The Cross-Sectional Shapes of Longitudinal Hydraulic Fractures

A mathematical formulation has been developed for calculating the cross-sectional shape of hydraulic fractures. This formulation treats the problem as a free-boundary-type problem and is modeled after mathematical formulations developed for contact and lubrication problems. Numerical solution of the resulting equations has been used to address problems involving particularly difficult in-situ stress distributions, including problems in which the fracture breaks through high-stress barriers. The technique is illustrated on two example problems.