MultiScale finite volume method for finite-volume based poromechanics simulations

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Abstract

We propose a multiscale finite volume method (MSFV) for simulation of coupled flow-deformation in heterogeneous porous media under elastic deformation (i.e., poroelastic model). The fine-scale fully resolved system of equations is obtained based on a conservative finite-volume method in which the displacement and pore pressure unknowns are located in a staggered configuration. The coupling is treated through a fully-coupled fully-implicit formulation. On this fully-coupled finite-volume system, coarse-scale grids for flow and deformation are imposed. Local basis functions for scalar pore pressure and vectorial displacement unknowns are then solved over their respective local domains at the beginning of the simulation, and reused for the rest of the time-dependent simulations. These local basis functions are then clustered to form the prolongation operator. As for the finite-volume nature of the proposed multiscale system, finite-volume restriction operators for poroelastic systems are utilised. Once the coarse-scale system is solved, its solution is prolonged back to the original fine-scale resolution, providing approximate fine-scale solution. The finite-volume multiscale formulation provides conservative stress andmass flux both at fine and coarse scale. Several numerical test cases are provided first to validate the fine-scale finite-volume discrete fully-implicit simulation, and then to investigate the accuracy of the proposed multiscale formulation. Our multiscale method allows for quantification of the elastic geomechanical behaviour with using only a fraction of the fine-scale grid cells, even for highly heterogeneous time-dependent models. As such, it casts a promising approach for field-scale quantification of the mechanical deformation and stress field due to injection and production in a subsurface formation. In order to extend the fine-scale finite volume (FV) framework for fractured media, we implement a discontinuity enriched FV method for mechanical deformation. We model fracture shear failure, based on static friction law. We demonstrate the results, obtained for a single fracture test case and show convergence of shear slip solution. The discontinuity enriched FV method is a basis for promising developments within a coupled flow-deformation framework for fractured reservoirs.