UNCERTAINTY QUANTIFICATION FOR SUBSURFACE FLOW PROBLEMS USING COARSE-SCALE MODELS

Fine-scale features can have a large impact on key subsurface flow quantities such as fluid injection or production rates. Because the geological characteristics of subsurface formations are highly uncertain, multiple realizations are typically simulated in an attempt to capture the impact of geological uncertainty on flow behavior. It is, however, expensive to perform flow simulation on highly resolved models; for this reason a number of upscaling and multiscale procedures have been devised. Most such techniques aim to provide coarse models that reproduce the fine-model response on a realization-by-realization basis. This may not be necessary, however, when the goal is to replicate the statistics of the flow responses of multiple realizations. In this work, we present an upscaling approach that entails the statistical assignment of upscaled functions. This approach is more efficient than traditional treatments as it greatly reduces the most time-consuming upscaling computations. We will also describe new procedures for upscaling in the vicinity of injection and production wells. Numerical results demonstrate that, by combining near-well upscaling and statistical assignment of coarse-scale flux functions, coarse models that are well suited for computing ensemble quantities can be efficiently constructed. These coarse models will be shown to provide cumulative distribution functions for key two-phase flow quantities that are in close agreement with those computed using the underlying ensemble of fine-scale geological models.