Growth of a hydraulically pressurized fracture

A general formulation for hydraulic fracture in an elastic medium is presented. The analysis develops the governing equations, initial conditions, boundary conditions and solution process. A complete numerical analysis for the axially symmetric case is presented and an index M, which is related to solution stability, is found. For small values of M, the prevailing method of using an equivalently constant fluid pressure proves to be a very good approximation. For this case, the equations for the fluid become unnecessary to solve and the initial conditions are relatively unimportant.