Phase-Field Modeling of Hydraulic Fracture Propagation in Mechanically Heterogeneous Formations

Abstract

Understanding the mechanisms behind the nucleation and propagation of cracks is of considerable interest in engineering applications and design decisions. In hydraulic fracturing treatments of unconventional formations, complex hydraulic fracture geometries and propagation behaviors are encountered. As a result, the development of modeling approaches that can capture the physics of non-planar crack evolution while also being computationally tractable is a critical challenge. The phase-field approach to fracture has been shown to be a powerful tool for simulating very complex fracture topologies, including the turning, splitting, and merging of cracks. In contrast to fracture models that explicitly track the crack surfaces, crack propagation and the evolution thereof arise out of the solution to a partial differential equation governing the evolution of a phase-field damage parameter. As such, the crack growth emerges naturally from solving the set of coupled differential equations linking the phase-field to other field quantities that can drive the fracture process. In the present model, the physics of flow through porous media and cracks is coupled with the mechanics of fracture. Darcy-type flow is modeled in the intact porous medium, which transitions to a Stokes-type flow regime within open cracks. This phase-field model is implemented to investigate how fluid-driven cracks interact with material interfaces. The problem of an induced hydraulic fracture interacting with a layer possessing contrasting mechanical properties is studied. Several factors that influence the fracture behavior when encountering such a layer are presented in the simulations. Simulation results have shown that a very tough layer has the ability to deflect the induced fracture. Interestingly, the contrast in the modulus of elasticity of the layer relative to the matrix is not sufficient to make the layer act as a barrier in the absence of a contrast in the layer toughness. Additionally, a layer with a steep orientation relative to the crack direction has less of a tendency to deflect the fracture. Also, a thicker layer has a greater tendency to deflect the induced crack than a thin layer. Finally, it appears that the distance between the injection point and the layer does not play a significant role in deflecting the fracture.