The effect of stochastic relative permeabilities in reservoir simulation

Abstract

During recent years Norsk Hydro has developed a 3D model for the simultaneous generation of stochastic absolute and relative permeabilities. By using a unique set of core data containing relative permeability curves measured on 85 core plugs from one single well in the North Sea, the authors have been able to model relative permeability curves (represented by endpoints and exponents) stochastically for four different depositional environments ranging from highly permeable mouthbar sands to low permeable tidal deposits. The authors will show that for all the four depositional environments represented here, the stochastic variation of the relative permeabilities have only marginal, if any, effect on the production characteristic, compared to keeping the relative permeabilities constant at their mean. Based on the fractional flow theory, for unit mobility ratio and ingnoring capillary forces, this paper presents both a theoretical and empirical statistical analysis of the correlation between the water shock front velocity and the absolute permeability for the different depositional environments. It is shown that in specific cases this correlation can serve as an indication of the potential effects of stochastically varying relative permeability curves. The main conclusion, which must be very comforting to practicing engineers, is that in within a wide range of depositional environments, stochastic modelling of the relative permeability curves is of minor importance. However, the choice of mean relative permeabilities may be crucial.