Improved Geological Model Calibration Through Sparsity-Promoting Ensemble Kalman Filter

Abstract Calibrating complex subsurface geological models against dynamic well observations yields to a challenging inverse problem which is known as history matching in oil and gas literature. The highly nonlinear nature of interactions and relationships between reservoir model parameters and well responses demand automated, robust and geologically consistent inversion techniques. In the recent years, there has been significant progress in automated history matching methods mostly categorized as gradient-based and ensemble-based techniques. Ensemble-based methods such as ensemble Kalman filter (EnKF) have proved to be successful in adjusting reservoir parameters to match observed dynamic data. To calibrate the reservoir model and update the distributed parameters in geologically robust way it is crucial to utilize a parameterization method. Parameterization techniques also aim to make the inversion process more efficient by reducing the dimension of the model parameter. Recently in the fields of image processing and data mining, sparse parameterization and image reconstruction are gained considerable attention. We propose a novel automated history matching method by employing EnKF along with a sparsity-promoting parameterization technique. To improve the performance of EnKF in capturing complex geological features such as channelized reservoirs, we employ sparse constraints to construct the reservoir model from the observed dynamic well data. For the parameterization purpose we investigate utilizing various basis functions or models such as singular value decomposition (SVD) and discrete cosine transform (DCT). The combination of EnKF analysis equation with sparse reconstruction algorithm such as Matching Pursuit (MP) will enhance the inversion results. We also investigated effects of different geologically trained dictionaries or basis such as K-SVD and also the impact of combining various basis sets. We applied the proposed sparsity-promoting EnKF to several numerical examples to estimate reservoir distributed properties from well production data. The enhanced EnKF method with sparse constrained parameterization showed promising improvement comparing to standard EnKF and also EnKF with standard parameterization. The proposed inversion technique propagates and updates an ensemble of geological models through integration steps and provides more consistent distributed parameter fields with the prior geology of the subsurface formation. The sparsity-promoting EnKF is a derivative free history matching method which is also able to perform uncertainty assessment because of its ensemble based nature. Parameterizations along with sparse selection of basis functions make the calibrated solutions of this method more geologically consistent. This method is especially suitable for resolving more complex geological structures such as channelized formations which are generated with multi-point geostatistics techniques.