Adjoint Gradient, Commercial Simulator Combine for Efficient History-Matching

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 223837, “Combining Adjoint Gradient With Commercial Reservoir Simulator For Efficient History Matching,” by Duc Le, Krishna Nunna, SPE, and Amir Shahbazi, SPE, Occidental Petroleum, et al. The paper has not been peer-reviewed. _ Efficient history-matching of reservoir simulation models remains a paramount challenge in the oil and gas industry. Traditional approaches often require computationally expensive simulations, performed either manually by reservoir engineers or by algorithms that treat the reservoir simulator as a black box. In contrast, the adjoint method facilitates efficient determination of sensitivities to all parameters in a single backward calculation. However, its implementation requires knowledge of the partial differential equations used to develop the forward model, which is not available for commercial simulators. This study demonstrates how such calculations can be performed even when a commercial reservoir simulator is used for forward simulations. Methodology The complete paper provides equations necessary for the adjoint state method. The steps described there are optimally performed by the forward simulator. However, the lack of support for this functionality from commercial simulators necessitates those steps be executed by an external tool. External Adjoint Calculation. In this study, the MATLAB Reservoir Simulation Toolbox (MRST) is used to calculate adjoint gradients. Coupling open-source tools such as the MRST with established commercial simulators is a promising approach for agile and efficient reservoir model calibration. One of the key features of MRST is its extensive support for Eclipse keywords and binary output files. This compatibility with industry-standard input and output files enables MRST to seamlessly communicate and transfer data with commercial software workflows. In practice, this means that MRST can be used as a pre- and post-processing tool for complex simulations. The seamless data transfer between the two platforms minimizes errors related to reformatting. Another noteworthy feature within MRST is its support for automatic differentiation, which facilitates the computation of accurate derivatives without the need for symbolic manipulation. This capability is particularly valuable for external adjoint calculations. The external tool development is further aided by MRST’s integration with the MATLAB environment. The latter’s scripting and visualization tools allow users to customize MRST’s source code, creating tailored workflows that align with specific simulation needs. The ability to experiment with new approaches, adjust model details, and build custom modules enables MRST users to explore solutions without the rigidity often evident in a commercial simulation setting. It is important to note that history-matching constitutes merely one step in the comprehensive process of reservoir characterization. The property modifications created by history-matching must be examined by the geomodeler to interpret these changes as possible missing geological features and incorporate them into the updated geomodel. In this context, possessing a powerful tool such as the adjoint gradient significantly expedites the feature-discovery process.