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 permeabillty by using the fundamental solutions obtained in a previous paper and the concept of a dislocation segment. The transverse isotropy with its axis being vertical is a more realistic model for oil/gas 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 and include the known solutions for the isotropic case and for the case of zero permeability in one direction as limiting cases. These integral equations are intended to be implanted in a 3D hydraulic fracturing simulator.
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