A Novel Bayesian Optimization Framework for Computationally Expensive Optimization Problem in Tight Oil Reservoirs

Abstract

AbstractMulti-well pad has been considered as the most efficient horizontal-well drilling technique in unconventional reservoir development since it not only greatly maximizes the oil production, but also significantly reduces environmental impact and operation costs by drilling group of wells on a single pad. To optimize both hydraulic fracture parameters of each well and well placement simultaneously is still largely unexplored and remains to be a challenging task. Conventional optimization techniques, such as genetic algorithm, particle swarm optimization, and differential evolution algorithm are inadequate to optimize production performance in the multi-well pad, because it may take hours to days to run a single reservoir simulation, leading to an unaffordable computational cost for the optimization processes.To speed up the search process of global optimization in reservoir simulations, a novel optimization framework for computationally expensive simulations is developed based on Bayesian optimization algorithm. The newly developed optimization algorithm constructs a probabilistic model for the objective function and then exploits this model to make decisions about where in search space to next evaluate the function. In this study, Gaussian Process (GP) is utilized to construct the prior distribution over the objective function. Then, the posterior over functions is obtained based on the prior distribution and evaluations of objective functions. Finally, acquisition function is developed through maximizing the expected improvement over the current best from the posterior, allowing us to determine the next point to evaluate in search space.It is shown that GP Bayesian optimization framework can successfully optimize the hydraulic fracture parameters and horizontal well placement simultaneously in tight oil reservoirs. 19 parameters involve well spacing, well length, fracture spacing, fracture half-length, and fracture conductivity in a four-well pad were optimized and a high net present value (NPV) was achieved. The oil recovery and NPV of the optimum scenario derived through the Bayesian optimization technique are increased by 36.0% and 55.7% respectively in comparison with a field reference case. The proposed Bayesian optimization framework is found to be a promising and efficient optimization strategy, which takes full advantage of the information available from previous evaluations of objective function, in handling the computationally expensive optimization problems.