Typical optimization problems in reservoir management (e.g. injection rates allocation in a waterflooding project) usually involve a high number of variables to be controlled. Model-based optimization techniques can be used to seek for control strategies able to maximize the asset performance. Another key issue is that model parameters are always affected by uncertainty, even after being conditioned to the historical data. Objective of this paper is to present a robust ensemble-based optimization methodology (EnOpt) for maximizing reservoir life-cycle production under geological uncertainty.

EnOpt is a simulator-independent technique which attempts to maximize an objective function by iteratively updating an ensemble of control variables along the direction of an estimated gradient. This method was applied for the control optimization of a 6-wells model inspired on a real field case, which is a heavy oil reservoir characterized by line-drive waterflood patterns with horizontal wells. We first evaluated different control strategies assuming perfect knowledge of model parameters (nominal optimization). Then, an ensemble of updated model realizations was included within the optimization framework (robust optimization) to represent the residual uncertainty after history matching.

In the nominal case we optimized the cumulative oil production over a period of 10 years using the injection bottom hole pressures as control variables. In order to investigate the possibility of limiting the water production, we also evaluated an alternative strategy based on the optimization of the Net Present Value. The overall results showed that the methodology is able to improve the selected objective function (up to 6% average increase with respect to a traditional pressure maintenance strategy), even though the associated optimal controls could be conditioned by the kind of information included in the gradient evaluation. In the robust case, optimization was intended as the maximization of the expected value of the objective function (here the cumulative oil production). In addition, the robust framework was implemented considering two alternative schemes, which differ by the ratios used for coupling the ensemble of model realizations with the ensemble of controls. The standard approach uses a one-to-one relationship between the two ensembles, whereas the second one is based on the application of a full set of controls to a smaller ensemble of representative models. We observed that the former performed slightly better (and with lower computational cost), although this behavior was ascribed to the relatively low degree of uncertainty. However, in both the cases we achieved an average increase in the objective function comparable to the optimization based on the hypothesis of known geology.

Effectiveness and flexibility are well-known strengths of EnOpt. Considering reservoir complexity and model uncertainty, the results of this application give further evidence of its feasibility and robustness for the production optimization of real cases on a larger scale.

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