Process synthesis of natural gas to liquid transportation fuels (GTL) has demonstrated the impact that the growing natural gas supply can have on the national energy landscape [1, 2]. In the search for domestic feedstocks to replace petroleum, natural gas is appealing due to low costs, growing supply, and the ability to operate at equal, or lower, levels of greenhouse gas (GHG) emissions as petroleum operations [1, 3, 4]. However, due to constantly changing energy markets, the pricing of natural gas, gasoline, diesel, and kerosene, can be unpredictable; design of refineries with uncertainty in mind is vital in order to ensure profitability. Robust optimization provides a key methodology for incorporating uncertainty into process synthesis of GTL plants. The robust counterpart framework incorporates the uncertainty of model parameters into model constraints in order to ensure that each uncertain constraint is not violated for all possible parameter values in the given uncertainty set [5,6,7].
As seen in previous studies, the primary methods for GTL conversion involve reforming to synthesis gas via autothermal reforming or steam reforming, before further upgrading to fuels via methanol synthesis and conversion or Fischer-Tropsch processes . These conversion methods, in addition to other important refinery components including hydrogen and oxygen production, light gas handling, and wastewater treatment, are rigorously modeled for inclusion in a mixed-integer non-linear program (MINLP). A branch-and-bound algorithm is used to solve the MINLP to global optimality . The superstructure also includes simultaneous heat and power integration . The inclusion of uncertainty through robust optimization directly impacts the feedstock and product cost constraints, which must be converted from equality to inequality constraints for robust optimization theory to apply .
The resulting robust counterpart formulation allows for uncertainty to be handled with box, ellipsoidal, polyhedral, interval+ellipsoidal, or interval+polyhedral uncertainty sets . The uncertainty of natural gas, butane, liquefied petroleum gas, electricity, gasoline, diesel, and kerosene pricing was characterized using historical data from the past five years, in order to derive nominal values and the maximum perturbation values to consider. Ninety-six case studies were conducted on a 50,000 barrel per day plant in order to compare the impact of each uncertainty set at probabilities of constraint violation ranging from 5% to 95% . Using a priori and a posteriori bounds for the probability of constraint violation, an iterative method is utilized to guarantee the quality of the robust solutions . The distinct impact of uncertainty on the overall profit and plant topology is discussed, with direct comparison to the nominal case study. Other key considerations in plant design, including GHG emissions and investment costs, are also presented.
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 J. A. Elia, R. C. Baliban, and C. A. Floudas, “Nationwide, regional, and statewide energy supply chain optimization for natural gas to liquid transportation fuel (GTL) systems,” Industrial & Engineering Chemistry Research, vol. 53, no. 13, pp. 5366–5397, 2014.
 U.S. Energy Information Administration, “United States natural gas industrial price,” October 2014.
 U.S. Energy Information Administration, “Monthly biodiesel production report,” April 2015.
 Z. Li, R. Ding, and C. A. Floudas, “A comparative theoretical and computational study on robust counterpart optimization: I. Robust linear optimization and robust mixed integer linear optimization,” Industrial & Engineering Chemistry Research, vol. 50, no. 18, pp. 10567–10603, 2011.
 Z. Li, Q. Tang, and C. A. Floudas, “A comparative theoretical and computational study on robust counterpart optimization: II. probabilistic guarantees on constraint satisfaction,” Industrial & Engineering Chemistry Research, vol. 51, no. 19, pp. 6769–6788, 2012.
 Z. Li and C. A. Floudas, “A comparative theoretical and computational study on robust counterpart optimization: III. improving the quality of robust solutions,” Industrial & Engineering Chemistry Research, vol. 53, no. 33, pp. 13112–13124, 2014.
 R. C. Baliban, J. A. Elia, R. Misener, and C. A. Floudas, “Global optimization of a MINLP process synthesis model for thermochemical based conversion of hybrid coal, biomass, and natural gas to liquid fuels,” Computers & Chemical Engineering, vol. 42, no. 0, pp. 64 – 86, 2012. European Symposium of Computer Aided Process Engineering.
 R. C. Baliban, J. A. Elia, and C. A. Floudas, “Simultaneous process synthesis, heat, power, and water integration of thermochemical hybrid biomass, coal, and natural gas facilities,” Computers & Chemical Engineering, vol. 37, no. 0, pp. 297 – 327, 2012.
 X. Lin, S. L. Janak, and C. A. Floudas, “A new robust optimization approach for scheduling under uncertainty: I. Bounded uncertainty,” Computers & Chemical Engineering, vol. 28, pp. 1069 – 1085, 2004. FOCAPO 2003 Special issue.