Numerical solution of plane hydrofracture problem in modified formulation under arbitrary initial conditions

Abstract

The solution to a hydraulic fracture problem for the model of Khristianovich–Geertsma–de Klerk is obtained on the basis of the modified formulation of the problem, which, in contrast with the conventional approach, employs the particle velocity rather than the flux. This served to complement the system of ordinary differential equations, resulting after spatial discretization, with the speed equation. The complete system is solved by the Runge–Kutta method for arbitrary initial conditions. The decaying influence of the initial conditions on key characteristics of a fracture (opening and length) at the end of a treatment, is established and numerically analyzed.