The impact of viscosity contrast on the error of heterogeneity loss in upscaling of geological models

Abstract

Multiphase flow simulation is widely used to evaluate different production plans in petroleum engineering. In order to solve the flow equation efficiently, upscaling is applied to transform a fine grid geological model into a coarser one. The coarse model result, however, may be inaccurate due to heterogeneity loss, connectivity distortion and numerical dispersion. Each source of upscaling error has its own influential factors. Knowledge about these factors and error behavior is useful in design of appropriate sizes for coarse grid blocks. Although numerous methods have been developed for upscaling, few works may be found on the related error itself.This paper studies how a major source of upscaling error, heterogeneity loss, changes with viscosity contrast in water-oil displacement. The fBm process is used to create very heterogeneous fine models that are upscaled by Renormalization method. For separating the effect of heterogeneity loss from numerical dispersion, refined upscaled models are derived. Water flooding is then simulated on fine and refined upscaled models at 3 different ratios of oil to water viscosity. For each ratio, a heterogeneity loss plot is prepared. This plot is a powerful tool for evaluating the performance of an upscaling method. The result shows the heterogeneity loss error heavily depends on viscosity contrast. Moreover, the limit of coarsening is determined for each case and it is discussed why that limit is lower when water has higher viscosity than oil.