What is flow-based permeability upscaling?

In reservoir simulation multiple scales are useful to consider: from pore-scale all the way up to full field scale. Often one may have some knowledge of the petrophysical properties (permeability, porosity) of a field at a finer scale than one is able to use in a simulation, due to time or memory constraints.

In such situations, it is useful to simulate on a coarser scale than that on which the properties are defined. However, properties appropriate to that larger scale are then needed, and these properties must in a faithful way represent the fine-scale information.

While porosity is simple to upscale, since it is just the ratio of pore volume to total volume, permeability is not so simple, since it should induce the same flow as the fine-scale permeability. While there are analytic solutions for simple cases (such as a layered structure with uniform layers), for more heterogenous cases such methods cannot produce coarse-scale permeabilities that preserve the major features of the fine-scale flow.

Flow-based upscaling is one method that aims to solve this problem. It consists of solving several flow (pressure) problems on the fine scale, and computing coarse-scale permeability tensors to be consistent with the solutions to the fine-scale problems. There are two further variants: global upscaling, where the solutions of a few global fine-scale problems are used, and local upscaling, where the solutions of many local fine-scale problems are used.

The OPM upscaling module implements local flow-based permeability upscaling.