Practical Use of the Ensemble-Based Conjugate Gradient Method for Production Optimization in the Brugge Benchmark Study

摘要

The concept of the ensemble-based optimization has matured over the last several years and is rooted in the field of reservoir-model-based production optimization. Usually, a backtracking line search scheme is used, but this approach often leads to inefficient searching path direction (e.g. zig-zag patterns). As such, it has some redundancies in finding an optimal solution effectively, increasing the computational overhead with greater risk of problematic numerical instability. Here, we introduce a trust-region conjugate gradient method embedded in EnOpt, motivated by the general applicability and the success in practice. The approach is tested on a synthetic truth model developed by TNO, namely the Brugge benchmark model. The optimization strategy is to control maximum allowed water cut in each connection at which control valves (ICVs) are closed, and the objective is to maximize the net-present-value (NPV). Injectors are controlled using voidage replacement. The methodology performs well on the case considered here. In particular, we use the entire ensemble of controls to adapt the covariance matrix. As such, the gradient estimate of EnOpt is statistically equivalent to that of a Gaussian Mutation Optimization (GMO) algorithm.