On the Computation of the Three-Dimensional Geometry of Hydraulic Fractures

Abou-Sayed, A.S., and Clifton, R.J.
Presented at: SPE/DOE Symposium of Low-Permeability Gas Reservoirs, Denver, Colorado, May 20-22, 1979.


A computational method is outlined for modelling the three-dimensional development of hydraulic fractures due to the injection of a non-Newtonian fluid at the well bore. The rock formation is modelled as an infinite, homogeneous, isotropic, elastic solid with in situ stresses that vary with depth. The three dimensional problem is made two-dimensional by assuming that the velocity profile through the thickness of the crack opening is the same as for flow between parallel plates and by reducing the elasticity problem to an integral equation that relates pressure on the crack faces to crack openings. Crack openings for a given crack geometry and pressure distribution are obtained by using properties of two-dimensional Chebyshev polynomials to properties of two-dimensional Chebyshev polynomials to facilitate inversion of the integral equation. Two-dimensional fluid flow between the crack faces is analyzed using a finite element method.