Multiscale Finite Volume Method For Finite-Volume-Based Poromechanics Simulations

Accurate reservoir simulations that quantify mutual effect of reservoir flow and mechanical deformation demand for large-scale heterogeneous computational models: while fluid flow occurs inside heterogeneous reservoirs, stress and deformation fields span the entire geological domain. A conservative nature of mass and momentum balance governing equations motivates a locally conservative representation of the unknowns in discrete space. Accurate simulation of these large-scale heterogeneous coupled phenomena with sufficient resolutions remains computationally challenging for state-of-the-art simulators. To resolve this challenge, we develop the first multiscale finite volume (FV) method for elastic poromechanics model, where the displacement-pressure system is solved fully implicitly using finite volume method. This finite volume discrete fine-scale system is obtained based on the Biot’s theory. Independent coarse grids for flow and deformation are imposed on this fine-scale computational domain, allowing for targeting larger domains for mechanical deformation simulations. Fully implicit coarse-scale quantities are obtained via sets of local basis functions, for both flow and deformation unknowns. These basis functions are calculated once at the beginning of the simulation, and are re-employed to construct and solve the coarse-scale systems during the entire simulation. The coarse-scale solution is interpolated to the fine scale using the same basis functions. This method provides stable (fully implicit), efficient (multiscale), and locally conservative (FV for all unknowns) solution for the coupled flow-deformation system of equations. We study several test cases, including benchmarking ones, to illustrate consistency, order of accuracy, convergence, and applicability of our method. Importantly, we show that our multiscale method allows for quantification of the geomechanical behavior with using only a fraction of the fine-scale grid cells, even for highly heterogeneous time-dependent models.