In the ensemble-based approach to production optimization (EnOpt), a steepest-ascent direction is computed from an ensemble of controls to iteratively improve a set of control settings. The method was shown to work well in maximizing field net present value (NPV) with an ensemble size of 104 on the Brugge SPE comparative test case for closed-loop optimization that had 84 controllable completion intervals (and 3,360 control variables), but performance of the method with smaller ensemble size or on larger problems might be difficult. Without regularization, the crosscovariance between control variables and the objective function is often likely to be dominated by spurious correlations. Because the update to the control variables is proportional to the covariance, spurious correlations will result in poor control settings.
We propose a localization method that updates the control setting to optimize the field production while reconciling information from each individual well. The proposed localization method reduces the effect of spurious correlations for improved performance. The Brugge test case is used as an example to show that with covariance localization, greater efficiency could be achieved through the use of a smaller ensemble, or that for a given ensemble size, the optimization results can be improved.