Partially separated meta-models with evolution strategies for well placement optimization

Finding the optimal location of non-conventional wells increases significantly the project's Net Present Value (NPV). This problem is nowadays one of the most challenging problems in oil and gas fields development. When dealing with complex reservoir geology and high reservoir heterogeneities, stochastic optimization methods are the most suitable approaches for optimal well placement. However, these methods require in general a considerable computational effort (in terms of number of reservoir simulations, which are CPU time demanding). This paper presents the use of the CMA-ES (Covariance Matrix Adaptation - Evolution Strategy) optimizer, which is recognized as one of the most powerful derivative free optimizers, to optimize well locations and trajectories. A local regression based meta-model is incorporated into the optimization process in order to reduce the computational cost. The objective function (e.g., the NPV) can usually be split into local components referring to each of the wells: it depends in general on a smaller number of principal parameters, and thus can be modeled as a partially separable function. In this paper, we propose to exploit the partial separability of the objective function into CMA-ES coupled with meta-models, by building partially separated meta-models. Thus, different meta-models are built for each well or set of wells, which results in a more accurate modeling. An example is presented. Results show that taking advantage of the partial separability of the objective function leads to a significant decrease in the number of reservoir simulations needed to find the "optimal" well configuration, given a restricted budget of reservoir simulations. This approach is practical and promising when dealing with a large number of wells to be located.