The need to reconcile conflicting objectives regarding project value often arises. When reservoir uncertainty is represented with a set of alternative reservoir models (robust approach), typical conflicting objectives are the maximization of project value and the minimization of the risk, which, in turn, could be expressed as the maximization of the minimum project value under the uncertainties affecting it.
Unfortunately, multi-models based optimization often requires large computational costs, imposing severe limitations to the industrial applications, especially with large-scale cases with hundreds of reservoir model realizations.
This work aims at developing a new methodology able to achieve an affordable robust multi-objective optimization with a reasonable computational effort. The main feature of the proposed approach is the use of "proxy models", analytical functions that, conveniently calibrated, can approximate the reservoir behaviour and surrogate the full model simulator with very low computational cost. Proxy models are commonly adopted within reservoir uncertainty estimations; the new approach herein presented extends the idea of building proxy models considering both uncertainty parameters and control variables related to the development strategy.
The validation on a real case (a complex offshore reservoir) confirms the possibility to explore many alternative control strategies keeping the computational costs within reasonable limits, with a benefit for the decision-making process.
Reservoir engineering problems often involve conflicting objectives, such as the short-term oil production and the ultimate oil recovery [1], the recovery factor and the production plateau length [2], the undiscounted and the highly discounted Net Present Value [3]. In such cases, the identification of a set of optimal solutions (rather than a single one) is recommended to properly support the decision-making process (multi-objective optimization). Moreover, as the reservoir characterization always comes with uncertainties, it is preferable to consider an ensemble of plausible reservoir models to account for such uncertainties on forecasts (robustness of solution). The optimization accounting for uncertainties is known in this context as "robust optimization". When the reservoir uncertainty is represented by a set of alternative models (reservoir model realizations), two strategies are usually adopted to deal with robust multi-objective optimization problems.
