| A computer model was developed for describing the propagation of hydraulically induced fractures. In this model, the fracture was treated as a planar fracture of arbitrary shape in an infinite elastic medium, and the influence of in-situ stress and other reservoir conditions on the propagation of fracture was considered.;The integral equation, which relates the fracture opening displacement to the fluid pressure on the fracture surfaces, is a two dimensional Cauchy singular integral equation. In order to achieve numerical accuracy and efficiency, a new method for obtaining a solution from this equation was developed. The Cauchy integral in the equation was transformed to a singular integral with a removable singularity by formulating the equation in a weak form. The fluid flow equation and the fracture opening displacement equation were then solved numerically by applying the finite element method and an iterative method. The moving fracture front was treated by assuming a successive stationary front which was followed by an incremental fracture extension. The incremental fracture front extension was calculated by comparing the calculated stress intensity factors along the fracture front with the critical stress intensity factor of the rock medium.;The numerical method was proven to be accurate and efficient. The calculated dimensions for propagating circular fractures were compared with those calculated from the Geertsma formulas. A good agreement was noted. The characteristics of fracture propagation under different reservoir conditions were presented and discussed. |
