Two-phase flow upscaling with heterogeneous tensorial relative permeability curves.

A.Genty, C. Le Potier, P. Renard proceedings du XIII International Conference on Computational Methods in Water Resources. Calgary, Canada - Computational Methods in Water Resources XIII, Bentley et al. (eds), Balkema, Rotterdam, ISBN 90 5809 123 6, pp. 749-754

This paper focuses on the effects of the heterogeneity of small scale variability of the absolute permeability (and possibly relative permeability) on upscaled relative permeability curves. First we present a technique to upscale "tensorial" relative permeability curves based on block inversion. Then, we build a new two-phase flow upscaling technique based on the combination of upscaled absolute permeability and upscaled "tensorial" relative permeability. We conducted numerical simulations to analyze the reliability of this method in two dimensions on a stochastic anisotropic sand-shale medium with a new two phase flow mixed-hybrid finite element technique which ensures the continuity of fluxes. The analysis shows that the new method gives good results, however the use of upscaled "tensorial", relative permeability for this medium does not improve the results given by simplified renormalization.