Rigorous modeling of coupled flow and geomechanics in largely deformable anisotropic geological systems

Copyright 2016 ARMA, American Rock Mechanics Association. We propose and investigate formulation and numerical simulation for largely deformable anisotropic reservoirs in this study. We employ the total Lagrangian method (TL) for coupled flow and geomechanics, which does not need to update the coordinate system each time step. The use of the deformation gradient as well as the first and second Piola stresses reflects the change of reservoir configuration, being mathematically equivalent to the updated Lagrangian method. To accurately model full-tensor permeability derived from the Piola transformation in permeability, we use the multi-point flux approximation (MPFA). The total Lagrangian method with MPFA can provide high accurate and rigorous modeling. We thus consider the total Lagrangian method with MPFA as the reference method in this study. Then, we compare it with two other methods: Total Lagrangian method with the two-point flux approximation (TPFA) and infinitesimal transformation assumption with TPFA. From numerical simulation, we find differences between the reference method and the other two methods. Displacement based on the assumption of the infinitesimal transformation is different from that of the total Lagrangian method. Also, we find that volumetric strain and pressure of TL-MPFA are different from those of TL-TPFA. As the anisotropy ratio of permeability increases, the errors between MPFA and TPFA increases.

Rigorous modeling of coupled flow and geomechanics in largely deformable anisotropic geological systems Conference Paper