This paper is concerned with the analysis of a low-viscosity fluid injection into a pre-existing, fingerlike crack within a linear elastic, permeable rock, and of the conditions leading to the onset of the fracture propagation (i.e., the breakdown). The problem is of interest in reservoir waterflooding, supercritical CO2 injection for geological storage, and other subsurface fluid injection applications. Fluid injection into a stationary crack leads to its elastic dilation and pressurization, buffered by the fluid leak-off into the surrounding rock. The solution of the problem, therefore, requires coupling of the crack deformation and the full-space pore-fluid pressure diffusion in the permeable rock. Contrary to the case of propagating hydraulic fractures, when significant part of the energy input is dissipated in the viscous fluid flow in the fracture, we find that the viscous fluid pressure drop inside a stationary fracture can be often neglected (we establish the conditions when one can do so). This, in turn, allows for a semi-analytical solution of the problem using the Green's function method, and, furthermore, for the full analytical treatment of the small/large injection time asymptotics. We apply the transient pressurization solution to predict the onset of the propagation based on the criteria derived from the energy considerations for a fingerlike crack.

References

References
1.
Keck
,
R. G.
, and
Withers
,
R. J.
,
1994
, “
A Field Demonstration of Hydraulic Fracturing for Solids Waste Injection With Real-Time Passive Seismic Monitoring
,”
Society of Petroleum Engineers Annual Technical Conference and Exhibition
(
SPE
), New Orleans, LA, Sept. 25–28, Paper No. SPE-28495-MS.10.2118/28495-MS
2.
Moschovidis
,
Z. A.
,
Gardner
,
D. C.
, and
Veatch
,
R. W.
,
1994
, “
Disposal of Oily Cuttings by Downhole Periodic Fracturing Injections, Valhall, North Sea: Case Study and Modeling Concepts
,”
SPE Drill. Completion
,
9
(
4
), pp.
256
262
.10.2118/25757-PA
3.
Willhite
,
G. P.
,
1986
,
Waterflooding
(SPE Textbook Series),
SPE
,
Richardson, TX
.
4.
Deutsch
,
M.
,
1963
, “
Groundwater Contamination and Legal Controls in Michigan
,” U.S. Geological Survey of Water Supply–Paper 1691.
5.
Raleigh
,
C. B.
,
Healy
,
J. H.
, and
Bredehoeft
,
J. D.
,
1976
, “
An Experiment in Earthquake Control at Rangely, Colorado
,”
Science
,
191
(
4233
), pp.
1230
1237
.10.1126/science.191.4233.1230
6.
Talwani
,
P.
, and
Acree
,
S.
,
1985
, “
Pore Pressure Diffusion and the Mechanism of Reservoir-Induced Seismicity
,”
Pure Appl. Geophys.
,
122
(
6
), pp.
947
965
.10.1007/BF00876395
7.
Hsieh
,
P. A.
, and
Bredehoeft
,
J. D.
,
1981
, “
A Reservoir Analysis of the Denver Earthquakes: A Case of Induced Seismicity
,”
J. Geophys. Res. B: Solid Earth
,
86
(
B2
), pp.
903
920
.10.1029/JB086iB02p00903
8.
A.
Daubrée
,
1879
,
Etudes synthetiques de geologie experimentale
,
Dunod Éditeur
,
Paris
.
9.
Becker
,
G. F.
,
1891
, “
The Structure of a Portion of the Sierra Nevada of California
,”
Geol. Soc. Am. Bull.
,
2
(
1
), pp.
49
74
.10.1130/GSAB-2-49
10.
Pollard
,
D. D.
, and
Aydin
,
A.
,
1988
, “
Progress in Understanding Joints Over the Last Century
,”
Geol. Soc. Am. Bull.
,
100
(
8
), pp.
1181
1204
.10.1130/0016-7606(1988)100<1181:PIUJOT>2.3.CO;2
11.
Hodgson
,
R. A.
,
1961
, “
Classification of Structures on Joint Surfaces
,”
Am. J. Sci.
,
259
(
7
), pp.
493
502
.10.2475/ajs.259.7.493
12.
Engelder
,
T.
,
1982
, “
Is There a Genetic Relationship Between Selected Regional Joints and Contemporary Stress Within the Lithosphere of North America?
,”
Tectonics
,
1
(
2
), pp.
161
177
.10.1029/TC001i002p00161
13.
Pointe
,
P. R.
, and
Hudson
,
J. A.
,
1985
, “
Characterization and Interpretation of Rock Mass Joint Patterns
,”
Geol. Assoc. Am. Spec. Pap.
,
199
, pp.
1
38
.10.1130/SPE199
14.
Perkins
,
T. K.
, and
Kern
,
L. R.
,
1961
, “
Widths of Hydraulic Fractures
,”
J. Pet. Technol.
,
13
(9), pp.
937
949
.10.2118/89-PA
15.
Kovalyshen
,
Y.
, and
Detournay
,
E.
,
2010
, “
A Reexamination of the Classical PKN Model of Hydraulic Fracture
,”
Transp. Porous Media
,
81
(
2
), pp.
317
339
.10.1007/s11242-009-9403-4
16.
Castillo
,
J. L.
,
1987
, “
Modified Fracture Pressure Decline Analysis Including Pressure-Dependent Leakoff
,”
Society of Petroleum Engineers Low Permeability Reservoirs Symposium
(
SPE
), Denver, May 18–19, Paper No. SPE-16417-MS.10.2118/16417-MS
17.
Barree
,
R. D.
, and
Mukherjee
,
H.
,
1996
, “
Determination of Pressure Dependent Leakoff and Its Effect on Fracture Geometry
,”
Society of Petroleum Engineers Annual Technical Conference and Exhibition
(
SPE
), Denver, Oct. 6–9, Paper No. SPE-36424-MS, pp.
85
94
.10.2118/36424-MS
18.
Howard
,
G. C.
, and
Fast
,
C. R.
,
1957
, “
Optimum Fluid Characteristics for Fracture Extension
,”
Drilling and Production Practices
, American Petroleum Institute, New York, pp.
261
270
.
19.
Gordayev
,
Y. N.
, and
Zazovsky
,
A. F.
,
1992
, “
Self-Similar Solution for Deep-Penetrating Hydraulic Fracture Propagation
,”
Transp. Porous Media
,
7
(
3
), pp.
283
304
.10.1007/BF01063964
20.
Gordayev
,
Y. N.
, and
Entov
,
V. M.
,
1997
, “
The Pressure Distribution Around a Growing Crack
,”
J. Appl. Math. Mech.
,
61
(
6
), pp.
1025
1029
.10.1016/S0021-8928(98)80005-1
21.
Mathias
,
S. A.
, and
Reeuwijk
,
M.
,
2009
, “
Hydraulic Fracture Propagation With 3-D Leak-Off
,”
Transp. Porous Media
,
80
(
3
), pp.
499
518
.10.1007/s11242-009-9375-4
22.
Kovalyshen
,
Y.
,
2010
, “
Fluid-Driven Fracture in Poroelastic Medium
,” Ph.D. thesis, University of Minnesota, Minneapolis, MN.
23.
Detournay
,
E.
, and
Cheng
,
A. H.-D.
,
1991
, “
Plane Strain Analysis of a Stationary Hydraulic Fracture in a Poroelastic Medium
,”
Int. J. Solids Struct.
,
27
(
13
), pp.
1645
1662
.10.1016/0020-7683(91)90067-P
24.
Nordgren
,
R. P.
,
1972
, “
Propagation of Vertical Hydraulic Fractures
,”
SPE
,
12
(4), pp.
306
314
.10.2118/3009-PA
25.
Hutchinson
,
J. W.
, and
Suo
,
Z.
,
1992
, “
Mixed Mode Cracking in Layered Materials
,”
Adv. Appl. Mech.
,
29
, pp.
63
191
.10.1016/S0065-2156(08)70164-9
26.
Nolte
,
K. G.
,
1991
, “
Fracturing-Pressure Analysis for Nonideal Behavior
,”
J. Pet. Technol.
,
43
(
2
), pp.
210
218
.10.2118/20704-PA
27.
Bear
,
J.
,
1988
,
Dynamics of Fluids in Porous Media
,
Dover
,
New York
.
28.
Carslaw
,
H.
, and
Jaeger
,
J. C.
,
1959
,
Conduction of Heat in Solids
,
2nd ed.
,
Oxford University
,
London
.
29.
Stehfest
,
H.
,
1970
, “
Algorithm 368: Numerical Inversion of Laplace Transforms [D5]
,”
Commun. ACM
,
13
(
1
), pp.
47
49
.10.1145/361953.361969
30.
Khristianovic
,
S. A.
, and
Zheltov
,
Y. P.
,
1955
, “
Formation of Vertical Fractures by Means of Highly Viscous Fluids
,”
4th World Petroleum Congress
,
Rome
, June 6–15, Vol.
II
, pp.
579
586
.
31.
Geertsma
,
J.
, and
de Klerk
,
F.
,
1969
, “
A Rapid Method of Predicting Width and Extent of Hydraulic Induced Fractures
,”
J. Pet. Technol.
,
21
(12), pp.
1571
1581
.10.2118/2458-PA
32.
Tada
,
H.
,
Paris
,
P. C.
, and
Irwin
,
G. R.
,
2000
,
The Stress Analysis of Cracks Handbook
,
ASME
,
New York
, pp.
55
56
.
33.
Michael
,
K.
,
Golab
,
A.
,
Shulakova
,
V.
,
Ennis-King
,
J.
,
Allinson
,
G.
,
Sharma
,
S.
, and
Aiken
,
T.
,
2010
, “
Geological Storage of CO2 in Saline Aquifers—A Review of the Experience From Existing Storage Operations
,”
Int. J. Greenhouse Gas Control
,
4
(
4
), pp.
659
667
.10.1016/j.ijggc.2009.12.011
34.
Rutqvist
,
J.
,
Donald
,
W. V.
, and
Larry
,
M.
,
2010
, “
Coupled Reservoir-Geomechanical Analysis of CO2 Injection and Ground Deformations at in Salah, Algeria
,”
Int. J. Greenhouse Gas Control
,
4
(
2
), pp.
225
230
.10.1016/j.ijggc.2009.10.017
35.
Bandis
,
S. C.
,
Lumsden
,
A. C.
, and
Barton
,
N. R.
,
1983
, “
Fundamentals of Rock Joint Deformation
,”
Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
,
20
(
6
), pp.
249
268
.10.1016/0148-9062(83)90595-8
36.
Detournay
,
E.
, and
Cheng
,
A. H.-D.
,
1993
, “
Fundamentals of Poroelasticity
,”
Comprehensive Rock Engineering
,
Pergamon
,
New York
, Vol.
2
, pp.
113
171
.
37.
Sedov
,
L. I.
,
1971–1972
,
A Course in Continuum Mechanics
,
Walters-Noordhoff Publishing
,
Groningen, The Netherlands
.
38.
Zehnder
,
A. T.
,
2012
,
Fracture Mechanics
(Lecture Notes in Applied and Computational Mechanics),
Springer
,
London
.
39.
Patankar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
Hemisphere Publishing
,
Washington, DC
.
40.
Abramowitz
,
M.
, and
Stegun
,
I. A.
, ed.,
1972
,
Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables
,
Dover
,
New York
.
41.
Watson
,
G. N.
,
1995
,
A Treatise on the Theory of Bessel Functions
,
Cambridge University Press
,
London
.
42.
Erdogan
,
F.
,
Gupta
,
G. D.
, and
Cook
,
T. S.
,
1973
,
Numerical Solution of Singular Integral Equations
(Mechanics of Fracture, Vol.
1
),
Noordhoff International Publishing
,
Leyden
, The Netherlands, pp.
368
425
.
You do not currently have access to this content.