Fundamental solutions for an instantaneous point force and an instantaneous fluid point source are derived for an infinite, fluid-saturated, poroelastic solid with zero permeability in one direction. Applying these solutions and Cleary’s reciprocal theorem to the three-dimensional problem of a pressurized plane crack yields two integral equations, which relate normal tractions and fluid pressure on the crack faces to crack opening and fluid injection rate per unit fracture area. An important application of these equations is the prediction of hydraulic fractures induced during water-flooding of reservoirs to enhance gas and oil recovery. Zero permeability in one direction may be a good approximation for the case in which the reservoir is sandwiched between two impermeable rock layers.

Issue Section:
Technical Papers
Topics:
Fluids, Fracture (Materials), Integral equations, Permeability, Fracture (Process), Reservoirs, Approximation, Floods, Fluid pressure, Petroleum extraction, Rocks, Theorems (Mathematics), Water
1.
Cleary
M. P.
,
1977
, “
Fundamental Solutions for a Fluid-Saturated Porous Solid
,”
International Journal of Solids and Structures
, Vol.
13-9
, pp.
785
–
806
.
2.
Clifton, R. J., and Abou-Sayed, A. S., 1979, “On the Computation of the Three-Dimensional Geometry of Hydraulic Fractures,” Paper SPE 7943 presented at the 1979 SPE symposium on low permeability gas reservoirs, Denver, May, pp. 20–22.
3.
Clifton, R. J., and Wang, J. J., 1991, “Modeling of Poroelastic Effects in Hydraulic Fracturing,” Paper SPE 21871 presented at the 1991 SPE Rocky Mountain Regional Meeting/Low-Permeability Reservoirs Symposium, Denver, Apr., pp. 15–17.
4.
Gradshteyn, I. S., and Ryzhik, I. M., 1965, Tables of Integrals, Series, and Products, Academic Press, New York.
5.
Hirth, J. P., and Lothe, J., 1982, Theory of Dislocations, John Wiley and Sons, New York.
6.
Kurashige, M., and Clifton, R. J., 1992, “Integral Equations for the Problem of a 3D Crack in an Infinite, Fluid-Filled, Poroelastic Solid,” SPE Production Engineering, Feb., pp. 34–38.
7.
Sneddon, I. N., 1951, Fourier Transforms, McGraw-Hill, New York.
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