Application of Statistical Proxies to Speed Up Field Development Optimization Procedures
Authors: Onwunalu Jerome , Litvak Michael , Durlofsky Louis J. , Aziz Khalid 
Published: June 2009

Abstract
Field development optimization is a computationally intensive task due to the large number of reservoir simulation runs required. These simulations can be expensive, especially for large and complex reservoir models. Proxies can be used to efficiently estimate the objective function value for new scenarios and can act to reduce the number of simulations required. Thus they can be very useful for speeding up field development optimization.
In this paper a procedure that combines an optimization algorithm (in this case a genetic algorithm or GA) and a new statistical proxy is described. The statistical proxy has the following key elements. First, a new selection procedure called individual-based selection is applied to decide which individuals (scenarios) are to be simulated. Second, the new approach uses multiple proxies for optimization problems involving multiple reservoir models, which are needed to account for geological uncertainty. Third, the statistical proxy is modified to work efficiently in distributed computing environments. Finally, the proxy procedure is successfully incorporated into an existing general field development optimization package (Williams et al., 2004; Litvak et al., 2007a).
In the individual-based selection method, for each scenario the proxy estimate of the objective function is compared to a threshold. If the estimate exceeds the threshold, then the case is simulated (otherwise it is not simulated). The threshold corresponds to a specified percentile of the cumulative distribution function constructed from previously simulated cases and therefore changes during the course of the optimization. In cases with multiple reservoir models, each model has its own corresponding proxy. This eliminates the problem of duplicate objective function estimates for different reservoir models, which may occur with previous proxy-based methods. The individual-based selection method is shown to perform better for a particular example than the population-based method published previously.
The overall procedure is applied to the optimization of infill drilling where we maximize the incremental net present value (NPV) by optimizing new well locations, well type and rig schedule, subject to field development constraints. We demonstrate the capabilities of the proxy using synthetic reservoir models and a real field in the Gulf of Mexico. In the first example, two optimization cases are considered, corresponding to the use of single and multiple reservoir models. In the case with one reservoir model, the hybrid procedure found the same field development scenario compared to GA only, and required 85% fewer simulations. In the case with multiple reservoir models, the hybrid procedure found a slightly different field development scenario than the pure GA approach, though the NPV from the hybrid procedure was within 1% of that using only GA. The hybrid approach, however, required 91% fewer simulations for this case. In the field application, a better field development scenario with 45% fewer simulations was found using the hybrid algorithm (GA and proxy) compared to using only GA. These examples clearly demonstrate the effectiveness of the statistical proxy procedure for accelerating field development optimization.