Integral Equations for a 3D Crack in a Fluid-Saturated Poroelastic Infinite Space of Transversely Isotropic Permeability

(Case of Anisotropy Axis Perpendicular to Crack Face)

Abstract

A pair of integral equations are derived for a non-uniformly pressurized vertical planar crack of arbitrary shape in a fluid-saturated, poroelastic, infinite space of transversely isotropic permeability with its anisotropy axis perpendicular to the crack surface, by using the fundamental solutions obtained in a previous paper and the concept of a dislocation segment. This anisotropy assumption is more realistic for many oil reservoirs. The equations obtained relate normal tractions and fluid pressure on the crack faces to crack opening gradients and fluid injection rate per unit fracture area nad include the known integral equations for an isotropic permeability as a limiting case. These integral equations are intended to be implanted in a 3D hydraulic fracturing simulator.