Modified Ensemble Kalman filter for reservoir parameter and state estimation in the presence of model uncertainty

Abstract

Ensemble Kalman filter (EnKF) is widely used in reservoir modelling for on-line history matching. Typically, it is assumed that structurally the model is an accurate representation of the reservoir and uncertainty exists only in the parameters. This paper focuses on estimating reservoir static parameters (i.e., porosity and permeability) and dynamic states using EnKF in the presence of mismatch between the reservoir and the model. An in depth investigation of the application challenges of EnKF is reported. Two modifications are introduced for joint state-parameter estimation: i) addition of error to the model to represent the mismatch between the predictive model and real system, and ii) introduction of a tuning parameter called ‘forcing data’ to the perturbation variable for dealing with a noisy system. A benchmark problem defined as ‘tank series model’ has been designed for the verification of the EnKF algorithm. Using the simplified model mathematical formulation of state estimation combined with parameter calibration is presented systematically. Later similar approach is applied to a nonlinear two-dimensional reservoir under water flooding operation. To assess the performance in history matching, a sensitivity analysis is conducted. It was observed that due to forcing data perturbation, about 13.6% and 9% improvement is possible in history matching of the tank and reservoir cases respectively when model mismatch and uncertainty in measurement is high.