Abstract
The scheduling of drilling and hydraulic fracturing of wells in an unconventional oil field plays an important role in the profitability of the field. A key challenge arising in this problem is the requirement that neither drilling nor oil production can be done at wells within a specified neighborhood of a well being fractured. We propose a novel mixed-integer linear programming (MILP) formulation for determining a schedule for drilling and fracturing wells in an unconventional oil field. We also derive an alternative formulation which provides stronger relaxations. In order to apply the MILP model for scheduling large fields, we derive a rolling horizon approach that solves a sequence of coarse time-scale MILP instances to obtain a solution at the daily time scale. We benchmark our MILP-based rolling horizon approach against a baseline scheduling algorithm in which wells are developed in the order of their discounted production revenue. Our experiments on synthetically generated instances demonstrate that our MILP-based rolling horizon approach can improve profitability of a field by 4–6%.
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References
Arps JJ (1945) Analysis of decline curves. Trans AIME 160(1):228–247
Arredondo-Ramirez K, Ponce-Ortega J, El-Halwagi M (2016) Optimal planning and infrastructure development for shale gas production. Energy Convers Manag 119:91–100
Cafaro C, Grossmann I (2014) Strategic planning, design, and development of the shale gassupply chain network. AIChE J 60:2122–2142
Cafaro C, Drouven M, GI E (2016) Optimization models for planning shale gas well refracture treatments. AIChE J 62:4297–4307
Cafaro DC, Drouven M, Grossmann I (2018) Continuous-time formulations for the optimal planning of multiple refracture treatments in a shale gas well. AIChE J 64:1511–1517
Carvalho MCA, Pinto J (2006) A bilevel decomposition technique for the optimal planning of offshore platforms. Braz J Chem Eng 23(1):67–82
Crafton J, Noe S (2013) Factors affecting early well productivity in six shale plays. In: SPE annual technical conference and exhibition. Society of Petroleum Engineers https://www.onepetro.org/conference-paper/SPE-166101-MS
Drouven M, Grossmann I (2017) Stochastic programming models for optimal shale well development and refracturing planning under uncertainty. AIChE J 63(11):4799–4813
Drouven MG, Grossmann I (2016) Multi-period planning, design, and strategic models for long-term, quality-sensitive shale gas development. Process Syst Eng 62:2296–2323
Etherington J, McDonald IR (2004) Is bitumen a petroleum reserve? In: SPE annual technical conference and exhibition. Society of Petroleum Engineers
ExxonMobil-Newsroom (2017) Exxonmobil to acquire companies doubling Permian basin resource to 6 billion barrels. https://corporate.exxonmobil.com/news/newsroom/news-releases/2017/0117_exxonmobil-to-acquire-companies-doubling-permian-basin-resource-to-6-billion-barrels
ExxonMobil-Newsroom (2019) Exxonmobil to increase, accelerate Permian output to 1 million barrels per day by 2024. https://corporate.exxonmobil.com/News/Newsroom/News-releases/2019/0305_ExxonMobil-to-increase-accelerate-Permian-output-to-1-million-barrels-per-day-by-2024
Garey M (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, NewYork
Goel V, Grossmann I (2004) A stochastic programming approach to planning of offshore gas field developments under uncertainty in reserves. Comput Chem Eng 28(8):1409–1429
Gupta J (1988) Two-stage, hybrid flowshop scheduling problem. J Oper Res Soc 39(4):359–364
Iyer RR, Grossmann IE, Vasantharajan S, Cullick AS (1998) Optimal planning and scheduling of offshore oil field infrastructure investment and operations. Industrial and Engineering Chemistry Researchl 37:1380–1397
Knudsen B, Foss B (2013) Shut-in based production optimization of shale-gas systems. Comput Chem Eng 58:54–67
Kondili E, Pantelidas C, Sargent R (1993) A general algorithm for short-term scheduling of batch operations, milp formulation. Comput Chem Eng 17:211–227
Lee T, Loong Y (2019) A review of scheduling problem and resolution methods in flexible flow shop. Int J Ind Eng Comput 10:67–88
Lin X, Christodoulos A (2003) A novel continuous-time modeling and optimization framework for well platform planning problems. Optim Eng 4:65–95
Manchanda R, Bhardwaj P, Hwang J, Sharma M (2018) Parent–child fracture interference: explanation and mitigation of child well underperformance. In: SPE annual technical conference and exhibition. Society of Petroleum Engineers. https://www.onepetro.org/conference-paper/SPE-189849-MS
Marquant JF, Evins R, Carmeliet J (2015) Reducing computation time with a rolling horizon approach applied to a milp formulation of multiple urban energy hub system. In: ICCS 2015 international conference on computational science, pp 2137–2146
Office of Fossil Energy (2013) Natural gas from shale. US Department of Energy, Washington
Ondeck A, Drouven M, Blandino N, Grossmann I (2019) Multi-operational planning of shale gas pad development. Comput Chem Eng 126:83–101
Rahmanifard H, Plaksina T (2018) Application of fast analytical approach and ai optimization techniques to hydraulic fracture stage placement in shale gas reservoirs. J Nat Gas Sci Eng 52:367–378
Sam M, DAriano A, Pacciarelli D (2013) Rolling horizon approach for aircraft scheduling in the terminal control area of busy airports. Procedia Soc Behav Sci 80:531–552
Silvente J, Kopanos GM, Pistikopoulos EN, Espuna A (2015) A rolling horizon optimization framework for the simultaneous energy supply and demand planning in microgrids. Appl Energy 155:485–501
Spratt B, Kozan E (2018) An integrated rolling horizon approach to increase operating theatre efficiency. https://arxiv.org/abs/1808.10139
Tarhan B, Grossmann I, Goel V (2009) Stochastic programming approach for the planning of offshore oil or gas field infrastructure under decision-dependent uncertainty. Ind Eng Chem Res 48(6):3078–3097
US Energy Information Administration EIA (2019) Tight oil development will continue to drive future U.S. crude oil production. Today in Energy
Wang H (2016) Numerical investigation of fracture spacing and sequencing effects on multiple hydraulic fracture interference and coalescence in brittle and ductile reservoir rocks. Eng Fract Mech 157:107–124
Xie J, Wang X (2005) Complexity and algorithms for two-stage flexible flowshop scheduling with availability constraints. Comput Math Appl 50(10–12):1629–1638
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Soni, A., Linderoth, J., Luedtke, J. et al. Mixed-integer linear programming for scheduling unconventional oil field development. Optim Eng 22, 1459–1489 (2021). https://doi.org/10.1007/s11081-020-09527-6
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DOI: https://doi.org/10.1007/s11081-020-09527-6