(778d) Process Synthesis of Natural Gas to Liquid Transportation Fuels Under Uncertainty: A Robust Optimization Approach

As discussed in a recent perspective [1], natural gas has been explored as an exciting feedstock for the production of liquid transportation fuels [2], olefins [3], and aromatics [4] through advanced process synthesis and global optimization techniques in recent years. The growing abundance of natural gas as a feedstock, coupled with the importance of these products in society, provides substantial motivation for the discovery of optimum refinery topologies and product distributions. Focusing on natural gas to liquid transportation fuels (GTL) specifically, there are many different natural gas conversion routes using synthesis gas as an intermediate and processes such as methanol synthesis or Fischer-Tropsch conversion for final fuel production in the form of gasoline, diesel, and kerosene. Identifying the most cost-effective method for fuel production is imperative.

Process synthesis as a whole, however, has many areas in which uncertainty can appear in model parameters. This uncertainty can be detrimental to the optimal solutions, which may become infeasible or give objective function values worse than expected due to uncertain parameter realizations. To include parameter uncertainty in the model, uncertain constraints are reformulated using robust optimization [5]. The robust counterparts ensure that constraints will feasible for an uncertainty set of parameter realizations; the size of the uncertainty set can be determined using probabilistic bounds, in which considerable advances have recently been made [6-9]. These probabilistic bounds are utilized a priori and a posteriorito give robust solutions with minimal conservatism and known levels of risk.

Uncertainty has been included in the GTL process synthesis superstructure in order to incorporate price uncertainty from the key feedstocks and products through reformulation of the objective function. Uncertain parameters such as investment costs are also considered and discussed. The non-convex mixed-integer nonlinear optimization problems are solved to global optimality to give optimal solutions at known probabilities of constraint violation [10]. As the uncertainty appears in the objective function alone, probabilistically guaranteed levels of profit can be found with conservative assumptions about the probability distributions for uncertain parameters. An iterative method will be utilized to provide high quality robust solutions at low probabilities of constraint violation using the box, interval + ellipsoidal, and interval + polyhedral uncertainty sets [11]. The guaranteed and expected profit levels, optimal product distributions, and overall investment costs of the robust solutions will be discussed at varying probabilities of constraint violation. These insights will provide key information on the best GTL refinery topologies moving forward under uncertainty.

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[2] Baliban, R. C.; Elia, J. A.; Floudas, C. A. Novel Natural Gas to Liquids Processes: Process Synthesis and Global Optimization Strategies. AIChE Journal 2013, 59 (2), 505-531.

[3] Onel, O.; Niziolek, A. M; Floudas, C. A Optimal Production of Light Olefins from Natural Gas via the Methanol Intermediate. Industrial & Engineering Chemistry Research 2016, 55 (11), 3043-3063.

[4] Niziolek, A. M.; Onel, O.; Floudas, C. A. Production of benzene, toluene, and xylenes from natural gas via methanol: Process synthesis and global optimization. AIChE Journal 2016, 62(5), 1531-1556.

[5] Li, Z.; Ding, R.; Floudas, C. A. A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization. Industrial & Engineering Chemistry Research 2011, 50, 10567-10603.

[6] Li, Z.; Tang, Q.; Floudas, C. A. A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: II. Probabilistic Guarantees on Constraint Satisfaction. Industrial & Engineering Chemistry Research 2012, 51 (19), 6769-6788.

[7] Guzman, Y. A; Matthews, L. R; Floudas, C. A New a priori and a posteriori probabilistic bounds for robust counterpart optimization: I. Unknown probability distributions. Computers & Chemical Engineering 2016, 84, 568-598.

[8] Guzman, Y. A; Matthews, L. R; Floudas, C. A New a priori and a posteriori probabilistic bounds for robust counterpart optimization: II. A priori bounds for known symmetric and asymmetric probability distributions. 2016, In Preparation.

[9] Guzman, Y. A; Matthews, L. R; Floudas, C. A New a priori and a posteriori probabilistic bounds for robust counterpart optimization: III. A posteriori bounds for known probability distributions. 2016, In Preparation.

[10] Baliban, R. C; Elia, J. A; Misener, R.; Floudas, C. A. 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 2012, 42, 64-86.

[11] Li, Z.; Floudas, C. A. A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: III. Improving the Quality of Robust Solutions. Industrial & Engineering Chemistry Research 2014, 53 (33), 13112-13124.