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Coupled Hydro-Mechanical Response of a dual porosity coal seam. EGEE 520 Shugang Wang. Introduction. Dual porosity media. Matrix block 1 : high porosity, low permeability Fracture system 2 : low porosity, high permeability . a. b. - PowerPoint PPT Presentation
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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
References1. C Zhao, TP Xu, S Valliappan - Computers & structures, 1994 2. D Elsworth, M Bai - J. Geotech. Eng. Div., ASCE, 19923. GI Barrenblatt, P Zehltov Iu, IN Kochina – J Appl Math Mech, 19604. H Zhang, J Liu, D Elsworth - Int. J. Rock Mech., Min. Sci., 20085. I Gray - SPE Reserv. Eng, 1987 6. JE Warren, PJ Root - SPE Journal, 19637. JP Seidle, DJ Jeansonne, DJ Erickson - SPE, 19928. J Rutqvist, CF Tsang - Environ Geol , 20029. J Yi, IY Akkutlu, CÖ Karacan, CR Clarkson - Int J of Coal Geol , 200910. M Bai, D Elsworth, JC Roegiers - Water. Resour. Res., 200311. M Bai, D Elsworth, ASCE, 200012. S Valliappan, Z Wohua - J. Numer. Anal. Methods Geomech, 199613. S Harpalani, RA Schraufnagel - Fuel, 199014. S Harpalani, G Chen - Geotech. Geol. Eng, 199715. T Xu, CA Tang, TH Yang, WC Zhu, J Liu - Int. J. Rock Mech. Min. Sci., 200616. WC Zhu, J Liu, JC Sheng, D Elsworth - Int. J. Rock Mech. Min. Sci., 2007 17. YS Wu, K Pruess, Persoff - Transp. in P. Media. , 199818. Y Wu, J Liu, D Elsworth, in Submittal, 200919. Y Zhao, Y Hu, B Zhao, D Yang - Transp. in P. Media. , 200420. Y Zhao, Z Jin, J Sun – J Appl Math Mech, 1994