Polynomial Chaos Expansion for Uncertainty Quantification in Closed-Loop Reservoir Management

Closed-loop reservoir management (CLRM) is a model-based optimal control procedure that aims at optimizing oil and gas production strategies under both physical and operational constraints and large model uncertainties. Using stochastic simulation in this decision-making process is imperative due to the large uncertainties that impact the model predictions. However, this often involves performing a large number of model evaluations repeatedly to integrate an ensemble of realizations that represent the input uncertainty. In CLRM, this requires excessive computational effort due to the complexity of the nonlinear and high-dimensional reservoir simulation models. In this study, a surrogate modeling technique, namely, polynomial chaos expansion (PCE), is leveraged for efficient and accurate implementation of the stochastic reservoir simulation in CLRM. A PCE for the reservoir dynamics is computed and employed to propagate the uncertainty without the need for additional expensive model evaluations. This can reduce the computational burden in both the forward and inverse problems of the CLRM. Results show that the PCE surrogate model can accurately quantify the uncertainty and evaluate a large number of model realizations at the cost of evaluating a polynomial, compared to the full model evaluations using Monte Carlo simulations.