Robust optimization of subsurface flow using polynomial chaos and response surface surrogates

Abstract

This study employs an inclusive framework for surrogate model-based optimization in the presence of parametric and spatial uncertainties. The framework is applied to optimize water injection rate for optimal hydrocarbon recovery from a synthetic subsurface model with uncertainty in the geological and fluid relative permeability properties. In one model of parametric uncertainty, geological properties such as the channel’s absolute permeability and the fault transmissibility multiplier and the fluid relative permeability parameters such as the residual oil saturation to water and the water relative permeability at residual oil are assumed to be non-informative. In another model, the channels positions are assumed uncertain and various realizations of the channelized permeability are parameterized and the spatial uncertainty is accounted for in the optimization. The uncertainty is quantified in each evaluation of the objective function via polynomial chaos expansions. The coefficients of polynomial chaos expansion are solved by probabilistic collocation method. The objective function is assigned with a risk-averse net present value computed from a distribution of values obtained from the probabilistic proxies. The proxies are updated for each round of objective function evaluation. Monte-Carlo simulations are also conducted to verify accuracy and to demonstrate the computational efficiency of the probabilistic collocation approach. The optimization is conducted in various random input cases (depending on the number of uncertain parameters) and for each case net present value is successfully maximized and optimal solutions of the water injection rates are determined.