Coupling of meshfree peridynamics with the Finite Volume Method for poroelastic problems

Peridynamics is a non-local theory of continuum mechanics that has been developed primarily for understanding material failure due to different mechanisms, including fluid-driven crack propagation during hydraulic fracturing of subsurface reservoirs. Because of its non-local nature, this theory is computationally expensive. To improve its performance, a scheme was recently proposed for coupling Peridynamics (PD) with less expensive Finite Element Method (FEM) for static equilibrium problems. This scheme has been adapted in the current paper to couple a PD-based poroelastic model with the Finite Volume Method (FVM) for simulating problems in porous media. Coupling is implemented by dividing the computational domain into two subdomains, one of which is discretized and solved with PD and the other with FVM. The formulation is developed for porous flow involving fluid mass balance and is extended for poroelastic problems to include rock momentum balance. The coupled model is verified against the analytical solutions to classical problems. No spurious behavior is observed near the PD-FVM interface region. Improvements in computational performance over the pure PD model are demonstrated. Moreover, due to differences in the sparsity patterns and the magnitudes of PD and FVM transmissibility/Jacobian terms, it is shown that appending the PD equations after all the FV equations in the global matrix has additional computational benefits.