Robust optimization of the production profile of the steam assisted gravity drainage reservoir using a polynomial chaos expansion-based proxy model

Uncertainty quantification is essential to ensure robustly stable operation in many engineering applications. Steam assisted gravity drainage (SAGD) reservoirs are large scale distributed parameter dynamical systems and pose significant challenges in quantifying the uncertainty. An effective data driven method to develop computationally inexpensive proxy models for the dynamic outputs and their uncertainty would be valuable for optimization and control. In this work, we present a proxy model developed using polynomial chaos expansion (PCE) for the cumulative oil production (COP) of a SAGD reservoir at different steam injection rates. The proxy model is used in robust optimization using statistical metrics of COP calculated over the entire parameter space. An ensemble of realizations of the cumulative oil production is simulated corresponding to the ensemble of the petro-physical properties over which the PCE model coefficients are estimated using collocation points over the orthogonal polynomial basis under an inner product relationship. Robust optimization is performed as a trade-off between maximum nominal performance and robustness and used to find the optimum steam injection rate for maximum oil production with minimum variability.