Applications of phase-field modeling in hydraulic fracture
Creators: name: Alotaibi, Talal Eid
Publisher: name: The University of Texas at Austin
Year: 2019
Subjects: Phase-field modeling
Hydraulic fracture
Fracture mechanics

description: Understanding the mechanisms behind the nucleation and propagation of cracks is of considerable interest in engineering application and design decisions. In many applications in the oil industry, complicated 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 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 gain insights into the propagation behavior of fluid-injected cracks. One outstanding issue with phase-field fracture models is the decomposition of the strain energy required to ensure that compressive stress states do not cause crack propagation and damage evolution. In the present study, the proper representation of the strain energy function to reflect this fracture phenomenon is examined. The strain energy is constructed in terms of principle strains in such a way that it has two parts; the tensile and the compressive. A degradation function only applies to the tensile part enforcing that the crack is driven only by that part of the strain energy. We investigated the split operator proposed by Miehe et al. [1], and then proposed a split approach based on masonry-like material behavior [2, 3]. We have found that when using Miehe’s form for the strain energy function, cracks can propagate under compressive stresses. In contrast, the approach based on a masonry-like materials constitutive model we proposed ensures that cracks do not grow under compressive stresses. To demonstrate the capabilities of phase-field modeling for fluid-driven fractures, four general types of problems are simulated: 1) interactions of fluid-driven, natural, and proppant-filled cracks, 2) crack growth through different material layers, 3) fluid-driven crack growth under the influence of in-situ far-field stresses, and 4) crack interactions with inclusions. The simulations illustrate the capabilities of the phase-field model for capturing interesting and complex crack growth phenomena. To understand how fluid-driven cracks interact with inclusions, AlTammar et al. [4] performed experiments. Three tests with tough inclusions were performed to understand the effects of orientation angle, thickness, and material properties. Additionally, one test with a weak inclusion was performed to compare the results with those of the tough inclusion cases. The experiments show a clear tendency for the fluid-driven hydraulic fracture to cross thick natural fractures filled with materials weaker and softer than the matrix and to be diverted by thick natural fractures with tougher and stiffer filling materials. To replicate these experiments numerically and to gain a mechanistic understanding, in the present study, we ran simulations using phase-field modeling. Results from both the experiments and the simulations provide clear evidence that inclusion width, angle, material properties, and distance from the injection point affect the outcome of the crack evolution. Phase-field modeling was able to capture the trends of crack deflection/crossing in all the test cases. Finally, we extended the phase-field model has been extended to three dimensions and tested it on bench-mark problems. The first bench-mark problem is a compact test for a CT specimen. In this problem, the mechanical equations are only considered. The simulation shows that the CT specimen is split into two symmetric parts. The second bench-mark problem is a fluid-driven circular crack. The simulation for this problem shows that the crack grows in a radial direction.