Fluid flow in fractured porous media has always been important in different engineering applications especially in hydrology and reservoir engineering. However, by the onset of the hydraulic fracturing revolution, massive fracturing jobs have been implemented in unconventional hydrocarbon resources such as tight gas and shale gas reservoirs that make understanding fluid flow in fractured media more significant. Considering ultralow permeability of these reservoirs, induced complex fracture networks play a significant role in economic production of these resources. Hence, having a robust and fast numerical technique to evaluate flow through complex fracture networks can play a crucial role in the progress of inversion methods to determine fracture geometries in the subsurface. Current methods for tight gas flow in fractured reservoirs, despite their advantages, still have several shortcomings that make their application for real field problems limited. For instance, the dual permeability theory assumes an ideal uniform orthogonal distribution of fractures, which is quite different from field observation; on the other hand, numerical methods like discrete fracture network (DFN) models can portray the irregular distribution of fractures, but requires massive mesh refinements to have the fractures aligned with the grid/element edges, which can greatly increase the computational cost and simulation time. This paper combines the extended finite element methods (XFEM) and the gas pseudo-pressure to simulate gas flow in fractured tight gas reservoirs by incorporating the strong-discontinuity enrichment scheme to capture the weak-discontinuity feature induced by highly permeable fractures. Utilizing pseudo-pressure formulations simplifies the governing equations and reduces the nonlinearity of the problem significantly. This technique can consider multiple fracture sets and their intersection to mimic real fracture networks on a plain structured mesh. Here, we utilize the unified Hagen–Poiseuille-type equation to compute the permeability of tight gas, and finally adopt Newton–Raphson iteration method to solve the highly nonlinear equations. Numerical results illustrate that XFEM is considerably effective in fast calculation of gas flow in fractured porous media.

References

References
1.
Dahi Taleghani
,
A.
, and
Olson
,
J.
,
2011
, “
Analysis of Multi-Stranded Hydraulic Fracture Propagation: An Improved Model for the Interaction Between Induced and Natural Fractures
,”
SPE J.
,
16
(
3
), p.
124884
.
2.
Shojaei
,
A.
,
Dahi Taleghani
,
A.
, and
Li
,
G.
,
2014
, “
A Continuum Damage Failure Model for Hydraulic Fracturing of Porous Rocks
,”
Int. J. Plasticity
,
59
, pp.
199
212
.
3.
Bautista
,
J. F.
, and
Dahi Taleghani
,
A. A.
,
2016
, “
The State of the Art and Challenges in Geomechanical Modeling of Injector Wells: A Review Paper
,”
ASME J. Energy Resour. Technol.
,
139
(
1
), p.
012910
.
4.
Li
,
J.
,
Guo
,
B.
, and
Ling
,
K.
,
2013
, “
Flow Diverting for Reducing Wellbore Erosion in Gas-Drilling Shale Gas Wells
,”
ASME J. Energy Resour. Technol.
,
135
(
3
), p.
031501
.
5.
Du
,
X.
,
Gu
,
M.
,
Duan
,
S.
, and
Xian
,
X.
,
2017
, “
The Influences of CO2 Injection Pressure on CO2 Dispersion and the Mechanism of CO2–CH4 Displacement in Shale
,”
ASME J. Energy Resour. Technol.
,
140
(
1
), p.
012907
.
6.
Guo
,
B.
,
Yu
,
X.
, and
Khoshgahdam
,
M.
,
2009
, “
A Simple Analytical Model for Predicting Productivity of Multifractured Horizontal Wells
,”
SPE Reservoir Eval. Eng.
,
12
(
6
), pp.
879
885
.
7.
Ozkan
,
E.
,
Brown
,
M. L.
,
Raghavan
,
R.
, and
Kazemi
,
H.
,
2011
, “
Comparison of Fractured-Horizontal-Well Performance in Tight Sand and Shale Reservoirs
,”
SPE Reservoir Eval. Eng.
,
14
(
2
), pp.
248
259
.
8.
Brown
,
M.
,
Ozkan
,
E.
,
Raghavan
,
R.
, and
Kazemi
,
H.
,
2011
, “
Practical Solutions for Pressure-Transient Responses of Fractured Horizontal Wells in Unconventional Shale Reservoirs
,”
SPE Reservoir Eval. Eng.
,
14
(
6
), pp.
663
676
.
9.
Medeiros
,
F.
, Jr.
,
2007
, “Semi-Analytical Pressure-Transient Model for Complex Well- Reservoir Systems,”
Ph.D. thesis
, Colorado School of Mines, Golden, CO.
10.
Medeiros
,
F.
,
Kurtoglu
,
B.
,
Ozkan
,
E.
, and
Kazemi
,
H.
,
2007
, “
Analysis of Production Data From Hydraulically Fractured Horizontal Wells in Tight, Heterogeneous Formations
,” SPE Annual Technical Conference and Exhibition, Anaheim, CA, Nov. 11–14,
SPE
Paper No. SPE-110848-MS.
11.
Cipolla
,
C. L.
,
Lolon
,
E. P.
,
Erdle
,
J. C.
, and
Rubin
,
B.
,
2010
, “
Reservoir Modeling in Shale-Gas Reservoirs
,”
SPE Reservoir Eval. Eng.
,
13
(
4
), pp.
638
653
.
12.
Sheng
,
M.
,
Li
,
G.
,
Shah
,
S. N.
, and
Jin
,
X.
,
2012
, “
Extended Finite Element Modeling of Multi-Scale Flow in Fractured Shale Gas Reservoirs
,” SPE Annual Technical Conference and Exhibition, San Antonio, TX, Oct. 8–10,
SPE
Paper No. SPE-159919-MS.
13.
Ren
,
G.
,
Jiang
,
J.
, and
Younis
,
R.
,
2016
, “
A Fully Coupled XFEM-EDFM Model for Multiphase Flow and Geomechanics in Fractured Tight Gas Reservoirs
,”
Procedia Comput. Sci.
,
80
, pp.
1404
1415
.
14.
Mirzaei
,
M.
, and
Cipolla
,
C. L.
,
2012
, “
A Workflow for Modeling and Simulationof Hydraulic Fractures in Unconventional Gas Reservoirs
,” SPE Middle East Unconventional Gas Conference and Exhibition, Abu Dhabi, United Arab Emirates, Jan. 23–25,
SPE
Paper No. SPE-153022-MS.
15.
Li
,
L.
, and
Lee
,
S. H.
,
2008
, “
Efficient Field-Scale Simulation of Black Oil in a Naturally Fractured Reservoir Through Discrete Fracture Networks and Homogenized Media
,”
SPE Reservoir Eval. Eng.
,
11
(
4
), pp.
750
758
.
16.
Moinfar
,
A.
,
Varavei
,
A.
,
Sepehrnoori
,
K.
, and
Johns
,
R. T.
,
2014
, “
Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs
,”
SPE J.
,
19
(
2
), pp.
289
303
.
17.
Ţene
,
M.
,
Al Kobaisi
,
M. S.
, and
Hajibeygi
,
H.
,
2016
, “
Algebraic Multiscale Method for Flow in Heterogeneous Porous Media With Embedded Discrete Fractures (F-AMS)
,”
J. Comput. Phys.
,
321
, pp. 819–845.
18.
Moës
,
N.
,
Dolbow
,
J.
, and
Belytschko
,
T.
,
1999
, “
A Finite Element Method for Crack Growth Without Remeshing
,”
Int. J. Numer. Methods Eng.
,
46
(
1
), pp.
131
150
.
19.
Strouboulis
,
T.
,
Copps
,
K.
, and
Babuška
,
I.
,
2001
, “
The Generalized Finite Element Method
,”
Comput. Methods Appl. Mech. Eng.
,
190
(
32–33
), pp.
4081
4193
.
20.
Belytschko
,
T.
, and
Black
,
T.
,
1999
, “
Elastic Crack Growth in Finite Elements With Minimal Remeshing
,”
Int. J. Numer. Methods Eng.
,
45
(
5
), pp.
601
620
.
21.
Melenk
,
J. M.
, and
Babuška
,
I.
,
1996
, “
The Partition of Unity Finite Element Method: Basic Theory and Applications
,”
Comput. Methods Appl. Mech. Eng.
,
139
(
1–4
), pp.
289
314
.
22.
Daux
,
C.
,
Moës
,
N.
,
Dolbow
,
J.
,
Sukumar
,
N.
, and
Belytschko
,
T.
,
2000
, “
Arbitrary Branched and Intersecting Cracks With the Extended Finite Element Method
,”
Int. J. Numer. Methods Eng.
,
48
(
12
), pp.
1741
1760
.
23.
Sukumar
,
N.
,
Moës
,
N.
,
Moran
,
B.
, and
Belytschko
,
T.
,
2000
, “
Extended Finite Element Method for Three-Dimensional Crack Modelling
,”
Int. J. Numer. Methods Eng.
,
48
(
11
), pp.
1549
1570
.
24.
Moës
,
N.
,
Gravouil
,
A.
, and
Belytschko
,
T.
,
2002
, “
Non‐Planar 3D Crack Growth by the Extended Finite Element and Level Sets—Part I: Mechanical Model
,”
Int. J. Numer. Methods Eng.
,
53
(
11
), pp.
2549
2568
.
25.
Duarte
,
C. A.
,
Hamzeh
,
O. N.
,
Liszka
,
T. J.
, and
Tworzydlo
,
W. W.
,
2001
, “
A Generalized Finite Element Method for the Simulation of Three-Dimensional Dynamic Crack Propagation
,”
Comput. Methods Appl. Mech. Eng.
,
190
(
15–17
), pp.
2227
2262
.
26.
Belytschko
,
T.
,
Moës
,
N.
,
Usui
,
S.
, and
Parimi
,
C.
,
2001
, “
Arbitrary Discontinuities in Finite Elements
,”
Int. J. Numer. Methods Eng.
,
50
(
4
), pp.
993
1013
.
27.
Molino
,
N.
,
Bao
,
Z.
, and
Fedkiw
,
R.
,
2005
, “
A Virtual Node Algorithm for Changing Mesh Topology During Simulation
,”
ACM SIGGRAPH 2005
Los Angeles, CA, Aug. 8–12, pp. 385–392.
28.
Sukumar
,
N.
,
Dolbow
,
J. E.
, and
Moës
,
N.
,
2015
, “
Extended Finite Element Method in Computational Fracture Mechanics: A Retrospective Examination
,”
Int. J. Fract.
,
196
(
1–2
), pp.
189
206
.
29.
Li
,
Y.
,
Jiang
,
Y.
,
Zhao
,
J.
,
Liu
,
C.
, and
Zhang
,
L.
,
2015
, “
Extended Finite Element Method for Analysis of Multi-Scale Flow in Fractured Shale Gas Reservoirs
,”
Environ. Earth Sci.
,
73
(
10
), pp.
6035
6045
.
30.
Mohammadnejad
,
T.
, and
Khoei
,
A. R.
,
2013
, “
An Extended Finite Element Method for Hydraulic Fracture Propagation in Deformable Porous Media With the Cohesive Crack Model
,”
Finite Elem. Anal. Des.
,
73
, pp.
77
95
.
31.
Civan
,
F.
,
Rai
,
C. S.
, and
Sondergeld
,
C. H.
,
2011
, “
Shale-Gas Permeability and Diffusivity Inferred by Improved Formulation of Relevant Retention and Transport Mechanisms
,”
Transp. Porous Media
,
86
(
3
), pp.
925
944
.
32.
Martin
,
V.
,
Jaffré
,
J.
, and
Roberts
,
J. E.
,
2005
, “
Modeling Fractures and Barriers as Interfaces for Flow in Porous Media
,”
SIAM J. Sci. Comput.
,
26
(
5
), pp.
1667
1691
.
33.
Zi
,
G.
,
Song
,
J. H.
,
Budyn
,
E.
,
Lee
,
S. H.
, and
Belytschko
,
T.
,
2004
, “
A Method for Growing Multiple Cracks Without Remeshing and Its Application to Fatigue Crack Growth
,”
Modell. Simul. Mater. Sci. Eng.
,
12
(
5
), p.
901
.
34.
Dranchuk
,
P. M.
,
Purvis
,
R. A.
, and
Robinson
,
D. B.
,
1973
, “
Computer Calculation of Natural Gas Compressibility Factors Using the Standing and Katz Correlation
,” Annual Technical Meeting, Edmonton, AB, Canada, May 8–12, Paper No.
PETSOC-73-112
.
35.
Puyang
,
P.
,
Dahi Taleghani
,
A.
, and
Sarker
,
B.
,
2016
, “
An Integrated Modeling Approach for Natural Fractures and Post Treatment Fracturing Analysis: A Case Study
,”
J. Interpret.
,
4
(
4
), p. T485.
36.
Puyang
,
P.
,
Sarker
,
B.
, and
Dahi Taleghani
,
A.
,
2015
, “
Multi-Disciplinary Data Integration for Inverse Hydraulic Fracturing Analysis
,” Unconventional Resources Technology Conference, San Antonio, TX, July 20–22, Paper No.
URTEC-2153945-MS
.
37.
Dahi Taleghani
,
A.
, and
Olson
,
J.
,
2013
, “
How Natural Fractures Could Affect Hydraulic Fracture Geometry
,”
SPE J.
,
19
(
1
), pp. 161–171.
38.
Teng
,
B.
,
Cheng
,
L.
,
Huang
,
S.
,
Li
,
H.
,
2018
, “
Production Forecast for Shale Gas Reservoirs With Fast Marching-Succession of Steady States Method
,”
ASME J. Energy Resour. Technol.
,
140
(3), p. 032913.
You do not currently have access to this content.