Nonlinear Two-Point Flux Approximations for Simulating Subsurface Flows with Full-Tensor Anisotropy

Full-tensor anisotropy effects are often encountered in subsurface flow due to either grid nonorthogonality or permeability anisotropy. A multipoint flux approximation (MPFA) is generally needed to accurately simulate flow for such systems, though the resulting discrete system is more complex and may be less robust than that resulting from a two-point flux approximation (TPFA). In this paper, we present and apply a different approach, nonlinear two-point flux approximation (NTPFA), for modeling systems with full-tensor effects and grid nonorthogonality. NTPFA incorporates global flow into the determination of the two-point flux transmissibilities, which is analogous to the use of two-point flux transmissibility in global and local-global upscaling procedures. For a given flow scenario, the global MPFA solution can be used to compute the two-point flux transmissibility, leading to a global NTPFA scheme. To avoid solving the full global MPFA system, we have also developed a local-global NTPFA procedure, in which the global flow is approximated by local MPFA solutions iteratively coupled with a global TPFA solution. The NTPFA methods described here are applied to 2D parallelogram grids, heterogeneous full-tensor permeability fields, and a 3D multiblock model with grid nonorthogonality. Results from both NTPFA schemes are generally in close agreement with the MPFA solution and provide considerable improvement over the standard TPFA scheme.