Partially Separated Metamodels With Evolution Strategies for Well-Placement Optimization

Abstract

Summary The net present value (NPV) of a project can be significantly increased by finding the optimal location of non-conventional wells. This optimization problem is nowadays one of the most challenging problems in oil-and gas-field development. Suitable methods to tackle this problem include stochastic optimization algorithms, which are particularly robust and able to deal with complex reservoir geology with high heterogeneities. 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, recognized as one of the most powerful derivative free optimizers, to optimize well locations and trajectories. A local-regression-based metamodel 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 that moreover 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 metamodels by building partially separated metamodels. Thus, different metamodels 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. The proposed approach is practical and promising to deal with the placement of a large number of wells.