On the hydraulic fracture of poroelastic media

Abstract

The problems of quasi-static poroelasticity for stationary and extending cracks in an isotropic homogeneous medium are considered. The crack driving forces are caused by pressure of fluid injected inside the crack by external sources. Using simple and double layer potentials of poroelasticity, the problems are reduced to systems of 2D-integral equations on the crack surface. The integral equations contain operators with various time-asymptotics at infinity. Neglecting operators rapidly vanishing with time results in an approximate formulation of the crack problems. In this formulation, the process of filtration of fluid from the crack surface into the host medium is independent on the medium deformation. For numerical solution, the integral equations are discretized with respect to spatial and time variables. Examples of solutions of the filtration problem are presented for penny shape cracks with constant and extending radii. The three parameter model is used for simulation of hydraulic fracture crack propagation in poroelastic media. Time-dependencies of the crack radius, pressure distribution, and fluid flux on the crack surface are studied for various permeability parameters of the host medium.