Analysis of the impacts of relative permeability and mobility ratio on heterogeneity loss error during upscaling of geological models

Abstract

The detailed geological fine grids are upscaled to create reliably sized simulation coarse models to solve flow equations in a more efficient way. Any upscaling process results in a loss of accuracy, along with an increase of errors. Numerical dispersion, heterogeneity loss, and connectivity misrepresentation are responsible for the upscaling errors. Recognizing the source of each error, and the behavior of influential factors through upscaling process could provide an optimum level of upscaling and an evaluation of upscaling methods’ accuracy. Despite the importance of upscaling error, little attention has been paid to this subject. This paper represents a rigorous analysis of the heterogeneity loss behavior associated with the relative permeability contrast and the mobility ratio under a waterflooding process. For this purpose, heterogeneous fine grid models are constructed by the fractional Brownian motion process. The models are upscaled by three upscaling factors. The models achieved are implemented to eliminate the impact of numerical error among upscaling errors in order to focus strictly on heterogeneity loss. Water–oil displacement simulation is then performed on fine and corresponding refined upscaled models at three different ratios of relative permeabilities and mobility ratios. In the next stage, the relation between flow performance error and heterogeneity loss is investigated by the heterogeneity loss plot. The slope of this plot provides the reservoir engineer an insight to evaluate the performance of upscaling methods and the behavior of the influential factors on upscaling errors. Moreover, by using the heterogeneity loss plot for each ratio, a limit of coarsening is presented. Based on the results, the heterogeneity loss error is affected more by the mobility ratio contrast than the relative permeability difference. Also, it is demonstrated that water-wet reservoirs with light oil are more sensitive to the level of upscaling.

Simulation study of water and gas injection process into the Azadegan reservoir for enhanced oil recovery

“…For the case of Rp <1, which means that the water permeability is less than oil and consequently oil is displaced by water with a favorable relative permeability ratio. It should be noted that the presence of the geological heterogeneity has a significant effect on the fluid displacement and the shape of the flood‐front 21 . The following figure analyzes the degree of heterogeneity in different ratios of relative permeability.…”

“…It should be noted that the presence of the geological heterogeneity has a significant effect on the fluid displacement and the shape of the flood-front. 21 The following figure analyzes the degree of heterogeneity in different ratios of relative permeability. According to these results, it can be said that the simulation results are reliable.…”