Hybrid derivative-free technique and effective machine learning surrogate for nonlinear constrained well placement and production optimization

It is imperative that wells in an oil field be located and controlled in an optimal fashion to maximize asset value while satisfying the optimization constraints which can be in the form of production limits, water cut, or well spacing. Computational optimization algorithms coupled with a reservoir simulator have become increasingly popular in determining the optimal locations of wells and the optimal controls to be imposed on them. These algorithms should be able to deal with highly non-linear objective functions, the absence of gradient information, and a limited reservoir simulation budget. In this work, we considered derivative-free and non-invasive techniques: Enhanced Success History-Based Adaptive Differential Evolution (ESHADE) strategy with linear population size reduction, which is a variant of L-SHADE (recognized as one of the state-of-the-art global stochastic optimizers for continuous variable), and a Mesh Adaptive Direct Search (MADS) local pattern search method. These two methods are hybridized to develop a hybrid framework (E-MADS) that combines the advantageous aspects of both methods in order to improve optimization efficiency. In order to further improve the efficiency of the framework, gradient boosting machine learning technique is used to generate proxy model, based on regression and classification methods, to predict the objective function and classify optimization solutions into feasibless (satisfies all prescribed constraints) and infeasible groups. This information is then used to screen out solutions that are not expected to improve the objective function. Applications of these algorithms to the joint optimization of well location and time-varying control problem, with bounds and nonlinear constraints, are presented in this work. ESHADE is shown to outperform traditional global optimization algorithms such as Particle Swarm Optimization (PSO) and a real-coded Genetic Algorithm (GA). The E-MADS hybrid is also shown to have a superior performance relative to the standalone ESHADE and MADS methods for the joint optimization problem.