Three-Dimensional Crack Propagation Algorithms Based on Universal Meshes and their Application to Fracking

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Accurate prediction of when and how a crack will grow and propagate through a rock formation is an important yet unsolved problem in engineering. Crack growth and prediction models guide the design of strategies to frack oil and gas reservoirs and to inject fracking fluids and waste water back underground, and help assess the resulting seismicity. Crack growth models are also used in evaluating the stability of reservoirs for carbon sequestration, and in the engineering of geothermal reservoirs. Additionally, they play an important role in developing understanding of geophysical phenomena, such as volcanic eruptions and fracture of glaciers. This award supports fundamental research to formulate and implement numerical algorithms and methods to simulate the propagation of cracks through structures and underground rocks. The outcomes of this project will reduce the predictive uncertainty to the understanding of the physics and the structure of the rock being fractured. It will alleviate or remove uncertainties associated with the computational methods. By improving the way such predictions are made, the project has the potential to impact energy production and associated concerns for years to come. Additionally, this project will train a graduate student in an area in which experts are highly sought, as well as involve undergraduate students from predominantly underrepresented minority institutions, training and exposing them to research in engineering. To attain control of the numerical errors associated with simulating the propagation of cracks, this project will combine three novel developments. First, the formulation of a robust algorithm to deform a single background mesh of tetrahedra so that it exactly meshes every cracked geometry obtained as the fracture propagates in three dimensions. Such mesh is called a universal mesh. Second, the formulation of a class of numerical methods that enable the computation of stress intensity factors along a crack front with high-order of accuracy. Third, the creation of an algorithm to compute convergent evolution of brittle and hydraulic fractures in three dimensions. Working jointly, the universal mesh algorithm and the high-order method should enable the computation of very accurate crack evolutions without constant re-meshing around the crack front.