Finite Volume Schemes for Multiphase Flow Simulation on Near Well Grids

In reservoir engineering a proper well modeling requires to simulate accurately multiphase flow taking into account the singular pressure distribution in the well vicinity and the large difference of scales between the wellbore radius and the reservoir dimension. This paper investigates the numerical simulation of a 3D near-well model using a radial mesh exponentially refined down to the well boundary. The radial and the reservoir CPG grids are matched using either hexahedra or both tetrahedra and pyramids. Various multipoint finite volume methods are compared such as the O and L schemes, and the newer G and GradCell schemes which are briefly described. Our first objective is to introduce a new scheme which includes the advantages of compact stencil, symmetry and convergence. Our second objective is to study the behavior of these schemes on the above two types of meshes. First, their convergence behavior are compared for the deviated well single-phase flow analytical solution described in the literature with an homogeneous anisotropic permeability tensor. Second, the influence of the type of mesh is studied on a CO2 injection test case in an aquifer with solubility of CO2 in the water phase and anisotropic permeability fields.