Robust optimization of well location to enhance hysteretical trapping of CO2: Assessment of various uncertainty quantification methods and utilization of mixed response surface surrogates

Abstract

The paper aims to solve a robust optimization problem (optimization in presence of uncertainty) for finding the optimal locations of a number of CO2 injection wells for geological sequestration of carbon dioxide in a saline aquifer. The parametric uncertainties are the interfacial tension between CO2 and aquifer brine, the Land's trapping coefficient and the boundary aquifer's absolute permeability. The spatial uncertainties are due to the channelized permeability field which exhibits a binary channel-non-channel system. The objective function of the optimization is the amount of residually trapped CO2 due to the hysteresis of the relative permeability curves. A risk-averse value derived from the cumulative density function of the distribution of the amount of trapped gas is chosen as the objective function value. In order to ensure that the uncertainties are effectively taken into account, Monte Carlo simulation and Polynomial Chaos Expansion (PCE)-based methods are used and compared with each other. For different cases of parametric and spatial uncertainties, the most accurate uncertainty quantification (UQ) method is chosen to be integrated within the optimization algorithm. While for parametric uncertainty cases of up to two uncertain variables, PCE-based methods computationally outperform Monte Carlo simulations, it is shown that for the multimodal distributions of the function of trapped gas occurring for the spatial uncertainty case, Monte Carlo simulations are more reliable than PCE-based UQ methods. For the discrete (integer) optimization problem, various mixed response surface surrogate models are tested and the robust optimization resulted in optimal CO2 injection well locations.