Abstract

Abstract An infinite homogeneous, isotropic and elastic medium with a penny-shapedhydraulic fracture is considered. The hydraulic fracture is subjected to the pressure of fluid injectedfrom its center with a positive injection rate. Description of the hydraulic fracture growth is based on the lubrication equation (balance of the injected fluid and the crack volume), equation for hydraulic fracture opening caused by fluid pressure on the hydraulic fracture surface, the Poiseullie equation related local fluid flux with the hydraulic fracture opening and the pressure gradient and classical criterion of hydraulic fracture propagation from lineal elastic fracture mechanics. The hydraulic fracture growth is simulated by a discrete process consisting of three basic stages: increase of the hydraulic fracture volume by a constant hydraulic fracture size, hydraulic fracture jump to a new size defined by the fracture criterion, and filling of the new appeared hydraulic fracture volume by the fluid. It is shown that the model results in a reasonable dependence of the hydraulic fracture radius with time as well as the pressure distribution on the hydraulic fracture surface. Comparisons withother solutions of hydraulic fracture problems for penny-shaped geometry existing in the literature are presented. The model is applied to the case of media with leakoff, and numerical examples of hydraulic fracture propagation with the leakoff effect are presented.

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