Simulation of the hydraulic fracture process in two dimensions using a discrete element method

We introduce a discrete element simulation for the hydraulic fracture process in a petroleum well which takes into account the elastic behavior of the rock and the Mohr-Coulomb fracture criterium. The rock is modeled as an array of Voronoi polygons joined by elastic beams, which are submitted to tectonical stresses and the hydrostatic pressure of the fracturing fluid. The fluid pressure is treated like that of a hydraulic column. The simulation reproduces well the time and dimensions of real fracture processes. We also include an analysis of the fracturing fluid loss due to the permeability of the rock which is useful in an efficiency analysis of the treatment. The model is a first step for future applications in the petroleum industry.