Polymer Flooding (Developments in Petroleum Science)

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Developments in Petroleum Science, 24

polymer flooding

DEVELOPMENTS IN PETROLEUM SCIENCE Advisory Editor: G.V. Chilingarian Volumes 1 , 3 , 4 , 7 and 13 are out of print. 2. W.H.FERTL ABNORMAL FORMATION PRESSURES 5. T.F. YEN and G.V. CHILINGARIAN (Editors) OIL SHALE 6. D.W. PEACEMAN FUNDAMENTALS OF NUMERICAL RESERVOIR SIMULATION 8. L.P.DAKE FUNDAMENTALS OF RESERVOIR ENGINEERING 9. K.MAGARA COMPACTION AND FLUID MIGRATION 10. M.T. SILVIA and E.A. ROBINSON DECONVOLUTION OF GEOPHYSICAL TIME SERIES IN T H E EXPLORATION FOR OIL AND NATURAL GAS 11. G.V. CHILINGARIAN and P. VORABUTR DRILLING AND DRILLING FLUIDS 12. T.D. VAN GOLF-RACHT FUNDAMENTALS OF FRACTURED RESERVOIR ENGINEERING 14. G. MOZES (Editor) PARAFFIN PRODUCTS 15A O.SERRA FUNDAMENTALS OF WELL-LOG INTERPRETATION 1. T H E

ACQUISITION OF LOGGING DATA

15B O.SERRA FUNDAMENTALS OF WELL-LOG INTERPRETATION 2. T H E INTERPRETATION OF LOGGING DATA

16. R.E. CHAPMAN PETROLEUM GEOLOGY 17A E.C. DONALDSON, G.V. CHILINGARIAN and T.F. YEN ENHANCED OIL RECOVERY, I FUKDAMENTALS AND AXALYSES

18A A.P. SZILAS PRODUCTION AND TRANSPORT OF OIL AND GAS A. FLOW MECHANICS AND PRODUCTION second completely revised edition

18B A.P. SZILAS PRODUCTION AND TRANSPORT OF OIL AND GAS B. GATHERING AND TRANSPORTATION second completely revised edition

19A G.V. CHILINGARIAN, J.O. ROBERTSON Jr. and S.KUMAR SURFACE OPERATIONS IN PETROLEUM PRODUCTION, I 19B G.V. CHILINGARIAN, J.O. ROBERTSON Jr. and S. KUMAR SURFACE OPERATIONS IN PETROLEUM PRODUCTION, I1 20. A.J. DIKKERS GEOLOGY IN PETROLEUM PRODUCTION 21. W.F. RAMIREZ APPLICATION OF OPTIMAL CONTROL THEORY TO ENHANCED OIL RECOVERY E.C. DONALDSON, G.V. CHILINGARIAN and T.F. YEN (Editors) 22. MICROBIAL ENHANCED OIL RECOVERY 23. J. HAGOORT FUNDAMENTALS OF GAS RESERVOIR ENGINEERING

Developments in Petroleum Science, 24

polymer flooding

W. LITTMANN

ELSEVIER - Amsterdam - Oxford - New York - Tokyo 1988

ELSEVIER SCIENCE PUBLISHERS B.V. Sara Burgerhartstraat 25 P.O. Box 211,1000 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.

LIBRARY OF CONGRESS L i b r a r y o f Congress C a t a l o g i n g - i n - P u b l i c a t i o n

Littmann,

kd.

Data

fhclfgang)

Polymer f l o o d i n g

1 W. Littmann. crn. -- ( D e v e l o p m e n t s i n p e t r o l e u m s c i e n c e 241 Bibliography p. Includes indexes. ISBN 0 - 4 4 4 - 4 3 0 0 1 - 6 I. O i l w e l l f l o o d i n g . 2. P o l y m e r s and p o l y m e r i z a t i o n . 11. S e r i e s . TNE71.1547 l9@8 622'.3382--dc19

D.

.

I.

Title.

88- 1 9 2 1 8 CIP

ISBN 0-444-43001-6 (Vol. 24) ISBN 0-444-41625-0 (Series)

0Elsevier 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

CONTENTS 1

1

Introduction

2

Mechanics of polymer flooding

3

Screening procedures

10

3.1

Reservoir geometry

10

3.2

Reservoir rock

11

3.3

Reservoir depth and temperature

12

4

3.4

Crude oil

13

3.5

Reservoir brine

13

3.6

Polymer selection

14

3.7

Resistance factor

18

3.8

Injectivity testing

20

3.9

Thermal and chemical stability

21

3.10

Displacement tests

22

3.11

Adsorption

22

Chemistry of EOR-polymers

24

4.1

Synthetic polymers

24

4.1.1

Polyacrylamides

24

4.1.2

Other synthetic polymers

28

4.2

4.3

4.4

5

3

Polysaccharides

29

4.2.1

Hydroxyethylcellulose

29

4.2.2

Xanthan

30

4.2.3

Other polysaccharides

32

Degradation mechanisms

32

4.3.1

Mechanical degradation

32

4.3.2

Chemical degradation

32

4.3.3

Biological degradation

33

4.3.4

Stabilisation of polymer solutions

34

Polymer production

34

4.4.1

Synthetic polymers

34

4.4.2

Fermentation processes

35

Physics of EOR-polymers

39

5.1

39

5.2

Rheology 5.1.1

Definitions

39

5.1.2

Friction laws

40

Flow in cylindrical pipes

44

5.2.1

44

5.2.2

General flow equations Flow o f Newtonian fluids in pipes Hagen-Poisueille’s law

V

46

5.3

5.2.3

Laminar flow of pseudo plastic liquids through pipes

46

5.2.4

Reynold’s criterium

47

Measurement of flow curves

48

5.3.1

Capillary viscometers

49

5.3.2

Rotational viscometers

51

5.3.3

Other viscometers

Molecule size, structure and viscosity

58

5.5

Elastic viscosity

62

5.5.1 5.6

Flow of polymer solutions in porous media

64 65

5.6.1

Darcy’s law

65

5.6.2

Flow of pseudo plastic liquids

66

5.6.3

Viscoelastic effects in flow

5.6.4

Calculation of pressure drop in

Measuring elastic viscosity

through porous media

5.6.5 5.7

5.8

6

57

5.4

70

flood tests

71

Shear stability

72

Inaccessible pore volume

73

5.7.1

Pore size distribution

74

5.7.2

Dispersion

76

Adsorption

77

5.8.1

Adsorption isothermes

79

5.8.2

Adsorption isothermes of xanthan

83

5.8.3

Heat of adsorption

85

5.8.4

Measuring adsorption isothermes

87

5.8.4.1

Static experiments

88

5.8.4.2

Flow experiments

89

5.8.4.3

Calorimetric methods

91

Laboratory testing of EOR-polymers

95

6.1

Polymer mixing

95

6.1.1

Polyacrylamides

96

6.1.2

Xanthan

99

6.1.3

Hydroxyethyl cellulose

99

6.1.4

Shearing of polymer solutions

6.2

6.3

100

Stability testing

102

6.2.1

Solution stability

102

6.2.2

Long term thermal stability

105

6.2.3

Biological stability

106

Injectability testing

107

6.3.1

108

Filter tests

6.3.2

Injoctivity testing on core plugs 110

and sand packs 6.4

7

Oil displacement tests

115

6.4.1

Crude oil

115

6.4.2

Porous medium

116

6.4.3

Saturating with water

116

6.4.4

Saturating with oil

117

119

Reservoir engineering aspects Evaluation of reservoir characteristics

119

7.2

Injection wells

119

7.3

Pressure distribution in the reservoir

121

7.3.1

Injection pressure

121

7.3.2

Pressure testing

7.1

8

124

7.4

Flood patterns

125

7.5

Numerical reservoir simulation

126

7.6

Other applications of polymers

128

7.6.3

Profile modification

128

7.6.2

Polymer flooding and steam flooding

130

Surface and subsurface equipment

136

8.1

Injection water

136

8.1.1

Preparation of injection water

136

8.1.2

Injection water quality

137

8.2

Polymer mixing

141

8.2.1

141

Shipping

8,2,2

Storage

142

8.2.3

Mixing powders and gels

142

8.2.4

Mixing liquid polymers

143

8.2.4.1

Polyacryamide emulsions

143

8.2.4.2

Xanthan broths

144 145

8.2.5

Pumps

8.2.6

Static mixers, injectors and 146

she a I* i n g d ev i c e s

8.3

9

8.2.7

Filters

8,2.8

Material s

149 ,

corit 1-01equipment

149

149

Injection wells

151

Case histories Chateaurenard

3 51

9.2

North Stanley

152

9.3

Hankensbuettol

154

9.4

Eddesse-Nord

156

9.5

Profile modification

158

9.1

VII

9 6 10

rro.icct design

Appraisal and economics

162

10.1 Numerical simulation of a five spot pattern

162

10.2

165

Economics

10.3

10.2.1

Valuation of the producde oil

166

10.2.2

Investments

166

10 .2.3

Lifting costs

167

10.2.4

Chemical costs

167

10.2.5

Specific costs

168 168

Outlook

169

List of symbols and units Appendices

A

Chemical structure of polysaccharides

n

Chemical analysis of polymers in produced

171

field waters

174

B.l

Polyacrylamide B . 1 . 1 Turbidimetry

174

B.1.2

Iodometric method

175

B.1.3

Ammonium detection

B.2

174 175 175

Xanthan

c

Measurement of flow curves

177

D

Example calculation for pressure drop in pipes

181

D.l

Pressure drop for water

183

D.2

Pressure drop for a polymer solution

184

D.3

Pressure drop for a xanthan broth

185

E F

El.astic viscosity - flood experiments

186

Rate of shear strain in perforations

189

G

Accuracy of calculations of rate of shear strain a porous medium

191

G.l

Comparison of different equations

191

G.2

Relevance to two-phase flow

3 94

iI

Example calculation on dispersion

196

I

Polymer mixing in the laboratory

198

1.1

198

1.2

Mixing powders

198

Mixing emulsions

I .2 . 1

Activator

199

1.2.2

Mixing water

199

1.2.3

Preparing a stock solution

199

1.2.4

Preparing a final solution

201

Vlll

1.3

Shearing

J

201

L E I V O of ~ ~ s h e a r p1tr;es

1.3.1

C h e m i s t r y of i r o n h y d r o x i d e s a n d iron o x i d e s

I1

J.l

Iron

J.2

Dissolved iron

J.3

Iron stabilizing agents

-

-

202 204 204

hydroxide I11 - h y d r o x i d e s

204

205

Author Index

206

Subject index

208

IX

This Page Intentionally Left Blank

1 INTRODLJCTI ON

I t might hbve been a mere coincidence that published

two papers

in its

January 1981

Scientific American

edition which

at

the

first glence hfive nothing to do with one another. One is troleum

an article

by MENARD (19811, which deals with the pe-

reserves that still may be discovered in the USA, where he

concluded fields

that the

barrels)

probability

of

discovering new, large oil-

an oil content of more than 10,106 t (or 100 million

with

not very

is

the

conclusion that

met

by more

big. This

the demand

efforts in

judgement very quickly leads to for new petroleum may not only be

exploration but

also

by

improving

the

production of known reservoirs. The his

other article

studies TANAKA

polymer for

deals with gels and their properties. F o r

(1981) chose

polyacrylamide, a

water soluble

which has become more and more important in the last gears

the improvement of oil recovery using a process called polymer

flooding. The production history of a petroleum reservoir may be divided into

different phases. The first, where oil is flowing freely from

the

reservoir to

most

cases also

the production the shortest.

the best known. but in

Very early in the life of a reser-

voir,

energy must

bears

the crude o i l , so that i t continues to flow to the producing

wells.

usually be

well, is

This energy

or gas.

water

supplied to the porous medium which

is brought

into the reservoir by injection of

With these secondary methods about 30 to 40 percent

of

the original oil in place may be recovered, while the rest must

be

left in

well,

the earth.

In order

tertiary methods

to recover

have been

some of

developed which

this oil as

are still

the

subject of research. The forces that hold back the oil in the porous body of the reservoir of

are the

oil, water of the

sity

interfacial tension

and gas flowing in the porous medium and the viscocrude oil. The interfacial tension may be overcome by

injection

of surface

of

that is

a gas

using

C02 at

duced

bj applying

displacing which

active agents

miscible with

(surfactants) or by injection

the crude oil (miscible flooding

high pressures). The viscosity of the oil may be reheat to

the reservoir, or the viscosity of the

phase may be adapted to the viscosity of the crude oil,

is accomplished

floodwater.

between the different phases

This method

by adding

a water

of enhanced

flooding. is the subject of this book.

soluble polymer

to the

oil recovery, called polymer

Beginning

of

Ihe

pi'nc't

icirl

phy!;i<,:; diid,

w

i th

l h e hook

floocjing,

t.hrx p h i l o s o p h y c o \ n r ' < ~the

flow of

which

t;t.ands

chemistry of

behind

r)olymer

EOR--polymers a n d

the

polymet. s o l u t i o n s i n p i p e s atid p o r o u s m e

sc:~.cenirlg procedures, methods of

h i n t s on r e s e r \ , o i r e n g i n e e l - .

hand1 i n g polymers

in

t,hc? I n b o ~ - a t o r y

iiig

p i ~ i > b l t r r n ~i:t ,r i d

arid

i n l h e oj 1 f i n l d . C a s e h i . s i o t , i e s a r e d i s c u s s e d wi t h a r i o u t l o o k

or1

ei.otioinic e f f i c i e r i c y o f

t h i s petroleum

rr?c:over~F ) I - O C ~ . S S ,

REFERENCES M e n a r d . Fi W . . S c i e n t i f i c American. J a n . 1981 Ttlnaka, T . : S c i e n t i f i c American. Jan 1981

2

OF POLYMER FLOODING

2 MECHANICS

Flooding petroleum be

regarded as

though

by definition

croscopic of

economic tertiary

polymer flooding

oil recovery

does not

method,

increase the mi-

sweep efficiency of reservoir rock; the remaining volume

o i l in the porous media is assumed to be the same after a poly-

mer

flood as

for

water flooding

lutions. be

reservoirs with water soluble polymers may

the most

after a

The two

described by

displacement

water flood. Thus the physical laws derived

may be applied to the injection of polymer sophase flow of crude oil and polymer solution may

using the

of oil

by a

relative permeability concept. For the polymer solution

the

fractional

flow

equation derived by BUCKLEY and LEVERETT (1942) may be used. According to these concepts and the experimental work of DYES, CAUDLE and ERICSON (19541, the mobility ratio

M

(kw/uw)/(ko/uo)

(2.1)

(krw/uw)/(kro/uo)

influences the areal sweep efficiency as shown in fig. 2 . 1

M=0.45

M=1.67

/ y / v Mobility Ratio

Flooded Area a t Breakthrough at f, = 90 %

10 2 1 0.5 0.25

0.51 0.60 0.70 0.82 0.87

0.83 0.88 0.98 0.99 0.995

Flooded Area a t Breakthrough

Fig. 2.1 Influence of mobility ratio on areal sweep efficiency

3

Different mobility

DYES, CAUDLE and oil

phases of

flooding

ratios in

the experiments

ERICSON ( 1 9 5 4 )

different

the mobility

were obtained

viscosities.

In

carried out by

by using miscible

the

case

of

polymer

ratio is influenced by thickening the flood

water, e . g . increasing the viscosity by a factor of 10 to 5 0 . In fig. 2 . 2 the influence of viscosity ratio on oil recovery is shown the

TUNN

according t o improvement in

oil recovery

displacing

phase. The

saturation

after

volumes

a

in oil

related to

irreducible oil sufficiently

should, however,

improvement

This figure clearly demonstrates

(1974).

the viscosity of the

saturation or residual oil

high

number

of

flooded

pore

be the same for all vicosity ratios. The

recovery is

that the oil is recovered earlier

at a lower water cut and thus in practice at lower lifting costs.

///,25

2ok 0

0

I

1

t

2

irreducible oil saturation

‘///

I

I

I

I

I

3

1,

5

6

7

I 1

Flooded Pore Volumes

2.2 Influence of eiccording to TUNN.

Fig.

These explanations

viscosity ratio

on the

effect of

recovery pro c e ss

viscosity and

mobility

on oil recovery do not consider the fact that mobility ratio not constant during the flood but varies according t o the

ratio is

on oil

4

saturations

of the flowing phases. Typical relative permeabilities

for a water wet sandstone are plotted in fig. 2.3.

’,S

0

1.0

0.5

Fig.

2.3 Typical relative permeabilities for oil and water of a water wet sandstone and fractional flow curves for the displacement of oil by water and polymer solution. (Viscosity of oil 15 mPas; viscosity of water 1 mPas: viscosity of polymer solution 15 mPas)

The fractional flow curves

fw

=

1 / ( 1 t 1/M)

for

the displacement

water in

(2.2)

the same

the also

of an

oil having

a viscosity of 15 mPas by

of 1 mPas and a polsmer solution of 1 5 mPas are also plotted graph. According

front for

the water

to WELGE ( 1 9 5 2 1 , the saturations at

flood Swf

and the polymer flood Spf and

the saturation at breakthrough Sbtw and Sbtp are given in fig

The saturations both at the front and at breakthrough are distinctly higher for the polymer flood than for the water flood.

2.3.

This pared

reflects the to a

better performance

of a

polymer flood as com-

water flood. Fig. 2 . 4 shows the corresponding mobility

5

I t can be seen that the mobility ratio in a water flood at water saturations may also be below 1 , and that at high

ratios.

low

saturations

the mobility

ratio for

the polymer

flood may become

greater than 1 .

100

I

kWater

M 10

I

-

1 -

Polymer 0.1 -

0.01

0

0.5

sw

Fig. 2 . 4 Mobility ratio for the displacement of oil by water and polymer solution as a function of the saturation of the displacing phase.

Apart from the microscopic and areal sweep efficiency, the vertical

sweep efficiency

determines

the

performance

of

a

water

in many cases more than any other parameter. Before the that may improve the vertical sweep efficiency during polymer flooding is discussed, some introductory remarks on the rheology of pseudo plastic liquids are necessary. For water and oil the viscosity is, in most cases, a constant value. For polymer solutions this is more or less not the case. The viscosity is in bold outlines a function of the rate of shear flood,

mechanism

strain. Fig. 2 . 5 shows flow curves of commomly employed in polymer flooding. a

aqueous polymer solutions

The viscosity, or more exactly apparent viscosity, may vary as function of shear strain within a wide range. This behavior in

a wel.1-determined range may be described by a power law

6

500 ppm Xanthan in 0 formation water

500 ppm Polyacrylamide in x fresh water 0 formation water I" I

v)

m

n

-

E

102

5

i

c

g

10'

.-v) > €lo*; 100

,

h

- 01 0.1

1

10

Rate of shear strain,

100

9 (s-’)

Fig. 2.5 Typical flow curves of aqueous polymer solutions applied in polymer flooding

In regard

to the

viscous flow of a liquid, the rate of shear

strain is a function of both flow geometry and flow velocity. For flow in porous media this means that in narrow pores the rate of shear

strain is

troleum the

shear rate

having 0.2

of

a

in low

in larger pores, o r , in terms of pethat at

permeable zones

good permeabilities.

the same Darcg velocities is higher

than in

zones

Hence, e . g . , for a Darcy velocity of

m/d in a sandstone with a porosity of 2 5 % and a permeability 2 0 0 0 m D , the rate of shear strain is 8.6 s - ' for a polymer

solution at

higher than

reservoir engineering,

with H=40 mPasn and nz0.6. For the same polymer solution

the same

Darcy velocity rate of shear strain in sandstone with

porosity of 20

%

and a permeability of 2 0 0 m d , the rate of shear

7

is 30

strain solution

s

’’This

flowing

permeability

is

means that higher

(16.9mPas)

in

than

of the p o l v m o ~ ~

the viscosily the

in

sandstone

the

with

sandstone

the

with

high

the

low

permeability (10.2 mPas). Usually high permeable zones are preferentially invaded by the water during

flood

and

low permeable

these

parts

of

secondary operations zones are

vertical

sweep efficiency

solution

of course

then

not flooded

reservoir.

a

or natural

During

may be

first follows

so that

polymer

water drive, oil is left in

flooding

improved, because

a

the

poor

polymer

the paths prepared by water and

because of its high viscosity tends to "block" these parts of

the

reservoir, so

flowing. those

that oil

The pressure

zones where

that was

previously immobile

starts

gradient in the reservoir and especially in

oil was

immobile becomes

higher in

a polymer

flood than i t was during water drive.

I

d

g

20

o

tf

t

0

0

1

2

3 0

3

2.6 Improvement SANDIFORD (1977))

Fig. 2 . 6 ( 1 9 7 7 ) . In a perrneabilities,

3

2

Injected Pore Volume

Injected Pore Volume

Fig.

1

of

vertical

sweep

efficiency

(acc.

to

shows the results of a flood experiment by SANDIFORD system of

two parallel

the

recovery

oil

8

flooded cores due

to

polymer

of different flooding is

significantly

higher than

during a

flood in

one core of uniform

permeability.

REFERENCES Buckley, S . E . and Leverett M . C . : Mechanism of Fluid Displacement in S a n d s , Trans. AIME ( 1 9 4 2 ) 146 107-116 Dyes, A . B . , Caudle, B.H.and Ericson, R . A . : Oil Production after Breakthrough - As Influenced by Mobility Ratio , Trans. AIME ( 1 9 5 4 ) 201 81-86 Sandiford, B . B . : Improved Oil Recovery by Surfactant and Polymer Flooding , D . O . Shah, R . S . Schechter (editors) Academic Press (1977) 4 8 7 - 5 1 0 Tunn, W . : Gedanken uber Einsatzmoglichkeiten von Tensiden zur Erhohung der Ausbeute von Erdollagerstatten , Erd61 - Erdgas - Zeitschrift (1974) 90 5 0 - 5 3 Welge, H . J . : A Simplified Method for Computing Oil Recovery by Gas or Water Drive , Trans. AIME ( 1 9 5 2 ) 195 3 9 - 4 6

9

3 SCREENING PROCEDURES

Because polymer servoir,

flooding is not always ,suitable for every re-

in this chapter the most important screening criteria are

outlined.

Before a

polymer project

may be

planned

in detail a

screening of the reservoir parameters may give a first indication as to whether a polymer flood is at all possible which polymer is

most likely

successful

to be

with

successful, and

respect

to

technical

if the project might prove performance

and

profit-

ability . Usually the situation is such that the recovery of a particular oilfield

is poor,

consequentially

that the

the economic

producing water cut is high, and that efficiency of

oil production is not good. In such cases there is an urgent need for a decision about a suitable EOR-method that should be made before expensive research is started.

In order to be able to make a clear decision whether polymer flooding is suitable in a reservoir before going into more this chapter provides some assistance. I t is self-evident

details, that

less attention

more or

other,

should be

given to one point or the

depending on the specific reservoir case, and that for some

of these points additional research work may also be necessary. 3.1 Reservoir geometry The reservoir geometry should be examined first while screening reservoirs for an EOR-application, especially chemical flooding. Chemical flooding very

in the

servoirs flooded servoirs of too

even be impossible because the flow of the che-

difficult or

micals

of the

reservoir cannot be regulated. Strongly dipping reshoe-string type

with respect have only

a flood

in a reservoir with bottom water may become

are also very difficult to be to the control of chemical loss. If such re

a small

oil bearing zone, the economic design

pattern may not be possible. This basically means that

many injection

and production

wells are necessary to produce

the oil. For reservoirs done

to control

of chemicals, the which are usually production pressure aquifer

having large

aquifers specific work should be

the flow of fluids. In order to minimize the loss pressure gradient from the injection wells - located near the oil-water-contact -- to the

wells, should be sufficiently large. To maintain such a gradient, back

pressure wells

may

be

drilled

in

the

into which water is being injected. The importance of this

10

point

with

respect

disregarded, to

4 0 % of

calculate In

to

economic

efficiency

should

not

be

as the loss of chemicals into an aquifer may reach up

the injected

volume.

The

best

method

to

plan

and

fluid flow within the reservoir is numerical simulation.

this manner, even i f the simulation program that is used cannot

properly

handle the

physics of

polymer flow,

i t may nonetheless

provide a solution to this problem. Reservoirs having gas caps are also not easy to handle with respect to the control of fluid flow in the reservoir. Hence for such

reservoirs, too,

numerical

simulation is the best means of

planning an injection and production project The reservoir geometry that is most suitable flooding

for

chemical

is that of separated block, or that the reservoir is that

big that pattern flooding is possible. 3 . 2 Reservoir rock The type

of reservoir

ralogy, porosity and important with respect Porosity for

and more

rock is important with regard to mine-

permeability. Mineralogy, in turn, is of the compatibility of polymer solutions.

permeability and

the injectability

its variation are significant

of the polymer solution and, as pointed out

above, for the performance and benefit of the polymer flood. At high clay concentrations the compatibility of the formation with fresh water may become a problem if fresh water is being used as mixing water, e.g. when polyacrylamide is employed in a salt reservoir. If

water

possible fresh

clay swelling

or mobilization

of

fines

is

by using fresh water, a polymer which can only be used in

water is

not applicable.

Further attention should be given

to chemical loss due to adsorption that is usually higher at high clay concentrations. This applies also to high carbonate contents. When

flooding with

fresh water

content, attention should temperature and pH-value, fresh

water may

solution

become harder,

may change.

significantly,

This

especially

in reservoirs with high carbonate

be given to the fact that, depending on the carbonate dissolves, the injected and the properties of the polymer

means that the viscosity may decrease for

polyacrylamides

mixed

in

fresh

water. cal

Permeability and its distribution is important for the techniand also economic success of a polymer project. It is evident

that permeability determines the injectability of the polymer solution - end thus the duration of the project. A high permeability

11

1 pm2

above values

and should not be below 0 . 5 urn2. These

is desirable,

are guidelines a n d , as already stated qbove, are given here

for screening purposes. Polymer flooding in reservoirs with

0 1

pm2 should

injection

not be

permeabilities lower than

generally excluded

i f a sufficiently high

rate can be achieved and the necessary amount of polymer

solution can be injected within a reasonable time.

As described polymer

in the

flooding, a

reservoir

is the A high

benefit.

breakthrough flooding

preceding chapter about the mechanics of

high vertical

case where contrast in

variation may have

permeability leads

during secondary

may be

permeability

polymer flooding operations. In

economicallv attractive,

to

in

early

such cases

since large

a

the most water polymer

&mounts of

o i l are left in the reservoir that is bypassed by the flood water.

3 . 3 Reservoir depth and t e m p e r a t u r ~ Reservoir depth pressure.

Injection pressure

flooding is

For

bv

than in

given by

trired.

is important

an injection

injection

higher in

polymer

attained when

the reservoir

is frac-

the fracture gradient should be determined

and breakdown test using water. But in many cases

reservoirs also

therefore

is significantly

the

depth may be a restriction for polymer flooding.

shallow reservoirs

shallow

to

water flooding. The limit for injection pressure

that pressure

Hence low

in relation

relatively

consist of ’weak’

unconsolidated sand: they a r e

and

do

not

exhibit

a

fracture

pressure, so that low depth is not always a severe problem. The

temperature of

the reservoir

thereof,. Reservoir temperat,ure too

high. Thougli

arid

more for

limit

Some products.

be seen

to the

depth

f 1 oodiiig shotild not hc

of up t o 1 2 0 O C

give values

their products, t h e iii>pet’

st.ability of

should nevertheless

problems.

in polymer

many manufacturers

the thermal

is related

at 70

O C

in

especially synthetic

order

avoid

to

polymers, may also

b e employed at temperatures up to 9 0 " C .

I t should be noted that the viscosity decreases with increasing. temperature, technical dependence products, the

so

that

is

desired purposes at

temperatures also an

different

s o while

consideration. behavior

high

restriction but

for

about

various

screening polymers find

for

Most products

70

OC.

every show’ a

e:'g:

12

represent

not

only

a

economic one. This temperature types

polymer change in

polymers

of

it, should

and

be measured for

being

taken

into

their temperature

polyacrylamides

demonstrate

a

stronger

tendency to flocculate at this temperature. Decomposition

reactions

are

also

accelerated

at

higher

temperatures

and

adsorption on the reservoir rock ’may increase. Another factor that is influenced by temperature is the use of other

chemicals needed

high

for polymer flooding, such as biocides and

scavengers. F o r

oxygen

example,

concentrations as

temperature because

may also

a

formaldehyde may only be used at

biocide

up

have adverse

the activities

to

effects

of bacteria

about

50

on

polymer

are generally

A

OC.

low

flooding

higher at such

temperatures. 3 . 4 Crude oil

The properties determine thus

of the

low mobility

polymer case

meability

Low oil viscosities and

only allow

compared to flooding is

variations. At

mobility

to be recovered essentially

to be applied.

ratios often

flooding as

when polymer

between

crude oil

the EOR-process

small impi*ovements by

water flooding.

except for

favourable because

high oil

of

viscosities the

high

the per

reduction

in

for polymer flooding may be considerable. Oil viscosities 5 and

5 0 mPa’s

in

mobility ratio

of

the polymer

are regarded as advantageous. A reduction

far below

1 is favorable, so that the mobility

solution is

lower than

the mobility of the crude

under reservoir flowing conditions. I t is obvious that the oil

oil

saturation oil

in the reservoir should be substantially below residual

saturation.

better

The earlier

a polymer

project is

started, the

i t will have. This will be discussed later

the performance

in the presentation of results of laboratory flood tests. 3 . 5 Reservoir brine

The brine that saturates the pores of a r o s r : ~ . ~ ~ hooides u i ~ , tho oil

itself, is one of the most important parameters for the selec-

tion

of a

salinity be

preconditioned by

preconditioning mineralogy a

I f the

suitable polymer. the polymer

should he a preflush

with fresh

reservoir water

is of

high

salt stable or the reservoir must of fresh

water is

water. Whether

or not

possible also depends on the

of the reservoir as discussed above. Preconditioning of

reservoir with

fresh water

presupposes slug sizes of 0 . 5 - 1.0

pore

volumes. So for economic reasons, preconditioning may be done

with

a salt-tolerant

of

the polymer

polymer as proposed by VOLZ ( 1 9 8 3 )

slug is

relatively

small

(0.05

compared with preconditioning only with fresh water

13

-

0 1

The size PV)

as

In some fresh

cases of high saline reservoirs, preconditioning with

water

may

possibility no

not

be

to dispose

fresh water

applicable,

because

there

is

no

of the produced reservoir brine or because

is available.

In these

cases only those polymers

which are salt stable may be utilized. 3 . 6 Polymer selection

I f , with respect to the has

been chosen

of

the adequate

criteria described above, a reservoir

as a candidate for a polymer flood, the selection polymer may

begin. This

means

first

that

the

demands on the desired polymer solution should be defined. T o begin polymer

with, the

solution should

appropriate efficiency

of a

permeabilities

give a

reasonable value

polymer

solution

is

not

for the readily

above, mobility ratio determines the sweep In Fig.

2 . 3 the

relative

for two-phase flow in a typical water wet sandstone for

respectively. polymer

the

displacement process.

shown together

viscosities solution

be. To

viscosity of A s mentioned

possible.

are

question arises what the viscosity of the

with the water

and

Furthermore, a

was computed solution of

permeabilities

is

corresponding

fractional flow oil

were

1

fractional flow

assuming both

curves for

valid

for

and

mobility ratio

mPa’s,

viscosity of the

the same

the

15

curve for a polymer

a constant

15 m P a s s and that also

curve of water. The

mPa’s

set of relative

polymer

solution.

were presented

in

The Fig.

2 4.

Detailed discussions placement SMITH fw=O

are given

in many

reservoir engineering books, e . g . by

( 1 9 6 6 ) and CRAIG ( 1 9 7 1 ) . on

the

fractional flow he

tangency

of

on the concepts of immiscible fluid dis-

water or

curves in F i g . 2 . 3 yield at the point

polymer saturation

these tangents

extrapolating

The tangents from point Sw=Swc and

to fw=l

at

the

yields the

front

and

values at break

through. This is illustrated once more in Fig. 3 . 1 . As

water more a is

shown

n Fig. 2 . 3 , the water saturation at the front

during

flood is lower than during a corresponding polymer flood. So oil is left behind the front during a water flood than during

polymer flood, also below

ratio

in water

saturation

though the mobility ratio during the water flood

1 at

the front.

flooding is

at the

front is

But at breakthrough the mobility

about 10. nearly the

14

In the

polymer flood

same as

the

at breakthrough:

because of difference The

the shape

of the

between saturation

saturation of

that

for the

more

of the

the polymer

water flood original oil

fractional flow at the

front and

solution at

0 . 6 2 . This

in place

curve there is no at breakthrough.

breakthrough is 0 . 7 2 ,

means that about 10 percent may be

recovered by

polymer

flooding during the early stages of a flood.

Fig. 3 . 1 Fractional flow curve showing graphical construction for average displacement phase saturations for continued injection after breakthrough. (according to SMITH ( 1 9 6 6 ) , p . 1 6 5 )

Another factor viscous

fingering.

investigated periment BLACKWELL

fluid

The

by BLACKWELL

are shown

influence et a l .

of

the

( 1 9 5 9 ) . The

in Fig. 3 . 2 and Fig. 3 . 3 .

( 1 9 5 9 ) used

two miscible

mobility

ratio

was

results of his exIn his experiments,

fluids, dyeing the displacing

to observe viscous fingering. I t is

reservoir and

that influences the displacement efficiency is

a well-known is the

assumption that recovery in a homogeneous

same for polymer flooding as for water flooding,

polymer flooding only serves to accelerate

this is true, then

the acceleration

15

is

o i l production. If

tremendous.

In order to

Fig

3.2

Displacement et a1 (1959))

(R1.ACKWEI.L

front

for

different

rnobilitv

ratios

100

-

80

5

60

W

> 0 U L W

LO

W

> .-+

m

d

3

20

5

U

0 0

0.2

0.11

0.6

0.8

1.4

1.2

1.0

6

Solvent injected, (pore volumes) 3 . 3 Effect of m o b i l i t y (BLACKWELL et. al. (1959))

ratio

Fig.

obtain about

on

cumulative

recovery

t h e s a m e r e c o v e r y i n w a t e r f l o o d i n g as in polymer f l o o d i n g ,

10

-

20 t i m e s m o r e p o r e v o l u m e s m u s t b e f l o o d e d , as i s s h o w n

in F i g . 3 . 4 .

16

P

s c’

0 .c

m

L

5l

+ =l 10 m v)

.-

O

aJ

sorw

' Sorp

m

10

-

~~

Sandstone Core

/

o S/A-9

8-

6-

-i3

4-

d

m + c

al

f -

2-

U L C

" I

100

'

'

"""I

I

I

,

I

I

10'

Polymer Viscosity,

,,,I

102

p (mPa . s)

Fig. 3 . 5 Incremental oil recovery as a f u n c t i o n of polymer v i s cosity for d i f f e r e n t p o l y m e r s m e a s u r e d in s a n d s t o n e c o r e s . (S/A-9: p o l y s a c c h a r i d e ; C / U - 2 : h y d r o x y e t h y l c e l l u l o s e ; P/H-5: p o l y a c r y l a m i d e ; 60 m P a ’ s ; v i s c o s i t y of p o l y m e r s o l u t i o n u n d e r oil v i s c o s i t y f l o w i n g c o n d i t i o n s ; s l u g s i z e 1 V p : f l o w i n g v e l o c i t y 134 c m / d ; T=50 O C ; DIETZEL (1982))

17

This figure polymer

flooding with

viscosity. ence

also illustrates

In his

the recovery

to he obteined by

respect to polymer ,concentration or polymer ( 1 9 8 2 ) measured

experiments DIETZEL

the influ-

of polymer viscosity on incremental oil recovery, as shown in

Fig. 3 . 5 . Fig 3 . 5

viscosity

that should

recovered. polymer

demonstrates that

be exceeded

(1982)

DIETZEL

types. For

found

the case

before any different

incremental oil is values

various 3.5, a

polymer viscositv

may he

value for

read.

This viscosity i s roughly the oil viscosity of 6 0 m P a ~ s .For

are

required minimum

for

from Fig.

of polyacrylamide

clear

polysaccharide

the

there is an onset value of polymer

the onset

value and the minimum required viscosity

about the same and are also in the range of the oil viscosity. viscosity significantly

A

above that

of o i l

viscosity

is

only

necessary for hydroxyethylcellulose. shown

As

necessary

above,

viscosity

conditions)

is to

oil

reservoir

under

solution strain

to take

a of

first

approach

the

polymer

approximating

for

solution

(under

the

flowing

assume a viscosity that is equal to that of the conditions.

the apparent

This

means

viscosity at

the

for

the

rate

polymer of

shear

under mean reservoir flowing conditions, i . e . approximately

10 s - 1 . The viscosity factor,

and so

of the

this point

polymer solution

is also

an

economic

should be of great interest in further

experimental work in the laboratory. 3 . 7 Resistance factor

.

In order

during

to characterize

the behavior

of pressure

built up

flooding of different polymers, the resistance factor Rf is

often used.

(3.1)

The resistance water

to

resistance to

the

of

defined as the ratio of mobility of a

polymer

solution.

The

residual

factor Rrf is the ratio of the mobility of water before

that after

expressed

factor is

mobility

the injection of a polymer solution. It can also be

as the

ratio of the permeability of water initially and

after polymer injection.

18

(3.2)

100

-

a- 80L

0 +

y

60-

Y-

U W

5

c .-VI VI

40-

p:

/XYX

‘ X

W

/

200-

I

I

I

I I0

D a r c y velocity, v o (m/d) Fig. 3 . 6 Resistance factor of a polyacrylamide solution vs. Darcy velocity according to MARTISCHIUS et al. (1985).

In Fig. 3 . 6 the dependence of the resistance factor on tho flowing velocity is shown as measured by MARTISCHIUS (1985).

At low velocities the resistance factor is constant flects the Newtonian of flowing velocity. shear

which r e -

thinning starts, where the resistance factor decreases, and

subsequently increases now

,

flow behavior of the solution in that range Then, at higher velocities, the so-called

at

again due

rules the

behavior molecular

much

higher to the

weight. The

significantly

the

elastic behavior

resistance to

strongly depends

velocities flow

on the

in

the

type of

elasticity of

resistance

factor

of the polymer that porous

the

medium.

polymer

and

polyacrylamide molecules

This its is

higher than that of, for example, xanthan molecules,

which have stiffer polymer chains.

19

The residual resistance factor is a measure of the tendency of the

adsorb and t h u , s partially block the porous medium,

polymer t o

as shown schematically in F i g . 3 . 7 .

Fig. 3 . 7 Adsorbed polymer molecules reducing the diamet,er of the pores in a sandstone. The adsorbed molecules are surrounded by 1)ound solvent.

of this

The appeararice post-flood with

a are

water some characterist,ics of the polymer flood

still present.

:;olutior~, and the as if

flow

efficiency i ) ur e

the flood fov

R

adsorbed molecules

water had

desorb and g o jnto

a l s o cause

a higher

FA

resistance to

viscosity.

the

sweep

water post-flood is a l s o increased as compar3ed to

F o r practical

flush. he

As the

adsorbed molecules

water f I ood ins.

fresh 1

phenomenon is in ono way desired, be-

i t prolongs the characteristics of the polymer flood. During

iause

w ~ t e rpolymer

purposes, this flood were

means that

i f . for instance. a

performed for the following watov

fresh water should be used, because salt wat.er would r e d u c , e

residual resistance factor more rapidly. The salt wat.er’ lowers

t h e biscosity of the polymer solution remaining

in the pore

space.

3 8 Injectivity testing

Good injectability of a polymer solution into is

the most

ii

rcsorvoir r o ~ k

impoi tant requirement for a successful polvmer flood

Good

injectability means

the

solution

into

that the

the

pressure loss

reservoir than i t

is,

when

while injecting

to

compared

water

injection,

not higher

viscosity.

The injectability may also be influenced by the elastic

properties

of some polymers. Beyond that, good injectability means

that

should be

because of

the

raised

the pressure drop remains constant during injection. The pore

space should not be irreversibly blocked by the polymer. Undesired blocking One

is that

flow

through the

Solid the

of the

pores, which

particles in case

of

is often the case for biopolymers.

xanthan solutions may be bacterial debris from

or bacteria or fungi from infections. In

fermentation process

the

porous medium may have two causes.

a solution still contains solid particles that cannot

hydroxycellulose,

cellulose

particles

may

cause

plugging. Another reason contains happens using

why

gel particles when powder

an adequate

plugging from

the

polymers are

occurs

is

dilution

that

the

process.

used. This

may be

qolution

This

often

avoided

by

dilution procedure, including proper mixing and

shearing . The presence and kind of plugging particles in polymer solution may

be detected by filter tests or injectivity tests on core plugs

and

sand packs

Details about these tests are given in Chapter 6 ,

which deal.; with laboratory methods. 3 . 9 Thermal and chemical stabili.ty

Flood processes in an oil reservoir last for a relatively long period not

of time.

The chemicals

used for enhanced oil recovery are

indefirlitely stable. This means tho1 a flood project should be

planned

for as

requirernerits

ori

short a the

period of time as possible, and that iiome

long-term stability

of such chemicals should

be fulfilled. For polymers temperature water

this means

of the

should be

that a

reservoir and

obtained, and

good aqueous solution at, t,he

at the

that

salinity of

they

must

not

the

flood

flocculate.

Degradation of t,he p o l y m e r should be as small as possible. Reasons fot’ flocculation are the presence of multivalerit metal ions and to

like Ca2+

and F e 3 +

bacteria. Biopo1ymei.s

,

Degradation may be caused by oxidation such as xanthan are extremely sensitive

biological degi,odation. Thus i t

injection

is very

important

that

the

water is free of oxygen, and that effective biocides are

ZJ

used.

Methods and

facilities for

and control of

the preparation

mixing waters are discussed elsewhere. 3. 1 0 Displacement tests For the final design of a polymer flood, displacement tests in the

laboratory under

are

necessary. Such displacement tests should be made at different

flow

similar conditions to those in the reservoir

velocities, thereby

reservoir.

and if

way

a

that

viscosities

of the

and those enable a

sible,

possible

measured in

between

the

derived from the a

scale-up to

input data

the

apparent

pressure drop

viscometer. Only

field conditions.

such

and lead to

for numerical reservoir simulation. If pos-

the experiments simulation

is

polymer solutions

correlations

servoir

occurring in

possible flood tests should be carried out in a

correlation

measurements reasonable

simulating conditions

should be

program

matched with

before

simulating

a

numerical the

field

reper-

formance. Other data

that can

be obtained

by flood

tests include the

necessary polymer concentration, slug sizes and slug design.

3.11 Adsorption retention of

Adsorption or influences

its

effectiveness important

concentration

for

the

flood

screening parameter

a chemical

in

the

process.

at the

solution, Hence

rock and

surface thus

adsorption

is

its an

for polymers as well, but even more

so for surfactants. A certain rate of adsorption i s even desired

to oblaiii adequate

values for the residual resistance factor.

REFERENCES Blackwell, R . J . . Rayne. J . R . and Terry, W . M . : "Factors influencing the efficiency of miscible displacement", Trans. AIME ( 1 9 5 9 ) 216 1 Craig, F . F . : "The reservoir engineering aspects of water flooding". S O C . Petr. Eng. (1971) Dietzel , H .J . : "Untersuchung uber die Eignung von Polymerlosungen z u r Erhohung des Entolungsgrades" , PhD Thesis, Techn. Univers. Clausthal ( 1 9 8 2 )

22

Martischius, F . D . , B a r t h o l d . K . , H o v e m a n n , F . : " O p t i m i s a t i o n of the p r o p e r t i e s of polymer s o l u t i o n s for enhanced oil recovery". 3 r d E u r . M e e t . I m p r . O i l R e c . R o m e ( 1 9 8 5 ) Smith, C . R . : " M e c h a n i c s of s e c o n d a r y oil r e c o v e r y " , Krieger Publishing Company ( 1 9 6 6 ) Volz. H . : P a t e n t DE 3 2 1 1 1 6 8 C1, E 2 1 B 43/22 ( 1 9 8 3 )

23

J CHEMISTRY O F EOH TOJ,I'MERS Wal.c?r ! : r ~ l u t ) l e

that

po1ymel.r;

p o l y m e ~ ~t.ha s t

groups: Hrt?

IIR

f o r EOR

usad

a r e produced

t,ui%al p i , o d u c 1.:;

mas b e d i v i d e d i n l o two

s y n t h e t i c a l 1.v.

f {'om w o o d ,

seeds e f r

.

or

,

and

polymers

1 hose

prod(iced

Syntliotic polvmei,s

4 .1

4 . 1 .I l'o'yocrylamidew a t e r s o l u b l e p o l y m e r s wh

Polyacrylamides a r e many m a n u f a c t u r e i - s

by

instance

acrylarnide is

monomer

most

i n many

as f l o c c u l a t i n g

ways f o r

agents in

a compound

important representatives

of

waste derived

CH2 = CH CH2

= CH

CH2 = CH

treatment,

a c r y l i c a c i d . The

t h e chemical

group t h a t aci'ylic

acrylic acid

-

CN

acrylni t r i l

-

COOR

acrvlic acid ester acrvlumide

-. CONH2 -

ac1.01 e i n

CIIO

The c h e m i c a l

s t r u c t u r e o f p o l y a c r y l a m i d e i s shown i n F i g . J . 1

H

H

H

H

H

I

I

I

I

I

-c -

c -

c -

c -

c -

I

I

I

I

I

H

C = O

H

C = O

H

H

I c -

I

c=o

I

I

I

NY

NH2

NH2

F i g . 4 . 1 S t r u c t u r e of

polyacrylamide

24

for The

from

CH2 = CH - COOH

= CH

water

t o are

a c i d belongs

CH2

d i f f e r e n t purposes,

(not hydrolized)

The molecul.ar

The size

W1O6. HI

weight of

polycryamides is

molecules is about 0 . 1

of the

between 3

.lo6

and

0 . 3 i i m ( I I N S A I . et

-

(1979)). By

lisdrolvsis

to

reect

pt'oups

in

cnu:;tic w h t e r solution some of the CONH2

R

carboxyl

form

(COOHI.

groups

degree

perties

polyacrylamide in aqueous solutions as used in enhanced

of

:; nti

recovei'y.

solution.

The

carboxyl

groups

of a

The structure

which determines dissociate

in

the

of

i

oil

impovtaiit parameter

The

hydrolysis

an

pro-

aqueous

polyacrylamide molecule is as shown

in F i g . 4 . 2 .

H

H

H

H

H

H

I

I

I

I

I

I c -

-c -

c -

c -

c -

c -

I

I

I

I

I

I

H

C = O

H

C = O

H

c=o

I

I

I

NH2

0-

NH2

H*

Fig. 4.2 acrylamide

Molecular

of

structure

partially

hydrolized

poly-

This structure is representative for a polyacrylamide with a 25 degree of

percent

hydrolysis. The

negative charges

solution

so that

polarity

keep the molecule chain in a more or less stretched form.

a

of the

pure,

distilled

charges having

the

water same

produces a molecule coil in solution that assumes the largest

volume the

the repulsion

in

dis-

carboxyl groups

This

interact

of the

sociated

possible in

molecule

according later.

the solution (together with bounded solvent in

coil),

what

to Einstein’s

I f only

a low

results

viscosity

amount of

in

law

a

high

that

will

vicosity be

yield

discussed

cations is present in the water,

25

the

negative

molecule solution. may

charges

of

the

oxygen

are

compensated

Rnd

the

tends to c u i . 1 , s o that i t a s sumes,a smaller volume in t,he With higher

amounts of

be cross--linked hy this

divalent cations

the molecules

mechanism, so that a gel may form if

the

polymer concentration

are

formed that fall out of solution. The configuration of a poly-

is high enough, or molecular aggregates

mer

molecule in

the

influence of

illustrated in F i g . 4 . 3 . In Table 4 . 1

solution is

N n C l concentration

on intrinsic

viscosity

and

thus molecular size is shown.

I "Bound" ] Solvent

wA

"Free" Solvent

coil Volume

1-1 Fig 4 . 3 Illustration of a (from VOLLMERT ( 1 9 8 0 ) )

coiled polymer

Chain Substance

molecule in

solution.

Table 4.1 Effect of NaCl on molecular size (according to UNSAL et al. ( 1 9 7 9 ) ) The molecular weight is calculated using the Mark-Houwink equation with the constants K m = 3 . 7 3' and az0.66. These are typical values for polgacrglamide according to MEISTER et a l . ( 1 9 8 0 ) . NaCl concentration ( ppm 1 200 1000 10000

Intrinsic vi scos i ty

Molecular size

(l/g)

(urn)

9.90 7.18 6.42

0.2950 0.2650 0.2550

26

Molecular weight Z 5,106 %

5.10;

z 5.10

K', Na', Li*, NHL* Ba2*, Sr*+, M$+, cd** ~ a ~ C+O ,~ *

0

1

2

Cation concentration,

3

4

(meq/Ll

Fig. 4.4 Influence of v a l e n c y of c a t i o n s agar s o l u t i o n a c c o r d i n g t o PHILIPOFF ( 1 9 4 4 )

lo-'

loo

10’

lo2

o n t h e v i s c o s i t y of a n

lo3

Rate o f shear s t r a i n , t (s-') F i g . 4 . 5 F l o w c u r v e s of a s o l u t i o n of 1000 ppm p o l y a c r y l a m i d e at d i f f e r e n t h a r d n e s s e s of m i x i n g w a t e r : 1 ) 1 . 6 " d H ; 2 ) 5 O d H ; 3 ) 15 OdH; 4 ) 25 OdH. ( 1 "dH 10 m g CaO/l)

The influence of small amounts of electrolytes on viscosity was PHILIPOFF (1944). He called i t the "electro-

already

described by

viscous

effect". and showed that this effect significantly depends

on

the valency of the cations. The decrease in viscosity is at its

smallest

for cations

La3+,Co3+ and Pt4’,

such as

In F i g . 4 . 5 the effect viscosity flow

yield is

curves. The

centration measured high

is

K+,Na+,NH4’ and

at its highest for

as shown in Fig.4.4 for a solution of agar. of the

shown as

mixing waters

on

it results on the characteristics of

decrease in

significant.

hardness of

viscosity due that

As

part

to raised of

the

salt con-

flow

curves

at low rates of shear strain stands for the amount of the

molecular portion (high volume molecules) in the solution, i t

is

obvious that

this part in the distribution of molecular weight

in

the polymer

solution is influenced predominantly by the raised

salt. concentration. Thus at.

least the

co--polyrner of acrylic acrylic percent. zero

and

acrylamide.

The

percentage

of

for EOR

But products

have degrees

having degrees

of hydrolysis

of 25-30

of hydrolysis approximating

are also available. These products do not exhibit as strong a

sensitivity do.

to salts

They may

in

aoj d

R

acid in the molecule chain gives the degree o f hydi’olysis.

piboducts used

Most

polymer usually called polracrslamide is

as products

be used

the previous

chapter. But

concentration

of

flooding

rssttrvoi r

in a

of a

high degree of hydrolysis

for preconditioning reservoirs as mentioned

these

one must keep in mind that a higher

products

is

needed,

and

that. during

hydvolysi s always takes place which

sonic

niey chnnge the chemical charactel’ of the product. 4 . 1 . 2 O t h e r synthe lic p o l ymers Some

tjf

f o r t . hns

beer made

poly~ci~ylamidns,i . e . , thnl S

H

c g ,

v i riy

,

(1985).

tho disddvanlage of

they cannot. be u s e d i n waters o f h i g h

raised temperctturel.;. T h e s e p o l y m e r s are. 1 5 t i 1 f o n a t. r) / \ iriy 1 an1i d e c o - p t o 1 y m c) r s . R s d e r , 1 , i b e d b y H I L L E

nspe(:iallu at

i~ n i t y , ,

to overcome

c;

They

teiiipernture

wei'tl

we1

originally developed f o r d r i l l i n # fluids in h i g h

1 5 ,

Another p o l 5 i n e r

pr’oposed by

Volz as

a saci.ificia1

i n

with xanthan

po1y:iiers

examined for EOR. e . g . by WILLHITE and DOMINGUEZ. hut not

gums

is

called polyethylene

figen1

flooding

28

glycol. O t h e r

tested

jrl

field

Rpplications. are:

polvethylene oxide, polyvinyl

acetate, polysterene, and p o l y m e t h y l m e t h a , c r y l a t e . 4 . 2 Polysaccharides In

order

solutions cription given

of the a

in

nomenclature abundant

to

understand

the

properties

of

polysaccharide

as hydroxyethyl cellulose or xanthan gums a general dessaccharides is

chemistry of

brief

form

in

and chemistry

organic matter.

A,

Appendix

of sugars.

essential. This

which

discusses

is the

Polysaccharide is the most

I t is present as cellulose to supply the

material for cell w a l l s , or as starch, etc. 4 . 2 . 1 Hydroxyethyl cellulose (HEC)

The component thHt

is

positions possible

structure of the molecule is given in F i g . 4 . 5 . The basic is cellulose the

smallest

where an

(see Appendix

A ) . Within the glucose ring

unit

molecule

in

addition o r

without destroying

the

thei’o

are

three

reaction with

other chemi.ca1s is

of

the molecule. These

the character

positions are the two OH groups and the CH20H group.

woa" C H20C y CH2OH

CH,

CHZOCH~CH~OH

F

I 1 ~6

M o l e c u l n r structii~e of

Tn the

case o f

OC H2 CH2OH

OH

hydroxyethyl cellulose

hydroxyethyl cellulose,

thra.~ CH2CHOH (hydroxyethyl)

groups are

29

as shown in F i g 3 . 6 ,

added

at

the

possible

positions. polymers

By adding other groups (methyl. ethyl, carboxyl), other such as carboxylme,thyl cellulose (CMC) or

are obtained,

ethylhydroxyethyl cellulose. 4 . 2 . 2 Xanthan

Xanthan is xanthomonaa

a. polysaccharide

campestris. It

produced by bacteria of the type

is assumed

that the

bacteria produce

the polymer to protect themselves from dehydration. The backbone different The Every the

of the

side chains

side chains

molecule is a cellulose chain having two

at every second glucose ring ( E L glucose).

also have

saccharide rings

as

basic

elements.

side chain is made up of three monosaccharides. Beginning at end of

the first

side chain

is a

mannose,

followed

gluceron acid, and then a mannose having an acethyl group at the

I

AcOCH~

I

0 /

0

II

Fig

4 . 7 Molecular structure of xenthan

30

by

sixth but

carbon atom.

it

distribution known

The second side chain is similar to the first.

contains of

a

The pyruvato

molecule

an anionic

acrylamide,

pyruvate

the pyruvate group and

unit

at

the

end

mannose.

The

within the molecule is not exactlv the two

character. Though

gluceron acids

lend

this molecule,

the

like poly-

also carries electrical charges at its side chain, its

behavior

is totally different in high salinity waters. The xanthan

molecule

shows practically

function

of rising

molecule stiffer

i s , because than the

no decrease

salinity. The of the

of viscosity

reason for

side

chain

this

yield as is

structure,

polyacrylamide molecule.

This may

that

a the

essentially also be

the

reason for its good shear stability. But if the pyruvate content

Table 4 . 2 Polysacchai%ides used in technology which microorganisms (according to CRUEGER (1986))

1

o 1 ys acchn r i d e

panthan

St I' u c t u re

~blginate

produced

Microorganism

~

Glc I D 4 Glc 3 n l Mann 6 - O A c 2 P 1 GlcA 4 p l Mann 4 f i - 0 f x r u v a t e

Xanthomonas canipestri s

~

-4 D-MannA I D 4 D-Mann 1 - - ; - 4 L - - G u l A la4 I.--GulA

Pseudomonas aeroginosa, Azetobacter vinelandi i

Curd 1an

--Glc 1 p 3 G l c -

Alcaligenes

S c 1 e r og 111can

-Glc 1133 G l c -

Sclerotium glucanicum. S . delphinii, S. rolfsii

~

by

__

~

I

1

are

~

~

1

6 8 1 Glc

~

_____--.__-

Ipu 1 1u 1 an

-

boxtran

- G ~ 'la6 c Glc -also some 1 - 2 , l - 3 . and 1--4bonds

6(Glc l a 4 G l c 104 Glc)l

--

Pullaria piillans

~ _ _ _ - . _ _ - ~

~

i

Acetobactev sp I .eu c o n 0 s to c mesenteroides I.e u c on o z i t o c dextranicum, st I'E? p t o c o c C U 5 mu t a11s ~

= Glucose, Mann = Mannose, G l c A Gluceron acid, MannA Mann-G u l o r o n acid, Ac = Acetni.e, 1 - - 2 bond between ose acid, GulA carbon atom 1 and 2 , n or 0 position of OH-group in bond (see also Appendix A )

Glc

31

becornerr wl: t h

too

h i g h the ~ ~ o l o c u lmom y birlrcrvo n i g i l e v t o polgacrylami.do

r e s p e c l . to clromicnl s t a b i l l 1.v ( p r e c i p i t a t i o n . gel f o r m a t i o n )

arid t h o fldsorptiiJri mug i r i c v n s e o . 4 . 2 . 3 Other polysaccharides

Other polysaccharides that may be produced by fermentat.ion with bmcteria profile

or fungi

scleroglucan, being

also been

that are

investigated for

disadvanlage I-eadily

a

product. that has been used foi,

production wells

which has

some others

and

are: nlginate,

modification in

to

reduce

water

cut:

proposed for polymer flooding:

listed in

Table 4 . 2 . The scleroglucan

polymer flooding is produced by fungi. The

of this

product is

that t.he

removed from

the highly

viscous broth, so that they lead

micellae

may

not

be

t o formEition plugging when injected into a well bore.

3 . 3 Degradation mechanisms

There

atTe

mechanisms

basically

t,hree different

of

types

dogrndatiot~

possible: mechanical degradation. chemical degradalion.

and biological degradation. 3 . 3 . 1 Mechanical degradation

When a polymer solution is exposed to high shear conditions the molecule mixing

may be

scissored. High

shear

conditions

occur

during

of polymer solutions. or during the conveyance of a polymer

solution

in pumps and chokes, or during injection in perforations,

or

in the

is

flowing at

formation near the well bore where the polymer solution high

velocities.

Some

of

these

mechanisms

are

discussed in papers by MAERKER ( 1 9 7 5 ) and SERIGHT ( 1 9 8 0 ) . Polyacrylamide is dation. has

But this

to be

excluded from

polyacrylamide GRODDE rate tions

particularly sensitive to mechanical degra--

sensitivity is not so severe that polyacrylamide being used for EOR. During the mixing of

some shearing

( 1 9 8 0 ) and

is also

MARTISCHIUS et

necessary

as

proposed

a l . ( 1 9 8 5 ) . In Appendix

by

F the

of shear strain that might occur during injection in perforais calculated,

and i t

may be

concluded that

under normal

conditions no shear degradation should happen. Polysaccharides are not as sensitive to mechanical degradation as polyacrylamides. and for mixing very high shear is appropriate.

32

4 , 3 . 2 Chemical degrade!. i o n

The, c ~ l e m i c a ~ effected by

mairl]y

the

dearsdo~,ionof .the presence

temperature, Divalent

influence

the

too, as

brines. I f ,

introduced

into such

FeSt

which in

such

Ca2+,

as

polyacrylamides

tendency to

magnesium, iron,

formation

solution3 is

R ~ U ~ O U T ;

of-divalent ions and oxygen, and

cations,

hsd~,olvsis of

s o ~ u t i o r l stability or

and

polymer s i n

and

MgZt

etc-9

thus

their

flocculate. Apart from calcium

~ e 2 +is present in small amounts in

from the handling at the surface, oxygen is waters, the

turn may

iron cation

flocculate

may be oxidized to

polyacrylamides

well

RS

as

polysaccharides. Temperature accelerates these mechanisms. I f the temperature is below

70 OC,

tions

of about

degree

polyacrylamide may

of

mg/1

water with a

1 degree of hardiiess

of

that

thumb a paper

performed on

but some

for every

to fresh

2 5 , where

found in

have been

SORBIE ( 1 9 8 5 ) ) ,

respect

rule

was also

investigations necessary

(this corresponds

of about

This

CaO).

manufacturers and

200 ppm

of hardness

be used up to calcium concontra-

is

given

by RYLES

by

10 mans

( 3 9 8 5 ) . MHns

this subject (see CLIFFORD

laboratory testing

particular project,

as the

will always conditions

be with

to the chemical nature of the polymer, temperature, compo-

sition of mixing water and field brine are always different. Hydroxyethyl cellulose four

pronounced positions

molecule is

the bond

reaction has

the

be attacked at the

OH-groups

in

the

glucose

as discussed above. One of these positions

between different

glucose rings.

Here any

chemical

results in a loss of viscosity. As hydroxyethyl cellulose character, i t

no ionic

actions, Some

are situated,

may preferentially where

which is

does not participate in any ionic re-

the reason

for its

good stability

in brines.

details about the reaction mechanisms are discussed by VETTER

(1980).

Above 6 5 O C most HECs tend to flocculate, as indicated by

some manufacturers. 4 . 3 , 3 Biological degradation

Biological degradation is mainly a problem for biopolymers, and preferentinlly degradation

at lower temperatures and salinities. BY biological

is meant

that the

polymer molecule

is destroyed

by

bacteria or by chemical processes governed by enzymes. The xanthan ditions

molecule may

by fermenting

be destroyed

bacteria that

33

attack

under anaerobic mainly

the

con-

glucose

n i o l e c ~ i l r ~ ’ . backbone ;

The

slahilitv

of

a

polVmer

u r i i l ~ , of

Ihr,

.;elution

against bacteriul degration should he tested under

condi t,ions polsmer high, The

Biocides

,

a r e necessary

i f the

solutions a n d , must be

used along

reservoir tempe-rature is not very

with the

biological degradation

field

for surface handling of the injected solutions

of xanthanes

as

well.

was intensively investi.-

gated by BRAGG et a l . (1983) for Exxon s Loudon field pilot. Enzymes processes

are

biological

in

nature,

po1ysacc:harides. PlRrits

appropriate

palysaccharide. temporarily

a special enzyme

catalyze the

enzymes are the

of

called hydrolases. also contain

decomposition

treatments where

different

hydrolysis

polysaccharide often

for

In reservoir

that

example

These particular

that produce

the

catalysts for

R

of

this

polymer- gel

is

used, enzymes are applied for the decomposition of the

gel plug. Enzymes d e g r a d e cellulose polymers especially well.

4 . 3 . 3 Stabilization of polymer solutions

In chemical

low concentrations

very reason

also plays

an important

role. For

this

oxygen scavengers are often applied in polymer flooding. In oxygen scavengers i t should be noted that they may interfere

using with

the polymer

polymer of

polymers a r e degraded, oxygen in

processes where

if there

should only

the oxygen

is

be added

scavenger and

still

some

oxygen

present.

The

to the mixing water if the reaction the oxygen

is

complete.

The

most

common oxygen scavengers are sulfide and thiosulfate. The most common means of preventing the formation of Fe3+-ions is

citric acid.

these

Because the

citric acid hinders the formation of

i t may be used to prevent flocculation and thus improve injectivity of polymer solutions.

iron ions,

polymers course

other chemicals

that form

of

Of

complexes with iron may also be

used. In order

to prevent biological degradation biocides are used.

Several

authors have

biocide

for EOR

chemical

that

flooding,

may

also

be

Concentrations of

concentrations effect

found that

and i t

formaldehyde is a very effective

field applications. used 500 -

as

Formaldehyde is a

tracer

2000 ppm

a low

during

cost

polymer

are suggested. Below

of about

100 ppm, formaldehyde looses its biocidal

may, on

the contrary, serve as a nutrient for some

bacteria

34

4 . 4 Polymer production

4 4 . 1 Synthetic polymers Polymers mas merisationl, In

the

case

of

polymerisation with

a

be synthesized

from a single monomer (homopoly-

or two or more different monomers (copolymerisation).

per tially

hydrolyzed

polyacrylamide

the

may be homopolymerisation of the monomer acrylamide

subsequent

saponification

as

described

above,

a

or

copolymerisation of acrylic acid and acrylamide. The technical pure

monomer

polymerisation), polymerisate

or from

settles

polymerisation), liquid

production of polymers may be done by using the substance

from a

without

out

described

the

of

~

(emulsion polymerisation). in the

solvent

of the

suspension of

(suspension polymerisation)

monomers

any

a solution

solution

an emulsion

These processes for the

the

(precipitate

non-soluble monomers

or from

following paragraphs

(substance

monomers, where

ere

in a

of

the

roughly

polymerisation of

polyacrylamide. Substance polymerisation: By irradiating solid acrylamide with

X

rays or by heating i t up to about 150 ’C, a polymer is obtained.

Its solubility depends on the intermolecular structure. Precipitate poylmerisation: regular for

organic solvents.

Polyacrylamide is

not soluble in

For the polymerisation process solvents

the monomer, such as dioxane, methanol or toluol, may be used.

A

peroxide is used as a catalyst for the polymerisation. T o obtain

a

well water soluble product the process is performed in a mixture

of

acetone and

water (maximum 10%). The polymerisate precipitates

and is completely water soluble. Suspension organic

polymerisation:

Acrylamide

medium (polyvinylacetate),

performed

in an

organic reaction

is

dispersed

in

an

and the polymerisation is then medium. A

polymerisate in

the

form of small beads or coarse powder is obtained. Emulsion polymerisation: emulgated

by means

of a

A water

solution of

the monomer is

surfactant. The polymer that is obtained

is a fine, dispersed emulsion similar to rubber latex. The processes applied to produce water soluble polyacrylamides for nical

EOR are

precipitate and

processes are

emulsion polymerisation. These tech-

of course

more sophisticated

than described

herein. A more in-depth discussion is given by VOLLMERT (1980).

35

4 . 4 . 2 Fermentation processes

Biopolymers are process

shall

production, selected

be as

produced in

described shown

strain, i . e .

in

fermentation processes.

below

in

the

example

F i g . 4 . 8 . Bacteria

from

of a

Such

a

xanthan carefully

with respect to their capability to produce

the desired xanthan, are grown in a nutrient liquid.

0-

F i g . , 4 . 8 Scheitie o f the xanthan ferrnentatioii p t ' o c e s n . 1 : s t e i ~ 1i e riiit.t,ient.; 2: ait, (sterile.); 3 : Trioculum ctili,tii,il; 3 : pt'e 7' : p r o d u z t. i o n 6: c o n d i 1. i on i n g , r e r m n n tat. i on : 5: f e rmen t. 8 Ii on ; .;torRge t.ank

The v o l u m e ii\iniber

of t h e

of b a c t e r i a

fernienter

T h e miiin

enough

large

augmented grow

l o

in in

steps until

thv

1hp

over-

T h e n i i t i , i e n l . i s e s s c n t i ~ i ll y sirgai'

some s e 1 i . s .

problem

~ ; o t.lint

ferrnnntntiorr pi'oduct.

ic;

rneasuriiig about 50 rn3.

w i t h the a d d i t i o n o f

sterile,

c u l l . i r ~ ei s

in

no

Fei*menI.ation i s

other

is stoppod

that is obtained

bitcteri(4

by c 2 n d i n g i s

ii

or

t.o k e t t p

fungi

the CHIL

fermentor. grow.

The

the \ ( ~ n t i l a i . i o r i w i l h e i r . T h e

s ~ l l o w i n h ,h i g h l y v i s c o i ~ sb r o l h with

a

concentration of

depending

on the

active

polymers

between

micrograph

4

percent,

In

containing

dead bacteria is shown. The bacteria are separated from

another in

a

and

bacteria. one

Fig.4.9

2

and the activity of the

fermentation conditions of

a

fermentation

broth

the solution, The length of one bacterium is about

0 . 8 um.

The product

may be

concentrated

by

precipitation

with

an

alcohol and subsequent vaporisation of the water up to a powder

Fig. 4 9 M j (

i-ogi

aph of

pl'ade,

by

( 1 1 I . 1 . a - f i 1 tral

or’

p a r c ~ r ~ t ,It, i:;

d

xanthan broth showirig dead hacterjt\

itin

c!vidcri~t that.

3

i s

t.hc

r ' d ~ i i i lt . .

iii

~ ~ ~ ~ l i t i oc:oc;l:: t i ~ l in

relatively l o w

I.i.irn’;po~~I.al ion

high

ndtli t i c > r l a l

field.

costs.

up

t.o

c o r i c . ~ ~ ~ i 1 . i ~ ~ l t oi f~ r 1 1 s 0-12

{he ~ ~ i ~ o h lwith em such

R

fermentation

concentration o f the pi.oducI. This concen1rat.iiig o r ' d r , y i i i g i t , o r i n

I n using

a high concentrate or powder

a l s o arise in mixing the polymei. at. t h e o i l

<:ost.s w i l l

Putting a powder into solution requires more steps a n d more f o i - mixing

H I I ~ I ' ~ ~

and shearing than does the dissolution of

8

low

concen t r a l ion broth. Orie way

oil

field,

Rdvaritages fermoritat ion

the

to avoid these costs i s to produce the polymer at the where

a

c:oritinuousls

woi%kinr; p r o c e s s

will

have

o v e r a bHt.ch-w i s e production. I r i R continuously workirig

process, the

f(1rrnenter.d f l c r

product is

the latter

withdrawn f r o m

has bean

17

brought

one side o f

stepwisct

into

production,

and the

problem

continuous

in

nutrient is

fed in

fermentation

is

from the other side. One to

keep

the

fermenter

sterile and to sterilize the nutrient.

REFERENCES Bragg, J . R . . Maruca, S . D . ,G a l e , W . W . , Gall, L . S . : "Control of Xanthan-Degrading Organisms in the Loudon Pilot: Approach, Methodology, and Results", SPE 11989 (1983) Clifford, P . J . ,Sorbie, K . S . : "The Effects of Chemical Degradation on Polymer Flooding", SPE 13586 (1985) Crueger, W . and A . : "Biotechnologie-Lehrbuch der angewandt.en Mikrobiol-ogie", Oldenbourg Verlag, Oldenburg (1986) Fieser, L . F . , Fieser, M . : "Organic Chemistry", 3*’d edition (1956) Grodde , K . --H. , Schnef er , W . : "Erfahrungen in der Anwendung von Polymer als Fluthilfsmittel in Dogger-L.agerstatten des Cifhorner Troges", Erdol-Erdgas-2. (1978) 7 252-259 Grodde, K . - H . : "Verfahren z u r Scherbehandlung waessriger Polyacrylamidloesungen", FRG Patent DE 27 33 852 B2 Inl.Cl. E 21 B 43/22 (1980) Hille, M . : " V i n y l s u l f o n a t e / V i n y l a n i d e Copolymers i n Drilling Fluids for Deep", High-Temperature Wells, SPE-paper 13558 (1985) Maerker, J . M . : "Shear Degradation of Patially Hydrolized Polyacrylamid Solutions", SOC.Petr. Eng. J (1975) Meister, J . J . , Pledger Jr.H..Hogen-EschT . E . , B u t l e rC . B . : "Retention of polyacrylamide by Berea sandstone, Baker dolomite,and sodium’kaolinite during polymer flooding", SPE-paper 8971 (1980) Phjlipoff, W . : "Kolloidchemisches Taschenbuch", Editor: A . K u h n ; Akademische Ver,lagsgesellschaft, Leipzig (19441, p 327 Ryl e s , R . G .: "Chemical Stabi 1 i ty of Water-Soluble Polymers lJsed in Oil Recovery Processes", SPE 13585 (1985) Sevjght, R . S .: "The Effect,s of Mechanical Degradetion and ' d i s c o E l a s l i c Behavior of Polyacrylfimide Solutions", SPE 9297 (1980) Llnsal, E . , Duds, I . . J . , K l a u s , E . : "Compfirison of Solut,ion Propertior; o f Mohil ity Con-trol Polymers", in: "Chemistry of Q i1 Recovery", JohHnsen arid Berg (editors), ACS Syposium S e r i e s (1979) 91 V e i t e ~ , ,O . J . , T y s s e e , D . A . : "Chemical Characterizetioil Prohlrn~s o f Water Soliihle P o l ~ v m e ~ ~ SPE i ' ' , 8977 (1980) Vol linert , B . : "Grundris:: der Makron~oleki~larenChemie" , B d ,4 p . 1 3 E . Vol.lmer-t Verlag Karlsruhe (1980) o r Polymer Chemi stry,Springer. Verlag N e w York ( 3 973) V o l z , H . V . : " A Method for Reducing Polymer Retention in Chemical Flooding for EOR under High Salinity Conditions", Proc. ACS Division of Polymeric Matei,ials: Science & Engineering (1986) 5 5 055-859 Willhite. G . P . , Dorninguez, J . G .: "Mechanisms of Polymer Retention in Porous Media", in: D . O . S h & h , R . S .Schechter (editors): "Improved o i l recovery by surfactant and polymer flooding" Academic Press (1977)

5 PHYSICS OF EOR-POLYMERS

5.1 Rheology Engineering of with

petroleum reservoirs

the description

of fluid

flow in

deals to porous

a great extent

media.

For

this

the rheology of pseudoplastic liquids, like aqueous polymer

reason

solutions, includes

should be given close attention. Therefore this chapter

some basic

definitions as

well as

a discussion

of the

most important physical laws concerning rheology

5 . 1 . 1 Definitions In the following, some definitions are given that are necessary to

describe fluid

shown if

in F i g . 5 . 3 , the solid

two parallel

body

flow. If a force is applied to a solid body, as forces of

i s sheared

length I,,

at the

is strained over the distance 6 1 , or

different directions

angle y .

The distance

is the linear strain F , and

a r e applied, the 61 divided by the

y the angle of shear strain.

F Fig

c Y

6 . 1

S ~ I ~ H and ~ Ishear. I o f a solid bods

= 61/1*

1 inear s l pain

angle of shear

39

s l r ~ i t i

( 5 . 1 .a)

(5.l.b)

The chengw

OP sl.t-ein

HS

' . n f u n c t i o n of time,. i

- 8 .

l.hu

tnn1.e of

s t r n l r i is g i v o n by t h e o q i i n t i o n

€

=

d€/dl.

The f o i - c e that c a u s e s lhe strain rate nornielized by the a r e a t o which

0

=

it

is n p p l ied. is l . h n stress

F/I\

(5.3)

stress

Stress has t h e same dimension a s pressure. and the strnjrt r a t e has the dimension o f reciprocnl time.

f 8.i

Friction lnws

Fr irtjon law.; describe the relation

of

stress tirtd

s1 r n i t i

( 5 . 4 ,b )

Liquids f o r

which the relation between stress and strain is a

simple linear equation are called Newtonian liquids.

y

(5.5)

U/Ll

The constant strain

rate is

JJ

s-',

stands and

for viscosity. that u f

Since the dimension of

stress is

the

same

as

of

a

P H = ? ? / I I L the ~,

pressut.e

Ihn

visualize h y p o i 1 ~ e l . cal i

and

H

A

chsractor

physjcal

experiment s h a l l

m,~vshln p l a n e is d . To

ihickries.;

with

dimerir;ion of

corist.arit

IUOVG

the

of

v i r ; c o s i tg

he perfoi’med.

thin

layer of

then

P a ’ a . To

the

following

Between a fixed wal 1

a liquid, which has t h e

the platin (having the area A ) along the wall

vclocily

5 . 2 For Fig. v i s c os i 1.Y

H

viscosity is

\*

the force F i s needed (see F i g . 5 . 2 )

explanation

of

the

physical

character

of

(5.6)

The constant liquid: the only the

i t is

is a measure of the frictional properties of a

y

the viscosity or dynamic viscosity. In equation 5 . 6

same correlation difference being ratio of

as in

equation 5 . 5 is represented, with the

that the

rate of

shear strain is given by

a velocity to the distance within which the velocity

decreases from a particular value to zero. The Newtonian simplest.

model of

But there

friction in

fluid flow is surely the

exist, of course, other friction laws, depen-

ding on the characteristics of the fluid, as shown in Fig.5.3.

41

a

b

c

b'

a'

C'

.P

.-i ID c L v) L

m al

r

v)

+ 0

c al

m

a

00

Stress, U F i g 5 . 3 Different types of flow curves

C u r v e b is that of the Newtonian fluid, whilst curve b’ is that

> f t h e ideal B i r i g h a n i body

y

I :

-

(IT

up

must I S

ao)

(5.7)

/ U

represents

be applied

a threshold before the

called plastic

value, i . e . a minimum stress that

fluid starts to flow. The viscosity U

viscosity. The

other types

of flow curves are

represented by equations 5 . 8 ( a ’ , c ’ ) and 5.9 ( a , b).

(5.8)

(5.9)

For N

curve

> 1 and

u o = O the curve

EI

is obtained. This type of flow

describes the behavior of polymer solutions usually employed

42

EOR

for

In

e r ~ c ~ l l ~m eo ?r ~e ~ c o m n i o n l y used

notation. with n=l/N and

r = H e N 3 equ~tiori 5 . 9 is written

Accordir~y to viscosity

the viscosi ty of Newtonion liquid.;. the apparent

o f these

’pseudoplastic’

liquids

may

be

defined

as

follows.

(5.11)

Equation 5 . 1 1 petroleum liquids. of

i s usually

indust.ry are If the

a viscosity,

referred

to

when

people

in

the

speaking of pseudoplastic or non-Newtonian

apparent viscosity which is

shall also have the dimension

expressed in

P a ’ s , then the constant H

must have the dimension P a . s n

Fig.

5.4

Construction of

fluid flow through a short cylindrical

pipe

43

5 . 2 Flow in cylindrical pipes 5 . 2 . 1 General flow equations If

In Fig.5.4 a short cylindrical pipe with the radius a is shown. a particular hypothetical cylinder of radius r

we consider

within a

to

the pipe,

fluid is outlet of

the surface area of this cylinder is A=27cr’l. If

flowing through the pipe at a pressure drop from inlet A p . then

a force

F=

7cr2*Ap is

acting

upon

the

cylinder surface. The stress at radius r is

(5.12)

The total liquid flow rate through the pipe V is given by the integration

of the

infinitesimal liquid cylinders where the fluid

flows at the velocity v .

The relation between volume flow rate V=dV/dt and stress may be derived as follows

Integrating this from

v to

0 , and

equation within

correspondingly for

the limits for the velocity the stress from u to w ( w =

a,Ap/21 is the stress at the pipe wall, where v=O) yields

v

(21/Ap)

w/

f(u) do

(5.15)

U

B y putting v of equation 5 . 1 5 into equation 5 . 1 3 one obtains

(5.16)

"[

By substituting x = 3 / 2 o 2 and one a r r i v e s e t t h e f o l l o w i n g : a,j

f(o) d v

y

, x’=

a

and y ' = f ( c ~ )

(5.17)

45

This equation describes the relation between volume flow rate and stress for fluid flow in cylindrical pipes in a general form. 5.2.2

Flow of Newtonian fluids in pipes - Hagen-Poiseuille s law

F o r Newtonian fluids the friction law is stated by:

IIsing equation 5 . 1 5 results in

cr3/p

ilnd with

w

do

(T

a3/w3)

.

(w4/4u)

= (za3/4u)

w

= a Ap / 2 1 , one obtains

(5.18)

This equation

is well

known as

Hagen-Poiseuille s

law;

it

tiescribes the laminar flow of a Newtonian liquid through a pipe. Laminar flow of pseudo plastic liquids through pipes

7.3.2

The same applied

iiescrjbes Ihr

procedure as

for pseudoplastic the laminar

pipe is

riot a

above for liquids

flow through

Newtonian

to

derive

liquids an

pipes. Since flow velocity in

a mean

rate of

shear strain

and put an

,~pproj>riate apparent viscosity into Hagen-Poiseuille s law. The friction law for a pseudoplastic liquid is

( 7 )

= r

be that

constant but varies with the radius, i t i s not

~.irfficierit to c,slculate

I(

may

equation

oN

Hr~ewi th the integration of equation 5 . 1 7 yields

46

r

n a3

9 = -

,N+3

~

w3

(5.19)

3 t N

I f the average velocity of the liquid in the pipe is the volume flow rate divided by the pipe cross-section

then

the pressure drop in the pipe and the rate of shear strain at

the wall may be calculated. Using n=l/N and r=H-N

(5.20)

3ntl

i,=- n

? -

(5.21)

a

5 . 2 . 4 Reynold’s criterion During the flow of liquids in pipes the pressut’e drop increases significantly reached. I

disturbed. turbulent

as a

as s o o n

Instead o f This is

critical value

laminar flow usually

called

flow occ,urs at. Reynold

the

in flow

observed

turbulent

velocity

streamlines flow.

numbers greeter

In

is are

general

than 2320. The

Reynold number i s defined as

( 5 22)

O r - , oxpressed n s may

H

evil j , e I

vcl

i l y

f o r N e r u t o r i i n r i liquids, i l

he w r i l ten

(5.23)

47

U s i n g eqimtiotis t.irrbrrlon1 f l o w

5 . 1 0 and

s ~ . H I * ~ . Rl

T h i s show!;

l.hn crilical v n l c > c i t y o f

that

t . h ~ nt h a t

sigiiif i(:aritl? h i g h e t .

is

the

r'etison why

for

in

flow

5 . 2 1 , tho R n y i r o l d ' s numbnt* a t which

o

polynters a r e

pipe

Flow

i/

streill iiist

curves or

t.unients

6,

where

the

this

D.

relation

tho s t r a i n

ti)

measure

v i s c : c ~ m e i . e r s . IJr;iially two <

c i l l i : i i l ~ t i o ~f~o r

flow curves

describe

used

T h i s ir;

l i q u i d s a s "di.ag. t ~ o d u r : e r ~ : "

typiral

A

" ~ I i e r i ~ ~ t n e n o i!; n" g i v e n i n Appendix

5 . 3 hleasurenleni. uf

f o r Newtonitin liquid:;.

added to

lines.

p s e u d o p l ~ s i . i cl i q i i i d s

usually these

different

d p i l l . H r y or t u b e v i s c o m n t e r s

and

sires5 n

of

and

i,nte

( i f

is w s h e a r s t r a i n . T h e flow

l.,ypes o f

curves

a1.e

cal 1ed

v i s c o t n e t ~ t ? ~a~r nc i i s e d :

r o t ~ t i o n e lv i s c o n l e t e r s .

Tube Viscometers A

8

Flg.

C /A

5.5

Fenske.

\

C a p i l l a r y v i s c o m e t e r s . a ) O s t w a l d b ) Ubbelohde c ) Cannon A , B , C , a n d D a r e filling or t i m i n g m a r k s

48

5 . 3 . 1 Capi 1 1 ~ 1 . yvisconreterss

In c a p i 1 l a i . y Capil

1at.y

viscoineters, viscosii,y can be mensured directly.

v i ~ ; c o ~ n e f e r . IIIBY s

The tYpicR1

vis(:o!:i 1 y .

be caliira-Led with fluids

make-up o f

r;uch instruiiier~ls

of a

known

i s sliowri- in

Fig.5.5.

I n these

viscometers the flowing time t through tho capillary

of

a known

If

the f l o w i n g

v-iscosity

of the liquid

volunie

time t o

measured before,

wns

)to

t.o be investigated is measured.

for the same volume of a liquid o f known

then

the

viscosity

for

the

liquid is

Different

densilies of

the calibrating

liquid and the liquids

.O

be measured should be considered As shown above the stress w at the tube wall is

Since

the viscosity

and

the

of shear

viscosity

are

also

directly,

(i/ =

T o obtain flow curves the viscosity must be measured at

U/LI),

the rate

apparent

meaCjurPd

strain may be calculated

stresses. This can be done by measuring the flowing time For these different pressures applied to the capillary

different at

measurements viscometer

a

capillnry

of the

atmospheric

viscometer

Ilbbelohde type

pressure. Another

must

usually

mod fied,

be can

only

as

measure

way to obtain differen

a at

stresses is

to use capillaries of different diameters or lengths. The constants rising raG

r

or n and H may be obtained directly by

equation 5 19. If the log of the volume flow rate divided by is plotted

gives

N and

N and

versus the log of stress w , the slope of the curve

the intersection

at the

ordinate yields

r / ( 3 t N ) as

shown in Fig. 5 . 6 . The results of measurements with capillary viscometers may have an

error due

pressure

to

drop may

end

effects.

occur when

This

means

the liquid

capillary. Although such end effects

49

that

enters

cannot be

an or

totally

additional leaves

the

avoided,

log

w

5 . 6 Plot of volume flow rate versus slress t o obtain N and from measuremerils with capillary viscometers.

Fig.

they the

can nevei*theless be minimized capillary inlets

effects

may be

ahd outlets.

measured by

by lending The

r

a special form to

influence

of

these

end

letting the liquid to be investigated

flow at a particular rate through capillaries of the same diameter

2 ci 0

U L L W

3 vl vl W

&

Capillary length, l Fig. 5.7 Pressure drop capillary viscorneters.

due to

end effects

50

in

measuring

with

diffni.ari1. 1 c ~ n g l . h s . l3v plcill

but.

versus

tube 7nngt.h

Ihe

the

iiig

~J'C+SSUYC?.

measrirod

d r o p dun

pressure

effects mag be

end

1.0

drop

determined as shown in Fig.5.7.

I f viscosity culated

during flow for

directly, e . g . law

Poiseui l e ’ s factor

through capillaries

Newtonian

liquids

( E q u . 5 . 3 8 ) , knowledge

i s necessary.

by

the

of

is to

be cal-

using end

Hagen-

correction

The Hagenbach correction gives the following

form to Hagen-Poiseuille’s law

Whe1.e

a factor that has to be measured.

c ’ is

I f pressure is kept

constant, this equation may be written IJ

= A’t

A'

B’/t

-

and B’ are constants for

the

flowing time

for a

R

particular tube viscometer. nnd t is

well-defined volume

of the

liquid to be

measured. Especially while such

as

measuring liquids with an elastic character,

polyacrylamide

solutions,

end

effects

may

become

a

problem.

5 . 3 . 2 Rotational vjscometers In rotational gap

between

cylinder torque

proportional the

also

the

rotated at other

mounted

cylinders.

a constant

cylinder

is

angular

measured,

While

one

velocity,

the

This

torque

is

to the stress that the liquid flowing in the annullus

to the

cylinder wall. The rate of shear strain applied to

liquid depends

angular shown

concentrically

is being at

applies

viscometers the liquid to be measured fills the

two

on the

velocity with

geometry

which the

of

the

cylinder is

cylinders

and

the

rotated. A s will be

later for non--Newtonian liquids, the rate of shear strain is a function of the liquid’s properties. The typical setup of a

rotational viscometer is shown in Fig. 5.8.

51

c

I

I

i i

h

I Fig. 5 . 8

Typical setup of a rotational viscometer

D that is measured at the non-rotating cylinder is

The torque proportional cylinder

to the

wall with

stress applied

by the

liquid flowing to the

the distance R 1 from the center and the wetted

A , which is 2 z R 1 times the height h u p to which the system is

area

filled with liquid.

(5.26)

The torque normalized to the length 1 is G . where

Thus. in talculated shear

strain m u s t

liquid. one

a rotational

directly from

viscometer, the the measurement

be calculated

shear stre’js u o f torque

may

be

Thc ralc of

from the flowing velocity of the

This velocity depends on the angular velocity 0 with whtch

cylinder is

rotating, while

the

52

other

cylinder

where

the

torque gap.

is measui,ed, stands still,

The whole

hypothetical with

a

and the

setup of

the apparatus

experiment as

shown in

liquid between

them are

width of the cylinder

is similar to that of the

Fig. 5 . 2 ,

where two planes

moved against

one another at a

determined velocity, but with rotational symmetry. The angular between 0 strain is y

r

is

n. By

and

definition

= dy/dt. For

mN

~

velocity of the liquid in the cylinder gap varies (Equ.5.2b), the rate

pseudoplastic

(Equ. 5 . 9 ) .

of

shear

liquids, the friction law

Applying this friction law and equation

5 . 2 7 gives rise to

i/

r’dW/dt =

Case a : while the

r

( G / 2 ~ c r ~ ) ~

the torque

the other

(5.28)

is being

measured at

the inner cylinder

cylinder is rotated. A s the torque is measured at

inner cylinder, the corresponding rate of shear strain

must,

be

calculated at the inner nyljnder wall,

(5.30)

(5.31)

A

lypicml constant of

t h e instrument is the retin of t h e irrtier

and outer- cylinder i,adius:

(5.32)

Using this

ratio i n

equation 5 . 3 1

equation :

53

leads

to

lhe

following

(G/2zRl2) i s a c t u a l l y t h e s t r e s s u a t t h e i n n e r

Since the t e r m

w a l l with

cylinder

R1,

radius

the rate

of

shear

s t r a i n may

be

c a l c u l a t e d by a p p l y i n g t h e f r i c t i o n l a w ( E q u . 5 . 2 8 ) a t r a d i u s R 1 .

the rate

This produces

shear s t r a i n at the inner cylinder

of

wall:

(5.35)

Thei,efore t h e velocity, depends

not

a

r a t e of

constant parameter

on t h e f r i c t i o n l a w o f

Newtonian calculated

d i r e c t l y . Foi.

if

flow

is;

curve

sho.wn

Ic,g$

different with

diffei,enl N

Llie

1 ) . plot

of

i/

Usually

of

vei,:;us

liquids,

in

shear which

thus

ri

strain

uijo

with be

typical

flow

i t

may

01’

are

slope

es!;ontialIy

i n - t o lwo

theit

two

moi-e p a r l s

be

somf?rvliiiI

a f l o w c u t - v e . To g e t t h e is

assumed

t h e new

curves

have c o n s t a n t

c u r v e s show

shows

may

be

the

’ r i g h t ’ v a l u e s of

arid

strain

a t a p a r t i c u l a r p o i n t of

be d i v i d e d

s I ~ . a i r i w i t h an

shear

only

N ~ r i i t e r a i i v e pr’occ)ss

sheat,

1 i o n o f y , an(]

rate

the

l o obtain

rather

s u c h a s EOR-polymers

these curves

values. T h i s

values for ratr

may

of

shear

examples of

p l o t . The o t h e r

logo

s l o p e s and

difficult

right

-

of N

exact, v a l u e

k n o b n , Some

annular

apparatus, but

rate

the

r a t e of

F i g 4 . 4 O n l y a few o f

iri

in the

the

the

other liquids

p~eudoplastic behavior, the calculated

of

a given

t h e f l u i d s t o b e measured. Only f o r

N = l may

l i q u i d s where

is, at

shear s t r a i n

N

!:uggor;lt!d:

vnlue

caloulate

N (e.g.

for

f o r anoI.ho!

cslvula

on.

tic

EOR p u b 1 i c ; a t i o n s d e a l i n g w i t h p o l y m e r f l o o d i l l y i h e strain is

is

c a l c u l a t e d wi-t.h

not corre(-t.

The

54

ei’r-ot’

N=l

as

made i s

for

Newl.oniari

about

1 0 % . An

typical

r,tilriiI~tion

calculations that

t h e appai-erit

measurement verb

given

b.

irt

Appendix

C.

Hence

for

all

p o l y m e r f l o o d i n g o n e m u s t k e e p i n mind

v i s c o s i t v b e i n g used may n o t be c o r r e c t , as t h e

made w i t h

s i m p l e , may Case

is

b e i n g done for

a rotational

v i s c o m e t e r , though

it

looks

riot b e c o r r e c t .

for

measuring

at

the

outer

cylinder,

the

same

c a l c u l a t i o n may b e d o n e , a n d

(5.36)

Tn t.he were the

t h e c y l i n d e r systems

t.he c y l i n d o r

i s a l s o a p l a n e , and

neglected.

If

t h o bottom o f

d i s t a n c e between w ~ t l l ~t h~e ,

cylindei.

must

above c a l c u l a t i o n s end e f f e c t s of

a l s o bo

sheel,

s

11'23

flowing c.e~iter

i

11

liiken nrid

velocily

these planes

c : o t i I r i b i ~ t i o n of

mi+Fi~-,ui'cd

the l i q u i d

~ ; o i n i ~n s t . i ~ i r m e r ~ t sa

a:.;

a t

d e p e n d s on 11s

pl.ate

t.he

end parts

t.he d i : ; t a n c n

the

fi,i-)m t h e

tind c.ono a:; shown i n

Fjg. 5.9.

,\\\\\\\\\\\\\\\\\,\\\\\\\

the

t h e insl.runinnI.

~ ~ l ~ u l k ~ tloi o t , hnr 1 . 8 1 ~o f

t o r q u e , As

r e buill

t h e gap between

I h e s e p ~ t ' t so f

iiito ~+ccoi~n -iii t the

tht?

in

small

HS

\\\\Y R

I n t h e p l ~ i l cand r o n e system the rjse in flowiria veloritv when from the

going

center

compensat~d by the

to

the

outer

growing distance,

parfs

of

and thus

the

system

is

the rate o f shear

strain is constant for Newtonian ljquids Another way to minimi38 the error due to end effects is to use n

double cylirid~t-system as shown in Fig. 5.10.

Fig. 5.10 Rotational viscometer with double cylinder system

With such a system the stress at an inner and an outer cylinder system rotated

is measured. So i f , for example, at a

constant angular

the cylinders 1 and 4 are

velocity, the rate of shear strain

the inner wall and the outer wall of the middle cylinder ( 2 / 3 ) ,

at

where the stress is measured, should be the same.

Y1

=

(5.37)

Y2

when

56

S1

1

H2/R1

The

obeyed

i

H I I ~

Sp-

elation

( 5 38)

H J / R ~

between tlic

two cylillder systc,ms thtit ~ ~ l i o u lbt= d

i r . given b y :

(5.39)

T t is

obvious t h n i

Newtonian

liquids;

must n o t

such syslems for

and

Newtonian

be used

liquids

for n o n N=l

with

the

fullowing equtttion is v a l i d .

s p

s22

t

=

2

(5.40)

This mefins impossible, Sl

=

01'

that o n l y

f o r cylinder systems with S - 1 ,

which is

for systems with S near 1 , the convention of taking

S 2 may be used.

5 . 3 . 3 Other. viscometers Besides tube exist; fluid A

and

one other

rotational

main class

flows around

viscometers

thereof are

other

instruments

instruments

where

the

a solid body, which is in most cases a sphere.

well-known instrument of this type is called the Hoeppler visco-

meter, time

where a

the ball

measured,

ball is needs

and the

rolling in

for

a

FA

defined

viscosity is

slightly deviated tube. The distance

in

calculated from

the

this

tube time.

is

The

principal setup of this viscometer is shown in Fig. 5 . 1 1 . As

the

calculate, curves for

fluid flow

in the

this instrument

of polymer

Hoeppler viscometer is not easy to

is not

solutions, This

viscosity measurements

suitable

for

measuring

viscometer is

flow

usually applied

of live crude o i l s , because it is easy

to measure under high pressures. Another instrument which

is

a

is called

rotational

the

viscometer

Zimm-Crothers used

to

viscosities. I t is described in the next chapter.

57

viscometer,

measure

relative

Measuring Tube

Ball

Outer Tube Measuring Distance

Spirit Level

/

Tripod

Calibrating Screw

Fig 5 . 1 1 Principal setup of the Hoeppler viscometer

5 . 4 Molecular s i z e , structure and viscosity The viscosity of a polymer solution depends on the size and the struct.ure stages by

of the

of colloid

molecules that

are dissolved.

In

the

initial

science, the first systematic research w a s done

STAUDINGER ( 1 9 4 4 1 , 0STWAL.D ( 3 9 4 4 ) , and KUHN (1944). Before some

aspec.ts of the dependence of the viscosity behavior of a liquid on the ing,

characterjslics o f

the molecule

are discussed i n the follow--

the essential definitions and terms about viscosity are given

in Table 5 . 1 .

58

fr>rmulat.ndthe following l ~ i w aboul t h e ~ ' e l a -

ETNSTEIN ( 1 9 0 6 ) tion

belwec?n the

resulting v i r , c o s i

N*

s i z e of l y

t h e number-

is

dir,solved splierical

V the volunte of the solution. The ratio o f

the

particle N * . v

to the

porosity.

Einstein’s

’porosity’

influences the

of the

particles

icles n n d

of part.iclos. v the volume of

and

size

porl

the

[ i f the solution.

particles

pai,t.icle,

volume of the liquid is compavable to a law

visc0sit.y or

OIIFL

the total voliinie of

viscosity of their

states

that

only

this

the solution, and not the

number.

This

means

that

lo3

of volume 1 result in the same viscosity as one particle

of volume 1 0 3 .

A 5 N*=b.I.,/M ( b = amount of soluted substance; M = molecular weight; I, Avogadro’s number) equation 5.41 mag be written

(5.42)

and as the concentration c is b/V

(5.43)

59

Macromolecules in globules, these

but more

filaments

cylinders the

that of

may

be

v=n;r21, where end by

~iic~lecule is

not have

long curled

approximated 2 r is

the form

of

small

filaments. The volume of by

the

volume

of

small

the diameter d and 1 the length of

the diameter of a particular macromolecule is

cylinder. Since

constant, the

solutions do

molecular weight only the length of

varying the

5 . 4 3 may

changed, equation

be

written

in

the

following, simple form

where

cIIl is

the concen1.ration

equ~t,ion says t.hat weight, we

niolecular

not

s

tr.ue, for

weight,

macromolecule on

with respect to t.he moi~omer~s. This is

not

a

function

of

molecular.

but only of the concentration of the monomers. This is, as

know,

diameter

viscosity

may be

is also

I.he molecular

The

viscosity

assumption

approximated by

not true.

increases that

the

with volume

increasing of

the

small cylinders of constant

The volume of a macromolecule depends

weight v=f(M), forming a

non-linear curve. Some

t.ntistica1 assunip-tions lead t o the relation

(5.45)

(M

mean molecular weight),

This, together

with equation 5 . 4 3 ,

1 eads to

(5.46)

The influence of different conformations of the molecular filaments, sidered

of temperature,

in the

and of solvent on the coil volume, is con-

molecular weight

- viscosity

Houwink. as follows:

60

equation by Mark and

By determination information may

weight.

The stiffer

deviates from

In the

the more its

rising

stiffer the

coil decreases

in. turn

polyacrylamide

means

has the

stiffer xanthan

means the

of the

which

chain is,

curl with

polyacrylamide chain

type. This

density

a molecule

a random

in F i g . 4 . 3 , and the

rod

and the exponent a , some

molecular

case of EOR-polymers, this means that the molecule

the flexible

shown

constant K,

about the conformation of the molecule in the solution

be obtained.

conformation of

of the

that

the exponent

form of a curl, as

molecule i s more of a

chain

is,

with increasing the

a in

exponent the

the

more

the

moleculfir weight. is

a

higher.

For is

Mark~-IIouwink equation

about 2/3, and for xanthan i t is close to 1 . The constant

K,

may

be described

by t.he

following equation

derived by VOLLMERT ( 1980 )

(5.48)

the factor Fm is a measure of the deviation of the coil form

where from

that of

lmon

chain, and Mmon

a sphere, AmO is a measure of the flexibility of the is

the length

Because, e g . affected least that

of a is if

molecular shear

this viscosity

of shear

molecule is

also

strain), which

at

altered, the vis-

should be measured at ’zero’ shear,

is to be used for the determination of

strain, constructed by ZIMM and CROTHERS (1962), is shown in

and

stator are

swimming

is

of the

is

weight. An instrument for measuring at very low rates of

5 . 1 2 . The

the

liquids, viscosity

forces (rate

the size

polymer solution

Fig.

that

structural unit of the molecule,

for pseudoplastic

by mechanical

means that

cosity

of a

the molecular weight of the monomer.

in the

i t is

instrument is made of

a rotational

glass tubes.

liquid to

The

viscometer, the rotor inner

glass

tube

is

be tested, i t is equilibrated in a way

wetted up to its border so that the surface tension of

liquid keeps i t centered. In the inner cylinder a metal pellet f?xed so

that i t will rotate

when a magnet is rotated outside

61

tho

whole s e t u p

by means

of a

synchronous mol.or.

The

relative

xiscosity is obtained by the ratio of the rotational

Circulating Fluid Inlet Tube Meniscus Rotor Stator Steel Pellet Iron Pole Piece T e s t Fluid Magnet

Motor Shaft Synchronous Motor

F i g , 5 12 Schematic diagram of Zimm-Crothers viscometer

l > r ? r i ~ > i i sof

the

ild\,nniages o f shear

t t i t , i ~ s of

the1.e is

hf?r:nu!,e c,i

rec:~,

r o t o r for

the

the test

instrument a r e ,

strain a n d ,

solution and the s o l v e n t . T h e first., that i t measures

s e c o n d , that

i.1

is

very

a t

low

sensitive

no ~~dditional friction i n a device that measures

such a s in the ball bearings of other viscometers.

5 . 5 E l a s 1 i c vi s c o s i ty In

the

flow of

a l i q u i d , linear strain i s another mechanical

foi,ce besides shear strain which effects a molecule ( s e e F i g . 5 . 1 ) .

I inear

s t r a j n occurs

during the

f1.ow of

a polymer s o l u t i o n when

the

flow velocity c h a n g e s , and if this chenge is relatively rapid.

The

equtition that describes the relation between stress and linear

strain

j s

called Hook’s law

o = E . E

(5.49)

62

E is

the elasticity

module. Analogous t o s h e a r v i s c o s i t y , an

e l a s t i c v i s c o s i t y may b e d e f i n e d

h = u/€

(5.50)

is

observed

when

particular rate;

t h i s may

occur in

This e l a s t i c strained

at a

viscometer gular

when

viscosity

the

cyl-inders a r e

v e l o c i t y , but

rather a t

not

a

one.

e.g.

-is o s c i l l a t i n g a 1 ci p f i r t j c u 1 . a r f r e q u e n c y . A

cylinder rate

may a l s o

rate

chnnyn!;

bot tltsnncks.

be produced

molecule

is

rotational

r o t a t i n g a t a c o n s t a n t an-

changing

n

the

when

one

linear strain

i n f l o w i n porous rnedie, where t h e f l o w

sigrlificnrltls

when

the f l u i d is flowing through pore

I n hot11

the

m o l e c u l e r e a c t s w i t . h EL damped 0 s - -

C H T ; ~ S

ci 11a t i o n .

The gener,al f o r m o f t i l e d i f f e 1 , e r l t i a l e q u a t i o n t h a t d e s c r i b e s a n i n d u c e d damped o s c i l l n t i < > r io f

. . inx t c x t F x

Fo i n quency.

=

Fo

H

rnnss

point

i s

wt.

(5.51)

L C ~ S

the+ f o 1 , c : n

With k = f i / 2 m .

that

i n d u c e s t.he o s c i l l a t i o n , a n d W i t s f r e -

W o 2 = c / m , arid f o = F o / m , E q u a t i o n 5 . 5 2 b e c o m e s

.. x t

2kx t W o 2 x

and f o r W o 2

=

> k2

(5.521

f o coswl,

t h e s o l u t i o n of

t h i s e q u a t i o n becomes

(5.53)

63

T h i s d i f f o r o t i l i a l equation arid its s o l u t i o n are o n l y v s l i d for

thi:

o s i . i l 3 r i t i o n of

only

p o i n t ' , and

n iiiissfs

i t s representntion here is

t o p r o v i d e n iiiearir; of visualizing t h e physical bar;kgl*o(Jtbd. An

anHlc,goias an

e q u a t i o n mny

be d e r i v e d f o r a system o'f mnss p o i n t s , by

a largw niolecule may be r e p r e s e n t e d . E q u a t i o n 5 . 5 3 desc1.i bes

wh i c h

undamped

harmonic

oscillation

o s ~ . i l l n t . i o n . The r e l a x a t i o n

together

tiroe f o r

with

the damped

a

damped

oscillation

is

de iI o t e d by

e =

i l k

of

an " e l a s t i c " polymoi. s o l u t i o n . T h e dimensionless D e h o p H h riuniher,

( 5 . 5 3 )

Thir;

D,.

r e l ~ ~ x iao lr i

which is

is

i s o f t e n used

1:irne

the r n l o o f

i o

der;c~.ihc?i h e

p t , ~ p e i 'ies l

linear sttsain times the relaxatjori t i m e ,

o f t e n a 1 5 0 ti>;ed t.o describe the elastic propc~rtins o f

R

polynii~r

solution.

(5.55)

5

'>

1 Measuring

elastic viscosity

Measuring elastic viscosity r e q u i r e s a dynamicthat

mean5 that

the applied

shear streqs

tesl

changes in

ing method a harmonic

mariner

C T

(5.56)

00 cosut.

This oscillating shear stress produces a strain

y = yo cos(0t-6)

where

viscous

the phase

(5.57)

lag 6

properties of

is a

measure of the a m o u n t of elastic and

the liquid.

64

I f the liquid h a s only viscous

elastic

propri’ties the

visualized series,

whei’e the

pr.ndiices

cui~t-ent

i s

i s zet'o;

plra!;r woiilrl

resistor sinrids e l a s t i c part..

bet.wnen

c i i i ~ i ' e r ti

Llie

z e 1 ~ 0 ,1 h c i t (sf

rid

if

8

Ihi.

l i q r i i d had o r i l s

Tliis t ) e h ~ v i ~ rm'a y h e

he 9 O 0 ,

by a n e l e : r . t , r i c circuit o f

iridiictoi~ for t,he alotie

lag F

t h e phfise

properties,

resistor

Hnd

illductor. in

on

visoou>:.- o f l r l

for the

Tha phase

lag t.htit

~ n d v o l tage

an

of

inductor alone is 9 0 ' .

and the

the resistor alterntiting

If

they ctre in

series, l h e pha:ie lag is r’epresented by

(5.58)

Ail

rotatinrial viscometet~ is u s e d i n rheomet.rs for

osrillaling

these

kinds of

where

the imyedaticn

H

complex

imaginary

measiireni~rits,A n r t l o g o u s miiy

viscosity

t o Iho

be described in terms of may

JI*

parts represent

be

defined,

the viscous

electric a

wher’e

and the

circrii t

complex number, l.he

t.ae1

and

elastic. pot.tions.

The quantities

.

J"=

yo/uo

are

called storage compliance J’and loss compliance J " .

procal

(5.60)

sin6

values of

the compliances

are

called

storage

The rociand

loss

moduli G’and G". The dynamic analysis of fluids mag give an impressiort of their properties

(ratio elastic/viscous), but seems to be unsuitable for

the

application in

reservoir engineering

the

elastic viscosity

of a

problems. To

polymer solution,

a

flood

cal rul~1.e test

as

described in Appendix E may be more helpful. 5 . 6 Flow of polymer solutions in porous media 5 . 6 . 1 Darcy’s equation

The flow of fluids in a Dorous body may be described by Darcy’s equation

65

k is the permeability, u the viscosity of the flowing fluid.

where

the pressure drop. The Darcy velocity VD is the volume

,+rid A p / l

flow rate V divided by the area A

of the flooded cross section of

ihe porous body.

VD

=

V/A

(5.62)

5 . 6 . 2 Flow of pseudoplastic liquids

The Dercy liquids, rate

equal ion describes

media, and

porous

is not

t,he flow of Newtonian fluids in

valid for

the

flow

of

pseudoplastic

as the viscosity of these liquids depends on the effected

of shear

strain during

flow through

the porous medium. The

,,ate of shear strain depends on the pore structure and the flowing velocity. For the description of the pore geometry, the definition of the hydraulic radius ’ H

or diameter D H is helpful:

(5.63)

where

VF is

the volume

occupied by the fluid and SV i s the inner

~ ~ u r f a a eof the solid body. V shall be the volume of the entire PO-roils

body and

that

VF

is

VR the bulk volume. In the following i t is supposed

t h e pore

v o l u m e Vp.

The specific

surface of

B

solid

p o r o u s body is then given by:

so

SV/VB

and

thus for

(5.64)

the hydraulic

diameter of

written as follows:

66

a

porous

body

may

be

(5.65)

where

0 is

the porosity

in fraction, which is distinguished from

porosity in percent, for which the letter rD is used. The rela-

the tion

between the

actual flowing

velocity vm

of the fluid in the

pore space and the DRI CYvelocity is:

i t is

where the

fluid flows.

does Its

not flow way is

dead

the smaller the porosity i s , the faster

On the

other hand, the fluid in a porous medium

along the

shortest path from one end to the other.

actually longer

because

the

single

pores

are

not

t v each other in a direct manner, but there exist, e . g . ,

connected

end pores

longation the

obvious that

which have to be bypassed. The measure of the pro-

of the

square of

flow path

is the

tortuosity factor T , which is

the ratio of the actual flow path L, and the length

I. of the porous body

T = (L,/L)

2

(5.67)

By combining Equation 5 . 6 1 and the Darcy Equation 5 . 5 6 , and by assuming, is

first, that the flow of a liquid through the porous body

similar to the flow through a body consistin8 of interconnected

and, second, that the following Equation 5 . 6 8 (see 5 . 1 9 ) for the flowing velocity of pseudoplastic liquids is valid

capillaries

r

V@

= - mN . a

(5.68)

3tN

67

and,

Equation 5 . 5 8

lastly, that

valid,

for the

hydraulic

diameter

is

equation for the rate of shear strain for pseudo-

then the

plastic liquids in porous media may be derived as follows: The

hydraulic radius of the porous medium shall be equal to

the radius of a cylindrical capillary 40

= 2a

DH

so (1-0) and

substituting this

into Equation

5.68

one obtains f o r

the interstitial velocity v0

r.P

as

is

power la

the rate

of shear

strain in

the equation for

fluids, one can write

So(l-0)

$

(3tN 20

or,

us ng

"0

the

relation

between

Darcy

velority

and

interstitial velocity of Equation 5 . 6 6 , SO(l.-@)

= (3tN) 20 Writing

n=l/N,

JT - VD

'

0

one

obtaiti!; en

expression f o r t

the r a t e o f

shear stvain in the porous medium:

(5.69)

KOZENY (1927)

and CARMAN (1937,1938) derived an equation that

calculates the permeability of well-sorted sands:

(5.70)

68

equation may be solved for the specific surface S o . and

This

into Equation 5 . 6 9 . Thus an equation is obtained which

substituted expresses power

the rate

law fluid

factor k,, is set

3nt 7

l o

$2

sand pack for a

2 , and the tortuosity factor diminishes.

-"D

Equation 5 . 7 1 pack, arid, a power

has

a porous

(5.71)

Ik5

4n

of

strain in

of permeability and porosity. The shape

1

y = -

send

of shear

in terms

allows one i n most

law fluid

bean measured,

this

flow curve

flow

in the

to calculate the pressure drop in a

cases, in consolidated sand for the flow Once a

flow curve for the power law fluid

the viscosity

at the

rote of

porous medium.

of the

fluid may

sheer strain

The pressure

be read from

determined for the

d r o p may then easily be

calculated using the Darcy equation. Other authors have found some similar equations for the rate of shear strain in a porous medium.

HIRASAKT tlnd POPE ( 1 9 7 2 ):

ri/(n-l)

'n+'

y -

(-

12

)

If 5 0 k p

4n

VD

(5.72)

GOGARTY ( 1 9 7 5 ) ( 1 9 7 9 ) :

3nt 1

50

3n

I t 50ko

y = -

\' D

(5.73)

ODEH and Y A N C :

i, =

Ck0 1

i c '

VD

(5.74)

The

constants used

equations

in equations

are semi-empirical.

describing

the flow

in a

5.72 -

5 . 7 4 show

The accurracy

porous

medium

of

will

that these

these be

equations

discussed - i n

Appendix G . 5 . 6 . 3 Viscoelastic effects in flow through porous media

mentioned above, the elasticity of macromolecules, which is

As

like

that of

a rubber string, plays an important role in pressure

drop

in flow

through a

phenomenon un:iform. always

does not In a

is flowing

solute

oscillations may

drop

h

relfites

of

sandstone i . R t e

1

where the

fact

that

diameter

the

flow the

of

is

pores

or elongate

the liquid and thus the

an oscillation

energy

that

is

is

induced

needed

in

for

the these

by

like shear to the

an

elastic

viscosity, a rate o f

lirleilr s-train in f l o w 01’

n

viscosity.

The

elastic

m a t e r i ~ l constant

11~~11

linear strain ( E q u . 5 . 5 5 ) .F n r through a por’ous solid. such a s

send pack, the following approximation is made:

of l i r i c ~ i r r s t v d + i n H S defined in E q u . 5 . 2 a i s :

dl

-

F = -

rlt

l o

Tn

is

The

described is

the stress

vale

the

increases the pressure drop. The increase in pressure

be

viscosiiy

The

that press

molecules.

to

sometimes very suddenly. forces occur while a

macromolecirles. Hence

polymer

thf.

porous medium,

changes, and

fluid

porous medium. In flow through pipes this

occur due

tlirs

FL

p r ~ r o u sbody d l / d t

rlii3nietnr.

r.l

i s the intnrr;tiiinl velocity v o Hrid 10

of a sand grain that must bt, bypassed in

R

pore

neck. S o the r a t e of linear strain may be expressed b y :

(5.75)

70

(5.76)

A s shown by an experiment described in Appendix E , the elastic

h

viscosity depend

of

a polyacrylamide so1ut.ion .is constant and does not.

on str-ain rate within

particular range of strain rate, as

H

inli-ently evidenced in Equation 5 . 5 5 . A t high rates of shear strain, shown i n

a polyacry1amide

increase. is

This

solution

t.o

WHY

vo1cJcjt y ,

flow

trbserved in

i::

viscosity

may

called dilel.ancs, and i t

clnsl.ic viscc2sit.s. The opposite

1 . 1 : ~ ~ n i i i e a::

is t l ~ i x o t r ~ o p y . 81:;

repr~crsnri1nLive

on

solidificetion’ i!,

'shetir-

not. nncesnni’ily

effect

for the dependence of t h e i.c?r,i!;tancefnctor

F i g . 1.6

as

of

drilling muds. The most

nieasur’e elastic viscosity and its dependenc,e

on

strain raie

is

hereforn from flood experiments like in Appendix E .

for purposes of reservoir ongineering ctrlculations

5 . 6 4 Calculation of pressure drop jn flood tests

Laboratory flood jec ability measuring

of a polymer solution, in adsorption measurements, for elestic: viscosity,

phenomena.

pressure drop

being measured.

pressure

inaccessible pore volume, dispersion

and displacement

experiments, is

experiments are performed to measure the in-

drop in

T o get the

efficiency mlong the an

for

is

these

core piece or the sand pack

impression

experiment

In , a l l

oil.

whether

reasonable,

the

observed

the

equations

derived above to calculate presliui’e drop can be used. The

si tiintion

is

q i i i (.A

nof

exhibit

simple

solul i o n s which do For s u ~ : h liquids.

p i ~ o s s i i ~ ~drop e

equations

derived

above.

obtained,

a s is shown in Appendix

experimeri t s may

also

that pressui-e be

used

for

and

for

liquids

like

xanthan

considerable elastic viscosity.

R

can

quite

be

calculated

reasonable

using

values

can

the be

E. If i t is proven in laboratory

drop calculations pressure

are reasonable, they

calculations

in

reservoir

engineering and numerical reservoir simulation.

For liquids elastic must

assure that

experiments. as

that have

viscosity can

no plugging

Then the

measured in

a significant

be calculated

a flow

of the

elastic viscosity, this

from flood pore space

experiments. One occurs in these

pressure drop due to the apparent viscosity curve may

71

be calculated, and the pressure

fi.om ela.;tic

CJI o p

t h e difference b e t w e e n c a l c u l ~ ~ t c ~ d

viscosjty is

arid obt,r+i,vedp i '

Kiiowi~ig these

date

is

impor ! , a n t

the

c ~ l ~ : u l i ~ t i o n s ,because

elastic

for

in.jecI. ion

effects

may

pi'nssure

sipif icantly

the effect of shear thinning.

o\-crcoiiic?

I t is important that all data are measured on the system t o be

field, for not only shear vitjcosity may depend on the

used

in the

sc+lt

content of

tho nixing

influenced. The

is

water, but. a l s o the elastir. vis1:o:;i t.y

elastic visc,osity

of polyacrylnmide solui i o n s

dr.ci~t.?~ses i r l propot’tion with the increasing haitdrless of the mixing Since the

w-1

niolecul e

c:\rrled,

is

c,,~t.ion$,, thi:; t ) n h a v i o r -

is quite

c ( ~ m p r o ~ ; ~ ; e co rl ' el ~

1 hat,

arid

H

of

i S1 y . ar; i f i I. had

g r c ' a 1 + ? I ' volume

H

ions.

6 5 Sheer stabilily

was

As

solutions ~

~

presence

t.he

p ~ ~ r lof s -thc niolnculn were not sti~cinglybound b y , foi, example,

divaleril

5

i i g t i o t d

in

as

obvious. The molecule may n o t be

R

W

shown above, high molecular weight polymers in aqueous have a viscous behavior that may be described by

This behavior

cc lloid

science

Gcrinan

This means

this

laminar flow

the

viscosity

of the

If the

tilone

are not

tllat

filaments apparent

is called behavior

was

In

called

power

R

the beginning of

"strukturvi skos"

in

that the colloid or the macromolecule disturbs of

the

solvent

solution is

rate of

thus

and

obtained than

shear strain

i.;

R

highets

the solvent

that of

increased,

apparent

the molecules

globules but more ellipsoids. discs, rods, o r curled

are orjentod

the

in

viscosity decieasrs

slructbre

pseudoplastic

flowing

s o l v ~ n t , arid

thus

the

This means Ihat the particles form

H

I t i s evident that if the rate of sheer

in the solution

strain becomes very high, even the molecule may be destroved While mixing and pumping polymer solutions in the oilfield, or when of

pressing the polymer solutions through the small perforations an injection

to

well, the

rate of

shear strain

may become very

It may therefore be possible that some polymers are strained

high

such an

rpsult

extent that

that the

the molecule

may be

scissored, with the

viscosity yield of the polymer solution decreases

drastically. Polysaccharides such eben mixing

high shear

as xanthans

are not shear sensitive and

is employed to xanthan solutions to obtain proper

Pressing these

polymer

solutions

72

through

small

chokes

(shc:av

plates) is

common

H

teclriiique

used

to

homogenize

the

s o l u t . i o t i s and improve injectability.

Polyacrylamides & r e more shear sensitive, but this is n o reason why

they cilnnot

shes;’

plates

be applied for polymer flooding. has

also

been

proposed

Jetting through

GRODDE

by

for

mixing

pol yacrylairiides. T h o rat.es of shear, strain occurirrg in flow through perforations

may

also become

prr?sent,ed much, strain

exenlples

as

perforations.

very high.

T o prove

flood tests and

the

nieasut.ed. A s is

for

the

that the

may be

rate

viscosity Appendix E ,

in

of

occurr~jng in regultli. opnrntions of

calculations are shear

polymer will

carried out

possible shown

E some

In Appendix

strain

in

not be damaged -loo

at 1 . h ~ s n v a t e s

degradation

may

of

!;hr.niS

t.hus

be

the r e 1 , e s

o f shear s t r a i n

an injection

well are not so

high that severe damage to the polymer must be feared. 5 . 7 1naccer;sjble pore volume

When investigators

performing

e ~ r l i e r than the

with

flooding

experiments,

many

breakthrough of a tracer that was injected along

the polymer.

attributed

polymer

have observed that the polymer breakthrough occurred

to

the

This

phenomenon, as shown in Fig.5.13, may be

fnct

that

some

of

the

pore

volume

is

inaccessible to the polymer solution.

U O

’ 1

0

2

1

Injected pore volumes

Fig. 5.13 Inaccessible pore volume

73

A reason

f o r this

the polymer

that

order.

to be l o

ricces:iai,y

may he

that some pores are t,oo small, and

molecules therefore cannot. enter these pores. In

a b l c s 1.0 decide whether or not this is the case, i t is

more c l o s e l y

look

-the pore sizes of a petroleum

fit

reset’\oir. 5 . 7 . 1 Pore size distribulion

The pore forniation

is

s i z e and

of

its distribution in-terest to

great

flow

The

tho

rock with oil and water, and to two--phase or three-phase

gas or

pressure measurement. The porous solid is saturated with tl

liquid. This phase is then displaced b y another phase.

pressure that. i s needed to displace the phase which originally

satu~.att-:dthe pores two

the

in the reservoir. The pore si7.e distributiori is determined b y

capillary H

reservoir ~ ' o c k

R

urtderst.nnding of

i s with i’espoct to the s a t i r i ' ~ t i c , r i o f

t-esei~voir behavior, that. reservoir

wit.hin

the

phases, and

r ~ i i ~ is

pet.roleum

often

depends on

the interfacial

their different displaced

by

laboratories the

t~rine displaced b y

mercury,

rock is

an oil,

tension of these

wetting angles. for

or

For porosometry measurements

saturated with

so that

the

two

in

brine and the

phases

are

quite

similar to those in a reservoir. In F i g . 5 . 1 4 , capillary pressure

100

I

I I

80-

I

I,

\

60-

\

L\

,, 40-

1

2 '\

\

*\

, 20-

'.

'a.

x - 4

0

v

0

I

20

I

I

I

40

I

r

60

Brine saturation, S, Fig. 5.14 Capillary stone core samples.

-

1

80

100

(O/O)

pressure curves (drainage) o f water wet sand1 : 9 ~ 1 8 . 5 % , k Z 1 . 1 3 urn2 2 : @ = 2 4 . 8 % kz0.062

,1111’

74

~ u r v e s for core pormeabil i tic?:; wetting

The

&rid

thHt

at'e

displaced ly

wet 5;howri.

the

sandstone In

of

this

non-wet.ting

different

exiimplc?

the

phpse,

and

the

peed

from

the

i s meH!::IJred.

irreducible

%

p(7r.c:

i s when

for

.SHIUI'RI ion may

water I t

prrr,sure c u r v e .

rieai' 5 0

cut~ves,

a water

tind p o i , o s i l i n s

phnse i s

draineye curve

rapillary

samples of

is

2 . From

r o c k sample

bn

1 8 % f o r t h e r o c k sample 1

eboul

Ihe

capillary

pi'essuve

s i z r ~ ,a n d p o r e s i z e d i s t r i b u t i o n s may b e r . a l c u l a t c d . tlio

i n t c + i , f n r . i H l l e r i s i o n arid

t h e wettitig

a n g l e 8t'c

k n o w n , a c c o r d i rig t o E q u i i t .i o n 5 . 7 7 .

1'

=

(5.77)

2u’c0s8/pc

F o r t h e c a p i l l a r y p r e s s u r e c u r v e s shown a b o v e , a p o r e s i z e d i s t r i b u t i o n a s shown i n F i g . The p o r e the

5 . 1 5 may be c a l c u l a t e d .

size distribution

r o c k s a m p l e l ) , 20 % o f

t h e pores are s m a l l e r than 0 . 3 him,

a n d a b o u t 1 0 % s m a l l e r t h a n 0 . 1 urn,

0

10

20

5 . 1 5 show t h a t for

curves i n Fig.

30

40

I n r o c k s a m p l e 2 ) , 50 % o f

50

60

70

80

90

and the

100

Percentage

Fig. lated

mN/m

5 . 1 5 P o r e s i z e d i s t r i b u t i o n for t w o s a n d s t o n e s a m p l e s , c a l c u from t h e capillary pressure c u r v e s i n F i g . 5 . 1 4 . ( u O l w = 20 8 = 50°)

75

are smaller than 0 . 2 um. Even if the calculation of the pore

pores size

distributions does

ties

in interfacial

gives

evidence that

smaller

than the

wetting

angle,

it

nonetheless

a considerable portion of a reservoir rock is

molecular size

polymer. A s shown in Table

of a

the molecular size of a polyacrylamide is 0.25 - 0 . 3 pm. This

4 1, means

sample 1 )

that for

inaccessible as

have a small error due to some uncertain-

tension and

to polymer

about

20

%

molecules, and

of

the

pore

volume

is

in rock sample 2) as much

about 50 % . This approach to inaccessible pore volume is in good agreement measurements made

that

inaccessible pore volume does not detract from the benefit of

polymer the

flooding, as

same one

by different

i t also

with

that portion

that i s

authors. But of the

shows

pore volume is usually

filled with water (irreducible water) in an

o i l reservoir.

5 , 7 . 2Dispersion Another approach to the phenomenon of inaccessible i c i

dispersion. The of a

(mtlet

different tracer

dispersion o r

and a

tliat

diffusion coefficients.

In the case o f a

polymc:r, the Iracer, which is u s i r n l l y o salt. sho~ild diffiisioii o r dispersion coefficient than l l i e poly-

because the polgiiinr inolncules ere much l a ~ g c r 1 . h s n s a l t

Dispersion and

fact that one component arrives eai,lier at the

core or sand pack than the other may b e attributed t o

hCive a. greater in(.r,

volume

pore

always 1nkt)s

i I_ should

ions,

place i r i displacement o f miscible f l u i d . ; ,

b e considered i n all Itihoratorg t e s t . % . The equHiion

tlesci,ibesdispersion

o r diffusion

is

Firk’s

2nd

law,

as

wi,itten below in Equation 5 . 7 8 .

d /dt

I

D d20/dx2

(5.78)

(5.79)

with 2

= -

erf x

Jz

erf x

e-k2dk

(5.80)

OJ

is the error function. The values of the error function

are tabulated or may be approximated by polynomes. Either diffusion or dispersion is responsible for the fact that a

flood front is not sharp, but rather smeared. The breadth of the

transition of

zone is often measured between the 10 % and 90 % vRlues

the measured

diffusion the

concentration at

coefficient may

transition

concentration should

zone.

c , the

the outlet.

be quickly To

obtain

argument of

be 1.1631, and to

or

estimated from the width of a

value

the error

obtain a

The dispersion of

0 . 9 for

function

value of

0 . 1 , it

0.0886. Thus the width of the transition zone Ax90/10

the

( X ~ ~ / Z J D ~ ) should

be

is

(5.81)

An example

of a

calculation

for

dispersion

together

with

results of a flood test are given in Appendix H . The above

considerations and

discussed

in Appendix

important

role in

the results

of the experiments

H show that dispersion or diffusion play an

flood tests. Dispersion should be distinguished

from such effects as inaccessible pore volume or adsorption. 5 . 8 Adsorption

the enrichment

Adsorption is interface. phases, liquid an

a particular component at an

may be the interface between two liquid

interface between

a gas

or a solid, or between a

phase and a solid surface. The enrichment of a component at

interface causes

phase. of

This interface

or the

of

the l o s s

The concentration

a liquid

or the

of this component in the continuous

of the component in the continuous phase

partial

pressure

in

a

gas

phase

are

in

equilibrium with the amount of substance adsorbed. The science that deals with the nature of particles of the size between of

molecular size

colloids. I t

and macroscopic size is called the science

deals with

colloidal particles

77

such as

sols or

surfactants molecular

in interfaces, weight of

and also

some hundred

macromolecules. which have a

thousands to

several millions.

The word colloid is derived from the Greek word for glue, k o l l a .

So

not surprising that materials like polymers for EOR that

it is

are

used in

solid

normal life

surface of

form

interfaces as

active

at the

chemical less

surfactants (surface

For

adsorb.

decreases

or that chemicals that are used to active agents)

are also

surface of a grain of sand. All substances used for

flooding have

adsorption,

as glue for wall paper also stick to the

a sandstone,

the

these properties, and thus they do more or

polymer

flooding

concentration

and thus

of

the viscosity

this

polymer of the

means in

that,

the

due

flood

displacing

to

water

phase

also

decreases. Adsorption mechanisms adsorption. between

Physical

the

(adsorptive). chemical

are divided

adsorption

surface

(adsorbent)

The forces

adsorption a

into physical and chemical

means

a

and

relatively the

are electrostatic

weak

adsorbed

(van der

bond

species

Waals).

In

chemical reaction between adsorbent and ad-

sorptive takes place. The consequence which adsorption has on polymer flooding shall be

visualized by

scientific vg/g

in

the following arbitrary example. I t has become a

convention to

(polymer/rock).

calculated

express the amount of adsorbed substance This amount

of adsorbed polymer shall be

for a clean silica sand with a well-defined grain size.

A representative grain diameter of a good, permeable sand is d

=

7 0 vm

The specific surface of such a grain of sand is g i v e n by:

SO

= 3.5

where

'

l/r

l.10-5 rn-l

3 . 5 is

density

= 1 . 5 . 1 0 - 5 m2/m3

3 7 . 7 m2/kg

a typical value for a well rounded sand. (The matrix

of the

sand is

2 6 5 0 kg/m3.)

For a polyacrylamide. a r e is 0 . 3 vm (Table 4 . 1 ) . So

presentative

diameter of

the

area of

an adsorption site may be calculated as the square of

the

diameter of

weight

of the

the molecule

the molecule polymer is

with 0 . 0 9 . 1 0 - 1 2 m2

5 , 1 0 6 (Table

4 . 2 ) , With

.

The molecular the

Avogadro

NL = 6,1OZ3 molecules/mol, the number of adsorbed molecules

number

in a monolayer is

1.0’1013

molecules/m2,

or

3 . 8 .1014

molecules/kg sand

or

6 . 0 . 1 0 - 1 0mol/kg

01'

3.0.10--3 g/kg

I

3

or

Natural sands content below

and a 20 p m ,

kaolinite hundred

Ilg/e

or grounded

grain size have

reservoir rocks

distribution with

specific

surfaces

of

having some

clay

a significant amount about

m2/g

2

and

a

clay of about 13 m2/g (see Table 5.2). This is about one times higher

than for

the sand

in the

adsorption model

above. So adsorption may become 30 - 300 pg/g. For such

calculated high

values of

adsorption, all

of the substance that is injected

into

a

medium

adsorbed,

porous

may

be

as

indicated

by

the

measurement of LOTSCH (1986) for Xanthan (see Table 5.2). 5 . 8 . 1 Adsorption isotherms Adsorption isotherms perature,

the

equilibrium

give,

at

of

the

dependence

concentration c .

a

particular

amount

The amount

constant

adsorbed

ns

tern

on

the

of substance adsorbed in

one monolayer is n S m . The coverage of the surface is defined as

0

(5.82)

ns/ns m

The simplest adsorption isotherm is the Henry-isotherm, which describes

a linear dependence of adsorbed particles on equilibrium

concen t re t ion b’c

€3

In the particles

(5.83)

case of that hit

a Henry isotherme the the

surface are

it

is

~ s s u m e d that

adsorbed with

the

all same

adsorption energy. In the case of the LANGMUIR-isotherm (1916):

e = -

bc ( 5 .€44)

1 tbc

79

Msorptioa Data

Table 5.2

olymer

Concentr.

kg/m3 AA

-

-

0.500 0.187 0.250 0.250 0 -500

Retention-Acbarption

w/9 w/m2 10.2 8.3 9.4 17.8 1.9 8.4 9.5 15.3 360.4 18.0 9.0 20.0 80.0 160.0 208.0 356.0 494.0 692.0 135.0 21 1 .o 237.0 408.0 104.0 143.0 273.0 185.0 283.0 364.0 484.0 10.0

b/m3

-

W

F

Adsorbent

’C -

~

Sandstone

0.105 0.080 0.102 0.176 0.015 0.097 0.101 0.177 0.123

Dolomite

Clay -

-

80 137 190 266 52 81 91 157 40 55 105 71 109 141 186 100

23

k

Mioc. Sdst Ottawa Sd Sand Pack

llmz

1-12; 1.34f 1.151 1.175 1.07: 1.09' 1.09' 1.06; 1.04! 1.17: 1.17: 1.081

-5

Salinity of solven

Molecula Weight

% ppn 20.: ?2-( 19.' ?2.( 19.: t2.1 20.! Z0.f

15. *

1 1 5 1 1 1 5 1 1 20 200 30 30

Specific Surf ace m2/g 6.28 6.21 6.25 6.12 3.21 3 .OO 3.11 3 -23 13.14

901 710 150 900 852 710 150 900 600 000 000 000 000

Author

MEISTER

1980)

e t .al.

SZABO (1975) DOMINWZ WNGAN (1969)

0

,I ,I

50

75 23 I,

-

90 000 58 000 230 000 0 90 000 58 000 230 000 0 58 000 230 000 0 90 000 58 000 230 000 40 000

2.7-106

,

2.60

KLEIN (1978

1.0.106

CHAWETEAU (1987)

bncentr.

kanthan

kg/m3

w/9

0.58 0.63 1.35 2 -45 3.10

70.0 83.0 151 .O 114.0 123.0 116.0 81 .O1 64.02 20.03 3.0 0.4 10.0

0.40 0 -05

Sclerqluca

l--Polymer4

Retention-Adsorption

kg/m3 0.62 0.69 1.11 0.88 0.99

TemF

17.0 35.0 58.0 117.0 126.0 149.0

(59)

1.20

173.0 92.0

149) (41)l)

(10)

55

Bentheim Sandstone

56

R e s . Core

(78)

55

I * ) Data

,I

I

56

i n ( ): " i r r e v e r s i b l e " adsorption i n w / g

%lecular Weight

specific

Res. Gore

Author

Surf ace m2/g

i

170 000

1 100 000

S d 0.13 0.27 0.47 0.90 0.98 1.11

F of solven

"C -

100

0.10 0.31 0.56 0.85 0.92 1.45

Adsorbent

1 ) w i t h Dreflush of 0.3 ,V 2 k / m 3 PAA 3, with s e f l u s h of 0.3 VL 2 k&n3 mlyethylenglycol molecular weight 1000

170 000

SORBIE CHAUVETEAU (1987)

L h S C H (1986)

w>Lz (1986)

2! with preflush of 0.3 , Vr 2 &/m3

4, HILLE cfrapter 3

HEC

it

is also

find

necessary that

only those particles are adsorbed that

a free adsorption site when hitting the surface. The constant

b i s , as the kinetic derivation of the L.angmuir-isotherm shows.

b

s’t/l(2zMRT)

where

s

portion

is

(5.85)

an adhesion

of the

coefficient, which helps to determine the

particles hitting

the surface

that are adsorbed,

and t is the residence time of the particles on the surface. The sticking

coefficient s

is a

function of

the activation

energy of adsorption Etad and temperature, as follows:

(5.86)

whereas

the residence

time is a function of the activation energy

of desorption Etdes and temperature:

(5.87)

In

the

adsorption

case is

of

physisorption,

zero,

and

E*des

the

is

activation

equal

to

the

energy

of

energy

of

desorption, so that

(5.88)

The Langmuir-isotherm requires that adsorption energy does not depend

on the degree of coverage 8 . But in most cases the possible

adsorption these

sites do

cases

the

not have

the same

Freundlich-isotherm

mechanism

82

adsorption describes

energies. the

In

adsorption

(5.89) where a

= RT/q,

and

(5.90)

4 , is

a constant

in the

assumed exponential distribution of

adsorption energy (TAYLOR and HALSEY (1947)). Beyond these

three basic types of adsorption isotherms, other

adsorption models have been developed according to literature. 5 . 8 . 2 Adsorption isotherms of xanthan In Table faces than

5 . 2 adsorption values for some polymers on sand sur-

The values measured by LOTSCH (1986) for xan-

are compiled. on a

sandstone are plotted in F i g . 5 . 1 6

-

5 . 1 8 in the form of

a Henry-isotherm, Freundlich-isotherm, and a Langmuir-isotherm. F i g . 5 . 1 6 shows versus

that in

a linear

polymer concentration,

plot of the adsorbed amount

a value of saturation is roRched at

a polymer concentration of about 1300 ppm. The last measured

-

1.4

m

& urn

1.2 1.0

i al

0.8 d

0

a.

0.2 0 0

0.2

0.4

0.6

1.0

0.8

1.2

1.4

1.6

1.8

2.0

Polymer concentration, c (g/l) Fig. 5.16 Adsorption Henry-isotherm.

of xanthan on sandstone. Values plotted as a

83

0.1

1.0

0.5

0.2

5.0

2.0

Polymer concentration, c (g/l) Fig. 5.17 Adsorption Freundlich-isotherm.

o

1

of x a n t h a n o n s a n d s t o n e . V a l u e s plotted a s a

2

3

II

5

6

I

a

9

10

l/c Fig. 5 . 1 8 A d s o r p t i o n of x a n t h a n o n s a n d s t o n e . b’alues p l o t t e d a s a Langmuir type isotherm.

84

value,

if true, indicates that at higher concentrations adsorption

decreases.

of

The plot

adsorption on

also shows that there is no linear dependence

concentration: the

assumption

for

the

Henry-

isotherm is not valid. Fig.5.17 shows a plot of the log of adsorbed polymer versus the

log

of the

plot,

concentration. There

is also no straight line in this

which means that a Freundlich-isotherm does not describe the

adsorption mechanism. In Fig.5.18 should type.

yield a

the measured

plotted in

a way

that

straight line if the adsorption is of the Langmuir

The reciprocal

versus

values are

value of

the reciprocal

lution.

This plot

others,

but i t

the adsorbed

value of

gives a

the polymer

line somewhat

is obvious

polymer

is

plotted

concentration in so-

straighter than the two

that insufficient adsorption data have

been measured at low polymer concentration. At least the plots discussed above show that the measured data follow

more

or

less

the

adsorption

mechanism

based

on

the

assumptions of the Langmuir-isotherm. 5 . 8 . 3 Heat of adsorption The heat of adsorption is a measure of the strength of the bond between

the adsorbed

adsorption should

be measured.

isotherms

to be

The way

for different

adsorption,

e.g. a

concentrations be

polymer and

mechanism is

read from

the solid surface. Thus, if the

explained, the to do

this is to measure adsorption

temperatures. At

in the

a particular

0 of

surface coverage

polymer solution

the isotherms.

heat of adsorption

0.5,

the

value for equilibrium

at these temperatures may

According to

the Clausius-Clapayron

equation, the heat of adsorption is

(5.91)

where

i t is assumed that the heat of adsorption is constant in the

interesting determined

temperature range. Hence the heat of adsorption may be from the

slope of a plot of In c versus the reciprocal

absolute temperature 1/T. Unfortunately there sorption isotherms

are no data in the literature for the ad--

of EOR-polymers, were measured

i . e . in

experiments

at different

85

where

adsorption

temperatures and from which

it

is possible

so

that at a particular amount of adsorption different equilibrium

to read

adsorption data at low surface coverages,

concentrations in the solution may be read. The data completely

KLEIN et

measured by

5 . 2 . are for

al. (19781, as shown in Table

maximum adsorption, where

saturated

with

polymer

the surface

molecules.

seems to be

These

data

were

measured at 296 K , 3 2 3 K , and 349 K . The decrease of adsorption with rising temperature, as measured by

KLEIN et

the from

be interpreted as a desorption, and thus in

following an attempt is made to calculate a heat of desorption these

constant are

a l . , may

data.

The

and the

read from

concentration

concentration

in

corresponding values

the isotherms. of

The data

polyacrylamide

2 . 7 . 1 0 6 are listed

in Table

for

having

5 . 3 . The

the

solution

is

kept

of the adsorbed amount cad a

a

constant

molecular

polymer

weight

of

plots of In Cad versus 1/T

are shown in F i g . 5 . 1 9 . 5.5

5.0 0 U

c

4

4.5

L.0

3.5

1

I

I

I

I

I

2.9

3.0

3.1

3.2

3.3

3.4

1/T

(K-’/10-3)

Fig. 5 . 1 9 Plot of In Cad versus 1/T t o calculate t h e h e a t of adsoi,ption/desorption. Sallnity is taken a s a parameter.

The values amount was

said above,

needed

for the

of substance

for the

heat of

desorption are obtained from the

that remains

where the

adsorbed, just contrary to what

concentration in

Clausius-Clapayron equation.

86

the excess So the

phase is

sign of

the

obtained

values for

the enthalps

has to be changed, and the heat

of desorption becomes positive. heats of desorption, as listed in Table 5 . 3 . are

The measured

values for physisorption. The values are in the same range

typical as

those values typical for the heat of vaporisation, heat of

the

2 3 . 1 5 3 kJ/mol

vaporisation is

e.g.

for C 0 2

(Handbook of Chemistry

and Physics).

Adsorption data according to KLEIN et a 1 . ( 1 9 7 8 ) . Computed data for calculation of the heat of desorption.

Table 5 . 3

O'O

~

9.0 58.0

130,O

296 323 348

1

52

4.382 3.951 13.689

1

i

1400

111.6

3.378 3.096

4.920 4.394

2100

17.5

296 323 348

190 91 55

3.378 3.096 2.874

5.247 4.511 4.007

2500

20.8

296 323 348

266 157 105

3.378 3.096 2.874

5.583 5.056 4.654

2000

16.6

shows that

something

learned

isotherms.

A s one

aim of research

always be

taken

3.378 3.096 2.874

81

may be

factors

hHdes/

137

This example

feasibility

,’lope D1Ot

1Il

296 323

adsorption will

1

I

ISalinityI Temperature NaCL

arid

from

to optimize

economic

like adsorption

the

about

the

measurement

work

mechanism of

1

of

adsorption

in enhanced oil i’eco\*erv

the process with respect to technical success,

mechanisms

thst

influonce

should be understood before any action is

to minimize adsorption by adding, for instance, sacrificial

agents . 5 . 8 . 4 Measuring adsorption isotherms

Adsorption isotherms the

main thing

is to

may be measured in different ways, where

determine the

87

amount of

adsorptive on the

surface

aiid

j

ts

coriconti*ation i n tho soliition at equilibrium. One

must be sure in all experiments that equilibrium is reached. The amount directly and

particles on

a solid

surface mas bo

measured, e . g . by determining the mass of a sample before

after

adsorption.

adsorption This

of adsorbed This

method

is

applied

for

measuring

from a gas phase by using very sensitive microbalances.

method also

allows one to observe the kinetics of adsorption

processes. Another method defined

is to

amount of

adsorptive pressure

adsorptive and

then measure

the

decrease

of

concentration in a particular volume. An example is the

BET-method, number

bring the adsorbent into contact with a

in which

a

is brought

defined

volume

of

with

the

into contact

of adsorbed

particles is

gas

under

a

adsorbent.

calculated from

known

and

the

the decrease in

pressure. Adsorption measurement is

isotherms

possible to

may

also

be

measured

from

direct

of adsorption with calorimetric methods if i t

of heat

recalculate the

adsorbed amounts from calibration

measurements. Besides these calculated

from flow

catalytic designed

’static’ experiments,

research,

experiments. This as

such

flow

adsorption may is done,

experiments

also

be

for example, in may

be

closely

to technical applications. F o r enhanced oil recovery such

experiments

are appropriate,

since the

conditions during

a flow

experiment are the closest to reservoir conditions.

5.8.4.1Static experiments Samples of measurements to

a liquid

the

this

adsorption to

surface. As phase, it

liquid) the

measure

rock

of adsorption

the solid

from

reservoir

is as

measure these

grounded

for

static

so that the adsorptive has good access

EOR-polymers is measured

mag be difficult to measure directly (in weight, but it should be possible to

increase

high as

be

adsorption of

increase in

weight

should

after

the

sample

is

dried.

If

noted above, it should not be difficult

masses, a s scales with such high resolutions are

available today in every laboratory. Usually the adsorbed substance is determined from the decrease in

concentration of the polymer solution after it has been brought

into The in

contact with

the adsorbent and equilibrium has been reaLhed.

experiment should concentration is

be designed in such a way that the decrease significant and

88

can be

easily measured; the

mass

of the

adsorbent should

not be

too small and the volume of

the solution not too big. The concentration of the polymer may be determined by chemical analysis

(see

calibration been

B),

appendix

curves (flow

or

by

viscosity

measurement,

if

curves at different concentrations) have

measured before. From a change in the shape of the flow curve

some

information

may

molecular

weight

example,

particles

preferentially, should

are

be

deduced.

adsorbed of

high

in

If

molecules

varying

molecular

of

different

amounts,or weight

are

if,

for

adsorbed

the molecular weight distribution is changed. This

change the

part of

the flow

curve at

low rates of shear

In such cases the polymer solution and its distribution in

strain. molecular

weights may

also be

characterized

by

chromatographic

techniques (GP C ) . 5.8.4.2

Flow experime-

In flow experiments adsorption mas be examined under conditions that

are similar to reservoir conditions. In such flow experiments

a polymer solution of known concentration is flooded through a

0

1.0

2.0

Injected pore volumes Fig. 5.20 experiment.

Concentration

profile

89

at

outlet

in

a

core

flood

reservoir at

core or

sand pack. and the development of concentration

the outlet is observed. In this manner, a concentration profile

as shown in F i g . 5 . 2 0 is obtained.

The amount Ncap

of polymer

is proportional

that is

to the

captured in the porous medium

shaded area

in Fig.5.20. The amount

adsorbed is given by:

Nad

(5.92)

= Ncap - Npve

where

Npve is

volume

the amount that is retained in solution in the pore

of the

core. The

pore volume is the effective pore volume

that

is filled

that

are not invaded by the polymer solution, such

pore

volume or

considered. pore

long

oil and

solution. Parts

gas saturated

of the RS

pore volume, should not be

volume, the surface affected by adsorption should the core

pore volume inaccessible

If the effective pore volume is not equal to the total

respectively. at

with polymer

The equilibrium inlet when

enough so

concentration is

the flood

that this

be reduced

the concentration

experiment has

been performed

concentration is almost obtained at the

outlet.

0

5

c'

0 .c

2

c

c U u c U 0

kl

5

d

0

a

0.8

1.0

1.2

1.4

1.6

Injected pore volumes Fig 5 . 2 1 Concentration profile in a slug experiment.

90

1.8

In F i g . 5 21 a flow experiment is shown in which a slug process is

applied. Only a small slug of polymer solution is injected into core and then followed by water. The water is injected as long

the as

almost zero

material

concentration is

balance an

measured at the ou%let. From the

irreversible

adsorbed

amount

may

be

cal

culated. If the due

amount of

to adsorption,

in

such slug

If

this is

place fallen

adsorption mechanism is physisorption

experiments, then

all of the polymer should desorb

not the case, mechanisms other than physisorption take

in the out of

plugged

polymer retained in a porous medium is only

and the

pores. The

polymer may

solution, or

the pores.

be retained

gels have

These mechanisms

formed and that are

because

it

has

have partially

not exactly known,

together with adsorption, are often called retention.

5 . 8 . 4 . 3Calorimetric methods The heat static

of adsorption

may be

measured in

a calorimeter in

experiments or in flow experiments. Flow experiments may be

performed

as core floods using a microcalorimeter (GROSZEK ( 1 9 7 0 ) .

TEMPLER). This type of measurement has the disadvantage that the

Desorption with n-Heptane

Fig. 5 . 2 2 Adsorption of n-Butanol from n-Heptane on washed reservoir sand (according to a MICROSCAL publication)

91

oil

amount

of adsorbed substance has to be recalculated from other ad-

sorption quick

isotherms, but

and simple,

observed

as

desorption. agents)

may

adsorption directly this

well The

the advantage

and that as

the

of

difference

influence

be

is that the method is very

the kinetics of

determined

other

easily.

adsorption

between

adsorption

adsorptives The

may

be and

(sacrificial

difference

between

on a clean surface and a precovered surface may be seen from the

method is

change in

heat of

adsorption. Measurement for

shown as a n example in Fig.5.22 for the adsorption

of n-Butanol in a reservoir sand formation.

36.0 mJ/g rock

Fig. 5.23 Adsorption of Xanthan f r o m tl 1000 ppm s o l u t i o n i n reservoir brine (50 g/l TDS) on grounded reservoir rock at 20 O C ( S o E 2 rn2/g). (Courtesy to Microscal, London)

In Fig. adsorption measured

was

This is

when the used to

totally

results of

xanthan on

an experiment are shown for the

reservoir rock.

The

amount

of

heat

during adsorption is lower than the heat developed d u r j n g

desorption. cell

5.23 the

of

due to

the heat of mixing that occurs in the

Xanthan solution displaces the reservoir brine that

wet the

desorbed, the

rock before. heat of

Assuming that

mixing is

92

the Xanthan

- 1 4 . 8m J / g .

is

and so the

heat

of adsorption

more

detailed investigations the heat of mixing should be measured

separately

is 2 1 . 2 mJ/g of reservoir rock. For deeper and

using an

medium (such as glass or Teflon

inert porous

beads with a small surface). The heat

of

polyacrylamide, adsorption of

adsorption, is

for Xanthan

reservoir rock.

the

as

kJ/mole.

20

leads to

One mag

calculated

in

Assuming

the

Table same

5.3

for

heat

of

an adsorption of 1 . 6 . 1 0 - 6 mole/g

asssume that

the interaction between

macromolecule and the surface is of the same character as bet-

w e e n ’ the monomers and the surface. The xanthan molecule monomer is in

principle a

This

sugar ring

produces an

which

is

methods,

somewhat but in

interaction of

the sugar reported in

higher

the same

with a

as

with a molecular weight of 164 g/mole.

adsorption of 300 pg/g (Xanthan/reservoir rock). than

the

range of

heat exchange

values

measured

magnitude. If

by

other

one assumes an

of 20 kJ/mole at the five edges

ring, the adsorption would be about 6 0 pg/g, a value Table 5 . 2 .

In this context entropy effects should

also be considered. The experiment orienting for that

step to

described

adsorption measurements microcalorimetry,

measurements,

is

above

was

performed

as

a

first

show that microcalorimetry is a method feasible

a

in

good

of EOR-chemicals. I t may be concluded conjunction method

for

other

adsorption

investigating

with

adsorption

mechanisms.

REFERENCES Carman. P . C . : Trans. Inst. Chem. Eng London 15 ( 3 9 3 7 ) , 150 Carrnan, P . C . : J . SOC. Chem. Irid. 57 ( 1 9 3 8 1 , 225 Carman, P . C . : "Flow of Gases in Porous Media", Butterworth’s London Chauveteau, G . . Lecoutier. J . . Lee, L . T . : "Polymer Flooding: A New Method for Selecting the Optimal Polymer Chemical Structure for Given Reservoir Conditions", 4th Europ. Symposium on Enh. Oil Recov., Hamburg (FRG) ( 1 9 8 7 ) Dominguez. J . G . , Willhite, G . P . : "Polymer Retention and Flow Characteristics of Polymer Solutions in Porous Media" SPE-paper 5835 ( 1 9 7 6 ) Einstein,A.: Ann. Physik 19 ( 1 9 0 6 ) 289 Gogarty, W . B . , Levy G . L . ,F o x , V . G . : "Viscoolastic effects in polymer flooding through porous media", SPE-paper 4025 ( 1 9 7 5 ) Grodde, K . - H . : "Verfahren zur Scherbehandlung waessriger Polymer Loesungen*’, FRG Patent DE 27 33 8 5 2 B 2 Int.Cl. E 2 1 B 43/22 ( 1 9 8 0 ) Groszek, A . J . : Transactions ASLE 13 ( 1 9 7 9 ) 2 7 8

93

Groszek A ,J , , Andrews , G . I , : Proceedings of 3rd Conference on Industrial Carbons and Graphite, SCI (1970) 156 Halsey, G . , Taylor, H . S . : J . Chem. Phys. ’15 (1947) 624 Hirasaki, G . J . , Pope G . A . : "Analysis of factors influencing mobility ratio and adsorption in the flow of polymer solutions through porous media", SPE-paper 9710 (1972) Klein, J . , Martin, V . , Borkowski, N . , v . Diiszeln, J . . Klare, J . , Mansouri, A . , Westerkamp, A . : "Entwicklung neuer Polymertypen z u r Tertiarforderung von Erdol aus Lagerstatten hoher Salinitat". DGMK-Forschungsbericht 165, Hamburg (1978) Kozeny, J . : Royal Academy of Science, Vienna Proc. Class I 136 (1927) 271 Kuhn, A . : (editor) Kolloidchemisches Taschenbuch Leipzig 1944 Langmuir: Phys. Rev. 8 (1916) 149 Lotsch, T . : "Untersuchungen z u m Retentionsverhalten von Polymeren beim viskosen Fluten". Thesis, Techn. U . Clausthal (1986) Meister. J . J . , Pledger J r . , H . ,Hogen-Esch, T . E . ,Butler, G . B . : "Retention of polyacrylamide by Berea sandstone", Baker dolomite, and sodium kaolinite during polymer flooding", SPE-paper 8981 (1980) Mungan, N . : "Rheology and adsorption of aqueous polymer solutions" J . Cdn. P e t . Tech. 8 (1969) 45 Ostwald, W . : "Begriff und Systematik der Kolloidwissenschaft" Kolloidcheniisches Taschenbuch Leipzig 1944 p . 1 Odeh, A . S . ,Yang, H . T . : "Flow of non-Newtonian power law fluids through porous media", SPE-paper 7150 (1979) Pusch, G . , Lotsch, T . : "Eigenschaften wasserloslicher Polyniere z u m Fluten in hochsalinaren Erdollagerstatten", Erdol Erdgas Kohle 103 (1987) 272 Sorbie, K . S . , Parker, A . . Clifford, P . J . :"Experimental and Theo-retical Study of Palymer Flow in Porous Media", SPE Reservoir Engineering 2 (1987) 281 Staudinger, H . : "Organische Kolloide als Makromolekule". Kolloidchemisches Taschenbuch Leipzig 1944 p.291 Szabo, M . T . : "Some aspects of polymer retention in porous media using a C1* tagged hydrolyzed polyacrylamide", SOC. Petr. Eng. J . (Aug. 1975) 323 Templer, C . E . : " Characterization of powdered coal by flow micro calorimetry", Microscal Publication, Microscal Ltd. 79 Southern Row, London W105AL Vollmert , B .: "Grundriss der Makromolekularen Chemie" , E . Vollmert Verlag Karlsruhe (1980) or Polymer Chemistry.Springer Verlag New York (1973) V o l z . H . V .: " A Method for Reducing Polymer Retarition in Cliemical Flooding for EOR under High Salinity Conditions". Proc. ACS Division of Polymeric Materials: Science & Engineering ( 1 986) 55 855-859 Zimm, B . H . ,Crothers, D . M . : "Simplified rotating cylindrical. viscometer for DNA", Proc. N . Aca. of Sciences. 4 8 (1962) 905

94

OF EOR-POLYMERS

6 LABORATORY TESTING

At the beginning,of a polymer flood, extensive laboratory work is

necessary. The

the

task is

conditions in

tolerance, economic only

a particular

conditions. The

needed to

the

also other

more per

than

of a

kilogram of

another product

price,

mixing

water,

chemicals, that

is

and not

chemicals such as surfactants that

that reduce

economic efficiency

costs

quality of

consumption of

mix emulsion polymers, oxygen scavengers, biocides,

sacrificial agents

or

a polymer product suitable to

oilfield with respect to salinity

temperature stability,

polymers, but

are

to find

adsorption, mainly

polymer flood.

determines

Thus a polymer that

active substance may be more economic

having the

same viscosity

yield at a lower

if fewer additional chemicals are needed. The profitability

of

a high-price

of

the mixing

polymer may be better if no expensive preparation water is

necessary, or

lower, or a

adsorption is

smaller slug size is needed. A l l these factors influencing the

mer

flood and

laboratory.

its economic

Therefore in

technical success of a poly-

efficiency are to be evaluated in the

this chapter

the basic

descriptions of

laboratory work are presented. 6 . 1 Polymer mixing The main preceding solution ticles

pages

is that

of single in that

small in

prerequisite and

much

the polymer

macromolecules in

solution should

enough to

a polymer

assumption that

was made

aolut.ion is

in

the

a homogeneous

water. The size of the par-

not vary

too much

and should be

pass through the pores of a reservoir rock. Hence

solution no

precipitates or

gel particles that are

bigger than .the single molecule should be present. This means

that

proper

mixing

of

the

polymers

is

necessary

for

any

applica+.ion in the field. For this purpose adequate mixing methods must

be developed

as well as methods to test the injectability of

the polymer solution into a reservoir rock formation. The polymers vered

that are

applied in field projects may be deli-

in different states. They may be a fermentation broth with a

of

2

25

"6,

-

10 X

concentration of active product, or an emulsion with

or a gel with about 6 0 % ,

or a 100 % powder. A l l

these forms

demand

different mixing procedures. The fermentation brolh in most

cases

only needs a dilution, t.he emulsion must be broken down, arid

the

gel takes

assure

thHt the

some time

to swell.

dry powdei,

I n mixing

powders

one

must

is well dispersed in the solLrent,’arid

95

that to

the gels that form from the powder particles have enough time swell. This

processes before

shows that

an optimum

cooking

for a

at

the

first

Anybody who

by mixing

cream, knows

glance,

simple

has ever

done

some

starch for a sauce, o r diluting of how tricky

this mag b e , and that i t

does not heed the experience laid down in r ecjpes. A

fails

if one

thick

solution of

and

is obtained.

and started

gelatine

such,

as mixing and stirring may also require some development

starch must

be prepared before i t can be used,

gelatine must be allowed to swell at raised temperature before

further application. 6 . 1 . 1 Polyacrylamides The hardness of the mixing water is a very important factor in the

properties

of

polyacrylamides. is

generally not

hand,

the

The use

solution

of

partially

hydrolysed

of distilled water is unrealistic, as i t

be available

in field

operations. On the other

the viscosity of partially hydrolysed polyacrylamide is very

high

in distilled

mixing used

water, but

water effect in the

only small

a drastic

amounts of salts in the

decrease in

viscosity. The

water

field should be as fresh as possible, but one must be

certain that i t will not become harder during the flood. The water standard in

used in

the field.

composition. that

the laboratory

for testing

should

be

a

fresh water, similar to that water that w i l l be available Tap water

The test

is mixed

is not

recommended as it may change its

water should

with salts

be made

in accordance

from distilled water

with the

results of

an

analysis of the fresh water to be used for mixing in the field. The concentrations of a polymer solution used for flooding are usually

very low.

Diluting

difficult.

1000 ppm

are common.

in one step - down to these concentrations is

The formation

of big

gels

(fish eyes)

may be

con-

more effectively if a more highly concentrated stock solu-

trolled tion

500 -

Concentrations of

polymers -

is first

needed

in a

prepared which is then diluted to the concentration second step.

concentrations

a stirrer

In preparing a stock solution at higher is recommended to disperse the particles

in the solvent. TANAKA (1981)

gels, The

and found

volume of

perature

investigated the

properties of

polyacrylamide

that these gels show discontinuous phase changes. the gels changes very abruptly at a particular tem-

or salinity

of the water. This behavior is shown in Fig.

96

6.1

for the

temperature and

Fig.6.2 f o r

the salt content of the

mixing water, The results plotted in Fig.6.1/6.2 show that a

120 100

0 80 Q

60 a

c m

l+o

E l-

20 0

-20

t 35 0.1 0.2

0.5

1

2

5

10

20

50 1

0

Swelling ratio (final volume/initial volume) Fig. 6 . 1 Dependence of the swelling ratio (end volume / initial volume) on temperature for polyacrglamide according to TANAKA

0

Swelling ratio (final volume/initial volume] Fig 6 . 2 Swelling ratio as accordinn to TANAKA

a function of salinity of mixing water

97

minimum mixing the

temperature water salt

of about 20

O C

is necessRry and that above a NaC1. or 1 mg/l MgC12,

1 g/l

concentration of

gels do not swell. A swelling of a gel is necessary before its

molecules

can go

separated

molecules, and

several

for EOR,

influence

of temperature

dissolution This

means

as

single

and

phase behavior of the

TANAKA may be different from that

the results

and hardness

process. Furthermore,

swelling process

there

a microgel that may be formed of Though the

investigated by

polymers used

the

and exist

not as

cross-linked molecules.

polyacrylamides of

into solution

shown above of

mixing

reflect water

on

the the

TANAKA’s work demonstrated that

goes faster

the smaller

the gel volume is.

that a fine and homogeneous dispersion of the polymer

in the water is necessary for the dissolution of polyacrylamide. The concentration of stock solutions of powders should be about 5

-

g/l. To

10

improve the swelling of the powder a good disper-

sion

in the

water is

the

powder

particles

particles wetting of

the well phase, as

the water

and

thus

dried powder an alcohol

prevent the agglomeration of

the

formation

may be

of

bigger

gel

"pre-dispersed" in a non

or mineral oil.

After the addition

a relatively long swelling time is necessary. During

period of

this

necessary. T o

about 12

hours

the

solution

should

be

gently

stirred with a magnetic stirrer. I f the polymer is delivered in tho form of a g e l , i t should be

cut

into small

pieces, which

gel

pieces are

relatively large

that

form while

are then diluted in water. As these as compared to the gel particles

putting a powder into solution, a longer swelling

time is essential. Emulsion polymers consist of an emulsion of water droplets in a matrix

of a

droplets.

mineral oil. The polymer exists as a gel in the water

About one

third of

the emulsion

is oil,

one third is

water, and one third is polymer. a solution of the polymer in water i t is necessary

T o prepare to

break the

mixing

emulsion and

water. The

to disperse

finely dispersed

the water droplets in the

polymer

particles

may

then

swell and dissolve in the mixing water. Emulsion polymers the

advantage of

small

as or

have, with respect to the solution process,

both a powder and a gel. The particle size is as

even smaller

than in

a powder,

and the

polymer is

already in contact with water. T o prepare to

convert the

a stock solution from the emulsion i t is necessary emulsion from

water in

98

oil to

oil in water. For

this

purpose a

some

products the

Instructions

surfactant should be added to the mixing water surfactant is

for mixing

already added

polymers in

to the

the laboratory

In

emulsion.

are given in

Appendix I . A final

solution having the concentration needed for flooding

may be easily prepared by simply diluting the stock solutjons.

6 . 1 . 2 Xanthan Xanthan is available in different forms. The easiest to handle is

the fermentation

tration

of 2

2% are

about sugars

broth. Fermentation

% --

5

-

other organic

and salts

broths

sometimes up to 7 %

that were

--

have

a

matters, including

mainly

used as

for

nutrients

concen-

of active polymer, rests

growing

of the

bacteria, and the remains of the dead bacteria. Xanthan is water

often chosen for a field application when no fresh

is available

solution broths

directly in

when

these broths

made

of a

the

produced

This

means

reservoir

that

brine.

the

polymer

Mixing

xanthan

such reservoir brines is usually feasible. But are concentrated

powder product.

polymer in

structure for

for flooding.

of

is made

it may

fresh water.

or when

the solution must be

become necessary to pre-dilute

In this

case a

swelling of

a

gel

is necessary, and the same mechanisms as discussed above

polyacrylamide are valid. The swelling of polymer gels is more

effective

in fresh

water and

at raised temperatures. This should

be considered when mixing procedures are worked out in the lab. A concentrated xanthan broth ( 5 - 12 % )

in

fresh water

should first be diluted

to a concentration of about 2 % before i t is mixed

to a high salinity reservoir brine. For mixing connection the

powder

products

with polyacrylamide

preparation of

the

same

procedure

powders should

stated

in

be considered, and

a stock solution in fresh water is easier than

directly diluting the polymer in a brine. 6 . 1 . 3 Hydroxyethyl cellulose Hydroxyethyl cellulose mixing as

it is

a very

is usually

delivered as a powder, and

well-known procedure because i t is also used

glue for wall paper. For mixing hydroxyethyl cellulose, a stock

solution

should

concentrations

also

be

necessary for

prepared

as

described

above.

hydroxyethyl

cellulose

are

than those for polyacrylamide and xanthan.

99

The

higher

6 . 1 . 4 Shearing of polymer solutions In mixing polymer solution, shearing the stock solution and the dilute

solution may

improve injectability. *Shear

treatment

was

(1974) and UNSAL et al. (1979) for biopolymer by GRODDE ( 1 9 8 0 ) , shear treatment to improve injectability was extended to polyacrylamide solutions.

described

by LIPTON

solutions,

In a

patent

Fermentation broths of xanthan having a concentration of 2 may

Shearing and to

-

4%

usually be diluted with reservoir brines without any problems. the broth

shearing the

before mixing

improve injectability.

speed

stirrer as

it with the saline field water,

diluted polymer solution are sometimes necessary Shearing may

shown in

be performed

F i g . 6 . 3 , or

through shear plates as shown in Fig.6.4.

by

jetting

in

a

the

high liquid

Shear plates consist of

6.3 High speed stirrers for shearing of polymer solutions (ultra turrax; courtesy of Janke & Kunkel GmbH, D-7813 Stauferi)

rig.

a

plate with

:,hearing

one

01’

several holes that is mounted in a pipe. For

xanthan solutions,

as a rule of thumb I h r e o sheer r ) l & t e s

re necessary with e pressure drop of 10 bar at each plate.

Shear plates

mas a l s o

be easily

mounted in

a

cotitinuo~~sly

operating

mixing device i n t,he field. High speed stirrer’s are also

availtnble

as in--line machines that

device in the field.

100

can be

mounted in

a

mixing

Nz

-

pressure

Sealing

Diameter - 1

cm

Sealing

Distance ring Shear plate cap

Rubber stopper

Fig. 6 . 4

Laboratory shearing assembly

The use of shear plates has the advantage that a scale-up from laboratory

to field

scale may

be done

very easily. The pressure

drop at a nozzle is described by the Bernoulli equation

(6.1)

v = V / (n

The velocity and

A is

, where n is the number of holes area of one hole. The factor

factor f o r non-Newtonian behavior of a liquid

correction factor

A)

the cross-sectional

j has

beeii determined

for

H

j

is a

Once the

particular polymer solution,

stock

solution. broth, or final solution. the pressure drop at t h o

shear

plate may

calculation shearing

be calculated

for every

is given in Appendix I )

a polymer

flow

rate

(a

typical

The optimal pressure drop for

solution, or a stock solution from which a f i -

101

nal

solution is

periments sheared well

in

must be

the laboratory.

polymer solutions,

as the

optimum

loss of

determined by a series of ex-

For

such

differently

injectability must

viscosity yield

be

due to

mixed

and

determined

shearing.

as

Once

an

pressure drop for shearing is found, the scale up to field

conditions rates

prepared

may be

effected by

6 . 1 . For high flow

using Equation

in a field mixing device the holes may be made bigger or the

number of holes may be increased. Shear treatment shown

in F i g . 6 . 4 may be

polymer vessel the

solution is

solutions using

completed very

filled into

the assembly

quickly and

the vessel.

as

easily. The

The outlet

of

the

behind the shear plates is closed by a rubber stopper. When

vessel is

nitrugen, plates the

of polymer

closed, a pressure may be applied to it by means of

and the

polymer solution

is pressed

through the shear

under this pressure drop. In the assembly shown in F i g . 6 . 4 .

shear plates

may be

changed by unscrewing the cap that holds

the plates within the short tube. 6 . 2 Stability testing

A s chemical

flood projects

chemicals

used should ,be

Polymers

should

flocculate

The

are

stability. should not pass

throughout these

their

viscosity,

long

they

periods.

should

not

stability

criteria

that

should

be

applied

to

solution stability, thermal stability and long-term

This means

remain at

that the

the initial

precipitate or

stability

stable

loose

to 10 years, the

of 5

or change their behavior in any way that could plug the

reservoir. polymers

not

last from

value, and

cross link

tests described

successfully,

are

viscosity of the polymer solution that the polymer should

and thus

below, which chosen

with

plug the a polymer respect

reservoir. The solution

to

the

must

possible

degradation mechanisms. A polymer molecule may be destroyed by high shear treatment as

discussed chemical

in

the

previous

reactions which

chapter,

or

by

high

temperature,

are accelarated with rising temperature.

and biologic~l degradation. 6 . 2 . 1 Solution stability

Solution stability stable

and neither

means that

the polymer

precipitates nor

creams

solution must

Polyacrylamides

be may

precipitate

i f the salinity or hardness of the mixing water is too

high.

solution

The

stabi itg

of

102

polyacrylamides

depends

on

molecular

weight, degree

of

hydrolysis

and

temperature.

Small

amounts of iron in the mixing water may, for example, gel xanthan broths. The solution stability can be tested by storing the solutions at the required temperatures. Such tests are the first in a series , and they often give the first rough impression about the weak points of a polymer. Fig.6.5 and Fig.6.6 show the results of a test on xanthan broth and xanthan solutions. The tests were performed to check the sensitivity of xanthan to different metals. Screws made of iron, stainless steel and brass were put into the solution and then the solutions were stored at a temperature of 60 OC for 10 days. The xanthan broth in contact with the piece of iron became red and the polymer gelled. The gel was very stiff and not pumpable; a dissolution of these gels not being possible. The broth in contact with the brass screw gelled too. The xanthan in contact with the stainless steel showed no changes. But after longer periods ( > 60 days) these broths, too, showed a slight gellation. Citric acid also stabilizes the solution. Citric acid forms a complex with the

Fig. 6 . 5 Solution stability of xanthan broth and xanthan solution in contact with different metals.

a

1000

ppm

iron. This may be tested simply: rusty iron in a citric acid solution changes its color very quickly from brown to black (dark

103

green)

and afterwards becomes blank iron again. An overview of the

chemistry of iron is given in Appendix J .

Fig. 6 . 6 Stability of a described in Fig. 6.5)

These experiments

1000 ppm

Xanthan

solution

as

were performed to test the applicability of

different materials for use in xanthan mixing

equipment

and

for

tanks. It is obvious that all parts with which the xanthan

storage broth

(stored

comes into

contact

should

be

stainless

steel

or.

even

better. plastics. The 1000

ppm solutions only showed a gelation when in contact

with iron.

As these neither as the

experiments were

free of

an orienting

performed with solutions that were

oxygen and nor sterile. they may only be regarded first step.

dilute polymer

But these

solution undergoes

experiments did show that no changes even in contact

with iron when an iron complexing agent is present. Such different

experiments may compatabilities of

hydrolysis

of about

hydrolysis

of

polyacrylamide

also be

performed to

investigate the

polyacrylamide with

a low degree of

5 % and and a polyacrylamide with a degree of

approximately with the

25

%.

low degree

104

The

experiments

of hydrolysis

show

that

has the better

stability

in reservoir

brine. In

frosh water

both products

are

stable. These simple decision

experiments are

concerning

whether

not to

a

be used for an ultimate

product

is

applicable

for

a

particular project or not. They can, however, help to find the weak points in a system and give indications for the choice of materials. 6 . 2 . 2 Long term thermal stability

If a polymer solution is kept for a longer period at high tem-

i t can degrade and loose its viscosity. peratures (50 - 90 ' C ) , The degradation may coincide with a precipitation. Detecting the thermal

stability

measuring

the

polymer

loss of

the solutions

is

usually

a polymer

should be

accomplished

solution.

For

by

those

free of both oxygen and any

may gel the polymer. I t is also necessary to keep

ions that

solutions sterile.

high,

a

the viscosity

measurements metal

of

sterility is

If the

not a

testing temperature

very big

is relatively the

are obtained by using oxygen scavengers or by evacuating

because oxygen

these chemicals is still

sulfite mixed

may also

present. Oxygen

should be into i t ,

oxygen scavengers destroy

may the

Oxygen

of

decreases

use of

temperature.

growth

solutions

solution. The

increasing

as

bacteria the

with

problem,

cause polymer

scavengers like

free

problems

if

thiosulfate

some or

added to the mixing water bsfore the polymer is

and the

reaction of the oxygen scavenger with the

oxygen should be complete. To mix oxygen-free solutions in the laboratory, a glove box is needed inert be

in which

the sample

may be prepared under a blanket of an

gas like nitrogen. If possible, the polymer solutions should

mixed using

a continuously

operating method, such as a mixing

device used in field operations. For testing the thermal stability of sufficiently prepared. similar.

large number

The samples A blanket

of samples

are sealed

in a

a polymer

of this

solution, a

solution

glass tube

or

must

be

something

of an inert gas should be present in the glass

tube to allow the liquid to expand when heated. The samples viscosity viscosity product.

are then

stored at the required temperature, and

is measured at regular intervals. The decrease of gives an impression of the thermal stability of the An example

is shown

in Fig.6.7 for xanthan

environments.

105

in various

100

Q

0

0

42. .L4

s

VI .->

-.I0

+ .c '-

50

'c

0

+

c

al L u

T r a c e s O p F e (1 day)

al

a

A

T r a c e s 02+Fe

0

Ot*Fe

, 0

I

,Y, ,

,

,

1

100

10

Time, (days1 Fig. 6 . 7 S tability of xanthan in the presence of steel (variable contact time ) and oxygen (different concentrations), according to CHAUVETEAU et al. (1985)

If samples of a greater volume are stored, injectability tests solution was might plug a

also be performed. Such tests indicate that the either gelled or something else happened with it that porous medium. Long-term thermal stability is often tested at peratures than the reservoir temperature at which the

may

higher tempolymer will

be used, because chemical reaction rates, as a rule of thumb, double every 10 " C , and thus the testing time may be reduced.

6 . 2 . 3Biological stability

The

biological

stability

of

effec iveness

a

polymer

solution

or

the

of a biocide may be tested in a manner analogous to that used for thermal stability by measuring the viscosity loss of a polymer solution as a function of time. Another testing method is to observe the growth of a particular species of bacteria by determining the number of germs using light scattering or other methods, or to observe the metabolism of the

106

c

m

0

Fig. 6 . 8 Biological degradation of xanthan. Product formation during anaerobic degradation. (CORDRUWISCH et a l . ( 1 9 8 5 ) )

bacteria.

In

degradation oculated

Fig.6.9

products

observed

during

bacterial

of xanthan a r e plotted versus time. The sample was in-

with bacteria

gradation

the

mechanism may

found in produced oil field water. T h e debe observed

by the

metabolism

of

fer-

menting

bacteria.

Microbiological investigations have shown that

xanthan

i s , under

anaerobic conditions, a substrate for bacterial

growth. 6 . 3 Injectability testing Good injectability into a porous medium is a basic requirement for

any polymer

tability

and how

essentially through

solution. T h e may it

two methods

question is: What is a good injec-

be measured i n the laboratory? There are currently

in

use:

filterability

tests

membrane filters: and injectivity tests in a porous medium

such as sandstone cores or sand packs.

107

6 . 3 . 1Filter tests For these tests filter membranes having pore sizes of 0 . 8 - 3pm are

utilized. These

tions,

since

tests are

polyacrylamides

usually show

a

applied to xanthan solusignificant

viscoelastic

effect that may cause extraordinary pressure drops and thus lead to wrong conclusions about the results of such tests. BY definition,

a filter

solutions.

In xanthan

of

form a filter cake and reduce filterability. A microphotograph such a

taken filter and

only detect solid particles in the

solutions bacterial debris are present that

to fall out of the solution, or may produce agglomerates that

tend can

test can

of the is also

not a

whether

filter is

shown in

edge of

SEM-photograph

was

a cleaved filter. It is obvious that such a

a porous

sieve having

Fig.6.9. This

medium, having a pore size distribution, well defined

holes. It

may be

doubtful

such a porous medium having pore sizes much smaller than a

reservoir rock is which are pressed

the proper medium to test polymer solutions, through this filter with pressure gradients of

several thousand bar/m.

F i g . 6 . 9 Microphotograph of a membrane filter measuring 0 . 8 pm

108

The materials these filters are made of are cellulose acetate, cellulose nitrate, polyamide, etc. The micrograph in Fig.6.8 shows that the filters do not have only one particular pore size, but rather a distribution in pore size. In Fig.6.10 the result of a filter test on different xanthan solutions is shown. The filtration rate is plotted versus the cumulatively filtered polymer solution. The tests were made for one xanthan solution mixed from a broth and two solutions made of powder grade xanthan. Curve 1 shows that the filtration rate remains constant during the whole experiment, whereas in the experiment with the solutions made of the powder grade xanthan, the filter is plugged. The plugging of the filters may be due to insufficient dissolution of the polymer. A curve such as No. 1 in Fig.6.10 is seldom encountered in such filtration tests. Usually the curves dip after a certain amount of

50

-p

-E .>

10

5

a i l

4-

m

c

0.5

0 .c L m

f .LL

0.1 0.05

0.01

.

0

200

400

600

.

BOO

1000

Cumulative filtered polymer solution, (mi) Fig. 6 . 1 0 Filtration test on differently solutions, 3 pm-filter (LITTMANN et al.)

109

prepared

xanthan

polymer

filtered. This does not necessarily mean that

solution is

such polymer solutions may not be used in polymer flooding. Such solutions may perform very well in an injectability test as described in the next chapter. Filtration tests should only be used as a means of compar son, for

instance, of

pressure the

different mixing procedures for one polymer. The

drop at

a membrane

hydraulic radius

filter may

concept

as

also be calculated using

derived

for

porous

media

in

5. A method for calculating pressure drops across random -

Chapter

fiber filters was evaluated by KAPLAN et a1.(1979). The results of the

tests depend, at the same pore size, on the type of filter pa-

per

that is used (sometimes even on the batch number), or the wet-

tability

of the

polymer solution.

If the

filter paper

is

pre-

wetted with a surfactant, better results are obtained. As the filtration test is very quick and easy to perform, i t is very

popular. But as stated above, it should only be used to check

the

values known from other tests for one particular polymer, e . g .

to control the performance of a mixing unit. 6 . 3 . 2 Injectivity testing on core plugs and sand packs ,

A good

obtained the

by injecting

reservoir rock.

ducible. in

idea of the injectability of a polymer solution may be a porous medium that is similar to

porous medium

should be

well repro-

Core material from the reservoir is usually not available

sufficiently large

often

vary within

tests

may be

amounts, and

a wide

be obtained

its porosity and permeability

range. Other

obtained from

or Bentheim

sandstone also

it into

Such a

core material

quarries like

the

sandstone. Synthetic

by fritting

for

flood

well-known

Berea

porous

together small

material

may

glass beads (DEURER

(1982)).

The sand pack is a good reproducible porous medium. Sand packs for

injectivity testing,

should

be

made

distribution.

of

as proposed

a

sand

A plexiglass

with

by KOHLER a

et

al.

well-defined

(19811,

grain

size

cell as shown in Fig.6.11 may be used

to prepare the sand packs. At the bottom of the cell a plexiglass disk with several holes is mounted which supports a fine overlying sieve

On

with a

the

wall

approximately

mesh width of

the

the size

smaller than the grain size of the sand.

cell

small

rills

are

turned

that

have

of one sand grain. These rills prevent the

fluid from bypassing along the wall.

110

End cap 0

-

ring

Rough wall

Sand

Fine plastic sieve Coarse Plastic sieve

End cap

1 Fig. 6 . 1 1

Plexiglass cell for sand packs

g-Q

1

I Pressure tranducer

I

0

0

Sand-

I I I

I

Fig. 6 . 1 2

Injectivity testing assembly

111

H

The plexiglass cell is mounted in an assembly as shown in Fig. 6 . 1 2 . The polymer solution is pumped through the sand pack at a

constant rate by means of a piston pump. The injection pressure is measured and recorded on an x-t chart recorder. to make

In order sand

should always

should

be dry

Afterwards.

reproducible sand packs, the same amount of

be filled

and may

the sand

The vacuum produced the cell.

into the

be condensed pack is

plexiglass cell. The sand

by shaking

the whole

cell.

evacuated and saturated with water.

by a water jet pump is sufficient to evacuate

The sand packs obtained have porosities of about 40 % and permeabilities, depending on the grain size distribution of the

100

m

F

i

3

10

U 0

.-v) '

c

5

c

1

0.1

05

5

1

Rate o f shear strain,

50

10

100

+ (s-’)

Fig. 6 . 1 3 Flow curves of polymer solutions 1: 1000 ppm polyacrylamide - degree of hydrolysis 25 X - in water of 5 OdH=50 mg/l CaO 2: P A A in water of 3 0 "dH=300 mg/l CaO 3 : 600 ppm xanthan ; temperature 20 OC

sand, may

between 1

be calculated

curves

of three

and 5

urn2. The

using Equation

permeabilities of the sand packs 5.70.

In

Fig.6.13,

the

flow

different polymer solutions are plotted which are

in turn employed in injectivity tests to be dlscussed below.

112

The injectivity

tests of the two polyacrylamide solutions are

shown in Fig.6.14.Solution 1 exhibits a higher pressure drop than solution 2. This is in agreement with the higher viscosity of solution 1. The increase in pressure drop from 10 pore volumes injected polymer solution to 270 injected pore volumes is from 510 hPa to 660 hPa. This increase of 100 hPa represents 19.6 % of the initial value. The residual resistance factor is measured when flooding the sand pack after the test with water. The pressure drop for water after polymer flooding is 90 hPa. The initial value was 20 hPa. Hence the residual resistance factor is 4.5.

800 m

f

300

v)

200

n

100

90 hPaI

0

40

80

I

120

I

I

160

I

200

I

I

I

2kO

10

injected pore volumes Fig. 6.14

Injectivity tests on polyacrylamide solutions

Polymer solution 2 is made of the same polyacrylamide, but in a harder mixing water, The viscosity of the solution is therefore lower, as is the pressure drop in the injectivity test. The increase in pressure drop is 125 X of the initial value. The residual resistance factor is 10. A s a result, the injectivity of solution 1 is better than that solution 2 . The reason for this may be the harder mixing water. Gels may have formed while mixing the polymer. A blocking of the pore space is also indicated by the higher residual resistance

of

factorI

113

In Fig.6.15 an analogous injectivity test is shown for a xanthan solution. The solution was prepared from a fermentation broth. It is

obvious that

the pressure

loss is

lower than that of the two

polyacrylamide solutions, though the viscosity

L

o

6 hPa

l

!

,

,

,

,

40

0

is-higher than for

,

,

,

,

120

80

,

,

,

,

, 240

200

160

2 0

Injected pore volumes Fig. 6.15

Injectivity test on a xanthan solution

solution

2.

demonstrate

This

is

because

elastic viscosity.

the

xanthan

A 16

solution

does

not

percent increase in pressure

drop arises. The residual resistance factor is 1 . 6 . For this xanthan solution a pressure drop may also be calculated

using Equation 5.71. The porosity of the sand pack was 5 4 . 9 X ,

the

length 4

rate

was 80

Darcy

c m , the cross-sectional area 2.84 cm2, the injection cm3/h, and

velocity is

7.8

the water

.

m/s,

viscosity 1.16 mPa.s. So

the

and the permeability is 2.250

For flow curve 3 shown in Fig.6.13, the power law exponent is 0 738 in the interesting region of rates of shear strain above 10 pm2.

s-'.

The rate

of shear strain may thus be calculated according to

Equation 5 . 7 1 . is 108 s - ' . curve. 65

This yields

a value of

4 . 7 mPa.s from the flow

With this viscosity the pressure drop in the sand should be

hPa. This

is a little below the measured value of 7 4 hPa. This

114

error

is tolerable

if one

considers the errors that may occur in

the determination of porosity and length of this small sand pack. The results shows

of the test are, first, that the xanthan solution

good injectability- and, second, that a solution having such

an injectability may be used for field applications. 6 . 4 Oil displacement tests

Oil displacement screening

to

concentration economic

tests are

determine

and incremental

data. These

performed at the end of a polymer

the

optimum

slug

oil recovery

flood tests

must be

size,

polymer

for the evaluation of performed in

a

well-

defined manner and with a good reproducibility. When performing flood tests, several points should be carefully considered.

6.4.1 Crude oil The crude oil to be used should be thoroughly dehydrated. Most crude such

oils produced as sand,

filters such of

from well

bores contain some solid particles

silt or clay, so the oil should be filtered through

of about

3

filters are

urn. The filters

should have a large surface:

available which withstand differential pressures

several bar. To improve filterability, the oil may be heated or

solvents

may be

added, if

experiment. After filtration above

should be

at which

do not spoil the flood topped at

the flood

a temperature

experiments are

to be

By adding solvents that are similar to the original low

performed.

components of the oil, the viscosity of the oil may be to the viscosity required for the experiment, i.e. the oil

viscosity

under

advantage

that the

pressures, employed

reservoir

and no

petroleum the

the oil

the temperature

boiling adapted

these solvents

gas are

high

composition

pressure

necessary.

in polymer

most

conditions.

flood experiments

important

This

may be

cells

Such

model

and

procedure

has

the

performed at normal recombination

oils

should

with

only

be

flood tests where the viscosity of the oil is factor.

For

flood

tests

where

the

oil

is important, such as for surfactant or carbon dioxide

flooding, such model oils cannot be used. A procedure in which the oil is recombined is recommended for every

flood experiment,

since the

oil sampled from the well head

usually does not have the same properties as the life crude oil under reservoir conditions. The recombination of the oil may be done similar to a PVT-analysis.

115

6 4 . 2 Porous medium

The porous comparable during

medium will

to the

which a

usually be a reservoir rock or a rock

reservoir rock.

But for

particular parameter

series of experiments

is changed, natural rocks do

have the required reproducibility. A preflush with citric acid

not

hydrochloric acid

or

remove

movable fines

is therefore

recommended for

many rocks to

or iron often present in rocks obtained from

outcrops. To avoid these difficulties, and because core material is often of limited length, flood tests should be performed in sand packs.

A mixture of several sand fractions similar to a representative grain

size distribution

model

sand. The

ogeneous sizes

grain size

as this

and thus

should

of the

reservoir rock

may be

used as a

distribution should not be too heter-

may cause

a separation

of the

different grain

plug the sand pack. According to the reservoir, it

be decided

whether a

crushed sand

or a

rounded sand

is

appropriate. The tube length

and

experimental

of

a

material

temperatures. At

that

may

low temperatures,

be

used

at

the

plexiglass cells

be used which allow one to observe the experiment. A length of

may 1

to be used for the sand pack should be of sufficient consist

m and

a diameter

of 2 - 3 cm usually meet most requirements of

an experiment.

If the

sand packs

reproducible Porosities

are always

produced in the same w a y , good

values for porosity and permeability may be obtained. packs are 4 0 - 50 % , and permeabilities in the

of sand

range of 0 . 5 - 4 Jim2 may be easily produced. 6 4 . 3 Saturating with water

the sand pack or core with water the tube or core

T o saturate holder

should be

should

be well

pressure must

and then

in the

is to

flood the

water. If

the core

the lower

water saturation

with C O P

saturated,

evacuated before

flooded from

a good

dissolved the

(sand

pack)

evacuated, and while saturating with water, vacuum

should be

achieve

The core

should be applied. It is also self-evident that the water

be thoroughly

water pores

mounted perpendicularly.

a core

is saturated.

side. Another exchange the

water. The or sand

The

method to air in

CO2 will

the

then be

pack is sufficiently

i t may be checked by weighing, since the bulk volume of

core, the

density of

the s a n d ,

116

the porosity

as well as the

density not

of the

easily

water are known. Complete saturation with water is

obtained,

and

a

poorly

saturated

core

may

cause

incorrect results that may be misinterpreted.

6.4.4 Saturating with oil In order mounted upper

to saturate

perpendicularly end. Several

water

is

and the latter should be flooded from the

pore volumes

displaced.

accomplished

the core with oil, the former should be should be

Determination

by material

flooded until no more

of

the

oil

saturation

balance, where

the

volumes

of

is

tubes,

valves, etc. must be considered. The flood velocity is important for the saturation process, and to

achieve good

reproducibility the

same flood

velocity

should

always be assumed.

0

0.5

1.0

2.0

1.5

2.5

3.0

Flooded pore volumes Fig.

6.16

Result of

a typical

flood experiment,

according

to

DIETZEL (1982)

6 . 4 . 5 Displacement test A result

polymer

of a

injection is

displacement test is shown in Fig.6.16. Before started, a

water flood is usually performed

until a well-defined water cut is reached. From such an experiment

117

the thus

ultimate recovery the incremental

for a

water flood may be extrapolated, and

oil recovery by polymer flooding can be cal-

culated as shown in F i g . 6 . 1 6 .

REFERENCES Chauveteau, G . , Combe, J . , Latil, M . , Zaitoun, A . , Truchetet, R . , Turta, M . , Blank, L . , Panaitescu, A , , Barsan, P . : "Preparation d ’ u n pilote d’injection de polysaccharide dans le reservoir de Surani-Carbunesti",3rd Eur. EOR Symp. Rome (1985) Cordruwisch, R . , Kleinitz, W . , Widdel, F . : "Sulfate reducing bacteria and their economic activities", SPE-paper 13554 (1985). Deurer, R . , Klose, P . - S t . : "Herstellung kunstlicher Kapillarsysteme", Erdol- Erdgas- Zeitschrift 98 (1982) 25. Dietzel, H . - J . : "Untersuchung uber die Eignung von Polymerlosungen z u r Erhohung des Entolungsgrades", Thesis, Technical U n . Clausthal ( F R G ) , 1982. Grodde, K.-H.: "Verfahren zur Scherbehandlung waessriger Loesungen von partiell hydrolysierten Polyacrylamiden" Int. Cl.: E 21 B 43;22 (1980). Patent DE 27 33 852 B 2 Kaplan, S . J . , M o r l a n d ,C . D . , H s u , S.C.: "Predict non-Newtonian fluid pressure drop across random-fiber filters", Chem. Eng.(Aug.1979). Kohler, N . , Chauveteau, G . : "Xanthan polysaccharide plugging behavior in porous media - preferential use of fermentation broth", J . Petr. Techn. (Febr. 1981) 349 Littmann. W . , Westerkamp, A . : "Xanthan-biopolymer flooding in a north German oilfield, q t h European Symp. on EOR", Hamburg (Oct. 1987) Lipton, D . : "Improved injectability of biopolymer solutions". SPE paper 5099. Tanaka. T . : Scientific American. Jan. 1981. Unsal, E . , Duda, L . J . ,Klaus, E . : "Comparison of Solution Properties of Mobility Control Polymers", in: "Chemistry of Oil Recovery", Johansen and Berg (editors), ACS Syposium Series (1979) 91

118

7

RESERVOIR ENGINEERING ASPECTS For a polymer flood project some reservoir engineering aspects

have

to

be

operations. pressure wells

recognized These are:

that

from

differ

higher injection

normal

water

pressures;

a

flood

different

distribution in the reservoir; another ratio of injection

to production

wells; and

special

features

for

numerical

reservoir simulation,

7.1 Evaluation of reservoir characteristics

A good necessary data to

understanding

on permeability the mechanisms

of

the

reservoir

characteristics

is

the performance of a polymer flood. So good

to evaluate

and its distribution are essential according

that influence

the

incremental

oil

recovery

possible during polymer flooding as discussed in Chapter 2 . Knowledge of important due

to

the mineral composition of the reservoir rock is

in order adsorption.

parameters

to be An

able to overview

influencing the

estimate the loss of chemicals dealing

performance of

with

such

chemical

geological flooding

is

given by GAIDA et a1.(1985). The geological should

a reservoir

or reservoir block

be as well known as possible, because this, apart from

turation the

boundaries of

data, determines

sa-

the amount of chemicals needed and also

chemicals that may be lost into an aquifer or other

amount of

parts of the reservoir where no oil may be recovered.

For the evaluation of the reservoir behavior it is necessary to have

a sufficiently

This

i s , of

long and

well-documented production history.

course, also important if a numerical reservoir simu-

lation will be performed.

7 . 2 Injection

w a s

A s a polymer flood is relatively expensive, i . e . as compared to

regular

water flood

location located

and number in such

possible. wells On that be

that the

loss of chemicals is as small as

As an example, in a reservoir with an aquifer, injection drilled near

the oil

water contact, so that the

do not have to pass a long distance through the aquifer.

the other no oil

chemicals

should be given to the

of injection wells. Injection wells should be

a way

should be

chemicals

operations, attention

hand, the is displaced

into an

balanced in

injection wells into the

aquifer, injection

should be

aquifer.

To

situated such avoid

loss

of

and production rates should

such a manner that the flow of fluids is mainly in

119

the

direction of

drilling

the producing

back pressure

wells. This

wells into

may be

which water

amplified by

is injected, thus

forcing the chemical slug to flow in the desired direction. If the injection water is oxygen free, which is normally a prerequisite for polymer flooding, no special coating of the tubing is necessary. As was shown in the previous chapter, the iron

that may

normally

go into

does no

solution from

harm to

a dilute

iron parts

such as tubings

polymer solution,

especially

when iron sequestering agents are added. The perforations should be clean and the number thereof as high as possible. In any case, especially at old wells, a reperforation with high density perforators (tubing conveyed guns) is recommended. check the

If an

open hole

whether the well bore

completion is

reservoir region

radius

should

be

possible, one should

can be underreamed. Moreover, as

large

as

possible.

Small

fracture jobs may also be performed to improve injectivity. Injection wells the

that are

located in an oil saturated area of

reservoir, or production wells that have been converted to the

injection that is

type, usually exhibit an injectivity which is worse than

of wells due to

located in

the small

the aquifer of the same formation. This

relative

permeability

to

water.

Even

at

residual oil saturation the relative permeability to water is only about 10 to 20 percent of the absolute permeability. In such cases a

stimulation of

done oil

the injection well may be necessary. This can be

by acidizing or by using surfactants that reduce the residual saturation and

thus increase

the

relative

permeability

to

water. In most cases the limiting parameter for injection pressure is the

fracture pressure

should,

in most

of the

formation.

The

fracture

pressure

be exceeded so as to prevent un-

reservoirs, not

controlled fracturing of the reservoir and thus uncontrolled fluid losses during injection. In deep formations ( > l o 0 0 m), the fracture

pressure

is

normally

fracture

not

pressure

may

obtained, already

but

shallow

the

relatively

small injection rates. In such cases it is necessary to

evaluate the fracture pressure by means of a Shallow formations are often "weak" with the

be

in

formations

exceeded

at

breakdown test. result that no

fracturing is possible. The pressure loss in the tubing, the perforations and the formation Example

may be calculated using the equations derived in Chapter 5 . calculations for

the pressure

120

drop in pipes are given in

D. The calculation of the pressure drop in the reservoir,

Appendix

and thus injection pressures, is described in the next chapter. 7 . 3 Pressure distribution in the reservoir from

In polymer flooding the pressure distribution is very different that found in primary production or water flooding. As was

discussed

in the

solution

previous chapters,

the viscosity of the polymer

is not constant, but rather varies with the flow velocity

in

the reservoir.

in

the reservoir

This makes the calculation of the pressure drop and the

calculation of injection pressures more

complicated than for water flooding. 7 . 3 . 1 Injection pressure A first approach to calculating injection pressure is to ignore production or flood radial flow

assuming from

patterns, and

a constant

to use

the Darcy equation for

boundary pressure pe at a particular distance injection pressure or pressure dis-

the injection

well. The

tribution

in the

injection

rate. For Newtonian liquids like water, this calculation

is

reservoir may

rather simple,

solutions, constant,

because the but depends

for non-Newtonian liquids like polymer

viscosity of

the polymer

solution is not

on the rate of shear strain and thus on the

velocity. An equation to calculate the pressure distribution

Darcy may

but not

then be calculated for a constant

be obtained

by substituting the viscosity in the linear Darcy

equation by a power law, and within the power law the rate of shear strain in the porous medium by Equation 5 . 7 1 . By integrating this one

equation, as

injection becomes the

the

calculation

of

in

the

in radial

and so

reservoir

it may

stepwise,

increments. This

be easier to calculate assuming

a

constant

procedure has the advantage

it is not necessary to use only one power law with a constant

and H

values

enables

pressure for non-Newtonian liquids. But such an equation

pressure

that

equation which

rather complicated

viscosity n

in the derivation of the radial Darcy equation,

obtains another

for the

for n

calculation, but i t is possible to use different

and H for the different regions of a flow curve. For

121

particular

a

calculated, shear

strain for

determine

increment,

the

Darcy

velocity

may

be

this Darcy velocity the, corresponding rate of

the polymer

the apparent

apparent the

radial

and for

solution, which

is

then

used

to

viscosity from a measured flow curve. This

viscosity 1.1,

is then

used in

Equation 7 . 1 to calculate

pressure drop for this radial increment. If the increments are

chosen

in the

right manner,

the obtained

result

will

be

good

enough for further reservoir engineering considerations. In Table 7 . 1 the reservoir data and the rheological data of the polymer the

solution for a calculation example are shown. In Table 7 . 2

results of

polymer

the calculation

solution that

are listed

exhibits no

for

the

elastic viscosity.

case

of

This table

also outlines the calculation procedure.

Table 7 . 1

Data for calculation example

Injection rate: Bore hole radius: Net thickness: Porosity : Permeability: Power law exponent: Power law constant:

,Distance Darcy from velocity well

, ~

I

I

i’

VD

= 24 m3/d = 2 . 7 8 . 1 0 - 4 m 3 / s rw= 3 . 5 " 8.89.10-2 m h = l m 0 = 0.3 k = 2.5,10-12 m2 n 0.5 H 5 0 mPa.sn V

Rate of Viscosity ln(ri/ Ap(rishear in reserri-1) ri-1) strain voir

i,

(m)

(m/s)

0.1 0.3

4 . 4 2 . 1 0 - ~ 902 300 1 . 4 7 ' 10-4 180 8.85.10-5 90 4.42.10-5 1.47.10-5 30 18 8.85.10-6 9.0 4.42.10-6 3.0 1.47. 1.8 8.85'10-7 4.42.10-7 0.9

0.6 1.0

3.0 5.0 10.0

30.0 50.0 100.0

(s-1)

Ma (mPa.s) 1.66 2.89 3.73 5.27 9.13

11.8 16.7 28.9 36.3 52.7

122

(pa) 0.118 1,099 0.511 0.693

1.099 0.511 0.693 1.099 0.511 0.693

3 . 4 6 103 5.62, lo4 3.34, lo4 6.46.104 1 . 7 8 ' lo5 1.07.105 2 . 0 5 105 5.62. lo5 3.28' lo5 6.46' lo5

a

Ap( ri )

( kPa 1

3.5 59.7 93.4 158 336 443 648 1210 1538 2134

In Table 7 . 3 the same calculation is made for a polyacrylamide solution

assuming a

,

constant elastic

viscosity of

30

rnPa.s

in

accordance with Section 5 . 6 . 3 and Appendix E.

Table 7 . 3 Results of calculation 30 mPa.s) (elastic viscosity

example

polyacrylamide

for

iato of Viscosity sheer in reser;train voir

0.1 0.3 0.5 1.o 3.0 5.0 10.0 30.0 50.0 100.0

4 . 42 . 1 0 902 1 .47.10-4 300 8.85. 180 4.42’10-5 90 1.47.10-5 30 8.85.10-6 18 4.42’10-6 9.0 3.0 1 . 4 7 ,low6 8.85.10-7 1.8 4.42.10w7 0.9

0.118 1.099 0.511 0.693 1.099 0.511 0.693 1.099 0.511 0.693

31 33 34 35 39 42 47 59 66 82

6 . 4 7 ’104 6 . 4 2 .lo5 3.08.105 4 . 2 9 .lo5 7 . 5 8 .lo5 3 . 8 0 ’lo5 5 . 7 6 .lo5 1 . 1 5 ,lo6 5.97 105 1.01 ' 106

106

1014 1443 2201

2581 3157 4307 4904 5914

lo3

€

a"

<

d

c

2 102

10'

0

j U v)

.->

al

L

a

c

v)

c

v)

al

&

64.7 706

10’

100

!! a.

4 I I

I

10-1

100

10-2

10-1

100

10’

102

Distance from well bore, r (ml Fig. 7.1 Pressure distribution Injection of different polymers.

123

around

an

injection

well.

In Fig.

7 . 1 the

results of

these calculations

are

plotted

together with the pressure distribution that would be obtained for water

flooding. These

calculations did not copsider the fact that

during a polymer flood, or water flood, the effective viscosity is a function of the saturation of the displacing phase. These simple calculations

should only

be used

to get a first impression about

the injection pressure that may occur during polymer flooding. The calculation shows that for flooding with a polyacrylamide solution under

having a

considerable elastic

viscosity, the

viscosity

reservoir conditions for the calculation of pressures may be

assumed

as nearly

constant. Whether

this is

also true

for

the

displacement mechanism is not clear, but may be doubted. In order to clarify this matter, laboratory oil displacement tests are needed which should be performed using viscoelastic polymers.

at different

Darcy

velocities

7 . 3 . 2 Pressure testing During every

pressure measurement

in the

oilfield, such

as

bottom hole flowing pressure, pressure build-up, or pulse testing, 10

9 ’

8 1

'.

I

I

r

before po\ymer injection

-

n Y I

3

2

1

Fig. 7 . 2 Pressure fall-off test in an injection well in the Eddesse-Nord polymer pilot project (LITTMANN (1988)). Curve 1 after water injection, curve 2 after 1 . 5 years polymer injection. (analysis acc. to MATTHEWS (1967))

124

the

result of

fluids methods in

the reservoir.

Therefore, by

using these test

in polymer flooding the effective viscosity of the poylmer

the reservoir

extension For

the test is also determined by the viscosity of the

flowing in

may be

of the

determined,

polymer slug

such purposes

or

in the

an

impression

of

the

reservoir may be obtained.

conventional pressure

analyses such

as Horner

plot, type curve matching, e t c . , may be used. In Fig 7 . 2 the analysis of two pressure fall-off tests is shown as

an example,

polymer

one test

after water

injection before start of a

and the other after 1 1/2 years of polymer

flood project,

injection. Test It1 Assuming

calculated.

permeability.

the viscosity

in

the

reservoir

was

The viscosity measured in this way was 2 . 7 mPa’s. This

not as high as the viscosity of the injected polymer solution, was 10 mPa.s at a rate of shear strain of 10 s-’.

which

this result

during polymer result be

reservoir

same permeability and the same remaining

test # 1 ,

as in

the

significantly higher than the viscosity of the reservoir water,

but for

to determine

#2 the

in test

parameters is

was used

the polymer

amount

flood or

solution was shows that

performed in

The reason

could be that the permeability to water increased that the

presumably too

whenever it a polymer

of information

radius influenced large.

In

any

by

the

case,

this

is possible, pressure tests should

flood in

about the

order to

obtain

a

maximum

behavior of the polymer solution

in the reservoir. 7 . 4 Flood patterns

As shown

for is

above, injection

polymer injection

than for

pressures are significantly higher water injection,

which in itself

a trivial statement. And yet the assumption may arise that in a

polymer

flood more

injection wells

are needed

than in

a

water

flood. This is not necessarily true. In Fig. 7 . 3 the pressure distribution in a quarter of a 5-spot between

the injection

well and

the production well is shown. The

calculation was performed using numerical reservoir simulation. For a whereas

water flood the pressure drop is about 8 bar ( 8 0 0 kPa),

for the

simulation

model

polymer flood the

pressures

it is are

120 bar block

( 1 2 MPa). pressures.

In

the

For

the

polymer flood not only the injection pressure is higher than for

125

200

-x e

150

aL a v)

a

v)

t

Water

1

100

Injection

50

Production I

I

40

0

120

80

Distance, [m)

140

Fig. 7 . 3 Pressure distribution in a quarter of a 5-spot pattern. Calculated using numerical reservoir simulation.

the

water flood,

significantly solution

but also

lower. The

is of

flood

the pressure at the production well is reason for

course not

this

flowing as

is

that

the

polymer

well as the water having a

lower visco;ity. For polymer flooding this means that the flood pattern and the ratio

of injectors

flooding. production flowing

to producers

In contrast,

it may

should be happen that

the same as for water the capacity

of

the

wells is not sufficient, as in a polymer flood the well

pressures are

also

significantly

lower

than

in

water

flooding. 7 . 5 Numerical reservoir simulation Numerical reservoir for to

modeling the describe the

simulators for the

modeling models,

flow of

oil, water

were developed.

compositional and

simulation is

a well-developed technique

flow of fluids in petroleum reservoirs. In order Besides

and gas, so-called black oil these

widely

used

programs

simulators for the modeling of miscible C02 flooding modeling

of polymer and not

of

surfactant

flooding is

very much

flooding

usually only

attention is

also

exist.

one part

given to

these

The

of these polymer

options.

A well-known method for the simulation of polymer flooding was developed by BONDOR, HIRASAKI and THAM (1972). Their model

126

represents

the polymer

significant

solution as

as introducing

a fourth

phase, what is more

the polymer only as a fourth component

in the aqueous phase. Modeling the fourth

polymer only

phase has

dispersed

as a fourth component and not as a

the disadvantage

that the

polymer front may be

too much in the model, because whenever a polymer enters

a block it is "soluted" in the entire water present in this block. Hence the concentration of the polymer in this block is very low and

the polymer

not very "effective". To get a sharp front in the

model,

some mixing

mixing

parameters is

procedures

parameters are

introduced. Finding

the

best

not easy, due to the fact that no comparable

have been

performed, except

those from

corresponding

laboratory experiments. In most viscosity this

polymer options

is assumed to be constant in the reservoir. We know that

is not true. The fact that these polymer options demand power

law

parameters as

for

the calculation

flowing

input only means that these parameters are used of injection pressures. To determine the well

pressure during polymer injection, a pseudo skin factor is

calculated is

of black oil simulators, the polymer

using the

then used

flowing

in the

power law

equation. This pseudo skin factor

regular equation for the calculation of well

pressures. This i s , as shown above, only valid for polymer

solutions having no elastic viscosity. Although these polymer models have some disadvantages, they may nonetheless aware

be used to plan a polymer flood project if one is well

of the

things

fact that

may not

sweep

be calculated,

are not exact and that some

e . g . the

improvement in

vertical

efficiency in some reservoirs can only be described using 3 -

dimensional practicable.

models

The optimum flood

with

questions

reservoir

are

layers,

what

is

often

not

the influence of adsorption, the best

injection and often

simulation. The

this oil

many

slug size,

pattern, possible

related when

some results

production rates and other

accurately

answered

by

numerical

incremental oil production and the time

is produced are frequently predicted conservatively

by numerical simulation. In many a technically successful project, the incremental oil production has been higher than predicted by simulation

and the

oil bank observed earlier in the field than in

the simulation model (see Chapter 9). Some simulation models especially floodi-ng do nut

have the

developed

for

chemical

"disadvantages" discussed above. A one-

127

dimensional to

model developed by POPE and NELSON ( 1 9 7 7 ) is also able

model polymer viscosity as a function of electrolyte concentra-

tion.

The model

accessible these

proposed by

pore volume

models

were,

in

CHASE ( 1 9 7 9 ) considers in-

TODD and

and retention the

first

of

polymer

place,

solution.

But

developed

for

simulation

for

also

surfactant flooding. One important polymer water

aspect of

flooding is

that a

flooding, and

base

reliable prediction

that this

prediction can

can be

made for

be accepted as the

determining the incremental oil recovery in a field

case for

project,

numerical reservoir

and thus

allows one

to assess

the benefit of a polymer

flood. 7 . 6 Other applications of polymers

Water soluble polymers also play an important role in other applications

in petroleum

engineering. There

is, for

example, the

of hydroxyethyl cellulose and other polymers in drilling muds workover fluids, or the polymers as sand carriers in hydraulic

use and

fracturing.

In well stimulations, e.g. acidizing, polymer gels are

used to temporarily plug some parts of a formation. 7 . 6 . 1 Profile modification

In some breakthrough efficiency. changed

reservoirs high of

the

The

flood

injection

by blocking

that was

improvement near a

coarse Ottawa

thus such

to

a

early

low

sweep

formations

may

be

NAVRATIL et al. (1982) to investigate the

recovery by

an injection

and of

an

is only a few meters, and thus the chemical low. In Fig. 7 . 4 , an experimental setup is

used by

in oil

water

profile

lead to

the high permeable layers with a polymer gel.

The penetration depth consumption is rather shown

permeable layers

blocking high

permeable

streaks

well. The high permeable streaks are modeled by

sand, and

a sand-blasting

sand was used for the

reservoir. The result of such an experiment is shown in Fig. 7 . 5 . The oil revovery Without was

is plotted

versus the

polymer blocking

recovered in

injected pore

about 50

volumes of

this experiment, with blocking

more of the oil could be recovered.

128

brine.

X of the original oil in place

about 15

-

20 X

displacing fluid port

coarse sand

fine sand

fluid/oil outlet Fig. 7.4 Experimental sand beds for simulation of high permeable zones according to NAVRATIL et a l . ( 1 9 8 2 )

70

-

60 -

10

//

----- no blocking ---- 0.1 PV gel blocking

-

0

1

0

2

4

6

8

10

'

1

12

.

1

14

.

16

Volume of brine injected, [PV)

F i g . 7 . 5 Effect of blocking high permeable streaks on oil recovery according t o NAVRATIL et a l . ( 1 9 8 2 )

129

The treatment is done by injecting a polymer solution together with

a cross-linking agent. The polymers are polyacrylamide or As cross-linkers Cr3+ and A13+ are used. The gelation

xanthan. time the

and the gel strength cross-linking agent,

are determined by the concentration of the polymer concentration, and the

salinity and pH-value of the reservoir brine. Another well-known silicate.

method of

blocking utilizes gelled sodium

Sodium silicate may be gelled by decreasing the pH-value

or by the addition of Ca2+ ions.

For

producing

offered to

wells,

by service

block the

there

are

companies. The

ways by

which the

also

some

well

treatments

purpose of these treatments is water flows

to

the

production

wells. Here also polymers are used that are gelled in reservoir. The philosophy behind these treatments is that polymer that

mainly flows

then mostly

reservoirs

the the

along the water path into the reservoir, and

oil flows

such treatments

to

the

production

have been

wells.

applied with

In

some

success,

but

wells,

the

this success is usually only temporary. In treating

injection wells

as well

production

volume of the reservoir which is influenced is small. The injection profile in the,. well may be changed, but at some distance from

the well

the flood

water may

once again

follow the highly

permeable path. The same seems to apply for production wells. In the experiment shown in Fig. 7 . 5 , the treatment volume was 0.1

pore volumes, which is about the total pore volume of the high

permeable to

zone. If

be blocked

large.

On the

in a field case most of the thief zone is also

by a polymer gel, the treatment volume must be very other hand,

the volume

that can

be

injected

is

limited by the gelation time. In some field applications profile modification has been rather successful, Profile

though the volume influenced is normally rather small.

modification may

make sense

in

some

oil

fields

under

certain economic considerations. 7 . 6 . 2 Polymer flooding and steam flooding The recovery of heavy oil by application of thermal recovery methods caused adverse flood, still

is usually by an

very low

most of

the poor

sweep efficiency

unfavorable mobility ratio, steam override and other

effects. After be the

owing to

the oil

completion of a steam drive or a hot water remains in

the reservoir.

This oil

may

target for other enhanced oil recovery processes.One

130

of

these i s ,

steam

for instance,

to improve

polymer

the

the addition of foaming agents to the

sweep

efficiency.

Another

process

using

to a hot water flood or a steam flood

flooding subsequent

is discussed here (LITTMRNN ( 1 9 8 5 ) ) .

2 106

5 2

7

lo3

2E 5

I

2

5 .-

102

0U

5

II)

Possible temmrature

II)

5

2

flooding

10'

5 2 100

l l 0 Y 80° 50'

30 C

2.5 3.0 3.5 Reciprocal temperature, 1/T t103K-')

Fig. 7.6 Viscosity of a heavy oil as a function of temperature

Heavy oils

are often deposited i n shallow reservoirs, so that

the

reservoir temperature

the

oil can

reservoir.

is l o w .

be significantly In F i g .

In such cases the viscosity of

decreased by

pumping heat into the

7 . 6 the viscosity of a heavy oil is shown as a

function of temperature. In F i g , 7.6 the temperature region is marked in which a n application ween

of polymers 7 0 and

reservoir mPa’s, once

110

The

temperature of

has in

a heavy

heavy

oil,

about 20

O C

this region

which a

has

under

normal

viscosity of some 10 000

a viscosity of only 10 - 100 mPa’s. So

oil reservoir is heated u p to temperatures of 70-100

O C ,

the oil

may

be recovered

the

is still possible. T h e s e are temperatures betOC.

viscosity is decreased to values where additional oil

viscosity

by polymer region

have

flooding. T h e temperature as well as values

where

polymer

applicable, as pointed out in the previous chapters.

131

flooding

is

Steam flooding and hot water flooding are not performed at such low

temperatures, but rather at temperatures that are much higher. injection temperatures are about 300 “ C . At these tempera-

Typical tures not

polymer flooding stable. But

during tion

on the

steam flooding in the

losses

is not other is not

possible because hand,

the

the polymers are

reservoir

temperature

constant. The temperature distribu-

reservoir depends on the injection rates and the heat

to overburden

and underlying

strata. In

the same

way as

during steam injection, the reservoir is heated and a

Table 7 . 4

Data for a typical calculation

Reservoir 1.5 Permeability 0.3 Porosity 8.5 Reservoir thickness 23 Initial reservoir temperature 0.3 Irreducible water saturation Oil viscosity at reservoir temp. 1600 10000 Pattern area Hot water 5 Injection rate 270 Injection temperature 50 Injection pressure Po 1yme r 5 Injection rate 20 Injection temperature 50 Viscosity of polymer solution

temperature

distribution

temperature

at the

wells

the

m O C

mPa . s m2 m3/h O C

bar m3/h o c

mPa ’ s

reservoir

develops

with

high

low temperature at the producing

respectively, the reservoir is cooled when a cold water slug

follows hot

in

injector and

um

the injection

of steam.

In the following an example of a

water

flood followed by an injection of cold water is calculated. The data used for the calculations are listed in Table 7.4. In Fig different

LAUWERIER

7.7 the temperature distribution in the reservoir after hot water injection are plotted according to 1955).

periods of

The temperature 500

days of

calculation water in

distribution in

the reservoir achieved after

hot water injection was then taken as a basis for the of the

flood. The

the reservoir

temperature distribution for a subsequent cold results are plotted in Fig. 7.8. The temperature is equal

to that

132

of

the

cold

water

at

the

injection again

well, then

to the

rises to a maximum, and afterwards decreases

temperature at

the production well. The dashed line

in Fig. 7 . 8 represents the temperature obtained at the front of

260 220

0

0 180 W-

5

:

140

0

100

I-

60 20 10

Fig. 7 . 7 Radial temperature distribution different times of hot water injection.

the

in

a

reservoir

after

cold water flood. This temperature lies between 80 and 100

This

is a

temperature region

where

polymer

flooding

is

O C .

still

applicable. A cold

follows follows But after the

as the

water

is usually

example calculation

a steam

flood is

reservoir may

simulation, may

water flood

not very

effective

when

it

a steam drive or hot water flood, because the cold water the path of the steam and thus breaks through very early.

and so

be determined preflush,

above has

shown, a polymer flood

possible. The temperature distribution in

be easily determined by numerical reservoir the temperature for a subsequent polymer flood as well.

e t c . , may

The optimum

injection rates,

be

by

planned

simulation.

133

numerical

a cold

reservoir

260

- - Temperature distribution a f t e r 500 d h o t water flood

- \

220

0

e

180

6

2 +

140

m

L 0)

CL

5

100

+

60

20 0

40

20

60

80

100

120

140

160

180

Radius, (m) 7 . 8 Temperature distribution after following 500 days of hot water i n j e c t i o n

Fig.

-

U

a

cold

water

flood

32

\ m

E

.24

a-

c

2

.-cc0

16

u

a

U

0L

8

0.

0

250

750

500

1000

Time, (dl 7 . 9 Oil production rates and recovery factor for a hot water flood and a subsequent polymer flood

Fig.

134

The conditions usually

not bad,

for polymer

flooding after

a steam flood are

because steam flooding requires a good permeable

reservoir

and high

steam injection

patterns,

water supply .and most

rates. In

addition, the well

other requirements

for

polymer

flooding are already present in the field The oil

recovery and oil production rates are plotted in Fig.

7.9

for the

example discussed

to

MYHILL and

polymer

flood

Leverett.

It is

STEGEMEIER was

then

above, w th calculations according

(1978).

The performance of a subsequent

calculated

obvious that

according

to

Buckley

and

a considerable amount of oil may be

recovered with polymer flooding.

REFERENCES Bondor, P . L . .Hirasaki, G . J . , Tham, M . J . : "Mathematical simulation of polymer flooding in complex reservoirs", SPE reprint series no. 11 ( 1 9 7 2 ) Gaida. K . H . ,Kessel, D . G . , V o l z , H . , Zimmerle, W . : "Geological parameters of reservoir sandstones as applied to enhanced oil recovery", SPE-paper 1 3 5 7 0 ( 1 9 8 5 ) Lauwerier, H.A.: "The transport of heat in an oil layer by injection of hot fluid", Appl. Sci. Res., Sec A , Vol. 5 ( 1 9 5 5 ) p.

145

Littmann, W . , Kleinitz, W.: "Polymerflutprojekt Eddesse-Nord", Statusreport 1 9 8 8 Geotechnik und Lagerstatten, Projektleitung Enegieforschung, KFA Jiilich (1988) Littmann, W.:"Method of Increasing the Yield of Hydrocarbons from a Subterranean Formation", U . S . Patent 4 , 5 0 8 , 1 7 0 ( 1 9 8 5 ) Matthews, C . S . , Russel, D . G . : "Pressure buildup and flow tests in wells", monograph vol. 1 , Henry L. Doherty Series, SPE (1967)

Myhill, N . A . , Stegemeier, G . L . : "Steam drive correlation and prediction", J . Petr. Techn. (Feb. 1 9 7 8 ) 1 7 3 - 1 8 2 Navratil. M . , Sovak, M . , Mitchell, M . S . : "Diverting trgents for sweep improvements in flooding operations-Laboratory studies", SPE-paper 1 0 6 2 1 , 1 9 8 2 SPE Int. S y m p . Oilfield and Geoth. Chem. Pope, G . A . ,Nelson, R . C .: " A chemical flooding compositi.ona1 simulator", SPE reprint series numerical simulatj.on vol. 2 (1977)

Todd, M R,. , C,hase, C . A . : " A numerical simulator f o r predicting chemical flood performance", SPE-paper 7 6 8 9 ( 1 9 7 9 )

135

8 SURFACE AND SUBSURFACE EQUIPMENT

Storing and materials

mixing polymers

for pipes or the

completions

in

and tanks,

the

question what

the

field,

necessi’ty

kind of

the

of

choice

special

pumps may

of well

be used for

pumping polymer solutions are the subjects of this chapter. 8 . 1 Injection water

Water of a good quality for polymer mixing, preconditioning of the pro

efterflush are

reservoir or ect.

the

The flood

prerequisites

in

a

flood

water should be free of solids that might plug

reservoir. One

with

all

must also

ensure that the water is compatible

the reservoir

rock and other waters it may possibly be mixed different. incompatible waters may cause scale

with. Mixing of formation.

The quality of the mixing water, especially produ ed reservoir brines, should be monitored continuously. This means that i t must be

good quality means, and also that nie hods must be

defined what

developed to check this quality. 8 . 1 . 1 Preparation of injection water

Water supplied by fresh water wells usually needs no filtration or

treatment. When

the

water is

lifting these waters one should take care that

free of

oxygen, this means that no air is accident-

ally mixed into the water in pumps, valves or leaks in the system. Reservoir brine solids

are also

production

in

especially

the

reservoir

must be

more or

oil

wells,

fines

carefully separated from the oil. As

less produced in conjunction with liquid

may

these

reservoir

cause

trouble

sand when

particles

and

reinjecting

the

brine. Rests of oil in the separated reservoir brine may

form films around the fines and thus cause conglomeration of these particles. In preparing these waters a thoroughly selected demulsifier of

the fines

in

deep bed

Deep

filters may

beds that

then lead to the required water quality.

may be

performed in

gravel

filters

or

in

consist of fine walnut shells: these filters may

easily backflushed.

preparation

these conglomerates and make the surface

accessible to acid treatments. Subsequent filtration

bed filtration

filter be

may separate

depends on

T h e best

method to use in injection water

the special conditions i n , a n oil field and

will therefore not be discussed in this context.

136

8 . 1 . 2 Injection water quality The quality

of an

injection water as to injectability into a

reservoir is determined by the content of solids that may plug the pores of the rock. The mechanisms that may lead to well impairment by

suspended solids

may be

one of the following, as investigated

by BARKMAN and DAVIDSON (1972). -the

solids form a filter cake on the face of the well bore

(well bore narrowing) --the solids

invade

the

formation,

bridge

and

form

an

internal filter cake (invasion) -the

solids become

plugging) -the solids settle fillup)

lodged in the perforations (perforation at the

bottom of

the

well

(wellbore

The content of solids in a water and their capability to form a filter

cake is characterized by the water quality ratio. The water

quality

ratio may

being tested is pore size. When

be measured

in a

filtration test.

The

water

filtered through a filter membrane having a small a filter cake is formed, the pressure drop across

the filter increases. The rate at which the pressure drop increases depends on the concentration of the suspended solids as well

as the

permeability of

the filter cake. For the filter cake

itself Darcy’s law may be applied.

The thickness d of the filter cake increases during the filtration; C/PW

it depends (measured

filtration filter

on in ppm

rate V ,

the concentration - in

of the suspended solids

relation to the water density), the

the filtration

time

t , the

density

of the

cake pc, and is reciprocal to the cross section of the fil-

ter A .

137

Combining Equations 8 . 1 and 8 . 2 leads to Equation 8 . 3

S2 = Q2t/2

with

The water defined

quality ratio

c/kc (usually measured in ppm/mD) as

8 . 3 may

be used as a measure to characterize

in Equation

the quality of a floodwater. The water quality ratio may be measured, as described above, by a

filtation test.

The water is filtered through a filter membrane

at a constant pressure drop and the time that is needed for the

Time, t 1s) 2000

0

5

20

40

60

50

60

1800

-

-5 -gg

1600

m

a

1400 1200 1000

V

t

800

f i i

600

OI

400

200

-

0 0

10

20

Time, 8 . 1 Measurement and DAVIDSON (1972)

Fig.

30

40

1)G-I

of water quality ratio according to

138

BARKMAN

con trolling calculation

El Printer

Fig. 8 . 2 S e t u p for automatic measurement of water quality ratio. Hydroguard system Preussag (KLEINITZ ( 1 9 8 7 ) ) . Principle setup and photograph of apparatus.

139

filtration

is measured.

filtered

volume the

Equation

8.3 from

It versus

When plotting

water quality

ratio may

the

cumulative

be calculated using

the slope S of the filtration curve as shown in

Fig. 8 . 1 .

The water shown

quality ratio

a flow

line and

it may

be bypassed

tion

membrane is

pressure between

and

unit A .

to the

A to

holding valve

transported

a tape pressed

to

F and

the contacts given to

yalues

according to

ratio.

The

an apparatus as

is sampled

directly

filter that is G is

a microcomputer Fig. 8.1

sampling

outlet or fed through a constant

the filtration membrane. The filtra-

of filter

The time

signal

measured in

stands at a particular pressure at valve C .

from Here

pressure

may be

Fig. 8 . 2 . The water

schematically in

paper that

is

automatically

E

by

the

vessel needed to

measured

and

which both

and calculates

intervals,

sampling

constant

fill up the volume a

corresponding

plots

the

the

water

rates,

and

measured quality break-off

conditions may be programmed in the computer.

In Fig. 8 . 3 the impairment of the injectivity of a well due to waters ing

with different qualities is shown for the well bore narrow-

mechanism. For

different injection

capacities of a well, the

half-life time is shown as a function of water quality ratio. The

lo-'

100 10’ 102 Injection capacity, (m3. mD/d.m)

lo3

8 . 3 Calculated well bore half-life for the case of well bore narrowing (BARKMAN and DAVIDSON ( 1 9 7 2 ) )

Fig.

140

half-life have

of a

well is

dropped to

the time after which injection rate would

half of

the initial

rate at

constant injection

pressure. At high ratios same

capacities of

(i.e. better

half-life as

shown

an injection well, lower water quality

water quality) for low

graphically in

are necessary

injection capacities.

the

calculation,

Fig. 8 . 3 , for a well with an injection capa-

100 m3.mD/d.m yields a water quality ratio of

city

to obtain A Z5

ppm/mD which

is needed to obtain a half-life of 10 years and Z50 ppm/mD for a half-life of 1 year. T o obtain a water quality ratio of 5 ppm/mD intensive filtering of the water is often needed. So i t might be more economical to periodically work over the well than to supply water of excellent quality. In the nisms

paper by

that lead

BARKMAN and DAVIDSON (1972) the other mecha-

to well

impairment are

also discussed

and

the

corresponding equations are given. For polymer possible, solutions

flooding the

because may

be

water quality

should be as good as

well impairment by solids suspended in polymer more

severe

than

that

of

pure

water.

The

injection water quality should be continuously monitored. The water quality ratio is a good measure for the water quality, whatever the mechanism of well impairment may be. For polymer mixing waters a value below 50 ppm/mD is recommended. 8 . 2 Polymer mixing discussed in Chapter 6 for polymer mixing have

The procedures to

be adapted

Facilities work

to

the

that are

technical

used for

continuously and

not

conditions

polymer mixing

batchwise,

and

in

an

oil

field.

in the field should these

mixing

plants

should run automatically. The methods of mixing polymers and the components that are needed are described below. 8 . 2 . 1 Shipping Dry polymers

drums.

Bulk handling

hygroscopicity make

are usually

further

homogeneous obtained.

of dry

of these use

and

powders is

powders, which

impossible. highly

shipped in

With

injectable

paper bags

or

plastic

difficult because of the may clump

clumped polymer

and

therefore

polymer

powders

solution

cannot

Gels are shiDDed in loes measuring approximately 30 x 50 cm.

141

a be

iquids are capacity that

the tanks

loaded

shipped in

20 -

of about

tank cars

30 m3.

or tank

containers with a

Shipping liquid polymers requires

are meticulously

clean and that the liquid can be

and unloaded in a way that no a i r , moisture or bacteria are

mixed into it. 8 2 . 2 Storage

Powders should precautions

be stored

in

cool

and

dry

places.

Health

should be taken when handling the powders. The powders

should not be inhaled. Liquid polymers are to be stored in fiberglass tanks. When tanks

are emptied

sions

are sensitive

emulsion.

they must

be ventilated.

to moisture,

Polyacrylamide emul-

which may cause clumping of the

The tanks should therefore be ventilated with dry air or

nitrogen.

The air

emulsions

may separate

and

agitation

is sometimes

needed. This

liquid

the

from the

may be

bottom to

dried wit,h a silica gel. As the polymer settle

into

the

may be

tank

some

done by

slight

pumping the

the top of the tank. The emulsions are

OC.

usually still pumpable at temperatures of about - 2 0

Xanthan broths may as well be stored in fiberglass tanks. Storing

in stainless

time

is not

too long

and the temperature not too high. At raised

temperatures

the iron

that is

also

steel tanks

gelation. At

cause a

storage

tank must

sterile

air or

is also

possible if the residence

soluted from

stainless steel

may

below 0

the

outside temperatures

be heated.

nitrogen. The

The tank

O C

should be ventilated with

use of a sterile filtration for the

air or nitrogen used during ventilation is recommended. 8 . 2 . 3 Mixing of powders and gels

In Fig. shown.

8 . 4 the mixing procedure for powders is schematically

is supplied from the paper bags, in which i t is

The powder

stored,

to a

hopper. From

amount

needed, into

water.

The polymer

is may

further mixed be taken

this hopper

a mixing

solution is

and stirred. From this tank the polymer solution

to mix

needed

concentration. Before as

i t is mixed with the

then flowing into a tank where i t

for further application. As shown in Chapter 6 it is

better prepared

the powder is fed, in the

funnel, where

a stock shown

solution first, in

Fig.

and then

dilute

to

the

the polymer stock solution, that was 8.4,

is

diluted

to

the

final

concentration i t may be stored for some time to allow swelling, i t

142

-

-

t o further application

Fig. 8.4 Mixing of polymer powders

may

mixers, or

pass static

i t may

be sheared in shear plates or

dynamic mixers. Gels must be grounded before they can be diluted in water. A l s o here

a higher

gels

may not

have,

solution should be prepared. As

concentrated stock

be grounded to a size that the particles of a powder

gels need

longer swelling times. During this time the solu-

tion of the gel should be stirred. 8 . 2 . 4 Mixing of liquid polymers

In Fig. 8 . 5 the principles of mixing liquid polymers are shown. Nearly

the same

procedures may

be applied

to xanthan broths and

polyacrylamide emulsions. 8 2 . 4 . 1 Polyacrylamide emulsions

A l s o in

solution emulsions final the

mixing liquid

should be a 5

solution is

emulsion

prepared first.

- 10

activator is

polymers a

times higher recommended

added at

To

higher concentrated

stock

In the case of polyacrylamide

concentration than

that of the

the water stream I in F i g . 8 . 5

the required

concentration, then

the

is added t o t h o water strc-am The stock solution may then

be

mixed and sheared and pass a long tube to allow proper swelling

of

the polymer before i t is then diluted in water stream I 1 to the

143

final

concentration. The

static 11

mixers and

biocides and

operation

polymer solution

may

then

pass

again

shearing devices, if necessary. T o water stream sequestering agents

of mixing

chambers, static

may be

added. The

mixers, dynamic

mode

of

mixers and

s h e a r plates is described below.

shearing I

I water I

chamber

mixer

sequestering agents

biocide

I

I

--I water ti

t o injection

mixing chamber

static mixer

shearing

Fig. 8 . 5 Sceme for mixing liquid polymers

8 2 . 4 . 2 Xanthan broths

Xanthan broths may have concentrations of 2 % up to 10 % . A 2 % xanthan

broth may

usually

needs only a dilution in water stream 1 1 . The water stream

I1

the

is a

already be regarded as a stock solution, and it

reservoir brine of a good water quality. Before mixing to

brine the polymer broth may also be sheared like a stock solu-

tion, if necessary. The residence tube is not necessary. Higher concentrated diluted a

In

xanthan broths

may not

that

easily

be

in salt water. It is recommended to predilute the broth in

fresh water

(water stream I) to a concentration of about 2 - 4 % .

this case the residence tube allows further swelling of the po-

lymer

before i t is added to the salt water. Of course no activator

is needed for diluting xanthan broths.

144

8 . 2 . 5 Pumps When choosing pumps for polymers, one should notice that the polymer may be sheared in these pumps. Especially centrifugal pumps cannot be recommended for pumping polymer soltuions. Within mixing plants as shown in Fig. 8 . 5 centrifugal pumps may be taken for transporting water before the polymer is added. For loading storage tanks with emulsions and xanthan broths pumps may be taken, as the shearig in these pumps is not very

gear high

I

A problem is often the metering of the viscous emulsions and highly viscous xanthan broths. Membrane pumps and piston pumps having valves need high inlet pressures.

Fig. 8.6 Piston pump without valves for metering of high viscous polymer solutions (courtesy to Orlita GmbH, Giessen. FRG)

The metering pump shown in Fig. 8.6 is well suited for viscous liquids, The piston is rotating 180 at one By this rotation the inlet or the outlet is opened by a the piston. The piston is hollow at the front end, and the

high

pumping stroke. slot in face of

the piston lies behind the slot. The stroke of the piston may be adjusted oontinously, so that the flow rate may be varied in a

145

range. The

wide

more. A t

and

pumps are

pressures up to 100 bar

available for

pressures below 1 bar are sufficient. The

the inlet

are applicable for metering polyacrylamide emulsions as well

pumps

as xanthan broths.

F . 2 . 6 Static mixers, injectors and shearing devices Static mixers

are used

flowir~g in pipe-lines. liquid has

sfter

i t

passed a

needed that

are

are

known since

in an

specially

years. The

other trade

formed barriers

liquids

poor mixing

while occurs

liquid stream, turn i t over and put

appropriate manrier.

about 30

besides numerous

different

flow only

barrier. In such cases mixing elements

separate the

together again

mixer

for mixing

In laminar

These static mixers

most famous

marks. The

is the

Kenics

Kenics mixer uses

that are mounted in e pipe in different

positions. The principle is shown in Fig. 8 . 7 .

Fig. 8 . 7 Principle of a static mixer (Kenics)

Also great liquid good

attention should be given to the device, where the

polymer is

injected to

mixing especially

for

the water

polyacrylamide

stream. At this place a emulsions

should

achieved.Usually the liquid polymer is jetted at a high speed and

146

be

liquid polymer

polymer solution

F i g . 8 . 8 P r i n c i p l e of a mixing chamber or

8 . 9 D y n a m i c mixer ( D i s p a x 7813 S t a u f e n , F R G )

Fig.

injector

r e a c t o r , courtesy J a n k e & K u n k e l ,

147

pressure chamber

into the

water stream,

or injector

The principle

of such

a mixing

descibed by PAHL et al. ( 1 9 7 9 ) is shown in

as

Fig. 8 . 8 .

Dynamic mixers are also available to be mounted in a pipe-line construction. In Fig. 8 . 9 such a mixer is shown. The mixer solution.

Such mixers

conditions. selected

Fig. 8 . 9

shown in

are available

The s i z e ,

according to

is also

speed, and

shearing

polymer

for different flow and shear

number of

the experience

the

shear wheels

gained with

may be

such mixers in

the laboratory (see 6 . 1 . 4 ) . Another method gel

particles still

plates. the

The size

present in

and number

the solution

of shear

is the use of shear

holes may be determined in

laboratory (see 6 . 1 . 4 ,Appendix I ) . Shear plates may easily be

mounted shear

to homogenize polymer solutions and to destroy

in pipe flanges as shown in Fig. 8 . 1 0 . The function o f plates may

be controlled

by monitoring

the pressure

the drop

across them.

Fig 8 . 1 0 Shear plates mounted in a LIPlON ( 1 9 7 4 ) ) . The shear plates

disconnecting the flanges

148

f l a n g e of a flow line ( t i f t e t , may

easily

be

chatiped

by

Shearing of Filters

with a

polymer solutions large surface

( e . g . P a l l , FRGI. to

allow higher

at

these filters

xanthan

possible in

filters.

pore sizes are available

may be assembled to larger units

flow rates. The pressure drop that may be applied bar. A good shearing is obtained e . g . for

is 10

filter having a pore size of 2 0 j.un at a

such a 0.5 -

drop of

observed,

and small

These filters

broths in

pressure

is also

the standing

1 - 5 bar. A plugging of the filter was !lot

time in

a pilot

0 . 5 - 1 year (LITTMANN and WESTERKAMP

polymer mixing plant was

(1987)).

8 . 2 . 7 Filters

In a at

polymer mixing unit filters and sieves should be mounted

some places,

Filters mixers

even if

or sieves

no plugging

should be

I t is

from damage.

used to

are still

By instal ing

polymer is

protect pumps

always possible

present from

shreds pipes.

of the

that

the costruction

filter bags malfunctions

feared.

and

sand

dynamic or

metRl

phase in tanks

01'

n the mixing plant

be detected. Precipitates from the water or growth of bacteria

may

may be early seen in such filter bags. 8 . 2 . 8 Materials. control equipment

As already pointed out before i n a polymer mixing plant plastic or

stainless steel

ferent

should be

metals must

steel

will gel

used for all paJ,ts. Tlie use of d i f

b e avoided.

the polymer

Copper or

brass in

contact with

very rapidly. Also valves, gcluges etc

should be made of stainless steel or plastic, if possible. For means of control flow meters for the water streams and t h e polymer tored that

storage tank. Highly sensitive devices & r e available

measure the

using to

should be installed. Polymer consumption may also be moniin the

position of

the liquid

face in

the tank: e . g .

supersonic. Pressure gauges mounted in flow l i n e s a r e t i c e d e d

allow a

good control

of

the

mixing

process,

as

e . g . the

performance o f shear plates. residence tubes. or p u m p s . 8.3

Injection w e l l s Injection wells for polymer’ solutions mag’ b e iiist~illed s i r n i l a t ,

to

water injection

wells. Piston pumps usually used f o r injection

do

not shear

do

riot need any coating i f the polymer solut.iori is o x s g e r i f v e e arid

the polymer

solution uncunti,olled. 'Ttrbittgs r i o i ~ ~ i i c t l l s

thouroughly prepared.

149

Perforations should voir. high be

If an

( e . g . tubing

conveyed guns)

should

be

open hole completion is possible the bore hole should

underreamed to

%hen

and deeply penetrate the reser-

In old wells a reperforation is recommended. For perforation density perforators

used.

be clean

very high

increase the

well bore

radius. In

some cases

injection rates are needed are small fracturing of

the reservoir may be necessary. The installation of downhole pressure transducers helps to perform

pressure fall

off tests

periodically and

thus observe

the

performance of the well.

REFERENCES Barkman, J . H . ,Davidson, D . H . :"Measuring water quality and predicting well impairment", JPT (July 1 9 7 2 ) Chamberlain, R . J . : in "Polyelectrolytes for waste water treatment", editor: Schwoyer. W . L . K . , CRC Press, Inc. Boca raton, Florida. U S A ( 1 9 8 1 ) Chen. S . J . et a l . : (Kenics mixer) AICHE J . 18 ( 1 9 7 2 ) 984 Kleinitz. W . : private communication ( 1 9 8 7 ) Littmann, W . . Westerkamp, A Xanthan-Biopolyrner flooding in a North German oilfield, 4" Eur. Symp. on EOR, Hamburg F R G (Okt. 1 9 8 7 ) Lipton, D . : "Improved injectability of biopolymer solutions". SPE-paper 5 0 9 9 ( 1 9 7 4 ) Pahl, M . H . , Muschelknautz, E . : "Einsatz und Auslegurig statischcr Mischor", Chem.--1ng.-Tech. 5 1 ( 1 9 7 9 ) 347

150

9 CASE HISTORIES Polymer flooding has become a widely used EOR-method, and about 200

projects have

is given by LEONHARD (1986). In the USA 178 projects were

projects active is

worldwide. A good review of these

been started

in 1986

Outside

with a total oil production of 15,313 bbl/d, which

of the

90 X

the USA

total

production

of

chemical

5 polymer

there were

flood

projects.

projects, with a total oil

production of 3402 bbl/d active in 1986. Though such scant

a large

number of projects exists, there is only

literature available

formance.

In the

discussed. (France),

about case

following some

These are

histories and project per-

of these

the polyacrylamide

North Stanley

projects projects

are

briefly

Chateaurenard

(USA), and Hankensbuettel (West Germany),

and the xanthan project Eddesse-Nord (West Germany). Furthermore, some are

discussed, and

results of

profile modification treatments

some considerations

about project

design are

handled, 9 . 1 Chateaurenard The Cateauronard Cretaceous) basin the

oilfield is

part of

the

Neocomian

(lower

oil reservoirs found in the southern part of the Paris

in France.

The reservoir

Chateaurenard polymer

characteristics and other data of

flood field

test, as

discussed

in

paper by LABASTIE and VIO (19811, are given in Table 9 . 1 .

Table 9 . 1 Chateaurenard polymer flood data 600 m

Depth Pay thickness

Porosity Permeability Clay content Tempe r a t u r e Oil density O i l viscosity Water hardness ( M g t C n ) Number of wells Injection wells Production wells Pat tern conf igu1.nt i on Pattern ai’ee Pore volume Polymer slug Po 1 y m e r c on c en t r a t i on

5

m

30 x 1 Hm* 2

15 30 890 40

x

’C kg/m3 mPa s 7 0 ppm 8

I 3

~ r i \ t : r t e d7 c g u t

(one: o x t i s w e l l

4 1 0 000 m 700 000 , 3

235 000

m3

7 0 0 ppm

151

0 33 Vp

irls~do)

a

The oil viscosity appeared

very early

relatively high (40 m P a s ) , so that water

was

in the

the

production

and

increased

very

quickly. For the polymer flood pilot project an inverted 7-spot pattern was chosen with a distance from the center injection well to the production wells of 400-500 m. As the thereof

reservoir water

was very

sweet and

the

temperature

low, a

partially hydrolyzed polyacrylamide was chosen for A polymer slug of 0.33 pore volumes at a polymer

flooding.

concentration of 700 ppm was injected.

-- ----c<

100

-*

90

80

I

50

’

observed

I

i

I I

L

2

--- 2

I

3 60 U

I

I

70

3

- predicted

.

\ a \ \

40

*//

\

\

.idaf

+

20

a

,

-a .b

10

0

/

/

/

\

30

/

r

a

l

0 .

a

‘.+&A

a

a

a

m

I

3

Fig. 9 . 1 Development of water cut in one well in the Chateaurenard polymer flood (LABASTIE and VIO (1981))

The performance seen

in Fig.

from

95

seems

%

to

performance

of the polymer flood is impressive, as can be

9 . 1 . The

in a production well is reduced to nearly zero. This clear response to polymer flooding

be

water cut

possible,

due

to

the

because reservoir

water

flooding

heterogeneity

had

and

a high

poor oil

viscosity. 9 . 2 North Stanley

The North

Stanley field is located in Osage County, Oklahoma,

USA. The presence of a fracture system in the reservoir effected a

152

Table 9 . 2

North Stanley polymer flood

Area Depth Porosity Pore volume Permeability Temperature Oil viscosity Water viscosity (105 O F ) Original oil in place Ultimate recovery - primary - water flood - polymer flood Number of wells - injection - production - inactive Fresh water preflush Polymer slug (0.1 lb/bbl) Fresh water afterflush

-

1024 47 18

pro.iect data acres -ft

4 143 000 m 2

14 m

%

10 440 0 0 0 m 3

300 105 2.36 0.63 39.106 26.8 14.8 1.1 55 17 28 10 3 980 000 11 963 000 3 088 000

mD

OF CP CP

=

40

6 200 000 m3

bbl % % %

bbl bbl bbl

= = =

0.06 V p 0.18 V p 0.05 V,

170 150

99.3

100

90 80 o- 7 0

99.0 90.9 90.0 90.6

m

60

90.4

.-0

50

98.0

a

3”

.c

L

kl *

3”

OC

-s-

2 f Y

40

91.6

30

96.8

c m

95.2

20 0

1

2

3

4

Cumulative oil production, (lo6 bbl) Fig. 9 . 2 Water-to-oil ratio versus cumulative oil recovery North Stanley polymer flood project (SMITH and BURTCH (1980))

153

in

poor.

water

flooding, were

flood

performance,

treatments with

also performed.

SMITH

fracture during

The reservoir

( 1 9 8 0 ) are

and BURTCH

system was

and

in

gelled polvmer

addition dii some

and project

listed in

to

data as given by 9.2.

Table

polvmel,

selected wells Whether

the

natural or induced by high injection pressure

polymer flooding

was not

quite clear

from the literature

available. The data 9.2

Fig.

listed in

the

Table 9 . 2

are partially recalculated. In

project performance

is shown in a plot of water-to-

oil ratio versus cumulative oil recovery. The decrease in water cut is relatively low. Some possible reasons,

similar to

given in a paper by SMITH and BURTCH

those also

( 1 9 8 0 ) , may be:

-

the injection

thus

pressures might

have been

too high,

and

fractures were opened in the reservoir which led to

early water breakthrough.

-

the size of the polymer slug is relatively small. Just a s

in

a fractured

system, the

polymer slug should be bigger,

if a polymer flood is to be at all successful.

-

the fresh

precondition

water preflush

might have

the reservoir

for

been too

flooding

with

small to polyacryl

amide.

-

the afterflush

may

be seen

stopped

with fresh water was also too small. This 9.2,

in Fig.

a short

a s the decrease in water cut was

time after

the afterflush

with reservoir

brine had been started. 9 . 3 Hankensbuettel

The Hankensbuettel oil field is located in the Gifhorn trough, one this

of the

main oil producing sediment basins in West Germany. In

and adjacent oil fields several commercial scale polymer pro-

jects

have been

Block

2 is

performed. In

briefly described

the following

the project in West

in accordance with a paper given by

MAITIN (1985). The project data are listed in Table 9.3. The preconditioning project more

was not

effective and

polymer

of the

high salinity

accomplished with smaller slug

reservoir in

this

a fresh water slug, but with a of a salt-tolerable polymer. The

was a polyacrylamide with a low degree of hydrolysis. This

seems to be

more effective

because

154

the

slug

needed

for

T a b l e 9 . 3 t i ~ ~ i h e r i s b u c i i e Wnst l B l o c k 2 polvmct, f l o o d data Depth 1500 m Net thickness 28 m Porosi ty 28 % Permeability 2 - 4 um2 Oil density 888 kg/m3 Oil viscosity 1 1 - 1 5 mPa’s Salinity of brine 175 kg/m3 Temperature 58 " C Flood pattern confined structure (line drive) 9 Number of wells Injection wells 3 Production wells 6 Original oil in place I 4 7 5 000 m3 Pref lush with polyacrylamide (low degree of hydrolysis) 0 . 6 Vp ( 6 0 0 ppm) Polymer slug after fresh water flush Incremental oil recovery 1 6 . 5 96 OOIP

preconditioning does

not follow

is smaller the paths

when using of the

a polymer, and the polymer

flood water,

as a fresh water

slug would.

0

10

20

40

30

Recovery, 9 . 3 Performance flood ( M A I T I N ( 1 9 8 5 ) )

Fig.

of the

(Oh

50

Hankensbuettel West

155

60

0

OOIP) Block 2 polymer

In Fig.

results of the polymer flood in West Block 2

9 . 3 the

are

shown. A decrease in water cut from 8 5 % , t o 40 % was observed,

and

the additional oil recovery was about 15 % of

he original oil

i n place.

Another interesting

aspect of

this project

s

shown if Fig.

9.4. The salt concentration of the produced reservoir brine in one well 80

decreases from

1 2 0 g/l to 40 g/l and then increases again to

g/l before the banked oil reaches the production well. Then the

salinity the

decreasing water cut. With polymer breakthrough and increasing

water

cut after

decreases polymer of

of the produced water decreases again simultaneously with the oil

to nearly

bank has

zero. The

breakthrough indicates

the reservoir

been

produced,

increase of

the

the

salinity

salinity before

that during polymer flooding parts

have been swept which had not been influenced by

the preceding water flood.

200

160

m -

120

E

kl Y s; 80 .-

.-cc 4

m

vl

Time, (years) Fig. 9 . 4 Production performance of well 7 8 in Hankcnsbuettel West Block 2 polymer flood (MAITIN (1985))

9 . 4 Eddesse-Nord

The oil produces

field Eddesse-Nord

from Wealden

is located

on North

Germans and

and Valanginian sandstones. A polymer flood

156

using

xanthan was

started in

October 1 9 8 5 .

The project data are

listed in Table 9 . 4 .

Table 9 . 4 Polymer flood Eddesse Nord - project data 350 m Depth 5 m Thickness 24 % Porosity Permeability 0 . 9 - 1 . 7 Mm2 7 mPa’s Oil viscosity 22 o c Temperature Salinity of reservoir brine 120 k g / m 3 Salinity of flood water 5 0 kg/rn3 5 Number of wells 2 Injection wells 3 Production we1 1 s single block with active aquifer and Pat tern secondary gas cap; injection from OWC 2 1 2 0 0 m2 Pattern area Original oil in place 2 1 200 m3 Hydrocarbon pore volume 27 5 0 0 m 3 xanthan Polymer 0 . 5 vp Slug size Polymer concentration 1 kg/m3 Incremental oil recovery 7 % vp

water flood prediction polymer flood prediction

1985

1987

1989

1991

1993

1995

Time, (years) F i g . 9 . 5 Performance of production well in the xanthan project Eddesse-Nord (LITTMANN and WESTERKAMP ( 1 9 8 7 ) )

157

flood

The performance

WESTERKAMP the

( 1 9 8 7 ) is

field followed

very

closely during

response

to

polymer

of one

well as

described

LITTMANN

by

and

shown in Fig. 9.5. The water cut measured in the curve

predicted by

the first

numerical

year after

flooding,

a

simulation

polymer injection. The

decrease

in

water

cut,

was

observed earlier than predicted and also more significantly.

9 . 5 Profile modification The modification of the production profile or injection profile (flood ing

water diversion)

is a

layers

are present

flood

to improve the efficiency of water flood-

method that is used in reservoirs where highly permeable

water in

in contrast

such cases

to lower

flows

permeable

through

the

layers.

highly

The

permeable

streaks and almost no oil can be recovered from the other layers. In the Dillard ABDO

following the

in the

et a l .

(Stephens

(1984),

is

diversion

project

Myrtle

field, as presented in a paper by

briefly discussed.

County, Oklahoma)

Pennsylvanian, performed

flood water

Sho-Vel-Turn oil

is producing

The Sho-Vel-Turn field

from zones

of Permian,

Mississippian, and Ordivician ages. The project was

in the Dillard Permian sand. The project data are listed

in Table 9 . 5 .

Table 9 . 5 Myrtle Dillard flood water diversion project data Depth ReserLoir rock Porosity Permeability, average , maximum 1 empei ature 0 1 1 viscosity humbei of wells Injection wells Product ion we1 1s hater flood recovery Polymer consumption (complexed with CrC13) Incremental oil recovery

400

--

6 5 0 ft

=

120

-

200 m

Sands tone 20 0.13R 2.1 69 50 44 12 32 16 % 3 6 0 0 0 lbs

=

6 4 7 0 0 bbl

= 10300

1 6 3 1 0 kg

m3

The response to the gelled polymer treatments in the injection \\ells is shown 7032

bbl of

in Fig.

water per

9.6.

The

day ( 1 1 1 8

total water

injection rate was

m3/d). The total oil production

158

before

treatment

augmented

by the

was

227

bbl/d

m3/d),

300 bbl/d

treatment to

production of 326 bbl/d

(36

it

and

(48 m3/d)

could

with a

be peak

( 5 2 m3/d).

1000

-

700

h

4 500

2e

.zc-300 U

a

U

L 0

izoo171p Time, (years)

100

1986

F i g , 9 . 6 Production performance of the Myrtle Dillard flood water diversion project (ABDO et a l . (1984))

The performance of this proiect shows that such treatments may be

very successful

and also

economically attractive

consumption for the incremental 011 is 0 56 lbo/bbl

The polymer

( 1 6 kg/m )

9 . 6 Pro.iect design

In this section the results of the projects described above are summarized,

and some

conclusions are drawn for the general design

of polymer flooding. The

projects discussed

above are

technically and probably

economically successful. In

flooding with polyacrylamides precondj tioning of the re-

servoir

and afterflush

are important.

in particular be considered.

1 59

These points should

Preconditioning with

with salt

tolerable polymers

polyacrylamides seems

to be

for flooding

more effective than with

fresh water only. The

afterflush should

Afterflushing

only be performed using fresh water.

with salt

water is

detrimental

to

polymer

flooding with polyacrylamides. Naturally

fractured or

fissured reservoirs

are not easily

flooded.

Fracturing of the reservoii. caused b y too high i n

jection

pressures

during

polymer

injection

should

be

avoided. Polymer

slug size

be too small. A slug size of

should not

0 . 3 - 0 . 5 pore volumes is to be recommended. In

the flood

seems This

to be may also

project using

xanthan,

slightly higher

than in

polymer

consumption

the other

projects.

be due to losses of polymer into the aquifer

in this project. Only

in

one

difficulties plugging

the

projects

in polymer

of

injection

of the

reservoir

is

not

described occur. the

above

did

Injectivity

main

or

problem

in

polymer flooding. Profile lymer

modification or flood water diversion by gelled p o treatment seems

to be

an appropriate method in some

reservoirs with high permeability contrasts. Polymer kg/m3

consumption for for flooding

incremental oil

with polyacrylamide,

is roughly

xanthan, and 1 - 2 kg/m3 in flood water diversion.

160

3

-

8

about 7 kg/m3 for

REFERENCES Abdo, M . K . , Chung, H . S . , Phelps, C . H . ,Field experience with flood water diversion by complexed biopolymers, SPEpaper 12642, Fourth Symp. E O R , Tulsa (Apr. 1984) Maitin. B . , Application of chemical flood processes in the oilfield Hankensbuettel, g r d Europ. Meeting EOR, Rome (Apr. 1985) Labastie, A , , Vio. L . , The Chateaurenard (France) polymer flood field test, Eur. Symp. E O R , Bournemouth (Sept. 1981) Leonhard, J . , Increased rate of EOR brightens outlook. Oil and Gas Journ. (Apr 1 4 , 1986) 71 Littmann, W . , Westerkamp, A . Xanthan-Biopolsmer flooding in a North German oilfield. 4tA Eur. Ssmp. on E O R , Hamburg FRG (Okt. 1987) Smith, R . V . . B u r t c h ,F . W . , Study shows North Stanley field polymer flood economics, Oil and Gas J . ( N o v . 2 4 , 1980)

161

1 0 APPRA I S A L AND ECONOMICS The appraisal economic basis of

for any

planned project and the evaluation of its be illustrated

economic considerations

be recovered

may

of a

efficiency shall

in the

following.

The

is the additional oil that

as compared to a water flood, and the total cost

investments, chemicals, operation and maintenance. Examples are

ciilcul~ted for a viscosities.

typical five-spot

Incremental oil

with regard

recovery by

to different oil

polymer flooding due to

reservoir heterogeneities are not considered. 10 1 Numerical simulation of a five-spot pattern The performance of water flooding and polymer flooding was calculated block

using numerical was

pattern voir

was sized parameters

permeabilities in

A closed reservoir

of the

300 x 300 m , the thickness was 10 m . The reser are

listed

that have

Fig. 10.1.

ties

reservoir simulation.

chosen with one injection and four production wells. The in

Table

10.1,

the

relative

been used for the simulation are plotted

The simulation was performed for different viscosi-

reservoir oil

( 5 , 1 5 , and 30 mPa’s). The calculation

was only done for one quarter of that five-spot pattern, so that

Table 1 0 . 1 Parameters used five-spot pattern Grid system: d i r e c t i on )

for the Block

numerical simulation

length:

30 m (in x-

of

a

and

y-

Block thickness: 10 m Number of blocks: 25 (one quarter of 5-spot) Number of layers: 1 Reservo4r:

Depth:

1000 m sub sea level

Dip:

0 0 %

Porosity : 25 Permeability: 1 Pore volume: 56 250 OOIP: 39 375

Oil:

Bo: Viscosity:

R, Water:

:

urn2 m3 m3

1 5 , 1 5 , 3 0 mPa’s 16 m3(Vn)/m3

at 2 MPa

1 mPa’s

Viscosity:

(The model was set up in a way that the oil-water contact and gas-oil contact were below and above the reservoir limits. PVT-data were simplified, Bo was set to 1 to simplify material lance and the pressure in the reservoir was always kept above bubble point.)

162

the The ba-the

the

values given five-spot. A

plete was

be,low should

modelled using

be multiplied by four for the com-

black oil model was used, and polymer flooding the theory

proposed by

BONDOR, HIRASAKI, and

THAM ( 1 9 7 2 )

L

c aJ

B

2 0

Water saturation, 5,

(%I

1 0 . 1 Relat ive permeabilities to oil and water

Fig

The results Fig.

of the simulation runs are shown in Fig. 10.2 and

1 0 . 3 . In Fig. 1 0 . 2 the development of water cut for the three

different cases (oil viscosity = 5 , 1 5 , and 30 mPa.s) is shown for water flooding and polymer flooding. Polymer injection in all three

cases was

viscosity that

in the

water

case of

equal to

oils. Hence

the oil

the reservoir

breakthrough occurs

viscous the

started after 6 years of water injection, polymer

was chosen

viscosity. It

with the

earlier than

in

is obvious

highly viscous oil, the

cases

of

lower

the benefit of polymer flooding is greater in

case of the high viscous oil than if viscosity were lower. The

decrease in water cut during polymer flooding is in all cases significant. In the case of the 30 mPa s oil, water cut decreases from about 95 % to about 5 0 % . This is in good agreement with the results of the case histories dicussed in Chapter 9 .

163

100

80

20

0

.

I

1

2

4

3

I

5

6

I

7

I

I

9

8

I

10

1

11

I

I

1213

I

14

15

Time, (years) 10.2 Water cut versus time for three different reservoir Results of a numerical reservoir simulation for water flooding and polymer flooding for a quarter of a five-spot.

Fig.

oils.

- 250

m

E

N

s

.-

200 150

u

L

a

0

e

30 m P a . s

A E = 18

.-0

15 m P a . s

A E = 15 % OOlP

a 100

d

5 mPa.s

g 50

AE =

OOlP

9 ’1- OOlP

Start o f polymer injection

=I U I

0

1

I

2

I

3

I

4

~ l , l l j , l l

I

5

6

7

8

Time,

9

1011

1 2 1 3 1 4 1 5

(years)

Fig. 10.3 Cumulative oil production versus time for three different oil viscosities. Results of a numerical reservoir simulation for water flooding and polymer flooding for a quarter of a five-spot.

164

Figure 1 0 . 3 shows the results of the simulation runs with respect

to cumulative

to 4 8

%

38

of

%

For the 5 mPa’s case, 19,000 m 3

oil recovery.

be recovered by water flooding after 11 years, which amounts

could

polymer

of the original oil in place. In the 3 0 mPa’s the original

oil in

place could

case

only

be recovered. By using

flooding, an additional 9 % of the OOIP could be recovered

in the 5 mPa.s case, and 18 % in the 3 0 mPa’s case. Though water flood recovery is already excellent in this homogeneous

reservoir, the

additional oil

that may still be recoverd

by polymer flooding is remarkable. 1 0 . 2 Economics

For an example calculation of the economics of a polymer flood, the

case with the 3 0 mPa’s oil was chosen. This does not mean that

polymer

flooding in

economical. covered

Though the

is not

worthwhile

reservoirs having lower viscosity oils is not

so

as well,

amount of

high,

such

since the

additional oil a

project

cost for

may

that may be rebe

a polymer

economically slug of lower

viscosity is also lower. The production

data for

the

30

mPa’s

case

that

will

be

discussed here are listed in Table 1 0 . 2 .

Table 1 0 . 2 Net oil production for water flooding and pol mer flooding. 30 mPa’s case. Wet oil production rate 3 0 m B / d , injection rate 3 0 m3/d. Quarter of a 5-spot.

Waterflood 7 11 12 13 13

600 200 300 000

7 600 3 600

500

500 400 300 300

13 9 0 0 14 2 0 0 8 9 10

11 12 13 14

1 4 500 2 4 750 15 000 15 200 15 400 1 5 570

15 730 1 5 880

*

Polymerflood

Annual oil production m3 Waterflood Polymer f loo(

900 700

14 200 1 5 150 1 9 200 21 2 0 0 2 2 000 22 400 2 2 650 22 8 5 0 23 000

250 250 200 200 170 160

150

Start of polymer flood at January lSt of year 7

165

0 950 4 050 2 000 800 400 250 200 150

1 0 . 2 . 1 Valuation of the produced oil

for a polymer flood has to be made 2 - 3 years

The investment before for

any incremental

any

calculation

simulated calculated in

Table

above, the

At

an

Thus,

the incremental

interest

oil produced

polymer flood m3. For

4960

profitability.

value of

for

the

example

produced oil

was

for the time at the start of the polymer flood as shown 10.3.

incremental the

oil is produced. This has to be considered of

would not

the

10

of

%,

the

value

of

the

first 5 years after the start of

in the

of 6860 m3 but only that of

be that

total five-spot

which is

dealt with

in

the

further calculations, this figure is 1 9 , 8 4 0 m3.

Table 10.3 Net present value of polymer flood. Interest 10 % .

Year

Di s coun t

Incremental oil product ion m3

7 8 9

0 650 3800 1750 600

10

11

6860

incremental oil

factor

I

at

start

of

Present value (at start of polymer in.i.) m3

0,9091 0.8264 0.7513 0.6830 0.6209

1

0 537 2855 1195 - - 373 - .. - 4960

1 0 . 2 . 2 Investments Investments in this example are only necessary for storage and mixing might

of the

polymer. The

be necessary

for a

costs for project like

the mixing facilities that the 5-spot described here

a r e , according to the author s experience, about US $200,000. Other investments, e . g . for water treatment and filtration, are not considered. Such costs should be borne by the whole field.

166

10.2.3 Lifting costs

Lifting costs m a y , b e a controversially discussed factor, mainly when these costs are already high, because the oil field is already producing at a high water cut. I t is evident that if the field

is only

should

operated with

also be

polymer flooding

credited with

the lifting

the

tertiary

oil

costs. This can make a

polymer flood economically unattractive. On

the other

windfall,

hand, the

tertiary oil

may be

regarded as a

oil that is lifted instead of water. This may reduce the

specific production costs significantly. Reduction of water cut from 99 % to 98 % is a reduction of the water-to-oil ratio from 100 to 5 0 , or a reduction in lifting costs by

a factor

So polymer

of 2 .

flooding may

economic i f

also be

water cut is only decreased slightly. In the following lifting costs are not considered. 1 0 . 2 . 4 Chemical costs 1 0 . 4 the

In Fig.

viscosity yield

of two typical xanthans is

shown. T o obtain a viscosity equal to the oil viscosity in the above-mentioned 30 m P a . s case, a polymer concentration of 800-1000 LO

'I

1

.

l

~

0 Fig. 10.4 at 54 OC.

100

.

I

l

200

~

300

~

LOO

I

,

l

500

,

600

~

700

.

800

~

,

900

~

1000

Polymer concentration, (ppm) Viscosity yield of two xanthann in a 2 0 0 g/l TDS water

167

,

~

ppm at a tcmpei,ature of 54 ’C is necessary. The price of xanthan is

about US $3

costs. some for

--

4 / h n , depending on the product and transportation

S o at a concentration of 1 kg/m3, and also considering

that

other chemicals like biocides are needed, a price of US $ 6 / m 3 a 30

mPa.s polgmer

solution seems

to be

realistic.

In the

case of polyacrylamide the cost may be slightly lower. 1 0 . 2 . 5 Specific costs Calculations for

the following

specific costs of incremental

oil are based on the costs given above.

us

Investment:

$200 0 0 0

Lifting costs: Chemical costs

vp

(Slug of 0 . 5

= 112 5 0 0 in3; 6 US $ / m 3 ) :

US $675 000

= = > Specific costs:

4 4 US $/m3 7 US $/bbl

1 0 . 3 Outlook The calculations made above show that total costs of 7 US $/bbl of

incremental oil

is

of course a rough figure and not representative for every field

and

case, but

produced by

it illustrates

polymer flooding are neoded. This that polymer

flooding

may

be

an

attractive enhanced oil recovery method even at low oil prices.

For the temperat’ures products oil

futuro, polymer of more

have been

industry may

polymers

then 90

flooding may OC, when

be extended

other

to higher

temperature-stable

developed. A more intensive application by the also enable

the chemical

industry

to

provide

at lower prices, so that polymer flooding might become as

common a technique in the oil field as i t is water flooding today.

REFERENCES Bondor, P.L.,Hirasaki, G . J . ,Them, M . J . : "Mathematical simulation of polymer flooding in complex reservoirs", SPE reprint series no. 11 (1972)

168

SYMBOLS A

De

D

E E F G

H L

ia M N

R R Re Rf

Rr f ;O

T T V

v "P

a b C

d fW

k 1 n P r S

t V W 0

U )1

Y T

.\i E E

n w

r 0

P

area Debo r ah n um b e 1' torque elasticity modulo adsorption energy force nomalized torque power law coefficient length Avogadro’s number mobility ratio molecular weight power law exponent radius gas constant 8,31431 Reynold’s number resistance factor residual resistance factor specific surface totuosity factor temperature absolu to temperature volume

m2

volume flow rate p o r e volume

, 3 . ,-1

N’m Pa

J N N Pa.sn m -

m r a d i us constant in Langmuir i sotherme concentration m diameter, thickness fractional flow permeability m 2 (mD) m length power law exponent Pa pressure m radius sticking coefficient S time m8s-l velocity Pa stress (at wall)

expon. Freundlich isotherme stress viscosity angle of shear residence time rate of shear strain linear strain rate of linear strain angular velocity angular velocity power law coefficient porosity, % porosity, fraction density

169

A

elastic viscosity

Pa’s

indices C

f 0 W

r i a e

P P

D C

B V 0

filter cake formation oil water relative initial after elastic polymer porous Darcy critical bulk volume porous

units length

m ka

mass

time force pressure concentration

S

N=kg,m . s 2

meter ki 1ogr amm second Newton Pascal

Pa=N’m2 kg kg/ks ppm parts per million for permeability sometimes the Darcy is still used

micro milli centi hekto kilo mega

10-6 10-3 10-2 102 103 106

170

A CHEMICAL STRUCTURE OF S A C C H A R I D E S I n the

and

following some

bi,ief explanations about the structure

nomenclature of baccharides

carbohydrates

is Cm(H20),.

are given

T h e general formula of

Saccharides are carbohydrates with the

genaral formula CnHZnOn. They are divided into three groups:

Polysaccharides (contain one CH20H group)

Bisaccharides Trisaccharides

Aldoses (contain one aldehyde group - CHO)

~

etc.

1 Trioses Tetroses Pent oses

Ketoses

IAldohexoses

I L-Aldohexoses (1" OH-group at 5th C-atom in chain notation (see below) is at the left side)

I D-Aldohexoses the give

D-Aldohexoses have

the OH-group

right side.

and

The

the position

structure,

Q

B

at the penultimate C-atom on

in the

notation of the aldohexoses

of the OH-group at the first C-atom in the ring

as shown

in Fig.A.l.

A

+

or - marks the direction in

which the polarized light is rotated. The position specifies

the name

of the

OH-group on the pnd, g r d , and q t h C-atom

as shown in the ’linear’ notation in the upper

part of Fig.A.2.

171

a - position Fig. A . l

p-

position

Position o f the OH-group at the l S t C-atom

ChOH CHzOH

CHzOH CHzOH

H O OH H OH i H OH a-D Glucose

HO OH HO OH H O H H a-D Mannose

CHzOH

CYOH

H

CHzQH CYOH

H~JH HO

H OH

OH OH (1-0 Allose

H

OHO H OOH H OH a-L Galaktose

CYOH

CYOH CYOH

CYOH

CYOH

HH HO ' H OH

CYQH CYOH

H

o H Ob H

PH HOH O0 H

1

' ; O O H 3

OH

OH H a-0 Altrose

OH

a-L Gulose

a-L Talose

2

OH

H

a-1 ldose

Fig.A.2 Aldohexoses in notation as a chain and as a ring. A l l are a - a l d o h e x o s e s in D and L p o s i t i o n . At the idose ring the counting of the C - a t o m s , as used for t h e notation of bonds between different rings ( e . g . c e l l u l o s e ) , is g i v e n .

172

Oligosaccharides

are made up of two monosaccharides)

Disaccharides

HJ - ( OJ - OH ( H OH

H

H

a -0 Glucose ig. A . 3

H

OH

OH

a - 0 GLucose

Maltose

CHzOH

H

p-0 Glucose Fig. A . 4

Maltose is unit being and

H

OH

OH

a-0 Glucose

Cellubiose

the basic unit of starch, and cellubiose the basic

of cellulose. that maltose

Both

consist of two glucoses, the difference

is built

from two

glucoses of ihe same t y p e ,

cellubiose is built of an a- and a 8-glucose. The bond between

the two glucoses in the cellubiose is l j 3 4 .

173

B CHEMICAL ANALYSIS OF POLYMERS IN PRODUCED FIELD WATERS The determination portant the

of polymers in produced field waters is im-

for the analysis of the performance of a polymer flood. In

following some

methods for the analysis of polyacrylamide and

xanthan are described. In some of these analyses the determination of the polymer may be a

disturbed by sample may

may

be used.

high salt concentrations. The content of salts in

be reduced by dialysis. An ordinary laboratory setup The content

of salts

may be

reduced to 30 mg/l in

about 1 hour. The polymer content is usually determined by measuring the turbidity

or extinction

reagents

of a

colour that develops after the testing

have been added to the sample. A calibration curve has to

be prepared for every polymer and testing method.

B . l Polyacrylamide The analysis of polyacrylamides in water may basically be done by

utilizing three

method,

and by

principles: turbidimetry,

hydrolysis with

the detection

the of

starch the

iodide

resulting

ammonia.

B . l . l Turbidimetry One method aL(1987). reservoir

using turbidimetry

This method brine. The

is

described

by

ALLISON

et

may also be applied for samples containing presence of

iron does

interfere

with

the

method. The procedure as follows:

- 50 ml of the sample are diluted with 30 ml of deionized water.

- 10 ml of 5 % sodium citrate solution are added and mixed. -

10 ml of Hyamine 1622 reagent are added.

-

turbidity develops within 30

-

5 0 minutes.

- turbidity is measured at 500 nm with any standard colorimeter. This method may be used for up to 20 ppm concentrations of polydcrylamide.

At higher

ted.

A similar

uses

the reaction

sodium

method is

concentrations the sample should be diludescribed by FOSHEE et a l . (1976) which

of polyacrylamide

in

an

acid

solution

with

hypochlorite. During this reaction an insoluble chloroamide

174

is

produced, and

turbidity is measured. The method may be applied

in brines and the rang,e is 0 - 500 ppm of polyacrylamide.

- pipette 1 m l polymer solution in a test tube.

-

add 1 ml acetic acid ( 5 N ) and stir.

- add 1 ml bleach (1.31 X sodium hypochlorite), mix gently and stand 5 minutes

- read turbidity B . 1 . 2 Iodometric method The method,

pH

of 5 . 5 ,

mine

is described

by FOSHEE et a l . (1976). The excess bro-

is reduced by sodium formate. The N-bromo amide then oxidizes

iodide, iodide

It

where the amide group is brominated at a buffered

which in

the presence that any

filtered. I t

thoroughly

forms the

blue starch-

intensity of the color is measured at 580 n m .

complex. The

is self-evident

of starch sample of

may also

reservoir brine should be

be recommended

to

remove

the

brine by dialysis.

- place 15 ml of the sample in a 100 ml bottle. - add 0 . 5 ml of a 50% sodium formate solution and wait for exactly 10 minutes.

- add 1 . 5 ml of a 10% potassium iodide and shake. - add 1 ml of starch indicator (0.1 g soluble starch in 5 ml of distilled water) and shake again.

- measure the absorbance of the solution at 580 nm B . 1 . 2 Ammonia detection

By hydrolysis reacts may

in a

caustic water

carboxgl group

R

be detected

reacts The

to

in a

solution the CONH2

and ammonia

color reaction.

--

group

is produced. The ammonia "Neslers reagent." K2(HgJ4 1

with ammonia to form an orange brown complex Hg(HgJ3(NH2)).

absorbance may

calibration

he

curves have

detected to be

using

a

colorimeter.

prepared just

as

for

Standard

the

other

methods, too.

B . 2 Xanthan A method described

for the

determination of xanthan in fresh waters is

by GRAHAM (1971). Samples containing brines and rests of

sugars should be prepared by dialysis.

175

- 1 m l of the sample is mixed with 1 ml of a 4 % resorcin solution (the solution should be fresh, prepare daily! 1

- 6 ml of concentrated sulphuric acid are added quickly (Caution! The sample becomes hot)

- the sample is cooled in ice-water to room temperature - turbidity is measured at 4 9 4 nm The method

may be

used for xanthan gum concentrations of 5 -

2 5 0 ppm.

REFERENCES Allison, J . D . . Wimberley, J . W . ,E l y , T . L . . : "Automated and manual methods for the determination of polsacryamide arid other anionic polymers", SPE Res. Eng. 2 ( 1 9 8 7 ) 1 8 4 Foshee, W . C . , Jennings, R . R . , West, T.J.:"Preparation and testing partially hydrolyzed polyacrylamide solutions", SPE-paper 6 2 0 2 ( 1 9 7 6 ) Graham, H . D . : "Microdetermination of Keltrol (Xanthan g u m ) " , J . Dairy Sci 5 4 ( 1 9 7 1 ) 1 6 2 2 Hoyt, J . R . : "Automated method for the detection of polyacrylamides in brine solutions", Adv. Automated Analysis, Technicon Intl. Congr. 2 ( 1 9 6 9 ) 6 9 Scoggins, M . W . , Miller, J . W . : "Determination of water soluble polymers containing primary amide groups using the starchtriodide method", SPE J . (June 1 9 7 9 ) 151

176

C MEASUREMENT OF FLOW CURVES A s already

measurement angular the

pointed out

in rotational

the rate of shear strain in viscosity viscometers not

only

depends

on

the

velocity and some constants of the apparatus, but also. in

case of non-Newtonian liquids, on the properties of the liquid

itself. In the calculated N

of a

double

following example, for different

power law

fluid. The

cylinder system,

the rate

of shear strain shall be

cylinder systems and different exponents cylinder system

will be

that of a

as shown in Fig. 5 . 1 0 . The ratio S of the

radii is to be the same for both systems.

The rate of shear strain will now be calculated for 0=1, Sz1.05 and 1 . 1 0 and N = l ,

1.5. 2 . 0 ,

The rate of shear strain

2.5

il for

the inner cylinder system shall

be calculated at the same location where the stress is measured, that is the inner wall of the middle cylinder and y 2 for the outer system at the outer wall of the middle cylinder. Thus for the inner system where the inner cylinder is rotated

and for the outer cylinder system

177

So the following values are obtained for the above parameters: Table C . l Rate of shear strain in a double cylinder system with the same S for different exponents N of a power law fluid.

=

N = l

21.51

N = 1.5

q1

N

2.0

i/l = 2 2 . 5 6

2.5

23.10

N

-~

=

= 22.03

This shows for

representative and

-4.9 %

q2 = i/2 =

18.56 18.10

=

8.62

13.19

q2

ql

behavior

19.03

y2

2.5

=

=

12.62

2.0

ql = ql =

N

y2

9.06

N

=

19.51

12.06

y1 = 1 1 . 5 2

N

=

q2 q2 =

N = l 1.5

<

y2

that the

error made

9.52

8.19

in assuming

Newtonian

flow

N=2 (n=0.5; value for polymer solutions used in EOR) is t 4 . 9 non-Newtonian

for cylinder

liquid

systems with

with

a %,

a very small gap ( S = l . O 5 ) ,

and t 9 . ' 5 % and - 9 . 5 % for S = 1 . 1 0 .

For example, 5 ~ 1 . 0 8 7for the Brookfield LV-viscometer with ULadapter

and

5 ~ 1 . 0 7 8 for

the

Haake

viscometer

with

a

double

cylinder system. Hence the

error that is made in calculating the rate of shear

strain is not negligible. If we

assume for

a double cylinder system that the effective

rate of shear strain is the mean value of both cylinder systems,

178

then

the

errors

compensate. liquids fluids

in

So such

and the

measuring

a system

procedure for

(apparent viscosities)

power

may be

law

fluids

calibrated

do

with

exactly

Newtonian

measuring flow curves of power law may be

the same

as for

Newtonian

liquids.

m

n E

30

c

c

zm 5 n n

a

3

Fig. C.l Typical flow xanthan solution

curves of

In Fig.C.l two typical

both a

polyacrylamide

and

a

flow curves of a polyacrylamide and a

xanthan solution are shown. The flow curves may each be represented by two

sections

of a straight

line in a logu,

-

log?

plot.

In Table C . 2 the values H and n for these two flow curves and of a flow curve of a xanthan broth are given. These values will be used in the following for further calculations.

179

Table C . 2 Parameters of flow curves

i/ =

0 . 3 - 3.0 3.0

-

90

s-l

H = 53.5 m P a * s n

: n

=

0.85

:

H = 7 6 . 8 mPa.sn

: n

=

0.56

-

20

o c

c 1000 ppm reservoir brine 60 g/l TDS

= 0.3 - 5.0 s - l

:

H

20.5 m P a . s n

: n

= 5 . 0 - 90

:

H = 26.4 mPa.sn

: n

Xanthan broth

-i/

:

t

Xanthan

-i/ -i/

c = 500 ppm fresh water of 50 m g CaO/l

t = 20 o c

Polyacrylamide

0.3

-

300 s-’

=

t :

30

O C

c

=

=

0.75

21 200 p p m

H = 25.7 Pa.sn

I80

0.94

: n

=

0.067

D EXAMPLE CALCULATIONS FOR PRESSURE DROP IN PIPES In the following examples, the pressure drop for water, a polyacrylamide pipe 10

solution and

a xanthan broth shall be calculated for a

with an inner diameter of 3" (76.2 m m ) , and for flow rates of m3/d and

5 0 m3/d. The flow curves described in Appendix C will

be used to calculate the pressure drop of the polymer solutions. In order

to distinguish whether the flow in a pipe is laminar

or turbulent, Reynold’s criterion may be used. I t states that for laminar flow the Reynold’s number should be smaller than 2320.

For 1amin.ar flow the Hagen-Poiseuille equation is used

The Hagen-Poiseuille above.

equation was

derived in

Section

5.2.2

For turbulent flow an equation that allows one to calculate

pressure d r o p may be derived as follows: The shear stress for laminar flow at a pipe wall is

The shear stress for turbulent flow may be expressed as kinetic energy per volume

183

A friction

factor that expresses the ratio of shear stress in

laminar flow to turbulent flow

mag

be defined as:

So the pressure drop for turbulent flow may be calculated, that is, if the friction factor is known,

with f = 4’f’

Equation D.6

is usually

used to

calculate pressure

drop in

for turbulent flow with the friction factor f . This friction

pipes factor

may be

determined using

the following empirically derived

equations: for pipes with smooth walls

or

1 f

.?

Re Sf

=

(D.8)

)

2 log(-

2.51

and for pipes with rough walls

182

1

3.71

-=

)

2 log(-

If

c/2r

c is a roughness factor. This fact r expresses

where the

rough parts

fluids

above the

enters the

pipe wall.

calculation of

Viscosity of

he height of the

flowing

the pressure drop via Reynold’s

number.

D.l Pressure drop for water In the

example for water flowing in a 3 " pipe at a rate of 10

m3/d and 5 0 m3/d, the following values are obtained.

10 m3/d: 1000~76.2~10-3~0.025

Re =

1905

<

2320

1.10-3 Therefore,

since the

flow is

still laminar, the Hagen-Poiseuille

equation is valid, and

AP

32.10-3.0. 025

1

0.07622

- -

= 0 . 1 4 Pa/m

50 m3/d:

Re = 9525 > 2320 Because

the flow

is turbulent, Equation D . 6 should be used. For a

smooth pipe, the friction factor is f

= 0.032

and so

AP

_ 1

0.032 .lo00' 0 . 1 2 5 2 3 . 2 8 Pa/m 2 ’0.0762

183

D . 2 b e s s u r e drop for a polymer solution The same calculation as made above

for water

shall now

be

performed for a polymer solution. 10 m3/d:

To estimate xiscosity obtain

the velue

of the

Ihe right

for

Reynold’s

polymer solution value for

number,

shall be

the apparent

the

npparent

assumed. In order to

viscosity, the

rate of

strain in the pipe for the flow of t h e polmyer solution must

’shear

be first determined. The average flowing velocity in the pipe is

V =

V/(7cr2)

=

0 . 0 2 5 m/s

This average velocity as well as the data used in the flow curve of

the polyacrylamide

strain

between 3 . 0

solution in

and 90

s-',

Appendix C for a rate of shear

will b e used to calculate the rate

of shear strain in the pipe (nz0.56, H z 7 6 . 8 mPa*s")

3n+l

9 = n

ua = H

'

V -

= 3.14 , - I

r

yn-'

4 6 . 4 mPa’s

p.2’r.G Re

= 41 < 2310

= Ma

Since the flow is still laminar, Equation 5.20 is used to calculate the pressure drop

AP 1

=

3n+l 2(-)"

n

H .n+ 1

Vn

=

7 . 6 5 Pa/m

184

5 0 m3/d:

V

0.125

i/

= 15.7

pa

=

Re

m/s s-1

22.8

mpa’s

<

418

2320

Though the flow rate is raised by a factor of 5 , the pressure drop

increases only

turbulent

flow of

by a

factor of

2 . 5 and,

as compared to the

water, the presssure drop increases at the same

rate only by a factor of 5 . 8 even though the viscosity of the

flow

fluid is 2 2 times higher. D . 3 Pressure drop for a xanthan broth

To calculate the presure drop for a xanthan broth the data from the flow curve described in Appendix C are taken. 10 m3/d; 3": Ap/l

=

(9

0.012 s-1;

1 5 7 4 Pa/m

Though the

the

11,

1592 Pa’s)

viscosity is

pressure drop

is only

lo6

times higher than that of water,

a factor

water.

10 m3/d; 1":

Ap/l = 5 8 9 0 Pa/m

185

of l o 5

higher than that for

E ELASTIC VISCOSITY

FLOOD EXPERIMENT

In order to determine the elastic viscosity of a polyacrylamide solution,

a flood

measured

in a

i n Table

performed. The

flow

curve

as

rotational viscometer with a double cylinder system

already shown

was

in Appendix

C. These data are listed once more

E.l.

Table E.1

Data of a flow curve of a polyacrylamide solution

t = 20

Polyacrylamide

y

experiment was

= 0.3 - 3.0

$ = 3 . 0 - 90

c = 500 ppm fresh water of 50 mg CaO/l

C

s-l

:

H = 53.5 mPa.sn

;

n

s-’

:

H = 76.0 m P a s s n

;

n

The flood

experiment was

=

0.85

0.56

performed in a sand pack. The para-

meters are listed in Table E . 2 .

Table E . 2

Parameters of the sand pack

Sand : broken sand with sharp edges grain diameter: 6 3 - 90 um Tube :

.

4 Length: 1.9 Diameter: 49 Porosity : Permeability: 3 . 2

cm cm 95

urn2

The means of calculation may be seen from Table E . 3 . By knowing the

flow rate,

a Darcy

space

may be

Darcy

equation (5.61).

of

viscosity that

is effective

in the pore

calculated from the measured pressure drop using the With the data from the flow curve the rate

shear strain in the porous medium during flow may be calculated

according

to Equation

viscosity

and the

since

the higher

5.71. The

difference between

viscosity calculated

the measured

is the elastic viscosity,

viscosity measured in the pore space during flow

is due to the elastic properties of the polyacrylamide solution.

186

Fable E.3

Calculating pressure drop in a sand pack at different flow rates, determination of pressure

drop due to elastic viscosity and determination of elastic viscosity

Flow rate,

Darcy velocity

Pressure drop

Darcy viscosity

Calculated shear rate

cm3/h

m3/s

m/s

Pa

LID(mPa-s)

(s-1)

Elastic

viscosity v,(mPa.s)

viscosil pD-pa(mPi

80

2.22-1 0-8

7.83 10-5

-

49 600

35.9

168

8.1

27.8

40

1.11.10-8

3.91-10-5

24 900

36.8

84

10.9

25.9

20

5.56-10-9

1.96-10-5

14 200

41 .1

42

14.8

26.3

8

2.22-10-9

7.83-10-6

7 150

51 .8

16.8

22.2

29.6

4

1.11 -10-9

3.91 -10-6

4 300

62.3

8.4

30.1

32.2

2

0.56-10-9

1.96-10-6

2 400

68.9

4.2

40.9

28.0

The results in Table E . 3 demonstrate that the, elastic viscosity is

nearly

increasing

constant flow rate.

and

does

Viscosity

not

increase

or

decrease

with

data measured in this relatively

simple way can be used to calculate pressure drops in a reservoir.

188

F RATE OF SHEAR STRAIN IN PERFORATIONS To estimate the rates of shear strain that mag occur in the vicinity ration

of a

well bore, the rate of shear strain around a perfo-

is calculated

in the

following

for

two

different

flow

rates.

a)

$' =

4 m3/d

b)

V

=

2 4 m3/d

The thickness perforations diameter

of 1

of the

per meter cm and

formation is 1 m. It is assumed that 10

are open a length

and that the perforations have a of 20

cm. Radial flow around the

perforation is assumed as illustrated in Fig F . l .

Fig. F.l

Radial flow around a perforation

189

The Darcy velocity at the border of the perforation is a ) VD

= 7.35

'

m/s

b ) VD

4.43

'

m/s

Assuming a solution

= 64 m/d = 380 m/d

permeability

of

the

formation

to

the

polymer

of 0 . 5 urn2 and a n effective porosity of 20 % , the rate of

s h e a r strain will be

b)

2 8 000 s-l

These

are relatively high values, but they are not so high that

the polymer solution may be degraded.

190

G ACCURACY OF CALCULATIONS OF SHEAR RATE IN A POROUS MEDIUM G . l Comparison of different equations

In the

following the pressure drop for a flood test on a sand

pack

is calculated

flow

curve of

using the different equations ( 5 . 7 1 - 5 . 7 3 ) . The

a xanthan

solution is

shown in

Fig. G . 1 , and the

result of the flood test in Fig. G . 2 .

-'!'

100

50

m

n E

1

.-L ul 4-

lo

U 0

.-ul> 4 - 5 c W

k n n

U

1

+ (s-')

Rate of shear strain,

Flow curve of a xanthan solution used for flood test in Fig G.l a sand pack.

--m

160 -

r

140

-

120

-

v =

180 I

n

8 &

Y

vD

cm3/h

80

= 7.84.

m/s

k = 3.52. 0 = 55.5

+=

,

0

.

T

40

1

I

80

-

T

120

~

1

160

.

1

mz % mPa. s

1.16

.

200

I

240

.

1

280

.

!O

Flooded pore volumes Fig. G . 2 Flood test with a xanthan solution on a sand pack.

191

The data for the sand PHck a r c K i v o n in Table G . l . I n the test

the

sand

pack

permeability polymer

*us

first

flooded

with

water,

and

then

the

was determined. After flooding the sand pack ~ i t hthe

solution. the

sand pack was flooded with water again, and

the permeabilty was calculated.

Table G.l Data from an injectivity test of a xanthan solution on a .;and pack. Length. Cross sectional area: Porosity: Pei,meabil i ty : Permeability to water after polymer flood: Dai cy velocity: Power law exponent: Power law factor:

4 2.84 55.5 2.85

cm cm2 %

wn2

2 . 1 3 urn'

7 . 8 . 1 W 5m / s 0.68 30.1 mPa.sn

The pressure drops measured during the flood test are given in F i g . G . 2 .

In

the

following

the

results

obtained

by

the

different

equations are given for the calculation of rate of shear strain:

HIRASAKI and POPE (1972) (Equ. 5.72)

48

s-l

ua = 8.72 mPa’s Ap = 9 5 . 5 hPa

192

GOGARTY: ( 1 9 7 5 ) ( E q u , 5 . 7 3 ) 3nt 1

50

4n

J150km

y = -

VD

-i, = 283 s - ' ua = 4.94 mPa’s Ap = 54

hPa

This book: ( 5 . 7 1 ) 3nt 1 y =-$2 4n

1 - VD Ikvj

-i,

2

pa

= 6 . 9 4 mPa’s

98

5-1

Ap = 76

hPa

This comparison and

that of

measured these

shows that

HIRASAKI and

value of

8 9 hPa

two equations,

the equation derived in this book

POPE (1972) lies between

give the best results. The the results

obtained

by

whereas the result obtained by equation 5.73

(GOGARTY (1975)) is too low. Fom Fig.G.2 i t may be seen that the xanthan solution shows a slight

tendency to plug the formation. This to some extent desired

behavior water the

leads to

flooding. If end of

a permeability

the pressure

reduction

for

the

subsequent

drop for the polymer solution at

the polymer flood is calculated using this permeabili-

ty, the following results are obtained:

193

HIRASAKI and POPE (1972):

i/

= 55.5

s-1

= 8 . 3 3 mPa’s A P = 122 hPa 1-1,

GOGARTY ( 1 9 7 5 ) :

9

= 327

Ap

s-'

4 . 7 mPa’s

pa

= 69

hPa

This book:

i/ 11 .,

= 113.4 = 6.6 mPa’s

Ap

= 97

hPa

These figures show that the equation derived in this book gives the

best result,

measured

where the

value of

calculated value

of 97

hPa fits the

96 hPa very well, whereas the value obtained by

HIRASAKI and POPE’S equation (1972) is too high. The results not

used for

solution this

of the injectability test shown in Fig. 6 . 1 5 were

such a calculation, due to the fact that the polymer

in this test was plugging the porous medium too much. But

t e s t would

also

show

that

the

results

obtained

by

the

worked out by HIRASAKI and POPE (19721, as well as by the

equation

equation derived in this book are reasonable. G . 2 Relevance to two-phase flow

Equation 5.71 may also be used in two-phase flow, e . g . oil and polymer

solution, if

effective effective solution effective solution

one takes

porosity for

the flow

porosity, the should be

effective

permeability

and

of the polymer solution. For the

fraction that

taken. For

permeability to

the

the

water at

is saturated

effective

with polymer

permeability,

the

the saturation of the polymer

may be calculated from the relative permeabilities of oil

194

and

water.

This

permeability

should

then

be

reduced

by

the

residual resistance factor as shown above. There is practica’lly no literature dealing with two-phase flow of

polymer solutions.

research, with

both in

respect to

This should therefore be subject to further

the laboratory

and

numerical reservoir

theoretically,

especially

simulation for polymer flood

processes.

REFERENCES Gogarty, W . B . , Levy G . L . , Fox, V.G.: "Viscoelastic effects in polymer flooding through porous media", SPE-paper 4025 ( 1 9 7 5 ) Hiresaki, G . J . , Pope G . A . : "Analysis of factors influencing mobility ratio and adsorption in the flow of polymer solutions through porous media", SPE-paper 9710 (1972)

195

H EXAMPLE CALCULATION ON DISPERSION In an occurring

experiment described while displacing

in the

fresh water

following, the dispersion from a sand pack with a

NaC1-brine shall be examined. Table H.l

Data for dispersion calculation experiment

T = 60

Temperature: Diameter: Cross sectional area: Porosity : Length : Pore volume:

d = 3 A Q

1

=

7.07

O C

cm cm2

= 37.2 x 21

cm

V, = 55.2 cm3

v = 5 cm3/h Injection rate: Salinity of fresh water: cf = 15 m g Catt/l Salinity of brine: Cb = 2900 m g Ca++/l The results

of

the

displacement

experiment

Fig.H.l.

5000

P-

1000

i Y

d

c

a

500

0

4-

m

c

0 .c

m c L

100

c U Y

c U 0

50

N m

U

10

0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0

Injected pore volumes Fig. H . l Breakthrough curve of Ca2’

196

26 m g CaC12/1 5000 mg ~ a ~ 1 2 / 1 E 0.05 m o l / l are

shown

in

The width of the breakthrough curve between the value of 10% of the

initial brine

concentration and

that

of

90%

0.4 pore

is

volumes o r , expressed as a length, 8.4 cm. The diffusion coefficient for strong electrolytes may be calculated

according to

tables.

Nernst’s relation, or looked up i n appropriate

The Handbook

of Chemistry and Physics gives the following

values for CaC12:

= 1.1

D

Diffusion coefficient:

=

'

cm2s-l

at 25 OC

cm2s-’

at 60 OC

1.23’

Using Equation 5 . 8 1 , a width of the breakthrough curve Ax90/10 may be calculated. At the injection rate given, the front of the injected brine should reach the outlet of the sand pack after of about

injection leads

to a

considerable of

fusion

volume after width of

11.04 h or 39744 s . This

about

1.5

cm.

This

is

a

value that should not be neglected as i t is about 8 %

the length

experiment indicates

1 pore

diffusion zone of the

flooded distance. The value measured in the

is about 5 times higher than the value calculated. This

that dispersion only.

coefficients

In

his

of about

in core

flooding is

work

BLACKWELL

1,10-4 ,

which

(1962) are

higher than gave

nearly

the

dispersion same

measured here.

REFERENCES Blackwel1,R.J.: "Laboratory Studies of Microscopic Dispersion Phenomena", SPEJ March 1962, p . 1 .

197

difas

I POLYMER MIXING IN THE LABORATORY Some parts of the mixing procedures given below and in previous chapters here

of the

is based

book may be subjects of patents. The advice given on the

author’s experience.

It is not meant as an

invitation to violate any patents.

1 . 1 Mixing of powders

A stock solution should be prepared in fresh water. Two methods may be applied in principle:

I:

The

The

water is

the required amount of water is put into a beaker.

that a

so

vor ex,

stirred using a propeller or magnetic stirrer

vortex is

created. The

powder is spread in the

is continued for several hours ( 5 - 2 0 )

and stirring

unt 1 the powder is totally hydrated. 11:

The the

beaker, while by

required amount

and the

of powder

corresponding amount

is of

put

into

water

is

the

added

stirring. The hydration of the powder may be improved

wetting

ethanol)

(dispersing)

with

it

an

alcohol

(methanol,

before the water is added. Stirring should also be

continued for several hours. Dilute

solutions with the final concentration may be prepared from

these stock solutions. 1 . 2 Mixing of emulsions Polyacrylamide emulsion The

polymer is

dispersed it

in the

in the

is necessary

the

polymers are

form of

oil phase.

a gel

in

water in oil emulsions. small

water

droplets

When mixing the emulsions with water

to disperse the polymer as quickly as possible in so that no agglomeration of bigger gel particles

water phase,

may occur. the

The polymer

concentration in the emulsion varies depending on

product and

for one

batches. which

When mixing

may

particular product within the production

the polymer

be determined

the content

by evaporating

of active

the emulsion,

matter, must

be

droplets

to

considered. Some emulsions settle.

When storing

show a

tendency for

samples of

the

such products

198

water

for a longer time

bottles should

the

be shaken

at regular

intervals (about once a

week 1.2.

Activator The activator is a surfactant for breaking the emulsion. Polyproducers often

mer

activators these

deliver

or

recommend

an

activator.

These

are often poorly soluble in water. Diluted solutions of

activators ( 2 0

% ) may

be handled

more easily. They can be

quickly diluted in the mixing water. 1 . 2 . 2 Mixing water

The mixing water should be of constant quality and composition. 1 . 2 . 3 Preparing a stock solution

Preparation of recommended. same

activator

inverted.

10 10

a stock

Thus the

solution of

higher concentration

activator concentration

consumption,

The concentration

and

the

is higher

emulsion

may

is

at

be

the

better

of the stock solution should be about

times higher than that of the final solution. This is about 5 g/1.

A

beaker (1

mixing

1 , high

water. The

shape) is

water is

0.5 1

filled with

stirred with

of the

a propeller.

so

that a vortex develops, but no air is drawn into the water. Note:

of the

The material

propeller should

be

stainless

steel. The

activator is added to the water. This is about 5 % mass

(active matter) based on the polymer emulsion to be mixed. Example: content means 490

A stock

solution of

of active

matter in

5 g/l shall be prepared. The the emulsion

is 25

%.

This

that 10 g of the emulsion are needed for 0 . 5 1 (exact g) of water. The necessary amount of activator is 0 . 5 g

or 2 . 5 ml of a 20 % prediluted activator solution.

The

required amount

syringe.

The polymer

shoulder

of

adjusted

so that

about stem

the

of polymer

emulsion is

emulsion is

vortex.

The

the vortex

quickly jetted

speed is

loaded into a

of

still

the

into the

stirrer

maintained.

is

After

2 minutes the polymer solution starts creeping up the

of the

stirrer

Stirring

of the solution should then

be continued for another 2 or 3 minutes. The mixing procedure is visualized in F i g . I . l - 1 . 3 .

199

Fig.

1 . 1 P i p e t t i n g the a c t i v a t o r to t h e m i x i n g water

F i g . 1 . 2 A d d i n g the polymer e m u l s i o n by m e a n s of a s y r i n g e .

200

Fig. 1 . 3 The inverted emulsion thickens the water, and the polymer solution starts creeping up the stirrer shaft.

1.2.4 Preparing a final solution Dilute polymer solutions may be obtained by simply diluting the required

amount of

stock solution

into

the

water.

Only

short

mixing is necessary. 1 . 3 Shearing Shearing of a polymer solution may be effected with high speed stirrers through

as shown in Fig. 6 . 3 , or by passing the polymer solutions

orifices (shear

plates) as

shown in

Fig. 6 . 4 . Shearing

through shear plates has been proposed by LIPTON (1974), GRODDE ( 1980), or in a rhone poulenc product information. Passing of polymer

solutions through

orifices in

a device, as shown in Fig.

6 . 4 , was proposed by UNSAL et al. (1977). If shearing (e.g.

air

in an

is performed,

exsiccator) before

the solution further use,

should be

evacuated

because nitrogen or

is mixed into the solution while shearing. The gas bubbles may

only be removed by evacuation.

201

1 . 3 . 1 Layout of shear plates

The best

layout of

injectability (stock

tests

shear plates may be found by carrying out

of

solutions and/or

differently final

sheared’ polymer

solutions).

The

shear

solutions at

shear

plates may be varied by applying different pressure drops. Whenever an laboratory,

adequate layout

it may

be easily

of shear

scaled up

plates is found in the to the requirements in a

field mixing unit. Examp1 e : The

flow rate of a xanthan broth through a hole of l m m dia-

meter

was measured

in the laboratory at different pressure

d r o p s . The results are listed in Table 1 . 1 .

1 1

Flow rates of a xanthan broth through a l m m hole

Table 1 . 1 I

I

1

Pa

m3/s

1.105 2’ 105 3,105 7.105 10.105

The

8.1.10-6 12.5.10-6 14.6.10-6 20.6.10-6 26.9.10-6

factor j

in the

lo;ls 15.9 16.6 26.2 34.3

0.70 0.77

1176

Bernoulli equation

( 6 . 1 ) is

on

the

average 0 . 7 5 . By

using this factor the cross sections of the hole(s) in a

shear plate of a field unit may be calculated. The

velocity for

drop of 10 bar (1 MPa) is ( p =

a pressure

1000 kg/m3)

v

(A

=

: A

V/A

=

cross

holes; a

=

=

n’a

sectional area

of the

holes; n

cross sectional area of one hole)

202

=

number

of

for

the flow

rate of

500

l/h

(=1.39.10-4 m3/s)

and

a

pressure drop of 1 MPa

So

each

one hole with a

with a diameter of 2 . 3

mm,

diameter of

are necessary to obtain

1.33

mm,

or e.g. three holes

the desired shear.

REFERENCES Cyanamid, product information, Cyanatrol, Cyanamid Plaza, Wayne, NJ 07470 (USA) Dow Chemical, product information, Pusher 700 Grodde, K . - H . : "Verfahren zur Scherbehandlung waessriger Loesungen von partiell hydrolysierten Polyacrylamiden" Patent DE 27 33 852 B 2 Int. Cl.: E 21 B 43j22 (1980) Kelco, product information, Keltrol, Okmulgee, Oklahoma (USA) Lipton, D . : "Improved injectability of biopolymer solutions", SPE paper 5099 (1974) Nalco, product information, Nalflo, 1801 Diehl Road, Naperville, IL 60586 Pfizer, product information, Flocon 4800, Eastern Point Road, Groton. CT 06340 (USA) rhone poulenc, product information, Rhodoflood X R , 125 bis rue Raspail, 69150 Decines (France) Unsal, E . , Duda, J . L . ,Klaus, E . : "Comparison of solution properties of mobi1it.y control polymers", in Chemistry of oil recovery, Johansen, R . T . , Berg, R.L.(editors) Unsal, E . , Duda, J . L . , Klaus, E . E . ,Liu, H.T.: "Solution properties of mobility control polymers", Eastern Regional Conference SPE, Pittsburg (19771, SPE-paper 6625

203

J CHEMISTRY OF IRON HYDROXIDES AND IRON OXIDES The chemistry of iron compounds, especially that of iron oxides and

iron hydroxides,

necessary iron

is not very clear. As a certain knowledge is

to understand

in water,

the solution

which are

and reaction

essential for

polymer

processes flooding,

of some

basic explanations are given below. J . l Iron - I1 - hydroxide The hydroxide soluble

of the

compound. I t

divalent iron

may fall

(Fa (OH)2)

is a

poorly

out of a solution of Fe -11- salts

by addition of alcaline hydroxide. The precipitate is white.

By oxidation built

that are

of the

white Fe(OH12,

dark green compounds are

called ferroferrite. This name stands for a number

of compounds of F e - 1 1 - 1 1 1 - h y d r o x i d e s / o x i d e s . J . 2 Dissolved iron-111-hydroxides

Fe(OH)3 exists only in solution and only then when the solution has

a particular

mean pH-value.

Fe(II1) forms

salts

with

most

anions, except, of course, reducing anions. The most solutions

remarkable characteristic of Fe(II1)-ions in aqueous

is to

hydrolyse and/or

to form complexes. Two Fe(II1)-

ions form a structure as shown in Fig. J . l .

H

Fig

J . l Structure of two Fe(III)-.ions in an aqueous solution

A t pH-values shown so

i n Fig

thht ~t

above 2

J . 1 and

least gels

-

3

the tendency to form structures as

st.ructures of an higher order is increased, are formed

red hi,own gelatinous substance

204

that fall out o f solution as a

Aqueous F e ( 1 1 1 ) hydroxides are soluble in acids. Fe (111) will be

reduced by

overview

many rdducing

of the

compounds, e . g iodine or sulfide. An

most important

iron compounds

is given in Table

J.1. Table J.l Characteristics of some corrosion products of iron Compound

Color

Remarks

Fe(OH)2 a- FeOOH v- FeOOH 6- FeOOH FeO

white yellow-blackbrown red-yellow yellow black

Fe304

black-blue black

a -Fez03 Y-Fe203

red-black brown

ferromagnetic in a fine dispersed form well soluble in acids ferromagnetic: soluble only in HF well soluble in HF ferromagnetic; well soluble in acids

J . 3 Iron stabilizing agents The

characteristics

described

above

of

Fe(II1)

to

form

complexes are also one reason why iron stabilized or sequestered in solutions,

may be relatively well so that i t cannot react

with

commonly used are citric

acid,

polymers. Sequestering

agents most

acetic acid, mixtures of citric acid and acetic acids, EDTA.

and NTA.

REFERENCES Crowe, C . W . : "Evaluation of agents for preventing precipitation of ferric hydroxide from spent treating acid" JPT (1985) 691 Crowe, C . W . : "Method of inhibiting crosslinking of aqueous xanthan gums in the presence of ferric acid ions", U.S. Patent No. 4 , 3 1 7 , 7 3 5 (1982) Homig: "Physicochemische Grundlagen der Speisewasserchemie", Vulkan Verlag Essen. 1963 Kleinitz, W . : private communication (1987)

205

HOGEN-ESCH, T.E. (1980) 80 HOMIG, ( 1 9 6 3 ) 205 HOVEMANN, F . (1985) 1 9 , 32 ABDO, M.K. ( 1 9 8 4 ) 158 HOYT, J.R. ( 1 9 6 9 ) 176 ALLISON, J.D. ( 1 9 8 7 ) 174 HSU, S.C. ( 1 9 7 9 ) 109 ANDREWS, G . I . ( 1 9 7 0 ) 91 JENNINGS, R . R . (1976) 174f BARKMAN, J.H. ( 1 9 7 2 ) 137f KAPLAN, S.J. ( 1 9 7 9 ) 109 BARSAN, P. ( 1 9 8 5 ) 186 KESSEL, D.G. ( 1 9 8 5 ) 119 BARTHOLD, K. ( 1 9 8 5 ) 19, 32 KLARE, J . (1978) 80 BLACKWELL, R.J. ( 1 9 5 9 ) 1 5 KLAUS, E. ( 1 9 7 9 ) 2 5 , 100 BLACKWELL, R.J. ( 1 9 6 2 ) 197 KLAUS, E . E . ( 1 9 7 7 ) 201 BLANK, L. ( 1 9 8 5 ) 186 KLEIN, J . ( 1 9 7 8 ) 80 BONDOR ( 1 9 7 2 ) 128, 163 KLEINITZ, W . (1985) 107 BORKOWSKI, N . (1978) 80 KLEINITZ, W . ( 1 9 8 7 ) 139, 205 BRAGG, J.R. (1983) 34 KLEINITZ, W. (1988). 124, 157 BUCKLEY, S.E. ( 1 9 4 2 ) 3 KLOSE, P.-ST. (1982) 110 BURTCH, F.W. ( 1 9 8 0 ) 153 KOHLER. N ( 1 9 8 1 ) 1 1 1 BUTLER, G . B (1980) 80 KOZENY, J ( 1 9 2 7 ) 68 CARMAN, P.C ( 1 9 3 7 , 1 9 3 8 ) 6 8 KUHN, A . 1944) 58 CAUDLE, B.H (1954) 3 LABASTIE, A. ( 1 9 8 1 ) 1 5 1 f CHAMBERLAIN R.J. (1981) LANGMUIR 1916) 79 CHASE, C.A. ( 1 9 7 9 ) 128 LATIL, M . ( 1 9 8 5 ) 186 CHAUVETEAU, G . (1981) 1 1 1 LAUWERIER H . A . (1955) 132 CHAUVETEAU, G . ( 1 9 8 5 ) 106 LEONHARD, J . ( 1 9 8 6 ) 1 5 1 CHEN, S . J . 1972) 150 LEVERETT. M.C. ( 1 9 4 2 ) 3 CHUNG. H . S . ( 1 9 8 7 ) 158 LEVY G . L . ( 1 9 7 5 ) 6 9 , 193 CLIFFORD, P.J. ( 1 9 8 5 ) 33 LIPTON, D . ( 1 9 7 4 ) 100, 1 4 8 , 201 CLIFFORD, P.J. ( 1 9 8 7 ) 81 LITTMANN, W. ( 1 9 8 5 ) 131 COMBE, J . ( 1 9 8 5 ) 186 LITTMANN, W . ( 1 9 8 7 ) 149 CORDRUWISCH, R . ( 1 9 8 5 ) 107 LITTMANN, W . ( 3 9 8 8 ) 124, 157 CRAIG, F.F. ( 1 9 7 1 ) 14 LIU, H . T . ( 1 9 7 7 ) 201 CROTHERS, D . M . ( 1 9 6 2 ) 61 LOTSCH, T. ( 1 9 8 6 ) 7 9 , 8 1 , 8 3 CROWE, C . W . ( 1 9 8 5 , 1982) 235 LOTSCH, T. ( 1 9 8 7 ) 83 CRUEGER, W . AND A . ( 1 9 8 6 ) 31 MAERKER, J . M . ( 1 9 7 5 ) 32 DAVIDSON, D . H . ( 1 9 7 2 ) 137f MAITIN, B . ( 1 9 8 5 ) 154 DEURER, R . ( 1 9 8 2 ) 110 MANSOURI, A . ( 1 9 7 8 ) 80 DIETZEL, H.J. ( 1 9 8 2 ) 117 MARTIN, V . ( 1 9 7 8 ) 80 DOMINGUEZ, J.G. ( 1 9 7 6 ) 80 MARTISCHIUS, F.D. (1985) 1 9 , 3 2 DOMINGUEZ. J.G. (1977) 28 MARUCA, S.D. ( 1 9 8 3 ) 34 DUDA, J . L . ( 1 9 7 7 ) 201 MATTHEWS, C . S . (1967) 124 DUDA, L . J . ( 1 9 7 9 ) 2 5 , 100 MEISTER, J . J . ( 1 9 8 0 ) 80 DUSZELN V . , J . ( 1 9 7 8 ) 80 MENARD, H . W . ( 1 9 8 1 ) 1 DYES, A , B . ( 1 9 5 4 ) 3 MILLER, J . W . ( 1 9 7 9 ) 176 EINSTEIN, A . ( 1 9 0 6 ) 61 MITCHELL, M . S . (1982) 129 ELY, T . L . ( 1 9 8 7 ) 174 MORLAND, C . D . ( 1 9 7 9 ) 109 ERICSON, R.A. (1954) 3 MUNGAN, N. ( 1 9 6 9 ) 80 FIESER, L . F . ( 1 9 5 6 ) 171 MUSCHELKNAUTZ, E . (1979) 148 FIESER, M . ( 1 9 5 6 ) 171 MYHILL, N.A. ( 1 9 7 8 ) 135 FOSHEE, W.C. ( 1 9 7 6 ) 174F NAVRATIL, M . ( 1 9 8 2 ) 129 FOX, V . G . ( 1 9 7 5 ) 6 9 , 193 NELSON, R.C. ( 1 9 7 7 ) 128 GAIDA. K.H. ( 1 9 8 5 ) 119 ODEH, A.S. (1979) 69 GALE, W . W . (1983) 34 OSTWALD, W . ( 1 9 4 4 ) 58 GALL, L.S. ( 1 9 8 3 ) 34 PAHL, M . H . ( 1 9 7 9 ) 148 GOGARTY, W.B. ( 1 9 7 5 ) 69. 193 PANAITESCU, A . (1985) 186 GRAHAM. H . D . ( 1 9 7 2 ) 174 PARKER. A . ( 1 9 8 7 ) 81 GRODDE. K . - H . ( 1 9 7 8 ) 38 GRODDE, K.H. ( 1 9 8 0 ) 3 2 , 7 3 , 1 0 0 ,201PHELPS, C . H . ( 1 9 8 4 ) 158 GROSZEK, A . J . (1970,1979) 91 PHILIPOFF, W. (1944) 27 HALSEY, G . ( 1 9 4 7 ) 83 PLEDGER J R . , H . (1980) 80 HILLE, M . ( 1 9 8 5 ) 28 POPE, G.A. ( 1 9 7 2 ) 6 9 , 128 HIRASAKI, G.J. ( 1 9 7 2 ) 128, 163 POPE, G . A . ( 1 9 7 2 ) 6 9 , 192 HIRASAKI, G.J. ( 1 9 7 2 ) 6 9 , 192 POPE, G . A . ( 1 9 7 7 ) 128 AUTHOR INDEX

206

PUSCH, G . ( 1 9 8 7 ) 83 RAYNE, J.R. ( 1 9 5 9 ) 15 RUSSEL, D.G. ( 1 9 6 7 ) 124 RYLES, R.G. ( 1 9 8 5 ) 33 SANDIFORD, B.B. ( 1 9 7 7 ) 8 SCHAEFER, W . ( 1 9 7 8 ) 38 SCOGGINS, M.W. ( 1 9 7 9 ) 176 SERIGHT, R.S. ( 1 9 8 0 ) 32 SMITH, C . R . ( 1 9 6 6 ) 14 SMITH, R . V . ( 1 9 8 0 ) 153 SORBIE, K.S. ( 1 9 8 5 ) 33 SORBIE, K.S. ( 1 9 8 7 ) 81 SOVAK, M . ( 1 9 8 2 ) 129 STAUDINGER, H . ( 1 9 4 4 ) 58 STEGEMEIER, G.L. ( 1 9 7 8 ) 135 SZABO, M.T. ( 1 9 7 5 ) 80 TANAKA, T. ( 1 9 8 1 ) 1 , 98f TAYLOR, H.S. ( 1 9 4 7 ) 83 TAYLOR, H.S. ( 1 9 4 7 ) 83 TEMPLER, C.E. 91 TERRY, W.M. ( 1 9 5 9 ) 1 5 THAM, M . J . ( 1 9 7 2 ) 128, 163 TODD, M.R. ( 1 9 7 9 ) 128 TRUCHETET R . ( 1 9 8 5 ) 186 TUNN, W . 1974) 4 TURTA, M . ( 1 9 8 5 ) 186 TYSSEE, D A . ( 1 9 8 0 ) 33 UNSAL, E . ( 1 9 7 7 ) 201 UNSAL, E. ( 1 9 7 9 ) 2 5 , 100 VETTER, 0 J . ( 1 9 8 0 ) 33 VIO, L . , 1986) 1 5 1 f VOLLMERT B . ( 1 9 7 3 , 1980) 26 VOLZ, H . ( 1 9 8 5 ) 119 VOLZ, H.V. ( 1 9 8 3 ) 1 3 , 81 VOLZ. H . V . ( 1 9 8 6 ) 83. WELGE. H.J. ( 1 9 5 2 ) 5 WEST, T . J . ( 1 9 7 6 ) 174f WESTERKAMP, A . ( 1 9 7 8 ) 80 WESTERKAMP, A . ( 1 9 8 7 ) 149 WIDDEL, F . ( 1 9 8 5 ) 107 WILLHITE, G . P . ( 1 9 7 6 ) 80 WILLHITE, G . P . ( 1 9 7 7 ) 28 WIMBERLEY, J . W . ( 1 9 8 7 ) 174 YANG, H . T . ( 1 9 7 9 ) 69 ZAITOUN, A . ( 1 9 8 5 ) 186 Z I M M , B.H. ( 1 9 6 2 ) 61 ZIMMERLE, W . ( 1 9 8 5 ) 119

207

SUBJECT INDEX A acceleration 15 acetic acid 2 0 5 acidizing 120 acrylamide 35 acrylic acid 2 4 , 35 acrylic acid ester 2 4 acrylnitril 2 4 ac tivatiori energy 8 2 activator 1 4 4 , 1 9 8 adhesion coefficient 82 adqorbent 7 8 adsorption 11, 2 0 , 2 2 , 7 7 adsorption energy 82 adsorption isotherms 7 9 adqorpt ion measurement 88 adsorption mechanism 8 5 ad<-orptionsite 82 adsorption, ’static’88 adsorption. data for polymers 8 0 , 81 adsorption, from flow experiments 8 9 adsorption, heat of 8 5 , 8 7 adsorption, kinetics 9 2 adsorptive 7 8 afterflush 160 agar 2 7 , 2 8 aldose 1 7 1 alginate 31 alginate 32 ammonia detection 1 7 5 analysis of polymers 8 9 , 1 7 4 angle of shear 3 9 angular velocity 52 apparent viscosity 6 , 42 aquifer 1 0 , 1 1 areal sweep efficiency 3 , 6 , 1 5 6

B back pressure well 10, 11 bacteria 2 1 , 36 bacterial growth 107f Bernoulli equation 101, 198 Bingham body 4 2 biocides 1 3 , 2 1 , 33 biological dgradation 2 1 , 32 biological stability 107 blocking 130 bound solvent 26 break down test 12 breakthrough 5 brine 1 3 bromine 1 7 5

calcium 3 2 calorimetry 8 8 , 9 1 Cannon Fenske viscometer 48

capillary pressure 7 4 capillary viscometer 4 8 , 4 9 carbonate 11 , carboxyl group 25 carboxymothyl cellulose 30 case histories 1 5 1 collubiose 173 cellulosn 2 1 , 2 9 centrifugal pumps 145 Chateaurenerd polvmer flood 151 chemical degradation 3 2 chromatography 8 9 citric acid 3 4 , 103 citric acid, preflush in cores, 116 Clausius-Clapasron-equation 85 clay 1 1 , 7 9 coil, of molecule 26 colloid 7 2 , 7 7 colloid science 7 2 , 7 7 colorimeter 175 compatibility 11 complex 3 4 complex viscosity 65 compliance 65 conformation, of molecule in solution 61 continous fermentation 37 copolymerisation 35 costs 168 coverage 7 9 critical velocity 47 cross-linking 26 crude oil 1 3 , 115 curdlan 31 cylinder 4 4 cylinder , rotational viscometer 53

D Darcy’s equation 66 Deborah number 64 degradation 21, 32 degradation, biological 32 degradation, chemical 32 degradation, mechanical 32 degradation, shear 32 degree of hydrolysis 25,28 desorption 82 dextran 31 dialysis 1 7 4 diffusion 76 dioxane 35 dip, reservoir 10 dispersion 7 6 , 98, 196 displacement tests 8 , 2 1 , 2 2 115,118 distilled water 96 drae reducer 4 8 , 184 drilling muds 128 dynamic mixer 147

208

dynamic viscosity 41 E economics 162. 165 Eddesse-Nord polymer flood 156 EDTA 205 Einstein’s viscosity law 59 elastic properties 1 9 , 2 1 elastic viscosity 6 2 f , 124, 186 elas tic t. iscosi t y , measuring of 64 elasticity module 6 3 emulsion polymerisation 35 emulsion polymers 98 end effects, viscometer, 51f enzymes 33f error function 76 ethylhydroxyethyl cellulose 30 exploration 1 exsiccator 201

F fermentation 3 2 , 35 fermentation, continous 37 fermenter 36 Fick’s law 76 filter bags 149 filter tests 108ff fish eyes 96 flocculation 13 flood pattern 11 flood performance 13 flood test 8 , 2 1 , 2 2 , 115 flood water 136 flow curve, measurement of 54. 177 flow curves 48, 112 flow rate 44 flow velocity 45 flow, in pipes 44 flow, in porous media 65f flow, laminar 46 flow, pseudo plastic liquids 68 flow, turbulent 47 formaldehyde 1 3 , 34 fractional flow 5 , 14 fracture gradient 1 2 fresh water 1 1 , 96 fresh water post-flood 20 fresh water preflush 1 1 . 13 Freundlich-isotherm 82 friction factor 181f friction laws 40 fungi 2 1 , 36 G

gas cap 11 gear pumps 145 gel particles 21 gels, properties of 96f giants 1

glove box 106 gluceron acid 30 glucose 2 9 , 171 g l u e 78

H Hagen -Poiseuille’s law 46 Hagenbach correction factor 51 Hankensbuettel polymer flood 154

hardness, of mixing water 2 7 , 2 8 , 96 heat of adsorption 8 5 , 87 heavy oil 131 Henry-isotherm 79 hexose 171 Hoeppler viscometer 58 homopolymerisation 34 Hook’s law 6 2 hopper 143 hot water flooding 132 hydraulic radius 66 hydrochloric acid, preflush in cores 116 hydrolysis 2 5 , 32 hydroxyethyl cellulose 1 8 , 29 hydroxyethyl cellulose, degradation 33 hydroxyethyl cellulose, mixing 98 1

immiscible fluid displacement14 inaccessible pore volume 73f,90 incremental oil recovery 1 5 , 17 infections 21 injectability 1 1 , 2 1 , 71. 186 injectability testing 108 injection pressure 1 2 , 119, 121 injection water 136 injection water quality 136f injection wells 119, 149 injectivity 160 injectivity testing 2 1 , llOf injectivity, of wells 120 injectors 146 inoculum culture 36 interface 77f interfacial tension 1 , 75 intrinsic viscosity 59 investments 166 iodometry 175 iron 33 iron hydroxide 204 iron sequestering agents 120 irreducible oil saturation 4 irreducible water saturation 75

K kaolinite 79 Kenics mixer 146

209

I. 1a bo r a t o r y t e s t i rig of

polgmors 95f laminar flow 4 6 1-angniuiP - i sotherni 79 latex 35 lifting costs 167 limiting vjscosity number 59 1 ineai, strain 7 0 long term stability 105 l o s s compliance 65 l o s s of chemicals 10, 1 1 , 119

M macromolecule 78 magnesium 3 2 maltose 171 mannose 3 0 , 171 Mark-Houwink equation 6 0 , 6 1 mechanical degradation 32 metering pumps 145 methanol 3 5 micellae 3 2 micro flow calorimeter 91 microscopic sweep efficiency 6 mineralogy 11 minimum polymer viscosity 18 miscible flooding 1 mixer, dynariiic 147 mixer, static 142, 1 4 6 mixing chamber 147 mixing funnel 142 mixing of emulsions 198 mixing of polymers 95 mixing of powders 198 mixing procedures 95 mixing water 198 mixing, in the oil field 142 mixing, of polyacrylamide emuLsions 143 mobility ratio 3 , 6 , 16 molecular size 58 molecular structure 5 8 , 6 0 molecular weight 25 molecule size 76 monolayer 79 monomer 3 4 Myrtle Dillard flood water diversion 158

N Newtonian liquids 40 North Stanley polymer flood 1 5 2 NTA 205 numerical simulation 1 1 , 22, 1 6 2 nutrient 3 5 , 3 6

0 oil recovery 8

o i l saturation 5 oil viscosity 13 oil-water-cdntact 1 0 oscillation, damped 63 Ostwald viscomnter 4 8 oxygen 32, 34 oxvgeri scavenger 1 3 , 3 4 , 106

P pattern, of wells 12t perforations 1 2 0 , 150 performance 11 performance. flood 13 permeability 6 , 7 , llf, 6 6 permeability distribution 11 permeability variation 1 1 , 13 phase lag 6 4 , 6 5 physical adsorption 78 physisorption 82 plastic viscosity 42 plate and cone system 5 5 plugging 21, 1 6 0 polyacrylamide 1, 11, 1 8 , 2 4 polyacrylamide, chemical structure 2 4 polyethylene oxide 2 9 polymer consumption 1 6 0 polymer flooding, after steam flooding 130 ff polymer flooding, in low voscosity oil reservoirs 1 6 5 polymer mixing 1 4 1 , 198 polymer option 127 polymer production 3 4 polymer saturation 14 polymer selection 1 4 polymer stability 12 polymer viscosity, minimum needed 1 4 polymer viscosity, needed 18 polymethylmethacrylate 29 polysaccharide 29, 30, 3 2 , 171 polystyrene 29 polyvenyl acetate 2 9 , 3 5 pore size distribution 74f pore volume, inaccessible 7 3 f , 90 porosity 1 1 post flood 2 0 powder 3 6 power law 6 precipitation 3 6 preconditioning 159f preconditioning, reservoir 13 preconditioning, with polymer 1 4 pressure distribution, in reservoir 121f pressure drop, in pipes 120f, 181 pressure drop, in pipes 46, 47

210

pressure fall off test 124f , pressure gisadient 8 pressure, well flowing p . 126 productioii wells 126 profile modification 128, 1 5 8 , 160 project design 159 pseudo plastic liquids 6 , 4 2 , 72 pseudomonas acroginosa 31 pullulan 31 pumps 145 pyruvate 31

Q quality, of injection water 136f

R rate of shear strain 6 rate of shear strain, in porous media 6 9 f , 1 9 1 rate of strain 40 recovery, by polymer flooding 15 relative permeabilities 5 , 14 relaxation time 64 reservoir characteristics 119 reservoir depth 12 reservoir dip 10 reservoir geometry 10 reservoir preconditioning 13 reservoir rock 1 1 reservoir temperature 12 reservoir, shoe-string type 10 residual resistance factor 18,19,20f resistance factor 18 retention 2 2 , 91 retention 91 Reynold’s criterion 47 Reynold’s number 47 rheology 6 , 39 rheology, definitions 39 rotational viscometer 5 1 , 5 2 , 177

S saccharides 171 sand 78 sand packs 110 saponification 35 saturating sand packs 116f scleroglucan 31f screening 10 secondary methods 1 separated block 1 1 shear 39f shear degradation 32 shear degradation in perforations 3 2 , 189 shear plates 7 3 , 142, 148, 202 shear pletes, lay out 202 shear rate, 6 , 40

shear stabilit,~3 1 , 72 shear thinning 19 sheer, in perforarions 190 shearing 100, 201 shearing devices 146 shipping, of polymers 141 shoe-string type reservoir 10 simulation, numerical 126 sodium silicate 130 sol 77 solution stability 102f specific costs 168 specific surface 6 6 , 78 specific viscosity 59 stability testing 102 stability. of polymer solutions 21 stability, shear 72 starch iodide method 174 static mixer 142, 146 Staudinger index 59 steam flooding 130 ff sticking coefficient 82 stimulation, of injection wells 120 stock solution 9 8 , 198f storage compliance 65 storage of emulsion polymers 198 storage, of polymers 142 strain 39 stress 40, 44 sugar 29, 36 sulfide 34 sulfite 106 surface facilities 136 surface, specific 66 surface, specific of sand 78 surfactants 1 , 77 sweep efficiency, areal 156 swelling, of gels 97f synthesis 34

T tap water 96 testing of polymers 9 5 f thermal stability 106 thiosulfate 3 4 , 106 toluol 35 torque 5 1 , 52 tortuosity factor 67 tracer 73 transition zone 77 transportation costs 37 tube viscometer 40 tubing 120 turbidimetry 174 turbidity 174 turbulent flow 47

U Ubbelohde viscometer 48

211

V vaporisation 36 vel oci t y , angular 52 velocity, critical 47 ventilation 36 vinylamide 28 vinylsulfonate 28 vinylsulfonate/vinylamide

co-polymer 28 viscoelastic effects, in porous media 70f. 186f viscometer 48 viscometer, capillary 4 8 , 4 9 viscometer, double cylinder 56 viscometer, Hoeppler 58 viscometer, plate and cone 55 viscometer, rotational 177 viscometer, rotational 51 viscometer, tube 48 viscometer, Zimm-Crothers 5 7 , 6 2 viscosity number 59 viscosity of crude oil 1 viscosity ratio 59 viscosity, apparent 42 viscosity. complex 65 viscosity, definition 4 0 , 41 viscosity, elastic 62 viscosity, influence of electrolytes 28 viscosity, nomenclature of 59 viscosity, of heavy oil 131 viscosity, plastic 42 viscous fingering 1 5 , 16 volume flow rate 44

W wall, of pipe 45 water quality ratio 137f water saturation, irreducible 75 water wet 74 water, for mixing 96 well impairment 137 well pattern 125 well treatments 130

X xanthan 29, 31 xanthan broth 36, 37 xanthan production 35 Xanthan, mixing 98 xanthomonas campestris 3 0 , 31

2 Zimm-Crothers viscometer 5 7 , 62

212