Uncertainty Quantification and Management in Model Calibration and History Matching with Ensemble Kalman Methods

Abstract History matching field performance is a time-consuming, complex and ill-posed inverse problem that yields multiple plausible solutions. This is due to the inherent uncertainty associated with geological and flow modeling. The history matching must be performed diligently with the ultimate objective of availing reliable prediction tools for managing the oil and gas assets. Our work capitalizes on the latest development in ensemble Kalman techniques, namely, the Ensemble Kalman Filter (EnKF) and Ensemble Smoother (ES) to properly quantify and manage reservoir models’ uncertainty throughout the process of calibration and history matching. Iterative ensemble algorithms have been developed to overcome the shortcomings of the existing methods such as the lack of data assimilation capabilities and abilities to quantify and manage uncertainties, in addition to the huge number of simulations runs required to complete a study. In this work, NORNE benchmark model was used to generate an initial ensemble of 40 to 50 equally probable reservoir models was generated with variable areal, vertical permeability and porosity. The initial ensemble captured the most influencing reservoir properties, which will be propagated and honored by the subsequent ensemble iterations. Data misfits between the field historical data and simulation data are calculated for each of the realizations of reservoir models to quantify the impact of reservoir uncertainty, and to perform the necessary changes on horizontal, vertical permeability and porosity values for the next iteration. Each generation of the optimization process reduces the data misfit compared to the previous iteration. The process continues until a satisfactory field level and well level history match is reached or when there is no more improvement. The application of the Iterative ensemble algorithms is demonstrated by history matching NORNE benchmark model. Multiple iterative ensemble smoothers with adaptive inflation and localization techniques were implemented and compared. The ES algorithms preserved key geological features of the reservoir model throughout the history matching process. During this study, ES served as a bridge between classical control theory solutions and Bayesian probabilistic solutions of sequential inverse problems. The methods demonstrated good tracking qualities while giving some estimate of uncertainty as well. The updated reservoir properties (horizontal, vertical permeability and porosity values) are conditioned throughout the ES iterations (cycles), maintaining consistency with the initial geological understanding. The workflow resulted in enhanced history match quality in shorter turnaround time with much fewer simulation runs than the traditional genetic or evolutionary algorithms. The geological realism of the model is retained for robust prediction and development planning.