Modeling the connectivity and intersection of hydraulically loaded cracks with in situ fractures in rock

Summary The interaction of an advancing hydraulically loaded crack and in situ fracture network can yield highly complex patterns. We model the connectivity of cells in a finite element domain and in a fracture network by a simplicial complex data structure. The complete adjacency information between cells is determined by one level down facet and one level up cofacet neighborhood information. Combined with a disjoint set data structure, explicit algorithms are derived to efficiently track network connectivity and load transfer between independent fracture sets. We also propose an approach to regularize the application of hydraulic load to newly intersected in situ cracks to smoothen the transition of pressure on intersected cracks from ambient to hydraulic pressure and to avoid the sudden loading of the entire length of these cracks. Numerical results demonstrate the performance of crack connectivity and load transfer models and the effect of regularization model. The results show that as the angle between an incoming hydraulically loaded crack and an in situ crack increases, the effect of in situ crack shifts from slight realignment to diversion/offsetting of the loaded crack. As the angle difference approaches the normal angle, the loaded crack tends to penetrate through the in situ crack. The proposed schemes are also used for transient simulation of 2D reservoirs with multiple perforations surrounded by in situ cracks with and without a bias in the distribution of their orientation. It was shown that from 2 perforations with angles closer to in situ cracks at low loading rates to all perforations at higher loading rates can result in active hydraulic crack propagation. The h‐adaptive method of asynchronous space‐time discontinuous Galerkin method is used to exactly track complex fracture patterns in these dynamic fracture simulations.