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 €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

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
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"

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

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

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