Coupled Hydro-Mechanical Response of a dual porosity coal seam

EGEE 520Shugang Wang

Introduction

• Migration process of gas in dual porosity coal seams

• Dual porosity media Matrix block 1: high porosity, low permeability

Fracture system 2: low porosity, high permeability a

b

Introduction• Coupled physical behavior in dual porosity coal seams

Volumetric strain

Porosity of matrix

Permeability of matrix

Porosity of fracture

Permeability of fracture

Sorption or desorption -induced strain

1

v

1k

s

2k

2

Governing Equations#

, 1 1, 2 2,( )1 2i j ji i i ij s ij iGG u u p p K b

#

1 1s

KK

#

2n

1 KK a

1

1s L

L

pp p

• Mechanical Behavior with hydrological and sorption effects

21 11 2 1( )ts

p k p p pt

1 1 1 1 1 1 1 1 11 2 2

1 1 1

( ) ( ) ( )( ) (1 ) (1 )( ) (1 )

L L L L vts a c

L S L

V p p p p ppp p S K S p p S p

1v s

S

pSK

1

#e

v sK

1 0 10 1 01 (1 ) ( )1

S S SS

3

10 10 1 0

10

1 (1 ) ( )1

k S S Sk S

Matrix

2 20 1 100

2 20 exp ( )e e e es sKn K

2 20 1 100

2 20 exp 3 ( )e e e es sk k

Kn K

Fracture

22 2 2 22 2 2 11 ( )

n

p p k p p p RK t

1 2 1 1 2 22 2

1

1 1( ) 3

L L kk

L n

p p p p pRK p p t K K t

• Hydrological Behavior

12

60 ka

FormulationModels

Axial Symmetric Stress-Strain uaxi, w

Diffusion Equation (matrix) p1

Diffusion Equation (fracture) p2

( )c u F

( )tsc D c Rt

2

2( )tsc D c Rt

( )i iu u t ( )ij j in F t

0(0)iu u0(0)ij

1 1( )p p t 111 ( )s

kn p Q t

2 2( )p p t 222 ( )s

kn p Q t

1 10(0)p p2 20(0)p p

BCs and ICs

Solution• Gas flow in matrix and fracture

• Matrix pore pressure and permeability evolution

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.50.0

0.2

0.4

0.6

0.8

1.0

Matrix pore pressure (MPa)

Mat

rix p

erm

eabi

lity

ratio

(k1/

k10)

0 30 60 90 120 150 1800

1

2

3

4

5

6

7

8

Time (Day)

Mat

rix p

ore

pres

sure

(MPa

)

Solution

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5-20%

0%

20%

40%

60%

80%

100%

free-phase gasadsorped-phase gascoal gain deformationcoal grain swellingbulk skeletal deformation

Matrix pore pressure (MPa)

Cont

ributi

on to

mat

rix st

orati

vity

• Matrix storativity and volumetric strain

0.50 1.50 2.50 3.50 4.50 5.50 6.50 7.50-0.01

-0.005

0

0.005

0.01

0.015

Sorption-induced

Total

Effective stress induced

Matrix pore pressure (MPa)

Volu

met

ric st

rain

• Fracture pore pressure and permeability evolution

0 1 2 3 4 5 6 70

2

4

6

8

10

Time (Minute)

Frac

ture

pre

ssur

e (M

Pa)

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+70.98

0.99

1.00

1.01

1.02

Time (Second)

Frac

ture

per

mea

bilit

y ra

tio

Validation

0 30 60 90 120 150 1800

1

2

3

4

5

6

7

8

Time (Day)

Mat

rix p

ore

pres

sure

(MPa

)

0 1 2 3 4 5 6 70

2

4

6

8

10

Time (Minute)

Frac

ture

pre

ssur

e (M

Pa)

• Pressure transient in a typical dual-porosity reservoir

• Pressure transient in a dual-porosity coal seam

(Bai and Elsworth, 2000)

1 2 3 4 5 6 7 80

2

4

6

8

10

12

Time [log (t), sec.]Pr

essu

re (M

Pa)

Measured dataCalculation

slope change due to fluid supply from matrix to fractures

Parametric study

0 30 60 90 120 150 1800.0

0.2

0.4

0.6

0.8

1.0

7.5 & 5

15 & 1030 & 20

Time (Day)

Mat

rix p

erm

eabi

lity

ratio

In situ stress

0 100 200 300 400 500 600 700 8000

0.2

0.4

0.6

0.8

1

1.2

0.010.05

0.1

Time (Day)

Mat

rix p

erm

eabi

lity

ratio

Fracture spacing

0 30 60 90 120 150 1800.0

0.2

0.4

0.6

0.8

1.0

K_#/K_S=1/2

K_#/K_S=1/5

K_#/K_S=1/10

Time (Day)

Mat

rix p

erm

eabi

lity

ratio

Bulk modulus ratio

Conclusions and future work Gas sorption or desorption is the primary mechanism for either gas

sequestration (sorption) or production (desorption) The greater the ratio of coal bulk modulus to coal grain modulus, the more

rapid the reduction in matrix permeability ratio The lower the in situ stresses, the more rapid the reduction in matrix

permeability ratio Injection-induced permeability within the fracture system initially increases

and subsequently decreases as sorption induced stress builds up Initial matrix permeability and fracture spacing has important effects on the

timing of gas flow in matrix ( 1 -1 and 1 2)

#, 1 1, 2 2, ,( )

1 2i j ji i i ij sd ij T i iGG u u p p K T b

• Conclusions

• Future work Consider thermal effects

Image mechanical failure process under constant loading rate

wFailure criterion Damage factor

(1 )new oldE w E exp( )new old Dk k w

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