Upscaling Reservoir Models with Piecewise Constant Permeability

Xiao-Hui Wu, Matthew T. Stone, Rossen R. Parashkevov, Steve L. Lyons

Email: xiao-hui.wu@exxonmobil.com
Postal address: Reservoir Properties & Modeling, URC-URC-SW424, ExxonMobil Upstream Research Company

Modern geostatistical techniques often produce geo-cellular models with discontinuous permeability distributions.  Jumps in permeability cause well-known singularities in the flow solutions and hence slow convergence of standard numerical methods.  Depending on the discretization used, i.e. finite element or finite volume, these singularities have differing impact on the solution. In scale-up, this can be seen as significant differences in upscaled permeabilities calculated by using finite element and finite volume methods.  Such differences lead to high uncertainty in upscaled permeability and hence reservoir performance predictions.  In this presentation, we introduce a hybrid approach to overcome the difficulty by taking advantages of both methods.  Using standard Galerkin finite element method and an L2 projection of the fluxes calculated from the finite element solutions, we obtain a practical method that gives more accurate scale-up and reduced uncertainty in the upscaled permeabilities.  We present extensive numerical tests on different reservoir models to show the accuracy and robustness of this approach. This is a joint work with Matthew T. Stone, Rossen R. Parashkevov, Steve L. Lyons.