A practical numerical simulator for three-dimensional fracture propagation in heterogeneous media

A numerical simulator capable of predicting fracture geometries during propagation in both height and length directions has been developed. The simulator is capable of handling random spatial variations in elastic properties, confining stress, pore pressure, and rock strength. Fracture fluid pressures, fracture widths, and net stresses are calculated at uniformly spaced points over the entire fracture face. The solution of the problem combines a finite difference formulation for calculation of fluid flow within the crack with an integral equation for fracture width. The fracture width equation is based on the work of I. N. Sneddon, but eliminates some of the simplifying assumptions he introduced. Results of simulation of laboratory fractures under various stress conditions are presented. The effects of varying rock properties and stresses on fracture containment are shown. The general nature of the formulation, with its flexibility in handling any number of randomly arranged rock formations, is ideal for application of the simulator to the prediction of hydraulic fracture geometries under field conditions. Input and output of the model are easily comprehensible and convenient to the user.