Abstract
Being able to understand and predict flow and transport processes in porous subsurface rocks is decisive for oil and gas recovery, carbon sequestration, and groundwater management. Porous rocks are typically highly heterogeneous and exhibit a multiscale behavior in the sense that small-scale flow paths dominate the overall displacement of fluids in a reservoir. Describing all pertinent flow processes with a single model is impossible and flow modeling is therefore divided into separate steps according to physical scales. In the first part of the lecture series, I will introduce the basic modeling concepts and review standard upscaling methods used to transfer effective properties between models on different scales. Multiscale methods offer a systematic framework for model reduction and bridging scales. In these methods, sub-scale information is incorporated into model equations on a coarser scale in a consistent way. I will present a few examples of such multiscale methods. Most attention will be devoted to a class of approximate multiscale methods that solve local problems to numerically construct a set of basis functions that later can be used to compute global solutions that describe the flow on both the coarse computational scale and the underlying fine parameter scale. This way, one is able to account for both effective coarse-scale properties and sub-scale variations. The methods are particularly efficient when the flow field must be updated repeatedly. Because temporal changes in the flow equations are moderate compared to the spatial variability, it is seldom necessary to recompute basis functions each time the global flow field is recomputed.