Estimation of Relative Permeability and Capillary Pressure for Hydrocarbon Reservoirs Using Ensemble-Based History Matching Techniques

Abstract

Reservoir simulation is generally used in modern reservoir management to make sound reservoir development strategies, requiring a reliable and up-to-dated reservoir model to predict future reservoir performance in an accurate and efficient way. It is the history matching that is able to provide a reliable reservoir model by using the observed data to calibrate the reservoir model parameters. In this study, assisted history matching techniques have been developed to inversely and accurately evaluate relative permeability and capillary pressure for the hydrocarbon reservoirs. An assisted history matching technique based on the confirming Ensemble Kaman Filter (EnKF) algorithm has been developed, validated, and applied to simultaneously estimate relative permeability and capillary pressure curves by assimilating displacement experiment data in conventional reservoirs and tight formations, respectively. Subsequently, the confirming EnKF algorithm has been extended its application to a synthetic 2D reservoir model where two-phase and three-phase relative permeability and capillary pressure curves are respectively evaluated by assimilating field production data. The power-law model and/or B-spline model can be used to represent relative permeability and capillary pressure curves, whose parameters are to be tuned automatically and finally determined once the measurement data has been assimilated completely and history matched. The estimated relative permeability and capillary pressure curves, in general, have been found to improve progressively, while their associated uncertainties are mitigated gradually as more measurement data is assimilated. Finally, there exists a generally good agreement between both the updated relative permeability and capillary pressure curves and their corresponding reference curves, leading to excellent history matching results. As such, the uncertainties associated with both the updated relative permeability and capillary pressure curves and the updated production profiles are reduced significantly. In addition, a novel damped iterative EnKF (EnKF) algorithm has been proposed and applied to evaluate relative permeability and capillary pressure for the laboratory coreflooding experiment. It has been found that relative permeability and capillary pressure can be simultaneously determined by using the damped IEnKF algorithm to only assimilate the cumulative oil production and pressure drop, while there exist better history matching results than those of the confirming EnKF. Compared with the initial cases, the uncertainties associated with both updated relative permeability and capillary pressure curves and the updated production history profiles have been decreased greatly. Finally, the standard test case based on a real field, i.e., PUNQ-S3 reservoir model, is used to further evaluate performance of the damped IEnKF algorithm. After assimilating all of the measurement data, the three-phase relative permeability and capillary pressure curves can be estimated accurately. The damped IEnKF algorithm is found to reduce the uncertainties associated with both the updated relative permeability and capillary pressure curves and the updated production profiles significantly compared with their corresponding initial cases. In addition to its better performance than the confirming EnKF algorithm, the damped IEnKF algorithm is found to be special suitable for the strongly nonlinear data assimilation system, though there still exist certain variations in the updated relative permeability and capillary pressure curves as well as the predicted production profiles.