Upscaling Simulations of 3D Displacement Processes that Include Change of Wettability using Analytically Derived Relative Permeability

Abstract

Summary We introduce an upscaling method that can be used to improve the accuracy of forecasts of EOR processes that involve changes to fluid mobility either by modifying wettability and interfacial tension as in surfactant flooding, alkaline flooding and low salinity water flooding, or by increasing the injectant viscosity as in polymer flooding. The suggested upscaling method is designed to solve the two numerical artefacts associated with discretization of these processes which include well know dispersion effects as well as more recently reported pulses. Simulations involving changes to wettability or interfacial tension usually require two sets of input relative permeability curves. In this newly derived upscaling method, we show how to develop a single set of pseudorelative permeability curves for coarse scale models to represent fine scale behaviour. The shape of the derived properties is based on the analytical solution of the fractional flow theory of chemical flooding. Using this analysis, we are able to build a pseudo relative permeability that honours the correct velocity of the formation and chemical waterfronts with an appropriate oil banking interval. It also ensures the sharpness of the shock fronts. We derived a single set of relative permeability curves, avoiding numerically based pulses. We built pseudo-relative permeability curves that includes the impact of effective concentration range and physical dispersion induced by geological heterogeneity. The numerical results of the upscaled models were compared against the fine scale models. We analysed the flow behaviour in 1D homogenous models and 2D models of communicating and non-communicating layers. We also analysed flow in 2D and 3D models of correlated random permeability. Our method is shown to work for all of these cases. However, for unfavourable displacement in strongly heterogenous models of correlated random permeability, some tuning was required due to significant fingering effects. Secondary and tertiary flooding were considered in the analysis. This novel upscaling method was able to control the artefacts of numerical pulses and dispersion. It also simplified the complex modelling of these processes, improving the upscaling step and decoupling the representation of solutes. We reduced the requirement for relative permeability curves to one set, and removed the need to simulate solutes such as polymers and salinity. This means that simplified fast simulations of oil displacement can be run.