A Multiscale Finite-Volume Framework for Modeling Multiphase Flow
A multi-scale finite-volume (MSFV) method for solving multiphase flow
problem in highly heterogeneous media was recently developed. In
contrast with classical upscaling techniques, the goal of multiscale
methods is not simply to capture the large-scale effects of the
fine-scale heterogeneity, but to provide an efficient tool for solving
large flow problems with fine-scale resolution.
The MSFV is based on a fractional flow formulation of the problem:
first an equation for the total velocity is solved, then a fine-scale
velocity field is reconstructed, finally the phase-saturation
distribution is obtained by solving the nonlinear transport equations.
In addition to the original fine grid the MSFV method employs an
imposed coarse grid and a dual coarse grid. The first step is to
compute the effective parameters that have to be used for solving the
global flow problem on a coarse grid. This is done by means of a set of
basis functions, which are numerical solutions computed on the cells of
the dual grid. From these basis functions, the fluxes across the
coarse-block boundaries are computed and the transmissibilities are
extracted. Then the conservative fine-scale total-velocity field is
reconstructed by solving a local flow problem in each coarse cell.