Sensitivity of Steam Displacement Predictions to Three-Phase Relative Permeability Models

Abstract

Abstract Users of thermal simulators usually provide data in terms of two sets of two phase relative permeability functions: (1) krow and krw in a water-oil system, and (2) krog and krg in an oil-gas system. Within the thermal simulator two-phase relative permeabilities are used to predict effective permeability of each phase when all three phases are flowing simultaneously in a block. The most frequently used models for making these predictions are due to Stone (Model I and Model II) and their modifications. The literature does not provide clear guidance on the selection of a relative permeability model for a given problem. In this paper we present theoretical and numerical analyses of three-phase relative permeability models for steamflood problems. Our analysis shows that relatively high krw and krg (from two-phase data) lead to higher kro from Model I than Model II, and the reverse is true when krw and krg are relatively low. The differences in predicted kro by the two models are greatest in the range of low oil saturations. We have selected three sets of relative permeability data from the literature that have been previously used for the modelling of steamfloods. Data Sets 1, 2 and 3 are characterized by moderate, low and high values of krw and krg, respectively. The oil relative permeability (kro) predicted for Data Set 1 by the Stone's two models is about the same. As expected from our theoretical analysis, Stone's two models yield quite different kro's for Data Sets 2 and 3. However, oil production predictions with Model I and Model II for Data Set 3 are not too different, but these two models show significant differences in the simulation results for Data Set 2. Investigation of saturation profiles near production and injection wells show that low krw and krg values (Data Set 2) tend to drive saturations into the range where Stone's two models give different results, and high krw and krg values (Data Set 3) tend to keep saturations in the range where the two models give similar results. The results of this study should be of value in selecting three-phase relative permeability models for steamflood simulations.