A fully implicit mimetic finite difference scheme for general purpose subsurface reservoir simulation with full tensor permeability

• Published in: Journal of computational physics 2020-04, Vol.406, p.109194, Article 109194
• Main Authors: Abushaikha, Ahmad S., Terekhov, Kirill M.
• Format: Article
• Language: English
• Subjects: Computational physics; Computer simulation; Cubic equations; Discretization; Finite difference method; Finite element method; Fully implicit; Mass balance; Mathematical analysis; Mimetic finite difference; Mixed formulation; Newton-Raphson method; Permeability; Reservoir simulation; Reservoirs; Robustness (mathematics); Tensor permeability; Tensors; Unstructured grids; Unstructured grids (mathematics)
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2019.109194

•Fully-implicit temporal discretization for mimetic finite difference (MFD) method.•Numerical analysis of MFD versus TPFA and MPFA schemes.•Measure the method's performance for full tensor permeability applications.•Application of MFD for challenging and realistic full tensor permeability and unstructured grids cases. In the previous article Abushaikha et al. (2017) [1], we presented a fully-implicit mixed hybrid finite element (MHFE) method for general-purpose compositional reservoir simulation. The present work extends the implementation for mimetic finite difference (MFD) discretization method. The new approach admits fully implicit solution on general polyhedral grids. The scheme couples the momentum and mass balance equations to assure conservation and applies a cubic equation-of-state for the fluid system. The flux conservativity is strongly imposed for the fully implicit approach and the Newton-Raphson method is used to linearize the system. We test the method through extensive numerical examples to demonstrate the convergence and accuracy on various shapes of polyhedral. We also compare the method to other discretization schemes for unstructured meshes and tensor permeability. Finally, we apply the method through applied computational cases to illustrate its robustness for full tensor anisotropic, highly heterogeneous and faulted reservoirs using unstructured grids.