Advancing fractures during the hydraulic fracturing process can produce complicated growth pattern when propagating in a pre-exiting natural fracture network. A proper network representation for simulating pressure-driven and natural fracture interactions is crucial as these occurrences may result in significant diversion of fracture paths which potentially generate difficulties in proppant transport and ineffectiveness of the treatment. In this study fracture network and propagation patterns are modeled with a simplicial complex network representation and geometrical information are analyzed with a graph theoretic approach. In conjunction with graph theoretic algorithms, a disjoint-set data structure is employed to track fracture connectivity, dynamic hydraulic load advancing in the fracture network and load transfers between independent sets of fractures. This permits imposing independent loading conditions for arbitrary sets of fracture sets. The procedure is implemented in a spacetime discontinuous Galerkin finite element scheme, whose efficiency and accuracy are very important for the type for fracture simulations considered herein. In addition, the SDG method's powerful mesh adaptive operations enable direct tracking of arbitrary crack propagation patterns. Numerical results, of the dynamics problem solution, from various crack configurations and loading conditions will be presented which can have applications in the stability analysis of natural faults close to hydraulic fracturing reservoirs. For all case studies, the rock matrix domain is subject to confinement (compressive) stress conditions on the boundary; the simplicial complex network is capable to incorporate the connectivity of the main crack with natural fissures and microcracks that are generated due to dynamic loading.


Among the variety of ubiquitous engineering applications of the hydraulic fracturing process, the most common representation is within the energy industry; this involves the treatment of tight geological formations by inducing hydro-fractures into natural fracture networks to enhance the production rate of low-permeability reservoirs. To increase the efficiency of this costly process, it is essential to understand the mechanisms involved which can be difficult due to complex fracture networks both natural and created by the hydraulic fracture process. An accurate representation of the hydraulic and natural fracture network is insightful in determining: i) mechanics of applying hydraulic load during the treatment process, ii) the mechanical properties and mechanical integrity of the rock matrix and reservoir, and iii) the reservoir product yield (e.g., hydrocarbon recovery).

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