The Multiscale Finite-Volume (MSFV) method was originally proposed to solve elliptic problems arising from incompressible multiphase flow in highly heterogeneous porous media at reduced computational cost. However, when phases are compressible, especially when the reservoir contains gas, mathematical formulations lead to a parabolic equation to be solved for pressure. In this paper we introduce a general MSFV method to deal with such parabolic problems. In this scheme, the basis and correction functions are numerical solutions of the full parabolic problems in localized domains. Hence compressibility effects are represented by a stencil in the coarse-system matrix, i.e. not only by a diagonal entry. Furthermore, to enhance the computational efficiency of the scheme, the basis functions are kept independent of the pressure field. As a result, only the correction functions (1 per dual-coarse cell) have to be updated during the iterative procedure. It is an important property of this approach that it requires no additional simplifications. Finally, its good efficiency is demonstrated for a number of challenging test cases.


Article metrics loading...

Loading full text...

Full text loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error