Two-Phase Relative Permeability Prediction: A Comparison of the Modified Brooks-Corey Methodology with a New Carman-Kozeny Based Flow Formulation

Abstract

Abstract The prediction of relative permeability has been in the past and is currently a very active research area, with theoretical, experimental and empirical approaches under consideration. However, it is fair to say that the complexities of relative permeability have to date eluded researchers and practitioners alike, in that there is no universal formulation that is able to predict two-phase relative permeability for the wide range of rock and wettability characteristics observed. This paper presents a new, generalised formulation, one that is truly predictive, and compares the same with the industry standard - the modified Brooks-Corey (MBC) formulation. The MBC formulation is perhaps the most widely used, practical method describing laboratory-derived relative permeability relationships in terms of simple power functions. The shortcomings of this formulation are that it has no real predictive capability and the relative contributions due to pore structure components as compared to variation in wettability cannot be resolved. The new two-phase flow formulation presented is based on a phenomenological approach related to the Carman-Kozeny equation, and is able to resolve the above mentioned shortcomings. Included are several laboratory examples and the results of a comparison of the two formulations is presented. It is shown how the new formulation is able to predict "the curvature" of relative permeability curves when only the endpoints are known, duplicating observed behaviour from steady-state relative permeability experiments. Alternatively, if the endpoints can be derived, correlated or estimated with the use of more fundamental data, the entire prediction of relative permeability is possible. In conclusion, the formulation presented is able to predict two-phase relative permeability under steady-state conditions, not just merely fit data. The second advantage of this method is that it is theoretically based and does not involve any fitting parameters but involves relatively simple analytical expressions.