Advancing Predictive Capability for Brittle Failure Using Dynamic Graphs

1. After the breakthrough in the modeling of hydraulic fracture process in shale, published in January 2019 in PNAS, it is necessary to extend these results in several ways. One proposed extension will be to include in the hydraulic crack system vertically inclined shear cracks in the model. This will a problem both for programming and physical modeling: a) The programming will require extending the crack band concept from quadrilateral to triangular elements in 2D, and tetrahedral elements in 3D. b) The physical modeling will involve formulation of the opening and slip of a shear crack. A frictional slip law, in which the opening of the shear crack is propped by asperities, and the shear stress on the crack drops to the sliding friction value, will be formulated. The filling of these shear cracks by viscous flow of the fracking water will have to be modeled as well. 2. Further it is proposed to work on extending the computational model in two ways: a) First, the simulations need to be generalized to full three dimensions, including independent propagation of the vertical hydraulic cracks in both the horizontal and vertical directions, and instructing a full three-dimensional permeability matrix for the flow of fracking water along the cracks. The permeable weak layers with orientation dependent Biot coefficient, paralleling the natural cracks, will have to be generalized to three dimensions as well, and so will the diffusion of water through the microcracks in these layers. 3. Next, a major challenge is how to scale the model published in PNAS to the full scale of a fracking stage, typically 70 m x 150 m x 500 m. Using the same method as we did in PNAS, it would be a problem with several billion unknowns. It is necessary to develop some methods of “reduced-order” to much larger finite elements. 4. After completing the model to be able to simulate hydraulic fracturing process in full scale, the possible methods to improve the production rate of fracking process can be studied. Especially, the effect of different pumping and of pulses in the pressure of fracking fluid can be analyzed to find the best fracking strategy for different wells with different geological features. 5. Finally, the Northwestern researchers will collaborate with LANL in the planning and evaluation of the experiments demonstrating the branching of hydraulic cracks propagating under fluid pressure into preexisting perfectly closed fractures that simulate natural fractures in the shale mass. This will consist of analytical modeling and simulations.