A novel stabilized NS-FEM formulation for anisotropic double porosity media

Abstract

Self-consistent extension of linear poroelasticity to overlapping scales of porosity within fluid-saturated anisotropic materials is developed. The coefficient matrix of poromechanical properties considering anisotropy is firstly derived from the corresponding intrinsic properties of its single porosity constituents. The momentum supply term arising from the mass transfer is also quantitatively analyzed. To provide further insight into the theory, numerical values of the poroelastic coefficients are calculated for sandstone that are consistent with the material parameters reported by prominent authors. Then, the node-based smoothed finite element method (NS-FEM) is extended to implement the coupled double porosity flow and deformation formulation. In order to provide numerical stability and accuracy, a modified nodal integration scheme based on multiple stress points over the smoothing domain (SD) and the polynomial pressure projection (PPP) scheme are further implemented in the NS-FEM. Next, four benchmark tests are simulated and compared with reference solutions, based on which the correctness of the proposed NS-FEM formulation is verified and the generalizability of the derived anisotropic double porosity model is confirmed. Finally, the elastoplastic response of double porosity media is investigated, including the impact of permeability anisotropy, the impact of permeability contrast, and the impact of strain-softening.