Upscaling of reservoir permeability will remain an issue in the oil and gas industry as long as static and dynamic models are limited by computing power and memory constraints. At the same time, flow predictions are required at the scale of the static model. A feasible approach is the subsequent application of upscaling and downscaling: upscaling to be able to make reservoir-scale flow simulations and downscaling to map the results of these calculations on the underlying geological grid.
We propose a procedure which mimics the behavior of non-scaled reservoir models better than conventional methods. Our method entails a new non-local upscaling and downscaling procedure inspired by effective medium theories. The most important difference with standard techniques is the choice of boundary conditions. Our boundary conditions are based on the physical situation rather than on an ad-hoc pressure and/or flow condition on the boundaries of the region to be upscaled.
We demonstrate our procedure with three examples. The first example entails a simple problem where a 2x2 block region is upscaled and it is shown that conventional procedures break down. The physical explanation is given in terms of a flow disturbance outside the scaled area not honored by these techniques.
The second example is a more complicated problem with apparent geological channeling. In the first place, the upscaling provides a good match of the fine-scale dynamic model. Even more important, however, are the downscaled flow velocities resulting when introducing the boundary conditions obtained from the coarse scale for the local fine scale. These show a faithful representation of the channel flow as also obtained with the fine-scale model, while results of attempts to achieve the same with conventional technology did not.
The third example is a 3-dimensional model available from the literature. Again, our upscaled and downscaled results were in close agreement with the full fine-scale simulation.
The current technique does not account for relative permeabilities and capillary pressures. It may be possible to complement our workflow with already existing techniques for these. This is, however, still a matter of research.