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The geology of oil reservoirs is largely unknown. Consequently, the reservoir models used for production optimization are subject to significant uncertainty. To minimize the associated risk, the oil literature has mainly used ensemble-based methods to optimize sample estimated risk measures of net present value (NPV). However, the success in reducing risk critically depends on the choice of risk measure. As a systematic approach to risk mitigation in production optimization, this paper characterizes proper risk measures by the axioms of coherence and aversion. As an example of a proper measure, we consider conditional value-at-risk, $\text{CVaR}_{\alpha}$, at different risk levels, $\alpha$. The potential of $\text{CVaR}_{\alpha}$ to minimize profit loss is demonstrated by a simulated case study. The case study compares $\text{CVaR}_{\alpha}$ to real-world best practices, represented by reactive control. It shows that for any risk level, $\alpha$, we may find an optimized strategy that provides lower risk than reactive control. However, despite overall lower risk, we see that all optimized strategies still yield some unacceptable low profit realizations relative to reactive control. To remedy this, we introduce a risk mitigation method based on the NPV offset distribution. Unlike existing methods of the oil literature, the offset risk mitigation approach minimizes the risk relative to a reference strategy representing common real-life practices, e.g. reactive control. In the simulated case study, we minimize the worst case profit offset to reduce the risk of realizations that do worse than the reactive strategy. The results suggest that it may be more relevant to consider the NPV offset distribution than the NPV distribution when minimizing risk in production optimization. |
