Transmissibility Upscaling on Unstructured Grids for Highly Heterogeneous Reservoirs

One critical point of modeling of flow in porous media is the capacity to consider parameters that are highly variable in space. It is then very challenging to simulate numerically fluid flow on such heterogeneous porous media. The continuous increase in computing power makes it possible to integrate smaller and smaller heterogeneities into geological models of up to tens of millions of cells. On such meshes, despite computer performance, multi-phase flow equations cannot be solved in an acceptable time for hydrogeologists and reservoir engineers, especially when the modeling considers several components in each fluid and when taking into account rock-fluid interactions. Taking average reservoir properties is a common approach to reducing mesh size. During the last decades, many authors studied the upscaling topic. Two different ways have been investigated to upscale the absolute permeability: (1) an average of the permeability for each cell, which is then used for standard transmissibility calculation, or (2) computing directly the upscaled transmissibility values using the high-resolution permeability values. This paper is related to the second approach. The proposed method uses the half-block approach and combines the finite volume principles with algebraic methods to provide an upper and a lower bound of the upscaled transmissibility values. An application on an extracted map of the SPE10 model shows that this approach is more accurate and faster than the classical transmissibility upscaling method based on flow simulation. This approach keeps the contrast of transmissibility values observed at the high-resolution geological scale and improves the accuracy of field-scale flow simulation for highly heterogeneous reservoirs. Moreover, the upper and lower bounds delivered by the algebraic method allow checking the quality of the upscaling and the gridding.