Iterative Ensemble Kalman Filter and genetic algorithm for automatic reconstruction of relative permeability curves in the subsurface multi-phase flow

Abstract

Relative permeability curves are one of the main factors that control the behavior of multi-phase flow in underground energy resources. The incorrect selection of relative permeability curves can lead to inaccurate predictions of the reservoir's future behavior. Accurate prediction of the reservoirs transient behavior is therefore vital as it influences subsequent political and management decisions. In this study, two different algorithms, namely GA (Genetic Algorithm) and Iter EnKF (Iterative Ensemble Kalman Filter), were used to estimate the optimal set of relative permeability curves aiding Corey's three-phase relative permeability correlation. A synthetic reservoir model was used as a benchmark to compare the accuracy and efficiency of the utilized algorithms. Sensitivity analysis was conducted over the type of cost function used within the optimization algorithm. Graphical results, such as time-evolved reservoir parameters, saturation maps, and mismatch of the relative permeability curves were used for comparison purposes. The comparison study unveiled that oil recovery is the best option to be included in the cost function with a mean AARD (Average Absolute Relative Deviation) of around 6%. Nonetheless, the inherent non-uniqueness of the problem showed that the best optimal case based on the mismatch analysis might not necessarily represent the true relative permeability curves. Overall, parameters such as “oil recovery” and “cumulative gas production” better captured the evolution of the well and reservoir state variables with time, probably due to the consideration of the history of production at each data point. Finally, a comparison between GA and Iter EnKF showed that the difference between the optimal solutions obtained using these two algorithms is almost insignificant. Computational time analysis showed that both algorithms have almost the same running time for small population sizes while Iter EnKF leads to lower computation times for population sizes larger than 50.