An integral method for predicting hydraulic fracture propagation driven by gases or liquids

Hydraulic fracture propagation is predicted by a general numerical procedure which satisfies the transport equations in a global or integral sense over the entire fracture and over a small control volume near the leading edge. At each discrete time step the pressure distribution is selected from a four-parameter family of profiles such that the stress intensity is equal to the critical value at the tip of the fracture and the integral equations are satisfied. Comparisons with previous analytical and, numerical solutions indicate accuracy within 10 per cent for a variety of test problems include wedge-shaped and envelope-shaped fractures, laminar and turbulent flows, incompressible liquids and ideal gases, permeable and impermeable media, prescribed inlet pressure and prescribed flow rates. CPU time is typically a few seconds for a tenfold increase in fracture length. The method has been applied to explosively driven and propellant-driven gas fracturing problems as well as the traditional pump-driven hydraulic fracturing problem.