Modified Multiscale Finite Volume Method for Two Phase Flow in Porous Media

Abstract

Multiscale finite volume (MSFV) method have been developed and applied in various complicated physics. The most important advantage of MSFV method is its computational efficiency. In this paper we present a new set of boundary condition for calculation of basis and correction functions which leads to further reduction in computational time in problems with medium heterogeneity and therefore improves computational efficiency. In standard MSFV (sMSFV) method reduced boundary condition is used to determine the basis and correction functions which is based on local information, however in modified MSFV (mMSFV) method global information is used at initial time for constructing boundary condition which is needed for computing basis functions. The main idea of the method is to use global initial pressure distribution to determine the boundary condition for the basis and correction functions. There is no need to update these basis and correction functions in porous media with medium heterogeneity at each time step and they are calculated only once at the initial time step. This boundary condition allows us to enter nonlocal effect in to the calculation of basis and correction functions which has great importance especially in highly heterogeneous reservoirs. The two difficulties of sMSFV method are problems with high permeability contrast and problems with course grid aspect ratio. This mMSFV can overcome the limitation of high permeability contrast partly.