Abstract
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.
Similar content being viewed by others
References
Brouwer, D.: Dynamic water flood optimization with smart wells using optimal control theory [D]. Delft University of Technology, Delft (2004)
Van den Hof, P.M., J.D. Jansen, and A. Heemink. Recent developments in model-based optimization and control of subsurface flow in oil reservoirs. in Proceedings of the 2012 IFAC Workshop on Automatic Control in Offshore Oil and Gas Production. 2012
Foss, B.: Process control in conventional oil and gas fields—challenges and opportunities. Control. Eng. Pract. 20(10), 1058–1064 (2012)
Van den Hof, P.M., et al. Model-based control and optimization of large scale physical systems-challenges in reservoir engineering. In Control and Decision Conference, 2009. CCDC’09. Chinese. 2009. IEEE
van Essen, G., et al.: Robust waterflooding optimization of multiple geological scenarios. SPE J. 14(01), 202–210 (2009)
Capolei, A., et al.: Waterflooding optimization in uncertain geological scenarios. Comput. Geosci. 17(6), 991–1013 (2013)
Siraj, M.M., Van den Hof, P.M., Jansen, J.D.: Robust optimization of water-flooding in oil reservoirs using risk management tools. IFAC-PapersOnLine. 49(7), 133–138 (2016)
Alhuthali, A.H., et al.: Optimizing smart well controls under geologic uncertainty. J. Pet. Sci. Eng. 73(1–2), 107–121 (2010)
Capolei, A., L.H. Christiansen, and J.B. Jørgensen, Risk minimization in life-cycle oil production optimization. ar**v preprint ar**v:1801.00684, 2018
Capolei, A., Foss, B., Jørgensen, J.B.: Profit and risk measures in oil production optimization∗. IFAC-PapersOnLine. 48(6), 214–220 (2015)
Yeten, B., Durlofsky, L.J., Aziz, K.: Optimization of nonconventional well type, location, and trajectory. SPE J. 8(03), 200–210 (2003)
Bailey, W.J., Couët, B.: Field optimization tool for maximizing asset value. SPE Reserv. Eval. Eng. 8(01), 7–21 (2005)
Capolei, A., et al.: A mean–variance objective for robust production optimization in uncertain geological scenarios. J. Pet. Sci. Eng. 125, 23–37 (2015)
Hauser, R., V. Krishnamurthy, and R. Tütüncü, Relative robust portfolio optimization. ar**v preprint ar**v:1305.0144, 2013
Kouvelis, P. and G. Yu, Robust discrete optimization and its applications. Vol. 14. 2013: Springer Science & Business Media
Wen, T., Waterflood optimization using streamlines and reservoir management risk analysis with market uncertainty. 2014, Stanford University
Bashiri Behmiri, N. and J.R. Pires Manso, Crude oil price forecasting techniques: a comprehensive review of literature. 2013
Lee, C.-Y., Huh, S.-Y.: Forecasting long-term crude oil prices using a Bayesian model with informative priors. Sustainability. 9(2), 190 (2017)
Rockafellar, R.T., Uryasev, S.: Conditional value-at-risk for general loss distributions. J. Bank. Financ. 26(7), 1443–1471 (2002)
Ben-Tal, A., L. El Ghaoui, and A. Nemirovski, Robust optimization. Princeton series in applied mathematics. 2009, Princeton University Press Princeton
Mohammadi, S.E. and E. Mohammadi, Robust portfolio optimization based on minimax regret approach in Tehran stock exchange market
Baumeister, C., Kilian, L.: Forty years of oil price fluctuations: why the price of oil may still surprise us. J. Econ. Perspect. 30(1), 139–160 (2016)
Yergin, D., The prize: the epic quest for oil, money & power. 2011: Simon and Schuster
https://www.macrotrends.net/1369/, crude-oil-price-history-chart
Kilian, L.: Not all oil price shocks are alike: disentangling demand and supply shocks in the crude oil market. Am. Econ. Rev. 99(3), 1053–1069 (2009)
Bodenstein, M., Guerrieri, L., Kilian, L.: Monetary policy responses to oil price fluctuations. IMF Econ. Rev. 60(4), 470–504 (2012)
Kilian, L., Lee, T.K.: Quantifying the speculative component in the real price of oil: the role of global oil inventories. J. Int. Money Financ. 42, 71–87 (2014)
Armstrong, J.S., Evaluating forecasting methods. In Principles of Forecasting. Kluwer Academic Publishers: Norwell, MA, USA, 2001. pp. 443–472
Yildirim, I., Bayesian inference: Gibbs sampling. Technical Note, University of Rochester, 2012
Geweke, J., et al., The Oxford handbook of Bayesian econometrics. 2011: Oxford University Press
Organization of the Petroleum Exporting Countries (OPEC). 2017 World oil outlook; OPEC secretariat: Vienna, A., 2017
British Petroleum (BP). BP statistical review of world energy 2017; BP: London, U., 2017
https://www.macrotrends.net/1329/us-dollar-index-historical-chart
Energy, B., Marginal cost curve - understanding the link between growth and returns. 2016
Kennedy, J. and R. Eberhart, Particle swarm optimization, Proceedings of IEEE International Conference on Neural Networks (ICNN’95) in. 1995
Jansen, J., et al.: The egg model–a geological ensemble for reservoir simulation. Geosci. Data J. 1(2), 192–195 (2014)
Onwunalu, J.E., Durlofsky, L.J.: Application of a particle swarm optimization algorithm for determining optimum well location and type. Comput. Geosci. 14(1), 183–198 (2010)
Siavashi, M., Doranehgard, M.H.: Particle swarm optimization of thermal enhanced oil recovery from oilfields with temperature control. Appl. Therm. Eng. 123, 658–669 (2017)
Jesmani, M., et al. Particle swarm optimization algorithm for optimum well placement subject to realistic field development constraints. In SPE Reservoir Characterisation and Simulation Conference and Exhibition. 2015. Society of Petroleum Engineers
Ding, S., et al., Optimization of well location, type and trajectory by a modified particle swarm optimization algorithm for the PUNQ-S3 model. Journal of Industrial and Intelligent Information. 4(1), (2016)
Jansen, J.-D., R. Brouwer, and S.G. Douma. Closed loop reservoir management. In SPE reservoir simulation symposium. 2009. Society of Petroleum Engineers
Shi, Y. and R. Eberhart. A modified particle swarm optimizer. In 1998 IEEE international conference on evolutionary computation proceedings. IEEE world congress on computational intelligence (Cat. No. 98TH8360). 1998. IEEE
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mohammadi, M., Ahmadi, M. & Kazemi, A. Comparative study of different risk measures for robust optimization of oil production under the market uncertainty: a regret-based insight. Comput Geosci 24, 1409–1427 (2020). https://doi.org/10.1007/s10596-020-09960-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10596-020-09960-7