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Constitutive Modeling of Chalk with Considering Effect of Intergranular Physicochemical forces

Changfu Wei（韦昌富）

Institute of Rock and Soil Mechanics

Chinese Academy of Sciences

Dec. 14-17, 2016, HKU

IGSCSRM-2016, Hong Kong

1971

Oil production began

Depletion method

1984

Oil field compression

Settlement: 3 m

1987

Inject seawater

Platform jacked up 6 m

1993-1994

Reservoir pressure recovered

2007

Total settlement: 8-9 m

A notorious example: Subsidence of Ekofisk oil field

Water-weakening effect of chalk

Microstructure and features of Chalk Material

Coccoliths

Rosettes Calcite

“grains” originated

from the skeleton

of algae organism

High porosity (40%

- 50%)

Large surface area

(~2.0 m2/g)

Chemically active

SEM image 1 m

Zeta potential data Equilibrium water: - 20 mV

Methanol: +10 mV

Oil: 0 mV

Our working hypothesis

What is the relevance of these features

Intergranular stress

Hypothesis: Mechanical behavior of

chalk is governed by Intergranular

stress but NOT effective stress! op

wpFree or capillary water ( )

Adsorbed water ( ) w

disjoiningp

Outline

1. Surface forces & surface potential

2. Matric potential & Chemical potential

3. Pore water pressure & effective stresses

4. Constitutive modeling of chalk

5. Concluding remarks

1. Surface forces and surface potential

Surface forces in the soil pores saturated with water solution:

capillary forces (in case of unsaturation)

interactions between water dipoles and charged solid surfaces

electrostatic forces (Columbic force)

van der Waals forces

hydrogen bonding forces

diffuse double layer repulsion

others …

1. Surface forces and surface potential

How to characterize these surface forces?

ˆ f fA w A

f w

ˆf f fA A

【Definition】 Surface potential ˆ fA

fA

Porous medium Reservoir

Solution (water) is moved

slowly from the reservoir

to the porous medium

wWork input:

Energy conserved:

Chemical potential of a species in the pore fluid

, , ,

( )

( )k

kff f m

f f ff

ff

T Jn m k

Jn A

Jn

2. Matric and chemical potentials

0 0( , , , , ) ( , ) ln ( , , ) ( , , )j jk k kf ff f ff f f f f f k

k k

RTT p C n T p a T p C T n

m m

F

Classical chemical potential

Surface potential

Definition:

Surface potential

1. Between two bulk phase:

2. In an individual phase:

0 0( , , , , ) ( , , , , )j jk kf gf gf f g gT p C n T p C n

0 0( , , , , ) ( )jkff f fT p C n const g Z Z

2. Matric and chemical potentials

1

0 +

r

f f f f

r M D r

S

S s dS Equilibrium conditions:

H O H O2 2

H O2

2H O

= ln

f f

WD f

RT a

a

m

Donnan osmotic pressure

Matric suction


Equilibrium solution

f f

A Bp p k kf f

A B f f

B Ap p

H O2f f

D

H O H O2 2

H O2

2H O

= ln

f f

WD f

RT a

a

m

0

1

+

r

f f f f

r

M D r

S

S

s dS

What is the pore water pressure?

Generalized osmotic pressure


H O H O2 2

H O2

2H O

= ln

l l

WD l

B

RT a

a

m

0

l l

D D

0 0.09 0.18 0.27 0.36 0.45nl

10

100

1000

10000

100000

D [

kP

a]

c0 [moles/m3]

n = 0.45

cfix= 100 [moles/m3]

1000400

100

10

rS

Effective stresses of unsaturated soils are given by

Int

op p σ σ 1 1

o w

Ms p p Matric suction:

Generalized osmotic pressure:

Donnan osmotic pressure:

Surface potential:

= ln

wweq

D w

w pore

aRT

a

m

w w

D

1

0 =

r

w w w w

r M D r

S

S S dS

Int r Mp S s

@ full saturation


wp σ σ 1 1

Physical significance of average intergranular stress


w

neutralp p

op

wpFree or capillary water ( )

Adsorbed water ( )

For oil- AND water- saturated:

For water-saturated

w

disjoiningp

neutralp σ σ 1

op

op

(1 )

1

o w

neutral r r

r M r

p S p S p

S s S


0 20 40 60 80 100Sr [%]

-100

-80

-60

-40

-20

0

pin

tGR

[kP

a] c0 [moles/m3]

n=0.6

T=296 K

cfix = 30 [moles/m3]

10

100

500

0 20 40 60 80 100Sr [%]

1

10

100

1000

10000

100000

D o

r s M

[kP

a]

D

sM

n = 0.6

T = 296 K

c0 = 100 [moles/m3]

cfix= 30 [moles/m3]

The average intergranular stress ( ) in a clay during drying intGRP

intGR

1P

3kk eqp


-2 0 2 40

2

4

6

8

10

q (

MP

a)

p' (MPa)

Equilibrium water

250g/l NaCl

700g/l CaCl2

Glycol

-2 0 2 40

2

4

6

8

10

q (

MP

a)

pI' (MPa)

Equilibrium water

250g/l NaCl

700g/l CaCl2

Glycol

Critical state line

Failure lines for the chalks saturated by various fluids

wp 1 w w w

Dp σ σ 1 1Terzaghi: Current:


Apparent cohesive pressure of various chalks

0 25 50 75 1000

1

2

3

4

c (M

Pa)

Mole % water

Traditional effective stress


High-porosity outcrop chalk (Risness et al. 2005)

0.0 0.1 0.2 0.3

1

2

3

c (M

Pa)

w

Net stress


Lewes chalk (Taibi et al. 2009)


M

q

p

Oil-saturated

Water-saturated c

/c M

Constitutive framework: The Modified Cam Clay model

0 0 Int,p

c c vp p h p

0 0 0 0, exp expp

p vc v cp p

Int Mrp S s

Int Intexph p p

Intergranular PhysicoChemical pressure

Int@ 100% : 0, 1.0rS p h

0( 0 )

0( 0 )

cpcp


Material parameters

Conventional: (as in the Modified CamClay model)

Physicochemical Effect:

Water Retention Characteristics:

*

0, , , , , , cE M c p

0, ,fixc

, n

11

M

1

1

n

r nS

s

0 0 For oil-saturated,

can be estimated using CEC value fixc


1 10 1000.3

0.4

0.5

0.6

Dry chalk

sM

=1.5MPa

Water saturated

Simulated

e

Vertical stress (MPa)

Water injection

Compression of Estreux chalk (De Gennaro et al. 2005 )


1 10 1000.64

0.68

0.72

0.76

Soltrol

Water

Simulation

e

p' (MPa)

Mechanical behavior of water- or saltrol-saturated chalk

(Homand and Shao 2000a)

0 10 20 30

0

10

20

30 Initial yield stress for soltrol

Yield stress for soltrol after hardening

Initial yield stress for water

Failure stress for water

Failure stress for soltrol

Simulation

q (

MP

a)

p' (MPa)

c/M


-2 0 2 4 6 8 10

0

2

4

6

8

10

1 (%)

3 (%)

Water saturated

5 MPa confining pressure


Simulation

q (

MP

a)

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00

4

8

3 (%)

1 (%)

Soltrol saturated




Simulation

q (

MP

a)




-4 0 4 80

8

16

(%)

(%)

Sotrol satuarted




Simulation

q (

MP

a)

0 2 4 6

0

5

10

15

20

1 (%)

3 (%)

Soltrol saturated



Simulation

q (

MP

a)



5. Concluding remarks

Physicochemical effect remains elusive in the classical theory of

geomechanics, due to its microscopic nature, which is closely

related to many unresolved geomechanical problems.

A theoretical continuum framework has been recently developed

for describing coupled physical and chemical processes (C. Wei,

2014, Vadose Zone Journal).

The proposed theory addresses well the constitutive behavior of

chalk materials.

Thank you for your attention!