A Variational Approach to the Prediction of the Three-Dimensional Geometry of Hydraulic Fractures

Abstract

ABSTRACT A computational method is outlined for modeling the three-dimensional development of hydraulic fractures due to the injection of a non-Newtonian fluid at the well bore. The rock formation is modeled as an infinite, homogeneous, isotropic, clastic solid with in situ stresses that vary with depth. This three-dimensional problem is made two-dimensional by reducing the elasticity problem to an integral equation that relates pressure on the crack faces to crack openings and by neglecting the component of the fluid velocity in the direction perpendicular to the fracture plane. Variational principles are used to derive the discrete form of the governing equations that are used for the computations. Preliminary computations indicate that the essential features of the approach are suitable for use in a numerical method for predicting the three-dimensional geometry of an advancing crack.