Well Placement Optimization with the Covariance Matrix Adaptation Evolution Strategy and Meta-Models

The amount of hydrocarbon recovered can be considerably increased by finding optimal placement of non-conventional wells. For that purpose, the use of optimization algorithms, where the objective function is evaluated using a reservoir simulator, is needed. Furthermore, for complex reservoir geologies with high heterogeneities, the optimization problem requires algorithms able to cope with the non regularity of the objective function. In this paper, we propose an optimization methodology for determining optimal well locations and trajectories based on the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) which is recognized as one of the most powerful derivative-free optimizers for continuous optimization. In addition, to improve the optimization procedure two new techniques are proposed: – Adaptive penalization with rejection in order to handle well placement constraints; – Incorporation of a meta-model, based on locally weighted regression, into CMA-ES, using an approximate stochastic ranking procedure, in order to reduce the number of reservoir simulations required to evaluate the objective function. Z. Bouzarkouna · D. Ding IFP Energies nouvelles 1 & 4 avenue de Bois-Préau 92852 Rueil-Malmaison cedex, France E-mail: [email protected] D. Ding E-mail: [email protected] Z. Bouzarkouna · A. Auger TAO Team INRIA Saclay-̂Ile-de-France LRI Paris-Sud University 91405 Orsay cedex, France A. Auger E-mail: [email protected] The approach is applied to the PUNQ-S3 case and compared with a Genetic Algorithm (GA) incorporating the Genocop III technique for handling constraints. To allow a fair comparison, both algorithms are used without parameter tuning on the problem, standard settings are used for the GA and default settings for CMA-ES. It is shown that our new approach outperforms the genetic algorithm: it leads in general to both a higher net present value and a significant reduction in the number of reservoir simulations needed to reach a good well configuration. Moreover, coupling CMA-ES with a metamodel leads to further improvement, which was around 20% for the synthetic case in this study.