Modeling of hydraulically induced fractures in elastic‐plastic solids

Abstract

Fracking, i.e. inducing fractures by hydraulic means, is a technique used for extraction of gas and petroleum from rock formations in the subsurface. Thereby a well is stimulated via fractures induced by a pressurized fluid which is injected into the wellbore. This leads to an increased permeability within the deep‐rock formations and finally to an increased flow of petroleum and natural gas out of the well. Because of its risks due to environmental issues, such as increased seismic activity or drinking water contamination, this technique is highly controversial in many countries. Numerical simulations can be used to gain a profound understanding of the involved physical processes leading to more precise estimates of associated risks and potentials. Of course, reliable numerical simulations must be based on accurate models and stable algorithms. Many of the existing models for hydraulically induced fractures are based on the assumption that the solid skeleton undergoes only non‐dissipative elastic deformations. However, there is experimental evidence that field measurements (e.g. net pressure) cannot be described with an elastic material law [1]. Hence we propose a framework that accounts also for dissipative plastic deformations within the solid skeleton. The elastic‐plastic material behavior is described by a Drucker–Prager‐type plasticity model based on [2,3]. It is linked to an elastic‐plastic failure criterion that drives the fractures. The fractures in turn are modeled by a phase‐field approach characterizing a regularization of a crack surface that converges for vanishing length‐scale parameter to a sharp crack [4]. Fluid contribution and interaction are incorporated by a Darcy–Biot‐type constitutive formulation [5]. By means of a representative numerical example the model capabilities are demonstrated.