Estimation of Relative Permeability by Assisted History Matching Using the Ensemble-Kalman-Filter Method

An ensemble-based history technique has been applied to implicitly estimate three-phase relative permeability curves from production data. A power law representative of relative permeability curves is used. Both endpoints and shape factors of relative permeability curves are included in state vectors that are updated sequentially by assimilating observation data. This method has been validated by accurately evaluating relative permeability in a synthetic reservoir with 2D, three-phase flow. It is shown from the synthetic case that good estimation of relative permeability curves can be obtained by assimilating the observed oil rates, gas/oil ratios, and bottomhole pressures of production wells. Both shape factors and endpoints of relative permeability curves are accurately evaluated; however, a larger ensemble size is needed to avoid filter divergence. Compared with the existing implicit methods, the ensemble-based history matching technique does not require the gradient of the objective function, which makes the technique easy to implement.