Model-based production optimization relies on a dynamic model that simulates the fluid flow in the oil reservoirs, and an economic objective function that assigns an economic measure to the recoverable oil reserves. An optimization algorithm utilizes the dynamic model to find the production scenario which maximizes the economic measure of profit. However, due to incompleteness and doubtfulness of available data, the reservoir model describing the complex subsurface geology is quite uncertain. Moreover, the definition of the economic objective functions such as net present value (NPV) requires economic variables such as oil price, interest rate, and production costs which unpredictably vary with time. In recent years, robust optimization (RO) has been widely used as an appropriate tool for handling the uncertainties in production optimization problems. However, previous works on robust optimization paid less attention to economic uncertainties arising from market volatility. Instead, they are mostly focused on geological uncertainties. This paper is devoted to production optimization under oil market uncertainty. To narrow down the range of economic uncertainties, a Bayesian framework for oil price history matching and forecasting has been developed which allows generating more reliable realizations of oil price future trend. It is common to include a measure of risk-averse in the objective function of RO problems. However, the quality of the solutions depends directly on the used risk measure. In the oil industry, risk measures such as worst-case scenario and CVaR (Conditional Value at Risk) have been used to mitigate the risk of low-profit realizations. These risk measures are appropriate in many cases for measuring the robustness. Though, they are inadequate in evaluating robustness in a relative sense in cases where the worst-case realizations have an undue effect on the final decisions. The risk measure defined based on the minimax regret approach takes into account all realizations instead of just considering the worst-case realizations. In this research, RO has been performed to maximize NPV using the minimax regret approach. In addition, the results are compared with the common risk measures used in the oil industry including expected profit, CVaR, and worst-case. Results show that while worst-case scenario and CVaR perform better than other risk measures in lower-profit realizations, they give inappropriate results for other scenarios. In contrast, regret-based approach and expected profit give nearly optimum solutions for all realizations. In this paper, the minimax regret approach was compared with other risk measures in the presence of oil price uncertainty. However, the results might be extended to optimization under geological uncertainty.

中文翻译：

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市场不确定性下用于稳健优化石油生产的不同风险措施的比较研究：基于遗憾的见解

基于模型的生产优化依赖于模拟油藏中流体流动的动态模型，以及为可采石油储量分配经济指标的经济目标函数。优化算法利用动态模型来找到使利润的经济度量最大化的生产方案。但是，由于可用数据的不完整和可疑性，描述复杂地下地质的储层模型是非常不确定的。此外，诸如净现值（NPV）之类的经济目标函数的定义要求诸如油价，利率和生产成本之类的经济变量，这些变量会随时间而变化。最近几年，稳健优化（RO）已被广泛用作处理生产优化问题中不确定性的适当工具。但是，先前关于鲁棒优化的工作很少关注市场波动引起的经济不确定性。相反，他们主要集中在地质不确定性上。本文致力于石油市场不确定性下的生产优化。为了缩小经济不确定性的范围，已经开发了用于油价历史匹配和预测的贝叶斯框架，该框架允许生成更可靠的油价未来趋势实现。在反渗透问题的目标函数中通常包括规避风险的措施。但是，解决方案的质量直接取决于所使用的风险度量。在石油工业中 最坏的情况和CVaR（有条件的风险价值）等风险衡量指标已被用来减轻低利润实现的风险。在许多情况下，这些风险措施都适用于测量鲁棒性。但是，在最坏情况的实现对最终决策产生不适当影响的情况下，它们不足以相对意义上的评估鲁棒性。基于最小极大后悔法定义的风险度量考虑了所有实现，而不仅仅是考虑最坏情况的实现。在这项研究中，使用最小最大后悔方法进行了反渗透以最大化NPV。此外，将结果与石油行业中使用的常见风险度量（包括预期利润，CVaR和最坏情况）进行比较。结果表明，在利润较低的情况下，最坏情况和CVaR的表现要好于其他风险度量，但对于其他情况，它们却给出了不适当的结果。相反，基于遗憾的方法和预期利润为所有实现提供了几乎最佳的解决方案。在本文中，在油价存在不确定性的情况下，将最小最大后悔法与其他风险措施进行了比较。但是，结果可能会扩展到地质不确定性条件下的优化。