Up-Scaling Two-Phase Flow in Heterogeneous Reservoirs: Current Trends

In this paper, we review the main upscaling techniques of two phase flow. Purely numerical fine to coarse gridding methods are investigated, as well as more physical approaches where the focus is on the algebraic form of the averaged transport equations. A detailed numerical and analytical study of the dynamics of the water-oil front shows that stochastic approaches cannot neglect the viscous coupling between the pressure and saturation. A very strong interaction exists between the heterogeneity and the stable or unstable character of the fluid flow displacement. This coupling is responsible of a qualitative and quantitative change of the form of the large scale equations, that must be accounted for by any upscaling procedure. Once this problem is solved, it is easier to devise optimal physically based discretisation procedures, that allows Monte-Carlo studies to be accelerated. Examples dealing with stratified or stochastic media will also be presented.

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