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

为了提高原油采收率，许多威尔斯生产井都采用了水力压裂技术。水力压裂模拟器（在许多情况下是二维的）已经开发了很长时间，其中只考虑了油层的各向同性弹性，而没有考虑油和压裂液的扩散，也没有考虑几乎所有地层的各向异性。本文的主要目的是在考虑流体在地层中的扩散和地层的各向异性的情况下，用积分方程描述地层的各向同性弹性，并考虑流体在地层中的扩散和地层的各向异性。成功地得到了：[○！1]利用传统的Fourier变换和拉普拉斯变换，得到了无限大水力横截面各向异性而弹性各向同性空间的基本解，[○！2]基本解水力以及弹性横观各向同性孔隙弹性，通过诉诸Kupperten的方法，[○！3]耦合积分方程的三维裂纹在流体饱和多孔弹性无限空间的横观各向同性渗透率，和[○！4]任意载荷作用下平面裂纹的耦合积分方程。

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.