Joint estimation of absolute and relative permeabilities using ensemble-based Kalman filter

Abstract

An ensemble-based, sequential assimilation procedure is developed and successfully applied to estimate absolute and relative permeabilities jointly under multi-phase (oil, gas and water) flow condition in the porous media. Two-phase oil–water and gas–oil relative permeabilities are represented by power-law models, and Stone's Model II is used to calculate three-phase oil relative permeability. Prior absolute permeability field is also generated with isotropic Gaussian covariance. The proposed method is validated by a twin numerical setup with three different case studies, in which a synthetic 2D reservoir under multi-phase flow condition is considered. In the first case, there is simultaneous flow of oil, water, and gas phases within the reservoir. In the second, only oil and water phases are present; and, only oil and gas phases are mobile for the third case. By assimilating measured production rates of the producers and bottomhole pressure of the injector, relative permeability curves and absolute permeability field are accurately estimated. Therefore, simultaneous estimation of absolute and relative permeabilities from measured production data is feasible if there exists a prior model for the absolute permeability field and relative permeability curves.