Comparative study of different risk measures for robust optimization of oil production under the market uncertainty: a regret-based insight

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.