Relative Permeability Estimation from Displacement Experiments Using EnKF Method

Abstract

The relative permeability is a crucial parameter for accurately evaluating reservoir performance. Two-phase relative permeability curves are normally obtained by either directly or indirectly interpreting the displacement experiment data. As for the direct interpretation, the core samples are assumed to be homogeneous, while the capillary forces are normally neglected. Although the indirect interpreting approach is able to take heterogeneity of the core sample into account, calculating the derivatives of the objective functions through the graphical or numerical methods is prone to considerable errors. In this paper, a new method is developed to calculate the absolute and relative permeability from unsteady-state, two-phase immiscible displacement experiments. The permeability data is determined by history matching the experimentally observed pressure drop, production data and water saturation profiles via the ensemble Kalman filter (EnKF) algorithm. The power-law model is utilized to represent the relative permeability. Both the absolute and relative permeability are calculated simultaneously by assimilating the observed data. The newly developed method is validated using a numerical coreflooding experiment. It has been found that estimations of absolute and relative permeability are improved progressively as more observation data are assimilated. In addition, this method is convenient to be implemented as the derivative of the objective function is not required.