Modeling compressible gas flow in anisotropic reservoirs using a nonlinear finite volume method

A nonlinear two-point flux approximation (NTPFA) finite volume method is applied to the modeling of compressible gas flow in anisotropic reservoirs. Gas compressibility factor and gas density are calculated by the Peng-Robinson equation of state. The governing equations are discretized by NTPFA in space and first-order backward Euler method in time. Newton-Raphson iteration is used as the nonlinear solver during each time step. The NTPFA method employs the harmonic averaging points as auxiliary points during the construction of onesided fluxes. A unique nonlinear flux approximation is obtained by a convex combination of the one-sided fluxes. Since a Newton-Raphson nonlinear solver is used, NTPFA will have a denser discretized coefficient matrix compared to the widely used Two-Point Flux Approximation (TPFA) method on grids that are not K-orthogonal. However, its coefficient matrix is still much sparser than the classical Multi-Point Flux Approximation O (MPFAO) method. Results of numerical examples demonstrate that the pressure profile and gas production rate of NTPFA is in close agreement with that of MPFA-O for most cases while TPFA is inconsistent since the grid is not Korthogonal. The MPFA-O method is well known to suffer from monotonicity issues for highly anisotropic reservoirs and our numerical experiments show that MPFA-O can fail to converge during the Newton-Raphson iterations when the permeability anisotropy is very high while NTPFA still enjoys good performance.