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0.0004
L=400–450m L=250–300m
0.0003
L=100–150m 0.0002 0.0001 0 0
(b)
2000
4000
6000
8000 10000 t (year)
12,000 14,000 16,000
0.05 L=850–900m
0.045
L=700–750m
Q
0.04
L=550–600m
0.035
L=400–450m
0.03
L=250–300m L=100–150m
0.025 0.02 0.015 0.01 0.005 0
2000
4000
6000
8000 10,000 12,000 14,000 16,000 t (year)
FIGURE 18.4 Q is the total solute flux over the control plane. (a) Expected solute breakthrough curves with the source line at different locations. (b) Variances about the mean predictions. (Figure 2 from Cushman et al., 2002, Adv. Water Resour. 25, 1043–1067.)
Consider the normalized concentration, C(x, t ). The dilution index E(t ) is an entropy-like measure defined by E(t ) = exp −
C(x, t ) ln C(x, t )dV
(18.27)
V
The theoretical maximum of this quantity can be considered for systems and the dilution index compared to this maximum quantity, yielding the reactor ratio. The dilution index and reactor ratio have been thoroughly explored for unbounded domains via the advection-dispersion equation with constant coefficients as well as other systems. In addition, E(t ) has been related to the concentration variance (Kitanidis, 1994; Kapoor and Kitanidis, 1997; Pannone and Kitanidis, 1999). Kapoor and Gelhar (1994) examined spreading vs. dilution in the Cape Cod bromide tracer data via peak concentration. They found that the macroscale dispersion tensor was not a very accurate predictor of the peak concentration (their measure of dilution) and that, at best, the macroscale dispersion tensor
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can be used to describe the plume spread in terms of the second moment of concentration. Additionally, it was found through numerical simulations in a heterogeneous conductivity field that an n-fold increase in the covariance of the concentration in the mean flow direction does not result in an n-fold decrease in the peak concentration as would occur in a homogeneous conductivity field. A hundred fold decrease in covariance resulted in only a tenfold decrease in peak concentration. This indicates in heterogeneous aquifers that care should be taken in contamination transport in relating dilution and spreading.
18.10 Experiments 18.10.1 Lab Experiments The majority of laboratory experiments involve the analysis from an Eulerian perspective by looking at solute concentration (breakthrough curves), porosity, pore-velocity, and hydraulic conductivity and employ a Fickian estimate for the dispersion tensors by using the velocity covariance (Harleman and Rumer, 1963; Klotz et al., 1980; Eidsath et al., 1983; Rashidi et al., 1996). An alternative method that allows greater freedom in analysis and more detailed information is Particle Tracking Velocimetry (PTV). Particle Tracking Velocimetry has been utilized by Moroni and Cushman (2001) in the investigation of the generalized hydrodynamic approach (Section 18.7.1) and to study the validity of the ADE. PTV has the benefit that Lagrangian trajectories of the passive tracer are obtained for analysis. In a time stationary system one can then convert this information to an Eulerian frame. To utilize PTV in a porous medium the matrix must be made invisible. This can be accomplished using a fluid and matrix that have matching refractive indices (matched-index system). One naturally occurring system is cryolite and water, however to develop a laboratory system another possibility is glycerol and Pyrex at 23◦ C in natural light. Moroni and Cushman (2001) used Pyrex beads and cylinders to create both homogeneous and heterogeneous media. Air bubbles, of an appropriate size, were used as the passive tracer (they have a different refractive index than the glycerol and Pyrex) and the flow of the bubbles in the glycerol was tracked with different flow velocities in the various media. Through reconstruction techniques, three-dimensional (3D) trajectories of the air bubble paths were followed and analyzed. A sample of 3D trajectories from the “homogeneous” medium is shown in Figure 18.5. It was found that all media have anomalous flow characteristics at some scale, even “homogeneous” media, (see Figure 18.5) and thus reinforces the notion that homogeneity is a scale dependent concept.
18.10.2 Field Experiments Many large scale field experiments have been performed over the past several decades to examine and compare theories of macrodispersion. The largest such natural gradient experiments are the Borden, Cape Cod, and the MADE tests. A comprehensive discussion of field-scale dispersion experiments can be found in Gelhar (1992). The Borden aquifer, located in Canada, is a sand quarry with medium and fine-grained sands. Chloride and bromide were used as the conservative tracers. Discussions of this test can be found in Sudicky (1986) and Freyberg (1986). Scale-dependent dispersion is present in this experiment and has mainly been studied using the ADE. The Cape Cod (Massachusetts) site is a sand and gravel aquifer with a low level of heterogeneity and both reactive and nonreactive tracers were used. The Cape Code site has been analyzed with stochastic theories and the first and second moments of the tracer plumes have fit well with these theories (Garabedian et al., 1991; Kapoor and Gelhar, 1994), but these theories have not held up well in the more heterogeneous case of the MADE site. The concept of spreading vs. dilution has also been investigated for the Cape Cod site through the covariances. The MADE site (Mississippi) is substantially more heterogeneous than the other sites and also involved the use of reactive and nonreactive tracers (Adams and Gelhar,1992; Boggs et al.,1992; Benson et al., 2000). The FADE has been studied relative to this data as discussed in Section 18.7.3. Further discussion on the MADE site can be found in Chapter 26 (C. Zheng).
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18-15
900 800 700 600 500 400 300 200 800
700
600
500
400
300
200
300
400
500
600
700
800
900
FIGURE 18.5 Example of trajectories obtained via Particle Tracking velocimetry through a bench scale porous medium. Trajectories are of length greater than 12 sec. (Figure 7 in Moroni and Cushman, 2001, Phys. Fluids 13, 81–91.)
These large-scale field experiments are providing a basis for the testing of new theories and a better understanding of when classical theories break down; it is expected that they will continue to play an important role in the modeling of transport in porous media.
Glossary Passive tracers Solute that does not react with the porous medium or the suspending solution. Conservative tracer Solute that maintains its mass in the fluid volume. Heterogeneity The occurrence of variability of the values of field properties in space. Stochastic model A mathematical model that involves spatially or temporally material parameters or a random forcing function. Structural vs. functional hierarchy Structural hierarchy refers to nested physical subunits of the medium whereas functional hierarchy refers to nested processes. Discrete vs. continuous hierarchy Discrete hierarchy involves a finite number of nested subunits (subprocesses) whereas in a continuous hierarchy the number of such subunits goes to infinity. Pore scale The scale of the pore. The pore velocity is the velocity measured at this scale. Darcy scale A scale large enough so that Darcy’s law holds. The Darcy velocity is the velocity used at the Darcy scale. Hydraulic conductivity The constant of proportionality in Darcy’s law between the Darcy velocity and the gradient of the hydraulic head. Macrodispersivity tensor The dispersivity tensor in the ADE when it is used on a Darcy scale or higher. Pathline A particles trajectory in time. Nonlocal constitutive law One that involves integral or higher order gradients. Covariance The average of the product of a random variable at two different spatial points (example velocity covariance Cv (x, y) = E[v(x)v(y)]). Steady flow A flow where the properties do not depend explicitly on time. Stationarity May be temporal or spatial. Refers to dependence of a property only on the time lag or spatial displacement instead time and location. In a random variable the most common types are
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strict stationarity (statistically homogeneous) and second order or weak stationarity. Strict stationarity means that the probability density function is invariant to spatial shifts. In weak stationarity the mean and variance are constant and the covariance depends only on the displacement vector between the two points and is symmetric. Probability density function Function describing the probability of event. The sum (or integral) over all possible events must be 1.
Acknowledgments This work was funded under the support of the National Science Foundation under Contract Nos 0310029EAR, 0417555-EAR, and 0003878-EAR.
References Adler, P.M. 1992. Porous Media: Geometry and Transports. Butterworth/Heinemann. Adams, E.E. and Gelhar, L.W. 1992. Field study of dispersion in a heterogeneous aquifer 2. Spatial moments analysis. Water Resour. Res. 28, 3293–3307. Bear, J. 1972. Dynamics of Fluids in Porous Media, Elsevier. Benson, D.A., Schumer, R., Wheatcraft, S.W., and Meerschaert, M.M. 2001. Fractional dispersion, Levy motion and the MADE tracer tests. Transp. Porous Media 42, 211–240. Benson, D.A., Wheatcraft, S.W., and Meerschaert, M.M. 2000. The fractional-order governing equation of Levy motion. Water Resour. Res. 36, 1413–1423. Berg, H.C. 2000. Motile behavior of bacteria. Phys. Today 53, 24–29. Berkowitz, B., Klafter, J., Metzler, R., and Scher, H. 2002. Physical pictures of transport in heterogeneous media: Advection–dispersion, random-walk, and fractional derivative formulations. Water Resour. Res. 38, Art 1191. Berkowitz, B. and Scher, H. 2001. The role of probabilistic approaches to transport theory in porous media. Transp. Porous Media 42, 241–263. Boggs, J.M., Young, S.C., Beard, L.M., Gelhar, L.W., Rehfeldt, K.R., and Adams, E. 1992. Field study of dispersion in a heterogeneous aquifer 1. Overview and site description. Water Resour. Res. 28, 3281–3291. Bonilla, F.A. and Cushman, J.H. 2002. Effect of alpha-stable sorptive waiting times on microbial transport in microflow cells. Phys. Rev. E 66, 031915. Bouleau, N. and Leìpingle, D. 1994. Numerical Methods for Stochastic Processes. Wiley, New York. Brenner, H. and Edwards, D.A. 1993. Macrotransport Processes. Butterworth-Heinemann, MA. Cortis, A. and Berkowitz, B. 2004. Anomalous transport in “classical” soil and sand columns. Soil Sci. Soc. Am. J. 68, 1539–1548. Creswick, R.J., Farch, H.A., and Poole, C.P. Jr. 1992. Introduction to Renormalization Group Methods in Physics. Wiley, New York. Cushman, J.H. (Ed.) 1990. Dynamics of Fluids in Hierarchical Porous Media. Academic Press. Cushman, J.H. 1997. The Physics of Fluids in Hierarchical Porous Media: Angstroms to Miles. Kluwer. Cushman, J.H. and Ginn, T.R. 1993. Nonlocal dispersion in media with continuously evolving heterogeneity. Transp. Porous Media, 13, 123–138. Cushman, J.H. and Ginn, T.R. 2000. Fractional advection–dispersion equation: A classical mass balance with convolution-Fickian flux. Water Resour. Res. 36, 3763–3766. Cushman, J.H., Bennethum, L.S., and Hu, B.X. 2002. A primer on upscaling tools for porous media. Adv. Water Resour. 25, 1043–1067. Dagan, G. 1989. Flow and Transport in Porous Formations. Springer-Verlag, New York. Dagan, G. 1994. An exact nonlinear correction to transverse macrodispersivity for transport in heterogeneous formations. Water Resour. Res. 30, 2699–2705.
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Dagan, G., Cvetkovic, V., and Shapiro, A. 1992. A solute flux approach to transport in heterogeneous formations, 1. The general framework. Water Resour. Res. 28, 1369–1376. Dentz, M. and Berkowitz, B. 2003. Transport behavior of a passive solute in continuous time random walks and multirate transfer. Water Resour. Res. 39, Art. 1111. Eidsath, A., Carbonell, R.G., Whitaker, S., and Herrmann, L.R. 1983. Dispersion in pulsed systems-III. Comparison between theory and experiments for packed beds. Chem. Eng. Sci. 38, 1803–1816. Freyberg, D. 1986. A natural gradient experiment on solute transport in a sand aquifer, 2. Spatial moments and the advection and dispersion of nonreactive tracers. Water Resour. Res. 22, 2031–2046. Garabedian, S.P., LeBlanc, D.R., Gelhar, L.W., and Celia, M.A. 1991. Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts 2. Analysis of spatial moments for a nonreactive tracer. Water Resour. Res. 27, 911–924. Gelhar, L.W., Gutjahr, A.L., and Naff, R.L. 1979 Stochastic analysis of macrodispersion in a stratified aquifer. Water Resour. Res. 15, 1387–1397. Gelhar, L.W. 1993. Stochastic Subsurface Hydrology. Prentice-Hall, NJ. Gelhar, L.W. 1986. Stochastic subsurface hydrology from theory to application. Water Resour. Res. 22, S135–S145. Gelhar, L.W. 1992. A critical review of data on field scale dispersion in aquifers. Water Resour. Res. 28, 1955–1974. Harleman, D. and Rumer, R.R. 1963. Longitudinal and lateral dispersion in an isotropic porous medium. J. Fluid Mech. 16, 385–394. Hsu, K.C., Zhang, D.X., and Neuman, S.P. 1996. Higher-order effects on flow and transport in randomly heterogeneous media. Water Resour. Res. 32, 571–582. Kapoor, V. and Gelhar, L.W. 1994. Transport in three-dimensionally heterogeneous aquifers: 2. Predictions and observations of concentration fluctuations. Water Resour. Res. 30, 1789–1801. Kapoor, V. and Kitanidis, P. 1997. Advection–diffusion in spatially random flows: Formulation of concentration covariance. In Stochastic Hydrology and Hydraulics, vol. 11, pp. 397–422, Springer-Verlag. Kitanidis, P. 1994. The concept of the dilution index. Water Resour. Res. 30, 2011–2026. Kleinfelter, N., Moroni, M., and Cushman, J.H. 2005. Application of a finite size Lyapunov exponent to particle tracking velocimetry in fluid mechanics experiments. Phys. Rev. E 72(5), Art. 056306, Part 2. Klotz, D., Selier, K.-P., Moser, M., and Neumaier, F. 1980. Dispersivity and velocity relationship from laboratory and field experiments. J. Hydrol. 45, 169–184. Lee, K.K. and Cushman, J.H. 1993. Multiscale adaptive estimation of the conductivity field using pump test data. Stoch. Hydrol. Hyd. 7, 241–254. Liu, Y.P., Steenhuis, T.S., and Parlange, J.Y. 1994. Closed-form solution for finger width in sandy soils at different water contents. Water Resour. Res. 30, 149–952. Meerschaert, M., Benson, D.A., and Bäumer, B. 1999. Multidimensional advection and fractional dispersion. Phys. Rev. E 59, 5026–5028. Metzler, R. and Klafter, J. 2000. The Random walk’s guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339, 1–77. Moroni, M. and Cushman, J.H. 2001. Statistical mechanics with three-dimensional particle tracking velocimetry in the study of anomalous dispersion. 1. Experiments, Phys. Fluids 13, 81–91. Pannone, M. and Kitanidis, P. 1999. Large-time behavior of concentration variance and dilution in heterogeneous formations. Water Resour. Res. 35, 623–634. Quintard, M. and Whitaker, S. 1987. Ecoulement monophasique en milieu poreus: Effect des heterogeneities locales. J. Mec. Theo. Appl. 6, 691–726. Rashidi, M., Peurrung, L., Tompson, A.F.B., and Kulp, T.J. 1996. Experimental analysis of pore-scale flow and transport in porous media. Adv. Water Resour. 19, 163–180. Sanchez-Palencia, E. 1980. Non-Homogeneous Media and Vibration Theory. Lecture Notes in Physics, 127, Springer-Verlag, New York.
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Scher, H. and Montroll, E.W. 1975. Anomalous transit time dispersion in amorphous solids. Phys. Rev. B. 12, 2455–2477. Selker, J.S., Steenhuis, T.S., and Parlange, J.Y. 1996. An engineering approach to fingered vadose pollutant transport. Geoderma 70, 197–206. Shapiro, H. and Brenner, H. 1988. Dispersion of a chemically reactive solute in a spatially periodic model of a porous medium. Chem. Eng. Sci. 43, 551–571. Simmons, C.S. 1982. A stochastic-convective transport representation of dispersion in one-dimensional porous-media systems. Water Resour. Res. 18, 1193–1214. Sudicky, E.A. 1986. Natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersive process. Water Resour. Res. 22, 2069–2082. Wheatcraft, S.W. and Tyler, S.W. 1988. An explanation of scale dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry. Water Resour. Res. 24, 566. Winter, C.L. and Tartakovsky, D.M. 2000. Mean flow in composite porous media. Geophys. Res. Lett. 27, 1759–1762. Winter, C.L., Tartakovsky, D.M., and Guadagnini, A. 2002. Numerical solutions of moment equations for flow in heterogeneous composite aquifers. Water Resour. Res. 38, 1055. Wu, J.C., Hu, B.X., and Zhang, D.X. 2003a. Applications of nonstationary stochastic theory to solute transport in multi-scale geological media. J. Hydrol. 275, 208–228. Wu, J.C., Hu, B.X., Zhang, D.X., and Shirley, C. 2003b. A three-dimensional numerical method of moments for groundwater flow and solute transport in a nonstationary conductivity field. Adv. Water Resour. 26, 1149–1169. Zhang, D.X. 2002. Stochastic Methods for Flow in Porous Media: Coping with Uncertainties. Academic Press. Zhang, D.X., Andricevic, R., Sun, A.Y., Hu, B.X., and He, G.W. 2000. Solute flux approach to transport through spatially nonstationary flow in porous media. Water Resour. Res. 36, 2107–2120.
Further Information We have presented a brief outline of some of the methods and resources that have been employed in the study of conservative tracers. Zhang (2002) provides a good introduction to stochastic methods for the flow problem. An introduction to stochastic numerical methods can be found in Bouleau and Lépingle (1994). The books of Adler (1992), Brenner and Edwards (1993), Cushman (1990, 1997), Dagan (1989), and Gelhar (1993) are useful references on transport problems.
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19 Reactive Contaminant Transport in the Saturated Zone: Review of Some Upscaling Approaches 19.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.2 Physical, Chemical, and Microbiological Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.3 Scale of Observation and Constitutive Concepts . . . . . . 19.4 Upscaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19-2 19-4 19-5 19-5
Methods for Chemical Heterogeneity
19.5 Linearity and Nonequilibrium Eulerian Stochastic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-7 Deterministic Nonequilibrium Sorption • Random Nonequilibrium Sorption • Random Nonequilibrium Sorption and Equilibrium Microbial Decay • Numerical Results for Random Kd and No Degradation • Numerical Results with Random Chemical and Microbiological Conditions
19.6 Upscaling Microbial Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 19-11 19.7 Lagrangian Stochastic Models for Nonlinear Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-13 Streamtube Formulation • Stochastic–Convective Averaging • Travel-Time Distribution Function • Some Reaction System Examples • Toward Handling Heterogeneity in Reactive Properties
J. H. Cushman Purdue University
T. R. Ginn University of California at Davis
19.8 Connection between Approaches . . . . . . . . . . . . . . . . . . . . . . . Definition of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19-22 19-23 19-24 19-25 19-25 19-29
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19.1 Introduction We extend the discussion of the previous chapter to a setting wherein the dissolved chemical reacts with its environment. The catalogue of natural geochemical reactions and transformations associated with man-made contaminants that have entered the saturated zone is essentially limitless, but for the most part these reactions can be categorized according to speed, reversibility, and phase association. A relevant subset of the classification scheme of Rubin (1983) includes the four cases (1) reactions that are fast (equilibrium) and reversible involving aqueous–aqueous or (2) aqueous–solid phase interactions; and (3) reactions that are not fast (nonequilibrium) involving aqueous–aqueous or (4) aqueous–solid phase interactions. The terms “fast” and “not fast” are defined relative to the other transformation processes involved, including other reactions and convective and dispersive transport on the observation time scale. Aqueous–aqueous (Categories 1 and 3) are termed “homogeneous” and aqueous–nonaqueous (2 and 4) are termed “heterogeneous” (regarding phase; not to be confused with spatial variability). This scheme is useful because there is a distinct mathematical approach for each of these categories. The chemical mechanisms driving general reactions and the mass balance approaches for formulating representative transformation models are beyond the present scope, and are summarized at various levels in for instance Rubin (1983), Fetter (1993), Marsily (1986), Sposito (1994), and Lichtner et al. (1996). Here we will be restricted to some of the simpler (but representative) reaction mechanisms in categories 2 (sorption) and 4 (biodegradation), and focus on scaling issues associated with transport in heterogeneous porous media. We begin with a brief summary of reaction-transformation formulations and then describe concepts of heterogeneity, scale, and upscaling. The remainder of the chapter describes current methods for scaling plume behavior involving linear reactions (Eulerian approaches), and for scaling contaminant arrival behavior involving nonlinear reactions (Lagrangian approaches). We start with a simple illustrative example of an equilibrium heterogeneous reaction, involving the single electrolyte NaCl. Dissolved chloride is a simple anion and generally moves in accordance with the local pore-water velocity, much as the water molecules themselves do (with some exception due to the repulsive electrostatic potential between the anion and the mineral surfaces in, for example, quartzitic or kaolinitic materials). Thus chloride is often reasonably treated as an inert or “passive” tracer using methods described in the previous chapter. Sodium, however, tends to be both transported and exchanged with other cations on the negatively charged mineral surfaces. That is, aqueous sodium reacts with the solid phase by cation-exchange, one of a number of mechanisms by which aqueous species may associate with the mineral surfaces. Other mechanisms include precipitation (e.g., Novak and Sevougian, 1993), surface complexation (e.g., Dzombak and Morel, 1990), hydrophobic sorption of organic species to organic solids (Karickhoff, 1983), colloid filtration (Tien, 1976), and intergranular diffusion (Wood et al., 1990). Reaction transformations are formally captured via augmenting the basic solute transport rate equation (Equation 13.1 of the previous chapter) with a generalized mass loss rate, nr = [∂C/∂t ]transformation , here written as mass transfer to the solid phase, with constant porosity n: ∂(Vi C) ∂ ∂C + − ∂t ∂xi ∂xi
∂C dij ∂xj
=
∂C ∂t
≡− transformation
ρb ∂S n ∂t
(19.1a)
where C is the aqueous concentration [M/L3 ], S is the sorbed concentration per unit mass of solid [M/M], ρb is the bulk density of the aquifer material [M/L3 ], n is the porosity, and dij is the symmetric dispersion tensor. A majority of sorption and other heterogeneous transformations may be represented by specifying this mass transformation rate as a function of the departure of the system from an equilibrium state. The first-order form is ∂S = Kr (Kd C − S) ∂t
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(19.1b)
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19-3
where Kr is the desorption rate [1/T] and Kd is the equilibrium distribution coefficient [L3 /M]. Equation 19.1b specifies a linear nonequilibrium (“not fast”) reversible mass transformation rate that approximates numerous sorption processes (of category 4) in natural media. Alternatively, one may express the right-hand side of Equation 19.1b as [Kf C − Kr S], where Kf = Kr Kd is the forward sorption rate [1/T]. Reactive solutes undergoing transport according to Equation 19.1 exhibit attenuation. If Kr is very large so that Equation 19.1b responds much more quickly than local conditions change (due to other mass fluxes in Equation 19.1a), then the “local equilibrium assumption” is invoked and the chemical partitioning is taken to occur instantaneously. That is, ironically, the reaction rate in Equation 14.1b is so fast that it occurs over a negligibly short time, and literally most of the time, Equation 14.1b is zero. Note that this is not to be confused with assuming steady state conditions for S; S will change, instantaneously with changes in C. We may then use the equilibrium solution to Equation 19.1b, S = Kd C, as an algebraic relation for S in terms of C in the derivative on the right-hand side of Equation 19.1a (to express the dependence of S on C). Differentiating and grouping terms gives from Equation 19.1a 1 ∂(Vi C) 1 ∂ ∂C + − ∂t R ∂xi R ∂xi
dij
∂C ∂xj
=0
(19.2)
where R = 1 + ρb Kd /n is known as the retardation factor. When transport is governed by an equation involving equilibrium reactions such as Equation 19.2, the solute(s) are retarded (as opposed to attenuated), as is clear upon recognizing that R reduces the transport parameters Vi and dij . Equation 19.1 and Equation 19.2 illustrate the simplest case of heterogeneous mass transformations of the nonequilibrium and equilibrium types. This example illustrates the different mathematical approaches for the two cases. For nonequilibrium reactions we specify a (“kinetic”) function for ∂S ≡ r(S, C) ∂t and for equilibrium we specify the algebraic relation (termed “isotherm”) of the form S = r(C), so that ∂C ∂S ≡ r (C) ∂t ∂t and r(C) becomes involved in the transport operator. More complex forms of r arise when the mass transformations are nonlinear in C and in S, when multiple processes are in effect, when the nonaqueous phase (for S) undergoes transformations, and when multiple interacting solutes are involved, to note only a few cases. In the case of multiple interacting solutes and solid-phase species, an evolution equation is written for each component, and these equations are coupled through the (multiple) reaction terms appearing. Such systems present special issues requiring attention in their solution depending on the character of the reactions (cf. review in Yeh and Tripathi, 1989). When all interactions are at equilibrium, the transport equations are coupled with a set of algebraic equations relating mobile to immobile species that complicate the solution via integration schemes designed for the transport operator alone. Recent approaches use iterative solutions between the algebraic and differential equations (Yeh and Tripathi, 1989) or a decoupling of the system (Rubin, 1990). In the other limiting case where all the reactions have a finite rate, then a sink term appears for each species in the evolution equation and the solution can proceed conventionally through operator-splitting (e.g., Chiang et al., 1990; Valocchi and Malmstead, 1992) or explicit integration schemes (e.g., Widdowson et al., 1988; Celia et al., 1989). Finally, a mixture of both nonequilibrium and equilibrium transformations results in a“differential-algebraic equation”(DAE) system that may be solved, under particular conditions regarding the “index” of the system (Gear and Petzold, 1984; Gear, 1988), through specialized iterative or noniterative decoupling approaches (e.g., Steefel and MacQuarrie, 1996). We now turn our attention to a demonstration of some of the available approaches for dealing with reactions in the presence of physical and chemical heterogeneities in natural media. The goal of the
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scaling approaches is to derive maximum information about the solute fate and transport when data on the spatial variability of the natural media is limited. We describe two such approaches, an Eulerian stochastic-analytic method that is useful for describing expected plume behavior under linear reactions, given statistical (correlation) properties of the spatially variable aquifer flow and reaction characteristics; and a Lagrangian-streamtube approach useful for predicting solute arrivals at observation locations (as opposed to plume evolution) when the reactions involve nonlinear transformations. Beyond the current scope is a third approach that is quite useful when available aquifer data includes conditioning data on the flow and reaction property values on significant scales, such as identification and incorporation of hydrofacies geometry (Bierkens and Weerts, 1994; Scheibe and Freyberg, 1995). In the following sections, we introduce concepts of heterogeneity defined as spatial variability in physical, or chemical, or microbiological properties, within the context of scales of observation, to set the stage for upscaling or averaging methods, that is the topic of this chapter. We then turn to some basic demonstrations of how one can upscale various occurrences of heterogeneity. This is first described in the Eulerian setting for some elementary single-component reactions. Next, the Lagrangian perspective is described and demonstrated for a multicomponent reaction network with nonlinear kinetics. Finally, we describe a connection between the Eulerian and Lagrangian settings. This review is not comprehensive either with respect to reactions encountered in the subsurface or with respect to most up-to-date contributions. Our target is rather to demonstrate some of the basic results in upscaling solute fate and transport in heterogeneous formations, for some simple cases of reactions. Thus, our goal is to provide an introductory review of the concepts and some approaches used in dealing with subsurface heterogeneity and its effects on solute fate and transport.
19.2 Physical, Chemical, and Microbiological Heterogeneity It is clear that transport models for multiple species of reactive and degradable chemicals in a homogeneous environment must be very complicated. Couple this already complicated transport phenomena with heterogeneity, and the resultant problem increases by an order of magnitude in complexity. To date, only the simplest of such problems have been solved analytically, and even Monte Carlo methods have been applied to only moderately complex systems. Aquifer properties are commonly found to vary on multiple spatial scales in a variety of settings, including alluvial (e.g., Weissman and Fogg, 1999; Schulmeister et al., 2003) and marine depositional (Tompson et al., 1996; DeFlaun et al., 2001) environments. Such heterogeneity arises in part from aquifer depositional structures that exhibit variations from the centimeter (e.g., cross-bedding) to the meter (lithofacies) scales. In the previous chapter, physical heterogeneity was discussed in the context of a random hydraulic conductivity field. There are two other commonly encountered forms of physical heterogeneity: a spatially variable porosity field and a spatially variable “local” dispersivity field. Both are commonly considered of secondary importance to flow and transport, though recent Monte Carlo simulations (Hassan et al., 1998) suggest that the correlation between conductivity and porosity may play a significant role in transport. As in Chapter 18, however, we will equate physical heterogeneity with ignorance about the values of particular parameters and how they vary over space. This will usually be approached by conceptualizing, for example, the hydraulic conductivity as a “random” conductivity field. In such a field the value of a parameter such as conductivity is viewed as a random deviate from a distribution that can be characterized by its moments and the like (mean, standard deviation, etc.). When the moments of the distribution themselves do not depend on space, the random field is termed “stationary”or, equivalently,“statistically homogeneous.” While stationary field representations are among the simplest (and most commonly relied upon), they are not to be confused with “homogeneous” fields where conductivity value is the same everywhere. Another critically important aspect of a “random” field is “ergodicity.” In loose terms, a field is ergodic if the probability distribution of values that can occur at a point in space is equivalent to the frequency distribution of values over space for the given subsurface in question. Ergodicity is critically important because if it holds for a given aquifer, then the statistics for
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describing the random field can be estimated to some degree by compiling data from boreholes and other (e.g., geophysical) sources from different locations within the given subsurface in question. Unfortunately, proof of ergodicity would require not only exhaustive characterization of an entire subsurface domain, but also definition and identification of a set of subsurface domains that could arguably serve as a probability space with samples from each one at a consistent point in space — clearly an impossibility. Therefore ergodicity can not be proved. Superimposed on the random conductivity field is a random geochemical field. Historically and spatially varying distributions of mineral deposition, formation, diagenesis, and weathering and organic matter occurrence and deposition give rise to this natural heterogeneity. Superimposed over both the physically and chemically heterogeneous fields is a dynamic random distribution of microbial populations. The major difference between physical/chemical heterogeneity and microbial heterogeneity is the dynamic nature of the latter. Microbes are transported and adsorbed as much as are chemicals and other colloidal particles, though the adsorptive mechanisms are completely different, with physiologically dependent residence times on surfaces leading in some cases to biofilm formation and eventual decay.
19.3 Scale of Observation and Constitutive Concepts Engineered porous media are generally designed to be homogeneous when viewed over the scale on which they are to be used in a given technology. Natural porous formations, on the other hand, are almost always inhomogeneous on any relevant scale of observation. As mentioned in the previous section these natural formations are not only inhomogeneous physically, but chemically and biologically as well. However, the degree and type of these heterogeneities depends to a large extent on the scale of observation. It is for this reason that “effective” parameters such as so-called macro dispersivity have little meaning in natural systems. A primary goal of modelers of transport in heterogeneous media is to develop functional forms for constitutive variables and to know the regions of space-time that are important to their definition. If the constitutive theory depends upon what is happening at a point (here a point has meaning only with respect to the window and scale of resolution associated with the measurement process) in space-time, or a very small neighborhood of the point, then the theory is said to be local. On the other hand, if information is needed to define the constitutive theory from regions of space-time distinct from a neighborhood of the space-time point where evaluation of the theory is to be made, then the model is said to be nonlocal. These ideas will be made more concrete in subsequent sections.
19.4 Upscaling The concept of “upscaling” is one of the most important in modern hydrological modeling circles. Upscaling simply means taking information on scales smaller than those of interest, homogenizing it, and studying the resultant “larger” scale system. The rationale behind the need to upscale is that we simply cannot make enough detailed measurements at the smaller scales to be of much use on the larger scales wherein relevant transport processes are taking place. There are numerous methods that may be used to upscale physics in hydrology, including matched asymptotic expansions, Taylor–Aris–Brenner method of moments, renormalization group theory, transform methods, volume averaging, particle tracking, and so on. Many of these are illustrated in Cushman et al. (2002) and the interested reader is referred there. The next subsection reviews works regarding mineralogical or otherwise reactivity-associated properties and the effects of heterogeneity therein.
19.4.1 Methods for Chemical Heterogeneity Here we review some concepts and results in the use of the Lagrangian approach when not only physical but also chemical and microbiological properties are heterogeneous. First, we term any reactive property
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of an aquifer “aquifer reactivity.” This includes any immobile reactive component, for example, sorbed organic matter, organic mineral assemblages, (co-)precipitated minerals, mineral-oxide surface coatings, or biotic phases such as microbial colonies or biofilms. Glassley et al. (2001) characterized a small sample of fractured rock from Yucca Mountain, Nevada, and compared both high-resolution (modeled aquifer porosity and reactivity) and effective-homogeneous models and found that the effect of mineralogical heterogeneity on reactive solute transport depends on how solute flux is distributed over contact times with minerals. At larger scales this dependency is often viewed in the context of how reactive transport depends on the way in which the patterns of geochemical and physical properties are overlain in space. Investigations have involved both deterministic patterns of geochemical and physical properties in experimental (e.g., Knapp et al., 1998) and simulated (e.g., Burr et al., 1994) settings. In sandy aquifer materials metal (iron, aluminum, manganese) oxides are among the most important solid species that impart the positively charged sites on an otherwise negatively charged silicate surface, thus controlling the sorption of negatively charged solute particles. The occurrence of these microscale heterogeneities in reactivity and the impact on transport of colloidal and viral tracers in particular has been studied by Elimelech and coworkers (e.g., Ryan et al., 1999; Elimelech et al., 2000; Chen et al., 2001; Bhattacharjee et al., 2002). There, negatively charged colloidal depositions are demonstrated to be influenced by the positively charged surface (e.g., Chen et al., 2001). The presence of organic matter absorbed on the mineral surface decreases the electrostatic force between the positively charged surface and negatively charged colloids (Ryan et al., 1999). The overall impacts of such “patchwise” heterogeneity of positively charged metal oxyhydroxide grain coatings, on the transport of virus tracers is described for instance in Bhattacharjee et al. (2002). Larger scales of variation were examined, in that both layered and randomly (log-normally) distributed physical and geochemical heterogeneities were considered. The most direct and simple approach to upscaling microscale (e.g., patchwise) heterogeneity of reactivity, in both Eulerian and Lagrangian settings, is by replacing the heterogeneous medium with an effective homogeneous medium (HEM) with the same total reactive surfaces available (but distributed now, homogeneously). This usually involves the assumption that the solute has equal access to reactive surfaces occurring within any representative elementary volume (REV) that is complete mixing. In one study without this assumption, Lichtner and Tartakovsky (2003) show that even with a single sorption rate but surface area variable within the REV due to a log-normal grain size distribution, the effective rate is not a constant but varies with time. When complete mixing is assumed and the sorption reaction is fast but involves multiple sorbents (e.g., mineralogies) that are spatially variable at the grain scale, equilibrium models written for homogeneous reactivity can give wrong simulations especially when calibrated in batch but applied in the presence of transport (e.g., Bosma et al., 1993; Wise, 1993; Chen and Wagenet, 1995; Szecsody et al., 1998 for a multicomponent reaction system). When kinetically controlled sorption reactions are involved, this situation can give rise to multi-rate or multi-site reaction kinetics at the continuum and larger scales. Sposito (1993) points out how multiple reactive mineral phases involved in a surface reaction with a single reversibly sorbing solute give rise to the multi-rate reaction model (e.g., Haggerty and Gorelick, 1995) and under Gamma-distribution of reactivity, a power-law distribution of sorption rates and thus residence times (e.g., Metzler and Klafter, 2002). If some of the reactions in a multi-rate model are fast on the timescale of transport and the remaining reactions, then they can in general be combined to a single equilibrium reaction that operates in parallel with the remaining kinetically controlled reactions. Various combinations of serial and parallel reactions models can be constructed from particular conceptual models of grain surfaces, sometimes involving intra-granular porosity and diffusion limitations approximated as kinetically controlled reactions (e.g., Villermaux, 1981; Valocchi, 1990; Cunningham et al., 1997). Approaches to dealing with heterogeneity in reactive properties on larger (e.g., meter) scales are often based on hypothesized correlations between macroscopic physical properties and reactive properties. Kabala and Sposito (1991) derive an effective convective-dispersive transport equation for the expected value of a solute undergoing transport and equilibrium sorption in random velocity and distribution coefficient fields, in the absence of microscopic dispersion. Their results are extended to higher moments
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and higher order statistics in Kabala and Sposito (1994). Burr et al. (1994) present a numerical study of three-dimensional reactive transport with a geostatistical description of hydraulic conductivity and sorption equilibrium distribution coefficient designed to resemble Borden aquifer characteristics. Using spatial moment analyses on a small Monte Carlo ensemble, the authors showed that a negative correlation between the physical and reactive properties led to an increased spreading of solute plumes, as reflected in the second spatial moment within individual plumes. Similar results are reflected in Dagan (1989), Chrysikopoulos et al. (1990), and Bellin et al. (1993). Tompson et al. (1996) provide nine separate case simulations of multicomponent reactive transport of a uranyl–citric acid mixture in multi-dimensional physically and chemically heterogeneous media, with speciation and surface-complexation (equilibrium) reactions involving hydrous-ferric oxide (goethite) coatings on aquifer materials (sand). The authors highlight the importance of the third space dimension in mixing, the effect of multicomponent interactions, and showed that fate is controlled by the abundance of the oxide as a function of the specific sand surface area as well as by larger scale patterns of oxide occurrence. Burr et al. (1994) also showed that the joint variability induces a pseudokinetic behavior, in that the ensemble mean bulk retardation factor can increase with time and plume displacement distance, even though the sorption reaction is equilibrium. The same result is obtained by Espinoza and Valocchi (1997) in a perturbation analysis and Monte Carlo study of one-dimensional solute transport with kinetically controlled sorption, and by Mishra et al. (1999) for reversible kinetic sorption. The usefulness of HEM models noted above for upscaling grain-scale reactivity heterogeneity has also been examined at larger scales. For instance, Chen et al. (2001) and Knapp et al. (1998) investigated transports of colloids and bacteria, respectively, in experimental columns with porous media that were physically homogenous but chemically heterogeneous. They compared results to reactivity-homogenized cases where aquifer reactivity patterns were erased and replaced with homogeneous material containing equivalent total reactivity. They concluded that the actual spatial distribution of iron-coated surfaces did not affect the column-scale attenuation and transport of the solutes as long as the overall fractions of reactive surface area in the column were the same. However, these results are restricted to one-dimensional transport with chemical heterogeneity occurring in the same dimension (e.g., varying along the flow path). If reactivity were arranged in a second space dimension, for example, in bands aligned parallel to the direction of the flow, the colloidal and bacterial breakthrough curves would indeed depend on pattern, because some of the solute flux would experience zero reactivity. This dependence is partly reflected in two of the nine experiments of Tompson et al. (1996) that involved banded goethite patterns, although the only pattern tested was banding diagonal to flow that spanned the no flow boundaries (e.g., parallel-to-flow banding was not examined). The authors state that the impact of correlation between reactive surface area and hydraulic conductivity seemed less significant than the overall abundance and distribution of the reactive area, such as the kind of banded goethite patterns observed in a coastal sand body. Finally, studies with unidirectional flow cannot reflect the coupled effects of physical and reactivity heterogeneity that occur via nonuniform flow in multiple dimensions (including dilution, e.g., Tompson et al., 1996). Thus, conclusions for unidirectional flow cases are not generally applicable in naturally heterogeneous porous media because in natural systems solute flux may experience a variety of “frequency of reaction sites” exposures. This is the same notion constructed by Glassley et al. (2001).
19.5 Linearity and Nonequilibrium Eulerian Stochastic Models 19.5.1 Deterministic Nonequilibrium Sorption It is assumed the chemical is transported by convection and local dispersion under steady, saturated, incompressible groundwater flow in a nondeformable porous medium, of constant porosity. The chemical undergoes first-order linear nonequilibrium kinetics with its surroundings. We assume a natural scale exists, the “Darcy” scale (as in Chapter 18), and we wish to upscale without knowledge of a scale separation between the Darcy and the “Reservoir” scale. Darcy-scale transport is governed by Equation 19.1. It is assumed the mean-flow is in the x1 -direction, that Kr and Kd are deterministic constants, and as a result
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of randomness in ln K , Vi , S, and Care random. Solving for the mean and fluctuation equations for Equation 19.1 and using a transform analysis gives (Cushman et al., 1996), assuming triplet correlation fluxes can be neglected, t ¯ ∂ ∂ C(y, t ) ∂ C¯ ∂ C¯ ¯ − Dij (x − y, t − t ) dydt + V1 ∂t ∂x1 ∂xj ∂yi 0 3
t ¯ = −Kr Kd δ(t − t ) − e−Kr (t −t ) C(x, t )dt + Kr e−Kr t S0
(19.3)
0
where Dij (x − y, t − t ) = dij δ(x − y, t − t ) + vi vj (x − y)G(x − y, t − t )
(19.4)
−1 K r Kd 2 + di ki + ik1 V1 G (k, ω) = ω 1 + ω + Kr
(19.5)
and ◦
where vi vj is the assumed stationary fluctuating-velocity covariance, S0 and C0 are initial concentrations, the ◦ represents Fourier–Laplace transform where t is dual to ω and x is dual to k. The form of the mean Equation 19.3 is quite different from the original local scale Equation 19.1. This dispersive flux is nonlocal (third term of the left-hand side of Equation 19.3), as is the source (left-hand side of Equation 19.3) term. The upscaling process is the source of nonlocality and it results from a lack of information on the small-scale details of the transport process.
19.5.2 Random Nonequilibrium Sorption Here the local-scale model is exactly as the previous case except it is assumed Kd is a random spatial field that may be correlated with ln K . In this case, the resultant mean equation is more complicated and given by Hu et al. 1995: t ∂ ∂ ∂ C¯ ∂ C¯ ¯ ¯ + V1 − Dij (x − y, t − t ) C(y, t ) dy dt ∂t ∂x1 ∂xj ∂yi 0 3
−
∂ ∂xj
t
¯ G(x − y, t − t )kd vj (x − y)C(y, t ) dy dt
0 3
t t −Kr t −Kr (t −t ) ¯ ¯ = −Kr Kd C − e δ(t − t ) − Kr e−Kr (t −t ) C(x, t ) dt − S 0 − K r Kd e 0
t ¯ × G(x − y, t − t )kd kd (x − y)C(y, t ) dy dt 0
t + 0 3
0
B(x − y, t − t )kd vi (x − y)
∂ ¯ C(y, t ) dy dt dt ∂yi
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with Dij (x − y, t − t ) = dij δ(x − y, t − t ) + vi vj (x − y)B(x − y, t − t )
(19.7)
K r Kd (k, ω) = ω 1 + + di ki2 + ik1 V ω + Kr
(19.8)
◦
B
−1
and ◦
◦
G (k, ω) = B (k, ω)
ωKr ω + Kr
(19.9)
The addition of randomness in Kd again increases the complexity of the mean equation. In this case, in addition to nonlocal sources/sinks and dispersion, there is also nonlocality in the convective flux (fourth term on the left-hand side of Equation 19.6).
19.5.3 Random Nonequilibrium Sorption and Equilibrium Microbial Decay It is possible to generalize the previous results to the case where there is linear first order microbial degradation. In this case, the local scale Equation 19.1 is replaced by ∂C ∂S ∂ + = ∂t ∂t ∂xj
dij
∂C ∂xi
−
∂(Vi C) − Kc C − K s S ∂xi
(19.10)
which is coupled with Equation 19.2. Here Kc and Ks are the solute degradation rates in the solution and sorbed phases. The mean equation can be obtained for this problem, but it is too complicated to present here (see Hu et al. [1997] for its presentation and development). In the next subsection we will, however, present some numerical solutions to it.
19.5.4 Numerical Results for Random Kd and No Degradation To apply Equation 19.6, one needs to know three covariance functions vi vj , kd kd , and kd vi and where vi and kd are the fluctuating velocity in the ith-direction and the fluctuating partition coefficient, respectively. As it is difficult, if not impossible, to measure vi , it is common to functionally relate vi to f (the fluctuating log-conductivity) and then to measure the covariance of f and its cross-covariance with kd . First-order expressions relating vi to f and vi to kd are (Gelhar and Axness, 1983; Hu et al., 1995) v i vj (k) =
Qg n
2 δi1 −
k1 ki
2
|k|2
ff (k)
(19.11)
and Qg k1 ki vi kd (k) = δi1 − 2 fkd (k) n |k|
(19.12)
where Qg is the product of the geometric mean conductivity with the mean gradient in the x1 -direction, n is the porosity, and caret indicates Fourier space transform. Both ff and fkd must be obtained from field experiments. For illustrative purposes, we assume various correlation structures for these covariances. For perfect positive correlation (Model A) or perfect negative correlation (Model B) to first order, we have 2 2 kd kd (k) = KdG eσf ff (k)
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(19.13)
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and 2 kd f (k) = ±KdG eσf ff (k)
(19.14)
with plus for Model A and minus for Model B, where KdG is the geometric mean of Kd (x). For uncorrelated Kd (Model C), to first order, 2 2 kd kd (k) = KdG eσW WW (k)
(19.15)
fkd (k) = 0
(19.16)
and
2 , and covariance where W is a normally distributed random space function with zero mean, variance σW
(z) = σ 2 e−zl/lw WW W
(19.17)
where lw is the integral scale of W and l is the correlation length of ln K . We take the initial concentration C0 to be constant, Cm over a rectangular prism 2a1 × 2a2 and assume S0 ≡ 0. The log-conductivity is chosen to be exponential ff (z) = σf2 exp − |z|2 /l 2
(19.18)
Model D will correspond to deterministic and constant Kd . In Figure 19.1 (from Hu et al., 1995, Figure 3), we plot the various spatial moments as a function ¯ where R¯ = 1 + Kd . It is seen that the first moment is little of nondimensional time t = t V¯ /Rl affected by the models irrespective of Kr . Relative to the uncorrelated model, negative correlation between the chemical heterogeneity and physical heterogeneity increases the second longitudinal moment and positive correlation decreases it. The difference between the three models becomes larger as Kr increases. Deterministic Kd can produce significantly different results from random Kd . Figure 19.1c shows the difference in the second transverse moments between the four models is small, but distinct at large time.
19.5.5 Numerical Results with Random Chemical and Microbiological Conditions The mean concentration for this case can be obtained given a much larger number of covariance functions, vi vj , vi kd , vi kc , vi ks , kd kd , kd ks , kd kc , kc kc , ks ks , and ks kc . We call the case without degradation model D. In this case, Ks ≡ Kc ≡ 0. We again must relate vi , kd , kc , and ks to f and in general, it follows to first order (with a = d, c, s). Qg k1 ki vi ka (k) = δi1 − 2 fka (k) n |k|
(19.19)
For illustrative purposes, we assume kc and ks are Gaussian and kc ks = σc σs exp −r 2 /lc2
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(19.20)
(a)
20
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Kr = 0.10 Kr = 100.
10
² ²
Model A Model B Model C
0
X1(t)/l2
Kdconstant
0.4
20
(c)
0
0.0
0.1
0.2
X22(t)/l2
10
X11(t)/l2
0.3
(b)
10 tV/Rl
20
0
0
10 tV/Rl
20
0
10 tV/Rl
20
FIGURE 19.1 Spatial moments for various models with KdG = 0.2: (a) first moment, (b) second longitudinal moment, c) second transverse moment. (Adapted from Figure 3 of Hu et al., 1995, Water Resour. Res. 31(9):2219–2237.)
We assume positive (Model A), negative (Model B), and uncorrelated (Model C) covariance structures in the form kc f = ±σc σf exp[−r 2 /lcf2 ] ks f = ±σs σf exp[−r 2 /lf2 ] where + is for Model A, and − for Model B, and kd is linearly negatively correlated with f . Use the same initial data as the previous case with lc = lcf = lf = 1.0 m, σf2 = 0.2, V1 = 1.0 m/day, d1 = 0.05 m2 /day, d2 = 0.005 m2 /day, cm = 1, Kd =1/day, Kc = 0.01/day, Ks = 0.003/day, σc2 = 0.01, σs2 = 0.003. Figure 19.2 plots mean concentration contours for the various models at 80 days. Models A, B, and C produce similar mean distributions. The shape of Model D’s contours are similar to the others, but they are larger in area and have higher mean concentrations, owing to a lack of degradation.
19.6 Upscaling Microbial Dynamics Even when microbes do not stick to the porous medium, they should be considered as reactive. This is because their self-motility allows them to move in a nonpassive way. They can move against the mean flow, transverse to it, or move rapidly in the direction of the mean flow and effectively can behave as retarded or enhanced particles. Initially this behavior was modeled as enhanced diffusion, however, in recent years researchers have begun to model microbial transport as nonlocal via Lévy motions (see Figure 1, Park et al., 2005a, 2005b). One of the biggest challenges faced when modeling microbial dynamics is how to
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Y(m)
5
Model A
0
0.03 0.02 0.01 0.005
–5 0
10
20
30
40
50 X(m)
60
70
Y(m)
5
80
90
100
Model B
0
0.03 0.02 0.01 0.005
–5 0
10
20
30
40
50 X(m)
60
70
Y(m)
5
80
90
100
Model C
0
0.03 0.02 0.01 0.005
–5 0
10
20
30
40
50 X(m)
60
70
Y(m)
5
80
90
100
Model D
0
0.05 0.03 0.02 0.01 0.005
–5 0
10
20
30
40
50 X(m)
60
70
80
90
100
FIGURE 19.2 Concentration contours for various models at t = 80 days for Kr = Kd = 1/day, Kc = 0.01/day, and Ks = 0.003/day. (Adapted from Figure 1 of Hu et al., 1997, Adv. Water Resour. 20(5–6):293–308.)
upscale from the pore to the Darcy to the field scale, especially when the field scale may be fractal. One method of attack, proposed in Park et al. (2005a, 2005b) is via the use of generalized central limit theorems (CLT). Essentially one writes the stochastic differential equation that the microbe obeys on the smallest scale and then applies the CLT to upscale. We present only a rudimentary summary of the results here. On the pore scale, the stochastic ordinary differential equation (SODE) the motile particle is assumed to satisfy has the form
X (0) (t ) = X (0) (0) +
t
v (0) (X (0) (r))dr + ρ (0) L (0) (t )
(19.21)
0
where the drift velocity v (0) (X (0) (r)) is assumed stationary, ergodic, and Markov with mean v and the fluctuating position L (0) (t ) is αl -stable Lévy and accounts for the self-motility. A classical CLT (Bhattacharya, 1982; Bhattacharya and Gupta, 1990) coupled with the fact that Lévy motions dominate Brownian shows X (0) (nt)→ L (1) (t ), where L (1) (t ) is a Darcy-scale Lévy motion which is a renormalized pore trajectory.
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Thus the Darcy scale SODE is X
(1)
(t ) = X
(1)
t
(0) +
v (1) (X (1) (r))dr + ρ (1) L (1) (t )
(19.22)
0
where v (1) (X (1) ) is the Lagrangian velocity, V (1) . In form, the previous two equations are identical, but mathematically v (1) (X (1) (r)) is rarely stationary and so the classical CLT cannot be applied to obtain the field scale trajectory X (2) . However, generalized CLTSs can be proved (Park, 2005a) and applied if it is assumed the Lagrangian drift velocity at the Darcy scale can be modeled as an αv -stable Levy process. With this assumption and a few technical constraints, it can be shown that at the field scale the ADE for the transition density (concentration) in 1-D is ∂f ∂ αv f ∂f = −v (2) + D(t ) α ∂t ∂x ∂x v
(19.23)
where (1)
v (2) = [v (1) ] + µl v (1) = E
1 |A| |B|
(19.24a)
v (1) (t , x0 ) dt dx0
(19.24b)
A = A(x0 (ω)) = {x0 (ω) : x0 (ω) ∈ [0, 1]}
(19.24c)
B = B(t , ω) =
A B
t t ≥ 0; 0
X (1) (τ , ω)dτ ∈ [0, 1]
(19.24d)
where ω is an elementary event. The αv derivative ∂ αv f /∂x αv is the well-known fractional derivative, and D(t ) = −(t σv )αv / cos(π αv /2) with σv a parameter in the definition of the αv stable Lévy motion; Sαv (t 1/αv σv , 1, v (1) ) is the distribution for the Lévy motion.
19.7 Lagrangian Stochastic Models for Nonlinear Reactions Mass transfer equations representing natural biological and chemical transformations in saturated subsurface systems typically involve strongly nonlinear transformations among multiple species. Eulerian methods that result in ensemble-averaged expected plume behavior have been successful in upscaling the effects of idealized heterogeneities on the fate and transport of linearly sorbing solutes at both equilibrium (e.g., Berglund and Cvetkovic, 1996) and nonequilibrium rates (e.g., above, cf. also Dagan and Cvetkovic, 1993; Quinodoz and Valocchi, 1993; Andricevic, 1995), and solutes undergoing linear decay (e.g., Hu et al., 1995; Miralles-Wilhelm and Gelhar, 1996). These methods are however, generally inappropriate for the application to reactive transport where nonlinearities exist in nonequilibrium transformations or in multicomponent (coupled) dependencies. Sudicky et al. (1990) point out that the ergodic requirement (that, simply, the solute domain is large relative to the dominant scale of heterogeneity) is invalid for a nonconservative (e.g., sorbing or degraded) solute whose domain shrinks with time. Also, the use of a macrodispersion parameter effectively represents as mixing what may actually be plume deformation due to nonuniform convections, as described in the previous chapter. In the case of dually-limiting reactants (interior and exterior to the plume, such that reactions only occur at the mixing fringe), this artificial mixing will significantly overestimate the reaction sink. The scaling procedure, as an equation averaging operation, is valid when the averaging operator commutes with the (linear) kinetic reaction operator, so
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that the average of quantities within the reaction term may be obtained. When nonlinearities exist in the kinetics of transformation, the averaging and reaction operations do not generally commute, and so the scaling approach fails to generate useful equations for average plume behavior. An approach to scaling complex reactive transport in heterogeneous materials may be obtained when one first applies the reaction operation to solute parcels as they follow nonuniform convective paths, and then averages the resulting reacted solute convections over the appropriate convective paths contributing to an observation. In this approach, known as the solute flux-based (Cvetkovic and Dagan, 1996; Cvetkovic et al., 1998) or stochastic-convective reaction (SCR) method (Simmons et al., 1995), the reactions are cast in terms of the solute residence-time during convection. The method is based in the stochastic-convective representation of dispersive transport of a passive tracer (Simmons, 1982). The travel-time of the solute is defined as the time of residence of solute moving through the aquifer, from the point of spill or contamination entry to the system, to the observation location or regulatory boundary. Solute particles that enter the system and arrive at the observation location follow particular paths, or streamtubes, and the set of streamtubes delivering solutes to an observation sampler (point), line (well), or plane (regulatory boundary) makes up an ensemble of travel paths, and so the travel-time describing the ensemble is a distributed quantity, characterized by a distribution function. When the reactive transport model along any given streamtube can be expressed in terms of travel-time, the solution to the model is in terms of travel-time, and the solute arrival at the observation is recovered by averaging the solution of the model against the travel-time distribution function. The advantages of this approach are (1) the reliance upon travel-time, a global measure of the effects of locally-varying Eulerian velocities, as opposed to estimates of the full nonuniform velocity field, and (2) the solution for each streamtube equation system can be obtained before averaging, thus eliminating the operator commutation problem with scaling nonlinearly reactive transport. This latter feature, it should be noted, results from the assumption that lateral mixing between streamtubes is negligible, that is, the flow in which the transport occurs is “segregated.” Recent work by Viswanathan and Valocchi (2004) and by Robinson and Viswanathan (2003) provides some innovative effective methods to deal with the occurrence of lateral mixing. This scaling approach is usually applied to provide predictions of observed solute arrivals at observation samples, or arrivals at an imaginary control plane. It is a direct although cumbersome matter to use the SCR approach to reconstruct estimates of plume evolution, which may be done if the travel-time distribution function is given or estimated at many points in the aquifer. Similar streamtube principles have been used to gain computational speedup in two- and three-dimensional reactive transport simulations in a deterministic setting (Thiele et al., 1995a, 1995b). The method proceeds in three basic steps. First, the existence of an ensemble of streamtubes that is suitable for averaging must be ensured by checking the validity of the SCR assumptions for the particular reaction system, initial, and boundary conditions. Second, the reaction system must be solved for the streamtube ensemble (or canonical streamtube, defined below, when it exists). Finally, the travel-time distribution function must be determined for the particular flow regime and initial and boundary conditions. The following two subsections borrow heavily from Simmons et al. (1995).
19.7.1 Streamtube Formulation The concept of the streamtube as a path taken by solute parcels from a source to an observation is made under the requirement that flow in it (a subset of the total flow domain) is constant for both space and time. The assumptions under which such an ensemble of streamtubes may exist are as follows: The members of the ensemble are physically independent, with no mass transfer among streamtubes. This allows treatment of the solute paths as integral, averagable quantities. This restricts diffusive/dispersive mass transports lateral to streamtubes; for example, this representation is incapable of incorporating local transverse dispersion. For simplicity we ignore also longitudinal mixing processes, although this is not a requisite assumption as a longitudinal mixing may be incorporated within the streamtube (Ginn, 2001). Second, the streamtube orientation in Eulerian space is arbitrary save that it must of course connect the source to the measurement location, and that the projection of its axis, s, onto the x-axis connecting the
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source and observation be one-to-one (such that the x(s) is monotone increasing). This assumption allows us to associate with each streamtube a 1D velocity function v(x)ε{v(x)} that is positive, and so allows the definition of an associated travel-time function. Further, each streamtube obeys a known reaction function r. A streamtube in three-space (which may have variable areal cross section) is defined such that its average cross-sectional velocity vs (x ) times the corresponding cross-sectional water content ns (x ) is a constant, q. To represent a streamtube in three-dimensions with an equivalent 1D streamtube with the same flow q we must honor the velocity to preserve the transport characteristics. Velocity is defined by vs (x ) = q/ns (x ) in the streamtube and by v(x ) = q/n(x ) in the equivalent 1D system. Mass balance implies vs (x )ns (x )As (x ) = v(x )n(x )Ao where Ao is a (constant) reference area, and so we may define an effective porosity n(x ) = ns (x )As (x )/Ao to give v(x ) = vs (x ) along the equivalent 1D system. Under this construction the convective-reactive transport along a given streamtube is represented in the 1D form ∂(nC) ∂(nvC) + = nr ∂t ∂x
(19.25)
By construction n(x)v(x) = q is a constant of x, and n is assumed constant of t , so Equation 19.25 simplifies to ∂C ∂C + v(x) =r ∂t ∂x
(19.26)
A simple change of variables in Equation 19.26 allows expression of velocity in terms of solute travel-time. The travel-time corresponding to the streamtube velocity v(x) is the time elapsed as a tracking particle is transported from x0 to x, x T (x; x0 ) = x0
dx /v(x ) =
x 0
dx /v(x ) −
x0
dx /v(x ) = T (x) − T (x0 )
(19.27)
0
where T (x) means T (x , 0). By positivity of velocity, T (x) is a monotone increasing function in x and the inverse function, (T (x)) = T 1 (τ ) = x, exists and is monotone increasing in variable τ . Note that mass loss over the ensemble corresponds to the case where ensemble maximum travel-time is infinity. In this case, a finite T ∗ would be used that represents the largest travel-time of a tracer particle captured at a measurement location, and the mass lost would be accounted in the specification of the streamtube frequency distribution. Now invoking the chain rule with dT (x) = dx/v(x) and incorporating the inverse function (T ) we may write for Equation 19.26: ∂C ∂C + = r((T ), t , C) ∂t ∂T
(19.28)
This last form expresses the result that C can be obtained explicitly as a function of global travel-time. Equation 19.7 is the basic streamtube model. Note that if r is streamtube invariant (requiring that r contain effective streamtube porosity as factor) the solution to Equation 19.26 depends only on v. Any set of streamtubes for which the velocity statistics are identical to those of {v} (determined from the observation of conservative tracer breakthrough or from conductivity statistics), and for which r accurately represents the reactions, suffices. A working hypothesis of this approach is that the streamtube model more closely represents the actual conditions for the definition and calibration of the kinetic model r than does the conventional averaging approach. Closed-form solutions to Equation 19.26 may be found under general conditions on r, including nonlinear and dynamic forms (e.g., r depends on a parameter such as microbial mass that evolves according to its own differential equation). We will return to a few examples after introducing the travel-time distribution function.
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Ensemble averaging of the solution to Equation 19.28, described next, is greatly simplified when the solution to Equation 19.28 may be written in terms of dimensionless travel-time, and rescaled to fit any particular travel-time. When the solution to the streamtube equation is rescalable over travel-time, the solution is termed “canonical.”
19.7.2 Stochastic–Convective Averaging Here we examine averaging of the foregoing solutions according to the travel-time pdf, a measure of streamtube frequency. Once a canonical solution of Equation 19.7 is obtained as C(T , t ), the streamtube ensemble average solution, C(x, t ), is found by averaging C(T , t ) over the travel-time pdf p(τ ; x) for the streamtube travel-times to location x. This pdf is defined over the streamtube ensemble in the frequency sense as (Simmons, 1982; Shapiro and Cvetkovic, 1988; Dagan and Nguyen, 1989) p(τ ; x) = δ(τ − T (x))
(19.29)
where δ is the Dirac distribution function and the angle brackets indicate average over the streamtube ensemble. The expectation can be expressed as ∞ C(τ , t )p(τ ; x) dτ
C(x, t ) =
(19.30)
0
In Equation 19.30, p(τ ; x) is the pdf for random travel-time τ to a plane normal to the major flow axis at x, measured along that axis (Simmons, 1982; Dagan and Nguyen, 1989). The averaging in Equation 19.30 is over the realizations of (random) travel-time at a certain point in x space, and not over the deterministic measure of travel-time T (x) itself. That is, the average in the right-hand side of Equation 19.30 is exactly the streamtube ensemble average, as is demonstrated on substitution of Equation 19.29: ∞ C(τ ; t )p(τ ; x) dτ ≡ 0
∞
∞ C(τ ; t )δ(τ − T (x)) dτ = 0
C(τ ; t )δ(τ − T (x)) dτ = C(T (x), t )
0
(19.31) The numerical calculation Equation 19.31 via discrete integration requires first the enumeration of the surfaces Ci (T , t ) for each realization of travel-time function Ti (x). When a canonical solution is available this is accomplished by simply rescaling the travel-time axis of the canonical solution C(T , t ) to the indicated Ti (x). This approach is used by Wise and Carbeneau (1994), whose averaging is associated with the measured cumulative passive breakthrough (which they term the “fractional breakthrough,” that is the integral part of our travel-time pdf). Finally, one may also introduce heterogeneity into the reaction term through either the space-time dependency or the solute component dependency in the right-hand side of Equation 19.30 (for instance, when r(x, t , C) = g (x, t )h(C), and g indicates concentration of reactive iron oxides or attached biomass). Further, correlations between the flow properties and the reaction properties may be cast as a conditioning of the travel-time pdf upon the value of the reaction properties. When such heterogeneity is represented through pdfs of the random properties and when these pdfs are known, the expectation may be computed in many cases by simple sequential averaging of C(T , t ) according to each random property (with pdfs appropriately conditioned to reflect correlations). Suppose, for instance, randomness in the case of a factorable hyperbolic kinetic decay (e.g., biodegradation following Michaelis–Menten kinetics), is such
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that we write Equation 19.30 as r(x, t , C) = {g }(x, t )h(C)
(19.32)
where g represents time evolution of a random space function selected from the ensemble {g }. That is, Equation 19.32 is the reactive term written for one realization (streamtube) of the random pathways. In this case (Simmons et al., 1995) the streamtube solution is cast in terms of not only travel-time (cumulative reciprocal velocity) but also cumulative “reaction property” G, defined as the integral of g along the streamtube coordinate. Then the travel-time averaging in Equation 19.30 is followed by averaging over the ensemble distribution of G, appropriately conditioned; ∞ C(x, t )G =
C(τ , t )p(τ ; x|G) dτ
(19.33a)
C(τ , t )G p(G; x) dG
(19.33b)
0
∞ C(x, t ) = −∞
19.7.3 Travel-Time Distribution Function The travel-time T (x) determines the mapping of the random velocity along a streamtube onto a random velocity field for an equivalent one-dimensional system with distance coordinate x. Thus the travel-time pdf is experimentally observed as the conservative tracer breakthrough curve at the control plane at x in response to a unit Dirac-δ input function. Alternatively, the pdf may be deconvolved from the observed response to other known input functions (e.g., Ginn et al., 1995). In either case, it should be noted that pore-scale mixing processes (such as diffusion and pore-scale dispersion) serve to smooth the observed breakthrough curve in an irreversible way. One may also hypothesize forms for p(τ ; x), a priori, such as lognormal or inverse-Gaussian (Simmons, 1982). Frequently, tracer test results are not available for characterizing transport between a source and an observation location. It is possible to estimate the expected travel-time distribution function that corresponds to the average arrival time distribution over an ensemble of flow fields. To derive the expected travel-time distribution for particles arriving at an observation point at distance x1 from source centroid, g (t ; x1 ), at first order, we follow Dagan (1989, chap. 5.8; see also Appendix A in Cvetkovic and Dagan 1996). For simplicity it is assumed that all particles start within a finite plane source that is oriented normal to the average flow direction. A particle starts at coordinates (0, a2 , a3 ), at initial velocity parallel to x-axis v0 = V1 (0, a2 , a3 ). The probability that a solute particle has crossed the regulatory control plane (assumed normal to the flow direction x, ¯ located at x1 ) at time t = τ is the same as the probability that the particle’s displacement along the flow axis is larger than the distance to the control plane, that is, X1 > x1 . Hence, with φ(X1 , v0 ; t ) as the joint pdf of X1 , v0 , at time t , one has for the cumulative arrival distribution ∞ G(τ ; v0 , x1 ) =
φ(X1 ; v0 , τ ) dX1
(19.34)
x1
It is important to note that the concentration probability function φ is a statistical construction that is not equivalent to any particular physical realization unless the transport is ergodic, for example, that the lateral domain of the source is large compared to the heterogeneity scale. Various models for φ have been derived based on different constructs of the statistical description of the controlling (conductivity) field and boundary conditions (Dagan, 1991; Dagan et al., 1992). The expected travel-time pdf is obtained from the cdf G by averaging Equation 19.34 over possible initial velocities v0 (where v0 is assumed Gaussian
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with mean U ) and differentiating with respect to τ . 1 g (τ ; x1 ) = U
1 ∂ v0 g (τ , v0 ; x1 ) dv0 = U ∂τ
∞ ∞ v0 φ(X1 , v0 ; τ ) dX1 dv0
(19.35)
0 x1
For instance, for asymptotic conditions where the impact of v0 and τ correlations vanish, g is given by 1 −(x1 − U τ )2 ∂ x1 − U τ g (t ; x1 ) = − √ exp √ 2X11 ∂τ X11 2π
(19.36)
where X11 is the longitudinal particle covariance, a measure of the ensemble-averaged longitudinal second spatial moment, and U is the source-averaged initial velocity.
19.7.4 Some Reaction System Examples Here we summarize some recent examples of reaction systems that have been constructed for particular biogeochemical systems and used in streamtube-ensemble reactive transport models. The examples include a generalized linear sorption model, and a model of aerobic biodegradation with microbial transport. Lassey (1988) provided a generalized formulation of a model combining equilibrium, kinetic-reversible, and kinetic-irreversible sorption processes and its solution for particular boundary conditions. The solution to the streamtube Equation 19.30 with r given by the kinetic reversible sorption model of Equation 19.1a and Equation 19.1b (e.g., r = −(ρb /n)∂S/∂t ), in the case of an instantaneous injection at the upstream boundary, is adopted from Lassey (1988; cf. Also Cvetkovic and Dagan, 1996; Cushman et al., 1996) C(τ , t ) = e−Kr Kd t δ(t − τ ) + Kr2 Kd τ e[−Kr Kd t −Kr (t −τ )] I1 [Kr2 Kd τ (t − τ )H (t − τ )]
(19.37)
where I1 (z) = z −1/2 I1 (2z 1/2 ), and I1 is the modified Bessel function of the first kind of order one. This solution is appropriate for averaging as indicated in Equation 19.30. Note that as pointed out in Simmons et al. (1995) and Theile (1995a), the so-called initial value problems, for example, those involving the initial distribution of a reactant (such as attached biomass) in space, impose certain restrictive assumptions on the use of the streamtube approach. In the most restrictive case, uniformity of the distributed property over the streamtube ensemble is required. (This is only slightly less restrictive than the requirement of spatial biochemical homogeneity overall.) In the event of spatially nonuniform initial distribution of biomass, full averaging of the streamtube-component evolution equations is feasible, but requires the joint probability of biomass occurrence and streamtube travel-time (as in Equation 19.33). Biogeochemical and biodegradation systems involving attached phase biomass or biofilms are typically formulated as initial value problems, and thus may be complicated by heterogeneity in not only initial microbial distributions, but also by the dynamic microbial heterogeneity associated with microbial growth. This is the case in the next example, involving nonlinear degradation of an organic solute by a microorganism that is initially uniformly attached to the solid phase but partitions to the aqueous phase according to a nonequilibrium and nonlinear rate equation. This example describes meter-scale laboratory experiments in aerobic biodegradation in physically heterogeneous media, and is greatly condensed from Murphy et al. (1997) and Ginn et al. (2001). Simplified evolution equations for the organic substrate benzoate, oxygen, mobile microbes, immobile microbes, and passive tracer bromide, are shown here in one-dimensional (streamtube projection) format. Because we have retained one-dimensional longitudinal dispersivity d in the transport operation in Equation 19.38, to preserve the mixing between oxygenated and oxygen-depleted waters that is important to degradation, the equations are cast in terms of their streamtube velocity projected onto the x-axis, as opposed to travel-time. This aspect, and the possibility
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of nonuniformities in the initial biomass concentrations, violates the requirements for a travel-time (i.e., constant-velocity) representation of streamtube velocities. Nevertheless for simplicity in calculating the SCR predictions, a constant velocity ensemble, corresponding to an equivalent travel-time ensemble, is used as an approximation of the transport. The reactions involve degradation of benzoate (Cb , Equation 19.38a) as the electron-donor, with oxygen consumed as the terminal electron-acceptor (Co , Equation 19.38b). Degradation induces an increase in biomass, the rates of which are the same for aqueous (Cmm , Equation 19.38c) and attached (Cim , Equation 19.38d) biomass. The mass transformations associated with the degradation are governed by the bracketed dual-Monod terms in (Equations 19.38a, b, c) that effectively shut down the transformation rate under limiting conditions, for example, when C0 or Cb values drop to the order of K0 or Kb , respectively. Biomass partitions kinetically and reversibly, but with the added complexity that the equilibrium partition coefficient is dependent on the local ionic strength, changes in which are due to the presence of an inert bromide tracer (CT , Equation 19.38e) that effectively compresses the electrostatic repulsive layer of the quartzitic solid phase. For simplicity, attached biomass is treated as a stationary volumeless dissolved species. These transformations incur a strong nonlinear coupling among the four mobile components (organic solute, oxygen, aqueous biomass, and bromide) and the one immobile component (attached biomass). More complex forms, involving microbial metabolic lag and dynamic endogenous respiration, are described in Murphy et al. (1997). The transport takes place at average pore-water velocity of 50 cm/d through a 1 m flow cell that is 0.1 m × 0.2 m in cross-section, in inoculated porous media consisting of high hydraulic conductivity sand containing a set of randomly located low conductivity inclusions. Details on the heterogeneity pattern and pre-experimental modeling are found in Ginn et al. (1995). C0 ∂vx Cb ∂ 2 Cb µ Cb ∂Cb + −d (C = − + C ) · mm im ∂t ∂x ∂x 2 Y (K0 + C0 ) (Kb + Cb )
(19.38a)
∂Co ∂vx Co ∂ 2 Co µ C0 Cb + −d = −F (Cmm + Cim ) · ∂t ∂x ∂x 2 Y (K0 + C0 ) (Kb + Cb )
(19.38b)
∂Cmm ∂vx Cmm ∂ 2 Cmm C0 Cc + −d = −µCmm − Kr Kd (CT )Cmm + Kr Cim ∂t ∂x ∂x 2 (K0 + C0 ) (Kc + Cc ) (19.38c) ∂Cim C0 Cc = −µCim · + Kr Kd (CT )Cmm − Kr Cim ∂t (K0 + C0 ) (Kc + Cc )
(19.38d)
∂CT ∂vx CT ∂ 2 CT + −d =0 ∂t ∂x ∂x 2
(19.38e)
The initial conditions in the flow cell are fully oxygenated water (Co = 8 mg/l) with equilibrium distributed biomass at 5 × 106 cells/ml in the aqueous phase. The distribution coefficient is roughly 2/3 in the absence of bromide and doubles at 300 mg/l bromide. The boundary conditions are continuous injection of oxygenated (8 mg/l) water with a 1d pulse of benzoate (300 mg/l) and bromide (392 mg/l) in solution injected to evaluate the resulting biodegradation. Data collected include breakthrough curves at the outlet of the flow cell for benzoate, oxygen, and aqueous microorganisms. The first step in obtaining the SCR solution is the determination of a travel-time distribution function, which was taken from the breakthrough curve of the bromide tracer, shown by the “+” marks in the top panel of Figure 19.3. Using the principle of superposition in reverse allows deconvolution of the breakthrough curve to determine the breakthrough curve expected to result from an instantaneous injection (Dirac pulse) at the boundary, that is, the travel-time distribution function. This is shown in the bottom panel of Figure 19.3, and the reconvolved simulation of the bromide breakthrough is shown as the solid line in the top panel of Figure 19.3. (The deconvolution is not a trivial exercise because it involves solving a Volterra integral equation and
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Bromide [mg/l]
300 250 200 150 100 50 0 0.05
Frequency
0.04 0.03 0.02 0.01 0.00 24
48
72 96 Time [hours]
120
144
FIGURE 19.3 Top panel: Observed breakthrough of bromide (+) and reconstituted breakthrough curve (solid line) using convolution of the system travel-time distribution function with the 1-day square impulse function. Bottom panel: Travel-time distribution function.
is usually unstable numerically, although a unique solution exists.) In the second step, the SCR solution ensemble was generated by solving Equation 19.38 for 100 different but constant velocities corresponding to the travel-time domain shown in Figure 19.3. That is, effective velocities were selected according to v = x/T , where T is discretized at 40, 120 h. These solutions were obtained using RAFT, a deterministic flow and reactive transport simulator capable of general reaction systems (Chilakapati, 1995). The SCR predictions are obtained in the third step by averaging the ensemble of breakthrough curves per solute against the travel-time distribution function shown in Figure 19.3. This average was carried out by solving a discrete form of Equation 19.30 using an ensemble of 100. The resulting predictions are shown with observed data for benzoate, oxygen, and aqueous microbes in Figure 19.4. Numerous reactions systems have been addressed with the streamtube approach, in part because of the facility in developing solutions in one transport dimension. In addition to the foregoing, generalized solution surfaces C(τ , t ) have been derived for multicomponent nonlinear equilibrium sorption (Charbeneau, 1988; Dagan and Cvetkovic, 1996; Ginn, 2001), immiscible two-phase displacement (the Buckley–Leverett problem, Thiele et al., 1995a), and simplified nonlinear decay, precipitation, or dissolution rate equations (Simmons et al., 1995; Dagan and Cvetkovic, 1996; Cirpka and Kitanidis, 2000), to name a few.
19.7.5 Toward Handling Heterogeneity in Reactive Properties As was pointed out in Section 19.4.1, a number of works (Tompson, 1993; Szecsody et al., 1998; Glassley et al., 2001; Bhattacharjee et al., 2002) state explicitly that upscaling reactive transport in natural porous media requires not necessarily the aquifer reactivity volume fraction or otherwise Eulerian information, but the distribution of flux over cumulative reactivity. Simmons et al. (1995) describe such an approach involving the distribution of solute flux over both travel-time τ and cumulative reactivity (defined as the integral along a streamtube path of the spatially
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Benzoate [mg/l]
250 200 150 100 50
Aqueous microbes [cells/ml]
Oxygen [mg/l]
0 8 6 4 2 0 1.2e+07 1.0e+07 7.5e+06 5.0e+06 2.5e+06 0.0e+00 0
30
60 90 Time [hours]
120
150
FIGURE 19.4 Top panel: Observed (+) and simulated (solid line) breakthrough of benzoate. Middle panel: Observed (+) and simulated (solid line) breakthrough of oxygen. Bottom panel: Observed (+) and simulated (solid line) breakthrough of aqueous microorganisms.
variable reactivity), G. The field scale solute flux is reconstructed as an integral over the ensemble of streamtubes with joint frequency distribution p(τ , G) of flux (Simmons et al., 1995, Equation 36). The method is outlined for general linear or nonlinear kinetically controlled irreversible reactions and is shown admissible for any kinetic where the reaction rate factors into (explicitly) spatially dependent term and concentration-dependent terms. Cvetkovic et al. (1998) provide a stochastic interpretation of the same basic approach and define a “reaction flow path” µ as the cumulative reactivity G above, and describe p(τ , µ) in terms of the stochastic Lagrangian transport approach of Dagan (1989). They show first-order analytical and Monte Carlo methods to obtain statistics of p(τ , µ). The conceptual model also differs in that transport is via advective streamlines whereas Simmons et al. (1995) conceptualize streamtubes. Cvetkovic et al. (1998) provide detailed temporal and spatial moment analyses for several equilibrium and kinetically controlled reactions in statistically homogeneous, stationary, and isotropic media. This approach is subsequently focused to the case of reactive transport in fractures in Cvetkovic et al. (1999) and used to simulate sorbing tracer transport at Yucca Mountain in Painter et al. (2001) and in a network model based on the Äspö (Sweden) site in Cvetkovic et al. (2004). The authors point out that their results stress the need for further studies on the upscaling of travel-time and cumulative reactivity distributions.
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19.8 Connection between Approaches The Eulerian methods described in Section 19.6 and the Lagrangian approach described above can be examined in light of one another through the use of a formal coordinate transformation that shows the particle (Lagrangian) paths in terms of the spatial (Eulerian) velocities (Dagan et al., 1992; Dagan and Cvetkovic, 1993; Cvetkovic and Dagan, 1994, 1996; Cushman et al., 1996). In this section, we present this coordinate transformation for reference. We begin conceptually again with Equation 19.1, taking dij = 0 and steady divergence-free velocity field v(x), the mean of which is in the x1 direction. Further, the magnitude of v1 (x) is restricted to be positive. Now to trace the path of a solute parcel or particle in such a system, define a particle coordinate tracking function X(t ; t 0 ,x0 ) as a solution to the Lagrangian equation dX/dt = V(X), with the initial condition X(t 0 ; t 0 , x 0 ) = x 0 . Under steady velocity, we have also X(t ; t 0 , x 0 ) = X(t − t 0 ; x 0 ). We restrict ourselves to the tracking of the particle path until it strikes an infinite plane positioned normal to the axis of mean flow, at x1 , and introduce the following coordinates to put transport in the x1 -direction in terms of travel-time and transport in the remaining two directions in terms of deviations from the starting point x0 . T (x; x0 ) = t − t0
(19.39)
η(x; x0 ) = X2 (τ ; x0 )
(19.40)
ξ(x; x0 ) = X3 (τ ; x0 )
(19.41)
The travel-time function T is defined as the inverse of the particle position function X. The new coordinate system satisfies by construction τ = 0, η = x2 , and ξ = x3 for x1 = x10 , and 1 dτ = dx1 v1 (x1 , η, ξ )
(19.42a)
dη dτ v2 (x1 , η, ξ ) dη = = dx1 dτ dx1 v1 (x1 , η, ξ )
(19.42b)
dξ dτ v3 (x1 , η, ξ ) dξ = = dx1 dτ dx1 v1 (x1 , η, ξ )
(19.42c)
Thus x2 = η(x1 , x 0 ) and x3 = ξ(x1 , x 0 ) are equations of streamlines (streamtube centerlines) for the particle path. In this coordinate system, along the streamlines, Equation 19.1a takes the form of Equation 19.30, with r given by Equation 19.1b [e.g., r = −(ρb /n)∂S/∂t ]. Thus the transformation Equation 19.39 to Equation 19.42 formally translates the governing equations into each other. Cushman et al. (1996) have used this transformation to compare the spatial moments of a plume evolving according to Equation 19.1 obtained by both the Eulerian and Lagrangian (according to Dagan and Cvetkovic [1993], using Lassey’s solution, [Equation 19.37]) approaches. In that case the zero and first spatial moments are equivalent between the two approaches, but the second moments of the Eulerian solution contain a linear dependence on time with coefficient in dij . In particular, the long-time transverse second moment is linear in time and otherwise constant, so the Eulerian approach predicts the plume width will grow linearly in time while the Lagrangian approach predicts the plume width will reach a constant. Note that this discrepancy is not inherent to any fundamental difference between the approaches themselves; rather, it arises from the assumption of zero dispersion dij in the Lagrangian approach. In
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the previous chapter, the importance of pore-scale mixing (e.g., nonzero dij ) to average plume dilution is illustrated and in the previous section; the effect of mixing on scaling multicomponent nonlinear reactions is noted. This highlights a subtle aspect of mathematical scaling of processes in general. The total mass moved by pore-scale mixing is in general relatively small as the process is small scale in space and time (it is slow) — however it can play a significant role in the eventual large scale and longtime behavior of the system.
Definition of Symbols Mathematical Adornments ◦
represents Fourier–Laplace transform where t is dual to ω and x is dual to k represents Fourier space transform where x is dual to k − represents expected value
Principal Actors Ao C C0 Co , Cb , Cmm , Cim , CT Dij (x − y, t − t ) dij δ(t ) F f φ(X1 , v0 ; t ) G g (x) H (t ) I1 K Kr Kd KdG kd Kf Kr Kc Ks Ko Kb µ p(τ ; x) R ρb n r(C) r S
constant reference area for effective streamtube [L2 ] aqueous concentration [M/L3 ] initial condition for aqueous concentration [M/L3 ] aqueous concentrations of oxygen, benzoate, mobile microbes immobile microbes, and bromide tracer, respectively nonlocal dispersion tensor defined in Equation 19.4 symmetric microscale dispersion tensor [L2 /T] Dirac-delta function mass ratio of oxygen consumed per benzoate consumed by microbial degradation [1] fluctuation in the natural log of K = ln K − ln K joint probability distribution of X1 , v0 , at time t cumulative reactivity, integral of g along a streamtube, a distributed quantity reaction rate coefficient along a given streamtube, a random field Heaviside function, integral of δ(t ) modified Bessel function of the first kind of order one hydraulic conductivity tensor [L/T] desorption rate [1/T] equilibrium distribution coefficient [L3 /M] geometric mean of Kd (x) fluctuation in Kd from its expected value = Kd − Kd = Kr Kd is the forward sorption rate [1/T] desorption rate [M/TL3 ] solute degradation rate in the solution [1/T] solute degradation rate in the sorbed phase [1/T] half-saturation constant for oxygen biodegradation [M/L3 ] half-saturation constant for benzoate biodegradation [M/L3 ] specific growth rate for microbial degradation of benzoate [1/T] distribution of solute flux over travel-times = 1 + ρb Kd /n is the retardation factor [1] bulk density of the aquifer material [M/L3 ] porosity algebraic relation specifying S as a function of C at equilibrium reaction rate in streamtube [M/L3 T] sorbed concentration per unit mass of solid [M/M]
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So t τ T (x; xo ) V v v(x) (T ) Y W
initial condition for sorbed concentration [M/M] ¯ where R¯ = 1 + Kd nondimensional time = t V¯ /Rl travel-time [T] as a distributed variable deterministic travel-time along streamtube from xo to x porewater velocity vector [L/T] fluctuation in V from its expected value = V − V Lagrangian velocity along a streamtube [L/T] inverse function of travel-time (delivering x) yield coefficient for microbial degradation of benzoate [M/M] normally distributed random space function
Variances, Symbolically σa2
the variance of the fluctuation a of the quantity A
Covariances, Symbolically ab ff fkd vi v j kd vj kd kd WW
the expected value of the product of the fluctuations a and b (of A and B, respectively), that is, the covariance. Some examples: fluctuating log-conductivity covariance fluctuating log-conductivity-partition coefficient covariance fluctuating velocity covariance fluctuating velocity-partition coefficient covariance fluctuating distribution coefficient covariance covariance of W
Integral Scales (a.k.a., Correlation Lengths) lw l
is the integral scale of W , [L] is the correlation length of ln K [L]
Glossary Cumulative reactivity: integral of reactivity along a streamtube. Equilibrium reaction: a chemical or biological transformation that occurs at a rate much faster than the other fate and transport processes governing a particular species. Eulerian: referring to a coordinate system that is independent of the motion of groundwater, solutes, and other items of interest, that is, fixed. First-order kinetics: a means of expressing the rate of a kinetically controlled reaction as proportional to the difference between the current state of the reactants and their equilibrium point. Fluctuation: departure of the value of a property from some defined mean or expected value of that property. Half-saturation constant: parameter of the Monod kinetic rate formula for biodegradation. Heterogeneous (property): a property (e.g., porosity) whose value varies with spatial location. Heterogeneous reaction: a chemical or biological transformation that involves a change of phase (typically between solid and aqueous phases, such as a sorption reaction). Homogeneous (property): a property (e.g., porosity) whose value is not dependent on spatial location. Homogeneous reaction: a chemical or biological transformation that involves a single phase. Inhomogeneous: heterogeneous.
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Isotherm: a means of expressing the equilibrium relationship among reactants and products of an equilibrium reaction (defined at a given temperature, thus the name), typically as an algebraic relation. Kinetically controlled reaction: a chemical or biological transformation that occurs at a rate on the same order as that of the other fate and transport processes governing a particular species. kinetics: the expressions of the rates of reactions for kinetically controlled reactions. Lagrangian: referring to a coordinate system that is associated with a point moving with the groundwater flow. Monte Carlo: a computational strategy for dealing with uncertainty, where unknown parameters are characterized by some frequency distribution and repeated simulations are made using values chosen from such distribution(s). Operator-splitting: a computational scheme wherein distinct fate and transport processes are treated within a given time step by overlaying their effects sequentially for that time step; this is an approximation. Pseudokinetic: rates of transformation that appear kinetically controlled but are associated with (multiple) equilibrium reactions in heterogeneous media. Random: uncertain. Reactivity: reactive site density (sites per bulk volume) associated with surfaces within aquifer materials. Streamtube: REV-scale (e.g., super-pore scale) path associated with streamlines of transport that is steady state in direction. Travel-time distribution: distribution of fractional flux over travel-time from start location to observation location.
Acknowledgments This work was supported by the Environmental Management Science Program, Office of Health and Environmental Research and Office of Science and Technology, United States Department of Energy. The second author was supported by the National Science Foundation through the project grant no. 0420374 entitled “Biogeochemical cycling of heavy metals in lake Coeur d’Alene sediments: The role of indigenous microbial communities.”
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Dzombak, D.A. and Morel, F.M.M. 1990. Surface Complex Modeling; Hydrous Ferric Oxide. WileyInterscience, New York. Elimelech M., Nagai, M., Ko, C.H., and Ryan, J.N. 2000. Relative insignificance of mineral grain zeta potential to colloid transport in geochemically heterogeneous porous media. Environ. Sci. Technol. 34:2143–2148. Fetter, C.W. 1993. Contaminant Hydrology. Macmillian Publishing Co., New York. Gear, C.W. 1988. Differential–algebraic equation index transformations. SIAM J. Sci. Comput. 9(1):39–47. Gear, C.W. and Petzold, L.R. 1984. ODE methods for the solution of differential/algebraic systems. SIAM J. Numer. Anal. 21:716–728. Gelhar, L.W. and Axness, C.L. 1983. Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour. Res. 19:161–190. Ginn, T.R. 2001. Stochastic–convective transport with nonlinear reactions and mixing: finite streamtube ensemble formulation for multicomponent reaction systems with intra-streamtube dispersion. J. Contam. Hydrol. 47:1–28. Ginn, T.R., Murphy, E.M., Chilakapati, A., and Seeboonruang, U. 2001. Stochastic–convective transport with nonlinear reactions and mixing: application to intermediate-scale experiments in aerobic biodegradation in saturated porous media. J. Contam. Hydrol. 48:121–149. Ginn, T.R., Simmons, C.S., and Wood, B.D. 1995. Stochastic–convective transport with nonlinear reaction: biodegradation and microbial growth. Water Resour. Res. 31:2689–2701. Haggerty, R. and Gorelick, S.M. 1995. Multiple-rate mass transfer for modeling diffusion and surface reactions in heterogeneous media. Water Resour. Res. 31(10):2383–2400. Hassan, A.E., Cushman, J.H., and Delleur, J.W. 1998. The significance of porosity variability to flow and transport in random heterogeneous porous media. Water Resour. Res. 34(9):2249–2259. Hu, B.X., Cushman, J.H., and Deng, F.W. 1997. Nonlocal theory of reactive transport with physical, chemical, and biological heterogeneity. Adv. Water Resour. 20(5–6):293–308. Hu, B.X., Deng, F.W., and Cushman, J.H. 1995. A nonlocal theory of reactive transport with physical and chemical heterogeneity: linear nonequilibrium sorption with random Kd . Water Resour. Res. 31(9):2219–2237. Kabala, Z. and Sposito, G. 1991. A stochastic model of reactive solute transport with time-varying velocity in a heterogeneous aquifer. Water Resour. Res. 27(3):341–350. Kabala, Z. and Sposito, G. 1994. Statistical moments of reactive solute concentration in a heterogeneous aquifer. Water Resour. Res. 30(3):759–768. Karickhoff, S. 1983. Organic pollutant sorption in aquatic systems. J. Hydraul. Eng. 110:707–733. Knapp, E.P., Herman, J.S., Hornberger, G.M., and Mills, A.L. 1998. The effect of distribution of ironoxyhydroxide grain coatings on the transport of bacterial cells in porous media. Environ. Geol. 33:243–248. Lichtner, P.C., Steefel, C.I., and Oelkers, E.H. (eds.) 1996. Reactive Transport in Porous Media; Reviews in Mineralogy, Volume 34. P.H. Ribbe, series editor. Mineralogical Society of America, Washington, D.C. Lichtner, P.C. and Tartakovsky, D.M. 2003. Upscaled effective rate constant for heterogeneous reactions, Stochast. Environ. Res. Risk Assessment (SERRA) 17(6):419–429. Metzler, R. and Klafter, J. 2000. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339:1–77. Miralles-Wilhelm, F. and Gelhar, L.W. 1996. Stochastic analysis of transport and decay of a solute in heterogeneous aquifers. Water Resour. Res. 32(12):3451–3459. Murphy, E.M., Ginn, T.R., Chilakapati, A., Resch, C.T., Phillips, J.L., and Wietsma, T.W. 1997. The influence of physical heterogeneity on microbial degradation and distribution in porous media. Water Resour. Res. 33:1087–1104. Novak, C.F. and Sevougian, S.D. 1993. Propagation of dissolutin/precipitation waves in porous media. In Migration and Fate of Pollutants in Soils and Subsoils, D. Petruzzelli, F. G. Helffereich (eds.) NATO ASI Series, Series GL Ecological Sciences, vol. 32. Springer-Verlag, Berlin.
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Painter S., Cvetkovic, V., and Turner, D.R. 2001. Effect of heterogeneity on radionuclide retardation in the alluvial aquifer near Yucca Mountain, Nevada. Ground Water 39:326–338. Park, M., Kleinfelter, N., and Cushman, J.H. 2005a. Scaling laws and Fokker–Planck equations for 3-dimensional porous media with fractal mesoscale. SIAM Multiscale Model. Simul. 4(4): 1233–1244. Park, M., Kleinfelter, N., and Cushman, J.H. 2005b. Renormalizing chaotic dynamics in fractal porous media with application to microbe motility. Geophysical Res. Ltr. 33(1), Art. No. L01401. Quinodoz, H.A.M. and Valocchi, A.J. 1993. Stochastic analysis of the transport of kinetically sorbing solutes in aquifers with randomly heterogeneous hydraulic conductivity. Water Resour. Res. 29(9):3227–3240. Robinson B.A. and Viswanathan, H.S. 2003. Application of the theory of micromixing to groundwater reactive transport models, Water Resour. Res. 39(11). Rubin, J. 1983. Transport of reacting solutes in porous media: relationship between mathematical nature of problem formation and chemical nature of reactions. Water Resour. Res. 19(5):1231–1252. Rubin, J. 1990. Solute transport with multisegment, equilibrium-controlled reactions: a feed forward simulation method. Water Resour. Res. 26(9):2029–2055. Ryan, J.N., Elimelech, M., Ard, R.A., Harvey, R.W., and Johnson, P.R. 1999. Bacteriophage PRD1 and silica colloid transport and recovery in an iron oxide-coated sand aquifer. Environ. Sci. Technol. 33:63–73. Scheibe, T.D. and Freyberg, D.L. 1995. Use of sedimentological information for geometric simulation of natural porous media structure. Water Resour. Res. 31:3259–3270. Schulmeister, M.K., Healey, J.M., McCall, G.W., Birk, S.M and Butler, Jr, J.J. 2003. High-resolution chemical characterization of an alluvial aquifer. In Modelcare 2002: Calibration and Reliability in Groundwater Modeling: A Few Steps Closer to Reality, K. Kovar and Z. Hzkal (eds.), IAHS Publication 277, International Association of Hydrological Sciences, Wallingford, UK, pp. 419–423. Simmons, C.S. 1982. A stochastic–convective transport representation of dispersion in one-dimensional porous media systems. Water Resour. Res. 18:1193–1214. Simmons, C.S., Ginn, T.R., and Wood, B.D. 1995. Stochastic-convective transport with nonlinear reaction: mathematical framework. Water Resour. Res. 31:2674–2688. Sposito, G. 1993. Chemical Equilibria and Kinetics in Soils. Oxford University Press, Inc., New York. Steefel, C.I. and MacQuarrie, K.T.B. 1996. Approaches to modeling of reactive transport in porous media. In Reactive Transport in Porous Media; Reviews in Mineralogy, Volume 34. Lichtner et al. (eds.), P.H. Ribbe, series editor. Mineralogical Society of America, Washington, D.C. Sudicky, E.A., Schellenberg, S.L., and MacQuarrie, K.T.B. 1990. Assessment of the behavior of conservative and biodegradable solutes in heterogeneous porous media. In Dynamics of Fluids in Hierarchical Porous Media. J.H. Cushman (ed.), pp. 429–462. Academic, New York. Szecsody, J.E., Chilakapati, A., Zachara, J.M., and Garvin, A.L. 1998. Influence of iron oxide inclusion shape on CoII/III EDTA reactive transport through spatially heterogneeous sediment. Water Resour. Res. 34(10):2501–2514. Thiele, M.R., Blunt, M.J., and Orr, Jr, F.M. 1995a. Modeling flow in heterogeneous media using streamtubes I. Miscible and immiscible displacements. In Situ 19:299–339. Thiele, M.R., Blunt, M.J., and Orr, Jr, F.M. 1995b. Modeling flow in heterogeneous media using streamtubes II. Compositional displacements. In Situ 19:367–391. Tompson, A.F.B., Schafer-Perini, A.L., and Smith, R.W. 1996. Impacts of physical and chemical heterogeneity on co-contaminant transport in a sandy porous medium. Water Resour. Res. 32(4):801–818. Valocchi, A.J. 1990. Use of temporal moment analysis to study reactive solute transport in aggregated porous media. Geoderma 46:233–247. Valocchi, A.J. and Malmstead, M. 1992. Accuracy of operator splitting for advection–convection–reaction problems. Water Resour. Res. 28(5):1471–1476.
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Villermaux, J. 1981. Theory of linear chromatography, In Percolation Processes, Theory and Applications, A.E. Rodrigques and D. Tondeur (eds.), NATO ASI Series, Serial E, Vol. 33, pp. 83–140. Viswanathan, H.S. and Valocchi, A.J. 2004. Comparison os streamtube and three-dimensional models of reactive transport in heterogeneous media. J. Hydraul. Res. 42:141–145. Widdowson, M.A., Molz, F.J., and Benefield, L.D. 1988. A numerical transport model for oxygen- and nitrate-based respiration linked to substrate and nutrient availability in porous media. Water Resour. Res. 24(9):1553–1565. Wise, W.R. 1993. Effects of laboratory-scale variability upon batch and column determinations of nonlinearily sorptive behavior in porous media. Water Resour. Res. 29:2983–2992. Wood, W.W., Kramer, T.P., and Hearn, Jr, P.P. 1990. Intergranular diffusion: an important mechanism influencing solute transport in clastic aquifers? Science 247:1569–1572. Yeh, G.T. and Tripathi, V.S. 1989. A critical evaluation of recent developments in hydrological transport models of reactive multichemical components. Water Resour. Res. 25(1):93–108.
Further Reading Regarding Reactive Transport Modeling in Hydrogeology Schulz, H. D. and Teutsch, G. (Ed.). 2002. Geochemical Processes: Conceptual Models for Reactive Transport in Soil and Groundwater. Research Report, Wiley Publishing Company. Lichtner, P. C., Steefel, C. I., and Oelkers, E. H. (Ed.). 1997. Reactive Transport in Porous Media, Volume 34, Reviews in Mineralogy, American Mineralogical Society.
Regarding Eulerian Upscaling Approaches to Reactive Transport Cushman, J. H. (Ed.). 1990. Dynamics of Fluids in Hierarchical Porous Media. Academic Press, London. Cushman, J.H., Bennethum, L.S., and Hu, B.X. 2002. A primer on upscaling tools for porous media. Adv. Water Resour. 25, 1043–1067.
Regarding Lagrangian/Streamtube Approaches to Reactive Transport Cirpka, O.A. and Kitanidis, P.K. 2000. An advective-dispersive stream tube approach for the transfer of conservative-tracer data to reactive transport. Water Resour. Res. 36:1209–1220. Cvetkovic, V. and G. Dagan 1996. Reactive transport and immiscible flow in geological media. II. Applications. Proc. R. Soc. Lond. A 452:303–328. Ginn, T. R. 2001. Stochastic-convective transport with nonlinear reactions and mixing: Finite streamtube ensemble formulation for multicomponent reaction systems with intra-streamtube dispersion, J. Contam. Hydrol. 47:1–28.
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20 Groundwater Flow and Solute Transport in Fractured Media 20.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-1 20.2 Structural Geology of Fractured Rock . . . . . . . . . . . . . . . . . 20-2 20.3 Fundamentals of Groundwater Flow and Solute Transport in a Single Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . 20-4 Groundwater Flow in a Single Fracture • Solute Transport in a Single Fracture
20.4 Field Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-9 Fracture Mapping • Core Analysis • Borehole Geophysical Methods • Hydraulic Testing Methods • Single-Well Hydraulic Tests • Multiwell Hydraulic Tests • Point Dilution Method • Tracer Experiments • Borehole Instrumentation
20.5 Conceptual Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-26
K.S. Novakowski
Conceptual Models for a Single Fracture • Conceptual Models for a Fracture Network
20.6 Modeling Flow and Transport in Fractures and Fracture Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-31
Queen’s University
P.A. Lapcevic British Columbia Ministry of the Environment
E.A. Sudicky University of Waterloo
Flow in Discrete Fracture Networks • Solute Transport in a Discrete Fracture Network
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-37 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-38 Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-43
20.1 Introduction Many of the world’s largest aquifers reside in fractured consolidated media. Studies have shown that even media traditionally considered to be of low permeability, such as shale and granite, are fractured to the extent that significant groundwater flow may occur. In North America, there are many locales at which bedrock of either sedimentary or crystalline origin is used for either domestic or commercial water supply. In many geological settings, the lack of a protective layer of low-permeability clays or clay tills makes these water supplies particularly vulnerable to groundwater contamination. Understanding groundwater flow in fractured consolidated media has long been important when undertaking engineering tasks such as dam construction, mine development, the abstraction of petroleum, 20-1
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slope stabilization, and the construction of foundations. To study groundwater flow in support of these tasks, often only relatively simple measurements of permeability conducted in situ are required. More recently, the discovery of groundwater contamination in fractured bedrock materials has led to the advent of many new investigative techniques that are quite different from those previously used in the geotechnical and petroleum industries. In particular, the focus of most hydrogeological investigations has been on the characterization of the transport properties of the higher permeability fractures in the rock mass. On many occasions, groundwater investigations benefit from the application of a numerical model that is used to simulate the flow system. However, because groundwater flow is primarily governed by discrete fractures at the local scale, traditional mathematical methods, in which it is assumed that the hydrogeological properties vary in a smooth and continuous fashion (a single continuum), provide a poor approximation. Only at large, regional scales of groundwater flow or where fracturing is very dense might continuum methods be applied in fractured media. Further, the often complex and heterogeneous arrangement of discrete fractures makes for difficulties in the representation of these features on an individual basis. There are several modeling approaches that can be used to circumvent this problem, including the use of stochastic or mixed deterministic-stochastic techniques (e.g., Smith and Schwartz 1984) and the use of scale-dependent multi-continua (e.g., Bear, 1993). However, numerical models that can represent two-dimensional groundwater flow and solute transport in each discrete fracture within a three-dimensional randomly fractured domain of practical size have yet to be widely applied. As it is extremely expensive to characterize a field site to the degree necessary to support this type of model, a compromise such as the alternate approaches suggested above will almost always be required. In this chapter, we will try to provide a basic theory and practical advice for guiding investigations of the hydrogeology of fractured rock sites. Our aim has been to focus on the hydrogeological representation of fractured rock systems at scales below which an equivalent porous media (EPM) approach is adequate. To this end, the modeling and field sections will outline techniques to characterize and simulate discrete fractures and fracture networks in the subsurface. A basic introduction to structural geology will be provided to assist in determining how the features that govern groundwater flow in fractured media are formed and how to go about finding them. A brief outline of the principal processes involved in the flow of groundwater and transport of contaminants in individual fractures is presented. In addition, some methods commonly used in the field characterization of fractured rock will be described. These elements become the building blocks for the development of a conceptual model of groundwater flow. A discussion of conceptual models for both single fractures and fracture networks is included. Finally, an overview of analytical and numerical modeling techniques for fractured rock will be presented.
20.2 Structural Geology of Fractured Rock In this chapter, the term fracture is used to refer to any discontinuity in a solid material. In geological terms, a fracture is any planar or curviplanar discontinuity that has formed as a result of a process of brittle deformation in the earth’s crust (Engelder et al., 1993). Planes of weakness in rock respond to changing stresses in the earth’s crust by fracturing in one or more ways depending on the direction of the maximum stress and the rock type. Three broad types of fractures have been identified based on the motion involved in the formation of the fracture. Opening mode (Mode I) cracks form by the separation of the crack walls, under the action of tensile stresses normal to the crack plane (Figure 20.1a). Mode I fractures are thus extension fractures in which the fracture walls have displaced normal to the crack plane and no appreciable displacement parallel to the fracture plane has occurred. Sliding mode (Mode II) cracks propagate by mutual shearing of the crack walls with the shearing oriented in the direction normal to the crack front (Figure 20.1b). Tearing mode (Mode III) cracks advance when the crack walls are subject to a shearing aligned parallel to the crack front (Figure 20.1c). Mode II and III features are defined as shear fractures. Joints (Mode I fractures) are the most common type of fracture structure and are found in all types of rocks as well as in partly consolidated to unconsolidated sediments. Joint sets are characterized as
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(b)
20-3 (c)
FIGURE 20.1 Schematic diagram showing mechanism of fracture formation: (a) Mode I (opening), (b) Mode II (sliding), (c) Mode III (tearing). (From Atkinson, B.K., 1987. Fracture Mechanics of Rock, Academic Press, Orlando, FL, 534 pp.)
systematic or nonsystematic. Joints belonging to a set maintaining consistent characteristics such as orientation, morphology, mineralization, and distribution between outcrops in a local and regional scale are defined as systematic (Engelder et al., 1993). Nonsystematic joints have highly curved and irregular fracture surfaces and are not easily related to a recognizable stress field. Groundwater movement in fractured rock depends on discontinuities at a variety of scales ranging from microcracks (micrometers, µm, in length and width) to faults (kilometers in length and meters in width). Fracturing in a large-scale rock mass can be loosely classified on the basis of three scales of discontinuity (1) microscopic, (2) mesoscopic, and (3) megascopic. At the microscopic scale, isolated or continuous disk-shaped microcracks ranging in length from 100 to 1000 µm and 1 to 2 µm in width are common to both crystalline and sedimentary rocks. Microcracks are normally Mode I fractures, and often form in a disk-shape. In some cases, particularly adjacent to shear fractures, microcracks may form under Mode II conditions. In crystalline rocks, the total porosity of the rock matrix (i.e., the rock bounded by macroscale fractures) is due to microcracks and may range from 0.01 to 1.0%. In sedimentary rock, in addition to microcracks, significant porosity in the matrix may also occur due to incomplete cementation, the weathering of vugs, or imperfect lattice development. Matrix porosity in sedimentary rock may range from less than 1% to as much as 50%. At the mesoscopic scale, fractures (or joints) ranging between <0.5 m and >1000 m in length with widths ranging from <10 µm to >10 mm predominate the groundwater flow system. These fractures are often grouped in sets having similar orientation that are related to the mode of fracture genesis. Fracture zones at this scale are defined as sets of closely spaced fractures contained within a narrow band. Shear fractures are also observed at this scale. A common and extremely important class of fractures at this scale is known as sheeting structure (Holzhauser, 1989). Sheeting structure forms due to the vertical expansion of the rock resulting from erosional unloading. Sheeting structures are present in all types of rock, often found parallel to the earth’s surface, and are common conduits for groundwater flow at the regional scale. In plutonic and metamorphic rocks they are often independent of the original macrostructure and fabric of the rock and are found at decreasing frequency with increasing depth (Trainer, 1988). At the megascopic scale, faults and shear zones dominate the fracture morphology. A fault is defined as a planar discontinuity between two blocks of uniform rock where displacement has taken place parallel to the discontinuity. These are large-scale fractures with many associated features and may be either of high or low permeability depending on infilling and local stress fields. Faults may be of any orientation, although it is the sub-vertical features that are most easily identified through air-photo or map interpretation. Shear zones are similar to faults (i.e., a large-scale fracture zone that has undergone shearing) and are typically found in metamorphic terrain. These features are often of high permeability. In many fractured rock environments, the frequency and spacing of faults and shear zones is sparse. For example, Figure 20.2 illustrates in plan view the possible surface expression of a hypothetical distribution of vertical faults in the southern Ontario region of central Canada. These faults are postulated to vertically penetrate the entire thickness of the sedimentary strata that ranges from ∼200 m to ∼2 km, in this area (Sanford et al., 1985).
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LAKE HURON LAKE ONTARIO
0
km
50
LAKE ERIE GSC
FIGURE 20.2 Distribution of regional faults in Southern Ontario. (From Sanford, B.V., Thompson, F.J., and McFall, G.H., 1985. Phanerozoic and recent tectonics of the Canadian Craton, in The Geoscience Program — Proceedings of the Seventeenth Information Meeting of the Nuclear Fuel Waste Management Program, Atomic Energy of Canada Limited, TR-299, pp. 334–352.)
Note that the spacing between faults is several to tens of kilometers. Thus, at the local to regional scale, any one of these faults may dominate the groundwater flow system. Karst aquifer systems develop due to the extensive dissolution of fractured carbonate rock by flowing groundwater. The hydrogeology of this type of rock terrain is discussed in the following chapter.
20.3 Fundamentals of Groundwater Flow and Solute Transport in a Single Fracture 20.3.1 Groundwater Flow in a Single Fracture Groundwater flow in a single fracture is often interpreted by assuming the fracture walls are analogous to parallel plates separated by a constant aperture. Using this analogy, solution of the Navier–Stokes equations for laminar flow of a viscous, incompressible fluid bounded by two smooth plates leads to an expression referred to as the cubic law. Figure 20.3 shows the parabolic distribution of velocity predicted by the solution to the Navier–Stokes equations in a cross section of a fracture having parallel walls. A rigorous mathematical development of the cubic law can be found in Bear (1972). Expressed as volumetric flow rate, Q, per unit drop in hydraulic head, h, the cubic law can be written as Q = C(2b)3 h
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Groundwater Flow and Solute Transport in Fractured Media
vx (y) vmax Direction of flow
y x
20-5
Smooth walls
FIGURE 20.3 Schematic diagram showing the parabolic distribution of velocity in a fracture having parallel walls.
Fracture aperture (m)
10,000
1,000
100
c −3 m/se K=10 c −4 m/se K=10 c −5 m/se K=10 c −6 m/se K=10 c −7 m/se K=10
10 1 10 100 1,000 Thickness of porous medium equivalent to one fracture (m)
FIGURE 20.4 Comparison of aperture of a single fracture to equivalent thickness of porous media. (From de Marsily, G., 1986. Quantitative Hydrogeology, Academic Press, Orlando, FL.)
where 2b is fracture aperture and C is a constant related to the properties of the fluid and the geometry of the flow domain. Thus, the flow rate is proportional to the cube of the aperture, hence the term cubic law. For straight uniform flow, the constant of proportionality is C=
ρg W 12µ L
(20.2)
where ρ is fluid density, g is acceleration of gravity, µ is kinematic viscosity, W is the width of the fracture, and L is the length of the fracture. For flow in radial domain, C is given as C=
2π ρg 12µ ln(re /rw )
(20.3)
where rw is well radius and re is radius of influence. By substitution of the cubic law into Darcy’s law, the transmissivity (Tfr ) and hydraulic conductivity (Kfr ) of a fracture can be defined as Tfr =
ρg (2b)3 = Kfr 2b 12µ
(20.4)
Thus, using Equation 20.4 we can relate terms typically used to describe the permeability of a porous medium to that for discrete fractures. Figure 20.4 illustrates for a range of hydraulic conductivities, the thickness of porous medium that would be equivalent to a single fracture of a given aperture. For example, using Figure 20.4, we see that the volume of groundwater passing through a 10-m section of porous media having K =10−4 m/sec is
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The Handbook of Groundwater Engineering 1000 100 v (m/day)
10 1 0.1
.01 x=0 dh/d .001 x=0 d / 1 h d 000 =0. x d / dh
0.01 0.001 0.0001 10
100 Fracture aperture (µm)
1000
FIGURE 20.5 Groundwater velocity in a single fracture as predicted by the cubic law.
the same as can pass through a fracture less than 1 mm in width under the same driving force. Thus, even in sparsely fractured rock, considerable volumes of groundwater are moved about under typical hydraulic gradients. The average groundwater velocity in a fracture can be found by combining Equation 20.4 and Darcy’s Law: v¯ = −
dh ρg (2b)2 12µ dx
(20.5)
Groundwater velocity predicted using the cubic law over a range of hydraulic gradients is presented in Figure 20.5. Note that even for very small hydraulic gradients, groundwater velocity in discrete fractures is very high in comparison to velocities typical of porous media. As in open-channel or closed-pipe regimes, turbulent flow is possible where very large hydraulic gradients are present. To estimate the onset of turbulent flow in a discrete planar fracture, the transition from laminar to turbulent flow is defined using the Reynolds number, Re : Re =
v¯ Dh ρ µ
(20.6)
where v¯ is mean velocity, and Dh is the hydraulic diameter. For planar fractures, Dh is defined as: Dh = 2 · 2b
(20.7)
In addition, the relative roughness of a fracture, Rr , can be defined as Rr =
ε Dh
(20.8)
where ε is the mean height of the asperities (the peaks in the topographic surface of the fracture walls). The transition from smooth to rough flow occurs at a Rr of 0.033 and the transition from laminar to turbulent flow at a Re of 2300 (de Marsily, 1986). Using the expression for velocity (Equation 20.5) and the definition of Re , it is found that extremely high hydraulic gradients are required to generate turbulent conditions in smooth fractures. For example, using an aperture of 1000 µm (on the higher end of the range typically found in nature) and a hydraulic gradient of 0.01 (very high end of the range observed in nature), a Re of only 8.5 is calculated.
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Z
Porous matrix
Matrix diffusion
2b
X
V
Fracture Porous matrix
FIGURE 20.6 Schematic diagram of a single fracture in a porous rock.
20.3.2 Solute Transport in a Single Fracture The transport of both conservative and reactive aqueous constituents in discrete fractures is governed by (1) hydrodynamic dispersion, (2) advection, (3) radioactive or biological decay, and (4) diffusion into the rock matrix. In addition, the transport of reactive compounds is influenced by geochemical processes such as acid–base reactions, oxidation–reduction reactions, precipitation–dissolution, or adsorption–desorption. The governing equation for solute transport in a single fracture (Figure 20.6) which incorporates advective transport, longitudinal dispersion, molecular diffusion from the fracture into the matrix, adsorption onto the face of the matrix, adsorption within the matrix, and radioactive decay is written as (Tang et al., 1981): ∂c ∂c ∂ 2c + v¯ − DL 2 + λRa c + 2q = 0 2b Ra ∂t ∂x ∂x
0≤x≤∞
(20.9)
where the x-coordinate is in the direction of the fracture axis, λ is a decay constant, and q is the diffusive flux perpendicular to the fracture axis. The retardation factor, Ra , is defined by Ra = 1 + Kdf /b
(20.10)
where Kdf is the distribution coefficient for the fracture walls defined as mass of solute adsorbed per unit area of surface divided by the concentration of solute in solution. To relate this to the distribution coefficient for the rock matrix, Kd , which is based on the bulk density of the material, an estimate of internal specific surface area of the medium, γ , is required. The specific surface area is defined as the area of the pore walls exposed to the fluid and has units of area per unit mass. Thus, the relation is given as Kd = γ Kdf
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(20.11)
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The hydrodynamic dispersion coefficient, DL , is defined following the standard formulation for porous media: DL = αL v¯ + D
(20.12)
where αL is the longitudinal dispersivity in the direction of the fracture axis and D is the effective diffusion coefficient which incorporates the geometric effect of the pathways in the pore space. The governing equation for the matrix as derived by Tang et al. (1981) is D ∂ 2c
∂c
− 2 + λc = 0 b ≤ z ≤ ∞ ∂t R ∂z
(20.13)
assuming a single fracture penetrating an infinite medium where c is concentration in the matrix, and the matrix retardation coefficient R is defined as R = 1 +
ρb Kd θm
(20.14)
where ρ b is the bulk density of the matrix, and θ m is matrix porosity. The diffusive loss term q in Equation 20.9 represents diffusive mass flux crossing the fracture–matrix interface. Using Fick’s first law this can be expressed as ∂c q = −θm D ∂z z=b
(20.15)
Thus, the final coupled equation for the fracture becomes
∂c ∂c ∂ 2c
∂c 2b Ra + v¯ − DL 2 + λRa c − 2θm D =0 ∂t ∂x ∂x ∂z z=b
0≤x≤∞
(20.16)
In porous and fractured rock, the loss of solute from the fractures into the rock matrix through the process of diffusion can be significant. To illustrate the effect of matrix diffusion, Figure 20.7 uses the solution 1.0 1% 0.8 5% 0.6
v = 1 m/day
C/C
Θm = 1 %
v = 10 m/day
10%
0.4
5%
0.2
10% 0.0 0
10
20
30
40
Time [day]
FIGURE 20.7 Dimensionless concentration profiles in a 500-µm fracture, 50 m from a continuous source, illustrating the influence of matrix porosity on solute transport in a single fracture.
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to Equation 20.16 to show the relative concentration of solute in a single 500 µm fracture pervading a medium having a porosity of 1 to 10%. The velocity in the fracture ranges from 1 to 10 m/day and dispersivity is varied from 0.05 to 0.5 m. Concentration input is continuous and the point of measurement is 50 m from the source. It is immediately evident that the effect of solute loss to the matrix is profound. The effect is so significant that the influence of hydrodynamic dispersion in the longitudinal spreading of solute is completely overwhelmed (i.e., different α L results in little change in the shape of the curve). The loss of solute to the matrix results in an additional problem when undertaking the clean-up of a fractured porous aquifer. Removal of the source of aqueous contamination to a fracture network may be conducted via a number of means (e.g., pump-and-treat), however, the back diffusion process will continue to supply contamination from the matrix for many years, depending on the porosity of the matrix rock. This is shown in Figure 20.8 where Equation 20.16 is used to simulate the exposure of a single fracture–matrix system to a source of aqueous contamination (5000 ppb) for a period of 10 years. The fracture aperture is 100 µm, the groundwater velocity is 1 m/day, the point of observation is 45 m down-gradient from the source, and the results for three matrix porosities (0.5%, 2%, and 10%) are shown. Although the influence of matrix diffusion at the lowest porosity does not appear significant, note that for a contaminant having a low drinking water limit (e.g., 5–10 µg/L), the presence of contaminants above that limit will persist for many years following the cutoff of the source. At higher matrix porosity this problem is significantly exacerbated, with contamination persisting for many decades. It is the process of back diffusion that presently confounds efforts to remediate contaminated bedrock aquifers.
20.4 Field Techniques To develop a defensible conceptual model for a given flow system in fractured rock, some characterization of the medium is necessary. The degree of characterization is dependent on a variety of factors including the inherent complexity of the fracture system (i.e., sedimentary versus crystalline rock), the type of conceptual model desired, and the amount of funding available. Because of the inherent heterogeneity of fractured rock masses (e.g., presence of sheeting structures), some characterization of the subsurface is essential in supporting conceptual models based only on surface measurements (i.e., fracture maps). In the following, methods for the measurement of the surface and subsurface expression of fractures will be discussed. In addition, techniques for the measurement of the hydraulic parameters of both the fractures and unfractured matrix are discussed and an overview of tracer methods that are used 4,500 4,000
Conc. (ppb)
3,500
0.5%
3,000 2,500 2,000
2%
1,500 1,000 500
10%
0 0
2,000
4,000
6,000
8,000
10,000
Time (day)
FIGURE 20.8 Concentration profiles in a 100-µm fracture, 45 m from a source having a concentration of 5000 ppb, lasting 10 years. Groundwater velocity is 1 m/day.
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to measure solute transport parameters in fractured rock, is presented. Finally, permanent multilevel borehole instrumentation specifically designed for fractured rock investigations is described. An essential component of comprehensive investigations of groundwater flow and solute transport in fractured media is the geochemistry of the groundwater. A discussion of groundwater geochemistry in fractured media, however, is beyond the scope of this chapter. An example of using inorganic and isotopic geochemistry to conceptualise groundwater flow pathways can be found in Zanini et al. (2000).
20.4.1 Fracture Mapping To determine the distribution of systematic fractures, outcrops, quarry walls, pavements, or mine tunnels are mapped to estimate the strike, dip, and spacing of individual fractures. In practise, reference lines are established on the rock surface using a measuring tape oriented from the north. The orientation, spacing, and trace length of all fractures intersecting these scanlines are measured. The bias introduced by the intersection of the fractures with an oriented scanline in this type of sampling must be considered during post-processing (LaPointe and Hudson, 1985). Other useful observations of the fractures on traces include the nature of the termination, mineralization, staining, and surface roughness. Qualitative observations of water or fluid seepage along fractures in road cuts or gorge faces can also be useful indicators of groundwater flow. It is important to note that in many cases surface fracture measurements will be reflective of near surface stress conditions or may be influenced by the removal of the overlying rock in quarrying operations. Consequently, physical estimation of fracture aperture cannot reliably be conducted from surface measurements. In addition, due to the presence of sheeting structure, the fracture measurements obtained from surface exposures may not agree with those obtained in situ. Measurements of fracture orientation are usually presented in one of two ways (1) rose diagrams or (2) stereographic plots. Rose diagrams are histograms in which the frequency (usually as a percentage of total measurements) of joint orientations within 5–10◦ intervals is plotted by azimuth. Rose diagrams are commonly used in flat-lying sedimentary rock where most non-horizontal fractures are vertical in orientation. Figure 20.9 shows a rose diagram developed from core collected in a Silurian-aged dolostone. The diagram indicates the presence of a dominant fracture set oriented at approximately 100◦ and two secondary sets oriented at approximately 10◦ and 140◦ . In crystalline rock or deformed sedimentary rock with fracture sets of more random orientation, data are often presented as the projection of the poles of the planes (fractures) plotted on equal-area stereonets (Ragan, 1973). An example of this method is given in Figure 20.10 using fracture data collected in monzonitic gneiss. There are two dominant fracture sets and one minor set shown by the concentration of the poles.
N
N = 75
2%
FIGURE 20.9 Rose diagram of orientations of vertical fractures intersecting seven boreholes to depths of 60 m in a flat-lying Silurian dolostone.
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20.4.2 Core Analysis Boreholes installed for groundwater investigations in fractured rock, using either percussion, tri-cone, or diamond drilling techniques, generally range in diameter from 48 to 152 mm. In North America, 76 or 96 mm diameter boreholes are generally drilled as test or monitoring wells while 152 mm or greater diameter boreholes are used for water supply. Rock core obtained from diamond-drilled boreholes can be used to determine the subsurface pattern of fractures. While it is common to install only vertical boreholes, for most hydrogeological site investigations, installing boreholes in the inclined orientation will maximize the number of non-horizontal and vertical fractures intersected. There is only a nominal cost differential between inclined and vertical boreholes and working in inclined boreholes is no more difficult than vertical boreholes. In flat-lying sedimentary rock, inclined boreholes may be of better quality and less prone to blockages due to spalling rock. The physical examination of rock core can be used to identify potentially open fractures through which groundwater flows. Natural fractures can be distinguished from mechanical breaks (breaks resulting from drill vibration etc.) using the following criteria (1) roughness of the fracture surface (wavy irregular fracture traces in natural fractures contrast to sharp, clean mechanically induced breaks), (2) presence N
Contours of pole density (% of total poles) 0-1 Poles to planes projected on lower hemisphere of equal area diagram
1-2 2-3 3-4 4-6.8 Total poles = 1489
FIGURE 20.10 Equal area stereonet of fracture orientations plotted as poles to planes. (From Raven, K.G., 1986. Hydraulic characterization of a small ground-water flow system in fractured monzononitic gneiss, Nat. Hyd. Res. Inst. Scientific Series No. 149, No. 30, 133pp.)
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of infilling (normally, calcite or sulfate mineralization), and (3) in crystalline or deformed sedimentary rock, evidence of shear or slickenside structure. Evidence of weathering or iron staining is indicative of groundwater flow. Examination of the core in detail for lithological changes is also important because discontinuities at geological contacts are frequently water-bearing fractures. In a detailed comparison between core analysis and subsequently-obtained hydraulic testing results (West et al., 2005), a ranking system ranging from 1 to 10 based on the likelihood of a specific core break being open to flow was shown to have a good correlation to the hydraulic results. It is important to note that the aperture or width of naturally open fractures cannot be determined from physical measurements on the core. This is because removing core from the subsurface disrupts the natural stress conditions such that aperture values become arbitrary. If the orientation of bedding is known or the core is oriented using an orientation device, it is a relatively simple procedure to obtain the orientation of non-horizontal fractures by measuring the arc length of the fracture elipse in the core (Lau, 1983). Orientation data may be displayed using the same methods as used for surface fractures. Fracture spacing from the core can be determined as the spacing between naturally open fractures (eliminating all other fractures). Further discussion of the analysis of core, particularly in sedimentary rock is provided by Kulander et al. (1990).
20.4.3 Borehole Geophysical Methods There are a broad number of borehole geophysical tools available for the investigation of hydrogeological features in fractured rock aquifers. Many such as the gamma, neutron, and electric logs are most helpful with lithological interpretation and of limited application in identifying fracture features relevant to groundwater flow. Identification of fractures and other hydraulic features is best determined using calliper, temperature, conductivity, borehole flowmeter, and borehole image logs. Borehole acoustic televiewer, is one of the most useful borehole geophysical tools for determining the location and orientation of fractures in an open borehole (Zemanek et al., 1969). As the televiewer probe travels the borehole length, a rotating electronic transducer emits a pulsed ultrasonic beam. The reflection of this acoustic energy from the borehole wall produces an image that can be used to identify the strike, dip, and relative size of the fractures intersecting the borehole. The system characterizes fractures only in the immediate vicinity of the borehole. Additionally, it is often difficult to distinguish open fractures from the effects of drilling damage. Recent developments in acoustic probe hardware, optical televiewer probes , and the software for the interpretation of the acoustic or optical signal (Deltombe and Schepers, 2004) have made for more automated and accurate assessment of the presence of fractures in a variety of borehole conditions. Many geophysical logging companies in North America and abroad have the capability to conduct televiewer logs. A borehole video camera (BVC) survey is a cost-effective alternative to acoustic or optical televiewers, particularly in shallow boreholes (<100 m depth). BVC’s film the borehole walls and produce either a color or black and white image of the borehole. Many of the cameras designed to inspect sewers or pipelines are easy to adapt to a borehole application. Automated depth counters allow for the location of specific features such as fractures, vugs, precipitates, mineralization, changes in lithology, or the presence of flowing fractures. Mirrors can be attached to permit a side view of the borehole walls. A BVC survey conducted prior to hydraulic testing or the installation of permanent packer strings will reduce the chances of packer damage or zone leakage due to the inflation of packers over an enlarged portion of the borehole. Recently, borehole temperature probes and borehole flowmeters have been used to detect the presence of large, open fractures using either ambient flow in the borehole (Paillet and Kapucu, 1989), or pumpinginduced vertical flow (Hess and Paillet, 1990; Paillet, 2004). In both cases, these methods are sensitive only to the largest one or two fractures, although quantitative information about the hydraulic properties of these features can be obtained with manipulation and correction of the data (Paillet, 2004). Other geophysical logging tools suitable for fracture detection in open boreholes include (1) multi-arm caliper, (2) formation microscanner, and (3) azimuthal laterlog. Conventional and imaging logs are compared for their ability to detect fractures in Jouanna (1993).
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20.4.4 Hydraulic Testing Methods The characterization of groundwater flow systems in fractured rock is generally dependent on measurements of the permeability of the rock (hydraulic testing). The principal aim of hydraulic testing is to determine the permeability of the fractures and of the rock mass to assist in the estimate of groundwater velocity through the fractures and to appraise groundwater resources. The key to successful field characterization of fractured rock systems lies in the design of hydraulic testing programs. This design should be developed from a preliminary conceptual model of the fracture framework and groundwater flow system. The choice of hydraulic test will depend on several factors including the expected permeability, fracture frequency, matrix properties, and type of rock, depth of the borehole, inter-borehole spacing, and purpose of investigation. In this section, constant-head injection tests, and pulse interference testing will be described. In addition, some of the concepts important in the interpretation of pumping tests (i.e., wellbore storage and skin effects) will be introduced. A general description of various testing methods applicable to hydrogeological investigations in fractured rock can be found in Doe et al. (1987), and a comprehensive case study is provided by Novakowski et al. (1999). 20.4.4.1 Hydraulic Testing Equipment Essential equipment for testing the hydraulic properties of open boreholes in rock, are packers of some type and devices to measure pressure (i.e., pressure transducers). Packers are used to temporarily seal portions of an open borehole to allow for testing in specific zones. In some instances, hydraulic testing is carried out after the installation of permanent borehole instrumentation (discussed later in this section). Typically, for studies conducted at shallow depth (i.e., <100 m) in open boreholes, test zones may range from 2 to 10 m in length with packer seal lengths ranging from 1 to 2 m. In shallow systems, packers are normally inflated with compressed air or nitrogen. In deeper systems or in low-permeability rock, water can be used to provide a stiffer seal. Commercially available packers generally consist of a gland of rubber, steel-reinforced rubber or neoprene over steel or PVC pipe with either a fixed-head or sliding-head design. Fixed-head packers rely on the stretch of the gland material during inflation to provide the seal. Conversely, with sliding-head packers, o-rings in the bottom head of the packer permit the gland to slide upward during inflation. This latter design allows for the use of stiffer (i.e., reinforced) materials to inflate against the borehole wall. The fixed-head design is adequate for shallow rock systems with competent borehole walls, while sliding-head packers are more suitable for use in deeper flow systems. A two-packer system having a single isolated zone is usually adequate for hydraulic testing programs conducted in moderate to sparsely fractured rock. For conditions where fracture frequency is high and packer leakage or short-circuiting effects around the main packers are anticipated, additional packers may be installed above and below the test section to monitor these effects. For multiwell testing, multiple-packer strings are normally used in the observation boreholes. In some cases, it may be convenient and cost-effective to install permanent packer strings in the observation boreholes (described later in this section). The pressure response in the isolated source zone or in the observation zones to perturbations generated by injecting or withdrawing water from the source zone is usually measured using pressure transducers or transmitters. The most commonly used types of pressure transducers are based on either strain gauge or vibrating wire membranes. Descriptions of transducer electronics and other geotechnical instrumentation useful to hydrogeological studies can be found in Dunnicliff (1988).
20.4.5 Single-Well Hydraulic Tests 20.4.5.1 Constant-Head Injection Tests As open fractures may intersect a borehole at any depth, a continuous measurement of permeability with depth is necessary to locate these features. The most widely used method for testing individual boreholes is the constant-head injection technique. The principle behind a constant-head injection test (CHIT) is to inject or withdraw water at a constant hydraulic head into an isolated portion of the borehole and
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The Handbook of Groundwater Engineering Water injection line (Nylon tubing)
Compressed nitrogen
Data aquisition system Borehole
Pressure transducer
Constant head injection tanks
Packer Test interval
Control panel
FIGURE 20.11 Schematic diagram of a typical constant-head injection testing system. A series of five tanks is shown on the right while the left shows the downhole instrumentation consisting of a two-packer system and pressure transducer.
measure the flow rate at steady-state conditions (Ziegler, 1976). CHITs may also be referred to as “Lugeon tests,” or “constant pressure tests.” While a pump and water supply could be used to inject water into the test zone, a series of different diameter tanks fitted with manometers is more commonly used and extends the limits of the testing apparatus to generate a wide range of injection flow rates (Figure 20.11). A range of 10−10 to 10−3 m2 /sec in transmissivity, T , can typically be determined using a series of three or more tanks ranging in diameter from 0.01 to 0.3 m. Flow rate is measured by timing the change in water level as viewed through the tank manometers. Compressed nitrogen gas added above the water in each tank ensures a constant pressure as the tank empties. Flow meters can be used to measure the flow rate; however, most flow meters have a very limited measurement range and thus a complex series of flow meters connected by valves would be required to achieve a range in measurement of T similar to the tank system. Thus, the great advantage to this testing method is the broad range of measurement. Using measurements of flow rate, Q, and the change in pressure expressed as a change in hydraulic head, H , at steady conditions, the T of the tested zone is calculated using the Theim equation: re Q ln T = H 2π rw
(20.17)
The radius of influence, re , or outer flow boundary, can generally be assumed to be between 10 and 15 m for moderate values of T (Bliss and Rushton 1984). To improve the estimate of re , the following simple expression can be used by assuming a value for storativity, S: re = 2 T /S · t
(20.18)
where t is the duration of the injection period for the test. The value of S can be estimated or determined from a slug or pumping test. The initial value of re is calculated using an estimate of T and then revised using the result from Equation 20.17. Following a few iterations, re and T stabilize and a more accurate
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194
184
Elevation (masl)
174
164
154
144
134
T below testing limit (~1 x 10-10 m2/sec)
124 –11.0
–9.0
–7.0
–5.0
–3.0
log (T ) (m2/sec)
FIGURE 20.12 Typical profile of T with respect to depth obtained from a borehole drilled in Silurian dolostone and tested with constant-head injection tests using a 2-m packer test interval.
estimate of T is obtained than when using Equation 20.17 alone (Novakowski, 2005). Further discussion of the re issue can be found in Doe and Remer (1980). For tests in which it is assumed that only one fracture intersects the test section, an equivalent single fracture aperture, 2beq , can be determined from the test results by using the cubic law: 12µ 1/3 2beq = T · ρg
(20.19)
The vertical distribution of T or 2beq is determined by systematically testing the length of the borehole in sections, using a two-packer system. If possible, two to three increasing increments of pressure should be used during each test. In most studies, injection pressures leading to H ≤ 10 m are recommended. Care must be taken not to use pressures that generate fracture dilation or hydro-fracturing. Figure 20.12 shows a typical profile of T with respect to depth obtained from a borehole drilled in Silurian dolostone. T varies by over seven orders of magnitude over 50 m of elevation illustrating the heterogeneity commonly observed in fractured rock. It is important to note that a single permeable fracture within a test zone will predominate the permeability measurement. Thus, the choice of test zone length will depend on the expected fracture spacing with depth. A test interval too short in length will lead to an unnecessarily large number of tests while a test interval too long in length will not capture any of the variability in T and lead to general overestimates of the permeability of the rock mass. To properly characterize a borehole in detail, an initial survey using a large packer separation length will identify the more permeable zones while a subsequent second survey using a shorter packer separation length can be used to characterize the properties of individual permeable features and fracture zones (Figure 20.13).
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Lithology 184
Broken Core Fractures
0.5 m packer spacing
2-m packer spacing
178
176
174
172
Upper vinemount
Elevation (masl)
180
Eramosa
182
T below testing limit (~1 x 10-10 m2/sec) 170 Lower vinemount
–11.0
–9.0 –7.0 log (T) (m2/sec)
–5.0
–11.0
–9.0 –7.0 log (T) (m2/sec)
–5.0
FIGURE 20.13 Results of two testing surveys (2-m and 0.5 m packer intervals) compared to fractures and broken core zones identified in core examination.
20.4.5.2 Slug Tests The slug (pulse or bail) test is a transient single-well method that is also frequently used in hydrogeological studies of fractured rock to obtain estimates of the hydraulic properties of a given length of borehole. Type curves based on radial flow in a confined porous aquifer are usually employed to obtain estimates of T and S (Cooper et al., 1967). Although, in principle, this method should provide estimates of T that are more accurate than CHITs, slug tests conducted in fractured rock, frequently exhibit results that deviate from the ideal (Cooper et al. 1967) response. This has led to the development of numerous conceptual models that consider the effects of alternate boundary geometries, composite zones, and the other physical conditions more typically found in fractured rock systems. For example, in the presence of a damaged zone around the well, known as wellbore skin, T and S determined from a slug test may reflect only the skin zone (e.g., Faust and Mercer, 1984; Sageev, 1986). Wellbore skin can refer to a zone of enhanced permeability (negative skin) or of reduced permeability (positive skin). Double porosity effects (e.g., Doughtery and Babu, 1984), where both the fractures and matrix contribute to the flow system can also be incorporated. Composite models are used to account for separate regions surrounding the well, which have properties that are individually different from the formation properties as a whole (e.g., Moench and Hsieh, 1985; Karasaki et al., 1988). Open-hole slug tests are generally limited to zones of T ≥ 10−7 m2 /sec due to the time required to achieve sufficient recovery for interpretation. In lower permeability material (T < 10−10 m2 /sec) slug tests are conducted under shut-in (no free-water surface) conditions, reducing the effects of storage in the borehole (Bredehoeft and Papadopulos, 1980; Neuzil, 1982).
20.4.6 Multiwell Hydraulic Tests 20.4.6.1 Interference Tests In the following, the term “interference testing” is used to refer to all types of multiwell hydraulic tests. Interference testing between specific zones in two or more boreholes serves two main objectives
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20-17
(1) establish the presence of hydraulic connection between the zones and (2) obtain estimates of interwell T and S. In the case of isolated discrete fractures, interwell aperture can also be calculated. In hydrogeological investigations, the choice of interference test method will be influenced by the diameter of the borehole, ability or desire to pump, or inject large quantities of water into the formation, and the presence of a water table. Pumping tests conducted in fractured rock are done in a similar manner to those conducted in porous media. The difference lies in the factors influencing the response to pumping. Similar to the case for slug tests, pumping interference tests are influenced by (1) wellbore storage, (2) skin effects, (3) double porosity, (4) boundary effects (e.g., a linear feature), and (5) vertical or near-vertical fractures. Interpretation of interference tests is accomplished by matching the pressure or hydraulic head response in both the source and observation zones to theoretically derived response curves. This is accomplished by either manually matching field data to generate theoretical type curves (e.g., Earlougher, 1977) or using automated algorithms (e.g., Piggott et al., 1996). 20.4.6.2 Wellbore Storage Fracture apertures usually range from a few microns to a few millimeters. Consequently, the volume of water stored in an open borehole will be several orders of magnitude greater than the volume of water found in the fractures intersecting the borehole. This will influence the pressure response measured in the well during pulse interference and pumping tests. The wellbore storage factor, Cs , for an open well, is defined as πr2c where rc is the radius of the casing. The dimensionless wellbore storage coefficient, CD , is defined as CD =
Cs 2π rw S
(20.20)
In low storativity media (most fractured rock systems), wellbore storage will significantly influence the early time response to a pressure disturbance in either a source or observation well. To accurately measure the hydraulic properties of low storativity media, wellbore storage must either be eliminated (by eliminating the free-water surface in the testing equipment) or accounted for in the interpretation of transient multiwell tests. 20.4.6.3 Pulse Interference Tests Single-pulse interference tests are an easy yet powerful extension to single-well slug tests. In this case, the pressure response in one or more observation zones due to the introduction of an instantaneous slug of water in a nearby source well is measured (Figure 20.14). A pulse interference test can be analyzed quickly using a graphical method (Novakowski, 1989). To do so, the magnitude of peak response and time lag in the observation zone must be measured. Peak response is defined as the ratio of the maximum rise in hydraulic head at the observation well (h), divided by the initial rise in hydraulic head in the source well (H0 ). Time lag (tL ) is the elapsed time between the start of the slug test in the source well and the maximum peak response in the observation well. The remaining required dimensionless parameters (rD , tD , and dimensionless wellbore storage coefficients in both the observation and source well (CDO , CDS ) are defined as follows: rD =
r rw
CDS =
CS 2π rw2 S
CDO =
CO 2π rw2 S
tD =
TtL rw2 S
hDO =
h H0
(20.21)
where r is the distance between the source and observation boreholes and Cs , and Co are the storage coefficients in the source and observation boreholes, respectively. One of two sets of graphs is used to determine T and S via the dimensionless variables. Set 1 (Figure 20.15) is used when there is no observation well storage (CDO = 0) whereas Set 2 (Figure 20.16) is used when the storage capacity in the source well is equal to the storage capacity in the observation well (CDO = CDS ). First, using hDO and rD , a value for CDS is determined from the graphs in part (a) and S is calculated from the definition
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The Handbook of Groundwater Engineering To data acquisition
Standpipe Deflated single packer Pressure transducer
H0
Static water level
Straddle packers
Fracture zone Source well
Observation well
FIGURE 20.14 Schematic diagram showing field setup for pulse interference tests. (From Novakowski, K.S., 1989. Water Resour. Res., 25(11): 2377–2387.)
of CDS in Equation 20.21. Second, using hDO and rD again, a value for tD is determined from the graphs in part (b) and T is calculated from the definition of tD in Equation 20.21. Figure 20.17 shows an example of both source and observation zone responses to a typical pulse interference test where r = 22 m, T = 5 × 10−4 m2 /sec and S = 4 × 10−5 . This method was recently employed in the development of a detailed conceptual model for groundwater flow pathways in a structurally complex folded limestone (Stephenson et al., 2006)
20.4.7 Point Dilution Method Measuring groundwater velocity in discrete fractures is often difficult due to the large uncertainty associated with estimates of low hydraulic gradient (i.e., hydraulic head varies by only centimeters over distances of many meters). The point dilution method may be employed to determine direct measurements of groundwater velocity. This method is based on the decay in concentration with time of a mixed tracer in a single well due to dilution caused by the natural groundwater flow through the borehole (Drost et al., 1968; Grisak et al., 1977). To conduct a point dilution experiment, a small section of the borehole having one or more fractures is isolated using a set of two pneumatic packers. To minimize the duration of the experiment, the mixing volume must be reduced by using a short spacing between the two packers. The experiment is initiated by instantaneous injection of a small volume of conservative tracer into the test zone and mixing is continued throughout the duration of the experiment. Figure 20.18 shows schematically a typical arrangement for a point dilution experiment. Suitable conservative tracers include bromide or chloride, some fluorescent dyes (e.g., Lissamine FF), radioactive isotopes (e.g., Tritium), or stable isotopes (e.g., Deuterium). The decay in concentration is interpreted using (Drost et al., 1968): c dc = −Ava dt V
(20.22)
where A is the cross-sectional area available to flow, va is the apparent velocity of groundwater flowing through the wellbore and V is the volume of the sealed off portion of the borehole in which the dilution occurs. The solution to Equation 20.22 for the case of instantaneous injection and relating the apparent
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20-19
6 5 4
Part a 3
∆hDO
2
10–1 9 8 7 6 5 4 3
2
A
rD A–B : 100–600 step of 25 B–C : 600–1300 step of 50 C–D : 1300–3000 step of 100 D–E : 3000–4000 step of 200
E
10–2 9 8 7 6
C
D
B 102 2
3 4 5 6789103
2
3 4 5 6789104
2
3 4 5 6789105
2
3 4 5 6789106
2
3 4 5 6789107
2
3 4 5 6789108
CDS (b)
6 5 4
Part b 3
∆hDO
2
10–1 9 8 7 6
A
5 4 3
E 2
10–2 9 8 7 6
C
B 104
2
3
4 5 6789105
rD A–B : 100–600 step of 25 B–C : 600–1300 step of 50 C–D :1300–3000 step of 100 D–E :3000–4000 step of 200
D 2
3
4 5 6789106
2
3
4 5 6789107
2
3
4 5 6789108
2
3
4 5 6789109
tD
FIGURE 20.15 Type curves used to interpret pulse interference tests by graphical method when there is no observation well storage (a) curves used to calculate S and (b) curves used to calculate T . (From Novakowski, K.S., 1989. Water Resour. Res., 25(11): 2377–2387.)
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The Handbook of Groundwater Engineering 6 5 4
Part a 3
∆hDO
2
10–1 9 8 7 6 5 4 3
2
A
10–2 9 8 7 6
C
rD A–B : 100–600 step of 25 B–C : 600–1300 step of 50 C–D : 1300–3000 step of 100 D–E : 3000–4000 step of 200
E
D
B 102
3 4 56789103
2
3 4 5 6789104
2
2
3 4 5 6789105
2
3 4 5 6789106
2
3 4 5 6789107
2
3 4 5 6789108
CDS = CDO (b)
6 5 4
Part b 3
∆hDO
2
10–1 9 8 7 6 5 4
A 3
2
10–2 9 8 7 6
rD A–B : 100–600 step of 25 B–C : 600–1300 step of 50 C–D : 1300–3000 step of 100 D–E : 3000–4000 step of 200
E C
B 104
2
3 4 5 678 9 105
2
3 4 5 678 9 106
D 2
3 4 5 678 9 107
2
3 4 5 678 9 108
2
3 4 5 678 9 109
tD
FIGURE 20.16 Type curves used to interpret pulse interference tests by graphical method when observation well storage = source well storage (a) curves used to calculate S and (b) curves used to calculate T . (From Novakowski, K.S., 1989. Water Resour. Res., 25(11): 2377–2387.)
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Groundwater Flow and Solute Transport in Fractured Media 1
20-21 0.012 0.01
0.8
source 0.008
0.6 hDS
0.006 hDO 0.4 0.004 observation
0.2 0
0.002 1
10
100
1,000
0 10,000
Time (sec)
FIGURE 20.17 Example of source well pulse and observation zone response. Test was conducted in a 500-µm fracture where the observation zone was approximately 22 m from the source zone.
Mixing pump
Tracer injection
Valve
Sample collection To data acquisition
Pressure transducer
Mixing zone
Packer
Fracture zone Borehole
FIGURE 20.18 Schematic diagram of a point dilution experimental setup.
velocity in the test section to the true formation velocity, vf , yields (Drost et al., 1968): vf =
c V ln ξ At co
(20.23)
where co is the initial concentration at t =0, c is the concentration at time t after the tracer was injected, and ξ is a dimensionless correction factor accounting for additional flow captured by the open well due to the convergence of flowlines in the neighborhood of the wellbore. Groundwater velocity in a single fracture intersecting the test zone (vf ) is determined from the measurements of dilution of tracer in the sealed off portion of the borehole by plotting the results in the form of ln c vs. t and fitting a linear regression
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The Handbook of Groundwater Engineering
c/co
1
0.1
0.01 0
20
40
60
80
Time (h)
FIGURE 20.19 Example point dilution response curve. In this test a velocity of 4 m/day was measured in a 220 µm fracture.
1,200
Aperture (m)
1,000 800 600 400 200 0 1
10
100
1,000
Groundwater velocity (m/day)
FIGURE 20.20 Average groundwater velocity vs. fracture aperture for point dilution experiments conducted in an orthogonal fracture network.
line to the data (Figure 20.19). Using the time (tm ) at c/co =0.5 from the regression line, Equation 20.23 reduces to: vf =
0.693V ξ Atm
(20.24)
In the case of a zone containing a single fracture, A equals the diameter of the borehole times the hydraulic aperture and ξ =2. Where more than one fracture intersects the borehole, the interpretation is more complicated. To accurately estimate velocity, the aperture of each individual fracture must be known, otherwise the result will represent an average. In a detailed study of groundwater velocity conducted in a fracture network that pervades a flat-lying Silurian dolostone in southern Ontario (Novakowski et al., 2006), a range in velocity from 3 to 388 m/day was observed. The aperture of the fractures ranged from approximately 130 to 1100 µm. Figure 20.20 shows the relation between aperture size and groundwater velocity. Although it might be anticipated that velocity would be proportional to aperture, no such relation is evident. This is attributed to the nature of the fracture interconnections at this site where some smaller aperture fractures act as a limit to the overall groundwater flux through the domain and thus experience large hydraulic gradients and high velocities.
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Groundwater Flow and Solute Transport in Fractured Media (a)
(b)
so-
Source Borehole Observation Borehole
20-23
(c)
- Streamline - Equipotential line
FIGURE 20.21 Flow field geometry commonly used for tracer experiments: (a) injection-withdrawal, (b) radial convergent, and (c) radial divergent.
20.4.8 Tracer Experiments Tracer experiments conducted in fractured rock provide a means of determining solute transport parameters (i.e., velocity, dispersivity, and matrix porosity) of individual fractures or fracture zones at the field scale. Similar to tests in porous aquifers, tracer experiments conducted in fractures can be carried out using either forced hydraulic gradient or natural gradient flow conditions. Because of the difficulty and cost associated with natural gradient tracer experiments, very few of these have been conducted and no further discussion of this method will be presented here. In the following sections, the common methodologies used to carry out multiwell tracer experiments under conditions of forced gradient are outlined. The three flow field geometries that are commonly used when conducting tracer experiments under forced gradient in fractured rock are (1) injection-withdrawal, (2) radial convergent, and (3) radial divergent. In the injection-withdrawal format, an artificial steady-state flow field between two wells is established where the injection flow rate is equal to the withdrawal flow rate (Figure 20.21a). Tracer is introduced either as a finite slug or continuously into the injection well and the concentration is monitored at the withdrawal well. An example of this type of experiment can be found in Novakowski et al. (2004). The water removed from the withdrawal well can be re-circulated back into the system via the injection well, but this will complicate the interpretation of the test. The advantage to this test method is the development of a well-controlled flow field where recovery of the tracer should approach 100%. A radialconvergent experiment is conducted by passively injecting tracer into one borehole and withdrawing by pumping at a second borehole (Figure 20.21b). Multiple boreholes can be used by introducing a different tracer in each borehole. An example of the use of this experimental method is outlined in Shapiro and Nicholas (1989). Radial-divergent experiments are conducted by injection of tracer in a single well and passively monitoring the tracer arrival in one or more observation wells (Figure 20.21c). An example of this experiment is presented in Novakowski and Lapcevic (1994). The choice of methodology will be dependent on the objectives of the experiment, the number of boreholes available for study, the ease of pumping and sampling, and the type of tracer used. To date most forced-gradient experiments have been conducted in discrete fractures or fracture sets in which the geometry of the fracture is well known (e.g., Raven et al., 1988; Shapiro and Nicholas, 1989; Abelin et al., 1991; McKenna et al., 2001; Mazurek et al., 2003). The scale of these experiments has been limited to interwell travel distances of 50 m or less. In future, tracer experiment methodology should prove very useful in confirming the geometry of fracture intersections over larger scales, the presence of which may be surmised from the results of interwell hydraulic tests. Interpreting these experiments is limited at present due to computational requirements for managing the matrix diffusion process (more discussion of this in the modeling section).
20.4.9 Borehole Instrumentation Permanent completion of boreholes drilled in bedrock is generally carried out in one of two ways (1) using technology designed for piezometer construction in unconsolidated porous media or (2) through the use
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The Handbook of Groundwater Engineering
Sample tubing Port stem
Filter retaining clamp Sample entry port Filter screen
Port
FIGURE 20.22 Components of the Solinst® system of permanent multilevel instrumentation for use in the rock boreholes. Access lines may be electrical cables for pressure transducers installed in the ports or tubing to sample the isolated zones. Pumps (triple tube or double valve types) may be dedicated to specific zones or lowered into the sampling tubing as required. Manual water level measurements are obtained through the tubing.
of multilevel borehole casing or liners. Only the latter will be discussed in this chapter as the former is covered in discussions of well completions for unconsolidated porous media. Multilevel completions are primarily designed to (1) obtain measurements of hydraulic head and (2) obtain representative samples of groundwater. This is accomplished by isolating sections of the borehole using a series of permanent packers joined by casing or riser pipe or by the installation of a liner material that directly contacts the wall of the borehole. Access to the isolated zones is through manometers or access ports. Currently, two commercial systems for multilevel casing completions are widely used around the world. These are the Solinst® system (Cherry and Johnson, 1982) and the Westbay® system (Black et al., 1987). The FLUTe® liner system is a relatively new product that provides similar advantages as the more traditional multilevel casing with the added flexibility of temporary completions. The Solinst® system (Figure 20.22) is based on packer elements that are filled with a sealant chemical that is activated with the introduction of water into the casing after the complete casing string has been lowered into the borehole. Sampling ports and manometers of thin nylon or teflon tubing provide access
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Casing string
20-25
Data acquisition unit Packer
Measurement/ sampling port
Casing Transducer O-ring
Mechanical foot Probe
Pumping port
Packer
Sample container
FIGURE 20.23 Components of the Westbay® system of permanent multilevel instrumentation for use in the rock boreholes. Note that no tubing or electrical cable is permanently installed in the casing string as the probe is lowered to each zone to either measure water pressure or obtain a groundwater sample.
to each sealed off zone to measure water levels and withdraw groundwater samples. Triple-tube sampling pumps can either be installed in each zone or lowered into the manometers. These pumps allow sampling in zones where pumping from the surface is not feasible. Additionally, pressure transducers or transmitters can be included in each zone to electronically measure water pressure. Depending on the objectives of the study and specific site conditions, the modular instrumentation system can be customized to maximize the amount of data obtained. The number of zones sampled or measured is limited by the diameter of the borehole (and thus the diameter of the casing) as each transducer, pump, or sampling port requires access to the surface through tubing or electrical cable. The Westbay® System is also a modular design having water-filled packers connected by casing elements and specially designed pumping and measurement/sampling ports (Figure 20.23). Water pressure is measured and representative groundwater samples are obtained using a submersible probe that is lowered into the casing and connected to an electronic data acquisition device on the surface. The probe has a small arm that is used to locate each measurement port inside the casing. Once positioned on the port, a mechanical foot on one side of the probe is activated and presses against the inner casing wall. This causes an o-ring on the opposite side of the probe to seal around a ball bearing and exposes the pressure transducer in the probe to water pressure outside the casing. Groundwater samples can be obtained using the same port by opening a valve from the surface unit and allowing water to fill a sample container attached below the probe (Figure 20.23). Multiple probes can be installed temporarily in individual casing strings allowing for simultaneous sampling or water level observation. The FLUTe® liner system was developed initially to provide a temporary seal in open boreholes in bedrock (i.e., to prevent cross contamination between fractures via the borehole). The liner is constructed of a flexible polyurethane-coated nylon fabric and is inverted into the borehole from a reel. The liner is inflated by providing an interior water head greater than that in the fractures and borehole. Sampling is conducted through interior tubing that access a port in the wall of the liner. The port is located behind a geotextile that provides a fluid pathway from the fracture to the sample tubing. Multilevel completions provide an excellent measurement platform for interwell hydraulic tests. For example, a borehole instrumented with several zones, used as an observation well during a pumping test
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can provide information on the vertical connection of fracture zones. To maximize the data obtained from permanently instrumented boreholes, care must be taken in designing appropriate isolated zones. Careful examination of rock core, geophysical surveys, and hydraulic testing results prior to installation of the instrumentation will ensure that the isolated zones appropriately define the three-dimensional nature of the groundwater flow system.
20.5 Conceptual Models In formulating an understanding of groundwater flow and contaminant transport for a given site or region at which flow is predominated by the presence of fractures, it is important to develop a reasonable conceptual model as a starting point. In many cases, the conceptual model may incorporate elements of the flow system at a variety of scales. This may include processes at the microscopic scale such as matrix diffusion and processes at the single-continuum scale such as recharge or discharge. In the following section, a variety of conceptual models for flow and transport at the scale of a discrete fracture and a fracture network are discussed. In all cases, it is assumed that the cubic law, hydrodynamic dispersion, and matrix diffusion apply at the microscopic scale. Bear (1993) defined four operational scales in a fractured medium, at which different conceptual approaches might be applied (Figure 20.24). At the very-near field scale, flow and solute transport are dominated by a single fracture. At the near field, flow and transport are dominated by a few well-defined fractures and interaction between the fractures and the matrix may play a role. At this scale discrete fracture models may be used in which the major fractures are defined deterministically and the minor fractures are specified stochastically. Depending on the type of fractured rock and the nature of the problem, it is likely the near-field scale is of most interest to practising hydrogeologists. At the far-field scale, multiple continua are defined using at least one continuum for the unfractured matrix, possibly one for the minor fractures and another for the major fractures. At the very-far-field scale, a single continuum can be applied. In particular cases, it may be found that a mixture of conceptual approaches is required. For example, in some sedimentary rock environments, sheeting fractures along bedding planes may predominate in one stratigraphic horizon, while in another the fracturing is so frequent as to warrant the use of a continuum or a multi-continuum approach.
20.5.1 Conceptual Models for a Single Fracture Numerous studies have been conducted in which the roughness of natural fracture walls and the distribution of fracture aperture have been measured (e.g., Brown et al., 1986; Gentier and Billaux, 1989; Piggott, 1990; Konzuk and Kueper, 2004). These studies have been conducted on fracture samples ranging in scale between 0.1 and 1 m. The results indicate that the surfaces of fracture walls can be rough and undulating with numerous contact points between the walls. In general, it is concluded that (1) fracture aperture may fit into one of several statistical distributions, (2) aperture is correlated spatially, and (3) aperture distributions are scale invariant. The distribution of apertures at the laboratory scale has been observed to follow either a log-normal distribution (Gentier and Billaux, 1989; Hakami, 1995), a Gaussian distribution (Piggott, 1990; Brown, 1995; Hakami, 1995), or a gamma distribution (Tsang, 1984). Additionally, spatial distributions of aperture are often observed to have a large variance, indicating a high level of heterogeneity in the fracture plane (e.g., Hakami, 1995). The roughness of fracture surfaces has also been determined to display fractal properties implying that variable aperture distributions may be scale invariant (e.g., Brown et al., 1986; Wang et al., 1988). Fractures with similar statistical distributions of aperture may have very different flow properties due to the spatial relation of the aperture variations. Fracture surfaces have been determined to be correlated spatially with the degree of correlation related to the scale of measurement. Brown et al. (1986) determined
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Porous medium Fracture
Well
Fracture Porous medium Repository
(b)
Well
Fractures
Fracture continuum
(c)
Exchange
Well
Porous medium continuum (d) Well
FIGURE 20.24 Operational scales in a fractured medium: (a) very-near field, (b) near field, (c) far field, and (d) very-far field. (From Bear, J., 1993. Modeling Flow and Contaminant Transport in Fractured Rocks. In Flow and Contaminant Transport in Fractured Rocks, eds. J. Bear, C.-F. Tsang, and G. de Marsily, pp. 1–37. Academic Press Inc., San Diego, CA.)
correlation lengths from between 0.5 and 5.0 mm for sample lengths and diameters of 25.4 mm. Vickers et al. (1992) studied surface roughness of a single fracture in a block of welded tuff (0.15 × 0.40 m) and found the resulting aperture distributions close to normal except at the tails. The apertures were also found to be correlated at two scales, one on the order of millimeters and the other on the order of tens of centimeters. In addition, Vickers et al. (1992) found that apertures increased consistently along the entire length of the fracture suggesting that a third spatial correlation occurs at a scale well in excess of the sample dimensions. Hakami (1995) compiled experimental results of aperture measurements at the lab scale and concluded that both the variance and spatial correlation length increase with increasing mean aperture. It is also well recognized that the regions in which the fracture surfaces are in contact and closed to water flow will strongly influence flow and transport. Experiments conducted by injecting wood’s metal into fractures in granitic cores, have shown contact areas ranging from 8% to 15% with a normal stress of 3 MPa (Pyrak-Nolte et al., 1987). At the field scale, hydraulic aperture measurements in two fractures at depths less than 15 m in sedimentary rock (shale/limestone) in an area roughly 30 m×30 m, indicate fracture closure between 20 and 30% (Lapcevic et al., 1990). Smooth fractures will display many small areas of contact with complex outlines resulting in a complex distribution of fluid flow among many
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(b) P2
L ∆x ~ b(x)
P1
FIGURE 20.25 (a) Channel representation of fluid flow in a single fracture, and (b) schematic sketch of one channel, where b(x) is the aperture distribution, and λ is the spatial correlation length of the distribution. (From Tsang, Y.W., and Tsang, C.F., 1987. Water Resour. Res., 23(3): 467–479).
small channels. In contrast, rough fractures display fewer, larger contact areas with smoother outlines concentrating flow in a few large channels (Odling, 1994). Tsang (1984), observed that increases in contact area results in a reduction in mean aperture, an increase in tortuosity and a decrease in the connectivity of the fluid flow paths. Tortuosity factors determined through comparisons of measured hydraulic versus physical apertures have been determined to be a good approximation to account for closure (e.g., Piggott and Elsworth, 1993). Experimental studies of flow and transport in laboratory scale fractures have been used to investigate the relationship between measured apertures and resultant flow characteristics within the fracture. Results of flow experiments on fractures in laboratory studies with known aperture distribution show that the ratio between mean aperture and hydraulic aperture is 1.1–1.7, for 0.1 < 2b < 0.5 mm (Hakami, 1995). The lower value of the hydraulic aperture is to be expected as the variation in aperture of natural fractures forces the flow to be tortuous. It is well recognized that fluid flow in natural fractures will be controlled by the distribution of asperities leading to tortuous paths and areas in which no flow occurs. There are several conceptual models for transport in a fracture of variable aperture. For example, the “channel model” for flow and transport through a single fracture is based on a series of one-dimensional channels of constant aperture oriented in the direction of flow (Tsang and Witherspoon, 1983). Tsang and Tsang (1987) extended this model to include a limited number of tortuous and intersecting channels each characterized by an aperture density distribution, effective channel width, and correlated in length and aperture (Figure 20.25). A gamma function was used to characterize the aperture distribution and standard geostatistical techniques used to calculate distributions. Johns and Roberts (1991) presented a two-aperture channel model in which lateral transfer of mass from large to small aperture regions of the fracture plane and vertical diffusion into the rock matrix were considered. Moreno et al. (1988) presented a stochastic model where flow and transport in the entire fracture plane was considered. The aperture of the fracture was lognormally distributed and possessed a spatial correlation length (λ). From this it was concluded that a broad distribution of apertures with spatial correlation length on the same order of magnitude as the scale of measurement is responsible for flow channeling phenomena. Determining the spatial distribution and correlation of fracture aperture at the field scale is difficult due to the extreme cost required to obtain sufficient field data. Consequently, conceptual models of variable aperture based on surface roughness are well verified at scales up to a meter but have yet to be verified with field data at scales in the tens to hundreds of meters. Thus, we are left with using simple correction factors such as macroscopically defined tortuosity to account for this variability.
20.5.2 Conceptual Models for a Fracture Network In all rock types, fractures of various sizes and lengths together combine to form three-dimensional networks of interconnected groundwater pathways. At scales less than that defined for a single continuum, determining an appropriate conceptual model for the three-dimensional arrangement of fractures is essential in understanding and predicting groundwater flow and solute transport in fractured rock. In general, a distinction must be made between conceptual network models for sedimentary rock and those for crystalline rock. In most sedimentary rock environments, the directions of the principal fractures follow bedding planes and other pre-existing planes of weakness related to deposition. These fractures
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20-29 Cross joints
Joints
Mechanical layer thickness
beddin
g Systematic joints
FIGURE 20.26 Typical three-dimensional view of conceptual fracture framework for a layer-cake stratigraphy. (From Engelder, T., Fischer, M.P., and Gross, M.R., 1993. Geological Aspects of Fracture Mechanics, A Short Course Manual, Geological Society of America, 281pp.)
A B
D C
F3
F5 F4
F2
F1
FIGURE 20.27 A three-dimensional depiction of the conceptual model developed using pulse interference tests for fracture planes (dark) and interconnections in a complex limestone site. The light vertical lines indicate the position of the boreholes that were used to conduct the interference testing.
are often connected by near-orthogonal fractures whose geneses are related to paleo- and neotectonic stresses (Holst, 1982; Williams et al., 1985). For flat-lying stratigraphy, this results in a relatively simple fracture framework that can be conceptualized by several discrete horizontal fractures connected by statistically defined sets of sub-vertical fractures. Figure 20.26 illustrates a typical three-dimensional view of a conceptual fracture framework for a layer-cake stratigraphy. Note that the vertical fractures are constrained by the bedding and have a preferred orientation. There are exceptions to this scenario, however, for sedimentary environments that have undergone considerable deformation. In such cases, the stratigraphy tends to be inclined and folded. This concentrates vertical fractures in the vicinity of fold axes and leads to shearing movement on some bedding planes. An example of this is provided in Figure 20.27 which illustrates the primary interconnected fractures in a folded and faulted limestone (Stephenson et al., 2006). This conceptual model was developed primarily from the results of pulse interference tests and was verified by comparison to the results of a steam flood in which the pathways of the hot water front was monitored. Conceptual models for crystalline rock environments are usually more complex than that for sedimentary rock, although the example shown in Figure 20.27 for limestone is an exception. In uniform granitic rock, fractures may be oriented in preferred directions according to magma emplacement and cooling
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FIGURE 20.28 Three-dimensional conceptual model of disc-shaped fractures that are of random size and oriented orthogonally. (From Long, J.C.S., Gilmour, P., and Witherspoon, P.A., 1985. Water Resour. Res. 21(8): 1105–1115.)
(polygonal fracture sets), local deformation, regional deformation, and erosional unloading (sheeting fractures). One of the earliest conceptual models for flow in crystalline rock was based on the assumption of an equivalent porous medium (Snow, 1969). The concept was developed to relate the results of permeability measurements obtained from boreholes to a hydraulic conductivity ellipsoid that defines the anisotropic permeability of the bulk rock. To conduct the interpretation, it was assumed that flow was predominated by the fractures, all fractures contributed to the flow system, and the orientations of the fractures intersecting the boreholes were known. The hydraulic conductivity ellipsoid was constructed by summing the permeability contributions of each fracture intersecting each test interval. It has long been recognized that fractures form disc-shaped discontinuities, particularly in granitic environments. Figure 20.28 shows a three-dimensional conceptual model in which disc-shaped fractures are of random size but oriented orthogonally. This concept can be extended to the general case for more
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(b)
Fracture plane
Flow channels
20-31
δ
2rc
W=0.2 m
Mixing point
Mixing point (c) δ W
FIGURE 20.29 Three types of interconnecting flow channels in a fracture network: (a) tubular flow channels, (b) parallel plate channels with constant width, and (c) parallel plate channels with width equal to the fracture intersection line. (From Dverstorp, B., Andersson, J., and Nordqvist, W., 1992. Water Resour. Res. 28(9): 2327–2343.)
random orientations of discs. For example, Cacas et al. (1990) and Dverstorp et al. (1992) developed numerical flow and transport models based on a three-dimensional distribution of discs randomly placed in space and of random radius, but given a specific spatial orientation to simulate fracture sets. Groundwater flow and solute transport were then assumed to follow one of three types of linear flow channels that interconnect the individual fractures in the network (Figure 20.29). Recently, scaling relations have been introduced into these types of conceptual models through the use of fractals and other methods (Piggott et al., 1997; Mazurek et al., 2003) thus providing a means of using field data in the generation of artificial fracture networks. Figure 20.30 illustrates the generation of a three-dimensional network of fractures based on fracture traces measured from outcrop scan lines, air photographs, and geophysical data (Piggott et al., 1997). From the trace data (Figure 20.30a) statistically generated two-dimensional traces are extended to produce the three-dimensional network of fractures (Figure 20.30b). A detailed three-dimensional view of a portion of the fracture network in Figure 20.30b is shown in Figure 20.30c.
20.6 Modeling Flow and Transport in Fractures and Fracture Networks In some cases, such as where sheeting fractures dominate the groundwater flow system, it may be necessary only to model these discrete features and not the flow system as a whole. Simple analytical models for flow and transport in a single fracture (e.g., Tang et al., 1981) or a set of parallel fractures (Sudicky and Frind, 1982; West et al., 2004) may suffice. For example, transport calculations such as that shown in Figure 20.7 or Figure 20.8 may provide the information necessary in illustrating the potential importance of matrix diffusion at a given site. Non-uniform aperture in the fracture plane, as discussed in the previous section, will influence solute transport in single fractures. Direct solution of the flow and transport in a fully defined aperture distribution can be conducted using numerical models (e.g., Lapcevic, 1997). For example, Figure 20.31 compares a tracer plume created assuming a constant aperture to one simulated assuming spatially variable aperture. Note that the variability in aperture leads to a plume of much greater irregularity in shape and of lower concentration. Thus, for some distributions of aperture it may be necessary to consider aperture variable in simulation at the discrete fracture scale. Unfortunately, in almost all field studies there is insufficient information to generate a defensible model of variable aperture.
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N
Ottawa river
Location of the CRL site
Fracture traces 0
5 Km
(c)
(b)
FIGURE 20.30 Generation of a conceptual model of fracture network using field data and fractal relations: (a) fracture traces measured from outcrop scan lines, air photographs, and geophysical surveys, (b) statistically generated two-dimensional traces (top) extended to form three-dimensional network of fractures (bottom), and (c) detailed portion of network shown in bottom part of (b). (From Piggott, A., Moltyaner, G., Yamazaki, L., and Novakowski, K., 1997. Preliminary characterization of fracturing at the site of the Chalk River Laboratories, In Proceedings of 50th Canadian Geotechnical Conference, Ottawa, Canada [also NWRI No. 97-126].)
(a)
(b)
c/C0
c/C0
0.06
0.023
0.05
0.020 0.017
0.04
0.014
0.03
0.011
0.02
0.008
0.01 5m
0.00
0.005 5m
0.00
FIGURE 20.31 Two-dimensional concentration plumes in a single fracture illustrating the effect of variable aperture on plume dimensions: (a) tracer plume assuming a constant aperture and (b) tracer plume assuming aperture of the fracture is variable.
Modeling approaches to simulate flow and transport in fracture networks fall into one of three categories within the range of conceptual models for fractured rock (1) equivalent porous medium (EPM), (2) dual porosity, and (3) discrete fracture representation. In addition, fracture network models may be implemented in either two or three dimensions.
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Groundwater Flow and Solute Transport in Fractured Media 0 0
100
20-33
Distanc
e (m)
Depth (m)
200 10
300
20 30 40
FIGURE 20.32 Network of orthogonal fractures generated based on a conceptual model of layered sedimentary rock where each layer has differing fracture spacing and connectivity parameters. System is divided into three layers: a densely fractured zone (0–26 m), a relatively unfractured zone (26–28 m) and a more sparsely fractured zone (28–45 m).
Models based on equivalent porous medium treat the fractured porous rock as equivalent to a nonfractured continuum. Bulk parameters for the permeability of the rock mass are used and the geometry of individual fractures or the rock matrix is not considered. This is a reasonable approach for the simulation of flow if fracturing is intense or the study domain is sufficiently large that individual fractures have no influence on the overall flow system (e.g., some regional systems of the scale of kilometers). Berkowitz et al. (1988) and Schwartz and Smith (1988) discuss the fundamentals of continuum models for fractured rock systems and Min et al. (2005) provide a recent example of the application at large scale. Double porosity models are used to attempt to bridge the gap between the simplifications of EPM models and the details of the discrete fracture models by treating the fracture system and the porous matrix as two separate inter-related continua (Barenblatt et al., 1960). In this approach, equations of flow and transport for each system are linked by a source/sink term that describes the fluid or solute exchange between the two systems each of which may have very different properties relative to the other. Examples of the use of semi-analytical and numerical models having this approach can be found in Huyakorn et al. (1983); Rowe and Booker (1990); Sudicky (1990); Hassan and Mohamed (2003); and Nair et al. (2004). Some limitations to the double-porosity approach include the assumption that the matrix blocks are of simple (and possibly unrealistic) geometry and that advection of solutes in each block is ignored. The discrete fracture approach will result in the most physically representative simulation of flow and transport processes at the sub-continuum scale. However, discrete fracture models require the generation of fracture networks based on a conceptual model developed using information on both the individual fractures and the geometry of inter-fracture relationships. A network of fractures is characterized by a distribution of fractures of fixed or variable aperture, finite length, regular, or random orientations, and some degree of connectivity with other individual fractures. Thus, the development of the conceptual model strongly influences the outcome of the model simulations. Figure 20.32 illustrates a fracture network generated using a conceptual model of fracturing in a layered sedimentary sequence of dolostone and shale. To generate this network minimum horizontal and vertical fracture spacings of 1.5 and 3.5 m were set for the entire sequence. Within each geologic unit a range of fracture lengths and fracture density were set. Note the denser fracture zones at the top of the sequence (0–26 m), a relatively unfractured zone at 26 m and a more sparsely fractured zone from 28 to 45 m.
20.6.1 Flow in Discrete Fracture Networks The modeling of flow in discrete fracture networks may be conducted to estimate groundwater flux for the purpose of groundwater resource evaluation or to provide an estimate of the distribution of groundwater
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velocity in individual fractures as input to a solute transport model. In the former case, transient hydraulic head conditions may be of interest, whereas in the latter, only steady conditions are considered. In the following, two approaches to the modeling of flow in discrete features are described, both of which are suitable for either transient or steady flow conditions. Barker (1991) developed a robust semi-analytical method that can be used to determine the distribution of groundwater flux and velocity in a two-dimensional network of fractures having random orientations. The fracture network is conceptualized as a linked system of linear elements for both steady and transient flow conditions (e.g., Dverstorp et al., 1992). Flux into each node is calculated by summing the contribution from each fracture using Darcy’s law. The cubic law is used to relate the fracture aperture to elemental hydraulic conductivities. The system of Laplace transformed equations is solved by direct or iterative methods depending on the size of the network and the results numerically inverted from the Laplace domain to obtain values in real space. Modeling groundwater flow in three-dimensional fracture networks is considerably more difficult than for two-dimensional slices. For conceptual models involving sparsely distributed fractures in impermeable rock, randomly oriented fracture discs and fracture intersections of various orientations must be discretised. However, the mesh generation required for solution with standard finite element or finite difference techniques is very difficult, even for small solution domains. Alternative solution methods have been attempted including a hybrid analytical-numerical scheme (Long et al., 1985) and a boundary element formulation (Elsworth, 1986), but were found not to be generally useful for large complex networks. At present the most widely used model for simulating flow in networks is the proprietary code package known as FracMan/Mafic (Golder Associates Inc.). Example applications using this code are found in Kim et al. (2004) and Pashin (2005). Therrien and Sudicky (1996) derived a model for a variably saturated fracture–matrix system having three dimensions in which advective fluid exchange is allowed between the fractures and matrix. A modified form of the Richards’ equation was used for determining hydraulic head in the matrix and an extension to the variably saturated flow equations was used for hydraulic head in the fracture. The fractures were idealized as two-dimensional parallel plates and fluid leakage flux was used to link the equations for the fracture with that of the matrix. The resulting system of governing equations was solved using the control-volume finite-element method in conjunction with Newton–Raphson linearization. Oxtobee and Novakowski (2003) used this model to simulate groundwater–surface water interchange in a stream flowing directly on bedrock. Connection between the stream and the underlying orthogonal fracture network was simulated through sparsely distributed vertical fractures. The results showed that capture zones in the fracture network could develop over a substantial width (several hundreds of meters) even though discharge to the stream was limited to a single fracture no larger than 1000 µm. Although there is no technical limitation to the method in the simulation of flow in a non-orthogonal fracture system, as aforementioned, any problem simulated using this model would be significantly limited in scale. Recent advances in the formulation of the model, however, have shown that large-scale non-orthogonal fractures can be accommodated under some conditions (Graf and Therrien, 2005).
20.6.2 Solute Transport in a Discrete Fracture Network Solute transport in fracture networks can be simulated in two ways (1) using particle tracking, and (2) direct solution of the governing equations for solute transport. Of the two methods, the former has received more widespread use. In the following sections, both particle tracking and methods for direct solution will be described, with focus on the former. In modeling solute transport in fracture networks, the presence of fracture intersections where solute must be apportioned according to the flux entering and leaving the intersection node, must be incorporated. There are two approaches to this (1) assume complete mixing at the node, and (2) use streamtube routing. For the former, concentration entering the intersection is assumed to completely mix resulting in a uniform distribution of concentration leaving the intersection. For the latter, mass is distributed at the intersection according to the distribution of streamtubes and no mixing is assumed to occur (Figure 20.33).
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Groundwater Flow and Solute Transport in Fractured Media (a)
Q1
(b)
Q3
Q1
Q4
Q3
in = 1,2 out = 3,4
in = 2,3 out = 1,4
Q2
20-35
Q2
Q4
FIGURE 20.33 Schematic diagram showing mass transfer at a fracture intersection according to the distribution of streamtubes. (a) Q2 = Q3 and transport is split evenly into Q1 and Q4 and (b) Q1 > Q2 and transport is split unevenly between Q3 and Q4 .
Complete mixing at an intersection having n incoming fractures is described by (Küpper et al., 1995a): n ci Q i c = i=1 n i=1 Qi
(20.25)
where c is the concentration in the intersection, and Qi and ci are the volumetric flux and concentrations in the incoming fractures, respectively. The development required for a rigorous implementation of streamtube routing is considerably more complex (e.g., Philip, 1988). Berkowitz et al. (1994) suggested that diffusional transfer between streamtubes at intersections may smear the distinction between streamtubes, resulting in a distribution of concentration more like that observed with complete mixing. However, Küpper et al. (1995b) showed that, even in the absence of diffusion, for three of four possible flow conditions at intersections, the complete mixing assumption and streamtube routing produce identical results. In addition, it was also shown that for some types of flow (i.e., radial flow in a network), the flow condition giving rise to the difference is rare. Thus, in practical terms, the degree of error introduced into a model by assuming complete mixing at every intersection, is likely not significant. However, it is important to note that these concepts apply only to mixing at linked one-dimensional elements. In the more realistic case where two-dimensional planes intersect, the hydraulic head will be non-constant along the intersection resulting in much more complex mixing arrangements. To date, this issue has not been rigorously addressed. Particle tracking is a means to simulate solute transport by following the residence times of particles released into the flow system at a given boundary or internal location. In the most rudimentary implementation, a given number of particles, usually 20,000–30,000, are released into the flow system, routed at fracture intersections according to volumetric flux (i.e., assume perfect mixing at the intersection node) and eventually tracked to an exit boundary (Schwartz et al., 1983). The number of particles are summed at the exit boundary resulting in a breakthrough curve equivalent to a dirac input. Integration of the breakthrough curve with respect to time yields a breakthrough curve equivalent to a step-function input. The use of particle tracking methods was expanded in the 1990s to account for solute retardation (Dverstorp et al., 1992), and variable aperture fracture elements (Nordqvist et al., 1992). Retardation is accounted for by manipulating the travel time in individual fracture elements using the expression: tR = tC Ra
(20.26)
where tR is the travel time adjusted for sorption, tC is determined from the cubic law, and Ra is as defined in Equation 20.10. Nordqvist et al. (1992) also manipulated residence time in fracture elements to account for the influence of variable-aperture fractures. This was conducted by generating a spectrum of residence times using a variety of realizations of a variable aperture fracture having different mean apertures and
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3-D Fracture network 30 m
Single fracture library 30 m b0 ,σb
3m 30 m
om Rand ion t c sele
τ1 , τ2 ,..., τi ..., τn gi(t)
t
FIGURE 20.34 The incorporation of variable aperture fractures is introduced in a fracture network model. Here, bo and σb are the two parameters describing the lognormal aperture distribution (mean aperture and standard deviation). The τi are effective transmissivities of the fractures in the library. The gi (t ) plots are graphical illustrations of the residence time spectra for the fractures in the library. (From Nordqvist, A.W., Tsang, Y., Tsang, C.-F., Dverstorp, B., and Andersson, J., 1992. Water Resour. Res. 28(6): 1703–1713).
different properties of the log-normal aperture distribution. To develop the residence time distribution for the system of linked linear elements, the residence time spectrum was randomly sampled for each fracture element (Figure 20.34). Recent work by Tsang and Doughty (2003) showed that matrix diffusion along with heterogeneity of the aperture distribution, the presence of fracture gouge, and mineral alteration can also be accommodated using particle tracking techniques. For two-dimensional networks of linked linear fracture elements, direct solution offers the most robust means of simulating transport in the fractures and interactions with the matrix. Sudicky and McLaren (1992) and Novakowski and Bogan (1999) describe finite-element and semi-analytical approaches, respectively. The solution method described by Sudicky and McLaren (1992) accommodates advection–dispersion, retardation, and decay in the fracture and the same in the matrix. A third-type boundary condition is used for the exchange between fracture and matrix. This solution method can therefore simulate fractured domains having a permeable matrix (e.g., fractured clays). The finite element method is used to discretise the equations in the spatial coordinates and the Laplace transform is used to manage the time derivative. To minimize the difficulties in discretisation and to maximize the domain size for tractable problems, fracture geometry has been limited to orthogonal systems. For two-dimensional networks having more random fracture orientations, the solution method of Novakowski and Bogan (1999) offers a practical alternative. In this case, only diffusive transport is allowed between the fracture and matrix. A semi-infinite domain is also defined for the diffusive transport in the matrix. Clearly, this is an approximation that is viable only for geological material having sparse fractures and low matrix porosity. In some settings, the conceptual model for transport has been developed to the degree where a threedimensional discrete fracture simulation is viable. In three dimensions, the direct solution method of Therrien and Sudicky (1996) for a variably saturated fractured medium can be employed. The two governing equations for the fracture planes and matrix blocks are linked using continuity between the concentration in the fracture and that in the matrix at the fracture wall. As the transport equations are linear, solution is based on a standard time-marching Galerkin scheme. Two-dimensional rectangular elements are used for the fractures and three-dimensional rectangular prisms were used for the matrix.
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As with the flow case, non-orthogonal fractures present a difficulty, although the newest version of the model (Graf and Therrien, 2005) can accommodate these. At present, in the general practice of hydrogeology, the modeling of flow and transport in fractured rock systems is often conducted using EPM models. As we have suggested above, this approach will lead to error in the prediction of both groundwater flux and solute travel time, depending on the size of the domain modeled. At a domain scale of several hundreds of meters, or more, however, prediction of groundwater flux may be conducted with only minor error using EPM models, provided the characteristics of the major fracture zones and unfractured rock are known and appropriately represented. Thus, the hydraulic effects of short or long-term pumping or changes in boundary conditions such as recharge, can be reliably explored using this approach. Unfortunately, the prediction of solute transport using the EPM approach at this scale can be substantially erroneous. Thus, as a general rule of thumb, all predictions of contaminant transport and the design of remedial facilities at the scale of a contaminated site should be conducted using a model which, at a minimum, incorporates multi-continuum concepts. In some cases, a defensible modeling strategy may be to simulate transport in the fracture system with simple analytical models that incorporate a parallel system of fractures and matrix diffusion. Although the fracture system may not be well represented by this approach, it is likely that this approach will lead to substantially more accurate predictions of contaminant transport than were an EPM model employed. For conditions where more accurate simulations of contaminant transport are required, such as for large-scale groundwater remediation program, the simulation of controlled tracer experiments conducted in fracture networks, or investigations of intrinsic bio-remediation, there are now very robust modeling tools available that account for fractures on a discrete basis. Unfortunately, there are significant practical limitations in the application of some models that are directly related to the ability to discretise the fractures and matrix in detail sufficient enough to provide the necessary accuracy in the predicted transport rate and concentration. For example, a radially divergent tracer experiment conducted in a discrete fracture in a slightly porous dolostone over a distance of approximately 125 m (Novakowski et al., 1999) has yet to be successfully interpreted using a direct numerical solution. This is because of the computational limitations which, for this problem, are related to the excessive number of elements required (over 60 million estimated).
Glossary Aperture: Separation distance between two fracture surfaces used as a measure of fracture width. Borehole: Drilled open hole in rock. Boreholes may be of any orientation and plunge from vertical to horizontal in relation to the earth’s surface. Channel: Preferred pathway in a single fracture plane or fracture network. Conceptual Model: Geological or hydrogeological image representing natural system. Fracture Network: Two- or three-dimensional arrangement of intersecting fractures. Fractures in a network may be of identical aperture, length, or orientation or may represent a distribution of fractures of varying parameters. Fracture: Any planar or curviplanar discontinuity or break in a rock mass that has formed as a result of a brittle deformation process. Joints, shear fractures, faults, microcracks etc. are all examples of fractures. Hydraulic Test: Test involving the injection or withdrawal of water into a given test zone to determine the permeabilitiy of the zone. Either the transient or steady-state response can be used. Interference Test: Hydraulic test conducted between two or more hydraulically connected zones. A vertical interference test can be conducted between two isolated zones in a single borehole. Joint: A mesoscopic fracture in rock exhibiting purely opening mode displacement, with no appreciable shear offset. Matrix Diffusion: Process whereby solute from water in fracture is transferred to water in pore spaces of rock through chemical diffusion.
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Sheeting Structure: Mesoscopic fractures formed due to the vertical expansion of the rock resulting from erosional unloading. Sheeting structures are often found parallel to earth’s surface in all types of rock and are common conduits for groundwater flow at the regional scale. Skin: Zone around borehole that has different properties than the bulk rock mass. A positive skin suggests the permeability around the borehole is less than the bulk rock whereas a negative skin suggests greater permeability. Skin zones may be caused by fracture infilling due to rock flour, drill bit damage or invasion of drilling muds. Surface Roughness: Texture of fracture surface due to asperities in the plane. Roughness can range from smooth planes to highly irregular surfaces. Rock Matrix: Structure of unfractured bulk rock mass composed of mineral grains, cement, pore water, and pore space. Wellbore Storage: Volume of water in the borehole which, when pumping is initiated, is first depleted prior to water stored in fracture or rock matrix.
References Abelin, H., Birgersson, L., Gidlund, J., and Neretnicks, I., 1991. A large-scale flow and tracer experiment in granite 1. Experimental design and flow distribution, Water Resour. Res., 27(12): 3107–3117. Atkinson, B.K., 1987. Fracture Mechanics of Rock, Academic Press, Orlando, FL, 534 pp. Barenblatt, G.I., Zheltov, I.P., and Kochina, I.N., 1960. Basic concepts in the theory of seepage if homogeneous liquids in fissured rocks, J. Appl. Math. Mech., (Engl. Transl.) 24(5): 852–864. Barker, J.A., 1991. Reciprocity principle and analytical solution for Darcian flow in a network, Water Resour. Res., 27(5): 743–746. Bear, J., 1972. Dynamics of Fluids in Porous Media, Elsevier, New York, 764 pp. Bear, J., 1993. Modeling flow and contaminant transport in fractured rocks. In Flow and Contaminant Transport in Fractured Rocks, eds. J. Bear, C.-F. Tsang, and G. de Marsily, pp. 1–37. Academic Press Inc., San Diego, CA. Bear, J., Tsang, C.-F., and de Marsily, G., 1993. Flow and Contaminant Transport in Fractured Rocks, Academic Press Inc., San Diego, CA, 560 pp. Berkowitz, B., Naumann, C., and Smith, L., 1994. Mass transfer at fracture intersections: an evaluation of mixing models. Water Resour. Res., 30(6): 1765–1773. Berkowitz, B., Bear, J., and Braester, C., 1988. Continuum models for contaminant transport in fractured porous formations, Water Resour. Res., 24(8): 1225–1236. Black, W.H., Smith, H.R., and Patton, F.D., 1987. Multiple-level groundwater monitoring with the MP system. In Proc. NWWA-AGU Conf. on Surface and Borehole Geophysical Methods and Groundwater Instrumentation, NWWA, Dublin, Ohio. Bliss, J.C. and Rushton, K.R., 1984. The reliability of packer tests for estimating the hydraulic conductivity of aquifers, Q. J. Engrg. Geol., 17: 88–91. Bredehoeft, J.D. and Papadopulos, S.S., 1980. A method for determining the hydraulic properties of tight formations, Water Resour. Res., 16(1): 233–238. Brown, S.R., Kranz, R.L., and Bonner, B.P., 1986. Correlation between the surfaces of natural rock joints, Geophys. Res. Lett., 13(13): 1430–1433. Brown, S.R., 1995. Simple mathematical model of a rough fracture, J. Geophys. Res., 100(B4): 5941–5952. Cacas, M.C., Ledoux, E., de Marsily, G., Tillie, B., Barbareau, A., Calmels, P., Gaillard, B., and Margritta, R., 1990. Modelling fracture flow with a stochastic discrete fracture network: calibration and validation 1. The flow model. Water Resour. Res. 26(3): 479–489. Cherry, J.A. and Johnson, P.E., 1982. A multilevel device for hydraulic head monitoring and groundwater sampling in fractured rock. Ground Water Monitoring Rev., 2(3): 41–44. Cooper, H.H., Bredehoeft, J.D., and Papadopulos, I.S., 1967. Response to a finite diameter well to an instantaneous charge of water, Water Resour. Res., 3(1): 263–269.
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Deltombe, J.-L. and Schepers, R., 2004. New developments in real-time processing of full waveform acoustic televiewer data. J. Appl. Geophys., 55(2004): 161–172. de Marsily, G., 1986. Quantitative Hydrogeology, Academic Press, Orlando, FL. Doe, T. and Remer, J. 1980. Analysis of constant-head well tests in non-porous fractured rock. In Third Invitational Well-Testing Symposium — “Well testing in Low Permeability Environments”, Berkeley, California, pp. 84–89. Doe, T., Osnes, J., Kenrick, M., Geier, J., and Warner, S., 1987. Design of well testing programs for waste disposal in crystalline rock. In Proceedings of 6th Congress of the International Society for Rock Mechanics, Montreal, Canada. Dougherty, D.E. and Babu, D.K., 1984. Flow to a partially penetrating well in a double porosity reservoir, Water Resour. Res., 20(8): 1116–1122. Drost, W., Klotz, D., Koch, A., Moser, H., Neumaier, F., and Werner R., 1968. Point dilution methods of investigating ground water flow by means of radioisotopes, Water Resour. Res., 4(1): 125–146. Dunnicliff, J., 1988. Geotechnical Instrumentation for Monitoring Field Performance, John Wiley & Sons, Canada, Ltd. Dverstorp, B., Andersson, J., and Nordqvist, W. 1992. Discrete fracture network interpretation of field tracer migration in sparsely fractured rock. Water Resour. Res., 28(9): 2327–2343. Earlougher, R.C., Jr., 1977. Advances in Well Test Analysis, Monogr. 5, Society of Petroleum Engineers, Dallas, TX. Elsworth, D., 1986. A model to evaluate the transient hydraulic response of three-dimensional sparselyfractured rock masses. Water Resour. Res., 22(13): 1809–1819. Engelder, T., Fischer, M.P., and Gross, M.R., 1993. Geological Aspects of Fracture Mechanics, A Short Course Manual, Geological Society of America, 281 pp. Faust, C.R. and Mercer, J.W., 1984. Evaluation of slug tests in wells containing a finite-thickness skin, Water Resour. Res., 20(4): 504–506. Ford, D.C., Palmer, A.N., and White, W.B., 1988. Landform development:karst. In Hydrogeology, eds. Back, W., Rosenshein, J.S., and Seaber, P.R. Vol. O-2, pp. 401–412, Geological Society of America, Boulder, CO, The Geology of North America. Gentier, S. and Billaux, D., 1989. Caracterisation en laboratoire de l ’espace fissural d’une fracture, In Proceedings of the International Symposium on Rock at Great Depth, Vol.1, pp. 425–431, A.A. Balkema, Rotterdam, The Netherlands. Graf, T. and Therrien, R. 2005. Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures Adv. Water Resour., 28: 1351–1367. Grisak, G.E., Merritt, W.F., and Williams, D.W., 1977. A fluoride borehole dilution apparatus for groundwater velocity measurements, Can. Geotech. J., 14: 554–561. Hakami, E. 1995. Aperture Distribution of Rock Fractures, Ph.D. thesis, Dept. of Civil and Environmental Engineering, Royal Institute of Technology, Stockholm, Sweden. Hassan, A.E. and Mohamed, M.M., 2003. On using particle tracking methods to simulate transport in single-continuum and dual continua media. J. Hydrol., 275: 242–260. Hess, A.E. and Paillet, F.L., 1990. Applications of the thermal-pulse flowmeter in the hydraulic characterization of fractured rocks, ASTM STP, 1101: 99–112. Holst, T.B., 1982. Regional jointing in the northern Michigan Basin. Geology., 10: 273–277. Holzhauser, G.R., 1989. Origins of sheet structure, 1. Morphology and boundary conditions. Engng. Geol. 27: 225–279. Huyakorn, P.S., Lester, B.H., and Mercer, J.W. 1983. An efficient finite element technique for modeling transport in fractured porous media, 1. Single species transport, Water Resour. Res., 19(3): 841–854. Johns, R.A. and Roberts, P.V., 1991. A solute transport model for channelized flow in a fracture, Water Resour. Res., 27(8): 1797–1808. Jouanna, P., 1993. A summary of field test methods in fractured rocks, In Flow and Contaminant Transport in Fractured Rocks, eds. J. Bear, C.-F. Tsang, and G. de Marsily, pp. 437–543. Academic Press Inc., San Diego, CA.
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Karasaki, K., Long, J.C.S., and Witherspoon, P.A. 1988. Analytical models of slug tests, Water Resour. Res., 24(1): 115–126. Kim, H.-M., Inoue, J., and Hideyuki, H., 2004. Flow analysis of jointed rock masses based on excavationinduced transmissivity change of rough joints. Int. J. Rock Mech. Mining Sci., 41(6): 959–974. Konzuk, J. and Kueper, B., 2004. Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture. Water Resour. Res., 40(2), W02402, doi:10.1029/2003WR002356. Kulander, B.R., Dean, S.L., and Ward, B.J., 1990. Fractured Core Analysis: Interpretation, Logging and Use of Natural and Induced Fractures in Core: AAPG Methods in Exploration Series. No. 8, American Association of Petroleum Geologists, Tulsa, Ok, 88 pp. Küpper, J.A., Schwartz, F.W., and Steffler, P.M., 1995a. A comparison of fracture mixing models, 1. A transfer function approach to mass transport modeling. J. Contam. Hydrol. 18: 1–32. Küpper, J.A., Schwartz, F.W., and Steffler, P.M., 1995b. A comparison of fracture mixing models, 2. Analysis of simulation trials. J. Contam. Hydrol. 18: 33–58. La Pointe, P.R. and Hudson, J.A., 1985. Characterization and interpretation of rock mass joint patterns, Geological Society of America Special Paper 199, 37pp. Lapcevic, P.A., Novakowski, K.S., and Cherry, J.A., 1990. The characterization of two discrete horizontal fractures in shale, In Proc. Technology Transfer Conference, Ontario Ministry of Environment, Nov., Toronto, Ontario. Vol II, pp. 486–495. Lapcevic, P.A., 1997. Tracer Experiments Conducted in a Discrete Horizontal Fracture under Conditions of Forced Hydraulic Gradient and Natural Groundwater Flow, MSc. Thesis, University of Waterloo, Waterloo, ON, 98 pp. Lau, J.S.O., 1983. The determination of true orientations of fractures in rock cores, Canad. Geotech. J., 20: 221–227. Long, J.C.S., Gilmour, P., and Witherspoon, P.A., 1985. A model for steady fluid flow in random threedimensional networks of disc-shaped fractures. Water Resour. Res., 21(8): 1105–1115. Mazurek, M., Jakob, A., and Bossart, P., 2003. Solute transport in crystalline rocks at Aspo I: Geological basis and model calibration. J. Contam. Hydrol., 61: 157–164. McKenna, S.A., Meigs, L.C., and Haggerty, R., 2001. Tracer tests in fractured dolomite, 3. Double porosity, multiple-rate transfer processes in two-well convergent-flow tests.Water Resour. Res., 37(5): 1143–1154. Min, K.-B., Rutqvist, J., Tsang, C.-F., and Jing, L., 2005. Thermally induced mechanical and permeability changes around a nuclear waste repository — a far-field study based on equivalent properties determined by a discrete approach. Int. J. Rock Mech. Mining Sci., 42: 765–780. Moench, A.F. and Hsieh, P.A., 1985. Analysis of slug test data in a well with finite thickness skin, In Memoirs of the 17th International Congress on the Hydrogeology of Rocks of Low Permeability, Vol. 17, pp.17–29, International Association of Hydrologists, Tucson, AZ. Moreno, L., Tsang, Y.W., Tsang, C.F., Hale, F.V., and Neretnieks, I., 1988. Flow and tracer transport in a single fracture: a stochastic model and its relation to some field observations, Water Resour. Res., 24(12): 2033–2048. Nair, R., Abousleiman, Y., and Zaman, M., 2004. A finite-element porothermoelastic model for dualporosity media. Int. J. Numer. Anal. Meth. Geomech., 28: 875–898 (DOI: 10.1002/nag.336) Neuzil, C.E., 1982. On conducting the modified > slug = test in tight formations, Water Resour. Res., 18(2): 439–441. Nordqvist, A.W., Tsang, Y., Tsang, C.-F., Dverstorp, B., and Andersson, J., 1992. A variable aperture fracture network model for flow and transport in fractured rocks. Water Resour. Res. 28(6): 1703–1713. Novakowski, K.S., 1989. Analysis of pulse interference tests, Water Resour. Res., 25(11): 2377–2387. Novakowski, K.S., 2005. Use of the Theim equation to interpret constant head tests conducted in boreholes. J. Hydrol., submitted. Novakowski, K.S. and Lapcevic P.A., 1994. Field measurement of radial solute transport in fractured rock, Water Resour. Res., 30(1): 37–44.
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Novakowski, K.S. and Bogan, J.D., 1999. A semi-analytical model for the simulation of solute transport in a network of fractures having random orientations. Int. J. Num. Anal. Meth. Geomech., 23: 317–333. Novakowski, K.S, Lapcevic, P., Bickerton, G., Voralek, J., Zanini, L., and Talbot, C., 1999. The development of a conceptual model for contaminant transport in the dolostone underlying Smithville, Ontario. Final report prepared for the Smithville Phase IV Remediation Program (Available on CD), 175 pp. Novakowski, K.S., Bickerton, G., and Lapcevic, P. 2004. Interpretation of injection-withdrawal tracer experiments conducted between two wells in a large single fracture. J. Contam. Hydrol., 73: 227–247. Novakowski, K.S., Bickerton, G., Lapcevic, P.A., Voralek, J., and Ross, N., 2006. Measurement of groundwater velocity in discrete fractures. J. Contam. Hydrol., 82: 44–60. Odling, N.E., 1994. Natural rock profiles, fractal dimensions and joint roughness coefficients, Rock Mech. Rock Engng., 27(3): 135–153. Oxtobee, J. and Novakowski, K.S., 2003. A numerical investigation of the principal processes governing the exchange of groundwater between a bedrock stream and a fractured rock aquifer. J. Groundwater, 41(5): 667–681. Paillet, F.L. and Kapucu, K., 1989. Characterization of fracture permeability and fracture flow modeling at Mirror Lake, New Hampshire, U.S. Geological Survey Water Resources Investigations Report 89-4058, 49p. Paillet, F.L., 2004. Borehole flowmeter applications in irregular and large-diameter boreholes. J. Appl. Geophys., 55: 39–59. Pashin, J.C., 2005. Compartmentalization analysis of coalbed methane resources in the Black Warrior Basin; using 3-D computer models to balance industrial and environmental concerns. AAPG Bull., 89(1): 151. Philip, J.R., 1988. The fluid mechanics of fractures and other junctions. Water Resour. Res., 24(2): 239–246. Piggott, A.R. 1990 Analytical and Experimental Studies of Rock Fracture Hydraulics, Ph.D. thesis, Pennsylvania State Univ., University Park, PA. Piggott, A.R. and Elsworth, D., 1993. Laboratory assessment of the equivalent apertures of a rock fracture, Geophys. Res. Lett., 20(13): 1387–1390. Piggott, A.R. Huynh, T.N.T., Lapcevic, P.A., and Novakowski, K.S. 1996. Automated analysis of hydraulic and tracer tests conducted in fractured rock, Hydrogeology J., 4(3): 84–93. Piggott, A., Moltyaner, G., Yamazaki, L., and Novakowski, K.S. 1997. Preliminary characterization of fracturing at the site of the Chalk River Laboratories, In Proceedings of 50th Canadian Geotechnical Conference, Ottawa, Canada (also NWRI No. 97-126). Pyrak-Nolte, L.J., Myer, L.M., Cook, N.G.W., and Witherspoon, P.A., 1987. Hydraulic and mechanical properties of natural fractures in low permeability rock, In Proceedings of 6th Congress of the International Society for Rock Mechanics, Montreal, Canada, pp. 225–231. Ragan, D.M. 1973. Structural Geology: An Introduction to Geometrical Techniques, John Wiley & Sons, New York, NY, 208 pp. Raven, K.G. 1986. Hydraulic characterization of a small ground-water flow system in fractured monzononitic gneiss, Nat. Hyd. Res. Inst. Scientific Series No. 149, No. 30, 133pp. Raven, K.G., Novakowski, K.S., and Lapcevic, P.A., 1988. Interpretation of field tracer tests of a single fracture using a transient solute storage model, Water Resour. Res., 24(12): 2019–2032. Rowe, R.K., and Booker, J.R. 1990. Contaminant migration through fractured till into an underlying aquifer, Can. Geotech. J., 27(4): 484–495. Sageev, A., 1986. Slug test analysis, Water Resour. Res., 22(8): 1323–1333. Sanford, B.V., Thompson, F.J., and McFall, G.H., 1985. Phanerozoic and recent tectonics of the Canadian Craton, in The Geoscience Program — Proceedings of the Seventeenth Information Meeting of the Nuclear Fuel Waste Management Program, Atomic Energy of Canada Limited, TR-299, pp. 334–352. Schwartz, F.W., Smith, L., and Crowe, A., 1983. A stochastic analysis of macroscopic dispersion in fractured media. Water Resour. Res. 19(5): 1253–1265.
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Schwartz, F.W. and Smith, L. 1988. A continuum approach for modeling mass transport in fractured media, Water Resour. Res., 24(8): 1360–1372. Shapiro, A.M. and Nicholas, J.R. 1989. Assessing the validity of the channel model of fracture aperture under field conditions, Water Resour. Res., 25(5): 817–828. Smith, L. and Schwartz, F.W., 1984. An analysis of the influence of fracture geometry on mass transport in fractured media. Water Resour. Res. 20(9): 1241–1252. Snow, D.T., 1969. Anisotropic permeability of fractured media. Water Resour. Res., 5(6): 1273–1289. Stephenson, K., Novakowski, K.S., Davis, E., and Heron, G., 2006. Hydraulic characterization for steam enhanced remediation in fractured rock. J. Contam. Hydrol., 82: 220–240. Sudicky, E.A. and Frind, E.O. 1982. Contaminant transport in fractured porous media: analytical solution for a system of parallel fractures, Water Resour. Res., 18(6): 1634–1642. Sudicky, E.A., 1990. The Laplace transform galerkin technique for efficient time-continuous solution of solute transport in double-porosity media, Geoderma, 46: 209–232. Sudicky, E.A. and McLaren, R.G., 1992. The Laplace transform Galerkin technique for large-scale simulation of mass transport in discretely fractured porous formations. Water Resour. Res., 28(2): 499–514. Tang, D.H., Frind, E.O., and Sudicky, E.A., 1981. Contaminant transport in fractured porous media: analytical solution for a single fracture, Water Resour. Res., 17(3): 555–564. Therrien, R. and Sudicky, E.A., 1996. Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media, J. Contam. Hydrol., 23(1–2): 1–44. Trainer, F.W. 1988. Hydrogeology of the plutonic and metamorphic rocks, In Hydrogeology, eds. Back, W., Rosenshein, J.S., and Seaber, P.R. Vol. O-2, pp. 367–380, Geological Society of America, Boulder, CO, The Geology of North America. Tsang, Y.W. and Witherspoon, P.A., 1983. The dependence of fracture mechanical and fluid flow properties on fracture roughness and sample size, J. Geophys. Res., 88(B3): 2359–2366. Tsang, Y.W., 1984. The effect of tortuosity on fluid flow through a single fracture, Water Resour. Res., 20(9): 1209–1215. Tsang,Y.W. and Tsang, C.F., 1987. Channel model of flow through fractured media, Water Resour. Res., 23(3): 467–479. Tsang, C.-F. and Doughty, C., 2003. A particle-tracking approach to simulating transport in a complex fracture. Water Resour. Res., 39(7): 1174, doi:10.1029/2002WR001614. Vickers, B.C., Neuman, S.P., Sully, M.J., and Evans, D.D., 1992. Reconstruction and geostatistical analysis of multiscale fracture apertures in a large block of welded tuff, Geophys. Res. Lett., 19(10): 1029–1032. Wang, J.S.Y., Narasimhan, T.N., and Scholz, C.H. 1988. Aperture correlation of a fractal fracture, J. Geophys. Res., 93(B3): 2216–2224. West, M.R., Kueper, B.H., and Novakowski, K.S., 2004. Analytical solutions for solute transport in fractured porous media using a finite width strip source. Adv in Water Resour, 27: 1045–1059. West, A.C.F., Novakowski, K.S., and Gazor, S., 2005. Usefulness of core logging for the identification of conductive fractures in bedrock. Water Resour. Res., 41: W03018, doi:10.1029/2004WR003582. Williams, H.R., Corkery, D., and Lorek, E.G., 1985. A study of joints and stress-relief buckles in Paleozoic rocks of the Niagara Peninsula, southern Ontario. Can. Geotech. J., 22: 296–300. Zanini, L., Novakowski, K., Lapcevic, P., Bickerton, G., Voralek, J., and Talbot, C., 2000. Regional groundwater flow in the fractured carbonate aquifer underlying Smithville, Ontario, inferred from combined hydrogeological and geochemical measurements. J. Groundwater, 38(3): 350–360. Zeigler, T.W., 1976. Determination of Rock Mass Permeability, Waterways Experiment Station, Technical Report S-76-2, Vicksburg, MI. Zemanek, J., Caldwell, R.L., Glenn, E.E., Holcomb, S.V., Norton, L.J., and Strauss, A.J.D., 1969. The borehole televiewer — A new logging concept for fracture location and casing inspection, J. Pet. Technol., 21(12): 762–774.
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Further Information Engleder et al. (1993) presents a thorough overview of the geological aspects of fracture mechanics and includes a comprehensive glossary of terms. deMarsily (1986) is a general text in quantitative hydrogeology that discusses flow and transport in fractures in an easy to follow manner. Kulander et al. (1990) discusses in detail core analysis and the identification and classification of breaks in rock core. Doe et al. (1987) discusses various techniques and strategies for hydraulic testing in fractured rock. Earlougher (1977) provides a comprehensive look at standard well testing methods in the petroleum industry that can be adapted to hydrogeological investigations. Bear et al. (1993) provides a compilation of chapters investigating flow and contaminant transport in fractured rock and in addition to theoretical discussions has sections of flow and solute transport in fracture networks.
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21 Groundwater Flow in Karstic Aquifers 21.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-2 21.2 Karst Aquifers: The Conceptual Framework . . . . . . . . . . . 21-2 Groundwater Basins • Allogenic Recharge • Internal Runoff • Dispersed Infiltration and the Epikarst • Infiltration Pathways in the Vadose Zone • Subsurface Drainage Patterns • Groundwater Discharge: Karst Springs • The Geologic Boundary Conditions • The Conceptual Model
21.3 Permeability and Flow Dynamics in Karst Aquifers . . . 21-8 Matrix and Fracture Flow • Conduit Permeability and Flow Dynamics • Sediment Fluxes and Transport Mechanisms • Caves and Conduits: Hydrologic Interpretation of Cave Patterns • Paleohydrology
21.4 Chemistry of Carbonate Rock Dissolution . . . . . . . . . . . . 21-17 Chemical Equilibrium • Chemical Parameters for Karst Aquifers • Dissolution Kinetics of Limestone and Dolomite
21.5 Evolution of Karst Aquifers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-24 Life History of a Conduit • Initiation and Critical Thresholds • Enlargement, Maturity, and Decay
21.6 Quantitative Hydrology of Karst Aquifers . . . . . . . . . . . . . 21-27 Water Budget • Base Flow/Runoff Relations • Tracer Studies • Well Tests and Water Table Mapping • Hydrographs of Karst Springs • Chemographs of Karst Springs
21.7 Modeling of Karst Aquifers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-37 Evolutionary Models • Equivalent Porous Media Models • Pipe Flow Models • Coupled Continuum Pipe Flow Models • Input–Output Models
21.8 Water Resource Issues in Karst Hydrology . . . . . . . . . . . . . 21-39 Water Supplies in Karst • Flood Flows in Karst: Sinkhole Flooding • Contaminants and Contaminant Transport in Karst Aquifers • Water Quality Monitoring
21.9 Land Instability and Sinkhole Development . . . . . . . . . . . 21-41 Sinkholes as Land Use Hazards • Mechanisms of Sinkhole Development • Hydrologic Factors in Sinkhole Development • Sinkhole Remediation
William B. White The Pennsylvania State University
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-43 Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-47
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21.1 Introduction Karstic aquifers are those that contain dissolution-generated conduits that transport groundwater, often localized, fast-moving and in a turbulent regime. The ability of the conduit system to transport a sediment load, sometimes with associated contaminants, is an additional feature. Such aquifers are found mainly in limestone, dolomite and gypsum as the commonly occurring soluble rocks. In most aquifers there is a mismatch of many orders of magnitude between groundwater flow rates in the aquifer and stream flow rates on the land surface above. In karstic aquifers there is a continuum of flow rates such that the groundwater system in karstic aquifers takes on the characteristics of both surface water and groundwater. Further, because of the presence of sinking streams and large springs, there is a complex interplay between surface water and groundwater. Karst regions display a characteristic suite of landforms. On the surface are sinking streams and dry channels linked by underground routes to large springs. There are closed depressions on many size scales and elaborately sculptured bedrock surfaces that may or may not be mantled with soil. Underground, there are cave systems which may or may not be accessible through entrances from the surface. Some caves are dry and abandoned except for drip water, some carry active streams, and some may lie below local base levels and be completely water-filled. Karst regions are often classified by their dominant landforms such as fluviokarst for mixed carbonate — clastic rock regions, cone-and-tower karst, pavement karst, sinkhole karst, and others. They are also sometimes classified by climate as in alpine karst, tropical karst, arid karst, and others. The emphasis of this chapter is on fluviokarst because this is the form of karst most commonly encountered by engineers and resource managers in the United States.
21.2 Karst Aquifers: The Conceptual Framework 21.2.1 Groundwater Basins The physical framework for discussion of groundwater is the aquifer. Usually, an aquifer is a specific rock formation with a well-defined thickness but an indefinite lateral extent. One can speak of the “area” of an aquifer only in a rough sense. The physical framework for discussion of surface water is the drainage basin. Drainage basins have an arbitrary downstream limit determined by the choice of gauge point but once the gauge point is fixed, a drainage divide can be drawn and the basin has a well-defined area. Karst aquifers share the properties of both groundwater and surface water which lead to the concept of groundwater basins with well-defined boundaries which do not necessarily coincide with the boundaries of overlying surface water basins. The essential components are sketched in Figure 21.1. The sketch is appropriate to the mixed carbonate/clastic rock terrain that makes up the fluviokarst of the eastern United States. There are three main components to the catchment system: (1) allogenic recharge, (2) internal runoff, and (3) dispersed (diffuse) infiltration. The groundwater basin arises when the aquifer acquires a well-developed conduit system. The conduit system provides a flow path of low hydraulic resistance. It also acts as a drain for matrix and fracture flow so that there is the subsurface equivalent of a drainage divide. However, unlike surface divides which are fixed by topography, groundwater basin divides may shift depending on groundwater levels. High-level spillovers between adjacent basins are common.
21.2.2 Allogenic Recharge Streams rising on adjacent or overlying clastic rocks often sink underground near the clastic rock/carbonate rock contact when they flow onto the karst. These sinkpoints are called swallow holes or swallets. Each sinking stream derives water from its own small surface catchment with a well-defined area. The sink point acts as the gauge point. Sinking streams inject large quantities of water into the carbonate aquifer at single points. Allogenic recharge often has a different chemistry, is exceptionally vulnerable to contamination, and exhibits the rapid response to storm flow characteristic of surface runoff. The total area providing
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Allogenic recharge
Swallow holes Internal runoff
ide
Diffuse infiltration
Ba
sin
div
Spring
Gauge
FIGURE 21.1 Map showing a groundwater basin with areas of allogenic recharge, internal runoff and diffuse (or dispersed) infiltration. The area of the basin is defined by the dashed line showing the basin divide which in turn is determined by the choice of gauge location.
allogenic recharge, Aa , is simply the sum of the areas of the individual sinking stream basins Ai : Aa =
Ai
(21.1)
i
Swallets take many forms. In some cases the allogenic streams have downcut upstream from the swallet forming blind valleys so that all allogenic runoff feeds into the groundwater regardless of the magnitude of flow. In other cases, a dry surface channel continues downstream from the swallet so that during flood flows, only a portion of the flow enters the aquifer and the remainder remains as surface flow. Some streams lose a portion of their water through the channel but do not go completely dry even during base flow. In physical appearance, swallets range from open cave mouths with streams flowing into them to inconspicuous loosing reaches of stream channel. In regions such as the Appalachian Plateaus, the Illinois Basin, and the Ozark Plateau, karstic carbonate aquifers underlie extensive plateaus capped with clastic rocks. Surface water catchments on the plateaus provide allogenic runoff that enters the carbonate aquifer from the top. These waters tend to be chemically aggressive and enlarge fractures into open shafts which in turn permit very rapid movement of water through the unsaturated zone.
21.2.3 Internal Runoff Some karst terrains are so densely packed with closed depression that overland storm flow is entirely captured by the depressions and does not reach surface stream channels. Closed depressions — also known as sinkholes and dolines — vary widely in their ability to accept storm flow. In the eastern United States, most closed depressions are mantled with soil of widely varying thicknesses. Some have open drains at the bottom which carry storm flow directly into tributary channels of the conduit drainage system. In some, the storm flow must infiltrate through the soil mantle, a situation that can change rapidly if a soil
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piping failure opens a throat in the bottom of the depression. Some depressions are mantled with clay-rich soils that act as effective seals thus producing perennial sinkhole ponds. Calculation of the internal runoff contribution to the overall water balance is difficult. In principle, the collection area for internal runoff would be the sum of the areas of enclosed depressions. However, intense storms may be required to saturate the soils and produce enough overland flow to reach the bottom of the depression. Less intense storm flow infiltrates the soils on the walls of the depression and becomes part of the dispersed infiltration. The distinction between internal runoff and dispersed (or diffused) infiltration is based on transit time. Overland flow directly into open drains will have a different chemistry from water that permeates slowly through the soil. There is a continuum between the two recharge types.
21.2.4 Dispersed Infiltration and the Epikarst
Internal runoff from storm flow
Sinkhole drain
Vadose zone
Dispersed infiltration
Epikarst soil
The entire area of the karst groundwater basin receives rainfall. What does not drain into closed depressions by overland flow infiltrates slowly as the soil gradually becomes saturated. In karst terrain, the soils are strongly leached, with few carbonate rock fragments remaining in the soil. The C-horizon is usually absent; there is a sharp contact between the B-horizon and limestone or dolomite bedrock. The bedrock surface is often highly irregular with deep channels and trenches dissolved along fractures, sometimes known as “cutters” (or “grikes” in the UK). Between the fractures are irregular pinnacles of residual bedrock. Cavities may occur within the bedrock mass. The zone of regolith plus the cutter and pinnacle zone in the bedrock has a thickness of meters to tens of meters and is known collectively as the epikarst (Jones et al., 2003) (Figure 21.2). The bulk bedrock usually has a very low permeability so that the infiltrating water can reach the subsurface only by moving laterally along the crevices and trenches until it reaches an open fracture or shaft descending into the aquifer below. Because the irregular cutters are soil-filled, flow rates are slow
Water table Stream cave at base flow
Phreatic zone
Dry cave
FIGURE 21.2 Cross-section of a karst surface showing a closed depression collecting internal runoff and the epikarst collecting dispersed infiltration.
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and storm water may be stored for periods of days to weeks. The epikarst is the reservoir that supplies cave dripwater during drought periods.
21.2.5 Infiltration Pathways in the Vadose Zone Movement of water through the vadose zone is highly anisotropic and often very rapid. Pathways for the vertical movement of water that has penetrated the epikarst include: 1. Slow percolation through the matrix porosity of the bedrock. This component is important in young limestones, such as those in Florida and the Bahamas, for example, that have not been compacted by deep burial or compressed by orogenic processes. Infiltration through the matrix is usually negligible in the dense Paleozoic limestones of eastern United States. 2. Vertical flow through fractures at the base of the epikarst. 3. Dissolutionally widened fractures and open throats that serve as sinkhole drains. 4. Larger shafts that carry the runoff from caprocked upland surfaces and discharge from overlying perched aquifer system. 5. Open channels that carry water from sinking streams. Allogenic streams often sink into open cave systems at elevations well above regional base levels. The underground streams descend rapidly, often in open channels with a stair-step profile. In high-relief terrains, the profile may consist of a sequence of steep channels with interspersed waterfalls. These input channels are often large enough for human exploration and many have been mapped. The explorable allogenic stream inputs and some large closed depression drains have been classified as vadose caves. The internal relief varies from a few meters in low-relief terrains to more than 1000 m in high-relief terrains. Water draining from upland areas underlain by clastic rock is injected into vertical pathways when it reaches the top of the carbonate aquifer. Because allogenic recharge tends to be highly aggressive, dissolution by the water moving along vertical pathways enlarges the initial fractures into shafts with diameters of meters to tens of meters and depths of tens to hundreds of meters. Some shafts have irregular shapes dictated by the shape of the fracture system that provided the initial pathway. With time, the shafts take the form of near-perfect cylinders with vertical walls that slice across beds of varying lithology (Brucker et al., 1972). Drains from closed depressions have dimensions from centimeters to meters and are sometimes large enough to permit human exploration. Flow velocities are high and sufficient to transport sediment. Soil piping processes in closed depressions and above open fractures are an important source of sediment injected into the conduit system. The walls of closed depression drains are often jagged and corroded showing the highly aggressive chemistry of the water collected in the closed depressions and injected into the drain. The Paleozoic carbonate aquifers of the eastern United states are highly fractured. The fractures provide effective pathways for infiltration of water into the subsurface. If the chemical reaction between the aggressive water of the epikarst with the carbonate bedrock goes to equilibrium, there may be relatively little dissolutional enlargement of these fractures. If the fractures are closely spaced, they provide a very important pathway for dispersed infiltration. In contrast to the open shafts and drains, because of the long residence time at the base of the epikarst, the fracture water is often near saturation with calcium carbonate.
21.2.6 Subsurface Drainage Patterns The mixed groundwater/surface water character of karst aquifers is best revealed in the flow pattern in the subsurface. Instead of a uniform flow field mapped by isopotential contours, groundwater in karstic aquifers moves through an interconnected system of fractures, small solution channels, and large conduits. Travel times in the conduit system are often very short, hours to days per kilometer. The water may flow
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as open channel underground streams or as pipe flow with varying degrees of pressure head. Gradients within the matrix and fracture flow portions of the aquifer are usually oriented toward the conduits. Sinking surface streams for the most part inject water directly into the conduit system. Drains from closed depressions also feed into the conduit system. Dispersed infiltration recharges the matrix and fracture system which in turn discharges into the conduit system. Each of these subsystems has different storage capacities and travel times.
21.2.7 Groundwater Discharge: Karst Springs Most groundwater discharge from karst aquifers is through high volume springs. Sometimes a groundwater basin discharges through a single spring and sometimes the water is distributed over multiple springs including wet-weather spillover springs. As more tracer data accumulates, groundwater distributed to multiple springs is being shown to be common. Diffuse discharge of groundwater in valley bottoms certainly occurs, but in well-developed karst aquifers, it constitutes only a small portion of the total discharge. As an example, measurements show that 95% of the discharge from groundwater basins in the southcentral Kentucky karst aquifer is through a few large springs (Hess and White, 1989). The springs along the Green River in south-central Kentucky can be divided into a small number of large regional springs draining groundwater basins of more than 100 km2 , a somewhat larger number of valleys drain springs with catchments of a few tens of km2 , and a large number of very small local springs are fed by small catchment areas near the river. Water balance shows, however, that the large springs account for most of the discharge.
21.2.8 The Geologic Boundary Conditions The hydrologic components of the karst groundwater system must be superimposed on the geologic framework of the drainage basin because much of the detail in the pattern and development of the internal drainage system is guided and controlled by the local geology. The details of the geologic framework are highly site-specific but the main factors can be listed. 1. Physiographic factors (a) Placement of the karst aquifer within the regional drainage basin (b) Relief between recharge area and springs 2. Structural factors (a) Folded vs. non-folded rocks (b) Dip with respect to groundwater flow directions (c) Faults (d) Regional scale fracture systems (e) Local pattern of joints and bedding plane partings 3. Stratigraphic and lithologic factors (a) Thickness of carbonate or gypsum rocks (b) Location of soluble rock sequences with respect to clastic rock sequences (c) Limestone vs. dolomite vs. gypsum (d) Lithologic characteristics: pure limestones, shaley limestones, marls (e) Presence and location of confining layers — thin shales and sandstones — within the soluble rock sequence (f) Confined vs. unconfined aquifer Conduit development seeks out optimum flow paths through the available fractures and bedding plane partings. Conduits are deflected by relatively minor impermeable layers and by unfavorable lithologies. Fine-grained (micritic) pure limestone are favorable; shaley limestones, dolomitic limestones, and dolomites are unfavorable. Folds and faults guide possible flow paths by controlling the placement of favorable
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Dispersed infiltration Losing stream basins
Perched catchment
Internal runoff
Epikarst
Sinking stream basins
Surface overflow channel
Fracturematrix system
Shafts Exchange
Sinking stream basins
Overflow spring
Conduit system Deep fractures
Baselevel stream
Underflow spring
Phreatic lift Confined flow
FIGURE 21.3 Conceptual model for the internal structure and flow paths in a karst aquifer. This is the current version of a sketch that has been drawn and re-drawn by the author and by J.A. Ray of the Kentucky Division of Water since its first publication (White, 1999).
rock lithologies. The final arrangement of internal flow paths represents a balance between hydraulic gradients and geologic constraints.
21.2.9 The Conceptual Model The hydrogeologic concepts can be reduced to a conceptual model based on overall water balance and internal flow paths (White, 1999). A variety of these models can be drawn. One that applies to many fluviokarst groundwater basins in eastern United States is shown in Figure 21.3. The spring (or springs) where groundwater and spillover surface water are recombined into a single surface stream is the effective gauge point for the system. The flow paths shown in the conceptual model are schematic and generalized. Allogenic recharge and internal runoff feed mainly into the conduit system. Throughput times are short. A well-developed conduit system exhibits a fast response to storm recharge. Rising and falling stage levels in the conduit system force the exchange of water into and out of the matrix and fracture systems. Dispersed infiltration recharges mainly the matrix and fracture system. There is a substantial time lag due to water stored in the epikarst. Overall throughput times for the dispersed infiltration are long, generally longer than the mean spacing between storms. Not all of these components are present in all karst aquifers. There are carbonate aquifers to which there is no allogenic recharge and those in which the conduit system is absent. These have been called diffuse flow aquifers. In some aquifers, notably, aquifers in young limestones of Florida and the Caribbean, matrix flow is a dominant component of the groundwater system. In the dense Paleozoic limestones of the eastern United States, matrix flow rarely makes much of a contribution. Beyond visualizing the internal workings of a karst aquifer, the principal value of the conceptual model is that it forms the framework for writing water budgets. Karst aquifers have the virtue that they provide many sites for flow measurements. Flow rates can be measured in sinking streams, in cave streams, and in springs. Measurable areas within the karst groundwater basin allow additional estimates of input. Such measurements provide the necessary data for input–output type of water balance calculations.
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21-8 TABLE 21.1 Permeability
The Handbook of Groundwater Engineering The Component of the Triple Permeability Model for Karstic Aquifers Aperture
Travel Time
Flow Mechanism
Matrix
µm to mm
Long
Darcian flow field. Laminar
Fracture
10 µm to 10 mm
Intermediate
Cube law. Mostly laminar; may be nonlinear components
Conduit
10 mm to 10 m and greater
Short
Darcy–Weisbach. Open channel and pipe flow. Turbulent
Guiding Equation hf =
ηvL ρg (Nd 2 )
Q C = b3 h f
hf =
fLv 2 4gr
Distribution Continuous medium Localized but statistically distributed
Localized
21.3 Permeability and Flow Dynamics in Karst Aquifers A central requirement for any theoretical description of groundwater flow is that the permeability remains a fixed-quantity characteristic of particular rock units. Discontinuities in permeability across geologic boundaries can be accommodated. Likewise, expressing permeability in tensor form accounts for the anisotropy of bedded rock units. Within these constrains, permeability remains scale-independent and time independent. Aquifer behavior can be described theoretically or modeled by computer programs with reasonable accuracy. The permeability in karst aquifers is often described by the “triple porosity” or “triple permeability” model. It is the conduit permeability that sets karst aquifers apart from other water-bearing units (Table 21.1). As a consequence of the permeability distribution, the hydraulic conductivity varies by many orders of magnitude on different size scales (Sauter, 1991). Karst aquifers are not only anisotropic with respect to orientation but they are also anisotropic with respect to measurement scale and with respect to specific points in the aquifer where measurements are to be made.
21.3.1 Matrix and Fracture Flow Ground water flow through the limestone or dolomite bedrock is not intrinsically different from groundwater flow in any other aquifer. The guiding equation is Darcy’s law. Q = −AK
AρgNd 2 h h =− L η L
(21.2)
Q is flow volume (m3 sec−1 ) , A is cross-sectional area of aquifer (m2 ), K is the hydraulic conductivity (m sec−2 ), ρ is density of water (kg m−3 ), Nd 2 is permeability (m2 ), and η is viscosity of water (Pa sec). h/L is the hydraulic gradient. The true matrix component of the flow must be based on the hydraulic conductivity of the unfractured bedrock. Such data are sparse. Most hydraulic conductivities are based on pump tests on wells and those data are dominated by the fracture flow. Intrinsic hydraulic conductivities must be determined from laboratory measurements on unfractured core samples. Estimates for the Mississippian limestone in which Mammoth Cave is formed and for a Silurian dolomite in Ontario are K = 2 × 10−11 and K = 10−10 m sec−1 , respectively (Worthington, 1999). These may be contrasted with K = 10−8 m sec−1 for the Cretaceous Edwards Aquifer in Texas (Worthington et al., 2002) and 3.65 × 10−6 m sec−1 as a mean value for the Floridan Aquifer (Budd and Vacher, 2002). What is clear from the observed hydraulic conductivities is that matrix flow is a negligible part of the overall flow field in the compacted Paleozoic limestones. Matrix flow is important in the Floridan aquifer and many other young, undisturbed limestones in the Yucatan and in the Caribbean islands.
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The idealized model for fracture flow assumes a fracture with plane parallel walls and a uniform aperture. For this ideal geometry, the flow is described by the cubic law which can be derived theoretically from the fundamental Navier–Stokes equations:
Q=−
W ρgb 3 h 12η L
(21.3)
In Equation (21.3) W is the total width of fractures (m) and b is the full aperture of the fracture (m). Other symbols are as defined for Equation 21.2. It has long been recognized that real fractures do not have uniform apertures and that the walls are not parallel. An empirical approach (Witherspoon et al., 1980) was to compact the constants of Equation (21.3) into a single constant, C, and add an empirical fraction factor, ff . Q=
C 3 h b ff L
(21.4)
Good agreement was obtained with laboratory measurements with values of ff ranging from 1.04 to 1.64. Real carbonate aquifers contain a complex suite of fractures. These are typically rough-walled, of varying aperture, and which may or may not be interconnected. Describing the flow through such fracture networks is the object of much current research (Brush and Thomson, 2003; Konzuk and Kueper, 2004). See Chapter 20.
21.3.2 Conduit Permeability and Flow Dynamics For reasons to be discussed later, the aperture marking the transition from fracture permeability to conduit permeability is taken to be 1 cm. Within a mature karst aquifer is a network of solutionally widened fractures and bedding plane partings less than 1 cm in aperture, widened fractures and small solution channels with dimensions of centimeters to tens of centimeters, and conduits with dimensions of meters to tens of meters. All of these are interconnected in complex ways, sometimes in an ordered branchwork pattern as an underground analogy of a surface stream, but more often with multiple interconnections of closed loops. The conduits have very low hydraulic resistance and can carry large volumes of water at high velocities. Knowledge of the conduit system is mainly obtained by tracer tests and by direct observation and survey. Given 0.5 m as a practical lower limit for human exploration, there is a very large portion of the conduit permeability in the scale range from 0.01 to 0.5 m which cannot be directly probed by any presently available technique. Because hydraulic conductivity has units of velocity, there is a temptation to equate travel time to an effective “hydraulic conductivity.” This is erroneous. Use of hydraulic conductivity implies a linear relationship between hydraulic head and discharge and a continuous medium. Most flow in conduits is turbulent and the flow is localized. Further, the travel time represents an average. The actual flow path may contain reaches of high-velocity flow interspersed with reaches where the water is ponded. To a certain extent, groundwater flow in conduits can be treated as flow in pipes. However, conduit geometry is highly variable with cross-sections ranging from uniform elliptical shapes, to high and narrow fissures, to irregular shapes partly filled with rock fragments. Most conduits contain a bed of clastic sediments on their floors and some of these are armored with cobble and boulder-size material in the manner of surface streams. Water may flow in conduits in an open-channel regime subject only to gravitational gradients, or as pipe flow under substantial pressure heads. Both regimes frequently occur in different reaches of the same conduit. Rising and falling water levels in response to storm recharge can shift the regime from open channel flow to pipe flow and back again. Passages that flood to the ceiling during storms are well known to cave explorers.
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Flow velocities in conduits become sufficiently large to drive the system into a turbulent regime. The flow regime in closed pipes is described by a Reynolds number defined as: NR =
ρvR η
(21.5)
Again, ρ and η are the fluid density and viscosity, respectively and v is the flow velocity. R is the hydraulic radius. Although the hydraulic radius for circular pipes is often defined as the pipe diameter, it is more useful to define the hydraulic radius of irregular karst conduits as the cross-sectional area divided by the perimeter. With this definition R = 2r/4 (2r = pipe diameter) with a corresponding scaling of the numerical value of the Reynolds number for circular conduits. If Equation 21.5 is written in consistent units, the Reynolds number is dimensionless. At low Reynolds numbers, the flow regime will be laminar; at high Reynolds numbers it will be turbulent. The transition from laminar to turbulent flow occurs over a range of Reynolds numbers. The onset depends on the wall roughness of the conduit and will be in the range of NR = 50 to 500. At Reynolds numbers greater than 500 (with the definition of hydraulic radius given above), fully developed turbulent flow will occur even in smooth-walled conduits. For a circular conduit of radius, r, containing water flowing in a laminar regime, the flow volume is described by the Hagen–Poiseuille equation: Q=
πρgr 4 h 8η L
(21.6)
There is no corresponding equation for turbulent flow derived from first principles. Instead, the usual starting point is an empirical relation, the Darcy–Weisbach equation. The Darcy–Weisbach equation is shown as a head loss in Table 21.1. As a calculation of flow volume in a circular conduit, it takes the form: Q = 2π
1/2 h 1/2 g r 5/2 f L
(21.7)
The parameter, f , is a dimensionless friction factor. Its determination is one of the serious problems in modeling conduit flow in karst aquifers. If the flow is laminar, the friction factor is exactly determined by the Reynolds number: 64 (21.8) f = NR In the limiting case of turbulent flow in a smooth-walled conduit, unlikely to be found in a karst aquifer, the friction factor is given by the Prandl–Von Karman equation: 1 = 2 log(NR f ) − 0.8 f
(21.9)
Determination of the Darcy–Weisbach friction factor for real karst conduits has taken two approaches. For uniform conduits, the friction factor can be calculated from the wall roughness. Turbulent flow over a smooth wall produces a laminar sublayer separating the mass of the fluid from the rock wall. The wall roughness of rock conduits depends on the irregularities on the conduit wall and on the lithologic characteristics of the bedrock. The thickness of the laminar sublayer, δ is determined by the dimensionless equation: 32.8 δ = (21.10) 2r NR f The relief of surface irregularities, e, is given in the same units as the conduit dimensions. A rough surface is one where the surface roughness is greater than the thickness of the laminar sublayer. For very rough
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Estimates of the Darcy–Weisbach Friction Factor
Location Mendips (UK) Castleguard (Canada) Morecombe Bay (UK) Glomdalsvatn (Norway) Turnhole (KY) Friars Hole (WV) Holloch (Switzerland) Maligne Basin (Canada)
From Discharge
From Roughness
Reference
24–340 0.87–2.31 — 0.116 27 46–74 — 130
— 0.33–0.90 0.077 0.039 — — 0.322 —
[1] [2] [3] [4] [5] [5] [6] [7]
References for Table 21.2: [1] Atkinson (1977); [2] Atkinson et al. (1983); [3] Gale (1984); [4] Lauritzen et al. (1985); [5] Worthington (1991); [6] Jeannin (2001); [7] Smart (1988).
surfaces the friction factor is given by: 1 2r + 1.14 = 2 log e f
(21.11)
For the friction factor to be calculated from wall roughness, the conduit must be uniform. Most karst conduits are not uniform. An alternative approach is to monitor a karst drainage basin and measure all parameters in the Darcy–Weisbach equation except the friction factor. Then calculate the effective friction factor for the entire conduit from the measurements. Table 21.2 is a summary of Darcy–Weisbach friction factors determined either from wall roughness or from drainage basin calculations. The resulting numbers vary by more than two orders of magnitude, with the wall-roughness friction factor always smaller than those calculated from the entire basin. Open channel flow is described by the Manning equation: v=
M 2/3 1/2 R S n
(21.12)
In the Manning equation, v is the mean channel velocity, R is a hydraulic radius, and S is the channel slope. The constant, n (known as “Manning’s n”) is a roughness factor. It has been the custom to let n have the same numerical values regardless of units. The parameter, M , adjusts the units: M = 1 for velocity in m sec−1 and hydraulic radius in meters. M = 1.486 for velocity in ft/sec and hydraulic radius in feet. The hydraulic radius of an irregular channel is defined as the cross-sectional area divided by the wetted perimeter. Values for Manning’s n have been determined for a range of surface stream bed materials (Table 21.3). These are the best available approximations for underground stream channels since no direct experimental determinations of the roughness characteristics of karst conduits seem to have been made. Water may flow in open channels in either laminar or turbulent regimes, although most underground free-surface streams have dimensions and velocities that place them in the turbulent regime. Open channel flows are also subject to a balance between inertial forces and gravity forces described by a dimensionless Froude number: v (21.13) NF = √ gD D is the hydraulic depth, equal to the actual water depth in a rectangular channel. Flows with NF < 1 are termed subcritical; flows with NF > 1 are termed supercritical. The transition from supercritical to subcritical flow is abrupt, with considerable release of energy producing a hydraulic jump. Most underground streams flow in a subcritical regime, but supercritical flows occur in steep gradient vadose streams carrying water from allogenic catchments down to base level. Supercritical flows also occur in the shafts and drains that carry internal runoff through the unsaturated zone down to the water table.
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The Handbook of Groundwater Engineering TABLE 21.3 Manning’s n for Open Channels Bed Material Smooth concrete Good ashlar masonry Rubble masonry Firm gravel Clay Clay and silt Sand and clay Sand and gravel Gravel over rock Coarse sand with some gravel Gravel, rock, and boulders Large angular boulders
n 0.010 0.013 0.017 0.020 0.026 0.046 0.030 0.042 0.027 0.049 0.055 0.079
Source: Data from Vennard, J. K. (1962) Elementary Fluid Mechanics, Wiley, New York and Barnes, H. H. (1967) Roughness Characteristics of Natural Channels, U.S. Geological Survey Water Supply Paper 1849, Washington, D.C.
21.3.3 Sediment Fluxes and Transport Mechanisms Consider the drainage basin illustrated in Figure 21.1. Various tributary surface streams sink into blind valleys. There is no overland flow path for these streams. All surface water moves into the groundwater system to appear eventually at the spring where it returns to a surface route. These tributary surface streams also carry a clastic load. Some clastic particles, mostly clay and some silt will be moved in suspension during storm flow. Other material, particularly the coarser material, will be dragged along the bed as bedload during periods of high flow. Both suspended and bedload sediments are transported into the underground system. They eventually reappear at the spring although there may be a substantial time delay. Clastic sediments are held in temporary storage in the conduit system until the occurrence of storm flows of sufficient magnitude to move the material through the system. If the clastic sediment did not move through the system, the conduit system would eventually clog and force the sinking streams back onto surface routes. However, the transport is episodic with sediments moving only during periods of high discharge. Sampling of the sediment load is possible by examining the sediments in caves which, in the active passages, can be taken as sediment in temporary storage, waiting for the next storm episode. Sediment transport is now considered an important part of karst hydrology and many studies have been undertaken (Sasowsky and Mylroie, 2004). A flow sheet for the transport of clastic sediment through the conduit system is shown in Figure 21.4. In additional to the sediment carried into karst aquifers by sinking streams, there is also soil-washdown due to gradual flushing of soils from the epikarst, and plug injections of sediment from soil-piping failures in sinkholes. A fourth component is the insoluble residue from the dissolution of the bedrock to form the conduit system. The clastic sediments that are flushing into the conduit system are reworked considerably as they are transported through the system. As sediments are transported in the conduit system mainly during storm events, direct investigation of the transport processes is difficult. Suspended sediment can be captured at the springs where the concentration can be related to the discharge hydrograph. Observations on springs give information mainly on the very small particle end of the sediment size scale. Many karst springs are perennially turbid to various degrees, reflecting the concentration of suspended material. Particles in the colloid size range and also larger particles of organic material remain in suspension indefinitely. Larger particles settle out and move only during storm flow when some springs become visually muddy. Transport of even larger particles, in the gravel to cobble range, only occurs during extreme storms which are infrequent and also when measurements are not likely to be possible.
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Sediment load in sinking streams
Spring discharge
Soil washdown
Compacted sediment
Mobilization of stored sediment
Recent siltation
Residuum from dissolution
FIGURE 21.4 Flow chart for the sources of clastic sediment in a karst aquifer. A distinction is made between compacted sediments which tend to be immobile in the conduit system except during extreme storms and recent siltation which is easily remobilized and appears at the spring during very moderate storms.
meters 5— Limestone 4—
Ceiling clay Red sandy silt
3— Gravel 2—
1—
Sandy silt Gravel Sand Gravel Sand Floor
0—
FIGURE 21.5 The clastic in-filling of Dismal Valley, an occluded master conduit in the Salts Cave section of Mammoth Cave, Kentucky. The bulk of the deposit is the channel facies with a layer of slackwater facies (clay) on top. Drawing from Davies, W.E. and Chao, E.C.T. (1958) Report on sediments in Mammoth Cave, Kentucky. Administrative Report to National Park Service by U.S. Geological Survey, 117 pp.
A more representative sampling of the total sediment flux can be obtained by examining sediment piles in caves. In caves that are part of active conduit systems, these deposits represent the sediment flux, although movement might be on very long time scales. Sediment piles in dry caves are samples of the material that was moving through the system when the cave passage was abandoned and which may represent flow conditions that are no longer present in the drainage basin. Sorting and reworking of the sediment in the conduit system results in recognizable lithofacies that can be distinguished by particle size and by sorting (Bosch and White, 2004). Two of these are illustrated (Figure 21.5) from Mammoth Cave, Kentucky. Channel facies are those sediments likely to be moved as bedload during storms of moderate intensity. They typically consist of interbedded sand, silt and sometimes gravel, often with a rough sorting into distinct beds as shown in Figure 21.5. However, these beds cannot be traced continuously for distances
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of more than a few tens of meters along the passageway. Bedload transport consists of material being dragged along the bed by the shearing action of water flowing above the bed. The shear is related to the velocity of the moving water by Newton’s stress law: τ=
1 ρfv 2 8
(21.14)
The symbols are τ = boundary shear, N m−2 ; ρ = fluid density, kg m−3 ; f = dimensionless friction factor; v = fluid velocity at the boundary, m sec−1 . The boundary shear necessary for bedload movement has been extensively investigated for surface channels (Vanoni, 1975) and is related to sediment particle size by the regression equation: 1.08 (21.15) τc = 0.067D50 D50 is the mean particle diameter in mm. The presence of channel facies sediments in long horizontal conduits far from any possible sediment inlets is evidence that the flow velocity in these conduits must be in the range of tenths of a meter per second or the sediments would not be where they are observed. The uppermost bed in many sediment deposits is a layer, typically a few centimeters thick, of finegrained laminated clay. Note that this layer of clay, termed the slackwater facies in Figure 21.5 completely fills the passage between the top of the channel facies and the limestone ceiling. The slackwater facies provides a sample of the suspended load. During storm flow, base level conduits are frequently flooded to the ceiling. All recesses are filled with muddy water. This water is stagnant during the time in which the passage is flooded, and suspended sediment settles, forming a layer of clay. Successive floods add additional layers and thus is formed the bed of laminated clay. The sediments in active stream channels are often well-winnowed so that the stream bed has a gravel or cobble armoring much like many surface streams. Sometimes, very coarse cobbles occur, tens of centimeters in diameter or larger. These can move as bedload only during exceptional floods whereas the smaller particles are stripped away during more frequent, but less intense storms. These stream channel deposits have been referred to as thalweg facies. There is evidence in a few caves for a diamicton facies. These are masses of completely unsorted and unstratified material, apparently thrust into the conduit as a debris flow traveling in suspension at high velocity. The term and the first observations came from the high relief caves of the New Guinea Highlands (Gillieson, 1986). Since then similar deposits have been found in other caves, some with only modest relief.
21.3.4 Caves and Conduits: Hydrologic Interpretation of Cave Patterns It is important to distinguish between caves and conduits. Conduits are solutionally formed pathways on many size scales that serve to transmit water from recharge points to discharge points. Some portions of the conduit system are below base level and are continuously water-filled. Some portions lie between the elevations of base flows and flood flows and are therefore used intermittently depending on the groundwater stage. Still other portions are abandoned as base levels are lowered and groundwater levels fall below the elevations of the conduits. Caves are those fragments of the conduit system that are accessible to human exploration. Cave explorers traditionally include all accessible passages as part of the same cave. Thus a cave map may show fragments of several conduits interconnected by collapse or secondary dissolution. The cave map may also include conduit segments of greatly different ages ranging from abandoned high-level passages that may date from the Pliocene to vertical shafts that are apart of the contemporary groundwater system. Cave maps, in brief, are composites of all parts of the conduit system that are interconnected and which can be accessed by cave exploration. Although they provide valuable data on the conduit system, they must be interpreted with some care. Although cave maps reveal a great diversity of patterns, some common features can be recognized. The important variables are the local geologic structure that determines many of the details of the cave
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(a)
(b)
Swallet
1000 m
500 m Branchwork (c)
Master conduit (d)
50 m 20 m Network maze
Anastomotic maze
FIGURE 21.6 Patterns of conduit drainage systems: (a) Branchwork pattern with most tributaries originating as sinkhole drains. (b) Master conduit with surface streams making up most of the tributaries. (c) Network maze. (d) Anastomotic maze.
pattern, the overall hydraulic gradient of the drainage basin, and the relative contributions of allogenic, internal runoff, and dispersed infiltration recharge (Palmer, 1991). Some of the possibilities are shown in Figure 21.6. The conduit systems within aquifers dominated by recharge through internal runoff often exhibit branchwork patterns as small tributaries draining individual closed depressions merge to form larger drainage channels which ultimately lead to a spring. The smallest tributaries of the systems are often too small for human exploration. Branchwork patterns require sufficient gradient to allow a free-flowing drainage to develop. There may appear closed loops and spillover routes used during periods of high discharge. In detail, the branching tributaries are guided by joints or bedding plane partings. If the aquifer is dominated by allogenic recharge, the underground drainage may be through a single large conduit with few tributaries. In the limit, a large surface catchment could have a short segment of underground route that would be almost completely decoupled from the groundwater system. These systems are most like underground rivers and least like aquifers. Large conduits can be nearly linear, can be angulate following structural features in the bedrock or can be sinuous. Caves frequently occur with maze patterns consisting of many closed loops along the same flow route. Maze caves may take the form of anastomotic mazes or network mazes depending of whether the fracture permeability is dominated by bedding plane partings or by joints. Both require that the dissolution process proceed along all possible pathways without the concentration of flow along a single pathway that leads to branchwork and single conduit caves. Anastomotic mazes generally have their greatest cross section developed along bedding planes. Freedom for water to select optimum pathways along the bedding plane parting leads to the gently curving loops on many size scales. Network mazes generally have their greatest cross section developed along joints so that the pattern is constrained by the joint pattern to produce the characteristic “city block” pattern. Anastomotic mazes generally occur in low gradient systems in nearly flat-bedded rock where many percolation paths would be possible. Network mazes are sometimes related
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to dispersed infiltration through an overlying permeable caprock into a jointed limestone mass below the water table (Palmer, 1975). Other network mazes are the result of backflooding from surface streams, a form of bank storage. In a different category are floodwater mazes that occur in very high gradient conduit systems with large contributions of allogenic recharge where high hydraulic heads from flood flows can force water along all possible joints and fractures. To a certain extent, branchwork patterns are the subsurface analogs of surface tributary stream patterns. Single conduit patterns are the subsurface analogs of high-order surface streams. Anastomotic maze patterns may be taken as the subsurface equivalent of braided rivers, but most generally, maze patterns are the subsurface equivalent of swamps.
21.3.5 Paleohydrology Unlike deepening surface valleys and their drainage systems which usually destroy their past as the valleys downcut, caves provide useful records of the history of the conduit drainage system. Vertical sequences of abandoned conduit fragments (tiered caves) may reveal changing drainage patterns and changing discharges. To be useful, the paleohydrologic record must be tied to the time sequence of the evolving surface drainage basin. U/Th isotope dating of calcite speleothems, useful in the age range back to 0.5 Myr, can place some limits on the ages of various passage levels (Richards and Dorale, 2003). Magnetic reversals preserved in cave sediments provide absolute time markers when they can be found and when the correct reversal can be identified (Schmidt, 1982). Most relevant to paleohydrology is the dating of clastic sediment by cosmogenic isotopes (Granger et al., 2001; Anthony and Granger, 2004). SiO2 in the form of quartz sand and pebbles exposed on the land surface is subject to the bombardment by cosmic rays. The bombardment coverts minute amounts of 28 Si to 26 Al and 16 O to 10 Be, both radioactive isotopes. When the irradiated quartz is swept into a cave and deposited there, the quartz is shielded from cosmic rays. The isotopes begin to decay but at different rates. Measurement, by means of an accelerator mass spectrometer, of the 26 Al/ 10 Be ratio, permits the calculation of the time at which the sediment was transported into the cave. This is only the minimum age for the cave passage but is likely to be close because most sediment deposition takes place when the conduit is an active part of the groundwater system. Cave walls often exhibit a pattern of scallops (Figure 21.7) which record both the flow direction and the paleoflow velocity. The scallop’s length is inversely related to velocity through a Reynolds number
Downstream
Plan view
l1
l2
l3
Profile view
FIGURE 21.7 Plan and profile of a scalloped cave wall. Characteristic lengths of the scallops are measured along the flow direction.
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1,000
Conduit diameter (m) 0.3 1
Water velocity (cm sec–1)
100
3 10
10
1.0
0.1 1
10 L32 (cm)
100
FIGURE 21.8 Calculated water velocity as a function of mean scallop length. L32 = Sauter mean. Curves based on the equations of Curl (1974).
(Curl, 1974):
ρvL32 = NR = 22,500 η
(21.16)
The parameter L32 is the Sauter mean of a population of measured scallop lengths: 3
L32 = i i2 i i
(21.17)
A detailed analysis of the transport processes shows a dependence on conduit size (Figure 21.8). Measurement of the Sauter mean on a population of scallops gives paleoflow velocity, which, combined with conduit cross-sectional area gives a paleodischarge. With some assumptions the paleodischarge allows an estimate of the paleocatchment areas. Calculations of hydraulic parameters from scallops in both paleoconduit and active conduits have produced reasonable agreement with the parameters determined by other measurements (Gale, 1984; Lauritzen et al., 1985; White and Deike, 1989).
21.4 Chemistry of Carbonate Rock Dissolution 21.4.1 Chemical Equilibrium The primary process in karstic weathering and in the development of fracture and conduit permeability in karst aquifers is the dissolution of carbonate rocks in weak solutions of carbonic acid. Carbonate chemistry has been extensively investigated, and more detail may be found in the aqueous geochemistry textbooks of Drever (1997) and Langmuir (1997). Carbon dioxide occurs in the atmosphere at a volume fraction of 3.75 × 10−4 (2003 values). This reservoir provides a constant atmospheric background that CO2 partial pressures in karstic waters rarely fall below. Much greater concentrations of CO2 are generated in the soil due to respiration from roots,
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from decay of organic matter, and from the action of microorganisms. CO2 generation in the soil is a sensitive function of temperature and, in temperate and subpolar climates, exhibits a seasonal periodicity. The volume fraction of CO2 in the soil varies from 0.01 to 0.1 with excursions to both greater and smaller values. Some of the soil CO2 diffuses upward to be lost to the atmosphere, while some dissolves in infiltrating groundwater. Carbonic acid is formed from gaseous CO2 by a two-step process: CO2 (gas) → CO2 (aqueous) CO2 (aqueous) + H2 O → H2 CO3 Molecular carbonic acid is a minor species and comprises only about 0.17% of the dissolved CO2 . Nonetheless, it is convenient to consider both reactions together and write the equilibrium constant as: aH2 CO3 = KCO2 PCO2
(21.18)
The symbol “a” in this and the following equations is the thermodynamic activity. H2 CO3 ionizes: H2 CO3 → H+ + HCO− 3 2− + HCO− 3 → H + CO3
The equilibrium expressions are: aH+ aHCO− 3
aH2 CO3 aH+ aCO2− 3
aHCO−
= K1
(21.19)
= K2
(21.20)
3
Calcite (limestone) is only slightly soluble in pure water: CaCO3 → Ca2+ + CO2− 3 aCa2+ aCO2− = KC
(21.21)
3
Solving Equation 21.21 gives the concentration of dissolved calcite as 6 to 7 mg/L, less then the solubility of quartz. The difference is that the solubilities of carbonate minerals are highly sensitive to the presence of weak acids whereas the solubility of quartz is not. The dissolution of dolomite can be described by a similar reaction: CaMg(CO3 )2 → Ca2+ + Mg2+ + 2CO2− 3 2 aCa2+ aMg2+ aCO 2− = Kd
(21.22)
3
The equilibrium constants for Equations 21.18 through 21.22 have been refined and evaluated (Table 21.4). In overall terms, the dissolution of limestone and dolomite in carbon dioxide-rich waters is described by the reactions: CaCO3 + CO2 + H2 O → Ca2+ + 2HCO− 3 CaMg(CO3 )2 + 2CO2 + 2H2 O → Ca2+ + Mg2+ + 4HCO− 3
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Groundwater Flow in Karstic Aquifers TABLE 21.4 T (◦ C) 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
21-19
Equilibrium Constants for Carbonate Reactions
pKw
pKCO2
pK1
pK2
pKCaHCO+
pKCaCO3
pKc
pKa
pKd
14.938 14.727 14.528 14.340 14.163 13.995 13.836 13.685 13.542
1.108 1.192 1.269 1.341 1.407 1.468 1.524 1.577 1.625
6.579 6.516 6.463 6.419 6.382 6.352 6.328 6.310 6.297
10.629 10.554 10.488 10.428 10.376 10.329 10.288 10.252 10.222
−0.820 −0.901 −0.968 −1.023 −1.069 −1.106 −1.135 −1.159 −1.179
−3.134 −3.127 −3.134 −3.154 −3.185 −3.224 −3.271 −3.325 −3.383
8.381 8.394 8.410 8.430 8.453 8.480 8.510 8.543 8.580
8.218 8.235 8.255 8.279 8.306 8.336 8.370 8.406 8.446
16.56 16.63 16.71 16.79 16.89 17.00 17.12 17.25 17.39
3
pK = −log K . Kw taken from Handbook of Chemistry and Physics, 84th edn., pp. 8–87 (2003). Kd taken from Langmuir (1971). All other K ’s calculated from fitting equations of Plummer and Busenberg (1982).
These equations leave aside possible reactions with organic acids and also leave aside reactions involving sulfuric acid which is known to be an important mechanism in the development of some cave systems. A discussion of the sulfuric acid mechanism for the formation of Carlsbad Caverns and other caves of the Guadalupe Mountains of New Mexico may be found in Hill (1990). To calculate the solubilities of the carbonate minerals requires that all of these reactions be simultaneously in equilibrium. Because carbonic acid and its ionization products are involved, one further reaction must be considered, the ionization of water: H2 O → H+ + OH−
(21.23)
aH+ aOH− = Kw
Considering the case of pure calcite, the simplest case, crystalline calcite would be in equilibrium with an aqueous phase and with a gas phase containing a variable concentration of CO2 . The system would 2− + require the determination of seven variables — the concentrations of Ca2+ , H2 CO3 , HCO− 3 , CO3 , H , − and OH plus the partial pressure of CO2 . Seven unknowns require seven independent equations. The equilibrium expressions 21.18, 21.19, 21.20, 21.21, and 21.23 provide five of these. The requirement that positive and negative electric charges must balance gives a sixth relationship. For the determination of the seventh constraint on the system, three cases are of interest: 1. Available CO2 is a fixed quantity (closed system) 2. The CO2 pressure is fixed by the environment (open system) 3. The pH (hydrogen ion activity) is fixed by the environment Closed system conditions occur only rarely in karst. Case 1 is relevant but complicated to describe. Langmuir (1997) discusses this case in some detail. If pH is fixed by some external buffering system (Case 3) such as might be relevant to the analysis of limestone barriers for the remediation of acid mine drainage, the individual equations can be solved and no elaborate calculations are necessary. Case 2 is of most interest in karst hydrology because the CO2 partial pressure is usually fixed by the rate of CO2 generation in the soil. The calculations involving the various equilibrium expressions, the charge balance requirement, and the constraint that PCO2 = constant yield the equilibrium concentration of dissolved Ca2+ (as molal concentration):
mCa2+
1/3 K K K 1 c CO2 1/3 = PCO2 2 4K2 γCa2+ γHCO − 3
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(21.24)
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Cave seepage water
PCO of soil air 2
2
300
PCO of cave air
400
PCO2 of atmosphere
Disolved carbonate as mg/L CaCO3
500
200
100 Calcite solubility
Soil water
Rain water 0 0.001
0.01 CO2 Pressure (atm)
0.1
FIGURE 21.9 Solubility curve for calcite at 10◦ C as a function of CO2 partial pressure. The chemical composition of dispersed infiltration water is shown at three locations along its flow path.
If the groundwater is at equilibrium with calcite at a given CO2 partial pressure, the pH is also fixed. 2 1 pH = − log PCO2 − log 3 3
K12 K2 KCO2 γCa2+ 2Kc γHCO−
(21.25)
3
The symbol γ in these equations is the activity coefficient which links thermodynamic activity to molal concentration. The solubility of calcite (and dolomite) is somewhat temperature dependent. The temperature dependence is incorporated in the temperature dependence of the equilibrium constants. The solubility of calcite, expressed as mass concentration of CaCO3 , is displayed in Figure 21.9. The solubility increases from 6 mg/L in the absence of CO2 to 50 mg/L in equilibrium with atmospheric CO2 to several hundred mg/L in equilibrium with the CO2 pressures found in many soils.
21.4.2 Chemical Parameters for Karst Aquifers As a practical tool in karst hydrology, neither the underlying physical chemistry as described above nor raw chemical analyses of groundwater are the most useful. Parameters, solidly based on theory, but using analytical data are the hardness, the Ca/Mg ratio, saturation indices for calcite and dolomite, and the calculated CO2 partial pressure. Hardness is one of the oldest water quality parameters. It is defined as: Hd = MCaCO3 (mCa + mMg )
(21.26)
MCaCO3 is the molecular weight of calcium carbonate. Concentrations of dissolved Ca and Mg are given in molal units. The hardness describes the total dissolved calcium and magnesium but expresses the result
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as mg/L CaCO3 . Mainly, it is a measure of the total dissolved carbonate rock although all other sources of Ca and Mg are included. The parameter has little theoretical significance but is very important for water supplies, particularly those in which precipitated carbonates in the plumbing and in boilers are important (Loewenthal and Marais, 1976). The Ca/Mg ratio is simply the relative concentrations of Ca2+ and Mg2+ on an atomic scale (molal concentration): mCa Ca = (21.27) Mg mMg The Ca/Mg ratio provides information on the rock units through which the groundwater has passed. The Ca/Mg ratio = 1 to 1.5 for dolomite aquifers and 6 to 8 for limestone aquifers. Intermediate values imply a dolomitic limestone or mixed limestone/dolomite sequence. The degree of disequilibrium between groundwater and the carbonate wall rock is given by the saturation index, defined for calcite as: SIc = log
aCa2+ aCO2− 3
Kc
= log
Kiap Kc
(21.28)
Kiap is the ion activity product derived from actual analyses of the water. Kc , as above, is the solubility product constant for calcite. Saturation indices can be written for any mineral in a similar fashion. If the water is exactly at equilibrium, the experimental ion activity product will be exactly equal to the solubility product constant and SIc = 0. If the water is undersaturated with respect to calcite, Kiap will be less than Kc and the saturation index will be negative. For a supersaturated water, SIc will be positive. Calcium ion activity can be determined directly from the analyzed calcium concentration. The carbonate ion, however, is a minority species in most carbonate groundwaters. Its activity must be calculated from the measured bicarbonate ion concentration and the pH. A final expression for saturation index as a function of experimentally determined quantities is: SIc = log
γCa2+ mCa2+ γHCO− mHCO− K2 3
K1 10−pH
3
(21.29)
See White (1988), Drever (1997), or Langmuir (1997) for a full discussion of the thermodynamics. The effective concentrations of carbonate species in the groundwater are related to the CO2 partial pressure in the source area through Equations 21.18 and 21.19. These reactions may be combined to allow the calculation of carbon dioxide pressure from the water analysis PCO2 =
γHCO− mHCO− 10−pH 3
3
K1 KCO2
(21.30)
Because the observed CO2 partial pressures in karst systems are rarely lower than the atmospheric background, it is often helpful to normalize the calculated CO2 pressure by dividing by the background atmospheric CO2 pressure. The result expresses the CO2 in the groundwater sample as an enhancement over background.
21.4.3 Dissolution Kinetics of Limestone and Dolomite The central role of dissolution kinetics is a unique characteristic of karst aquifers. In porous media aquifers and in most fracture aquifers, travel times and surface/volume ratios are both large. The groundwater is in intimate contact with the mineral grains of the aquifer rock and remains in contact for long periods of time. As a result, there is sufficient time for chemical reactions to proceed to completion, and it is generally safe to assume that chemical reactions are at equilibrium. Geochemical modeling of aquifer chemistry can make use of speciation and reaction path programs such as WATEQ4F, PHREEQC, and MINTEQA2.
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In karst aquifers, travel times are measured in hours or days which are on the same order of magnitude as the reaction time of the water with the rock. As a result, karst groundwater can travel the entire width of the aquifer without coming into chemical equilibrium. The rates of dissolution reactions are an essential part of any attempt to model the evolution of a karst aquifer. The characteristic time scales for the various carbonate reactions are: 1. Dissociation of carbonic acid into bicarbonate ion and bicarbonate ions into carbonate ions: milliseconds. 2. Hydration of aqueous CO2 to form carbonic acid: 30 sec. 3. Dissolution of calcite: 2 to 3 days. 4. Dissolution of dolomite, 1st stage: 3 to 5 days. 5. Dissolution of dolomite, 2nd stage: months to years. 2− It can be assumed from (21.1) that the concentrations of H2 CO3 , HCO− 3 , and CO3 in solution are always in equilibrium. The 30 sec time scale for producing carbonic acid from aqueous CO2 is important for sheet flow of thin films of rapidly moving water in shafts and chimneys in the vadose zone. The dissolution kinetics of calcite and dolomite are central to the interpretation of the evolution of karst aquifers. The raw data for limestone and dolomite dissolution are deceptively simple (Figure 21.10). The rate is proportional to the slope of the curve. The rate is initially rapid as the rock is attacked by highly undersaturated water but then slows as the solution approaches saturation. Fitting the experimental curves to theoretical models has been challenging and there have been a tremendous number of investigations many of which are reviewed by Morse and Arvidson (2002). A useful and widely adopted rate equation was developed by Plummer et al. (1978; 1979).
Rate = k1 aH+ + k2 aH2 CO3 + k3 aH2 O − k4 aCa2+ aHCO−
(21.31)
3
In Equation 21.31, k1 , k2 , and k3 are forward rate constants and k4 is the backward rate constant. The rate is given in units of millimoles cm−2 sec−1 .
Saturation pH 6.0 stone
e Clover Lim
5.5
Dolomite
pH
Tea Creek
PCO = 0.97 atm
5.0
2
T = 30.5°C
4.5
4.0 0
50
100 150 Time (h)
200
250
FIGURE 21.10 Rate curve for the dissolution of an Ordovician limestone and an Ordovician dolomite. These data are plotted in terms of the changing pH of a fixed volume of solution maintained at a fixed CO2 pressure of one atmosphere. Based on unpublished data from author’s laboratory.
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The first term shows that the rate is directly proportional to the hydrogen ion activity and dominates in strongly acid solution. It describes, for example, the interaction of acid mine water with limestone. The first component of the forward rate is mass-transport controlled so that the rate depends on the rate of flow of water across the rock surface. The second term describes the dissolution process driven by carbonic acid. It is dependent on the available CO2 but is surface-reaction controlled and does not depend strongly on fluid motion. The third term describes a constant background rate of limestone dissolving directly in water and is usually a minor contribution because the solubility of limestone in pure water is very low. All three forward rate constants are known functions of temperature: 444 T
(21.32)
2177 T
(21.33)
log k1 = 0.198 − log k2 = 2.84 − log k3 = −5.86 −
317 T
(T < 298 K)
(21.34)
log k3 = −1.10 −
1737 T
(T > 298 K)
(21.35)
The backward reaction rate constant can be calculated from the forward rate constants:
K2 1 [k2 aH2 CO3 + k3 aH2 O ] k4 = k + KC 1 aH+
(21.36)
K2 and KC are equilibrium constants (Table 21.4) and k1 refers to the hydrogen ion concentration at the dissolving interface. Experimental comparisons have been made by setting k1 = k1 . When dissolution rate is plotted against some measure of saturation, the rate is found to be a function of CO2 partial pressure but only slightly dependent on undersaturation until the saturation index reaches values near −0.3. Between this value and equilibrium the rate plummets by orders of magnitude (Berner and Morse, 1974; White, 1977). This abrupt decrease in dissolution rate in waters that remain somewhat undersaturated is a crucial feature in explaining the development of long conduits in karst aquifers. Recently, researchers (e.g., Dreybrodt and Buhmann, 1991; Palmer, 1991) have found it convenient to use a genetic rate equation that does not attempt to separate the components of the dissolution reactions C n A dC =k 1− Rate = V dt CS
(21.37)
In this equation, A = surface area of limestone, V = volume of water in contact with the limestone, k = rate constant, C = instantaneous concentration, CS = saturation concentration, and n = reaction order. For values of C/CS less than 0.83, the reaction order, n = 1 and reaction rates are fast. As the solution approaches saturation and C/CS becomes greater that 0.83 (approaching unity when the solution reaches equilibrium), the reaction order shifts abruptly to n = 4 and reaction rates greatly decrease. Many factors influence the rate at which carbonate rocks dissolve in CO2 -containing groundwater. New factors appear when the flows are turbulent and when the groundwater is close to equilibrium. Among those identified (Dreybrodt and Buhmann, 1991; Svensson and Dreybrodt, 1992; Dreybrodt et al., 1996; Liu and Dreybrodt, 1997) are: 1. The hydration reaction of aqueous CO2 to carbonic acid, which has a time constant of about 30 sec, is shown to be rate-controlling at high A/V ratios and under some conditions of turbulent flow. 2. Adsorption of impurity ions on the reactive surface becomes rate-controlling when the solution is near saturation. 3. A diffusion boundary layer becomes important under conditions of turbulent flow.
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Karst development in dolomite is generally more subdued than karst development in limestone. It is not a matter of solubility. The equilibrium solubilities of limestone and dolomite are very similar. However, the kinetics of dolomite dissolution is more sluggish than the kinetics of limestone dissolution. The dissolution of dolomite in highly unsaturated water can be described by a rate equation of the form (Busenberg and Plummer, 1982; Herman and White, 1985) n n n Rate = k1 aH + + k2 aH2 CO3 + k3 aH2 O − k4 aHCO− 3
(21.38)
The exponent, n = 0.5 for temperatures below 45◦ C. However, unlike the calcite rate curve which approaches the equilibrium value on times on the order of a few days, the dolomite rate curve flattens out at a saturation index of SId = −2. A different and slower mechanism takes effect. The final approach to equilibrium requires times on the order of months to years. Groundwater in dolomite aquifers does eventually come into equilibrium with the wall rock because well waters from dolomite are found to be near saturation. As a result of slower dissolution kinetics, conduit systems are generally less well developed in dolomite aquifers. Dissolution tends to follow pathways through limestones if these are available. If there are no alternative pathways available, large conduits do develop in dolomite but appear to do so at a much slower rate.
21.5 Evolution of Karst Aquifers 21.5.1 Life History of a Conduit Although all aquifers evolve in the sense that the permeability distribution varies as minerals are dissolved or precipitated and the overlying land surface is lowered by erosion, these processes are generally very slow. Karst aquifers, in contrast, evolve on a time scale as short as 104 years as bedrock is dissolved and new conduits are developed. A particular pathway through the mass of soluble rock will have a “life history” as sketched in Figure 21.11. It is assumed that the initial state is obtained by mechanical fracturing of the bedrock. The initial pathway is along a sequence of joints, fractures, or bedding plane partings, more rarely a fault or sequence of primary vuggy porosity. The initiation phase is that time during which the primary mechanical openings are enlarged by dissolution from their initial apertures of tens to hundreds of micrometers to a width on the order of 10 mm. When the aperture reaches 10 mm, the flow regime crosses a set of critical thresholds in the dissolution and transport processes so that a 10-mm aperture is the practical boundary between openings that would be considered part of the fracture permeability and openings that would be part of the conduit permeability. Once the critical thresholds have been passed, the conduit enters an enlargement phase and grows to dimensions typical of cave passages by the continued dissolutional retreat of its walls. As the enlargement phase comes to a close, several alternative scenarios are possible. If the conduit is so situated that it remains water-filled, solution will continue until the ceiling span becomes mechanically unstable and the passage will collapse. As the flooded passage enlarges, however, velocities decrease, the water will become more saturated, solution rates will slower, and so water-filled passages may persist for long periods of time. If the recharge source for the conduit remains constant as base levels are lowered, the passage will eventually grow to a size where the available recharge will not fill it and a free air surface will develop. If the recharge source is not diverted, there will be a transition from a tubular conduit to a canyon morphology and the canyon will continue deepening as base level continues to lower. If the recharge source is diverted to some lower route with lowering base levels, the conduit will be drained but will persist as an abandoned dry tube. Those tubes and canyons, which by chance circumstances develop entrances, are the population of explorable caves. After the conduit has been drained, it enters a stagnation phase that may persist for millions of years. The clastic sediments in dry caves were mostly deposited at the transition from the enlargement to stagnation phases. Speleothems are deposited during the stagnation phase. These are the deposits that make caves an important paleoclimate archive. Eventually, however, erosional lowering will sweep the land surface past
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Fl oo co ded nd ui t
Slow growth and collapse 50 meters
Stagnation
Decay
Enlargement Dry tube
Passage diameter
3 meters
Transition to canyon Transitional
Initiation
5-10 mm 100 µm 0
Fragmentation and removal by surface erosion
Critical thresholds
3000-20,000
104 105 Time (years)
106- 107
FIGURE 21.11 Schematic illustration of the “life history” of a conduit. The time scale is derived from geochemical modeling in the initiation and enlargement phases and from geologic and age-dating evidence in the stagnation and decay phases.
the cave passage. The conduit will be fragmented and ultimately destroyed. The later part of this sequence has been sketched separately as a final decay phase when cave passages are truncated by collapse and broken into short passage fragments, as many caves are observed to be, before they are destroyed completely. One of the objectives of cave development theories is to assign a time scale to the various phases in the life history of the conduit, particularly the early ones where dissolution of the bedrock is the dominant process. The time scale of Figure 21.11 is based on calculations for the early stages and on geomorphic and age-dating evidence for the later stages. The stagnation and decay phases are determined by events elsewhere in the drainage basin or by regional tectonics. It is not possible to calculate what happens from a general model although events in specific drainage basins can sometimes be interpreted. A question not yet addressed by any model is whether, given the calculations and analysis for single passages, the results could be put together too obtain the equivalent “life history” for an entire conduit system and its associated groundwater basin. If one could, it would allow us to say something about the historical development of the drainage, and still further extrapolated, to say something about events in the regional climatic and tectonic setting in which the drainage basin is embedded. Overall, a formidable task, but an important one.
21.5.2 Initiation and Critical Thresholds In compact and impermeable limestones, the initial hydraulic pathway from recharge point to discharge point is along a sequence of joints, fractures and bedding plane partings with mechanical apertures in the range of tens to hundreds of micrometers. The discharge through the fracture system is described by the cubic law (Equation 21.4 and its recent modifications). The volume and velocity of water flowing through the fractures both increase rapidly as the fractures widen. When unsaturated water from the recharge source reaches the carbonate bedrock, much of the dissolutional capacity is consumed by reaction at the bedrock interface because of the rapid kinetics and high undersaturation. Water that enters the fracture system remains slightly undersaturated because of the very slow rate of reaction in water close
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to equilibrium. In spite of the small fracture aperture and long travel times, slightly undersaturated water penetrates deep into the aquifer where the fractures are slowly enlarged. As the fractures enlarge, the volume of flow increases with the cube of the aperture and the saturation index becomes more negative. Eventually, the fracture system will become sufficiently enlarged that water undersaturated at the critical value of SIC = −0.3 penetrates the entire length of the hydraulic pathway, a condition called “breakthrough” by some authors. The dissolution kinetics shift from fourth order to first order and dissolution rates increase rapidly. This transition occurs when the aperture reaches about ten mm. Calculations based on a range of reasonable hydraulic gradients and carbon dioxide partial pressures gave a time scale for the initiation phase in the range of 5000 years (White, 1977). More elaborate calculations based on computer models give a range from 3000 to 20,000 years (Groves and Howard, 1994; Dreybrodt, 1996; Siemers and Dreybrodt, 1998). The elapsed time from initial fracture to breakthrough is a sensitive function of the initial fracture aperture By coincidence, when the aperture of the enlarging fracture system reaches ten mm, not one, but three thresholds are crossed. These thresholds mark the transition from fracture permeability of conduit permeability: 1. The onset of turbulence 2. The penetration (breakthrough) of the aquifer by undersaturated water 3. The onset of clastic sediment transport For a fixed input and fixed output defining the hydraulic gradient across an aquifer, the flow velocity within a widening fracture can be calculated. From the velocity and fracture aperture, the Reynolds number can be calculated and tracked as both velocity and aperture increase as dissolution proceeds. For a range of hydraulic gradients from 10−4 to 10−2 , the onset of turbulence occurs at an aperture of 10 to 5 mm, respectively. The onset of turbulence marks the beginning of a regime where a linear relation between head and flow velocity can no longer be used to construct models of groundwater flow. When one of the possible hydraulic pathways through the aquifer achieves an aperture that permits highly undersaturated water to penetrate the aquifer, the dissolution kinetics shifts from the slow regime to the fast regime. Dissolution rates then increase rapidly so that the hydraulic pathway that first achieves breakthrough will undergo a runaway process and grow at the expense of alternate hydraulic pathways. It is this kinetic trigger that is responsible for the aquifer containing a small number of large conduits rather than an arrangement of small opening along all possible pathways. For the kinetic trigger and associated runaway process to function, the aquifer must have sufficient hydraulic gradient to permit velocity to increase in response to increasing aperture. A failure of the kinetic trigger to function leads to the development of maze caves. Carbonate aquifers maintain a flux of clastic sediment. Sediment can be transported as bedload or as suspended load both of which move through the aquifer mainly during flood flow. Bedload transport requires a finite boundary shear between the bedded sediment and the flowing water. The velocity to initiate sediment movement is or the order of 0.1 m sec−1 . This will occur, depending on hydraulic gradient, when the aperture reaches the range of 10 mm.
21.5.3 Enlargement, Maturity, and Decay The selection of hydraulic pathway during the initiation phase is determined by the arrangement of fractures and bedding plane partings, by changes in lithology that influence dissolution rates, and by the presence of confining layers and other geological barriers. The pattern of the conduit system is set at the initiation phase. Once the water in the growing conduit reaches the fast kinetics regime, dissolution rates are nearly constant and enlargement is uniform along the entire conduit. If Equation (21.37) is accepted as a description for the dissolution rate of limestone, the retreat of conduit walls can be described by Palmer (1991): 31.56k(1 − (C/CS ))n (21.39) S= ρr
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S is the rate of wall retreat in cm/year, k is the dissolution rate constant, CS is the saturation concentration of dissolved carbonate, and ρr is the density of the wall rock. The effect of temperature and variations in the dissolution rates for rocks of different lithology are incorporated in the rate constant, k. The available CO2 and also temperature determines the saturation concentration CS . Palmer finds good agreement between observed dissolution rates and those predicted by Equation (21.39). Typical calculated values for the retreat of a conduit wall are in the range of 40 cm/1000 years, a rate that would produce a conduit 4 m in radius in 10,000 years. These results represent an upper limit. Other factors such as walls coated with insoluble residue from the limestone or with mud carried into the cave from the land surface would slow down the dissolution process. Generally, the rapid enlargement converts the initial fracture geometry into a more nearly tubular cross section. The rate of enlargement depends on the path length and on the hydraulic gradient. Under the high gradients and short path lengths that would be found in such locations as dam abutments, significant dissolutional enlargement could take place within the design lifetime of the structure (Dreybrodt, 1992). Because development of conduit permeability in karst aquifers takes place on very short time scales, continuous conduit development at successively lower elevations can easily keep pace with downcutting of surface river valleys. Geological evidence that the theoretical predictions are reasonable is provided by caves that are known to have developed in the 11,000 years since the retreat of the last Pleistocene ice sheet and also by caves in the Bahamas that have developed in limestones that themselves are only 85,000 years old (Mylroie and Carew, 1987). In many karst regions, conduits are graded to local base levels. The conduits that can be readily explored are in the later stages of the enlargement phase or in the early stages of the stagnation phase. They are often occupied by free-surface streams and subject to flooding. Many conduits have alternating reaches of air-filled passage (at least during base flow) and permanently water-filled passage. The streams in these conduits and the springs where the water returns to the surface are usually undersaturated with respect to calcite, with saturation indices typically in the range of −0.5 to −0.3, exactly what is expected for continuous enlargement by dissolution in the fast kinetics mode. Mature conduits lying close to regional base levels act as low gradient master drains for the matrix and fracture portions of the aquifer. Conduits may be blocked by rockfalls which pond the water and thus create sediment traps. Bypass routes and flood spillover routes evolve. Continually lowering base levels shift hydraulic gradients. The new gradients initiate new conduit development at lower elevations, and eventually the recharge sources are diverted into the new conduits. The original conduits may survive as dry cave passages for long time periods in the stagnation phase. These abandoned conduits provide useful records of past base levels and are markers for the geomorphic history of the drainage basin. Cosmogenic isotope dating of quartz sand and pebbles in the cave sediment can be used to establish an absolute chronology for the conduits. Such dating gives a sequence of tiered cave passages in Mammoth Cave extending back 3 million years (Granger et al., 2001), a sequence in the Cumberland Plateau of Tennessee extending to 5 million years (Anthony and Granger, 2004), and a sequence in the California Sierra extending to 1.2 million years (Despain and Stock, 2005). Shafts and chimneys carrying vadose water from overlying perched aquifers or from closed depressions sometimes intersect the older conduit system. Underground waterfalls and segments of very high gradient streams display contemporary drainage moving nearly vertically in the vadose zone as it passes through the abandoned conduits.
21.6 Quantitative Hydrology of Karst Aquifers 21.6.1 Water Budget The concept of the groundwater basin allows the water budget to be used as a powerful tool in the evaluation of karst aquifers. The framework for an overall water balance as an input/output calculation is implied by Figure 21.3. Spring discharge and allogenic recharge can be gauged directly. Diffuse infiltration and internal runoff can be estimated from catchment areas providing that they can be corrected for
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evapotranspiration losses. High internal runoff tends to lower evapotranspiration losses because of the rapid transport of water underground. The calculation requires that the basin area be known and for this the divides for groundwater basins must be drawn. As the divides for groundwater basins cannot be directly observed, they must be constructed from as much available evidence as possible: 1. Results of tracer tests linking sinking streams, cave streams, and other accessible inputs to the discharging spring. 2. Water table slopes determined from well inventories. 3. Geological constraints imposed by folds and faults, regional dips, fracture patterns, confining layers, and the upper and lower boundaries of the carbonate rocks. 4. Chemical fingerprinting — comparing spring water chemistry with water chemistry within the aquifer. The groundwater basin as finally drawn must be consistent with the water budget. A seriously unbalanced budget is an indication that the boundaries of the groundwater basin have not been drawn correctly. Water budgets should be constructed under both high and low flow regimes. Spillover routes that transport water across basin boundaries are common and may become active only during high flow regimes.
21.6.2 Base Flow/Runoff Relations Base flow in surface streams is maintained by groundwater discharge. If the region has a distinct dry season, the mean base flow for the surface streams gives a measure of the regional base flow. This is normalized to basin area to yield a unit base flow: QN =
¯B Q A
(21.40)
Springs fed by conduits behave much like surface streams and exhibit a low storage and therefore a low base flow. For those aquifers for which the spring discharge reaches base flow conditions, Equation (21.40) can used to estimate the area of the groundwater basin (E.L. White, 1977). Tests of the relationship by Quinlan and Ray (1995) suggest that the method is reasonably accurate provided that it is calibrated for the climate and geologic setting of the aquifer of interest.
21.6.3 Tracer Studies Much of the advance in understanding karst aquifers in the past several decades have come from tracer studies (Jones, 1984; Mull et al., 1988; Käss, 1998). An identifiable substance is placed in a sinking stream, cave stream, well, or flushed into a closed depression. The substance is later detected at an outlet point, usually a spring but sometimes an underground stream or another well. Tracers that have been used include: • • • • • •
Fluorescent dyes Spores Salt Rare elements (e.g., bromide) Noble gases Other substances
Although tracing using colored lycopodium spores received a great deal of attention in Europe, it has not proved useful in the conduit aquifers of eastern United States where springs are frequently muddy and the plankton nets used to capture the spores easily become clogged. Traces using NaBr combined with neutron activation analysis to detect low levels of Br− have been used but are expensive because of the
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analytical methods. Traces with massive injections of salt allow easy detection by measurement of specific conductance but are generally unacceptable from environmental considerations. Injections of noble gases are useful for tracing fracture flows. A noble gas, typically helium or neon, is bled continuously into the groundwater through a well drilled along the fracture. Water collected from another well or spring is then analyzed for the noble gas by mass spectrometry. Unlike other tracers which use a single spike of the tracer material, noble gas traces use a continuous injection over a long period of time. It is thus suitable for traces through tight fractures where long travel times are expected. By far the most important tracers for characterizing karst aquifers are fluorescent dyes. The technique is the same as with other tracer tests. Dye is injected into the aquifer at points of interest and detected at springs or other discharge points. With increasing levels of sophistication, these detection methods are: • • • • •
Visual observation of dye Visual test with dye receptor Fluorescence detection with dye receptor Quantitative test with automatic sampler Quantitative test with on-site spectrofluorophotometer
Visual tests require the injection of sufficient dye to visibly color the water at the discharge point. Other than the inconvenience of positioning observers and the possibility of dye coming through at night, visual traces require such large quantities of dye that the test would be a source of groundwater contamination. Further, injection of large quantities of dye may be prohibitively expensive, particularly if multiple traces are needed. Direct visual observation has been used historically but is now rarely used. A major advance made in the late 1950s was the introduction of packets of activated charcoal as dye receptors. A few grams of high-grade coconut charcoal contained in mesh bags are placed in all suspected resurgent points. Dye is strongly adsorbed onto the charcoal and is not desorbed by continuing flow of water. The packets are collected at convenient intervals and replaced by fresh packets. The dye is elutriated with an alcoholic solution of strong base. The detection of dye by visual observation of the elutriate can be improved by observing the fluorescence of the solution under ultraviolet light. Use of the charcoal receptors permits many possible discharge points to be tested at the same time. Optical brighteners can also be used for qualitative traces. These are agents widely used in laundry detergents so background should be checked. The receptors are wads of unsized cotton onto which the brightening agent strongly adsorbs. The presence of the brightener on the cotton is determined by observing its bright blue luminescence under long wave ultraviolet radiation. Charcoal packets will also adsorb optical brightener. A more quantitative trace can be made by installing automatic water samplers at suspected discharge points. These can be programmed to collect water samples at prescribed intervals. The water samples are analyzed by spectrofluorimetry. As the analysis is of the water itself rather than an elutriate, the analysis can be calibrated to determine fraction of dye recovered. A plot of dye concentration as a function of time gives a breakthrough curve (Figure 21.12) that shows the exact travel time. The shape of the dye pulse often gives other clues to the nature of the flow path. To carry out tests on more than one injection point requires the use of multiple dyes. The fluorescence bands are broad and overlap so that the identification of mixed dyes is difficult by visual observation alone. However, fluorescence spectra can be deconvoluted with suitable software, allowing quantitative determination of the different dye combinations. A recent development is the use of fiber optic probes and portable spectrofluorophotometers directly at the detection site. The fluorescence signal is recorded on a data logger and transferred to a computer. This technique permits a much greater density of measurement points and eliminates the need for collecting large numbers of samples. As a guideline, charcoal packets are very inexpensive, automatic water samplers are expensive, and portable spectrofluorophotometers more expensive. The requirements for tracers is that they be nontoxic, stable in the groundwater environment, non adsorbent on clays, silts and the carbonate wall rock, and detectable at very low concentrations. Tracers that are most widely used are listed in Table 21.5. Details on the chemistry, properties and toxicity of these
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The Handbook of Groundwater Engineering Eosine levels at Lost River Rise 9.0 8.0
Concentration (ppb)
7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0
3
6
9
12 15 18 21 Hours after dye injection
24
27
30
FIGURE 21.12 Dye breakthrough curve for the Lost River Rise, Warren County, Kentucky. Plot courtesy of the Crawford Hydrology Laboratory, Western Kentucky University. TABLE 21.5
Commonly Used Tracer Dyes for Karst Hydrology Fluorescence Wavelength (nm)
Common Name Sodium fluorescein (uranine) Eosine Rhodamine WT Sulphorhodamine B Optical brightener
Color Index
Elutriate
Water
Acid yellow 73 Acid red 87 Acid red 388 Acid red 52 Tinopal CBS-X
515.5 542 568.5 576.5 398.0
508 535 576 585 397
Data courtesy of Crawford Hydrology Laboratory, Western Kentucky University.
and other tracer dyes may be found in Smart and Laidlaw (1977) and Smart (1984). Use of fluorescein as a water tracer has a 100-year history and remains the most popular tracer. It decomposes in sunlight and so does not persist after emerging from the groundwater system. The main drawback of fluorescein is that it is used in many common products such as antifreeze and toilet bowl cleaners, which often produce an unacceptable background. If there are many potential discharge points to be tested, a qualitative investigation with dye receptors can be used to delineate the overall drainage pattern. These results can be followed up with quantitative studies to obtain travel times and flow characterization. When legal and regulatory issues are involved, the quantitative trace provides an objective record to be entered into evidence. Tracer testing is by far the most powerful technique available for working out the conduit system of a carbonate aquifer. Combined with direct exploration and survey of such parts of the active conduits as may be accessible, it should be possible to delineate the groundwater basin, determine piracy routes, specify allogenic recharge and base level discharge points, and set down at least a rough plan of the conduit system.
21.6.4 Well Tests and Water Table Mapping The literature is ambiguous concerning the properties of the karst water table and even its very existence. Many examples are known where air-filled cave passages lie below flowing streams. Certain alpine caves
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ingest snow melt and runoff as turbulent frothing streams and crashing waterfalls. These have been cited as evidence for the absence of a water table in karst aquifers. Much of the confusion appears to arise from a failure to appreciate the dynamic response of the conduit system to storm runoff and failure to appreciate the mismatch in hydraulic conductivity between the conduit system and the associated fracture and matrix systems. Because of their high flow capacity, conduits cannot support much hydraulic head and thus create a trough in the water table during periods between storms. Because of their rapid response to recharge, conduits quickly fill during storm flow and the groundwater trough may become a groundwater mound. Losing surface streams perched over conduits that are air-filled at base flow may become gaining streams when the conduit is flooded. If the hydraulic conductivities of the fracture and matrix systems are low, the conduit system, particularly one with a large component of allogenic recharge, may act as a decoupled set of pipes with little influence on the water table. The fracture and matrix permeability portions of the aquifer support a well-defined water table that can be mapped if a sufficient number of wells is available. Water tables that have been mapped in karst areas appear reasonable and the locations of conduits are often revealed by the groundwater troughs. Drilling test wells is an appropriate way to probe the fracture and matrix component of the aquifer. However, account must be taken of the heterogeneous distribution of fracture permeability on the borehole scale. Wells drilled on fracture intersections may produce several orders of magnitude, more water than wells drilled in the same formation in rock between fractures. When the bedrock is not masked by thick soils or overlying caprock, and where the permeability is dominated by fractures rather than by bedding plane partings, air photographs can be used to map fracture traces at the land surface (Lattman and Parizek, 1964). These are then used to select drilling sites. Standard pump tests must be used and interpreted with great care in carbonate aquifers. In the unlikely event of a well penetrating a master conduit, the yield will be high and the drawdown low. If the well happens to penetrate mostly unfractured rock, the yield will be low and the drawdown very large. It is possible that these two wells could be drilled within a few meters of each other. In either case, the pump test gives a very misleading interpretation of the overall properties of the aquifer. A better technique is to test the well in segments using packers to isolate the segments. Such tests carried out in the Silurian dolomite aquifer of the Door Peninsula of Wisconsin (Figure 21.13) shows the extreme variability in hydraulic conductivity found in a single well (Muldoon et al., 2001). Downhole video cameras are a useful tool for locating fracture zones and directly examining solution features intersected by wells. If the well can be pumped dry, the camera can be used to observe which of the solution openings is actually discharging water into the well. Packers can then be used to isolate productive zones and these can be pump tested or injection tested independently of the remainder of the well bore.
21.6.5 Hydrographs of Karst Springs While exploration and tracer studies reveal something of the conduit system and wells and pump tests characterize the fracture and matrix systems, the only hydraulic response that depends on both systems is that of the spring that drains the aquifer. Spring hydrographs and fluctuations in spring water chemistry provide very useful guides to aquifer hydraulics. Spring hydrographs can be grouped into three types (Figure 21.14) depending on the response time of the aquifer compared with the mean spacing between storms. In fast response aquifers (Type I), storm pulses can pass completely through the aquifer and conditions return to base flow before the next storm pulse arrives. Each storm produces its own hydrograph at the spring which is not different in overall characteristics from hydrographs of surface streams. In slow response aquifers (Type III) the throughput time is sufficiently long to completely flatten the individual storm hydrographs and all that remains is a broad rise and fall relating to wet and dry seasons. In the limit, the slow response aquifer may produce only a horizontal straight line, a spring of constant flow. When the response time is comparable to the mean spacing between storms (Type II), some structure appears in the hydrograph but the individual storm pulses are not resolved.
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K segments
Facies Mudstn Wackesin Packstn Grainstn
20
DR-394
30
9
40
8
50 67
60
5
70 80
4
Byron Dol.
Hendricks Dol. Manistique Fm. Depth below ground surface in DR-394 (m)
Texture
90 3
100
2
120 1
Mayville Dolomite
110
130 10-6
10-4
10-2
140 K (cm/sec) 150 160
FIGURE 21.13 Distribution of hydraulic conductivity along the well bore for a well drilled in Silurian dolomite in Door County, Wisconsin. (Adapted from Muldoon, M.A., Simo, J.A. and Bradbury, K.R. (2001) Hydrogeol. J. 9, 570–583.)
1.6
Discharge (m3/sec)
0.01
Jack Daniel Spring, TN Type I
13.4
Greer Spring, MO Type II
4.3
24.6 Rainbow Spring, FL Type III 20.5
FIGURE 21.14 Types of spring hydrographs. Maximum and minimum discharges are given numerically. The x-axis represents one water year. Data from U.S. Geological Survey surface water records.
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Factors that determine the type of spring hydrograph include degree of conduit development, the mix of matrix and fracture flow, area of groundwater basin, proportion of allogenic recharge, and hydraulic gradient from input to output. Small basins with well-developed conduit systems are more flashier than larger basins with the same degree of conduit development. Longer travel times in large basins tend to smooth out the hydrograph even if there are open conduits. Very low gradients reduce travel times and produce the same effect. Both factors seem to be operating in the large springs of Florida which are known from divers’ explorations to be fed by large conduits yet have Type III hydrographs. A useful parameter for describing the flashiness of an aquifer is the ratio of the maximum annual discharge, the quantity known in surface water hydrology as the annual flood, to the base flow, averaged over the number of years of record. n 1 (Qmax )i (21.41) Qf = n (Qbase )i i=1
Type I responses have Qf in the range of 70 to 100, Type II in the range of 5 to 10, and Type III in the range of 1 to 2, based on relatively sparse data. Individual storm hydrographs can be further analyzed (Figure 21.15). There is a lag between the rainfall event and the arrival of the storm pulse at the spring. This lag, however, does not measure the time required for storm water to traverse the aquifer. The injection of water into the upstream reaches of the aquifer raises hydraulic gradients, floods conduit, and forces out by piston flow, water that has been stored in continuously flooded parts of the conduit system. The recession limb of the hydrograph can be described by one or more functions of the form (21.42) Q = QO e−εt The coefficient, ε, sometimes called an exhaustion coefficient, has units of reciprocal time and is inversely related to the response time of the aquifer, tR = 1/ε. Very characteristically, the recession limb of spring storm hydrographs will consist of a fast response segment and a slow response segment (Figure 21.16). Sometimes there are more than two distinct segments. The fast response segment can be assigned to the conduit portion of the aquifer which drains rapidly when the storm input ceases. The slow response segment can be assigned to the fracture system draining into the conduit after the conduit itself has emptied. During storm flow, flooded conduits have
Discharge, Q
Rainfall
Rising limb
Qmax
d2Q
=0
dt 2
–t Q = Q0e
Lag time
tR
Recession limb
Base flow QB T=0
Time
FIGURE 21.15 Sketch showing components of a storm hydrograph at a karst spring.
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Big Spring, MO
Ln Q
tR = 9 days
tR = 25 days
Time (days)
FIGURE 21.16 Semi-log plot of hydrograph recession curve showing fast response and slow response components. Data from U.S. Geological Survey surface water records.
gradients that force water into the surrounding aquifer. As the conduit drains after the storm, gradients reverse and the water stored in the fractures is released into the conduits. Analysis of the recession limb of the spring hydrograph gives some information on the relative importance of the conduit and fracture systems and the coupling between them. The exhaustion coefficient gives an estimate of the volume of water in dynamic storage above regional base level (Burdon and Papakis, 1963): 86,400Qmax (21.43) V = ε V is the volume of stored water in m3 , 86,400 is the number of seconds in a day, Qmax is the peak discharge in m3 sec−1 and ε is in units of days−1 . The exhaustion coefficient is also related to the transmissivity, T , and storativity, S, through (Milanovi´c, 1981): ε=
2T SL 2
(21.44)
L is the horizontal distance from recharge point to discharge point. The storage derived from the recession curve is what may be termed “dynamic storage.” It is the water stored above the local base level defined by the elevation of the spring. The deep storage below local base level is not probed by these measurements and requires wells of sufficient depth to penetrate the bottom of the aquifer.
21.6.6 Chemographs of Karst Springs The chemical composition of karst springs varies depending on the hydrogeology of the specific spring and for some springs, the chemistry also varies with season and with storm flow. Plots of various chemical parameters as a function of time are referred to as “chemographs” in analogy to the term hydrograph. Any chemical parameter can be used to construct a chemograph but hardness and specific conductance are most commonly used. Specific conductance is especially valuable in that it is linearly proportional to the concentration of dissolved ions in carbonate aquifers and conductance probes and data loggers are both reliable and relatively inexpensive.
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+2 Rapid precipitation +1
SIC
Slow precipitation
0
Slow dissolution
Internal runoff
–1
Drip waters Diffuse springs
Tropical springs
Conduit springs
Rapid dissolution
PCO2 of atmosphere –2 –4
–3 –2 Log PCO (atm) 2
–1
FIGURE 21.17 Schematic plot of karst water as a function of saturation index and calculated carbon dioxide partial pressure. The horizontal dashed lines indicate the saturation index at which carbonate dissolution shifts from fast kinetics to slow kinetics and the supersaturation at which nucleation barriers to calcite precipitation are exceeded.
The chemical compositions of ground and surface waters are commonly displayed as Piper or Stiff diagrams. These are useful when waters of widely varying composition are being compared but are less useful for karst waters, all of which are intrinsically carbonate type. The karst water parameters described in Section 21.4.2 are more useful as plotting variables. Figure 21.17 displays many of the chemical characteristics of karst waters. The enclosed areas labeled with various water types are generalized from a large body of data that have accumulated. Waters from various sources are often clearly distinguished by their chemistry. When spring water chemistry is monitored over time periods of months to years, it is found that some spring waters have essentially no chemical variability while others undergo excursions of 25 to 50%, often in an erratic manner (Shuster and White, 1971). For drainage basins of modest size, in the range of tens of km2 , the constant chemistry springs are mainly those discharging from fractures (called diffuse flow springs in the original report). Highly variable chemistry is associated with springs discharging from conduits and from drainage basins with large components of allogenic recharge. Interpretation of data collected at weekly or longer intervals is limited. Continuous records, or point-by-point records that can map the chemistry over individual storm hydrographs are more useful. Chemographs record events on many time scales (Figure 21.18). The chemograph of CO2 pressure from a large basin reveals the seasonal oscillation due to the coming and going of the growing season. The concentration of Ca2+ ions measured on the Maramec Spring, Missouri, exhibits dips corresponding to individual storm events. Like the recession limb of the hydrograph, the chemograph has an exponential recovery tail. However, the recovery time for the chemistry is substantially longer than the hydrograph recession. Continuous chemographs recorded as specific conductance reveal details within individual storm events with time resolution as short as 15 min. This fine structure has been interpreted as the arrival of storm water from different tributaries of the conduit system. Chemographs are most useful when they can be directly superimposed on hydrographs of individual storm events. The sudden decrease in specific conductance (hardness) is an indication of dilution of the spring water by storm water from the surface. If the decrease in conductance aligns with the rising limb
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PCO2 / [PCO2 (atm)]
(a)
40 Turnhole Spring, KY 30 20 10 0 Nov
Jan
Mar
May
Jul
Sep
Nov
Water year 1974
mg/L m3/sec
(b)
Maramec Spring, MO 15 5 35 25 15
Discharge Ca2+ Nov
Jan Mar May Jul
Sep Nov
Specific conductance (µs/cm)
(c) 400 300 200
Onset of intense storm
100 0 21
22 July 1973
23
FIGURE 21.18 Chemographs for selected karst springs. (a) CO2 partial pressure normalized to atmospheric CO2 , Turnhole Spring, Kentucky. (Data from Hess, J.W. and White, W.B. (1993) Appl. Geochem. 8, 189–204.) (b) Relation of Ca2+ ion concentration to discharge, Maramec Spring, Missouri. (Adapted from Dreiss, S.J. (1989) Water Resour. Res. 25, 117–125). (c) Response of specific conductance to a single intense storm, Turnhole Spring, Kentucky. (Adapted from Hess, J.W. and White, W.B. (1986) J. Hydrol. 99, 235–252.)
of the hydrograph, it is an indication that the system is open and the rise in the hydrograph is due to the arrival of storm water at the spring. If, as is often observed, there is a lag between the rising limb of the hydrograph and the falling limb of the chemograph, the indication is that water stored in continuously water-filled portions of the conduit system is being forced out by rising hydraulic head in the recharge region. Combining the lag time with the hydrograph allows calculation of the volume of water displaced (Ryan and Meiman, 1996). Comparison of chemographs and hydrographs have been used as a means of hydrograph separation to distinguish storm flow from phreatic storage and other sources of water appearing at the spring during storm discharge (Padilla et al., 1994; Grasso and Jeannin, 2002; Birk et al., 2004). Profiles of oxygen isotope ratios can also serve as a chemograph (Winston and Criss, 2004). Chemographs of other parameters can be superimposed on storm hydrographs (Figure 21.19). In the example shown, the falling limb of the conductance curve is synchronous with the rising limb of the hydrograph. However, the CO2 pressure, initially low and remaining low through the peak of the hydrograph, rises on the recession limb of the hydrograph. This can be interpreted as the arrival of soil water from the epikarst which brings in higher CO2 concentrations to the receding storm flow.
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140
520 III
IV
Discharge
Spc PCO 2 SIC
120
480
440
100
120
400
380 80
-0.4
80
320
SIC
Discharge (L/sec)
0.0
SC (µs/cm)
II
I
-0.8
60
40 0
Enhanced CO2
40 -1.2
20 175.5
176.1
176.7 Julian Date 1999
177.3
FIGURE 21.19 Hydrograph and selection of chemographs for a single storm at Beaver Spring, Fort Campbell Army Base, western Kentucky. (Adapted from Vesper, D.J. and White, W.B. (2004) Hydrogeol. J. 12, 135–143.)
21.7 Modeling of Karst Aquifers The word “model” is used here in the sense of a quantitative description of some aspect of karst aquifers as distinguished from the various conceptual models presented earlier in this chapter. Karst aquifer models come in two varieties. There are models that attempt to describe the evolution of the aquifer or groundwater basin through time as dissolution of the bedrock progresses and conduit permeability is developed. The second variety of model is concerned with the recharge, flow, and discharge of groundwater through the aquifer, assuming a time scale sufficiently short that the permeability distribution may be taken as fixed. These models differ from models used for non-karstic aquifers in that they must take into account the breakdown of Darcy’s law in the conduit permeability and the extreme contrast in hydraulic conductivity in different parts of the aquifer. Karst aquifer modeling has been a very active field of research and the sections that follow only briefly mention some of the approaches that have been used. For a broader perspective, see Palmer et al. (1999) and Sasowsky and Wicks (2000).
21.7.1 Evolutionary Models The qualitative concepts underlying evolutionary models were discussed earlier. The models that have been developed have been mainly a matter of reducing the qualitative ideas to computer programs. The usual starting point is a network of fractures for which the aperture distribution and connectivity are adjustable parameters. Some equation for the dissolution kinetics of carbonate rock is inserted and standard fluid mechanics is used to describe fracture flow and flow in conduits. These models show the evolution of
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the fracture and conduit system as a function of time with the objective of replicating permeability patterns seen in real aquifers (Kaufmann and Braun, 1999; Kaufmann, 2002, 2004; Gabrovsek et al., 2004).
21.7.2 Equivalent Porous Media Models Models adapted from standard porous media models such as the MODFLOW program developed by the United States Geological Survey assume that at large enough scales, the heterogeneities of the karst aquifer are smoothed out and can be represented by an average hydraulic conductivity. Scanlon et al. (2003) had some success in applying this type of model to the Edwards Aquifer in Texas. Equivalent porous media models work best for aquifers in which the karstic flow paths are dispersed and consist mainly of solutionally widened fractures. They work least well for aquifers with well-developed conduit systems, particularly those with large inputs of allogenic recharge. Establishing a suitable value for the average hydraulic conductivity is also difficult because hydraulic conductivity is scale dependent. For some spring basins in Missouri, the hydraulic conductivity was found to increase with scale up to a certain limit after which it became scale independent (Rovey, 1994). For highly karstic aquifers, the hydraulic conductivity continues to increase with scale until the scale length becomes equal to the size of the groundwater basin (Sauter, 1991). In general, equivalent porous media models should be used with great care.
21.7.3 Pipe Flow Models Equivalent porous media models ignore the conduit systems and their localized turbulent flows. Pipe Flow models focus entirely on the conduit system. Pipe flow models treat the conduit system as a network of pipes. Flow through the pipes is described by the Darcy–Weisbach equation (Equation 21.7). The drawback of the pipe flow models is that conduits are not exactly pipes. They have varying cross sections, complicated interconnections, and are often further modified by breakdown and sediment infillings. Much detail about conduit pattern is needed. However, calculations of travel times, head losses, and discharges for known conduit systems have been generally successful (Halihan and Wicks, 1998; Jeannin, 2001).
21.7.4 Coupled Continuum Pipe Flow Models Realistic models for maturely developed karst aquifers must take account of both the conduit system which carries most of the flow and the fracture and matrix system which holds most of the storage (Worthington et al., 2000). The conduit system is strongly coupled to surface water through sinking streams and closed depressions and so has a very dynamic response to storms. The fracture and matrix system receives most of its recharge through the epikarst and has a slower response. A dominant component of the total flow system is the exchange flow between the conduits and the surrounding fractured matrix. During storm flow, heads in the conduit system rise rapidly and water is forced into the surrounding fractures. After the storm flow recedes, the conduit system drains rapidly, heads reverse, and the water stored in the fractures drains into the conduits. Models have been constructed in which the fracture and matrix system is described as a continuum with Darcy flow. The conduits are put in“by hand”and described by pipe flow models. There is an exchange term that describes the influx and outflux of water between the fracture system and the conduits. These models have worked well in the sense that they reproduce storm hydrographs measured at the spring (Mohrlok and Sauter, 1997). The drawback is that independent information is required on the distribution of conduits. Tracer studies and cave exploration must supplement the strictly model calculation. Continued development of this approach to modeling has been very promising (Bauer et al., 2003; Liedl et al., 2003).
21.7.5 Input–Output Models All of the modeling approaches described above are built on considerable knowledge of the aquifer being modeled — the geometry of the conduit system, the hydraulic conductivity of the fracture and matrix
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system, and any geologic boundary conditions. In general, the more knowledge available, the more accurate the model. The diametrically opposite approach is to treat the aquifer as a black box and assume nothing about its internal properties. Instead, models are built from inputs and outputs, both of which can be measured directly. The relationship between input and output is described by linear systems theory as pioneered by Dreiss (1982, 1989) with more recent applications described by Wicks and Hoke (1999). The relationship between input of water to the aquifer and output of water as discharge from springs is given by: ∞ h(t − τ )i(τ ) dτ (21.45) O(t ) = −∞
The function O(t ) is the output — either a hydrograph or a chemograph. The function i(τ ) is the input of the same variable but not necessarily on the same timescale. The quantity h(t − τ ) is the kernal function that describes what goes on inside the black box. The kernal function must be calibrated by measuring both inputs and outputs for a range of discharges. Once the kernal function is known, it can then be used to relate output to input for future behavior of the aquifer.
21.8 Water Resource Issues in Karst Hydrology 21.8.1 Water Supplies in Karst Water supplies in karst are obtained from springs and wells. Karst springs’ draining fracture systems, as indicated by uniform discharge, lack of turbidity, and small chemical variation, provide reliable water supplies generally of good quality except for high hardness. Springs’ draining conduit systems have a highly variable discharge, sometimes become turbid to muddy after-storms, and are at risk from pollutants introduced through sinking streams and sinkholes. The conduit systems offer very little filtration. Injected pollutants can be quickly transmitted to the spring with little purification except for dilution. Location of production wells in karst is challenging except for wells in young limestones (e.g., the Floridan) with a high matrix permeability. Fractured limestone and dolomite aquifers provide the most reliable supplies of good quality water if the wells are drilled on fracture intersections. In favorable localities these can be determined by mapping lineaments seen on air photographs (Lattman and Parizek, 1964). Locations of wells in aquifers dominated by conduit permeability is difficult because conduits cannot generally be located from the surface. If the conduit is an accessible cave, wells can be located by use of a magnetic induction device (cave “radio”) from within the cave. Wells drilled into conduits face the same uncertainty of discharge, turbidity, and pollution risk as conduit springs. Farm wells are sometimes placed in conduits; municipal water supply wells are usually not placed in conduits.
21.8.2 Flood Flows in Karst: Sinkhole Flooding Karst aquifers serve to modify the flood flows in the associated surface water basins. Flood pulses of intermediate magnitude in tributary streams are injected into the conduit system at swallets. The conduit system holds the water in temporary storage and bleeds it out more slowly through the spring. The response time of even the most flashy conduit system is usually longer than the response time of flood pulses in surface channels. This has the effect of clipping the top of the hydrograph and spreading it out, thus reducing the flood crest downstream (E. L. White and Reich, 1970). Extreme floods may override swallets and send flood waters down dry valleys where there is no stream channel. In developed areas, buildings constructed in dry swales and valleys may be damaged by the unexpected invasion of flood waters. Sinkhole terrain is prone to flooding. One mechanism is that storm water ponds in closed depressions if the drain is plugged with clay. A second and more important mechanism is flooding from below. Storm flow into the conduit system quickly fills the groundwater trough and turns it into a groundwater mound. If the temporary water table created by flooding of the conduit system rises above the level of
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the bottoms of closed depressions, water will be forced up sinkhole drains and create ponds. High level sinkhole flooding may occur only during exceptional storms. If the sinkholes are broad and shallow, urban development may spread across them. All is well until the exceptional storm causes water to rise from below (Quinlan, 1986).
21.8.3 Contaminants and Contaminant Transport in Karst Aquifers Karst aquifers are highly vulnerable to groundwater contamination because of the negligible filtering of surface runoff into sinkholes and water from sinking streams. Contaminants can travel long distances constrained to the conduit systems rather then spreading to form plumes. The contaminants themselves are the same as those that impact other aquifers but some unique threats arise because of the flow paths in karst. Fecal material from septic tanks, leaky sewer lines, barnyard, and manure spread on fields migrates downward to the epikarst and then through the fractures in the vadose zone to the aquifer below. Cave streams and conduit springs frequently contain colliform bacteria and high nitrate levels. Agricultural chemicals including insecticides and herbicides have been reported in karst groundwater in many farming areas in the United States (Katz et al., 2004; Panno and Kelly, 2004). Household waste water becomes a contaminant in karst area. Pharmaceuticals are now being found in karst waters (Wicks et al., 2003). Sinkholes have long been used for solid waste disposal in rural areas. Household waste, junk, paint and chemical containers and dead, often diseased, farm animals end up in sinkholes. These wastes are leached by runoff into the sinkholes and carried down the sinkhole drain into the underlying conduit system. Solid waste can be flushed down open drains and dispersed along the conduit system where it continues to leach, but is impossible to clean up. Contaminants can be incorporated into the clastic sediments and flushed by flood flows deep into the aquifer. Likewise, trash discarded into sinking surface streams can be carried into the conduit system by flood flows. Liquid wastes from improper disposal of solvents, from industrial outfalls directed into fractures and sinkholes, and from leaking pipelines and storage tanks can make their way into karst aquifers though any of the recharge routes. Soluble wastes dissolve in the karst groundwater and are carried along with it. Insoluble liquids with a density less than water (LNAPLs) float on underground streams or on the karst waters table. Insoluble liquids with a density greater than water (DNAPLs) sink to the bottom of the karst groundwater system and may continue downward into fractures and indeed travel in directions other than that of the main groundwater flow. The most common LNAPLs are gasoline, diesel fuel, and heating oil from leaking underground storage tanks. Toxic substances — the BTEX components benzene, tolune, ethyl benzene, and xylene — are found in LNAPL hydrocarbons. Because LNAPLs float, they tend to pond behind sumps in the conduit system and tend to be trapped in pockets and other irregularities in the conduit system (Ewers et al., 1991). Rising flood waters can force the LNAPLs upward through fractures and sinkhole drains. They may invade basements and crawl spaces beneath buildings where they produce both toxic fumes and also an explosion hazard (Stroud et al., 1986). DNAPLs consist mainly of chlorinated hydrocarbons used as solvents and degreasers. When such materials reach the conduit system, they may pool in low places in stream channels or be adsorbed into sediment piles. DNAPLs have a finite, although usually low, solubility so that the pooled liquid is eventually dissolved in the conduit water and carried away although this may take a long time. DNAPLs in sediment piles and in the fractures in the limestone may remain in place for very long times (Loop and White, 2001). DNAPLs spilled into karst aquifers often do not reappear at springs and wells. Storm flows may eject a slug of DNAPL that had remained sequestered in the aquifer. The movement of suspended sediments through karst aquifers is an important mechanism for contaminant transport. Metals tend to adsorb onto clay particles and are carried through the system with the suspended particles. For the carbonate aquifer at Fort Campbell in western Kentucky, there was a close correlation between concentrations of nickel, lead, chromium, cadmium and arsenic with the concentration of aluminum in the analysis of unfiltered water samples (Vesper and White, 2003). Aluminum
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was taken as a proxy for suspended clay minerals. Likewise, bacteria have been found to be transported through karst aquifers attached to suspended particles (Mahler et al., 2000).
21.8.4 Water Quality Monitoring United States Environmental Protection Agency and state regulation require legally established landfills and other disposal sites to install a network of monitoring wells. Samples are drawn from these wells at prescribed intervals and analyzed for contaminants. A typical requirement is three down-gradient wells and one up-gradient well to be installed on the perimeter of the waste disposal site. The strategy is to detect any contamination before it moves offsite and to take early remedial action. The concept does not work in karst. Because of the heterogeneous distribution of conduit permeability and the general impossibility of locating subsurface conduits from the land surface, there is a very real possibility of contaminants moving offsite through the karst conduits while leaving no trace in the monitoring wells. As contaminants, once in the conduit system, move rapidly, detection and remedial action must be prompt. To monitor waste sites in karst requires a different strategy. Trenches should be excavated to bedrock and tracers injected into the bedrock fractures with a water flush. The spring or springs to which the aquifer drains must be identified must be used as a monitoring site regardless of the difficulties of offsite monitoring. Likewise, more frequent monitoring, especially following storm events, is necessary because of the rapid transport of contaminants though the conduit system (Quinlan, 1990).
21.9 Land Instability and Sinkhole Development 21.9.1 Sinkholes as Land Use Hazards The term “sinkhole” is used for any closed depression in karst terrain. In this broad usage, sinkholes range in size from a few meters to kilometers in diameter and from fractions of a meter to kilometers in depth. Processes include bedrock dissolution, bedrock stoping and collapse of underlying solution cavities, and soil collapses resulting from piping. The sinkholes that are of main concern as land-use hazards are of the soil piping variety. Unlike processes of dissolution, which are slow on human time scales, soil piping failures are abrupt with time scales in the range of seconds to days. Residents of karst may be dismayed to discover soil collapses — sinkholes — meters in diameter and meters deep appearing in their yards or, worse, under their houses after heavy rains or after the thawing of frozen ground. These sinkholes occur in two end-member varieties: (1) cover collapse sinkholes that form abruptly as a plug of soil falls into an underlying cavity and (2) raveling sinkholes that form gradually as loose, poorly cohesive soils drain away into the subsurface. The size and depth of sinkholes depend on the thickness of the regolith and also on the cohesive strength of soil and regolith. Damage to buildings, paved areas, and highways can be extensive with some sinkholes of sufficient size to swallow entire buildings.
21.9.2 Mechanisms of Sinkhole Development The essential steps in the development of a cover collapse sinkhole are shown in Figure 21.20. In the pre-sinkhole stage there is an opening in the bedrock, which may be a solutionally widened fracture or a tubular throat that connects at the bottom with a conduit system that contains flowing water. Above is a cohesive soil of some specified thickness. The throat is assumed to be plugged with soil. The throat may be the drain for a larger area of the epikarst. As infiltrating water descends the throat, the clastic sediment is gradually flushed into the underlying conduit that must have sufficient flow velocity, at least during storm flow, to carry the material away. When the throat has been cleared, sediment from the base of the regolith column is also flushed down the throat, creating a cavity. As more and more of the regolith is carried into the subsurface, the cavity and its regolith arch roof continue to grow. The final step in the process is the collapse of the regolith arch. When the cavity reaches a critical size, the roof becomes mechanically unstable. Collapse is usually instantaneous with the fallen plug of roof material blocking the throat.
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The Handbook of Groundwater Engineering (a)
(b)
(c) Thick Cohesive soil
Sinkhole throat
Stream-carrying conduit Initial state
Development of soil arch
Final state: Collapse of arch
FIGURE 21.20 Components of a cover collapse sinkhole. (a) Initial conditions of thick, cohesive soil over karsted limestone. (b) Lowering water table increases hydraulic gradient so that storm runoff down the sinkhole throat flushes soil into the underlying cave passage and creates a soil arch. (c) The soil arch reaches a size where it becomes mechanically unstable. The remaining plug of soil near the surface collapses, forming a sinkhole.
21.9.3 Hydrologic Factors in Sinkhole Development Sinkholes are a natural part of landscape evolution. Closed depressions are natural routes by which internal runoff reaches karst aquifers. Soils accumulate in the closed depressions and piping failures occur. When failures happen, a plug of soil is flushed into the underlying conduit system, the walls of the sinkhole slump and the throat reseals, more soil accumulates, and the cycle repeats. These sinkholes are found in rural areas, far from any human influence. Excess runoff from roofs, parking lots, and other pavement concentrates the amount of water injected into the ground into a few locations. Increased hydrostatic heads and increased flow volumes focused on the pathways at the base of the epikarst accelerates the transport of regolith down sinkhole throats and thus the development of sinkholes. Detention basins for the management of storm runoff are particularly susceptible to the creation of sinkholes. Broken water mains or broken sewer lines are a common local cause of sinkholes. Dewatering of karst aquifers also accelerates sinkhole development. If at least the lower portion of the throat is below the water table, sediment choking the throat will be water-saturated and less mobile. If the water table is lowered by excessive pumping from the aquifer, by quarry dewatering, or by other means, sediment plugs will drain and dry, hydraulic gradients will increase, and the system will be more susceptible to sinkhole development. Quarry dewatering has been a common source of sinkhole problems in surrounding areas.
21.9.4 Sinkhole Remediation Sinkholes are part of hydrologic system and for this reason must be repaired with some care. Often sinkholes are repaired by simply filling them with soil or other material. This is seldom a long term solution. Plugging one sinkhole is likely to initiate another sinkhole somewhere in the vicinity as a drainage route for surface water must be maintained. A useful technique is to excavate the sinkhole to bedrock, expose the throat, then fill the bottom of the excavation with a stone too large to fit into the throat. Continue upward with progressively less coarse stone and gravel. The top can be capped with a geofabric and then
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with soil. The objective is to provide a pathway that will allow free drainage of water but which will block the movement of soil and regolith. Many ingenious schemes have been devised for sinkhole remediation as discussed in detail by Sowers (1996) and Waltham et al. (2005).
References Anthony, D.M. and Granger, D.E. (2004) A late Tertiary origin for multilevel caves along the western escarpment of the Cumberland Plateau, Tennessee and Kentucky, established by cosmogenic 26 Al and 10 Be. J. Cave Karst Stud. 66, 46–55. Atkinson, T.C. (1977) Diffuse flow and conduit flow in limestone terrain in the Mendip Hills, Somerset (Great Britain). J. Hydrol. 35, 93–110. Atkinson, T.C., Smart, P.L. and Wigley, T.M.L. (1983) Climate and natural radon levels in Castleguard Cave, Columbia Icefields, Alberta, Canada. Arc. Alpine Res. 15, 487–502. Barnes, H.H., Jr. (1967) Roughness Characteristics of Natural Channels, U.S. Geological Survey Water Supply Paper 1849, Washington, D.C. Bauer, S., Liedl, R. and Sauter, M. (2003) Modeling of karst aquifer genesis: Influence of exchange flow. Water Resour. Res. 39, doi:10.1029/2003WR002218. Berner, R.A. and Morse, J.W. (1974) Dissolution kinetics of calcium carbonate in sea water IV. Theory of calcite dissolution. Amer. J. Sci. 274, 108–154. Birk, S., Liedl, R. and Sauter, M. (2004) Identification of localized recharge and conduit flow by combined analysis of hydraulic and physico-chemical spring responses (Urenbrunnel, SW-Germany). J. Hydrol. 286, 179–193. Bonnaci, O. (1987) Karst Hydrology, Springer-Verlag, Berlin. Bosch, R.F. and White, W.B. (2004) Lithofacies and transport of clastic sediments in karstic aquifers. In Studies of Cave Sediments, Sasowsky, I.D. and Mylroie, J.E., Eds., Kluwer Academic/Plenum Publishers, New York, pp. 1–22. Brucker, R.W., Hess, J.W. and White, W.B. (1972) Role of vertical shafts in movement of groundwater in carbonate aquifers. Ground Water. 10, 5–13. Brush, D.J. and Thomson, N.R. (2003) Fluid flow in synthetic rough-walled fractures: Navier–Stokes, Stokes, and local cubic law simulations. Water Resour. Res. 39, doi:10.1029/2002WR001346. Budd, D.A. and Vacher, H.L. (2002) Facies control on matrix permeability in the upper Floridan Aquifer, west-central Florida. Karst Waters Inst. Spec. Pub. 7, 14–24. Burdon, D.J. and Papakis, N. (1963) Handbook of Karst Hydrogeology, United Nations Special Fund, Institute for Geology and Subsurface Research, Athens, Greece. Busenberg, E. and Plummer, L.N. (1982) The kinetics of dissolution of dolomite in CO2 –H2 O systems at 1.5 to 65◦ C and 0 to 1 atm PCO2 . Amer. J. Sci. 282, 45–78. Curl, R.L. (1974) Deducing flow velocity in cave conduits from scallops. Natl Speleol. Soc. Bull. 36, 1–5. Davies, W.E. and Chao, E.C.T. (1958) Report on sediments in Mammoth Cave, Kentucky. Administrative Report to National Park Service by U.S. Geological Survey, 117 pp. Despain, J.D. and Stock, G.M. (2005) Geomorphic history of Crystal Cave, southern Sierra Nevada, California. J. Cave Karst Studies 67, 92–102. Dreiss, S.J. (1982) Linear kernels for karst aquifers. Water Resour. Res. 18, 865–876. Dreiss, S.J. (1989) Regional scale transport in a karst aquifer. 1. Component separation of spring flow hydrographs. Water Resour. Res. 25, 117–125. Drever, J.I. (1997) The Geochemistry of Natural Waters, 3rd ed. Prentice Hall, Englewood Cliffs, NJ. Dreybrodt, W. (1988) Processes in Karst Systems, Springer-Verlag, Berlin. Dreybrodt, W. and Buhmann, D. (1991) A mass transfer model for the dissolution and precipitation of calcite from solutions in turbulent motion. Chem. Geol. 90, 107–122. Dreybrodt, W. (1992) Dynamics of karstification: A model applied to hydraulic structures in karst terranes. Appl. Hydrogeol. 3, 20–32.
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Dreybrodt, W., Lauckner, J., Liu, Z., Svensson, U. and Buhman, D. (1996) The kinetics of the reaction CO2 + H2 O → H+ + HCO− 3 as one of the rate limiting steps of the dissolution of calcite in the system H2 O–CO2 –CaCO3 . Geochim. Cosmochim. Acta 60, 3375–3381. Dreybrodt, W. (1996) Principles of early development of karst conduits under natural and man-made conditions revealed by mathematical analysis of numerical models. Water Resources Res. 32, 2923–2935. Ewers, R.L., Estes, E.K., Idstein, P.J. and Johnson, K.M. (1991) The transmission of light hydrocarbon contaminants in limestone (karst) aquifers. Proc. Third Conf. Hydrogeology, Ecology, Monitoring and Management of Ground Water in Karst Terranes, Nashville, TN, pp. 287–306. Ford, D.C. and Williams, P.W. (1989) Karst Geomorphology and Hydrology, Unwin Hyman, London. Gabrovsek, F., Romanov, D. and Dreybrodt, W. (2004) Early karstification in a dual-fracture aquifer: The role of exchange flow between prominent fractures and a dense net of fissures. J. Hydrol. 299, 45–66. Gale, S.J. (1984) The hydraulics of conduit flow in carbonate aquifers. J. Hydrol. 70, 309–327. Gillieson, D. (1986) Cave sedimentation in the New Guinea Highlands. Earth Surf. Proc. Landforms 11, 533–543. Granger, D.E., Fabel, D. and Palmer, A.N. (2001) Pliocene-Pleistocene incision of the Green River, Kentucky, determined from radioactive decay of cosmogenic 26 Al and 10 Be in Mammoth Cave sediments. Geol. Soc. Amer. Bull. 113, 825–836. Grasso, D.A. and Jeannin, P.-Y. (2002) A global experimental system approach of karst springs’hydrographs and chemographs. Ground Water. 40, 608–617. Groves, C.G. and Howard, A.D. (1994) Early development of karst systems. 1. Preferential flow path enlargement under laminar flow. Water Resour. Res. 30, 2837–2846. Halihan, T. and Wicks, C.M. (1998) Modeling of storm responses in conduit flow aquifers with reservoirs. J. Hydrol. 208, 82–91. Herman, J.S. and White, W.B. (1985) Dissolution kinetics of dolomite: Effects of lithology and fluid flow velocity. Geochim. Cosmochim. Acta 49, 2017–2026. Hess, J.W. and White, W.B. (1986) Storm response of the karstic carbonate aquifer in Southcentral Kentucky. J. Hydrol. 99, 235–252. Hess, J.W. and White, W.B. (1989) Water budget and physical hydrology. In Karst Hydrology: Concepts from the Mammoth Cave Area, White, W.B. and White, E.L., Eds, Van Nostrand Reinhold, New York, Chap. 4, pp. 105–126. Hess, J.W. and White, W.B. (1993) Groundwater geochemistry of the carbonate karst aquifer, Southcentral Kentucky, U.S.A. Appl. Geochem. 8, 189–204. Hill, C.A. (1990) Sulfuric acid speleogenesis of Carlsbad Caverns and its relationship to hydrocarbons, Delaware Basin, New Mexico and Texas. Amer. Assoc. Petrol. Geol. Bull. 74, 1685–1694. Jeannin, P.Y. (2001) Modeling flow in phreatic and epiphreatic karst conduits in the Hölloch Cave (Muotatal, Switzerland). Water Resour. Res. 37, 191–200. Jones, W.K. (1984) Dye tracer tests in karst areas. Natl. Speleol. Soc. Bull. 46, 3–9. Jones, W.K., Culver, D.C. and Herman, J.S. (2003) Epikarst, Spec. Pub. 9, Karst Waters Institute, Charles Town, WV. Käss, W. (1998) Tracing Technique in Geohydrology, A.A. Balkema, Rotterdam. Katz, B.G., Chelette, A.R. and Pratt, T.R. (2004) Use of chemical and isotopic tracers to assess nitrate contamination and ground-water age, Woodville Karst Plain, USA. J. Hydrol. 289, 36–61. Kaufmann, G. and Braun, J. (1999) Karst aquifer evolution in fractured rocks. Water Resour. Res. 35, 3223–3238. Kaufmann, G. (2002) Karst aquifer evolution in a changing water table environment. Water Resour. Res. 38, doi:10.1029/2001WR000259. Kaufmann, G. (2003) Modelling unsaturated flow in an evolving karst aquifer. J. Hydrol. 276, 53–70. Konzuk, J.S. and Kueper, B.H. (2004) Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture. Water Resour. Res. 40, doi:10.1029/2003WR002356.
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Langmuir, D. (1971) The geochemistry of some carbonate ground waters in central Pennsylvania. Geochim. Cosmochim. Acta 35, 1023–1045. Langmuir, D. (1997) Aqueous Environmental Geochemistry, Prentice Hall, Upper Saddle River, NJ. Lattman, L.H. and Parizek, R.R. (1964) Relationship between fracture traces and the occurrence of groundwater in carbonate rocks. J. Hydrol. 2, 73–91. Lauritzen, S.E., Abbott, J., Arnesen, R., Crossley, G., Grepperud, D, Ive, A. and Johnson, S. (1985) Morphology and hydraulics of an active phreatic conduit. Cave Sci. 12, 139–146. Liedl, R., Sauter, M., Hückinghaus, D., Clemens, T. and Teutsch, G. (2003) Simulation of the development of karst aquifers using a coupled continuum pipe model. Water Resour. Res. 39, doi:10.1029/2001WR001206. Liu, Z. and Dreybrodt, W. (1997) Dissolution kinetics of calcium carbonate minerals in H2 O–CO2 solutions in turbulent flow: The role of the diffusion boundary layer and the slow reaction H2 O + CO2 → H+ + HCO− 3 . Geochim. Cosmochim. Acta 61, 2879–2889. Loewenthal, R.E. and Marais, G.V.R. (1976) Carbonate Chemistry of Aquatic Systems: Theory and Application, Ann Arbor Science, Ann Arbor, MI. Loop, C.M. and White, W.B. (2001) A conceptual model for DNAPL transport in karst aquifers. Ground Water. 39, 119–127. Mahler, B.J., Personné, J.-C., Lods, G.F. and Drogue, C. (2000) Transport of free and particulate-associated bacteria in karst. J. Hydrol. 238, 179–193. Milanovi´c, P.T. (1981) Karst Hydrogeology, Water Resources Publications, Littleton, CO. Milanovi´c, P.T. (2004) Water Resources Engineering in Karst, CRC Press, Boca Raton, FL. Mohrlok, U. and Sauter, M. (1997) Modelling groundwater flow in a karst terrane using discrete and double-continuum approaches — importance of spatial and temporal distribution of recharge. Proc. 12th Internatl. Congress Speleol., La Chaux de Fonds, Switzerland, Vol. 2, pp. 167–170. Morse, J.W. and Arvidson, R.S. (2002) The dissolution kinetics of major sedimentary carbonate minerals. Earth-Sci. Rev. 58, 51–84. Muldoon, M.A., Simo, J.A. and Bradbury, K.R. (2001) Correlation of hydraulic conductivity with stratigraphy in a fractured-dolomite aquifer, northeastern Wisconsin, U.S.A. Hydrogeol. J. 9, 570–583. Mull, D.S., Liebermann, T.D., Smoot, J.L. and Woosley, L.H. Jr. (1988) Application of dye-tracing techniques for determining solute-transport characteristics of groundwater in karst terranes. U.S. Environmental Protection Agency Report, EPA 9045/6-88-001. Mylroie, J.E. and Carew, J.L. (1987) Field evidence of the minimum time for speleogenesis. Natl Speleol. Soc. Bull. 49, 67–72. Padilla, A., Pulido-Bosch, A. and Mangin, A. (1994) Relative importance of baseflow and quickflow from hydrographs of karst springs. Ground Water. 32, 267–277. Palmer, A.N. (1975) Origin of maze caves. Natl Speleol. Soc. Bull. 37, 57–76. Palmer, A.N. (1991) Origin and morphology of limestone caves. Geol. Soc. Amer. Bull. 103, 1–21. Palmer, A.N., Palmer, M.V. and Sasowsky, I.D. (1999) Karst Modeling, Spec. Pub. 5, Karst Waters Institute, Charles Town, WV. Panno, S.V. and Kelly, W.R. (2004) Nitrate and herbicide loading in two groundwater basins of Illinois’ sinkhole plain. J. Hydrol. 290, 229–242. Plummer, L.N., Wigley, T.M.L. and Parkhurst, D.L. (1978) The kinetics of calcite dissolution in CO2 –water systems at 5◦ to 60◦ C and 0.0 to 1.0 atm CO2 . Amer. J. Sci. 278, 179–216. Plummer, L.N., Parkhurst, D.L. and Wigley, T.M.L. (1979) Critical review of the kinetics of calcite dissolution and precipitation. In Chemical Modeling in Aqueous Systems, Jenne, E.A., Ed., Amer. Chem. Soc. Symposium Ser. 93, Washington, DC, Chap. 25, pp. 537–573. Plummer, L.N. and Busenberg, E. (1982) The solubilities of calcite, aragonite and vaterite in CO2 –H2 O solutions between 0 and 90◦ C, and an evaluation of the aqueous model for the system CaCO3 –CO2 –H2 O. Geochim. Cosmochim. Acta 46, 1011–1040.
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Quinlan, J.F. (1986) Legal aspects of sinkhole development and flooding in karst terranes: 1. Review and synthesis. Environ. Geol. Water Sci. 8, 41–61. Quinlan, J.F. (1990) Special problems of ground-water monitoring in karst terranes. In Ground Water and Vadose Zone Monitoring, Nielsen, D.M. and Johnson, A.I. Eds., ASTM STP 1053, American Society for Testing Materials, Philadelphia, PA, pp. 275–304. Quinlan, J.F. and Ray, J.A. (1995) Normalized base-flow discharge of groundwater basins: A useful parameter for estimating recharge area of springs and for recognizing drainage anomalies in karst terranes. In Karst Geohazards, Beck, B.F., Ed., A.A. Balkema, Rotterdam, pp. 149–164. Richards, D.A. and Dorale, J.A. (2003) Uranium-series chronology and environmental applications of speleothems. Rev. Mineral. 52, 407–460. Rovey, C.W. II. (1994) Assessing flow systems in carbonate aquifers using scale effects in hydraulic conductivity. Environ. Geol. 24, 244–253. Ryan, M. and Meiman, J. (1996) An examination of short-term variations in water quality at a karst spring in Kentucky. Ground Water. 34, 23–30. Sasowsky, I.D. and Wicks, C.M. (2000) Groundwater Flow and Contaminant Transport in Carbonate Aquifers, A.A. Balkema, Rotterdam. Sasowsky, I.D. and Mylroie, J. (2004) Studies of Caves Sediments, Kluwer Academic/Plenum Press, New York. Sauter, M. (1991) Assessment of hydraulic conductivity in a karst aquifer at local and region scale. Proc. Third Conf. of Hydrogeology, Ecology, Monitoring, and Management of Ground Water in Karst Terranes, Nashville, TN, pp. 39–57. Scanlon, B.R., Mace, R.E., Barrett, M.E. and Smith, B. (2003) Can we simulate regional groundwater flow in a karst system using equivalent porous media models? Case study, Barton Springs, Edwards Aquifer, USA. J. Hydrol. 276, 137–158. Schmidt, V.A. (1982) Magnetostratigraphy of sediments in Mammoth Cave, Kentucky. Science 217, 827–829. Shuster, E.T. and White, W.B. (1971) Seasonal fluctuations in the chemistry of limestone springs: A possible means for characterizing carbonate aquifers. J. Hydrol. 14, 93–128. Siemers, J. and Dreybrodt, W. (1998) Early development of karst aquifers on percolation networks of fractures in limestone. Water Resour. Res. 34, 409–419. Smart, C.C. (1988) Quantitative tracing of the Maligne Karst System, Alberta, Canada. J. Hydrol. 98, 185–204. Smart, P.L. and Laidlaw, I.M.S. (1977) An evaluation of some fluorescent dyes for water tracing. Water Resour. Res. 13, 15–33. Smart, P.L. (1984) A review of the toxicity of twelve fluorescent dyes used for water tracing. Natl Speleol. Soc. Bull. 46, 21–33. Sowers, G.F. (1996) Building on Sinkholes, American Society of Civil Engineers, New York, NY. Stroud, F.B., Gilbert, J., Powell, G.W., Crawford, N.C., Rigatti, M.J. and Johnson, P.C. (1986) Environmental Protection Agency emergency response to toxic fumes and contaminated ground-water in karst topography, Bowling Green, Kentucky. Proc. Environmental Problems in Karst Terranes and Their Solutions Conference, Bowling Green, KY, pp. 197–226. Svensson, U. and Dreybrodt, W. (1992) Dissolution kinetics of natural calcite minerals in CO2 –water systems approaching calcite equilibrium. Chem. Geol. 100, 129–145. Vanoni, V.A. (1975) Sedimentation Engineering, American Society of Civil Engineers, New York. Vennard, J.K. (1962) Elementary Fluid Mechanics, Wiley, New York. Vesper, D.J. and White, W.B. (2003) Metal transport to karst springs during storm flow: An example from Fort Campbell, Kentucky/Tennessee, U.S.A. J. Hydrol. 276, 20–36. Vesper, D.J. and White, W.B. (2004) Storm pulse chemographs of saturation index and carbon dioxide pressure: Implications for shifting recharge sources during storm events in the karst aquifer at Fort Campbell, Kentucky/Tennessee, USA. Hydrogeol. J. 12, 135–143.
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Waltham, T., Bell, F. and Culshaw, M. (2005) Sinkholes and Subsidence: Karst and Cavernous Rocks in Engineering and Construction, Springer-Verlag, Berlin. White, E.L. and Reich, B.M. (1970) Behavior of annual floods in limestone basins in Pennsylvania. J. Hydrol. 10, 193–198. White, E.L. (1977) Sustained flow in small Appalachian watersheds underlain by carbonate rocks. J. Hydrol. 32, 71–86. White, W.B. (1977) Role of solution kinetics in the development of karst aquifers. In Karst Hydrogeology, Tolson, J.S. and Doyle, F.L., Eds., Internatl. Assoc. Hydrogeologists Memoir 12, pp. 503–517. White, W.B. (1988) Geomorphology and Hydrology of Karst Terrains, Oxford University Press, New York. White, W.B. and Deike, G.H. (1989) Hydraulic geometry of cave passages, In Karst Hydrology: Concepts from the Mammoth Cave Area, White, W.B. and White, E.L., Eds., Van Nostrand Reinhold, New York, Chap. 9, pp. 223–258. White, W.B. (1999) Conceptual models for karstic aquifers. Karst Waters Inst. Spec. Pub. 5, 10–16. Wicks, C.M. and Hoke, J.A. (1999) Linear systems approach to modeling groundwater flow and solute transport through karstic basins. Karst Waters Inst. Spec. Pub. 5, 97–101. Wicks, C.M., Kelley, C. and Peterson, E. (2003) Estrogen in a karstic aquifer. Ground Water. 42, 384–389. Winston, W.E. and Criss, R.E. (2004) Dynamic hydrologic and geochemical response in a perennial karst spring. Water Resour. Res. 40, doi:10.1029/2004WR003054. Witherspoon, P.A., Wang, J.S.Y., Iwai, K. and Gale, J.E. (1980) Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour. Res., 16, 1016–1024. Worthington, S.R.H. (1991) Karst hydrogeology in the Canadian Rocky Mountains. Ph.D. thesis, McMaster University, Hamilton, Ontario. Worthington, S.R.H. (1999) A comprehensive strategy for understanding flow in carbonate aquifers. Karst Waters Inst. Spec. Pub. 5, 30–37. Worthington, S.R.H., Ford, D.C. and Davies, G.J. (2000) Matrix, fracture and channel components of storage and flow in a Paleozoic limestone aquifer. In Groundwater Flow and Contaminant Transport in Carbonate Aquifers, Sasowsky, I.D. and Wicks, C.M., Eds. A.A. Balkema, Rotterdam, pp. 113–128. Worthington, S.R.H., Schindel, G.M. and Alexander, E.C. (2002) Techniques for investigating the extent of karstification in the Edwards Aquifer, Texas. Karst Waters Inst. Spec. Pub. 7, 173–175.
Further Information It has been estimated that 15 to 20% of the Earth’s land surface is karst. As a result, there is a very large literature in many languages. The study of karst has traditionally been the province of physical geographers and geomorphologists and most books approach the subject from this point of view. Useful books that emphasize the hydrogeologic aspects of karst include Bonacci (1987), White (1988), Dreybrodt (1988), Ford and Williams (1989), and Milanovi´c (1981, 2004).
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22 Contaminant Transport in the Unsaturated Zone: Theory and Modeling 22.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-1 22.2 Variably Saturated Water Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 22-3 Mass Balance Equation • Uniform Flow • Preferential Flow
22.3 Solute Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-8 Transport Processes • Advection–Dispersion Equations • Nonequilibrium Transport • Stochastic Models • Multicomponent Reactive Solute Transport • Multiphase Flow and Transport • Initial and Boundary Conditions
Ji˘rí Šimunek ˚ University of California, Riverside
Martinus Th. van Genuchten George E. Brown, Jr, Salinity Laboratory, USDA-ARS
22.4 Analytical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-22 Analytical Approaches • Existing Models
22.5 Numerical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-27 Numerical Approaches • Existing Models
22.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-36 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-38
22.1 Introduction Human society during the past several centuries has created a large number of chemical substances that often find their way into the environment, either intentionally applied during agricultural practices, unintentionally released from leaking industrial and municipal waste disposal sites, or stemming from research or weapons production related activities. As many of these chemicals represent a significant health risk when they enter the food chain, contamination of both surface and subsurface water supplies has become a major issue. Modern agriculture uses an unprecedented number of chemicals, both in plant and animal production. A broad range of fertilizers, pesticides and fumigants are now routinely applied to agricultural lands, thus making agriculture one of the most important sources for non-point source pollution. The same is true for salts and toxic trace elements, which are often an unintended consequence of irrigation in arid and semiarid regions. While many agricultural chemicals are generally beneficial in surface soils, their leaching into the deeper vadose zone and groundwater may pose serious problems. Thus, management processes are being sought to keep fertilizers and pesticides in the root
22-1
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zone and prevent their transport into underlying or down-gradient water resources. Agriculture also increasingly uses a variety of pharmaceuticals and hormones in animal production many of which, along with pathogenic microorganisms, are being released to the environment through animal waste. Animal waste and wash water effluent, in turn, is frequently applied to agricultural lands. Potential concerns about the presence of pharmaceuticals and hormones in the environment include: (1) abnormal physiological processes and reproductive impairment; (2) increased incidences of cancer; (3) development of antibiotic resistant bacteria; and (4) increased toxicity of chemical mixtures. While the emphasis above is mostly on non-point source pollution by agricultural chemicals, similar problems arise with point-source pollution from industrial and municipal waste disposal sites, leaking underground storage tanks, chemicals spills, nuclear waste repositories, and mine tailings, among other sources. Mathematical models should be critical components of any effort to optimally understand and quantify site-specific subsurface water flow and solute transport processes. For example, models can be helpful tools for designing, testing and implementing soil, water, and crop management practices that minimize soil and water pollution. Models are equally needed for designing or remediating industrial waste disposal sites and landfills, or for long-term stewardship of nuclear waste repositories. A large number of specialized numerical models now exist to simulate the different processes at various levels of approximation and for different applications. Increasing attention is being paid recently to the unsaturated or vadose zone where much of the subsurface contamination originates, passes through, or can be eliminated before it contaminates surface and subsurface water resources. Sources of contamination often can be more easily remediated in the vadose zone, before contaminants reach the underlying groundwater. Other chapters in this Handbook deal with water flow (Chapter 4) and solute transport (Chapter 18 and Chapter 19) in fully saturated (groundwater) systems and with water flow in the unsaturated zone (Chapter 6). The focus of this chapter thus will be on mathematical descriptions of transport processes in predominantly variably saturated media. Soils are generally defined as the biologically active layer at the surface of the earth’s crust that is made up of a heterogeneous mixture of solid, liquid, and gaseous material, as well as containing a diverse community of living organisms (Jury and Horton, 2004). The vadose (unsaturated) zone is defined as the layer between the land surface and the permanent (seasonal) groundwater table. While pores between solid grains are fully filled with water in the saturated zone (groundwater), pores in the unsaturated zone are only partially filled with water, with the remaining part of the pore space occupied by the gaseous phase. The vadose zone is usually only partially saturated, although saturated regions may exist, such as when perched water is present above a low-permeable fine-textured (clay) layer or a saturated zone behind the infiltration front during or after a high-intensity rainfall event. As the transport of contaminants is closely linked with the water flux in soils and rocks making up the vadose zone, any quantitative analysis of contaminant transport must first evaluate water fluxes into and through the vadose zone. Water typically enters the vadose zone in the form of precipitation or irrigation (Figure 22.1), or by means of industrial and municipal spills. Some of the rainfall or irrigation water may be intercepted on the leaves of vegetation. If the rainfall or irrigation intensity is larger than the infiltration capacity of the soil, water will be removed by surface runoff, or will accumulate at the soil surface until it evaporates back to the atmosphere or infiltrates into the soil. Part of this water is returned to the atmosphere by evaporation. Some of the water that infiltrates into the soil profile may be taken up by plant roots and eventually returned to the atmosphere by plant transpiration. The processes of evaporation and transpiration are often combined into the single process of evapotranspiration. Only water that is not returned to the atmosphere by evapotranspiration may percolate to the deeper vadose zone and eventually reach the groundwater table. If the water table is close enough to the soil surface, the process of capillary rise may move water from the groundwater table through the capillary fringe toward the root zone and the soil surface. Because of the close linkage between water flow and solute transport, we will first briefly focus on the physics and mathematical description of water flow in the vadose zone (Section 22.2). An overview is given of the governing equations for water flow in both uniform (Section 22.2.2) and structured (Section 22.2.3)
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Transpiration Interception Irrigation Rainfall Evaporation
rag
Root water uptake
Sto
Unsaturated zone
Root zone
e
Runoff
Deep drainage Capillary rise
zone
Saturated
Water table Groundwater recharge
FIGURE 22.1 Schematic of water fluxes and various hydrologic components in the vadose zone.
media. This section is followed by a discussion of the governing solute transport equations (Section 22.3), again for both uniform (Section 22.3.2) and structured (fractured) (Section 22.3.3) media. We also briefly discuss alternative formulations for colloid (Section 22.3.3.2.2) and colloid-facilitated transport (Section 22.3.3.3), multicomponent geochemical transport (Section 22.3.5), and stochastic approaches for solute transport (Section 22.3.4). This is followed by a discussion of analytical (Section 22.4) and numerical (Section 22.5) approaches for solving the governing flow and transport equations, and an overview of computer models currently available for simulating vadose zone flow and transport processes (Sections 22.4.2 and 22.5.2).
22.2 Variably Saturated Water Flow In this section, we briefly present the equations governing variably saturated water flow in the subsurface. More details about this topic, including the description of the soil hydraulic properties and their constitutive relationships, are given in Chapter 6. Traditionally, descriptions of variably saturated flow in soils are based on the Richards (1931) equation, which combines the Darcy–Buckingham equation for the fluid flux with a mass balance equation. The Richards equation typically predicts a uniform flow process in the vadose zone, although possibly modified macroscopically by spatially variable soil hydraulic
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properties (e.g., as dictated by the presence of different soil horizons, but possibly also varying laterally). Unfortunately, the vadose zone can be extremely heterogeneous at a range of scales, from the microscopic (e.g., pore scale) to the macroscopic (e.g., field or larger scale). Some of these heterogeneities can lead to a preferential flow process that macroscopically is very difficult to capture with the standard Richards equation. One obvious example of preferential flow is the rapid movement of water and dissolved solutes through macropores (e.g., between soil aggregates, or created by earthworms or decayed root channels) or rock fractures, with much of the water bypassing (short-circuiting) the soil or rock matrix. However, many other causes of preferential flow exist, such as flow instabilities caused by soil textural changes or water repellency (Hendrickx and Flury, 2001; Šimunek ˚ et al. 2003; Ritsema and Dekker 2005), and lateral funneling of water due to inclined or other textural boundaries (e.g., Kung 1990). Alternative ways of modeling preferential flow are discussed in a later section. Here we first focus on the traditional approach for uniform flow as described with the Richards equation.
22.2.1 Mass Balance Equation Water flow in variably saturated rigid porous media (soils) is usually formulated in terms of a mass balance equation of the form: ∂qi ∂θ =− −S (22.1) ∂t ∂xi where θ is the volumetric water content [L3 L−3 ], t is time [T], xi is the spatial coordinate [L], qi is the volumetric flux density [LT−1 ], and S is a general sink/source term [L3 L−3 T−1 ], for example, to account for root water uptake (transpiration). Equation 22.1 is often referred to as the mass conservation equation or the continuity equation. The mass balance equation in general states that the change in the water content (storage) in a given volume is due to spatial changes in the water flux (i.e., fluxes in and out of some unit volume of soil ) and possible sinks or sources within that volume. The mass balance equation must be combined with one or several equations describing the volumetric flux density (q) to produce the governing equation for variably saturated flow. The formulations of the governing equations for different types of flow (uniform and preferential flow) are all based on this continuity equation.
22.2.2 Uniform Flow Uniform flow in soils is described using the Darcy–Buckingham equation: ∂h + KizA qi = −K (h) KijA ∂xj
(22.2)
where K is the unsaturated hydraulic conductivity [LT−1 ], and KijA are components of a dimensionless anisotropy tensor KA (which reduces to the unit matrix when the medium is isotropic). The Darcy– Buckingham equation is formally similar to Darcy’s equation, except that the proportionality constant (i.e., the unsaturated hydraulic conductivity) in the Darcy–Buckingham equation is a nonlinear function of the pressure head (or water content), while K (h) in Darcy’s equation is a constant equal to the saturated hydraulic conductivity, Ks (e.g., see discussion by Narasimhan [2005]). Combining the mass balance Equation 22.1 with the Darcy–Buckingham Equation 22.2 leads to the general Richards equation (Richards, 1931) ∂ ∂h ∂θ (h) = + KizA − S(h) K (h) KijA ∂t ∂xi ∂xj
(22.3)
This partial differential equation is the equation governing variably saturated flow in the vadose zone. Because of its strongly nonlinear makeup, only a relatively few simplified analytical solutions can be derived. Most practical applications of Equation 22.3 require a numerical solution, which can be obtained
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using a variety of numerical methods such as finite differences or finite elements (Section 22.5a). Equation 22.3 is generally referred to as the mixed form of the Richards equation as it contains two dependent variables, that is, the water content and the pressure head. Various other formulations of the Richards equation are possible.
22.2.3 Preferential Flow Increasing evidence exists that variably saturated flow in many field soils is not consistent with the uniform flow pattern typically predicted with the Richards equations (Flury et al., 1994; Hendrickx and Flury, 2001). This is due to the presence of macropores, fractures, or other structural voids or biological channels through which water and solutes may move preferentially, while bypassing a large part of the matrix pore-space. Preferential flow and transport processes are probably the most frustrating in terms of hampering accurate predictions of contaminant transport in soils and fractured rocks. Contrary to uniform flow, preferential flow results in irregular wetting of the soil profile as a direct consequence of water moving faster in certain parts of the soil profile than in others. Hendrickx and Flury (2001) defined preferential flow as constituting all phenomena where water and solutes move along certain pathways, while bypassing a fraction of the porous matrix. Water and solutes for these reasons can propagate quickly to far greater depths, and much faster, than would be predicted with the Richards equation describing uniform flow. The most important causes of preferential flow are the presence of macropores and other structural features, development of flow instabilities (i.e., fingering) caused by profile heterogeneities or water repellency (Hendrickx et al., 1993), and funneling of flow due to the presence of sloping soil layers that redirect downward water flow. While the latter two processes (i.e., flow instability and funneling) are usually caused by textural differences and other factors at scales significantly larger than the pore scale, macropore flow and transport are usually generated at the pore or slightly larger scales, including scales where soil structure first manifests itself (i.e., the pedon scale) (Šimunek ˚ et al., 2003). Uniform flow in granular soils and preferential flow in structured media (both macroporous soils and fractured rocks) can be described using a variety of single-porosity, dual-porosity, dual-permeability, multi-porosity, and multi-permeability models (Richards, 1931; Pruess and Wang, 1987; Gerke and van Genuchten, 1993a; Gwo et al., 1995; Jarvis, 1998; Šimunek ˚ et al., 2003, 2005). While single-porosity models assume that a single pore system exists that is fully accessible to both water and solute, dualporosity and dual-permeability models both assume that the porous medium consists of two interacting pore regions, one associated with the inter-aggregate, macropore, or fracture system, and one comprising the micropores (or intra-aggregate pores) inside soil aggregates or the rock matrix. Whereas dual-porosity models assume that water in the matrix is stagnant, dual-permeability models allow also for water flow within the soil or rock matrix. Figure 22.2 illustrates a hierarchy of conceptual formulations that can be used to model variably saturated water flow and solute transport in soils. The simplest formulation (Figure 22.2a) is a singleporosity (equivalent porous medium) model applicable to uniform flow in soils. The other models apply in some form or another to preferential flow or transport. Of these, the dual-porosity model of Figure 22.2c assumes the presence of two pore regions, with water in one region being immobile and in the other region mobile. This model allows the exchange of both water and solute between the two regions (Šimunek ˚ et al., 2003). Conceptually, this formulation views the soil as consisting of a soil matrix containing grains/aggregates with a certain internal microporosity (intra-aggregate porosity) and a macropore or fracture domain containing the larger pores (inter-aggregate porosity). While water and solutes are allowed to move through the larger pores and fractures, they can also flow in and out of aggregates. By comparison, the intra-aggregate pores represent immobile pockets that can exchange, retain, and store water and solutes, but do not contribute to advective (or convective) flow. Models that assume mobile–immobile flow regions (Figure 22.2b) are conceptually somewhere in between the singleand dual-porosity models. While these models assume that water will move similarly as in the uniform flow models, the liquid phase for purposes of modeling solute transport is divided in terms of mobile and
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22-6
The Handbook of Groundwater Engineering (a) Uniform flow
(b) Mobile-immobile water
Water
Water
(c) Dual-porosity Water Mobile Immob.
Solute Solute
Immob.
Mobile
= im + mo
Solute Immob.
Mobile
= im + mo
(d) Dual-permeability Water Slow
Fast
Solute Slow
Fast
= m + f
FIGURE 22.2 Conceptual models of water flow and solute transport (θ is the water content, θmo and θim in (b) and (c) are water contents in the mobile and immobile flow regions, respectively, and θm and θf in (d) are water contents in the matrix and macropore (fracture) regions, respectively).
immobile fractions, with solutes allowed to move by advection and dispersion only in the mobile fraction and between the two pore regions. This model has long been applied to solute transport studies (e.g., van Genuchten and Wierenga, 1976). Finally, dual-permeability models (Figure 22.2d) are those in which water can move in both the interand intra-aggregate pore regions (and matrix and fracture domains). These models in various forms are now also becoming increasingly popular (Pruess and Wang, 1987; Gerke and van Genuchten, 1993a; Jarvis, 1994; Pruess, 2004). Available dual-permeability models differ mainly in how they implement water flow in and between the two pore regions (Šimunek ˚ et al., 2003). Approaches to calculating water flow in the macropores or inter-aggregate pores range from those invoking Poiseuille’s equation (Ahuja and Hebson, 1992), the Green and Ampt or Philip infiltration models (Ahuja and Hebson, 1992), the kinematic wave equation (Germann, 1985; Germann and Beven, 1985; Jarvis, 1994), and the Richards equation (Gerke and van Genuchten, 1993a). Multi-porosity and multi-permeability models (not shown in Figure 22.2) are based on the same concept as dual-porosity and dual-permeability models, but include additional interacting pore regions (e.g., Gwo et al., 1995; Hutson and Wagenet, 1995). These models can be readily simplified to the dual-porosity/permeability approaches. Recent reviews of preferential flow processes and available mathematical models are provided by Hendrickx and Flury (2001) and Šimunek ˚ et al. (2003), respectively. 22.2.3.1 Dual-Porosity Models Dual-porosity models assume that water flow is restricted to macropores (or inter-aggregate pores and fractures), and that water in the matrix (intra-aggregate pores or the rock matrix) does not move at all. This conceptualization leads to two-region type flow and transport models (van Genuchten and Wierenga, 1976) that partition the liquid phase into mobile (flowing, inter-aggregate), θmo , and immobile (stagnant, intra-aggregate), θim , regions [L3 L−3 ]: θ = θmo + θim (22.4) The dual-porosity formulation for water flow can be based on a mixed formulation of the Richards Equation 22.3 to describe water flow in the macropores (the preferential flow pathways) and a mass balance equation to describe moisture dynamics in the matrix as follows (Šimunek ˚ et al., 2003): ∂ ∂hmo ∂θmo (hmo ) = + KizA − Smo (hmo ) − w K (hmo ) KijA ∂t ∂xi ∂xj (22.5) ∂θim (him ) = −Sim (him ) + w ∂t
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where Sim and Smo are sink terms for both regions [T−1 ], and w is the transfer rate for water from the inter- to the intra-aggregate pores [T−1 ]. Several of the above dual-porosity features were recently included in the HYDRUS software packages (Šimunek ˚ et al., 2003, 2005). Examples of their application to a range of laboratory and field data involving transient flow and solute transport are given by Šimunek ˚ et al. (2001), Zhang et al. (2004), Köhne et al. (2004a, 2005), Kodešová et al. (2005), and Haws et al. (2005). 22.2.3.2 Dual-Permeability Models Different types of dual-permeability approaches may be used to describe flow and transport in structured media. While several models invoke similar governing equations for flow in the fracture and matrix regions, others use different formulations for the two regions. A typical example of the first approach is the work of Gerke and van Genuchten (1993a, 1996) who applied Richards equations to each of two pore regions. The flow equations for the macropore (fracture) (subscript f) and matrix (subscript m) pore systems in their approach are given by:
and
∂ w ∂θf (hf ) A ∂hf A = + Kiz Kf (hf ) Kij − Sf (hf ) − ∂t ∂xi ∂xj w
(22.6)
∂θm (hm ) ∂ w A ∂hm A = + Kiz Km (hm ) Kij − Sm (hm ) + ∂t ∂xi ∂xj 1−w
(22.7)
respectively, where w is the ratio of the volumes of the macropore (or fracture or inter-aggregrate) domain and the total soil system [−]. This approach is relatively complicated in that the model requires characterization of water retention and hydraulic conductivity functions (potentially of different form) for both pore regions, as well as the hydraulic conductivity function of the fracture–matrix interface. Note that the water contents θf and θm in Equation 22.6 and Equation 22.7 have different meanings than in Equation 22.5 where they represented water contents of the total pore space (i.e., θ = θmo + θim ), while here they refer to water contents of the two separate (fracture or matrix) pore domains such that θ = wθf + (1 − w)θm . 22.2.3.3 Mass Transfer The rate of exchange of water between the macropore and matrix regions, w , is a critical term in both the dual-porosity model (Equation 22.5) and the dual-permeability approach given by (Equation 22.6) and (Equation 22.7). Gerke and van Genuchten (1993a) assumed that the rate of exchange is proportional to the difference in pressure heads between the two pore regions: w = αw (hf − hm )
(22.8)
in which αw is a first-order mass transfer coefficient [T−1 ]. For porous media with well-defined geometries, the first-order mass transfer coefficient, αw , can be defined as follows (Gerke and van Genuchten, 1993b): αw =
β K a γw d2
(22.9)
where d is an effective diffusion path length [L] (i.e., half the aggregate width or half the fracture spacing), β is a shape factor that depends on the geometry [−], and γw (= 0.4) is a scaling factor [−] obtained by matching the results of the first-order approach at the half-time level of the cumulative infiltration curve to the numerical solution of the horizontal infiltration equation (Gerke and van Genuchten, 1993b). Several other approaches based on water content of relative saturation differences have also been used (Šimunek ˚ et al., 2003).
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The Handbook of Groundwater Engineering
22.3 Solute Transport Similarly, as shown in Equation 22.1 for water flow, mathematical formulations for solute transport are usually based on a mass balance equation of the form: ∂JTi ∂CT =− −φ ∂t ∂xi
(22.10)
where CT is the total concentration of chemical in all forms [ML−3 ], JTi is the total chemical mass flux density (mass flux per unit area per unit time) [ML−2 T−1 ], and φ is the rate of change of mass per unit volume by reactions or other sources (negative) or sinks (positive) such as plant uptake [ML−3 T−1 ]. In its most general interpretation, Equation 22.10 allows the chemical to reside in all three phases of the soil (i.e., gaseous, liquid, and solid), permits a broad range of transport mechanisms (including advective transport, diffusion, and hydrodynamic dispersion in both the liquid and gaseous phases), and facilitates any type of chemical reaction that leads to losses or gains in the total concentration. While the majority of chemicals are present only in the liquid and solid phases, and as such are transported in the vadose zone mostly only in and by water, some chemicals such as many organic contaminants, ammonium, and all fumigants, can have a significant portion of their mass in the gaseous phase and are hence subject to transport in the gaseous phase as well. The total chemical concentration can thus be defined as: CT = ρb s + θc + ag
(22.11)
where ρb is the bulk density [ML−3 ], θ is the volumetric water content [L3 L−3 ], a is the volumetric air content [L3 L−3 ], and s[MM−1 ], c[ML−3 ], and g [ML−3 ] are concentrations in the solid, liquid, and gaseous phases, respectively. The solid phase concentration represents solutes sorbed onto sorption sites of the solid phase, but can include solutes sorbed onto colloids attached to the solid phase or strained by the porous system, and solutes precipitated onto or into the solid phase. The reaction term φ of Equation 22.10 may represent various chemical or biological reactions that lead to a loss or gain of chemical in the soil system, such as radionuclide decay, biological degradation, and dissolution. In analytical and numerical models these reactions are most commonly expressed using zeroand first-order reaction rates as follows: φ = ρb sµs + θcµw + ag µg − ρb γs − θ γw − aγg
(22.12)
where µs , µw , and µg are first-order degradation constants in the solid, liquid, and gaseous phases [T−1 ], respectively, and γs [T−1 ], γw [ML−3 T−1 ], and γg [ML−3 T−1 ] are zero-order production constants in the solid, liquid, and gaseous phases, respectively.
22.3.1 Transport Processes When a solute is present in both the liquid and gaseous phase, then various transport processes in both of these phases may contribute to the total chemical mass flux: J T = Jl + J g
(22.13)
where Jl and Jg represent solute fluxes in the liquid and gaseous phases [ML−2 T−1 ], respectively. Note that in Equation 22.13, and further below, we omitted the subscript i accounting for the direction of flow. The three main processes that can be active in both the liquid and gaseous phase are molecular diffusion, hydrodynamic dispersion, and advection (often also called convection). The solute fluxes in the two phases
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22-9
are then the sum of fluxes due to these different processes: Jl = Jlc + Jld + Jlh Jg = Jgc + Jgd + Jgh
(22.14)
where the additional subscripts c, d, and h denote convection (or advection), molecular diffusion, and hydrodynamic dispersion, respectively. 22.3.1.1 Diffusion Diffusion is a result of the random motion of chemical molecules. This process causes a solute to move from a location with a higher concentration to a location with a lower concentration. Diffusive transport can be described using Fick’s law: ∂c ∂c = −θDls ∂z ∂z ∂g ∂g = −aξg (θ)Dgw = −aDgs ∂z ∂z
Jld = −θ ξl (θ)Dlw Jgd
(22.15)
where Dlw and Dgw are binary diffusion coefficients of the solute in water and gas [L2 T−1 ], respectively; Dls and Dgs are the effective diffusion coefficients in soil water and soil gas [L2 T−1 ], respectively; and ξl and ξg are tortuosity factors that account for the increased path lengths and decreased cross-sectional areas of the diffusing solute in both phases (Jury and Horton, 2004). As solute diffusion in soil water (air) is severely hampered by both air (water) and solid particles, the tortuosity factor increases strongly with water content (air content). Many empirical models have been suggested in the literature to account for the tortuosity (e.g., Moldrup et al., 1998). Among these, the most widely used model for the tortuosity factor is probably the equation of Millington and Quirk (1961) given by: ξl (θ) =
θ 7/3 θs2
(22.16)
where θs is the saturated water content (porosity) [L3 L−3 ]. A similar equation may be used for the tortuosity factor of the gaseous phase by replacing the water content with the air content. 22.3.1.2 Dispersion Dispersive transport of solutes results from the uneven distribution of water flow velocities within and between different soil pores (Figure 22.3). Dispersion can be derived from Newton’s law of viscosity which states that velocities within a single capillary tube follow a parabolic distribution, with the largest velocity in the middle of the pore and zero velocities at the walls (Figure 22.3a). Solutes in the middle of a pore, for this reason, will travel faster than solutes that are farther from the center. As the distribution of solute ions within a pore depends on their charge, as well as on the charge of pore walls, some solutes may move significantly faster than others. In some situations (i.e., for negatively charged anions in fine-textured soils, leading to anion exclusion), the solute may even travel faster than the average velocity of water (e.g., Nielsen et al., 1986). Using Poiseuille’s law, one can further show that velocities in a capillary tube depend strongly on the radius of the tube, and that the average velocity increases with the radius to the second power. As soils consist of pores of many different radii, solute fluxes in pores of different radii will be significantly different, with some solutes again traveling faster than others (Figure 22.3b). The above pore-scale dispersion processes lead to an overall (macroscopic) hydrodynamic dispersion process that mathematically can be described using Fick’s law in the same way as molecular diffusion, that is, ∂c ∂c ∂c = −θ λv = −λq (22.17) Jlh = −θDlh ∂z ∂z ∂z
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22-10
The Handbook of Groundwater Engineering (a)
(b)
R
0
C=0
C = C0
–R Velocity
FIGURE 22.3 system (b).
Distribution of velocities in a single capillary (a) and distribution of velocities in a more complex pore
where Dlh is the hydrodynamic dispersion coefficient [L2 T−1 ], v is the average pore-water velocity [LT−1 ], and λ is the dispersivity [L]. The dispersion coefficient in one-dimensional systems has been found to be approximately proportional to the average pore-water velocity, with the proportionality constant generally referred as the (longitudinal) dispersivity (Biggar and Nielsen, 1967). The discussion above holds for onedimensional transport; multi-dimensional applications require a more complicated dispersion tensor involving longitudinal and transverse dispersivities (e.g., Bear, 1972). Dispersivity is a transport property that is relatively difficult to measure experimentally. Estimates are usually obtained by fitting measured breakthrough curves with analytical solutions of the advection– dispersion equation (discussed further below). The dispersivity often changes with the distance over which solute travels. Values of the longitudinal dispersivity typically range from about 1 cm for packed laboratory columns, to about 5 or 10 cm for field soils. Longitudinal dispersivities can be significantly larger (on the order of hundreds of meters) for regional groundwater transport problems (Gelhar et al., 1985). If no other information is available, a good first approximation is to use a value of one-tenth of the transport distance for the longitudinal dispersivity (e.g., Anderson, 1984), and a value of one-hundreds of the transport distance for the transverse dispersivity. 22.3.1.3 Advection Advective transport refers to solute being transported with the moving fluid, either in the liquid phase (Jlc ) or the gas phase (Jgc ), that is, Jlc = qc Jgc = Jg g
(22.18)
where Jg is the gaseous flux density [LT−1 ]. Advective transport in the gaseous phase is often neglected as its contribution in many applications is negligible compared to gaseous diffusion. The total solute flux density in both the liquid and gaseous phases is obtained by incorporating contributions from the various transport processes into Equation 22.14 to obtain Jl = qc − θDls Jg =
∂c ∂c ∂c − θDlh = qc − θDe ∂z ∂z ∂z
∂g −aDgs
(22.19)
∂z
where De is the effective dispersion coefficient [L2 T−1 ] that accounts for both diffusion and hydrodynamic dispersion. Dispersion in most subsurface transport problems dominates molecular diffusion in the liquid phase, except when the fluid velocity becomes relatively small or negligible. Notice that Equation 22.19 neglects advective and dispersive transport in the gaseous phase.
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22.3.2 Advection–Dispersion Equations 22.3.2.1 Transport Equations The equation governing transport of dissolved solutes in the vadose zone is obtained by combining the solute mass balance (Equation 22.10) with equations defining the total concentration of the chemical (Equation 22.11) and the solute flux density (Equation 22.19) to give ∂ ∂(ρb s + θc + ag ) = ∂t ∂xi
∂c θDeij ∂xj
∂ + ∂xi
s aDgij
∂g ∂xj
∂ qi c −φ − ∂xi
(22.20)
s are Notice that this equation is again written for multidimensional transport, and that Deij and Dgij thus components of the effective dispersion tensor in the liquid phase and a diffusion tensor in the gaseous phase [L2 T−1 ], respectively. Many different variants of Equation 22.20 can be found in the literature. For example, for one-dimensional transport of nonvolatile solutes, the equation simplifies to
∂(θRc) ∂ ∂(ρb s + θc) = = ∂t ∂t ∂z
θDe
∂c ∂z
−
∂(qc) −φ ∂z
(22.21)
where q is the vertical water flux density [LT−1 ] and R is the retardation factor [−] R =1+
ρb ds(c) θ dc
(22.22)
For transport of inert, nonadsorbing solutes during steady-state water flow we obtain ∂c ∂ 2c ∂c = De 2 − v ∂t ∂z ∂z
(22.23)
The above equations are usually referred to as advection–dispersion equations (ADEs). 22.3.2.2 Linear and Nonlinear Sorption The ADE given by Equation 22.20 contains three unknown concentrations (those for the liquid, solid, and gaseous phases), while Equation 22.21 contains two unknowns. To be able to solve these equations, additional information is needed that somehow relates these concentrations to each other. The most common way is to assume instantaneous sorption and to use adsorption isotherms to relate the liquid and adsorbed concentrations. The simplest form of the adsorption isotherm is the linear isotherm given by s = Kd c
(22.24)
where Kd is the distribution coefficient [L3 M−1 ]. One may verify that substitution of this equation into Equation 22.22 leads to a constant value for the retardation factor (i.e., R = 1 + ρb Kd /θ). While the use of a linear isotherm greatly simplifies the mathematical description of solute transport, sorption and exchange are generally nonlinear and most often depend also on the presence of competing species in the soil solution. The solute retardation factor for nonlinear adsorption is not constant, as is the case for linear adsorption, but changes as a function of concentration. Many models have been used in the past to describe nonlinear sorption. The most commonly used nonlinear sorption models are those by Freundlich (1909) and Langmuir (1918) given by: s = Kf c β s=
Kd c 1 + ηc
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(22.25) (22.26)
22-12
1
(b)
1.4
0 0.5 0.75 1 1.5 2 2.5 3 5
0.9
1.2 1
Sorbed concentration [M/M]
Sorbed concentration [M/M]
(a)
The Handbook of Groundwater Engineering
0.5 0.75 1 1.5 2 2.5 3 5
0.8 0.6 Increasing 0.4 0.2
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
0 0
0.5 1 Dissolved concentration [M/L3]
Increasing
0
1.5
0
0.5
1
1.5
Dissolved concentration [M/L3]
FIGURE 22.4 Plots of the Freundlich adsorption isotherm given by (22.25), with Kd = 1 and β given in the caption (a), and the Langmuir adsorption isotherm given by (22.26), with Kd = 1 and η given in the caption (b).
TABLE 22.1
Equilibrium Adsorption Equations adapted from van Genuchten and Šimunek ˚ (1996)
Equation
Model
s = k1 c + k2 s= s=
k1 c k3 1 + k2 c k3 k1 c k3 c + 1 + k2 c 1 + k4 c
s = k1 c c s=
k2 /k3
k1 c √ 1 + k 2 c + k3 c
Reference
Linear
Lapidus and Amundson (1952) Lindstrom et al. (1967)
Freundlich–Langmuir
Sips (1950), Šimunek ˚ et al. (1994, 2005)
Double Langmuir
Shapiro and Fried (1959)
Extended Freundlich
Sibbesen (1981)
Gunary
Gunary (1970)
s = k1 c k2 − k3
Fitter–Sutton
Fitter and Sutton (1975)
s = k1 {1 − [1 + k2 c k3 ]k4 }
Barry
Barry (1992)
Temkin
Bache and Williams (1971)
s=
RT ln(k2 c) k1
s = k1 c exp(−2k2 s) s = c[c + k1 (cT − c) exp{k2 (cT − 2c)}]−1 sT
Lindstrom et al. (1971) van Genuchten et al. (1974) Modified Kielland
Lai and Jurinak (1971)
k1 , k2 , k3 , k4 : empirical constants; R: universal gas constant; T : absolute temperature; cT : maximum solute concentration; sT : maximum adsorbed concentration. Source: Adapted from van Genuchten, M.Th. and Šimunek, J. In P.E. Rijtema and V. Eliáš (Eds.), Regional Approaches to Water Pollution in the Environment, NATO ASI Series: 2. Environment. Kluwer, Dordrecht, The Netherlands, pp. 139–172, 1996.
respectively, where Kf [M−β L3β ] and β [−] are coefficients in the Freundlich isotherm, and η [L3 M−1 ] is a coefficient in the Langmuir isotherm. Examples of linear, Freundlich and Langmuir adsorption isotherms are given in Figure 22.4. Table 22.1 lists a range of linear and other sorption models frequently used in solute transport studies.
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22.3.2.3 Volatilization Volatilization is increasingly recognized as an important process affecting the fate of many organic chemicals, including pesticides, fumigants, and explosives in field soils (Jury et al., 1983, 1984; Glotfelty and Schomburg, 1989). While many organic pollutants dissipate by means of chemical and microbiological degradation, volatilization may be equally important for volatile substances, such as certain pesticides. The volatility of pesticides is influenced by many factors, including the physicochemical properties of the chemical itself as well as such environmental variables as temperature and solar energy. Even though only a small fraction of a pesticide may exist in the gas phase, air-phase diffusion rates can sometimes be comparable to liquid-phase diffusion as gas-phase diffusion is about four orders of magnitude greater than liquid phase diffusion. The importance of gaseous diffusion relative to other transport processes depends also on the climate. For example, while transport of MTBE (gasoline oxygenate) is generally dominated by liquid advection in humid areas, gaseous diffusion may be equally or more important in arid climates; this even though only about 2% of MTBE may be in the gas phase. The general transport equation given by Equation 22.20 can be simplified considerably when assuming linear equilibrium sorption and volatilization such that the adsorbed (s) and gaseous (g ) concentrations are linearly related to the solution concentration (c) through the distribution coefficients, Kd in (22.24) and KH , that is, (22.27) g = KH c respectively, where KH is the dimensionless Henry’s constant [−]. Equation 22.20 for one-dimensional transport then has the form: ∂ ∂(ρb Kd + θ + aKH )c = ∂t ∂z or
∂c θDe ∂z
∂ ∂θRc = ∂t ∂z
∂c θDE ∂z
∂ + ∂z
∂c aDgs KH
∂z
∂ qc −φ − ∂x
∂ qc −φ − ∂x
(22.28)
(22.29)
where the retardation factor R [−] and the effective dispersion coefficient DE [L2 T−1 ] are defined as follows: ρb Kd + aKH θ aDgs KH D E = De + θ
R =1+
(22.30)
Jury et al. (1983, 1984) provided for many organic chemicals their distribution coefficients Kd , Henry’s constants KH , and calculated percent mass present in each phase.
22.3.3 Nonequilibrium Transport As equilibrium solute transport models often fail to describe experimental data, a large number of diffusion-controlled physical nonequilibrium and chemical-kinetic models have been proposed and used to describe the transport of both non-adsorbing and adsorbing chemicals. Attempts to model nonequilibrium transport usually involve relatively simple first-order rate equations. Nonequilibrium models have used the assumptions of two-region (dual-porosity) type transport involving solute exchange between mobile and immobile liquid transport regions, and one-, two- or multi-site sorption formulations (e.g., Nielsen et al., 1986; Brusseau, 1999). Models simulating the transport of particle-type pollutants, such as colloids, viruses, and bacteria, often also use first-order rate equations to describe such processes as attachment, detachment, and straining. Nonequilibrium models generally have resulted in better descriptions of observed laboratory and field transport data, in part by providing additional degrees of freedom for fitting observed concentration distributions.
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The Handbook of Groundwater Engineering
22.3.3.1 Physical Nonequilibrium 22.3.3.1.1 Dual-Porosity and Mobile–Immobile Water Models The two-region transport model (Figures 22.2b and Figure 22.2c) assumes that the liquid phase can be partitioned into distinct mobile (flowing) and immobile (stagnant) liquid pore regions, and that solute exchange between the two liquid regions can be modeled as a first-order exchange process. Using the same notation as before, the two-region solute transport model is given by (van Genuchten and Wagenet, 1989; Toride et al., 1993): ∂f ρsmo ∂ ∂θmo cmo + = ∂t ∂t ∂z
θmo Dmo
∂cmo ∂z
−
∂qcmo − φmo − s ∂z
∂(1 − f )ρsim ∂θim cim + = −φim + s ∂t ∂t
(22.31)
for the mobile (macropores, subscript mo) and immobile (matrix, subscript im) domains, respectively, where f is the dimensionless fraction of sorption sites in contact with the mobile water [−], φmo and φim are reactions in the mobile and immobile domains [ML−3 T−1 ], respectively, and s is the solute transfer rate between the two regions [ML−3 T−1 ]. Notice that the same Equation 22.31 can be used to describe solute transport using both the mobile–immobile and dual-porosity models shown in Figures 22.2b and Figure 22.2c, respectively. 22.3.3.1.2 Dual-Permeability Model Analogous to Equations 22.6 and Equation 22.7 for water flow, the dual-permeability formulation for solute transport can be based on advection–dispersion type equations for transport in both the fracture and matrix regions as follows (Gerke and van Genuchten, 1993a): ∂ρsf ∂ ∂θf cf + = ∂t ∂t ∂z ∂ρsm ∂θm cm ∂ + = ∂t ∂t ∂z
∂cf θf D f ∂z
θ m Dm
∂cm ∂z
−
s ∂qf cf − φf − ∂z w
(22.32)
−
s ∂qm cm − φm + ∂z 1−w
(22.33)
where the subscript f and m refer to the macroporous (fracture) and matrix pore systems, respectively; φf and φm represent sources or sinks in the macroporous and matrix domains [ML−3 T−1 ], respectively; and w is the ratio of the volumes of the macropore-domain (inter-aggregate) and the total soil systems [−]. Equation 22.32 and Equation 22.33 assume complete advective–dispersive type transport descriptions for both the fractures and the matrix. Several authors simplified transport in the macropore domain, for example, by considering only piston displacement of solutes (Ahuja and Hebson, 1992; Jarvis, 1994). 22.3.3.1.3 Mass Transfer The transfer rate, s , in Equation 22.31 for solutes between the mobile and immobile domains in the dual-porosity models can be given as the sum of diffusive and advective fluxes, and can be written as s = αs (cmo − cim ) + w c ∗
(22.34)
where c ∗ is equal to cmo for w > 0 and cim for w < 0, and αs is the first-order solute mass transfer coefficient [T−1 ]. Notice that the advection term of Equation 22.34 is equal to zero for the mobile– immobile model (Figure 22.2b) as the immobile water content in this model is assumed to be constant. However, w may have a nonzero value in the dual-porosity model depicted in Figure 22.2c. The transfer rate, s , in Equation 22.32 and Equation 22.33 for solutes between the fracture and matrix regions is also usually given as the sum of diffusive and advective fluxes as follows (e.g., Gerke and van Genuchten, 1996): (22.35) s = αs (1 − wm )(cf − cm ) + w c ∗
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in which the mass transfer coefficient, αs [T−1 ], is of the form: αs =
β Da d2
(22.36)
where Da is an effective diffusion coefficient [L2 T−1 ] representing the diffusion properties of the fracture– matrix interface. Still more sophisticated models for physical nonequilibrium transport may be formulated. For example, Pot et al. (2005) and Köhne et al. (2006) considered a dual-permeability model that divides the matrix domain further into mobile and immobile subregions and used this model successfully to simulate bromide transport in laboratory soil columns at different flow rates or for transient flow conditions, respectively. 22.3.3.2 Chemical Nonequilibrium 22.3.3.2.1 Kinetic Sorption Models An alternative to expressing sorption as an instantaneous process using algebraic equations (e.g., Equation 22.24, Equation 22.25 or Equation 22.26) is to describe the kinetics of the reaction using ordinary differential equations. The most popular and simplest formulation of a chemically controlled kinetic reaction arises when first-order linear kinetics is assumed: ∂s = αk (Kd c − s) ∂t
(22.37)
where αk is a first-order kinetic rate coefficient [T−1 ]. Several other nonequilibrium adsorption expressions were also used in the past (see Table 2 in van Genuchten and Šimunek, ˚ 1996). Models based on this and other kinetic expressions are often referred to as one-site sorption models. As transport models assuming chemically controlled nonequilibrium (one-site sorption) generally did not result in significant improvements in their predictive capabilities when used to analyze laboratory column experiments, the one-site first-order kinetic model was further expanded into a two-site sorption concept that divides the available sorption sites into two fractions (Selim et al., 1976; van Genuchten and Wagenet, 1989). In this approach, sorption on one fraction (type-1 sites) is assumed to be instantaneous while sorption on the remaining (type-2) sites is considered to be time-dependent. Assuming a linear sorption process, the two-site transport model is given by (van Genuchten and Wagenet, 1989) ∂ ∂sk ∂(f ρb Kd + θ )c + ρb = ∂t ∂t ∂z
∂c θDe ∂z
∂ qc − φe − ∂z
∂sk = αk [(1 − f )Kd c − sk ] − φk ∂t
(22.38)
where f is the fraction of exchange sites assumed to be at equilibrium [−], φe [ML−3 T−1 ] and φk [MM−1 T−1 ] are reactions in the equilibrium and nonequilibrium phases, respectively, and the subscript k refers to kinetic (type-2) sorption sites. Note that if f = 0, the two-site sorption model reduces to the one-site fully kinetic sorption model (i.e., when only type-2 kinetic sites are present). On the other hand, if f = 1, the two-site sorption model reduces to the equilibrium sorption model for which only type-1 equilibrium sites are present. 22.3.3.2.2 Attachment/Detachment Models Additionally, transport equations may include provisions for kinetic attachment/detachment of solutes to the solid phase, thus permitting simulations of the transport of colloids, viruses, and bacteria. The transport of these constituents is generally more complex than that of other solutes in that they are affected by such additional processes as filtration, straining, sedimentation, adsorption and desorption, growth, and inactivation. Virus, colloid, and bacteria transport and fate models commonly employ a
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modified form of the ADE, in which the kinetic sorption equations are replaced with equations describing kinetics of colloid attachment and detachment as follows: ρ
∂s = θka ψc − kd ρs ∂t
(22.39)
where c is the (colloid, virus, bacteria) concentration in the aqueous phase [Nc L−3 ], s is the solid phase (colloid, virus, bacteria) concentration [Nc M−1 ], in which Nc is a number of (colloid) particles, ka is the first-order deposition (attachment) coefficient [T−1 ], kd is the first-order entrainment (detachment) coefficient [T−1 ], and ψ is a dimensionless colloid retention function [−]. The attachment and detachment coefficients in Equation 22.39 have been found to strongly depend upon water content, with attachment significantly increasing as the water content decreases. To simulate reductions in the attachment coefficient due to filling of favorable sorption sites, ψ is sometimes assumed to decrease with increasing colloid mass retention. A Langmuirian dynamics (Adamczyk et al., 1994) equation has been proposed for ψ to describe this blocking phenomenon: ψ=
s smax − s =1− smax smax
(22.40)
in which smax is the maximum solid phase concentration [Nc M−1 ]. A similar equation as Equation 22.39 was used by Bradford et al. (2003, 2004) to simulate the process of pore straining. Bradford et al. (2003, 2004) hypothesized that the influence of straining and attachment processes on colloid retention should be separated into two distinct components. They suggested the following depth-dependent blocking coefficient for the straining process: ψ=
dc + z − z0 dc
−β (22.41)
where dc is the diameter of the sand grains [L], z0 is the coordinate of the location where the straining process starts [L] (the surface of the soil profile, or interface between soil layers), and β is an empirical factor (Bradford et al., 2003) [−]. The attachment coefficient is often calculated using filtration theory (Logan et al., 1995), a quasiempirical formulation in terms of the median grain diameter of the porous medium (often termed the collector), the pore-water velocity, and collector and collision (or sticking) efficiencies accounting for colloid removal due to diffusion, interception, and gravitational sedimentation (Rajagopalan and Tien, 1976; Logan et al., 1995): 3(1 − θ ) ηαv (22.42) ka = 2dc where dc is the diameter of the sand grains [L], α is the sticking efficiency (ratio of the rate of particles that stick to a collector to the rate they strike the collector) [−], v is the pore-water velocity [LT−1 ], and η is the single-collector efficiency [−]. In related studies, Schijven and Hassanizadeh (2000) and Schijven and Šimunek ˚ (2002) used a twosite sorption model based on two equations (22.39) to successfully describe virus transport at both the laboratory and field scale. Their model assumed that the sorption sites on the solid phase can be divided into two fractions with different properties and various attachment and detachment rate coefficients. 22.3.3.3 Colloid-Facilitated Solute Transport There is an increasing evidence that many contaminants, including radionuclides (Von Gunten et al., 1988; Noell et al., 1998), pesticides (Vinten et al., 1983; Kan and Tomson, 1990, Lindqvist and Enfield, 1992), heavy metals (Grolimund et al., 1996), viruses, pharmaceuticals (Tolls, 2001; Thiele-Bruhn, 2003), hormones (Hanselman et al., 2003), and other contaminants (Magee et al., 1991; Mansfeldt et al., 2004) are transported in the subsurface not only with moving water, but also sorbed to mobile colloids. As many
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colloids and microbes are negatively charged and thus electrostatically repelled by negatively charged solid surfaces, which may lead to an anion exclusion process, their transport may be slightly enhanced relative to fluid flow. Size exclusion may similarly enhance the advective transport of colloids by limiting their presence and mobility to the larger pores (e.g., Bradford et al., 2003). The transport of contaminants sorbed to mobile colloids can thus significantly accelerate their transport relative to more standard advection– transport descriptions. Colloid-facilitated transport is a relatively complicated process that requires knowledge of water flow, colloid transport, dissolved contaminant transport, and colloid-contaminant interaction. Transport and mass balance equations, hence, must be formulated not only for water flow and colloid transport, but also for the total contaminant, for contaminant sorbed kinetically or instantaneously to the solid phase, and for contaminant sorbed to mobile colloids, to colloids attached to the soil solid phase, and to colloids accumulating at the air–water interface. Development of such a model is beyond the scope of this chapter. We refer interested readers to several manuscripts dealing with this topic: Mills et al. (1991), Corapcioglu and Jiang (1993), Corapcioglu and Kim (1995), Jiang and Corapcioglu (1993), Noell et al. (1998), Saiers et al. (1996), Saiers and Hornberger (1996), van de Weerd et al. (1998), and van Genuchten and Šimunek ˚ (2004).
22.3.4 Stochastic Models Much evidence suggests that solutions of classical solute transport models, no matter how refined to include the most relevant chemical and microbiological processes and soil properties, often still fail to accurately describe transport processes in most natural field soils. A major reason for this failure is the fact that the subsurface environment is overwhelmingly heterogeneous. Heterogeneity occurs at a hierarchy of spatial and time scales (Wheatcraft and Cushman, 1991), ranging from microscopic scales involving timedependent chemical sorption and precipitation/dissolution reactions, to intermediate scales involving the preferential movement of water and chemicals through macropores or fractures, and to much larger scales involving the spatial variability of soils across the landscape. Subsurface heterogeneity can be addressed in terms of process-based descriptions which attempt to consider the effects of heterogeneity at one or several scales. It can also be addressed using stochastic approaches that incorporate certain assumptions about the transport process in the heterogeneous system (e.g., Sposito and Barry, 1987; Dagan, 1989). In this section we briefly review several stochastic transport approaches, notably those using stream tube models and the transfer function approach. 22.3.4.1 Stream Tube Models The downward movement of chemicals from the soil surface to an underlying aquifer may be described stochastically by viewing the field as a series of independent vertical columns, often referred to as “stream tubes” (Figure 22.5), while solute mixing between the stream tubes is assumed to be negligible. Transport V3 V2
Vn Vn –1
V1
FIGURE 22.5 Schematic illustration of the stream tube model (Toride et al., 1995).
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in each tube may be described deterministically with the standard ADE, or modifications thereof to include additional geochemical and microbiological processes. Transport at the field scale is then implemented by considering the column parameters as realizations of a stochastic process, having a random distribution (Toride et al., 1995). Early examples are by Dagan and Bresler (1979) and Bresler and Dagan (1979) who assumed that the saturated hydraulic conductivity had a lognormal distribution. The stream tube model was implemented into the CXTFIT 2.0 program (Toride et al., 1995) for a variety of transport scenarios in which the pore-water velocity in combination with either the dispersion coefficient, De , the distribution coefficient for linear adsorption, Kd , or the first-order rate coefficient for nonequilibrium adsorption, αk , are stochastic variables (Toride et al., 1995). 22.3.4.2 Transfer Function Models Jury (1982) developed an alternative formulation for solute transport at the field scale, called the transfer function model. This model was developed based on two main assumptions about the soil system: (a) the solute transport is a linear process, and (b) the solute travel time probabilities do not change over time. These two assumptions lead to the following transfer function equation that relates the solute concentration at the outflow end of the system with the time-dependent solute input into the system: t cout (t ) =
cin (t − t )f (t ) dt
(22.43)
0
The outflow at time t , cout (t ) [ML−3 ], consists of the superposition of solute added at all times less than t , cin (t − t ) [ML−3 ], weighted by its travel-time probability density function (pdf) f (t ) [T−1 ] (Jury and Horton, 2004). One important advantage of the transfer function approach is that it does not require knowledge of the various transport processes within the flow domain. Different model distribution functions can be used for the travel-time probability density function f (t ) in Equation 22.43. Most commonly used (Jury and Sposito, 1985) are the Fickian probability density function L (L − vt )2 f (t ) = √ exp − 4Dt 2 πDt 3
(22.44)
1 (ln t − µ)2 f (t ) = √ exp 2σ 2 2π σ t
(22.45)
and the lognormal distribution
where D[L2 T−1 ], v[LT−1 ], µ , and σ are model parameters, and L is the distance from the inflow boundary to the outflow boundary [L]. To accommodate conditions when the water flux through the soil system is not constant, Jury (1982) expressed the travel-time pdf as a function of the cumulative net applied water I : t I=
q(t ) dt
(22.46)
0
leading to the following transfer function equation: I (t ) cout (I ) = cin (I − I )f (I ) dI 0
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22.3.5 Multicomponent Reactive Solute Transport The various mathematical descriptions of solute transport presented thus far all considered solutes that would move independently of other solutes in the subsurface. In reality, the transport of reactive contaminants is more often than not affected by many often interactive physico-chemical and biological processes. Simulating these processes requires a more comprehensive approach that couples the physical processes of water flow and advective–dispersive transport with a range of biogeochemical processes. The soil solution is always a mixture of many ions that may be involved in mutually dependent chemical processes, such as complexation reactions, cation exchange, precipitation–dissolution, sorption– desorption, volatilization, redox reactions, and degradation, among other reactions (Šimunek ˚ and Valocchi, 2002). The transport and transformation of many chemical contaminants is further mediated by subsurface aerobic or anaerobic bacteria. Bacteria catalyze redox reactions in which organic compounds (e.g., hydrocarbons) act as the electron donor and inorganic substances (oxygen, nitrate, sulfate, or metal oxides) as the electron acceptor. By catalyzing such reactions, bacteria gain energy and organic carbon to produce new biomass. These and related processes can be simulated using integrated reactive transport codes that couple the physical processes of water flow and advective–dispersive solute transport with a range of biogeochemical processes. This section reviews various modeling approaches for such multicomponent transport systems. 22.3.5.1 Components and Reversible Chemical Reactions Multi-species chemical equilibrium systems are generally defined in terms of components. Components may be defined as a set of linearly independent chemical entities such that every species in the system can be uniquely represented as the product of a reaction involving only these components (Westall et al., 1976). As a typical example, the chemical species CaCO03 Ca2+ + CO2− ⇔ CaCO03 3
(22.48)
consists of the two components Ca2+ and CO2− 3 . Reversible chemical reaction processes in equilibrium systems are most often represented using mass action laws that relate thermodynamic equilibrium constants to activities (the thermodynamic effective concentration) of the reactants and products (Mangold and Tsang, 1991; Appelo and Postma, 1993; Bethke, 1996). For example, the reaction bB + cC ⇔ dD + eE
(22.49)
where b and c are the number of moles of substances B and C that react to yield d and e moles of products D and E, is represented at equilibrium by the law of mass action
K =
aDd aEe aBb aCc
(22.50)
where K is a temperature-dependent thermodynamic equilibrium constant, and ai is the ion activity, being defined as the product of the activity coefficient ( γi ) and the ion molality (mi ), that is, ai = γi mi . Single-ion activity coefficients may be calculated using either the Davies equation, an extended version of the Debye–Hückel equation (Truesdell and Jones, 1974), or by means of Pitzer expressions (Pitzer, 1979). Equation 22.50 can be used to describe all of the major chemical processes, such as aqueous complexation, sorption, precipitation–dissolution, and acid–base and redox reactions, provided that the local chemical equilibrium assumption is valid (Šimunek ˚ and Valocchi, 2002).
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22.3.5.2 Complexation Equations for aqueous complexation reactions can be obtained using the law of mass action as follows (e.g., Yeh and Tripathi, 1990; Lichtner, 1996): xi =
Na Kix x (γka ck )aik x γi
i = 1, 2, . . . , Mx
(22.51)
k=1
where xi is the concentration of the ith complexed species, Kix is the thermodynamic equilibrium constant of the ith complexed species, γix is the activity coefficient of the ith complexed species, Na is the number of aqueous components, ck is the concentration of the kth aqueous component, γka is the activity coefficient of the kth aqueous component species, aikx is the stoichiometric coefficient of the kth aqueous component in the ith complexed species, Mx is the number of complexed species, and subscripts and superscripts x and a refer to complexed species and aqueous components, respectively. 22.3.5.3 Precipitation and Dissolution Equations describing precipitation–dissolution reactions are also obtained using the law of mass action, but contrary to the other processes are represented by inequalities rather than equalities, as follows (Šimunek ˚ and Valocchi, 2002): p
p
Ki ≥ Qi =
Na
p
(γka ck )aik
i = 1, 2, . . . , Mp
(22.52)
k=1 p
where Mp is the number of precipitated species, Ki is the thermodynamic equilibrium constant of the p ith precipitated species, that is, the solubility product equilibrium constant, Qi is the ion activity product p of the ith precipitated species, and aik is the stoichiometric coefficient of the kth aqueous component in the ith precipitated species. The inequality in Equation 22.52 indicates that a particular precipate is formed only when the solution is supersaturated with respect to its aqueous components. If the solution is undersaturated then the precipitated species (if it exists) will dissolve to reach equilibrium conditions. 22.3.5.4 Cation Exchange Partitioning between the solid exchange phase and the solution phase can be described with the general exchange equation (White and Zelazny, 1986): zj · A zi + Xzi + zi · B zj + ⇔ zi · B zj + Xzj + zj · A zi +
(22.53)
where A and B are chemical formulas for particular cation (e.g., Ca2+ or Na+ ), X refers to an “exchanger” site on the soil, and zi is the valence of species. The mass action equation resulting from this exchange reaction is zj z + zi j z+ cj γia ci i + Kij = (22.54) zj + z γja cj cii where Kij is the selectivity coefficient, and c i is the exchanger-phase concentration of the ith component (expressed in moles per mass of solid). 22.3.5.5 Coupled System of Equations Once the various chemical reactions are defined, the final system of governing equations usually consists of several partial differential equations for solute transport (i.e., ADEs for each component) plus a set of nonlinear algebraic and ordinary differential equations describing the equilibrium and kinetic reactions, respectively. Each chemical and biological reaction must be represented by the corresponding algebraic or ordinary differential equations depending upon the rate of the reaction. Since the reaction of one
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species depends upon the concentration of many other species, the final sets of equations typically are tightly coupled. For complex geochemical systems, consisting of many components and multidimensional transport, numerical solution of these coupled equations is challenging (Šimunek ˚ and Valocchi, 2002). As an alternative, more general models have recently been developed that also more loosely couple transport and chemistry using a variety of sequential iterative or non-iterative operator-splitting approaches (e.g., Bell and Binning, 2004; Jacques and Šimunek, ˚ 2005). Models based on these various approaches are further discussed in Section 22.5b.
22.3.6 Multiphase Flow and Transport While the transport of solutes in variably saturated media generally involves two phases (i.e., the liquid and gaseous phases, with advection in the gaseous phase often being neglected), many contamination problems also increasingly involve nonaqueous phase liquids (NAPLs) that are often only slightly miscible with water. Nonaqueous phase liquids may consist of single organic compounds such as many industrial solvents, or of a mixture of organic compounds such as gasoline and diesel fuel. Some of these compounds can be denser than water (commonly referred to as DNAPLs) or lighter than water (LNAPLs). Their fate and dynamics in the subsurface is affected by a multitude of compound-specific flow and multicomponent transport processes, including interphase mass transfer and exchange (also with the solid phase). Multiphase fluid flow models generally require flow equations for each fluid phase (water, air, NAPL). Two-phase air–water systems hence could be modeled also using separate equations for air and water. This shows that the standard Richards Equation 22.3 is a simplification of a more complete multiphase (air–water) approach in that the air phase is assumed to have a negligible effect on variably saturated flow, and that the air pressure varies only little in space and time. This assumption appears adequate for most variably saturated flow problems. Similar assumptions, however, are generally not possible when NAPLs are present. Hence mathematical descriptions of multiphase flow and transport in general require flow equations for each of the three fluid phases, mass transport equations for all organic components (including those associated with the solid phase), and appropriate equations to account for interphase mass transfer processes. We refer readers to reviews by Abriola et al. (1999) and Rathfelder et al. (2000) for discussions of the complexities involved in modeling such systems subject to multiphase flow, multicomponent transport, and interphase mass transfer. An excellent overview of a variety of experimental approaches for measuring the physical and hydraulic properties of multi-fluid systems is given by Lenhard et al. (2002).
22.3.7 Initial and Boundary Conditions 22.3.7.1 Initial Conditions The governing equations for solute transport can be solved analytically or numerically provided that the initial and boundary conditions are specified. Initial conditions need to be specified for each equilibrium phase concentration, that is, c(x, y, z, t ) = ci (x, y, z, 0)
(22.55)
where ci is the initial concentration [ML−3 ], as well as for all nonequilibrium phases such as concentrations in the immobile region, sorbed concentrations associated with kinetic sites, and initially attached or strained colloid concentrations. 22.3.7.2 Boundary Conditions Complex interactions between the transport domain and its environment often must be considered for the water flow part of the problem being considered since these interactions determine the magnitude of water fluxes across the domain boundaries. By comparison, the solute transport part of most analytical and numerical models usually considers only three types of boundary conditions. When the concentration
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at the boundary is known, one can use a first-type (or Dirichlet type) boundary condition: c(x, y, z, t ) = c0 (x, y, z, t )
for (x, y, z) ∈ D
(22.56)
where c0 is a prescribed concentration [ML−3 ] at or along the D Dirichlet boundary segments. This boundary condition is often referred to as a concentration boundary condition. A third-type (Cauchy type) boundary condition may be used to prescribe the concentration flux at the boundary as follows: −θDij
∂c ni + qi ni c = qi ni c0 ∂xj
for (x, y, z) ∈ C
(22.57)
in which qi ni represents the outward fluid flux [LT−1 ], ni is the outward unit normal vector and c0 is the concentration of the incoming fluid [ML−3 ]. In some cases, for example, when a boundary is impermeable (q0 = 0) or when water flow is directed out of the region, the Cauchy boundary condition reduces to a second-type (Neumann type) boundary condition of the form: θDij
∂c ni = 0 for (x, y, z) ∈ N ∂xj
(22.58)
Most applications require a Cauchy boundary condition rather than Dirichlet (or concentration) boundary condition. Since Cauchy boundary conditions define the solute flux across a boundary, the solute flux entering the transport domain will be known exactly (as specified). This specified solute flux is then in the transport domain divided into advective and dispersive components. On the other hand, Dirichlet boundary condition controls only the concentration on the boundary, and not the solute flux which, because of its advective and dispersive contributions, will be larger than for a Cauchy boundary condition. The incorrect use of Dirichlet rather than Cauchy boundary conditions may lead to significant mass balance errors at an earlier time, especially for relatively short transport domains (van Genuchten and Parker, 1984). A different type of boundary condition is sometimes used for volatile solutes when they are present in both the liquid and gas phases. This situation requires a third-type boundary condition, but modified to include an additional volatilization term accounting for gaseous diffusion through a stagnant boundary layer of thickness d [L] above the soil surface. The additional solute flux is often assumed to be proportional to the difference in gas concentrations above and below this boundary layer (e.g., Jury et al., 1983). This modified boundary condition has the form: −θDij
Dg ∂c (kg c − gatm ) ni + qi ni c = qi ni c0 + ∂xj d
for (x, z) ∈ C
(22.59)
where Dg is the molecular diffusion coefficient in the gas phase [L2 T−1 ] and gatm is the gas concentration above the stagnant boundary layer [ML−3 ]. We note that Jury et al. (1983) assumed gatm in Equation 22.59 to be zero. Still other types of boundary conditions can be used. One example is the use of the Bateman equations (Bateman, 1910) to account for a finite rate of release of multiple solutes that are subject to a first-order sequential decay (e.g., radionuclides, nitrogen species). These solutes are typically released from a waste site into the environment as a consequence of decay reactions in the waste site (e.g., van Genuchten, 1985).
22.4 Analytical Models A large number of computer models using both analytical and numerical solutions of the flow and solute transport equations are now available for a wide range of applications in research and management of natural subsurface systems (Šimunek, ˚ 2005). Modeling approaches range from relatively simple analytical
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and semi-analytical models, to more complex numerical codes that permit consideration of a large number of simultaneous nonlinear processes. While for certain conditions (e.g., for linear sorption, a concentration independent sink term φ , and a steady flow field) the solute transport equations (e.g., Equation 22.20, Equation 22.21, Equation 22.23, Equation 22.31, and Equation 22.38) become linear, the governing flow equations (e.g., Equation 22.3) are generally highly nonlinear because of the nonlinear dependency of the soil hydraulic properties on the pressure head or water content. Consequently, many analytical solutions have been derived in the past for solute transport equations, and are now widely used for analyzing solute transport during steady-state flow. Although a large number of analytical solutions also exist for the unsaturated flow equation, they generally can be applied only to relatively simple flow problems. The majority of applications for water flow in the vadose zone require a numerical solution of the Richards equation. Analytical methods are representative of the classical mathematical approach for solving differential equations to produce an exact solution for a particular problem. Analytical models usually lead to an explicit equation for the concentration (or the pressure head, water content, or temperature) at a particular time and location. Hence, one can evaluate the concentration directly without the time stepping that is typical of numerical methods. While exceptions exist (e.g., Liu et al., 2000), analytical solutions usually can be derived only for simplified transport systems involving linearized governing equations, homogeneous soils, simplified geometries of the transport domain, and constant or highly simplified initial and boundary conditions. Unfortunately, analytical solutions for more complex situations, such as for transient water flow or nonequilibrium solute transport with nonlinear reactions, are generally not available and cannot be derived, in which case numerical models must be employed (Šimunek, ˚ 2005).
22.4.1 Analytical Approaches Analytical solutions are usually obtained by applying various transformations (e.g., Laplace, Fourier or other transforms) to the governing equations, invoking a separation of variables, and using the Green’s function approach (e.g., Leij et al., 2000). 22.4.1.1 Laplace Transformation The Laplace transform, £, of the solute concentration with respect to time is defined as follows: ∞ c(x, t ) exp(−st ) dt
c¯ (x, s) = L[c(x, t )] =
(22.60)
0
where s is the transform variable [T−1 ]. Laplace transforms can greatly simplify the governing solute transport equations by eliminating one independent variable, usually time. They also transform the original transport equation from a partial to an ordinary differential equation. Using Laplace transforms, one thus obtains a governing ADE in the Laplace domain that is much simpler to solve analytically than the original equation. The analytical solution in the Laplace space is subsequently inverted to the real space using either a table of Laplace transforms, by applying inversion theorems, or by using a numerical inversion program. 22.4.1.2 Fourier Transformation Two- and three-dimensional problems often require not only Laplace transforms with respect to time (transformation from t to s) and one spatial coordinate (usually x being transformed to r), but often also a double Fourier transform with respect to two other spatial coordinates (y and z), which is given by (Leij and
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Toride, 1997): 1 FYZ [¯c (r, y, z, s)] = c˜ (r, γ , κ, s) = 2π
∞ ∞ c(r, y, z, s) exp(iγ y + iκz) dy dz
(22.61)
−∞ −∞
where i 2 = −1 and γ and κ are transformation variables pertaining to the y and z coordinates. Similarly as for Laplace transforms, Fourier transforms lead to an equation that can be solved analytically more easily. One also needs to transform this analytical solution from the Laplace and Fourier domains back to the original time and space domains. Several analytical solutions, including the derivation process, for different initial and boundary conditions, and different transport domain geometries are given by Leij and Toride (1997) in the N3DADE manual. 22.4.1.3 Method of Moments Statistical moments are often used to characterize the statistical distribution of the solute concentration versus time and space. For example, moments can be used to evaluate the average residence time or the width of the residence time distribution. These attributes can be quantified with the moments of the distribution (Skaggs and Leij, 2002). The pth time moment, mp , is defined as: ∞ t p c(t ) dt
mp =
(p = 0, 1, 2, . . .)
(22.62)
0
where c(t ) is the breakthrough curve measured at a certain location. The zeroth moment is related to the mass of solute contained in the breakthrough curve, while the first moment is related to the mean residence time. Normalized and central moments are defined as: Mp =
mp m0
Mp =
1 m0
∞ (t − M1 )p c(t ) dt
(22.63)
0
The second central moment relates to the degree of solute spreading. Similar expressions can be written also for the spatial (depth) moments characterizing the spatial solute distribution. Moments for particular problems or processes can then be obtained by substituting appropriate analytical solutions in the above equations.
22.4.2 Existing Models Numerous analytical solutions of the linear advection–dispersion solute transport equations (e.g., Equation 22.21, Equation 22.23, Equation 22.31, and Equation 22.38), or their two- and threedimensional equivalents, have been developed during the last 40 years and are now widely used for predictive purposes and for analyzing laboratory and field observed concentration distributions. The majority of these solutions pertain to solute transport equations assuming constant water content, θ, and flux, q, values (i.e., for steady-state water flow conditions in a homogeneous medium). 22.4.2.1 One-Dimensional Models Some of the more popular one-dimensional analytical transport models have been CFITM (van Genuchten, 1980b), CFITIM (van Genuchten, 1981), CXTFIT (Parker and van Genuchten, 1984), and CXTFIT2 (Toride et al., 1995). While CFITM considers only one-dimensional equilibrium solute transport in both finite and infinite solute columns, CFITIM additionally considers physical and chemical
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nonequilibrium transport (i.e., the two-region mobile–immobile model for physical nonequilibrium and the two-site sorption model for chemical nonequilibrium). CXTFIT further expanded the capabilities of CFITIM by considering more general initial and boundary conditions, as well as degradation processes. CXTFIT2 (Toride et al., 1995), an updated version of CXTFIT, solves both direct and inverse problems for three different one-dimensional transport models (1) the conventional advection–dispersion equation, ADE; (2) the chemical and physical nonequilibrium ADEs; and (3) a stochastic stream tube model based upon the local-scale equilibrium or nonequilibrium ADE. These three types of models all consider linear adsorption, and include zero- and first-order decay/source terms. All of these models may be used also to solve the inverse problem by fitting the analytical ADE solutions to experimental results. 22.4.2.2 Multi-Dimensional Models Some of the more popular multi-dimensional analytical transport models have been AT123D (Yeh, 1981), 3DADE (Leij and Bradford, 1994), N3DADE (Leij and Toride, 1997), and MYGRT (Ungs et al., 1998). These programs provide analytical solutions to transport problems in two- and three-dimensional domains. 3DADE also included parameter estimation capabilities. A large number of analytical models for one-, two-, and three-dimensional solute transport problems were recently incorporated into the public domain software package STANMOD (STudio of ANalytical MODels) (Šimunek ˚ et al., 1999a) (http://www.hydrus2d.com). Figure 22.6 shows a STANMOD dialog window where users can make a selection of the analytical program to be used. This Windows-based computer software package includes not only programs for equilibrium advective-dispersive transport (i.e., the CFITM of van Genuchten 1980b) for one-dimensional transport and 3DADE (Leij and Bradford, 1994) for three-dimensional problems (Figure 22.7), but also programs for more complex problems. For example, STANMOD also incorporates the CFITIM (van Genuchten, 1981) and N3DADE (Leij and Toride, 1997) programs for nonequilibrium transport (i.e., the two-region mobile–immobile model for physical nonequilibrium and the two-site sorption model for chemical nonequilibrium) in one and multiple dimensions, respectively.
FIGURE 22.6 Selection of an analytical model in the STANMOD software package (Šimunek ˚ et al., 1999a).
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FIGURE 22.7 Selection of the geometry of the transport domain for the 3DADE code (Leij and Bradford, 1994) within the STANMOD software package (Šimunek ˚ et al., 1999a).
Figure 22.7 shows a dialog window of STANMOD in which users can select the geometry of the transport domain for use in the 3DADE program. STANMOD also includes CXTFIT2 (Toride et al., 1995) as discussed earlier, and the CHAIN code of van Genuchten (1985) for analyzing the advective– dispersive transport of up to four solutes involved in sequential first-order decay reactions. Examples of the latter are the migration of radionuclides in which the chain members form first-order decay reactions, and the simultaneous movement of various interacting nitrogen or organic chemicals. The latest version of STANMOD also includes the screening model of Jury et al. (1983) for describing transport and volatilization of soil-applied volatile organic chemicals. An application of CFITIM within of the STANMOD program is demonstrated in Figure 22.8, which shows measured and fitted breakthrough curves of a nonreactive (3 H2 O) solute for transport through a saturated Glendale clay loam soil. In this example, a tritiated water pulse of 3.102 pore volumes was applied to a 30 cm long column, with the breakthrough curve being determined from the effluent concentrations. An analytical solution for two-region (mobile–immobile) physical nonequilibrium transport (van Genuchten, 1981) was used for the analysis. With the pore-water velocity known (v = 37.54 cm d−1 ) and assuming that the retardation factor R for 3 H2 O was equal to one (no sorption or anion exclusion), only three parameters were optimized against the breakthrough curve, that is, the dispersion coefficient D (= 15.6 cm2 d−1 ), a dimensionless variable β (= 0.823) for partitioning the liquid phase in mobile and immobile regions, and a dimensionless mass transfer coefficient ω (= 0.870). An example application of the 3DADE program (Leij and Bradford, 1994) in the STANMOD package is demonstrated in Figure 22.9, which shows calculated concentration contours for a transport problem in which solute is applied at a concentration C0 = 1, assuming a third-type boundary condition, to a rectangular area of the soil surface (or within groundwater) of 15 × 15 cm2 . Other transport parameters were as follows: v = 10 cm d−1 , Dx = 100 and Dy = Dz = 10 cm2 d−1 , and R = 1. Figure 22.9 shows concentration contours in the xy-plane at t = 1 days, and z = 0.
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1.2
Concentration [–]
1 Measured
0.8
Fitted 0.6 0.4 0.2 0 0
2
4 Pore volumes [–]
8
6
FIGURE 22.8 Breakthrough curve for nonreactive tritium transport as analyzed with the two-region physical nonequilibrium program CXTFIT2 (Toride et al., 1995) within STANMOD (Šimunek ˚ et al., 1999a). 20
0
y
–20 0 0.0
0.2
x 0.4
30 0.6
0.8
1.0
FIGURE 22.9 Solute distribution in the xy-plane for continuous application at x = 0 and −7.5 < y < 7.5 cm after 1 days, with v = 10 cm d−1 , Dx = 100 and Dy = Dz = 10 cm2 d−1 as calculated with 3DADE (Leij and Bradford, 1994) within STANMOD (Šimunek ˚ et al., 1999a).
22.5 Numerical Models 22.5.1 Numerical Approaches While analytical and semi-analytical solutions are still popularly used for many relatively simple applications, the ever-increasing power of personal computers, and the development of more accurate and
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stable numerical solution techniques, have led to the much wider use of numerical models in recent years. Numerical methods are in general superior to analytical methods in terms of being able to solve much more practical problems (Šimunek, ˚ 2005). They allow users to design complicated geometries that reflect complex natural geologic and hydrologic conditions, control parameters in space and time, prescribe more realistic initial and boundary conditions, and permit the implementation of nonlinear constitutive relationships. Numerical methods usually subdivide the time and spatial coordinates into smaller pieces, such as finite differences, finite elements, and finite volumes, and reformulate the continuous form of governing partial differential equations in terms of a system of algebraic equations. To obtain solutions at certain times, numerical methods generally require intermediate simulations (time-stepping) between the initial condition and the points in time for which the solution is needed. Reviews of the history of development of various numerical techniques used in vadose zone flow and transport models are given by van Genuchten and Šimunek ˚ (1996) and Šimunek ˚ (2005). Here we will summarize only the main principles behind some of the more popular techniques. 22.5.1.1 Finite Differences The method of finite differences is generally very intuitive and relatively easy to implement. Time and space are both divided into small increments t and z (or x and z) (Figure 22.10). Temporal and spatial derivatives in the governing equation are then replaced with finite differences (formally using Taylor series expansions). For example, the standard advection–dispersion equation for steady-state water flow: ∂J ∂ 2c ∂c ∂c =− =D 2 −v ∂t ∂z ∂z ∂z
(22.64)
can be approximated as follows using an explicit (forward-in-time) finite difference scheme: j
j
j j j j j j Ji+1/2 − Ji−1/2 ci+1 − 2ci + ci−1 ci+1 − ci−1 − ci =− =D −v t z 2z (z)2
j+1
ci
(22.65)
where subscripts refer to spatial discretization and superscript to temporal discretization (j and j+1 are for the previous and actual time levels, respectively; see Figure 22.10), t is the time step, and z is the spatial step (assumed to be constant). Notice that this equation contains only one unknown variable (i.e., j+1 the concentration ci at the new time level), which hence can be evaluated directly (explicitly) by solving the equation.
ti
(a)
zi+1
t i+1 j
(b)
zj+1
j +1
ci +1
ci +1
xi + 1
xi
xi –1 ci –1, j +1
ci, j +1
ci +1, j +1
∆zi zi
ci
j
cij +1
z
∆zj
∆z
zj
j +1 ci – 1
j ci – 1
∆t t
ci+1, j
ci, j
∆zj – 1
∆zi–1 z
zi –1
ci–1, j
∆z
zj – 1
ci–1, j –1
ci, j–1
ci+1, j–1
∆x ∆xi–1
∆xi
x
FIGURE 22.10 Examples of the spatial and temporal finite difference discretization of a one-dimensional problem (a), and the finite difference discretization of a two-dimensional domain (b).
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By comparison, a fully implicit (backward-in-time) finite difference scheme can be written as follows: j+1
j+1
j+1
j+1
j+1
j+1
j+1
j Ji+1/2 − Ji−1/2 c c − 2ci + ci−1 − ci−1 − ci =− = D i+1 − v i+1 2 t z 2z (z)
j+1
ci
(22.66)
and an implicit (weighted) finite difference scheme as: j+1
j+1
ci
j+1
j ε(c − 2ci − ci = D i+1 t j+1
−v
j+1
j
j
j
+ ci−1 ) + (1 − ε)(ci+1 − 2ci + ci−1 ) (z)2
j+1
j
j
ε(ci+1 − ci−1 ) + (1 − ε)(ci+1 − ci−1 )
(22.67)
2z
where ε is a temporal weighting coefficient. Different finite-difference schemes results depending upon the value of ε, that is, an explicit scheme when ε = 0, a Crank–Nicholson time-centered scheme when ε = 0.5, and a fully implicit scheme when ε = 1. Of these, the latter two cases lead to several unknown concentrations in each equation at the new time level. Consequently, equations for all nodes of the transport domain need to be assembled into an algebraic system of linear equations to produce a matrix equation of the form (22.68) [P]j+1 {c}j+1 = {F } in which [P] is a tridiagonal matrix given by:
d1
b
2
0
[P] =
0
0
0
e1 d2 b3
0 e2 d3 .. . 0
0 e3 .. . bN −2 0
0 .. . dN −2 bN −1 0
0
eN −1
dN 0 0 0
eN −2 dN −1 bN
(22.69)
Equation 22.68 is subsequently solved using a matrix equation solver to yield the concentrations at the new time level. The problem becomes more complex for problems involving transient flow. In that case one must first obtain estimates of the water contents and fluxes at the new time level using a numerical solution of the Richards equation. These water contents and fluxes are subsequently used for assembling the matrix equations for solute transport. While finite differences are relatively straightforward to implement for many transport problems, one major disadvantage is that this method cannot be easily applied to relatively complicated (irregular) transport domains in two and three dimensions. 22.5.1.2 Finite Elements Finite element methods can be implemented in very much the same way as finite differences for one-, two-, and three-dimensional problems. A major advantage of the finite elements is that they are much easier used to discretize complex two- and three-dimensional transport domains (Figure 22.11). As an example, Figure 22.11 shows triangular unstructured finite element grids for a regular rectangular and an irregular domain as generated with the automated MeshGen2D mesh generator of HYDRUS-2D (Šimunek ˚ et al., 1999b). Note that even though the figure on the right (Figure 22.11) has an irregular soil surface, as well as a tile drain within the transport domain, MeshGen2D could easily discretize/accommodate this transport domain using an unstructured triangular finite element mesh. The finite element method assumes that the dependent variable in the advection–dispersion equation (e.g., the concentration function c(x, t ) in (22.64)) can be approximated by a finite series c (x, t ) of
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(a)
(b)
Z
X
FIGURE 22.11 Examples of the triangular finite element grids for regular (a) and irregular (b) two-dimensional transport domains.
(a) 1 1
i–1
i
2
∆xi
i+1
x
(b)
c ci
ci–1
ci+1
1
i -1
i
i +1
x
FIGURE 22.12 Example of one-dimensional linear basis functions (a) and their use to approximate solution c(x, t ) of the advection–dispersion equation (b).
the form (Figure 22.12b): c (x, t ) =
N
φm (x)cm (t )
(22.70)
m=1
where φm are the selected linear basis functions that fulfill the condition φm (xn ) = δnm , δnm is Kronecker delta ( δnm = 1 for m = n, and δnm = 0 for m = n), cm are the unknown time-dependent coefficients which represent solutions of (22.64) at the finite element nodal points, and N is the total number of nodal points. For example, for the one-dimensional finite element xi < x < xi+1 , linear basis functions have
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the following form (Figure 22.12a): x − xi x x − xi φ2 = x
φ1 = 1 −
xi ≤ x ≤ xi+1
(22.71)
where x (= xi+1 − xi ) is the size of a finite element [L], that is, the distance between two neighboring nodal points. The approximate solution c (x, t ) converges to the correct solution c(x, t ) as the number of basis functions N increases. Application of the Galerkin method, which postulates that the differential operator associated with the transport equation is orthogonal to each of the N basis functions (e.g., Pinder and Gray, 1977), leads to the following system of N time-dependent differential equations with N unknown values cn (t ): L − 0
∂ 2c ∂c ∂c +D 2 −v ∂t ∂x ∂x
φn dx = 0
(22.72)
where φn are the selected linear weighting functions that can be the same as the basis functions φm . Integrating by parts the terms containing the spatial derivatives to remove the second-order derivatives, and substituting (22.70) for c(x, t ) leads to the following equation: Le Le ∂cm ∂φm ∂φn φm φn dx − dx − qsL φn (L) + qs0 φn (0) = 0 − − vcm φm Dcm ∂t ∂x ∂x e e 0
0
(22.73) where qs0 and qsL are solute fluxes across the left and right boundaries, respectively; e is the element index, Le is the size of an element e, and L is the size of the transport domain (length of the soil profile). The integrals in Equation 22.73 can be evaluated either numerically or analytically, depending upon the type of invoked basis and weighting functions ( φm and φn , respectively). The equation can be rewritten in matrix form similarly as Equation 22.68 and then solved using a matrix equation solver. For a detailed derivation of the matrix equation we refer to standard finite element textbooks (e.g., Pinder and Gray, 1977; Zienkiewicz, 1977; Huyakorn and Pinder, 1983) or manuals of some of the models (e.g., the HYDRUS models by Šimunek ˚ et al., 1998a, 1999b). 22.5.1.3 Stability and Oscillations Numerical solutions of the transport equation often exhibit oscillatory behavior and/or excessive numerical dispersion near relatively sharp concentration fronts (Huyakorn and Pinder, 1983; Šimunek ˚ et al., 1998a). These problems can be especially serious for advection-dominated transport characterized by small dispersivities. One way to partially circumvent numerical oscillations is to use upstream weighing in which case the flux term of Equation 22.64 is not weighted using regular linear basis functions φn , but instead with nonlinear quadratic functions φnu . Undesired oscillations can often be prevented also by selecting an appropriate combination of the space and time discretizations. Two dimensionless numbers may be used to characterize the discretizations in space and time. One of these is the grid Peclet number, Pee , which defines the predominant type of solute transport (notably the ratio of the advective and dispersive transport terms) in relation to coarseness of the finite element grid: Pee =
vx D
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where x is the characteristic length of a finite element [L]. The Peclet number increases when the advective part of the transport equation dominates the dispersive part (i.e., when a relatively steep concentration front is present). To achieve acceptable numerical results, the spatial discretization must be kept relatively fine to maintain a low Peclet number. Numerical oscillations can be virtually eliminated when the local Peclet numbers do not exceed about 5. However, acceptably small oscillations may be obtained with local Peclet numbers as high as 10 (Huyakorn and Pinder, 1983). Undesired oscillations for higher Peclet numbers can be effectively eliminated by using upstream weighing. A second dimensionless number, the Courant number, Cre , may be used to characterize the relative extent of numerical oscillations in the numerical solution. The Courant number is associated with the time discretization, t [T], as follows: vt (22.75) Cre = x Given a certain spatial discretization, the time step must be selected such that the Courant number remains less than or equal to 1. Perrochet and Berod (1993) developed a criterion for minimizing or eliminating numerical oscillations that is based on the product of the Peclet and Courant numbers: Pe · Cr ≤ ωs (=2)
(22.76)
where ωs is the performance index [−]. This criterion indicates that advection-dominated transport problems having large Pe numbers can be safely simulated provided Cr is reduced according to (22.76) (Perrochet and Berod, 1993). When small oscillations in the solution can be tolerated, ωs can be increased to about 5 or 10.
22.5.2 Existing Models 22.5.2.1 Single-Species Solute Transport Models A large number of numerical models are now available for evaluating variably saturated water flow and solute transport processes in the subsurface. Some of these models are in the public domain, such as MACRO (Jarvis, 1994), SWAP (van Dam et al., 1997), UNSATH (Fayer, 2000), VS2DI (Healy, 1990), and HYDRUS-1D (Šimunek ˚ et al., 1998a, 2005), while others are in the commercial domain, such as HYDRUS2D (Šimunek ˚ et al., 1999b) and MODFLOW-SURFACT (HydroGeoLogic, 1996). These models vary widely in terms of their complexity, sophistication, and ease of use. Although some models are still being run under the DOS operating system, with associated difficulties of preparing input files and interpreting tabulated outputs, many others, especially those in the commercial domain, are supported by sophisticated graphics-based interfaces that greatly simplify their use (Šimunek ˚ et al., 1998a; 1999b). Several studies have recently reviewed and compared various numerical models for vadose zone applications (e.g., Wilson et al., 1999; Scanlon et al., 2002; MDH Engineered Solutions Corp., 2003; Vanderborght et al., 2005). These studies typically evaluated comparable precision, speed, and ease of use of the codes involved. While many of the early numerical models were developed mostly for agricultural applications (e.g., optimizing soil moisture conditions for crop production), this focus has increasingly shifted to environmental research, with the primary concern now being the subsurface fate and transport of various agricultural and other contaminants, such as radionuclides, hydrocarbons, fumigants, pesticides, nutrients, pathogens, pharmaceuticals, viruses, bacteria, colloids, and/or toxic trace elements. The earlier models solved the governing flow and transport equations for relatively simplified system-independent boundary conditions (i.e., specified pressure heads or fluxes, and free drainage). Models developed recently can cope with much more complex system-dependent boundary conditions evaluating surface flow and energy balances and accounting for the simultaneous movement of water, vapor, and heat. Examples are DAISY (Hansen et al., 1990), TOUGH2 (Pruess, 1991), SHAW (Flerchinger et al., 1996), SWAP (van Dam et al., 1997), HYDRUS-1D (Šimunek ˚ et al., 1998a, 2005), UNSATH (Fayer, 2000), and COUP (Jansson
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and Karlberg, 2001). Several models now also account for the extremely nonlinear processes associated with the freezing and thawing cycle (e.g., DAISY, SHAW, and COUP). Models have recently also become increasingly sophisticated in terms of the type and complexity of solute transport processes that can be simulated. Transport models are no longer being limited to solutes undergoing relatively simple chemical reactions such as linear sorption and first-order decay, but now consider also a variety of nonlinear sorption and exchange processes, physical and chemical nonequilibrium transport, volatilization, gas diffusion, colloid attachment/ detachment, decay chain reactions, and many other processes (e.g., the HYDRUS-1D and -2D codes of Šimunek ˚ et al., 1999b, 2005, or MODFLOW-SURFACT of HydroGeoLogic, Inc., 1996). For example, the general formulation of the transport equations in the HYDRUS codes permit simulations of not only non-adsorbing or linearly sorbing chemicals, but also of a variety of other contaminants, such a viruses (Schijven and Šimunek, ˚ 2001), colloids (Bradford et al., 2002), cadmium (Seuntjens et al., 2001), and hormones (Casey et al., 2003, 2004), or chemicals involved in the sequential biodegradation of chlorinated aliphatic hydrocarbons (Schaerlaekens et al., 1999; Casey and Šimunek, ˚ 2001). Much effort has recently been directed also toward improving models for purposes of simulating nonequilibrium and/or preferential flow. Examples of this are the TOUGH codes (Pruess, 1991, 2004), MACRO (Jarvis, 1994), and HYDRUS-1D (Šimunek ˚ et al., 2003, 2005). These models typically assume the presence of dual-porosity and dual-permeability regions, with different fluxes possible in the two regions. As discussed in detail in Section 22.2b, dual-porosity, mobile–immobile water flow models result when the Richards or kinematic wave equations are used for flow in the fractures, and immobile water is assumed to exist in the matrix, whereas dual-permeability models assume that water is mobile in both the matrix and fracture domains, while invoking terms accounting for the exchange of water and solutes between the two regions. Example applications of these dual-porosity and dual-permeability models are given by Šimunek ˚ et al. (2001), Haws et al. (2005), Köhne et al. (2004b, 2005), and Pot et al. (2005), among many others. As an example of available vadose zone flow and transport models, we discuss here in somewhat greater detail the HYDRUS software packages of Šimunek ˚ et al. (1999b, 2005) and the MODFLOW-SURFACT model developed by HydroGeoLogic (1996). 22.5.2.1.1 The HYDRUS Software Packages HYDRUS-1D (Šimunek ˚ et al., 2005) and HYDRUS-2D (Šimunek ˚ et al., 1999b) are software packages (www.hydrus2d.com) that simulate the one- and two-dimensional movement of water, heat, and multiple solutes in variably saturated media, respectively. Both programs use finite elements to numerically solve the Richards equation for saturated–unsaturated water flow and Fickian-based advection–dispersion equations for both heat and solute transport. The flow equation includes a sink term to account for water uptake by plant roots as a function of both water and salinity stress. The flow equation may also consider dual-porosity-type flow with a fraction of water content being mobile, and fraction immobile. The heat transport equation considers conduction as well as advection with flowing water. The solute transport equations assume advective-dispersive transport in the liquid phase, and diffusion in the gaseous phase. The transport equations also include provisions for nonlinear and/or nonequilibrium reactions between the solid and liquid phases, linear equilibrium reactions between the liquid and gaseous phases, zero-order production, and two first-order degradation reactions: one which is independent of other solutes, and one which provides the coupling between solutes involved in the sequential first-order decay reactions. In addition, physical nonequilibrium solute transport can be accounted for by assuming a two-region, dual-porosity type formulation which partitions the liquid phase into mobile and immobile regions. Alternatively, the transport equations include provisions for kinetic attachment/detachment of solute to the solid phase and thus can be used to simulate the transport of viruses, colloids, or bacteria (Schijven and Šimunek, ˚ 2002; Bradford et al., 2003). Both programs may be used to analyze water and solute movement in unsaturated, partially saturated, or fully saturated media. The flow region itself may consist of nonuniform (layered) soils. HYDRUS-2D additionally can handle flow regions delineated by irregular boundaries. The flow region itself may be
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composed of nonuniform soils having an arbitrary degree of local anisotropy. Flow and transport can occur in the vertical plane, the horizontal plane, or in a three-dimensional region exhibiting radial symmetry about the vertical axis. The unsaturated soil hydraulic properties (the constitutive relationships) can be described using van Genuchten (1980a), Brooks and Corey (1964), Kosugi (1996), and Durner (1994) type analytical functions, or modified van Genuchten type functions that produce a better description of the hydraulic properties near saturation. HYDRUS-1D incorporates hysteresis by assuming that drying scanning curves are scaled from the main drying curve, and wetting scanning curves from the main wetting curve. Root growth is simulated by means of a logistic growth function, while root water uptake can be simulated as a function of both water and salinity stress. The HYDRUS-1D software package additionally includes modules for simulating carbon dioxide and major ion solute movement (Šimunek ˚ et al., 1996). Diffusion in both the liquid and gas phases ˚ and advection in the liquid phase are considered as the main CO2 transport mechanisms (Šimunek and Suarez, 1993). The major variables of the chemical system are Ca, Mg, Na, K, SO4 , Cl, NO3 , H4 SiO4 , alkalinity, and CO2 (Šimunek ˚ and Suarez, 1994; Šimunek ˚ et al., 1996). The model accounts for equilibrium chemical reactions between these components such as complexation, cation exchange and precipitation-dissolution. For the precipitation-dissolution of calcite and dissolution of dolomite, either equilibrium or multicomponent kinetic expressions are used, involving both forward and back reactions. Other dissolution-precipitation reactions considered include gypsum, hydromagnesite, nesquehonite, and sepiolite. Since the ionic strength of soil solutions can vary considerably with time and space and often reach high values, both modified Debye–Hückel and Pitzer expressions were incorporated into the model as options to calculate single ion activities. In addition, both HYDRUS programs implement a Marquardt-Levenberg type parameter estimation technique (Marquardt, 1963; Šimunek ˚ and Hopmans, 2002) for inverse estimation of soil hydraulic (Šimunek ˚ et al., 1998b,c; Hopmans et al., 2002) and/or solute transport and reaction (Šimunek ˚ et al., 2002) parameters from measured transient or steady-state flow and/or transport data. The HYDRUS packages use a Microsoft Windows based Graphics User Interface (GUI) to manage the input data required to run the program, as well as for nodal discretization and editing, parameter allocation, problem execution, and visualization of results. All spatially distributed parameters, such as those for various soil horizons, the root water uptake distribution, and the initial conditions for water, heat and solute movement, are specified in a graphical environment. HYDRUS-2D includes the MeshGen2D mesh generator, specifically designed for variably-saturated subsurface flow transport problems, for defining more general domain geometries, and for discretizing the transport domain into an unstructured finite element mesh. The program offers graphs of the distributions of the pressure head, water content, water and solute fluxes, root water uptake, temperature, and solute concentrations in the soil profile at preselected times. Also included is a small catalog of unsaturated soil hydraulic properties (Carsel and Parish, 1988), as well as pedotransfer functions based on neural networks (Schaap et al., 2001). Many different applications of both software packages were referenced throughout this book chapter.
22.5.2.1.2 MODFLOW-SURFACT MODFLOW-SURFACT (HydroGeoLogic, 1996) is a fully integrated flow and transport code, based on the MODFLOW groundwater modeling software package of the U.S. Geological Survey (McDonald and Harbaugh, 1988). While MODFLOW (see detailed discussion in Chapter 23) deals only with fully saturated groundwater flow, MODFLOW-SURFACT expands the applicability of the code to unsaturated domains. MODFLOW-SURFACT includes new flow packages that enhance schemes for performing unconfined simulations to rigorously model desaturation and resaturation of aquifers. It provides an option for discretizing the domain using an axi-symmetric geometry for efficient simulation of pumping tests, recovery tests, etc. In addition to normally allowed external stresses in MODFLOW (i.e., constant head, constant flux, areal recharge, evapotranspiration, drains, and streams), MODFLOW-SURFACT provides a rigorous well withdrawal package, unconfined recharge boundary conditions, and seepage face boundary conditions. Additionally, MODFLOW-SURFACT also includes options for adaptive time-stepping and
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output control procedures, and a new solution package based on the preconditioned conjugate gradient method. MODFLOW-SURFACT includes new Analysis of Contaminant Transport (ACT) modules that allow simulations of single-species and multi-component contaminant transport. The program can handle up to 5 chemical species, which may undergo linear or nonlinear retardation, first-order decay and biochemical degradation, as well as generate transformation products. MODFLOW-SURFACT also permits mass partitioning of a single or multicomponent contaminant with diffusive mass movement in the inactive phase, and mass partitioning of a single or multicomponent contaminant from a depleting immobile NAPL phase with advective and dispersive transport in the active phase and diffusive transport in the inactive phase. 22.5.2.2 Geochemical Transport Models Significant efforts have recently been carried out also in coupling physical flow and transport models with geochemical models to simulate ever more complex reactions, such as surface complexation, precipitation/dissolution, cation exchange, and biological reactions. Recent reviews of the development of hydrogeochemical transport models involving reactive multiple components are given by Mangold and Tsang (1991), Lichtner (1996) and Steefel and MacQuarrie (1996), Šimunek ˚ and Valocchi (2002), and Bell and Binning (2004). Most modeling efforts involving multicomponent transport have thus far focused on the saturated zone, where changes in the water flow velocity, temperature and pH are often much more gradual and hence less important than in the unsaturated zone. Consequently, most multicomponent transport models assumed one- or two-dimensional steady-state saturated water flow with a fixed value of the flow velocity, temperature and pH. Only recently have several multicomponent transport models been published which also consider variably saturated flow; these include DYNAMIX (Liu and Narasimhan, 1989), HYDROGEOCHEM (Yeh and Tripathi, 1990), TOUGH-REACT (Pruess, 1991), UNSATCHEM (Šimunek ˚ and Suarez, 1994; Šimunek ˚ et al., 1996, 1997), FEHM (Zyvoloski et al., 1997), MULTIFLO (Lichtner and Seth, 1996), OS3D/GIMRT (Steefel and Yabusaki, 1996), HYDROBIOGEOCHEM (Yeh et al., 1998), FLOTRAN (Lichtner, 2000), MIN3P (Mayer et al., 2002), HP1 (Jacques et al., 2002; Jacques and Šimunek, ˚ 2005), and HYDRUS-1D (Šimunek ˚ et al., 2005). Geochemical models can be divided into two major groups: those with specific chemistry and general models (Šimunek ˚ and Valocchi, 2002). Models with specific chemistry are limited in the number of species they can handle, while their application is restricted to problems having a prescribed chemical system. They are, however, much easier to use and computationally can be much more efficient than general models. Typical examples of models with specified chemistry are those simulating the transport of major ions, such as LEACHM (Wagenet and Hutson, 1987), UNSATCHEM (Šimunek ˚ and Suarez, 1994; Šimunek ˚ et al., 1996), and HYDRUS-1D (Šimunek ˚ et al., 2005). Models with generalized chemistry (DYNAMIX, HYDROGEOCHEM, MULTIFLO, FLOTRAN, OS3D/GIMRT, and HP1, all referenced above) provide users with much more freedom in designing a particular chemical system; possible applications of these models are also much wider. 22.5.2.2.1 HP1 HYDRUS-1D was recently coupled with the PHREEQC geochemical code (Parkhurst and Appelo, 1999) to create a new comprehensive simulation tool, HP1 (acronym for HYDRUS1D-PHREEQC) (Jacques et al., 2003; Jacques and Šimunek, ˚ 2005). The combined code contains modules simulating (1) transient water flow in variably saturated media, (2) the transport of multiple components, (3) mixed equilibrium/kinetic biogeochemical reactions, and (4) heat transport. HP1 is a significant expansion of the individual HYDRUS-1D and PHREEQC programs by preserving most of their original features and capabilities. The code still uses the Richards equation for simulating variably saturated water flow and advection– dispersion type equations for heat and solute transport. However, the program can now simulate also a broad range of low-temperature biogeochemical reactions in water, the vadose zone and in ground water systems, including interactions with minerals, gases, exchangers, and sorption surfaces, based on thermodynamic equilibrium, kinetics, or mixed equilibrium-kinetic reactions.
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0.01
Concentrations [mol/L]
Concentrations [mol/L]
(a) 0.012
0.008 Na 0.006
Ca
0.004
Zn
0.0006
0.0004
Pb
0.0002
0.002
Cd
Al 0
0 0
3
6
9
12
Time [days]
15
0
3
6
9
12
15
Time [days]
FIGURE 22.13 Major ions (a) and heavy metals (Zn, Pb, and Cd) (b) concentrations in the effluent of an 8-cm soil long column.
Jacques et al. (2003) and Jacques and Šimunek ˚ (2005) demonstrated the versatility of the HP1 model on several examples such as (a) the transport of heavy metals (Zn2+ , Pb2+ , and Cd2+ ) subject to multiple cation exchange reactions, (b) transport with mineral dissolution of amorphous SiO2 and gibbsite (Al(OH)3 ), (c) heavy metal transport in a medium with a pH-dependent cation exchange complex, (d) infiltration of a hyperalkaline solution in a clay sample (this example considers kinetic precipitation– dissolution of kaolinite, illite, quartz, calcite, dolomite, gypsum, hydrotalcite, and sepiolite), (e) long-term transient flow and transport of major cations (Na+ , K+ , Ca2+ , and Mg2+ ) and heavy metals (Cd2+ , Zn2+ , and Pb2+ ) in a soil profile, (f) cadmium leaching in acid sandy soils, (g) radionuclide transport (U and its aqueous complexes), and (h) the fate and subsurface transport of explosives (TNT and its daughter products 2ADNT, 4ADNT, and TAT) (Šimunek ˚ et al., 2006). 22.5.2.2.2 Leaching of Heavy Metals from a Soil Column As an example application of HP1, Figure 22.13 shows calculated effluent concentrations of heavy metals (Zn2+ , Pb2+ , and Cd2+ ) leached from an 8-cm long soil column having an initial solution as defined in Table 22.2, and with its ion-exchange complex in equilibrium with this solution. Heavy metals initially present in the soil column are leached from the exchange complex by major ions (Ca2+ , Mg2+ , and Al3+ ). Water was applied to the top of the column at a steady flow rate of 2 cm day−1 and having a chemical composition as given in Table 22.2. Details are given by Jacques and Šimunek ˚ (2005).
22.6 Concluding Remarks This chapter demonstrates the abundance of models and modeling approaches that are currently available for simulating variably saturated water flow and contaminant transport at various levels of approximation and for different applications. Models range from relatively simple analytical approaches for analyzing solute transport problems during one-dimensional steady-state flow, to sophisticated numerical models for addressing multi-dimensional variably saturated flow and contaminant transport problems at the field scale. One may expect that unsaturated zone flow and transport models will be used increasingly as tools for developing cost-effective, yet technically sound strategies for resource management and pollution remediation and prevention. Improved understanding of the key underlying processes, continued advances in numerical methods, and the introduction of more and more powerful computers make such simulations increasingly practical for many field-scale problems. For example, models can be helpful tools for designing, testing and implementing soil, water and crop management practices that minimize soil and water pollution. Models are equally needed for designing or remediating industrial waste disposal
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TABLE 22.2 Chemical Components (mmol/L) and Species Considered, and Elemental Compositions of Initial and Boundary Solutions Used in the Column Simulation. X Refers to Ion Exchanger Solutions Components Species Al Br Cl Ca K Na Mg Cd Pb Zn X
− 0 Al3+ , Al(OH)2+ , Al(OH)+ 2 , Al(OH)3 , Al(OH)4 Br− Cl− (and Cd, Pb, and Zn-species, see below) Ca2+ , Ca(OH)+ K+ , KOH0 Na+ , NaOH0 Mg2+ , Mg(OH)+ 2− + Cd2+ , Cd(OH)+ , Cd(OH)02 , Cd(OH)− 3 , Cd(OH)4 , CdCl , CdCl2 , CdCl− 3 2− 0 + Pb2+ , Pb(OH)+ , Pb(OH)02 , Pb(OH)− 3 , Pb(OH)4 , PbCl , PbCl2 , 2− PbCl− , PbCl 3 4 2− 0 + Zn2+ , Zn(OH)+ , Zn(OH)02 , Zn(OH)− 3 , Zn(OH)4 , ZnCl , ZnCl2 , − 2− ZnCl3 , ZnCl4 AlX3 , AlOHX2 , CaX2 , CdX2 , KX, NaX, MgX2 , PbX2 , ZnX2 (mmol)
Boundary
Initial
0.1 3.7 10 5 0 0 1
0.5 11.9 0 0 2 6 0.75
0
0.9
0
0.1
0 NA
0.25 11
sites and landfills, for predicting contaminant transport from mining wastes, or for long-term stewardship of nuclear waste repositories. The main challenge is to make the models as realistic as possible for the various applications. Continued progress in subsurface flow and transport modeling requires equal advances in both numerical techniques as well as the underlying science. Addressing preferential flow phenomena, and the related problems of subsurface heterogeneity, including the stochastic nature of boundary conditions (precipitation and/or evapotranspiration), will continute to pose formidable challenges. The same is true for improving multicomponent geochemical transport modeling for the vadose zone. For example, numerical algorithms and databases for multicomponent transport models must be extended to higher temperatures and ionic strengths, complex contaminant mixtures (including especially mixed organic and inorganic wastes), multiphase flow, redox disequilibria for low-temperature systems, and coupled physicochemical systems to account for possible changes in the soil water retention and hydraulic conductivity functions. Better integration is also needed between variably saturated subsurface and existing largerscale surface numerical models, which in turn requires further research on such issues as spatial and temporal scaling of hydrological, chemical and biological processes and properties, linking constitutive (soil hydraulic) relationships to measurements scales, preferential flow, and issues of parameter and model uncertainty. Many science questions related to colloid and colloid-facilitated transport are also still largely unresolved. This is an area of research where our understanding lags far behind current numerical capabilities. Much work is needed to better understand the processes of filtration, straining, size exclusion, colloid–colloid interactions, mobilization of colloids and microorganisms; accumulation at air–water interfaces, interactions between microorganisms and contaminants (including biodegradation), the effects of both physical factors (water content, flow velocity, textural interfaces) and chemical processes (ionic strength, solution composition, pH) on colloid retention and mobilization, and modeling colloid-facilitated transport during conditions of transient flow. Also, to the best of our knowledge, no models are currentely available that consider all the various processes simultaneously and in their full complexity, including their mutual interactions. That is, no models exist that consider transient preferential flow and transport in structured soils or fractured rocks, while simultaneously considering complex biogeochemical reactions between contaminants, organic and inorganic colloids and/or organic complexes, and solid and air phases of a soil, including widely
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varying rates of these various reactions. Further integration of the different types of numerical models is needed to address practical problems of contaminant transport (trace elements, radionuclides, organic contaminants) in complex vadose zone environments.
References Abriola, L.M., Pennell, K.D., Weber, Jr., W.J. Lang, J.R., and Wilkins, M.D., Persistence and interphase mass transfer of organic contaminants in the unsaturated zone: Experimental observations and mathematical modeling. In J.Y. Parlange and J.W. Hopmans (Eds.) Vadose Zone Hydrology: Cutting Across Disciplines. Oxford University Press, New York, pp. 210–234, 1999. Adamczyk, Z., Siwek, B., Zembala, M. and Belouschek, P., Kinetics of localized adsorption of colloid particles. Adv. Coll. Interf. Sci. 48, 151–280, 1994. Ahuja, L.R. and Hebson, C., Root Zone Water Quality Model. GPSR Tech. Rep. No. 2, USDA, ARS, Fort Collins, CO, 1992. Anderson, M.P., Movement of contaminants in groundwater: Groundwater transport–advection and dispersion. In Groundwater Contamination, Studies in Geophysics, National Academy Press, Washington, D.C. pp. 37–45, 1984. Appelo, C.A.J. and Postma, D., Geochemistry, Groundwater and Pollution. A. A. Balkema. Rotterdam, 1993. Bache, B.W. and Williams, E.G., A phosphate sorption index for soils. J. Soil Sci. 27, 289–296, 1971. Barry, D.A., Modelling contaminant transport in the subsurface: theory and computer programs. In H. Ghadiri and C.W. Rose (Eds.), Modelling Chemical Transport in Soil: Natural and Applied Contaminants, Lewis Publishers, Chelsea, MI, pp. 105–144, 1992. Bateman, H., The solution of a system of differential equations occurring in the theory of radioactive transformation. Proc. Cambridge Philos. Soc. 15 (pt V) 423–427, 1910. Bear, J., Dynamics of Fluids in Porous Media, Elsevier Science, New York, 1972. Bell, L.S.J. and Binning, P.J., A split operator approach to reactive transport with the forward particle tracking Eulerian–Lagrangian localized adjoint method. Adv. Water Resour. 27, 323–334, 2004. Bethke, C. M., Geochemical Reaction Modeling — Concepts and Applications. Oxford University Press, New York, p. 397, 1996. Biggar, J.W. and Nielsen, D.R., Miscible displacement and leaching phenomena. Agronomy 11, 254–274, 1967. Bradford, S.A., Yates, S.R., Bettahar, M. and Šimunek, ˚ J., Physical factors affecting the transport and fate of colloids in saturated porous media. Water Resour. Res. 38, 1327, doi:10.1029/2002WR001340, 2002. Bradford, S.A., Šimunek, ˚ J., Bettahar, M., van Genuchten, M.Th. and Yates, S.R., Modeling colloid attachment, straining, and exclusion in saturated porous media. Environ. Sci. Technol. 37, 2242–2250, 2003. Bradford, S.A., Bettahar, M., Šimunek, ˚ J. and van Genuchten, M.Th., Straining and attachment of colloids in physically heterogeneous porous media. Vadose Zone J. 3, 384–394, 2004. Bresler, E. and Dagan G., Solute dispersion in unsaturated heterogeneous soil at field scale: I Applications. Soil Sci. Soc. Am. J. 43, 467–472, 1979. Brooks, R.H. and Corey, A. T., Hydraulic properties of porous media. Hydrol. Paper No. 3, Colorado State University, Fort Collins, CO, 1964. Brusseau, M.L., Nonideal transport of reactive solutes in porous media: Cutting across history and disciplines. In Parlange, M.B. and Hopmans, J.W. (Eds.), Vadose Zone Hydrology: Cutting Across Disciplines, Oxford University Press, New York, pp. 130–154, 1999. Carsel, R.F. and Parrish, R.S., Developing joint probability distributions of soil water retention characteristics. Water Resour. Res. 24, 755–769, 1988. Casey, F.X.M. and Šimunek, ˚ J., Inverse analyses of the transport of chlorinated hydrocarbons subject to sequential transformation reactions. J. Environ. Qual. 30, 1354–1360, 2001. Casey, F.X.M., Larsen, G.L., Hakk, H. and Šimunek, ˚ J., Fate and transport of 17β-Estradiol in soil-water systems. Environ. Sci. Technol. 37, 2400–2409, 2003.
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Casey, F.X.M., Larsen, G.L., Hakk, H. and Šimunek, ˚ J., Fate and transport of testosterone in agriculturally significant soils. Environ. Sci. Technol. 38, 790–798, 2004. Corapcioglu, M.Y. and Jiang, S., Colloid-facilitated ground-water contaminant transport. Water Resour. Res. 29, 2215–2226, 1993. Corapcioglu, M.Y. and Kim, S., Modeling facilitated contaminant transport by mobile bacteria. Water Resour. Res. 31, 2639–2644, 1995. Dagan G. and E. Bresler, Solute dispersion in unsaturated heterogeneous soil at field scale: I Theory. Soil Sci. Soc. Am. J. 43, 461–467, 1979. Dagan G., Flow and Transport in Porous Formations, Springer-Verlag, Berlin, 1989. Durner, W., Hydraulic conductivity estimation for soils with heterogeneous pore structure. Water Resour. Res. 32, 211–223, 1994. Fayer, M.J., UNSAT-H Version 3.0: Unsaturated Soil Water and Heat Flow Model. Theory, User Manual, and Examples. Pacific Northwest National Laboratory 13249, 2000. Fitter, A.H. and Sutton, S.D., The use of the Freundlich isotherm for soil phosphate sorption data. J. Soil Sci. 26, 241–246, 1975. Flerchinger, G.N., Hanson, C.L. and Wight, J.R., Modeling evapotranspiration and surface energy budgets across a watershed. Water Resour. Res. 32, 2539–2548, 1996. Flury, M., Fluhler, H., Jury, W. and Leuenberger, J., Susceptibility of soils to preferential flow of water: a field study. Water Resour. Res. 30, 1945–1954, 1994. Freundlich, H., Kapillarchemie; eine Darstellung der Chemie der Kolloide und verwandter Gebiete, Akademische Verlagsgellschaft, Leipzig, Germany, 1909. Gelhar, L.W., Mantaglou, A., Welty, C. and Rehfeldt, K.R., A review of Field Scale Physical Solute Transport Processes in Unsaturated and Saturated Porous Media, EPRI Topicl Report EA-4190, Electric Power Research Institute, Palo Alto, CA, 1985. Gerke, H.H. and van Genuchten, M.Th., A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media. Water Resour. Res. 29, 305–319, 1993a. Gerke, H.H. and van Genuchten, M.Th., Evaluation of a first-order water transfer term for variably saturated dual-porosity flow models. Water Resour. Res. 29, 1225–1238, 1993b. Gerke, H.H. and van Genuchten, M.Th., Macroscopic representation of structural geometry for simulating water and solute movement in dual-porosity media. Adv. Water Resour. 19, 343–357, 1996. Germann, P.F., Kinematic wave approach to infiltration and drainage into and from soil macropores. Trans. ASAE 28, 745–749, 1985. Germann, P.F. and Beven, K., Kinematic wave approximation to infiltration into soils with sorbing macropores. Water Resour. Res. 21, 990–996, 1985. Glotfelty, D.E. and Schomburg, C.J., Volatilization of pesticides. In B.L. Sawhney and K. Brown (Eds.), Reactions and Movement of Organic Chemicals in Soils, Special Publ. No. 22, Soil Science Society of America, Madison, WI, pp. 181–208, 1989. Grolimund, D., Borkovec, M., Barmettler, K. and Sticher, H., Colloid-facilitated transport of strongly sorbing contaminants in natural porous media; a laboratory column study. Environ. Sci. Technol. 30, 3118–3123, 1996. Gunary, D., A new adsorption isotherm for phosphate in soil. J. Soil Sci. 21, 72–77, 1970. Gwo, J.P., Jardine, P.M., Wilson, G.V. and Yeh, G.T., A multiple-pore-region concept to modeling mass transfer in subsurface media. J. Hydrol. 164, 217–237, 1995. Hanselman, T.A., Graetz, D.A. and Wilkie, A.C., Manure-borne estrogens as potential environmental contaminants: A review. Environ. Sci. Technol. 37, 5471–5478, 2003. Hansen, S., Jensen, H.E., Nielsen, N.E. and Svendsen, H., DAISY: Soil Plant Atmosphere System Model. NPO Report No. A 10. The National Agency for Environmental Protection, Copenhagen, 272 pp, 1990. Haws, N.W., Rao, P.S.C., Šimunek, ˚ J., and Poyer, I.C., Single-porosity and dual-porosity modeling of water flow and solute transport in subsurface-drained fields using effective field-scale parameters. J. Hydrol. 313, 257–273, 2005.
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Healy, R.W., Simulation of solute transport in variably saturated porous media with supplemental information on modifications to the U.S. Geological Survey’s computer program VS2D. U.S. Geological Survey, Water-Resources Investigation Report 90-4025: 125, 1990. Hendrickx, J.M.H., Dekker, L.W. and Boersma, O.H., Unstable wetting fronts in water repellent field soils. J. Env. Qual. 22, 109–118, 1993. Hendrickx, J.M.H. and Flury, M., Uniform and preferential flow, Mechanisms in the vadose zone. In Conceptual Models of Flow and Transport in the Fractured Vadose zone. National Research Council, National Academy Press, Washington, D.C., pp. 149–187, 2001. Hopmans, J.W., Šimunek, ˚ J., Romano, N. and Durner, W., Inverse modeling of transient water flow. In J.H. Dane and G.C. Topp (Eds.), Methods of Soil Analysis, Part 1, Physical Methods, Chapter 3.6.2, Third edition, SSSA, Madison, WI, pp. 963–1008, 2002. Hutson, J.L. and Wagenet, R.J., A multiregion model describing water flow and solute transport in heterogeneous soils. Soil Sci. Soc. Am. J. 59, 743–751, 1995. Huyakorn, P.S. and Pinder, G.F., Computational Methods in Subsurface Flow, Academic Press, London, 1983. HydroGeoLogic, Inc., MODFLOW-SURFACT, A Comprehensive MODFLOW-Based Flow and Transport Simulator, Version 2.1, HydroGeoLogic, Inc., 1996. Jacques, D., Šimunek, ˚ J., Mallants, D. and van Genuchten, M. Th., Multicomponent transport model for variably-saturated porous media: Application to the transport of heavy metals in soils. In S.M., Hassanizadeh, R.J. Schotting, W.G. Gray, and G.F. Pinder (Eds.) Computational Methods in Water Resources, XIVth International Conference on Computational Methods in Water Resources, June 23–28, 2002, Delft, The Netherlands. Elsevier, Developments in Water Science, 47, 555–562, 2002. Jacques, D., Šimunek, ˚ J., Mallants, D. and van Genuchten, M. Th., The HYDRUS-PHREEQC multicomponent transport model for variably-saturated porous media: Code verification and application, MODFLOW and More 2003: Understanding through Modeling, Conference Proceedings, E. Poeter, Ch. Zheng, M. Hill, and J. Doherty, (Eds.), Int. Ground Water Modeling Center, Colorado School of Mines, pp. 23–27, 2003. Jacques, D. and Šimunek, ˚ J., Multicomponent — Variable Saturated Transport Model, Description, Manual, Verification and Examples, Waste and Disposal, SCKCEN, BLG-998, Mol, Belgium, 79 pp, 2005. Jansson, P.-E. and Karlberg, L., Coupled heat and mass transfer model for soil-plant-atmosphere systems. Royal Institute of Technology, Dept of Civil and Environmental Engineering, Stockholm 325 pp, 2001. Jarvis, N.J., The MACRO model (Version 3.1), Technical description and sample simulations. Reports and Dissertations 19. Dept. Soil Sci., Swedish Univ. Agric. Sci., Uppsala, Sweden, 51 pp, 1994. Jarvis, N. J., Modeling the impact of preferential flow on nonpoint source pollution. In H.M. Selim and L. Ma (Eds.), Physical Nonequilibrium in Soils: Modeling and Application. Ann Arbor Press, Chelsea, MI, pp. 195–221, 1998. Jiang, S. and Corapcioglu, M.Y., A hybrid equilibrium model of solute transport in porous media in the presence of colloids. Coll. Surf. A: Physicochem. Eng. Aspects 73, 275–286, 1993. Jury, W.A., Simulation of solute transport using a transfer function model. Water Resour. Res. 18, 363–368, 1982. Jury, W.A., Spencer, W.F. and Farmer, W.J., Behavior assessment model for trace organics in soil: I. Description of model. J. Env. Qual. 12, 558–564, 1983. Jury, W.A., Spencer W.F. and Farmer, W.J., Behavior assessment model for trace organics in soil: I. Chemical classification and parameter sensitivity. J. Env. Qual. 13, 567–572, 1984. Jury W.A. and Sposito, G., Field calibration and validation of solute transport models for the unsaturated zone. Soil Sci. Soc. Am. J. 49, 1331–1341, 1985. Jury, W.A. and Horton, R., Soil Physics, Sixth ed, John Wiley & Sons, Inc., New York, 2004.
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23 Groundwater Modeling 23.1 23.2 23.3 23.4
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow and Transport Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23-1 23-2 23-3 23-3
Groundwater-Flow Equation • Seepage Velocity • Solute-Transport Equation
23.5 Numerical Methods to Solve Equations . . . . . . . . . . . . . . . . 23-7 Basics of Finite-Difference Methods • Basics of Finite-Element Methods • Basics of Method-of-Characteristics Methods • Matrix Solution Techniques • Boundary and Initial Conditions • Generic Model Verification
23.6 Model Design, Development, and Application . . . . . . . . 23-19 Grid Design • Model Calibration • Model Error • Mass Balance • Sensitivity Tests • Calibration Criteria • Predictions and Postaudits • Model Validation
23.7 Overview of Representative Generic Models. . . . . . . . . . . 23-28 MODFLOW-2000 • SUTRA
23.8 Case Histories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-31 Flow and Transport in a Shallow Unconfined Aquifer • Delineation of Contributing Areas to Water-Supply Wells, Rhode Island • Seawater Intrusion in a Coastal Aquifer
Leonard F. Konikow, Thomas E. Reilly, Paul M. Barlow, and Clifford I. Voss U.S. Geological Survey
23.9 Available Groundwater Software. . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23-44 23-45 23-46 23-46 23-50
23.1 Introduction Effective management of groundwater requires the ability to predict subsurface flow and transport of solutes, and the response of fluid and solute flux to changes in natural or human-induced stresses. One popular type of tool that has been evolving since the mid-1960s is the deterministic, distributedparameter, computer simulation model for analyzing flow and solute-transport in groundwater systems.
23-1
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The Handbook of Groundwater Engineering
The development of the computer simulation model has paralleled the development and increasing availability of faster, more capable, yet less expensive computer systems. The purpose of this chapter is to review the state of the art in deterministic modeling of groundwater flow and transport processes. This chapter is aimed at practitioners and is intended to describe the types of models that are available and how to apply them to complex field problems. Our discussions of transport modeling are focused on nonreactive dissolved constituents, and we do not address multicomponent reactive transport or multiphase flow phenomena, such as the transport of nonaqueous phase liquids (NAPL). The chapter discusses the philosophy and theoretical basis of deterministic modeling, the advantages and limitations of models, the use and misuse of models, how to select a model, and how to calibrate and evaluate a model. However, as this chapter is only a review, it cannot offer comprehensive and in-depth coverage of this complex topic; instead, it guides the reader to references that provide more details.
23.2 Models The word model has so many definitions and is so overused that it is sometimes difficult to discern its meaning (Konikow and Bredehoeft 1992). A model is perhaps most simply defined as an approximate representation of a real system or process. A conceptual model is a hypothesis for how a system or process operates. This hypothesis can be expressed quantitatively as a mathematical model. Mathematical models are abstractions that represent processes as equations, physical properties as constants or coefficients in the equations, and measures of state or potential in the system as variables. Most groundwater models in use today are deterministic mathematical models. Deterministic models are based on conservation of mass, momentum, and energy and describe cause and effect relations. The underlying assumption is that given a high degree of understanding of the processes by which stresses on a system produce subsequent responses, the response of the system to any set of stresses can be predetermined, even if the magnitude of the new stresses falls outside the historically observed range. Deterministic groundwater models generally require the solution of partial differential equations. Exact solutions can often be obtained analytically, but analytical models require that the parameters and boundaries be highly idealized. Some deterministic models treat the properties of porous media as lumped parameters (essentially, as a black box), but this precludes explicit representation of heterogeneous hydraulic properties in the model. Heterogeneity, or variability in aquifer properties, is characteristic of all geologic systems and is recognized as important in affecting groundwater flow and solute transport. Thus, it is often preferable to apply distributed-parameter models, which allow the representation of more realistic distributions of system properties. Numerical methods yield approximate solutions to the governing equation (or equations) through the discretization of space and time. Within the discretized problem domain, the varying internal properties, boundaries, and stresses of the hydrogeologic system are approximated. Deterministic, distributed-parameter, numerical models can relax the rigid idealized conditions of analytical models or lumped-parameter models, and they can, therefore, be more realistic and flexible for simulating field conditions (if applied properly). The number and types of equations to be solved are determined by the dominant governing processes. The coefficients of the equations are parameters that are measures of the properties, boundaries, and stresses of the system; the dependent variables of the equations are measures of the state of the system and are mathematically determined by the solution of the equations. When a numerical algorithm is implemented in a computer code to solve one or more partial differential equations, the resulting computer code can be considered a generic model. When the grid dimensions, boundary conditions, and other parameters (such as hydraulic conductivity and storativity) are specified in an application of a generic model to represent a particular geographical area, the resulting computer program is a site-specific model. The capacity of generic models to solve the governing equations accurately is typically demonstrated by example applications to simplified problems. This capacity does not guarantee a similar level of accuracy when the model is applied to a complex field problem.
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If the user of a model is unaware of or ignores the details of the numerical method, including the derivative approximations, the scale of discretization, and the matrix solution techniques, appreciable errors can be introduced and remain undetected. For example, if the groundwater-flow equation is solved iteratively, but the convergence criterion is too coarse, then the numerical solution may converge to an inaccurate solution. The inaccuracy of the solution may or may not be reflected in the mass-balance error. The mass-balance error itself may not be readily observed by inexperienced model users. Moreover, the potential for unrecognized errors in numerical models is increasing because “user-friendly” commercially available graphical user interfaces (GUIs) make it easier for models to be used (and to be misused). These interfaces effectively place more “distance” between the modeler and the numerical method that lies at the core of the model. When developing a complex three-dimensional (3D) groundwater model, however, a GUI may be a necessity.
23.3 Flow and Transport Processes The process of groundwater flow is generally assumed to be governed by the relations expressed in Darcy’s law (see Chapter 3) and the conservation of mass. However, Darcy’s law does have limits on its range of applicability, and these limits must be evaluated in any model application. The purpose of a model that simulates solute transport in groundwater is to compute the concentration of a dissolved chemical species in a groundwater system at any specified time and place. The theoretical basis for the equation describing solute transport has been well documented in the literature (e.g., Bear 1979; Domenico and Schwartz 1997). Reilly et al. (1987) provide a conceptual framework for analyzing and modeling physical solute-transport processes in groundwater. Changes in chemical concentration occur within a dynamic groundwater system primarily because of four distinct processes: (1) advective transport, in which dissolved chemicals are moving with the flowing groundwater; (2) hydrodynamic dispersion, in which molecular and ionic diffusion and small-scale variations in the flow velocity through the porous media cause the paths of dissolved molecules and ions to diverge or spread from the average advective flow path; (3) fluid sources, where water of one composition is introduced into and mixed with water of a different composition; and (4) reactions, in which some amount of a particular dissolved chemical species may be added to or removed from the groundwater as a result of chemical, biological, and physical reactions in the water or between the water and the solid aquifer materials or other separate liquid phases. The subsurface environment constitutes a complex, 3D, heterogeneous hydrogeologic setting. This variability strongly affects groundwater flow and transport, and such settings can be described accurately only through careful hydrogeologic practice in the field. Regardless of how much data are collected, uncertainty always remains about the properties and boundaries of the groundwater system of interest. Stochastic approaches have resulted in many significant advances in characterizing subsurface heterogeneity and dealing with uncertainty (see Gelhar 1993). Parameters often are treated in stochastic modeling as random variables and deterministically solve the governing equations for many realizations.
23.4 Governing Equations The mathematical equations that describe groundwater flow (see Chapter 4) and transport processes (see Chapter 18 and Chapter 19) may be developed from the fundamental principle of conservation of mass of fluid or of solute. Given a representative elementary volume (REV) of porous medium, a general equation for conservation of mass for the volume may be expressed as rate of mass inflow − rate of mass outflow + rate of mass production/consumption = rate of mass accumulation
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(23.1)
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This statement of conservation of mass (or continuity equation) may be combined with a mathematical expression of the relevant process to obtain a differential equation that describes flow or transport.
23.4.1 Groundwater-Flow Equation The rate of flow of water through a porous media is related to the properties of the water, the properties of the porous media, and the gradient of the hydraulic head, which can be written using Darcy’s law as qi = −Kij
∂h ∂xj
(23.2)
where qi is the specific discharge, LT−1 ; Kij is the hydraulic conductivity of the porous medium (a secondorder tensor), LT−1 ; h is the hydraulic head, L; and xj are the Cartesian coordinates, L. A general form of the equation describing the transient flow of a slightly compressible fluid in a nonhomogeneous anisotropic aquifer may be derived by combining Darcy’s law with the continuity equation. A general groundwater-flow equation may be written in Cartesian tensor notation as ∂ ∂xi
Kij
∂h ∂xj
= Ss
∂h + W∗ ∂t
(23.3)
where Ss is the specific storage, L−1 ; t is time, T; and W ∗ the volumetric flux per unit volume (positive for outflow and negative for inflow), T−1 . The summation convention of Cartesian tensor analysis is implied in Equation 23.2 and Equation 23.3. Equation 23.3 can generally be applied if isothermal conditions prevail, the porous medium only deforms vertically, the volume of individual grains remains constant during deformation, Darcy’s law applies (and gradients of hydraulic head are the only driving force), and fluid properties (density and viscosity) are homogeneous and constant. Aquifer properties can vary spatially and fluid stresses (W ∗ ) can vary in space and time. If the aquifer is relatively thin compared to its lateral extent, it may be appropriate to assume that groundwater flow is areally two dimensional. This assumption allows the 3D flow equation to be reduced to the case of two-dimensional (2D) areal flow, for which various additional simplifications are possible. The advantages of reducing the dimensionality of the equation include less stringent data requirements, smaller computer memory requirements, and shorter computer execution times to achieve numerical solutions. An expression similar to Equation 23.3 may be derived for the 2D areal flow of a homogeneous fluid in a confined aquifer and written as ∂ ∂xi
Tij
∂h ∂xj
=S
∂h +W ∂t
(23.4)
where Tij is the transmissivity, L2 T−1 ; and Tij = Kij b; b is the saturated thickness of the aquifer, L; S is the storage coefficient (dimensionless); and W = W ∗ b is the volume flux per unit area, LT−1 . When Equation 23.4 is applied to an unconfined (water-table) aquifer, it must be assumed that flow is horizontal and equipotential lines are vertical, that the horizontal hydraulic gradient equals the slope of the water table, and that the storage coefficient is equal to the specific yield (Sy ) (Anderson and Woessner 1992). Note that in an unconfined system, the saturated thickness changes as the water-table elevation (or head) changes. Thus, the transmissivity also can change over space and time (i.e., Tij = Kij b, where b(x, y, t ) = h − hb , and hb is the elevation of the bottom of the aquifer). The cross-product terms of the hydraulic conductivity tensor drop out when the coordinate axes are aligned with the principal axes of the tensor; that is, Kij = 0 when i = j. Therefore, the only hydraulic conductivity terms with possible nonzero values are Kxx and Kyy . Under this assumption, Equation 23.4
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23-5
may be simplified to ∂ ∂x
∂h Txx ∂x
∂ + ∂y
∂h Tyy ∂y
=S
∂h +W ∂t
(23.5)
for 2D flow. In some field situations, fluid properties, such as density and viscosity, may vary significantly in space or time. This may occur where water temperature or dissolved-solids concentration changes significantly. When the fluid properties are heterogeneous and (or) transient, the relations among water levels, hydraulic heads, fluid pressures, and flow velocities are neither simple nor straightforward. In such cases, it is impossible to solve the groundwater-flow equation in terms of the fluid potential (hydraulic head), and the flow equation is written and solved in terms of fluid pressures, fluid densities, and the intrinsic permeability of the porous media as ∂p kij ρ ∂ρ ∂ω ∂ ∂p ∂z + ε − + ρg = Qp ρS0p ∂t ∂ω ∂t ∂xi µ ∂xj ∂xj
(23.6)
where S0p is the specific pressure storativity [ML−1 T−2 ]−1 ; ρ is the fluid density [ML−3 ]; p is the fluid pressure [ML−1 T−2 ]; Qp is a fluid mass source [ML−3 T−1 ]; kij is the intrinsic permeability of the porous medium (a second-order tensor) [L2 ]; µ is the dynamic fluid viscosity [ML−1 T−1 ]; g is the gravitational acceleration [LT−2 ]; and ω is the solute mass fraction (mass of solute/mass of fluid) [dimensionless]. The specific pressure storativity is related to the specific storage coefficient as Ss = ρ|g |S0p .
23.4.2 Seepage Velocity The migration and mixing of chemicals dissolved in groundwater is affected by the velocity of the flowing groundwater. The specific discharge calculated from Equation 23.2 is sometimes called the Darcy velocity. However, this nomenclature can be misleading because qi does not actually represent the speed of water movement. Rather, qi represents a volumetric flux per unit cross-sectional area. To calculate the mean seepage velocity, one must account for the cross-sectional area through which flow is occurring by dividing the specific discharge by the effective porosity of the porous medium, ε, resulting in Vi =
Kij ∂h qi =− ε ε ∂xj
(23.7)
where Vi is the seepage velocity (also commonly called average linear velocity or average interstitial velocity), LT−1 . For variable-density flow, the fluid velocity is given by kij ερ ∂z ∂p + ρg Vi = − µ ∂xj ∂xj
(23.8)
23.4.3 Solute-Transport Equation An equation describing the transport and dispersion of a dissolved chemical in flowing groundwater may be derived from the principle of conservation of mass by considering all fluxes into and out of a REV, as described by Bear (1979, p. 29). A generalized form of the solute-transport equation is presented by Grove (1976), in which terms are incorporated to represent chemical reactions and solute concentration both in the pore fluid and on the solid surface, as ∂ ∂(εC) = ∂xi ∂t
εDij
∂C ∂xj
−
∂ (εCVi ) − C ∗ W ∗ + CHEM ∂xi
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(23.9)
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where CHEM equals one or more of the following: − ρb s
∂ C¯ ∂t
Rk
for linear equilibrium controlled sorption or ion-exchange reactions,
for s chemical rate-controlled reactions, and (or)
k=1
¯ − λ(εC + ρb C)
for decay,
and where C is the volumetric concentration (mass of solute per unit volume of fluid, ML−3 ), Dij is the coefficient of hydrodynamic dispersion (a second-order tensor), L2 T−1 ; C ∗ is the concentration of the solute in the source or sink fluid; C¯ is the concentration of the species adsorbed on the solid (mass of solute/mass of solid); ρb is the bulk density of the sediment, ML−3 ; Rk is the rate of production of the solute in reaction k, ML−3 T−1 ; and λ is the decay constant (equal to ln 2/half life), T−1 (Grove 1976). For cases of variable-density fluids without reactions, the solute mass balance may be expressed as ∂ ∂ω = (ερ) ∂t ∂xi
∂ω ερDij ∂xj
− ερVi
∂ω + Qp (ω∗ − ω) ∂xi
(23.10)
The first terms on the right sides of Equation 23.9 and Equation 23.10 represent the change in concentration because of hydrodynamic dispersion. This expression is analogous to Fick’s law describing diffusive flux. This Fickian model assumes that spreading is driven by the concentration gradient and that the dispersive flux occurs in a direction from higher concentrations toward lower concentrations. However, this assumption is not always consistent with field observations and is the subject of much ongoing research and field study (see, e.g., Gelhar et al. 1992; Carrera et al. 2005). The coefficient of hydrodynamic dispersion is defined as the sum of mechanical dispersion and molecular diffusion (Bear 1979), commonly expressed as Dij = αijmn
Vm Vn + D∗ |V |
i, j, m, n = 1, 2, 3
(23.11)
where αijmn is the dispersivity of the porous medium (a fourth-order tensor), L; Vm and Vn are the components of the flow velocity of the fluid in the m and n directions, respectively, LT−1 ; D ∗ is the effective coefficient of molecular diffusion, L2 T−1 ; and |V | is the magnitude of the velocity vector, LT−1 , defined as |V | =
Vx2 + Vy2 + Vz2 (Bear 1979; Domenico and Schwartz 1997). Mechanical
dispersion is a function both of the intrinsic properties of the porous medium (such as heterogeneities in hydraulic conductivity and porosity) and of the fluid flow. Molecular diffusion in a porous medium will differ from that in free water because of the effects of tortuous paths of fluid connectivity in porous media. The dispersivity of an isotropic porous medium can be defined by two constants. These constants are the longitudinal dispersivity of the medium, αL , and the transverse dispersivity of the medium, αT . These constants are related to the longitudinal and transverse dispersion coefficients by DL = αL |V | and DT = αT |V |. Most documented applications of transport models to groundwater contamination problems have been based on this conventional formulation, even for cases in which the hydraulic conductivity is assumed to be anisotropic, despite the conceptual inconsistency. However, some models (e.g., Voss and Provost 2002) incorporate an additional level of sophistication by allowing αL and (or) αT to vary with direction. Flow-direction-dependent dispersivity is indeed a useful generalization of the classical dispersion paradigm. For example, it may be expected that flow parallel to layering in a layered medium and flow perpendicular to the layering do not necessarily have the same longitudinal dispersivity. For seawater intrusion, as considered in cross section, solutes may travel several kilometers inland from the
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23-7
sea within a given aquifer layer with an effective longitudinal dispersivity of hundreds of meters. After transport inland, the solutes may be induced to travel upward to an overlying aquifer layer when shallow wells are pumped; this transport occurs over the distance of aquifer thickness of a few tens of meters. A dispersivity value of hundreds of meters is not appropriate or meaningful for quantifying transport with flow over a vertical distance of tens of meters. Rather, a dispersivity of a few meters is more reasonable. Thus, for simulating this hydrogeologic system using flow-direction-dependent dispersivity, longitudinal dispersivity for flow in the horizontal direction would be specified to be about 100 m and for flow in the vertical direction would be specified to be about 1 m. Although conventional theory holds that αL is generally an intrinsic property of the aquifer, it is found in practice to be dependent on and proportional to the scale of the measurement. Most reported values of αL fall in a range from 0.01 to 1.0 times the scale of the measurement, although the ratio of αL to scale of measurement tends to decrease at larger scales (see Anderson 1984; Gelhar et al. 1992). Field-scale dispersion (commonly called macrodispersion) results from large-scale spatial variations in hydraulic properties. Consequently, the use of relatively large values of dispersivity together with uniform hydraulic properties (Kij and ε) is inappropriate for describing transport in geological systems (Smith and Schwartz 1980). Part of the scale dependence of dispersivity may be explained as an artifact of the models used, in that a scaling up of dispersivity will occur whenever an (n − 1)-dimensional model is calibrated or used to describe an n-dimensional system (Domenico and Robbins 1984). Furthermore, if mean values are applied in a model of a system with variable hydraulic conductivity and thereby does not explicitly represent the variability, the model calibration will likely yield values for the dispersivity coefficients that are larger than would be measured locally in the field area. Similarly, representing a transient flow field by a mean steady-state flow field, as is commonly done, inherently ignores some of the variability in velocity and must be compensated for by using increased values of dispersivity (primarily transverse dispersivity) (Goode and Konikow 1990). Overall, the more accurately a model can represent or simulate the true velocity distribution in space and time, the less of a problem will be the uncertainty concerning representation of dispersion processes. The mathematical solute-transport model requires at least two partial differential equations. One is the equation of flow, from which groundwater-flow velocities are obtained, and the second is the solutetransport equation, whose solution gives the chemical concentration in groundwater. If the properties of the water are affected appreciably by changes in solute concentration, as in a seawater intrusion problem in a coastal aquifer, then the flow and transport equations should be solved simultaneously (or at least iteratively). For such a variable-density problem, the flow and transport equations must be linked by a functional relation between concentration and fluid density. If the transport problem is such that the properties of the water remain constant, then the flow and transport equations can be decoupled and solved sequentially, which is simpler numerically.
23.5 Numerical Methods to Solve Equations The partial differential equations describing groundwater flow and transport can be solved mathematically using either analytical or numerical solutions. The advantages of an analytical solution, when it is possible to apply one, are that it usually provides an exact solution to the governing equation and is often relatively simple and efficient to use. Many analytical solutions have been developed for the flow equation; however, most applications have been limited to well hydraulics problems involving radial symmetry and to 1D and 2D problems involving stream–aquifer interactions. The familiar Theis type curve represents the solution of one such analytical model. Analytical solutions are also available to solve the solute-transport equation (e.g., Bear 1979; Javandel et al. 1984; Wexler 1992). In general, obtaining the exact analytical solution to the partial differential equation requires that the properties and boundaries of the flow system be highly and perhaps unrealistically idealized. For modeling most field problems, the mathematical benefits of obtaining an exact analytical solution can be outweighed by the errors introduced by the simplifying assumptions required to apply the analytical approach to the field setting.
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For problems where simplified analytical models cannot describe the physics of the situation, the partial differential equations of groundwater flow and transport can be approximated numerically. In so doing, the continuous variables are replaced with discrete variables that are defined throughout a spatial grid. Thus, the continuous differential equation, which defines hydraulic head or solute concentration everywhere in the groundwater system, is replaced by a finite number of algebraic equations that defines the hydraulic head or concentration at specific points. This system of algebraic equations generally is solved using matrix techniques. This approach constitutes a numerical model. Two major classes of numerical methods have come to be the most widely used and accepted for solving the groundwater-flow equation. These classes are finite-difference and finite-element methods. Each of these two major classes of numerical methods includes a variety of subclasses and implementation alternatives. Comprehensive treatments of the application of these numerical methods to groundwater problems are presented by Remson et al. (1971) and Wang and Anderson (1982). Both these numerical approaches require that the area of interest be subdivided into a grid (or mesh) of smaller sub-areas (cells or elements) that are associated with nodal points (either at the centers or peripheries of the sub-areas). In addition to finite-difference and finite-element methods, boundary integral equation methods and analytical element methods can also be applied to solve the flow equation (e.g., Haitjema 1995). The main advantage of these methods is that, for homogeneous regions, they can provide precise solutions without discretization. Thus, if the heterogeneity of a groundwater system can be adequately represented by using only a few very large elements, the methods can be efficient in terms of computer time. If heterogeneities are such that a large number of elements are required to describe them adequately, then finite-difference or finite-element methods may be preferable. Finite-difference methods approximate the first derivatives in the partial differential equations as difference quotients (the differences between values of the independent variable at adjacent nodes with respect to the distance between the nodes, and at two successive time levels with respect to the duration of the time-step increment). Assumed functions of the dependent variable and parameters are used in the finite-element methods to evaluate equivalent integral formulations of the partial differential equations. Huyakorn and Pinder (1983) present a comprehensive analysis of the application of finiteelement methods to groundwater problems. In both numerical approaches, the discretization of the space and time dimensions allows the continuous boundary-value problem for the solution of the partial differential equation to be reduced to the simultaneous solution of a set of algebraic equations. These equations can then be solved using either iterative or direct matrix methods. Each method described here has advantages and disadvantages, but there are very few groundwater problems for which either is clearly superior. In general, the finite-difference methods are conceptually and mathematically simpler, and are easier to program. The finite-difference equations typically are derived for a relatively simple, rectangular grid, which also eases data entry. Finite-element methods generally require the use of more sophisticated mathematics but, for some problems, may be more accurate numerically than standard finite-difference methods. A major advantage of the finite-element methods is the flexibility of the finite-element grid, which allows a close spatial approximation of irregular boundaries of the aquifer and (or) of parameter zones within the aquifer when they are considered. However, the construction and specification of an input data set are much more difficult for an irregular finite-element grid than for a regular rectangular finite-difference grid. Thus, the use of a model preprocessor, which includes a mesh generator and a scheme to number the nodes and elements of the mesh and to specify the spatial coordinates of each node, is recommended. A hypothetical aquifer system that has been discretized using finite-difference and finite-element grids is illustrated in Figure 23.1. Conceptually how the finitedifference and finite-element grids can be adjusted to use a finer mesh spacing in selected areas of interest are illustrated in Figure 23.1b and Figure 23.1c. The rectangular finite-difference grid approximates the aquifer boundaries in a step-wise manner, resulting in some nodes and cells that lie outside of the aquifer. In contrast, the finite-element mesh can closely follow the outer boundary of the aquifer using a minimal number of nodes. The solute-transport equation is more difficult to solve numerically than the groundwater-flow equation, largely because the mathematical properties of the transport equation vary depending upon
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(c)
Well field
Active cell
Aquifer boundary
Inactive cell
Element
FIGURE 23.1 Application of a numerical model to a simple hypothetical problem, showing (a) an irregularly bounded aquifer discretized using (b) a finite-difference grid and (c) a finite-element mesh. (From Konikow, L. F. (1996) In Manual on Mathematical Models in Isotope Hydrogeology, International Atomic Energy Agency, Vienna, Austria.)
which terms in the equation are dominant in a particular situation. When solute transport is dominated by advective transport, as is common in many field problems, then Equation 23.9 or Equation 23.10 approximates a hyperbolic type of equation (similar to equations describing the propagation of a wave or of a shock front). However, if transport is dominated by dispersive fluxes, such as might occur where fluid velocities are relatively low and aquifer dispersivities are relatively high, then Equation 23.9 or Equation 23.10 becomes more parabolic in nature (similar to the transient groundwater-flow equation). The numerical methods that work best for parabolic partial differential equations are not best for solving hyperbolic equations, and vice versa. Thus, no single numerical method or simulation model will be ideal for the entire spectrum of groundwater-transport problems likely to be encountered in the field. Further compounding this difficulty is that in the field, the seepage velocity of groundwater can be highly variable because of heterogeneous aquifer properties and (or) boundary conditions. Thus, in low permeability zones or near stagnation points, the velocity may be close to zero and the transport processes will be dominated by dispersion processes; in high permeability zones or near stress points (such as pumping wells), the velocity may be several meters per day and the transport processes will be advection-dominated. In other words, for the same system, the governing equation may be more hyperbolic in one area (or at one time) and more parabolic in another. Therefore, no numerical method will be ideal or optimal over the entire domain of the problem, and appreciable numerical errors may be introduced somewhere in the solution. The transport modeling effort must recognize this inherent difficulty and strive to minimize and control the numerical errors. Additional complications arise when the solutes of interest are reactive. The reaction terms included in Equation 23.9 are mathematically simple ones that may not necessarily represent the true complexities of many reactions. Also, particularly difficult numerical problems arise when reaction terms are highly nonlinear, or if the concentration of the solute of interest is strongly dependent on the concentration of other chemical constituents. In reality, the transfer of solute between the liquid and solid phases may not be linear or equilibrium controlled. For field problems in which reactions appreciably affect solute concentrations, simulation accuracy is less limited by mathematical constraints than by data constraints. That is, the types and rates of reactions for the specific solutes and minerals in the particular groundwater system of interest are rarely known and often highly variable, and require an extensive amount of data to assess accurately. Finite-difference and finite-element methods also can be applied to solve the transport equation, particularly when dispersive transport is large compared to advective transport. However, numerical errors, such as numerical dispersion and oscillations, may be important for some problems. The numerical errors can generally be reduced by using a finer discretization (either shorter time steps or finer spatial grid). An example of a documented 3D, transient, finite-difference model that simultaneously solves the
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The Handbook of Groundwater Engineering Observation wells
(a)
Confining bed
Observation wells
(b)
h2
Potentiometric surface
h4
Confining bed h0
h0
Potentiometric surface
h3
h1 Aquifer ∆x
∆x
1
d
Aquifer
0 ∆x
e
∆y
x 3
2
f
∆y
0 ∆y
g
y 4
FIGURE 23.2 Schematic cross section through confined aquifer to illustrate numerical approximation to derivatives of head, (a) ∂h/∂x and (b) ∂h/∂y. (Adapted from Bennett, G. D. (1976) Introduction to ground-water hydraulics: A programmed text for self-instruction, Techniques of Water-Res. Invests. of the U.S. Geol. Survey, Book 3, Ch. B2.)
fluid pressure, energy-transport, and solute-transport equations for nonhomogeneous miscible fluids is HST3D (Kipp 1987). An example of a 3D finite-element transport model is SUTRA, documented by Voss and Provost (2002). Although finite-difference and finite-element models are commonly applied to transport problems, other types of numerical methods also have been used, including the method of characteristics, random walk, Eulerian–Lagrangian methods, and adaptive grid methods. All of these methods have the capacity to track sharp fronts accurately with a minimum of numerical dispersion. Documented models based on variants of these approaches include Konikow et al. (1996), Prickett et al. (1981), Zheng and Wang (1999), and Heberton et al. (2000). None of the standard numerical methods is ideal for a wide range of transport problems and conditions. Thus, there is still much research being done to develop better mixed or adaptive methods that aim to minimize numerical errors and combine the best features of alternative standard numerical approaches.
23.5.1 Basics of Finite-Difference Methods The partial differential equations describing the flow and transport processes in groundwater include terms representing derivatives of continuous variables in space and time. Finite-difference methods are based on the approximation of these derivatives (or slopes of curves) by discrete linear changes over discrete intervals of space or time. If the intervals are sufficiently small, then all of the linear increments will represent a good approximation of the true curvilinear surface or hydrograph. If we consider three observation wells spaced an equal distance apart in a confined aquifer, as illustrated in Figure 23.2a, Bennett (1976) shows that a reasonable approximation for the derivative of head, ∂h/∂x, at a point (d) midway between wells 1 and 0 is
∂h ∂x
≈ d
h0 − h 1 x
(23.12)
Similarly, a reasonable approximation for the second derivative, ∂ 2 h/∂x 2 , at point 0 (the location of the center well) can be given as
∂ 2h ∂x 2
≈ 0
((h2 − h0 )/ x) − ((h0 − h1 )/ x) h1 + h2 − 2h0 (∂h/∂x)e − (∂h/∂x)d ≈ = x x ( x)2
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(23.13)
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If we also consider wells 3 and 4 shown in Figure 23.2b, located on a line parallel to the y-axis, we can similarly approximate ∂ 2 h/∂y 2 at point 0 (the same point 0 as in Figure 23.2a) as (Bennett 1976):
∂ 2h ∂y 2
≈ 0
h3 + h4 − 2h0 ( y)2
(23.14)
If we consider a case of 2D horizontal flow only for the uniform spacing of wells in Figure 23.2b (i.e., x = y = a), then we can develop the following approximation: ∂ 2h h1 + h2 + h3 + h4 − 4h0 ∂ 2h + 2 ≈ 2 ∂x ∂y a2
(23.15)
These approximations can also be obtained through the use of Taylor series expansions. A certain error is involved in approximating the derivatives by finite-differences, but this error will generally decrease as a (or x and y) is given smaller and smaller values. This error is called a “truncation error” because the replacement of a derivative by a difference quotient is equivalent to using a truncated Taylor series, so that the exact solution of a difference equation differs from the solution of the corresponding differential equation (Peaceman 1977). Also, it may not be possible to achieve an “exact” solution of the difference equation because of precision limits in storing numbers in a digital computer. In solving a large set of difference equations, many arithmetic operations are performed, and round-off errors may sometimes accumulate. Next, consider the construction of a rectangular finite-difference grid. Two possible modes of grid construction are illustrated in two dimensions in Figure 23.3a and Figure 23.3b. In Figure 23.3a, the calculation points (or nodes) are located at the centers of the blocks (or cells) formed by the grid lines. This type of grid is commonly called a block-centered grid. In the second grid type (Figure 23.3b), the nodes are considered to be located at the intersections of the grid lines. This type has been variously called a point-, node-, mesh-, or lattice-centered grid. Although there is no overall inherent advantage of one type over the other, there will be some operational differences between the two approaches in the treatment of boundaries and in areas of influence around nodes. Most, but not all, finite-difference groundwater models are based on the use of block-centered grids. Double indexing is normally used to identify functions and variables within the 2D region. For example, hi,j is the head at node i, j, where i and j are the row and column locations in the finite-difference grid. This procedure is easily extended to three dimensions, as illustrated in Figure 23.3c. Here the vertical dimension (or z-direction) is indexed by the subscript k and hi,j,k would represent the head at node i, j, k. We must also consider the discretization of time, which may be viewed as another dimension, and, hence, represented by another index. If we consider a representative segment of a hydrograph (see Figure 23.4), in which head is plotted against time for a transient flow system, n is the index or subscript used to denote the time at which a given head value is observed. The slope of the hydrograph at any point is the derivative of head with respect to time, and it can be approximated as ∂h/∂t ≈ h/ t . In terms of the (a)
(b)
(c) ∆y
∆x ∆z
∆y ∆x
Node
FIGURE 23.3 Examples of finite-difference grids: (a) 2D block-centered grid, (b) 2D node-centered grid, and (c) 3D block-centered grid. (Modified from Konikow, L. F. (1996) In Manual on Mathematical Models in Isotope Hydrogeology, International Atomic Energy Agency, Vienna, Austria.)
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Approximate slope at tn hn+1 ∆h
h hn
∆h hn-1 ∆t tn–1
∆t tn
tn+1 Time
FIGURE 23.4 Part of a hydrograph showing that the derivative (or slope, ∂h/∂t ) at time tn may be approximated by h/ t . (From Konikow, L. F. (1996) In Manual on Mathematical Models in Isotope Hydrogeology, International Atomic Energy Agency, Vienna, Austria.)
heads calculated at specific time increments (or time steps), the slope of the hydrograph at time n can be approximated by
∂h ∂t
≈
hn+1 − hn t
(23.16)
≈
hn − hn−1 t
(23.17)
n t
or
∂h ∂t
n t
Calculation of the derivative at t = n t using Equation 23.16 takes a “forward difference” from time n to time n+1, and calculation using Equation 23.17 takes a “backward difference.” In terms of solving the groundwater-flow equation for a node (i, j) of a 2D finite-difference grid, we have to consider heads at five nodes and at two time levels, as illustrated in Figure 23.5. In Figure 23.5a, we have expressed the spatial derivatives of head at time level n, where all values are known, and the time derivative as a forward difference to the unknown head at time step n+1. Then for every node of the grid, we will have a separate difference equation, each of which contains only one unknown variable. Thus, these equations can be solved explicitly. Explicit finite-difference equations are simple and straightforward to solve, but may have stability criteria associated with them. If time increments are too large, small numerical errors or perturbations may propagate into larger errors at later stages of the computations. In Figure 23.5b, we have expressed the time derivative as a backward difference from the heads at time level n, which are the unknown heads, to the heads at the previous time level, n − 1, which are known (either from initial conditions specified for the first time step or from the solution for previous time steps). The spatial derivatives of head are written at time level n, where all values are unknown; so, for every node of the grid, we will have one difference equation that contains five unknowns, which cannot be solved directly. However, for the entire grid, which contains N nodes, we would have a system of N equations containing a total of N unknowns. Such a system of simultaneous equations, together with specified boundary conditions, can be solved implicitly. Although implicit solutions are more complicated, they also have the advantage of generally being unconditionally stable. This stability implies that a solution will be obtained; although not necessarily that the estimate of the derivative that is calculated will be accurate,
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(a) time tn + 1
hi,j,n + 1
time tn
hi,j +1,n hi –1,j,n
hi,j,n
hi +1,j,n
hi,j + 1,n hi,j –1,n tn
hi –1,j,n
hi,j,n
hi +1,j,n
tn –1
hi,j,n –1
EXPLANATION
hi,j –1,n
Known head Unknown head
FIGURE 23.5 Grid stencil showing discretization of time at node (i, j) in a 2D finite-difference grid: (a) explicit (forward-difference) formulation, and (b) implicit (backward-difference) formulation. (From Konikow, L. F. (1996) In Manual on Mathematical Models in Isotope Hydrogeology, International Atomic Energy Agency, Vienna, Austria.)
even if the time steps are large relative to the rate of change of head. Most available groundwater-flow models solve an implicit finite-difference approximation to the flow equation. We may next consider Equation 23.5, a 2D groundwater-flow equation for a heterogeneous, anisotropic aquifer, in which the coordinate system is aligned with the major axes of the transmissivity tensor. This may be approximated by the following implicit finite-difference equation for representative node (i, j) as
hi−1,j,n − hi,j,n hi+1,j,n − hi,j,n + T xx[i+1/2,j] ( x)2 ( x)2 hi,j−1,n − hi,j,n hi,j+1,n − hi,j,n + Tyy[i,j−1/2] + T yy[i,j+1/2] ( y)2 ( y)2 hi,j,n − hi,j,n−1 qi,j Kz − (Hs[i,j] − hi,j,n ) =S − t x y m
Txx[i−1/2,j]
(23.18)
where qi,j is the volumetric rate of withdrawal (negative in sign) or recharge (positive) at the i, j node, L3 T−1 . This formulation assumes that any stresses, such as represented by qi,j , are applied over the entire surface area of cell i, j rather than at a point (or at node i, j). This condition implies that if a pumping well is represented at node i, j, then the head will be calculated as if it were being withdrawn from a well that had a cross-sectional area for the borehole equal to x y, rather than the actual cross-sectional area of the well. In Equation 23.18, the transmissivity terms represent the harmonic means of the transmissivity of the two adjacent cells. The harmonic mean can be shown to be appropriate and consistent with the assumption that transmissivity is constant and uniform within each cell but may differ between cells. Other types of means for interblock transmissivity may be more appropriate for other assumptions about the transmissivity distribution, such as smoothly varying transmissivity (Goode and Appel 1992).
23.5.2 Basics of Finite-Element Methods The finite-element method (FEM) is a numerical analysis technique for obtaining approximate solutions to a wide variety of problems in physics and engineering. The method was originally applied to structural mechanics but is now used in all fields of continuum mechanics. Huebner (1975) describes four different approaches to formulate the finite-element method for a problem, which are, the direct approach, the variational approach, the weighted residual approach, and the energy balance approach. In groundwater problems, the approach frequently used is either the weighted residual or variational approach. The concept of “piecewise approximation” is used in the FEM. The domain of the problem, that is, the extent of the groundwater system to be simulated, is divided into a set of elements or pieces. In theory,
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the elements can be of different shapes and sizes. Most FEM computer programs use one shape element, most commonly either triangular or quadrilateral elements. In the groundwater model MODFE (Torak, 1993 and Cooley, 1992) triangular elements are used, whereas in the groundwater model SUTRA (Voss and Provost, 2002), quadrilateral (2D) or hexahedral (3D) elements are used. Point values of the dependent variable (e.g., head, pressure, or concentration) are calculated at nodes, which are the corners or vertices of the elements; a simple equation is used to describe the value of the dependent variable within the element. This simple equation is called a basis function and each node that is part of an element has an associated basis function. The simplest basis functions that are usually used are linear functions. The solution to the differential equation for flow (Equation 23.3 or Equation 23.6) or transport (Equation 23.9 or Equation 23.10) is approximated by a set of elements in which the dependent variable only varies linearly within the element, but the entire set of elements approximates the complex distribution of head or concentration. The approximate modeled hydraulic head distribution (Figure 23.6c) is comprised of a set of triangular elements (Figure 23.6a) having a linear approximation of head variation within each element (Figure 23.6b). In the method of weighted residuals, the “piecewise” continuous surface is obtained by minimizing the difference between the approximate surface and the continuous surface. The method of weighted residuals is summarized by Huyakorn and Pinder (1983, p. 39) as follows. Any differential equation L(h), such as the steady-state form of Equation 23.3 (the groundwater-flow equation) can be written as L(h) = 0
(23.19)
over the domain of the problem R. The first step in obtaining the approximate solution is to define the approximate solution as the sum of all the simple basis functions as hˆ =
n
Ni Zi
(23.20)
i=1
where hˆ is the approximate solution, n is the number of linearly independent basis functions, Ni are the linearly independent basis functions defined over the entire domain, and Zi are the unknown coefficients to be determined (there is one coefficient for each node in the finite-element mesh). The trial function hˆ is an approximation, so that when it is substituted into Equation 23.19 there will be some error, ξ , defined as ˆ ξ = L(h)
(23.21)
The method of weighted residuals determines the unknown coefficients by minimizing the error. This minimization is accomplished by weighting the error, integrating the error, and setting the error equal to zero over the entire domain. A weighting function, Wi , can be specified for each basis function and the resulting integration is ˆ dR = 0, i = 1, 2, . . . , n Wi ξ dR = Wi L(h) (23.22) R
R
Equation 23.20 is substituted into Equation 23.22 and weighting functions are specified. There are then n equations and n unknowns. The selection of the weighting functions and the simplification of the integral in Equation 23.22 into a linear algebraic equation is mathematically straightforward, but not intuitive. In the Galerkin method, the weighting functions are chosen to be identical to the basis functions and Equation 23.22 is simplified by using integration by parts. Because the basis functions and weighting functions are defined to be of a specific algebraic form (e.g., linear basis functions), the modified integral is straightforward to solve and becomes a set of n simultaneous algebraic equations. After Equation 23.22 is mathematically evaluated into a set of n simultaneous equations, they are solved using matrix solution techniques for the n unknown coefficients Zi , and the approximate solution hˆ is
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(a)
Aquifer region
Finite elements
m
e k
l Typical element e and nodes k, l, and m
hm
(b)
h = Ae + Bxe + Cye hl hk m h y
k
True hydraulic head, h, approximated by hk, hl, hm and at nodes k, l, and m, respectively, of element e
l x
(c)
h
True hydraulic head h represented by finiteelement mesh
y
x
Finite-element mesh
FIGURE 23.6 Diagram showing (a) aquifer region partially subdivided by finite elements and typical element e, ˆ and (c) finite-element mesh configuration for approximating (b) finite-element representation of hydraulic head h, true hydraulic head. (From Torak, L. J. (1993) A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 1: Model description and user’s manual, Techniques of Water-Res. Invests. of the U.S. Geol. Survey, Book 6, Ch. A3.)
determined at each node. The time derivative is frequently approximated by finite differences as discussed in the previous section. Huyakorn and Pinder (1983), Huebner (1975), Zienkiewicz (1971), Wang and Anderson (1982), and Cooley (1992) provide more comprehensive explanations of the method.
23.5.3 Basics of Method-of-Characteristics Methods The method-of-characteristics (MOC) was developed to solve hyperbolic differential equations (advectively dominated transport equations). A major advantage of this over other methods is that MOC minimizes numerical dispersion (Garder et al. 1964; Reddell and Sunada 1970; Zheng and Bennett 2002). The approach taken with the MOC is not to solve Equation 23.9 directly, but rather to solve an equivalent
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system of ordinary differential equations. A form of Equation 23.9, accounting for equilibrium-controlled sorption or exchange and first-order irreversible rate reactions, can be further modified for improved compatibility with this method by expanding the advection term, substituting relations from Darcy’s law and the flow equation, and rearranging terms to obtain 1 ∂ ∂C = ∂t Rf ∂xi
Dij
∂C ∂xj
−
W ∗ (C − C ∗ ) Vi ∂C + − λC Rf ∂xi εRf
(23.23)
where Rf is defined as a dimensionless retardation factor, Rf = 1 + (ρb Kd /ε), and Kd is the distribution coefficient, L3 M−1 . If we consider the material derivative of concentration with respect to time, dC/dt , as describing the change in concentration of a parcel of water moving at the seepage velocity of water, it may be defined for a 3D system as ∂C ∂C dx ∂C dy ∂C dz dC = + + + . dt ∂t ∂x dt ∂y dt ∂z dt
(23.24)
The second, third, and fourth terms on the right side include the material derivatives of position, which are defined by the velocity in the x, y, and z directions. We then have Vx dx = dt Rf
(23.25)
Vy dy = Rf dt
(23.26)
Vz dz = dt Rf
(23.27)
and 1 ∂ dC = dt Rf ∂xi
Dij
∂C ∂xj
+
W ∗ (C − C ∗ ) − λC εRf
(23.28)
The solutions of the system of equations comprising Equation 23.25 through Equation 23.28 may be given as x = x(t ), y = y(t ), z = z(t ), and C = C(t ), and are called the characteristic curves of Equation 23.23. Given solutions to Equation 23.25 through Equation 23.28, a solution to the partial differential equation may be obtained by following the characteristic curves, which are defined by the particle pathlines. This may be accomplished by introducing a set of moving points (or reference particles) that can be traced within the stationary coordinates of a finite-difference grid. Each particle corresponds to one characteristic curve, and values of x, y, z, and C are obtained as functions of t for each characteristic (Garder et al. 1964). Each point has a concentration and position associated with it and is moved through the flow field in proportion to the flow velocity at its location (see Figure 23.7). The concentrations at the nodes of the fixed finite-difference grid may then be estimated as an arithmetic or weighted mean of the concentrations of all particles contained within the cell area for that node. In the traditional MOC, the nodal concentrations are used to estimate spatial concentration gradients for an explicit or implicit finite-difference solution to Equation 23.28. However, the transfer between the moving grid of particles and the fixed grid of finite-difference nodes involves a loss of accuracy (generally seen as a small amount of numerical dispersion). An alternate approach is to use a particle strength exchange method, which uses particle positions at the end of each time increment as quadrature points in what is essentially a finiteelement solution to Equation 23.28 (Zimmermann et al. 2001). This eliminates the problems involved in interpolating from particles to nodes and back again to compute the changes in concentration caused by hydrodynamic dispersion, but does so at a cost of increased computational effort.
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o
o
x o
xo
o
xo
x o
EXPLANATION Flow line and direction of flow Computed path of particle originally in cell j,i,k Computed path of particle entering cell j,i,k
x x
x
Node of finite-difference cell x
Initial location of particle
o
New location of particle
FIGURE 23.7 Part of a hypothetical finite-difference grid showing relation of flow field to movement of particles in method of characteristics model for simulating solute transport. (Adapted from Konikow, L. F. and Bredehoeft, J. D. (1978) Computer model of two-dimensional solute transport and dispersion in ground water, Techniques of Water-Res. Invests. of the U.S. Geol. Survey, Book 7, Ch. C2.)
23.5.4 Matrix Solution Techniques As indicated previously, the finite-difference and finite-element approximations lead to an algebraic equation for each node point. The set of algebraic equations may be solved numerically by one of two basic methods: direct or iterative. In direct methods, a sequence of operations is performed only once to solve the matrix equation, providing a solution that is exact, except for machine round-off error. Iterative methods arrive at a solution by a process of successive approximation. The process involves making an initial guess at the solution, then improving this guess by some iterative process until an error criterion is satisfied. Therefore, in these techniques, convergence and the rate of convergence are of concern. Direct methods have two main disadvantages when compared to indirect methods. The first problem is one of computer resource requirements, including large storage (memory) requirements and long computation times for large problems. The matrix is sparse (contains many zero values) and to minimize computational effort, various techniques have been proposed. However, for finite-difference and finiteelement methods, storage requirements may still prove to be unavoidably large for 3D problems. The second disadvantage of direct methods is round-off error. As many arithmetic operations are performed, round-off errors can accumulate for certain types of matrices. Iterative schemes avoid the need for storing large matrices, which make them attractive for solving large problems. Numerous schemes have been developed (Barrett et al. 1994). A few of the more commonly used ones include successive over-relaxation methods, iterative alternating-direction implicit procedure, the strongly implicit procedure, and conjugate-gradient methods with various types of preconditioning. As iterative methods start with an initial estimate for the solution, the efficiency of the method depends somewhat on this initial guess. To speed up the iterative process, relaxation and acceleration factors are sometimes used. Unfortunately, the definition of best values for these factors commonly is problem dependent. In addition, iterative approaches require that an error tolerance be specified to stop the iterative process. An optimal value for the tolerance, which is used to evaluate when the iterative calculations have converged on a solution, may also be problem dependent. If the tolerance is set too large, then the iterations may stop before adequate numerical accuracy is achieved. If the tolerance is set too small, then the iterative process may consume excessive computational resources in striving for numerical precision that may be orders of magnitude smaller than the precision of the field data, or the iterative process may even fail to converge.
23.5.5 Boundary and Initial Conditions To obtain a unique solution to a partial differential equation corresponding to a given physical process, additional information about the physical state of the process is required. This information is supplied
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The Handbook of Groundwater Engineering TABLE 23.1 Common Designations for the Three Common Mathematical Boundary Conditions Specified in Mathematical Analyses of Groundwater-Flow and Transport Systems (n is directional coordinate normal to the boundary (L)) Boundary Type and Name
Formal Name
Mathematical Designation (Equation for head and equation for concentration)
Type 1 Specified value
Dirichlet
Type 2
Neumann
h(x, y, z, t ) = constant C(x, y, z, t ) = constant dh(x, y, z, t ) = constant dn dC(x, y, z, t ) = constant dn dh + ah = constant dn dC + aC = constant dn (where a is also a constant)
Specified flux Type 3 Value-dependent flux
Cauchy
Sources: Franke, O.L., Reilly, T.E. and Bennett, G.D. (1987) Definition of boundary and initial conditions in the analysis of saturated groundwater flow systems — An introduction, Techniques of Water-Res. Invests. of the U.S. Geol. Survey, Book 3, Ch. B5; and Reilly, T.E. (2001) System and boundary conceptualization in ground-water flow simulation: Techniques of Water-Res. Invests. of the U.S. Geol. Survey, Book 3, Ch. B8.
by boundary and initial conditions. For steady-state problems, only boundary conditions are required, whereas for transient problems, boundary and initial conditions must be specified. Mathematically, the boundary conditions include the geometry of the boundary and the values of the dependent variable or its derivative normal to the boundary. Internal sources and sinks are also considered as boundary conditions in the solution to the governing equations. In physical terms, for groundwater-model applications, the boundary conditions are generally of three types (Table 23.1): (1) specified value (head or concentration), (2) specified flux (corresponding to a specified gradient of head or concentration), or (3) value-dependent flux (or mixed boundary condition, in which the flux across a boundary is related to both the normal derivative and the value) (Mercer and Faust 1981; Franke et al. 1987; Reilly 2001). The third type of boundary condition might be used, for example, to represent leakage or exchange between a stream and an adjacent aquifer, in which the leakage may change over time as the head in the aquifer changes, even though the head in the stream might remain fixed. A noflow boundary is a special case of the second type of boundary condition. A fourth type of boundary condition that is important in many groundwater-flow problems is the free-surface boundary, in which head in the groundwater system is a function of only the potential energy of a water particle because of its position above some datum, that is, its elevation head (Franke et al. 1987). The most common type of free-surface boundary is the water table, which is the boundary surface between the saturated flow field and the atmosphere. The types of boundaries appropriate to a particular field problem require careful consideration. The initial conditions are simply the values of the dependent variable specified everywhere inside the boundary at the start of the simulation. Preferably, the initial conditions are specified from a steady-state simulation of the groundwater system. If, however, initial conditions are directly specified on the basis of field measurements, they may not be consistent with the model conceptualization or the stresses specified in the model. In that event, transient flow and (or) transient solute transport may occur in the system at the start of the simulation in response to both the new hydrologic stresses and the initial conditions (Franke et al. 1987; Reilly and Harbaugh 2004).
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23.5.6 Generic Model Verification It must be demonstrated that the generic model accurately solves the governing equations for various boundary value problems, an evaluation that is often called model “verification.” This evaluation is checked by demonstrating that the code gives good results for problems having known solutions. This test is usually done by comparing the numerical model results to those of an analytical solution. Numerical accuracy is rarely a problem for the solution to the flow equation, but may sometimes be a major problem in transport modeling. Numerical solutions are sensitive to spatial and temporal discretization. Therefore, even a perfect agreement for test cases only proves that the numerical code can accurately solve the governing equations, not that it will accurately solve problems under any and all circumstances. Analytical solutions generally require simple geometry, uniform properties, and idealized boundary and initial conditions. The power of the numerical methods is that they are not constrained by the simplification imposed by analytical methods and allow the introduction of nonhomogeneous, anisotropic parameter sets, irregular geometry, mixed boundary conditions, and even nonlinearities into the boundary value problems. Usually, analytical solutions approximating these complexities are unavailable for comparison. Therefore, once these complexities are introduced, there is no definitive basis for verifying the numerical model. One approach that improves confidence for complex heterogeneous problems is to compare the model results to experimental data, to results of other well-accepted models, or to some other accepted standard. Such evaluations might best be termed benchmarking. The HYDROCOIN Project used standardized problem definitions as a basis for intercode comparisons (Swedish Nuclear Power Inspectorate 1987). Although this type of benchmarking helps ensure consistency, it does not guarantee or measure accuracy (Konikow et al. 1997). A collection and detailed discussion of a number of classical groundwater problems that have been used historically as a basis of model evaluation are presented and documented by Ségol (1994).
23.6 Model Design, Development, and Application The first step in model design and application is to define the nature of the problem and the purpose of the model (Figure 23.8). Although this may seem obvious, it is an important first step that is sometimes overlooked in a hasty effort to take action. This step is linked closely with the formulation of a conceptual model, which is required prior to the development of a mathematical model. In formulating a conceptual model, the analyst must evaluate which processes are important in the groundwater system being investigated for the particular problem at hand. Some processes may be important to consider at one scale of study, but negligible or irrelevant at another scale of investigation. The analyst must similarly decide on the appropriate dimensionality and resolution for the numerical model. Good judgment is required to evaluate and balance the tradeoffs between accuracy and cost, with respect to model development, model use, and data requirements. The key to efficiency and accuracy in modeling a system probably is more affected by the formulation of a proper and appropriate conceptual model than by the choice of a particular numerical method or code. Once a decision to develop a model has been made, a code (or generic model) must be selected (or modified or constructed) that is appropriate for the given problem. Next, the generic code must be adapted to the specific site or region being simulated. Development of a numerical deterministic, distributedparameter, simulation model involves selecting or designing spatial grids and time increments that will yield an accurate solution for the given system and problem. The analyst must then specify the properties of the system (and their distributions), stresses on the system (such as recharge and pumping rates), boundary conditions, initial conditions (for transient problems), and geochemical processes/reactions (if appropriate). All of the parameter specifications and boundary conditions must be consistent with the overall conceptual model of the system, and the initial numerical model reflects the analyst’s conceptual model of the system.
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Hypothesis testing
Management decisions
Postaudits
Predictions
Calibration of model & sensitivity tests Models of groundwater flow, transport, & reactions
Site specific Data
Conceptual models of governing Processes
Definition of problem and model Objectives Start
FIGURE 23.8 The use and application of models in the analysis of groundwater problems. (From Konikow, L. F. (1996) In Manual on Mathematical Models in Isotope Hydrogeology, International Atomic Energy Agency, Vienna, Austria.)
A model is a simplified approximation of a complex reality, but the model should capture the essential features and processes relative to the problem at hand. The selection of the appropriate model and appropriate level of model complexity (or, rather, simplicity) remains subjective and dependent on the judgment and experience of the analysts, the objectives of the study, the level of prior information available for the system of interest, and the complexity of the system being modeled. The trade-off between model accuracy and model cost will always be difficult to resolve, but will always have to be made. Water managers and other users of model results must be made aware that these trade-offs and judgments have been made and may affect model reliability. Reilly and Harbaugh (2004) discuss many of these design decisions and their trade-offs in the context of developing guidelines to aid water managers in their evaluation of the usefulness and appropriateness of a groundwater-flow model. In general, it is more difficult to calibrate a solute-transport model of an aquifer than it is to calibrate a groundwater-flow model. Fewer parameters need to be defined to compute the head distribution with a flow model than are required to compute concentration changes with similar confidence using a solutetransport model. Also, in typical field problems, defining the source term for a solute-transport model is especially difficult for point-source contamination problems because the timing, location, and strength of releases of solute mass into an aquifer system are rarely known or reported accurately (and is commonly the very point of contention in litigation). Groundwater seepage velocity is determined from the head distribution, and because both advective transport and hydrodynamic dispersion are functions of the seepage velocity, a model of groundwater flow typically is calibrated before a pathline or solute-transport model is developed. In a field environment, perhaps the single most important key to understanding a solute-transport problem is the development of an accurate description (or model) of flow. This is particularly relevant to transport in fractured rocks, where simulation is commonly based on porous-media concepts. In highly heterogeneous systems, the head distribution and flow directions often can be simulated fairly accurately, whereas the calculated velocity field still may be greatly in error, which results in considerable errors in transport simulations.
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23.6.1 Grid Design The dimensionality of the model (i.e., one, two, or three dimensions) should be selected during the formulation of the conceptual model. If a 1D or 2D model is selected, then it is important that the grid be aligned with the flow system so that there is no unaccounted flux into or out of the line or plane of the grid. For example, if a 2D areal model is applied, then there should be no significant vertical components of flow and any vertical leakage or flux must be accounted for by boundary conditions. If a 2D profile model is applied, then the line of the cross section should be aligned with an areal streamline, and there should not be any significant lateral flow into or out of the plane of the cross section. To minimize a variety of sources of numerical errors, the model grid should be designed using the finest mesh spacing and time steps that are possible, given limitations on computer memory and computational time. The boundaries of the grid should be aligned, to the extent possible, with natural hydrologic and geologic boundaries of the groundwater system. Where it is impractical to extend the grid to a natural boundary, then an appropriate boundary condition should be imposed at the edge of the grid to represent the net effects of the continuation of the aquifer beyond the grid. This representation can typically be accomplished using head-dependent leakage (third type) boundary conditions. However, this would preclude calculating (and accounting for) any storage changes outside the active grid. These boundaries should also be placed as far as possible away from the area of interest and areas of stresses on the system, so as to minimize any effect of conceptual errors associated with these artificial boundary conditions. Note that it is possible for certain types of hydraulic boundaries, such as a groundwater divide, to change location over time if they are located near a major hydraulic stress. If such a boundary shift is anticipated, it might be preferable to extend the boundary of the grid some distance beyond the location of such a natural boundary. In designing the grid, the length to width ratio (or aspect ratio) of cells or elements should be kept as close to one as possible. Long linear cells or elements can lead to numerical instabilities or errors, and should be avoided, particularly if the aspect ratio is greater than about five (Bear and Verruijt 1987). However, this is not a stringent guideline as aspect ratios exceeding 1000 : 1 are routinely used with the SUTRA code (Voss and Provost 2002) without numerical problems. For example, a ratio of 500 : 1 was used by Voss and Souza (1998) in a model of the Pearl Harbor aquifer, Oahu (Section 23.8.3). In specifying boundary conditions for a particular problem and grid design, care must be taken not to over constrain the solution. That is, if dependent values are fixed at too many nodes of a grid, the model may have too little freedom to calculate a meaningful solution. At the extreme, by manipulating boundary conditions, one can force any desired solution at any given node. Although a forced solution may ensure a perfect match to observed data used for calibration, such a match is of course not an indicator of model accuracy or reliability, and can be meaningless (Franke and Reilly 1987). To optimize computational resources in a model, it sometimes is advisable to use an irregular (or variably-spaced) mesh in which the grid is finest in areas of point stresses, where gradients are steepest, where data are most dense, where the problem is most critical, and (or) where greatest numerical accuracy is desired. Similarly, the length of time steps can often be increased geometrically during a transient simulation. At the initial times or after a change in the stress regime, small time steps should be imposed, as that is when changes in the dependent variable over time are the greatest. With increased elapsed time, the rate of change in head typically decreases, so time steps can often be safely increased. Because transmissivity (or hydraulic conductivity) is a property of the porous media, the cross-product terms of the transmissivity tensor drop out of the governing flow equation that is solved in a model by aligning the model grid with the major axes of the transmissivity tensor (as represented in Equation 23.5). This makes the code simpler and more efficient, and is a required assumption for most finite-difference models. However, this same simplification typically is not possible for the dispersion tensor in the transport equation because it depends on the flow direction, which changes orientation over space and time. In general, it is not possible to design a fixed grid that will always be aligned with a changing flow field.
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23.6.2 Model Calibration Deterministic groundwater-simulation models impose large requirements for data to define all of the parameters at all of the nodes of a grid. To determine uniquely the parameter distribution for a field problem, so much expensive field testing would be required that it is seldom feasible either economically or technically. Therefore, the model typically represents an attempt, in effect, to solve a large set of simultaneous equations having more unknowns than equations. It is inherently impossible to obtain a unique solution to such a problem. Uncertainty in parameters logically leads to a lack of confidence in the interpretations and predictions that are based on a model analysis, unless the model can be demonstrated to be a reasonably accurate representation of the real groundwater system. To demonstrate that a deterministic groundwatersimulation model is realistic, usually field observations of aquifer responses (such as changes in water levels and fluid flux for flow problems or changes in concentration for transport problems) are compared to corresponding values calculated by the model. The objective of this calibration procedure is to minimize differences between the observed data and calculated values. Usually, the model is considered calibrated when it reproduces historical data within some acceptable level of accuracy. The level of acceptability is, of course, determined subjectively. Although a poor match provides evidence of errors in the model, a good match in itself does not prove the validity or adequacy of the model (Konikow and Bredehoeft 1992). Because of the large number of variables in the set of simultaneous equations represented in a model, calibration will not yield a unique set of parameters. Where the match is poor, it suggests (1) an error in the conceptual model, (2) an error in the numerical solution, and (or) (3) a poor set of parameter values. Even when the match to historical data is good, the model may still fail to predict future responses accurately, especially under a new or extended set of stresses than experienced during the calibration period. The calibration of a deterministic groundwater model is often accomplished through a trial-and-error adjustment of the model input data (aquifer properties, sources and sinks, and boundary and initial conditions) to modify model output. As a large number of interrelated factors affect the output, trialand-error adjustment may become a highly subjective and inefficient procedure. Advances in automated parameter-estimation procedures help to eliminate some of the subjectivity inherent in model calibration. The newer approaches generally treat model calibration as a statistical procedure using multiple regression approaches. This is sometimes called inverse modeling because instead of using defined parameter values to solve the governing flow equation for head, the procedure strives to achieve a best fit to observed heads by adjusting (in effect, solving for) unknown or uncertain parameter values. The procedure to achieve a best fit uses sensitivity coefficients that are based on the change in calculated value divided by the change in the parameter (e.g., the change in head with changing hydraulic conductivity). The sensitivity coefficients may be useful in the consideration of additional data collection. Hill (1998) provides an overview of methods and guidelines for effective model calibration using inverse modeling. Parameter-estimation procedures improve the efficiency of model calibration and allow the simultaneous construction, application, and calibration of a model using uncertain data. Statistical measures are used to quantify the uncertainties both in model parameters and in predictions. One example of a parameter-estimation program is UCODE (Poeter and Hill 1998; Poeter et al. 2005), which performs inverse modeling using nonlinear regression. UCODE is a powerful public domain code because it will work with any model — not just a groundwater-flow model. An estimated parameter can be a quantity that appears in the input files of the model (such as hydraulic conductivity in a flow model); observations to be matched in the regression can be any quantity for which a simulated equivalent value can be produced (such as head or outflow to a stream) (Poeter and Hill 1998). Even with regression modeling, the hydrologic experience and judgment of the modeler in formulating a proper conceptual model continues to be a major factor in calibrating a numerical simulation model both accurately and efficiently. The modeler should always be familiar with the specific field area being studied to ensure that both the database and the numerical model adequately represent prevailing field conditions. The modeler must also recognize that uncertainty in specification of sources, sinks, and boundary and initial conditions should be evaluated during the calibration procedure in the same manner
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as uncertainty in aquifer properties. Failure to recognize the uncertainty inherent both in the input data and in the calibration data may lead to “fine-tuning” of the model through unjustifiably precise parameter adjustments strictly to improve the match between observed and calculated variables. This may serve only to provide a false confidence in the model without producing an equivalent (or any) increase in the predictive accuracy of the model or any improved conceptual understanding of the real groundwater system. Freyberg (1988) illustrated this in an exercise in which several groups were given the task of modeling a particular hypothetical groundwater problem. The group that achieved the best calibration, as measured by the minimum root mean square error, was not the group that developed the model that yielded the best prediction (measured by the same criterion). Freyberg (1988, p. 360) concluded that “simple measures of the goodness of a calibrated fit to head data are inadequate to evaluate the true worth of a calibrated parameter set.” The use of deterministic models in the analysis of groundwater problems is illustrated, in a general sense, in Figure 23.8. Perhaps the greatest value of the modeling approach is its capacity to integrate site-specific data with equations describing the relevant processes as a quantitative basis for predicting changes or responses in a groundwater system. There must be allowances for feedback from the stage of interpreting model output both to the data collection and analysis phase and to the conceptualization and mathematical definition of the relevant governing processes. One objective of model calibration should be to improve the conceptual model of the system. As the model quantitatively integrates the effects of the many factors that affect groundwater flow or solute transport, the calculated results should be internally consistent with all input data, and it can be determined if any element of the conceptual model should be revised. Prior concepts or interpretations of aquifer parameters or variables, such as represented by potentiometric maps or the specification of boundary conditions, may be revised during the calibration procedure as a result of feedback from the model output. Another objective of modeling should be to define inadequacies in the database and help set priorities for the collection of additional data. Automated parameter-estimation techniques improve the efficiency of model calibration and have two general components — one that calculates the best fit (sometimes called automatic history matching) and one that evaluates the statistical properties of the fit. The objective of automatic history matching is to obtain the estimates of system parameters that yield the closest match (minimize deviations) between observed data and model calculations. Least squares deviation is usually chosen as a criterion. The minimization procedure uses the sensitivity coefficients described previously. Parameter uncertainty is commonly addressed using a sensitivity analysis. A major objective of sensitivity analysis of simulation models is to determine the change in model results as a result of changes in the model input or system parameters. Direct parameter sampling in which parameters are perturbed one by one and the complete set of system equations is resolved is used in conventional sensitivity analysis (Konikow and Mercer, 1988).
23.6.3 Model Error Discrepancies between observed and calculated responses of a groundwater system are the manifestation of errors in the conceptual or mathematical model. In applying groundwater models to field problems, there are three sources of error, and it may not be possible to distinguish among them (Konikow and Bredehoeft, 1992). One source is conceptual errors — that is, misconceptions about the basic processes that are incorporated in the model. Conceptual errors include both neglecting relevant processes as well as inappropriate representation of processes. Examples of such errors include the use of a 2D model where appreciable flow or transport occurs in the third dimension, or the application of a model based upon Darcy’s law to media or environments where Darcy’s law is inappropriate. A second source of error involves numerical errors arising in the equation-solving algorithm. These errors include truncation errors, round-off errors, and numerical dispersion. A third source of error arises from uncertainties and inadequacies in the input data that reflect our inability to describe comprehensively and uniquely the aquifer properties, stresses, and boundaries. In most model applications, conceptualization problems and uncertainty concerning the input data are the most common sources of error.
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FIGURE 23.9 Representative breakthrough curves for a simple flow and transport problem to illustrate types of numerical errors that may occur in numerical solution to transport equation: (a) plug flow having no dispersion, (b) “exact” solution for transport with dispersion, (c) numerical solution for case B that exhibits effects of numerical dispersion, and (d) numerical solution for case B with oscillatory behavior. (From Konikow, L. F. (1996) In Manual on Mathematical Models in Isotope Hydrogeology, International Atomic Energy Agency, Vienna, Austria.)
Numerical methods, in general, yield approximate solutions to the governing equations. There are a number of possible sources of numerical error in the solution. If model users are aware of the source and nature of these errors, they can control them and interpret the results in light of the presence of error. For example, if the spatial grid spacing is too coarse, truncation errors affect the accuracy of the solution. In solving advection-dominated transport problems in which a relatively sharp front (or steep concentration gradient) is moving through a groundwater system, it is numerically difficult to preserve the sharpness of the front. Obviously, if the width of the front is narrower than the node spacing, then it is inherently impossible to calculate the correct values of concentration in the vicinity of the sharp front. However, even in situations where a front is less sharp, the numerical solution technique can calculate a greater dispersive flux than would occur by physical dispersion alone or would be indicated by an exact solution of the governing equation. That part of the calculated dispersion (or spreading of solute about the center of mass) introduced solely by the numerical solution algorithm is called numerical dispersion. Calculated breakthrough curves at a particular point in time for a hypothetical problem of 1D uniform flow and transport, after a tracer having a relative concentration of 1.0 was continuously injected at some point upstream, are illustrated in Figure 23.9. Curve A represents the breakthrough curve and position of a sharp front for a case having no dispersion (plug flow). Curve B represents an exact analytical solution for a nonzero dispersivity. Curve C illustrates the breakthrough curve calculated for the same conditions as B, but using a numerical method that introduces numerical dispersion. Major differences exist between the analytical solution (B) and the numerical solution (C) in parts of the domain. Therefore, care must be taken to assess and minimize such numerical errors that would artificially add “numerical” spreading or mixing to the calculated dispersion attributable to physical and chemical processes. Numerical dispersion can be controlled by reducing the grid spacing ( x, y, and z). However, reduction to a tolerable level may require an excessive number of nodes and render the computational costs unacceptably high. It may also be controlled in finite-element methods by using higher order basis functions or by adjusting the formulation of the equations (using different combinations of forward, backward, or centered in time and (or) space, or using different weighting functions). Unfortunately, many approaches that eliminate or minimize numerical dispersion introduce oscillatory behavior, causing overshoot behind a moving front and possibly undershoot ahead of the front (see curve D in Figure 23.9),
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and vice versa. Undershoot can result in the calculation of negative concentrations, which are obviously unrealistic. Overshoot can introduce errors of equal magnitude that may go unnoticed because the value is positive in sign (although greater than the source concentration, so still unrealistic). Oscillations generally do not introduce any mass-balance errors, and often dampen out over simulation time. However, in some cases, oscillatory behavior can become unbounded, yielding an unstable solution or failure to converge numerically. In solving the advective–dispersive transport equation, some numerical errors (mainly oscillations) can be related to two dimensionless parameter groups (or numbers). One is the Peclet number, Pe , which may be defined as Pe = l/α, where l is a characteristic nodal spacing (although it should be noted that there are several alternative, though essentially equivalent, ways to define Pe ). Anderson and Woessner (1992) recommend that the grid be designed so that l < 4α (or Pe < 4); Ségol (1994) recommends that the nodal spacing be adjusted so that Pe ≤ 2. Similarly, time discretization can be related to the Courant number, Co , which may be defined as Co = V t / l (Anderson and Woessner, 1992). Anderson and Woessner (1992) recommend that time steps be specified so that t < l/V (or Co < 1.0), which is equivalent to requiring that no solute be displaced by advection more than the distance across one grid cell or element during one time increment. In finite-difference transport models, there may also be a grid-orientation effect in which the solute distribution, calculated for the same properties and boundary conditions, will vary depending on the angle of the flow relative to the grid. This effect is largely related to the cross-product terms in the governing equation, and generally is not a serious source of error, but the model user should be aware of this error.
23.6.4 Mass Balance One measure of numerical accuracy is how well the model conserves mass. This can be measured by comparing the net fluxes calculated or specified in the model (e.g., inflow and sources minus outflow and sinks) with changes in storage (accumulation or depletion). Mass-balance calculations should always be performed and checked during the calibration procedure to help assess the numerical accuracy of the solution. For direct matrix equation solution methods, the mass-balance error should always be negligible. Mass-balance errors can be introduced by an inaccurate iterative solution of the matrix equations for flow or solute transport. As part of these calculations, the hydraulic and chemical fluxes contributed by each distinct hydrologic component of the flow and transport model should be itemized separately to form hydrologic and chemical budgets for the system being modeled. The budgets are valuable assessment tools because they provide a measure of the relative importance of each component to the total budget. Errors in the mass balance for flow models should generally be less than 0.1%. However, because the solute-transport equation is more difficult to solve numerically, the acceptable mass-balance error for a solute may be greater than for the fluid, but this will depend also on the nature of the numerical method implemented. Finite-difference and finite-element methods are inherently mass conservative, whereas some implementations of the method of characteristics and particle-tracking approaches may not be (or their mass-balance calculations themselves are only approximations). Also, whereas a large mass-balance error provides evidence of a poor convergence of the iterative solution, a perfect mass balance in itself does not and cannot prove that a true or accurate solution has been achieved or that the overall model is valid. That is, a perfect mass balance can be achieved if the model includes compensating errors. For example, the solutions C and D in Figure 23.9 that exhibit substantial numerical dispersion or oscillatory behavior arise from solutions that show a near-perfect mass balance, but they are still wrong.
23.6.5 Sensitivity Tests Systematically varying values for given parameters helps to achieve another objective of the calibration procedure, namely to determine the sensitivity of the model to factors that affect groundwater flow and transport and to errors and uncertainty in the data. Evaluating the relative importance of each factor helps
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determine which data must be defined most accurately and which data are already adequate or require only minimal further definition. If additional field data can be collected, such a sensitivity analysis helps in deciding which types of data are most critical and how to get the best information return on the costs of additional data collection. If additional data cannot be collected, then the sensitivity tests can help assess the reliability of the model by demonstrating the effect of a given range of uncertainty or error in the input data on the model output. The relative sensitivities of the parameters that affect flow and transport will vary from problem to problem. Furthermore, the sensitivities may change over time as the stress regime imposed on a system evolves. Therefore, a sensitivity analysis should be performed during the early stages of a model study. The sensitivity of the solution to the spatial grid design (or spacing), time-step size, nature and placement of boundary conditions, and other numerical parameters also should be evaluated. This step is frequently overlooked, but failure to do so may cause critical design flaws to remain undetected. For example, parameter-estimation models cannot evaluate the sensitivity to grid spacing or certain boundary conditions that are fixed in the model by the user. It is generally recommended that after a preliminary calibration has been achieved, the model should be rerun for the same stresses and properties using a finer grid, smaller time steps, and perhaps alternative boundary conditions. If such a test yields significantly different results, then the model should be recalibrated using design criteria that yield a more accurate numerical solution. If such a test yields no significant differences, then the coarser design is probably adequate for that particular problem. For example, Bower et al. (2005) found that grid resolution was a critical issue for simulating groundwater flow and solute transport at Yucca Mountain, Nevada. The use of a GIS-based GUI with automatic regridding capability can greatly facilitate the assessment of grid sensitivity.
23.6.6 Calibration Criteria Model calibration may be viewed as an evolutionary process in which successive adjustments and modifications to the model are based on the results of previous simulations. The modeler must decide when sufficient adjustments have been made to the representation of parameters and processes and at some time accept the model as being adequately calibrated (or perhaps reject the model as being inadequate and seek alternative approaches). This decision is often based on a mix of subjective and objective criteria. The achievement of a best fit between values of observed and computed variables is a regression procedure and can be evaluated as such. That is, the residual errors should have a mean that approaches zero and the deviations should be minimized. Cooley (1977) discusses several statistical measures that can be used to assess the reliability and “goodness of fit” of groundwater-flow models. The accuracy tests should be applied to as many dependent variables as possible. The types of observed data that are most valuable for model calibration include head and concentration changes over space and time, and the quantity and quality of groundwater discharges from the aquifer. Although it is necessary to evaluate the accuracy of the model quantitatively, it is equally important to ensure that the dependent variables that serve as a basis for the accuracy tests are reliable indicators of model accuracy. For example, if a particular dependent variable was relatively insensitive to the governing parameters, then the presence of a high correlation between its observed and computed values would not necessarily be a reflection of a high level of accuracy in the overall model. Head values are the most common basis for model calibration, but water-level (head) measurements are subject to error, even if precisely measured. If the well is a long open borehole or has a long screen, then the measured water level represents some integrated mean head, and if the vertical discretization of the model does not correspond closely to the sampled interval, forcing a match may induce a bias in the model parameters. In addition, if the water levels were measured at various points in time, but the model is developed to simulate a long-term steady-state condition, then even if the water levels had been measured accurately, there may be a disconnect between the data and the supposedly corresponding model-computed values. Similarly, caution must be exercised when the “observed data” contain an element of subjective interpretation. For example, matching an observed potentiometric surface or concentration distribution is
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sometimes used as a basis for calibrating groundwater models. However, a contoured surface is itself interpretive and can be a weak basis for model calibration because it includes a variability or error introduced by the contouring process, in addition to measurement errors present in the observed data at the specific points.
23.6.7 Predictions and Postaudits As model calibration and parameter estimation are keyed to a set of historical data, the confidence in and reliability of the calibration process is proportional to the quality and comprehensiveness of the historical record. The time over which predictions are made with a calibrated model should also be related to, and limited by, the length of the historical record. A reasonable guideline is to predict only for a period of time comparable in length to the period that was matched. The accuracy of a model’s predictions is the best measure of its reliability. Predictive accuracy, however, can be evaluated only after the fact. Anderson and Woessner (1992) summarize several published studies in which the predictive accuracy of a deterministic groundwater model was evaluated several years after the prediction had been made. The results suggest that extrapolations into the future were rarely accurate. Predictive errors often were related to having used a time period for history matching that was too short to capture an important element of the model or of the groundwater system, or to having an incomplete conceptual model. For example, processes and boundary conditions that are negligible or insignificant under the past and present stress regime may become important under a different set of imposed stresses. Thus, a conceptual model founded on observed behavior of a groundwater system may prove to be inadequate in the future, when present stresses are increased or new stresses are added. A major source of predictive error is sometimes attributable primarily to the uncertainty of future stresses, which is often affected by demographic, political, economic, and (or) social factors. If the range or probability of future stresses can be estimated, then the range or probability of future responses can be predicted. When using a model to predict future responses in a groundwater system, it is important to place confidence bounds on the predictions arising out of the uncertainty in parameter estimates. However, these confidence limits still would not bound errors arising from the selection of a wrong conceptual model or from problems in the numerical solution algorithms (Bredehoeft and Konikow 1993). If a model is to be used for prediction relating to a problem or system that is of continuing interest or importance to society, then field monitoring should continue and the model should be periodically postaudited, or recalibrated, to incorporate new information, such as changes in imposed stresses or revisions in the assumed conceptual model. A postaudit offers a means to evaluate the nature and magnitude of predictive errors, which may itself lead to a large increase in the understanding of the system and in the value of a subsequently revised model. Revised predictions can then be made with greater reliability.
23.6.8 Model Validation It is natural for people who apply groundwater models, as well as those who make decisions based on model results, to want assurance that the model is valid. Groundwater models are embodiments of various scientific theories and hypotheses. Popper (1959) argues that“as scientists we can never validate a hypothesis, only invalidate it.” The same philosophy has been applied specifically to groundwater models (Konikow and Bredehoeft 1992; Oreskes et al. 1994). The criteria for labeling a model as validated are inherently subjective. In practice, validation is attempted through the same process that is typically and more correctly identified as calibration, that is, by comparing calculations with field or laboratory measurements. However, the non-uniqueness of model solutions means that a good comparison can be achieved with an inadequate or erroneous model. Also, because the definition of “good” is subjective, under the common operational definitions of validation, one competent and reasonable scientist may declare a model as validated, whereas another may use the same data to demonstrate that the model is invalid. To the general public, proclaiming that a groundwater model is validated carries with it an aura of correctness that many modelers would not claim (Bredehoeft
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and Konikow 1993). Because labeling a model as having been “validated” has little objective or scientific meaning, such “certification” does little beyond instilling a false sense of confidence in such models. Konikow and Bredehoeft (1992) recommend that the term validation not be applied to groundwater models.
23.7 Overview of Representative Generic Models A large number and variety of generic groundwater models are documented and available at the present time. Two widely used public domain models are explained in more detail as illustrative examples.
23.7.1 MODFLOW-2000 One of the most popular and comprehensive deterministic groundwater models available today is the United States Geological Survey’s (USGS) MODFLOW code (McDonald and Harbaugh 1988; Harbaugh and McDonald 1996; Harbaugh et al. 2000; Harbaugh 2005). This model is actually an integrated family of compatible codes that centers on an implicit finite-difference solution to the 3D flow equation. The model was coded in a modular style to allow and encourage the development of additional packages or modules that can be added on or linked to the original code. MODFLOW-2000 (Harbaugh et al. 2000) is a major revision of the previous MODFLOW computer programs (McDonald and Harbaugh 1988; Harbaugh and McDonald 1996). MODFLOW-2000 is organized by “Processes,” which currently (2005) include the Ground-Water Flow, Observation, Sensitivity, Parameter-Estimation, Ground-Water Management, and Ground-Water Transport Processes. The Ground-Water Flow Process uses a block-centered finite-difference grid that allows variable spacing of the grid in three dimensions. Flow can be steady or transient. Layers can be simulated as confined or convertible between confined and unconfined. Aquifer properties can vary spatially and hydraulic conductivity (or transmissivity) can be anisotropic. Flow associated with external stresses, such as wells, areally distributed recharge, evapotranspiration, drains, lakes, and streams, can also be simulated through the use of specified head, specified flux, or head-dependent flux boundary conditions. The implicit finite-difference equations can be solved using one of several available solver packages. Although the input and output systems of the program were designed to permit maximum flexibility, usability and ease of interpretation of model results can be enhanced by using one of several commercially available preprocessing and postprocessing packages; some of these packages operate independently of MODFLOW, whereas others are directly integrated into reprogrammed and (or) recompiled versions of the MODFLOW code. MODPATH (Pollock 1989, 1994) is a particle-tracking postprocessor for the MODFLOW GroundWater Flow Process that calculates flowpaths and traveltimes of water particles through a simulated groundwater system for steady-state or transient conditions. Particles can be tracked in the direction of groundwater flow (forward tracking) or backwards towards points of recharge (backward tracking). A companion program, MODPATH-PLOT, provides a graphics interface package to visually display the results of a MODPATH simulation. A semi-analytical method is used in MODPATH to determine each particle’s flowpath within a grid cell. The method is based on heads calculated by MODFLOW, from which the volume flow rate and average linear velocity of groundwater are calculated across each of the six faces of a grid cell. An analytical expression is then obtained on the basis of the cell-face velocities to compute the 3D movement of a particle within each grid cell, given the initial particle position anywhere within the cell. A particle’s complete flowpath through the model domain is obtained by tracking particles from one cell to the next until the particle reaches a model boundary, an internal sink or source of water, or a termination site (or zone) specified by the user. The development of MODPATH in the late 1980s coincided with the initiation of many source-water and wellhead-protection programs in the United States designed to protect water supplies from contamination. Partly because of these programs, MODPATH has been used widely to determine the sources of water to wells, aquifers, and other features represented
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in MODFLOW simulations, as well as to assist hydrologists and water managers understand and visualize water flow through complex groundwater systems. The Observation, Sensitivity, and Parameter-Estimation Processes are all documented in Hill et al. (2000). The Observation Process generates model-calculated values for comparison with measured, or observed, quantities. The Sensitivity Process calculates the sensitivity of hydraulic heads throughout the model with respect to specified parameters. The Parameter-Estimation Process uses a modified GaussNewton method to adjust values of user-selected input parameters in an iterative procedure to minimize residuals. Parameters are defined in the Ground-Water Flow Process input files and can be used to calculate most model inputs such as horizontal hydraulic conductivity, horizontal anisotropy, vertical hydraulic conductivity or vertical anisotropy, specific storage, and specific yield. In addition, parameters can be defined to calculate the hydraulic conductance of the River, General-Head Boundary, and Drain Packages; areal recharge rates of the Recharge Package; maximum evapotranspiration of the Evapotranspiration Package; pumpage or the rate of flow at defined-flux boundaries of the Well Package; and the hydraulic head at constant-head boundaries. Groundwater models often are developed to address specific questions (or problems) that arise in the management of groundwater systems. For example: What is the maximum amount of water that can be pumped from a particular aquifer without causing unacceptable groundwater-level declines or reductions in streamflow? What is the least-cost pumping strategy to capture or contain a contaminant plume? What is the best strategy to conjunctively use the groundwater and surface-water resources of a basin? During the past two decades, much effort has been directed toward developing computer models that can simultaneously account for the physical processes that affect flow and transport in a groundwater system and the large number of engineering, legal, and economic factors that can affect the development and management of groundwater resources. Such models couple the capabilities of groundwater simulation with mathematical optimization techniques (such as linear and nonlinear programming) that solve properly formulated management problems. An optimization problem (or formulation) is a model of the management decision-making process, and has three primary components — an objective function, a set of constraints, and a set of decision variables (Ahlfeld and Mulligan 2000). The decision variables of a management problem are the quantities that are determined by solution of the management problem — for example, the rates, locations, and timing of groundwater withdrawals from a set of available pumping wells. As implied by its name, the objective function defines the objective of the management problem — such as “maximize total pumping from the set of pumping wells.” The constraints of the problem limit the values that can be taken by the decision variables in the solution of the problem. Several codes have been developed for groundwater simulation-optimization modeling (Lefkoff and Gorelick 1987; Greenwald 1998; Zheng and Wang 2002; Ahlfeld and Riefler 2003; Peralta 2004; Ahlfeld et al. 2005). These codes differ in (1) the numerical model that is used to represent the groundwater-flow system, (2) the types of groundwater-management problems that can be solved, and (3) the approaches that are used to mathematically solve the management problems. Recently, the Ground-Water Management (GWM) Process has been developed for MODFLOW-2000 (Ahlfeld et al. 2005). A response-matrix method is used in the GWM Process to solve various types of linear, nonlinear, and mixed-binary linear groundwater management-formulations. The method is based on the determination of functional relations (called response coefficients) between stresses imposed at the decision-variable locations and the resulting changes in state variables (heads or streamflows) at the constraint locations; these functional relations are calculated by the MODFLOW Ground-Water Flow Process. Decision variables that can be specified in GWM include withdrawal and injection wells, artificial-recharge basins, and imports and exports of water. The types of constraints that can be specified include upper and lower bounds on withdrawal and injection rates, water-supply demands, hydraulic-head constraints such as drawdowns and hydraulic gradients, and streamflow and streamflow-depletion constraints. A variety of other MODFLOW accessory codes, packages, and features are available. Most of these were developed by the USGS and reports documenting them are available with the latest versions of MODFLOW-2000 and related models. Examples include coupled surface-water and groundwater flow, aquifer compaction, transient leakage from confining units, rewetting of dry cells, horizontal flow barriers,
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alternative interblock transmissivity computations, cylindrical flow to a well, a statistical processor, a data input program, multi-node wells, and a program that calculates water budgets. The Ground-Water Transport Process (MODFLOW-GWT) includes the capability to solve the solute-transport equation using several optional solution methods, including the method of characteristics (Konikow et al. 1996). Other packages have been developed by non-USGS sources to work with MODFLOW; one example is the advective–dispersive solute transport model MT3DMS (Zheng and Wang 1999). This model solves the solute-transport equation for one or more solutes on the basis of a flow field calculated using MODFLOW. MT3DMS offers several different numerical methods to solve the transport equation, including an advanced finite-difference method to reduce numerical dispersion. Langevin et al. (2003) have integrated MT3DMS directly into a modified version of MODFLOW-2000, which is called the Variable-Density Flow Process (VDF). In the VDF Process, the governing flow equation is modified for application to variable-density problems (Equation 23.6, but developed in terms of equivalent freshwater head rather than pressure), and the resulting code is called SEAWAT-2000. A comprehensive watershed simulation system based on MODFLOW has been documented by Panday and Huyakorn (2004). This model, called MODHMS, includes a 3D saturated–unsaturated flow equation for the subsurface, coupled with the diffusion wave equation for overland flow, both of which are coupled with the diffusion wave equation for flow through a network of streams, channels, and hydraulic structures (Panday and Huyakorn 2004).
23.7.2 SUTRA The USGS’s SUTRA code is one of the most widely used simulators in the world for seawater intrusion and other variable-density groundwater-flow problems based on solute transport or heat transport. Since its initial release in 1984, SUTRA (acronym for Saturated-Unsaturated TRAnsport) (Voss 1984; Voss and Provost 2002) has also been widely used for many other types of groundwater problems. The code is routinely used for hydrogeologic analyses and for many practical engineering studies. The SUTRA code offers the means to numerically simulate a variety of subsurface physical processes and situations. It robustly and reliably provides simulation results for well-posed problems. Although the SUTRA code can be used to simulate saturated–unsaturated systems with subsurface energy transport or single-species reactive solute transport, this discussion focuses only on seawater intrusion. Application to seawater-intrusion problems is based on the capability of SUTRA to simulate saturated variable-density flow with non-reactive solute transport. SUTRA is a finite-element code designed to solve a general set of single-phase subsurface fluid flow and single-species transport problems. The code was written to solve the basic equations presented by Bear (1979), which cover most types of groundwater flow and transport physics known. The two equations solved in 2D or 3D are a fluid mass balance for unsaturated and saturated groundwater flow, and a unified energy and solute mass balance. The unified balance provides a single equation that describes either solute or energy transport simply by changing the definition of parameters in the equation. The coding style of SUTRA is modular with each routine serving a special function, and coding simplicity is stressed over code efficiency to allow users to make easy changes and additions of processes to the code. A robust direct solver was selected to avoid the convergence difficulties associated with iterative matrix solvers, despite that such a solver would be less efficient for problems with large meshes. The code is written in standard FORTRAN. Recent developments for SUTRA include a complete GUI that provides a geographical information system (GIS) type of functionality together with automatic mesh generation (Voss et al. 1997; Winston and Voss 2003). The SUTRA GUI consists of public-domain USGS codes that connect SUTRA with the commercial Argus ONE™ software package that provides meshing and GIS capabilities. This GUI provides SUTRA users with new analytic power, making it easy to set up, run, and view results for even complex 3D SUTRA models. Computer speed and size have been the only limiting factors for practical application since the code was released, and will likely continue to be so. Computer speed and size have increased substantially since SUTRA’s original 1984 release, allowing more complex 2D and 3D simulations to be done regularly on a
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personal computer. The numerical effort for a simulation (i.e., computer time and memory) is determined by the density of spatial discretization and the number of time steps simulated. The numerical technique employed by the SUTRA code to solve the governing equations uses a modified 2D and 3D Galerkin finite-element method with bi- and tri-linear quadrilateral and hexahedral elements. Solution of the equations in the time domain is accomplished by the implicit finite-difference method. Modifications to the standard Galerkin method that are implemented in SUTRA are as follows: All terms of the equations not comprised of spatial gradients (e.g., time derivatives and sources) are assumed to be constant in the region surrounding each node (cell) in a manner similar to integrated finite differences. Parameters associated with the non-flux terms are thus specified nodewise, whereas parameters associated with flux terms are specified elementwise. This achieves some efficiency in numerical calculations while preserving the accuracy, flexibility, and robustness of the Galerkin finite-element technique. A very useful ad hoc generalization of the dispersion process is included in SUTRA, which allows the longitudinal and transverse dispersivities to vary in a time-dependent manner at any point depending on the direction of flow (as discussed above). Voss and Provost (2002) give a complete description of these numerical methods as used in the SUTRA code. An important modification to the standard finite-element method that is required for variable-density flow simulation is implemented in SUTRA. This modification provides a velocity calculation within each finite element based on consistent spatial variability of pressure gradient, ∇p, and the buoyancy term, ρg , in Darcy’s law. Without this “consistent velocity” calculation, the standard method generates spurious vertical velocities everywhere there is a vertical gradient of concentration within a finite-element mesh, even with a hydrostatic pressure distribution (Voss 1984; Voss and Souza 1987). The spurious velocities make it impossible to simulate, for example, a narrow transition between freshwater and seawater with the standard method, irrespective of how small a dispersivity is specified for the groundwater system. The two governing equations, fluid mass balance and solute mass (or energy) balance, are solved sequentially for each iteration or time step. Iteration is carried out by the Picard method with linear half-time-step projection of nonlinear coefficients on the first iteration of each time step. Iteration to the solution for each time step is optional. Velocities required for solution of the transport equation are the result of the flow equation solution (i.e., pressures) from the previous iteration (or time step for non-iterative solution). SUTRA is coded in a modular style, making it convenient for sophisticated users to modify the code (e.g., replace the existing direct banded-matrix solver) or to add new processes. Addition of new terms (i.e., new processes) to the governing equations is a straightforward process usually requiring changes to the code in very few lines. Also to provide maximum flexibility in applying the code, all boundary conditions and sources are allowed to be time-dependent in any user-specified manner.
23.8 Case Histories A large number of documented examples of the application of groundwater models to a variety of hydrogeologic problems are available in the literature. Three case studies have been selected to help illustrate modeling philosophy and practice, including aspects of model conceptualization, model implementation, and interpretation of results.
23.8.1 Flow and Transport in a Shallow Unconfined Aquifer Reilly et al. (1994) combined the application of environmental tracers and deterministic numerical modeling to analyze and estimate recharge rates, flow rates, flow paths, and mixing properties of a shallow groundwater system near Locust Grove in eastern Maryland. The study was undertaken as part of the USGS’s National Water-Quality Assessment Program to provide flow paths and traveltime estimates to be used in understanding and interpreting water-quality trends in monitoring wells and stream base flows. The study area encompassed about 2.6×107 m2 of mostly agricultural land on the Delmarva Peninsula.
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The Handbook of Groundwater Engineering
Task: Preliminary Calculations Method: Calculation of ranges of travel times to shallow wells using known ranges of recharge and porosity. Purpose: To check consistency of CFC ages. Task: First-level groundwater-flow model calibration. Method: MODFLOW (McDonald & Harbaugh,1988) Purpose: To calibrate a groundwater-flow model to known heads and flows. Task: Second-level calibration of flow model and pathline analysis. Method: MODFLOW & MODPATH (Pollock,1988,1989,&1994) Purpose: To recalibrate the groundwater-flow model with the additional information of traveltimes based on CFC age data. And to determine flow paths and time of travel in the groundwater system.
Plausible simulated advective flow system.
Task: Simulation of observed tritium concentrations. Method: MOC (Konikow & Bredehoeft,1978) Purpose: To simulate the transport of tritium with radioactive decay, and test the sensitivity of the system to dispersion. Also to corroborate the plausible advective flow system.
Evaluation of conceptualization of transport and flow system.
FIGURE 23.10 Flow diagram of the steps taken to quantify the flow paths in the Locust Grove, Maryland, groundwater-flow system. (Adapted from Reilly, T.E., Plummer, L.N., Phillips, P.J. and Busenberg, E. (1994) Water Resour. Res., 30: 421–433.)
The surficial aquifer includes unconsolidated permeable sands and gravel that range in thickness from less than 6 m to more than 20 m. This surficial aquifer is underlain by relatively impermeable silt and clay deposits, which form a confining unit. In this study, chlorofluorocarbons (CFCs) and tritium were analyzed from a number of water samples collected from observation wells to estimate the age of groundwater at each sampling location and depth. Because inaccuracies and uncertainty are associated with estimates of age based on environmental tracers, just as inaccuracies and uncertainty are associated with deterministic models of groundwater flow and transport, the authors applied a feedback or iterative process based on comparisons of independent estimates of traveltime. Their approach is summarized and outlined in Figure 23.10. Each task shown was designed to improve either the estimates of parameters or the conceptualization of the groundwater system. The preliminary calculations (first task) were used to set bounds on the plausibility of the results of the more complex simulations and chemical analyses. The first-level calibration of a groundwater-flow model (second task) provided the initial system conceptualization. The third task was a second-level calibration and analysis involving simulation of advective transport, which provided quantitative estimates of flow paths and time of travel to compare with those obtained from the CFC analyses. The fourth task involved the application of a solute-transport model to simulate tritium concentrations in the groundwater-flow system as affected by the processes of advection, dispersion, radioactive decay, and time-varying input (source concentration) functions. The sampling wells were located approximately along an areal flow line, and a 2D cross-sectional model was developed for the simulation of processes occurring along this flow line. The MODFLOW model (McDonald and Harbaugh 1988) was used to simulate groundwater flow and advective transport. The finite-difference grid consisted of 24 layers and 48 columns of nodes, with each cell having dimensions of 1.14 by 50.80 m, as shown in Figure 23.11, which also shows the wells that lie in the cross section. The simulation was designed to represent average steady-state flow conditions. After the flow model was calibrated, 2D pathline and traveltime analyses were undertaken and comparisons to CFC age estimates were made. The pathlines calculated using MODPATH (Pollock 1989) after the second-level calibration with MODFLOW are shown in Figure 23.12. The comparison with CFC estimates was generally good. However, Reilly et al. (1994) note that close to the stream, many flow lines converge, and the convergence of pathlines representing the entire range of traveltimes present in the aquifer causes waters of different ages to be relatively near each other. Thus, at the scale and grid spacing of the model, in the area near the stream the convergent flow lines cannot be readily differentiated in the
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23-33 Inactive cells above water table Free surface with constant-flux boundary
S
53
9.1 m (30 ft)
52 164
62
61
64
163
161 160
Sea Level
63
162
No-flow boundary
59 No-flow boundary
Altitude above sea level, in meters (feet)
N 18.3 m (60 ft)
No-flow boundary 159
–9.1 m (−30 ft) 2440 m (8000 ft)
1220 m (4000 ft)
0 m (0 ft)
Horizontal Distance, in meters (feet) Explanation Stream Node 62 Well location and number Inactive part of grid
FIGURE 23.11 Model grid used to simulate Locust Grove cross section, showing well locations. (Adapted from Reilly, T.E., Plummer, L.N., Phillips, P.J. and Busenberg, E. (1994) Water Resour. Res., 30: 421–433.)
0.8
Explanation
6.0 8.1 23.5
17.5
3.9
Simulated pathline, marker 6.0 indicates location of well screen. Value is simulated traveltime in years
2.6 15.6
8.8 12.3
36.7 65.6
Area above the water table or below the lower confining unit.
27.1 0
300 Meters
0
1,000 Feet
Vertical exaggeration is 50.0
FIGURE 23.12 Pathlines (calculated using MODPATH after second-level calibration) in Locust Grove cross section to observation wells showing time of travel (in years) from the water table. (Adapted from Reilly, T.E., Plummer, L.N., Phillips, P.J. and Busenberg, E. (1994) Water Resour. Res., 30: 421–433.)
model and the ages at individual well screens cannot be accurately represented directly under the stream. After the second-level calibration, the root mean squared error between the simulated ages and the CFC ages for the ten wells farthest from the stream (i.e., excluding wells 159, 160, and 161) was 3.4 years. Tritium concentrations of recharge waters have varied considerably over the last 40 years. Thus, the time of travel would not always be readily apparent from the tritium concentration in a water sample. Also, mixing of waters recharged during periods of these relatively sharp changes of input concentrations
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(a)
--14.8 15.3 25
31.5
13.7
16.5
50.0 100
25
75
16.5
50
38.5
25
Explanation 16.5 Location of well, tritium concentration measured Nov. 1990.
100
0.9
25
---
Area above the water table or below the lower confining unit.
(b)
14.8 15.3
25 31.5
50
50.0
75
13.7
16.5
16.5
Contour of simulated tritium distribution for 1990, contour interval 25 Tritium Units (TU).
0
300 Meters
0
1,000 Feet
25
50 25
38.5
Vertical exaggeration is 50.0
0.9 25
FIGURE 23.13 Simulated tritium distribution at the end of 1990: (a) with dispersivity αL = 0.0 m and αT = 0.0 m, and (b) with dispersivity αL = 0.15 m and αT = 0.015 m. Contour interval 25 tritium units (TU). (Adapted from Reilly, T.E., Plummer, L.N., Phillips, P.J. and Busenberg, E. (1994) Water Resour. Res., 30: 421–433.)
can make the interpretation of time of travel from tritium concentrations even more uncertain. Thus, the investigators simulated solute transport of tritium within the system using a model that accounts for mixing (dispersion), radioactive decay, and transient input functions, which also allowed a further evaluation of consistency with the results of the previous flow and advective transport model. They applied the MOC solute-transport model of Konikow and Bredehoeft (1978) and Goode and Konikow (1989) for this purpose. The results of the simulation of the tritium distribution assuming (1) no dispersion and (2) assuming αL of 0.15 m and αT of 0.015 m are shown in Figure 23.13. The limiting case simulation of no dispersion yielded acceptable results and was used as the best estimate of the tritium distribution in November 1990 (Reilly et al. 1994). This case reproduces the sharp concentration gradients required to reproduce the low tritium values that were observed. The MOC model was advantageous for this problem because it minimizes numerical dispersion and it can solve the governing equations for αL of 0.0, which transport models based on finite-difference or finite-element methods often cannot solve. The results of the solute-transport simulation are consistent with the advective flow system determined by the secondlevel calibration and thus strengthen the case for the conceptual model. The coupling of the tritium analyses and the transport model indicates where discrepancies between the measured and simulated concentrations occur, where additional data collection would be most useful, and where refinement of the conceptual model may be warranted. The case study described above illustrates that environmental tracers and numerical simulation methods in combination are effective tools that complement each other and provide a means to estimate the flow rate, time of travel, and path of water moving through a groundwater system. Reilly et al. (1994) found
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that the environmental tracers and numerical simulation methods also provide a “feedback” that allows a more objective estimate of the uncertainties in the estimated rates and paths of movement. Together, the two methods enabled a coherent explanation of the flow paths and rates of movement while identifying weaknesses in the understanding of the system that require additional data collection and refinement of conceptual models of the groundwater system.
23.8.2 Delineation of Contributing Areas to Water-Supply Wells, Rhode Island One type of water-resource management issue to which groundwater modeling and particle tracking are often applied is the delineation of contributing areas to water-supply wells. The contributing area of a well is defined as the surface area of the water table (and, possibly, the beds and banks of surface-water bodies) where water entering the groundwater system eventually flows to the well (Franke et al. 1998). The delineation of contributing areas has become an important component of many wellhead-protection programs because the land surface that overlies the contributing area to a well can be identified and protected from activities that may cause groundwater contamination. Contributing areas to several supply wells in the Hunt River Basin of Rhode Island were determined to identify the sources of water to the wells, the land area that contributes recharge to the wells, and the travel times of recharge to the wells (Barlow and Dickerman 2001). The aquifer from which the wells pump consists of highly permeable, stratified sand-and-gravel sediments deposited by glacial meltwater. The aquifer covers a 19 square-mile area, which is about half the total drainage area of the basin; the remainder of the basin consists of upland areas of primarily till and bedrock that drain to the aquifer (Figure 23.14). The aquifer is unconfined and in direct hydraulic connection with several shallow rivers, streams, and ponds that generally penetrate only a thin portion of the top of the aquifer. However, this connection allows for extensive interaction between the groundwater and surface-water systems, which occurs as groundwater discharge (base flow) to the streams, streamflow leakage to the aquifer from natural stream-channel losses, and induced infiltration of streamflow caused by pumping at the supply wells. This hydraulic interaction was a key factor in the development of the conceptual and numerical models of the groundwater system. Groundwater flow in the aquifer was simulated using the MODFLOW model (Harbaugh and McDonald 1996). The model grid was aligned approximately parallel to the northeast-trending Hunt River Valley (Figure 23.14). The model domain was discretized into a grid of 205 rows and 197 columns of square cells that were 200 ft on each side. Vertically, the model consists of a maximum of four layers that extend from the water table to the intersection of the aquifer with underlying bedrock. The uppermost layer of the model was relatively thin (a maximum of 10 ft) to simulate shallow groundwater flow near surface-water bodies as accurately as possible. The thickness of the remaining layers was specified partly on the basis of the vertical locations of the screened intervals of supply wells that pump from the aquifer. Areas of the aquifer where saturated thickness was less than 5 ft were made inactive to ensure numerical stability. This criterion resulted in many cells near the contact between the aquifer and adjoining upland areas being made inactive and a modeled area that was smaller than the measured extent of the aquifer (Figure 23.14). Boundary conditions specified for the model consisted of several variants of the specified flow and head-dependent flow boundary condition types defined in Table 23.1. No-flow boundary conditions were specified along groundwater-flow lines and drainage divides that separate the modeled area from adjacent aquifer areas that were not simulated. Nonzero flow rates were specified to represent (1) groundwater inflow from the upland areas, which was simulated using injection wells located within the active area of the model at the contact between the aquifer and upland areas; (2) pumping from 18 supply wells; and (3) recharge at the water table. Two types of head-dependent flow boundary conditions were simulated — evapotranspiration from the water table and hydraulic interaction between the aquifer and overlying streams, rivers, and ponds. Interactions between groundwater and surface water were simulated by use of the streamflow-routing (STR) package of MODFLOW (Prudic 1989). This package calculates the flow rate (Qs ; L3 /T) between each simulated stream reach and surrounding model cell by use of the following
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o
71 45'
71 30'
o
42 00'
Rhode island
Study Area
71°32'30"
o
41 30'
0
10 Miles
71°27'30"
10 Kilometers
30
0
10
9A KC1 NK9 NK10
14A 20
30
3A 60
41°37'30"
40
nt
R iv
er
IW
–1 2 100 0
Hu
40
60
50
50
NK6
50
60
80
Explanation Stratified deposits
SFH2 0
SFH1
10
120
Aquifer boundary
50
SFH3 140
180 160
Till and bedrock
NK1 NK2 NK4
Boundary of active area of model
40 50
NK5
Drainage boundary 0
.5
0 0
.5
NK8
10
100
20
40
50 60
30
Water-supply well and identifier
10
NK2
120
Water-table contour—in feet above sea level. Interval is variable
80
41°32'30" 100
50
60
NK3
NK7
1 Mile 1 Kilometer
FIGURE 23.14 Model-calculated steady-state water table, Hunt River Basin, Rhode Island. (Modified from Barlow, P.M. and Dickerman, D.C. (2001) Numerical-simulation and conjunctive-management models of the Hunt-Annaquatucket-Pettaquamscutt stream-aquifer system, Rhode Island. U.S. Geol. Survey Prof. Paper 1636.)
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equation: Qs = Cs (Hs − h)
(23.29)
where Cs is the streambed conductance of the stream reach (L2 /T), Hs is the average stream stage in the reach (L), and h is the groundwater head calculated for the model cell (L). Streambed conductance is a function of the thickness and hydraulic conductivity of the streambed and width and length of the stream reach within each model cell. Cs and Hs were estimated primarily on the basis of field data, including measurements of the hydraulic conductivity of streambed sediments, width of the streams, and streamstage elevation, but the estimates of Cs were highly uncertain and subsequently modified during model calibration. The steady-state model was calibrated to groundwater levels measured at 23 observation wells, average annual streamflow measured at a USGS gauging station on the Hunt River, and estimated average annual streamflows for four additional streams in the basin. During the calibration process, initial estimates of several model parameters were modified to improve the match between observed and simulated water levels and streamflow. These modifications included increasing the initial estimate of aquifer recharge by 10% (to 28.0 inches per year), increasing estimates of hydraulic conductivity in several areas, and decreasing the largest estimates of streambed conductance by about one-third. Contributing areas and sources of water were delineated for 13 supply wells within the study area by use of the MODPATH particle-tracking program (Pollock 1994). Potential sources of water to the wells are recharge to the water table, streamflow leakage, and simulated groundwater inflow from uplands. The contributing area to each well was delineated by overlaying a 2×2 array of particles onto the simulated water table of each grid cell. Particles were then tracked in the forward direction from the water table to their points of discharge. The origin of those particles captured by each well defined the well’s contributing area. The amount of streamflow leakage contributing to each well’s withdrawal also was determined by tracking particles from losing stream reaches to their point of discharge from the flow system. Twentyseven particles were distributed uniformly in a 3D array (3×3×3) within each losing stream cell. To estimate the amount of streamflow leakage reaching each of the supply wells, a volumetric flow rate was assigned to each particle by dividing the streamflow-leakage rate to the aquifer in the cell in which the particle originated by the number of particles placed in each cell (27). The contribution of streamflow leakage to each supply well was then calculated by summing the individual flow rates of all particles captured by each well. The contributing areas for the four northernmost wells as determined using MODPATH are shown in Figure 23.15 to illustrate some of the complicated spatial patterns that are often determined for contributing areas, particularly for groundwater systems where several wells are located in close proximity to one another. Each well’s contributing area is a function of various hydrogeologic and well-design factors, including the structure and hydraulic properties of the aquifer; the thickness, width, and hydraulic conductivity of streambed sediments near the wells; the withdrawal rate of each well; and the position of the screened interval of each well. This last factor is likely to be one of the primary reasons why the contributing areas for wells NK9, KC1, and 14A extend to the opposite side of the Hunt River from which the wells pump. Also note that the contributing area to well KC1 does not overlie the wellhead. The contributing area to well 9A is completely enveloped by that to well 14A; this results, in part, because the screened interval of well 9A is at a shallower depth than that of well 14A. Streamflow leakage was determined to be a source of water to 7 of the 13 supply wells (Table 23.2). The largest contribution was calculated for well 3A, which captures an estimated 95% of its discharge from a nearby stream. Streamflow leakage also is a substantial source of water to wells 9A, 14A, and KC1. The total travel time of each simulated water particle from its entry at the water table to its withdrawal at a supply well also was calculated by MODPATH, and zones of equal travel time to each well are shown in Figure 23.15. Model-calculated travel times for particles captured by the four wells (for a uniform porosity of 0.35) ranged from a minimum of 45 days (to well 14A) to a maximum of 24.7 years (to well NK9).
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71°27'30" 41°38'45"
20
30
41°38'45"
9A KC1 NK9
71°28'45"
14A
P
ot ow
om
Hu
ond ut P
Ri
ver
nt
20
30
41° 37' 30"
Explanation
Traveltime to well, in years
Contributing areas to water-supply wells
40
>20 >10 - 20 >5 - 10 >2.5 - 5 0 - 2.5 NK9
KC1
14A
9A
Water-supply well identifier Boundary of active area of model—dashed where active area extends beyond area shown.
Inactive area of model
30
Model-calculated water-table countour—contour interval is 10 feet. Datum is sea level.
NK9 Water-supply well and identifier Base from U.S. Geological Survey digital data, 1:24,000, Rhode Island stateplane projection. 1983 North American datum
FIGURE 23.15 (See color insert following page 23-52) Model-calculated steady-state contributing areas and traveltimes to water-supply wells in the northern part of the Hunt River Basin, Rhode Island. (Modified from Barlow, P.M. and Dickerman, D.C. (2001) Numerical-simulation and conjunctive-management models of the Hunt-Annaquatucket-Pettaquamscutt stream-aquifer system, Rhode Island. U.S. Geol. Survey Prof. Paper 1636.)
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TABLE 23.2 Model-Calculated Sources of Water to Supply Wells in the Hunt River Basin, Rhode Island. Values Shown are Percent of Well’s Simulated Withdrawal Rate Well Identifier 9A 14A KC1 NK9 3A NK6 NK1 NK2 NK4 NK5 SFH1 SFH2 NK3
Percent Contribution from Recharge and Uplands
Percent Contribution from Streamflow Leakage
24.1 24.2 27.2 83.8 5.3 100.0 100.0 100.0 100.0 100.0 69.8 100.0 92.6
75.9 75.8 72.8 16.2 94.7 0 0 0 0 0 30.2 0 7.4
Sources: Modified from Barlow, P.M. and Dickerman, D.C. (2001) Numerical-simulation and conjunctive-management models of the HuntAnnaquatucket-Pettaquamscutt stream-aquifer system, Rhode Island. U.S. Geol. Survey Prof. Paper 1636.
23.8.3 Seawater Intrusion in a Coastal Aquifer The main population center of the volcanic Hawaiian Island chain in the north-central Pacific Ocean, is on the island of Oahu. Oahu depends on groundwater for its potable water supply, and most of it is produced from coastal aquifers. Oahu has high rainfall, highly permeable aquifers, and a coastal semi-confining layer above many of the aquifers. The coastal confining unit keeps heads high at the coast, and creates a very thick freshwater lens. This combination of high recharge, high permeability, and impeded discharge provides an ample supply of fresh groundwater for both drinking and irrigation. Seawater is present at the base of Oahu’s coastal aquifers, and water supplies are potentially threatened by seawater intrusion. A major issue in Oahu that remains unresolved is how much groundwater may be safely withdrawn from each aquifer. This is an important issue as limited availability of freshwater may potentially limit further economic growth. On the other hand, over-development of groundwater may lead to deleterious impacts on local groundwater supplies from seawater intrusion. Such intrusion may be difficult to reverse quickly. A careful quantitative analysis of aquifer hydraulics and the physics of seawater intrusion will give water managers a reliable scientific basis for managing Oahu’s aquifer systems. The primary aquifer of interest underlies the Pearl Harbor area of southern Oahu (Figure 23.16). The SUTRA code was applied first to evaluate aquifer hydraulics, and then to evaluate seawater intrusion. The objective of the hydraulic analysis was to find the simplest possible variable-density flow and transport model that reproduces the measured large-scale hydraulic behavior of the system and to elucidate the major hydrologic controls on the system. SUTRA was modified to include a water table in cross-sectional simulation. The cross-sectional 2D-model domain represents the basal aquifer and caprock containing the basal freshwater lens, the transition zone (TZ) between freshwater and seawater, and deeper seawater to the right of the dike zone (Figure 23.17). A 2D representation is appropriate for evaluation of aquiferwide response in this system because (1) flow is approximately perpendicular to the coastal boundary; (2) permeability anisotropy is primarily horizontal and vertical; (3) the caprock is parallel to the coast; and (4) sources and sinks are distributed evenly along bands parallel to the coast. When analyzing water resources in a coastal aquifer system where water quality may be affected by seawater intrusion, relatively low concentrations of solute are critical for water supply. The limiting concentration of potable water is defined here as the equivalent of freshwater containing about 2%
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The Handbook of Groundwater Engineering 160°
158°
22°
Kauai Niihau
N
3
20°
t rif
PACIFIC
1
7
Vo Pearl Harbor (244) area ? ? 6 (213) 7.3 lley Va Ho i lih n Ka 8.1 a re olu (183) a lu 8.4 (2.7) (0.9) 8.1 valley fill northeast trending dikes
on
e
bo
un
da
ry
confining bed
ry
Major hydrogeologic boundary
(274)
tz
no
unda
Explanation
(305)
rif
lca
Wai anae
85
no
Vo
ne bo
lca
ae
rift zo
ry
au
an
7
da
ol
ai
5
Hawaii
un
Ko
W
7
6
8
OCEAN
bo
5
7
ne zo
1 1.5 valley fill ? ? 3.5 4 rift 6 zo (50) ne bo (40) un da ry Schofield (488) area (61) 8.5 8
Molokai Maui
Lanai Kahoolawe
4 5 6
0 2 4 km
HAWAII
Oahu
Honolulu
6
156°
6
(244)
8.1
Subordinate hydrogeologic boundary—Queried where uncertain Water-level contour—Shows altitude of water level in the mid-1950's. Contour interval, in meters, is variable. Datum is sea level Point observation of altitude of water level in the mid-1950's, in meters above sea level Representative mid-1950's water level where water table is too flat to be contoured, in meters above sea level
FIGURE 23.16 Location and relative positions of Hawaiian Islands and surface locations of hydrogeologic barriers, water levels in principal aquifers, and inferred freshwater flow directions on Oahu, Hawaii. (From Gingerich, S.B. and Voss, C.I. (2005) Hydrogeol. J., 13: 436–450; after Hunt, C.D., Jr. (1996) Geohydrology of the island of Oahu, Hawaii, U.S. Geol. Surv. Prof. Paper 1412-B.)
seawater (∼700 ppm total dissolved solids). Tracking the boundary of potable water as delineated by this relatively low concentration requires use of a numerically accurate solute-transport model with variable fluid density applied using a fine mesh to minimize numerical dispersion. A 2D cross-sectional model was initially developed for analyzing the TZ and used to predict the general evolution of water quality that will be drawn from the coastal pumping zone. The finite-element mesh (Figure 23.18) encompasses the entire aquifer to a depth of 1800 m below sea level, the deepest extent of permeable basalts. The vertical discretization is only schematically represented in Figure 23.18; the actual discretization in the top 600 m of the mesh is actually 2 m. Recharge in the model-simulated aquifer enters through the water table and through the upstream boundary of the aquifer (representing inflow from dike compartments and the central plateau), both at prescribed rates. The seaward model boundary is held at hydrostatic seawater pressure and the top boundary above the caprock is held at a pressure of zero. The other boundaries are modeled as impermeable (no flow). More details are provided by Souza and Voss (1989) and Voss (1999). The period 1980–2080 is considered, and the effect of various alternative pumping-recharge scenarios is evaluated (Souza and Voss 1989). Pumping is simulated by withdrawing water from the model area identified as the pumping zone in Figure 23.18, which represents a strip of scattered wells along the coast about 1.5 km (5000 ft) wide. In a practical sense, a regional-scale model cannot be used to predict the salinity of the water pumped from an individual well in the zone. Because of the large scale of processes modeled, only some average concentration in the zone may be considered when analyzing the general salinity changes expected. Thus, meaningful salinity values of the pumped water are the mean
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A East Trace of section
A
1,200 900
OAHU Recharge
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Perched water Springs, discharge
Unsaturated zone
Springs
A'
300 Sea level Seawater
Dike complex with dikeimpounded freshwater
Basal water (freshwater)
–150 sition Tran
zone
–300 Saline groundwater –450 Vertical exaggeration increased x3 below sea level Explanation Water table Generalized direction of groundwater flow
Basalt
Caprock - sedimentary
FIGURE 23.17 Schematic cross section of typical groundwater bodies in Hawaii. (From Gingerich, S.B. and Voss, C.I. (2005) Hydrogeol. J., 13: 436–450; after Hunt, C.D., Jr. (1996) Geohydrology of the island of Oahu, Hawaii, U.S. Geol. Surv. Prof. Paper 1412-B.)
concentrations of the three nodes that represent the pumping center. This represents the average salinity of the water pumped from the areally extensive well field that is present in a strip across the aquifer system underlying the Pearl Harbor area. The TZ evolution was modeled from predevelopment conditions (1880) through recent time (1990). The calculated distribution of seawater, freshwater, and irrigation water in 1990 (Figure 23.19) and the concurrent flow field (Figure 23.20) represented the starting conditions for the simulation of water-quality evolution in the pumping center for the period 1980–2080 for eight scenarios, which had different assumed withdrawal rates and different recharge rates for future conditions. These numerical experiments were used to help assess management alternatives. The results show that careful management of groundwater system withdrawals during droughts can preserve water quality. An analysis of controls on water-quality evolution indicates that the key control on long-term saltwater intrusion is the net system discharge (equal to the difference between total recharge and pumpage), not the percentage of recharge pumped, and the maximum safe withdrawal will vary depending on the actual long-term recharge rate (Souza and Voss 1989). The effect is illustrated in Figure 23.21 wherein the average concentration of seawater in water produced at the pumping center in the year 2080 is a strong function of net system discharge. This curve is the result of several independent simulations, each with different recharge and withdrawals. The net system discharge is important because it controls the ultimate thickness of the freshwater lens downstream of the pumping center. A “minimum safe discharge” from the aquifer underlying the Pearl Harbor area is defined on the basis of simple interpretations of what the average salinity of water produced in the coastal pumping zone means in terms of a “safe yield,” and indicates the least quantity of water that must be allowed to discharge naturally from the aquifer to ensure production of potable water in 2080 from the zone of pumping (Voss 1999). This modeling indicates that if the long-term net system discharge rate drops to within the range
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e
Recharge from irrigation
Zone of pumping Specified pressure = 0
Water Table 0
Low permeability caprock
Hydrostatic seawater pressure
High permeability –600 Basalt
Aquifer –900
Leakance Boundary
Elevation, in meters from sea level
–300
–1200
–1500
No flow –1800 –10
–8
–6
–4
4 –2 0 2 Distance, in kilometers from caprock boundary
6
8
10
FIGURE 23.18 Schematic SUTRA finite-element mesh for transition zone modeling showing boundary conditions applied to model and regions of constant permeability. Actual vertical discretization is finer than illustrated. (From Voss, C.I. and Souza, W.R. (1998) Dynamics of a regional freshwater–saltwater transition zone in an anisotropic coastal aquifer system, U.S. Geol. Survey Open-File Rept. 98-398.)
of minimum safe discharge (1.7 to 2.9 × 105 m d−1 ), then significant seawater intrusion in parts of the Pearl Harbor area pumping zone will occur by 2080. A 3D model of the aquifer underlying the Pearl Harbor area was developed subsequently as a lateral expansion of the 2D cross-sectional model by incorporating realistic areal distributions of hydrogeologic structure, recharge, and pumping (Gingerich and Voss 2005). One obvious advantage of 3D modeling is the ability to include realistic areal distributions allowing the model to be used as a management tool for testing or optimizing various pumping distribution schemes. An objective in constructing the 3D model was to maintain the general spatial geometry and boundary conditions of the 2D cross-sectional model as well as the 2D physical property and parameter values, and to add no additional complexity except for the realistic areal geometry of model features and the extra parameters required in 3D (one additional permeability and several dispersivity parameters). It was expected that, without significant adjustments, this 3D model should be a good representation of the aquifer because of the descriptive strength and functional simplicity of the 2D model upon which it is based. One of the most useful applications of a 3D variable-density model is to simulate the response of the TZ to pumping stresses on the aquifer. The simulated rise and spread of the TZ at well 2300-18 (an open borehole) during 100 years of pumping is illustrated in Figure 23.22 where salinity concentrations equivalent to 2, 10, 50, and 90% seawater concentration are shown. The simulated trends of the four
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–300
75 90 95 98
–600
–900 –10
–8
–6
–4
–2
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2
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8
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Distance from shoreline (km)
FIGURE 23.19 Modeled cross section of aquifer underlying Pearl Harbor area showing seawater distribution from 1880 to 1990 transient simulation (lower set of contours in units of percent seawater), irrigation recharge water distribution (upper set of contours in units of percent irrigation water), and location of monitor wells. Upper half of model section is shown. (Adapted from Voss, C.I. and Wood, W.W. (1994) In Mathematical Models and their Applications to Isotope Studies in Groundwater Hydrology, International Atomic Energy Agency (IAEA) Vienna, Austria, IAEA-TECDOC-777, pp. 147–178.)
0
Elevation, in meters from sea level
Velocity (m/s)
4 × 10−8
−300
4 × 10−7 4 × 10−6 4 × 10−5
−600
−900 −10
−8
−6
−4
−2
0
2
4
6
8
10
Distance from shoreline (km)
FIGURE 23.20 Modeled cross section of aquifer underlying Pearl Harbor area showing velocity distribution in 1990 from transient simulation. Upper half of model section is shown. (Adapted from Voss, C.I. and Wood, W.W. (1994) In Mathematical Models and Their Applications to Isotope Studies in Groundwater Hydrology, International Atomic Energy Agency (IAEA) Vienna, Austria, IAEA-TECDOC-777, pp. 147–178.)
salinity-concentration lines are generally parallel to each other, but show more spreading below the 50% line. The periods of most rapid rise in the TZ near the well were between 1910–15 (5 m/ year) and 1970–75 (2.6 m/year) (Gingerich and Voss 2005). In many field situations, where TZ information from wells is lacking, the Ghyben–Herzberg (G–H) relation is commonly used to estimate the position of the TZ and the amount of freshwater available in the aquifer. The relation indicates that the depth of the interface between freshwater and saltwater below sea level is 40 times the altitude of the water table above sea level. The validity of this assumption can be checked by comparing the depth of this theoretical freshwater– saltwater interface with the simulated salinity-concentration lines (Figure 23.22). In this simulation, the
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Concentration, % seawater
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0
25
50
75
100
125
Minimum safe discharge
4
2 0.67 0
0
1
2 3 4 Net system discharge, 105 m3/day
5
Depth (m below sea level)
FIGURE 23.21 Dependence of average salinity of water produced in the Pearl Harbor area aquifer’s zone of pumping after 100 years of pumping (1980–2080) on the quantity of water that still discharges naturally from the aquifer after water is removed by pumping (net system discharge). (From Voss, C.I. (1999) In J. Bear et al. (eds.) Seawater Intrusion in Coastal Aquifers, Kluwer Academic Publ., Dordrecht, pp. 249–313.)
0
−250
Well 2300-18 2% 10%
theoretical interface depth
50% 90%
−500 1880
1900
1920
1940
1960
1980
FIGURE 23.22 Position of simulated transition zone and theoretical (Ghyben–Herzberg) interface depth at well 2300-18, 1880–1980. (From Gingerich, S.B. and Voss, C.I. (2005) Hydrogeol. J., 13: 436–450.
depth of the theoretical interface is nearly always shallower than the 50% seawater concentration depth, indicating that the G–H relation is not a good predictor of the transition-zone position. The general approach to coastal seawater intrusion modeling, as applied in Oahu, provides reasonable predictions of changes in the regional position of the potable-water boundary above the transition zone that result from changes in stress in a coastal aquifer. A strategy that controls withdrawals on the basis of (1) accurate estimates of recharge and (2) water-quality predictions from coastal aquifer modeling should be a major component of a total management scheme for a coastal aquifer water resource.
23.9 Available Groundwater Software A large number of generic deterministic groundwater modeling software packages, based on a variety of numerical methods and a variety of conceptual models, are available. The selection of a numerical method or generic model for a particular field problem depends on several factors, including accuracy, efficiency/cost, and usability. The first two factors are related primarily to the nature of the field problem, availability of data, and scope, or intensity of the investigation. The usability of a method may depend partly on the mathematical background of the modeler, as it is preferable for the model user to understand the nature of the numerical methods implemented in a code. In selecting a model that is appropriate for a particular application, it is most important to choose one that incorporates the proper conceptual model; one must avoid force fitting an inappropriate model to a field situation solely because of the
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FIGURE 23.23 (See color insert following page 23-52) Example plot generated with Model Viewer software showing the grid shell, selected model features and boundary conditions, particle pathlines (shaded by time of travel), and a solid rendering of a contaminant plume for a 3D MODFLOW simulation. (From Hsieh, P.A. and Winston, R.B. (2002) User’s guide to Model Viewer, a program for three-dimensional visualization of ground-water model results, U.S. Geol. Survey Open-File Rept. 02-106.)
model’s convenience, availability, or familiarity to the user. Usability is also enhanced by the availability of preprocessing and postprocessing programs or features, and by the availability of comprehensive yet understandable documentation. Many groundwater models are in the public domain and available for downloading from the internet at no cost; some are proprietary codes available for purchase. However, most GUIs, GIS Packages, and visualization software are commercial products that must be purchased. One available public domain postprocessor, which works with output from several different specific models, is Model Viewer (Hsieh and Winston 2002). Scalar data (such as hydraulic head or solute concentration) may be displayed as a solid or a set of isosurfaces, using a red-to-blue color spectrum to represent a range of scalar values. Vector data (such as velocity or specific discharge) are represented by lines oriented to the vector direction and scaled to the vector magnitude. Model Viewer can also display pathlines, cells, or nodes that represent model features (such as constant-head boundary cells, streams, and wells), and auxiliary graphic objects (such as grid lines and coordinate axes). Figure 23.23 represents an illustrative example showing the grid outline, selected model features and boundary conditions, particle pathlines, and a solid rendering of a contaminant plume. Users may rotate and crop the model grid in different orientations to examine the interior structure of the data. For transient simulations, Model Viewer can animate the time evolution of the simulated quantities.
Glossary Analytical Model A closed-form exact mathematical solution, which is continuous in space and time. Conceptual Model A hypothesis for how a system or process operates. Deterministic Model A mathematical model based on conservation of mass, momentum, and energy. Discretization The process of representing a continuous system by a set of discrete blocks, cells, or elements. Generic Model The computer code used to solve one or more governing differential equations. Mathematical Model A set of equations, which include mathematical variables, constants, and coefficients, that represents relevant processes. Model A representation of a real system or process. Numerical Model An approximate solution of a differential equation obtained by replacing the continuous variables with a set of discrete variables defined at grid blocks, cells, or nodes. Site-Specific Model A numerical model with the parameters (such as hydraulic conductivity, dispersivity, etc.), boundary conditions, and grid dimensions of the generic model specified to represent a particular geographical area.
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Stochastic Involving random variables or random processes, and amenable to analysis using probabilistic concepts.
Acknowledgments The authors appreciate the helpful review comments provided by Robert Nicholson and Michael Planert of the USGS, and by Mary P. Anderson of the University of Wisconsin-Madison, on the first edition of this chapter, and by Brendan A. Zinn, Philip T. Harte, and Angel Martin, Jr. of the USGS on this revised version for the second edition.
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Hsieh, P.A. and Winston, R.B. (2002) User’s guide to Model Viewer, A program for threedimensional visualization of ground-water model results, U.S. Geol. Survey Open-File Rept. 02-106. Huebner, K.H. (1975) The Finite Element Method for Engineers, John Wiley & Sons, New York. Hunt, C.D., Jr. (1996) Geohydrology of the island of Oahu, Hawaii, U.S. Geol. Surv. Prof. Paper 1412-B. Huyakorn, P.S. and Pinder, G.F. (1983) Computational Methods in Subsurface Flow, Academic Press, New York. Javandel, I., Doughty, D. and Tsang, C.-F. (1984) Groundwater Transport: Handbook of Mathematical Models, Am. Geophysical Union, Water Res. Monograph 10. Kipp, K.L., Jr. (1987) HST3D: A computer code for simulation of heat and solute transport in threedimensional ground-water flow systems, U.S. Geol. Survey Water-Res. Inv. Rept. 86-4095. Konikow, L.F. (1996) Numerical models of ground-water flow and transport. In Manual on Mathematical Models in Isotope Hydrogeology, International Atomic Energy Agency, Vienna, Austria. Konikow, L.F. and Bredehoeft, J.D. (1978) Computer model of two-dimensional solute transport and dispersion in ground water, Techniques of Water-Res. Invests. of the U.S. Geol. Survey, Book 7, Ch. C2. Konikow, L.F. and Bredehoeft, J.D. (1992) Ground-water models cannot be validated. Adv. Water Resour., 15: 75–83. Konikow, L.F., Goode, D.J. and Hornberger, G.Z. (1996) A three-dimensional method-of-characteristics solute-transport model (MOC3D), U.S. Geol. Survey Water-Res. Inv. Rept. 96-4267. Konikow, L.F. and Mercer, J.M. (1988) Groundwater flow and transport modeling. J. Hydrol., 100: 379–409. Konikow, L.F., Sanford, W.E. and Campbell, P.J. (1997) Constant-concentration boundary condition: Lessons from the HYDROCOIN variable-density benchmark problem. Water Resour. Res., 33: 2253–2261. Lambert, P.M. (1996) Numerical simulation of the movement of sulfate in ground water in southwestern Salt Lake Valley, Utah, Tech. Pub. No. 110-D, Utah Dept. of Natural Resources, Salt Lake City, UT. Langevin, C.D. (2001) Simulation of ground-water discharge to Biscayne Bay, Southeastern Florida: U.S. Geol. Survey Water-Res. Inv. Rept. 00-4251. Langevin, C.D., Shoemaker, W.B. and Guo, W. (2003) MODFLOW-2000, The U.S. Geological Survey modular ground-water model — Documentation of the SEAWAT-2000 version with the variabledensity flow process (VDF) and the integrated MT3DMS transport process (IMT), U.S. Geol. Survey Open-File Rept. 03-426. Lefkoff, L.J. and Gorelick, S.M. (1987) AQMAN-Linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling. U.S. Geol. Survey Water-Res. Inv. Rept. 87-4061. Masterson, J.P. (2004) Simulated interaction between freshwater and saltwater and effects of ground-water pumping and sea-level change, lower Cape Cod Aquifer System, Massachusetts: U.S. Geol. Survey Scientific Inv. Rept. 2004–5014. Masterson, J.P., Walter, D.A. and Savoie, J. (1996) Use of particle tracking to improve numerical model calibration and to analyze ground-water flow and contaminant migration, Massachusetts Military Reservation, western Cape Cod, Massachusetts, U.S. Geol. Survey Open-File Rept. 96–214. McAda, D.P. and Barroll, P. (2002) Simulation of ground-water flow in the Middle Rio Grande Basin between Cochiti and San Acacia, New Mexico: U.S. Geol. Survey Water-Res. Inv. Rept. 02-4200. McDonald, M.G. and Harbaugh, A.W. (1988) A modular three-dimensional finite-difference groundwater flow model, Techniques of Water-Res. Invests. of the U.S. Geol. Survey, Book 6, Ch. A1. Mercer, J.W. and Faust, C.R. (1981) Ground-Water Modeling, Natl. Water Well Assoc., Worthington, OH. Oreskes, N., Shrader-Frechette, K. and Belitz, K. (1994) Verification, validation, and confirmation of numerical models in the earth sciences. Science, 263: 641–646.
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Panday, S. and Huyakorn, P.S. (2004) A fully coupled physically-based spatially-distributed model for evaluating surface/subsurface flow. Adv. Water Resour., 27: 361–382. Peaceman, D.W. (1977) Fundamentals of Numerical Reservoir Simulation, Elsevier, Amsterdam. Peralta, R.C. (2004) Simulation/Optimization MOdeling System (SOMOS). Logan, UT, Utah State University Department of Biological and Irrigation Engineering. Poeter, E.P. and Hill, M.C. (1998) Documentation of UCODE, A computer code for universal inverse modeling, U.S. Geol. Survey Water-Res. Inv. Rept. 98-4080. Poeter, E.P., Hill, M.C., Banta, E.R., Mehl, S. and Christensen, S. (2005) UCODE_2005 and six other computer codes for universal sensitivity analysis, calibration, and uncertainty evaluation: U.S. Geol. Survey Techniques and Methods 6-A11. Pollock, D.W. (1988) Semianalytical computation of path lines for finite-difference models. Ground Water, 26: 743–750. Pollock, D.W. (1989) Documentation of computer programs to compute and display pathlines using results from the U.S. Geological Survey modular three-dimensional finite-difference ground-water flow model, U.S. Geol. Survey Open-File Rept. 89-381. Pollock, D.W. (1994) User’s guide for MODPATH/MODPATH-PLOT, version 3: A particle tracking post processing package for MODFLOW, the U.S. Geological Survey finite-difference ground-water flow model, U.S. Geol. Survey Open-File Rept. 94-464. Popper, K. (1959) The Logic of Scientific Discovery, Harper and Row, New York. Prickett, T.A., Naymik, T.G. and Lonnquist, C.G. (1981) A “random-walk” solute transport model for selected groundwater quality evaluations, Ill. State Water Survey Bulletin 65. Prudic, D.E. (1989) Documentation of a computer program to simulate stream-aquifer relations using a modular, finite-difference, ground-water flow model. U.S. Geol. Survey Open-File Rept. 88-729. Reddell, D.L. and Sunada, D.K. (1970) Numerical Simulation of Dispersion in Groundwater Aquifers, Colorado State University, Ft. Collins, Hydrology Paper 41. Reilly, T.E. (2001) System and boundary conceptualization in ground-water flow simulation: Techniques of Water-Res. Invests. of the U.S. Geol. Survey, Book 3, Ch. B8. Reilly, T.E., Franke, O.L., Buxton, H.T. and Bennett, G.D. (1987) A conceptual framework for groundwater solute-transport studies with emphasis on physical mechanisms of solute movement, U.S. Geol. Survey Water-Res. Inv. Rept. 87-4191. Reilly, T.E. and Harbaugh, A.W. (2004) Guidelines for evaluating ground-water flow models: U.S. Geol. Survey Scientific Inv. Rept. 2004-5038. Reilly, T.E., Plummer, L.N., Phillips, P.J. and Busenberg, E. (1994) The use of simulation and multiple environmental tracers to quantify groundwater flow in a shallow aquifer. Water Resour. Res., 30: 421–433. Remson, I., Hornberger, G.M. and Molz, F.J. (1971) Numerical Methods in Subsurface Hydrology, Wiley, New York. Ségol, G. (1994) Classic Groundwater Simulations: Proving and Improving Numerical Models, PTR Prentice Hall, Englewood Cliffs. Smith, L. and Schwartz, F.W. (1980) Mass transport, 1, A stochastic analysis of macroscopic dispersion. Water Resour. Res., 16: 303–313. Souza, W.R. and Voss, C.I. (1989) Assessment of potable ground water in a fresh-water lens using variabledensity flow and solute transport simulation. In: Proceedings, National Water Well Association (NWWA) Conference on Solving Ground Water Problems with Models, Indianapolis, Indiana, Feb. 7–9, 1989, pp. 1023–1043. Swedish Nuclear Power Inspectorate (1987) The International HYDROCOIN Project — Background and Results, OECD, Paris. Tenbus, F.J. and Fleck, W.B. (2001) Simulation of ground-water flow and transport of chlorinated hydrocarbons at Graces Quarters, Aberdeen Proving Ground, Maryland: U.S. Geol. Survey Water-Res. Inv. Rept. 01-4106.
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Torak, L.J. (1993) A modular finite-element model (MODFE) for areal and axisymmetric ground-waterflow problems, Part 1: Model description and user’s manual, Techniques of Water-Res. Invests. of the U.S. Geol. Survey, Book 6, Ch. A3. Turco, M.J. and Buchmiller, R.C. (2004) Simulation of ground-water flow in the Cedar River alluvial aquifer flow system, Cedar River, Iowa: U.S. Geol. Survey Scientific Inv. Rept. 2004-5130. Voss, C.I. (1984) SUTRA — Saturated Unsaturated Transport — A finite-element simulation model for saturated-unsaturated fluid-density-dependent ground-water flow with energy transport or chemically-reactive single-species solute transport, U.S. Geol. Survey Water-Res. Inv. Rept. 84-4369. Voss, C.I. (1999) USGS SUTRA Code — History, practical use, and application in Hawaii. In J. Bear et al. (eds.) Seawater Intrusion in Coastal Aquifers, Kluwer Academic Publ., Dordrecht, pp. 249–313. Voss, C.I., Boldt, D. and Shapiro, A.M. (1997) A graphical-user interface for the U.S. Geological Survey’s SUTRA code using Argus ONE (for simulation of variable-density saturated-unsaturated groundwater flow with solute or energy transport): U.S. Geol. Survey Open-File Rept. 97–421. Voss, C.I. and Provost, A.M. (2002) SUTRA, A model for saturated–unsaturated variable-density groundwater flow with solute or energy transport, U.S. Geol. Survey Water-Res. Inv. Rept. 02-4231. Voss, C.I. and Souza, W.R. (1987) Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater–saltwater transition zone. Water Resour. Res., 23: 1851–1866. Voss, C.I. and Souza, W.R. (1998) Dynamics of a regional freshwater–saltwater transition zone in an anisotropic coastal aquifer system, U.S. Geol. Survey Open-File Rept. 98-398. Voss, C.I. and Wood, W.W. (1994) Synthesis of geochemical, isotopic and ground-water modeling analysis to explain regional flow in a coastal aquifer of southern Oahu, Hawaii. In Mathematical Models and their Applications to Isotope Studies in Groundwater Hydrology, International Atomic Energy Agency (IAEA) Vienna, Austria, IAEA-TECDOC-777, pp. 147–178. Wang, J.F. and Anderson, M.P. (1982) (reprinted, 1995). Introduction to Groundwater Modeling, Academic Press, San Diego, CA. Wexler, E.J. (1992) Analytical solutions for one-, two-, and three-dimensional solute transport in groundwater systems with uniform flow, Techniques of Water-Res. Invests. of the U.S. Geol. Survey, Book 3, Ch. B7. Winston, R.B. and Voss, C.I. (2003) SutraGUI: A Graphical User Interface for SUTRA, A model for ground-water flow with solute or energy transport: U.S. Geol. Survey Open-File Rept. 03-285. Yager, R.M. (1997) Simulated three-dimensional ground-water flow in the Lockport Group, a fractured dolomite aquifer near Niagara Falls, New York, U.S. Geol. Survey Water-Supply Paper 2487. Zheng, C. and Bennett, G.D. (2002) Applied Contaminant Transport Modeling, 2nd ed., Wiley-Interscience, New York. Zheng, C. and Wang, P.P. (1999) MT3DMS: A modular three-dimensional multispecies model for simulation of advection, dispersion and chemical reactions of contaminants in groundwater systems; Documentation and User’s Guide, Report SERDP-99-1, U.S. Army Engineer Research and Development Center, Vicksburg, MS. Zheng, C. and Wang, P.P. (2002) MGO — A Modular Groundwater Optimizer incorporating MODFLOW and MT3DMS, Documentation and user’s guide. The University of Alabama and Groundwater Systems Research Ltd., Tuscaloosa, AL. Zienkiewicz, O.C. (1971) The Finite Element Method in Engineering Science, McGraw-Hill, London. Zimmermann, S., Koumoutsakos, P. and Kinzelbach, W. (2001) Simulation of pollutant transport using a particle method. J. Comput. Phys., 173: 322–347.
Further Information Text books and examples of good reports on site-specific models are provided as a starting point for readers who would like to obtain more information or study representative applications.
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Text Books Ahlfeld and Mulligan (2000) provide an introduction to combined simulation-optimization modeling of groundwater flow. Anderson and Woessner (1992) present an overview of applied groundwater flow and advective transport modeling. Zheng and Bennett (2002) present an overview of the theory and practice of contaminant transport modeling.
Examples of Reports on Site-Specific Models Comprehensive reports on site-specific models provide insight into applied groundwater simulation. A few examples from the work of the United States Geological Survey are provided below. Obviously, this list is not inclusive and many other reports could have been listed.
Regional Flow Models Buxton and Smolensky (1999) simulate the effects of water use on the groundwater-flow system on Long Island, New York. McAda and Barroll (2002) describe a 3D flow model of the Albuquerque Basin in New Mexico.
Local Flow Model Turco and Buchmiller (2004) Simulated groundwater flow in the Cedar River alluvial aquifer flow system, Cedar River, Iowa.
Local Advective-Transport Model Barlow and Dickerman (2001) examined contributing areas to public-supply wells in Rhode Island.
Solute-Transport Model Lambert (1996) used a 3D model to simulate contaminant plume in approximately 480-km2 area in Utah. Tenbus and Fleck (2001) simulated the transport of chlorinated hydrocarbons at a site on Aberdeen Proving Ground, Maryland.
Variable-Density Flow Models Langevin (2001) simulated groundwater discharge to Biscayne Bay, Southeastern Florida. Masterson (2004) simulated the effects of groundwater pumping and sea-level change on the lower Cape Cod Aquifer System, Massachusetts.
Model Calibration Masterson et al. (1996) used particle tracking and contaminant plumes to improve calibration of a 3D flow model. Yager (1997) used a parameter-estimation model (MODFLOWP) to help calibrate a 3D flow model for a fractured dolomite aquifer system.
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Internet A number of sites on the internet provide compendiums of codes and sources of information about groundwater modeling, as well as providing links to other Web sites related to groundwater modeling. Many of these sites allow codes to be downloaded. Examples of several groundwateroriented Home Page locations are: http://www.thehydrogeologist.com/, http://hydrologyweb.pnl.gov/, http://www.mines.edu/igwmc/, and http://www.ggsd.com/. Also, many of the U.S. Geological Survey public domain codes are available from the “Software” tab on the USGS Water Resources Information Home page at: http://water.usgs.gov/.
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24 Groundwater Model Validation 24.1 24.2 24.3 24.4
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Practical Views of Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Proposed Model Validation Process . . . . . . . . . . . . . . . Acceptance Criteria for Stochastic Model Realizations and Application to PSA Model. . . . . . . . . . . . . . . . . . . . . . . . . .
24-1 24-2 24-3 24-6
Proposed Acceptance Criteria for PSA • Single Validation Target Illustration • Testing the Efficacy of P 1 for a Single Validation Target • Multiple Validation Targets Illustration • Testing the Efficacy of P 1 for Multiple Validation Targets • Testing the Efficacy of P 2 for Multiple Validation Targets
24.5 Uncertainty Reduction Using Validation Data and Application to the Amchitka Model . . . . . . . . . . . . . . . . . . . . 24-18 Model Background • Bayesian Framework for Uncertainty Reduction • Application to the Milrow Site in Amchitka
Ahmed E. Hassan Desert Research Institute, Las Vegas, Nevada, and Cairo University, Giza, Egypt
24.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24-22 24-23 24-24 24-24 24-27
24.1 Introduction The term validation has been the subject of literature debate for more than a decade. Some skeptics argue the term should not be used as it implies correctness and accuracy for a groundwater model that no one can claim. Similarly, others believe it is impossible to validate a groundwater numerical model because such a claim would assert a demonstration of truth that can never be attained for our approximate solutions to subsurface problems (Oreskes et al., 1994). Anderson and Bates (2001) edited a book covering the issue of model validation in hydrological sciences. Some of the quotes they presented from the skeptics and opponents to the use of the term “validation” include: Absolute validity of a model is never determined. (National Research Council 1990). “What is usually done in testing the predictive capability of a model is best characterized as calibration or history matching; it is only a limited demonstration of the reliability of the model. We believe the terms validation and verification have little or no place in groundwater science; these terms lead to a 24-1
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false impression of model capability. More meaningful descriptors of the process include model testing, model evaluation, model calibration, sensitivity testing, benchmarking, history matching, and parameter estimation.” (Konikow and Bredehoeft 1992). The above views consider validation in the strictest definition of the word. That is, they refer to validation as a demonstration of the accuracy of the model in representing the true system and they warn against misconception of the public about the meaning of the term. As discussed in Hassan (2004a), most models, if not all, are not being used to reveal the truth of a system (an objective they simply cannot achieve). Models are in many cases decision-making tools. When a model successfully passes a rigorous development, calibration, and testing process, it becomes a reasonable decision-making tool, often the best available for subsurface problems that demand answers now. The model validation process can be regarded as an additional filter for independent model evaluation to assess the suitability of a model for its given purpose (likely to be decision-making). Most of the literature debate focuses on validation terminology and not on the process. No one argues the process is unimportant, unneeded, or useless and no one disagrees on the concept of using an independent data set to test the model. The disagreement is on what we call it and what the implications are for the term we use. This lack of focus on the development of model validation processes or tools is reflected clearly in Vogel and Sankarasubramanian’s (2003) discussion about the validation of watershed models. “When one considers the wide range of watershed models and the heavy emphasis on their calibration (Duan et al., 2003), it is surprising how little attention has been given to the problem of model validation. In three recent reviews of watershed modeling (Singh 1995; Hornberger and Boyer 1995; Singh and Woolhiser 2002) and watershed model calibration (Duan et al., 2003), there was little attention given to developments in the area of model validation. Although there is rough agreement on the goal of model validation, no agreement exists on a uniform methodology for executing model validation.” There is an urgent need for a model validation process that can be used to evaluate model performance and build confidence in a model’s suitability for making decisions. This confidence building is a long-term iterative process and it is the author’s belief that this process is what should be termed model validation. Model validation is a process, not an end result. That is, the process of model validation cannot always assure acceptable model predictions or quality of the model. Rather, it provides safeguard against faulty models or inadequately developed and tested models. If model results end up being used as the basis for decision-making, then the validation process indicates the model is valid for making decisions (not necessarily an absolute representation of truth). Again, such a process should not be viewed as a mechanism for proving that the model is valid, but rather as a mechanism for enhancing the model, reducing its uncertainty, and improving its predictions through an iterative, long-term confidence-building process. The process should contain trigger mechanisms that will drive the model back to the characterization–conceptualization–calibration–prediction stage (i.e., back to the beginning), but with a better understanding of the modeled system. Following this introduction, a brief review of practical definitions of the term validation is presented in Section 24.2. A description of a proposed model validation process for stochastic groundwater models (Hassan, 2004b) is presented in Section 24.3. The details of this process will not be repeated here, but rather more explanation and discussion of some of the challenging aspects of the process will be addressed as they apply to two actual field sites: the Project Shoal Area (PSA) in Nevada and the Amchitka site in Alaska. In particular, we focus on two main aspects (1) the selection of the acceptance criteria for the stochastic model realizations for PSA presented in Section 24.4, and (2) the evaluation of model input parameters and the reduction of their uncertainty at Amchitka presented in Section 24.5. A wrap up and concluding remarks are presented in Section 24.6.
24.2 Practical Views of Validation Refsgaard (2001) defines model validation as the process of demonstrating a given site-specific model is capable of making accurate predictions for periods outside a calibration period. He also adds that a
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model is said to be validated if its accuracy and predictive capability in the validation period have been proven to lie within acceptable limits or errors. de Marsily et al. (1992) argued that using a model in a predictive mode and comparing it with new data does not (and does not have to) prove the model is correct for all circumstances, it only increases the confidence in the model’s value. They added “We do not want certainty; we will be satisfied with engineering confidence.” Neuman (1992) defines the validation of safety assessment models as the process of building scientific confidence in the methods used to perform such assessment. However, he recognizes that this confidence-building approach to validation is possibly open-ended, as many iterations between modelers and regulators may be needed. Eisenberg et al. (1994) support the idea of confidence building and indicate this term recognizes that full scientific validation of models of performance assessment may be impossible and the acceptance of mathematical models for regulatory purposes should be based on appropriate testing, which will lead to a reasonable assurance that the results are acceptable. Hassanizadeh (1990) differentiates between research (or analysis) model validation and safety assessment modeling (or predictive modeling) validation. The former is a tool to help understand processes, uncertainties, and the like, whereas the latter is a goal to help the decision-making process. Sargent (1990) regards validation as a process that consists of performing tests and evaluations during model development until sufficient confidence is obtained that a model can be considered valid for its intended application. There is a general consensus that the main concern is whether or not a model is adequate for its intended use and whether or not there is sufficient evidence that the model development followed logical and scientific approaches and did not fail to account for important features and processes. It should be noted that determining the adequacy of a model or building confidence in its prediction is not ideally a one-time exercise. It can be considered an iterative process that should be viewed as part of an integral loop with trigger mechanisms or decision points that force the model back to the data collection–conceptualization– calibration–prediction phase if the model validation process indicates the need to do so. Key to this process is the use of a diverse set of tests that should be designed to evaluate a diverse set of aspects related to the model. It is clear that often-quoted statements such as “groundwater models cannot be validated” and “groundwater models can only be invalidated” (Konikow and Bredehoeft 1992, 1993; Bredehoeft and Konikow 1992, 1993) refer to validation in only the strictest sense, responding to a concern regarding layman’s possible misconceptions. Unfortunately, such statements may lead to a relaxed attitude on the part of researchers, consultants, and even regulatory agencies when it comes to evaluating model predictions. With the perception that the groundwater model will never be validated, there may be a temptation to believe good model development, building, and calibration are sufficient and nothing more can be done. All groundwater modelers agree that their models cannot be validated in the strictest sense (at least with present-day technology) but similarly agree on the importance of post-prediction testing and evaluation. By expanding our definition of validation to encompass a long-term process of confidence building, modelers and model users can develop rigorous validation processes that will ultimately improve the models and the quality of decisions based on those models.
24.3 The Proposed Model Validation Process Hassan (2004b) proposed an approach for the validation process of stochastic numerical models. The details of the process will not be repeated here, but rather more explanation and discussion of some of the challenging aspects will be addressed as they apply to two actual field sites. However, for completeness, the overall validation approach is briefly discussed here. The validation process is designed to account for the stochastic nature of some groundwater models. The focus of the process is centered around the following three main themes (1) testing if predictions of numerical groundwater models and the underlying conceptual models are robust and consistent with regulatory purposes, (2) improving model predictions and reducing uncertainty using data collected
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through field activities designed for model validation, and (3) linking validation efforts to long-term monitoring and management of the site. Figure 24.1, adapted from Hassan (2004b), displays the step-by-step approach for performing the validation and post-audit processes for a typical stochastic groundwater model. The proposed steps of the model validation process are described below:
Step 1: Identify the data needed for validation, the number and location of the wells, and the type of laboratory or field experiments needed. Well locations can be determined based on the existing model and should favor locations likely to encounter fast migration pathways. Step 2: Install the wells and collect the largest amount of data possible from the wells. The data should include geophysical logging, head measurements, conductivity measurements, contaminant concentrations, and any other information that could be used to test the model structure, input, or output. Step 3: Perform different validation tests to evaluate various components of the model. The stochastic validation approach proposed by Luis and McLaughlin (1992) is an example of an approach that can be used to test the flow model output (heads) under saturated conditions. Other goodness-offit tests can be used for the heads to complement this stochastic approach. The philosophy here is to test each individual realization with as many diverse tests (in terms of the statistical nature of the test and the tested aspect of the model) as possible and have a quantitative measure of the adequacy of each realization in capturing the main features of the modeled system. It is important to note that goodness-of-fit results and other statistical results for the current realization will be used after analyzing all realizations to obtain some of the acceptance criteria measures, P1 through P5 , which are discussed in detail in Section 24.4. Step 4: Link the results of the calibration accuracy evaluations performed during the model-building stage and the validation tests (step 3) for all realizations and sort the realizations in terms of their adequacy and closeness to the field data. A subjective element may be invoked in this sorting based on expert judgment and hydrogeologic understanding. The objective here is to filter out the realizations that show a major deviation in many of the tested aspects and focus on those that “passed” the majority of the tests. By doing so, the range of output uncertainty is reduced and the subsequent effort can be focused on the most representative realizations and scenarios. To continue reducing the uncertainty level, a refinement of the conductivity or other input distribution can be made based on information collected from the validation wells as presented in Section 24.5 for the Amchitka site. Step 5: Step 4 results will determine the subsequent step and guide the decision of whether there is a sufficient number of realizations with high scores or not. 5a. If the number of realizations with high scores is very small compared to the total number of model realizations (the P1 measure discussed in Section 24.4), it could be an indication that the model has a major deficiency or conceptual problem or it could be that the input is not correct. In the latter case, the model may be conceptually good, but the input parameter distributions are skewed one way or another. Generating more realizations and keeping those fitting the validation criteria can shift the distribution to the proper position. This can be done using the existing model without conditioning or using any of the new validation data. If the model has a major deficiency or conceptual problem, generating additional realizations will not correct it and continued failure per the validation criteria will be obvious. The importance of the distinction between conceptualization problems and inappropriate input distributions has been discussed by Bredehoeft (2003). He states one should carefully ask the question of whether the mismatch between the model and the field observations is a result of poor parameter adjustments or does it suggest we rethink the conceptual model. The use of different metrics such as P1 and P2 discussed in Section 24.4 provides a tool for making this distinction.
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Start Analyze refined model for new round of data collection
Select well locations based on model results (First stage monitoring design)
Step 1
Field work and data collection activities
Step 2
Start analysis of the stochastic model Realization = 1
Compute and save goodness-of-fit and results of hypothesis testing on linear regression line based on the numeric validation targets (to get P1)
Step 3 Model refinement using new and original data (e.g., using MCMC)
Stochastic validation approach and other hypothesis testing and linear regression analysis (P3 and P4 measures)
Realization = realization +1
Evaluate results of tests of model structure and failure possibility (P5)
Link and evaluate calibration and validation tests for current realization
Step 4
No
Refine the model (e.g., update model input and refine prediction) using the original data
Did we analyze all realizations?
Yes Sort all realizations using a composite score measure and subjective judgment
Continue interactive process of validation, refinement and monitoring
Step 5
Did enough realizations attain a satisfactory score?
Step 5b
Step 5a
No
Yes
Produce regulatory quantity of interest using the satisfactory realizations
Step 6a No
Did validation results meet regulatory objectives?
Step 6b
Yes
Design the long-term monitoring plan taking into account the existing validation wells
Steps using prevalidation data only
Step 6
Step 7
Stop
FIGURE 24.1 Details of the proposed model validation processes for stochastic groundwater models. (Reprinted from Ground Water with permission of the National Ground Water Association Press. Copyright 2004.)
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5b. If the number of realizations with high scores is found sufficient, this indicates the model does not have any major deficiencies or conceptual problems. Based on the realizations retained in the analysis and deemed acceptable, the regulatory quantity of interest can be calculated and compared to the original model-predicted quantity. This comparison will be presented for reference by decision makers in step 6. Step 6: Once the model performance has been evaluated per the acceptance criteria, the model sponsors and regulators have to answer the last question in Figure 24.1. This question will determine whether the validation results meet the regulatory objectives or not. This is the trigger point that could lead to significant revision of the original model. 6a. If the answer to the question is no, then the left-hand side path in Figure 24.1 begins, and a new iteration of model development will begin using the original data plus data collected for validation. Steps 1 to 6 will be eventually repeated. 6b. If the answer to the question is yes, validation is deemed sufficient and the model is considered adequate or robust and the process proceeds to step 7, which starts the development of the long-term monitoring program for the site. It can be seen and expected that the process of validating a site-specific groundwater model is not an easy one. Throughout the structured process described above, there may be a desire to confirm that the work is on the right track. The way to this confirmation is the cumulative knowledge gained from the different stages of the validation process. That is, a set of independent tests and evaluations will provide knowledge about the model performance, and the test results will provide some incremental, but additive, pieces of information that will be of importance. While there are no guarantees of success (attaining a conclusive outcome about model performance), the combined presence of these different results and evaluations sharply improves the odds that one can make a good decision about the model performance. Two aspects of the validation process are explained in detail in the following subsections. These are (1) the criteria for determining the sufficiency of the number of acceptable realizations, which are demonstrated for the Project Shoal Model (PSA) model, and (2) the reduction of uncertainty of model input parameters, which is demonstrated for the Amchitka model. Other aspects of this validation approach need further analysis and development. The work on developing a model validation process is still at its infancy and the hope is that more attention will be devoted to the development of rigorous approaches for conducting groundwater model validation processes.
24.4 Acceptance Criteria for Stochastic Model Realizations and Application to PSA Model The Project Shoal Area (PSA), about 50 km southeast of Fallon, Nevada, is the location of the Shoal underground nuclear test. The nuclear device was emplaced 367 m below ground surface, about 65 m below the water table, in fractured granite. Details of the geology and hydrogeology of the site are provided in Pohll et al. (1999). Ongoing environmental remediation efforts at the PSA have successfully progressed through numerous technical challenges related to the substantial uncertainties present when characterizing a heterogeneous subsurface environment. The original Corrective Action Investigation Plan (CAIP) for the PSA described a plan to drill and test four characterization wells, followed by flow and transport modeling. The data analysis and the first modeling effort are described in Pohll et al. (1999). After evaluating the modeling effort, the model sponsor determined the degree of uncertainty in transport predictions for PSA remained unacceptably large. Thus, a second CAIP was developed prescribing a rigorous analysis of uncertainty in the PSA model and quantification of methods for reducing uncertainty by collecting additional data. This analysis formed the basis for a second major characterization effort, where four additional characterization wells were drilled during summer and fall of 1999. A key component of the second field program was a tracer test conducted between two of the new four wells, which is described in Reimus et al. (2003).
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Results of the tracer test and new characterization efforts produced a new groundwater flow and radionuclide transport model that was approved by the model sponsor and regulators (Pohlmann et al., 2004). The next step in the environmental management of the PSA is to start the validation process and develop the long-term monitoring network. This section focuses on the selection of acceptance criteria and how they can be applied for PSA model. An attempt is made to develop and test some acceptance criteria to be used through the model validation process. It is important to note that this analysis is still in the development stage and the application here is made for hypothetical cases (i.e., hypothetical validation data). Field data will be collected for the validation process of the PSA model at the time when this book will be in press.
24.4.1 Proposed Acceptance Criteria for PSA According to the validation approach shown in Figure 24.1, the first set of analyses using the field data collected for validation purposes will yield results that will be evaluated to determine the path forward. The first “if ” statement in the validation approach pertains to whether a sufficient number of realizations attained satisfactory scores on how they represent the field data used for calibration (old) and for validation (new). The determination of whether a sufficient number exists will be based on five criteria with the decision made in a hierarchical manner as will be discussed later. The five criteria are summarized below: 1. Individual realization scores (Sj , j = 1, . . ., number of realizations), obtained based on how well each realization fits the validation data, will be evaluated. The first criterion then becomes the percentage of these scores, P1 , that exceeds a certain reference value. 2. The number of validation targets where field data fits within the inner 95% of the probability density function (pdf) of these targets as used in the model is the second criterion, P2 . 3. The results of hypothesis testing to be conducted using the stochastic perturbation approach of Luis and McLaughlin (1992) as described in detail in Hassan (2004b), P3 , represent the third criterion. 4. The results of linear regression analysis and other hypothesis testing (e.g., testing error variance based on calibration data and based on validation data) that could be feasible (depending on the size of data set obtained in the field), P4 , are considered the fourth criterion. 5. The results of the correlation analysis where the log-conductivity variance is plotted against the head variance for the targeted locations and the resulting plot for the model is compared against the field validation data, P5 . The hierarchical approach to make the above determination is described by a decision tree. This decision tree for the acceptance of the realizations and for passing the first decision point on the validation approach is shown in Figure 24.2. First Sj is evaluated to determine whether the percentage of realizations with scores above the reference value, P1 , is more than 40%, between 30% and 40%, or less than 30%. If the number is more than 40%, it is deemed sufficient. If it is between 30% and 40% or less than 30%, the second criterion, P2 , is used as shown in Figure 24.2. The second criterion represents the number of validation targets where the field data lie within the inner 95% of the pdf for that target as used in (input) or produced by (output) the model. Then if P1 is between 30% and 40% and P2 is between 40% and 50% or if P1 is less than 30% but P2 is greater than 50%, the number of realizations is deemed sufficient. If P1 is less than 30% and P2 is less than 40%, then the remaining three measures, P3 , P4 , and P5 , are used to determine whether the model needs revision or whether more realizations can be generated to replace some of the current realizations. In this latter case, the model may be conceptually good but the input parameter distribution is skewed or inappropriate and by generating more realizations and keeping the ones fitting the above criteria, the distribution attains the proper position. This can be done using the existing model without conditioning or using any of the new validation data (i.e., no additional calibration). The rationale for selecting the above thresholds (30–40% for P1 and 40–50% for P2 ) is described through an example and when these metrics are evaluated with statistical hypothesis testing later in this section.
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Start Here
Percentage of realizations where Sj is larger than reference value (P1)
> 40%
Between 30% and 40%
The number with satisfactory score is sufficient
> 50% The number with satisfactory scores is sufficient
< 30%
Percentage of validation targets within the inner 95% of the pdf (P2)
Percentage of validation targets within the inner 95% of the pdf (P2)
Between 40% and 50%
< 40%
The number with satisfactory scores is sufficient
The number with satisfactory scores is not sufficient and the RHS loop on the validation plan takes effect
> 50% The number with satisfactory scores is sufficient
Between 40% and 50%
< 40%
The number with satisfactory scores is not sufficient and the RHS loop on the validation plan takes effect
P3,P4, and P5 evaluation
Model needs revision
FIGURE 24.2 A decision tree chart showing how the first decision (step 6) in the validation process will be made and the criteria for determining the sufficiency of the number of acceptable realizations.
150
Frequency
h50 ho
100
h
2.5
h
97.5
50
0 1275
1280 1285 1290 Validation target
1295
FIGURE 24.3 The head distribution as obtained from the PSA model with the 2.5th, 50th, and 97.5th percentiles shown with the solid symbols and the hypothesized field data shown by the open circle.
24.4.2 Single Validation Target Illustration The first criterion is to compute the number of realizations with scores Sj above a reference value. To demonstrate how this reference value is computed, assume we only have one validation target (e.g., the head measurement in one interval in a well). Figure 24.3 shows the head distribution as produced by the stochastic PSA model where the solid symbols represent the 2.5th, 50th, and 97.5th percentiles and the open circle indicates a hypothesized field measurement, ho . The reference value and the score for any
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individual realization for this simple case can be computed as
Reference value(RV ) =
(ho − h2.5 )2 exp − (h97.5 − h2.5 )2 (h − h97.5 )2 exp − o (h97.5 − h2.5 )2
(ho − hj )2 Realization score (Sj ) = exp − (h97.5 − h2.5 )2
P1 =
for ho < h50 (24.1) for ho > h50
for j = 1, . . . , NMC
# of Realizations where Sj > RV NMC
(24.2)
(24.3)
where j is the realization index and it varies from 1 to NMC (number of Monte Carlo realizations) with NMC being 1000 realizations for the PSA model. This leads to all realizations with absolute errors smaller than min {(|ho − h2.5 |), (|ho − h97.5 |)}, attaining a score higher than the reference value. Figure 24.4 shows the resulting scores and how they compare to the reference value, RV as obtained from the above equations. It can be seen from Equations 24.1–24.3 that the maximum value RV or Sj can attain is 1.0. Thus if the observed value, ho , is equivalent to the 2.5th or the 97.5th value, P1 becomes zero because RV becomes 1.0 and all Sj values will be less than 1.0. Also, if the observed value is found to be less than h2.5 or greater than h97.5 , P1 will be automatically set to zero. In such cases, one may conclude the model output is skewed toward higher or lower values than indicated by field data. However, this does not necessarily indicate conceptual problems and it may be an indication of incorrect input parameter distributions. The other tests and evaluations can help identify the reasons for this output skewness. When the measured value coincides with the 50th percentile of the target output, h50 , then P1 will approximately be 95% indicating that 95% of the realizations attained scores higher than RV .
24.4.3 Testing the Efficacy of P 1 for a Single Validation Target To investigate the P1 metric for the case of a single validation target, a distribution form for the model output is assumed. For simplicity, it is assumed that the model predictions follow a standard normal distribution with zero mean and unit variance, so h50 = 0.0, h2.5 = −1.96, and h97.5 = 1.96. The performance of this metric is tested for a range of measurement values (hypothesized values for the single field data point) between −10.0 and +10.0. For each one of these hypothesized values, the RV can be obtained according to Equation 24.1 and the results are shown in Figure 24.5. The RV metric decreases rapidly as the observation value approaches the median, h50 . When the measured value lies outside the middle 95% of the output distribution (i.e., outside the range [−1.96, 1.96]), RV is not computed as P1 becomes zero. Also, as shown in the figure, when ho equals −1.96 (h2.5 ) or 1.96 (h97.5 ), RV equals 1.0. Due to the exponential form in Equation 24.2, all Sj values will be less than 1.0 resulting in a zero value for P1 when ho is at the 2.5th or 97.5th percentile. The next step is to calculate the Sj score for each Monte Carlo realization, with Sj being a similar measure to the RV , but using individual realization predictions for the head. The Sj score is compared to the RV score and the relative number of Sj values that exceed the RV are tallied to obtain P1 . The Sj values and the corresponding P1 value were tallied for a range of single observation values in the range [−10, 10] as shown in Figure 24.6. Figure 24.6 also compares the P1 metric to the t -distribution with one degree of freedom. The t -distribution is commonly used to test the statistical differences among means when the variance of the distribution is not known. The distribution plotted with the solid line in the figure simply shows the
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The Handbook of Groundwater Engineering Number of Realizations where Sj ≥ RV = 979 & Number of Realizations where Sj < RV = 21
1
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0
0
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FIGURE 24.4 Realizations scores, Sj , relative to the reference value, RV for the single validation target case. The P1 value here is 97.9% (= 979/1000).
value of the significance level, α, at which each observation on the range [−10, 10] would be rejected in a hypothesis testing evaluating the statistical difference between the mean of the model output (assumed standard normal distribution) and each observed value (assuming each observed value represents a distribution with only one [n = 1] sample). The one-degree of freedom used in this plot is not exactly correct as the degrees of freedom are actually n − 1 = 0. To avoid this limitation, we employ the Z -test that is commonly used for the same purpose, but it assumes the variances of the distributions are known. It is assumed that each observation is a mean of a normal distribution and each output realization represents a mean of a normal distribution. For each observation value, we then test the following hypothesis: H 0 : h j = ho
for j = 1, . . . , NMC
H1 : hj = ho
for j = 1, . . . , NMC
(24.4)
Then the proportion of Monte Carlo realizations where the null hypothesis, H0 , above is not rejected is plotted against each observation value as shown with the dashed line in Figure 24.6. The plots in Figure 24.6 provide an indication of how the P1 test compares against standard statistical tests. According to the figure, one would accept all model realizations for any of the observed values [−10, 10] based on the student t -test. In other words, if the t -test is used, one would not reject any of the
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RV
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0.75 –1.5
–1
–0.5
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1
Measurement ho
FIGURE 24.5 The reference value, RV for the single validation target case as a function of the measured field value.
1 P1 Metric 0.9
Proportion of accepted realizations
0.8 0.7
Z test t Distribution
α value necessary to reject the corresponding observation based on student t test
0.6
Hypothesis testing results for each ho : H0 : hj = ho for j = 1, ..., NMC H1 : hj ≠ ho for j = 1, ..., NMC Proportion of NMC where Ho is not rejected is plotted
0.5 0.4 0.3 0.2 0.1 0 –10
–8
–6
–4
–2 0 2 4 Hypothetical field observation
6
8
10
FIGURE 24.6 The P1 metric, student t distribution, and the results of hypothesis testing using the Z -test.
model realizations until approximately the absolute value of the observation is well above 10 (at the 95% confidence level). On the other hand, the P1 measure and the Z -test both indicate decreasing proportions of acceptable realizations as one deviates from the median of the model output distribution which is zero in this test case. At the 5% significance level and if the observed value coincides with the median of the model output, only 95% of the realizations are deemed acceptable using the P1 measure and the Z -test.
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When the observed value deviates from the median, the proportion of acceptable realizations drops faster using the P1 measure compared to the Z -test. For example, 40% or more of the model realizations would be accepted using the Z -test for any observation value in the range [−2.22, 2.22], whereas the P1 measure gives this level of acceptance for a narrower range of observation values [−1.07, 1.07]. At first glance it appears that the two methods (the P1 measure versus the Z -test or the t -test) are in large disagreement. But Type I error (rejecting a model realization when in fact it is a good one) versus Type II error (accepting a poor model realization) must be considered. The P1 metric is essentially reducing Type II error at the expense of Type I error. As discussed by Sargent (1990), the probability of Type I error is called model builder’s risk, whereas the probability of Type II error is called model user’s risk, and in model validation, model user’s risk is extremely important and must be kept small. As a result, it is believed that the restrictiveness of the P1 measure helps minimize Type II error and thus reduce the model user’s risk (both model sponsor and regulators) at the expense of increasing model builder’s risk (supposedly the research team constructing the model).
24.4.4 Multiple Validation Targets Illustration For the general case of having N validation targets, the above equations should be modified to account for these different validation targets. In this case, the RV and the individual scores, Sj , will depend on the sum of squared deviations between each observation, ho , and the corresponding h2.5 or h97.5 . The equations thus become RV = exp −
N
N 2 min[(hoi − h2.5i ) , (hoi − h97.5i ) ] [h97.5i − h2.5i ] 2
2
i=1
Sj = exp −
N
i=1
[hoi − hj ]
(24.5)
i=1
2
N
[h97.5i − h2.5i ]
2
for j = 1, . . . , NMC
(24.6)
i=1
For demonstration purposes and as an example, assume the hypothetical case that data are collected on 18 validation targets. These, for example, could be conductivity data in three wells, three measurements each (i.e., nine intervals) and head data for the same intervals. For each one of these targets, the current stochastic PSA model provides a distribution of values. It is then assumed that the values of the field data are known (we pick at random one realization to provide an example observation for all targets). Figure 24.7 and Figure 24.8 show the results of this example (Example 24.1) where P1 is found to be about 76.7%. In this case, we do not check for P2 and accept the sufficiency of the number of realizations having acceptable scores. Note, however, that if we were to check P2 , it would be about 94% (= 17/18) because 17 data points lie between the 2.5th and the 97.5th percentiles for the corresponding targets. Using another set of random values to hypothesize the field data, a different result is obtained as shown in Figure 24.9 and Figure 24.10, for Example 24.2. In this case, both P1 and P2 are less than 40% (as the number of validation targets where the open circle is between the 2.5th and the 97.5th percentiles is only 2–11%). In this case, the additional hypothesis tests and linear regression evaluations will be performed to assert whether the model needs to be revised or if the parameter distributions need to be modified. In Example 24.1, the field data values are hypothesized to be equivalent to one of the model realizations. That is, the values of the 18 validation targets are obtained from one single realization and assumed to represent field data collected for the validation analysis. In spite of assuming field values exactly matching one of the model realizations, the P1 metric was found to be about 76.7%. This value is obviously dependent on which realization is selected. Therefore, we repeated the above example 1000 times with each of the model realizations assumed to represent the field data in one of those times (similar to a jackknife method). The P1 metric is obtained for these 1000 experiments and its mean value was found to be about 43%. Given the actual field data to be collected for the validation analysis are very unlikely
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2.5th percentile
50th percentile
100 50 −6 −4 −2 Validation target #1
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150 Frequency
150 Frequency
Frequency
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97.5th percentile
100 50 0 1275 1280 1285 1290 1295 Validation target # 18
FIGURE 24.7 Example 24.1 showing the distributions for validation targets 1 through 18 with the 2.5th, 50th, and 97.5th percentiles shown with the solid symbols and the hypothesized field data shown by the open circles.
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1
0.9
0.8
0.7
Scores ( Sj )
0.6
0.5
0.4 Individual Scores (Sj ) Reference Value (RV )
0.3
0.2
0.1
0
0
100
200
300
400 500 600 Realization Number (j )
700
800
900
1000
FIGURE 24.8 Example 24.1 showing individual realization scores, Sj , relative to the reference value, RV ; the P1 value here is about 76.7% (= 767/1000).
to exactly match any of the PSA model realizations, the 30–40% threshold forP1 is considered realistic. In other words, if one, on average, obtains 43% for P1 when one of the model realizations is assumed to match real field conditions, one can safely assume the model conceptually valid if P1 is between 30% and 40% when using the actual validation data.
24.4.5 Testing the Efficacy of P 1 for Multiple Validation Targets A numerical experiment is performed to evaluate the P1 metric for the case of multiple validation targets. The experiment is run as follows: 1. A model is assumed to produce multiple outputs, each following a standard normal distribution with zero mean and unit variance. 2. To test the sensitivity of the P1 metric, 30 observations are randomly selected, with the mean value of the observation set being constant. A range of observation set means is used to determine at what point the model will be rejected. The mean of each observation set is tested over the range −4.0 to 4.0 (i.e., −4.0, −3.9, … , 4.0). 3. For each mean value, 30 observations are randomly drawn from a normal distribution with the mean equal to the current mean value (i.e., −4.0, −3.9, … , 4.0) and a standard deviation = 1.0. 4. The RV value for the 30 validation targets is computed using Equation 24.5. 5. For each observation mean, the scores Sj for 10,000 realizations of a model (model is assumed to be standard normal) are computed and the metric P1 is obtained according to Equation 24.3. 6. Steps 3–5 are then repeated for each observation mean in the range [−4.0, 4.0].
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24-15 50th pecentile
100 50 0 −8
50 0 −8
50 0 −8
1270 1280 1290 1300 Validation target # 16
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Field Observation 150
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1280 1290 1300 Validation target # 17
100 50 0
1280 1290 1300 Validation target # 18
FIGURE 24.9 Example 24.2 showing the distributions for validation targets 1 through 18 with the 2.5th, 50th, and 97.5th percentiles shown with the solid symbols and the hypothesized field data shown by the open circles.
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The Handbook of Groundwater Engineering Number of realizations where Sj ≥ RV = 51 & Number of realizations where Sj < RV = 949
0.35
0.3
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0.25
0.2
0.15
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Individual Scores (Sj)
0.05
Reference Value (RV )
0
0
100
200
300
400 500 600 Realization Number ( j )
700
800
900
1000
FIGURE 24.10 Example 24.2 showing individual realization scores, Sj , relative to the reference value, RV . The P1 value here is about 5.1% (= 51/1000).
The purpose of this experiment is to determine the point at which a model will be considered invalid. Each observation set represents data that are either close to the model predictions (i.e., mean values close to zero), or poor fitting data with mean values far away from zero. This experiment allows us to compare the rejection region for using a simple hypothesis test (i.e., Z -test) versus the P1 measure. Due to the random nature of the distributions generated in the above procedure, we repeated the above experiment 100 times and the average results are shown in Figure 24.11. The dots in the figure represent the results for the P1 metric, the dashed line shows the results of the Z -test that is similar to the test conducted for the single validation target case, the thin solid line represents the mean value (of 100 values) of the P1 metric at each observation mean, and the thick solid line represents a normal distribution that best fits the P1 results. For the Z -test, we assume each output realization represent a mean of a normal distribution. For each observation mean value, we then test the following hypothesis: H0 : h j = ho
for j = 1, . . . , NMC
H 1 : h j = ho
for j = 1, . . . , NMC
(24.7)
Then the proportion of Monte Carlo realizations (assumed 10,000 in this experiment) where the null hypothesis, H0 , above is not rejected is plotted against each observation mean as shown with the thin solid
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1 P1 metric Z test Student t distribution Mean of P1 at each obs. mean Best normal fit to P1 results
0.9
Proportion of accepted realizations
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –4
–3
–2
–1
0
1
2
3
4
Hypothetical observation mean FIGURE 24.11 The P1 metric (dots), its mean (thin solid line), its best fit normal distribution (thick solid line), student t distribution (line with circles), and the results of hypothesis testing using the Z -test (dashed line) for the multiple validation targets case.
line in Figure 24.11. According to the figure, the t -test would suggest accepting all model realizations if the mean value of the observations is inside the range [–2.2, 2.2] at 95%. The P1 criterion has a narrower acceptance region ([–1.6, 1.6] according to the thick or thin solid line) again suggesting the P1 metric is overemphasizing (i.e., trying to reduce) Type II error. Therefore, the P1 criterion is more stringent than typical hypothesis tests and provides a useful method to test multiple validation targets, which is a more difficult task with standard hypothesis test procedures. It is important to note that according to P1 and the Z -test, decreasing proportions of acceptable realizations are obtained as one deviates from the median of the model output distribution (zero in this test case). At a 5% significance level and if the observed mean value coincides with the median of the model output, 95% of the realizations are deemed acceptable using the Z -test, whereas only 60% of the model realizations are deemed acceptable using the P1 measure. Therefore, a rejection region of less than 30% for the P1 criteria is very stringent and should not be confused with the 95% confidence interval used for presenting the output uncertainty.
24.4.6 Testing the Efficacy of P 2 for Multiple Validation Targets A numerical experiment is constructed to test the efficacy of the P2 metric as follows: 1. A model is assumed to produce output according to a standard normal distribution. 2. Observations are assumed to follow a normal distribution with mean µ and unit variance. The numerical experiment chooses mean values µ from an observation distribution range −4.0 to 4.0 (i.e., −4.0, −3.9, … ,4.0).
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Proportion of accepted realizations
0.8 0.7 0.6 0.5 0.4 0.3 0.2 P2 Metric
0.1 0 −4
Mean of P2 at each observation mean
−3
1.96 −2
1.96 −1 0 1 2 Hypothetical observation mean
3
4
FIGURE 24.12 The P2 metric (dots) and its mean (solid line) for the multiple validation targets case. The horizontal and vertical lines show that at the 50% threshold, the acceptance region is [−1.96, 1.96] which is the same acceptance region for a standard t test at the 95% confidence level.
3. For each mean value, a random sample of 30 observations is drawn from a normal distribution with the mean equal to the current mean value (i.e., −4.0, −3.9, … , 4.0) and a standard deviation equal to 1.0. 4. Each of the 30 observations is then compared to the model’s distribution N (0, 1) to determine what percentage falls outside of the 95% confidence interval (i.e., −1.96 to 1.96). 5. The process is repeated for all observation means [−4.0, 4.0]. Due to the random nature of the distributions generated in the above procedure, we repeated the above experiment about 100 times and the results are shown in Figure 24.12. The figure shows that if 50% is chosen as the rejection threshold for the P2 metric, then the model would be accepted for µ = [−1.96, 1.96]. This is a very interesting result as one might initially think 95% should be the acceptance threshold, but 50% yields the same acceptance region as a standard t - test at a 95% confidence level. This warrants further analysis, and as stated earlier, the different aspects of the validation process need more attention for the ultimate goal of arriving at a rigorous set of steps for conducting a model validation process.
24.5 Uncertainty Reduction Using Validation Data and Application to the Amchitka Model The use of validation data to evaluate input parameter distributions and reduce their uncertainty level is demonstrated for the Amchitka site as a case study. Amchitka is the southernmost island of the Rat Island Group of the Aleutian Island chain extending southwestward from mainland Alaska. The focus here is on one of three underground nuclear tests conducted on the island, a test known as Milrow.
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24-19 Total mass flux Q (t ) = Σq
Recharge
q (xi, t )
q (xi+6, t ) Point mass flux
40 Specified pressure (P = γh) Island center (GW Divide) Contaminant release from Transition Zone test cavity
No-flow Boundary
P = γh
Advection, dispersion, retardation, matrix diffusion and decay Kzz
Kxx C = Cs
∂C/∂x = 0
No-flow boundary
–4000
∂C/∂z = 0
0
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FIGURE 24.13 Milrow model domain showing boundary conditions, simulated processes, test cavity transition zone location and resulting velocity vectors as obtained from one realization.
24.5.1 Model Background The groundwater flow and radionuclide transport at the Milrow test was modeled using two-dimensional numerical simulations as described in Hassan et al. (2002). The Milrow model involved solving a densitydriven flow problem (seawater intrusion problem) to obtain the salinity distribution and the groundwater velocities followed by solving the transport problem to predict radionuclide mass fluxes leaving the groundwater system and discharging into the sea. A multi-parameter uncertainty analysis was adapted and used to address the effects of the uncertainties associated with the definition of the modeled processes and the values of the parameters governing these processes. Details of the modeling efforts at Amchitka can be found in Hassan et al. (2001, 2002) and Pohlmann et al. (2002). With uncertain parameters, the output of the seawater intrusion problem (i.e., the location of the transition zone between freshwater and saltwater in the groundwater system) varies between model realizations with significant impacts on the solution of the transport equation. This location is mainly determined by the recharge-conductivity ratio. This ratio varies dramatically in the model due to the large parametric uncertainty built into the conductivity and recharge distributions. Figure 24.13 shows the model domain, boundary conditions of the density-driven flow problem, the radionuclide source, transport processes considered and an example transition zone location and velocity vectors as produced by one realization. Although the analysis conducted in Hassan et al. (2002) conservatively accounted for parametric uncertainty, the need remained for the validation of the numerical groundwater model with an independent data set. The Consortium for Risk Evaluation with Stakeholder Participation II (CRESP II), which represents an Organization of the Institute for Responsible Management, initiated a field expedition in the summer of 2004 for the purpose of collecting data as part of the Amchitka Independent Assessment Science Plan.1 One of the objectives of this data collection campaign was to provide data to reduce uncertainty about the risk of radionuclide release through the groundwater system to the marine environment. Of great importance to the groundwater model are the magnetotelluric (MT) measurements for determining the subsurface salinity and porosity structure of the Island, which were recently released in a report 1 http://www.cresp.org/
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by Unsworth et al. (2005). MT data were collected on profiles that passed through the contaminant source at Milrow. The data presented in Unsworth et al. (2005) showed the presence of a pattern of increasing, decreasing, and increasing resistivity with increasing depth at the site. The depth at which there is an inflection point of the resistivity profile where resistivity begins to decrease is interpreted by Unsworth et al. (2005) as corresponding to the top of the transition zone (TZ) as the salinity increases. The deeper inflection point (increase in resistivity after its decrease with depth) is interpreted as corresponding to the base of the transition zone, as salinity remains constant and the decreasing porosity causes a rise in resistivity (Unsworth et al., 2005). This independent set of data provides an opportunity for applying the validation process to the groundwater flow model at the Milrow site and reducing the uncertainty in the model parameters and subsequently the model output. To accomplish this, data pertaining to the location of the freshwater lens (from the interpretation of the MT data) could be compared to the groundwater model input distributions as part of the validation process, and then the distributions tightened around the new data for uncertainty reduction.
24.5.2 Bayesian Framework for Uncertainty Reduction In hydrologic modeling, the uncertainty of parameter estimation needs to be accounted for and the impact on the model output uncertainty needs to be quantified. Bayesian inference provides a framework within which these issues can be addressed with the end product of models being a probability distribution known as the posterior distribution of the model parameters (input) and predictions (output) quantifying uncertainty after data have been collected and incorporated. Although a number of recent studies used this framework for rainfall-runoff modeling and parameter estimation (e.g., Kuczera, 1983; Freer et al., 1996; Kuczera and Parent, 1998; Kuczera and Mroczkowski, 1998; Bates and Campbell, 2001; Marshall et al., 2004), its application to other areas has been limited due to computational difficulties. The advent of Markov Chain Monte Carlo (MCMC) methods has helped address some of these computational difficulties (Marshall et al., 2004). For certain simple analyses, the posterior distributions (on which inferences are usually made) can be derived analytically, which means they can be written down in standard statistical notation. When this is not possible, a Bayesian solution can still be obtained through the use of simulation methods, such as the MCMC methods. Some details about the Bayesian framework and the MCMC method are presented next in relation to the Milrow model. For the stochastic groundwater flow model at Milrow, it is assumed that the newly collected data are expressed by the data vector D. One of the elements in this data vector would be the groundwater salinity profile beneath the island, C, which also represents the steady-state output of the model. One can express the model as C(x) = M (G, x; ) + ε(x)
(24.8)
where C(x) is the observed data at location x, M (G; ) is the model output for location x, G is the set of model input describing domain geometry, boundary conditions, and discretizations, is the vector of unknown model parameters to be estimated from the data (e.g., hydraulic conductivity, recharge, porosity), and ε(x) is an error term that is assumed to be a normally distributed random variable having zero mean and variance σε2 . At this point it is also assumed that the error terms are all mutually independent. The set of model input G includes those aspects that do not change from one realization to another. The set of model parameters includes all the uncertain parameters needed to run the model and that change from one model realization to another. The vector is treated as a random variable distributed according to a probability density function. This density function expresses our uncertainty about . Before considering the newly collected data, the knowledge about the model parameter set can be summarized in a distribution P() called the prior distribution.
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The posterior distribution of the parameter set, P(|C) can be obtained through the application of Bayes’ theorem P(|C) =
P() P(C|) P(C)
(24.9)
where P(C|) is the likelihood function that summarizes the model relation to the collected data given the parameters used in the model and P(C) is a proportionality constant required so that P(|C) is a proper density function. It is important to note that the posterior distribution assumes a shape similar to the prior when available data are limited. But when there are large data sets, the posterior distribution will be influenced more by the data than by the assumed prior distribution. Also, the information in the new sample data will dominate the posterior if the prior distribution is selected to represent vague prior knowledge. P(|C) thus contains all of the available information about coming from both prior knowledge and collected data. Bayesian inference, therefore, reduces to summarizing the posterior density P(|C). MCMC sampling explores the posterior distribution by generating a random process (a Markov process) that eventually converges to the stationary, posterior distribution of the parameters. While many different MCMC sampling algorithms may exist, the Metropolis–Hastings algorithm is the most commonly used. Details of this algorithms are beyond the scope of this chapter, but can be found in Bates and Campbell (2001), Campbell et al. (1999), Marshall et al. (2004), Kuczera and Parent (1998), to name a few sources.
24.5.3 Application to the Milrow Site in Amchitka The validation data at Milrow are obtained from the MT data and the interpretation of the measured MT signals. Specifically, this provided identification of the top and bottom bounds of the transition zone from freshwater to seawater beneath the island. This set of data is used with MCMC to develop the posterior distributions for conductivity, recharge, and conductivity–recharge ratio. The development of the posterior distribution serves to evaluate the original (prior) distribution selection and to reduce the uncertainty in the parameter distributions, both of which are objectives of the validation process. In the original Milrow model (Hassan et al., 2002), lognormal distributions were assumed for both recharge and conductivity and they were assumed to be uncorrelated. These prior distributions were based on calibrating the model to a set of salinity data that was available from one borehole at the site. This data set clearly defines the increase in salinity with depth to near-seawater concentrations. Therefore, the location of the transition zone separating the shallow freshwater from the deep saltwater provided by this data set guided the selection of the distributions used in the original model. These distributions are used here as the prior distributions for the MCMC analysis and with the help of the MT data, posterior distributions are developed. Figure 24.14 shows the potential of the MCMC approach to help in the validation process and uncertainty reduction by conditioning on field data. The figure compares the prior distributions for the recharge, conductivity, and the recharge–conductivity ratio to the posterior distributions for these parameters obtained utilizing the prior knowledge and the new MT-related data. It is clear that the posterior distributions are very different than the prior ones, especially for the recharge–conductivity ratio. The interpretation of the MT data indicated a deeper transition zone than what was used in the model. This translated into the posterior distribution of conductivity being skewed to lower values relative to the prior and that of recharge being skewed to the higher values. The end result is a higher recharge–conductivity ratio for which the posterior distribution has a sharp peak and a much smaller range compared to the prior indicating a dramatic reduction in uncertainty of this ratio. Although the posterior distributions of model input parameters are different than the prior, no parameter value in the posterior range is outside the ranges implemented in the original model. The MCMC tool has the potential to be a very useful tool in the validation process and in particular for uncertainty reduction of model input parameters and consequently model output.
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= 0.017 & = 1.10e004
P(θ ) p (K )
2
P(θ |D) = 0.014 & = 2.53e005 50
0 0
0.01
0.02
0.03 K
0.04
0.05
0.06
0.8 2
= 2.08 & = 1.90
P(θ ) p (R )
0.6
2
P(θ|D) = 2.07 & = 0.58
0.4 0.2 0 0
1
2
3
4
5 R
6
p (R/K )
P (θ )
7
8
9
10
2
= 166.42 & = 26773.8
P (θ|D) = 151.93 & 2 = 8.45
0.1 0.05 0 0
50
100
150
200
250 R/K
300
350
400
450
500
FIGURE 24.14 Comparison between the prior (solid lines) and posterior (dashed lines) distributions obtained using validation data and the MCMC approach for conductivity, K , recharge, R, and recharge-conductivity ratio.
24.6 Summary and Conclusions Models have an inherent uncertainty. The difficulty in fully characterizing the subsurface environment makes uncertainty an integral component of groundwater flow and transport models, which dictates the need for continuous monitoring and improvement. Building and sustaining confidence in closure decisions and monitoring networks based on models of subsurface conditions require developing confidence in the models through an iterative process. The definition of model validation is postulated as a confidence-building and long-term iterative process (Hassan, 2004a). Model validation should be viewed as a process, and not an end result. Following Hassan (2004b), an approach is proposed for the validation process of stochastic groundwater models. The approach is briefly summarized here and detailed analyses of acceptance criteria for stochastic realizations and of using validation data to reduce input parameter uncertainty are presented and applied to two case studies. During the validation process for stochastic models, a question arises as to the sufficiency of the number of acceptable model realizations (in terms of conformity with validation data). We propose to use a hierarchical approach to make this determination. This approach is based on computing five measures or metrics and following a decision tree to determine if a sufficient number of realizations attain satisfactory scores regarding how they represent the field data used for calibration (old) and for validation (new). The first two of these measures are applied to hypothetical scenarios using the first case study and assuming field data are consistent with the model or significantly different than the model results. In
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both cases it is shown how the two measures would lead to the appropriate decision about the model performance. Standard statistical tests are used to evaluate these measures with the results indicating they are appropriate measures for evaluating model realizations. The use of validation data to constrain model input parameters is shown for the second case study using a Bayesian approach known as Markov Chain Monte Carlo. The approach shows a great potential to be helpful in the validation process and in incorporating prior knowledge with new field data to derive posterior distributions for both model input and output.
Glossary Model: An abstraction or a simple representation of a real system or process. Conceptual Model: A hypothesis for how a system or a process operates. Mathematical Model: A quantitative expression of the system processes, forces, and events. Computer Code: An algorithm to implement the mathematical model and perform the model computations. Generic models: The computer codes that are used to solve the mathematical flow and transport equations. Site-Specific Models: The computer codes combined with the conceptual models (model structure), input data and boundary conditions for a particular geographical area. Research or Analysis Models: Models used for studying and understanding different phenomena in the subsurface and they usually rely on hypothetical domains or very well characterized field sites. Predictive or Decision-making Models: Models that are mainly used to support and aid a regulatory decision regarding a subsurface issue. Model Calibration: The process of tuning the model to identify the independent input parameters by fitting the model results to some field data or experimental data, which usually represent the dependent system parameters. History Matching: Using historical field data during the model building and calibration process and trying to match them before using the model to predict future system response. Computer Code Verification: Verification of a mathematical model or its computer code; it is obtained when it is shown that the model behaves as intended and that the equations are correctly encoded and solved. Model Verification: A process aimed at establishing a greater confidence in the model by using a set of calibrated parameter values and stresses to reproduce a second set of field data that is available during the model-building process. Model Validation: A process, not an end result, aimed at building confidence in the model predictions through a structured set of tests and evaluations with trigger mechanisms that forces the process back to the model-building stage if model is not consistent with field data collected for validation. Research Model Validation: Validation of a research model that helps one understand processes, uncertainties, and the like. Predictive Validation: Performing a validation process for a site-specific, predictive model for the goal of helping the decision-making process. Validation Target: The model output for which filed data will be collected for validation purposes. Bayesian Inference: An alternative to the classical approach to statistical analysis that benefits from prior knowledge as well as newly collected data to quantify parameter uncertainty. Markov Chain Monte Carlo (MCMC): A form of Bayesian inference that can be used to simulate the posterior distribution of model parameters. Prior Distribution: The parameter distribution that summarizes all the knowledge about the parameter before collecting new data. Posterior Distribution: The parameter distribution that is obtained through Bayesian inference and it relies on both prior knowledge and newly collected data.
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Likelihood Function: A probability function describing the probability of seeing the observed data (newly collected data) given that a certain model or assumption is true. Density-driven Flow: A groundwater flow problem in which the flow depends on (or is driven by) the variations in groundwater density (e.g., due to thermal effects or salinity effects). Transition Zone: The varying salinity zone separating shallow freshwater (mainly from recharge) from deep saltwater (from the ocean or the sea).
Acknowledgments The author would like to express his special thanks to Greg Pohll, Jenny Chapman, and Karl Pohlmann for very helpful comments and stimulating discussions and also for the help on the statistical evaluation of the acceptance criteria. Appreciation is extended to Hesham Bekhit for his help on the Metropolis Algorithm. This work was performed under the auspices of the U.S. Department of Energy by the Desert Research Institute under contract number DE-AC08-00NV13609.
References Anderson, M.G. and Bates P.D. (2001) Model Validation: Perspectives in Hydrological Science. New York, NY: John Wiley & Sons, Ltd. Andersson, K., Grundfelt, B., Larsson, A. and Nicolson, T. (1989) INTRAVAL as an integrated international effort for geosphere model validation — A status report. Proceedings of Symposium on Safety Assessment of Radioactive Waste Repositories, Paris, October 9–13, OECD Nuclear Energy Agency. AWR (1992a) Special issue: Validation of Geo-Hydrological Models — Part 1. Advances in Water Resources 15, 1–87. AWR (1992b) Special issue: Validation of Geo-Hydrological Models — Part 2. Advances in Water Resources 15, 153–217. Balci, O. (1988) Credibility assessment of simulation results: The state of the art, methodology and validation. Simulation Series, The Society for Computer Simulation 19, 19–25. Balci, O. (1989) How to assess the acceptability and credibility of simulation results. In Proceedings of the 1989 Winter Simulation Conference, Washington, DC. Edited by E. MacNair, K. Musselman, and P. Heidelberger. Balci, O. and Sargent, R.G. (1981) A methodology for cost-risk analysis in the statistical validation of simulation models. Communication of the ACM 24, 190–197. Balci, O. and Sargent, R.G. (1982) Validation of multivariate response simulation models by using Hotelling’s two-sample T2 test. Simulation 39, 185–192. Balci, O. and Sargent, R.G. (1984) A bibliography on the credibility, assessment and validation of simulation and mathematical models. Simuletter 15, 15–27. Bates, B. C. and Campbell, E. P. (2001) A Markov chain Monte Carlo scheme for parameter estimation and inference in conceptual rainfall runoff modeling. Water Resources Research 37, 937–947. Beljin, M.S. (1988) Testing and validation of models for solute transport in groundwater: Code intercomparison and evaluation of validation methodology. International Ground Water Modeling Center, Holcomb Institute, Butler Univ., Indianapolis, Indiana. Report GWMI 88–11. Bredehoeft, J.D. and Konikow, L.F. (1992) Reply to comment. Advances in Water Resources 15, 371–372. Bredehoeft, J.D. and Konikow, L.F. (1993) Ground water models: Validate or invalidate. Ground Water 31, 178–179. Bredehoeft, J.D. (2003) From models to performance assessment: The conceptualization problem. Ground Water 41, 571–577. Broyd, T., Read, D. and Come, B. (1990) The CHEMVAL Project: An international study aimed at the verification and validation of equilibrium speciation and chemical transport computer programs.
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In Proceedings of GEOVAL90 Symposium, Stockholm, May 14–17, 1990, Swedish Nuclear Power Inspectorate (SKI), Stockholm. Campbell, E. P., Fox, D. R. and Bates, B. C. (1999) A Bayesian approach to parameter estimation and pooling in nonlinear flood event models. Water Resources Research 35, 211–220. de Marsily, G., Combes, P. and Goblet, P. (1992) Comment on ‘Groundwater models cannot be validated,’ by L.F. Konikow and J. D. Bredehoeft. Advances in Water Resources 15, 367–369. Duan, Q., Gupta, H.V., Sorooshian, S., Rousseau, A.N. and Turcotte, R. (Eds.) (2003) Calibration of watershed models, Water Sci. Appl. Ser., Vol. 6, AGU, Washington, D.C. Eisenberg, N., Federline, M., Sagar, B., Wittmeyer, G., Andersson, J. and Wingefors, S. (1994) Model validation from a regulatory perspective: A summary. In GEOVAL 94, Validation Through Model Testing, Proceedings of an NEA/SKI Symposium, Paris, France, 11–14 October, pp. 421–434. Freer, J., Beven, K. and Ambroise, B. (1996) Bayesian estimation of uncertainty in runoff prediction and the value of data: An application of the GLUE approach. Water Resources Research 32, 2161–2173. Gass, S.I. (1983) Decision-aiding models: Validation, assessment, and related issues for policy analysis. Operations Research 31, 601–663. Gass, S.I. and Thompson, B.W. (1980) Guidelines for model evaluation: An abridged version of the U.S. General Accounting Office exposure draft. Operations Research 28, 431–479. GEOVAL87 (1987) Proceedings of Symposium on Verification and Validation of Geosphere Performance Assessment Models, organized by Swedish Nuclear Power Inspectorate, Stockholm, Sweden, April 7–9. GEOVAL90 (1990) Proceedings of Symposium on Validation Geosphere Flow and Transport Models, organized by Swedish Nuclear Power Inspectorate, Stockholm, Sweden, May 14–17. GEOVAL94 (1994) Proceedings of Symposium on Verification through Model Testing, organized by OECD Nuclear Energy Agency and the Swedish Nuclear Power Inspectorate, Paris, France, October 11–14. Grundfelt, B., Lindbom, B., Larsson, A. and Andersson, K. (1990) HYDROCOIN level 3 — Testing methods for sensitivity/uncertainty analysis. Proceedings of GEOVAL9O Symposium, Stockholm, May 14–17, 1990. Swedish Nuclear Power Inspectorate, (SKI), Stockholm. Grundfelt, B. (1987) The HYDROCOIN Project — Overview and results from level one. Proceedings of International GEOVAL-87 Symposium, Swedish Nuclear Power Inspectorate, (SKI), Stockholm. April 7–9, 1987. Hassan, A.E. (2004a) Validation of numerical groundwater models used to guide decision making. Ground Water 42, 277–290. Hassan, A.E. (2004b) A methodology for validating numerical groundwater models. Ground Water 42, 347–362. Hassan, A.E., Pohlmann, K., and Chapman, J. (2001) Uncertainty analysis of radionuclide transport in a fractured coastal aquifer with geothermal effects. Transport in Porous Media 43, 107–136. Hassan, A., Pohlmann, K. and Chapman, J. (2002) Modeling Groundwater Flow and Transport of Radionuclides at Amchitka Island’s Underground Nuclear Tests: Milrow, Long Shot, and Cannikin. Desert Research Institute, Division of Hydrologic Sciences, Publication No. 45172, DOE/NV/11508–51. Hassanizadeh, S.M. 1990. Panel discussion. In GEOVAL-90, Symposium on Validation of Geosphere Performance Assessment Models, Stockholm, Sweden, 14–17 May, pp. 631–658. Herbert, A., Dershowitz, W., Long, J. and Hodgkinson, D. (1990) Validation of fracture flow models in the Stripa project. Proceedings of GEOVAL90 Symposium, Stockholm, May 14–17, Swedish Nuclear Power Inspectorate (SKI). Huyakorn, P.S., Kretschek, A.G., Broome, R.W., Mercer, J.W. and Lester, B.H. (1984) Testing and validation of models for simulating solute transport in groundwater. International Ground Water Modeling Center, Holcomb Research Institute, Butler University, Indianapolis, IN. Report GWMI 84–13. Hornberger, G.M. and Boyer, E.W. (1995) Recent advances in watershed modeling. U.S. Natl. Rep. Int. Union Geod. Geophys. 1991–1994, Rev. Geophys., 33, 949–957. INTRACOIN (1984) Final report level 1, Code verification. Report SKI 84:3, Swedish Nuclear Power Inspectorate, Stockholm, Sweden.
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INTRACOIN (1986) Final report levels 2 and 3, Model validation and uncertainty analysis. Report SKI 86:2, Swedish Nuclear Power Inspectorate, Stockholm, Sweden. Konikow, L.F. and Bredehoeft, J.D. (1992) Groundwater models cannot be validated. Advances in Water Resources 15, 75–83. Konikow, L.F. and Bredehoeft, J.D. (1993) The myth of validation in groundwater modeling. In Proceedings 1993 Groundwater Modeling Conference, IGWMC, Golden, CO, pp. A-4. Kuczera, G. (1983) Improved parameter inference in catchment models: 1. Evaluating parameter uncertainty. Water Resources Research 19, 1151–1162. Kuczera, G. and Mroczkowski, M. (1998) Assessment of hydrologic parameter uncertainty and the worth of multiresponse data. Water Resources Research 34, 1481–1489. Kuczera, G. and Parent, E. (1998) Monte Carlo assessment of parameter uncertainty in conceptual catchment models: The Metropolis algorithm. Journal of Hydrology 211, 69–85. Luis, S.J. and McLaughlin, D. (1992) A stochastic approach to model validation. Advances in Water Resources 15, 15–32. Marshall, L., Nott, D. and Sharma, A. (2004) A comparative study of Markov chain Monte Carlo methods for conceptual rainfall-runoff modeling. Water Resources Research 40, W02501, doi:10.1029/2003WR002378. Miller, R.E. and van der Heijde, P.K.M. (1988) A groundwater research data center for model validation. Proceedings of the Indiana Water Resources Assoc. Symposium, June 8–10, Greencastle, IN. Moran, M.S. and Mezgar, L.J. (1982) Evaluation factors for verification and validation of low-level waste disposal site models. Oak Ridge National Laboratory, Oak Ridge, TN. Report DOE/OR/21400-T119. National Research Council (1990) Groundwater Models; Scientific and Regulatory Applications. National Academy Press, Washington, D.C., 303 pp. Neuman, S.P. (1992) Validation of safety assessment models as a process of scientific and public confidence building. In Proceedings of HLWM Conference, Vol. 2, Las Vegas. Nicholson, T.J. (1990) Recent accomplishments in the INTRAVAL Project — A status report on validation efforts. Proceedings of GEOVAL90 Symposium, Stockholm, Sweden, May 14–17, Swedish Nuclear Power Inspectorate (SKI). Oren, T. (1981) Concepts and criteria to assess acceptability of simulation studies. A Frame of Reference. Communication of the ACM 24, 180–189. Oreskes, N., Shrader-Frechette, K., and Belits, K. (1994) Verification, validation, and confirmation of numerical models in the earth sciences. Science 264, 641–646. Pohll, G., Hassan, A.E., Chapman, J.B., Papelis, C. and Andricevic, R. (1999) Modeling groundwater flow and radioactive transport in a fractured aquifer. Ground Water 37, 770–784. Pohlmann, K., Hassan, A.E. and Chapman, J. (2002) Modeling density-driven flow and radionuclide transport at an underground nuclear test: Uncertainty analysis and effect of parameter correlation. Water Resources Research 38, 10.1029/2001WR001047. Pohlmann, K., Pohll, G., Chapman, J., Hassan, A.E., Carroll, R. and Shirley, C. (2004) Modeling to support groundwater contaminant boundaries for the Shoal underground nuclear test. Division of Hydrologic Sciences, Desert Research Institute, Publication No. 45184-revised, pp. 197. Refsgaard, J.C. (2001) Discussion of model validation in relation to the regional and global scale. In Model Validation: Perspectives in Hydrological Sciences, M.G. Anderson and P.D. Bates (Eds.) John Wiley & Sons, New York. Reimus, P., Pohll, G., Mihevc, T., Chapman, J., Haga, M., Lyles, B., Kosinski, S., Niswonger, R. and Sanders, P. (2003) Testing and parameterizing a conceptual model for solute transport in a fractured granite using multiple tracers in a forced-gradient test. Water Resources Research 39, 1356–1370. Sargent, R.G. (1984) Simulation Model Validation. In Simulation and Model-based Methodologies: An Integrative View. Edited by Oren et al., Springer-Verlag. Sargent, R.G. (1988) A tutorial on validation and verification of simulation models. Proceedings of 1988 Winter Simulation Conference. Edited by M. Abrams, P. Haigh, and J. Comfort, pp. 33–39.
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Sargent, R.G. (1990) Validation of mathematical models. In GEOVAL-90, Symposium on Validation of Geosphere Performance Assessment Models, Stockholm, Sweden, 14–17 May, pp. 571–579. Schruben, L.W. (1980) Establishing the Credibility of Simulations — The Art and the Science. Prentice-Hall. Singh, V.P. (1995) Computer Models of Watershed Hydrology, 1129 pp, Water Resour. Publ., Highlands Ranch, Colorado. Singh, V.P. and Woolhiser, D.A. (2002) Mathematical modeling of watershed hydrology. Journal of Hydrol. Eng. 7, 270–292. SSI (Swedish National Institute of Radiation Protection) (1990) Proceedings of Symposium and Workshop on the Validity of Environmental Transfer Models (BIOMOVS), October 8–12, 1990. Swedish National Institute of Radiation Protection (SSI), Stockholm. Swedish Nuclear Power Inspectorate (1987) The International HYDROCOIN Project — Background and Results. OECD, Paris. Swedish Nuclear Power Inspectorate (1990) The International INTRAVAL Project — Background and Results. OECD, Paris. Tsang, C.F. (1991) The modeling process and model validation. Ground Water 29, 825–831. van der Heijde, P.K.M., Huyakorn, P.S. and Mercer, J.W. (1985) Testing and validation of groundwater models. Proceedings of the NWWA/IGWMC Conference on “Practical Applications of Ground Water Models.” August 19–20, Columbus, OH. van der Heijde, P.K.M. (1987) Quality assurance in computer simulations of groundwater contamination. Environmental Software 2. van der Heijde, P.K.M., Elderhorst, W.I.M., Miller, R.A. and Trehan, M.F. (1989) The establishment of a groundwater research data center for validation of subsurface flow and transport models. International Ground Water Modeling Center, Holcomb Research Institute, Butler Univ., Indianapolis, IN. Report GWMI 89-01. Vogel, R.M., Sankarasubramanian (2003) Validation of a watershed model without calibration, Water Resources Research 39, 1292, doi:10.1029/2002WR001940. Unsworth, M., Soyer, W. and Tuncer, V. (2005) Magnetotelluric measurements for determining the subsurface salinity and porosity structure of Amchitka Island, Alaska. In Biological and Geophysical Aspects of Potential Radionuclide Exposure in the Amchitka Marine Environment, edited by Powers et al. Consortium for Risk Evaluation with Stakeholder Participation, Institute for Responsible Management, Piscataway, New Jersey. Zeigler, B.P. (1976) Theory of Modeling and Simulation. John Wiley & Sons, Inc., New York.
Further Information This chapter attempts to introduce a newly proposed validation methodology for numerical groundwater models cast in a stochastic framework. Research on model validation is extensively reported in the literature, but mostly focuses on process models and definitions of the term. In the area of toxic waste management, a number of authors (e.g., Moran and Mezgar, 1982; Huyakorn et al., 1984; van der Heijde et al., 1985; Van der Heijde, 1987; Beljin, 1988) have considered the question of whether a model used in a safety assessment program is valid in making appropriate long-term predictions. During the late 1980s, an effort was made to establish a groundwater research data center for the validation of subsurface flow and transport models (Miller and Van der Heijde, 1988; Van der Heijde et al., 1989). In the area of nuclear waste management, the need to validate groundwater models has received increased emphasis. This has led to institutionalized and publicized programs for validation of hydrogeological models. A number of international cooperative projects such as INTRACOIN (1984, 1986), HYDROCOIN (Grundfelt, 1987; Grundfelt et al., 1990), INTRAVAL (Andersson et al., 1989; Nicholson, 1990), STRIPA (Herbert et al., 1990), CHEMVAL (Broyd et al., 1990), BIOMOVS (SSI, 1990) were devoted to the validation of models. Model validation was also extensively discussed in symposia including GEOVAL87 (1987), GEOVAL90 (1990), and GEOVAL94 (1994). The journal Advances in Water Resources
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dedicated two special issues to the topic of model validation (AWR, 1992a, 1992b). Additionally, a wealth of literature has been published on validation in the field of systems engineering and operations research (Tsang, 1991), some of which may be useful for subsurface model validation. Examples cited by Tsang (1991) include Balci (1988, 1989), Balci and Sargent (1981, 1982, 1984), Gass (1983), Gass and Thompson (1980), Oren (1981), Sargent (1984, 1988), Schruben (1980), and Zeigler (1976). The Swedish Nuclear Power Inspectorate, SKI, initiated and completed three international cooperation projects to increase the understanding and credibility of models describing groundwater flow and radionuclide transport. The INTRACOIN project is the first of these, and it focused on verification and validation of transport models. The HYDROCOIN study was the second study and represented an international cooperative project for testing groundwater-modeling strategies for performance assessment of nuclear waste disposal. The SKI initiated the study in 1984, and the technical work was finalized in 1987 (Swedish Nuclear Power Inspectorate, 1987). The participating organizations were regulatory authorities as well as implementing organizations in ten countries. The study was devoted to testing of groundwater flow models and was performed at three levels: computer code verification, model validation, and sensitivity/uncertainty analysis. Based upon lessons learned from INTRACOIN and HYDROCOIN, international consensus grew prior to and during the GEOVAL Symposium in Stockholm in April 1987 to begin a new project dealing with the validation of geosphere transport models. This new international cooperative project, named INTRAVAL, began in October 1987. As with the preceding projects, INTRAVAL was organized and managed by the SKI. The INTRAVAL project was established to evaluate the validity of mathematical models for predicting the potential transport of radioactive substances in the geosphere (Swedish Nuclear Power Inspectorate, 1990). The unique aspect of INTRAVAL was the interaction between the experimentalists and modelers simulating the selected test cases for examining model validation issues. The test cases selected consisted of laboratory and field transport experiments and natural analogue studies that incorporate hydrogeologic and geochemical processes relevant to safety assessments of radioactive waste repositories.
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25 Scale Issues 25.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-1 Scale, Definition, and Issues • A Brief Background • A Rich Literature
25.2 Measurement and Interpretation . . . . . . . . . . . . . . . . . . . . . . . 25-5 25.3 Upscaling and Downscaling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-7 Upscaling • Downscaling
25.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-10 Alternative Characterizations of Spatial Variability at the Catchment Scale • Extrapolation from Site to Region • Querying the Effect of Upscaling
Keith Loague Stanford University
Dennis L. Corwin USDA-ARS
25.5 Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25-14 25-15 25-16 25-16
Anything you build on a large scale or with intense passion invites chaos. Francis Ford Coppola
25.1 Introduction 25.1.1 Scale, Definition, and Issues One of the many definitions for scale in Webster’s dictionary is a system of grouping or classifying in a series of steps or degrees according to a standard of relative size, amount, importance, perfection, etc. The jargon used to describe scales in earth science includes, for example, continuum, correlation, integral, microscopic, macroscopic, local spatial average, REA (representative elementary area), and REV (representative elementary volume). The objective of this chapter is to introduce the subject of scale as it relates to hydrology, the entirety of which could easily fill several volumes. Dooge’s (1989) classifications for length and time scales in hydrology are given in Table 25.1. Relative to Dooge’s scheme, it is worth pointing out that some scale classifications include a mega class. A relationship between scale and model type, relative to non-point source pollution models, is given in Figure 25.1. An important consideration for conceptualization of a given problem is for the model to account for the predominant processes occurring at the spatial and temporal scales of interest (Corwin and Loague, 2005). The issue of scale (both spatial and temporal) is ever present in modern hydrology. Whether one is engaged in laboratory or field experiments, parameter estimation or modeling, scale is an important 25-1
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The Handbook of Groundwater Engineering TABLE 25.1
Spatial and Temporal Scales in Hydrology Spatial Scale
Temporal Scale
Class
System
Length (m)a
Class
System
Time (s)b
Micro Micro Micro Meso Meso Meso Macro Macro Macro
Molecular cluster Continuum point REVc Module Sub-catchment Small catchment Large catchment Continental Planetary
1 × 10−8 1 × 10−5 1 × 10−2 1 × 102 1 × 103 1 × 104 1 × 105 1 × 106 1 × 107
Micro Micro Micro Meso Meso Meso Macro Macro Macro
Water cluster Continuum point Experimental plot Earth rotation Moon orbit Earth orbit Sun spots Orbital eccentricity Stellar evolution
1 × 10−13 1 × 10−6 1 1 × 104 1 × 106 1 × 107 1 × 108 1 × 1012 1 × 1016
a Typical. b Order of magnitude. c REV, representative elementary volume.
Source: After Dooge (1989).
Hierarchy of spatial scales
i+6
World
i+5
Continent
i+4
Region
County/state i+3 Functional modets i+2
Watershed
i+1
Field
Qualitative models i Soil horizon
i–1
Peds, Aggregates
i–2
Pedon Quantitative models
Mechanistic models Basic structures i–3 Molecular
i–4
FIGURE 25.1 Organization hierarchy of spatial scales pertinent to non-point source pollution models. (Redrawn from Wagenet, R.J. and Hutson, J.L., Journal of Environmental Quality, 25, 499, 1996.)
consideration. At the surface the focus can be on the land phase, the channel phase, or the combined land and channel phase. In the subsurface the focus can range from an individual soil profile through an entire continent. For coupled atmospheric–surface and surface–subsurface problems the spatial and temporal scales can be significantly different. The water balance estimates in Table 25.2 illustrate the considerable range in volumes and residence times for the various components of the hydrologic cycle. One must also recognize that the underlying spatial and temporal scales can be different for water movement than they are for solute–sediment transport. For example, Figure 25.2 illustrates the tremendous range in spatio-temporal scales for hydrologically driven soil erosion processes.
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TABLE 25.2 World Water Balance Estimates System
Surface Area (km2 × 106 )
Volume (km3 × 106 )
Volume (%)
Equivalent Depth (m)a
Residence Time (sec)
361 1.55 <0.1 <0.1 130 130 17.8 504 <0.1
1,370 0.13 <0.01 <0.01 0.07 60 30 0.01 <0.01
94 <0.01 <0.01 <0.01 <0.01 4 2 <0.01 <0.01
2,500 0.25 0.007 0.003 0.13 120 60 0.025 0.001
∼1.3 × 1011 ∼3.2 × 108 3.2 × 107 ⇒ 3.2 × 108 ∼1.2 × 106 1.2 × 106 ⇒ 3.2 × 107 1.2 × 106 ⇒ 3.2 × 1011 3.2 × 108 ⇒ 3.2 × 1010 ∼8.6 × 105 ∼6.1 × 105
Oceans and seas Lakes and reservoirs Swamps Rivers and channels Soil moisture Groundwater Icecaps and glaciers Atmospheric water Biopsheric water
a Computed as though storage were uniformly distributed over the entire surface of the earth.
Source: Freeze, R.A. and Cherry, J.A., Groundwater, Prentice-Hall, Englewood Cliffs, NJ, 1979.
Log space km
1 Minute
–6
1 Day
1 Hour
1 Month
Infiltration/soil moisture
–2
Interrill/Hortonian overland flow Breeze
0
10 100 1000 10000 Years Years Years Years
Soil structure
Soil texure
Grass
Splash –4
1 Year
Tillage ridge
Canopy
Gully
Thunder storm
Long waves
Weather/climate Erosion and runoff frocess
–2
El Nino 0
100 m 1 km
Sub-
Landscape evolution
Front
–4
10 m
Catena Wood
2
–6
1m
Hillslope
Stand
Fluvial
4
Soil depth
Crop Forest
1 dm
Plot
Buffer strip
Rill/saturated overland flow
1 cm
Micro
100 km 1000 km
Basin
Climate change 2
10 km
Watershed
4
Log time years
Vegetation
Soil/lithology
Management
Topographic scale
FIGURE 25.2 Temporal and spatial extent of hydrological processes and natural phenomena with special consideration for soil erosion. (Redrawn from Renschler, C.S., Strategies for implementing natural resource management tool — A geographical information science perspective on water and sediment balance assessment at different scales, PhD dissertation, University of Bonn, Germany, 2000.)
The spatial variability of surface, near surface, and subsurface hydrologic parameters is well known (e.g., de Marsily et al., 2005). Perception plays a major role in the characterization of spatial variability and, subsequently, scale. The two-part Figure 25.3 cleverly illustrates that what appears at first blush to be the visible variability at an assumed scale is in fact the variability at a much larger scale. It is also critically important to recognize that not all hydrologic parameters are time invariant. The development of a grid or mesh for process-based simulations of hydrologic response requires a level of discretization sufficient to represent spatial variations in hydrologic parameters. For transient hydrologic-response simulation
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(a)
(b)
FIGURE 25.3 (a) Photograph of a section of heterogeneous porous media, with an Olympus camera lens cap for scale. (b) Photograph of the same section of heterogeneous porous media, showing that the diameter of the camera lens cap is much larger (i.e., 1 m) than was most likely assumed for the initial inspection of (a). Scott Tyler shot the two photographs [Stephen Wheatcraft provides the correct length scale in (b)]. Note, Tyler and Wheatcraft (1990) show alternative versions of these photos.
(e.g., event-based versus long-term) the proper selection of a minimum and maximum time step is critical. Not withstanding the type of model, all hydrologic response simulation efforts are faced with the daunting task of effectively representing the spatial and temporal variability for the parameters associated with the problem. Most often these parameters are measured for a scale that is much smaller (with a characteristic variability) than the level of discretization to be employed for the simulation, requiring an upscaling protocol. When the objective is to reconstruct small-scale variability from a larger scale average, a downscaling protocol is required.
25.1.2 A Brief Background Much of the backbone of modern hydrology was developed before scale was the center stage issue it is today (e.g., Darcy, 1856; Buckingham, 1907; Terzaghi, 1925; Richards, 1931; Hubbert, 1940; Biot, 1941; Horton, 1945; Penman, 1948). For nearly half a century, high-speed digital computers have facilitated the development of physics-based hydrologic response models (e.g., Freeze, 1971; Harbaugh and McDonald, 1996; Zheng and Wang, 1998; VanderKwaak, 1999). The simulation scale in hydrology ranges from the soil profile (e.g., Freeze, 1969) to the continental scale (e.g., Garven, 1995). Segol (1994) and Beven (2000) review many of the classic groundwater and rainfall-runoff simulations. There is a large spectrum of modeling approaches that have been used in hydrology (e.g., continuum, stochastic continuum, porescale network, effective domain network, percolation theory, stochastic stream-tube, transfer function), each of which is impacted by the problems of scale. Earlier, it was assumed that sophisticated deterministic-conceptual simulations, employed in parallel to exhaustive plot- or well-scale information, could easily be scaled up to simulate process-based hydrologic response at larger scales. This assumption, grounded in the fact that plots make up hillslopes, hillslopes make up catchments, and catchments make up watersheds, was shortsighted as, to date, no data set has allowed for the complete characterization, with high levels of confidence in both space and time, at the larger scales. In the context of scale-dependent deterministic-conceptual simulation, equifinality is a wellknown problem (Beven, 1993, Savenije, 2001, Beven, 2005). Freeze (1975, 1980) was a pioneer in the use of stochastic-conceptual simulation for unraveling scale issues in both groundwater flow and rainfall-runoff processes, considering the variability and uncertainty in both inputs and outputs (Gelhar, 1974). Five significant scale-related contributions to our improved understanding of hydrologic response are (i) the Miller and Miller (1956) theory for similar media (i.e., similitude analysis), (ii) the Pilgrim
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(1983) identification of the problems associated with transferring hydrological relationships between regions, (iii) the Klemes (1983) argument that the level of scale at which meaningful conceptualizations of physical processes are possible are not arbitrary and their ranges are not continuous, (iv) the Cushman (1986) discussion of the relationships between measurements, scale, and scaling, and (v) the Woolhiser and Goodrich (1988) work showing the effects of storm rainfall intensity patterns on surface runoff. Obviously, the five contributions listed here are just the tip of the proverbial iceberg.
25.1.3 A Rich Literature Four of the earliest workshops that focused entirely on the problems of scale in hydrology were the 1982 meeting in Caracas, Venezuela (Rodriguez-Iturbe and Gupta, 1983), the 1984 meeting at Princeton University (Gupta et al., 1986), the 1993 meeting in Robertson, Australia (Kalma and Sivapalan, 1995; Sivapalan and Kalma, 1995), and the 1996 meeting at Krumbach, Austria (Bloschl et al., 1997). Other meetings have also resulted in special issues focused on scale and scaling in hydrology (e.g., Sivapalan et al., 2003a, 2004). There are several excellent books dealing with scale-related issues in hydrology and related fields (e.g., Cushman, 1990; Hillel and Elrick, 1990; Feddes, 1995; Stewart et al., 1996; Rodriguez-Iturbe and Rinaldo, 1997; Sposito, 1998; Bierkens, et al., 2000; Grayson and Bloschl, 2000; Pachepsky et al., 2003). There are also several outstanding review and commentary papers on scale issues in hydrology and related fields (e.g., Church and Mark, 1980; Wood et al., 1990; de Boer, 1992; Gelhar et al., 1992; Koltermann and Gorelick, 1996; Shuttleworth et al., 1997; Mayer et al., 1999; Dodds and Rothman, 2000; Beven, 2001; Bloschl, 2001a,b; Cushman et al., 2002; Farmer, 2002; Grayson et al., 2002; Western et al., 2002; Lin, 2003; Neuman, 2003; Skoien et al., 2003; Sivapalan, 2003; Sivapalan et al., 2003b; Shaman et al., 2004; Bloschl, 2005; Noetinger et al., 2005).
25.2 Measurement and Interpretation More than 20 years ago Gupta et al. (1984) reported an amazingly detailed large-scale saturated subsurface interpretation for groundwater flow simulations within a multiaquifer system. The 3D finite-element representation of Long Island, New York by Gupta et al. was based upon six hydrogeologic units that were gleaned from stratigraphic maps. To the best of our knowledge, the finite-element mesh in Gupta et al. is the only foldout ever to be published in Water Resources Research. Characterization of the unseen subsurface, with the information that is typically available, is difficult at best. Even an accurate representation of surface topography (e.g., identifying size from digital elevation models) can be troublesome (Montgomery and Foufoula-Georgiou, 1993). Notwithstanding the information problem, the underlying foundation to the success of any hydrologic-response simulation is the best possible conceptualization of the problem. Bredehoeft (2005) defines surprise as new data that renders a prior conceptualization invalid. More data is generally better; however, the $64,000 question of when enough information is really enough (James and Gorelick, 1994) is important for the problems of scale. The size of the area of influence for a given hydrogeologic parameter measurement is often related to the scaling problem. For example, saturated hydraulic conductivity measurements can be made at the column, point, plot, and local scales. Figure 25.4 illustrated that data from different measurement scales can have different correlation lengths. One of the implications of invasive measurement techniques is that the system is changed, which can result in measurement error. Data collected from small areas are often employed in hydrologic response simulations to represent larger areas (Hopmans et al., 2002). Soil texture is often used as a surrogate for soil-hydraulic properties when no data are available (Rawls et al., 1991). Pedotransfer functions, remote sensing, and other non-invasive techniques are also used to estimate near-surface hydraulic and hydrogeologic parameters at larger scales (Corwin et al., 1999). Water balance and hydrologic-response simulations are often used (in a residual or inverse mode) to estimate hydrologic parameters at regional scales. The use of electrical resistivity and electromagnetic induction methods
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Semivariance
25-6
Regional Local Core
Lag (separation distance)
FIGURE 25.4 Hypothetical variogram for scale-dependent hydraulic conductivity. (Redrawn from Gelhar, L.W., Water Resources Research, 22, 1355, 1986.)
104
101 100
Tracer tests Contam. models Envir. tracers
10–1 10–2
10–1
100
101
102 103 Scale (m)
104
Fractured
102
Porous
Longitudinal dispersivity (m)
103
105
106
FIGURE 25.5 Longitudinal dispersivity as dependent on an overall displacement scale for different types of observations and media. (Redrawn from Gelhar, L.W., Welty, C., and Rehfeldt, K.R., Water Resource Research, 28, 1955, 1992.)
to interpret between widely spaced conventional hydrogeologic measurements is extremely promising (Corwin and Plant, 2005; Day Lewis et al., 2006). Davis (1969) was one of the first to thoroughly summarize porosity and permeability values for earth materials. Nielsen et al. (1973) and Philip (1980) were among the first to discuss spatial variability for nearsurface soil-hydraulic properties. A big dilemma in employing data from different measurement scales for hydrologic-response simulations is the quantification of reliability for the mixed information (e.g., hydraulic conductivity correlated to grain size analysis and hydraulic conductivity from pump test results). An important problem for simulating hydrologic response is the identification and characterization of small-scale preferential flow paths located within larger systems (e.g., Clothier, 2002; Zheng and Gorelick, 2003). An often ignored obstacle related to effectively exciting physics-based models is the poor assumption of time invariance for many near-surface hydraulic and hydrogeologic parameters. For example, Loague and VanderKwaak (2004) report permeability values for a single location where the measurement was repeated and the difference was greater than 700%. Figure 25.5 and Figure 25.6, from the pioneering work of Gelhar et al. (1992), clearly illustrate scale impacts for longitudinal (along the flow path) dispersivity for both porous and fractured media. Some researchers take dispersivity as a characteristic property used to estimate the magnitude of hydrodynamic
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Longitudinal dispersivity (m)
104 103 102 101 100 Reliability Low Intermediate High
10–1 10–2 10–3 –1 10 100
101
102 103 104 Scale (m)
105
106
FIGURE 25.6 Field longitudinal dispersivity data classified according to reliability. (Redrawn from Gelhar, L.W., Welty, C., and Rehfeldt, K.R., Water Resource Research, 28, 1955, 1992.)
dispersion in solute transport simulations; others argue that it is a calibration parameter employed because there is insufficient information to describe the flow regime. The dispersivity values shown in Figure 25.5 were estimated from a mixed set of tracer experiments (smaller scales), environmental tracers (larger scales), and numerical simulations. The estimated dispersivities in Figure 25.5 range from 0.01 m to 10 km. The dispersivity estimates shown in Figure 25.5 are presented again in Figure 25.6, now classified based upon their reliability. Figure 25.6 shows that most of the reliable information falls within a scale of less than approximately 100 m and that most of the least reliable data is from scales over a kilometer. Geostatistics and geographic information system (GIS) technology are well-established tools for the characterization/representation of spatial variability relative to assessing hydrologic response at different scales (e.g., Burrough and McDonnell, 1998; Deutsch and Journel, 1998; Webster and Oliver, 2001; Longley et al., 2005). The Netherland of geostatistical theory [e.g., use of training images (Caers, 2003)] and the array of GIS methods are well beyond the scope of this chapter. Fractal mathematics (e.g., Rodriguez-Iturbe and Rinaldo, 1997), fuzzy rules (e.g., Bardossy et al., 2002), neural networks (e.g., Tsegaye et al., 2003), and wavelet analysis (e.g., Chu et al., 1998), as they are related to scale problems in hydrology, are not covered in this chapter. The term “scaling”, to many, is veiled in a nimbus of exciting mystery. At a basic level, part of the mystery simply comes from confusion of two connotations of the word — meaning either scale invariance (i.e., processes behaving similarly at small scales) or upscaling/downscaling (i.e., aggregating/disaggregating data). Bloschl (2001b)
25.3 Upscaling and Downscaling The material in this section is gleaned in large part from the lucid contributions of Bierkens et al. (2000) and Bloschl (2005). From a generic prospective there are two types of upscaling or downscaling methods: (i) how model equations/parameters change with scale, and (ii) how to best represent variability (space and time) at various scales. Bierkens et al. (2000) use the term scale for the concept of support, where support is defined as the largest area [L2 ], volume [L3 ], or time interval [T] for which the property of interest is considered homogeneous. The scale triplet (spacing, extent, support), defined by Bloschl and Sivapalan (1995), is illustrated in Figure 25.7 and Figure 25.8. The scale triplet applies to both
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The Handbook of Groundwater Engineering Extent
Support
Distance
Quantity
Quantity
Quantity
Spacing
Distance
Distance
FIGURE 25.7 Schematic illustration of the scale triplet. (Redrawn from Bloschl, G. and Grayson, R., Spatial Patterns in Catchment Hydrology: Observations and Modeling, Cambridge University Press, Cambridge, United Kingdom, 2000, Chap. 2.)
Observa
tion
Support dow
Win
ng aci Sp Resolution
FIGURE 25.8 Scales affecting hydrogeologic variables. (Redrawn from Neuman, S.P. and and Di Federico, V., Review of Geophysics, 41, 4–1, 2003.)
measurements and simulations (Bloschl and Grayson, 2000). Discussing the scale triplet Bloschl (2005) writes: In dedicated studies, soil hydraulic conductivity measurements, for example, may have spacings of decimeters, while rain gauges in a region are typically spaced at tens of kilometers. The extent, which is the overall size of the domain sampled, may again range from meters to hundreds of kilometers in hydrological application. The support is the integration volume or area of the samples ranging from, say 1 dm2 in the case of time domain reflectometry in situ probes, to hectares in the case of groundwater pumping tests (Anderson, 1997) or micrometeorological studies of the atmosphere (Schmid, 2002), and square kilometers in the case of remotely sensed data (Western et al., 2002). In hydrology, the catchment area can also be thought of as a support scale (Bierkens et al., 2000). In case of a model, the notion of a scale triplet is similar. For example, for a spatially distributed hydrologic model the scale triplet may have typical values of, say 25 m spacing (i.e., the grid spacing), 1 km extent (i.e., the size of the catchment or aquifer to be modeled), and 25 m support (the cell size). Analogue scales apply to the temporal domain. In terms of extent, upscaling is usually referred to as extrapolation (with the opposite being singled out). In terms of spacing, downscaling is usually referred to as interpolation (with the opposite being singled out). In terms of support, both upscaling and downscaling are referred to as aggregation and disaggregation, respectively. Skoien and Bloschl (2006) performed Monte Carlo experiments to examine the nuances associated with the scale triplet. The typical upscaling–downscaling exercise involves the following four steps (Bloschl, 2005): (i) analyzing the local data and scrutinizing the literature to decide on the model type, (ii) estimating the parameters from the data, (iii) verifying the upscaling–downscaling model against an independent data set, and (iv) performing the actual upscaling–downscaling step. Bloschl (2005) discusses upscaling–downscaling for
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six important cases: (i) upscaling point rainfall to catchments, (ii) temporal disaggregation of rainfall, (iii) statistical downscaling of the output of global circulation models, (iv) flood frequency as a function of catchment scale, (v) upscaling and downscaling soil moisture, and (vi) subsurface media characterization and generation. Overviews of both upscaling and downscaling methods are provided in the following subsections.
25.3.1 Upscaling Upscaling methods can be divided into four major classes (Bierkens et al., 2000): (i) averaging observations or model outputs, (ii) finding representative parameters or input variables, (iii) averaging model equations, and (iv) model simplification. The different classes are based upon five criteria (Bierkens et al., 2000): (i) if a model is involved, (ii) if the model is linear in its input variables and parameters, (iii) if the model can be employed at many locations or time steps, (iv) if the form of the model is the same at the two scales involved, and (v) if the larger scale model can be analytically derived from the smaller scale model. When no model is involved the upscaling problem is trivial, with observed information at a given scale (S1 ) used to represent the larger scale (S2 ). When the model is linear the upscaling problem is relatively simple [i.e., (i) conduct many simulations at S1 then average the S1 outputs to S2 or (ii) average the S1 model inputs to S2 , then conduct a single simulation at S2 ]. When the model can be applied at many locations or time steps, simulations are conducted for all the scenarios where information at S1 is available; the S1 outputs are averaged for S2 (i.e., calculate first, average later). If the information coverage at S1 is insufficient (i.e., the data crisis) or if the model is computational inefficient (i.e., too much time or storage) it is preferable to conduct simulations at S2 directly. When the model has the same form for both scales, representative values for the input information are needed (i.e., the representative value for the support unit at S1 produces output at S2 ). When the model does not have the same form for both scales, a relationship between the S1 and S2 models is needed (e.g., the form of the S2 model depending on the S1 information, the S1 model, and the support ratio S2 /S1 ). When the larger scale model can be analytically derived from the smaller scale model it usually involves averaging the equations, with supplementary assumptions regarding the input information within the support units at S2 . If linear, both models will have the same form. When the larger scale model cannot be analytically derived from the smaller scale model the upscaling must be accomplished in another manner [e.g., (i) input information for S1 support units are determined, (ii) the S1 model is employed for the support units with the outputs averaged for S2 , (iii) a simplified model is postulated for S2 , and (iv) outputs from the simplified model are compared to outputs from the S1 model for the support units; if the comparisons are unacceptable the simplified model can either be calibrated or reformulated]. Approaches for averaging non-exhaustive (i.e., the trivial case) information include auxiliary information, deterministic functions, and geostatistical methods (Bierkens et al., 2000). Auxiliary information can be either quantitative or qualitative (note, both deterministic functions and geostatistical methods can sometimes be applied to auxiliary information). Deterministic functions usually involve interpolation where the weights depend solely on the sample configuration (e.g., Thiessen polygons). Geostatistical methods estimate variability as a realization from a stochastic function, where the weights depend upon both the sample configuration and a model of spatial-temporal structure estimated from the data (e.g., block Kriging). Approaches for finding non-exhaustive representative information include deterministic functions and stochastic methods (Bierkens et al., 2000). Deterministic functions provide full coverage with a method of interpolation. Stochastic methods, with statistics estimated from known information, describe unknown variations with conditional realizations from a stochastic function, ultimately yielding a single probability distribution. Methods for averaging model equations (i.e., temporal/volume and ensemble averaging) and model simplification (i.e., lumped conceptual and meta modeling) are discussed by Bierkens et al. (2000). It is worth pointing out that Bierkens et al. (2000) provide excellent schematic diagrams for all the upscaling methods described herein. As well, there are many examples of upscaling in the hydrology
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related literature (e.g., Desbarats, 1987; Rubin and Gomez-Hernadez, 1990; Indelman and Dagan, 1993a, 1993b; Sanchez-Villa et al., 1995; Christie, 1996; Dolman and Blyth, 1997).
25.3.2 Downscaling Downscaling is a more homogeneous problem than the upscaling problem. Essentially each downscaling problem consists of reconstructing (often a non-unique solution) the variation of a given property at some smaller scale (S1 ) from information at a larger scale (S2 ), given only the value (arithmetic average) at the larger scale. Downscaling problems can be classified as deterministic, conditional stochastic, and unconditional stochastic (Bierkens et al., 2000). For the deterministic downscaling problem the average value of the property is known exactly at scale S2 . The task with this method is to find a single deterministic function that describes the variation (temporal or spatial) of the property at S1 with the condition that the S2 average value of the function is the same as the known average. For the conditional stochastic downscaling problem the average value of the property is known exactly (as in deterministic downscaling) at scale S2 . The task with this method is to find a set of equally probable functions (an ensemble) describing the variation of the property at S1 with the condition that the S2 average value for each function (a realization) are the same as the known average (i.e., conditional). It is often necessary to constrain the functions to prevent negative values (e.g., precipitation, soil-water content). For the unconditional stochastic downscaling problem the average value of the property is not known exactly at scale S2 , rather a probability distribution function (PDF) for the property is known. The task with this method is to find a set of equally probable functions describing the variation of the property at S1 with the condition that the PDF of the S2 averages of these functions is the same as the known PDF of the average (i.e., each individual realization is not required to have the same average for S2 ). The type of functions used for deterministic or stochastic downscaling can be classified as auxiliary information, mechanistic, or empirical (Bierkens et al., 2000). Deterministic and stochastic functions can both be employed with auxiliary information [i.e., a property (e.g., topography) strongly related to the target property (e.g., soil-water content) at S1 ] available to explain the variation of the property at S1 within S2 . For example, deterministic functions can be employed when the average value of the property is known exactly for S2 and the variation of the property at S1 within S2 is described with a single deterministic function. When auxiliary information is not available both deterministic and stochastic functions can be employed when there is a mechanistic model (e.g., groundwater flow equation) describing the unknown variation of the property at S1 within S2 . For example, deterministic functions can be employed when the average value of the property is known exactly for S2 and the variation of the property at S1 within S2 is described with a single deterministic function. Deterministic and stochastic empirical functions, describing the unknown variation of a property at S1 within S2 , can be used when neither auxiliary information nor mechanistic models are available. For example, deterministic empirical function (e.g., spline, linear, additive) can be employed when the average value of the property is known exactly for S2 and the variation of the property at S1 within S2 is described with a single deterministic function. It is worth pointing out that Bierkens et al. (2000) provide excellent schematic diagrams for all the downscaling methods described herein. As well, there are many examples of downscaling in the hydrology related literature (e.g., Rodriguez-Iturbe, 1986; Robinson and Sivapalan, 1997; Wilby et al., 1998; Bishop et al., 1999; Prudhomme et al., 2002; Wood et al., 2004).
25.4 Examples 25.4.1 Alternative Characterizations of Spatial Variability at the Catchment Scale The 0.1-km2 rangeland catchment (known as R-5) located near Chickasha, Oklahoma has been host to considerable work focused on characterizing near-surface hydrologic response via simulation. A critical
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Saturated hydraulic conductivity (m/s), x 10–6 9.5 13.4 19.9
Permeability (m2), x 10–12 (c)
6.0 5.0 4.0 3.0 2.0 1.0
(d)
FIGURE 25.9 Alternative characterizations of spatially variable near-surface permeability based upon the same 157 steady-state infiltration experiments (Loague and Gander, 1990) across the 0.1-km2 R-5 catchment. (a) Average saturated hydraulic conductivity values for three soil series (Loague, K., Water Resources Research, 26, 973, 1990), (b) Permeability (corrected for temperature) tapestry based upon the x ≈ y ≈ 25 m measurement grid (Loague, K. and Kyriakidis, P.C., Water Resources Research, 33, 2883, 1997), (c) Permeability (corrected for temperature) estimated with geostatistical methods (VanderKwaak, J.E. and Loague, K., Water Resources Research, 37, 999, 2001), and (d) Permeability (corrected for temperature and scaled by the measurement chronology) estimated with geostatistical methods (Heppner, C.S. and Loague, K., Earth Surface Processes and Landforms, 2006).
piece of information in these simulations has been the spatial variability of surface permeability. Loague and Gander (1990) reported the results from 157 steady-state infiltration experiments (over a 51-day period in 1984) across a relatively uniform R-5 grid (i.e., x ≈ y ≈ 25 m; see Figure 25.9a). As illustrated in Figure 25.9 these data have been interpreted in several different ways over the past 20 years.
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The data were used to (i) estimate average saturated hydraulic conductivity values for the three R-5 soil series (see Figure 25.9a), (ii) prepare saturated hydraulic conductivity and permeability (corrected for temperature) tapestries based upon the measurement grid (see Figure 25.9b), and (iii) estimate the spatial structure of permeability (corrected for temperature) with geostatistical methods (see Figure 25.9c). Most recently, Heppner and Loague (2006) used the data to estimate the spatial structure of permeability (corrected for temperature and scaled by the measurement chronology) with geostatistical methods (see Figure 25.9d). The four scenarios in Figure 25.9, albeit all defendable and well within the same overall range of values, are strikingly different in their spatial representation. The scenarios shown in Figure 25.9a to 25.9c, were each used for rainfall-runoff simulations with a relatively simple Horton type model (see summary in Loague et al., 2000). More recently, the scenarios shown in Figure 25.9c and Figure 25.9d were each used for comprehensive hydrologic-response simulations with a physics-based model (VanderKwaak and Loague, 2001; Loague and VanderKwaak, 2002; Loague et al., 2005; Heppner et al., 2006). When used to simulate hydrologic response, with either the Horton or comprehensive models, each of the four scenarios produced different results. It is worth pointing out that an order of magnitude estimate for permeability, which is often taken as sufficient for groundwater simulations, is not good enough for the catchment-scale near-surface simulations, whose success is based upon capturing the nuances of infiltration and exfiltration, especially when the rainfall rates and the surface permeabilities are similar in magnitude. There is no easy method for upscaling soil-hydraulic property data in the near surface.
25.4.2 Extrapolation from Site to Region One method of upscaling is extrapolation by means of soil taxonomy. Soil taxonomy (Soil Survey Staff 1999) is a hierarchical classification system that establishes several successive categories of soils. Taxonomic levels in the U.S. system include: order, suborder, great group, subgroup, family, and series. The variability of a given soil property within a taxa increases at higher taxonomic categories. The classification was designed to bring out natural relationships among soils and enhance prediction about the behavior of a given kind of soil in relation to other kinds of soil for which information is available. Classification criteria include a wide range of morphologic, chemical, and physical characteristics. Average values of a given soil property are determined for a specific category and the average values are used wherever the taxonomic category is found in the region of interest. Upscaling by soil taxonomy is based on an approximation that soils of similar taxonomy have similar values for the soil property. Figure 25.10 shows an illustrative example of upscaling by soil taxonomy as discussed by Loague et al. (1989). One consideration in the use of such approximations is that, as more soils are grouped into larger categories, the variation within the group becomes larger. It is desirable to form as few groups as possible while not increasing the withingroup variation too rapidly. The relation between the number of groups and the within-group variance can be represented by plotting the within-group variance versus the number of categories one obtains in the hierarchy.
25.4.3 Querying the Effect of Upscaling Between the late 1950s and the time of its statewide cancellation in August of 1977, there was widespread use of DBCP (1, 2-dibromo-3-chloropropane) throughout California’s San Joaquin Valley. Almost three decades after its cancellation, DBCP-contaminated groundwater persists as a problem in the San Joaquin Valley. The objective of the Fresno Case Study (FCS) was to address, from a simulation perspective, if labelrecommended NPS applications were the principal source of DBCP-contaminated groundwater for an area approximately coincident with east-central Fresno County (Loague et al., 1998a,b). The FCS consisted of two 35-yr (1960–1994) simulation phases. In Phase I, the potential fate and transport of DBCP between the surface and the water table for multiple applications was quantitatively estimated with 1172 separate 1D simulations (Loague et al., 1998a). In Phase II, the aggregate of the DBCP concentrations loaded to the water table (from Phase I) were input to 3D transient saturated subsurface transport simulations (Loague et al., 1998b). Loague et al. (1998a) identify upscaling as a potential source of uncertainty in the FCS.
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Soil map
Soil map
(series level)
(Family level)
Ai
A C
Extrapolation by
Ci
Soil taxonomy Ak
Bi
A
B
Ai
A Taxonomic groups
Bi Ck
Ck
Series: Ai, Ak, Bi, Ci, Ck Family: A, B, C
BC
C
Soil parameter sampling site
FIGURE 25.10 Schematic illustration of how soil parameter information is extrapolated from a lower taxonomic category to a higher taxonomic category (Loague, K.M., Yost, R.S., and Liang, T.C., Journal of Contaminant Hydrology, 4, 139, 1989). In (a) there are five soil series within three soil families. Each soil family has one site at which soil properties (e.g., saturated hydraulic conductivity) are measured. In (b) the measured soil properties are assumed to represent the soil series from which they were sampled and are then extrapolated to other soil series from the same soil family where no measurements were made.
Each of the near-surface FCS simulations represented a 1 km2 area and required estimates of four soil properties (changing with depth): (i) soil-water content at the wilting point, (ii) soil-water content at field capacity, (iii) fraction of soil organic carbon, and (iv) bulk density. The FCS soil database was developed by averaging individual properties from the soil orders covering at least one-third of any 1-km2 element. Records of changing crop cover were used (as a surrogate) to approximate multiple and variable DBCP applications in the FCS area. DBCP applications were estimated from the label-recommended rates for a specific crop weighted by the fractional area of an element containing that particular crop at a given time. With the upscaled soil and crop information, DBCP-concentration profiles were estimated via PRZM-2 (Mullins et al., 1993) simulations. The year-end mosaics of water-table concentrations indicated that DBCP had leached to groundwater (Loague et al., 1998a). The FCS upscaling approach was limited by averaging both multiple soil orders and different application rates. Soutter and Loague (2000) critically examined the FCS water-table loading concentrations by comparison with new scenarios developed from simulations that did not employ the same upscaling. Figure 25.11 is a schematic illustration of the steps used by Soutter and Loague (2000) for simulating the worst-case DBCP water-table loading concentration scenarios without upscaling. The Soutter and Loague (2000) results indicated that (i) the areas most sensitive to upscaling were small relative to the total study area, (ii) the new concentration estimates were within the range of concentrations reported by Loague et al. (1998a), and (iii) the impacts from upscaling soil information exceeded the impacts from upscaling crop information. In as much as the Soutter and Loague (2000) study demonstrated that a somewhat coarse grid may be suitable for certain locations, thoughtful planning for variations in the grid size should help to target where upscaling is a potential problem for future regional-scale NPS simulation efforts. There are two recently reported efforts related to the FCS. First, Stewart and Loague (2003, 2004) reported on the development (and San Joaquin Valley testing) of a type transfer function approach for regional-scale NPS groundwater vulnerability assessments. Second, Loague and Soutter (2006) reported
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Step 1. Deconstruct the upscaled information from Loague et al. (1998a) into the unique single soil/single crop pairs.
Step 1. Simulate DBCP water-table loading concentrations with PRZM-2 for each single soil/single crop pair from Step 1.
PRZM-2
Upscaled inputs
Single Soil/Single Crop Pairs Mollisols
Citrus
Vertisols
Peaches
0.1 Compare 0.0 1960
1994
Loague et al. (1998a)
DBCP (µg/L)
DBCP (µg/L)
PRZM-2
0.1
DBCP (µg/L)
0.1
0.0 0.1
0.0 1960
1994
1960
1994
Step 3. Combine the Step 2 results to contruct new DBCP water-table loading concentration scenarios.
0.0 1960 1994 Worst Case
FIGURE 25.11 Schematic illustration (for a single 1 km2 element) of the three steps used for simulating the worstcase DBCP water-table loading concentration scenarios without upscaling for comparison with the DBCP water-table loading concentration scenario with upscaling from the original Fresno case study. (Soutter, L.A. and Loague, K., Journal of Environmental Quality, 29, 1794, 2000.)
on the cause for small-scale high-concentration DBCP hotspots within regional-scale (San Joaquin Valley like) groundwater plumes.
25.5 Epilogue First and foremost, scale does matter in the earth sciences. For example, agricultural engineers, biometeorologists, climatologists, ecologists, geomorphologists, hydrologists, hydrogeologists, petroleum engineers, and soil physicists who attempt to understand process-based hydrologic response at the surface, in near surface, and within the saturated subsurface (for applications such as climate change, flooding, landscape evolution, surface and groundwater contamination) are all faced with scale-related problems. Relative to process-based simulation of hydrologic response, computers, and to a lesser extent theory, are not the delimiters they were just a few decades ago. However, insufficient data remains a major obstacle in hydrologic modeling. For example, it is unlikely that anytime soon there will be enough information available to rigorously quantify the impacts of small-scale preferential flow in the unsaturated and saturated subsurface flow at regional scales. Bloschl (2001b) points out that Maybe, instead of trying to capture everything when upscaling we should be developing methods to identify dominant processes that control hydrological response in different environments and at different scales, and then develop models to focus on these dominant processes, a notion we might call the ‘Dominant Processes Concept’ (DPC). Bredehoeft (2005) describes the conceptualization problem as the thorniest issue in modeling today and suggests that the best tack (today) is to consider alternative scenarios, rejecting the ones whose
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estimates are unacceptable when compared to observed information. Bredehoeft (2005), faced with the problem of conceptualization (which is obviously scale related), answers of course to the question of whether hydrogeologists should continue to model. For example, deterministic-conceptual simulation facilitates (i) concept development, (ii) hypothesis testing, (iii) evaluation of existing (and future) data sets, (iv) design of new field experiments, (v) creation of synthetic data sets, (vi) hosting of Monte-Carlo experiments, (vii) driving physics-based solute transport and landscape evolution models, and (viii) the development and testing of simpler models (Loague and VanderKwaak, 2004). The measure and model approach, pioneered by Robert E. Horton (Beven, 2004a, 2004b), is without question the best protocol in hydrology. Heeding the call for cooperative work between the Cains and Ables of hydrology (Dunne, 1983) is critical in the future if progress is to be made in wrestling the scale behemoth closer to the ground. The various calls for detailed long-duration field monitoring programs at selected experimental locations (e.g., Dunne, 1998; Entekhabi et al., 1999) are renewed here.
Glossary Conceptual model A model is conceptual if their functional form is derived from consideration of physical processes. Deterministic model A model is deterministic if all the variables are (viewed as) free from random variations. Dispersion The spread of solute due to heterogeneities in the pore sizes and shapes (mechanical dispersion) and heterogeneities in the aquifer (macrodispersion). Empirical model A model is empirical if their functional form is not derived from consideration of physical processes. Equifinality Refers to more than one parameter set (for deterministic-conceptual simulation) providing an equally good representation of overall hydrologic response. Geographic information system An organized collection of computer hardware, software, and geographic data, to efficiently capture, store, update, manipulate, analyze, and display geographically reference information. Geostatistics A method of estimation for spatial variables, based upon the theory of random functions. Heterogeneity The occurrence of variations in the value of a field property at different points in space. Kriging Denotes a geostatistical method of interpolation or averaging. Model A representation of a real system or process. A mathematical model is a set of equations (with variables, constants, and coefficients) that represents relevant processes. Non-point source pollution Contaminants entering the environment over an extensive area, which are difficult (at best) or impossible to trace to a specific location and have the potential for maintaining a relatively long active presence on entire ecosystems. Upscaling Representing the heterogeneous domain for modeling purposes through elements larger than the scales of heterogeneity but not large enough to warrant the use of effective properties. The effects of subelement heterogeneity are represented using coefficients that depend on the element size. Pedotransfer function Transfer function that use particle-size distribution, bulk density, or soil organic-carbon content to yield soil-water retention or unsaturated hydraulic conductivity functions. Preferential flow Local subsurface pathways, such as structural voids or biological channels, which can carry water at velocities much greater than those of the surrounding matrix. Representative elementary area The scale at which a statistical treatment of spatial variability can replace a deterministic description, or where small-scale complexity gives way to larger scale simplicity.
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Representative elementary volume The exact size is not determined, but it is assumed that the size is much larger than the pore scale and much smaller than the scale of the porous medium. Scale of observation Window in space or time through which the environment or some property of the environment is viewed or measured. Stochastic model A model is stochastic if any of the variables are described by a probability distribution. Water balance An accounting for the inflows and outflows for a fluid control volume.
Acknowledgments We are very grateful to Professor Gunter Bloschl for generously sharing his in press papers/book on scale issues. We also thank Scott Tyler and Stephen Wheatcraft for the use of the photos in Figure 25.3 and Chris Heppner for his help in preparing Figure 25.9.
References Anderson, M.P., Characterization of geological heterogeneity, in Subsurface Flow and Transport: A Stochastic Approach, Dagan, G. and Neuman, S.P., (eds.), Cambridge University Press, Cambridge, United Kingdom, 1997, chap. 1. Bardossy, A., Stehlik, J., and Caspary, H.J., Automated objective classification of daily circulation patterns for precipitation and temperature downscaling based on optimized fuzzy rules, Climate Research, 23, 11, 2002. Beven, K., Prophecy, reality and uncertainty in distributed hydrological modeling, Advances in Water Resources, 16, 41, 1993. Beven, K.J., Rainfall-Runoff Modelling: The Primer, John Wiley and Sons, Chichester, England, 2000. Beven, K., On landscape space to model space mapping, Hydrological Processes, 15, 323, 2001. Beven, K., Infiltration excess at the Horton hydrology laboratory (or not?), Journal of Hydrology, 293, 219, 2004a. Beven, K. Robert E., Horton’s perceptual model of infiltration processes, Hydrological Processes, 18, 3447, 2004b. Beven, K., A manifesto for the equifinality thesis, Journal of Hydrology, 320, 18, 2006. Bierkens, F.P., Finke, P.A., and de Willigen, P., Upscaling and Downscaling Methods for Environmental Research, Kluwer Academic Publishers, Dordrecht, the Netherlands, 2000. Biot, M.A., General theory of three-dimensional consolidation, Journal of Physics, 12, 155, 1941. Bishop, T.F.A., McBratney, A.B., and Laslett, G.M., Modelling soil attribute depth functions with equal-area quadratic smoothing splines, Geoderma, 91, 27, 1999. Bloschl, G., Scaling issues in snow hydrology, Hydrological Processes, 13, 2149, 2001a. Bloschl, G., Scaling in hydrology, Hydrological Processes, 15, 709, 2001b. Bloschl, G., Statistical upscaling and downscaling in hydrology, in Encyclopedia of Hydrological Sciences (Part 1. Theory, Organization and Scale), Anderson, M., (ed.), John Wiley and Sons, Chichester, England, pp. 135–154, 2005. Bloschl, G. and Grayson, R., Spatial observations and interpolation, in Spatial Patterns in Catchment Hydrology: Observations and Modeling, Grayson, R. and Bloschl, G., (eds.), Cambridge University Press, Cambridge, United Kingdom, 2000, chap. 2. Bloschl, G. and Sivapalan, M., Scale issues in hydrological modelling — a review, Hydrological Processes, 9, 251, 1995. Bloschl, G., Sivapalan, M., Gupta, V., and Beven, K., Preface to the special section on scale problems in hydrology, Water Resources Research, 33, 2881, 1997. Buckingham, E., Studies on the movement of soil moisture, Bulletin 38, U.S. Department of Agriculture Bureau of Soils, Washington D.C., 1907.
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Burrough, P.A. and McDonnell, R.A., Principles of Geographical Information Systems, Oxford University Press, New York, 1998. Bredehoeft, J., The conceptualization model problem — surprise, Hydrogeology Journal, 13, 37, 2005. Caers, J., History matching under training-image-based geological model constraints, Society of Petroleum Engineers Journal, 8, 218, 2003. Christie, M.A., Upscaling for reservoir simulation, Journal of Petroleum Technology, 48, 1004, 1996. Chu, L.F., Schatzinger, R.A., and Tham, M.K., Application of wavelet analysis to upscaling of rock properties, SPE Reservoir Evaluation and Engineering, 1, 75, 1998. Church, M. and Mark, D.M., On size and scale in geomorphology, Progress in Physical Geography, 4, 342, 1980. Clothier, B.E., Rapid and far-reaching transport through structured soils, Hydrological Processes, 16, 1321, 2002. Corwin, D.L. and Loague, K., Multidisciplinary approach for assessing subsurface non-point source pollution, in Soil-Water-Solute Process Characterization: An Integrated Approach, Alvarez-Benedi, J. and R. Munoz-Carpena, R., (eds.), CRC Press, Boca Raton, FL, 2005, chap. 1. Corwin, D.L. and Plant, R.E., Applications of apparent soil electrical conductivity in precision agriculture, Computers and Electronics in Agriculture, 46, 1, 2005. Corwin, D.L., Loague, K., and Ellsworth, T.R., (eds.), Assessment of Non-Point Source Pollution in the Vadose Zone, Geophysical Monograph 108, American Geophysical Union Press, Washington, D.C., 1999. Cushman, J.H., On measurement, scale, and scaling, Water Resources Research, 22, 129, 1986. Cushman, J.H., (ed.), Dynamics of Fluids in Hierarchical Porous Media, Academic Press, San Diego, CA, 1990. Cushman, J.H., Bennethum, L.S., and Ju, B.H., A primer on upscaling tools for porous media, Advances in Water Resources, 25, 1043, 2002. Darcy, H., Les fontaines publiques de la ville de Dijon, Victor Dalmont, Paris, France, 1856. Davis, S.N., Porosity and permeability of natural materials, in Flow Through Porous Media, DeWiest, R.J.M., (ed.) Academic Press, New York, 1969, chap. 2. Day-Lewis, F.D., Lane, J.W., and Gorelick, S.M., Combined interpretation of radar, hydraulic, and tracer data from a fractured-rock aquifer near Mirror Lake, New Hampshire, USA, Hydrogeology Journal, 14, 1, 2006. de Boer, D.H., Hierarchies and spatial scale in process geomorphology: A review, Geomorphology, 4, 303, 1992. de Marsily, Gh., Delay, F., Goncalves, Ph., Teles, V., and Violette, S., Dealing with spatial heterogeneity, Hydrogeology Journal, 161, 2005. Desbarats, A.J., Numerical estimation of effective permeability in san-shale sequences, Water Resources Research, 23, 273, 1987. Deutsch, C.V. and Journel, A.G., GSLIB: Geostatistical Software Library and User’s Guide, 2nd ed., Oxford University Press, New York, 1998. Dodds, P.S. and Rothman, D.H., Scaling, universality, and geomorphology, Annual Reviews of Earth and Planetary Sciences, 28, 571, 2000. Dolman, A.J. and Blyth, E.A., Patch scale aggregation of heterogeneous land surface cover for mesoscale meteorological model, Journal of Hydrology, 190, 253, 1997. Dooge, J.C.I., Scale problems in hydrology, Fifth Memorial Chester C. Kisiel Lecture, University of Arizona, Tucson, 1989. Dunne, T., Relation of field studies and modeling in the prediction of storm runoff, Journal of Hydrology, 65, 25, 1983. Dunne, T., Wolman lecture: Hydrologic science . . . in landscapes . . . on a planet . . . in the future, in Hydrologic Sciences: Taking Stock and Looking Ahead, National Academy Press, Washington, D.C., 1998, chap. 1.
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Entekhabi, D., Asrar, G.R., Betts, A.K., Beven, K.J., Bras, R.L., Duffy, C.J., Dunne, T., Koster, R.D., Lettenmaier, D.P., McLaughlin, D.B., Shuttleworth, W.J., van Genuchten, M.T., Wei, M.-Y., and Wood, E.F., An agenda for land surface hydrology research and a call for the second international hydrological decade, Bulletin of the American Meteorological Society, 80, 2043, 1999. Farmer, C.L., Upscaling: A review, International Journal for Numerical Methods in Fluids, 40, 63, 2002. Feddes, R.A., (ed.), Space and Time Scale Variability and Interdependencies in Hydrological Processes, Cambridge University Press, Cambridge, United Kingdom, 1995. Freeze, R.A., The mechanism of natural groundwater recharge and discharge: 1. One-dimensional, vertical unsteady, unsaturated flow above a recharging or discharging groundwater flow system, Water Resources Research, 5, 153, 1969. Freeze, R.A., Three-dimensional, transient, saturated-unsaturated flow in a groundwater basin, Water Resources Research, 7, 347, 1971. Freeze, R.A., A stochastic-conceptual analysis of one-dimensional groundwater flow in non-uniform homogeneous media, Water Resources Research, 11, 725, 1975. Freeze, R.A., A stochastic-conceptual analysis of rainfall-runoff processes on a hillslope, Water Resources Research, 16, 391, 1980. Freeze, R.A. and Cherry, J.A., Groundwater, Prentice-Hall, Englewood Cliffs, NJ, 1979. Garven, G., Continental scale groundwater flow and geologic processes, Annual Reviews of Earth and Planetary Sciences, 23, 89, 1995. Gelhar, L.W., Stochastic analysis of phreatic aquifers, Water Resources Research, 10, 539, 1974. Gelhar, L.W., Stochastic subsurface hydrology from theory to applications, Water Resources Research, 22, 135S, 1986. Gelhar, L.W., Welty, C., and Rehfeldt, K.R., A critical review of data on field-scale dispersion in aquifers, Water Resources Research, 28, 1955, 1992. Grayson, R. and Bloschl, G., (eds.), Spatial Patterns in Catchment Hydrology: Observations and Modelling, Cambridge University Press, Cambridge, United Kingdom, 2000. Grayson, R.B., Bloschl, G., Western, A.W., and McMahon, T.A., Advances in the use of observed spatial patterns of catchment hydrologic response, Advances in Water Resources, 25, 1313, 2002. Gupta, S.K., Cole, C.R., and Pinder, G.F., A finite-element three-dimensional groundwater (FE3DGW) model for a multiaquifer system, Water Resources Research, 20, 553, 1984. Gupta, V.K., Rodriguez-Iturbe, I., and Wood, E.F., (eds.), Scale Problems in Hydrology: Runoff Generation and Basin Response, D. Reidel Publishing Company, Dordrecht, Holland, 1986. Harbaugh, A.W. and McDonald, M.G., Programmer’s documentation for MODFLOW-96, an update to the U.S. Geological Survey modular finite-difference ground-water flow model, U.S. Geological Survey Open-File Report 96-486, U.S. Geological Survey, Federal Center, Denver, CO. 1996. Hillel, D. and Elrick, D.E., (eds.), Scaling in Soil Physics: Principles and Applications, Soil Science Society of America, Madison, WI, 1990. Heppner, C.S. and Loague, K., Hydrologic response and sediment transport for the R-5 catchment: 1. Analysis of long-term observed data, Earth Surface Processes and Landforms, 2006 (in review). Heppner, C.S., Loague, K., and VanderKwaak, J.E., Hydrologic response and sediment transport for the R-5 catchment: 2. Long-term simulations with InHM, Earth Surface Processes and Landforms, 2006 (in review). Hopmans, J.W., Nielsen, D.R., and Bristow, K.L., How useful are small-scale soil hydraulic property measurements for large-scale vadose zone modeling? in Environmental Mechanics: Water, Mass, Energy Transfer in the Biosphere, Raats, P.A., Smiles, D., and Warrick, A.W., (eds.), Geophysical Monograph 129, p. 247, American Geophysical Union Press, Washington, D.C., 2002. Horton, R.E., Erosional development of streams and their drainage basins: Hydrophysical approach to quantitative morphology, Bulletin of the Geological Society of America, 56, 275, 1945. Hubbert, M.K., The theory of groundwater motion, Journal of Geology, 48, 785, 1940. Indelman, I. and Dagan, G., Upscaling of permeability of anisotropic heterogeneous formations, 1: The general framework, Water Resources Research, 29, 917, 1993a.
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Indelman, I. and Dagan, G., Upscaling of permeability of anisotropic heterogeneous formations, 2: General structure and small perturbation analysis, Water Resources Research, 29, 925, 1993b. James, B. and Gorelick, S.M., When enough is enough: The worth of monitoring data in aquifer remediation design, Water Resources Research, 30, 3499, 1994. Kalma, J.D. and Sivapalan, M., (eds.) Scale Issues in Hydrological Modelling, John Wiley and Sons, Chichester, England, 1995. Klemes, V., Conceptualization and scale in hydrology, Journal of Hydrology, 65, 1, 1983. Koltermann, C.E. and Gorelick, S.M., Heterogeneity in sedimentary deposits: A review of structureimitating process-imitating and descriptive approaches, Water Resources Research, 32, 2617, 1996. Lin, H., Hydropedology: Bridging disciplines, scales, and data, Vadose Zone Journal, 2, 1, 2003. Loague, K., R-5 revisited: 2. Reevaluation of a quasi-physically based rainfall-runoff model with supplemental information, Water Resources Research, 26, 973, 1990. Loague, K. and Gander, G.A., R-5 revisited: 1. Spatial variability of infiltration on a small rangeland catchment, Water Resources Research, 26, 957, 1990. Loague, K. and Kyriakidis, P.C., Spatial and temporal variability in the R-5 infiltration data set: Deja vu and rainfall-runoff simulations, Water Resources Research, 33, 2883, 1997. Loague, K. and Soutter, L.A., Desperately seeking a cause for hotspots in regional-scale groundwater plumes resulting from non-point source pesticide applications, Vadose Zone Journal, 5, 204, 2006. Loague, K. and VanderKwaak, J.E., Simulating hydrologic response for the R-5 catchment: Comparison of two models and the impact of the roads, Hydrological Processes 16, 1015, 2002. Loague, K. and VanderKwaak, J.E., Physics-based hydrologic response simulation: Platinum bridge, 1958 Edsel, or useful tool, Hydrological Processes 18, 2949, 2004. Loague, K.M., Yost, R.S., Green, R.E., and Liang, T.C., Uncertainty in a pesticide leaching assessment for Hawaii, Journal of Contaminant Hydrology, 4, 139, 1989. Loague, K., Lloyd, D., Nguyen, A., Davis, S.N., and Abrams, R.H., A case study simulation of DBCP groundwater contamination in Fresno County, California: 1. Leaching through the unsaturated subsurface, Journal of Contaminant Hydrology, 29, 109, 1998a. Loague, K., Abrams, R.H., Davis, S.N., Nguyen, A., and Stewart, I.T., A case study simulation of DBCP groundwater contamination in Fresno County, California: 2. Transport in the saturated subsurface, Journal of Contaminant Hydrology, 29, 137, 1998b. Loague, K., Gander, G.A., VanderKwaak, J.E., Abrams, R.H., and Kyriakidis, P.C., Simulating hydrologic response for the R-5 catchment: A never ending story, Floodplain Management, 1, 57, 2000. Loague, K., Heppner, C.S., Abrams, R.H., VanderKwaak, J.E., Carr, A.E., and Ebel, B.A., Further testing of the Integrated Hydrology Model (InHM): Event-based simulations for a small rangeland catchment located near Chickasha, Oklahoma, Hydrological Processes, 19, 1373, 2005. Longley, P.A., Goodchild, M.F., Maguire, D.J., and Rhind, D.W., Geographic Information Systems and Science, 2nd ed., John Wiley & Sons, New York, 2005. Mayer, S., Ellsworth, T.R., Corwin, D.L., and Loague, K., Estimating transport parameters for nonpoint pollution transport models, in Assessment of Non-Point Source Pollution in the Vadose Zone, Corwin, D.L., Loague, K., and Ellsworth, T.R., (eds.), Geophysical Monograph 108, p. 119, American Geophysical Union Press, Washington, D.C., 1999. Miller, E.E. and Miller R.D., Physical theory for capillary flow phenomena, Journal of Applied Physics, 4, 324, 1956. Montgomery, D.R. and Foufoula-Georgiou, E., Channel network source representation using digital elevation models, Water Resources Research, 29, 3925, 1993. Mullins, J.A., Carsel, R.F., Scarbough, J.E., and Ivery, A.M., PRZM-2, a model for predicting pesticide fate in the crop root and unsaturated soil zones: Users manual for release 2, EPA-600/R-93/046, U.S. Environmental Protection Agency Environmental Research Laboratory, Athens, GA, 1993. Neuman, S.P. and Di Federico, V., Multifaceted nature of hydrogeologic scaling and its interpretation, Reviews of Geophysics, 41, 4–1, 2003.
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Nielsen, D.R., Biggar, J.W., and Em, K.T., Spatial variability of field-measured soil–water properties, Hilgardia, 42, 215, 1973. Noetinger, B., Artus, V., and Zargar, G., The future of stochastic and upscaling methods in hydrology, Hydrogeology Journal, 13, 184, 2005. Pachepsky, Y., Radcliffe, D.E., and Selim, H.M., (eds.), Scaling Methods in Soil Physics, CRC Press, Boca Raton, FL, 2003. Penman, H.L., Natural evaporation from open water, bare soil, and grass, Proceedings of the Royal Society London, A, 193, 120, 1948. Philip, J.R., Field heterogeneity: Some basic issues, Water Resources Research, 16, 443, 1980. Pilgrim, D.H., Some problems in transferring hydrological relationships between small and large drainage basins and between regions, Journal of Hydrology, 65, 49, 1983. Prudhomme, C., Reynard, N., and Crooks, S., Downscaling of global climate models for flood frequency analysis: Where are we now? Hydrological Processes, 16, 1137, 2002. Rawls, W.J., Gish, T.J., and Brakensiek, D.L., Estimating soil water retention from soil physical properties and characteristics, Advances in Soil Science, 16, 213, 1991. Renschler, C.S., Strategies for implementing natural resource management tools — A geographical information science perspective on water and sediment balance assessment at different scales, PhD dissertation, University of Bonn, Germany, 2000. Richards, L.A., Capillary conduction of liquids through porous mediums, Physics, 1, 318, 1931. Robinson, J.S. and Sivapalan, M., Temporal scales and hydrological regimes: Implications for flood frequency scaling, Water Resources Research, 33, 2981, 1997. Rodriguez-Iturbe, I., Scale of fluctuation of rainfall models, Water Resources Research, 22, 15S, 1986. Rodriguez-Iturbe, I. and Gupta, V.K., Introduction, Journal of Hydrology, 65, vi, 1983. Rodriguez-Iturbe, I. and Rinaldo, A., Fractal River Basins: Chance and Self-Organization, Cambridge University Press, Cambridge, United Kingdom, 1997. Rubin, Y and Gomez-Hernadez, J.J., A stochastic approach to the problem of upscaling of conductivity in disordered media: Theory and unconditional numerical simulations, Water Resources Research, 26, 691, 1990. Sanchez-Villa, X., Girardi, J.P., and Carrera, J.A., synthesis of approaches to upscaling of hydraulic conductivities, Water Resources Research, 31, 867, 1995. Savenije, H.H.G., Equifinality, a blessing in disguise? Hydrological Processes, 15, 2835, 2001. Schmid, H.P., Footprint modeling for vegetation atmosphere exchange studies: A review and perspective, Agricultural and Forest Meteorology, 113, 159, 2002. Segol, G., Classic Groundwater Simulations: Proving and Improving Numerical Models, Prentice Hall, Englewood Cliffs, NJ, 1994. Shaman, J., Stieglitz, M., and Burns, D., Are big basins just the sum of small catchments? Hydrological Processes, 18, 3195, 2004. Shuttleworth, W.J., Yang, Z.-L., and Arain, M.A., Aggregation rules for surface parameters in global models, Hydrology and Earth System Sciences, 1, 217, 1997. Sivapalan, M., Process complexity at hillslope scale, process simplicity at the watershed scale: Is there a connection? Hydrological Processes, 17, 1037, 2003. Sivapalan, M. and Kalma, J.D., Scale problems in hydrology: Contributions of the Robertson workshop, Hydrological Processes, 9, 3, 1995. Sivapalan, M., Zhang, L., Vertessy, R., and Bloschl, G., Preface: Downward approach to hydrological prediction, Hydrological Processes, 17, 2099, 2003a. Sivapalan, M., Bloschl, G., Zhang, L., and Vertessy, R., Downward approach to hydrological prediction, Hydrological Processes, 17, 2101, 2003b. Sivapalan, M., Grayson, R., and Woods, R., Preface: Scale and scaling in hydrology, Hydrological Processes, 18, 1369, 2004. Skoien, J.O. and Bloschl, G., Sampling scale effects in random fields and implications for environmental monitoring, Environmental Monitoring and Assessment, 114, 521, 2006.
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Skoien, J.O., Bloschl, G., and Western, A.W., Characteristic space scales and timescales in hydrology, Water Resources Research, 39, doi:10.1029/2002WR001736, 2003. Soil Survey Staff, Soil Taxonomy: A Basic System of Soil Classification for Making and Interpreting Soil Surveys, 2nd ed., Agriculture Handbook Number 436, U.S. Department of Agriculture, Natural Resources Conservation Service, U.S. Government Printing Office, Washington, D.C., 1999. Soutter, L.A. and Loague, K., Revisiting the Fresno DBCP case study simulations: The impact of upscaling, Journal of Environmental Quality, 29, 1794, 2000. Sposito, G., (ed.) Scale Dependence and Scale Invariance in Hydrology, Cambridge University Press, Cambridge, United Kingdom, 1998. Stewart, I.T. and Loague, K., Development of type transfer functions for regional-scale nonpoint source groundwater vulnerability assessments, Water Resources Research, 39, doi:10.1029/2003WR002269, 2003. Stewart, I.T. and Loague, K., Assessing ground water vulnerability with the type transfer function model in the San Joaquin valley, California, Journal of Environmental Quality, 33, 1487, 2004. Stewart, J.B., Engman, E.T., Feddes, R.A., and Kerr, Y., Scaling Up in Hydrology Using Remote Sensing, John Wiley and Sons, Chichester, England, 1996. Terzaghi, K., Erdbaumechanic auf Bodenphysikalischer Grundlage, Franz Deuticke, Vienna, 1925. Tsegaye, T.D., Crosson, W.L., Laymon, C.A., Schamschula, M.P., and Johnson, A.B., Application of a neural network-based spatial disaggregation scheme for addressing scaling of soil moisture, in Scaling Methods in Soil Physics, Pachepsky, Y., Radcliffe, D.E., and Selim, H.M., (eds.), CRC Press, Boca Raton, FL, 2003, chap. 15. Tyler, S.W. and Wheatcraft, S.W., The consequences of fractal scaling in heterogeneous soil and porous media, in Scaling in Soil Physics: Principles and Applications, Hillel, D. and Elrick, D.E., (eds.), Soil Science Society of America, Madison, WI, 1990, chap. 8. VanderKwaak, J.E., Numerical simulation of flow and chemical transport in integrated surface-subsurface hydrologic systems, PhD dissertation, University of Waterloo, Ontario, Canada, 1999. VanderKwaak, J.E. and Loague, K., Hydrologic-response simulations for the R-5 catchment with a comprehensive physics-based model, Water Resources Research, 37, 999, 2001. Wagenet, R.J. and Hutson, J.L., Scale-dependency of solute transport modeling/GIS applications, Journal of Environmental Quality, 25, 499, 1996. Webster, R. and Oliver, M.A., Geostatistics for Environmental Sciences, John Wiley & Sons, Chichester, England, 2001. Western, A.W., Grayson, R.B., and Bloschl, G., Scaling of soil moisture: A hydrologic perspective, Annual Reviews of Earth and Planetary Sciences, 30, 149, 2002. Wilby, R.L., Wigley, M.L., Conway, D., Jones, P.D., Hewitson, B.C., Main, J., and Wilks, D.S., Statistical downscaling of general circulation model output: A comparison of methods, Water Resources Research, 34, 2995, 1998. Wood, A.W., Leung, R.R., Sridhar, V., and Lettenmaier, D.P., Hydrologic implications of dynamical and statistical approaches to downscaling climate model outputs, Climate Change, 62, 189, 2004. Wood, E.F., Sivapalan, M., and Beven, K., Similarity and scale in catchment storm response, Reviews in Geophysics, 28, 1, 1990. Woolhiser, D.A. and Goodrich, D.C., Effects of storm rainfall intensity patterns on surface runoff, Journal of Hydrology, 102, 335, 1988. Zheng, C. and Gorelick, S.M., Analysis of solute transport in flow fields influenced by preferential flowpaths at the decimeter scale, Ground Water, 41, 142, 2003. Zheng, C. and Wang P.P., MT3DMS: A Modular Three-Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems, Release DoD_3.00A, Waterways Experiment Station, U.S. Army Corps of Engineers, Vicksburg, MS, 1998.
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26 Accounting for Aquifer Heterogeneity in Solute Transport Modeling: A Case Study from the Macrodispersion Experiment (MADE) Site in Columbus, Mississippi 26.1 26.2 26.3 26.4
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Site Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Natural-Gradient Tracer Tests . . . . . . . . . . . . . . . . . . . . . . . . . . Modeling of the MADE-2 Tritium Tracer Test. . . . . . . . .
26-2 26-2 26-4 26-6
Objectives and Approaches • Model Setup and Boundary Conditions • Assignment of Hydraulic and Transport Properties
26.5 Analysis of Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 26-10 Advection-Dispersion Model • Dual-Domain Mass Transfer Model • Sensitivity Analysis
Chunmiao Zheng University of Alabama
26.6 Summary and Concluding Remarks . . . . . . . . . . . . . . . . . . . Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26-13 26-14 26-14 26-15 26-17
26-1
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26.1 Introduction Field studies at well-instrumented sites have played a preeminent role in our efforts to better understand and characterize solute transport processes in geologic media. In particular, several field tracer tests conducted at well-known sites such as those in Borden, Canada (MacKay et al., 1986), Mobile, Alabama (Molz et al., 1986), Twin Lake, Minnesota (Killey and Moltyaner, 1988), Cape Cod, Massachusetts (LeBlanc et al., 1991) and Columbus, Mississippi (Boggs et al., 1992) have provided new insights and extensive data sets for development and testing of transport theories and mathematical models. The case study presented in this chapter concerns the natural-gradient tracer tests conducted at the Columbus Air Force Base in Mississippi, southeastern United States, more commonly known as the Macrodispersion Experiment (MADE) site. Since the early 1990s, the data collected at the MADE site has been used extensively by numerous researchers around the world to gain insights into contaminant transport processes in highly heterogeneous aquifers. It has also served as a catalyst for the development of new and improved theories and computer models that enable more accurate description and prediction of contaminant transport and remediation. Recent studies related to the MADE site include Adams and Gelhar (1992), Boggs and Adams (1992), Boggs et al. (1992), Rehfeldt et al. (1992), MacIntyre et al. (1993), Eggleston and Rojstaczer (1998), Berkowitz and Scher (1998), Zheng and Jiao (1998), Harvey and Gorelick (2000), Feehley et al. (2000), Stapleton et al. (2000), Benson et al. (2001), Brauner and Widdowson (2001), Julian et al. (2001), Lu et al. (2002), Zheng and Gorelick (2003), Liu et al. (2004), Barlebo et al. (2004), Bowling et al. (2005), and Molz et al. (2006). In this chapter, we will first describe the hydrogeologic setting of the MADE site and the details of the three natural-gradient tracer tests that have been conducted at the MADE site since 1986. We will then discuss the application of two modeling approaches, the classical advection-dispersion model and the alternative dual-domain (dual-porosity) mass transfer model, to interpret and analyze the tracer test data. The model application will elucidate the difficulties encountered by the classical advection-dispersion model in characterizing solute transport in an extremely heterogeneous aquifer, and reveal to what extent the dual-domain mass transfer model can be used effectively to lessen and overcome such difficulties. Finally, we will evaluate the sensitivity of the simulation results to key dual-domain model parameters and comment on the applicability of the dual-domain model under field conditions.
26.2 Site Description
Buttahatchee river
5 I-4
Tombigbee river
Figure 26.1 shows the location of the MADE site located inside the Columbus Air Force Base in Mississippi, Southeastern U.S. The shallow unconfined aquifer that immediately underlies the site consists of alluvial
MADE site Columbus air force base Quarry
N 1 km
FIGURE 26.1 Location of the MADE site in Columbus, MS.
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terrace deposits with an average thickness of 11 m. Pleistocene river deposits associated with nearby Tombigbee and Buttahachee Rivers may account for the heterogeneity observed in the field. The heterogeneous aquifer is composed of poorly sorted to well-sorted sandy gravel and gravelly sand with significant amounts of silt and clay. Sediments are generally unconsolidated. Soil facies occur as irregular lenses and layers having horizontal dimensions ranging up to 8 m and vertical dimensions of less than 1 m. Marine sediments, which belong to the Eutaw Formation and consist of clay, silts, and fine-grained sands, form an aquitard beneath the alluvial aquifer. Figure 26.2 shows a geologic facies model for the MADE site based on geophysical and sedimentological investigations (Bowling et al., 2005). A more detailed description of the site condition is provided in Boggs et al. (1990, 1992). The spatial distribution of horizontal hydraulic conductivity (K ) at the test site was first determined on the basis of 2187 measurements obtained from the borehole flowmeter tests conducted in 58 fully penetrating wells by Rehfeldt et al. (1992). The locations of these flowmeter test wells are shown in Figure 26.3. The vertical spacing of K measurements within each flowmeter well was approximately
0 3 10
Depth (m)
MLS boundary
14 Silt and Clay fraction:
0–20%
Depostional unit:
Braided fluvial system
20–40%
40–60%
>60%
Fine Meandering grained fluvial sands system
Channel fill or Clay aquitard
FIGURE 26.2 Geologic facies model of the MADE site based on resistivity and GPR data. (Bowling, J.C., A.B. Rodriguez, D.L. Harry, and C. Zheng, Ground Water, 43:890–903, 2005.) Z Y X
Z axis (m)
Injection site
60 ler amp 200
el s ltilev
55
Mu
250
150 X
er met Flow 50
0
ax
is
(m
)
50
100
)
is (m
Y ax
0
FIGURE 26.3 Three-dimensional view of the monitoring network at the MADE site. Vertical lines consisting of closely spaced dots indicate the locations of flowmeter test wells. Circles indicate multilevel sampler (MLS) locations.
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15 cm. Details of the borehole flowmeter tests are described in Rehfeldt et al. (1992). More flowmeter test wells were added in subsequent studies, resulting in a cumulative total of 3925 measurements from 86 test wells (Boggs et al., 1995; Julian et al., 2001). The geometric mean of the 2187 measured horizontal K data is approximately 5 × 10−3 cm/s, but the variations in these data range from two to four orders of magnitude. The overall variance of the natural logarithm of horizontal hydraulic conductivity is 4.5 (Rehfeldt et al., 1992), which is significantly greater than that of any previously reported tracer test sites. For example, the reported variance of ln K is 0.29 for the Borden site (Sudicky, 1986), 0.26 for the Cape Cod site (LeBlanc et al., 1991), and 0.031 for the Twin Lake site (Killey and Moltyaner, 1988). The hydraulic head field at the experiment site was monitored with piezometers installed at the flowmeter wells. The general direction of groundwater movement was northward along the y axis of Figure 26.3. The hydraulic head field was subject to complex temporal and spatial variability, resulting from the heterogeneity in the hydraulic conductivity distribution and large seasonal fluctuations of the water table. The averaged hydraulic gradient across the test site was approximately 0.03 with a 20–30% variation in the saturated thickness of the aquifer (Boggs et al., 1992).
26.3 Natural-Gradient Tracer Tests Three natural-gradient tracer tests have been conducted at this site since 1986. In the first test (MADE-1) conducted between October 1986 to June 1988 (Boggs et al., 1990, 1992), a number of conservative tracers including bromide were injected into five source wells spaced 1 m apart in a linear array. Each well was screened between the elevations of 57.5 and 58.1 m above the mean sea level, or approximately halfway between the water table and the aquifer bottom. At the start of the test, approximately 10 m3 of solution containing a bromide concentration of 2500 mg/l was injected into the source wells at a uniform rate over 48.5 h. The tracer injection was so designed as to mimic a pulse release of tracers into the middle of the saturated aquifer zone with minimal disturbance to the natural flow field (Boggs et al., 1992). The migration of the bromide plume in three dimensions was monitored through a network of 258 multilevel samplers (MLS) (increased to 328 for subsequent studies) (see Figure 26.3). Each MLS was equipped with 20 to 30 sampling points spaced 0.38 m apart in the vertical dimension. The network used for the MADE-1 test consisted of approximately 6000 sampling points. The groundwater samples collected from MLS were analyzed using high-pressure liquid chromatography (HPLC). Eight sampling events were conducted over a total monitoring period of 20 months. Each sampling event was designed to capture a “snapshot” of the evolving 3-D bromide plume. Figure 26.4 shows a 3-D visualization of the 503-day snapshot of the bromide plume (Harvey and Gorelick, 2000). A 2-D contour map of vertically integrated concentrations is also shown beneath the 3-D rendering of the plume. The most noticeable aspect is the asymmetrical distribution of the plume along the general flow direction with the high-concentration region remaining close to the injection point (<20 m) and the low-concentration front spreading far down-gradient (>160 m) after 503 days. In the second test (MADE-2) conducted between June 1990 and September 1991 (Boggs et al., 1993; MacIntyre et al., 1993), a tritium tracer was injected into the aquifer for 48.5 h at a uniform rate of 3.3 l/min, using the same experimental setup established for the MADE-1 test. The injected fluid had a tritium concentration of 55,610 pCi/ml, representing a total injected mass (activity) of 0.5387 Ci. Five snapshots of the tracer plume were taken over a period of 15 months from the 328 MLS at over 6,000 sampling points. The tritium concentration present in field samples was measured with a liquid scintillation analyzer. Figure 26.5 shows the observed tritium plume snapshot of 328 days after the start of injection. Similar to the observed bromide plume for the MADE-1 test, the high-concentration region of the observed tritium plume stayed close to the injection point while the low-concentration front traveled far down-gradient. The location of the observed maximum concentration after 328 days (4721 pCi/ml) was within several meters of the injection point, while the leading plume edge as defined by the low concentration of 5 pCi/ml traveled more than 200 m from the injection point.
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IsoConcentration Surface of MADE-1 Bromide Plume (503 days After Injection) Bottom contour plot represents vertically integrated concentration
100 m
FIGURE 26.4 Observed MADE-1 bromide plume at 503 days after injection. (Harvey, C.F. and S.M. Gorelick, Water Resour. Res., 36:637–650, 2000.) Z Y
Z axis (m)
X
60 250
55
200 150
X
100 0 is (m )
ax
50 50
)
is (m
Y ax
0
Concentration (pCi/ml)
300 100 50 25 10 5
FIGURE 26.5 Observed MADE-2 tritium plume at 328 days after injection.
In the third test (MADE-3), also referred to as the Natural Attenuation Study or NATS, conducted between December 1995 and September 1997 (Boggs et al., 1995; Libelo et al., 1997; Stapleton et al., 2000; Julian et al., 2001), the injection well array was replaced by a source trench measuring approximately 14 m × 0.8 m × 1.7 m. The source trench was emplaced in the aquifer between the elevations of 58.6 and 60.3 m with 30 m3 of coarse sand coated with six hydrocarbon compounds and bromide. This setup was intended to approximate an instantaneous release for hydrocarbon and bromide tracers. A total of six snapshots of the plume were measured over 20 months. Figure 26.6 shows a 2-D contour map of the observed “peak” bromide concentrations 152 days after the source release; this map was constructed using the highest concentrations measured among multiple sampling elevations at each MLS location. As in the case of the bromide plume for MADE-1
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Bromide (ppm)
40
10
30
Y (m)
6
20
MLS 0.6
10 0.06
Source Trench
0 –10 –30
–20
–10
0 X (m)
10
20
FIGURE 26.6 Observed MADE-3 bromide plume at 152 days after trench source release. The 2D contour map is constructed from the peak concentrations at each MLS location.
and the tritium plume for MADE-2, the bromide plume for MADE-3 shows the presence of a high concentration region close to the source trench and a low concentration front spreading to far-field, truncated by the extent of the sampling. This indicates that the characteristics of the conservative tracer plumes at the MADE site is independent of the method used for introducing the source into the aquifer. The highly asymmetrical nature of the bromide and tritium plumes observed in the MADE-1, MADE-2, and MADE-3 experiments may be explained by the fact that the aquifer is extremely heterogeneous and the tracer source was located in a zone of relatively low hydraulic conductivity, thereby leading to the trapping of the tracer mass close to the source. The extensive spreading down-gradient may have been caused by the presence of small-scale preferential flow paths as discussed in subsequent sections.
26.4 Modeling of the MADE-2 Tritium Tracer Test 26.4.1 Objectives and Approaches The data sets from the three natural-gradient tracer tests at the MADE site, described in the preceding section, provided unprecedented opportunities to test and evaluate various theories and mathematical models of solute transport in highly heterogeneous aquifers. The case study presented in this chapter focuses on the modeling of the MADE-2 test, adopted from the work of Zheng and Jiao (1998) and Feehley et al. (2000). The primary objectives of the transport modeling in this case study are to (1) test the applicability of the classical advection-dispersion model (ADM) to represent solute transport processes in the presence of extreme aquifer heterogeneity, and (2) evaluate the usefulness of the dual-domain (dual-porosity) mass transfer model (DDMT) as an alternative to the classical ADM. The classical advection-dispersion transport equation for conservative tracers is (e.g., Bear, 1961; Zheng and Bennett, 2002),
θ
∂ ∂C = ∂t ∂xi
θDij
∂C ∂xj
−
∂ (qi C) + qs Cs ∂xi
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FIGURE 26.7 A newly exposed aquifer cross section near the MADE site indicating the existence of a decimeter-scale preferential flow path.
where C is the solute concentration, θ the porosity, t time, Dij the hydrodynamic dispersion coefficient (including mechanic dispersion and molecular diffusion), qi the Darcy flux, qs the rate of fluid sink/source, and Cs the concentration of the fluid sink/source. The classical advection-dispersion model, first introduced by Taylor (1953) and Bear (1961) among others, has been the basis of practical field-scale transport modeling since the early 1970s (e.g., Bredehoeft and Pinder, 1973; Anderson, 1979). A fundamental assumption embedded in Equation 26.1 is that the mechanical dispersion, caused by variations in seepage velocity due to aquifer heterogeneity, is analogous to molecular diffusion governed by Fick’s law. Under this assumption, the mechanical dispersivities can be estimated from the geostatistical properties of the hydraulic conductivity field (e.g., Gelhar and Axness, 1983; Dagan, 1989). For solute transport in relatively homogeneous aquifers, as at the Borden site (MacKay et al., 1986) or the Cape Cod site (LeBlanc et al., 1991), the classic ADM has been shown to be a good one (e.g., Sudicky, 1986). However, for solute transport in extremely heterogeneous aquifers, such as at the MADE site, the classical ADM may be grossly inadequate (e.g., Carrera, 1993; Harvey and Gorelick, 2000; LaBolle and Fogg, 2001). This inadequacy could be attributed to the inability of the classical ADM to account for solute transport along connected preferential pathways that may persist at scales smaller than those that can be practically represented in numerical flow and transport models (Zheng and Gorelick, 2003; Liu et al., 2004). An example of such a small-scale preferential flow path from an aquifer outcrop adjacent to the MADE site is illustrated in Figure 26.7. An alternative to the single-porosity advection-dispersion model is the dual-porosity or dual-domain mass transfer model, given below for conservative tracers (e.g., Coats and Smith, 1964; van Genutchen and Wierenga, 1976; Zheng and Bennett, 2002): θm
∂ ∂Cm ∂Cim + θim = ∂t ∂t ∂xi
θm Dij
∂Cm ∂xj
−
∂ (qi Cm ) + qs Cs ∂xi
∂Cim = β(Cm − Cim ) θim ∂t
(26.2)
where θm is the porosity of the “mobile” domain, or pore spaces filled with mobile water, θim the porosity of the “immobile” domain, or pore spaces filled with immobile water, β the mass transfer rate coefficient between the mobile and immobile domains, Cm the concentration in the mobile domain, and Cim the concentration in the immobile domain.
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The DDMT partitions transport into two domains: transport in the mobile domain is primarily by advection, while transport in the immobile domain is mostly by diffusion. The mobile and immobile domains are defined by two porosities: mobile (θm ) and immobile (θim ) porosities, with the total porosity θ = θm + θim . The connection between the zones of mobile and immobile fluids is governed by a firstorder mass transfer equation, with the transfer rate proportional to the concentration difference between the two zones multiplied by a coefficient of proportionality β. Other factors affecting mass transfer include sorption, measurement scale, fluid velocity, and characteristics of preferential flow paths (Griffioen et al., 1998; Haggerty et al., 2004; Gorelick et al., 2005). The larger the rate coefficient β, the faster mass transfer occurs between the mobile and immobile zones for a given concentration difference. As β approaches infinity, the connection is instantaneous, and the system acts like a single-porosity ADM with the porosity approaching total porosity. Conversely, as β approaches zero, the system behaves as a single-porosity ADM with the total porosity equal to θm . The mass transfer rate coefficient can be determined through laboratory and field procedures of Clothier et al. (1992), Jaynes et al. (1995), Hollenbeck et al. (1999), and Haggerty et al. (2001) or through trial-and-error model calibration (Feehley et al., 2000; Julian et al., 2001).
26.4.2 Model Setup and Boundary Conditions Zheng and Jiao (1998) applied the classical ADM; Feehley et al. (2000) applied both the classical ADM and alternative DDMT to simulate and analyze the MADE-2 tritium tracer test. The 3-D finite-difference model grid used by Feehley et al. (2000) consists of 55 columns, 153 rows, and 22 layers, covering a model domain of 110 m × 306 m × 11 m. The grid spacing is 2 m × 2 m in the horizontal direction and 0.5 m in the vertical direction. Specified-head boundaries along the north and south, and no-flow boundaries to the east and west, bound the model domain laterally. The Eutaw Formation acts as a no-flow boundary at the bottom and a uniform recharge rate is specified at the water table. Transport simulation was conducted using the mesh developed for the flow model. The boundary conditions for the transport model are zero-mass flux at all boundaries except at the northern boundary where dispersive flux is assumed to be zero and advective flux is determined by outflow rate and concentration. Only steady-state flow simulation was attempted using the MODFLOW code (McDonald and Harbaugh, 1988; Harbaugh et al., 2000) because the detailed data required for transient calibration (such as specific yield, storage coefficient, and time-dependent recharge distribution) were not available. Values along the specified-head boundaries were calibrated to achieve the best match between the calculated and observed heads at 48 piezometers. The calibration was done manually by minimizing the root mean of squared differences between the calculated and observed heads. More details of model development and calibration are provided in Zheng and Jiao (1998) and Feehley et al. (2000). As noted above, the tritium tracer was injected into the aquifer over a period of two days. This case study only considered the 328-day plume snapshot because the plumes at earlier times were not as extensive, and the plume at 440 days was not sampled completely. To accommodate the injection in the flow model, the total transport simulation time of 328 days was approximated by two steadystate stress periods, one representing conditions during the two-day period of injection and the other representing conditions during the subsequent 326 days. In the first stress period, the tracer injection through five wells was represented by three cells with a total injection rate of 3.3 l/min and a concentration of 55,610 pCi/ml. The transport model was solved using the MT3DMS code (Zheng and Wang, 1999), which includes both the standard advection-dispersion approach and the alternative dual-domain mass transfer approach.
26.4.3 Assignment of Hydraulic and Transport Properties The ordinary kriging technique was used to construct the hydraulic conductivity distributions needed by the numerical model. Ordinary kriging is a simple interpolation technique commonly used in field
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Z Y
Z axis (m)
X
60 50 55
200 150 100
X
0
ax
is
is
Y ax
InK (cm/sec)
(m)
50
(m
)
50
0
–3 –4 –5 –6 –7
FIGURE 26.8 3D hydraulic conductivity field generated with ordinary kriging from over 3000 measurements. (Feehley C.E., C. Zheng, and F.J. Molz, Water Resour. Res., 36:2501–2515, 2000.)
applications. In the kriging approach, the statistical parameters, such as the mean, variance and correlation scales, were determined from the flowmeter data and input into a three-dimensional ordinary kriging program (Deutsch and Journel, 1998). The result is a deterministic three-dimensional hydraulic conductivity field as shown in Figure 26.8. The corner of the cutaway block represents the approximate location of the observed tritium plume centerline. A stochastic fractal based method was also used by Feehley et al. (2000) to investigate the effect of different K generation schemes on the simulated plumes. An average total porosity of 0.35 was used for the entire model area, which is close to the value of 0.32 determined from the soil cores collected from the test site (Boggs et al., 1990). The difference in the two values was intended to account for potential consolidation during handling of the core samples (Adams and Gelhar, 1992). A uniform recharge rate of 1.4 × 10−4 m/day was used for the steady-state flow model. Different values of longitudinal dispersivity were tested. The ratios of the transverse and vertical dispersivities to the longitudinal dispersivity were fixed at 0.01 and 0.001, respectively, consistent with the very limited transverse and vertical dispersion as observed at the MADE site and other field sites (Gelhar et al., 1992). For the dual-domain mass transfer model, it is also necessary to specify mobile and immobile porosities and a mass transfer rate coefficient. These parameters were estimated through trial-and-error calibration based on a comparison of observed and calculated tritium plumes. In all simulations conducted, a mobile porosity of one-eighth of the total porosity was judged to produce the most consistent match between observed and calculated plumes. The mass transfer rate coefficient was found to be sensitive to the hydraulic conductivity distribution. For simulations with the kriged K field, a uniform value of 0.001 day−1 was used for the entire model domain. The effect of the mass transfer rate coefficient on the simulated plume is addressed subsequently. The model domain was divided into six equally spaced zones along the general flow direction (the y axis) in which the mobile-domain mass (i.e., the zeroth moment) of the simulated plume was calculated and compared with that of the observed plume. The mass of each zone is determined by computing the mass per zone and dividing it by the total mass of all zones. This relative mass instead of absolute mass is used for the convenience of comparison.
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26.5 Analysis of Simulation Results 26.5.1 Advection-Dispersion Model For the advection-dispersion model, a single porosity equal to the total porosity of 0.35 was used. In a previous study by Zheng and Jiao (1998), a longitudinal dispersivity value of 5.0 m was found to result in a reasonable match of the overall plume configuration to the observed plume above a certain concentration limit. The longitudinal dispersivity was varied spatially during the calibration process, but the overall match was not significantly improved; thus, those results are not reported here. Figure 26.9 shows the calculated tritium plume based on the single-porosity ADM and the kriged hydraulic conductivity field. A large amount of mass is retained near the injection wells, as was observed in the measured data (Figure 26.5). However, the simulated plume fails to represent rapid, anomalous spreading at low concentrations. Furthermore, the resulting plume does not reproduce the fringy appearance of the observed plume. The distribution of calculated relative mass in the different zones (shown in Figure 26.10 as columns with a darker shade) does not closely mimic the observed distribution (shown as columns with a light shade). In the injection area, zone 1, the relative mass of the calculated plume is much higher than that of the observed plume. There is a steady decline in calculated relative mass with increasing distance from the injection zone, while the relative mass for the observed plume shows a sharp decrease from zone 1 to zone 2, but increases and decreases again with distance. In the far-field (zone 5 and zone 6), the relative mass for the calculated plume is zero even though the observed plume shows significant mass in these zones. Several possible reasons exist for the discrepancies between the observed and calculated plumes. First, the characterization of solute transport in highly heterogeneous porous media is inherently difficult; it is practically impossible to represent heterogeneity at a level where its effects on solute transport will be reproduced completely. Measured hydraulic conductivity distributions are incorporated into models by assigning a different hydraulic conductivity value to each model node, generally using interpolation. Interpolation methods, such as ordinary kriging, generate a unique hydraulic conductivity field, preserving local accuracy only near data points while smoothing data in areas of sparse sampling Z Y
Z axis (m)
X
60 50 55
200 150 100
X
0
ax
is
50
(m
)
50
0
)
is (m
Y ax
Concentration (pCi/ml)
300 100 50 25 10 5
FIGURE 26.9 Simulated tritium plume at 328 days after injection with the advection-dispersion model (Feehley C.E., C. Zheng, and F.J. Molz, Water Resour. Res., 36:2501–2515, 2000.). The longitudinal dispersivity used is 5 m.
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0.80 Observed
0.70
ADM DDMT
0.60
Mass (%)
0.50 0.40 0.30 0.20 0.10 0.00 1
2
3
4
5
6
Aquifer zones along the flow direction
FIGURE 26.10 Bar graph showing results of the advection-dispersion model (ADM) and the dual-domain mass transfer model (DDMT). (Feehley C.E., C. Zheng, and F.J. Molz, Water Resour. Res., 36:2501–2515, 2000.)
(Deutsch and Journel, 1998). Commonly, therefore, these methods fail to reproduce preferential pathways, which tend to be characterized by sharp local contrast in hydraulic conductivity. Furthermore, even if a more sophisticated hydraulic conductivity generation methodology were used, it would generally still be impossible to achieve a sufficiently accurate representation of the true hydraulic conductivity field and the resulting velocity field, particularly if the macroscopic or local scale heterogeneities in the aquifer are smaller than the numerical grid spacing, or if they occur in preferential directions. The failure to account for preferential pathways eliminates the mechanism for rapid spreading of a part of the tracer mass; this is probably the reason that the simulated plume in Figure 26.9 does not show mass transported a significant distance downstream.
26.5.2 Dual-Domain Mass Transfer Model The second simulation was based on the DDMT with the same kriged hydraulic conductivity distribution as used in the first simulation. The mass transfer rate coefficient used for this simulation is 0.001 day−1 , and the mobile porosity was set to one-eighth of the total porosity. The longitudinal dispersivity used in the dual-domain mass transfer model is 1.0 m, compared to 5.0 m used in the single-porosity ADM. Note that the dispersivity is the driving force for all mechanical dispersion and mixing in the ADM. However, the dispersivity becomes secondary in the DDMT as much of the mechanical dispersion and mixing are accounted for by mass transfer between the mobile and immobile domains at each model cell. Thus, the dispersivity used in this simulation is necessarily smaller than that in the previous simulation, and is intended to account for the randomly occurring local dispersion not already accommodated by the mass transfer process. Additional analysis has shown that the simulated plume in the DDMT is not sensitive to the dispersivity value. The overall configuration of the simulated plume, shown in Figure 26.11, resembles that of the observed plume, shown in Figure 26.5. There is a large amount of mass trapped near the source area, and also sufficient downstream spreading of low concentration fronts. The narrowing of the plume front as simulated by the ADM (Figure 26.9) has disappeared. The relative mass for the DDMT simulation is shown in
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Z axis (m)
X
60 50 55
200 150 100
X
0
ax
is
(m
)
50 50
0
is Y ax
(m)
Concentration (pCi/ml)
300 100 50 25 10 5
FIGURE 26.11 Simulated tritium plume at 328 days after injection with the dual-domain mass transfer model. (Feehley C.E., C. Zheng, and F.J. Molz, Water Resour. Res., 36:2501–2515, 2000.). The longitudinal dispersivity used is 1 m; the ratio of mobile/total porosities used is 1/8; and the mass transfer rate coefficient is 0.001 day−1 .
Figure 26.10 as columns with the darkest shade. The calculated relative mass in each zone closely resembles that of the observed plume. While the match is not exact (the simulated plume is considerably smoother than the observed plume), the result is much more satisfying than that from the previous simulation based on the ADM. By simulating a mobile and an immobile domain, the dual-domain mass transfer model allows for advective transport to occur in the mobile region at velocities increased in inverse proportion to the ratio of mobile/immobile porosities, thus providing a mechanism for rapid spreading of a certain amount of mass downstream, while retaining a bulk of mass near the source area. The smooth contour surface appears for the same reason as for the ADM simulation (i.e., due to the use of the kriging-generated hydraulic conductivity field), but the DDMT simulation shows a significant improvement in matching the overall size and shape of the observed plume compared to the ADM simulation.
26.5.3 Sensitivity Analysis Many DDMT simulations, based on the kriging-generated hydraulic conductivity distribution, were run with different combinations of the dual-domain model parameters. The results of a sensitivity analysis showing how relative mass varies with changes in mass transfer rate coefficient are shown in Figure 26.12. In all the runs shown in Figure 26.12, mobile porosity, θm , was set to one-eighth of the total porosity. When the mass transfer rate coefficient is low, the transport regime approaches the behavior of a single-domain system having a total porosity equal to the mobile porosity of the dual-domain system. Therefore, the plume moves downstream at a faster rate, causing higher relative mass to appear in the last three zones. If the mass transfer rate coefficient is increased substantially, the connection between the domains becomes very rapid. The system acts like a single-domain regime having a porosity approaching the total porosity of the dual-domain system. Thus the plume travels through the domain at a slower rate; mass is trapped in the first zone due to the faster connection between mobile and immobile zones, and less mass moves downstream. These results suggest that a combination of mass transfer rate coefficients might best model the characteristics of the observed plume.
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0.50 Observed β = 0.0010 (1/day) β = 0.0008 (1/day)
0.40
β = 0.0006 (1/day)
Mass (%)
β = 0.0004 (1/day) 0.30
0.20
0.10
0.00 1
2 3 4 5 Aquifer zones along the flow direction
6
FIGURE 26.12 Bar graph showing the sensitivity of calculated relative mass to changes in mass transfer rate coefficient for the dual-domain mass transfer model. (Feehley C.E., C. Zheng, and F.J. Molz, Water Resour. Res., 36:2501–2515, 2000.) Mobile porosity equal to one-eighth of total porosity is used.
The results of an analysis of how relative mass varies with changes in the ratio of mobile/total porosity are shown in Figure 26.13. The mass transfer rate coefficient of 0.0006 day−1 is used in the model and the ratio of mobile over total porosities is allowed to vary. It is clear that the calculated relative mass is not particularly sensitive to changes in the ratio of mobile over total porosities within the range examined (1 : 4–1 : 8).
26.6 Summary and Concluding Remarks Three natural-gradient tracer tests have been conducted at the MADE site since 1986. The plumes for the conservative tracers used in all three tests exhibited a strongly asymmetrical pattern, with a more concentrated region remaining close to the source and a front of dilute concentration traveling far downgradient. The non-Gaussian behavior was apparently caused by the extreme heterogeneity in the hydraulic conductivity distribution, which had a natural logarithm variance of 4.5. The same behavior was observed regardless of whether the tracers were introduced to the aquifer by injection wells or through an excavated trench. A fundamental difficulty with applying the classical Fickian advection-dispersion model to the MADE site appears to be the existence of preferential flow pathways (high conductivity lenses) whose scale (cm to dm) is smaller than the grid spacing (0.5 ∼ 2 m) of the numerical model (e.g., Figure 26.7). Without hydraulic conductivity data sufficient to delineate these preferential flow pathways explicitly, and without the grid resolution required to incorporate them fully in the numerical model, the advection-dispersion approach cannot reproduce the observed plume behavior adequately, even when a large number of K measurements are available. More discussion on this subject can be found in Zheng and Gorelick (2003) and Liu et al. (2004). The results of the dual-domain mass transfer model show a significant improvement over the advectiondispersion model in matching the observed plume. While the dual domain model does not represent preferential pathways explicitly, the possibility of reducing porosity for the mobile domain allows for
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m / = 1/4 m / = 1/7
Mass (%)
m / = 1/8
0.30
0.20
0.10
0.00 1
2 3 4 5 Aquifer zones along the flow direction
6
FIGURE 26.13 Bar graph showing the sensitivity of calculated relative mass to changes in mobile porosity ratio for the dual-domain mass transfer model. (Feehley C.E., C. Zheng, and F.J. Molz, Water Resour. Res., 36:2501–2515, 2000.) Mass transfer rate coefficient of 0.0006 day−1 is used.
rapid solute movement, mimicking the effects of movement along preferential pathways. At the same time, the storage of mass in the immobile domain adequately represents the retention of mass in lowpermeability regions of the subsurface. The DDMT simulation results in a satisfactory match between calculated and observed plumes and mass distributions, particularly in areas of low concentration; this represents a significant improvement over the ADM simulation. It is noteworthy that although this case study focuses only on the MADE-2 tritium plume, the DDMT approach has also been applied successfully to the MADE-1 and MADE-3 bromide plumes, respectively, by Harvey and Gorelick (2000) and Julian et al. (2001) with dual-domain model parameters similar to those used in this case study.
Acknowledgments The funding for some of the materials presented in this chapter was provided by grants from the National Science Foundation and the U.S. Army Engineer Research and Development Center. Many individuals have contributed to the research discussed in this chapter, including Fred Molz, Steve Gorelick, Gaisheng Liu, Erin Feehley, Mark Boggs, Hank Julian, Tom Stauffer, Mark Dortch, Charles Harvey, Mary Hill, and Eileen Poeter. The author is grateful to Prabhakar Clement for reviewing this manuscript.
Glossary Advection: Movement of solutes in groundwater with average seepage velocities. Advection-dispersion model (ADM): A mathematical model for solute transport that is characterized by advection and hydrodynamic dispersion. Dual porosity: A term used to describe the type of porous media where the total porosity can be separated into mobile and immobile porosities; equivalent to dual domain. Dual-domain mass transfer model (DDMT): A mathematical model that conceptualizes solute transport as occurring in two overlapping domains: advection and hydrodynamic dispersion in the mobile domain, and rate-limited mass transfer between the immobile and mobile domains. Fick’s law: A mathematical equation that quantifies the diffusive mass flux as proportional to the concentration gradient.
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Flowmeter test: An aquifer test technique in which the horizontal flow at multiple elevations in a single borehole is measured and differentiated to determine the vertical profile of hydraulic conductivity at the borehole location. Heterogeneity: Variation of any aquifer property such as hydraulic conductivity with space or time. Hydrodynamic dispersion: Sum of mechanical dispersion and molecular diffusion. Immobile porosity: Ratio of the pore space filled by immobile or stagnant fluids to the total pore space. Mass transfer: Exchange of solute mass between two regions such as between the mobile and immobile domains. Mechanical dispersion: Spreading of solutes in groundwater due to variations in flow velocities. Mobile porosity: Ratio of the pore space filled by mobile fluids to the total pore space. Molecular diffusion: Movement of solutes in fluids induced by concentration gradients. Natural gradient tracer test: A type of tracer tests in which conservative or reactive tracers are injected into the aquifer under natural conditions and their movement is monitored by a network of monitoring and sampling wells. Ordinary kriging: A geostatistical method for estimating an unknown value from neighboring sampled data based on the minimization of interpolation error variance. Preferential flow paths: Parts of porous media that are comprised of high conductivity materials to permit flow and/or solutes to move through preferentially. Sensitivity analysis: A numerical procedure to quantify the effect of change in one variable on another variable.
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Brauner, J.S. and M.A. Widdowson. Numerical simulation of a natural attenuation experiment with a petroleum hydrocarbon NAPL source. Ground Water, 39:939–952, 2001. Bredehoeft, J.D., and G.F. Pinder, Mass transport in flowing groundwater, Water Resour. Res., 9:194–210, 1973. Carrera, J., An overview of uncertainties in modeling groundwater solute transport, J. Contam. Hydrol., 13:23–48, 1993. Clothier, B.E., M.B. Kirkham, and J.E. Mclean, In situ measurements of the effective transport volume for solute moving through soil, Soil Sci. Soc. Am. J., 56:733–736, 1992. Coats, K.H. and B.D. Smith, Dead-end pore volume and dispersion in porous media, Soc. Petrol. Eng. J., 4:73–84, 1964. Dagan, G., Flow and Transport in Porous Formation, Springer-Verlag, New York, 465 p., 1989. Deutsch, C.V. and A.G. Journel, GSLIB: Geostatistical Software Library and User’s Guide, 2nd edn., Oxford University Press, New York, 1998. Eggleston, J. and S. Rojstaczer, Identification of large-scale hydraulic conductivity trends and the influence of trends on contaminant transport, Water Resour. Res., 34:2155–2168, 1998. Feehley C.E., C. Zheng, and F.J. Molz, A dual-domain mass transfer approach for modeling solute transport in heterogeneous porous media, application to the MADE site, Water Resour. Res., 36:2501–2515, 2000. Gelhar, L.W. and C.L. Axness, Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resour. Res., 19:161–189, 1983. Gelhar, L.W., C. Welty, and K. Rehfeldt, A critical review of data on field-scale dispersion in aquifers, Water Resour. Res., 28:1955–1974, 1992. Gorelick, S.M., G. Liu, and C. Zheng, Quantifying mass transfer in permeable media containing conductive dendritic networks, Geophys. Res. Lett., 32:L18402, doi:10.1029/2005GL023512, 2005. Griffioen, J.W., D.A. Barry, and J.Y. Parlange, Interpretation of two-region model parameters, Water Resour. Res., 34:373–384, 1998. Haggerty, R., S.W. Fleming, L.C. Meigs, and S.A. McKenna, Tracer tests in a fractured dolomite. 2. Analysis of mass transfer in single-well injection-withdrawal tests, Water Resour. Res., 37:1129–1142, 2001. Haggerty, R., C.F. Harvey, C.F. von Schwerin, and L.C. Meigs, What controls the apparent timescale of solute mass transfer in aquifers and soils? A comparison of diverse experimental results. Water Resour. Res., 40: W01510, doi:10.1029/2002WR001716, 2004. Harbaugh, A.W., E.R. Banta, M.C. Hill, and M.G. McDonald, MODFLOW-2000: U.S. Geological Survey Modular Ground-water Model — User Guide to Modularization Concepts and the Ground-Water Flow Processes, U.S. Geological Survey Open-File Report 00–92, 121 p., 2000. Harvey, C.F. and S.M. Gorelick, Rate-limited mass transfer or macrodispersion: which dominates plume evolution at the Macrodispersion Experiment (MADE) site? Water Resour. Res., 36:637–650, 2000. Hollenbeck, K.J., C.F. Harvey, R. Haggerty, and C.J. Werth, A method for estimating distribution of mass transfer rate coefficients with application to purging batch experiments, J. Contam. Hydrol., 37:367–388, 1999. Jaynes, D.B., S.D. Logson, and R. Horton, A field method for measuring mobile/immobile water content and solute transport rate coefficient, Soil Sci. Soc. Am. J., 59:352–365, 1995. Julian, H.E., J.M. Boggs, C. Zheng, and C.E. Feehley, Numerical simulation of a natural gradient tracer experiment for the Natural Attenuation Study: flow and physical transport, Ground Water, 39:534– 545, 2001. Killey, R.W.D. and G.L. Moltyaner, Twin Lake tracer tests: methods and permeabilities. Water Resour. Res., 24:1585–1613, 1988. LaBolle, E.M. and G.E. Fogg, Role of molecular diffusion in contaminant migration and recovery in an alluvial aquifer system, Transport Porous Med., 42:155–179, 2001. LeBlanc, D.R., S.P. Garabedian, K.M. Hess, L.W. Gelhar, R.D. Quadri, K.G. Stollenwerk, and W.W. Wood, Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts. 1. Experimental design and observed tracer movement. Water Resour. Res., 27:895–910, 1991.
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Libelo, E.L., T.B. Stauffer, M.A. Geer, W.G. MacIntyre, and J.M. Boggs, A field study to elucidate processes involved in natural attenuation, 4th International In Situ and On-Site Bioremediation Symposium, New Orleans, LA, 1997. Liu, G., C. Zheng, and S.M. Gorelick, Limits of applicability of the advection-dispersion model in aquifers containing high-conductivity channels, Water Resour. Res., 40:W08308, doi:10.1029/2003WR002735, 2004. Lu, S., F.J. Molz, and G.J. Fix, Possible problems of scale dependency in applications of the threedimensional fractional advection-dispersion equation to natural porous media, Water Resour. Res., 38, doi:10.1029/2001WR000624, 2002. MacIntyre, W.G., J.M. Boggs, C.P. Antworth, and T.B. Stauffer, Degradation kinetics of aromatic organic solutes introduced into a heterogeneous aquifer, Resour. Res., 29:4045–4051, 1993. MacKay, D.M., D.L. Freyberg, P.V. Roberts, and J.A. Cherry, A natural gradient experiment on solute transport in a sand aquifer. 1. Approach and overview of plume movement, Water Resour. Res., 22:2017–2029, 1986. McDonald, M.G. and A.W. Harbaugh, A modular three-dimensional finite-difference ground-water flow model, U.S. Geological Survey Techniques of Water Resources Investigations, Book 6, U.S. Geological Survey, Reston, VA, 1988. Molz, F.J., O. Guven, J.G. Melville, R.D. Crocker, and K.T. Matteson, Performance, analysis, and simulation of a two-well tracer test at the Mobile site, an examination of scale-dependent dispersion coefficients, Water Resour. Res., 22:1031–1037, 1986. Molz, F.J., C. Zheng, S.M. Gorelick, and C.F. Harvey, Discussion of “Investigating the Macrodispersion Experiment (MADE) site in Columbus, Mississippi, using a three-dimensional inverse flow and transport model” by H.C. Barlebo, M.C. Hill, and D. Rosbjerg, Water Resour. Res., doi:10.1029/2005WR004265, 2006. Rehfeldt, K.R., J.M. Boggs, and L.W. Gelhar, Field study of dispersion in a heterogeneous aquifer. 3. Geostatistical analysis of hydraulic conductivity, Water Resour. Res., 28:3309–3324, 1992. Stapleton, R.D., G.S. Sayler, and J.M. Boggs, Changes in subsurface catabolic gene frequencies during natural attenuation of petroleum hydrocarbons, Environ. Sci. Technol., 34, 2000. Sudicky, E.A., A natural gradient experiment of solute transport in a sand aquifer: spatial variability of hydraulic conductivity and its role in the dispersion process, Water Resour. Res., 22:2069–2082, 1986. Taylor, G., Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. R. Soc. London, A, 219:186–203, 1953. van Genutchen, M.Th. and P.J. Wierenga, Mass transfer studies in porous media. 1. Analytical solutions, Soil Sci. Soc. Am. J., 40:473–450, 1976. Zheng, C. and G.D. Bennett, Applied Contaminant Transport Modeling, Second Edition, Wiley, New York, 621 p., 2002. Zheng, C. and S.M. Gorelick, Analysis of the effect of decimeter-scale preferential flow paths on solute transport, Ground Water, 41:142–155, 2003. Zheng, C. and J.J. Jiao, Numerical simulation of tracer tests in a heterogeneous aquifer, J. Environ. Eng., 124:510–516, 1998. Zheng, C. and P.P. Wang, MT3DMS: A modular three-dimensional multispecies model for simulation of advection, dispersion and chemical reactions of contaminants in groundwater systems; Documentation and User’s Guide, Contract Report SERDP-99-1, U.S. Army Engineer Research and Development Center, Vicksburg, MS, 1999.
Further Information For a comprehensive treatment of the MADE-1 test, refer to a 4-part series of papers by Adams and Gelhar (1992), Boggs and Adams (1992), Boggs et al. (1992), and Rehfeldt et al. (1992). The information on
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the MADE-2 test can be found in Boggs et al. (1993) and MacIntyre et al. (1993). The MADE-3 test is covered in Boggs et al. (1995), Libelo et al. (1997) and Stapleton et al. (2000). Zheng and Jiao (1998), Harvey and Gorelick (2000), Feehley et al. (2000), and Julian et al. (2000) provide an in-depth discussion of the difficulties in using the classical advection-dispersion model to simulate the MADE tracer tests and the applicability of the dual-domain mass transfer model as a practical alternative to the advectiondispersion model. Zheng and Gorelick (2003) and Liu et al. (2004) explore the concept of connected decimeter-scale high-conductivity networks as an explanation for the dual-domain mass transfer model applied to the MADE site.
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27 Determining Sustainable Groundwater Development
John D. Bredehoeft
27.1 Sustainability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.2 Quantitatively Maintaining a Groundwater Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.3 Analytical Methods in Hydrogeology . . . . . . . . . . . . . . . . . . 27.4 The Water Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.5 Aquifer Dynamics and Models . . . . . . . . . . . . . . . . . . . . . . . . . . 27.6 The Dynamics of a Basin and Range Aquifer . . . . . . . . . . 27.7 Paradise Valley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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27.1 Sustainability The concept of sustainable development focuses on the concept of limiting resource use to levels that can be sustained over the long term. The Brundtland Commission (1987), known formerly as the World Commission on Environment and Development, defined sustainable development as that which meets the needs of the present without compromising the ability of future generations to meet their own needs. Implicit in this definition is a conservation ethic that states our generation should not use the resources of the planet, in the broadest context, in a manner that leaves our children and grandchildren (future generations) with problems of degraded, or impossibly depleted resources. The idea introduces a whole host of value judgments to be made by both individuals, and society collectively. History tells us that society’s values with respect to the use of the planet’s resources change with time. Society’s judgment of what is sustainable today is different from that of older generations, and in turn, our children’s and our grandchildren’s societal values are likely to be different than ours. The idea of this chapter is to introduce the concept of sustainability into groundwater development. Alley and Leake (2004) discuss how our ideas about groundwater developments that can be maintained indefinitely have evolved from the concept of safe yield to one of sustainability. Many things can degrade 27-1
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the prolonged use of a groundwater system; the degradations generally fall in the categories of degraded groundwater quality, or a depletion of the quantity of water available from the resource, or a combination of both. Degradation is a serious issue that impacts groundwater sustainability. It is often important, especially in problems involving changes in groundwater quality to understand aquifer systems; this includes both the recharge and discharge from the systems. This is especially true where recharge brings with it undesirable water quality. However, the focus in this chapter is on the quantitative issues associated with sustainability. Somehow the idea persists within the groundwater community that the sustained yield of an aquifer is some arbitrary fraction of the virgin recharge. Theis (1940) showed the fallacy of this notion, yet the idea persists. A second intent of this paper is to reinforce Theis’ concept of how a groundwater system responds to development.
27.2 Quantitatively Maintaining a Groundwater Development Much of our understanding of how groundwater systems respond to development goes back to the early work of Theis. Theis (1940) in a paper entitled: The source of water derived from wells: essential factors controlling the response of an aquifer to development, introduced the principle of capture. One can explain the principle in the following manner: before development a groundwater system is in a state of equilibrium in which the recharge is balanced by the discharge from the system. Pumping imposes an additional stress on the system. If the system is to reach a new equilibrium state, in which there is no further change in storage attributable to the pumping, then there must be an increase in the recharge, or a decrease in the discharge, or some combination of both. The United States Geological Survey (Lohman, 1972) in Definitions of selected groundwater terms published the following definition of capture: Water withdrawn artificially from an aquifer is derived from a decrease in storage in the aquifer, a reduction in the previous discharge from the aquifer, an increase in recharge, or a combination of these changes. The decrease in discharge plus the increase in recharge is termed capture. Neither the (virgin) recharge nor discharge is of interest in determining the long-term productivity of an aquifer; rather it is the changes in these quantities, caused by the pumping, that one seeks. The purpose of this chapter is to show that the relevant quantity in determining the long-term productivity of a groundwater system is capture.
27.3 Analytical Methods in Hydrogeology Before digital computer modeling codes, groundwater hydrologists used traditional analytical methods to assess the impacts of wells on groundwater systems. The traditional method of analysis used the principle of superposition (Reilly et al., 1987, see also Section 10.2.5). In this approach one assumes that the hydraulic head (or the water table) before development resulted from the inputs and outputs (recharge and discharge) from the system. One analyzes the impact of pumping independent of the initial (or virgin) hydraulic head. The cone of depression is calculated as a function of time. This cone of depression is then superposed upon the existing hydraulic head (or water table); the resulting head after superposition is the solution to the development. What information does one need to make such a superposition calculation? One needs (1) the transmissivity and storativity distribution within the aquifer, (2) the boundary conditions that will be reached by the cone of depression, and (3) the rate of pumping. Those trained in classical hydraulic theory are well aware of reflection boundaries and image wells to account for the boundary conditions. Missing from the classical analysis is any mention of recharge. The recharge is taken into account by the initial hydraulic head (or the water table). The initial head is a solution to initial boundary value problem that includes both the recharge and discharge.
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Prior to the widespread use of digital computer models most analyses in groundwater flow were made using the principles of superposition. This was also the methodology used in the analog computer models of the 1950s, 1960s, and 1970s. With the advent of digital computer models it became feasible to specify the varying distributions of recharge and discharge with the idea of solving for the virgin water table. The calculated water table can then be compared to the observed water table (or hydraulic head). Such an analysis requires knowledge of the distribution of the virgin rate of both recharge and — in addition to the transmissivity distribution, and the boundary conditions for the aquifer of interest. Usually one has an estimate of the rainfall; however, one has no idea of how large the recharge is except that it cannot exceed some unknown fraction of rainfall. One may know the transmissivity of the aquifer at a few places, and may also know that the aquifer discharge that makes up the baseflow of streams associated with the aquifer. Based upon this set of limited information a steady-state model analysis is made in an attempt to estimate the transmissivity of the aquifer. This is a common digital computer model analysis. In this context, knowledge of the virgin recharge and discharge are useful in estimating the transmissivity. The recharge and the discharge are the inputs and outputs from a groundwater system. Both quantities are important in understanding how a particular groundwater system functions. However, it is not the purpose of this chapter to discuss recharge or discharge. The focus is in how recharge and discharge enter into the determination of the long-term quantitative yield of a groundwater system. In the classical analytical method the important variables for determining the impacts of pumping are those that describe the dynamic response of the system — the distribution of aquifer diffusivity and the boundary conditions. This argument was the thrust of Brown’s (1963) paper. The argument makes sense to one trained in classical analytical methods; it is obscure to others. Brown’s paper made almost no impact on the profession. This chapter will attempt to further simplify the mathematical argument.
27.4 The Water Budget To illustrate the basic principle, consider a simple aquifer system. A permeable alluvial aquifer underlies a circular island in a freshwater lake. The intent is to develop a well on the island. The island aquifer is shown schematically in Figure 27.1. Before development, recharge from rainfall creates a water table. The recharge over the island is balanced by discharge from the permeable aquifer directly to the lake. One can write the following water balance for virgin conditions on our island: R 0 = D0
or
R0 − D 0 = 0
where R0 is the virgin recharge (this is the recharge one generally refers to), and D0 is the virgin discharge. A water table develops on the island in response to the distribution of recharge and discharge and the transmissivity of the alluvial aquifer.
Well
Water table Aquifer Lake
Lake
FIGURE 27.1 Cross-section of hypothetical island aquifer.
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The discharge to the lake can be obtained at any point along the shore by applying Darcy’s Law: dD = T (dh/dl) where D is the discharge through the aquifer at any point along the shore, T is the transmissivity at the same point, and dh/dl is the gradient in the water table at that point. If one integrates the point discharge along the entire shoreline of the island one obtains the total discharge from the island: T (dh/dl) ds = D0 Now at the middle of the island a well is installed and pumping is initiated (see Figure 27.1). At any time one can write a new water balance for the island: (R0 + R0 ) − (D0 + D0 ) − P + dV /dt = 0 where R0 is the change in the virgin rate of recharge caused by the pumping, D0 is the change in the virgin rate of discharge caused by the pumping, P is the rate of pumping, and dV /dt is the rate at which pumping removes groundwater from storage on the island. The virgin rate of recharge, R0 , equals the virgin rate of discharge, D0 , the water budget equation following the initiation of pumping reduces to R0 − D0 − P + dV /dt = 0
or
R0 − D0 − P = −dV /dt
For a long-term development one requires the rate of water taken from storage to be zero; in other words, we define prolonged development that can be maintained indefinitely as: dV /dt = 0
as t goes to ∞
where dV /dt goes to zero at some future time. As long as the system can reach a future state where there is no continued depletion of storage we define the system as capable of being maintained indefinitely. The water budget for long-term development (at t = ∞) is: R0 − D0 = P This states that in order to reach a development that can be maintained indefinitely the pumping must be balanced, at some future time, by a change in the virgin rate of recharge, R0 , or a change in the virgin rate of discharge, D0 , caused by the pumping. Traditionally, the sum of the change in recharge and the change in discharge caused by the pumping, the quantity (R0 − D0 ), is defined as the capture attributable to the pumping. For a development to be maintained indefinitely the rate of pumping must equal the rate of capture, at some future time. Notice that to determine a development that can be prolonged we do not need to know the recharge. The recharge may be of interest as are all the facets of the hydrologic budget, but it is not a determining factor in our analysis of quantitative sustainability. Recharge is often a function of external conditions — rainfall, vegetation, soil permeability, and the like. In many, if not most, groundwater situations, the rate of recharge cannot be impacted by the pumping; in other words in terms of our water budget: R0 = 0
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In most situations, prolonged development occurs when the pumping captures an equal amount of virgin discharge: P = D0 It is interesting to see how in the island aquifer, capture occurs conceptually. When pumping is initiated a cone of depression is created. Figure 27.1 (cross-section) shows the cone of depression at an early stage in the development of the island aquifer. The natural discharge from the island does not start to change until the cone of depression changes the slope in the water table at the shore of the island — remember Darcy’s Law controls the discharge at the shoreline. Until the slope of the water table at the shoreline is changed by the pumping, the natural discharge continues at its virgin rate. Up until the point in time that the cone reaches the shore and changes the water table gradient significantly, all the water pumped from the well is supplied totally from storage in the aquifer. In other words, the cone of depression must reach the shoreline before the natural discharge is impacted. The rate at which the cone of depression develops, and reaches the shoreline, and changes the slope of the water table there, depends on the dynamics of the aquifer system — its transmissivity, storativity (or specific yield), and its boundary conditions. The rate of capture in a groundwater system is a problem in the dynamics of the system. Capture has nothing to do with the virgin rate of recharge. At some point in time, if the pumping is large enough, the natural discharge will be almost eliminated — this occurs when the slope of the water table is flat everywhere at the shoreline. The island aquifer is an aquifer system in which one can induce water to flow from the lake into the aquifer (Figure 27.1). In this instance a prolonged development can exceed the virgin recharge (or the virgin discharge). This again suggests that the recharge is not a relevant input in determining the magnitude of a development that can be maintained indefinitely if another source of water is available — a lake, or stream. Often the geometry of the aquifer restricts the capture. For example, were the aquifer on the island to be thin, one might run out of water at the pump long before the pumping could capture any fraction of the discharge. In this case, all the water pumped would come from storage — it would be “mined.” In the island example, with a thin aquifer, the well could run dry before it could impact the discharge at the shoreline. This again points out that the dynamic response of the aquifer system is all important to determining the impacts of development. It is for these reasons that hydrogeologists are concerned with the dynamics of aquifer system response. Hydrogeologists model aquifers in an attempt to understand their dynamics. Clearly, the circular island aquifer example is a simple system. Even so, the principles explained in terms of this simple aquifer apply to all groundwater systems. It is the dynamics of how capture takes place in an aquifer that ultimately determines how large a prolonged groundwater development can be maintained. Whether a groundwater system that can be maintained indefinitely is sustainable is an entirely different question having to do with the social, political, and ethical consequences of the development. Creating a groundwater system in which the pumping is balanced by the capture, a system that can be maintained indefinitely, may be a necessary condition for sustainability, but by itself it is not a sufficient condition. In an earlier paper (Bredehoeft, 2002) I argued that a system balanced at some future time by capture was both necessary and sufficient for sustainability; however, I no longer believe it to be sufficient — I stand corrected by my colleagues.
27.5 Aquifer Dynamics and Models Since the development of the Theis equation in 1935 hydrogeologists have been concerned with the dynamics of aquifer response to stress — pumping or recharge. Once Theis (1935) and later Jacob (1940) showed the analogy of groundwater flow to heat flow, the groundwater community has been busy solving the appropriate boundary value problems that describe various schemes of development. This endeavor has gone through several stages.
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The 1940s and 1950s were a time during which the groundwater profession was concerned with solving the problems of flow to single well. Numerous analytical solutions to the single well problem were produced. These solutions were used both to predict the response of the aquifer system, as well as to estimate aquifer properties — transmissivity (or permeability) and the storativity. Hydrogeologists of that day saw the limitations in analyzing wells and sought a more robust methodology by which to analyze an entire aquifer, including complex boundary conditions and aquifer heterogeneity. The search led a group at the USGS to invent the analog model in the 1950s; the genius behind this development was Herb Skibitski — Herb was one of those individuals who rarely published. The new tool was the electric analog computer model of the aquifer. In the analogous system, voltage is equivalent to hydraulic head; electrical current is equivalent to the flow of water (see Section 3.4.1). The model consisted of a finite-difference network of resistors and capacitors. In the analog computer aquifer transmissivity is represented by the network of resistors; the storativity is represented by the network of capacitors. The resulting resistor–capacitor network is excited by electrical function generators that simulated pumping, or other stresses. In reality, the analog models were elegant finite-difference computer models of aquifer systems. By 1960, the USGS had a facility in Phoenix, Arizona where analog models of aquifers were routinely built on a production basis. At about the same time, The Illinois Water Survey established an analog model facility in Urbana, Illinois. Some of these analog models had multiple aquifers; some had as many as 100,000 nodes. At the time, it was infeasible to solve the same problems with digital computers; the digital computers of the day were too small and too slow. However, by 1970, the power of the digital computers increased to the point that digital aquifer models could begin to compete with the analog models. By 1980, digital computer models had replaced the analog models, even at the USGS. The models of the 1980s have now grown to include solute transport, pre- and post-processors, and automatic parameter estimation. By far the vast majority of groundwater flow problems are simulated using the USGS code MODFLOW; there is a new version MODFLOW 2000 (see Chapter 23). The groundwater model is a tool with which to investigate the dynamics of realistic aquifer systems. As suggested above, it is only through the study and understanding of aquifer dynamics that one can determine the impact of an imposed stress on an aquifer system.
27.6 The Dynamics of a Basin and Range Aquifer One can illustrate the dynamic response of aquifers using as the prototype a closed basin aquifer like those in the Basin and Range of Nevada. The aquifer geometry is illustrated in plan view in Figure 27.2. The basin is approximately 50 miles in length by 25 miles in width. At the upper end of the valley are two streams that emerge from the nearby mountains and recharge the aquifer at an average combined rate of 100 cfs (∼70,000 acre-feet annually). At the lower end of the valley an area of phreatophyte vegetation discharges groundwater as evapotransipation (ET) at an average rate of 100 cfs. The system before development is in balance; 100 cfs is being recharged, and 100 cfs is being discharged by ET. Two scenarios of groundwater development are of interest in this aquifer. The size of both developments is the same, and is equal to the recharge (and the discharge) 100 cfs. Two locations for the well field are considered — shown as Case I and Case II in Figure 27.2. The Case II well field is closer to the area of phreatophyte vegetation. To simulate the system one needs aquifer properties; the aquifer properties are specified in Table 27.1. In the hypothetical system, phreatophyte groundwater consumption is eliminated as the pumping lowers the water table in the area containing phreatopyhtes. This is a groundwater system in which capture of ET can occur. A linear function is used to cutoff the phreatophyte consumption. As the water table drops between 1 and 5 ft, the phreatophyte use of groundwater is linearly reduced. The reduction in phreatophyte use does not start until the groundwater declines 1 ft, by the time the water table drops 5 ft the phreatophyte use is eliminated in that cell. The phreatopyhte-reduction function is applied cell by cell in the model.
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Valley Fill Aquifer Stream
Case I
Case II
Phreatophytes
Stream
FIGURE 27.2 Plan of hypothetical valley fill aquifer. The two streams, to the left, provide on average 100 cfs of recharge to the aquifer. The area of phreatophytes, to the right, discharges on average 100 cfs of groundwater through ET before groundwater development. We consider two scenarios of groundwater development located as Case I and Case II; each development pumps at a rate equal to the recharge — 100 cfs. TABLE 27.1 Aquifer Properties Basin size Model cell dimensions Hydraulic conductivity Saturated thickness Transmissivity Storage coefficient Phreatophyte consumption Well field pumping Recharge
50 × 25 miles (see Figure 27.2) 1 × 1 mile 0.00025 ft/sec 2000 ft 0.5 ft2 /sec (∼43,000 ft2 /day) 0.1–10% specific yield 100 cfs 100 cfs 100 cfs
For this system to reach a new equilibrium state, in which the yield can be maintained indefinitely, the phreatophyte consumption must be eliminated entirely. Using the model we can examine the phreatophyte use as a function of time. Figure 27.3 is a plot of the phreatophyte use in the system vs. time since pumping was initiated. The ET is reduced faster where the pumping is closer to the phreatopytes — Case II. The point of considering Case I and Case II is to show that the location of the pumping makes a difference in the dynamic response of the system. In Case II, where the pumping is close to the phreatophytes, the ET is reduced by approximately 40 cfs in 10 years. In contrast in Case I, the ET is reduced by only approximately 5 cfs in 10 years. Both scenarios, Case I and Case II, take a long time to fully eliminate the ET; it takes almost 1000 years before the ET is totally eliminated. Even seasoned hydrologists are surprised at how long it takes a water table groundwater system to reach a new equilibrium state in which no more water is removed from storage. One can examine the output from the model in another way by investigating the total amount of water removed from storage in the hypothetical valley fill aquifer (Figure 27.4). Both scenarios of development, Case I and Case II, take approximately the same time to reach a new equilibrium state. In Case II, where the pumping is close to the phreatophytes, the amount of water removed from storage is approximately 60% less than in Case I. It is important to notice, that even though the two developments (Case I and Case II) are equal in size, the aquifer responds differently depending upon where the developments are sited. This again emphasizes the importance of studying the dynamics of the aquifer response — the response is different depending on where the development is located.
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–20
–40 ET (cfs)
Case II
–60
Case I –80
–100 0.1
1
10
100
1000
Year
FIGURE 27.3 ET vs. time in our hypothetical valley-fill aquifer.
This example, of an overly simplified Basin and Range valley fill aquifer, illustrates the importance of understanding the dynamics of aquifer systems. Again, while this is a simple example, the principles illustrated apply to aquifers everywhere. It is the rate at which the phreatopyte consumption can be captured that determines how this system can be maintained indefinitely; this is a dynamic process. Capture always entails the dynamics of the aquifer system. The question arises — is the basin and range aquifer described in this simple example sustainable? This depends upon one’s values. To reach the new equilibrium state, in which the pumping can be maintained indefinitely, one has to eliminate all the phreatophyte consumptive use — kill the phreatophytes. This vegetation provides cover for wildlife in the area — is it reasonable to kill this vegetation? Nevada law restricts groundwater pumping to the natural recharge. Implicit in the law is a value judgment that discounts the value of phreatophyte vegetation that pumping to the full amount of the recharge will usually eliminate.
27.7 Paradise Valley Paradise Valley is a real development in Nevada. Alley and Leake (2004) explored the concept of sustainability; they used as their example a development in Paradise Valley in northern Nevada. The Humboldt River flows across the southern end of the valley. They simulated groundwater pumping near the southern end of the valley, not far to the north of the Humboldt River. Alley and Leake (2004) examined the source of the groundwater pumped vs. time. There are four sources of water that support the pumping (1) water from storage, (2) capture of ET, (3) capture of water leaving the valley, and (4) induced recharge
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Removed from storage (billions of cubic ft)
0
–100
–200 Case II
–300
Case I –400
–500 0
200
400
600
800
1000
Year
FIGURE 27.4 The volume of water removed from storage as a function of time in the hypothetical valley fill aquifer with two developments — Case I and Case II.
from the Humboldt River. Each of these sources varies with time. Figure 27.5 is a plot of the four sources of water that supply the pumping vs. time. One sees the principal source of groundwater in Paradise Valley, during the early period, is from storage in the system. The storage declines to only 3% of the supply in 300 years. The capture of water from phreatophyte ET grows from 20% in 1 year, to approximately 74% of the total in 300 years. The induced recharge from the Humboldt River grows from zero in the early years to approximately 19% of the total in 300 years. The capture of outflow from the valley grows to 3% in 300 years. The groundwater system in Paradise Valley takes a long time to reach a new equilibrium state. The time is similar to the valley fill aquifer explored above. Even after 300 years 3% of the water pumped is still coming from storage. The analysis suggests that the Paradise Valley pumping can be maintained indefinitely, that is, the pumping will at some point after 300 years be balanced by the capture. Nowhere in the analysis by Alley and Leake (2004) does the recharge enter into the calculation of sustainability. The important quantities are the removal of groundwater from storage, the capture of ET, and capture (induced recharge) from the Humboldt River. The groundwater system described by Alley and Leake (2004) can be maintained indefinitely. However, it reaches a new steady state by depleting streamflow in the Humboldt River; this is streamflow that is already claimed, and to which the downstream users have water rights. Any reasonable application of sustainability suggests that the Paradise Valley groundwater development is not sustainable; it infringes on the prior rights of others. Again, such a conclusion depends upon one’s perspective. The Paradise Valley farmers are pumping groundwater to irrigate potatoes, while the downstream users are using the streamflow of the Humboldt River to irrigate alfalfa. Were the upstream users pumping to supply the nearby town of Winnemucca, the value judgment might not be so clear.
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Source of groundwater pumped (%)
80 ET capture
60
40 Storage
Induced recharge from Humboldt River
20
Outflow captured 0 0
100
200
300
Year
FIGURE 27.5 Sources of groundwater that supply the pumping in Paradise Valley, Nevada. (From Alley, W.M. and Leake, S.A., Ground Water, 42, 12–16, 2004.)
27.8 Conclusions The important quantity in determining how a groundwater system reaches a new equilibrium is capture. Capture in an aquifer system is a dynamic process. For this reason hydrologists are occupied in studying aquifer dynamics. The principal tool for these investigations today is the groundwater model. These ideas are not new; Theis (1940) articulated this basic principle. Nowhere in the quantitative determination of long-term maintenance of pumping is the virgin groundwater recharge relevant. Sustainability, on the other hand, is a much broader question that involves the application of societal values. In the final analysis, hydrogeologists seek to be good stewards of that small part of the earth for which they bear some management responsibility. Hopefully, one can apply the ethics of sustainability wisely.
References Alley, W.M. and Leake, S.A., The journey from safe yield to sustainability. Ground Water, 42, 12–16, 2004. Bredehoeft, J.D., The water budget myth revisited: why hydrogeologists model. Ground Water, 49, 340–345, 2002. Brown, R.H., The cone of depression and the area of diversion around a discharging well in an infinite strip aquifer subject to uniform recharge. U.S. Geological Survey Water-Supply Paper 1545C: pp. C69–C85, 1963. Brundtland (Report), Our common future, World Commission on Environment and Development. New York, Oxford University Press, 1987.
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Jacob, C.E., On the flow of water in an elastic artesian aquifer. Transactions of American Geophysical Union, Part 2: pp. 585–586, 1940. Lohman, S.W., Definitions of selected ground-water terms — revisions and conceptual refinements, Water Supply Paper 1988, U.S. Geological Survey, Reston, VA, 1972. Reilly, T.E., Franke, O.L., and Bennett, G.D., Principle of superposition and its application in groundwater hydraulics, Techniques of Water-Resources Investigations, Book 3: Application of Hydraulics, Chapter B6. U.S. Geological Survey, Denver, CO, 1987. Theis, C.V., The relation between lowering the piezometric surface and the rate and duration of discharge of a well using groundwater storage. Transactions American Geophysical Union, 16th Annual Meeting, Part 2: pp. 519–524, 1935. Theis, C.V., The source of water derived from wells: essential factors controlling the response of an aquifer to development. Civil Engineer, 10, 277–280, 1940.
Further Reading Alley, W.M. and Leake, S.A., The journey from safe yield to sustainability. Ground Water, 42, 12–16, 2004. This paper explores sustainability using as an example a groundwater development in Paradise Valley, Nevada. Devlin, J.F. and Sophocleous, M., The persistence of the water budget myth and its relationship to sustainability. Hydrogeology Journal, 13, 549–554, 2005. This paper further explores the idea of capture and its relationship to sustainability.
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28 The Impact of Climate Change on Groundwater 28.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28-1 28.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28-2 Climate Change • Impact of Climate Change on Water Resources • Groundwater Recharge • Factors Affecting Recharge • Recharge Estimation Methods • Recharge in Groundwater Modeling
28.3 A Case Study: Recharge Analysis of the Grand River Watershed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28-20
Mikko I. Jyrkama and Jon F. Sykes University of Waterloo
Introduction • Input Data • Methodology • Results • Conclusions
28.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28-34 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28-34
28.1 Introduction The growing and competing demand for domestic, agricultural, industrial, and recreational water has made clean and safe drinking water a scarce natural resource in many regions of the world. Increasing populations, especially in urban areas, are not only stressing the capacity and sustainability of the existing water supplies, but they are also placing the supplies at a greater risk of contamination. Humans are also affecting the global water resources through climate change. Increases in the atmospheric concentrations of greenhouse gases and aerosols, as well as changes in land use due to deforestation and urbanization already have, and will continue to impact the Earth’s climate, and hence the terrestrial hydrologic cycle in the future (IPCC, 2001). The human impacts on Earth’s water resources are not only being felt in developing countries, but they are increasingly, and often dramatically, being noticed in developed nations such as the United States and Canada. Understanding the interaction between the various components of the hydrologic cycle is, therefore, essential for the management of watershed and for ensuring the quality and sustainability of safe and clean drinking water resources. The surface water and groundwater systems have often been considered as separate due to the pervasive complexity and increased computational effort required by their integration (El-Kadi, 1989). The systems, however, are intrinsically linked through the processes of recharge and discharge, and their interaction constitutes an essential part of the hydrologic cycle. 28-1
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According to Robins (1998), “the management of both groundwater resources and of individual groundwater sources cannot sensibly be undertaken without some knowledge of recharge: its quantity, its seasonality and, above all, the different routes through the sub-soil and the unsaturated zone by which it can occur”. Recharge also plays an important role in the assessment of aquifer vulnerability to contamination. According to Foster (1998) “since the transport of most groundwater contaminants, with the exception of density driven contaminants such as DNAPLs, to saturated aquifers occurs in the aqueous phase as part of the recharge process, assessing aquifer pollution vulnerability is inextricably linked with understanding groundwater recharge mechanisms.” Aquifer vulnerability maps can provide valuable guidance to municipal planners and developers regarding land use allocation, well locations, and pumping regulations. This is especially important in areas where the underlying aquifers are exploited extensively for drinking water purposes. Changes in future climate will alter regional hydrologic cycles and subsequently impact the quantity and quality of regional water resources (Gleick, 1989). While climate change affects surface water resources directly through changes in the major long-term climate variables such as air temperature, precipitation, and evapotranspiration, the relationship between the changing climate variables and groundwater is more complicated and poorly understood. Groundwater resources are related to climate change through the direct interaction with surface water resources, such as lakes and rivers, and indirectly through the recharge process. Therefore, quantifying the impact of climate change on groundwater resources requires not only reliable forecasting of changes in the major climatic variables, but also accurate estimation of groundwater recharge. Accurate spatial and temporal characterization of groundwater recharge can be difficult, due to its dependence on a multitude of physical factors such as land use and hydrogeological heterogeneity (Lerner et al., 1990). Groundwater recharge can also be significantly impacted by snowmelt and frozen soil conditions in northern climates, and furthermore be complicated by the issue of scale. It is evident that assessing the impact of climate change on groundwater resources requires a physically based approach for estimating groundwater recharge. The method must not only account for temporal variations in the climatic variables and their impact on the hydrologic cycle, but also consider the spatial variation of surface and subsurface properties across the study area. Many climate change studies have generally focused on modeling the temporal change in the hydrologic processes and ignored or relied on average spatial characteristics due to model limitations or coarse discretization schemes. This chapter outlines a physically based methodology that can be used to characterize not only the temporal impact, but also the spatial effect of climate change on groundwater recharge. The method is based on the hydrologic software package HELP3 coupled with a geographic information system (GIS). The method is used in an example application to simulate the past conditions and possible future changes in the hydrologic cycle of the Grand River watershed in Ontario, Canada.
28.2 Background 28.2.1 Climate Change The Earth’s energy cycle is driven by short wave radiation from the sun and balanced by the outgoing long wave terrestrial radiation. Any changes in this radiative balance will alter the global hydrologic cycle, and hence, the groundwater recharge as well as the atmospheric and oceanic circulation, thereby resulting in climate change. According to the Intergovernmental Panel on Climate Change (IPCC), the key climate variables impacted by changes in the Earth’s energy balance include temperature, precipitation and atmospheric moisture, snow cover, extent of land and sea ice, sea level, patterns in atmospheric and oceanic circulation, and extreme weather and climate events (IPCC, 2001). The Earth’s radiative balance can be affected not only by human impacts, but also by a multitude of natural factors, resulting in both cooling and warming of the climate system. While increases in greenhouse gases, such as carbon dioxide, ozone, methane, and nitrous oxide, reduce the outgoing terrestrial radiation (i.e., heat) to space, thereby resulting in warming of the lower atmosphere and the Earth’s surface,
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anthropogenic aerosols, such as those derived from fossil fuels and biomass burning, can reflect the incoming solar radiation, leading to cooling of the climate systems (IPCC, 2001). Changes in volcanic activity, the energy output of the sun, and slow variations in the Earth’s orbit, not only have, but will also continue to impact the Earth’s climate in the future. Climate variations can also occur in the absence of external factors, as a result of complex interactions between the components of the climate system, such as the coupling between the atmosphere and the oceans. Variations in climate occur across a range of temporal and spatial scales, making both observation and modeling highly uncertain (Goddard et al., 2001). Nevertheless, advanced remote sensing from Earthobservation satellites is providing increasingly detailed images of our current climate, while the growing amount of paleoclimatic core data from trees, sediments, and ice are providing information about the Earth’s climate in the distant past. At the same time, the continuing increase in computing power has led to the development of more detailed and sophisticated global climate and general circulation models (GCMs). The interaction between the Earth’s orbit, ocean circulation, and atmosphere has contributed to nine glacial episodes in the northern hemisphere over approximately the past 900,000 years. Tarasov and Peltier (2004) integrated a GCM with a glacial model to simulate the evolution of ice coverage over the North American continent. McGuffie and Henderson-Sellers (2001) provide a review of climate modeling over the past 40 years. Significant improvements in hydrological parameterizations and grid resolution have also allowed coupling between the atmospheric circulation and hydrologic surface water models (Stewart et al., 1998; Pitman, 2003). The greatest uncertainty in future predictions by climate models arises from clouds and their interactions with radiation. Clouds can both absorb and reflect solar radiation and absorb and emit long wave radiation, thereby either cooling or warming the Earth’s surface. The variation in the two states is controlled by many factors and is difficult to model. Therefore, clouds represent a significant source of potential error in climate simulations (IPCC, 2001). Through the co-ordination of researchers from around the world, and after a comprehensive and careful review of a vast number of observational records and results from a number of simple and complex GCM models, the IPCC has arrived at the following general predictions for the global climate during this century (IPCC, 2001): • The global average surface air temperature is predicted to increase by 1.5 to 4.5◦ C. Furthermore, it is very likely that nearly all land areas will warm more rapidly than the global average, particularly those at northern high latitudes in the cold season. • Globally averaged water vapor, evaporation, and precipitation are projected to increase. Both increases and decreases in precipitation are seen at the regional scale. • Precipitation extremes are projected to increase more than the mean, and the intensity and frequency of extreme precipitation events are projected to increase. • Ice caps and glaciers will continue their widespread retreat during the 21st century while sea ice and snow cover in the Northern Hemisphere are projected to decrease further. • The global average sea level is predicted to increase by 0.09 to 0.88 m, with regional variations.
28.2.2 Impact of Climate Change on Water Resources Various hydrologic models have been used to study the impact of climate change on water resources (e.g., Wilkinson and Cooper, 1993; Gureghian et al., 1994; Cooper et al., 1995; Bobba et al., 1997; Querner, 1997; Rosenberg et al., 1999; Kirshen, 2002). The hydrological effects of climate change are commonly evaluated by estimating the sensitivity of model outputs, such as streamflow hydrographs or soil moisture contents, to hypothetical changes in the magnitude and temporal distribution of model inputs such as precipitation and temperature. In addition to hypothetical perturbations, however, the results inferred from the GCMs have also been used to predict the effects of climate change on regional hydrology. In one of the early studies, Vaccaro (1992) used a deep percolation model (DPM) to estimate the influence of climate change on recharge variability in a basin in north-western United States. In addition
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to historical records, climate predictions from the synthetic weather generator WGEN (Richardson and Wright, 1984) and three GCMs were considered along with two different land use conditions. The results of the study indicated that the variability in annual recharge was less under the GCM conditions than using the historic data. The objective of the study was to investigate the degree of variability in climate and its impact on future recharge predictions, and not explicitly to predict the impact of climate change on recharge rates in the basin. Bouraoui et al. (1999) developed a methodology to disaggregate the outputs of large-scale GCMs for use in hydrologic models. The method was used in conjunction with the runoff and sediment transport model ANSWERS to investigate the impact of doubling CO2 on groundwater recharge in a watershed in France. The methodology was based on a statistical approach requiring a large number of simulations. The results of the study indicated that recharge would decrease in the basin due to increase in atmospheric CO2 . Rosenberg et al. (1999) used the GIS-based program HUMUS and the hydrologic model SWAT (Arnold et al., 1998) to study the impact of climate change on the water yield and groundwater recharge of the Ogallala aquifer in the central United States. Three different GCMs were used to predict changes in the future climate due to anticipated changes in temperature and CO2 concentrations. The study found that recharge was reduced under all scenarios, ranging up to 77%, depending on the simulation conditions. Kirshen (2002) used MODFLOW to study the impact of global warming on a highly permeable aquifer in the northeastern United States. The lumped hydrologic model HSPF was used to compute streamflows from rainfall, temperature, and potential evapotranspiration, while groundwater recharge was estimated using a separate model based on precipitation and potential evapotranspiration. The sensitivity of the aquifer system to the possible effects of global climate change was simulated by introducing both hypothetical and GCM predicted changes to the input parameters of the HSPF and recharge models, and then running MODFLOW based on the outputs. The results of the study were mixed, showing higher, no different, and significantly lower recharge rates and groundwater elevations, depending on the climate scenario used. Croley and Luukkonen (2003) studied the impact of climate change on groundwater using a regional scale MODFLOW model of Lansing, Michigan. The results from two separate GCMs were first used in an empirical streamflow model to estimate baseflow rates. The recharge in the regional groundwater model was then adjusted on the basis of the differences in baseflow from the two GCMs. The study used a steady-state approach and hence the transient changes in groundwater levels were not captured in the analysis. The results of the study indicated that the simulated groundwater levels were generally predicted to increase or decrease due to climate change, depending on the GCM used. Eckhardt and Ulbrich (2003) used a revised version of the SWAT model to investigate the impact of climate change on groundwater recharge and streamflow. The model was applied to a small catchment in Germany. Climate change was simulated by adjusting stomatal conductance and leaf area in the SWAT model as a response to increased CO2 levels. Four different climate scenarios were considered based on simulations from five different GCMs. The results of the study indicated that more precipitation will fall as rain in winter due to increased temperatures resulting in higher recharge and streamflow in January and February. They also found that the snowmelt increase in recharge in March disappears, while recharge and streamflow were shown to be potentially reduced in the summer months. Loaiciga (2003) conducted a review of climate change predictions and associated hydrologic consequences and presented the results of a case study of an aquifer in south-central Texas. The study considered a confined karst aquifer that receives recharge only in sections of streams that are hydraulically connected to the underlying water table. The impact of climate change on the indirect recharge was estimated using runoff scaling factors based on the ratio of historical and future streamflows predicted from linked general and regional climate models. The study also considered the impact of changes in pumping rates (i.e., predicted changes in groundwater use) on groundwater resources of the aquifer. The study concluded that the rise in groundwater use associated with predicted growth would pose a higher threat to the aquifer than climate change. Allen et al. (2004) used Visual MODFLOW to study the impact of climate change in an aquifer in southern British Columbia, Canada. The recharge boundary condition for the groundwater model was
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estimated using Visual HELP, while rivers were represented using constant heads. Constant recharge was assumed across the domain in a steady-state analysis. The base case recharge analysis was based on synthetic weather generated with WGEN (Richardson and Wright, 1984) using Canadian weather normals (i.e., thirty-year averages) from a nearby weather station as input. Four climate change scenarios were considered based on general predictions for the study area. The average temperature and precipitation were perturbed based on the predictions and were then used in WGEN to generate synthetic records. Average annual recharge rates were then computed for each of the scenarios and applied across the whole domain. Results of the study indicated that there was little change in the overall water table configuration as a result of potential climate change. This is to be expected, however, as constant recharge (i.e., spatially) was assumed across the domain. Brouyere et al. (2004) investigated the impact of climate change on a chalky groundwater basin in Belgium using the integrated hydrological model MOHISE. The integrated model was composed of three submodels, each for soil, surface water, and groundwater, which were linked through flux boundaries. Three GCMs were used to compute monthly change rates in precipitation and temperature that were then used to adjust the daily historical record to obtain climate change scenarios. The results showed decreases in groundwater levels for two scenarios, while one of the models showed no significant change. Instead of seasonal changes in groundwater levels, a monotonic increase over time was observed. The impact of seasonal variation was likely smoothed out by a thick saturated zone found at their basin. Understanding the impact of climate change is most crucial for studies concerned with the storage and containment of high-level nuclear waste. Due to the slow decay of nuclear materials, modeling efforts must be concerned with changes in boundary conditions over very long periods of time. However, predictions of climate change are highly uncertain even for shorter periods such as the next century, making the predictions for the next 10,000 to 100,000 years extremely uncertain. Yucca Mountain in Nevada is being evaluated as a potential site for high-level nuclear waste disposal in the United States. Because the proposed repository is to be located within the deep unsaturated zone, estimating rates of groundwater recharge at the site is critically important (Flint et al., 2002). Gureghian et al. (1994) studied the impact of climate change on the groundwater recharge rate at Yucca Mountain using a quasi-linear form of the Richards’ equation. They used two different climatic variation models for temperature and precipitation over the next 10,000 years based on the recommendations by a panel of experts. The results of the study indicate minimal differences between the two climate models on the overall movement of the wetting front. In summary, climate change will have an impact on future recharge rates and hence on the underlying groundwater resources. The impact may not necessarily be a negative one, as evidenced by some of the investigations. Quantifying the impact is difficult, however, and is subject to uncertainties present in the future climate predictions. Simulations based on general circulation models have yielded mixed and conflicting results, raising questions about their reliability in predicting future hydrologic conditions. Groundwater recharge is influenced not only by hydrologic processes, but also by the physical characteristics of the land surface and soil profile. Many climate change studies have focused on modeling the temporal changes in the hydrologic processes and ignored the spatial variability of physical properties across the study area. While knowing the average change in recharge and groundwater levels over time is important, these changes will not occur equally over a regional catchment or watershed. Long-term water resource planning requires both spatial and temporal information on groundwater recharge to properly manage not only water use and exploitation, but also land use allocation and development. Studies concerned with climate change should therefore also consider the spatial change in groundwater recharge as a result of future changes in hydrologic processes.
28.2.3 Groundwater Recharge The word “recharge” has several meanings in the groundwater literature. Generally, it means any water that is added as an input to the system, while discharge is normally considered to be any water that exits the groundwater system. Within the context of this chapter, groundwater recharge is defined as the soil
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FIGURE 28.1 The hydrologic cycle.
water (from precipitation) in the vadose zone that crosses the water table into the saturated zone. Recharge of deeper confined aquifers can also occur both laterally and vertically through aquitard leakage in the saturated zone (Gerber and Howard, 2000). Groundwater recharge is part of the vadose zone soil water budget. Figure 28.1 illustrates the main processes. For clarification, infiltration is defined as the volume rate of water flowing into a unit area of soil surface, whereas percolation is the process by which water migrates down through the soil profile in the unsaturated zone. Deep soil water percolation, often referred to as groundwater recharge by soil scientists, is the water that has moved past the evaporative and root zones in the vadose zone and is no longer available to plants. The driving force for natural recharge is precipitation; however, groundwater recharge may also result from other processes. According to Lerner et al. (1990) groundwater recharge can be divided into three distinct processes: • direct recharge, which is water added to the groundwater system in excess of soil moisture deficits and evapotranspiration by direct vertical percolation of precipitation through the unsaturated zone. • localized recharge is an intermediate form of recharge resulting from the horizontal surface concentration of water in local joints and depressions. • indirect recharge is the flow of water to the water table through the beds of surface water courses, such as rivers and lakes. As direct recharge due to precipitation forms the highest contribution to the groundwater system in humid climates (Knutssen, 1988), it will receive the main focus in this section. Surface water bodies commonly act
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as discharge areas rather than recharge areas in humid climates and therefore provide a minor contribution to the overall production of groundwater recharge. However, for areas of an aquifer in close proximity to a surface water body, seasonal variations in surface water levels may result in alternating periods of groundwater recharge and discharge. Climate change can impact the levels of the surface water and hence the relative importance of the recharge and discharge. As shown in the hydrologic cycle in Figure 28.1, precipitation is formed either as rain or snow. Before reaching the ground, however, the vegetation canopy intercepts some of the precipitation, which then either evaporates, or is channeled to the ground via stemflow, or drips directly to the ground as part of throughfall. Depending on the rainfall intensity and ground surface cover, the precipitation reaching the ground surface may then flow overland directly into streams and ditches, or infiltrate into the soil. The infiltrated water then percolates downwards through the vegetative root zone or evaporative zone where a portion of it may be taken up by the plant roots and subsequently transpired through the vegetation canopy. The remaining water will continue percolating deeper into the soil column, eventually becoming groundwater recharge when crossing the water table into the saturated zone. The percolating soil water can also partition into the air phase in the vadose zone through evaporation at any time, depending on the moisture content and distribution in the unsaturated zone.
28.2.4 Factors Affecting Recharge 28.2.4.1 Precipitation Precipitation is the most important parameter in the groundwater recharge process. It is the driving force in the hydrologic cycle and provides the water that will eventually recharge the groundwater system. Precipitation is effected by climatic factors such as wind and temperature, resulting in a very complex and dynamic distribution. Therefore, determining the amount and rate of precipitation over an area is exceedingly difficult due to the high spatial and temporal variation. Storm events can vary widely in duration, velocity, and intensity, while lower temperatures can result in snowfall or mixed precipitation. Singh (1997) provides a literature review on the effects of rainfall variability across a watershed on streamflow hydrographs. He concludes that the velocity and direction of a storm has a significant impact on the hydrographs and that temporally varying rainfall leads to higher peak flows than constant rainfall. In addition, low intensity rainfall may cause no recharge due to a high rate of evapotranspiration, whereas the same amount in a shorter time period may be sufficient to saturate the soil and cause recharge (Lerner et al., 1990). In arid and semiarid areas, where evaporation dominates the water balance, recharge is determined by the distribution of extreme events in excess of threshold levels (Lloyd, 1986). In addition to estimation, accurate measurement of precipitation is also very difficult. Point measurements using standard rain gauges, such as weighing, capacitance, tipping-bucket, and optical types, are often used to measure the accumulation of rainfall at a particular location. However, these instruments can be subject to large measurement errors (Habib et al., 2001), and provide poor estimates of the spatial distribution of rainfall over a catchment. Ball and Luk (1998) analyzed the spatial distribution of rainfall over a catchment using several mathematical models in the GIS environment. They showed that all the methods based on spatial extrapolation of point data, such as Theissen polygons, inverse distance weights, kriging, and surface fitting, can result in significant errors in predicted rainfall distributions. An accurate representation of rainfall is especially difficult in remote areas where the available information is limited. In many cases, synthetic weather generators based on historical weather records and stochastic analysis, such as WGEN (Richardson and Wright, 1984) and MORECS (Hough and Jones, 1998) are often used to generate synthetic weather data and rainfall distributions. However, these methods commonly use the extrapolation methods described by Ball and Luk (1998) and hence are subject to potentially large errors. The use of weather radar to predict precipitation distributions seems promising; however, it is also subject to errors (e.g., due to signal noise) and problems with scale or resolution (Kouwen and Garland, 1989). In most groundwater modeling applications, rainfall rates are often considered constant spatially, or averaged over time in steady state analyses. Individual storm events are rarely accounted for and monthly
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or annual averages are commonly used. The assumption of temporally averaged rainfall seems reasonable, at least for shorter time periods, as the fluxes in the vadose zone contributing to recharge are usually much slower than an individual storm. However, rainfall varies considerably even over short distances, and therefore, the spatial variation in precipitation should not be ignored, especially in larger scale modeling studies. 28.2.4.2 Land Use and Cover The type of land cover can have a significant impact on infiltration, and hence on groundwater recharge. For example, the clearing of native vegetation and replacing it with shallow-rooted annual crops and pastures have resulted in substantial waterlogging and salinity problems in Australia due to increased recharge rates (e.g., Peck, 1978; Williamson, 1990; Walker et al., 2002). Urban areas can also have a profound impact on groundwater recharge by increasing the amount of impervious areas and generally altering the land surface from its natural state (Lerner et al., 1990; Lerner, 2002). However, the most significant impact of urbanization is often its adverse impact on the quality of recharge, rather than on its quantity (Foster, 2001). The impact of land use changes on groundwater recharge has been the focus of modeling studies. Walker et al. (2002) give a comprehensive review of modeling approaches used in Australia to combat dryland salinity problems. Carmon et al. (1997) and Collin and Melloul (2001) investigated the impact of urbanization and changes in land use types in the context of sustainable groundwater development in Israel. They concluded that measures should be taken to reduce the negative effects of urban development on groundwater quality. Finch (2001) estimated the response of mean annual groundwater recharge to land cover changes in a rural catchment in southern England. He observed that land use changes lead to changes in the recharge pattern, but had no impact on the overall catchment total. Bellot et al. (2001) studied the impact of land use changes on runoff and recharge due to wildfires, afforestation, and land abandonment in Spain. They found that the increase in vegetated land cover has a negative effect on human water availability in semiarid areas, due to decreased aquifer recharge rates. Batelaan et al. (2003) used MODFLOW to study land use changes in Belgium by perturbing recharge rates at selected areas. Their study yielded mixed results. 28.2.4.3 Vegetation Vegetation reduces recharge by directly interfering with the passage of precipitation from the atmosphere to the water table. The vegetation canopy intercepts a portion of the rainfall, which then either evaporates, or is channeled to the ground through stemflow, or drips directly to the ground as part of throughfall (Le Maitre et al., 1999). Arguably, these processes are very difficult to quantify as they are dependent on a multitude of climatic parameters, such as intensity and duration of rainfall, temperature, wind speed, as well as the physical characteristics of the individual plants (Larcher, 1983). However, they can still have a significant effect on the recharge process as shown by Taniguchi et al. (1996) and Finch (1998). Perhaps the greatest influence on recharge by vegetation is through evaporation and transpiration. These terms are often lumped together with direct evaporation from the soil and referred to as evapotranspiration. Evapotranspiration is an important component of the water budget with up to 40 to 60% of the annual rainfall being lost through it in humid climates (Knutssen, 1988). Methods to calculate actual evapotranspiration include the Bowen ratio method, derived from a simplified energy balance, and the eddy correlation method based on the correlation between wind speed and vapor density (e.g., Dingman, 1994). The downside of these models is that they require variables, such as aerodynamic, thermal, and plant specific parameters, which are very difficult to measure in practice. Other methods, such as Penman (1948), Penman-Monteith (Monteith, 1965), Thornthwaite and Mather (1957), and Priestley and Taylor (1972) have been developed to estimate evapotranspiration. However, these models also require many parameters that are derived from ideal conditions. Furthermore, most of these methods estimate potential evapotranspiration, which is not always equal to actual evaporation rates. The Penman–Grindley model (Grindley, 1969) is a widely used and simple soil moisture budgeting
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and evaporation model, which also allows for the determination of recharge indirectly. Like the other models, however, it can be very sensitive to errors in the input parameters (Finch, 1998). Plant roots also play an important role in the recharge process. Not only do they enable plants to draw water from deep in the vadose zone (and even from the saturated zone), thereby reducing the amount of percolating water that reaches the water table, but they also create preferential flow paths and channels that aid water flow through the soil profile (Le Maitre et al., 1999). Studies have revealed that in addition to absorption, plant roots can also exude water into the soil in response to gradients in water potential between themselves and the soil (Burgess et al., 1998; Schulze et al., 1998). When root systems span soil layers of different moisture content, water is redistributed by the roots in the direction of the difference in water potential. This hydraulic redistribution of water not only removes excess water from the topsoil and out of the reach of evaporation, shallow-rooted competitors, runoff, and lateral subsurface flow, but it may also increase the capture of mobile nutrients such as nitrogen from the topsoil (Burgess et al., 2001). Although the water stored at depth is unlikely to be significant for drought avoidance by plants, the downward transfer of water to dry soil layers following rain my be important to plant establishment and the reduction of water logging in certain soil types (Burgess et al., 2001). Both Finch (1998), and Zhang et al. (1999b, 1999c) found that rooting depth, which depends on soil type, available water, and the type of plant, had a significant impact on groundwater recharge rates. The depth of plant root penetration is difficult to measure and can vary significantly even within the same plant community (Canadell et al., 1996; Jackson et al., 1996). Furthermore, only a few roots penetrating deep into the ground can sustain large plant communities (Le Maitre et al., 1999). Finch (1998) and Zhang et al. (1999b, 1999c) also found that the leaf area index, or the ratio of leaf area to ground cover, has a significant influence on groundwater recharge. Larger leaf areas result in greater interception of precipitation as well as potentially higher transpiration rates leading to decreased groundwater recharge. Although standard methods exist for measuring the leaf area index (Pearcy et al., 1989), these methods are impractical for large areas. The values for leaf area index reported in the literature are also very difficult to apply to many sites due to the high variability of types of vegetation across catchments and watersheds. In addition, the leaf area index not only has high variability between different plants, but it also varies seasonally due to climatic changes. In summary, the effect of vegetation on recharge can be both positive and negative. Vegetation intercepts rainfall and transpires water obtained from the rooted soil profile; however, it can also facilitate infiltration by reducing overland flow and creating surface storing opportunities. Plant root systems may also increase recharge rates by creating macropores and channels in the soil profile (Le Maitre et al., 1999), and by downward transfer of water due to differences in moisture potentials (Burgess et al., 2001). 28.2.4.4 Urbanization The water balance of an area can be drastically altered by urbanization. Not only is the recharge rate affected, but the entire climate can also be altered (Lerner et al., 1990). A micro-climate may develop in large urban centers, causing changes in temperature, humidity, wind speed, and air clarity (Hall, 1984). While surface runoff is considerably increased due to increased imperviousness, the amount of direct groundwater recharge due to precipitation is decreased (Burges et al., 1998; Rose and Peters, 2001). However, most urban centers import their water for consumption from outside sources thereby increasing the amount of water in the area. A portion of this imported water then becomes recharged through septic tanks and leaking sewer and water distribution systems, and over-irrigation of lawns and parks (Lerner et al., 1990; Simmers, 1998; Yang et al., 1999; Foster, 2001; Lerner, 2002). This kind of indirect or maninduced recharge can result in higher recharge rates, or balance the loss of precipitation recharge due to impermeable areas (Lerner, 2002). However, determining the exact spatial and temporal distribution of this indirect recharge is exceedingly complicated and difficult to account for in any modeling efforts (Yang et al., 1999). In summary, any changes in land cover, whether seasonal changes in vegetation or permanent changes due to urbanization, can impact groundwater recharge by altering the interception, infiltration, surface runoff, evaporation, and transpiration processes.
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28.2.4.5 Overland Flow Overland flow is a rare event in humid climates due to less intensive rainfall, well-developed vegetation, and sufficient infiltration capacity of most soils (Knutssen, 1988). Surface runoff occurs only over short distances or during special events such as intense snowmelt over frozen ground (Johnsson and Lundin, 1991). Furthermore, overland flow only takes place in the discharge areas, which usually occupy only a small part of a catchment (Knutssen, 1988). In areas of high topographic relief, with very low permeability soils such as clays and tills near the ground surface, surface ponding can occur, resulting in overland flow. Overland flow can be estimated using the diffusion wave approximation of the depth-integrated shallow water equations with Manning’s equation used for velocity calculations (Woolhiser et al., 1996; VanderKwaak, 1999). Due to small-scale variations in surface slope, the estimation of Manning’s roughness coefficients across a catchment is difficult and subject to spatial averaging. A popular method among surface hydrologists to estimate overland flow is using the Natural Resources Conservation Service (NRCS, formerly the Soil Conservation Service) curve number method (NRCS, 1986). This rainfall-runoff analysis method is based on a simple relationship between precipitation, infiltration, an initial abstraction, which is a function of interception and surface ponding, and an empirical curve number obtained from numerous field experiments. This method is widely applied due to its simplicity (e.g., Colosimo and Mendicino, 1996; Srinivas et al., 1999); however, it only provides estimates of runoff volumes, and ignores any subsurface flow mechanisms. 28.2.4.6 Infiltration and Flow in the Unsaturated Zone Infiltration is the volume rate of water flowing into a unit area of soil surface. It is generally considered to be one-dimensional in the vertical direction; however, as noted before, local changes in ground cover and near surface permeability can lead to lateral flows. Percolation is the process by which water migrates down through the soil profile, whereas deep soil water percolation is the water that has moved past the evaporative and root zones in the unsaturated zone and is no longer available to plants. Both infiltration and percolation are very complicated processes as they are governed by such factors as the rate of precipitation, antecedent moisture conditions in the soil, soil hydraulic properties, topography, and others. While infiltration equations (e.g., Green and Ampt, 1911; Horton, 1940; Philip, 1957) simply describe the rate of water movement into the soil at the ground surface, other relationships (e.g., Richards, 1931) are used to describe the percolation of water through the unsaturated zone. The processes of infiltration and flow in the unsaturated zone have been much studied with many methods derived for their estimation. These processes are examined in detail in other chapters of this book. 28.2.4.7 Soil Properties The hydraulic properties of the soils in the unsaturated zone are very sensitive to the moisture content and pressure head distributions. A small change in the volumetric water content can often result in a change in the hydraulic conductivity by two or more orders of magnitude (Rushton, 1988). In addition, the soils in the unsaturated zone rarely exhibit homogeneous properties, often consisting of layered sands, silts, and clays, resulting in non-uniform moisture distributions. Instability in the wetting front and subtle changes in the permeability structure can also lead to flow fingering (Kung, 1990; Selker et al., 1992). The fingering process is enhanced by initially dry, layered, coarse-grained systems (Sililo and Tellam, 2000); however, the antecedent moisture contents prevalent in the field in humid climates will generally inhibit its occurrence. The unpredictable occurrence of preferred pathways, due to plant roots, cracks, and fissures, in even relatively homogeneous materials furthermore complicates the hydraulic characterization of soils in the unsaturated zone (Simmers, 1990). Large variations in recharge can also occur even across uniform soils due to topography, resulting in depression focused recharge (e.g., Freeze and Banner, 1970; Winter, 1983; Schuh et al., 1993).
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28.2.4.8 Temperature In northern climates, subzero temperatures result in snow accumulations in winter time, as well as frost formation in the near surface soil layers due to pore water freezing. Furthermore, in northern Canada, the layer of frost remains in the ground throughout the entire year and is referred to as permafrost. The presence of both a snowpack and a frozen soil layer will clearly have a significant impact on the recharge process. Similar to rainfall, the spatial and temporal distribution of snow accumulation is very complex, and even further complicated by its high sensitivity to temperature and wind velocities (i.e., drifting) (Deng et al., 1994). Snowpack melting is a fairly well-understood process and is primarily based on the energy balance at the air–snow interface, and on the physical characteristics of the snowpack (Harms and Chanasyk, 1998). However, the presence and extent of the frost layer influences the amount and distribution of the infiltrating snowmelt. Snowmelt or rain located in one portion of a watershed may be redistributed by either surface runoff or interflow on top of the frozen soil layer depending on the topography (Johnsson and Lundin, 1991). As the soil frost layer develops, the water in the soil pores freezes. The growing ice constricts or blocks the infiltrating water, thereby increasing the tortuosity and producing a net reduction in hydraulic conductivity and infiltration rates (Kane and Stein, 1983; Granger et al., 1984; Black and Miller, 1990). Infiltration rates can also vary depending on the initial soil water content before freezing (Engelmark, 1988). The depth of the frozen soil layer is dependent on several factors such as temperature, the duration of freezing temperatures, snow depth at the ground surface, and initial soil water content (Daniel and Staricka, 2000). The porosity of the frozen soil may also change due to expansion caused by ice formation. The freeze–thaw process can also create large, temporary fractures resulting in higher hydraulic conductivities as the ice melts (Johnsson and Lundin, 1991). As shown by Jyrkama (1999), during and immediately after thawing of the frozen soil layer in the spring, rapid infiltration of the accumulated snowmelt can create a transient groundwater mound, resulting in significant recharge to the water table. Therefore, due to the complex interaction of all the above processes, modeling unsaturated zone flow in a seasonally (or permanently) frozen environment is very challenging.
28.2.5 Recharge Estimation Methods The link between climate change and groundwater is the precipitation recharge at the land surface and the recharge and discharge that occurs at surface water bodies. Reviews on the unsaturated zone flow processes and methods to quantify groundwater recharge rates from precipitation can be found in texts by Lerner et al. (1990) and Stephens (1996). In addition, Simmers (1988) and Sharma (1989) provide several examples on how these methods have been applied in many field studies. An overview of estimation problems and developments in groundwater recharge are also given by Simmers (1998) and the special theme issue of the Hydrogeology Journal (vol. 10, 2002). It should be noted that much of the literature and the associated methods have been developed for estimating recharge in arid and semiarid areas, where recharge plays both an economically and environmentally critical role. Lerner et al. (1990) highlight five main methods of estimating direct recharge from precipitation: • • • • •
direct measurement empirical methods water budget methods Darcian approaches tracers.
Other methods include, for example, plane of zero flux, temperature and electromagnetic methods, baseflow separation, remote sensing, and inverse groundwater modeling (Stephens, 1996). A brief discussion of these and other additional methods is presented in the following sections.
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28.2.5.1 Field (or Direct) Techniques The most common and practical instrument to measure recharge directly is with a lysimeter. A lysimeter is a block of soil instrumented such that all the parameters in the water budget can be quantified, with the recharge flux being either measured directly at the bottom (e.g., Lerner et al., 1990), or estimated based on the changes in the block weight (Kirkham et al., 1984; Yang et al., 2000). The inherent problems with lysimeters are that they are difficult and expensive to construct and only provide a point or an average value of recharge for the materials within the block. Soil disturbance is also a problem, as well as leaks and other failures resulting in potentially erroneous measurements. The major difficulty with weighing lysimeters is in measuring small weight changes in relation to the large and heavy soil mass. As an example, Fayer et al. (1996) used three lysimeters, in conjunction with other methods, to estimate recharge rates at the Hanford nuclear waste site in the United States. They measured drainage from the bottom of each instrument over several years to estimate an average annual recharge rate. The lysimeters were of different depths and filled with soils typical of their surroundings. The main problem with their measurements, however, was that the instruments were too shallow (i.e., within or above the root or evaporative zone). Therefore, in spite of the long measurement period used, the collected drainage may have overestimated the actual recharge rates in the area. To avoid problems with the larger size instruments, Holder et al. (1991) developed a special wick pan lysimeter, also called the passive capillary sampler (PCAPS). The PCAPS is generally constructed from a small sealed bucket and instrumented with a wetted fiberglass wick that acts as a hanging water column and develops suction in the soil water depending on the flux. Louie et al. (2000) used a number of PCAPS and found them to perform satisfactorily under various field conditions. The matric potential and water content measurements using tensiometers and time-domain reflectometry (TDR) can also be used in the field to estimate hydraulic gradients and storage changes in the vadose zone. As a pulse of infiltrated water moves through the unsaturated zone, a plane of zero flux, that is, where the hydraulic gradient is zero, may develop as the water above the plane moves upward due to evapotranspiration while below the plane, water moves downward due to gravity (e.g., Scanlon et al., 2002). Water below the zero flux plane will therefore become recharged, and the amount or rate can be calculated by monitoring the change in water content below the plane. However, this requires extensive monitoring in the field and is therefore unfeasible for large areas. Furthermore, the location of the zero flux plane changes with time and only applies to a pulse of infiltrated water. Therefore, the method breaks down when there is a downward hydraulic gradient due to a continuous precipitation event (Stephens, 1996). Temperature and electromagnetic methods have been developed based on the fact that surface waters and groundwaters have different temperatures and chemical compositions. The rate of recharge can be estimated based on measured borehole temperature profiles (Taniguchi, 2002) or through soil temperature measurements (Taniguchi and Sharma, 1993). Electromagnetic methods are mostly used for reconnaissance investigations to screen sites where more quantitative methods for recharge could be applied (Cook and Kitty, 1992). Similarly, remote sensing, such as Landsat imagery (Salama et al., 1994) or InSAR analysis of ERS-1 and ERS-2 images (Lu and Danskin, 2001) have been used to distinguish regions of recharge and discharge over larger areas. 28.2.5.2 Empirical Methods Recharge rates have been estimated by correlating precipitation with recharge using an empirical relationship often based on regression (e.g., Sinha and Sharma, 1988; Shade and Nichols, 1996; Yang et al., 1999; Nichols and Verry, 2001; Xu and van Tonder, 2001; Chen et al., 2002) or stochastic analysis (Wu et al., 1997; Gau and Liu, 2000). Although these methods may be adequate for the particular study area and purpose, they are not applicable to other areas. Expressing recharge as a function of precipitation has no physical basis, as all the unsaturated zone processes described in the previous section are completely ignored. Methods have also been developed to quantify groundwater recharge based on the analysis of the recession curve in the streamflow hydrographs (e.g., Rorabaugh, 1964; Chapman, 1999; Wittenberg and
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Sivapalan, 1999; Arnold et al., 2000). It is assumed that the recession part of the hydrograph represents primarily groundwater discharge to the river as a direct result of precipitation recharge to the aquifer. Erskine and Papaioannou (1997) further developed a relationship called the aquifer response rate based on maximum permissible abstraction and minimum flow requirements for a river. Halford and Mayer (2000) studied various hydrograph separation techniques and concluded that baseflow is frequently not equivalent to groundwater discharge because other hydrologic phenomena can significantly affect stream discharge during the recession periods. Drainage from bank storage, wetlands, surface water bodies, soils, and snowpacks also decreases exponentially during recession periods, and along with evapotranspiration, were shown to affect the stream discharge more than groundwater discharge during the recession periods. These methods have obvious limitations, therefore, and at best only provide an approximation of the overall volume of groundwater recharge over a selected time period. 28.2.5.3 Water Budget Methods Soil water budget methods are based on a soil moisture balance whereby all the components of the water balance equation are estimated with groundwater recharge being the residual (also see Figure 28.1) R = P − ET ± O ± S
(28.1)
where R is the recharge, P is precipitation, ET is actual evapotranspiration, O is the lateral surface runoff in and out of the area, and S represents the change in water storage in the unsaturated zone. Assuming a unit cross-sectional area, each process can be described as a rate or a flux. As indicated, water is added or depleted from the soil storage with any excess becoming groundwater recharge. Due to the difficulty in accurately estimating each of the processes, propagation of errors in the water budget method can result in large uncertainty in the calculated recharge. Furthermore, this method ignores the movement of moisture, that is, percolation, through the unsaturated zone, and therefore fails to account for the time it takes for the infiltrated water to reach the water table. Recharge is assumed to occur instantaneously as water is released from soil storage. Therefore, the temporal recharge pattern or the timing of recharge is difficult to capture with this method. The water budget method has been used to calculate average recharge rates in various situations (e.g., Bekesi and McConchie, 1999; Srinivas et al., 1999; Finch, 2001; Chapman and Malone, 2002). 28.2.5.4 Darcian Approaches Water movement in the unsaturated zone can be modeled based on Darcy’s equation and conservation of mass (Richards, 1931). The strength of this method is that it is physically based, however, in addition to the uncertainty in the antecedent moisture conditions and heterogeneities of the soil column, the high nonlinearity between the hydraulic conductivity, pressure head, and water content in the unsaturated zone pose several difficulties in its application. This method is therefore computationally intensive and requires detailed information about the hydraulic characteristics of the unsaturated zone. These inherent difficulties are compounded by the potential presence of root channels and other fissures, which may dominate the recharge process. However, accounting for the moisture movement through the unsaturated zone explicitly provides a robust method of estimating groundwater recharge (assuming errors in the input data can be minimized). 28.2.5.5 Tracers A host of environmental tracers have been used to estimate groundwater recharge. These include tritium and chlorine-36, chloride, carbon-14, chlorofluorocarbons, and stable isotopes such as deuterium, and 18 O. These methods require the measurement of a concentration profile in the soil column, which provides information about water movement in the unsaturated zone. Recharge is then estimated based on a tracer mass balance, total water content analysis, or numerical modeling. These methods usually assume piston displacement and result in an estimate of either a long-term average recharge rate or a total volume of recharge (e.g., Allison, 1988; Scanlon et al., 2002).
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28.2.5.6 Inverse Groundwater Modeling Recharge is commonly used purely as a calibration parameter in many groundwater modeling studies (e.g., Martin and Frind, 1998; Bonomi and Cavallin, 1999; Javed and Bonnell, 1999; Varni and Usunoff, 1999; Ella et al., 2002). Therefore, the resultant recharge pattern can potentially be used to quantify recharge rates in the area. Zoning of recharge into equivalent areas is often used to reduce the total number of calibration parameters. The concepts of inverse calibration and zoning are based on earlier conceptual models (e.g., Toth, 1963; Freeze and Witherspoon, 1968; Winter, 1978, 1983) where the specific recharge and discharge zones emerge naturally as a response to geologic or topographic conditions. The distribution of recharge can therefore be delineated with the knowledge of the depth of the water table and the underlying hydraulic conductivity distribution, while the rate of recharge can furthermore be estimated using the Darcy equation. Stoertz and Bradbury (1989) and Levine and Salvucci (1999) used this approach with numerical groundwater flow modeling to delineate recharge areas and rates. Using the same concept, Lin and Anderson (2003) developed a recharge and discharge mapping procedure based on pattern recognition and image analysis. Similar to Stoertz and Bradbury (1989) their method is based on a mass balance calculation performed using MODFLOW, and therefore is critically dependent on the accuracy of the water table interpolation. Zoning is used to smooth out the results as “it is not practical to work with numerous grid specific rates in a parameter estimation code, nor are the individual values expected to be very accurate” (Lin and Anderson, 2003). Scale is also a major problem with this method as the resolution of the hydraulic gradient between adjacent model cells decreases with finer grid spacing. As the method ignores all the physically based processes in the hydrologic cycle contributing to recharge, and only considers parameters used in the groundwater flow model, Lin and Anderson (2003) admit that the method may result in unreasonable estimates of groundwater recharge, for example, recharge greater than precipitation. The main problem with inverse groundwater model calibration is that it relies entirely on the accuracy of the groundwater flow model which often has great uncertainty associated with it due to limitations in the input data. Small changes in the calculated hydraulic conductivity field, for example, can result in potentially large variations in the recharge estimates. Furthermore, because hydraulic conductivity ranges over several orders of magnitude, estimated recharge rates are highly uncertain. The results are also nonunique because the same distribution of hydraulic heads can be produced with a range of recharge rates, as long as the ratio of recharge to hydraulic conductivity remains the same (Scanlon et al., 2002). This approach, therefore, ignores all the physical processes in the hydrologic cycle and disregards the dynamic interaction between the surface water and groundwater systems. 28.2.5.7 Combined Modeling Groundwater recharge has also been estimated by using a mixed approach, based on a combination of the water budget methods and the Darcy equation. The problem with the Darcian approach alone is that it lacks the description of many of the important hydrologic processes. It simply calculates the movement of water through the soil column based on limited boundary conditions. Using the water budget method first to estimate important processes such as surface runoff, evapotranspiration, and snowmelt, for example, and then calculating percolation through the unsaturated zone using the Darcy equation, will preserve the hydrologic moisture balance and allow recharge to be quantified in both space and time. This approach is also well suited to the investigation of the impact of land use and climate changes on groundwater recharge. The various weather input parameters, such as precipitation and temperature, can be perturbed according to predicted changes in the future climate, while the ground surface properties, such as runoff potential and rooting depths, can be modified due to expected changes in land use. Examples of combined models include Bauer and Vaccaro (1987), UNSAT-H (Fayer and Jones, 1990), TOPOG_IRM (Dawes and Hatton, 1993), PRZM-2 (Mullins et al., 1993), HELP3 (Schroeder et al., 1994), Sandstrom (1995), ANSWERS (Bouraoui and Dillaha, 1996), PERFECT (Abbs and Littleboy, 1998), SWAT (Arnold et al., 1998), and WAVES (Zhang and Dawes, 1998). The rate of recharge in each model is simulated using a combination of various vegetation, climate, and hydrologic models.
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28.2.6 Recharge in Groundwater Modeling 28.2.6.1 Introduction Groundwater models are employed for numerous hydrologic investigation purposes such as vulnerability assessments, remediation designs, and water quantity estimations. Most often, however, they are used in groundwater quality studies dealing with the increasing number of emerging groundwater contamination problems. Groundwater models are applied across various scales, from very small scale flow analyses (e.g., Srinivas et al., 1999; Ella et al., 2002), to the regional, or even national scale groundwater flow studies (e.g., Brodie, 1999; Varni and Usunoff, 1999; Vermulst and De Lange, 1999). Both steady-state and transient modeling strategies are employed, depending on the extent and nature of the particular problem. Whereas fully saturated models, such as the United States Geological Survey (USGS) modular finitedifference groundwater model MODFLOW (McDonald and Harbaugh, 1996), only simulate groundwater flow below the water table, variably saturated models that depict flow in the unsaturated zone also exist, and are used in some instances (e.g., Freeze, 1971; Huyakorn et al., 1986; Deng et al., 1994; Therrien and Sudicky, 1996). Infiltration at the ground surface is used as the top boundary condition in variably saturated models, while groundwater recharge is calculated explicitly as part of the flow solution. Although subsurface fluid flow (both air and water) is therefore modeled as a continuum, this approach is still limited by the scaling problem. The highly nonlinear relationships between water content, pressure head, and unsaturated hydraulic conductivity requires very fine discretization, limiting the application to smaller areas due to increased computational costs. In addition to added input data, variably saturated models also need to account for the near surface hydrologic processes such as infiltration, evapotranspiration, frost penetration, and snowmelt that influence not only the top boundary condition, but also the upper few meters of the unsaturated zone. Fully saturated groundwater models, on the other hand, only require the specification of the recharge boundary condition at the water table and are therefore more commonly used in most groundwater modeling investigations. Variably saturated flow is described by the Richards’ equation, while transient three-dimensional saturated groundwater flow in heterogeneous anisotropic porous media is expressed as (Bear, 1972) ∂ ∂xi
Kij
∂h ∂xj
+ Q = Ss
∂h ∂t
(28.2)
where Kij is the hydraulic conductivity tensor, h is the hydraulic head, Q represents sources or sinks, and Ss is the specific storage. As fully saturated models only describe groundwater flow below the water table, the specification of either the location of the water table (Dirichlet — Type I) or the recharge flux (Neumann — Type II) is required at the top or upper boundary. Depending on the model, the flow equations are commonly solved either by the finite difference method, for example, MODFLOW (McDonald and Harbaugh, 1996), or the finite element method, for example, WATFLOW (Molson et al., 1992). As the exact location of the phreatic surface is often difficult to determine, and small errors in its location may potentially lead to large errors in groundwater fluxes, the recharge flux is often specified as the upper boundary condition. However, due to the many difficulties in recharge estimation, as alluded to earlier, the recharge boundary condition is commonly used purely as a calibration parameter to improve the model fit (e.g., Martin and Frind, 1998; Bonomi and Cavallin, 1999; Varni and Usunoff, 1999). Where information about precipitation is available, a fraction of it is also often assigned as the recharge boundary condition (Kennett-Smith et al., 1996; Brodie, 1999). The concept of the recharge spreading layer (RSL) has also been proposed to redistribute recharge from areas of low permeability to areas of relatively high permeability (Therrien and Sudicky, 1996; Martin and Frind, 1998; Beckers and Frind, 2000). Although these assumptions may be reasonable for the long-term simulation of a regional groundwater flow system or flow in a deep confined aquifer, a physically based and more accurate description of the recharge
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boundary condition is required for studies involving climate change, where the detailed knowledge of the spatial and temporal variation of the recharge is imperative. 28.2.6.2 Coupled Models To obtain a more physically based recharge boundary condition for saturated groundwater models, several researchers have adopted a coupled approach (Chiew et al., 1992; Prathapar et al., 1994; Fayer et al., 1996; Beverly et al., 1999; Srinivas et al., 1999; Vermulst and De Lange, 1999; Zhang et al., 1999a; Sophocleous and Perkins, 2000; Batelaan and De Smedt, 2001; Ruud et al., 2001; Coppola et al., 2002). Groundwater recharge is estimated separately, using methods described Section 28.2.5, and the results are then used as a boundary condition in a saturated groundwater flow model. While most, if not all, of the methods presented in Section 28.2.5 have been used in groundwater modeling studies, the following discussion will focus on combined vadose zone–water budget modeling, as it provides the most versatile and physically based means of estimating the recharge boundary condition. Chiew et al. (1992) developed a coupled approach based on the rainfall-runoff model HYDROLOG and the finite element groundwater flow model AQUIFEM-N to estimate regional groundwater recharge rates. The surface hydrologic model was used to calculate daily recharge rates, which were then summed over a month and input into the groundwater flow model as the recharge flux boundary condition. While their methodology may provide improved results as calibration is conducted against both streamflow and potentiometric head data, there are still many shortcomings and limitations in their approach. First, they divided their catchment into ten sub-areas based on drainage divides, rather than into areas with similar hydrologic characteristics. This resulted in spatially averaged values being used for each sub-area in the recharge analysis. Second, the rainfall-runoff model HYDROLOG completely ignores flow in the unsaturated zone and is simply calibrated against streamflow hydrographs with recharge estimated as a result. Even though the analysis is conducted based on daily precipitation records, the combination of ignoring the unsaturated zone and using average parameters to represent each sub-area results in an averaged estimate of recharge for a given sub-area. This is clearly shown in their simulated groundwater levels, which fail to match the transient variations observed in the groundwater flow field resulting from significant recharge events. Prathapar et al. (1994) developed a soil water and groundwater simulation model SWAGSIM to estimate water table fluctuations in extensively irrigated regions. They calculated daily recharge at the water table based on an analytical solution to the Richards’ equation and added it to a two-dimensional finite difference groundwater flow model through the source/sink term. The main problems with their model include the simplification of important hydrologic processes, the requirement of homogeneous and isotropic conditions for the analytical solution, and the two-dimensional nature of the groundwater flow model (essentially assumes a one-layer system with assigned transmissivities and specific yields). Therefore, their model is only applicable to very simple systems. Using a geographic information system (GIS), Fayer et al. (1996) estimated the spatial distribution of recharge with four different methods for their groundwater study at the Hanford nuclear waste site in the United States. They used a combination of field techniques such as lysimeters, water content measurements, and tracer studies in conjunction with numerical modeling (UNSAT-H) to generate a temporally averaged recharge boundary condition map for their groundwater flow model of the study area. The use of the GIS aided significantly in the analysis by allowing the identification of all possible combinations of soil type and vegetation in the area that could be assigned an appropriate estimate of recharge. The inclusion of field studies provided additional confidence to the unsaturated zone modeling results. However, the resulting recharge map only depicts average annual recharge rates and neglects to provide information regarding the change of recharge over time. The results from the groundwater model were not discussed. Due to data limitations required by more physically based models, Beverly et al. (1999) developed a simple unsaturated module SMILE to provide recharge estimates to MODFLOW. Their model accounts for overland flow and evaporation from both the unsaturated and saturated zones and recharge is calculated based on either a matrix or crack flow approximation, or an empirical Darcy approach. The two models
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are again linked through the recharge boundary condition; however, their approach also allows for groundwater discharge, due to heads in excess of the ground surface, to be distributed in overland flow and reinfiltrated in the subsequent time steps. This dynamic linking seems very attractive with a small computational burden due to the simplicity of the model; however, the process descriptions are overly simplified and may lead to significant errors in the results. Srinivas et al. (1999) used the water budget method to calculate monthly recharge rates for their nested squares groundwater flow model NEWSAM of a small fractured granitic aquifer in India. They used the SCS curve number method to calculate an average curve number for the watershed and applied the water balance method on a monthly basis to estimate recharge. The estimated temporal recharge pattern was then coupled to the groundwater flow model through the boundary condition. Their results showed the importance of including temporally varying recharge in groundwater flow modeling to capture the temporal fluctuations observed at the water table. However, their model consistently over predicted the observed water levels by a wide margin, although it seemed to capture the timing of changes in the flow field. Using the water budget method across the entire watershed leads to spatial averaging, which may account for the problems in their simulated data. As mentioned previously, the water budget method ignores percolation through the unsaturated zone resulting in average results. Vermulst and De Lange (1999) used a GIS interface to link the unsaturated flow model MOZART and the analytic element groundwater flow model NAGROM to aid in national groundwater policy analysis in the Netherlands. As their models operated at different spatial and temporal scales, they coupled them through the Cauchy boundary condition using up- and down-scaling procedures. The models were run sequentially until a steady state was obtained. Although recharge was averaged both spatially and temporally, their model provides a valuable tool for policy decisions at the national scale. However, the model has limited potential for groundwater quality studies of point source contamination. To simulate catchment scale responses under different land management options in the context of salinity control, Zhang et al. (1999a) used a distributed parameter ecohydrological model TOPOG-IRM to estimate soil moisture and groundwater recharge rates. The model accounts explicitly for the spatial distribution of topography, soil characteristics, and vegetation properties and predicts the dynamic interactions within the soil–vegetation–atmosphere system. It also uses the Richards’ equation to simulate water movement in the unsaturated zone and links soil and canopy processes with catchment topography. Evapotranspiration is based on a Penman–Monteith type approach, with transpiration based on a canopy resistance model. The model uses daily climate variables such as precipitation, temperature, vapor pressure deficit, and solar radiation to estimate the recharge rate at the bottom of the soil column. Their model, therefore, seems to offer a very sophisticated approach for estimating groundwater recharge. Using the results from the recharge analysis, Zhang et al. (1999a) also used MODFLOW to simulate groundwater flow in their catchment. The simulated water levels, however, failed to match the temporal variations in the observed data. This was likely not caused by problems in the recharge analysis, but by the simplicity of the groundwater flow model. Due to the lack of soil information in the study area, they assumed homogeneous conditions across the entire site. Furthermore, the calculated recharge was only approximately 5% of the annual rainfall in the area, resulting in a very small recharge boundary flux. Sophocleous and Perkins (2000) combined the semi-distributed agricultural watershed model SWAT (Arnold et al., 1998) with MODFLOW to study conjunctive water use and management scenarios in three watersheds in Kansas. They developed a linking routine where the results from SWAT were distributed or averaged over the groundwater model grid and passed as inputs into MODFLOW at each MODFLOW time step. They also utilized GIS to aid in parameterization of hydrologic variables using overlaying and averaging operations. They calibrated the model against actual streamflows and groundwater levels in three watersheds and found reasonable agreement between the simulated and observed results. In addition to allowing calibration to multiple targets, the main advantage of their method is in the flexible modular linking approach that allows other watershed models to be used in place
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of SWAT. The main shortcoming, however, is that the linked model is based on the HRU concept resulting in averaging of important parameters. Mean sub-basin responses are first estimated by averaging the mean results from each of the HRUs within the sub-basin, and then distributed over the underlying groundwater model grid. The inputs to the groundwater model are therefore not only averaged temporally, but spatially as well. Batelaan and De Smedt (2001) developed a GIS-based methodology to provide recharge estimates for regional groundwater modeling. Their model, WetSpass, estimates recharge on a raster cell basis using a simplified water balance formulation. They used the results of the recharge analysis as boundary conditions in MODFLOW to study the effect of land use changes on groundwater discharge in a catchment in Belgium (Batelaan et al., 2003). While their method may provide reasonable estimates of average annual recharge rates at the regional scale, it is unsuitable for small temporal and spatial scales. One of the main drawbacks of the method is the coarseness of the raster approach, which requires average parameter values to be used for each raster cell. However, the central weakness of their method is the crude water balance, which employs simple empirical relationships to describe important hydrologic processes, with recharge estimated as the residual. Ruud et al. (2001) used a similar GIS-based approach in their coupled groundwater and surface water flow model at the basin scale. They linked a surface water model, a land–atmosphere interface and unsaturated zone model, and a groundwater flow model (MODFLOW) in GIS to evaluate conjunctive use alternatives and their impacts on groundwater resources in response to land use demands and potential changes to surface water deliveries in their study area. Monthly rates of recharge were calculated from the surface water models and input as the recharge flux boundary condition in MODFLOW. The main weakness in their approach is that the modeling is conducted at a very large scale leading to spatial averaging of important processes and parameters. Furthermore, they used the water budget method (and a quasi-hydraulic model) to compute the recharge rates at the water table which ignores or simplifies the impact of the unsaturated zone soil column. As part of a groundwater flow study in New Jersey, Coppola et al. (2002) developed a fuzzy-rule based approach to estimate monthly recharge rates for the groundwater flow model. Instead of estimating recharge using a physically based description of hydrologic processes, they employed a fuzzy-rule based approach relating monthly groundwater recharge to mean monthly air temperature, monthly precipitation, and the previous month’s total streamflow. They used the method to estimate monthly basin wide recharge values during transient calibration of the groundwater flow model. Similar to other empirical approaches, however, their method is only a statistical tool and lacks physical basis. Furthermore, at best, it can only estimate average basin wide values as the analysis is based on monthly streamflow totals from the basin. In summary, various types of coupled models have been developed for different purposes and applications. The approaches portray various degrees of sophistication, from the rigorous numerical treatment of many hydrologic processes, to simple water budget or empirical models. Regardless of the many obvious weaknesses present in many of the models, these methods provide a more versatile and practical way to estimate groundwater recharge than the more expensive and intensive field methods. Physically based method are especially useful, as they not only provide current estimates of recharge, but they can also be used to study the impact of changes in the physical processes, for example, in temperature and precipitation due to climate change, on recharge distribution and rates. 28.2.6.3 Integrated Models To overcome the problems inherent in the coupled approaches, several researchers have attempted to model the entire hydrologic system as a whole. The basic design of the integrated surface–subsurface modeling approach was first outlined by Freeze and Harlan (1969). Yan and Smith (1994) proposed a framework for an integrated approach based on integrating a surface water management model SFWMM with MODFLOW. Although the idea of integrating existing and widely used models sounds appealing, their approach, however, suffers from many simplifying assumptions common with the coupled methods.
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Furthermore, besides the proposed framework, details of model development and applications have not been found in literature to date. Using the GIS, Xiao et al. (1996) developed a raster-based spatially and temporally continuous surface– subsurface hydrologic flow model. The model is based on a dynamic linkage between precipitation, surface flow, infiltration, and subsurface flow submodels and uses simple physical relationships instead of the more rigorous higher order transient differential equations. The processes of interception and evapotranspiration are ignored due to sparse vegetation and the assumption that evapotranspiration rates would be low during a rainfall event due to high humidity. The equations are solved sequentially, and the percolation of water through the unsaturated zone is ignored. The model was applied to a large watershed in northern Alaska to simulate the system response to a single rainfall event. In addition to the inherent problems with a simplified model, the lack of evapotranspiration, snow pack, and snowmelt processes limit the application of the model to simple systems. Querner (1997) developed a physically based groundwater and surface water model MOGROW and used it to investigate the effects of human interventions and natural factors on groundwater recharge at the regional scale in the Netherlands (Querner, 2000). The model combines a variably saturated finite element groundwater flow model SIMGRO with a surface water model SIMWAT. Although advertised as an integrated model, the two models operate at different time steps and are linked through the surface boundary condition. Furthermore, the flow in the unsaturated zone is modeled with a pseudo-steady-state approach with empirical parameters introduced for surface runoff, perched water tables, and preferential flow. Results from their study indicate that the model may be suitable for long-term assessments of changes in the groundwater flow field due to changes in land use, groundwater abstractions, and meteorological conditions. VanderKwaak (1999) developed a fully integrated surface water and groundwater model that rigorously considers the flow and transport processes on the land surface and in the variably saturated, dualcontinua subsurface. The two-dimensional diffusion wave equation is used to describe the shallow surface water flow, while groundwater flow is described using the three-dimensional form of the Richards’ equation. The linkage between the surface and subsurface systems is through first-order, physically based flux relationships or through continuity assumptions. The entire system of equations is also solved simultaneously resulting in a truly integrated model. The weakness of the model, however, is that it ignores important hydrologic processes such as interception and evapotranspiration, which can account for significant losses in long-term flow simulations. Snowmelt processes are also ignored, limiting the application of the model to warmer climates or short-term simulations. Parameterization and the scaling problem between the surface and subsurface processes furthermore restrict the application of the model to smaller areas with small variations in properties or characteristics (VanderKwaak and Sudicky, 2000). Montgomery Watson (1993) has also created an Integrated Groundwater Surface Water Model (IGSM) based on a quasi three-dimensional finite element approach. The major components of the hydrologic cycle simulated by the model include rainfall, runoff, groundwater recharge, pumping, consumptive use, evaporation, subsurface flows, and seawater intrusion. As stated by Fuller (1995) “integration of groundwater and surface water flows is carried out using a soil mixture accounting and unsaturated flow model. This, combined with runoff and soil percolation, allows for full interaction between surface and groundwater. Water quality simulation is also included which can track a contaminant through the processes of advection, dispersion, and dissolution.” The model has been applied in basin management studies in California, Florida, and Colorado. Due to its increasing popularity, LaBolle et al. (2003) conducted a comprehensive review of the underlying assumptions and mathematical formulations present in the IGSM model. In addition to using empirical land use and vadose zone models to compute net percolation or recharge to the water table, they found that “the model fails to properly couple and simultaneously solve groundwater and surface water models with appropriate mass balance and head convergence under reasonable conditions” (LaBolle et al., 2003). They further concluded that due to instabilities and errors caused by some of the algorithms in the model, the model results may produce misleading predictions and interpretations that may influence planning and management decisions.
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HydroGeoLogic (2002) developed an integrated hydrologic modeling system MODHMS based on the USGS MODFLOW model. They added modules for three-dimensional flow in the unsaturated zone using the Richards’ equation, two-dimensional overland flow using the diffusion wave approximation, and flow through a network of one-dimensional channels or pipes using the diffusion wave approximation with Priesmann Slot conceptualization for pressurized flow in pipes. The model is fully compatible with GIS and provides an interface with ArcView for accessing and analyzing spatially distributed input parameters. The model has been applied to various problems, such as groundwater interaction with rivers and saltwater intrusion analysis. Due to the lack of published data, however, a more detailed description of the model cannot be given here. Graham and Refsgaard (2001) give a descriptive overview of the fully distributed hydrologic model MIKE-SHE, which is an extension of the original Systeme Hydrologique Europeen (SHE) code (Abbott et al., 1986). They assert that “MIKE-SHE is one of the only distributed, physically based, fully integrated surface water/groundwater models available today.” The model includes descriptions for many of the important hydrologic processes, including snowmelt, with well-known non-empirical equations used to represent the physical processes in the different parts of the hydrologic cycle (Graham and Refsgaard, 2001). The model and its earlier versions have been around for quite some time and therefore have been applied to numerous hydrologic problems. One of the weaknesses of the model includes the strictly one-dimensional flow assumption in the unsaturated zone and sheet flow approximation of overland flow. Furthermore, as with any of the integrated hydrologic models, the central problem is with parameterization and increased computational requirements due to rigorous mathematical equations as well as coupling, or integration, of processes that take place on vastly different spatial and temporal scales. Singh and Woolhiser (2002) give a comprehensive review of hydrologic models reported in literature over the years. While most of the models listed in their paper deal only with surface water hydrology, references to more comprehensive models are also included. In the end, the problem comes down to the purpose and scope of the model, and its associated conceptual model. As Reddi and Danda (1994) pointed out, “while simple lumped parameter models may be adequate in regional groundwater quantity studies on homogeneous soil domains, models addressing multidimensionality and spatial heterogeneity are necessary in groundwater quality studies, such as remediation designs at contaminated sites.” Therefore, depending on the objectives and purpose of the model, the use of steady-state or average parameters may very well be appropriate. However, this does not imply that using average values, especially across many spatial or temporal scales, results in an accurate model. Parameter sampling and modeling must be done at the appropriate scale to accurately describe the processes that the model intends to simulate.
28.3 A Case Study: Recharge Analysis of the Grand River Watershed 28.3.1 Introduction The Grand River watershed is located in south-western Ontario, draining an area of nearly 7000 km2 into Lake Erie. The location of the watershed is shown in Figure 28.2. The main tributary is approximately 290 km in length with an elevation differential of about 362 m from its source to the mouth. The landscape of the watershed has mainly been shaped by the last period of glaciation, resulting in highly variable soils and topography. The southern part of the watershed consists of low permeability lacustrine clay deposits and low topographic relief. The central part is formed mostly of higher permeability sand and gravel kame moraines with moderately high relief, while the northern portion of the watershed is comprised of lower permeability till plains with varying surface relief (Holysh et al., 2000). Although 90% of the watershed is classified as rural, the watershed contains some of the fastest growing urban areas in Ontario, such as the cities of Kitchener, Waterloo, Cambridge, and Guelph. Not only is
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FIGURE 28.2 Location of the Grand River watershed.
increasing urbanization stressing the existing water supply, but it is also placing the supply at a greater risk of contamination. There is growing concern about the environmental impact of such rapid urbanization and the ability of the river and groundwater systems to meet the rising demand for water. The recent and continuing drought conditions in southern Ontario have also placed an additional stress on the hydrology and water resources of the watershed. The objective of this study is to assess the spatial and temporal distribution of groundwater recharge in the Grand River watershed and to estimate the impact that climate change may have on groundwater recharge, evapotranspiration, and runoff. Approximately 80% of the population in the watershed derive their drinking water from groundwater. Therefore, quantifying the input to the groundwater system is critical for developing an effective groundwater management strategy that will ensure an adequate and clean supply of drinking water, now and in the future.
28.3.2 Input Data Numerical modeling at the regional watershed scale, such as the Grand River, involves the handling of large amounts of input and output data. A geographic information system (GIS) is ideally suited for this purpose as it provides an integrated platform to manage, analyze, and display model parameters and results. Due to the large volume of temporally varying climate data (e.g., daily precipitation, temperature, and solar radiation), a separate relational database management system (RDBMS) was also utilized in this work to facilitate data organization and storage. The physically based hydrologic model HELP3 was used to calculate the spatially varying daily groundwater recharge rates for the watershed. The model was linked to ArcView GIS and the database management system (MS Access) using simple Visual Basic and ArcView Avenue scripts. Details of the methodology can be found in Jyrkama et al. (2002). HELP3 was chosen mainly because it was readily available and easy to use. Furthermore, HELP3 simulates all of the important hydrologic processes in the water budget, including the effects of snowmelt and freezing temperatures. Following is a summary of the input data used in the model.
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Legend Built-up (industrial) Built-up (residential) Dense forest (conifer) Dense forest (deciduous) Dense forest (mixed) Pasture/sparse forest Golf courses Extraction/bedrock/roads Forage Marsh Bare agricultural fields Plantation ( mature) Rowcrops Small grains Open water close-up
10
0
10 20 Km
FIGURE 28.3 Land use/land cover (LULC) map.
28.3.2.1 Land Use/Land Cover Data Digital land use and land cover (LULC) data for the Grand River watershed were obtained using 1999 satellite imagery from the Landsat 7 thematic mapper. As shown in Figure 28.3, the raster LULC coverage is based on a 25-m grid with 15 unique field descriptors. 28.3.2.2 Soil Data The surface soil information in Figure 28.4, was assembled from various regional soil surveys conducted in the watershed. All the information was obtained from the Canadian Soil Information System (CANSIS) website in digital form. However, several difficulties were encountered during the construction of the soil map and the associated database for the watershed. The Grand River watershed spans a number of different counties and municipalities, each with its own soil survey and database, as shown in Table 28.1 and Figure 28.2. Due to differences in scales and mapping methods, relatively minor to severe discontinuities and overlaps existed between adjacent soil map sheets. Therefore, to generate a continuous soil map for the entire watershed, these gaps and overlaps needed to
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ON17 ON38
ON35 ON43
ON13
close-up
ON44
ON32 ON28
10
0
ON55
10
20 Km
ON57
FIGURE 28.4 Soil surveys and soil map. TABLE 28.1 Soil Surveys in the Grand River Watershed Survey
County
Scale
Year
ON13 ON17 ON28 ON32 ON35 ON38 ON43 ON44 ON55 ON57
Perth Grey Oxford Wentworth Wellington Dufferin Halton Waterloo Brant Haldimand-Norfolk
1 : 63360 1 : 63360 1 : 63360 1 : 63360 1 : 63360 1 : 63360 1 : 63360 1 : 20000 1 : 25000 1 : 25000
1975 1981 1961 1965 1963 1963 1971 1971 1989 1984
be corrected. It was assumed that newer maps and maps with finer scales were more accurate and therefore were used to fill gaps (by extending edge polygons), and to trim the surrounding map sheets. There were a total of 723 unique soil types identified in the watershed. In addition to physical and chemical details, the associated soil database also contained information on soil type, number of layers, layer depths, and soil texture classifications. 28.3.2.3 Vegetation Data Plant roots can have a significant impact on recharge as they remove infiltrated water from the soil. However, the determination of plant root penetration and subsequently the evaporative zone depth are very difficult tasks. In this study, the average evaporative zone depths (based on the combination of soils
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Mount Forest Elora Research Station Fergus Shand Dam
Toronto Pearson Int’l Airport
UW Weather Station Waterloo/Wellington Airport Hamilton Marine Police Hamilton RBG Hamilton Airport
London Airport
Simcoe FIGURE 28.5 Zones of uniform meteorology (ZUM), sub-basins, and location of relative humidity and average wind speed observations.
and land cover types) were estimated using the guidelines given in the recharge methodology developed by the New Jersey Geological Survey (NJGS) (Charles et al., 1993). HELP3 also requires a value for the maximum leaf area index (LAI) to calculate transpiration rates for the vegetative cover. Following the guidelines in HELP3, where the LAI ranges from 0 for bare ground to 5.0 for maximum vegetal leaf coverage, the values for LAI were assigned based on the LULC data. For example, the maximum LAI for bare agricultural fields was assumed to be 0, and for golf courses 2.0. 28.3.2.4 Weather Data Due to its large size, the weather varies significantly across the Grand River watershed. Actual daily precipitation and temperature records from January 1960 to December 1999 were obtained from the Grand River Conservation Authority (GRCA) for the watershed. The data were based on point observations at various locations within (as well as outside) the watershed that were then used to represent the weather patterns within 13 subregions, or zones of uniform meteorology (ZUM) shown in Figure 28.5. The builtin weather generator in HELP3 was then used to generate daily synthetic solar radiation values for each ZUM as a function of latitude, precipitation, and temperature. A preliminary study revealed, however, that these subregions were still quite large resulting in discontinuities in recharge along their boundaries. Therefore, a new method based on an interpolation algorithm was developed. The Grand River watershed was divided into 293 smaller sub-basins, also shown in Figure 28.5, each with its distinct values of daily precipitation, temperature, and solar radiation. The values were interpolated using the inverse distance squared (IDS) algorithm as 13 P
SUB
=
ZUM /d 2 i=1 Pi i 13 2 1/d i=1 i
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where P is the daily precipitation, temperature, or solar radiation, and d is the distance from the centroid of each ZUM to the centroid of each sub-basin. This provided a much smoother transition of weather data across the entire watershed, while still honouring the original observations. The average quarterly relative humidities and average annual wind speeds were obtained from Environment Canada as well as the University of Waterloo weather station for various locations in and around the watershed, as shown in Figure 28.5. As before, the inverse distance squared weighting scheme was then used to estimate values for each of the 293 sub-basins. The dates for the start and end of growing season were estimated using guidelines provided in HELP3 (Schroeder et al., 1994). The values were estimated for each ZUM, therefore, constant growing season dates were assumed for each sub-basin within each of the ZUM areas. Growing season starting dates varied from May 2nd to May 6th, while the ending dates ranged from October 7th to October 12th.
28.3.3 Methodology As mentioned previously, the methodology was based on the work by Jyrkama et al. (2002), therefore, only a brief description is given in the following. Figure 28.6 illustrates a schematic diagram of the method. First, the LULC and soil maps were overlaid in the GIS to produce a combination map. These combinations were then used to determine vegetation data such as evaporative zone depths, as well as curve numbers used by HELP3 in the recharge analysis. HELP3 was then run daily from January 1960 to December 1999 for each of the unique combinations within each of the 293 sub-basin using the interpolated weather data for each sub-basin. This resulted in a total of approximately 47,000 unique combinations of LULC, soil,
FIGURE 28.6 Methodology for estimating groundwater recharge. (After Jyrkama, M.I., Sykes, J.F., and Normani, S.D. 2002. Ground Water, 40, 638–648.)
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Close-up
Legend 0 98 123 170 191 209 229 253 290 345 421 mm
FIGURE 28.7 Average annual recharge for the Grand River watershed (mm/yr).
and weather data (i.e., ∼47,000 HELP3 simulation runs). Areas classified as open water were ignored in the recharge analysis.
28.3.4 Results Figure 28.7 shows the average annual recharge rates obtained from the HELP3 analysis for the Grand River watershed. Figure 28.8 illustrates the histogram of the same distribution. The average annual groundwater recharge in the watershed is approximately 200 mm/yr, which is approximately one-fifth of the average annual precipitation (950 mm/yr). As shown in Figure 28.7, recharge varies considerably across the watershed, responding directly to variations in land use and the hydraulic characteristics of the underlying soils. As discussed previously, areas of high recharge may indicate areas where the underlying aquifers are subjected to increased vulnerability from contamination. This may have significant implications on land use planning near the urban areas, where existing lands are rapidly being converted into residential subdivisions and industrial areas. The recharge rates also vary considerably over time, as shown by the monthly rates in Figure 28.9. Due to warmer temperatures in December 1992, most of the precipitation is able to infiltrate and become groundwater recharge, while during the much colder period in December 1998, most of the precipitation occurs as snow over frozen ground resulting in negligible recharge rates across the watershed. As shown in Figure 28.9a, there is also considerable variation in recharge rates across the watershed. This variation is not only due to the variations in the land cover and soils, as discussed previously, but
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4.5 binSize = 2 mm
Base case 4
Avg. R: 189.1 mm/yr 3.5
Open water
% of total area
3 2.5 2 1.5 1 0.5 0 50
100
150
200
250
300
350
400
450
Average recharge (mm/yr)
FIGURE 28.8 Recharge histogram.
(a)
(b)
N
Legend 0 1 30 58 71 81 88 94 100 107 119 mm
10
0
10 20 km
FIGURE 28.9 Monthly recharge rates for (a) December 1992 and (b) December 1998 (mm/month).
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Legend 62 116 139 163 186 208 230 257 299 383 642 mm
10
0
10
20 km
FIGURE 28.10 Average annual surface runoff (mm/yr).
also as a response to variations in climatic conditions across the watershed. Contrary to what might be expected, the northern portion of the watershed has considerably higher recharge rates in December 1992 than the southern end. This is explained by lower precipitation rates and unusually cool temperatures prevalent in the southern part of the watershed at the time. The physically based recharge methodology also provides estimates of evapotranspiration and surface runoff, shown in Figure 28.10 and Figure 28.11, respectively, which can be used in an assessment of the watershed’s overall water budget. As expected, both evapotranspiration and surface runoff vary considerably across the watershed, responding directly to variations in the land cover and soils. The northern portion of the watershed has significantly higher surface runoff rates, as expected, due to the presence of low permeability tilly soils. Approximately 210 mm of annual precipitation is subjected to overland flow while approximately 510 mm is evapotranspired by the vegetation in the watershed on an annual basis. Evapotranspiration, therefore, constitutes the largest portion of the watersheds’ overall water budget. As demonstrated by the above results, the methodology can potentially be used to assess the impact of climate change and changes in land use due to urbanization. The results further prove the applicability of the methodology across various scales, that is, from the small sub-basin level analysis to the regional watershed scale. 28.3.4.1 Impact of Climate Change As discussed previously, climate change has the potential to significantly impact and alter the key processes in the Earth’s water and energy cycles. Specific evidence from a wide variety of General Circulation (GC) and other climate models predict increases in the globally averaged surface air temperature, water vapor, evaporation, and precipitation. The intensity and frequency of extreme events is also projected to grow
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Legend 208 378 447 490 505 521 536 551 571 597 683 mm
10
0
10
20 km
FIGURE 28.11 Average annual evapotranspiration (mm/yr).
(IPCC, 2001). Understanding the impact of these potential changes in the hydrologic cycle is essential for ensuring the quality and sustainability of water resources in the Grand River watershed. The impact of climate change was modeled by perturbing the HELP3 model input parameters using predicted changes in the climate of the Grand River watershed. In addition to global changes, the IPCC reported the following general predictions for the regional climate in north-eastern North America over the next 100 years (IPCC, 2001): • precipitation is projected to increase with an average change between 5 and 20% in the winter • precipitation extremes are projected to increase more than the mean with higher intensities and higher frequency of extreme events • greater than average warming in both summer and winter temperatures • a possible reduction in incoming solar radiation due to increases in greenhouse gases. Using the actual historical weather data as a reference for the Grand River study area, several scenarios were constructed to simulate the impact of climate change on the hydrologic cycle in the future. These scenarios are shown in Table 28.2. All of the simulation parameters were scaled over the length of the study period. That is, they were assumed to increase linearly over time. For example, the temperature change of +0.016◦ C/yr corresponds to a predicted increase of 1.6◦ C in 100 years, or to a daily increase of approximately 4.4 × 10−5◦ C. The changes in precipitation intensity were simulated using N P ·δ x = i=1 N i=1 iP
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(28.4)
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Description
Base
Actual daily temperature, precipitation, and simulated solar radiation Precipitation +5% for Dec, Jan, and Feb Precipitation +20% for Dec, Jan, and Feb Precipitation +20% for all months Temperature +0.016◦ C/yr Temperature +0.070◦ C/yr Solar radiation 2% for all months Combination of Cases 1, 5, and 6 Combination of Cases 3, 5, and 6
1 2 3 4 5 6 7 8
and Picc = Pi (1 + ix)
(28.5)
where P is the actual daily precipitation on day i, P cc is the new daily precipitation due to climate change, x is the calculated change in daily precipitation, δ is the percent change in the average precipitation, and N is the total number of days in the study. Figure 28.12 presents the cumulative differences in surface runoff, evapotranspiration, and recharge between all the cases and the Base Case scenario, for the Grand River watershed, averaged spatially over the study area. As shown, changing the precipitation (Case 1 to Case 3) has the highest influence on the hydrologic cycle, while solar radiation (Case 6) has a minimal impact. Groundwater recharge is predicted to increase under all scenarios, while evapotranspiration increases in all cases, except when incoming solar radiation is reduced (Case 6). Figure 28.12a illustrates that, as expected, surface runoff increases with increasing precipitation. Furthermore, increasing the precipitation rate will generally increase all three hydrologic parameters as there is more water available in the system. Increasing temperature, however, has both a negative and positive impact on the hydrologic processes. As demonstrated by Case 4 and Case 5 in Figure 28.12a for the Grand River watershed, temperature has a significant influence on the runoff process. The cumulative surface runoff decreases with increasing temperature mainly due to a reduced period of ground frost. Due to warmer winter temperatures, less water is stored in the snowpack and more water is able to infiltrate into the ground thereby reducing runoff and increasing groundwater recharge. This effect is less pronounced for more southerly study areas where the average winter temperatures are generally higher. At the watershed scale, climate change has the highest relative impact on groundwater recharge resulting in a 53% increase over 40 years, while surface runoff and evapotranspiration increase by 10% and 12%, respectively, over the same time period. The temporal variabilities in the hydrologic processes are further demonstrated using the results from Case 8. Figure 28.13 shows the spatially averaged monthly differences for Case 8 and Base Case for the Grand River watershed. The increase in temperature and precipitation intensity over time is directly reflected in the hydrologic processes. Figure 28.14 shows the same results for each month. As shown in Figure 28.14 for the Grand River watershed, it is evident that there is a significant reduction in the average runoff in the spring (e.g., April) as the springmelt is shifted into the winter months due to warmer temperatures. The amount of runoff is consequently increased during January, February, and March as moisture is released from the snowpack (as opposed to being stored or accumulated). Groundwater recharge also increases significantly during the winter months as more water is able to infiltrate into the ground. Evapotranspiration rates are increased for the study area during the summer months due to higher temperatures and increased amount of available water.
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4 Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8
Runoff cumulative difference (m)
3.5 3 2.5 2 1.5 1 0.5 0 –0.5 –1 –1.5 0
10
20
30
40
30
40
30
40
Time (yr) (b)
4 Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8
ET cumulative difference (m)
3.5 3 2.5 2 1.5 1 0.5 0 –0.5 –1 –1.5 0
10
20 Time (yr)
(c) Recharge cumulative difference (m)
4 Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8
3.5 3 2.5 2 1.5 1 0.5 0 −0.5 −1 −1.5 0
10
20 Time (yr)
FIGURE 28.12 Cumulative differences between the climate change scenarios and the Base Case for (a) surface runoff, (b) evapotranspiration, and (c) groundwater recharge.
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∆ Precip (mm)
0.08 0.06 0.04 0.02
∆ Runoff(mm)
0 0.15 0.1 0.05 0 –0.05 –0.1 –0.15
∆ ET (mm)
0.04 0.02 0 –0.02
∆ Recharge (mm)
–0.04 0.15 0.1 0.05 0 –0.05 30
31
32 33 Time (years)
34
35
FIGURE 28.13 Monthly differences in precipitation, surface runoff, evapotranspiration, and groundwater recharge between Case 8 and the Base Case for a selected time period. 25
Average difference (mm)
20 15 10 5 0 –5 Runoff –10
Evapotranspiration Recharge
–15 –20 Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
FIGURE 28.14 Average differences for each month between Case 8 and the Base Case.
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Legend 0 72 92 97 101 105 109 113 117 123 146 mm
10
0
10
20 km
FIGURE 28.15 Average annual change in recharge between Case 8 and the Base Case.
Figure 28.15 shows the temporally averaged groundwater recharge rates for the Grand River watershed for the Base Case and Case 8. As illustrated, there is an overall increase in the recharge rate across the areas due to climate change. The average rate is predicted to increase by approximately 100 mm/yr from 189 mm/yr to 289 mm/yr over the 40-year study period for the Grand River watershed. Unlike the significant reduction in recharge rates as predicted by Rosenberg et al. (1999) for the Ogallala aquifer in the United States, the results of this study predicted increased recharge rates for the study area due to climate change. The reason for the contrasting results is not only due to the temperature impacts in cooler climates, but also due to differences in the input data. Rosenberg et al. (1999) only included predicted changes in temperature and CO2 concentrations in their simulations. As shown by the results for the Grand River watershed study area, increased precipitation has a significant influence on the estimated recharge rates. Land use changes due to potential increases in urbanization, especially in the Grand River watershed, will also impact the hydrologic processes beyond the possible effects of climate change. The predicted increases in overall groundwater recharge due to climate change will, therefore, not necessarily guarantee sustainability in the future because human impacts, such as increased pumping, also exert a major influence in the aquifer system and can lead to depletion of the drinking water resources. In conclusion, understanding the impact of potential changes in the hydrologic cycle due to climate change is essential for ensuring the quality and sustainability of our water resources in the future. The results of the study demonstrate the benefit of using the developed recharge methodology to address these issues.
28.3.5 Conclusions Estimating groundwater recharge is critical for developing an effective watershed management strategy that will ensure the protection of the fresh water resources of the watershed. The physically based hydrologic
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model HELP3 was integrated with ArcView GIS to estimate spatially distributed daily groundwater recharge rates for the Grand River watershed over a period of 40 years, from January 1960 to December 1999. The use of the GIS and a relational database management system (RDBMS) was essential due to the large volume of data required for numerical modeling of watershed processes at the regional scale. The results of the study indicated that on average, only one-fifth of the overall precipitation in the watershed contributes to direct groundwater recharge, with an average recharge rate of approximately 200 mm/yr. In addition to quantifying the temporal distribution and amount of recharge, the results also identify areas of varying recharge potential. As the transport of most groundwater contaminants to saturated aquifers occurs in the aqueous phase as part of the recharge process, areas of high recharge may indicate areas where the underlying aquifers are subjected to increased vulnerability from surface contamination. This may have significant implications on land use planning, especially near urban areas. The developed recharge methodology also provides estimates of evapotranspiration and surface runoff, which may be used in estimating the watershed’s overall water budget. The results also demonstrate the applicability of the methodology across various scales. The method can easily be applied to hydrologic analyses, for example, due to climate change, at the regional watershed scale, or a detailed evaluation of the impact of land use changes at the much smaller sub-basin scale.
28.4 Chapter Summary Climate change can directly affect the water balance of a surface water system; the impact on the groundwater system is indirect and is influenced through the spatially and temporally varying recharge and discharge boundary conditions that link the groundwater system to the surface water system. Recharge can occur as a result of precipitation events while both recharge and discharge can occur at surface water bodies. Assessing the impact of climate change on groundwater systems will generally require physically based models of these boundary conditions. Alternatively, fully integrated or coupled surface water and groundwater models can be used to assess climate change impact. Regardless of the modeling methodology used, it is essential that an assessment include the evaluation of historical conditions. For some groundwater systems, the spatial and temporal variation in historical groundwater recharge and discharge rates may be greater than the perturbation caused by climate change. In this chapter, the model HELP3 has been used as a simple tool to assess both the historical recharge and the impact of climate change for the Grand River Ontario watershed. For engineers and scientists, the value of the tool lies in the model’s ready availability and its easy-to-use database. However, there are many other physically based models that are suitable for the assessment of the impact on groundwater of climate change. This chapter has reviewed many of these models and analyses.
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Reddi, L.N. and Danda, S.K.R. 1994. Unsaturated flow modeling — Exact solution to approximate problem? Journal of Water Resources Planning and Management, 120, 186–198. Richards, L.A. 1931. Capillary conduction of liquids in porous mediums. Physics, 1, 318. Richardson, C.W. and Wright, D.A. 1984. WGEN: A model for generating daily weather variables. ARS-8. Agricultural Research Service, US Department of Agriculture. Robins, N.S. (ed.) 1998. Ground-water Pollution, Aquifer Recharge and Vulnerability. Geological Society, London, Special Publications, 130, 107–115. Rorabaugh, M.I. 1964. Estimating changes in bank storage and groundwater contribution to streamflow. International Association of Scientific Hydrology Publication, 63, 432–441. Rose, S. and Peters, N.E. 2001. Effects of urbanization on streamflow in the Atlanta area (Georgia, USA): a comparative hydrological approach. Hydrological Processes, 15, 1441–1457. Rosenberg, N.J., Epstein, D.J., Wang, D., Vail, L., Srinivasan, R., and Arnold, J.G. 1999. Possible impacts of global warming on the hydrology of the Ogallala Aquifer Region. Climatic Change, 42, 677–692. Rushton, K.R. 1988. Numerical and conceptual models for recharge estimation in arid and semi-arid zones. In: Simmers, I. (ed.) Estimation of natural groundwater recharge. NATO ASI Series C, vol. 222 (Proceedings of the NATO advanced research workshop, Antalya, Turkey, March 1987), D. Reidel Publication Company, Dordrecht, pp. 223–238. Ruud, N., Harter, T., and Naugle, A. 2001. A conjunctive use model for the Tule River groundwater basin in the San Joaquin Valley, California. In: M.A. Marino and S.P. Simonovic. (eds.) Proceedings of the Conference on Integrated Water Resources Management. IAHS Publication No. 272, pp. 167–174. Salama, R. B., Tapley, I., Ishii, T., and Hawkes, G. 1994. Identification of areas of recharge and discharge using Landsat-TM satellite imagery and aerial photography mapping techniques. Journal of Hydrology, 162, 119–141. Sandstrom, K. 1995. Modeling the effects of rainfall variability on groundwater recharge in semi-arid Tanzania. Nordic Hydrology, 26, 313–330. Scanlon, B.R., Healy, R.W., and Cook, P.G. 2002. Choosing appropriate techniques for quantifying groundwater recharge. Hydrogeology Journal, 10, 18–39. Schroeder, P.R., Dozier, T.S., Zappi, P.A., McEnroe, B.M., Sjostrom, J.W., and Peyton, R.L. 1994. The Hydrologic Evaluation of Landfill Performance (HELP) Model: Engineering Documentation for Version 3. EPA/600/R-94/168b, U.S. Environmental Protection Agency Office of Research and Development, Washington, DC. Schuh, W.M., Meyer, R.F., Sweeney, M.D., and Gardner, J.C. 1993. Spatial variation of root-zone and shallow dose-zone drainage on a loamy glacial till in a sub-humid climate. Journal of Hydrology, 148, 27–60. Schulze, E.D., Caldwell, M.M., Canadell, J., Mooney, H.A., Jackson, R.B., Parson, D., Scholes, R., Sala, O.E., and Trimborn, P. 1998. Downward flux of water through roots (i.e. inverse hydraulic lift) in dry Kalahari sands. Oecologia, 115, 460–462. Selker J.S., Parlange, J.-Y., and Steenhuis, T. 1992. Fingered flow in two dimensions, 2, Predicting finger moisture profile. Water Resources Research, 28, 2523–2528. Shade, P.J. and Nichols, W.D. 1996. Water budget and the effects of land-use changes on ground-water recharge, Oahu, Hawaii. USGS Professional Paper 1412-C. Sharma, M.L. (ed.) 1989. Groundwater Recharge. Proceedings of the Symposium on Groundwater Recharge, Mandurah, Australia, 6–9 July 1987, A.A. Balkema, Rotterdam. Sililo, O.T.N. and Tellam, J.H. 2000. Fingering in unsaturated zone flow: a qualitative review with laboratory experiments on heterogeneous systems. Ground Water, 38, 864–871. Simmers, I. 1990. Part I: Aridity, groundwater recharge and water resources management. In: Lerner, D., A.S. Issar, and I. Simmers. (eds.). Groundwater recharge: a guide to understanding and estimating natural recharge. Heise, Hannover. Simmers, I. 1998. Groundwater recharge: an overview of estimation ‘problems’ and recent developments. In: Robins, N.S. (ed.) Ground-water Pollution, Aquifer Recharge and Vulnerability. Geological Society, London, Special Publications, 130, 107–115.
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Singh, V.P. 1997. Effect of spatial and temporal variability in rainfall and watershed characteristics on stream flow hydrograph. Hydrological Processes, 11, 1649–1669. Singh, V.P. and Woolhiser, D.A. 2002. Mathematical modeling of watershed hydrology. Journal of Hydrologic Engineering, 7: 270–292. Sinha, B.P.C. and Sharma, S.K. 1988. Natural groundwater recharge estimation methodologies in India. In: Simmers, I. (ed.) Estimation of natural groundwater recharge. NATO ASI Series C, vol. 222 (Proceedings of the NATO advanced research workshop, Antalya, Turkey, March 1987), D. Reidel Publication Company, Dordrecht, 301–311, 1988. Sophocleous, M. and Perkins, S.P. 2000. Methodology and application of combined watershed and ground-water models in Kansas. Journal of Hydrology, 236, 185–201. Srinivas, A., Venkateswara Rao, B.V., and Gurunadha Rao, V.V.S. 1999. Recharge process and aquifer models of a small watershed. Hydrological Sciences Journal, 44, 681–692. Stephens, D.B. 1996. Vadose Zone Hydrology. Lewis Publishers, Florida. Stewart, J.B., Engman, E.T., Feddes, R.A., and Kerr, Y.H. 1998. Scaling up in hydrology using remote sensing: Summary of a Workshop. International Journal of Remote Sensing, 19, 181–194. Stoertz, M.W. and Bradbury, K.R. 1989. Mapping recharge areas using a ground water flow model: A case study. Ground Water, 27, 220–228. Taniguchi, M. 2002. Estimations of the past groundwater recharge rate from deep borehole temperature data. Catena, 48, 39–51. Taniguchi, M. and Sharma, M.L. 1993. Determination of groundwater recharge using the change in soil temperature. Journal of Hydrology, 148, 219–229. Taniguchi, M., Tsujimura, M., and Tanaka, T. 1996. Significance of stemflow in groundwater recharge. 1: Evaluation of the stemflow contribution to recharge using a mass balance approach. Hydrological Processes, 10, 71–80. Tarasov, L. and Peltier, W.R. 2004. A geophysically constrained large ensemble analysis of the deglacial history of the North American ice-sheet complex. Quaternary Science Reviews, 23, 359–388. Therrien, R. and Sudicky, E.A. 1996. Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media. Journal of Contaminant Hydrology, 23, 1–44. Thornthwaite, C.W. and Mather, J.R. 1957. Instructions and tables for computing potential evapotranspiration and the water balance. Publications in Climatology, 10, 185–311. Toth, J. 1963. A theoretical analysis of groundwater flow in small drainage basins. Journal of Geophysical Research, 68, 4795–4812. Vaccaro, J.J. 1992. Sensitivity of groundwater recharge estimates to climate variability and change, Columbia Plateau, Washington. Journal of Geophysical Research, 97, 2821–2833. VanderKwaak, J.E. 1999. Numerical Simulation of Flow and Chemical Transport in Integrated SurfaceSubsurface Hydrologic Systems. PhD thesis, Department of Earth Sciences, University of Waterloo, Waterloo, Ontario, Canada. VanderKwaak, J.E. and Sudicky, E.A. 2000. Application of a physically based numerical model of surface and subsurface flow and solute transport. In: Stauffer, F., W. Kinzelbach, K. Kovar, and E. Hoehn. (eds.) Proceedings of ModelCARE 1999, Calibration and Reliability in Groundwater Modelling. IAHS Publication No. 265, pp. 515–523. Varni, M.R. and Usunoff, E.J. 1999. Simulation of regional-scale groundwater flow in the Azul River basin, Buenos Aires Province, Argentina. Hydrogeology Journal, 7, 180–187. Vermulst, J.A.P. and De Lange, W.J. 1999. An analytic-based approach for coupling models for unsaturated and saturated groundwater flow at different scales. Journal of Hydrology, 226, 262–273. Walker, G.R., Zhang, L., Ellis, T.W., Hatton, T.J., and Petheram, C. 2002. Estimating impacts of changed land use on recharge: review of modelling and other approaches appropriate for management of dryland salinity. Hydrogeology Journal, 10, 68–90. Wilkinson, W.B. and Cooper, D.M. 1993. Response of idealized aquifer/river systems to climate change. Hydrological Sciences Journal, 38, 379–389.
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Williamson, D.R. 1990. Salinity — An Old Environmental Problem (abstract). Technical Memorandum 90/7, CSIRO Division of Water Resources, Institute of Natural Resources and Environment. Winter, T.C. 1978. Numerical simulation of steady state three-dimensional groundwater flow near lakes. Water Resources Research, 14, 245–254. Winter, T.C. 1983. The interaction of lakes with variably saturated porous media. Water Resources Research, 19, 1203–1218. Wittenberg, H. and Sivapalan, M. 1999. Watershed groundwater balance estimation using streamflow recession analysis and baseflow separation. Journal of Hydrology, 219, 20–33. Woolhiser, D.A., Smith, R.E., and Gilardez, J.-V. 1966. Effects of spatial variability of saturated hydraulic conductivity on Hortonian overland flow. Water Resources Research, 32(3), 671–678. Wu, J., Zhang, R., and Yang, J. 1997. Estimating infiltration recharge using a response function model. Journal of Hydrology, 198, 124–139. Xiao, Q., Ustin, S.L., and Wallender, W.W. 1996. A spatial and temporal continuous surface-subsurface hydrologic model. Journal of Geophysical Research, 101, 29565–29584. Xu, Y. and van Tonder, G.J. 2001. Estimation of recharge using a revised CRD method. Water South Africa, 27, 341–344. Yan, J. and Smith, K.R. 1994. Simulation of integrated surface water and ground water systems — model formulation. Water Resources Bulletin, 30, 879–890. Yang, Y., Lerner, D.N., Barrett, M.H., and Tellam, J.H. 1999. Quantification of groundwater recharge in the city of Nottingham, UK. Environmental Geology, 38, 183–198. Yang, J., Li, B., and Liu, S. 2000. A large weighing lysimeter for evapotranspiration and soil-watergroundwater exchange studies. Hydrological Processes, 14, 1887–1897. Zhang, L. and Dawes, W.R. 1998. WAVES — An Integrated Energy and Water Balance Model. Technical Report 98(31), CSIRO Land and Water Division. Zhang, L., Dawes, W.R., Hatton, T.J., Reece, P.H., Beale, G.T.H., and Packer, I. 1999a. Estimation of soil moisture and groundwater recharge using the TOPOG_IRM model. Water Resources Research, 35, 149–161. Zhang, L., Hume, I.H., O’Connell, M.G., Mitchell, D.C., Milthorpe, P.L., and Yee, M.D.H. 1999b. Estimating episodic recharge under different crop/pasture rotations in the Mallee region. Part 1. Experiments and model calibration. Agricultural Water Management, 42, 219–235. Zhang, L., Dawes, W.R., Hatton, T.J., Hume, I.H., O’Connell, M.G., and Mitchell, D.M.Y. 1999c. Estimating episodic recharge under different crop/pasture rotations in the Mallee region. Part 2. Recharge control by agronomic practices. Agricultural Water Management, 42, 237–249.
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29 Ecohydrology: Water, Carbon, and Nutrient Cycling in the Soil– Plant Atmosphere Continuum 29.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-2 29.2 Atmospheric Controls on Photosynthesis and Transpiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-2 Scalar Mass Balance and Turbulent Transport • Scalar Transfer from Leaf Stomata and Resistance Parameterization • Photosynthesis and Ci Parameterization • Radiative Transfer • Parameterization of Ti and qi : The Leaf Energy Budget • Modeling the Flow Field inside Canopies • Modeling Ecosystem Fluxes • Transpiration and Hydraulic Controls
29.3 Soil Water Balance in the Vadose Zone . . . . . . . . . . . . . . . . . 29-13 Instantaneous Equation for Soil-Moisture Dynamics • Soil-Moisture Dynamics at the Daily Time Scale • Long-Term Water Balance • Heat Flow into the Soil
29.4 Soil Moisture Deficit and Plant Water Stress . . . . . . . . . . . 29-19 Physiological Impact of Soil Moisture Deficit on Plants • Modeling Plant Water Stress • Soil-Climate-Vegetation Control on Plant Water Stress and Plant Carbon Assimilation
29.5 Soil Nutrient Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-24 Brief Review of Soil Carbon and Nitrogen Cycles • Model Structure • System Behavior under Constant and Stochastic Soil Moisture Conditions • Soil Organic Matter and Soil Hydraulic Properties
Edoardo Daly, Gabriel Katul, and Amilcare Porporato Duke University
29.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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29.1 Introduction The vadose zone is located between the land surface and the water table within which the soil moisture content is below saturation (except in the capillary fringe) and the water pressure is less than atmospheric. In this zone, the soil pore space typically contains air and other gases (e.g., O2 , CO2 ) that are central to the biogeochemistry of the soil-plant-atmosphere system. The dynamics of water and nutrients in this zone impact groundwater quality and quantity through intricate interconnections between physical, biological, and chemical processes attributed to the presence of vegetation, soil microorganism, and their interaction with local climate and above-ground micrometeorology. The urgency of linking carbon-nutrient-water activities in the vadose zone to simultaneous plant activities and ground recharge cannot be underemphasized. Management strategies to reduce anthropogenic CO2 from the atmosphere are now providing incentives for timber-product companies to increase the managed plantation acreage and shortening stand rotations. For example, in the Southeastern United States, managed pine plantations are projected to increase by up to 30% of the entire timberland area in 2050. Naturally, to increase aboveground net primary productivity, nitrogen fertilization is routinely employed with application rates well in excess of 10 g N m−2 yr−1 (natural N deposition rates in the Southeast are on the order of 0.5 g N m−2 yr−1 ). While nitrogen amendments can increase aboveground biomass and leaf area density as well as leaf photosynthetic capacity, the impact of such high N fertilization on groundwater quality cannot be ignored. A detailed description of such dynamics requires taking into account the water, energy, carbon, and nutrients budgets in the soil-plant-atmosphere system, where fluxes and state and forcing variables fluctuate on a broad range of spatial and temporal scales, making the entire system extremely complex and high-dimensional. The modeling difficulty is compounded by the central role played by the biological components, going from the plant stomatal control of transpiration and photosynthesis to plant nutrient uptake, litter production, and the dynamics of soil organic matter (SOM) and microbial biomass. The focus of this chapter is the mathematical modeling of carbon-nutrient-water cycling in the soilplant-atmosphere system with particular attention to time scales most relevant to groundwater quality and quantity. Our review will be centered on the temporal dynamics, while spatial issues will not be directly considered. At the finest scale, describing water vapor exchange (and transpiration) over vegetated surfaces commands simultaneous considerations of heat and CO2 exchanges, as all these exchange processes are intertwined at the most fundamental level, the leaf stomata. Hence, a logical starting point of this chapter is to describe the basic formulations for computing maximum CO2 uptake through the stomata and maximum H2 O loss out of the stomata based on hydro-meteorological conditions and photosynthetic demands (Section 29.2). We then progress toward a discussion of the impact of soil-water availability on these maximum rates and their implications to soil biogeochemistry and groundwater recharge. Section 29.3 presents a stochastic model for soil-moisture dynamics in the vadose zone, along with the consequent implications in the long-term water balance and the soil heat balance. The main relations between soil water availability and vegetation behaviors are described in Section 29.4, where plant water stress is modeled and its influence on vegetation carbon assimilation is analyzed. Section 29.5 is finally dedicated to soil biogeochemical cycles, and particularly to modeling soil carbon and nitrogen, whose dynamics is strongly dependent on soil-moisture level and variability.
29.2 Atmospheric Controls on Photosynthesis and Transpiration This section investigates recent developments in multi-layer methods needed for computing distributions and strengths of H2 O, heat, and CO2 (often referred to as scalars) sources and sinks within the above-ground canopy volume using basic radiative transfer schemes, turbulent transport theories, and physiological principles assuming water loss is entirely “slaved” to the carbon needs of leaf photosynthesis.
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Hence, the resulting carbon-water rates from these models represent the maximum transpiration and photosynthesis for a set of physiological properties and microclimate conditions (e.g., radiative load, vapor pressure deficit, air temperature, etc.). The conservation equations and parameterization schemes used in such methods are reviewed next. In multi-layer models, the canopy is represented by a sequence of finite layers (Figure 29.1), each of thickness dz, and encompassing leaf area density a(z). The leaf area index (LAI) of the stand is given by h LAI = 0 a(z)dz, where h is the mean canopy height.
29.2.1 Scalar Mass Balance and Turbulent Transport For a horizontally uniform and rigid canopy, the time and horizontally averaged one-dimensional scalar mass conservation equations for mean carbon dioxide (Ca ), water vapor (qa ), and temperature (Ta ), within a layer of thickness dz (Figure 29.1) can be written as ∂Fc ∂Ca + = Sc ∂t ∂z ∂Fq ∂qa + = Sq ∂t ∂z
(29.1)
∂FT ∂Ta + = ST ∂t ∂z where t is time, z is height above the forest floor (this notation for z will reverse once we consider the vadose zone), Fc , Fq , and FT are the turbulent vertical fluxes of CO2 , water vapor, and heat, and Sc , Sq , and ST are the vegetation source (or sink) strength of CO2 , water vapor, and heat, respectively. Mean quantities are subject to both time and horizontal averaging as discussed in Raupach and Shaw (1982). Temporal averaging, often on the order of 1/2 h, is needed to average out turbulent eddies responsible for much of the mass transport to and from the canopy, and spatial averaging, often on the order of few canopy heights, is needed to include the effects of the canopy on the airflow. Equation 29.1 represents three equations with nine unknowns necessitating additional formulations to solve for Ca , qa ,Ta , Fc , Fq , FT , Sc , Sq , and ST . The required additional formulations can be derived from the relationship between source strength and mean concentration via basic fluid mechanics principles. A set of prognostic equations describing the Atmospheric surface layer ~3–5 h
Canopy sub layer a(z) h S
dz
Ca
dz
Vadose zone
FIGURE 29.1 Schematic representation of a canopy with a mean height h and leaf area density a(z) (foliage area per unit volume) showing an arbitrary layer of thickness dz. The leaves are assumed to exchange heat, water vapor, and CO2 with the neighboring atmosphere via source terms S. The term a(z) is analogous to the porosity distribution in groundwater flow. (Modified from Katul, G.G. and Siqueira, M., Vadose Zone J., 1, 58, 2002.)
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relationship between concentration and source (or sink) for CO2 , water vapor, and temperature can be formulated in the Lagrangian or Eulerian frame of reference. In the Lagrangian frame of reference, these equations take the form of an arbitrary scalar s (representing here either CO2 , H2 O, or temperature) 1 s¯ = ρa
P(z, t ; z0 , t0 )Ss (z0 , t0 )dzdt0
(29.2a)
where ρa is the mean air density, P(z, t ; z0 , t0 ) is the transition probability density function determined from measured or modeled turbulent flow statistics within the canopy volume, and Ss is the source (or sink) strength of scalar s, and s¯ is the mean concentration. For practical estimation of P(z, t ; z0 , t0 ), Lagrangian analytical models were developed and tested for a wide range of vegetation types (Raupach, 1989a,b; Katul et al., 1997; Warland and Thurtell, 2000). In particular, the Localized Near Field theory (LNF) proposed by Raupach (1989a,b) proved to be a parsimonious model for such applications (Gu et al., 1999; Denmead et al., 2000; Leuning, 2000; Siqueira et al., 2000; Katul and Siqueira, 2002) though its ability to explicitly deal with thermal stratification within the canopy remains absent. In the Eulerian frame of reference, the time and horizontally averaged conservation equation for the vertical scalar flux budget s (=s − s¯) can be expressed as ∂w s ∂ s¯ ∂w w s ∂p = 0 = −w 2 − − s ∂t ∂z ∂z ∂z
(29.2b)
0 = P1 + P2 + P3 where w is the turbulent vertical velocity, and terms P2 and P3 are unknowns requiring closure approximations if the velocity statistics are known. Note that Equation 29.2b neglects buoyancy, scalar drag, and waving source production though they can be readily included in such formulations as discussed in Finnigan (1985) and Siqueira and Katul (2002). Using higher order closure models and detailed measurements within a pine forest, Siqueira and Katul (2002) showed that accounting for thermal stratification during day-time conditions is important for matching the sensible heat flux, and accounting for thermal stratification at night is important for modeling CO2 storage dynamics within the canopy volume. Below, we show the near-neutral stratification for illustration purposes though the more general case is derived and discussed elsewhere (Siqueira and Katul, 2002). The flux transport term (P2 ) can be modeled after Meyers and Paw U (1987) and the dissipation term (P3 ) can be modeled after Finnigan (1985). These approximations often lead to standard closure schemes given by w w s s
∂ s¯ ∂w w ∂w s τ −w w w −w s − 2w w = C8 ∂z ∂z ∂z
∂p w s = C4 ∂z τ
where C4 and C8 (the subscripts here are retained for consistency with standard nomenclature in turbulent transport theories) are closure constants and τ is an Eulerian relaxation time scale given by τ=
σe2 , ε
where σe = ui ui is a characteristic turbulent velocity (proportional to the turbulent kinetic energy), and ε is the mean rate of turbulent kinetic dissipation, and ui are the velocity components in the x1 (or x), x2 (or y), and x3 (or z) directions, respectively, with x1 aligned along the mean wind direction so that u2 = 0. The relaxation time τ is strictly dependent on the velocity statistics and can be computed from
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momentum higher-order closure models (Katul and Albertson, 1998, 1999; Katul and Chang, 1999) or LES techniques. Upon combining these closure approximations with the scalar budget equation, for example, Equation 29.2b, a second order ordinary differential equation (ODE) can be derived to describe the variations of the scalar turbulent flux with height (Siqueira et al., 2000; Katul and Albertson, 1998), as A1 (z)
∂ 2w s ∂w s + A3 (z) w s = A4 (z) + A2 (z) 2 ∂z ∂z
where A1 (z) =
2τ ww C8
∂ τ τ ∂w w +2 ww C8 ∂z ∂z C8 ∂ 1 τ ∂w w − C4 A3 (z) = ∂z C8 ∂z τ τ ∂ 2 s¯ ∂ ∂ s¯ τ ∂ s¯ A4 (z) =w w − − www www . ∂z ∂z C8 ∂z C8 ∂z 2
A2 (z) =
Combining Equation 29.1 and either Equation 29.2a or Equation 29.2b to estimate Ca , qa , Ta , Fc , Fq , FT , Sc , Sq , and ST reduces now the problem to six equations with nine unknowns and still remains unsolvable. To mathematically close this system of equations, three additional relations describing mass transfer from the leaves to the atmosphere are required. These are described next.
29.2.2 Scalar Transfer from Leaf Stomata and Resistance Parameterization The scalar source strength can be related to the atmospheric concentration by a Fickian diffusion formulation through the stomatal cavity and the leaf boundary layer. These formulations lead to the following expressions: Ca (z) − Ci (z) rb (z) + rs (z) qa (z) − qi (z) Sq (z) = −λw a(z) rb (z) + rs (z) Sc (z) = −ρa(z)
ST (z) = −ρCp a(z)
Ta (z) − Ti (z) rb (z)
(29.3a) (29.3b) (29.3c)
where subscripts “a” and “i” represent the “free” atmosphere and stomata sub-cavity space concentration values, λw is the latent heat of water vaporization, Cp is the specific heat of dry air under constant pressure, a(z) is, as before, the leaf area density, and rb (z) and rs (z) are the mean boundary layer and stomatal resistances at a given z, respectively. For simplicity, all the symbols representing mean resistances (or conductance) are shown without overbar throughout. Combining Equation 29.1 to Equation 29.3, Ca , qa ,Ta , Fc , Fq , FT , Sc , Sq , and ST can be solved if rb (z), rs (z), Ci , qi and Ti are modeled or parameterized. Modeling rb (z), rs (z), Ci , qi and Ti is discussed next. The estimation of rb is based on flat plate theory (Schuepp, 1993; Baldocchi and Meyers, 1998), and requires the mean wind speed within the canopy, which in turn is modeled from second order closure principles (and will be reviewed later).
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0.16
0.14
gs
0.12 0.1 0.08 0.06 0.04 0.02 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
An hs/Ca
FIGURE 29.2 Comparison between measured and modeled leaf stomatal conductance (gs ) using Equation 29.4 for sunlight Loblolly pine needles under ambient (=380 ppm) and elevated (=580 ppm) atmospheric CO2 concentration levels. The gs , leaf photosynthesis (An ), and the surface relative humidity (hs ) data are collected using leaf-level gas exchange porometry within the Free Air CO2 Enrichment (FACE) facility at the Blackwood division of the Duke Forest, near Durham, NC.
Collatz et al. (1991) developed a semi-empirical physiological model to relate stomatal conductance gs = rs−1 to leaf photosynthesis, given by gs = m
A n hs +b Ca
(29.4)
where m and b are species-specific parameters, often determined by gas-exchange measurements, An is the net leaf-scale assimilation rate, and hs is the mean air relative humidity near the leaf surface (not to be confused with canopy height h). Equation 29.4 has been tested for a wide range of climatic conditions, including elevated atmospheric CO2 as shown in Figure 29.2. The experiments in Figure 29.2 suggest the parameters m and b are robust to such wide range of variations in atmospheric CO2 conditions and do reflect “internal” physiological properties. While there is some debate as to whether relative humidity or vapor pressure deficit ought to be used in such models (e.g., Leuning, 1995; Katul et al., 2000; Kumagai et al., 2004), the data-model comparison in Figure 29.2 suggests that Equation 29.4 (or variants on it) is sufficient to link leaf conductance to photosynthesis, at least for the purposes of modeling “maximum” leaf photosynthesis and subsequent carbon input to the vadose zone.
29.2.3 Photosynthesis and Ci Parameterization According to Farquhar et al. (1980), the net photosynthetic rate at the leaf scale depends on light, CO2 , and leaf temperature and can be described as An ≈ min
JE − Rd , Jc
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where JE and Jc are the assimilation rate restricted by light and ribulose bisphosphate (Ru BP) carboxylase (or Rubisco) respectively, and Rd is the respiration rate during daytime without photorespiration. The flux per unit leaf area, JE , describes the light restriction on photosynthesis, given by J E = αl × e m × Q p
Ci − ∗ Ci + 2 ∗
where αl is the leaf absorptivity for photosynthetically active radiation (PAR), em is the maximum quantum efficiency for CO2 uptake, Qp is the PAR irradiance on the leaf surface (and varies significantly inside the canopy), Ci , as before, represents mean intercellular mean CO2 concentration. The CO2 compensation point, ∗ , is the CO2 concentration at which An = 0 in the absence of photorespiration, and is given by: ∗ =
[O2 ] 2ω
where [O2 ] is the oxygen concentration in air (≈210 mmol mol−1 ), and ω is a ratio of kinetic parameters describing the partitioning of Ru BP to the carboxylase or oxygenase reactions of Rubisco (Campbell and Norman, 1998). The leaf flux Jc is the Rubisco-limited rate and is estimated from Jc =
Vc max (Ci − ∗ ) Ci + Kc (1 + [O2 ]/Ko2 )
where Vc max (µmol m−2 sec−1 ) is the maximum catalytic capacity of Rubisco per unit leaf area, Kc and Ko2 are the Michaelis constants for CO2 fixation and O2 inhibition with respect to CO2 , respectively. Note that Jc increases linearly with increasing Ci , but approaches a maximum Vc max under high CO2 concentration state, which is rarely encountered under natural conditions. Following Collatz et al. (1991), the respiration rate Rd can be estimated as Rd = 0.015Vc max . Temperature dependence of kinetic variables is computed following the equations in Campbell and Norman (1998). Five kinetic parameters are needed to adjust for temperature, namely Kc , Ko , ω, Vc max and Rd . For the first three parameters, an exponential temperature function is employed: k = k25 exp[y(Ts − 25)] with k defined at leaf surface temperature Ts , and where k25 is the value of the parameter at 25◦ C, and y is the temperature coefficient for that parameter. In addition, Vc max and Rd are adjusted by a more complex function incorporating deactivation effects at extremely high temperatures (see Figure 29.3), such as Vc max =
Vc max,25 exp[0.031(Ts − 25)] 1 + exp[0.115(Ts − 41)]
and Rd =
Rd,25 exp[0.069(Ts − 25)] 1 + exp[1.3(Ts − 55)]
where Vc max,25 and Rd,25 are the values of Vc max and Rd at 25◦ C, respectively. Again, this strong dependency of Vc max on leaf temperature necessitates simultaneous modeling of heat, water vapor, and CO2 exchange. Finally, at the leaf scale, Cs , Ci , and Ca are related by Ci = Cs − An /gs and Cs = Ca − An /gb .
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The Handbook of Groundwater Engineering 140
120
Vc max ( mol m–2 s–1)
100
80
60
40
20
0
0
5
10
15
20 25 30 Leaf temperature (C)
35
40
45
FIGURE 29.3 Typical relationship between Vc max and leaf temperature for a southern Loblolly pine stand. Note the deactivation effects at air temperatures in excess of 36◦ C.
29.2.4 Radiative Transfer Radiation attenuation inside the canopy is critical to both the Farquhar photosynthesis model (through JE ) and the leaf energy budget. The light transmission model of Campbell and Norman (1998) is perhaps among the most parsimonious models and is briefly described below. The solar (short-wave) radiation can be decomposed into direct beam, diffuse, and reflective radiation. For thermal or long-wave radiation, the atmosphere can be assumed to function as a gray body (e.g., Campbell and Norman, 1998). This permits using an averaged sky emissivity for calculating atmospheric thermal emittance. For simplicity, a constant emissivity of 0.97 can be employed. Light transmission through the canopy is computed for sunlit and shaded portions separately to estimate PAR and near-infrared (NIR) irradiance absorbed at each canopy level. This waveband decomposition is necessary because leaf absorptivity is different for these two spectral bands (Monteith and Unsworth, 1990; Campbell and Norman, 1998). The fraction τb (ψ) of incident beam radiation from a zenith angle ψ penetrating through the canopy is given by √ (29.6) τb (ψ) = exp(− αl Kbe (ψ)al ), where Kbe (ψ) is the extinction coefficient for an ellipsoidal leaf distribution (see Campbell and Norman, z 1998), al (=− h a(z)dz) is the cumulative leaf area density integrated from the canopy top, and is the clumping factor of leaf distribution ( = 1 when leaves are randomly distributed in space).
29.2.5 Parameterization of Ti and qi : The Leaf Energy Budget The energy budget at the leaf surface is used to solve for surface variables (i.e., Ti and qi ) and absorbed radiation for estimating gs . Due to the strong nonlinearity in the leaf energy budget, a Taylor series expansion along with a Penman approximation were used to derive an explicit algebraic equation for mean leaf surface temperature (Ts ), given by 4
3
Ts = Ta + (Qab − λw gv Dv /pa − εl σ Ta )/(hc + λw gv s /pa + 4εl σ Ta )
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z (m)
(a) 12 8 4 0
1
2
3
4
5
6
0
1
2
3
4
5
6
0
1
2
3 4 Time (d)
5
6
Rn (W m–2)
(b) 700 300 100
T (°C)
(c) 40 30 20
FIGURE 29.4 (a) Modeled radiation attenuation inside a 17-year-old pine canopy at the Blackwood division of the Duke Forest, near Durham, North Carolina. Regions of maximum radiation absorption are in dark. (b) Comparison between modeled radiation absorbed by the canopy and net radiation measured above canopy. (c) Comparison between remotely sensed, measured, and modeled skin temperature in the upper third of the canopy. (Revised from Lai, C.T., et al. Bound. Lay. Meteorol., 95, 91, 2000.)
where Qab is the absorbed energy at each canopy layer, gv is the water vapor conductance (derived from gs and gb for water vapor), Dv is the vapor pressure deficit, pa is the atmospheric pressure, εl is the leaf emissivity, σ is the Stefan-Boltzmann constant, hc is a convection coefficient (not to be confused with canopy height), and s is the slope of the curve relating saturation vapor pressure to temperature. A comparison between modeled absorbed radiation and measured net radiation, and measured and modeled remotely sensed skin temperature are shown in Figure 29.4. The agreement between modeled and measured surface temperature in the figure for the canopy morphology of a pine forest is encouraging despite the simplifications in the radiative transfer schemes.
29.2.6 Modeling the Flow Field inside Canopies To predict the flow statistics for Equation 29.2, particularly the second-moment statistics such as σw = ¯ needed (w w )1/2 , σu = (u u )1/2 , σv = (v v )1/2 , σe = (σu2 + σv2 + σw2 )1/2 , and the mean velocity (u) for the calculation of rb , second-order closure principles can be used. One simple approach is to consider the analytical theory of Massman and Weil (1999), hereafter referred to as MW99, which assumes an exponential mean velocity profile given by u(z) ¯ = e−nγ (z) u(h) ¯ and results in w u (z) = e−2n(γ (z)) , u∗2
σe (z) σu = Au υ 1 , u∗ u∗
σe (z) σv = A v υ1 , u∗ u∗
σe (z) σw = Aw υ1 u∗ u∗
where σe = [υ3 e−ς (h)γ (z) + B1 (e−3nγ (z) − e−ς(h)γ (z) )]1/3 , u∗
ς (z) , γ (z) = 1 − ς (h)
z ς (z) =
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Cd a(z)dz 0
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The Handbook of Groundwater Engineering
and the constants are given by n=
1 2
u∗ u(h) ¯
−2
ς (h),
B1 =
υ1 = (Au2 + Av2 + Aw2 )−1/2 ,
−9u∗ /u(h) ¯
, 2 4 2αυ1 9/4 − u∗4 /(u(h)) ¯
υ3 = (Au2 + Av2 + Aw2 )3/2 ,
and
2 =
3υ1 α2
υ2 =
A2 υ3 − w 6 2 υ1
where, u∗2 = −u w defined above the canopy (and assumed to be independent of zup to the atmospheric surface layer, see Figure 29.1). The MW99 model computes the zero displacement height (d) from the centroid of the momentum sink using 1 u w (r) d =1− d(r) h u∗2 0
where, r = z/h. Above the canopy, the flow is assumed to attain its atmospheric surface layer state (see Figure 29.1) with uw = −1, u∗2
z −d u¯ 1 = log , u∗ κ zo
σu = Au , u∗
σv = Av , u∗
σw = Aw u∗
where zo /h = (1 − d/h)e−kv (u¯ h /u∗ ) , and κ = 0.4 is the von-Karman constant, and zo is the momentum roughness length. This model has been tested for a wide range of canopies ranging from uniform rice fields to hardwood forest, as shown in Figure 29.5. In Equation 29.2b, a simplified gradient-diffusion model for w w w = −C6 σe2 τ (dw w /dz) can be used. Common values for the constants Au = 2.1–2.4, Av = 1.8–2.2, and Aw = 1.1–1.3.
29.2.7 Modeling Ecosystem Fluxes When combining the scalar continuity equations, the turbulent flux budget equations, the radiation balance, the leaf energy balance, and the Farquhar model, it is possible to solve for Ca , qa ,Ta , Fc , Fq , FT , Sc , Sq , and ST . The concentration and fluxes within and above the canopy can be compared to measurements for well-water conditions. For example, Figure 29.6 compares eddy-covariance measured and modeled scalar fluxes above a six-year-old pine canopy for an ambient and a fertilized stand at the South-Eastern Tree Research and Education Site (SETRES) in North Carolina, where the fertilization increased LAI by a factor of two, the respiring biomass by a factor of 1.5, and Vc,max by 20%. In both, ambient and N-fertilized stands, the formulation here reproduced well the eddy-covariance measured fluxes of heat, water vapor, and CO2 .
29.2.8 Transpiration and Hydraulic Controls The method described so far can determine plant transpiration for conditions in which soil moisture does not limit stomatal conductance using h Tr,max (t ) =
Sq (t , z)dz 0
Because Sq and the leaf-conductance in Equation 29.4 do not include any hydraulic limitations (e.g., leaf pressure), the model cannot account for cavitation and other hydraulic-related phenomena leading to stomatal shutdown as drought progresses. This shutdown is crucial in shallow-rooted plants because
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3
3
3
3
2
2
2
2
2
1
1
1
1
1
3
z/h
Rice
0 0
10
20
0
0
5
10
0 0 15 –1.5 –1 –0.5 0 0.5 0
1
2
0
3
3
3
3
2
2
2
2
2
1
1
1
1
1
3
0
5
10
0
5
10
0
5
10
0
5
10
0
5
10
0
5
z/h
Corn
0
0
10
20
3
0
0
5
10
0 15 –1.5 –1 –0.5 0
0
0
1
2
0
3
3
3
3
2
2
2
2
2
1
1
1
1
1
z/h
Aspen
0
0
10
20
3
0
0
5
10
0 0 15 –1.5 –1 –0.5 0 0.5 0
1
2
0
3
3
3
3
2
2
2
2
2
1
1
1
1
1
z/h
L. Pine
0
0
10
20
0
0
5
10
0 0 15 –1.5 –1 –0.5 0 0.5 0
1
2
0
3
3
3
3
2
2
2
2
2
1
1
1
1
1
3
z/h
S. Pine
0
0
10
20
3
0
0
5
10
0 0 15 –1.5 –1 –0.5 0 0.5 0
1
2
0
3
3
3
3
2
2
2
2
2
1
1
1
1
1
z/h
Hardwood
0
0
10 a (z) h
20
0
0
5
10 U/u*
0 0 15 –1.5 –1 –0.5 0 0.5 0 2
uw/u*
1 uw/u*
2
0
2
10 2
K/u*
FIGURE 29.5 Comparison between measured and MW99 modeled velocity statistics for a wide range of canopy morphologies, including a rice- and a cornfield, an aspen forest, a southern Loblolly pine stand, a Scots pine forest, and a southern hardwood forest (see Nathan and Katul, 2005 for further details). Here K = 12 σe2 is the turbulent kinetic energy, U is the mean wind speed, and uw and ww represent the momentum flux and the vertical velocity variance.
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The Handbook of Groundwater Engineering Fortilized 0.3
0.2
0.2
Fc–EC (mg cm–2 s–1)
Fc–EC (mg cm–2 s–1)
Control 0.3
0.1 0 –0.1 –0.2
–0.1
0.3
–0.2 –0.1 0 0.1 0.2 Fc–EC (mg cm–2 s–1)
350
350
300
300
250
Fq–CV (W m–2)
Fq–CV (W m–2)
0
–0.2 –0.2 –0.1 0 0.1 0.2 Fc–EC (mg cm–2 s–1)
200 150 100 50
0.3
250 200 150 100 50
0
0
–50
–50 0
100 200 Fq–EC (W m–2)
300
350
350
300
300
250
Fh–CV (W m–2)
Fh–CV (W m–2)
0.1
200 150 100
0
100 200 Fq–EC (W m–2)
300
0
100 200 Fh–EC (W m–2)
300
250 200 150 100
50
50
0
0 –50
–50 0
100 200 Fh–EC (W m–2)
300
FIGURE 29.6 Comparison between 1/2-hourly measured (subscript EC for eddy-covariance) and modeled (subscript CV for canopy – vertically resolved) scalar fluxes of CO2 (top), water vapor (middle), and sensible heat (bottom) for the 6-year-old ambient and fertilized pine stands at SETRES for control and fertilized plots. (From Lai, C.T., et al. Plant Cell Environ., 25, 1095, 2002, with permission.)
the soil moisture reservoir is rather limited and can be depleted rapidly. Using sapflow and soil moisture measurements for the entire root zone (=30 cm), Oren et al. (1998) reported a reduction in transpiration of more than 60% in a southeastern Loblolly pine forest as the root-zone soil moisture content is reduced from 0.20 to 0.13. The actual transpiration is thus a function of the Tr,max , that is, of the evaporative demand, and soil-water content (e.g., Guswa, 2005). For the sake of simplicity, in the following, the effect of evaporative demand on actual evapotranspiration will be neglected with respect to the influence of
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29-13
water availability. Hence, for soil biogeochemical models, running on time-scales of months to decades, it is possible to represent the transpiration rate as Tr = Tr,max f (θ) where Tr,max is the maximum loss of water that can occur if the plant is permitted to satisfy its carbon uptake demand for a given set of light and micrometeorological conditions above the canopy (as determined from the model earlier described), and f (θ) is the soil moisture reduction function that accounts for stomatal shutdown to prevent runaway cavitation (e.g., Bohrer et al., 2005 for additional developments taking into account plant architecture). This is the basic transpiration-assimilation model used in the coupled C-N-H2 O described next.
29.3 Soil Water Balance in the Vadose Zone As noted earlier, a correct description of soil-moisture dynamics is essential to predict plant uptake and evapotranspiration (see Section 29.2.8) and the related plant water stress, the soil energy balance and deep percolation of water and nutrients to groundwater, as well as the decomposition of SOM and the nutrient availability to plants. The main processes involved in the soil water balance are schematically described in Figure 29.7. We will start with the balance equation of soil water at a point in space and time and then proceed with formal averaging procedures to describe the soil water balance at the daily time scale and vertically averaged over the root zone to provide a simplified but realistic equation to couple with the stochastic rainfall variability.
29.3.1 Instantaneous Equation for Soil-Moisture Dynamics The three-dimensional continuity equation for soil moisture is given by ∂qi ∂θ =− − Sr (θ) ∂t ∂xi
(29.7)
where θ is the volumetric soil moisture content at some arbitrary point xi in the soil, qi is the water flux in direction xi , xi (i = 1, 2, 3) being the Cartesian coordinates for the longitudinal (x1 = x), the lateral (x2 = y), and the vertical (x3 = z, directed into the soil) direction, and Sr now represents the local sinks of water by the rooting system. For a planar homogeneous flow ∂(.)/∂x1 = ∂(.)/∂x2 = 0, and the continuity equation in the vertical direction reduces to ∂q3 ∂θ =− − Sr (θ) ∂t ∂x3 Upon depth averaging this equation from the soil surface (x3 = z = 0) to the root-zone depth (z = Zr ), we obtain Zr Zr ∂θ dz = q(0) − q(Zr ) − Sr (θ)dz ∂t 0
0
where q(0) is the amount of water infiltrating or evaporating from the soil system, q(Zr ) is the drainage Z loss from the rooting system (that percolates to groundwater), and 0 r Sr (θ)dz is the actual plant-water
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The Handbook of Groundwater Engineering Rainfall h
t
InterceptionEvaporation
Evapotranspiration
Throughfall Runoff
Runoff Zr Zr
Effective porosity, n
Effective porosity, n
Leakage
FIGURE 29.7 Schematic representation of the key processes controlling the soil water balance. (From Laio, F., et al. Adv.Water Resour., 24, 707, 2001a, with permission.)
uptake or transpiration, Tr . Defining the normalized depth-averaged soil moisture content by Zr sm (t ) = 0
1 θ (t , z) dz, Zr (t ) n(t , z)
where n(t , z) is the soil porosity, and using Leibniz’s theorem, leads to the simplified hydrologic balance nZr
dsm d(nZr ) + sm = q(0) − q(Zr ) − Tr dt dt
In the following, n and Zr will be assumed not to change appreciably with t so that the term sm d(nZr )/dt is neglected compared to nZr dsm /dt .
29.3.2 Soil-Moisture Dynamics at the Daily Time Scale For hydrologic models, the logical time scale for resolving the soil moisture dry-down period is daily. Hence, it becomes necessary to apply an additional averaging operator to the previous formulation that
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reduces the daily hydrologic balance to nZr
d¯sm = q(0) − q(Zr ) − Tr dt
where the overbar represents time averaging over a day (rather than over turbulent time scales as earlier defined). For prognostic (vis-à-vis diagnostic) models of subsurface flow, the daily rainfall depth, which determines q(0), is not known; only its statistical properties are available from historical records (or climate forecasts in the future). Consequently, it is reasonable to treat q(0) as a stochastic process and consider the probabilistic treatment of soil moisture in relation to these precipitation statistics (the evaporation component of q(0) is described later). This approach, pioneered by Eagleson (1978), gives rise to several simplified models accounting for rainfall stochasticity (e.g., Cordova and Bras, 1981; Hosking and Clarke, 1990; Milly, 1993; RodriguezIturbe et al., 1999; Laio et al., 2001a; Porporato et al., 2004; Daly et al., 2004b). Although, it is not our intent to provide a detailed or chronological review of all the work already reported on this topic, as it is well beyond the scope of a single chapter, the salient points alone are repeated. Using a simplified scheme, Milly (1993) derived an analytical expression of the asymptotic soil moisture probability distribution (pdf). Milly’s model, however, lacks the dependence of evapotranspiration on the soil water level and therefore cannot account for the impact of soil-moisture dynamics on vegetation (Milly, 2001). This problem was addressed by Rodriguez-Iturbe et al. (1999) and Laio et al. (2001a) and further pursued by Daly et al. (2004a,b) and Porporato et al. (2004), who modeled the soil water losses from drainage and evapotranspiration using a nonlinear function of soil moisture (e.g., Federer, 1979; Cordova and Bras, 1981; Gollan et al., 1985; Crago and Brutsaert, 1992), aimed at reproducing the effect of reduced soil water potential on water movement through the plant and the highly nonlinear form of deep infiltration (Daly et al., 2004a). In what follows, we will briefly present the approach of Rodriguez-Iturbe et al. (1999), Laio et al. (2001a), and Porporato et al. (2004) as it combines a simplified approach that allows analytical solutions to a realistic description of rainfall stochasticity and nonlinearity in soil water losses. According to this approach, the arrival of rainfall events is described as a Poisson process, assuming that each event carries a random amount of water extracted from an exponential distribution with mean α. During rainfall events, the soil accumulates water by infiltration to successively lose it by means of evapotranspiration and leakage. Hence, for simplicity, the water balance of the so-called hydrologically active soil is re-written as nZr
dsm = I [sm (t ), t ] − E[sm (t ), t ] − L[sm (t )] dt
(29.8)
where I [sm (t ), t ] is infiltration from rainfall given by the rainfall rate minus runoff and canopy interception (q(0)), E[sm (t ), t ] is evapotranspiration, and L[sm (t )] is deep infiltration or drainage (q(Zr )). Since I [sm (t ), t ] depends on soil moisture and rainfall variability, it represents the state-dependent stochastic forcing of the system, while evapotranspiration and drainage are nonlinear function of soil moisture content. Infiltration depth into the soil is taken to be the minimum of the rainfall amount, hr , and nZr (1−sm ), to reflect the fact that only a fraction of hr can infiltrate when the rainfall amount exceeds the storage capacity of the soil column. Excess rainfall is considered to produce runoff according to the mechanism of saturation from below, which is a reasonable assumption in vegetated areas (no soil crust) with negligible-to-mild topography. Canopy interception, which is responsible for the capture and subsequent direct evaporation of some of the precipitation prior to its arrival at the soil surface, is included in the model by assuming a threshold of rainfall depth, (not to be confused with the slope of the saturation vapor pressure s ) below which no water effectively penetrates the canopy. Then, analytically, the only change necessary is to modify the rate
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of storm arrivals, λ (not to be confused with the latent heat of water vaporization, λw ), to λ = λe −/α (see Rodriguez-Iturbe et al. (1999) for details). The link between daily evapotranspiration and soil moisture can be obtained by upscaling the fast dynamics of evapotranspiration (e.g., Daly et al., 2004a). The resulting behavior can be approximated by three regimes: a linear increase from E = 0 at the hygroscopic point, sh , to Ew , at the wilting point, sw (soil evaporation regime). For larger values of s, E(s) has a linear rise (stressed evapotranspiration regime) from Ew at sw to Emax at s ∗ , where s ∗ is the soil moisture level at which the plant begins to close stomata in response to water stress and Emax is the climate- and vegetation-dependent maximum daily evapotranspiration rate. For values of s exceeding s ∗ , evapotranspiration is decoupled from soil moisture and remains constant at Emax (unstressed evapotranspiration regime), which represents the average daily evapotranspiration rate during the growing season under well-watered conditions. Recall that the maximum transpiration contribution Emax can be theoretically determined by “slaving” the water loss to the biochemical carbon demand through leaf photosynthesis as earlier described. Assuming no interaction with the underlying soil layers and water table and the absence of significant topographic gradients, L(s) represents vertical percolation forced by a unit gradient and is equal in magnitude to the unsaturated soil hydraulic conductivity. For reasons of analytical tractability, Laio et al. (2001a) adopted an exponential function (over the customary power law) increasing from 0 at field capacity, sfc , to the saturated hydraulic conductivity at s = 1. The sum of the evapotranspiration and drainage losses is shown in Figure 29.8; its behavior is similar to the ones employed in previous studies (Cordova and Bras, 1981) and measured in field experiments (Salvucci, 2001). The values of sh , sw , s ∗ , and sfc are related to the corresponding soil matric potentials through the soil–water retention curves. The model allows one to obtain analytically the steady state (i.e., under the assumption of a homogeneous growing season) soil moisture pdf as a function of the parameters defining climatic conditions, soil type, and vegetation characteristics. As an example, Figure 29.9 shows an analysis of the role of changes in the frequency of storm events λ on the soil moisture pdf. A coarser soil texture corresponds to a consistent shift of the pdf toward drier conditions. The shape of the pdf also undergoes marked changes and resembles the one empirically measured elsewhere (e.g., Salvucci, 2001). The broadest pdfs are found for shallower soils. Several applications demonstrate the good adaptability of the model to very different environmental conditions, from semiarid, temperate, to tropical (Salvucci, 2001; Laio et al., 2001b; Fernandez-Illescas et al., 2001; Porporato et al., 2003a). Other applications of the probabilistic approach to soil-moisture dynamics have regarded the seasonal water balance (Laio et al., 2002), as well as the role of inter-annual climate variability (D’Odorico et al., 2000; Porporato et al., 2003a). Guswa et al. (2002) also explored the importance of the assumption of vertically averaging the soil moisture equation, noting that the main differences are in the transpiration temporal dynamics in case of deep-rooted plants with little active control on their water uptake from different soil layers (see also Guswa et al. (2004) and Puma et al. (2005)). losses (cm/d) Ks 2 1.5 1 0.5
Emax Ew 0 Sh Sw S*
Sfc
s
1
FIGURE 29.8 Soil water losses as a function of relative soil moisture content. (From Laio, F., et al. Adv. Water Resour., 24, 707, 2001a, with permission.)
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Water, Carbon, and Nutrient Cycling in the Soil–Plant Atmosphere Shallow soil
Deep soil
Dry climate
(a) p(s) 10
(b)
p(s) 10
8
8
6
6
4
4
2
2 s 0.2
0.4
0.6
0.8
1
(c) p(s) 10
(d)
8
6
6
4
4
2
2
Wet climate
s 0.4
0.6
0.8
1 (f)
(e) p(s) 10
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
s
p(s) 10
8
0.2
29-17
s
p(s) 10
8
8
6
6
4
4 2
2 0.2
0.4
0.6
0.8
1
s
s 1
FIGURE 29.9 Examples of pdf ’s of relative soil moisture for different type of soil, soil depth, and mean rainfall rate. Continuous lines refer to loamy sand, dashed lines to loam. Left column corresponds to Zr = 30 cm, right column to 90 cm. Top, center, and bottom graphs have a mean rainfall rate λ of 0.1, 0.2, and 0.5 d−1 respectively. Common parameters to all graphs are α = 1.5 cm, = 0 cm, Ew = 0.01 cm/d, and Emax = 0.45 cm/d. (From Laio, F., et al. Adv. Water Resour., 24, 707, 2001a, with permission.)
29.3.3 Long-Term Water Balance The different terms of the long-term water balance are the averages of the respective components of the soil-moisture dynamics. Rainfall is first partitioned into interception, runoff, and infiltration. Infiltration is then divided into leakage and evapotranspiration. For purposes of describing vegetation conditions, the amount of water transpired can be further divided into water transpired under stressed conditions and water transpired under non-stressed conditions (e.g., for soil moisture below and above s ∗ , respectively; see Section 29.4). The long-term water balance of the stochastic model presented above can be obtained analytically by multiplying the terms of Equation 29.8 by the steady state soil moisture pdf and then integrating between 0 and 1 (e.g., Rodriguez-Iturbe et al., 1999). Figure 29.10 presents examples of the dependence of the water-balance components — normalized by the mean rainfall rate — on some characteristics of rainfall regime, soil, and vegetation. The influence of the rainfall rate λ is shown in Figure 29.10a for the case of a shallow loam. As interception is a linear function of the rainfall rate, it is not surprising that the fraction
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The Handbook of Groundwater Engineering (a) 100
Rainfall (%)
80 60
40 <Ens>
<Es>
20
0.1
0.2
0.3
0.4 (d–1)
0.5
0.6
(b) 100
Rainfall (%)
80
<Ens>
60 <Es> 40 20
0.1
0.2
0.3
0.4 (d
0.5
0.6
–1)
FIGURE 29.10 Components of the water balance normalized by the total rainfall for a shallow loamy sand. (a) Water balance as a function of the frequency of rainfall events, λ (Zr = 30 cm, α = 2 cm). (b) Water balance as a function of λ for a constant mean total rainfall during a growing season of 60 cm. Parameters are sh = 0.08, sw = 0.11, s ∗ = 0.31, sfc = 052, Ew = 0.01 cm/d, Emax = 0.45 cm/d, and = 0.2 cm. I , Q, L, Ens , and Es are the long-term averaged interception, runoff, leakage, evapotranspiration in non-stressed and stressed conditions, respectively. (From Laio, F., et al. Adv. Water Resour., 24, 707, 2001a, with permission.)
of water intercepted remains constant in the normalized equation. The percentage of runoff, however, increases almost linearly. More interesting is the interplay between leakage and the two components of evapotranspiration. The fraction of water transpired under stressed conditions rapidly decreases, while the evapotranspiration under non-stressed conditions evolves in a much more gradual manner. As discussed by Porporato et al. (2001), this last aspect has interesting implications for vegetation productivity. It is clear that in semiarid conditions most of the water that actually reaches the soil is lost by evapotranspiration (in particular transpiration), consistent with many field experiments. Figure 29.10b shows the terms of the water balance when both the frequency, λ, and the average storm depth, α, change but the total amount of rainfall in a growing season (i.e., αλ) is kept constant. The result is interesting, due to the existence of two opposite mechanisms regulating the water balance. On the one hand, for a given seasonal amount of rain, runoff production strongly depends on the ratio between soil depth and the mean depth of rainfall events. On the other hand interception increases almost linearly with λ. The interplay between these two mechanisms determines a maximum of both leakage and evapotranspiration at moderate values of λ (of course, the position of the maxima changes according to the parameters used). This interplay is particularly important to ecosystem productivity given the intimate linkage between transpiration,
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photosynthesis, and carbon gain (Kramer and Boyer, 1995). Not only the amount but also the frequency of rainfall is important for the existence of an optimum transpiration (a surrogate for productivity).
29.3.4 Heat Flow into the Soil Given that all the kinetic rates and respiration terms in the soil carbon-nitrogen dynamics, which will be described in detail in Section 29.5, depend on soil temperature (in addition to soil moisture), we end this section with a brief summary on modeling soil temperature dynamics in depth and time. The heat flow into the soil is highly impacted by soil moisture and the incident radiation and leaf area density. The heat flow conduction in a soil is given by qh,i (t , xi ) = −Kh
∂Tt (t , z) ∂xi
where qh,i is the heat flux along direction xi (i = 1, 2, 3), Tt is the soil temperature, and Kh is the thermal conductivity of the soil, which varies with the mineral type and soil moisture. The energy conservation in a soil layer can be expressed as ∂Tt ∂qh,i =− ρt cm ∂t ∂xi with ρt soil density, and cm the soil specific heat capacity per unit mass. In the case of vertical heat flow the balance reduces to 1 ∂ ∂Tt ∂Tt = Kh ∂t ρcm ∂z ∂z where z in this case is directed upward. The simplest method to determine “effective” thermal properties of the bulk soil is from its constitutive components using a volume-based aggregation scheme, Kh = fa Kh,a + θKh,w + (1 − fa − θ )Kh,s ρcm = fa (ρa cm,a ) + θ (ρw cm,w ) + (1 − fa − θ)(ρs cm,s ) where subscripts a, w, and s represent the air, water, and solid components of the soil matrix, respectively, and fa is the air-filled porosity. Roughly, the value of the parameters is Kh,s = 2.9 W m−1 K−1 , Kh,w = 0.57 W m−1 K−1 , and Kh,a = 0.025 W m−1 K−1 , ρa cm,a = 1.25 × 103 J m−3 K−1 , ρw cm,w = 4.2 × 106 J m−3 K−1 , and ρs cm,s = 2.0 × 106 J m−3 K−1 . A volume-based parameter averaging may not be valid for the effective thermal properties in a heterogeneous soil with dense rooting system. This, in part, can be attributed to the temperature difference between the precipitation water and the soil and the rooting system. We tested this aggregation methodology in a grass-covered forest clearing in which the soil heat flux at the ground surface was measured by soil heat flux plates every 20 min, and soil temperature and soil moisture were measured at depths of −2, −5, −10, −15, and −30 cm. Figure 29.11 shows the measured soil heat flux and the measured soil temperature, and Figure 29.12 compares measured and modeled soil temperatures using the volume-based aggregation scheme (the porosity of the soil also varied with zand was taken as the maximum measured θ in the 1-year time series) using the one-dimensional version of the soil heat flow model. The agreement between measured and modeled fluxes is rather encouraging — at least for the purposes of modeling microbial activity and respiration rates.
29.4 Soil Moisture Deficit and Plant Water Stress In many ecosystems, and especially in arid and semiarid climates, soil moisture deficit is often the most important stress factor for vegetation. In fact, other important sources of stress such as nutrient limitation
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The Handbook of Groundwater Engineering Soil heat flux (W m–2)
Gs
30 20 10 0 –10 0
20
40
60
80
100
120
140
160
120
140
160
Soil temperature (°C)
Depth
–20 –40 –60 –80 0
20
40
60
80 100 Time (hr)
FIGURE 29.11 (See color insert following page 23-52) Measured soil heat flux (Gs ) near the land–atmosphere interface and measured soil temperature (ranging from 12, black, to 18◦ C, white) within a grass-covered surface illustrating the warming and cooling heat waves.
z = –5 cm
z = –2 cm 20
18
18
16
16
14
14
12
12
Tt ( C)
20
10
0
50
100
150
200
10
0
50
100
150
200
z = –15, –30 cm
z = –10 cm 17
18
16
16 Tt ( C)
15
14 14
12
13 12
10 0
50
150 100 Time (hr)
200
0
50
100 150 Time (hr)
200
FIGURE 29.12 Comparison between measured (symbols) and modeled (line) soil temperature at different soil layer depths (z) for a grass-covered forest clearing at the Blackwood division of the Duke Forest, near Durham, NC. The “forcing” input is the measured soil heat flux at z = 0 (shown in Figure 29.11). The locally measured soil moisture content at each depth was used in the volume aggregation scheme of model parameters.
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Soil moisture deficit
Plant water potential
Water pressure in the protoplast (Turgor, cell water content)
Effects on physiology (Growth, cell ultrastructure, photosynthesis, dark respiration, carbohydrate and nitrogen metabolism...)
Vegetation water stress temporal-permanent damages
FIGURE 29.13 Schematic representation of the process linking soil moisture deficit to plant water stress. (Modified from Porporato, A., et al. Adv. Water Resour., 24, 725, 2001.)
are frequently initiated by the occurrence of water stress (e.g., Larcher, 1995; Nilsen and Orcutt, 1998). A large number of studies on physiological plant ecology has dealt with the problem of plant water stress (e.g., Hsiao, 1973; Lange et al., 1976; Levitt, 1980; Bradford and Hsiao, 1982; Smith and Griffith, 1993; Larcher, 1995; Ingram and Bartels, 1996; Nilsen and Orcutt, 1998). Porporato et al. (2001) provided a simplified mathematical description of plant water stress and linked it to the model of stochastic soil-moisture dynamics previously described.
29.4.1 Physiological Impact of Soil Moisture Deficit on Plants As noted earlier, plants need to maintain an adequate level of hydration in their tissues to ensure both growth and survival; they also require a continuous flux of water from the soil to perform vital processes such as photosynthesis and nutrient uptake. The reduction of soil moisture content during droughts lowers the plant water potential and leads to a decrease in transpiration. This in turn causes a reduction of cell turgor and plant water content, which brings about a sequence of damages of increasing seriousness. Figure 29.13 presents a simplified scheme of the steps linking soil moisture deficit to plant water stress. Figure 29.14 reproduces a typical sequence of effects caused by a decrease in cell water potential. As can be seen, during drought conditions this decrease triggers a series of harmful events on plant physiology whose number and seriousness grows with the intensity and duration of water deficit. As the plant water potential is reduced, the first effect is a reduction of cell growth and wall-cell synthesis; then nitrogen uptake from soil is diminished due to the sharp decrease in nitrate reductase, an enzyme that catalyzes the reduction of nitrate to nitrite (which is the first internal step for nitrogen assimilation after nitrate has been taken up by the plant). The stomatal closure and the related reduction in CO2 assimilation also follows: at first, stomatal closure is mostly a way to reduce water losses while maintaining carbon uptake and does not produce permanent damage to the plant. Soon after, however, respiration is affected. Changes in the patterns of resource allocation are then induced, including the accumulation of amino acid proline, whose increase is a characteristic disturbance in protein metabolism. Sugar accumulation, along with possible
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Reduction in tissue water potential, ψp (MPa), required to affect process*
Process affected 0
1
2
Cell growth Cell-wall synthesis Protein synthesis Nitrate reductase Stomatal closure CO2 assimilation Respiration Proline accumulation Sugar accumulation
* With Ψp of well-watered plants under mild evaporative demand as the reference point
FIGURE 29.14 Typical sequences of plant physiological effects caused by a decrease in cell water potential. Redrawn after Hsiao, T.C. Ann. Rev. Plant Physiol., 24, 519, 1973.
flowering reduction, inhibition of seed production, and fruit abortion are possible further effects of higher levels of water stress (Nilsen and Orcutt, 1998). At the same time, reduction in transpiration inhibits the cooling effect and radiation stress more likely. Finally, at very low water potentials, complete stomatal closure occurs followed by turgor loss and wilting (Bradford and Hsiao 1982, p. 309) as well as widespread cavitation. The interplay between cavitation in the xylem system and turgor pressure remains a subject of active research. This, in part, is due to the fact that stomatal closure often occurs at leaf pressures much less negative than the pressure of turgor loss. Recent studies on plant hydraulics seem to indicate that evolution of vascular plants was associated with some loss of “lower plants” to survive desiccation (Sperry, 2000), as processes associated with the evolution of a larger and more complex plant body became more limiting to gas exchange than those occurring within individual cells (Sperry, 2000; Katul et al., 2003). The vascular tissue is a vital whole-plant process that can be impaired by water supply to the photosynthetic tissue. As soil water deficit develops, events in plant and soil make it increasingly difficult to keep the hydraulic pipelines between soil and leaf hydraulically intact. The transport characteristics of this network of pipelines impose physical limits on the rate at which water can be supplied to the leaves, and on the potential rate of transpiration allowed by stomata (Tyree and Sperry, 1989; Bohrer et al., 2005). In a recent review, Sperry (2000) suggested that much of the stomatal closure observed during drought is a result of a decline in plant hydraulic conductance in the xylem of the root system because roots can be substantially more susceptible to cavitation than shoots. This explains why stomatal conductance shuts down at suction levels well below the turgor suction. On re-watering, there is also the potential for considerable hysteresis in the recovery of conductance to “pre-drought” values. Recovery can occur by refilling of cavitated vessels by root pressure (short time scale), and by growth of new roots (intermediate time scale). Stomatal closure is thus an important process for the description of plant response to water deficit. It is controlled by the pressure of the guard cells surrounding the stomata: high guard-cell turgor produces
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stomatal opening, while low turgor induces stomatal closure (e.g., Salisbury and Ross, 1992; Larcher, 1995). Stomatal closure and xylem cavitation are the main mechanisms that lead to a nonlinear relationship between bulk canopy conductance (and thus transpiration) and soil water content. Furthermore, this relationship need not be unique at a given soil moisture state because of this hysteresis — which is driven by soil moisture history and carbon uptake. The sequence of events shown in Figure 29.14 is related to the intensity of the soil moisture deficit without specifically considering its duration. It is clear that this “static” description of the physiological effects is not sufficient to describe the development of plant sufferance; water stress is a gradually intensifying process in which the time dimension is particularly important. This is especially true for semiarid ecosystems, where drought is often a prolonged and frequent phenomenon, more than an isolated event. Duration and frequency of periods of water stress are therefore as important as the reduction in water potential to model plant water stress.
29.4.2 Modeling Plant Water Stress Porporato et al. (2001) used a “static” vegetation water stress index to relate the actual value of soil moisture to two levels of the same variable associated with important changes in the physiological activities of the plant, namely the point at which transpiration (and thus photosynthetic activity) starts being reduced, s ∗ , and the point at which plants begin to wilt, sw . These two levels correspond to the point of incipient and complete stomatal closure, respectively. Static stress is assumed to be equal to zero when soil moisture is above s ∗ and equal to one when soil moisture is at or below sw . In between these soil moisture levels, the static stress is given by s − sw q ζ = ∗ s − sw where q is a measure of the nonlinearity of the effects of soil moisture deficit on plant conditions (not to be confused with the water flux qi ). This simple relationship between ζ and s permits the derivation of the pdf of static stress as a derived distribution of the steady state pdf of soil moisture. Using this relationship, the mean value of water stress ζ¯ , given that the plant is under stress, can be derived (Porporato et al., 2001). Besides the information given by ζ¯ , the dynamical aspects of the water deficit process, namely the duration and frequency of the stress periods, should also be taken into account to describe the plant stress conditions. To this purpose, Porporato et al. (2004) derived the expressions for the mean duration, T¯ ξ , of an excursion below an arbitrary soil moisture threshold, ξ , as well as the mean number, n¯ ξ , of such intervals during the growing season. Using s ∗ as a meaningful threshold to mark the onset of water stress, the stress intensity, its mean duration, and its frequency of occurrence may be combined to define an overall indicator of plant conditions under given edaphic and climatic factors, called the dynamic plant water stress, as −r ζ¯ T¯ s∗ n¯ s∗ if ζ¯ T¯ s∗ > kTseas (29.9) ϑ¯ = kT s 1 otherwise where k is an indicator of plant resistance to water stress and Tseas is the duration of the growing season and r is a nonlinearity coefficient to account for the importance of sequence of stress events. The reader is referred to Porporato et al. (2001) for the derivation and discussion of this dynamic water stress function.
29.4.3 Soil-Climate-Vegetation Control on Plant Water Stress and Plant Carbon Assimilation The above formulation of the total dynamic water stress permits a quantitative study of its dependence on climate, soil, and vegetation. As an example, Figure 29.15 shows the interplay between the timing and amount of rainfall, similar to Figure 29.10 where the storm frequency λ is varied while fixing the
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The Handbook of Groundwater Engineering 1 Θ = 400 mm 0.8
Θ = 450 mm
0.6
Θ = 500 mm
0.4
Θ = 800 mm
0.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(d–1)
FIGURE 29.15 Impact of timing and amount of rainfall on dynamic water stress. Each curve corresponds to a constant total rainfall, , during the growing season, q = 2, k = 0.5, and r = 0.5. Parameters: Tseas = 200 d, Zr = 60 cm, Emax = 0.45 cm d−1 , sw = 0.24, s ∗ = 0.57, sfc = 0.65. (Modified from Porporato, A., et al. Adv. Water Resour., 24, 725, 2001.)
total precipitation per growing season. Except for very wet climates, there exists a clear optimal trade-off between timing and amount of rainfall, which provides the best condition for vegetation (minimum of the dynamic water stress). The minima decrease and move toward the right-hand side of the diagram for larger values of total rainfall. Such evidence provides interesting connotation to the concept of effective rainfall (i.e., an event that is intense enough to stimulate biological processes, particularly growth and reproduction), and whose importance is well known in the ecology of arid and semiarid ecosystems (e.g., Noy-Meir, 1973). The dynamic water stress defined above has been used in Porporato et al. (2003a) to describe the tree-grass coexistence in the Kalahari transect. Porporato et al. (2004) and Daly et al. (2004b) have extended it to include plant carbon assimilation. In particular, Figure 29.16, shows a comparison of the experimental results with the theoretical mean carbon assimilation as a function of the frequency of rainfall events for fixed total rainfall during a growing season in mesic grassland in Kansas (Knapp et al., 2002). The 20% decrease in measured net assimilation for the altered rainfall pattern (when total rainfall is the same but concentrated in fewer events) is well reproduced. As shown by the effective relative soil moisture pdfs, the shift in the rainfall frequency changes qualitatively the soil moisture pdf and thus the grassland water balance. The figure also shows that in such an ecosystem, the impact on carbon assimilation of a decrease in total rainfall is more pronounced when such a decrease is accompanied by a reduction in the frequency of rainfall events.
29.5 Soil Nutrient Dynamics Having completed the precipitation and vegetation controls on soil-moisture dynamics, we proceed next to soil biogeochemical cycles. While the former is critical to modeling groundwater recharge, the latter exerts significant controls on groundwater quality. Soil biogeochemical cycles are characterized by complex dynamics, acting at different spatial and temporal scales, and remain crucial for modeling groundwater recharge (on multiple time scales) and quality. They are impacted by vegetation and hydrometeorological forcing and, in turn, exert various feedbacks on the ecosystems, atmosphere, and climate dynamics. In particular, the hydro-climatic variability and soil-moisture dynamics regulate the sequence of fluxes between different components of soil nutrient cycles and determine the temporal dynamics of the system state variables at different time scales. Moreover, the soil moisture and temperature regimes control decomposition, leaching, and plant uptake and, indirectly, influence vegetation growth and composition of plant residues. Various models have been proposed in the past to investigate these dynamical processes for a wide range of ecosystems and climatic conditions (e.g., Parton et al., 1988; Hunt et al., 1991; Melillo et al., 1995;
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p(x) 3 24
Altered
2
( mol m–2 s–1)
1 x 20
0.15
0.3
0.45
0.6
p(x) 3
16
Ambient 2 1
12
x 0.15 0.05
0.1
0.3
0.45
0.15
0.6 0.2
(d–1)
FIGURE 29.16 Mean daily carbon assimilation rate as a function of the frequency of rainfall events for constant total amount of precipitation during a growing season. The lines are the theoretical curves derived from the soil moisture probability density function, while the two points are field data published by Knapp et al. (2002). The point on the right corresponds to the ambient conditions (λ = 0.19 d−1 ), and the other point to artificially modified conditions (λ = 0.08 d−1 ) while keeping the total rainfall the same. The continuous line is for mean total rainfall during a growing season of 507 mm, the dashed line for 600 mm, and the dotted line for 400 mm. The two insets show observed and theoretical soil moisture probability density functions for ambient and altered conditions (Emax = 0.63 cm d−1 , sh = sw = 0.25, s ∗ = 0.65, sf = 0.8, n = 0.55, Zr = 30 cm). Revised from Porporato, A., Daly, E., and Rodriguez-Iturbe, I. Am. Nat., 164, 625, 2004.
Gusman and Marino, 1999; Benbi and Richter, 2002; Porporato et al., 2003b; Schimel and Weintraub, 2003; Schimel and Bennett, 2004, and references therein).
29.5.1 Brief Review of Soil Carbon and Nitrogen Cycles The carbon cycle in the soil-plant system is dominated by a sequence of biochemical processes including assimilation (photosynthesis), residues production and deposition, and decomposition (litter mineralization), which releases carbon as CO2 back to the atmosphere (Figure 29.17). Assuming a longterm equilibrium condition of ecosystems, the total respiration is generally balanced by the input of plant residues while at shorter time scales (e.g., seasonal-to-interannual) the carbon content is subject to fluctuations induced by hydro-climatic and other environmental forcing. Carbon is stored in the SOM, which is a complex and varied mixture of organic substances, with three main components: plant residues, microbial biomass, and humus. Plant residues accumulate on the soil surface where they are degraded by both physical and biological agents. The organic compounds are then partially assimilated and partially oxidized by the microbial biomass in the soil. The biomass provides a high turnover rate of C and N in the SOM pool, with release of stable mineralized products of the catabolic processes (e.g., CO2 ) at each turnover (Molina and Smith, 1998). The carbon assimilation and respiration processes are affected by the composition of organic compounds and by climatic conditions. The presence of water and elevated soil temperatures are key factors to provide a fast decomposition and biomass growth. The relation between biomass activity and soil water content is strongly nonlinear (Brady and Weil, 1996). In particular, low soil moisture levels reduce diffusion of nutrients, limiting their availability to microbes, and lower hydration, and enzymatic
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The Handbook of Groundwater Engineering Plants C
Atmosphere Photosynthesis
CO2
N2
Atmospheric deposition and biological fixation
N Respiration
SOM Plant residues and humus
Microbial biomass C
C Assimilation
N
N
Uptake
Biomass recycling
N mineralization Immobilization
Remineralization
Inorganic nitrogen NH3 NO2– NH4+ NO3– Leaching
FIGURE 29.17 Schematic representations of the soil carbon and nitrogen cycles, with particular attention to the interactions among the three main components of the SOM: plant litter, humus, and biomass. Thick lines: C fluxes; thin lines: N fluxes. (Modified after Mary, B., et al. Plant Soil, 181, 71, 1996.)
activity of microbes causing water stress. Interestingly, the water stress of soil microbes has characteristics similar to plant water stress. The dependence of decomposition on soil temperature is also nonlinear, rising from zero at low temperatures (∼−5◦ C) to a maximum at around 40◦ C (although these values tend to be site-specific). When the conditions are favorable, nitrification is quite rapid. As a result, in hot and dry environments, sudden water availability can cause a flush of soil nitrate production (see Figure 29.18), which may greatly influence the growth patterns of natural vegetation (Cui and Caldwell, 1997; Fierer and Schimel, 2002). Depletion of soil mineral nitrogen, through plant uptake and deep percolation (leaching), also depends nonlinearly on soil moisture. As described in Porporato et al. (2001), plant nitrogen uptake is typically a nonlinear function of soil moisture with some similarities with the transpiration function. Leaching is an increasing nonlinear function of soil water content (related to soil hydraulic conductivity) and occurs intermittently following intense rainfall events. The so-called Mineralization-Immobilization Turnover (MIT) and the C/N ratio of microbial biomass are also very important for the entire soil biogeochemistry. To maintain a constant C/N ratio during its growth, the microbial biomass needs to assimilate proportional amounts of carbon and nitrogen, independently of the composition of the organic compounds of the substrate (Brady and Weil, 1996). As a consequence, if the nitrogen content of the decomposed compounds is high, mineralization proceeds unrestricted and mineral components in excess are released into the soil, while if such compounds are nitrogen poor, the microbes immobilize mineral nitrogen for their growth (Figure 29.18). If mineral nitrogen is not available, immobilization is halted. The MIT is thus characterized by an extremely strong nonlinearity that acts as a threshold-process and determines the conditions of when the growth of soil microbial biomass is carbon or nitrogen limited.
29.5.2 Model Structure Various models of different complexity have been proposed in the literature and a full review would be outside of the scope of this chapter. Here, we provide a brief description of the “low-dimensional” model
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Respiration
Plant residues
rrDEC1 rrDECh ADD BD
Litter C1 DEC1 (1 − rh − rr)DEC1 +(1 − rr)DECh
rhDEC1
Biomass Cb
DECh Humus Ch (b) Plant residues
Plant uptake
ADD (C/N )ADD BD (C/N )b
Litter N1
MIN
DEC1 (C/N )1 rhDEC1 (C/N )h
DECh (C/N )h Humus Nh
UP
(C/N )1 DEC1 + + 1 − rh (C/N )h (C/N )1
Biomass Nb
Mineral nitrogen IMM
DECh + (C/N )h LE
Leaching
FIGURE 29.18 Schematic representation of the main components of the model. (a) Soil carbon cycle; (b) soil nitrogen cycle. (Modified from Porporato, A., et al. Adv. Water Res., 26, 45, 2003b.)
proposed by Porporato et al. (2003b) because of its simple yet realistic structure of the soil C-N cycles for vertically averaged concentrations over the active soil depth, Zr . The carbon and nitrogen cycles are modeled using four different pools, one for each main component of the system (Figure 29.18). The only external input of carbon and nitrogen to the system is through vegetation litter. Respiration is the only carbon output, while the nitrogen losses are leaching and plant uptake. Fluxes such as ammonium adsorption and desorption, deposition, and volatilization are neglected, being of lesser importance for the soil C-N balances at the daily-to-seasonal time scale (Mary et al., 1996; Baisden and Amundson, 2003; D’Odorico et al., 2003). SOM is divided into three compartments, representing litter, humus, and microbial biomass. For simplicity, we lump ammonium and nitrate into a single mineral nitrogen pool. Once plant residues enter the litter pool, they move partially to humus and partially to the biomass pool, losing a respired fraction during the decomposition process. The approach here differs from the widely
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used CENTURY model (Parton et al., 1988) because decomposition is explicitly considered to account for the fact that it also depends on the amount of biomass, in agreement with Schimel and Weintraub (2003). The model requires seven state variables, each in terms of mass per unit volume of soil (e.g., g m−3 ), six of them to describe carbon and nitrogen concentrations in the three SOM pools, and one for the soil mineral nitrogen (see the scheme in Figure 29.18): Cl , carbon concentration in the litter pool; Ch , carbon concentration in the humus pool; Cb , carbon concentration in the biomass pool; Nl , organic nitrogen concentration in the litter pool; Nh , organic nitrogen concentration in the humus pool; Nb , organic nitrogen concentration in the biomass pool; N , mineral nitrogen concentration in the soil. The temporal dynamics of such variables is controlled by a system of seven coupled differential equations that describe the balance of carbon and nitrogen in the various pools and the fluxes among them, in terms of mass per unit volume per unit time (e.g., g m−3 d−1 ). As many of the fluxes are controlled by environmental fluctuations, their modeling explicitly accounts for soil moisture and temperature conditions. The system of first order nonlinear differential equations in describing these processes is given by dCl = ADD + BD − DEC dt ADD BD DECl dNl = + − dt (C/N )ADD (C/N )b (C/N )l dCh = rh DECl − DECh dt dNh DECl DECh = rh − dt (C/N )h (C/N )h dCb = (1 − rh − rr )DECl + (1 − rr )DECh dt DECl dNb (C/N )l DECh BD = 1 − rh + − − dt (C/N )h (C/N )l (C/N )h (C/N )b dN = − LE − UP dt The first six equations represent the balances of litter (l subscript), humus (h subscript), and biomass (b subscript) pools, while the last one is the balance equation for the mineral nitrogen, N . A brief description of the terms is given next. The term ADD is the external input into the system, representing the rate at which carbon in plant residues is added into the soil and made available to the microbial colonies. Here ADD is assumed to be constant in time. The term BD is the rate at which carbon returns to the litter pool due to the death of microbial biomass. Porporato et al. (2003b) simply used a linear dependence on the amount of microbial biomass, that is, BD = kd Cb . DECl represents the carbon output due to microbial decomposition, modeled using a first order kinetics with respect to the carbon concentration in the litter pool, Cl , as well as to the carbon in the biomass pool, Cb , DECl [ϕkl f (s, T )Cb ]Cl where the coefficient ϕ is a nondimensional factor accounting for a possible reduction of the decomposition rate when the litter is very poor in nitrogen and immobilization is not sufficient to integrate the nitrogen required by bacteria. The constant kl defines the rate of decomposition for the litter pool as a weighted average of the decomposition rates of the different organic compounds in the plant residues. Its average value is usually much higher than the corresponding value for humus, kh . The close relationship between the decomposition rate and the microbial biomass is due to the role of exoenzymes in the depolymerization process. The factor f (s, T ) describes soil moisture (s) and soil temperature (T ) effects on decomposition. The dependence of microbial activity on soil temperature is described by a
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quadratic relation, while the soil moisture control on aerobic microbial activity and decomposition is modeled via a linear increase from sb up to field capacity, sfc , and a hyperbolic decrease from there to soil saturation. The parameter sb represents a sort of permanent “wilting” point for soil microbial biomass and its relationship with the plant wilting point, sw , that defines the level at which transpiration and passive nitrogen uptake are stopped, provides a way to account for the impact of water stress on the competition for nutrients between plants and soil microbial biomass (Kaye and Hart, 1997). The second equation in the system represents the nitrogen balance in the litter pool. This is similar to that of carbon, with each term divided by the C/N ratio of its respective pool. (C/N )ADD is the C/N ratio of added plant residues, whose variability can produce pronounced changes in the C/N ratio of the litter pool and on the MIT turnover. The balance equation for carbon in the humus pool has a single input flux, represented by the fraction rh of the decomposed litter undergoing humification. The input of carbon in the biomass pool is represented by the fraction of organic matter incorporated by the microorganisms from litter and humus decomposition. The constant rr defines the fraction of decomposed organic carbon that goes into respiration, usually estimated to be in the interval 0.6 to 0.8 (Brady and Weil, 1996), while is the net mineralization defined so to ensure that (C/N )b is constant. The explicit modeling of mineralization/ immobilization dynamics is quite complicated and the reader is referred to Porporato et al. (2003b) for details. The last equation of the system describes the balance of mineral nitrogen, in which mineralization is the only input, while plant uptake (UP) and leaching (LE) are the two losses. The latter is simply modeled as proportional to the deep infiltration L(s) losses through a solubility coefficient (see Porporato et al., 2003b), while the plant uptake involves a passive and an active process, which can be regarded as additive processes. The passive uptake is assumed to be proportional to the plant transpiration rate and to the nitrogen concentration in the soil solution. The active uptake is assumed to help compensate the nitrogen deficit only if the passive uptake is lower than a given plant demand.
29.5.3 System Behavior under Constant and Stochastic Soil Moisture Conditions In steady-state conditions, the SOM carbon and nitrogen concentrations can be analytically determined from the full system (e.g., Manzoni et al., 2004). The steady solutions for humus and biomass nitrogen are simply proportional to the humus and biomass carbon, according to their C/N ratios. At steady state, Cb is the only state variable that depends on the climate forcing, while the other SOM pools accumulate carbon and nitrogen when the decomposition efficiency is low and lose them when the decomposition efficiency is high (i.e., near field capacity) and under elevated soil temperature conditions. Figure 29.19 shows the dynamics of carbon biomass toward equilibrium as a function of soil moisture and under constant temperature conditions (for reference). The trajectories are obtained by numerically integrating the system using a standard ordinary differential equation solver. At very low soil moisture, decomposition is not sustained and equilibrium is degenerate. Following the usual classification of the different equilibrium points of dynamical systems, equilibrium is a stable focus with damped oscillation to equilibrium. If the soil moisture approaches field capacity, a dynamic bifurcation takes place and in the region where the decomposition is more efficient, the equilibrium point becomes a stable node. The situation is inverted at high soil moisture values where damped oscillations leading to a stable focus reappear. The damped oscillations are determined by the dead biomass recycling in the litter pool, which introduces a feedback in the system, and by the biomass control on decomposition. The duration of these oscillations ranges between 1 and 8 years, depending on soil moisture level and system initial conditions. D’Odorico et al. (2003) analyzed the C-N dynamics under the more realistic conditions of stochastic soil moisture forcing using the model described in the previous section for the case study of the waterlimited savanna of Nysvley in South Africa. As shown in Figure 29.20, depending on the inertia of the various pools and on the degree of dependence on soil moisture, the random fluctuations imposed by precipitation are filtered by the temporal dynamics of the state variables in a very interesting manner. Some variables (e.g., NO− 3 ) preserve much of the high-frequency variability imposed by the random
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FIGURE 29.19 Qualitative representation of the temporal dynamics of biomass (plots in the left column) and the biomass-carbon litter trajectories (plots in the right column) for different soil moisture values.
forcing of precipitation, while some others (Ch , Cl , and Cb ) show smoother fluctuations (Figure 29.20 and Figure 29.21). Nitrate dynamics is the final product of a number of intertwined processes in which both high- and low-frequency components interact. In particular, the high-frequency component of NO− 3 fluctuations (period of days to weeks) can be linked to the direct dependence of mineralization and nitrification on soil moisture (panels e and f), which transfers the random fluctuations of the rainfall forcing to the budget of nitrate. On the other hand, the low-frequency variability (period of seasons to years) resembles the one of organic matter (in particular of microbial biomass; e.g., panel d) and depends on the inertia imposed on the dynamics by the dimension of the soil carbon and nitrogen pools, which is very large compared to the fluxes (see Figure 29.21). Notice that the same low frequency component also characterizes the litter dynamics, which is negatively correlated to Cb (see Figure 29.21b) as the growth of one of these pools occurs at the expense of the other one. The different time scales occurring in the carbon and nitrogen cycles were analyzed by means of the power spectra of the different variables. Figure 29.22 shows the logarithmic plot of the normalized spectral density of s, Cb , and NO− 3 . As expected, the energy associated to the high frequencies is higher for soil moisture than for nitrate and microbial biomass, while the converse is true for the low frequencies. The crossing between the Cb , (or NO− 3 ) and s power spectra is located at frequencies corresponding to periods of seasons to years. The model thus reproduces the change in time scales occurring from the soil-moisture dynamics to the nutrient dynamics observed by Schimel et al. (1997). This indicates that, while in semiarid ecosystems soil moisture is not able by itself to provide memory to the system at scales larger than one year (due to the complete depletion of soil water content by the end of the dry season, for example (Nicholson, 2000)), nutrient and vegetation dynamics may have a much longer memory responsible for
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FIGURE 29.20 Temporal dynamics of relative soil moisture (a), carbon litter (b), carbon humus (c), carbon biomass (d), ammonium (e), and nitrate (f) simulated for the case of the broad-leafed savanna at Nylsvley. The broken lines represent the average values or the range of values observed at Nylsvley except in (f), where the broken line is an upper limit for nitrate concentration in the nitrogen-poor savanna. The broken lines are reported whenever observations are available. Parameters: n = 0.4, sfc = 0.3, sh = 0.02, Ks = 1.1 m d−1 , Zr = 0.80 m, α = 11 mm, λ = 0.23 d−1 , Emax = 4.5 mm d−1 , Add = 1.5 gC m−2 d−1 , s ∗ = 0.17, sw = 0.065, (C/N )add = 58, (C/N )bio = 11.5, (C/N )h = 22. (From D’Odorico, P., et al. Adv. Water Res., 26, 59, 2003, with permission.)
the interannual persistency observed both in hydro-climatic and ecosystem processes (Parton et al., 1988; Schimel et al., 1996, 1997). A closer inspection of the time series of soil moisture and nitrate reveals that such a phenomenon is due to the presence of sudden flushes of nitrate, following a prolonged wet period after a drought (see Figure 29.23). In these conditions, first the dry soil hinders decomposition and favors SOM accumulation, then the subsequent wet period elicits biomass growth and enhances mineralization (e.g., Cui and Caldwell, 1997; Scholes et al., 1997). Episodic changes in nitrate levels greatly influence plant growth, because plants’ response to increased availability of nitrogen tends to be very quick (e.g., Brady and Weil, 1996). These pulses of nitrate are therefore of considerable importance for natural ecosystems. From the previous results, it is clear that the high frequency variability of soil moisture and the low frequency variability of SOM combine to produce complex temporal dynamics of soil mineral nitrogen, while the nonlinear mutual interactions between the processes may either enhance or reduce the effect of changes in the climatic regime. Moreover, the occurrences of exceptional hydrologic conditions, such as
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FIGURE 29.21 Simulated rates of litter decomposition (a), net mineralization (b), nitrate uptake (c) and nitrate leaching (d) in the broad-leafed savanna at Nylsvley. The broken lines represent the average values observed at Nylsvley. The nitrate leaching (d) is reported to be negligible at Nylsvley. (From D’Odorico, P., et al. Adv. Water Res., 26, 59, 2003, with permission.) Parameters as in Figure 29.20.
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prolonged rainfall or drought, are capable of affecting the dynamics of the slow-varying pools inducing long-lasting effects.
29.5.4 Soil Organic Matter and Soil Hydraulic Properties In the soil biogeochemical cycle models, the soil hydraulic properties are assumed to be static. However, there are significant (yet indirect) effects of SOM dynamics on the hydrological processes. The most crucial of them is the role of SOM (especially humus and soil microbial biomass) on changes in hydraulic properties such as porosity, hydraulic conductivity, and soil water retention functions. Despite intense experimental and theoretical research, a clear link between results from field and laboratory experiments and detailed dynamical description of SOM evolution and interaction with the soil matrix remains elusive and the long-term projections of soil biogeochemistry models still rely on semi-empirical relationships whose range of applicability and physical underpinning are un-assessed. The interaction between SOM and soil-moisture dynamics depends on the relationship between (1) hydraulic properties and geometric structure of the soil matrix, (2) organic matter and soil matrix, and (3) soil water content and microbial activity in the SOM. The hydraulic properties of soils are inseparable from their physical/geometrical characteristics. Thus the link between Pore Size Distribution (PSD) functions and Water Retention Curves (WRC) has received increasing attention in soil physics also in relation to pedo-transfer functions (e.g., Wosten et al., 2001; Aubertin et al., 2003; Rawls et al., 2003), stochastic and fractal models of soil structure (Tyler and Weathcraft, 1990; Rieu and Sposito, 1991; Hueckel et al., 1997; Chan and Govindaraju, 2003), and percolation theory (e.g., Hunt and Gee, 2002). SOM plays a significant role in determining the chemical and physical properties of soils because of its biotic and abiotic shares (Sollins et al., 1996; Neff et al., 2003). From the recent review by Six et al. (2004), it appears that the conceptual advances in understanding the soil matrix structure (microaggregate theory, aggregate hierarchy theory, flocculation, etc.) were not equally accompanied by an improved description of SOM–soil matrix interaction. On the other hand, the literature in soil bioremediation and soil sciences has shown how SOM and microorganisms growth determines substantial changes in the PSD and permeability of saturated soils. Using micro-models of triangular pore networks, Kim and Fogler (2000) found steep decreases in relative permeability with increasing SOM content. In similar experiments, Stewart and Kim (2004) found that microorganisms cluster thereby inducing periodic dynamics, alternating proliferation and starvation, hence causing periodic clogging of soil microporosity. Two mechanisms for bioclogging of saturated porous media have been investigated in Thullner et al. (2002): biofilm and colony. The results showed that colony-type development has more important consequences on
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the PSD than the biofilm-type. Furthermore, they found that increased pore-size heterogeneity yields faster bioclogging. Exoenzymes produced by bacteria appear to be responsible for the increase in microbial volume contributing to bioclogging (Schimel and Weintraub, 2003). Relatively simple models have been proposed to describe the effects of bacterial microfilm and aggregates on soil hydraulic properties (e.g., Taylor et al., 1990; Vandevivere, 1992). In unsaturated soils, Rawls et al. (2003) have shown that SOM somewhat tempers the soil hydraulic behavior, increasing the WRC in sandy soils and lowering it in fine-textured soils. As the WRC is sensitive to the PSD, it is inferred that SOM affects the structural organization of the pore network. Indirectly, also infiltration, evaporation, deep percolation, and plant water and nutrient uptake depend on the SOM dynamics with important consequences on the soil water balance and related processes. The effects of SOM in unsaturated soils range from modifying fluid properties such a viscosity, surface tension, and wetting characteristics, to reducing the effective porosity and PSD via microfilms and aggregates (Rockhold et al., 2002). Thus a comprehensive model requires a dynamic microscopic description of SOM growth and decay and its physical properties coupled with the detailed representation of the complex geometry of the soil matrix. As pointed out by Rockhold et al. (2002) modeling of these processes in unsaturated soils is still in its infancy, and is an emerging frontier in biogeoscience research.
29.6 Summary and Conclusions The compass of this chapter was on the description and the mathematical formulation of temporal dynamics of water and carbon inputs from the surface and of their regulation of percolation and biogeochemistry of the soil-plant system within the vadose zone. Our intent was not to cover all the above issues in detail, but we aimed at providing a mathematical framework that can guide groundwater hydrologists and hydrogeologists on various approaches used to quantify the carbon-nitrogen-water fluxes through the soil-plant-atmosphere system. The chapter commenced with the mathematical formulation for water-carbon cycling above ground as a means of determining the maximum CO2 uptake and hence maximum water loss by plants (i.e., water is slaved to the carbon needs of the plant) based on leaf area density, physiological, drag, and radiative properties of the plants, and forced by standard meteorological drivers, such as air temperature, mean wind speed above the canopy, vapor pressure deficit, incident shortwave radiation (or photosynthetically active radiation), and atmospheric CO2 concentration. This framework is timely, given the recent advances in remote sensing products (e.g., MODIS platform) to map leaf area over large spatial scales and at time scales relevant to plant phenology (e.g., weeks), and the availability of higher resolution re-analysis meteorological data. We then explored how soil moisture controls reduce these rates (i.e., the carbon uptake now becomes “slaved” to the soil-plant hydraulics). We showed how to upscale these processes in time “prognostically” by assuming precipitation as a random forcing with known statistics. This approach is much more suited to questions relevant to long-term carbon sequestration in future climate as the precise time series of precipitation, the key driver of the hydrological cycle, is unknown. We then examined how the basic elements of the soil biogeochemical cycle, including nitrate leaching (relevant to groundwater quality), is impacted by the soil-plant characteristics and precipitation statistics. We also discussed (more accurately speculated on) some long-term feedbacks from the soil-biogeochemical cycles on soil (and possibly plant) hydraulics, rarely investigated in current biogeochemistry or hydrology models. The latter feedbacks remain a knowledge gap and are likely to gain broader attention in the near future.
List of Symbols a(z) m2 leaf m−2 ground m−1 m2 leaf m−2 ground al ADD g m−3 d−1 mol m−2 s−1 An
leaf area density cumulative leaf area density soil carbon input rate net leaf-scale assimilation
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BD Ca Cb Ch Ci Cl cm Cp DEC Dv d em E Emax Ew fa Fx gb Gs gs gv h hc hr hs Jc JE k Kbe Kh kx LAI LE n n¯ ξ Nb Nh Nl pa Qab Qp q rb Rd rh rr rs q¯ a s sm s∗
g m−3 d−1 mol CO2 mol−1 air g m−3 g m−3 mol CO2 mol−1 air g m−3 J kg−1 K−1 J kg−1 K−1 g m−3 d−1 Pa m
soil carbon input rate due to microbial death mean atmospheric carbon dioxide concentration biomass carbon concentration humus carbon concentration intercellular stomata carbon dioxide concentration litter carbon concentration soil specific heat capacity specific heat of air soil carbon output rate vapor pressure deficit Zero-plane displacement height maximum quantum efficiency for CO2 uptake Evapotranspiration rate cm d−1 cm d−1 potential evapotranspiration rate cm d−1 soil evaporation at sw rate air filled soil porosity [x] t−1 m turbulent vertical fluxes of x mol m−2 s−1 mean boundary layer conductance W m−2 Soil heat flux at the surface mol m−2 s−1 mean stomatal conductance kg m−2 s−1 water vapor conductance m canopy height W m−2 K−1 convection coefficient cm rainfall amount g water g−1 air mean air relative humidity near the leaf surface molm−2 s−1 assimilation rate limited by Rubisco mol m−2 s−1 assimilation rate limited by light plant resistance to water stress leaf extinction coefficient W m−2 K−1 soil thermal conductivity rate of decomposition for x pool m2 leaf m−2 ground leaf area index leaching g m−3 d−1 soil porosity mean number of excursions below ξ in a growing season g m−3 biomass organic nitrogen concentration g m−3 humus organic nitrogen concentration g m−3 litter organic nitrogen concentration Pa atmospheric pressure W m−2 canopy absorbed energy mol m−2 s−1 leaf PAR irradiance static water stress parameter m2 s mol−1 mean boundary layer resistance molm−2 s−1 leaf respiration rate decomposed litter fraction undergoing humidification organic carbon fraction going into respiration m2 s mol−1 Mean stomatal resistance g water g−1 air Mean atmospheric water vapor turbulent concentration fluctuation for an arbitrary scalar relative soil moisture value of sm below which water stress occurs
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sfc sh sw Sx Ta T¯ ξ Tr Tr,max Ts Tt Tseas U , v, w u∗ UP Vcmax Zr zo α αl ε εl κ ζ ψ θ ϑ¯ λ λw ρa ρt σ σe σu,v,w τ τb ω ∗ s
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sm at field capacity sm at the hygroscopic point sm at the wilting point [x] t−1 sink/source of x K mean air temperature d mean time duration of an excursion below ξ in a growing season cm d−1 actual transpiration rate cm d−1 potential transpiration rate K leaf surface temperature ◦C Soil temperature d growing season duration wind speed components along x, y, and z directions m s−1 m s−1 friction velocity nitrogen plant uptake g m−3 d−1 mol m−2 s−1 maximum Rubisco capacity cm soil root depth m Momentum roughness length cm mean depth of rainfall events leaf absorptance for PAR turbulent kinetic dissipation m2 s−3 leaf emissivity Von Karman constant (=0.4) static plant water stress coefficient zenith angle volumetric soil moisture dynamic plant water stress mean rainfall frequency d−1 J kg−1 latent heat of water vaporization kg m−3 air density kg m−3 soil density Stefan-Boltzman constant W m−2 K−4 m s−1 Velocity scale related to the turbulent kinetic energy m s−1 Longitudinal, lateral, and vertical velocity standard deviations s relaxation time incident beam radiation CO2 /O2 specification ratio mol CO2 mol−1 air compensation point Cm threshold for rain interception Pa K−1 slope of saturation vapor pressure-temperature net mineralization rate g m−3 d−1 cm total rainfall amount in a growing season clumping factor of leaf distribution
Glossary Available nutrient The portion of any element in the soil that can be adsorbed and assimilated by growing plants. Available water The portion of water that can be freely up-taken by plant roots. Therefore, it is the amount of water between field capacity and wilting point. Autotroph An organism able to use carbon dioxide or carbonates to obtain energy for life processes from the oxidation of inorganic elements.
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Biomass The total mass of living material of a specified type in a given environment. Carbon cycle The sequence of transformations through which carbon dioxide is fixed in living organisms by photosynthesis or chemosynthesis, is produced by respiration and by the death and decomposition of living organisms, is used by heterotrophic species and is returned to its original state. Compensation point It is the carbon dioxide concentration at which plant carbon assimilation vanishes in the absence of photorespiration. Decomposition Chemical breakdown of organic matter into simpler compounds, often accomplished by the aid of microorganisms. Field capacity Water content remaining in a soil after it has been saturated and after free drainage is practically ceased. Fixation Process or processes by which elements essential for vegetation growth are converted from a soluble or exchangeable form to a less soluble or non-exchangeable form. In particular, nitrogen is chemically combined with hydrogen to produce ammonia. Groundwater Subsurface water in the saturated soil free to move under the influence of gravity. Heterotroph Organism capable of deriving energy for life processes only from the decomposition of organic compounds. Humus The partially stable fraction of the soil organic matter remaining after the major portions of added plant and animal residues have decomposed. Immobilization The conversion of an element from the inorganic to the organic form in microbial or plant tissues, thus making the element not available to other organisms or plants. Leaching The removal of materials in solution from the soil by percolating water. Mineralization The conversion of an element from an organic form to an inorganic state as a result of microbial decomposition. Nitrogen cycle The sequence of changes undergone by nitrogen as it moves from the atmosphere into water, soil, and living organisms and upon death of such organisms is recycled through a part or all of the entire process. Runoff The portion of the precipitation on an area that is discharged from the area through stream channels. In soil science it usually only refers to the water lost by surface flow (e.g., surface runoff). Vadose zone The aerated region of soil above the permanent water table. Wilting point The soil-moisture content at which plants wilt.
References Aubertin, M., et al. A model to predict the water retention curve from basic geothecnical properties, Can. Geotech. J., 40, 1104, 2003. Baisden, W.T. and Amundson, R. An analytical approach to ecosystem biogeochemistry modeling, Ecol. Appl., 13, 649, 2003. Baldocchi D. and Meyers, T. On using eco-physiological, micrometeorological and biogeochemical theory to evaluate carbon dioxide, water vapor and trace gas fluxes over vegetation: A perspective, Agric. Forest Meteor., 90, 1, 1998. Benbi, D.K. and Richter, J. A critical review of some approaches to modeling nitrogen mineralization, Bio. Fertil. Soils, 35, 168, 2002. Bohrer, G., Mourad, H., Laursen, T.A., Drewry, D., Avissar R., Poggi, D., Oren, T., and Katul, G. Finite element tree crown hydrodynamics model (FETCH) using porous media flow within branching elements: A new representation of tree hydrodynamics, Water Resour. Res., 41, W11404, doi:10.1029, 2005. Bonan, G., Ecological Climatology: Concepts and Applications, Cambridge University Press, Cambridge, 2002.
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Bradford, K.J. and Hsiao, T.C. Physiological responses to moderate water stress, in Physiological Plant Ecology II, Water Relations and Carbon Assimilation, O. L. Lange, P. S. Nobel, C. B. Osmond, and H. Ziegler (eds.), Springer-Verlag, New York, 1982. Brady, N.C. and Weil, R.R. The Nature and Properties of Soil, 11th ed., Prentice Hall, Upper Saddle River, NJ, 1996. Brutsaert, W. Evaporation into the Atmosphere: Theory, History, and Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1982. Campbell, S.G. and Norman, J.M. An Introduction to Environmental Biology, Springer-Verlag, New York, 1998. Chan, T.P. and Govindaraju, R.S. A new model for soil hydraulic properties based on a stochastic conceptualization of porous media, Water Resour. Res., 39, Art. No. 1195, 2003. Collatz, J.G., Ball, J.T., Grivet, C., and Berry, J.A. Physiological and environmental regulation of stomatal conductance, photosynthesis and transpiration: A model that includes a laminar boundary layer, Agric. For. Meteorol., 54, 107, 1991. Cordova, J.R. and Bras, R.L. Physically based probabilistic models of infiltration, soil moisture, and actual evapotranspiration, Water Resour. Res., 17, 93, 1981. Crago, R.D. and Brutsaert, W., A comparison of several evaporation equations, Water Resour. Res., 28, 951, 1992. Cui, M. and Caldwell, M.M. A large ephemeral release of nitrogen upon wetting soil and corresponding root responses in the field, Plant Soil, 191, 291, 1997. Daly, E., Porporato, A., and Rodriguez-Iturbe, I. Coupled dynamics of photosynthesis, transpiration, and soil water balance. Part I: Upscaling from hourly to daily level, J. Hydrometerol., 5, 546, 2004a. Daly, E., Porporato, A., and Rodriguez-Iturbe, I. Coupled dynamics of photosynthesis, transpiration, and soil water balance. II. Stochastic dynamics and ecohydrological significance, J. Hydromet., 5, 559, 2004b. Denmead, O.T., Harper, L.A., and Sharpe, R.R. Identifying sources and sinks of scalars in a corn canopy with inverse Lagrangian dispersion analysis: I. Heat, Agric. For. Meteorol., 104, 67, 2000. Dingman, S.L. Physical Hydrology, Prentice Hall, Upper Saddle River, NJ, 1994. D’Odorico, P., et al. Preferential states of seasonal soil moisture: The impact of climate fluctuations, Water Resour. Res., 36, 2209, 2000. D’Odorico, P., et al. Hydrologic control on soil carbon and nitrogen cycles. II: A case study, Adv. Water Res., 26, 59, 2003. Eagleson, P. S. Climate, soil, and vegetation. 1. Introduction to water balance dynamics, Water Resour. Res., 14, 705, 1978. Farquhar, G.D., von Cammerer, S., and Berry, J.A. A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species, Planta, 149, 78, 1980. Federer, C.A. A soil-plant-atmosphere model for transpiration and availability of soil water, Water Resour. Res., 15, 555, 1979. Fernandez-Illescas, C., et al. The role of soil texture in water controlled ecosystems, Water Resour. Res., 37, 2663, 2001. Fierer, N. and Schimel, J.P. Effects of drying-rewetting frequency on soil carbon and nitrogen transformations, Soil Biol. Biochem., 34, 777, 2002. Finnigan, J. Turbulent transport in plant canopies, in The Forest-Atmosphere Interactions, Hutchinson, B.A. and Hicks, B.B. (eds.) D. Reidel, Norwell, 1985, pp. 443. Finnigan, J. Turbulence in plant canopies, Annu. Rev. Fluid Mech., 32, 519–571, 2000. Gollan, T., Turner, N.C., and Schulze, E.D. The responses of stomata and leaf gas exchange to vapour pressure deficit and soil water content, III. In the schlerophyllous woody species Nerium Oleander, Oecologia, 65, 356, 1985. Gu, L.H., et al. Micrometeorology, biophysical exchange and nee decomposition in a two-story boreal forest – development and test of an integrated model, Agric. For. Meteorol., 94, 123, 1999.
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Gusman, A.J. and Marino, M.A. Analytical modeling of nitrogen dynamics in soils and ground water, J. Irrig. Drain. Eng., 125, 330, 1999. Guswa, A.J. Soil-moisture limits on plant uptake: An upscaled relationship for water-limited ecosystems, Adv. Water Resour., 28, 543–552, 2005. Guswa, A.J., Celia, M.A., and Rodriguez-Iturbe, I. Effect of vertical resolution on predictions of transpiration in water-limited ecosystems, Adv. Water Resour., 27, 467, 2004. Guswa, A.J., Celia, M.A., and Rodriguez-Iturbe, I. Models of soil-moisture dynamics in ecohydrology: A comparative study, Water Resour. Res., 38, Art. No. 1166, 2002. Hillel, D. Environmental Soil Physics, Academic Press, San Diego, 1998. Hosking, J.R.M. and Clarke, R.T. Rainfall-runoff relations derived from the probability-theory of storage, Water Resour. Res., 26, 1455, 1990. Hsiao, T.C. Plant responses to water stress, Ann. Rev. Plant Physiol., 24, 519, 1973. Hueckel, T., Kaczmarek, M., and Caramuscio, P. Theoretical assessment of fabric and permeability changes in clays affected by organic contaminants, Can. Geotech. J., 34, 588, 1997. Hunt, A.G. and Gee, G.W. Application of critical path analysis to fractal porous media: Comparison with examples from the Hanford site, Adv. Water Resour., 25, 129, 2002. Hunt, H.W., et al. Simulation model for the effects of climate change on temperate grasslands ecosystems, Ecol. Modell., 53, 205, 1991. Ingram, J. and Bartels, D. The molecular basis of dehydration tolerance in plants, Ann. Rev. Plant Physiol. Plant Mol. Biol., 47, 377, 1996. Jones, H.G. Plants and Microclimate: A Quantitative Approach to Environmental Plant Physiology, Cambridge University Press, Cambridge, 1992. Katul, G.G. and Albertson, J.D. An investigation of higher-order closure models for a forested canopy, Bound.-Lay. Meteorol., 89, 47, 1998. Katul, G.G. and Albertson, J.D. Modeling CO2 sources, sinks and fluxes within a forest canopy, J. Geophys. Res., 104, 6081, 1999. Katul, G.G. and Chang, W.-H. Principal length scales in second-order closure models for canopy turbulence, J. Appl. Meteorol., 38, 1631, 1999. Katul, G.G. and Siqueira, M. Modeling heat, water vapor, and carbon dioxide flux distribution inside canopies using turbulent transport theories, Vadose Zone J., 1, 58, 2002. Katul, G.G., et al. A Lagrangian dispersion model for predicting CO2 sources, sinks, and fluxes in a uniform loblolly pine (Pinus taeda L.) stand, J. Geophys. Res., 102, 9309, 1997. Katul, G.G., Ellsworth, D., and Lai, C.T. Modeling assimilation and intercellular CO2 from measured conductance: A synthesis of approaches, Plant Cell Environ., 23, 1313, 2000. Katul, G., Leuning, R., and Oren, R. Relationship between plant hydraulic and biochemical properties derived from a steady-state coupled water and carbon transport model, Plant Cell Environ., 26, 339, 2003. Kaye, J.P. and Hart, S.C. Competition for nitrogen between plants and soil microorganisms, Trends Ecol. Evol., 12, 139, 1997. Kim, D.S. and Fogler, H.S. Biomass evolution in porous media and its effects on permeability under starvation conditions, Biotechnol. Bioeng., 69, 47, 2000. Knapp, A. K., et al. Rainfall variability, carbon cycling, and plant species diversity in a mesic grassland, Science, 298, 2202, 2002. Kramer, P.J. and Boyer, J.S. Water Relations of Plants and Soils, Academic Press, London, 1995. Kumagai, T., et al. Water cycling in a Bornean tropical rainforest under current and projected precipitation scenarios, Water Resour. Res., 27, 1135, 2004. Lai, C.T., et al. Modeling vegetation-atmosphere CO2 exchange by a coupled Eulerian-Lagrangian approach, Bound. Lay. Meteorol., 95, 91, 2000. Lai, C.T., et al. Modeling the limits on the response of net carbon exchange to fertilization in a southeastern pine forest, Plant Cell Environ., 25, 1095, 2002.
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Laio, F., et al. Plants in water-controlled ecosystems: Active role in hydrological processes and response to water stress. II. Probabilistic soil-moisture dynamics, Adv. Water Resour., 24, 707, 2001a. Laio, F., et al. Plants in water controlled ecosystems: Active role in hydrological processes and response to water stress. IV. Applications to real cases, Adv. Water Res., 24, 745, 2001b. Laio, F., et al. On the seasonal dynamics of mean soil moisture, J. Geophys. Res., 107, 10.1029/2001JD001252, 2002. Lange, O.L., Kappen, L., and Schulze, E.D. Water and Plant Life: Problems and Modern Approaches, Springer-Verlag, Berlin, 1976. Larcher, W. Physiological Plant Ecology, 3rd ed., Springer-Verlag, Berlin, 1995. Leuning, R. A critical appraisal of a combined stomatal-photosynthesis model for C3 plants, Plant Cell Environ., 18, 339, 1995. Leuning, R. Estimation of scalar source/sink distributions in plant canopies using Lagrangian dispersion analysis: Corrections for atmospheric stability and comparison with a multilayer canopy model, Bound.-Lay. Meteorol., 96, 293, 2000. Levitt, J. Responses of Plants to Environmental Stresses, vol. I, 2nd ed., Academic Press, New York, 1980. Manzoni, S., et al. Soil nutrient cycles as a nonlinear dynamical system, Nonlinear Proc. Geophys., 11, 589, 2004. Mary, B., et al. Interactions between decomposition of plant residues and nitrogen cycling in soil, Plant Soil, 181, 71, 1996. Massman, W.J. and Weil, J.C. An analytical one dimensional second-order closure model of turbulence statistics and the Lagrangian time scale within and above plant canopies of arbitrary structure, Bound.-Lay. Meteorol., 91, 81, 1999. Melillo, J.M., Borchers, J., and Chaney, J. Vegetation ecosystem modeling and analysis project — comparing biogeography and biogeochemistry models in a continental-scale study of terrestrial ecosystem responses to climate change and CO2 doubling, Global Biogeochem. Cycles, 9, 407, 1995. Meyers, T. and Paw U, K.T. Modeling the plant canopy micrometeorology with higher- order closure principles, Agric. For. Meteorol., 41, 143, 1987. Milly, P.C.D. An analytical solution of the stochastic storage problem applicable to soil water, Water Resour. Res., 29, 3755, 1993. Milly, P.C.D. A minimalistic probabilistic description of root zone soil water, Water Resour. Res., 37, 457, 2001. Molina, J.A. and Smith, P. Modeling carbon and nitrogen processes in soils, Adv. Agron., 62, 253, 1998. Monteith, J.L. and Unsworth, M. Principles of Environmental Physics, 2nd ed., Butterworth-Heinemann Publishers, 1990. Nathan, R. and Katul, G.G. Foliage shedding in deciduous forests lifts up long-distance seed dispersal by wind, Proc. Natl. Acad. Sci., 102, 8251–8256, 2005. Neff, J.C., Chapin III, F. S., and Vitousek, P. Breaks in the cycle: Dissolved organic nitrogen in terrestrial ecosystems, Front Ecol. Environ., 1, 205, 2003. Nicholson, S. Land surface processes and Sahel climate, Rev. Geophys., 38, 117, 2000. Nilsen, E.T. and Orcutt, D.M. Physiology of Plants Under Stress: Abiotic Factors, Wiley, New York, 1998. Nobel, P.S. Physicochemical and Environmental Plant Physiology, Academic Press, San Diego, CA, 1999. Noy-Meir, I. Desert ecosystems: Environment and producers, Annu. Rev. Ecol. Syst., 4, 25, 1973. Oren, R., et al. Water balance delineates the soil layer in which moisture affects canopy conductance, Ecol. Appl., 8, 990, 1998. Parton, W.J., Steward, J., and Cole, C. Dynamics of C, N and S in grassland soils: A model, Biogeochemistry, 5, 109, 1988. Peixoto, J.P. and Oort, A.H. Physics of Climate, Springer-Verlag, New York, 1992. Porporato, A., et al. Plants in water-controlled ecosystems: active role in hydrologic processes and response to water stress. III. Vegetation water stress, Adv. Water Resour., 24, 725, 2001. Porporato, A., et al. Soil moisture and plant stress dynamics along the Kalahari precipitation gradient, J. Geophys. Res.–Atmos., 108, 4127, 2003a.
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Porporato, A., et al. Hydrologic controls on soil carbon and nitrogen cycle. I: Modelling scheme, Adv. Water Res., 26, 45, 2003b. Porporato, A., Daly, E., and Rodriguez-Iturbe, I. Soil water balance and ecosystem response to climate change, Am. Nat., 164, 625, 2004. Puma, M.J., et al. Functional relationship to describe temporal statistics of soil moisture averaged over different depths, Adv. Water Resour., 28, 553, 2005. Raupach, M.R. Applying Lagrangian fluid mechanics to infer scalar source distributions from concentration profiles in plant canopies, Agric. For. Meteorol., 47, 85, 1989a. Raupach, M.R. A practical Lagrangian method for relating scalar concentrations to source distributions in vegetation canopies, Q. J. Roy. Meteorol. Soc., 115, 609, 1989b. Raupach, M.R. and Shaw, R.H. Averaging procedures for flow within vegetation canopies, Bound.-Lay. Meteorol., 22, 79, 1982. Rawls, W.J., et al. Effect of soil organic carbon on soil water retention, Geoderma, 116, 61, 2003. Rieu, M. and Sposito, G. Fractal fragmentation, soil porosity, and soil-water properties. 1. Theory, Soil Sci. Soc. Am. J., 55, 1231, 1991. Rockhold, M.L., et al. Considerations for modeling bacterial-induced changes in hydraulic properties of variably saturated porous media, Adv. Water Resour., 25, 477, 2002. Rodriguez-Iturbe, I. and Porporato, A. Ecohydrology of Water-Controlled Ecosystems, Cambridge University Press, Cambridge, 2004. Rodriguez-Iturbe, I., et al. Probabilistic modeling of water balance at a point: The role of climate, soil and vegetation, Proc. R. Soc. Lond. A, 455, 3789, 1999. Salisbury, F.B. and Ross, C.W. Plant Physiology, 4th ed., Wadsworth Publishing Company, Belmont, 1992. Salvucci, G.D. Estimating the moisture dependence of root zone water loss using conditionally averaged precipitation, Water Resour. Res., 37, 1357, 2001. Schimel, J.P. and Bennett, J. Nitrogen mineralization: challenges of a changing paradigm, Ecology, 85, 591, 2004. Schimel, J.P. and Weintraub, M.N. The implications of exoenzyme activity on microbial carbon and nitrogen limitation in soil: A theoretical model, Soil Biol. Biochem., 35, 549, 2003. Schimel, D.S., et al. Climate and nitrogen controls on the geography and timescales of terrestrial biogeochemical cycling, Global Biogeochem. Cycles, 10, 677, 1996. Schimel, D.S., Braswell, B.H., and Parton, W.J. Equilibration of terrestrial water, nitrogen and carbon cycles, Proc. Natl. Acad. Sci. USA, 94, 8280, 1997. Scholes, M.C., et al. NO and N2 O emissions from savanna soils following the first simulated rains of the season, Nutr. Cycl. Agroecosys., 48, 115, 1997. Schuepp, P.H. Tansley Review n. 59, Leaf boundary-layers, New Phytologist, 125, 477, 1993. Siqueira, M. and Katul, G. Estimating heat sources and fluxes in thermally stratified canopy flows using higher-order closure models, Bound. Lay. Meteorology, 103, 125, 2002 Siqueira, M., Lai, C.T., and Katul, G. Estimating scalar sources, sinks and fluxes in a forest canopy using Lagrangian, Eulerian and hybrid inverse models, J. Geophys. Res., 105, 19475, 2000. Six, J., et al. A history of research on the link between (micro)aggregates, soil biota, and soil organic matter dynamics, Soil Till. Res., 79, 7, 2004. Smith, J.A.C. and Griffith, H. Water Deficits: Plant Responses from Cell to Community, Bios Scientific Publishers, Oxford, 1993. Sollins, P., Homann, P., and Caldwell, B.A. Stabilization and destabilization of soil organic matter: mechanisms and controls, Geoderma, 74, 65, 1996. Sperry, J.S. Hydraulic constraints on plant gas exchange, Agric. For. Meteorol., 104, 13, 2000. Stewart, T.L. and Kim, D.S. Modeling of biomass-plug development and propagation in porous media, Biochem. Eng. J., 17(2), 107–119, 2004. Stull, R.B., An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988.
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Taylor, S.W., Milly, P.C.D., and Jaffe, P.R. Biofilm growth and the related changes in the physical properties of a porous medium. 2. Permeability, Water Resour. Res., 26, 2161, 1990. Thullner, M., Zeyer, J., and Kinzelbach, W. Influence of microbial growth on hydraulic properties of pore networks, Transport Porous Med., 49, 99, 2002. Tyler, S.W. and Wheatcraft, S.W. Fractal processes in soil-water retention, Water Resour. Res., 26, 1047, 1990. Tyree, M.T. and Sperry, J.S. Vulnerability of xylem to cavitation and embolism, Annu. Rev. Plant Physiol. Plant Mol. Biol., 40, 19, 1989. Vandevivere, P. Bacterial clogging of porous media: A new modeling approach, Biofouling, 8, 281, 1992. Warland, J.S. and Thurtell, G.W. A Lagrangian solution to the relationship between a distributed source and concentration profile, Bound.-Lay. Meteorol., 96, 453, 2000. Wosten, J.H.M., Pachepsky, Ya.A., and Rawls, W.J. Pedotransfer functions: Bridging the gap between available basic soil data and missing soil hydraulic characteristics, J. Hydrol., 251, 123, 2001.
Further Information A general introduction on plant-atmosphere exchange and its role in climate science can be found in Peixoto and Oort (1992), Dingman (1994), and Bonan (2002). Campbell and Norman (1998) focus on modeling radiative and eco-physiological processes related to various components of the soil-plantatmosphere system. A detailed description of boundary-layer dynamics along with Reynolds-Averaged turbulence closure models can be found in Stull (1988) or Brutsaert (1982). Finnigan (2000) provides a review of the structure of turbulence inside canopies. A number of books treat hydrological and physiological features of vegetation and their relationship to microclimate . We suggest three of them: • Jones (1992) provides a description of the interactions between plants and their aerial environment accompanied by explanations of the state-of-the-art models now adopted. • Larcher (1995) is an accurate synthesis of the vast number of processes linking plants and their environment. • Nobel (1999) provides a mathematical treatment of the physical and chemical processes occurring inside plant cells and tissues. Regarding the physical properties of soils, two good references are Hillel (1998) and Brady and Weil (1996); both give an exceptionally well-documented description of the soil properties and its role in the terrestrial energy exchange and water cycle. Finally, the material related to stochastic soil-moisture models and soil nutrient dynamics is extensively presented in the book by Rodriguez-Iturbe and Porporato (2004).
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30 The Role of Geographical Information Systems in Groundwater Engineering 30.1 Introduction to Geographic Information Systems . . . . 30-1 Overview of GIS
30.2 GIS Components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30-2 Software • Hardware • Data
30.3 30.4 30.5 30.6
Bernard Engel and Kyoung Jae Lim Purdue University
Kumar C.S. Navulur Digital Globe
Data Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis Capabilities of GIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Web GIS Services. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Application of GIS to Groundwater Engineering. . . . . .
30-3 30-3 30-5 30-6
Mapping the Occurrence of Groundwater and Groundwater Features • Managing Spatial Data Aspects of Groundwater Projects • Spatial Data Analyses Using Spatial Statistics • Surface Fitting and Interpolation • Visualization • Modeling Water Vulnerability Using Spatial Data • Modeling Groundwater Movement • Implementation of Policies Involving Spatial Dimensions
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30-14 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30-15 Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30-17
30.1 Introduction to Geographic Information Systems Geographic Information Systems (GIS) have become important tools in efficiently solving many problems in which spatial data is important. Natural resources and environmental concerns, including groundwater, have benefited greatly from the use of GIS. This chapter provides a brief introduction to GIS and some of its applications in addressing groundwater issues. 30-1
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30.1.1 Overview of GIS GIS have evolved rapidly in the last decade, becoming powerful computer tools for varied applications ranging from sophisticated analysis and modeling of spatial data to simple inventory and management. The rapid growth, diversity, and commercial orientation of GIS have resulted in multiple definitions of the term GIS. GIS can be described as a collection of computer software and hardware for storing, manipulating, analyzing, and displaying spatial or geographically referenced data. GIS can also be described as a combination of computer tools: cartographic and tools for displaying data and making maps, a database for storing spatial data, and an analysis tool for manipulating data. As a visualization tool, GIS allows graphical display of maps, tabular information, statistical summaries, and modeling solutions. As a database, GIS can store, maintain, and update spatial data and associated descriptive information. GIS supports most database functions such as browsing, tabular queries, updating data, and functions supported by commonly used computer software such as spreadsheets and statistical packages. The most significant difference between GIS and other information systems and databases is the spatial nature of the data in a GIS. The analysis functions in a GIS allow manipulation of multiple themes of spatial data to perform operations such as overlays, buffering, and arithmetic operations on the data. The application of GIS has grown dramatically since the 1980s with yearly expenditures on GIS experiencing double digit growth. Estimated expenditures within the US on GIS were approximately $6 billion in 1995 and are estimated at $75 to $95 billion in 2005 [1,2]. The ability of GIS to perform analysis on spatial data and corresponding attribute data and to integrate different types of data at high speeds are unmatched by manual methods. There is an increasing trend within organizations and public agencies at all levels to develop GIS for the management and analysis of spatial data. The ability of a GIS to perform complex spatial analyses rapidly provides a quantitative, as well as qualitative, advantage in planning scenarios, decision models, change detection and analyses, and other problems requiring refinements to successive analyses. Digital databases like SSURGO (Soil Survey Geographic), NASIS (National Soil Information System), land use data, satellite imagery, Digital Elevation Model (DEM) data, and NHD (National Hydrography Dataset) river reach data are now being distributed in GIS formats, and efforts are ongoing to integrate more data into GIS formats.
30.2 GIS Components GIS, like other information systems, are integral parts of applications to address various problems and issues. To create successful GIS applications, there must be an organization of people, facilities, equipment, and data to successfully implement and maintain the GIS. Four essential elements that constitute a GIS are computer software, hardware, data, and personnel.
30.2.1 Software GIS software are extremely diverse in functionality, database structure, and hardware requirements. A GIS user today is presented with a wide variety of commercial GIS software. Popular GIS software includes ArcGIS, ArcView, Arc Internet Map Server (IMS), MapServer, MapInfo, MGE (Modular GIS Environment), Genasys, ERDAS, GRASS, IDRISI, GeoMedia, and Atlas. These software tools are sophisticated and have a variety of functionalities for GIS applications and analyses. Most of these software tools have capabilities to handle data in various formats, thereby facilitating data transfer between GIS software. Some of the above software are hardware specific and others run on a variety of platforms. The marketing of GIS software today is increasingly oriented to an open system or platform-independent approach.
30.2.2 Hardware The large memory and disk requirements of GIS software and data resulted in a trend toward workstations running the UNIX operating system in the late 1980s and early 1990s. However, rapidly declining computer hardware costs and increasing capabilities of personal computers have made GIS software available on
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a wide variety of computer platforms including personal computers, high performance workstations, Windows CE devices, and PDAs. GIS applications often require the use of special peripherals such as digitizers and scanners for developing digital data. Global Positioning System (GPS) units with handheld and mobile devices running the ArcPad or similar programs have become widely used to locate and collect points and define lines and boundaries for developing, analyzing, and displaying spatial data in GIS formats. Other hardware requirements for GIS applications include plotters and printers for output of the final GIS products, including hard copy maps and summaries.
30.2.3 Data Even though hardware and software may be available, GIS users cannot perform analysis, visualization, or modeling without data. Non-spatial data with spatial indexing as well as spatial data are used in GIS projects. In the early stage of the GIS era, a GIS user had to develop spatial digital data by digitizing or scanning paper maps, which was an extremely time-consuming job and often introduced error in developing the digital data. However, many national, state and local level GIS projects have now been completed to provide digital datasets. Many of these GIS data have been extracted from airborne or remotely sensed image data with digital image processing techniques. The GIS data model has evolved with the introduction of relational and spatial database management systems. Maintenance of metadata (data describing other data) is a critical aspect of successful GIS projects.
30.3 Data Representation Data are the most important resource in a GIS. Digital data are usually very expensive to develop and require large quantities of storage space. GIS data are commonly stored in one of two forms: (1) vector or (2) raster. Vector data are the set of points, lines, and polygons that are used to represent map feature locations (see Figure 30.1). The spatial relationships between various features must be explicitly coded by the GIS software for vector data. A topological data structure may be used to store the relationships between objects. Well locations, streams, and state boundaries are some of the examples of point, line, and polygon vector features, respectively. Vector data can be represented in various formats such as shape files, DXF, DLG, MOSS, and SDTS. GIS software is generally designed to accept and export data in one or more of these formats. Raster data can be described as a matrix of columns and rows or as a regular grid of square or rectangular data. Location in raster data is defined by row and column numbers and size of each cell or pixel. The value assigned to a grid or cell indicates the value of the attribute it represents. Figure 30.1 shows a comparison of vector and raster representation of GIS data sets. Airborne and satellite data are typical examples of raster data. Various graphic interchange formats for raster data are GIF, TIFF, BIL, BIP, BSQ, JPEG, DEM, ASCII, and SDTS. The choice between vector and raster GIS is usually driven by application requirements. The most important aspects of data quality are accuracy, time, scale, and completeness of data sets. The error associated with each of the data sets will affect the accuracy of the final product and therefore defines the usefulness of the final products. Hence, GIS data developers are encouraged to document the data or create metadata to facilitate the sharing of spatial information with other GIS users. Metadata for a GIS data layer includes the scale of the data, projection, how the data were developed, and many other items of information useful in understanding the GIS data layer. Metadata is typically stored in either ASCII text file format or Extensible Markup Language (XML) format. Metadata in an XML format has become widely accepted and used because of its ease for data sharing. The XML format has also become the standard for data sharing through the Internet.
30.4 Analysis Capabilities of GIS Analysis of spatial and attribute data in a GIS can be classified into five main types of procedures: (1) data transformation and restructuring, (2) data retrieval, classification, and measurement, (3) overlay,
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Point
Line
Polygon Vector representation
Raster representation
FIGURE 30.1 Vector and corresponding raster representation.
(4) neighborhood and statistical measures, and (5) connectivity. Each of these is discussed briefly in the remainder of this section. Data transformation functions allow mathematical manipulation of raster or vector data to rotate, translate, scale, or mosaic different map layers. Such efforts are often necessary when acquiring GIS data sets. Transformation of data may be required to convert the data being developed by digitizing or scanning into useful forms. Restructuring functions include data conversion from raster to vector, vector to raster, and converting data between different formats. Retrieval functions allow the query and retrieval of spatial and tabular data stored in the GIS database. They also facilitate spatial queries specific to a region on single or multiple map layers. Classification allows the user to rename attributes, such as to indicate that areas within 0.5 miles of a well are sensitive areas and special precautions should be taken with potential contaminants in this area. Generalization allows the combining of classes such as considering all water table depths less than 15 ft as “shallow” for a particular application. Measurement functions allow the user to determine distance from a feature, or length, area, volume, and perimeter of a feature or features. Overlay functions constitute the third set of GIS analysis tools. Overlay allows the user to combine and overlay multiple thematic data (map layers) at different scales and in different formats. Overlay functions can also perform arithmetic operations such as addition, division, or multiplication on map layers and logical operations between map layers such as AND, OR, and NOT. A typical logical operation might be finding areas with soils having high permeabilities and areas with shallow depths to water tables and defining areas having this combination as being susceptible to groundwater contamination. The fourth set of analysis procedures includes neighborhood functions that involve calculations based on the value of neighboring cells. For example, a search technique can be used to find the maximum contamination level in an area. The Thiessen polygon technique can be used to construct polygons
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around a set of points such as rain gages or groundwater monitoring wells. Interpolation procedures, such as inverse distance weighting, kriging, and splines, can be used for interpolating a value based on the values of neighboring locations. Such procedures are useful to create continuous surfaces from point data, such as data observed in groundwater monitoring wells. The fifth group of analysis procedures contains connectivity functions such as contiguity measures that can be used to determine the size of a catchment. Proximity can be used to determine distance from a feature and generate buffer zones. Network functions can be used to predict water flow in a stream network, and other connectivity functions can be used to define drainage basins, determine sinks in watersheds, and generate perspective views. Statistical measures allow calculation of spatial auto-correlation, correlation between maps, and confidence intervals.
30.5 Web GIS Services With the introduction of the Internet in the early 1990s, data and information sharing has become easier and faster than ever before. With advances in GIS and information technologies, including the World Wide Web (WWW), spatial data sharing over the Internet has grown rapidly. Many Web GIS software tools have been developed to provide spatial information through the Web. Commercially available and public domain Web GIS software includes ArcIMS, AspMap, GeoTools, JShape, MapServer, MapGuide, and GeoServ. Beyond just providing spatial information using Web GIS software, many Web GIS-based decision support systems have been developed to overcome data availability, expertise, ease-of-use, and access difficulties in solving real world problems, especially in natural resources and environmental areas. With the rapidly growing numbers of Internet users in the United States and beyond, the Web presents a means to supply large numbers of tools, databases, and other information to decision makers and other potential users. In addition, the Web-based approach provides opportunities to increase involvement of stakeholders in the decision making process by providing them with the required knowledge and data through these accessible, easy to use Web GIS-based systems. The following are examples of Web GIS-based decision support systems to help solve natural resource and environmental concerns [3–8]. • NAPRA WWW (http://danpatch.ecn.purdue.edu/∼napra): estimates impacts of agricultural management systems on surface and subsurface hydrology and water quality, and to identify location specific environmentally friendly agricultural management practices • L-THIA WWW (http://www.ecn.purdue.edu/runoff/lthianew): estimates impacts of land use changes on hydrology and water quality • ROMIN WWW (http://pasture.ecn.purdue.edu/∼romin): provides assistance with environmentfriendly land use planning • SEDSPEC (http://pasture.ecn.purdue.edu/∼sedspec): assists in analyzing runoff and erosion problem by determining the peak rate of runoff from the area and providing information about different types of runoff and erosion control structures • WATERGEN (http://pasture.ecn.purdue.edu/∼watergen): provides online watershed delineation tool and serves as an interface for other spatial decision support systems • WHAT (http://pasture.ecn.purdue.edu/∼what): provides automated baseflow separation and a hydrograph analysis tool to complement the USGS daily stream flow web site with a Web GIS interface The Web GIS-based decision support systems overviewed above provide numerous advantages over traditional systems. In general, making such models, decision support tools, and databases accessible on the Web gives users access to vast and diverse options. Users of Web GIS-based systems do not need to learn how to use expensive and complex GIS software, and large databases including GIS data required to
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run the model are also stored on a central server. This has a twofold advantage of significant financial and time savings for users of the Web GIS-based system.
30.6 Application of GIS to Groundwater Engineering Typical examples of GIS applications in groundwater studies include site suitability analyses; mapping information such as water table depths, aquifer type and material, aquifer recharge, and groundwater remediation areas; managing site inventory data; computing statistics to estimate spatial correlation of a process occurring over a region such as non-point source pollution; estimating vulnerability of groundwater to pollution potential from non-point sources of pollution; integrating groundwater quality assessment models with spatial data to create spatial decision support systems; modeling groundwater and contaminant movement: advection and dispersion modeling, developing flow field or vector fields representing groundwater seepage velocities, tracking particle movement, and particle retardation; modeling solute transport and leaching; and evaluating soil salinity and salt loading into groundwater.
30.6.1 Mapping the Occurrence of Groundwater and Groundwater Features Maps play an important role in portraying information about groundwater systems. GIS can be used to store these maps, allowing the user to create the desired map products. GIS further provide the ability to manipulate the mapped data. Mapping the material of underlying aquifer systems requires information of geologic strata and other data including soil properties and depth to bedrock. Soil databases such as SSURGO and NASIS contain information that can be used in conjunction with glacial geology to interpret the material of the aquifers. Figure 30.2 shows the aquifer media data layer developed from the glacial geology map of Indiana at a 1:100,000 scale. Another application is estimating the recharge flux to the water table. GIS can be utilized to evaluate and delineate patterns of recharge within a region by incorporating available information about observed temporal fluctuations of recharge at specified locations. Continuous remote acquisition of water table depths combined with GIS capabilities for distributing the flux spatially across the study region can result in near-real-time monitoring of spatial variability in recharge flux [9]. Recharge can also be estimated using information including current climate, soil, and vegetation/land use patterns and estimates of recharge for various soil-vegetation combinations [10].
30.6.2 Managing Spatial Data Aspects of Groundwater Projects Siting a waste disposal facility is an example for which GIS can help manage the spatial data considerations including the potential impacts on groundwater. State and federal regulations for a site location can be implemented using GIS functions such as overlays, buffers, and arithmetic computations on data layers. For example, regulations for a hazardous waste landfill may indicate that they should not be located: (1) within 100 ft of any lake reservoir or continuously flowing stream, (2) within 100 ft from any of the site’s property boundaries, (3) within 600 ft of potable domestic water supplies, (4) within 600 ft of any dwelling, and (5) within 1200 ft of a public water supply. Such exclusionary areas are easily computed as buffers within GIS. Further, GIS maps of soils, geology, and climate, hydrological and cultural data sets can be integrated in a GIS to develop maps showing areas suitable for hazardous waste landfill siting that meet the above and other regulations. Figure 30.3 shows the areas suitable for hazardous waste landfill siting in Tippecanoe County, Indiana that were identified using such an approach [11].
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Glacial till, Limestone, Beddrock, Sandstone Sand and gravel
Karst limestone
N
FIGURE 30.2 Aquifer material map of Indiana.
30.6.3 Spatial Data Analyses Using Spatial Statistics Spatial statistics are a rapidly emerging field being applied to many diverse applications [12]. Spatial auto-correlation studies are often used in geo-statistics for determining the spatial dependencies of the factors being studied. In groundwater studies, spatial statistics can be computed to study the distributions of non-point source (NPS) contamination of groundwater on a regional scale, and spatial variation of hydrogeologic factors affecting solute transport including hydraulic conductivity of the aquifer, slope, and groundwater properties. Spatial auto-correlation refers to the spatial ordering of a single variable and to the relationship between pairs of observations of this variable. The ordering of n observed values of some variable X is usually described with the aid of a connectivity matrix, C. Non-zero cij entries in the n × n matrix indicate that the corresponding polygons are juxtaposed. For data measured on an interval/ratio scale, Moran coefficient statistics can be used [13] for assessing spatial correlation. These spatial statistics can be used to determine
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(1) Unacceptable sites (2) Poor sites (3) Average sites (4) Good sites
FIGURE 30.3 Sites suitable for hazardous waste disposal in Tippecanoe County, Indiana.
the spatial correlation of NPS pollution and to eliminate detections from point sources of pollution in a water quality database.
30.6.4 Surface Fitting and Interpolation Surface fitting and interpolation techniques are commonly employed for creating continuous data (raster data) from a distributed set of data points over a geographical region (e.g., creating a depth to groundwater map from observations of water depth in wells). The underlying assumption in these techniques is that the data points are random, well-sampled, and are representative of the spatial distributions of the attribute. Commonly employed techniques for interpolation include inverse distance weighting interpolation (IDW), kriging using a semi-variogram, polynomial regression, and spline fitting [14,15]. Inverse distance weighting interpolation computes a cell value using a linear weighting combination of the set of sample points surrounding the cell. The weight is a function of inverse distance to the observed values. Usually a power of two is adopted for inverse distance and values greater than two will increase the influence of nearby data. Also the interpolated value can be controlled by limiting the search radius or by limiting the number of sample points to be used for interpolation. Kriging is based on the regional variable theory that assumes the spatial variation of an attribute is statistically homogeneous throughout the surface. The variation of the attribute is measured using a semivariogram, a graphical plot of semi-variance against the distance between pairs of sample points. Using the surface estimators, ordinary kriging, and universal kriging, the value at a cell can be interpolated. Polynomial regression interpolation depends on the order of polynomial used for fitting the surface. A first-order polynomial regression simply performs a least-squares fit of a plane to the set of data points. As the order of the polynomial increases, the interpolation becomes more complex. Polynomial regression generally creates smooth surfaces, and the surface created seldom passes through the original data points. Spline interpolation is a two-dimensional (2D) minimum curve interpolation that creates a smooth surface, and unlike polynomial regression, the surface passes through the input data
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Water table depth >100 feet 75–100 feet 50–75 feet 25–50 feet
FIGURE 30.4 Interpolated water table depths based on water depths in wells.
points. The commonly used minimum-curvature technique is also called thin plate interpolation. Spline interpolation ensures a smooth surface together with continuous first-derivative surfaces. Functions for conducting surface fitting and interpolation are often included in commercial GIS software [14,15]. These techniques are commonly used in geo-statistics and can be applied in groundwater studies. The distribution of sample points will determine which method is appropriate. An example application of these techniques within GIS includes developing groundwater table depths for a region in unconfined aquifers using observed water table depths in drinking water wells. Figure 30.4 shows the map of water table depths in southern Indiana developed using the inverse distance weighting method. Another example is the study in northeastern Colorado where inverse distance weighting interpolation was used for mapping spatial distributions of nitrate contamination in groundwater for the region [16].
30.6.5 Visualization The saying “A picture is worth a thousand words” is certainly relevant to GIS. One of the advantages of using a GIS is its visualization capability. Visualization is a way of interpreting an image in digital format and improving human perception. When visualizing 3D phenomena in a 2D environment, a significant amount of information is lost. With advances in GIS technology, visualization of the phenomena in a 3D environment has become easier and more accurate, which provides opportunities for diverse analysis and exploitation of the data. Visualization of contaminant transport, plume movement, and delineation of remediation areas are typical 3D visualization examples in the groundwater engineering discipline. Many efforts are underway and have been completed to develop 3D visualization for groundwater modeling systems, such as MODFLOW, MODPATH, MT3DMS, MOC3D, and SUTRA. For example, Model Viewer, developed by the US Geological Survey, is a public domain program for 3D visualization of groundwater model results. The Visual MODFLOW and GMS software are commercially available visualization programs.
30.6.6 Modeling Water Vulnerability Using Spatial Data Non-point sources are often responsible for nitrates and pesticides in groundwater and surface water. However, it is difficult to predict NPS pollution in groundwater and surface water due to agricultural
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activities because numerous factors including soil, climate, crop, rate, and timing of pesticide and nutrient applications and tillage affect the movement of NPS pollutants. GIS are increasingly being integrated with groundwater and surface water quality assessment models [17–21] to facilitate model use. The data required for these models can be stored and managed in a GIS to facilitate the model simulations. GIS maps showing the areas vulnerable to groundwater contamination for a region would have many potential uses, such as implementation of groundwater management strategies to prevent degradation of groundwater quality and locating groundwater monitoring systems. These maps would also be helpful in evaluating existing and potential policies for groundwater protection. Groundwater vulnerability mapping can be classified into two categories: sensitivity mapping and vulnerability mapping. Sensitivity of groundwater to pollution is determined based on hydrogeologic setting, such as depth to groundwater, presence of confining layer, groundwater recharge, and hydraulic conductivity [20,21]. Groundwater vulnerability estimates how groundwater sensitivity is modified with human activities such as land use practices, pesticide and nutrient uses, and water use [20,21]. To develop regional maps of groundwater vulnerability to agricultural NPS pollution in Indiana, simple techniques like DRASTIC and SEEPAGE have been applied. DRASTIC is a regional scale groundwater quality assessment model that estimates groundwater vulnerability of aquifer systems based on the hydrogeologic factors of a region [22]. It is an empirical model and was developed by the National Well Water Association in conjunction with USEPA in the 1980s for evaluating pollution potential of groundwater systems on a regional scale. The factors considered in DRASTIC are: Depth to water table, Recharge (aquifer), Aquifer media, Soil media, Topography, Impact of vadose zone media, and Conductivity (hydraulic) of the aquifer. A region to be rated by DRASTIC is subdivided into smaller areas in which the factors considered are nearly homogeneous. A grid cell subdivision is often used and thus a raster GIS approach is well suited for conducting DRASTIC analyses. Each of the subdivisions of the factors considered in the model is weighted based on the factor values. The DRASTIC Index [21,22], a measure of pollution potential, is computed by summing the weighted factors of each subdivision. The higher the DRASTIC index, the greater the relative pollution potential. The DRASTIC Index can be converted into qualitative risk categories of low, moderate, high, and very high. Existing spatial databases like SSURGO contain inputs required for these groundwater models. GIS can be used to develop and store data representing hydrogeologic settings of a region required for DRASTIC and SEEPAGE. GIS classification, overlay, and arithmetic operations can be used for integrating the data layers to develop maps showing areas vulnerable to groundwater contamination from non-point source pollution. Figure 30.5 shows the vulnerability of groundwater systems in Indiana as predicted by DRASTIC analyses. Using a GIS, a comparison of the predictions of DRASTIC analyses with a GIS-based water quality database of nitrate detections in drinking water wells from USGS showed that 80% of nitrate detections >2 ppm were within the DRASTIC highly and very highly vulnerable areas [23]. The DRASTIC map is useful as a preliminary screening tool for policy and decision making in groundwater management strategies on a regional scale. The DRASTIC approach considers only soil structure but not other soil properties such as texture. However, studies have shown that soil structure is important in estimating water and pollutant transport through preferential flow [24–26]. Thus, soil structure information with land use and agricultural chemical use data were used to improve the DRASTIC methodology for groundwater vulnerability mapping using fuzzy rules [23]. The fuzzy rule based DRASTIC results considering soil structure were better correlated with measured water quality data [23]. However, the DRASTIC and SEEPAGE approaches do not consider the effects of temporal changes in variable agronomic management, crop growth, land use, climate, and properties and amounts of nutrients and pesticides applied to local areas. The Web GIS-based National Agricultural Pesticide Risk Analysis (NAPRA) system [3], available at http://danpatch.ecn.purdue.edu/∼napra, was developed to estimate the site-specific effects of land use and management on groundwater vulnerability. The NAPRA system builds the input parameter files for the Groundwater Loading Effects of Agricultural Management Systems
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DRASTIC vulnerability ratings Low High Moderate Very high 25
0
25
50 Miles Developed at 1:250,000
FIGURE 30.5 DRASTIC groundwater vulnerability map of Indiana.
(GLEAMS) [27] model from user provided crop management, pesticide, and nutrient data in the input interface by querying databases and by running weather generator models (Figure 30.6). The NAPRA postprocessor generates pesticide and nutrient loss probability of exceedance and historic loss curves and GIS maps. The NAPRA system was used to simulate state average nutrient and atrazine application rates for continuous corn in Indiana to develop a regional scale shallow groundwater vulnerability map. The NAPRA system simulates the movement of nitrate and atrazine below the root zone, and it can be assumed that much of the atrazine and nitrate leached below the root zone is lost to shallow groundwater. Figure 30.7 shows the NAPRA predicted nitrate losses to shallow groundwater. The natural break classification method was used to classify the NAPRA predicted nitrate values in Figure 30.7. The NAPRA predicted nitrate loss map could be used to identify areas that are vulnerable to NPS nitrate reaching groundwater. Statistical techniques used in conjunction with GIS show promise for various groundwater applications, including identifying and assessing nitrate leached to groundwater on a regional scale [28,29]. The Bayesian approach uses prior and posterior probabilities of occurrence of an event for combining data sets. The posterior probability can be computed and updated based on the prior probability and addition of new evidence. The Bayesian model, in a log-linear form, known as the weights of evidence model, is a datadriven model that estimates the relative importance of evidence of data by statistical means. The Bayesian approach can be used to build a map showing areas vulnerable to groundwater contamination from nitrates and other pollutants using factors considered in DRASTIC or SEEPAGE and a water quality database of observed contamination levels in drinking water wells in a region. Figure 30.8 shows the Bayesian risk map for Indiana developed using the USGS water quality database and DRASTIC factors as evidence [23]. The data layers required for the analyses were integrated within the ARC/Info GIS.
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Nutrient Enabled NAPRA WWW Input Interface (JavaScript, Java, DHTML, Database, Web GIS Tool, and CGI/Perl)
HTTP/Internet with WWW Browse S E R V E R
[INPUT]
[MODEL]
[OUTPUT]
Pesticide/Nutrient Losses Probability table & Yearly/Probability graphs
Management, pesticide, Nutrient data from client Pre-processor GLEAMS
Post-processor
STATSGO soil, pesticide prop. Weather data (30–50 years) CLIGEN & GEM Input
CLIGEN & GEM
NAPRA Predicted Pesticide/Nutrient Database file to be used in ArcView GIS (Perl/Avenue)
FIGURE 30.6 Overview of the NAPRA WWW System [3].
30.6.7 Modeling Groundwater Movement Groundwater flow modeling is usually completed using a 2D or 3D finite-difference or finite-element approach. In 2D, the finite-difference method employs a rectangular discretization in which input parameters are assigned to each pixel and hydraulic head is computed for each cell. A 3D finite-difference can be visualized as a stack of grids with interaction between the grids as specified. Both common GIS data models, vector and raster, can be used to model groundwater movement using a finite-difference approach, but the grid/raster approach is more analogous to a finite-difference approach as each parameter/input into the model can be represented as a separate GIS data layer [30]. In the finite-element approach, a polygon network, typically a triangular network, is used to represent 2D flow in the aquifer [31]. GIS are often equipped with functions for creating triangular irregular networks (TIN), and this approach is similar to the finite-element approach. Hence, a vector data model with TIN capabilities may be more suitable for finite-element mesh generation for modeling groundwater movement. GIS can facilitate the development, calibration, and verification of models as well as the display of model parameters and results in modeling groundwater movement. Spatial statistics and grid design capabilities of GIS can improve the modeling effort and aid in reliability assessment. A GIS-MODFLOW interface is an example of a groundwater finite-difference model linked with a GIS. Most parameters to the MODFLOW need to be represented in a raster format. There may be the case that there are no data in a cell after conversion to the raster data. Spatial interpolation algorithms in the GIS, such as Inverse Distance Weighting (IDW), can be used to interpolate point data [32]. Usually GIS and the model are autonomous and are linked by an interface or a set of programs. Typically, these programs simply convert the data from
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NAPRA WWW predicted nitrate losses to shallow groundwater Low Medium High Very high
FIGURE 30.7 NAPRA WWW predicted nitrate losses to shallow groundwater [28].
the GIS to a format that can be read by the model and the model output is converted for display in a GIS. GIS is primarily used for data management and spatial analysis capabilities in such interfaces. Various functions are also generally available in a GIS that can be used for modeling groundwater advection and dispersion. The first step in groundwater flow modeling is to determine the flow velocity and direction at each point in the flow field. A flow field can be generated using Darcy’s law for a regular grid. A volume balance can be computed for each cell. A zero volume balance residual might indicate a balance between inflow and outflow in a cell. This represents the steady state condition of groundwater flow.
30.6.8 Implementation of Policies Involving Spatial Dimensions Groundwater is clearly one of the most important natural resources. The government has mandated protection of groundwater systems through programs that identify and protect municipal wellfields by designating wellhead protection areas. A wellhead protection area (WHPA) is defined as the surface and subsurface areas surrounding a public well or wellfield through which contaminants are likely to move toward and reach the well or wellfield. Five general criteria in wellhead protection as identified by EPA are: (1) distance, (2) drawdown, (3) time of travel, (4) flow boundaries, and (5) assimilative capacity. A GIS can be used to integrate the above concepts and synthesize the inputs and outputs required for the analysis [33]. The analytical capabilities of GIS software can be used for site characterization. Both the logical and visual overlay functions, as well as distance measurement capabilities in a GIS, can be used to define conditions and locations meeting specified protection criteria.
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25
0
25
50 Miles
Probability of nitrate detection <25% 25–50% 50–75% 75–100%
FIGURE 30.8 Bayesian risk map of nitrate detections in groundwater using DRASTIC factors.
GIS technology can be used for supporting remedial investigation of groundwater contamination. GIS can be used to integrate several software packages required for assessing environmental contamination during site characterization. Interfacing GIS with a groundwater movement model, such as MODFLOW, can facilitate investigation of 3D plumes [34]. GIS technology helps organize data about problems occurring over a geographic region and understand their spatial association, and provides a powerful means of analyzing and synthesizing information of such problems. GIS can also provide information to decision makers about the limitations of the accuracy of the data and the final products produced by GIS analyses.
Glossary Buffer A zone of a specified distance around coverage features. Buffers are useful for proximity analysis (e.g., find all wetlands within 150 m of streams). Cell Basic element of spatial information in a grid or raster data set. Coordinate system A system used to measure horizontal and vertical distances on a planimetric map. Its units and characteristics are defined by a map projection. A common coordinate system is used to spatially register geographic data for the same area. Coverage A set of thematically associated data considered as a unit. A coverage usually represents a single theme or layer such as roads, streams, land use, or aquifer depth. Digitize To encode map features as x, y coordinates in a digital form. A digitizer (a table device with a cursor and keys for tracing map features) is used to create GIS coverages. Geographic data The locations and descriptions of geographic features. The composite of spatial data and descriptive data.
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Geographic database A collection of spatial data and related descriptive data organized for efficient storage and retrieval. Georeference To establish the relationship between coordinates on a planar map and known real-world coordinates. GIS Geographic information system. An organized collection of computer hardware, software, geographic data, and personnel to efficiently capture, store, update, manipulate, analyze, and display geographically referenced information. Intersect Topological integration of spatial data sets. Common analysis function within GIS software. Layer A set of thematic data stored for use within GIS. Layers organize data by subject matter (e.g., aquifer depths, slope, roads). Line A set of ordered coordinates that represent the shape of linear features within a GIS coverage or layer. Data such as streams and roads are commonly represented as lines. Map projection Conversion of locations on the Earth’s surface from spherical to planar coordinates. A projection is required to define a map’s coordinate system. Point An x, y coordinate that represents a geographic feature. Data representation technique used within GIS to represent small features such as well locations. Polygon A multisided figure used to represent an area on a map. A polygon is defined by series of arcs. Data such as the locations of soil series are commonly represented as polygons within a GIS coverage or layer. Raster A cellular or grid data structure composed of rows and columns. Groups of cells represent features such as land use or elevation. The value of each cell represents the value of the feature. Image and remotely sensed data is commonly stored in this format. Resolution Resolution is the accuracy at which a map scale can depict the location and shape of map features. As map scale decreases, resolution diminishes and feature boundaries must be smoothed, simplified, or not shown at all. Scanning Data input in raster format with a device called a scanner. Used to convert paper-based maps into GIS coverages or layers. Spatial analysis The process of modeling, examining, and interpreting model results. Spatial analysis is the process of extracting or creating new information about a set of geographic features. Spatial analysis is useful for evaluating suitability and capability, for estimating and predicting, and for interpreting and understanding. Spatial data Information about the location, shape of, and relationships among geographic features usually stored as coordinates and topology. Surface Representation of geographic information as a set of continuous data in which the map features are not spatially discrete. Surfaces are used to represent spatial features such as depth to groundwater and are generally created by fitting a surface to point data. Topology The spatial relationships between connecting or adjacent coverage features. Topology is useful in GIS because many spatial analysis functions do not require coordinates, only topological information.
References [1] Alterkawi, M.M. Measures towards a comprehensive municipal GIS-the case of Ar-Riyadh Municipality. Habitat International 29:689–698. 2005. [2] Griffin, C.B. Introduction to GIS for Public Agencies. Technical Report, Conservation Technology Information Center, State University of New York, College of Environmental Science and Forestry, Syracuse, NY, 1995. [3] Lim, K.J. and Engel, B.A. Extension and enhancement of national agricultural pesticide risk analysis (NAPRA) WWW decision support system to include nutrients. Computers and Electronics in Agriculture 38: 227–236. 2003.
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[4] Pandey, S., Gunn, R., Lim, K.J., Engel, B.A., and Harbor, J. Developing web-based tool to assess long-term hydrologic impacts of land use change: information technology issues and a case study. Journal of Urban and Regional Information System Association (URISA) 12: 5–17. 2000. [5] Lim, K.J. and Engel, B.A. RunOff MINimization (ROMIN) Web GIS for environment-friendly land use planning. 2004. http://pasture.ecn.purdue.eud/∼romin. Accessed September 2005. [6] Tang, Z., Engel, B.A., Choi, J., Sullivan, K., Sharif, M., and Lim, K.J. A Web-based DSS for erosion control structure planning. Applied Engineering in Agriculture 20:707–714. 2004. [7] Engel, B.A., Choi, J., Harbor, J., and Pandey, S. Web-based DSS for hydrologic impact evaluation of small watershed land use changes. Computers and Electronics in Agriculture 39: 241–249. 2003. [8] Lim, K.J., Engel, B.A., Tang, Z., Choi, J., Kim, K., Muthukrishnan, S., and Tripathy, D. Automated Web GIS-based hydrograph analysis tool, WHAT. Journal of American Water Resource Association 41(6):1407–1416. 2005. [9] Keen, K.L. and Queen, L.P. An approach for continuously monitoring the recharge flux to the water table: Integration of field monitoring, laboratory characterization, and theory within GIS framework. In D.L. Corwin and R.J. Wagnet (ed), Applications of GIS to the Modeling of Non-Point Source Pollutants in the Vadose Zone. 1996 Bouyaucos Conference, USDA-ARS. 1996. [10] Fayer, M.J., Gee, G.W., Rockhold, M.L., Freshley, M.D., and Walters, T.B., Estimating recharge rates for a groundwater model using GIS. In D.L. Corwin and R.J. Wagnet (ed), Applications of GIS to the Modeling of Non-Point Source Pollutants in the Vadose Zone. 1996 Bouyancous Conference, USDA-ARS. 1996. [11] Levine, N.S. The Development and Use of a GIS-Based Expert System for Hazardous Waste Landfill Siting. Ph.D. thesis, Purdue University, December, 1995. [12] Schubert, M., Pena, P., Balcazar, M., Meissner, R., Lopez, A., and Flores, J.H. Determination of radon distribution patterns in the upper soil as a tool for the localization of subsurface NAPL contamination. Radiation Measurement 40:633–637. 2005. [13] Winiwarter, W., Dore, C., Hayman, G., Vlachogiannis, D., Gounaris, N., Bartzis, J., Ekstrand, S., Tamponi, M., and Maffeis, G. Methods for comparing gridded inventories of atmospheric emissions — application for Milan province, Italy and Greater Athens Area, Greece. The Science of the Total Environment 303:231–243. 2003. [14] ESRI. Using ArcGIS Geostatistical Analyst. Redlands, CA. 2004. [15] Ruhaak, W. A Java application for quality weighted 3-d interpolation. Computers & Geosciences 32:43–51. 2006. [16] Follet, R.F., Shaffer, M.J., Brodahl, M.K., and Reichman, G.A. NLEAP simulation of residual soil nitrate for irrigated and non-irrigated corn. Soil and Water Conservation 49:375–382. 1994. [17] Tait, N.G., Davison, R.M., Whittaker, J.J., Leharne, S.A., and Lerner, D.N. Borehole Optimisation System (BOS) — A GIS-based risk analysis tool for optimising the use of urban groundwater. Environmental Modeling & Software 19:1111–1124. 2004. [18] Wylie, B.K., Shaffer, M.J., and Hall, M.D. Regional assessment of NLEAP NO3-N leaching indices. Water Resources Bulletin 31:399–408. 1995. [19] Luzio, M.D., Srinivasan, R., and Arnold, J.G. Integration of Watershed Tools and SWAT model into BASINS. Journal of the American Water Resources Association 38:1127–1141. 2002. [20] Dixon, B. Groundwater vulnerability mapping: A GIS and fuzzy rule based integration tool. Applied Geography 25:327–347. 2005. [21] Aller, L., Bennett, T., Lehr, J.H., and Petty, R.J. DRASTIC: A standardized system for evaluating groundwater using hydrogeologic settings. Technical report, USEPA EPA/600/2-85/0108, Robert S. Kerr Environmental Research Laboratory, Ada, OK. 1985. [22] Aller, L., Bennet, T., Lehr, J.H., Petty, R.J., and Hackett, G. DRASTIC: A standardized system for evaluating groundwater pollution using hydrogeologic settings. Technical report, USEPA EPA-600/2-87-035. 1987. [23] Navulur, K.C. and Engel, B.A. Groundwater vulnerability assessment to nonpoint source nitrate pollution on a regional scale using GIS. Transaction of ASAE 41:1671–1678, 1998.
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[24] Quisenberry, V.L., Smith, B.R., Phillips, R.E., Scott, H.D., and Norcliff, S. A soil classification system for describing water and chemical transport. Soil Science Society of America Journal 156:306–315. 1993. [25] Lin, H.S., McInnes, K.J., Wilding, L.P., and Hallmark, C.T. Effects of soil morphology on hydraulic properties: I. Quantification of soil morphology. Soil Science Society of America Journal 63:948–953. 1999. [26] Scott, H.D. Soil Physics: Agricultural and Environmental Applications. Ames, IW: Iowa State University Press. 2000. [27] Leonard, R.A., Knisel, W.G., and Still, D.A. 1987. GLEAMS: Groundwater loading effects of agricultural management systems. Transactions of ASAE 30:1403–1418. [28] Lim, K.J., Engel, B.A., and Tang, Z. Identifying regional groundwater risk areas using a WWW GIS model system. Accepted for the Special issue of International Journal of Risk Assessment and Management. 2006. [29] Bates, L.E., Barber, C., and Otto, C.J. Aquifer vulnerability mapping using GIS and Bayesian weights of evidence: Review of application. In Hydro GIS, Vienna, Austria, 1996. [30] Bonham-Carter, G.F. Geographic Information Systems for Geoscientists: Modeling with GIS. Computer Methods in Geosciences 13:302–303. 1994. [31] Watkins, D.W., McKinney, D.C., Maidment, D.R., and Lin, M., Use of Geographic Information Systems in Ground-Water Flow Modeling. Water Resources Planning and Management 122:88–96. 1996. [32] Fetter, C.W. Applied Hydrogeology. Third Edition. Prentice Hall, Upper Saddle River, NJ, USA. 1994. [33] Vieux, B.E., Mubaraki, M.A., and Brown, D. Wellhead protection area delineation using a coupled GIS and groundwater model. Journal of Environmental Management 54:205–214. 1998. [34] Juan, C.S. and Kolm, K.E. Conceptualization, characterization and numerical modeling of the Jackson Hole alluvial aquifer using Arc/INFO and MODFLOW. Engineering Geology 42:119–137. 1996.
Further Information Aronoff, S. 1989. Geographic Information Systems: A Management Perspective, WDL Publications, Ottawa, Canada. Bolstad, P. 2002. GIS Fundamentals: A First Textbook on Geographic Information Systems. Eider Press, OH. Clarke, K.C. 1997. Getting Started with Geographic Information Systems. Prentice Hall, Upper Saddle River, NJ. Corwin, D.L., Loague, K., Bigham, J.M., Kral, D.M., and Viney, M.K. 1996. Applications of GIS to the Modeling of Non-Point Source Pollutants in the Vadose Zone, SSSA No. 48. Soil Science Society of America, Madison, WI. Goodchild, M.F., Parks, B.O., and Steyart, L.T. (ed). 1993. Environmental Modeling with GIS. Oxford University Press, New York NY. Goodchild, M.F., Steyaert, L.T., Parks, B.O., Johnston, C., Maidment, D., Crane, M., and Glendinning, S. (eds). 1996. GIS and Environmental Modeling: Progress and Research Issues. GIS World, Fort Collins, CO. Heit, M. and Shortreid, A. 1991. GIS Applications in Natural Resources, GIS World, Fort Collins, CO. Longley, P.A., Goodchild, M., Maguire, D.J., and Rhind, D.W. 2002. Geographic Information Systems and Science. John Wiley & Sons, New York, NY. Maguire, D., Goodchild, M., and Rhind, D. (eds). 1991. Geographical Information Systems. John Wiley & Sons, New York, NY. Pinder, G.F. 2002. Groundwater Modeling Using Geographic Information Systems. John Wiley & Sons, New York, NY.
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31 Biodegradation 31.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31-1 Subsurface Microbiology and Geochemistry • Environmental Conditions That Influence Biodegradation • Biotransformations • Limits to Biodegradation
31.2 Quantitative Description of Reactive Transport and Biodegradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31-12 Microbial Reaction Kinetics • Sorption as a Reactive Kinetic Process • Microbial Reactions and Sorption in a Batch System • Microbial Reaction, Sorption, and Transport
31.3 Field Applications of Bioremediation . . . . . . . . . . . . . . . . . . 31-20 Intrinsic Bioremediation • Engineered Bioremediation • Case Histories • Emerging Technologies
Loring F. Nies and Chad T. Jafvert Purdue University
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31-22 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31-23 Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31-27
31.1 Introduction The objective of this chapter is to present the basic principles and concepts of groundwater microbiology and transport processes as they relate to biodegradation. Understanding of these processes is necessary to model, forecast, and manipulate subsurface contaminant transport and biodegradation. The basic principles presented may be applied to the biorestoration of contaminated groundwater, a field now commonly called “bioremediation” (Lee et al., 1988; National Research Council 1993; Thomas and Ward 1989).
31.1.1 Subsurface Microbiology and Geochemistry 31.1.1.1 Basic Microbiology Microorganisms mediate the biotransformation of many different chemicals in the subsurface. Historically there has been much scientific debate over the relative contribution of abiotic and biotic chemical processes in the subsurface. Until the last 50 years, very little was known about microorganisms in groundwater, and thus abiotic transformations were thought to dominate. However, more recent research has contributed new knowledge about microbial life in the subsurface and this view has changed. While our understanding of subsurface microbiology and biogeochemistry is far from complete, biologically mediated reactions of both inorganic and organic compounds in groundwater are known to be significant, and in many cases control groundwater chemistry (Chapelle, 1993). With respect to the biotransformation of organic 31-1
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pollutants, microbially mediated reactions are by far the most important. The abiotic transformation of pollutants does occur (e.g., dehalogenation, polymerization, and hydrolysis reactions), however, the environmental significance of these abiotic reactions relative to microbially mediated reactions is difficult to assess. This is partly due to the difficulty in distinguishing between abiotic and biotic processes in situ. In addition, certain abiotic reactions are dependent on two environmental parameters that are often controlled by microbial processes, redox, and pH. Thus these latter types of abiotic reactions are indirectly mediated by microorganisms as well. Microorganisms can be classified in a number of different ways (e.g., phylogenetically). However, for the purpose of understanding biodegradation, it is most useful to begin the characterization of microorganisms according to their source of energy and their source of carbon for cell growth. Potential energy sources are organic carbon (including pollutants), inorganic compounds, and sunlight. Microbes that oxidize organic compounds to obtain energy are organotrophs and those that oxidize inorganic compounds are lithotrophs. Potential sources of carbon for cell growth are either organic carbon or inorganic carbon (HCO− 3 , CO2 ). Microbes that degrade organic compounds to obtain carbon for the synthesis of cellular constituents are heterotrophs and those that utilize inorganic carbon are autotrophs. Logically, most lithotrophs are also autotrophs and most organotrophs are also heterotrophs. Photoautotrophs and photoheterotrophs may exist in groundwater, but their utilization of photometabolism is obviously limited by access to sunlight (Brock et al., 1997; Gottschalk, 1986). The types of microorganisms found in groundwater include protozoa, fungi, bacteria (this chapter includes both bacteria and archaea), and viruses. For purposes of examining microscale phenomena (biodegradation) relative to macroscopic subsurface particle and pore sizes, it is useful to consider the size of the microorganism. Protozoa have a size range of approximately 2 to 200 µm, the smallest single-celled fungi are approximately 2 µm, and bacteria range in size from 0.1 to 15 µm, although a bacterium which is 500 µm long has recently been discovered. Viruses are much smaller, ranging from approximately 0.01 to 0.1 µm (Brock et al., 1997). Protozoa are relatively large heterotrophic microorganisms whose distribution in groundwater has not been thoroughly studied. Protozoa are not known to be significant biodegraders of organic pollutants, although many protozoa do feed on bacteria. This predation is thought to reduce bacterial numbers in some groundwater (Chapelle, 1993). Thus, it is possible that protozoa could indirectly and adversely influence biodegradation rates in groundwater by reducing populations of pollutant biodegrading bacteria. Some protozoa are also human pathogens; therefore their distribution in groundwater is a public health interest (e.g., Entamoeba histolytica, the causative agent of dysentery). Drinking water is the primary route of human exposure to pathogenic protozoa. Fortunately, the cysts of the problematic pathogenic protozoa Cryptosporidium and Giardia are primarily detected only in surface waters (LeChevallier and Norton, 1995). However, groundwater under direct influence of surface water also very frequently tests positive for Cryptosporidium and Giardia (Hancock et al., 1998). Fungi are heterotrophic biodegraders of immense capability. There are many types of single-celled microscopic fungi as well as multicelled macroscopic organisms, such as mushrooms. The ability of fungi to biodegrade organic pollutants is well known; however in groundwater the bacteria dominate in terms of both biomass and as catalysts of biodegradation. Therefore, all microbial biodegradation discussed in this chapter can be assumed to be mediated by bacteria, unless stated otherwise. Viruses are obligate parasites whose hosts include bacteria as well as macroscopic organisms. The transport and survival of viruses in groundwater is of interest with respect to the control of infectious diseases (Bitton et al., 1983). Viruses have no catabolic capability and therefore do not contribute directly to biodegradation. The influence of the viral infection of bacteria on biodegradation, and on microbial ecology in general, has not been systematically examined. As viruses are essentially containers of genetic material that is inserted into the host, they can be used as gene vectors to insert desirable genetic information (e.g., biodegradation genes) into bacteria. While this type of technology is available in the laboratory, it is not currently used in the field. Bacteria are ubiquitous in groundwater, and in addition, they have very diverse catabolic abilities, morphology, physiology, and biochemical constituents. This diversity allows bacteria to survive in some
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of the most extreme environments on earth. Bacteria have been found up to 2.8 km below the surface (Fredrickson and Onstott, 1996). Although they are microscopic, bacteria are the dominant biodegraders and drivers of biogeochemical cycling in groundwater. Bacteria live attached to subsurface particles as individuals or in colonies and also as unattached motile organisms. Attached microbes conserve energy while removing nutrients from the surrounding water, as well as deriving some protection from predation. The growth and survival of attached organisms is dependent on obtaining nutrients by transport through groundwater. Motile organisms are known to move in response to chemical gradients (chemotaxis), moving toward higher concentrations of nutrients and away from toxics. Bacterial transport in groundwater and environmental factors that induce bacteria to exhibit attached or motile phenotypes have been studied (Dawson et al., 1981; Fletcher and Marshall, 1982; Corapcioglu and Haridas, 1984, 1985; Harvey et al., 1989). However, our ability to control and influence these processes in the subsurface to promote biodegradation is still under development (Gentry et al., 2004). 31.1.1.2 Basic Metabolism All living organisms obtain energy by mediating oxidation/reduction reactions. Reduced organic and inorganic compounds serve as the reductant (electron donor) in the reaction. Oxidized, usually inorganic, species serve as the oxidant (electron acceptor). Aerobic respiring organisms utilize oxygen, which is the most ubiquitous electron acceptor in the environment, as an oxidant. However, the solubility of oxygen in water is relatively low (∼8 mg/l @ 20◦ C) and the oxygen diffusion rate is slow, therefore, the availability of oxygen in groundwater is significantly limited by mass transfer. A variation of typical oxidation/reduction reactions occurs when a fraction of a compound is oxidized and the remaining fraction is reduced. This type of catabolism is called fermentation, in contrast to respiration. Almost all fermenting bacteria cannot tolerate oxygen and are found in anaerobic environments living in close association with sulfate reducing or methanogenic bacteria (Brock et al., 1997; Chapelle, 1993; Gottschalk, 1986). Organisms have evolved elegant mechanisms for converting the electron transfer that occurs during oxidation/reduction reactions into energy. Respiring organisms oxidize their energy source, stripping off the high energy electrons. The electrons are shuttled on electron carriers (NADH) to the cell membranes where electron transport phosphorylation occurs (Figure 31.1). Respiring organisms use electron transport to pump protons across the membrane to create a pH differential (charge and proton gradient) between the inside and outside of the cell. In this energized state, protons are driven by the gradient through specialized enzymes which convert the “proton motive force” into stored chemical energy, adenosine triphosphate (ATP). Driving the proton pumps consumes the electron’s energy. At the terminal end of the electron transport chain the now low energy electrons are transferred to a terminal electron acceptor. Fermenting bacteria make ATP through the direct conversion of chemical bond energy, in a process called “substrate level phosphorylation (SLP).” The energy-producing steps primarily occur during oxidation of carbonyl groups (Figure 31.2). As no external electron acceptor is utilized, and biological electron carriers are in limited supply and must be recycled, the electrons generated from the energyproducing oxidations of SLP must be discarded. This is accomplished by reducing some of the substrate, producing alcohols, or by reducing protons, producing hydrogen. Thus fermenters produce a mixture of both oxidized and reduced products such as CO2 , carboxylic acids, alcohols, and H2 . Anaerobic respiration occurs when oxygen is depleted and other suitable oxidized species are available to act as an electron acceptor. Common anaerobic electron acceptors are oxidized nitrogen compounds ◦ (nitrate, nitrite), iron(III), oxidized sulfur compounds (sulfate, sulfite, S ), and CO2 . Other oxidized inorganic species are utilized in anaerobic respiration as well, and in addition, some organic compounds, such as fumarate, may also serve as electron acceptors (Zehnder, 1988). The widespread existence of anaerobic respiration can be exploited for groundwater remediation when the contaminants of interest can function as microbial electron acceptors. Examples include nitrate, nitrite, perchlorate, chlorate, and oxidized species of chromate and arsenate. It is critically important to have a thorough understanding of the chemodynamics of inorganic species, particularly chromate and arsenate for example, as redox transformations alter speciation, solubility, and toxicity. Reduction of chromate species reduces mobility
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(decane) O2
Alkane hydrocarbon biodegradation CH2OH O
COOH β-oxidation (n)CH3C)CoA (decanoic acid) (acetyl-coenzyme A)
Electron transport NAD+ phosphorylation (electron shuttle) e– NADH
TCA cycle
H+
CO2 OH COOH CHO O2
CO2 ATP] (energy)
Aromatic hydrocarbon biodegradation
O2 OH
(benzene)
O2 Potential – NO 3 electron acceptors R–Cl
OH (catechol)
H+
H2O NO2– R–H +Cl–
FIGURE 31.1 Idealized schematic of hydrocarbon biodegradation by a respiring organism. ATP
NADH + (electron shuttle) NAD
2 CH3CHO
CH3COOH
CH3CH2OH
FIGURE 31.2 Schematic of fermentation.
and toxicity, while reduction of arsenate species may actually increase mobility in some instances. Therefore, redox transformations of inorganics may be desirable or undesirable and their long-term impacts must be assessed as well. Perchlorate is one inorganic groundwater contaminant with a high potential for successful biological transformation to the harmless end-product, chloride ion (Logan, 1998, 2001). Acquisition of fundamental knowledge about the microbiology and genetics of perchlorate reduction has been very significant (Bender et al., 2005). Bacteria obtain less energy from using electron acceptors other than oxygen. The amount of energy obtained from the oxidation of a given substrate is proportional to the reduction potential (E ◦ ) of the electron acceptor (Table 31.1). Electron acceptors that yield the largest amount of energy (e.g., oxygen) tend to be utilized preferentially over others that are available, probably because bacteria with access
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31-5 TABLE 31.1 Reduction Potentials of Important Biological Oxidants (electron acceptors) E ◦ (Volts) 1 O (g) + H+ + e− = 1 H O 4 2 2 2 1 MnO (s) + 1 HCO− (10−3 ) + 3 H+ + e− = 1 MnCO (s) + H O 2 3 2 3 2 2 2 2 1 NO− + H+ + e− = 1 NO− + 1 H O 2 3 2 2 2 2 1 NO− + 4 H+ + e− = 1 NH+ + 1 H O 2 4 3 3 2 6 6 −3 + − FeOOH(s) + HCO− 3 (10 ) + 2H + e = FeCO3(s) + 2H2 O 1 SO2− + 4 H+ + e− = 1 S(s) + 2 H O 4 3 3 2 6 6 1 S(s) + H+ + e− = 1 H S(g) 2 2 2 1 CO (g) + H+ + e− = 1 CH (g) + 1 H O 2 4 8 8 4 2 H+ + e− = 12 H− 2
0.820 0.527 0.423 0.344 −0.047 −0.195 −0.243 −0.244 0.414
Values apply for unit activity (1 M or 1 atm) in water at pH 7.0 and 25◦ C, except −3 M which more typically represents environmental conditions. HCO− 3 = 10 ◦ G = −nFE ◦ , where n is the number of electrons transferred and F is Faraday’s constant. F = 96.5 kJ/V-mol. Source: Adapted from (Brock, T.D., M.T. Madigan, J.M. Martinko, and J. Parker. 1997. Biology of Microorganisms, Prentice Hall, Upper Saddle River, NJ.; Stumm, W. and J.J. Morgan. 1981. Aquatic Chemistry, John wiley & Sons, Inc., New York.; Thauer R.K., K. Jungermann, and K. Decker. 1977. Bacteriol. Rev., 41:100–180.)
to more energy can grow faster and compete for resources more successfully. In addition, biochemical mechanisms exist that maximize energy production. For example, facultative aerobes that can use both oxygen and nitrate as electron acceptors are common. The presence of oxygen inhibits synthesis of the enzyme at the terminus of the electron transport chain that transfers electrons to nitrate (nitrate reductase), thus ensuring more energetically favorable oxygen utilization whenever possible. During biodegradation of organic compounds, large molecules are broken down into small molecules, which are oxidized, yielding electrons for energy production. For example, aromatic rings are cleaved open to form aliphatic chains, which are then cleaved into two-carbon pieces, which are subsequently oxidized to CO2 (Figure 31.1). Likewise, long alkanes are cleaved into two-carbon pieces prior to oxidation to CO2 . However, the initiation of biodegradation of many compounds requires “activation” by the insertion of molecular oxygen (O2 ) into the hydrocarbon, forming mono- and dihydroxylated compounds. Oxygenase enzymes perform this function. Once activated by oxygenase enzymes, further biodegradation of hydrocarbons often does not require molecular oxygen. An exception is the biodegradation of aromatic rings, during which oxygen is used as a reactant for ring activation and ring cleavage. Thus, it should be observed that oxygen can be utilized by bacteria as both an electron acceptor and as a reacting co-substrate for initiating biodegradation reactions. A critical issue in biodegradation is that there are many alternatives to oxygen as an electron acceptor, while there are few alternatives to oxygen as a reactant for initiating hydrocarbon biodegradation. For this reason, when more rapid and complete biodegradation of certain hydrocarbons is desired, aerobic conditions are preferred. The bioremediation of groundwater aquifers that are contaminated with hydrocarbons is often limited by insufficient oxygen. Hydrogen peroxide, which decomposes to oxygen, is often used as a highly soluble source of oxygen for groundwater systems (Pardieck et al., 1992). One good alternative to oxygen as an electron acceptor is nitrate (NO− 3 ). Significant research also has been devoted to the feasibility of using nitrate as a supplemental electron acceptor (Dolfing et al., 1990; Evans et al., 1991; Hutchins, 1991a, 1991b). Nitrate is more soluble in water than oxygen, is a strong oxidant, and could potentially be more readily introduced into groundwater aquifers through injection wells. Interestingly, many monoaromatic compounds (BTEX) are biodegraded under anaerobic nitrate reducing conditions, although unlike oxygen, the nitrate is used only as an electron acceptor and not as a reactant in biotransformation reactions. Nitrate has relatively low toxicity, but does have known health
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hazards (methemoglobinemia) and is a regulated drinking water contaminant, and therefore, is used as a supplemental electron acceptor only under carefully controlled situations.
31.1.2 Environmental Conditions That Influence Biodegradation The activity and types of microorganisms present in groundwater are greatly influenced by subsurface physical and chemical properties (Alexander, 1994). Biodegradation kinetics are generally highly dependent on temperature because enzyme function is temperature sensitive. Bacteria can be classified by the range of temperature within which they can grow. At optimum temperatures biodegradation kinetics reach maximum rates, while slightly above optimum temperature, cell constituents usually begin to degrade. As temperatures decrease below the optimum, biodegradation rates decrease until enzymes function at rates too slow to support growth. Temperature extremes will select for climate-adapted organisms. For example, cold-loving bacteria (psychrophiles) can grow at temperatures below 0◦ C and generally die at temperatures greater than 20◦ C. Mesophilic bacteria thrive at temperatures that are comfortable to humans. Although the vast majority of biodegradation studies have been done with mesophilic bacteria at temperatures ranging between 15 and 45◦ C, some evidence exists that suggests that psychrophilic (or at least psychrotolerant) (Kellems et al., 1994) and thermophilic bacteria also possess pollutant biodegrading ability (Chen and Taylor, 1995). Bacteria can also be classified according to the pH range within which they can grow. Our knowledge of biodegradation has been derived chiefly from studies conducted in the “neutral” pH range between approximately 6 and 8. Most groundwater falls within this pH range as well. Acidophilic bacteria can tolerate a pH as low as 2, although most are lithoautotrophs that do not degrade organics. Alkaline conditions exist (pH 9 to 11) in certain areas where carbonate rocks predominate. Sodium concentrations in these alkaline environments are often more than 10× greater than seawater, thus indigenous bacteria are halophiles in addition to their adaptation to extreme pH. Knowledge of pollutant biodegradation in extreme pH environments is scarce. Bacteria are sensitive to salinity. Halophilic bacteria have evolved a mechanism to counteract the tendency for cells to become desiccated by high salt concentrations. Numerous studies have demonstrated that marine bacteria are capable of hydrocarbon biodegradation, however, knowledge about pollutant biodegradation by extreme halophiles is lacking. Because a primary concern is the bioremediation of contaminated aquifers that are sources of potable water, acquiring knowledge about organisms adapted to extreme environments has not been a high priority. All living things, including bacteria require inorganic nutrients for growth, in addition to a source of energy and carbon. Nitrogen and phosphorus are the nutrients that are most likely to be a limiting factor for biodegradation and, similar to agricultural applications, are often added to the environment to remove potential nutrient limitations. Oxidation/reduction potential is by definition the electrical potential (in volts) of the oxidation/reduction reaction occurring between the electron donor and electron acceptor. In practice, when considering conditions in the environment the term “redox” potential is commonly used. Redox potential typically refers to the reduction potential of the dominant electron acceptor in the environment. Probes are available to measure environmental redox potential; however, when assessing biodegradation, actual measurement of the electron acceptor of interest is more useful. For example, if aerobic biodegradation is desired oxygen concentrations should be monitored. Likewise, the simultaneous disappearance of nitrate and organics, with the concurrent appearance of nitrite is better circumstantial evidence of the existence of denitrifying bacteria than a redox measurement. More reducing, anaerobic conditions can be inferred from measurements of sulfate, sulfide, and the production of methane, as well as redox measurements.
31.1.3 Biotransformations Bacteria biodegrade organic compounds by breaking large molecules apart with an array of biotransformation reactions such as hydrolysis, oxidation, reduction, dehalogenation, deamination,
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TABLE 31.2
Biotransformation Reactions Mediated by Oxygenase Enzymes
Biotransformation Deamination Dehalogenation Ether cleavage Aromatic ring hydroxylation Aromatic ring fission Alkane hydroxylation
Compound
Reference
Aniline Pentachlorophenol 2,4,-dichlorophenoxyacetate Benzene Benzene Octane
Bachofer et al. (1975) Xun et al. (1992) Tiedje and Alexander (1969) Gibson (1984) Gibson (1984) Watkinson and Morgan (1990)
decarboxylation, and rearrangement reactions. As mentioned previously, molecular oxygen participates directly in a number of biotransformation reactions (Table 31.2). Anaerobic bacteria can perform many of the biotransformation reactions listed in Table 31.2 by different mechanisms without molecular oxygen (Schink, 1988). In addition, anaerobic bacteria can mediate reductive dehydroxylation, reductive deamination, and reductive dehalogenation reactions. Of these, reductive dehalogenations are of the greatest interest with respect to the biotransformation of hazardous pollutants. No anaerobic bacteria have been shown to be able to hydroxylate alkanes, thus saturated hydrocarbons persist under anaerobic conditions. While BTEX biodegradation by denitrifying and iron reducing bacteria has been well documented, and a few reports of aromatic hydrocarbon degradation under sulfate reducing and methanogenic conditions exist, detailed knowledge about the biochemistry of anaerobic aromatic hydrocarbon transformation is limited (Evans, 1988; Lovley et al., 1989; Lovley and Lonergan, 1990). In most cases, bacteria biodegrade organic compounds to obtain energy for growth. Due to the relaxed specificity of some enzymes, bacteria perform certain biotransformation reactions on compounds that are not growth substrates. The term “cometabolism” can be broadly taken to mean the “gratuitous biotransformation of a compound from which the organism derives no benefit.” Often these gratuitous reactions produce products that can be more easily biodegraded by other organisms. 31.1.3.1 Hydrocarbons Biodegradation of alkanes is usually initiated with terminal hydroxylation by a monooxygenase enzyme and subsequent oxidation of the alcohol to a carboxylic acid. The initial step requires oxygen, and thus far, no other anaerobic mechanism for the initiation of biodegradation of alkanes has been reported. The carboxylic acid can easily be further oxidized to CO2 through two nearly universal biochemical pathways, ß-oxidation and the Krebs (tricarboxylic acid) cycle (Figure 31.1). Branched alkanes can be more difficult to degrade depending on the degree of branching. Branching interferes with ß-oxidation and significant branching can result in complete inhibition of biodegradation (Watkinson and Morgan, 1990). Alkenes can be aerobically biodegraded similarly to alkanes, however the double bond can also be hydrolyzed to initiate biodegradation under anaerobic conditions (Schink, 1988). As alkanes have relatively low water solubilities they are less of a hazard to migrate as soluble constituents of groundwater. Biodegradation of alkanes often occurs at the hydrocarbon/water interface and is mediated by bacteria that produce biosurfactants for hydrocarbon uptake. As described previously, aerobic biodegradation of aromatic compounds is initiated by the hydroxylation of the ring by oxygenase enzymes. Ring cleavage also requires oxygen. The aromatic compounds of most common concern are benzene, ethylbenzene, toluene, o-xylene, m-xylene, and p-xylene (BTEX). Initiation of the biodegradation of the alkylbenzenes occurs either by dioxygenase attack on the aromatic ring or by monooxygenase attack on the alkyl group followed by a dioxygenase mediated ring cleavage (Smith, 1990). Biodegradation rates are generally observed in the following order which may vary from site to site: toluene, ethylbenzene > benzene > m-xylene, p-xylene > o-xylene. BTEX are constituents of gasoline and therefore often appear together as a mixture in contaminated groundwater. Interactions between bacteria and BTEX mixtures may be complex and site-specific (Alvarez and Vogel, 1991). Biodegradation of monoaromatic hydrocarbons (e.g., toluene, ethylbenzene) also occurs under anaerobic
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nitrate reducing conditions. Benzene appears to be more recalcitrant under anaerobic conditions than other monoaromatics. The biodegradation of aromatic rings has also been observed under iron reducing, sulfate reducing, and methanogenic conditions (Grbic-Galic and Vogel, 1987; Lovley et al., 1989; Edwards et al., 1992). Simple nonhalogenated hydrocarbon solvents such as ethanol, methanol, and acetone are easily biodegraded at dilute concentrations (e.g., 0.1% or less). The cyclical ethers, and ether structures in general, are typically recalcitrant; however the biodegradation of furans and 1, 4-dioxane has been reported, although biochemical mechanisms and the distribution of this ability in the environment remains unknown. Space limitations prohibit an exhaustive review of the biodegradation of all large production organics that might be found in groundwater, but several more complete references are available (Gibson, 1984; Howard, 1989; Leahy and Colwell, 1990; Young and Cerniglia, 1995). 31.1.3.2 Halogenated Compounds Halogenated organic compounds are among the most problematic environmental pollutants encountered (Chaudhry and Chapalamadugu, 1991). Halogenation typically increases environmental stability and toxicity, and significantly alters the kinds of biochemical and chemical reactions compounds undergo (Vogel et al., 1987). Halogenation increases the oxidation state of a compound relative to analogous nonhalogenated compounds, and this significantly influences biodegradation as well. Several reviews of microbial transformation of halogenated compounds exist (Fetzner and Lingens, 1994; Mohn and Tiedje, 1992; Neilson, 1990). Biodegradation of halogenated compounds can be considered from two perspectives, bioenergetics and biochemical mechanisms. In general, extremely oxidized compounds are thermodynamically less favorable electron donors than reduced compounds, and therefore, as the degree of halogenation (and oxidation) increases compounds have fewer and fewer electrons to give up as electron donor and they potentially would yield correspondingly less energy when microorganisms oxidize them. Alternatively, polyhalogenated compounds are potentially good electron acceptors (Figure 31.3). Halogenated compounds acting as electron acceptors can undergo a reaction called reductive dehalogenation, in which two electrons are transferred to the compound, the halogen leaves as a halide ion, and is replaced by a hydrogen atom. Depending on the degree of halogenation, and the type of environment and microorganisms present where it is found, halogenated compounds may be used as either electron donors or electron acceptors, with the more halogenated compounds making better electron acceptors and the less halogenated compounds making better electron donors. Consideration of thermodynamics suggests that sequential anaerobic dechlorination followed by aerobic biodegradation would be successful. Halogenated organics influence biodegradation mechanistically because of the large atomic size of halogens relative to hydrogen (which halogens usually replace), halogen electronegativity, and the strength of the carbon–halogen bond. Halogen size may prevent biochemical reactions simply due to steric hindrance. Halogen electronegativity causes charge separation in bonds and may result in dipole moments in molecules, profoundly affecting chemical reactivity. For example, halogen substitution may result in compounds more susceptible to nucleophilic substitution reactions (e.g., hydrolysis) whereas many oxygenases enzymes are strong electrophiles that are better suited to attack saturated non-halogenated hydrocarbons. Strong bonds require large activation energies for cleavage and may prevent reactions from occurring. For example, the carbon–fluorine bond is exceptionally strong and is rarely broken during biological processes. 31.1.3.3 Halogenated Aliphatic Solvents The halogenated aliphatic solvents that are most commonly found in groundwater are the chlorinated methanes (e.g., carbon tetrachloride (CCl4 )) and chlorinated ethenes (tetrachloroethene or “perc” (PCE) and trichloroethene (TCE)) (Vogel et al., 1987; Schwarzenbach et al., 1993). Under anaerobic conditions, PCE can undergo stepwise reductive dechlorination to TCE, then dichloroethene (DCE), chloroethene (i.e., vinyl chloride (VC)), and finally ethene. The rates of dechlorination tend to be proportional to the number of chlorine, thus PCE dechlorinates faster than dichloroethene. In groundwater systems where PCE and TCE undergo reductive dechlorination, vinyl chloride often accumulates. As vinyl chloride is a
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E '(Volts) 1.2
Halogenated Solvents Alkane
Alkene
1.0
Halogenated Solvents R-H R-X
O2/H2O 0.8
0
Halogenated Aromatic Ar-X Ar-H
NO3− /NO2− 0.4
0.2
0.0
−0.2
−0.4
Fe 3+/ Fe 2+
SO42− / HS− CO2 / CH4 H+/H2
FIGURE 31.3 Redox potentials of biological electron acceptors and chlorinated compounds. (Brock, T.D., M.T. Madigan, J.M. Martinko, and J. Parker. 1997. Biology of Microorganisms, Prentice Hall, Upper Saddle River, NJ.; Dolfing, J. and B.K. Harrison. 1992. Environ. Sci. Technol., 26:2213–2218.; Thauer R.K., K. Jungermann, and K. Decker. 1977. Bacteriol. Rev., 41:100–180.; Holmes, D.A., Harrison, B.K., and Dolfing, J. 1993. Environ. Sci. Technol., 27:725–731.; Schwarzenbach, R.P., P.M. Gbchwend, and D.M. Impoden. 1993. Environmental Organic Chemistry, John wiley & Sons, Inc., New York.; Vogel, T.M., Criddle, C.S., and McCarty P.L. 1987. Environ. Sci. Technol., 21: 2213–2218.)
known human carcinogen, the presence of this metabolite is extremely undesirable. It has recently been elucidated that there is a genetic basis for this phenomena and detection methods for the microbial ability to completely dechlorinate chloroethenes to ethene have been developed (Löffler et al., 2000). These novel microorganisms carry out “halorespiration” during which the chlorinated solvent is utilized as an energy producing electron acceptor. Molecular techniques have been used to characterize microbial communities with halorespiring capabilities at chlorinated solvent contaminated sites throughout North America and Europe (Hendrickson et al., 2002). Despite a generally poor history of success with bioaugmentation attempts, more recently a large number of successful field demonstrations have been completed with halorespiring bacteria (Ellis et al., 2000; Major et al., 2002). Advances and applications of halorespiration bioaugmentation in chlorinated solvent contaminated aquifers have been so substantial that the US Environmental Security Technology Certification Program commissioned a study to document them (Parsons Engineering Science, Inc., 2002).
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Aerobically, TCE, DCE, and VC, but typically not PCE, can be co-metabolized by certain bacteria with monooxygenase enzymes. This phenomenon can potentially be exploited for use in the restoration of contaminated aquifers. These bacteria require specific growth substrates (e.g., methane or phenol) which induce synthesis of the monooxygenase enzymes that act on the chlorinated compounds. The metabolites of (at least TCE) co-metabolism are potentially toxic, and kill the cells mediating the reaction. As the growth substrate and the co-metabolized pollutant both compete for the same reactive enzyme site, a balance must be achieved between maintaining sufficient growth rates and acceptable degradation rates. Optimizing growth with excessive substrate could inhibit degradation of the pollutants, while low substrate concentrations may not induce the monooxygenase enzymes and biomass could be lost due to the production of suicide metabolites. For effective biodegradation, cell growth and pollutant biotransformation could potentially be separated in either space or time. This could be accomplished in groundwater by alternating periods of growth enhancement (adding growth substrate) with periods of starvation (Alvarez-Cohen and McCarty, 1991; Nelson et al., 1987). 31.1.3.4 Halogenated Aromatic Compounds The biodegradation of halogenated aromatic compounds is highly dependent on the position and number of halogen substituents (Reineke and Knackmuss, 1988). It is useful to subdivide halogenated aromatics into two groups, non-ionizable compounds and ionizable compounds. PCBs and chlorobenzenes are examples of non-ionizable halogenated aromatic compounds found in the environment. In general, increased halogen substitution results in greater hydrophobicity. Therefore, the more soluble, less chlorinated PCB and chlorobenzene congeners are a greater threat to migration in groundwater relative to more highly chlorinated congeners. The biodegradation of PCBs and chlorobenzenes is highly dependent on the degree of chlorination as well (Furukawa et al., 1978; Bedard and Haberl, 1990). PCBs and chlorobenzenes can be aerobically degraded similar to non-halogenated aromatics; however, chlorine substitution often inhibits one or more enzymatic reactions. Thus, less chlorinated congeners are significantly more easily biodegraded by aerobic microorganisms than highly chlorinated compounds. Anaerobically, highly chlorinated PCBs and chlorobenzenes undergo microbially mediated reductive dechlorination to less chlorinated congeners that could potentially be biodegraded aerobically, but tend to persist under anaerobic conditions (Abramowicz, 1990). A well-documented field demonstration of PCB bioremediation was described by Harkness et al. (1993) during which it was found that bioavailability of PCBs severely limited biodegradation. The behavior of ionizable aromatic compounds, such as phenols, anilines, and benzoates, is dependent on groundwater pH. For example, at a typical pH of 7, greater than 99% of the dissolved pentachlorophenol (PCP) (pKa = 4.75) will exist in the more soluble, less hydrophobic, ionized form. Unlike most PCB and chlorobenzene congeners, the complete biodegradation of PCP to CO2 occurs under both aerobic and anaerobic conditions. In the better understood aerobic process, a single microorganism can catabolize PCP for energy and carbon. Anaerobically, PCP is sequentially dechlorinated to phenol, which can be further degraded to methane and CO2 . Relatively little is known about the microbiology and biochemistry of anaerobic PCP biodegradation (Haggblom and Valo, 1995; McAllister et al., 1996).
31.1.4 Limits to Biodegradation It should be mentioned that the environmental conditions that influence biodegradation and the limits to biodegradation are intrinsically related, and therefore, should not necessarily be viewed as separate topics. The most extreme limit to biodegradation is the absence of any known biochemical mechanism for the transformation of a specific compound (McCarty and Semprini, 1993). Discoveries of new transformations and microbial evolution of new enzymes will continue to challenge this limitation (Shannon and Unterman, 1993). Biodegradation potential can often be predicted from structure-activity models and a review of the biodegradation literature (Scow, 1990; Huesemann, 1995). However, as microbial distribution and environmental conditions are extremely heterogeneous, actual site-specific assays, such as laboratory treatability studies, provide the most reliable evidence that in situ biodegradation is possible.
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31.1.4.1 Toxic Environmental Conditions As discussed previously, microorganisms have adapted to life in many naturally occurring extreme environments; however, most of these organisms are autotrophs that will not significantly biodegrade organic pollutants. Extreme toxic conditions resulting from human activities and chemical releases to the environment are more difficult to ameliorate. The addition of oxygen and nutrients, as well as a moderate ability to influence pH, comprise the options currently available to influence environmental conditions. High concentrations of pollutants may cause toxic conditions and prevent biodegradation. Under these circumstances removal of source material might lower groundwater concentrations to non-toxic levels at which biodegradation could occur. Moderate environmental conditions at near neutral pH, with adequate moisture, nutrients, and electron acceptors are the most likely to promote biodegradation. 31.1.4.2 Bioavailability and Mass Transfer Limitations Most bacteria take up dissolved nutrients and substrate from the surrounding water. Phenomena that lower the dissolved concentrations or dissolution rate of compounds will limit biodegradation. Sorption of hydrophobic compounds to soils results in significant mass fractions of these compounds being unavailable to microorganisms. Biodegradation of the soluble phase results in desorption to reestablish the phase distribution equilibrium. In this situation, desorption rates may control biodegradation kinetics (Bosma et al., 1997). Long-term exposure of hydrophobic compounds to soils often results in a fraction of compound that remains unavailable for biodegradation due to mechanisms that are not yet fully understood (Hatzinger and Alexander, 1995). Therefore, it should be clear that in situ biodegradation kinetics may reflect processes other than microbial metabolism such as desorption of the pollutants, pollutant transport, and availability of electron acceptors. 31.1.4.3 Absence of Organisms In some cases, novel pollutant degrading microorganisms have been isolated and cultured in laboratories, while the widespread existence of these microorganisms in the environment has not been observed. The introduction of novel non-indigenous pollutant degrading microorganisms to resolve this situation has several potential problems. The survival and effectiveness of non-indigenous microorganisms in situ has rarely been carefully documented. Current research is attempting to assess the transport and survival of introduced organisms in contaminated zones. Recent success with the bioaugmentation of halorespiring microorganisms into chlorinated solvent contaminated sites has firmly established this method as a viable remediation technique. An outstanding overall review of bioaugmentation applications and principles is now available (Gentry et al., 2004). However, the well-known ecological problems caused by the introduction of invasive non-indigenous macroscopic organisms (e.g., zebra mussels, invasive weeds, rabbits) should provoke careful evaluation of the practice of introducing non-native organisms, even at the microscopic scale. 31.1.4.4 Co-occurring Contaminants Mixtures of different chemicals may influence biodegradation in several ways. Microorganisms have biochemical mechanisms for optimizing energy production by specifically utilizing preferred substrates while repressing catabolism of other substrates. Thus, compounds that are readily biodegraded when present individually, may persist when present in a mixture. Studies of BTEX biodegradation have revealed that substrate interactions are important, and are likely complex and diverse (Alvarez and Vogel, 1991). Compounds that require different redox conditions for biotransformation may further complicate the biodegradation of mixtures. For example, aerobic conditions are desirable for petroleum hydrocarbon biodegradation, but anaerobic conditions are necessary for reductive dechlorination of chlorinated solvents. Thus it may not be possible to have optimum biodegradation conditions for all compounds present in a mixture. Furthermore, readily biodegradable constituents of mixtures, such as ethanol in gasoline, may exert an oxygen demand sufficient to cause anaerobic conditions that result in a spatial expansion of BTEX plumes in groundwater (Ruiz-Aguilar et al., 2002).
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31.2 Quantitative Description of Reactive Transport and Biodegradation A quantitative understanding of coupled chemical transformation, sorption, and transport processes is required to predict, control, and possibly optimize biodegradation in natural and engineered environments. In this section, the basic mass conservation statements and idealized constitutive models that provide a framework for reactive transport modeling are presented. First, basic microbial reaction kinetics are discussed followed by a discussion of the most basic ways in which sorption can be idealized in reactive transport systems, and finally, the interactions that can be expected among these “reactive” mechanisms and the transport mechanisms are presented.
31.2.1 Microbial Reaction Kinetics Probably the most familiar expression for microbial growth kinetics is attributed to Jacques Monod, after whom the general expression is named, although this equation by no means was Monod’s greatest contribution to science. Later, he, along with F. Jacob and A. Lwoff conducted experiments on lactose metabolism by E. coli that led to the discovery of the lac-operon and the overall science of regulatory genes for which they were awarded the Nobel Prize in Medicine in 1965. A major milestone in Monod’s contributions to the area of microbial growth kinetics came in 1942 with the publication of the first of his two books, Recherches Sur la Croissance des Cultures Bactériennes. Surprisingly and unfortunately, an English translation of this book was never published; consequently the writers of many current English textbooks, not only ignore the development of the equation, but tend to refer to many different equations as the Monod equation, with these alternate equations being variations on the same theme. An excellent discussion of Monod’s equation and its development is provided by Panikov (1995) and is summarized here. For E. coli and B. subtilis cultures, Monod observed that after complete substrate utilization, the biomass yield per unit mass of substrate, Y, was nearly constant, independent of culture age or initial substrate concentration, (31.1) [X ]m = [X ]0 + [S]0 · Y where [X ]m is the final biomass concentration after complete consumption (ML−3 ), [X ]0 is the initial biomass concentration(ML−3 ), [S]0 is the initial substrate concentration (ML−3 ), and Y is the yield coefficient for a specific substrate by a specific organism (MM−1 ). For batch short-term-duration growing cultures, this relationship provided a material balance between substrate and biomass concentration that was employed to calculate the substrate concentration at any point along the growth curve, [S] = [S]0 −
([X ] − [X ]0 ) Y
(31.2)
where X is the biomass concentration (ML−3 ). Plotting the calculated values of S against the instantaneous growth rate (µ = d(ln(X )/dt ), ML−3 T−1 ) for various points along the growth curve resulted in a relationship that was best fit with an empirical equation with two fitting parameters, µm and Ks, that is generally considered in the strictest sense the Monod equation, [S] (31.3) µ = µm Ks + [S] where µm is the maximum rate (ML−3 T−1 ) and Ks is the saturation constant (ML−3 ). The simple lesson of this equation is that at large substrate concentrations, where µ → µm , microbial growth is limited by factors other than substrate concentration, and at small substrate concentrations, utilization is first-order in substrate concentration. Apparently, at the time of publishing his book, Monod was unaware of Michaelis and Menten’s much earlier paper (1913) where an identical mathematic equation
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was developed to describe the kinetics of substrate utilization by enzymes. The Michaelis–Menten equation is easily derived from the following reaction sequence, k1
k2
E + S −→ E · S −→ E + P
(31.4)
k−1
E · S −→ E + S where E is the enzyme, S is the substrate, E · S is the enzyme-substrate complex, and P is the product of the enzymatic reaction. In the derivation, it is assumed that the change in concentration of the enzyme–substrate complex over time is negligible (i.e., at pseudo-steady-state), d[E · S] = k1 [E][S] − k−1 [E · S] − k2 [E · S] = 0 dt
(31.5)
leading to an approximation of the complex concentration at any point in time equal to, [E · S] =
[S][E]tot [S] + Ks
(31.6)
where [E]tot is the total concentration of enzyme (=[E] + [E · S]), (ML−3 ), and Ks now is defined by the ratio (k−1 + k2 )/k1 , (M). By measuring the velocity of product appearance, and realizing the maximum rate of product appearance defined by vmax = k2 [E]tot (i.e., [E]tot = vmax /k2 ), the rate of product appearance is defined by, dP [S] = k2 [E · S] = vmax v= (31.7) dt Ks + [S] analogous mathematically to Equation 31.3. The right-hand-side of Equation 31.7 is obtained by substituting vmax /k2 for [E]tot in Equation 31.6, and substituting the resulting term for [E · S] into Equation 31.7. As discussed by Panikov (1995), Monod cleverly invoked material balance constraints in developing Equation 31.3, yet the utility of this equation by itself in describing microbial kinetics is limited. Monod (1942) however proceeded further, defining the rate of microbial growth as a first-order process in biomass concentration, with the rate constant obviously being a function (e.g., f (x)) equal to the instantaneous growth rate, µ(S) (where the substrate concentration, S, is the function variable), [S] d[X ] = µ(S) · [X ] = µm · · [X ] dt Ks + [S]
(31.8)
After substituting Equation 31.2 into Equation 31.8, separating variables and integrating, the following relationship was obtained, (1 + P) ln([X ]/[X ]0 ) − P ln(Q − [X ]/[X ]0 ) + P ln(Q − 1) = µm · t
(31.9)
where P = Ks · Y /(Y · [S]0 + X0 ), and Q = (Y · [S]0 + X0 )/[X ]0 . Equation 31.9 has three parameters, µm , Ks , and Y , that upon determining their values experimentally for any substrate-organism combination and set of environmental conditions (i.e., pH, temperature, mineral content), can be applied in a predictive manner to estimate the growth dynamics from the initial (boundary value) concentrations of substrate and biomass. Depending upon the magnitude of the three “fitting” parameters, plotting X versus t often results in the characteristic S-shaped growth curve generally associated with the “Monod kinetics.” For example, Figure 31.4 is a plot of Equation 31.9 and a plot of the corresponding substrate concentration for the case where µm = 1.2 h −1 , Y = 0.3, and Ks = 75 mg/l.
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500
Biomass (mg/l)
150
400 300
100 200 50
Substrate (mg/l)
Biomass Substrate
100 0
0 0
1
2 Time (h)
3
FIGURE 31.4 Substrate utilization curve with initial concentrations of substrate and biomass equal to 400 and 10 mg/l, respectively, and µm = 1.2 h−1 , Y = 0.3, and Ks = 75 mg/l.
The ensuing literature on microbial growth kinetics over the past ∼7 decades is replete with examples where either Monod’s original model has been invoked to interpret experimental data or where modified versions have been used (see e.g., Simkins and Alexander, 1984; Brezonik, 1994). One such form is the generalized kinetic model that considers simultaneous utilization of numerous substrates by numerous microbial species, and includes reaction terms to account for organism death (Schnoor, 1996), m µi,j Sj Xi dXi − b i Xi = dt Ksi,j + Sj
(31.10)
j=1
n −µi,j Sj Xi dSj 1 = · dt Ksi,j + Sj Yi,j
(31.11)
i=1
where all terms are as previously defined, with n denoting the number of chemical substrates, and m denoting the number of microbial species, and bi is the death rate constant of species i (T−1 ). While Equation 31.10 and Equation 31.11 are mathematically straightforward, they are very impractical for the purpose of evaluating chemical transformation in groundwater, or essentially any complex system for that matter. Even for the simple case of one organism utilizing four substrates, a 13 parameter model results. For the case of BTEX (including all three xylene isomers) being metabolized by four organisms a model with 76 coefficients results, and we have yet to consider sorption and transport! Clearly, the model must be simplified for practical purposes, and with reasonable insight into underlying metabolic processes, this can be accomplished for many specific cases. In many cases, for example, metabolism of the chemical substrate of interest is very slow, as it may be an anthropogenic chemical at low concentration that may not act as the main carbon source. In a non-engineered system where the biomass concentration and supply of electron acceptors (i.e., redox condition) are relatively constant, the transformation kinetics of such a chemical may easily be characterized as pseudo-first order, as simplification of Equation 31.11 for such conditions suggests. Hence, environmental half-lives of many chemicals often vary little from site to site at similar temperatures, with this being particularly true for agricultural pesticides in groundwater. Alternatively, in many highly contaminated systems and engineered systems, the overall rate of degradation is established (i.e., controlled) by one or two “limiting factors.” A large input of reduced carbon, for example, may drive the system to a low redox potential, such that all organisms capable of specific transformations do not continue to grow, effectively stopping transformation of certain
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chemicals. High redox potentials have similar effects on the transformation of other chemicals. In such cases, the kinetics of degradation often are directly controlled by the rate of input of a suitable electron acceptor, leading to zero-order kinetics with respect to substrate concentration. Additional factors limiting degradation include, but are not limited to, toxicity to the chemical or to other chemicals present in the system including reaction products; extreme system conditions such as very low or very high pH; and insufficient concentrations of essential elements in absorbable forms, including phosphorus and nitrogen.
31.2.2 Sorption as a Reactive Kinetic Process Sorption of chemicals to soils, sediments, and aquifer solids has been an area of extensive research over the past several decades. As with biological transformation and growth kinetics, a large portion of this effort has been devoted to the discovery of generalized models that can be used in predictive ways to characterize chemical behavior in natural and contaminated environments, and in engineered environments. Obviously, similar to biological transformations, sorption affects chemical transport and fate, often in a big way. Hence, well-trained quantitative algorithms for such processes become essential components in evaluating the overall risks associated with existing contaminated sites, in evaluating the risk of new chemicals before they are approved for use for various purposes within our society, and in evaluating treatment efficacy and potential costs associated with remediation technologies at existing contaminated sites. 31.2.2.1 Sorption Thermodynamics While modern site remediation efforts and associated costs generally have been concerned with several hundred chemicals, with a few dozen chemicals marshalling major attention (PCE, MTBE, BTEX components, etc.), the development of quantitative sorption algorithms has been largely through successful elucidation of coefficients, consistent with physical chemistry theory that can be easily measured or estimated for thousands of chemicals. As the first studies examined non-polar organic chemicals, including PAHs, PCBs, pesticides, and chlorinated solvents, the dominant influence of soil organic matter as the sorptive phase was noted with the linearity of sorption isotherms indicating that partitioning (i.e., solubilization) was occurring, rather than adsorption to a surface, leading to the common expressions for phase distribution, [C]s foc · [C]oc = Koc · foc = (31.12) Kp = [C]aq [C]aq where [C]s is the chemical concentration in the bulk solid (MM−1 ), [C]aq is the chemical concentration in the aqueous phase (ML−3 ), [C]oc is the chemical concentration in the solid normalized to organic carbon mass in the solid phase (MM−1 ), Kp is the partition coefficient (L3 M−1 ), Koc is the carbon-normalized partition coefficient (L3 M−1 ), and foc is the fraction of organic carbon in the solid phase (MM−1 ). Correlations of Koc with the octanol–water partition coefficient, Kow , (Karickhoff et al., 1979) and water solubility, Sw (Chiou et al., 1979; Karickhoff et al., 1979) were reported within the same year, with Karickhoff et al. correctly noting that a much better correlation existed between Koc and Kow than with Sw because of the fact that in these early correlations, the crystal energy contributions of those chemicals that are solids at room temperature were not quantitatively taken into consideration. This has led to the concept of adjusting the solubility of room-temperature solids to the hypothetical solubility value that would occur if the chemical were a liquid at room temperature (see e.g., Schwarzenbach et al., 1993), referred to as the hypothetical sub-cooled (also, super-cooled) liquid solubility. The log of this hypothetical solubility is inversely proportional to the energy change in transferring the chemical’s molecules from the hypothetical liquid phase to water, as the energy required to “break” the crystal is eliminated from consideration (i.e., not involved). If S ∗ is defined as the water solubility of ambient-temperature liquids or the hypothetical sub-cooled solubility of ambient temperature solids, correlations between − log S ∗ and log Kow have a sound theoretical basis, and correlations between − log S ∗ and log Koc are generally robust and can be considered semi-empirical.
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In the case of partitioning between water and either sediment organic carbon (oc) or octanol, the distributions involve only solvent–solute interactions, and crystal energy need not be considered. Karickhoff et al. (1979) determined the relationship between the associated partition coefficients as, Koc = 0.63 · Kow
(31.13)
To this day, this relationship remains a reasonable approximation for thousands of non-polar chemicals over numerous soil, sediment, and aquifer media classifications. In a paper two years later, Karickhoff (1981) reported on a slightly different proportionality constant of 0.411 (rather than 0.63) based on the sorption of benzene and four polycyclic aromatic hydrocarbons to soils. This new, trained model was then used to estimate the Koc values of 38 other chemicals for which Koc (i.e., Kp and foc ) values were reported in the literature with agreement between estimated and measured values generally agreeing within a factor of three. While this error may seem large, it should be noted that Karichkoff ’s data set included chemicals that vary by over six orders in magnitude in Kow (=101.0 –106.5 )! One may ask why this rather simple correlation works so well. For example, soil organic carbon is derived from different sources and exists at different stages along its diagenetic path. The simple answer is because it is the interactions between the solutes with water, rather than with the organic or solid matrix, that influence the magnitude of these phase distribution processes most significantly. Basic physical chemistry demonstrates that by invoking the same standard (i.e., reference) state (i.e., pure liquid or hypothetical subcooled liquid phase) the thermodynamic (i.e., equilibrium) chemical potentials, hence the activities, of a chemical solubilized within different phases are equal, where activity is defined as the product of the chemical concentration and the activity coefficient, γ1 · [C]1 = γ2 · [C]2
(31.14)
An important system for which this relationship applies is the distribution of a chemical between its pure liquid phase (i.e., liquid benzene) and water, defining the chemical’s “water solubility.” With the pure liquid as the reference state, it can be shown that the activity of chemical in the pure liquid phase equals 1 (1 = γ · [C]), in which case the solubility of the chemical in the water phase, S ∗ equals the reciprocal of the associated activity coefficient (=1/γ ). Equation 31.14 also applies to partitioning of a chemical, C, between octanol and water, Kow =
γaq [C]o = [C]aq γo
(31.15)
As Kow of nonpolar organic compounds increases through a series of chemicals, the respective water phase activity coefficients increase almost proportionally, as the respective octanol phase activity coefficients remain nearly constant, and actually increase very slightly. This can be shown by applying Equation 31.15 to chemical distributions at the solubility limit (or hypothetical sub-cooled liquid solubility limit). For example, from the Koc and Kow values reported by Karickhoff (1981) for benzene, naphthalene, phenanthrene, anthracene, and pyrene and the corresponding solubilities, S ∗ , reported by Schwarzenbach et al. (1993), the solubility of each chemical in water-saturated octanol and soil organic carbon can be calculated with Equation 31.15 or Equation 31.12, respectively. Figure 31.5 shows these solubility values (S ∗ ) regressed against Kow values on logarithmic scales. Clearly, the aqueous phase solubility decreases as Kow increases, however solubility in octanol and soil organic carbon also slightly decreases as Kow increases! Hence, partitioning to soil organic matter by these solutes is not because of a greater affinity of the low solubility compounds for this natural organic carbon phase; rather it is because of their much less favorable affinity for water: The molecules truly are hydro-phobic. The affinity, or attractive forces, for soil organic carbon actually decreases slightly with increasing Kow ; however, the much more significant decrease in affinity for water is what results in larger partition coefficients. The parallel slopes of the octanol and organic carbon solubility lines in Figure 31.5 indicate that octanol has about twice the affinity
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31-17 1 0
log (S *)
–1 –2 –3 –4
water octanol
–5
organic carbon –6 1
2
3
4
5
log (Kow)
FIGURE 31.5 Solubility or sub-cooled liquid solubility (S ∗ ) of benzene, naphthalene, phenanthrene, anthracene, and pyrene in regressed against.
for these compounds as soil organic carbon, independent of the specific chemical’s Kow value. At the macro-scale, this same phenomenon of very weak attractive forces between nonpolar molecules accounts for the low surface tension of organic liquids such as gasoline that spread easily across a surface, as the cohesive forces holding the molecules together are very weak. The significance of these predictive algorithms for a priori estimation of contaminant transport in porous media was quickly recognized, resulting in the ASCE Hydraulics Division Committee on Hydrologic Transport and Dispersion to solicit from S. W. Karickhoff a review paper on the subject in 1984 (Karickhoff, 1984). Importantly, in this paper, situations where Equation 31.12 and Equation 31.13 are poor estimators of chemical distribution are reviewed. These situations include (1) high clay to organic carbon content soils; (2) low (<0.05%) organic carbon soils; and (3) systems where the specific chemical interacts with the solid matrix through polar or ionic (i.e., non-hydrophobic) forces. In the case of surface soils and sediments, there is much recent interest on nonlinear and enhanced sorption caused by char and soot content in some soils (Bucheli and Gustafsson, 2000; Zhu and Pignatello, 2005), although characterization of char and soot in soils is difficult at best. Clearly, for the idealized case, where all partition processes are assumed linear, the partition equation can easily be generalized to consider sorption to numerous sorptive components (i.e., organic carbon, amorphous oxides, and aged clay minerals), each with unique affinities, [C]aq =
n
(Kpi · [C]si )
(31.16)
i=1
Whether sorption to phases other than organic carbon ought to be considered generally can be gleaned from the polarity of the chemical of interest and the organic carbon content of the matrix. For some extremely hydrophobic chemicals, partitioning to aqueous phase humic acids or colloidal particles is important and can result in “facilitated” transport through porous media. 31.2.2.2 Time-Dependent Sorption An additional consideration is the rate at which thermodynamic equilibrium is achieved. Sorption requires diffusion of chemical to the solid matrix, often through the matrix, and often through tortuous pores within the solid matrix. As a result, whether or not local sorption equilibrium can be presumed depends
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on the relative characteristic times of other processes to that of the sorption process. In the case of sandy aquifer material, any time-dependency can be approximated quite reasonably with a model that accounts for chemical mass transfer, via diffusion, through a film-layer around the sand grains, with local sorption equilibrium occurring at the surface of the particles, as sorption may occur within a thin organic coating, or for very low organic carbon sands, may occur directly on the silica surface. For cohesive soils and sediments, approach to equilibrium can be modeled either as a kinetic process or a diffusive process, with sorption occurring throughout the soil pods. One of the simplest empirical kinetic models for this type of matrix is a “2-box model,” in which sorption occurs rapidly to a portion of the matrix (i.e., always at equilibrium with the surrounding solution), and sorption is treated as a kinetic process to the remaining portion (Karickhoff, 1980), Kp
k
Caq ←→ CS1 ←→ CS2
(31.17)
where Kp is the equilibrium partition coefficient (L3 M−1 ), CS1 is chemical concentration in the fraction of sites (X ) accessed rapidly (MM−1 ), CS2 is the chemical concentration in sites accessed slowly, (1 − X ), (MM−1 ), and k is the first-order exchange constant for chemical passing from the equilibrium to kinetically accessed sites (T−1 ). The advantages of this model are that only two additional model parameters exist (k and X ), and the temporal dependency is treated as a first-order process and can be easily encoded within larger flow models. If approach to equilibrium is treated as a diffusive process, then definition of particle geometry is required, along with definition of the active matrix through which diffusion is occurring (i.e., water pores versus organic matrix). Excellent descriptions of these types of models exist in the literature (Wu and Gschwend, 1986).
31.2.3 Microbial Reactions and Sorption in a Batch System Before considering flowing systems, much can be gleaned from simple systems where only first-order microbial transformation of a chemical and equilibrium sorption are considered. In most cases, microbial transformation does not occur if the chemical is partitioned to a solid matrix, especially if this matrix is the organic fraction of a soil, in which case the chemical may be considered “dissolved” by the organic matrix and unavailable to the microorganisms. Hence, only chemical dissolved in the water phase is readily accessible. A sufficient set of equations that may define this system include partition, mass balance, and biodegradation kinetic equations, respectively, Kp =
[C]s = Koc · foc = 0.411 · Kow · foc [C]aq
Vtot [C]tot = Vaq [C]aq + Ms [C]s d[C]tot = −kbio [C]aq dt
(31.18) (31.19) (31.20)
where Vtot is total (or unit) volume (L3 ), [C]tot is the total chemical mass divided by the total volume (ML−3 ), Ms is the mass of the soil (M), Cs is the chemical concentration in the soil (MM−1 ), and kbio is the pseudo-first order biodegradation rate constant of aqueous phase chemical (T−1 ). Substitution of Equation 31.18 and Equation 31.19 into Equation 31.20 yields Equation 31.21 that is easily solved by separation of variables, d[C]tot = −keff [C]tot dt
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(31.21)
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where keff = kbio ·
Vaq 0.411 · Kow · foc · Ms + Vtot Vtot
−1 (31.22)
For any first-order process such as this, the observed or “effective” half-life of any chemical in the system is defined by t1/2,eff = 0.693/keff . To evaluate the influence that sorption has on the effective half-life of several chemicals in this system, the pseudo-first order biodegradation rate constant, kbio , can be held constant for the purpose of demonstration (say, kbio = 0.173 d−1 for a half-life in the water phase of 4 days) while varying Kow . For this comparison, assume constant soil mass (10 g), organic carbon content (2%) soil density (2 g/ml), and water volume (100 ml). Under these conditions, while the rate of decay in the aqueous phase is set to be the same with a half-life of 4 days, the effective half-lives of total chemical mass in the system for chemicals with hydrophobicities equal to: chlorobenzene (log Kow = 2.84), 1, 2, 3, 4-tetrachlorobenzene (log Kow = 4.60), and p,p’-DDT (log Kow = 6.36) are 6 days, 128 days, and 19.7 years, respectively. Note that these effective half-lives are in general agreement with observed loss rates of these compounds in the environment (i.e., days, months, years) under reducing conditions. Interestingly, some chemicals like p,p’-DDT are known to undergo facile reduction in organic solvents like hexane or acetonitrile as long as a suitable reducing agent is present, again indicating that the environmental recalcitrance of chemicals like this may result more from their limited availability rather than from limited reactivity.
31.2.4 Microbial Reaction, Sorption, and Transport These same idealized processes of first-order microbial transformation and sorption equilibrium can be considered in a 1-dimensional (1-D) saturated porous media flowing system. Because concentration, and hence total chemical mass, may vary with distance, x, along the 1-D path, sorption equilibrium occurs only locally at each discrete value of x. The equation that describes transport in 1-D for this simplest of cases is, ∂[C]aq = −µ · ∂t
∂[C]aq ∂x
+D·
∂ 2 [C]aq ∂x 2
±
(rxn)
(31.23)
where µ is the water velocity (LT−1 ), D is the dispersion coefficient (L2 T−1 ) and the reaction terms (rxn) that are considered include those for pseudo first-order biodegradation and mass transfer of chemical from the aqueous phase to the solid phase, respectively, d[C]aq = −kbio [C]aq dt d[C]aq −(1 − n)ρ d[C]s = dt n dt
(31.24) (31.25)
where n is the bulk porosity of the media (water volume/total volume), ρ is the density of the solid phase (ML−3 ), and again [C]s is the concentration of chemical in the solid phase, MM−1 . Equation 31.25 is derived strictly via mass balance, as any chemical that leaves the aqueous phase due to sorption must accumulate in the solid phase and vice versa. Because, locally [C]aq and [C]s are in equilibrium, Equation 31.12 can be substituted into Equation 31.25 eliminating [C]s as a parameter, and the resulting two reaction equations can be substituted into Equation 31.23, which upon rearrangement yields, −µ · (∂[C]aq /∂x) + D · (∂ 2 [C]aq /∂x 2 ) − kbio [C]aq ∂[C]aq = ∂t tr
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(31.26)
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Kp (1 − n)ρ tr = 1 + n
The sorption term, tr is commonly referred to as the retardation factor and may be thought of as the ratio of the water flow rate to the chemical transport rate. A value of 5, for example, implies that the chemical on average is moving through the porous media at one-fifth the rate of the water. A large retardation factor therefore attenuates the chemicals advective transport (the first term on the right-hand side of Equation 31.26); however, because tr is the denominator of all three terms on the right-hand-side, it also attenuates dispersive transport, and as before, biological degradation. Many analytical solutions exist for this equation as the solution depends upon the boundary conditions of interest. Very often, numerical solutions are used to solve for [C]aq as a function of time and distance, as additional factors are considered that prohibit finding a suitable analytical solution, such as media heterogeneity with distance (variation in Kp , n, etc.), variable flow rates, etc. Additional variations to this simplest construct include accounting for (1) advective and dispersive flow in three dimensions, (2) sorption nonlinearity, (3) sorption dynamics, (4) the simultaneous transport of substrate and electron acceptors (i.e., higher order biodegradation kinetics), (5) biomass growth, and the list goes on. Very importantly, even for this simplest of cases, the solution to Equation 31.26 is only half the answer. The other half is in calculating [C]s with time and distance; however, because local equilibrium is assumed in the derivation, this becomes a trivial task. For any chemical that has a retardation coefficient greater than two, however, more than half the total chemical mass will be found sorbed on the media.
31.3 Field Applications of Bioremediation Bioremediation is the utilization of naturally occurring microbial biodegradation processes to restore a site to a non-hazardous condition. A detailed discussion of bioremediation application and design is presented elsewhere (King et al., 1992; Riser-Roberts, 1992; Baker and Herson, 1994; Flathman et al., 1994; Cookson, 1995). There are many advantages to using bioremediation. As pollutant destruction occurs in situ, the potential liability and environmental risk associated with the removal, handling, transport, and storage of hazardous contaminated materials is eliminated. An additional important advantage of bioremediation is that it is often the most economical solution available. Successful bioremediation requires a thorough site investigation and evaluation of treatment options. A site history is compiled which should include property uses, chemicals stored, and location of utilities and buildings, as well as the location of nearby wells. Available information about local hydrogeology, geology, and topography should also be included. Soil and groundwater samples are obtained to identify the contaminants present, and estimate their concentration and distribution. Soil borings are made to determine the local hydraulic gradient and sometimes in conjunction with pumping tests, the hydraulic conductivity is estimated. Whenever possible, an assessment of the local groundwater geochemistry should be made by measuring alternative electron acceptor concentrations (nitrate, sulfate), pH and aquifer buffering capacity. Data from samples taken outside the zone of contamination are useful for assessing background microbiological and geochemical conditions. Laboratory studies are currently the most reliable method for assessing the biodegradation potential of the indigenous organisms. From the assembled information, predictions of contaminant migration and biodegradation can be used to evaluate the current hazard posed and potential remediation options.
31.3.1 Intrinsic Bioremediation Intrinsic bioremediation is the natural in situ biodegradation of pollutants without the engineered manipulation of environmental conditions. Intrinsic bioremediation is appropriate when a site investigation shows that natural biodegradation processes are sufficiently attenuating the migration of contaminants and there is little imminent risk or liability associated with the site. An ongoing monitoring program is essential to regularly evaluate the progress of intrinsic bioremediation until site closure.
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31.3.2 Engineered Bioremediation Engineered systems are installed when it is necessary to overcome some limitation to biodegradation, or health and liability concerns make it desirable to accelerate naturally occurring processes. In current practice, the addition of some form of oxygen to the aquifer is usually the primary objective. Nutrients (N&P) are often added as well, usually without site-specific evidence of a nutrient deficiency, but because it is an easy and inexpensive option. Pumping wells, injection wells, infiltration galleries, vacuum pumps, and compressors may be installed in various combinations and configurations depending on the design objective. In addition to adding an electron acceptor or nutrients to an aquifer, it may be desirable to attempt to contain the contaminant plume, install a groundwater recirculation system, or combine bioremediation with other remediation processes.
31.3.3 Case Histories The objective of listing a few case histories is to provide the reader with references to further study and well-documented examples of applied bioremediation. Therefore, only brief summaries of several types of bioremediation field studies are presented and the interested reader is encouraged to obtain the cited references for detailed descriptions. 31.3.3.1 Aerobic Petroleum Hydrocarbon Bioremediation The aerobic bioremediation of motor oil, diesel fuel, and gasoline that had leaked from a used oil sump into groundwater was described by Nelson et al. (1994). Hydrogen peroxide and nutrients were infiltrated into the contaminated zone through an installed groundwater recirculation system. A vapor extraction system was combined with bioremediation to enhance hydrocarbon removal in the unsaturated zone. 31.3.3.2 BTEX Bioremediation under Denitrifying Conditions The use of nitrate as an electron acceptor for the bioremediation of JP-4 jet fuel was described by Hutchins et al. (1991). The system consisted of an infiltration gallery, interdiction wells, pumping wells, and monitoring wells. The bioremediation was effective in removing BTEX constituents; however, a significant amount of relatively insoluble alkanes remained as NAPL. 31.3.3.3 Aerobic Chlorinated Aliphatic Hydrocarbon Bioremediation The feasibility of in situ methanotrophic co-oxidation of chlorinated ethenes was tested at Moffett Naval Air Station, CA (Roberts et al., 1990; Semprini et al., 1990). With sufficient oxygen and methane the methanotrophic bacteria cometabolized TCE, DCE, and VC in a 2-m long biostimulated zone. Approximately 90% of the VC and 80 to 90% of the trans-DCE was biodegraded in this short distance. TCE and cis-DCE were more recalcitrant; however, longer residence times in biostimulated zones would improve the extent of removal. 31.3.3.4 Anaerobic Chlorinated Aliphatic Hydrocarbon Bioremediation Several excellent case studies involving bioaugmentation of chlorinated solvent contaminated sites with halorespiring bacteria are available (Ellis et al., 2000; Major et al., 2002). In addition, an extensive compilation of the specific techniques used at different sites and the cost of application and other information is available as well (Parsons Engineering Science, Inc., 2002). 31.3.3.5 Intrinsic Bioremediation Intrinsic biodegradation processes have been responsible for the containment of petroleum hydrocarbons from a pipeline leak in Minnesota (Baedecker et al., 1993). Careful monitoring has confirmed that the soluble BTEX constituents are not migrating with the groundwater flow. This is due to the biodegradation rate being equal to the release rate of BTEX from the residual hydrocarbon mixture.
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31.3.4 Emerging Technologies Increased utilization of bioremediation will depend on technological advances that will remove limitations to when bioremediation can be reliably and effectively applied (Atlas, 1995). Advances in understanding novel bioremediation technologies have been made in several areas, for example, bioavailability, molecular biology, microbiology, and anaerobic biodegradation. Microbially produced biosurfactants and synthetic surfactants increase the apparent solubility of hydrophobic compounds and could potentially reduce bioavailability limitations. However, much remains to be learned about the biodegradation of surfactant solubilized compounds and potential surfactant toxicity, as well as cost and effectiveness. A combined treatment process consisting of surfactant/solvent soil washing followed by bioremediation to remove residual contamination has potential for the remediation of NAPL (Non-Aqueous Phase Liquids) contaminated sites. However, the microecological effect of the soil washing is unknown. Advances in molecular biology have contributed much to our understanding of the biochemistry and microbiology of biodegradation, and will continue to do so. Use of molecular techniques is now commonplace in biodegradation research. The importance of understanding the biochemistry, genetics, and microbiology of biodegradation cannot be overestimated. In the coming years, molecular techniques for detecting and enumerating bacteria in situ will likely become routine. These techniques have been used to characterize anaerobic chlorinated solvent sites (Hendrikson et al., 2002) and aerobic petroleum contaminated sites (Baldwin et al., 2003). Genetic techniques are being used to construct novel biodegradation pathways, essentially creating organisms with new capabilities. Additional examples of emerging technologies include water recirculation systems, oxygen releasing peroxides, the use of zero valent metals to enhance reductive dechlorination, as well as advances in in situ measurement of physical, chemical, and biological parameters. Ongoing development of pollutant degrading thermophiles, alkaline tolerant bacteria, and bacteria with membranes resistant to high solvent concentrations will ensure that biodegradation will continue to grow as a primary groundwater remediation option.
Glossary Aerobic Microorganisms that use molecular oxygen as a terminal electron acceptor or an environment that contains molecular oxygen. Anaerobic Microorganisms that do not use molecular oxygen as a terminal electron acceptor or an environment that contains no molecular oxygen. Autotroph An organism that uses inorganic carbon as a source for biosynthesis of cellular constituents. Bacteria In this chapter, bacteria includes all prokaryotic organisms. In fact, Achaea and Bacteria are separate phylogenetic domains of prokaryotic organisms. Bioavailability Refers to the availability of a substance for uptake and transformation by living organisms. Bioremediation The use of naturally occurring biodegradation processes for the remediation of sites contaminated with pollutants. Cell An assembly of highly structured macromolecules which is the smallest living unit. Bacteria are single-celled organisms. Citric Acid Cycle A nearly universal biochemical cycle that oxidizes organic carbon to CO2 and NADH. Cometabolism A gratuitous biochemical reaction from which the microorganism derives no benefit. Electron acceptor The terminal oxidant in respiratory processes. Oxygen is the electron acceptor of aerobic organisms. Electron donor The compound that is oxidized as a source of energy by organisms. Eukaryote Organisms that have a membrane enclosed compartment containing their DNA (a nucleus).
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Fermentation Substrate transformation without the use of an external electron acceptor, therefore the substrate serves as both electron donor and electron acceptor. Halogens Elements in group VII of the Periodic Table. F, Cl, Br, I, At are halogens. Heterotroph An organism that uses organic carbon as a source for biosynthesis of cellular constituents. Lithotroph An organism that oxidizes inorganic compounds for energy. Organotroph An organism that oxidizes organic carbon for energy. pH A logarithmic unit of H+ ion concentration, pH = − log[H+ ]. Prokaryote Single-celled organisms without a membrane enclosed compartment containing DNA. Redox potential The electrical potential of a given oxidation–reduction reaction. Reductive Dechlorination Removal of halogens as halide ions by the reduction of the organic compound with the replacement of the halogen by a hydrogen atom. Respiration Substrate transformation in which an external oxidant is used as a terminal electron acceptor.
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Hancock, C.M., Bose, J.B., and Callahan, M. 1998. Crypto and Giardia in US groundwater. J. Am. Water Works Assoc., 90:58–61. Harkness, M.R., McDermott, J.B., Abramowicz, D.A., Salvo,J.J., Flanagan, W.P., Stephens, M.L., Mondello, F.J., May, R.J., Lobos, J.H., Carroll, K.M., Brennan, M.J., Bracco, A.A., Fish, K.M., Warner, G.L., Wilson, P.R., Dietrich, D.K., Lin, D.T., Morgan, C.B., and Gately, W.L. 1993. In situ stimulation of aerobic PCB biodegradation in Hudson River sediments. Science, 259:503–507. Harvey, R.W., George, L.H., Smith, R.L., and LeBlanc, D.R. 1989. Transport of microspheres and indigenous bacteria through a sandy aquifer: Results of natural and forced gradient tracer experiments. Environ. Sci. Technol., 23:51–56. Hatzinger, P.B. and Alexander, M. 1995. Effect of aging of chemicals in soil on their biodegradability and extractability. Environ. Sci. Technol., 29:537–545. Hendrickson, E.R., Payne, J.A., Young, R.M., Starr, M.G., Perry, M.P., Fahnestock, S., Ellis, D.E., and Ebersole, R.C. 2002. Molecular analysis of Dehalococcoides 16S rRNA DNA from chloroethenecontaminated sites throughout North America and Europe. Appl. Environ. Microbiol., 68:485–495. Holmes, D.A., Harrison, B.K., and Dolfing, J. 1993. Estimation of Gibbs free energies of formation for polychlorinated biphenyls. Environ. Sci. Technol., 27:725–731. Howard, P.H. 1989. Handbook of Environmental Fate and Exposure Data for Organic Chemicals, Lewis Publishers, Inc., Chelsea, MI. Huesemann, M.H. 1995. Predictive model for estimating the extent of petroleum hydrocarbon biodegradation in contaminated soils. Environ. Sci. Technol., 29:7–18. Hutchins, S.R. 1991a. Biodegradation of monoaromatic hydrocarbons by aquifer microorganisms using oxygen, nitrate, or nitrous oxide as the terminal electron acceptor. Appl. Environ. Microbiol., 57:2403–2407. Hutchins, S.R. 1991b. Optimizing BTEX biodegradation under denitrifying conditions. Environ. Toxicol. Chem., 10:1437–1448. Hutchins, S.R., Downs, W.C., Wilson, J.T., Smith, G.B., Kovacs, D.A., Fine, D.D., Douglas, R.H., and Hendrix, D.J. 1991. Effect of nitrate addition on biorestoration of fuel-contaminated aquifer: field demonstration. Ground Water 29:571–580. Karickhoff, S.W. 1980. Sorption kinetics of hydrophobic pollutants in natural sediments. In Robert A. Baker (ed.), Contaminants and Sediments, Vol. 2, Ann Arbor Science, Ann Arbor, MI, pp. 193–205. Karickhoff, S.W. 1981. Semi-empirical estimation of sorption of hydrophobic pollutants on natural sediments and soils. Chemosphere, 10:833–846. Karickhoff, S.W. 1984. Organic pollutant sorption in aqueous systems. J. Hydraul. Eng., 110:707–733. Karickhoff, S.W., Brown, D.S., and Scott, T.A. 1979. Sorption of hydrophobic pollutants on natural sediments. Water Res., 13:241–248. Kellems, B.L., Leeson, A., and Hinchee, R.E. 1994. Review of bioremediation experience in Alaska, p. 438–443. In R.E. Hinchee, B.C. Alleman, R.E. Hoeppel, and R.N. Miller (ed.), Hydrocarbon Bioremediation, Lewis Publisher, Boca Raton, FL. King, R.B., Long, G.M., and Sheldon, J.K. 1992. Practical Environmental Bioremediation, Lewis Publishers, Boca Raton, FL. Leahy, J.G. and Colwell, R.R. 1990. Microbial degradation of hydrocarbons in the environment. Microbiol. Rev., 54:305–315. LeChevallier, M.W. and Norton, W.D. 1995. Giardia and Cryptosporidium in raw and finished water. J. Am. Water Works Assoc., 87:54–68. Lee, M.D., Thomas, J.M., Borden, R.C., Bedient, P.B., Ward, C.H., and Wilson, J.T. 1988. Biorestoration of aquifers contaminated with organic compounds. CRC Crit. Rev. Environ. Control, 18: 29–88. Löffler, F.E., Sun, Q., Li, J., and Tiedje, J.M. 2000. 16S rRNA gene-based detection of tetrachloroethenedechlorinating Desulfuromonas and Dehalococcoides species. Appl. Environ. Microbiol., 66: 1369–1374.
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Logan, B.E. 1998. A review of chlorate- and perchlorate-respiring microorganisms. Bioremediation J. 2:69–79. Logan, B.E. 2001. Assessing the outlook for perchlorate remediation. Environ. Sci. Technol., 482A–487A. Lovley, D.R. and Lonergan, D.J. 1990. Anaerobic oxidation of toluene, phenol and p-cresol by the dissimilatory iron-reducing organism, GS-15. Appl. Environ. Microbiol., 56:1858–1864. Lovley, D.R., Baedecker, M.J., Lonergan, D.J., Cozzarelli, I.M., Phillips, E.J.P., and Siegei, D.I. 1989. Oxidation of aromatic contaminants coupled to microbial iron reduction. Nature, 339:297–299. Major, D.W., McMaster, M.L., Cox, E.E., Edwards, E.A., Dworatzek, S.M., Hendrickson, E.R., Starr, M.G., Payne, J.A., and Buonamica, L.W. 2002. Field demonstration of successful bioaugmentation to achieve dechlorination of tetrachloroethene to ethene. Environ. Sci. Technol., 36:5106–5116. McAllister, K.A., Lee, H., and Trevors, J.T. 1996. Microbial degradation of pentachlorophenol. Biodegradation, 7:1–40. McCarty, P.L. and Semprini, L. 1993. Engineering and hydrogeological problems associated with in-situ treatment. Hydrol. Sci. J., 38:261–272. Michaelis, L. and Menten, M.L. 1913. The kinetics of invertin action, Biochemische Zeutschrift, 49:333. Mohn, W.W. and Tiedje, J.M. 1992. Microbial reductive dehalogenation. Microbiol. Rev., 56:482–507. Monod, J.K. 1942. Recherches Sur la Croissance des Cultures Bactériennes, Herman et Cie, Paris. National Research Council. 1993. In Situ Bioremediation. When does it work? National Academy Press, Washington, D.C. Neilson, A.H. 1990. A review — the biodegradation of halogenated organic compounds. J. Appl. Bacteriol., 69:445–470. Nelson, M.J.K., Montgomery, S.O., Mahaffey, W.R., and Pritchard, P.H. 1987. Biodegradation of trichloroethylene and involvement of an aromatic biodegradative pathway. Appl. Environ. Microbiol., 53:949–954. Nelson, C.H., Hicks, R.J., and Andrews, S.D. 1994. In situ bioremediation: an integrated systems approach, pp.125–132. In R.E. Hinchee, B.C. Alleman, R.E. Hoeppel, and R.N. Miller (ed.), Hydrocarbon Bioremediation, Lewis Publishers, Boca Raton, FL. Panikov, N.S. 1995. Microbial Growth Kinetics, Chapman and Hall, London. Pardieck, D.L., Bouwer, E.J., and Stone, A.T. 1992. Hydrogen peroxide use to increase oxidant capacity for in situ bioremediation of contaminated soils and aquifers: A review. J. Contam. Hydrol., 9:221–242. Parsons Engineering Science, Inc. 2002. Evaluation of performance and costs associated with anaerobic dechlorination techniques. ESTCP. http://www.estcp.org/documents/techdocs/Phase%20I% 20Site%20Survey-Final%20Version%20(3).pdf Reineke, W. and Knackmuss, H.J. 1988. Microbial degradation of haloaromatics. Annu. Rev. Microbiol., 42:263–287. Riser-Roberts, E. 1992. Bioremediation of Petroleum Contaminated Sites, C.K. Smoley, Boca Raton, FL. Roberts, P.V., Hopkins, G.D., Mackay, D.M., and Semprini, L. 1990. A field evaluation of in-situ biodegradation of chlorinated ethenes: part I, methodology and field site characterization. Ground Water, 28:591–604. Ruiz-Aguilar, G.M, O’Reilley, K., and Alvarez, P.J.J. 2002. A comparison of benzene and toluene plumes for sites contaminated with regular versus ethanol-amended gasoline. Ground Water Monit. R., 23:48–53. Schink, B. 1988. Principles and limits of anaerobic degradation: Environmental implications and technological aspects, pp. 771–846. In A.J.B. Zehnder (ed.), Biology of Anaerobic Microorganisms, John Wiley & Sons, New York. Schnoor, J.L. 1996. Environmental Modeling, Fate and Transport of Pollutants in Water, Air, and Soil, John Wiley and Sons, Inc., New York. Schwarzenbach, R.P., Gschwend, P.M., and Imboden, D.M. 1993. Environmental Organic Chemistry, John Wiley & Sons, Inc., New York. Scow, K.M. 1990. Rate of Biodegradation, In W.J. Lyman, W.F. Reehl, and D.H. Rosenblatt (ed.), Handbook of Chemical Property Estimation Methods, American Chemical Society, Washington, D.C.
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Semprini, L., Roberts, P.V., Hopkins, G.D., and McCarty, P.L. 1990. A field evaluation of in-situ biodegradation of chlorinated ethenes: Part 2. Results of biostimulation and biotransformation experiments. Ground Water, 28:715–738. Shannon, M.J.R. and Unterman, R. 1993. Evaluating bioremediation: distinguishing fact from fiction. Annu. Rev. Microbiol., 47:715–738. Simkins, S. and Alexander, M. 1984. Models for mineralization kinetics with the variables of substrate concentration and population density. Appl. Environ. Microbiol., 47:1299–1306. Smith, M.R. 1990. The biodegradation of aromatic hydrocarbons by bacteria. Biodegradation 1:191–206. Stumm, W. and Morgan, J.J. 1981. Aquatic Chemistry, John Wiley & Sons, Inc., New York. Thauer, R.K., Jungermann, K., and Decker, K. 1977. Energy conservation in chemotrophic anaerobic bacteria. Bacteriol. Rev., 41:100–180. Thomas, J.M. and Ward, C.H. 1989. In situ biorestoration of organic contaminants in the subsurface. Environ. Sci. Technol., 23:760–766. Tiedje, J.M. and Alexander, M. 1969. Enzymatic cleavage of the ether bond of 2,4-dichlorophenoxyacetate. J. Agric. Food Chem., 17:1080–1084. Vogel, T.M., Criddle, C.S., and McCarty, P.L. 1987. Transformations of halogenated aliphatic compounds. Environ. Sci. Technol., 21:722–736. Watkinson, R.J. and Morgan, P. 1990. Physiology of aliphatic hydrocarbon degrading microorganisms. Biodegradation, 1:79–92. Wu, S. and Gschwend, P.M. 1986. Sorption kinetics of organic hydrophobic compounds to natural sediments and soils. Environ. Sci. Technol., 20, 717–725. Xun, L., Topp, E., and Orser, C.S. 1992. Confirmation of oxidative dehalogenation of pentachlorophenol by a Flavobacterium pentachlorophenol hydroxylase. J. Bacteriol., 174:5745–5747. Young, L.Y. and Cerniglia, C.E. 1995. Microbial Transformation and Degradation of Toxic Organic Chemicals, Wiley-Liss, New York. Zehnder, A.J.B. 1988. Biology of Anaerobic Microorganisms, John Wiley & Sons, New York. Zhu D.Q. and Pignatello, J.J. 2005. Characterization of aromatic compound sorptive interactions with black carbon (charcoal) assisted by graphite as a model. Environ. Sci. Technol., 39:2033–2041.
Further Information Brock et al. (1997) provides an excellent comprehensive work on microbiology covering introductory cell chemistry and cell biology as well as much more advanced material. Environmental Security Technology Certification Program, (http://www.estcp.org/index.cfm). Gottschalk (1986) is an outstanding reference that describes basic bacterial biochemistry. National Research Council (1993) describes the basic fundamental principles and limitations of bioremediation. Office of Superfund Remediation and Technology Innovation (http://clu-in.org).
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32 Legal Framework for Groundwater Protection in the United States 32.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32-2 Relationship between Laws and Regulations • Relationship between Federal, State, and Local Laws and Regulations • Interaction between Surface Water and Groundwater • Organization of Chapter
32.2 Groundwater Allocation and Management . . . . . . . . . . . . 32-3 The Need for Regulation • State Groundwater Rights Systems • Federal and Indian Groundwater Rights • Takings Issues
32.3 Clean Water Act (CWA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32-7 CWA Legislative Background • CWA Regulations • CWA Summary
32.4 Safe Drinking Water Act (SDWA) . . . . . . . . . . . . . . . . . . . . . . 32-10 SDWA Legislative Background • SDWA Regulations • SDWA Summary
32.5 Resource Conservation and Recovery Act (RCRA) . . . . 32-16 RCRA Legislative Background • RCRA Regulations • RCRA Summary
32.6 Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA) . . . . . . . . . . 32-23 CERCLA Legislative Background • CERCLA Regulations • CERCLA Summary
John A. Veil, Deborah Elcock, Nancy L. Ranek, and Markus G. Puder Argonne National Laboratory
32.7 Other Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32-28 SMCRA • FIFRA
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32-29 Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32-32
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32.1 Introduction This chapter describes the four major Federal environmental laws that place controls on the management of groundwater. These are: • The Clean Water Act (CWA), based on the Federal Water Pollution Control Act (FWPCA) Amendments of 1972, Public Law 92-500, 42 U.S.C. §1251 et seq.1 • The Safe Drinking Water Act (SDWA), Public Law 93-523, 42 U.S.C. §300f et seq. • The Resource Conservation and Recovery Act of 1976 (RCRA), Public Law 94-580, 42 U.S.C. 3251 et seq., and • The Comprehensive Environmental Response, Compensation, and Liability Act of 1980 (CERCLA or Superfund), Public Law No. 96-510, 42 U.S.C. §9601 et seq., as amended. The chapter also offers a brief discussion of groundwater protection themes in two other laws: • The Surface Mining Control and Reclamation Act of 1977 (SMCRA), Public Law 95-87, 30 U.S.C. §1201 et seq. • The Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA) of 1947, Public Law 80-104, 7 U.S.C. §136 et seq. The legal framework for groundwater protection has been summarized as concisely as possible while still presenting the important issues. We strongly recommend that readers consult the authentic source texts of the relevant laws and regulations before forming opinions and making decisions. Copies can be obtained from Federal and State agencies. Also, various online services and agency homepages offer electronic access. The first edition of this handbook did not delve into water quantity issues. This second edition includes a new section (32.2) that describes groundwater allocation and management. Again, readers are encouraged to investigate the law in the light of the specific facts of their case.
32.1.1 Relationship between Laws and Regulations A law, or statute, is a formal written enactment of a legislative body — the Congress or a State legislature. Normally, laws outline general requirements and programs without prescribing in great detail the specific methods to accomplish the statutory objectives. A regulation is a type of “delegated legislation”promulgated by a state, federal, or local administrative agency that has been given the regulatory authority by the appropriate legislature (e.g., the U.S. Environmental Protection Agency [EPA] or State and local environmental, health, or natural resources agencies). Regulations generally are very specific in nature. They are also referred to as “rules.” Regulations are promulgated following a more or less lengthy administrative procedure that includes opportunity for public comment. All Federal regulations are codified in the Code of Federal Regulations (CFR).
32.1.2 Relationship between Federal, State, and Local Laws and Regulations Groundwater protection efforts are managed at all three levels of government. Federal laws and regulations establish basic frameworks and minimum national standards, and entrust Federal agencies with program administration. In many statutes Congress enabled the federal agencies entrusted with program management to give authority (primacy) to willing and able States. Other responsibilities, such as funding programs, conducting large research programs, and preparing baseline regulatory criteria, remain with the Federal government. When States assume Federal programs, their programs must be at least as strict 1 This is the reference for section 1251 forth following in title 42 of the United States Code. The United States Code (U.S.C.) is the codification by subject matter of the general and permanent laws of the United States. It is published by the Office of the Law Revision Counsel of the U.S. House of Representatives. The U.S.C. is divided by broad subjects into 50 titles.
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or as effective as the Federal programs. States may choose to fashion stricter programs. In addition, States can adopt groundwater protection programs that are not considered under the Federal laws. For example, many States operate groundwater discharge permit programs that cover a wider range of discharges than the corresponding Federal program — the Underground Injection Control (UIC) program. Local governments also play a role in groundwater protection. Local health departments frequently represent the first line of defense against unsound septic system installation and operation. Local and State governments are the driving force behind source water protection programs that are geared to prevent pollution from entering a drinking water aquifer. Under RCRA, for example, local governments must protect groundwater by complying with all applicable Federal and State regulations governing municipal solid waste landfills (MSWLFs).
32.1.3 Interaction between Surface Water and Groundwater Surface water and groundwater are intimately linked through the hydrologic cycle. Water tables move up and down seasonally, and can either contribute water to or take water from surface water bodies. This interchange of water can also carry contaminants. The technical aspects of the hydrologic cycle and surface water/ground water exchange are described in other sections of this handbook. For the most part, the major laws and regulations governing groundwater do not extensively address the overlap and exchange of surface water and groundwater. One of the few examples relates to EPA’s efforts over the past decade to promote a watershed management approach.
32.1.4 Organization of Chapter The remainder of this chapter discusses in detail the CWA, SDWA, RCRA, and CERCLA, including the legislative backgrounds, statutory authorities, implementing regulations, and broader perspectives. A final section highlights the SMCRA and FIFRA.
32.2 Groundwater Allocation and Management 32.2.1 The Need for Regulation Groundwater in the United States faces increasing demands from multiple parties. In a scenario where several interests compete for the same groundwater, one person’s extensive use can deny the resource to other parties. Groundwater overdraft and drawdown can create significant problems for sustaining groundwater resources over time. When groundwater stocks are exhausted, costs for drilling and pumping rise because the distance between the water stored in an aquifer and the surface increases. In addition, water quality suffers because groundwater pumped from greater depths typically contains more salts and minerals. More dramatically, the eventual depletion of the supply can create regional problems, including reductions in spring and stream flows, saltwater intrusions in coastal areas, and adverse consequences to wetlands and riparian ecosystems. Finally, in areas of severe groundwater loss, a sinking land surface can cause subsidence by creating cracks or fissures with the potential to damage roads, foundations of buildings, and underground structures. The expected population growth, especially in the southeastern and western parts of the United States, will only compound the pressures faced by a relatively limited groundwater resource. Groundwater rights law governs the rights associated with the use of water in the ground portion of the hydrologic cycle, including the type and scope of the right, and the point in time when the right arises. Conceptually, the existence of the groundwater must be distinguished from the right to lift the groundwater. The right to lift, which involves the energy contained in the groundwater pool, allows users to withdraw a volume of groundwater by reasonable means from a water table at a fairly stable level without having to deepen their wells and use more powerful pumps. In practice, most disputes revolve around the right to lift.
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Groundwater rights law in the United States is highly fragmented. Each State has developed its own unique system based on English common law, Spanish-Mexican law elements, and administrative law. Also, federal and tribal groundwater rights law exists. Sources of groundwater rights law include constitutions, statutes, administrative regulations and practice, and court decisions. In light of the complexities associated with groundwater rights law, this section only highlights key elements of the issues.
32.2.2 State Groundwater Rights Systems The distinctions among State systems involve the foundation and scope of groundwater rights. In most States, groundwater rights spring from ownership of the overlying land surface. Several subcategories of systems have developed: absolute dominion (English rule or rule of capture), reasonable use (American rule), Restatement of Torts, and correlative rights (common resource rule). Other States separate water rights from the rights of land ownership. Groundwater belongs to the State, and any rights are based on specific administrative authorization. These jurisdictions follow the law of prior appropriation. A survey conducted by the Water Systems Council identifies the States following the different subcategories of groundwater rights law (see Table 32.1). It is often difficult to determine a State’s particular type of groundwater rights system. The courts and legislatures in the different jurisdictions have crafted specific exceptions and limitations to the various rules. Further, administrative permitting systems as well as local and regional groundwater management and conservation schemes can modify the traditional rule frameworks. 32.2.2.1 Absolute Dominion Under the absolute dominion doctrine, landowners have the right to withdraw and use, as they please, unlimited amounts of groundwater lying beneath their surface land, unconstrained by liability to surrounding landowners who might claim that the pumping operations have depleted their wells. The absolute dominion doctrine is based on a right to pump groundwater. This includes capturing and selling the groundwater for offsite use, but does not cover the right to save it in place for subsequent use and protect it against the potential use by others. Eight States — Connecticut, Indiana, Louisiana, Maine, Massachusetts, Mississippi, Rhode Island, and Texas — have adopted or indicate a preference for the absolute dominion rule. Among the arid western TABLE 32.1
State Survey of Groundwater Rights Rules
Doctrine Absolute dominion
Reasonable use
Number of States
States in Alphabetical Order
8
Connecticut, Indiana, Louisiana, Maine, Massachusetts, Mississippi, Rhode Island, and Texas Alabama, Arizona, Arkansas∗ , Delaware∗ , Florida, Georgia, Illinois, Kentucky, Maryland, Missouri∗ , Nebraska∗∗ , New Hampshire, New York, North Carolina, Oklahoma, Pennsylvania, South Carolina, Tennessee, Virginia, West Virginia, and Wyoming∗ Michigan, Ohio, and Wisconsin California, Hawaii, Iowa, Minnesota, New Jersey, and Vermont Alaska, Colorado, Idaho, Kansas, Montana, Nevada, New Mexico, North Dakota, Oregon, South Dakota, Utah, and Washington
21
Restatement of torts Correlative use
3 6
Prior appropriation
12
Note: In conjunction with the prior appropriation rule ∗∗ In conjunction with the correlative rights rule. Source: Water Systems Council.
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states, Texas represents the lone holdout for its version of the absolute dominion doctrine — the rule of capture. 32.2.2.2 Reasonable Use Like the absolute dominion doctrine, the reasonable use rule allows landowners to pump and use as much groundwater as they choose, as long as they make “reasonable use” of the withdrawn groundwater. This means that withdrawals must be reasonably related to the overlying land and do not result in waste. The reasonable use rule does not provide for proportional sharing or preference for prior users. Neighbors injured by reasonable use have no recourse. However, unreasonable groundwater uses that injure adjacent landowners can result in lawsuits. In traditional reasonable use jurisdictions, offsite uses, including selling and transportation, have been presumed to be unreasonable. The considerations for determining reasonableness generally include the purpose, suitability, economic and social value of the use, the overall supply quantities, the presence or absence of competition, the extent and equity of harm caused by the use, and the efficiency or wastefulness of competing uses. For example, persons are generally allowed to withdraw a fair share of the groundwater for their artificial wants (irrigation); however, natural needs (household use) enjoy priority over artificial wants. Recognizing the need for efficient and effective groundwater management, especially in times of water scarcity, many reasonable use jurisdictions have implemented regulatory and administrative variants of the doctrine. For example, certain groundwater users who pump in quantities that exceed a regulatory threshold (e.g., 100,000 gallons per day) are held to comply with all applicable notification and permitting requirements. Twenty-one states — Alabama, Arizona, Arkansas, Delaware, Florida, Georgia, Illinois, Kentucky, Maryland, Missouri, Nebraska, New Hampshire, New York, North Carolina, Oklahoma, Pennsylvania, South Carolina, Tennessee, Virginia, West Virginia, and Wyoming — have adopted or indicate a preference for the reasonable use rule. Arkansas, Delaware, Missouri, and Wyoming combine the reasonable use rule with the prior appropriation doctrine. Nebraska blends the reasonable use and correlative rights rules. 32.2.2.3 Restatement of Torts Restatements are collections of law published by the American Law Institute. Although they do not have binding authority, Restatements are highly persuasive because they reflect long periods of effort and receive extensive input from law professors, practicing attorneys, and judges. Section 858 of the Restatement of Torts (second edition) “Liability for Use of Groundwater” provides specific criteria for comparing the reasonableness of competing uses of groundwater. A well owner is not liable for withdrawal of groundwater unless the withdrawal causes well interference by lowering the water table or by reducing water pressure, involves pumping more than the well owner’s reasonable share, or interferes with levels of streams and lakes that depend on groundwater. This language protects against over-pumping, and seems flexible enough to take into account uses that are more beneficial than others. Three states — Michigan, Ohio, and Wisconsin — have adopted or indicate a preference for the Restatement of Torts approach. Also, most States with a reasonable use approach rely on some of the considerations offered in the restatement. 32.2.2.4 Correlative Rights The correlative rights doctrine realizes that landowners using groundwater from a common pool share common rights and duties with respect to one another. Landowners may withdraw only their portion of water for reasonable use. Groundwater is prorated among the overlying landowners. When conflicts or shortages occur, each owner is entitled to a share of the available supplies that is proportionate to the amounts allocated to that landowner’s use. Unlike absolute dominion and reasonable use, a correlative rights system attempts to accommodate all overlying owners through proportional reductions when all reasonable needs cannot be met. Six states — California, Hawaii, Iowa, Minnesota, New Jersey, and Vermont — have adopted or indicate a preference for the correlative rights rule. The doctrine originated in California. Interestingly, California
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also recognizes the municipal pueblo water right possessed by a municipality as successor of a Spanish or Mexican pueblo. The pueblo right entitles the municipality to the beneficial use of all needed, naturally occurring groundwater of the original pueblo watershed. Water use under a pueblo right must occur within the modern city limits, and excess water may not be sold outside the city. 32.2.2.5 Prior Appropriation Following the concept that water rights are separate from the rights of land ownership, Spanish and Mexican water law required specific authorization to use water. Under the appropriative rights doctrine, groundwater is allocated according to the temporal sequence of use (“first come first serve”). The first person to use water (“senior appropriator”) acquires the right (“priority”) to future use against all subsequent users (“junior appropriators”). In almost all prior appropriation states, the water right is regulated and managed by a permit system that specifies pumping rates, well spacing, and construction requirements. Groundwater permits generally require actual and beneficial use. Permits reflect seniority, recognizing the higher priority legal right in the first user. Landowners whose usage predates the permitting system receive grandfathered rights. The appropriation date of a water right reflects the point in time when the applicant successfully demonstrates the initiation of the appropriation. Prior appropriation can apply to all groundwater, although in some states, the doctrine applies only to particular sources (underground streams). Twelve states — Alaska, Colorado, Idaho, Kansas, Montana, Nevada, New Mexico, North Dakota, Oregon, South Dakota, Utah, and Washington — have adopted or indicate a preference for the prior appropriation rule. 32.2.2.6 Prescriptive Rights Prescriptive rights, which exist outside the relationships among and between common law and appropriative users, are gained by trespass or unauthorized taking. The title is based on conduct allowed to continue beyond the applicable statute of limitations. Prescriptive rights can only be obtained against private entities. The claim of a prescriptive water right to non-surplus water requires that pumping was actual, open and notorious, hostile, adverse to the original rights holder, continuous and uninterrupted, and under a claim of right. 32.2.2.7 Conjunctive Management A common practice among western states with respect to groundwater involves conjunctive management — the coordinated and integrated management of surface and groundwater resources. Groundwater is often connected to surface water. For example, seepage from a stream may recharge an underlying aquifer, or a particular stream may be fed by an aquifer. Several states are managing interconnected surface water and groundwater in a single system that recognizes the importance of the whole hydrological cycle, and facilitates better management of water resources.
32.2.3 Federal and Indian Groundwater Rights Federal authority and jurisdiction over groundwater rights is based on several clauses of the U.S. Constitution. The Commerce Clause permits federal regulation of groundwater that may be involved in or affect interstate commerce. The Property Clause allows federal regulation of groundwater as necessary for the beneficial use of federal property. The Compact Clause bars state compacts without the consent of Congress; for example, the creation of interstate river basin commissions regulating groundwater withdrawals through permits and fee schedules. In many instances, federal law requires federal agencies managing groundwater resources to defer to state laws and cooperate with state regulators. Examples of such legislation include the Reclamation Act, the Water Supply Act, the McCarren Amendment, and the Endangered Species Act. In interstate disputes over groundwater rights federal courts resolve the issue through equitable apportionment. Reasonable and efficient usage and volumes of prior appropriation constitute important factors for making groundwater allocations among states. In controversies among appropriative rights
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systems, the groundwater supply is generally allocated by way of seniority. In disputes involving states that follow ownership doctrines, courts will generally follow a reasonableness standard to maintain groundwater availability to all states concerned. Finally, the US Supreme Court has held that states are barred from obstructing the exportation of groundwater to other states. Indian groundwater rights law must be carefully evaluated and administered within the prevailing groundwater allocation systems. In light of the early establishment of Indian reservations often predating the onset of most other water uses, especially in the west, tribes generally retain the oldest and most valuable groundwater rights. Indian groundwater rights generally fall into aboriginal, pueblo, and Winters rights. Aboriginal groundwater rights attach to lands occupied since time immemorial. They are accorded a corresponding priority date. Pueblo groundwater rights enjoy early priority dates in the wake of Spanish land grants and the US Treaty of Guadalupe Hidalgo with Mexico. Most federal Indian groundwater rights are examined in light of the Winters decision by the US Supreme Court. In Winters, the high court held that when ceding to the federal government vast territories of land in return for permanent reservations for Indian occupation and use, the tribes reserved, along with the land, the amount of water required to meet the needs and purposes of the reservation. This means that Indian water rights are created according to the date of the reservation. Actual quantification and sizing of vested Indian water rights occurs through litigation and congressional action. The most widely used method is the practicable irrigation acreage approach, which quantifies the amount of water needed to irrigate the reservation’s arable lands. In general, the amounts are measured in terms of (future) needs, as opposed to the quantities in actual use. On reservations where state, federal, and tribal jurisdictional interests and concerns compete, courts will regularly fashion the type of applicable scheme of groundwater rights administration. In general, courts have recognized important tribal sovereignty interests to regulate Indian and non-Indian water use on a reservation.
32.2.4 Takings Issues Questions of property takings through governmental action can be associated with groundwater use and regulation. Groundwater pumping operations by governmental entity (municipality) pumps can physically invade the landowner’s property by diverting water from beneath the landowner’s property. And high-volume groundwater pumping can deny the landowner all economically viable uses of the property. Other issues of regulatory property takings are raised when a state converts groundwater rights under ownership doctrines to an appropriative rights system. In all scenarios, courts will need to determine whether a governmental action rises to the level of a taking. The outcome will depend on the specific facts of each case.
32.3 Clean Water Act (CWA) 32.3.1 CWA Legislative Background 32.3.1.1 Historical Perspective The CWA was passed in 1972 as a comprehensive package of amendments to the Federal Water Pollution Control Act of 1948. The name “Clean Water Act” was not applied to the law until 1977, when another round of amendments was enacted. The 1972 amendments, which gave the law its current shape, serve as the Federal foundation for water quality protection and water pollution control. Through the CWA Congress responded to the country’s growing public concerns over water quality degradation in its rivers, lakes, and oceans. Only a few years earlier the Cuyahoga River in Cleveland had actually caught fire due to floating oils and other flammable contaminants. In the light of the Nation’s greater awareness of surface water issues, the CWA is mainly geared to the surface water component of the hydrological cycle. The amendments of 1977, 1981, and 1987 did little to change this focus of the CWA. This also holds true for the minor revisions to the CWA made by Congress since 1987.
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32.3.1.2 Goals and Objectives The 1972 law declared as its objective “to restore and maintain the chemical, physical, and biological integrity of the Nation’s waters.” The phrase “Nation’s waters” is never explained, but the term “navigable waters,” defined as “the waters of the United States,” is used throughout the CWA. The definition, which determines the reach of the CWA, has been litigated on numerous occasions over the recent years. Navigable waters include surface water bodies but not groundwater. The goals listed in §101 of the CWA do not directly speak to groundwater. However, §102(a) states that EPA “shall, after careful investigation . . . prepare or develop comprehensive programs for preventing, reducing, or eliminating the pollution of the navigable waters and ground waters and improving the sanitary condition of surface and underground waters.” Through summer 2005, no regulatory programs have been promulgated under the CWA to implement this section. Several other references to groundwater are sprinkled throughout the CWA. §104 directs EPA to maintain a groundwater monitoring network. Under §208, states are to identify areas that have substantial water quality problems and develop areawide waste treatment management plans. The plans must include, among others, processes that identify contaminated underground mine drainage, recognize salt water intrusion due to excessive groundwater extraction, and control disposal of pollutants on the land or in subsurface excavations within such area to protect groundwater quality. §304 requires EPA to develop and publish water quality criteria that reflect the latest scientific knowledge on effects on health and welfare, which result from the presence of pollutants in groundwater. Under §304 EPA must develop and publish information on the factors necessary to restore and maintain the chemical, physical, and biological integrity of all navigable waters and groundwater. §304 also directs EPA to issue to appropriate Federal agencies, the states, water pollution control agencies, and certain agencies processes, procedures, and methods to control pollution resulting from various sources, including: underground mining activities; the disposal of pollutants in wells or in subsurface excavations; salt water intrusion resulting from reductions of fresh water flow (e.g., in the wake of extraction of ground water); and changes in the movement, flow, or circulation of any navigable waters or ground waters. EPA has fulfilled some of these obligations through other programs, particularly those under the SDWA, but has not developed a comprehensive program under the CWA. §319 — discussed below — offers the only program specifically geared toward protecting groundwater. States have accessed grant funding under §106 to develop their State groundwater protection and wellhead regulations. 32.3.1.3 General Provisions The primary regulatory control mechanism of the CWA — the National Pollutant Discharge Elimination System (NPDES) program (§402) — covers point source discharges (mainly from industries and sewage treatment plants, including publicly owned treatment works — POTWs). Congress also established a comparable pretreatment program for industries that discharge wastewater to POTWs rather than directly to navigable waters. Nonpoint sources of pollution are not subject to a formal Federal regulatory program such as the NPDES program. Under §319, states are required to submit nonpoint source management programs to EPA for approval. The State programs must outline the best management practices and measures that will be used to reduce nonpoint source pollution, and the regulatory or non-regulatory programs (including enforcement, technical and financial assistance, education, training, technology transfer, and demonstration projects) designed to achieve implementation. §319 represents one of the few sections of the CWA that explicitly references groundwater protection by name. State management programs are to consider impacts of the recommended practices on groundwater quality (§319(b)(2)(A)). When making Federal nonpoint source grants, EPA must give priority to projects that will protect groundwater from nonpoint sources (§319(h)(5)(D)). Further, EPA may make grants that assist states in carrying out groundwater protection activities designed to implement a comprehensive nonpoint source program (§319(i)). Unfortunately, nonpoint source control programs have not been widely successful. This may be attributable to the lack of a strong Federal program, insufficient levels of Federal financial support, and
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the absence of responsible and financially viable parties (such as industries or POTWs) willing and able to carry out the control program. Although the Federal NPDES program is limited to discharges to surface water, many State water pollution control laws are broader and mandate regulatory programs to protect both the surface water and groundwater of their state. For example, some states require permits for discharges of wastewater not only to surface water but also to groundwater or the land surface. Septic systems for disposal of sewage or household wastes are not regulated at the Federal level through the CWA, but are controlled by State and local regulations. As the details of these State programs vary widely, readers are advised to consult with the appropriate State regulatory agencies. 32.3.1.4 Issues and Outlook As of mid-2005, Congress is not working on any significant revisions to the CWA in the area of groundwater quality and protection. Over the past decade, EPA has emphasized a watershed management approach that involves consideration of all activities occurring within a watershed rather than focusing on a single regulatory program. A well-designed and operated watershed management program ideally considers impacts of various activities on groundwater quantity and quality. EPA has begun to encourage watershed management programs; however, these programs might have greater success and clout if backed up by explicit statutory authority.
32.3.2 CWA Regulations The CWA regulations do not exercise direct regulatory controls over groundwater. However, the point source stormwater regulations (40 CFR 122.462 ), which require that stormwater discharges associated with industrial activity, stormwater discharges from construction sites, and discharges from large and medium municipal separate storm sewer systems must be covered by NPDES permits, do indirectly affect groundwater. In most instances, stormwater permits do not use numerical limits as compliance tools. Instead, they require that permittees adopt best management practices (BMPs), which can be grouped into three categories. A first type of BMPs prevents clean stormwater from coming into contact with contaminant sources. This can for example be accomplished through berms, curbing, and roofing. Another category of BMPs treats the contaminated runoff to lower pollutant levels. Treatment technologies in this category include oil/water separators, straw bale dikes, and sediment ponds. A third type of BMPs involves reducing the total volume or rate of runoff to surface waters — for example, through detention and retention ponds, or stormwater drainage wells. The third category of BMPs represents a very effective mechanism for controlling surface water quality, but can conceivably contribute to groundwater contamination. For example, dissolved pollutants contained in the stormwater can infiltrate through the bottom of detention or retention ponds and enter the groundwater. Disposal of stormwater into drainage wells directly introduces pollutants into the groundwater. Nonpoint source and point source stormwater discharges contain the same contaminants. EPA has not adopted nonpoint source stormwater regulations; rather control programs in this area rely almost entirely on BMPs, and groundwater contamination scenarios comparable to the point source category described above exists. EPA’s sewage sludge regulations (40 CFR 503) represent another example of CWA regulations with indirect effects on groundwater quality and protection. Two of the approved methods for sewage sludge management involve land application and surface disposal. The land application and surface disposal regulations do not contain direct groundwater protection controls. Rather, the prescribed application rates and management practices are designed to protect surface water from excessive land application of sludge contaminants.
2 40
CFR 122.46 refers to Section 122.46 in Part 122 of Title 40 of the Code of Federal Regulations.
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32.3.3 CWA Summary Only a few sections in the CWA speak directly to groundwater. Yet, §319 — the nonpoint source control program — offers a statutory lever for imposing groundwater protection requirements on landowners, businesses, farmers, or other dischargers.
32.4 Safe Drinking Water Act (SDWA) 32.4.1 SDWA Legislative Background 32.4.1.1 Historical Perspective The SDWA, Title XIV of the Public Health Service Act, was passed in 1974 to establish a national framework for ensuring a clean drinking water supply. The SDWA establishes two main programmatic themes. The public water system program specifies how clean drinking water must be when it is delivered to customers. A variety of other programs protect underground sources of drinking water (USDWs). Minor amendments to the SDWA were made in 1976, 1977, and 1980, and the first significant changes were adopted in 1986. The 1986 amendments greatly expanded the scope of contaminants subject to drinking water standards, and increased the level of monitoring for nonregulated contaminants. States were required to establish wellhead protection areas. In 1996, Congress passed another round of comprehensive amendments to the SDWA. Many of those have affected the public water supply system requirements by changing how drinking water standards are established and implemented. Consideration was given for small public systems with limited economic resources. Much greater emphasis was placed on protecting source water, and the new source water requirements have indeed helped to improve ground water quality. 32.4.1.2 Goals and Objectives The public water system program strives to ensure that drinking water at the tap is clean and safe to drink. This is accomplished through a combination of treatment requirements (like filtration and disinfection) and numerical quality standards for individual contaminants. The SDWA focuses solely on public water systems, which are defined as those that have at least 15 service connections or that serve at least 25 persons. The SDWA does not require testing, controls, or standards for those drinking water systems that supply fewer than the specified number of connections or persons (e.g., private wells). The remaining SDWA programs are designed to protect USDWs from contamination by restricting activities in sensitive areas and controlling discharges of contaminants to groundwater or to the subsurface soils. The SDWA does not contain program components specifically requiring protection of surface water supplies. Under the SDWA, not all groundwater must be protected; protection is required only for USDWs. 32.4.1.3 General Provisions All major SDWA programs affect groundwater to varying degrees. The national primary drinking water regulations form the heart of the public water system program. EPA has published maximum contaminant levels (MCLs) and maximum contaminant level goals (MCLGs) for more than 75 contaminants (see Table 32.2). The MCLGs reflect the levels of contaminants in drinking water below which no known or expected risk to health exists. MCLGs allow for a margin of safety and represent non-enforceable public health goals. For many contaminants, MCLGs cannot be economically or technically achieved. MCLs are the highest concentrations of contaminants allowed in drinking water. MCLs are established as close to MCLGs as feasible using the best available treatment technology and taking cost into consideration. In some cases, EPA has the authority to establish treatment requirements that control a particular contaminant in lieu of promulgating a numerical MCL. Under the SDWA, variances and waivers from meeting MCLs or treatment requirements are available for public drinking water systems. The primary
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EPA’s National Primary Drinking Water Standards
Contaminant Inorganics Antimony Arsenic Asbestos (>10 um) Barium Beryllium Cadmium Chromium (total) Copper Cyanide Fluoride Lead Mercury (inorganic) Nitrate Nitrite Selenium Thallium Coliform and surface water treatment Cryptosporidium Giardia lambia Legionella Heterotrophic plate count Total coliform Turbidity Viruses Organics Acrylamide Alachlor Atrazine Benzene Benzo-a-pyrene Carbofuran Carbon tetrachloride Chlordane Chlorobenzene 2,4-D Dalapon 1, 2-Dibromo-3-chloropropane o-Dicholorobenzene p-Dichlorobenzene 1, 2-Dichloroethane 1,1-Dichloroethylene cis-1, 2-Dichloroethylene trans-1, 2-Dichloroethylene Dichloromethane 1, 2-Dichloropropane Di(2-ethylhexyl) adipate Di(2-ethylhexyl) phthalate Dinoseb Diquat Dioxin Endothall Endrin Epichlorohydrin Ethylbenzene
MCLG (mg/l)
MCL (mg/l)
0.006 0 7 MFLa 2 0.004 0.005 0.1 1.3 0.2 4 0 0.002 10 1 0.05 0.0005
0.006 0.010 7 MFL 2 0.004 0.005 0.1 TTb 0.2 4 TT 0.002 10 1 0.05 0.002
0 0 detected 0 detected N/A 0 detected N/A 0 detected
TT TT TT TT
0 0 0.003 0 0 0.04 0 0 0.1 0.07 0.2 0 0.6 0.075 0 0.007 0.07 0.1 0 0 0.4 0 0.007 0.02 0 0.1 0.002 0 0.7
TT 0.002 0.003 0.005 0.0002 0.04 0.005 0.002 0.1 0.07 0.2 0.0002 0.6 0.075 0.005 0.007 0.07 0.1 0.005 0.005 0.4 0.006 0.007 0.02 0.00000003 0.1 0.002 TT 0.7
c
TT TT
Continued
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Continued
Contaminant Ethylene dibromide Glyphosate Heptachlor Heptachlor epoxide Hexachlorobenzene Hexachlorocyclopentadiene Lindane Methoxychlor Oxyamyl PCBs Pentachlorophenol Phthalate (di-2-ethylhexyl) Picloram Simazine Styrene Tetrachloroethylene Toluene Toxaphene 2, 4, 5-TP 1, 2, 4-Trichlorobenzene 1,1,1-Trichloroethane 1,1, 2-Trichloroethane Trichloroethylene Total trihalomethanes Vinyl chloride Xylenes (total) Disinfectants and disinfectant byproducts Bromate Chloramines (as Cl2 ) Chlorine (as Cl2 ) Chlorine dioxide (as ClO2 ) Chlorite Haloacetic acids (HAA5) Total trihalomethanes (TTHMs) Radionuclides Radium 226 + radium 228 Alpha particles Beta particle + photon radioactivity Uranium
MCLG (mg/l)
MCL (mg/l)
0 0.7 0 0 0 0.05 0.0002 0.04 0.2 0 0 0 0.5 0.004 0.1 0 1 0 0.05 0.07 0.2 0.003 0 N/A 0 10
0.00005 0.7 0.0004 0.0002 0.001 0.05 0.0002 0.04 0.2 0.0005 0.001 0.006 0.5 0.004 0.1 0.005 1 0.003 0.05 0.07 0.2 0.005 0.005 0.080 0.002 10
0 4.0 d 4.0d 0.8d 0.8 N/A N/A
0.010 4.0d 4.0d 0.8d 1.0 0.06 0.080
0 0 0 0
5 pCi/l 15 pCi/l 4 mrem/yr 0.030
a MFL = million fibers per liter. b TT = treatment techniques in lieu of a numerical standard. c No more than 5% of samples can be total coliform-positive. d Expressed as maximum residual disinfectant.
MCLs described above regulate the concentration of numerous naturally occurring and synthetic, organic, and inorganic contaminants in drinking water. Primary MCLs are enforceable. EPA also has adopted secondary MCLs for 16 drinking water contaminants or constituents. Secondary MCLs are suggested guidelines that are related to aesthetic qualities (taste and smell) of drinking water. They rarely present health threats to consumers because the drinking water in question would become unpalatable well before the constituents could possibly reach harmful levels. Secondary MCLs are not enforceable. The public water system requirements under the SDWA do not directly control groundwater quality. They are designed to protect drinking water consumers and not the groundwater itself. For example, a water supplier can withdraw groundwater that does not meet all MCLs, treat it, and then supply it to customers. However,
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MCLs play important roles in several other regulatory programs. The Underground Injection Control (UIC) program frequently requires that MCLs must be met at the point where waste injection occurs, where the discharge plume intersects the USDW, or where the USDW leaves the property boundaries. Under CERCLA, the MCLs are often enlisted as applicable or relevant and appropriate cleanup standards. This is discussed in Section 32.6.2.1. The SDWA contains several important USDW protection programs. The UIC program governs injection of fluids into wells (§§1421–1424). The SDWA envisions that willing and able states will have the opportunity to gain UIC program primacy (§§1422 and 1425). Many states have been granted UIC program authority over certain or all classes of injection wells. Otherwise EPA’s regional offices administer the UIC program in direct implementation. Underground injection operations are subject to authorization by permit or rule, and must not endanger USDWs. The second USDW protection program is the sole source aquifer program. Under §1424(e) and §1427, EPA has the authority to designate certain aquifers as the sole or principal drinking water source for a given area. When an aquifer is designated as the sole source aquifer, EPA is barred from committing Federal financial assistance (through a grant, contract, loan guarantee, or otherwise) for any project deemed to contaminate such aquifer through a recharge zone and create a significant public health hazard. As of 2005, EPA has designated more than 70 aquifers as “sole source.” State and local governments and regional planning entities with jurisdiction over certain critical aquifer protection areas may apply to EPA for demonstration-program funding. When selecting critical aquifer protection areas EPA must consider the vulnerability of the aquifer to contamination, the population using the aquifer as their drinking water source, the economic, social, and environmental benefits resulting from protecting the aquifer, and the economic, social, and environmental costs resulting from aquifer degradation. The application for a demonstration program must include a comprehensive management plan for the proposed protection area. Such plans would, among other items identify existing and potential point and nonpoint sources of ground water degradation; assess the relationship between activities on the land surface and ground water quality; specify implementation and management activities and practices for preventing adverse impacts on ground water quality in the critical protection area; determine the quality of the existing groundwater recharged through the special protection area, and the natural recharge capabilities of the special protection area watershed; provide requirements designed to maintain existing underground drinking water quality or improve underground drinking water quality if prevailing conditions fail to meet drinking water standards; and describe actions in the special protection area that would avoid adverse impacts on water quality, recharge capabilities, or both. The third USDW protection program relates to protection of wellheads. Under this program, states are directed to protect the areas around water supply wellheads from contaminants (§1428). Wellhead protection programs must delineate the size of the protection area for each wellhead and identify the activities that will be undertaken for protecting the water supply within wellhead protection areas from contaminants. The Federal requirements for the wellhead protection program provide a framework and funding for the program. The actual regulatory requirements and controls are designed and administered at the State or local levels. With the advent of source water protection programs in the wake of the 1996 amendments, many wellhead protection programs have been made part of new source water protection programs. Two new USDW protection programs were added to the SDWA in 1996. §1429 authorizes EPA to make grants to states for developing and implementing comprehensive programs for groundwater protection. Under §1453, states are required to develop and implement source water assessment programs protective of surface water and groundwater drinking water. State source water assessment programs must delineate the boundaries of assessment areas, identify contaminants deemed to be a public health threat, and trace the origins of those contaminants. Under §1454, states may establish programs that enable community water systems or local governments to submit source water quality protection partnership petitions to the state requesting assistance in developing voluntary, incentive-based partnerships to reduce the presence of contaminants in drinking water, receive financial or technical assistance, and develop a long-term source water protection strategy.
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32.4.1.4 Issues and Outlook The SDWA was reauthorized and amended in 1996. No significant revisions have been made since then.
32.4.2 SDWA Regulations EPA’s extensive regulations for the public drinking water program are codified in 40 CFR Parts 141–143. As discussed above, most of the drinking water requirements are not directly based on protecting groundwater. As this chapter concerns groundwater issues, only the MCLs and MCLGs portions, as opposed to the full range of drinking water programs, are discussed here. Many parts of the drinking water regulations were adopted at different times; therefore, not all MCLs or MCLGs are housed in one single consolidated section of the regulations. MCLs are found in 40 CFR §§141.11–.16, 141.61–.64, and 141.66; and MCLGs in 40 CFR §§141.50–.53, and .55. All MCLs and MCLGs that have been promulgated by EPA are listed in Table 32.2. EPA’s detailed UIC regulations are codified in 40 CFR Parts 144–148. Underground injection, unless authorized by permit or rule, is prohibited by §144.11. Moreover, §144.12 states: “no owner or operator shall construct, operate, maintain, convert, plug, abandon, or conduct any other injection activity in a manner that allows the movement of fluid containing any contaminant into underground sources of drinking water, if the presence of that contaminant may cause a violation of any primary drinking water regulation under 40 CFR Part 142 or may otherwise adversely affect the health of persons.” §146.4 provides for aquifer exemptions if the aquifer does not currently serve and cannot in the future serve as a USDW by virtue of its depth, location, existing contamination, or its use for mineral or hydrocarbon extraction; the total dissolved solids content of the aquifer’s ground water is more than 3,000 mg/l and less than 10,000 mg/l; and the aquifer is not reasonably expected to supply a public water system. §146.5 establishes five classes of injection wells. Class I wells are used for the disposal of industrial hazardous, industrial non-hazardous wastes, and municipal (non-hazardous) waste below the lowermost USDW. §§146.11–.14, and .61–.73 contain detailed requirements for siting, constructing, operating, monitoring, and closing Class I wells to ensure that contaminants are unable to migrate into a USDW. Parts 144.60–.70 define the financial responsibilities for Class I well owners and operators. Nearly 500 Class I injection wells at more than 290 active facilities are scattered throughout the United States in 19 states. The greatest concentration of Class I wells occurs in the Gulf Coast, Great Lakes, and Florida regions. Class II wells are used for injection of oil and gas industry wastes, injection of fluids for enhanced oil recovery, or underground storage of liquid hydrocarbons. §§146.21–.24 provide detailed requirements for construction, monitoring, operations, and closure. Approximately 170,000 Class II wells exist in 31 states. Class III wells are used for mineral extraction. The two primary mining processes that use Class III wells are solution mining and in situ leaching. §§146.31–.34 contain detailed requirements for construction, monitoring, operations, and closure. The Class III category includes approximately 20,000 wells at 200 facilities in 18 states, primarily in the South and Southwest. Under the Federal UIC regulations, all Class I, II, or III wells must be permitted by the EPA or an approved primacy state (§144.31). Class IV wells inject hazardous or radioactive wastes into or above a USDW (§144.13). Class IV wells, which are considered to be a threat to USDWs, are prohibited, except when used for CERCLA or RCRA cleanups, or injections to exempted aquifers. Identified Class IV wells must be closed and considered for remediation. The final class of injection wells is not a specific type of well but serves as a catch-all for injection wells that do not fall into one of the other classes. Class V wells include drywells, sumps, drain fields, drainage wells, and some septic systems, among others. Class V wells have been widely used in many parts of the country without having typically been subjected to extensive permitting requirements. Most Class V wells are drainage wells or wells involving sewage disposal — septic tanks, drain fields, and cesspools. EPA does not have an accurate count or even rough estimate of the number of Class V wells in the United States. The number very likely exceeds 1 million wells.
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New Class V regulations were adopted in 2002 (144.79–.89). Class V wells are generally authorized by rule — a type of authorization given through blanket regulatory approval. However, large-capacity cesspools and motor vehicle waste disposal wells located in a groundwater protection area or sensitive groundwater area must be permitted or closed. Other types of Class V wells are subject to various regulatory requirements. Movement of fluid into USDWs that might cause endangerment is not permitted. Moreover, well owners must comply with other Federal or State UIC requirements. And finally, wells must be properly closed. Under certain circumstances EPA can require a permit for individual wells (§§144.24–.25). §§144.51–.55 contain various conditions that are applicable to all UIC permits. In 40 CFR Part 147 the applicable Underground Injection Control (UIC) programs for the states, territories, and possessions are codified. The applicable UIC program for a state is either a State-administered program approved by EPA, or a federally administered program promulgated by EPA. In some cases, the UIC program may consist of a State-administered program applicable to some classes of wells and a federally administered program applicable to other classes of wells. In all cases readers should consult 40 CFR Part 147 concerning the current program authorization status for UIC activities in a particular state. 40 CFR Part 148 identifies hazardous wastes that are restricted from disposal into Class I hazardous waste injection wells, and defines those circumstances under which a waste that is otherwise prohibited from injection may be injected. EPA’s hazardous waste injection restrictions actually implement §3020 of RCRA, but are discussed here because EPA’s UIC regulatory program covers both SDWA and RCRA requirements. EPA’s sole source aquifer regulations are codified in 40 CFR Part 149. Federal regulations are minimal as the language in the SDWA (§§1424(e) and 1427) is already rather specific. Subpart A (§§149.1–.3) provides two alternative sets of criteria for identifying critical aquifer protection areas (§149.3). A critical aquifer protection area is an area designated as a sole or principal source aquifer prior to June 19, 1986, and for which an areawide groundwater quality protection plan was approved prior to that date. A critical aquifer protection area is also a major recharge area of a sole or principal source aquifer, designated before June 19, 1988, for which the sole or principal source aquifer is particularly vulnerable, contamination is likely to occur without a control program, and significant cost would accrue. Subpart B (§§149.100–.110) describes Federal requirements for protecting the Edwards Underground Reservoir. This is the sole or principal drinking water source for the San Antonio area, and if contaminated, would create a significant hazard to public health. The Edwards Underground Reservoir is the only aquifer subject to specific regulations promulgated by EPA. EPA’s Office of Ground Water and Drinking Water periodically publishes a list of the sole source aquifers in the United States. The types of requirements placed on these sole sources aquifers through State programs are similar to the Federal regulations governing the Edwards Underground Reservoir. EPA has not adopted regulations governing wellhead protection programs, although EPA does require states to submit wellhead protection plans (§1428 of the SDWA). As in the case for the sole source aquifer program, the SDWA language for the wellhead protection program is rather specific. Most states have developed wellhead protection programs, and the actual implementation of most wellhead protection programs occurs at the state and local levels. Over 4000 communities nationwide conduct some form of wellhead protection. This section has only presented the Federal SDWA regulations. As states take a lead role in groundwater protection activities, readers are encouraged to work with state regulatory agencies to determine specific groundwater protection requirements. Although not required by the SDWA, EPA has encouraged each state to develop a Comprehensive State Ground Water Protection Program (CSGWPP) that focuses on a hierarchy of priorities: prevention of contamination whenever possible; prevention of contamination based on the relative vulnerability of the resource, and where necessary, the groundwater’s use, value, and vulnerability; and remediation commensurate with the relative use and value of groundwater. A CSGWPP incorporates goal and priority setting, assignment of responsibilities to different stakeholders, implementation, data collection, and public participation. States with CSGWPPs are eligible for greater flexibility in grant funding and program administration.
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32.4.3 SDWA Summary The SDWA places indirect and direct controls on groundwater quality. The MCLs serve as overriding targets for groundwater quality even though they are intended as drinking water standards that must be met at the tap. The UIC program regulates injection of fluids and wastes into underground formations. The sole source aquifer, wellhead protection, groundwater protection, and source water protection programs are designed to prevent drinking water aquifers from becoming contaminated. States play the largest role in program managing and receive extensive support from local governments.
32.5 Resource Conservation and Recovery Act (RCRA) 32.5.1 RCRA Legislative Background 32.5.1.1 Historical Perspective RCRA, as enacted in 1976, gave EPA broad authority to develop a hazardous and solid waste management regulatory program to promote recycling and ensure protective waste management practices. However, little guidance was included on how to do it, and EPA first focused on the regulation of non-hazardous solid wastes. As a result, by 1984, the Agency had managed to issue permits (EPA’s approach to ensuring protective waste management practices) to only five of the thousands of operating hazardous waste land disposal facilities. Meanwhile, Congress had become even more aware of the effects that land disposal of hazardous wastes was having on the environment (especially groundwater). Congress was intent on preventing contaminated sites that could require future cleanups under CERCLA, but lacked confidence in EPA’s ability to develop an effective program. Hence, the Hazardous and Solid Waste Amendments of 1984 (HSWA) were passed, containing a level of detail unprecedented in environmental law and fundamentally altering the RCRA program. Provisions were included that would automatically take effect unless EPA issued within specified time frames regulations to significantly reduce, and comprehensively control, land disposal of hazardous wastes. As a result, between 1986 and 1998, treatment standards specifying the method or level of treatment for all hazardous wastes were identified. After 1998, development and updating of hazardous waste treatment standards became an ongoing process that continues as new hazardous wastes are identified. The HSWA also mandated that EPA create a Corrective Action Program under which cleanups have been initiated at RCRA-permitted hazardous waste treatment, storage, and disposal facilities where waste has been determined to be leaking into the environment from any source. 32.5.1.2 Goals and Objectives §1003(b) of RCRA declares the national policy of the United States to be: “wherever feasible, the generation of hazardous waste is to be reduced or eliminated as expeditiously as possible. Waste that is nevertheless generated should be treated, stored, or disposed of so as to minimize the present and future threat to human health and the environment.” 32.5.1.3 General Provisions In general, RCRA regulates solid waste, which includes nonhazardous solid waste and hazardous waste produced by industrial processes. Subtitle D of the statute deals with nonhazardous solid waste by directing EPA to promulgate guidelines for use by states, which are directed to develop and implement solid waste management plans and to establish permitting programs for certain solid waste management facilities. Subtitle C, on the other hand, authorizes EPA to develop and implement all or portions of an extensive Federal program for regulating the management of hazardous wastes. Upon request, qualified states can be authorized by EPA to implement the Federal hazardous waste program. State regulations must be at least as stringent as EPA’s. When EPA finalizes new Federal hazardous waste regulations, EPA implements them in all states until the states become authorized, unless the new Federal regulations are based on RCRA authority that pre-dated HSWA, or are less stringent than existing ones. In the latter two situations,
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the new Federal regulations usually take effect in a state only after the state has adopted and received EPA approval for implementing its regulations. States also sometimes use their own laws as authority to regulate hazardous wastes, independent of RCRA. Readers should check with the state waste management agencies to determine which state and federal hazardous waste regulations are applicable to their facilities. Also of interest in RCRA is Subtitle I, which regulates underground storage tanks (USTs) containing petroleum and hazardous substances as defined by the CERCLA. Subtitle I does not cover USTs containing hazardous wastes that are regulated under Subtitle C. Like Subtitle C, Subtitle I allows states to be authorized by EPA to implement the Federal UST program, provided that their regulations are no less stringent than the corresponding EPA requirements. 32.5.1.4 Issues and Outlook During the mid- and late 1990s, leaders in both the Administration and Congress were interested in amending RCRA in ways that would speed the cleanup of hazardous waste sites. However, despite much discussion of draft legislation at the time, no bills were passed, and the momentum for such legislation subsided significantly after 2000. Notwithstanding, improvements in the coordination, speed, and effectiveness of cleanups continues to be an issue. EPA’s One Cleanup Program (http:www.epa.gov/oswer/onecleanupprogram/) was established to address this issue by (1) promoting more consistent and effective cleanups, (2) providing clear and useful information to stakeholders about the cleanup of contaminated properties, and (3) developing meaningful measures to demonstrate the overall effectiveness and benefit of cleanup efforts. Another primary focus of EPA’s RCRA regulatory activities is the goal of reducing the amount of waste generated and changing the ways in which society identifies materials as wastes. In furtherance of this goal, EPA continues to pursue finalization of its proposed rule entitled “Revisions to the Definition of Solid Waste,” which would revise the regulatory definition of solid waste by identifying certain recyclable hazardous secondary materials as not “discarded” and thus not subject to regulation as wastes under Subtitle C of RCRA (68 FR 61558; October 28, 2003). In addition, EPA is promoting legislation, regulations, and voluntary programs that encourage the reuse or recycle of electronic products. EPA also supports development and use of Environmental Management Systems by all types of organizations to provide a structured approach for managing environmental and regulatory responsibilities.
32.5.2 RCRA Regulations Because of the large number of RCRA regulations that deal with groundwater protection, this section of the chapter relies primarily on summary tables. 32.5.2.1 Hazardous Waste 32.5.2.1.1 Introduction Regulations implementing RCRA Subtitle C, “Hazardous Waste Management,” are located in 40 CFR 260–279. Of these, Part 264, “Standards for Owners and Operators of Hazardous Waste Treatment, Storage and Disposal Facilities,” Part 265, “Interim Status Standards for Owners and Operators of Hazardous Waste Treatment, Storage and Disposal Facilities,” and Part 280, “Underground Storage Tanks,” contain specific groundwater monitoring provisions. HSWA created two regulatory programs particularly designed to prevent the migration of hazardous constituents into groundwater as a result of hazardous waste management activities: the Land Disposal Restrictions (LDR) program and the Corrective Action program. Regulations addressing corrective action are located in Part 264, Subparts F, “Releases from Solid Waste Management Units,” and S, “Special Provisions for Cleanup.” The LDR program is governed by Part 268, “Land Disposal Restrictions,” which identifies hazardous wastes that are restricted from land disposal and defines the limited circumstances under which an otherwise restricted waste may continue to be stored and land disposed. Elsewhere in Title 40 of the CFR, Part 260 contains definitions and general provisions that apply to all facilities and wastes governed by RCRA Subtitle C. Part 261 defines the terms solid waste and hazardous
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waste. For a waste to be regulated under RCRA Subtitle C, it must first fall within the definition of solid waste. Waste that does not meet this definition cannot be RCRA hazardous waste. Unfortunately, the definitions of solid waste and hazardous waste are very complicated, making it sometimes difficult to determine whether a particular waste is regulated. 32.5.2.1.2 Facility Standards Once a waste meets EPA’s hazardous waste definition, generators, transporters, and all facilities that treat, store or dispose of it, must comply with applicable RCRA regulatory requirements. Such requirements are intended to encourage minimization of hazardous waste generation, and ensure that hazardous waste management facilities and practices prevent migration of hazardous constituents into the environment, including groundwater. They are also intended to ensure that if hazardous constituents do migrate into the environment, corrective action will occur. Of particular concern with respect to groundwater protection are hazardous waste facilities and practices involving placement of hazardous waste on or into the land. Therefore, RCRA regulations governing such facilities and practices contain specific groundwater protection provisions, which are summarized briefly in Table 32.3 and Table 32.4. Table 32.3 covers the regulations applicable to owners and operators of hazardous waste treatment, storage and disposal facilities that hold RCRA permits (Part 264). Table 32.4 covers the regulations applicable to interim status facilities (Part 265). To qualify for interim status, the owner or operator must: (a) have been treating, storing, or disposing of the hazardous waste, or commenced facility construction on or before October 31, 1976 (the date RCRA was enacted), or on or before the date on which the waste being managed became subject to RCRA permitting requirements; (b) notify EPA of hazardous waste activities, as required in RCRA §3010; and (c) apply for a permit under Part 270. Generally, the Part 265 regulations specify a minimal groundwater monitoring program to detect hazardous releases to the uppermost aquifer at interim status surface impoundments, landfills, and land treatment facilities. In contrast, Part 264 imposes minimum technology designs on tanks, surface impoundments, waste piles, land treatment facilities, and landfills that are seeking RCRA permits, and requires all solid waste management units (SWMUs) at facilities seeking RCRA permits to comply with corrective action requirements designed to identify and remediate hazardous releases. 32.5.2.1.3 Land Disposal Restrictions Under the LDR program, no hazardous waste can be land disposed after a specified date unless it has been: (a) treated prior to disposal in accordance with standards established by EPA; (b) treated prior to disposal in accordance with a case-by-case treatability variance granted by EPA; (c) disposed of in a facility that will prevent migration of hazardous constituents for as long as the waste remains hazardous; (d) approved for a national capacity variance granted by EPA; or (e) approved for a case-by-case capacity variance granted by EPA. In addition, storage of untreated hazardous waste beyond one year is prohibited, unless the storage occurs in tanks, containers, or containment buildings solely to facilitate proper recovery, treatment, or disposal and certain labeling and record keeping requirements are met. While this program does not directly address groundwater monitoring or remediation, its treatment requirements and limitations on storage of hazardous waste have significantly affected hazardous waste management practices that could result in groundwater contamination. 32.5.2.1.4 Corrective Action Program Prior to HSWA, corrective action requirements under RCRA were applicable only to onsite releases of hazardous waste to groundwater from surface impoundments, waste piles, land treatment units, and landfills that received wastes after July 26, 1982 (referred to as regulated units). HSWA expanded corrective action requirements to cover both onsite and offsite releases to all environmental media from solid waste management units at all facilities seeking RCRA permits, including interim status facilities. EPA incorporated the HSWA language regarding corrective action very quickly into its rules (existing 40 CFR 264.90–.101). Even so, the Agency did not propose comprehensive implementing regulations until 1990 (55 FR 30798; July 27, 1990). As proposed, these regulations (referred to as the “1990 Subpart S
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TABLE 32.3 Groundwater Protection Provisions for Hazardous Waste Treatment, Storage and Disposal Facilities with RCRA Permits Provision
Description
40 CFR 264.90
40 CFR 264.91
40 CFR 264.92
40 CFR 264.93 40 CFR 264.95 and 264.96
40 CFR 264.97 40 CFR 264.98–264.100 40 CFR 264.101
40 CFR 264, Subpart G, Closure and Post Closure (264.110–264.120) 40 CFR 264.193, 264.221, 264.251, 264.272, and 264.301 40 CFR 264.551
40 CFR 264.552
Requires solid waste management units to comply with corrective action requirements in 40 CFR 264.101, but allows surface impoundments, waste piles, land treatment units or landfills that received hazardous waste after July 26, 1982 (referred to as “regulated units”) to comply with 40 CFR 264.91–264.100 in lieu of 264.101 and, under certain circumstances, allows the EPA Regional Administrator to replace all or part of the requirements in 40 CFR 264.91–264.100 with alternative requirements for groundwater monitoring and corrective action for releases to groundwater. (1) Requires owner/operator to implement compliance monitoring under 264.99 whenever hazardous constituents under 264.93 from a regulated unit are detected at a compliance point under 264.95; (2) Requires owner/operator to institute corrective action under 264.100 whenever the groundwater protection standard under 264.92 is exceeded; (3) Requires owner/operator to institute corrective action under 264.100 whenever hazardous constituents under 264.93 from a regulated unit exceed concentration limits under 264.94 in groundwater between the compliance point under 264.95 and the downgradient facility property boundary; and (4) in all other cases, requires owner/operator to institute detection monitoring under 264.98. Requires owner/operator to comply with permit conditions designed to ensure that hazardous constituents detected in the groundwater from a regulated unit do not exceed concentration limits in the uppermost aquifer underlying the waste management area beyond the point of compliance during the compliance period. Indicates that facility permit will specify the hazardous constituents to which the groundwater protection standard of 264.92 applies. Provides that facility permit will specify the point of compliance at which the groundwater protection standard applies and at which monitoring must be conducted, as well as the compliance period. Requires groundwater monitoring programs to satisfy Parts 264.98–264.100. Establishes owner/operator responsibilities to develop detection monitoring, compliance monitoring and corrective action programs, respectively, for regulated units. Requires applicants for RCRA permits to establish corrective action programs, but clarifies that the requirement does not apply to remediation waste management sites unless they are part of a facility subject to a permit for treating, storing or disposing of hazardous wastes that are not remediation wastes. Requires closure of hazardous waste management units in a manner that, among other things, protects groundwater. Requires closure and post-closure plans that include groundwater monitoring corrective action provisions, if applicable. Establishes unit-specific design and operating requirements for tanks, surface impoundments, waste piles, land treatment units and landfills, respectively, to prevent migration of hazardous wastes or hazardous constituents into groundwater. Establishes requirements for CAMUs that were approved before April 22, 2002, or for which substantially complete applications (or equivalents) were submitted on or before November 20, 2000 (referred to as “grandfathered CAMUs”). Among other things, requires that groundwater monitoring provisions and closure/post-closure provisions that meet certain criteria be specified in a permit or order applicable to the CAMU. Establishes requirements for CAMUs that are not grandfathered CAMUs. Allows certain wastes to be prohibited from placement in a CAMU. Prohibits placing liquids in a CAMU, except under specified conditions. Requires that a permit or order applicable to the CAMU include the specification of design, operation, treatment and closure requirements. Specifies minimum design requirements for CAMUs that include installation of a composite liner, but allows approval of alternative design and operating practices where justified. Specifies minimum treatment requirements for wastes prior to placement into a CAMU, but allows the treatment levels to be adjusted based on certain factors. Establishes requirements for groundwater monitoring, corrective action, and closure/post-closure care.
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TABLE 32.4 Groundwater Protection Requirements for Hazardous Waste Treatment, Storage and Disposal Facility with Interim Status Provision
Description
40 CFR 265.90
40 CFR 265.91 and 265.92 40 CFR 265.93
40 CFR 265.94 40 CFR 265, subpart G, Closure and Post-Closure (265.110–265.120)
Requires owners/operators of interim status surface impoundments, landfills, or land treatment facilities that are used to manage hazardous waste to implement, and operate during the active lives of the facilities as well as during post-closure, groundwater monitoring programs that meet the requirements of 265.91, and comply with 265.92–265.94. Under certain circumstances, alternative groundwater monitoring requirements may be developed and set out in an approved closure or post-closure plan or in another enforceable document. Establish requirements for groundwater monitoring systems and sampling and analysis plans at interim status units, respectively. Requires more comprehensive, alternative groundwater monitoring when an owner/operator of an interim status unit assumes (or knows) that monitoring of indicator parameters in accordance with 265.91 and 265.92 would show statistically significant increases (or decreases in the case of pH) when evaluated under 265.93(b). Establishes record keeping and reporting requirements for groundwater monitoring programs at interim status units. Establishes requirements for closure and post-closure care of interim status units in a manner protective of human health and the environment, including post-closure groundwater monitoring. Mandates corrective action if migration of hazardous constituents is detected.
proposal”) required the collection of enough information to support determinations of whether corrective action would be needed and if so, to support selection and implementation of appropriate corrective action. EPA received numerous comments on the 1990 Subpart S proposal. As a result of this and other pressures and changing priorities, EPA never finalized the proposal, except for a small section dealing with corrective action management units (CAMUs) and temporary units (TUs) (58 FR 8658; February 16, 1993), which are units limited to handling remediation wastes. Notwithstanding, the Agency used the 1990 Subpart S proposal as guidance for many years, and a number of states still have corrective action programs based largely on it. Under the guidance in the 1990 Subpart S proposal, groundwater monitoring frequently is required to satisfy the proposed information collection requirements, and selected corrective actions often include groundwater remediation, with accompanying monitoring to evaluate success. On May 1, 1996 (61 FR 19432), the Agency published an advance notice of proposed rule making, which introduced the “Subpart S Initiative.” The Subpart S Initiative was designed to identify and implement improvements to the protectiveness, responsiveness, speed, and efficiency of the corrective action program. The Agency also discussed corrective action implementation and the evolution of the program since 1990, and set forth its goals and strategy for the future of the corrective action program. The 1996 advance notice provided guidance on areas of the program not addressed by the 1990 proposal, and replaced the 1990 proposal as the primary guidance for much of the corrective action program. In 1999, EPA officially withdrew the 1990 Subpart S proposal and announced that it had determined that such regulations were not necessary to carry out the Agency’s statutory corrective action duties (64 FR 54604; October 7, 1999). Rather, a strategy of reliance on existing regulations (including those provisions of the Subpart S proposal already promulgated), supplemented by guidance and enhanced training was revealed. Accordingly, EPA subsequently issued dozens of guidance documents and interpretive memoranda intended to facilitate corrective action. Of particular interest with respect to groundwater protection is the Handbook of Groundwater Protection and Cleanup Policies for RCRA Corrective Action, which was published in October 2001 and updated in April 2004. Topics addressed in this guidance document include: Groundwater protection and cleanup strategy; short-term protection goals; intermediate performance goals; final cleanup goals; groundwater cleanup levels; point of compliance; cleanup timeframes; source control; groundwater use designations; institutional controls; monitored natural attenuation; technical impracticability; reinjection of contaminated groundwater; performance
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TABLE 32.5 Groundwater Protection Standards for Non-Municipal Non-Hazardous Waste Disposal Units That Receive Conditionally Exempt Small Quantity Generator (CESQG) Waste Provision
Description
40 CFR 257.8 and 257.9 40 CFR 257.22–257.28
Establish criteria for locating non-municipal non-hazardous waste disposal units that receive CESQG waste with respect to floodplains and wetlands. Requires groundwater monitoring systems for contaminant detection at non-municipal non-hazardous waste disposal units that receive CESQG waste. Establishes requirements for groundwater monitoring system design and sampling and analysis. Requires assessment monitoring program, as well as corrective measures evaluation, selection, and implementation, if contaminants are detected.
monitoring; and, completing groundwater remedies. As a guidance document, the Handbook does not impose legally binding requirements, and it expressly acknowledges that its provisions may not apply to a particular situation based upon the specific circumstances of the corrective action facility. The Handbook also recognizes that most states have their own requirements and policies aimed at cleaning up contaminated groundwater, which may vary from federal guidance and policies. Hence, professionals involved in groundwater monitoring and cleanups under RCRA Corrective Action will need to determine on a case-specific basis the requirements of the state where each cleanup is located. 32.5.2.2 Nonhazardous Waste 32.5.2.2.1 Introduction Guidelines for state and regional solid waste plans are located in 40 CFR 255–258. Parts 255 and 256 cover the process by which states are expected to develop and implement solid waste management plans. Part 257 sets criteria for determining which solid waste disposal facilities and practices pose a reasonable probability of adverse effects on health or the environment. Such facilities and practices must be appropriately addressed in the state’s waste management plans. Part 257 also contains criteria for ensuring that non-municipal non-hazardous waste disposal units that receive conditionally exempt small quantity generator (CESQG) waste do not adversely affect human health and the environment. Specifically, Part 257, Subpart B establishes restrictions on locating this type of disposal unit in floodplains and wetlands and establishes requirements for groundwater monitoring and implementation of corrective action at these units. Table 32.5 summarizes provisions of Part 257, Subpart B pertinent to groundwater protection. Finally, Part 258 establishes minimum national standards for location, operation, design, closure, postclosure care, and financial assurance of MSWLF units. It also delineates minimum national standards for corrective action and groundwater monitoring at MSWLFs, and therefore, is of particular interest with respect to groundwater protection issues. Table 32.6 summarizes provisions of Part 258 pertinent to groundwater protection. 32.5.2.3 Underground Storage Tanks 32.5.2.3.1 Introduction In 1984, HSWA added Subtitle I, “Regulation of Underground Storage Tanks,” to RCRA as a result of Congress’ realization that, of several million USTs containing petroleum or hazardous substances in the United States, tens of thousands were leaking, and more would leak in the future. As leaking USTs can cause fires or explosions and can contaminate drinking water and groundwater, Subtitle I was designed to address these issues. EPA’s regulations implementing Subtitle I are located in Parts 280, 281, and 282. Parts 281 and 282 deal primarily with the process by which EPA (1) approves State UST programs, and (2) documents such approvals. Part 280, however, sets technical standards and corrective action requirements for owners and operators of USTs, and is of most interest with respect to groundwater protection planning.
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The Handbook of Groundwater Engineering Groundwater Protection Guidelines for Municipal Solid Waste Landfill Units
Provision
Description
40 CFR 258, subpart B, Location Restrictions (258.10–258.19) 40 CFR 258, subpart C, Operating Criteria (258.20–258.29) 40 CFR 258, subpart D, Design Criteria (258.40) 40 CFR 258, subpart E, Corrective action and Groundwater Monitoring (258.50–258.58) 40 CFR 258, subpart F, Closure and Post-closure Care (258.60–258.74)
TABLE 32.7
Establishes criteria for locating MSWLFs with respect to airports, wetlands, floodplains, seismic zones, fault areas, and unstable areas. Establishes criteria for operating MSWLFs, including among other things, procedures for excluding the receipt of hazardous waste, cover material requirements, requirements for runon/runoff control systems, limitations on surface water discharges, and restrictions on placing liquids in a landfill. Requires design of MSWLFs to assure that concentrations of specified constituents do not exceed certain limits in the uppermost aquifer, and requires composite liners and leachate collection systems. Requires groundwater monitoring systems for contaminant detection at MSWLFs. Establishes requirements for groundwater monitoring system design and sampling and analysis. Requires assessment monitoring program, as well as corrective measures evaluation, selection, and implementation if contaminants are detected. Requires all MSWLF units to prepare a closure plan, install a final cover system designed to minimize infiltration and erosion, and conduct post-closure care for 30 years, including monitoring the groundwater and maintaining the groundwater monitoring system, if applicable.
Groundwater Protection Standards for Underground Storage Tanks
Provision
Description
40 CFR 280.20 40 CFR 280.21 40 CFR 280.30–280.33 40 CFR 280.40–280.43
40 CFR 280.50–280.52 40 CFR 280.53 40 CFR 280.60–280.67
40 CFR 280.70–280.72
Establishes performance standards for new USTs to prevent releases due to structural failure, corrosion, or spills, and overfills. Requires upgrading of existing USTs. Requires operating practices to prevent releases caused by spills, overfills, corrosion, incompatibility of content and tank materials, or repairs. Requires new and existing UST systems to be equipped with a method, or combination of methods, of release detection, and establishes standards for such methods. Standards for groundwater monitoring are included. Requires reporting and investigation of suspected releases. Requires reporting and cleanup of spills and overfills. Requires response and corrective action for confirmed releases, including reporting, initial abatement, initial site characterization, free product removal, site investigations for soil and groundwater contamination, preparation of corrective action plan, and public notice. Establishes requirements for temporary and permanent closure, including measurements for the detection of releases.
32.5.2.3.2 Groundwater Protection at USTs USTs are identified and classified by Part 280 according to five criteria: (a) physical characteristics; (b) exclusions; (c) deferrals; (d) contents (i.e., hazardous substance or petroleum); and (e) age (i.e., new or existing). Together, these criteria define how each UST is regulated. Table 32.7 briefly summarizes the UST groundwater protection provisions of Part 280.
32.5.3 RCRA Summary RCRA, as amended by HSWA, attempts to protect groundwater quality through various programs. States are required to regulate land disposal of nonhazardous solid waste (Subtitle D). EPA is required to regulate underground storage tanks containing petroleum and hazardous substances (Subtitle I), as well as the generation, transportation, treatment, disposal, and release remediation of hazardous waste (Subtitle C).
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32.6 Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA) 32.6.1 CERCLA Legislative Background 32.6.1.1 Historical Perspective In the late 1970s, many US citizens were becoming distressed about the dangers of sites contaminated with hazardous wastes. Perhaps the most famous case was Love Canal. Residents of this small New York community were evacuated after authorities learned that hazardous waste buried over a 25-year period had contaminated the groundwater and surrounding soils. Responding to concerns over Love Canal and similar sites, Congress passed CERCLA, popularly known as the Superfund law, in 1980. (The term “Superfund”refers to the trust fund that Congress established to pay for CERCLA cleanup and enforcement activities.) Because it covers all environmental media (groundwater, surface water, air, and soil), the scope of the Superfund law is broader than most environmental laws. CERCLA also differs from other environmental laws in that it requires EPA to move beyond its traditional regulatory authority and to provide response authority to clean up hazardous waste sites. In 1986, Congress passed the Superfund Amendments and Reauthorization Act (SARA), which reauthorized CERCLA for five years and expanded and strengthened many of its provisions. In 1990, Congress reauthorized CERCLA through 1994 but made no other significant changes. Since then, Congress has introduced several bills to reauthorize the program, but none has passed. In the meantime, many of the reauthorization proposals have been addressed through administrative reforms or court decisions, and annual appropriations have extended the program’s authority. In 2002, the President signed the Small Business Liability Relief and Brownfields Revitalization Act, which facilitated cleanup and revitalization of underutilized, contaminated sites. 32.6.1.2 Goals and Objectives A primary goal of Superfund is to ensure protection of human health and the environment by preventing further contamination and cleaning up contamination at sites to levels called for in existing standards, or, where existing standards do not exist, to acceptable risk levels. Wherever technically practicable, groundwater is to be cleaned up to levels that correspond to those in existing standards, such as MCLs. Another goal is to maximize the involvement of potentially responsible parties in conducting site cleanups. In 1989, EPA conducted the first in a series of evaluations to identify ways to improve the program. Goals resulting from this first evaluation included controlling acute threats immediately; monitoring sites over the long term; developing and using new technologies; and improving efficiency. Between 1993 and 1995, EPA initiated three rounds of administrative reforms designed to meet goals that included enhancing cleanup effectiveness and protectiveness and consistent program implementation. Goals articulated in the most recent administrative review, completed in 2004, included increasing the pace of site cleanups and controlling the risks to human health and the environment by remediating and restoring contaminated sites or properties to appropriate levels. Over the past few years, the goals and performance measures in Superfund have shifted from output-oriented measures (e.g., the number of cleanup completions) to results-oriented measures (e.g., controlling the migration of contaminated groundwater). There are two specific results-oriented goals for groundwater. The first is to control, by 2008, all identified unacceptable human exposures from site contamination to health-based levels or below for current land and groundwater use conditions at 84% (1,259) of the 1,494 Superfund human exposure sites (as of FY 2002). The second is to control, by 2008, the migration of contaminated groundwater through engineered remedies or natural processes at 65% (832) of the 1,275 Superfund groundwater exposure sites (as of FY 2002). 32.6.1.3 General Provisions CERCLA provides Federal funding and enforcement authority to clean up hazardous waste sites that were created in the past. It also provides for response to hazardous spills and requires businesses to report releases of hazardous substances. Pertinent portions of this broad law that pertain to groundwater are summarized below.
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32.6.1.3.1 §104 — Response Authorities §104 authorizes EPA to respond when an actual or threatened release of a hazardous substance may endanger public health or welfare. CERCLA provides for two types of response actions. Removal actions are short-term responses that stabilize or clean up a hazardous site that poses a threat to public health or the environment. Removal actions include capping of contaminated soils to reduce migration of hazardous substances into groundwater and providing temporary alternate sources of drinking water to local residents. The second type of response action is a remedial action. Remedial actions are taken instead of or in addition to removal actions to minimize the migration of hazardous substances so that they do not cause substantial danger to present or future public health or the environment. Remedial actions include the study, design, and construction of longer term actions aimed at permanent remedy. Typical actions include constructing underground walls to control the movement of groundwater and pumping and treating of contaminated groundwater. Both removal and remedial actions must be conducted in accordance with the National Contingency Plan (NCP). 32.6.1.3.2 §105 — National Contingency Plan CERCLA requires EPA to revise and republish the NCP for the removal of oil and hazardous substances, originally prepared and published pursuant to §311 of the CWA. CERCLA requires that the plan reflect the responsibilities created by CERCLA, including the establishment of procedures for responding to releases of hazardous substances. The NCP is published as an EPA regulation in 40 CFR 300. It specifies procedures for identifying, removing, and remedying releases of hazardous substances. §105 also provides for the Hazard Ranking System (HRS). The HRS is a scoring system used to evaluate potential relative risks to human health and the environment from releases or threatened releases of hazardous substances. EPA uses the HRS to determine if a site should be on the National Priorities List (NPL). The NPL is EPA’s list of the most serious hazardous waste sites identified for possible long-term remedial response using money from the Trust Fund. The NCP and the HRS are described further under CERCLA Regulations. 32.6.1.3.3 §121 — Cleanup Standards §121 provides principles governing the cleanup of hazardous substances. §121(a) states that remedial actions are to be selected in accordance with the NCP. §121(b) states that remedies in which treatment permanently and significantly reduces the volume, toxicity, or mobility of the hazardous substances are preferred over remedies that do not provide such treatment. CERCLA requires that remedial actions are to be protective of human health and the environment, cost-effective, and utilize permanent solutions and alternative treatment technologies to the maximum extent practicable. In determining the degree of cleanup, CERCLA provides no standards of its own. However, §121(d)(2) requires site cleanups to attain standards from other Federal and State environmental programs that are applicable or relevant and appropriate requirements (ARARs). §121(d)(2)(A)(ii) states that such remedial actions shall require a level or standard of control which at least attains MCLGs established under the SDWA and water quality criteria established under the CWA, where such goals or criteria are relevant and appropriate under the circumstances of the release or threatened release. §121(d)(2)(B) states that in determining whether or not any water quality criteria under the CWA is relevant and appropriate under the circumstances for the release or threatened release, the designated or potential use of the groundwater must be considered. §121(d)(4) provides limited waivers for achieving ARARs. §121(e) provides that CERCLA cleanups require no Federal, State, or local permits for the portion of any removal or remedial action conducted entirely onsite, where such remedial action is selected and executed in compliance with the rest of §121. §121(f) provides for “substantial and meaningful” State involvement in initiation, development, and selection of remedial actions to be undertaken in that state. §107(a) provides that owners, operators, transporters, or generators potentially responsible for contamination problems at a Superfund site are liable for natural resource damages (NRD) resulting from a release of a hazardous substance. NRD are monetary compensations for injury to, destruction of, or loss of natural resources. Natural resources are land, fish, wildlife, biota, air, water, groundwater, drinking water supplies, and other such resources belonging to, or otherwise controlled by the United States; a state,
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local, or foreign government; or Indian tribe. NRD are distinct from response costs, which are the costs of actions taken under the NCP to remove threats to human health and the environment caused by hazardous substance releases. §301 (c) of CERCLA requires the Department of Interior to promulgate regulations for assessing NRD resulting from hazardous substance releases. The regulations include two types of assessment procedures. “Type A” procedures are standard procedures for simplified assessments, and “Type B” procedures are “alternative protocols for conducting assessments in individual cases.” Unlike many environmental regulatory programs, CERCLA does not provide for State delegation. EPA and its ten Federal regions administer site cleanups financed by the Superfund trust fund. Before the Federal government initiates a fund-financed remedial action, the state in which the site is located must assure that it will provide for future maintenance of response actions and pay for 10% of all costs of remedial action, or 50% if the state had operated the facility undergoing cleanup. Many states have comparable programs that provide for the cleanup of contaminated sites that are not on the Federal NPL. In all cases, concerns of the state and local community are considered in cleanup decisions. 32.6.1.4 Issues and Outlook When CERCLA was enacted 25 years ago, Congress expected that only a few hundred sites would require cleanup and that the program would require relatively modest funding. As of June 2005, there were 1242 sites on the NPL and 64 sites proposed to be added; 298 sites have been dropped. Over the past 10 years, new sites have been added to the NPL at the rate of about 28 per year. At sites with completed RODs, about 85% have required groundwater remediation. Assuming these trends continue, there will be ample opportunity to address groundwater contamination at Superfund sites well into the future. The Superfund program has many critics. Although Congress has struggled to modify and reauthorize CERCLA since 1991, no comprehensive bills have been passed. Key issues pertain to the liability system and to the remedy selection process. CERCLA’s provision that parties are liable for cleanup costs for which they may not have been the cause can result in excessive litigation and other transaction costs that divert money from actual cleanup. Regarding remedy selection, many believe that the prescriptive, cumbersome, and confusing nature of the process has delayed cleanups. Minor amendments have been made to the law to help address some of the liability issues, and EPA has undertaken administrative reforms to respond to the remedy selection issues. In 2005, comprehensive reauthorization of CERCLA is not as high a priority as it was in the 1990s.
32.6.2 CERCLA Regulations Superfund regulations are contained in the NCP (40 CFR 300) and in the Natural Resource Damage Assessment (NRDA) regulations (43 CFR 11). 32.6.2.1 National Contingency Plan The NCP contains procedures for responding to discharges of oil and hazardous substances. Subpart E describes methods and criteria for assessing sites and determining the appropriate response to hazardous substance releases. Site assessment determines whether a site is eligible for cleanup funding and includes the following activities: • • • •
Site Discovery — Identifies hazardous substance releases. Preliminary Assessment — Evaluates existing data to determine need for further action. Site Investigation — Assesses onsite conditions to determine need for HRS scoring. HRS scoring — Applies a mathematical approach to assess the relative risk of a site and determine its eligibility for the NPL. The HRS considers four exposure pathways: groundwater migration, surface water migration, soil exposure, and air migration. The groundwater migration pathway is based on three factor categories: likelihood of release, waste characteristics, and targets. The HRS evaluates these pathways and then combines them to produce an overall score for the site. Appendix A to Part 300 provides details on HRS scoring calculations; §3.0 of that appendix pertains to groundwater pathway calculations.
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• NPL listing — Determines sites eligible for Superfund-financed remedial action. If the unitless score resulting from the HRS process is at least 28.5, the site is placed on the NPL. Once a site is placed on the NPL, the remedial process begins. The NCP provides general expectations to help identify and implement appropriate remedial actions. Some of these pertain to groundwater. For example, 40 CFR 300.420(a)(iii) expects EPA to use institutional controls such as water use restrictions to supplement engineering controls in limiting exposure to hazardous substances. However, institutional controls cannot substitute for active response measures (e.g., restoration of groundwater to its beneficial uses) as the sole remedy, unless such active measures are determined not to be practicable. EPA expects to return usable groundwater to its beneficial uses whenever practicable within a time frame that is reasonable; when restoration of groundwater to beneficial uses is not practicable, EPA expects to prevent further migration of the plume, prevent exposure to the contaminated groundwater, and evaluate further risk reduction. The NCP prescribes the following specific activities for the remedial action process: • Remedial investigation (RI) — Determines the nature and extent of the problem presented by a release. The RI includes field investigations to assess the characteristics of groundwater and other environmental media. A site-specific risk assessment is conducted to characterize the current and potential threats to human health and environment that may be posed by contaminants migrating to groundwater, surface water, and other pathways. The results of the baseline risk assessment help establish acceptable exposure levels for developing remedial alternatives in the feasibility study. • Feasibility study — Develops and evaluates options for remedial action. Remediation goals are set to establish acceptable exposure levels that are protective of human health and the environment. For groundwater, MCLGs established under the SDWA that are set at levels above zero are to be attained by remedial actions for ground or surface waters that are current or potential sources of drinking water, where the MCLGs are relevant and appropriate. If an MCLG is determined not to be relevant and appropriate, the corresponding MCL is to be attained where relevant and appropriate. Where the MCLG for a contaminant has been set at zero, the MCL is to be attained by remedial actions for ground or surface waters that are current or potential sources of drinking water, where the MCL is relevant and appropriate. • Remedy selection — Identifies the likely remedial alternative and provides for public comment. The Record of Decision (ROD) is the official report that documents the background information on the site and describes the chosen remedy and the justification for that remedy. • Remedial design — Prepares technical plans for implementing the chosen remedy. • Remedial action — Implements the remedial design. • Operation and Maintenance — Ensures that the cleanup methods are working properly after a response action occurs. A groundwater restoration activity will be considered administratively complete when: (a) actions restore ground or surface water quality to a level that assures protection of human health and the environment; (b) actions restore groundwater or surface water to such a point that reductions in contaminant concentrations are no longer significant; or (c) ten years have elapsed, whichever is earliest. Ground or surface water measures initiated for the primary purpose of providing a drinking water supply and not for the purpose of restoring groundwater do not constitute treatment. 32.6.2.2 Natural Resource Damage Assessments CERCLA authorizes the United States, individual States, Indian Tribes and foreign governments to act on behalf of the public as Natural Resource Trustees for natural resources under their respective trusteeship. Natural Resource Damage Assessments (NRDA) regulations (43 CFR 11) define the process whereby a natural resource trustee may pursue compensation on behalf of the public for injury to natural resources resulting from releases of hazardous substances. Individual NRDAs follow specific procedures for determining whether an injury has occurred to groundwater (and other) resources and for determining if the exposure pathway was through groundwater or another medium. Procedures also exist for testing
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and sampling to determine injury and for quantifying baseline conditions and effects of the release on groundwater (and other) resources to determine the appropriate amount of compensation. 32.6.2.3 CERCLA Guidance Guidance is designed to implement national policy, but it does not substitute for statutes or regulations, and, unlike regulations, does not require a public notice and comment process. Guidance provides direction but does not impose legally binding requirements on EPA, states, or the regulated community. EPA has issued guidance relevant to groundwater in the areas of monitored natural attenuation, presumptive remedies, vapor intrusion, and technical impracticability. 32.6.2.4 Monitored Natural Attenuation Natural attenuation processes include natural physical, chemical, and biological process that act to reduce the mass, toxicity, mobility, volume, or concentration of contaminants in groundwater or soil. These processes include biodegradation, dispersion, dilution, sorption, volatilization, radioactive decay, and chemical or biological stabilization, transformation, or destruction of contaminants. As the understanding of these processes has increased, so too has the interest in using Monitored Natural Attenuation (MNA) as a component of groundwater treatment strategies. MNA refers to the reliance on natural attenuation processes that are part of a controlled and monitored cleanup approach to achieve sitespecific remediation objectives in a reasonable time frame. Potential advantages of using MNA compared with active remediation include reduced potential for cross-media transfer of contaminants, reduced risk of human exposure to contaminants, reduced intrusion from fewer surface structures, and potentially lower overall remediation costs. Potential disadvantages can include increased time to achieve remediation objectives, toxicity and or mobility products that may be more hazardous than the parent compound, and the need for institutional controls to ensure long-term protection. In 1999, EPA issued guidance entitled Use of Monitored Natural Attenuation at Superfund, RCRA Corrective Action, and Underground Storage Tank Sites, which clarified the Agency’s policy on the use of MNA for the cleanup of contaminated groundwater and soil. The guidance states that EPA considers MNA to be a means of addressing contamination under a limited set of site circumstances where its use meets the applicable statutory and regulatory requirements. It also said that a decision to implement MNA should include comprehensive site characterization, risk assessment where appropriate, and measures to control sources. 32.6.2.5 Presumptive Remedies Since the 1980s, EPA has found that certain categories of sites have similar characteristics. By using information acquired from evaluating and cleaning up such sites, EPA has developed “presumptive remedies” to accelerate future cleanups of these sites. Presumptive remedies are preferred technologies for common categories of sites that are developed on the basis of historical patterns of remedy selection and EPA’s scientific and engineering evaluation of performance data on technology implementation. In October 1996, EPA issued guidance entitled, Presumptive Response Strategy and Ex-Situ Treatment Technologies for Contaminated Ground Water at CERCLA Sites, Final Guidance. This guidance outlines a “phased approach” for addressing contaminated groundwater, which integrates the site characterization, early actions, remedy selection, design, implementation, and performance-monitoring phases. The strategy suggests ways to optimize the selected remedy to improve effectiveness and decrease costs and time. It identifies and describes presumptive technologies for treatment of extracted groundwater. These technologies include air stripping, granular/activated carbon, chemical/ultraviolet oxidation, aerobic biological reactors, chemical precipitation, ion exchange/adsorption, electrochemical methods, and aeration of background metals. Since issuing the guidance, EPA has been investigating additional ways to streamline groundwater response strategies. For example, for removing volatile organic compounds from groundwater, the Agency could modify its current practice of developing a unique design for each site, to developing standard designs that could be adapted to a particular site, water chemistry, and suite of chemicals.
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32.6.2.6 Vapor Intrusion Volatile chemicals in contaminated groundwater or soils can emit vapors that may migrate through subsurface soils. Vapor intrusion is the upward migration and entry of contaminants to indoor air from underlying groundwater or soil contamination sources. It is commonly associated with petroleum products, chlorinated solvents, and other volatile organic chemicals in groundwater and soil. High water tables and coarsely grained soils can increase the likelihood of intrusion. Vapor intrusion is of concern because in extreme cases, the accumulated vapors may cause safety hazards (e.g., explosion), acute health effects, or aesthetic problems (e.g., odors). Vapor intrusion has direct links to CERCLA cleanups. The potential for subsurface migration of vapors via the indoor air pathway, particularly at cleaned up sites that are being redeveloped, is a growing concern, and investigations are becoming increasingly common. In 2002, EPA issued Draft Guidance for Evaluating the Vapor Intrusion to Indoor Air Pathway from Groundwater and Soils, and many states are issuing their own guidance on the subject. EPA’s guidance provides a tool for conducting a screening evaluation to determine whether the vapor intrusion exposure pathway is complete (i.e., that humans are exposed to vapors originating from site contamination) and, if so, whether it poses an unacceptable risk to human health. At the time of this writing, EPA is considering revising the guidance to, among other things, more accurately address the actual risks associated with vapor intrusion. 32.6.2.7 Technical Impracticability The remediation of the most highly contaminated groundwater sites, such as those with dense nonaqueous phase liquids, is technically challenging. While the goal of groundwater cleanup at Superfund sites is to restore contaminated groundwater to ARAR-based levels where technically practicable, EPA studies indicate that complex site hydrogeology, contaminant characteristics, and other factors make complete restoration of some contaminated groundwaters technically impracticable with available technologies. Both CERCLA and the NCP allow for the waiving of ARAR-based levels for technical impracticability from an engineering perspective. In 1993, EPA issued Guidance for Evaluating the Technical Impracticability of Ground-water Restoration, which explains how EPA determines whether groundwater restoration at Superfund sites is technically impracticable, and, if so, the alternative measures that must be undertaken to ensure that a final remedy is protective. The guidance covers the types of technical data needed to determine technical impracticability, decision criteria, and alternative remedial strategies.
32.6.3 CERCLA Summary In summary, CERCLA provides for the cleanup of groundwater and other media at old or abandoned sites contaminated by releases of hazardous substances. The law contains no cleanup standards of its own, relying instead on requirements from other Federal and State environmental programs such as the CWA and the SDWA. Many Superfund critics blame the law and its regulations for high cleanup costs and slow cleanup progress. Congress has been trying to reauthorize and improve the law since 1991. Over the years, the scope of the Superfund program has expanded. Response actions aimed at rapid site cleanup to eliminate immediate threats to human health and the environment have expanded to include responses to terrorist activities and other non-waste site cleanup emergencies. In the early years, remedial actions focused on drum disposal sites and landfills; today they include sediments in harbors and mining sites. The universe of Superfund sites has also expanded, with many sites requiring multiple cleanup remedies. Many sites have moved from the assessment phase to the cleanup phase, and today, many are entering the post-construction completion phase, which often requires groundwater monitoring and institutional controls to ensure that the cleanup remains effective.
32.7 Other Laws Two other laws are of interest in the area of groundwater regulation: • The Surface Mining Control and Reclamation Act of 1977 (SMCRA), Public Law 95-87, 30 U.S.C. §1201 et seq.
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• Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA) of 1947, Public Law 80-104, 7 U.S.C. §136 et seq.
32.7.1 SMCRA SMCRA provides general regulatory requirements governing surface coal mining and the surface impacts of underground coal mining. SMCRA requires the Office of Surface Mining (OSM) in the US Department of Interior to promulgate a federal program that controls surface coal mining and reclamation operations, and serves as a model for authorized state programs. The minimum general environmental protection performance standards established by the law include those directed at minimizing disturbances to the quality and quantity of water in groundwater systems. OSM has implemented general standards governing groundwater protection performance (30 CFR §715.17(h)) and water rights and replacement (30 CFR §715.17(i)). The groundwater protection performance standard requires that the recharge capacity of reclaimed lands must be restored to approximate pre-mining capacity. In addition, backfilled material must be placed on reclaimed land in a fashion that minimizes adverse impacts on groundwater flow and quality. Finally, groundwater monitoring must be conducted to determine the effects of mining and reclamation operations relative to the recharge capacity of reclaimed land as well as the water quantity and quality in groundwater systems at the mine area and in associated offsite areas. OSM’s water rights and replacement standard is triggered when mining activities affect the underground water supply source of an owner with interest in real property who uses the water for domestic, agricultural, industrial, or other legitimate purposes. In the overall context of SMCRA implementation, the absence of historic data allowing interested parties to systematically track groundwater quality and quantity impacts from mining and reclamation activities has been identified as one of the principal issues.
32.7.2 FIFRA FIFRA requires EPA to regulate the sale and use of pesticides in the United States through registration and labeling requirements. EPA is given the mandate to restrict the use of pesticides as necessary for the purpose of preventing unreasonable adverse effects on humans and the environment. FIFRA does not specifically mention groundwater. However, FIFRA does address concerns related to user risk, risk-benefit relationships, and consumption of food and drinking water.
Glossary The following definitions are provided for the readers’ better understanding and are not necessarily the same as the applicable legal definitions. Absolute dominion The right of the landowner to capture the groundwater beneath the surface land. The doctrine is also known as the English rule or rule of capture. ARARs Applicable or relevant and appropriate requirements include any standard, requirement, criteria, or limitation under any Federal environmental law, (e.g., CWA, SDWA, TSCA (Toxic Substances and Control Act), RCRA) and any promulgated standard, requirement, criteria, or limitation under a State environmental or facility siting law that is more stringent than any Federal standard requirement, criteria, or limitation. CAMUs Corrective action management units are land areas, located within a RCRA-regulated facility, that have been designated by EPA or the authorized state for the purpose of managing remediation wastes generated from corrective action activities at that facility. CESQG A generator is a conditionally exempt small quantity generator in a calendar month if he generates no more than 100 kg of hazardous waste in that month.
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Conjunctive management The coordinated and integrated management of surface and groundwater resources. Corrective action A corrective action is any action taken to remedy a hazardous release. Correlative use The right of landowners to withdraw groundwater from a common pool according to their respective proportions of overlying land. The doctrine is also known as the common resource rule. CSGWPP The Comprehensive State Ground Water Protection Program is an EPA program that attempts to focus State resource on prevention of contamination and remediation based on the relative use and value of groundwater. Hazardous substance A hazardous substance includes but is not limited to any substance designated under the CWA, the Clean Air Act (CAA), TSCA, or any “hazardous waste” under RCRA. Hazardous waste A hazardous waste is defined as any solid waste that is not excluded from RCRA Subtitle C regulation, and that exhibits a hazardous characteristic, is listed as hazardous waste under RCRA regulations, or is mixed with or derived from hazardous waste. HRS The Hazard Ranking System is a scoring system used to evaluate potential relative risks to human health and the environment from releases or threatened releases of hazardous substances. Injection well Practically speaking, an injection well is a hole in the ground that is deeper than it is wide and that receives wastes or other fluids. Under the UIC program, drain fields, leach fields, drywells, and sumps are considered to be injection wells even though traditionally they have not been thought of as wells. LDRs Land disposal restrictions treatment standards are EPA regulations adopted under RCRA specifying concentration levels or methods of treatment that substantially diminish the toxicity or likelihood of migration of hazardous constituents from hazardous wastes placed into or onto the land. MCLs Maximum contaminant levels are enforceable standards for drinking water quality. MCLs may be less stringent than MCLGs as they consider not only human health protection but also the availability of economically achievable treatment technology. MCLGs Maximum contaminant level goals are nonenforceable targets set to protect human health. MSWLF A municipal solid waste landfill is a discrete, publicly or privately owned area of land that receives household waste (e.g., garbage, trash and sanitary waste from homes, hotels, campgrounds, etc.), and may receive commercial and industrial solid waste, nonhazardous sludge, or hazardous waste from generators exempt from RCRA Subtitle C because they produce such small quantities. NCP Officially known as the National Oil and Hazardous Substances Pollution Contingency Plan (40 CFR 300), the NCP outlines the responsibilities and authorities for responding to releases into the environment of hazardous substances and other pollutants and contaminants under the statutory authority of CERCLA and §311 of the CWA. NPDES The National Pollutant Discharge Elimination System is a Federal program that issues wastewater discharge permits to all point source discharges to surface water. NPL The National Priorities List is EPA’s list of the most serious hazardous waste sites identified for possible long-term remedial response using money from the Superfund Trust Fund. NRD Natural Resource Damages are monetary compensations for injury to, destruction of, or loss of natural resources. NRDA Natural Resource Damage Assessments are processes whereby a trustee assesses the damages to natural resources resulting from a release of a hazardous substance under the Superfund law. Natural resources Natural resources are the land, fish, wildlife, biota, air, water, groundwater, drinking water supplies, and other such resources controlled by Federal, State, local, or foreign governments, or Indian tribes. Nonpoint sources Nonpoint sources of pollution are those that do not enter surface or groundwater through discrete pipes or conveyances. They include agricultural runoff, atmospheric deposition, groundwater inflow to stream beds, acid mine drainage, and some types of stormwater runoff.
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POTW A publicly owned treatment works is a wastewater treatment plant owned by a state or local government. Prescription Acquisition of a personal right to use water by reason of continuous usage. Prior appropriation The landowner’s right to use available water based on dates of appropriation pursuant to a government-administered permit system. RCRA base program The RCRA base program is defined as all RCRA Subtitle C requirements imposed prior to enactment of the Hazardous and Solid Waste Amendments of 1984. RI A Remedial Investigation is a process used under the National Contingency Plan to determine the nature and extent of the problem(s) presented by a release of a hazardous substance ROD A Record of Decision is a public document that explains which cleanup alternative(s) will be used at a National Priorities List site. Reasonable use The right of the landowner to capture the groundwater beneath the surface land, subject to making reasonable use of the resource. The doctrine is also known as the American rule. Remediation wastes Remediation wastes are wastes managed for the purpose of implementing corrective action. Restatement of Law A series of volumes authored by the American Law Institute that describe the law in a general area; for example, Restatement of the Law of Torts. Release A release is any spilling, leaking, pumping, pouring, emitting, emptying, discharging, injecting, escaping, leaching, dumping, or disposing into the environment. Excluded from the definition of release are workplace exposures covered by OSHA, vehicular engine exhausts, radioactive contamination covered by other statues, and the normal application of fertilizer. Sole source aquifer A sole source aquifer is a sole or principal drinking water source for an area. Solid waste A solid waste is any material that has been discarded by being abandoned, recycled, or considered inherently waste-like, and that is not excluded from RCRA Subtitle C requirements. Source water protection program A program that protects drinking water supplies through evaluation of the activities that might cause undesirable pollutants to enter drinking water source waters and the system’s susceptibility to contamination and implementation of controls. SWMU A solid waste management unit is any discernable unit at which solid wastes have been placed at any time, irrespective of whether the unit was intended for the management of solid or hazardous wastes. Takings The Fifth Amendment to the US Constitution prohibits the government from taking private property for public use without paying the owner just compensation. Regulatory takings issues involve the allegations by owners that the government’s regulations restrict the use of their property and cause reductions in property values. TUs Temporary units are tanks or container storage units, located within the boundaries of a RCRAregulated facility, that have been designated by EPA or the authorized state for use in treating and storing remediation wastes generated from corrective action activities at that facility, and that will operate for no longer than one year. UIC The Underground Injection Control program is a Federal program that regulates injection of fluids underground through injection wells. USDW An underground source of drinking water is an aquifer that presently serves or could reasonably be expected to serve as drinking water supply. USTs Under RCRA, USTs are underground storage tanks containing petroleum and hazardous substances. Watershed management approach The watershed management approach is a framework for environmental management that focuses efforts to address the highest priority problems within hydrologically defined geographic areas, taking into consideration both ground and surface water flow. Wellhead protection programs Wellhead protection programs are designed to impose controls on activities located in surface and subsurface areas surrounding a well that supplies a public water system, through which contaminants are reasonably likely to move toward and reach the well.
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Further Information Groundwater Allocation and Management Henley, T., Arizona Department of Water Resources, Groundwater Resources of the Lower Colorado Region, in University of Colorado School of Law, Natural Resources Law Center, 2004 Summer Conference, Groundwater in the West, available at http://www.colorado.edu/ law/centers/nrlc/publications/Groundwater Conference/papers/Session5/henley.pdf (last visited September 13, 2005). Offers an excellent explanation of the need for regulation from a regulator’s perspective. Water Systems Council, Who Owns the Water: A Summary of Existing Water Rights Laws, Washington, D.C., 2002. Provides the source for the state-survey numbers displayed in Table 32.1. Ferry, S., Environmental Law, Aspen Publishers, New York, NY, 2004. Discusses the rights associated with use of water resources in the surface and ground portions of the hydrological cycle. Ashley, J.S. and Smith, J.A., Western Groundwater Wars, Forum for Applied Research and Public Policy, Knoxville, TN, pp. 33–39, spring 2001. Summarizes major groundwater rights doctrines, legal concepts, and future perspectives. Government Accountability Office, Freshwater Supply — States’ Views of How Federal Agencies Could Help Them Meet the Challenges of Expected Shortfalls, GAO-03-514, Washington, D.C., pp. 19–21, July 2003. Summarizes federal authorities to manage water resources. Williams, S.M., Overview of Indian Water Rights, Water Resources Update, Universities Council on Water Resources, issue number 107, Carbondale, IL, pp. 6–8, spring 1997, available at http://www. ucowr.siu.edu/updates/pdf/V107_A1.pdf (last visited May 7, 2005). Describes reservation, quantification and scope of use, and administration of Indian water rights. Richardson, J.J., Legal Impediments to Utilizing Groundwater as a Municipal Water Supply Source in Karst Terrain in the United States, Environmental Geology, vol. 42, Springer, Berlin, pp. 532–538, 2002. Discusses groundwater use and taking issues.
CWA and SDWA Readers are encouraged to visit the EPA Office of Water website at http://www.epa.gov/water. The CWA topics of interest are primarily located in the Office of Wetlands, Oceans, and Watersheds website at http://www.epa.gov/owow. The SDWA topics of interest are primarily located in the Office of Ground Water and Drinking Water website at http://www.epa.gov/safewater/index.html. The website offers a great deal of explanatory information and links to relevant reports.
RCRA and CERCLA Readers are encouraged to visit the following EPA websites, which contain links to or searchable databases containing RCRA policy and guidance documents: • http://www.epa.gov/swerrims (EPA’s Office of Solid Waste and Emergency Response website). • http://www.epa.gov/rcraonline/ (EPA’s RCRA Online database, which enables users to locate RCRA policy and guidance documents on topics including cleanup and groundwater monitoring). • http://www.epa.gov/epaoswer/hazwaste/ca/index.htm (EPA’s RCRA Corrective Action website). • http://www.epa.gov/epaoswer/osw/hazwaste.htm (EPA’s RCRA Hazardous Waste website). • http://www.epa.gov/epaoswer/osw/non-hw.htm (EPA’s RCRA Non-Hazardous Waste website). Information on Superfund and links to laws, policies, and guidance and other documents are on EPA’s Superfund website, http://www.epa.gov/superfund. EPA’s CLU-IN website (http://www.clu-in.org/) is a source of on-line and downloadable information on site remediation and field analytical technologies, including those pertaining to ground water. The Federal Remediation Technologies Roundtable website (http://www.frtr.gov) was developed by a consortium of EPA and six other federal agencies to improve
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the availability of innovative technologies and contains information on groundwater characterization and cleanup technologies. The following documents concerning groundwater remediation and groundwater investigations at remediation sites are referenced in the text of this chapter.
Groundwater Remediation EPA, Use of Monitored Natural Attenuation at Superfund, RCRA Corrective Action, and Underground Storage Tank Sites, OSWER Directive 9200.4-17P, April 21, 1999. EPA, Presumptive Response Strategy and Ex-Situ Treatment Technologies for Contaminated Ground Water at CERCLA Sites, Final Guidance, OSWER Directive, EPA 9283.1-12, EPA/540/R-96/023, October 1996. EPA, Guidance for Evaluating the Technical Impracticability of Ground-Water Restoration, OSWER Directive No. 9234.2-25, October, 1993.
Groundwater Investigation at Remediation Sites EPA, Handbook of Groundwater Protection and Cleanup Policies for RCRA Corrective Action, EPA530-R04-030, April 2004. EPA, Draft Guidance for Evaluating the Vapor Intrusion to Indoor Air Pathway from Groundwater and Soils, November 2002, available at http://www.epa.gov/correctiveaction/eis/vapor/complete.pdf.
FIFRA Lee, M., Summary of Environmental Laws Administered by the EPA, Congressional Research Service Report RL30022, January 12, 1999, available at http://www.ncseonline.org/nle/crsreports/ briefingbooks/laws/index.cfm (last visited May 7, 2005). Provides a comprehensive overview of FIFRA.
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33 Landfills 33.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33-1 33.2 Regulatory Considerations and Landfill Siting . . . . . . . . 33-2 Subtitle D • Clean Water Act • Clean Air Act • State and Local Regulations • Landfill Siting • Hydrogeologic and Geotechnical Considerations
33.3 Site Master Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33-5 33.4 Landfill Configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33-6 33.5 Conceptual Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33-7 Landfill Footprint • Subbase Grading • Sedimentation/Detention Basins • Borrow Areas • Final Cover Grading • Cell Layout and Filling Sequence • Other Factors
33.6 Detailed Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33-12 Mechanical Properties of Waste • Liner System • Final Cover System • Berms • Storm Water Management System • Leachate Collection and Removal System • Gas Management System • Bioreactor Landfills • Alternative Final Covers
33.7 Liner and Cover System Materials . . . . . . . . . . . . . . . . . . . . . . 33-22 Soil Materials • Geosynthetic Materials
33.8 Environmental Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33-25 Groundwater Monitoring • Gas Monitoring
33.9 Performance of Landfill Elements . . . . . . . . . . . . . . . . . . . . . . 33-26 Geotechnical and Geosynthetics Analysis • Storm Water Management • Leachate Collection and Removal System
Beth A. Keister and Pedro C. Repetto URS Corporation
33.10 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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33.1 Introduction Landfills may be classified in accordance with several criteria. The most common criteria used to classify landfills are type of waste, type of liner system, and geometric configuration. Based on current federal regulations, landfills are classified with respect to the type of waste. They contain: municipal solid waste, hazardous waste, and other types of solid waste. Federal regulations regarding these three types of landfills are published in Section 258, Section 264, and Section 257, respectively, of the Code of Federal Regulations. State regulations are, however, frequently more stringent than federal regulations. State regulations 33-1
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frequently include specific regulations for landfills where other types of waste will be disposed, such as industrial waste, construction demolition debris, and residual waste. Development of a landfill project requires proper attention to the diverse and, sometimes, conflicting array of regulatory, physical, and technical considerations relevant to siting and design. Two initial and essential steps for the development of a landfill project are site selection and preparation of a Site Master Plan. A thorough understanding of the physical setting of the site and the regulatory requirements for the design and permitting are of paramount importance for the successful development of a project. Landfill designers must keep in mind that environmental regulations are intended to protect human health and the environment, and though they tend to be prescriptive, they do not necessarily incorporate all the requirements of a sound engineering design. Therefore, as part of the design process, appropriate engineering analyses must be performed to ensure adequate performance of the final landfill and all of its interrelated systems. These include leachate, landfill gas, and surface water management systems, to name a few to be discussed in this chapter.
33.2 Regulatory Considerations and Landfill Siting The basic federal regulation for sanitary municipal solid waste landfills in the United States is the Environmental Protection Agency (EPA) Criteria for Municipal Solid Waste Landfills (MSWLF) (40 CFR 258), generally referred to as Subtitle D (of the Resource Conservation and Recovery Act). Other federal regulations that apply to MSWLFs have been promulgated under the Clean Water Act and the Clean Air Act. The regulations for the design of hazardous waste landfills have been promulgated under Subtitle C of the Resource Conservation and Recovery Act. The regulations for the design of municipal and hazardous waste landfills are similar, except for the requirements for liner and final cover systems. The discussion presented in this chapter is applicable, in general, to both municipal and hazardous waste landfills, except for the details related to liner and final cover systems where this paper focuses on MSWLFs.
33.2.1 Subtitle D The purpose of the Subtitle D regulations is to establish minimum national criteria for MSWLFs. As is common with many Federal regulations, the Federal Government has delegated the responsibility to implement their regulations to each individual state. Each state was required to submit to the EPA a plan for implementation of the Subtitle D regulations. Most states have received approval of their implementation plan and are designated “approved states.” Subtitle D regulations are organized into the following subparts: Location Restrictions, Operating Criteria, Design Criteria, Groundwater Monitoring and Corrective Action, Closure and Post-Closure Care, and Financial Assurance Criteria. The Location Restrictions specified under Subtitle D are discussed in the section below on landfill siting. Other Subtitle D requirements are discussed throughout the chapter.
33.2.2 Clean Water Act The regulations applicable to MSWLFs promulgated under the Clean Water Act are the wetlands regulations and the National Pollutant Discharge Elimination System (NPDES) program. For MSWLF units, the NPDES program is applicable to discharges from storm water management systems and leachate treatment plants or ponds, as well as storm water discharges during construction. The NPDES program establishes discharge criteria and standards for the imposition of technology-based treatment requirements in permits issued under the Clean Water Act.
33.2.3 Clean Air Act The EPA has promulgated standards and guidelines under the authority of the Clean Air Act entitled “Standards of Performance for New Stationary Sources and Guidelines for Control of Existing Sources: Municipal Solid Waste Landfills.” These standards and guidelines, promulgated in 1996, regulate MSWLF
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emissions, commonly referred to as“landfill gas,” which is composed primarily of carbon dioxide, methane, and non-methane organic compounds (NMOCs). These gasses are produced as the waste decomposes and may be discharged from the gas collection system or directly from the waste mass itself. As with Subtitle D, the responsibility of implementing the New Source Performance Standards (NSPS) lies with the EPA. However, the EPA has the ability to delegate authority to the State and in many cases, has done so. A set of rules are included in the federal rules specifically to deal with Emissions Guidelines (EG) for existing landfills; these rules require a State to submit plans that establish emission standards for an existing source when NSPS have been promulgated for a designated pollutant, such as landfill gas, and establishes minimum requirements as guidance. The provisions of the NSPS and EG rule apply to all new landfills with a maximum design capacity equal to or greater than 2.5 million Mg or 2.5 m3 . The provisions include criteria for determining landfill control requirements, design and operating specifications for control equipment, compliance schedules, and criteria for removal of controls. The provisions also include a series of monitoring, record keeping, and reporting requirements. A three-tiered calculation process is applied to identify landfills that exceed 50 Mg (55 tons) of NMOC emissions annually. The NMOC emission rate has been selected as a surrogate for total landfill gas emissions because it is relatively easy and inexpensive to measure.
33.2.4 State and Local Regulations State and local regulations vary significantly and may affect both the lateral and vertical limits of landfill development. These frequently include minimum setback distances from: • • • • • • • • • •
Surface water bodies Sources of drinking water Public roadways Property lines Structures such as homes, schools, hospitals, and nursing homes Cultural resources such as historic parks, monuments, structures, and museums Recreational parks Designated wild and scenic rivers Coal seams or limestone outcrops Gas or oil wells
Other regulatory aspects that may affect the design or permitting are: • • • • • • • •
Zoning Buffers Deed restrictions Special protection areas Traffic/access roads Height restrictions Groundwater separation Maximum/minimum final cover slopes
Typically, State regulations are administered by the State’s pollution control agency. Local regulations are most often found with the jurisdiction that has land use control, that is, the city, county or township.
33.2.5 Landfill Siting 33.2.5.1 State and local considerations The majority of these local regulations control landfill siting. The siting phase of landfill projects is often the most labor and cost intensive and often involves some level of federal review even for states that have
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been approved by EPA to administer their own programs. In Minnesota, for example, State rules identify the size of a proposed facility or facility expansion that requires the preparation of a state Environmental Impact Statement (EIS). This state process is analogous to the federal EIS process. During the siting phase, hydrogeologic and geotechnical investigations are completed as are master planning and conceptual design. Often several sites are included in initial planning and siting, each undergoing investigation and evaluation, until one site is identified as the most cost-effective site meeting regulatory approval. 33.2.5.2 Federal considerations At a minimum, Subtitle D specifies the following location restrictions: Airport Safety, Floodplains, Wetlands, Fault Areas, Seismic Impact Zones, and Unstable Areas. A brief description of each of these restrictions is presented below. 1. Airport Safety: Existing units, new units, and lateral expansions located within 10,000 ft of any airport runway end used by turbojet aircraft, or within 5,000 ft of any airport runway end used only by piston-type aircraft must demonstrate that the facility does not pose a bird hazard to aircraft. 2. Floodplains: Existing units, new units, and lateral expansions located in 100-year floodplains must demonstrate that the facility does not restrict the 100-year flood flow, reduce the temporary water storage capacity of the floodplain, or result in the washout of solid waste so as to pose a hazard to human health or the environment. 3. Wetlands: This restriction requires that new units and lateral expansions shall not be located in wetlands, unless the following demonstrations are made: • Where applicable under Section 404 of the Clean Water Act, a demonstration must be made that no practicable alternative to the proposed landfill is available. • Construction and operation of the MSWLF unit will not cause or contribute to: – Violations of any applicable state water quality standard – Violate any applicable toxic effluent standard or prohibition under Section 307 of the Clean Water Act – Jeopardize the continued existence of threatened or endangered species or result in the destruction or adverse modification of a critical habitat protected under the Endangered Species Act of 1973 – Violate any requirement under the Marine Protection, Research, and Sanctuaries Act of 1972 for protection of a marine sanctuary • To the extent required under Section 404 of the Clean Water Act or applicable state wetlands regulations, a demonstration that steps have been taken to attempt to achieve no net loss of wetlands (as defined by acreage and function). This is to be done by first avoiding impacts to wetlands to the maximum extent practicable, minimizing unavoidable impacts to the maximum extent practicable, and finally offsetting remaining unavoidable wetland impacts through all appropriate and practicable compensatory mitigation actions. 4. Faults: New units and lateral expansions may not be located within 200 ft of faults that have experienced displacement in Holocene time, unless it is demonstrated that a smaller setback distance will be protective of human health and the environment. 5. Seismic Impact Zones: New units and lateral expansions may not be located in seismic impact zones, unless it is demonstrated that the facility is designed to resist the maximum horizontal acceleration in lithified material for the site (Seed and Bonaparte, 1992). 6. Unstable Areas: Existing units, new units, and lateral expansions located in unstable areas must demonstrate that engineering measures have been incorporated into the design to ensure that the integrity of the structural components of the unit will not be disrupted. Unstable areas include areas subject to instability due to local soil or geologic conditions or conditions made potentially unstable due to adjacent development or human intervention.
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33.2.6 Hydrogeologic and Geotechnical Considerations To verify that the contemplated landfill development will not adversely affect existing groundwater quality and availability, regulations require that a number of aspects be adequately addressed. These include: • • • •
Depth to groundwater Delineation of regional confined and unconfined aquifers Direction and rate of groundwater flow, including possible spatial and temporal variations Aquifer characteristics including thickness and saturated (and, as applicable, unsaturated) hydraulic conductivity • Regional uses of the groundwater • Background groundwater quality
A complete characterization of the hydrogeologic regime must include an understanding of the current and previous uses of the regional groundwater. A full understanding of the site aquifer characteristics and soil permeability is also needed. For example, an understanding of both saturated and unsaturated hydraulic conductivity may be required to accurately model how contaminants may be transported. Many state regulations include specific requirements related to hydrogeologic and geotechnical field investigations, such as the minimum number and depth of test borings, test pits, piezometers, and monitoring wells. The number is based in part on the size of the proposed facility and on adjacent land uses. Depths are based on the proposed base grades (bottom of base liner), depth to the water table, and presence of additional lower aquifer units. Some regulations may provide guidance to use supplemental investigative techniques such as geophysics and other remote sensing methods. Some state regulations specify in situ hydrogeologic testing of aquifers using individual well or multi-well pumping tests to determine aquifer characteristics. These tests may be essential in determining the presence of an aquitard. Frequencies of groundwater level measurements may be specified to construct appropriate seasonal or regional groundwater potentiometric surface maps. Often, specific soil laboratory tests and frequencies are specified to characterize subsurface soils or to evaluate suitability of potential borrow soil sources for construction, operation, and closure of the MSWLF unit. This can avoid the need for additional testing in the future. Additional geotechnical factors that must be considered in the formulation of investigation programs include: • • • • • •
Proposed height of landfill at full development and total depth of waste deposited Presence of near-surface bedrock Interrelated topographic/geotechnical considerations (e.g., substantial cuts or fills) Stability of natural and cut slopes The presence of soft, compressible, collapsible, or otherwise unsuitable foundation soils Availability of cover materials and uses for any excavated soils
33.3 Site Master Plan Preparation of the Site Master Plan should consider the facilities required at the site, site-specific constraints (setbacks, buffer zones, wetlands, etc.), and optimal use of the land. The main objectives of preparing the Site Master Plan are: (1) to optimize the use of the land and resources that will be used for waste disposal; (2) to ensure that the relative locations of support facilities are convenient for landfill operation; and (3) to limit future changes to accommodate facilities that were not initially included in the original design and construction (Repetto and Foster, 1993). The type of facilities required and their sizes depend mainly on the desired facility life (total airspace required), the expected waste stream, composition and intake rates, and specific regulatory requirements.
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Typically, a Site Master Plan includes at least the following facilities: • • • • • • • • • • • •
Waste disposal area Buffer zones Access, entrance, and internal roads Sedimentation/detention basin(s) Scale(s) and scale house Office building Maintenance building Stockpile area(s) Leachate loadout Landfill gas management system, including blower and flare or gas-to-energy plant Perimeter fence and gate Environmental monitoring equipment (groundwater monitoring wells and piezometers, landfill gas monitoring probes, surface water monitoring locations, settlement plates, leachate level monitoring wells or manholes, and others).
A Site Master Plan may also include facilities for recycling and composting, leachate pretreatment or treatment, vehicles storage, and on-site borrow.
33.4 Landfill Configuration A typical landfill design includes the following: landfill footprint; subbase grading; final cover grading; cell layout; perimeter and intercell berms; liner system section; final cover section; storm water management system; leachate collection, recirculation, and removal system; gas management system; and, environmental monitoring system. The interdependence between the various landfill elements and the sequence in which they are considered in the design plays a very important role in landfill design. The most common landfill types, from geometrical configurations are (Figure 33.1): • Area fill: Landfilling progresses with little or no excavation. Normally used in relatively flat areas with a shallow groundwater table • Above-ground and below-ground fill: The landfill consists of a two-dimensional arrangement of large cells that are excavated one at a time. Once two adjacent cells are filled, the area between them is also filled. Normally used in relatively flat areas without a shallow water table • Valley fill: The area to be filled is located between natural slopes. It may include some below ground excavation • Trench fill: This method is similar to the above-ground and below-ground configuration, except that the cells are narrow and parallel. It is generally used only for small waste streams. The valley fill and trench fill configurations are shown primarily for historical purposes when dealing with existing landfills that have been filled over the last several decades and are, for the most part, now closed. Present day designs try to avoid valley locations to avoid troublesome surface water issues and associated geotechnical issues. Trench fills are avoided because the soils remaining between the trenches are essentially wasted airspace and waste streams are now larger than in the past. The new sites accommodate the existing terrain and use constructed berms, usually 6 to 8 ft in height, in the base of the landfill to delineate cell boundaries and serve as markers for construction of future adjacent cells. The base liner, including any geosynthetic layers, runs up the side of the berm and is buried into it. A styrofoam or plywood marker is used to indicate the edge of liners. Cells are filled to predetermined heights and at predetermined slopes, usually in lifts of 6 to 10 ft. Waste is deposited by packer trucks and rolloff vehicles directly onto the “open face,” where loaders or compactors wait to compact it into place. Present day landfills can be more than 300 ft deep and cover hundreds of
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al c
III
II
ove
IV
r
I Existing ground Area fill In
te
Fin
rm
al c
ed
ia
II
te
ove
r
III
co
ve
I
r
Existing ground Above and below ground fill Fina
l cov
er
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rme
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Existing ground
II
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te c
ove
r
I Valley fill
Fina
Inte IV
rme
III I
l cov
dia
te c
ove
r
er
V
II
Existing ground Trench fill
FIGURE 33.1 Landfill configurations.
acres. Waste acceptance rates are usually limited by traffic considerations and large new facilities include access roadways designed to allow placement of more than 2000 tons of waste daily.
33.5 Conceptual Design The design of a landfill must take into account the interdependence of the various landfill elements, which can lead to several design iterations. To minimize design iterations, the design is generally subdivided into two stages: conceptual design and detailed design. The conceptual design comprises the basic elements that define the cost of the project and its economic feasibility. These basic elements are those related to optimal use of the land, the airspace, and the soil balance. The airspace should include an allowance for daily, intermediate, and final covers. Soil balance is defined as the comparison between the volume of soil to be excavated and the volume of soil required for the entire project. Soil is excavated at landfill projects for cell development and for sedimentation/detention
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basins. Excavated soil can be used for structural fill (subgrade fill, perimeter, and intercell berms); daily, intermediate and final covers; soil liners; sedimentation/detention basin berms; roads; and final land forms required by a particular end use. The soil balance applies not only to the total volume, but to soil of specific properties, as soil used for different purposes have different specifications. The basic elements that must be included in the conceptual design are the landfill footprint, the subbase grading plan, the final grading plan, sedimentation/detention basins, borrow areas, stockpile areas, cell layout, and entrance and internal roads. The final grading plan and access roadways are often defined with a specific end use of the property in mind. Closed landfills are currently in use as parking facilities, golf courses, and various other innovative uses. Detailed design of the other elements, such as the leachate collection and removal system, the storm water management system, and the gas management system is not needed until the conceptual design has been completed. Although the conceptual design must account for all the site constraints, end use plans, and regulatory requirements, it should be preliminary and simplified. The landfill elements included in a conceptual design are discussed below.
33.5.1 Landfill Footprint The landfill footprint is generally selected by maximizing its area, considering the rest of the required facilities and site constraints (see Figure 33.2). Prime importance must be given to critical issues addressed during the permitting process (e.g., wetlands, groundwater issues, environmental monitoring requirements). At the conceptual design level, selection of the footprint does not need to be entirely accurate; for example, an allowance should be included for the width of perimeter berms, but the berms do not need to be designed. The landfill footprint selected in the conceptual design stage will require some adjustments when other landfill elements are designed as part of the final design. However, if the conceptual design has been Setback Sedimentation basin
Limits of waste
Perimeter ditch Phase 6
Phase 5 Solid waste boundary Property line
Access road
Phase 4
Phase 3
Access road and perimeter berm Setback
Maintenance facility Blower and flare Office
Phase 2
Phase 1
Access road Recycling center
FIGURE 33.2 Landfill footprint and cell layout.
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xxx
xxx
Proposed leachate sideslope/extraction point (typical)
xx
xx
x
xx
x
xx
xx
xx
Phase 5 xx
Phase 6
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xx xx
x
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xx
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xx
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xx xxx xxx
xxx
642
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Perimeter ditch
xx
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Phase 3
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Access road and perimeter berm
Phase 2
xxx
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xx
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xx xx
xxxx xxxx
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Phase 4
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xx xx
xxxx xxxx
xxxx xxxx
Phase 1
Limits of waste
FIGURE 33.3 Subbase grading plan.
properly developed, the adjustments will not significantly modify the soil balance or the location of other facilities at the site.
33.5.2 Subbase Grading Once the footprint has been defined, the next step is to prepare a subbase grading plan (see Figure 33.3), which identifies areas and depths of excavation, as well as areas and heights of fill. Selection of the landfill footprint and the subbase grading plan is an iterative process that depends significantly on the soil balance. At the conceptual design level, the subbase grading should be sufficient to obtain a preliminary estimate of excavation and fill volumes, and, together with the final cover grading, to estimate the airspace. It should consider vertical separation from groundwater, side slopes, and overall leachate collection system slope. However, at this level it need not include detailed subbase grading (leachate collection swales) or design of the intercell berms. Subbase grades are generally set as deep as possible, so that airspace is maximized and soil is made available for landfill development. However, the footprint shape and extent, cell layout, excavation depth, and subbase design are strongly influenced by a number of factors, such as: • Depth to the water table or uppermost aquifer: Some regulations require a minimum vertical separation from groundwater. Even if regulations do not require separation from groundwater, the cost of constructing base liner below the water table is usually prohibitive. • Depth to bedrock: The cost of hard rock excavation negatively impacts the economic feasibility of a project. Additionally, excavated rock generally has little use in a landfill project unless it is processed (e.g., by crushing and sorting). • Stability of the foundation: Areas previously mined or susceptible to sinkhole development may cause instability problems. In addition, areas with underlying peat or soft soils subject to
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consolidation are unsuitable, as the base liner grades must remain as designed to accommodate leachate collection. Differential settlement of the base grade could damage geosynthetic liner components or leachate collection piping. Site topography and stability of slopes: In flat areas, only fill embankments and cut slopes for cell excavation need to be considered, whereas valley excavations can affect natural slopes. Excavation close to natural slopes may affect their stability and need to be considered in selecting the landfill footprint. Stability of cut slopes: The stability of cut slopes is a function of their height, inclination, groundwater conditions, and the strength and unit weight of the in situ soils. The inclination and height of the cut slopes affect the landfill airspace and the volume of soil to be excavated. Permeability of natural soil: In some cases a natural clay liner may be acceptable, which would eliminate the need for low permeability borrow for an engineered liner. Soil balance: An adequate soil balance allows a sufficient volume of soil to be available from on-site excavations and, at the same time, avoids excessive excavation that would have to be disposed. Required airspace and available area: Most landfill projects include requirements for airspace and daily waste acceptance rates that are predetermined based upon financial considerations and the population they are intended to serve. Slope of the landfill subbase: A minimum slope is required for the leachate collection system.
As discussed previously, perimeter and intercell berms do not need to be designed as part of the conceptual design. However, an estimate of their volume needs to be considered in the soil balance and subtracted from the available airspace.
33.5.3 Sedimentation/Detention Basins Sedimentation/detention basins are used to collect, treat, and control the discharge of surface water collected on the site. The location and size of sedimentation/detention basins is one of the basic elements to be considered at the beginning of the design process, as they frequently occupy significant area and influence the landfill footprint. Sedimentation/detention basins also influence the soil balance, as they require excavation and the construction of berms. A detailed design of sedimentation basins is not required at the conceptual design level, as only their location, areal extent, and volume are important at this level. The depth to groundwater at sites with a high water table may limit the effective volume of the sedimentation basins. State and local regulations may also have a bearing on function and configuration of these facilities.
33.5.4 Borrow Areas Borrow areas need to be evaluated as part of the conceptual design, as they have a significant influence on the landfill footprint and the soil balance. Borrow areas may be located on-site or off-site. This decision depends on-site topography, soil types available on-site, land availability, desired airspace, cost of imported borrow, and final site layout. Generally, soils from cell excavation are used as borrow material; however, the need for stockpiling for future use must be considered. The selection of on-site borrow areas may affect the landfill footprint, cell development, and the sequence of filling.
33.5.5 Final Cover Grading At the conceptual design level, the final cover grading should be sufficient to obtain a preliminary estimate of the airspace. It should consider maximum and minimum regulatory slopes, any height restrictions, slope stability, and allowance for appropriate runoff control (see Figure 33.4). However, at this level it does not need to include design of the benches/channels for runoff control; the influence of the channels/benches in the airspace can be considered by assuming an average slope.
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Access road 5' × 3' Concrete Box culvert Sedimentation basin
Setback xxx
xxx
xxx 700710 720 730 140 150 160170 180
xx
Channel/perimeter ditch confluence Access road
x xx x
Sedimentation outlet structure
Perimeter drain
xxx
xx
200 210
x xx x xx x
xxx xxx
xxx
xxx xxx
xxx
xxx
xxx
xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx xxx
Down slope channel
647 640
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xxx xxx
Solid waste boundary
xxx
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12" f RCP
Setback
xxx xxx
xxx
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xxx xxx
xxx xxx xxx
xxx xxx xxx
xxx xxx
620 600 790
780 770 760 750
xxx
740 730 720 710 700 xxx xxx
xxx xxx
FIGURE 33.4 Final cover grading.
The final grading is generally designed as steep and high as possible, so that the maximum airspace is attained. However, both steepness and height need to be compatible with other requirements, such as regulatory restrictions regarding side slopes and height, overall stability of slopes and sliding of the final cover, and storm water management and erosion control.
33.5.6 Cell Layout and Filling Sequence Once the overall landfill configuration (footprint, subbase grading, and final grading) has been decided, the landfill has to be divided into cells (see Figure 33.2). The objective of dividing the landfill into cells is to provide separate operational units by constructing one cell at a time, so that the initial capital investment is limited and the period of time over which the liner would be exposed is limited. Cell sizes are selected based mainly on the waste stream and the desired life of each cell. In general, it is unusual for cells to be less than two acres or more than eight acres. The desired life of each cell is generally decided as a function of the desired schedule of construction operations. When analyzing the life of individual cells, it should be remembered that isolated cells form a single mound, while cells adjacent to a previously filled cell also add a wedge on the interim slope of the previous cell.
33.5.7 Other Factors Other important factors to take into account in designing the cell layout are leachate collection and removal, and the filling sequence. Generally, the cells are designed with slope toward the landfill perimeter, so that leachate can be removed without crossing other cells. The cell layout plan should show all the leachate sumps and riser pipes. It is generally advantageous to design the cell layout and the filling sequence so that excessive stockpiling of excavated soil is avoided and part of the final slopes are formed as early as possible. Once a part of
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a final slope has been formed, final cover can be placed on that area. This reduces the cost of leachate treatment, as placement of final cover reduces contact water volume and infiltration into the waste.
33.6 Detailed Design The detailed design includes refining the design of the basic landfill elements. The following sections discuss only the additional landfill elements not included in the conceptual design. The main containment systems used in modern landfills are the bottom liner, the final cover, and the storm water management system. The function of the liner system is to prevent leachate from migrating into the subsoil. The primary function of the final cover is to minimize infiltration of precipitation into the refuse. The storm water management system controls runoff on the landfill itself to prevent erosion of the final cover, and run-on from the surrounding areas. Other types of containment systems associated with landfills are cut-off walls and blanket drains.
33.6.1 Mechanical Properties of Waste Mechanical behavior of the waste mass, as it is deposited and after the landfill is filled to capacity, is a key factor in planning the hydrogeologic and geologic investigations, as well as in the final design of the facility and operation of the facility after it is constructed. Substantial work is being done by numerous entities to better characterize this markedly heterogeneous material (Fassett et al., 1994; Langer and Dixon, 2004). Unit weight, compressibility, shear strength, lateral stiffness and hydraulic conductivity have been studied in both the laboratory and in situ. An internationally vetted classification system and test standards are envisioned that will lead to the development of models using standardized input on waste composition to better predict behavior of the constructed system after placement. Such analysis will enhance the landfill design process by allowing a more indepth evaluation of interaction between liner designs, management systems designs, and surrounding geologic and hydrogeologic settings. This is particularly important as leachate recirculation within landfills becomes more common. Liquid absorptive capacity of the waste mass is key to determining the amount of leachate recirculation that can occur initially and over time. Leachate application rates are dependent upon the hydraulic capacity of the liner drainage layer, the liquid absorptive capacity of the waste mass, and the hydraulic capacity of the waste mass. Of these three, only the hydraulic capacity of the liner system can currently be calculated with standard methods and techniques. Operation as a bioreactor landfill also necessitates evaluation of stability of the waste mass under saturated conditions. Quantifying these characteristics in a standard manner will also allow better planning by facility operators who deal daily with ramifications of several properties of waste as it is received at the site, including compressibility to determine compaction rates, and its ability to accept and conduct liquids when leachate is recirculated.
33.6.2 Liner System Liner systems are containment elements constructed under the waste to prevent or minimize infiltration of contaminated liquids into the subsoil or groundwater. The contaminated liquid, or leachate, may be part of the waste itself or may originate from precipitation that has infiltrated into the waste. Landfill liner systems consist of multiple layers that fulfill specific functions. Landfill liner systems may consist, from top to bottom, of the following functional layers: • Protective layer: This layer of soil, or other appropriate material, separates the refuse from the rest of the liner to prevent damage from large objects placed in the landfill. • Leachate collection layer: This permeable layer collects leachate from the refuse and conveys it to sumps from where it is removed. Frequently, the functions of the protective layer and the leachate collection layer are integrated in one single layer of coarse granular soil.
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• Primary liner: This primary low permeability layer (or composite of two different low-permeability materials in direct contact to each other) prevents or minimizes the movement of landfill leachate into the subsoil. Primary liners typically consist of low permeability soil or geosynthetics. • Secondary leachate collection layer (or leakage detection layer): This high permeability (or transmissivity, if geosynthetic) layer is designed to detect and collect any leachate infiltrating through the primary liner. This layer is included only when a secondary liner is used. Collection layers typically consist of high permeability non-calcareous aggregate or rock, as well as several types of geosynthetics. • Secondary liner: This is a second or backup low permeability layer (or composite of two different low-permeability materials in direct contact with each other). Not all liner systems include a secondary liner. Secondary liners typically consist of low permeability soil or geosynthetics. • Drainage layer: In cases where the liner system is close to or below the water table, a highpermeability (or high-transmissivity, if geosynthetic) soil blanket drainage layer is generally placed under the liner system to control migration of moisture from the foundation to the liner system. • Subbase: This bottom layer, generally site soil of intermediate permeability, separates the liner system from the natural subgrade or structural fill. These layers are often separated by geotextiles to prevent migration of particles between layers, or to provide cushioning or protection of geomembranes. Each of the liners (primary or secondary) may consist of one layer (clay, geomembrane, or geosynthetic clay liner [GCL]) or two adjacent layers of these materials, in which case it is called a “composite” liner. Liner systems comprising only the primary liner are called “single” liner systems. Liner systems comprising a primary and a secondary liner, with an intermediate secondary leachate collection layer, are called “double” liner systems. Sample liners are presented in Figure 33.5. The leachate collection layer(s) may be constructed of a permeable soil, a geonet, or a geocomposite. The geocomposite used for leachate collection layers consists of a geonet welded between two nonwoven geotextiles. According to Subtitle D, the liner system must comply with either a design standard or a performance standard. The design standard under Subtitle D is a single composite liner comprised of a minimum 30-mil geomembrane placed over at least a 2-ft layer of compacted soil with a hydraulic conductivity of no more than 1 × 10−7 cm/sec. If the geomembrane is made of high density polyethylene (HDPE) the minimum thickness is specified to be 60 mils due to the effects of welding. The geomembrane must be placed in direct and uniform contact with the compacted soil. Any alternative liner system design must demonstrate compliance with the performance standard. The performance standard requires demonstration that the maximum concentration levels of 24 chemical parameters listed in Subtitle D will not be exceeded in the uppermost aquifer at the relevant point of compliance. The relevant point of compliance must be located no more than 150 m from the waste management unit boundary and on land owned by the facility. To perform the demonstration required for an alternative liner system design, it is necessary to conduct an assessment of leachate quality and quantity, leachate leakage through the liner system, and subsurface transport to the relevant point of compliance. The EPA has developed a modeling package to perform these analyses, called the Multimedia Exposure Assessment Model (MULTIMED, EPA, 1992), which is intended for sites where certain simplifying assumptions can be made.
33.6.3 Final Cover System A low-permeability cover is a containment system constructed on top of the waste, primarily to control the infiltration of precipitation. Cover systems control infiltration by providing a low-permeability barrier and by promoting runoff with adequate grading of the final surface. Other functions of cover systems are to prevent contact of runoff with waste, to prevent spreading or washout of wastes, to reduce disease vectors, such as rodents, and to control the emission of gases from the decomposing refuse.
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The Handbook of Groundwater Engineering Protective/primary leachate collection layer Cushion geotextile Primary geomembrane liner Primary soil liner Secondary leachate collection layer (geonet composite) Secondary geomembrane liner Secondary soil liner Berm
Protective/primary leachate collection layer Cushion geotextile Primary geomembrane liner Primary soil liner
Filter geotextile Secondary leachate collection layer Cushion geotextile Secondary geomembrane liner Secondary soil liner Filter geotextile Subbase Filter geotextile Subgrade
FIGURE 33.5 Double composite liner systems.
Cover systems also consist of multiple layers with specific functions related to the management of storm water. A low permeability cover system may include, from top to bottom, the following functional layers (see Figure 33.6): • Erosion (vegetative) layer: This layer of soil is capable of supporting vegetation (typically grass) and has good resistance to erosion. • Infiltration layer: The functions of this layer, also frequently called cover material, are to provide a minimum thickness of cover over the waste and to protect the underlying barrier layer from frost penetration. • Drainage layer: This is a permeable layer whose function is to convey the water that infiltrates through the upper layers of the cover system to a perimeter collection system. A cover without
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33-15 Erosion layer ff
no
Ru
Infiltration layer
Drainage layer Barrier layer
w
Flo
Intermediate layer (buffer layer)
Refuse
FIGURE 33.6 Final cover system functional layers.
a drainage layer is susceptible to damage occurring if the layers above the barrier layer become saturated. The drainage layer usually includes a toe drain at the toe of the final cover slope and may incorporate intermediate collector drains throughout. • Barrier layer: This is a low-permeability layer (or layers of two different low-permeability materials in direct contact with each other), whose function is to minimize infiltration into the waste. • Intermediate layer: This layer is placed primarily for operational reasons. It is placed directly upon the waste and is used as a subbase for the placement of the final cover system. It is often referred to as the buffer layer. The erosion and infiltration layers are normally constructed of soil, as they must support vegetation and provide a minimum thickness for frost protection. The drainage layer can be constructed of a permeable soil, a geonet, or a geocomposite. The barrier layer can be constructed of compacted low-permeability soil, a geomembrane, a geosynthetic clay liner (GCL), or adjacent layers of two of these materials, in which case it is called a composite barrier layer. Some of these layers can also be separated by geotextiles. Of the precipitation that falls on the cover, a part becomes surface water runoff, a portion infiltrates through the cover into the drainage layer, a part is retained in the cover soil, a small amount infiltrates into the waste through the barrier layer, and the remainder is lost through evapotranspiration. The runoff can produce erosion of the cover surface and must be controlled by means of a storm water management system. The infiltrated water primarily flows through the drainage layer, which must have adequate hydraulic capacity to convey the expected flow.
33.6.4 Berms The design of landfills includes perimeter and intercell berms. The primary functions of the perimeter berms are to prevent the spreading of refuse outside of the disposal area during filling operations and to protect the landfill from storm water run-on from surrounding areas. The intercell berms provide separation between active cells and the rest of the landfill area. This allows construction of new cells to be performed simultaneously to the filling of active cells, and to prevent runoff from inactive cells and undeveloped areas from coming into contact with waste. The perimeter and intercell berms are subject to driving forces produced by refuse slopes and, therefore, require structural strength. They also function to contain leachate; clayey soil works well in this regard. As long as the configuration and the material allow for adequate stability design, both clayey and granular structural fill materials can be used.
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In addition to the landfill berms, sedimentation/detention basins may also include perimeter berms. These berms require low permeability in addition to structural strength.
33.6.5 Storm Water Management System The storm water management system consists of two parts. One part controls runoff on the landfill itself to prevent erosion of the final cover. The other part is external to the landfill and its objective is to prevent run-on to the landfill from surrounding areas. Subtitle D specifies that storm water management systems be designed to collect and control at least the water volume resulting from the 24-h, 25-year recurrence interval design storm. Some state regulations also require verification of the outlet structures of sedimentation/detention basins for the 100-year recurrence interval design storm. The runoff control system on the landfill consists generally of a system of benches or diversion berms located on the final cover (Figure 33.4). It is difficult to control runoff without benches, although it is possible for short slopes or on final covers flatter than 4H:1V. The vertical distance between the benches/channels is generally selected such that erosion of the final cover, calculated by the US Department of Agriculture Universal Soil Loss Equation, does not exceed two tons/acre/year as recommended by the EPA. An additional criterion to select the vertical distance between benches/channels is to prevent the surface water flow regime changing from sheet flow to shallow concentrated flow. By preventing this change in flow regime, the storm water has less energy with which it can mobilize soil. The final cover channels are designed with minimal longitudinal slope, more or less paralleling the final cover contours. Depending on the flow velocity, the channels may be lined with grass or rip-rap. A good rule of thumb for distance between diversion berms is 100 to 150 ft Benches are typically spaced slightly farther apart. The final cover channels generally discharge into gabion-lined or ungrouted rip-rapped downslope channels. A gabion lining or ungrouted rip-rap is generally used because of its ability to withstand settlements and the relatively high water velocities resulting from steep slopes. Sometimes pipes are used to convey the flow downslope; however, pipes are susceptible to damage from waste settlements. The downslope channels, in turn, discharge to other channels that convey the flow to sedimentation/detention basins. These other channels typically collect runoff from the final cover and run-on from the surrounding areas, and discharge to sedimentation basins that are often converted to detention basins after closure of the facility. The design of the runoff control system on the final cover should be performed simultaneously to the detailed design of the final grading. At this stage, the need for a permanent access road on the final cover should also be evaluated. If such a road is required, it should be designed in conjunction with the runoff control system. These designs should also be coordinated with the design of the gas management system, as the location of gas vents or extraction wells may require the widening of benches in some areas.
33.6.6 Leachate Collection and Removal System Landfills generate excess liquid as a byproduct of waste decomposition. This liquid, referred to as leachate, is collected by the leachate collection system (LCS), a series of pipes and trenches located at the bottom of the cell, immediately above the primary liner. The purpose of the LCS is to collect leachate from the waste and to convey it to sumps, where pumps remove it from the cell. This high-permeability collection layer oftentimes contains perforated pipes in swales surrounded by gravel (see Figure 33.7). The collection layer generally consists of noncalcareous gravel, and the perforated pipes are made of HDPE or PVC (see Figure 33.8); crushing of the collection pipes is a critical design factor. Subtitle D requires the LCS to be designed to maintain less than 1 ft of leachate head over the liner. The LCS transfers the leachate to sumps located at the lowest point of each cell, preferably adjacent to the toe of the inside slope of the perimeter berm. The leachate is typically pumped from the sump, up the side slope of the landfill, and into a leachate storage tank or to a treatment facility. The leachate removal system typically consists of a riser pipe that parallels the inside slope of the perimeter berm commonly called a side slope riser (see Figure 33.9). The system requires a submersible
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33-17 Sump Setback xxx
xxx
Typical leachate collection pipe Perimeter ditch
xx xx xx
x
Phase 5
xx
xx
xxx
Phase 6
Solid waste boundary
xx
x
xx
x
xx
xxx
xxx xxx
xx
xx
xx
xx xx
xxx
xx
xx
xx xx
xx xx
xx
xx
Sedimentation outlet structure 12" f RCP
xx
xx
63
5
3
63
631
xxx
63
xx
7
633 xxxx xxxx
xxxx xxxx 63
5
5
Phase 4 xx
xx xx
xx 7 64
5
Phase 2
3
64 xx
64
xx
8
64
xx xx
63
3
xxx
Phase 3 xx
xxx
7
xx xx
Typical sump house
63
63
xxxx
xx
xx xx
1 xx
xxxx xxxx
63
Cell 4 East sump Anchor trench
Phase 1
Sump riser
FIGURE 33.7 Leachate collection system.
pump to remove the leachate. Landfills constructed in the late 1980s and early 1990s may have accomplished leachate removal by means of a gravity flow pipe passing through the perimeter berm. This avoids the need for pumping, but requires a liner penetration that often affected liner performance; this is no longer a common practice (see Figure 33.9). The leachate removed from the cells is generally conveyed by a header pipe to holding tanks or ponds. The header pipe may be gravity or force, depending on the site topography. The holding tanks or ponds are generally designed to hold 30 days of leachate production. Some regulations require double containment for leachate header pipes and holding tanks. Finally, the leachate may be discharged to an on-site treatment plant, or it may be piped or transported by truck to an off-site treatment facility. The design of the final subbase grades should be performed simultaneously with the design of the leachate collection system. The modifications to the subbase grading prepared during the conceptual design phase should be such that the soil balance and the airspace should not change significantly.
33.6.7 Gas Management System Landfills generate landfill gas as a product of decomposition of waste. Landfill gas is approximately 50% methane, 50% carbon dioxide and less than 1% trace contaminants referred to as Non-Methane Organic Compounds (NMOCs). Gas management systems can be passive or active. The type of system depends on state regulations, the size of the landfill, and site-specific issues related to odor control. As discussed under regulatory considerations related to the Clean Air Act, the NSPS and EG regulations establish that an active gas extraction system must be installed if the design capacity of the MSWLF exceeds 2.5 million tons and the total emission of NMOCs exceeds 55 tons per year. When determining the landfill gas and the NMOC emission rate, the entire landfill must be considered, even if portions are closed. If installation of collection and control systems is required, these systems are required by rule to be installed in the entire landfill. Typical collection systems include gas extraction wells, trenches, and collection header piping and laterals. Typical control devices include flares, gas turbines,
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The Handbook of Groundwater Engineering Coarse drainage stone Excavated trench width
Perforated pipe
Filter geotextile
Sand drainage layer
Waste
Cushion geotextile
Geomembrane
Compacted clay liner
Manhole
FIGURE 33.8 Leachate collection trench and collector pipe.
Waste Leak detection pipe
Antiseep collars
Necessary penetration of secondary liner
Leachate collection system with liner penetration circa 1980
Leachate extraction pump Solid waste Geomembrane (rubsheet) Cushion Geotextile
Sidewall riser (= 24 in. dia.)
Removal and monitoring shed
Geotextile
Gravel
Geomembrane (primary)
Perforated T-section within gravel Leachate collection system typical today
FIGURE 33.9 Leachate removal systems. (Courtesy Prof. R.M. Koerner.)
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Stack sampling ports (typical of 4) From landfill gas collection wells
Enclosed flare
Condensate knockout chamber
M Flow control valve
Flame arrestor Drain to condensate collection system
FIGURE 33.10 Landfill gas blower and flare schematic.
internal combustion engines, and boilers. All but flares provide the opportunity for energy recovery, and federal tax credits are periodically available to offset increased costs associated with power generation. A typical landfill gas blower and flare system is shown in Figure 33.10. The NMOC emission rate is calculated as a function of the mass and age of the refuse, the gas generation constant (k), and the concentration of NMOCs (CNMOC ) allows the calculation of gas emissions to be based on conservative default values of k and CNMOC provided by the EPA, or by using site-specific values determined from gas samples and pumping tests. A passive system is designed to vent the gas by providing a path for gas flow without the use of additional mechanical components. A passive system generally consists of perforated pipes in rock-filled trenches embedded into the waste or a high permeability layer located within the waste mass or directly under the final cover to allow ventilation of the gas. The primary components for an active system are gas extraction wells, trenches or layers, piping network, condensate collection traps, blowers or compressors with related power and control equipment, and disposal. From the piping network, the gas is transferred to the disposal point where the gas can be destroyed by means of open gas flares, or it can be utilized in energy generation, heating, or purified for other uses. When designing an active system, careful consideration should be given to the location of condensate traps and header pipes on the final cover, so that unnecessary iterations of the final grading plan are avoided.
33.6.8 Bioreactor Landfills Many landfills are incorporating leachate recirculation and other operational changes that promote degradation of the waste mass at an accelerated rate. Subtitle D of RCRA allows for leachate recirculation in Section 258.28(a)(2), which provides for the placement of landfill gas condensate and leachate as the only allowable bulk noncontainerized liquid wastes to be placed in the landfill. Leachate recirculation can be accomplished by several means, including spray irrigation, steam injection, vertical well injection, horizontal trench injection, and horizontal distribution layers. Horizontal injection trenches have pressure piping in the center to distribute the leachate to areas determined by sensors and monitored to be optimal for accepting additional moisture. Horizontal distribution layers operate under similar conditions, with pressure piping feeding geonet, stone, or other synthetic distribution layers. These two most common types of systems are used in landfills actively operating as bioreactor landfills. Spacing of the distribution system is dependent upon assumed hydraulic conductivity (horizontal and vertical) of the waste mass and the distribution medium, and the pressure used to distribute the leachate. Bioreactor landfills show evidence of treatment of leachate over time. There are four phases of treatment during a process referred to as landfill organic stabilization. Assuming leachate starts as clean water that infiltrates into the waste mass, it starts with a pH of 7 and contaminant concentrations of zero. During
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The Handbook of Groundwater Engineering Changes in leachate composition
Leachate characteristics (mg/I)
25
I
II
III
Landfill organic stabilization phase IV
V 8
Cod 20
pH
7 pH
15
6 10
Volatile fatty acids 5
5
0 Time (non–liner scale)
FIGURE 33.11 Changes in landfill leachate composition during landfill organic stabilization. (From Spear, J.W.Sr. (2004), Bioreactors and Leachate Recirculation Systems Design, Section 8 of Proceedings for Sanitary Landfill Design course offered through the University of Wisconsin, Madison, February 11–13, 2004.)
Phase I, the water begins to pick up contamination as it moves through the waste mass and because the contaminants are acidic, its pH drops below 7. During Phase II, the chemical oxygen demand (COD) and pH of the leachate reach extremes. During Phase III, the recirculated leachate serves as a catalyst to treatment of the organics in the landfill. Waste degrades and settlement of the landfill waste mass occurs. The level of contaminants in the leachate decrease and the pH again approaches 7. During Phase IV, this process is completed and the low levels of remaining contaminants in the leachate reach zero and the pH reaches 7. Some resources identify a fifth phase of operation where the leachate is essentially water percolating through biologically inert material. Figure 33.11 shows these five phases in sequence (Spear, 2004). Times for these phases vary depending on many factors and predictive models are not available at this point to identify either timing or the level of the contamination relative to waste composition. A similar process occurs with the landfill gas production. As leachate is recirculated, gas generation increases and peaks as the contaminants in the leachate are consumed. As shown in Figure 33.12 (Spear, 2004), gas production can reach twice the levels otherwise expected when leachate is recirculated. At present, the NSPS of the Clean Air Act do not address bioreactor landfills, but the increased production rates and other operational considerations will necessitate some additional regulatory consideration with regard to action levels and post-closure care periods. The biology of bioreactor landfills is similar to traditional landfills, being largely dependent on anaerobic decomposition of organic matter and water into biodegraded organic matter, methane, carbon dioxide, and other gases. The limiting factor in the equation is moisture, thus the reliance on leachate recirculation and precipitation to promote the process. During initial stages, additional water is often permitted into the system based upon a “variance” or “pilot-study” allowed by regulatory agencies. Several states have issued state rules or guidance for leachate recirculation. Bioreactor landfills have several recognized economic advantages over traditional landfills focused on safely entombing the waste. These include a delay in the need to perform leachate treatment, accelerated waste and leachate degradation, increased gas production rates, reduced post-closure care periods, all resulting in increased design capacity for the same air space and footprint. These factors change the economic models used to identify required design capacity, taking the designer back to the initial stages of the Master Planning process. As bioreactor technology reaches its full potential, landfills become more like traditional treatment facilities. Design of such facilities is in its infancy, requiring better methods to estimate landfill gas and leachate generation, to define interaction between landfill systems, and to define optimal waste type and intake rates.
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Methane production rate (ft3/yr)
6.00E+08 5.00E+08 4.00E+08 3.00E+08 2.00E+08 1.00E+08 1.00E+08 0
20
40
60
80
100 Traditional Bioreactor
FIGURE 33.12 Methane production in traditional and bioreactor landfills. (From Spear, J.W.Sr. (2004), Bioreactors and Leachate Recirculation Systems Design, Section 8 of Proceedings for Sanitary Landfill Design course offered through the University of Wisconsin, Madison, February 11–13, 2004.)
To that end, EPA promulgated additional CAA regulations for MSWLF that require those sites operated as a landfill bioreactor and subject to existing CAA regulations (i.e., landfills containing over 2.5M3 of waste) to collect and control LFG emissions within 6 months of liquid additions (Thornloe, 2004). Using results from a study under way by the National Risk Management Research Laboratory (NRMRL), the EPA will be able to establish updated LFG emission factors for use with conventional landfilling operations. In addition, this research will establish emission factors for bioreactor operations. The research is being conducted in partnership with Waste Management, Inc. These data will be used to update the existing set of landfill gas emission factors, defined in AP-42 for EPA’s landfill gas emissions model (LandGEM), used to define emissions associated with the NSPS and EG of the Clean Air Act.
33.6.9 Alternative Final Covers The water balance models employed in designing a RCRA Subtitle D or Subtitle C final cover have been useful tools in identifying an alternative to these prescriptive cover systems. In arid or semiarid climates, water balances indicate that precipitation is so low that percolation never reaches the geosynthetic or clay barrier layer included in the final cover section. In regions where precipitation is less than 70% of potential evapotranspiration, water balance models such as UNSAT-H and the Hydrologic Evaluation of Landfill Performance (HELP) Model indicate that effective alternatives to the clay and geosynthetic layers may include capillary or other barrier systems (Khire et al., 2000). The acceptance of Alternative Final Cover (AFC) design received a substantial boost when EPA undertook evaluation of 24 test covers at 11 sites in seven states. The Alternative Cover Assessment Program (ACAP) includes primarily sites in the dry western United States, but also includes sites in Nebraska, Iowa, and Georgia. More information on ACAP can be obtained at the EPA’s ACAP web site (www.acap.dri.edu). AFCs typically fall into two categories: Monolithic and Capillary Barrier final covers. Monolithic final covers rely on a loosely compacted fine-grained soil layer designed with a thickness that will allow it to store infiltration. The water balance is used to verify that the thickness of the cover is sufficient to store infiltration during months when vegetation is dormant and evaporation is lower.
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Capillary Barrier systems rely on capillary breaks, created by placing a high permeability granular layer beneath a fine-grained soil that holds infiltration. AFCs can incorporate more than one capillary break and several layers. The costs of these covers are substantially less than covers incorporating geosynthetics and granular or synthetic drainage layers with their associated collection systems, particularly if the required soils are readily available (Koerner and Daniel, 1992).
33.7 Liner and Cover System Materials Materials used for the construction of liner and cover systems can be classified with respect to their origin and function. With respect to their origin they are classified into natural soils and geosynthetic materials. With respect to their function the classification is more complex and includes the following: • • • • • •
Barrier layers Drainage layers Fill Vegetative layer Filtration/protection/cushion layers Tensile reinforcement
33.7.1 Soil Materials 33.7.1.1 Barrier Layers Barrier layers constructed of natural soils may consist of clay or a soil-bentonite admixture. In the case of admixtures, the required bentonite content is selected based on laboratory permeability tests performed with different bentonite percentages. The typical requirement for barrier layers is to have a permeability not exceeding 10−7 cm/sec. The main factors that influence the permeability of a given soil or soil-bentonite admixture are: • Compaction dry density: For all other factors being constant, the higher the compaction dry density of a soil, the lower its permeability. • Compaction moisture content: For all other factors being constant, the permeability of a given soil decreases with increasing compaction moisture content. • Compaction procedure: It has been observed that specimens compacted to identical dry densities and moisture contents may exhibit different permeabilities if compacted using different procedures. • Consolidation pressure: Barrier layers are subjected to high permanent loads while in service in the case of landfill liner systems. On the other hand, permanent loads are minimal on cover systems and an increase in dry density with time should not be expected. Therefore, permeability tests should be performed using a consolidation pressure consistent with the expected loads. In landfills, the permeant is water in the case of covers or leachate in the case of liners. The flow of leachate through cohesive soils may produce changes in the permeability of the soil. These changes are evaluated by means of leachate compatibility tests. These are long-duration permeability tests, comparing effects on the liner material when distilled water is used initially as the permeant and then leachate from the facility (or a similar leachate) is used as the permeant. 33.7.1.2 Drainage Layers Drainage layers constructed of natural soils consist of sands or gravels, and may be used in liners or covers. Drainage layers are designed to have a hydraulic capacity adequate to convey the design flow rate without significant head build up. The hydraulic capacity of a drainage layer is a function of its permeability, thickness, and slope. Frequently the transmissivity, defined as the product of the permeability times the thickness, is used to characterize a drainage layer.
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33.7.1.3 Fill The requirements for fill material includes the following general categories: • Grading fill: There are no strict requirements for grading fills in which fill slopes are not constructed. Depending on the thickness of the fill and the loads to be applied on them, compressibility may become an important consideration. • Structural fill: This category comprises fill used for elements such as intercell berms and perimeter berms in landfills, or perimeter berms for leachate ponds. When these elements will be subjected to significant lateral pressures, these berms are constructed of coarse granular soils. These berms are generally lined, so permeability is not an issue. • Water-containment berms fill: Berms containing water-retaining structures, such as sedimentation and detention basin berms, require a combination of low permeability and high shear strength. 33.7.1.4 Vegetative Layer Vegetative layers must be adequate to support vegetation, generally shallow-rooting grasses when synthetic or clay barriers are included, and must have adequate resistance to erosion. To support vegetation, the soil must contain sufficient nutrients. Nutrients can also be supplied by adding limestone or other fertilizers. The erosion that a vegetative layer may suffer is a function of the soil type and the slope inclination and length. The soil loss is estimated by means of the Universal Soil Loss Equation, published by the US Department of Agriculture. The maximum allowable soil loss recommended by the EPA for landfill covers is 2 tons/acre/year.
33.7.2 Geosynthetic Materials There are a large number of geosynthetic materials used in environmental applications and many different tests to characterize their properties. A comprehensive discussion of geosynthetic materials is presented in another chapter of this Handbook. Therefore this section presents a brief summary of the most common types of geosynthetic materials generally used in landfills. For a detailed discussion on the applications of geosynthetic materials, product data, and manufacturers, the Specifier’s Guide of the Geotechnical Fabrics Report (Industrial Fabrics Association International (IFAI), updated annually) is recommended. The Geosynthetics Research Institute (GRI), Drexel University, has defined specifications for most common geosynthetic materials and test methods. ASTM methods and standards have also been written for many soils and geosynthetic materials used in landfill applications. In general, two types of tests are included in geosynthetic specifications: conformance tests and performance tests. Conformance tests are performed prior to installing the geosynthetics, to demonstrate compliance of the material with the project specifications. Performance testing is performed during the construction activities, to ensure compliance of the installed materials and the installation procedures with the project specifications. 33.7.2.1 Barrier Layers Geosynthetic barrier layers may consist of geomembranes, also called flexible membrane liners, or GCLs. The most common polymers used for geomembranes are HDPE, linear low density polyethylene (LLDPE), polypropylene, ethylene propylene diene monomer (EPDM) and polyvinyl chloride (PVC). Selection of the polymer is based primarily on chemical resistance to the substances to be contained. The polymer most widely used for landfill liner systems is HDPE, as it has been shown to adequately resist most landfill leachates. In the case of cover system barrier layers, flexibility is frequently an important selection factor, as landfill covers are subjected to significant settlements. LLDPE geomembranes are generally more flexible than HDPE and therefore are frequently used for cover systems. GCLs consist of a thin layer of dehydrated bentonite placed between two geotextiles or bonded to a geomembrane. The geotextiles are fixed to the bentonite layer by means of adhesives, needle-punched fibers, or stitches.
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33.7.2.2 Drainage Layers Geosynthetic drainage layers used as part of liner and cover systems may consist of geonets or geocomposites. Polymers used for geonets are polyethylene, HDPE, and medium density polyethylene (MDPE). Geotextiles of various types and weights are attached to geonets to manufacture geocomposites. In addition to the properties of the geonet or geocomposite, the properties of the geotextiles attached to the geonet are generally specified separately as discussed below. Seaming of geonets is performed by means of nylon ties, which are not intended to transfer stresses. For geocomposites, the lower geotextiles are generally overlapped, the geonets are joined with nylon ties, and the upper geotextiles are sewn. 33.7.2.3 Geotextiles Geotextiles may be used in landfills to perform several different functions. The most important are: • Separation: Consists of providing separation between two different materials to prevent mixing. A typical application is placement of a granular fill on a soft subgrade. • Reinforcement: Applications of geotextiles for reinforcement are identical to those of geogrids, discussed below. • Filtration: The geotextile is designed as a filter to prevent migration of soil particles across the geotextile. • Drainage: In-plane capacity to convey flow or transmissivity. • Cushioning/Protection: The geotextile serves to separate a geomembrane from a granular soil, to prevent damage to the geomembrane. The polymers most commonly used to manufacture geotextiles are polypropylene and polyester. With respect to their structure, geotextiles are classified primarily as woven and nonwoven. Each of these types of structure is in turn subdivided depending on the manufacturing process. 33.7.2.4 Geogrids Geogrids may be used in landfill liners and covers to provide tensile reinforcement if needed, as well as other types of reinforcement. Typical applications in landfill projects include: • Reinforcement of slopes and embankments: Potential failure surfaces would have to cut across layers of geogrid. The resisting forces on the potential failure surface are the shear strength of the soil and the tensile strength of the geogrid. • Reinforcement of retaining structures: In this application, some of the soil pressure that would act against the retaining wall is transferred by friction to the part of the reinforcing geogrid layer adjacent to the wall, while the rest of the geogrid layer provides passive anchorage. • Unpaved roads: The stiffness of the geogrid allows distribution of loads on a larger area and prevents excessive rutting. • Reinforcement of cover systems: A potential mode of failure of relative steep covers is sliding of a soil layer on the underlying layer (veneer-type sliding). To control this type of failure, a geogrid layer is embedded within the unstable soil layer to provide a stabilizing tensile force. The opposite side of the geogrid must be anchored in an anchor trench or have sufficient length to develop sufficient passive resistance to restrain its displacement. • Bridging of potential voids under liner systems: When liner systems are constructed on existing waste (vertical expansions) or in areas where sinkholes may develop, geogrids are used within the liner system to allow bridging of voids. Geogrids are made of polyester, polyethylene, and polypropylene. If exposed to waste or leachate, selection of the polymer is based on chemical resistance, as in the case of geomembranes. Depending on the direction of greater strength and stiffness, geogrids are classified as uniaxial or biaxial.
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33.8 Environmental Monitoring Landfill projects must include groundwater and landfill gas monitoring systems. If there are important water bodies nearby, surface water monitoring may also be required.
33.8.1 Groundwater Monitoring The groundwater monitoring system specified by Subtitle D consists of a sufficient number of wells installed at appropriate locations and depths to yield groundwater samples from the uppermost aquifer at the site. A number of wells must provide samples representative of groundwater reaching the site (background) and others of the quality of groundwater passing the relevant point of compliance (downgradient). The monitoring plan should include procedures for: • • • • • • •
Frequency of sampling Sample collection Sample preservation and shipment Analytical procedures Chain-of-custody control Quality assurance and quality control Statistical method for data evaluation
Groundwater elevations must be measured in each well immediately prior to purging, each time groundwater is sampled. Two types of monitoring programs are included in Subtitle D: detection monitoring and assessment monitoring. Detection monitoring is required semi-annually at all monitoring wells during the active life of the facility and post-closure period, for 62 constituents listed in Appendix I of Subtitle D. Four independent samples from each monitoring well must be collected and analyzed for the Appendix I constituents during the first semi-annual event. At least one sample from each well must be collected and analyzed during subsequent semi-annual sampling events. If a statistically significant increase over background concentration for one or more of the Appendix I constituents occurs, and no demonstration can be made to disassociate the increase from the MSWLF, an assessment monitoring program must be initiated within 90 days. Assessment monitoring includes sampling and analysis for 213 constituents listed in Appendix II of Subtitle D within 90 days of triggering the assessment monitoring program and annually thereafter. At least one sample from each downgradient well must be collected and analyzed during each sampling event. If any Appendix II constituents are detected, four independent samples from background and downgradient wells must be collected and analyzed to establish the background for the constituents. Additionally, a groundwater protection standard must be established for each Appendix II constituent detected. Within 90 days of detection of Appendix II constituents, and on a semi-annual basis thereafter, all wells must be resampled and analyzed for Appendix I constituents and for the Appendix II constituents that were detected. At least one sample from each well (background and downgradient) must be collected during each sampling event. The facility may return to detection monitoring if all of the detected Appendix II constituents are at or below background levels for two consecutive sampling events. If subsequent monitoring indicates concentrations of Appendix II constituents above background but below groundwater protection standards, the facility must continue assessment monitoring. If one or more Appendix II constituents are detected at statistically significant levels above the groundwater protection standard, the following actions must be initiated within 90 days: characterize the nature and extent of the release; install at least one additional monitoring well; notify all adjacent landowners or residents over the contaminant plume; and initiate assessment of corrective measures.
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33.8.2 Gas Monitoring The gas monitoring program generally consists of performing methane concentration measurements by means of a portable gas probe indicator. Depending on state regulations, permanent gas monitoring wells or probes may also be required as part of the design. Subtitle D specifies the following limits with respect to gas monitoring: • Methane concentrations within on-site structures must not exceed 25% of the lower explosive limit (LEL) • Methane concentration at the site boundary must not exceed the LEL
33.9 Performance of Landfill Elements 33.9.1 Geotechnical and Geosynthetics Analysis Liner and cover systems typically consist of multiple layers of soil and geosynthetic materials. This creates a complex system of materials with different strengths, moduli, and interface frictions in which geotechnical and geosynthetic analyses must be conducted to evaluate their performance. These materials are susceptible to damage by tensile stresses and strains in the geosynthetic materials and tensile cracks in the earth materials. Geotechnical analyses normally conducted for the design of landfills include overall slope stability, stability under seismic loading, sliding of the liner system on berm slopes during construction, sliding of the final cover, settlement of the landfill bottom, settlement of the final cover, and bearing capacity. Overall slope stability and stability under seismic loading are frequently some of the most critical and are briefly discussed below. Overall slope stability analyses are performed to evaluate the stability at critical times during the filling sequence and at the end of filling. The stability analyses include slip surfaces and wedges through underlying soils, surrounding soils, refuse, and interfaces between layers of the liner system. A detailed discussion of the potential failure modes has been published by Mitchell and Mitchell (1992). Geotechnical properties of refuse and interface friction between layers of the liner system are unconventional geotechnical parameters that present significant uncertainties; reviews of available data have been published by Landva et al. (1984), Martin et al. (1984), Mitchell et al. (1990a, 1990b), Landva and Clark (1990), Singh and Murphy (1990), Fassett et al. (1994), Kavazanjian et al. (1995), and Singh (1995). Due to the diversity of materials, strain compatibility of shear strength parameters should be an important consideration in these analyses. The analysis of landfill stability under seismic loading is required under the location restrictions specified in Subtitle D for sites located in seismic impact zones. The seismic loading in the landfill is generally determined by wave propagation analysis. The stability under seismic loading is then analyzed by means of pseudo-static slope stability analysis or calculation of seismically induced displacements. Detailed discussion of the method for seismic analysis of landfills has been published by Repetto et al. (1993a, 1993b), Augello et al. (1995), and Bray et al. (1995). Performance of geosynthetic materials generally includes analysis of tensile stresses and strains, leachate compatibility, durability, puncture resistance, permittivity and clogging of geotextiles, and transmissivity of geonets and geocomposites. Methods to evaluate the performance of geosynthetic materials have been developed and are discussed in detail by Koerner (1994).
33.9.2 Storm Water Management Subtitle D and State regulations typically require the design of run-on and runoff control systems for the 25 year, 24 hour storm event. Methods outlined by the US Department of Agriculture, Soil Conservation Service in the publication entitled “TR55: Urban Hydrology for Small Watersheds” (USDA 1986) and “TR-20: Computer Program for Project Formulations — Hydrology” are generally used to calculate flow
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rates for the design and size of storm water control structures. Several commercial computer programs based upon these methods are available with user-friendly interfaces. Finally, Manning’s Equation for open channel flow is used to analyze channel capacity. The base width, side slopes, and longitudinal slope for the channels can be selected at this time. In general, the minimum slope used for the channels on the final cover is 2% to allow for settlement and subsidence.
33.9.3 Leachate Collection and Removal System The size and spacing of the leachate collection pipes are dependent upon the amount of leachate generated. That can be calculated using two methods: the water budget (or balance) method and the HELP model. The water budget method, based upon the interrelationship of precipitation, evapotranspiration, runoff, soil moisture storage, and infiltration as discussed by Viessman et al. (1989), is a manual computation that can be performed using a spreadsheet type setup. This method does not, however, allow the consideration of a geomembrane component in the cover. Conversely, the HELP model, developed by the US Army Corps of Engineers (EPA 1994), allows the inclusion of geomembranes within the cover or liner. This program requires similar input parameters to the water budget method, yet the program includes significant default data (e.g., climatological for 102 cities, soil and vegetation types, etc.). The results of the program include runoff, evapotranspiration, vertical drainage through the liner, percolation through the layers, peak daily leachate generation rates, average annual and monthly leachate generation rates, and lateral drainage from layers above the liner. The program output also provides data to select pipe spacing, which is most dependent upon the head of leachate over the primary liner. Once the leachate generation rates have been developed and the collection pipe spacing has been selected, the size and slot parameters for the pipes are calculated.
33.10 Summary and Conclusions Development of a landfill project is a complex process that requires a thorough understanding of the physical setting of the site, relevant regulatory requirements, and engineering principles to ensure adequate performance of the various landfill elements. The design of a landfill must consider the interdependence of airspace, soils balance, geotechnical stability, current and ultimate land use plans, environmental monitoring and operation of the gas, surface water, and leachate management systems. With all of these interdependent elements, design is an iterative process, initiated with the Master Plan, followed by the Concept Plan for permitting purposes, and finally Detailed Design for construction documents. Once constructed, a monitoring program is needed to verify environmental compliance of the facility.
Glossary The definitions presented in this section have been extracted from the Code of Federal Regulations (CFR), 40 CFR 258, EPA Criteria for Municipal Solid Waste Landfills, and 40 CFR 261, Identification and Listing of Hazardous Waste. Definitions not available in the federal regulations were obtained from the Virginia Solid Waste Management Regulations. Agricultural Waste All solid waste produced from farming operations or related commercial preparation of farm products for marketing. Commercial Solid Waste All types of solid waste generated by stores, offices, restaurants, warehouses, and other nonmanufacturing activities, excluding residential and industrial wastes. Construction/Demolition/Debris Landfill A land burial facility engineering, constructed, and operated to contain and isolate construction waste, demolition waste, debris waste, inert waste, or combinations of the above solid wastes. Construction Waste Solid waste that is produced or generated during construction, remodeling, or repair of pavements, houses, commercial buildings, and other structures. Construction wastes
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include, but are not limited to, lumber, wire, sheetrock, broken brick, shingles, glass, pipes, concrete, paving materials, and metal and plastics if the metal or plastics are part of the materials of construction or empty containers for such materials. Paints, coatings, solvents, asbestos, any liquid, compressed gases or semi liquids, and garbage are not construction wastes. Cover Material Compactable soil or other approved material, which is used to blanket solid waste in a landfill. Debris Waste Wastes resulting from land-clearing operations, including, but not limited to, stumps, wood, brush, leaves, soil, and road spoils. Demolition Waste Solid waste that is produced by the destruction of structures and their foundations and includes the same materials as construction wastes. Garbage Readily putrescible discarded materials composed of animal, vegetal, or other organic matter. Hazardous Waste The definition of hazardous waste is fairly complex and is provided in 40 CFR Part 261, Identification and Listing of Hazardous Waste. The reader is referred to this regulation for a complete definition of hazardous waste. A solid waste is classified as hazardous waste if it is not excluded from regulations as hazardous waste; it exhibits characteristics of ignitability, corrosivity, reactivity, or toxicity as specified in the regulations; or it is listed in the regulations (the regulations include two types of hazardous wastes: those from nonspecific sources and those from specific sources). Household Waste Any solid waste (including garbage, trash, and sanitary waste in septic tanks) derived from households (including single and multiple residences, hotels, motels, bunkhouses, ranger stations, crew quarters, campgrounds, picnic grounds, and day-use recreation areas). Industrial Solid Waste Solid waste generated by a manufacturing or industrial process that is not a hazardous waste regulated under Subtitle C of RCRA. Such waste may include, but is not limited to waste resulting from the following manufacturing processes: electric power generation; fertilizer/agricultural chemicals; food and related products/by-products; inorganic chemicals; iron and steel manufacturing; leather and leather products; nonferrous metals manufacturing/foundries; organic chemicals; plastics and resins manufacturing; pulp and paper industry; rubber and miscellaneous plastic products; stone, glass, clay, and concrete products; textile manufacturing; transportation equipment; and water treatment. This term does not include mining waste or oil and gas waste. Industrial Waste Landfill A solid waste landfill used primarily for the disposal of a specific industrial waste or a waste that is a by-product of a production process. Inert Waste Solid waste that is physically, chemically, and biologically stable from further degradation and considered to be nonreactive. Inert wastes include rubble, concrete, broken bricks, whole bricks, and blocks. Infectious Waste Solid wastes defined as infectious by the appropriate regulations. Institutional Waste All solid waste emanating from institutions such as, but not limited to, hospitals, nursing homes, orphanages, and public or private schools. It can include infectious waste from health-care facilities and research facilities that must be managed as an infectious waste. Leachate A liquid that has passed through or emerged from solid waste and contains soluble, suspended, or miscible material removed from such waste. Liquid Waste Any waste material that is determined to contain free liquids. Liner A continuous layer of natural or synthetic materials beneath or on the sides of a storage or treatment device, surface impoundment, landfill, or landfill cell that severely restricts or prevents the downward or lateral escape of hazardous waste, hazardous waste constituents, or leachate. Litter Any solid waste that is discarded or scattered about a solid waste management facility outside the immediate working area. Monitoring All methods, procedures, and techniques used to systematically analyze, inspect, and collect data on operational parameters of the facility or on the quality of air, groundwater, surface water, and soils.
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Municipal Solid Waste Waste that is normally composed of residential, commercial, and institutional solid waste. Municipal Solid Waste Landfill Unit A discrete area of land or an excavation that receives household waste, and that is not a land application unit, surface impoundment, injection well, or waste pile. A municipal solid waste landfill unit may also receive other types of RCRA Subtitle D wastes, such as commercial solid waste, nonhazardous sludge, small-quantity generator waste, and industrial solid waste. Such a landfill may be publicly or privately owned. Putrescible Waste Solid waste that contains organic material capable of being decomposed by microorganisms and causing odors. Refuse All solid waste products having the character of solids rather than liquids and that are composed wholly or partially of materials such as garbage, trash, rubbish, litter, residues from cleanup of spills or contamination, or other discarded materials. Release Any spilling, leaking, pumping, pouring, emitting, emptying, discharging, injection, escaping, leaching, dumping, or disposing into the environment solid wastes or hazardous constituents of solid wastes (including the abandonment or discarding of barrels, containers, and other closed receptacles containing sold waste). This definition does not include any release that results in exposure to persons solely within a workplace; release of source, by-product, or special nuclear material from a nuclear incident, as those terms are defined by the Atomic Energy Act of 1954; and the normal application of fertilizer. Rubbish Combustible or slowly putrescible discarded materials that include but are not limited to trees, wood, leaves, trimmings from shrubs or trees, printed matter, plastic and paper products, grass, rags, and other combustible or slowly putrescible materials not included under the term garbage. Sanitary Landfill An engineered land burial facility for the disposal of household waste, which is located, designed, constructed, and operated to contain and isolate the waste so that it does not pose a substantial present or potential hazard to human health or the environment. A sanitary landfill also may receive other types of solid wastes, such as commercial solid waste, nonhazardous sludge, hazardous waste from conditionally exempt small-quantity generators, and nonhazardous industrial solid waste. Sludge Any solid, semisolid, or liquid waste generated from a municipal, commercial, or industrial wastewater treatment plant, water supply treatment plant, or air pollution control facility exclusive of treated effluent from a wastewater treatment plant. Solid Waste Any garbage (refuse), sludge from a wastewater treatment plant, water supply treatment plant, or air pollution control facility, and other discarded material, including solid, liquid, semi-solid, or containing gaseous material resulting from industrial, commercial, mining, and agricultural operations and from community activities. Does not include solid or dissolved materials in domestic sewage, or solid or dissolved materials in irrigation return flows or industrial discharges that are point sources subject to permit under 33 U.S.C 1342, or source, special nuclear, or by-product material as defined by the Atomic Energy Act of 1954, as amended. Special Wastes Solid wastes that are difficult to handle, require special precautions because of hazardous properties, or the nature of the waste creates management problems in normal operations. Trash Combustible and noncombustible discarded materials. Used interchangeably with the term rubbish. Vector A living animal, insect, or other arthropod that transmits an infectious disease from one organism or another. Washout Carrying away of solid waste by waters of the base flood. Yard Waste That fraction of municipal solid waste that consists of grass clippings, leaves, brush, and tree prunings arising from general landscape maintenance.
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References Augello, A.J., Bray, J.D., Leonards, G.A., Repetto, P.C., and Byrne, R.J. (1995), Response of Landfills to Seismic Loading, Proceedings of GeoEnvironment 2000, Special Geotechnical Publication, ASCE. Bray, J.D., Augello, A.J., Leonards, G.A., Repetto, P.C., and Byrne, R.J. (1995), Seismic Stability Procedures for Solid-Waste Landfills, Journal of Geotechnical Engineering, ASCE, 121, 139–151. Fassett, J.B., Leonards, G.A., and Repetto, P.C. (1994), Geotechnical Properties of Municipal Solid Wastes and Their Use in Landfill Design, Proceedings of the WasteTech ’94, Charleston, SC, National Solid Waste Management Association. Geosynthetic Research Institute, Drexel University, GRI Test Methods and Standards, www.geosyntheticinstitute.org Industrial Fabrics Association International, Geotechnical Fabrics Report — Specifier’s Guide, December. Kavazanjian, E., Jr., Matasovic, N., Bonaparte, R., and Schmertmann, G.R. (1995), Evaluation of MSW Properties for Seismic Analysis, Proceedings of the GeoEnvironment 2000, Special Geotechnical Publication, ASCE. Khire, M.V., Benson, C.H., and Bosscher, P.J. (2000), Capillary Barriers: Design Variables and Water Balance, Journal of Geotechnical and Geoenvironmental Engineering, August 2000, pp. 695–708. Koerner, R.M. (1994), Designing with Geosynthetics, 3rd Ed., Prentice Hall, Englewood Cliffs, NJ. Koerner, R.M. and Daniel, D.E. (1992), Better Cover-Ups, Civil Engineering, May, Vol. 62(5), pp. 55–57. Landva, A.O. and Clark, J.I. (1990), Geotechnics of Waste Fills, ASTM, STP 1070, Geotechnics of Waste Landfills — Theory and Practice, A. Landva and G.D. Knowles, ed., American Society for Testing and Materials, pp. 86–106. Landva, A.O., Clark, J.I., Weisner, W.R., and Burwash, W.J. (1984), Geotechnical Engineering and Refuse Landfills, Proceedings of the 6th National Conference on Waste Management in Canada, Vancouver. Langer, U. and Dixon, N. (2004), Mechanical Properties of MSW: Development of a Classification System. 4th BGA Geoenvironmental Engineering Conference, Startford-upon-Avon, UK, Thomas Telford, London, pp. 267–274. Martin, R.B., Koerner, R.M., and Whitty, J.E. (1984), Experimental Friction Evaluation of Slippage Between Geomembranes, Geotextiles and Soils, Proceedings of the International Conference on Geomembranes, Denver, pp.191–196. Mitchell, R.A. and Mitchell, J.K. (1992), Stability Evaluation of Waste Landfills, Proceedings of the ASCE Specialty Conference on Stability and Performance of Slopes and Embankments — II, Berkeley, CA, June 28–July 1, pp. 1152–1187. Mitchell, J.K., Seed, R.B., and Seed, H.B. (1990a), Kettleman Hills Waste Landfill Slope Failure. I: Liner System Properties, Journal of Geotechnical Engineering, ASCE, 116, 647–668. Mitchell, J.K., Seed, R.B., and Seed, H.B. (1990b), Stability considerations in the design and construction of lined waste repositories, ASTM STP 1070, Geotechnics of Waste Landfills — Theory and Practice, A. Landva and G.D. Knowles, ed., American Society for Testing and Materials, pp. 207–224. Repetto, P.C., Bray, J.D., Byrne, R.J., and Augello, A.J., (1993a), Applicability of Wave Propagation Methods to the Seismic Analysis of Landfills, Proceedings of the WasteTech ’93, National Solid Wastes Management Association, California, January. Repetto, P.C., Bray, J.D., Byrne, R.J., and Augello, A.J., (1993b), Seismic Analysis of Landfills, 13th Central Pennsylvania Geotechnical Seminar, Hershey, PA, April. Repetto, P.C. and Foster, V.E. (1993), Basic Considerations for the Design of Landfills, Proceedings of the First Annual Great Lakes Geotechnical/Geoenvironmental Conference, The University of Toledo, Toledo, OH. Seed, H.B. and Bonaparte, R. (1992), Seismic Analysis and Design of Lined Waste Fills: Current Practice, Proceedings of the ASCE Specialty Conference on Stability and Performance of Slopes and Embankments — II. Berkeley, CA, June 28–July 1, pp. 1521–1545.
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Singh, S. (1995), Geotechnical Considerations in the Strength Characterization of Municipal Solid Waste, Proceedings of the 10th Pan-American Conference on Soil Mechanics and Foundation Engineering, Guadalajara, Mexico, November. Singh, S. and Murphy, B. (1990), Evaluation of the Stability of Sanitary Landfills, ASTM STP 1070, Geotechnics of Waste Landfills — Theory and Practice, A. Landva and G. D. Knowles, ed., American Society for Testing and Materials, pp. 240–258. Spear, J.W.Sr. (2004), Bioreactors and Leachate Recirculation Systems Design, Section 8 of Proceedings for Sanitary Landfill Design course offered through the University of Wisconsin, Madison, February 11–13, 2004. Thornloe, Susan A. (2004), U.S.EPA’s Field Test Programs to Update Data on Landfill Gas Emissions, Air Pollution Prevention and Control Division, Office of Research and Development, USEPA, Research Triangle Park, NC. United States Code of Federal Regulations, Title 40 (1991), Protection of the Environment, Part 258, EPA Criteria for Municipal Solid Waste Landfills. United States Department of Agriculture (1986), Soil Conservation Service, Engineering Division, TR-55: Urban Hydrology for Small Watersheds. United States Environmental Protection Agency (1992), Center for Environmental Assesment Modeling, The Multimedia Exposure Assesment Model (MULTIMED), Computer program available at: http://www.epa.gov/ceampubl/mmedia/multim1/ United States Environmental Protection Agency (1994), Office of Research and Development, The Hydrological Evaluation of Landfill Performance (HELP) Model, User’s Guide for Version 3 (EPA/600/R-94/168a) and Engineering Documentation for Version 3 (EPA/600/R-94/168b). This software is available through the Site Characterization Library, Volume 1, Release 2 (EPA report number 600/C-98/001) through the EPA’s National Service Center for Environmental Publications (800-490-9198) (http://www.epa.gov/ncepi). Viessman, Jr., W., Lewis, G., and Knapp, J. (1989), Introduction to Hydrology, 3rd Edition, Harper & Row Publishers, New York.
Further Information Geosynthetic Research Institute, www.geosynthetic-institute.org International Geosynthetics Society, www.geosyntheticssociety.org North American Geosynthetics Society, www.nagsigs.org USACE Geosynthetics, www.geosynthetica.net/tech_docs/USACEdocs.asp USEPA. 1993. Office of Research and Development. Quality Assurance and Quality Control for Waste Containment Facilities, Technical Guidance Document. EPA/600/R-93/182. USEPA. 1993. Office of Research and Development. Proceedings of the Workshop on Geosynthetic Clay Liners. EPA/600/R-93/171 USEPA. 1993. Office of Research and Development. Report of Workshop on Geomembrane Seaming. EPA/600/R-93/112. USEPA. 1988. Risk Reduction Engineering Laboratory. Guide to Technical Resources for the Design of Land Disposal Facilities. EPA/625/6-88/018. USEPA. 1986. Office of Solid Waste and Emergency Response. Technical Guidance Document: Construction Quality Assurance for Hazardous Waste Land Disposal Facilities. EPA/530-SW-86-031. USEPA. 1982. Office of Solid Waste and Emergency Response. Evaluating Cover Systems for Solid and Hazardous Waste. EPA/SW-867.
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34 Evapotranspirative Cover Systems for Waste Containment 34.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34-1 34.2 Unsaturated Soil Hydraulic Concepts Relevant to Evapotranspirative Cover Performance . . . . . . . . . . . . . . . . 34-3 Water Flow through Unsaturated Porous Media • Unsaturated Soil Hydraulic Properties
34.3 Types of Evapotranspirative Covers . . . . . . . . . . . . . . . . . . . . 34-9 Monolithic Covers • Capillary Barriers • Anisotropic Barriers
34.4 Relevant Issues for Design of Evapotranspirative Covers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34-13 Design Strategies • Performance Criteria and Regulatory Issues • Important Design Variables • Numerical Modeling Issues
34.5 Performance Monitoring of Evapotranspirative Covers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34-16 Monitoring Strategies • Regulatory Issues Specific to Compliance Demonstration • Lysimetry • Monitoring of Moisture and Suction Profiles • Monitoring of Meteorological Variables and Overland Runoff
34.6 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34-19 Site Survey • OII Landfill • Rocky Mountain Arsenal
Jorge G. Zornberg and John S. McCartney University of Texas at Austin
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34-27 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34-27 Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34-31
34.1 Introduction The management of hazardous and municipal wastes may have important implications on groundwater quality. The current trend in waste management in the United States involves its disposal and isolation within containment facilities to minimize human and environmental contact. One of the key engineered components in municipal and hazardous waste containment systems is the cover system. The cover system is the surface culmination of a landfill, so it interacts closely with the atmosphere. Cover design and analysis involves concepts from various disciplines such as geotechnical engineering, environmental 34-1
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engineering, soil science, agriculture engineering, climatology, biology, and hydrology. Integration of concepts from these various disciplines presents important challenges to researchers, designers, regulators, and stakeholders. This is particularly the case in evapotranspirative covers, the understanding of which relies heavily on the quantification of atmospheric processes at the land surface and of water flow though unsaturated soil. The water balance components used to quantify the conservation of water mass in an engineered cover may include evaporation and plant transpiration (together referred to as evapotranspiration), precipitation, overland runoff, soil moisture storage, lateral drainage, and basal percolation. Basal percolation, an important variable to quantify the overall performance of landfill covers, is the volume of water that exits the lower boundary of the engineered cover with time. The water that cannot be removed from the cover by evapotranspiration or lateral drainage reaches the underlying waste mass, possibly mobilizing contaminants that may eventually reach the groundwater. Accordingly, one of the primary objectives of a landfill cover system is to control basal percolation. Additional objectives of landfill covers include accommodating differential settlements without compromising its performance, and controlling landfill gas release. In addition, the cover should remain stable under static and seismic conditions, minimize long-term maintenance, allow land re-use, and provide an aesthetic appearance. The design of final cover systems for new municipal and hazardous waste containment systems in the United States is prescribed by the US Resource Conservation and Recovery Act (RCRA) Subtitles D and C, respectively. Federal- and state-mandated cover systems for municipal and hazardous waste landfills have endorsed the use of resistive barriers. Resistive cover systems involve a liner (e.g., a compacted clay layer) constructed with a low saturated hydraulic conductivity soil (typically 10−9 m/sec or less) to reduce basal percolation. Figure 34.1(a) shows the water balance components in a resistive system, in which basal percolation control is achieved by maximizing overland runoff. To enhance cover performance and lower construction costs, RCRA regulations allow the use of alternative cover systems if comparative analyses and field demonstrations can satisfactorily show their equivalence with prescriptive systems. Evapotranspirative covers are alternative systems that have been recently proposed and successfully implemented in several high-profile sites. Evapotranspirative covers are vegetated with native plants that survive on the natural precipitation and have been shown to be stable over long periods of time. Figure 34.1(b) shows the water balance components in an evapotranspirative cover system. Evapotranspiration and moisture storage are components that influence significantly the performance of this system. Internal lateral drainage may also be a relevant component in some cover types (capillary barriers on steep slopes). The novelty of this approach is the mechanism by which basal percolation control is achieved: an evapotranspirative cover acts not as a barrier, but as a sponge or a reservoir that stores moisture during precipitation events, and then releases it back to the atmosphere as evapotranspiration or lateral drainage. Silts and clays of low plasticity are the soils most commonly used in evapotranspirative covers, as they can store water while minimizing the potential for cracking upon desiccation.
(b)
(a)
Precipitation Overland runoff
Precipitation Overland runoff Moisture storage
Lateral drainage
Basal percolation Resistive cover
Evapotranspirative cover
Basal percolation
FIGURE 34.1 Water balance components: (a) in a resistive barrier and (b) in an evapotranspirative cover
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Additional advantages of evapotranspirative covers over typical clay barrier systems include minimizing desiccation cracking, ease of construction, and low maintenance. Also, effective evapotranspirative covers can be constructed with a reasonably broad range of soils, which can lead to significant cost savings. The adequacy of evapotranspirative cover systems has been verified by field experimental assessments (Anderson et al., 1993; Dwyer, 1998), and procedures have been developed for quantitative evaluation of the variables governing their performance (Khire et al., 1999; Zornberg et al., 2003). The scope of this chapter includes: (i) basic hydraulic concepts for unsaturated soils relevant to evapotranspirative covers, (ii) types of evapotranspirative covers, (iii) design and modeling issues, (iv) field monitoring approaches, and (v) case studies.
34.2 Unsaturated Soil Hydraulic Concepts Relevant to Evapotranspirative Cover Performance 34.2.1 Water Flow through Unsaturated Porous Media Designing a truly impermeable barrier (i.e., one leading to zero basal percolation) should not be within an engineer’s expectations. Instead, the objective of the cover should be to minimize the basal percolation of water to acceptable levels. Quantification of the basal percolation is challenging as it involves analysis of water flow through unsaturated soils subject to complex atmospheric boundary conditions. Both air and water are present in the voids of unsaturated soils. The relative amounts of water and air in the soil, typically quantified on a volumetric basis, highly influence the soil hydraulic behavior. Figure 34.2 illustrates some of the common phase relationships used for the analysis of water flow processes in unsaturated soils. The volumetric moisture content θ, is defined as the ratio between the volume of water and the total control volume. The porosity n, which is the ratio between the volume of voids and the total control volume, corresponds to the volumetric moisture content at saturation (i.e., n = θs ). The degree of saturation S, commonly used to normalize the moisture content of a soil is the ratio between the volumetric moisture content and the porosity. Finally, the volumetric air content is the difference between the porosity and the volumetric moisture content. In an unsaturated soil, water is held within the pores against the pull of gravity by a combination of adsorptive and capillary pressures (Olson and Langfelder, 1965). Adsorptive pressures are present in soils due to electrical fields and short-range attractive forces (van Der Waal forces) that tend to draw water toward the soil particles in highly plastic clays, where the net negative charges on water dipoles and surface of clay particles interact with the cations in the pore water. The capillary pressure is quantified as the difference between the pore air pressure and the pore water pressure. Water is a wetting fluid for most soil particles, which implies that the air-water menisci between individual soil particles are convex, tensioned membranes. Accordingly, the air pressure is greater than the water pressure, which has a negative magnitude. The adsorptive and capillary pressures are typically considered together as a single
Air
Va
=
Vv Water
Vw Vt
s= S=
Solid particles
Vs
Vs
Vw VT Vv VT Vw Vv
=
s
FIGURE 34.2 Volumetric phase diagram for unsaturated soils.
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variable, referred to as the matric suction, ψ, which has units of pressure (kPa). The capillary rise in a pipette provides an analogy useful to assess the influence of pore sizes on the matric suction, given by the following expression 2σaw cos γ (34.1) ψ = Pa − Pw = hc ρw g = R where Pa is the pore air pressure, Pw is the pore water pressure, hc is the height of capillary rise in a pipette of radius R, ρw is the density of water, g is the acceleration of gravity, σaw is the surface tension between water and air, and γ is the wetting contact angle (typically 10◦ for quartz minerals). Equation 34.1 assumes that air is under atmospheric pressure (Pa = 0) and indicates that the suction is inversely proportional to the pore radius. Accordingly, for the same volumetric moisture content, a fine-grained soil (with comparatively small pore radii) will have a higher suction than a coarse-grained soil. The relationship between moisture content and suction is thus related to the pore size distribution of the soil as discussed in Section 34.2.2. Flow of water through soils is driven by a gradient in the hydraulic energy, which is quantified by the fluid potential (energy per unit mass of water). The fluid potential is given by an expanded form of Bernoulli’s equation: Po 1 v 2 −ψ + + (34.2) = gz + 2 n ρw ρw where is the fluid potential, z is the vertical distance from the datum, v is the water discharge velocity, n is the porosity, and Po is the osmotic suction. In Equation 34.2, the four terms on the right-hand side correspond to the potential energy, the kinetic energy, the energy due to the water pressure (ψ = −Pw if Pa = 0), and the energy due to osmosis. The discharge velocity (v/n) is comparatively small, leading to a negligible kinetic energy component. The osmotic suction is typically considered constant throughout an evapotranspirative cover, and consequently does not lead to a contribution to the hydraulic gradient. As in the case of water-saturated soils, Darcy’s law for unsaturated soils indicates that flow is driven by the gradient in total hydraulic potential. However, the available pathways for water flow in unsaturated soil decrease as the moisture content decreases (or as suction increases). This is quantified by the hydraulic conductivity function K (ψ), which accounts for the decrease in conductivity with increasing suction (or decreasing moisture content). The K -function is discussed in Section 34.2.2.2. The discharge velocity through a soil in the vertical direction z can be estimated using Darcy’s law and Equation 34.2, as follows: K (ψ) ∂ ∂ Q =− = −K (ψ) v= A g ∂z ∂z
1 ∂ψ 1− ρw g ∂z
(34.3)
where Q is the volumetric flow rate, and A is the area of soil perpendicular to the flow direction. Figure 34.3 shows a control volume of thickness dz for one-dimensional (1-D) water flow through a soil layer with thickness L using the base of the soil layer as datum. The continuity principle in this control volume can be expressed by: ∂v ∂θ =− (34.4) ∂t ∂z where the left-hand side represents the change in moisture storage in the control volume, and the righthand side represents the change in flow rate across the control volume. Substitution of Equation 34.3 into Equation 34.4 leads to the governing equation for 1-D flow through unsaturated porous materials, referred to as Richards’ equation: ∂ 1 ∂ψ ∂θ ∂ψ = K (ψ) 1 − ∂ψ ∂t ∂z ρw g ∂z
(34.5)
Richards’ equation is a coupled, nonlinear parabolic equation, which can be solved using finite differences or finite elements. Numerical solutions to Richards’ equation can be challenging because the constitutive function [K (ψ) and θ (ψ)] are highly nonlinear and may have undefined or zero derivatives. Further,
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dz
L +
g
∂ dz ∂z
z
FIGURE 34.3 Control volume for vertical flow through an evapotranspirative cover
1.0
Nonwoven geotextile Sand Low plasticity clay High plasticity clay
0.9
Degree of saturation
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1.E–01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Suction, kPa
FIGURE 34.4 Typical SWRCs for different geotechnical materials
selection of boundary conditions may not be straightforward for several practical problems. Boundary conditions typically used for evapotranspirative covers include atmospheric flux boundary conditions at the surface (infiltration or evaporation), and unit hydraulic gradient (i.e., zero change in suction with depth) at the base. A discussion on the boundary conditions for evapotranspirative covers may be found in Fayer and Jones (1990). Additional difficulties for solving water flow problems for unsaturated soils arise when considering moisture removal from plant roots, desiccation cracking, animal intrusion, and volumetric changes.
34.2.2 Unsaturated Soil Hydraulic Properties 34.2.2.1 Soil Water Retention Curve The moisture storage of the soil is an important performance variable of evapotranspirative covers. The moisture storage is typically quantified using the relationship between volumetric moisture content and soil suction, referred to as the Soil Water Retention Curve (SWRC). Figure 34.4 shows the SWRCs for different geotechnical materials. The coarser materials (sand and geotextile) show a highly nonlinear
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response, with a significant decrease in moisture content (or degree of saturation) in a narrow range in suction. The fine-grained materials (silt and clay) show a more gradual decrease in moisture content with increasing suction. The nonlinearity observed in these relationships is partly caused by the range of pore size distributions for these materials. An important characteristic in a SWRC is the air entry value. During initial drying of a fully saturated soil specimen water does not flow from the soil until the suction corresponding to the air entry value is reached. When this suction is reached, air enters the specimen and the moisture content decreases. Once the air entry value is reached, the moisture content drops from saturation to a value that remains approximately constant with increasing suction. This low moisture content value is often referred to as the residual moisture content. The residual condition occurs because the water becomes occluded (or disconnected) within the soil pores, with no available pathways for water flow to occur. The SWRC for a given material is not only sensitive to the pore size distribution, but also the soil mineralogy, density, and pore structure (Hillel, 1988). The SWRC can show significantly different wetting and drying paths, a phenomenon referred to as hysteresis (Topp and Miller, 1966; Kool and Parker, 1987). During drying, the largest pores drain first, followed by the smaller pores. During wetting, the smaller pores fill first, but the presence of large pores may prevent some from filling. Also, wetting of a dry media often leads to entrapment of air in the larger pores, which prevents saturation of the media unless positive pressure is applied to the water. Air entrapment causes the wetting path to be relatively flat for high suctions (e.g., over 100 kPa), with a steep increase in volumetric moisture content at lower suctions. Several techniques are available to determine the SWRC experimentally (Klute et al., 1986; Wang and Benson, 2004). Two main groups of techniques have been used to define the SWRC. The first group of techniques (“physical”techniques) involves an initially water-saturated material from which water is slowly expelled by imposing a suction to a specimen boundary. Flow continues until it reaches a condition at which the moisture content and suction are in equilibrium. The most commonly used physical technique is the axis translation technique. A common test that is based on this technique is the pressure plate test (Figure 34.5(a)), which involves placing a soil specimen on a high air-entry ceramic plate and applying air pressure to the specimen. The air pressure causes the pore water to pass through the ceramic plate since the water pressure on the effluent side of the plate is kept at atmospheric pressure (zero). At equilibrium, the air pressure corresponds to the suction. The outflow volume is measured using a constant head Mariotte bottle. This approach is repeated for successively higher pressures that gradually dry the specimen, after which the pressure may be decreased to measure the wetting behavior. At the end of the testing, the gravimetric moisture content may be measured destructively, and the moisture content at each pressure increment can be back-calculated from the outflow measurements. Additional details can be found in the ASTM standard for SWRC determination (ASTM D6836 2002). Another technique, the hanging column, is shown in Figure 34.5(b). This test also involves a ceramic plate, but connects the bottom of the plate to a manometer tube. A negative water pressure is imposed on the water level in the ceramic plate by holding the manometer tube beneath the plate. The second group of techniques (“thermodynamic” techniques) involves allowing water to evaporate from a specimen in a closed chamber under controlled relative humidity. The relative humidity is controlled by allowing water to evaporate from a saturated salt solution placed within the chamber, as shown in Figure 34.5(c). Another commonly used thermodynamic technique is the chilled mirror
(a)
Soil specimen
O-ring seal Water outlet
Air pressure inlet
(b)
Buchner funnel Retaining ring Soil specimen Fritted glass disk
(c)
Soil specimens
Water manometer
Retaining ring
Oversaturated salt solution
Desiccator Supports
Ceramic plate
FIGURE 34.5 Conventional methods to determine the SWRC: (a) pressure plate; (b) hanging column; and (c) saturated salt solutions.
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hygrometer (Wang and Benson, 2001). This device infers the total soil suction (matric and osmotic) by measuring the vapor pressure in the soil, which is related to the temperature at which moisture condenses on a mirror. When condensation occurs, a change in the optical properties of the mirror is detected. In general, physical techniques are used for relatively low suctions (e.g., under 1500 kPa), while thermodynamic techniques are used for higher suctions. Conventional techniques to define the SWRC require significant time to obtain limited data. For example, determination of the SWRC for a high-plasticity clay specimen may take several months. Also, conventional determination methods require the use of several specimens and destructive measurement of moisture content. Problems specific to SWRC testing involve diffusion of air across porous ceramics, lack of control of volume change during drying and wetting (e.g., Cabral et al., 2004), and inability to impose a stress state representative of field conditions. Centrifugation can be used to alleviate shortcomings of conventional characterization of the SWRC. Centrifugation increases the body forces on a porous media, accelerating fluid flow as time increases quadratically with g-level. Centrifuges were first used in the early 1930s to define the SWRC by soil scientists and petroleum engineers (Gardner, 1937; Hassler and Bruner, 1945). Saturated specimens can be placed upon a saturated ceramic plate that conducts only liquid. During centrifugation, the increased body force causes water to exit the specimen through the ceramic while air enters the surface of the specimen. The suction profile within the specimen can be defined if the bottom boundary is maintained saturated (zero suction). The suction distribution obtained at equilibrium (i.e., when flow ceases) is: ψ(r) =
ρw ω 2 2 [r0 − r 2 ] + ψ(0) 2
(34.6)
where r0 is the outer radius of the centrifuge specimen, r is the distance toward the center of rotation with a datum at the outer radius, ω is the angular velocity, and ψ(0) is the suction at the bottom boundary of the specimen (zero if a saturated ceramic plate is used as the bottom boundary condition). Analytical techniques can be used to associate the average moisture content (measured destructively) with the suction at the soil surface (Forbes, 1994). A SWRC is typically quantified by fitting experimental data to power law, hyperbolic, or polynomial functions (Brooks and Corey, 1946; van Genuchten, 1980; Fredlund and Xing, 1994). Although the Brooks and Corey (1946) model is able to represent a sharp air entry suction, the van Genuchten (1980) model is most commonly used in numerical analyses because it is differentiable for the full range of suctions. The van Genuchten model is given by: θ = θr + (θs − θr )[1 + (αψ)N ]−(1−(1/N ))
(34.7)
where θr is the residual moisture content, θs is the saturated moisture content (porosity), and α (units of kPa−1 ) and N (dimensionless) are fitting parameters. Preliminary estimates of the SWRC could be obtained using databases that rely on the granulametric distribution of soils (Fredlund and Xing, 1994). 34.2.2.2 Hydraulic Conductivity Function The relationship between hydraulic conductivity and suction, also referred to as the K -function, provides a measure of the increased impedance to moisture flow with decreasing moisture content. The saturated hydraulic conductivity Ks provides a measure of the minimum impedance to moisture flow through soil. Figure 34.6 shows K -functions for different geotechnical materials. Near saturation, the coarser materials (sand and geotextile) have high hydraulic conductivity, while the fine-grained materials (silt and clay) have lower hydraulic conductivity. However, as the soil dries, the coarse materials end up being less conductive than the fine-grained materials. That is, as the fine-grained materials can retain more water in the pores as suction increases, they still have available pathways for water flow, and are thus more conductive than coarser materials. The superior performance in arid climates of evapotranspirative covers relative to conventional resistive covers can be attributed to the lower unsaturated hydraulic conductivity of the selected cover soils.
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The Handbook of Groundwater Engineering 1.E–01 Nonwoven geotextile Sand Silt Clay
Hydraulic conductivity, m/s
1.E–03 1.E–05 1.E–07 1.E–09 1.E–11 1.E–13 1.E–15 1.E–17 1.E–19 1.E–21 1.E–01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Suction, kPa
FIGURE 34.6 Typical K -functions for different geotechnical materials.
in from flow pump Permeameter wall
Moisture content sensors
Suction sensors
out measured with pressure gauge or tipping bucket
FIGURE 34.7 Parameter set up for measurement of K -function.
Conventional methods used to define the K -function are costly, time consuming, and prone to experimental error. Accordingly, the K -functions (e.g., such as those in Figure 34.6) are often predicted based on pore size distributions such as van Genuchten–Mualem model (1980), as follows: K (θ ) = Ksat
1/(1−N) 2 θ − θr 1−N θ − θr 1− 1− θs − θ r θs − θ r
(34.8)
K (ψ) can be defined by substituting Equation 34.7 for θ into Equation 34.8. Other predictive relationships for the K -function are given by Burdine (1953) and Campbell (1974). Several techniques have been proposed for direct determination of the K -function in the laboratory (Benson and Gribb, 1997). Conventional techniques to measure the K -function involve flow of liquid through a specimen confined within a permeameter. Flow is applied using either ceramic plates or flow pumps. Figure 34.7 shows a typical permeameter setup used to measure the hydraulic conductivity (Meerdink et al., 1996; Lu and Likos, 2005; McCartney et al., 2005b). Permeameters have differed in
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specimen confinement and size, control of boundary conditions, and availability of instrumentation. The K -function can be estimated using steady or transient flow processes. During steady moisture infiltration with a deep water table, a unit hydraulic gradient (e.g., i = 1) is typically observed in the soil profile, sufficiently far from a water table boundary. Accordingly, suction does not change with depth and water flow is driven only by gravity. In this case, the hydraulic conductivity equals the imposed steady-state discharge velocity. Additional points are obtained by changing the imposed flow. During transient flow processes, the suction and moisture content profiles are measured as a function of depth and time, and the K -function can be estimated using the instantaneous profile method (Watson, 1966; Olson and Daniel, 1979; Meerdink et al., 1996). While techniques based on transient processes yield more information about the K -function, steady state techniques provide more reliable information. As for the SWRC, conventional techniques used to define the K -function require significant time to obtain limited data. Problems specific to K -function testing include boundary effects on the flow process, difficulties in uniformly distributing water from flow pumps to the specimen, and tedious testing procedures. To alleviate these shortcomings, centrifuge testing has been used to define the K -function in geotechnical projects involving the design of ET covers (Zornberg et al., 2003; Dell’Avanzi et al., 2004). Nimmo et al. (1987) developed the Internal Flow Control Steady-State Centrifuge (IFC-SSC) method, which uses a system of reservoirs to control the fluid flow rate and suction at the upper and lower surfaces of a specimen. Conca and Wright (1994) developed the Unsaturated Flow Apparatus (UFA), which uses a sophisticated rotary joint to a low fluid flow rate into the specimen. The UFA uses open-flow centrifugation, which does not impose a suction value on the specimen. For steady state conditions, the SSC and UFA use Darcy’s law to determine the K -function: K (ψ) =
−v [−(1/(ρw g ))(dψ/dz) − ((ω2 r)/g )]
(34.9)
where v is the imposed discharge velocity. Points on the K -function curve are defined using Equation 34.9 after reaching steady state flow conditions. The SSC and UFA do not allow the direct monitoring of the relevant variables (suction, moisture, discharge velocity) in-flight during testing. If the suction gradient in Equation 34.9 is assumed to be negligible, the hydraulic conductivity becomes inversely proportional to ω2 . The SSC and UFA centrifuges must be periodically stopped to measure the specimen mass to ensure steady state flow, and the moisture content must be measured destructively at the end of the test. Although the SSC and UFA allow a faster testing time than conventional K -function testing methods, their shortcomings led to the development of an improved centrifuge device, referred to as the Centrifuge Permeameter for Unsaturated Soils (CPUS) (McCartney and Zornberg, 2005a). This device incorporates the use of a low-flow hydraulic permeameter and a high-g centrifuge capable of continuously, nondestructively, and non-intrusively measuring suction, moisture content, and fluid flow rate in a single specimen during centrifugation. Accordingly, CPUS allows an expedited determination of both the SWRC and K -function from a single specimen in a single test. Measuring the SWRC and K -function during a flow process is consistent with actual flow problems, unlike conventional techniques such as the axistranslation technique. Figure 34.8(a) shows a view of the CPUS centrifuge and Figure 34.8(b) shows a schematic view of the CPUS permeameter and its instrumentation layout. A special low-flow fluid union is used to supply fluid from the stationary environment to the rotating specimen within the centrifuge. CPUS facilitates the use of experimentally obtained, rather than theoretically derived hydraulic properties in the design of evapotranspirative cover systems.
34.3 Types of Evapotranspirative Covers 34.3.1 Monolithic Covers Monolithic covers are evapotranspirative covers that consist of a single soil layer placed directly over the waste (Zornberg et al., 2003). Figure 34.9a shows a schematic view of a monolithic soil cover. The soil layer
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(a)
(b)
Inflow port Fluid distribution cap
Rotary fluid union
TDR cable tester and multiplexer
Permeameter
Air release
Air entry port (for drying) High-speed data acquisition system
Time domain reflectometry probes
Heat dissipation units
Vibration isolators Base pedestal
Porous support platen Air release
Water table control port
Outflow reservoir
Pressure transducer
FIGURE 34.8 Centrifuge parameter for unsaturated soils: (a) centrifuge layout and (b) Permeameter. (a)
Vegetative surface
(b)
t4 t5
t1 t2
t6
t3
t7
Monolithic cover
Monolithic cover Depth of significant moisture fluctuations Depth Foundation layer Waste
Initial moisture content in monocover
Foundation layer
Infiltration Evapotranspiration
FIGURE 34.9 Monolithic cover: (a) soil profile and (b) typical seasonal moisture content fluctuations.
acts both as a substrate for vegetation and a hydraulic barrier. A foundation layer consisting of the same soil type is typically used to provide a level surface above the waste. Early research focused on investigation of the long-term behavior of natural soil layers in arid regions, assuming that the behavior is analogous to that of an engineered monolithic cover (Waugh et al., 1994). These studies found that moisture content fluctuations in natural analogues in recent geologic history are typically confined to the upper few feet of soil, indicating the adequacy of monolithic covers as an acceptable long-term solution to waste disposal. The major aspects in monolithic covers are the proper characterization of the hydraulic properties (K -function and SWRC) of the soils as well as the determination of the appropriate thickness of the engineered soil cover. Figure 34.9b shows schematic moisture profiles, illustrating typical seasonal fluctuations in a properly performing monolithic cover. The moisture profiles illustrate wetting during infiltration events and subsequent drying due to evapotranspiration. Although some moisture fluctuations
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are expected to reach the base of the cover in extreme events, most of the moisture fluctuations are expected to take place only within the upper portion of the cover. Monolithic cover design requires selection of the cover thickness and soil moisture storage necessary to keep the basal percolation below a minimum allowable (design) value, given the expected weather conditions for a site. The soil moisture storage of a cover can be calculated as the integral of the volumetric moisture content profile with depth. The upper bound on soil moisture storage depend on the shape of the SWRC. The greater the moisture retained in a soil for the suction values expected in the field, the greater the moisture storage. A parameter that has been used to quantify the moisture storage is the field capacity, which is defined as the threshold moisture content value above which the soil no longer retains water by capillarity under the effects of gravity (Zornberg et al., 1999). When water is added to a soil that is at field capacity, drainage occurs. The field capacity may be obtained from infiltration tests, although a generally accepted value for silt and low plasticity clay soils is the moisture content corresponding to a suction of 33 kPa (Nachabe, 1998; Meyer and Gee, 1999). The storage capacity of a monolithic cover can be preliminarily estimated by multiplying the volumetric moisture content at field capacity (obtained using the SWRC) by the cover thickness.
34.3.2 Capillary Barriers Capillary barriers are evapotranspirative covers that consist of a layered soil system typically involving a fine-grained soil (silt, clay) placed over a coarse-grained material (sand, gravel, nonwoven geotextile). Capillary barriers use the contrast in hydraulic properties between the fine- and coarse-grained soils to enhance the ability of the fine-grained material to store moisture (Shackelford et al., 1994; Stormont and Anderson, 1999; Khire et al., 1999; 2000). Figure 34.10a and Figure 34.10b show SWRCs and K -functions for sand (coarse-grained component), and low plasticity clay (fine-grained component). The capillary break concept relies on the continuity of suction, even at the interface between two different materials. Figure 34.10a shows that when a clay–sand system is at an initially high suction (e.g., 1000 kPa), the clay has a degree of saturation of 0.2 while the underlying sand is at residual moisture content. Figure 34.10b indicates that at this high suction, the clay has a hydraulic conductivity of approximately 1 × 10−13 m/sec while the sand has an even higher impedance to flow. Consequently, if moisture infiltrates into the fine-grained material after a precipitation event and reaches the interface with the coarse-grained material it can only progress into the coarse-grained material at a very slow rate. Consequently, water will accumulate at the interface until the suction at the interface reaches a value at which the hydraulic conductivity of the coarse grained material is no longer below that of the fine-grained material (3.0 kPa in Figure 34.10b). This suction value is referred to as the breakthrough suction. A breakthrough suction of 3.0 kPa is significantly below the suction corresponding to field capacity (typically considered at 33 kPa for clay), which indicates that the degree of saturation in the clay will be relatively high (95%) when breakthrough occurs. For suction values less than that corresponding to field capacity, water would have drained downwards by gravity had the capillary break not been present. When the breakthrough suction is reached, leakage is observed in the coarse-grained layer at a rate approaching that corresponding to the saturated hydraulic conductivity of the barrier layer. Figure 34.10c shows a schematic view of a capillary break cover. Similar to the monolithic cover, the soil layer acts both as a substrate for vegetation and a hydraulic CRL (or capillary retention layer, CRL). However, a coarse-grained material (capillary break layer, CBL) is placed over the foundation material to create a capillary break at the interface between the CRL and the CBL). Figure 34.10d shows schematic moisture profiles illustrating the expected seasonal fluctuations in a properly performing capillary break cover. Unlike the monolithic cover, the moisture front can reach the bottom of the barrier layer without resulting in basal percolation, provided that the moisture at the interface does not exceed the breakthrough value. An important benefit of capillary breaks is that the moisture storage within the fine-grained soil can exceed its freely draining state (field capacity). Consequently, more water can be stored in a capillary break cover than in a monolithic cover of equivalent thickness. Alternatively, a thinner fine-grained layer can be used in a capillary break cover to obtain the same moisture storage as in a monolithic cover. The magnitude
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1.0
(b)
Degree of saturation
0.8
0.6 0.5 0.4 0.3
0.1
Breakthrough suction of 4.0 kPa
0.0 1.E–01
Sand
1E–03
Low plasticity clay SWRC
0.7
0.2
1E–01
Sand Sand SWRC Low plasticity clay
0.9
Hydraulic conductivity, m/s
(a)
The Handbook of Groundwater Engineering
1E–05
Low plasticity clay
Breakthrough Suction of 4.0 kPa
1E–07 1E–09 1E–11 1E–13 1E–15 1E–17 1E–19 1E–21
1.E+00
1.E+01
1.E+02 1.E+03 Suction, kPa
(c)
1.E+04
1.E+05
1.E–01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Suction, kPa
Vegetative surface
(d)
t5
t1
t6 t7
t2 Fine-grained (CRL) layer
t8 t9
Fine-grained (CRL) layer
Coarse-grained (CBL) layer
Depth
Foundation layer Waste
t3
t4
Coarse-grained (CBL) layer Foundation layer Initial moisture content in fine-grained layer Infiltration Evapotranspiration
FIGURE 34.10 Capillary barrier details: (a) conceptual SWRC illustration of the capillary break effect; (b) conceptual K -function illustration of capillary break effect; (c) capillary break soil profile; and (d) typical seasonal moisture content fluctuations.
and long-term changes in the conditions leading to breakthrough are aspects under current investigation, especially in inclined covers (Parent and Cabral, 2004). Inclined covers may experience lateral diversion, which leads to greater moisture contents in the lower portion of a slope, resulting in a greater likelihood for breakthrough. Conservatism should be used in capillary barrier design, as these barriers have typically been reported to experience breakthrough during spring snowmelt when plant evapotranspiration is at a minimum (Khire et al., 1999; 2000). In addition, preferential flow through larger pores may lead to significant variability in the breakthrough suction (Kampf and Holfelder, 1999).
34.3.3 Anisotropic Barriers Anisotropic barriers are similar to capillary barriers, but their design accounts for the internal lateral drainage through one or more drainage layers resulting from the inclination of the cover (Stormont, 1995; Bussiere et al., 2003; Parent and Cabral 2005). Figure 34.11a shows a schematic view of an anisotropic barrier. Anisotropic layers typically involve a soil vegetation substrate overlying a coarse-grained drainage layer, which are in turn underlain by a primary barrier layer and a second coarse-grained layer to provide a capillary break. The coarse-grained drainage layer functions both as a capillary break to the vegetation substrate and as a drainage layer for breakthrough water. The water collected by the drainage layer, along with moisture migrating laterally within the vegetation substrate is typically diverted to a ditch before a significant amount of water can infiltrate into the primary barrier. Figure 34.11b shows moisture profiles
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(b) t1 t2 t3 t4
Vegetation layer
At breakthrough, water moves laterally through drainage layer t1 t2 t t 3 4
Drainage layer Primary barrier layer
Depth
Secondary capillary break layer
Depth
Increased water flux into barrier layer down slope
FIGURE 34.11 Anisotropic barrier: (a) soil profile and (b) typical moisture content fluctuations during infiltration.
illustrating the expected trends along the length of an anisotropic barrier during a wet season. The capillary break at the drainage layer increases the moisture storage capacity of the vegetative substrate. Infiltration of water into the barrier layer generally occurs toward the toe of the slope due to water accumulation from infiltration and lateral drainage. Design of anisotropic covers is more complex than that of monolithic or capillary break covers due to the need to quantify the required hydraulic properties for the layered profile as well as the volume of laterally diverted water. Field comparisons between the performance of test-scale capillary break, anisotropic, and monolithic covers performed by Dwyer (1998) indicate that the anisotropic cover performed well compared to the other covers for the same weather conditions over a five-year monitoring program. However, its construction was the most difficult of the three covers.
34.4 Relevant Issues for Design of Evapotranspirative Covers 34.4.1 Design Strategies Despite the conceptual simplicity of evapotranspirative covers, their design is not trivial and typically involves numerical and field demonstration components. The design of an evapotranspirative cover involves the identification of performance criteria that are used to evaluate the suitability of different design alternatives. This phase typically requires close interaction between the designer, site stakeholders, and local regulators. The goal is to identify the criteria that will provide for human safety, constructability, and cost effectiveness. The design process typically involves identification of different cover design alternatives. This includes: (i) identification of suitable local borrow soil sources, (ii) characterization of the hydraulic properties of pre-selected soils under different placement conditions, (iii) determination of the cover geometry, (iv) identification of site-specific critical meteorological conditions, and (v) identification of suitable plant communities and vegetative cover properties. Design typically involves use of numerical models to predict the cover performance and field demonstrations aimed at evaluating the different design alternatives. Performance monitoring programs have been typically implemented after construction to verify the adequacy of the selected design alternative. Recent developments in evapotranspirative cover design have employed decision analysis, statistical characterization of design variables, and cost estimations to identify the optimal combination of performance variables. Such design approaches may help optimize the collection of laboratory data, identify if a site-specific field testing program is necessary, and quantify the risk of failure associated with design alternatives.
34.4.2 Performance Criteria and Regulatory Issues Evapotranspirative covers are considered alternative covers and, as such, their design involves comparison of their performance with that of prescriptive cover systems (i.e., equivalency demonstration). Development of suitable performance criteria for ET cover systems generally involves equivalence demonstration with prescriptive covers (Morris and Stormont, 1997; McCartney and Zornberg, 2002; Albright et al., 2004). Because of the site-specific interactions between an evapotranspirative cover and the
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local climate and environment, performance criteria for evapotranspirative covers must account for sitespecific conditions. This section outlines different types of performance criteria that have been put forth for evapotranspirative covers. The type of performance criteria will impact both the design procedures and the methods of post-closure monitoring. Determination of a percolation criterion has been approached from two different perspectives, at least in recent evapotranspirative cover projects in the United States. The first involves defining a quantitative maximum value of basal percolation (e.g., expressed in mm/year) that should not be exceeded. The second involves a comparative approach aiming at achieving a basal percolation value in the evapotranspirative cover that is smaller than that through a prescriptive cover under the same weather conditions. The maximum basal percolation value (quantitative percolation criterion) is typically defined in agreement with regulatory agencies, yet it should be based on actual performance data from prescriptive type covers or on the results of verified numerical models. A quantitative criterion establishes that the basal percolation through the evapotranspirative cover, Pe (mm/year), should be less than the Maximum Quantitative Percolation Value, MQPV (e.g., mm/year), deemed to satisfy equivalence, as follows: Pe < MQPV
(34.10)
where MQPV is a predefined criterion and Pe is determined from field monitoring and from numerical simulations. The choice of a quantitative percolation criterion implies that the cover must be designed for a wide range of possible meteorological conditions to ensure fulfillment of the criterion for worst case scenarios. On the other hand, if the MQRV is selected conservatively, the cover design may lead to unrealistically high material and construction costs. A comparative percolation criterion for evapotranspirative covers involves defining the maximum ratio between the basal percolation through an evapotranspirative cover and that through a prescriptive cover. This percolation criterion recognizes that the performance of the evapotranspirative cover should be compared to that of a resistive cover under the same meteorological conditions. Specifically, the basal percolation through the evapotranspirative cover (Pe ) should be less than that through the prescriptive cover (Pp ), affected by the Maximum Comparative Percolation Ratio (MCPR) established for the project. That is, equivalence is deemed satisfied when the following condition is fulfilled: Pe < MCPR · Pp
(34.11)
where MCPR is dimensionless and Pe and Pp are basal percolation values (e.g., in mm/year). Adopting an MCPR of 1.0 implies that the evapotranspirative cover should perform better than a prescriptive cover under the same weather conditions. The methods used to define basal percolation values Pe and Pp may involve the use of a numerical model or of monitored field test plots. The first approach may not account for factors that are not adequately modeled using unsaturated flow models such as desiccation, surface settlement, animal burrowing, and fingering. The second approach may result in additional costs and may not account for critical weather conditions and long-term factors. Performance criteria may also involve interpretation of the moisture profiles in the cover rather than quantification of percolation values. Specifically, quantitative criteria can involve comparison of the moisture storage within the cover with a certain threshold value. Similarly, criteria may involve comparison of the moisture at the base of the cover with a certain threshold moisture value (that can in turn correspond to a maximum value of K (θ ) calculated from Equation 34.8). Ideally, performance criteria would involve interpretation of both basal percolation and moisture profile information (McCartney and Zornberg, 2002).
34.4.3 Important Design Variables 34.4.3.1 Soil Hydraulic Properties The soil hydraulic properties relevant to the performance of evapotranspirative covers include the saturated hydraulic conductivity (Ks ), the soil-water retention curve (SWRC), and the K -function.
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Determining the required soil hydraulic properties is a challenging aspect of evapotranspirative cover design. Target values of the hydraulic properties are typically selected based on the required cover performance and on the expected weather conditions at the site. An important difficulty in the methods used to evaluate hydraulic properties in the laboratory is their high sensitivity to sample preparation and testing procedures. For example, the relative compaction of the soil and its compaction moisture content will typically affect the soil hydraulic properties. Finally, the differences between hydraulic properties determined in the laboratory and those in the field add to the difficulty in soil characterization. In addition to specimen preparation variability, the hydraulic properties in the field may change with time due to hysteresis (different behavior during wetting and drying), soil cracking, settlement, plant or animal intrusion, and erosion. 34.4.3.2 Cover Geometry Cover geometry variables include the thickness of the cover, as well as the cover inclination. As the performance of the soil cover depends on its capacity to store liquid, a thicker cover will have a higher moisture storage capacity. The slope of the cover will impact its stability, the amount of water drained laterally, as well as the amount of overland runoff during precipitation events. Some evapotranspirative covers have been constructed with significantly high slope inclinations (as high as 1.5H:1V). This is the case of the OII landfill in Pomona, California (see Section 34.6.2). Steep slopes may require stabilization to account for seismic and static stability. 34.4.3.3 Critical Meteorological Variables Critical meteorological conditions are site specific and play a significant role in the selection of the required soil properties, cover thickness, and slope inclination. A general guideline is that evapotranspirative covers are suitable for regions in which the potential evapotranspiration is greater than the precipitation. An important aspect of the design process involves identification of a worst-case precipitation record. Multiyear records must be obtained to consider the patterns in cover performance over both wet and dry years. In addition to the precipitation, the solar radiation, minimum and maximum air temperatures, wind speed, relative humidity, and percentage cloud cover are often used in numerical models to calculate the potential evapotranspiration. These variables are generally available from local or national weather station databases. 34.4.3.4 Vegetation Parameters Vegetative cover properties determine the amount of water that can be removed from the cover by transpiration. Water uptake by plants has been quantified empirically as a function of variables such as the wilting point suction, leaf area index, evapotranspiration partitioning model parameters, and root density distribution. Although researchers have been incorporating plant behavior in numerical models since the 1950s, the quantification of these variables is still unclear. The wilting point suction is the suction above which the plants are unable to draw water from the soil. Plants will typically stop transpiring and grow dormant under such conditions. The leaf area index is the leaf area coverage per unit ground area, and is typically correlated with the moisture demand of plants. A plant with more foliage will be able to photosynthesize faster, leading to more transpiration. Evapotranspiration can be estimated using the Penman-Monteith model (Monteith, 1965), which requires knowledge of the daily maximum and minimum temperatures, dew point temperature, solar radiation, percent cloud cover, wind speed, and precipitation (Zornberg and McCartney, 2003). However, once the evapotranspiration has been estimated, it must be partitioned into evaporation and transpiration components for use in numerical models (Fayer et al., 1992). The Ritchie model can be used to correlate the relative contribution of the plant transpiration with the leaf area index. The root density distribution depends on the particular plant, although it is typically measured to avoid plants with roots deeper than the cover thickness. A diverse group of native shrubs and grasses is recommended. Selection
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of plants with different heights also prevents intrusion of burrowing animals while providing erosion control.
34.4.4 Numerical Modeling Issues Analysis of the performance of alternative covers has been performed using: (i) unsaturated flow analyses, and (ii) simplified water balance analyses (Albright et al., 2002). Unsaturated flow analysis entails solving Richards’ equation for certain surface boundary conditions (e.g., water infiltration, overland runoff, evaporation, transpiration) and bottom boundary conditions (e.g., unit hydraulic gradient, seepage face). The governing equations are solved using numerical techniques such as the finite element method or the finite difference method. Relevant outputs from these analyses include the transient moisture redistribution and basal percolation. Four commonly used Richards’ equation-based codes that have been used in the analysis of evapotranspirative covers are UNSAT-H (Fayer and Jones, 1990), HYDRUS-1D (Simunek et al., 1998), LEACHM (Hutson and Wagenet, 1992), and Vadose/W (GeoSlope, 2004). The current version of UNSAT-H allows modeling of hysteresis in the SWRC, and was observed to have a close fit to observed data (Khire et al., 1999). HYDRUS-1D is more user-friendly and has built-in libraries for soil hydraulic properties and initial estimates for most performance variables. LEACHM has the distinct advantage of being an open-source code, while being particularly useful for conducting sensitivity analyses that allow identification of relevant variables (Zornberg et al., 2003). VADOSE/W is a commercial code that considers fully coupled heat and mass transfer with vapor flow, vegetation, gas diffusion and ground freezing in a finite element formulation in one or two dimensions. It solves a modified form of the Richards’ equation with pressure as the dependent variable, not water content, which improves solution stability. Despite their ability to solve Equation 34.5 subject to complex boundary conditions, it is still challenging to use Richards’ equation-based codes for predicting small basal percolation values with a high level of accuracy. It should be noted that the mass balance errors for numerical models may be of the same order of magnitude as basal percolation values of relevance for the analysis of evapotranspirative covers. Analyses involving water balance use the conservation of mass at the soil surface to estimate the basal percolation through the cover. This approach treats the soil layer as a sponge, able to hold a certain maximum amount of water (at the field capacity suction) against the pull of gravity. Basal percolation is calculated as the volume of moisture in the cover that exceeds the field capacity moisture storage after accounting for moisture removed by evapotranspiration and lateral drainage. Water balance codes that have been used for evapotranspirative cover include the Hydrologic Evaluation of Landfill Performance (HELP) (Schroeder et al., 1994), which is distributed by the US Environmental Protection Agency (EPA), and the Erosion Productivity Impact Calculator (EPIC) (Williams et al., 1984). A significant limitation of the water balance approach is that it does not consider transient moisture redistribution, which plays an important role in moisture removal from the cover by evapotranspiration. Also, as the water balance approach considers that the only driving mechanism for water flow is gravity, it implicitly considers that the hydraulic gradient is always equal to 1.0.
34.5 Performance Monitoring of Evapotranspirative Covers 34.5.1 Monitoring Strategies In the past decade, there has been a significant effort to expand the evapotranspirative cover knowledge base by constructing full-scale field test plots involving the monitoring of basal percolation and moisture profiles (Benson et al., 1999, 2001; Dwyer, 1998; O’Kane et al., 1998; Zornberg and McCartney, 2003). Monitoring schemes allow direct quantification of the response of evapotranspirative covers to atmospheric conditions. The field monitoring program should be consistent with the performance criteria used for the cover design. Different technologies have been considered to evaluate the basal percolation, moisture profiles, suction profiles, and meteorological variables, as discussed further in the following sections.
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34.5.2 Regulatory Issues Specific to Compliance Demonstration The selection of a quantitative or comparative percolation criterion for an evapotranspirative cover project (Section 34.4.2) may have significant implications on the compliance demonstration for the cover. As mentioned, the threshold basal percolation (MQPV) to be used in a quantitative percolation criterion is difficult to define. However, once the MQPV has been defined the monitoring program used for compliance demonstration phase using a quantitative percolation criterion is reasonably straightforward, as it involves monitoring the basal percolation to verify that it remains below the MQPV. Yet, limitations in field monitoring and numerical modeling must be understood to correctly interpret the data collected for compliance demonstration. On the other hand, the monitoring program used for compliance demonstration when using a comparative percolation criterion for the design may not be straightforward. For example, an approach could involve continued comparison monitored in the basal percolation values of two covers (prescriptive and alternative) over the lifetime of the evapotranspirative cover. Accordingly, the time period used for compliance demonstration is a key factor. For instance, compliance could be based on either the average basal percolation value during a time period or on the maximum basal percolation amounts associated with specific precipitation events.
34.5.3 Lysimetry Gravity lysimeters are the most common tools for directly monitoring basal percolation. They typically consist of a drainage layer underlain by a hydraulic barrier (Benson et al., 1999, 2001), such as a geocomposite or gravel drainage layer placed on top of a geomembrane. The geocomposites used in gravity lysimeters consist of a geonet sandwiched between two nonwoven geotextiles. A geonet is a thin polymeric sheet with slotted grooves that provide high lateral transmissivity. Geotextiles are polymeric fabrics used as filters, protection layers, and drainage layers. Geomembranes are polymeric sheets that have equivalent hydraulic conductivity values on the order of 10−15 m/sec. When a soil cover is placed above the lysimeter, it is intended that percolation through the cover soil will reach the geocomposite, and be transmitted down-slope to a collection bin. For effective performance, it is important to avoid that the presence of the lysimeter interferes with water flow (i.e., by introducing a capillary break). The main advantage of lysimeters is that they can be constructed to cover large areas (10 to 100 ft on side), which allows a spatial averaging of the water flow through a potential system of saturated preferential pathways in the cover (areas with lower density, cracks, animal burrows, or decayed plant roots). However, lysimeters have several shortcomings, the most significant being that they provide little insight into reasons for poor or adequate cover performance. Another shortcoming is that, despite their high transmissivity and permittivity when saturated, the geotextile component of a lysimeter may cause a capillary break when in contact with unsaturated soils (Stormont and Morris, 2000; Zornberg and McCartney, 2003; McCartney et al., 2005b). A capillary break at the lysimeter–soil interface distorts the suction and moisture content profiles in an evapotranspirative cover and may lead to significant underestimation of basal percolation. In addition, lysimeters create barriers to upward flow from lower depths (Scanlon and Milly, 1994). This is typically caused by water vapor flow in response to thermal gradients, and may lead to overestimation of the basal percolation at the site.
34.5.4 Monitoring of Moisture and Suction Profiles As the overall performance of an evapotranspirative cover system relies on its ability to store moisture until it is removed by evapotranspiration, moisture content or suction profiles can be monitored to assess why the evapotranspirative cover performs adequately (or not). Continued monitoring of in situ soil volumetric moisture content profiles is important in many geoenvironmental engineering and hydrological projects. In particular, monitoring of soil volumetric moisture content can provide relevant feedback on the migration of moisture through evapotranspirative covers. Time Domain Reflectometry (TDR) technology has been used to measure the volumetric moisture content in evapotranspirative covers (Dwyer, 1998; O’Kane et al., 1998; Siddiqui et al., 2000; Albright and
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Benson, 2002; Zornberg and McCartney, 2003). TDR involves measuring the velocity of an electromagnetic pulse applied to a transmission line that terminates in a shielded probe placed within the soil mass (Topp et al., 1980; Siddiqui et al., 2000; Suwansuwat and Benson, 1999). The pulse is reflected due to changes in impedance along the transmission line-probe system (e.g., the beginning of the probe and the end of the probe). The velocity of the reflected pulse is affected by the dielectric constant of the water within the soil mass, which is an order of magnitude greater than that of air and soil particles. The bulk dielectric constant of the soil mass, calculated from the velocity of the reflected pulse, can then be correlated with the soil volumetric moisture content. Conventional TDR systems use a cable tester to generate high frequency electromagnetic pulses (∼10 to 100 GHz) and measure the reflected waveform (with a resolution on the order of nanoseconds). Although conventional TDR systems are generally adequate for a wide range of soil types, their accuracy decreases for high moisture contents, saline soils, and highly conductive clays. Their shortcomings include the relatively high cost of probes and cable tester systems and comparatively complicated installation procedures to prevent probe damage. Water content reflectometer (WCR) probes have often been used as an alternative to conventional TDR probes (Dwyer, 1998; Albright and Benson, 2002; Chandler et al., 2004). WCR probes infer the moisture content by measuring the dielectric content of the soil, similar to TDRs. However, WCRs use smaller electronic circuitry placed within the probe itself that generate a lower frequency electromagnetic pulse (∼40 MHz) (Chandler et al., 2004). WCR probes have lower power requirements and allow longer cable lengths than conventional TDRs. In addition, WCR probes can use conventional field dataloggers instead of cable testers, which makes them attractive for field applications. Despite these advantages, the use of comparatively low frequencies may lead to decreased resolution in volumetric moisture content measurements and to correlations that are more sensitive to the soil electrical conductivity and temperature than TDRs (Kim and Benson, 2002). Suction measurements can also be made to complement moisture content evaluations. Concurrent suction and moisture content monitoring can provide data suitable to interpret evapotranspirative cover performance. Specifically, the suction and moisture content measurements can provide information for in situ determination of the SWRC. This can be used to interpret the SWRC during wetting and drying, interface phenomena like capillary breaks, and optimization of the SWRC to be used in numerical models. Suction measurements have been conducted in the field using several types of techniques, such as tensiometers (Ridley and Burland, 1995; Sisson et al., 2002; Tarantino and Mongiovì, 2003) and heat dissipation units (HDUs) (Flint et al., 2002; Nichol et al., 2003). Tensiometers consist of a pressure transducer with a porous ceramic stone filter. Due to continuity of suction, the suction within the ceramic stone will come into equilibrium with that of the surrounding soil. As water is drawn from the ceramic stone, the pressure transducer will measure a negative pressure value. HDUs consist of a heating unit and a thermocouple placed within a ceramic stone. The HDU infer the soil suction by applying a heat pulse to the heating unit in the ceramic stone, and measuring the transient changes in temperature of the ceramic stone using the thermocouple. The thermal properties of the ceramic are related to its moisture content, with a wet ceramic having higher thermal conductivity than a dry ceramic. Accordingly, the thermal response of the ceramic to the applied heat pulse can be calibrated against the suction in the ceramic, which is the same as the suction in the soil.
34.5.5 Monitoring of Meteorological Variables and Overland Runoff Site-specific monitoring of meteorological variables is important to proper interpretation of evapotranspirative cover performance, as these variables vary on a regional and local scale. Precipitation is generally measured using tipping bucket rain gauges. These gauges collect water in a two-sided bucket with a capacity of approximately 4 ml. The bucket is placed on a pivot so that water flowing into the gauge is funneled into one side of the bucket. After the capacity of the bucket is reached, the weight of the water causes the bucket to tip on the pivot, spilling the water and allowing water to be funneled into the other side of the bucket. The gauge records the time of each tip. Overland runoff has been typically measured using geomembrane swales anchored on the soil surface on the perimeter of the cover. Difficulties have
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been encountered in the use of such swales due to thermal expansion of the exposed geomembranes. Other variables typically measured on the site include wind speed and direction using an anemometer, temperature, and solar radiation.
34.6 Case Studies 34.6.1 Site Survey Table 34.1 shows a survey of evapotranspirative covers in the United States that have implemented field monitoring programs. A total of 53 evapotranspirative covers were identified at 48 sites in the United States. Among these, 19 of the sites have undergone or are undergoing construction or closure of an evapotranspirative cover, while the rest involve compliance demonstration using test covers. The number of sites with performance monitoring shown in this table reflects the growing number of alternative cover construction projects because of their technical and economic benefits. The table also provides the water balance variables monitored at each site and the study period. Although information is limited for some of the private covers, it appears that most covers have used lysimetry and moisture profile monitoring as part of compliance demonstration programs. Two of the sites, the OII landfill in Monterey Park, California, and the Rocky Mountain Arsenal, near Denver, Colorado, are discussed next.
34.6.2 OII Landfill The first evapotranspirative cover system approved by the US EPA for a hazardous waste Superfund site was in 1997 (Zornberg et al., 2003). The cover was constructed at the OII Superfund site in Monterey Park, California, approximately 16 km east of downtown Los Angeles. The design of this cover involved five phases that were undertaken to define the cover layout configuration. The design phases included: (i) evaluation of a baseline evapotranspirative cover, (ii) equivalence demonstration of the baseline cover by comparison with the basal percolation through a prescriptive cover, (iii) evaluation of the sensitivity of different design parameters (e.g., cover thickness, soil characteristics, rooting depth, and potential use of irrigation schemes) on the basal percolation through the cover, (iv) use of compilation of the results of this analysis as basis for the design of the final evapotranspirative cover, and (v) equivalence demonstration using soil-specific hydraulic properties of each cover soil. The criterion used for the design of the cover system at the OII Superfund site was comparative, and required that the basal percolation through the proposed evapotranspirative cover be less than the basal percolation through a prescriptive, resistive cover. That is, the Maximum Comparative Percolation Ratio (MCPR) at this project was 1.0. The prescriptive cover, defined by a consent decree, consisted of a 1200-mm thick system, which included a 300-mm thick vegetative layer, a 300-mm thick clay layer, and a 600-mm thick foundation layer. The vegetative and foundation layers both were considered to have a saturated hydraulic conductivity of 1 × 10−6 m/sec, and the clay layer to have a saturated hydraulic conductivity of 1 × 10−8 m/sec. A laboratory testing program was implemented to characterize the candidate borrow soils using soil specimens remolded under different compaction and moisture conditions. The experimental program included determination of hydraulic, shear strength, desiccation potential, and edaphic properties. Table 34.2 summarizes the laboratory test results for one of the candidate borrow soils measured in the laboratory for use in the equivalence demonstration. Following identification of the candidate soil borrow sources and determination of their hydraulic properties, soil-specific equivalence demonstrations were performed for the proposed evapotranspirative cover. Soil-specific parameters used in the unsaturated flow analyses included the SWRC, saturated hydraulic conductivity and K -function (obtained by centrifugation). In addition, soil-specific information from compaction tests was used in the analyses to define the soil placement conditions (unit weight and moisture content) that would optimize the performance of the cover.
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Wentachee, WA Wentachee, WA Atlanta, GA Sacramento, CA MD Sacramento, CA NM
Reedsburg, WI Sierra Blanca, TX
Twentynine Palms, CA
HI Sheffield, IL Hamburg, Germany Milwaukee, WI Los Alamos, NM Los Alamos, NM Richland, WA Richland, WA
Richland, WA Richland, WA Las Cruces, NM Mojave Desert, NV Richland, WA UT
Monolithic
Monolithic Monolithic Monolithic Monolithic Monolithic
Monolithic Monolithic
Monolithic
Monolithic Monolithic
Capillary break Capillary break Capillary break
Capillary break
Monolithic
Capillary break
Capillary break Monolithic Monolithic
Monolithic Monolithic Capillary break
Cover location
Capillary break
Cover type
Cover details
Survey of ET Cover Case Studies
Greater Wenatchee Regional Landfilla Greater Wenatchee Regional Landfilla Live Oak Landfilla Sacramento sitea Beltsville facilitya Phelan landfilla National Council for Air and Stream Improvementa Grede Foundriesa Texas Low-Level Radioactive Waste Disposal Authority Facilitya US Marine Corps Air and Ground Combat Centera Marine Corps Basea US Ecology Co. Landfilla Hamburg Test Site Omega Hills Landfilla Los Alamos National Laboratorya Los Alamos National Laboratorya Arid Lands Ecology Reserve, Hanforda Hanford Field Lysimeter Test Facilitya Hanforda Hanforda NMSU Las Cruces Sitea Beatty Sitea Hanford Sitea Hill AFBa
Site name
TABLE 34.1
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X X X
X
X
X
X
X
X X
X
X X
X X X
X
X
X
Meterological variables
X X X X X
X X
X X X X X
X X
X X X X X X
X X
X X X X
X
1987
X X
? 1987 ? ? ? 1990
X X X X
X X X X X
X
X
1985
X X
1991
X
1988 ? 1991
? ?
1998
1995 1995
1993 1999 ? ? ?
1992
1992
Start date
? ? 1993
? 1989 ?
1996
1990
1995
1992 ? 1995
? ?
1999
1996 1997
1996 2002 ? ? ?
1995
1995
End date
Study period
X
X
X X
X X
X X
X X X X X
X
X
X
X
X
X
Runoff
X
Suction
Water content
Percolation
Water balance variables measured
1 test section 1 test section 2 test sections
2 test sections 6 test sections 1 test section
8 test sections
4 test sections
2 test sections
1 test section 1 test section 1 test section
Test section
Test section
Test section Test section
1 test section 2 test sections Test section Test section Test section
1 test section
0 test sections
Full scale or test section
34-20 The Handbook of Groundwater Engineering
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a ACAP Sites.
Vereenigning Ash Dump F. R. Bowerman Landfill Operating Industries, Inc. (OII) Puente Hills Yucaipa Lopez Canyon Yeermo Riverside Co. 29 Palms Marine Base Potrero Hills Chiquita Canyon Needles Landfill Fairmead Landfill Rocketdyne Site China Grade Landfill McPherson Area Solid Waste Utility Ft. Carson Lakeside Reclamation Landfill MSW Landfill Duvall Custodial Landfill
Equity Silver Mine
Sandia National Laboratories Sandia National Laboratories Sandia National Laboratories Rocky Mountain Arsenala Nevada test site Idaho National Engineering and Environmental Laboratorya El Paso Site Questa Mine
CA Orange Country, CA Los Angeles, CA Los Angeles, CA Riverside Country, CA CA CA CA CA CA Chattsworth, CA Kern Country, CA McPherson, KS CO Beaverton, OR NE WA
Monolithic Monolithic
Monolithic Monolithic
X
X
X
BC, Canada South Africa
X X
X X
X
X
X
X
El Paso, TX NM
Monolithic Monolithic Monolithic Monolithic Monolithic Monolithic Monolithic Monolithic Monolithic Monolithic Monolithic Monolithic Monolithic
NV ID
Monolithic Monolithic
Monterey Park, CA
Denver, CO
Monolithic
Monolithic
Albuquerque, NM
Anisotropic
CA
Albuquerque, NM
Monolithic
Capillary break Monolithic/ Oxygen cover Monolithic/ Oxygen cover Ash Dump cover Monolithic
Albuquerque, NM
Capillary break
X
X X
X
X X
X
X X
X X
X X X X X X X X X X X X
X
X
X
X
X
X
X
X X
X
X
X
X
X
X
X
X
X
X
X X
X
X
X
a
X
X
X
? ?
? ?
? ? ? ? ? ? 1997 ? ? ? ? ? ?
?
?
1995
1992
2000 2000
1996 1984
1992
1997
1997
1997
? ?
? ?
? ? ? ? ? ? 1999 ? ? ? ? ? ?
?
?
1995
1995
2001 2001
2002 1995
2003
2002
2002
2002
Full scale Full scale
Full scale Full scale
Full scale Full scale Full scale Full scale Full scale Full scale Full scale Full scale Full scale Full scale Full scale Full scale Full scale
Full scale
Full scale
1 test section
1 test section
1 test section 1 test section
2 test sections 1 test section
4 test sections
1 test section
1 test section
1 test section
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TABLE 34.2
Series
Hydraulic and Geotechnical Properties for OII Landfill Cover Soils
USCS classification (ASTM D2487)
Average % passing #200 sieve (% fines)
Average PL (%)
Average LL (%)
Saturated hydraulic conductivity (m/s)
CL CL CL CL CL CL
66 66 66 66 66 66
43 43 43 43 43 43
18 18 18 18 18 18
2.80E-06 1.10E-05 3.70E-05 3.30E-06 1.70E-05 1.90E-04
T1 T2 T3 T4 T5 T6
Atterberg limits
Campbell model parameters a
b
Relative compactiona (%)
−4.89 −4.89 −4.89 −4.89 −4.89 −4.86
7.028 6.328 5.495 7.278 6.463 6.678
93.9 87.2 83.1 88.5 87.8 77.7
a In relation to standard Proctor test (ASTM 698).
350 300
Liquid quantity (mm)
250
Infiltration
200 Evapotranspiration 150 100
Moisture storage change Percolation
50 0 –50 Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Time
FIGURE 34.12
Seasonal variation in the water balance variables (Zornberg et al. 2003).
The code LEACHM (Hutson and Wagenet, 1992) was used to predict the basal percolation through both the prescriptive and the evapotranspirative covers to compare their performance using site-specific soil and meteorological conditions. LEACHM uses Campbell’s (1974) equation to describe the relationship between suction and volumetric moisture content for soil: ψ = a(θ/θs )b
(34.12)
where a and b are constants obtained from curve fitting. The a and b values as well as the saturated hydraulic conductivity for one of the candidate evapotranspirative cover soils are listed in Table 34.2. The simulated water balance variables for the OII site are shown in Figure 34.12. This figure indicates that the moisture storage of the cover increases during periods of infiltration and subsequently decreases during period of evapotranspiration. The infiltration is typically higher in the early party of the year, while the evapotranspiration is higher in the late spring and summer months. Figure 34.13a shows equivalence results, as quantified by the percolation ratio (basal percolation through the ET cover divided by the basal percolation through the prescriptive cover) with time. This equivalence demonstration shown in the figure corresponds to an evapotranspirative cover system constructed using soils placed under compaction conditions defined by series T1 (Table 34.2). The percolation ratio is below 0.1 (and well below the MCPR
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1.0
(a)
Percolation ratio (PR)
0.8
0.6
0.4
0.2
0.0 0
2
4
6
8
10
Time (years) (b) 0 Year 3 250
1-Jan 1-Feb 8-Feb 1-Mar 1-Apr 1-May 1-Jun 1-Jul 1-Aug 1-Sep 1-Oct 1-Nov 1-Dec
Depth (mm)
500
750
1000
1250
1500 0
0.05
0.1
0.15 0.2 0.25 Volumetric moisture content (vol/vol)
0.3
0.35
FIGURE 34.13 Performance variables for the O11 landfill evapotranspirative cover estimated using LEACHM: (a) comparative percolation ratio and (b) volumetric moisture content profiles during wettest simulation year (Zornberg et al. 2003).
of 1.0) for each year of the soil-specific, 10-year simulation. The engineered evapotranspirative cover constructed using the local soils, and placed under conditions defined by the T1 series, was then deemed to satisfy compliance with the prescriptive cover according to this demonstration. Figure 34.13b shows a prediction of the typical moisture content profiles expected for the cover. This figure indicates that the moisture fluctuations take place within the top meter of the soil cover, which reflects proper monolithic cover performance as discussed in Section 34.3.1.
34.6.3 Rocky Mountain Arsenal Almost 200 acres of RCRA-Equivalent evapotranspirative covers have been recently designed to contain contaminated materials at the Rocky Mountain Arsenal (RMA), located near Denver, Colorado, USA. The climate in Denver is semiarid, with an average annual precipitation of 396 mm and an average pan evaporation of 1394 mm (as quantified for the 1948 to 1998 period). The wettest months of the year
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Soil type 2
Soil type 1
Cover A
Nest D3 Nest D2
Cover C
Cover B
Nest C
Nest B
Nest A
Cover D
Nest D1
WCR cables
Percolation Extents collection of fill soil tank
Runoff collection tank
Perimeter fence
(b)
WCR multiplexer and datalogger
All season rain gauge
Runoff collection tank
WCR probes
Geocomposite drainage layer
(c)
Cover B
Cover A 9.14 m
1.067 m
Soil type 1
Geomembrane
4.8 m
9.14 m
1.219 m
Percolation collection tank
Cover C 4.8 m
9.14 m
1.524 m
Soil type 2
Cover D 4.8 m
9.14 m
1.067 m
Foundation soil
FIGURE 34.14 Layout for the monitoring program at the Rocky Mountain Arsenal: (a) plan view; (b) schematic view of instrumentation; and (c) elevation view.
(April to October) are also the months with the highest pan evaporation, which is appropriate for an evapotranspirative cover. The Record of Decision (ROD) for the site requires a compliance demonstration to show equivalence of the alternative design with a prescriptive cover before construction of the final evapotranspirative covers. The design and compliance of the covers at the RMA site is governed by a quantitative percolation criterion. A MQPV threshold of 1.3 mm/year was selected at this site, which was based on eight years of leachate data collected from two landfill covers built to RCRA Subtitle C standards in Hamburg, Germany, according
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1143 1270 1676 1168
SC CL CL CL
43.4 60.2 59.2 61.5
Average % passing #200 sieve (% fines)
a In relation to standard Proctor test (ASTM 698).
A B C D
Cover
USCS classification (ASTM D2487) 9 12.8 11.7 12
Average PL (%) 24.4 27.6 26.7 26.8
Average LL (%)
Atterberg limits
1.60E-05 4.70E-06 4.70E-06 4.70E-06
Saturated hydraulic conductivity (m/s)
Hydraulic and Geotechnical Properties for Rocky Mountain Arsenal Cover Soils
Soil cover thickness (mm)
TABLE 34.3
0.6118 0.3386 0.3386 0.3386
α (kPa−1 )
1.39 1.335 1.335 1.335
N
0.03 0.025 0.025 0.025
θr
0.482 0.470 0.470 0.470
θs
van Genuchten model parameters
72.9 72.8 72.8 72.8
Relative compactiona (%)
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Barrier soil with organic amendments (0.152 m)
1.219 m
Barrier soil Nonwoven geotextile Chokestone (min = 0.025 m)
0.457 m varies
Biotic barrier Foundation soil Waste
FIGURE 34.15
Final cover design at the Rocky Mountain Arsenal
to analyses described by Melchior (1997). This type of criterion was selected for its simplicity, as it sets a benchmark to be used in post-closure monitoring to demonstrate compliance, and is representative of the basal percolation for resistive covers. The compliance demonstration at the Rocky Mountain Arsenal involved a field demonstration, which was complemented by comparative numerical analyses and a field demonstration (Kiel et al., 2002). Four evapotranspirative test covers were constructed on a rolling plain at the site in the summer of 1998. A plan view of the four test covers, referred to as covers A, B, C, and D, is shown in Figure 34.14a. The test covers were constructed using site-specific clays of low plasticity (CL), compacted atop large pan lysimeters (9.1 m by 15.2 m) placed on a 3% grade to allow gravity drainage to a collection tank. The geotechnical and hydraulic properties of the cover soils are summarized in Table 34.3. Figure 34.14b shows a schematic view of the monitoring layout used in the test covers. The instrumentation program involved monitoring of the basal percolation, precipitation, soil volumetric moisture content profile, and overland runoff in the four test covers. Basal percolation was collected in a gravity lysimeter, which consists of a geocomposite underlain by geomembrane. The lysimeters were constructed without sidewalls. Rain and snow were monitored using an all-season rain gauge. Surface water was collected in polyethylene geomembrane swales constructed around the cover perimeters. WCR probes were used to measure volumetric moisture content. Specifically, the covers were instrumented with nests of eight WCR probes. This included six WCR probes placed in a vertical nests of WCR probes and spaced evenly with depth. In addition, redundant WCR probes were placed at the same depth as the top and the bottom probes, approximately 1 foot aside from the vertical profile of WCR probes. Cover D was instrumented using three vertical profiles. Figure 34.14c shows an elevation view of the covers, indicating the depth of each cover. The covers are separated from each other by 2.4 m-wide buffer zones, and the entire area is vegetated with local grasses and shrubs. The four test covers at the RMA were constructed to verify that the moisture flux through site-specific soils under local weather conditions remains below the MQPV of 1.3 mm/year (Kiel et al., 2002). The test plots at the Rocky Mountain Arsenal satisfied the quantitative percolation criterion over the period 1998 to 2003 of operation. That is, all four of the covers showed a yearly basal percolation rate below the MQPV despite having complemented the natural precipitation with irrigation. Although Cover D showed surface
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depression, possibly due to the installation of moisture probes or burrowing animals, the collected basal percolation over this cover was still below the MQPV percolation threshold. The monitoring results of the field demonstration program were used to develop the final cover design. As shown in Figure 34.15, the final cover design is a capillary barrier with a 1.067 m barrier layer, similar to that used in covers A and D. An additional 0.152 m of topsoil is used for vegetation. The specifications for the final cover soil are based on those for soil type I used in cover A. The final design includes a nonwoven geotextile over a chokestone layer (coarse gravel) to form a capillary break at the bottom interface of the barrier soil. The geotextile also helps prevent barrier soil particles from migrating into the chokestone layer. The chokestone is underlain by a biotic barrier consisting of crushed concrete from a demolition site. The biotic barrier is design to prevent plants and burrowing animals from reaching the waste. The final cover will be instrumented with gravity lysimeters placed within the final cover to measure basal percolation and WCR probes to measure moisture profiles within the barrier soil.
Glossary Anisotropic barrier Evapotranspirative cover with a system of barrier and drainage layers placed on a slope so that water is removed from the cover by lateral drainage. Basal percolation Water that passes through a cover system into the underlying waste. Biota barrier Layer of gravel or crushed concrete beneath the cover used to prevent entry of plants or animals into the waste. Capillary break cover Evapotranspirative cover that exploits the increased moisture storage arising from placing a fine-grained soil over a coarse-grained soil. Degree of saturation Ratio of the volumetric moisture content and the porosity. Evapotranspirative cover systems Class of alternative landfill cover systems that functions by storing water from precipitation until it may be removed by evapotranspiration. Field capacity Moisture content at which water will drain from a soil by gravity. Geocomposite Drainage material consisting of a geonet with high transmissivity sandwiched between two nonwoven geotextile filters. Geomembrane Low permeability geosynthetic used in hydraulic barriers. HDU Heat dissipation unit, a device used to measure soil suction. Lysimeter Device used to measure the basal percolation through a saturated soil layer. MCPR Maximum comparative percolation ratio, a percolation criterion relying on comparison of the performance of an evapotranspirative cover and a prescriptive cover. Monolithic cover Evapotranspirative cover with a single layer of soil acting as a hydraulic barrier and vegetation substrate. MPQV Maximum percolation quantitative value, a percolation criterion relying on comparison of the performance of an evapotranspirative cover with a selected basal percolation value. Prescriptive cover Landfill cover prescribed by government regulations that limits percolation by maximizing overland runoff. Richards’ equation Governing equation for water flow through unsaturated porous media. Suction Difference between the pore air pressure and pore water pressure. TDR Time domain reflectometry, a device used to infer the soil volumetric moisture content. Volumetric moisture content Volume of water in a soil divided by the total volume of the soil. Porosity Ratio of the volume of voids and the total volume. WCR Water content reflectometer, a device used to measure volumetric moisture content in the field based on TDR technology.
References Albright, W.H. and Benson, C.H. (2002). Alternative Cover Assessment Program 2002 Annual Report. US EPA Publication No. 41182. 48 p.
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Albright, W.H., Gee, G.W., Wilson, G.V., and Fayer, M. (2002). Alternative Cover Assessment Program Phase 1 Report. US EPA Publication 41183. 203 p. Albright, W.H., Benson, C.H., Gee, G.W., Roesler, A.C., Abichou, T., Apiwantragoon, P., Lyles, B.F., and Rock, S.A. (2004). “Field water balance of landfill final covers.” Journal of Environmental Quality. 33, 2317–2332. Anderson, J.E., Nowak, R.S., Ratzlaff, T.D., and Markham, O.D. (1993). “Managing soil moisture on waste burial sites in arid regions.” Journal of Environmental Quality. 22, 62–69. Benson, C. and Gribb, M. (1997). “Measuring unsaturated hydraulic conductivity in the laboratory and field.” In Unsaturated Soil Engineering Practice. Houston, S. and Wray, W. (eds). ASCE. Reston, VA. 113–168. Benson, C., Abichou, T., Wang, X., Gee, G., and Albright, W. (1999). Test section installation instructions — Alternative Cover Assessment Program. Environmental Geotechnics Report 99-3, Department of Civil & Environmental Engineering, University of Wisconsin-Madison. Benson, C., Abichou, T., Albright, W., Gee, G., and Roesler, A. (2001). “Field evaluation of alternative earthen final covers.” International Journal of Phytoremediation. 3, 1–21. Brooks, R.H. and Corey, A.T. (1964). “Hydraulic properties of porous medium.” Colorado State University (Fort Collins). Hydrology Paper No. 3. March. Burdine, N.T. (1953). “Relative permeability calculations from pore-size distribution data.” Petroleum Transactions of the American Institute of Mining and Metallurgical Engineering. 198, 71–77. Bussiere, B., Aubertin, M., and Chapuis, R. (2003). “The behavior of inclined covers used as oxygen barriers.” Canadian Geotechnical Journal. 40, 512–535. Cabral, A.R., Planchet, L., Marinho, F.A., and Lefebvre, G. (2004). “Determination of the soil water characteristic curve of compressible materials: Case study of de-inking residues.” ASTM Geotechnical Testing Journal. 27(2): 154–162. Campbell, G. (1974). “A simple method for determining unsaturated conductivity from moisture retention data.” Soil Science. 117(6): 311–314. Chandler, D.G., Seyfried, M., Murdock, M., and McNamara, J.P. (2004). “Field calibration of water content reflectometer.” Soil Science Society American Journal. 68: 1501–1507. Conca, J. and Wright, J. (1992). “Diffusion and flow in gravel, soil, and whole rock.” Applied Hydrogeology. 1, 5–24. Dell’Avanzi, E., Zornberg, J.G., and Cabral, A.R. (2004). “Suction profiles and scale factors for unsaturated flow under increased gravitational field.” Soils and Foundations. 44, 1–11. Dwyer, S.F. (1998). “Alternative landfill covers pass the test.” Civil Engineering. ASCE. 68(9): 50–52. Dwyer, S.F. (2003). Water balance and computer simulations of landfill covers. Doctoral thesis. The University of New Mexico. Albuquerque. Fayer, M. and Jones, T.L. (1990). “UNSAT-H version 2.0: Unsaturated soil water and heat flow model.” PNL-679, Pacific Northwest Laboratory, Richland, Washington. Flint, A.L., Campbell, G.S., Ellet, K.M., and Calissendorff, C. (2002). “Calibration and temperature correction of heat dissipation matric potential densors.” Soil Science Society of America Journal. 66, 1439–1445. Forbes, P.L. (1994). “Simple and accurate methods for converting centrifuge data into drainage and imbibition capillary pressure curves.” The Log Analyst. 35, 31–53. Fredlund, D.G. and Xing, A. (1994). “Equations for the soil-water characteristic curve.” Canadian Geotechnical Journal. 31, 521–532. Gardner, R.A. (1937). “The method of measuring the capillary pressures in small core samples.” Soil Science. 43, 277–283. GeoSlope International Ltd. (2004). Vadose/W Technical Overview. Calgary, Canada. Hassler, G.L. and Brunner, E. (1945). “Measurements of capillary pressure in small core samples.” Transactions of AIME. 160, 114–123. Hillel, D. (1998). Environmental Soil Physics. Academic Press. San Diego, CA.
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Hutson, J.L. and Wagenet, R.J. (1992). “Leaching Estimation and Chemistry Model, LEACHM.” New York State College of Agriculture and Life Sciences, Cornell University. Kampf, M. and Holfelder, T. (1999). “Designing capillary barriers.” Seventh International Waste Management and Landfill Symposium. CISA. Environmental Sanitary Engineering Centre, Sardinia. pp. 381–388. Khire, M.V., Meerdink, J.S., Benson, C.H., and Bosscher, P.J. (1995). “Unsaturated hydraulic conductivity and water balance predictions for earthen landfill final covers.” Soil Suction Applications in Geotechnical Engineering Practice, Geotechnical Special Publication No. 48. ASCE, 38–57. Khire, M.V., Benson, C.H., and Bosscher, P.J. (1999). “Field data from a capillary barrier and model predictions with UNSAT-H.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 125, 518–527. Khire, M., Benson, C., and Bosscher, P. (2000). “Capillary Barriers in Semi-Arid and Arid Climates: Design Variables and the Water Balance.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 126, No. 8, pp. 695–708. Kiel, R.E., Chadwick, D.G., Lowrey, J., Mackey, C.V., and Greer, L.M. (2002). “Design of evapotranspirative (ET) covers at the Rocky Mountain Arsenal.” Proceedings: SWANA 6th Annual Landfill Symposium. Kim, K.C. and Benson, C.H. (2002), Moisture Content Calibrations for Final Cover Soils, University of Wisconsin-Madison Geotech. Eng. Report 02-12, Madison, WI, 122 p. Klute, A. (1986). Water Retention: Laboratory Methods. Methods of Soil Analysis, Part 1: Physical and Mineralogical Methods SSSA. Madison, WI. 635–662. Kool, J.B. and Parker, J.C. (1987). “Development and evaluation of closed-form expression for hysteretic soil hydraulic properties.” Water Resources Research, 23, 105–114. Lu, N. and Likos, W.J. (2005). Unsaturated Soil Mechanics. Wiley. New York. 584 p. McCartney, J.S. and Zornberg, J.G. (2002). “Design and performance criteria for evapotranspirative cover systems.” Fourth International Congress on Environmental Geotechnics. Rio de Janeiro, Brazil. McCartney, J.S. and Zornberg, J.G. (2005a). “The Centrifuge Permeameter for Unsaturated Soils (CPUS).” Proceedings of the International Symposium on Advanced Experimental Unsaturated Soil Mechanics, Experus 2005. Trento, Italy, June 27–29, A.A. Balkema, pp. 299–304. McCartney, J.S., Kuhn, J.A., and Zornberg J.G. (2005b). “Geosynthetic drainage layers in contact with unsaturated soils.” 16th ISSMGE Conference: Geotechnical Engineering in Harmony with the Global Environment. 12–16 September 2005. Osaka, Japan. Meerdink, J.S., Benson, C.H., and Khire, M.V. (1996). “Unsaturated hydraulic conductivity of two compacted barrier soils.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 122, 565–576. Melchior, S. (1997). “In-situ studies of the performance of landfill caps (Compacted clay liners, geomembranes, geosynthetic clay liner, capillary barriers).” Land Contamination and Reclamation. 5, 209–216. Meyer, P.D. and Gee, G.W. (1999). “Flux-based estimation of field capacity.” Journal of Geotechnical and Geoenvironmental Engineering. 125, 595–599. Monteith, J.L. (1965) “Evaporation and environment.” Symposia of the Society for Experimental Biology. Morris, C.E. and Stormont, J.C. (1997). “Capillary barriers and Subtitle D covers: Estimating equivalency.” Journal of Environmental Engineering, ASCE, 123, 3–10. Nachabe, M.H. (1998). “Refining the definition of field capacity in the literature.” Journal of Irrigation and Drainage Engineering. 124, 230–232. Nichol, C., Smith, L., and Beckie, R. (2003). “Long-term measurement of matric suction using thermal conductivity sensors.” Can. Geotech. J. 40: 587–597. Nimmo, J.R., Rubin, J., and Hammermeister, D.P. (1987). “Unsaturated flow in a centrifugal field: Measurement of hydraulic conductivity and testing of Darcy’s law.” Water Resources Research. 23, 124–134. O’Kane, M., Wilson, G.W., and Barbour, S.L. (1998). “Instrumentation and monitoring of an engineered soil cover system for mine waste rock.” Canadian Journal of Geotechnical Engineering. 35, 828–846.
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Olson, R.E. and Langfelder, L.J. (1965). “Pore water pressures in unsaturated soils.” Journal of the Soil Mechanical and Foundation Division ASCE, 91, 127–151. Parent, S.E. and Cabral, A.R. (2004). Procedure for the design of inclined covers with capillary barrier effect. Proc. 57th Canadian Geotechnical Conference, Québec, October, 24–28. Ridley, A.M. and Burland, J.B. (1995). “A pore pressure probe for the in-situ measurement of soil suction”. Proceedings of Conference on Advances in Site Investigation Practice. I.C.E.:London. Scanlon, B.R. and Milly, P.C.D. (1994). “Water and heat fluxes in desert soils 2. Numerical simulations.” Water Resources Research. 30, 721–733. Schroeder, P.R., Dozier, T.S., Zappi, P.A., McEnroe, B.M., Sjostrom, J.W., and Peyton, R.L. (1994). “The Hydrologic Evaluation of Landfill Performance (HELP) Model: Engineering documentation for Version 3, EPA/600/R-94/168b.” US EPA Risk Reduction Engineering Laboratory, Cincinnati, OH. Shackelford, C.D., Chang, C.-K., and Chiu, T.-F. (1994). "The capillary barrier effect in unsaturated flow through soil barriers." 1st ICEG Conference. Edmonton, CA, pp. 789–793. Siddiqui, S.I., Drnevich, V.I., and Deschamps, R.J. (2000). “Time domain reflectometry development for use in geotechnical engineering,” Geotechnical Testing Journal. 23, 9–20. Simunek, J., Sejna, M., and van Genuchten, M. 1998. HYDRUS-1D: Code for Simulating the OneDimensional of Water, Heat, and Multiple Solutes in Variably Saturated Porous Media. Version 2.02. International Groundwater Modeling Center. Colorado School of Mines. Golden, CO. Sisson, J.B., Gee, G., Hubbell, J.M., Bratton, W.L., Ritter, J.C., Ward, A.L., and Caldwell, A.C. (2002). “Advances in tensiometry for long-term monitoring of soil water pressures.” Vadose Zone Hydrology. 1, 310–315. Stormont, J. (1995). “The effect of constant anisotropy on capillary barrier performance.” Water Resources Res. 32, 783–785. Stormont, J.C. and Anderson, C.E. (1999). “Capillary barrier effect from underlying coarser soil layer.” Journal of Geotechnical and Geoenvironmental Engineering. 125, 641–648. Stormont, J.C. and Morris, C.E. (2000). “Characterization of unsaturated nonwoven geotextiles.” In Advances in Unsaturated Geotechnics: Proceedings of Sessions of Geo-Denver 2000. Chang, N.-Y., Houston, S.L., and Shackelford, C.D. (eds) August 5–8, 2000. Denver, Colorado. pp. 153–164. Suwansuwat, S. and Benson C.H. (1999). “Cell size for water content-dielectric constant calibrations for time domain reflectometry.” Geotechnical Testing Journal. 22, 3–12. Tarantino, A. and Mongiovì, L. (2003). “Calibration of tensiometer for direct measurement of matric suction.” Géotechnique. 53, 137–141. Topp, G., Davis, J., and Annan, A. (1980). “Electromagnetic determination of soil water content: Measurement in coaxial transmission lines.” Water Resources Research. 16, 574–582. Topp, G.C. and Miller, E.E. (1966). “Hysteretic moisture characteristics and hydraulic conductivities for glass-bead media.” Soil Science Society of American Proceedings. 30, 156–162. van Genuchten, M. (1980). “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” SSSA. 44, 892–898. Wang, X. and Benson, C.H. (2004). “Leak-free pressure plate extractor for the soil water characteristic curve.” Geotechnical Testing Journal. 27, 1–10. Watson, K.K. (1996). “An instantaneous profile method for determining the hydraulic conductivity of unsaturated porous materials.” Water Resour. Res., 2, 709–715. Waugh, W.J., Petersen, K.L., Link, S.O., Bjornstad, B.N., and Gee, G.W. (1994). “Natural analogs of the long term performance of engineered covers.” In situ Remediation: Scientific Basis for Current and Future Technologies, Gee, G.W. and Wing, N.R. (eds), Battelle Press, Richland Washington. pp. 379–409. Williams, J.R., Jones, C.A., and Dyke, P.T. (1984). “The EPIC model and its application.” Proceeding of ICRISAT-IBSNAT-SYSS Symposium on Minimum Data Sets for Agrotechnology Transfer. March 1993.
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Zornberg, J.G. and McCartney, J.S. (2003). Analysis of monitoring data from the evapotranspirative test covers at the Rocky Mountain Arsenal. Geotechnical Research Report, US Environmental Protection Agency, Region 8, December 2003, 227 p. Zornberg, J.G., Jernigan, B.L., Sanglerat, T.R., and Cooley, B.H. (1999). “Retention of free liquids in landfills undergoing vertical expansion.” Journal of Geotechnical and Geoenvironmental Engineering. ASCE, 125, 583–594. Zornberg, J.G., LaFountain, L., and Caldwell, J.C. (2003). “Analysis and design of evapotranspirative cover for hazardous waste landfill.” Journal of Geotechnical and Geoenvironmental Engineering. ASCE. 129, 427–438.
Further Information Further information on the hydraulic properties of unsaturated soils may be found in Lu and Likos (2005). Descriptions of common techniques used to determine the SWRC can be found in Wang and Benson (2004) and the proceedings of Experus (2005). Descriptions of common techniques used to determine the K -function can be found in Benson and Gribb (1997). The ACAP Phase 1 report provides a comparative analysis of available numerical models for evapotranspirative cover performance evaluation, while the 2002 ACAP Annual Report provides a summary of field monitoring programs for evapotranspirative covers. An overview of current research topics in monitoring and analysis of evapotranspirative covers can be found in ASCE Geotechnical Special Publication 142 “Waste Containment and Remediation,” held at GeoFrontiers 2005 in Austin, TX.
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35 Groundwater Monitoring 35.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35-1 Introduction • Purpose of Groundwater Monitoring • Regulatory Requirements for Groundwater Monitoring • Groundwater Monitoring Strategy Considerations
35.2 Groundwater Monitoring Plans . . . . . . . . . . . . . . . . . . . . . . . . 35-7 Introduction • Developing a Groundwater Monitoring Plan
35.3 Design and Installation of Groundwater Monitoring Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35-13 Overview of Groundwater Monitoring Devices • Groundwater Monitoring Wells • Piezometers • Groundwater Discharges • Alternative Groundwater Monitoring Devices
35.4 Groundwater Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35-24 General Approach to Sampling Groundwater Monitoring Wells • Overview of Groundwater Sampling Techniques • In Situ or Alternative Monitoring Techniques • Quality Assurance and Quality Control Samples • Sample Handling and Preservation • Documentation of Sampling Events
35.5 Analysis of Groundwater Samples . . . . . . . . . . . . . . . . . . . . . . 35-34 Field Chemical Analyses • Laboratory Chemical Analyses
35.6 Evaluation of Groundwater Monitoring Data . . . . . . . . . 35-37 Data Validation • Evaluations of Groundwater Elevation Measurements or Depths to Groundwater • Groundwater Quality Data Analysis • What to Do if a Statistical Analysis Indicates the Presence of Contaminants
Michael F. Houlihan and Paul J. Botek GeoSyntec Consultants
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35-43 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35-45 Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35-47
35.1 Fundamentals 35.1.1 Introduction In this chapter on groundwater monitoring, a summary of approaches and techniques for sampling, analyzing, and evaluating the quality of groundwater is provided. In the remaining portion of this subsection on fundamentals, the purpose of groundwater monitoring is addressed and an overview of the regulatory
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requirements for groundwater monitoring is provided; also, strategies for developing groundwater monitoring programs are provided. In other sections of this chapter, descriptions are provided for the design and installation of groundwater monitoring systems, sampling and analysis of groundwater, and evaluation of groundwater monitoring data. The primary focus of this chapter is on groundwater monitoring at sites where contaminant releases, or potential releases, have impacted, or could impact, groundwater quality.
35.1.2 Purpose of Groundwater Monitoring Groundwater is used for a variety of purposes, including irrigation, drinking, and manufacturing. Groundwater is also the source of a large percentage of surface water. To verify that groundwater is suited for its purpose, its quality can be evaluated (i.e., monitored) by collecting samples and analyzing them. In simplest terms, the purpose of groundwater monitoring is to define the physical, chemical, and biological characteristics of groundwater. If the characteristics of the groundwater do not meet the requirements of its intended use, or if the groundwater could be harmful to human health or the environment, then it may need to be remediated. Groundwater remediation is discussed in Chapter 36 of this handbook. The purpose of a groundwater monitoring program should be defined before monitoring begins so that appropriate procedures, techniques, and analyses can be planned that will meet the specific needs of the project. Detection monitoring programs are used to detect the impact to groundwater quality. Assessment monitoring programs are used: (1) to assess the nature and extent of contaminants that have been detected in groundwater; and (2) to collect data that may be needed to perform a design for remediation of the groundwater. Corrective action monitoring programs are used to assess the impact of a groundwater remedy on contaminant concentrations as a tool in evaluating the success of a remedy. Performance monitoring programs are used to evaluate the effectiveness of an element of a groundwater remediation system in meeting the design criteria for the element. These four types of monitoring programs, which are commonly required at facilities regulated under the Resource Conservation and Recovery Act (RCRA), are the focus of this chapter. More detailed descriptions of the requirements of these programs are provided by the United States Environmental Protection Agency (USEPA) (1986a, 1992a, 1993c) and may also be contained in other applicable state, local, or federal guidance documents. Although the monitoring programs described in this chapter are based on the requirements of RCRA, the elements of these monitoring programs may also be useful and applicable to non-RCRA groundwater monitoring programs, such as groundwater monitoring programs at Superfund sites, at sites that are being voluntarily remediated, and at sites where a legally binding agreement has been made (e.g., a “consent agreement”) requiring monitoring of the site. A flow diagram showing the typical sequence of groundwater monitoring activities is presented in Figure 35.1. A description of the characteristics of the groundwater monitoring program types identified above is provided in the following subsections. 35.1.2.1 Detection Monitoring Programs For sites where regulated materials or contaminants of concern are used, stored, or contained a detection monitoring program is often implemented to evaluate whether or not a release has occurred. A detection monitoring program typically involves obtaining samples from wells located proximal to the location where regulated substances are present or in a downgradient area where these constituents would be expected to migrate if released. The samples are then analyzed for a constituent or series of constituents that are indicative of a release (i.e., indicator parameters). A sampling frequency is also typically established to ensure that data are collected often enough to identify potential releases before the contaminants migrate beyond the monitoring well network. The groundwater quality data from a detection monitoring program are typically compared to background concentrations to identify changes in groundwater quality that would confirm a release. Background concentrations are usually established by collecting four initial samples (N = 4) from a newly installed monitoring well. The sample interval for the N = 4 sampling event is normally within the first three months after well installation. These comparisons may include interwell comparisons against data collected at wells outside of the presumed area of interest (e.g., upgradient wells) or through intrawell comparisons to evaluated temporal trends in the data that may indicate an
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Groundwater Monitoring Prepare groundwater monitoring plan Step 1. Understand hydrogeologic/geochemical setting Step 2. Establish data needs and data quality objectives Step 3. Design groundwater monitoring network Step 4. Establish sampling and analysis methods Step 5. Establish data evaluation methods Step 6. Develop response criteria and response actions Step 7. Evaluate background conditions
35-3 Install groundwater monitoring features Step 1. Select appropriate installation technique Step 2. Procure appropriate monitoring feature construction materials Step 3. Install monitoring features according to design presented in groundwater monitoring plan Step 4. Update conceptual model of site hydrogeology based on findings of installation program
Sample / analyze groundwater
Analyze data: perform contingency actions
Step 1: Inspect wells and area surrounding well Step 2: Measure depth to groundwater and total depth of well Step 3: Purge groundwater from well Step 4: Collect groundwater samples Step 5: Document sampling event Step 6. Analyze groundwater samples for presence of contaminants
Step 1. Select appropriate statistical analysis method Step 2. Perform statistical analysis of data Step 3. If statistically significant increase is detected, reevaluate validity of analysis Step 4. If statistically significant increase is confirmed, them implement appropriate response actions
FIGURE 35.1 Sequence of activities for groundwater monitoring.
increase or decrease in a particular constituent. These comparisons typically require statistical analyses of the background and monitoring data to verify that a change in groundwater quality is verifiable. Statistical analysis of groundwater quality data is described in Section 35.6.3.2. 35.1.2.2 Assessment Monitoring Programs For sites where a release to groundwater is known to have occurred, a monitoring program should be implemented to assess the nature and extent of the release. The purpose of assessment monitoring is to evaluate the nature and extent of the release and, if it is found that corrective action is needed, to identify potentially applicable corrective actions. An assessment monitoring plan establishes the thresholds for implementing a corrective action. Many times these thresholds would include establishing a groundwater protection standard, or a concentration that would trigger a corrective action. Typically, the groundwater protection standard is defined as the constituent’s maximum contaminant level (MCL) (which is defined by the USEPA) or the background concentration, whichever is greater, or an alternate concentration limit (ACL). An alternative concentration limit is a concentration for a particular contaminant that is often times higher than background or MCL value but that provides continued protection of human health and the environment. An ACL must be established during the permitting process and included in the Facility permit. A detailed discussion of ACL development and permitting is provided in USEPA (1987). If the groundwater is discharging to surface water, concentrations protective of aquatic life may also need to be considered. A point of compliance is also another common aspect of an assessment monitoring program that should be established prior to implementing an assessment monitoring program. The point of compliance is a point (or line) at which an exceedance of the groundwater protection would trigger a corrective action. The point of compliance is often established by the regulatory requirements and typically includes features such as the site property boundary or groundwater discharges where potential receptors may be exposed to groundwater contaminants. As the purpose of the assessment monitoring program is also to evaluate the nature and extent of contamination, the assessment monitoring field exploration should be focused primarily on providing data to fill gaps in the detection monitoring database or to provide data related to suspected contaminants. Also, if the results of assessment monitoring indicate that corrective action is required, a list of technically feasible corrective measures should be developed. It is useful to develop this
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list during assessment monitoring so that data can be collected during the assessment monitoring field exploration and subsequently used to perform a preliminary assessment of the feasibility of the candidate remedial alternatives. The assessment monitoring plan should contain criteria for either returning to detection monitoring or proceeding to corrective action. For example, corrective action may be warranted if the presence of contaminants is confirmed and the contaminants are present at concentrations that are greater than either background concentrations or the groundwater protection standard. A return to detection monitoring may be warranted for any of the following reasons: (1) through additional sampling and analysis, the detection monitoring results are found to have given a false positive indication of a release from the potential source; (2) none of the parameters on the expanded list of analytes is detected at a statistically significant level above background concentrations; or (3) the concentrations of contaminants do not exceed the groundwater protection standard. 35.1.2.3 Corrective Action Monitoring Programs If the assessment monitoring data confirm that contaminants are present at concentrations that exceed the groundwater protection standard, then corrective action may be required. Corrective action of contaminated groundwater is described in Chapter 36 of this handbook. During corrective action, a groundwater monitoring program can be implemented to evaluate the effectiveness of the remedy. As an example, for a remedy involving extraction of groundwater to reduce contaminant concentrations in a plume of contaminated groundwater, corrective action monitoring could involve sampling and analysis of groundwater at wells (i.e., “compliance” wells) located within the plume of contamination to evaluate whether or not contaminant concentrations are decreasing at these locations. If it is found that contaminant concentrations in groundwater are not decreasing, then either the remediation system could be adjusted so that it will more likely achieve the remediation goal or it could be demonstrated that groundwater remediation at that site is technically impracticable (as described in the next chapter in Section 36.2.2). Finally, the conditions that trigger the end of corrective action (e.g., attainment of the groundwater protection standard at the compliance wells) or the need for alternative corrective action (e.g., continued exceedance of the groundwater protection standard or significant increase in the concentrations of detected contaminants) should be defined. 35.1.2.4 Performance Monitoring Programs Monitoring the performance of a corrective action system is a useful approach for verifying that the features of the system are fulfilling their respective design criteria. As described in Chapter 36, groundwater remediation system features may include groundwater extraction wells, groundwater extraction trenches, or low-permeability subsurface barriers. A performance monitoring program typically involves monitoring to evaluate whether a feature of the remediation system is fulfilling its intended function. An example of performance monitoring for a groundwater extraction system is presented in Figure 35.2. If monitoring results indicate that the design criteria is not being satisfied by the feature, then the design should be reviewed and improvements should be identified that will more likely provide the desired result. Performance monitoring is described in more detail by USEPA (1994) and by Rumer and Mitchell (1995).
35.1.3 Regulatory Requirements for Groundwater Monitoring Federal and state regulations have been established to provide for protection of groundwater resources. An extensive discussion of these regulations is provided in Chapter 32 of this handbook. As described in Chapter 32, these regulations require monitoring of groundwater quality near operations where materials are managed that could have an adverse impact on groundwater quality. The following questions are provided as a guide to identifying applicable groundwater monitoring regulations for a particular site or operation. • What is the activity (e.g., underground storage of petroleum hydrocarbon products) that could have an adverse impact on groundwater quality? Are there related activities (e.g., transmission
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Plume of contaminated groundwater
Groundwater quality monitoring well (typ.)
Perimeter containment system
Stream
Potential source
Groundwater extraction well (typ.)
Performance monitor wells Plan view
Potential source
Plume of contaminated groundwater
Performance monitor wells
Groundwater extraction well (typ.)
q q
Groundwater quality monitoring well (typ.) Stream
Cross section
FIGURE 35.2 Performance monitoring of groundwater extraction system. (From USEPA, 1990. Handbook — Ground Water, Volume I: Ground Water and Contamination. EPA/625/6-90/016a. Washington, DC.)
of petroleum products to the storage tank through underground pipes) that could also have an adverse impact on groundwater quality? • What regulations govern the activity or activities, and what portions of those regulations address either groundwater monitoring or potential impacts to groundwater quality? • What specific requirements do the regulations contain for planning groundwater monitoring events, for sampling groundwater, for analyzing groundwater samples, and for evaluating data from groundwater sampling events? • Do the regulations contain specific requirements for action in the event that impacts to groundwater quality are identified during the monitoring program? Once applicable regulatory requirements have been identified, a program can be developed for addressing each applicable regulatory requirement. A useful tool for addressing the requirements is the groundwater monitoring plan. Guidelines for developing a groundwater monitoring plan are presented in Section 35.2.2.
35.1.4 Groundwater Monitoring Strategy Considerations After identifying applicable regulatory requirements and before preparing a groundwater monitoring plan, the overall strategy of the groundwater monitoring program should be defined to guide the development of the plan. In this sense, “strategy” refers to the manner in which a hypothetical release from a regulated unit will be detected or measured. Examples of issues that should be addressed when developing a monitoring strategy include: (1) the type of monitoring data needed; (2) the locations (both horizontal and vertical) from which the samples are to be collected (i.e., definition of “target monitoring zones”); (3) the manner
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in which the samples will be obtained; and (4) the ability of the monitoring features to rapidly detect a change in groundwater quality. For detection monitoring programs, the types of data needed are usually defined by regulation; for other types of monitoring programs, the types of data needed are typically based on site-specific considerations. Selection of target monitoring zones is described in Section 35.2; design of groundwater monitoring devices is described in Section 35.3; and the ability of a monitoring system to rapidly detect an impact on groundwater quality is discussed in Section 35.2.2 (see “Phase II” of Step 3 of a groundwater monitoring system design). See Chapter 2 of Nielsen (1991) for additional discussion of groundwater monitoring strategy. Development of a groundwater monitoring strategy is illustrated in Figure 35.3 to Figure 35.5. As shown in these figures, the potential sources of contamination and the aquifers of concern should be characterized before developing a groundwater monitoring strategy because selection of target monitoring zones cannot be made until the source and the aquifer of concern have been evaluated, usually through a detailed hydrogeologic evaluation of the site. When evaluating the ability of a monitoring system to rapidly detect a release from the potential source, the impact of preferential flow paths and vertical gradients should be carefully evaluated; a two-dimensional analysis of groundwater elevation may not reveal actual upgradient
Generalized groundwater flow direction
Upgradient monitoring wells Potential source
Downgradient monitoring wells
FIGURE 35.3 Plan view of typical unconfined aquifer groundwater monitoring system.
Potential source Downgradient well Upgradient well
Shallow unconfined aquifer
Generalized groundwater flow direction
FIGURE 35.4 Section of typical unconfined aquifer groundwater monitoring system.
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Groundwater flow direction (type)
(a)
Potential source
Stream
Target upgradient monitoring zone
Upgradient wells (b)
Target downgradient monitoring zone Potential source Downgradient wells
Zone A Unconfined aquifer Zone B Aquitard Confined aquifer
Zone C
FIGURE 35.5 (a) Horizontal target monitoring zones; (b) vertical target monitoring zones.
or downgradient locations of groundwater flow. The presence of vertical gradients may significantly affect the selection of monitoring locations.
35.2 Groundwater Monitoring Plans 35.2.1 Introduction Successful implementation of a groundwater monitoring strategy requires a well-planned approach and an understanding of the factors that could affect the quality, validity, or representativeness of groundwater samples. A groundwater monitoring plan is an effective tool for systematically addressing these factors. Groundwater monitoring plans are required on a site-by-site basis for facilities that are regulated under RCRA and the Comprehensive Emergency Response and Compensation Liability Act (CERCLA), and may also be required for facilities that are regulated under various state and local programs. Groundwater monitoring plans are usually prepared to describe each aspect of groundwater monitoring and to control monitoring activities so that they fulfill the overall goals of the groundwater monitoring strategy. A comprehensive groundwater monitoring plan addresses each activity that will occur during sampling, analysis, and data interpretation, as well as response actions to be taken based on the results of monitoring.
35.2.2 Developing a Groundwater Monitoring Plan Developing a groundwater monitoring plan requires an in-depth understanding of site conditions, contaminant properties, regulatory requirements, and other technical considerations. When developing a groundwater monitoring plan, a stepwise approach is recommended to minimize omissions and to
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TABLE 35.1
Sample Outline — Groundwater Monitoring Plan
1. Introduction 2. Site Conditions 2.1 Site Topography and Surface-Water Hydrology 2.2 Site Geology 2.3 Site Hydrogeology 3. Groundwater Monitoring System 3.1 Introduction 3.2 Existing Groundwater Monitoring Wells 3.3 Construction of New Groundwater Monitoring Wells 3.4 Development of New Groundwater Monitoring Wells 4. Groundwater Sampling Procedures 4.1 Introduction 4.2 Health and Safety Procedures 4.3 Recordkeeping 4.4 Equipment Use, Cleaning, Decontamination 4.5 Preparation for Sampling 4.6 Groundwater Sample Collection Procedures 4.7 Groundwater Sample Handling and Preservation 4.8 Shipment of Groundwater Samples 5. Laboratory Groundwater Analytical Program 6. Quality Assurance and Quality Control Procedures 6.1 Data Quality Objectives 6.2 Field Sampling QA/QC Requirements 6.3 Laboratory QA/QC Requirements 7. Evaluation of Groundwater Data 7.1 Introduction 7.2 Groundwater Quality Data Validation 7.3 Evaluation of Static Groundwater Elevations 7.4 Statistical Analysis Procedures for Groundwater Quality Data 7.5 Response Actions 7.6 Reporting Requirements for Groundwater Quality Data 8. References
provide a clear and concise strategy for identify the goals, requirements, and limitations of the groundwater monitoring program. In this section, a procedure is presented for developing a thorough groundwater monitoring plan. Additional guidance on addressing the elements described in this section is presented by USEPA (1992a) and Nielsen (1991). An example outline for a groundwater monitoring plan is presented in Table 35.1. 35.2.2.1 Step 1: Understand Hydrogeologic/Geochemical Setting A comprehensive understanding of the hydrogeologic and geochemical setting of the site is an essential prerequisite to designing a groundwater monitoring system that can reliably detect a release to groundwater. This understanding should be based on an analysis of hydrogeologic and geochemical data from site explorations, literature reviews, and experience with similar hydrogeologic and geochemical settings. The types of hydrogeologic and geochemical information that should be collected and the general data needs for each type of information are described below, along with recommended means for obtaining the data. Aquifer Hydrogeologic Parameters: The transmissivity, porosity, and storage properties (i.e., specific yield or specific capacity) of the aquifer should be evaluated. Transmissivity and storage properties are typically calculated based on the results of aquifer tests, as described in Chapter 10 of this handbook and by Freeze and Cherry (1979). Porosity is typically determined in the laboratory or estimated from the literature. Effective porosities can be estimated for bedrock aquifers by assuming that fractured rock acts as an equivalent porous medium.
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Geologic Information: Characterization of the geologic units beneath the site is important to developing an understanding of the pathways that contaminants could take if introduced into groundwater (fate and transport of contaminants is described in detail in Chapter 18 and Chapter 19 of this handbook and in USEPA [1989c]). Examples of information that should be obtained before installing groundwater monitoring features include the horizontal and vertical limits of the aquifers, horizontal and vertical limits of confining units or aquitards, presence of interconnections between aquifers, anisotropies in aquifer material, presence of discontinuities (e.g., fractures, solution cavities, channel deposits, etc.) within or between stratigraphic units, gradual variations of the stratigraphic units with depth or with horizontal location, and the nature of the earth materials within the aquifers (e.g., particle size, angularity, dispersion-related properties, etc.). Topographic Information: The surface topography of a site may provide important clues to the presence or extent of geologic/stratigraphic units at the site and, accordingly, may provide an indication of the potential impact of a release of contaminants to groundwater. An understanding of site topography may provide valuable insight into: (1) the manner in which contaminants may have reached groundwater after being released to the ground surface; (2) past waste management practices at the site; (3) the interconnection between surface water and groundwater; and (4) aspects of the depositional history of the subsurface soils, which may give clues to the subsurface lithology and the manner in which it might control groundwater flow and contaminant transport. A discussion of terrain evaluation approaches and their use in site investigations is provided by Lueder (1959). Potentiometric Surface Information: Knowledge of the potentiometric surface elevation is essential to understanding the direction of groundwater flow and the fate of contaminants. Potentiometric surface information is also important for evaluating whether an aquifer is unconfined, confined, or perched. Potentiometric surface information should be obtained for the uppermost aquifer and for any underlying aquifer that could be interconnected with the uppermost aquifer, as well as unconnected aquifers that could be impacted by a release from the potential source. Subsurface monitoring data can sometimes be supplemented with surface-water elevation data (e.g., springs, streams, etc.) to provide a better understanding of groundwater flow patterns. Geochemical Conditions: Contaminants can chemically react with geologic media. Several types of reactions are common in aquifers (e.g., sorption, chelation, complexation, ion exchange, precipitation/dissolution, and hydrolysis, which are described in Chapter 18 and Chapter 19 of this handbook). Characterizing the geochemical properties of the aquifer materials is important when evaluating the effect of these reactions on fate and transport of contaminants. Detailed discussions of groundwater geochemistry are provided in Chapter 17 of this handbook and by Chappelle (1993). 35.2.2.2 Step 2: Establish Data Needs and Data Quality Objectives When developing a groundwater monitoring plan, a decision should be made regarding the types and quality of data needed to support decisions regarding the presence of groundwater contamination. To guide such decisions, data quality objectives (DQOs) can be established in the groundwater monitoring plan. DQOs can be specified as either qualitative (i.e., as a specific set of procedures to follow for collecting data) or quantitative (i.e., as the amount of imprecision or bias error that may be tolerated in data without incurring an unacceptable probability of making incorrect or inappropriate decisions). A more detailed discussion of DQOs is presented by USEPA (2000, 2002). Figure 35.6 depicts the DQO process. An important step in this process is determining an appropriate sampling schedule or frequency. Many regulatory programs, such as RCRA, prescribe the minimum sampling frequencies and these requirements should be verified prior to implementing a groundwater monitoring program. If a prescribed sampling frequency is not provided, the groundwater professional must establish a sampling frequency that provides sufficient data to evaluate changes in groundwater quality over time at an interval that will not potentially miss contaminants as they migrate through the monitoring network. When developing the sampling schedule and frequency, one must consider temporal variations in the hydrogeologic conditions, such as seasonal variations in flow or timing of dewatering activities, if any, in nearby locations, and the fate and transport conditions for the contaminants of concern including groundwater, and the affect of sampling frequency on data evaluations such as statistical analyses.
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Step 1. State the problem Define the problem; identify the planning team; examine budget, schedule
Step 2. Identify the decision State decision; identify study question; define alternative actions
Step 3. Identify the inputs to the decision Identify information needed for the decision (information sources, basis for action level, sampling/analysis method)
Step 4. Define the boundaries of the study Specify sample characteristics; define spatial/temporal limits, units of decision making
Step 5. Develop a decision rule Define statistical parameter (mean, median); specify action level; develop logic for action
Step 6. Specify tolerable limits on decision errors Set acceptable limits for decision errors relative to consequences (health effects costs)
Step 7. Optimize the design for obtaining data Select resource-effective sampling and analysis plan that meets the performance criteria
FIGURE 35.6 Data quality objectives process. Source: USEPA. 2000. Guidance for the Data Quality Objectives Process — EPA QA/G-4 EPA/600/R-96/055. Washington, DC, 100 p. August.
35.2.2.3 Step 3: Design Groundwater Monitoring Network After hydrogeologic conditions have been evaluated and the DQOs have been established, the groundwater monitoring system can be designed. A three-phased procedure for designing a groundwater monitoring system is described below. Phase I: Select Monitoring Locations: Locating the appropriate monitoring point locations is essential in designing a monitoring network capable of providing data of adequate quality to achieve the program objectives. At times, monitoring well locations may be prescribed by the regulations under which the groundwater monitoring program is being developed. For example, some regulations require monitoring locations be placed at a designated “point of compliance,” which is often at the property boundary or a groundwater discharge location. For other groundwater monitoring programs, the groundwater professional should select monitoring locations that provide the most reliable data needed to detect or assess a groundwater contaminant plume. To verify that the monitoring network can accomplish this goal, target monitoring zones must be selected based on the site hydrogeologic conditions and anticipated contaminant pathways, which are discussed in detail in Chapter 18 and Chapter 19. Examples of monitoring well location layouts for a detection monitoring program in both a typical unconfined and layered aquifer system are provided in Figure 35.4 and Figure 35.6, respectively. As shown in Figure 35.5, the locations and orientation of confining units have a significant effect on potential contaminant migration paths and therefore the vertical spacing of monitoring wells. Additionally, the physical and chemical characteristics contaminant must also be considered when identifying target
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monitoring zones and selecting monitoring locations. For example, the presence of LNAPLs (i.e., floaters) or DNAPLS (i.e., sinkers) in groundwater would require that monitoring locations be installed at the water table or at the top of confining units, respectively. To facilitate the selection of monitoring locations, numerical groundwater flow models with particletracking capabilities (e.g., MEMO [Wilson et al. 1992], MODFLOW [McDonald and Harbaugh 1988]) can be used to predict contaminant migration pathways and identify potential target monitoring zones. Additionally, geostatistical analyses can also be used to optimize monitoring well layout both prior to implementing the groundwater monitoring program or during periodic reassessments of the groundwater monitoring program. Additional guidance for monitoring well optimization is provided by the U.S. Air Force Center for Environmental Excellence (1997). Phase II: Select Monitoring Devices: Appropriate monitoring devices should be selected for obtaining the required samples or data from the target monitoring zones. Groundwater monitoring programs most often incorporate monitoring wells, piezometers, and groundwater discharge features as monitoring points. However, in some instances, alternative monitoring devices such as lysimeters, soil gas probes, direct push technology (DPT) samplers or other devices may be incorporated into the monitoring program. A description of alternative monitoring devices is provided in Section 35.3.5. Phase III: Design the Monitoring Features: Finally, after the monitoring features have been identified, they should be designed as described in Section 35.3 to meet the specific goals of the monitoring program and to provide accurate, representative samples of groundwater. 35.2.2.4 Step 4: Establish Sampling and Analysis Methods Each aspect of groundwater sampling and analysis, from extraction of the sample from the aquifer to laboratory analysis, can affect the results of the monitoring event. Therefore, it is important to specify sampling and analysis procedures that promote collection of samples representative of groundwater quality. When establishing the sampling procedures the groundwater monitoring professional must consider several factors including the monitoring point condition and design (e.g., depth, diameter, etc.), the type and properties of contaminants of concern (COCs) that will be monitored, access restrictions, availability of resources such as electric power, and any special sample or purge water handling requirements. The correct sampling procedure is an essential element of the groundwater monitoring planning process, as many of the errors or data quality issues associated with groundwater data collection occur as a result of bias introduced by the sampling procedure. Guidelines for sampling are presented in Section 35.4. Some regulatory programs, such as RCRA Subtitle C and Subtitle D, prescribe a specific list of analytes that must be monitored at a particular site. At other sites, the groundwater professional needs to identify the COCs that are the basis of the monitoring program. COCs typically include the regulated substances contained in the source, as well as any daughter products that might be produced by reactions as the contaminants migrate. To minimize the number of tests required to characterize groundwater quality, the presence of chemical constituents is sometimes evaluated by measuring “indicator parameters,” including pH, total organic carbon (TOC), total organic halides (TOX), and specific conductance; these parameters may be indicative of the presence of elevated concentrations of organic, chloride-based, or metallic constituents, respectively, in groundwater. Use of appropriate sampling and analysis methods (as described in Section 35.4 and Section 35.5) promotes the development of consistent, high-quality data and minimizes the possibility of invalid or incomplete data. Guidelines for analysis of groundwater samples are presented in Section 35.5. 35.2.2.5 Step 5: Establish Data Evaluation Methods After the groundwater samples have been analyzed, the data should be evaluated to provide a basis for concluding the presence or absence of groundwater contaminants. Such evaluations typically involve statistical analysis of the data to identify significant differences in groundwater quality. To guide the data evaluation process, the groundwater monitoring plan should contain descriptions of the methods that will be used to evaluate the monitoring data and the criteria for initiating response actions. Data evaluation methods are described in Section 35.6 of this chapter.
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The Handbook of Groundwater Engineering Example Response Criteria and Corresponding Response Actions for Detection Monitoring Program
Response criteria
Response action
• Significant change in groundwater elevation • Change in total depth of well
• Statistically significant increase in monitored parameters • Statistically significant increase not attributable to source or found to be invalid • Statistically significant increase confirmed and attributed to the potential source being monitored
• Consider seasonal effects on water level, or impacts from groundwater withdrawals (e.g., water supply or irrigation wells) • If necessary, remeasure groundwater levels • Redevelop well • If necessary, reconstruct well • Evidence of intrusion in well • Evaluate possibility of vandalism or tampering • Protective cover damage • If necessary, reconstruct well • Reevaluate validity of monitoring data • Resample wells to confirm statistically significant increase • Continue detection monitoring • Revise groundwater monitoring plan to prevent recurrence of problem during future monitoring events. • Consider validity of statistical analysis • Evaluate possibility of release from monitored source • Consider possibility of impact by other sources • Notify appropriate regulatory authorities • Develop plan of action with regulators; possible plans could require the following: • Prepare assessment monitoring plan • Submit assessment monitoring plan to regulatory agency for review (if necessary) • Implement assessment monitoring plan
35.2.2.6 Step 6: Develop Response Criteria and Response Actions Response criteria are results of groundwater monitoring events for which specific responses must be implemented. For example, in a detection monitoring program, an appropriate response action for the response criteria “if a statistically significant increase in a contaminant concentration is observed” could be “begin assessment monitoring.” Examples of response criteria for a detection monitoring program and potentially appropriate response actions are provided in Table 35.2. The response actions for a detection monitoring program should be designed to confirm the presence of the detected contaminant or the statistically significant increase; detailed assessment or remediation of the detected contaminants may be delayed until the start of an assessment monitoring program (see Section 35.1.2.2) or a corrective action monitoring program (see Section 35.1.2.3). The groundwater monitoring plan should also identify follow-on activities for each possible outcome of a response action (e.g., “prepare, submit, and implement an assessment monitoring program” if the presence of contaminants is confirmed, or “continue detection monitoring program” if the presence of contaminants is not confirmed). 35.2.2.7 Step 7: Evaluate Background Conditions To evaluate the impact of a potential source on groundwater quality, the characteristics of nonimpacted (i.e., upgradient) or baseline (i.e., existing conditions in the study area) groundwater must first be evaluated. This step is usually performed concurrently with the collection and analysis of geochemical conditions and includes an assessment of the ambient concentrations of target constituents. Background water quality data provide a baseline against which the results of future groundwater monitoring events can be compared. When establishing background conditions, a careful examination of the site should be made to verify that the location selected for the background sample is unaffected by either the potential source or by other sources; for example, locations that could be impacted by incidental spills (such as waste material storage areas or parking areas) should not be selected as background sampling locations. In
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Typical Groundwater Monitoring Features Primary use
Wells
Groundwater sampling
Piezometers
Groundwater potentiometric surface measurement
Lysimeters
Sampling liquid from vadose zone
Seeps
Surface sampling of groundwater seepage
Geophysical techniques
Plume delineation
Sampling probes (e.g., HydroPunch® , Geoprobe® )
Plume delineation
Advantages and limitations Extensive record of successful use; can be targeted to specific site limitations and contaminants of concern; flexible design. Allows measurement of potentiometric surface at a point; can be outfitted to provide continuous monitoring of groundwater elevation; not well suited for groundwater sampling. Allows characterization of liquid that could eventually impact groundwater quality; may allow loss of VOCs in samples; construction materials (usually ceramic) may affect chemical composition of samples. Low cost for establishing sampling point; gives good indication of quality of water with which humans or organisms may come into contact. Large areas can be quickly delineated at the “survey” level, inexpensively; can be used on ground surface or in boreholes; cannot be used to detect presence of specific constituents. Allows quick sample collection without incurring the cost of installing a monitoring well; limited to one-time sampling of groundwater.
addition, sufficient baseline data should be collected to evaluate temporary variations such as tidal effects or seasonal effects. Following collection of sufficient baseline data, the monitoring program can begin.
35.3 Design and Installation of Groundwater Monitoring Devices 35.3.1 Overview of Groundwater Monitoring Devices The purpose of this section is to identify and describe installation methods for typical groundwater monitoring devices. In Table 35.3, some typical groundwater monitoring features are identified. Each feature has a purpose and a situation for which it is best suited. The most common device used to monitor groundwater quality is the monitoring well. Installation of groundwater monitoring wells is described in Section 35.3.2.3, and other types of monitoring features are described in the remainder of this section.
35.3.2 Groundwater Monitoring Wells 35.3.2.1 General Design of Groundwater Monitoring Wells The purpose of a groundwater monitoring well is to provide access to the target monitoring zone for collection of a representative sample of groundwater. The representativeness of the sample may be affected by installation of the well or by the materials used to construct the well; the design of the well must account
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for these factors. In this section, groundwater monitoring wells and their applicability are described. The discussion presented in this section should be considered to be a general guide; site-specific conditions and applicable regulatory requirements should be considered over these guidelines when designing a groundwater monitoring well. Standard approaches for design of groundwater monitoring wells are presented by a number of agencies and organizations, including the USEPA (1991a, 1992a) and the American Society for Testing Materials (ASTM, 1995). Examples of typical groundwater monitoring well designs are presented in Figure 35.6. The design shown in Figure 35.5(a) incorporates several features that minimize the possibility of introducing contaminants into the well (e.g., the protective cover, the bentonite seal, and the well apron). The monitoring well design shown in Figure 35.5(b) is typically used in situations where the well must be installed either: (1) beneath a confining feature (e.g., clay aquitard), where the additional casing prevents leakage from the upper aquifer to the lower aquifer; or (2) through a heavily contaminated soil layer, where the additional casing prevents mixing of drill cuttings from the target monitoring zone with the contaminants in the overlying or underlying portion of the aquifer. These designs can be modified as needed to meet site-specific conditions or regulatory requirements. For example, the number of monitoring points can be increased by installing multiple, discrete sampling points within a well; also, uncased, open boreholes can be used to monitor bedrock aquifers where migration of soil particles into the well is not expected to occur. Some of the key features of the groundwater monitoring well, shown in Figure 35.7, are the wellscreen, filter pack, bentonite seal, cement grout backfill, concrete apron, and protective cover. The most important aspect of monitoring well design is the proper sizing and placement of the wellscreen or open-interval. When sizing the wellscreen, one must consider both the screen-interval size (i.e., slot size and screen type) and screen length for the proposed monitoring well. The screen-interval of the monitoring wellscreen should be sized based on the geologic materials outside of the screened interval and the proposed filter materials. Various guides have been established for well slot size selection including those described in USEPA (1991) and ASTM (1998). The wellscreen or open-interval length should be limited to the target monitoring zone. Monitoring wellscreen lengths typically range from 2 to 10 ft, with rare occurrences of up to 20 ft (EPA, 1991). To the extent possible, the screen length should be minimized to avoid dilution in the screened zone and to minimize interactions with, and potential contaminant migration to other zones within the aquifer. Also, as previously discussed, some regulatory agencies prescribe well design requirements particularly screen or open interval dimensions. The filter pack is intended to promote formation of a graded filter outside of the well to prevent migration of fine-grained soils into the well (because soil particles are composed of minerals that may be constituents of concern, the presence of fine-grained soils in a well can cause inaccurate groundwater monitoring results, as well as clog the well). The filter pack material should also have a characteristic particle size (i.e., the diameter greater than 85%, by weight, of the soil particles) that is bigger than the wellscreen slot size to prevent clogging of the wellscreen by the filter pack material. Similarly, the filter pack material should be capable of retaining the coarsest 15% of materials in the adjacent geologic formation. The bentonite seal is intended to prevent the cement grout backfill from migrating into the filter pack; the presence of grout in the filter pack could permanently compromise the validity of groundwater samples from the well. The concrete apron is intended to route surface water away from the well and to prevent downward migration of surface water into the wellscreen. The protective cover is intended to prevent unauthorized access to the well and to protect the exposed portion of the riser pipe from damage due to incidental contact. When installing a groundwater monitoring well, the following potential problems should be anticipated and avoided to the extent possible (after Nielsen 1991; USEPA, 1993c): • Use of well construction materials that are physically or chemically incompatible with either the surrounding natural earth materials or contaminants in the target monitoring zone and strong enough to prevent collapse under the stress applied by the soil. • Improper selection of wellscreen sizes (screen sizes that are too large may allow siltation of the well, and screen sizes that are too small may prevent proper development of a graded filter around the well).
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FIGURE 35.7 Monitoring well design.
Plug
Centralizer(s) as necessary
Borehole
Centralizers as necessary
Minimum 2 in (50mm) ID riser with flush threaded connections wrapped with PTFE tape or with O-rings (varies with riser material)
Dry bentonite pellets
Slope grout away from casing or riser to prevent infiltration, but do not create a mushroom for grout which will be subject to frost heave
Top of riser 3 ft (1.0ms) Above grade Slope bentonite/soil mixture or 4 in (101 mm) thick concentrate pad away from casing
6 in (152 mm) clearance for sampler
Sediment sump (as appropriate)
Well screen length varies
3 ft – 2 ft (303mm to 608 mm) first secondary filter pack where conditions warrant extend primary filter pack 20% of screen length or 2ft (608 mm) above slotted well screen, unless conditions warrant less
3 ft – 5 ft (1.0 m to 1.5 m) Bentonite seal
6 ft – 1 ft (152 mm to 304 mm) Final secondary filter pack
Grout length varies
3 ft – 5ft (1.0 to 1.5 m) extend protective casing depth to below frost line Steel casing installed and stabilized at a minimum 2 ft (608 mm) into confining layer Dry bentonite pellets
Slope concrete grout away from casing or riser to prevent infiltration, but do not create a mushroom which will be subject to frost heave
Plug
Centralizer as necessary
Borehole
Centralizers as necessary
(b)
Sediment sump (as appropriate)
Well screen length varies
1 ft – 2 ft (303mm to 608 mm) secondary filter pack where conditions warrant extend primary filter pack 20% of screen length or 2ft (608 mm) above slotted well screen, unless conditions warrant less
3 ft – 5 ft (1.0 m to 1.5 m) Bentonite seal
6 ft – 1 ft (152 to 304 mm) Secondary filter pack
Grout length varies
3 ft – 5ft (1.0 to 1.5 m) extend protective casing depth to below frost line
1µm (6.3 mm) weep hole at 6 in above ground level
Protective casing Washed pea gravel or coarse sand mixture
Vented cap
Well identification labeled inside and outside the cap
Protective cover with locking cap
Top of riser 3 ft (1.0ms) Above grade Slope bentonite/soil mixture or 4 in (101 mm) thick concentrate pad away from casing
6 in (152 mm) clearance for sampler
Minimum 2 in (50mm) ID riser with flush threaded connections wrapped with PTFE tape or with O-rings (varies with riser material)
1µm (6.3 mm) weep hole at 6 in above ground level
Washed pea gravel or coarse sand mixture
Protective casing
Vented cap
Well identification labeled inside and outside the cap
Protective cover with locking cap
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• Placement of the screened interval of the well across stratigraphic zones, if the intent of monitoring is to sample discrete zones of the aquifer (this problem could also limit the use of the well for hydraulic conductivity testing of the aquifer). • Improper selection or placement of filter pack material that could cause either siltation of the well or plugging of the wellscreen. • Improper selection or placement of annular seal materials that can allow plugging of the filter pack, cross-linking of discrete water-bearing units, or migration of grout into the filter pack. • Poor surface-protection measures that can allow damage to well casing materials or introduction of surface water into the well at the ground surface. • Poor well development and evacuation techniques that may alter the aquifer formation around the wellscreen, cause excessive siltation of the filter pack and groundwater samples, or compromise well yield. 35.3.2.2 Drilling Methods There are numerous drilling methods available for installing groundwater monitoring wells, each of which has attributes that may make it suited for a particular drilling location and well type. A summary of drilling methods that are commonly used to install groundwater monitoring wells is presented in Table 35.4. Also, the situations where each method is best suited are identified. More comprehensive discussions of drilling methods are presented by Hvorslev (1949), Driscoll (1986), ASTM (1998), and USEPA (1991). 35.3.2.3 Monitoring Well Installation Careful installation of groundwater monitoring wells is an important step in producing representative samples of groundwater from the target monitoring zone. In this section, a generalized approach to installation of monitoring wells is presented. Further information and guidance on design and installation of monitoring wells is presented by USEPA (1975, 1989d) and ASTM (1990). Prepare for Field Work: Before beginning monitoring well installation activities in the field, the groundwater field professional should develop as complete an understanding as possible of the conditions that will be encountered. This can be accomplished by reviewing the groundwater monitoring plan, regional and site-specific hydrogeologic information, the site health and safety plan (which must be prepared if hazardous conditions might be encountered), and the logs for installation of existing wells or other borings near the proposed well locations. The equipment that will be needed for the field work (e.g., waterlevel measuring instrument, personal protective equipment, sample jars, field analytical equipment, etc.) should be assembled well in advance of the field work. Monitoring equipment (e.g., water-level measuring equipment, field analytical equipment, etc.) should be calibrated. Well construction materials should be specified in advance of field work; recommendations for selection of well construction materials are provided in Table 35.5. Finally, the groundwater field professional should verify that the well construction materials that are procured by others meet the specific requirements of the groundwater monitoring plan. Lay Out Location for Monitoring Well: The well location specified in the monitoring plan should be laid out before drilling begins. After the location is marked, the groundwater field professional should verify that the location is suitable for the well (e.g., not in a location where it is likely to be damaged, or in standing water, or where conditions are encountered that were not anticipated in the groundwater monitoring plan). The well location should also be sited in a location that will not encounter or interfere with underground utilities or structures. Most states require that public utility companies be notified prior to drilling or excavating activities so that underground utility lines are marked prior to performing the work. In addition, many industrial, commercial, and military facilities contain private underground utilities that may also need to be marked prior to well installation. Note that, after the well has been installed, the location should be surveyed by a licensed professional surveyor to provide an exact record of the location and top of casing elevation of the well. Decontaminate Drilling Equipment and Well Construction Materials: Equipment or construction materials should be decontaminated before being introduced into the borehole using a high-pressure steam wash or other appropriate decontamination methods (see Moberly [1985] for a discussion of
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Soil, rock Soil, rock
Yes Yes
Air, water, foam Water
Soil, rock, boulders Soil Soil
Yes Yes Yes No Yes
Air, water, mud None None, water, mud, air Water Water
Soil, rock, boulders Soil
Soil, rock Rock, boulders Soil, rock Soil, rock
Yes Yes Yes Yes
Air, water, foam Air, water, foam Air, water, foam Water, mud
Soil, rock
Soil
Yes
No
Soil, weathered rock
Soil, weathered rock
No No
Soil, weathered rock
Type of material drilled
Yes
Casing advance
Water, mud
None, water (below water table) None
None, water, mud Water, mud
Drilling fluid
18–48
2–6 2–36 2–36 4–16 3–6 12–36 12–36 4–35 2–16 1.5–3 4–12 2–4 4
<70 (above water table only) >1000 >1500 <2000 >1000 <2000 >1000 >5000 <2000 <100 <500 <50 <50
2–10
<150 <150
5–22
Typical range of borehole sizes, in in.
<150
Typical drilling depth, in fta
S S
S, R, F
S, R, F (F-below water table) S, R, F S, F
S, R, F
S, R, F R S, R, F S, R, F
S, R
S
S
S
S, F
Samples obtainableb
No No
Yes
Yes Yes
Yes
Yes
Yes Yes Yes Yes
Yes
Yes
Yes
Yes
Yes
Coring possible
12 12
11
9 10
8
7.7
7.4 7.5.1 7.6 7.8
7.3
6.5
6.4
6.3
6.2
Reference section
achievable drilled depths will vary depending on the ambient geohydrologic conditions existing at the site and size of drilling equipment used. For example, large high-torque rigs can drill to greater depths than their smaller counterparts under favorable site conditions. Boreholes drilled using air/foam can reach greater depths more efficiently using two-stage positive-displacement compressors having the capability of developing working pressures of 250 to 250 psi and 500 to 750 cfm, particularly when submergence requires higher pressures. The smaller rotary-type compressors only are capable of producing a maximum working pressure of 125 psi and produce 500 to 1200 cfm. Likewise, the rig mast must be constructed to safely carry the anticipated working loads expected. To allow for contingencies, it is recommended that the rated capacity of the mast be at least twice the anticipated weight load or normal pulling load. b Soil = S (Cuttings), Rock = R (Cuttings), Fluid = F (some samples might require accessory sampling devices to obtain). Source: From American Society for Testing and Materials (ASTM), Standard D 6286 -98 “Standard Guide for Selection of Drilling Methods for Environmental Site Characterization.” 1998. West Conshohocken, Pennsylvania.
a Actual
Casing-advancer Direct-push technology Sonic (vibratory) Jet percussion Jetting
Direct fluid rotary Direct air rotary DTH hammer Wireline Reverse fluid rotary Reverse air rotary Cable tool
Hand auger
Power auger (Hollow-stem) Power auger (Solid-stem) Power bucket auger
Drilling method
TABLE 35.4 Well Drilling Selection Guide
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Recommendations for Selection of Well Casing Materials
If
Use
Well depth in range of 225–375 ft (68.6–114 m) Well depth in range of 1200–2000 ft (366–610 m) pH < 7.0, DO > 2 ppm, H2 S ≥ 1 ppm, TDS > 1000 ppm, CO2 > 50 ppm, or Cl– > 500 ppm A neat PVC solvent/softening agent is present or if the aqueous concentration of the PVC solvent/softening agent exceeds 0.25 times its solubility in water
Do not use
PVC, ABS, SS
PTFE
SS
PVC or ABS
PVC, ABS, or PTFE
SS
SS or PTFE
PVC
In All Cases Do not use Solvent bonded joints for PVC casings Welded stainless joints Any PVC well casing that is not NSF-ASTM approved — D-1785 and F-480 Any stainless steel casing that is not ASTM approved — A312 Any ABS well casing that is not ASTM approved
Use Threaded PVC casings Threaded SS casings ASTM-NSF approved PVC well casings — D-1785 and F-480 ASTM approved SS 304 and SS 316 casings — A312 ASTM approved ABS casings — F-480
DO = dissolved oxygen; TDS = total dissolved solids; PVC = polyvinyl chloride; SS = stainless steel; ABS = acrilonitrile-butydiene-styrene; PTFE = polytetrafluoroethylene Source: From USEPA. 1992a. RCRA Groundwater Monitoring: Draft Technical Guidance, Office of Solid Waste, EPA/530-4-93-001, PB93-139-350, Washington, DC.
decontamination procedures). Decontamination minimizes the possibility of unintentionally introducing contaminants into the borehole. Drilling fluids should be inert; the use of oil and grease on drilling equipment should be restricted. Drill Borehole: The borehole should be drilled using a technique that minimizes disturbance to the aquifer formation and does not impact the ability of the well to produce a representative groundwater sample. The potential impacts of drilling on groundwater samples are illustrated in Table 35.6, and candidate drilling techniques are identified in Table 35.6. During drilling of the borehole, the cuttings should be examined by the driller and the groundwater field professional, and a stratigraphic log should be made of the materials that are encountered; a sample boring log form is shown in Figure 35.8. The drill cuttings, drill fluid, or cores should be examined for unexpected materials (e.g., soils that are not described on logs for nearby wells, contaminants, indications of stratigraphic units at unexpected locations, etc.). The groundwater field professional should verify that the borehole is open throughout its depth, is reasonably straight, and is terminated within the target monitoring zone so that the well can be properly constructed; these can be verified by measuring the total depth of the boring after the drilling equipment has been removed from the boring. If downhole geophysical logging is required by the groundwater monitoring plan, then it may be performed at this time. (Note that for some geophysical logging techniques, logging must be performed while the borehole is open, prior to well construction.) Inspect Well Construction Materials: Well construction materials should be inspected to verify that they meet the requirements of the groundwater monitoring plan. Wellscreen and riser pipes should be clean and undamaged; screen slots should be uniform, open, and continuous throughout the screened interval;
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Groundwater Monitoring TABLE 35.6
35-19
Effects of Drilling Methods on Water Samples
Methods
Advantages
Air rotary
• Drilling fluid is not always used, minimizing contamination and dilution problems
Mud rotary
• Borehole can be kept open inexpensively • Sample collection is relatively easy
Bucket auger
Solid stem auger
Hollow stem auger
Cable tool
Jetting
• No drilling fluid is used, minimizing contamination and dilution problems • No drilling fluid is used, minimizing contamination and dilution problems • Can avoid use of lubricants
• No drilling fluid is used, minimizing contamination and dilution problems • Can avoid use of lubricants • Formation waters can be sampled during drilling • Well can be installed as augers are removed, decreasing interaction with water from higher water-bearing zones • Little or no drilling fluid required
• May be only alternative where drill rig access is poor
Disadvantages • When more than one water-bearing zone is encountered and hydrostatic pressures are different, flow between zones occurs after drilling is completed but before the hole is cased and grouted • Oil from compressor may be introduced to geologic formation • Use of foam additives containing organic materials can interfere with both organic and inorganic analyses • Drilling fluid that mixes with formation is difficult to remove and can cause contamination • Fluid circulation can cause vertical mixing of contaminants • Drilling fluids and additives can interfere with subsequent water quality analyses • Lubricants may cause contamination • Large-diameter hole makes it difficult to assure adequate grouting • Because auger must be removed before well can be set, vertical mixing can occur between water-bearing zones • Must continuously add water in soft or loose formations • Can cause vertical mixing of both formation water and geologic materials • Can cause vertical mixing of geologic materials • Can cause vertical mixing of formation waters if augers are removed before well is installed
• Contamination of aquifer is possible if drilling • fluid is used • Slight potential for vertical mixing as casing is driven • Large quantities of water or drilling fluid are introduced into and above sampled formation • Cannot isolate target monitoring zone with a grout seal
Source: From Driscoll, F.G. 1986. Groundwater and Wells. Johnson Division, St. Paul, MN. With permission.
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FIGURE 35.8 Typical boring/well installation form. (From Nielsen, D.M., ed. 1991. Practical Handbook of Ground-Water Monitoring. Lewis Publishers, Chelsea, MI. With permission.)
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threaded connections at ends of pipes should be properly formed and should provide a tight connection. Bentonite seal materials should be delivered to the site in sealed containers and should not be allowed to hydrate before installation in the borehole. Filter pack material should be tested for particle-size distribution to verify that it meets the gradation requirements of the groundwater monitoring plan. Before installation, the length of each section of the riser pipe should be measured to the nearest hundredth of a foot or to the nearest centimeter so that, once installed, the depth to the top and bottom of the wellscreen is known. Install Wellscreen and Riser Pipe: The riser pipes should be installed carefully to prevent damage during installation. The completed riser pipe should extend about 3 ft (1m) above the ground surface, as shown in Figure 35.7. Alternatively, if the presence of an above-ground riser causes an unacceptable obstacle at the site, the riser pipe can be terminated at ground level in a vault that is specially designed to prevent leakage into the well or damage to the well. The wellscreen should be in the borehole, using a centralizer if necessary; if the wellscreen is not centered in the borehole, it might not be possible to install the filter pack material evenly around the pipe, which might prevent proper development of a graded filter around the wellscreen. Install Filter Pack, Seal, and Backfill Material: The filter pack material should be installed around the wellscreen slowly, to prevent bridging of the material between the wellscreen and the soils in the adjacent aquifer. Bridging, which leaves a portion of the wellscreen unsupported, could result in crushing of the riser pipe or migration of fine-grained soil particles into the well. For deep boreholes, the filter pack material may need to be installed using a tremie pipe, which is used to deposit the material from the bottom up (see Driscoll [1986, p. 477] for additional discussion). The bentonite seal should be installed evenly, above and on all sides of the top of the filter pack using either dry bentonite pellets or bentonite slurry. If dry bentonite is used, then it should be allowed to hydrate in the well for a period of at least one hour (preferably overnight) before the grout backfill material is installed over the seal. The backfill material should be installed carefully to prevent damage to the bentonite seal; backfill materials may include cement grout, drill cuttings (if uncontaminated), or stabilized soil, depending on the requirements of applicable regulations. The depth to the top of the filter pack, seal, and backfill material should be measured and recorded before the overlying component of the well is installed; when making these measurements, the groundwater field professional should confirm that the wellscreen section is located completely within the filter pack. Samples of well construction materials should be retained by the contractor for a period of time designated in the well construction specifications. Complete Above-Ground Portion of Well: The above-ground portions of the well should be constructed in a manner that accommodates sampling of the well and protects the well from incidental damage. The actual configuration of the aboveground portion of the well may depend on applicable regulations; a recommended configuration is shown in Figure 35.7. For above-ground risers, the riser should be located at short depth (i.e., about 3 to 6 in., (75 to 150 mm)) beneath the top of the protective casing, and the reference point (for measuring the depth to groundwater and total depth of the well) should be clearly and permanently marked on the riser pipe. The annular space between the protective casing and the riser pipe can be filled with sand or gravel (so that items dropped in the casing can be easily retrieved) and a hole should be drilled in the casing about 6 in. (150 mm) above the ground surface to allow drainage of water that may collect in the casing during sampling. A concrete pad should be constructed around the protective casing at the ground surface and sloped downward, away from the protective casing, to prevent accumulation of standing water around the well and infiltration of surface water into the well. The volume of grout placed above ground should be minimized to prevent frost heave of the grout pad during freezing weather. 35.3.2.4 Well Development Techniques The purposes of well development are to remove sediment from the well and surrounding aquifer materials impacted by well installation, and to form a graded filter at the interface between the aquifer materials and the filter pack material. Well development involves removing water from the well after construction is completed. Development prior to initial well sampling is essential if a representative sample is to be obtained. Common well development techniques are described by Driscoll (1986) and ASTM (1994). Hand-bailing techniques are widely used but are time consuming and may alter the geologic formation
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that surrounds the filter pack, resulting in high values of suspended solids in groundwater samples or even failure of the filter pack. Mechanical development techniques (e.g., swabbing, surging, or lowflow pumping) require less physical effort and can be tailored to the specific limitations of the aquifer and well construction features. Wells should be developed until the pH, specific conductivity, and color (i.e., cloudiness) of the water stabilize; note that, if pH and specific conductivity remain consistently higher in the well than in the aquifer, there may be leakage into the filter pack from the overlying cement grout (grout typically has a pH of about 10 and a specific conductivity of about 1500 (µmhos/cm). Cloudy development of water may be an indication that the filter pack is not filtering the aquifer formation material effectively. Such problems indicate that groundwater samples from the well may not be representative of groundwater in the aquifer near the well. Problems encountered during development should be examined carefully and, if necessary, the well should be redeveloped or decommissioned (using techniques described in Section 35.3.2.6) and then reinstalled. Also, a water level inconsistent with surrounding water levels can indicate a problem with well completion. 35.3.2.5 QC/QA of Drilling and Well Installation To verify that the monitoring well is installed properly, the groundwater professional should implement a program of Quality Control and Quality Assurance (QC and QA) during drilling and installation. In the context of monitoring well installation, QC refers to the procedures used to confirm that the materials and methods used meet the requirements of the groundwater monitoring well design, and QA refers to the activities that are performed to verify that QC procedures were properly implemented. QC and QA procedures are typically specified in the groundwater monitoring plan. QC activities could include testing well construction materials, verifying that appropriate drilling methods are used, observing the performance of the drilling equipment, and documenting drilling and well construction details. QA is typically provided by the groundwater field professional (i.e., a geologist, an engineer, or an engineering technician) and includes oversight of the drill crew’s activities, inspection of the materials of construction, and review of submittals from the driller (e.g., material specification sheets, results of filter pack laboratory gradation tests, etc.) Cooperation between the driller and the groundwater field professional is essential for quick resolution of problems that may arise during well installation. An essential element of QC/QA is documentation of field activities. Well installation activities should be recorded in a boring log; a sample boring log form is provided in Figure 35.8. The details of well development should also be documented (e.g., pH and specific conductivity measurements for each purged well volume, cloudiness of purge water, time required to purge the well, etc.) 35.3.2.6 Decommissioning of Groundwater Monitoring Wells In many jurisdictions, groundwater monitoring wells that are not actively used must be decommissioned (also, the terms “destroyed” or “abandoned” are used in some jurisdictions to denote decommissioning). Decommissioning involves removing the well from use so that the well does not act as either a possible conduit for contaminant migration or uncontrolled access to groundwater resources. Decommissioning can be performed either by: (1) installing cement grout within the wellscreen and filter pack and then removing the casing and riser pipe (if possible); or (2) over coring the well and removing all of the well construction materials from the ground, then backfilling the borehole with appropriate material (e.g., a bentonite seal in low-permeability zones, soil in unconsolidated soil zones, or cement grout in rock formations).
35.3.3 Piezometers A piezometer is used to measure the hydraulic head at a specific location within the aquifer. As piezometers are not designed for the collection of groundwater samples, their design may be different from the design of a groundwater monitoring well. Attributes typical of a piezometer include a small diameter borehole, casing, and screen (to minimize the impact of the piezometer on groundwater flow in the aquifer), small screened interval (because piezometers having long screened intervals provide the average head over a
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35-23
large depth, instead of the head at a specific location), small or no filter pack (because the filter pack may impact the hydraulic head near the screened interval of the piezometer), and a very effective seal at the top of the screened interval (to prevent intrusion of water from above the measuring point).
35.3.4 Groundwater Discharges Groundwater quality samples and data can also be obtained from groundwater discharge to the surface at locations such as springs, seeps, or drains or from other groundwater discharges such as production/extraction wells. These discharge locations are often incorporated into groundwater monitoring programs because they typically provide a measure of groundwater quality at a location where a receptor may be present (i.e., drinking water well, discharge to a surface water body) and are therefore often used as a point of compliance. When using discharge locations as monitoring points, the DQOs of the groundwater monitoring program should be carefully considered to verify that the groundwater quality obtained at the discharge locations are comparable to the data collected at other monitoring points in the program. Variability in groundwater quality and sampling error at discharge locations can occur through interaction with the atmosphere and dilution with surface water bodies or groundwater from outside of the study area (depending upon the capture zone of the well or discharge feature). This variability can affect contaminant concentrations observed in discharge samples and bias the results of the analysis.
35.3.5 Alternative Groundwater Monitoring Devices At times, groundwater monitoring programs may incorporate alternative monitoring devices that either provide short-term data to supplement the conventional monitoring program, provide indirect data that can be inferred to assess potential releases (i.e., geophysical variations); or provide data regarding conditions outside of the target monitoring zone (e.g., soil gas, vadose zone, etc.) that can be extrapolated to assess groundwater quality within the target monitoring zone. These techniques are often incorporated into monitoring programs at sites that may be small, dry, or remote, where the use of conventional groundwater monitoring devices and sampling techniques may be impractical or cost-prohibitive. A detailed discussion of alternative monitoring techniques for these types of sites is provided by USEPA (1995). Alternative monitoring devices that are used to collect and extract samples of groundwater include direct push technology (DPT) samplers such as GeoProbe® , Hydropunch® (Edge and Cordry 1989), or other specialized grab samplers equipped on DPT or cone penetrometer testing (CPT) devices. These devices allow discrete groundwater samples to be collected directly from the formation. Some DPT equipment can also be fitted with specialized probes to monitor constituent concentrations or other parameters (e.g., specific conductance) vertically through saturated and unsaturated zone. Some examples of specialized probes include membrane interface probes (MIP), electrochemical sensors, and Site Characterization and Analysis Penetrometer (SCAP) or ROST™ probes, which analyze the groundwater in situ rather than extracting a sample to the surface. Descriptions of selected monitoring probes and sensors are provided in Section 35.4.3. DPT techniques are typically used during site characterization and assessment because they provide only temporary access to the formation and therefore allow only one-time sampling. However, they can be incorporated into monitoring programs if data is needed to supplement long-term monitoring results. The advantages of DPT techniques are that they are low cost, allow rapid collection of samples, and are applicable to a wide range of soil types. Additional detail regarding DPT groundwater sampling methodologies is provided in ASTM (1996). Various surface and borehole geophysical methods including electrical induction, electrical resistivity, electromagnetic induction and induced polarization, and complex resistivity can be used to monitor variations in aquifer and groundwater properties that can be indicative of releases. Geophysical evaluations are useful in plume delineation and monitoring as they can provide a gross measure of changes in an aquifer system, but most are not sensitive enough to detect minor changes in concentrations or provide precise concentrations values for specific contaminants that may be of interest.
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Soil gas probes and soil gas survey data can be used to infer groundwater quality impacts from some volatile compounds in shallow groundwater regimes. Soil gas surveys involve inserting a temporary or permanent probe or tube into the vadose zone and extracting gas from the subsurface to collect a sample. The soil gas data do not provide a direct measurement of groundwater quality and are limited to assessing volatile compounds. In addition, soil gas samples require special handling and shipping considerations. More information on soil gas survey procedures, requirements, and limitations is provided by ASTM (2001) and USEPA (1995). Lysimeters are used to collect water samples from the vadose zone either passively (by gravity collection) or through applying a vacuum or pressure to extract water from the unsaturated soils. The use of lysimeter in a groundwater monitoring program typically occurs in recharge areas near source zones. Lysimeter data from these areas can be used to obtain concentration data for waters recharging the aquifer through the source zone that may be used to evaluate contaminant flux and fate and transport. However, lysimeter samples are often difficult to obtain and pressure changes induced by some lysimeters may affect the solution chemistry of some contaminants thereby affecting data quality.
35.4 Groundwater Sampling 35.4.1 General Approach to Sampling Groundwater Monitoring Wells A general approach to the sampling of groundwater monitoring wells is presented in a stepwise fashion in this section. The following procedures are a compilation of groundwater sampling techniques recommended by the USEPA Yeskis and Zavala (2002), Puls and Barcelona (1996), Nielsen (1991), Driscoll (1986), and ASTM (2001). In contaminated areas, sampling should proceed from the least contaminated well to the most contaminated well if any sampling equipment is to be used at more than one well. 35.4.1.1 Step 1: Inspect Wells and Area Surrounding Wells The well should be examined for evidence of tampering, damage, or other activity that could compromise the ability of the well to produce a representative groundwater sample. The ground surface near the well should be examined for signs of recent activity (including accidental spills of constituents that could impact groundwater quality) and the area being monitored should be examined for changes since the last sampling event (e.g., new construction, new storage activities for waste materials, agricultural activity, etc.); such changes may require reexamination of the adequacy of the monitoring well network layout. Observations should be recorded by the field sampling professional for future reference. 35.4.1.2 Step 2: Measure Depth to Groundwater and Total Depth of Well The first activity to be performed after the well is inspected should be measurement of the depth to groundwater and the total depth of the well. There are many techniques available for measuring the depth to groundwater in a well, as shown in Table 35.7, including hand measurement using a wetted tape (which is simple and inexpensive, but somewhat time consuming) and electronic measurement (which is more expensive but less time consuming, and can be configured to provide a continuous record of data, if needed). All measurement equipment should be decontaminated (as described by USEPA [1992a]) before introducing it into the well. Measurements of the depth to groundwater that are made shortly after sampling the well may not be representative of the actual depth to groundwater. Measurement of the total depth of a well is important for evaluating changes in the total depth; for example, a decrease in the total depth could be indicative of siltation in the bottom of the well, or a crushed wellscreen or riser pipe. 35.4.1.3 Step 3: Purge Groundwater from Well The purpose of purging the well is to remove stagnant water from the well and to cause groundwater from the aquifer formation around the well to flow into the well, allowing collection of a representative groundwater sample from the target monitoring zone. Depending upon the hydrogeologic conditions and monitoring device design, purging may not be necessary. However, most commonly used groundwater
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TABLE 35.7 Summary of Methods for Manual Measurement of Well Water Levels in Nonartesian and Artesian Wells Measurement method
Wetted-tape Air-line Electrical Transducer Acoustic probe Ultrasonics
Measurement accuracy (ft)
Major interference or disadvantage
Nonartesian Wells 0.01 Cascading water or casing wall water 0.25 Air line or fitting leaks; gauge inaccuracies 0.02 to 0.1 Cable wear; presence of hydrocarbons on water surface 0.01 to 0.1 Temperature changes; electronic drift; blocked capillary 0.02 Cascading water; hydrocarbon on well water surface 0.02 to 0.1 Temperature changes; well pipes and pumps; casing joints
Artesian Wells Casing extensions 0.1 Limited range; awkward to implement Manometer/pressure 0.1 to 0.5 Gauge inaccuracies; calibration required gauge Transducers 0.02 Temperature changes; electronic drift Source: From Nielsen, D.M., ed. 1991. Practical Handbook of Groundwater Monitoring. Lewis Publishers, Chelsea, MI. With permission.
sampling techniques require purging to ensure that a sample representative of the formation water is obtained. Purge water may need to be collected and treated if there is a chance that it could be contaminated. 35.4.1.4 Step 4: Collect Groundwater Samples Groundwater in the well should be sampled using the techniques described in Section 35.4.2 or Section 35.4.3. Extreme care should be used when collecting, preserving, storing, and shipping groundwater samples (as described in Section 35.4.5) to provide samples to the laboratory that are representative of groundwater quality. Sample quality is much more likely to be compromised in the field than in the controlled environment of a laboratory. 35.4.1.5 Step 5: Document Sampling Event During the sample event, each step of the sampling process should be documented to allow detailed examination of the sampling procedures in the future. Recommended documentation procedures are described in Section 35.4.6. Good documentation is essential because it provides the basis for verifying the validity of the monitoring event. Also, if monitoring problems cannot be traced to laboratory error or resolved using field logs, then the notes of the field sampling professional may be valuable in identifying the source of the problem.
35.4.2 Overview of Groundwater Sampling Techniques Groundwater sampling typically requires extracting and collecting a volume of groundwater from a monitoring device for subsequent analysis. A variety of sampling devices are used to extract an aliquot of groundwater from the target monitoring zone for use as a sample. Table 35.8 provides a groundwater sampling device matrix that details the characteristics of most common sample extraction devices (get rid of in situ and portable determination, most portables can be dedicated). In addition to the characteristics provided in the matrix in Table 35.8, the groundwater professional should consider factors such as the sampling technique, access to the monitoring locations, availability of power, and ease of operations when identifying the appropriate monitoring devices. Additionally, the groundwater professional must examine the potential for the sampling device to affect data quality. For example, although bailers have historically
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•
• • • •
•
•
• • • • • •
•
•
•
0.01–0.2 gal 0–0.5 gpm 0–2 gpm 0–1.2 gpm 0–0.5 gpm Variable
0.01–0.3 gpm
Variable 0.2 gpm
0.01–0.13 gpm
1–1/2 in 2 in 1–1/2 in 2 in 1–1/2 in 2 in
1/2 in
1 in 1 in
No limit
•
•
•
•
•
• •
Variable Variable
•
Redox
1/2 in 1/2 in
pH
•
•
•
•
•
•
•
•
•
• •
Major ions
Inorganic
•
•
•
•
•
•
•
•
• •
Trace metals
•
•
•
•
•
•
•
•
•
• •
Nitrate fluoride
•
•
•
•
•
•
•
•
•
•
•
•
•
• •
Non-volatile
Dissolved gases
•
•
•
•
•
•
Volatile
Organic
Groundwater parameters
•
•
•
•
•
TOC
•
•
•
•
•
TOX
•
•
•
•
•
•
•
•
•
• •
Radium
•
•
•
•
•
•
•
•
Gross alpha and beta
Radioactive
•
•
•
•
•
• •
Coliform bacteria
Biological
installed. Sampling device construction materials (including tubing, haul lines, etc.) should be evaluated for suitability in analyzing specific groundwater parameters. It is assumed on this chart that existing monitoring wells are properly installed and constructed of materials suitable for detection of the parameters of interest. • Indicates device is generally suitable for application (assuming device is cleaned and operated properly and is constructed of suitable materials). Indicates device may be unsuitable or is untested for application. Source: From USEPA. 1992a. RCRA Groundwater Monitoring: Draft Technical Guidance, Office of Solid Waste, EPA/530-4-93-001, PB93-139-350, Washington, D.C.
b Sampling devices on this chart are divided into two categories: (1) portable devices for sampling existing monitoring wells, and (2) in situ monitoring devices (often multilevel) that are permanently
conditions, and depth to sampling point. For all devices, delivery rate should be carefully controlled to prevent aeration and degassing of the sample.
a Sample delivery rates and volumes are average ranges based on typical field conditions. Actual delivery rates are a function of diameter of monitoring well, size, and capacity of sampling device, hydrogeologic
Portable Sampling Devices GRAB Open bailer No limit Point Source No limit Bailer Syringe No limit Submersible Gear-drive 200 ft pump Bladder 400 ft pump Helical rotor 160 ft pump Gas-driven 500 ft piston pump Centrifugal Variable (low-rate) pump Suction Peristaltic 26 ft pump Gas Contact Gas-lift pump Variable Gas-drive 150 ft pump In Situb Sampling Devices Pneumatic No limit pump
EC
Device
Delivery sample rate or volumea
Approx. maximum sample depth Minimum well diameter
Generalized Groundwater Sampling Device Matrixa
TABLE 35.8
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been commonly used in groundwater sampling activities, they are prone to disturbing the water column and sediments in the well that can significantly affect sample quality. In addition, the use of peristaltic or suction pumps for collection of samples for volatile organic compounds is often not recommended due to potential off-gassing resulting from the negative pressure exerted on the sample as it is being extracted. The groundwater professional should also determine whether portable sampling equipment or dedicated sampling equipment should be used in the groundwater monitoring program. This decision should be based on factors such as the proposed frequency of sampling, duration of the monitoring program, decontamination requirements, overall data quality, and cost analyses. The groundwater sampling techniques most often used to collect samples from monitoring wells include: (1) the low-stress approach (or low-flow sampling, minimal drawdown sampling); (2) the well volume approach; (3) minimal purge approach; (4) discrete interval sampling; and (5) passive sampling. Selecting the appropriate sampling technique is based on several factors including well construction, hydrogeologic characteristics of the formation, and the proposed analytical requirements. Guidelines for selection of monitoring well purging and sampling approaches are provided in Table 35.9 and ASTM (2001). 35.4.2.1 Low-Stress (Minimal Drawdown) Approach The low-stress approach is based on the assumption that purging and sampling at a low-flow rate that minimizes stress (drawdown) in the well allows a sample to be obtained from the aquifer formation at a discrete interval (i.e., the pump intake elevation) with minimal interaction with stagnant water in the well column. The low stress approach is performed using a variable speed sampling pump to extract water from the screen interval at a low-flow rate, typically between 0.1 and 0.5 l/min. During well purging, drawdown within the well is monitored and the flow rate is adjusted to minimize drawdown to less than 0.1 m (0.33 ft) from the static water level in the well. The pump intake should be positioned in the center, or just above the center of the wellscreen, to minimize the potential to entrain solids that may have collected at the bottom of the well. In wells where the wellscreen spans the water table, the pump intake should be positioned near the center of the water column rather than the wellscreen. During well purging, the discharge is typically routed through a flow through cell and selected water quality parameters are monitored using portable field monitoring probes. These parameters typically include pH, ORP, specific conductance, dissolved oxygen, and turbidity. Purging is continued until the values for these parameters stabilize to established criteria. Table 35.10 provides stabilization criteria for common water quality indicator parameters. Following stabilization, samples are collected directly from the discharge of the pump at the same flow rate that was used during well purging. This approach has become widely accepted in recent years and is often the preferred technique under many regulatory programs. This approach has become popular because it provides samples that are representative of the mobile load of contaminants present (i.e., dissolved and colloidal phases); minimizes sample disturbance and artifacts; and reduces the volume of purge water that oftentimes is subject to special treatment or disposal requirements. The disadvantages of this approach include: additional capital costs for specialized equipment, additional personnel training requirements, greater set up times in the field. 35.4.2.2 Well Volume Approach Another sampling approach that is commonly used is the well volume approach. In this approach, the volume of the standing water column in the monitoring well is calculated based on water level measurements and well construction details. The well is then purged until a minimum number of well volumes (typically between three and five volumes) have been evacuated. This approach is typically performed using either dedicated or portable pumping systems. When using this approach the pump intake is placed in the water column to a depth that will not result in drawdown below the pump intake that could allow air to enter the pump. The pump should also be lowered slowly and set sufficiently above the bottom of the well to minimize disturbance of sediments in the well that could affect sample integrity.
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TABLE 35.9 Applicability of Different Approaches for Purging and Sampling Monitoring Wells
Low-stress approach Applicable Geologic Materialsa
Materials with moderate to high hydraulic conductivities. May be applicable to some low hydraulic conductivities, if can meet minimal drawdown criteria. High definition of vertical hydraulic conductivity distribution and vertical containment distribution.
Aquifer/Plume Characterization Data Needs prior to Choosing Sampling Method
Constituent Types Mainly recommended for Method is Applicable constituents that can be biased by turbidity in wells. Applicable for most other contaminants
Data Quality Objectives
1) High resolution of plume definition both vertically and horizontally. 2) Reduce bias from other sampling methods if turbidity is of concern. 3) Target narrow sections of aquifer.
Others (such as passive diffusion samplers, in situ samplers, and other non-traditional groundwater sampling pumps
Well-volume approach Materials with low to high hydraulic conductivities
Materials with very low to high hydraulic conductivities
Plume and hydraulic conductivity distributions are less critical
May need to consider the degree of hydraulic and contaminant vertical distribution definition dependent on Data Quality Objectives and sampler type.
Applicable for all sampling parameters. However, if turbidity values are elevated, low-stress approach may be more applicable if constituents of concern are turbidity sensitive. 1) Basic characterization 2) Moderate to high resolution of plume definition (will be dependent on screen length). 3) Target sample composition to represent entire screened/open interval.
Constituents of concern will be dependent on the type of sampler.
1) Can be applicable to basic site characterization, depending on sampler and methodology used. 2) Can reduce bias from other sampling methods. 3) May yield high resolution of plume definition.
a Hydraulic conductivities of aquifer materials vary from low hydraulic conductivities (clays, silts, very fine sands) to high
conductivities (gravel, sands, weathered bedrock zones). This term for the use on this table is subjective, and is more dependent on the drawdown induced in a monitoring well when sampled with a groundwater sampling pump. For instance, in a well being pumped at 4 liters per minute (l/min) with less than 0.1 ft of drawdown, can be considered to have high hydraulic conductivity. A well that can sustain a 0.2 to 0.4 l/min pumping rate, but has more than 0.5 ft of drawdown, can be considered to have low hydraulic conductivity. To assign absolute values of hydraulic conductivities to well performance and sustainable pumping rate cannot be completed because of the many factors in monitoring well construction, such as well diameter, screen open area, and length of screen. Source: Yeskis, D. and Zavala, B., 2002. Groundwater Issue Paper: Groundwater Sampling Guidelines for Superfund and RCRA Project Managers, U.S. Environmental Protection Agency, EPA/542/S-02-001. 53 p.
TABLE 35.10
Stabilization Criteria with References for Water-Quality Indicator Parameters
Parameter
Stabilization Criteria
pH
±0.1
Specific electrical conductance (SEC) Oxidation-reduction potential (ORP) Turbidity
±3% ±10 mV ±10 % (when turbidity is greater than 10 NTUs) ±0.3 mg/l
Dissolved oxygen (DO)
Reference Puls and Barcelona 1996; Wilde et al., 1998 Puls and Barcelona 1996 Puls and Barcelona 1996 Puls and Barcelona 1996; Wilde et al., 1998 Wilde et al., 1998
Source: Yeskis, D. and Zavala, B., 2002. Groundwater Issue Paper: Groundwater Sampling Guidelines for Superfund and RCRA Project Managers, U.S. Environmental Protection Agency, EPA/542/S-02-001. 53 p.
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To minimize potential effects to the quality of the sample obtained, the well should be purged at a flow rate that does not produce turbulence within the well. Minimizing turbulent flow in the well will reduce the potential for volatilization or excessive turbidity. Care should also be taken to minimize drawdown below the top of the screened interval of the monitoring well that could expose the aquifer to the atmosphere. When the minimum number of well volumes is purged, samples containers are filled directly from the pump discharge and prepared for analysis. Although the well volume approach has been replaced with the low-stress approach in many groundwater monitoring programs, regulations, and guidance, some regulatory agencies continue to require the well volume purge approach. The advantages to this approach are ease of implementation, cost and availability of sampling equipment, comparability with historical results, and minimal training requirements for field personnel. However, the representativeness of the samples obtained using this approach are sometimes compromised due to increased stress on the formation that may allow preferential flow from areas outside of the discrete zone. In addition, increased flow rates often create turbulence in the well that can result in loss of volatile compounds, oxidation of samples, and entrainment of sediments into the sample; all of which can affect data quality. 35.4.2.3 Minimal Purge Approach The minimal purge approach is used in low-yielding zones where extensive well purging prior to sample collection may not be feasible. The minimal purge approach is typically performed with dedicated, downhole sampling equipment set at a discrete depth within the screened interval. Purging is performed to the extent that only the volume of water contained within the sampling system (tubing, sample intake, bladder, etc.) is evacuated with no attempt to remove water from the well casing or formation. The sample is then collected directly from the discharge of the sampling equipment. When minimal purging is used attempts should be made to minimize the purge volume by using small diameter tubing and the smallest feasible sampling chamber. The minimal purge approach may also be used in high-yielding aquifers where sufficient flow across the open interval is occurring such that formation water mixing with the stagnant water in the well column is minimal. 35.4.2.4 Discrete Interval Sampling Discrete interval sampling requires no purging and is performed with down-hole, typically non-dedicated, samplers that are slowly lowered into the well to a discrete depth within the screen interval. A sample is then drawn into the sampling chamber and extracted. Several discrete interval samplers are commercially available and most common samplers operate using either a mechanical trigger mechanism to release a check valve at the desired depth that allows a sample to fill the sample chamber or pressurized systems that are lowered to the desired depth where the pressure is released or hydrostatic pressure forces water into the sampling chamber. Discrete interval sampling is often used in extremely low yielding wells where even minimal purging efforts are not possible. This method could also be used in higher yielding wells where flow across the screen interval is sufficient to minimize mixing with stagnant water from above the screen interval. 35.4.2.5 Passive Sampling Passive sampling techniques include sampling protocols that are used to collect a sample of environmental media for analysis, but the sample is not an aliquot of groundwater. Passive samplers also rely on formation water moving through the wellscreen or open interval, rather than forcing water through the well by evacuating groundwater from the wellscreen or applying a vacuum. Passive samplers typically utilize specialized sampling media that interact with the groundwater in the well. The contaminants in the well are then transferred to the media via physical processes such as diffusion or sorption and the sampling media is extracted and analyzed. The most common passive samplers are polyethylene diffusive bag (PDBs) samplers. A PDB consists of a low density polyethylene (LDPE) tube filled with distilled water that is lowered into the well. The PDB operates by allowing compounds to diffuse from the groundwater through the semi-permeable LDPE
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membrane and into bag. When the concentration of compounds within the sampler reaches equilibrium with the surrounding groundwater, the bag is removed and the sample is extracted from the bag and analyzed. PDBs are not useful for all contaminants such as metals and other inorganics; however, many VOCs have been demonstrated to be reliably monitored using this technology. A detailed discussion of PDBs is provided by ITRC (2004).
35.4.3 In Situ or Alternative Monitoring Techniques As an alternative to extracting and analyzing groundwater samples from a conventional groundwater monitoring device, some groundwater monitoring programs may include the use of direct monitoring devices, such as downhole sensors or probes that can analyze groundwater quality in situ. Direct monitoring devices are commonly used in groundwater monitoring programs because they provide capabilities such as long-term deployment, automated data collection functions, and data logging that can provide low-cost data collection with minimal effort. The following is a description of several direct monitoring devices that are commonly deployed at groundwater monitoring sites. Multi-parameter probes: Various commercially available multi-parameter probes or sondes are available that can be used to collect in situ groundwater quality data for various analytes. Typically, these devices include single or multiple electric sensors that are capable of analyzing one or more of a variety of parameters, such as head pressure, pH, specific conductance, dissolved oxygen, or ORP. Ion-selective probes: These probes can be used to detect specific ions in groundwater. The probes are designed to detect specific ions by producing an electric signal that can be compared to a reference signal for a specific ionic constituent. This method is particularly useful for preliminary groundwater characterization and tracer studies. Fiber optic chemical sensors: These are also designed to detect a specific chemical in groundwater. The sensor is made of a reagent that is physically confined or chemically immobilized at the end of a fiber optic cable. The cable is inserted into a monitoring well, piezometer, or borehole, and then a signal is transmitted through the cable, which detects the constituent, if it is present. This method, which is also in the developmental stages, can be used on an extremely wide variety of constituents, uses portable equipment, and produces results at very low cost. Specialized DPT or CPT probes: As described in Section 35.3.5, various types of CPT and DPT probes are available to obtain in situ measurement of contaminant concentrations in groundwater as boreholes are being advanced. Some DPT or CPT probes, such as the MIP, utilize a semi-permeable membrane to collect vapor samples that are extracted to the surface and analyzed using a variety of instruments. Other DPT probes utilize technologies such as laser-induced fluorescence (e.g., the ROST™ system or SCAP) or x-ray fluorescence to assess organic or metal contaminant concentrations in soils or groundwater within the borehole. These systems are generally used for site characterization rather than long-term monitoring events because they are deployed during DPT or CPT borehole installation.
35.4.4 Quality Assurance and Quality Control Samples Most groundwater monitoring programs will incorporate the collection and analysis of quality assurance and quality control (QA/QC) samples to assess the precision, accuracy, representativeness, completeness and comparability (PARCC) of the data. The type and frequency of QA/QC data collection necessary for any groundwater monitoring program depends upon the DQOs and the checks that need to be performed to verify that the data collected achieve the DQOs. QA/QC samples can generally be categorized as blanks, spikes, calibration checks, and duplicate or replicate samples. Blanks are samples that are intended to contain none of the analytes of interest and are therefore analyzed to assess bias that may be introduced to the field samples during field or laboratory processes. Spikes are samples in which a known quantity of a substance is added to the sample and the sample is analyzed for that substance to assess the accuracy of the analytical method.
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Groundwater Monitoring TABLE 35.11
35-31 Project Quality Control Checks
QC check Blanks bottle blank field blank reagent blank rinsate or equipment blank method blank Spikes matrix spike matrix spike replicate analysis matrix surrogate spike Calibration check samples zero check span check mid-range check Replicate, splits, etc. field collocated samples field replicates field splits laboratory splits laboratory replicates analysis replicates
Information provided
cleanliness of sample bottles transport, storage, and field handling bias contaminated reagent contaminated equipment response of an entire analytical system analytical (preparation + analysis) bias analytical bias instrument bias analytical bias calibration drift and memory effect calibration drift and memory effect calibration drift and memory effect sampling + measurement precision precision of all steps after acquisition shipping + interlaboratory precision interlaboratory precision analytical precision instrument precision
Source: USEPA. 2002. EPA Guidance for the Quality Assurance Project Plans — EPA QA/G-5 EPA/240/R-02/009. Washington, DC, 111 p. December.
Calibration Checks are standards containing a known concentration of the subject analyte that are analyzed typically at the beginning, middle, and end of the analyses of the batch of field samples. Calibration checks are performed to verify that the analytical equipment is producing accurate results within the anticipated range of the analytical method. Replicates or duplicates are samples that are obtained at the same time from the same population of a particular media. The duplicate samples are analyzed and compared to assess the precision and reproducibility of the analytical method. There are several specific QA/QC samples that fit into the categories described above that are intended to assess specific aspects of the sampling program. Table 35.11 provides a summary of the specific QA/QC samples that are commonly used in groundwater monitoring programs and the information that they provide. More detailed discussions of QA/QC sampling is provided by USEPA (1992a, 1998).
35.4.5 Sample Handling and Preservation After the well has been sampled, the sample must be properly transferred to the sample container and preserved for transport to the laboratory. During sampling, every effort must be made to minimize changes in the chemistry of the sample. To minimize such changes in chemistry, samples should be collected, preserved, and stored correctly. Guidelines for each of these activities are presented by USEPA (1992a) and Nielsen (1991) and are summarized below. A generalized groundwater sampling protocol is presented in Table 35.12. Sample collection refers to the transfer of the sample from the sampling device to the sample container. The contents of the sampling device should be transferred in a controlled manner that minimizes sample agitation and aeration, which can cause gasification of samples, allow release of volatile organics, or cause oxidation and precipitation of metals in the sample. Groundwater samples should be collected soon after the well is purged to prevent interaction of the samples with the atmosphere and well casing. In samples that will be tested for volatile organic constituents, there should be no air in the sample containers
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35-32 TABLE 35.12
The Handbook of Groundwater Engineering Generalized Groundwater Sampling Protocol Steps Goal
Recommendations
1. Hydrologic measurements 2. Well purging 3. Sample collection 4. Filtration
Establish nonpumping water level. Remove or isolate stagnant H2 O that otherwise bias representative sample. Collect samples at land surface or in well-bore with minimal disturbance of sample chemistry. Filtration permits evaluation of characteristics of soluble constituents. It should be performed in the field as soon as possible after sample collection.
5. Preservation
Retard chemical changes that could affect the chemistry of a sample after it is extracted from the well. Field analyses of samples will effectively avoid bias in determining parameters/constituents that can change significantly after sample collection (e.g., temperature, alkalinity, pH). These blanks and standards will permit the correction of analytical results for changes that may occur after sample collection, preservation, storage, and transport. Refrigerate and protect samples to minimize their chemical alteration prior to analysis.
Measure the water level to ±1 cm (±0.01 ft). Pump water until well purging parameters (e.g., pH, temperature, specific conductance, Eh) stabilize to ±10 percent over at least two successive well volumes pumped. Pumping rates should be limited to ∼100 mL/min for volatile organics and gas-sensitive parameters. Filter trace metals, inorganic anions/cations, alkalinity. Do not filter samples to be analyzed for TOC, TOX, volatile organic compounds, other organic compounds. See Table 35.13.
6. Field determinations 7. Field blanks/standards 8. Sample storage/transport
Parameters or constituents that are not preservable should be analyzed in the field if at all possible. At least one blank and one standard for each sensitive parameter should be made up in the field on each day of sampling. Spiked samples are also recommended for complete QA/QC. Observe maximum sample holding or storage periods recommended by the agency. Actual holding periods should be carefully documented.
Source: Data from USEPA. 1990. Handbook — Groundwater, Volume I: Groundwater and Contamination. EPA/625/690/016a. Washington, D.C.; USEPA. 1992a. RCRA Groundwater Monitoring: Draft Technical Guidance, Office of Solid Waste, EPA/530-4-93-001, PB93-139-350, Washington, DC.
(which would allow volatilization of the compounds during shipment). Also, the samples should be transferred from the sampling device directly into the sampling container to minimize the opportunity for contamination of samples or changes in sample chemistry. Filtration of samples is frequently performed to provide samples that do not contain suspended solids. Filtration is usually performed by draining or forcing samples through a filter having openings of 0.45 µm. The advantage of filtering samples is that the constituents adsorbed to the suspended solids can be distinguished from constituents that travel in dissolved phase in the groundwater. Potential disadvantages of filtering include changes in groundwater chemistry during filtration and the removal of some solid particles (e.g., colloids) that may actually travel with groundwater. More detailed discussions of the advantages and disadvantages of filtering groundwater are provided by Puls and Barcelona (1989) and USEPA (1995). In monitoring scenarios where significant quantities of suspended solids exist, it may be useful to analyze both filtered and unfiltered samples to allow a comprehensive evaluation of groundwater quality. Sample preservation refers to actions taken to minimize changes to the chemistry of the sample after it is removed from the well. As there are significant changes to the environment of the sample after it is removed from the well (e.g., temperature, light, presence of air, etc.), the sample can experience geochemical changes that could render the sample unrepresentative if it is not properly preserved. Sample preservation methods are intended to retard volatile loss and chemical reactions such as oxidation, biodegradation, and sorption. Preservation methods are generally limited to pH adjustment, refrigeration, and protection from light. A list of appropriate preservation measures is presented in Table 35.13.
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Groundwater Monitoring TABLE 35.13
35-33
Sample Preservation Measures Volume required (ml) 1 samplea
Parameters (type) Well purging pH (grab) specific conductivity (grab) T (grab) Eh (grab) Contamination indicators pH, specific conductivity, (grab) TOC TOX Water quality dissolved gases (O2, CH4, CO2) Alkalinity/Acidity Fe, Mn, Na+ , K+ , Ca++ , Mg++ PO4, Cl, Silicate
Container (material)
Preservation and storage requirements
Maximum holding period
50 100 1000 1000
T,SS,P,G T,SS,P,G T,SS,P,G T,SS,P,G
None; field det. None; field det. None; field det. None; field det.
<1 hb <1 hb None None
As above
As above
As above
As above
40 500
G,T G,T
Dark, 4◦ C Dark, 4◦ C
35 h 5 days
10 ml minimum
G,S
Dark, 4◦ C
<35 h
100 (filtered) All filtered, 1000 ml
T,G,P T,P
<6 hb /<35 h 6 months
@50
(T,P,G glass only)
4◦ C/None Field acidified to pH < 2 with HNO3 4◦ C
NO− 3 SO− 4 NH+ 4
100 50 400
T,P,G T,P,G T,P,G
Phenols
500
T,G
Same as above for water quality cations (Fe, Mn, etc.) Same as chloride above
Same as above for water quality cations (Fe, Mn, etc.) Same as chloride above
Drinking water suitability As, Ba, Cd, Cr, Pb, Hg, Se, Ag F−
4◦ C 4◦ C 4◦ C/H2 SO4 to pH < 2 4◦ C/H3 PO4 to pH < 4 Same as above for water quality cations (Fe, Mn, etc.) Same as chloride above
Remaining organic parameters As for TOX/TOC, except where analytical method calls for acidification of sample
35 h/7 days; 7 days 35 h 7 days 35 h/7 days 35 h
6 months
7 days
35 h
Modified after Scalf, M.R., McNabb, Dunlap, W.J., Crosby, R.L., and Fryberger, J. 1981. Manual of Groundwater Quality Sampling Procedures. EPA/600/2-81/160 (NTISPB82-103045). a It is assumed that at each site, for each sampling date, replicates, a field blank, and standards must be taken at equal volume to those of the samples. b Temperature correction must be made for reliable reporting. Variations greater than ±10 percent may result from longer holding period. In the event that HNO cannot be used because of shipping restrictions, the sample should be refrigerated to 4◦ C, 3 shipped immediately, and acidified on receipt at the laboratory. Container should be rinsed with 1:1 HNO3 and included with sample. Note: T = Teflon, SS = stainless steel, P = PVC, polypropylene, polyethylene. G = borosilicate glass. From USEPA. 1993a. Office of Research and Development. Subsurface Characterization and Monitoring Techniques: A Desk Reference Guide, Volume I: Solids and Groundwater, Appendices A and B. U.S. Environmental Protection Agency, Washington, D.C. EPA/625/R-93-003a.
Sample storage refers to measures used to maintain sample quality during transportation. Samples should be cooled to a temperature of 4◦ C as soon as possible after they are collected and should be maintained at that temperature until they are received at the laboratory. Samples should be shipped in containers that minimize agitation of the samples and should be accompanied by proper documentation
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(see Section 35.4.6). Note that most samples must be analyzed within a specified period (i.e., holding time) after the sample is collected; data from samples that are analyzed after the holding time limit has been exceeded are considered to be unreliable. Coordination between the field sampling team and the laboratory can help to prevent exceedance of holding times. Sample storage requirements and maximum recommended holding times are listed in Table 35.13.
35.4.6 Documentation of Sampling Events Each sampling event should be documented so that the validity of the sample collection, preservation, and storage techniques can be verified in the future. If this information cannot be verified, then (depending on the data quality objectives specified for the project) the data could be rendered invalid and resampling could be required. An example field sampling documentation log form is presented in Table 35.14. As shown in the table, each aspect of the sampling event should be recorded, including the time of sampling, ambient weather conditions, time required to purge the well and the volume of water purged, purge water characteristics, decontamination procedures, sample equipment calibration, and procedures for preservation of samples. Also, chain-of-custody of documentation should be prepared. The record of sampling should be stored in the project files for future reference.
35.5 Analysis of Groundwater Samples 35.5.1 Field Chemical Analyses Many analyses can be performed in the field using electronic sensors or other field methods such as reagent test kits or bioassay tests; in fact, several parameters must be measured in the field to be relevant. Analyses that should be performed in the field include measurement of temperature, pH, specific conductance, redox potential, dissolved oxygen, sulfides, nitrate, and ferrous iron. Temperature measurements that are not made in the field immediately after the sample is collected are not representative of in situ conditions because the temperature of the sample may change rapidly after the sample is removed from the well. Measurements of pH and redox potential are strongly affected by temperature and, therefore, should also be measured in the field. Other measurements such as sulfide, dissolved oxygen, nitrates, and ferrous iron may be significantly affected by exposure to the atmosphere. These analyses can be performed quickly using readily available, relatively inexpensive equipment. A good discussion of field measurement techniques is presented by USEPA (1993a). Many of the analyses that are typically performed in the laboratory (which are described in Section 35.5.2) can be performed in the field by setting up a field laboratory. Field laboratories have become increasingly common as manufacturers of analytical equipment have developed increasingly reliable, portable analytical devices. The advantages of performing analyses in the field include fast return of results, decreased chance of sample disturbance or changes in sample chemistry during shipment, ability to obtain an additional sample quickly if problems occur during analysis, and lower cost per sample (if large quantities of analyses are performed). The disadvantages of performing analytical tests in the field include difficulty in implementing quality assurance measures, increased potential for contamination of samples and equipment, less sophisticated instrumentation (which usually results in higher method detection limits and lower precision and accuracy), and correspondingly less reliable test results. However, in spite of these shortcomings, field analysis can be an extremely valuable and time-saving approach for site characterization studies and for monitoring of remediation activities.
35.5.2 Laboratory Chemical Analyses Most analyses of groundwater samples are performed in an offsite, permanent laboratory to provide a high level of quality control of analyses. Laboratory analyses may be conducted using a variety of analytical techniques and methods. Analytical “technique” refers to a particular procedure and type of instrument
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TABLE 35.14
Example of a Field Sampling Log (Source: USEPA, 1993)
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that is used in the laboratory to analyze the sample; an analytical technique may incorporate one or more analytical methods to analyze a sample. An analytical method refers to the requirements and protocols that are employed when using a particular analytical technique to evaluate a specific group or subset of constituents. Note that appropriate methods and techniques will be a function of required detection limits, regulatory requirements, and DQOs. Laboratories will often recommend an appropriate technique and method depending upon your site-specific conditions and data needs. The most commonly used laboratory analytical techniques include chromatography (i.e., detection of constituents based on the rate that they migrate through a stationary medium), spectroscopy (i.e., identification of constituents based on the changes in light spectrum caused by irradiated light as the light passes through the groundwater sample), and photometry (i.e., the measurement of the intensity of light or the relative intensity of different lights as they pass through a groundwater sample) (USEPA, 1993b). Some of the more commonly used laboratory analytical techniques are described below (USEPA, 1993b). Gaseous-phase analyses are performed using instruments designed to detect constituents in gases or that require conversion of the sample to the gaseous phase before analysis. Gaseous-phase techniques include photo-ionization, flame-ionization, explosimetry, gas chromatography, mass spectrometry, and atomic adsorption spectrometry. Luminescence/spectroscopic analyses involve exciting a sample (e.g., x-rays or other means of radiation), and measuring the radiation emitted by the compound, either during excitation or as the electrons in the constituent return to their original state. Luminescence/spectroscopic techniques include x-ray fluorescence (i.e., measurement of the secondary radiation emitted when a sample is excited using x-rays), fluorometry (i.e., measurement of the radiation emitted when electrons in a molecule return to their original state after excitation), or spectrometry (i.e., measurement of the absorption spectra of narrow bandwidths of radiation from the sample). Wet chemistry analyses include a wide range of colorimetric (e.g., titration, colorimetry, filter photometers, and spectrophotometers), immunochemical (e.g., enzyme immunoassay and fluoroimmunoassay), liquid chromotography, and electrochemical (e.g., voltammetry, polargraphy, pH, Eh, dissolved oxygen, and electrical conductance) techniques. These procedures are relatively straightforward and inexpensive but they require strict application of QA/QC procedures, are time consuming, require different reagents for each analyte of concern, and have limited application for some toxic chemicals. Other analytical techniques include radiological, gravimetric, magnetic, microscopic, biological, and chemical sensor techniques. Each of these applies to particular constituents. The potential advantages of these techniques include: (i) economy of scale when analyzing for a small list of constituents from a large number of samples; (ii) better reliability of results for certain compounds; and (iii) (in some cases) simple operation of equipment. Disadvantages could include expensive equipment, difficult QA/QC procedures, and high cost of analyses. Refer to USEPA (1993b) for a discussion of these and other candidate analytical techniques. The specific analytical method used in a groundwater monitoring program is often specified by the regulations. For example, most groundwater monitoring data collected under RCRA or other federal or state cleanup programs require that analyses be performed in accordance with USEPA methods for evaluating solid waste contained in USEPA (1996). These analytical methods specify the analytical technique, requirements, and protocols that need to be implemented to perform the required analysis and requisite quality control for a specific group of compounds or elements. Other standard analytical methods may also be applicable, for example, USEPA drinking water test methods for projects where groundwater from residential or public water supply wells is evaluated. At times, specialized methods must be developed to detect a particular contaminant for which a standard methodology does not exist or to increase the precision, accuracy, and sensitivity of a standard method to achieve DQOs. If such specialized methods are required, they should be developed by an experienced analytical chemist. When reporting analytical results, the laboratory may present a qualifier with the data to clarify the validity of the test result. Qualifier types and definitions vary between laboratories, but some qualifiers are used widely by most laboratories. Typical qualifiers are presented below (USEPA, 1992a); the laboratory
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should be required to submit a list of qualifier definitions with the reports of laboratory analyses. J = value is estimated (typically below the method detection limit). U = compound analyzed for but undetected (value presented is the quantitation limit). R = data does not meet laboratory QC requirements and is rejected. N = compound is tentatively identified (i.e., its presence is likely, based on the judgment of the laboratory, but not conclusively confirmed by the test result).
35.6 Evaluation of Groundwater Monitoring Data 35.6.1 Data Validation Data validation refers to the process of verifying that the groundwater sampling and analysis was performed in accordance with the requirements of the groundwater monitoring plan and in accordance with the requirements of applicable QA/QC procedures. Data that does not comply with these specific requirements must be considered to be potentially invalid. Example causes of invalid data include insufficient purging affecting representativeness of the sample; improper sampling, filtration, and preservation techniques; failure to analyze the samples before the recommended holding time is exceeded; the presence of air in VOC sample containers; failure to properly implement chain-of-custody procedures; improper calibration of laboratory analytical equipment; presence of contaminants in field blank, method blank, or trip blank samples; or failure of the analytical laboratory to properly implement or document QA/QC procedures. If data has been found to be potentially invalid, then one of the following may be required: (i) if remaining portions of the samples exist, then they may be analyzed and substituted for the invalid data; (ii) additional samples can be collected and analyzed; or (iii) documentation of the sampling event can be reviewed and, if it is found that the improper procedure would not have impacted the analytical results, notations can be made in the project files regarding the occurrence and resolution of the problem, with the analytical result tentatively used in data evaluations.
35.6.2 Evaluations of Groundwater Elevation Measurements or Depths to Groundwater The elevation of the groundwater potentiometric surface is typically evaluated by measuring the depth to groundwater at several locations, calculating the elevation of groundwater at each location, and then interpolating contours of groundwater elevation for the area. The groundwater elevation can be calculated for the well location by subtracting the depth to groundwater from the surveyed elevation of the reference measuring point on the monitoring well casing. Measurements of the depth to groundwater can be complicated by the presence of LNAPLs in the monitoring well or piezometer, as shown in Figure 35.9 and as discussed by Blake and Hall (1984). As shown in the figure, the thickness of LNAPLs (e.g., petroleum hydrocarbon products) in an aquifer can be significantly different from the thickness of LNAPL in a well. LNAPLs typically “float” on groundwater at the top of the capillary fringe. LNAPLs flow into the well until the elevation of the top of LNAPL above the capillary fringe equals the elevation of the top of LNAPL inside the well. As groundwater in the capillary fringe does not flow into the well, the thickness of LNAPL present in the well (TA ) is typically greater than the actual thickness of LNAPL in the aquifer (HM + TM − HC ). The actual thickness of LNAPL, and a more accurate estimate of depth to groundwater, can be estimated from: TM = TA − (DWT + HM )
(35.1)
where TM = thickness of mobile LNAPL (ft), TA = apparent thickness of LNAPL (ft), HM = distance from bottom of the mobile LNAPL layer to the water table, and DWT = depth of LNAPL in the well below
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Mobile LNAPL Immobile LNAPL
HM
HC
Capillary fringe Water table
TA DWT
P1 At equilibrium: P1 = P2 P2
FIGURE 35.9 Distribution of LNAPL and groundwater in a well within an LNAPL-contaminated aquifer.
the actual water table (ft). DWT can be calculated as DWT = HM γLNAPL /(γw − γLNAPL )
(35.2)
where γLNAPL = the specific weight of LNAPL (lb/ft3 ), and γw = the specific weight of water (lb/ft3 ). HM is approximately equal to the thickness of the capillary fringe, which can be estimated based on the grain-size distribution of the soil (see Lambe and Whitman 1969). Once the elevation of groundwater has been calculated for the wells at a site, the configuration of the potentiometric surface can be estimated to provide an indication of the likely direction of groundwater flow and the gradient of the potentiometric surface. There are numerous techniques for interpreting the contours of the potentiometric surface, the most common and basic of which is manual contouring based on the triangular linear interpolation of hydraulic head data from a minimum of three monitoring wells. Often, more complex computer-generated contouring programs are available such as kriging, triangulation with linear interpolation, inverse distance weighted averaging, or minimum curvature. Representations of the potentiometric surface are typically generated using specialized software such as CADD or geographic information systems equipped with geostatistical packages or specialized groundwater modeling software. Additional information regarding potentiometric surface contouring is provided by Kresic (1997). An illustration of a potentiometric surface map, as interpreted from groundwater elevations at several wells, is provided in Figure 35.10. As shown in the figure, a potentiometric surface can be produced by interpolating data between monitoring wells; the groundwater professional should carefully consider all available site data when evaluating groundwater flow direction to prevent the type of problem illustrated in Figure 35.10, which shows that a limited subset of the data would imply an incorrect groundwater flow direction. Surface-water features that are connected with groundwater can also provide valuable information regarding the configuration of the potentiometric surface. The gradient of the potentiometric surface is calculated as the ratio of vertical change of elevation in the potentiometric surface to the distance over which the change occurred. The velocity of groundwater can then be calculated for a given area as (Freeze and Cherry 1979): v=−
Ki ne
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(35.3)
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18.73
18.30
.0
18
17.58
.5
18
.0
19
5
19.
A
19.43
20.10 20
.0
18.42
Area of Leaking pipe
20.0
20.0
19.9
19.9
19.8
19.8 19.7
19.7
19.6
19.31
Groundwater elevation contour Actual based on 9-wall array Apparent based on 3-well array
19.60
19.53 B
C
Groundwater flow direction
19.0
FIGURE 35.10 Potentiometric surface mapping. (From Nielsen, D.M., ed. 1991. Practical Handbook of Ground-Water Monitoring. Lewis Publishers, Chelsea, MI. With permission.)
where v = groundwater flow velocity [ft/sec], K = hydraulic conductivity [ft/sec], i = groundwater hydraulic gradient (which is usually a negative number) [−], and ne = effective porosity of the aquifer material [−]. This velocity can be used as an initial estimate of the speed at which a nonreactive solute might move through the aquifer.
35.6.3 Groundwater Quality Data Analysis 35.6.3.1 Comparisons to Standards Some simple, yet common, type groundwater quality data evaluation are comparisons to published values such as ranges of naturally occurring groundwater quality, regulatory standards, or site-specific criteria established in permits or the groundwater monitoring plans. Typical ranges of physical, chemical, and biological characteristics of uncontaminated groundwater are presented in Table 35.15. It should be noted that the ranges provided in Table 35.15 are generalities and that natural groundwater quality varies widely depending upon geologic conditions and other environmental and geographic factors. More specific information regarding natural groundwater quality for a particular geographic location and geologic formation can often be obtained from state or federal geologic survey publications or from other local organizations. The most common regulatory standards by which groundwater data are compared are
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The Handbook of Groundwater Engineering Key Physical, Chemical, and Biological Properties of Groundwater Standard range of values in natural groundwater
Property
Physical
Temperature Elevation of potentiometric surface, or depth below land surface Presence of NAPLs Total suspended solids Total dissolved solids Chemical pH Dissolved oxygen Total organic carbon Specific conductance Manganese Iron Ammonium Chloride Sodium Volatile organics Sodium, calcium, bicarbonate, magnesium, arsenic, cadmium, iron, lead, nickel, selenium, zinc Beryllium, Mercury, Silver, Thallium Biological Coliforms, viruses
10–20◦ C Varies widely None 100–500 ppm 100–1000 ppm 6.5–8.5 standard units 2–5 ppm 1–10 ppm 100–1000 µmhos/cm 0–0.1 ppm 0.01–10 ppm 0–2 ppm 2–200 ppm 1–100 ppm <40 ppb 1000 to 1,000,000 ppb 1 to 1,000 ppb <1 ppb 0 organisms
Source: Data from Driscoll, F.G. 1986. Groundwater and Wells. Johnson Division, St. Paul, MN.; Freeze, R.A. and Cherry, J.A. 1979. Groundwater. Prentice–Hall, Inc., Englewood Cliffs, NJ.; Hem, J.D. 1989. Study and Interpretation of the Chemical Characteristics of Natural Water. U.S. Geological Survey Water Supply Paper 2254, 3rd Edition.
drinking water standards established by USEPA, which include maximum contaminant levels (MCLs) and secondary maximum contaminant levels (SMCLs). Many states have also developed numeric standards for groundwater cleanup sites based on contaminant toxicity and risk. Although a comparison to a particular value or standard is a simple method, a statistically valid comparative approach is often required to confirm the validity of the findings, as described below. 35.6.3.2 Statistical Evaluations of Data Another common approach used to evaluate groundwater quality data is to statistically assess the monitoring data to identify spatial or temporal variations in the data. After data have been validated, they should be evaluated to determine if groundwater quality conditions have changed since the last sampling event. As a first step in this process, the presence of the contaminants should be confirmed and an evaluation of the contribution of the contaminants by the potential source should be performed. This first step is typically made by analyzing the data using statistical analyses, which can be used as the basis for concluding whether a contaminant is present in groundwater. An adequate quantity of data is required before a statistical analysis can be performed; often, samples from multiple background wells and from multiple sampling events must be available. A discussion of statistical analysis of groundwater analytical data is presented in USEPA (1989b). Statistical analyses are based on the probability theory that the likely range of all values (e.g., constituent concentrations at any location within the monitored area) can be estimated based on the distribution of the known values. If a groundwater quality dataset is found to be consistent with a standard distribution (e.g., normal, lognormal, etc.), then the probability that the concentration will exceed a certain value (e.g., a groundwater protection standard) can be estimated. Two key parameters that are used in nearly all statistical analyses are the mean and the standard deviation of the data set: n n xi x¯ = i=1
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(35.4)
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s=
n
1/2 ¯ (n − 1) (xi − x)
(35.5)
i=1
where x = sample mean; i = observation number; xi = the value for the ith observation; n = total number of observations; and s = sample standard deviation. Groundwater quality data are usually well characterized by a normal or lognormal distribution, although some data cannot be adequately characterized by any common distribution (USEPA, 1989b). As most statistical tests are based on an assumption regarding normality or lognormality, the data must be tested for conformance to either a normal distribution or other type of distribution that is assumed by the particular statistical test. One test for evaluating the fit of a data set to a normal distribution is the coefficient of variation test. To perform this test, the sample mean and standard deviation are first calculated. Then the sample standard deviation is divided by the sample mean; if the result is greater than one, then the data do not fit a normal distribution well. If the data are found not to fit a normal distribution, then a log transformation should be performed on the original data and the coefficient of variance test rerun to see if the data fit a lognormal distribution. If the data fit either a normal or a lognormal distribution, then a parametric approach (described in Section 35.6.3.2) to statistical analyses can be used; otherwise, a nonparametric analysis (also described in Section 35.6.3.2) must be used. Other more accurate but more complicated tests are available to test the fit of the data to a normal or lognormal distribution (e.g., probability plots, coefficient of skewness, the Shapiro-Wilk test, and the probability plot correlation coefficient, all described in USEPA (1989b)). 35.6.3.3 Tests for Statistical Significance of Detected Constituents To select a statistical approach, the type of comparison being made (e.g., compliance well vs. background, intrawell, etc.) must be selected, and then a method that best suits the approach. Types of comparisons and recommended statistical methods are presented in Table 35.16. As shown in the table, the recommended method of statistical analysis varies based on the type of comparison being made and the number of times the compound of concern was detected. If the constituent was not previously detected, then the analytical results should simply be compared to the quantitation limit of the test apparatus.
TABLE 35.16
Recommended Statistical Methods for Groundwater Monitoring
Compound
Type of comparison
Any compound in background ACL/MCL specific Many nondetects in database(synthetic)
Recommended method
Background vs. compliance well Intrawell Fixed standard % nondetects
ANOVA tolerance intervals, prediction intervals, Control charts
0 ≤ x ≤ 15%
Replace nondetect values with one half the method detection limit or quantitation limit (as appropriate), then proceed with any of the following parametric procedures: ANOVA Tolerance intervals Prediction intervals Control charts. If residuals from transformed do not meet parametric ANOVA requirements, use nonparametric approaches. Treat nondetect values as ties, then either proceed with nonparametric ANOVA, or use Cohen’s adjustment, then proceed with: Tolerance intervals, Confidence intervals Control charts Test of proportions Compare sample best result values to sample quantitation limits
15% ≤ x < 50%
50–99% 100%
Confidence intervals, tolerance intervals Recommended method
Key: ND = Nondetect QL = Quantitation Limit MDL = Method Detection Limit ACL = Alternate Concentration Limit From USEPA. 1989b. Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Interim Final Guidance. Office of Solid Waste, Washington, DC.
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One of the most powerful statistical tests for groundwater monitoring is the Analysis of Variances (ANOVA) test, also known as the “general linear model procedure.” This method is useful for comparing background data to compliance well data and is useful in situations where constituents are detected in many wells at differing concentrations. The method is used to compare the means of different groups of observations (i.e., from different wells on the same sampling date) and to identify significant differences among the groups; if there are significant differences, then the data can be further analyzed to identify contrasting aspects of the dataset. If the compound is not routinely detected in groundwater, then the nondetect data points are replaced with nonzero approximations of data before proceeding with the statistical test. The analysis can be performed using either a parametric or a nonparametric approach. The parametric ANOVA procedure assumes that the differences (called residuals) between the mean of the values and the values themselves are normally distributed with equal variance; this case can be checked as described in Section 35.6.3.1. If this test shows that the residuals do not meet this assumption, then the nonparametric ANOVA procedure must be performed. For a nonparametric ANOVA, it is first assumed that there is no contaminant present (i.e., all of the data comes from uncontaminated groundwater having the same continuous distribution of constituents) and that, therefore, the median concentration of contaminants must be the same at all wells. The nonparametric ANOVA is performed by comparing the median concentration of hazardous constituents for all wells and then, if the median differs significantly, by comparing the average rank of each of the compliance wells with the average rank of the background well.
35.6.4 What to Do if a Statistical Analysis Indicates the Presence of Contaminants If the results of a statistical analysis indicate that contaminants are present in a particular groundwater monitoring well, then the data should first be reexamined to verify that the test results were not a falsepositive indication of contamination. The data should be examined for the following problems that may cause a false-positive indication of groundwater contamination. See also Nielsen (1991), USEPA (1989b), and Miller and Miller (1986) for discussions of false-positive groundwater monitoring results. Natural variation in groundwater quality: Groundwater quality sometimes varies naturally according to season, temperature, geology, or a number of other factors. If the statistically significant increase is due to a constituent that is present in uncontaminated groundwater (e.g., manganese, sodium, iron, etc.), then the historic data for the site should be reexamined to evaluate the expected range of values for the detected constituent. Constituents of concern may be naturally present in groundwater and may not be the result of the potential source; for example, arsenic and lead are naturally present at levels exceeding MCLs in uncontaminated groundwater in many parts of the United States. These false positives can be identified and resolved by obtaining adequate representative background data. Contaminant source different from the potential source: The potential source being monitored may not be the actual source of contamination. This could be confirmed by either demonstrating that a hydraulic interconnection exists between an alternative source and the well having the statistically significant increase or by showing that the contaminants present in the well could not have been derived from the potential source, given the type of waste in the potential source. Another type of false-positive result is the contamination of groundwater samples by condensation of landfill gas in monitoring wells. Well construction problems: The statistically significant increase may be due to a problem with well construction. For example, high pH or alkalinity values may indicate that grout from the well is “bleeding” down into the filter pack, either through the aquifer formation or through an inadequate bentonite seal. Alternatively, the statistically significant increase may be a result of poor well maintenance; an example of such a problem is infiltration of contaminated surface water ponded around the well at the ground surface. Analytical error: The statistically significant increase may be the result of laboratory error. For example, methylene chloride and acetone (which are commonly used in the laboratory to clean test devices) are routinely detected in groundwater samples but are often a false-positive indication of contamination. Such analytical errors can usually be detected by preparing and analyzing laboratory, trip, and method
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blanks. Contaminants present in laboratory or trip blanks that are also present in groundwater samples are not indicative of groundwater contamination. Good QA/QC procedures and documentation by the laboratory can usually lead to resolution of analytical errors. Statistical error: These errors are typically mathematical errors or inappropriate application of statistical procedures (e.g., improper consideration of nondetects in sample datasets). If such a problem is expected, then the results of the statistical analysis should be reviewed by an expert in statistical analysis. Sampling error: These errors include problems in the field that occur during sampling, such as improper filtering of samples, improper evacuation of wells before sampling, agitation of wells during sampling, agitation of samples during transfer to sample containers, and improper preservation of samples. This source of error is typically the most difficult to evaluate because, usually, very little documentation is generated during actual handling of the sample (because the sample technician’s hands are occupied), making it difficult to isolate the source of the problem. The best method of preventing such problems is to use properly trained professional field technicians and to routinely implement good QA/QC procedures during sampling. The use of good field forms is an effective way of ensuring that key observations are made and recorded. If no alternate source can be identified for the statistically significant increase, then the statistically significant increase should be attributed to the potential source being monitored and subsequent measures (such as those described in Section 35.2.2, Step 6) should be implemented.
Glossary Anisotropy Variation in geologic formations in the vertical or horizontal direction. Anthropogenic Resulting from, or caused by, human activities. Aquitard A lithologic unit that impedes, but does not completely prevent, groundwater movement. Background Sampling Evaluation of initial water quality conditions. Bridging The development of gaps caused by obstructions in either grout or filter pack materials. Also refers to blockage of particles in natural formation materials or artificial filter pack materials that may occur during well development. Casing An impervious, durable pipe placed in a borehole to prevent the walls of the borehole from caving and to prevent flow of undesirable groundwater, surface water, gas, or other fluids into the well. Chain of Custody A method for documenting the possession history of a sample from the time of its collection through its final disposition. Confining Unit A relatively low-permeability material stratigraphically adjacent to one or more aquifers. Contaminant A substance that is not normally present in groundwater or that is present at an unusually high concentration. Cross-Contamination The movement of contaminants between aquifers or water-bearing zones through an unsealed or improperly sealed borehole or other conduit. Detection Limit The lowest concentration of a chemical that can be reliably detected by an analytical device. Development The act of removing materials introduced during drilling from a well and adjacent aquifer formation. DNAPL A dense nonaqueous phase liquid that is relatively immiscible and has a density greater than that of water. Also known as “free product” or a “sinker.” Downgradient In the direction of decreasing hydrostatic head. Drilling Fluid A fluid (liquid or gas) that is used in drilling operations to remove cuttings from the borehole, to clean and cool the drill bit, and to maintain the integrity of the borehole during drilling. Equipotential Surface A surface, in a three-dimensional groundwater flow system, for which the total hydraulic head is the same at every point on the surface.
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False Negative A condition for which contamination is present, but the results of sample analyses fail to indicate its presence. False Positive A condition for which no contamination is present, but the results of sample analyses indicate presence of contamination. Field Blank A laboratory-prepared sample of known properties that is transported to the sampling site for use in validating field sampling procedures. Filter Pack A clean silica-sand or sand and gravel mixture that is installed in the annular space between the borehole wall and the wellscreen for the purpose of retaining and stabilizing the particles from the adjacent strata. Groundwater Protection Standard The acceptable quantity of contaminants in groundwater; the groundwater protection standard could be an MCL or another value. LNAPL A light nonaqueous-phase liquid. Also known as “free product” or a “floater.” Maximum Contaminant Level (MCL) The concentration at which the excess cancer risk of exposure to humans is estimated to be 1 × 10–6 , as defined by the USEPA. Nonaqueous Fluids that are relatively insoluble. Parts Per Billion (ppb), or Parts Per Million (ppm) Unit weight of solute per billion (or per million, respectively) unit weights of solution (solute, plus solvent). Piezometer A well that is used only to measure the elevation of the water table or the potentiometric surface. Potentiometric Surface A surface that represents the level to which water will rise in a tightly cased well. The “water table” is the potentiometric surface for an unconfined aquifer. Preservation Measures taken during sample storage to minimize the change in concentration of a constituent of interest until analyses can be performed (e.g., storage of sample in acidic solution). Quantitation Limit The lowest concentration at which a chemical can be accurately and reproducibly quantitated. Usually equal to the instrument detection limit times a factor of three to five. Quality Assurance A management function used to establish and monitor quality control protocols and to evaluate their outcomes. Quality Control Technical and operational procedures that are used to investigate and confirm the proper conduct of field, sample transportation, and laboratory activities necessary to assure accuracy and precision in the data. Statistically Significant Exceedance of a certain level of probability, based on the results of a statistical analysis. Target Monitoring Zone The portion of an aquifer for which there is a reasonable likelihood that a vertically placed well will intercept migrating contaminants. Upgradient In the direction of increasing hydrostatic head. Volatile Organic Compounds (VOCs) Compounds that will partition relatively easily into the air phase, sometimes defined as compounds with Henry’s law constant greater than around 10−6 atm-m3 /mol. Wellscreen A filtering device used to retain the filter pack and aquifer materials while allowing groundwater to enter the well, commonly constructed of slotted or perforated casing material.
References American Society for Testing and Materials (ASTM) 1998. Standard D 6286-98 Standard Guide for Selection of Drilling Methods for Environmental Site Characterization 16 p., West Conshohocken, PA. American Society for Testing and Materials Standard D5092-90. 1990. Standard Practice for Design and Installation of Groundwater Monitoring Wells in Aquifers. Philadelphia. American Society for Testing Materials (ASTM) 1992. Standard Guide for Sampling Groundwater Monitoring Wells, Standard D4448-85a; ASTM Standards on Environmental Sampling. 1995. Philadelphia, 220–233
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ASTM 1994. Standard D5521-94, Standard Guide for Development of Groundwater Monitoring Wells in Granular Aquifers 17 p., West Conshohocken, Pennsylvania. ASTM 1995b. Standard D5792-95, Standard Practice for Generation of Environmental Data Related to Waste Management Activities: Development of Data Quality Objectives 17 p. ASTM 1996. Standard D6001-96, Standard Guide for Direct-Push Water Sampling for Geoenvironmental Investigations 14 p., West Conshohocken, Pennsylvania. ASTM 1998. Standard D5092-90 (reapproved 1995) Standard Practice for Design and Installation of Groundwater Monitoring Wells in Aquifers 14 p., West Conshohocken, Pennsylvania. ASTM 2001. Standard D5314-92 (reapproved 2001), Standard Guide for Soil Gas Monitoring in the Vadose Zone 36 p., West Conshohocken, Pennsylvania. Barcelona, M.J., Gibb, J.P., Helfrich, J.A., and Garske, E.E. 1985. Practical Guide for Groundwater Sampling. EPA/600/2-85/104. Blake, S.B. and Hall, R.A. 1984. Monitoring petroleum spills with wells: some problems and solutions. Proceedings of the Fourth National Symposium and Exposition on Aquifer Restoration and Groundwater Monitoring. National Water Well Association. Columbus, OH. 305–310. Chappelle, F.H. 1993. Groundwater Microbiology and Geochemistry. John Wiley & Sons, New York. Cohen, R.M. and Mercer, J.W. 1993. DNAPL Site Evaluation. C. K. Smoley, Boca Raton, FL. Driscoll, F.G. 1986. Groundwater and Wells. Johnson Division, St. Paul, MN. Edge, R.W. and Cordry, K. 1989. The HydroPunch® : An in situ sampling tool for collecting groundwater from unconsolidated sediments. Groundwater Monitoring Review, 177–183. Fetter, C.W. 1993. Contaminant Hydrogeology. Macmillan Publishing Co., New York. Freeze, R.A. and Cherry, J.A. 1979. Groundwater. Prentice-Hall, Inc., Englewood Cliffs, NJ. Hem, J.D. 1989. Study and Interpretation of the Chemical Characteristics of Natural Water. U.S. Geological Survey Water Supply Paper 2254, 3rd Edition. Hvorslev, M.J. 1949. Subsurface Exploration and Sampling of Soils for Civil Engineering Purposes. U.S. Waterways Experiment Station, Vicksburg, MS. (Reprinted by Engineering Foundation, New York.) Kresic, Neven, 1997. Quantitative Solutions in Hydrogeology and Groundwater Modeling Law Engineering and Environmental Services, Inc. Lewis Publishers, New York. Lambe, T.W. and Whitman, R.W. 1969. Soil Mechanics. John Wiley & Sons, New York. Lueder, D.R. 1959. Aerial Photographic Interpretation. McGraw-Hill Book Company, New York. McDonald, M.G. and Harbaugh, A.W. 1988. A Modular Three-Dimensional Finite-Difference Groundwater Flow Model. USGS Techniques of Water-Resources Investigations, Book 6, Chapter A1, USGS, Reston, VA. Miller, J.C. and Miller, J.N. 1986. Statistics for Analytical Chemistry. John Wiley & Sons, New York. Moberly, R.L. 1985. Equipment Decontamination. Groundwater Age, 19:36–39. Nielsen, D.M., ed. 1991. Practical Handbook of Groundwater Monitoring. Lewis Publishers, Chelsea, MI. Puls, R.W. and Barcelona, M.J. 1989. Filtration of groundwater samples for metals analysis. Hazardous Waste and Hazardous Materials. 6. Puls, R.W. and Barcelona, M.J. 1996. Groundwater Issue Paper: Low-Flow (Minimal Drawdown) Groundwater Sampling Procedures; U.S. Environmental Protection Agency, EPA/540/S-95/504, 12 p. Rumer, R.R. and Mitchell, J.K. 1995. Assessment of Barrier Containment Technologies — A Comprehensive Treatment for Environmental Remediation Applications. National Technical Information Services, Springfield, VA. Scalf, M.R., McNabb, J. F., Dunlap, W.J., Crosby, R.L., and Fryberger, J. 1981. Manual of Groundwater Quality Sampling Procedures. EPA/600/2-81/160 (NTISPB82-103045). The Interstate Technology & Regulatory Council (ITRC), February, 2004. Technical and Regulatory Guidance for Using Polyethylene Diffusion Bag Samplers to Monitor Volatile Organic Compounds in Groundwater 78 p. U.S. Air Force Center for Environmental Excellence. 1997. Long-Term Monitoring Optimization Guide. Version 1.1. USEPA. 1975. Manual of Water Well Construction Practices. USEPA Office of Water Supply, Report No. EPA-5709-75-001. Washington, D.C.
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USEPA. 1986a. RCRA Groundwater Monitoring Technical Enforcement Guidance Document. Office of Waste Programs Enforcement and Office of Solid Waste and Emergency Response, OSWER-9950.1. Washington, D.C. USEPA. 1986b. Test Methods for Evaluating Solid Wastes. Office of Solid Waste and Emergency Response, Washington, D.C., SW-846. USEPA. 1987. Alternate Concentration Limit Guidance, Interim Final EPA/530-SW-87-017. 114 p. July. USEPA. 1989a. Risk Assessment Guidance for Superfund: Interim Final Guidance. Office of Emergency and Remedial Response (EPA/540/1-89/002). Washington, D.C. USEPA. 1989b. Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Interim Final Guidance. Office of Solid Waste, Washington, D.C. USEPA. 1989c. Seminar Publication — Transport and Fate of Contaminants in the Subsurface. EPA/625/489/019. Washington, D.C. USEPA. 1989d. Handbook of Suggested Practices for the Design and Installation of Groundwater Monitoring Wells. PB90-159-807. Washington, D.C. USEPA. 1990. Handbook — Groundwater, Volume I: Groundwater and Contamination. EPA/625/6-90/016a. Washington, D.C. USEPA. 1991. Handbook — Groundwater, Volume II: Methodology. EPA/625/6-90/016b. Washington, D.C. USEPA. 1992a. RCRA Groundwater Monitoring: Draft Technical Guidance, Office of Solid Waste, EPA/530-4-93-001, PB93-139-350, Washington, D.C. USEPA. 1992b. Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Addendum to Interim Final Guidance, Office of Solid Waste, Washington, D.C. USEPA. 1993a. Office of Research and Development. Subsurface Characterization and Monitoring Techniques: A Desk Reference Guide, Volume I: Solids and Groundwater, Appendices A and B. U.S. Environmental Protection Agency, Washington, D.C. EPA/625/R-93-003a. USEPA. 1993b. Office of Research and Development. Subsurface Characterization and Monitoring Techniques: A Desk Reference Guide, Volume II: The Vadose Zone, Field Screening and Analytical Methods; Appendices C and D. U.S. Environmental Protection Agency, Washington, D.C. EPA/625/R-93/003b. USEPA. 1993c. Technical Manual — Solid Waste Disposal Facility Criteria. EPA530-R-93-017, PB94-100450. USEPA. 1994. Handbook — Groundwater and Wellhead Protection. EPA/625/R-94/001. USEPA. 1995. Groundwater Sampling — A Workshop Summary, November 30 to December 2, 1995, Dallas, Texas. EPA/600/R-94/205. USEPA. 2000. Guidance for the Data Quality Objectives Process — EPA QA/G-4 EPA/600/R-96/055. Washington, D.C., 100 p. August. USEPA. 2002. EPA Guidance for the Quality Assurance Project Plans — EPA QA/G-5 EPA/600/R-98/018. Washington, D.C., 111 p. December. Wilde, F.D., Radtke, D.B., Gibs, J. and Jwatsubo, R.T. eds. 1998. National Field Manual for the Collection of Water Quality Data: US Geological Survey Techniques of Water-Resources Investigations. Book 9 Handbooks for Water-Resources Investigations, Variously Paginated. Wilson, C.R., Einberger, C.M., Jackson, R.L., and Mercer, R.B. 1992. Design of groundwater monitoring networks using the monitoring efficiency model (MEMO). Groundwater Age, 30:965-970. Yeskis, D. and Zavala, B., 2002. Groundwater Issue Paper: Groundwater Sampling Guidelines for Superfund and RCRA Project Managers, U.S. Environmental Protection Agency, EPA/542/S-02001. 53 p.
Further Information Nielsen (1991) gives a good, broad description of groundwater monitoring techniques. Driscoll (1986) gives a thorough discussion of groundwater well construction techniques and materials of construction for groundwater wells. USEPA (1993a, b) gives a detailed description of monitoring and analytical techniques for subsurface media. Complete citations for these works can be found in References.
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36 Remediation of Contaminated Groundwater 36.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36-1 Introduction • Groundwater Remediation Goals • Risks Associated with Contaminated Groundwater
36.2 Groundwater Remediation System Design. . . . . . . . . . . . . 36-6 Introduction • Step 1. Define the Problem • Step 2. Define the Goal of Groundwater Remediation • Step 3. Screen Candidate Remedies • Step 4. Prepare Detailed Design • Step 5. Implement the Design • Step 6. Confirm the Effectiveness of the Design
36.3 Hydraulic Containment of Groundwater . . . . . . . . . . . . . . 36-13 Overview • Physical Barriers • Hydraulic Barriers • Other Options for Hydraulic Containment
36.4 Design of Groundwater Extraction Systems . . . . . . . . . . . 36-21 Introduction • Extraction Well Systems • Extraction Trench Systems • Time Required to Extract a Plume of Contaminated Groundwater • Other Groundwater Extraction Approaches
36.5 Treatment of Contaminated Groundwater . . . . . . . . . . . . 36-30 Introduction • In Situ Treatment • Ex Situ Treatment
Michael F. Houlihan and Michael H. Berman GeoSyntec Consultants
36.6 Performance Monitoring of Groundwater Remediation Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36-43 36-44 36-45 36-48
36.1 Fundamentals 36.1.1 Introduction This chapter presents comprehensive approaches for developing and implementing programs for the remediation of contaminated groundwater. It also presents references for further information on such approaches. In this section on fundamentals, the purpose of, and typical goals for, groundwater remediation programs are addressed, and the role of risk assessment in groundwater remediation programs is
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described. Approaches to groundwater remediation are described based on the current requirements of the United States Environmental Protection Agency (USEPA) for remediating sites that are regulated under the Resource Conservation and Recovery Act (RCRA), the Comprehensive Environmental Response, Compensation and Liability Act (CERCLA), or analogous state programs. Other requirements, such as local regulations (as described in Chapter 32) and the need to mitigate human health or other environmental concerns posed by the contaminated groundwater may also define the needs of a groundwater remediation program.
36.1.2 Groundwater Remediation Goals Groundwater is an extremely important source of water. In the United States, one-third of all drinking water is obtained from groundwater sources (Hutson et al., 2004). Further, a significant majority of Americans live near industrialized population centers, which are typically located near viable groundwater supplies. In the past several decades, instances of groundwater contamination have illustrated the adverse impacts that contaminated groundwater can have on human health. For all of these reasons, protecting the integrity of groundwater supplies is crucial to the protection of human health and the environment. The need for remediation of contaminated groundwater is typically established based on the results of a groundwater assessment or monitoring program (see Chapter 35). In general, if the results of groundwater monitoring indicate that groundwater contains contaminants at concentrations that make it a threat to human health or the environment, then the groundwater may need to be remediated. Remediation, in this sense, is a broad term that refers to the reduction of risk caused by exposure to contaminated groundwater. One of the most important steps in a remediation program is defining the goals of the program. There are many different goals that can be defined for a groundwater remediation program, including the following (see NRC, 1994): • Complete restoration, which involves returning the aquifer to its condition prior to being contaminated • Nondegradation, which involves removal of contaminants that exceed either the detection limits of available analytical equipment or background concentrations • Remediation to health-based standards, which involves removal of contaminants that are present at a concentration that could cause adverse health effects (some examples of health-based standards are maximum contaminant levels (MCLs), alternate concentration limits (ACLs; see Section 36.1.3) and local or Federal drinking-water standards) • Remediation to risk-based standards, which involves removal of contaminants that are present above a concentration that is determined to present an unacceptable risk to site-specific receptors based on anticipated use of the site • Remediation to the limits of technology-based standards, which involves use of the best available technology to remove as much of the contaminants as possible • Partial-use restrictions (or institutional controls), such as legal restrictions on the use of groundwater in areas where groundwater has been contaminated, or physical barriers (e.g., fences) to prevent access to contaminated media • Containment, which involves the use of engineered systems for preventing migration of the contaminants to locations where receptors could be exposed to the contaminants. A brief summary of the advantages and disadvantages of each of these remediation goals is presented in Table 36.1. When selecting a remediation goal, the degree to which groundwater can actually be remediated should be examined. For example, until the 1990s, pump-and-treat was considered one of the best technologies available for restoring groundwater quality. However, based on studies by the USEPA and others, the actual success rate for pump-and-treat remedies is extremely low. A summary of the USEPA’s findings, as presented by the National Research Council (NRC) (1994), is provided in Table 36.2. Although there were various reasons for the failure of the systems to meet their goals, the data strongly suggest that, for most circumstances, groundwater pump-and-treat technologies alone are not capable of
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- - - - - - - - - - Increasing Protection - - - - - - - - - -
- - - - - - - - - - - - Increasing Cost - - - - - - - - - - - -
- - - - - - - - - - Increasing Flexibility - - - - - - - - - -
TABLE 36.1 Advantage and Disadvantage of Cleanup Goals Goal
Advantages
Complete restoration Nondegradation
Eliminates all risk
Likely impossible
Reduction of contaminants to lowest level measurable
Extremely difficult, expensive, and time-consuming for many contaminants and hydrogeologic settings Health-based standards are difficult to define and may not accurately address all possible health impacts of exposure to contaminated groundwater May not reduce risk to acceptable levels if site use changes; may need to be used in conjunction with partial use restrictions May not reduce risk to a level that is protective of human health and the environment Leaves contaminants that could cause risk if partial use restrictions are ineffective Leaves contamination that could migrate if containment system fails
Health-based standards
Designed to prevent measurable impacts to human health or environment
Risk-based standards
Designed to remove unacceptable risk to actual and anticipated site receptors based on anticipated use of site Allows treatment to the best standards capabilities of current technology Prevents contact between contaminants and receptors in a cost-effective manner Relatively predictable and reliable; typically less costly than other remediation approaches
Technology-based standards
Partial use restrictions
Containment
Disadvantages
Source: Adapted from National Research Council (NRC), Water Science and Technology Board. 1994. Alternatives for Groundwater Cleanup. Washington, DC. With permission.
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Categorya 1 2 3 4
Summary of Pump-and-Treat System Performance Data
No. of sites
No. of sites containment achieved
No. of sites cleanup goal achieved
No. of sites goal not achieved
2 13 19 36
1 8 12 18
1 4 4 0
1 9 15 36
Note: a Indicates relative ease of cleanup, with 1 easiest and 4 hardest, as defined by NRC (1994) and as illustrated in Table 36.8. This summary is based on information provided by NRC (1994) for sites where data were available regarding attainment of the cleanup goal. Source: Adapted from National Research Council (NRC), Water Science and Technology Board. 1994. Alternatives for Groundwater Cleanup. Washington, DC. With permission.
restoring groundwater to its original quality or health-based standards. However, returning groundwater to its useful purpose, or eliminating health and environmental risks, does not always require restoration to original quality. Accordingly, a growing number of remediation systems are being designed with the goal of either containment or remediation to health-based standards. A typical approach for achieving this remediation goal is, first, to estimate the risk associated with exposure to the contaminated groundwater and then design a remediation system that will improve groundwater quality to a level that is protective of human health and the environment (i.e., health-based standards). It has become commonplace for regulators to approve remedies involving in situ remediation technologies (ISRTs, see Section 36.5.2) or monitored natural attenuation (MNA, see Section 36.5.2.5), to meet such goals. An approach for deriving an achievable, health-based remediation goal is presented in Section 36.1.3. After a remediation goal has been selected, a remedy must be implemented to achieve the goal. In general, groundwater can be remediated in one or more of the following three manners. • Containment. Containment of a plume of contaminated groundwater involves preventing the plume from migrating to a location where receptors can be exposed to it. Techniques for containing contaminated groundwater are described in Section 36.3. • Extraction. For some remediation approaches, groundwater must be extracted from the ground, either to allow ex situ treatment or to provide hydraulic control of contaminated groundwater. Groundwater extraction approaches are described in Section 36.4. • Treatment. Contaminated groundwater can be treated, either in situ or ex situ, using a variety of physical, chemical, or biological methods. Techniques for treatment of contaminated groundwater are described in Section 36.5. Before beginning a program of groundwater remediation, it is recommended that the groundwater professional define a stepwise approach to developing and implementing the program. Recommended steps for developing and implementing a plan for groundwater remediation are presented in Section 36.2.
36.1.3 Risks Associated with Contaminated Groundwater Contaminated groundwater may pose a risk to human health or the environment if it comes into contact with receptors and if the groundwater contains concentrations of constituents that could affect the health of the receptors. Risk can be defined as the probability of occurrence of human health or environmental impacts due to a release of contaminants to the environment. Risk can be evaluated by performing a baseline risk assessment, as described by USEPA (2000b) and as summarized in Figure 36.1. The goal of performing a baseline risk assessment is to estimate the current and future risks associated with contaminated groundwater and to compare the estimated risk to the acceptable threshold of risk (definition
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Data collection and evaluation • Gather and analyze relevant site data • Identify potential chemicals of concern
Toxicity assessment
Exposure assessment • Analyze contaminant releases • Identify exposed populations • Identify potential exposure pathways • Estimate exposure concentrations for pathways • Estimate contaminant intakes for pathways
• Collect qualitative and quantitative toxicity information • Determine appropriate toxicity values
Risk characterization • Characterize potential for adverse health effects to occur: --Estimate cancer risks --Estimate noncancer hazard quotients • Evaluate uncertainty • Summarize risk information
FIGURE 36.1 Baseline risk assessment. (From USEPA. 2000b. Risk Assessment Guidance for Superfund: Interim Final Guidance. Office of Emergency and Remedial Response. Washington, DC.)
of an “acceptable” level of risk is addressed at the end of this subsection); if the acceptable threshold level of risk is exceeded, groundwater remediation is likely warranted. Risk assessment techniques can also be used to estimate the risk that would remain after a remediation program has been implemented. Estimating the resulting future risk for several candidate remedies can provide a basis for selecting a remedy that reduces risk most effectively. Based on the results of a risk assessment, a non-zero concentration limit for contaminants in groundwater could be proposed that results in an acceptable risk to potential future receptors. For several contaminants, USEPA has defined exposure concentrations that result in a risk of 10−6 (i.e., or one additional cancer case in 1,000,000 people), these concentrations are defined as “Maximum Contaminant Levels” (or MCLs). USEPA also allows owners of contaminated sites to propose, on a case-by-case basis, Alternate Contaminant Levels (ACLs) that result in a site-specific exposure level (after considering the fate and transport of the contaminants) of 10−6 . There are numerous sources of uncertainty in currently available risk-assessment methods (NRC, 1994). First, there is very little data to establish a conclusive link between human exposure to specific contaminants and specific health or environmental impacts. The accuracy of epidemiologic studies performed on humans to date is limited, with significant uncertainties related to: (1) exposure quantity and duration; (2) latency of observable impacts; (3) the relatively small size of the study populations; (4) inadequate control over comparison (i.e., “control”) groups; (5) inability to attribute observed health problems to only the known exposure; and (6) the synergistic effects in humans of exposure to some contaminants. Similarly, the accuracy of epidemiologic studies on animals is limited by: (1) the need to extrapolate the results of largedose impacts on animals to estimate impacts of small doses on humans; and (2) the focus of such studies on single-contaminant exposures. Finally, because the concentrations of contaminants in groundwater may change over time due to factors such as treatment or attenuation over the exposure period (i.e., a lifetime), the quantity of contaminants to which a receptor may be exposed (as calculated in Step 2, Exposure
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Assessment) could change during the period under consideration. Because of these uncertainties, risk assessment results have a degree of uncertainty. To account for this degree of uncertainty, very conservative assumptions are typically used when estimating toxicity and exposure quantity to minimize the possibility of underestimating the actual risk. Therefore, the estimated risk may be extremely conservative. After the risk of exposure to contaminated groundwater has been estimated, the groundwater professional, stakeholder, or regulator must decide whether or not the risk is high enough to warrant remediation. This decision process, which is referred to as risk management (a process that is separate from risk assessment), is typically performed based on input from both regulatory agencies and the population likely to be exposed to the risk. For example, a decision has been made by the US Congress, as presented in the National Contingency Plan, that a risk level of 10−4 to 10−6 is acceptable for contaminants at Superfund sites. The USEPA typically considers a similar range of risk to be acceptable at RCRA sites. The acceptable level of risk may vary from location to location and is a balance between the benefits to the public of a clean environment and the public cost of attaining a clean environment. The benefit of a clean environment is difficult to determine, but can be estimated in terms of dollars that the public would be willing to spend to clean up the environment (i.e., the “contingent valuation” approach); however, this approach is complex because of the great number of site-specific variables and non-quantifiable factors that must be considered (NRC, 1994; USEPA, 2002). Because of difficulties in obtaining an accurate estimate of the value of a clean environment, the commonly used value for acceptable risk (e.g., 10−6 ) has been assigned.
36.2 Groundwater Remediation System Design 36.2.1 Introduction The design of an efficient, cost-effective groundwater remediation system requires a comprehensive understanding of the nature and extent of contamination, the remediation objectives, and a careful evaluation of remedial technologies and their abilities to meet the objectives. When preparing a remediation system design, the use of a stepwise approach can simplify the design process and minimize the chances of failure of the system to achieve the remediation goal. In this section, recommended steps are presented for preparing a design to remediate contaminated groundwater. In subsequent sections, approaches to the design of some typical remediation systems are described.
36.2.2 Step 1. Define the Problem The first step in the design of the groundwater remediation system is to define the problem in adequate detail to allow the design of an efficient and cost-effective groundwater remediation system. The problem should be defined in terms of the extent of contamination, the risk associated with the contaminated groundwater, the regulations that apply to the problem, the degree of remediation required, and the subsurface conditions. The extent of contamination may be defined using procedures described by the USEPA (2004a) and others. If the vertical and horizontal extent of contamination have not been adequately evaluated during the site characterization or groundwater monitoring program, then additional field exploration data should be collected to complete this evaluation. In some cases, such as sites contaminated with DNAPL, it may not be economically feasible to fully define the source of contamination. The risk associated with contaminated groundwater can be estimated as described in Section 36.1.3 of this chapter. The regulations that apply may be identified based on the information presented in Chapter 32 of this handbook, and based on input from legal counsel, if necessary. Subsurface conditions may be defined as described in Chapter 2. The various manners in which groundwater can become contaminated are illustrated in Figure 36.2; hydrogeologic considerations for groundwater remediation are summarized in Table 36.3 and Table 36.4. It should be noted that the hydrogeologic properties described in Table 36.3 also are a key component in understanding how treatment agents injected in association with some ISRTs will be transported. As illustrated in Table 36.5, the hydrogeology of the site (as well as other factors) has a strong bearing on the type of remediation system that can be considered.
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36-7 Source
LNAPL pool
VOC vapor plume
High-permeability sand lenses
Residual product
Groundwater flow Dissolved contaminant plume Aquifer DNAPL pool
Aquitard
FIGURE 36.2 Groundwater contamination by dissolved vapor and nonaqueous phase constituents. TABLE 36.3
Hydraulic Properties of Aquifers Important for Groundwater Cleanup
Property
Description
Porosity
Volume of pore space relative to the total volume Interconnected pore space that can transmit fluid Rate of fluid movement
Effective porosity Groundwater velocity Hydraulic gradient Hydraulic conductivity
Elevation and pressure differences that cause fluids to flow Ease with which water can move through a geologic formation
Transmissivity
Product of formation thickness and hydraulic conductivity
Storage coefficient
Volume released by pressure changes per unit area during pumping in a confined aquifer Fraction of total pore volume released as water by gravity drainage during pumping of an unconfined aquifer Fraction of total aquifer volume retained as water above the water table after pumping an unconfined formation
Specific yield
Specific retention
Importance for groundwater cleanup Pores store water and contaminants Water and contaminants flow through interconnected pores Influences the direction and velocity of dissolved contaminant movement Influences the direction of contaminant movement Influences the rate at which fluid can be pumped for treatment, as well as the rate and direction of groundwater migration Influences the rate at which a plume of contaminants migrates and the rate at which fluid can be pumped for treatment Influences the quantity of fluid that can be obtained by pumping Influences the quantity of fluid that can be obtained by pumping Influences the quantity of contaminant that remains in the subsurface after pumping
Source: Adapted from National Research Council (NRC), Water Science and Technology Board. 1994. Alternatives for Groundwater Cleanup. Washington, DC. With permission.
36.2.3 Step 2. Define the Goal of Groundwater Remediation The next step in designing a groundwater remediation system is to define the goal of remediation. This step involves: (1) identifying remediation technologies that could possibly be used to remediate the contaminated groundwater; then (2) screening the list to identify remediation technologies that could be
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The Handbook of Groundwater Engineering TABLE 36.4 Summary of the Mechanisms Influencing the Fate of Contaminants in the Environment Process
Environmental conditions
Movement (i.e., advection)
Retention (physical processes affecting transport) Reaction (chemical processes affecting transport)
Water flow rate Formation permeability Water motion Gravity Surface tension Soil/Sediment Organic matter content Sorptive capacity pH Redox status Microbial communities
Contaminant Amount of material Physical state Solubility Viscosity Aqueous solubility Ionic character Chemical transformation Biodegradability
Source: From USEPA. September 1989. Seminar Publication — Transport and Fate of Contaminants in the Subsurface. EPA/636/4-89/019. Washington, DC.
successfully implemented at the site; and finally (3) selecting an appropriate remediation goal based on the remedies that can be successfully implemented. A summary of remediation technologies that could be used is presented in Table 36.6. Candidate goals for remediating contaminated groundwater are described in Section 36.1.2; candidate remediation approaches that correspond to these goals are presented in Table 36.7. For sites where it is demonstrated that remediation is needed, the remediation goal should be developed with as complete an understanding as possible of the goals that are actually attainable. This begins with an understanding of the difficulty of remediating or restoring groundwater quality in certain hydrogeologic settings, as summarized in Table 36.5. Then, the possibility of achieving the remediation goal should be evaluated based on past experience with similar problems in similar hydrogeologic settings. For example, the likelihood of success of groundwater restoration (based on the profession’s documented experience in achieving health-based remediation goals) is illustrated in Table 36.8, which was developed based on an analysis of the information presented in Table 36.2. As shown in Table 36.8, it is currently feasible to remediate some types of sites to health-based standards (e.g., homogeneous aquifers contaminated with dissolved, mobile contaminants, as shown in “Group A” in Table 36.8), but not other types of sites (e.g., heterogeneous or fractured rock aquifers contaminated with non-aqueous phase liquid contaminants “Group C” in Table 36.8). As a further consideration, restoration of groundwater to original quality represents a significant financial burden to the nation, as illustrated in Table 36.9. Regardless of the goal selected, it should be noted that, as stated by the NRC (1994), “The attainment of zero contaminant concentration as an outcome for groundwater remediation should be recognized as an unattainable goal no matter how far cleanup technologies advance in the future.” The difficulty of restoring groundwater quality at some sites is also addressed by the USEPA in its document entitled, Guidance for Evaluating the Technical Impracticability of Ground-water Restoration (1993). In this document, the USEPA identifies several hydrogeologic settings (based on information in Table 36.5) in which, based on the USEPA’s experience, groundwater quality likely cannot be restored to background conditions. Once the remediation goal has been selected and feasible remedies have been identified that could be implemented at the site, the groundwater professional should screen the list of candidate remedies to those that, based on experience, can be expected to achieve the remediation goal. These remedies should then be further evaluated during Step 3.
36.2.4 Step 3. Screen Candidate Remedies After a list of feasible candidate remediation technologies has been prepared, the remedies should be screened to identify the remedy that can most efficiently and cost effectively achieve the remediation goal. Screening involves evaluating the likely effectiveness and cost of the feasible remediation technologies
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36-9
Examples of Factors Affecting Groundwater Remediation
Characteristic
Generalized remediation difficulty scale ———————————
Less difficult
More difficult
Nature of release
Small volume Short duration Slug release
——————————— ——————————— ———————————
Large volume Long duration Continual
Biotic/Abiotic decay potential Volatility Contaminant retardation (sorption) potential Tendency for larger plume Difficulty removing contaminants
High
Chemical properties ———————————
Low
High
———————————
Low
High
———————————
Low
Low
———————————
High
Aqueous, gaseous Small
Stratigraphy
Simple geology, (e.g., planar bedding)
Texture of unconsolidated deposits Degree of heterogeneity
Sand
———————————
Homogeneous (e.g., well-sorted sand)
———————————
Hydraulic conductivity Temporal variation Vertical flow
Shallow
High (10−2 cm/sec) Little/None Little
——–
Contaminant distribution Sorbed ——– LNAPLs ———————————
Contaminant phase Volume of contaminated media Contaminant depth
——————————— Geology ———————————
Hydraulic/Flow ——————————— ——————————— ———————————
——–
DNAPLs Large Deep Complex geology, (e.g., interbedded and discontinuous strata, fractured media) Clay
Heterogeneous (e.g., interbedded sand and silts, clays, fractured media, karst) Low (10−6 cm/sec) High large downward flow component
Source: From USEPA. 1993. Guidance for Evaluating the Technical Impracticability of Ground-Water Restoration. EPA-540R-93-080. Washington, DC.
and selecting a remedy for detailed design based on the results of this evaluation. Three valuable steps in performing the evaluation are described below. • Prepare Preliminary Conceptual Design for Each Candidate Remedy. By preparing a conceptual design, the effectiveness and cost of the remedy can be evaluated, as described below. Developing and implementing design criteria can be an effective way to focus the conceptual design effort on the keys to success for the project. Design criteria are guidelines to be used during design that, if achieved, will likely result in successful performance of the remediation system. These criteria are defined by the owner, engineer, and the operator. Design criteria should consider
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The Handbook of Groundwater Engineering Summary of Commonly Used Groundwater Remediation Technologies Residual groundwater concentration
Alternative technology Source remediation Conventional pump-and-treat Vacuum extraction and bioventing Air sparging (vertical or horizontal wells) In situ bioremediation-hydrocarbons In situ bioremediation-chlorinated solvents Cosolvent and surfactant flushing Steam stripping Resistivity heating In situ thermal desorption In situ chemical oxidation In situ bioremediation-metals Monitored natural attenuation Plume remediation Conventional pump and treat Air sparging (vertical or horizontal wells) In situ bioremediation- hydrocarbons In situ bioremediation-chlorinated solvents In situ reactive barriers Monitored natural attenuation
Residual sorbed concentration in source area
Cleanup timea
Number of peer-reviewed publicationsb
Low to medium NA Low to medium
Medium to high Low to medium Low to medium
Long Short Short to medium
Some Some Limited
Low to medium Low to medium
Low to high Low to high
Short to medium Medium to long
Some Some
Low to medium Low to medium Low to medium Low to medium Low to medium Low to medium Low to medium
Low to medium Low to medium Low to medium Low to medium Medium to high Low to high Low to high
Short to medium Short Short Short Medium Medium to high Long
Some Some Limited Some Some Limited Limited
Low Low to medium
Medium to high Low to medium
Long Medium to long
Many Some
Low to medium Low to medium
Low to high Low to high
Medium to long Medium to long
Many Many
Low Low to medium
NA Low to medium
Long Long
Some Many
Note: A “low” residual concentration and “medium” cleanup time reflect relatively good performance, while a “high” residual concentration and “long” cleanup time reflect much less effective performance. “NA” denotes that the technology is not applicable to this situation. Cost of the technology and feasibility for different situations are not addressed in this table but should be carefully evaluated before selecting a technology. a Because few cases of achieving cleanup goals have been reported, these qualitative assessments reflect the judgment of NRC. b “Limited” indicates that very little information about this technology is available in peer-reviewed publications, while “some” indicates a greater availability of information. Source: Modified from National Research Council (NRC), Water Science and Technology Board. 1994. Alternatives for Groundwater Cleanup. Washington, DC. With permission.
constructability concerns, performance limitations of the technology, budget constraints, operation and maintenance requirements, and regulatory requirements. The candidate remedies can be compared by examining the results of these evaluations and selecting remedies that can most costeffectively achieve the remediation goal. Conceptual designs should then be prepared that address the design criteria that are relevant at the conceptual design stage. • Evaluate Effectiveness of Conceptual Designs. The effectiveness of the designs in meeting the remediation goal should be evaluated next. This evaluation can be performed objectively (e.g., by modeling the performance of the remediation system as described in Chapter 18 and Chapter 19 of this handbook) or subjectively (using the information on remedies presented in Table 36.6 and the information on remediation feasibility presented in Table 36.8). Also, the time required to achieve the remediation goal should be estimated for use in the subsequent cost evaluation. • Evaluate Cost of Remedies. The cost of each remedy should be estimated. A good reference for remediation cost estimating techniques is presented in USEPA (2000a). In particular, the presentworth value of each remedy should be calculated, considering both capital and long-term operation and maintenance costs, to provide a consistent basis for comparing the costs of the candidate remedies.
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TABLE 36.7 Candidate Groundwater Remediation Goals and Corresponding Remediation Approaches Examples of candidate remediation approaches
Remediation goal Groundwater restoration
Nondegradation
Return aquifer to health-based standards
Apply technology-based standards
Implement restricted-use policies Containment
Monitored natural attenuation Bioremediation Combinations of conventional remediation approaches Source removal Conventional pump-and-treat Bioremediation Soil vapor extraction/Air sparging Source removal Conventional pump-and-treat Bioremediation Soil vapor extraction/Air sparging Phytoremediation Electrokinetics Solvent extraction Thermal desorption Deed restrictions Local ordinances Physical barriers Hydraulic barriers Capping Reactive barriers
Source: Adapted from National Research Council (NRC), Water Science and Technology Board. 1994. Alternatives for Groundwater Cleanup. Washington, DC. With permission.
TABLE 36.8
Likelihood of Success of Groundwater Restoration Contaminant chemistry
Mobile, dissolved (degrades/ volatilizes)
Hydrogeology Homogeneous, single layer Homogeneous, multiple layers Heterogeneous, single layer Heterogeneous, multiple layers Fractured
Mobile, dissolved
Strongly sorbed, dissolved (degrades/ volatilizes)
Strongly sorbed, dissolved
Separate phase LNAPL
Separate phase DNAPL
A (1)
A (1-2)
B (2)
B (2-3)
B (2-3)
B (3)
A (1)
A (1-2)
B (2)
B (2-3)
B (2-3)
B (3)
B (2)
B (2)
B (3)
B (3)
B (3)
C (4)
B (2)
B (2)
B (3)
B (3)
B (3)
C (4)
B (3)
B (3)
B (3)
B (3)
C (4)
C (4)
Note: Group A represents types of sites for which cleanup of the full site to health-based standards should be feasible with current technology. Group C represents types of sites for which full cleanup of the source areas to health-based standards will likely be technically infeasible. Group B represents sites for which the technical feasibility of complete cleanup is likely to be uncertain. The numerical ratings indicate the relative ease of cleanup, where 1 is easiest and 4 is most difficult. Adapted from National Research Council (NRC), Water Science and Technology Board. 1994. Alternatives for Groundwater Cleanup. Washington, DC. With permission.
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The Handbook of Groundwater Engineering TABLE 36.9 Costs of Various National Policies for Hazardous Waste Site Remediation Present value of resource cost (billions of 1991 U.S. dollars) National policy
Lower bound
Best guess
Upper bound
Current policya
180 140 360
280 180 440
390 260 630
Less stringent policyb More stringent policyc
Note: This table converts the figures in Russell et al. (1991) to present value by assuming that costs are prorated equally each year for a 30-year time period and that the discount rate is 4 percent. a According to Russell et al. (1991), current policy means “the set of principles and practices for hazardous waste remediation that are inferred to be in place in the period 1988–91 when the experience base and data for this study were collected.” b According to Russell et al. (1991), less stringent policy means relying more on containment and less on full cleanup. c According to Russell et al. (1991), more stringent policy means application of more intensive treatment technologies and reduced burden on future generations. Source: Adapted from National Research Council (NRC), Water Science and Technology Board. 1994. Alternatives for Groundwater Cleanup. Washington, DC. With permission.
For remedies that require more technically complex remediation technologies, the process of screening candidate remedies tends to incorporate a more gradual scale up to a full-scale remedy through bench studies and pilot tests. Bench studies are often employed during the early stages of the screening process. For example, if bioremediation were to be considered as a remedy, a bench study would be conducted to determine whether native microbes present in the aquifer at the site are capable of degrading the contaminants. Then, pilot studies are used during the latter stages of technology screening, or even after a remediation technology has already been selected, to provide confirmation that a particular approach will be effective for the specific site and to obtain additional data that can be used during the detailed design stage (Section 36.2.5).
36.2.5 Step 4. Prepare Detailed Design After the preferred remedy has been selected, a detailed design of the approach should be prepared that is suitable for construction of the system. Recommendations for design of specific elements of some of the more commonly used groundwater remediation systems are presented in Section 36.3, Section 36.4, and Section 36.5. USEPA (1995a) provides an overall framework for developing a remedial design. It is recommended that detailed calculations be performed to demonstrate that each of the design criteria is satisfied. Also, it is recommended that the ability of the design to mitigate adverse impacts to human health or the environment be demonstrated; ideally, this is accomplished by performing a risk assessment (as described in Section 36.1.3) for the conditions that will exist during and after operation of the remediation system. An effective remedy will achieve the remediation goal, mitigate the risk of exposure to contaminated groundwater, and provide reliable service throughout the design life of the system. Like all engineering design activities, remedial design is an iterative process. Therefore, the design should be critiqued several times to identify improvements that can be made to enhance the performance or reduce the cost of the system. Such an evaluation could be performed by subjecting the preliminary design to a detailed review by: (1) a peer reviewer who is qualified in the technology being considered and who has not been an integral part of the design process (to provide an unbiased, critical evaluation of the design); (2) a contractor (to provide an evaluation of the constructability of the design); (3) a risk
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assessment professional (to give an indication of the ability of the design to meet the remedial action objectives for mitigation of risks to human health or the environment); or (4) an operator of a similar system (for a value-engineering review or an evaluation of the potential costs or difficulties in operating the proposed system). Although such reviews may appear to be somewhat time consuming, they frequently result in valuable input that can improve the likelihood that the design criteria will be met. Also, because such reviews reduce the possibility of failure of the remediation system, they can be an effective component of a liability and loss prevention program.
36.2.6 Step 5. Implement the Design After the design has been completed and reviewed, it must be implemented, which involves constructing and operating the system. The first step in constructing the system is deciding how and by whom the system will be constructed. There are several methods of arranging to construct a remediation system, including: (1) construction by the owner; (2) soliciting competitive bids from independent contractors qualified to perform the work; (3) negotiating a contract with an independent contractor; or (4) retaining a design/build contractor. For the last three approaches to construction, a detailed set of bid documents should be prepared that can be used by the bidder to prepare a responsive bid. The advantages of procuring a contractor through a competitive bid process include: (1) a generally lower construction cost, resulting from the competitive nature of the bid process; (2) well-defined roles of each party to the construction contract and well-defined terms of the construction contract; and (3) documentation of the information that the contractor used to prepare its bid, which can be valuable if additions or subtractions to the contract scope of work and budget are required. The disadvantages of competitively bidding work are: (1) the formality required, which involves a preparation of detailed plans and legal documents, sometimes at a significant cost; and (2) difficulty in factoring in “subjective” criteria in the bid evaluation, such as the contractor’s qualifications for performing the work and the contractor’s past performance on similar projects.
36.2.7 Step 6. Confirm the Effectiveness of the Design The final step of a remediation program is confirmation of the effectiveness of the system in achieving the remediation goal. The effectiveness of the design can be evaluated simply by reviewing the data from a performance-monitoring program (as described in Chapter 35) and assessing whether or not the remediation goals and the performance criteria are being satisfied. The effectiveness of the design should be evaluated both during the startup of operations (if the system contains components that require operation and maintenance) and at specified time intervals after startup. As an example of confirming the effectiveness of a groundwater pump-and-treat system design that is intended to prevent migration of contaminants beyond a line of extraction wells, the system could be monitored to ensure that the groundwater downgradient of the extraction wells does not exceed design cleanup criteria; similarly, if the system is designed to remove contaminants in the aquifer, then groundwater collected by the removal wells could be tested to confirm that groundwater quality is improving as predicted. As a subsequent step after evaluating the performance of the remediation system, the system should be modified as needed to improve the system’s ability to achieve the remediation goal and performance criteria. As described in Section 36.6, the performance-monitoring program should contain criteria for “shutting off ” the system (as verified using data collected during performance monitoring); also, the performance-monitoring program should contain criteria for reevaluating the adequacy of the design if the system has failed to meet the remedial design criteria.
36.3 Hydraulic Containment of Groundwater 36.3.1 Overview There are many alternatives for providing hydraulic containment of groundwater. The most widely used features for containing groundwater are physical barriers and hydraulic barriers. Therefore, this section
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The Handbook of Groundwater Engineering TABLE 36.10
Types of Physical Barriers
Barrier type
Width (ft)
Maximum depth (apx) (ft)
Unit cost ($[1995]/sf)
Production rate per 10 hrs (sf)
Soil bentonite Cement bentonite Biopolymer drain Deep mixing DM structural Jet grouting Grout curtain Sheet piling Geochemical barrier
2–3 2–3 2–3 2.5 2.5 1.5–3 One row One sheet Varies
80 80 70 90 90 200 200 150 Hundreds
2–8 5–18 7–36 6–15 15–30 30–80 40–100 15–40 8–400
2,500–15,000 1,000–8,000 1,500–5,000 1,000–8,000 1,000–3,000 300–2,500 200–1,000 2,000–15,000 100–1,000
Source: From Rumer, R.R. and Mitchell, J.K. 1995. Assessment of Barrier Containment Technologies — A Comprehensive Treatment for Environmental Remediation Applications. National Technical Information Services, Springfield, VA.
is focused on physical barriers (Section 36.3.2) and hydraulic barriers (Section 36.3.3). Also, innovative hydraulic containment methods are described in Section 36.3.4. Recommended methods for performance monitoring of hydraulic containment features are summarized in Section 36.6.
36.3.2 Physical Barriers Physical barriers are vertical features in the ground that provide a barrier to groundwater flow. Physical barriers can be formed using a variety of materials and can be either nonselective (i.e., a barrier to the flow of all groundwater) or selective (i.e., a barrier to only the migration of target contaminants). In this section, only nonselective physical barriers are discussed; selective physical barriers (i.e., “permeable reaction barriers”) are described in Section 36.5.2.5. A list of several of the most commonly used physical barriers is presented in Table 36.10, along with their typical dimensions, range of unit costs, and approximate production (i.e., construction) rates. The oldest and most commonly used types of physical barriers are cutoff walls; several types are illustrated in Figure 36.3. Cutoff walls limit the migration of groundwater by forming a physical impediment to groundwater flow. The effectiveness of the wall is a function of its continuity, its resistance to degradation by contaminants in groundwater, and its resistance to physical degradation. Note that, because it impedes groundwater flow, the elevation of groundwater may rise (or “mound”) on the upgradient side of the barrier; to prevent overtopping or flanking of the barrier by contaminated groundwater, other controls may be needed, such as (1) groundwater extraction wells or trenches adjacent to the barrier to route mounded groundwater to a discharge point; or (2) permeable segments in the barrier to allow water to pass through controlled locations in the wall. Soil-bentonite slurry walls are, by far, the most common type of physical barrier used in geotechnical and environmental remediation projects. Slurry walls have been used in the U.S. since the 1940s. Construction of a slurry wall consists of installing a mixture of soil (or other material) and bentonite clay into a vertical trench to form a very low-permeability, vertical barrier to groundwater flow. A general approach for slurry wall construction is illustrated in Figure 36.4 and includes: (1) excavation of a narrow (i.e., about 2 to 3 ft, or 0.6 to 1 m, wide) vertical trench (if the unsupported trench could cave, then the trench should be temporarily supported using a bentonite slurry); and (2) placing the soil-bentonite mix in the slurry-filled trench in a manner that displaces the bentonite slurry and forms a continuous vertical wall of lowpermeability soil-bentonite material. A typical soil-bentonite mix contains about 2 to 4% bentonite clay, 20 to 35% water, 15 to 40% soil finer than the No. 200 U.S. standard sieve, and about 40 to 60% material coarser than the No. 200 U.S. standard sieve (Inyang, 1992). In many cases, the material excavated from the trench can be used as an economical source of the soil component of the soil-bentonite mix. Factors that must be considered in selecting a source for soil to be mixed with the bentonite include: (1) the grain-size
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a. Linear barrier
b. Arcuate barrier
Slurry wall
Slurry wall
Plume
Waste
c. Recillinear barrier Slurry wall
Plume
Ground water
Ground water
River
Waste
River
River
Waste
Plume
Ground water
Plan views of upgradient slurry walls for partial containment of buried waste and/or plume
a. Linear barrier
b. Arcuate barrier
Slurry wall Plume
c. Recillinear barrier
Slurry wall Plume
Waste
Ground water
Plume
Waste
Ground water
River
River
River
Waste
Slurry wall
Ground water
Plan views of downgradient slurry walls for partial containment of buried waste and/or plume
a. Circular perimeter
b. Rectangular perimeter
Waste
Waste
Slurry wall
Slurry wall
Plan views of waste totally enclosed by slurry walls
FIGURE 36.3 Examples of physical barrier configurations. (From GeoSyntec Consultants. 1994. Subsurface Barriers. Report to the United States Navy, Contract SBIR Topic N93-130. Atlanta, Georgia. 80 pages.)
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The Handbook of Groundwater Engineering
Soil-bentonite backfill
Emplaced backfill
Soil-bentonite backfill placed here
Excavated soil
Area of active excavation Bentonite-water slurry
Bentonite-water slurry
Backfill movement downslope Unexcavated soil
1
Emplaced backfill
Low hydraulic conductivity stratum
6 to 12 typical
Low hydraulic conductivity stratum
Overall operation
Backfilling schematic
FIGURE 36.4 Soil-bentonite slurry wall construction. (From GeoSyntec Consultants. 1994. Subsurface Barriers. Report to the United States Navy, Contract SBIR Topic N93-130. Atlanta, Georgia. 80 pages.)
10–2 Well graded coarse gradations (30–70% +20 sieve) w/10 to 25% NP fines
Permeability of SB backfill (cm/sec)
10–3 10–4 10–5
Poorly graded silty sand w/30 to 50% NP fines
10–6 10–7 10–8 10–9
Clayey silty sand w/30 to 50% fines 0
1
2
3
4
5
Bentonite by dry wight of SB backfill (%)
FIGURE 36.5 Permeability as a function of percent bentonite. (From GeoSyntec Consultants. 1994. Subsurface Barriers. Report to the United States Navy, Contract SBIR Topic N93-130. Atlanta, Georgia. 80 pages.)
distribution of the soil; (2) treatment and disposal costs for excavated trench soils that are contaminated; and (3) the chemical composition of the soil (e.g., soil that is contaminated with metals or VOCs could inhibit the ability of the bentonite to hydrate and, therefore, compromise the permeability of the wall). An excellent reference for design and construction of slurry walls is provided by Xanthakos (1979). The effectiveness of a soil-bentonite slurry wall in preventing flow through the wall is a function of: (1) the environment of the wall (i.e., the nature of the chemicals in groundwater to which the soil-bentonite mix will be exposed); (2) the percentage of bentonite clay used in the soil-bentonite mix (as illustrated in Figure 36.5); (3) the type and gradation of soil used typically measured as a percentage of the soil that is finer than the No. 200 U.S. standard sieve (as illustrated in Figure 36.6); and (4) the quality of wall construction. When designing a soil-bentonite slurry wall, laboratory hydraulic conductivity tests are typically performed on candidate mixtures of soil and bentonite clay, and the test results are used to select the proportions of soil and bentonite that will produce the desired in situ hydraulic conductivity.
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80
Minus #200 sieve (%)
70 Plastic fines
60
Non-plastic or low plasticity fines
50 40 30 20 10
0
10–9
10–8 10–7 10–6 SB backfill permeability (cm/sec)
10–5
10–4
FIGURE 36.6 Permeability as a function of soil fines content. (From GeoSyntec Consultants. 1994. Subsurface Barriers. Report to the United States Navy, Contract SBIR Topic N93-130. Atlanta, Georgia. 80 pages.)
Based on widespread experience with soil-bentonite slurry walls over the past half century, it is generally recognized that the lowest in-place hydraulic conductivity that can reasonably be achieved for a soilbentonite slurry wall is typically between 10−6 cm/sec and 10−7 cm/sec, with hydraulic conductivities in the lower end of this range attainable only under ideal circumstances and using excellent construction practices (GeoSyntec 1994). Finally, note that the performance of a soil-bentonite slurry wall can be adversely affected by exposure of the wall to VOCs, aqueous salts (such as those contained in seawater), or NAPLs. Sai and Anderson (1992) reported an increase of two to three orders of magnitude in hydraulic conductivity for soil-bentonite slurries that were permeated with the VOCs xylene and methanol. To improve the resistance of slurry walls to permeation by VOCs, some researchers are experimenting with the addition of activated carbon to the slurry.
36.3.3 Hydraulic Barriers The term hydraulic barrier is used to describe a feature that causes a depression in the piezometric surface of groundwater and acts as a barrier beyond which groundwater within the zone of influence of the barrier should not flow. Hydraulic barriers may be formed using trenches, wells, or other features that remove groundwater, thus depressing the potentiometric surface. Groundwater collection trenches and groundwater extraction wells, which are the most common types of hydraulic barriers, are described in this section. Groundwater Collection Trenches. Trenches can be installed in an aquifer to produce an induced hydraulic barrier by depressing the potentiometric surface of the aquifer. A typical groundwater extraction trench system is illustrated in Figure 36.7. During design, the designer must identify the depth to which the trench must be constructed to induce a hydraulic barrier. The depth of the trench should be carefully selected based on consideration of the seasonal variations in the elevation of groundwater, the location of contaminants (i.e., “floating” LNAPLs, dissolved constituents, or “sinking” DNAPLs), and the depth of contaminants in the aquifer. Trenches may be more cost-effective than wells for extracting groundwater if contaminants are located at a shallow depth below ground (i.e., less than about 50 ft [15 m]) and the aquifer materials are relatively easy to excavate (e.g., no excavation of bedrock). The depth of influence of a groundwater collection trench in an isotropic, homogeneous aquifer is illustrated in Figure 36.8 and
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36-18
The Handbook of Groundwater Engineering Groundwater flow direction
Contaminant source
Discharge to treatment system
Electrical/mechanical control panel (1 per sump) Soil trench backfill
Removal pipe Manhole/sump (typical)
Pump (typical) Gravel trench backfill Aquitard
FIGURE 36.7 Typical groundwater extraction trench system.
can be estimated using the equation (Zheng et al., 1988): D=
2S π
1/2 (36.1)
where S is defined by the following equation: S = 2a(h0 − hd )
(36.2)
and D is the depth of influence of the ditch (ft), a is equal to one half the width of the ditch (ft), h0 is the head in the aquifer beneath the ditch (ft), hd is the head in the ditch (ft), and i is the uniform water table gradient in the aquifer. The flow rate of groundwater to the trench per unit width of trench can be estimated using the following equation: Q = KiD
(36.3)
where Q is the volumetric flow to the trench (ft3 /sec), K is the hydraulic conductivity of the aquifer material, i is the uniform slope of the potentiometric surface in the aquifer, and D is the depth of influence of the trench calculated from Equation 36.3. Equation 36.1 and Equation 36.3 apply only to isotropic, homogeneous aquifers; for aquifers that contain vertical or horizontal variations in stratigraphy (e.g., clay lenses, sand seams, coarsening-with-depth deposits, etc.), or anisotropies, a more complicated model (see, for example, Chapter 18 and Chapter 19) may be needed. In such environments, the designer must be aware of the presence of such features and, if necessary, extend the depth or lateral extent of the trench to intercept contaminated groundwater that could flow through these features. Groundwater Extraction Wells. Wells can also be installed in an aquifer to induce a hydraulic barrier to groundwater flow. In fact, because most groundwater plumes are located at depths or in locations where collection trenches are not practical, groundwater extraction wells are more commonly used. A typical groundwater extraction well is illustrated in Figure 36.9. The radius of influence and depth of influence of a single well can be calculated based on the properties of the aquifer, the geometry of the well (i.e., depth and radius), and the pumping rate of the well. Analytical solutions are provided for several combinations
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General groundwater flow direction
Extraction trench
4 972
97 0
086
97
6
984
97
978
982
972
8
96
Vertical capture zone
Key Potential line (ft)
984
Groundwater flow direction
FIGURE 36.8 Vertical zone of influence of partially penetrating groundwater extraction trench. Radius of influence (r0)
Extracted groundwater
Grout
Depressed potentiometric surface Filter sand Wellscreen
Ho
Sediment trap Hw
Datum
FIGURE 36.9 Groundwater extraction well.
of these variables as summarized by Cohen and Miller (1983). The zone of influence of a single well in a homogenous, isotropic, confined aquifer having a non-zero gradient is illustrated in Figure 36.10 and can be estimated as (USEPA, 1994): W =
Q Ti
(36.4)
where W is the width of the zone of influence (ft), Q is the pumping rate (cfs) of the extraction well, T is the transmissivity of the confined aquifer (or the equivalent transmissivity of the unconfined aquifer) (sec−1 ),
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The Handbook of Groundwater Engineering w = Q/2T
+
Q 2Ti
Q Ti
Q 2Ti
w=0
y=0 sp
–
w = –Q/2T x=0
–
+
Sp = stagnation point
FIGURE 36.10 Single-well capture zone. (Data from USEPA. 1994. Monitoring the Performance of Groundwater Pump and Treat Systems. EPA/600/R-94/123. Washington, DC.)
and i is the hydraulic gradient (dimensionless). Zones of influence can be estimated for wells in unconfined aquifers using this equation by substituting Kb (where b is the full thickness of the unconfined aquifer at the pumping well) for T if drawdown is small compared to the thickness of the aquifer. More accurate estimates of capture zone geometry in unconfined aquifers can be made using numerical models. The value Q in Equation 36.4 can be estimated for fully penetrating wells in an unconfined, zero gradient aquifer, where drawdown is small compared to the depth of the aquifer, as (Bear, 1979): Q = πK
Ho2 − Hw2 ln(ro /rw )
(36.5)
where Q is the pumping rate (cfs), K is the hydraulic conductivity of the aquifer (ft/s), Ho is the hydraulic head at the limit of the zone of influence, Hw is the hydraulic head at the well (ft), ro is the distance to the limit of the zone of influence (ft), and rw is the radius of the pumping well screen (ft). The relationship between Q, Ho , Hw , ro , and rw is best estimated based on the results of a pump test, performed as described in Chapter 10 and Chapter 11. When evaluating the combined zone of influence of a network of extraction wells, the location of the stagnation point and the overlap of adjacent zones of influence should be carefully examined. For aquifers where the hydraulic gradient is steep, the path taken by water flowing toward the network of wells could pass between and beyond the network of wells. To minimize this problem, zones of influence should be overlapped significantly (e.g., wells should be spaced at a distance of approximately Q/(π Ti ) for two extraction wells and slightly greater for increasing numbers of extraction wells [USEPA, 1994]). The capture zone of a group of extraction wells is illustrated in Figure 36.11. To perform a more accurate estimate of the dimensions of the capture zones or to more accurately evaluate the possibility of groundwater flow past the induced barrier, a particle tracking groundwater model can be used, as described in Chapter 18 and Chapter 19.
36.3.4 Other Options for Hydraulic Containment Numerous alternative approaches to hydraulic containment have been developed over the past two decades. Some promising approaches are described below. • Horizontal drains (Cohen and Miller, 1983) induce a barrier to groundwater flow in a manner similar to trenches. With recent advances in horizontal “directional” drilling technologies, the accuracy of placement for horizontal wells has improved significantly. Horizontal drains may be
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36-21 Double-well capture-zone type curves 1500
Single-well capture-zone type curves 1000
(a) Y
Meters
500
0
Q/8U = 2000m 1600 1200 800 400 Regional flow X
1000
(b) Q/8U = 2000m 1600 1200 800
Y 500
400 X
Regional flow
0 –500 –500 –1000 –500
0
500
1000
1500
2000
–1000
2500
–1500 –500
0
Three-well capture-zone type curves 1500
1500
2000
2500
3000
Four-well capture-zone type curves
(d)
Q/8U = 1000m Y
1000
U Q/8
X
Regional flow
–500
–1000
–1000
500
1000
1500
2000
2500
200
3000
–1500 –500
Regional flow
X
0
–500
0
400
500
200
0
m 000 = 1 800 600
Y
400 500 Meters
1000
1500
(c)
1000
–1500 –500
500
0
500
1000
1500
2000
2500 3000
FIGURE 36.11 Capture zone of extraction well network. (From USEPA. 1994. Monitoring the Performance of Groundwater Pump and Treat Systems. EPA/600/R-94/123. Washington, DC.)
particularly useful in locations where access for excavation of a trench is not available (e.g., beneath a building or roadway). • Geomembranes (see Rumer and Mitchell, 1995) can be incorporated into vertical barriers (as shown in Figure 36.12) to provide an extremely low-permeability barrier to groundwater flow. Geomembranes offer excellent compatibility with subsurface contaminants and have highly uniform properties. However, for the barrier to perform properly, joints between adjacent geomembrane panels must be carefully made to prevent leaks at these locations. Some commonly used installation methods for geomembrane barrier walls are summarized in Table 36.11. • Wellpoints (see Driscoll, 1986) are discrete groundwater extraction devices that are typically jetted or driven into the ground. Wellpoints are useful in aquifer formations where a filter pack is not needed and where groundwater is at a relatively shallow depth. Typically, groundwater is extracted by suction or by using air-lift techniques from wellpoints; pumps are typically not used in wellpoint systems. A good discussion of other remediation techniques is presented in USEPA (2003), and a market evaluation of these technologies is presented in USEPA (2004b).
36.4 Design of Groundwater Extraction Systems 36.4.1 Introduction In Section 36.3, the design of groundwater extraction features was addressed, particularly groundwater extraction wells and trenches. In this section, the design of the other features of groundwater extraction
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100-mil HDPE geomembrane
Monitoring well
HDPE geomembrane
Existing grade
Soil permeated with bentonite
Grout monitoring layer HDPE geomembrane
Backfill (Excavated soil, SB, CB, SC, etc.)
Sand backfill
Clay layer or bedrock
3'0" 3'0"
FIGURE 36.12 Geomembrane lined cutoff trench. (From Rumer, R.R. and Mitchell, J.K. 1995. Assessment of Barrier Containment Technologies — A Comprehensive Treatment for Environmental Remediation Applications. National Technical Information Services, Springfield, VA.) TABLE 36.11 Method No. 1 2
3
4 5
Installation Methods for Geomembrane Barrier Walls
Method or technique
Geomembrane configuration
Trench support
Typical trench width mm (in.)
Trenching machine Vibrated insertion plate Slurry supported
Continuous
None
300–600 (12–24)
Panels
None
100–15 (4–6)
Panels
Slurry
600–900 (24–36)
Segmented trench box Vibrating beam
Panels or continuous Panels
None
900–1200 (36–48)
Slurry
150–220 (6–9)
Typical trench depth m (ft.)
Backill type
1.5–4.5 (5–15) 1.5–6.0 (5–20)
Sand or native soil
No limit, except for trench stability 3.0–9.0 (10–30) No limit
SB, SC, CB, SCB, sand or native soil Sand or native soil
Native soil
SB, SC, CB, SCB slurry
Key: SB = soil bentonite; SC = soil cement; CB = cement bentonite; SCB = soil cement bentonite. From Rumer, R.R. and Mitchell, J.K. 1995. Assessment of Barrier Containment Technologies — A Comprehensive Treatment for Environmental Remediation Applications. National Technical Information Services, Springfield, VA.
systems (e.g., pumps, controls, etc.) is presented. Groundwater extraction systems are a combination of both subsurface features (i.e., wells or trenches, which provide access to the contaminated groundwater) and above-ground features (which are used to regulate and monitor the extraction process). In Section 36.4.2 and Section 36.4.3, features of groundwater extraction well and trench systems are described. Then, in Section 36.4.4, methods for estimating the volume of water and time required to
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Check Throttle valve Pressure gauge valve Wellhead
Electrical/mechanical control panel
Cement grout or Bentonite seal Casing
Wellscreen Discharge column Pump Motor Well filter patch
Wellscreen Valve Filter piezometer Means for measuring operating level Height x Depth z Detail of air line for measuring operating level
FIGURE 36.13 Typical groundwater extraction system. (From USEPA. 1995b. Ground-Water and Leachate Treatment Systems. EPA/636/R-94/005. Washington, DC.)
remove a plume of contaminants from the subsurface by extraction are presented and critiqued. Finally, innovative groundwater extraction approaches are described in Section 36.4.5. Note that groundwater extraction is only one step of the two-step extraction/treatment process; treatment processes are described in Section 36.5.
36.4.2 Extraction Well Systems Groundwater extraction wells are typically more cost-effective for removing groundwater than trenches if the depth of contamination is great or if construction of the trench to the required depth in the aquifer is complex. In addition to extraction wells, extraction well systems contain the pumps, power sources, and controls that are needed to actually remove the contaminated groundwater from the aquifer and transmit it to the treatment or disposal system. A schematic diagram of a typical groundwater extraction well system is presented in Figure 36.13. The typical features of the system are briefly described below. • Well: The well provides access to the groundwater in the aquifer. The well may be designed using techniques as described in Section 24.3.2.1, except the design of an extraction well should be different from the design of a groundwater monitoring well to improve the long-term performance of the extraction well and minimize the need for maintenance. Design of groundwater extraction well components (i.e., wellscreen, filter pack, etc.) is addressed by Driscoll (1986). • Pump and Motor: The pump raises the groundwater from the aquifer to the above-ground wellhead assembly. The pump and motor should be selected according to the specific operating conditions that will exist during groundwater extraction; for example, some pumps are very well suited for operation under low-flow conditions, and other pumps are better suited for operation under high-flow conditions. In Table 36.12, information is presented for several types of pumps that are commonly used in groundwater extraction wells. • Wellhead: The wellhead is the above-ground assembly that contains the features used to transfer groundwater from the extraction well to the transmission piping. Typical components of the wellhead assembly include valves, fittings, flowmeters, pressure gauges, and sampling ports. The wellhead can be designed to be either in an above-ground shed or in a below-ground vault, depending on the use of the area surrounding the well.
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50–400 (15.2–121.9)
2. All electrical components are accessible, above ground 1. Same as shallow well turbine 2. Short pump shaft to motor 3. Quiet operation
1. Same as straight centrifugal except not suitable for pumping water containing sand or silt 2. Self–priming 1. Same as shallow well turbine
2. Usually reliable and good service life
1. Pumps water containing sand and silt
1. Same as shallow well jet 2. Well straightness not critical
1. Pumps water containing sand and silt 2. Especially adapted to low capacity and high lifts 1. High capacity at low heads 2. Simple operation
Advantages
Source: From Corbitt, R.A., editor. 1990. Standard Handbook of Environmental Engineering. McGraw–Hill, New York. With permission.
a Practical suction lift at sea level. Reduce lift 1 ft for each 1000 ft above sea level.
(30.5–243.8)
(15.2–91.4)
N/A (impellers submerged) N/A (pump and motor submerged)
100–800
100–200 (30.48–45.72)
a. Vertical line shaft turbine (multistage) b. Submersible turbine (multistage)
28 (8.5)
28 (8.5) max.
(30.5–45.7)
100–150
80–150 (24.4–45.7)
80–150 (24.4–45.7)
100–2,200 (30.5–670. 6)
50–300
(3 –6.1)
36–120 (7.62–36.58) below ejector 10–20
15–20 (4.57–6.10) below ejector
20 ft (6.10) max.
15–20 (4.6–6.1) below ejector 15–20 (4.6–6.1) below ejector
22–36 (6.7–7.6)
Usual pressure heads ft (m)
Deep well
3. Centrifugal Shallow well a. Straight centrifugal (single stage) b. Regenerative vane turbine type (single impeller)
b. Deep well
2. Ejector a. Shallow well
22–36 (6.7–7.6)
Practical suction lifta ft (m)
Usual well-pumping depth ft (m)
Groundwater Extraction Pump Information
1. Positive displacement
Type of pump
TABLE 36.12
1. Repair requires pulling from well 2. Sealing of electrical equipment from water vapor critical 3. Abrasion from sand
1. Efficiency depends on operating under design head and speed 2. Requires large, straight well
1. Same as straight centrifugal except maintains priming easy
2. Efficiency depends on operating under
1. Loses prime easily
1. Same as shallow well jet 2. Lower efficiency, especially at greater lifts
1. Capacity reduces as lift increases 2. Air in suction or return line will stop
1. Subject to vibration and noise 2. Maintenance cost may be high
Disadvantages
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• Transmission Piping: The transmission piping is used to transmit the extracted groundwater from the wellhead to the treatment or discharge location. The following should be considered when designing the piping: (1) the required quantity of flow (as described by Corbitt [1990]); (2) damage due to overburden stresses (using analysis techniques described by Merritt [1989]), including stress caused by vehicles if appropriate; (3) resistance of the piping to degradation by the contaminants in groundwater; and (4) constructability of the piping system (note that difficult-to-construct systems are less likely to be well constructed). • Power Source: A source of power is typically needed for operation of the extraction system components. Power can be provided by electricity, compressed air, solar energy, or by natural gas. Local building codes should be checked to identify any specific requirements for design of electrical components of the system. • Electrical/Mechanical Control Panel: The control panel contains the electrical controls (e.g., alarms, programmable logic controls, etc.) for the extraction system. Functions that are typically controlled at a panel include pump cycle time, pump temperature, monitoring for alarm conditions, and transmittal of the data collected at the wellhead (e.g., groundwater elevation, pump flow rate, etc.) to a central processing unit. Control systems often incorporate remote monitoring and/or control components that can help to optimize system O&M. • Discharge Point: The discharge point is the feature at which the extracted groundwater is transferred to either the treatment system or the ultimate discharge point. It is recommended that the following factors be considered when designing a groundwater extraction system (Driscoll, 1986): • Because of the high quantity of groundwater that flows through an extraction well, very durable materials (such as stainless steel wellscreen) should be specified, and the open area of the well should be maximized, but carefully balanced against the strength requirements of the wellscreen. • The chemical compatibility of each component of the extraction, transmission, and pump systems with the contaminated groundwater should be carefully examined before the final selection of the extraction system components and materials. • The health and safety of the well installation crew should be considered when developing the plan for installation of the groundwater extraction wells (the well installer should be required to prepare a health and safety plan for well installation activities). • The impact of naturally occurring compounds in extracted groundwater on the durability and performance of the extraction system components should be evaluated, including the effects of low and high pH (a pH significantly lower than 7 indicates acidic, possibly corrosive conditions), iron (as little as 0.36 mg/l can cause fouling of a wellscreen or groundwater treatment system), hydrogen sulfide (as little as 1 mg/l can be corrosive), dissolved solids (>1000 mg/l can cause electrical corrosion), carbon dioxide (>50 mg/l can produce carbonic acid and result in corrosive conditions), and encrusting conditions (which are typically caused by conditions of pH > 7.5, hardness (as CaCO3 ) > 300 mg/l, iron > 0.5 mg/l, or manganese > 0.2 mg/l).
36.4.3 Extraction Trench Systems Groundwater extraction trenches will likely be more cost-effective than extraction wells if the depth of contamination is relatively shallow and when it is relatively simple to install a trench to the required depth. Before beginning detailed design of the extraction trench system, the groundwater professional should have already identified the depth of the trench and the location where the trench must be installed (using techniques described in Section 36.3.3). In addition to an extraction trench, an extraction trench system consists of the pumps, power sources, and controls that are needed to actually remove the contaminated groundwater from the trench. A schematic diagram of a typical groundwater extraction trench system is presented in Figure 36.7. The typical features of the system are briefly described below.
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• Trench: Trenches used for extraction of groundwater may be installed using any of a number of methods (e.g., backhoe, slurry trench backfilled with aggregate, biodegradable slurry trenches, trench machines that install the pipe in a single operation, etc. Backfill materials used in most types of groundwater extraction trenches include collection piping and aggregate; these materials should be designed to withstand degradation by the chemicals in groundwater that they will be exposed to and to resist damage caused by the stresses that they would be exposed to. Design of plastic pipes (which are typically used in extraction trenches because of their resistance to chemical degradation) is addressed by Merritt (1989). • Pump: The pump should be designed using the criteria presented in Section 36.4.2 for extraction well pumps. Because groundwater extraction trenches are typically several feet wide, large-diameter sumps can be placed in the trench, which can accommodate relatively large pumps. Large pumps can be designed to be resistant to clogging by soil particles, typically have a much longer service life, and are typically more reliable and less costly to maintain than smaller pumps. A sump should be located at each low point in the trench. • Transmission Piping, Power Source, Control Panel, Discharge Point: These features may be designed using the recommendations presented for extraction well systems in Section 36.4.2.
36.4.4 Time Required to Extract a Plume of Contaminated Groundwater
Pump
In this section, the concept of restoring an aquifer to its useful purpose and the reasonableness of restoration as a cleanup goal are addressed. Aquifer restoration is based on the concept that the quantity of groundwater that must be removed to restore the aquifer can be calculated based on the physical properties of the aquifer. If there were no continuing source of contamination and if contaminated groundwater flowed uniformly unimpeded to the extraction wells or trench, then the time required to “restore” the aquifer could be estimated simply by dividing: (1) the distance from the farthest part of the plume of contaminated groundwater to the extraction wells or trench (ft) by (2) the average linear groundwater flow velocity (ft/day). The volume of groundwater pumped under this scenario would be equal to the cleanup time (as calculated above) times the combined pumping rate of all of the groundwater extraction features (Figure 36.14). Experience has shown (NRC, 1994) that, in nearly all cases, other factors affect the time and the quantity of groundwater that must be extracted to remediate a contaminated aquifer. Some of the more significant of these other factors are sorption, hydrolysis, cosolvation/ionization, volatilization/ dissolution, complexation, oxidation/reduction, and biodegradation, each of which may increase or decrease the time required On Off
t1
t2
t3
t4
t5
t6
t7
t8
Concentration
Max
0 Time Residual contamination
FIGURE 36.14 Use of a pulsed pumping scheme to maximize reduction of contaminant concentration. (From Keely, J.F. 1989. Performance of Pump-and-Treat Remediations, EPA Superfund Groundwater Issue, EPA/540/4-89/005. Washington, DC.)
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36-27
Partitioning Characteristics for Selected Chemicals
Chemical Aldrin Benzene DDT Tetrachloroethene (PCE) Trichloroethene (TCE) Vinyl chloride
Water solubility (mg/l)
Vapor pressure (torr)
Henry’s Law constant, KH (atm-m3 /mol)
Organic carbon partition coefficient, Kow (unitless)
1.7 × 10−2 1.8 × 103 2.5 × 10−2 2.0 × 102 1.5 × 103 8.8 × 103
6.0 × 10−6 9.5 × 10−1 1.6 × 10−1 1.9 × 101 7.3 × 101 3.0 × 103
1.7 × 10−4 5.6 × 10−3 1.6 × 10−6 1.8 × 10−2 1.0 × 10−2 2.7 × 10−2
5.5 2.1 6.4 3.4 2.4 1.4
Source: From USEPA 2004c. Superfund Chemical Data Matrix. Washington, DC.
for remediation. A concise discussion of these processes and their impact on remediating a contaminated aquifer is presented in USEPA (1989). Sorption typically has a significant impact on remediation, although other factors could have a greater impact depending on the specific site features and the particular contaminants that are present in groundwater. Sorption is described in Chapter 18. In general, sorption is the dual process of: (1) adsorption of dissolved contaminants in groundwater to the surface of soil particles, and (2) subsequent desorption of the contaminants from the soil particles when equilibrium conditions in the aquifer change. As equilibrium conditions change in the aquifer, “partitioning” of contaminants between the dissolved phase and the solid (i.e., adsorbed) phase changes, causing contaminants to either sorb to soil particles from groundwater or to desorb from soil particles to groundwater. Contaminants become sorbed to soil particles as a result of electrochemical forces (i.e., either ion exchange reactions or van der Waals forces) between the soil particles and the dissolved contaminants. Partitioning coefficients for some common organic contaminants are presented in Table 36.13. Ions that have a high valence charge (e.g., Cr+6 , Al+3 ) and molecules that are either large (e.g., chlorine-based compounds, such as TCE) or long-chained (e.g., polynuclear hydrocarbons) tend to sorb strongly to soil particles. Because desorbed contaminants can adversely impact groundwater quality, aquifer materials having sorbed contaminants act as a continuing “source” of groundwater contamination, allowing uncontaminated groundwater that flows past the sorbed contaminants to become contaminated until all of the sorbed material has been desorbed. There are numerous models available for evaluating the time required to remediate an aquifer for which the effects of sorption are significant. The models range from simple (e.g., the batch-flush model using simple hydraulic “pore-volume” approaches, or advective-dispersive approaches) to complex (e.g., finite-element models incorporating data from bench-scale tests, pilot tests, etc.). A simple and reasonably accurate analytical method for estimating the time and quantity of extracted groundwater required to remediate an aquifer is the batch-flush model. The batch-flush model is based on the ideal assumptions that: (1) upon becoming contaminated, groundwater is perfectly mixed within the aquifer; and (2) sorption is linear, reversible, and rapid. The analysis does not account for nonhomogeneities or anisotropies within the aquifer, dispersion, or any other mechanism of contaminant transport described in Chapter 18 and Chapter 19. The batch-flush approach is based on the explicit, finite-difference approximation of the one-dimensional differential equation for groundwater transport, which is: Vo
Vo dS dC +ρ = −QC dt n dt
(36.6)
where C is the concentration of the contaminant in water (mg/l), S is the sorbed-phase concentration of the contaminant (mg/l), Vo is the volume of contaminated water (i.e., the pore-volume water) (m3 ), ρ is the bulk density of the porous media (g/m3 ), n is the effective porosity (dimensionless), Q is the volumetric groundwater extraction rate (m3 /sec), and t is time (sec). Because sorption is linear, reversible, and rapid,
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S can be substituted with KdC1 , where Kd is the soil-water partitioning coefficient. Finally, substituting and rearranging gives the equations:
Ct Tt = R − ln Co tt =
Vo Tt Q
(36.7)
(36.8)
where Co is the initial concentration of contaminant in the aquifer, Tt is the number of pore volumes that must be extracted to “restore” the aquifer to the desired cleanup concentration (Ct ), and tt is the time required to achieve Ct . In Equation 36.9, the term R is known as the retardation factor and is defined as: R =1+
ρ Kd n
(36.9)
where ρ, n, and Kd are as previously defined. Values of Kd may be measured in the laboratory; however, because the value of Kd is primarily a function of sorption to organic material, a useful approximation of Kd can be found using the equation: Kd = Koc × foc
(36.10)
where Koc is a proportionality constant (which can be estimated based on the octanol-water partitioning coefficient, Kow , of the contaminant) and foc is the fraction of organic carbon in the aquifer soils. Estimates of Koc for several common organic contaminants are provided in Table 36.13. Because desorption is a function of the ratio of the concentration of sorbed contaminant to the concentration of dissolved contaminant, sorbed contaminants could be expected to desorb indefinitely, which (depending on the desired cleanup concentration, Ct ) could make it impossible to restore groundwater quality in a reasonable period of time, if at all. Batch flush models are useful for estimating cleanup times for simple aquifer systems in which sorption is nearly linear. However, the model typically underestimates cleanup times because it does not account for any of the following: (1) heterogeneities; (2) continuous releases from a source of contamination; (3) the presence of separate-phase contaminants; or (4) the effects of nonlinear sorption. These limitations also apply to models that are more complex than the batch flush model. Because of the effects of sorption, the cost to clean up an aquifer to a very low level of contamination can be significantly greater than the cost to achieve a slightly higher level of contamination; an example of this problem is shown in Figure 36.15 and in Table 36.14, which illustrates groundwater quality as a function of the number of pore volumes removed for a simple pump-and-treat groundwater remediation system in a homogeneous sand aquifer. Remediation cost can be expected to increase substantially as the retardation factor increases (as shown in Figure 36.16), and a substantial additional cost can be expected for achieving very high cleanup efficiencies (as shown in Figure 36.17 and Table 36.14). If it is found that the groundwater remediation goal cannot be achieved through extraction, then either a different groundwater remediation goal should be selected or a complementing remediation technique should be considered to enhance remediation of groundwater.
36.4.5 Other Groundwater Extraction Approaches There are many groundwater extraction approaches available to the groundwater professional in addition to vertical wells and trenches, including both innovative approaches for removing groundwater and approaches that enhance the extraction of contaminants from the subsurface. Other groundwater extraction techniques include the use of horizontal wells and wellpoints. Some of the more promising innovative approaches to enhance extraction efficiency include pneumatic hydraulic fracturing
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1
Relative concentration
0.8 Field experiment Batch-flush model Hydraulic (advection only)
0.6
Ideal-advection dispersion
0.4
0.2
0
0
5
10 15 20 Number of pore volumes
25
30
FIGURE 36.15 Elution curve for diethylether. (From Brusseau, M. 1996. Evaluation of Simple Methods of Estimating Contaminant Removal by Flushing. Groundwater, p. 19–22. With permission.) TABLE 36.14 Impact of Cleanup Goal on Cost of a Conventional Pump-and-Treat System Percent removal required 80 90 99 99.9 99.99
Calculated years to achieve goal
Present worth
15 21 42 63 84
$ 2,800,000 $ 3,360,000 $ 4,750,000 $ 5,600,000 $ 6,000,000
Source: Adapted from National Research Council (NRC), Water Science and Technology Board. 1994. Alternatives for Groundwater Cleanup. Washington, DC. With permission.
(i.e., fracturing subsurface media using water pressure or explosives to increase the permeability of the media and the groundwater extraction efficiency), flushing (i.e., reinjecting treated groundwater upgradient of the source area to increase the hydraulic gradient toward the extraction feature), surfactant flushing or chemical extraction (i.e., flushing using surfactants or other chemicals that are designed to increase the mobility or solubility of the contaminants in the aquifer), electroacoustical decontamination (i.e., use of electrokinetic and acoustical waves to reduce surface tension and viscosity of separate-phase contaminants, increasing their mobility and the opportunity to extract them), and steam extraction (i.e., injection of steam into the aquifer to either decrease the viscosity of a contaminant or to volatilize contaminants). When evaluating reinjection techniques that involve the use of chemicals, the groundwater professional should be careful to evaluate the potential adverse impact of the chemicals, which may be toxic, on human health and the environment. When evaluating groundwater extraction approaches, separate attention should be given to extraction of NAPLs. Because they represent a significant source of potential contamination, removal of NAPLs can significantly decrease the amount of time required to achieve a groundwater remediation goal using pumpand-treat techniques. Dual-phase pumping approaches can be effective for removing both LNAPL and DNAPL products; examples of dual-extraction systems for LNAPL and DNAPL products are illustrated in Figure 36.18.
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6,000,000 5,000,000 4,000,000 3,000,000 2,000,000
99.9% removal 90% removal
1,000,000 0 1
2
3
4
5 6 7 Retardation factor
8
9
10
FIGURE 36.16 Cost of pump-and-treat system as a function of the retardation factor of the contaminant. (Adapted from National Research Council (NRC), Water Science and Technology Board. 1994. Alternatives for Groundwater Cleanup. Washington, DC. With permission.)
10,000,000 9,000,000
Present worth in dollars
8,000,000 7,000,000 6,000,000 5,000,000 4,000,000 3,000,000 2 percent discount rate 3.5 percent discount rate 5 percent discount rate
2,000,000 1,000,000 0 0
90 99 99.9 Percent of contaminant removed
99.99
FIGURE 36.17 Cost of pump-and-treat system as a function of the cleanup goal. (Adapted from National Research Council (NRC), Water Science and Technology Board. 1994. Alternatives for Groundwater Cleanup. Washington, DC. With permission.)
36.5 Treatment of Contaminated Groundwater 36.5.1 Introduction There are many techniques available for treatment of contaminated groundwater. Over the past 20 years, a large number of groundwater treatment techniques has been developed; these techniques are described by the Federal Remediation Technology Roundtable (2002), USEPA (1995c), and GAO (2005). In this section, brief descriptions of the most widely used standard treatment techniques and the most promising innovative treatment techniques are presented. Candidate treatment technologies that are addressed in this
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(a)
Contaminated groundwater
Treatment system
36-31
LNAPL Storage tank Pump
Pump
LNAPL pump LNAPL product
Surface of LNAPL Static groundwater level Conductance sensor Large diameter borehole Contaminated groundwater
(b) Treatment system
Aquifer Groundwater pump
DNAPL Storage tank
Pump
Static groundwater level
Pump
Groundwater pump
Aquifer
Static DNAPL level
Conductance sensor DNAPL pump DNAPL product
Large diameter borehole Aquitard
FIGURE 36.18 (a) LNAPL Dual-extraction system; (b) DNAPL Dual-extraction system.
section are presented in Table 36.15. For the purposes of this section, these technologies are categorized as either in situ or ex situ techniques. In situ techniques are generally intended to either render a contaminant nontoxic through treatment (e.g., bioremediation) or to enhance extraction of the contaminant from the aquifer (e.g., air sparging). Ex situ techniques can be used only to treat groundwater that has been extracted from the aquifer. In situ treatment techniques are described in Section 36.5.2, and ex situ treatment techniques are described in Section 36.5.3.
36.5.2 In Situ Treatment 36.5.2.1 Introduction In situ treatment techniques are described in this section in three categories. First, techniques that incorporate biological processes (e.g., bioventing, bioremediation) are described in Section 36.5.2.2. Next, techniques that incorporate volatilization processes (e.g., air sparging, soil vapor extraction) are described
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36-32 TABLE 36.15
The Handbook of Groundwater Engineering Summary of Candidate Treatment Technologies Treatment type
In Situ Bioremediation
Destruction
Soil vapor extraction Air sparging Permeable reaction barriers Chemical Oxidation/Reduction
Destruction Extraction Destruction Destruction
Ex Situ Bioreactor
Destruction
Air stripping Carbon adsorption Ion exchange Chemical precipitation
Extraction Extraction Extraction Extraction
Membrane Separation
Extraction
Wetlands treatment
Destruction/ Extraction Destruction
Electrokinetic decontamination Advanced oxidation process
Destruction
Process description
Biological degradation of contaminants by stimulation of naturally occurring microbes in soil or non-native (exogenous) cultures introduced to target-specific contaminants Volatilization of contaminants that are present in the vadose zone Volatilization of contaminants in the saturated zone Physical or chemical treatment in a trench Chemical degradation of contaminants using injected oxidants (e.g., permanganate) or reducing agents (e.g., nanoscale zero-valent iron) Biological degradation of contaminants (activated sludge, fixed-film biological reactor, biophysical treatment or slurry phase treatment) Volatilization of contaminants Adsorption of contaminants to activated carbon Exchange-type attachment of contaminants to ion-exchange resin Alteration of water quality (usually pH adjustment) to conditions in which concentration exceeds the solubility limit of the compound, causing precipitation Separation of solids from water using membranes (reverse osmosis, ultrafiltration) Uptake of contaminants by wetland features Desorption of contaminants by “acidic front” of groundwater caused by hydrolysis of the groundwater Destruction of contaminants by contacting them with oxidizing environments typically containing free hydroxyl radicals
in Section 36.5.2.3. Then, techniques that incorporate a chemical or physical process (e.g., permeable reaction barriers) are described in Section 36.5.2.4. Finally, some promising innovative in situ treatment approaches are described in Section 36.5.2.5. In some cases, in situ treatment technologies may offer a viable alternative to more conventional remediation approaches (e.g., pump-and-treat) and may improve the chances of achieving the ultimate remediation goal (in some cases, even aquifer restoration). 36.5.2.2 Biological Remediation In situ biological treatment of groundwater — commonly referred to as enhanced in situ bioremediation (EISB) — involves creating conditions in the subsurface that promote the growth of microorganisms that can degrade contaminants. The popularity and use of EISB for groundwater remediation increased significantly during the 1990s, and today EISB is transitioning from a developing technology to mature technology. Technical guidance for designing and applying EISB is available in a variety of government reports, including USEPA, 2000c; Hughes et al., 2002; ITRC, 2002; and USAFCEE, 2004. Many of these reports are available on-line (see links to world-wide-web provided in the reference list). In this section, a brief overview of biological remediation is presented; a more detailed discussion of bioremediation is presented in Chapter 31 (i.e., Bioremediation). EISB exploits the capabilities of naturally occurring subsurface microorganisms, which can derive energy and often reproduce while metabolizing contaminants. Biodegradation reactions may involve destruction of organic contaminants, such as fuel hydrocarbons and chlorinated solvents, but can also involve transformation of inorganic contaminants to less toxic or immobile forms (e.g., nitrate to nitrogen gas or hexavalent chromium to trivalent chromium). EISB involves the perfusion of treatment agents that stimulate biological growth and catalyze biodegradation reactions. Bioremediation agents can include edible organic substrates (e.g., soybean oil, ethanol, molasses), air, oxygen gas, hydrogen gas, nutrients
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(nitrogen and phosphorus), wood mulch, specialized bacterial cultures, and vitamins. These agents can be delivered via batch-type injections into the subsurface, or via groundwater recirculation type designs. Numerous and diverse types of bacteria are naturally present in the subsurface, and many of these bacteria possess the capability to degrade common groundwater contaminants (e.g., fuel hydrocarbons or nitrate). Many organic contaminants (e.g., polycyclic aromatic hydrocarbons and fuel hydrocarbons) are degraded by the process of heterotrophic metabolism, in which bacteria use the contaminant as an electron donor and gain energy for maintenance and growth via microbial respiration. The by-products of complete biodegradation include carbon dioxide, water, and biomass. Biodegradation of synthetic organic contaminants in the subsurface may occur in a series of several steps, in which a contaminant is degraded into intermediate products before it is completely degraded. For example, under certain aquifer conditions, tetrachloroethylene is biodegraded to ethene and ethane by the following sequential steps: tetrachloroethene => trichloroethene => cis-1, 2-dichloroethene => vinylchloride => ethene => ethane. Bioremediation is often most successful in aquifers that are contaminated with chemicals that are easily metabolized by the indigenous microorganisms; in general, the more closely a contaminant resembles a naturally occurring compound, the more likely it is that there exists a microorganism in the aquifer that is capable of biodegrading the contaminant. Fuel hydrocarbons such as benzene and naphthalene, for example, are naturally occurring compounds that can be easily biodegraded under aerobic conditions by many subsurface bacteria. Certain synthetic organic compounds, such as chlorinated ethenes or chlorofluorocarbons, are more difficult to biodegrade, and there are fewer species of bacteria capable of completely biodegrading these compounds. An illustration of the relative biodegradability of organic contaminants under aerobic conditions is shown in Figure 36.19. Note that while some inorganic compounds are easily biodegraded (e.g., nitrate=>nitrogen gas), many inorganic compounds (e.g., heavy metals) cannot be biodegraded. Nevertheless, EISB systems can be used to engineer favorable biological treatment reactions, such as the reductive precipitation of hexavalent chromium and hexavalent uranium to precipitated end products. Also, note that the ambient conditions within the aquifer have a significant effect on the potential for successful bioremediation; a summary of the environmental factors that affect bioremediation and the range of optimum values for each factor are presented in Table 36.16. The rate of biodegradation (and, generally, the consumption of any material at relatively low concentration by biological activity) is often expressed by the first-order rate equation defined below: ln
Ct Co
= −kt
(36.11)
Easier to biodegrade Hydrocarbons Subsituted hydrocarbons: phenols, esters, alcohols, nitrates, partially chlorinated compounds Pesticides
Highly chlorinated compounds
Polychlorinated biphenyls
More difficult to biodegrade
FIGURE 36.19 Relative biodegradability of organic compounds.
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Environmental Factors That Affect Biodegradability
Environmental factor Available soil water Oxygen
Redox potential pH Nutrients
Temperature
Optimum levels 36–85% of water holding capacity; −0.01 Mpa Aerobic metabolism: >0.2 mg/l dissolved oxygen, minimum air-filled pore space of 1% by volume Anaerobic metabolism: oxygen concentrations <1% by volume Facultative anaerobes: >50 mV Obligate anaerobes: <50 mV pH values of 5.5–8.5 Sufficient nitrogen, phosphorus, and other nutrients so as to not limit microbial growth (Suggested C:N:P ratio of 120:10:1) 15–45◦ C (Mesophiles)
Source: Modified from USEPA. 1991. Handbook — Ground Water, Volume II: Methodology. EPA/636/690/016b. Washington, DC.
where k is the first-order reaction rate coefficient (sec−1 ), Ct is the concentration of constituent remaining at time t (mg/l), Co is the initial concentration of the constituent (mg/l), and t is time (sec). Biodegradation rate coefficients are often estimated based on the results of bench-scale testing performed prior to field implementation. In the case of pre-design analyses, the time required for degradation of a particular plume of contamination can be estimated by solving Equation 36.11 for t . In evaluating the field performance of EISB systems, the rate coefficient can be estimated by comparing contaminant concentrations over time and space relative to the initial concentration (Co ). It should be noted that, at high contaminant concentrations, biodegradation reaction rates are often more accurately described by variable- or zeroorder (Monod) kinetics. In the case of contaminant source areas or high-concentration plumes, use of first-order rate models to quantify biodegradation rates can significantly underestimate the time needed to achieve cleanup criteria. The design effort for a bioremediation system is typically focused on (1) identifying the additives (e.g., organic substrates, nutrients, oxygen, and microorganisms, etc.) that will promote biodegradation; and (2) determining effective approaches for delivering those additives to the subsurface. The most effective EISB systems are typically those that have been designed via the traditional engineering scale-up process of bench testing, followed by pilot testing, followed by full-scale application (EPA, 2000a). Laboratory bench testing is a simple and low-cost step for identifying effective treatment additives and assessing treatment rates for design of full-scale systems. Bench testing, as well as pilot-scale testing, is a prudent approach for determining effective additives, identifying potential inhibitory factors, and avoiding wasteful expenditures on unsuccessful full-scale designs in the field. 36.5.2.3 Volatilization Processes Volatilization is the transfer of a chemical from the liquid state to the gaseous state. Remediation techniques that employ volatilization processes promote the change of contaminants from liquid phase (including dissolved) to the vapor phase. Vapor-phase contaminants are typically easier to remediate than liquidphase contaminants because aquifer materials are significantly more permeable to vapors than to liquids, making vapors easier to remove from the aquifer (see discussion of intrinsic permeability in Chapter 2). Remediation technologies that employ volatilization processes include both soil vapor extraction (which is applicable to contaminants adsorbed to soil in the vadose zone) and air sparging (which is applicable to both dissolved and adsorbed contaminants in the saturated zone). Both processes are based on the principle of molecular diffusion of contaminants from the dissolved or nonaqueous phase to the vapor phase, which is described by Fick’s Law for diffusion. The principles of soil vapor extraction (SVE) and air sparging (AS) are described below.
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36-35 Vapor treatment unit Vacuum pump
Vapor extraction well
Vapor flow
Contaminated soil
Groundwater table
Vapor flow Free-liquid hydrocarbon
Soluble plume
FIGURE 36.20 “Basic” soil vapor extraction system. (From Johnson, P.C., Stanley, C.C., Kemblowski, M.W., Byers, D.I., and Colthart, J.D. 1990. A practical approach to the design, operation, and monitoring of in situ soil venting systems. Groundwater Monitoring Review, Spring 1990, 159–178. With permission.)
Soil Vapor Extraction. An example of an SVE system is illustrated in Figure 36.20. The concentration of a particular contaminant in the extracted vapor can be estimated using Fick’s Law as follows: Cest =
xi P v M w i i
i
RT
(36.12)
where Cest is the estimated concentration of contaminant in the vapor (mg/l), xi is the mole fraction of component i in the liquid-phase contaminants, P1v is the vapor pressure of component i at temperature T (atm), Mw is the molecular weight of component i (mg/mole), R is the gas constant (i.e., 0.0821 l-atm/mole ◦ K ), and T is the absolute temperature of the contaminant residual (K ). Note that contaminant concentrations will decline with time as the concentration of the contaminant adsorbed to the subsurface soils decreases; therefore, the contaminant vapor concentration will change over time. SVE is potentially suitable for contaminants that have a vapor pressure conducive to volatilization (usually greater than about 1 × 10−4 atm at the average subsurface temperature); a summary of vapor pressures for some typical contaminants is presented in Table 36.13. Using the value of Cest , the removal rate can be estimated by multiplying Cest by the expected air flow rate Q. The achievable air flow rate can be estimated using the following equation (Johnson et al., 1990): k [1 − (Patm /Pw )2 ] Q = π Pw H µ ln(Rw /Ri )
(36.13)
where Q/H is the flow rate per unit thickness of wellscreen (cm3 /sec), k is the soil permeability to air flow (cm2 ), µ is the viscosity of air (1.8 × 10−4 g/cm-s, or 0.018 cp), Pw is the absolute pressure at the extraction well (atm), Patm the absolute atmospheric ambient pressure (i.e., 1.01 × 106 g/cm-s2 , or 1 atm), Rw is the radius of the extraction well (cm), and RI is the radius of influence of the extraction well (cm). The reasonableness of the expected gas flow rates for the permeability of the site soils
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1100 Rw =5.1 cm (2") R1 = 12 m (40')
10
110 Pw = 0.40 atm = 20.3 ft H2O
1
Pw = 0.60 atm = 13.6 ft H2O
11
(m3/m-min) .1
1.1
Vapor flow rate (scfm/ft)
Pw = 0.80 atm = 6.8 ft H2O .01
Pw = 0.90 atm = 3.4 ft H2O
0.011
Pw = 0.95 atm = 1.7 ft H2O .001
0.0011 Clayey sands
Fine sands
Medium sands
Coarse sands
.0001
0.0011 10 100 1000 1 Soil permeability (darcy) [ft H2O] denote vacuums expressed as equivalent water column heights .01
.1
FIGURE 36.21 Predicted steady-state flow rates (per unit wellscreen thickness) for a range of soil permeabilities and applied vacuums (Pw ). (From Johnson, P.C., Stanley, C.C., Kemblowski, M.W., Byers, D.I., and Colthart, J.D. 1990. A practical approach to the design, operation, and monitoring of in situ soil venting systems. Groundwater Monitoring Review, Spring 1990, 159–178. With permission.)
may be confirmed using Figure 36.21. In some cases, there may be a significant quantity of residual contamination adsorbed to soil particles located a short depth below the water table as a result of changes in groundwater elevation since contaminants were released. In this case, it may be efficient to implement a “dual extraction” (i.e., air and groundwater) system similar to the dual extraction system illustrated in Figure 36.18A for groundwater and LNAPLs. By depressing the groundwater table below the residual contamination, the residual contamination can be extracted using SVE techniques, which are much more efficient than groundwater extraction techniques for removing adsorbed or residual contamination. Air Sparging/Biosparging/Bioventing. An illustration of an air-sparging (AS) system is presented in Figure 36.22. Air sparging involves introducing air into the aquifer to volatilize and biodegrade groundwater contaminants. To prevent uncontrolled migration of contaminated sparge air, AS systems are typically used in conjunction with SVE systems, which capture the sparged air and volatilized organic compounds after they rise from groundwater into the vadose zone, as shown in Figure 36.22. Biosparging is a form of AS that involves injection of air into contaminated groundwater at low flow rates (e.g., 2 to 5 cfm), to maximize in situ biodegradation and minimize volatilization. Similarly, bioventing involves injection of air and, in some cases, gaseous nutrients) above the water table to stimulate biodegradation of vaporand sorbed-phase contaminants in the vadose zone. The US Department of Defense has applied AS, biosparging, and bioventing technologies at hundreds of sites, and achieved success particularly at fuel spill sites. Useful guidance manuals for these technologies include (Leeson and Hinchee, 1996a and 1996b; and Leeson et al., 2002).
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36-37 Atmospheric discharge Vapor treatment
Compressor (air sparging)
Blower (SVE)
Air flow Air flow
Vapor phase Absorbed phase Dissolved phase
Air flow
Air flow
FIGURE 36.22 Typical air-sparging system configuration. (From Hinchee, R.E. 1994. Air Sparging for Site Remediation. Lewis Publishers, Chelsea, Michigan.)
In general, the physics of air movement in the saturated zone is currently not well understood, which limits the predictability of AS system performance; in fact, the decisions regarding sparge well location and spacing are usually based on experience rather than calculation. Still, because it has a relatively low cost, AS can be a costeffective approach to groundwater remediation. As presently understood, air discharged to groundwater by a sparge well typically flows upward to the vadose zone through air channels (as illustrated in Figure 36.22) that are established at first operation of the system. These air channels directly impact only a very small quantity of groundwater and soil. Contaminants partition between the sparge air, groundwater, and soils; the portion that partitions to vapor in the sparge air rises with the sparge air to the ground surface. For AS to be effective, adsorbed contaminant mass must be transported by diffusion from the surface of soils through the groundwater to the air–water interface of the air channels, which is a slow process. The minimum air pressure required to operate a sparge system is provided by the equation (Johnson et al., 1993): PH = rw g (Ls − Lgw )
(36.14)
where PH is the hydrostatic pressure corresponding to the water column height that is displaced (atm), rw is the density of water (1000 kg/m3 ), g is the acceleration due to gravity (9.8 m/sec2 ), Ls is the depth below ground to the top of the sparge wellscreen (m), and Lgw is the depth to groundwater (m). Two concerns exist related to the performance of air sparge systems, both of which can be addressed through monitoring. First, the introduction of air below the water table could raise the elevation of the water table, possibly changing groundwater flow direction. This first concern can be addressed by monitoring groundwater elevations near the sparge area to confirm that groundwater elevations are not changing. The second concern is that sparge gas may migrate horizontally in more permeable zones resulting in an increase in the lateral extent of contamination. This concern can be addressed by monitoring the chemical characteristics of soil vapor at locations beyond the sparge wells to verify that contaminated vapors are not migrating offsite in an uncontrolled manner and, if necessary, by using SVE to prevent offsite migration of vapors. In Situ Thermal Treatment. Beginning in the 1980s, in situ thermal remediation technologies were developed and have more recently been employed to enhance the mobility and extraction of volatile
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and semi-volatile contaminants from groundwater. Variations of in situ thermal treatment technologies include steam injection, resistive heating, in situ thermal desorption, hot air injection, and radio frequency (RF) heating. A useful summary of in situ thermal treatment technologies is provided by EPA (2004d). Each of the variations of in situ thermal treatment functions by increasing subsurface temperatures, thereby increasing the mobility of subsurface contaminants and facilitating their removal from the subsurface. Therefore, they typically are used in conjunction with extraction technologies, primarily SVE. The mechanisms by which in situ thermal treatment technologies enhance mobilization, even within highly contaminated source areas, for less volatile contaminants, or in low permeability aquifers, have been described by USEPA (Davis, 1997; USEPA, 2004). In addition to increasing mobility, some applications of in situ technologies have the added effect of increasing subsurface temperatures to an extreme where contaminants may be thermally destroyed. One potential concern with in situ thermal treatment technologies is the potential for spreading of contaminant plumes if appropriate vapor or groundwater capture systems are not employed. 36.5.2.4 Chemical and Physical Processes Chemical and physical processes are often used to promote in situ treatment of contaminated groundwater. The range of chemical processes that can be applied in situ includes reduction with chemical reducing agents (e.g., sodium dithonite), reduction with zero-valent iron, and chemical oxidation with permanganate. For a chemical treatment process to be carried out to a high rate of completion, groundwater must be well mixed with reagents, which can be difficult to achieve in heterogeneous formations, low-permeability formations, and large plumes. Still, under some conditions, in situ chemical and physical treatment of contaminated groundwater is possible, particularly in situations where contaminated groundwater can be routed to a collection point before it is treated and where contaminated groundwater can be well mixed with treatment reagents. Chemical processes that can be considered for in situ application include adsorption, precipitation, oxidation/reduction, fixation, and physical transformation. Such processes can be promoted by: (1) installing a permeable reaction barrier (also known as a “reaction trench,” or “in situ reactive barrier,” or “selective” barrier) in the aquifer to intercept contaminated groundwater and provide a controlled environment for the reaction; or (2) by applying reagents directly to groundwater through wells or by infiltration from the ground surface. The barrier can be constructed using the techniques described in Section 36.4.3 and can be backfilled with reagents, such as activated carbon (for treatment of volatile organic contaminants), limestone (to promote precipitation of dissolved metal ions), or iron filings (to capture organic carbon compounds [Focht et al., 1996]), to provide the desired treatment of groundwater. A variation of the permeable reaction barrier is the “funnel and gate” reaction barrier, which is illustrated in Figure 36.23. This approach uses relatively impermeable barrier walls (i.e., the “funnels”) to route groundwater to the permeable, reactive portion of the barrier (i.e., the “gate”) and minimizes the length of barrier that must be maintained or reconditioned as the reaction sites in the barrier wall become exhausted. The range of treatment technologies that can be used for permeable reaction barriers is illustrated in Table 36.17. The primary advantages of permeable reaction barriers are a result of the passive nature of the technology; for example, there is no need for a power source, which typically represents the majority of long-term operation and maintenance costs for active (e.g., pump-and-treat) remediation systems. There is a large variety of technical guidance in the public domain regarding design and application of in situ chemical treatment technologies and permeable reactive barriers. Example guidance regarding zero-valent iron reactive barriers includes Blowes et al. (1999a, 1999b) and Blowes and Mayer (1999); example guidance regarding chemical oxidation is provided in USEPA (1998a); ITRC (2005); Yin and Allen (1999). 36.5.2.5 Monitored Natural Attenuation Monitored natural attenuation (also known as “MNA”) involves the evaluation and monitoring of naturally occurring processes that prevent the migration of contaminants to receptors. Currently, MNA is most frequently used to describe biodegradation of contaminants by naturally occurring microorganisms;
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(a) Single gates
(b) Multiple gates Treatment cells
Treatment cell Contaminant plume
Cleaned water
Contaminant plume
Waterloo sealable joint sheet piling
Waterloo sealable joint sheet piling
(c) Multiple cells Treatment cells
Cleaned water
Contaminant plume
Waterloo sealable joint sheet piling
FIGURE 36.23 Funnel and gate system configuration. (From Rumer, R.R. and Mitchell, J.K. 1995. Assessment of Barrier Containment Technologies — A Comprehensive Treatment for Environmental Remediation Applications. National Technical Information Services, Springfield, VA.)
TABLE 36.17
Treatment Technologies Applied in Permeable Reactive Barriers
Treatment medium Zero-valent iron Zero-valent iron Limestone Precipitation agents (gypsum, hydroxyapatite) Sorptive agents (Fe hydroxide, GACa , zeolites, coal) Chemical reducing agents (dithionite, hydrogen sulfide) Chemical oxidants (e.g., potassium permanganate) Metal couplesb Oxygen to stimulate aerobic bioremediation (e.g., via hydrogen peroxide, air, or oxygen gas) Methane, propane, and oxygen to stimulate co-cometabolic bioremediation (e.g., biosparging in horizontal wells) Organic electron donors (organic compost and mulch, alcohols, sugars, soybean oil, and fatty acids)
Target contaminants
Technology status
Halocarbons Reducible metals (Cr+6 , U6+ ) Metals, acid waters Metals
Commercially applied Commercially applied In practice (mining) Laboratory studies
Metals and organics
Reducible metals
Field demonstration and/or laboratory studies Field demonstration
Halocarbons
Field demonstration
Halocarbons Fuel hydrocarbons
Laboratory studies Commercially applied
Halocarbons, MTBE
Commercially applied
Halocarbons
Commercially applied
a GAC = granulated activated carbon. b Coupled oxidation of metal and reduction of halocarbon to produce chloride and Fe+2 in solution.
Source: Modified from Rumer, R.R. and Mitchell, J.K. 1995. Assessment of Barrier Containment Technologies — A Comprehensive Treatment for Environmental Remediation Applications. National Technical Information Services, Springfield, VA.
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however, other natural physical or chemical processes (e.g., adsorption) may effectively prevent the migration of contaminants. Under the MNA approach, natural forces are allowed to act on the contaminated groundwater, without any human intervention, to remediate groundwater. Because microorganisms are present in nearly all aquifers and because other naturally occurring processes (e.g., sorption, complexation, precipitation, etc.) can mitigate groundwater contamination by attenuating contaminants, these naturally occurring processes can have a beneficial impact on groundwater quality. A key component of MNA is a program of groundwater monitoring to verify that natural processes are, indeed, resulting in the degree of attenuation required. MNA can be used alone or to supplement conventional remediation techniques. For example, a contaminant source could be removed prior to beginning a program of MNA to reduce contaminant loading in the aquifer and thereby improve the performance of MNA (National Academy of Sciences, 2000, USEPA, 1998b). 36.5.2.6 Innovative In Situ Treatment Approaches A large number of innovative techniques for in situ remediation of groundwater have been developed in the past several years that promise to provide a higher degree of permanence, a higher contaminant removal efficiency, or lower remediation cost for some groundwater contamination problems. A good summary of available innovative technologies is presented in USEPA (2003). Descriptions of some promising innovative in situ remediation techniques are presented below. • Nanoscale Zero-Valent Iron. Since the late 1990s, nanoscale zero-valent iron (nZVI) has emerged as a promising new technology for in situ remediation of halogenated organics and heavy metals in groundwater. Laboratory Research over the past several years has demonstrated that nZVI and bimetallic Pd-Fe nanoparticles can destroy chlorinated biphenyls, ethenes, methanes, benzenes, and certain pesticides at rates that are orders of magnitude faster than can be achieved by granular ZVI and ZVI powder (Wang and Zhang, 1997; Lien and Zhang, 1999; Xu and Zhang, 2000; Masciangioli and Zhang, 2003). The faster transformation by nZVI has been shown to be due to higher specific surface area (the surface area of NZVI and commercial iron powder are 33.5 m2 /g, and < 1 m2 /g, respectively). In addition to rapid transformation rates, a key benefit of nZVI is that it can be delivered to the subsurface via aqueous suspension. In contrast to granular ZVI, nZVI does not require trenching. A field pilot test in 2001 demonstrated that nZVI injected into the subsurface was well distributed and achieved effective treatment of chloroethenes and chloromethanes (Elliott and Zhang, 2001). However, nZVI is still an emerging technology, and additional development is required before the technology can be widely deployed. In particular, research and development is required regarding methods for improving delivery of nZVI to the subsurface. • Groundwater Circulation Well (GCW) Technologies. GCW is a general term that describes groundwater remediation technologies that treat groundwater by creating a circulation cell around each individual treatment well. The treatment cells are typically created using wells with two screened intervals at the top and bottom of the treatment zone; groundwater is drawn in the bottom screen and reintroduced to the aquifer through the upper screen. Different variations of this technology employ different mechanisms to effect groundwater treatment. One variation used to strip VOCs from groundwater injects air into the bottom of the well; as the air lifts groundwater through the well, VOCs are stripped from the groundwater. Off gas from such a system can be treated above ground. Allmon et al. (1999) provides a detailed description and assessment of this variation of the technology. Other configurations of GCW technology may employ active pumping and other treatment technologies, such as bioremediation or carbon adsorption. GCW technology has been tested at more than 50 sites in the United States with mixed results. The application of GCW technology may be limited by the presence of highly anisotropic conditions or layers of variable permeability, which can preclude the formation of a recirculation cell, or the potential for biofouling in the circulation well screens (Allmon et al., 1999; Parson, 2001). • Surfactant Enhanced Aquifer Remediation. A primary challenge of remediating chlorinated solvent DNAPL source areas is the slow rate of dissolution of DNAPL. Surfactant Enhanced Aquifer
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Remediation (SEAR) is an emerging technology that offers promise for effective remediation of DNAPL source areas via enhanced solubilization of DNAPL. Surfactants, or Surface Active Agents, are chemicals that possess a molecular structure that is hydrophobic at one end of the molecule, and hydrophilic at the other the end. In the presence of hydrophobic compounds, such as fats or chlorinated solvents, surfactants can form micelles, where the hydrophobic end of the surfactant joins with fat or solvent, and the hydrophilic tail of the surfactant facilitates solubilization of the compound. Chemical engineers have exploited surfactants for decades, using them in household detergents and as food-grade additives. Over the past several years, engineers and academic researchers have performed laboratory column and sand box tests to demonstrate that food-grade surfactants can be highly effective for enhanced recovery of DNAPLs. More recently, a handful of carefully controlled field pilot tests have shown that while SEAR can achieve effective results in the field (e.g., Ramsburg et al., 2005; Abriola et al., 2005), more testing is required before the technology can be widely applied. The ability of SEAR to solubilize and mobilize DNAPL requires that groundwater extraction systems be carefully designed to prevent any uncontrolled migration of DNAPL during remediation with SEAR. Technical guidance on SEAR is provided in NAVFAC, 2002.
36.5.3 Ex Situ Treatment 36.5.3.1 Biological Processes Ex situ biological processes involve treatment of extracted groundwater in vessels until the concentration of the remaining contaminants is below a predefined level. Biological processes have been widely used for the past 40 years in the United States to treat municipal wastewater. A good general reference for biological treatment is presented by Corbitt (1990). The processes used to treat municipal wastewater are generally applicable to treatment of contaminated groundwater except in circumstances where the contaminants in groundwater are toxic to the microbes in the biological treatment system. Ex situ biological treatment processes include bioreactor and slurry-phase treatment, among others. A brief description of these two processes is presented below. • Bioreactors. In this approach, contaminants are degraded by placing them in contact with microbes in an environment where biological growth is promoted. This can be accomplished using either suspended (i.e., activated sludge) or attached (i.e., rotating biological contactors or trickling filters) growth systems. The microbial population can be either derived from the contaminated groundwater or added to the system. • Slurry-Phase Treatment. In this approach, extracted groundwater is mixed with soil and nutrients and then routinely agitated in a controlled environment to promote biodegradation of the contaminants. The slurry is typically placed in a lined area and left until the desired degree of biodegradation occurs. Finally, the slurry is dewatered, and then the water and soil (both should be uncontaminated after biodegradation is completed) are properly disposed of as nonhazardous wastes. This process offers much better control of process variables than the bioreactor approach but is slow and requires a larger area for implementation. 36.5.3.2 Volatilization Processes As described in Section 36.5.2.5 and as shown in Table 36.13, volatilization processes are effective in treating groundwater that is contaminated with organic chemicals that have a high vapor pressure. Volatilization processes may also be effective at removing nonorganic contaminants that have a relatively high vapor pressure (e.g., mercury). Volatilization processes, or “air stripping,” involve mixing of contaminated groundwater with air to allow the volatile contaminants that are dissolved in groundwater to partition from the dissolved phase to the vapor phase, allowing them to be removed from groundwater. The efficiency of the volatilization processes depends on the number of air/water contacts. Air/water contacts can be maximized by using spray aeration, diffused-air aeration, packed column air
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stripping, tray aerators, or rotating disk aerator techniques. The primary advantage of ex situ over in situ volatilization approaches is the flexibility of ex situ systems and the high efficiency rates of these systems. 36.5.3.3 Chemical and Physical Processes Numerous well-developed technologies are available for treating extracted groundwater by chemical or physical means. Useful summaries of these processes are presented by the Federal Remediation Technology Roundtable (FRTR) (2002) and by Corbitt (1990). In general, chemical and physical processes are available for ex situ treatment of nearly all types of contaminants that occur in groundwater. Ex situ chemical and physical treatment techniques typically have the following advantages over in situ treatment techniques: (1) the ability to maintain uniformity of the influent by using equalization features (i.e., tanks etc.) at the point of inflow to the treatment system; (2) the ability to easily evaluate the effectiveness of the treatment process by monitoring the quality of treated groundwater; and (3) ease in adjusting the treatment system components in response to changes in influent quality to optimize groundwater treatment efficiency. In Table 36.18, several chemical and physical treatment technologies are identified, and examples of their use are illustrated. Below, descriptions are provided for the ex situ treatment techniques that are most
TABLE 36.18
Summary of Selected Ex Situ Groundwater Treatment Technologies
Treatment technology Organic Contaminants Air stripping Liquid-phase
Steam stripping Membranes Oxidation Activated sludge Fixed-film biological reactors Biophysical Inorganic Contaminants Alkaline precipitation Coagulation Ion exchange Adsorption Filtration Reduction Membranes
Oxidation
Representative examples
Packed towers, surface or diffused aeration removal of volatile compounds; soil venting GAC removal of broad spectrum of VOCs
Packed tower with steam stripping, removal of low volatile organics Ultrafiltration for removal of selected organics Ozone/UV, or ozone/H2 O2 , destruction of chlorinated organics Oxygen or air biological oxidations for removal/destruction of degradable organics Fixed-film fluidized bed, for oxidation of less degradable organics Powdered carbon, with activated sludge, treatment of high strength waste waters
Status of technology
Residual streams
Air stream with VOCs GAC for regeneration or disposal Recovered solvent
Commercial Commercial
Some commercial
Concentrated brine side stream None
Commercial Some commercial
Sludge
Commercial
Sludge
Commercial
Powdered carbon and bacterial
Commercial, PACT process
Heavy metals removal Ferric sulfate or alum for heavy metals removal Heavy metals; nitrate Selenium removal on activated alumina Removal of clays, other particulates SO2 reduction of Cr (VI) Reverse osmosis, ultrafiltration for removal of metals, other ions
Hazardous sludge Hazardous sludge
Commercial Commercial
Regeneration stream Regeneration stream Backwash wastes Sludge Concentrated liquid waste
Fe (II) and Mn (II)
Sludge
Commercial Commercial Commercial Commercial Commercial, new membranes are under development Commercial
Source: From USEPA. 2003. Superfund Innovative Technology Evaluation Program, Technology Profiles, Eleventh Edition. EPA/540/C-03/501. Washington, DC.
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commonly used to treat contaminated groundwater. • Carbon Adsorption: For this approach, groundwater is typically pumped through a series of canisters containing activated carbon, to which contaminants from the groundwater are adsorbed. Because activated carbon offers “attractive” locations for adsorption of organic carbons (i.e., because of the similarity between the carbon atoms on the contaminant molecule and the carbons in the activated carbon), carbon adsorption is a very effective technique for removing VOCs from contaminated groundwater. Periodically, the activated carbon must be either replaced or regenerated as the adsorption sites become saturated with VOCs. For some application, biologically activated carbon (BAC) treatment may be employed to enhance removal efficiency of minimize the need for carbon replacement. • Precipitation: Precipitation occurs when a constituent exists at a concentration in groundwater that is greater than its solubility limit. Solubility is a function of many factors, including pH, temperature, and the presence of other dissolved constituents. Precipitation of a target constituent is caused by manipulating these factors to change the equilibrium in the direction that promotes precipitation of that constituent. Typically, the least-soluble constituent at a given pH will precipitate from the solution. Note that precipitation can also occur in situ in response to changes in groundwater chemistry. Because solubility is affected by many factors, changes in groundwater quality over time may cause changes in the solubility of constituents of concern. Precipitation and dissolution may be slow reactions, depending on the solubility of the constituent; therefore, after a change occurs in groundwater chemistry that increases the constituent’s solubility (e.g., drawing groundwater having lower pH through a contaminated aquifer), the previously precipitated minerals may require a long time to redissolve and be removed from the aquifer. • Reverse Osmosis: In reverse osmosis (RO) (USEPA, 1996), solids are separated from water by creating a concentration gradient across a semipermeable membrane (i.e., a membrane that is “selectively” permeable to only the solids of choice, based on size of molecules, but not to other compounds or solids). To prevent water from also passing through the membrane, a pressure gradient is applied to the opposite side of the membrane that exceeds the osmotic pressure (hence the use of the term “reverse” osmosis). The technology is extremely effective at removing dissolved solids from groundwater, but RO capital equipment is very expensive.
36.6 Performance Monitoring of Groundwater Remediation Systems Monitoring the performance of a groundwater remediation system allows evaluation of the success of the system in meeting the remediation goal and the design criteria for the system. Different approaches are typically used to monitor the performance of groundwater extraction, barrier, and treatment remediation systems. Performance monitoring of groundwater extraction systems typically includes at least the following activities (USEPA, 1994): • Confirming that the system is extracting groundwater at flow rates similar to those predicted in the predesign pump test (by measurement using a flowmeter at the wellhead) • Verifying that groundwater elevations near the extraction system are being affected as needed to control groundwater flow direction and gradient (by measuring groundwater elevations at wells or piezometers located near the extraction well(s)) • Verifying that there are no significant breaches in the groundwater extraction system that would allow contaminated groundwater to flow past the extraction system (using the groundwater elevation data collected at the wells and piezometers) • Confirming that the system components perform consistently throughout the operational life of the facility (by routinely inspecting the components of the system and checking for signs of operational problems).
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Performance monitoring of a groundwater treatment system (both in situ and ex situ) typically includes the following: • Periodic analysis of influent groundwater quality to evaluate changes in the quality of water requiring treatment • Periodic analysis of effluent groundwater quality, to evaluate the success of the system at meeting treatment goals • Routine inspection of the components of the system to identify potential future problems. Performance monitoring of subsurface barriers (see Rumer and Mitchell, 1995) typically includes the following activities: • Verifying that the barrier is having the desired impact on groundwater flow direction and gradient (by measuring groundwater elevations at wells or piezometers near the barrier) • Verifying that contaminated groundwater is not passing through or around the barrier (by monitoring groundwater quality beyond the barrier) • Verifying that the barrier is not degrading over time. These activities can be monitored in a variety of ways using a system of piezometers or wells, as described in Section 36.3.5. When the purpose of the performance-monitoring program is to verify that nearby receptors are not at risk of contaminated groundwater, external monitoring features should be located downgradient of the hydraulic containment system near receptors or near a property boundary.
Glossary Adsorption The adherence of ions or molecules in solution to the surface of solids. Anisotropy The condition under which one or more of the hydraulic properties of an aquifer vary with direction. Biodegradation The biologically mediated conversion of a compound to simple products. Contaminant An undesirable substance that is not normally present in groundwater or a substance that may naturally occur in groundwater, but that is present at an undesirably high concentration. Desorption The release of sorbed molecules from the solid into solution (the reverse of adsorption). DNAPL An acronym for denser-than-water nonaqueous-phase liquid; a liquid, composed of one or more contaminants, that does not mix with water and is denser than water. Fraction of Organic Carbon The organic carbon content of soil, expressed as a mass fraction of the dry soil. Hydraulic Control Prevention of the spread of contaminated groundwater using physical features to control groundwater flow. Ion A molecule or atom that has a positive or negative electric charge. LNAPL An acronym for less-dense-than-water (i.e., “light”) nonaqueous-phase liquid. Maximum Contaminant Level (MCL) The maximum amount of a compound allowed in drinking water under the Safe Drinking Water Act. Octanol-Water Partition Coefficient A measure that indicates the extent to which a compound is attracted to an organic phase (for which octanol is a proxy) and, hence, the tendency of the compound to sorb to subsurface materials. Partitioning A chemical equilibrium condition in which the concentration of a chemical is apportioned between two different phases according to the partition coefficient. Plume A zone of contaminated groundwater. Receptor An organism that is exposed to a contaminant. Retardation The movement of a solute through a geologic medium at a velocity less than that of the groundwater as a result of phenomena that separate a fraction of the solute mass from the groundwater.
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Sorption Refers to a reversible process involving physical reaction of aquifer material and dissolved constituents. Upgradient In the direction of increasing hydrostatic head. Volatilization The transfer of a chemical from the liquid to the gas phase.
References Abriola, L.M., Drummond, C.D., Hahn, E.J., Hayes, K.F., Kibbey, T.C.G., Lemke, L.D., Pennell, K.D., Petrovskis, E.A., Ramsburg, C.A., and Rathfelder, K.M. 2005. Pilot-scale demonstration of surfactant-enhanced PCE solubilization. 1. Site characterization and Test Design. Environ. Sci. Technol. 39: 1778–1790. Allmon, W.E., Everett, L.G., Lighter, A.T., Alleman, B., Boyd, T.J., and Spargo, B.J. 1999. Groundwater Circulating Well Technology Assessment. Report No. NRL/PU/6115-99-384. Naval Research Laboratory, Washington, DC. http://www.estcp.org/projects/cleanup/199602v.cfm. Bear, J. 1979. Hydraulics of Groundwater, McGraw-Hill, New York. Blowes, D.W., Gillham, R.W., Ptacek, C.J., Puls, R.W., Bennett, T.A., O’Hannesin, S.F., Hanton-Fong C.J., and Bain, J.G. 1999a. An In Situ Permeable Reactive Barrier for the Treatment of Hexavalent Chromium and Trichloroethylene in Ground Water: Volume 1 Design and Installation. Office of Research and Development. EPA/600/R-99/095a. http://www.epa.gov/ada/download/reports/ prbdesign_v1.pdf. Blowes, D.W., Puls, R.W., Gillham, R.W., Ptacek, C.J., Bennett, T.A., Bain, J.G., Hanton-Fong, C.J., and Paul, C.J. 1999b. An In Situ Permeable Reactive Barrier for the Treatment of Hexavalent Chromium and Trichloroethylene in Ground Water: Volume 2 Performance Monitoring. Office of Research and Development. EPA/600/R-99/095b. http://www.epa.gov/ada/download/reports/ prbperformance_v2.pdf Blowes, D.W. and Mayer, K.U. 1999. An In Situ Permeable Reactive Barrier for the Treatment of Hexavalent Chromium and Trichloroethylene in Ground Water: Volume 3 Multicomponent Transport Modeling. Office of Research and Development. EPA/600/R-99/095c. http://www.epa.gov/ada/download/reports/prbmodel_v3.pdf Brusseau, M. 1996. Evaluation of simple methods of estimating contaminant removal by flushing. Groundwater 34:19–22. Cohen, R.M. and Miller, W.J. III, 1983. Use of analytical models for evaluating corrective actions at hazardous waste sites. Proceedings of the Third National Symposium on Aquifer Restoration and Ground-Water Monitoring. Nielson, D.M., ed. National Water Well Association. Worthington, OH, 86–97. Corbitt, R.A. (ed.) 1990. Standard Handbook of Environmental Engineering. McGraw-Hill, New York. Davis, E.L. 1997. Ground Water Issue: How Heat Can Enhance In-situ Soil and Aquifer Remediation: Important Chemical Properties and Guidance on Choosing the Appropriate Technique. EPA/540/S97/502. Washington, DC. Driscoll, F. 1986. Groundwater and Wells, Johnson Division, St. Paul, MN, Second Edition. Elliott, D. and Zhang, W. 2001. Field assessment of nanoparticles for groundwater treatment. Environmental Science & Technology 35: 4922–4926. Federal Remediation Technology Roundtable, 2002. Remediation Technologies Screening Matrix and Reference Guide. EPA 542-B-93-005. Washington, DC. Focht, R., Vaughn, S., and O’Hannesin. 1996. Field application of reactive iron walls for in-situ degradation of volatile organic compounds. Remediation. Summer 1996. GAO. 2005. Groundwater Contamination: DOD Uses and Develops a Range of Remediation Technologies to Clean Up Military Sites. Washington, DC. GeoSyntec Consultants. 1994. Subsurface Barriers. Report to the United States Navy, Contract SBIR Topic N93-130. Atlanta, GA. 80 pages. Hinchee, R.E. 1994. Air Sparging for Site Remediation. Lewis Publishers, Chelsea, MI.
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Hughes, J.B., Duston, K.L., and Ward, C.H. 2002. Engineered Bioremediation. Technology Evaluation Report TE-02-03. Ground-Water Remediation Technologies Analysis Center, Pittsburgh, PA. http://www.groundwatercentral.info/org/pdf/E_bio.pdf Hutson, S.S., Barber, N.L., Kenny, J.F., Linsey, K.S., Lumma, D.S., and Maupin, M.A. 2004. Estimated Use of Water in the United States in 2000. U.S. Geological Survey Circular. 1268, Reston, VA. Interstate Technology and Regulatory Council. 2002. A Systematic Approach to In Situ Bioremediation in Groundwater. http://www.itrcweb.org/Documents/ISB-8.pdf. Interstate Technology and Regulatory Council. 2005. Technical and Regulatory Guidance for In Situ Chemical Oxidation of Contaminated Soil and Groundwater. http://www.itrcweb.org/Documents/ ISCO-2.pdf. Inyang, 1992. Selection and design of slurry walls as barriers to control pollutant migration. A seminar Presentation, Office of Solid Waste and Emergency Response, USEPA, Washington, DC. Johnson, P.C., Stanley, C.C., Kemblowski, M.W., Byers, D.L., and Colthart, J.D. 1990. A practical approach to the design, operation, and monitoring of in-situ soil-venting systems. Groundwater Monitoring Review, Spring 1990, 159–178. Johnson, R.I., Johnson, P.C., McWhorter, D.B., Hinchee, R.E., and Goodman, I. 1993. An overview of in situ air sparging. Groundwater Monitoring and Remediation. Fall 1993, 127–135. Keely, J.F. 1989. Performance Evaluations of Pump-and-Treat Remediations, EPA Superfund Groundwater Issue, EPA/540/4-89/005. Washington, DC. McCoy and Associates. September/October 1992. The Hazardous Waste Consultant. 4.1–4.38. Leeson A., Johnson, P.C., Johnson, R.L., C.M. Vogel, R.E. Hinchee, M. Marley, T. Peargin, C.L. Bruce, I.L. Amerson, C.T. Coonfare, R.D. Gillespie, and D.B. McWhorter. 2002. Air Sparging Design Paradigm. Battelle Memorial Institute, Columbus, Ohio. http://www.estcp.org/documents/ techdocs/Air_Sparging.pdf. Leeson, A. and Hinchee, R.E. 1996a. Principles and Practices of Bioventing Volume I: Principles and Practices. Battelle Memorial Institute, Columbus, OH. Leeson, A. and Hinchee, R.E. 1996b. Principles and Practices of Bioventing Volume II: Bioventing Design. Battelle Memorial Institute, Columbus, OH. Lien, H. and Zhang, W. 1999. Reactions of Chlorinated Methanes with Nanoscale Metal Particles in Aqueous Solutions. J. Environ. Eng., 136: 1042–47. Masciangioli, T. and Zhang, W. 2003. Environmental Nanotechnology: Potential and Pitfalls. Environmental Science & Technology, 37:102A–108A. Merritt, F.S. 1989. Standard Handbook for Civil Engineers. McGraw-Hill, New York. National Academy of Sciences. 2000. Natural Attenuation for Groundwater Remediation. Water Science and Technology Board. Washington, DC. National Research Council (NRC), Water Science and Technology Board. 1994. Alternatives for Groundwater Cleanup. Washington, DC. Naval Facilities Engineering Command. 2002. Surfactant-Enhanced Aquifer Remediation (SEAR) Design Manual. Technical Report TR-2206-ENV. Washington, DC. Parsons Engineering Science, Inc. 2001. Groundwater Circulation Well Technology Evaluation at Facility 1381 Cape Canaveral Air Station, Florida. Technical Summary Report. Ramsburg, C.A., Pennell, K.D., Abriola, L.M., Daniels, G., Drummond, C.D., Gamache, M., Hsu, H.-L., Petrovskis, E.A., Rathfelder, K.M., Ryder, J.L., and Yavaraski, T.P. 2005. Pilot-scale demonstration of surfactant-enhanced PCE solubilization. 2. System operation and evaluation. Environ. Sci. Technol. 39:1791–1801. Rumer, R.R. and Mitchell, J.K. 1995. Assessment of Barrier Containment Technologies — A Comprehensive Treatment for Environmental Remediation Applications. National Technical Information Services, Springfield, VA. Russel, M., Colglazier, E.W., and English, M.R. 1991. Hazardous Waste Site Remediation: The Task Ahead. Waste Management Research and Education Institute. University of Tennessee, Knoxville, TN.
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Sai, J.O. and Anderson, D.C. 1992. Barrier wall materials for containment of dense nonaqueous phase liquid (DNAPL). Hazardous Waste and Hazardous Materials. 9, 4, 317–330. U.S. Air Force Center for Environmental Excellence. 2004. Principles and Practices of Enhanced Bioremediation of Chlorinated Solvents. San Antonio, TX. http://www.afcee.brooks.af.mil/products/techtrans/ bioremediation/downloads/PrinciplesandPractices.pdf. USEPA. 1989. Seminar Publication — Transport and Fate of Contaminants in the Subsurface. EPA/636/489/019. Washington, DC. USEPA. 1991. Handbook — Groundwater, Volume II: Methodology. EPA/636/6-90/016b. Washington, DC. USEPA. 1993. Guidance for Evaluating the Technical Impracticability of Ground-Water Restoration. EPA540-R-93-080. Washington, DC. USEPA. 1994. Monitoring the Performance of Groundwater Pump and Treat Systems. EPA/600/R-94/123. Washington, DC. USEPA. 1995a. Remedial Design/Remedial Action Handbook. EPA 540/R-95/059. Washington, DC. USEPA. 1995b. Ground-Water and Leachate Treatment Systems. EPA/636/R-94/005. Washington, DC. USEPA. 1995c. Evaluation of Technologies for In-Situ Cleanup of DNAPL Contaminated Sites. EPA/600/R94/0120. Washington, DC. USEPA. 1996. Capsule Report: Reverse Osmosis Process. EPA/636/R-96/009. Washington, DC. USEPA. 1998a. Field Applications of In Situ Remediation Technologies: Chemical Oxidation. Office of Solid Waste and Emergency Response. EPA 542-R-98-008. http://www.cluin.org/download/remed/chemox.pdf. USEPA. 1998b. Technical Protocol for Evaluating Natural Attenuation of Chlorinated Solvents in Ground Water. Office of Research and Development. Washington, DC. USEPA. 2000a. A Guide to Developing and Documenting Cost Estimated During the Feasibility Study. EPA 540-R-00-002. Washington, DC. USEPA. 2000b. Risk Assessment Guidance for Superfund: Interim Final Guidance (Parts A through E). Office of Emergency and Remedial Response. Washington, DC. USEPA. 2000c. Engineered Approaches to In Situ Bioremediation of Chlorinated Solvents: Fundamentals and Field Applications. Office of Solid Waste and Emergency Response. EPA 542-R-00-008. http://www.epa.gov/tio/download/remed/engappinsitbio.pdf. USEPA. 2002. A Framework for the Economic Assessment of Ecological Benefits. Ecological Benefit Assessment Workgroup, Social Sciences Discussion Group, Science Policy Council. Washington, DC. USEPA. 2003. Superfund Innovative Technology Evaluation Program, Technology Profiles, Seventh Edition. EPA/540/R-94/526. Washington, DC. USEPA. 2004a. Handbook of Groundwater Protection and Cleanup Policies for RCRA Corrective Action for Facilities Subject to Corrective Action Under Subtitle C of the Resource Conservation and Recovery Act. EPA 530-R-04-030. Washington, DC. USEPA. 2004b. Cleaning up the Nation’s Waste Sites: Markets and Technology Trends. 2004 Edition. EPA 542-R-04-015. Washington, DC. USEPA. 2004c. Superfund Chemical Data Matrix. EPA/540-R-94-009. Washington, DC. USEPA. 2004d. In Situ Thermal Treatment of Chlorinated Solvents: Fundamentals and Field Applications. Office of Solid Waste and Emergency Response, Office of Superfund Remediation and Technology Innovation. EPA-542-R-04-010. http://www.clu-in.org/download/remed/ epa542r04010.pdf USGS, 2005. Estimated Use of Water in the United States in 2000. NRL/PU/6115-99-384. Wang, C. and Zhang, W. 1997. Nanoscale Metal Particles for Dechlorination of PCE and PCBs, Environmental Science & Technology, 31: 2154–2156. Xanthakos, P. 1979. Slurry Walls. McGraw-Hill, New York. Xu, Y. and Zhang, W. 2000. Subcolloidal Fe/Ag Particles for Reductive Dehalogenation of Chlorinated Benzenes. Industrial & Engineering Chemistry Research, 39: 2238–2244. Yin, Y. and Allen, H.E. 1999. In Situ Chemical Treatment. Ground-Water Remediation Technologies Analysis Center. Technology Evaluation Report No. TE-99-01. http://www.groundwatercentral.info/ org/pdf/E_inchem.pdf.
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Zheng, C., Wong, H.F., Anderson, M.P., and Bradbury, K.R. 1988. Analysis of interceptor ditches for control of groundwater pollution. J. Hydrol. 98: 67–81.
Further Information USEPA (2000b) presents a good discussion of the basic approaches involved in performing a risk assessment. A discussion of selection of cleanup goals and current issues in groundwater remediation technology is presented by NRC (1994). USEPA (2003) evaluates emerging remediation technologies and routinely publishes updates of the results of the program.
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37 Geosynthetics 37.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37-1 37.2 Geosynthetic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37-3 Design by Function of Geosynthetics • Separation Function • Reinforcement Function • Filtration Function • Drainage Function • Barrier Function • Protection Function
37.3 Geosynthetic Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37-10 Geotextiles • Geomembranes • Geogrids • Geosynthetic Clay Liners • Geocomposite Sheet Drains • Geocomposite Strip (Wick) Drains • Geocells • Erosion Control Products • HDPE Vertical Barrier Systems
37.4 Geosynthetic Applications in Landfill Design . . . . . . . . . 37-27 37.5 Case Histories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37-28
Jorge G. Zornberg University of Texas at Austin
Barry R. Christopher Independent Consultant
Case History of Vertical Barrier System • Case History of Multiple Use of Geosynthetics in Landfill Cover Design
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37-31 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37-34 Further Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37-35
37.1 Introduction Geosynthetics can be defined as planar products manufactured from polymeric material, which are used with soil, rock, or other geotechnical engineering-related material as an integral part of a manmade project, structure, or system (ASTM, 1995). Geosynthetics are widely used in many geotechnical, environmental, and hydraulic applications related to groundwater quality and control. One of the most common examples is the use of geotextile filters in trench (i.e., French) drains. Base and cover liner systems for modern landfills also make extensive use of geosynthetics with the main purpose of minimizing the potential for groundwater contamination. Furthermore, the use of geosynthetics is rapidly increasing in applications related directly to groundwater control. This is the case of high density polyethylene (HDPE) vertical barrier systems, which can be used instead of traditional soil-bentonite cutoff walls in projects involving groundwater remediation and control. The geosynthetics market is strong and rapidly increasing due to the continued use of geosynthetics in well-established applications and, particularly, due to the increasing number of new applications that make use of these products. The strength of the geosynthetics market can be appreciated by evaluating the growth in the estimated amount of geosynthetics in North America over the years. Table 37.1 shows the estimated North American shipments of geosynthetics for 2001. While the total amount of geosynthetics 37-1
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The Handbook of Groundwater Engineering TABLE 37.1 North American Shipments of Geosynthetics Material 1995–2001 (in million m2 )
Geotextiles Geomembranes Geogrids Geosynthetic clay liners Erosion-control products Specialty geosynthetics
1995
1996
1998
2001
346.2 62.4 22.4 5.0 72.7 16.7
356.2 64.4 24.3 5.4 77.8 20.1
419.7 74.6 29.1 6.1 82.8 25.9
477.4 86.8 36.8 8.2 93.6 31.8
Source: Industrial Fabrics Association International (1996).
produced in North America was slightly over 83 million m2 in 1980, the production of geosynthetics was approximately 1 billion m2 in 2005. Geosynthetics applications are very diverse. To fulfill different functions in the design of geotechnical-, environmental-, and hydraulic-related systems, the geosynthetic industry has developed a number of products to meet engineers’ needs. In addition to the use of geotextiles as filters in trench drains, geomembranes in landfill liner systems, and HDPE vertical panels in groundwater control projects, other examples of geosynthetics applications include the use of geotextiles as filtration elements in dams and waste containment systems, the use of geocomposites as erosion control elements in channels and slopes, and the use of geogrids as reinforcement elements in soil embankments, to mention just a few. Numerous tests have been developed to characterize the hydraulic and mechanical properties of geosynthetics. Many of these properties are important in the manufacture and quality control of geosynthetics; however, many others are also important in design. The material properties that are primarily related to the manufacture and quality control of geosynthetics are generally referred to as index properties and those related to the design are referred to as performance properties. When properly correlated to performance properties, some index properties may also be used for design. As the various geosynthetic products can perform different functions, they should be designed to satisfy minimum criteria to adequately perform these functions in a given design. The different functions performed by geosynthetics are discussed in Section 37.2. The functions that geosynthetics may provide are as follows: separation, reinforcement, filtration, drainage, barrier, and/or protection (or stress relief). Geosynthetics are manufactured in sheet form in a factory-controlled environment. They are most often packaged in rolls for transporting to the site. They may also be folded or cut and stacked and placed in cartons. At the project site the geosynthetic sheets are unrolled on the prepared subgrade surface, overlapped to form a continuous geosynthetic blanket, and often physically joined to each other, for example, by welding (geomembranes) or sewing (geotextiles). The different types of geosynthetics are discussed in Section 37.3. They include geotextiles, geomembranes, geogrids, geosynthetic clay liners (GCLs), geocomposite sheet drains, geocomposite strip (wick) drains, geocells, erosion control products and HDPE vertical barrier systems. Different types of geocomposite drains and HDPE vertical barriers, a special form of geomembranes, are considered separately in the list above. These geosynthetics are described separately in this chapter because of their particular relevance in groundwater-related applications. Geotechnical, environmental, and hydraulic systems frequently incorporate several types of geosynthetics, which are designed to perform more than one function in the system. The bottom and cover liner systems of waste containment facilities are good examples of applications that make use of geosynthetics for multiple purposes. In these facilities, the different geosynthetic products are combined to create the liner system, the components fulfill the functions of infiltration barrier, filtration, separation, drainage, protection, and reinforcement. The multiple uses of geosynthetics in the design of modern landfills are described in Section 37.4. Finally, a case history illustrating the use of HDPE panels as vertical barrier in a groundwater control project is presented in Section 37.5. A glossary of relevant terms and a list of sources are also included for further information.
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37.2 Geosynthetic Functions 37.2.1 Design by Function of Geosynthetics As with other engineering materials, there are several design approaches that could be used during the selection process of geosynthetic products. The most common methods are design by experience, by specification, or by function (Koerner, 2005). Design-by-experience is generally based on the use of manufacturer’s literature and of the designer’s experience and familiarity with specific geosynthetic products. An extension of design by experience is design-by-specification, which consists of selecting geosynthetic products for common application areas based on basic minimum or maximum specified property values. These methods may be acceptable for routine, repeat, non-critical applications. Design-by-function is the preferred approach. Design-by-function should be performed as a check for applications covered by specifications and required for applications not covered by specifications or of such a nature that large property or personal damage would result in the event of a failure. A generic design process that applies to the different geosynthetic functions is summarized as follows (Koerner, 2005): 1. 2. 3. 4. 5.
Evaluate the critical and severe nature of the application Determine the function(s) of the geosynthetic Calculate, estimate, or otherwise determine the required property value for the function(s) Test or otherwise obtain the allowable property of the candidate geosynthetic material(s) Calculate the factor of safety (FS) as follows: FS =
allowable (test) value required (design) value
(37.1)
6. Determine if the resulting factor of safety is adequate for the site-specific situation under consideration 7. Prepare specifications and construction documents 8. Observe construction and post-construction performance If the factor of safety is sufficiently high for the specific application, the candidate geosynthetic(s) is (are) deemed acceptable. The same process can be repeated for a number of available geosynthetics, and the final selection among acceptable products is based on availability and cost. The design-by-function approach is the general approach to be followed in the majority of the projects. As mentioned, the primary function(s) of geosynthetics can be separation, reinforcement, filtration, drainage, infiltration barrier, or protection. However, a certain geosynthetic product can perform different functions and, similarly, the same function can often be performed by different types of geosynthetics. Geosynthetic applications are usually defined by the primary or principal function. In addition, geosynthetics can perform one or more secondary functions, which must also be considered when selecting the geosynthetic characteristics for optimum performance. For example, a geotextile can provide separation of two dissimilar soils (e.g., gravel from clay in a road), but the geosynthetic may also be required to provide the secondary function of filtration to minimize the build up of excess pore water pressure in the soil beneath the separator. The specific function(s) of the different geosynthetic(s) are presented in Table 37.2. Each of these functions is described in Section 37.2.2 to Section 37.2.7.
37.2.2 Separation Function Separation is the introduction of a flexible, porous geosynthetic product between dissimilar materials so that the integrity and functioning of both materials can remain intact or be improved. For example, a major cause of failure of roadways constructed over soft foundations is contamination of the aggregate base course with the underlying soft subgrade soils (Figure 37.1a). Contamination occurs both due to: (1) penetration of the aggregate into the weak subgrade due to localized bearing capacity failure under
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37-4 TABLE 37.2
The Handbook of Groundwater Engineering Function of Different Geosynthetic Products
GeoGeotextile membrane Geogrid GCL Separation Reinforcement Filtration Drainage Barrier Protection
X X X X Xa X
X
Geocomposite strip Geocomposite (wick) sheet drain drain
Geocell
Erosion control product
HDPE vertical barrier
X X
X X X
X
X X
X X
X
X
X
a Asphalt-saturated geotextiles.
Transition zone of intermixed material
(a)
(b)
FIGURE 37.1 Separation function of a geotextile placed between road aggregate and soft saturated subgrade. (a) Without geotextile and (b) With geotextile.
stresses induced by wheel loads, and (2) intrusion of fine-grained soils into the aggregate because of pumping or subgrade weakening due to excess pore water pressure. Subgrade contamination results in inadequate structural support that often leads to premature failure of the system. A geotextile can be placed between the aggregate and the subgrade to act as a separator and prevent the subgrade and aggregate base course from mixing (Figure 37.1b). Among the different geosynthetics, geotextiles have been the products generally used in the function of separation. Examples of separation applications are the use of geotextiles between subgrade and stone base in roads and airfields, and between geomembranes and drainage layers in landfills. In addition to these applications, in which separation is the primary function of the geotextile, it could be said that most other geosynthetic applications generally include separation as a secondary function. The design of geosynthetics for separation applications is provided by Holtz et al. (1997, 1998) and Koerner (2005).
37.2.3 Reinforcement Function Geosynthetic inclusions within a soil mass can provide a reinforcement function by developing tensile forces that contribute to the stability of the geosynthetic-soil composite (a reinforced soil structure). Design and construction of stable slopes and retaining structures within space constrains are major economical considerations in geotechnical engineering projects. For example, when geometry requirements dictate changes of elevation for a retaining wall, or dam project, the engineer faces a variety of distinct alternatives for designing the required earth structures. Traditional solutions have been either a near vertical concrete structure or a conventional, relatively flat, unreinforced slope (Figure 37.2). Although simple to design, concrete wall alternatives have generally led to elevated construction and material costs. On the other hand, the construction of unreinforced embankments with flat slope angles dictated by stability considerations is an alternative often precluded in projects where design is controlled by space constraints. As shown in
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37-5 Increasing right-of-way
(a)
(b)
(c)
(d)
Increasing construction cost
FIGURE 37.2 Reinforcement function of geosynthetics used to optimize the design of earth retaining structures: (a) concrete retaining wall; (b) reinforced wall; (c) reinforced slope; (d) unreinforced slope.
Figure 37.2, an alternative would be to place horizontal, geosynthetic reinforcing elements in the soil to allow construction of very steep embankment side slopes or a vertical reinforced soil wall. For example, vertical reinforced soil walls have been used to both construct dams for reservoirs and increase the height of existing dams. Geosynthetic products typically used as reinforcement elements are geotextiles and geogrids. Additional products include geocells and fiber reinforcement. Reinforced soil walls generally provide vertical grade separations at a lower cost than traditional concrete walls. Reinforced wall systems involve the use of facing elements such as precast panels, cast-in-place concrete panels, or modular block systems. Alternatively, steepened reinforced slopes (with facing inclination below approximately 70◦ ) may eliminate the use of facing elements, thus saving material costs and construction time in relation to vertical reinforced walls. As indicated in Figure 37.2, a reinforced soil system generally provides an optimized alternative for the design of earth retaining structures by combining lower cost and decreased right-of-way requirements. The effect of geosynthetic reinforcements on the stability of slopes is illustrated in Figure 37.3, which shows a reduced scale geotextile-reinforced slope model built using dry sand as backfill material. The maximum slope inclination of unreinforced sand under its own weight is the angle of repose of the sand, which is well below the inclination of the slope face of the model in the figure. Horizontal geotextile reinforcements placed within the backfill provided stability to the steep sand slope. In fact, not only did the reinforced slope model not fail under its own weight, but its failure only occurred when the unit weight of the backfill was increased 67 times by placing the model in a geotechnical centrifuge (Zornberg et al., 1998). Figure 37.4 shows the reinforced slope model after centrifuge testing. The use of inclusions to improve the mechanical properties of soils dates to ancient times. However, it is only within the last 35 years (Vidal, 1969) that analytical and experimental studies have led to the contemporary soil reinforcement techniques. Soil reinforcement is now a highly attractive alternative for embankment and retaining wall projects because of the economic benefits it offers in relation to conventional retaining structures. Its acceptance has also been triggered by a number of technical factors including aesthetics, reliability, simple construction techniques, good seismic performance, and the ability to tolerate large deformations without structural distress. The design of reinforced soil walls is based on earth pressure theory while the design of reinforced slopes is based on the use of limit equilibrium methods. The design process involves evaluation of the external (global), internal, and compound stability of the structure. The required tensile strength of the reinforcements is selected in design so that the margins of safety to prevent internal failure, such as that shown in Figure 37.4, are adequate. Guidance in soil reinforcement design procedures is provided by Elias et al. (2001), Holtz et al. (1997, 1998), and NCMA (1997).
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FIGURE 37.3 Model of a sand slope reinforced with geosynthetics.
FIGURE 37.4 Reinforced slope model brought to failure by increasing the unit weight of the backfill.
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A special form of geosynthetic reinforcement is the mixing of fibers with the soil. Fiber reinforcement is used in applications such as stabilization of thin soil veneers, localized repair of failed slopes and increasing the seismic performance. Randomly distributed fibers can provide isotropic strength increases to the soil and avoid the existence of the potential planes of weakness that can develop on the soilreinforcement interface. The design of fiber-reinforced soil slopes has typically been performed using composite approaches, where the fiber-reinforced soil is considered as a single homogenized material. Accordingly, fiber-reinforced soil design has required non-conventional laboratory testing of composite fiber-reinforced soil specimens, which has discouraged implementation of fiber-reinforcement in engineering practice. A new discrete approach was recently proposed (Zornberg, 2002), which predicts the “equivalent” shear strength of the fiber-reinforced soil based on the independent properties of fibers (e.g., fiber content, fiber aspect ratio) and soil (e.g., friction angle and cohesion).
37.2.4 Filtration Function The filtration function involves movement of liquid through the geosynthetic and, at the same time, retention of soil on its upstream side. As indicated in Table 37.2, geotextiles are the product generally used for the function of filtration. Applications include geotextile filters for trench drains, blanket drains, interceptor drains, structural drains, toe drains in dams, filters for hard armor (e.g., rip-rap, gabions, fabric-form) erosion control systems, silt fences, and silt curtains. Both adequate hydraulic conductivity (provided by a geotextile with a relatively porous structure) and adequate soil retention (provided by a geotextile with a relatively tight structure) should be offered by the selected product. In addition, considerations should be made regarding the long-term soil-to-geotextile flow compatibility such that the flow through the geotextile will not be excessively reduced by clogging during the lifetime of the system. The geosynthetic-to-soil system should then achieve an equilibrium that allows for adequate liquid flow with limited soil loss across the geotextile throughout a service lifetime compatible with the application under consideration. Filtration concepts are well established in the design of soil filters, and similar concepts are used in the design of geotextile filters. As the flow of liquid is perpendicular to the plane of the geosynthetic, filtration refers to the crossplane hydraulic conductivity. Some of the geosynthetics used for this purpose are relatively thick and compressible. For this reason, geosynthetics are generally characterized by their permittivity, which is defined as: ψ = kn /t
(37.2)
where ψ is the permittivity, kn is the cross-plane hydraulic conductivity, and t is the geosynthetic thickness at a specified normal pressure. Testing procedures for geotextile permittivity follow similar guidelines used for testing the hydraulic conductivity of the soil. Some designers prefer to work directly with hydraulic conductivity and require the geotextile’s hydraulic conductivity to be some multiple of the adjacent soil’s hydraulic conductivity (Christopher and Fischer, 1992). As the flow of liquid through the geotextile increases, the geotextile voids should be larger. However, large geotextile voids can lead to an unacceptable situation called soil piping, in which the soil particles are continuously carried through the geotextile, leaving large soil voids behind. The liquid velocity then increases, which accelerates the process and may lead to the collapse of the soil structure. This process can be prevented by selecting a geotextile with voids small enough to retain the soil on the upstream side of the fabric. It is the coarser soil fraction that must be initially retained. The coarser-sized particles eventually create a filter “bridge,” which in turn retains the finer-sized particles, building up a stable upstream soil structure (Figure 37.5). Several methods have been developed for soil retention design using geotextiles; most of them compare the soil particle size characteristics to the 95% opening size of the geotextile (defined as O95 of the geotextile). The test method used in the United States to determine the geotextile opening size is called the apparent opening size (AOS) test (ASTM D 4751).
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Filter
FIGURE 37.5 Geotextile providing adequate filtration through selection of adequate opening size and formation of soil filter bridge.
Some of the soil particles will rest on or embed them within the geotextile structure, and will cause a reduction in the hydraulic conductivity or permittivity of the geotextile. Although some partial clogging should be expected, the designer should ensure that the geotextile will not become excessively clogged, that is, that the flow of liquid will not be decreased to a point in which the system will not adequately perform its function. Thus, the geotextile voids should be large enough to allow the finer soil particles to pass. Clogging potential creates a special problem when geotextiles are used to wrap pipes due to the restricted area available for flow (i.e., a portion of the geotextile is covered by the pipe walls). Any clogging will significantly reduce the flow into the pipe. Either the flow capacity of the geotextile should be increased proportionally to the covered area (i.e., the total pipe area divided by geotextile area available for flow, which is usually the area of the holes in the pipe) or the geotextile should only be used to wrap gravel placed around the pipe. Design guidelines are available for clogging evaluation of non-critical, non-severe cases (Holtz et al., 1997, 1998; Koerner, 2005), but laboratory testing is strongly recommended in important applications. The gradient ratio test (ASTM D 5101), the long-term flow test (Halse et al., 1987), or the hydraulic conductivity ratio test (ASTM D 5567) should be performed. An evaluation of the filtration function of geotextiles is provided by Giroud (1996), Bhatia and Smith (1996a,b), Bhatia et al. (1996), Holtz et al. (1997, 1998), and Palmeira and Fannin (2002). Proper construction is a critical factor in the performance of the filtration function. To develop and maintain the filter bridge, the geotextile must be placed in continuous (intimate) contact with the soil to be filtered such that no void spaces occur behind the geotextile. Placement granular material (e.g., gravel, drain rock, or rip rap) must also be consistent with the strength and durability of the geosynthetic to prevent damage during construction.
37.2.5 Drainage Function Geosynthetics provide a drainage function by transmitting liquid within the plane of their structure. As shown in Table 37.2, the geosynthetics generally used for drainage purposes are geotextiles and geocomposites. The drainage function of geosynthetics allows for adequate liquid flow with limited soil loss within the plane of the geotextile over a service lifetime compatible with the application under consideration. Thick, needle-punched nonwoven geotextiles have considerable void space in their structure and can convey liquid in their plane (on the order of 0.01 to 0.1 l/sec/m width of geotextile). Geocomposite drains can transmit one to two orders of magnitude more liquid than geotextiles. Proper design should dictate what type of geosynthetic drainage material is necessary. The soil retention and the long-term compatibility considerations regarding the drainage function of geosynthetics are the same as those discussed in Section 37.2.4 regarding the filtration function of geosynthetics. As the geosynthetic thickness decreases with increasing normal stress, the in-plane drainage
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of a geosynthetic is generally quantified by its transmissivity, which is defined as: θ = kp · t
(37.3)
where θ is the transmissivity, kp is the in-plane hydraulic conductivity, and t is the geosynthetic thickness at a specified normal pressure. The in-plane flow capacity of geosynthetic will reduce under compression and with time (due to creep). Therefore, the transmissivity should be evaluated under normal pressures that are comparable to field conditions with a factor of safety included in the design to account for the design life of the project. Design guidance is provided by Holtz et al. (1997, 1998) and Koerner (2005). Calculating the thickness of the liquid in or above a liquid collection layer is an important design step because one of the design criteria for a liquid collection layer is that the maximum thickness of the liquid collection layer must be less than an allowable thickness. The thickness of liquid in a liquid collection layer depends on the rate of liquid supply. A typical case of liquid supply is that of liquid impinging onto the liquid collection layer. Two examples of liquid collection layers with such a type of liquid supply can be found in landfills: (1) the drainage layer of the cover system, where the liquid that impinges onto the liquid collection layer is the precipitation water that has percolated through the soil layer overlying the drainage layer; and (2) the leachate collection layer, where the liquid that impinges onto the leachate collection layer is the leachate that has percolated through the waste and through the protective soil layer overlying the leachate collection layer. Equations are available (Giroud et al., 2000) to calculate the maximum thickness of liquid in a liquid collection layer located on a single slope with a perfect drain at the toe.
37.2.6 Barrier Function The barrier function can be performed by geosynthetic products that have adequately low hydraulic conductivity as to provide containment to liquid or vapor. As shown in Table 37.2, the barrier function may be provided by several types of geosynthetics, namely, geomembranes and geosynthetic clay liners (GCLs). Other geosynthetic products also used as infiltration barriers include membrane-encapsulated soil layers (MESLs) used with paved or unpaved road construction, asphalt-saturated geotextiles used in the prevention of bituminous pavement crack reflection problems, and geofoam used for insulation against moisture and extreme temperatures. Geosynthetic barriers are commonly used as liner for surface impoundments storing hazardous and nonhazardous liquids, as covers above the liquid surface of storage reservoirs, and as liner for canals used to convey water or chemicals. Geosynthetic barriers are also used as secondary containment for underground storage tanks, and in applications related to dams and tunnels. Of particular relevance for groundwater applications is the use of geosynthetic barriers for seepage control (HDPE vertical barrier systems). A common application of geosynthetics as infiltration barriers is base and cover liners for landfills. In landfill applications, infiltration barriers are typically used instead of (or in addition to) low-hydraulic conductivity soils. Base liners are placed below the waste to prevent liquids from the landfill (leachate) contaminating the underlying ground and the groundwater. Geosynthetic cover liner systems are placed above the final waste configuration to keep precipitation water from entering the waste and generating leachate. If a building or other structure is constructed on a landfill, a geosynthetic barrier may be placed under the building foundation to provide a barrier for vapors such as landfill gas. The use of geosynthetics in infiltration barriers is further described in Koerner (2005). Dams are among the most critical hydraulic structures and stand to benefit the most from the use of geosynthetics. Deterioration and structural damage due to seepage are major concerns that have been addressed by placement of geomembrane liners. Geosynthetic systems as hydraulic barriers in dams are effective solutions to the problem of degradation. Accordingly, geosynthetics have been used in a wide range of dam types and dam sizes. The first installation of a geomembrane in a dam was in Italy in 1959. Since then, geosynthetics have been installed in dams worldwide as part of new projects and rehabilitation projects. Most recently, the Olivenhain Dam in San Diego was built with a geosynthetic system as an infiltration barrier. Significant advances have taken place in geosynthetics engineering since
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geomembranes were first used in hydraulic structures. A good example is the current confidence on the extended service life of geomembranes. Additional information on the use of geosynthetics in dams is provided by and can be found in Christopher and Dahlstrand (1989), Zornberg and Weber (2003), Zornberg (2005), and Scuero et al. (2005).
37.2.7 Protection Function Geosynthetics (mainly geotextiles) can be used to provide stress relief and protect other materials such as geosynthetics (mainly geomembranes) against damage. A common example is the use of geotextiles to provide protection against puncture of geomembranes in waste and liquid containment systems. Adequate mechanical protection must be provided to resist both short-term equipment loads and long-term loads imparted by the waste. Experience has shown that geotextiles can play an important role in the successful installation and long-term performance of geomembranes by acting as a cushion to prevent puncture damage of the geomembrane. In the case of landfill base liners, geotextiles can be placed (1) below the geomembrane to resist puncture and wear due to abrasion caused by sharp-edged rocks in the subgrade, and (2) above the geomembrane to resist puncture caused either by the drainage aggregate or direct contact with waste materials. In the case of landfill cover liners, geotextiles can be placed below the geomembrane to reduce risk of damage by sharp objects in the landfill and above the geomembrane to prevent damage during placement of drainage aggregate or cover soil. Key characteristics for the geotextile cushions are polymer type, mass density, method of manufacture, and construction survivability. The selection process of a geotextile that fulfills a protective function of a geomembrane involves the following three steps: (1) selection of polymer type and method of manufacture; (2) evaluation of the geotextile’s capacity to provide puncture protection for the geomembrane; and (3) evaluation of construction survivability. Detailed procedures and methods for conducting these evaluations are described by Holtz et al. (1997, 1998), Koerner (2005), Narejo et al. (1996), and Wilson-Fahmy et al. (1996). Another protection application associated with groundwater is erosion control blankets and mats. In this case, the geosynthetic protects the ground surface from the prevailing atmospheric conditions (i.e., wind, rain, snow, etc.). Specialty geocomposites have been developed for the specific purpose of erosion control. The general goal of these products is to protect soil slopes from both sheet and gully erosion, either permanently or until vegetation is established. Information on the design of geosynthetics for separation applications is provided by Holtz et al. (1997, 1998) and Koerner (2005).
37.3 Geosynthetic Types As indicated in the introduction Section 37.1, there are a number of different geosynthetics. The characteristics of these materials vary considerably, primarily due to the method of manufacturing and the types and amount of polymers used for their production. This section provides a brief description of these materials and their primary characteristics. Additional information on the manufacturing process and characteristics of geosynthetics is provided by Koerner (2005) and Holtz et al. (1997, 1998) as well as by manufacturer’s organizations, such as the Geosynthetic Manufacturer’s Association (www.gmanow.com) and the PVC Geomembrane Institute (pgi-tp.ce.uiuc.edu).
37.3.1 Geotextiles Among the different geosynthetic products, geotextiles are the ones that present the widest range of properties. They can be used to fulfill all the different functions listed in Table 2.2 for many different geotechnical, environmental, and hydraulic applications. For example, Figure 37.6 shows the construction of a reinforced slope in which geotextiles were selected as multipurpose inclusions within the fill, as they can provide not only the required tensile strength (reinforcement function), but also the required transmissivity (drainage function), needed for that particular project (Zornberg et al., 1995).
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FIGURE 37.6 Placement of a high-strength nonwoven geotextile to perform a dual function of reinforcement and in-plane drainage in a reinforced slope.
Geotextiles are manufactured from polymer fibers or filaments that are later formed to develop the final product. Approximately 85% of the geotextiles used today are based on polypropylene resin. An additional 10% are polyester and the remaining 5% is a range of polymers including polyethylene, nylon, and other resins used for specialty purposes. As with all geosynthetics, however, the base resin has various additives, such as for ultraviolet light protection and long-term oxidative stability. The most common types of fibers or filaments used in the manufacture of geotextiles are monofilament, multifilament, staple filament, and slit-film. If fibers are twisted or spun together, they are known as a yarn. Monofilaments are created by extruding the molten polymer through an apparatus containing small-diameter holes. The extruded polymer strings are then cooled and stretched to give the filament increased strength. Staple filaments are also manufactured by extruding the molten polymer; however, the extruded filaments are cut into 25- to 100- mm portions. The staple filaments or fibers may then be spun into longer yarns. Slit-film filaments are manufactured by either extruding or blowing a film of a continuous sheet of polymer and cutting it into filaments by knives or lanced air jets. Slit-film filaments have a flat, rectangular cross-section instead of the circular cross-section shown by the monofilament and staple filaments. The filaments, fibers, or yarns are formed into geotextiles using either woven or nonwoven methods. Figure 37.7 shows a number of typical woven and nonwoven geotextiles. Woven geotextiles are manufactured using traditional weaving methods and a variety of weave types. Nonwoven geotextiles are manufactured by placing and orienting the filaments or fibers onto a conveyor belt, which are subsequently bonded by needle punching or by melt bonding. The needle-punching process consists of pushing numerous barbed needles through the fiber web. The fibers are thus mechanically interlocked into a stable configuration. As the name implies, the heat (or melt) bonding process consists of melting and pressurizing the fibers together. Common terminology associated with geotextiles includes machine direction, cross machine direction, and selvage. Machine direction refers to the direction in the plane of fabric in line with the direction of
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Woven geotextiles
Nonwoven geotextiles
FIGURE 37.7 Typical woven and nonwoven geotextiles.
manufacture. Conversely, cross machine direction refers to the direction in the plane of fabric perpendicular to the direction of manufacture. The selvage is the finished area on the sides of the geotextile width that prevents the yarns from unraveling. Adjacent rolls of geotextiles are seamed in the field by either overlapping or sewing. Sewing is generally the case for geotextiles used as filters in landfill applications, but may be waived for geotextiles used in separation. Heat bonding may also be used for joining geotextiles used in filtration and separation applications. Numerous tests have been developed to evaluate the properties of geotextiles. In developing geotextile specifications, it is important that the designer understands the material tests and that material properties important for the geotextile’s intended use are specified. Table 37.3 describes the tests commonly performed in geotextile products (ASTM, 1995). Geotextiles can generally be specified with index and performance properties. As previously discussed, critical filtration applications are exceptions and the use of pre-qualified specific products from performance flow tests are strongly recommended.
37.3.2 Geomembranes Geomembranes are flexible, polymeric sheets that have very low hydraulic conductivity (typically less than 10−11 cm/sec) and, consequently, are used as liquid or vapor barriers. The most common types of geomembranes are high density polyethylene (HDPE), very flexible polyethylene (VFPE), polyvinyl chloride (PVC), flexible polypropylene (fPP) and reinforced chlorosulfonated polyethylene (CSPE). Figure 37.8 shows a number of geomembranes currently available in the geosynthetics market. Polyethylene is the type of geomembrane most commonly used in landfill applications for base and cover liner systems. This is primarily because of its high chemical resistance and durability. Specifically, high-density polyethylene (HDPE) is typically used in base liner systems. This material is somewhat rigid but generally has good physical properties and can withstand large stresses often imposed on the geomembrane during construction. VFPE and PVC are the most commonly used geomembrane materials besides HDPE. The term VFPE encompasses various polyethylene grades such as very low density polyethylene (VLDPE) and certain types of linear low density polyethylene (LLDPE). The linear structure and lack of long-chain branching
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Standard Tests for Geotextiles
Property
Test standard
Thickness
ASTM D 5199
Mass per Unit Area
ASTM D 5261
Grab rupture
ASTM D 4632
Uniaxial tensile strength geotextiles Geogrids
ASTM D 4595 ASTM D 6637
Multiaxial tensile, puncture or burst tests Trapezoid tear strength Apparent opening size
ASTM D 6241 ASTM D 4533 ASTM D 4751
Permittivity
ASTM D 4491
Gradient ratio
ASTM D 5101
Transmissivity
ASTM D 4716
Ultraviolet resistance
ASTM D 4355
Seam strength Seam strength
ASTM D 1683 ASTM D 4884
Test name Standard Test Method for Measuring Nominal Thickness of Geotextiles and Geomembranes Standard Test Method for Measuring Mass per Unit area of Geotextiles Standard Test Method for Breaking Load and Elongation of Geotextiles (Grab Method) Standard Test Method for Tensile Properties of Geotextiles by the Wide-Width Strip Method Standard Test Method for Determining Tensile Properties of Geogrids by the Single or Multi-Rib Tensile Method Standard Test Method for the Static Puncture Strength of Geotextiles and Geotextile Related Products Using a 50-Mm Probe Standard Test Method for Trapezoid Tearing Strength of Geotextiles Standard Test Method for Determining Apparent Opening Size of a Geotextile Standard Test Methods for Water Permeability of Geotextiles by Permittivity Standard Test Method for Measuring the Soil-Geotextile System Clogging Potential by the Gradient Ratio Standard Test Method for Constant Head Hydraulic Transmissivity (In-Plane Flow) of Geotextiles and Geotextile Related Products Standard Test Method for Deterioration of Geotextiles from Exposure to Ultraviolet Light and Water (Xenon-Arc Type Apparatus) Failure in Sewn Seams of Woven Fabrics Standard Test Method for Seam Strength of Sewn Geotextiles
Geomembranes
FIGURE 37.8 Typical geomembranes.
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Criteria for Selection of HDPE, PVC, or CSPE Geomembranes Considerations for selection
Liquid barrier
Mechanical properties
Construction survivability
Installation
Chemical resistance
Long-term durability
All three polymers have acceptable characteristics as liquid barriers, although HDPE geomembranes have the best characteristics in terms of chemical resistance and long-term durability. All three have extremely low hydraulic conductivity and are impermeable for practical purposes. Although the mechanical properties vary somewhat with geomembrane thickness, HDPE is relatively stiff and has relatively small yield strain. PVC, in contrast, is relatively extensible and does not exhibit yield. The tensile properties of CSPE often fall between those of HDPE and PVC but are difficult to generalize because CSPE is usually made with embedded reinforcing fabrics which affect tensile response. All three polymers have an acceptable ability to maintain integrity when subjected to concentrated stresses. However, the best performance is obtained with more extensible geomembranes. Therefore, based on the relative extensibility, PVC generally offers the most favorable performance. Key considerations include ease of placement and seaming. PVC and CSPE are easier to place than HDPE because their greater flexibility makes them conform more easily to the foundation and makes them less prone to thermal expansion wrinkles. Acceptable placement and wrinkle control, however, can be achieved with all three polymers if appropriate installation procedures are used. All three polymers are easily seamed, with HDPE usually achieving the highest seam strength and quality. HDPE has the highest degree of compatibility with a wide variety of chemicals encountered in wastes. CSPE has good resistance to many chemicals, but is attacked by some that are relatively common, namely chlorinated solvents and hydrocarbons. PVC typically is the least chemically resistant of these polymers. HDPE offers the best performance. HDPE is a highly inert and durable material that is not susceptible to chemical degradation under conditions generally encountered in landfills. In addition, HDPE is not susceptible to physical degradation (extraction). The durability of PVC geomembranes is less favorable than that of HDPE. This is because PVC geomembranes are composed of approximately two-thirds PVC resin and one-third plasticizers. Over time, physical degradation (extraction) may cause plasticizer loss which results in reduced geomembrane flexibility. The durability of CSPE geomembranes is typically between that of HDPE and PVC.
in both LLDPE and VLDPE arise from their similar polymerization mechanisms. Due to the large settlements that may occur, cover liner systems commonly require a flexible geomembrane. VFPE is often used in this application as it provides similar chemical resistance as HDPE but is more flexible and can more readily conform to underlying refuse settlements without puncturing. Flexible polypropylene (fPP) geomembranes have recently (1990) been developed by combining the polypropylene (PP) and the ethylene propylene elastomer (EPE). This product was developed to obtain physical characteristics similar to the low density polyethylene while offering the flexibility similar to the polyvinyl chloride geomembranes. PVC geomembranes are used in liners for many waste containment applications, such as contaminated soils containment and liquid storage ponds. While PVC may not be as durable as polyethylene geomembranes, the merits of PVC geomembranes are that they are generally less expensive than polyethylene geomembrane and can be factory manufactured in relatively large panels. The large panel sizes allow easier installation as there are fewer field fabricated seams. In landfill applications, geomembranes are typically used as a base or a cover liner in place of or in addition to low-hydraulic conductivity soils. The key performance factors related to the selection of geomembrane polymer types for landfill applications are summarized in Table 37.4. Geomembrane thickness ranges from 0.75 to 2.5 mm (30 to 100 mils). Table 37.5 summarizes the key performance factors related to
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TABLE 37.5
Criteria for Minimum Thickness of HDPE Geomembrane
Criteria
Considerations for selection of thickness
Abrasion resistance Response to differential settlements
Effective welding
The abrasion resistance of HDPE geomembranes increases with geomembrane thickness. Experience indicates that geomembranes with thickness < 1 mm may not have acceptable abrasion resistance. The thicker the HDPE geomembrane, the higher its stiffness. This issue is more significant for geomembrane cover systems than for geomembrane base liner systems because the cover system must be flexible enough to accommodate differential settlements. From this viewpoint, a thickness of not more than 2 mm is desirable. The thinner the HDPE geomembrane, the more difficult is the welding of adjacent panels. For most effective welding, a desirable thickness is of at least 1 mm (40 mils), and preferably 1.5 to 2 mm.
the selection of the thickness of HDPE geomembranes for landfill applications. Geomembranes are placed after subgrade preparation, and placement is followed by seaming, inspection, and backfilling. A properly designed geomembrane has the potential of hundreds of years of service lifetime, but installation must follow high quality management principles. In the early uses of geomembranes for waste containment applications, the main concerns were related to the chemical compatibility between geomembranes and waste, and to the service life of geomembranes. Now, construction quality issues are viewed as the principal limitations to the performance of geomembranes. For continuity of the impermeable barrier, geomembranes should be seamed in the field. The fundamental mechanism of seaming polymeric geomembrane sheets together is to temporarily reorganize (melt) the polymer structure of the two surfaces to be joined in a controlled manner. This reorganization can be done either through thermal or chemical processes. These processes may involve the addition of extra polymer in the bonded area. There are four general categories of seaming methods: extrusion welding, thermal fusion or melt bonding, chemical fusion, and adhesive seaming. Thermal fusion and extrusion welding are the methods most commonly used, and are described next. In thermal fusion or melt bonding (the most common seaming method), portions of the opposing surfaces are truly melted. Temperature, pressure, and seaming rate play important roles as excessive melting weakens the geomembrane and inadequate melting results in low seam strength. The hot wedge, or hot shoe, method consists of an electrically heated resistance element in the shape of a wedge that travels between the two sheets to be seamed. A standard hot wedge creates a single uniform width seam, while a dual hot wedge (or “split” wedge) forms two parallel seams with a uniform unbonded space between them. This space can then be conveniently used to evaluate seam quality and continuity by pressurizing the unbonded space with air and monitoring any drop in pressure that may signify a leak in the seam (Figure 37.9). Extrusion welding is at present used exclusively on geomembranes made from polyethylene. A ribbon of molten polymer is extruded over the edge of, or in between, the two surfaces to be joined. The molten extrudate causes the surface of the sheets to become hot and melt, after which the entire mass cools and bonds together. The technique is called extrusion fillet seaming when the extrudate is placed over the leading edge of the seam, and is called extrusion flat seaming when the extrudate is placed between the two sheets to be joined. Fillet extrusion seaming is essentially the only practical method for seaming polyethylene geomembrane patches, for seaming in poorly accessible areas such as sump bottoms and around pipes, and for seaming of extremely short seam lengths. The material properties of geomembranes are divided into the properties of the raw polymer or resin used in the manufacture of the geomembrane sheet and the manufactured geomembrane properties. Table 37.6 lists the tests commonly performed for evaluation of the raw polymer properties. Table 37.7 summarizes the tests commonly performed to evaluate the manufactured geomembrane sheet properties (ASTM, 1995). As with the geotextiles, many of these tests provide index or quality control properties.
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FIGURE 37.9 Monitoring seaming of a geomembrane liner.
TABLE 37.6
Tests for Raw Geomembrane Polymers
Property
Test standard
Test name
Density
ASTM D 792
Density
ASTM D 1505
Melt index
ASTM D 1238
Standard Test Method for Specific Gravity and Density of Plastics by the Density-Gradient Technique Standard Test Method for Density of Plastics by the Density-Gradient Technique Standard Test Method for Flow Rates of Thermoplastics by Extrusion Plastometer Thermogravimetric Analysis (TGA) Differential Scanning Calorimetry (DSC) Thermomechanical Analysis (TMA) Infrared Spectroscopy (IR) Chromatography (GC) Gel Permeation Chromatography (GPC)
Chemical identification methods (fingerprinting)
37.3.3 Geogrids Geogrids constitute a category of geosynthetics designed preliminary to fulfill a reinforcement function. Geogrids have a uniformly distributed array of apertures between their longitudinal and transverse elements. The apertures allow direct contact between soil particles on either side of the installed sheet, thereby increasing the interaction between the geogrid and the backfill soil. Geogrids are composed of polypropylene, polyethylene, polyester, or coated polyester. They are formed by several different methods. The coated polyester geogrids are typically woven or knitted. Coating is generally performed using PVC or acrylics to protect the filaments from construction damage and to maintain the grid structure. The polypropylene geogrids are either extruded or punched sheet drawn, and polyethylene geogrids are exclusively punched sheet drawn. Figure 37.10 shows a number of typical geogrid products. In the past several years, geogrids have also been manufactured by interlacing polypropylene or polyester strips together and welding them at their cross-over points (i.e., junctions).
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Geosynthetics TABLE 37.7
37-17
Standard Tests for Geomembranes
Property
Test standard
Test name
Thickness
ASTM D 5199
Tensile behavior
ASTM D 6693
Tensile behavior Tensile behavior
ASTM D 7003 ASTM D 882
Tensile behavior
ASTM D 4885
Tear resistance Puncture resistance Puncture resistance Puncture resistance Environmental stress crack Environmental stress crack Carbon black Carbon black
ASTM D 1004 ASTM D 2065
Standard Test Method for Measuring Nominal Thickness of Geotextiles and Geomembranes Test Method for Determining Tensile Properties of Nonreinforced Polyethylene and Nonreinforced Flexible Polypropylene Geomembranes Test Method for Strip Tensile Properties of Reinforced Geomembranes Test Methods for Tensile Properties of Thin Plastic Sheeting (Method A Used for PVC) Standard Test Method for Determining Performance Strength of Geomembranes by the Wide Strip Tensile Method Test Method for Initial Tear Resistance of Plastic Film and Sheeting Puncture Resistance and Elongation Test
Durability chemical resistance Seam strength
ASTM D 5721 ASTM D 5747 ASTM D 4437
Leak detection
ASTM D 7007
ASTM D 5494 ASTM D 5514
Test Method for the Determination of Pyramid Puncture Resistance of Unprotected and Protected Geomembranes Test Method for Large-Scale Hydrostatic Puncture Testing of Geosynthetics
ASTM D 1693
Standard Test Method for Environmental Stress-Cracking of Ethylene Plastics
ASTM D 5397
Test Method for Evaluation of Stress Crack Resistance of Polyolefin Geomembranes Using Notched Constant Tensile Load Test Standard Test Method for Carbon Black in Olefin Plastics Standard Practice for Microscopic Evaluation of the Dispersion of Carbon Black in Polyolefin Geosynthetics Practice for Air-Oven Aging of Polyolefin Geomembranes Practice for Tests to Evaluate the Chemical Resistance of Geomembranes to Liquids Standard Practice for Determining the Integrity of Field Seams Used in Joining Flexible Polymeric Sheet Geomembranes Practices for Electrical Methods for Locating Leaks in Geomembranes Covered with Water or Earth Materials
ASTM D 1603 ASTM D 5596
Although geogrids are used primarily for reinforcement, some products are used for asphalt overlay and some are combined with other geosynthetics to be used in water proofing or in separation and stabilization applications. In waste containment systems, geogrids may be used to support a lining system over a weak subgrade or to support final landfill cover soils on steep refuse slopes. Geogrids are also used for support of liners in the design of “piggyback” landfills, which are landfills built vertically over older, usually unlined landfills. Regulatory agencies often require that a liner system be installed between the old and new landfill. As the old refuse is highly compressible, it provides a poor base for the new lining system. A geogrid may be used to support the lining system and bridge over voids that may occur beneath the liner as the underlying refuse components decompose. As with other geosynthetics, geogrids have several physical, mechanical, and durability properties. Many of the test methods used for geotextiles and geomembranes also apply to geogrids. In particular, a key design parameter for reinforcement is the tensile strength, which is performed with the specimen width incorporating typically a few ribs of the geogrid. The allowable tensile strength of geogrids (and of other geosynthetics used for soil reinforcement applications) is typically significantly less than its ultimate tensile strength. The allowable tensile strength is determined by dividing the ultimate tensile strength by partial factors to account for installation damage, creep deformation, chemical degradation, and biological degradation. The partial factors for installation damage, chemical degradation, and biological degradation range from 1.0 to 1.6, with the partial factor of safety for creep ranging from 1.5 to 3.5 (Koerner, 2005). The design engineer should review all recommendations, available codes, national evaluations, and the like and determine appropriate partial factors for the specific projects (i.e., manufacturers’ recommendations should be carefully evaluated based on project-specific requirements and not blindly accepted).
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Geogrids
FIGURE 37.10
Typical geogrids.
37.3.4 Geosynthetic Clay Liners Geosynthetic clay liners (GCLs) are rapidly expanding products in the geosynthetics market. GCLs are infiltration barriers consisting of a layer of unhydrated, loose granular or powdered bentonite placed between two or on top of one geosynthetic layer (geotextile or geomembrane). GCLs are produced in panels that are joined in the field by overlapping. They are generally used as an alternative to compacted clay liners (Bouazza, 2002). Due to the inherent low shear strength of hydrated bentonite, GCL usage had initially been limited to applications where stability of the overlying materials was not a concern. In the late 1980s, however, methods were developed to reinforce the GCLs, producing a composite material with higher shear strength properties. This allowed the use of GCLs in landfill applications (Figure 37.11). Some advantages of GCLs over compacted clay liner are that they occupy significantly less space to achieve equivalent performance, plus they are flexible, self-healing, and easy to install. In locations where low hydraulic conductivity clays are not readily available, they may offer significant construction cost savings. In addition, as they are factory manufactured with good quality control, field construction quality assurance costs are typically less than with compacted clay liners. Bentonite is a clay formed primarily from the mineral montmorillonite. While several types of montmorillonite exist, including calcium and sodium montmorillonite, the term bentonite typically refers to a sodium montmorillonite. Water is strongly attracted to the surface of the negatively charged montmorillonite crystal and is readily absorbed by it. In its unhydrated state, the montmorillonite crystals are densely packed. Once hydrated, the structure becomes very open and swells. The high water absorption and swell characteristics of bentonite lead to its low hydraulic conductivity and low hydrated shear strength. Geosynthetic clay liners are manufactured by laying down a layer of dry bentonite, approximately 5 mm thick, on a geosynthetic material and attaching the bentonite to the geosynthetic. Two general configurations are currently employed in commercial processes (Figure 37.12): bentonite sandwiched between two geotextiles or bentonite glued to a geomembrane. The primary purpose of the geosynthetic component
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37-19
FIGURE 37.11 Installation of a GCL during construction of a landfill base liner.
(a)
4–5 mm
Bentonite + Adhesive
Adhesive bond between bentonite and geomembrane Geomembrane
Geotextile
(b)
5–7 mm
Bentonite + Adhesive
Geotextile
FIGURE 37.12 geotextiles.
GCL configurations: (a) bentonite glued to a geomembrane; (b) bentonite sandwiched between two
is to hold the bentonite together in a uniform layer and to permit transportation and installation of the GCL without loss of bentonite. The outer geosynthetic layer of GCLs can be mechanically bonded using stitching or needle punching (resulting in reinforced GCLs). A different process consists in using an adhesive bond to glue the bentonite to the geosynthetic (resulting in unreinforced GCLs). The mechanical bonding of reinforced GCLs increases their internal shear strength. Geosynthetic clay liners contain approximately 5 kg/m2 of bentonite that has a hydraulic conductivity of approximately 1 × 10−9 cm/sec. Infiltration under unit
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hydraulic gradient through a material with hydraulic conductivity of 1 × 10−9 cm/sec would result in an infiltration rate of 0.3 mm per year. As a GCL is a composite material, its relevant properties are those of the geotextile alone, of the bentonite alone, and of the composite. Geotextile properties were discussed in Section 37.3.1. The geotextile properties relevant to GCLs include mass per unit area, grab tensile, wide-width tensile, and puncture resistance. Relevant properties of the bentonite are obtained from free swell tests, which measure the absorption of water into a bentonite based on its volume change, and plate water absorption tests, which measure the ability of powdered bentonite to absorb water. The relevant properties of the composite GCL material include bentonite content, which is simply a measure of the mass of bentonite per unit area of GCL, permeameter testing (ASTM D 5084) used to estimate the GCL hydraulic conductivity, tensile strength characterized either by grab tensile or wide-width tensile tests, and puncture resistance tests performed to assess the relative puncture resistance between GCLs and geomembranes or other geosynthetics. The internal and interface shear strength of GCLs should also be determined as stability is a major concern for side slopes in bottom liner or cover systems that include GCLs. This is because of the very low shear strength of hydrated sodium bentonite. Proper shear strength characterization is needed for the different materials and interfaces in hydraulic barriers (Koerner, 2005). The analysis of a large database of test results on the internal shear strength of GCLs is presented by Zornberg et al. (2005).
37.3.5 Geocomposite Sheet Drains A geocomposite consists of a combination of different types of geosynthetics. In particular, the geosynthetics industry has developed a number of geocomposite drains, which are polymeric drainage cores with continuously open flow channels sandwiched between geotextile filters. Geocomposite sheet drains are discussed in this section while geocomposite strip (wick) drains are discussed in Section 37.3.6. Geocomposite sheet drainage systems have been engineered to replace costly aggregate and perforated pipe subsurface drainage systems. They have reached rapid acceptance because they provide adequate drainage and reduce the material cost, installation time, and design complexity of conventional aggregate systems. The core of geocomposite sheet drains are extruded sheets of plastic formed into a configuration that promotes drainage. The core of the geocomposite sheet drains are most commonly composed of polyethylene but may also be composed of polypropylene, polystyrene, high-impact polystyrene, or other materials. The structure of the core drainage products ranges from a dimpled core to a geonet. Geonets, a commonly used drainage product, generally consist of two or three sets of parallel solid or foamed extruded ribs that intersect at a constant angle to form an open net configuration. Channels are formed between the ribs to convey either liquid or gases. Figure 37.13 shows a number of geonets currently available in the market. Dimpled cores type products tend to have a greater flow capacity than geonets; however, they generally have a much lower crush resistance and tend to be more compressible than geonets. As indicated in Section 37.2.5, the transmissivity of the geocomposite drain must be evaluated under anticipated site-specific normal pressures and a factor of safety included to account for creep of the product over the life of the system (Koerner, 2005). The geotextile serves as both a separator and a filter, and the geonet or built-up core serves as a drain. There may be geotextiles on both the top and bottom of the drainage core and they may be different from one another. For example, the lower geotextile may be a thick needlepunched nonwoven geotextile used as a protection material for the underlying geomembrane, while the top geotextile may be a thinner nonwoven or woven product. Composite drainage nets are typically formed by thermally bonding the geotextile and geonet. Gluing and solvent welding can also be used to bond the geosynthetic core to the geotextile. In producing geocomposite drainage nets, the melt temperatures of the geotextile and geonet must be compatible so that the properties of each material are retained. Figure 37.14 shows a number of available geocomposite sheet drainage materials. As the purpose of the core is drainage, the most important properties to include in specifications are thickness, crush strength, and long-term transmissivity under load. Table 37.8 summarizes the tests
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Geonets
FIGURE 37.13 Typical geonets used as the core of geocomposite sheet drains.
Geocomposite drainage materials
FIGURE 37.14 Typical geocomposite sheet drains.
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The Handbook of Groundwater Engineering Standard Tests for Geocomposite Drainage Nets
Property
Test standard
Composite and core thickness Core crush strength Composite compression Composite compression Composite transmissivity
ASTM D 5199
Core carbon black
ASTM D 4218
Geotextile filter
See Table 37.3
ASTM D 1621 ASTM D 6244 ASTM D 6364 ASTM D 4716
Test name Standard Test Method for Measuring Nominal Thickness of Geotextiles and Geomembranes Standard Test Method for Compressive Properties of Rigid Cellular Plastics Test Method for Vertical Compression of Geocomposite Pavement Panel Drains Test Method for Determining Short-Term Compression Behavior of Geosynthetics Standard Test Method for Determining the (In-plane) Flow Rate per Unit Width and Hydraulic Transmissivity of a Geosynthetic Using a Constant Head Standard Test Method for Determination of Carbon Black Content in Polyethylene Compounds by the Muffle Furnace Technique Grab Tensile Tear Strength CBR Puncture Strength AOS Permittivity
commonly performed to evaluate the properties of geocomposite sheet drains. It is also important to evaluate filtration requirements for the geotextile. Design and specification of composite drains is covered by Giroud et al. (2000), Koerner (2005), and Holtz et al. (1997, 1998).
37.3.6 Geocomposite Strip (Wick) Drains Geocomposite strip drains, also called “wick drains,” have been developed to replace the use of sand drains in applications involving the increase in consolidation rate of soft, saturated fine-grained soils. Geocomposite strip drains actually do not wick moisture, but simply provide a conduit for excess pore water pressure induced flow. They are placed vertically through high water content silts and clays to produce shortened drainage paths and thus increase the rate of consolidation. Other names commonly used for these products are “band shaped drains” and “prefabricated vertical drains.” Sand drains were originally introduced in the 1930s as a method for improvement of soft soil foundations. The method of rapid consolidation of saturated fine-grained soils using sand drains involves placement of vertical columns of sand (usually 200 to 450 mm in diameter) at spacings of 1.5 to 6.0 m centers throughout the subsurface to be dewatered. Due to the low installed product cost and speed of installation, the use of geocomposite strip drains dominates over the use of sand drains in projects involving dewatering of saturated fine-grained soils. Their lengths are site-specific and extend to the bottom of the soft layer, and, thus, lengths generally will vary along a project. Once installed, a surcharge load is placed on the ground surface to mobilize excess pore water pressures. This surcharge load is placed in incremental lifts, which induce pore water pressure in the underlying soil. The pore water pressure is then dissipated through the vertical drains. Water takes the shortest drainage path (i.e., horizontally radial) to the vertical drain, at which point it flows vertically as the drain has a much higher hydraulic conductivity than the fine-grained soil being consolidated. The rate at which surcharge fill is added is critical in this process. Most commercially available geocomposite strip drains have adequate capacity to drain the water expelled during consolidation of the fine-grained soils. As their flow capacity is usually adequate, selection of the vertical drains is governed by the consolidation rate required in the project. Hansbo’s equation (Hansbo, 1979) is generally used to estimate the time required to achieve a desired percentage of consolidation as a function of the horizontal coefficient of consolidation of the foundation soil, the equivalent diameter of the geocomposite strip drain, and the spacing of the drains. As with geocomposite sheet drains,
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37-23
FIGURE 37.15 View of expanded geocell (photo courtesy of Presto Product Company).
the primary function of the geotextile covering is filtration. Determining the filtration requirements for the geotextile is an essential element of the design. Installation of geocomposite strip drains is very rapid and uses lightweight construction equipment fitted with hollow leads (called a “lance” or mandrel) for insertion to the desired depth. The bottom of the lance should be covered by an expendable shoe that keeps soil out of the lance so as not to bind the strip drain within it. The allowable flow rate of geocomposite strip drains is determined by the ASTM D4716 test method. Typical values of ultimate flow rate at a hydraulic gradient of 1.0 under 207 kPa normal stress vary from 1.5 to 3.0 m3 /sec.-m. This value must then be reduced on the basis of site-specific partial factors of safety. Specifications for geocomposite strip drains are provided by Holtz et al. (1997).
37.3.7 Geocells Geocells (or cellular confinement systems) are three-dimensional, expandable panels made from strips, typically 50 to 100 mm wide. When expanded during installation, the interconnected strips form the walls of a flexible, three-dimensional cellular structure into which specified infill materials are placed and compacted (Figure 37.15). This creates a system that holds the infill material in place and prevents mass movements by providing tensile reinforcement. Cellular confinement systems improve the structural and functional behavior of soil infill materials. Geocells were developed in the late 1970s and early 1980s for support of military vehicles on weak subgrade soils. The original type of geocell consists of HDPE strips 200 mm wide and approximately 1.2 mm thick. They are ultrasonically welded along their 200 mm width at approximately 330 mm intervals and are shipped to the job site in a collapsed configuration. At the job site they are placed directly onto the subgrade surface and propped open in an accordion-like fashion with an external stretcher assembly. They are then filled generally with gravel or sand (although other infill materials such as concrete, can be used) and compacted using a vibratory hand-operated plate compactor. Geocell applications include protection and stabilization of steep slope surfaces, protective linings of channels and hydraulic structures, static
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and dynamic load support on weak subgrade soils, and multilayered earth-retaining and water-retaining gravity structures. Geocells have proven very effective in providing a stable foundation over soft soils. The cellular confinement system improves the load-deformation performance of infill materials because cohesionless materials gain considerable shear strength and stiffness under confined conditions. Confining stresses are effectively induced in a geocell by means of the hoop strength developed by the HDPE cell walls. The overall increase in the load carrying performance of the system is provided through a combination of the cell wall strength, the passive resistance of the infill material in adjacent cells, and the frictional interaction between the infill soil and the cell walls. The cellular structure distributes concentrated loads to surrounding cells thus reducing the stress on the subgrade directly beneath the geocell. Infill selection is primarily governed by the nature and intensity of anticipated working stresses, availability and cost of candidate materials, and aesthetic requirements for a fully vegetated appearance. Aggregates, vegetated topsoil, and concrete constitute typical geocell infill types. A complete cellular confinement system may also include geotextiles, geomembranes, geonets, geogrids, integral polymeric tendons, erosion-control blankets, and a variety of earth anchors.
37.3.8 Erosion Control Products Erosion-control products represent one of the fastest growing application areas in the geosynthetics industry. Erosion-control products provide protection against sheet and gully erosion on soil slopes either until vegetation is established or for long-term applications. These products can be classified as temporary degradable erosion control blankets, long-term nondegradable erosion control mats, and permanent hard armored systems. Temporary degradable erosion control blankets are used to enhance the establishment of vegetation. These products are used where vegetation alone would provide sufficient site protection once established after the erosion control product has degraded. Some of these products are completely biodegradable (e.g., straw, hay, jute, and hydraulic mulches), while others are only partially biodegradable (e.g., erosion control meshes and nets). Long-term nondegradable erosion control mats provide permanent reinforcement of vegetation root structure. They are used in critical erosion-control applications where immediate high-performance erosion protection, followed by the permanent reinforcement of established vegetation is required. These soft armor related products provide erosion control, aid in vegetative growth, and eventually become entangled with the vegetation to provide reinforcement to the root system. Finally, the permanent hard armored systems include riprap on geotextile filters, modular concrete block over geotextile filter systems, gabions over geotextile filters, geocell products with gravel or concrete infill, vegetated concrete block systems, and fabric-formed revetments. Figure 37.16 shows an erosion control mat installed to help vegetation establishment on a steep reinforced soil slope. Installation of flexible erosion control products is straightforward. The products are usually placed on a prepared soil surface (e.g., facing of the reinforced embankment in Figure 37.16) by stapling or pinning them to the soil surface. Intimate contact between the blanket or mat and the soil is very important as water flow beneath the material has usually been the cause of poor functioning.
37.3.9 HDPE Vertical Barrier Systems The use of geomembranes (Section 37.3.2) as horizontal barrier layers has been extended for the case of seepage control in remediation projects, in which vertically deployed geomembranes are used in vertical cutoff trenches. The construction process involves excavation of a trench and placement of a seamed geomembrane in the open trench. This procedure is usually not possible for deep trenches due to the potential collapse of the sidewalls, so the use of slurry to stabilize the trench becomes necessary. The mixture of water and bentonite clay balances the pressures exerted by the in situ soils. The geomembrane
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FIGURE 37.16 slope.
37-25
Erosion control mat placed to help establish the vegetation on the face of a 1H:1V reinforced soil
GSE hypertiteTM seal
GSE 80 mil HDPE liner
Double wedge weld
Air test channel
FIGURE 37.17 Interlocking system for HDPE vertical barriers (figure courtesy of GSE Lining Technology, Inc.).
is placed in the slurry after trench excavation to the intended depth. Once the geomembrane is in place the backfill can be introduced, displacing the slurry and forcing the geomembrane to the side of the trench. As installation of vertically deployed conventional geomembranes is difficult, other systems have become available. These systems involve the use of thick HDPE or nonplasticized PVC geomembranes in the form of tongue-and-groove sheeting. Sealing of the interlocks is often achieved by using chloroprene-based, hydrophilic seals. Figure 37.17 shows one type of interlocking system with a hydrophilic seal. The seal is an extruded profile, typically 8 mm in diameter, which can expand up to eight times its original volume when exposed to water. These interlocking HDPE vertical barrier systems are being increasingly used as an alternative to soil-bentonite slurry walls, especially in projects involving areas of limited access, high disposal costs, depths where performance of a slurry wall is questionable and high concentrations of saline and chemicals. An additional advantage of the HDPE vertical barrier system is that it can work both as containment and a collection system (e.g., a composite sheet drain) and can be constructed in one trench. A recently developed method utilizes a biopolymer, or biodegradable, slurry. These slurries allow the HDPE panels and collection system (e.g., geocomposite sheet drains) to be installed in the same trench. Unlike bentonite, these slurries will either biodegrade or can be reversed to allow the collection system to drain clear and free of fines.
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Another method of achieving construction of a containment and collection system in the same trench has been developed which utilizes a trenchless, vibratory method for installation of the HDPE panels and geocomposite sheet drains. First, a collection trench is constructed to the required depth. This is followed with the installation of the geomembrane panel using modified pile-driving techniques. Panel widths ranging typically between 0.91 to 1.83 m are driven to depths up to 12 m. This construction method is most often reserved for sites on which excavation and disposal costs are high, access is limited, or the barrier is too close to a body of water. A case history in which this installation method was used for placement of an HDPE vertical barrier system is described in Section 37.5.1 . A recent development in the installation of these systems is the use of a “one-pass” deep trencher. Installation of HDPE vertical barrier systems using this technology has proven to be fast and safe. A special trencher equipment can install a vertical geomembrane wall with a collection system consisting of a HDPE pipe and gravel fill in one trench, in one pass. Figure 37.18 shows the placement of an HDPE panel using this one-pass deep trencher.
FIGURE 37.18 One pass trencher for installation of an HDPE vertical barrier system. (Photo courtesy of Groundwater Control, Inc.)
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37-27 Composite drainage net Geosynthetic erosion control system Geopipe
Geocomposite interceptor drain
Liquid extraction well
Geomembrane
Reinforcement (geogrid, geotextile, geocell)
Fiber reinforcement il
Geogrid
Cover so
HDPE vertical barrier Groundwater well GCL
Geotextile filter
Geocomposite for gas/leachate
Geotextile filter Clay blackfill Geonet Reinforcement (geogrid, geotextile)
Secondary geomembrane Fiber reinforcement Geotextile filter
Solid waste
Geonet Primary geomembrane Geopipe Gravel
Daily cover geotextile Geotextile filter
Compacted clay liner
Gradient control drain
FIGURE 37.19 Multiple use of geosynthetics in landfill design.
37.4 Geosynthetic Applications in Landfill Design The multiple uses of geosynthetics in the design of modern municipal solid waste landfills is a good illustration of an application in which different geosynthetics are used to perform all the functions discussed in Section 37.2. Virtually all the different types of geosynthetics discussed in Section 37.3 have been used in the design of both base and cover liner systems of landfill facilities. The extensive use of geosynthetics in modern landfills has been triggered by the economical and technical advantages that geosynthetics offer in relation to traditional liner systems. A geomembrane infiltration barrier and geocomposite sheet drain collection layers of a few millimeters in thickness can provide equivalent performance as a soil infiltration barrier with a gravel collection layer and graded granular filter layer of up to several meters in thickness. Landfill base liners are placed below the waste to minimize the release of liquids from the waste (i.e., leachate). Leachate is the main source of contamination of the soil underlying the landfill and, most importantly, the groundwater. Landfill cover liners are placed above the final waste configuration to prevent water, usually from rain or snow, from percolating into the waste and producing leachate. Waste containment systems employ geosynthetics to varying degrees. Figure 37.19 illustrates the extensive multiple uses of geosynthetics in both the cover and the base liner systems of a modern landfill facility. The base liner system illustrated in Figure 37.19 is a double composite liner system. Double composite liner systems are used in some instances for containment of municipal solid waste and are frequently used for landfills designed to contain hazardous waste. The base liner system shown in this figure includes a geomembrane/GCL composite as the primary liner system and a geomembrane/compacted clay liner composite as the secondary system. The leak detection system, located between the primary and secondary liners, is a geotextile/geonet composite. The leachate collection system overlying the primary liner on the bottom of the liner system consists of gravel with a network of perforated pipes. A geotextile protection layer beneath the gravel provides a cushion to protect the primary geomembrane from puncture by stones in the overlying gravel. The leachate collection system overlying the primary liner on the side slopes of the liner system is a geocomposite sheet drain (geotextile/geonet composite) merging into the gravel on the base. A geotextile filter covers the entire footprint of the landfill and prevents clogging of the leachate collection and removal system. The groundwater level may be controlled at the bottom of the landfill
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by gradient control drains built using geotextile filters. Different types of geosynthetics (e.g., geogrids, geotextiles, fibers) can be selected for stabilization of the foundation soils. The cover system of the landfill illustrated in Figure 37.19 contains a composite geomembrane/GCL barrier layer. The drainage layer overlying the geomembrane is a geocomposite sheet drain (composite geotextile/geonet). In addition, the soil cover system may include geogrid, geotextile, or geocell reinforcements below the infiltration barrier system. This layer of reinforcements may be used to minimize the strains that could be induced in the barrier layers by differential settlements of the refuse or by a future vertical expansion of the landfill. In addition, the cover system could include a geogrid or geotextile reinforcement above the infiltration barrier to provide stability to the vegetative cover soil. Fiber reinforcement may also be used for stabilization of the steep portion of the vegetative cover soil. A geocomposite erosion control system above the vegetative cover soil is indicated in the figure and provides protection against sheet and gully erosion. Figure 37.19 also illustrates the use of geosynthetics within the waste mass, which are used to facilitate waste placement during landfilling. Specifically, the figure illustrates the use of geotextiles as daily cover layers and of geocomposites within the waste mass for collection of gas and leachate. Geotextile filters are also extensively used for leachate collection and detection blanket drains and around the gravel in leachate collection trenches at the base of the landfill. Geosynthetics can also be used as part of the groundwater and leachate collection well system. The use of geotextiles as filters in groundwater and leachate extraction wells is also illustrated in the figure. Finally, the figure shows the use of a HDPE vertical barrier system and a geocomposite interceptor drain along the perimeter of the landfill facility. Although not all of the components shown in Figure 37.19 would normally be needed at any one landfill facility, the figure illustrates the many geosynthetic applications that can be considered in landfill design. Bouazza et al. (2002) provide an update on the use of geosynthetics in the design of waste containment facilities. A case history involving the design of a liner system with multiple uses of geosynthetics is described in Section 37.5.2.
37.5 Case Histories 37.5.1 Case History of Vertical Barrier System Although the use of geosynthetics in many geotechnical and environmental projects is related to groundwater applications (e.g., landfill liners, which prevent groundwater contamination), a geosynthetic application directly related to groundwater remediation and control is the use of HDPE panels as vertical barrier systems. A case history is presented herein to illustrate the use of HDPE panels as part of a remediation plan for a site contaminated with coal tar (Burson et al., 1997). The site was a defunct manufactured gas plant located in York, Pennsylvania. The site is surrounded by commercial and residential areas and a creek (Codorus Creek) borders the site for a distance of approximately 305 m. During years of operation and the subsequent closure of the manufactured gas plant, some process residuals migrated to the subsurface soils and groundwater. Over time, the presence of a coal tar-like material in the form of a dense non-aqueous phase liquid (DNAPL), was observed seeping from the bank of the Codorus Creek. DNAPL was also noted in some on-site monitoring wells. Several remediation scenarios were evaluated with the purpose of intercepting the tar-like material migrating through the soil and into groundwater, encountered approximately 5.0 m below ground surface. A system consisting of a combination of soil improvement by jet grouting, a vertical barrier using HDPE panels, and a network of recovery wells was finally selected. The use of vertical HDPE panels and trenchless technology allowed placement of the barrier as close as 3 m from the bank of the Codorus Creek, which was difficult to achieve with conventional slurry wall technology. The HDPE barrier system selected for this project was a 2 mm thick geomembrane, which allowed for the vibratory, trenchless installation. Sealing of the interlocks was achieved with a chloroprenebased, hydrophilic seal (see Figure 37.17). HDPE panels were keyed into the soil improved by jet grouting,
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FIGURE 37.20 Installation of HDPE barrier wall utilizing conventional pile driving equipment. (Photo courtesy of Groundwater Control Inc.)
as discussed below. The panels were installed using conventional vibratory pile driving equipment, without a trench, thus reducing the amount of contaminated spoils to be disposed (Figure 37.20). To complete closure of the contaminated material, jet grouting was used to provide a seal to control DNAPL migration between the bottom of the HDPE panels and the irregular bedrock contact. Jet grouting consists of high pressure injection of cement and bentonite slurry, horizontally into the soil strata to improve its mechanical and hydraulic properties. The containment wall was approximately 290 m in length. The soil along the alignment of the barrier system consisted of granular fills, with large amounts of cinder material. Also mixed into the fill were varying amounts of rubble and debris. These highly permeable soils were underlain by the competent bedrock. Holes were pre-drilled down to bedrock, and the jet grouting improvement was done by injecting the grout horizontally from the competent rock up to an elevation approximately 6 m below the ground surface. A groundwater recovery system was implemented once the barrier was completed. Since its installation in the fall of 1995, the HDPE panel jet grout barrier system has performed as intended.
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Cushion geotextile HDPE geomembrane
Vegetative Vegetative Cover Soil cover soil
Protection layer
Cobbles filled Cobbles Filled With sand Sand with
Mechanical barrier/ drainage layer
HDPE geomembrane backing HDPE gas extraction pipes
Sand Sand
Barrier layer Gas collection/ foundation sublayer
Reinforcing HDPE geogrid
Sand Sand
Reinforced foundation sublayer
Sand Sand
Unreinforced foundation layer
Geosynthetic clay liner
Existing Cover Existing cover
FIGURE 37.21
Cover system reinforced using geogrids.
37.5.2 Case History of Multiple Use of Geosynthetics in Landfill Cover Design The cover system at the McColl Superfund Site, Fullerton, California is a good example of a site where multiple systems of soil reinforcement were used for stabilization of the final cover system. One of these uses involves placement of geogrids along the cover system. The project also included the construction of conventional reinforced structures (Collins et al., 1998; Hendricker et al., 1998). The site has 12 pits containing petroleum sludge and oil-based drilling muds. The sludge was generated by the production of high-octane aviation fuel and was placed into the pits between 1942 and 1946. Between 1952 and 1964, the site was used for disposal of oil-based drilling muds. These wastes and their reaction products and byproducts were found as liquid, gas, and solid phases within the pits. At the time of deposition, essentially all of the waste materials were mobile. Over time, much of the waste had hardened. The drilling mud is a thixotropic semi-solid sludge, which can behave as a very viscous fluid. Key considerations for the selection of the final remedy were to: (1) provide a cover system that includes a barrier layer and a gas collection and treatment system over the pits to minimize infiltration of water and release of hazardous or malodorous gas emissions; (2) provide a subsurface vertical barrier around the pits to minimize outward lateral migration of mobile waste or waste byproducts and inward lateral migration of subsurface liquid; and (3) provide slope stability improvements for unstable slopes at the site. The geogrid reinforcement for the cover system over the more stable pits was constructed with two layers of uniaxial reinforcement placed orthogonally to one another. Connections at the end of each geogrid roll were provided by Bodkin joints. Adjacent geogrid panels did not have any permanent mechanical connections. This proved to be somewhat problematic, as additional care was required during placement of the overlying gas collection sand to minimize geogrid separation. Details of the cover system involving geogrid reinforcement are shown in Figure 37.21. A geocell reinforcement layer was constructed over the pits containing high percentages of drilling mud. While the construction of this reinforcement layer proceeded at a slower pace than the geogrid reinforcement, it did provide an immediate platform to support the load. As the bearing capacity of the underlying drilling mud was quite low, the geocell provided load distribution, increasing the overall bearing capacity of the cover system. Details of the cover system involving geogrid reinforcement are shown in Figure 37.22. In addition to reinforced covers, three conventional reinforced soil structures were constructed at the site. One of the structures was necessary to provide a working pad for construction of the subsurface vertical barrier. This reinforced earth structure had to support the excavator with a gross operating weight of 1100 kN that was used to dig the soil-bentonite cutoff wall. Another reinforced earth structure at the site
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37-31 Geocomposite
HDPE geomembrane
Vegetative Vegetative Cover Soil cover soil
Geosynthetic clay liner
Protection layer Drainage layer
HDPE geomembrane backing HDPE gas extraction pipes
Geotextile (for construction purpose only)
Sand Sand
Gas collection/ foundation sublayer
HDPE reinforcingGeocell geocell HDPE Reinforcing filled Filled with With sand Sand
Reinforced foundation sublayer
Sand Sand
Unreinforced foundation layer
Existing Existing Ground ground
FIGURE 37.22 Cover system reinforced using geocells.
Cap cover grade
Drainage and protection layers Property line
Barrier, gas extraction and foundation layers Reinforced slope
Sump Sump Geocell Low-permeability soil backfill
Abandoned soldier pile
Cutoff wall
FIGURE 37.23 Buttressing reinforced slope at McColl Superfund site.
had to span a portion of the completed cutoff wall. Due to concerns that the stress of the reinforced earth structure on the underlying soil-bentonite cutoff wall would lead to excessive deformation of the wall due to consolidation of the cutoff wall backfill, a flexible wall fascia was selected. As shown in Figure 37.23, a soldier pile wall was constructed to provide stability of the system during construction. The use of geosynthetic alternatives in this project was more suitable and cost effective than their conventional counterparts.
Glossary Alloys, polymeric a blend of two or more polymers (e.g., a rubber and plastic) to improve a given property (e.g., impact strength). Apparent opening size (AOS), O95 for geotextile, a property which indicates the diameter of the approximate largest particle that would effectively pass through the geotextile. At least 95% of the openings apparently have that diameter or are smaller as measured by the dry sieve test. Chemical stability stability of a geosynthetic; ability to resist degradation from chemicals, such as acids, bases, solvents, oils and oxidation agents; and chemical reactions, including those catalyzed by light.
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Chlorosulfonated polyethylene (CSPE) family of polymers that is produced by polyethylene reacting with chlorine and sulfur dioxide. Present CSPEs contain 25 to 43% chlorine and 1.0 to 1.4% sulfur. Clogging movement by mechanical action or hydraulic flow of soil particles into the voids of fabric and retention therein, thereby reducing the hydraulic conductivity of the geotextile. Cross-machine direction the axis within the plane of a fabric perpendicular to the predominant axis of the direction of production. Cross-plane The direction of a geosynthetic that is perpendicular to the plane of its manufactured direction. Referred to in hydraulic situations. Fiber basic element of fabrics and other textile structures, characterized by having a length at least 100 times its diameter or width that can be spun into a yarn or otherwise made into a fabric. Filament yarn the yarn made from continuous filament fibers. Filtration in geotextiles; the process of retaining soil in place while allowing water to pass from soil. In chemistry, removal of particles from a fluid stream. Geocell a three-dimensional structure filled with soil, thereby forming a mattress for increased stability when used with loose or compressible subsoils. Geocomposite a manufactured material using geotextiles, geogrids, and geomembranes in laminated or composite form. May or may not include natural materials. Geogrid open grid structure of orthogonal filaments and strands of polymeric material used primarily for tensile reinforcement. Geomembrane very low hydraulic conductivity synthetic membrane liners or barriers used with any geotechnical engineering related material so as to control fluid migration in a man-made project, structure, or system. Geonet a geosynthetic consisting of integrally connected parallel sets of ribs overlying similar sets at various angles for planar drainage of liquids or gases. Geopipe any plastic pipe used with foundation, soil, rock, earth, or any other subsurface related material as an integral part of a human-made project, structure, or system. Geosynthetic a planar product manufactured from polymeric material used with soil, rock, earth, or other geotechnical engineering related material as an integral part of a constructed project, structure, or system. Geosynthetic clay liner (GCL) factory-manufactured hydraulic barriers consisting of a layer of bentonite clay or other very low permeability material supported by geotextiles and geomembranes, and mechanically held together by needling, stitching, or chemical adhesives. Geotextile any permeable textile used with foundation, soil, rock, earth, or any other geotechnical engineering-related material as an integral part of a constructed project, structure, or system. Grab test in fabric testing, a tension test in which only a part of the width of the specimen is gripped in the clamps. Gradient ratio the ratio of the average hydraulic gradient across the fabric and the 25 mm of soil immediately next to the fabric to the average hydraulic gradient across the 50 mm of soil between 25 and 75 mm above the fabric, as measured in a constant head permeability test. Heat bonded thermally bonded by melting the fibers to form weld points. Hot wedge common method of heat seaming thermoplastic geomembranes by a fusing process wherein heat is delivered by a hot wedge passing between the opposing surfaces to be bonded. Hydraulic transmissivity for a geotextile or related product, the volumetric flow rate of water per unit width of specimen per unit gradient in a direction parallel to the plane of the specimen. Index test a test procedure that may contain a known bias but which may be used to establish an order for a set of specimens with respect to the property of interest. In-plane the direction of a geosynthetic that is parallel to its longitudinal, manufactured, or machine direction. Referred to in hydraulic situations. Leachate liquid that has percolated through or drained from solid waste or other human-emplaced materials and contains soluble, partially soluble, or miscible components removed from such waste.
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Liner a layer of emplaced materials beneath a surface impoundment or landfill that serves to restrict the escape of waste or its constituents from the impoundment or landfill. Machine direction the direction in the plane of the fabric parallel to the direction of manufacture. Mass per unit area the proper term to represent and compare the amount of material per unit area (units are or g/m2 ) of a geosynthetic. Monofilament a single filament of a fiber (normally synthetic). Mullen burst hydraulic bursting strength of textiles. Multifilament a yarn consisting of many continuous filaments or strands. Needlepunched in geotextiles, mechanical bonding of staple or filament fibers with barbed needles to form a compact fabric. Nonwoven fabric a textile structure produced by bonding or interlocking of fibers, or both, accomplished by mechanical, thermal, or chemical means. Permittivity of geotextiles and related products, the volumetric flow rate of water per unit cross sectional area per unit head under laminar flow conditions, in the normal direction through a geotextile. Plasticizer a plasticizer is a material, frequently solvent-like, incorporated in a plastic or a rubber to increase its ease of workability, its flexibility, or distensibility. Polyester fiber generic name for a manufactured fiber in which the fiber-forming substance is any long-chain synthetic polymer composed of an ester of a dihydric alcohol and terepthalic acid. Polyethylene a polyolefin formed by bulk polymerization (for low density) or solution polymerization (for high density) where the ethylene monomer is placed in a reactor under high pressure and temperature. Polymer a macromolecular material formed by the chemical combination of monomers having either the same or different chemical composition. Plastics, rubbers, and textile fibers are all highmolecular-weight polymers. Polyolefin a family of polymeric materials that includes polypropylene and polyethylene, the former being very common in geotextiles and the latter in geomembranes. Polyvinyl chloride (PVC) a synthetic thermoplastic polymer prepared from vinyl chloride. Quality assurance (QA) a planned system of activities whose purpose is to provide a continuing evaluation of the quality control program, initiating corrective action where necessary. It is applicable to both the manufactured product and its field installation. Quality control (QC) actions that provide a means of controlling and measuring the characteristics of (both) the manufactured and the field installed product. Separation the function of geosynthetics as a partition between two adjacent materials (usually dissimilar) to prevent mixing of the two materials. Specification a precise statement of a set of requirements to be satisfied by a material, product, system, or service that indicates the procedures for determining whether each of the requirements is satisfied. Spun-bonded fabrics fabric formed by continuous filaments that have been spun (extruded), drawn, laid into a web and bonded (chemical, mechanical, or thermal bonding) together in one continuous process. Staple fibers fibers of short lengths; frequently used to make needlepunched nonwoven fabrics. Subgrade intrusion localized aggregate penetration of a soft cohesive subgrade and resulting displacement of the subgrade into the cohesionless material. Subgrade pumping the displacement of cohesive or low-cohesion fines from a saturated subgrade into overlying aggregate as the result of hydraulic forces created by transmittal of wheel-load stresses to the subgrade. Survivability the ability of a geosynthetic to be placed and to perform its intended function without undergoing degradation. Tensile strength the maximum resistance to deformation developed for a specific material when subjected to tension by an external force.
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Trapezoid Tear Test test method used to measure the tearing strength of geotextiles. Transmissivity for a geosynthetic, the volumetric flow rate per unit thickness under laminar flow conditions, in the in-plane direction of the fabric or geocomposite. Ultraviolet degradation the breakdown of polymeric structure when exposed to natural light. Woven geotextilea planar geotextile structure produced by interlacing two or more sets of elements such as yarns, fibers, rovings of filaments where the elements pass each other usually at right angles and one set of elements are parallel to the fabric axis. Wide-width strip tensile test a uniaxial tensile test in which the entire width of a 200 mm wide specimen is gripped in the clamps and the gauge length is 100 mm. Yarn a generic term for continuous strand strands (1 or more) of textile filaments, monofilaments, or slit form suitable for knitting, weaving, or otherwise intertwining or bonding to form a textile fabric. Sources for these and other definitions of terms can be found in ASTM (1997) and Koerner (2005).
References ASTM. 1995. ASTM Standards on Geosynthetics. Sponsored by ASTM Committee D-35 on Geosynthetics, Fourth Edition, 178p. Bhatia, S.K. and Smith, J.L. 1996a. “Geotextile Characterization and Pore-Size Distribution: Part I. A Review of Manufacturing Processes,” Geosynthetics International, 3, 85–105. Bhatia, S.K. and Smith, J.L. 1996b. “Geotextile Characterization and Pore-Size Distribution: Part II. A Review of Test Methods and Results,” Geosynthetics International, 3, 155–180. Bhatia, S.K., Smith, J.L., and Christopher, B.R. 1996. “Geotextile Characterization and Pore-Size Distribution: Part III. Comparison of methods and Application to Design,” Geosynthetics International, 3, 301–328. Bouazza, A. 2002. Geosynthetic clay liners. Geotextiles and Geomembranes, 20, 1–17. Bouazza, A., Zornberg, J.G., and Adam, D. 2002. “Geosynthetics in Waste Containment Facilities: Recent Advances.” State-of-the-Art keynote paper, Proceedings of the Seventh International Conference on Geosynthetics, Nice, France, September 22–27, A.A. Balkema, Vol. 2, pp. 445–510. Burson, B., Baker, A.C., Jones, B., and Shailer, J. 1997. “Development and Installation of an Innovative Vertical Containment System," Proceedings of the Geosynthetics ’97 Conference, Long Beach, California, March, Vol. 1, pp. 467–480. Christopher, B.R. and Dahlstrand, T.K. 1989. Geosynthetics in Dams — Design and Use, Association of State Dam Safety Officials, Lexington, KY, 311 p. Christopher, B.R. and Fisher, G.R. 1992. “Geotextile Filtration Principles, Practices and Problems,” Journal of Geotextile and Geomembranes, Elsevier, 11, 4–6, 337–354. Collins, P., Ng, A.S., and Ramanujam, R. 1998. Superfund Success, Superfast. Civil Engineering, December, 42–45. Elias, V., Christopher, B.R., and Berg, R.R. 2001. Mechanically Stabilized Earth Walls and Reinforced Soil Slopes. Publication Number FHWA-NH-00-043, NHI-FHWA. Giroud, J.P. 1996. “Granular Filters and Geotextile Filters,” Proceedings of Geofilters ‘96, Montreal, pp. 565–680. Giroud, J.P. with cooperation of Beech, J.F. and Khatami, A. 1993. Geosynthetics Bibliography. Volume 1. IGS, Industrial Fabrics Association International (IFAI) Publishers, St. Paul, MN, 781 p. Giroud, J.P. with cooperation of Beech, J.F., Khatami, A., and Badu-Tweneboah, K. 1994. Geosynthetics Bibliography. Volume 2. IGS, IFAI Publishers, St. Paul, MN, 940 p. Giroud, J.P., Zornberg, J.G., and Zhao, A. 2000. “Hydraulic Design of Geosynthetic and Granular Liquid Collection Layers.” Geosynthetics International, Special Issue on Liquid Collection Systems, 7, 285–380.
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Halse, Y., Koerner, R.M., and Lord, A.E., Jr. 1987. “Filtration Properties of Geotextiles Under Long Term Testing,” Proceedings of ASCE/Penn DOT Conference on Advances in Geotechnical Engineering, Hershey, PA, pp. 1–13. Hansbo, S. 1979. “Consolidation of Clay by Band Shaped Perforated Drains,” Ground Engineering, July, 16–25. Hendricker, A.T., Fredianelli, K.H., Kavazanjian, E., and McKelvey, J.A. 1998. Reinforcement Requirements at a Hazardous Waste Site. Proceedings of the 6th International Conference on Geosynthetics. IFAI, Atlanta, Vol. 1, 465–468. Holtz, R.D., Christopher, B.R., and Berg, R.R. 1997. Geosynthetic Engineering. Bitech Publishers Ltd., Richmond, British Columbia, Canada, 452 p. Holtz, R.D., Christopher, B.R., and Berg, R.R. 1998. Geosynthetic Design and Construction Guidelines, U.S. Department of Transportation, Federal Highway Administration, Washington DC, Report No. HI-95-038, 396 p. Industrial Fabrics Association International. 1996. North American Market for Geosynthetics. 97 p. Koerner, R.M. 2005. Designing with geosynthetics, 5th ed. Prentice Hall, 783 p. Narejo, D., Koerner, R.M., and Wilson-Fahmy, R.F. 1996. “Puncture Protection of Geomembranes Part II: Experimental,” Geosynthetics International, 3, 629–653. Palmeira, E. and Fannin, J. 2002. “Soil-Geotextile Compatibility in Filtration.” State-of-the-Art keynote paper, Proceedings of the Seventh International Conference on Geosynthetics, Nice, France, September 22–27, A.A. Balkema, Vol. 3, pp. 853–872. Scuero, A. M., Vaschetti, G., Sembenelli, P., Aguiar Gonzalez, E., Bartek, P., Blanco Fernandez, M., Brezina, P., Brunold, H., Cazzuffi, D., Girard, H., Lefranc, M., do Vale, M., Massaro, C., Millmore, J., and Schewe, L. (2005). Geomembrane Sealing Systems for Dams. International Commission on Large Dams. Vidal, H. 1969. "La Terre Armée." Annales de l’Institut Technique du Bâtiment et des Travaux Publics, Series: Materials (38), No. 259–260, pp.1–59. Wilson-Fahmy, R.F., Narejo, D., and Koerner, R.M. 1996. “Puncture Protection of Geomembranes Part I: Theory,” Geosynthetics International, 3, 605–628. Zornberg, J.G. 2002. “Discrete Framework for Limit Equilibrium Analysis of Fibre-Reinforced Soil.” Géotechnique, 52, 593–604. Zornberg, J.G. (2005). “Advances on the Use of Geosynthetics in Hydraulic Systems.” Proceedings of the Nineteenth Geosynthetic Research Institute Conference (GRI-19), Geosynthetics Institute, Las Vegas, NV, December 14–16, pp. 1–17 (CD-ROM). Zornberg, J.G. and Weber, C.T. 2003. “Geosynthetics Research Needs for Hydraulic Structures” Proceedings of the Seventeenth Geosynthetic Research Institute Conference, Hot Topics in Geosynthetics IV, December 15–16, Las Vegas, Nevada, pp. 183–197. Zornberg, J.G., Barrows, R.J., Christopher, B.R., and Wayne, M.H. 1995. “Construction and Instrumentation of a Highway Slope Reinforced with High Strength Geotextiles." Proceedings of the Geosynthetics ’95 Conference, Nashville, TN, February, Vol. 1, pp.13–27. Zornberg, J.G., Sitar, N., and Mitchell, J.K. 1998. “Performance of Geosynthetic Reinforced Slopes at Failure.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 124, 670–683. Zornberg, J.G., McCartney, J.S., and Swan, R.H. 2005. “Analysis of a Large Database of GCL Internal Shear Strength Results,” Journal of Geotechnical and Geotechnical Engineering, ASCE, 131, 367–380.
Further Information Koerner (2005) provides an excellent, well-illustrated overview of the different types of geosynthetics and their applications. Holtz, Christopher and Berg (1997, 1998) provide well-documented practical design and construction information on the different uses of geosynthetic products.
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Giroud et al. (1993, 1994) provide a two-volume comprehensive database on technical literature relative to geosynthetics, including technical papers from conferences, technical papers from journals, books, theses, and research reports. Technical advances on geosynthetics are also published in the two official journals of the IGS: Geosynthetics International, and Geotextiles and Geomembranes. Similarly, the Geotechnical Fabrics Report (GFR), published by the Industrial Fabrics Association International (IFAI) provides updated information, including the annual Specifier’s Guide, which offers a summary of the properties of products available in the geosynthetics market. The ASTM Standards on Geosynthetics, sponsored by ASTM Committee D-35 on Geosynthetics (ASTM, 1995), provides information on the standard test procedures for the different types of geosynthetics. The proceedings of the International Conferences on Geosynthetics, organized by the International Geosynthetic Society (IGS), offer a relevant source of information on the different topics related to geosynthetics. These international conferences are organized every four years. Equally relevant are the proceedings of conferences organized by the regional chapters of IGS. Finally, the proceedings of the series of conferences organized by the Geosynthetics Research Institute (GRI) provide information on specific topics relevant to geosynthetic design. Geosynthetic manufacturers’ literature is also a valuable source of information, which provides product-specific properties, suggested design methods, and recommended factors of safety.
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Index
A Above-ground fill, landfill, 33-6 Absolute dominion doctrine, 32-4–32-5 Absolute pressure, 3-2–3-3 Absolute Thermodynamic Temperature Scale, see Kelvin scale Absorption, 17-10 Acetone, 31-8 Acid and chemicals in well development, 11-27–11-28 Acid–base behavior, 17-5–17-6 diagram, 17-12 reaction, 17-4, 17-8 Acid dissociation constants, 17-6 Acid mine drainage, 17-18–17-19 Acidophilic bacteria, 31-6 Acoustic logs, 14-19–14-20 Adenosine triphosphate (ATP), 31-3 Adhesion, 2-12, 2-14 Adsorbed contaminant, 3-29 Adsorption, 3-37, 17-10 Advection, 22-10 versus convection, 13-6 Advection–dispersion equation (ADE), 18-4 linear and nonlinear sorption, 22-11–22-12 transport equations, 22-11 volatilization, 22-13 Advection–dispersion model (ADM), 26-6, 26-8–26-9 Aeolian deposits, 2-9 Aerobic chlorinated aliphatic hydrocarbon bioremediation, 31-21 Aerobic petroleum hydrocarbon bioremediation, 31-21 Aerobic respiring organisms, 31-3 Aerosols, 17-16 Air entry pressure, see Bubbling pressure Air potential, 6-6 Air rotary, 11-25, 35-19 Air sparging (AS), 36-36–36-37 Air surging, 11-27 Airport safety, 33-4
Air-temperature changes, annual, 13-9 Akaike’s Information Criterion (AIC), 14-44 Alaska, 2-49 Aliphatic compounds, halogenated, 31-8–31-10 Alkanes, 31-7 Allogenic recharge, 21-2 Alluvium, 2-4, 2-9 Alpha particles, 17-25 Alternate concentration limit (ACL), 35-3 Amargosa Desert, 2-38 Amchitka model, uncertainty reduction, 24-18–24-22 background, 24-19–24-20 Bayesian framework, 24-20–24-21 Milrow site, 24-21–24-22 American Society for Testing and Materials (ASTM), 2-10 Amphoterism, 17-4 Amsterdam, 1-9 Anaerobic bacteria, 31-7 Anaerobic respiration, 31-3 Analysis of Contaminant Transport (ACT), 22-35 Analytical model, 23-2 Anchorage, 2-49 Anilines, 31-10 Anisotropic barriers, 34-12–34-13 Anisotropic media, 3-10 Anisotropy, 4-9–4-10, 15-7 and heterogeneity, 2-22–2-25 ANOVA, 35-42 Anthropogenic changes, in recharge areas, 2-51–2-52 Aperture, 20-31 Appalachians, 2-9, 2-50–2-51 Approximate mobility index (AMI), 2-49 Aqueous solubility, affecting factors pε, 17-11–17-13 pH and chemical composition, 17-3–17-10 sorption, to solids, 17-10–17-11 temperature, 17-13 Aquiclude, 2-27
I-1
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 1 — #1
I-2
Index
Aquifer, 1-15, 1-27, 2-25–2-28 artesian, 2-25,–2-26 basin and range, dynamics of, 27-6–27-8 coastal, 3-28 management, 12-5, 12-23–12-26 confined, 1-13, 2-25–2-26, 3-23, 3-25, 10-2–10-3 distance–drawdown analyses, 10-27–10-28 flow equation, 4-19–4-20 time–drawdown analyses, 10-17–10-19 well-flow equations, 10-5–10-6 dynamics and models, 27-5–27-6 exploration, 1-14–1-16 heterogeneous interpretation, 10-30–10-31 heterogeneity accounting in solute transport modeling, MADE site case study, 26-1–26-14 hydrogeologic parameters, 35-8 karstic, 20-3, 21-2 leaky, 3-14–3-15, 10-2, 10-3, 10-28–10-30 losses, 11-5–11-6, 11-16 well efficiency, 11-7 multilayered, 10-2 perched, 2-26–2-27 phreatic, 4-20–4-24 physical properties, 10-2–10-4 pumped, 10-6–10-9 reactivity, 19-5–19-6 restoration time, 36-26–36-28 semi-confined, 2-27, 2-28 shallow unconfined, flow and transport, 23-31–23-35 surficial, 23-32 tests, performance, 10-12–10-17 data processing, 10-15–10-17 date interpretation, 10-17 measurements, 10-13–10-15 pumping test duration, 10-15 3D modeling, 23-42 types, 10-2 unconfined, 2-26, 3-23, 3-25, 10-2–10-3 Aquitard, 2-27, 4-31 flow equation, 4-24 ArcGIS, 30-2 Archie’s relationship, 14-6 Archimedian screw, 1-3 ArcIMS, 30-2, 30-5 ArcView, 30-2 Area fill, landfill, 33-6 Arizona, 2-38 Arkansas, 2-38 Aromatic compounds, halogenated, 31-11 Aromatic rings, 31-5 Artesian aquifer, 2-25–2-26 Artesian pressure and surface effects, 2-50 Artesian wells, 1-3, 1-5, 1-8 Artificial drainage effects, 2-51 Artificial protective barriers, 2-45 Artois, 1-3, 2-7, 2-25 Arya–Paris model, 6-25–6-28 drawbacks, 6-27–6-28 ASCE Hydraulics Division Committee on Hydrologic Transport Dispersion, 31-14 Ash Meadows Springs, 2-38 AspMap, 30-5
Assessment monitoring programs, groundwater monitoring, 35-3–35-4 AT123D, 22-25 Atlantic Coastal Plain, 2-48 Atlas, 30-2 Atmospheric discharge and seepage face, 2-32–2-33 Attachment/detachment models, 22-15–22-16 Attenuation, 15-10, 15-14 difference tomography, 15-24–15-25 tomography, 15-18 Auger-hole test, 3-12 Aurora, 2-43 Automated parameter estimation techniques, 23-23 Automatic history matching, 23-23 Autotrophs, 31-2 Average pore diameter, 2-34 B B. subtilis, 31-12 BA model, 7-9 Backfill materials, 35-21 Bacteria, 31-2–31-4, 31-6 Balkan Peninsula, 2-7, 2-9 Bank storage, 2-42 Barrier function, geosynthetic, 37-9–37-10 Barrier layer, 33-15, 33-22–33-23 Base flow/runoff relations, 21-28 Baseflow recession constant, 2-36 Basin and range aquifer, dynamics of, 27-6–27-8 Basin and range areas, 2-38 Basin-area method, 2-37 Batch-flush model, 36-27–36-28 Bayesian approach, 30-11 geostatistics, 15-19 inversion approach, 15-20 for uncertainty reduction, 24-20–24-21 Bayesian Information Criterion (BIC), 14-44 Bedrock granitic, 14-5 surface, 21-4 Beerkan method, 6-22 Benchmarking, 23-19 Bentonite, 2-45, 35-14, 35-21, 37-10, 37-18 Benzene, 31-8 Benzoates, 31-10 Berms, 33-15–33-16 Bernoulli equation, 3-13, 5-3, 5-4 for conservation of energy, 1-5 Bessel equation, modified, 4-32 Beta distribution, 5-20–5-21 Beta particles, 17-25 Big Sioux River valley, 2-9 Big Springs, Texas, 2-38 Bi-modal behavior, 6-12, 6-14 Bioavailability and mass transfer limitations, 31-11 Biodegradation bioremediation field applications case histories, 31-21 engineered bioremediation, 31-21 intrinsic bioremediation, 31-20 technologies, emerging, 31-22 environmental conditions, influencing biotransformations, 31-6–31-10 limits, 31-10–31-11
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 2 — #2
Index
I-3
reactive transport and biodegradation, quantitative description microbial reaction kinetics, 31-12–31-15 microbial reactions and sorption, 31-18–31-20 sorption, as reactive kinetic process, 31-15–31-18 subsurface microbiology and geochemistry metabolism, 31-3–31-6 microbiology, 31-1–31-3 Biological remediation in ex situ treatment, 36-41 in in situ treatment, 36-32–36-34 Biomass, 19-19 Bioreactors, 36-41 landfills, 33-19–33-21 Bioremediation field applications, 36-32–36-34 case histories, 31-21 engineered bioremediation, 31-21 intrinsic bioremediation, 31-20 Biosparging, 36-36 Bioventing, 36-36 Bittern brines, 2-36 Black-centered grid, 23-11 Black Hills, 2-35 Blanks, QC check, 35-30 BLUE method, 16-10, 16-13, 16-14 Bog iron ore, 2-51 Boise, Idaho, 15-24 Book of Genesis, 2-8 Borden Aquifer, 15-3, 15-24, 18-14 Borehole, 20-10, 35-18 acoustic televiewer, 20-12 flow meters, 15-3, 15-5 geophysical methods, 14-16–14-20, 20-12 acoustic logs, 14-19–14-20 caliper logs, 14-17 electric logs, 14-17–14-19 nuclear logs, 14-19 instrumentation, 20-23–20-25 video camera (BVC), 20-12 Borrow areas, 33-10 Boulders, 2-8 Boundary conditions, 4-13–4-15 Boussinesq equation, 4-23 Branching, 31-7 Breakthrough curve, 3-34, 19-19, 23-24 boundary layer effect on, 9-12–9-14 British Columbia, 15-11 British Thermal Unit (BTU), 13-3 Bromide, 26-4–26-5 Brooks–Corey formula, 2-31, 6-13–6-15 Brundtland Commission, 27-1 Brussels World Exhibition, 1-22 BTEX 31-5, 31-7, 31-11, 31-14 bioremediation, 31-21 Bubbling pressure, 2-29 Bucket auger, 35-19 Buoyancy induced dispersion, 18-3 C C/N ratio, 29-26 C-14 dating, 1-3 Ca/Mg ratio, 21-21 Ca2+ , 17-7 Cable tool, 11-25, 35-19
Calcite, 2-9 dissolution, 21-18 Calibration checks, QC check, 35-31 criteria, 23-26–23-27 of deterministic groundwater model, 23-22 of model, 23-22–23-23 California, 1-16, 1-21, 2-45, 2-50, 3-28, 15-7, 15-17, 15-19 Caliper logs, 14-17 Calories, 13-3 Canada, 2-3, 2-38–2-39, 2-52, 18-14 Cape Cod Aquifer, 2-9, 15-3–15-4, 15-11, 18-14 Capillarity, 2-12–2-13, 2-50 barrier, 33-22, 34-11–34-12 fringe, 2-28, 2-32, 2-50, 15-12 potential, 1-13–1-14 water, 2-14 Capture, 27-2 Capture zone, 2-45 around pumping well, 2-47 Carbon, 17-27 adsorption, 36-43 cycle, in soil-plant system, 29-25 Carbon–nutrient–water cycle, 29-1 Carbonate, 2-9 dissolution chemistry, 21-17–21-24 system, 17-15 Carbonic acid, 17-15, 21-17–21-18 Cartesian coordinates, 4-10 Cartesian tensor, 23-4 Cation exchange, 22-20 Cauchy boundary condition, 22-22 Caves, 21-14 Cellular confinement system, 37-23–37-24 Celsius scale, 13-2–13-3 Centrifugation, 34-7 Centrifuge permeameter for unsaturated soils (CPUS), 34-9 CFITIM, 22-24–22-26 CFITM, 22-24–22-25 CHAIN code, 22-26 Channel model, 20-27 Charcoal, as dye receptor, 21-29 Chebyshev’s inequality, 5-14 Chemical and isotope method, 2-37 Chemical changes and surface-water interactions, 2-51 Chemical encrustation, 11-29 Chemical fencies, 1-27 Chemical hardness, 17-17 Chemical nonequilibrium attachment/detachment models, 22-15–22-16 kinetic sorption models, 22-15 Chemical precipitates, 2-9 Chemical transformations, microbiologically mediated, 17-15 Chemisorption, 17-10 Chemographs, of karst springs, 21-34–21-37 China, 1-3, 2-7, 2-10 Chlorinated congeners, 31-10 Chlorine, 11-29 Chlorobenzene, 31-10 Chlorofluorocarbons (CFC), 23-32 Chlorosulfonated polyethylene (CSPE), 37-12
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 3 — #3
I-4
Index
Chromatography, 17-11, 35-36 Churn drill, 2-7 Classical deterministic models, 18-4 Clay, 2-8–2-9 Clean Air Act (CAA), 17-24, 33-2–33-3 Clean Water Act (CWA), 32-7–32-10, 33-2 legislative background general provisions, 32-8–32-9 goals and objectives, 32-8 historical perspective, 32-7 issues and outlook, 32-9 regulations, 32-9 Cleanup Standards, 32-24–32-25 Climate change, impact of, 2-46–2-48, 28-1, 28-3–28-5 climate change, 28-2–28-3 Grand River watershed, case study, 28-20 conclusions, 28-33–28-34 input data, 28-21–28-25 methodology, 28-25–28-26 results, 28-26–28-33 groundwater recharge, 28-5–28-7 recharge, affecting factors infiltration and flow, in unsaturated zone, 28-10 land use and cover, 28-8 overland flow, 28-10 precipitation, 28-7–28-8 soil properties, 28-10 temperature, 28-11 urbanization, 28-9 vegetation, 28-8–28-9 recharge, in groundwater modeling, 28-15–28-20 coupled models, 28-16–28-18 integrated models, 28-18–28-20 recharge estimation methods, 28-11–28-14 combined modeling, 28-14 Darcian approaches, 28-13 empirical methods, 28-12–28-13 field techniques, 28-12 inverse groundwater modeling, 28-14 tracers, 28-13 water budget methods, 28-13 Climatic zonation, 1-26 Clogging, 37-7 Closed depressions, 21-3 CO2 , 1-12, 2-47, 2-51, 17-5, 17-15 Coastal aquifer, 3-28 management, 12-5, 12-23–12-26 water withdrawal, 12-25 Coastal collector, see Upconing Cokriging, 15-19, 16-13 Colloidal-facilitated solute transport, 22-16–22-17 Colophon, 1-4 Colorado, 2-38, 2-43, 2-52, 15-21, 30-9 Cometabolism, 31-7 Common midpoint (CMP), 14-10, 14-12 gathers, 15-9, 15-11 Complexation, 22-20 Comprehensive Environmental Response, Compensation and Liability Act (CERCLA), 3-39, 32-23–32-28, 36-2 legislative background general provisions, 32-23–32-24 goals and objectives, 32-23
historical perspective, 32-23 issues and outlook, 32-24 regulations guidance, 32-27 monitored natural attenuation, 32-27 National Contingency Plan, 32-25–32-26 Natural Resource Damage Assessments, 32-26–32-27 presumptive remedies, 32-27 technical impracticability, 32-28 vapor intrusion, 32-28 Computed axial tomography (CAT) 15-14 Computer code, 12-15 modeling, 1-29 Concentration moment analysis, 15-4 Conceptual errors, 23-23 Conceptual model, 23-2 Condensation, 1-4, 1-13 Conditional indicator simulation, 15-21 Conditional realization function simulation, 16-6 point simulation, 16-5–16-6 Conduction, of heat, 13-5 Conduits, 21-14 Cone of depression, 3-18 Cone penetrometer testing (CPT), 35-23, 35-30 Confined aquifer, 1-13, 2-25, 2-26, 3-23, 3-25, 10-2, 10-3 distance–drawdown analyses, 10-27–10-28 flow equation, 4-19–4-20 time–drawdown analyses, 10-17–10-19 well-flow equations, 10-5–10-6 Conformal mapping technique, 1-10 Congaree Bottomland Hardwood Swamp, see Congaree National Park Congaree National Park, 2-48 Congaree River, 2-48 Conjunctive management, 32-6 Connate water, 2-36 Connectivity function, in GIS spatial analysis, 30-5 Conservation of energy, for steady flow, 3-12 Conservation of mass, 23-3–23-4 Conservation tracer, 18-14 Conservative solutes, 3-29 Consortium for Risk Evaluation with Stakeholder Participation II (CRESP II), 24-19 Constant-head injection tests (CHIT), 20-13–20-16 Constant head permeameter, 3-11 Constant pressure tests, see Constant-head injection tests (CHIT) Construction, groundwater influence, 2-52 Contaminant adsorbed, 3-29 advection, 3-32 aqueous solubility, 17-3–17-13 diffusion, 3-32–3-33 dispersion, 3-34–3-37 dissolved, transport mechanisms of, 3-32–3-39 immiscible, 3-29 inorganic constituents, 17-14–17-19 maximum contaminant level (MCL), 35-3 miscible, 3-29 organic constituents, 17-19–17-24
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 4 — #4
Index
I-5
particulates, 17-29–17-30 plumes, dynamic imaging, 15-24–15-25 radioactive decay, 17-24–17-25 radioactive waste disposal, 17-28–17-29 radioactivity decay and degradation, 3-38–3-39 radionuclides, 17-24–17-29 remediation, 17-29 sorption, 3-37–3-38 sources, 17-26–17-28 units, 17-26 water physicochemical characteristics, 17-2–17-3 Contaminated groundwater, remediation of extraction systems design, 36-21–36-30 aquifer restoration time, 36-26–36-28 Contaminated groundwater (continued) extraction trench systems, 36-25–36-26 extraction well systems, 36-23–36-25 other approaches, 36-28–36-30 fundamentals, 36-1–36-6 associated risks, 36-4–36-6 remediation goals, 36-2–36-4 hydraulic containment, 36-13–36-21 alternative approaches, 36-20–36-21 hydraulic barriers, 36-17–36-20 physical barriers, 36-14–36-17 performance monitoring, of remediation system, 36-43–36-44 remediation system design candidate remediation, screening, 36-8–36-12 design effectiveness, confirmation, 36-13 design implementation, 36-13 detailed design, preparation, 36-12–36-13 problem defining, 36-6–36-7 remediation goals, defining, 36-7–36-8 treatment techniques, 36-30 ex situ treatment, 36-41–36-43 in situ treatment, 36-31–36-41 Contaminated transport, in unsaturated zone, 22-1 waterflow, variably saturated, 22-3–22-7 mass balance equation, 22-4 preferential flow, 22-5–22-7 uniform flow, 22-4–22-5 analytical models Fourier transformation, 22-23–22-24 Laplace transformation, 22-23 method of moments, 22-24 multi-dimensional models, 22-25–22-27 numerical models, 22-27–22-36 finite differences, 22-28–22-29 finite elements, 22-29–22-31 geochemical transport models, 22-35–22-36 single-species solute transport models, 22-32–22-35 stability and oscillations, 22-31–22-32 one-dimensional models, 22-24–22-25 solute transport advection–dispersion equation, 22-11–22-13 initial and boundary conditions, 22-21–22-22 multicomponent reactive solute transport, 22-19–22-21 multiphase flow and transport, 22-21 nonequilibrium transport, 22-13–22-17 stochastic models, 22-17–22-18
transport processes, 22-8–22-10 Continuity equation, 3-12, 4-2–4-5 Continuity principle, 1-10 Continuous hierarchy, 18-2 Continuous Time Random Walk (CTRW), 18-5–18-7 Contributing area, of well, 23-35 Convection, of heat, 13-5–13-6 Convective–dispersive equation (CDE), 9-2, 9-4 Convergent flow tracer tests, 15-7 Convolution–Fickian equation, 18-5 Core drilling, 1-3, 2-7 Corrective action monitoring programs, groundwater monitoring, 35-4 Correlation, 5-27–5-30 Correlative rights doctrine, 32-5–32-6 Coteau Des Prairies, 2-38 COUP, 22-32 Coupled continuum pipe flow models, for karst acquifer, 21-38 Coupled system of equations, 22-20–22-21 Courant number (Cre ), 22-32 Covariance, 5-28 Covariance matrix, 15-20 Crater Lake, 2-38 Creeping motion, 4-8 Cretaceous Period, 2-9, 2-26 Crosshole tomographic GPR techniques, 14-10 Cross-validation, 14-42–14-43 Cross-well radar tomography, 15-24–15-25 Cross-well tomography, 15-14–15-18 attenuation tomography, 15-18 travel time tomography, 15-16–15-18 Crusted soil infiltration rate, 7-13 Cryptosporidium, 31-2 Cryprosporidium parvum, 17-30 Crystalline rocks, 20-3, 20-29 Cubic law, 2-47–2-48, 20-3 Cubic packing, 2-11 Cumulative infiltration, 6-33, 7-4 Curve number method, 28-10 Curve tangent method, 2-37 CXTFIT, 22-18, 22-24–22-26 D DAISY, 22-32 Dakota aquifer, 2-26, 2-35 Dakota sandstone, 1-15, 1-16 Damming, 2-42 Dams, 37-9 Darcian velocity, 2-21 see also Specific discharge Darcy–Buckingham equation, 22-4 Darcy water flux density, 7-3 Darcy–Weisbach equation, 3-13, 21-10 Darcy’s law, 1-20, 2-20, 4-8–4-9, 5-3–5-5, 18-4, 20-34, 21-8, 23-4, 30-13, 3-7–3-12 extensions, 4-9–4-10 hydraulic conductivity field measurement, 3-11–3-12 laboratory measurement, 3-10–3-11 limitations, 3-9–3-10
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 5 — #5
I-6
Index
Data quality objectives (DQOs), groundwater monitoring, 35-9–35-10 Data transformation function in GIS spatial analysis, 30-4 DBCP (1,2-dibromo-3-chloropropane), 25-12–25-14 DC resistivity methods, 14-3–14-7 dipole–dipole array, 14-4 Schlumberger array, 14-4 Wenner array, 14-3 De Glee formula, 1-15 Death Valley, 2-38 Deep percolation model (DPM), 28-3–28-4 Deep surface pit mining, 2-50 Deep tunnel mining, 2-50 Degradation, mass transformation, 19-19 Degree of saturation, 2-12 Delayed yield principle, 1-17 Delmarva Peninsula, 23-31 DEM (Digital Elevation Model), 30-2 Dendro-chronologica dating, 1-3 Dense NAPL, 17-21 Depression springs, 2-38 Desalination, 1-3 Design optimization, of well fields, 11-22 Desorption, 3-37 Detection monitoring programs, groundwater monitoring, 35-2–35-3 Detergents, 17-3 Deterministic groundwater-simulation models, 23-2, 23-22 Deterministic nonequilibrium sorption, 19-7–19-8 Deterministic part, 16-2–16-3 Deuterium, 1-27–1-28 Diagenesis, 2-9 1,2-dibromo-3-chloropropane, see DBCP Dichloroethane (DCE), 31-8, 31-10 Dielectric permeativity, 15-12 Diffusion, 22-9 of heat, 13-6 Diffusion and back-diffusion modeling, 9-18–9-22 Diffusion driven dispersion, 18-3 Diffusive flux, 23-6 Digital computer, 2-2 simulation models, 1-29 Dijon, 2-20, 3-7 Dilution index, 18-12–18-13 Dimensional and inspectional analyses, 6-41, 6-42 1,4-dioxane, 31-8 Dipmeter, 14-17 Diprotic acid, 17-5 Direct-measurement method, 2-37 Direct methods, for algebraic equations, 23-17 Direct push technology (DPT) sampler, 35-23, 35-30 Direct recharge, 28-6 Direct rotary drilling method, 11-25 Dirichlet boundary condition, 22-22 Discharge phenomena, 1-22 Discharge point, 36-25 Discrete fracture networks, flow in, 20-33–20-35 Discrete hierarchy, 18-2 Discrete interval sampling, groundwater sampling, 35-29 Discrete matric potential regression methods, 6-23 Discretization, 23-2
Dispersion, 18-3 Dispersion tensor, 18-6 Dispersivity, 22-10, 23-6–23-7 flow-direction-dependent, 23-6 Dissolved chemical transport, 9-4 Dissolved chloride, 19-2 Distance–drawdown analyses, 10-26–10-30 confined and unconfined aquifer, 10-27–10-28 leaky aquifers, 10-28–10-30 DNAPLs, 21-40 Dolomite, 2-9 dissolution, 21-18 Dolostone, 2-9 Dose equivalent, 17-26 Double indexing, 23-11 Double porosity, 1-18 Downhole video camera, 21-31 Downscaling, 25-7–25-9, 25-10 Drainage function, geosynthetic, 37-8–37-9 Drainage layer, 33-15, 33-22–33-23 DRASTIC, 30-11 Index, 30-10 Drawdown, 3-14, 10-1 Drift, 2-8 Drilling, 21-31, 35-16–35-17, 35-19 QA/QC, 35-22 Dry bulk density, 6-5 Dual-domain mass transfer model (DDMT), 26-8, 26-11–26-12 Dual-permeability model, 22-5–22-7, 22-14 Dual-porosity and mobile–immobile water models, 22-14 Dual-porosity model, 22-5–22-7 with distribution layer at soil surface, 9-22–9-26 for gradual change at fracture–matrix interface, 9-9–9-22 boundary layer effect on BTC, at fracture outlet, 9-12–9-14 diffusion and back-diffusion modeling, 9-18–9-22 transition layer effect on concentration distribution, in matrix, 9-14–9-18 for sharp change at fracture–matrix interface, 9-3–9-9 first-order approximation, 9-8–9-9 zeroth-order approximation, 9-7–9-8 Dug wells, 1-3 Dune, 1-10, 1-19, 2-10 Dupit discharge formula, 4-24–4-27 Dupit–Forchheimer equation, 1-12 recharge basins, 3-17–3-18 seepage, from open channels, 3-16–3-17 steady flow in confined and unconfined aquifers, 3-18–3-20 over horizontal aquiclude, 3-15–3-16 Dynamic imaging, of tracer and contaminant plumes, 15-24–15-25 Dynamic plant water stress, 29-23 Dynamic viscosity, 2-18, 3-8, 13-4–13-5 DYNAMIX, 22-35 E E. Coli, 31-12 Earth materials
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 6 — #6
Index
I-7
minerals and rocks, 2-7–2-8 unconsolidated materials, 2-8–2-10 Ecohydrology, 29-1 photosynthesis and transpiration, atmospheric controls soil moisture deficit and plant water stress, 29-19–29-24 soil nutrient dynamics, 29-24–29-34 soil water balance, in vadose zone, 29-13–29-19 Effective porosity, 2-10, 3-8 Effective stress, 1-16 Effective velocity, 18-6 Egypt, 1-3, 2-7 Electric logs, 14-17–14-19 Electric Network Analogen for Groundwater Flow (ELNAG), 1-19 Electrical double-layer, 17-9 Electrical/mechanical control panel, 36-25 Electrical resistance methods, 6-17 Electrical resistance tomography (ERT), 14-5 Electroacoustical decontamination, 36-29 Electromagnetic (EM) induction, for hydrogeological characterization, 14-7–14-9 Electron, 17-25 Electron acceptors, 31-4–31-5, 31-8 nitrate, 31-5–31-6, 31-21 Electron transport phosphorylation, 31-3–31-4 Electrostatic forces of attraction and water states, in pores, 2-14 Elementary isotopes, 17-24 Elevation head, 3-3, 3-6, 3-8 Engineered bioremediation, 31-21 England, 3-28 Enhanced in situ bioremediation (EISB), 36-32 Entamoeba histolytica, 31-2 Envelope potential, 6-6 Environmental conditions, influencing biotransformations, 31-6–31-10 limits, 31-10–31-11 Environmental monitoring, in landfill projects, 33-25–33-26 Environmental problems, modern anthropogenic changes, in recharge areas, 2-51–2-52 artesian pressure and surface effects, 2-50 artificial drainage effects, 2-51 chemical changes and surface-water interactions, 2-51 climatic change, possible effects, 2-46–2-48 construction, groundwater influence, 2-52 excess evaporation and salt build up, 2-50 groundwater overdraft and consequences, 2-50 irrigation effects, 2-52–2-53 land subsidence, 2-49 mining effects, 2-50–2-51 soil liquefaction, 2-49 wetlands, 2-48–2-49 Environmental tracers, 1-28 EPA, 17-24, 30-10, 36-2 National Primary Drinking Water Standards, 32-11–32-12 Equilibrium flow, see Steady-state flow Equipotential lines, 3-20–3-21, 5-6–5-9 Equivalent porous media (EPM), 20-2 models, 20-37 for karst acquifer, 21-38
ERDAS, 30-2 Ergodicity, 19-4–19-5 Erkelenz, 1-3 Erosion control products, 37-24 Erosion layer, 33-14 Ethanol, 31-8, 31-11 Eulerian and Lagrangian perspectives, 18-3–18-4 Euphrates, 1-2 Europe, 31-9 Evapotranspiration, 1-24, 1-26, 2-13, 2-38–2-39, 2-48, 22-2, 28-8 Evapotranspirative cover systems, for waste containment, 34-1 case studies, 34-19–34-27 cover types anisotrophic barriers, 34-12–34-13 capillary barriers, 34-11–34-12 monolithic covers, 34-9–34-11 design numerical modeling issues, 34-16 performance criteria and regulatory issues, 34-13–34-14 strategies, 34-13 variables, 34-14–34-16 performance monitoring compliance demonstration, regulatory issues, 34-17 lysimetry, 34-17 meteorological variables and overland runoff, 34-18–34-19 moisture and suction profiles monitoring, 34-17–34-18 strategies, 34-16 unsaturated soils hydraulic concepts, 34-3–34-5 hydraulic conductivity functions, 34-7–34-9 hydraulic properties, 34-5–34-7 Everglades, 3-25 Evolutionary models, for karst acquifer, 21-37–21-38 Ex situ treatment biological processes, 36-41 chemical and physical processes, 36-42–36-43 volatilization processes, 36-41–36-42 Excess evaporation and salt build up, 2-50 Exit gradient, 5-46–5-47 Exoenzyme, 29-34 Expected spatial average infiltration rates, 8-7 Exploitation wells, 11-1 Extraction systems design, 36-21–36-30 aquifer restoration time, 36-26–36-28 extraction trench systems, 36-25–36-26 extraction well systems, 36-23–36-25 other approaches, 36-28–36-30 Extraction trench systems, 36-25–36-26 Extraction well systems, 36-23–36-25 Extrapolation, 25-8, 25-12 F Fahrenheit scale, 13-2 Falling head permeameter, 3-11 FAO, 1-27 Fault, 20-3, 33-4 FEAS code, 12-15 Federal and Indian groundwater rights, 32-6–32-7
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 7 — #7
I-8
Index
Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA), 32-29 Fermentation, 31-3 Ferralsols, 6-23–6-24 Fertigation, 2-51–2-52 Fiber optic chemical sensors, 35-30 Fiber reinforcement, 37-6–37-7 Fick’s law, 18-4, 20-8, 22-9, 23-6, 3-9 Field capacity, 1-14, 2-18 Field chemical analyses, 35-34 Field coefficient, of permeability, 2-20 Field scale infiltration, 8-3, 8-11 Field techniques, 20-9 borehole geophysical methods, 20-12 instrumentation, 20-23–20-25 core analysis, 20-10–20-12 fracture mapping, 20-10 hydraulic testing methods, 20-13 multi-well hydraulic tests, 20-17–20-18 point dilution method, 20-18–20-22 single-well hydraulic tests, 20-13–20-16 tracer experiments, 20-22–20-23 Field-scale dispersion, 23-7 Filter pack, 35-16, 35-21–35-22 Filtration function, geosynthetic, 37-7–37-8 Filtration theory, 22-16 Fingering, 9-2, 18-3, 22-5, 28-10 Finite-difference methods, 23-8–23-10, 23-10–23-13, 30-12 Finite Element Aquifer Simulator, see FEAS code Finite-element methods (FEM), 23-8–23-10, 23-13–23-15, 30-12 First-order approximation, 9-8–9-9 Fission fragments, 17-28–17-29 Fixed-head packers, 20-13 Flanders, 1-3 Flexible polypropylene (fPP), 37-12, 37-14 Flood plains, 2-9, 33-4 Florida, 1-19, 2-38, 3-25, 3-28 Flow analysis and aquifer tests, 1-16–1-18 Flow and transport, modeling, 20-31–20-38 Flow equation aquitard, 4-24 confined aquifer, 4-19–4-20 phreatic aquifer, 4-20–4-24 Flow mechanism, 8-2 Flow meter, 20-14 Flow model, of sea water intrusion, 12-12–12-13 Flow net, 3-20–3-22, 5-21–5-25 Flow systems, topography driven, 1-22 Flow work, 3-7 Flowing artesian well, 2-25 Fluid mechanics, 3-3, 4-1 Fluorescein, 21-30 Fluorescent dyes, 21-29 Flushing, 36-29 FLUTe® , 20-24–20-25 Flux, 20-34 boundary condition, 4-13 Flux–concentration relation, 6-36 Fokker–Planck equation, 6-32 Force potential, 1-20, 3-20 Forced gradient methods, 15-7
Forward modeling, with parameter error, 14-31–14-32 Fossil water, 2-36 Fourier transformation, 3-9, 18-8–18-10, 22-23–22-24 Fractional Advection-Dispersion (FADE), 18-7–18-8, 18-14 Fracture, 20-2 Fracture flow, 21-9 Fracture mapping, 20-10 Fracture–matrix interface dual-porosity models for gradual change, 9-9–9-23 for sharp change, 9-3–9-9 Fracture network, 20-28–20-31 Fracture zones, 20-3 Fractured media, groundwater flow and solute transport, 20-1 conceptual models, 20-25–20-31 discrete fracture networks, flow in, 20-33–20-35 flow and transport, modeling, 20-31–20-38 fracture network, 20-28–20-31 single fracture, 20-26–20-28 solute transport, in discrete fracture network, 20-35–20-38 field techniques, 20-9 borehole geophysical methods, 20-12 borehole instrumentation, 20-23–20-25 core analysis, 20-10–20-12 fracture mapping, 20-10 hydraulic testing methods, 20-13 multi-well hydraulic tests, 20-17–20-18 point dilution method, 20-18–20-22 single-well hydraulic tests, 20-13–20-16 tracer experiments, 20-22–20-23 single fracture, groundwater flow, 20-4–20-7 solute transport, in single fracture, 20-7–20-9 structural geology, of fractured rock, 20-2–20-4 France, 2-7, 2-9, 2-20, 2-25, 2-38 Freeze–thaw process, 28-11 Fresh-salt water interface problems, 1-18–1-19 Fresno Case Study, 25-12–25-14 Friction head loss, 3-13 Frontinus, 1-4 Fuel oxygenates, 17-24 Fulvic acid, 17-20 Function simulation, 16-6 Functional groups, oxygenated, 17-20 Functional hierarchy, 18-2 Functional normalization, 6-41 Functional regression methods, 6-23–6-25 Fungi, 31-2 Funnel and gate reaction barrier, 36-38 Funnel flow, 9-3 Furans, 31-8 G Gage pressure, 3-2–3-3 Gaining streams, 2-40–2-42 Galerkin method, 12-11, 22-31 Gamma–gamma log, 14-19 Gamma log, 14-19 Gamma particles, 17-25 Gamma rays attenuation method, 6-17 Gardner soil, 7-11 Gas management system, landfill gas, 33-17–33-19
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 8 — #8
Index
I-9
Gas monitoring, in landfill projects, 33-25 Gaseous-phase analyses, 35-36 Genasys, 30-2 Generalized linear estimation equations BLUE, 16-14 model, 16-13 parameter estimation, 16-14 Generalized Master Equation (GME), 18-6–18-7 Generic model, 23-2 Geocells, 37-23–37-24 Geochemical setting, 35-8–35-9 Geochemical transport models heavy metals leaching, from soil column, 22-36 HP1, 22-35–22-36 Geocomposite sheet drains, 37-20–37-22 Geocomposite strip (wick) drains, 37-22–37-23 Geographical information system (GIS), in groundwater engineering, 25-7, 30-1 analysis capabilities, 30-3–30-4 application groundwater movement modeling, 30-12–30-13 groundwater occurrence mapping, 30-6 policy implementation, involving spatial dimensions, 30-13–30-14 spatial data analyses, using spatial statistics, 30-7–30-8 spatial data aspects management, of groundwater projects, 30-6 surface fitting and interpolation, 30-8–30-9 visualization, 30-9 water vulnerability modeling, using spatial data, 30-9–30-12 components data, 30-3 hardware, 30-2–30-3 software, 30-2 data representation, 30-3 web services, 30-5–30-6 Geogrids, 33-23, 37-16–37-18 Geologic information, 35-9 Geological aspects, 1-12–1-13 Geological contact springs, 2-37 Geological occurrence, of groundwater, 2-2 anisotropy and heterogeneity, 2-22–2-25 aquifers, 2-25–2-28 capillarity, 2-12–2-13 Earth materials minerals and rocks, 2-7–2-8 unconsolidated materials, 2-8–2-10 electrostatic forces of attraction and water states, in pores, 2-14 environmental problems, modern anthropogenic changes, in recharge areas, 2-51–2-52 artesian pressure and surface effects, 2-50 artificial drainage effects, 2-51 chemical changes and surface-water interactions, 2-51 climatic change, possible effects, 2-46–2-48 construction, groundwater influence, 2-52 excess evaporation and salt build up, 2-50 groundwater overdraft and consequences, 2-50 irrigation effects, 2-52–2-53 land subsidence, 2-49
mining effects, 2-50–2-51 soil liquefaction, 2-49 wetlands, 2-48–2-49 groundwater importance, 2-3–2-7 groundwater supplies protection, 2-42–2-46 artificial protective barriers, 2-45 natural protective barriers and waste disposal, 2-44 water laws, 2-43–2-44 well-head protection programs, 2-45–2-46 hydraulic gradient, 2-20 hydraulic head, 2-16 intrinsic permeability, 2-18 moisture content, 2-12 porosity, 2-10–2-12 saturated media, hydraulic conductivity, 2-20–2-22 solid earth materials compressibility, 2-15 storage, 2-16–2-18 viscosity, 2-18–2-19 water, in saturated zone, 2-33 bank storage, 2-42 residence time, 2-35–2-36 streams, gaining and losing, 2-40–2-42 surface discharge, 2-36–2-40 water, in unsaturated zone atmospheric discharge and seepage face, 2-32–2-33 hydraulic conductivity and specific discharge, 2-31–2-32 moisture content vs depth, 2-28–2-29 recharge and infiltration capacity, 2-30–2-31 residence time, 2-32 subsurface stormflow, 2-32 water compressibility, 2-14–2-15 GeoMedia, 30-2 Geomembrane, 34-17, 36-21, 37-12–37-16 Geophysical and tracer data, combining, 15-18–15-24 geophysical and hydrogeologic properties relation, estimating, 15-23–15-24 geostatistical methods, 15-19–15-21 zonal inversion methods, 15-21–15-23 Geophysical methods, 35-13 borehole geophysical methods, 14-16–14-20 acoustic logs, 14-19–14-20 caliper logs, 14-17 electric logs, 14-17–14-19 nuclear logs, 14-19 to environmental problems surface seismic reflection and refraction surveys, 15-7–15-10 forward modeling, with parameter error, 14-31–14-32 for hydrogeological characterization DC resistivity methods, 14-3–14-7 electromagnetic induction, 14-7–14-9 ground penetrating radar, 14-9–14-11 seismic methods, 14-11–14-15 hydrogeophysical concepts, 14-20–14-29 hydrogeological mapping, 14-21–14-25 hydrogeological parameter estimation, 14-25–14-29 hydrological process monitoring, 14-29
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 9 — #9
I-10
Index
Geophysical methods (Continued) inverse modeling, 14-32–14-38 Bayesian estimators, 14-32–14-33 maximum likelihood method, 14-34–14-35 maximum a posteriori approach, 14-35–14-38 prior probability, defining, 14-33 model selection, 14-42–14-44 point estimation, with known parameters Bayesian point estimators, 14-39–14-42 potential field methods gravitational methods, 14-15–14-16 magnetic methods, 14-16 GeoServ, 30-5 Geostatistics, 16-1, 25-7 cokriging, 16-13 generalized linear estimation equations BLUE, 16-14 model, 16-13 parameter estimation, 16-14 inverse problems, 16-14–16-17 derivative computation, 16-17 methodology, 16-15–16-16 kriging variants, 16-11–16-12 ordinary kriging conditional realization, 16-5–16-6 function estimate, 16-4–16-5 interpolation, 16-3–16-4 preliminaries least squares, 16-2–16-3 model, 16-2 stochastic approach, 16-2 variogram calibration, 16-11 experimental variogram, 16-8–16-9 model, 16-6–16-7 nonnegativity, 16-11 residuals, 16-9 selection, 16-7–16-8 testing, 16-10–16-11 Geosynthetic, 37-1 applications, in landfill designs, 37-27–37-28 case histories multiple use, in landfill cover design vertical barrier system, 37-28–37-30 functions barrier function, 37-9–37-10 design by, 37-3 drainage function, 37-8–37-9 filtration function, 37-7–37-8 protection function, 37-10 reinforcement function, 37-4–37-7 separation function, 37-3–37-4 types erosion control products, 37-24 geocells, 37-23–37-24 geocomposite sheet drains, 37-20–37-22 geocomposite strip (wick) drains, 37-22–37-23 geogrids, 33-23, 37-16–37-18 geomembranes, 34-17, 36-21, 37-12–37-16 geosynthetic clay liners, 33-13, 37-18–37-20 geotextiles, 33-24, 33-26, 34-17, 37-7, 37-10–37-12 HDPE vertical barrier systems, 37-24–37-27 Geosynthetic clay liners, 33-13, 37-18–37-20 Geotechnical factors, 33-5, 33-26
Geotextiles, 33-24, 33-26, 34-17, 37-7, 37-10–37-12 cross machine direction, 37-12 machine direction, 37-11–37-12 manufacturing, 37-11 selvage, 37-12 Geothermal energy, for electric power, 13-7–13-9 GeoTools, 30-5 Ghyben–Hertzberg lens, 3-28 Ghijben–Herzberg principle, 1-9 Ghyben–Herzberg rule, 12-3 Giardia, 31-2 Giardian lambia, 17-30 GIS-MODFLOW, 30-12 Glacial drift, 2-8 Glacial ice, 2-8 Glacial till, 2-8 GLEAMS (Groundwater Loading Effects of Agricultural Management Systems), 30-10–30-11 Global neighborhood approach, 16-4 Global positioning system (GPS) 15-11, 30-3 GMS software, 30-9 Gobi Desert, 2-10 Golden, 15-21 Good Friday earthquake, 2-49 Grafton County, 15-25 Grand Island, 1-16 Grand River watershed, case study, 28-20 conclusions, 28-33–28-34 input data, 28-21–28-25 land use and land cover data, 28-22 soil data, 28-22–28-23 vegetation data, 28-23–28-24 weather data, 28-24–28-25 methodology, 28-25–28-26 results, 28-26–28-33 GRASS, 30-2 Gravel, 2-10 deposits, 2-8–2-9 pack, 11-19–11-20 Gravimetric method, 6-17 Gravitational methods, for hydrogeological characterization, 14-15–14-16 Gravitational water, 2-14 Gray, 17-26 Great Basin, 2-38 Great Lakes, 2-35, 2-38 Greece, 1-3, 2-7 Green and Ampt soils, 6-38–6-39 and Gardner soil, dynamical similarity, 6-45, 6-48 Greenhouse effect, 2-47 Greenhouse gas, 2-47 Green River, 21-6 Green’s function, 18-8–18-10 Grid design, 23-21 Ground penetrating radar (GPR), 14-9–14-11, 14-34, 15-10, 15-14, 15-24 Groundwater allocation and management federal and Indian groundwater rights, 32-6–32-7 property takings issues, 32-7 regulation, need for, 32-3–32-4 state groundwater rights systems absolute dominion, 32-4–32-5 conjunctive management, 32-6 correlative rights, 32-5–32-6
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 10 — #10
Index
I-11
prescriptive rights, 32-6 prior appropriation, 32-6 reasonable use, 32-5 torts restatement, 32-5 Groundwater and seepage flow net, 5-21–5-25 groundwater fundamentals, 5-2–5-9 Bernoulli’s equation, 5-3 Darcy’s law, 5-3–5-5 homogeneity and isotropy, 5-5 Reynolds number, 5-5 streamlines and equipotential lines, 5-6–5-9 introduction, 5-1–5-2 layered systems, flow in, 5-37–5-43 method of fragments, 5-31–5-37 piping, 5-43–5-46 Point Estimate Method (PEM) one random variable, 5-25–5-27 regression and correlation, 5-27–5-30 several random variable, 5-30–5-31 probabilistic fundamentals, 9 moments, 5-11–5-17 probability distribution, 5-17–5-21 Groundwater circulation well (GCW) technologies, 36-40 Groundwater contaminants aqueous solubility, affecting factors pε, 17-11–17-13 pH and chemical composition, 17-3–17-10 sorption, to solids, 17-10–17-11 temperature, 17-13 inorganic constituents source water, soil interaction, 17-17–17-19 source water composition, 17-14–17-17 organic constituents background organics, 17-19–17-20 fuel oxygenates, 17-24 high-profile organic contaminants, 17-21–17-24 nonaqueous phase liquids (NAPLs), 17-20–17-21 particulates, 17-29–17-30 radionuclides radioactive decay, 17-24–17-25 radioactive waste disposal, 17-28–17-29 remediation, 17-29 sources, 17-26–17-28 units, 17-26 water physicochemical characteristics, 17-2–17-3 Groundwater development, quantitative maintaining, 27-2 Groundwater dynamics, 1-6–1-12 Groundwater flow equations, 4-10–4-15, 23-4–23-5 boundary conditions, 4-13–4-15 Groundwater fundamentals, 5-2–5-9 Bernoulli’s equation, 5-3 Darcy’s law, 5-3–5-5 homogeneity and isotropy, 5-5 Reynolds number, 5-5 streamlines and equipotential lines, 5-6–5-9 Groundwater mining, 2-42, 23-1 case histories contributing areas delineation, 23-35–23-39 sea water intrusion, in coastal aquifer, 23-39–23-44 shallow unconfined aquifer, flow and transport, 23-31–23-35
equations, 23-3–23-7 groundwater-flow equation, 23-4–23-5 seepage velocity, 23-5 solute-transport equation, 23-5–23-7 flow and transport processes, 23-3 groundwater software, 23-44–23-45 model design and application, 23-19–23-28 calibration criteria, 23-26–23-27 grid design, 23-21 mass balance, 23-25 model calibration, 23-22–23-23 model error, 23-23–23-25 model validation, 23-27–23-28 predictions and postaudits, 23-27 sensitivity tests, 23-25–23-26 models, 23-2–23-3 MODFLOW-2000, 23-28–23-30 numerical methods, 23-7 boundary and initial conditions, 23-17–23-18 finite-difference methods, 23-10–23-13 finite-element methods (FEM), 23-13–23-15 generic model verification, 23-19 matrix solution techniques, 23-17 method-of-characteristics methods (MOC), 23-15–23-17 SUTRA, 23-30–23-31 Groundwater model validation, 24-1 Amchitka model, uncertainty reduction, 24-18–24-22 background, 24-19–24-20 Bayesian framework, 24-20–24-21 Milrow site, 24-21–24-22 practical views, 24-2–24-3 Project Shoal Area (PSA) model, 24-6–24-18 acceptance criteria, 24-7–24-8 multiple validation targets, 24-12–24-18 single validation target, 24-8–24-12 stochastic numerical models, 24-3–24-6 Groundwater monitoring, 35-1 data evaluation, 35-37 contaminant indications, responding to, 35-42–35-43 groundwater depths, 35-37–35-39 groundwater elevation measurement, 35-37–35-39 quality data, 35-39–35-42 devices, design and installation cone penetrometer testing, 35-23 direct push technology sampler, 35-23 groundwater discharge, 35-23 lysimeters, 35-24 piezometers, 35-22–35-23 soil gas probes, 35-24 wells, 35-14–35-22 groundwater sampling documentation, 35-34 field chemical analyses, 35-34 general approach, 35-24–35-25 in situ monitoring, 35-30 laboratory chemical analyses, 35-34–35-37 QA/QC samples, 35-30–35-31 sample handling and preservation, 35-31–35-34 techniques, 35-25–35-30
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 11 — #11
I-12
Index
Groundwater monitoring (Continued) in landfill projects, 33-25 plans developing, 35-7–35-13 purpose, 35-2 assessment monitoring programs, 35-3–35-4 corrective action monitoring programs, 35-4 detection monitoring programs, 35-2–35-3 performance monitoring programs, 35-4 regulatory requirements for, 35-4–35-5 statistical methods, 35-41 strategy considerations, 35-5–35-7 Groundwater overdraft and consequences, 2-50 Groundwater quality, 3-29–3-31 Groundwater whirl, 1-17 Gulf of Thailand, 15-9 H H2 CO∗3 , 17-5 H2 S, 17-5 Hagen–Poiseulle equation, 21-10 Halogenation compounds, 31-8 Halophilic bacteria, 31-6 Halorespiration, 31-9 Hantush leaky well flow equation, 4-31–4-33 Harris–Galveston area, 3-25 Haverkamp–Parlange model, 6-29 Hazardous waste, RCRA regulations, 32-17–32-21 corrective action program, 32-18–32-21 facility standards, 32-18 land disposal restrictions, 32-18 HDPE, see High density polyethylene Head loss, 2-35 Headwater, 5-22 Heat dissipation units (HDUs), 34-18 Heat flow, 13-1 advection versus convection, 13-6 applications different aquifers, distinguishing, 13-13 formation water expansion, 13-13 heat distributions, 13-11 hot and cold water storage, 13-13 temperature/depth profiles, in water wells, 13-11–13-13 basic thermodynamics heat as energy, 13-2 heat units, 13-3 specific heat of water, 13-3–13-4 temperature, 13-2–13-3 thermal and mechanical energy, relationship, 13-5 thermal conductivity, 13-3 thermal inertia, 13-4 thermal resistivity, 13-3 3D hexagon structures, of water, 13-4 viscosity and heat, 13-4–13-5 conduction, of heat, 13-5 convection, of heat, 13-5–13-6 different aquifers, distinguishing, 13-13 diffusion, of heat, 13-6 formation water expansion, 13-13 heat distributions, 13-11 heat flux, 13-5 hot and cold water storage, 13-13
into soil, 29-19 sources to and from Earth’s surface air-temperature changes, annual, 13-9 geothermal energy, for electric power, 13-8–13-9 geothermal gradient, 13-7 heat groundwater effects, upon hydrogeochemistry, 13-10–13-11 hydrothermal activity, 13-8 permafrost, 13-9–13-10 solar radiation, 13-6–13-7 surface water and groundwater, heat exchanges, 13-10 temperature/depth profiles, in water wells, 13-11–13-13 thermal gradients, 13-5 Heat flux, 13-5 Heat groundwater effects, upon hydrogeochemistry, 13-10–13-11 Heavy metals leaching, from soil column, 22-36 Hellenic–Roman civilization, 1-3–1-4 HEM, 19-6–19-7 Henry’s law, 17-4–17-5, 17-14–17-15 Heterogeneity, 19-4–19-5, 22-18, 23-2, 23-8 hierarchical, 18-2 in reactive properties, 19-20–19-21 Heterogeneity driven dispersion, 18-3 Heterogeneous aquifers, interpretation, 10-30–10-31 Heterotrophs, 31-2 High density polyethylene (HDPE), 37-12, 37-14 vertical barrier systems, 37-24–37-27 case history, 37-28–37-30 High-level waste (HLW), 17-28 High Plains Aquifer, 2-4, 2-52 High-profile organic contaminants, 17-21–17-24 High-velocity jetting, 11-27 History, of groundwater hydrology, 1-1 Hellenic–Roman civilization, 1-3–1-4 hydraulics and hydrology, 1-5 hydrochemistry, 1-25–1-27 isotope hydrology, 1-27–1-28 regional groundwater systems basic-scale analysis and evaluation, 1-20–1-21 flow systems, topography driven, 1-22 land drainage and groundwater discharge, 1-22–1-24 runoff generation, on sloping areas, 1-24–1-25 subsurface hydrology, developments in aquifer exploration, 1-14–1-16 flow analysis and aquifer tests, 1-16–1-18 fresh–salt water interface problems, 1-18–1-19 geological aspects, 1-12–1-13 groundwater dynamics, 1-6–1-12 hydrogeology consolidation, 1-19–1-20 soil water physics, 1-13–1-14 water management, in ancient societies, 1-2–1-3 water science evolution, during renaissance, 1-4–1-5 History matching, 16-14 HO model, 7-9–7-10 Hollow stem auger, 35-19 Homogeneity and isotropy, 5-5 Horizontal drains, 36-20–36-21 Hortonian runoff, 8-2–8-3 Hot Springs, Arkansas, 2-38
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 12 — #12
Index
I-13
HP1, 22-35–22-36 H-sigma bounds, 5-14, 5-16 Humic substances, 17-19–17-20 Hunt River Basin, 23-35 Hvorslev slug test equation, 4-27–4-28 Hydraulic approach, to groundwater flow aquitard, flow equation, 4-24 confined aquifer, flow equation, 4-19–4-20 motion equation, 4-15–4-19 phreatic aquifer, flow equation, 4-20–4-24 Hydraulic barriers, for hydraulic containment, 36-17–36-20 collection trenches, 36-17–36-18 extraction wells, 36-18–36-20 Hydraulic civilization, 1-2 Hydraulic conductivity, 6-9, 6-19–6-21, 21-9 functions, 6-15–6-16 instantaneous profile method, 6-19–6-20 pressure ring infiltrometer, 6-21 and specific discharge, 2-31–2-32 and suction, relationship, 34-7–34-9 tension disk infiltrometer, 6-20–6-21 Hydraulic containment, 36-13–36-21 alternative approaches, 36-20–36-21 hydraulic barriers, 36-17–36-20 physical barriers, 36-14–36-17 Hydraulic diameter, 20-6 Hydraulic gradient, 2-20, 3-5, 5-3 Hydraulic head, 2-16, 3-6, 3-8 measurement, 15-3 Hydraulic potential, 6-6 Hydraulic properties, of soil, 6-5–6-10 hydraulic conductivity, 6-9 soil water content, 6-5–6-6 soil water pressure, 6-6–6-7 water retention characteristic, 6-7–6-9 Hydraulic rotary method, 2-7 Hydraulic testing methods, 20-13 Hydraulics and hydrology, 1-5 Hydrocarbons, 31-5, 31-7–31-8 Hydrochemistry, 1-25–1-27 HYDROCOIN Project, 23-20 Hydrodynamic dispersion, 3-34, 23-6 Hydrofacies, 15-21 Hydrogen bonds, 17-2 Hydrogen peroxide, 31-5, 31-21 HYDROGEOCHEM, 22-35 Hydrogeologic factors, 33-5 Hydrogeologic setting, 35-8–35-9 Hydrogeology, analytical methods, 27-2–27-3 Hydrogeology consolidation, 1-19–1-20 Hydrogeophysical concepts, 14-20–14-29 hydrogeological mapping, 14-21–14-25 hydrogeological parameter estimation, 14-25–14-29 hydrological process monitoring, 14-29 Hydrographs, of karst springs, 21-31–21-34 Hydrology spatial scale, 25-2 temporal scale, 25-2 Hydrophobicity, 31-10 Hydrothermal activity, 13-8 HYDRUS software package, 22-33 HYDRUS-1D, 22-32–22-34, 34-16 HYDRUS-2D, 22-29, 22-32
Hygroscopic coefficient, 2-14 Hygroscopic water, 2-14 Hypochlorite, 11-29 Hypothetical solubility, 31-15 Hysteresis, 1-14, 2-29, 6-7, 6-9 I Idaho, 2-38 IDRISI, 30-2 Igneous rocks extrusives, 2-7 Immiscible contaminant, 3-29 In situ treatment, 36-31–36-41 biological remediation, 36-32–36-34 chemical and physical processes, 36-38 innovative treatment approaches, 36-40–36-41 monitored natural attenuation (MNA), 36-38–36-40 thermal treatment, 36-37–36-38 volatilization processes, 36-34–36-38 India, 1-3 Indiana, 2-8, 2-30, 2-38, 2-44, 2-49, 2-52, 30-6 Indicator seismic velocity thresholds, 15-21 Indirect recharge, 28-6 Infiltrability-depth approximation (IDA), 7-4 Infiltration, 1-24, 2-30, 3-2, 6-33–6-34, 7-1, 28-6, 28-10 capacity, 2-30–2-31 infiltration equations empirical equations, 7-9–7-10 Parlange et al. model (PA), 7-8–7-9 Philip infiltration equation (PH), 7-7–7-8 Swartzendruber (SW) model, 7-9 layer, 33-14 measurement methods permeameter method, 7-11 ring infiltrometer method, 7-10–7-11 sprinkler method, 7-10 rate prediction, 7-4 into sealed or crusted soils, 7-12–7-14 soil properties and process of infiltration, 7-2–7-7 spatial variability considerations, 7-11–7-12 Injection-withdrawal format, 20-22 Innovative in situ treatment approaches, 36-40–36-41 groundwater circulation well (GCW) technologies, 36-40 nanoscale zero-valent iron (nZVI), 36-40 surfactant enhanced aquifer remediation (SEAR), 36-40–36-41 Inorganic contaminants source water composition, 17-14–17-17 soil interaction, 17-17–17-19 Input–output models, for karst acquifer, 21-38–21-39 Instantaneous profile method, 6-19–6-20 Institute of Land and Water Management Research (ICW), 1-22 Integrated Groundwater Surface Water Model (IGSM), 28-19 Interface in confined aquifer, 12-4–12-5 in phreatic coastal aquifer, 1-5 Interference tests, 20-17 Intergovernmental Panel on Climate Change (IPCC), 28-2, 28-29 global climate predictions, 28-3
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 13 — #13
I-14
Index
Intermediate layer, 33-15 International Association of Hydrogeologist (IAH), 1-20, 1-28 International Association of Hydrological Sciences (IAHS), 1-20 International Association of Scientific Hydrology (IASH), 1-14, 1-20 International Atomic Energy Agency (IAEA), 1-28 International Hydrological Decade (IHD), 1-20 International Soil Science Society, 6-3 Interpolation and surface fitting, 30-8–30-9 Interpolation, see Geostatistics Intrinsic bioremediation, 31-20–31-21 Intrinsic permeability, 1-20, 2-18, 3-8 Inverse distance weighting, 30-12 interpolation, 30-8–30-9 Inverse flow modeling, 15-21 Inverse modeling, 14-32–14-38, 23-22 Bayesian estimators, 14-32–14-33 maximum a posteriori approach, 14-35–14-38 maximum likelihood method, 14-34–14-35 prior probability, defining, 14-33 Inverse problem, 3-20, 16-14–16-17 derivative computation, 16-17 methodology, 16-15–16-16 Ion exchange, 17-10 Ionizing radiation, 17-25–17-26 Ion-selective probes, 35-30 Iowa, 2-10 Iran, 1-3 Iron ore, 2-51 Irrigation effects, 2-52–2-53 Island aquifer, 27-3, 27-5 Isothermal compressibility, of water, 2-14–2-15 Isotope hydrology, 1-27–1-28 Isotropic media, 3-10 Isotropic tracers, 1-27 Israel, 1-19, 3-28 Iterative methods, for algebraic equation, 23-17 J Jacob’s method in step–drawdown tests, 11-8–11-11 Japan, 17-28 Jetting, 35-19 Joints, 20-3 JP-4 jet fuel, 31-21 Jshape, 30-5 K K -function, 34-7–34-9 Kankakee River Valley, 2-49 Kansas, 2-52, 3-25 Karst, 2-7, 3-25 Karst springs, 2-38 Karst terrane, 2-9 Karstic aquifers, 20-3 carbonate rock dissolution chemical equilibrium, 21-17–21-20 chemical parameters, 21-20–21-21 limestone and dolomite, dissolution kinetics of, 21-21–21-24 conceptual framework
allogenic recharge, 21-2–21-3 conceptual model, 21-7 dispersed infiltration and epikarst, 21-4–21-5 geologic boundary conditions, 21-6–21-7 groundwater basins, 21-2 groundwater discharge, 21-6 infiltration pathways, in vadose zone, 21-5 internal runoff, 21-3–21-4 subsurface drainage patterns, 21-5–21-6 evolution conduit life history, 21-24–21-25 enlargement, maturity, and decay, 21-26–21-27 initiation and critical thresholds, 21-25–21-26 modeling coupled continuum pipe flow models, 21-38 equivalent porous media models, 21-38 evolutionary models, 21-37–21-38 input-output models, 21-38–21-39 pipe flow models, 21-38 permeability and flow dynamics caves and conduits, 21-14–21-16 conduit permeability and flow dynamics, 21-9–21-12 matrix and fracture flow, 21-8–21-9 paleohydrology, 21-16–21-17 sediment fluxes and transport mechanisms, 21-12–21-14 quantitative hydrology base flow/runoff relations, 21-28 chemographs of karst springs, 21-34–21-37 hydrographs, of karst springs, 21-31–21-34 tracer studies, 21-28–21-30 water budget, 21-27–21-28 well tests and water table mapping, 21-30–21-31 sinkhole development hydrologic factors, 21-42 as landuse hazard, 21-41 mechanisms, 21-41 remediation, 21-42–21-43 water resource issues contaminants and transport, 21-40–21-41 sinkhole flooding, 21-39–21-40 water quality monitoring, 21-41 water supplies, 21-39 Kelvin scale, 13-2–13-3 Kentucky, 2-9, 2-38 Kesterson Aquifer, 15-7, 15-17, 15-19, 15-22–15-24 Kinematic viscosity, 2-19, 13-4–13-5 Kinetic energy, 3-6 Kinetic sorption models, 22-15 Kostiakov model (KO), 7-10 Kozeny–Carman equation, 1-8 Kriging, 14-39, 26-8–26-9, 30-8 variants, 16-11–16-12 Kurtosis coefficient of kurtosis, 5-17 L Laboratory chemical analyses, 35-34–35-37 Lacustrine materials, 2-9 Lagrangian perturbation approach, 18-10–18-11 Lagrangian stochastic models, for nonlinear reactions, 19-13–19-21 heterogeneity, in reactive properties, 19-20–19-21
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 14 — #14
Index
I-15
reaction system examples, 19-18–19-20 stochastic-convective averaging, 19-16–19-17 streamtube formulation, 19-14–19-16 travel-time distribution function, 19-17–19-18 Lakes and ponds, dynamic role, 2-38 Land drainage and groundwater discharge, 1-22–1-24 Land subsidence, 2-49, 4-12 calculation, 3-25–3-27 seepage force, 3-27 Landfills, 3-39, 33-1 Clean Air Act, 33-2–33-3 Clean Water Act, 33-2 conceptual design, 33-7–33-12 borrow areas, 33-10 cell layout and filling sequence, 33-11–33-12 final cover grading, 33-10–33-11 footprint, 33-8–33-9 sedimentation/detention basins, 33-10 subbase grading, 33-9–33-10 configuration, 33-6–33-7 detailed design alternative final covers, 33-21–33-22 berms, 33-15 bioreactor, 33-19–33-21 final cover system, 33-13–33-15 gas management system, 33-17–33-19 leachate collection and removal, 33-16–33-17 liner system, 33-12–33-13 mechanical properties of waste, 33-12 storm water management system, 33-16 elements, performance of, 33-26–33-27 environmental monitoring gas monitoring, 33-26 groundwater monitoring, 33-25 hydrogeological and geotechnical considerations, 33-5 linear and cover system materials geosynthetic materials, 33-23–33-24, 37-27–37-28, 37-30–37-31 geotextile, 37-10 soil materials, 33-22–33-23 Site Master Plan, 33-5–33-6 sitting federal considerations, 33-4 state and local considerations, 33-3–33-4 state and local regulations, 33-3 Subtitle D, 33-2 Laplace equation, 3-21, 4-32, 22-23 Las Vegas, 2-43 Law of continuity, 1-4 Law of hydrostatics, 3-3 Law of Tangents, 2-25 Layered systems, flow in, 5-37–5-43 Leachate, 37-27 collection system, 33-16, 33-27 removal system, 33-17, 33-27 LEACHM, 34-16, 34-22 Leaf area index (LAI), 28-9, 28-24, 29-3 Leaking underground fuel tanks (LUFTs), 17-21, 17-24 Leaky aquifer, 3-14–3-15, 10-2, 10-3 distance–drawdown analyses, 10-28–10-30 time–drawdown analyses, 10-22–10-24 well-flow equations, 10-7–10-9 see also Semi-confined aquifer
Least squares method, 15-2, 16-2–16-3 Legal framework for groundwater protection, in United States Clean Water Act (CWA), 32-7–32-10 legislative background, 32-7–32-9 regulations, 32-9 Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), 32-23–32-28 legislative background, 32-23–32-25 regulations, 32-25–32-28 Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA), 32-29 groundwater allocation and management federal and Indian groundwater rights, 32-6–32-7 property takings issues, 32-7 regulation, need for, 32-3–32-4 state groundwater rights systems, 32-3–32-6 laws and regulations, relationship, 32-2–32-3 Resource Conservation and Recovery Act (RCRA), 32-16–32-22 legislative background, 32-16–32-17 regulations, 32-17–32-22 Safe Drinking Water Act (SDWA), 32-10–32-16 legislative background, 32-10–32-14 regulations, 32-14 Surface Mining Control and Reclamation Act (SMCRA), 32-29 surface water and groundwater, interaction, 32-3 Leonardo da Vinci, 1-4 Ligands, 17-7 Light NAPL, see LNAPL Limestone, 2-9 Linear and nonlinear sorption, 22-11–22-12 Linear isotherm, 3-37–3-38 Linear law of groundwater flux and hydraulic gradient, 1-5 Linear reservoir, 9-23 Linear well losses, 11-6 Linearity and nonequilibrium Eulerian stochastic models deterministic nonequilibrium sorption, 19-7–19-8 random nonequilibrium sorption, 19-8–19-9 Liner system, 33-12–33-13 Liquid limit, of soil, 2-52 Lithitrophs, 31-2 Lithoautotrophs, 31-6 Lithologic heterogeneity, 15-12, 15-18 LNAPL, 17-21, 21-40, 35-37 Local equilibrium assumption (LEA), 9-4 Local neighborhood approach, 16-4 Local scale model, 8-5–8-6 Localized recharge, 28-6 Loess, 2-10 London, 17-10 Long Island, 1-20, 2-45 Long-term water balance, 29-17–29-19 Los Angeles, 2-45 Losing streams, 2-41 Low-level waste (LLW), 17-28–17-29 Low-stress approach, groundwater sampling, 35-27, 35-28 L-THIA, 30-5 Luminescence/spectroscopic analyses, 35-36
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 15 — #15
I-16
Index
Lungeon tests, see Constant-head injection tests (CHIT) Lwoff A., 31-12 Lysimeter, 28-12, 35-13, 35-24 Lysimetry, 34-17 M MACRO, 22-32 MacroDispersion Experiment Site (MADE), 15-3–15-4, 18-14 Macrodispersion Experiment (MADE) site, in Columbus advection-dispersion model (ADM), 26-6, 26-10–26-11 dual-domain mass transfer model (DDMT), 26-8, 26-11–26-12 natural-gradient tracer tests, 26-4–26-6 sensitivity analysis, 26-12–26-13 site description, 26-2–26-4 tritium tracer test hydraulic and transport properties assignment, 26-8–26-9 model setup and boundary conditions, 26-8 objectives and approaches, 26-6–26-8 Magnesite, 2-9 Magnetic methods, for hydrogeological characterization, 14-16 Magnrtotelluric (MT) measurements, 24-19–24-20 Manganese, 2-51 Manning equation, 21-11 MapGuide, 30-5 MapInfo, 30-2 Maps, 30-6 MapServer, 30-2, 30-5 Marion model, 15-23 Markov chain Monte Carlo (MCMC) method, 14-28, 24-20 Marl, 2-9 Mass balance equation, 2-16, 7-3, 9-5–9-8, 9-23, 12-4, 12-7–12-9, 18-4, 22-4, 22-6, 22-8 Massachusetts, 15-3 Mass-transfer coefficient, 9-12 Master Equation, 18-5–18-6 Mathematical model, 23-2 of sea water intrusion, 12-6–12-11 Matrix flow, 21-8 Matrix retardation coefficient, 20-8 Matrix solution techniques, 23-17 Maximum comparative percolation ratio, 34-14 Maximum contaminant level (MCL), 35-3 Maximum quantitative percolation value, 34-14 Mechanical dispersion, 3-34, 23-6 Mediterranean area, 2-9 Mendota, 3-25 Mesophilic bacteria, 31-6 Mesozoic Era, 2-9 Metabolism, 31-3–31-6 Metadata, 30-3 Metamorphic rock, 2-8 Meteorological variables, evapotranspirative covers, 34-15 Methane, 2-47 Methanol, 31-8 Method-of-characteristics methods (MOC), 23-15–23-17
Method of fragments, 5-31–5-37 form factor, 5-34 Method of moments, 22-24 Methyl tert-butyl ether (MTBE), 17-24 Mexico, 2-3 Mezencev (ME) model, 7-10 Mg2+ , 17-7 MGE (Modular GIS Environment), 30-2 Michaelis–Menten equation, 31-13 Microaerophiles, 17-19 Microbial dynamics, upscaling, 19-11–19-13 Microbial reaction kinetics, 31-12–31-15 and sorption, 31-18–31-20 Microbiology, 31-1–31-3 Microorganisms, 17-19, 17-29 Microresistivity logs, 14-17 Middle East, 2-10 Milrow model, 24-18–24-19, 24-21–24-22 Mineralization-immobilization turnover (MIT), 29-26 Minerals and rocks, 2-7–2-8 Mini-disk infiltrometer, 7-11 Minimal drawdown approach, see Low-stress approach Minimalpurge approach, groundwater sampling, 35-29 Minimum relative entropy (MRE), 14-33 Minimum safe discharge, 23-41–23-42 Mining effects, 2-50–2-51 Minnesota, 2-26, 2-30, 31-21 Miscible contaminant, 3-29 Miscible liquids, 12-2 Mississippi, 15-3–15-4 Mississippi River, 2-9–2-10, 2-35, 2-51 Missouri, 3-25 Missouri River, 2-9–2-10 Mobile–immobile model, 9-4, 9-6 time scale, 9-4–9-5 MOC3D, 30-9 Model, definition, 23-2, 23-20 Model calibration, 23-26 Model validation, 16-10 Model Viewer, 23-45, 30-9 Modena, 1-5 MODFLOW, 28-4, 28-17, 30-9 MODFLOW-2000, 23-28–23-30, 23-32, 23-35 Ground-Water Flow Process MODPATH, 23-28–23-29, 23-37 observation process, 23-29 parameter-estimation process, 23-29 sensitivity process, 23-29 MODFLOW-SURFACT, 22-32 MODHMS, 23-30 MODPATH, 30-9 Modules of elasticity, 3-25–3-26 Moffett Naval Air Station, 31-21 Moisture content vs depth, 2-28–2-29 Moisture content, 2-12 Molecular attraction, 2-14 Molecular diffusion, 3-28, 23-6 Molecular oxygen, 31-7 Molecular techniques, 31-9 Moments, 5-11–5-17 Monitored natural attenuation (MNA), 36-38–36-40 Monitoring wells, 11-23–11-24
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 16 — #16
Index
I-17
Monoaromatic hydrocarbons, 31-7–31-8 Monofilament, 37-11 Monolithic covers, 34-9–34-11 Monolithic final cover, 33-21 Montmorillonite crystal, 37-18 Motile organisms, 31-3 Motion equation, 4-6–4-9, 4-15–4-19 MT3DMS, 23-30 MTBE, 22-13 Mud rotary, 35-19 Multicomponent reactive solute transport cation exchange, 22-20 complexation, 22-20 components and reversible chemical reaction, 22-19 coupled system of equations, 22-20–22-21 precipitation and dissolution, 22-20 Multi-dimensional models, 22-25–22-27 Multilayered aquifer, 10-2 Multi-parameter probes, 35-30 Multi-permeability models, 22-6 Multiphase flow, 3-29 Multiple boreholes, 20-22 Multiple population inversion (MPI), 15-17 Multiple-packer strings, 20-13 Multiple scale roles, 18-2–18-3 Multi-pore group models, 9-26–9-28, 22-6 Multistep outflow method, 6-21 Multi-well hydraulic tests, 20-17–20-18 interference tests, 20-17 pulse interference tests, 20-17–20-18 wellbore storage, 20-17 Murot, 1-5 Mutually exclusive outcomes, 5-10 MYGRT, 22-25 N N3DADE, 22-25 Nanoscale zero-valent iron (nZVI), 36-40 NAPRA (National Agricultural Pesticide Risk Analysis), 30-5, 30-10–30-11 NASIS (National Soil Information System), 30-2, 30-6 National Bureau for Drinking Water Supply, 1-15, 1-21 National Contingency Plan, 32-24 National Research Council (NRC), 36-2, 36-8 National Well Water Association, 30-10 Natural Attenuation Study (NATS), 26-5 Natural gradient methods, 15-3–15-7 Natural pixels, 15-17 Natural protective barriers and waste disposal, 2-44 Natural Resources Conservation Service (NRCS), 7-10, 28-10 “Natural softening”, 1-26 Navier–Stokes equation, 1-20, 4-8, 21-9 Nebraska, 2-52 Negligible run-on spatial averages, 8-9–8-10 Neighborhood function, in GIS spatial analysis, 30-4 Neptunium, 17-27 Net system discharge, 23-41 The Netherlands, 1-9, 1-14, 1-16–1-18, 1-19, 1-21–1-24, 2-46, 3-28 Neutron thermalization, 6-17 Nevada, 2-10, 2-38, 2-43, 2-46, 17-28, 19-6
New Hampshire, 15-25 New Jersey Geological Survey (NJGS), 28-24 New Mexico, 2-9–2-10, 2-52, 3-25 New York, 2-45 Newton’s law of viscosity, 22-9 Newton’s stress law, 21-14 NHD (National Hydrography Dataset), 30-2 Nitrate, 31-5–31-6, 31-21 Nitrogen, 31-6 cycle, in soil-plant system, 29-26 N-nitrosamines N-nitrosodimethylamine (NDMA), 17-23–17-24 Noachian Flood, 2-8 Noble gas tracers, 21-29 Nonaqueous phase liquids (NAPLs), 17-20–17-21 Nonconservative solutes, 3-29 Nonequilibrium transport, 22-13–22-17 chemical nonequilibrium, 22-15–22-16 colloid-facilitated solute transport, 22-16–22-17 physical nonequilibrium, 22-14–22-15 see also Unsteady-state flow Nonhazardous waste, RCRA regulations, 32-21 Nonlinear well losses, 11-6–11-7, 11-13 Non-methane organic compounds (NMOCs), 33-17–33-19 Nonmicrobial colloidal particles, 17-30 Non-point source (NPS), 30-7, 30-9–30-10 Nonreactive contaminant transport, in saturated zone, 18-1 classical deterministic models, 18-4 Continuous Time Random Walk (CTRW), 18-5–18-7 dispersion, 18-3 Eulerian and Lagrangian perspectives, 18-3–18-4 field experiments, 18-14–18-15 Fractional Advection-Dispersion (FADE), 18-7–18-8, 18-14 heterogeneity, hierarchical, 18-2 lab experiments, 18-14 multiple scale roles, 18-2–18-3 spreading vs dilution, 18-12–18-14 stationary systems, locally, 18-11–18-12 statistical mechanical approach, 18-4–18-5 stochastic perturbation Fourier transform method and Green’s function approaches, 18-8–18-10 Lagrangian perturbation approach, 18-10–18-11 Noria, 1-3 Normal movement correction, 15-9, 15-20 Normality, 16-10 North Africa, 1-3 North America, 2-3, 20-10, 31-9 groundwater regions, 2-5 Norway, 2-49 NOx , 17-15–17-16 Nuclear logs, 14-19 Nuclear Waste Policy Act of 1982, 17-28 Numerical errors, 23-23 Numerical model, 23-2 evapotranspirative covers, 34-16 of sea water intrusion, 12-11–12-15 flow model, 12-12–12-13 specific discharge, calculation, 12-14–12-15 transport model, 12-13–12-14
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 17 — #17
I-18
Index
O Oahu island, 23-39 Observation wells, 11-24 Octanol : water partitioning coefficient (Kow ), 17-20 Ogallala Aquifer, 2-52 Ogallala formation, 2-4 Ohio River, 2-9 Ohm’s law, 3-9 OII landfill, evapotranspirative cover system, 34-19–34-23 Oklahoma, 2-52, 3-25 One-dimensional hydraulics, 3-12–3-13 One-dimensional models, 22-24–22-25 Ontario, 15-3, 20-21 Open-hole slug tests, 20-16 Optical brighteners, 21-29 Optimization problem, 23-29 Ordinary kriging, 16-3–16-6 conditional realization, 16-5–16-6 function estimate, 16-4–16-5 Oregon, 2-38 Organic contaminants background organics, 17-19–17-20 fuel oxygenates, 17-24 high-profile organic contaminants, 17-21–17-24 nonaqueous phase liquids (NAPLs), 17-20–17-21 Organotrophs, 31-2 Orthonormal, 16-9 Osmotic potential, 6-6 Outwash glacial, 2-8 sand, 2-8–2-9 Overdraft, 2-50, 2-52 Overland flow, 2-31 Overlay function, in GIS spatial analysis, 30-4 Overpumping method, 11-27 Oxbow lakes, 2-38 Oxygen, 1-27–1-28, 2-51, 17-15, 17-19 Oxygenase enzymes, 31-5, 31-7 Oyster, Virginia site, 15-20 P Pε, 17-11–17-13 Pε–pC diagram, 17-12 Pε–pH diagram, 17-12–17-13 Packers, 20-13 Paleohydrology, 21-16–21-17 Paleozoic carbonate acquifer, 21-5 Paradise Valley, 27-8–27-10 Parameter-estimation procedures, 23-22 Paris, 1-5 Park County, Colorado, 2-43 Parlange et al. model (PA), 7-8–7-9 Partial-area, 1-25 Particle pathlines, 23-16 Particle-size distribution, 6-11–6-13 bi-modal behavior, 6-12 particle-size scale parameter, 6-13 particle-size shape parameter, 6-12 Particle size limits, 6-3 Particle strength exchange method, 23-16 Particle tracking, 18-5, 20-35–20-36 Particle Tracking Velocimetry (PTV), 18-14 Particulates, 17-29–17-30
Passive capillary sampler (PCAPS), 28-12 Passive sampling, groundwater sampling, 35-29–35-30 Passive tracer, 19-2 PC–pH diagram, 17-6–17-8 PCBs, see Polychlorinated biphenyls PCE, see Perchloroethylene Pearl Harbor, 23-39, 23-41–23-42 Peat, 2-9 Peclet number (Pee ), 22-31–22-32 Pedo-Transfer Functions (PTF), 6-11–6-12, 6-24, 6-31 Pellicular water, see Capillarity Pentachlorophenol (PCP), 31-10 Perched aquifer, 2-26–2-27 Perchlorate, 31-4 Perchloroethylene (PCE), 17-21, 31-8, 31-10 Percolation, 1-5, 28-6, 28-10 Perennial streams, 2-40 Performance monitoring programs, groundwater monitoring, 35-4 remediation system, 36-43–36-44 Permafrost, 13-9–13-10 Permeability, 1-8, 2-39, 6-12 coefficient of, 5-5 conduit, 21-9, 21-17, 21-27 dual-permeability model, 22-5–22-7, 22-14 field coefficient of, 2-20 fracture, 21-17, 21-31 intrinsic, 1-20, 2-18, 3-8 karstic aquifers, 20-9 matrix, 21-31 multi-permeability models, 22-6 of natural soil, 33-10 Permeameter, 3-10–3-11, 7-11, 15-5 Permian basin, 3-25 Permittivity, 37-7 Petroleum hydrocarbon, 17-21, 31-11, 35-4 aerobic bioremediation, 31-21 Petrophysics, 14-11, 15-23 pF curve, 1-14 pH and chemical composition, 17-3–17-10 Phenols, 31-10 Philip infiltration equation (PH), 6-37, 7-7–7-8 Phosphorous, 31-6 Photoautotrophs, 31-2 Photoheterotrophs, 31-2 Photometry, 35-36 Photosynthesis and transpiration, atmospheric controls, 29-2 ecosystem fluxes modeling, 29-10 flow field inside canopies, 29-9–29-10 leaf energy budget, 29-8–29-9 radiative transfer, 29-8 scalar mass balance and turbulent transport, 29-3–29-5 scalar transfer from leaf stomata and resistance parameterization, 29-5–29-6 stomata sub-cavity space concentration parameterization, 29-6–29-8 transpiration and hydraulic controls, 29-10–29-13 Phreatic aquifer, 1-17, 4-15, 4-18 flow equation, 4-20–4-24 recharge, 1-21 PHREEQC, 22-35
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 18 — #18
Index
I-19
PHREEQE, 1-27 Physical barriers, for hydraulic containment, 36-14–36-17 cutoff walls, 36-14 soil-bentonite slurry walls, 36-14–36-17 Physical heterogeneity, 19-4 Physical nonequilibrium dual-permeability model, 22-14 dual-porosity and mobile–immobile water models, 22-14 mass transfer, 22-14–22-15 Physical properties, of soil, 6-4–6-5 and hydraulic properties, functional relationships hydraulic conductivity functions, 6-15–6-16 particle-size distribution, 6-11–6-13 water retention curves, 6-13–6-15 Physical techniques, soil water retention curve, 34-6 Physisorption, 17-10 Picard method, 12-11 Piecewise approximation, 23-13–23-14 Piezometer, 1-9, 2-50, 3-3, 3-12, 4-18, 35-13, 35-22–35-23 Piezometric head (potential), 3-3, 3-5, 3-7, 3-20 Piezometric surface, 2-25, 2-27 Pipe flow models, for karst acquifer, 21-38 Piping, 5-43–5-46 Plant roots, in recharge process, 28-9 Plant water stress modeling, 29-23 soil-climate-vegetation control and plant carbon assimilation, 29-23–29-24 Plastic limit, of soil, 2-52 Platte River, 2-52 Pleistocene, 2-10 Pleistocene Epoch, 2-8, 2-38, 2-46 Pleistocene fluvial sand, 1-15 Pneumatic hydraulic fracturing, 36-28–36-29 Point dilution method, 20-18–20-22 Point estimate method (PEM) one random variable, 5-25–5-27 regression and correlation, 5-27–5-30 several random variable, 5-30–5-31 Point estimation, with known parameters Bayesian point estimators, 14-39–14-42 normal linear methods, 14-40–14-42 Point simulation, 16-5–16-6 Point-water level, 1-19 Poiseuille’s law, 22-9 Polychlorinated biphenyls (PCBs), 31-10 Polyethylene, 37-12 Polyethylene diffusive bag (PDBs), 35-29–35-30 Polyhalogenated compounds, 31-8 Polymer, 37-11 Polynomial regression interpolation, 30-8 Polyphosphates, 11-27–11-28 Polyvinyl chloride (PVC), 37-12–37-14 Ponding, 1-24, 2-38, 6-33, 7-4, 8-1–8-2 time of, 7-4, 7-10–7-12, 7-14, 8-9 Pore pressure, 3-3 scale mixing, 19-17 size distribution, 7-3, 29-33, 34-6 space, 5-1 velocity, 3-8
Porosity, 2-8, 2-10–2-12, 3-2, 15-23 double, 1-18 dual-porosity models, 22-5–22-7 with distribution layer at soil surface, 9-22–9-26 for gradual change at fracture–matrix interface, 9-9–9-23 for sharp change at fracture–matrix interface, 9-3–9-9 effective, 2-10, 3-8 inter-aggregated, 9-3 primary, 2-10 secondary, 2-10 single-porosity model, 22-5 Porous-cup tensiometer, 1-14 Positrons, 17-25 Potential boundary condition, 4-13 Potential flow problem, 4-12 Potential theory, 5-6 Potentiometric surface, 2-27, 35-9 Prandl–Von Karman equation, 21-10 Precipitation, 2-48, 2-51, 36-43 and dissolution, 22-20 Predominance area diagram, 17-8 Preferential flow dual-permeability model, 22-5–22-7 dual-porosity models, 22-5–22-7 mass transfer, 22-7 Prescriptive rights, 32-6 Pressure energy, 3-7 Pressure head, 3-3, 3-7, 3-8 Pressure plate test, 34-6 Pressure ring infiltrometer, 6-21 Pressure surface, see Piezometric surface Primary porosity, 2-10 Prior appropriation, 32-6 Probabilistic fundamentals, 5-9 moments, 5-11–5-17 expected value, 5-12–5-13 probability distribution, 5-17–5-21 space, 5-18 Production casing, 11-15 Project Shoal Area (PSA) model, 24-6–24-18 acceptance criteria, 24-7–24-8 Corrective Action Investigation Plan (CAIP), 24-6 multiple validation targets, 24-12–24-18 single validation target, 24-8–24-12 Property taking issues, 32-7 Protection function, geosynthetic, 37-10 Protozoa, 31-2 Protozoan cysts, 17-30 Pseudo-steady state, 10-6 Psychrometer, 6-18 Psychrophiles, 31-6 Pulse interference tests, 20-17–20-18 Pumice, 2-7, 2-10 Pump and motor, 36-23, 36-26 in well design, 11-20–11-22 Pump housing length calculation, 11-15–11-17 Pumped aquifer confined and unconfined aquifer, differences, 10-6 leaky aquifers, 10-7–10-9 Pumping, 2-27, 23-40
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 19 — #19
I-20
Index
Pumping tests, 10-1 duration, 10-15 Pyrite oxidation, 17-18 Pyroclastic rock, 2-8 Q Q1 statistic, 16-10 Q2 statistic, 16-10 Qanat system, 1-2–1-3 Quantitative hydrology, 1-4 Quasi-exact infiltration solution, 6-38–6-39 Quasilinear approach, 16-16 Quicksand, 3-27, 5-43 R Radar, 6-18 signals, 15-14 Radial-convergent experiment, 20-22 Radial-divergent experiment, 20-22 Radial flow, 1-9 Radiative transfer, 29-8 Radiometers, 6-18 Radionuclides radioactive decay, 17-24–17-25 radioactive waste disposal, 17-28–17-29 remediation, 17-29 sources, 17-26–17-28 units, 17-26 Radium, 17-26–17-27 “Radius of influence”, 1-9 Radon, 17-26 Random field, 19-4–19-5 generation, 8-4–8-5 Random nonequilibrium sorption, 19-8–19-9 Random part, 16-2 Raster data, 30-3 Rate-limited model, 9-4–9-5 Raw variogram, 16-8 Raymonds number, 21-10 Reaction system examples, 19-18–19-20 Reactive contaminant transport, in saturated zone, 19-2 connection, between approaches, 19-22–19-23 heterogeneity, 19-4–19-5 Lagrangian stochastic models, for nonlinear reactions, 19-13–19-21 heterogeneity, in reactive properties, 19-20–19-21 reaction system examples, 19-18–19-20 stochastic-convective averaging, 19-16–19-17 streamtube formulation, 19-14–19-16 travel-time distribution function, 19-17–19-18 linearity and nonequilibrium Eulerian stochastic models deterministic nonequilibrium sorption, 19-7–19-8 random nonequilibrium sorption, 19-8–19-9 microbial dynamics, upscaling, 19-11–19-13 numerical results, 19-9–19-11 scale of observation, 19-5 upscaling chemical heterogeneity methods, 19-5–19-7 Reactive transport and biodegradation, quantitative description microbial reaction kinetics, 31-12–31-15 microbial reactions and sorption, 31-18–31-20
sorption, as reactive kinetic process, 31-15–31-18 Reactor ratio, 18-12–18-13 Reasonable doctrine, 32-5 Recharge, 28-2, 28-5–28-7 affecting factors infiltration and flow, in unsaturated zone, 28-10 land use and cover, 28-8 overland flow, 28-10 precipitation, 28-7–28-8 soil properties, 28-10 temperature, 28-11 urbanization, 28-9 vegetation, 28-8–28-9 estimation methods, 28-11–28-14 combined modeling, 28-14 Darcian approaches, 28-13 empirical methods, 28-12–28-13 field techniques, 28-12 inverse groundwater modeling, 28-14 tracers, 28-13 water budget methods, 28-13 in groundwater modeling, 28-15–28-20 coupled models, 28-16–28-18 integrated models, 28-18–28-20 Recharge and infiltration capacity, 2-30–2-31 Recharge basins, 3-17–3-18 Recharge estimation, to water table, 30-6 Recharge spreading layer (RSL), 28-15 Redox potential, 31-6 Redox reaction, 17-12 Redox transformation, 31-3–31-4 REELOGGER™, 13-12 Regional Aquifer System Analysis (RASA), 2-4 Regional groundwater systems basic-scale analysis and evaluation, 1-20–1-21 flow systems, topography driven, 1-22 land drainage and groundwater discharge, 1-22–1-24 runoff generation, on sloping areas, 1-24–1-25 Regression approach, 5-27–5-30, 15-2, 23-22 Reinforcement function, geosynthetic, 37-4–37-7 Relative roughness, of fracture, 20-6 Remediation goals, 36-2–36-4 advantages and disadvantages, 36-3 Remediation system design, of contaminated groundwater candidate remediation, screening, 36-8–36-12 design effectiveness, confirmation, 36-13 design implementation, 36-13 detailed design, preparation, 36-12–36-13 problem, defining, 36-6–36-7 remediation goals, defining, 36-7–36-8 Remediation wells, 11-22–11-23 Remote sensing, 6-18 radars, 6-18 radiometers, 6-18 Replicates, QC check, 35-31 Representative elementary volume (REV), 3-2, 3-34, 6-5, 18-2, 19-6 Residence time, 2-32, 2-35–2-36 Residual drawdown, 10-1 Resource Conservation and Recovery Act (RCRA), 3-39, 32-16–32-22, 36-2 legislative background general provisions, 32-16–32-17
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 20 — #20
Index
I-21
goals and objectives, 32-16 historical perspective, 32-16 issues and outlook, 32-17 regulations hazardous waste, 32-17–32-21 nonhazardous waste, 32-21 underground storage tanks, 32-21–32-22 Respiring organisms, 31-3 Response Authorities, 32-24 Response-matrix method, 23-29 Restatement doctrine, 32-5 Reston, Virginia, 2-4 Retardation factor, 3-38 Retrieval function, in GIS spatial analysis, 30-4 Reverse osmosis (RO), 36-43 Reversible chemical reaction and components, 22-19 Reynolds number, 2-33, 3-10, 3-13, 5-5, 20-6 Rhode Island, 23-35 Rhombohedral packing, 2-11 Richard’s equation, 1-14, 1-18, 20-34, 22-3–22-5, 34-16 Ring infiltrometers, 7-10–7-11 Riser pipe, 35-21 Risk, of contaminated groundwater, 36-4–36-6 Rock, 2-7–2-8 Rock flour, 2-10 Rock physics, see Petrophysics Rocky Mountain Arsenal, evapotranspirative cover system, 34-23–34-27 ROMIN, 30-5 Rorabaugh’s method in step–drawdown tests, 11-11–11-13 Rose diagrams, 20-10 Rotary drilling technique, 2-7 Runoff generation, on sloping areas, 1-24–1-25 Run-on process, 8-2 on Hortonian overland flow, 8-2 importance, 8-8–8-9 numerical simulation results discussion, 8-7–8-8 expected spatial average infiltration rates, 8-7 local scale model, 8-5–8-6 run-on importance, 8-8–8-9 soil properties and selected cases, 8-6 S Safe Drinking Water Act (SDWA), 32-10–32-16 legislative background general provisions, 32-10–32-13 goals and objectives, 32-10 historical perspective, 32-10 issues and outlook, 32-14 regulations, 32-14–32-15 Safe yield, 1-21, 2-42–2-43 Sahara, 2-10 Salinization, 1-18 Salt licks, 2-51 Salt transport model, 12-13–12-14 Salt water interfaces, 3-28–3-29 Salt water intrusion, 3-28 Salt Water Intrusion Meetings (SWIM), 1-19 Sample, in groundwater sampling analysis field chemical analyses, 35-34 laboratory chemical analyses, 35-34–35-37
collection, 35-31–35-32 filtration, 35-32 preservation, 35-32–35-33 storage, 35-33 San Francisco Bay, 2-49 San Joaquin Valley, 2-50, 3-25, 15-17, 15-19 Sand pumping, 11-29 Sand trap, 11-20 Saturated media, hydraulic conductivity, 2-20–2-22 Saturation indices, 21-21 Saturation ratio, 2-12 Scaling, 25-1 background, 25-4–25-5 catchment scale, spatial variability characterization, 25-10–25-12 extrapolation, 25-12 literature, 25-5 measurement and interpretation, 25-5–25-7 of soil water flow, 6-40–6-48 scaling evaporation, 6-47–6-48 scaling infiltration, 6-41–6-47 triplet, 25-7, 27-8 upscaling and downscaling, 25-7–25-10, 25-12–25-14 downscaling, 25-10 steps, 25-8 upscaling, 25-9–25-10 Scarborough, 1-5 Schofield, 1-14 Schoolcraft Plume-A Site, 15-5 Screen section, 11-17–11-18 length, 11-17 slot size, 11-17 well screens, calculation example, 11-18–11-19 Sea water intrusion, into coastal aquifers, 12-1, 23-39–23-44 coastal aquifer management, 12-23–12-26 examples in double-layered aquifer, 12-23 typical case, 12-15–12-18 with upconing, due to pumping, 12-18–12-23 mathematical modeling, 12-6–12-11 numerical modeling and computer code FEAS code, 12-15 numerical model, 12-11–12-15 Seal formation, 7-12–7-14 depositional or sedimentary seals, 7-13 structural seals, 7-12–7-13 Search technique, 30-4 SEAWAT-2000, 23-30 Secondary porosity, 2-10 Sedimentary rock, 2-8 Sedimentation/detention basins, 33-10 SEDSPEC, 30-5 SEEPAGE, 30-10–30-11 Seepage, from open channels, 3-16–3-17 Seepage face, 2-32–2-33 Seepage force, 5-43, 5-45 Seepage velocity, 3-8, 23-5 Seeps, 35-13 Seismic impact zones, 33-4 Seismic methods, for hydrogeological characterization, 14-11–14-15 petrophysics, 14-15 reflection methods, 14-12–14-14
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 21 — #21
I-22
Index
Seismic methods, for hydrogeological characterization (Continued) refraction methods, 14-14 tomography, 14-14–14-15 Semi-confined aquifer, 2-27–2-28 Semiphysical methods Arya–Paris model, 6-25–6-28 Haverkamp–Parlange model, 6-29 Sensitivity tests, 23-25–23-26 Separation function, geosynthetic, 37-3–37-4 Separation streamline, 12-16 Sequential Gaussian co-simulation, 15-19 Sequential imaging, of saline plume, 15-25 Shaduf, 1-2 Shallow unconfined aquifer, flow and transport, 23-31–23-35 Sharp interface approximation, 12-3 SHAW, 22-32 Shear fractures, 20-3 Shear zones, 20-3 Shearing stress, 2-19 Sheeting structure, 20-3 Silica sand, 17-9 Silt, 2-8–2-10 Silurian dolostone, 20-21 Silver springs, 2-38 Simulation experiments, 15-7 Simulation/optimization methods, for aquifer property estimation, 15-2–15-7 tracer tests forced gradient methods, 15-7 natural gradient methods, 15-3–15-7 Simultaneous iterative reconstruction technique, 15-17 Single fracture, 20-4–20-7, 20-26–20-28 Single point resistance, 14-17 Single-porosity model, 22-5 Single-species solute transport models, 22-32–22-36 HYDRUS software packages, 22-33–22-34 MODFLOW-SURFACT, 22-34–22-35 Single-well hydraulic tests, 10-24–10-26, 20-13–20-16 constant-head injection tests (CHIT), 20-13–20-16 slug tests, 20-16 Sinkhole, 3-25, 21-39–21-40 development hydrologic factors, 21-42 mechanisms of, 21-41–21-42 lakes, 2-38 as land use hazards, 21-41 remediation, 21-42–21-43 spring, 2-38 Site Master Plan, 33-5–33-6 Site remediation, 3-39 Site-specific model, 23-2 Skewness coefficient of skewness, 1-12, 5-17 Skibitski, Herb, 1-22, 27-6 Sliding-head packers, 20-13 Slit-film filament, 37-11 Slowness, 15-17 Sludge, 2-44 Slug test, 3-12, 20-16 Slurry-phase treatment, 36-41 Slurry wall, for contamination migration prevention, 2-45 Snowpack melting, 28-11
Sodium chloride, 17-19 Soft data, 16-8 Soil and rock, physical properties, 2-12 Soil-bentonite slurry walls, 36-14–36-17 Soil characteristics estimation techniques, 6-22–6-30 hydraulic conductivity relation, 6-29–6-31 water retention relation, 6-23–6-29 measurement, 6-16–6-22 hydraulic conductivity, 6-19–6-21 soil water content, 6-17–6-18 soil water pressure head, 6-18–6-19 water retention and hydraulic conductivity, combined, 6-21–6-22 spatial variability, of soil water properties, 6-31 Soil Conservation Service (SCS) method, 7-10, 28-10 Soil heterogeneity, 4-20 Soil infiltration capacity, 7-4–7-5 Soil liquefaction, 2-49 Soil moisture characteristic curves, 2-29 deficit, 29-19–29-21 physiological impact, on plants, 29-21–29-23 dynamics, 29-24–29-34 model structure, 29-26–29-29 soil carbon and nitrogen cycles, 29-25–29-26 soil organic matter and soil hydraulic properties, 29-33–29-34 system behavior, 29-29–29-33 Soil phases gaseous phase, 6-4 liquid phase, 6-4 solid phase, 6-3–6-4 Soil physics, 1-24 Soil properties functional relationships, 6-11–6-16 hydraulic properties, 6-5–6-10 physical properties, 6-4–6-5 soil phases, 6-3–6-4 Soil surface dual-porosity models with distribution layer, 9-22–9-26 Soil taxonomy, 25-12 Soil tests, 2-52 Soil vapor extraction (SVE), 36-34–36-35 Soil water balance, in vadose zone, 29-13–29-19 heat flow into soil, 29-19 long-term water balance, 29-17–29-19 soil-moisture dynamics at daily time scale, 29-14–29-17 instantaneous equation, 29-13–29-14 Soil water diffusivity, 6-32 Soil water physics, 1-13–1-14 Soil water retention curve, 34-5–34-7 function, 7-2–7-3 Solar radiation, 13-6–13-7 Solid earth materials compressibility, 2-15 Solid stem auger, 35-19 Solinist® system, 20-23 Solute transport advection–dispersion equation, 22-11–22-13 aquifer heterogeneity accounting MADE site in Columbus, case study, 26-1–26-14
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 22 — #22
Index
I-23
in discrete fracture network, 20-35–20-38 equation, 23-5–23-7 initial and boundary conditions, 22-21–22-22 multicomponent reactive solute transport, 22-19–22-21 multiphase flow and transport, 22-21 nonequilibrium transport, 22-13–22-17 in single fracture, 20-7–20-9 stochastic models, 22-17–22-18 transport processes, 22-8–22-10 Sorption, 36-27 as reactive kinetic process thermodynamics, 31-15–31-17 time dependent sorption, 31-17–31-18 to solids, 17-10–17-11 Sorptivity, 6-34–6-35, 6-37, 7-6 South Dakota, 2-9, 2-38, 2-52 SOx , 17-15–17-16 Spatial moments, 15-3 Spatial variability, 25-3 catchment scale, 25-10–25-12 characterization rainfall, 8-4 random fields, generation, 8-4–8-5 saturated conductivity, 8-3–8-4 considerations of infiltration, 7-11–7-12 infiltration and run-on numerical simulation results, 8-5–8-9 of rainfall, 8-4 random fields, generation, 8-4–8-5 of saturated conductivity, 8-3–8-4 theoretical results, 8-9–8-12 of soil water properties, 6-31 Specific discharge, 2-34, 2-37, 3-8 calculation, 12-14–12-15 Specific heat of water, 13-3–13-4 Specific retention, 2-17 Specific storage, 2-17, 4-12 coefficient, 3-23 Specific surface, 1-8 Specific yield, 1-17, 2-17, 2-27, 3-23 Spectroscopy, 35-36 Spent nuclear fuel (SNF), 17-28 Spikes, QC check, 35-30 Spline interpolation, 30-8–30-9 Split inversion method (SIM), 15-21–15-23 Spontaneous potential (SP) logs, 14-17–14-18 Spreading vs dilution, 18-12–18-14 Spring, 2-37–2-38 Sprinkler method, 7-10 SSURGO (Soil Survey Geographic), 30-2, 30-6 Stagnation point, 2-39 Standard deviation, 5-14 Standard pump test, 21-31 STANMOD, 22-25–22-26 Staple filament, 37-11 State groundwater rights systems absolute dominion, 32-4–32-5 conjunctive management, 32-6 corrective rights, 32-5–32-6 prescriptive rights, 32-6 prior appropriation, 32-6 reasonable use, 32-5
torts restatement, 32-5 Stationary systems, locally, 18-11–18-12 Statistical mechanical approach, 18-4–18-5 Steady flow in confined and unconfined aquifers, 3-18–3-20 over horizontal aquiclude, 3-15–3-16 Steady-state centrifuge (SSC), 34-9 Steady-state flow, 10-15 Steady-state laminar flow, 2-34 Steamboat Springs, Colorado, 2-38 Steam extraction, 36-29 Step–drawdown tests, 11-7–11-13 Jacob’s method, 11-8–11-11 Rorabaugh’s method, 11-11–11-13 Stochastic approach, 16-2, 23-3 heterogeneity, 22-18 stochastic numerical models groundwater model validation, 24-3–24-6 stream tube models, 22-17–22-18 transfer function models, 22-17 Stochastic-convective averaging, 19-16–19-17 Stochastic-convective reaction (SCR) method, 19-14 Stochastic perturbation Fourier transform method and Green’s function approaches, 18-8–18-10 Lagrangian perturbation approach, 18-10–18-11 Stomatal closure, 29-22 Storage coefficient, 1-16 Storativity, 3-23, 4-20 Storm runoff, 1-24 Storm water management system, 33-16, 33-26–33-27 Stratigraphy, 20-28 Stream beds, 2-9 Stream flow equation, 1-5 Stream flow hydrograph, 2-36 Stream lines, 3-20–3-21 Stream tube models, 22-17–22-18 Streamflow-routing (STR) package, 23-35–23-37 Streamlines, 5-6–5-9 Streamtube formulation, 19-14–19-16 Stress-balance diagram, 2-15 Strong acids, 17-17 Strontium, 17-28 Structural geology, of fractured rock, 20-2–20-4 Structural hierarchy, 18-2 Structural springs, 2-38 Student t -test, 24-10 Subbase grading, landfill, 33-9 Submerged unit weight, 5-43 Subsidence, see Land subsidence Substrate level phosphorylation (SLP), 31-3 Subsurface drainage patterns, karst acquifer, 21-5–21-6 Subsurface hydrology, 1-2 aquifer exploration, 1-14–1-16 flow analysis and aquifer tests, 1-16–1-18 fresh–salt water interface problems, 1-18–1-19 geological aspects, 1-12–1-13 groundwater dynamics, 1-6–1-12 hydrogeology consolidation, 1-19–1-20 soil water physics, 1-13–1-14 Subsurface microbiology and geochemistry metabolism, 31-3–31-6 microbiology, 31-1–31-3 Subsurface stormflow, 2-32
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 23 — #23
I-24
Index
Subtitle D, of Resource Conservation and Recovery Act, 33-2, 33-4 Suction, 3-3, 3-6 Sulfide ion, 17-5 Sumerians, 1-2 Surface charge, 17-9–17-10 Surface fitting and interpolation, 30-8–30-9 Surface mining, 2-50 Surface Mining Control and Reclamation Act (SMCRA), 32-29 Surface tension, 2-14 Surface water and groundwater, heat exchanges, 13-10 Surface-saturated zones, 1-25 Surfactant, 17-3 Surfactant enhanced aquifer remediation (SEAR), 36-40–36-41 Surfactant flushing, 36-29 Surficial aquifer, 23-32 Sustainable development, 27-1–27-2 aquifer dynamics and models, 27-5–27-6 basin and range aquifer, dynamics of, 27-6–27-8 groundwater development, quantitative maintaining, 27-2 hydrogeology, analytical methods, 27-2–27-3 Paradise Valley, 27-8–27-10 water budget, 27-3–27-5 SUTRA, 23-30–23-31, 23-39, 30-9 Swallets, 21-2 SWAP, 22-32 Swartzendruber (SW) model, 7-9 Synthetic organic compounds, 17-20 T Tailwater, 5-7, 5-9, 5-22–5-23, 5-37 Tarpon Springs, Florida, 2-38 Taylor series expansion, 23-11 Tectonic forces, 2-38 Temperature, 13-2–13-3 Tensiometer, 3-6, 6-18, 34-18 Tension disk infiltrometer, 6-20–6-21 Tertiary Ogallala Formation, 2-52 Texas, 2-38, 2-52, 3-25 Theis equation, 3-9, 4-28–4-30, 10-5 Thermal and mechanical energy, relationship, 13-5 Thermal conductivity, 13-3 Thermal energy, 17-13 Thermal gradients, 13-5 Thermal inertia, 13-4 Thermal resistivity, 13-3 Thermodynamics heat as energy, 13-2 heat units, 13-3 soil water retention curve, 34-6 specific heat of water, 13-3–13-4 temperature, 13-2–13-3 thermal and mechanical energy, relationship, 13-5 thermal conductivity, 13-3 thermal inertia, 13-4 thermal resistivity, 13-3 3D hexagon structures, of water, 13-4 viscosity and heat, 13-4–13-5 Thermophilic bacteria, 31-6 Thiem–Dupuit equation, 10-6
Thiem formula, 1-16 Thiessen polygon technique, 30-4–30-5 Thin plate interpolation, see Spline interpolation Thiobacillus ferrooxidans, 17-19 Thiobacillus thiooxidans, 17-19 Thixotropic system, 2-49 3D hexagon structures, of water, 13-4 3D modeling, of aquifer, 23-42 3DADE, 22-25–22-26 Tigris, 1-2 Time domain reflectometry (TDR) methods, 6-17–6-18, 34-17–34-18 Time–drawdown analyses aquifer test in confined aquifer, 10-17–10-19 in leaky aquifer, 10-22–10-24 in unconfined aquifer, 10-19–10-21 single-well tests, 10-24–10-26 Time-lapse imaging, 14-29 Tippecanoe County, 2-44, 30-6 Titrimetric procedures, 17-9 Top model, 1-25 Topography, 35-9 Tortuosity factor, 6-27 Total dissolved solids (TDS), 2-48, 12-7 Total head, 3-3 Total pressure, 3-6 Total soil water potential, 6-6 TOUGH codes, 22-33 TOUGH2, 22-32 TOUGH-REACT, 22-35 Toxic environmental conditions, 31-11 Tracer studies, 3-11, 20-22–20-23, 21-28–21-30 forced gradient methods, 15-7 natural gradient methods, 15-3–15-7 Tracers, 3-29 Transfer function models, 22-17 Transition layers, 9-18–9-22 Transmission piping, 36-25 Transmissivity, 2-21, 4-17–4-18, 23-4, 23-21, 37-9 Transnuranic waste (TRU), 17-28 Transport equations, 22-11 Transport mechanisms, of dissolved contaminants advection, 3-32 diffusion, 3-32–3-33 dispersion, 3-34–3-37 radioactivity decay and degradation, 3-38–3-39 sorption, 3-37–3-38 Transport processes, 22-8–22-10 advection, 22-10 diffusion, 22-9 Travel-time distribution function, 19-17–19-18 Travel-time of the solute, 19-14 Travel time tomography, 15-16–15-18 Treatment techniques, of contaminated groundwater, 36-30 ex situ treatment biological processes, 36-41 chemical and physical processes, 36-42–36-43 volatilization processes, 36-41–36-42 in situ treatment, 36-31–36-41 biological remediation, 36-32–36-34 chemical and physical processes, 36-38 innovative treatment approaches, 36-40–36-41
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 24 — #24
Index
I-25
monitored natural attenuation, 36-38–36-40 volatilization processes, 36-34–36-38 Trench, 36-26 Trench fill, 33-6 Trichloroethane, 31-8, 31-10 Trichloroethylene, 17-21 Triple permeability model components, for karst acquifer, 21-8 Tritium, 1-28, 2-30, 17-27, 23-32–23-34 Tritium tracer test, MADE site hydraulic and transport properties assignment, 26-8–26-9 model setup and boundary conditions, 26-8 objectives and approaches, 26-6–26-8 Truncation error, 23-11 Turbulent diffusion, 3-28 Turbulent flow, 2-34–2-35 Turgor, 29-22 Turning bands method, 8-4 Two- and three-dimensional flow, of groundwater continuity equation, 4-2–4-5 Darcy’s law extensions, 4-9–4-10 Dupuit discharge formula, 4-24–4-27 groundwater flow equations, 4-10–4-15 boundary conditions, 4-13–4-15 Hantush leaky well flow equation, 4-31–4-33 Hvorslev slug test equation, 4-27–4-28 hydraulic approach, to groundwater flow aquitard, flow equation, 4-24 confined aquifer, flow equation, 4-19–4-20 motion equation, 4-15–4-19 phreatic aquifer, flow equation, 4-20–4-24 macroscopic approach, 4-5–4-6 motion equation, 4-6–4-9 Theis well flow equation, 4-28–4-30 2-box model, 31-15 Two-packer system, 20-13 U UCODE, 23-22 Uncertainty reduction, using validation data, 24-18–24-22 background, 24-19–24-20 Bayesian framework, 24-20–24-21 Milrow site, in Amchitka model, 24-21–24-22 Unconfined aquifer, 2-26, 3-23, 3-25, 10-2, 10-3 distance–drawdown analyses, 10-27–10-28 time–drawdown analyses, 10-19–10-21 well-flow equations, 10-6–10-7 Unconfined compressive strength, of soil, 2-52 Unconsolidated materials, 2-8–2-10 Underground storage tanks, 32-21–32-22 groundwater protection, 32-22 UNESCO, 1-27 UNESCO-1HP, 1-28 Uniformity coefficient, 2-11 UNIX operating system, 30-2 UNSATCHEM, 22-35 UNSAT-H, 22-32, 34-16 Unsaturated flow apparatus (UFA), 34-9 Unsaturated flow equation, analytical solutions constant negative pressure head condition with gravity effects, 6-36–6-38 without gravity effects, 6-34–6-36
constant positive pressure head condition, 6-38–6-40 Unsaturated soil, evapotranspirative cover performance hydraulic properties conductivity functions, 34-7–34-9 soil water retention curve, 34-5–34-7 water flow, through unsaturated porous media, 34-3–34-5 Unsaturated soil water flow, conceptual aspects, 6-31–6-34 general flow equations, 6-32–6-33 infiltration, 6-33–6-34 Unsaturated zone, soil properties and moisture movement, 6-1 conclusions and future research perspectives, 6-48–6-49 flow equation, analytical solutions constant negative pressure head condition, 6-34–6-38 constant positive pressure head condition, 6-38–6-40 functional relationships, 6-11–6-16 hydraulic conductivity functions, 6-15–6-16 particle-size distribution, 6-11–6-13 water retention curves, 6-13–6-15 hydraulic properties, 6-5–6-10 hydraulic conductivity, 6-9 soil water content, 6-5–6-6 soil water pressure, 6-6–6-7 water retention characteristic, 6-7–6-10 physical properties, 6-4–6-5 scaling principles, 6-40–6-48 scaling evaporation, 6-47–6-48 scaling infiltration, 6-41–6-47 soil characteristics, estimation techniques, 6-22–6-30 hydraulic conductivity relation, 6-29–6-31 water retention relation, 6-23–6-29 soil characteristics, measurement, 6-16–6-22 hydraulic conductivity, 6-19–6-21 soil water content, 6-17–6-18 soil water pressure head, 6-18–6-19 water retention and hydraulic conductivity, combined, 6-21–6-22 soil phases, 6-3–6-4 soil water flow, conceptual aspects, 6-31–6-34 general flow equations, 6-32–6-33 infiltration, 6-33–6-34 spatial variability, of soil water properties, 6-31 Unstable areas, 33-4 Unsteady-state flow, 10-15 Upconing, 3-28–3-29, 12-23, 12-26 Upscaling, 25-7–25-10 chemical heterogeneity methods, 19-5–19-7 effect of, 25-12–25-14 extrapolation, 25-12 microbial dynamics, 19-11–19-13 spatial variability, at catchment scale, 25-10–25-12 Uranium, 17-27 Urbanization, 2-51 US, 1-13, 1-15, 2-2–2-3, 2-38, 2-43–2-44, 2-46, 2-52, 3-25, 17-17, 17-28, 2-9 groundwater regions, hydraulic characteristics, 2-6 legal framework, for groundwater protection, 32-1 US Department of Agriculture, see USDA US Department of Energy, 17-28
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 25 — #25
I-26
Index
US Environmental Security Technology Program, 31-9 US Geological Survey (USGS), 1-12, 1-15, 2-4, 27-2, 30-9 National Water-Quality Assessment Program, 23-31 US Geological Survey Fractured Rock Hydrology Research Site, 15-25 US Nuclear Regulatory Commission, 17-28 USDA, 6-3 soil textural classification chart, 6-4 USEPA, see EPA User index, 6-14 USSR, 1-26 Utah, 2-38 V Vadose zone, 22-2–22-4, 29-2 infiltration pathways in, 21-5 soil water balance, 2-13–29-19 see also Unsaturated zone Vadose/W, 34-16 Valley fill, 33-6 Van der Waal’s forces, 17-10 Variable-density flow process, 23-30 Variable-source area, 1-25 Variance, 5-13 Variation, coefficient of, 5-14 Variogram, 16-3 calibration, 16-11 experimental variogram, 16-8–16-9 model, 16-6–16-7 nonnegativity, 16-11 residuals, 16-9 selection, 16-7–16-8 testing, 16-10–16-11 Vector data, 30-3 Vegetative cover, 34-15–34-16 Vegetative layer, 33-23 Veihmeyer, 1-14 Velocity head, 3-6 Velocity potential, 3-20 Vertical rate of strain, 2-19 Very flexible polyethylene (VFPE), 37-12, 37-14 Vienna, 1-28 Vinyl chloride (VC), 31-8–31-10 Virginia, 2-4 Virus, 17-29, 31-2 Viscosity, 2-18–2-19, 18-3 Visual MODFLOW, 30-9 Void ratio, 2-11 Volatilization processes, 36-34–36-38 in ex situ treatment, 36-41–36-42 in in situ treatment, 36-34–36-38 Volatilization, 22-13 Volcanic craters, 2-38 Volume of voids, 2-10 W Wash River, 2-44 Valley, 2-8 Waste, mechanical behavior, 33-12 Waste containment evapotranspirative cover systems, 34-1 Waste Isolation Pilot Plant, 15-7
Water, in saturated zone, 2-33 artificial protective barriers, 2-45 bank storage, 2-42 groundwater supplies protection, 2-42–2-46 natural protective barriers and waste disposal, 2-44 residence time, 2-35–2-36 streams, gaining and losing, 2-40–2-42 surface discharge, 2-36–2-40 water laws, 2-43–2-44 well-head protection programs, 2-45–2-46 Water, in unsaturated zone atmospheric discharge and seepage face, 2-32–2-33 hydraulic conductivity and specific discharge, 2-31–2-32 moisture content vs depth, 2-28–2-29 recharge and infiltration capacity, 2-30–2-31 residence time, 2-32 subsurface stormflow, 2-32 Water and solute movement modeling, 9-1 dual-porosity models with distribution layer at soil surface, 9-22–9-26 for gradual change at fracture–matrix interface, 9-9–9-23 for sharp change at fracture–matrix interface, 9-3–9-9 multi-pore group models, 9-26–9-28 Water budget, 27-3–27-5 Water compressibility, 2-14–2-15 Water content reflectometer (WCR) probe, 34-18, 34-26 Water laws, 2-43–2-44 Water management, in ancient societies, 1-2–1-3 Water physicochemical characteristics, 17-2–17-3 Water retention and hydraulic conductivity, combined, 6-21–6-22 Beerkan method, 6-22 Water retention characteristic, 6-7–6-9 Water retention curves, 6-13–6-15 Water retention shape index, 6-14 Water science evolution, during renaissance, 1-4–1-5 Water table, 2-26–2-27, 4-14, 23-18, 30-6 Water vulnerability modeling, using spatial data, 30-9–30-12 WATERGEN, 30-5 Well, groundwater monitoring, 35-13 decommissioning, 35-22 design, 35-13–35-16 development techniques, 35-21–35-22 drilling methods, 35-16 QA/QC, 35-22 installation monitoring, 35-16–35-21 QA/QC, 35-22 Well, monitoring, 3-39 Well construction construction methods, 11-24–11-26 maintenance, 11-28–11-29 well development, 11-26–11-28 Well design, 11-13–11-24 casing section, 11-15 design optimization, 11-22 gravel-pack, 11-19–11-20 groundwater remediation wells, 11-22–11-23 monitoring wells, 11-23–11-24 pump, 11-20–11-22
JACQ: “4316_c038” — 2006/10/14 — 12:30 — page 26 — #26
Index
I-27
pump housing length, calculation example, 11-15–11-17 sand trap, 11-20 screen section, 11-17–11-18 well screen, calculation example, 11-18–11-19 Well development, 11-26–11-28 Well-drilling, 1-3 Well efficiency, 11-7 Well-fields equations, 11-2–11-5 aquifer and well losses, 11-5–11-7 partial penetration, 11-5 step–drawdown tests, 11-7–11-13 Well flow equations, 10-4–10-12 confined aquifers, 10-5–10-6 leaky aquifers, 10-7–10-9 partial penetration, 10-9–10-11 recovery well-flow equations, 10-11–10-12 unconfined aquifers, 10-6–10-7 Well head protection programs, 3-8 Well hydraulics and aquifer tests, 10-1 aquifer test performance, 10-12–10-17 data processing, 10-15–10-17 date interpretation, 10-17 measurements, 10-13–10-15 pumping test duration, 10-15 aquifer types, 10-2 distance–drawdown analyses, 10-26–10-30 heterogeneous aquifers, interpretation, 10-30–10-31 physical properties, of aquifers, 10-2–10-4 time–drawdown analyses aquifer test, in confined aquifer, 10-17–10-19 aquifer test, in leaky aquifer, 10-22–10-24 aquifer test, in unconfined aquifer, 10-19–10-21 single-well tests, 10-24–10-26 well-flow equations, 10-4–10-12 confined aquifers, 10-5–10-6 leaky aquifers, 10-7–10-9 partial penetration, 10-9–10-11 recovery well-flow equations, 10-11–10-12 unconfined aquifers, 10-6–10-7 Well losses, 11-6, 11-16 linear well losses, 11-6
nonlinear well losses, 11-6–11-7 well efficiency, 11-7 see also Head loss Well volume approach, groundwater sampling, 35-27–35-29 Wellbore skin, 20-16 Wellbore storage, 20-17 Wellhead protection area (WHPA), 30-13 Well-head protection programs, 2-45–2-46 Wellhead, 36-23 Wellpoints, 36-21 Wellscreen, 35-21 calculation example, 11-18–11-19 West Virginia, 2-38, 2-51 Westbay® System, 20-23 Wet chemistry analyses, 35-36 Wetlands, 2-48–2-49, 33-4 WHAT, 30-5 White Sulfur Springs, W. Virginia, 2-38 Wick pan lysimeter, see Passive capillary sampler (PCAPS) Wilting point, 2-13–2-14 Wind-powered mill, 1-4 World Commission on Environment and Development, see Brundtland Commission Wyoming, 2-26 X Xenophanes, 1-4 XML format, 30-3 Y Yarn, 37-11 Yucca Mountain, 17-28, 19-6 Yugoslavia, 2-9 Z Z -test, 24-10–24-12 Zero flux plane, 6-19–6-20, 28-12 Zeroth-order approximation, 9-7–9-8 Zonal inversion methods, 15-21–15-23 Zonal slowness model, 15-17 Zonation, 1-26
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100
0
90
10
80
20 30
70
50 Silty clay
Sandy clay Clay loam
30 Sandy clay loam
t
50
40
20
40
Si l
%
Clay
%
Cla y
60
60
Silty clay loam
70 80
Loam 10 0 100
Loamy Sand sand 90
80
Silt loam
Sandy loam
90 Silt
70
60
50 40 % Sand
30
20
10
100 0
FIGURE 6.7 Contour lines of the particle-size shape parameter M plotted on the basis of the USDA soil textural triangle as a function of the different soil texture classes.
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100
0
90
10
80
20 30
70
40 50 Silty clay
Sandy clay
40
Sandy clay loam
20
60
Silty clay loam
Clay loam
30
t
50
Sil
%
Clay
%
Cla y
60
70 80
Loam 10 0 100
Loamy Sand sand 90
80
Silt loam
Sandy loam
90 Silt
70
60
50 % Sand
40
30
20
10
100 0
FIGURE 6.8 Contour lines of the particle-size scale parameter Dpg (µm) plotted on the basis of the USDA soil textural triangle as a function of the different soil texture classes.
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Vertical direction (m)
20
(a) Natural equilibrium condition 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
0 Sea –20 –40 –60 –80
–100
Vertical direction (m)
20 0
Sea
–20
0.99 0.9 0.7 0.5 0.3 0.1 0.02
–40
0.5
–60 –80
–100
Vertical direction (m)
20 0
(b) Steady state under pumping 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
Sea
–20 –40 –60 –80
–100
Vertical direction (m)
20 0
Sea 0.99 0.9 0.7 0.5 0.3 0.1 0.02
–20 –40 0.5
–60 –80
–100 400
200
0 200 400 Horizontal direction (m)
600
800
1000
FIGURE 12.5 Numerical model results for (a) a sea water wedge under natural equilibrium conditions (no pumping) and (b) steady-state sea water intrusion under pumping conditions (three pumping wells). In each case, the figure shows the reference head distribution and streamlines in the top figure, and salt mass fraction in the bottom figure, as well as the separation streamline (in red solid line).
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–40
4.5
Sea
4
0
3.5
Vertical direction (m)
(a)
5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0
–80 –120 –160 –200
–400
–200
0
200 400 600 800 Horizontal direction (m)
1000
1200
1400
(b) Vertical direction (m)
0
Sea
–40
0.99 0.9 0.7 0.5 0.3 0.1 0.01
0.0
1
–80
0.1 0.3 0.9 0. 9 9 0.7 0.5
–120 –160 –200
–400
–200
0
200 400 600 800 Horizontal direction (m)
1000
1200
1400
FIGURE 12.7 Steady-state solution of a sea water wedge in a confined aquifer for Example B: (a) the reference hydraulic head distribution (in dashed lines), with the separation streamline (in red line) separating streamlines (in solid lines) originating at the fresh water zone and the sea water zone, and the zero-horizontal-flux line (in pink line), and (b) the mass fraction distribution within the transition zone, and the groundwater flow velocity vector.
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Sea
4
4.5
–40 3.5
Vertical direction (m)
0
–80 –120 –160 –200
–400
–200
0
200
400
600
800
1000
1200
4.5 4 3.5 3 2.5 2 1.5 1 0.5 0
1400
Horizontal direction (m)
Vertical direction (m)
0
Sea
–40 –80
0.9 0.7 0.5 0.3 0.1 0.05 0.02
0.1 0.5
–120 –160
0.9
–200
–400
–200
0
200
400
600
800
1000
1200
1400
Horizontal direction (m)
FIGURE 12.8 Transient sea water upconing in a confined aquifer at the end of 8.9 yr in Example B: (a) contours of reference hydraulic head (dashed lines), the separation streamline (red line), and streamlines (solid black lines) originating from the fresh water zone and from the sea water zone, and the capture zone (thicker solid black line), and (b) mass fraction contours (solid lines) with sea water upconing towards the pumping well, in comparison with the initial steady-state transition zone (dashed lines), and the separation streamlines for the upconing and the initial steady-state condition.
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(a)
(c)
Vertical direction (m)
–200 –200
–160
–120
-80
–40
0
200 –200
–160
–120
–80
–40
0
200
800 400 600 Horizontal direction (m)
0 200
800 400 600 Horizontal direction (m)
Upconing, C = 0.1
0
Upconing, C = 0.02
1000
1000
1200
1200
–80
–40
0
–80
–40
0
–200 –200
–160
–120
(d)
–200 –200
–160
–120
(b)
200
0
800
800 400 600 Horizontal direction (m)
200 400 600 Horizontal direction (m)
Decay, C = 0.1
0
Decay, C = 0.02
1000
1000
1200
1200
FIGURE 12.9 Transient upconing and decay processes in a confined aquifer (Example B). The times for the upconing process are 53, 239, 439, 839, and 3239 days (well’s shutoff), and 3239, 3439, 3639, 4039, and 4639 days for the decay process, all from the beginning of the pumping.
Vertical direction (m)
Vertical direction (m) Vertical direction (m)
71°27'30" 41°38'45"
20
30
41°38'45"
9A KC1 NK9
71°28'45"
Hu
P ond ut P om ow ot
Ri
14A
ver
nt
20
30
41° 37' 30"
Explanation
Traveltime to well, in years
Contributing areas to water-supply wells
40
>20 >10 - 20 >5 - 10 >2.5 - 5 0 - 2.5 NK9
KC1
14A
9A
Water-supply well identifier Boundary of active area of model—dashed where active area extends beyond area shown.
Inactive area of model
30
Model-calculated water-table countour—contour interval is 10 feet. Datum is sea level.
NK9 Water-supply well and identifier Base from U.S. Geological Survey digital data, 1:24,000, Rhode Island stateplane projection. 1983 North American datum
FIGURE 23.15 Model-calculated steady-state contributing areas and traveltimes to water-supply wells in the northern part of the Hunt River Basin, Rhode Island. (Modified from Barlow, P.M. and Dickerman, D.C. (2001) Numerical-simulation and conjunctive-management models of the Hunt-Annaquatucket-Pettaquamscutt stream-aquifer system, Rhode Island. U.S. Geol. Survey Prof. Paper 1636.)
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FIGURE 23.23 Example plot generated with Model Viewer software showing the grid shell, selected model features and boundary conditions, particle pathlines (shaded by time of travel), and a solid rendering of a contaminant plume for a 3D MODFLOW simulation. (From Hsieh, P.A. and Winston, R.B. (2002) User’s guide to Model Viewer, a program for three-dimensional visualization of ground-water model results, U.S. Geol. Survey Open-File Rept. 02-106.)
Soil heat flux (W m–2)
Gs
30 20 10 0 –10 0
20
40
60
80
100
120
140
160
120
140
160
Soil temperature (°C)
Depth
–20 –40 –60 –80 0
20
40
60
80 100 Time (hr)
FIGURE 29.11 Measured soil heat flux (Gs ) near the land–atmosphere interface and measured soil temperature (ranging from 12, black, to 18◦ C, white) within a grass-covered surface illustrating the warming and cooling heat waves.
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