Enhanced Nonlinear Finite Volume Scheme for Multiphase Flows

We present the latest enhancement of the nonlinear monotone finite volume method for the near-well regions. The original nonlinear method is applicable for diffusion, advection-diffusion and multiphase flow model equations with full anisotropic discontinuous permeability tensors on conformal polyhedral meshes. The approximation of the diffusive flux uses the nonlinear two-point stencil which reduces to the conventional two-point flux approximation (TPFA) on cubic meshes but has much better accuracy for the general case of non-orthogonal grids and anisotropic media. The latest enhancement of the nonlinear method takes into account the nonlinear (e.g. logarithmic) singularity of the pressure in the near-well region and introduces the nonlinear correction to improve accuracy of the pressure and the flux calculation. The new method is generalized for anisotropic media, polyhedral grids and nontrivial wells cases. Numerical experiments show the noticeable reduction of the numerical errors compared to the original monotone nonlinear FV scheme with the conventional Peaceman well model and even with the given analytical well rate.