Dynamics of polymers in porous mediagrigori.impa.br/site/arquivos/IPO/Polymer course at Juiz de Fora.pdf · (b) polymer transport in porous media and (c) the effect polymer adsorption

Challenge the future

DelftUniversity ofTechnology

Dynamics of polymers in porous media

Prof. Dr. P.L.J. (Pacelli) ZithaE-mail: [email protected]

2

3

DEPARTMENT OF GEOSCIENCES AND

ENGINEERING

Faculty of Civil Engineering and Goesciences

4

Course content

The course gives a introduction to polymer dynamics with emphasis on their use of polymers and gels for:

• water control during oil and gas production

• in-depth diversion for water flooding

• mobility control polymer flooding, alkali-surfactant-polymer (ASP)

The course starts with a brief overview of the above applications of polymers and gels for improving oil and gas recovery. Next it reviews the basics about polymer physics. Water control as this enables to illustrate the main advantages and issues when using polymers and gels in porous media: emplacement of the chemicals, permeability reduction concepts, etc. Operational aspects will also be briefly discussed.

5

Scope of the Course

The course is organized in three parts: (a) physics of liquid polymers, (b) polymer transport in porous media and (c) the effect polymer adsorption and gel retention on multiphase flow. The lectures on the physics of liquid polymers will focus on dynamic and static properties of dilute and semi-dilute polymer solutions. Polymers under deformation flows will be considered as an introduction to flow through porous media. Special efforts will be devoted to the behavior of polymers near surfaces. Whenever possible, the discussions will stress scaling laws approach. Concerning flow through porous media, we shall consider mostly rheology and polymer adsorption and shall discuss some of the most recent developments including contributions of our group. Microscopic aspects will focus on local dynamic adsorption and flow reduction. Simple statistical theories for up-scaling these properties will be briefly outlined. The numerical treatment of the macroscopic equations will be discussed. Finally the modification of the relative permeability for oil and water will be analyzed.

6

INTRODUCTION

Lecture 1

7

Primary Oil Recovery

8

Fracturing

Impermeable

Barrier

Natural

or Created

Fractures

Viscous

Fingering

Permeability

Contrast

Water production during oil

recovery

(Courtesy of Halliburton)

9

9

Polymer & polymers gels

X-linked polymer/gels block water thieve zones

(WELGEL project 1997-1999)

OIL, WATERWATER

Oil, low k

Water, low k

Water Flooding

(designer water)

Oil

Polymer Flooding

(Alkali-Surfactant Polymer)

Secondary

Tertiary Oil

WATER FLOODING

Recovery Factor (RF)

Less than 25% OIIP

POLYMER FLOODING

Increase in RF

5-10% OIIP

(15-30% OIIP)

(Lake, 2010;

Green and Willhite, 1998)

• Mobility control: better sweep

• DPR effect: higher oil

productivity

• Full blocking: water control,

higher oil productivity

(Seright, 1990; Zaitoun, 1995)

10

Introduction

• Polymers used for mobilitycontrol and better sweepefficiency.

• Commercial polymer EORprojects worldwide (see map*)rapidly expanding.

• Successfully applied examples:Angola (Dhalia Field), China(Daqing Field), India (MangalaField), Oman (Marmul Field),Suriname (Tambaredjo), …

• Polymer injectivity essential forextending the applicationenvelop to heavy oil reservoirs.

* Ref: http://www.snf-group.com/IMG/pdf/Oil_EOR-FLOPAAM-Desert.pdf

11

Polymer flow in porous media

• Polymer rheology

• Effect concentration above C*

• Effect of shear rates

• Polymer retention (adsorption

dominant)

C<C* C=C* C>C*

VIS

CO

SIT

Y

SHEAR RATERADIUS AROUND WELL(Rubinstein, 2010;Macosko, 1994, Sorbie, 1991, McLeish, 2008)

12

Polymer retention in porous media

13

Cross-linked polymer gels

fill/block the pores

Sand grains

Gelled water

Cross-linked polymer

Oil blob isolated by gel

14

References

• Introduction to Physical Polymer Science, 2nd Edition, Lesley H.

Sperling, Wiley Interscience (1992) ISBN 0-471-53035-2

• Principles of Polymer Chemistry, P.J. Flory (1953) Cornell

University Press, Inc., New York.

• The Physics of Polymers, Gert Strobl (1996) Springer-Verlag,

New York.

• Figures were reproduced from Polymer Physics, (1996) Ulf

Gedde, Chapman & Hall, New York.

15

POLYMERS: BASIC PROPERTIES, PHYSICS.

Lecture 1

16

Polymer StructureProperty Behavior

• chain thermodynamics

• chain dimensions

• chain environment

• chain topography

• mechanical behavior

17

Gaussian Chains

• Random Chain Conformation

• End-to-End Distance

• Radius of Gyration

18

r nl2 2

Mean Square End to End Distance

sr

2

2

6

Mean Square Radius of Gyration

Polymer Chain Size

19

Effect of Solvent quality

20

Kc

R M M

rA c

W W

1 1 16

3 6 222

2

2

2

2sin

where:K - contrast factorc - concentration of scattering speciesR - Rayleigh ratio (reduced intensity)r - distance from scattering center to detector.I0 - incident wave intensityA2 - 2nd virial coefficient

Measure of Chain Properties

Scattering Function

21

Determinenation of Chain

Generation of a Zimm Plot

lim

0 2

12

Kc

R MA c

W

lim sinc

W W

Kc

R M M

r 0

2

2

2

21 1 16

3 6 2

22

Chain Dimensions

Zimm Plot

23

WriteThesis

100

101

102

10-3

10-2

10-1

Shear Rate, (s-1)

Vis

co

sit

y,

p

(Pa.s

)

S

s 5 g/L

pH 5.8

o Experiments

-- Model

5000 ppm

4000 ppm

3000 ppm

2000 ppm

1000 ppm

500 ppm

250 ppm

Brine

Bulk polymer rheology

24

22

0'1 CkCwr

Ck

Crsp

2

00 '

1

CrC 1lim 00

Effect of Concentration on

Viscosity

Relative viscosity:

Reduced Specific Viscosity:

Intrinsic Viscosity:

wg MR3

0 Relation to Molecu;ar Weight:

25

51.66 10GR cm 0 1 2 3 4 5 6

x 10-3

0

1000

2000

3000

4000

5000

6000

7000

8000

Concentration, cp (g/cc)

s

p/c

p,

(cc/g

)

Ss 20 g/L

pH 5.8

o Experiments

-- Linear Fit

[mu] 1542

kH 0.25

*

pc

0[ ] lim

p

p b

cp bc

1/3[ ] w

G

MR

/cc g

[ ]

Dilute

Regime

Semi Dilute

Regime

(Chauveteau, 1989; Sorbie, 1991 ; Lake, 1989; Ait Kadi.et.al, 1987)

Intrinsic viscosity, radius of gyration

26

Summary

• Chain bond rotational potential energies dictate properties

• Chain dimensions can be calculated statistically or by vector

analysis

• Zimm Plots from scattering measurements give dimensions Mw

and Rg separately, along with A2

• Characteristic dimensions defined by structure and environment

27

Linear flexible polymers

Polymer

Monomer

Dilute Regime Semi Dilute Regime

Dilute

Regime

Semi Dilute

Regime

(Zitha, 1995, Macosko, 1994)

28

Complex fluids

(Complex fluids: Spread the word about nanofluids. Manoj K. Chaudhury

Nature 423, 131-132(8 May 2003)

(Complex fluids: Spread the word about nanofluids. Manoj K. Chaudhury

Nature 423, 131-132(8 May 2003)

29

Complex fluids

(http://www.physics.fudan.edu.cn/tps/people/jphuang/viewclass4_2.asp)

30

Complex fluids

(http://www.physics.fudan.edu.cn/tps/people/jphuang/viewclass4_2.asp)

31

Complex fluids

(http://www.cims.nyu.edu/cmcl/ComplexFluids/ComplexFluids.html)

32

Stick-beads network model


33

Complex fluids

(Extraction of physically realistic pore network properties from

three-dimensional synchrotron X-ray microtomography images

of unconsolidated porous media systems

R.I. Al-Raoush , C.S. Willson.

Journal of Hydrology

Volume 300, Issues 1–4, 10 January 2005, Pages 44–64

)

34

Complex fluids

(http://www.porexpert.com/Help/index.html?capillary_bundle_mo

del.htm)

35

Complex fluids


36

Modeling of Complex Fluids


37

EXAMPLE: PAPER SPE 165195 (2013)

Lecture 1

38

Problem statement

• Past polymer retention studies:

• Polymer concentrations lower than 1500 ppm.

• Filtered polymer solutions

• Scope of this study

• Polymer injectivity for unfiltered polymer at concentrations

higher than 1500 ppm ?

• Will unfiltered polymer solutions cause mechanical entrapment

under current experimental conditions ?

• Will there be any retention of the polymer at the inlet face of

porous medium ?

39

(Denys, 2003)

Polymer retention in porous media

40

• Overall objective: shed light into the interrelation

between polymer rheology and retention in porous

media and well injectivity and increase value of

polymer flooding.

• Specific objectives:

Model and interpret the rheology of HPAM solutions.

Quantification and modeling of the injectivity and transport

properties of polymer solutions in porous media.

Model validation and study the effect of physical and

numerical parameters on injectivity.

Objectives

41

Modeling: governing equations

Transport Equation for Polymer in Porous Media

2

2

(1 )p p p p

f p s s

c c cv D vc A

x x t t

Boundary Conditions ,

0

( 0, )p

p p init

x

cvc x t vc D

x

( , ) 0pc

x L tx

( , 0) 0pc x t

( , 0) 0p x t

Initial Conditions

Darcy Law

kA Pq

x

(Zitha, 2001, Sorbie 1991)

42

Model: polymer rheology

Bulk Polymer Viscosity(Flory-Huggins)

2 3

1 2 31 b

p b p p p sa c a c a c S

Apparent Viscosity inPorous Media

( , )( )

( , )

p p eq

p

p p ref

cSF c

c

,

,

, ,

(1 )

1

p sh

p app

p sh rel

, ( , )p sh p p refc SF

Polymer VelocityEnhancement

1pf

4

1 d

p Hr

Shear Rate in Porous Media

13 1

4

v

v

m

mv

eq

v

m uC

m k

(Sorbie, 1991; Stavland, 2010; Chauveteau, 1984)

43

PermeabilityReduction Model

( , )( , ) 1

p

k

x tR x t

4

1 H

pr

Mobility Reduction

Polymer Injectivity

0

p

m

b

PR

P

0

bp

p

PI

P

Model: polymer adsorption

Polymer AdsorptionEquilibrium

1

p e

p

e p

c k

k c

(Zitha, 2001, Chauveteau 1984)

44

Numerical solution

• finite difference method: Nx grid-blocks

• upwind approximation for advection term

• central difference approximation for dispersion

• implicit ‘Euler backward’ method for time

45

WriteThesis

100

101

102

10-3

10-2

10-1

Shear Rate, (s-1)

Vis

co

sit

y,

p

(Pa.s

)

S

s 5 g/L

pH 5.8

o Experiments

-- Model

5000 ppm

4000 ppm

3000 ppm

2000 ppm

1000 ppm

500 ppm

250 ppm

Brine

Bulk polymer rheology

a1 126.60

a2 15545.18

a3 14105109.79

Flory-

Huggins

Parameters

1

2 2

,0( ) 1vm

p b p b

46

51.66 10GR cm

0 1 2 3 4 5 6

x 10-3

0

1000

2000

3000

4000

5000

6000

7000

8000


s

p/c

p,

(cc/g

)S

s 20 g/L

pH 5.8

o Experiments

-- Linear Fit

[mu] 1542

kH 0.25

*

pc

0[ ] lim

p

p b

cp bc

1/3[ ] w

G

MR

/cc g

[ ]

Dilute

Regime

Semi Dilute

Regime

(Chauveteau, 1989; Sorbie, 1991 ; Lake, 1989; Ait Kadi.et.al, 1987)

Intrinsic viscosity, radius of gyration

47

Experimental setup

48

125 250 500 1000 2000 3000 5000

5.0

10.0

20.0

Overview of experiments

Porous material: Bentheim sandstone

Polymer: HPAM (AN 905 Lot E 2686, SNF-Floerger)

Brine: Sodium Chloride (NaCl); Potassium Iodide KI (Tracer)

Experiments: 9 single-phase core-floods: 7 polymer concentrations 3

salinities

Accuracy: salinities and polymer concetrations±0.1 g/L; pH = 5.8±0.1

49

p

s

c 250 (ppm)

S 20 ± 0.1 (g / L)

pH 5.8 ± 0.1

k 2.314 ± 0.11 (Darcy)

0.21 ± 0.01

q 1 ± 0.02 (cc / min)

0 2 4 6 8 10

1

1.2

1.4

1.6

1.8

2

PV

Mo

bil

ity R

ed

ucti

on

, R

m

Experiments

Model

0

p

m

b

PR

P

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

PV

Po

lym

er

Inje

cti

vit

y,

I p

Experiments

Model

0

bp

p

PI

P

ModelImprovement

0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

PV

Pre

ssu

re D

rop

,

Pp (

mB

ar)

Experiments

Model

Exp.Error ± 1.2 mBar

WriteThesis

B P

P

P B

Base case: pressure drops

50

WriteThesis

ModelImprovement

0 1 2 3 4 5 6

x 10-3

1

1.5

2

2.5

3

3.5


Reta

rdati

on

Facto

r, R

0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

PV

C/C

o

Tracer Experiments

Polymer Experiments

Tracer Model

Polymer Model

Exp.Error ± 0.05

R

0 1 2 3 4 5 6

x 10-3

0

0.5

1

1.5

2

2.5

3x 10

-3


d

p/d

cp,

(cm

)

Experiments

Curve Fitting

0 1 2 3 4 5 6

x 10-3

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2x 10

-4


Ad

so

rpti

on

,

p,

(g/g

)

sS 20 ± 0.1 (g / L)

pH 5.8 ± 0.1

q 1 ± 0.02 (cc / min)

ek

-6 2

2014.5 (cc / g)

Γ 1.46 × 10 (g / cm )

0

s

c 250 (ppm)

S 20 ± 0.1 (g / L)

pH 5.8 ± 0.1

sS 20 ± 0.1 (g / L)

pH 5.8 ± 0.1

q 1 ± 0.02 (cc / min)

ek

-6 2

2014.5 (cc / g)

Γ 1.46 × 10 (g / cm )

sS 20 ± 0.1 (g / L)

pH 5.8 ± 0.1

q 1 ± 0.02 (cc / min)

1

p e

p

e p

c k

k c

Base case: effluents

51

0 5 10 150

5

10

15

20

25

30

35

PV

Pre

ssu

re D

rop

,

Pp (

mB

ar)

20 g/L

10 g/L

5 g/L

pc 500 (ppm)

pH 5.8 ± 0.1

k 2 ± 0.1 (Darcy)

q 1 ± 0.02 (cc / min)

k 2 ± 0.1 Darcy


Effect of salinity

52

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

PV

C/C

o

Tracer Experiments

Polymer Experiments

Tracer Model

Polymer Model

125 ppm

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

PV

C/C

o

Tracer Experiments

Polymer Experiments

Tracer Model

Polymer Model

500 ppm

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

PV

C/C

o

Tracer Experiments

Polymer Experiments

Tracer Model

Polymer Model

1000 ppm

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

PV

C/C

o

Tracer Experiments

Polymer Experiments

Tracer Model

Polymer Model

2000 ppm

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

PV

C/C

o

Tracer Experiments

Polymer Experiments

Tracer Model

Polymer Model

3000 ppm

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

PV

C/C

o

Tracer Experiments

Polymer Experiments

Tracer Model

Polymer Model

5000 ppm

Effect of Concentration: adsorption

53

0 5 10 150

5

10

15

20

25

PV

Mo

bil

ity R

ed

ucti

on

, R

m

125 ppm

250 ppm

500 ppm

1000 ppm

2000 ppm

3000 ppm

5000 ppm

Model

0 5 10 150

0.2

0.4

0.6

0.8

1

PV

Po

lym

er

Inje

cti

vit

y,

I p

125 ppm

250 ppm

500 ppm

1000 ppm

2000 ppm

3000 ppm

5000 ppm

Model

0 5 10 150

50

100

150

200

250

300

350

PV

Pre

ssu

re D

rop

,

Pp (

mB

ar)

125 ppm

250 ppm

500 ppm

1000 ppm

2000 ppm

3000 ppm

5000 ppm

Model


Cp

[ppm]

Adsorption (g/g)

Permeability Reduction (Rk)

1252505001000200030005000

3.67E-55.60E-58.73E-51.13E-41.326E-41.583E-41.664E-4

1.021.041.061.081.101.111.12

pc

pH 5.8 ± 0.1

q 1 ± 0.02 (cc / min)

k 2 ± 0.1 Darcy

ok

d

kR

k

Effect of Concentration on injectivity

54

1D POLYMER FLOW. ANALYTICAL SOLUTIONS

Lecture 2

55

1D linear flow

• Basic assumptions Homogeneous and isotropic porous media Incompressible, non-inertial and isothermal flow Darcy’s flow equation

• Feature laboratory core-flood experiments

Polymer

2 3

...

Fraction Collector

k, f, As

Layer

adsorptionFree

polymer

coil

Grains of sand

or silicon carbide

56

Governing equations

tssxxt ACDCuC ff 12

dat C

Pu x

Mass conservation:

Adsorption kinetics:

Darcy’s equation:

57

Boundary conditions

00, txC

0

00,

xx

CDuCtxuC f

0, xx txC

OI PtLxPtPtxP ,;,0

Polymer

58

Special case: no dispersion and

instantaneous adsorption

0 CvCF xtR

CC eee 1

‘Langmuir’ isotherm:

fff uvAF essR

;11 1

Retardation factor, intersticial velocity:

Transport equation:

59

Solution to special case

0),0(;0)0,( tCxC

With front trajectory:

txxHCtxC f 0,

Solution:

Boundary conditions:

SLVVFQttx PPRf f ;

60

Solutions graphs

txC ,

x

0C

tx f

r

x

0r

tx f

22

001 CkCCr

kR

x

0kR

tx f

41 pk rR Effect of polymerpropagation relativeviscosity and permeabiltyreduction.

61

Pressure drop

x

rkww dxRkutxPtP0

,,0

General expression:

:txx f LxRPtP rkw /0

Behind the front:

txx f xxRPtP frkw /11 00

After the front:

62

Pressure drop graphs

tP

PVQtPV /

wP

pP

First polymerentry in PM

PolymerBreakthrouh

63

Steady-state flow in parallel cores

l2

POLYMER

OIL

WATER

L-l1

L-l2

l1

u2

u1

q2

q1

Q

s2

s1

64

Basic pressure drop equations

2,1,)()(

ipppi

lLi

li ii

2,1,)(

isk

qlp

ip

i

iip

iili

20

1,

)()(

iif

iifw

sk

qlLp

ii

iiiilL i

65

Pressure equations

11

111

11

1111

)(

sk

qlL

sk

qlp

w

w

p

p

2

2

2

222

22

222

2

)(

sk

qlL

sk

qlp

o

p

p

2,1,)( 11 idt

dxLsls

dt

dq i

iiii ff

powik

i

ii

,,;2,1,)(

)()(

66

First equation for the penetration

depths

( ) (2)

( ) 1

( ) (1)

2

, 1,2; , , , ;i

i wwwi

w

F i w o p F

f

f

dt

dxxF

k

Lp wpw

w1

1)1(

1

211

1 ]1)1[( f

dt

dxFxFF

k

Lp wowowpw

w2)2(

2)2()2(

2

222

2 ])[( f

(1) (2) (2) (2)1 21 2[( 1) 1] [( ) ] 0ww wp wp wo wo

dx dxF F x F F x F

dt dt

67

Second equation for the penetration

depths

t

LxsxsQdt0 222111 )(' ff

t

ss xrrxrrdttq0 1

)2()2(1

)1()1(')'( ff

S

srr

SL

tQtq ii

sii

)()(

,,)(

)(f

f

ff

t

ss xrrxrrdttq0 1

)1()1(1

)1()1()1)(2(')'( ff

1 2 1 2; 2S s s f f f

68

1D radial flow of polymer

• Basic assumptions Homogeneous and isotropic porous media Incompressible, non-inertial and isothermal flow Darcy’s flow equation

• Feature polymer injection in the field

Layer

adsorptionFree

polymer

coil

Grains of sand

or silicon carbide

WATER

69

Governing equations

tssrt ACuC ff 1

dat C

Pu r

Mass conservation:

Adsorption kinetics:

Darcy’s law

0 rur

70

Boundary conditions

wrrrC ,00,

eewfw PtrPtPtrP ,;,

0;,0 0 tCtC

wrrr ;00,

71

Integration of first equation

hQurconstruwrrw 2.

hrQru 2

PhrQ

C

AChrQC

r

dat

tssrt

ff

2

12

72

Instantaneous adsorption

CC

ChrQCF

eee

rtR

f

1

02

trC ,

r

0C

trfwr

rtrHCtrC f 0,

2/12 hQtrtr wf f

Solution:

73

Relative viscosity and

permeability rduction

r

x

0r

trf

22

001 CkCCr kR

x

0kR

trf

41

pk rR

74

Pressure drop

e

w

r

rrkwwew drrRhkQtrPtrPtP 12,,

wewww rrLnhkQP 2

wewfrkw rrLnrrLnRPtP 11

75

Pressure drop graphs

tP

t

wP

First polymerentry in PM

76

Polymer injection into a two-layer

reservoir

Penetration radii: r1 and r2 respectively

Pose: =Re/Rw, x1=r1/Rw and x2=r2/Rw.

)ln(2

1)1(

1

11 x

h

qpp

p

w

11 1(1)

1

ln( / )2

e

w

qp p x

h

q1 is the flow rate, and p(1)=k1p/1p and w(1)=k1w/1w

the mobilities of polymer and water respectively. The pressure drop over the reservoir: p1(t)=pw -pe

77

Semi-steady state flow, Pressure

drawdown, Productivity Index

Fwp(1) = w

(1)/ p(1) is the water-to-polymer mobility ratio

)]/ln()ln()1[(2

)( 11)1(

)1(1

11 xxF

h

qtp wp

w

dt

dxxRhq w

11

2111 2 f

)1(

21

1

w

wRC

f

dt

dxxFxCtp wp

11

)1(111 )]ln()ln()1[()(

78

Polymer/gelant placement in a two-

layer reservoir

Fwp(1) = w

(1)/ p(1) is the water-to-polymer mobility ratio

dt

dxFxFFxCtp wowowp

2)2(2

)2()2(222 )]ln()ln()[()(

)2(2

22

wwRC

f

79


layer reservoir

Fww = w(1)/ w

(2) is the mobility between the two layers

(1) (2) (2) (2)1 21 1 2 21 ln( ) ln( ) ln( ) ln( )ww wp wp wo wo

dx dxF x F x x F F x F

dt dt

80


layer reservoir

Q(t) = the total flow rate

])1()1([')'(0

2

222

2

111

2

t

w xhxhRdttQ ff

( ) ( )

1 22

( )( ) , , 2i ii i

h

w

hQ tq t r r

R H Hf

ff f f

f

(1) (1) 2 (1) (1) 2

1 20

( ') ' ( 1) (2 )(1 )( 1)t

h hq t dt r r x r r xf f

81



Q(t) = the total flow rate

])1()1([')'(0

2

222

2

111

2

t

w xhxhRdttQ ff

( ) ( )

1 22

( )( ) , , 2i ii i

h

w

hQ tq t r r

R H Hf

ff f f

f

(1) (1) 2 (1) (1) 2

1 20

( ') ' ( 1) (2 )(1 )( 1)t

h hq t dt r r x r r xf f

82


layer reservoir

2 (1)

1 2 1 1

2 (2) (2)

2 2

, { [( 1) ln( ) ] }

{ [( ) ln( ) ] }

ww wp wp wp

wp wo op op

x x F x F x

x F F x

ln2

1)1(

wp

wp

F

ln2

)2()2()2(

wowowp

op FFF

(1) (1) 2 (1) (1) 2

1 2( 1) (2 )(1 )( 1)h hqt r r x r r xf f

83



0)}ln()ln(])({[

)}ln()ln(]1)({[

22)2(

2)2(

2)2(

1111)1(

uxFxFuF

uxxuFF

wowowp

wpww

211

111

21

42

1

wRh

qux

dt

dx

f

222

222

22

42

1

wRh

qux

dt

dx

f

2

)2()2(

1

)1()1()1)(2( urrurrq hh ff

84



tuxxk

ik

ik

i 11

0

)}ln()ln(])({[

)}ln()ln(]1)({[

21)2(

2)2(

2)2(

1111)1(

kkwo

kwo

kwp

kkkkwpww

uxFxFuF

uxxuFF

])1)(2([222

)2()2(11

)1()1( kkh

kkh uxrruxrrq ff

85


layer reservoir

TABLE I: COMPUTATION SCHEME

STEP TIME x1 x2 u1 u2

0 0 x10=0 x2

0=0 u10 u2

0

1 t x11= t u1

0 x21= t u2

0 u11 u2

1

2 2t x12=x1

1 t u11 x2

2=x21 t u2

1 u12 u2

2

k k t x1k=x1

k-1 t u1k-1 x2

k=x2k-1 t u2

k-1 u1k u2

k

86

APPLICATIONS: WATER CONTROL USING

POLYMERS OR GELS. POLYMER

FLOODING

Lecture 3

87

Course contents

The Causes of Excessive Water ProductionWell Related Causes Mechanisms Reservoir Related MechanismsExercise 3: Prediction of Water Cut from a Model Reservoir

Identification the Water Production Mechanism in the Field Data Gathering and Analysis Role of the Information about the GeologyMultiple-Scenario Diagnosis of Water sourceExercise 4: Identify the Water Production Mechanism for a Given Case

88

A oil or gas well is producing at a

very high water cut!

89

Fracturing

Impermeable

Barrier

Natural

or Created

Fractures

Viscous

Fingering

Permeability

Contrast

Water production during oil

recovery

(Courtesy of Halliburton)

90

LOW kOIL or GAS

HIGH k WATER

Oil or Gas WATER CUT = 14.3 %Water

Higher oil rates during primary

secondary recovery

91

After sometime water cut increases

rapidly and oil cut decreases

LOW kOIL or GAS

HIGH k WATER

WATER CUT = 80 %Oil or Gas Water

92

The water cycle: opportunities and

challenges

27%

29%15%

29%

Shell Water Usage Options (1999)

Discharge to Sea

Re-injection for pressuremaintenance

Discharge to sweet water

Re-injection for disposal

93

Statistics of Water Production

• 70% production from mature fields (over 30 years production)

• Ratio of water to total production (water-cut) > 75% on

average (> 3 bbl/d water for 1 bbl/d oil)

• Average water cost $0.67/bbl ($0.17 to $2.50/bbl in U.S.)

• Cost component: lifting, pumping, separation, de-oiling,

filtering, and re-injecting

• Environmental aspects, disposing off the water

94

Produced Water Management

• Reduction of water

production (WATER SHUTOFF)

• Cement squeeze

• Mechanical methods (zone

isolation)

• Chemical water shutoff

(CWSO)

• Produced water

separation and re-injection

• Downhole dehydration and

produced water re-injection

• Surface separation and

produced water re-

reinjection (PWRI)

95

Surface treatment of oily water

•Plate separation

•Hydrocyclone

separation

•Gas flotation

•Oil coalescence

•Centrifugation

•Membrane filtration

96

Downhole separation and water

reinjection

• Separating water down-

hole reduces the cost of

lifting the excess water.

• Typical down-hole

separators are 50% efficient

97

Down-hole separation system

98

Produced Water Re-Injection

• Oil-water mixture exiting from a two-

dimensional micro-model

• Factors affecting separation efficiency and

re-injection

• Fluid production rates

• Droplet size distribution of the

dispersed phases

• the gas/liquid/oil ratios

• Phase densities and viscosities

• Interfacial tension

99

Re-injection of produced water

• Matrix injection Injection pressure is below fracturing pressure

• Fractured injectionInjection pressure is above fracturing pressure

100

Advantages of Reducing Water

Production

• Reduction of oil pumping costs (average cost

$0.67/bbl - $0.17 to $2.50/bbl in U.S.)

• Reduction of oil and water separation costs

• Reduction of equipment and platform space required

• Reduction of scaling, sand production, corrosion

problems and related costs

• Reduction of risk of adverse impact on the

environment

101

Benefits of Reducing Produced

Water

• Increases oil and gas production rates by reducing

hydrostatic column in the well and reducing bottom-

hole pressure

• Improve reservoir sweep efficiency

• Reduces formation damage due to scaling sand

production

• Extends the economic life of the reservoir and

ultimate recovery

102

Methods to reduce water cut

• Cement, sand plugs, calcium carbonate

• Packers, bridge plugs, mechanical patches

• Pattern flow control

• In fill drilling/well abandonment

• Horizontal wells

• Resins

• Foams, emulsions, particulates, precipitates, microorganisms

• Polymers and Polymer gels, Oil soluble chemicals

• Polymers flooding, Smart water flooding

103

Pressures in a production system

104

Well completion is critical

105

Well completion critical

106

Different pumping systems

107

Different pumping systems

108



wfP P P Pressure draw down: [psi]

QPI

P

Productivity Index: [psi/d/psi]

141.2 ln e

w

PkhQ

rB

r

[stb/d]Flow rate:

Field Units

109

Single phase

Liquid flow

Bubbly

flow

Slug

flow

Churn

flow

Annular

flowHomogeneous

flow

110

Categories of water-cut problems

111

Difficulty of water-cut problems

• Category A (Problems 1-3): easier to treat than the others in

the list. Therefore, one should look first for these types of

problems.

• Category D, (Problems 11-13): difficult, no easy, low-cost

solution. Gel treatments will almost never work for these

problems.

• Categories B and C (Problems 4-10): result from linear-flow

features (e.g. fractures, fracture-like structures, narrow

channels behind pipe, or vug pathways.

112

Data gathering for water production

diagnostics

• Analysis of well production data like rates, GOR, watercut, THP,

THT, deposits, sampling.

• Analysis of BHP surveys, production logging, PI surveys, PVT

samples

• Monitoring mechanical well status (sand, corrosion, wax, scale)

• Well stimulation.

Lack of data is often a problem for diagnosing high water-cut problems. Proper well surveillance, well performance analysis

helps solve this problem.

113

Reservoir Surveillance &

Performance

• GOR, BSW behaviour, movements of GOC,

OWC, displacement anomalies.

• Analysis of vertical and horizontal drainage

• Analysis of reservoir drive mechanism.

• Reservoir simulation model

• Reassessment of STOIIP, GIIP, reserves.

114

Polymers for water control

POLYMERS

PAM/HPAM Zaitoun et al.

polymer adsorption (k reduction)

temperature limit 70 0C

sensitive to reservoir pH and salinity

little enviromental issues

CPAM

Burrafato et al.

Mota et al.

Zaitoun et al.

Zitha et al.

stronger polymer adsorption (k

reduction)



little enviromental issues

115

Polyacrylamide and hydrolyzed

polyacrylamide

.

yCH2 CH .

CO

.

NH2PAM

CH2 CH

C O

NH2

CH CH

C

OH

O

MN

2CH2 CH

C O

NH2

CH CH

C

OH

O

MN

2Degree of hydrolysis is = N/(N+M). High Mw polymers: N+M=105-107

Random monomer distribution

HPAM

116

05.0 yx

x

CH2 CH .

CO

CH2 CH.

CO

O

CCH3 CH3

CH3

NH2

x y

PAtBA

.

yCH2 CH .

CO

.

NH2PAM

PAtBA and PAM

117

Metal ion cross-linker

Oligomers

ColloidalPrecipitate

C

C

C

COOHH

H

H2

2

O COOH

COOH

Citrate

Chromium in water

118

Cross-linking of polymer gels

Semi-dilute polymer(e.g. HPAM, PTBA), C >> C* Cross-linked gel

Cross-linker (e.g. Cr(III), PEI)

+

Cross-linked polymer gel

Cross-linker (e.g. Cr(III), PEI, etc.) Gelation times times can be minutes to days

119

Viscosity diverges at gel point

• Polyethyleneimine (PEI) is an

Organic Crosslinker

• PEI was nnown to crosslink

Polyacrylamide Copolymers

• Recent Work Indicated that

Simple Polyacrylamides Can Be

Crosslinked with PEI

0

4

8

12

16

20

0 20 40 60 80 100 120

Time, minutesV

isco

sit

y,

Pa

.s

PAtBA

PAM

7 wt% Polymer

1 wt% PEI

120oC

15,000 ppm Na

20.7 Bars

17.03 1/s

pH = 10.0

(Al-Muntasheri et al., SPE 104071, 2006)

120

Cross-linked polymer gels

Chemical References Features HPAM-Cr

3+ Sydansk et al.

Sright et al.

Lockhart et al.

etc.

weak and strong gels

temperature limit 70-90 0C


enviromental issues due to Cr3+

HPAM-Zr2+

(lactate)

Cui, Xia and Xu,

Moradi et al.

Bagassi et al.

weak and strong gels


sensitive to salinity, reservoir

conditions

enviromental issues due to chromium

PAM-HMTA

(phenyl-acetate)

Moradi et al. encapsulates


lower sensitive to salinity, reservoir

conditions

lesser enviromental issues but toxicity

PATBA-PEI

Hardy et al. strong gels


low sensitive to lithology reservoir

conditions

lesser enviromental issues

Oil soluble gelants Plazanet et al.

Thompson and

Folgler

strong or weak gels ???

temperature limit ???

sensitivity to reservoir pH, salinity ???

enviromental issues ???

121

Organically cross-linked polymer

gels

• t-butyacrylate/acrylamide (PTBA) copolymer-Polyethyleneimine

(PEI) (H2Zero)

• PAM and co- and terpolymers with HCHO, HMTA or

phenolic/hydroquinone crosslinkers (Phillips and Unocal

processes, Organoseal, Multigel)

• Crosslinked AMPS, NVP, acrylamide/acrylate co and terpolymers

(HE)

122

Chemical placement is a major issue

• Placement methods

• Zone isolation (using packers, plugs, etc.)

• Dual fluid injection (oil compatible and

polymer)

• Bullhead treatments (poorly known reservoir

properties, deviated and horizontal wells, etc.)

• Difficulty with bullhead treatments: risk

of penetration in oil layers

123

Options for chemical placement

Method References Features Zonal isolation

(Strong and weak

gels)

Seright et al. ok for clearly layered systems without

cross-flow

relies on detailed knowledge of

reservoir geology

impractical in many wells

Self-diversion or

diversion

Stavland et al.

Zaitoun et al.

Zitha et al.

combine adsorption and rheology

(bridging adsorption phenomenon)

relies on (strong) permeability contrast

probably inefficient if there is

crossflow

Diversion with a

viscous preflsuh

Stavland et al.

Vermolen et al.

experimental evidence is scarce

Self-selectivity

(selectivity of the

basis of saturation)

Stavland et al.

Zimmerman et al.

Zitha et al.

relies on saturation differences

low permeability contrast is not a

limitation

perhaps not efficient when cross-flow

is strong.

124

Water control/shutoff mechanisms

Type References Features (Full ??) Blocking

(strong gels)

Willhite et al.

Seright et al.

Stavland et al.

Lockhart et al

how full is full?

gel/longevity of blocking

Disproportionate

permeability

reduction (weak

gels, polymers)

Schneider and

Owens

sometimes it works: we just don't

know exactly when!!!

Self-diversion or

diversion

(polymers, weak

and strong gels)

Stavland et al.

Zaitoun et al.

Zitha et al.

combine adsorption and rheology

(bridging adsorption phenomenon)

relies on (strong) permeability contrast

probably inefficient if there is

crossflow

Diversion with a

viscous preflsuh

(???)

Stavland et al.

Vermolen et al.

experimental evidence is scarce

k reduction in the

presence of water

(not a classic

DPR!)

Stavland et al.

Zimmerman et al.

Zitha et al.

how does it work at intermediate

oil/water saturations?

125

Cross-linked polymer gels fill/block

the pores

Sand grains

Gelled water

Cross-linked polymer

Oil blob isolated by gel

126

Water shuttoff cross-linked polymer

gels

• Water shutoff technology:

• Inject a limited amount of chemicals

(cement, polymers, polymer gels, etc.)

• Chemicals reduce water flow but not oil

flow

• Tow main issues:

• Placement of chemicals (porous media

flow)

• Water flow reduction mechanism

(relative permeability, full blocking)

GRAINS GEL

127

Gels fill the pore and block flow

Gel has very low intrinsic permeability.

Grain

Pore

throat

2RP2(RP-eH)

128

Matrix versus well high water-cut

Leakage behind the casing

Channeling through high permeability layers

Oil

Water

Water Oil

Water

Water

129

Principle of a water-shutoff

treatment

• Injection of limited amount of

polymer solution or gelant

• Polymer adsorption, partial or

full blokking by gel

• Disproportionate permeability

reduction by the polymer or gel

LOW kOIL/GAS

HIGH k

SMALL DEPTH/NO GELIN OIL OR GAS LAYER

WATER

CHEMICAL

130

Polymer and gelant penetrate all layers!

LOW kOIL or GAS

HIGH k

Problem: penetration in oil or gas layers

Bull head treatments: penetration of polymer or gelantinto oil layers must be minimized

WATER

Polymer/Gelant

131

Bullhead water shutoff treatments

Polymer or Gel

LOW kOIL or GAS

HIGH k

Polymer or gel treatment: results in higher oil cuts.

WATER

132

How to size the treatment?

LOW kOIL or GAS

HIGH k WATER

Wellbore

h2

h1

hs

Re

Rw

k1, f1,As(1)

k2, f2,As(2)

Shale

Layer 2

Layer 1

PolymerGelant

Production packer

133

Penetration radius (single layer)

ttQShtr or )(1)( 1

2

1 fVolume conservation:

)(1 tr [ft]

1h [ft]f [-]

orS [ - ])(tQ [bbl/min]

Penetration radius

Reservoir height

Porosity Residual oil saturation

Injection rate t [hour]Time

134


0

5

10

15

20

25

30

0 2 4 6 8 10 12 14

TIME (hour)

RA

DIU

S (

ft)

135

Steady-state flow analysis

• Homogeneous and isotropic porous media

• Incompressible, non-inertial and isothermal

• Dispersion is negligible

• Instantaneous layer adsorption

• No desorption after bridging adsorption

• Steady state Darcy’s flow with RRF=RRF(t)

136



wfP P P Pressure draw down: [psi]

QPI

P

Productivity Index: [psi/d/psi]

141.2 ln e

w

PkhQ

rB

r

[stb/d]Flow rate:

Field Units

137

Exercise 1,2 : Water Production

Economics

• Consider a two layer reservoir with consisting of two layers L1

and L2 separated by an impermeable shale layer with thickness

Ls. Geophysical and geological data show that the reservoir is

bound by two sealing faults at a distance d = 1850 m and has

an average width w = 810 meters.

• The (average) properties of L1 and L2 are:

• L1: k1 = 250 mD, f1 = 0.22, h1 =10 m, Swi = 0.28

• L2: k2 = 1580 mD, f2 = 0.23, h2 = 45 m, Swi = 0.32

138


Economics

• Static reservoir pressure and temperature are: P = 1230 psi

and = 160 0F.

• Properties of the fluids in the reservoir at reservoir conditions

(for both layers):

• Oil: o = 8.53 cP, o = 0.70 g/cm3, co =1.34 1/bar

• Water: w = 1.00 cP, w = 1.00 g/cm3, cw = 0.86 1/bar

139


Economics

• Two identical wells are drilled in the reservoir at a distance of

234 m. One of the wells (IW) is used as an injector and the

second well (PW) is used as a producer.

• Well radius: 7 inch

• FBHP: 890 psi

• Compute the production history

• Compute the NPV for two scenarios:

• No water-control treatment

• Water treatment

140


Problem 1 : Consider the reservoir in the exercises 1,2. The high permeability layer totally watered out with Sor = 35%. We plan to carry out a gel treatment. A gelant with viscosity 10 cP gel time is 5 hours is used in this job.1) How much gelant is it needed to reach the target radius of 10 ft?2) At what rate must should the gelant bbe injected to reach the target radius of 10 ft at ½ of the gel time?3) Can this rate be sustained without fracturing the reservoir?

141

Excess Water Production

142

Flow-chart

Mahgoub, Mahmoud,

Abu El Ela, O&GJ,

105 (7), Feb 19, 2007

143

Water-cut increases rapidly

Mahgoub, Mahmoud, Abu El Ela, O&GJ, 105 (7), Feb 19, 2007

Bridge plug

144

Successful water-shutoff treatment:

general information

• A well in Kahraman-C41 field

• Field is in NW of Khalda concession, N part of Egypt’s western.

• Field discovery well, Kahraman-C2, was drilled in 1992.

• Field currently has 60 oil producers and 18 water-injectors

145

Field location

146


general information

• Kahraman-C mainly produces from Bahariya reservoirs,

laminated sandstone, two main horizons:

• Lower Bahariya (LBAH): main producing interval, good

quality sand, permeability up to 400 mD and porosity up to

24%, provides ~70% of the field’s total production.

• Upper Bahariya (UBAH): lower quality rock, thin sand

streaks inter-bedded with shale and carbonate barriers,

zone being developed with hydraulic fracturing (like most

other fields in the Khalda concession)

147

Successful water-shutoff:

petrophysics, testing

• The Bahariya reservoirs lie at about -5,700 ft subsea.

• Well Kahraman-C41 drilled in February 2005 as part of the

integrated development plan of both the upper and lower Bahariya

West of Kahraman-C field.

• Petrophysical analysis: 41 ft [12.5 m] of good quality pay with f =

23% and Sw = 40% on average

• The LBAH as good as the producing LBAH that produces west of

Kahraman-C field. No repeat formation tester (RFT), however, at

almost the same drilling time, but RFT was run in offset Kahraman-

C46 well, 560-m away.

148


lift testing

• The Kahraman-C46 RFT: pressure of 970 psi in the main producing sand, 1500 psi in the wet sand right below the main producing sand and 2600 psi in the wet sand further downhole.

• The initial LBAH intervals perforated in Kahraman-C41 were at 6,540-6,554 and 6,566-6,590. The test of the intervals with nitrogen lift produced all water at 960 b/d. The water had a 78,500-ppm chloride content, which is the same as in Bahariya water.

149


diagnosis

• Review of the cement-bond log-variable density (CBL-VDL) log showed bad cement behind the casing with almost free pipe.This indicated that cross flow from the high-pressure wet sand into the low-pressure oil zone through the channels behind the casing may be causing the water problem.

• To remedy the problem, the operator performed a cement squeeze with 17.5 bbl of cement through the perforated intervals. After drilling out the cement and cleaning the hole, the operator re-perforated the LBAH intervals 6,540-6,554 and 6,566-6,580.

150

Post-treatment testing

• The test of the well with nitrogen lift again produced 100%

water at 222 b/d. The water contained 79,900 ppm chlorides.

• A new CBL-VDL showed some cement improvement against the

LBAH compared to the original CBL-VDL that showed almost

free pipe.

• The offset well in the same reservoir, 560-m away, produced

oil with a low water cut, about 5%.

151

Refine diagnosis

• Based on this information, the conclusion was that water cross flowed from the high-pressure wet sand to the low-pressure oil zone through the channels behind the casing after the initial perforation of the LBAH and during the first test. During that period, water had moved from the wet sand into the oil zone because of the high-pressure difference. This resulted in the 100% water cut during the second test after the cement squeeze job.

• The cement squeeze job appeared successful, as indicated by the drop in production between the two tests, 950 b/d in the first and 222 b/d in the second.

152

Problem solved: diagnosis confirmed:

• The operator decided to complete the well and run an electric

submersible pump (FC-450) that could handle up to 500 b/d

and remove the water that had crossed flow into the oil zone.

This proved to be the right decision because a test 6 days later

produced 385 b/d of fluid with a 8% water cut or 354 bo/d.

153

Well producing at low water cut

Mahgoub, Mahmoud, Abu El Ela, O&GJ, 105 (7), Feb 19, 2007

154

POLYMER FLOODING. TWO-PHASE POLYMER-

OIL DISPLACEMENTS

Lecture 3

155

Hydrolyzed Polyacrylamide in Porous Media

• Polymer rheology: Polymer solutions

are non-Newtonian fluids.

• Polymer adsorption and

permeability reduction: Adsorbed

polymer chains form a layer, which leads

to a steady-state permeability reduction.

• Inaccessible pore volume: This

causes the polymer molecules to

travel faster through the porous

medium than inert tracer molecules.

• Physical dispersion: This smears

the interface between polymer and

brine.

156

Tambaredjo oilfield

• Field location: district of Saramacca, 45 kilometers west of the capital Paramaribo.

• Production is by primary recovery.

• The field has over 900 wells with a spacing of 200 meter.

• STOIIP (proven as per 2005) = 633 MMSTB.

• Ultimate recoverable reserves (proven as per 2005) = 65 MMSTB.

157

Tambaredjo oilfield

• Production comes from shallow unconsolidated sands (T-sands of Paleocene age).

• The sands are fluvial estuarine to coastal marine of origin.

• Reservoir is charged by Canje source rock.

• Shale forms the seal at the top, while to the south sands pinch out up dip

providing stratigraphic traps for oil.

158

Pilot Sector

• Reservoir properties (porosity, permeability

and water saturation) were determined from

multi-well petrophysical analysis.

• The model consists of 68, 54 and 16 cells in

respectively x, y and z direction, with a grid

size of 25 x 25 x 1 meter.

• The sector model is a relatively small part of

the overall reservoir model.

159

Model_ control volume

• The net pay zone of the reservoir was delimited based on the permeability and oil

saturation of the layers.

• A control volume was defined for which the oil in place was calculated

Perm. (mD) So

layer 2 225 0,18

layer 3 825 0,26

layer 4 1387 0,38

layer 5 2447 0,40

layer 6 3529 0,42

layer 7 1380 0,35

layer 8 2532 0,46

layer 9 4070 0,50

layer 10 6117 0,53

layer 11 5203 0,48

layer 12 301 0,20

Dx=Dy 25 m

Dz 1 m

Top reservoir 288 m

#Cells x 15

#Cells y 9

#Cells z 9

Porosity 0.34

Area 0.84×105 m2

BRV 7.59×105 m3

PV 2.58×105 m3

STOIIP 9.77×105 stb

160

Model_ reservoir fluids and rock-fluid properties

•The oil and water viscosity are respectively 240 cP

and 0.7 cP (at reservoir temperature of 36°C).

•PVT data for this area were scarce due to technical

difficulties in obtaining appropriate downhole

samples.

•The reservoir is water-wet.

0

0,2

0,4

0,6

0,8

1

0 0,2 0,4 0,6 0,8 1

kr

Sw

Water

Oil

161

Model_ polymer flow modeling: polymer viscosity

•Based on the flow velocity of polymer in the reservoir, an in-situ shear rate of 7s-1

was estimated. This was asserted on the rheological measurement of the polymer

for describing the polymer solution viscosity during numerical modeling.

0

10

20

30

40

50

60

0 200 400 600 800 1000

Po

lym

er

vis

co

sity (

cP

)

Polymer concentration (ppm)

Polymer viscosity (in-situ)

162

Model_ polymer flow modeling: polymer adsorption

•Adsorption of polymer was found to be 2×10-5 gram of polymer/gram of rock at a

polymer concentration of 1000 ppm.

•An adsorption isotherm was created by scaling data published by Zitha et al., 2002

for layer adsorption.

0,0E+00

5,0E-06

1,0E-05

1,5E-05

2,0E-05

2,5E-05

3,0E-05

0 500 1000 1500 2000

Ad

so

rptio

n le

ve

l (g

/g)

Polymer concentration (ppm)

Adsorption isotherm

163

Model_ polymer flow modeling:

permeability reduction and inaccessible pore volume

Permeability reduction

•The permeability reduction (Rk) was modeled as a function of polymer

concentration.

•Rk varies between one and the residual resistance factor (RRF). Likely levels of RFF

between 2 and 5 are reported.

Inaccessible pore volume

•The irreducible water saturation is used as an estimate for this.

max1 1

ap

k ap

CR RRF

C

164

Numerical details

•The numerical modeling and simulation was done using the Eclipse100 (2009.1)

software from Schlumberger.

•It includes the relevant polymer flooding mechanisms.

1w p a rw

r p w w z p w p

r w w peff k

V S C Tkd dV C P gD C Q C

dt B B dt B R

f

f

165

Numerical details (2)

•The model aims to capture both the effects of polymer concentration and physical

dispersion on polymer viscosity.

•An arbitrary parameter is used for this, which describes the degree of mixing

between polymer solution and brine at the leading edge of the slug.

•This parameter varies between 0 and 1 respectively describing zero and complete

mixing between polymer solution and brine within a grid block.

166

Results_ overview

1-D results

3-D results

• Forward simulation of primary recovery

• Polymer flooding simulations

• Fluid distribution

• Dispersion

• Production data

• Incremental oil recovery

• Sensitivity analysis

167

1D polymer flooding

One dimensional analysis has been done for:

• Validating the numerical model

• Verifying the consistency of results

0

0,2

0,4

0,6

0,8

0 0,2 0,4 0,6 0,8 1

Sw

X

Saturation profiles for polymer flooding

0.1 PV

0.3 PV

0.5 PV

numerical

168

Comparison between numerical and analytic results (2)

0

0,2

0,4

0,6

0,8

0 0,2 0,4 0,6 0,8 1

Sw

X

Saturation profile for water flooding (at 0.08 PV)

analytic

numerical

0

0,2

0,4

0,6

0,8

0 0,2 0,4 0,6 0,8 1

RF

PV

Oil recovery

polymerflooding

waterflooding

numerical

• The comparison shows a good to excellent match between both results, which validates the

use of the numerical model.

The numerical model can be used in the future for matching with experiments.

169

Results 3-D

•The history match of primary recovery was done earlier by Staatsolie (Falla et al., 2010)

using the oil production as a constraint.

•We just did one forward simulation of primary recovery to confirm that the results are

consistent.

0,E+00

1,E+06

2,E+06

3,E+06

4,E+06

jul-90 apr-93 jan-96 okt-98 jul-01 apr-04 jan-07

Oil

pro

du

ctio

n (

stb

)

Time

History match total oil production

Simulated

Measured

0,E+00

1,E+06

2,E+06


Wate

r pro

duction (

stb

)

Time

History match total water production

Simulated

Measured

Forward simulation of primary recovery

170

Forward simulation of primary recovery (2)

• The match for oil production is very good. But the minor mismatch in the

production of water is believed to be due to uncertainties about the static model,

PVT data and reservoir drive mechanisms.

• The oil is seemingly produced by a combination of several drive mechanisms,

including water influx, solution gas drive, rock compaction and oil expansion

0

0,2

0,4

0,6

0,8

1


Fra

ction o

f oil

pro

duction

Time

Drive mechanisms during primary recovery

Oil expansion

Rock compaction

Solution gas drive

Water influx

171

Polymer flooding simulations

• For the numerical simulations injection starts on the starting date of the pilot test,

12 September 2008.

• The polymer is injected at a concentration of 1000 ppm and at a fixed bottom-hole

pressure (BHP) of 800 psi.

• The polymer was only injected in the bottom part of the reservoir.

Polymer injection

172

Polymer flooding simulations

• First the results of a base case polymer flood are presented.

• Then the sensitivity to the physical parameters is described.

• An overview of these cases is shown below.

Polymer injection

Base case

Case1 Case2 Case3 Case4

Adsorption Yes Yes No Yes Yes

RRF 2.00 2.00 1.00 3.00 2.00

IPV 0.28 0.28 0.28 0.28 0.10

Mixing parameter

0.33 0.66 0.33 0.33 0.33

173

Fluid distribution_ cross sectional profile

Polymer injection

•Polymer concentration profile between injector and producer at 2008 (top-left), 2011 (top-right), 2013 (bottom-left) and 2015 (bottom-right). •Polymer breaks through in 2013 at 1M051

174

Fluid distribution

• Areal distribution of polymer, at 2013 (top-left) and 2017 (top-right), together with areal distribution of oil at 2008 (bottom-left) and 2017 (bottom-right). • Polymer propagates in a front like manner.• At 1M10 breakthrough occurs in 2017 • There is only residual oil in the swept area.

Polymer

injection

175

Dispersion

•In order to describe the effects of both

numerical and physical dispersion, we

zoom in on the polymer front.

•The absence of a sharp front is mainly

the effect of numerical dispersion

caused by the large grid blocks in the

model.

•The effect of physical dispersion is

relatively small.

•Numerical dispersion leads to lower

mobility control and earlier arrival of

polymer at the production wells.

0

200

400

600

800

1000

0,00 0,33 0,67 1,00Po

lym

er

co

nce

ntr

aio

n (

pp

m)

Distance between 1M101 and 1M051 (-)

Effect of dispersion on polymer front

mix=1/3

mix=2/3

176

Production data

• Polymer breakthrough times as

expected.

• Well 1M051, first increase in water-

cut due to oil bank breakthrough.

The second jump corresponds to

polymer breakthrough.

• Well 1M10 shows similar behavior.

• 1M09 the oil production is highest,

since this well produces the largest

oil bank.

• Well 1N06 is shut-in at 2017,

because pressure was low to

produce at required bottom-hole

pressure

0

0,2

0,4

0,6

0,8

1

0

5

10

15

2008 2012 2016 2020 2024 2027

Wate

r C

ut

+ C

/Co

Oil

rate

(stb

/day)

Time

1M051Oil rate

WatercutC/Co

0

0,2

0,4

0,6

0,8

1

0

5

10

15

2008 2012 2016 2020 2024 2027

Wate

r C

ut

+ C

/Co

Oil

rate

(stb

/day)

Time

1M10

Oilrate

Watercut

0

0,2

0,4

0,6

0,8

1

0

5

10

15

2008 2012 2016 2020 2024 2027

Wate

r C

ut

+ C

/Co

Oil

rate

(stb

/day)

Time

1M09

Oil rate

WatercutC/Co

0

0,2

0,4

0,6

0,8

1

0

5

10

15

2008 2012 2016 2020 2024 2027

Wate

r C

ut

+ C

/Co

Oil

rate

(stb

/da

y)

Time

1N06OilrateWatercutC/Co

177

Monitoring production data

• Breakthrough of polymer was measured within one year after start of injection.

• Clay tests were used for the measurement of polymer concentration at the

producers. However, it is mostly qualitative and cannot be used for accurate

estimates of polymer concentration.

• Only later this year, Staatsolie could get actual values of polymer concentration

using this test.

• The large difference in breakthrough time (measured and simulated) is due to

uncertainties in the reservoir and the polymer flow models.

Polymer injection

178

Incremental oil recovery

• These recovery factors for PF, WF and NFA

are respectively 40%, 37% and 32%. The

incremental recovery is therefore respectively

8% and 3%.

• The displaced oil fraction describes the oil

recovery for the control volume only. This is

respectively 34%, 28% and 22%.

• There exists a discrepancy between them.

The recovery factor is higher than the displaced

oil, which means that the control volume does

not only contribute to the oil production.

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45

jul-90 jul-94 jul-98 jul-02 jul-06 jul-10 jul-14 jul-18 jul-22 jul-26

Recovery

facto

r

Time

Incremental oil recovery

Polymerflooding

Water flooding

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45

jul-90 jul-94 jul-98 jul-02 jul-06 jul-10 jul-14 jul-18 jul-22 jul-26

Dis

pla

ced o

il fr

action

Time

Incremental displaced oil

Polymerflooding

Water flooding

179

Incremental oil (2)

• Until the start of both floods the displaced oil is half of the recovered oil, meaning that

the control volume only contributes to half of the total oil production.

• Considering the polymer flood

From 2008 till 2017 the oil recovery is 8%, while the displaced oil fraction is 10%.

If we consider the control volume only, then the oil recovery is roughly half of the

displaced oil.

From 2017 till 2030 the oil recovery is 3%, while the displaced oil fraction is 9%.

Therefore after 2017 even more oil will be swept out of the control volume rather

than produced, hence the pilot efficiency diminishes.

180

Incremental oil (3)

• If the incremental oil cannot offset the

extra costs for polymer flooding, water

flooding could be an alternative to

polymer flooding.

• With polymer flooding there is some

potential for increase in the incremental

oil, since only part of the swept oil is

produced.

• An extra case with three additional

wells was simulated for this. Here the

overall recovery factor increased with

3%, while the incremental oil recovery

increased with 1%.

181

Sensitivity analysis

• Considering the physics of polymer displacement, the breakthrough times are as

expected.

• The recovery factor on the other hand is only slightly affected by changes in

polymer adsorption and residual resistance factor.

Polymer injection

Polymer breakthrough

1M051 1M10 1M09 1N06 Recovery factor

Base case 2013 2017 - - 0.40

Case 1 (mixing parameter=0.66)

2011 2014 - - 0.40

Case 2 (No adsorption) 2010 2012 2021 - 0.42

Case 3 (RRF=3) 2016 2022 - - 0.39

Case 4 (IPV=0.1) 2014 2019 - - 0.40

182

Summary

• The numerical model for simulating polymer flooding is robust.

• Numerical dispersion leads to lower mobility control and earlier arrival of polymer

at the production wells.

• The large difference in breakthrough time (measured and simulated) is due to

uncertainties in the reservoir and polymer flow models.

• Based on these simulations, water influx appears to be the main drive mechanism,

while the effect of solution gas drive increases with time.

• The incremental oil recovery is 8% compared to NFA, however to water flooding

this is only 3%. Since only part of the swept oil is produced, there is some potential

for increasing the incremental oil by adding producers to the pilot area.

• Large uncertainties in the physical parameters have a direct impact on the

breakthrough time of polymer. The overall recovery factor however, is only slightly

affected. To resolve this at least partly, a detailed experimental study is needed.

183

Back-up_ effect of numerical dispersion in 1-D

0

0,2

0,4

0,6

0,8

0 0,2 0,4 0,6 0,8 1

Sw

X

Effect of numerical dispersion for polymer flooding

analytic

numerical

184

Back-up_ drive mechanisms

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 10 20 30 40 50

fraction o

f oil

pro

duction

Time (years)

fraction of oil produced by different mechanisms

oil expansion

solution gas drive

rock compaction

water influx

185

Swamp boats

186

Swamp Operations in the Tambaredjo Field

187

Intervention at the wellhead

188

Polymer injection data

189

ADEK students examine polymer facilities

190

Polymer mixing

191

Overview of polymer injection data

192


193


194


Documents

Dynamics of polymers in porous mediagrigori.impa.br/site/arquivos/IPO/Polymer course at Juiz de Fora.pdf · (b) polymer transport in porous media and (c) the effect polymer adsorption