Analysis of upscaling absolute permeability 论文

摘要

Flow based upscaling of absolute permeability has become an importantstep in practical simulations of flow through heterogeneous formations.The central idea is to compute upscaled, grid-block permeability from fine scalesolutions of the flow equation. Such solutions can be either local in each grid-blockor global in the whole domain. It is well-known that the grid-blockpermeability may be strongly influenced by the boundary conditions imposedon the flow equations and the size of the grid-blocks. We show that the upscalingerrors due to both effects manifest as the resonance between the smallphysical scales of the media and the artificial size of the grid blocks. To obtainprecise error estimates, we study the scale-up of single phase steady flowsthrough media with periodic small scale heterogeneity. As demonstrated byour numerical experiments, these estimates are also useful for understandingthe upscaling of general random media. It is further shown that the oversamplingtechnique introduced in our previous work can be used to reduce theresonance error and obtain boundary-condition independent, grid-block permeability.Some misunderstandings in scale up studies are also clarified in thiswork.