Upscaling of polymer adsorption

Abstract

Abstract This article considers upscaling of polymer adsorption. Input to adsorption values employed in reservoir simulation models are typically obtained from core plug measurements. There are several orders of magnitude in scale difference between core plugs and grid cells in reservoir simulation models, which foster a need for upscaling of the adsorption values. Polymer concentration distribution on the lithofacies scale is investigated in this article. The effect of diffusion on concentration distribution is investigated analytically. The slow diffusion of polymer molecules retards mixing even at the lithofacies scale. We introduce a formula to estimate the redistribution of polymer due to capillary forces in a layered model, and this formula is validated through numerical simulations. From our considerations we conclude that it is questionable to assume a constant polymer concentration in lithofacies models. This impedes applying steady-state upscaling techniques. Such upscaling techniques will over-predict polymer adsorption. Different methods for upscaling adsorption are presented in this paper, and applied to a simplified layered model and to more realistic fine-scale numerical models based on the SPE10 model. These numerical models were populated with adsorption values obtained from published experiments conducted on samples from the Brent sequence modeled in SPE10. Simulations of tertiary polymer flooding on the upscaled models were compared to simulations of the same flooding sequences on the original fine scale models. The tested upscaling methods include a volume averaging technique employed by other authors, and a method were we distribute the adsorption values by the same functional relationship as in the fine scale model. In addition we introduce upscaling methods were we assign zero adsorption to fine scale grid cells with permeability below a given cut-off value. The cut-off value is obtained from a single phase simulation on the fine scale model. In our models the cut-off value methods yield the best match between the coarse scale and fine scale simulation results. The volume averaging technique over-predict the polymer adsorption. Results from both the lithofacies and geomodel scale indicate a tendency to over-predict polymer adsorption, which could lead to conservative estimates for the effect of polymer flooding.