Data-Driven Spectral Methods for Stochastic Surrogate Modeling and Efficient Data Assimilation in Subsurface Flows

Abstract Subsurface flow dynamics are characterized by high uncertainties stemming from the scarcity of information regarding the subsurface formation. Quantifying these uncertainties, however, is imperative in simulating, predicting, optimizing, and managing the entire production process in hydrocarbon reservoirs. This study integrates stochastic surrogate modeling with Bayesian inference to accurately and efficiently quantify uncertainty in reservoir history matching, addressing the excessive computational burden in traditional methods. First, polynomial chaos expansion (PCE) is leveraged to model the distribution of the reservoir’s stochastic response, which is then used to efficiently propagate the uncertainty and simulate large ensembles of models. In tuning the PCE coefficients, an interpolation-based non-intrusive approach using sparse regression analysis is implemented to mitigate the curse of dimensionality in probabilistic collocation methods (PCM). In contrast to PCM, whose performance is limited by a fixed experimental design where the number of the required collocation points increases with the problem’s dimensionality, sparse regression analysis facilitates greater flexibility in selecting the number and locations of collocation points, significantly improving scalability and computational efficiency in high-dimensional problems. Consequently, the tuned PCE surrogate model is employed in a nonlinear sequential data assimilation procedure to update the reservoir model uncertainties by assimilating the production data. Specifically, sparse-regression-tuned PCE metamodels are integrated with the ensemble Kalman filter (EnKF) to reduce sampling errors in history matching allowing the use of large numbers of realizations without compromising the computational efficiency. Results demonstrate that sparse regression analysis enables tuning PCE surrogate models involving large numbers of uncertain variables compared to other approaches such as PCM. The resulting models provide accurate uncertainty quantification and can efficiently evaluate a large number of model realizations at the reduced computational cost of polynomial evaluations, in contrast to full-scale simulations. Furthermore, it provides comparable performance in history matching and reservoir management using the same number of realizations.