WATER AND WASTEWATER SYSTEMS ANALYSIS
DEVELOPMENTSIN WATER SCIENCE, 34 OTHER TITLES IN THlS SERIES (Volumes 1-3 are o...
349 downloads
74478 Views
3MB Size
Report
This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form
WATER AND WASTEWATER SYSTEMS ANALYSIS
DEVELOPMENTSIN WATER SCIENCE, 34 OTHER TITLES IN THlS SERIES (Volumes 1-3 are out of print)
4 J.J. FRIED GROUNDWATER POLLUTION 5 N. RAJARATNAM TURBULENT JETS 6 D. STEPHENSON PIPELINE DESIGN FOR WATER ENGINEERS
7 V. HALEK AND J. SVEC GROUNDWATER HYDRAULICS
B J.BALEK HYDROLOGY AND WATER RESOURCES IN TROPICAL AFRICA 9 T.A. M c M A H O N AND R.G. MElN RESERVOIR CAPACITY AND YIELD 10 0. KOVACS SEEPAGE HYDRAULICS 11 W.H. GRAF AND C.H. MORTIMER (EDITORS) HYDRODYNAMICS OF LAKES: PROCEEDINGS OF A SYMPOSIUM 12-13 OCTOBER 1978, LAUSANNE, SWITZERLAND 12 W. BACK A N D D.A. STEPHENSON (EDITORS) CONTEMPORARY HYDROGEOLOGY: THE GEORGE BURKE MAXEY MEMORIAL VOLUME 13 M.A. M A R l f l 0 A N D J . N . LUTHIN SEEPAGE AND GROUNDWATER 14 D. STEPHENSON STORMWATER HYDROLOGY AND DRAINAGE 15 D. STEPHENSON PIPELINE DESIGN FOR WATER ENGINEERS (completely revised edition of Vol. 6 in the series) 16 W. BACK A N D R. LkTOLLE (EDITORS] SYMPOSIUM ON GEOCHEMISTRY OF GROUNDWATER 17 A.H. EL-SHAARAWI (EDITOR) IN COLLABORATION W I T H S.R. ESTERBY TIME SERIES METHODS IN HYDROSCIENCES 18 J.BALEK HYDROLOGY AND WATER RESOURCES IN TROPICAL REGIONS 19 D. STEPHENSON PIPEFLOW ANALYSIS 20 I. ZAVOIANU MORPHOMETRY OF DRAINAGE BASINS 21 M.M.A. SHAHIN HYDROLOGY OF THE NILE BASIN 22 H.C. RlGGS STREAMFLOW CHARACTERISTICS 23 M. NEGULESCU MUNICIPAL WASTEWATER TREATMENT 24 L.G. EVERETT GROUNDWATER MONITORING HANDBOOK FOR COAL AND OIL SHALE DEVELOPMENT 25 W. KINZELBACH GROUNDWATER MODELLING: AN INTRODUCTION WITH SAMPLE PROGRAMS IN BASIC 26 D. STEPHENSON AND M.E. MEADOWS KINEMATIC HYDROLOGY AND MODELLING 27 A.H. EL-SHAARAWI A N D R.E. KWIATKOWSKI IEDITORS) STATISTICAL ASPECTS OF WATER QUALITY MONITORING - PROCEEDINGS OF THE WORKSHOP HELD AT THE CANADIAN CENTRE FOR ISLAND WATERS, OCTOBER 1985 28 M.JERMAR WATER RESOURCES AND WATER MANAGEMENT 29 G.W. ANNANDALE RESERVOIR SEDIMENTATION
30 D.CLARKE
MICROCOMPUTER PROGRAMS FOR GROUNDWATER
31 R.H. FRENCH HYDRAULIC PROCESSES ON ALLUVIAL FANS 32 L. VOTRUBA. Z.KOS. K. NACHAZEL. A. PATERA ANDV. ZEMAN ANALYSIS OF WATER RESOURCE SYSTEMS 33 L. VOTRUBA AND V. BROZA WATER MANAGEMENT IN RESERVOIRS
DAVD STEPHENSON Water Systems Research Group, University of the Witwatersrand, 1 Jan Smuts Avenue, Johannesburg, South Africa
ELSEVl ER Amsterdam
- Oxford - New York - Tokyo
1988
ELSEVIER SCIENCE PUBLISHERS B.V. Sara Burgerhartstraat 25 P.O. Box 21 1, 1000 AE Amsterdam, The Netherlands Distributors for the United States and Canada: ELSEVIER SCIENCE PUBLISHING COMPANY INC. 52, Vanderbilt Avenue New York, NY 10017, U S A .
ISBN 0-444-42945-X (Vol. 34) ISBN 0-444-41669-2 (Series)
0 Elsevier Science Publishers B.V., 1988 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V./Physical Sciences & Engineering Division, P.O. Box 330, 1000 AH Amsterdam, The Netherlands. Special regulations for readers in the USA - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred to the publisher. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Printed in The Netherlands
V
PREFACE
A systematic approach to decision m a k i n g i n water
resources p l a n n i n g
i s presented w i t h p a r t i c u l a r reference t o wastewater re-use. Various methods of system s i m u l a t i o n a n d o p t i m i z a t i o n a r e a p p l i e d number
of
case
studies.
Methods
of
analysis
and
numerical
in a
methods
(Chapter 2, 4 ) a r e described as well a s the b a s i s of p o l l u t i o n a n d water quality
(Chapter 1 ,
3).
The economics
of
desalination
a r e a l s o discussed
(Chapter 7 ) . The a u t h o r has considerable experience in p l a n n i n g and
recycling
systems
i n an a r i d
area,
Southern
premium f o r m i n i n g a n d i n d u s t r i a l development
a n d d i s t r i b u t i o n of water
resources can
purification
Water
i s at
a n d considerable money
spent on water treatment o r use of poor q u a l i t y water.
of money.
water
Africa.
a is
Careful management
i n these circumstances save a
lot
The general theory of o p t i m i z a t i o n subject to q u a l i t y c o n s t r a i n t s
i s presented i n Chapter 6. The internal are
examples
studied
re-circulation
considered
range
(Chapter
(Chapter
and
9)
sewerage systems (Chapter 1 1
from
,
regional
supplies
8). Groundwater stormwater
and
quality
12) a r e also covered.
(Chapter
artificial (Chapter
Computer
10)
to
recharge
5)
and
applications
e x i s t throughout and a number of s i m u l a t i o n a n d o p t i m i z a t i o n programs in BASIC a r e presented. Chapter 13 i s on an often ignored subject, sampling
procedures
in
monitoring
water
the necessity f o r s c i e n t i f i c
quality.
It
was
written
by
Professor Tom Sanders of Colorado State U n i v e r s i t y . The theory and case studies should p r o v e of v a l u e in many aspects of planning
use
of
water
resources
with
quality
constraints.
Wastewater
re-use and conservation therefore a r e promoted b y the approach adopted.
vi
CONTENTS CHAPTER 1 . WATER QUALITY IN INDUSTRIAL SYSTEMS Geochemical source o f p o l l u t i o n Effect o f e v a p o r a t i o n on c o n c e n t r a t i o n s Effects o f poor q u a l i t y w a t e r Scaling P r e d i c t i o n of s c a l i n g a n d corrosion P r e v e n t i o n of s c a l i n g Calcium c a r b o n a t e s c a l i n g Sulphate s c a l i n g A d d i t i v e s f o r t h e p r e v e n t i o n of s c a l i n g Fouling Control o f f o u l i n g O i l emulsion b r e a k d o w n Corrosion Types of corrosion Corrosion p r e v e n t ion P o t a b l e water s t a n d a r d s Agriculture and irrigation CHAPTER 2.
10 10 13 14 15 17
20 21 24 24 26 31 31
NON CONSERVATIVE PARAMETERS
Introduction B a s i c mass b a l a n c e e q u a t i o n Oxygen b a l a n c e in r i v e r s Coupled equations f o r DO a n d BOD Analytical solution C a l i b r a t i o n of a m o v i n g BOD model Oxygen b a l a n c e Fie1d measurements CHAPTER 4.
9
MATHEMAT I CAL MODELLING O F WATER QUAL I TY
Mass Balances M i x e d a n d p l u g f l o w systems Systems a n a l y s i s T e r m i n a l concentration in a w a t e r c i r c u i t A p p l i c a t i o n to a m i n e w a t e r c i r c u i t Computer s i m u l a t i o n model Mathematical b a s i s of model CHAPTER 3.
1 2 2 3 3 3 5 6 6 8
35 35 37 37 39 40 40 45
NUMERICAL METHODS
S i m u l a t i o n o f H y d r a u l i c Systems Two-step method Demonstration o f n u m e r i c a l i n a c c u r a c y I m p l i c i t f i n i t e d i f f e r e n c e schemes Comments on f i n i t e d i f f e r e n c e methods Numerical methods f o r t h e s o l u t i o n o f s i n g l e differential equations The E u l e r method The m o d i f i e d E u l e r method Runge-Kutta methods M u l t i s t e p methods F i n i t e elements Boundaries f o r n u m e r i c a l methods
51 52 52 55 56 57 57 59 60 61 62 62
vi i
CHAPTER 5. MASS BALANCE O F STORMWATER POLLUTANTS Introduction Catchmen t d e s c r i p t i o n Q u a l i t y Observations Fa1lout measurement Relationship between t o t a l p o l l u t a n t load a n d r u n o f f volume Chemical constituents Mass b a l a n c e f o r event of 18 January 1985 on H i l l b r o w catchment Mass b a l a n c e f o r event of 7 M a r c h 1983 on Montgomery P a r k catchment Conclusions
64 64 66 66 67 67 72 73 77
CHAPTER 6. OPTIMUM ALLOCATION O F WATER RESOURCES SUBJECT TO QUAL I T Y CONSTRA INTS
Int roduc t ion The system Solution method Discussion L i n e a r Programming Solution The I i n e a r programming technique w i t h separable programming a p p l i e d S e n s i t i v i t y study f o r v a r i o u s acceptable TDS values
79 80 82 85 85 91 95
CHAPTER 7. ECONOM I CS OF DESALINATION OF WASTEWATERS
I n t roduc t ion A l t e r n a t i v e s f o r optimal reuse of waste water Selection of optimum d e s a l i n a t i o n methods Relevant d e s l i n a t i o n methods I n d u s t r i a l wastewater treatment Reverse osmosis Membrane d e s c r i p t i o n EIect r o d i a I y s i s Ion exchange Cost a n a l y s i s C a p i t a l costs I n d i r e c t c a p i t a l costs Running costs L a b o u r costs Membrane replacement Conc Ius ions
99 99 101 103 1 04 104 105 105 105 107 107 108 108 108 108 111
CHAPTER 8. COMPUTER ANALYSIS JUST I F IES DESAL I NAT ION
I n t roduct ion A p p l i c a t i o n of o p t i m i z a t i o n of water s u p p l y Systems Analysis General o p t i m i z a t i o n problem Program a p p l i c a t i o n Optimization of mine water system Result o f a n a l y s i s Appendix 8.1 MlNSlM Program f o r s i m u l a t i n g flow a n d TDS in closed systems. Tape o r disc management MlNSlM l i s t of symbols
115 116 118 121 122 123 123 128 128 128 128 129
viii A p p e n d i x 8.2 MINOP p r o g r a m f o r o p t i m i z i n g d i s t r i b u t i o n MINOP l i s t o f symbols CHAPTER 9.
136 136 136
INTEGER PROGRAMMING PLANNING OF TREATED WASTEWATER CONVEYANCE FOR A R T I F I C I A L RECHARGE O F AN AQUIFER
Introduction Cost a n a l y s i s Mathematical formu tat ion Results Summary a n d conclusions
141 146 149 151 153
CHAPTER 10. OPTIMAL PLANNING OF REGIONAL WASTEWATER TREATMENT Introduction T h e m a t h e m a t i c a l model Optimization method
155 158 162
CHAPTER 1 1 . SIMULATION OF SEWER FLOW Int r o d u ct i o n Hydraulic analysis F low measurements H i g h e r income r e s i d e n t i a l L o w income r e s i d e n t i a I Apartment b u i l d i n g s Commercial a r e a s Industrial Conclusions Appendix P r o g r a m SEWSIM Effect of local p e a k s Routing effect Non-Circul a r Conduits I nf low components Data Program output Sample d a t a f i l e
166 167 167 169 170 171 171 172 172 174 174 1 74 175 175 1 76 177 177 186
CHAPTER 12. SEWERAGE SYSTEMS MANAGEMENT L e a r n i n g Simulation Program Optimization Optimal Control a s a L i n e a r Programming Problem Sewer M a i n t e n a n c e D a t a P r o c e s s i n g in J o h a n n e s b u r g A p p l i c a t i o n t o J o h a n n e s b u r g ' s System P r o c e s s i n g of Sewer M a i n t e n a n c e D a t a
190 192 193 195 197 198
CHAPTER 13. WATER QUAL I TY MON I TORlNG NETWORKS Necessity f o r Networks M o n i t o r i n g System F r a m e w o r k F a c t o r s in N e t w o r k D e s i g n S e l e c t i o n of Water Q u a l i t y V a r i a b l e s t o M e a s u r e Sampling Station Location Sampling Frequency Discussion
204 205 205 206 207 21 1 215
ix
AUTHOR SUBJECT
INDEX INDEX
21 7
21 9
This Page Intentionally Left Blank
1
CHAPTER 1
WATER QUALITY IN INDUSTRIAL SYSTEMS
GEOCHEMICAL SOURCE OF POLLUTANTS
Many
of
the
surroundings.
chemicals
?n
in
solution
water
originate
M i n e r a l s which form rocks may be dissolved
s u i t a b l e environment. certain
chemicals
assists
the
Acidic
waters
the rock,
in
reaction,
Iron
i n particular
Exposure to a i r ,
sulphide
i s one
a r e known which
such
from
the
in a
b y water to
contains
chemical
dissolve oxygen,
which
can
be
B a c t e r i a a r e also thought to p l a y a n important p a r t
o x i d i z e d to sulphate.
i n the leaching of sulphides.
The
s o l u b i l i t y of
chemicals
i s also dependent
on
temperature
the r a t e of
dissolution
s u l p h i d e from a rock r a p i dIy
.
When
a
chemical
positively
charged
Solubility
depends
s o l u b i l i t y K.
H 20
= H+
i s slow.
sample.
compound metal on
take
the other
dissolves
or
other
I t may
On
cations charges
to
dissolve
water
the
negatively
present
and
ions
the very
appear as
charged
is
In p a r t i c u l a r water i s ionized a s follows:
the
all
h a n d c h l o r i d e s dissolve
in
and
years
and
I n many cases
t o t a l dissolved s o l i d s i n the water amongst o t h e r factors.
anions.
expressed
as
a
(Brownlow, 1979).
+ OH-
The log of the hydrogen H+ ion concentration i s termed the pH: pH = -log(H+) Water w i t h a factors.
7 i s acidic.
pH below
be rendered so b y
many
For example absorption of carbon d i o x i d e C 0 2 from the a i r
I t may
forms
carbonic a c i d which c o u l d reduce the pH as l o w as 3.0. water d r a i n i n g from
O n the other hand
limestone o r s i l i c a t e m i n e r a l s may h a v e a pH g r e a t e r
than 7 ( P e l l e t i e r , 1964). The process of
l e a c h i n g s u l p h i d e from
s u l p h u r i c a c i d i s formed
i n the process.
minerals
i s self
stimulating
as
On exposure of s u l p h i d e b e a r i n g
horizons ferrous s a l t s o x i d i z e to the f e r r i c s t a t e a n d s u l p h i d e i s o x i d i z e d to sulphate:
4FeS2 + 1502 + 10H20
+ 4FeO(OH)
I n m i n i n g environments, further
promote
ferro-oxidans
the
oxidize
oxidizes only S
oxidation both
+' 8H2S04
bacteria
Fe
of
and
(Mrost a n d L l o y d ,
thrive
Fe
and
S
198Oj.
in the S.
whereas
The
acid
mine
bacteria
thiobacillus
water
and
thiobacillus thio-oxidans
EFFECT OF EVAPORATION ON CONCENTRAT IONS
The r a t e of concentration of t o t a l d i s s o l v e d s a l t s b y e v a p o r a t i o n may be p r e d i c t e d f o r any
ambient c o n d i t i o n s u s i n g psychrometric
a d d i t i o n to e v a p o r a t i o n in cooling towers, in
industrial
systems
dry-bulb
temperature
relative
humidity,
v a p o u r / k g of a i r . of 700 m’/s,
and of
ventilated
i s 31OC a n d
will
it
e v a p o r a t i o n of water takes p l a c e
particularly
air
the
in
increase
In
relationships.
water
For a n a i r d e n s i t y of 1.2
systems.
air
Thus
i s conveyed content
kg/m3
in
by
5
if
the
at
38%
g
water
and a ventilation rate be 5 l i t r e s p e r
the amount of water absorbed b y the a i r w i l l
second ( B a r e n b r u g , 1965). The loss of water b y e v a p o r a t i o n leaved b e h i n d s a l t s entered
the
system
c o n c e n t r a t i n g effect, depends on the
in
dilute
and
solution
the
rate
storage
volume of
of
initially. increase
in
which
There
Thus
if
have
therefore
concentration
in
the system.
is
may
in
there
a
time
is a
12
h o u r retention a n d the flow r a t e of service water i s 100 l i t r e s p e r second, the volume
i n the system w i l l
be 100 x
24/1000
3600 x
8640m’.
=
If
e v a p o r a t i o n loss i s 10 l i t r e s a second which i s 864 m 3 / d a y the i n i t i a l of concentration w i l l
be 10 percent
The s a l t concentration replaced.
would
of
the
increase
initial
unless
the
per day. water
was
The r a t e of concentration i s u s u a l l y offset b y the f a c t t h a t
i s a source of p u r e r water used f o r
make-up
t o t a l load unless there i s a blowdown (Porges, The concentration function
concentration
indefinitely
of
of
total
the e v a p o r a t i o n
dissolved r a t e as
b u t even
as
adds
there to
the
1971).
solids
well
this
the rate
at
equilibrium
will
be
the p u m p i n g d i s c h a r g e
a n d r a t e a t which s a l t s a r e introduced as a r e s u l t of make-up l e a c h i n g of chemicals from the environment (Van Staden,
a
rate
water a n d
1970).
EFFECTS OF POOR QUAL I TY WATER
H i g h t o t a l dissolved s a l t s concentration of
problems.
economic
concentration corrosion waters
The
nature
consequences o f
of
give
in
mine
pipework rise
to
exchange equipment.
of
the
poor
water and
scaling
problems
quality
is
and
varies,
water
suspected
equipment.
in water g i v e s r i s e to a number
are
to
be
Sulphates
blockages.
but
in
all
severe. one
of
and
Scaling
the
is
Plant has frequently
common
in in
of the
heat
in some a r e a s
to be r e p l a c e d a f t e r o n l y a
few years i n service i n many systems because of development of mechanized equipment
the
chloride
causes
carbonates
I n many systems there may be s c a l i n g
a n d corrosion in others.
cases
High
has g i v e n
these effects. rise
to
new
The recent
f e a r s of
the
3
consequences of poor q u a l i t y water. to operate and
the
hydraulically
hydraulic
Many of
using oil-in-water
circuits
could
be
these machines a r e designed emulsions.
already
Emulsion
affected
by
stability
poor
quality
water.
SCAL I NG
S c a l i n g i s the phenomenon of chemical deposition on submerged surfaces. The
deposits
place
are
because of
due the
to
crystallization
dissolved
salt
or
precipitation.
concentration
c o u l d be caused b y e v a p o r a t i o n loss of water,
i s also a
f u n c t i o n of
dissolved solids concentration, chemicals
most
3
whilst
solubility
temperature.
Figure 1 . 1
solubility
these
of
(CaS04). of
which
l e a c h i n g of chemicals from
the
The solubility
Other chemicals,
(e.g.
Mg(OH)2),
aluminium
and
scale
salts
ions i n solution. iron,
parameters such
are
as
pH,
calcium
Calcium carbonate
both
other
scales (Betz,
saturation
total
time a n d flow v e l o c i t y .
causing
illustrates
salts.
other
alkalinity,
frequently
and calcium s u l p h a t e
(CaCO ) insoluble
its
takes
o r a change i n temperature.
The s c a l i n g
The
exceeds
a r e s u l t of an excess of chemicals in solution
l i m i t and i s usually
surroundings,
Scaling
is
effects is
dependent
temperature
influenced
particularly
silica
is particularly
highly of
carbonate
by
oxides
a r e also
on
on
the
chlorides
and
of
magnesium
sometimes
found
in
1980).
P r e d i c t i o n of S c a l i n g and Corrosion
T h e factors
affecting
the e q u i l i b r i u m of
have a complex interdependence. predict
the tendency
calcium
carbonate
L a n g e l i e r (1954) developed
of calcium carbonate to form a
p r e f e r r e d to express the equation in terms of pH.
scale.
However
i n solution
an e q u a t i o n to Ryzner
(1944)
there a n y many
i n f l u e n c i n g effects a n d such formulae can o n l y o f f e r a g u i d e to the l i k e l y b e h a v i o u r of the water,
p a r t i c u l a r l y i n respect to corrosion.
Prevention of S c a l i n g
One way of p r e v e n t i n g s c a l i n g o r corrosion would be to d e s a l i n a t e water.
Possible
reverse osmosis,
methods
of
desalinating
mine
water
e l e c t r o d i a l y s i s a n d thermal procedures.
expensive t h e i r possibi I i ties a r e b e i n g re-assessed.
are
ion
the
exchange,
Although these a r e
4 Scale and,
prevention
where
necessary,
p r e v e n t excessive be
is
currently a
controlled
concentration of
supplemented
with
normally
the
use
undertaken
bleed
(waste)
the d i s s o l v e d s a l t s . of
scale
and
by
from
pH
adjustment
the
system
T h i s treatment
corrosion
additives.
3000 2800 2600 2400 2200
zoo0 1800
-E -I
1600 1400 1200 1000
800 600 400 200
100 50
0
0
20
40
60
80
100
120
140
160
TEMPERATURE O C
Fig.
1.1
Effect of temperature on s o l u b i l i t y of s c a l i n g s a l t s
to may
preventative
5 Calcium carbonate s c a l i n g
The f a c t o r s a f f e c t i n g have a complex
the e q u i l i b r i u m of
interdependence.
calcium
carbonate
In a d d i t i o n to temperature,
in s o l u t i o n the presence
Procedure : glven temp. OC TDS mgll Ca mgll Alkallnlty proceed 1-2-3-4-5
PHS Ryzner Stablllty Index RSI=lpH,-pH Calclum Carbonate S a l l n g Ilkely If LSI>O and R S l c 6 Colrorlon Ilkely If RSI>O
Fig.
1.2
L a n g e l i e r S a t u r a t i o n Index Chart f o r Carbonate S c a l i n g
6
of
other
dissolved
tendency
to form
nozzle can
solids,
especially
A
scale.
sudden
induce s c a l i n g ,
total
alkalinity
reduction
and suspended m a t t e r i n the
as n u c l e i f o r scale formation.
-
positive,
a
there
is
pHs,
where K(C,T)
tendency
can
negative
to
scale
and
a
serve
predict
it
if
pH.
is
I f the LSI
negative,
is
calcium
The pHs i s c a l c u l a t e d from the e q u a t i o n :
i s a f u n c t i o n of
represents
which
may to
the
at
+ pCa + pAPk
pHs = pK(C,T)
and
water
as
The L a n g e l i e r S a t u r a t i o n
where pHs i s the s a t u r a t i o n
carbonate tends to dissolve.
affect
such
L a n g e l i e r developed an equation
the tendency of calcium c a r b o n a t e to from scale. Index i s LSI = pH
a n d pH,
pressure
in
be
the
second
computed
logarithm
of
the temperature
dissociation
from the
thermo-dynamic
calcium
and total
constant
and
dissolved
solubility
considerations.
content,
and
pAPk
is
solids, constant
pCa the
is
the
negative
l o g a r i t h m of the e q u i v a l e n t concentration of the a l k a l i n i t y . The LSI can be computed r e a d i l y from F i g u r e 1.2. Ryzner proposed a d i f f e r e n t arrangement of equation.
The Ryzner S t a b i l i t y
-
R S I = ZpHs If
the
the terms
in
Langelier
the
Index ( R S I ) i s :
pH
RSI
is
less
t h a n 6,
scaling
tendency
increases,
and
if
it
is
g r e a t e r t h a n 8, corrosion i s in f a c t more l i k e l y . There
are
however,
many
and
particularly
other
such
effects
formulae
influencing
can
only
scaling
and
corrosion,
provide
preliminary
sulphate
i s higher
guides
i n r e l a t i o n to corrosion.
Sulphate s c a l i n g
The s o l u b i l i t y of v a r i o u s forms of calcium of
calcium
Calcium
but
s u l p h a t e occurs
CaS04.2H20 a n h y d r i te, The
carbonate
(gypsum),
in
is
also
three
highly
different
herni-hydrite
dependent
crystal line
CaS04.)H20
on forms:
(plaster
of
than that
temperature. dihydrate, paris)
and
CaS04.
solubility
temperature
it
of
(Figure
the 1.1
hernihydrite
1.
The
and
solubility
anhydrite increases
decreases with
with
chloride
concentration and i s affected b y t o t a l dissolved solids.
A d d i t i v e s for the p r e v e n t i o n of scale
I n most
systems,
dernineral i z a t i o n
or
softening the water w i t h r e s i n o r Zeolite i s not economically j u s t i f i a b l e .
In
some cases chemical
especially
once-through
systems,
i n h i b i t o r s a r e used to p r e v e n t the formation of
scale.
7 These
agents control
supersaturated
deposits
solution.
The
by
preventing
basic
crystal
mechanisms
of
growth, scaling
even and
in
a
deposit
control a r e :
(1
1
Control of i n t e r p a r t i c l e a t t r a c t i v e forces e.g.
(ii)
Control
of
particle-to
wetting
agents.
surface
These
involve
non-stoichiometrically possible. scal i n g
(iii)
They
.
and
are
forces,
used
Control of p r e c i p i t a t i o n
electrostatic
hence more
rate,
dispersants.
e.g.
low
for
e.g.
surfactants forces.
or
They
act
concentrations
preventing
flocculants.
are
fouling
These
than
are
high
molecu l a r weight pol ymers. Retardation of c r y s t a l growth, e.g.
(iv)
polyphosphates.
Some of t h e reagents used a r e l i s t e d below:
Polyphosphates:
Applied
in
rates
from
0,5
to 5
mg/O.
Absorbed
onto
surfaces of growing c r y s t a l s and i n i n c i p i e n t c r y s t a l n u c l e i .
They
the
successful
apparent
solubility
of
scale
forming
salts.
These
are
the
increase for
carbonates and h y d r o x i d e s b u t not f o r sulphates.
Organic Phosphates: Simi l a r to polyphosphates b u t they a r e more s t a b l e i n cooling
tower
successfu I
systems.
Phosphonic
acids
have
proved
particularly
.
Phosphate:
React w i t h calcium
p r e c i p i t a t e s out.
For
this
to
reason
form
i n s o l u b l e calcium
i t s use
has
largely
phosphate
been
which
replaced
by
d ispersan ts.
Polymers
(especially
polyacrylates):
growths.
Effectively
dispersants
crystals
i n suspension.
as
Absorbed they
Low molecular weight
onto
maintain
surfaces small
of
crystal
particles
of
polymers h a v e r e c e n t l y been
developed f o r t h i s purpose.
The reagents may be used on combination, reduce pH.
o r even together w i t h a c i d to
Carbon d i o x i d e can be added to closed systems to
reduce pH.
F e r r i c c h l o r i d e i s also used. Dispersants
or
sequestrants
are
sometimes
formation of i r o n h y d r o x i d e o r o x i d e in p a r t i c u l a r . agents a r e used to i s o l a t e and
used
to
prevent
scale
Chelants o r complexing
i n h i b i t scale formers.
It
should
be noted
8
that the
crystal systems
must
inhibitors as
be
a r e not
prevented
by
in e l i m i n a t i n g
effective
sol i d s .
suspended
Instead,
foulants
agglomeration
dispersants
such
as
of
entering
these
sol i d s
phosphonates
and
I igno-su I phates. The deposit of problem.
phosphates i n closed systems due to a d d i t i v e s can be a
The d u r a t i o n of effectiveness of
velocities
and
turbulence
can
affect
additives
i s also unknown.
low-concentration
High
dispersants
in
particular. The effects of
chemical
r e q u i r e consideration.
dissolved s o l i d s
on
Deposits may
may erode h i g h - v e l o c i t y total
additives
jets.
the
block
rest
of
pipes o r
the
will
system
machines.
also
Suspensions
Reactions w i t h o t h e r chemicals may a g g r a v a t e
problems.
There
may
also
be
an
effect
on
settlers
and demineralization plants.
FOUL I NG
Besides chemical which can
precipitates
there
are
many
substances
settle out o r block p i p e w o r k a n d m a c h i n e r y .
materialize
in
the
form
of
films
bridging
c a v i t i e s where water v e l o c i t i e s a r e slow.
openings
The
or
in suspension
deposits
building
may
up
in
The m a t e r i a l deposited may be:
Sediment from ore o r the atmosphere t r a n s p o r t e d in suspension Floc created b y chemical treatment Iron oxide ( r u s t ) Chemicals
used
for
scale
or
corrosion
inhibition
which
subsequently
cause deposits Oils Foam from chemical r e a c t i o n s o r a e r a t i o n B a c t e r i o l o g i c a l slime collected o r accumulated i n the system
The tendency water v e l o c i t y
to s e t t l e i s a
function
a n d a p p e r t u r e bore.
of
particle
Turbulence
due
size, to
shape,
flowing
density,
will
water
m a i n t a i n some p a r t i c l e s i n continuous suspension a l t h o u g h the concentration w i l l b e highest n e a r the bed i n the case of p a r t i c l e s denser t h a n water.
Once p a r t i c l e s particles.
s e t t l e out
Alternatively
they
they
may
may
stick
migrate
to
the
along
surface, the
bed.
or
to
other
Under
some
conditions the bed m a t e r i a l may move a s dunes w i t h p a r t i c l e s b e i n g p i c k e d up b y the flow upstream of resulting
rippled
surface
the dune c r e s t a n d deposited downstream. can
aggravate
friction
loss
in
conduits.
The In
9 addition
to
the
reduction
in
cross
sectional-area,
the
of
capacity
the
conduit i s reduced due t o the h i g h e r d r a g on the perimeter. Deposits may block f i n e pores o r o r i f i c e s completely. filter
media
particles
rapidly
block
thus
The gaps between
requiring
backwashing.
In
machines w i t h f i n e j e t s o r screens s i m i l a r blockages a r e possible. Deposits may
remain
i n flocculated
blanket
form,
or
time and i n c r e a s i n g deposits p r e s s i n g down from above.
consolidate
with
They may s t i c k
to
the surface due to chemical bonding. B i o l o g i c a l matter such as b a c t e r i a l slime o r f u n g i can build up w i t h i n a
water
system
sometimes
provided
carbon
and
r e q u i r i n g oxygen f o r
nutrients
silica,
are
such
as
present.
g r o w t h ) o r aerobic.
nitrogen,
They
may
phosphorous be
and
anaerobic
Some b a c t e r i a t h r i v e on
(not
iron o r
s u l p h a t e and cause d e t e r i o r a t i o n .
Control o f f o u l i n g
Deposits i n machinery and p i p e systems can be prevented o r reduced b y controlling
particle attraction
forces,
preventing
settling
by
turbulence,
i n s t a l l i n g s e t t l i n g b a s i n s o r keeping the p a r t i c l e s out of the system closed c i r c u it s )
(e.g.
.
Dispersants
are
p a r t i cI e- to-surface
used
forces.
o r create r e p e l l i n g charges.
control
to
particle-to-particle
and
n e u t r a I i ze e l e c t r o s t a t i c a t t r a c t ion charges
They
One problem w i t h
these
i s that
if
there
are
sedimentation b a s i n s i n the system they may h i n d e r s e t t l i n g there. High concentrations of dispersants may in f a c t be used f o r systems.
desludging
Surface w e t t i n g agents a r e sometimes used to p r e v e n t deposition of
o i l and grease. Biological
fouling
may
be
controlled
by
disinfection.
Shock
dosing
treatment appears more e f f e c t i v e a n d economic t h a n continuous dosing. Chlorine
i s widely
used as
o x i d i z i n g agent a n d reduces
a
the
biocide
hypochlorous a c i d a n d h y d r o c h l o r i c acid. of
less than 1 mg/t
i s usually
to combat
pH when
sufficient
dissolved
bio-matter. i n water
It
is
an
by
forming
A free r e s i d u a l c h l o r i n e
content
i f contact p e r i o d i s a n h o u r o r
more. Hypochlorite i s also used occasionaly. Non-oxidizing lesions
i n the
biocides act b y surface a c t i v a t i n g o r b y c a u s i n g s u r f a c e metabolism.
compounds ( q u a t s ) .
Into
this
category
fall
quarternary
ammonia
10
0 I L EMULS ION BREAKDOWN
Emulsions of amongst other the
form
of
in
oil
things. minute
water
are
used
for
driving
The emulsions consist o f droplets.
The
emulsion
oil is
prototype
dispersed
stabilized
machinery
in
water
by
in
electrical
charges on e m u l s i f y i n g agents. Chemicals emulsions
(such by
and
polymers
neutralizing
(coagulation), altering
as
precipitating
the e m u l s i f y i n g
cationic
o i I-in-water
emulsions.
are
opposite
repulsive or
out
i t can
particularly
Once charges
charge
charges
Crystallizing
so t h a t
film
polymers
of
polarity)
between
particles
emulsifying
readily
effective
break
agents
be broken.
Cations
separating
in
oi I
h a v e been n e u t r a l i z e d ,
or
dilute droplets
a n d suspended s o l i d s w i l l be absorbed on the surface of floc o r w i l l
break
out a n d f l o a t on top thereby d e s t r o y i n g the emulsion p r o p e r t i e s . Although
it
is
desirable
suspension w h i l s t in service, may
be d e s i r a b l e
place a t
to separate
controlled
machinery f u r t h e r been used
to
to
after
locations
the o i l to
in the cycle.
break
maintain
the
the emulsion and
prevent
emulsion
oil-in-water
i s d i s c h a r g e d to waste
the
water.
subsequent
This
slime
should
to
aluminium
raise
the
pH
emulsions.
again
Cationic
in
Acid a n d a l u m i n i u m s u l p h a t e ( a l u m ) h a v e
oil-in-water
hydroxide.
take
and caking
The
acid
lowers
the
about 3 a n d alum coagulates the o i l b y n e u t r a l i z i n g the charges. added
it
and
the
polymers
aluminium
are
is
preferred
pH
precipitated
and
to
Lime i s
often
used
as in
double a i r f l o t a t i o n (DAF) u n i t s which c o l l e c t s the o i l on the surface.
CORROS ION
Corrosion
is
electrochemical
the
attack
action.
due p r i m a r i l y
to
and
degradation
Pipework
highly
and
saline or
general o r i n i s o l a t e d p o i n t s .
of
machinery
acidic
water.
metal are
by
subject
chemical to
or
corrosion
The d e s t r u c t i o n may
be
I t may reduce the l i f e o f p i p e and steelwork
b y many years. I r o n corrodes
in
water
as
water since i t i s less noble i.e. Fe + 2H20 = Fe(OHl2
insoluble,
replaces
the
hydrogen
ion
in
i t i s less c a t h o d i c :
i s oxidized
which
further
to
i s usually ferric
i n solution
hydroxide,
b u t i s u l t i m a t e l y changed to f e r r i c
manifests a s p i t s i n the i r o n surface, 1.3).
It
+ H2
I n the presence of oxygen, ferrous oxide
follows:
oxide,
Fe203.
a form o f oxygen
in water,
Fe(OHl3.
This
the is
The
reaction
corrosion.
(Figure
11 TABLE 1.1
Nernst s c a l e of s t a n d a r d e q u i l i b r i u m p o t e n t i a l s r e l a t e d to the s t a n d a r d h y d r o g e n electrode a t 25OC (Metal immersed i n a normal s o l u t i o n of one of i t s s a l t s )
Metal
Electrode r e a c t i o n s
E q u i I ib r i u r n p o t e n t i a l (volts)
K
Potassi urn
=
+ e++ Ca + 2eK+
Calcium
Ca =
Sod i um
Na = Na+ + e-
Magnesium
Mg =
Al urn in iurn
~t
Manganese
Mn =
Zinc
Zn = Z n
C hrom i urn
Cr =
++ + Mg
= AI+++
++ Mn
- 2.922 - 2.87
-
2e-
+ 3e+ 2e-
++ + 2e+++ Cr + 3e++ Fe + 2e-
2.712 2.34 1.67
1.05 0.762 0.71
- 0.440
I ron
Fe =
Coba I t
Co = Co
2e-
-
Nickel
Ni =
2e-
- 0.250
Tin
Sn =
2e-
-
++ + ++ Ni + ++ + Sn
0.277
0.136
Lead
Pb = Pb++ + 2e-
Hydrogen
H2 = 2H+
- 0.000 b y convention
Copper
cu =
+ 2e++ cu + 2e-
+ 0.345
cu+
+ 0.522 + 0.800
Copper
cu
Silver
Ag = A g +
P I a t inum
Pt = P t
Gold
Au =
Gold
AU
a-
Fig.
1.3
=
+ e-
+ e+ 2e-
++ +++ Au
= AU+
+ 1.2 a p p r o x .
+ 1.42 + 1.68
+ 3e-
+ e-
Cathodic area
0.126
area Iron
Corrosion c e l l on the surface o f i r o n in water
12
L \
\
1
-
\ \ \
%
\ \ \
Potential o f Metal Eh relative 0 t o hydrogen
-1
F i g . 1.4 If they
the,
may
\
\ \
-
Oxidation Corrosion
-
%
-
Corrosion
-
Immunity due t o low i r o n p o t e n t i a l
% %
\
-
A s i m p l i f i e d form of the P o u r b a i x D i a g r a m f o r i r o n corrosion
or some of
the,
be eroded b y
iron
flowing
oxides water
are
present
especially
if
as
protective
sediment
layers
i s present.
C a v i t a t i o n can also erode the surface l a y e r s . The metal i s thereby exposed a n d corrosion i s accelerated. The e q u i l i b r i u m between i r o n and v a r i o u s compounds water
was
studied
by
Pourbaix.
He presented
i n the presence of
h i s results
in
a
diagram
( F i g u r e 1 .4 ) which shows three zones:
A corrosion zone f o r
low
pH
or
high
electrical
potential
relative
to
l i q u i d solution.
A corrosion i n h i b i t i o n zone f o r
h i g h pH due
to
passivation
by
a
film
found on the surface
A cathodic protection zone f o r low i r o n p o t e n t i a l r e l a t i v e to a s t a n d a r d elect rode.
13
Hydrogen
is
used
as
a
reference
electrode
in
the
of
i t s salts,
the s t a n d a r d
gives
in a normal solution of one
p o t e n t i a l s of metals immersed
r e l a t i v e to
The
Table 1 . 1
p o t e n t i a l of the i r o n w i l l depend on the reference system. the e q u i l i b r i u m
diagram.
hydrogen
electrode
25OC.
at
There
U h l i g (1963)
a r e many texts on f a c t o r s a f f e c t i n g corrosion e.g.
Types of Corrosion
in the presence of
There are many ways i n which corrosion can occur water.
Corrosion i s commonly an electro-chemical
phenomenon which occurs
a t an anode when electrons flow from an
anode
positively
oxygen.
corrode.
charged
anode
to
react
with
Ways i n which the electrons m i g r a t e
to a
cathode,
The
for
leaving
cathode
corrosion
a
does
not
to occur,
are
( U h l i g , 1963).
described below
G a l v a n i c Corrosion: When e l e c t r i c a l l y electrolyte,
dissimilar
metals
are
in
contact
a p o t e n t i a l difference i s established.
metal corrodes,
in o r
through
an
The more a c t i v e ( a n o d i c )
as i t i s least noble.
Selective Lea china: One element of an a l l o y can be corroded more r a p i d l y t h a n another.
Pitting: A shell of iron
surface.
permeable magnetite o r Salts
may
concentrate
ferric
h y d r o x i d e may
form
under
the
the
shell
and
over
an
resulting
env ironmen t becomes i n c r e a s i n g I y corrosive.
Stress Corrosion : Metals
in
stress
may
corrosive environment. to s a l t b u i l d - u p
exhibit
abnormal
Once a c r a c k
s i m i l a r to p i t t i n g .
corrosive
i s formed
properties
Chlorides a n d amonia appear
chief aggressors i n t h i s type of corrosion.
in
i t r a p i d l y deteriorates
Welding may also
a due
to be the
induce l i n e s
of corrosion unless stress r e l i e v e d .
A c i d Corrosion : Acids,
o r even carbon d i o x i d e i n solution,
ion concentration. chelants,
e.g.
NTA
they concentrate.
can
increase the hydrogen
T h i s r e s u l t s i n general loss of metal b y corrosion. (nitrilotriacetic acid)
may
also
Some
become c o r r o s i v e
as
14
B a c t e r i a l Corrosion : B a c t e r i a can cause biochemical a c t i o n which r e s u l t s i n corrosion.
This
t y p e of corrosion i s often encountered i n s u l p h u r i c c o n d i t i o n s .
E l e c t r i c a l Corrosion E l e c t r i c c u r r e n t s , d.c.
i n p a r t i c u l a r , may cause severe corrosion.
anode i s formed where the c u r r e n t
leaves
the
conductor,
corrosion
I f an occurs
there.
Reagent Corrosion : Certain
scale
preventing
agents
such
as
acids
and
chelants
and
complexing agents can promote corrosion
T h e effectiveness of a l t e r n a t i v e corrosion p r e v e n t i o n methods depends on the p r e v a i l i n g circumstances a n d system to be protected. cooling
systems
possible. the
relatively
high
concentrations
I n l a r g e c i r c u i t s a n d c o o l i n g systems,
treatment
dosage
concentration control
must
be
less;
sometimes
of
I n small
chemical
closed
dosage
are
i n o r d e r to be economic, little
more
pH
than
and
( b y b l e e d i n g o f f a n d r e p l a c i n g w i t h f r e s h w a t e r ) can
be accomp I i shed. I n c h i l l e d water human beings.
circuits
the
circulating
I n these circumstances
used i s non-toxic.
water
may
be
i t i s imperative that
T h i s requirement has the effect of
consumed any
severely
by
treatment
l i m i t i n g the
number of chemical corrosion i n h i b i t o r s which can be considered.
Corrosion p r e v e n t i o n
Corrosion can be reduced b y c h a n g i n g the c h a r a c t e r i s t i c s of
the water
o r c o a t i n g the metal. Metal i s sometimes i n f a c t coated n a t u r a l l y b y scale. A u n i f o r m deposit of calcium carbonate can be created b y dosing
w i t h lime,
soda ash o r c a u s t i c soda.
o r unstable,
and cannot be r e l i e d upon f o r 100 percent protection.
Deaeration of water w i l l also reduce i t s c o r r o s i v i t y . vacuum
deaeration
if
feasible.
Oxygen
corrosion a r e thus removed to some extent. remove oxygen
i n the water.
sulphate: 2Na2S03
+ O2
the water
The deposit i s f r e q u e n t l y non u n i f o r m
= 2Na2S04
and
carbon
I n closed systems, dioxide
which
aid
Sodium s u l p h i t e can be used to
The r e a c t i o n w i t h w i t h
oxygen
forms
sodium
15
Corrosion passivates magnetite
i n h i b i t o r s a r e a v a i l a b l e commercially. the
surface
(Fe304).
precipitates.
by
Other
forming
a
inhibitors
protective
react
and poly-
oxide
chemically
I n t o the l a t t e r category fa1 I zinc,
phosphate and ortho-
One t y p e of
to
and
include
film
such
form
insoluble
calcium carbonate,
as
calcium
phosphates.
Other i n h i b i t o r s act b y a b s o r b i n g o r b y p a s s i v a t i n g . protective f i l m
inhibitor
chromate,
nitrate,
The
molybdate
l a t t e r form a
and
tungstate.
Silicates also appear to work on s i m i l a r p r i n c i p l e s . In
general
oxygen.
the
corrosion
I t increases
significant
when
rate
is
dependent
w i t h c o n d u c t i v i t y up to a
the
pH
drops
below
4
(see
on
c o n d u c t i v i t y . pH
limit, Fig.
whereas
1.5).
and
it
i s most
Oxygen
content
increases corrosion r a t e , e s p e c i a l l y a t h i g h e r temperatures. Chromates a r e p a r t i c u l a r l y e f f e c t i v e corrosion up to 300 m i l l i g r a m s
per
litre
in open
I i t r e i n closed c i r c u i t s a r e used. a
deterrent.
Additives
of
circuits
inhibitors. and
I t i s therefore costly,
zinc
and
phophate
Concentrations
2000 m i l l i g r a m s
per
and its toxicity
reduce
the
is
chromate
r e q u i remen t s. To overcome the t o x i c i t y problem of chromates, and polyphosphate m i x t u r e s have been developed. of
calcium
milligrams
orthophosphate
at
per
inhibitor
Iitre,
an
Simultaneous p a s s i v a t ion of salts a t
orthophosphate such
as
phosphonate
the cathodic zone to form a p r o t e c t i v e
such
as
To p r e v e n t p r e c i p i t a t i o n
concentrations
above 5 can
the anodic areas a n d p r e c i p i t a t i o n
( r e f e r r e d to as d i a n o d i c protection, F i l m i n g amines
s u i t a b l e ortho-phosphate
layer
a p r o p r i e t r y name),
octadecylamine
act
differently.
7
be
added.
of
calcium
i s thereby (Betz,
to
possible
1980).
They
form
a
p h y s i c a l b a r r i e r , often monomolecular i n n a t u r e .
POTABLE WATER STANDARDS
Although
i n d u s t r i a l water
i s not often
intended f o r human
the q u a l i t y should b e adequate to ensure should be non-toxic,
no
harm
if
it
consumption
i s consumed.
It
and i f d r u n k in l i m i t e d q u a n t i t i e s showld show no i l l
effects.
The upper l i m i t s to dissolved s a l t s f o r p o t a b l e water a r e d i f f i c u l t
to f i x .
They
depend
on
the amount
consumed
and
it
should
be b o r n
in
m i n d t h a t men could d r i n k up to 2 l i t r e s a s h i f t . M i c r o b i o l o g i c a l m a t t e r in the water can be more concern salts.
After d i s i n f e c t i o n ,
not n o r m a l l y present made.
Toxic
nitrates,
with chlorine,
i n mine service water,
substances
some algae,
normally
include
organic
heavy
than dissolved
bacteria and viruses are
b u t r e g u l a r checks should be
metals,
phosphates and
concentrated
fluorides,
some poly-electrolytes
(the
16
l a t t e r two a r e used in t r e a t i n g water sometimes) Highly
mineralized
water
a f f e c t the sweating process, Often
human
possibility
of
perception unsafe
possesses
laxative
properties.
It
may
blood p r e s s u r e o r the c a r d i o - v a s c u l a r (taste,
water.
smell
Phenols,
or
colour)
chlorine
and
will organic
also
system.
identify
the
matter
are
e a s i l y detected b y taste. Suggested l i s t of l i m i t s to c e r t a i n substances f o r p o t a b i l i t y Table
1.2.
Table
1.3
indicates
the
maximum
allowable
i s given
in
concentrations
of
o t h e r t o x i c substances.
Fig.
1.5
The effect of pH on the corrosion r a t e .
TABLE 1.2
Recommended p o t a b l e water s t a n d a r d s .
Substance
Concentrat ion mg/e
A I k y I ben zenesu Ifona t e ( ABS )
,
tast e-produc in g
C h l o r i d e ( C 1 1,
250.0
taste-producing
Carbon chloroform e x t r a c t
(CCE),
taste-producing
0.2
possi b I y t o x i c
0.01
Cyanide (CN) I r o n ( F e ) , taste-
a n d colour-producing
Manganese ( M n ) , tasteN i t r a t e (NO ) ,
3
and colour-producing
p r o d u c i n g methemoglobinemia
P heno I s , t as t e-p r o d uc i n g a n d tox ic Sulphate (SO)&),taste-producing Total dissolved solids, Zinc
0.5 0.1
Arsenic ( A s )
laxative
( Z n ) , taste p r o d u c i n g
and l a x a t i v e
0.3
0.05 45.0 0.001 250.0
500.0 5.0
17
TABLE 1 . 3
Toxic concentrations in water
Substance
Concentration, mg/t
0.5
Arsenic (As) Barium ( B a )
1 .o
Cadmium (Cd)
0.01 6+) Cr
Chromium (hexavalent,
0.05
Cyanide ( C N )
0.02
Lead ( P b )
0.05
Selenium (Se)
0.01
Silver (Ag)
0.05
AGRICULTURE AND IRRIGATION
I r r i g a t i o n i s a major consumptive
use of water.
Crops cannot
tolerate
h i g h s a l t loads and y i e l d s d e t e r i o r a t e unless remedial a c t i o n i s taken.
The
f o l l o w i n g t a b l e shows levels of s a l t s which a f f e c t crops.
TABLE 1.4 Water Q u a l i t y which affect crops
T DS
mg/P
Lower l i m i t
Upper l i m i t
500
2000
150
350
Root a b s t r a c t i o n : Chloride
mg/P
L e a f water a b s t r a c t i o n (sprinkling) Chloride Nitrates
mg/P mg/P
Rapid assessment of The
conductivity
in
TDS
mS/m
100
1000
5
30
i s often is
possible
approximately
dissolved s o l i d s c o n c e n t r a t i o n ) i n m g / t
b y measuring equal
d i v i d e d b y 6.5.
to
the
conductivity. TDS
(total
F i g 1.6
shows the decrease
s o i l moisture salinity.Some
due to t h e i r p u r i f y i n g a b i l i t y . than f r u i t ,
yield
in
crops
are
for
some crops
more r e s i s t a n t
For instance,
as
than
a
function
others
to
of
salts
vegetables a r e more r e s i s t a n t
b u t a r e less p r o f i t a b l e .
There i s also the
gradual
deterioration
in s o i l
to contend
b u i l d s up due to e v a p o r a t i o n a n d t r a n s p i r a t i o n of water. leached out b y a p p l i c a t i o n of excessive water,
but,
for
with.
Salt
The s a l t s can b e instance,
at
least
25% more water would be r e q u i r e d to ensure good s o l i d c o n d i t i o n s w i t h the TDS l e v e l s of 800 mg/e.
More i r r i g a t i o n equipment
i s also r e q u i r e d
to cope
w i t h the h i g h e r flows. The a l t e r n a t i v e i s to change the c r o p p i n g p a t t e r n .
Crops r e q u i r i n g
water o r a d a p t a b l e to s a l i n e water would h a v e to be developed.
\
I
I
I
Lucerne\
\
\
I
C o n d u c t i v i t y of g r o u n d w a t e r (mS/m) Fig.
1.6
Crop y i e l d as a f u n c t i o n of water q u a l i t y
less
19 REFERENCES
Barenbrug, A.W.T., 1965. Psychrometry and psychrometric charts. T r a n s v a a l a n d O.F.S. Chamber of Mines. Johannesburg. Betz. 1980. Handbook of I n d u s t r i a l Water C o n d i t i o n i n g , 8 t h Ed., Betz, Trevose, 440 pp. Brownlow, A.H., 1979. Geochemisty, P r e n t i c e H a l l , N.J. 498 pp. L a n g e l i e r , W.F. 1954. Journal America1 Water Works Assn., 46, 461. Mrost, M. a n d L l o y d , P.J., 1980. B a c t e r i a l O x i d a t i o n of W i t w a t e r s r a n d Slimes, I .A.E.A. Johannesburg. P e l l e t i e r , R.A. 1964. M i n e r a l Resources o f South - C e n t r a l A f r i c a . O x f o r d U n i v e r s i t y Press. Cape Town. 277 pp. Porges, J. 1971. Handbook of Heating, V e n t i l a t i n g a n d A i r C o n d i t i o n i n g . 6 t h Ed., Newnes-Butterworths, London. Ryzner, J.W. A p r i l 1944. A new index f o r d e t e r m i n i n g t h e amount o f calcium carbonate scale formed b y water. JAWWA, 36, 472-473. U h l i g , H.H. 1963. Corrosion a n d Corrosion Control. John Wiley a n d Sons, N.Y. Van Staden, C.M.V.H., 1970. Steps Taken b y t h e M i n i n g I n d u s t r y to Prevent a n d Overcome Water P o l l u t i o n . Water f o r the F u t u r e Convention, Pretoria.
CHAPTER 2
MATHEMAT I CAL MODELL ING O F WATER QUALI TY
A f i e l d to which many systems concepts can be a p p l i e d q u a l i t y deterioration are
examples
predict
the
rate
concentrations of
in
where
industrial
quality
of
will
build-up
i n water
t h e complex n a t u r e of for
all
Cooling
of
in
dissolved
r e t i c u l a t i o n systems,
the o r i g i n s and methods of
accounting
systems. deteriorate
industrial
these
water
effects
in
and
time.
salts even
concentration
of
real
washing
It
is
or
easy
to
equilibrium
an
understanding
This
i s because of
systems.
system
water
systems
not
the
with
salts.
recirculation a
i s t h a t of
One
appears
way
of
be
by
to
m o d e l l i n g the system on a computer. Once a model i s produced a n d v a l i d a t e d ,
i t may be used to
improve the
operation of e x i s t i n g s e r v i c e water r e t i c u l a t i o n systems and f o r o p t i m i z i n g the design of new systems. The
build-up
of
impurities
in
water
can
together w i t h the water r e c i r c u l a t i o n cycle.
simulated
mathematically
The flows of water
o r i n vapour form i n the a i r in and out of The processes of e v a p o r a t i o n , condensation,
be
i n conduits
the system can be c a l c u l a t e d . p o l l u t i o n a n d make-up
can a l l
be modelled.
MASS BALANCES
For
the
purposes
of
mathematical
system must b e described described
in
terms
analytically. the
of
a
mass
balance
I n other more complex
equations
in
simulation
in terms of equations.
finite
equation
situations
difference
form
water
of
One-stage
and
which is
it
systems,
can
be
necessary
solve
the
systems can be
them
solved
to
express
numerically.
D i f f e r e n t types of models and the assumptions t h e r e i n a r e described below. Parameters whereby
pollution
i s measured may e i t h e r
be c o n s e r v a t i v e o r
non-conservative.
I n a c o n s e r v a t i v e system i n p u t to a n y p a r t of the system
equals
Thus,
outflow.
evaporation parameter
will is a
if
the
be neglected chemical
parameter in a
compound
studied
conservative it
is
is
model.
assumed
water
flow
Similarly
there
is
then if
the
no
reaction,
the
start-up
deposition o r s o l u t i o n i n a c o n s e r v a t i v e model. The model
may
be
mine as
steady-state concentrations
or
time-varying.
build
up
During
p e r i o d of
a
unsteady.
After a w h i l e the system may reach e q u i l i b r i u m . That
case of s a l t s in s o l u t i o n ,
the
system
is
said
to
be
is,
in the
the increases i n mass of d i s s o l v e d s o l i d s
in t h e
21 system
due
to
leaching
or
evaporation
equals
the
by
loss
pumping
or
deposition.
MIXED AND PLUG FLOW SYSTEMS
In a
plug-flow
through
the
pipes a n d d r a i n s a t a c e r t a i n r a t e , conveying i m p u r i t i e s a t t h a t r a t e .
The
s a l t s content as
water
a t any
with
completely
system,
An
input
so
that
the
divided
by
the
total
the
i s assumed
volume
of
and
cross
of
in a
in
at
that
will
salts
series of point.
be
the
instantaneously
increases water
travel
by the
the
mass
system.
Real systems w i l l
In
a
same
at
salt
This
probably
steps
through
of
the
input
simplified
to describe systems which e x h i b i t
change i n concentrations.
tubulence
to
arrives
to spread
concentration
p l u g flow and completely mixed, to
assumed
concentration
mechanism i s often s a t i s f a c t o r y r a t e s of
is
concentrations
system,
systems
water
p o i n t can therefore be affected
different
mixed
every p o i n t .
the
gradual
be between
as there w i l l be d i f f u s i o n and m i x i n g due
connections.
In
general
salts
are
conveyed
by
advection ( l a t e r a l t r a n s p o r t ) and dispersion.
Examples
The simplest i l l u s t r a t i o n of the use of the mass b a l a n c e equations i s f o r a
steady-state
concentration
Q
system.
i n mg/e.
is
I n f l o w of
flow
rate
e/s
in
water a n d of
outflow r a t e :
F i g 2.1 Point Node
Flow Balance Mass Balance
a, ale, .*.C
3
+ +
a2 = a3 a2c2 = a3 = alcl+a2c2 Q1
+Q2
or
MP/d,
salts per u n i t
C
is
the
time e q u a l s
22
e.g.
Q2
i f Q1 = 5 MP/d,
C 1 = 400 mg/P,
=
10 M e / d
( w a t e r flow r a t e )
C2 = 100 mg/P ( s a l t c o n c e n t r a t i o n )
C3 = 200 m g / t
then
a n d the t o t a l mass of s a l t discharged p e r day
Q3C3
=
=
15 x 200 = 3000 k g / d
A completely m i x e d
system can
(2.4)
be described
Subscript i r e f e r s to i n f l o w , e to e x i t ,
by
differential
equations:
s to i n i t i a l conditions:
Volume S Conc. C
Fig. 2.2
QiCi
=
=
.*.
M i x e d flow node
d (SC) Q C + -
e
dt
Q C +
SdC x
SdC
dt =
Qi C i-QeC
Fig. 2.3
Diffuse node
Integrating that C = C T = S
Qe
f o r constant S
en
and e v a l u a t i n g
the
constant
of
integration
from
the
fact
at t = 0 : QiCi-QsCs ( QiCi-QeC
(2.8)
1
23
QiCi/Qe-
QiCi
-- Qe
C =
or
e(
c
and a t t =
m
o r S = 0,
o r Be = -
,
(ai/ae)ci
=
i f Q . does not equal Qe,
Observe that losses, e.g. The
(2.9)
1
Qet/S
a t t = 0, C = C s ,
e.g.
Cs
there must be i n t e r n a l
gains or
due to evaporation.
previous
example
could
r e q u i r e s specific numbers,
it
is
be
studied
often
numerically.
the o n l y
Although
practical
way
of
this
solving
more complex problems. Assume S = 1000 m 3 , Q . = lm’/s Choose
~t
100
=
= Q
e’ The choice of ~t
5.
C s = 0, Ci = 500 mg/P. can affect
the speed of
the accuracy of r e s u l t s a n d the numerical s t a b i l i t y of must
be
determined
considerations. NOW Q.C.
- Q C
.’.
1
I
I
C2 = C
t
= 5-
5
by
trial,
from
experience
or
from
It
theoretical
c 2 -c 1
(2.10)
At
8 . ( C . -C 1
solution,
the computations.
1
1
) = C1
+ 0.1(500-C1)
(2.11)
The computations can be set out in t a b u l a r form as follows:
t
500-C1
c1
xo.l
c2
0
0
500
50
50
100
50
450
45
95
200
95
405
40
135
300
135
365
37
172
326
1 74
17
343 mg/t
0
0
0
1000
(2.9)
Equation comparable
with
would the
indicate
result
C =
316 mg/e
indicated
by
the
at
t
=
numerical
lOOOs, solution
which of
is 343
mde. A
plot
of
C
versus
t
is
called
a
pollutograph,
and CQ versus t a
loadograph. T h e numerical computations f o r change of p o l l u t a n t above
table
are
very
similar
to
flood
routing calculations
load i n t h e
assuming
for
example the Muskingum method. Reservoirs a r e g e n e r a l l y assumed to be completely mixed,
whereas r i v e r s
24 a r e sometimes assumed to be p l u g flow.
I n fact
i n b o t h there
i s a degree
of m i x i n g due to:
a)
Molecular
diffusion
b)
Turbulent mixing,
c)
Short
due
to Brownian
movement
in
(negligible
most
h y d r a u l i c systems).
circuiting
made across
due to eddies i n the stream. or
the
t r a c k i n g e.g.
water
body
by
reservoirs
in
the
flow.
The
a
track
is
stagnant
where
water
in
corners i s c a l l e d dead water d)
Wind m i x i n g
e)
Thermal m i x i n g a n d i n v e r s i o n (e.g.
Henderson-Sel lers,
The degree of m i x i n g can affect concentrations
1979).
so much t h a t m o n i t o r i n g
systems need to account f o r i t (Sanders, 1983).
SYSTEMS ANALYSIS
A
more
sophisticated
approach
than
the
simulation
above i s the use of systems a n a l y s i s a n d o p t i m i z a t i o n
method
assistance of computers i f necessary. The methods a l l o w to be selected from numerous a l t e r n a t i v e s alternative
The
o p t i o n from a few
standard
engineering
selected designs.
The
described
techniques,
the
with
an optimum design
(Thomann,
1374).
approach
is
to
l a t t e r approach
select is
the
tedious
best where
there are many a l t e r n a t i v e s . The
design o p t i m i z a t i o n
configuration
i n which
not been f i x e d .
the
approach
involves
the
numerical
v a l u e of
creation
of
independent
a
general
variables
A n o v e r a l l economic o b j e c t i v e i s defined a n d the system
has is
described i n terms of equations o r c o n s t r a i n t s .
TERMINAL CONCENTRATION I N A WATER C I R C U I T .
The t o t a l dissolved system w i l l
water
is
control
i n a closed water
b u i l d up due to e v a p o r a t i o n and a d s o r p t i o n o r
c o n c e n t r a t i n g effect
relative
s o l i d s concentration
replaced. proportion
will
continue indefinitely
Make-up of
rate
water of
will
the e q u i l i b r i u m d i s s o l v e d s o l i d s
leaching.
unless s a t u r a t i o n occurs,
replace
replacement
recirculation
to
polluted
water
concentration.
in
water
and
circulation
The or the will
Computation of
the
e q u i l i b r i u m concentration i s performed a s follows:
F
I
:~
ai ~ = aD
+
ae
(2.12)
25
c
I
c,
t
a.
P l u g flow
C
t
b.
Completely mixed system
t
c.
Fig. 2.4
D i f f u s e systea
Comparison of p l u g f l o w a n d m i x e d systems.
26 S a l t s : QiTi + QiTe -
(2.13)
- QPTP
where Qi
i s the
water
input
rate
(.e.g.
l i t r e s per' second
or
megalitres
per d a y ) ,
Q
P
i s the d i s c h a r g e pumping r a t e
Q
i s the e v a p o r a t i o n r a t e
T.
i s the concentration of s a l t s i n the replacement o r makeup water stream.
T
e
is
the
concentration
build
up
due
to
leaching,
expressed
in
terms of the incoming water flow r a t e here.
Tp
i s the concentration
in the pumped
water
which
i s the
same as
the c i r c u l a t i n g water f o r a mixed flow system.
I f Q i s i n m e g a l i t r e s a d a y and T k i l o g r a m s of s a l t p e r d a y .
then QT
i n mg/t
Solving f o r T
the
P'
salt
has
the
u n i t s of
concentration
in
the
system,
(2.14)
Thus f o r no l e a c h i n g ( T the pumping r a t e , T
=
0 ) and a n e v a p o r a t i o n r a t e equal to 50% of
=
1.5 Ti
i.e.
P be 150% of that of the make-up
the e q u i l i b r i u m s a l t concentration
will
water.
APPLICATION TO A MINE WATER CIRCUIT
South A f r i c a n g o l d mines use n e a r l y underground
(Holton a n d Stephenson,
f o r dust control
a n d cooling.
3000 metres below
surface,
Owing
rock
2000 m i l l i o n l i t r e s of water
1983).
The
to
great
the
temperatures
e f f i c i e n t method of c o o l i n g i s b y means of rock.
The water
water
is
depths
can
a day
used p r i m a r i l y i.e.
r e a c h 65°C.
often
over
The
most
s p r a y i n g c h i l l e d water onto the
i s also used f o r ore moving and to a
l i m i t e d extent
for
h y d r a u l i c emulsions in machinery. The
geological
formations
Free State and T r a n s v a a l
in
which
gold
i s mined
which s u f f e r water
imported from a d j o i n i n g catchments such as i n Natal purposes. encouraged
The
cost
both
to
pol l u t e d wastewaters
of
conserve
is
the requirement
therefore
water
i n t o surface
g o l d mines a r e therefore 10% of
water
and
streams.
high to The
made
up
from
minimize water
surface
in
the
Orange
is
i n fact
Water
f o r domestic d r i n k i n g
and
l a r g e l y met b y r e c y c l i n g is
are
shortages.
re-use the
water
is
discharge
of
of
requirements of
the
and only approximately water
resources.
Some
27
mines also have s u r p l u s
underground
water
from
infiltration
and
this
is
used where possible.
# Pure w a t e r
Remaining concentrated S a l i n e water
F i g . 2.5
Model of s a l t b u i l d u p due to e v a p o r a t i o n
The q u a l i t y content
of
surface
i s typically
water where there
less
i s any,
water than
is
good
and
500 mg p e r
i s also g e n e r a l l y
the
litre.
total The
Although
h a r d and contains magnesium and calcium carbonates,
on
the
i s r a r e l y above lOOOmg per
other
hand
the
natural
water
litre. is
In
,Qi
Fig.
2.6
of
ground
I
Model of s a l t e q u i l i b r i u m due to pumping
the water
the dissolved
the Orange
known
concentrations of chlorides.
Average salinity
quality
solids
good as the water o r i g i n a t e s
l a r g e l y from dolomitic a q u i f e r s in the upper s t r a t a .
concentration
dissolved
to
is
salts
Free State
contain
high
28
Despite the general p u r i t y of make-up
water,
a n d o r g a n i c s a l t s u n d e r g r o u n d can t y p i c a l l y per Iitre.
concentrations of d i s s o l v e d
vary
10000 mg
3000 to
from
T h i s water can therefore o n l y be used f o r l i m i t e d purposes.
has to be machines
taken and
to
ensure
with
heat
that
it
is
exchange
not
used
for
drinking,
In
apparatus.
many
mines
Care
certain
in
there
is
s c a l i n g a n d f o u l i n g of m a c h i n e r y a n d p i p e w o r k because of the poor q u a l i t y of
water
and
in
other
mines
there
is
corrosion
of
pipework
and
other
metal-work. Reasons for primarily are
the
l e a c h i n g from
to
brought
from
concentration effect i n cooling and
for
towers.
corrosion
contributor
deterioration
owing
the
the
source
due
to
service
mined ore. of
the
scaling
the
small
be
attributed
In a d d i t i o n c e r t a i n
pollutants
water
to the e v a p o r a t i v e
The chemical and
in mine
dosing of inhibition dosage
water
can
and
there
loss of
water
water can
rates
for
be
is
a
secondary
underground and
purification
ruled
relative
to
purposes
as
out
the
a
major
increase
in
dissolved solids i n the water.
Evaporation
Groundwater
F i g . 2.7 After water,
Mine water r e t i c u l a t i o n system i d e n t i f y i n g p o s s i b l e sources of
chemical
salts
appearing
r a t e of appearance of
s a l t s in
the
water.
The
complicated
n a t u r e of
geochemical environment make% a n exact q u a n t i t a t i v e estimation of in
any
in
the
l a b o r a t o r y a n d s i t e t e s t i n g were performed to e v a l u a t e the p o s s i b l e
particular
l e a c h i n g can
circumstance
be assessed
with
impossible.
Nevertheless
these methods.
Once
relative
pilot
tests
the
leaching r a t e s of had
been
29 conducted to i d e n t i f y the prime effects of water qua1 i t y d e t e r i o r a t i o n , parameters were s t u d i e d i n more d e t a i l . the
crushed
ore
originating
from
I t appeared t h a t
blasting
or
parameter i n a f f e c t i n g the r a t e of geochemical leaching. the reef
i.e.
the ore b e a r i n g stratum,
w i t h the water affects the amount of ore.
Temperature
water,
affects
the
the
drilling
these
fineness
was
a
of
prime
The composition
also i s a factor.
The contact
of
time
l e a c h i n g from any p a r t i c u l a r mass of
chemical
reaction,
as
does
the
pH
of
the in
a n d i n i s o l a t e d cases p o s s i b l y the presence of b i o l o g i c a l matter,
particular
thio-bacillus
ferro-oxidans
and
thio-oxidans.
The
presence
of
a i r appeared i n a l l cases s u f f i c i e n t to s a t u r a t e the water w i t h oxygen a n d therefore was not a l i m i t i n g factor.
Conditions unless otherwise stated 209 fine,
3OoC, a i r b u b b l e d t h r o u g h 2e
/' 5-409 fine crushed ore 100
-
00E
s,E
-
.-f> .-
60
-
" a
c
P
40-
d0VS
F i g . 2.8 L a b o r a t o r y l e a c h i n g tests on crushed o r e
L a b o r a t o r y tests were performed b y immersing samples , o f ore crushed to various
finenesses
one
in
to
two
litres
of
water.
Temperature
was
controlled b y means of a b a t h and a i r was b u b b l e d t h r o u g h the samples agitate
and
water
were
month
and
provide performed
sufficient
oxygen.
simultaneously.
conductivity
and
various
Datum
Tests
tests
were
dissolved
measured r e g u l a r l y as well as pH a n d temperature.
with
pure
for
longer
run salt
to
distilled than
parameters
a
were
30
The r a t e of l e a c h i n g of a t y p i c a l b a t c h of 2.8.
I t will
the f i r s t
be observed that
day a n d then
the l e a c h i n g r a t e s
gradually
the ore were depleted.
samples
decelerated
Confirmatory
i s indicated
were
most
the
reduction
crushed ore,
in
leaching
tests w i t h
rate,
d i f f e r e n t sizes of
The
rapid
during
in
as the s o l u b l e chemicals initial
water
a t v a r i o u s levels i n d i c a t e d t h a t s a t u r a t i o n of the water for
in F i g .
effects
particles and
of
concentrations
was
not
different
temperature,
the cause passes
of
presence of
air
a n d a g i t a t i o n were s t u d i e d i n d i f f e r e n t samples. v a r i e d from 5 to 30
The increase i n t o t a l dissolved s o l i d s in the water grams of dissolved s o l i d s per k i l o g r a m of crushed ore. The
following
a n a l ysed : sodium
inorganic
sulphates,
as
well
concentration
chlorides,
as o t h e r
of
salts
were
carbonates,
elements
in
sulphates
detected
in
the
nitrates, relative
milligrams
the
in
per
water
c a l c i urn order
Iitre
per
cent
sulphur
by
In the presence of
mass).
(mg/P)
r e a c t i o n was is
often
well
precipitated
known
in
both
as
iron oxide
coal
mining
and and
and The
The
SO4
of
was
i n mg/e.
in the ore
oxygen
s u l p h i d e forms in p a r t i c u l a r were o x i d i z e d to sulphates.
which
magnesi urn,
indicated.
t y p i c a l l y one h a l f of t h e t o t a l d i s s o l v e d s o l i d s concentration can be a t t r i b u t e d to the h i g h s u l p h i d e concentration
samples
This to
(up
water
8
some
i r o n from the
the
chemical
reaction
gold
mining
pollution
problems i s i n d i c a t e d below:
+ O2 + H20 4 FeO(OH) + H2S04
(2.15)
The pH of the s o l u t i o n remained between 6 a n d 8 f o r most cases.
By the end of
to below f o u r .
t h i r d week
the f i r s t
week
in
the pH often dropped
As the pH dropped an a c c e l e r a t i o n i n the l e a c h i n g r a t e ,
i n d i c a t e d b y an evidenced.
the second o r
increase
i n conductivity
The presence of
and total
b a c t e r i a was noticed
dissolved,
in
solids,
as was
i s o l a t e d samples a f t e r
a month of t e s t i n g , b u t not i n a l l samples in which the p H dropped o r r a t e of l e a c h i n g was noted to be p a r t i c u l a r l y It
is
therefore
geo-chemical
concluded
that
the
the
high.
leaching
reaction
is
primarily
to
be
r e a c t i o n a n d b i o l o g i c a l r e a c t i o n can be s a i d
small
a in
the environment studied. The
application
particularly generated exposed
of
the
by
mining
surface
of
It
leach a t
a
high
underground
fine
laboratory.
Tests
in
only
which
which
this
compared the
results
not
field
may
of out
Only
explain
with could
to
the
is
settles
to the s h a f t .
r a t e and as
is
operations
the
d r a i n s t a k i n g water back
rate
laboratory
complicated.
the total
field mass
importance, rapidly
the surface the
in
maximums
only
indicate
of but the
ore
also
the
horizontal
low
measured increase
is
fine
l a y e r appears
relatively
the
conditions
to
leaching in in
the total
31
dissolved solids of
the o r d e r of
100 to 300 mg/e
per
cycle
as
the
water
r a n from the workings back to the s h a f t . I t was therefore not possible to equation
form
into
r e l a t i o n s h i p s were
the
i n s e r t the complete chemical process
computer
therefore
used
model
and
of
these
will
the
system.
have
to
in
Empirical
be
verified
for
considerably
during
the
each mine and each o r e mined
COMPUTER SIMULATION MODEL
The day
r a t e s of
use of
and are highest
often
stored
various
in
the
stages.
rates
in
the
additions logical
underground
is
cascade
dams
at
dams in
volumes of
various
underground o r
water
all
conduits
the
quality storage
be
can
also
affect of
internal
volume,
simulating
the
in
is
surface
therefore
dams
modelled.
water removed w i t h the ore,
method
vary
Water
Fluctuation
p r e d i c t unless the
evaporation,
water
d u r i n g the d r i l l i n g a n d ore moving s h i f t s .
as
difficult
well
External
as
to
the
flows
flow
such
as
seepage a n d i n t e r m i t t e n t make-up
flow
process
rates was
and
with
quality. a
The
digital
most
computer
model. This was adapted to a micro computer w i t h considerable success. A
general
simulation
models of mine water
program
systems.
was
p a r t i c u l a r mines.
The sizes of dams,
conduits and the
usage
hydrographs
The o p e r a t i n g r e l a t i o n s h i p s rate,
criteria
for
then
be
used to
which,
adding
programmed as p a r t of
for
the
then
be
example, water,
source code.
model.
simulating i n general
p o s i t i o n s and
the
can
for
make-up
the model
simulate
developed
Models a r e constructed
Flow
starting
the
by
the
salt
pumps
The computer
rates,
for
the c a p a c i t i e s
specified
define
specific form
volumes
leaching etc.
program and
of
user.
are will
dissolved
s a l t s concentrations a r e d i s p l a y e d a t specified time i n t e r v a l s as output.
Mathematical Basis of Model
The computer model easy
updating
concentrations differential
and
was p r e p a r e d
in a
modification.
The
a r e described
equations.
i n models b y
Alternative
modular
structured
to s u i t
salt
means of
first-order
methods
the p a r t i c u l a r equations.
for
and
volumes
of
solving
n u m e r i c a l l y are b u i l t i n t o the s i m u l a t i o n p r o g r a m and selected
fashion
varying
the
ordinary equations
the methods can
I n many cases a fast
i s s u i t a b l e w h i l e i n o t h e r cases a more a c c u r a t e a l g o r i t h m
be
algorithm
i s r e q u i r e d to
solve the equations w i t h s u f f i c i e n t accuracy on a numerical basis. In a
mine
water
system
many
processes occur
simultaneously
and
the
32 net effect i s e i t h e r to increase o r decrease the d i s s o l v e d s a l t concentration of flows a n d water volumes w i t h time. storage element, volume of outflow.
such a s
water
dams,
i n storage,
on
the
mass
of
salts
a n d the s a l t c o n c e n t r a t i o n of a n y
Denote Q1 a n d Q2 as the i n f l o w a n d outflow
a n d C 2 as the corresponding
Cl
The s a l t concentration of water
depends
in a
and
the
inflaw and
to a dam,
a n d denote
I f M i s the mass of
s a l t concentrations.
dissolved s a l t a n d V the dam volume a t a c e r t a i n time t,
the r a t e o f
then
change of water volume a n d s a l t mass w i t h time i s
(2.16)
dM dt
and
If
-
= Qi.Cl
perfect
(2.17)
Q2.C2
mixing
is
assumed
concentration of the outflow M
c2
=
to
occur
in
the
dam
then
the
salt
is:
(2.18)
0
A mine water model b a s i c a l l y consists of e q u a t i o n s ( 2 . 1 6 ) and ( 2 . 1 7 ) f o r each storage element wherein
the volume and s a l t mass change w i t h time.
Other r e l a t i o n s h i p s govern flow r a t e s a n d changes i n s a l t concentrations of flows between storage elements. S t a r t i n g w i t h known o r assumed
initial
d i f f e r e n t i a l equations a r e n u m e r i c a l l y methods.
Values
time-increment
M,
of
V
and
C
V a n d C the
v a l u e s f o r a l l M,
solved u s i n g E u l e r a n d Runge-Kutta are
determined
at
each
iteration
d u r i n g the s i m u l a t i o n a n d can be d i s p l a y e d as o u t p u t .
s t a b i l i t y and accuracy of the solution depends v e r y much on
The
the time step
a n d numerical method selected. Considerable e f f o r t h a s to be expended it
i n g a t h e r i n g data for
the model
i s found. Owing to the u n p r e d i c t a b l e changes i n m i n i n g p a t t e r n s as the
of
characteristics
therefore
the
Reef
change,
the
b e i n g extended o r a l t e r e d .
continually
form
a
complex
storage
i s designed
monitored as
it
volumes and
times
of
distribution
to operate
makeup
water
were
reticulation
pattern
The c o n d u i t s and dams system
which
automatically.
therefore
often
is
Flow
often
rates,
difficult
to
in t h i s system
point
typical
for
variation
alternative
indicates
a
and Fig.
2.10 i n d i c a t e s the water q u a l i t y v a r i a t i o n
in
flow
operating
rate at
the
conditions. workings in
the
not
stored
ascertain.
The model can thus oe used to p r e d i c t the water q u a l i t y a t a n y any
is
constructed
time a t Fig,
2.9
underground water
to the surface a t the same g o l d mine over a p e r i o d of a week.
pumped
33
2.9
Fig.
Flowrate from Coldwell to u n d e r g r u n d (M4/d)
T h e i n i t i a l conditions varied
l2hOO
24h00
12h00
to
an extent.
in starting
That
i s the
up a n d
initial
running
water
the model
quality
could
could be
be
varied
assuming that d i f f e r e n t make-up q u a n t i t i e s of surface water c o u l d be used to replace poor q u a l i t y water i n the surface storage dams over a weekend when m i n i n g a c t i v i t i e s were m i n i m a l .
By comparing a l t e r n a t i v e management
p o l i c i e s i n t h i s manner i t i s possible to r e a c h a f o r m a i n t a i n i n g the water q u a l i t y usage
underground
was
minimum cost
a t a c e r t a i n selected
assumed
fixed
by
the
level.
mining
therefore o n l y storage dam c a p a c i t i e s and make-up
procedure
The r a t e of
operation
and
r a t e c o u l d be v a r i e d
in
t h i s way. I t i s also possible t h a t m i n i n g methods c o u l d water q u a l i t y .
I t was recognised t h a t the contact
be v a r i e d
to affect
time between f i n e ore
suspension and i n the r e t u r n water systems h a d a n important
bearing
the
methods
rate
returning water
of the
quality.
deterioration water
were
in
the
water
therefore
quality.
investigated
In t h i s manner the effects of
therefore r e q u i r i n g less surface make-up
p o l l u t i o n can
water
10000 8000
5000 4000 2000
TueS
F i g . 2.10
Yed
Thur
Fri
Sat
Sun
Hon
Tues
Salt concentration i n the settlers
to optimize
in on
of the
be minimized,
a n d r e d u c i n g m i n i n g costs
i n e l i m i n a t i n g to a l a r g e extent s c a l i n g and erosion.
12000
Alternate
i n order
the
34
REFERENCES
Henderson-Sellers, B. 1979. Re se rv o i rs , M c M i l l a n , 1 2 8 ' p . Holton, M.C. a n d Stephenson, D . , 1983. A computer model of c i r c u l a t i n g s e rv i c e wa t e r i n South A f r i c a n g o l d mines. I n t . J. M i n e Water , 2 ( 2 ) p 33-42. Sanders, T.G. ( E d . ) , 1983. Design of Networks for M o n i t o r i n g Water Q u a l i t y . Water Resources P u b l i c s . 328 p . Thomann, R . V . , 1974. Systems A n a l y s i s a n d Water Q u a l i t y Management. McGraw H i l l , 286 p .
35. CHAPTER 3
NON CONSERVATIVE PARAMETERS
INTRODUCTION
Mass
balances
are
not
always
possible.
waters change concentration n a t u r a l l y . d i f f e r e n t salts. total
Many
Some r e a c t chemically
I f a l l the s a l t s before and a f t e r
concentration of
dissolved
salt
in
same. Sometimes oxygen i s taken out of
mg/e
in
constituents
still
to r e s u l t
in
r e a c t i o n a r e s o l u b l e the
in
the water
the
water
remains
the
to release hydrogen gas
which i s more v o l a t i l e and escapes.
For instance ammonia
Oxygen i n water i s the cause of many changes. oxidized
to
nitrites,
n i t r a t e s cannot
biological
these
turn
in
be e l i m i n a t e d except
or biochemically, Absorption
and
of
oxidized
chemical
to
nitrates.
replacement,
is
The
absorption
as i s now done in some waste water treatment processes. oxygen
matter
by
are
in
and other
water.
Decay
chemicals
i n water
i s generally
may occur
approximated
by
due a
to
first
o r d e r equation
- _
at
-
KC
BASIC MASS BALANCE EQUATION
The
one-dimensional
balance
equation
allowing
for
dispersion,
and sources or s i n k s i s d e r i v e d below Source
I
SdtAdx
direct i o n
Decay Kc Adxdt
F i g . 3.1
Mass b a l a n c e
decay
36 Net increase i n mass of C i n element in time d t i s dC.Adx
= dt
(SAdx
-
aa
KC Adx - C a x dx
-
as
a x d x + a x ( A € aa sx ) d x j
Q
For a u n i f o r m channel A = constant and t = constant a n d Q = constant
...
s-
ac
-a + t k C + v
a2c
(3.3)
E,,I-~=O
1 )
i s r a t e of increase in concentration of p o l l u t a n t
2)
i s decay r a t e
3)
i s advection
4)
is diffusion
5)
i s source
E i s the t u r b u l e n t viscosity
which
diffusion
represents
coefficient.
transfer
of
It
is similar
momentum
to
between
the k i n e m a t i c layers
f r i c t i o n model, e.g. du = p E - against a wall, dy where
in
a
(3.4)
T
(3.5)
, where U=
v'(T/P)
= shear
velocity
a n d k i s the von Karman constant, 0.4. But i t
i s not t h a t simple
b u t macro turbulence, the action,
i n channels
tracking,
as
dead water,
not o n l y
molecular
s t r a t i f i c a t i o n etc.
diffusion complicate
therefore one needs to c a l i b r a t e models.
E l d e r ( D e i n i g e r , 1973) suggests
E = A h J(ghS)
where h = depth a n d A = coefficient
(3.7)
( a v e r a g i n g 0.07).
Normally d i f f u s i o n i s n e g l i g i b l e in r i v e r s , except estuaries. Thus one gets the Streeter-Phelps equation
-a_t
-
-_
- v ac
ax
KC
(3.8)
( o m i t t i n g sources)
(3.9) (3.10)
K ranges from 0.01
per day i n laboratory conditions
1980) w i t h p u b l i s h e d f i g u r e s f o r r i v e r s a v e r a g i n g 0.1
( a s found b y A r n o l d , per day.
37
t
or
C
X
F i g . 3.2
Decay curves
OXYGEN BALANCE I N R I V E R S
Oxygen concentration oxygen).
in a r i v e r i s measured in terms of DO ( d i s s o l v e d
Shortage o f oxygen
i s measured as
(COD) o r a biochemical oxygen demand (BOD). 1.45 x days,
a
BOD5 where BOD5 i s the BOD as measured a s t a n d a r d test (AWWA,
chemical
oxygen
The long term
in a
demand
BOO i s about
laboratory
over 5
1965).
Coupled equations for DO a n d BOD
I f DO concentration i s designated C and BOD i s L then
-a _t
a2c
ac
- E 7 ax - v~
-
K,L
+ K,(C
- C) * S c (3.11)
38
Dissolved Oxygen Sag Curve
Dernond Dissolved Oxygen
P-.L._-I
n-:-A
Lriilcui ruin1
R e oxygenot ion C u r v e Deoxygenalion Curve
Distance Downstream or Time
E f f luen t Outtall
Fig. 3.3
The d i s s o l v e d o x y g e n sag curve
J, Olcygen 0
F i g . 3.4
Carbonaceous plus
Carbonaceous and nitrogenous o x y g e n demand c u r v e s
39
where C aL and a t
= s a t u r a t i o n conc. =
E
a2L ax
7-
of oxygen (3.12)
aL v- K,L, ax
t S
L
These simultaneous equations can be solved a t p o i n t s a l o n g a r i v e r a n d over
time
K,
increments,
K~~~~
=
e (T-20)
i.e.
it
is
a
function
of
temperature.
charac t e r i s t i C
At n - l
F i g . 3.5
Solution g r i d
A s a n example of t h e solution of these two equations a
method
can
diffusion
be
employed
where
A x
f v
(Deininger
1973,
p
122).
One
two-step can
get
explicit pseudo (3.13)
A t
unless a c a r e f u l numerical procedure i s used. Where
the
river
is
depleted
of
oxygen,
the
BOD
equation
must
be
replaced b y KIL i.e.
( C - C ) - Sc 2 s the q u a n t i t y of oxygen consumed i s equal
(3.14)
= K
introduced i n the same time
(Thomann,
to the
quantity
of
oxygen
1972).
Ana I y t ica I solution dC I f - = - K L + K (C - C ) dt 1 2 s a n d oxygen d e f i c i t D = C - C
2:
_ - - KIL
-
(3.15) (3.16)
K2D
Integrating gives KILO -K,t -K,t D = (e -e Kz-Ki
(3.17)
-K, t
1
One can also e v a l u a t e K,
+ Doe
(3.18) and K2 a t t C ( D e i n i n g e r 1972 p 126).
40
CALIBRATION OF A MOVING BOD MODEL
As an a p p l i c a t i o n of the c a l i b r a t i o n of a r i v e r r i v e r in South A f r i c a was analyzed. effluent
from
major
municipal
underdeveloped township. t h r o u g h reed beds.
The
decay
the K l i p
The K l i p r i v e r h a s d i s c h a r g i n g sewage
works
and
runoff
into i t
from
an
The stream i s also h i g h l y m i n e r a l i z e d a n d flows DO o v e r
Measurements of BOD a n d
show r a p i d n a t u r a l self a e r a t i o n . o t h e r sources.
oxygen model,
summer
The waters a r e e v e n t u a l l y
and
winter
recycled w i t h
A numerical model p r e d i c t s d a i l y v a r i a t i o n s i n BOD a n d DO.
coefficient
and
sources
and
sinks
were
fitted
by
linear
programming opt im iza t ion. The
Klip
banks are area.
river
rises
in
three major
the
watershed
of
sewage
works
municipal
the
a
Separate s a n i t a r y sewers a r e p r o v i d e d g e n e r a l l y
l i t t e r i n g r e s u l t s in h i g h l y p o l l u t e d s u r f a c e The
population
consumption
within
of
the
the
m i l l i o n l i t r e s per day,
area
is
watershed
the
large
its
residential
but
a
tendency
Of
a
total
to
runoff.
nearly of
On
Witwatersrand.
and
2
million.
Klip
r i v e r of
water
500
approximately
n e a r l y 50 percent i s r e t u r n e d to the K l i p r i v e r v i a ( u n t r e a t e d ) i .e.
sewage p u r i f i c a t i o n works o r separate storm sewers
2m3/s.
The base flow of the r i v e r i n the reaches s t u d i e d amounts to o n l y lm’/s.
OXYGEN BALANCE
The dissolved oxygen content (DO) of ability
to support
A
life.
lower
water
i s a useful
level of 4 m g / t
i n d i c a t o r of
i s r e g a r d e d as the
its
limit
f o r f i s h l i f e i n the area studied. The
r a t e of
which
dissolved
demand i s dependent on
oxygen
reduces
the
biochemical
the level of free oxygen concentration.
l i m i t i s the s a t u r a t i o n concentration, C S (mg/e) = 14.6 - 0.41T
+ 0.008T‘
oxygen
The u p p e r
C s , estimated to be
- 0.000778T’
(3.19)
where T i s i n “C The DO i n a p o l l u t e d stream v a r i e s a l o n g the l e n g t h
i n accordance w i t h
the r a t e of takeup a n d the r a t e of re-oxygenation
(Fig.
to b i o d e g r a d a t i o n of carbonaceous o r g a n i c matter,
oxygen
nitrification, high
sulphur
oxidizing
i n o r g a n i c chemicals a n d p l a n t
concentration
in
oxygen requirement i s f a i r l y b y the h i g h llime content, Temperature demand.
and
sludge
the
high.
waters,
due
to
3.3).
respiration. mining
T h i s i s counterbalanced
as the waters o r i g i n a t e from a deposits
in
winter
also
I n addition
i s required With
activity,
for a the
to some extent dolomitic
influence
the
area. oxygen
41 Owing to deposits of t h a n 0.2 m/s) the
summer
in the slow
d u r i n g w i n t e r months,
rains
reoxygenation matter,
sludge
the
was
deposists
observed.
while benthal
stream v e l o c i t y
(less
BOD was observed to increase.
were
The
deposits
moving
scoured
sludge
out
arose
were considered
and
a
primarily
from
relatively
After
more
rapid organic
inactive
(Velz,
1970). There
are
nitrogen.
two
primary
biochemical
oxygen
abstractors;
carbon
and
The BOD removal c u r v e t y p i c a l l y e x h i b i t s a n i n i t i a l hump due to
carbon a n d a
subsequent
hump
due
to
nitrogen
(Fig.
3.4).
The
decay
equation smooths the c u r v e out. The coupled d i f f e r e n t i a l equations d e s c r i b i n g DO a r e 3.11
the v a r i a t i o n of
BOD a n d
and 3.12 r e w r i t t e n i n the form
(3.20) (3.21) A method of e v a l u a t i n g the coefficients K, sink
system, the
S
term,
and
so
total
equations 3.20
the
Linear
difference
3.21
and
and
equations
the above case,
Minimise
{
between
and
the
programming may
f u n c t i o n subject to c e r t a i n
K2,
the
actual
a n d the source a n d
represented
the
that
would
concentrations
concentrations
be used f o r
lead
to by
in
the
observed
the system
river
predicted
m i n i m i s a t i o n of
constraints provided
real
an objective is
In
linear.
the o b j e c t i v e f u n c t i o n would b e
z I Predicted BOD - observed BOD I
+Z
subject
that
would be to f i n d values f o r these parameters
minimum
field.
P,
I
Predicted DO
to the c o n s t r a i n t s
-
observed DO
formed
by
the
I}
(3.22)
system of
equations
and
to
the
c o n s t r a i n t that the e r r o r p l u s the p r e d i c t e d v a l u e must e q u a l the observed value. I n other
words
the
calibration
of
the
model
can
be
carried
out
by
m i n i m i s i n g the sum o f the absolute errors. Another method would be b y .means of This
has
been
attempted
survey on 21 March, and
3.21.
The
I inear
elsewhere,
least squares f i t t i n g
using
the
data
1979 (McPherson a n d S h a r l a n d , '
programming
method
has
been
from
techniques.
the
sampling
1979) equations 3.20 used
be
Kleinecke
(1971 f o r estimating geohydrologic parameters of groundwater basins.
O L - . ; ' . ' - . . . . I . . . . . 1 . . . . . .
6h00
l2hOO
18h00
Fig.
3.6
24h00
1 1 . .
...
I . . . . . .
06h00 06h00 12h00
. . a .
18h00
A
l
.
.
24h00
.
.
.
I
I1
.....
I
.
.
06h00 06h00 12h00
,
.
.
.
..... .....
18h00
Results of S i m u l a t i o n using minimum e r r o r c a l i b r a t i o n p a r a m e t e r s
I
24h00
I ,
06h00
43
I
1-1 x - t grid
F i g . 3.7
Considering the concentration-space how
x
1+1
the above coupled equations
grid
3.20
in
and
Fig.
3.21.
3.7 can
i t can be
be shown
formulated
for
l i n e a r programming e v a l u a t i o n of the parameters as follows: The BOD concentration a t a p o i n t
P can be w r i t t e n
in terms of
implicit
f i n i t e differences as:
- (L 2At
i,n + L i + l , n - Li,n-l
+
Li+l,n-l
1
For I i n e a r programming purposes two requirements must be met: (i) (ii)
a l l terms must be l i n e a r a l I v a r i a b l e s must be non-negative
I n the above f i n i t e difference form these c o n d i t i o n s a r e not s a t i s f i e d . F i r s t l y the term l i n e a r since both source/sink
the
+ L. + L. t , i /4 . ( L i - , , n 1-1 ,n-1 1In K1 and the L. a r e unknowns.
K
1,n
+ Li,n-l) Secondly
i s not the
net
term may be e i t h e r p o s i t i v e o r negative.
To overcome these problems the prediced L. a r e r e p l a c e d b y the known 1,n observed values b . a n d the source/sink term i s s p l i t i n t o a n i n p u t term 1,n + S and an output term - T where one of S a n d T w i l l be p o s i t i v e a n d the other zero.
The equation then becomes
44
( L 1. ,n
--
-UAt 2 Ax
+
-
Li+l,n)/2
+
(Li+l,n
+
+
(Li,n-l
-
Li+l,n-l
L .i+1 ,n-1 ) / 2
1
L .i,n - L i , n - l
- At T i
At Si
(3.24)
T h i s can be r e w r i t t e n as
1
(2
Li,n-l
*
1
U At
d
+
+
Li+l,n-l
(Z -
+
bi+l,n-l
+
UAt ~ x
-
-
(-1 ) i,n 2
-)-L. UAt 2Ax
UL!)
1
i+~,n
‘Z
+
2AX
K1 iAt
- +
AtSi
(bi+l,n
bi,n
+
bi,n-l
1
- AtTi = O
I n addition
(3.25)
another
set
of
equations
can
be w r i t t e n
in
terms
d i f f e r s from the e r r o r b y which the p r e d i c t e d v a l u e of L . 1,n of L . 1
. ,n
- Vi,n
L. + Ui,n ‘,n
Again
actual
= b.
the
value
(3.26)
i,n
the requirements that
the s p l i t t i n g of the e r r o r
of
the v a r i a b l e
must
be p o s i t i v e
necessitates
i n t o a p o s i t i v e e r r o r U o r a n e g a t i v e e r r o r -V,
one of which w i l l be zero i n the solution. Similarly
a
includes a
set
of
reaeration
equations term
can
which
be
i s also
written
for
non-linear
equation unless
3.22.
This
the observed
values a r e s u b s t i t u t e d f o r the p r e d i c t e d values. These equations a r e g i v e n below
- ci+l,n
1 (2
+
-
A t Pi
C.
1,n
+ M.
+
UAt
-126x
At R i
1,n
-
N.
1,n
=
o
=
d.
(3.27) 1,n
(3.28)
45
Equations 3.27 a n d 3.28 can be w r i t t e n f o r a l l p o i n t s i, except point,
a l o n g a study
to
be
the
last
i s a v a i l a b l e over
a
a n d di,n a t each v a l u e of n may i ,n observations taken a t o t h e r times. O n l y
The observed values b
p e r i o d of time. have
reach f o r which observed d a t a
inerpolated
from
equations 3.26 and 3.28 can be w r i t t e n f o r the p o i n t f u r t h e s t downstream. The o b j e c t i v e f u n c t i o n now becomes
;
+ V. + Mi,n + N. {; (Ui,n 1,n 1,n subject to the c o n s t r a i n t s g i v e n b y equations 3.27 a n d 3.28.
Minim i se
(3.29)
F I ELD MEASUREMENTS
The
length of
stream
modelled
6
was
km.
It
was
divided
reaches and two sets of samples were taken a s representative, mid w i n t e r and one i n mid summer.
into
four
one set
in
Samples were taken e v e r y hour f o r 24
hours of each section, which was p r o b a b l y a b i t sparse.
DO was measured
w i t h a p o r t a b l e meter.
and 20-day
COD a n d pH,
The samples were tested f o r 5-day
conductivity,
ammonia,
and suspended sol i d s were estimated
from
light
nitrate,
determined.
and
dark
nitrite,
chloride,
Photosynthetic oxygen
bottle
tests,
and
time
of
BOD,
alkalinity
release
was
passage
and
dispersion were determined w i t h f l u o r e s c i n dye, Various linear
methods
programming
were
employed
was
used
to
to
calibrate
minimize
the
the
simulation
absolute
model
value
of
: the
differences between observed and s i m u l a t i o n concentrations of BOD a n d DO. The
method
I inear,
is
the
described
theoretical
elsewhere.
In
concentrations
order were
render
the
equations
approximated
to
by
observed
values whenever p r o d u c t s of two unknowns appeared in the equations. may
have
been
the
result
of
often
apparently
high
unaccounted f o r sources a l o n g some of the reaches. extended
to
non-l i n e a r
equations
(McPherson
and
decay
This
rates
and
The methods a r e b e i n g Sharland,
1979)
with
encouraging results. The i n p u t parameters f o r the p l o t s g i v e n
in Table 3.2
were d e r i v e d b y
t r i a l a n d e r r o r f i t s i n the model. Even then,
there appeared
i n e x p l i c a b l y h i g h BOD o r COD sources a l o n g
the r i v e r reaches. These were a t t r i b u t e d to b e n t h i c deposits o r r u n o f f from adjacent
sewage
irrigation
works,
and
seepage
from
the
industrial
and
other townships to the north. The accuracy of the BOD measurements a t mg/4)
i s questionable,
the levels observed
due to the complex way of d e t e r m i n i n g i t .
(5 to
10
Various
46 researchers have proposed
TOC
(total
oxygen
carbon)
demand.
or
Due
to
COD
as
f r a c t i o n of COD,
the change i n COD may be a more a p p r o p r i a t e parameter
more
high
inert
and t h i s in f a c t gave b e t t e r r e s u l t s t h a n the BOD model.
The sampling frequency of 1 h o u r was r a t h e r coarse. plotted
the
(chemical
oxygen demand)
t h a n COD,
i n d i c a t o r s of
organic
it
was
likely
realized
due
to
that
pollution
surface
runoff
than
loading varied to
Once r e s u l t s were rapidly.
the e f f l u e n t
from
This the
was
sewage
works. The
decay
r a t e of
the
COD
was
which
i s h i g h i n comparison w i t h
data.
This
may
be due
to
high
estimated laboratory
turbulence,
to
be
up
to
3,O
per
day,
results
and other published
or
high salinity
the
of
the
water promoting reactions. Photosynthesis was noticeable o n l y on v e r y overgrown of 3 mg/P/day
reaches.
A value
was t y p i c a l .
Oxygen s i n k s were found to be l a r g e in w i n t e r
( u p to 75 mg/P/day)
but
n e g l i g i b l e i n summer ( t h e r a i n y season). The dissolved oxygen content
was found to be s u f f i c i e n t
to support
life
(above 3 mg/P) a t a l l stages. T y p i c a l r e s u l t s a r e i n c l u d e d as Tables 3.1
to 3.3 a n d F i g u r e 3.6.
REFERENCES
1%5. Standard Methods for the American Water Works Association, Examination of Water a n d Wastewater. 1980. M o d e l l i n g Water q u a l i t y in the u p p e r K I i p r i v e r . Arnold, R.W., MSc(Eng) Dissertation, U n i v e r s i t y of the Witwatersrand. Deininger, R.A., 1973. Models f o r Environmental P o l l u t i o n Control. Ann Arbor. D., 1971. Use of linear programming for estimating Kleinecke, geohydrologic parameters of groundwater basins. Water Resources Research, 7 ( 2 ) , p 367-374. McPherson, D.R. and Sharland, P.J., 1979. River Quality Tests. Undergraduate project, U n i v e r s i t y of the W i t w a t e r s r a n d . Thomann, R.V., 1972. Systems A n a l y s i s a n d Water Q u a l i t y Management. McGraw H i l l , N.Y. 1970. A p p l i e d Stream S a n i t a t i o n . Wiley Interscience, N.Y. Velz, C.J.,
TABLE
3.1
Results of c a l i b r a t i o n u s i n g d a t a of 21 M a r c h 1979 ( e n d of summer)
COD C a l i b r a t i o n
BOD C a l i b r a t i o n Value
Value jyrnbo
Parameter
Dispersion coeff i c i e n Decay c o e f f i c i e n t
K1
Reaeration coeff i c i e n
BOD source/sink
DO source/sink
(1) (2)
Photosynthetic DO ( 2 I n e r t source/sink
E
(1
K2
S R1 p1
Units
?each 1 3each 2
leach 3
Reach
:
Method of determination Reaches 1 a n d 2 Tracer studies Reach 3 - C a l i b r a t i o n
0.4
10.0
10.0
0.4
10.0
0.05
1.3
3.0
3.0
2.0
4.0
Ca I i b r a t ion
2.0
2.7
3.0
2.0
2.7
7 .o
Reaches 1 and 2 Formula Reach 2 - C a l i b r a t i o n
-1 80
330
100
75
30
-50
Calibration
8
10
0
30
10
20
Calibration
3
0
0
2
5
5
Bot t I e tests
-1 50
175
80
10.4
Not
) Notes
teach 1 Reach Z
1
applicable
-
(1)
A n e g a t i v e v a l u e i n d i c a t e s a source ( p o s i t i v e b e i n g a s i n k ) .
(2)
A p o s i t i v e v a l u e i n d i c a t e s a source ( n e g a t i v e b e i n g a s i n k ) .
The i n e r t f r a c t i o n o f t h e i n p u t COD was t a k e n a s 60% The BOD5/BOD20 r a t i o was t a k e n a s 0.69.
Calibration
48
TABLE 3.2
Results of model f i t t e d to COD d a t a of 18 J u l y 1978 (mid-w in t e r
Value ymbol
Parameter
--
-
each 1
each
2
each 3
10.4
0.4
10.0
-D i spers ion
E
Method of Det erm i n a t ion
Assumed same a s for March survey
coefficient Decay
K1
0.1
1.3
1 .o
Model f i t t i n g
2.0
2 .7
5 .0
Reaches 1 a n d
coefficient Reaera t ion
K2
2
coefficient
-
formula
Reach 3
-
model
fitting BOD source/
S
sink ( 1 )
-32
175
50
Model f i t t i n g
-1 3
13
-1 5
Model f i t t i n g
5
5
20
50
DO source/sinb
(2)
R1
Photosynthesis
(2) DO
p1
3
Bottle tests
~ n e r tsource/ (1)
-48
sink
Notes:
-
Model f i t t i n g
-
(1)
A n e g a t i v e v a l u e i n d i c a t e s a source ( p o s i t i v e b e i n g a s i n k )
(2)
A p o s i t i v e v a l u e i n d i c a t e s a source ( n e g a t i v e b e i n g a s i n k )
The i n e r t f r a c t i o n of the COD was taken as 60%
49
3.3
TABLE (.I
Program output mol
LISIIng (lor
D.I.
K l l p R l v w Slmlatlm
ENn Vn DFFN
-. . .-. . I
=
aa* KFm SINt 91RE
Po0 SINt I
1.7s 23.40
bn
kruleay
l0.00kruld.y 0.050 1/*y 2.00 I/&Y -190.0 n p / l / d a Y 8.0 n p / l / d a Y
3.0 np/l/dmy -150.0 np/l/dmy
5.30
bn
20.03 krulday 10.00 krulday 3.m I/&y 1.00 I/&Y 100.0 -/1/dmy 0.0 n p / l / d a Y 0.0 np/l/daY
lncrl F n c l l m :
0.00
0.00
m.0 np/i/ea~
-
O l u m l V a r l a l l m of Rolos,mlhesla used IFW
aLn
-
--
O a X I l l * 0.203 bn OELXIII 0.241 bn OaXl3l 0,174 km
NO of pace 1n1ew.I~ NX No of Ilm Inl.walsNT
-
IbI 1yplc.l
Lonplludlnal Oulpul
ULIPRIVER
SIMULATION
DI.l.nc. Ownsirearn
statim
VE IRO-ll
0.007 days
-
Run
Sirnulaled
9 o o w
m
E 27.0 35.6 15.0 52.3 5a.A . . 62.7
0.0 0.250 0.500 0,750
.ooo
I
1.250 1.500 1.7%
24.3 62.4
SIallm M
364
Tlm.
aO.00 h r s
Ov..r".d
moo
27.0
2.8
2.9
3. 0 3.2 3.3
1.5 _._
3.5 3.6 3.5
F
0 0 57.1
3.6
2.W 2 . m
54.6
3.1
2.503
49.7
i.1
0
44.0
3.4 3.5
0
Slallm
17.6 30.9
3.4
U.6
5.m
24.0 23.3 22.9 22.9 23.0 20.2
5.254
23.3
Slmllm No. HI41
0 0 0
0
0 0 22.0
b.0
11.9
4.0
3.9 1.9 4.3 4.1 4.1 4.2 4.2 4.2
0
0
0
0
1.7
M G
0
0 0
1.750 3.W 3.250
3.500 3.750 4.m 4.250 4.503 4.750
50.6
27 123
0 0 0
50 TABLE
3.3
Contd.
( c l T y p i c a l Time V a r i a t i o n Output KLlPRlVER
SIMULATION
-
RUN
eOp a n d 00 VARIATION = I T N TIME AT STATION F TIME
SIMULATED
OBSERVED
N0.5
m a ,
Kn
00
0.0 1.04
57.56 59.69 57.55 53.24 52.68 52.24 52.55 M.55 49.75 49.32
55.0 59.0 56.00 54.00 59.00 59.00 60.97 60.02 55.00 61.23 57.62 58.80 60.95 60.17 60.24 56.00 56.90 56.36 60.46 66.55 57.07 39.95 47.13 53.00 37.50 27.70
3.52 3.51 4.00 4.02 4.26 4.50 4.50 4.57 4.62 4.62 2.37 4.25 4.13 3.66 3.81 3.78 3.56 3.34 3.33 3.52 3.60 3.60 3.62 3.60 3.35 3.39
2.09 2.49 3.06 5.00 6.04 7.07 7.92 8.% 10.00 11.04
12.05 12.92 13.96 15.00 16.04 17.09 17.92 18.96 20.00 21.36 22.09 22.92 23.94 25.0
47.41
51.56 55.93 61.39 66.30 69.45 70.40 69.30 53.32 53.95 60.98 49.00 49.12 51.33 54.72 54.91
4.04
3.76 3.65 3.53 1.54 3.42 3.43 3.48 3.50 3.46 3.47 3.46
.
5 10 15 20 25 30 3 5 44 4 2 50 55 60 6: 0
3.38 3.45 3.52 3.65 3.91 4.21 4.47 4.56 4.71 4.76 4.73 4.65 4.48 4.19
ox on ON
on
0
.
?$ :7 80
0.
0.
.
.. ..
0%
0 .
a
XO SO
.
0
NO NO LO
0
.
.
0
SO
... . .... .
0
.
0.
*O SO
X
no
NO
no
.
0
I
.. . . 0
0 0
0 0
ON
.. I
.
.
0.
0
6
0 0
0
5
10
15
I
20
51
CHAPTER 4
NUMER ICAL METHODS
SIMULATION OF HYDRAULIC SYSTEMS
Simulation of systems described b y d i f f e r e n t i a l equations can be done in a number of ways:
F i n i t e elements Characteristics
-
Implicit
-
Four p o i n t
F i n i t e difference -
Explicit
-
Four p o i n t
F i n i t e difference
0-0
7 'V
Leap f r o g
Diffusive
Backward centred
L a x - Wendroff = d i f f u s i v e / l e a p
E x p l i c i t schemes a r e simple b u t schemes.
not
too
great.
(Deininger,
Ax2/At
or
2
At There
accurate o r
Problems which manifest w i t h e x p l i c i t
i n s t a b i l i t y and numerical d i f f u s i o n . is
as
The
accepted
stable
schemes
criterion
for
as
implicit
i n c l u d e numerical
I n s t a b i l i t y can occur
stability
frog
i f the time step
diffusive
schemes
is
1973);
2E
5 is
s p r e a d i n g of
(4.1
(4.2)
A x2/2 E
an
additional
the p o l l u t i o n
concentrations a t adjacent
problem, gradient
points.
the maximum numerical d i f f u s i o n Using the previous expression f o r be less than €/4.
that
due
to
From a is E At,
of
numerical
diffusion
successive c a l c u l a t i o n s second o r d e r
Taylor
i.e. using
expansion
max = A x 2 / 8 A t . ( D e i n i n g e r 1973) P we get the pseudo d i f f u s i o n cannot
52
Two-step
method
The water q u a l i t y
equation
i n c l u d i n g the d i f f u s i o n term
in two steps to ensure c o r r e c t a d v e c t i o n a n d d i f f u s i o n .
a‘c _ _ EaxZ
ac kC - v -
aC Ax
c. -
=
Cidl
(4.4)
Ax
ci+l -
a2c -
(4.3)
ax
at
use
can be solved
Thus s t a r t i n g w i t h
+ ci-l
2ci
ax7-
(4.5)
A X2
then C . i,n+l
=
The f i r s t equation
for
c.
+ EAt
i,n
and
last
two
advection
a p p r o x i m a t i o n to C .
I,
F i g . 4.1
Ci-l,n+Ci+l,n-2Ci,n Ax2
n+l
terms
and
on
decay
the can
-
- kC.
vAt ‘i+l,n-‘i,n
1,n
A X
right be
hand
side
used
to
(4.6) in
the
above
the
first
get
a n d then the d i f f u s i o n term.
Basic r e c t a n g u l a r x - t
grid
Demonstration of n u m e r i c a l i n a c c u r a c y
The
convection
term
in
the
water
quality
i I l u s t r a t e problems a n d i n a c c u r a c i e s d u e to a n
Neglecting the d i f f u s i o n a n d decay term, ‘i
,n+l
= C. 1,n
-
v
~
t‘i+l,n
equation
will
be
used
we h a v e
- ‘i,n A X
to
i n c o r r e c t n u m e r i c a l scheme.
(4.7)
53
We should have a wave of concentration move downstream a t a r a t e unattenuated o r changed i n concentration.
C i ,n
i-1
i it1
it2
AX
F i g . 4.2
Theoretical advection
I f Ax = vAt then u s i n g a f o r w a r d difference e x p l i c i t method
‘i
,n + l
i.e.
=
c.
=
2 which i s wrong,
- c.i , n )
1,n - (‘i+l,n = 1 - (0-1)
i t should be 0
dont use a f o r w a r d difference
ac/ax
Instead use a b a c k w a r d difference ac/ax Then ‘i,n+l
c .t,n -
= =
-
(‘i,n
1
1 - (1-0) = 0, correct.
on the other h a n d i f we use
=
‘i-l,n
1 -
0-0 =
1,
AX =
= (Ci+l = (Ci
-
-
Ci)/~x
Ci-l)/Ax (4.7b)
2vAt,
also wrong.
2 I f we continued w i t h t h i s scheme, the v a l u e of C o s c i l l a t e s (see below)
1
0
0.5 F i g . 4.3
O s c i l l a t i n g scheme
v,
54
O n the other h a n d i f one uses a
backward
difference
with
Ax
=
2vAt
n u m e r i c a l d i f f u s i o n occurs a s i n d i c a t e d below.
1
-
F i g . 4.4 I f At if
>
Numerical d i f f u s i o n Ax/v we get n u m e r i c a l i n s t a b i l i t y , e.g.
At = 2 Ax/v,
C.
= Ci,n
1
-
-
* Ax
( C .i,n - ‘i-1,n
1 (4.7d)
2 (1-0) = -1.
C o n t i n u i n g so, a n o s c i l l a t i n g c u r v e occurs:
I
F i g . 4.5
Instability
\
55
I m p l i c i t f i n i t e d i f f e r e n c e schemes
i-1
F i g . 4.6
i
X
i +1
I m p l i c i t scheme
(4.10) z c, - vAt becomes C. ('i,n+l ~,n+l i,n unknown and a set of i equations
method
is
unconditionally
equations can be l e n g t h y , use
the
hydrodynamic
since v .
I , n+l
stable
- 'i-1 , n + l is
with
A l l values
established
but
especially
equation
).
solution
for
of
i
the
a-t n + l a r e
unknowns.
for
non
l i n e a r systems,
the
term
v
( V i , n + l - ' i - l , n+l) i s parabolic.
ax
this
e.g.
is
('i,n+l
-
if
we
non-linear (4.11)
Ax
So r a t h e r use 'i,n
The
simultaneous
i
V.
I - 1 , n t l ) which i s l i n e a r .
(4.12)
A X
Methods of solution of i equations include ( F r i e d , 1975)
i)
Direct methods e.g.
ii)
I t e r a t i v e method
-
m a t r i x methods and Gauss e l i m i n a t i o n . i.e.
assume reasonable v a l u e s f o r
all
C's and
i t e r a t e the equations s u b s t i t u t i n g assumed values on the r i g h t h a n d side
until
the
left
h a n d side
o n l y converges i f At <
agrees
with
assumed
values.
This
AX/V.
... III)
Relaxation methods (Timoshenko,
iv)
A l t e r n a t i n g d i r e c t i o n i m p l i c i t procedure
1951). (Fried,
1975),
i.e.
compute
56
derivitive
w i t h respect to x
i m p l i c i t l y and y e x p l i c i t l y
a n d then
v i c e versa ( s t a b l e ) .
One (e.9.
also
gets
combined
explicit/implicit
McDonnel a n d O'Conner,
methods
for
more
accuracy
1977).
Comments on f i n i t e difference methods
E x p l i c i t method:
1.
T h i s must be designed to be s t a b l e i.e.
a n y e r r o r s due to 2nd o r d e r
terms in the T a y l o r expansion (we took j u s t the f i r s t o r d e r ) must decay d u r i n g comp u t ion. The
time
interval
For e x p l i c i t shown
must
t h r e f o r e be smaller
hydrodynamic
to be s t a b l e
if
equation,
2
using
-
Jgy
=
than
for
Fourier
wave
implicit series
celerity
it
i.e.
method. may
be
speed
of
computation g r e a t e r t h a n speed of a d i s t u r b a n c e i n the system.
2.
I t must
be accurate.
Check
with a
few
space a n d
time
intervals and
a g a i n s t an a n a l y t i c a l s o l u t i o n i f there i s one.
3.
I t shohld minimize numerical d i f f u s i o n
4.
One can use v a r y i n g g r i d s where g r e a t e r a c c u r a c y i s r e q u i r e d :
F i g . 4 . 7 V a r y i n g g r i d s p a c i n g (zooming)
57 NUMER I CAL METHODS FOR THE SOLUT ION OF SINGLE D IFFERENT IAL EQUATIONS
Numerical solutions appear i n the form of a t a b u l a t i o n o f the values of the functions of v a r i o u s values of as a f u n c t i o n a l r e l a t i o n s h i p .
the independent time v a r i a b l e
Numerical methods h a v e the a b i l i t y
p r a c t i c a l l y any equation b u t they
h a v e the d i s a d v a n t a g e t h a t
and
not
to s o l v e
the e n t i r e
t a b l e must be recomputed i f the i n i t i a l c o n d i t i o n s a r e changed.
I f a f u n c t i o n f ( t ) can be represented b y a
power series
i n a certain
i n t e r v a l then i t can be represented b y the T a y l o r series expanded about a p o i n t t = to,
i.e.
about the i n i t i a l value:
I
Y ( t ) = y (tO)+Y ( t o ) ( t - t O ) + y
II
( t o ) (t-t0)2+y
2!
L e t t i n g n represent
I1
( t o )(t-t0)3+
-
...
(4.13)
3!
the p r e v i o u s step
at
time
to a n d n + l
represent
the
next step a t t +h, the series can be w r i t t e n as:
0
Yn+l=~n+hyn l+h2 -yn I I + c y n 2 6
Ill+
*..
(4.14)
Consider the examp Ie p r o b lem
(4.15)
w i t h i n i t i a l conditions (4.16)
Y(0) = 1 This
is
a
linear
time
variant
1st
order
differential
equation.
The
a n a l y t i c a l solution to the problem,
y = 2e-t-1 w i l l be used to compare the t numerical r e s u l t s o f some of the methods a n d t o i l l u s t r a t e the e r r o r a t a n y step.
The E u l e r Method
The E u l e r method
i s the simplest b u t least accurate of a l l the methods
discussed. (4.151,
To o b t a i n a n exact numerical s o l u t i o n to the example problem II I l l, y I V a l l the d e r i v a t i v e s y , y must be e v a l u a t e d a n d
...
s u b s t i t u t e d i n t o the T a y l o r series (4.14). Knowing the i n i t i a l values of y n' I II Y,+~ c o u l d be e v a l u a t e d a f t e r a time increment h. The yn , yn
...,
values of a l l the d e r i v a t i v e s c o u l d then
be c a l c u l a t e d a t
could be evaluated a f t e r the next time increment a n d so on. a r b i t r a r y functions cannot e a s i l y be formulated derivatives y l ' ,
Y l I I , etc.
a r e easy
n+l,
and y n+2 D e r i v a t i v e s of
in computer programs.
to e v a l u a t e f o r
the example
The
(4.14)
58 b u t t h i s i s not g e n e r a l l y
the case.
The E u l e r method t r u n c a t e s t h e T a y l o r
series b y e x c l u d i n g the terms a f t e r the f i r s t problem o f
h a v i n g to
evaluaate
the
d e r i v a t i v e a n d e l i m i n a t e s the
second
and
subsequent
derivatives.
Then yn+l=yn+hynl+O(h')
error
Neglecting h ' y n " / 2 t r u n c a t i o n e r r o r of
(4.17)
and order
the
h'
subsequent
(4.14)
in
i s denoted O ( h * ) .
which
e r r o r a n d r e s u l t s from one step o n l y , t h a t the g l o b a l e r r o r
terms
i.e.
This
from n to n+l.
results is
in
a
the l o c a l
I t can b e shown
accumulated over many steps becomes O(h),
i.e.
an
e r r o r of o r d e r h. S u b s t i t u t i n g the example (4.15) Yn+l=Yn+h.
i n t o the E u l e r a l g o r i t h m (4.17)
gives:
(Yn+tn)
(4.18)
The i n i t i a l c o n d i t i o n y ( O ) = l means
that
y=O
at
increment h=0.02 a n d l e t t i n g the step number n=O a t
t=O.
Choosing
t=O,
the
time
the v a l u e s f o r y
can be evaluated a t successive time increments a s follows:
y =y + h ( y o + t O ) = 1+0.02(1+0) 1 0 +t ) = 1.0200+0.02( y =y +h 2 1 Yl 1 y =y +h y +t ) = 1.0408+0.02( 3 2 2 2
= 1.0200
(4.19)
.0200+0.02)
= 1.0408
(4.20)
.040+0.04)
= 1.0624
(4.21)
= 1 .ow0
(4.22)
= 1 .lo81
(4.23)
y4 y5 etc.
Anal y t i c a1 solution
.
c
F i g . 4.8 The Euler method
The numerical solution a f t e r 5 steps g i v e s the exact a n a l y t i c a l g l o b a l e r r o r i s 0.0022,
i.e.
solution as
i s y(0.10)=1 .lo81
y(0.10)=1.1103.
two-decimal-place
t
whereas y=2e -t-1
Hence
accuracy.
the a b s o l u t e
Since
the
global
59
e r r o r of the E u l e r method i s p r o p o r t i o n a l must b e reduced
at
least
22-fold
to h,
to g a i n
i.e.
O(h),
four-decimal
<0.004. T h i s would increase the computational e f f o r t 22-fold. how the slope a t the b e g i n n i n g o f the i n t e r v a l
ynl
t h e step size h
accuracy, Fig.
i s used
4.8
i.e.
h
shows
to determine
the f u n c t i o n v a l u e a t the end o f t h e i t e r a t i o n i n the E u l e r method. The slope a t the b e g i n n i n g of solution i s a s t r a i g h t l i n e .
the i n t e r v a l
i s a l w a y s wrong
unless t h e
Thus t h e simple E u l e r method s u f f e r s from t h e
d i s a d v a n t a g e of l a c k of accuracy,
r e q u i r i n g a n extremely s m a l l step size.
The M o d i f i e d E u l e r Method
F i g 4.8 a n d the subsequent discussion suggest how the E u l e r method c a n be
improved
with
little
additional
computational
effort.
The
arithmetic
average o f the slopes a t the b e g i n n i n g a n d the end o f t h e i n t e r v a l i s used ( o n l y the slope a t the b e g i n n i n g i s used in t h e E u l e r method).
1
1
yn+l
= Yn
+ h'n
(4.24)
+',+I 2
The E u l e r a l g o r i t h m must f i r s t can
be
estimated.
Applying
be
the
s u b s t i t u t i n g y1 = x+t i n t o (4.24)
used
same
to
predict
example
(4.15)
so as
I n+l before a n d that
y
gives
Y n + l --yn+h(Yn+tn)
+ (~,+~+t,+l) 2 S u b s t i t u t i n g the E u l e r e q u a t i o n (4.18)
'n+l
yn+l
= yn+h('n +t n 1 + (yn+h(Yn+tn)
+
(4.25) gives
f o r Yn+l
tn+l
1
(4.26)
2 Using h=0.02 a n d the i n i t i a l conditions:
y =l,t
0
=O
0
(4.27) =
1 + 0.02
(1+0)
+
(1+0.02(1+0)+0.02)
(4.28)
2 = 1.0204
(4.29)
60
+
1.0204
y 2=
0.02(1 .0204+0.02)+(1.0204+0.02(1.0204+0.02)+0.04) (4.30)
2
= 1.0416
(4.31)
y5= 1.1104 c f a n a l y t i c a l s o l u t i o n 1.1103
1 in the f o u r t h decimal p l a c e .
The answer agrees to w i t h i n
a s much work was done a s in the E u l e r method b u t times more that
would h a v e been needed
with
decimal p l a c e a c c u r a c y .
I t can be shown t h a t
of
method
the
Modified
Modified Euler
Euler and
the
are
simple
methods
method
not
to
twice the
attain
the l o c a l a n d g l o b a l
and
O(h3)
Euler
that
Nearly
certainly
O(h2)
are
referred
four
errors
respectively.
often
22
The to
as
second a n d f i r s t o r d e r methods r e s p e c t i v e l y .
Runge-Kutta Methods
The Fourth-Order
Runge- K u t t a methods a r e amongst
t h e greatest a c c u r a c y p e r u n i t o f c o m p u t a t i o n a l e f f o r t .
those which p r o v i d e The development of
t h e method i s a l g e b r a i c a l l y complicated a n d i s g i v e n completely and
Hainer
(1978)
while
Gerald
(1980)
derives
the
in Stummel
Second-Order
Runge-Kutta a l g o r i t h m a n d e x p l a i n s the p r i n c i p l e s b e h i n d t h e methods. t h e Runge-Kutta
methods use the simple E u l e r method a s a f i r s t
Improved estimates a r e
then
made u s i n g p r e v i o u s estimates
time-values
time
interval
within
the
estimates i s used to c a l c u l a t e are
the
most
widely
used
yn+l.
h.
weighted
The Fourth-Order
because of
f o l l o w i n g i s a p a r t i c u l a r Fourth-Order
A
their
power
method w h i c h
and different
average
of
Runge-Kutta and
Al I
estimate.
all
the
methods
simplicity.
The
i s commonly used a n d
w h i c h i s i n c l u d e d i n the s i m u l a t i o n p r o g r a m :
Yn+l
= y + I ( kl +2k2+2k3+k4) n6
(4.32)
(4.33)
= h f ( t n + i h , yn+gkl )
(4.34)
k3
= hf(t,+ih,yn+$k2)
(4.35)
k4
= hf(tn+l,yn+k3)
(4.36)
k2
61
Again
the problem g i v e n
in
(4.14)
above
T h i s time y ( 0 . 1 )
dy/dt=f(t,y)=t+y,y(O)=l.
whereas ~ ( 0 . 1 ) was c a l c u l a t e d
is
solved
as
an
example:
i s c a l c u l a t e d in one step
i n f i v e time increments
(h=0.02)
(h=0.1)
using
the
simple a n d modified E u l e r methods above.
kl
=h(tn+yn)
=o. 1 (0+1
= 0.10000
(4.37)
k 2 =0.1 (0.05+1 .05)
= 0.11000
(4.38)
k 3 =0.1 (0.05+1 .055)
= 0.11050
(4.39) (4.40)
= 0.12105 k 4 =0.1(0.10+1.1105 1 y(0.1)=1.000+ -(0.10000+2x0.11000+2x0.11050+0.12105) 6 =1.11034
(4.41 (4.42)
T h i s agrees to f i v e decimals w i t h the a n a l y t i c a l r e s u l t a n d i l l u s t r a t e s a f u r t h e r g a i n i n accuracy w i t h less e f f o r t t h a n r e q u i r e d b y the p r e v i o u s Euler methods. method
I t s computationally
because,
while four
each step r a t h e r than two,
steps
to
than
the modified
Euler
the f u n c t i o n a r e r e q u i r e d
the steps can be many-fold
l a r g e r for
for
the same
The simple E u l e r method would h a v e r e q u i r e d of the o r d e r of 220
accuracy.
only
more e f f i c i e n t
e v a l u a t i o n s of
achieve five-decimal
one
evaluation
of
accuracy
the
y(O.1)
in
function.
The
b u t each step
efficiency
of
the
involves
Euler
and
Runge-Kutta methods can be r o u g h l y compared b y c a l c u l a t i n g the number of function
evaluations
required
for
the
p a r t i c u l a r example the Runge-Kutta
same o r d e r
Runge-Kutta 4 would be about O(h 1.
algorith
In
accuracy.
this
method i s a p p r o x i m a t e l y 50 times more
e f f i c i e n t than the simple Euler method (220/4). Fourth-Order
of
(7.35)
is
The local e r r o r term f o r the 5 O(h ) a n d the g l o b a l e r r o r
M u l t i s t e p Methods
The
simple
Euler,
Modified
s i n g l e step methods
Euler
because
they
and
Runge-Kutta
use o n l y
the
methods
are
i n f o r m a t i o n from
called
the
last
I n t h i s they have the a b i l i t y to perform the next step w i t h
step computed.
a d i f f e r e n t step size a n d a r e i d e a l f o r b e g i n n i n g the s o l u t i o n where o n l y the
initial
method
is
conditions to
utilize
polynomial
that
this
the
into
are the
available. past
approximates next
time
The
values
the
of
principle y
derivative
interval.
Most
and/or function
multistep
behind yl and
to to
methods
a
multistep
construct
a
extrapolate have
the
d i s a d v a n t a g e that they use a constant step size h to make the c o n s t r u c t i o n of the polynomial easier.
Another d i s a d v a n t a g e of m u l t i s t e p methods i s t h a t
62 several past p o i n t s a r e a v a i l a b l e a t the s t a r t . the i n i t i a l
required
whereas
only
the
initial
conditions
are
The s t a r t i n g v a l u e s a r e g e n e r a l l y c a l c u l a t e d
conditions using
a
single-step
method
such
as
a
from
Runge-Kutta
method.
F I N I TE ELEMENTS
imp1 i c i t
An
method
involving
mass
balance
across
element
boundaries
(Connor a n d Brebbia,
1976) i s p o p u l a r i n f i x e d systems b u t has not g a i n e d
much
hydraulic
popularity
in
necessitating i t e r a t i v e methods.
systems
owing
to
changing
boundaries
The steps a r e as follows:
D i v i d e body i n t o elements ( 2 o r 3-
dimensional)
Define the nodal unknowns The
flow
across
an
external
boundary
can
be
approximated
as
a
ma themat i c a l f u n c t i o n .
F i g . 4.9 F i n i t e elements
One
sets
up
simu I taneousl y
equations
giving
balance
for
each
element
and
solve
.
Boundaries for numerical methods
Conditions on a b o u n d a r y may be e i t h e r constant p o t e n t i a l water
level
or
cencentration)
i.e.
flow
across
boundary,
flow across) o r mixed (same f u n c t i o n ) . One can use pseudo p o i n t s e.g. hi-,
= h. f o r no flow
h. -h. = h . - hi+, f o r flow p e r p e n d i c u l a r to b o u n d a r y . 1-1 I S i m i l a r schemes may be used f o r concentration d e f i n i t i o n .
( o r head o r
stream1 ines
(no
63 REFERENCES Connor, J.J. and B r e b b i a , C.A. 1976. F i n i t e e l e m e n t s f o r f l u i d f l o w . Newnes-Bu t t e r w o r t h s . D e i n i n g e r , R.A., 1973. M o d e l s f o r E n v i r o n m e n t a l P o l l u t i o n C o n t r o l . Ann A r b o r Science. F r i e d , J.J., 1975. G r o u n d w a t e r P o l l u t i o n , E l s e v i e r . G e r a l d , C.F., 1980. A p p l i e d N u m e r i c a l A n a l y s i s ; 2 n d Ed. A d d i s o n VJesley. 1977. H y d r a u l i c B e h a v i o u r of E s t u a r i e s . McDonell, D.M., O ' C o n n e r , B.A., Macmi I Ian. K., 1978. I n t r o d u c t i o n to N u m e r i c a l A n a l y s i s ; Sturnel, F . a n d H a i n e r , S c o t t i s h Academic P r e s s L t d . Timoshenko, S. and Goodier, J . M . , 1951. T h e o r y of E l a s t i c i t y , McGraw H i l l .
64 CHAPTER 5
MASS BALANCE O F STORMWATER POLLUTANTS I NTRODUCT ION
Pollution
l o a d i n g s from two catchments i n Johannesburg
1986) were i n v e s t i g a t e d . a n d t h e other, stormwater down
a
Montgomery
densely
r u n o f f and d r y weather
sources
process.
Hillbrow,
One,
of
pollutants and
I t i s r e p o r t e d that
t y p e of relate
contribution pollutant
hypothesis.
The
which
loads
to
in
source
i s detected
of
CATCHMENT DESCR I PT ION
Montgomery P a r k Catchment
runoff
A
area.
al.,
catchment
comparison of
b o t h catchments n a r r o w e d understanding
1979),
this
(Green et
suburban
pollution
here.
and
is a
city
from
(Wanielista,
landuse,
unpredictability
up
flows
assisted
a n d Kemp (1982) i s borne out though.
F i g . 5.1
built
non-point
70% of the load i n u r b a n r u n o f f
Park,
and
Bradford paper
qua1 i t y
the
washoff
is
responsible f o r
it
is largely this
(1977)
attempts
contributes
indicated
by
to
to
his
Simpson
65 The
Montgomery
Johannesburg estimated
at
remainder
and
Park
catchment
10.53
measures
15000.
includes
The
developed
parks,
a
is km2
6
situated
(1053
area
is
cemetery
km
ha).
The
75% of
the
and
north-west population total
undeveloped
s o l i d waste t i p in the catchment f r o m w h i c h seepage occurs. is fairly
hilly,
slopes
system
comprises
5.1).
Rainfall
over
ranging
the
from
natural catchment
0.02
and is
recorded
a u t o g r a p h i c r a i n gauges.
Runoff
catchment outlet
the measuring element
bubble
type
i n which
recorder.
Electrical
0.15
to
m/m
artificial
the The
There i s a
The catchment
m/m.
channels at
is
and
area.
development i s housing and some commercial a n d l i g h t i n d u s t r y .
drainage
of
five
The (see
main Figure
locations
by
i s measured a t a g a u g i n g s t a t i o n a t the
conductivity of
i s a Crump the
water
weir was
with
a
recorded
continuously since March 1983. The
Hillbrow
catchment
measures
67.2
u r b a n a r e a comprising h i g h - r i s e b u i l d i n g s , a school
and
is
illustrated
in
F i g u r e 2.
ha
and
is
a
fully
developed
some h i g h d e n s i t y housing a n d The
population
i s estimated
at
12000. There are f o u r r a i n g a u g e s a n d a streamgauge for t h i s catchment. Both
catchments
have
separate
seoarate from waste sewerage systems.
F i g . 5.2
H i l l b r o w Catchment
stormwater
drainage
systems
i .e.
66
Q U A L I T Y OBSERVATIONS
Fa1lout measurement
An
attempt
was
made
to
assess
the
level
of
TDS
occurring
as
atmospheric f a l l o u t on t h e Montgomery P a r k catchment. After a p e r i o d of 28 d a y s without
any r a i n f a l l ,
down" w i t h d i s t i l l e d water,
the r a i n g a u g e s in the catchment t h i s water
b e i n g collected
in a sample bottle.
I t was found t h a t the TDS w i t h i n the f u n n e l s averaged 9.5 was
deposited
equivalent kg/ha
a
fallout
over
28
kg/ha/annum. of 0.72
onto
funnel
loading
days.
If
was
188
the
0.020
m2 i t
Montgomery was
was
Park
omitted
mg.
catchment
this
would
i n a funnel
f a l l o u t was collected
Since t h i s
deduced
that
the
was
4.75
represent with
an
62
area
location n e a r the H i l l b r o w catchment over a p e r i o d of I t was found t h a t the TDS w i t h i n the funnel
d a y s w i t h no r a i n f a l l . case
on
washout
Atmospheric
mz a t a
a r e a of
were "washed
mg
in
resulting
an
atmospheric
loading
18
in t h i s
rate
of
48
kg/ha/annum. Stormwater r u n o f f qua1 i t y analyzed
to determine
data
whether
were
collected
for
relationships could
selected
storms
and
be e s t a b l i s h e d a n d
to
o b t a i n the p r o p o r t i o n s of the d i f f e r e n t constituents. C e r t a i n researchers h a v e observed a c o r r e l a t i o n between the number o f dry
d a y s preceding
runoff
(e.g.
maintain
that
Bedient,
1980).
An could
attempt be
a
Sartor no
such
was
related
storm
et
the
1974;
relationship
made to
and
al.,
to
the
see
level
of
p o l l u t i o n of
et
exists
(e.g.
whether
number
of
Colwill
the
al.,
Whipple
peak
antecedent
1984)
dry
the
resulting
while et
concentration days.
A
=568 P where C
C
1977;
TDS
of
regression
a n a l y s i s was performed on a l l the d a t a a v a i l a b l e a n d the best f i t from a l i n e a r r e l a t i o n s h i p ,
others
al.,
resulted
viz.
+ 68N
(5.1
i s the peak TDS concentration
in mg/l
and N
1
i s the number of
P antecedent d r y d a y s w th a maximum v a l u e of 5. The c o r r e l a t i o n c o e f f i c i e n t corresponding
i s 0.12
which
i s poor.
There
i s an
increase
in
TDS
with
l e n g t h of time between storms i t appears. a
further
condition
In
classes
tes
following relationship
Cp = 1020
-
,
TDS
proposed
by
was
and
with Stall
antecedent (1974)
used
moisture and
the
emerged.
163 AMC
w i t h a c o r r e l a t i o n coefficient of 0.29. mg/l
correlated
Terstriep
(5.2) C
i s the peak TDS concentration
P a n d AMC i s the antecedent moisture c o n d i t i o n class.
in
67
Relationship between Total P o l l u t a n t Load and Runoff Volume
A
regression
volume
data
established obtained
analysis
to
determine
between
from
was
these
linear
performed
whether
on
any
parameters.
pollutant
definite In
approximations
the
all
with
relationship
cases
the
reasonably
-
load
flow
could
best
high
be
fit
was
correlation
coefficients. Considering d a t a from Montgomery P a r k alone r e s u l t s in the equation
W = 3395 with
a
+ 23V
(5.3)
correlation
coefficient
W
0.84.
of
i s -the
mass
of
transported
dissolved solids i n k g a n d V i s the volume of r u n o f f in m’. With the i n c l u s i o n of the d a t a from H i l l b r o w ,
W = 1186
+
the e q u a t i o n becomes
= 0.27V
(5.4)
w i t h a c o r r e l a t i o n coefficient of 0.90. Treated
separately,
the
relationship
between
pollution
load
and
low
flow volume i s
+ 0.55V
W = 3.24
(5.5)
w i t h a coefficient of c o r r e l a t i o n of 0.97
Chem ica I Const ituen t s
The r e s u l t s of t h e chemical analyses of the “ g r a b “
samples collected
both the H i l l b r o w a n d the Montgomery P a r k catchments a r e l i s t e d
in
i n Tables
1 to 5 . These
results
were
analyzed
quantify
to
the
presence
chlorides and bicarbonates as i t was considered t h a t anions
present
bicarbonate,
in
wind
water.
The
highest
nitrates,
anion
concentration
was
followed b y sulphates d u r i n g storm r u n o f f a n d c h l o r i d e in d r y
weather conditions. be
the
of
these were the m a j o r
blown
Sulphates a r e predominant
from
neighbouring
mine
i n Johannesburg
waste
tips
which
and
could
have
high
Sulphates also reach concentrations over 300 mg/l
s u l p h a t e concentrations.
i n water supplies f o r the area. T h e p r o p o r t i o n of n i t r a t e s , total
dissolved
weather
flow
these anions runoff
salts
analyzed. whereas
( a v e r a g e d over
is
sulphates, c h l o r i d e s a n d bicarbonates to the
much I n the
this both
lower
in
storm
runoff
l a t t e r case 68.6% of
proportion
is
catchments)
as
low
as
indicating
than
the
in
TDS
38.8%
in
probable
constituents t h a t do not n o r m a l l y apear in the d r y weather flow.
the
dry
consists the
of
storm
washoff
of
68
TABLE
5.1
I l l
OM
Results o f chemical a n a l y s e s o n r a i n f a l l a n d r u n o f f samples f o r H i l l b r o w on 03/01/85
~~
conduct1V l t Y
TDI
taman
--
ma/.
.PI 1
2Ohl 1
6.20
14.31
138
1010
0.2
12
5.1
36
20hl4
6.30
13.12
112
242
0.3
10
4.1
31
20118
6.05
11.81
134
160
0.8
10
3.0
36
2ohz3
6.00
9.69
102
770
4.1
10
3.0
24
.?Oh26
5.55
9.91
100
512
8.6
11
5.1
10
2013 1
5.85
10.88
126
232
5.3
13
5.1
24
20150
5.45
13.37
120
110
15.0
16
1.1
10
2lho1
5.90
15.43
170
102
12.9
21
8.2
27
*/A
5.55
6.60
18
2.7
4
3.8
6
-
TABLE
&gl*
Yrh
T l l
5.2
pM
63
I
Results o f chemical a n a l y s e s on r a i n f a l l a n d r u n o f f samDles f o r H i l l b r o w o n 18/01/85
ODMYCLlVltY
UIICNt.
taWn
.s/*
1811
i ~ n 2 i 6.35
46.10
346
64
tO.l
6U
37.0
122
18/2
14132
6.35
35.50
265
84
57
30.0
90
18/3
lh138
6.15
2h.50
182
380
a3
12.3
85
18/U
14144
6.35
13.40
104
130
a.1
17
10.3
S6
18/5
14hM
6.15
8.88
69
2Oh
go.1
13
8.2
20
1016
14h52
5.05
8.23
65
u4
0.3
14
7.1
14
1811
1hh54
6.20
6.29
55
92
0.1
14
6.1
12
18/8
lhh57
5.60
7.03
65
56
0.2
12
10.2
7
18/9
15Mo
5.65
6.14
u
8
0.2
11
4.1
10
18/10
15hO4
5.10
5.95
60
(1
0.2
10
6.1
7
13/11
15hO9
5.85
5.92
49
0.2
11
6.1
7
18/12
15hl6
5.10
6.58
50
Y1
0.3
10
5.1
1
b.07
P.ZO
18
8.2
6
R
*/A
\
41
69 TABLE
LwIe mark
T i n
5.3
on
R e s u l t s o f c h e m i c a l a n a l y s e s o n r a i n f a l l and r u n o f f s a m p l e s f o r M o n t g o m e r y P a r k on 07/03/83
CO n a W t l v l t Y
auspewd
***
sol12
~~tntm
-1
I
-1 1
9 1I
-1 I
chiorlam
c. c.rbmet.
-1
1
-1 1
6.25
13.26
104
95
eo. 1
10
6.3
30
5.85
10.31
86
200
0.1
16
5.2
20
so113
6.00
12.91
112
450
2.2
Ylll
6.20
22.30
166
44
1.5
RFl/l*
1.25
10.86
52
TABLE
Su1ph.t.
so1 id. mSlm
50111
roa
taken
5.4
0.4
13
6. 3
31
25
16.0
16
..
..
21
R e s u l t s o f c h e m i c a l a n a l y s e s on d r y w e a t h e r f l o w s a m p l e s from Montgomery P a r k
TOI
8usp.na.a soilas
-11
-1
I
104
10
210.0
100
34
15
1625
4
91.0
15
480
456
314
12
10.0
16
45
175
544
12
11.8
64
101
202
446
10
30.4
kz
86
1@3
320
24
b.0
18
29
not aow
262
14
0.1
25
10
620
la
2.0
40
120
not aow not
row
70 TABLE
5.5
As
one
Results of chemical analyses o n d r y weather flow samples from H i l l b r o w
would
expect,
the
concentration
weather flow i s much lower t h a n
t r a n s p o r t r a t e of sediments as well the
samples
analyzed,
averaged o n l y 27 mg/l
the
of
suspended
i n the storm r u n o f f ,
solids
in
as p o s s i b l e erosion d u r i n g storms.
suspended
solids
in
dry
indicating a higher
the
dry
weather
compared w i t h a n average of 236 mg/l
for
For flow
the storm
flows. Comparing Tables 4 a n d 5 ( d r y weather
flows)
2 and 3
Tables 1,
with
r e v e a l s t h a t the TDS concentrations a r e c o n s i d e r a b l y h i g h e r in d r y flows
than
samples
in
storm
flows.
i s 644 mg/l
while
events a r e
125 mg/l,
The
average
average
1 1 3 mg/l
TDS
values
and
of
runoff.
The base load o f TDS from Montgomery
from
refuse
tip,
which
averages
averaged over the catchment
I t was mentioned
that
the
TDS
117 m g / l ,
weather flow has about f i v e times as h i g h a
a
for
for
to
detect
a
flushing
mg/l,
Park
runoff
the
at
The p r o p o r t i o n s of n i t r J t e s than
the
were
in the stormwater
are
also
the
that as
appears or
flow runoff
the
dry
stormwater
to be
largely
150 kg/ha/annum
o b t a i n e d on
runoff. viz.
the
effect
The
high
346 mg/l
much
higher
sampled in August and October 1982 (see T a b l e
and
TDS 265
to f i n a l
in accordance w i t h
1977; Helsel et a l . ,
I n the case of
rising
making i t possible
in TDS concentration
flush"
Cordery,
runoff.
of
runoff,
decrease
indicate a "first
the f i n d i n g s of many o t h e r s (e.g.
flow
start
stages of
followed b y a time-dependent
l e v e l s of about 60 mg/l
three
( B a l l , 1984).
samples of
effect
the
indicating
160000 kg/annum
weather
weather
concentration
l i m b of the h y d r o g r a p h of 18 J a n u a r y 1985 in H i l l b r o w ,
concentrations a t the e a r l y
dry
in
the
the d r y
1979). dry
weather
weather
flow
5. 4 ) the l e v e l s of n i t r a t e
71 mar
PH (mpnl 10
18 18
160-
14
6.5
14
140-
12
0.0
12
120-
10
5.5
10
100-
8
5.0
8 8 4
2
21
Fig.
5.3
Plot of p o l l u t a n t c o n c e n t r a t i o n event on H i l l b r o w on 03/01/85
--.-.
Nllrole
45
----Suop.
-
\
Sulohale
-.-
TO9
time f o r r a i n f a l l - r u n o f f
-
HW+I+WI
VS.
Conducllvlly pn cc CMorldoo
Solids
Flowale
-.18
40-
6.1
-.18
35-
8.t
-.14
30-
5.e
-
5.t
25
20 15105-
14h25 30
Fig.
5.4
35
40
50
45
P l o t of p o l l u t a n t c o n c e n t r a t i o n event on H i l l b r o w on 18/01/85
vs.
55
15hoo
5
10
15 T h
time f o r r a i n f a l l - r u n o f f
72
a r e so h i g h as to suggest resulting
overflow
p o s s i b l e blockage o f a s a n i t a r y sewer
entering
the
stream.
It
was
observed
w i t h the
for
all
three
r u n o f f events t h a t the n i t r a t e concentrations increased over the d u r a t i o n of each
hydrograph,
reaching their
maximum on
the recession
limbs of
respective h y d r o g r a p h s . A possible e x p l a n a t i o n f o r t h i s phenomenon lighting activity w i l l course of
the storm,
r u n o f f w i t h time. these
the
i s that
increase the n i t r a t e l e v e l s in t h e r a i n f a l l d u r i n g the r e s u l t i n g i n i n c r e a s i n g n i t r a t e concentrations
There
concentrations
were
between
however
large
events.
initial
concentrations from the H i l l b r o w catchment were 0.2 the r u n o f f on 3 J a n u a r y
1985 w h i l e
and
mg/l
final
nitrate
a n d 12.9 mg/l
in
the maximum n i t r a t e concentration
in
the r u n o f f on 18 J a n u a r y 1985 d i d not exceed 0.3 concentration of 2.2 mg/l
the
in magnitudes of
differences
The
in
mg/l.
A maximum n i t r a t e
was recorded i n the r u n o f f from the
Montgomery
P a r k catchment on 7 M a r c h 1983. The recommended n i t r a t e l i m i t i n domestic water i s 6.0 mg/l There
does
w i t h a n upper l i m i t of 10.0 mg/l
not
apear
to
be
any
definite
(SABS,
1984).
time-related
decrease
increase in the l e v e l s of the o t h e r c o n s t i t u e n t s i n the r u n o f f .
or
For example
s u l p h a t e concentrations increase w i t h time i n the r u n o f f from H i l l b r o w on 3 J a n u a r y 1985 w h i l e the converse i s t r u e f o r the r u n o f f on 18 J a n u a r y 1985 from the same catchment. Plots of p o l l u t a n t concentrations w i t h time f o r
the H i l l b r o w events a r e
presented i n F i g u r e s 5.3 and 5.4.
Mass Balance for event of 18 J a n u a r y 1985 on H i l l b r o w Catchment
A
rainfall
d e p t h of
6 mm was
measured
for
t h i s event
concentration in the r a i n f a l l was 18 mg/l
(see Table 2).
expressed
as a
rainfall
0.18
kg/ha
total.
For a
in
l o a d i n g r a t e of catchment
corresponds to 4030 rn3 of
size of
rainfall
over
kg/ha/mm
67.2 the
ha
this
catchment
and
TDS
the
T h i s can a l s o be of
or
rain
depth of mass of
1.08
rainfall 73
k g of
pollutants. For t h i s event a r u n o f f volume of 475 m’ pollutant
were
estimated.
There
p o l l u t a n t from the catchment.
was
thus
a n d a t o t a l load of
121 k g of
a
48
kg
the
runoff
1.8
kg/ha
net
washoff
E x p r e s s i n g the p o l l u t a n t
i n terms o f catchment a r e a a n d r a i n f a l l g i v e s 0.30
of
load i n
kg/ha/mm
or
of
total. The
sources
of
these
p o l l u t a n t s have
densely developed a r e a l i k e H i l l b r o w , of deposits
from
wind
and
w h i c h i s u s u a l l y present.
motor
not
the most
vehicles
and
been
identified,
but
in
a
l i k e l y sources a r e washoff s o l u b l e f r a c t i o n s of
litter
73
Since the r u n o f f was o n l y 12% of the r a i n f a l l experienced a
net
washoff
of
pollutants,
with
washed o f f than was deposited b y the r a i n f a l l ,
and
the catchment
66% more
pollutant
still being
i t i s conceivable t h a t
this
washoff may reach even h i g h e r percentages f o r events where the p r o p o r t i o n of
runoff
rainfall
to
is
greater.
Such
events
would
result
h a a v i n g a greater depth of h i g h e r i n t e n s i t y r a i n f a l l .
It
from
storms
i s also p o s s i b l e loss of moisture,
t h a t i n p u t d u r i n g one storm i s stored and released a f t e r to be washed o f f d u r i n g a subsequent storm.
A
p l o t of
hydrograph,
p o l l u t o g r a p h a n d TDS v a r i a t i o n
with
time
for
t h i s event i s presented i n F i g u r e 5.5.
Mass Balance for event of 7 March 1983 on Montgomery Park Catchment
On 7 March 1983 a t o t a l depth of 14 mm of the Montgomery P a r k catchment. exceeding f i v e concentration Hillbrow
on
days of
of
the
no
18 October
so
rain,
rainfall 1985
is
it
is
much
when
loading
rate
p o l l u t a n t s deposited
of
on
0.52
this
only
two
was
surprising than
recorded on
dry
that
that
days
km’
The
the
in
passed.
The
r e s u l t i n g in a
total
mass
of
was
thus
7666
catchment
TDS
measured
had
(see Table 5.31,
kg/ha/mm.
10.53
not
higher
measured TDS of the r a i n f a l l was 52 mg/l rainfall
rainfall
T h i s event was preceded b y a time p e r i o d
soluble kg
in
147420 m3 of r a i n f a l l . A r u n o f f volume of 5508 m3 w i t h a corresponding c u m u l a t i v e r u n o f f
of 1479 k g of dissolved p o l l u t a n t s was measured. pollutant
load
can
be
represents o n l y 4% of
expressed the
deposited b y the r a i n f a l l . a
net
gain
of
6187
kg
as
rainfall
0.10
and
kg/ha/mm.
pollutant,
or
k g / h a o r 0.42
pollutant
pollutant
net
deposition
of
( l o s s of
that
occurred
m a t t e r ) from
this
volume
19% of
that
deposited.
kg/ha/mm
catchment w h i l e net washoff occurred i n the densely Since there i s a deposit
runoff
therefore experienced
81% of
corresponds to a net g a i n of 5.87 i.e.
The
the TDS washed o f f
I n t h i s case the catchment of
load
I n terms of r a i n f a l l
in
of the
This
rain-borne peri-urban
developed catchment.
r a i n as
indicated b y
the
Montgomery P a r k catchment i t can be expected t h a t a s i m i l a r deposit would occur in H i l l b r o w , so the l i t t e r load must be h i g h e r . Once
again
it
is
p o l l u t a n t s washed o f f
difficult
to
attempt
t h i s catchment.
to
identify
the
sources
of
R e f e r r i n g to Tables 5.2
a n d 5.3
it
w i l l be seen that n i t r a t e levels in the r u n o f f a r e h i g h e r f o r t h i s catchment than
for
possible
the
Hillbrow
washoff
fertilizers.
This
of seems
catchment
decaying a
on
18
vegetation,
reasonable
January animal
deduction
as
1985,
signifying
faeces the
and
Montgomery
the
garden Park
74
r--,/-• --.----.
L*'
14hOO Fig.
16h00 5.5
lEhoO TIME
Hydrograph, p o l l u t o g r a p h a n d TDS f o r H i l l b r o w f o r event on 18/01/85
I 1,20
E 0,90 "
-
/--'
-
E
W
I-
U
d 0,60
s
s
-
LL
0,30
I
15h00
17h00
19hOO
2lhoo
23h0
TIME Fig.
5.6
Hydrograph, p o l l u t o g r a p h a n d TDS f o r Montgomery P a r k f o r event on 07/03/83
75
catchment consists of p r e d o m i n a n t l y s u b u r b a n r e s i d e n t i a l developments w i t h gardens.
Another
ground
(either
minerals).
source
in Montgomery
previously
deposited
I t i s noted that
Park
by
c o u l d be
rain
leachate from
seeping
or
in
the
from
soil
the p r o p o r t i o n of sulphates a n d carbonates i n
r u n o f f i s s i m i l a r to the r a i n , b u t c h l o r i d e s increase. It
appears
that
sulphates
d i f f e r e n t land-uses,
and
chlorides
are
the respective levels b e i n g of
unaffected
by
the
two
the same o r d e r f o r b o t h
catchments which also i n d i c a t e s they may be a i r - b o r n e
i n t o the catchment.
I t has also been observed that there a r e ( i l l e g a l ) discharges of
industrial
wastes i n t o the separate stormwater system in H i l l b r o w . The
hydrograph,
pollutograph
TDS
and
variation
with
time
for
this
event a r e i l l u s t r a t e d i n F i g u r e 5.6. I n the mass b a l a n c e of p o l l u t a n t s o u t l i n e d above i n both
the H i l l b r o w
pollutant runoff.
load
in
and
the
To determine
runoff
whether
g a i n of p o l l u t a n t s i t
to
the
i s also necessary
the
rainfall
to
causing
the that
the TDS concentration
know
TDS
levels
in
the r a i n f a l l
(Montgomery P a r k ) a n d 78 mg/l
concentration of 118 mg/l
relate
of
In the present p r o j e c t r a i n f a l l q u a l i t y
the r a i n f a l l as well a s the r u n o f f .
( H i l l b r o w ) , 52 mg/l
in
load
to
the catchment h a s experienced a net loss o r
was o n l y analyzed f o r three events, mg/l
i t was found p o s s i b l e
the Montgomery P a r k catchments
being
18
( H i l l b r o w ) . A TDS
i n r a i n f a l l was observed b y Madisha
(1983) a t a
location near the H i l l b r o w catchment. Assuming a r a i n f a l l l o a d i n g r a t e of 0.52 kg/ha/mm l o a d i n g r a t e of 0.71
and an average r a i n f a l l total
weight
computed f o r
of
dissolved
twelve
solids
deposited
rainfall-runoff
on
events f o r
e l e c t r i c a l c o n d u c t i v i t y d a t a were a v a i l a b l e .
f o r Montgomery P a r k
kg/ha/mm the
for
two
which
both
Hillbrow,
the
catchments
was
discharge
and
These r e s u l t s a r e presented in
Table 5.6. I t can be deduced from Table 5.6
runoff
expressed
in
terms
of
rainfall
Montgomery P a r k and 1.54 kg/ha/mm i s i n accordance Lanyon, of
with
1980; Mikalsen,
stormwater
is
the
is
from
the average 0.40
pollution
kg/ha/mm
of
of r a i n f a l l f o r H i l l b r o w .
f i n d i n g s of
1984), v i z .
higher
that
that
other
researchers
i n general
commercial
load of
rainfall
for
This f i n d i n g
(e.g.
Polls and
the level of p o l l u t i o n
and
downtown
land-use
developments than from r e s i d e n t i a l developments. Another
i n t e r e s t i n g deduction from Table 6 i s t h a t
deposited on the Montgomery P a r k catchment t h a t
more p o l l u t a n t
was
was washed o f f f o r
five
out of the seven events w h i l e t h i s was o n l y the case f o r events in the H i l l b r o w catchment.
two out of
five
The h i g h e r percentage imperviousness in
the H i l l b r o w catchment i s p o s s i b l y the reason f o r t h i s phenomenon.
76
TABLE
Comparison of p o l l u t i o n loads i n r a i n f a l l a n d r u n o f f w i t h r a i n f a l l depths
5.6
wation and
lainfall
U l p h t of
U i p h t 01
Ratio O f
dapth
dap0alt.d
106 In
runofr
load in
106
rumrr
I M d to
wnorr
data
?Oi I U t l O l
rainfall (-1
-
tho1
Ihal
I hg/h./rl
laad
mntwuw Pa~h 01/03/03
14
7666
1479
0.19
W/I2/01
11
7118
7356
1.03
0.54
12/12/83
17
9309
13086
1.41
0.73
21/01/85
46
25100
23451
0.93
0.40
30/10/85
55
30116
15872
0.53
0.27
0.10
3 I / 10185
24
13141
7680
0.59
0.30
0111 1/85
67
36607
26391
0.72
0.37
-
Avarmpa 10s for
ni I IbIOr
71 -/I
nlllb-
13/09/011
1
48
247
5.15
3.60
16/09/04
14
669
217
0.32
0.21
H)/lO/04
2
96
01
0.ou
0.60
21/10/04
1
48
193
4.02
2.07
18/01/85
6
73
121
1.66
0.30
-
r e l a t i o n s h i p s between d e p t h o r r a i n f a l I a n d
H a v i n g established of
pollutant
compu ted
washed
off
a
catchment,
precipitation
of
catchment
763
or
1190
loads
amount can
be
example
and
1981),
assuming a
the
total
mean
mass
of
will
be of the o r d e r of 80000 k g p e r
For
the
Montgomery
loading
will
be a p p r o x i m a t e l y
kg/ha/annum.
amount of a n n u a l p o l l u t a n t
for
(Adamson,
mm
p o l l u t a n t s washed o f f t h i s catchment annum
pollutant
.
Considering the H i l l b r o w annual
annual
Park
catchment
the
320 000 k g o r
305 kg/ha/annum. Assuming a n average d r y weather flow of 0.0015 m’/s H i l l b r o w a n d 310 d r y d a y s p e r annum flow
volume
of
a p p r o x i m a t e l y 40300 m’.
results
i n an
This
results
or
130 m’/day
annual in
dry
an
in
weather
annual
dry
weather p o l l u t a n t load of a p p r o x i m a t e l y 22100 k g o r 330 kg/ha/annum.
The
average d r y weather flow
i n Montgomery P a r k
the
annual
dry
off
which
corresponds
kg/ha/annum.
weather
flow to
a
this
total
catchment pollutant
i s about 0.004 is
due to d i r e c t stormwater r u n o f f i s about 3.6
approximately
load
Therefore i t can be deduced t h a t
m’/s
of
60500
so
110000 m’ kg
or
57
the a n n u a l p o l l u t a n t load
times t h a t due to d r y weather
77
flow
for
the
Hillbrow
catchment
and
about
5.3
times
that
due
to
dry
sources
are
weather flow f o r the Montgomery P a r k catchment. The
pollutant
loading
rates
derived
from
the
different
summarized i n Table 5.7.
TABLE
5.7
Summary of dissolved loads i n kg/ha/mm
CONCLUSIONS
Despite the l i m i t e d monitoring,
the f o l l o w i n g
tentative
conclusions c a n
be drawn. The t o t a l dissolved p o l l u t i o n from H i l l b r o w ,
a densely
load i n stormwater
a n d surface
populated c i t y a r e a i s about
which
i s about 3 times as great
Park.
The m a j o r i t y
from
a
s u b u r b a n catchment,
(70%-80%) occurs d u r i n g storm r u n o f f
Only about 430 kg/ha/annum
drainage
15000 kg/ha/annum Montgomery
in both
cases.
f a l l s o r i s washed out of the atmosphere.
The
m a j o r i t y i s therefore l i t t e r and from vehicles in the case o f H i l l b r o w ,
and
decaying vegetable matter o r leachate from Montgomery P a r k . There i s a net g a i n of p o l l u t a n t s from H i l l b r o w b u t in Montgomery P a r k the t o t a l washoff atmosphere.
i s about
the same o r d e r as the t o t a l deposited from
A s a l a r g e p r o p o r t i o n of r a i n seeps i n t o the ground,
store TDS to be released i n f u t u r e r u n o f f .
the
i t could
There i s a net g a i n of n i t r a t e
in Montgomery P a r k however.
Dry
weather
concentrations
seepage from a p o l l u t e d l a n d f i l l 1984)
and
illegal
waste
are
higher
in the case of
discharge
in
Hillbrow.
r u n o f f increase w i t h number of p r e v i o u s d r y sweeping would reduce loads.
in
both
catchments,
Montgomery
Park,
Concentrations
days,
due
signifying
to
(Ball,
in
storm
that
street
78
The m a j o r i t y o f d i s s o l v e d s a l t s i s washed o f f d u r i n g the r i s i n g the storms except n i t r a t e s w h i c h e x h i b i t a l a g . alternativley this.
the i n f l u e n c e of atmospheric
l i m b of
Release from the g r o u n d o r
l i g h t i n g could
Before p r e d i c t i o n b y m o d e l l i n g c a n be u n d e r t a k e n ,
b e the cause of intensive
further
i n v e s t i g a t i o n w i l l be r e q u i r e d .
REFERENCES
Adamson, P.T., 1981. Southern A f r i c a n Storm R a i n f a l l . D i r e c t o r a t e o f Water A f f a i r s , Department o f Environment A f f a i r s , Technical Report TR 102. B a l l , J.M., 1984. D e g r a d a t i o n o f g r o u n d a n d s u r f a c e w a t e r q u a l i t y in r e l a t i o n to a s a n i t a r y l a n d f i l l . MSc(Eng) D i s s e r t a t i o n , U n i v e r s i t y o f t h e W i twatersrand. Bedient, P.B., Lambert, J.L. and Springer, N.K., 1980. Stormwater p o l l u t a n t load-runoff r e l a t i o n s h i p s . Jnl. Water P o l l u t i o n Control Fed., 52, 2396-2404. B r a d f o r d , W.J., 1977. U r b a n stormwater p o l l u t a n t l o a d i n g s : a s t a t i s t i c a l summary t h r o u g h 1972. J n l . Water P o l l u t i o n Control Fed., 49, 613-622. C o l w i l l , D.M., Peters, C.J. a n d P e r r y , R., 1984. Water q u a l i t y o f motorway runoff. Transport and Road Research Laboratory, Dept. of the Environment a n d Dept. o f T r a n s p o r t , TRRL Supplementary Report No. 823. Cordery, I., 1977. Q u a l i t y c h a r a c t e r i s t i c s o f u r b a n stormwater in Sydney, A u s t r a l i a . Water Resources Research, 13, 197-202 Green, I.R.A., Stephenson, D. a n d Lambourne, J.J., 1986. Stormwater p o l l u t i o n a n a l y s i s . U r b a n H y d r o l o g y a n d D r a i n a g e Research Contract, Water Research Commission Report No. 115/10/86. Helsel, D.R., Kim, J.I., G r i z z a r d , T.J., R a n d a l l , C.W. a n d Hoehn, R.C., 1979. L a n d use i n f l u e n c e s o n m e t a l s in storm d r a i n a g e . Jnl. Water P o l l u t i o n Control Fed., 51, 709-717. Madisha, J.L., 1983. I n v e s t i g a t i o n p r o j e c t o n u r b a n stormwater p o l l u t i o n in Braamfontein. Department o f Civil Engineering, University of the W i twatersrand. Mikalsen, K.T., 1984. Assessment of water q u a l i t y changes r e s u l t i n g from urbanization, a g r i c u l t u r e and commercial f o r e s t r y in the s t a t e of Georgia, U.S.A. Proceedings o f t h e T h i r d I n t . Conf. "Urban Storm Drainage," Goteborg, Sweden, 801-810. 1980. P o l l u t a n t c o n c e n t r a t i o n s from hogeneous Pol Is, I . a n d L a n y o n , R., l a n d uses. Jnl. Environmental Eng. Div., ASCE, 106, 69-80. S a r t o r , J.D., Boyd, G.B. a n d A g a r d y , F.J., 1974. Water p o l l u t i o n aspects of street s u r f a c e contaminants. Jnl. Water P o l l u t i o n Control Fed., 46, 458-467. Simpson, D.E. a n d Kemp, P.H., 1982. Q u a l i t y a n d q u a n t i t y o f stormwater r u n o f f from a commercial land-use catchment in N a t a l , South A f r i c a . Water Sci. Tech., 14, 323-38. South A f r i c a n Bureau o f S t a n d a r d s (SABS), 1984. S p e c i f i c a t i o n f o r w a t e r f o r domestic supplies. SABS 241. Stephenson, D. and Green, I.R.A., 1987. Mass b a l a n c e o f stormwater p o l l u t a n t s . Water S.A. T e r s t r i e p , M.L. a n d S t a l l , J.B., 1974. The I l l i n o i s u r b a n d r a i n a g e a r e a s i m u l a t o r , ILLUDAS. I l l i n o i s State Water Survey, U r b a n a , B u l l e t i n 58. Wanielista, M.P., 1979. Stormwater Management Q u a n t i t y a n d Q u a l i t y . Ann A r b o r Science P u b l i s h e r s I n c . M i c h i g a n . Whipple, W., Hunter, J.V. a n d Yu, S.L., 1977. E f f e c t s o f storm f r e q u e n c y on p o l l u t i o n from u r b a n r u n o f f . Jnl. Water P o l l u t i o n Control Fed., 49, 2243-2248.
79
CHAPTER 6
OPT I MUM ALLOCAT ION OF WATER RESOURCES SUBJECT TO QUAL I TY CONSTRA I NTS I NTROOUCT ION
We a r e r e a c h i n g economic
benefit
an
cost
age of
compromise.
analysis,
1960's
The
1970's
the
saw
h a i l e d the e r a
the
appearance
of
of the
environmentalists and i d e a l i s t s a n d the 1980's appear to be p r o d u c i n g more realistic
planners.
Multiple
objectives
including
economic,
sociological,
p o l i t i c a l and environmental w i l l be considered b u t h o p e f u l l y perspectives.
High i d e a l s can o n l y r e s u l t
may h a v e detrimental The w a t e r i n g
down
effects
of
i n slow-down
development
e n g i n e e r i n g projects
stagnate the engineering profess ions
on
industry
and
of to
of
i n the correct
growth and t h i s
underdeveloped countries. meet
high
i d e a l s can
lose v a l u a b l e b r a i n power
also
to o t h e r
.
Water resources a r e regarded b y many as a never d i m i n i s h i n g asset. account mined.
of
annual
This i s a
replenishment fallacy,
basin deterioration, and
more
the
usage occurs
and poorer q u a l i t y water
for
it
apart
n a t u r e of so
is
there
assumed
from
the will
the
over-exploitation
resource can be g r e a t e r
i n our r i v e r s .
resource
cannot
and
be a l t e r e d .
waste
water
New g r o w t h can o n l y
On be
drainage
As
more
discharges be met from
these r i v e r s o r from water f u r t h e r a f i e l d i f surface waters a r e to be r e l i e d on. We can often not a f f o r d the l u x u r y of p u r e mountain waters p i p e d from many hundreds of kilometres away. water to acceptable s t a n d a r d s and n u t r i e n t removal f o r a l l uses. obtained
from
different
which quality
i n some cases.
i s particularly high.
containers
while
poorer
i n d u s t r i a l purposes. quality
water
a r e predominately water.
supplies.
be necessary
This
will
be
purify
waste
The cost of d e m i n e r a l i z a t i o n
quality
i s t r a n s p o r t e d separately water
Although separate expensive
h i g h density
to
T h i s cost may not be w a r r a n t e d
I n many countries p o t a b l e water
domestic and of
will
It
there
residential
i s used piped may
and
for
water be
or
general supplies
some
could j u s t i f y
areas high
Other areas r e q u i r i n g lower q u a l i t y c o u l d receive separate is particularly
the case
i n m i n i n g areas
in South
Africa
where these studies were i n i t i a t e d . P a r a l l e l studies a r e i n v e s t i g a t i n g the cost o f d e m i n e r a l i z a t i o n and h i g h q u a l i t y p u r i f i c a t i o n b u t that i s o n l y one of the options.
The others a r e to
seek f r e s h surface o r groundwater resources f u r t h e r away, poorer q u a l i t y of i n d i c a t e d here.
local resources o r to a l l o c a t e i n
to make do w i t h
an o p t i m a l
manner
as
80
Methods of research c o u l d e i t h e r adopt the g l o b a l systems approached o r a more s i m p l i s t i c b u t p e r h a p s easier
understood methodology.
number of sophisticated techniques f o r o p t i m i z a t i o n of water
systems
readily,
subject
to
constraints.
in fact sometimes too r e a d i l y ,
these methods may from a computer politicians.
form
follow
ideal
program
the
objectives.
subject
i s not easy
Simple g r a p h i c a l
to describe a n d present. to
various
The
There a r e a
linear and nonlinear use
of
computers
adopted b y eager students. matter
for
to e x p l a i n
dissertations
Whereas
the o u t p u t
to r e g i o n a l p l a n n e r s a n d
displays or tabular
results
a r e much easier
Simple h a n d c a l c u l a t i o n s o f t e n enable the a n a l y s t
alternatives
and
in m i n d
bear
marginal
costs
or
multiple
By f o l l o w i n g the e n t i r e p l a n n i n g process t h r o u g h the a n a l y s t
also able
to c l a r i f y
is
a l t e r n a t i v e objectives a n d
t h i s approach which i s adopted
i n the s i m p l i s t i c
allocate
priorities.
s t u d y below
It
is is
(Stephenson,
1982).
THE SYSTEM
Consider the t r a n s p o r t a t i o n problem depicted sources of
water a r e a v a i l a b l e
resources
indicated
as
10,
(A,
20
i n Fig.
6.1.
A number of
B a n d C ) a n d they each have
and
15
megalitres
per
day
limited
(Ml/day),
r e s p e c t i v e l y . T h e t o t a l a v a i l a b i l i t y may exceed the requirements of
demand
of users W,
in t h i s
example.
X,
and Y
The cost of
though, transport
a n d a g a i n i n the t r a n s p o r t a t i o n
which r e q u i r e 8,
12 a n d 16 M l / d a y
a l o n g each r o u t e i s i n d i c a t e d i n F i g . t a b l e a u Table 6 . 2 .
A s f a r as
6.1,
i t has been
described the system i s a simple t r a n s p o r t a t i o n example w h i c h could e a s i l y be optimized,
i.e.
the flow
a l o n g each r o u t e to r e s u l t
t r a n s p o r t a t i o n system c o u l d be d e r i v e d r e l a t i v e l y e a s i l y .
F i g . 6.1
Supply requirements a n d a l t e r n a t i v e s
i n a minimum t o t a l
81
The s i t u a t i o n
i s complicated b y the Fact t h a t
have c e r t a i n water q u a l i t y requirements.
TDS ( t o t a l dissolved s o l i d s ) i s in mg/l
i m p u r i t y , e.g. of
W,
X
and Y
respectively.
are
that
the TDS s h a l l
not
a n d the requirements
exceed
Note t h a t Ml/day m u l t i p l i e d b y mg/l
11
10,
8 mg/l
and
g i v e s k g / d a y of s a l t s ,
The TDS of the source waters from A,
mass flow rate. and 8 mg/l
the i n d i v i d u a l consumers
The measurements of the r e l e v a n t
B a n d C a r e 6,
a
11
respectively.
T h e lower l i m i t on TDS may be achieved b l e n d i n g d i f f e r e n t sources o r ,
i f economic,
the resources.
The l a t t e r option,
assuming
source
any
by
selecting
correct
sources,
p u r i f y i n g p a r t o r a l l of a n y of
namely p u r i f i c a t i o n ,
i s p u r i f i e d and adding
could be h a n d l e d b y
the cost
to
the conveyance
cost. Often the r e l a t i o n s h i p between cost of p u r i f i c a t i o n a n d r a t e of nonlinear
such as
w i t h desalination
be
reverse
becomes more complex.
I n such case,
possible
1978).
Alternatively
employed to seek a n optimum.
I f only par t
(Stephenson,
need be p u r i f i e d ,
separable a
osmosis
and
flow
the
is
system
programming methods a r e gradient
method
may
be
( a v a r i a b l e p a r t ) of a source
the d e s c r i p t i v e equations a r e more numerous b u t
linear
programming methods may be employed to optimize the system. I n the present example
(Fig.6.1)
the resource a n d demand c o n s t r a i n t s
may also be w r i t t e n a s l i n e a r c o n s t r a i n t s :
Demand
aAW + aBW + aCW= Q~~ + aBX + aCX = aAy + aBy + aCY =
8 12 16
The q u a l i t y c o n s t r a i n t s may be w r i t t e n : 6QAW + l l Q B W + 8QCW 1 1 0 x
+ 6QAy + 6QAx
8
llQBx
+ 8QCX 511 x 12,
llQBy
+ 8QBx
5
8 x 16
Provided there i s a feasible solution the set of m be analyzed b y l i n e a r programming methods. and n
the number
of
demand p o i n t s .
m
+
2n c o n s t r a i n t s c o u l d
i s the
Alternatively
the
number of
sources
availability
and
82
demand c o n s t r a i n t s c o u l d be considered i n a t r a n s p o r t a t i o n m a t r i x qua1 i t y c o n s t r a i n t s h a n d l e d separately of l i n e a r programmes ( D a n t z i g , This
is
u s i n g t h e p r i n c i p l e of decomposition
1963; Stephenson,
based
described
below.
additional
on
the
c o n s t r a i n t s on the d i s t r i b u t i o n s .
1969). A t h i r d method i s
transportation
computers
a n d more
interaction
between
method
with
The r e s u l t i n g advantages o v e r
the l i n e a r programming a l t e r n a t i v e s a r e s i m p l i c i t y , for
a n d the
the
rapidity,
no necessity
water
resources
planner
linear
programming
a n d the system. It
is
assumed
the
reader
is
familiar
with
and
t r a n s p o r t a t ion programming techniques.
SOLUTION METHOD
The d a t a a r e a r r a n g e d in a t a b l e a u s i m i l a r (Table
6.1).
Each
l a b e l led "slack"
demand
is
represented
by
to a
a
transportation row,
each source and there
i s an additional
column
including
A
since resources exceed demand here.
tableau
column
a
labelled "artificial
slack"
since the i n i t i a l assignment may not s a t i s f y q u a l i t y c o n s t r a i n t s w i t h o u t I n f a c t , a s there a r e three a d d i t i o n a l c o n s t r a i n t s , three a d d i t i o n a l of
the
artificial
v a r i a b l e s in the f i n a l slack
flow
variables
necessarily so f o r s a l t mass flow is
not
necessary
to
assign
should
artificial
cost
it.
one would expect u p to
programmme. be
s l a c k s since they
row
represents
The cost very
coefficients
large,
are of
the
but type.
not It
the
following
eliminate
artificial
coefficients
in
method.
TABLE 6.1
Transportation slack
X
Y
matrix
with
shuffling
to
83 An
initial
satisfied flow
-
i s made i n Table 6.1
assignment
r u l e (Loomba,
1964).
At each assignment,
water flow and
l i m i t s the number,
salt
balance.
i n b l o c k CY,
but
u s i n g the
Northwest corner
two types of c o n s t r a i n t must be Thus
i n most
blocks,
AW,
e.g.
TDS b a l a n c e l i m i t s flow
2.25
to
( a flow of 6 would otherwise have been assigned to t h i s b l o c k ) .
Ml/day
The f i r s t step a f t e r m a k i n g the i n i t i a l assignment should be to evacuate flows
from
the
artificial
slack
column.
s a t i s f y flow c o n s t r a i n t s and TDS Ml/day
corner
re-allocation,
6.1,
Thus 8/48
in k g / d a y .
each
re-assignment
that
indicates 8 Ml/day
r e s u l t i n g in TDS flow of 48 k g / d a y .
each
Note Observe
the
water
two
of
a
closed
and select
re-allocations
circuit
the lowest are
at
source
whether
water
to
evacuate
or
TDS o f
TDS
limit
allocation. block
in
a n d the
I t i s r e l a t i v e l y easy to check
p e r m i s s i b l e flow
necessary
a
must
flows
/
a r e w r i t t e n i n the bottom l e f t of each b l o c k followed b y
TDS flow mg/l
limits.
6 at
the
I n Table
LY.
a
feasible
(non o p t i m a l ) solution r e s u l t s . Now the o p t i m i z a t i o n proceeds a s f o r any t r a n s p o r t a t i o n exercise, for
the
column
additional and
row
constraint
cost
on
coefficient
vacant block w i t h a c t u a l costs
it
each and
re-al location. comparing
i s decided
to
After
calculating
implied
costs
in
each
re-allocate
to
block
BY.
Although flow consideration would l i m i t the a l l o c a t i o n to 1 M l / d a y , c o n s t r a i n t s l i m i t i t to 0.4 M l / d a y . eliminated.
Then a l l the slack i n TDS f o r
Table 6 . 2 r e s u l t s .
TABLE 6.2 T r a n s p o r t a t i o n m a t r i x step two
except
quality row Y
is
04 I t w i l l be observed t h a t there i s more than one p o s s i b l e cost coefficient f o r some blocks,
depending on which block i s used as a p i v o t .
This arises
because the number of occupied blocks i s g r e a t e r t h a n n + m - 1 a n d m a r e the number of a r t i f i c i a l slack column.
rows and columns
i n the t a b l e a u
where n
excluding
the
Each possible combination should be i n v e s t i g a t e d .
Where the p i v o t sequence AW,
AX,
B X , B Y , BS, CY i s used,
the maximum
difference between i m p l i e d cost a n d a c t u a l cost c o e f f i c i e n t appears i n block
C X , and i s 8 v s 4
( T a b l e 6.3).
It will
a r o u n d the closed p a t h CX-AX-AY-CY-CX 1.4
and then 0.9
ml/day
can
be found
t h a t b y proceeding f i r s t
a n d then CX-EX-BY-CY-CX
be a l l o c a t e d
to
CX
block
without
that f i r s t violating
flow and q u a l i t y c o n s t r a i n t s .
TABLE 6. 3
T r a n s p o r t a t i o n m a t r i x optimized
Dunand :
Subsequent improvement,
calculations i.e.
will
reveal
is
no
further
cost
no more i m p l i e d costs exceed a c t u a l costs once new cost
coefficients a r e ca Icu I a ted
.
The optimum p l a n , w h i c h s a t i s f i e s q u a l i t y F i g . 6.2.
there
requirements,
i s indicated
in
85
D iscussionl All
water
poorer
users do
quality
is
not
require
tolerable,
the
allocation
same of
high
quality
alternative
water.
sources
Where
may
be
considered. O v e r a l l economy of p u r i f i c a t i o n a n d d i s t r i b u t i o n r e s u l t .
F i g . 6.2
Optimum a l l o c a t i o n subject to c o n s t r a i n t s
A technique f o r a l l o c a t i n g water resources b y a form of programming simple and
has not
been
demonstrated
computer orientated.
with The
an
example.
transportation
The
technique
resulting distribution
system
is is
depicted a n d can r e a d i l y be updated as q u a l i t i e s of the sources v a r y .
T h e method distribution
i s therefore of use f o r management
systems
as
well
as
design.
In
and o p e r a t i o n of
fact
even
more
so,
water since
construction costs a r e not as a r u l e e a s i l y l i n e a r i z e d whereas pumping costs a r e g e n e r a l l y p r o p o r t i o n a l t o the r a t e of flow.
L I NEAR PROGRAMM I NG SOLUT ION
The p r e v i o u s sections high1 ighted the shortcomings of the t r a n s p o r t a t i o n and
transportation
extended
techniques.
The
techniques
onerous simp1 i f y i n g assumptions be made about parameters. an approach which do not model
require
They
that
thus o f f e r
the d i s t r i b u t i o n comprehensively
enough.
The most severe shortcomings are: a ) Qua1i t y
constraints
cannot
be
considered
in
Transportation
Programming.
b ) Optimization
of
the
amount
of
water
to
be
desalinated
and
hence
blended cannot be achieved in e i t h e r of the T r a n s p o r t a t i o n techniques.
86 c)
Non-Linear
cost f u n c t i o n s h a v e to be a p p r o x i m a t e d b y
l i n e a r functions
in both techniques.
Linear
programming
shortcomings can
techniques
be overcome.
In
provide linear
means
whereby
programming
q u a n t i t y c o n s t r a i n t s , a n d any o t h e r l i n e a r c o n s t r a i n t s , to
yield
an
optimum
solution.
However,
neither
al I
both
these
quality
and
can be m a n i p u l a t e d
a
non-linear
objective
f u n c t i o n n o r c o n s t r a i n t s c a n be used unless they a r e converted to a
linear
or
linear
piecewise
linear
form.
This
can
be
achieved
by
using
programming in c o n j u n c t i o n w i t h separable programming. This section describes how the d i s t r i b u t i o n problem i s transformed a
representative
mathematical
model
suitable
for
analysis
using
into
linear
programming (Grosman, 1981).
The sets of d a t a r e q u i r e d a r e summarized below;
Qua1i ty
Quantity
Water Board
500
mg/P
100.0 Me/d
Groundwater
600
mg/e
11.5 Me/d
Wastewater
1750 mg/l
Sources :-
Desalinated wastewater
Variable
175 mg/P
Variable
Demands:Transfer
1750 mg/e
7.0
Me/d
System 1
700 mg/e
9.5
Me/d
System 2
700 mg/e
0.7 Me/d
System 3
700 mg/e
0.5
Waste ( S l a c k )
1750 mg/P
The water b o a r d s u p p l y i s assumed o t h e r sources, b e used.
this is high,
Me/d
unused
to be 100 Me/d.
I n r e l a t i o n to the
a n d consequently o n l y a p o r t i o n
thereof
may
The p o r t i o n to be used w i l l b e optimized.
Wastewater to y i e l d a n
y i e l d s 10 Me/d,
improved qua1 i t y
This v a r i a b l e portion
i s an
of which a v a r i a b l e p o r t i o n i s d e s a l i n a t e d available unknown
from
and
the d e s a l i n a t e d
hence
it
should
wastewater.
be optimized.
The recovery r a t i o n of feed flow to product flow in a d e s a l i n a t i o n p l a n t 0,69 f o r t h i s case. U U
+ D /0.69 + 1.45 D
Expressing the above i n mathematical terms,
= 10
= 10
where U = Used MSW i n Me/d
D = Desalinated Wastewater in MP/d
(6.10)
is
87
Two
new
variables
(U
and
D)
and
a
new
constraint
Eq.
6.10
are
i n t r o d u c e d to c a t e r f o r t h e d e s a l i n a t i o n of a v a r i a b l e p e r c e n t a g e o f waste. U was assumed t o b e 7.5 Mk‘/d,
D w a s 1.73 Me/d.
The
m a g n i t u d e o f t h e s l a c k a l l o c a t i o n t o w a s t e (W) w i l l c o n s e q u e n t l y v a r y .
h e n c e f r o m Eq.
The
v a r i a t i o n i s a c c o r d i n g to E q . 6.11
6.10,
where the sources a r e b a l a n c e d a g a i n s t
the demands:
W + 7.0 + 9.5 + 0.7 + 0.5
-
D = (10
but
U ) 0.69
hence W = 93.8 + U + ( 1 0 W = 100.7 + 0.31
100 + 11.5 + U + D
=
f r o m Eq. 6.10 -
(6.11)
U ) 0.69
U
(6.12)
From a T r a n s p o r t a t i o n E x t e n d e d a n a l y s i s U w a s 7.5 Mt/d
was o n l y
with
a
1
maximum
hence W
MP/d, value
10
of
was
4.03
Me/d,
MP/d.
(that
Me/d,
However,
is
a n d t h e 100 U varies
without
now
desalination).
T h e r e f o r e from Eq. 6.12 W L 103.8 Me/d
(6.13)
The a c c e p t a b l e q u a l i t y assumed f o r t h e System 1 (S), System 2 ( V ) a n d System 3 ( M ) i s s t i l l 700 m g / Q . T h e n e x t s e c t i o n r e v i e w s a n a n a l y s i s of
a
r a n g e of acceptable q u a l i t i e s . The
only
unrealistic
linear programming, flow.
The
cost
assumption
i s that
the
coefficients
necessary
total
are
costs
are
summarized
this
in
analysis,
linearly below
r e l a t e d to in
Table
using feed 6.4.
Ab b r e via tio n s f o r the sources a n d demands a r e a l s o i n d i c a te d .
TABLE 6.4
Cost c o e f f i c i e n t s (c/m’)
u s e d in l i n e a r p r o g r a m m e
DEMANDS
I (c/m’
I TRANSFER I SYSTEM 1 I SYSTEM 2 1 SYSTEM 3
w l O / S
1
I
v
l M
WB
R
0.0
0.0
24.0
32.5
39.5
GROUND WATER
F
5.0
2.5
3.0
11.5
14.0
u
7.5
6.0
0.0
1 .o
0.0
D
44.0
43.0
38.0
-_ cn
WASTE
W
u
K
3
SI
WASTE WATER DESAL. WASTE WATER
46.0
51 .O
88 The f o r m u l a t i o n of t h e m a t h e m a t i c a l model b e g i n s b y e x p r e s s i n g the o b j e c t i v e f u n c t i o n i n terms of t h e e x p r e s s i o n
n
z =
x
c c.
J
(6.14)
J
Hence
+ O.O(RB) + 24.O(RS) + 32.5(RV) + 39.5(RM) + 5.0(FW) + + 3.0(FS) + 11.5(FV) + 14.O(FM) + 7.5(UW) + 6.0(UB) + O.O(US) + l.O(UV) + O.O(UM) + 44.O(DW) + 43.O(DB) + 38.O(DS) + 46.O(DV) + 51.5(DM) + O.O(U) + O.O(D)
Z = O.O(RW)
2.5(FB)
(6.15) where t h e terms
brackets represent
in
the
f l o w of
water
from
a
specific
source ( f i r s t l e t t e r ) to a s p e c i f i c demand (second l e t t e r ) a n d c o n s t i t u t e t h e The term U and D r e p r e s e n t the
unknowns. Desalinated
wastewater
respectively.
yields of
Consequently
the
they
wastewater have
zero
and cost
c o e f f i c i e n t s a n d a r e a l s o unknown. The o b j e c t i v e
2 must b e m i n i m i z e d s u b j e c t
function
to
the
following
l i n e a r constraints.
Source C o n s t r a i n t s :-
RW
+
RB
+ RS
t
R V t RM 5 100.0
FW + FB + FS + FV + FM = UW
+
(6.17)
+ UV + UM
=
U
(6.18)
+ DS + DV + DM
=
D
(6.19)
UB + US
DW + DB
(6.16)
11.5
Demand C o n s t r a i n t s : R W + FW + UW + DW
+ DB
RB + FB + UB RS + FS
+ US + DS
103.8 =
=
R V + FV + UV + DV =
RM + FM + UM + DM =
( f r o m 6.14)
(6.20)
7.0
(6.21)
9.5
(6.22)
0.7
(6.23)
0.5
(6.24)
Quality Constraints:500 R W 500 RB
+ +
600 600
500 RS + 600
+ FW + 1750 UW + 175 DW I 103.8 (1750) FB + 1750 UB + 175 DB 5 7.0 (1750)
+ +
FS + 1750 US + 175 DS
5 9.5
( 700)
+ 600 + FV + 1750 UV + 175 DV 5 0.7 ( 700) 0.5 ( 700) 500 RM + 600 + FM + 1750 UM + 175 DM 5
500 RV
(6.25) (6.26) (6.27) (6.28) (6.29)
89
B I end i n g Constraints:U
+ 1.45 D
= 10 ( from 6 . 1 0 )
( 6 .3 0 )
Non-nega t i v i t y constra i n ts:-
A l l unknowns It
is
(6.31 )
0
necessary
convert
to
unknowns on the r i g h t h a n d side.
UW + UB
DW
+
DB
The
+ US + UV + + DS + DV + set
optimized,
of
6.19
and
to
a
form
DM
-
(Eq.
no
Hence:
(6.32)
D = 0
subject to the objective
(6.33) 6.16,
6.17
6.20
and
f u n c t i o n of
Eq.
6.15,
to
6.33
can
be
u s i n g the manual
Since the r e s u l t a n t m a t r i x i s r a t h e r l a r g e ,
a computer
programme to solve I i n e a r programming problems b y the Simplex i s preferred.
with
UM - U = 0
constraints
Simplex Technique.
6.18
Eq.
Technique
The f o l l o w i n g i s noted :
a ) D i a g r a m m a t i c a l l y the solutions i s as i n d i c a t e d i n F i g . 6 . 3
b ) The
water
obtained
consequently
from
the
water
board
a l l o c a t e d to waste as slack.
is
not
This
is
required, interpreted
and
is
to mean
that i s i s not necessary to o b t a i n water from the water b o a r d . c ) Most
of
the
wastewater
ground
water
i s allocated
system
1
and
most
of
the
i s a l l o c a t e d to the t r a n s f e r .
I
/f
Optimal solution programming
WASTE
J
1750mg/L
/
11 .5MP/d
Fig. 6.3
to
to
the
distribution
problems
using
linear
90 The amount of water zero.
d r a w n from the d e s a l i n a t e d
T h i s implies t h a t no d e s a l i n a t i o n
being able
to
optimize
this
wastewater
i s required.
variable
is
source
is
The importance o f
enhanced
by
comparing
the
change in the values of the o b j e c t i v e f u n c t i o n . The
v a l u e of
the o b j e c t i v e
$453/day
compared
Solution,
solely
function
with
the
a
result
as
i s now
$1043/day,
Transportation of
allowing
a
decrease
of
Programming
Extended
an
variable
unknown
desal i n a t ion f r a c t i o n to be opt imized. The optimum solution
was reached,
unknowns were n e g a t i v e o r zero. function
would
occur
if
groundwater
to
$lO/day/unit
of water.
water,
waste.
i f water was
transfer.
TABLE 6.5
Table 6.5
a
The
since a l l
the shadow v a l u e s of
The
lowest
increase
of
water
was
unit cost
would
The highest
increase
in the o b j e c t i v e
allocated by
the
c/m'
or
increase would be $336/day/unit
a l l o c a t e d from
the d e s a l i n a t e d
wastewater
to
of the
summarizes the shadow values in ascending o r d e r .
DEMAND
SHADOW VALUE ( $ / d a y /un i t
Groundwater
Waste
10
Water Board
Transfer
15
Desal.
waste
System 2
225
Water Board
System 2
238
System 3
242
System 1
244
System 1
257
System 3
280
Desal.
Ww
Water Board Desa I.
WW
Water Board Desa I.
WW
Waste
331
Desa I.
WW
Transfer
336
g ) The assumption that cost i s l i n e a r l y r e l a t e d to feed flow Hence the r e s u l t s o b t a i n e d a r e not a ' t r u e '
the expected assumed,
from
1
only
Shadow v a l u e s of empty c e l l s u s i n g l i n e a r programming.
SOURCE
correct.
the
feed
and
assumptions
flow
hence
r a t e s from a
cost
( a n d consequently
was of
b y the comparisons i n Table 6.6.
each
source
derived. the cost
I t may,
overestimates cancel the underestimates.
to
The
each
demand
are
not
Initially,
inaccuracies
coefficients) however,
is clearly
optimum.
of
were the
borne o u t
be a r g u e d t h a t
the
91
TABLE 6.6
Errors
incurred
by
using
linear
cost
functions
instead
of
non-l i n e a r cost functions.
SOURCE
ASSUMED FLOWS OPT I MUM FLOWS AND CORRESPONDING FROM FIG. 6.3 COSTS AND CORRESPONDING COSTS
DEMAND
FLOW
COST
(Ml/d)
(c/m’)
FLOW
PERCENTAGE DIFFERENCE IN COSTS
COST
(Ml/d)
(c/m3 1
(c/m’)
Groundwater
System 1
3.0
3.0
8.7
1.6
47%
Wastewater
Waste
2.0
7.5
3.8
5.2
31 %
Wastewater
Transfer
2.0
6.0
5.3
4.5
25%
Groundwater
Transfer
5.0
2.5
1.7
3.1
-24%
THE
LINEAR
PROGRAMM ING
TECHN IQUE
WITH
PROGRAMM I NG
SEPARABLE
APPL I ED
The
assumption
function,
has
programming, programming, been
could
be
curve.
cost
throughout
transportation
that
the
function, the
and
discussion
programming
assumption
g r a p h s and t h a t employed
to
approximates n o n - l i n e a r accuracy
linear
made
depends on
in fact
avoid
on
onerous
by
of
objective
transportation and
Iinear
I t has consistently the
nature
of
the
the technique of s e p a r a b l e programming
this
functions
the
is
hence
extended
a n d the a p p l i c a t i o n of these techniques.
mentioned
cost-flow
a
of
been
assumption.
Separable
Programming
b y piecewise l i n e a r approximations.
d e v i a t i o n of
the
For non convex separable functions,
linear as
a p p r o x i m a t i o n from
i n t h i s case,
The the
the technique
does not guarantee a g l o b a l optimum. This
section
employs
the
separable
conjunction w i t h l i n e a r programming, mathematical model of
the system
f o r the objective function.
programming
to p r o v i d e a n o p t i m a l
technique,
in
solution.
The
i s described in the next section,
except
92 T h e model i s thus expressed as below:Minimize the o b j e c t i v e f u n c t i o n Z
subject
to
the
l i n e a r o r piecewise
linear
constraints
Z =
CRW
CRB t CRS
f
CRV
f
CRM
f
+ CFW
f
CFB + CFS
f
CFV
+ CUW
f
CUB + CUS
f
CUV + CUM
t
CDB
+
f
CDW
where CXY demand
Y
CDS
t
represents in
the
separable programming.
+
CDV total
dollars/day,
CFM
f
CDM
(6.34)
cost of
and
supplying
represents
water
a
DJXY represents the J t h
from
functional increment
source
X
equation
D or
to of
S f o r the
XY combination. CRW
=
CRB =
0 0
CRS = 117 DORS + 107 D l R S
+ 223 D2RS + 565 D3RS
1658 D4RS
f
CRV = 124 DORV + 108 D l R V t 227 D2RV + 565 D3RV
CFW =
37 DOFW +
25 D l F W
CFB =
13 DOFB +
19 D l F B +
4 0 D2FB +
CFS =
42 DOFS
20 D l F S +
24 D2FS
CFV =
4 9 DOFV t
22 D l F V
CFM =
42 DOFM +
20 D l F M
f
CUW =
6 2 DOUW +
38 DlUW
CUB =
42 DOUB
+
34 D l U B
cus
=
52 D2FW
f
f
1670 D4RV
f
CRM = 117 DORM + 107 D l R M + 223 DZRM + 565 D3RM
1658 D4RM
f
113 D3FW
+
80 D3FB +
+
29 D3FS
351 D4FW 156 D4FB
+
89 D4FS
t
26 D2FV +
30 D3FV +
+ + +
+ 89 D4FM 64 D2UW f 131 D3UW + 407 D4UW 5 7 DZUB + 109 D3UB + 236 D4UB 24 D2FM
f
29 D3FM
2 D2UV
f
3 D3UV
101 D4FV
0
CUV =
4 DOUV +
CUM =
0
CDW = 251 DODW CDB = 231 DODB
+ +
1 DlUV
229 DlDW 227 D l D B
f
+
6 D4UV
+ 583 D2DW + 1594 D2DW + 4595 D4DW + 574 DZDB + 1572 D3DB + 4424 D4DB
+ 1464 D3DS + 4287 D4DS + 1466 D3DV + 4194 D4DV 189 DODM + 193 D l D M + 517 D2DM f 1464 D3DM + 4287 D4DM
CDS = 189 DODS + 193 D l D S + 517 D2DS CDV = 193 DODV CDM =
+
194 D l D V
+
519 DZDV
(6.35) subject to source c o n s t r a i n t s 6.16, demand c o n s t r a i n t s 6.20
to 6.24,
qua1 i ty c o n s t r a i n t s 6.25
to 6.29,
6.17,
6.32
a n d 6.33,
b I end in g c o n s t r a i n t s 6.30, U
+
1.45 D = 10
Non-nega t i v i t y c o n s t r a i n t s , adjacent c o n s t r a i n t s f o r separable v a r i a b l e s : -
(6.30)
93
I f a n y DJXY i s non-zero, the v a l u e 1 ,
all
DJXY values
t h e preceding
must
take
on
and a l l the succeeding DJXY values must take the v a l u e 0.
where
RS
+
DORS + 0.6 DlRS
= 0.3
R V = 0.3 DORV t 0.6
+ 4.5 D3RS + 13 D4RS
1.6 D2RS
DlRV + 1.6 DZRV + 4.5
D3RV + 13 D4RV
RM = 0.3 DORM + 0.6 DlRM + 1.6 DZRM + 4.5
D3RM + 13 D4RN
+ 1.6 DZFW + 4.5 D3FW + 13 D4FW + 0.6 D l F B + 1.6 D2FB + 4.5 D3FB + 13 D4FB
FW = 0.3 DOFW + 0.6 DlFW FB = 0.3
DOFB
FS = 0.3 DOFS + 0.6
+
D l F S + 1.6 D2FS
DOFV + 0.6 D l F V + 1.6 DZFV
FV = 0.3
D3FS + 13 D4FS
4.5 4.5
.t
D3FV + 13 D4FV
+ 4.5 D3FM + 13 D4FM DlUW + 1.6 DZUW + 4.5 D3UW + 13 D4UW D l U B + 1.6 DZUB + 4.5 D3UB + 13 D4UB DlUV + 1.6 DZUV + 4.5 D3UV + 13 D4UV DlDW + 1.6 DZDW + 4.5 D3DW + 13 D4DW D l D B + 1.6 DZDB + 4.5 D3DB + 13 D4DB DlDS + 1.6 DZDS + 4.5 D3DS + 13 D4DS DlDV + 1.6 DZDV + 4.5 D3DV + 13 D4DV DlDM + 1.6 DZDM + 4.5 D3DM + 13 D4DM
FM = 0.3 DOFM + 0.6 D l F M + 1.6 DPFM UW = 0.3 DOUW
+
UB = 0.3
DOUB
+ 0.6
UV = 0.3
DOUV + 0.6
0.6
DW = 0.3 DODW + 0.6 DB = 0.3 DODB t 0.6 DS = 0.3 DODS + 0.6 DV = 0.3 DODV + 0.6 DM = 0.3 DODM + 0.6
(6.36) and where XY represents the unknown q u a n t i t y from source X to demand Y.
linear
programming
solution
was
Extended/370
in
obtained
(MPSX/370)
the
i n t o 6.34
equations,
conjunction using
supplied
represents the
.
S u b s t i t u t i n g the set of equations of 6.35 a s independent
i n MP/d,
i n 6.36
These set of equations
g r i d equa t ions of sepa r a b I e programm i n g
of equations of 6.36
of water
with
IBM
a n d r e t a i n i n g the set
the system
separable
Mathematical
i s solved u s i n g
programming. Programming
The
System
Software Package.
I n o r d e r to ensure the solution obtained
i s close to a
global
optimum
(as opposed to a local optimum) i t i s necessary to complete two computer runs.
The f i r s t ,
XSETLB = -1
with
after
the
the
control
programme,
l i n e BCDOUT
programming f o r non-convex
in
separable functions,
guarantee a g l o b a l optimum.
The reader
the
the control
second
the
information.
line
Separable
as in t h i s case,
i s r e f e r r e d to
Program Reference Manual (1976) f o r f u r t h e r
with
programme.
does not
the MPSX/370
IBM
The s a l i e n t r e s u l t s
and conclusions apear below: a ) Diagrammatically b ) The
100 MP/d
lOMP/d
is
returned.
t h e solution i s i n d i c a t e d below i n F i g . 6.4.
taken
assumed
from to
the
have
water
been
board
taken
is
from
in the
fact
not
board,
Hence the s u p p l y from the b o a r d i s also optimized.
used. it
is
If all
94
F i g . 6.4
Optimal
solution
using
l i n e a r programming
conjunction
in
with
separable programming
Most of
the
wastewater
ground
water
i s allocated
and
most
the
of
i s transferred.
The amount of water d r a w n from d e s a l i n a t e d implies that
no d e s a l i n a t i o n
the abundance of f a i r l y mg/e.
1
to system
i s required.
wastewater
The m a i n
good q u a l i t y g r o u n d water
I n t h i s case the acceptable s t a n d a r d of
i s zero.
reason f o r
This
this
w i t h a TDS of
700 mg/e
i s only
is 600
just
above the q u a l i t y of the groundwater s u p p l y . The
v a l u e of
$352/day
the o b j e c t i v e
compared
about solely
with
as a r e s u l t
function
the of
linear the
is
now
$691/day,
programming
i n t r o d u c t i o n of
a
solution.
decrease This
of
comes
a more r e p r e s e n t a t i v e
cost f u n c t i o n , u s i n g separable programming. Since
the o b j e c t i v e f u n c t i o n
obtained
is
not
necessarily
i s of the
the
non-convex
global
optimum.
type, When
the
solution
using
the
95
XSETLB=-1 command
( s e a r c h i n g from
lower
bound to u p p e r
v a l u e of the o b j e c t i v e f u n c t i o n was $714/d.
bound)
the
When d e l e t i n g t h i s command
( s e a r c h i n g from upper bound to lower b o u n d ) the v a l u e was reduced to $691/d.
Fig.
6.5
i n d i c a t e s the
$691/d
is
still
a
local
optimum.
The
g l o b a l optimum i s around $650/d. g ) There
is
no
difference
in
allocation
between
this
solution,
and
the
solution u s i n g l i n e a r programming ( w i t h o u t a n o n - l i n e a r cost f u n c t i o n ) .
h ) The accuracy optimum.
It
of
i s w i t h i n 5% -
the solution
would
be
improved
by
a
10% of
refinement
the of
true
the
global
grid
and
f u n c t i o n a l equations w i t h i n the v i c i n i t y of the c u r r e n t a l l o c a t i o n s .
S e n s i t i v i t y Study f o r v a r i o u s acceptable TDS v a l u e s
The case studies presented were based on a n acceptable Total Solids ( T D S ) of 700 mg/P System 3.
It
for
i s necessary
water
to
used on
examine
the
1,
System
the
optimal
Dissolved
System 2 a n d
solutions
for
various
possible acceptable TDS values i n o r d e r to e s t a b l i s h the best q u a l i t y .
This
would lead to the establishment of an optimum TDS value,
total
in terms of
combined costs, r e q u i r e d a t the demand zones mentioned above. here i s between 500 mg/O
The r a n g e of acceptable TDS values examined and 1200 m g / P closer
steps
i n discrete steps of 50 mg/O from 600 mg/P upwards, between
500
mg/O
and
r e q u i r e d to the mathematical model
mg/e.
i n Eq.
the e x i s t i n g system,
i g n o r i n g a l l q u a l i t y aspects.
to Eq.
presents the optimal
The
only
i s the s u b s t i t u t i o n of
values f o r 700 mg/P
Table 6.7
6.27
600
6.29.
water of
in
the r e l e v a n t TDS
Results a r e
a l l o c a t i o n of
and
modification
also
water
given
from
for
each
source to each demand,
the amount of wastewater used a n d the amount of
desalinated wastewater.
I t also
or
local
optimum,
and
shows
i n d i c a t e s whether the s o l u t i o n i s a g l o b a l the
value
of
the
objective
function
for
v a r i o u s selected TDS values. Fig.
6.5
procuring,
indicates desalinating
graphically and
the
variation
distributing
for
in
the
various
total
cost
acceptable
of TDS
values. From Table 6.7 a n d F i g . 6.5
the f o l l o w i n g conclusions a r e a p p a r e n t :
a ) The g r a p h i s c h a r a c t e r i z e d b y two p a r t s :
one w i t h acceptable q u a l i t i e s
g r e a t e r than 600 mg/e a n d the other w i t h q u a l i t i e s less t h a n 600 mg/O. The former has a f l a t slope of 0.2, l a r g e TDS
increases.
reverse tendency.
The
latter
i n d i c a t i n g small cost decreases f o r
has
a
slope
of
8.5,
displaying
the
96
TABLE
6.7
Comparison of optimal solutions f o r v a r i o u s TDS v a l u e s
RW 0.651
RB
4.339
3.409
2.661
3;591
7.000
RS RV RM 4.522
3.318
FW
2.059
FB
0.800
1.730
7,000
FS
7.265
8.382
9.500
8.674
7.848
7.022
6.196
FV
0.535
0.618
0.700
0.639
0.578
0.517
0.467
FM
0.382
0.441
0.500
0.457
0.413
0.370
0.326
3.326
3.800
3.800
8.139
7.209
6.278
4.941
6.200
uw UB
6.349
3.800
0.700
5.270
us uv
0.826
1.651
2.478
3.304
8.800
0.061
0.122
0.183
0.243
0.700
UM
0.043
0.087
0.130
0.174
0.500
10.000
10.000
10 .ooo
10.000
DW DB
DS
2.235
1.118
DV
0.165
0.082
DM
0.118
0.059
U
6.349
8.175
D
2.518
1.259
10.000
TYPE G L O B A L G L O B A L G L O B A L
.
OBJ. FN 1573 (R/d)
1213
698
LOCAL
691
GLOBAL
633
GLOBAL
LOCAL
GLOBAL
61 2
64 9
359
97
I1
1
FIG. 6.5
V A R I A T I O N I N T O T A L COST FOR
V A R I O U S A C C E P T A B L E TOS V A L U E S
LLL 1 6
u 7
800
900
1000
TOTAL D I S S O L V E D S O L I D S (mg/e)
1100
1200
The a b r u p t change in slope a t 600 mg/e p r o c u r i n g Desalinated wastewater water of
improved q u a l i t y
d e s a l i n a t i o n incrases,
for
i s a r e s u l t of the necessity f o r
lower
i s required,
acceptable
the amount
a n d consequently
TDS values.
of
water
As
requiring
1,
the a l l o c a t i o n s to System
2
and 3 increase. The p r e v i o u s argument v a l i d a t e s the selection of reach,
slightly
to the r i g h t of 600 m g / t .
a
quality
The exact
within
quality
the
would
be
Each successive increase i n acceptable TDS should cause a decrease
in
determined a f t e r a g r a p h was d r a w n .
the t o t a l least-cost. Not a l l the successive TDS increases manifest a decreased cost f o r p r e v i o u s TDS.
This
o b j e c t i v e function. t h a t 700 mg/4, they
not
do
occurs
as
However,
on
a
result
of
inspection
the of
non-convex
Fig.
6.5,
it
is
evident
1000 mg/e a n d 1100 mg/e a r e in f a c t local optima, follow
the
produced i n Table 6.7
expected
trend.
Consequently
the
f o r these TDS v a l u e s a r e also not
These problems may be overcome be p e r f o r m i n g a
the
separable
since
allocations
true
sensitivity
optima.
analysis,
o r p o s s i b l y b y r e v i s i n g the g r i d a n d f u n c t i o n a l equations. The absolute completely.
lowest cost The
occurs
resulting
when
cost
is
all
quality
$359/d,
a
aspects a r e
decrease
of
ignored
$34/d
in
comparison w i t h the s o l u t i o n u s i n g t r a n s p o r t a t ion programming a lone. Trends of
increases,
decreases a n d changes i n a l l o c a t i o n s as
v a r i e s a r e e v i d e n t from Table 6.6.
1)
An
increase
in
allocation
the TDS
Two t y p i c a l forms are: from
500
mg/Q
to
600
mg/e
and
a
decrease thereafter - Groundwater to System 1 . 2)
No
allocation
thereafter Most of
-
until
after
600
mg/e
and
a
steady
increase
Wastewater to System 2 .
the groundwater
is
allocated
to
System
1,
and
most
of
the
wastewater t r a n s f e r r e d a t low TDS values d i s c h a r a g e d to waste.
REFERENCES
Dantzig, G.B., 1963. L i n e a r Programming a n d Extensions. P r i n c e t o n U n i v . Press, Princeton. Grosman, D.D., 1981. Optimum a l l o c a t i o n of mine s e r v i c e water subject to q u a l i t y c o n s t r a i n t s . C i v i l Eng. in S.A. Lcomba, N.P., 1964. L i n e a r Programming. McGraw-Hill, NY. Stephenson, D., 1969. Optimum allocation of water resources by mathematical programming. J . H y d r o l . 9, 20-33. Stephenson, D., 1978. Optimum p l a n n i n g of r e g i o n a l waste water treatment. I n : Modelling the Water Q u a l i t y of the H y d r o l o g i c a l Cycle (Proc. Baden Symp., September 1978), 351-360. IAHS P u b l . No. 125. Stephenson, D., 1982. Optimum a l l o c a t i o n o f water resources subject t o q u a l i t y c o n s t r a i n t s . Proc. Exeter Symp. IAHS, P u b l i c . 135, 299-305
99
CHAPTER 7
ECONOMICS OF DESALINATION OF WASTEWATERS
I NTRODUCT ION
M u n i c i p a l wastewater
i s generally
and to n e u t r a l i s e the b i o l o g i c a l
treated
activity.
to remove suspended
It
i s disinfected and
innocuous before b e i n g discharged i n t o streams. water
however,
is,
not
affected
noticeably
The m i n e r a l content of
by
treatment
either
wastewater treatment works a n d a t the water p u r i f i c a t i o n works. o n l y i s there a m i n e r a l b u i l d - u p and
to some extent
contributed
to
by
domestic natural
phosphates and other
in the water
pollution, sources.
nutrient
but
in
the
at
the
Thus not
due to i n d u s t r i a l p o l l u t i o n
also
Thus
matter
rendered
this
mineral
addition
m i n e r a l s coming from
to
the
content
the
is
nitrates,
residential
type
areas, we also h a v e n a t u r a l m i n e r a l s such as calcium a n d s u l p h a t e b e i n g contributed dissolved
to
the
solids
system
thus
from
stormwater
discharged
by
runoff.
wastewater
The
works
total into
mass the
of
rivers
averages m i l l i o n s of tons p e r day. The magnitude of the problem of removing the dissolved m i n e r a l s i n the water
i s enormous.
There
reuse of t h i s wastewater.
a r e many
options
open,
however,
for
optimum
Some of the p o s s i b i l i t i e s a r e suggested below:
ALTERNATIVES FOR OPTIMAL REUSE OF WASTE WATER
Present p o l i c y for many affected water s u p p l i e s i s e f f e c t i v e l y
to d i l u t e
p a r t l y treated and r e t u r n e d wastewaters w i t h f r e s h water from r i v e r s a n d other
upstream
acceptable according concern.
sources.
limit, to
for
world
Provided
example health
500
that
the
mg/e
organisation
per
some of
the
wastewater
then
there
where
Alternative
other to t h i s
of f u r t h e r sources of f r e s h water (Stephenson a n d Corbetis, I t may be more p r u d e n t less c a p i t a l capital use
i s thought
steady
of
then
at
an
solids
is
little
in future users
will
i s the use
1984).
to adopt more o p e r a t i n g i n t e n s i v e schemes a n d
intensive schemes i n the l i g h t
i n t e n s i v e water
is
dissolved
i t may be necessary
downstream
have s i m i l a r o r more concentrated problems.
quality total
standards,
I n o r d e r to achieve t h i s d i l u t i o n ,
to discharge
water litre
supply
schemes.
high capital
economic
risks
,In p a r t i c u l a r
where
cost
of
schemes should
base load s u p p l y b a s i s whereas o p e r a t i n g
g e n e r a l l y be reserved f o r times of drought
be
involved
in
conjunctive used
on
a
i n t e n s i v e schemes would
i n s u r f a c e resources which a r e
100
Clarlflcatloi
Grit 500
Sand
50
10 1
0.1
Silt 0,Ol
SAND
FILTERS
Clay
0.00
EVAPORATION
Collolc
R E V E R S E OSMOSIS ,001
-
0001
I 1
F i g . 7.1
I 10
100
1000
10000
too
Selection of p u r i f i c a t i o n method based on water q u a l i t y
101
capital
intensive.
operative
intensive
procedures highly
Demineralisation than
those
i.e.
operating
and
surface
suitable
intensive
resources
for
as
desalination
development.
of
desalination
they
use
processes
large
sea
are
more
Desalination
water
are
of
power,
amounts
often for
example d i s t i l l a t i o n processes. On the o t h e r h a n d the t o t a l d i s s o l v e d s o l i d s content
of
sea
i s n e a r l y 35 000
water
t a l k i n g of dissolved s o l i d s contents of
mg/t
per
litre,
whereas
1 000 mg/P
less than
we
per
are
Iitre
in
into aquifers
is
wastewaters f o r a r t i f i c i a l recharge of g r o u n d water a q u i f e r s . The p o s s i b i l i t y of now
under
l i m i t e d treatment
consideration.
It
is
before d i s c h a r g i n g
possible
that
by
trickling
the
water
t h r o u g h the a q u i f e r s there w i l l b e n a t u r a l a e r a t i o n which would reduce the b i o l o g i c a l oxygen demand as well as p r o v i d e a degree of f i l t r a t i o n great
interest,
natural
n e u t r a l i s a t i o n of wastewaters
ion
some of
exchange
resulting
the dissolved
c o u l d be discharged
to
in
or
Alternatively,
the
s o l i d s content.
lower
levels o f
a n d of
demineralisation
the a c q u i f e r
thereby
l i f t i n g the fresher waters which have seeped there b y n a t u r a l means such as from r a i n w a t e r and i n f i l t r a t i o n from surface streams. Not o n l y
will
this
t y p e of
artificial
recharge
r e d u c i n g pumping costs b y keeping a h i g h water
have the a d v a n t a g e of table,
but
it
may
solve the problem of dewatering of dolomitic compartments which to geotechnical collapse
and
problems. dire
Previous
consequences
dewatering in
also
is linked
exercises have r e s u l t e d
residential
areas
and
at
in
mining
development so p a r t i e s concerned would be nervous about d e w a t e r i n g even i f o n l y i n t e r m i t t e n t l y to s u p p l y i n times of drought. Other
possibilities
particular
areas
possibility
of
to
include other
minimal
the
selected
if
treatment
local
recycling
In
areas. water
is
of
this
used
wastewater way
for
from
there
is
successive
a
lower
q u a l i t y - r e q u i r i n g uses. Yet another p o s s i b i l i t y i s the r e c y c l i n g w i t h f r e s h water pumped from r i v e r s
instead of
pumping costs a n d p i p i n g costs,
the n a t u r a l
as well
recycling.
as storage costs,
In
this
way
would be saved
f o r the water would be recycled a n d not have to be pumped.
SELECT ION OF OPT I MUM DESAL I NAT ION METHODS
Although h i g h d e s a l i n a t i o n costs a r e a deterrent desalination
for
water
supply,
considerably
more economic
than
an may
optimised first
to the general
system
appear.
The
may
in
location,
use of
fact
be
scale,
type and a d a p t a b i l i t y of a d e s a l i n a t i o n o r d e m i n e r a l i s a t i o n p l a n t can a l l be p u t to use i n r e d u c i n g t o t a l water costs. d e s a l i n a t i o n p l a n t may a v o i d the
Thus the location o f
necessity of
d i s p o s i n g of
in-house
effluents
into
102
collecting
sewers,
then
through
and
pumping
costs
Distribution
municipal are
wastewater
thereby
partly
treatment
reduced,
works.
w h i c h offset
d e s a l i n a t i o n costs. Studies f o r optimum location of d e s a l i n a t i o n p l a n t s have been conducted with the
the
assistance
reticulation
of
computer
system
and
simulation
alternative
programmes.
locations
for
The
depiction
desalination
p l u s a n a l y s i s h a v e p r o v e d t h a t such p l a n t s c a n be economically There may be s a v i n g s plants are
underground.
water
piping
and
pumping
in
There
costs.
is
costs
in
also
the
Desalination
has
c o n s i d e r a b l y b e t t e r water q u a l i t y
than
the
further
costs
of
imp1 i c a t i o n s
in
reducing
particular saving also
for
in
been
use of
heads
purchase
river
corrosion
installed.
high
shown
of
to
if
raw
give
water.
and
of
plants
This
a
has
deterioration
to
pipework due to other chemical a c t i v i t i e s such as s c a l i n g . The method of cost of energy.
d e s a l i n a t i o n may also depend to a
Whereas
l a r g e amounts of energy and a r e therefore fired
boilers,
low
energy
consumption
f r e q u e n t l y use e l e c t r i c i t y
from the g r i d systems. of
oil-from-coal more
for
heat
the
desalination
exchange
type
water
distribution may
methods.
before
prove
of most
sending ice
such
as
on
the
require
reverse
There a r e many
or
l a r g e amounts of
evaporation
Some mines c h i l l
contemplated
freezing
form
systems generate
suitable
cooling. even
some
extent
n o r m a l l y u n d e r t a k e n u s i n g coal
systems
which
have
large
d e s a l i n a t i o n methods such as e v a p o r a t i o n
heat
Some
and
Thus may
industries
The
In
such
vapour
be
require
underground and
underground.
viable.
industries
generation.
s u r p l u s heat
it
osmosis
have cases
compression
method i s also r e c e i v i n g close a t t e n t i o n i n t e r n a t i o n a l l y a t the moment. The scale of
the d e s a l i n a t i o n p l a n t a n d the q u a l i t y of
the
raw
h a v e a considerable effect on the optimum method of d e s a l i n a t i o n . size of p l a n t w i l l
water
Scale o r
i n f l u e n c e the o p e r a t i n g costs a n d these can be expected
to reduce the l a r g e r p l a n t a n d c a p i t a l costs such a s housing w i l l
reduce
p e r k i l o l i t r e of water t r e a t e d the l a r g e r the p l a n t . For low total dissolved sol i d s contents membrane-type
processes such a s
reverse osmosis a n d e l e c t r o d i a l y s i s h a v e p r o v e d most economical.
For very
low
problems
concentrations
ion exchange
i s economical.
There
a r e many
associated w i t h the membrane t y p e processes in p a r t i c u l a r where there i s a h i g h s u l p h a t e content. the c r y s t a l i s a t i o n dissolved a l s o effect
of
I n such cases seeded the
sulphates
s o l i d s in suspension. the f i n a l
on
The number o f stages
water q u a l i t y .
The
cost
removed may be a minimum f o r one p a r t i c u l a r k i l o l i t r e treated,
systems h a v e often p r e v e n t e d
the membrane a n d
per
in
ton of
kept such
the
dissolved
method whereas
total
p l a n t s cai solid
the cost pel
i f one i s not concerned w i t h the amount of s a l t s removed
103 F i g u r e s 7.7
may be cheaper f o r another system.
a n d 7.8
compare the costs
on these b a s i s f o r d i f f e r e n t methods. Multi-stage
demineralisation
applications. methods
are
brought
to
Thus
if
a
usually a
low
the
total
is
possible
that
most
Iitre,
also
water
be
suitable
is
quality
efficient
dissolved
than 10 m i l l i g r a m s per
It
may
high
and
solids
the
stages
final
particular multi-stage
effluent
concentration,
most economically
succession
for
required,
for
can
be
example,
less
t h r o u g h successive stages.
employ
different
techniques
e.g.
reverse osmosis coupled w i t h ion exchange. The
dispossl
of
the
brine
demineralisation
of
the b r i n e i s
l i t t l e concern
sea,
this
of
i s not
waste
the
most d e s i r a b l e that even
possibly
cost of
case
transport
in
where
also
a
Whereas the
problem
the
case of
the
brine
and
cases the b r i n e may
form
the cost of
disposal
be
to
to
of
sites
it
p l a n t s on
disposed
if
This
it
is
stored.
t h r o u g h successive
is
and
minimises
the
In
such
stages of
would b e designed d i f f e r e n t l y
stages
the
It
of.
h i g h concentration
inland.
have to be concentrated
the p l a n t . These concentration
of
desalination
has
before disposal
comes
concentration
when
volume
the b r i n e be b r o u g h t to a v e r y
solids
to
is
waters.
the
to
e f f l u e n t p u r i f i c a t i o n stages a n d may work on a d i f f e r e n t process a g a i n . Heat exchange p l a y s a n processes.
important
in the o p e r a t i n g costs of many
part
Thus i f e v a p o r a t i o n techniques a r e used
then
the e f f l u e n t
which
is a t a h i g h temperature can be used to heat the incoming stream to b r i n g it
to
nearly
evaporation could
be
evaporation
methods.
used
temperature. immaterial
to
In
cool
temperature
the the
case
of
i t may not
be wise
as
freezing
incoming
T h i s would be possible
but
such
stream if
in
multi-stage
processes of
the f i n a l
water
the to
ice
near
flash product
freezing
p r o d u c t temperature
i f c o l d water
i s a product
were
a s well
as
p u r e water. I t i s thus evident be
bought
practicability
in
that
the
of
desalination
form
the
of
a
be
designed
in
conjunction
costs
are
to
with
t h a n 50 cents p e r k i l o l i t r e ,
can
a s a whole.
the
be achieved.
plant In
The
plant.
d e m i n e r a l i s a t i o n process
considering the p l a n t and a l l factors
desalination
and d e m i n e r a l i s a t i o n cannot
package
of
this
only
easily
economics
and
be selected
when
The e n t i r e process must the
factory
case
effective
comparable w i t h r a w water,
if
optimum
costs
less
can be achieved.
RELEVANT D E S A L I N A T I O N METHODS
The p o t e n t i a l
for
desalination
r e s u l t there was a n increase
is
i n water
internationally
recognized
and
as
a
d e s a l i n a t i o n c a p a c i t y of 40% d u r i n g
104
the l a s t 5 years
(65% of which a r e m u l t i - s t a g e
flash distillation
seawater
p l a n t s a n d 25% reverse osmosis seawater a n d b r a c k i s h water p l a n t s ) . Membrane osmosis
was
methods
appear
restricted
y e a r ago a n d now
250000 m’/d
moving
Membrane
and
to
for
future
size p l a n t s
l a r g e scale
for
development.
brackish
plants.
water
Reverse until
Some examples
are
10 the
p l a n t in Jeddah f o r sea water treatment a n d the 400000 m’/day
p l a n t i n Yuma ( U S A ) ,
favourably
promising
small
to
f o r d e s a l i n a t i o n of d r a i n a g e .
methods
are
i n energy
scaling.
Where
competitive
consumption brine
with
as
disposal
well is
thermal as
a
processes,
susceptibility
problem
comparing
to
however
corrosion
(for
example
i n l a n d ) the cost of a d d i t i o n a l f a c i l i t i e s may d e t r a c t from the membrane processes.
I n d u s t r i a l Wastewater treatment
The
increased
research
and
costs
development
r e d u c i n g energy been
energy
work
consumption.
investigated
and
their
size of the p l a n t (Binnies,
during for
the
al I
Different
last
desalination
methods
applicability
1981; Larson,
decade
of
depends
have
directed
methods
towards
energy on
the
recovery costs
have
and
the
1979).
Some examples a r e : 1)
RO p l a n t energy can be recovered b y
installing
a
turbine
on
line
in
the ( h i g h p r e s s u r e ) b r i n e stream. 2)
Underground
installation
of
RO
plant
can
be
justified
based
on
u t i l i s a t i o n of the s t a t i c pressure instead of h i g h p r e s s u r e pumps. T h i s can be a p p l i c a b l e underground. In
the
to the m i n i n g
industry
has
it
(demineral i z a t i o n )
(USA)
plant,
production
The energy consumption costs w i l I n o r m a l l y be h i g h .
USA
for
been
suggested
domestic
and
that
where
the
RO
for
advanced
municipal
a l t e r n a t i v e f o r s o l v i n g the problems of Denver
f o r f r e s h water
water
treatment
wastewater
supply.
demineralization
is
This
is
methods the
best
is applied
included
in
iri
a
single
and
fresh
a n d i s now b e i n g contemplated elsewhere.
Reverse Osmosis
T h e n a t u r a l phenomenon
of
osmosis
occurs
water a r e separated b y a semi-permeable through when
the membrane
equilibrium
two solutions
to
dilute
i s established
the and
the
salt
water
membrane a n d f r e s h water flows
saline
i s c a l l e d osmotic pressure,
when
water.
This
water
flow
stops
p r e s s u r e d i f f e r e n c e between the
m a g n i t u d e of
which
the
depends
105 on
the s a l i n e
the s a l t
solution
solution
concentration.
greater
than
(DSS,
membrane free of s a l t
If
osmotic,
however, fresh
pressure
water
i s exerted
diffuses
through
in
the
1980).
1980; L u d w i g ,
Membrane Description
The cellulose
acetate membrane which
1 0 0 ~ thick,
approximately
approximately 0,2p
thick
of
which
in general
is currently
only
one
layer
is
active
use
is
and
is
(2000A) on top of the membrane surface w i t h the
r e s t a c t i n g as p h y s i c a l support f o r
the exerted pressure.
acts as a f i l t e r to r e t a i n the ions such as Na'
and
This t h i n
layer
Cl-.
E Iectrod ia I y s i s
I n the E l e c t r o d i a l y s i s process,
water
flows
between
alternately
placed
c a t i o n and a n i o n permeable membranes.
A
direct
electric
current
i s the
driving
force
for
the
ion
migration
through the membranes. A series of a l t e r n a t i v e c a t i o n a n d a n i o n membranes w i t h a p l a s t i c spacer between i s assembled hundred membranes
and
their
separating
i n t o membrane stacks. spacers
are
usually
Several
assembled
between a s i n g l e set of electrodes to form a membrane stack. The ion selection membranes a r e b a s i c a l l y
ion exchange r e s i n s i n sheet
90%. Normally
form w i t h s e l e c t i v i t i e s g r e a t e r
than
consists of one to s i x stages,
w i t h removal p e r stage v a r y i n g from 30
E l e c t r o d i a l y s i s systems to
60% ( n o r m a l l y 50%). Energy consumption i s based on F a r a d a y ' s Law, according
100 mg/e
removal
of
dissolved
ionised
solids
from
5m3
( D C ) a r e r e q u i r e d w i t h voltages 1 - 2 V.
amper-hours
kWh i s needed f o r
5m'
of
water
treated
in
to which f o r
of
200
water,
Therefore about 0,3
addition
to
which
2kWh
is
r e q u i r e d f o r pumping. Several
hundred
internationally
for
Electrodialysis
process
water
waters n o r m a l l y of less t h a n 3000 Reverse introduced
polarity
mg/t
(electrodialysis
commercially
to
plants
treatment
reduce
or
have
been
portable
water
i n s t a l led from
feed
has
been
salinity. reversal)
polarization
configuration and
scaling
in
the
membranes.
I o n Exchange
The ion exchange process has been used f o r many years
for
softening
106
iter
ter
'1
Fig. 7.2
10
100
1000 10 000 Product Solinity mg/l
S u i t a b l e feed s a l i n i t i e s a n d product s a l i n i t y f o r v a r i o u s d e s a l i n a t i o n processes. Recovery r a t i o s also i n d i c a t e d
100 1
107
of water and d e m i n e r a l i z a t i o n f o r v a r i o u s
i n d u s t r i a l uses.
r e s t r i c t e d to waters of not more than 1000 mg/4 The called
process zeolites
the c h a r a c t e r i s t i c
which
found
were
exchange r e s i n s have s u p e r i o r are
insoluable
solids
r e v e r s i b l e exchange Resins
normally
CP-
absorbs
with
mobile Na+
other
of
some
exchange a n d Ca
++
ions
neutral
fixed
ions of
ions
anions
cations
and
and
the other
+.
release
or
OH-;
these
+
ion
capable
in
of
solutions.
release
are
The ions release H
r e s i n s and base r e s i n s respectively.
the
be d e f i n i t i o n
sign and
for
Artificial
anions
opposite cations
minerals
suitable
f o r Na
exchange c h a r a c t e r i s t i c s a n d
containing
absorb
and
to
l i k e exchange of Mg'
i s normally
t o t a l dissolved solids.
i s based on
softening of water,
It
H+
called
a n d OH-
or
acid the
in
solution which combine to form H20. Ion exchange s a l i n i t y higher
is unlikely than
prove
to
1000 mg/4.
economical
However,
it
for
can
water
b e used
treatment
of
in c o n j u n c t i o n
w i t h a membrane process.
COST ANALYSIS
The
cost
cents/m' to take
of
desalination
of water produced. i n t o account a l l
techniques
i s often
expressed
in
terms
This approach can be m i s l e a d i n g as
the v a r i a b l e s
it
a f f e c t i n g t h e cost s t r u c t u r e .
of
fails Before
proceeding w i t h cost estimation the f o l l o w i n g parameters h a v e to be f i x e d :
1)
Product requirement,
p l a n t load f a c t o r a n d recovery.
The v a r i a b l e s affect the q u a n t i t y a n d q u a l i t y of r e l a t i o n s h i p between product the plant
operational
water
efficiency.
quantity,
Values
the f i n a l
feed
water
assumed f o r
product,
the
quantity
the cost
i n t h i s p a p e r a r e ; recovery r a t i o (Rc) 70% - 65% a n d p l a n t
and
estimate
load f a c t o r
90%.
2 ) Rate of
interest
which
for
present
purposes
is
taken
10% w i t h
as
a
redemp t ion p e r i o d of 20 years.
3)
P l a n t l i f e i s taken a t 30 years. The c a p i t a l and r u n n i n g costs a r e affected b y the above parameters.
C a p i t a l Costs
Capital development equipment
d i sposa I
.
costs
include
(roads, and
Civil
Engineering
electricity
controls
as
well
and as
water
and etc.
installation
plant
1. of
as
well
They
also
intake
as
and
site
include brine
108
I n d i r e c t C a p i t a l Costs
10 - 12% long term
interest
r a t e i s included d u r i n g p l a n t construction
a n d also labour costs w h i c h amount to 5
- 6% of the t o t a l c a p i t a l costs.
R u n n i n g Costs
Running costs a r e g e n e r a l l y d i r e c t l y p r o p o r t i o n a l and
include
energy
costs,
chemical
costs,
to p r o d u c t t h r o u g h p u t
labour
for
operation
and
ma i n tenance, membrane r e p lacemen t , o p e r a t i n g a n d maintenance costs. For
membrane
plants
100% load factor feed
water
of
it
2c/kWh.
characteristics,
is
reasonable
Chemical the
to
cost
process
assume
and used
electricity
treatment and
the
costs
cost
with
vary
with
plant's
recovery
ratio.
L a b o u r Costs
These depend on the requirements o f the p l a n t w i t h respect and
control.
also
It
depends
on
the
affects i t s maintenance l a b o u r cost.
of
reliability
the
to o p e r a t i o n
plant,
as
this
Costs g i v e n here a r e f o r p l a n t s u p to
10 000m3/day c a p a c i t y (medium s i z e ) .
Membrane Replacement
For E l e c t r o d i a l y s i s which
on
the
average
(ED)
20% of
have a
7
capital
year
cost
life.
For
is
spent
reverse
on
membranes
osmosis
treating
b r a c k i s h water the l i f e of the membrane i s o n l y 3 years. In
F i g u r e 7.3
Osmosis
include
capital
costs.
the
the
capital
site
Figure
cost
for
development
7.4
shows
both
costs,
the
Electrodialysis equipment
operating
costs
costs
and
Reverse
and
indirect
(running
i n c l u d i n g l a b o u r , energy a n d costs f o r both membrane processes. i s based upon a feed water w i t h a s a l i n i t y mg/e
costs)
This data
in the r a n g e of 1 000 t o 3 000
t o t a l dissolved sol ids.
The
capital
approximately
cost
for
$700/m3/day
the for
reverse a
osmosis
120rn3/day
$170/m3/day f o r a 10 000m3/day feed c a p a c i t y The cost a l l o w s f o r
feed
plant,
d i f f e r e n t equipment designs
process
varies
capacity
from
plant
to
based upon 3 stages.
and manufacturer's
prices
a n d s i t e costs which a r e dependent on t h e s i t e . The c a p i t a l cost
for
E l e c t r o d i a l y s i s depends
the feedwater hence the number of
stages
l a r g e l y on
involved
the s a l i n i t y
of
i n the process a s well
109
D E S R L I N R T I O N PROCESSES CFTXTRL L RUNNING co-
ro11 nLcmtornmysxs L IINLRSL
osnos~s
c
8
Fig
n \
I Fig.
7.4
Running cost versus P l a n t size (Feed) f o r ED & RO ED process RO process
(
(
-.-.d )
I10
D E S A L I N A T I O N PROCESSES ENERGY R f O U I R M W S (hl4hk) FOR CLCCTRODIRLYSIS h REVERSE OSMOSIS
Fig. 7.5
Energy Demand versus Feed Salinity for ED & RO
F i g . 7.6
Energy Demand versus P l a n t size (Prod) for ED & RO
ED
process (-.-.-
)
RO. p r o c c s d
)
111
as the p l a n t size. of
120m3/day
The costs v a r y from $760/m3/day
feed
capacity
10000m3/day feed c a p a c i t y .
a
to
$200/m3/day
f o r two 4-stage
for
2
a
I t can be seen i n F i g u r e 7.3
stage
plant
plant
of
t h a t c a p i t a l costs
f o r E l e c t r o d i a l y s i s a r e g e n e r a l l y h i g h e r than other methods. In
running
osmosis,
costs
varying
however
from
25c
electrodialysis 7c
to
as
osmosis from the same p l a n t c a p a c i t y 7.3
and 7.4
account
for
different
opposed
is
cheaper
( F i g u r e 7.5).
water
-
45c
to
than
reverse
for
reverse
in
Figures
1Oc
The costs
characteristics
and p l a n t
design
factors. water
The
temperature,
influence energy
and
pH,
turbidity,
pretreatment
costs.
suspended
Also
recovery
matter ratio
etc.
can
(Rc) v a r i e s
between 70 a n d 85% f o r E l e c t r o d i a l y s i s a n d 65 a n d 85% f o r reverse osmosis which can affect the energy requirement. The t o t a l for different
theoretical
cost of the water v a r i e s from 40c
to 20c
per
m3
size p l a n t s f o r E l e c t r o d i a l y s i s and 52c to 22c p e r m3 i n the
case of reverse osmosis (1983 f i g u r e s ) . In
Figure
7.5,
energy-consuming
it
can
be
seen
f o r a feed s a l i n i t y
that
Electrodialysis
is
r a n g e of 500 - 3 000 mg/Q.
less
This
is
due to the fact that energy demand i s d i r e c t l y p r o p o r t i o n a l to removal f o r the E l e c t r o d i a l y s i s .
The
energy
costs
account
for
different
plant
sizes,
assumed of the o r d e r of 1 000m3/day, F i g u r e 7.6 shows the v a r i a t i o n in energy requirements f o r d i f f e r e n t size p l a n t s . Energy f o r reverse osmosis changes w i t h recovery v a r y i n g from 70% to 85%. The e l e c t r o d i a l y s i s c u r v e assumes a recovery r a t i o of 75%.
CONCLUSIONS
It
is
evident
demineralization.
that
there
are
many
From
the
point
of
variables view
of
affecting the
the
costs
applicability
of
p a r t i c u l a r process and the optimum process f o r a p a r t i c u l a r a p p l i c a t i o n t h e f o l l o w i n g factors a r e r e l e v a n t :
Load factor
-
Locality
- affects power cost, construction a n d l a b o u r costs.
r e l a t e s c a p i t a l to r u n n i n g costs.
C a p i t a l cost a n d interest r a t e . Power and other o p e r a t i n g costs. TDS of r a w water. Q u a l i t y requirements f o r e f f l u e n t Method of b r i n e disposal.
of a
112
I f the costs a r e expressed a s cents p e r k i l o l i t r e , may p r o v e most economic,
i f they a r e expressed a s cents p e r
whereas
of dissolved s o l i d s removed,
of
k g of
per
membrane
and
ion
salt
removed
exchange
r e l a t e d to the amounts o f s a l t removed and they low TDS waters.
F i g u r e 7.7
however,
include scaling
There i s a tendency to use thermal methods
f o r h i g h TDS waters as the cost h a n d the cost
the incoming steam
In the case of e v a p o r a t i o n methods,
i s d i r e c t l y r e l a t e d to t h e TDS.
other
kg
another method may be optimal.
Methods r e l a t i v e l y i n s e n s i t i v e to the TDS o f the thermal methods.
one p a r t i c u l a r method
and
7.8
depict
is
low.
processes
are
therefore
the costs of
On
are lowest
different
the more for
method
p l o t t e d ( a ) versusflow r a t e a n d ( b ) versus r a t e of TDS removal. It
appears
industrial
that
wastwaters
membrane
type
(provided
Recent advances i n membranes now rates at
processes
adequate
are
most
economical
pre-treatment
is
i n c l u d e those c a p a b l e of
low pressures p r o v i d e d o n l y
limited
solids
removed
for
practical).
passing
high
i s required.
Using present d a y p r i c e s i t i s f e a s i b l e t h a t costs w i l l
be competitive w i t h
b u l k water
is
supplies from a f a r
reduced r e t i c u l a t i o n costs,
and
in
addition
there
a n d the p o s s i b i l i t i e s of use of
the
i n c e n t i v e of
the e f f l u e n t s f o r
specific a p p l i c a t i o n s o r f o r g r o u n d water recharge.
REFERENCES
B i n n i e a n d P a r t n e r s , 1981. D e s a l i n a t i o n methods a n d costs, Water Systems Research Programme, U n i v e r s i t y of the Witwatersrand. DSS Engineers Inc., 1980. Data Collection a n d A n a l y s i s of Commercial Membrane D e s a l i n a t i o n P l a n t s . 1979. D e s a l i n a t i o n of sea water a n d b r a c k i s h Larson T.J. and L e i t n e r G., water, A cost update. D e s a l i n a t i o n , 30, p525-539. L u d w i g , L., 1980. Reverse osmosis i n the d e s a l i n a t i o n of b r a c k i s h water a n d sea water, Desalination, 36, p 153-178. Stephenson, D. a n d Corbetis, S.S., 1984. Economics of D e s a l i n a t i o n of Wastewaters f o r the W i twatersrand. Water We1 I Assn. Conf. Johannesburg.
\ \
113
114
Fig. 7.8
Desalination costs per k g of dissolved solids removed as a function of f e e d s a l i n i t y , f l o w r a t e a n d method
115
CHAPTER 8
COMPUTER ANALYSIS JUSTIFIES DESALINATION
INTRODUCTION
Industry
uses
water
for
cleaning,
t r a n s p o r t amongst other purposes.
air
conditioning,
dilution
and
Water may be r e c y c l e d a n d d e t e r i o r a t e s
in q u a l i t y due to contact w i t h contaminants a n d discharges i n t o t h e system
(Holton
and
1983).
Stephenson,
The
total
dissolved
(TDS)
solids
concentration i n some waters can exceed 10000 mg/l. The
poor
pipework
water
and
refrigeration the
poor
quality
can
machinery.
plant
water
was
In
lead a
are
corrosion
particular
extremely
quality
to
severe.
the
health
and
system,
deterioration
hazard,
of
the
associated
with
corrosion
Other problems and
of
surface
effluent
discharge regulations. The problem has
been
aggravated
by
in
deterioration
surface
water
q u a l i t y over the last few years. The approach adopted resources,
can
(Stephenson,
in this
be a p p l i e d on
re-distributing
water
smaller scale f o r operating-cost
in
a much wider
to
scale
optimize than
the
economical
i n d u s t r i a l water systems.
sources
such
as
herein
way
to
discharge
The b a s i s f o r
desalination
lies
in
the
in
total,
problems
as may
the
water
be
may
reduced
as
of
described
purpose
meet
of
quality
justifying fact
that
be of the
high other costs.
a
higher
volume
of
( b r i n e ) i s c o n s i d e r a b l y less i f d e s a l i n a t i o n i s performed.
There
are
alternative
ways of
justifying
high
operating-cost
such as d e s a l i n a t i o n in comparison w i t h more conventional r i v e r water.
They l i e i n c o n j u n c t i v e use - namely
schemes to s u p p l y the base sources
the
use
namely p u m p i n g costs o r storage dam
Less water may be r e q u i r e d Effluent
most
the
I t could be a p p p l i e d on a r e g i o n a l b a s i s o r on a
costs may thereby be saved,
effluent
namely
1986). The computer program developed f o r
constraints i s universal.
quality.
study,
when
drought.
there
is
a
load,
use of c a p i t a l - i n t e n s i v e
and r e s o r t i n g to s t a n d y
shortfall
in
surface
systems
sources such as
resources
low c a p i t a l - c o s t e.g.
during
a
A l t e r n a t i v e l y d e s a l i n a t i o n could proceed on a r e g u l a r small scale,
d i s c h a r g i n g i n t o a r e s e r v o i r (e.g.
a q u i f e r ) which c o u l d be tapped i n times
of shortage elsewhere. The f i t t i n g i n o f a d e s a l i n a t i o n u n i t w i t h a system i s thus more l i k e l y to j u s t i f y from
a
desalination than a straight
plant
or
from
more
comparison
conventional
of
sources.
u n i t costs The
of
water
optimization
of
116
multi-source
systems
computer
is helpful.
analysis
can
reveal
be
balance
used.
of
builup
requires
over
at
nodes
analysis
various
Simulation
TDS
equation
careful
There a r e
time. will
ways
and
in
of
the
A
simultaneous
give
this
which
water
is
distribution
steady
where
computer
solution
system of
TDS
state
the
systems will
the
mass
loads,
and
o p t i m i z a t i o n can produce the best ( g e n e r a l l y the most economic) p l a n . The type of d e s a l i n a t i o n p l a n t most s u i t a b l e f o r a n y g i v e n system w i l l also depend on the circumstances (Stephenson a n d Corbetis, values
mentioned
demineralization processes,
e.g.
here
could
be
described
(usually
confined
reverse
osmosis,
to
as
TDS
lower
are
requiring
often
1983). The TDS desalination
water).
most
Membrane
suitable,
or type
although
freeezing d e s a l i n a t i o n i s now r e c e i v i n g a t t e n t i o n . Various attempts a t o p t i m i z i n g complex have
been
reported
(Rinaldi
al,
et
systems
1984).
In
i n v o l v i n g water general,
the
quality
problem
is
non-linear
so
little
use.
Search methods
used.
The technique described i n t h i s p a p e r i s one such method which uses
l i n e a r programming
packages
(Smeers a n d
(Loucks et
Tyteca,
known c h a r a c t e r i s t i c s o f
the system to speed
the cost
are
of
desalination
not e x p l a i n e d
studies have been r e p o r t e d ( A b u l n o u r et a l ,
1981)
al,
1967)
must
the search. in detail
are
generally
of be
The method a n d
here
although
such
1983).
APPL I C A T ION OF OPTIMIZATION O F WATER SUPPLY
The options studied,
in view
of
the poor
quality
of
the
water
on
an
i n d u s t r i a l system were:
1.
Accommodate
the
poor
quality
at
the
expense
of
higher
maintenance
costs of pipework a n d machinery.
2. Prevent d e t e r i o r a t i o n of the water a t the source o f p o l l u t i o n . 3.
Remove the TDS i n the water b y means of a d e s a l i n a t i o n p l a n t .
4.
Use g r e a t e r q u a n t i t i e s of f r e s h water.
5.
Re-distribute
the water i n a way w h i c h m a i n t a i n s h i g h e r q u a l i t y a t key
points.
Alternative 1 , was
quickly
namely c o n t i n u i n g w i t h the present
r u l e d out
pipework and machinery.
by
assessing
the
cost
of
poor
regular
quality
water,
replacement
of
Research was also i n p r o g r e s s to reduce l e a c h i n g
a t the source of p o l l u t i o n b u t no p o s i t i v e recommendations c o u l d b e made. The most economical combination of a l t e r n a t i v e s the computer program developed for the purpose.
3-5
was
investigated u s i n g
117
No.3 Shaft
Flsrure water
Mlm u r v l c a water
... . .....
-L
-. -
-----
C b r water return Ilne Carcmd. rvstem overflow F a d rate; Sludge llmr MIM wwklngs u r d water 6 nrsure water
chamber water system dam
F i g . 8.1 Section through a t y p i c a l mine
The water
d i s t r i b u t i o n system
not accurately documented. another
and
it
i s often complex
I n general,
i s collected
i n d r a i n s and
pumped
after
s e t t l i n g to remove suspended p a r t i c l e s .
dust
suppression
and
cooling.
(Stephenson,
1983) a n d
water i s p i p e d from one w o r k i n g to
Minimum
to
The water
flows
are
waste
or
recycled
may
be
used f o r
required
but
the
d i s t r i b u t i o n p a t t e r n a n d the amount r e c i r c u l a t e d o r pumped can b e v a r i e d .
118
Water from d i f f e r e n t evaporation
or
locations
draught
i s often blended.
towers
before
i s cooled
Water
refrigeration
by
an
in
spray
indirect
heat-exchange p l a n t i n c o o l i n g systems. The e v a p o r a t i o n i n the warm a r e a s as well a s i n e v a p o r a t i o n dams a g g r a v a t e s water.
F i g . 8.1
water
taken
the TDS concentration
in
the
i l l u s t r a t e s a section t h r o u g h a t y p i c a l mine w o r k i n g s w i t h
from
a
fresh
water
source
at
underground f o r cooling a t surface cooling
the
towers,
surface,
returned
from
and p a r t l y replaced b y
f r e s h water before r e c y c l i n g .
SYSTEMS ANALYSIS
One s h a f t
program
described
here.
must
equal
zero.
8.2,
reproduced
The h y d r a u l i c p r i n c i p l e
system i s the c o n t i n u i t y equation, node
in F i g .
i n the complex d i s t r i b u t i o n system depicted
be reduced to the flow d i a g r a m of F i g .
It
is
t h a t is,
possible
used
by
for
8.1
can
the computer analyzing
the
net i n f l o w minus outflow a t a n y
on
this
d i s t r i b u t i o n system out of a number of closed
basis
loops.
to close the system b y means of a dummy node i.e.
to
make
up
any
I t may be necessary
a n y loose i n p u t
to a n d
outflow from the system can be taken from o r to the dummy node.
Such a
dummy
quality
node
is
handled
differently
from
c o n s t r a i n t o r mass TDS b a l a n c e a p p l i e s to i t .
F i g . 8.2
Graphic of system a n a l y z e d
other
nodes
as
no
119
I t may be shown t h a t the minimum number of closed loops
in a network
1981):
of pipes and channels i s (Smith et a l ,
L = P - N + l where P
i s the
number
connecting N nodes.
conduits
of
Additional
loops
may be defined b y i n c l u d i n g pieces of o t h e r loops a n d the selection of
the
best loops can speed a n a l y s i s i f manual h y d r a u l i c a n a l y s i s i s performed. A n algorithm for f i n d i n g
nodes comprised p a r t of to
identify
conduits
as
flowing
s e p a r a t i n g adjacent loops, stage.
loops i n a system described o n l y
the program.
i.e.
in terms of
For p r a c t i c a l purposes i t
from
one
node
loops a r e not
to
another
i s easiest
and
not
i d e n t i f i e d a t the d a t a
as
input
The d e f i n i t i o n of loops a t d a t a i n p u t stage i s also irksome when
comes to r e v i s i n g ,
adding
flows i n t h e network,
to o r
however,
subtracting
conduits.
flows should a l w a y s b a l a n c e a t nodes.
simplest way of e n s u r i n g t h i s i s to a d j u s t
flows b y a d d i n g a flow
closed loops.
MAIN PROGRAM
SUB PROGS
~
IDENTIFY SYSTEM READ CONDUIT DATA IDENTlfY NODE CONS SEEK ML LOOPS
.
I I
I I
HYDRAULIC NETWORK ANALYSIS FOR CONDUITS I
I
I
SOLVE SIMULTANEOUS
MASS W C E TDS EOS AT ALL NODES XPT 0 ADJUST FLOW IN LOOPS IN BEST WAY UNTIL AU TDS's WITHIN LIMITS
RETC COST
F i g . 8.3
Program flow d i a g r a m
I
I
I I
TRYMTERNATNEDESM PUNT LOCATIONS AND-SCALE
it
D u r i n g r e v i s i o n of The
around
1 20
A computational a l g o r i t h m f o r loops
was
inserting
developed. dummy
The
selecting
algorithm
conduits and
nodes.
was r e q u i r e d as o n l y flow balance, nodes.
For instance,
8.3.
t h e minimum include
Special
h a n d l i n g of
closed
these
by
conduits
A flow d i a g r a m f o r the procedure i s g i v e n in
s t a r t s w i t h each p i p e in t u r n
i n the system.
flow
to bottom
(from
of
branches
not TDS b a l a n c e occurs a t some dummy
To ensure t h a t each p i p e i s i n c l u d e d in a
direction
number
unclosed
e v a p o r a t i o n can be represented a s a n e g a t i v e flow f o r
a dummy node w i t h zero TDS. Fig.
can
top
node
It
node)
loop,
proceeds from one
the procedure in
pipe
the
positive
to
another
l e a d i n g from i t . Where there i s more t h a n one p i p e e x i t i n g from a node, new
loop
i s created f o r each b r a n c h .
loop closure and then a n y p i p e s dropped.
in
At the
step not
a check in a
ignored.
A
negative
flow
from
node
i s made f o r
closed
Whenever a closed loop i s formed a check i s made,
w i t h o t h e r loops to ensure no d u p l i c a t i o n . are
each series
loop
are
pipe b y pipe,
Loops w h i c h h a v e n e g a t i v e f l o w s zero
(which
has
zero
TDS)
p r e s c r i b e d to represent e v a p o r a t i o n since node 0 i s a l w a y s a t zero TDS.
START WITH W C H PIPE IN TURN GO FROM TOP NODE TO BOTTOM OF SUCCESSIVE PIPES Where there Is a branch-off store plpedata up to branch for another loop CHECK FOR LOOP CLOSURE ELIMINATE REDUNDANT PIPES CHECK FOR LOOP DUPLICATION BY COMPARING PIPE FOR PIPE AND ELIMINATE DUPLICATES
GO BACK TO CHECK FOR BRANCH LOOPS
F i g . 8.4 Loop seeking a l g o r i t h m
a
is
121
Once a l l the loops a r e i d e n t i f i e d , a n increment i n flow i s added to one loop a t a time to determine the corresponding change in TDS a t each node
and the corresponding cost
increase.
comparison w i t h t a r g e t TDS,
i s i d e n t i f i e d a n d the
The
node
with
the
worst
TDS,
in
in TDS a t
improvement
the node p e r u n i t increment i s established.
T h i s i s repeated f o r each loop
a n d the one w i t h the maximum of d(TDS)/dC
i s selected where C i s the cost
of c i r c u l a t i o n .
The maximum necessary increase in flow i s made a r o u n d the
loop consistent w i t h
quality
constraints.
The procedure
i s repeated
until
a l l TDS's a r e w i t h i n specified l i m i t s . I t i s necessary time
an
i n the system each
to r e c a l c u l a t e TDS's a t each node
increment
is
made
to
flows
around
a
loop.
This
is
done
by
i t e r a t i n g f o r each node in succession the mass b a l a n c e equation z Q ( T + P)/YQ
T' =
flow from an upstream node to the node a t w h i c h T I
where Q i s the be determined.
and P
T i s the TDS a t the upstream node,
( o r decrease i n the case of
desalination)
of
TDS a l o n g
i s to
i s the p i c k u p
the conduit.
The
summation i s over a l l c o n d u i t s l e a d i n g to the node.
General o p t i m i z a t i o n problem
The problem to be solved can be described as follows: flow
requirements a n d maximum TDS requirements a t
network,
should
be
purchased
d e s a l i n a t i o n should flows
certain
as well as q u a l i t y of r a w water a v a i l a b l e ,
in water a t c e r t a i n p o i n t s a n d the network
in
each
objective
conduit
function
transport
per
from
to
Iitre
d e s a l i n a t i o n in c / l
the
raw
be performed? At and
quality
be minimized along
any
layout,
water
same
(TDS)
at
include
conduit,
each of
e.g.
a
what amount of water
time
cost
in
points
r a t e of d e t e r i o r a t i o n
source
the
g i v e n minimum
and the
what
node. raw
of
yields in
the
water,
Costs
cost
of
and
cost
of
pumping
f o r a l t e r n a t i v e l e v e l s of treatment (mg/l
level
program
removal).
A t r i a l a n d e r r o r process i s r e q u i r e d to e s t a b l i s h the best p o s i t i o n of the
desalination
plant
or
( p r o p o r t ion of TDS removed ) The
costs
were
a l t h o u g h non-linear
.
assumed
plants,
to
be
and
the
linearly
best
level
proportional
of
to
treatment
flow
rate
o b j e c t i v e functions could be h a n d l e d b y the program.
C a p i t a l costs of c o n d u i t s were not
i n c l u d e d a s the c o n d u i t s a l r e a d y
a n d can h a n g l e l a r g e r flows t h a n w i l l n o r m a l l y occur emergency c o n d i t i o n s ) .
Flows can be c o n t r o l l e d b y
exist
( t h e y a r e based on
valves
in
g r a v i t y lines and pumping power in the case of p u m p i n g lines.
the case of
122 PROGRAM APPL I CAT ION
The program handles
up
to
was
on
run
100
128 kb
a
conduits.
It
is
s i m u l a t i o n a n d g r a p h i c s program.
16
x
often
bit
run
m i c r o computer conjunction
in
The s i m u l a t i o n p r o g r a m a l l o w s
v a r i a t i o n in d r a w o f f s f o r meeting s p e c i f i c w a t e r demands, which
can
fluctuate
over
a
period.
It
does
not,
which with
for
a
time
a n d f o r storage
therefore,
assume
c o n t i n u i t y of flow a t nodes a n d i s useful f o r more r e f i n e d studies t h a n the o p t i m i z a t i o n program graphics
system
such
is
as
useful
r e q u i r e s co-ordinates
time
for
varying
quality
visualization
of nodes as i n p u t .
of
(see
the
8.5).
Fig.
system,
The
although
it
A common d a t a f i l e can b e used
f o r a l l programs a n d t h i s f i l e can be amended ( c o n d u i t s a l t e r e d ,
added o r
s u b t r a c t e d ) as a n a l y s i s proceeds. The o p t i m i z a t i o n p r o g r a m commences w i t h minimum flow d a t a . o n l y be increased to reduce TDS a t a n y p o i n t . p l a n t s must e.g.
be selected
i f s l i p stream
by
trial,
desalination
as
well
i s resorted
The location of d e s a l i n a t i o n
as
the
to,
level o f
it
desalination,
i s equivalent
removal. Although i t would be a simple m a t t e r to a u t o m a t i c a l l y desalination
plants
along
successive
conduits,
the
c o n s t r a i n t s l i m i t i n g d e s a l i n a t i o n p l a n t s to s p e c i f i c not
warrant
automatic
repositioning
of
Flows can
number
of
locations o r
plants.
Brine
to p a r t
investigate physical
l e v e l s does
disposal,
space
requirements and access a r e of p a r t i c u l a r concern i n mines.
0
1
2
F i g . 8 . 5 Deterioration simulation
3 of
TDS
5
4
at
a
,DAY 6
strategic
/
point
as
indicated
by
123
OPTIMIZATION O F MINE WATER SYSTEM
Mines s u f f e r from poor water q u a l i t y due to poor r i v e r q u a l i t y , concentrations of c h l o r i n e i n ground water, which
necessitates
particular
extensive
mine's
method
recycling.
of
a n d a severe shortage of water
(1985) r e p o r t e d on a
Baker-Duly
solving
large
the
problems
using
a
simulation
program. The p a r t i c u l a r mine presented as a n example of
the a p p l i c a t i o n of the
c u r r e n t o p t i m i z a t i o n p r o g r a m suffered the v a r i o u s problems out1 i n e d above. The s i m p l i f i e d system a n a l y z e d here i s depicted
i n Fig.
8.2,
r e a l mine i n v o l v e d 3 s h a f t s w i t h cross flows from one shaft the system
analyzed
2140m below surface, the
there
surface,
respectively.
lowest
level
and
and
i s one m a i n two
shaft
sub-shafts
from
down
the
the
water
water board. from
surface
In
down
to
There a r e s e t t l e r s f o r removing suspended sol i d s a t at
the
bottom o f
i s recycled
with
'fresh'
P r i o r to the study
groundwater
resulting
the
2430 and 2620m below
to
the
main
shaft.
s e t t l e r s i s d i v e r t e d i n t o sumps a n d thence pumped to of
whereas
to another.
totalled
22
23
I/s
water was
I/s
and
purchased thus
Water
higher from
purchased,
evaporation
a
the Part
regional
the makeup
amounted
i n a d i s c h a r g e to waste on the surface o f 29 I/s.
from
levels.
16
to
I/s
Owing to the
h i g h heads, cost of p u m p i n g to waste was h i g h a n d the purchase p r i c e of f r e s h water was also h i g h . making marginal
The q u a l i t y of ' f r e s h '
improvement to the system f o r
water was
in f a c t poor,
the p r i c e p a i d .
q u a l i t y was of p a r t i c u l a r concern a t the r e f r i g e r a t i o n p l a n t s , was directed s t r a i g h t to them. U n f o r t u n a t e l y , also sent to the r e f r i g e r a t i o n p l a n t s , poor q u a l i t y .
That
was
mine workings where the water h a d come i t s contamination,
and e v a p o r a t i o n a t
water
water from c o o l i n g dams was
a n d t h i s water was of
because the dams
As
f r e s h water
received
warm
i n t o contact
the w o r k i n g s
particularly
water
from
the
w i t h ore,
with
all
a n d the s p r a y i n g on
the dams had concentrated the dissolved s o l i d s even more b y e v a p o r a t i o n . T h e fact t h a t water i n the s p r a y dams was of p a r t i c u l a r l y poor q u a l i t y a n d that
i t h a d to be improved c o n s i d e r a b l y before re-use,
indicated
the
most a p p r o p r i a t e p o s i t i o n f o r a d e s a l i n a t i o n p l a n t .
RESULT OF ANALYSIS
Table 8.1 to
the
i n d i c a t e s flows a n d TDS's a t a l l p o i n t s in the system p r i o r
analysis
a n d Tables
8.2
a n d 8.3
present
the
optimum
TDS's r e s u l t i n g from the a n a l y s i s f o r the best p o s i t i o n of plant.
flows
and
the d e s a l i n a t i o n
1 24 Table quality over
8.1
was
was
obtained
arbitrarily
l i t t l e more
than
from
assumed
a
week
the
simulation
start
to
program,
500
at
to e q u i l i b r i u m
TDS's
of
where
before
mg/P
over
water
increasing
4000
mg/l
at
p I aces.
TABLE 8.1
Water Flows a n d TDS without d e s a l i n a t i o n
Cost, $/a = 1.056825E+6
~~
Pipe number
Node 2
Node 1
1 2 3 4 6 6 I 8 9 10 11 12 13 14 16 16 17 18 19 20 21 22
0 1 3 6 0 0 2 4 0 5
1 3 6 I 11 I 4 6
8 9 I 10 I 11 0
12 12 2 3
8.2
Table
4
summarizes
nodes 8 a n d 7,
(W
(will
(CPU
Equilibrium TDS (WlU
23 23 8 8 -8
800 0 0 0 0 0 0 0 1800 400 0 0 0 0 200 0 200 1800 0 0 0 0
80 0 0 0 0 0 0 0 0 0 6 0 20 0 0 0 0 0 10 60 16 0
i91 193 183 3296 4133 3296 2419 2298 2298 8180 8295 3174 8188 8138 8826 4183 3826 3138 3180 0 0 2419
-8
8 7 9 2 10 12 11 12 10 8 0 0
8
Increase TDS Cost
36 61 18 69 62 67 67 36 40 26 18 4 60 8 21 16
6
the
TDS's,
removing 1000 mg/l.
with
a
desalination
operating
cost
million/y.
I n f a c t a maximum TDS of 2000 mg/l
specified f o r
this
any re-distribution
run
a d e s a l i n a t i o n cost
whereas
plant
between
The h i g h e s t TDS in the system
mg/l a n d no a d d i t i o n a l f l o w s above minimum were r e q u i r e d . assuming
~
Water Flow
of
a maximum o f
100 c / k l ,
anywhere 1334 mg/l
i s 1334
The net system would
be
$2.9
in the mine was
resulted
without
or increase of flows.
For the r u n w i t h no d e s a l i n a t i o n i t was found t h a t i t was impossible to
achieve
a
maximum
TDS
as
low
r e c i r c u l a t i n g more f r e s h water. water
was
relatively
high
but
as
1334
mg/l
everywhere
purely
T h i s i s p a r t l y because the TDS of even
with
better
quality
raw
by
the r a w
water
a v a i l a b l e ) considerable geochemical d e t e r i o r a t i o n o c c u r r e d u n d e r g r o u n d ,
(if
so
125
there
were
limits
to
what
could
be
achieved.
Anyway,
even
maximum TDS of 1603 mg/l,
which exceeds the d e s a l i n a t i o n a l t e r n a t i v e f o r b e t t e r water. hand,
if
TDS
the
recirculation
limit
solution
with
a
the cost of c i r c u l a t i n g water was $6.5 m i l l i o n / y
was
became
relaxed
to
comparable
2000 with
mg/l, the
On
the
the o t h e r
cost
desal i n a t ion
of
the
solution,
namely $2.5 mi 1 I ion/year. should
It
be noted
that
the costs
purchases a n d d e s a l i n a t i o n . used
to pump
maintenance,
to
the m e t a l l u r g i c a l
especially
plant
replacement
c o n s t r a i n t s (maximum TDS)
only
B r i n e disposal
of
were set
include
where
corroded
it
was
only
a
question
of
it
whether
to
more
The
i s omitted
in s a v i n g s
use
Cost, $/a = 2.912175E+6
~~
1
Node1
3 4
0 1 3 6
6
0
6
0 2 4
2
7 8
9 10 11 12 1s 14 16 16 17 18 19 20 21 22
0 6
8 8 9 7 10 7
11 0 12 12 2 3
Node2 1 3 6 7 11 7 4 6 6 8 7 9
2 10 12 11 12 10 8 0 0
4
WatcrFlow
lncmrrTD8 Cod
BpuilibriumTD6
(Ud
(=g/l)
cwn,
(CW)
23 2s 8 8
800 0
30 0 0 0
-8
0
0
-8
0
0
36 61 18 69 62 67
0
0
0
67
36 40 26 18 4 60 8 21 16
0 0
797 798 783 448 843 448 1179 1339 1839 1844 448 1342 1348 681
0
0 0 0 100 0 20 0
200
0
799
0
0
643
200 1800 0 0 0 0
0
799
0 10
681 1344 0 0 1179
1800 400 -1000 0
0
60
16
0
is
cost
of
as
the The
i n replacements
raw
TABLE 8.2 New Water Flows and TDS w i t h d e s a l i n a t i o n
Pipe number
water
problems.
desalinate.
Max TDS 1344 mg/l,
raw
the b r i n e
i s used.
pipes,
to e l i m i n a t e corrosion
d e s a l i n a t i o n system cost i s more than j u s t i f i e d and
pumping,
i s not costed as
water
or
to
126
One
factor
additional
omitted
cooling of
The r a w water
at
this
stage,
the recirculated
however, water,
is
if
the
less
i s g e n e r a l l y a t a lower temperature
requirement
raw
water
for
i s used.
(2lOC) t h a n the water
r e t u r n e d from the mine w o r k i n g s (28OC). The a d d i t i o n a l cost of o p e r a t i n g a desalination
plant
underground
where
access
is
limited,
is
also
not
p r o p e r l y e v a l u a t e d a t t h i s stage. The most economical s i t i n g o f the d e s a l i n a t i o n p l a n t this
reduces p u m p i n g cost
highest TDS concentration
to as
the
surface.
this
results
It
i s u n d e r g r o u n d as
s h o u l d be a t
i n minimum p l a n t
the p o i n t capacity
of per
u n i t removed. The
example
illustrates
the
use
of
the
program
facilitated
rapid
comparison of a l t e r n a t i v e water management systems on a cost a n d q u a l i t y basis. costs
I n general quoted
additional cleaner
are
factors
water,
conservation
of
i t demonstrates t h a t , often
in
favouring less
excess
despite the f a c t t h a t raw
desalination
corrosion
natural
of
and
resources,
water in
industrial
blocking,
less
costs,
pumping
less costs,
Pipe number 1 2 3 4 6 6 7 8 9 10 11 12 13 14 16 16 17 18 19 20 21 22
Node 1
Node 2
Water Flow (116)
namely: greater
and
0 1 3 6
0 0 2 4 0 6 8 8 9 7 10
I 11 0 12 12 2 3
1 3 6 7 11 7 4 6 6 8 7 9 2 10 12 11 12 10 8 0 0 4
176 176 118 118 -8 -8 36 94 18 112 113 212 212 78 194 146 138 116 213 118 176 68
Cost, $/a = 6.544681E+6
Increase TDS Cost ( W l ) (c/W 800 0 0 0 0 0 0 0 1800 400 0 0 0 0 200 0 200 1800 0 0 0 0
30 0 0 0 0 0 0 0 0 0 6 0 20 0 0
0 0 0 10 60 16 0
Equilibrium TDS (mg/l) 800 799 798 1239 1303 1233 1106 1216 1216 1604 1233 1609 1603 1489 1697 1303 1697 1489 1604 0 0 1106
often
systems,
Optimum Flows to reduce TDS to 1603 mg/e
Best o b t a i n a b l e without d e s a l i n a t i o n ,
are
effluent,
consumption. TABLE 8.3
desalination
there
lower
water
127
REFERENCES
A b u l n o u r , A.M., S o r o u r , FA.H., Hammouda, F. and A b d a l Dayem, A.M., 1983. S q u e e z i n g d e s a l t e d w a t e r c o s t s b y p r o p e r c h o i c e o f t h e d e s a l t i n g t e c h n o l o g y a n d w a t e r management. D e s a l i n a t i o n , 44, 189-198. B a k e r - D u l y , H.L.G., 1985. O p t i m i z a t i o n o f w a t e r r e t i c u l a t i o n s y s t e m s a t L o r a i n e G o l d M i n e L i m i t e d , Proc. Mine V e n t i l a t i o n Society of South A f r i c a Conf. H o l t o n , M.C. and Stephenson, D., 1383. A c o m p u t e r model o f c i r c u l a t i n g s e r v i c e w a t e r i n S o u t h A f r i c a n g o l d m i n e s . I n t l . J. M i n e Water, 2 ( 2 ) 33-42. L o u c k s , D.P., R e v e l l e , C.S. and Lynn, W . R . , 1967. L i n e a r p r o g r a m m i n g m o d e l s f o r w a t e r p o l l u t i o n c o n t r o l . M a n a g e m e n t Science, 14, 8166-8181. Rinaldi, S., Soncini-Sessa, R., Stehfest, H. and T a m u r a , H., 1979. M o d e l l i n g and C o n t r o l o f R i v e r Q u a l i t y , McGraw H i l l , New Y o r k . Smeers, Y . and T y t e c a , D., 1981. On t h e o p t i m a l l o c a t i o n o f w a s t e w a t e r treatment p l a n t s , I n : J. T h i s s e and J. Z o l l e r ( E d s . ) , L o c a t i o n and A n a l y s i s o f P u b l i c F a c i l i t i e s , N o r t h H o l l a n d , Amsterdam. 1981. C i v i l E n g i n e e r i n g Systems S m i t h , A.A., H i l t o n , E. and L e w i s , R.W., A n a l y s i s and D e s i g n . Stephenson, D., 1983. D i s t r i b u t i o n o f w a t e r in g o l d m i n e s i n S.A., Intl. M i n e Water J . , 2 ( 2 ) 21-30. Stephenson, D., 1986. Computer analysis justifies desalination. Desa I i n a t i o n , 58, 155-167. Stephenson, D. a n d C o r b e t i s , S . , 1984. Economics o f d e s a l i n a t i o n o f w a s t e w a t e r s f r o m t h e W i t w a t e r s r a n d , Proc. I n t l . Conf. o n Water Resources and Desalination. Johannesburg, South A f r i c a , Water S u p p l y Improvement Assn.
128
APPENDIX 8.1
MlNSlM PROGRAM FOR SIMULATING FLOW AND TDS IN CLOSED SYSTEMS
The
program
is
for
simulating
r e t i c u l a t i o n systems.
It
concentration
nodes,
at
all
flow
TDS
and
and
plots
it
at
any
in
changes
i s based on nodes a n d l i n k s ,
and
water
TDS
calculates
selected
node.
Volume
v a r i a t i o n s a t nodes a r e p e r m i t t e d a l t h o u g h zero volume nodes can a l s o be specified.
will
The program
selected scale o r v i e w i n g
also draw
angle.
The
a
picture
program
of
is
the
system
BASIC 3.0
in
at
for
any
HP
a
9816 micro computer. To
account
for
TDS
build-up
along
a
route,
one
may
specify
the
increase in TDS a l o n g the r o u t e in mg/l. I f d e s a l i n a t i o n i s done, When
evaporation
a n e g a t i v e increment i n TDS i s inserted.
increases
TDS
the
concentration
specifies a n e g a t i v e flow to t h a t node from another
at
any
node
one
'0'
node such as node
a t the node of o r i g i n a n d zero increase i n TDS a l o n g the l i n k route. The volume a t each node i s set v a l u e i s zero o r n e g a t i v e , equal
outflow.
during
the
nodes,
It
day
is
from
a no-volume
therefore a
zero
node i s assumed a n d
not
possible
to
specify
volume
node.
From
other
t h e a v e r a g e flows
must
variations
positive
volume
Then
in o r d e r
i n t o a n d out of a l l nodes
not the p e a k s w h i c h a r e s p e c i f i e d in the
should b a l a n c e d u r i n g each d a y ,
i.e.
I f this
inflow
flow
the flow can be s p e c i f i e d over so many h o u r s a d a y .
not to cause extreme volumes,
data.
i n i t i a l l y a t a s p e c i f i e d value.
Q.Tin should = 0 over 24 hours.
A maximum of 5 p i p e s o r l i n k s a r e p e r m i t t e d to each node.
When before
inputting data
reading
in
dummy p i p e from
data
make sure on
the
the
( I ) node h a s been
'top'
'bottom'
(J)
node.
' 0 ' to the node i n question
Node 0 need not be so defined node 0 a r e p l o t t e d b u t
it
r e d e f i n e the TDS a t node 0,
wise
to
necessary
to d e f i n e
as no p i p e s from
i s not
If
use
a
i t s co-ordinates.
i t are plotted.
have pipes
defined
to 0 a s
Pipes they
to
will
w h i c h c o u l d otherwise b e used as a s i n k f o r
e v a p o r a t i o n and a source f o r f i s s u r e s w h i c h would then increase i n TDS b y a given figure. Costs a r e c a l c u l a t e d i n D o l l a r s p e r annum
if
prices
i n c/kl
are input
in d a t a .
Tape or Disc Management The
programme
MlNSlM
can
be
copied
onto
new
tapes.
Data
files
129
cannot.
They
have to be typed i n l i n e b y l i n e a f t e r the f o l l o w i n g
i s set
u p on the tape. CREATE "DATMIN",
100,88.
T h i s creates a f i l e o f
100 records
(for
p i p e s ) each 88 b y t e s long p e r m i t t i n g 11 x 8 b y t e numbers p e r record. erase a p r e v i o u s d a t a f i l e m i g h t have to
be closed
purge
manually
it
a n d re-create
after a
it.
bomb out.
executing the program i t pauses and asks whether
Note a
data
Alternatively
100 To file
while
graphics o r re-write
of
d a t a i s r e q u i r e d . A new tape could be inserted a t t h i s stage.
MlNSlM L i s t of Symbols A1 A2 B1-9 C c2
E( F( ) G( G1 GO
H( H1 I( J(
K ( I ,MI L( 1 L1 MO M M1 M2 M3 M5 N NO N1
N2 N3 N4 P( PO Q( 91
1
ZQ
R( S( s1 T1 T2 T3 T4
a n g l e of v i e w i n g p l a n e from X a x i s , degrees a n g l e of v i e w i n g p l a n e from 2 a x i s , degrees dummy i n p u t f o r a l t e r a t i o n s p r i c e c/kP t o t a l cost/rands p e r annum i n i t i a l volume, m3. Use n e g a t i v e o r zero v a l u e to s i g n i f y constant outflow over 24h. Must then b a l a n c e flows over 24h not a t peaks. new mg/P a t node p o l l u t a n t concentration mg/P a t node G counter f o r p l o t s used in c a l c u l a t i o n of TDS a t nodes head, m not used size of device top node of p i p e bottom of p i p e number of p i p e s connecting i n t o node ( u p to 5 p e r m i t t e d ) length, m distance to device p i p e counter Pipe number of nodes connecting p i p e counter counter f o r i n i t i a l flow c a l c u l a t i o n s p i p e no. of device node counter device p e r p i p e node a t w h i c h TDS i s to b e p l o t t e d 1 = TDS concentration p l o t r e q u i r e d 2 = volume a t node, m3 0 = o l d data, 1 = new, 2 = r e v i s e d 1 = g r a p h i c d i s p l a y , 0 = none, 2 = r e c o r d d a t a a n d stop i n p u t p o l l u t a n t concentration a t node 2, mg/e i n t o p i p e in it i a I concentration flow P / s
1
design flow i n p i p e P / s volume m3 S coun'ter f o r p l o t s d u r a t i o n of simuln. d a y s s i m u l a t i o n i n t e r v a l , hours d r a w o f f hours/day (1st hours of d a y ) time i n t e r v a l s f o r d r a w o f f p e r i o d
1 30 T5
device type; 1 = f l a n g e , 2 = v a l v e , 4 = a r r o w , 5 = square no. i t e r a t i o n s p e r d a y i t e r a t i o n counter d a y counter d a y counter screen X co-ordinate screen Z co-ordinate X m i n on screen X max on screen Z m i n on screen Z max on screen X co-ordinate Y co-ordinate Z co-ordinate
3 = tank,
Data Input
The computer asks f o r the f o l l o w i n g d a t a to be typed i n i n t e r a c t i v e l y :
Ll L2 L3 L4 L5 L6 L7
L B et seq
System name Simulation p e r i o d , d a y s Time increment, d a y s Period in h o u r s p e r d a y d u r i n g which d r a w o f f occurs. The b a l a n c e of the time water may flow to r e f i l l r e s e r v o i r s . I n i t i a l TDS of the e n t i r e systems, mg/P Node no. a t which a p l o t o f TDS versus time i s r e q u i r e d Type 0, 1 o r 2 depending on whether the o l d d a t a f i l e , a new one o r a r e v i s i o n of the o l d one i s r e q u i r e d Type the f o l l o w i n g separated b y commas, w i t h one l i n e p e r pipe o r conduit; Top ( u p s t r e a m ) end node no. Bottom (downstream) end node no. x-co-ordinate of bottom node ( h o r i z o n t a l l y from a d a t u m ) y-co-ordinate of bottom node ( v e r t i c a l l y ) z-co-ordinate of bottom node ( i n t o screen) Volume of storage a t bottom node, m’ Design flow in P / s ~ n p u tp o l l u t i o n , mg/e Cost a l o n g route, cents p e r u n i t o f flow (ke) Type a row of n i n e zeros to end t h i s d a t a L a t e r the program may c a l l f o r a d d i t i o n a l g r a p h i c s d a t a p e r pipe : Pipe no. (counted from the top of the l i s t ) Position ( d i s t a n c e from top end o f p i p e ) to a device Device t y p e ( 1 = f l a n g e , 2 = v a l v e , 3 = t a n k , 4 = a r r o w , 5 = square) Size, m to d r a w i t Cost p e r u n i t size
The d a t a w i l l then be f i l e d f o r subsequent re-use b y the second program MINOP. Examples of o u t p u t , g r a p h i c s a n d i n p u t a r e g i v e n in the char, ter.
131 Program listing 1 I RE-STORE"MINS1M'
10 I MINE WATER RETIC SIMULATION I"M1NSIM" 1 1 GRAPHICS OFF 12 DUMP DEVICE I S 707,EXPANDED 1 4 PRINTER I S 707 2 0 ASSIGN O P a t h l TO "DATMIN" I CREATE "FILNAM",100,88 ag"DATM1N" 2 1 D I S P "SYSTEM NAME"i 22 INPUT NS 2 4 PRINT NE 99 ) , J ( 99 ) ,K( 99.5 ) 2 5 INTEGER N ,NO ,N1 ,N2 ,N3 ,N4 ,M ,M0 ,M1 ,M2 ,M5 ,S I ,I( 2 7 D I M X ( 9 9 ) , Y ( 9 9 ) .Z( 9 9 ) ,U( 9 9 ) ,W(99) ,P( 9 9 ) , H ( 9 9 ) ,6( 9 9 ) , S ( 9 9 ) 30 D I M E( 9 9 ) ,R( 9 9 ) ,P( 9 9 ) ,L( 9 9 ) .F( 9 9 ) ,C( 99 ) 31 D I S P "DURN OF SIMULATION,DAYS"I 3 2 INPUT 1 1 33 D I S P "TIME 1NCREHENT.HOURS"t 3 4 INPUT 1 2 3 5 D I S P "FLO OVER HOURS/DAY"i 36 INPUT T3 37 D I S P " I N I T I A L TDS,mQ/l"( 3 8 INPUT P0 39 D I S P "PLOT TDS AT N0DE"i 4 0 INPUT N1 4 2 DEG 4 3 D I S P "OLD OR NEW OR REV D A T A ( 0 / 1 / Z ) " i 45 INPUT N3 61 NZ-1 62 T4-T3/T2 I I T S / d 66 1 7 - 2 4 / 1 2 70 G(O )=0 80 X ( 0 )-0 90 Y(0j-0 1 0 0 Z(0)-0 110 E ( 0 ) - 0 111 FOR N-1 TO 9 9 112 S ( N ) = 0 113 E ( N ) - 0 114 F ( N ) = 0 115 X ( N ) = 0 116 Y(N)=0 117 Z(N)=0 118 C(N)-0 1 1 9 NEXT N 120 c2-0 122 G( 1 )=P0 1 2 5 M1=0 130 FOR M=1 TO 9 9 1 4 0 I F N3C>1 THEN 190 1 4 5 I NEW PIPE DATA 150 DISP "N1 ,N2,X2,YZ,ZZ,U2,l/s,tmg/l,c/"i 1 6 0 INPUT I ( M ) , J ( M ) , X ( J ( M ) ) ,Y( J ( M ) ) ,Z( J ( M ) ) ,E( J ( M ) ) , R ( M ) ,P(M) ,C( M ) 170 OUTPUT @ P a t h 1.Mi I ( M ) , J ( M ) , X ( J ( M ) ) .Y( J ( M ) ) ,Z( J ( M ) ) ,E( J ( M ) ) , R ( M ) , P ( M ) ,C(M) 1 8 0 GOT0 2 10 1 8 5 I OLD PIPE DATA 1 9 0 ENTER @ P a t h 1, M i I ( M ) , J ( M ) , X ( J ( M ) ) , Y ( J ( M ) ) , Z ( J ( M ) ) ,E( J ( M ) ) ,R(M),P(M),C(M) 2 1 0 I F I ( M ) + J ( M ) = 0 THEN 228 212 S(J(M))=E(J(M)) 218 G(J(M))-P0 2 2 0 C2=CZtC( M )rR( M )*315 225 M l = M l + l
132
226 228 230 231 232 233 234 235 245 246 ?48 249 251 253 254 255 256 257 258
262 263 264 265 267 268 269 270 271 272 274 276 278
286 706 705 707 708 710 71 1 720 730 740 750 760 770 780 790 800 810 820 830 835 840 845 850 851 854 855
NEXT M I F N3<2 THEN 256 FOR M0=l TO 99 I REV P I P E DATA DISP "PIPE N o . " i INPUT M C2=CZ-C( M ) * R ( M ) * 3 1 5 DISP "N1 , N 2 , X 2 , Y 2 , ~ 2 , U 2 , l / s , t m g / l , c / " i INPUT I ( M ) , J ( M ) , X ( J ( M ) ) , Y ( J ( M ) ) ,Z( J ( M ) ) ,E( J ( M ) ) , R ( M ) , P ( M ) , C ( M ) OUTPUT B P a t h l , M i I ( M ) , J ( M ) , X I J ( M ) 1 , Y ( J ( M ) ) ,Z( J ( M ) ) ,E( J ( M ) ) , R ( M ) , P ( M ) ,C(M) I F I ( M ) t J ( M ) = 0 THEN 256 I F MCMl THEN 251
Ml=MI+l S ( J ( M ) )=E( J ( M ) ) G( J ( M ) )-P0 CZ=C2+C(M)*R(M)*315 NEXT M 0 FOR M - l TO M 1 L ( M ) = S Q R ( ( X ( J(M))-X(I(M)) ) ^ 2 + ( Y ( J ( M ) ) - Y ( I ( M ) ) ) * 2 + ( 2 ( J(M))-Z( I ( M ) ) ) ^ 2 1 NEXT M PRINT "N1 N2 X2 Y 2 22 U2 Q t m g c / " FOR M=1 TO M 1 PRINT USING 2651 I ( M ) , J ( M ) , X ( J ( M ) ) , V ( J ( M 1 ) ,Z( J ( M ) ) ,E( J ( M ) ) , R ( M ) . P ( M ) , C ( M ) IMAGE 20,2D ,5D, 4D,5D ,4D ,3D, 4D,3D NEXT M D I S P "LAYOUT GRAPHICS(0=NO,l=YES,2=RECORD DATA & STOP ) " I INPUT N4 I F N4<2 THEN 2 8 0 ASSIGN O P a t h l TO "DATMIN" FOR M=1 TO 99 OUTPUT @ P a t h 1, M i I ( M ) , J ( M ) ,XC J ( M ) ) , Y ( J ( M ) ) ,Z( J ( M ) ) ,E( J ( M ) ) , R ( M ) ,P(M) ,C(M 1 I F I ( M ) t J ( M ) = 0 THEN 2910 NEXT M I F N4-1 THEN 1570 ALPHA OFF GINIT GRAPHICS ON I F N2>1 THEN 8 5 0 WINDOW - . 5 , T I . - 2 0 0 , 2 * G ( I )t3000 C L I P 0 ,T1 ,0 ,2*Gc 1 )+3006 AXES 1 ,100 C L I P OFF MOUE T1-1,10 LABEL " O A Y " FOR T0=1 TO T I MOVE TO-.5,-200 LC\BEL UALO(T0) NEXT T0 FOR G I - 0 TO 2 * G ( l ) + 2 5 0 0 STEP 500 MOUE -.5,G1 LABEL UALS(G1 ) NEXT 61 MOUE .5,2*G( 1 )+600 LABEL "TDSmg/l NODE"LUALB(N1 ) 60TO 890 WINDOW -.5,Tl ,-10,E(NI ) t l U C L I P 0 , T l .-10,E(N1 ) + I 0 AXES 1 , l C L I P OFF
133 857 868 860 862 864
MOUE T l - 1 ,0 LABEL "DAY" FOR T0=l TO T1 MOUE T0-.5,-10 LABEL UALS(T0 ) 866 NEXT 1 0 8 6 8 FOR S l - 0 TO E ( N 1 ) t l O STEP 10 870 MOUE -.5,S1 872 LABEL UCILL(SI ) 874 NEXT S1 876 MOUE B,E(Nl ) + I 0 878 LABEL "UOLn3,NODE"bUALO(Nl) 890 I END OF LABELING 900 FOR N=1 TO M l t l I NODES CONS 905 M2=0 906 FOR M0=l TO 5 907 K ( N ,M0 )-0 908 I ( K ( N , M 0 ) ) = 0 909 J(K(N,M0))=0 910 NEXT MO 915 FOR M0=1 TO M 1 1 PIPES 920 I F I ( M 0 ) < > N THEN 940 925 MZ-M2tl 927 K ( N ,M2 )-M0 930 GOTO 960 940 I F J(M0)<>N THEN 968 945 M2=M2+1 950 K(N,MZ)=MB 960 I F M2-5 THEN 970 968 NEXT M0 970 NEXT N 975 I F NZ>l THEN 990 980 MOUE 0,G(N1 ) 985 GOTO 1090 990 MOUE 0,S(Nl ) 1090 FOR T=1 TO T l ! DAYS 1100 FOR T9=1 TO T7 1105 I F T9>T4 THEN 1160 1110 FOR M=1 TO M1 1145 Q ( M ) = R ( M ) 1155 NEXT M 1157 GOTO 1200 1160 I F E ( I ( M ) ) < = 0 THEN 1200 1195 Q(M)-0 1200 TDS a STORAGE TINS 1210 FOR N-1 TO M 1 + 1 1220 I F E ( N ) > 0 THEN 1340 1225 Gl=Q 1228 Q1=.001 1230 FOR M0-1 TO 5 I 2 3 5 I F J ( K ( N , M B ) ) O N THEN 1280 1236 I F G( I ( K ( N , M 0 ) ) )+P(K(N ,M0) )<=0 THEN 1255 1240 G1=( G( I ( K ( N ,M0) ) ) t P ( K ( N , M I ) ) )*Q(K(N .M0) )+G1 1255 01 =Ol + Q ( K ( N ,M0 ) ) 1280 NEXT MO 1282 G l = G l / Q l 1285 GOTO 1440 1340 G l m 0 1 S>0 1345 G0=G( N )*S( N )
134
1350 FOR MO-1 TO 5 1360 I F J(K(N,M0))<>N THEN 1390 1370 G1-61+(6( I ( K ( N,M0 ) ) )+P(K( N ,M0 ) ) )*Q( K ( N ,M0 ) ) 1375 S(N)=S(N)tQ(K(N,MB) )*T2*3.6 1380 GOT0 1420 1390 I F I(K(N,MB))<>N THEN 1420 i 400 GI=GI-G(N')*Q(K(N ,MQ ) ) 1412 S(N)=S(N)-Q(K(N,MQ) )*T2*3.6 1428 NEXT M 0 1430 61-( 61 *T2*3.6+60 ) / S ( N ) 1440 F ( N ) = G l 1472 NEXT N 1474 FOR N-1 TO M l + l 1476 G(N)=F(N) 1488 NEXT N 1492 I F N2>1 THEN 1488 1485 DRAW T - l t T g * T 2 / 2 4 , 6 ( N l ) 1486 60TO 1490 1488 DRAW T - l t T 9 * T 2 / 2 4 , S ( N l ) 1490 NEXT T9 1492 NEXT T 1494 DUMP GRAPHICS 8707 1496 GOT0 2920 1570 DISP "XMIN ,XMAX ,ZMIN ,ZMAX ,XANGL ,ZANGL' I 1580 INPUT ~ 0 , ~ 9 , ~ 0 , ~,AZ 9 , ~ 1 1590 GINIT 1592 GRAPHICS ON 1595 DEG 1600 WINDOW UQ,U9,W0,W9 1601 FOR M=1 TO M 1 ! NODES 1602 U(M)=X(M)*COS(Al ) t Y ( M ) + S I N ( A l ) 1604 W ( M )-Z( M )+COS( A2 ) t (Y ( M )tCOS( A1 )-X( M )*SIN( A 1 ) )*SIN( A2 1608 NEXT M 2170 FOR M=1 TO M l ! PIPES 2190 PEN 1 2195 I F I ( M ) - 0 THEN 2225 2196 I F J(M)-0 THEN 2230 2200 MOUE U ( I( M ) ) ,W( I( M ) ) 2210 DRAW U ( J ( M ) ) , W ( J ( M ) ) 2220 LABEL Uc\L$( J ( M ) ) 2223 GOT0 2230 2225 MOUE U( J ( M ) ) ,W ( J ( M ) ) 2228 LABEL UALO( J ( M ) ) 2230 NEXT M 2235 FOR N0=l TO 3 2240 FOR N=1 TO 100 2241 I F N>Ml THEN 2415 2242 I F NO-1 THEN 2256 2243 I F N0=3 THEN 2269 2246 M5-N I ARROWS 2247 I F I ( N ) = 0 THEN 2410 2248 L l = L ( N ) / 2 2249 I F J ( N ) - 0 THEN 2410 2250 T5=4 2251 Hl-L1/10 2254 C0-0 2255 GOTO 2320 2256 M5=N ! TANKS 2258 L l = L ( N ) 2260 1 5 1 3
)
135 2262 H l = E ( J ( N ) ) / 2 5 2264 C0=0 2266 GOT0 2320 2268 ALPHA ON 2 2 7 0 DISP "PIPEn ,X ,TYPE ,SIZE .COST/' 1 2280 INPUT M5,Ll ,T5,H1 ,C0 2 3 2 0 I F M5-0 THEN 2420 2340 X5=X( I ( M 5 ) ) + L l / L ( M 5 ) * ( X ( J(M5 1 )-X( I ( % ) ) ) 2350 Y5=Y( I ( M 5 ) )+Ll /L(M5 ) * ( Y ( J( M5 ) )-Y( I(M5 ) ) ) 2360 Z5=Z( I ( M 5 ) )+L1 /L(M5 )+(Z( J(M5) )-Z( I ( M 5 ) ) ) 2 3 7 0 US=XS*COS(AI ) t Y 5 * S I N ( A 1 ) 2 3 8 0 W5=Z5*COS(A2 )t(YS*CDS(Al )-XS*SSN(Al ) ) * S I N ( h Z ) 2390 ON T5 60TO 2460,2490,2540,2590,2850 2400 I l=FLANGE,Z=UALUE,3=TANK,4=~RROW,S=S~UARE 2 4 1 0 NEXT N 2415 NEXT N0 2420 MOUE U0,WB 2430 C2=1NT(C2 ) 2440 LABEL " R/s="LUALO(C2) 2445 DUMP GRAPHICS 2 4 5 0 60T0 7 0 0 2460 MOUE US ,W5tHI / 2 2 4 7 0 DRAW US ,W5-H1/2 2480 GOT0 2410 2 4 9 0 HOVE U5-H1/2,WStH1/2 2500 DRAW U 5 t H I 12 ,WS-HI / 2 2510 MOUE U5+Hl/2,WS+H1/2 2520 ORAW U5-H1/2,U5-H1/2 2530 GOTO 2410 2540 MOUE U5-HI / 2 ,WStWI 2550 DRAW U 5 - H l / 2 ,W5 2560 DRAW U S H 1 / 2 ,WE 2 5 7 0 DRAW U5+Hl/Z,W5+Hl 2580 60TO 2410 2590 I F U ( J ( M S ) ) < > U ( I ( M S ) ) THEN 2601 2591 IF W ( J ( f l S ) ) > W ( I ( M 5 ) ) THEN 2594 2592 U8=270 2 5 9 3 GOTO 2608 2594 U8=90 2595 GOT0 2608 2601 UE=ATN( (U( J( M 5 ) )-W( I( M5 ) ) ) / (U( J ( M 5 ) )-U( I( M5 ) ) ) ) 2602 I F U8>=0 THEN 2606 2603 I F W ( J(M5) ) < W ( I(M5) 1 THEN 2608 2604 GOTO 2607 2606 I F U ( J ( M S ) ) > W ( I ( M S ) ) THEN 2608 2607 U8=U8t180 2608 UG=U5-Hl*COS(U8-45) 2610 W6=W5-Ht*SIN(U8-45) 2 6 2 0 U7-U5-Hl*COS(U8t45) 2630 W7-W5-Hl*SIN(UEt45) 2 8 1 0 MOUE U6,W6 2820 DRAW U5,W5 2830 DRAW U7,W7 2 8 4 0 6QTO 2410 2850 MOUE US-H1/2,WStHl 2860 DRAW U5-H1/2 ,W5 2a70 DRAW u 5 + ~ 12 1 ,w5 2880 DRAW U5tH1/2,W5tHI 2890 DRAW U5-H1/2,W5tHl 2900 60TO 2410 2920 END
136
APPENDIX 8.2
MINOP p r o g r a m f o r o p t i m i z i n g d i s t r i b u t i o n
MlNOP List of Symbols p r i c e c/ke cost t o t a l cost dummy TDS max. TDS desired, o r G of node w i t h m a x . T D S increment i n TDS max. increment i n TDS t o t a l TDS - mg/s i n t o node t o t a l flow i n t o node TDS G(I) - H(I) max. TDS top node bottom node p i p e no. connecting to node ( u p to 5 p e r m i t t e d ) number of p i p e connecting number loops best loop no. branches i n loop p o s i t i v e loop p i p e s out node loop counter number loops a n d b e g i n number loop number connecting p i p e s to node p i p e number p i p e counter number of nodes number of p i p e s in loop number of connecting p i p e s from node dummy p i p e s out node number of p i p e s in loop r e d u c t i o n i n no. p i p e s in loop, o r , p i p e to node w i t h max. TDS p i p e number i n loop b e g i n p i p e f o r loops name node counter no. nodes p i p e no. i n p u t TDS, mg/e flow e/s dQ/dC dQ co-ord. not used i n MINOP 0,
I1
137
Notes on program
The program i s in BASIC for an HP 9816 series 200 micro computer. data f i l e i s obtained from the M l N S l M program in appendix 8.1.
The
138 Program
MINOP
listing
101 RE-STORE"MIN0P" 20 I "MINOP " OPTIMZS FLOS I N NETWORK SUBJECT TO TOS L I M I T S 3a PRINTER IS 707 40 A S S I G N @ P a t h 1 TO "DATMIN" 5 0 I D I S P "SYSTEM NAME"! 60!INPUT NO 7 0 I P R I N T NC DIM Q( 9 9 ) ,G(99) ,P( 9 9 ) ,C( 9 9 ) , L ( 9 9 ) ,H( 9 9 ) 80 , M 2 ( 5 0 , 5 0 ) , M 3 ( 9 9 ) .M4 ,M INTEGER I ( 9 9 ) , J ( 9 9 ) , K ( 9 9 , 5 ) , K 1 ( 9 9 , 9 ) , L l ,L2 ,L3,M,M0,Ml 90 S.M6(99),M7,M8,M9,N,Nl 1 0 0 M I 1 0 1 NO.PIPES 110 G ( 0 ) = . 1 120 N l = l 130 DISP "MAX TDS DES1RED"i 1 4 0 INPUT 6 0 1 5 0 FOR M=l TO 9 9 ENTER @ P a t h 1,M; I ( M ) , J ( M ) ,X ,Y ,Z ,E ,Q( M ) ,P( M ) ,C( M ) 160 H( .I(M ) )=G0 170 I F I ( M ) t J ( M ) = 0 THEN 2 5 0 180 I F I(M);=Nl THEN 2 1 0 190 Nl=I(M) 200 If J ( M ) < = N l THEN 2 3 0 216 N1 =.Jc M ) 220 MI-Mltl 230 2 4 0 NEXT M 250 H(0)-100000 2 6 0 FOR M0=l T O M 1 D I S P "ANY CHANGES? PIPENo,TOPn,BOTn,FLOI/s,POLmg/l , c / h 1 (O's=none ) " I 2 70 280 INPUT M , I ( M ) , J ( M ) ,QC M 1 ,P( M ) ,C(M ) 290 I F I ( M ) + J ( M ) = 0 THEN 3 2 0 I F M > M l THEN M l = M l t l 300 310 NEXT MO I NODES 3 2 0 FOR N-0 TO N l G( N )=G0 330 340 M3( N )=0 L( N )=0 350 FOR M=l T O M l I P I P E S FROM NODE 360 I F I ( M ) < > N THEN 4 0 0 370 M3( N )-M3( N ) t1 380 K l ( N ,M3( N ) )=M 390 NEXT M 400 FOR M0=1 TO M 1 I P I P E S TO NODE 410 I F J ( M Q ) < > N THEN 4 5 0 420 L( N )=L( N ) + 1 430 K ( N L ( N ) )=NO 440 NEXT M0 450 4 6 0 NEXT N 4 7 0 G( 0 1-0 4 8 0 L1=01LOOFS 4 9 0 FOR.M9=1 TO M1 IBEGINPIPE FOR LOOPS L 0 - L l t l ITRY LOOP 500 L8=0 51 0 M G ( L 0 ) = l I N O . P I P E S I N LOOP 520 M2(L0,1 )=M91PIFES I N LOOPI 530 LE=LBIPOS LOOP 540 FOR L 3 = 1 TO MlIBRANCH ROUTINE 550 L8=0 560 L4=M3( J ( M 2 ( L0 ,M6( L0 ) 1 ) ) 570 FOR M5=1 TO L 4 I P I P E S OUT NODE 580 ~
139 5 90 600 610 620 630 640 650 660
I F M5-1 THEN 670 L6=LG+lIANOTHER POS LOOP FROM BRANCH M6(L6 )=M6(L0) FOR M7=1 TO M6(L6)-1 MZ(L6 ,M7)42(LB,M7 )ICOPIES PIPES I N PREU LOOP NEXT M7 M 2 ( L6 ,M6(L6 ) )=K 1 ( J ( M 2 ( L 0 ,M6( LO ) - 1 ) ) ,M5 ) GOTO 690 M6(L0)=M6(L0)+1 IN0 PIPES I N LOOP 670 M2( L 0 ,M6( L 0 ) )=K 1 ( J ( M 9 ( L0 ,M6( L0 1- 1 ) ) ,M5 ) I NEXT PIPE 680 NEXT M51 CHEK LOOP CLOSURE 690 FOR M5-2 TO M6(L0) 700 71 0 FOR M7=1 TO M5 IF I( MZ(L0 ,M7) ) < > J M ( Z ( L 0 ,M5) ) THEN 800 720 L1=L1 t 1 730 M6(L1 )4lS+I-M71SHUFFLE UP PIPES 740 FOR M8=l TO M 6 ( L l ) 750 M Z ( L I ,M8 )-M2( L 0 ,M8+M7- 1 ) 760 NEXT ME 770 L6=1 780 GOTO 840 7 90 NEXT M7 800 NEXT M5 81 0 GOTO 1000 820 I CHEK DUP LOOP 830 I F L l ; = l THEN 1000 840 FOR LZ=1 TO L1-1 850 M=O 860 FOR M7=1 TO M6(Ll ) 870 M=Mt 1 880 ME-1 890 I F M Z i L l ,M)OM2(L2,M8) THEN 980 900 91 0 M8=M6+1 M=Mt 1 920 IF M:=MG(LI) THEN 950 930 M= 1 940 950 I F M8:=M6(L7) THEN 9G8 Ll=Ll-llREMOUE OUP L O O F 960 GOTO 1000 970 NEXT M7 980 NEXT L2 990 I F L 8 < - 0 THEN 1030 1000 I F L 6 ‘ = L 0 THEN 1040 1010 L0=L0+ 1 1020 1030 NEXl L3 1040 NEXT M9 I 0 5 0 FOR L:=l TO L I 1060 FOR M=I TO M 6 ( L 2 1 IQ701PRINT L:,MZ(L2,W) 1080 NEXT M 1090 NEXT L2 1100 GOSU8 1120 1110 GOTO 1300 1120 FOR L4=1 TO Mi 1130 G5-0 1140 FOR N=i T O N l 1150 Gl=.l 1160 G’L=.I 1170 FOR O=l TO L ( N ) Gl=Gl t Q ( K ( N,O ) * ( G : I ( k‘: N , O ) ) ) t F ( K ( N ,O ) ) ) 1180
140
1190 62=62tQ(K(N,O)) 1200 NEXT D 1210 63=6(N) 6(N )=GI 162 1220 64=AES( 6( N )-63)/G(N ) 1230 1240 I F 64<65 THEN 1260 1250 6544 1260 NEXT N 1270 I F 65<.00I THEN 12901 MAX FC 1280 NEXT L 4 1290 RETURN 1300 FOR M=1 TO N1 IITNS 1310 RI=BIDQ/DC 1320 R3=0IDQ 1330 FOR L 2 = l TO LllEEST LOOP 1340 C1=0 1350 H1=0 1360 M0=6 1370 FOR M8=1 TO MSfL2 ) C1 =C1tC(MZ(L2 ,M8 ) ) 1380 1390 I F Q ( M 2 ( L Z 3 M 8 ) ) < 0THEN 1540 1400 M0=M8 Q( M2( L2 ,M8 ) )=Q( M2( L2 ,M8 ) ) t1 14 10 1420 I F J(M2(L2,M8))=0 THEN 1470 1430 I F G( J ( M 2 ( L2 ,M8 ) ) )-H( J( M 2 ( L Z ,M8 ) ) )<=HI THEN HI =G( J( M 2 ( L2 ,M8 ) 1 )-H( J ( M 2 ( L2 ,M8 ) ) ) 1440 1450 M7=MZ(L2,MB)IPIPE TO NODEWITH MAX TDS 1460 60=G(J(MZ(LZ,M8))) 1470 NEXT ME 1480 I F H l i = l THEN 1540 1490 GOSUE 1120 1500 I F ( G Q - G ( J ( M 7 ) ) ) / C I ~ ' = R 1THEN 1540 1510 Rl=(G0-G( J(M7) ) ) / C l R3=(G0-H( J(M7)) ) / t G Q - G ( J ( M 7 ) ) ) 1520 1536 L3=L2 1540 FOR M8=1 TO MQ Q( MZ(L2 ,ME) )=Q(MZ(L? , M a ) ) - 1 1550 1560 NEXT M8 1570 NEXT L t 158@ FOR M7=1 TO M6(L3i 1590 Q ( M ~ ~ L ~ , M ~ ) ) I Q ( M ~ ( L )~t ,RM3 ~ ) 1600 NEXT M7 1610 NEXT M 1620 C 2 = 0 1630 PRINT " P n N l N2 1 / s tTDSng1 c / L 1 T D S 2 ' 1640 FOR M-1 TO M1 1650 PRINT USING 1660;M,I(M) , J ( M ) , Q ( M ) ,P(M) , C ( M ) ,G( 1660 IMAGE 2D ,4D ,4D ,4D ,6D ,50 ,SO 1670 C2=C2tC(fl)*Q(M)*315 1680 NEXT M 1690 C2=INT(C2 ) 1706 PRINT "COST ,R/a="i C Z 1710 ASSIGN 0Pathl TO 1720 EN0
INEXT LOOP
!NEXT PIPE 1470
J(M))
141
CHAPTER 9
INTEGER PROGRAMMING PLANN ING OF TREATED WASTEWATER CONVEYANCE FOR ARTIFICIAL RECHARGE OF AN AQUIFER
INTRODUCTION
The
international
growth
has been p e r s i s t e n t l y h i g h . l a r g e p r o p o r t i o n of living.
i n water
demand over
the
last
few
decades
T h i s r a t e of growth i s l i k e l y to c o n t i n u e a s a
the p o p u l a t i o n
is
increasing r a p i d l y
in
standard
of
The a v a i l a b i l i t y of new sources of water h a s tended to l a g b e h i n d
demand. Even i f new sources were a v a i l a b l e the cost of p r o v i d i n g to meet any
possible
drought
extreme
in
developing
account of the u n r e l i a b i l i t y of r i v e r flow.
areas
could
be
high,
on
Surface water can o n l y be used
i f a l t e r n a t i v e sources a r e a v a i l a b l e to meet essential
t o i t s f u l l e s t extent
demands i n times of d r o u g h t .
For t h i s reason the w o r l d i s now
l o o k i n g to
groundwater a n d wastewater to meet s h o r t f a l IS.
A scheme i s i n v e s t i g a t e d here to s u p p l y from groundwater o n l y a t
the
r a t e a t which i t can be n a t u r a l l y replenished.
Separate studies a r e b e i n g
conducted on t e r t i a r y
but
wastewater now
treatment of
to a r t i f i c i a l l y
wastewater
recharge groundwater
r e c e i v i n g consideration.
Such
research
with
is
cannot be expected to re1 ieve c u r r e n t droughts,
the
a
idea of
using
wastewater
long
term
the
is
only
project
and
w h i c h however p r e c i p i t a t e d
research i n t o a l t e r n a t i v e sources of water. It
i s proposed
resources
in
to
such
use groundwater
a
way
that
supplemented b y groundwater, Surface water
resources
can
groundwater reserves can r i v e r s (Paling, owing
to
natural
1984).
purification
and
resulting in a then
be u t i l i z e d
be d r a w n on
The
limited suitable
i n conjunction w i t h surface
deficiencies
r a t e of
surface
to
water
can
be
availability.
a g r e a t e r degree since
in times of
shortfalls
also
being available,
limited
water
higher overall
recharge w i l l
wastewater the
in
permeability
in surface
be r e l a t i v e l y the of
slow
possibility the
soil.
of The
h y d r a u l i c s of the recharge process should be i n v e s t i g a t e d w i t h s i t e tests. The case study a n a l y z e d i s the Witwatersrand area,
a h i g h growth r a t e
conurbation based o r i g i n a l l y on m i n i n g . Groundwater constitutes a t present o n l y one percent of the average d a i l y
2400 M l / d farming
to
and
the
Witwatersrand
gardening
purposes
supply
area. are
to t h e Rand Water Board of
Privately however
in
owned
boreholes
common
use
as
for
a
I
4
Fig. 9.1
Dolomite deposits i n the Witwatersrand a r e a
143
supplement to the formal
programmes intensified The
initiated,
of
around
source of
low r a i n f a l l
introduced,
of
of
1.
9.1
(Figure
Black
geological System, time
quartzites
is
in
outcrops
away
of
several
years
emergency
available
groundwater
weathered
zones,
Reef
from
of
occur
sources
deposits,
the centre a t
Series,
the
the
cavities
in
a
quartzites
a
wide
one
slope of
ten
and
Ventersdorp
the
mined
Pretoria
syenite
sanctioned
for
the
Series
dykes
groundwater compartments.
on
overly
Since some of
dewatering
in
these
the
order
pebble
W i twatersrand w h i c h were
The
series,
number of
some
small
and
Witwatersrand.
create a
shales and
virtually
vertical
independent
allow
safer
forming on the surface.
because of
The outcrops of
have
mining,
groundwater levels i n these compartments have dropped considerably. compartments have not been dewatered
and
r e s u l t i n g compartments to
and
circle
approximately
the l a t t e r renowned f o r i t s a u r i f e r o u s reefs,
extensively
intersections b y
which
These
the South dolomite o v e r l a y s
conglomerates
been
study
groundwater
thick, d i p gently To
one
the
dolomite deposits,
kilometer
at
and
Johannesburg
degrees.
F o l l o w i n g a series of
.
main
fissures
supply.
1980's water r e s t r i c t i o n s were
i n the e a r l y
the danger of
the Other
sinkholes
dolomite a r e g e n e r a l l y covered b y
a l l u v i a l deposits of v a r y i n g depth. Published studies on a r t i f i c i a l treated
wastewater
a r e almost
considerable depth,
recharge
entirely
u n d e r l a i n b y an
of the performance of
by
infiltration
conducted
with
in p r i m a r y
impermeable
layer.
partially
aquifers
Important
these schemes a r e the permanence of
of
aspects
the i n f i l t r a t i o n
r a t e and the reduction i n contaminants b y b a c t e r i o l o g i c a l processes a n d b y adhesion to soi I p a r t i c l e s .
1980),
(Bouwer et a l . , (Mathew
et
aquifer
Careful
selection
of
the
the p u r i f y i n g c a p a c i t i e s of in
the
Witwatersrand
the U.S.A.
1984) and A u s t r a l i a
I s r a e l ( l d e l o v i t c h and M i c h a i l ,
1982).
al.,
extensive testing of secondary
Successful p r o j e c t s a r e r e p o r t e d from
infiltration
site
and
the combined p r i m a r y and
area
will
have
to
precede
a
wil I
create
a
fluctuating
decision on the q u a l i t y of the i n f i l t r a t i o n water. An
actively
operated
groundwater t a b l e and
groundwater
reservoir
increased groundwater
flow
velocities.
Therefore a n
increased a c t i v i t y of s o l u t i o n a n d erosion processes i n the dolomite may be expected,
in
subsidence. certain
some
Built-up
compartments
cases areas
followed
by
the
occurence
located over some of
u n s u i t a b l e for
the
of
sinkholes
the dolomitic
envisaged
scheme.
areas
and leave
Simulation
of
groundwater movements a n d m o n i t o r i n g of the n a t u r a l freshwater/wastewater interfaces w i l l have to be done. Artificial
recharge
not
only
increases
the
available
amount
of
Fig.
9.2
S e w a g e w o r k s and r e c h a r g e s i t e s
145 groundwater,
it
schemes
groundwater
for
also
enables, use
by
its
more
stable
supply,
to
with
surface
waters.
conjunction
in
develop
A
s i m p l i s t i c model ( P a l i n g , 1985) indicates t h a t b y c o n j u n c t i v e use o f surface a n d groundwater the minimum guaranteed d r a f t can b e increased b y 10% of the total s u p p l y compared w i t h the s i t u a t i o n in w h i c h each source s u p p l i e s individually.
in the Witwatersrand a r e i s s t i l l m a i n l y o r g a n i z e d on
Sewage treatment a
municipal
watershed wastewater
basis.
which
collection
approximately
Johannebsurg
divides
the
is
located
three
two
with
(megalitres p e r
m u n i c i p a l i t i e s i s processed
the works
in
concerned,
500 M l / d
East of Johannesburg
operates
town
a
works
distinct combined
day).
South
areas
as
effluent
Sewage
from
in the m u n i c i p a l i t i e s of
as
output
of
as 6 Ml/d.
scheme c o u l d
Germiston,
the
surrounding
i n works w i t h c a p a c i t i e s a s small
a p o t e n t i a l a r t i f i c i a l recharge
of far
Boksburg,
involve Benoni,
B r a k p a n and S p r i n g s ( F i g u r e 9.2 and Table 9.1).
Table 9.1
Sewage works a n d Recharge site.
No.
Name
Discharge ( M l / d )
E l e v a t i o n (m)
a v e r a g e 1984
It that
1
Davey ton
8
1600
2
Mc Comb
6
1580
3
Jan Smuts
11
1610
4
Rynfield
11
1620
5
Ancor
30
1580
6
Benon i
15
1640
7
Mapleton
--
1580
8
Dekema
56
1530
9
Rondebul t
39
1560
10
Vlakp laas
44
1520
has been form
historical
t r i b u t a r i e s of
p r a c t i c e to
the' Vaal
discharge
River
the
upstream o f
in
effluent the
streams
intake
of
the
local Rand Water Board.
I n d i r e c t reuse in t h i s form h a s been p r a c t i s e d i n
the
since
Witwatersrand
area
1923
and
p u r i f i c a t i o n in streams and reedbeds, water.
I n t e n s i v e m o n i t o r i n g of
the
takes
place
after
and after d i l u t i o n with
streams
by
alleged fresh
the Rand Water
self river
Board
in
146
recent years h a s i n d i c a t e d a considerable contamination mainly
by
industrial
discharge
and
leaching
of
o f these
the
streams,
numerous
goldmine
dumps. Dolomite compartments are
limited.
suitable
Dewatered
compartments
with
for
artificial
compartments
built-up
a r e a s on
top
recharge and abstraction
the
gold
mining
have
been
mentioned.
in
area
and
Another
impediment c o u l d be t h e p e r c o l a t i o n from contaminated streams. Effluent
from
t r a n s p o r t e d to been a
established
sewage
water
works
by
pipeline.
the dolomite compartment
cheaper
alternative,
b u t closed
pipes
would
are
have
Canals
prefered
to
might for
be have
sanitary
For sewage works i n close p r o x i m i t y to each o t h e r in comparison
reasons.
w i t h the distance to a n y seepage a r e a combined c o n d u i t s be most economic whereas o t h e r sources may j u s t i f y minimizing
total
seperate conduits.
network
to be optimized.
I n the W i t w a t e r s r a n d s i t u a t i o n
clearly
distinct
clusters
are
which
of
network
enabled
model to be reduced to a minimum. works
cannot
be
the
Although
justified,
b u t may
be
considered
complexity
the
as
a
r e l o c a t i o n of e x i s t i n g sewage
future
economically s i t e d over the seepage areas. of economy of scale,
could
The
of
treatment
cost
probably
problem
discernable,
conveyance
would
new
works
T h i s would
may
be
more
use the a d v a n t a g e
increase conveyance cost due to the g r e a t e r
peak to average flow r a t i o f o r r a w sewage. Integer
network
programming
f i e l d of sewage conveyance. c e n t r a l i z a t i o n of Florida,
wastewater
has
Wanielista
found
treatment
Leighton a n d Shoemaker
several
a n d Bauer facilities
(1984) used
it
applications
(1972) a p p l i e d in
the
in
a
in
Econ R i v e r
similar
the r e g i o n a l i z a t i o n of wastewater c o l l e c t i o n and treatment
the
i t to the basin
fashion
for
systems
in Long
P i p e diameters were based on maximum p e r m i s s i b l e flow v e l o c i t i e s
decided
I s l a n d , New York.
COST ANALYSIS
for
p r a c t i c a l reasons.
The
was selected in each case.
next
larger
commercially
available
Based on a cost p e r metre
w i t h the length of the p i p e l i n e section known,
the t o t a l
pipe
size
in f i g u r e 9.3
and
costs f o r
supply
a n d construction may be c a l c u l a t e d . For
purposes
calculated using
of
estimating
the Darcy
pumping
equation.
w i t h the r e l a t i o n s h i p s i n Table 9.2. the
range
Q
interpolated.
=
10
-
50
Ml/d.
heads,
the
The costs f o r
friction pumps
was
head
was
estimated
The equations were based on d a t a f o r For
intermediate
heads
the
costs
are
w
c)
V
m
.r
0
-
u
0 0
E-
.
c
0 0 N
-
0
0
0 OD 0
0 L n
0
w 0
0
0 0 N
D
0 N 0
0
E
D 0
E 0
z N
D
D
z
D m 0
0
W 0
0 0 0
0
N 0
147
148 TABLE 9.2
The
Pump costs
Head (m 1
Cost
20
207.5
(Q i n Ml/d)
($1
40
217.5
* *
60
230.0
* a
costs
for
the
pump
motors
Q + 4625
Q + 4725 + 5800
were
based
on
the
shaft
power,
increased b y a 20% safety m a r g i n (see Table 9.3).
TABLE 9.3
Motor costs
Motor Power
Voltage
(kW)
(V)
0 - 250
400
250 - 1900 1900 - 6570
The number of
costs ($/kW
60
1000 - 3300
70
6600 - 11000
80
i n s t a l l e d pump sets depends on the flow
a n d the c o n t i n u i t y of t h i s b a s i c a n d one back-up
flow
volume.
set of pumps
was
For
h e l d to
under 50 M l / d a n d two b a s i c a n d one back-up F i n a l l y the costs f o r p i p e l i n e ,
the present
to be h a n d l e d
calculations
be s u f f i c i e n t
for
one
flows
sets f o r b i g g e r flows.
pumps a n d motors
are
added
procedure i s repeated f o r each of the 113 v a r i a b l e s p e r c l u s t e r .
up.
This
149
MATHEMAT I CAL FORMULAT ION
In
the
papers
by
Wanielista
Shoemaker
(1984) r e g i o n a l
plants
dealt
is
with
and
wastewater
in
one
Bauer
(1972)
conveyance
comprehensive
computer
W i twatersrand a r e a e f f l u e n t conveyance to recharge be
broken
down
in
a
number
of
Witwatersrand was developed that could
and
Leighton
to c e n t r a l i z e d model.
sites can
A
subsystems.
and
treatment For
the
successfully
network
of
the
In
incorporate a l l the subsystems.
p a r t i c u l a r the most complex subsystem comprises the s i x treatment works the
Benoni,
proposed
Brakpan
infiltration
and area
Springs municipalities at
Mapleton
1
(node
(node 7 ) .
The
6)
to
network
and with
in a its
possible flow d i r e c t i o n s i s presented in f i g u r e 9.4. I t i s the subsystems which could p o s s i b l y s u p p l y which a r e considered here.
At design stage i t i s u n c l e a r whether e f f l u e n t
should be conveyed from node 3 to node to minimize the costs. in the optimization
between nodes
5 o r the o t h e r way r o u n d in o r d e r
Both options a r e therefore l e f t f o r possible selection
procedure.
3 and 6.
The
The same considerations i n t r o d u c t i o n of
excludes the a p p l i c a t i o n of a dynamic Smith et a l . ,
the Mapleton a q u i f e r
apply
programming
approach
as
the
Rynfield
-
0----------------ODaveyton
,'; \,
-0'
i
MC
Maple1:on
Network w i t h possible flow d i r e c t i o n s
Comb
link
directions used b y
(1983). On the other h a n d integer programming can be
a p p l i e d to solve t h i s problem i n the f o l l o w i n g way.
F i g . 9.4
to
two p o s s i b l e flow
150
Each
plant
has
a
certain
design
o r i g i n a t i n g from a p l a n t must a t
discharge.
Every
pipeline
least be a b l e to convey
this
section
discharge.
As most l i n k s a r e supposed to convey e f f l u e n t from o t h e r p l a n t s a s w e l l , a series of flow r a t e s can be defined as a r e s u l t of d i f f e r e n t combinations o f By r e p r e s e n t i n g each flow r a t e in each p i p e l i n e section
d i s c h a r g e volumes. b y a seperate
i n t e g e r decision
v a r i a b l e the network o p t i m i z a t i o n c a n then
be formulated a s a n i n t e g e r programming problem.
The number of v a r i a b l e s
depends on the number of network nodes as well as on the number of In the present
w i t h t h e i r specific d i r e c t i o n .
example
the network
links
can
be
described b y 113 v a r i a b l e s . The flow required connected function
rate
pipe with can
dictates
diameter these
be
under
and
certain
pump
requirements
expressed
as
the
can
The
cost
factors
CCi
*
Ci
are
be
sum
v a r i a b l e s and the r e l a t e d cost factors, Objective f u n c t i o n =
conditions
capacities.
of
determined. the
products
below the
The of
the costs
objective
the
integer
or
Xi calculated
for
each
p i p e l i n e section as i n d i c a t e d i n the cost a n a l y s i s . developed to c a l c u l a t e
mentioned
Subsequently
thse cost
factors,
maximum flow volume from each node,
flow
volume
and
each
A separate p r o g r a m was
based on
the
input
of
(1)
the
( 2 ) the e l e v a t i o n of each node,
(3)
( 4 ) the maximum p e r m i s s i b l e flow v e l o c i t y a n d ( 5 )
the l e n g t h of each l i n k ,
the e f f e c t i v e p i p e roughness. P r o v i s i o n was made to e l i m i n a t e c e r t a i n
links
o r s u p p l y nodes i n o r d e r to m a i n t a i n the f l e x i b i i t y r e q u i r e d to a d j u s t network
for
other
program
was
program
makes
clusters
extended
u s i n g the I .B.M.
it
in
of such
immediately
treatment a
way
suitable
plants. that
for
the
The
cost
format
submission
of
for
the
calculation the
output
optimization,
mixed i n t e g e r programming p a c k a g e MPSX-370/MIP.
The c o n s t r a i n t m a t r i x
i s based on two simple p r i n c i p l e s
which exploit
the essential f e a t u r e of decision v a r i a b l e s : a) Y -
C Xi
5
zero
T h i s expression variables.
i s used to describe
I f Y = 1 at
least one X.
the
relationship
must b e present.
between
different
I n t e r a c t i o n s of
this
t y p e a r e m a i n l y of a p r o g r e s s i v e n a t u r e , but some r e g r e s s i v e steps h a d to be i n c l u d e d e.g.
i f l i n k 4-6 conveys Q1 + Q4, the
l i n k s 2-3,
2-5
and 2-7
may convey o n l y Q2.
b)
L X . = zero o r . u n i t y . For the r i g h t h a n d side t o equal one,
v a l u e one. zero.
only
I f the r i g h t h a n d side i s set a t
I f a l l p o s s i b l e flows
from a
one
zero,
particular
variable all
node a r e
a n d then set a t one, o n l y one flow w i l l be selected.
assumes
v a r i a b l e s must grouped
the be
together
151
The
combination
of
these
two
expressions
guarantee
unique
paths
through the network a n d together w i t h the o b j e c t i v e f u n c t i o n the p a t h w i t h the lowest costs w i l l be found.
RESULTS
Optimal artificial
effluent recharge
network
scheme c a r r i e d
appeared to i n d i c a t e f i g u r e 9.5a.
lising
velocity
2.2
of
configuration
configurations
the minimum
the flow m/s
would
the
be
around total
volumes total
$13.4
were computed
in
table
Under
Optimized c o n f i g u r a t i o n shown in f i g u r e 9.5b The r e l a t i o n between flow Since the p i p e diameter of
the
flow
velocity,
of
the
maximum
problem c o u l d be expanded
individually
separately,
to
one
potential inspection
a s estimated
and
a
for
maximum this
same
flow
the
( ~ / 4 D ) 2.
the s q u a r e root
velocity
to
1.2
m/s
million (figure 9 . 5 ~ ) .
slightly
by
the
inclusion
of
shows the s i t u a t i o n in which two c l u s t e r s
recharge
site.
Each
cluster
is
optimized
r e s u l t i n g in a cost of $11.2 m i l l i o n f o r the n o r t h e r n c l u s t e r as
indicated previously,
and $5.1
million for
the western
cluster,
bringing
the t o t a l to $16.3 m i l l i o n .
F i g . 9.5
in
selected
conditions
is Q = v
i n v e r s e l y p r o p o r t i o n a l to
reduction
sources 8 , 9 a n d 10. F i g u r e 9.6a supply
the
visual
was
costs
a
would cost $11.2 m i l l i o n .
r e s u l t e d i n a minimum construction cost of $17.5 The o r i g i n a l
9.1
r a t e and p i p e diameter
i s thus a
length
construction
million.
A
Mapleton.
pipe
for
Network o p t i m i z a t i o n . Node 1 to 6 represent sewage works and node 7 the i n f i l t r a t i o n site. See also T a b l e 9.1 a n d f i g u r e 9.1
152
L i n k a g e of networks. Node 1 to 6 a n d node 8 to 10 represent sewage works a n d node 7 the i n f i l t r a t i o n site. See a l s o Table 9.1 a n d f i g u r e 9.1
F i g . 9.6
An a l t e r n a t i v e arrangement from
the
northern cluster
via
which may save cost node 9
(see f i g u r e
i s to
supply
The
9.6b).
effluent
change
in
i n p u t d a t a f o r the n o r t h e r n c l u s t e r i n v o l v e s f i v e new v a l u e s f o r the l e n g t h of
the
the l i n k s between node 2, other,
resulting
in
a
3, 4, cost
5, of
6 on the one h a n d a n d node 9 on $11.1
million.
The
fact
that
the
c o n f i g u r a t i o n of the optimal network remains the same as i n f i g u r e 9.6a
is
coincidental. The
cost
increasing million
optimization
the flow
for
this
via
cluster.
of
the
node 9, The
western
resulting
total
cost
cluster i n an
thus
is
performed
optimized
amounts
to
cost $17.2
Hence the lay-out of the sewage works i n t h i s case i s such that of the two c l u s t e r s does not r e s u l t i n any f u r t h e r cost reduction.
+'
nodes 1 , 2
nodes 1 , 2 , 4 , 5 , 6
node 7 node 3 node 3'
-
-
- supply
points demand p o i n t l o c a t i o n of booster station alternative s i t e for
-
booster stati a,
F i g . 9.7
Optimum location f o r a booster s t a t i o n
a
after
of
$6.1
million. linkage
153
SUMMARY AND CONCLUS IONS
Integer programming p r o v e d to be a useful tool f o r the e v a l u a t i o n o f a least-cost
configuration
designed
to
a
It
takes
interrelations. computer
of
suit
node optimization
cases
with
seven
approximately
half
to c a l c u l a t e the cost factors and
f o r integer optimization.
I .B.M.
a p i p e l i n e network.
network
mixed can
support
a
and
second
p r o g r a m was
rather
on
an
complex
I.B.M.
3083
to compile a p r o g r a m s u i t a b l e
For a c l u s t e r of s i x s u p p l y nodes a n d one demand i n less t h a n 30 seconds u s i n g the
r e s u l t s were obtained
integer
be
The
nodes
programming
handled
by
package
subdividing
a
MPSX-37O/MIP.
system
into
Complicated
subsystems
and
o p t i m i z i n g each c l u s t e r i n d i v i d u a l l y . The f l e x i b i l i t y
of
the program enables one
to
i n t r o d u c e changes w i t h
minimal e f f o r t a n d to compare the r e s u l t i n g a l t e r n a t i v e s . This
feature
may
be
illustrated
by
the
follohing
example
of
an
economic o p t i m i z a t i o n of the location of a booster s t a t i o n ( f i g u r e 9.7). By v a r y i n g the d i s t a n c e between node 3 a n d
the other f i x e d
sequential search w i l l r e s u l t i n the optimum solution. o f MPSX-370/MIP prevent
the
applicability
each run g i v e a
can f o r
search
from
becoming
i s accompanied b y
a
The "range"
sensitivity
random
analysis
process.
the d i s a d v a n t a g e
nodes a
that
facility
and
The
thus
general
no p r o v i s i o n s a r e
made f o r i n t r o d u c i n g the costs f o r obstacles l i k e r o a d s a n d r i v e r s . Computer sewage
effluent
resulted visual
analysis
in a
the
conveyance
cost
inspection.
of
most
economic
an
artificial
to
r e d u c t i o n of A
lower
flow
16% over velocity
an
pipeline
configuration
groundwater optimum
increased
recharge
solution
the
total
based
for site on
construction
costs as the influence of a n increased p i p e diameter s t r o n g l y outweighs the reduced
cost
in
pumping
sewage works a f u r t h e r
equipment.
Depending
on
the
lay-out
of
the
r e d u c t i o n in the combined costs c o u l d p o s s i b l y be
a t t a i n e d b y i n t e g r a t i o n of i n d i v i d u a l clusters.
REFERENCES
H., Rice, R.C., Lance., J.C., and Gilbert, R.G., 1980. Bouwer, R a p i d - i n f i l t r a t i o n Research a t F l u s h i n g Meadows Project, Arizona. J. Water Polut. Control Fed., Vol. 52, No. 10, p 2457. I d e l o v i t c h , E. and M i c h a i l , M., 1984. S o i l - a q u i f e r Treatment - A New Approach to an O l d Method of Wastewater Reuse. J. Water P o l l u t . Control Fed., V o l . 56, No. 8, p 936. Leighton, J.P. and Shoemaker, C.A., 1984. An I n t e g e r Programming Analysis of the Regionalization of L a r g e Wastewater Treatment a n d Collection Systems. Water Resources Research, Vol. 20, No. 6, p 671.
154
Mathew, K., Newman, P.W.G. and Ho, G.E., 1982. G r o u n d w a t e r R e c h a r g e w i t h Secondary Sewage E f f l u e n t . A u s t r a l i a n Water Resources C o u n c i l , Technical P a p e r No. 71, C a n b e r r a . 1984. O p t i m i z a t i o n of C o n j u n c t i v e Use of G r o u n d w a t e r and P a l i n g , W.A.J., S u r f a c e Water Resources in t h e Vaal B a s i n . Proceedings o f t h e H a r a r e Symposium, IAHS P u b l . No. 144. P a l i n g , W.A.J., 1985. Economic O p t i m i z a t i o n of A l t e r n a t e Water Resources f o r the W i t w a t e r s r a n d . Water Systems Research Programme, U n i v e r s i t y o f the W i t w a t e r s r a n d , Report No. 4/1985. P a l i n g , W.A.J. and Stephenson, D., 1985. I n t e g e r P r o g r a m m i n g of T r e a t e d Wastewater Conveyance f o r A r t i f i c i a l Recharge o f a n A q u i f e r . J. Int. SOC. Ecol. M o d e l l i n g ( 7 ) . Smith, A.A., H i n t o n , E. a n d Lewis, R.W., 1983. C i v i l E n g i n e e r i n g Systems, A n a l y s i s and Design, John Wiley G. Sons. 1972. C e n t r a l i z a t i o n of Waste Treatment W a n i e l i s t a , M.P. and Bauer, C.S., F a c i l i t i e s , J. Water P o l l u t . Control Fed., V o l . 44, No. 12, p 2229.
155
CHAPTER 10
OPTIMAL PLANNING OF REGIONAL WASTEWATER TREATMENT I NTRODUCT ION i s a n elevated r i d g e in the
The Witwatersrand o r 'White Waters Ridge' h e a r t of South A f r i c a
formed
by
the
gold-bearing
quartzite
emerging above the surface of the s u r r o u n d i n g c o u n t r y . was
originally
secondary
in
discovered
industry
and
1886
tertiary
and
this
commercial
about f o u r m i l l i o n i n h a b i t a n t s of the area.
It
sparked
rock
strata
i s where the
development.
gold
growth
There
are
of now
The present water consumption
which i s s u p p l i e d b y the Rand Water Board,
averages 1700 Ml/day
and i s
i n c r e a s i n g a t a r a t e of 6 p e r cent a year. The Witwatersrand r u n s i n a n east-west watershed
(Fig.
10.1).
It
is
the
source
d i r e c t i o n a n d forms a n a t u r a l of
the
number
o r i g i n a l l y there were many s p r i n g s a l o n g the r i d g e , Waters R i d g e ' .
The
water
supply
of
streams
and
hence the name 'White
to Johannesburg
was o r i g i n a l l y
pumped
from the ground as the water resources of the a r e a were not p l e n t i f u l account
of
the
fact
that
the
r a t h e r than a r i v e r b a s i n ) .
elevated
ridge
was
an
origin
The streams to the n o r t h form
of
(on
streams
tributaries
of
the Limpopo R i v e r , a n ephemeral r i v e r w h i c h flows eastwards to the I n d i a n Ocean.
The streams to the south flow
i n t o the Vaal
River,
a tributary
of
the Orange R i v e r , which flows westwards to the A t l a n t i c Ocean. It water.
i s from The
constructed
the Vaal
Vaal in
River
Barrage,
1923,
r e l i a b l e sustained
50
followed
y i e l d of
that
the W i t w a t e r s r a n d d r a w s
km
by
these
south
the
sources
Water Board h a s r i g h t s to 2400 Ml/day. to downstream users. The Vaal, flashy Vaal
or
r i v e r a n d c a r r i e s much s i l t Dam.
On
the
other
hand
it
of
Vaal
the
is
3300
'murky'
(170 mg/l has
now
supplemented
by
r e l a t i v e l y untapped Tugela R i v e r , 300 km away. t a p p i n g the Orange R i v e r a t
The and
was
combined the
Rand
i s translated
is a
on the a v e r a g e ) beyond
relatively
o r i g i n a t i n g m a i n l y from s a l t s being
Ml/day
r i v e r as i t
( a v e r a g e 100 m g / l ) is
1933.
its
Some water must also be passed on
The Vaal
River
of
Witwatersrand,
in
Dam
most
little
dissolved
leached from water
diverted
the
salts
farmlands. from
the
P l a n s were considered f o r
i t s source a n d d i v e r t i n g these waters to the
Vaal b a s i n . These d i v e r s i o n schemes a r e expensive. On
the other
h a n d wastewater
treatment
technology
i s now
r a p i d l y and the cost of treatment i s a p p e a r i n g more a t t r a c t i v e . about 50 p e r cent
of
water
i s used consumptively
on
advancing Since o n l y
the Witwatersrand,
f
157
there
i s scope f o r
happening
water
indirectly.
Witwatersrand
finds
reclamation Most
and
water
i t s way,
In f a c t
recycling.
returned
a f t e r treatment,
to to
the
this
i s now
sewers
on
streams which
to the Vaal Barrage.
The Rand Water Board (1977) pumps 1000 M l / d a y
the Barrage. Most of
the b a l a n c e of
i t s supply
the
discharge
i s taken d i r e c t l y
from
from
the
Vaal Dam through a p i p e l i n e , which may be supplemented
i n the f u t u r e b y
a canal
leading
pumping
Some of
the e f f l u e n t
from
the
dam
from
wall
to
the Zuikerbosch
the Witwatersrand
which
finds
station.
i t s way
to
the
Vaal Barrage a n d i s not r e t u r n e d to the Witwatersrand
b y the Rand Water
Board,
The q u a l i t y of
i s consumed b y communities f u r t h e r downstream.
effluents
entering
the
Vaal
Barrage
thus
affects
the
cost
of
the
treatment
before f u r t h e r use of the water i s possible.
A
number
of
possible
schemes
to
re-use
the
wastewaters
of
the
Witwatersrand a r e possible:
1.
P a r t i a l treatment of waste water treatment p l a n t s on the Witwatersrand, and
return
of
the
effluent
f u r t h e r p u r i f i c a t i o n occurs. r i v e r water then, and/or
to
the
Vaal
Barrage
via
streams,
where
The e f f l u e n t s a r e d i l u t e d b y r e l a t i v e l y p u r e
a f t e r re-treatment,
pumped back
to the W i t w a t e r s r a n d
passed dOWnStream of the Barrage.
2.
Convey
3.
Reclaim e f f l u e n t on the Witwatersrand to a sub-standard
4.
Reclaim
wastewaters
Barrage,
from
the
Witwatersrand
to
the
banks
of
the
a n d p u r i f y them a t a combined works before r e - c y c l i n g .
i n a separate d i s t r i b u t i o n system f o r non-hygienic to
a
high
standard
and
re-cycle
and re-cycle
it
purposes.
together
with
the
water
pumped from the Vaal R i v e r .
5.
Install a
low-capital,
h i g h operating-cost,
reclamation f a c i l i t y
Witwatersrand and m a i n t a i n t h i s as a standby droughts. reliably
Draw be
from
drawn,
the Vaal
River
and
the
use
a
on
the
in case of n a t u r a l r i v e r
much h i g h e r d r a f t
reclamation
plant
than
when
could
shortfalls
occur.
6.
Install
low-capacity
reclamation
facilities
on
the
discharge the p u r i f i e d e f f l u e n t i n t o storage dams;
o r underground.
Draw on the Vaal
Witwatersrand
and
e i t h e r on the surface
R i v e r to a h i g h degree
as
for
(5)
and use the stored e f f l u e n t when s h o r t f a l l s occur in the Vaal R i v e r .
7.
Pass
partly
treated
effluents
downstream
of
the
Vaal
Barrage
in
constructed condu i t s.
Past p l a n n i n g and construction been
on
a
local
municipal
basis,
of waste water whereas
bulk
treatment water
facilities
supply
was
has the
158
r e s p o n s i b i l i t y of
the r e g i o n a l
Rand Water
Board.
The establishment This w i l l
r e g i o n a l waste water a u t h o r i t y i s now b e i n g contemplated. comprehensive facilities
planning
at
and combined
least
cost
to be achieved.
sewage o u t f a l l s can
be
s a v i n g s i n cost due to scale.
The location of
selected
overall
to
treatment,
result
in
least
cost
Regional
planned
i.e.
of
a
enable
treatment
with
treatment
of
consequent
facilities
sewers,
can
be
wastewater
and water s u p p l y .
I t i s w i t h these ideas i n m i n d t h a t a p r o j e c t to s t u d y the water s u p p l y
a n d waste water system of the Witwatersrand was embarked on.
THE MATHEMAT I CAL MODEL
The
system
of
dams,
streams,
wastewater
treatment
plants,
water works and c o n d u i t s between the W i t w a t e r s r a n d a n d the Vaal g r o w i n g more complex over the years. authority should
responsible
have
at
for
its
overall
disposal
As p o i n t e d out,
planning
data
a n a l y s i s models to f a c i l i t a t e p l a n n i n g . optimizing
planning
of
wastewater
is
Such
facilities
s u i t e of
A
treatment
is
a regional planning
desireable.
assimilation
potable River
computer
works,
a
and
body
systems
programs
for
sewers
and
outfall
water works should be a t hand. The system
i s described
in some cases not
linear,
to a r r i v e a t a least-cost
l a t e r b y equations a n d
The
chapter by
a
goes
master
on
to
methods
are
a r e needed
A s i m p l i s t i c mathematical model of p a r t o f
plan.
the system i s assembled below,
basins
constraints which
a n d n o n l i n e a r programming
and methods o f s o l u t i o n a r e o u t l i n e d l a t e r .
describe
program,
a
which
method
could
of
also
linking
neighbouring
consider
various
time
horizons. The set of c o n s t r a i n t s developed below i s f o r s t a t i c c o n d i t i o n s in a p a r t i c u l a r b a s i n . S t a t i s t i c a l l y averaged v a l u e s of flows,
water q u a l i t i e s
and
by
consumptions
distributions
are
would
taken. be
To
allow
for
variations
probability
possible
but
would
increase
F i g u r e 10.2.
The
diagram
embodies
theoretically
computat iona I time man yfo Id. Consider
the
simplistic
the f o l l o w i n g concepts: the Witwatersrand
system
in
the water requirements of a m a j o r consumer such a s
( 3 ) c o u l d be met from s u r f a c e resources
t r e a t e d wastewaters r e t u r n e d to the r i v e r a t from
(5).
The
wastewaters
from
(3)
could
Reclaimed
water
is
assumed
d i s t r i b u t i o n systems as r i v e r water.
to
partially
( 2 ) o r reclaimed waste water
be treated a t
t e r t i a r y treatment a t ( 5 ) o r d i s c h a r g e d i n t o the r i v e r a t treatment.
(11,
be
( 4 ) followed b y (6) after
circulated
in
the
limited same
The problem i s to determine what each
f l o w should be a n d what s t a n d a r d of treatment i s d e s i r a b l e .
159
SUE-SKTEM I
'. \ Fig.
\ 10.2 Water c i r c u l a t i o n d i a g r a m
Each source, node.
consumer,
treatment p l a n t o r j u n c t i o n
i s r e f e r r e d to as a
The v a r i a b l e s a r e the flow r a t e s between the nodes numbered
d i a g r a m and the respective p o l l u t a n t
concentrations,
i n the
.
and
are
all
designated Q. I-J
Pi-j
respectively
for
flow
from
node
to
i
node
The
j.
flows
expressed i n Ml/day. The p o l l u t i o n (TDS) o r a (BOD).
load may be conservative such as
non-conservative
total
dissolved solids
v a r i a b l e such as biochemical oxygen demand
I n the former case there must be a mass b a l a n c e of
pollutant
in
the system and i n the l a t t e r case the effect of the r i v e r a n d b a r r a g e s i n d i l u t i n g the p o l l u t a n t must be assessed. model.
BOD i s considered
Values of BOD a r e expressed i n mg/l
M l / d a y and p o l l u t i o n in mg/l
and
i n the present
the product
i s p r o p o r t i o n a l to the t o t a l
of
flow
in
load in tons/day
discharged b y a stream o r conduit. The object of
the study
i s to minimize
the cost
convenient to convert a l l costs to a common basis, redemption on c a p i t a l cost p l u s r u n n i n g costs, kilolitre.
Cost
coefficients,
or
variable.
Some
of
coefficients,
the
cost
water i n closed conduits, anticipated theoretically
incremental feasible,
are
It
is
a l l expressed in cents p e r
therefore
for
the system.
required
instance
for
for
each
conveyance
of
a r e n o n l i n e a r a n d must be approximated b y the
costs. it
rates,
of
say a n n u a l i n t e r e s t a n d
is
Although necessary
nonlinear to
objective
simplify
the
functions
model
as
far
are as
possible since there a r e f u r t h e r n o n l i n e a r c o n s t r a i n t s as w i l l be r e v e a l e d f u r t h e r on. capital
cost.
I f there a r e e x i s t i n g c o n d u i t s these w i l l But
existing capacity,
if
the
f u t u r e flow
along
a
route
e f f e c t i v e l y h a v e zero is
likely
to
exceed
i t i s o n l y the incremental cost of the new c o n d u i t s a n d
works which need to be considered. s i z i n g the v a r i o u s works.
Allowance f o r peak f a c t o r s i s made in
160
Associated
with
each
rate Q. .
flow
is a
conveyance cost
coefficient,
I-J
which
The v a r i a b l e p o r t i o n of
i s designated Ci.
the cost component
which
i s a f u n c t i o n of flow o n l y i s t h u s
‘1-2
’ ‘3‘3-6
‘2’2-3 Note that Q6-7
‘1
+
considered.
is
fixed
(10.1)
‘4‘4-3
+
its
so
cost
is
not
variable
i.e.
P u r i f i c a t i o n costs comprise a component p r o p o r t i o n a l component pollutant
proportional load
to
load removed,
pollutant
Q . . ( P . .-P.
removed,
conditions after
works
need
not
be
The cost of conveyance i n n a t u r a l channels i s zero.
I-J
I-J
treatment.
The
I-]
to
i.e.
effluent
of
.
and a
proportional
2
subscript
l a t t e r component,
produce a n
I-J
or
I-J
where
i s d i f f i c u l t to e s t a b l i s h a n d i n fact
a r e designed
.
Q. .P.
load
. ) l-J/2
to flow Q .
to
refers
to
cost p r o p o r t i o n a l
i t i s often assumed
reasonable
to
that
standard
with
treatment costs p r o p o r t i o n a l to flow r a t e . Vie w i l l consider the general case a n d designate
the coefficients
+ Q3-4
Since Q3-6
respectively.
of
Q
3-6 P3-4 a n d Q2-6 P2-3 as C5
is a
constant,
the
and
flow-proportional
C6 cost
can b e omitted. The equations o r c o n s t r a i n t s d e s c r i b i n g the system a r e formulated
Hall
(1977) formulated the system w i t h
similar
constraints,
but
next.
at
that
time was unaware of a simple method of solution. For flow b a l a n c e a t the v a r i o u s nodes: At
some source nodes such as
case we consider
(1
1,
the
yield
may
u n l i m i t e d augmentation possible,
be
limited
a t a cost.
but At
in our
consumer
nodes the s u p p l y must be s u f f i c i e n t :
42-3 ‘6-7
+
Q4-3
(10.2)
= a1
(10.3)
= a2
At consumer nodes the wastewater o u t p u t i s known:
(10.4)
‘3-4
+ ‘3-6 = a3 At treatment p l a n t s a n d o t h e r nodes the flows must balance:
Q3-4 - 44-2 ‘1-2
‘2-6
+ +
-
(10.5)
Q4-3 = 0
‘4-2
- ‘2-3
‘3-6
- ‘6-7
Note t h a t a l t h o u g h
-
‘2-6
=
‘6-8
=
the
(10.3) i t complicates
(10.6) (10.7)
v a r i a b l e Q6-7 the
cost
constants which may b e desired.
could
function
be e l i m i n a t e d
and
The number of
minimized i n simple cases b y s u b s t i t u t i n g Q
4-3
for
Q3-9 and Qg-6.
(10.2)-(10.7) c o n s t r a i n t s of
are the
It in
will fact
less-than
be all or
any
observed equations.
They
a slack
variable,
but
could
w i t h more meaning
in
The than
to
the
i s nevertheless a n d Q3-6 constraints
called
so
type,
v a r i a b l e s would be i n t r o d u c e d to form equations. fact
variables
the
equation
changes
f o r Q4-5 a n d
that
greater-than
later
using
equally which waste,
well
case
be
slack
Q6-8, i s i n
a purely
algebraic
161
slack
variable.
I n equation
(4)
the
waste
water
output
is
This constant i s in fact a f u n c t i o n of the consumption
constant.
given a2,
as
a
but i t
i s easier to i n s e r t a constant. There a r e other forms of c o n s t r a i n t s on the flow v a r i a b l e s
waste
water
barrage
C13-6
(10.2).
which c o u l d
For instance b a s i n c h a r a c t e r i s t i c s may l i m i t the amount of
be incorporated.
which
could
(economically)
O r i f the s u p p l y C12-3
be
discharged
beyond
the
was considered as two components;
one through e x i s t i n g c o n d u i t s a n d one t h r o u g h new conduits,
there
would
be a l i m i t on the c a p a c i t y of the e x i s t i n g conduits. The next set of c o n s t r a i n t s a p p l i e s to the p o l l u t a n t s .
Certain
l e v e l s of
p o l l u t i o n may be known: P I - 2 = a4
(10.8)
I n fact i t i s assumed f o r the BOD study t h a t P1-2 = 0. There may be t o l e r a b l e l i m i t s on c e r t a i n l e v e l s o f p o l l u t i o n : ‘4-2 ‘2-3 ‘6-7
5 5 5
a5
(10.9)
a6
(10.10
a7
(10.11
There i s an extent of n a t u r a l p u r i f i c a t i o n i n r i v e r s :
- ’4-2/2
’4-2
(10.12
= a8
(10.13) ( f o r f l o w 2 - 6) P2-3 - P2-3/2 = ag I n the case of TDS as the p o l l u t a n t there would b e n e g l i g i b l e r e d u c t i o n of P a t waste water treatment p l a n t s a n d the TDS a f t e r reclamation p l a n t s could be taken as zero. a n d P5-3 = 0,
-
‘3-4
‘4-2
i n the case of BOD,
i t can be assumed P1-2 = 0
and there i s some reduction i n P a t 4 a n d 9: (10.14)
=
(10.15)
- ‘9-6 = all ‘3-4 A mass balance of p o l l u t a n t s must be m a i n t a i n e d a t nodes:
(10.16)
(10.17)
Q3-4P3-4+Q3-6P3-4-Q2-3P2-3-Q4-3p5-3 Note P2-6 e q u a l s P2-3,
P4-5
= al 2
(10.18)
equals P4-2
a n d P3-9
e q u a l s P3-4
so these
s u b s t i t u t i o n s a r e made f o r s i m p l i f i c a t i o n . It
is
implicit
in
the
optimization
program
that
all
variables
are
non-negative a n d r e a l so these c o n s t r a i n t s a r e not s t a t e d e x p l i c i t l y . The general (10.2)-(10.17).
model
then
is
to
minimize
(10.1)
subject
to
constraints
A method of solution i s o u t l i n e d in the n e x t section.
162
OPTIMIZATION METHOD
It will linear
be
except
two-dimensional
observed for
that
the
constraints
objective
function
(16)-(18).
These
p r o d u c t s of v a r i a b l e s .
these products to separate functions,
and
constraints
constraints
are
involve
There a r e techniques f o r c o n v e r t i n g f o l l o w i n g w h i c h a technique known a s
separable programming may be employed to optimize the system. Hadley
(1964) proposed a simple method o f
transforming
a
p r o d u c t QP
b y i n t r o d u c i n g two new v a r i a b l e s M a n d N, such t h a t
+ P)/2,
M = (Q
-
N = (Q
P)/2
(10.19)
then
-
QP = M‘
NZ
(10.20)
and Q = M + N , P = M - N
(10.21) M and N a r e u n r e s t r i c t e d i n s i g n b u t t h i s i s p e r m i t t e d in the d e l t a method
of separable programming (IBM, The
separable
programming
1976). algorithm
is
based
on
the
fact
that
separable f u n c t i o n can be approximated b y piecewise
I i n e a r functions.
p o l y g o n a l a p p r o x i m a t i o n i s represented b y a set
special
of
variables,
a The
so
a n y v a l u e of M can be represented a s follows:
+
M = Mo
GIDl
+ G2D2 +
...Gk D k +...GRDR
(10.22)
where the Ds represent i n t e r v a l s of M a n d the special
v a r i a b l e s GI,
...,GR
a r e defined as follows: f o r M in i n t e r v a l k , G , = G 2 = G k-1 = 1
(10.23)
O(Gk(
( 10.24)
Gk+l
1
= Gk+2,..GR
= 0
(10.25)
M comprises a set o f i n t e g r a l i n t e r v a l s D u p to k - 1 p l u s a f r a c t i o n
i.e.
of i n t e r v a l k . Note that M’
=
where
+
+...
G E G E +... GRER 1 1 k k each i n t e r v a l Ek corresponds
Ma 0
approximations i n Fig.
10.3, Mo = 0,
(10.26) to
an
interval
Dk.
k = 4 a n d Gk = 0.3.
Thus
for
the
The v a l u e of M
can be confined to a known range. Although there i s a p o s s i b i l i t y of a t t a i n i n g a local optimum t h i s chance i s reduced i f the problem i s solved w i t h the special v a r i a b l e s set at
their
verify
upper bound,
the r e s u l t s .
a n d then w i t h
It will
them set
be observed
that
at
2R
their
lower
variables are
i n t o the model f o r each p r o d u c t in the o r i g i n a l c o n s t r a i n t s . d e s i r a b l e to s i m p l i f y
It
initially
bounds,
to
introduced i s therefore
the o r i g i n a l system a s much a s p o s s i b l e to minimize
163
the number o f products. The f o l l o w i n g s i m p l i f i c a t i o n s a r e introduced. i n t o two subsystems (see F i g .
10.21,
which
The system
will
i s subdivided
b e l i n k e d v i a a master
p r o g r a m a c c o r d i n g to D a n t z i g ' s decomposition p r i n c i p l e (Dantzig, a p p l i e d b y Stephenson (1970) to link r i v e r b a s i n s . considered
here and
there
will
be
shadow
1963) a n d
O n l y sub-system
values
imposed o n
1
the
is
cost
coefficients of Q (10.31,
P a n d Q2-6P2-3 b y the master p r o g r a m (C7 a n d C8). 3-6 9-6 (10.71, (10.11 1, (10.13) a n d (10.17) a r e thereby e l i m i n a t e d .
E l i m i n a t i n g Pg-6 C7,Cf5
using
Certain variables i s eliminated, and
(10.151,
= C5 + C7 a n d C I 6 = C6
(10.18)
,
and by
cost c o e f f i c i e n t s become C o g = C3
namely Plm2 substituting
respectively,
the
-
al 1
+ C8. a n d P5-3 a r e zero so c o n s t r a i n t (10.8) from
number
of
(10.12)
and
products
(10.4)
into
i s reduced.
(10.16) Now
the
problem i s :
subject
to: 0.28) 0.29) 0.30) 0.31) 0.32) (10.33) (10.34) ( 10.35) ( 10.36
(10.37) (10.38) Put
t
'4-2~4-2 = M - ~ ' Q2-3P2-3 = M i - N: Q2-6P2-3 = M =
-
N:
M Z - Nt
Q3-4p3-4 Then (10.37)
1
(10.39) (10.40) (10.41) (10.42)
a n d (10.38) c a n b e r e p l a c e d b y e q u a t i o n s (10.43)-(10.52):
164
(10.43 (10.44 (10.45 (10.46 (10.47) (10.48) (10.49) (10.50) (10.51) (10.52)
Each M2 a n d NZ comprises composite p o l y g o n a l
(10.22)
equation
and
computer d a t a i n p u t .
it
necessary
to
functions
define
the
according
intervals
c * ~ Q +~ c4a4-3 - ~
+ c;
(a3P3-&
-
to
in
The o b j e c t i v e f u n c t i o n must a l s o be r e - w r i t t e n
c1a1-2 + c2a2-3 +
min
is
the
as
+ N):
M:
(10.53)
b
t
Fig.
/
10.3 Polygonal a p p r o x i m a t i o n of a s e p a r a b l e f u n c t i o n
T h e problem may
once
the
expanded,
procedures using
the
thus
be solved
are
adequately
decomposition
by
straightforward
programmed, principle,
the
techniques, process
consider
to
horizons. The problem may also be considered i n more d e t a i l here.
Using decomposition
sub-programs
for
1975).
would
This
principles
individual ensure
waste
it
would
water
optimization
programming methods c o u l d be employed
be p o s s i b l e
treatment of
to
each
study
works
may
various
be time
than outlined to
incorporate
(e.g.
component.
pollution
and
along
CIRIA, Dynamic stream
reaches a n d optimize the s o a c i n g a n d s t a n d a r d of waste water p u r i f i c a t i o n
165
works d i s c h a r g i n g
i n t o the stream.
Where m u l t i p l e decisions a r e r e q u i r e d ,
f o r instance f o r a l t e r n a t i v e p u r i f i c a t i o n p l a n t
locations,
m i x e d integer p r o g r a m m i n g c o u l d be employed.
o r sewer o u t f a l l s ,
Computer s i m u l a t i o n s o f the
system a s a l s o r e q u i r e d t o study extreme c o n d i t i o n s a n d cost s e n s i t i v i t i e s t o supplement
the shadow
v a l u e s produced b y the o p t i m i z a t i o n .
There
o t h e r s o p h i s t i c a t e d techniques f o r o p t i m i z i n g n o n l i n e a r waste water (Chiang
and
Lauria,
above-formulated To would
recommended,
be
Pratishthananda
and
Bishop,
1977)
but
the
problem s i m p l i f i e d to a neat solution.
incorporate a l l not
1977;
are
systems
the
concepts
realistic
i.e.
c o u l d be continued
human
though,
in
a and
large number-crunching interactive
i n t e r v e n t i o n a t each step.
as data
are
updated
by
The p l a n n i n g
successive
program
programming
iteration
is
process of
the
master p r o g r a m a n d sub-programs.
REFERENCES
Chiang, C.H. a n d L a u r i a , D.T., 1977. H e u r i s t i c a l g o r i t h m f o r waste water p l a n n i n g . Proc. Amer. SOC. Civ. E n g r s 103 No. EE5, 863-876. CIRIA, 1975. Cost e f f e c t i v e sewage treatment - the c r e a t i o n of a n o p t i m i z i n g model. C l R l A Report 46, London. D a n t z i g , G.B., 1963. L i n e a r Programming a n d Extensions: P r i n c e t o n U n i v e r s i t y Press, Princeton, New Jersey, USA. H a d l e y , G., 1964. N o n l i n e a r a n d Dynamic Programming, pp. 448-465: Addi son-Wesley , Reading. 1977. A method f o r o p t i m i z i n g the c i r c u l a t i o n o f water in H a l l , G.C., u r b a n regions. N a t l . I n s t . Water Res. Council f o r Scient. a n d I n d u s t . Res. P r e t o r i a , R.S.A. IBM, 1976 Mathematical Programming System Extended/370, P r o g r a m Reference Manual, 2nd e d i t i o n , pp. 230-251. 1977. A n o n l i n e a r m u l t i l e v e l model P r a t i s h t h a n a n d a , S . a n d Bishop, A.B., f o r r e g i o n a l water resources p l a n n i n g . Waf. Resour. B u l l . 13 No. 3, 61 1-625. Rand Water Board, 1977. Annual Report. Stephenson, D., 1970. Optimum d e s i g n o f complex w a t e r resource projects. Proc. Amer. SOC. Civ. E n g r s 96, no. HY6, 1229-1246. Stephenson, D. 1978. Optimal p l a n n i n g of r e g i o n a l wastewater treatment. Proc. IAHS Symposium. Model I ing the Water Qua1i t y o f the H y d r o l o g i c a l Cycle. Baden, 125. 351-360.
166
CHAPTER 1 1
SIMULATION OF SEWER FLOW
I NTRODUCT ION
With the development of s u b u r b a n a r e a s w i t h i n c i t i e s to t h e i r
limits i t
i s becoming necessary to consider s u b d i v i s i o n a n d more intense r e s i d e n t i a l densities
i n suburbs which
were
previously
only
sparsely
effect of more intense development on the services,
populated.
The
such a s sewerage,
for
a n area must be considered before such increase i n d e n s i t y i s permitted. study of the consequences of increased l o a d i n g i s d i f f i c u l t , the
effect
may
cause
a
A method of
system.
p a s s i n g the
chain
reaction
identifying
increased
flow
was
down
possible
the
problem
A model
sought.
p a r t i c u l a r l y as
length areas
for
A
of
the
and
sewer
methods
rapidly
of
selecting a
p a r t i c u l a r area o r f o l l o w i n g the flows t h r o u g h a system was developed. There the
i s frequently
system
as
hydrograph,
well
i.e.
a n a p p r e c i a b l e time-lag as
attenuation
routing.
due
to
I n o r d e r to a l l o w
s i m u l a t i o n program seemed to b e the most
as h y d r o g r a p h s flow lateral
for
dispersion
down
of
the
these effects
a
computer
approach.
The
program
logical
can draw d a t a from e x i s t i n g l a n d use i n v e n t o r i e s wherein d a t a concerning a l l stands w i t h i n the m u n i c i p a l and
land
usage
type)
engineering data (i.e. and
condition)
are
are
area
(i.e.
floor
In
addition
retained.
sewer lengths,
compiled.
The
p r o j e c t s such as d a t a r e t r i e v a l
for
slopes, latter
areas,
number o f
data
connections,
data
drawing
may
files
containing
diameters,
be
sections,
rooms
used
drops
for
establishing
other depths
of connections a n d management o f the sewerage system a t a l a t e r stage. there a r e about 135 000 stands w i t h i n
As
the Johannesburg a r e a a systematic
a n d e f f i c i e n t way of s t o r i n g the d a t a was r e q u i r e d f o r t h i s a p p l i c a t i o n . The sewage
process design
of
computerization
flows
effectively.
also
enables
Whereas
it
design sewerage systems f o r
the estimated
over
it
ten
different manholes,
hours of
the d a y ,
components. leaks
from
Stormwater sanitary
accounted f o r separately. may
also
successive
be
considered.
hydrographs
i s now
peak
possible
ingress, fittings
was
engineers
flows to
sewage
estimate
necessary
based on
divide
infiltration and
to
previously
the
through
to
averages flow
into
joints
in
may
be
discharges
The a c t u a l time d i s t r i b u t i o n of sewage d i s c h a r g e s This
will
contribute
therefore h a d to be gathered
affect to
an
the
hydrograph
outfal I.
in o r d e r to p r o v i d e
the
lags
where
Considerable subdivision
a n a l y s i s a n d the development of c o n t r i b u t o r y h y d r o g r a p h s .
for
data the
167
Considerable
work
has been
done
South
in
Africa,
particular
in
by
Shaw (1963) a n d Crabtree (1976), on e s t a b l i s h i n g c o n t r i b u t o r h y d r o g r a p h s . The a c t u a l l a g g i n g of h y d r o g r a p h s a n d consideration of r o u t i n g effects a n d p r o b a b i l i t i e s of d i f f e r e n t
connections
been tackled on a r e a l scale. probably
received
synthesizing
more
inflow
discharging
The a n a l y s i s of
attention
and
the
larger
h a v e not
in storm d r a i n s has
1981)
(Stephenson
hydrographs
simultaneously
flow
due
to
the
scale
of
storm
ease
of
sewer
systems (Stephenson a n d Hine, 1986).
HYDRAULIC ANALYSIS
In employing backwater However,
a
effects,
routing
al I
if
computational
computer
these
time
simulation and
probability
components
would
method
be
were
effects
increased
and
so
on
can
also
be
shown
attenuated (Chan a n d Wang, One computer
model
to
simulates
the flow
types a n d
be
included. program, hydraulic
these effects
individual
and
lavatory
flushes
be
rapidly
theory
to
down sewers a n d accounts
times of
lengths of sewer number 135 000,
in fact a p p r o p r i a t e to a n a l y s e the flow therefore e x i s t s f o r
lag,
one The
some of
probability
time
1980).
time l a g as well as d i f f e r e n t individual
using
in
considerably.
Peaks due
for
could
considered
equations were therefore s i m p l i f i e d b y o m i t t i n g time l a g r o u t i n g was employed.
allowance
abstracting
data
inflow.
as
for the
i t i s often not convenient o r
in each sewer.
from
However
relevant
Another
areas
program
which
a n a l y s i s and even f o r condensing the d a t a so t h a t a number o f
require
lengths of
sewer could be considered together to speed a n a l y s i s (Constantinides, 1982). I t i s possible to i d e n t i f y build
the
correct
program i s to study times
of
day
at
the type of
contributor
the l a g and
which
the
inflow
hydrograph.
flows
One
i n each case i n o r d e r of
a t t e n u a t i n g effect start
and
the
to
of
the
on h y d r o g r a p h s .
The
increase
objects
and
subsequently
decrease a r e therefore important a n d f i e l d measurements were r e q u i r e d .
FLOW MEASUREMENTS
Measurements were made in manholes as n e a r a s possible to the source of sewage in o r d e r to minimize the time to r o u t i n g down the sewers.
l a g a n d t o a v o i d a t t e n u a t i o n due
The flow depths in t h e sewers wer gauged a t
manholes over a p e r i o d of weeks a n d the r e s u l t i n g h y d r o g r a p h s plotted. The v a r i a t i o n s from week to week
were s l i g h t and s i m i l a r
averaged f o r compil i n g the hydrographs.
weeks
The o b s e r v a t i o n s t a k e n a t
were night
168
in
dry
weather
were
assumed
comparing these r e a d i n g s a t dry
periods
infiltration during
was
it
and
and
possible
leakage
after
to
from
summer
indicate
the end of to
leakage
estimate
the
the
plumbing
storms
plus
summer a n d
indicated
infiltration.
the end of
relative
systems. storm
in
proportions
of
Observations
inflow
By
winter
to
the
made
system.
R a i n f a l l i n Johannesburg i s n o r m a l l y r e s t r i c t e d to the summer season when h i g h i n t e n s i t y storms of sewers
were
assumed
short to
duration
flow
occur
during
unsurcharged
surcharged conditions were d i s c a r d e d a s they
the
during
would
afternoons. storm
The
flow
and
h a v e been d i f f i c u l t to
use for e s t i m a t i n g a c t u a l c o n t r i b u t i n g flows. The peak flow r a t e d u r i n g the d a y f o r h i g h e r
1.17
I/min
ingress. system
per
house
leakage,
income housing averages
infiltration
and
stormwater
The amount of leakage from the p l u m b i n g system i n t o the sewerage i s estimated
to
throughout the year.
0.05
excluding
be
0.06
I/min
per
house,
in
sewers
poor
soil.
The
hours
additional
flow
during
the p r e c i p i t a t i o n over
and
after
suggested
two-year
storm of 5 mm/h.
to peak flow
to be 2 mm/h
i s 0.05
design
storms
the catchment.
T h i s flow i s also associated w i t h the one-year
storm over n h o u r s which i s estimated The flow
day
This i s greater for older
v a r y w i d e l y depending on the methods o f c o n t r o l l i n g stormwater gullies.
a
in l e a k i n g sewers i s estimated to be
The i n f i l t r a t i o n
I/min p e r metre of sewer p e r metre diameter.
estimated to a v e r a g e 1 % of
24
over
inflow
recurrence
f o r general
mm/h
which
The e f f e c t i v e c o n t r i b u t i n g area
is
This w i l l into
interval analysis.
is
1%
of
the
50 m
i s about
w i d t h of catchment p e r metre of sewer. Up to 5%, assumed
and
in
50 m wide
some cases.
i s o l a t e d cases even
strip
over
all
more,
of
was
found
sewers
The a c t u a l sewer flows often
the
rainfall
over
an
sewers
in
-
even
to
g l a s s f i b r e flume was used
in
to e n t e r
increased b y over 50%
69% d u r i n g a n d a f t e r a storm. I n the case of the
invert
of
a
the f l a t a r e a s a special manhole.
to measure
has
a
curved
that
the
results are
existence o f s i l t a n d so on. Where possible, to gauge flows. c i r c u l a r chart
a r e changed a t weekly P o r t e r meter was minute intervals.
integrated total intervals.
installed for
flow
a
block
which
273
affected
of
by
flume was
the used
these flumes was on a
r e a d on a
To g i v e continuous
several
not
a conventional
The normal method of r e c o r d i n g a t w i t h an
from
hump
T h i s e l i m i n a t e s the problem of a s c e r t a i n i n g e x i s t i n g sewer g r a d i e n t s . the fact
flows
a
flats.
is
small
and
it
advantage
relatively
bottom
made
Another
possible
This
meter;
flow
the
rates
a
weeks t o g i v e a c c u r a t e d a t a
charts Fisher at
15
169
The
input
hydrographs
were
reproduced
by
the
computer
using
a
F o u r i e r series t y p e of c u r v e f i t .
H i g h e r income r e s i d e n t i a l
An area o f houses
and
1220 h a w i t h
approximately
newer
houses
including
well
town
e s t a b l i s h e d medium-sized
houses
development of the h y d r o g r a p h taken in a h i g h e r (Fig.
11.1).
Equivalent
house u n i t s were
servant
accommodation
is
allowed
for
for
a
150 m2 f l o o r
the area area
to a l l o w f o r the r e d u c t i o n
in flow p e r u n i t of f l o o r a r e a as houses a n d f l a t s
and
selected
income r e s i d e n t i a l
based on
to the power of 0.8
normalized b y r a i s i n g t h a t
was
at
increase in size.
the
rate
of
one
Hotel house
e q u i v a l e n t u n i t f o r every three rooms. Shops, offices,
schools a n d churches
a r e allowed f o r a t the r a t e of one house e q u i v a l e n t
per
area.
Metered (November 1981) 58 5 67 8 1164 24 0
Daily Iota1 kl Average Its Peak 11s Minimum 11s
'"t
.-. 0.
300 m2 of
Calculated 58 7 68 0 1156 24 0
Calculated flow Melered llow
I
I
3
0
9
6
12 Time of day h
15
18
21
24
Comparison of c a l c u l a t e d a n d metered f l o w s in h i g h e r income r e s i d e n t i a l areas
Fig. 11.1
Minimum o r base flow was assumed to be due to i n f i l t r a t i o n a n d manholes o r to leakage w i t h i n equal to 41% of the average, At
5.15
a.m.
which occurs
at
the flow
8 a.m.
the b u i l d i n g s .
start
work
at
This
7
This
was
i n t o sewers shown
to
be
o r 20% of the maximum flow in d r y weather.
rises r a p i d l y flow
a.m.
congestion demands an e a r l y s t a r t
to
within
pattern
residents in Johannesburg get up a t 5 a.m. workers
city.
floor
and for
80% of maximum flow,
suggests onwards.
office
workers
that
higher
Generally, at
8
income
production
a.m.
Traffic
those t r a v e l l i n g the 12 km i n t o the
170 The evening meals,
peak occurs
at
a n d so on,
ablutions
7 p.m.,
about
and
activity
indicating
ceases
at
preparation
midnight.
of
Maximum
flow p e r u n i t was found to average 1.17 I/min.
Low income residential Detailed income
land
use d a t a
residential
area
were
not
available for
11.2).
(Fig.
Details
of
the study houses
of
and
the
low
flats
were
a b s t r a c t e d from c o n s t r u c t i o n d r a w i n g s a n d checked on s i t e before the sewer d a t a were used. Lenasia
-
monitored
The a r e a chosen embraced most of
-
a town 25 km south o f Johannesburg
A
a flume.
with
time
l a g of
comparing the h y d r o g r a p h measured
with
one
the newer
hour
the
sections of
a n d the sewage flow was
allowed
hydrograph
at
for
was when
the p o i n t
of
origin. Monday 461
Daily Iota1 kl Average. 11s Peak. Us Minimum. U s
,Tuesday
Wednesday
462 5 32 1532 0.28
531 14 77 0.15
460 5 30 1450 0.28
Average
Calculaled
461 531 1486
463 54 14 7
0.23
0.3
-- -
15
Calculaled l b w Monday 30 January 1984 Tuesday 31 January 1984 ........... Wednesday 1 February 1984
...
5
a
E
l 1
0
6
3
9
15
12
. 21
18
24
Time of day h
F i g . 11.2.
Comparison o f c a l c u l a t e d a n d metered f l o w s i n low income r e s i d e n t i a l a r e a s
Rapid increases i n flow occurred a t 5.30 smaller peak a t 10 a.m. departure
of
particularly
the on
a.m.,
p e a k i n g a t 7.15
a.m.
i n d i c a t e d g r e a t e r a c t i v i t y i n the home a f t e r
working
population
-
Mondays
the
than
traditional
p r o p o r t i o n of the f a m i l y c o u l d remain a t home,
in
higher
washing which
income
day.
A
A the
areas, greater
i s also indicated b y
the smaller evening peak a t 8 p.m. Maximum flow p e r house u n i t amounted to 0.46 flows
metered
b u i Idings.
are
due
to
the
recent
I/min.
construction
of
The low minimum all
sewers
and
171
Apartment buiIdi n g s
A
large
selected
complex
for
the
known
study
comprises 273 f l a t s
as
Helderberg
in
of
an
apartment
(flats)
a
total
with
of
Berea,
585 rooms.
Johannesburg,
area
(Fig.
Metering
was
was
11.3).
It
c a r r i e d out
close to t h e b u i l d i n g so the time l a g was minimal. Points infiltration
of
interest
and
m o r n i n g peak,
of
leakage,
the
hydrograph
the
sharp
rise
include and
have something
Inflow starts
later
to do than
with
the
i n other
p.m.
television
residential
g r e a t e r p r o x i m i t y of these f l a t s to places of work.
Monday
10
238 2 74 8 66 0 27
Tuesday 2295 2 66 7 45 041
-
Wednesday 241 9 2 82 8 66 0 46
---
-.-
Thursday 2374 276 8 31 052
of
in
the
p.m.
which
flat-dwellers.
possibly
due to
the
Maximum flows appear
2.05
i.e.
Average 2367 275 027
of
fall
a n d 9.30
areas,
level
each d a y except on
viewing
t o be h i g h e r t h a n i n other types of development, Daily lolal hI Average 11s Peak 11s Minimum lls
low
subsequent
the secondary morning peak a t 10 a.m.
the Thursday a n d the d i s t i n c t i v e peaks a t 7.30 may
the
I/min p e r u n i t .
Calculated 240 28
86 03
042
Calculated (low Monday 21 November 1983 Tuesday 22 N o v e m k 1983
G
Time 01 day h
F i g . 11.3
Comparison of c a l c u l a t e d a n d metered f l o w s i n a f l a t a r e a
Commercial a r e a s
For the study of a commerical a r e a ( F i g .
11.4)
business d i s t r i c t of Johannesburg was selected.
a p o r t i o n of t h e c e n t r a l
House e q u i v a l e n t u n i t s were
obtained on the b a s i s of 300 mz of f l o o r a r e a a n d amounted to 3026 u n i t s , i n d i c a t i n g a t o t a l f l o o r a r e a of
90.8
ha.
The development
i s exclusively
commerc i a I. A r a p i d increase in flows occurred a t
occurred a t 1 1 a.m. around
3
p.m.,
6 a.m.
The peak m o r n i n g flow
Flows then d e c l i n e d u n t i l a r a p i d increase o c c u r r e d a t
resulting
in
the
peak
daily
phenomena a r e i n d i c a t i v e of normal o f f i c e hours.
flow
at
4
p.m.
These
The afternoon peak must
b e due to the use of l a v a t o r i e s a n d washing j u s t before s t a f f l e f t work.
172
The base f l o w s
are
high
relative
to
higher
income r e s i d e n t i a l
areas,
w h i c h can be a t t r i b u t e d to a h i g h leakage r a t e . 20-23 April 1982 4955 6 57 4 90 5 31 9
Daily average total kl Average 11s Peak 11s Minimum 11s
150
I
5-8 July 1982 47185 54 6 94 7 30 0
Average 4837 0 56 0 92 6 30 9
Calculalecj 4849 8 56 1 93 2 30 3
-
Calculated llnw
......Weekday tlow 20-23 Aprll 1982 -..... . Weekday l l w 5-8 July 1981
I
I
0
3
6
9
12 Time 01 day h
15
18
21
24
F i g . 11.4 Comparison of c a l c u l a t e d a n d metered flows in a commercial
area
Industrial
Several
industrial
reasonably generally were
areas
were
r e a l i a b l e method of mixed b u t d i d not
established
based
investigated
simulating
include any
100
on
mn
of
in
flows. heavy
floor
detail
to
Types of industry.
area
establish industry
Initially
units
showed
large
which
discrepancies in flows due to t h e predominance of h i g h o r
low water
b y i n d i v i d u a l f i r m s w h i c h bore no r e l a t i o n to f l o o r a r e a .
Variation
f l o o r area p e r u n i t d i d not therefore g i v e consistent to another.
a
were
usage of
the
r e s u l t s from one a r e a
I t was found t h a t a c t u a l water s u p p l y g a v e the best i n d i c a t i o n
of e f f l u e n t discharge.
Water meter r e a d i n g s a r e n o r m a l l y taken e v e r y
months i n Johannesburg a n d stored
in
computer
e x t r a c t meter flows over a three-month average d a i l y flow of 800 I / d a y . f o r t h i s study
files.
It
was
three
possible
p e r i o d a n d then base u n i t s on
to an
An i n d u s t r i a l a r e a o f 160 h a was selected
( F i g . 5 ) . M a j o r i n d u s t r i e s i n c l u d e d yeast m a n u f a c t u r e w h i c h
has a v e r y h i g h water usage.
CONCLUSIONS
The composite h y d r o g r a p h s p r e p a r e d from sewer flow measurements 1 1 .l-11.5)
indicate
varying
peak
times
and
the
i n d i v i d u a l h y d r o g r a p h s i s thereby emphasized. be c u m u l a t i v e a n d as peaks.
The
time
a
l a g of
result
sewer
individual
Out-of-phase
capacities
contributor
importance
need not
of
(Fig.
assessing
peaks w i I I be
hydrographs
the
also
not
sum of adds
to
173
the attenuation effect. The computer s i m u l a t i o n program i s used f o r the p l a n n i n g a n d of
extensions to
the
sanitary
sewer
collection
network.
The
new
routes,
facilities,
size
temporary
diversion
works,
program
is
or subdivision,
used to i d e n t i f y bottlenecks, study the effects of re-zoning plan
design
plan
alternative
size t r u n k sewers a n d estimate loads a t o u t f a l l works.
The
program
is
contributions
and
sections.
is
It
to
linked plotting
proposed
to
to
a
land
program estimate
use
inventory
for
drawing
future
flows
for
sewer using
assessing longitudinal
a
land
use
c l a s s i f i c a t i o n established in the computer d a t a b a n k . Dailylolal k l Average I/s Peak lls Minimum 11s
300 -
Monday
Tuesday
Wednesday
Thursdav
Average
Calculated
10317 1194 216 5 60 2
11157 129 1 208 5 69 9
10565 122 3 208 5 75 0
10423 1206 2165 67 4
10615 1228 2125 68 1
10647 1232 2132 74 5
--..-.-........
Calculaled llow Monday 5 July 1982 Tuesday 6 J U I ~1982 Wednesday 7 July 1982 Thursaay 8 July 1982
,7 E FE R EN C ES Chan, W.Y.W. a n d Wang, L . K . , 1980. Re-evaluating H u n t e r ' s model f o r r e s i d e n t i a l water demand, J. Am. VJat. Wks Ass. Constantinides, C.A., 1982. Comparison o f time l a g and k i n e m a t i c flow i n conduits. Water Systems Research Programme, University of the Witwatersrand. Crabtree, P.R., 1976. Flow a n d i n f i l t r a t i o n g a u g i n g in sewers. N a t i o n a l B u i l d i n g Research Institute, Concil for Scientific and Industrial Research. P r e t o r i a . Shaw, V.A., 1963. The development of c o n t r i b u t o r h y d r o g r a p h s f o r s a n i t a r y sewers and t h e i r use in sewer designs. Civ. Engr. S. A f r . 5, No. 9, 246-252. Stephenson, D., 1981. Stormwater h y d r o l o g y a n d d r a i n a g e , E l s e v i e r , p 276. Stephenson, D. and Hine, A.E., 1986. Simulation of sewer flow. M u n i c i p a l Engineer, 3. 107-112.
174
APPENDIX 11.1
PROGRAM SEWS IM
T h i s i s a micro-computer
(HP9816) o r i e n t a t e d
version of
a
program
to
store d a t a and s i m u l a t e flows down s a n i t a r y sewage networks. Contributor
hydrograph
types of
development
(type 2),
industrial
flows
unit
per
number o f
e.g.
characteristics residential
(type 3)
(P/min/100m2)
programmed
100m’
in
various
lower
class
( t y p e 4). The
actual
peak
b e . inserted
in
the
t h e case of
a n d peak in P/min/HE
for
(type 11,
class
a n d commercial must
(HE) or
house u n i t s
r e q u i r e d f o r each p i p e ,
are
upper
data.
Equivalent
non-residential,
is
f o r each section.
Hydrographs a r e accumulated w i t h time l a g proceeding down a l l sewers. Time l a g s a r e based on f u l l p i p e v e l o c i t y a s h y d r o d y n a m i c a n a l y s i s would be too time consuming a n d not worth the e f f o r t . Hydrographs over a n y p e r i o d of f o r any time i n t e r v a l
(e.g.
maximum) a r e t a b u l a t e d , Also
indicated
overflow
volume
are
e.g.
24h
(starting at
midnight)
selected p i p e s ( s a y 10
and plotted i f required. maximum
i f not
time
l h ) f o r a n y number of
flow
adequate.
for
A
every
summary
pipe,
of
pipe
its
capacity
lengths
and
and inflow
areas i s t a b u l a t e d a t the end. Each sewer i s i d e n t i f i e d b y a number.
The n u m b e r i n g system f o r sewers
can be selected such t h a t the f i r s t two d i g i t s of a 6 - d i g i t the o u t f a l l region,
number i n d i c a t e
the second two the s u b u r b a n d the l a s t
two the a c t u a l
p i p e which i s assumed t h e same as the top end manhole.
Effect o f Local Peaks ( P r o b a b i l i t y a n d R o u t i n g )
The design flow from a house connection f o r sewer design 1,5P/min. effect
of
The a c t u a l peak d i s c h a r g e i s c o n s i d e r a b l y a
number
of
houses
is
accumulated
is typically
h i g h e r b u t when
the
above
the
figure
is
reasonable. A proof t h a t the instantaneous peaks c a n be neglected follows.
A
typical
toilet
f l u s h occurs a t
Frequency of f l u s h i n g p e r house.
a
rate
of
204
in
a t peak p e r i o d s i s once e v e r y 2,5
7
sec
i.e.
3P/s.
minutes = 1/150s
Therefore a f t e r 7 houses mean flow/house assuming o n l y 1 house
flushes a t a time,
i s 1,2P/min
-
w h i c h i s a normal design flow.
i.e.
after
10 houses o r so the flushes a v e r a g e to g i v e a normal flow design f i g u r e . The p r o b a b i l i t y 1/400,
of
any
two houses f l u s h i n g
a n d of 3 houses 1/8000 etc.
from each house together
i.e.
i s remote.
simultaneously
is
(7/150)’
=
remote so the coincidence o f a peak
I n any case those peaks a r e
rapidly
175 attenuated b y the r o u t i n g effect described below.
Routing effect (Graphs from Stormwater Hydrology a n d D r a i n a g e Stephenson,
1981 )
In
order
to
.
shorten
running
h y d r a u l i c r o u t i n g effects.
time,
the
program
does
The f o l l o w i n g section i s proof of
r o u t i n g has a n e g l i g i b l e effect on peak flows.
include fact
that
Routing i s the s p r e a d i n g of
in peak due to
a wave and corresponding reduction
not the
hydrodynamic
forces.
I t i s superimposed on the time l a g effect. f o r 7s in a
Consider the depth corresponding to a flow of 3P/s dia.
150mm
d r a i n a t a slope of 1/100:
From a c h a r t f u l l flow Qf = 2OP/s. Therefore Q/Qf
= 0.15.
Therefore r e l a t i v e depth a t 3 t / s from the c h a r t i s y/D = 0.25 Now f o r
a reduction
in
depth
from
0.25D
to
0.125D
(i.e.
half
original
d e p t h ) from the c h a r t
Ey
0 15*x ~0.013a100 - = 15m 0.003'7
.'. i.e.
x = t2m
depth h a l v e s i n 12m of sewer pipe.
Therefore the r o u t i n g effect
i s v e r y r a p i d to s t a r t w i t h i f the flow
is
v e r y low. On the other h a n d the r o u t i n g effect on a h y d r o g r a p h from 100 houses i s c a l c u l a t e d below: Flow r a t e q = 1.5P/min 0.003 x 8h x 3600. i.e.
x
i.e.
100/60s
depth w i l l
3e/s
=
as
well,
b u t Q(volume)
h a v e over 12rn x 3600 x 0/7
i s now
= 50
km
n e g l i g i b l e r o u t i n g over the f i r s t km o r so and b y then the number of
c o n t r i b u t i n g houses w i l l f a r exceed 100.
Non-Circular
Sewers
Conduits
are
sometimes
non-circular
e.g.
rectangular
culverts
or
egg
176
shaped.
Then
the
'diameter'
i s the h y d r a u l i c r a d i u s , a n d P the
wetted
equal
perimeter,
to A/P
at
full
results.
the c o n d u i t w i l l
and A i s t h e cross sectional flow.
correct time l a g i n the computations, flow c a p a c i t y of
where R
in the d a t a may be r e p l a c e d b y 4R
This
procedure
results
w h i c h i s taken f o r the f u l l
however b e i n c o r r e c t l y
The a c t u a l d i s c h a r g e c a p a c i t y
area, in
flow.
indicated
the The
in
the
is:
A
Q = A v =
-
De2 Qe
4
i.e.
the i n d i c a t e d flow Q
the
true
cross
i n the computer p r i n t o u t should be m u l t i p l i e d b y
sectional
e q u i v a l e n t diameter 4A/P
area i.e.
divided
( nDe'/4)
by
where
De
is
the
true capacity Q = (P2/4nA)Qe.
I n f l o w Components
I n f l o w to each sewer from connections, groundwater
i s assumed to comprise four
stormwater
ingress,
a
function
components; of
i n f i l t r a t i o n which i s a f u n c t i o n of s e w e r
sewer length,
sewage flow
length, and
steady
leakage.
Each parameter can be s u p p l i e d i n the d a t a a n d u n t i l more a c c u r a t e d a t a i s available,
the f o l l o w i n g f i g u r e s a r e suggested:
Sewage I n f l o w equivalent
: Peak net
i n f l o w r a t e of
1.0
litres
per
minute per
house
i s average i n m i d d l e c l a s s r e s i d e n t i a l areas.
:
Stormwater
From
gulleys,
I n f i l t r a t i o n : 0.15
manholes
and
leaks,
mm/h.
1%
About
of
1% x 10mm/h = O.lmm/h.
p r e c i p i t a t i o n r a t e . e.g.
l i t r e s p e r m i n u t e p e r metre of sewer p e r metre diameter.
Increase for o l d sewers.
L e a k s : from c i s t e r n s , equivalent.
Inflow
d r i p p i n g taps etc.
distribution
Q2 a n d 43
assumed
is
a
in
the
program.
The
series any
T21 a n d T31 a n d
(positive
start
half
only)
The f i r s t
are
T10,
wave should s t a r t
at
in
the
T20
of
sin
waves.
type hydrograph
time
peaks occur a r e T11,
hours).
l i t r e s p e r m i n u t e p e r house
Increase f o r o l d e r a n d l a r g e r p r o p e r t i e s .
peaks of each of the 3 s i n waves f o r Q1,
0.15
hours
time and
T10.
at T30
These
when which
The
a r e designated each the
of sin
respectively values
relative
are
those waves
(all
built
in into
177 the program a n d the p r o g r a m must be e d i t e d to change them.
DATA
Data can be stored a n d edited in a separate f i l e , establishment
and
identified
the d a t a
in
identified form.
when SEWSIM As
program a t the time of r u n n i n g should be equal lines.
to and
greater
the d a t a
named a t the time of
i s run. file
Data requirements
is
u s i n g the "GET"
appended statement,
to
the
are main
l i n e numbers
2000 to a v o i d o b l i t e r a t i n g program
than
The d a t a f i l e should end w i t h END. Data can b e i n free format w i t h
commas s e p a r a t i n g numbers. Three items of d a t a a r e not used
i n SEVJSIM.
These a r e
sewer
depth,
drop a n d g r o u n d level. They a r e intended f o r a d a t a l o g g i n g a n d p l o t t i n g program l a t e r . Zeros may be inserted a t t h i s stage.
Program Output
The program sorts the p i p e d a t a m a n h o l e ( s ) . I f there
i s more
the d a t a should be checked.
than
i n t o order
one
and
unconnected
A p i c t u r e i s d r a w n of
identifies
the
(downstream)
lowest
manhole
the system w h i c h
can
be copied u s i n g DUMP GRAPHICS. Then press CONTINUE f o r the p r o g r a m to i n each
r o u t e the flows through the system and t a b u l a t e maximum flow etc. pipe. Hydrographs
are
also
tabulated
for
nominated
pipes.
h y d r o g r a p h s a r e t a b u l a t e d a t the times corresponding reach the e x i t of the system ( t h e lowest time
at
which
the
tabulated
flow
manhole)
occurs
subtract
Note
that
the
to when they would
and the
to get lag
the time
actual of
the
correspond i ng p i pe from the t a b u I a t ed t ime. The h y d r o g r a p h s a r e a l s o p l o t t e d on the screen a t the correct times.
To
p l o t a h y d r o g r a p h DUMP GRAPHICS then/or continue. F i n a l l y a t a b l e summarizing t o t a l p i p e l e n g t h a n d house u n i t s f o r each type of development i s g i v e n .
.
'LO! Fi'E-Sl'OHE"SEWSI~1" W 1'1'8 7 16-2560 - 1b 03.87 15 N d = T 0 2 16 DlJMP O E V I C E I S Nd 18 PRINTER I S Nd 20 D I M M ( 4 0 0 ) . M d ( 4 0 0 ) . D ( 4 0 0 ) .S(408). X ( 4 0 0 ) .Hq(400) . Y ( 4 0 0 ) .H(40GI). I t (400) . T x (400) . T I (400) . Q ( 4 0 0 ) . Q c ( 4 0 0 ) . Q w ( 4 0 0 ) , G ! s ( 4 0 0 ) ,Qi (400) .Ql (400) . Q m ( 4 0 0 ) .Qv(4P)0) . J d ( 4 0 B ) 3v1 DJM I21 (99) . Q 2 ( 9 9 ) , Q 3 ( 9 9 ) . T 1 8 ( 9 9 ) . T 1 1 (99) . T 2 0 ( 9 9 ) . T 2 1 (99) . T 3 0 ( 9 9 ) , T 3 1 (99) . M h ( 9 9 ) , Jh (99) ,at (29.99) ,He(99) .G1 (400) 31 COM NSCZ03 40 I N P U T "NAME '?".NS 60 READ N s . T s . T i . N h , O l l !NO.SECNS. S I M L N h . T I N C h .Nhydqphs.GLmBOTMH 70 FOR Jn=l TO Nh ! HYDROGHAPHS 80 HEAD M h ( J n ) !PIPE NO OF HYGPHS 90 NEXT Jn 100 J2=B 110 FDR K = l TO Ns SECT DATA I20 READ Mb,Itk,Np,Am,Fw,Fs,Fi,Fl ! HOTM MH, ZONE TYPE,Npipes,MANNINljn.I-/MIN/HEQ ,mm/h STORM,INFIl/MIN/M/M.LK/MIN/HEQ 130 J2=J2+Np 140 M d ( J 2 ) = M b 150 FOR J=J2-Np+l TO J2 ! P I P E DATA 160 READ M ( J ) , D ( J ) . X ( J ) , S ( J ) , H q ( J ) ,Y(J) , H ( J ) ,G1 (;I) !NO. ,DIClmm,I..m,Sm/m.H~USE EQU VS(l00m2),DETTHm,DROP BOTMENDmm,GLmMH 180 I F J < = J Z - N p + l THEN 200 190 M d ( J - l ) = M ( J )
12 ! D. STEPHENSON
I
'
200 I t . ( J ) = I t k 205 Q v ( J ) = K 260 T x ( J ) =X ( J) +Am*4". ( 2 / 3 /) ( D ( J )/ 1000) ." ( 2 / 3 )/S( J)". 5 ! L..AG, 5 270 Qc ( J) =. 7 8 5 / A m / 4 . " ( 2 1 3 ) (D( J) / 1000) ( 8 / 3 +S ) ( J) 5+ 1000 !CAPAC I TY ,L./s 280 Qw (J)=Fw+Hq ( J ) /h0/ 1000 !PEAK M3/S INFLOW 290 Q s ( J ) = F s * X ( J ) * l 0 0 / 1 0 0 0 / ~ 6 0 0 ! DO. STORM 300 Qi ( J ) = F i + X (,I) +D ( J )/ 1 0 0 0 / 6 0 / 1000 ! DO. I N F I L T N 310 Q1 ( J ) = F l + H q ( J ) /60/1000 ! DO. L E A K S 320 NEXT J 330 0 (K)=J2-Np+l ! TEMP. TOPMH FOR PLAN P1.OT
*
,*%
340 350 400 410 420 430 440
450 460 470 480 490 500 510
9rn (F:) =Np NEXT K T40=12 T41-17 91(1)=.7 92(1)=.5 93(1)=.6 T10(1)=5 Tll(i)=9 T20(1)=7 T21(1)=13 T30(1)=14 T 3 1 ( 1 ) =20 91(2)=.8 92(2)=.7
520 530 c-13(2)=.6
T10(2)=6 T11 (2)=8 T20(2)=7 T Z 1 ( 2 )=13 T30(2)=16 590 T 3 1 ( 2 ) = 2 0 4500 01(3)=.4
!STORM START h !PEAK h ! RESID4UPCLAS. 1S T P E A K = l ! 2 N D PEAK ! 3 R D PEW !START h 1ST PEW MUST BE 1st HG TO START ' P E A K h 1ST PEAK ! S T A R T h ZND PEAK !PEAK h 2ND PEAK !START h 3RD PEAK !PEAK h 3RD PEAK !RESIDLPOOR
540 550 560 570 580
6llb 620 630 640
! INDUST
02(3)=.S 93 ( 3 ) =. 45
T10(3)=6 T 1 I ( 3 )= I 0 650 T 2 0 ( 3 ) = 4 660 T 2 1 (3)=13 670 T 3 0 ( 3 ) = 1 3 675 T 3 1 ( 3 ) = 1 6 680 01 (4)=.3 690 02(4)=.7 700 03(4)=.45 710 T 1 @ ( 4 ) = 6 720 1 1 1 ( 4 ) = 1 0 /d T 2 0 ( 4 ) = 6 740 T 2 1 ( 4 ) = 1 3
!COMMERCIAL
--.
d
W
i
61 4 IXI
B t.4
m iii L
I
z
2 W
I !-
w
t);
w
a
+
a
r.l
-
1030 1032 1033 1034 1035 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 104.9 1050 1051 1052
1053 1055 1060 1070 1071 1072 1073
1074 1075 1076 1077 1078 1080 J 090
1092 1093 1100
NEXT E GINIT GRAPHICS ON ! DRAW LAYOUT GCLEAR WINDOW - 1 0 0 0 . T l ( N l ) + 1 0 0 0 , 0 , N s + l FOR E = l TO Ns FOR J = B ( E ) TO O m ( K ) + O ( # ) - l MOVE T 1 ( N l ) - T l ( J ) . K DRAW T 1 ( N l ) - T l ( J d ( J ) ) - 2 0 . K L l = T l ( N l ) - T l (J)-20 C S I Z E 3..4 MOVE L1 .K ! D I R l+PT/b LABEL M ( J ) LDIR 0 NEXT J Jmm=Om ( K ) +O ( K ) - 1 I F J d ( J m m ) = 0 THEN 1055 MOVE T 1 ( N l ) - T l ( J d ( J m m ) ) - 1 0 . K DRAW 1 1 (N1 ) - T 1 ( J d ( J m m ) ) , G ! v ( J d ( J m m ) ) NEXT K PAUSE FOR J=1 TO J2 (;7m(J)=0 ! MAX. FLOW Qv(J)=0 !SPILL VOL. NEXT J Ti=0 !COUNTER FOR T H FOR T h = T i TO T s STEP T i ! T I M E h AT BOTTM FOR J=1 TO 52 I N I T I C I L I Z E FLOWS R(J)=0 NEXT J FOR J=1 TO 52 T S T h - T I ( J ) /3h00 !PIPE T I M E FOR REACHNG E X I T A T T h I F T : : . T 1 0 ( I t ( J ) ) THEN 1100 T=T+24 IF T > = T l B ( I t ( J ) ) THEN 1110 !HYOROGRAPH ORDINATE PER PIPE
1290 NEXT J 5 1300 NEXT J
1 3 1 0 FOR J = 1 TO J Z 1320 I F R(J)<=Qm(J)
THEN 1340 1 3 3 0 Qm(J)=Q(J) 1 3 4 0 I F Q ( J ) < P c ( J ) / l 0 0 0 THEN 1360 1350 R V ( J )=Qv (J)+ ( Q ( J )-Qc ( J )/ 1000)+3600+Ti 1360 NEXT J 1370 T i = T J + l 1380 FOR Jn=l TO Nh !HYDRAPH POTNTS 1 3 Y 0 R t (Jn,T j )=a ( J h ( J n )) + l B 0 0 1400 NEXT J n 1.410 NEXT T h 1420 PRINT "SEWER NETWORK ANALYSIS , " 1430 PRINT N8 1440 PRINT 'I P I P E D I A SLOPE HUNITS LAGh M A X L s QCAP XFIJL.1. OFL.Om3" 1450 IMAGE DDDDDD.DDDDD.D. DDDD.DDDDD.DDD. DD.DDDI)D.T)I)DDD.onnI>. D.DDDD. D 146R FnR J=l TO 52 1470 T 1 ( J ) = T l (J)/360cI 1400 Qm (J ) =Qm (J)+1800 1490 P f = a m (J) /Qc (J ) + 1 0 0 1500 PRINT USIND 1450:M(J) ,D(J) . S ( J ) .Hq(J) .T1 ( . 7 ) .Qm(,l) . R c ( , l ) . P f . R v ( J ) 1 5 1 0 NEXT 3 1520 IMAGE DDDDDDDD.# 1525 IMAGE DDDDD.DD.# 1526 IMAGE DDDDD.DD 1 5 2 7 IMAGE DDDDDDDD 1530 PRINT 1540 PRINT "SELECTED HYDROORAPHS AT":Ti ;"h 1NTVL.S STCIHTTNG A T - T l FKIR PTPF 1 5 4 5 PRINT USING 1520;Ti 1550 FOR Jn=l. 7'0 Nh-1 1551 PRINT USING 1520;M(Jh(Jn)) 1552 NEXT J n 1 5 5 3 PRINT USING 1 5 2 7 : M ( J h ( N h ) ) 1 5 6 0 FOR T k = l TO T i 1565 PRINT USING 15'20:Tk 1570 FOR Jn=l TO Nh-1 1571 PRINT I.JSING 1525:Qt (-7n.Tk) 1 5 7 2 NEXT J n 1573 PRINT IJSING 1526:Qt ( N h . T k )
1575 NEXT TIC 1380 GCLECIR 1600 FOR Jn=l TO Nh
1602 1603 1605 1610 1620 1630 1700 1701 1710 1711 1720 1721 1724 1725 1730 1740 1750 1755 1760 1765 1766 1770 1780 1790 1800 1810 1820 1830 1840 1850 1855
QCLEAR ! P L O T HYDROORCIPHS ON SCRNCSIZE 4 Omi=Qm(Jh(Jn)) WINDOW -3,24.5,-0.Qmj*l. 1 CIXES 1,1,0,0,12,10 MOVE l , Q m ( J h ( J n ) ) Qm (Jh (Jn ) ) = I N T (Qm ( Jh (Jn ) ) 1000)/ 1000 L A B E L Qm (Jh (Jn) ) ;" L / s PIPE" :Mh (Jn) MOVE 6,0 LCIBEL. N S
DUMP GRAPHICS & / O R CONT
*
MOVE 22.0 L A B E L "h 24" MOVE -2.10
LhBEL 10 FOR T=2 TO T i Th=(T)*Ti-Tl (Jh(Jn)) T h - T i .Qt ( J n , T - l ) Th,Qt ( J n . T ) T -T1 ( J h ( J n ) ). Q t ( J n , T - 1 ) DRAW T i - T l ( J h ( J n ) ) , Q t ! J n , l ) PAUSE ! T Y P E CONT NEXT Jn FOR 1 = 1 TO 6 MOVE DRAW NEXT MOVE
He(I)=0 NEXT I FOR J = 1 TO 52 H e ( 1 t ( J ) ) = H e ( I t (J)) + H q ( J ) XleX1+X(J) NEXT J PRINT
(El-)
TO DO NEXT t i Y B 13R DUMPFH TO DRAW EX
SEWSIM
DATA
FORM
NAME -2 W !
DATA
..........
NO. OF SECTIONS, 2010
DATA
SIMULATION DURATION h,
T I M E INCREMENT.h,
NO.
HYDROGRAPHS REQUIRED,
G.L.(M)
BOTM M i .
..................
....................................
........................
P I P E NO. OF HYDROGRAPHS
2020
DATA
..........................................................
SECTION DATA: BOTTOM MH NO.,
2030
DATA
( 1 L I N E PRECEEDING EACH SECN.)
ZONE TYPE (1-41,
P I P E DATA:
DATA
PIPES I N SECN,
MANNINGN,
SW/min/HE,
STORM Chnm/h,
I N F I L T N L/mm/m/m,
EAKG L/mi
/HE.
( I L PER P I P E )
P I P E NO.(=TOP MH NO.), 2040
NO.
........................................................................................................................... m -,
LENGTH m ,
SLOPE m/m,
HE=HDWE E a U I V S ( l W m ’ ) ,
(DEPTH TOP MHm,
DROP BOTM mm,
GLm
............................................................................................................................
G i v e e a c h d a t a f i l e a name
Store in ASCII form
e.g.
SAVE
c a l l e d up when SEWSIM i s RUN. “FILENAME”
187
SAMPLE DATA F I L E SEWDAT
(ASC I I
FORMAT)
7000 2001 ZQCI? 2061.3 2804 288'3
DATA 4 , 2 4 , 1 . 4 , 5 0 DATA lil,1'21,211,.311., 1 1 . 3 , 1 , 2 ,. 0 1 J , 1 1 , 0 WTA 111,100,100 ,.0100,100,1.30,49 DATA 1 1 2 , 3 0 0 , 3 0 0 , . 6 1 1 0 0 , l ~ 0 , 1 , 0 , 4 8 DATA 112,2,9, . 0 2 , I , 0 , . 1 , . 0 DATA 1 2 1 , 1 5 0 , 1 B 0 , . 0 1 5 , 1 0 0 , 1 , 0 , 4 7 2806 DATA 1 2 2 , 1 5 0 , 3 0 0 ,.004,75,1,C!Il46 2807 D(?ITA 123,200,i00,.802,95,1.5,30,45 2 0 0 8 DATA 122,3,1,.02,1,0,a..1 2089 DATA 211,150,100,.81,100,1,0,48 2 0 1 0 DATA 123,4,1,.02,1,0,0,0 2 0 1 1 DATA 311,100,iQ0,.002,100,1,0,47 100pI0 END
,.
:YF'B2'mX. 78B VOLUME LABEL: B982.5 F I L E NAME PRO TYPE FiEC/FILE HYTE/HEC
SEWDAT
BEWSIM
Note
_-__ SAME
ASCII PHDG
"SEWDAT",
3
256
7 _IL 3
256
don't STORE
,I...
ADDPESS
50 53
,
0
188
END P I P E WITH NO D . S . P I P E 2
SEWER NETWORK hNALYSIS
112
FOR
DIA SLOPE HUNITS LAGh MAXLs PCAP %FULL OFLOm3 100 .0100 100 .I2 2 4 37.3 0.0
PIPE
111 112
308 150 150 I23 200 211 150 311 100 121 122
.0100 100 .0150 100 .0840 75 .0020 95 .a100 100 .00?0 100
.07 .44 .40 .I6 .45 .31
10 2 4 7 2
2
84
12.1 14.0
12
6 69.3 10 73.3 10 16.7 2 112.5
0.0 0.0 0.0 0.0 0.0 0.0
SELECTED HYDROGRAPHS AT I h INTULS STfiRTING AT -TL FOR P I P E I 31 1 111 121 21 1 1 .I7 0.00 * 29 .03 L. 1
3 4
5 6 7
.03 0.00 0.0Q 0.00 a0
.
.79
8 9 10
1.25 1.56 I .67
11
1.57
1:
1.29 .96
13 13
.97
.03 .03 .03 -03 .03 .68 1.45
1.69 1 .?O
.96 1.11 1.18 1.18
.I7 .I7 .I7 .17 .17 .67 1.03 1.32 I .51 1.58 1.52
1.36 1.33 1.51 1.65 I .56
15
!.18
1.10
16 17 16 19 20 21 22
1.34
.94 .94 1.03
23
.73
.64 .56
.I7
24
.53
.20
.I7
1.40
1.36 1.21 1.17 1.07 .89
1.00 1.01 1 .OO
1 .:7
0.00 0.00 0.00 0.00 0.0Q .32 .7b
1.10 1.36 1.50 1 .5l 1 .41 1 .21 I .47 1 .69 I .43 *
76
.bl .51
.34
.37 .23
0.Q0
.08 0.08 0.08 0.00
...
189
I
1.684 L / s PIPE 121
1.688 L/s PIPE 31 1
-
h 24
190
CHAPTER 12
SEWERAGE SYSTEMS MANAGEMENT
The
in
interest
management
of
sewerage
existing
i n c r e a s i n g flows
and
systems
systems
to
improve
is
has
in
recent
order
to
increased
in
improved
catchment
water
balances.
years cope
The
as
with
design,
s i m u l a t i o n a n d management o f such systems i s t h e s u b j e c t of much r e s e a r c h (Yen,
1987).
Dual
p o l l u t i o n of old
systems
waterways
systems,
pose
particular
problems
i s becoming more o f
including
re-lining
p l a c e (Adams a n d Zukovs,
to
a
increase
older ,areas
as
Rehabilitation
of
in
problem.
i s also
throughput
taking
1987).
The o p e r a t i o n o f a l a r g e u r b a n sewer system was o p t i m i z e d b y S c h i l l i n g a n d Petersen sewer
(1987)
pumpstations,
using
in
system
storage
adequately controlled, severe
economic
conjunction
with
I i n e a r programming.
Brenner,
West
and
ponds
catchment
linear constraints.
Conduit
rate
the
given
by
wastewater
The
treatment
St.
optimization
s i m u l a t i o n model.
t h a t the o p t i m i z a t i o n model was,
as
a
comprises
combined
sewer
pipes,
plant.
Unless
t h e system i s l i a b l e to f l o o d l o w l y i n g s u b u r b s w i t h
consequences. a
The storm/waste
Germany,
o f necessity,
flow
in
run
was
this
was
a s i m p l i f i e d model assuming
s t o r a g e therefore, Venant
model
The reason f o r
a
complex
equations,
function
could
not
of
flow
easily
be
i n c l u d e d in a l i n e a r model. A r a i n d a t a c o l l e c t i o n n e t w o r k was coupled t o a catchment model o n a r e a l time b a s i s t o p r e d i c t flow r a t e s ( F u c h s e t al.,
1987).
LEARNING SIMULATION PROGRAM
The p r o g r a m used a n i t e r a t i v e l e a r n i n g process t o o p t i m i z e o p e r a t i o n o f t h e system.
That
is,
successive r u n s used p r e v i o u s r e s u l t s to
the operating r u l e using a r t i f i c i a l The sewer
system
studied
was
designed
o v e r f l o w i n storms r a n t o r i v e r s a n d lakes. forced t h e system t o b e improved.
to
treat
lower
flows
I n c r e a s i n g p o l l u t i o n awareness
.
The problem was set up t o m i n i m i z e a constraints.
A
formal
system
(referred
e s t a b l i s h e d w i t h t h r e e components:
whereas
At t h e same time a s r e d u c i n g overflows,
p a r a l l e l o b j e c t i v e s were t o reduce p u m p i n g e n e r g y costs a n d
f lood ing
improve o n
intelligence.
to
cost as
function a
avoid
without
production
street
violating
system)
is
191
A w o r k i n g memory w i t h a l l d a t a A r u l e base
A n i n t e r p r e t e r to choose and a p p l y p r o d u c t i o n s Improved control ones.
i s achieved b y a l t e r i n g the r u l e base o r
a d d i n g new
For each u n s a t i s f a c t o r y production a l i s t i s created.
A meta production systems was f u r t h e r added. a f f e c t the w o r k i n g memory b u t can change
Meta p r o d u c t i o n s do not
the content of
The meta system i s e v a l u a t e d b y the control
the r u l e base.
A simple example
interpreter.
demonstates the technique: Stormflow
could
be
stored
in
a
detention
f l o o d i n g would be an u n s a t i s f a c t o r y state.
basin
freely,
while
street
T h i s r u l e could be described b y
a meta f u n c t i o n as flows:
( W E > 1.0)
+
(pump too L O W ) (Value = - 1 )
Whenever the water level in the sewers i s h i g h e r t h a n manhole
level which
may cause street f l o o d i n g t h i s r u l e i s a p p l i e d . At a n y selected time i f the meta
production
rule
is applicable
the
decision
PUMP
=
OFF
is
counter
the corresponding productions a r e decreased b y 1 .
r u l e d i.e.
The facts i n the w o r k i n g memory a t the time may h a v e been
W E = 0.4
where W E = water e l e v a t i o n
R I = 10
where R I = r a i n f a l l i n t e n s i t y .
Another s i t u a t i o n may also have been stored in the experience memory, e.g. WE = low
R I = 10 I t i s possible b e t t e r productions c o u l d h a v e been a p p l i e d . The total l i s t i n memory may now be
WE -
Va Iue
RI -
-3
LOW
9
-1
LOW
10
-6
LOW
a
-10
LOW
11
A new p r o d u c t i o n i s created t a k i n g the c o n d i t i o n p a r t of the o l d one.
A
second condition i s added of the form
N I op x where op i s e i t h e r < o r experience memory,
> a n d x i s the median v a l u e of R I in the l i s t of
weighted w i t h the level of punishment.
Thus s t a r t i n g w i t h the o l d p r o d u c t i o n
(WE = LOW)
+
(pump = OFF)
192
the new p r o d u c t i o n w i l l s w i t c h pump on because the systems knows t h i s
is
connected w i t h h i g h r a i n f a l l i n t e n s i t y . Hence the new p r o d u c t i o n i s
( W E = L O W ) ( N I > 9.75)
+ (pump = O N )
The new p r o d u c t i o n i s assigned a v a l u a t i o n of
0 a n d stored
in
the
rule
base. I f the s i t u a t i o n WE = 0.4
R I = 10 occurs a g a i n the last r u l e s w i l l b o t h a p p l y ,
but
the
l a t t e r r u l e i s chosen
as h a v i n g lowest e v a l u a t i o n l e v e l . Street f l o o d i n g i s t h u s avoided.
OPT I M I ZAT ION
The
same
optimization
problem at
was
discrete
simplified times.
into
Sewers
a
linear were
subcatchments.
Wser
I1
Hbsssliisc
I2
-1
Fig.
12.1 Process v a r i a b l e s f o r the s i m p l i f i e d systems
system
lumped
for
direct
into
three
193
A rainfall/runoff
model
was
used
to compute
r e m a i n i n g system consists o f two o f f - l i n e backwater
effects from
v a r i a b l e s ( F i g . 12.11,
-
the
pumps.
inflow
hydrographs.
ponds a n d two t r u n k sewers w i t h
The
system
can
be
described
by
up
18
namely:
i n f l o w I 1 i n t o the pump sump of the downstream p u m p i n g s t a t i o n , 12 h a l f w a y
The
the
upstream
station,
and
13
into
the
sump
inflow of
the
upstream s t a t i o n .
-
the pumping r a t e s PR3
i n t o the
i n t o the downstream system,
upstream pond,
PRl
P2 from
the
i n t o the downstream pond,
upstream
a n d PKA to
the treatment p l a n t .
- recycled flow from the ponds to the system ( R R l a n d RR3, r e s p e c t i v e l y ) , - the stored sewage i n the t r u n k s (V12 a n d V3, r e s p e c t i v e l y ) and i n the ponds (R1 a n d R3, r e s p e c t i v e l y ) ,
-
overflow
PO1
Wasserlose,
-
flood
into
the
Weser
estuary,
01
into
the
downstream
creek
and 03 i n t o the upstream creek Krimpelfleet,
volumes
respectively
which
cannot
be
handled
by
the
system
(F12
and
F3,
1.
The s i m p l i f i e d model
was
verified.
This
was
done
through
a
detailed
a n d p h y s i c a l l y precise model.
Optimal Control a s a L i n e a r Programming Problem
The task
in
drainage (i.e.
the o p e r a t i o n of
the Bremen combined
m i n i m i z a t i o n of f l o o d i n g ) a n d environmental
m i n i m i z a t i o n of combined sewer f l o w ) as
low
as
sewer
possible.
Since
protection a n d no overflow
it
is
system
p r o t e c t i o n (i.e.
w h i l e keeping the cost of impossible
to
were
achieve
operations
perfect
flood
simultaneously p r i o r i t i e s h a v e to be specified.
They include:
1 . minimum f l o o d i n g (F12, F3) 2. minimum overflow i n t o the creeks (01, 0 3 ) , 3. minimum overlfow i n t o the e s t u a r y ( P o l ) ,
4. minimum pumping i n t o the ponds ( P R l , PR3),
5. minimum use of the ponds ( R l , R3) U n i t costs c a r e specified overflow.
etc.
Using the
for
every
technique of
c u b i c metre flooded,
l i n e a r programming
c u b i c metre
the o p e r a t i o n a l
o p t i m i z a t i o n problem was formulated a s n
z
min t = l
cv3tV3t + cR3tR3t + cv12tV12t + c r l t R l t + cRR3tRR3t + cP2tP2t
+ cPR3tPR3t + cF3tF3t + co3t03t + cRRltRRlt + cPKAtPKAt
+ cPRltPRlt
+ cF12tF12t + cPOltPOlt + c o l t O l t
1 94
12.1
TABLE
O p t i m a l Control S t r a t e g y f o r M a j o r Storm 0708
,----------------
----
0.0 1.0 .----------------
C
1 2
14268 1277 'I4268 10000 14268 10000 ill88 10000 14268 10000 14268 10000 14268 10000 14264 10000 13814 10000 13049 10000 13088 10000 11037 10000 10108 10000 9125 10000 a i r 4 10000 7163 10000 6182 10000 5201 10000 4220 10000 3231 10000 1612 -~~~ 9549 531 6560 531 6490' 531 4420 531 2350 531 260 531 0 531 0
3 4
6 6 7 8 9 10 11 12 13
14
16 16 17 18 19 20 21 22 23 24 25 28 27 28 29 t
.---__-----
R3
c
0.3
1 2 3
4944 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 6704 7615 6626 5437 4848 3269 2170 1081 0 0
.---------4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
93 ----0.26 -----
PM PRl Po1
t _---
10
1630 0 0 0 3800 1277 3600 9414 691 3600 Be68 9000 3600 6346 6346 3600 2946 2946 3600 1373 1373 3800 603 603
a
$600
3600 3600 3600 3600 3800
0
0 0
0 0
0
0
0
0
3600
0 0
0 0
3800 3600 3800 3600
0 0 0 0
0 0 0 0
3800 3600
0
0
0
0 0
0 0 0 0
0 0 0
0 0 0 451 0 989 0 2070 0 2070 0 2070 0 2070 0 280
0
0
0 0 0 0 0 0 0 0 0
3600 3600 3600 3800 3600 3600 1610 1530
0 0 0 0 0 0 0
0 0 0
0 0 0
0 0 0
0
0
0
0
0
0
0
1280 1280 1260 0 1260 1260 1260 1260 1260 1260 1260 1260 1260 1260
1730 1730 1730 1730 1730 1730 1730 1730 1730 1730 1262 193 0 0 0
1260 1260 1260 1260 1280 1260 171 171 171 171
0 0 0 0 0 0 0 0 0 0 0 0 0 0
171 171 171
PR3 F3 -----------1.0 1001 --__----_ 0 4944 6588 5710 6588 270 6032 0 3656 0 2047 0 2011 0 1577 0 997 0 396 0 0 0 0 0 0 0 0 0 0 0 0
0 0
0
0 0 0 0 0 0
0 0 0
0
896 1069 1089 1089 1089 1089 1089 1089 0 1081
0 0 0 0 0 0 0 0 0
0
1932 6588 6032 3656 2047 2011 1577 997 396 0 0 0 0 0 0 0 0
0 0 0 0
12283 9972 12715 8410 5080 3519 2752 2147 1701 1386 1170 1170 1170 1170 1170 1170 1170 1170 1170 1170
13558 6118 6032 4916 3307 3271 2837 2257 1656 812 171 171 171 171 171 171 171 171 171 171 171
3483 1762 752 ._ 275 205 194 191 189 189 189 i 89 189 189
ias
189 189 189 189 189 189 189 ~~~
195
subject to the c a p a c i t y c o n s t r a i n t s
5 R3 5 V12 5 R1 5 P2 5 PR3 5 PKA 5 PRI 5 PO1 5
V3
1730 m3 9600 rn’ 14268 m’ 10000 m3
0.70 m’/s 3.66 m’/s 2.00 m’/s 8.20 m’/s
5.00 m’/s
a n d the dynamic c o n s t r a i n t s f o r each of the f o u r storage u n i t s
-
V3t+l - V3t
RR3t + P2t + PR3t + F3t
= 13t
= o
R3t+l - R3t - PR3t + RR3t + 03t V12t+l
-
V12t
-
P2t-2
-
+ PKAt + P R l t + F12t
RRlt
R l t + l - R l t - P R l t + RRlt + POlt
The flow
time
from
the
taken as one time step
+
+
12t-1
= o
Olt
inflow
(i.e.
= Ilt
site
12
30 m i n ) and
to
the
downstream
the flow
pump
time between
was
the two
pumping stations as two time steps. The problem was
solved w i t h
presented i n Table 12.1 time step o n l y costs c of
A
s t a n d a r d software.
f o r a 210 m i n storm
and
(0 to 30 m i n from a c t u a l time).
the o b j e c t i v e function.
Sensitivity
c o u l d be specified q u i t e a r b i t r a r i l y ,
typical
inflow The
table
of
is one
includes u n i t
a n a l y s e s showed
provided that
result
forecasts
that
u n i t costs o f
these
different
o r d e r s of magnitude a r e a l l o c a t e d to objectives of d i f f e r e n t p r i o r i t y .
SEWER MAINTENANCE DATA PROCESSING IN JOHANNESBUG
Johannesburg
has
nearly
four
thousand
operate and m a i n t a i n on a continuous basis.
kilometres Many of
of
sewerage
to
the areas a r e prone
to abuse and blockage a n d the n a t u r e o f the topography a n d c l i m a t e make maintenance a h i g h cost i n the system. That is, in
ingress
into
sewers
and
f o r e i g n matter which block
in
many
sanitation
places system
it
is
are
this
suspected, often
may
the sewers.
found
as
in
bring
intense storms o f t e n r e s u l t surface
debris
and
other
There i s a l s o u n a u t h o r i s e d access articles sewers.
obviously Despite
the
not
from
high
rate
the of
1%
g r o w t h i n Johannesburg many o f the sewers a r e o l d a n d some a r e of poor q u a l i t y r e q u i r i n g r e g u l a r maintenance a n d replacement a n d r e p a i r s . While a t f i r s t i t may a p p e a r t h a t r e a d y a v a i l a b i l i t y of l a b o u r i n South Africa
should f a c i l i t a t e c l e a n i n g a n d
should
provide
obviously for
labour
imposes
severe
i d e n t i f y i n g trouble
managers
and
opportunities, problems a t
spots
sewerage
b u d g e t i n g f o r r e p a i r work
at
the
the
higher
i n the system
engineers.
same
time
management
This
levels. would
type
the
of
maintenance
such
a
system
Maintenance of
b e of
of
great
data
such a s to manholes a n d
even
is
logs
value useful
to for
pipes requiring
replacement as well a s m i n o r items such a s manhole l i d s a n d s t e p i r o n s a n d benching
i n manholes.
There i s also much to be g a i n e d
maintenance d a t a in the way o f types of blockage. where f o r e i g n objects a r e f r e q u e n t l y
encountered
from a n a l y s i s of
For instance l o c a l i t i e s can
be
narrowed
down
a n d the i n h a b i t a n t s o f t h a t township made a w a r e of the t r o u b l e s caused b y such p o l l u t i o n .
f o u n d in sewers i t may p o i n t
Where sand i s f r e q u e n t l y
r o a d s r e q u i r i n g s u r f a c i n g as stormwater
can
r e a c h sewers
by
to
unexpected
ways. Overflows a n d inadequate
l i f t i n g of
sewer
manhole
capacities.
lids
in c e r t a i n a r e a s may p o i n t
Alternatively
they
sewer l i n i n g s o r roots w h i c h b l o c k the sewers.
may
indicate
to
corroded
Here a g a i n i d e n t i f i c a t i o n of
frequency and l o c a l i t y o f such inadequacies i n d i c a t e s where maintenance i s most u r g e n t l y r e q u i r e d . The human management side
i s also v e r y complex.
The o u t l y i n g depots
where such maintenance takes p l a c e employ some s i x h u n d r e d people, w h i c h a r e g e n e r a l l y o r g a n i z e d i n t o gangs a t each depot. to managers who take messages a n d t r a n s m i t Even managers a n d f r e q u e n t l y type
of
logs
they
keep
The s u p e r v i s o r s r e p o r t
the teams to problem points.
s u p e r v i s o r s a r e not h i g h l y
are
often
difficult
to
trained
process.
a n d the
However
computerization of the l o g keeping on a n e x p e r i m e n t a l b a s i s a t one of depots has proved s a t i s f a c t o r y a n d w i t h i n t y p e of s t a f f .
the the
the c a p a b i l i t i e s of the e x i s t i n g
T e r m i n a l s connected to the m u n i c i p a l i t y ' s m a i n computer
at
head o f f i c e a r e used a n d once b a s i c k e y b o a r d s k i l l s h a v e been p i c k e d u p then spread sheet g r e a t advantage
type data
l o g g i n g h a s p r o v e d p o s s i b l e and
to the engineers a t
in
head o f f i c e concerned w i t h
fact
of
planning
a n d the engineers concerned w i t h b u d g e t i n g a n d maintenance a n d design. Although
Johannesburg's
obvious
computer w i t h o u t l y i n g t e r m i n a l s ,
solution
is
through
its
mainframe
in f a c t many s m a l l e r m u n i c i p a l i t i e s may
r e s o r t to m i n i o r even m i c r o computers to h a n d l e t h e i r system.
The l a t t e r
would be p o p u l a r w i t h the smaller m u n i c i p a l i t i e s where one s t a t i o n o n l y maintained.
is
197 The use of micro computers also enables micro g r a p h i c s to be used to identify
A
t r o u b l e areas.
blockages.
With
the
screen map can
advent
of
the
highlight
computers
many
zones
with
fields
in
frequent the
Civil
Engineering f i e l d have been opened up to the b e n e f i t s which can accrue in both
the
design
administration
and
areas.
constructional Due
to
initial
areas costs
and and
the
a
management
natural
and
reluctance
to
adopt new methods progress i s sometimes slow b u t i t can u s u a l l y be s a i d that
w h i l e computers do not
necessarily
save money
they
can
definitely
g i v e b e t t e r r e s u l t s a t the end of the day.
AppI i c a t i o n to Johannesburg's system
Thus
it
was
with
this
i n t e n t i o n of
giving
an
improved
Johannesburg h a s persevered w i t h computerization o f many of
service
that
i t s functions.
T h i s chapter o u t l i n e s the progress made in the p r o v i s i o n a n d maintenance of sewerage r e t i c u l a t i o n . The sewers
analysis has
townships
of
sewer
systems
already
been
established
for
s u b d i v i s i o n of
existing stands
and has
future
to
identify and
has
In
flows.
been assessed
potential been
some
overloading
used
cases
to
by
analyse
the
effect
a n d a c c u r a t e estimates of
of
costs
g i v e n f o r a d d i t i o n a l sewerage work (Stephenson a n d Hine, 1982 a n d 1985). Sewer r e t i c u l a t i o n s need r e g u l a r p l a n n e d c l e a n s i n g i f a n d subsequent danger to h e a l t h i s to be avoided.
serious f l o o d i n g
I f r e g u l a r c l e a n s i n g of
p u b l i c sewers i s well o r g a n i z e d many of the blockages which occur can be avoided.
Maintainance of p r i v a t e l y owned sewers i s not the r e s p o n s i b i l i t y
o f the sewerage a u t h o r i t y unblock these sewers owner
b u t i n Johannesburg i t i s the o f f i c i a l p o l i c y to
In many cases the
i f asked to do so b y the owner.
i s the local a u t h o r i t y
so t h a t there i s a vested
interest
to ensure
t h a t these a r e well m a i n t a i n e d so as to reduce the number of blockages. Conventional u s i n g c a r d s etc.
systems h a v e been which
used to r e c o r d the work
h a s been successful
considered t h a t records of
c l e a n s i n g work
but
and
c o u l d be more e f f e c t i v e l y done b y computer a n d
c a r r i e d out
time consuming.
the c l e a r i n g of that
I t was
blockages
r e t r i e v a l of
records
a n d p l a n n i n g o f work would be made easier. Consequently the M a i n t a i n a n c e Data System has been e s t a b l i s h e d a n d i s being applied
where Sewer
Data
has
been
established
giving
sizes
lengths of sewers together w i t h a u n i q u e manhole numbering system.
and
198
Data i s compiled b y depot a d m i n i s t r a t i v e
s t a f f on Forms wich
numerical format s u i t a b l e f o r i n p u t to the computer.
have a
Details are abstracted
from work r e p o r t s d a i l y . Forms used in the f i e l d g i v e township a n d street names which numerical
become
township codes a n d manhole numbers before b e i n g entered
the computer.
into
I n c o r p o r a t e d i n the c l e a n s i n g r e p o r t i s a n inspection of each
manhole a n d sewer l e n g t h i n c l u d i n g the measurement of the d e p t h o f flow.
Processing of Sewer Maintenance Data
The processing of
sewer maintenance
data
has
reached
an
advanced
stage u s i n g the programs and techniques d e s c r i b e d below. The workforce
i s d i v i d e d i n t o gangs w h i c h work
on e i t h e r c l e a n i n g of
sewers o r c l e a r i n g of blockages. The c l e a n i n g of sewers each
day
a n d manhole
i s recorded b y
the gang
numbers a r e o b t a i n e d
from
leaders keyplans
in
the f i e l d
showing
the
sewer network. On
the
following
working
day
information
is
abstracted
a d m i n i s t r a t i v e s t a f f a n d i n s e r t e d i n a numerical format.
TABLE 12.1 Cleansing of Sewers
nEcono OF SYSTEMATIC CLEANINO
L SEWERMANHOLE
CONDITION
by
( T a b l e 12.1)
depot
199 Program UPDATE i s then length
and
slope
which
is
used
to
added
to
provide the
details
data
file.
of
sewer
These
diameter,
details
are
o b t a i n e d from the Sewer Data F i l e ( T a b l e 12 .2 ) A MERGE program
i s used
to
add
new
data
to
a master maintenance
f i l e (Table 12.3). Program MAINTENANCE produces a r e p o r t of the sewers cleaned between g i v e n dates as r e q u i r e d a n d p r i n t e d out a c c o r d i n g to each township. Program GANGS produces a
r e p o r t of
work
c a r r i e d out
by
each g a n g
between g i v e n dates. T h i s r e p o r t could form t h e b a s i s f o r a bonus scheme ( T a b l e 1 2 . 4 ) . Blockages a r e recorded as reported The
details
of
actual
appear on work blockages
which
with
"Private"
number a n d "Main"
time
boundaries
started
recorded.
r e p o r t sheets a n d enable d a t a to be completed. stand
the
time a n d date
completed
within
giving
the
and
are
clearance
are
denoted
by
a
stand
blockages which occur in p u b l i c sewers a r e denoted b y
a manhole reference number. Reports which a r e
found
to
b e problems
i n the
storm water system a r e g i v e n a code which enables
water
reticulation or
the computer
to i g n o r e
t h a t report a p a r t from showing how many of the r e p o r t s h a v e been r e f e r r e d elsewhere f o r a c t i o n ( T a b l e 1 2 . 5 ) . Program
BLOCKMACRO
between g i v e n dates. possible cause
i s shown.
completion of clearance problems,
produces
a
The l e n g t h of The time
report
which
blockages
elapsed between
i s also c a l c u l a t e d
lack of s t a f f etc.
of
to
help
townships
in
time taken to c l e a r the
blockage
the
identify
report
and
administration
The s e v e r i t y of a blockage i s also shown b y
i n d i c a t i n g the number of houses flooded as the r e s u l t of a "main" and for a "private"
and
blockage
blockage i f the house o r y a r d i s flooded ( T a b l e 1 2 . 6 ) .
A macro program produces a r e p o r t of
all
done in u n b l o c k i n g sewers between g i v e n dates.
the
work
each
gang
has
Numbers of blockages a n d
t o t a l time spent i s shown ( T a b l e 1 2 . 7 ) .
A program produces a r e p o r t of a l l the stands a n d sewer lengths where there
has
been
information
can
overloading
of
more be
than very
public
one
blockage
useful
sewers
in
and
repeated blockages on p r i v a t e stands.
in
a
given
identifying
also
when
time
possible
answering
period. defects queries
This and about
TABLE 12.2
E x a m p l e of U p d a t e d Sewer D a t a F i l e
h)
0 0
35032913086120202 51.01.5 35032913186120203 41.01.0 35032913286120203 ti 1.0 1.0 01.5 35032913386120203 &l. 350329 13986120202 5 1.02.0 35032914086120202 51.02.5 35032914186120202 51.03.0 35132915086120103 01.01.0 35132915106120103 61.01.0 35132915286120103 41.02.0 35132915306120103 41.01.5 35132915486120102 51.02.0 35132915586120102 51.02.0 35132915686120102 51.01.5 35132315786120102 SO. 50.5
TABLE 12.3
1
1
2 2
3 2 2 1 1 3
3 5 1 2
1
152 152 152 152 152 152 152 152 152 152 152 152 152 152 152
5 6 2 4 3 6 3 2 2 1
1 6 1
1
5
4
1
1
15.54 70.26 57.79 60.01 49.22 75.68 49.10 76.90 70.73 64.00 62.97 65.40 62.97
100.0 100.0 100.0 00.0 80.0 00.0 110.0
70.0 70.0 60.0 60.0 66.0 46.0 79.2 79.2
63.03
63.00
Sewer M a i n t e n a n c e Records
I S E U E R PlCIINlEWNCE R M R D S
REOUESTED CTLIRT WITEX- 861201 REOUESTED END DRTE I- 861204
sso
TOUNSHIP
-
uwsm MRNMOLE CONDITION
DEBRIS GRNG tcIhlti NO No SIZE ~~~-W R S 2 S 1.0 329130 1.0 3-2131 S 0 3 A 1.0 3--91;2 z2913 1 A 1.0 2 S 1.0 229139 5 1.0 ‘329100 2 2 S 1.0 3,3101
SEWER LENGTH IS.%
!saNn
70--%
57.79
1.0 1.0
60.01
1-s
TOTnLSI
l4RN
~
7.0
BKTS 1.S
A9.22
2.0
75-68
A9.10
2. S J. 0
S77.60
12.S
ISEUER PlCIINlENRNCE RECORDS
0 0 0
0 0 0
0 0 0
0 0 0
DEPTH DF W SLBB COV FRR STEP COP FLOu RS X JNTS PIPE OIL 0 0 0 0 1 0 19. 0 1 0 0 0 0 0 0 1z. 0 0 0 0 0 0 12. 0 6 0 0 0 0 0
0
RUB R f f i MET YO00 GLRSS ROOTS FRT BEN 1NV U 0
1
0
0
0 0 0
0 1 1
0 0 0
0 0
0 0
0 1
0 0 0
0
0
0
1
2
1
0 0
0
0 0
SEUER CONDITION
0
6.
0
0
0
0
0
0
0
0
0
0
0 0 0
0
0
0
0
0
0
6
19.
0
6
0
0
0
0
0
0
0
0
6
22.
0
0 0 0
0
0 1
1
0
0
0
0
0
0
0
29.
0 0
6 0
0 0
0
1
0
0
1
0
0
0
0
0
1
1
6
1
6
0 0
1
c
0 N
86 T V 9
vv ' V S t
vs ' 6 8 I H18N31 1UlOl
00 ' 0 00 ' 0 666/00S
+OOOI
00 ' 0
oo ' 0 00 ' 0
00 '0
00 ' 0
86 'SVV
00 ' 0 vv ' f 6 Z 00 ' 0 9s '68 f 662/002 66f/001 Stj3M3S do S H U N 3 1
:tj313wu1a do U 3 N U 3 1 3
s 'L S T 0
'*
StlllOH NU313
- s7u101 :
-
I 1x3 UISUN31 f SS UI S U N 3 1 'OSZ 3WUN 3a03NMOI d IHSNMOl
N
0 N
TABLE 12.6
Output f i l e
1 S E U L R OLOCKAGC R C C O R D S
R L P U E S I E D S T A C T DATE:87ClUS *L:UC:TED CND D A T i :- 1175107 TOYNSnXP BLOCKAGL DCPORTFD MOUll DATE
-
52
BOSlOWT
PRIVATE: STAND NO
40.
nA1M: SLYER
OF S T A N D S
no
z z ~ i m 8 7 r i . r ~ iz:40
I ~ 7 ~ 1 ~ 0s
--
0 Z O n P L A I h T : R E F i R R E O TO b A T E R S R A N C M EC’PLAIhTS R L F E R R L O 1 0 R O A D S AND YORKS I S E Y i l l BLOCKAGE R C C O R D S
lOYNSHIP
iEPOPTlL
niui ?
DATL C7ulub
-
157
ELDORAEO PAPK
PRIVATE: STAGO
ID 4Jl
1418
87itios i 4 : o o
SEYER
DATL
L’J
o
30.
TIBE
I I C I ? ~ I:DD
JOB
TIRC
1.20
OF S T A W S
-
19n9
BLOCKAGE CLELRED START Fltiisn
RAIN:
AREA(WECTARES>
-
106.1 CIIVATL:
M O U I S FRO@!
RAIN:
I E P O R T l N G TO GANG GANG CORPLETIOM SUMDAT NO S I Z E CAUSE
L F F E C T E D FLOODED FLOODED
6
0
5
1
4
MOUSES 2
11110
I!
MOUSE
n
D
R L C U E S l r O S l 8 R T DATE:117OlOf D L i U C S T L D E k J C A T i :- 6 7 0 1 0 7
@LOCKAGE
-
I L O C K A G E CLEARED START FINISH DATF TlRf DATE T I R E
-
AREACMECTLRES)
JOB
DATE
TINE
TIME
87~106
a:so
0.30
128.6
cnon
MOURS
MA1N:
R E P O R T I N G TO GANG GAYG COfiPLETIOH SUMDAT N O S l Z E CAUSE
.
2
0
2
3
2
PRIVATE:
nousEs T A ~ D HOUSE A F F E C T E D FLOODED FLOFDED 0
1
1
20 3 REFERENCES
Adams, B.J. and Zukovs, G., 1987. P r o b a b i l i s t i c models f o r combined sewer systems r e h a b i l i t a t i o n s a n a l y s i s . In Beck (1987). Beck, M.B. (Ed.) 1987. Systems A n a l y s i s in Water Q u a l i t y Management. IAWPRC Conf. London, Pergamon Fuchs, L., M u l l e r , D. a n d Neumann, A., 1987. L e a r n i n g p r o d u c t i o n systems f o r the c o n t r o l o f u r b a n sewer systems. In Beck (1987). S c h i l l i n g , W. a n d Petersen, S.O., 1987. Real time o p e r a t i o n o f urban d r a i n a g e systems, v a l i d i t y a n d s e n s i t i v i t y o f o p t i m i z a t i o n techniques. In Beck (1987). Stephenson, D. a n d Hine, A.E., 1982. Computer a n a l y s i s o f Johannesburg Sewers. Proc. I n s t n . Munic. Engrs. S.A. IMESAF, 7 ( 4 ) A p r i l . p13-23 Stephenson, D. a n d Hine, A.E. 1985. Sewer Flow Modules f o r V a r i o u s t y p e s o f development in Johannesburg. Proc.. I n s t . Munic. Engrs. S.A. (10) Oct. p31-41. Stephenson, D. and Hine, A.E., 1987. Maintenance program for Johannesburg Sewerage Systems. Yen, B.C. ( E d . ) 1987. Proc. 4 t h I n t l . Conf. U r b a n Storm Water H y d r o l o g y a n d D r a i n a g e , Lausanne.
TABLE 12.7
Outout f i l e
SLYER BLOCKAGE
RECORDS
l E O U E S T E D S T l R l DATE:070105 SEOUESTED END DATE :- 870107 €AM:
1
SIZE:
ToYNsnIP
4 NO. OF PRIYITE
NO. OF nAIN
TOTAL NO. O f
PRIVATE- MAIN-
TOThL-
lOYNCODE lAME BLOCKbCLS BLOCKAGES BLOCKAGES JOB T I M E JOB T I M E JOE T I M E 155 E L D O R l D O PARK2 2 0 0.00 4.25 2 b.25 177 ELDORADO PARK4 4 0 4 7.25 0.00 7.25 342 K L I P S P R U I T YES 1 0 1 0.25 O.OG 0.25 TOTALS:-
7
0
7
12.15
0.00
12.15
204 CHAPTER 13
WATER
QUALITY MON I TOR I NG NETWORKS i Y
Colorado State U ive
b y Thomas G. Sanders,
NECESS I T Y FOR NETWORKS
Environmental
legislation
been responsible f o r recent streams.
Such m o n i t o r i n g
and
general
water
quality
awareness
have
increased m o n i t o r i n g a n d s a m p l i n g of water and
testing
can
be expensive
and
a
in
scientific
approach to m i n i m i z i n g costs w h i l s t m a x i m i z i n g b e n e f i t s i s d e s i r a b l e . The
assumption
trends
in
water
that
a
quality,
measure ambient
water
monitoring
actively
guide
implemented,
in
government's
however,
feasibi I i t y
obtaining
conclusive
compromises a n d
compliance etc.,
is
with
water
water
legal
the
view
being
is
the
of
more
which
to
When from
involved
resources force
of
for
water
efforts.
viewed
available
and
generated
problems
the consequences
detect
legislation
management
is,
can
standards,
into
The
monitoring
That
information w i t h measures,
stream
information
quality
quality
network
incorporated
conclusive
stand-point.
half
monitoring
the U n i t e d States.
envisages
technical
quality
check
quality,
water q u a l i t y management qua1 i t y
water
a
in
many
a r e often
not
f u l l y understood. Monitoring conducted
over
necessarily Simply
performed large
hydrologic
collecting
problem; cases, samples
or
ultimate
of
geographic
in
i n fact,
thought types
use
government
is
that
of
data
the
data.
(defined
covering
such
given
agencies
areas
boundaries)
samples
so major,
little
by
a
by
the
analysis
many
political
often
i t becomes a n end to
in
in
techniques
Consequently,
the
to
be
majority
a
used of
major
In many
itself. of
not
streams.
becomes
representativeness
cases, and
k i lometres of
many
situation
is,
the
or
water
even
the
resources
are
devoted to c o l l e c t i n g d a t a as i t i s the most immediate problem. By
using
most
resources
to
physically
collect
water
resources a r e l e f t to consider the representativeness of a n d space,
d a t a a n a l y s i s o r d a t a use.
m o n i t o r i n g system system
should
be
should
therefore
examined
and
samples,
the sample
little i n time
A b a l a n c e d ( c o l l e c t i o n versus
be developed designed
so
use)
the e n t i r e m o n i t o r i n g
simultaneously
(a
systems
the
system
approach). The purpose of
t h i s chapter
i s to r e v i e w
monitoring
and
then d e l i n e a t e the impacts t h a t such a systems a p p r o a c h of m o n i t o r i n g w i l l h a v e on network design b y c o n s i d e r i n g the w a t e r q u a l i t y
v a r i a b l e s to b e
205 monitored,
the sampling location a n d s a m p l i n g frequency.
MONITORING SYSTEM FRAMEWORK
Before
a
monitoring
network
can
be
m o n i t o r i n g program should be delineated, I n addition,
the decisions
designed
the
goals
of
the
and specific objectives applied.
to be made based
upon
information
network and the subsequent actions should also be well
from
the
developed p r i o r to
the collection o r a s i n g l e b i t of data. The a c t u a l
operation
of
a m o n i t o r i n g system can
be
categorized
into
f i v e major functions:
1.
Sample Collection
2.
Laboratory Analysis
3.
Data H a n d l i n g
4.
Data A n a l y s i s
5.
I nformation U t i I i z a t i o n
These f i v e functions serve as quality
conditions
of
water
management
agency
approvals,
regulations,
qua1 i t y . effects
Without of
those
a
the feedback
quality
loop from
management
i s c o n s t a n t l y m a k i n g decisions pollution
monitoring
decisions,
abatement,
feedback
the
loop
(e.g.
etc.)
past
water
making.
r e l a t i v e to
that
accurately
management's
in-stream
decision
affect
and
site
water
documenting
success
A
the
future
direction are uncertain. M o n i t o r i n g network design operational collection
i s an o v e r r i d i n g a c t i v i t y
f u n c t i o n s l i s t e d above) (e.g.
location
that
a n d frequency)
should c a r e f u l l y with
used to o b t a i n the i n f o r m a t i o n r e q u i r e d a n d making.
Thus,
the
type
actually
( c o v e r i n g the f i v e i n t e g r a t e sample of
data
utilized
analysis
in decision
the design of water q u a l i t y m o n i t o r i n g networks must
i n t o account the decision m a k i n g process,
take
the t y p e and level o f s t a t i s t i c a l
a n a l y s i s a p p l i e d to the d a t a , a n d u l t i m a t e use of the d a t a collected.
FACTORS I N NETWORK DESIGN
M o n i t o r i n g network
design,
guides m o n i t o r i n g operations,
as a p l a n n i n g / d e s i g n can
i t s e l f be broken
componen ts:
1.
Selection of Water Q u a l i t y V a r i a b l e s to Monitor
2.
Sampling Station Location
type function
down
which
i n t o three m a j o r
206
3.
Sampling Frequency
The
term
water
quality
variable
is
used
instead
of
water
quality
parameter because water q u a l i t y i s a random v a r i a b l e a n d c a n be d e f i n e d by
statistical
addition,
parameters
the term
deterministic
parameter
equations
a s the mean a n d
such
or
is
most
models
often
and
standard define
used
to
can
lead
it
deviation.
In
constants confusion
to
of by
i d e n t i f y i n g i t a s a random v a r i a b l e . the
monitoring
system's o p e r a t i o n a l f u n c t i o n s I i s t e d p r e v i o u s l y a n d v i c e versa.
Each
of
these
factors
The degree
of impact, however,
in
network
design
effects
all
depends upon the purpose a n d g o a l s of
the m o n i t o r i n g
system.
SELECT ION OF WATER QUALITY VARIABLES TO MEASURE
to
The selection of the water q u a l i t y
v a r i a b l e to be sampled w i l l
a
of
l a r g e extent
background developing network
frame
the of
its
objectives reference
the o b j e c t i v e s
has
stndards, for
or
on
of
primary
the
of
the
sampling
the
individuals
monitoring
objective
to
network
network.
monitor
the
responsible
for
When
a
compliance
sampl i n g
with
stream
the v a r i a b l e s sampled a r e the ones s p e c i f i e d i n the l e g i s l a t i o n ,
example,
dissolved
(DO).
oxygen
DO
is
sampled
because
s t a n d a r d s specify a minimum l e v e l which should not be v i o l a t e d .
s t a n d a r d l e g i s l a t i o n were those r e l a t e d to water s u p p l y , biochemical oxygen demand a n d dissolved solids,
(BOD),
stream
Dissolved
i m p o r t a n t a n d i n c l u d e d in stream
oxygen a n d o t h e r v a r i a b l e s deemed most
quality
depend
and
temperature,
col iform b a c t e r i a ,
turbidity,
and
suspended
because most i n d i v i d u a l s e n t e r i n g the f i e l d o f water
management d u r i n g
the
last
few
decades
have
a
background
in
s a n i t a r y engineering. Since i n d i v i d u a l s o t h e r t h a n besides s a n i t a r y became interested i n water q u a l i t y , which
should
be
sampled
( e n v i r o n m e n t a l ) engineers
the number of water
routinely
has
increased.
quality This
variables
compounding
syndrome cannot a n d should not be the major v a r i a b l e selection mode f o r a permanent,
routine
accommodated
in
sampling
the
p o p u l a r i t y of synoptic
much
program,
discussed
but
instead
synoptic
can
surveys.
be
The
easily
increasing
s u r v e y s w i t h s a m p l i n g agencies i s p r o b a b l y
due to
the f a c t t h a t the s u r v e y s a r e in fact a n a p p l i c a t i o n of a systems a p p r o a c h to
water
programs, sampling
quality
monitoring.
the objectives, frequency,
the
Unlike
the
permanent,
the use of the d a t a , variables
to
be
routine
the s a m p l i n g
sampled
as
well
sampling
locations, as
the
the data
207 analysis
procedures
and
decisions
to
be
made
should
be
developed
be
developed
completely before the survey i s undertaken. Both
sampling
independently
location
of
the
and
water
sampling
quality
frequency
variable
to
can
be
analyzed,
location and frequency a r e specified f o r the c o l l e c t i o n of ( t h e analyses a r e made l a t e r ) .
However,
water
monitored.
quality
week
at
a
monitoring
variable
single the
being
point
in
relatively
a
river
stable
For
may
river
the
variables
t h e i r n a t u r a l and/or
considered
when
be
more
temperature, coliform
sampling than
but
once
adequate
may
bacteria
water
delineated.
Network
concentration
qua1 i t y
is
concentration,
the
as
former
be
sample
in
if
opposed
being
a
to
an
result
24-hour
(generally
daily
in
space
In
several
period,
while
the daytime,
in a
be to
should
be
(flow
weighted)
grab
samples the
can
addition
units
mean
instantaneous
of
for
hardly
be s p e c i f i e d so
time a n d
respective
a
a
concentrations.
should
network.
their
differs
measurements spaced d u r i n g a single
variation
monitoring
variables,
design
needed
the
to be monitored
man-made
designing
considering
only a
example,
before a water q u a l i t y m o n i t o r i n g network can be designed
systematic fashion, that
both
both c r i t e r i a a r e affected b y the
adequate for m o n i t o r i n g r a p i d l y v a r y i n g Therefore,
as
the water sample
sample
with
latter
flow
comprises a.m.
between 8.00
and
4.30 p.m.1. In
reality,
the
specification
of
the
water
quality
variable
however, water
to
be
In p r a c t i c e ,
monitored p r i o r to i n i t i a t i n g network design would be ideal.
network design i s specified a n d one must know o r determine what
quality
variables
can
be
accurately
monitored
with
the
existing
a
water’
network.
SAMPL I NG STAT ION LOCAT ION
The
location
of
m o n i t o r i n g network design,
a
permanent
i s probably
b u t a l l too often
never
comprises lead i n many cases r i v e r g a u g i n g stations. the
gauging
sampled
is
collectors
station not
and
follow
when
most
properly
is
truly
addressed.
representative generally
of
the
water
the
in
aspect
of
quality
the
Expediency
network a n d cost
near existing
Whether the s i n g l e g r a b sample from the b r i d g e o r
but
users
station
critical
to s a m p l i n g from b r i d g e s o r
known,
e s t i m a t i n g discharge, indicate exactly
sampling
the
is
quality
of
the
assumed data.
measuring
discharge.
water
quality
However, variable
be
Using
measurement anywhere i n the river
water to
lateral
t h i s does
mass
being
by
both
the
river
stage
for
transect not
would
necessarily
concentrations.
In
fact
208
F i g , 13.1
Macrolocation of Sampling Stations W i t h i n a R i v e r Basin Using the Percent Areal Coverage a s the C r i t e r i a S p e c i f y i n g Locat ion
209 research
indicates
the
opposite,
that
will
rarely
a
single
sample
be
i n d i c a t i v e of the average water q u a l i t y i n a r i v e r cross section. Sampling
locations
for
a
c l a s s i f i e d i n t o two levels of
permanent design:
water
quality
network
former
b e i n g a f u n c t i o n o f the specific objectives o f the network
latter
being
independent
of
can
be
macrolocation a n d microlocation,
the
objectives
but
a
the
and
the
of
the
function
representativeness of the water sample to be collected. The political etc.
macrolocation
within
boundaries,
a r e a s of
Macrolocation can
a
river
basin
usually
major p o l l u t i o n
be specified,
coverage u s i n g b a s i n c e n t r o i d s
a s well,
(Sanders et
is
loads,
determined
population
a c c o r d i n g to percent
1986).
al,
This
locates sampling p o i n t s in a systematic f a s h i o n m a x i m i z i n g the e n t i r e b a s i n w i t h a few s t r a t e g i c a l l y an
example
of
locating
sampling
using
areal
methodology
information of F i g u r e 13.1
located stations.
stations
by
centres,
basin
centroids
is and
sub-basin centroids w i t h percent a r e a l coverage a s the c r i t e r i a . The procedure f o r l o c a t i n g sampling s t a t i o n s i s d e r i v e d b y d e t e r m i n i n g the c e n t r o i d o f a r i v e r system. i s a stream
without
defined
i n t e r i o r stream r e s u l t i n g from
value
equal
to
the
i s given
intersection
of
the v a l u e o f two e x t e r i o r
(this
one;
an
tributaries
Continuing downstream i n the same manner,
would have a v a l u e of two. streams intersect,
Each c o n t r i b u t i n g e x t e r i o r t r i b u t a r y
tributaries)
as
the r e s u l t a n t downstream s t r e t c h of r i v e r would h a v e a the
sum
of
the
values
of
the
preceeding
intersecting
stream. At the mouth of the r i v e r , the v a l u e o f the f i n a l r i v e r section w i l l be equal to the number o f c o n t r i b u t i n g e x t e r i o r t r i b u t a r i e s ,
22 in F i g u r e
13.1.
by
D i v i d i n g the
v a l u e of
the f i n a l
v a l u e of the c e n t r o i d of the b a s i n ,
s t r e t c h of
1 1 i s calculated.
h a v i n g a v a l u e equal to t h a t of the c e n t r o i d sections and
i s the
location of
the
the
river
r i v e r basin, of
I n many
sampling station
cases,
when
with
When
this
occurs,
closest to the c e n t r o i d i s chosen.
the
stream
highest
the
initial
river
basin
centroid.
segment
having
the two equal The
two
order
the mouth
t h i s procedure to
The n e x t o r d e r o f sampling
determined b y f i n d i n g the c e n t r o i d v a l u e of a n d below
applying
into
there i s u s u a l l y not a stream h a v i n g a v a l u e e q u a l to
the centroid.
the
The section of r i v e r
d i v i d e s the b a s i n
( t h e assumption i s made t h a t there e x i s t s a s a m p l i n g s t a t i o n a t of the r i v e r b a s i n ) .
two,
a
a
that value
locations
is
sections above
procedure
is
continued
u n t i l a percentage of a r e a l coverage i s a t t a i n e d . The percentage of area coverage specified b y the m o n i t o r i n g agency defined as the number of
sampling
the
this
basin.
sampling
Intrinsic
in
station hierarchy
stations d i v i d e d b y
objective
that
procedure
o r d e r s the
is
importance
is
the m a g n i t u d e of the of
concept each
of
a
sampling
210 station
in the b a s i n
1973). T h i s p r o v i d e s a
(Sharp,
r e a l i s t i c methodology
i n which a r a t i o n a l implementation progam c a n proceed: stations
(highest
available,
order)
additional
are
built
first
and
as
the most
the
important
resources
become
As each succeeding h i e r a r c h y
s t a t i o n s can be b u i l t .
of s t a t i o n s a r e e s t a b l i s h e d the percentage of a r e a l coverage i s increased. Having
established
microlocation
the
specifies
macrolocations
the
river
within
reach
to
a
be
river sampled
microlocation specifies the p o i n t i n the r e a c h to be sampled.
basin,
the
while
the
This point
is
t h e location of a zone in the r i v e r r e a c h where complete m i x i n g e x i s t s a n d
in o r d e r to o b t a i n a
o n l y one sample i s r e q u i r e d from the l a t e r a l transect
(in
representative
space)
sample.
Being
downstream from the nearest o u t f a l l ,
a
function
t h e zone of
of
the
distance
complete m i x i n g can
be
estimated u s i n g v a r i o u s methodologies. Given the assumptions t h a t a p o i n t
source
stream approximates a Gaussian d i s t r i b u t i o n , modelled
using
image
theory,
in a
d i s t a n c e downstream
the
following
straight,
pollutant
a n d t h a t b o u n d a r i e s can equation
u n i f o r m channel
-
-
(J
Y
where
a point
L
be the
source
1977).
2u
Y
(13.1) is
the
from
mixing
source
velocity and D Estimates of D
Y
predict
2oy
distance
D
can
from
p o l l u t a n t to a zone of complete m i x i n g (Sanders et a l . ,
LY
in a
distribution
distance farthest
for
complete
lateral
lateral
boundary,
u
mixing,
a y
is
stream
mean
is
i s the l a t e r a l t u r b u l e n t d i f f u s i o n coefficient.
Y
Y
to
can be made u s i n g e q u a t i o n 13.2
= 0.23 du'
(13.2)
where d i s depth of flow u* i s shear v e l o c i t y
g
i s acceleration flow
due to g r a v i t y R i s h y d r a u l i c r a d i u s S i s slope o r t h e h y d r a u l i c g r a d i e n t (Sanders e t al., Unfortunately,
1977). there may not e x i s t
in a g i v e n r i v e r
of complete m i x i n g due i n p a r t to the random n a t u r e of
mixing
distance,
determination of
inapplicability
of
the m i x i n g distance,
the
assumptions
o r more often
river
l e n g t h o r t u r b u l e n c e to assure complete m i x i n g
river
reach.
On
the o t h e r
hand field
reach any
within
in
used
t h a n not,
v e r i f i c a t i o n of
points
the aforementioned
not
the
enough
the s p e c i f i e d
a completely
mixed
zone p r i o r to l o c a t i n g a permanent s a m p l i n g s t a t i o n c a n be e a s i l y done b y collecting
m u l t i p l e samples
in the cross
u s i n g a we1 I-known one- o r two-way
section
and analyzing
the
a n a l y s i s of v a r i a n c e techniques.
data
21 1 If
there
sampled,
is
not
a
completely
mixed
zone
the
in
river
reach
to
be
there a r e three a l t e r n a t i v e s :
( 1 ) Sample anyway a t a s i n g l e p o i n t a n d assume i t i s r e p r e s e n t a t i v e ( t h i s i s a general approach adopted t o d a y ) ;
( 2 ) Don't sample the r i v e r reach a t a l l , obtained does not q u a l i t y o f the
represent
sample
because t h e d a t a w h i c h would be
the e x i s t i n g r i v e r
quality,
b u t only
In o t h e r words,
volume collected.
the
the data
is
useless;
( 3 ) Sample a t several p o i n t s in the l a t e r a l transect c o l l e c t i n g a composite mean, which would be r e p r e s e n t a t i v e of the water q u a l i t y
in the r i v e r
a t that p o i n t i n time a n d space.
I f the sample i s not r e p r e s e n t a t i v e of the water mass, sampling
as
presentation
well and
as the
the
mode
realistic
m a k i n g becomes inconsequential.
of
use
data of
analysis,
the
data
interpretation
for
I n s p i t e of t h i s f a c t ,
the frequency of
objective
and
decision
c r i t e r i a to e s t a b l i s h
s t a t i o n locations f o r r e p r e s e n t a t i v e s a m p l i n g h a v e received r e l a t i v e l y
little
a t t e n t i o n from many i n s t i t u t i o n s a n d agencies responsible f o r water q u a l i t y monitoring.
SAMPLING FREQUENCY
Once sampling
stations
a r e representative
have been
i n space,
located to ensure
sampling
frequency
samples collected
should
be
specified
so
t h a t the samples a r e r e p r e s e n t a t i v e in time. Sampling frequency basin
is
a
very
a t each permanent
important
parameter
sampling station w i t h i n a
which
must
be
considered
design of a water q u a l i t y m o n i t o r i n g network.
A l a r g e p o r t i o n of
o f o p e r a t i n g a m o n i t o r i n g network
r e l a t e d to
sampling.
However,
the
reliability
d e r i v e d from a m o n i t o r i n g network sampling.
Addressing
is directly
this
and
utility
of
river in
the
the costs
the frequency
water
quality
of
data
i s l i k e w i s e r e l a t e d to the frequency of
anomaly
Quimpo
(1968)
summarized
the
s i g n i f i c a n c e of sampling frequency a n d stated t h a t : On the one hand,
b y s a m p l i n g too often,
obtained i s r e d u n d a n t and t h u s expensive, hand,
the i n f o r m a t i o n a n d on the other
sampling too i n f r e q u e n t l y bypasses some i n f o r m a t i o n
necessitating an extended p e r i o d of observation. Significant v i o l a t ion
,
as
sampling
frequency
is
m a i n t a i n i n g e f f I uent standards,
i n ambient water q u a l i t y ,
very
to
detecting
stream
standards
a n d e s t i m a t i n g temporal changes
l i t t l e q u a n t i t a t i v e c r i t e r i a which designate
a p p r o p r i a t e sampling frequencies h a v e been a p p l i e d to the design of water
21 2 quality
monitoring
networks.
many
In
cases,
professional
judgment
cost c o n s t r a i n t s p r o v i d e the b a s i s f o r s a m p l i n g frequencies.
All
frequencies
upon
are
capabilities, only
the
same
at
once-a-month,
practical
means
each
station
once-a-week,
to
implement
etc.
a
frequencies
as
and
1978).
Adrian,
functions
of
the
variable
(Nyquist frequency),
maximum
to
minimum
flow
cyclic
methods
variations
and
(Ward et
possibly
the
considering
the
include
of
the
b a s i n area
water
and
19671,
Orlob,
specifying
of
a
test
measuring
the
confidence
1976; L o f t i s a n d Ward,
al,
water
quality
the r a t i o of
quality
intervention
1978),
1978), and
the number of d a t a p e r y e a r f o r hypotheses (Sanders and Ward, the power
routing
s a m p l i n g frequencies a t each
The
the d r a i n a g e
(Pomeroy
i n t e r v a l o f the a n n u a l mean
although
program
too often,
there do e x i s t many q u a n t i t a t i v e ,
s t a t i s t i c a l l y meaningful procedures to specify (Sanders
based
and
sampl i n g
s t a t i s t i c a l b a c k g r o u n d o f d a t a collectors,
station
and
and
(Lettenmaier,
1975).
A l l of the aforementioned procedures can b e a p p l i e d to the design of a water q u a l i t y m o n i t o r i n g network w i t h each r e q u i r i n g a d i f f e r e n t statistical
sophistication
assumptions app I y One of variable
the
.
simplest
(iid)
and
as
approaches
concentrations
distributed
insofar
are
is
data
to assume
random,
determine
the
requirements
that
the
independent
number
of
as
well
water
and
samples
level of as
quality
identically
per
year
as
a
f u n c t i o n o f an a l l o w a b l e ( s p e c i f i e d ) confidence i n t e r v a l of the mean a n n u a l concentration analyses of
( t h i s i s analogous to the procedure f o r d e t e r m i n i n g how many a
water
sample
should
be
made
to
determine
a
reasonable
estimate o f the mean water q u a l i t y v a r i a b l e c o n c e n t r a t i o n ) .
[
n =
aizS]
(13.3)
where n i s the number of e q u a l l y is a
constant
number
of
which
samples,
is a
S
is
spaced samples collected p e r y e a r ,
function the
of
the
standard
l e v e l of
deviation
concentrations a n d R i s s p e c i f i e d h a l f - w i d t h
of
significance of
the
water
the confidence
taI2
and
the
quality
interval
of
the a n n u a l mean. Using the same assumption,
t h a t the water
number of samples p e r
year
can
a n a l y s i s procedure as
well.
For
example,
variable i s iid,
quality
be s p e c i f i e d a s a
if
function
annual
of
means
tested f o r s i g n i f i c a n t changes u s i n g the d i f f e r e n c e in means,
the
the data
were
to
be
then to detect
a n assumed level of change, t h e number of samples c a n be specified.
A
more
sophisticated
procedure,
representing
a
higher
level
of
21 3
0.9
0.8
R vs. Number of Somples per Yeor I 2 3 4 5 6 7 8
0.7
0.6
Wore Conn. at Thompsonville Deerfield Conn. ot Montopue City Millers Conn.ot Vernon
Westfield Conn. ot Turners Falls
R
0.5
0.4
0.3
0.2
0. I
I
1
I
I
I
10
20
30
40
50
Number of Somples per Yeor
Fig 13.2
A p l o t n u m b e r o f s a m p l e s per y e a r of the expected h a l f - w i d t h of t h e c o n f i d e n c e i n t e r v a l of m e a n log f l o w , R , v e r s u s n u m b e r of S a m p l e s for S e v e r a l R i v e r s in t h e C o n n e c t i c u t R i v e r B a s i n
214 statistical
analysis,
may not be i i d ,
would
be
to recognize
b u t h i g h l y dependent,
that
water
seasonal v a r i a t i o n ,
a n d determine s a m p l i n g frequency
variability
water
of
the
quality
p e r i o d i c components h a v e daily
discharge,
data
been
variable
removed.
bases
of
quality
veriables
not i d e n t i c a l l y d i s t r i b u t e d ,
as a f u n c t i o n of
series
after
trend
Unfortunately,
other
than
water
time
having
quality
number, r e l i a b i l i t y a n d l e n g t h a r e g e n e r a l l y
variable
of
the and
mean
sufficient
not a v a i l a b l e f o r a p p l i c a t i o n
of t h i s procedure. Once utilized quality
a
uniform
to
objectively
interval
frequencies)
of
the
of
where
station.
Thus,
stations
more
frequently
little.
With
number
reference
of
of
sampling
annual
equality
sampled
these
samples
per
13.2
the
(for
it
can
within
a
varies
where which
of
specifying
in a
the is
mean
number
at
water
a
of
fashion sampling
tremendously
plot
of
samples
will
quality
log r i v e r
the
flow
the
sampling
each
water
be
of
consistent
half-widths
quality
interval
year,
frequencies
mean
stations
selected
the expected h a l f - w i d t h
expected
Figure
the confidence
is
basin-wide
water
than
to
criterion
For example,
approach c a n be a p p l i e d
specifying
half-width
frequency
distribute
m o n i t o r i n g network.
confidence
by
sampling
be
varies expected
versus
collected
at
the each
s t a t i o n w i t h i n the r i v e r b a s i n f o r a g i v e n R a r e determined b y d r a w i n g a horizontal abscissa curve.
line axis
through below
Figure
13.2
and
R
the
may
reading
intersections also
the
on
be used
number
the
i n an
of
samples
horizontal
line
i t e r a t i v e fashion
on
with to
the each
specify
s a m p l i n g frequencies a t each s t a t i o n when a t o t a l number o f samples from the b a s i n
i s specified.
For example,
collected a n d analyzed, horizontally;
a
v a l u e of
the number of
if
R
only
samples s p e c i f i e d
curves a r e summed a n d compared
to
N
samples
i s assumed
N.
If
the
by
and the
sum
a
per
year
line
is
were drawn
i n t e r s e c t i o n of
were not e q u a l
the to N
then another estimate of R would be made u n t i l the sum of a l l the samples i s equal to N. I t should be noted t h a t the expected h a l f - w i d t h o f the a n n u a l mean i s not the o n l y s t a t i s t i c
that
the expected h a l f - w i d t h a n d may
can
be used
to
specify
s a m p l i n g frequencies;
d i v i d e d b y the mean i s a measure o f r e l a t i v e e r r o r
be more a p p r o p r i a t e
when
assigning
sampling
frequencies
in
a
b a s i n where water q u a l i t y v a r i e s tremendously from r i v e r to r i v e r . When developing s a m p l i n g frequencies, important
cycles
concentrations,
which
can
have
one must keep i n m i n d two v e r y
immense
impact
on
the d i u r n a l c y c l e a n d the weekly cycle.
d i u r n a l cycle (which i s a
f u n c t i o n of
the r o t a t i o n
e l i m i n a t e d b y s a m p l i n g in e q u a l time i n t e r v a l s f o r
of a
water
The effect the e a r t h )
24-hour
quality of can
period
the be and
215 the effect of t h e weekly c y c l e ( w h i c h i s a f u n c t i o n of mans' be eliminated be m u l t i p l e s
by specifying of
seven,
that
and
sampling
occasional
i n t e r v a l s for a
sampling
on
a c t i v i t y ) can
network
weekends
cannot
would
be
necessary.
in terms of v a r i a b l e s
Perhaps the major impact between network design to
monitored,
be
operational
sampling
monitoring
consequently,
location,
functions
ultimate
v a l u e of
sampling program that
is
and
the
sampling
the
in
area
monitoring
frequency
of
data
network
and
the
analysis
and,
information.
Any
i s to generate conclusive r e s u l t s from o b s e r v i n g
stochastic process ( w a t e r q u a l i t y concentrations) must be well s t a t i s t i c a l l y designed.
S t a t i s t i c a l l y designed
implies
p l a n n e d ( i n p r o p e r locations and numbers) so t h a t
that
a
planned and
the
sampling
the s t a t i s t i c a l
techniques chosen w i l l be a b l e to y i e l d q u a n t i t a t i v e information.
is
analysis Thus,
the
d a t a a n a l y s i s techniques ( l e v e l and t y p e of s t a t i s t i c s ) to be used must be defined
in
order
to
know
how
to
compute
proper
sampling
frequencies,
locations, etc.
D ISCUSS ION
The above section has pointed out many problems due to not d e s i g n i n g a m o n i t o r i n g system that
all
accuracy. on
aspects
in a
of
For example,
nonrepresentative,
excessive segment
a
accuracy
systems
context.
monitoring
Perhaps
program
i t would not be wise to
grab
i n one
sample d a t a . segment
The
compared
the major
should
match
use
time
system to
concern
in
terms
series
would
be
the accuracy
is of
analysis providing another
in
.
I n a s i m i l a r manner, sophisticated
i t may be u n r e a l i s t i c to encourage use of
sample collection
and
laboratory
a n a l y s i s techniques
more
if
the
d a t a i s not to receive a thorough s t a t i s t i c a l a n a l y s i s . It
i s difficult
to
test
hypotheses,
make decisions
flow
weighted,
several
times
a
year,
from
and
i n i t i a t e action
in the daytime a n d not
u s i n g water q u a l i t y d a t a which a r e collected o n l y
locations
which
are
not
completely mixed a n d u s i n g l a b analyses procedures which may h a v e more variation
in
their
results
when
analyzing
the
same
sample
than
the
ambiant v a r i a t i o n of the water q u a l i t y v a r i a b l e in the r i v e r . Perhaps an even l a r g e r concern to those in m o n i t o r i n g network i s the
use of
water
quality
T h i s lowers the v a l u e of a n y t h a t of spot checks. standards
would
standards information
that
generally
ignore
design
statistics.
from a compliance v i e w p o i n t ,
I n c o r p o r a t i n g water q u a l i t y means a n d v a r i a t i o n
greatly
facilitate
incorporating
more
statistics
to into into
216 m o n i t o r i n g . T h i s would h a v e t h e effect of t y i n g network design to d a t a use in a much more concrete,
a l s o encourage use of would
be
a
s t a t i s t i c a l manner t h a n i s now possible.
the
statistical
system
thread
approach moving
to
network
through
the
design entire
I t would as
there
monitoring
operat ion.
REFERENCES
Lettenmaier, D.P., 1975. Design of M o n i t o r i n g Systems f o r Detection of Trends i n Stream Q u a l i t y . Technical Report No. 39, Charles W. H a r r i s H y d r a u l i c s L a b o r a t o r y , U n i v e r s i t y of Washington, Seattle. L o f t i s , J.C. a n d Ward, R.C., 1978. S t a t i s t i c a l Tradeoffs i n M o n i t o r i n g Network Design, presented a t AWRA Symposium Establishment of Water Q u a l i t y M o n i t o r i n g Programs. San Francisco, C a l i f o r n i a . Pomeroy, R.D. a n d Orlob, G.T., 1967. Problems of S e t t i n g S t a n d a r d s o f S u r v e i l l a n c e f o r Water Q u a l i t y Control. C a l i f o r n i a State Water Q u a l i t y Control Board P u b l i c a t i o n No. 65, Sacramento, C a l i f o r n i a . Quimpo, R.G., 1968. Stochastic A n a l y s i s of D a i l y R i v e r Flows. Journal o f H y d r a u l i c s , ASCE. 94(HY1) p43-47. Sanders, T.G., A d r i a n , D.D. a n d Joyce, J.M., 1977. M i x i n g L e n g t h f o r Representative Water Q u a l i t y Sampling. Journal Water P o l l u t i o n Control Federation. 49 p2467-2478. T.G. a n d Ward, R.C., 1978. R e l a t i n g Stream Standards to Sanders. Regulatory Water Q u a l i t y M o n i t o r i n g Practices. Presented a t the AWRA Symposium “Establishment of Water Q u a l i t y M o n i t o r i n g Programs, San Francisco, Ca I i f o r n i a . Sanders, T.G. and Adrian, D.D., 1978. Sampling Frequency f o r R i v e r Q u a l i t y M o n i t o r i n g . Water Resources Research. 1 4 ( 4 ) p 569-576. Ward, R.L. L o f t i s , J.G. Steel, T.D, Adrian, D.D. and Sanders, T.G., Yevjevich, V., 1986. Design of Networks f o r M o n i t o r i n g Water Q u a l i t y , 2nd E d i t i o n , Water Resources P u b l i c a t i o n s , Colorado. Sharp, W.E., 1973. A T o p o l o g i c a l l y Optimum R i v e r Sampling P l a n f o r South C a r o l i n a . Water Resources Research I n s t i t u t e Report No. 36, Clemson U n i v e r s i t y , Clemson , South Carol i n a . Ward, R.C., Neilsen, K.S. a n d Bundgaard-Nielsen, M., 1976. Design of M o n i t o r i n g Systems f o r Water Q u a l i t y Management. C o n t r i b u t i o n f o r the Water Q u a l i t y I n s t i t u t e , Danish Academy of Technical Science, No. 3, Horshdm, Denmark.
21 7
AUTHOR INDEX Abulnour, A.M. 116 Adarns, B.J. 190 Adarnson, P.T. 76 A d r i a n , D.D. 209,212 A g a r d y , F.J. 66 American Water Works Association 37 A r n o l d , R.W. 36 Baker-Duly, H.L.G. 123 B a l l , J.M. 70, 77 B a r e n b r u g , A.W.T. 2 Bauer, C.S. 143, 146, 149 Beck, M.B. 202 Bedient, P.B. 66 Betz, 3 Bishop, A.B. 165 Boyd, G.B. 66 B r a d f o r d , W. J 64 B r e b b i a , C.A. 62 Brownlow, A.H. 1 Bungaard-Nielsen, M. 210 Chan, W.Y.W. 167 Chiang, C.H. 165 CIRIA. 164 C o l w i l l , D.M. 66 Connor, J.J. 62 Corbetis, S. 116 Cordery, I. 70 Crabtree, P.R. 167
.
D e i n i n g e r , R.A. 36, 39, 51 D a n t z i g , G.B. 82, 163 F r i e d , J.J. 55 Fuchs, L. 190 G i l b e r t , R.G. 143 Goodier, J.M. 63 Green , I. R.A. 64 G r i z z a r d , T.J. 70 Grosman, D.D. 86 H a d l e y , G. 162 H a l l , G.C. 160 Helsel, D.R. 70 Henderson-Sel l e r s , B. 24 H i l t o n , E. 27, 119 Hine, A.E. 197 Hinton, E. 149 Ho, G.E. 143 Hoehn, R.C. 70 Holton, M.C. 75 Hunter, J.V.I. 66 IBM 162 Idelovitch,
E.
Joyce, J.M.
210
143
Kemp, P.H. 64 Kim, J.I. 70 Kleinecke, D. 41 Lance, J.C. 143 Larnbert, J.L. 66 Larnbourne, J.J. 66 L a n g e l i e r , W.F. 3, 5, 6 L a n y o n , R. 75 L a r s o n , T.J. 104 L a u r i a , D.T. 165 L e i g h t o n , J.P. 146, 149 Lettenmaier, D.P. 212 Lewis, R.W. 119, 149 L l o y d , P.J. 1 L o f t i s , J.C. 209, 212 Loucks, D.P. 116 L u d w i g , L. 9 L y n n , W.R. 116 M a d i s h a , J.L. 75 Mathew, K. 143 McDonell, D.M. 56 McPherson, D.R. 41, 45 M i c h a i l , M. 143 M i k a l s e n , K.T. 75 Mrost, M. 1 MOller, D. 190 Neilsen, K.5. 210 Neurnann, A. 190 Newrnan, P.W.G. 143 O'Conner, B.A. 56 Orlob, G.T. 212 P a l i n g , W.A.J. 141, 143, P e l l e t i e r , R.A. 1 P e r r y , R. 66 Peters, C.J. 66 Petersen, 5.0. 190 P o l l s , I. 75 Pomeroy, R.D. 212 Porges, J. 2 P r a t i s h t h a n a n d a , S. 165 Quimpo,
R.G.
145
211
R a n d a l l , C.W. 70 Rand Water B o a r d 155 Revelle, C.S. 116 Rice, R.C. 143 Rinaldi, S. 116 Ryzner, J.W. 36 Sanders, T.G. 24, 209, S a r t o r , J.D. 66 S c h i l l i n g , W. 190 S h a r l a n d , P.J. 41, 45 Sharp, W.E. 210
210,
212
21 8
S h a w , V.A. 167 Shoemaker, C.A. 146, 149 Simpson, D.E. 64 Smeers, Y. 116 Smith, A.A. 119, 149 Soncini-Sessa, R. 127 South A f r i c a n Bureau of S t a n d a r d s 72 S p r i n g e r , N.K. 66 Steel, T.D. 209, 212 Stehfest, H. 127 Stephenson, D. 27, 66, 80, 81, 82, 115, 116, 117, 163, 175, 197, 200
T e r s t r i e p , 66 Thomann, R.V. 39 Timoshenko, 5 . 55 Tyteca, D. 116 U h l i g , H.H. 13 Van Staden, C.M.V.H. Velz, C.J. 41
2
W a n i e l i s t a , M.P. 64, 146, 149 Ward, R.C. 209, 210, 212 Whipple, W. 66 Wang, L.K., 167 Yen, B.C., 190 Yevjevich, V . 209 Y u , S.L. 66 Zukovs, G.
190
21 9
SUBJECT INDEX Acid 1 Additives 6 Advection 21, 52 Aerobic 9 A g r i c u l t u r e 17 Antecedent moisture 66 Air 1 Alkalinity 3 A l l o c a t i o n 79 A l l o y 13 Ammonia 9 Anaerobic 9 Analyses 195 A n a l y t i c a l 39 Apartments 167 A q u i f e r 141 Arsenic 17 A r t i f i c i a l r e c h a r g e 141 Backwater 193 B a c t e r i a 9, 206, 207 B a r i u m 16 B a s i n 209 Benefits 126 Bicarbonate 67 Biocide 9 Blend 89 Blowdown 2 BOD (biochemical oxygen demand) 37 Booster 152 Bottleneck 173 Boundaries 62 Bremen 193 B r i n e 104, 122 Calcium carbonate 4 C a l i b r a t i o n 40 C a p i t a l 107, 157 Carbonaceous 38 Cathode 10 Catchment 64 Cellulose acetate 104 C h a r a c t e r i s t i c 39 Chelant 7 Chemical 67 C h l o r i d e 2, 67 Chlorine 9 C i v i l e n g i n e e r i n g 107 Commerci a I 1 70 Cleaning 115 Computer 20, 115, 128 Concentration 2, 71, 159, 212 C o n d u c t i v i t y 18 Conduit 175 Confidence 214 C o n s t r a i n t s 41, 86 Conveyance 141 Cooling 20
C o r r e l a t i o n 66 Corrosion 3, 13 Cost 79, 107, 146 C r i t e r i a 211 Crop 17 Crump w e i r 65 Crystal 7 C y a n i d e 16 Cycle 214 D a t a 177, 204 Dead water 24 Decomposition p r i n c i p l e 163 D e s a l i n a t i o n 99, 115 D e t e r i o r a t i o n 116 D i f f u s i o n 36 Disc 128 Dispersants 7 Dispersion 21, 166 D i s t i l l a t i o n 101 DO ( d i s s o l v e d o x y g e n ) 37, 206 Dissolved s o l i d s 206 Downstream 193 D r y d a y s 66 D r y weather 77 Economics 99 E l e c t r i c a l corrosion 14 E Iect r o d ia I v s i s 105 Emulsion 10 Env ironmenta I 193 Equipment 107 E r r o r 91 E s t u a r i e s 37 E u l e r 57, 59 Evaporation 2 E x p l i c i t 39, 51 F a l l o u t 66 F a r a d a y s l a w 14 Feedback 205 F i e l d 45 F i n i t e d i f f e r e n c e 55 F i n i t e elements 62 F i r s t f l u s h 70 F l o o d i n g 193 Flow 166 Foam 8 F o r m u l a t i o n 88 Fouling 9 Four p o i n t 51 F o u r i e r series 54, 169 Freezing 103 Frequency 21 1 Gain 23 G a l v a n i c corrosion 13 Geochemical 1 Geohydrology 41
220
G r a p h i c s 118, 177 Groundwater 98, 112, 143 Gypsum 6 H i e r a r c h y 209 H i l l b r o w 68 H y d r a u l i c 51, 167 Hydrodynamic 56 H y d r o g r a p h 166 IBM 150 I m p l i c i t 55 I n d u s t r i a l 1, 104, 112, 172 I n f i l t r a t i o n 143, 176 I n f l o w 177 I n a c c u r a c y 52 I n s t a b i l i t y 55 I n t e g e r Programming 141, 149 I n t e r e s t r a t e 107 I o n exchange 105 I r o n 3, 16 I r r i g a t i o n 17 I t e r a t i o n 165 Johannesburg 167 K l i p r i v e r 40 L a b o r a t o r y 205 L a b o u r 108 L a n g e l i e r index 5 L a x a t i v e 16 Leach 1 , 26, 75 L e a d 17 L e a k 166, 176 L e a p f r o g 51 Least squares 42 L e g i s l a t i o n 204 L i n e a r p r o g r a m m i n g 43, L o a d f a c t o r 107 Loops 119
85
Maintenance 116 Make-up 26, 33 Manhole 167 Mass b a l a n c e 20, 35, 64, 72, 161 Master programme 163 Mathematical models 20, 149, 158 Measurement 167 Membranes 105, 108 Meta p r o d u c t i o n 191 M i n e water 26, 117, 123 M i n i m i z e 41 M i x e d f l o w 21 M o n i t o r i n g 204 M u l t i - s t a g e f l a s h d i s t i l l a t i o n 103 M u l t i step 61 Network 146, 205 N i t r a t e 17, 72
Nodes 119, 128, 160 Non c o n s e r v a t i v e 35 Numerical 23, 51 d i f f u s i o n 35 O b j e c t i v e 41 O i l 10 O p e r a t i n g 157 Optimum 79 O p t i m i z a t i o n 116, 152, 162 Ore 30 Oxygen 10, 37, 40 Peak 146, 174 PH 3 Phenol 16 Phosphate 7 Photosynthesis 46 P i p i n g 2, 146 P l a n n i n g 149 P l a n t 122 P l u g f l o w 21 P o l l u t i o n 1 , 64 Pol l u t o g r a p h 23 Polymer 7 Polyphosphate 7 P o p u l a t i o n 166 P o t a b l e 15 P o u r b a i x d i a g r a m 12 P r o b a b i l i t y 167 P r o d u c t i o n system 190 P r o g r a m 122, 128, 136, 174, 179 P u r i f i c a t i o n 143 Rand Water Board 157 Random 212 Raw water 122 Reaction 14 Recharge 144 Recovery r a t i o 1 1 1 Reed beds 40 Regional 155 Regression 67 R e l i a b i l i t y 211 Reservoir 23 R e s i d e n t i a l 167 Re-use 99 Reverse osmosis 81, 104 R i v e r s 37, 214 R o u t i n g 166, 175 R u l e base 191 Runge Cutte 61 R u n n i n g 108 Runoff 67 Ryzner i n d e x 3 S a l t s 102 S a n i t a t i o n 195 S a n i t a r y e n g i n e e r i n g 206 Sample 68, 204, 205
221
Sampling frequency 206 Scale 102 Scaling 3 Sea water 101 Sediment 8 S e n s i t i v i t y 195 Separable programming 81, 95 S e n s i t i v i t y 95, 165 Sewage 144, 176 Sewer 72, 166, 190, 196, 198 Shadow v a l u e 165 Shops 169 Simulation 31, 51, 166 Simplex method 89 S i n k 42 Slack 82, 160 Software 195 Solution 82, 160 Source 43 Standards 15, 141 Station 210 S t a t i s t i c a l 205 S t a t i s t i c s 215 Steady s t a t e 20 Stormwater 64, 77, 166, 176 Stream 159, 204 Stream gauge 66 Streeter Phelps e q u a t i o n 37 Sub-programme 165 Sub-division 173 Sulphate 5, 16, 30, 67 Surcharge 168 Suspended 206 System 80 Systems a n a l y s i s 24, 118 Tape 128 Taste 16 T a y l o r series 53 TDS ( t o t a l d i s s o l v e d s o l i d s ) 2, 95 Temperature 3, 206, 107 Terminal concentration 24 Time l a g 166 Topography 1% Toxic 16 T r a f f i c 69 T r a n s p o r t a t i o n p r o g r a m m i n g 80 Treatment 141, 155, 157 T u r b i d i t y 206 Turbulence 8 Two step 39, 52 U n p r e d i c t a b l e 64 Upstream 193 V a a l r i v e r 155 Vapour compression 102 Vegetables 18 Ventilation 2
Washoff 67 Waste t i p 65 Waste water 99, 155 Water resources 79 Water s u p p l y 116 Waterways 190 Water v a p o u r 2 Welding 13 W i t w a t e r s r a n d 155 Zeolites 107 Z i n c 16 Zooming 56
This Page Intentionally Left Blank