A multi-resolution multiscale finite volume method for simulation of fluid flows in heterogeneous porous media

This paper presents an extension of the multiscale finite volume (MsFV) method to multi-resolution coarse grid solvers for single phase incompressible flows. To achieve this, a grid one level coarser than the coarse grids used in the MsFV method is constructed and the local problems are redefined to compute the basis and correction functions associated with this new grid. To construct the coarse-scale pressure equations, the coarse-scale transmissibility coefficients are calculated using a new multi-point flux approximation (MPFA) method. The estimated coarse-scale pressures are utilized to compute the multiscale pressure solution. Finally a reconstruction step is performed to produce a conservative velocity field which is used to solve the transport equations. The computational cost of the proposed method is compared with that of the MsFV method and the relevant time complexity formulas are given. Several two-dimensional test cases with permeability fields ranging from two-scale to multi-scale problems are solved. The performance of the proposed method in handling problems with shale layers or discrete fractures is assessed. Also, a number of layers from the tenth SPE comparative study problem are used to examine general abilities of the method when facing realistic reservoir problems. The results are compared with fine-scale reference solutions to assess the accuracy of the proposed method.