On the Implementation of the Planar3D Model Using the Explicit Time Integration Scheme and the Statistical Front Tracking Method

Nowadays, the relevance of problems associated with mathematical modelling of the propagation of hydraulic fractures is growing. In this paper, we consider a Planar3D plane crack model using the explicit numerical integration scheme over time to calculate the dynamics of crack propagation in a multilayer medium. When conducting numerical modelling, the key task is to ensure the speed of calculations while maintaining the stability of the calculation scheme. The present work is devoted to modelling the hydraulic fracturing of a layered formation under the influence of nonuniform injection of non-Newtonian fluid. We present the medium in the form of a set of horizontal layers, each of which is characterized by its own values of minimum compressive stress, toughness and leakage coefficient. To determine the geometry of the crack, we solve the front velocity equation and use universal asymptotes and the explicit time integration scheme.