A Multiscale Finite-Volume Framework for Modeling Multiphase Flow

Time:	January 10, 2006, 4:00 p.m. – 5:30 p.m.
Lecturer:	Dr. Ivan Lunati, Inst.f. Hydromechanik u. Wasserwirtschaft, ETH Zürich
Venue:	Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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A multi-scale finite-volume (MSFV) method for solving multiphase flowproblem in highly heterogeneous media was recently developed. Incontrast with classical upscaling techniques, the goal of multiscalemethods is not simply to capture the large-scale effects of thefine-scale heterogeneity, but to provide an efficient tool for solvinglarge 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-scalevelocity field is reconstructed, finally the phase-saturationdistribution is obtained by solving the nonlinear transport equations.In addition to the original fine grid the MSFV method employs animposed coarse grid and a dual coarse grid. The first step is tocompute the effective parameters that have to be used for solving theglobal flow problem on a coarse grid. This is done by means of a set ofbasis functions, which are numerical solutions computed on the cells ofthe dual grid. From these basis functions, the fluxes across thecoarse-block boundaries are computed and the transmissibilities areextracted. Then the conservative fine-scale total-velocity field isreconstructed by solving a local flow problem in each coarse cell.