A numerical simulation method applicable to staggered grids for two-phase reservoir flow problems

This paper studies the computational performance of the mimetic finite difference (MFD) method in staggered grids. First, the MFD discretization format of the mass conservation equation within each grid in staggered grids is derived. How to handle the distribution of each grid edge in the case of staggered grids and the flux continuity condition of each edge are clarified. Then, a fully implicit format is adopted to form a global equation system to simultaneously calculate the average water saturation of each grid, the pressure at the center of each grid, and the pressure values at the center of each grid edge. We implemented three numerical examples and verified that the MFD method can obtain simulation results very similar to the reference solutions using Cartesian grids in the cases of different types and degrees of staggered grids, anisotropic full-tensor permeability, and irregular computational domains, thus having reliable computational accuracy. In addition, the staggered grids do not increase the number of Newton iteration steps required by the nonlinear solver, but only slightly increase the computational time due to the increase in the bandwidth and dimension of the global equation system, while achieving a significant flexibility advantage in the discretization of the computational domain.