Ensemble-Based Relative Permeability Estimation Using B-Spline Model

A novel technique has been developed to implicitly estimate relative permeability by history matching the production data with the ensemble Kalman filter (EnKF) method. Water and oil relative permeability curves were approximated using the B-spline model, which has been modified to better represent the relative permeability curves. Compared to the existing implicit approaches, the newly developed technique did not require the use of the gradient of the objectives function and thus, was easy to implement. The newly developed technique has been validated by accurately evaluating relative permeability in a two-dimension synthetic heterogeneous reservoir. The case study showed that the estimated relative permeability was improved gradually as observation data were assimilated and that a good estimation of relative permeability curves can be effectively obtained. In this study, three estimation scenarios assimilating various types of observation data were examined and compared. It was also found that the oil relative permeability was sensitive to the oil production rate (OPR) data, as OPR was directly affected by oil relative permeability. On the other hand, water relative permeability was more sensitive to the bottomhole pressure data of the producers. Additionally, the production data, obtained prior to water breakthrough, contributed more to the estimation of the two-phase relative permeability curves.