DERIVATION OF COUPLED INTEGRAL EQUATIONS FOR A 3-D PLANAR HYDRAULIC FRACTURE IN AN OIL-BEARING FORMATION

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To enhance the productivity of oil recovery, hydraulic fracturing treatment is applied to many production wells. Simulators of hydraulic fracturing (2-D ones in many cases) have been developed for a long time, in which only the isotropic elasticity of oil bearing formations has been taken into account but neither the diffusion of oil and fracturing fluid nor the anisotropy of almost all formations.Major objects of this research is to take into account the fluid diffusion in and the anisotropy of the formations when integral equations describing the mechanics of hydraulic fracturing are derived.We successfully obtained : 【○!1】 fundamental solutions for an infinite space of hydraulically transverse is otropy but elastic isotropy, by usig the conventional Fourier and Laplace transformations, 【○!2】 fundamental solutions for a hydraulically as well as elastically transverse isotropic poroelasticity, by resorting to the Kuprae's method, 【○!3】 coupled integral equations for a 3-D crack in a fluid-saturated poroelastic infinite space of transversely isotropic permeability, and 【○!4】 coupled integral equations for a planar crack subjected to arbitrary loadings.