Microseismic imaging of the hydraulic fracturing operation in the naturally fractured rocks confirms the existence of a stimulated volume (SV) of enhanced permeability. The simulation and characterization of the SV evolution is uniquely challenging given the uncertainty in the nature of the rock mass fabrics as well as the complex fracturing behavior of shear and tensile nature, irreversible plastic deformation and damage. In this paper, the simulation of the SV evolution is achieved using a nonlocal poromechanical plasticity model. Effects of the natural fracture network are incorporated via a nonlocal plasticity characteristic length, . A nonlocal Drucker–Prager failure model is implemented in the framework of Biot's theory using a new implicit C0 finite element method. First, the behavior of the SV for a two-dimensional (2D) geomechanical injection problem is simulated and the resulting SV is assessed. It is shown that breakdown pressure and stable fracturing pressure are the natural outcomes of the model and both depend upon . Next, the post-shut-in behavior of the SV is analyzed using the pressure and pressure derivative plots. A bilinear flow regime is observed and it is used to estimate the flow capacity of the SV. The results show that the flow capacity of the SV increases as decreases (i.e., as the SV behaves more like a single hydraulic fracture); however, for 0.1m1m, the calculated flow capacity indicates that the conductivity of the SV is finite. Finally, it is observed that as tends to zero, the flow capacity of the SV tends to infinity and the SV behaves like a single infinitely conducting fracture.

References

References
1.
Mayerhofer
,
M. J.
,
Lolon
,
E.
,
Warpinski
,
N. R.
,
Cipolla
,
C. L.
,
Walse
,
D. W.
, and
Rightmire
,
C. M.
,
2010
, “
What is Stimulated Reservoir Volume?
,”
SPE Prod. Oper.
,
25
(
1
), pp.
89
98
.
2.
Dusseault
,
M. B.
,
2013
, “
Geomechanical Aspects of Shale Gas Development
,”
Rock Mech. Resour., Energy Environ.
,
39
, pp. 39–56.
3.
Dusseault
,
M. B.
,
McLennan
,
J.
, and
Shu
,
J.
,
2011
, “
Massive Multi-Stage Hydraulic Fracturing for Oil and Gas Recovery From Low Mobility Reservoirs in China
,”
Pet. Drilling Tech.
,
39
(
3
), pp.
6
16
.https://www.researchgate.net/publication/288812002_Massive_multi-stage_hydraulic_fracturing_for_oil_and_gas_recovery_from_low_mobility_reservoirs_in_China
4.
Cipolla
,
C. L.
,
Warpinski
,
N. R.
,
Mayerhofer
,
M.
,
Lolon
,
E. P.
, and
Vincent
,
M.
,
2010
, “
The Relationship Between Fracture Complexity, Reservoir Properties, and Fracture-Treatment Design
,”
SPE Prod. Oper.
,
25
(
4
), pp. 1–21.
5.
Maxwell
,
S.
,
2014
,
Microseismic Imaging Hydraulic Fracturing: Improved Engineering Unconventional Shale Reservoirs
, Society of Exploration Geophysicists, Tulsa, OK.
6.
Boroumand
,
N.
, and
Eaton
,
D. W.
,
2012
, “
Comparing Energy Calculations-Hydraulic Fracturing and Microseismic Monitoring
,”
74th EAGE Conference and Exhibition Incorporating EUROPEC
, Copenhagen, Denmark, June 4–7, Paper No. 58979.
7.
Garagash
,
D. I.
, and
Detournay
,
E.
,
2000
, “
The Tip Region of a Fluid-Driven Fracture in an Elastic Medium
,”
ASME J. Appl. Mech.
,
67
(
1
), pp.
183
192
.
8.
Tsai
,
Y. M.
,
1983
, “
Transversely Isotropic Thermoelastic Problem of Uniform Heat Flow Distributed by a Penny-Shaped Crack
,”
J. Therm. Stress
,
6
(
2–4
), pp.
379
389
.
9.
Garagash
,
D. I.
, and
Detournay
,
E.
,
2005
, “
Plane-Strain Propagation of a Fluid-Driven Fracture: Small Toughness Solution
,”
ASME J. Appl. Mech.
,
72
(
6
), pp.
916
928
.
10.
Detournay
,
E.
,
Adachi
,
J. I.
, and
Garagash
,
D. I.
,
2002
, “
Asymptotic and Intermediate Asymptotic Behavior Near the Tip of a Fluid-Driven Fracture Propagating in a Permeable Elastic Medium
,”
Structural Integrity and Fracture
,
A. V.
Dyskin
,
X.
Hu
, and
E.
Sahouryeh
, eds., pp.
9
18
,
Balkema
,
Lisse, The Netherlands
.
11.
Shimizu
,
H.
,
Murata
,
S.
, and
Ishidab
,
T.
,
2011
, “
The Distinct Element Analysis for Hydraulic Fracturing in Hard Rock Considering Fluid Viscosity and Particle Size Distribution
,”
Int. J. Rock Mech. Min. Sci.
,
48
(
5
), pp.
712
727
.
12.
B.
,
Damjanac
,
I.
,
Gil
,
M.
,
Pierce
,
M.
,
Sanchez
,
A.
,
Van
,
As
,
J.
, and
McLennan
,
2010
, “
A New Approach to Hydraulic Fracturing Modeling in Naturally Fractured Reservoirs
,”
44th U.S. Rock Mechanics Symposium and 5th U.S.-Canada Rock Mechanics Symposium
, Salt Lake City, UT, June 27–30, Paper No.
ARMA-10-400
https://www.onepetro.org/conference-paper/ARMA-10-400.
13.
Drucker
,
D. C.
, and
Prager
,
W.
,
1952
, “
Soil Mechanics and Plastic Analysis or Limit Design
,”
Q. Appl. Math.
,
10
(
2
), pp.
157
165
.
14.
Biot
,
M. A.
,
1941
, “
General Theory of Three-Dimensional Consolidation
,”
J. Appl. Phys.
,
12
(
2
), pp.
155
164
.
15.
De Borst
,
R.
, and
Pamin
,
J.
,
1996
, “
Some Novel Developments in Finite Element Procedures for Gradient-Dependent Plasticity
,”
Int. J. Numer. Methods Eng.
,
39
(
14
), pp.
2477
2505
.
16.
Pamin
,
J.
, and
De Borst
,
R.
,
1995
, “
A Gradient Plasticity Approach to Finite Element Predictions of Soil Instability
,”
Arch. Mech.
,
47
, pp. 353–377.
17.
Engelen
,
R. A. B.
,
2005
, “
Plasticity-Induced Damage in Metals: Nonlocal Modelling at Finite Strains
,”
Ph.D. thesis
, Technische Universiteit Eindhoven, Eindhoven, The Netherlands.https://research.tue.nl/en/publications/plasticity-induced-damage-in-metals-nonlocal-modelling-at-finite-
18.
Engelen
,
R. A. B.
,
Geers
,
M. G. D.
, and
Baaijens
,
F. P. T.
,
2003
, “
Nonlocal Implicit Gradient-Enhanced Elasto-Plasticity for the Modelling of Softening Behaviour
,”
Int. J. Plasticity
,
19
(
4
), pp.
403
433
.
19.
Nilson
,
R. H.
, and
Griffiths
,
S. K.
,
1983
, “
Numerical Analysis of Hydraulically-Driven Fractures
,”
Comput. Methods Appl. Mech. Eng.
,
36
(
3
), pp.
359
370
.
20.
Bourdet
,
D.
,
Ayoub
,
J. A.
, and
Pirard
,
Y. M.
,
1989
, “
Use of Pressure Derivative in Well Test Interpretation
,”
SPE Form. Eval.
,
4
(
2
), pp.
293
302
.
21.
Sarvaramini
,
E.
, and
Garagash
,
D. I.
,
2015
, “
Breakdown of a Pressurized Fingerlike Crack in a Permeable Solid
,”
ASME J. Appl. Mech.
,
82
(
6
), p.
061006
.
22.
Sarvaramini
,
E.
, and
Garagash
,
D. I.
,
2016
, “
Poroelastic Effects in Reactivation of a Fingerlike Hydraulic Fracture
,”
ASME J. Appl. Mech.
,
83
(
6
), p.
061011
.
23.
Nolte
,
K. G.
,
1979
, “
Determination of Fracture Parameters From Fracturing Pressure Decline
,”
SPE Annual Technical Conference and Exhibition
, Las Vegas, NV, Sept. 23–26, SPE Paper No.
SPE 8341
.
24.
Cinco
,
L. H.
,
Samaniego
,
V. F.
, and
Dominguez
,
A. N.
,
1978
, “
Transient Pressure Behavior for a Well With a Finite-Conductivity Vertical Fracture
,”
AIME Soc. Pet. Eng. J., Trans.
,
18
(
4
), pp.
253
264
.
25.
Babuška
,
I.
,
1971
, “
Error-Bounds for Finite Element Method
,”
Numerische Math.
,
16
(
4
), pp.
322
333
.
26.
Flügel
,
E.
,
2013
,
Microfacies Carbonate Rocks: Analysis, Interpretation Application
,
Springer Science & Business Media
, New York.
27.
Katz
,
A. J.
, and
Thompson
,
A. H.
,
1986
, “
Quantitative Prediction of Permeability in Porous Rock
,”
Phys. Rev. B
,
34
(
11
), p.
8179
.
28.
Rothenburg
,
L.
,
Bathurst
,
R. J.
, and
Dusseault
,
M. B.
,
1989
, “
Micromechanical Ideas in Constitutive Modelling of Granular Materials
,”
Powders Grains
,
90
, pp.
355
363
.
29.
Gringarten
,
A. C.
,
Ramey
,
H. J.
, Jr.
, and
Raghavan
,
R.
,
1975
, “
Applied Pressure Analysis for Fractured Wells
,”
J. Pet. Technol.
,
27
(
7
), pp.
887
892
.
30.
Bazant
,
Z. P.
, and
Oh
,
B. H.
,
1983
, “
Crack Band Theory for Fracture of Concrete
,”
Mater. Constr.
,
16
(
3
), pp.
155
177
.
31.
Simo
,
J. C.
, and
Hughes
,
T. J. R.
,
2006
,
Computational Inelasticity
, Vol.
7
,
Springer Science & Business Media
, New York.
32.
Djoko
,
J. K.
,
Ebobisse
,
F.
,
McBride
,
A. T.
, and
Reddy
,
B. D.
,
2007
, “
A Discontinuous Galerkin Formulation for Classical and Gradient Plasticity—Part 2: Algorithms and Numerical Analysis
,”
Comput. Methods Appl. Mech. Eng.
,
197
(
1–4
), pp.
1
21
.
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