##
462493 Robust Optimization of Biomass and Natural Gas to Liquid Transportation Fuel Refineries: Process Synthesis Under Uncertainty in Feedstock and Product Prices

In most process synthesis approaches, model parameters are assumed to be known and retain static parameter values. In reality, this is often not the case for parameters such as prices for feedstocks and products, among others; uncertain parameter realizations can have drastic impacts on the objective function values of the optimal solution, or even on overall model feasibility. Robust optimization is a framework for incorporating uncertainty which allows the optimization of large-scale process synthesis models which have uncertain parameters participating linearly in model constraints [8,9]. By imposing uncertainty sets for the parameters onto the model constraints, optimal solutions are found that ensure feasibility with known probabilities of constraint violation. Recent advances in robust optimization theory have greatly reduced the conservatism of robust solutions and allow the determination of competitive refinery topologies at known levels of risk through an iterative method utilizing *a priori *and *a posteriori* probabilistic bounds [10-13].

The process synthesis superstructure for converting biomass, specifically hardwood or switchgrass, and natural gas to liquid transportation fuels is a non-convex, nonlinear mixed-integer optimization problem, and is solved to global optimality using a rigorous branch-and-bound algorithm [14]. Robust solutions will be presented when robust optimization model counterparts are incorporated into the process synthesis superstructure for a refinery with uncertain price parameters. These parameters appear in the objective function, allowing probabilistic guarantees on the level of profit to be provided. The impact of uncertainty on the objective function value, feedstock utilization, product distribution, and investment costs will be discussed. Case studies will be conducted using the box, interval + ellipsoidal, and interval + polyhedral uncertainty sets, and an iterative method will be utilized in order to provide high quality robust solutions at low probabilities of constraint violation.

[1] Floudas, C. A.; Niziolek, A. M.; Onel, O.; Matthews, L. R. Multi-scale systems engineering for energy and the environment: Challenges and opportunities. AIChE Journal 2016, 62 (3), 602-623.

[2] Baliban, R. C.; Elia, J. A.; Floudas, C. A. Biomass to liquid transportation fuels (BTL) systems: process synthesis and global optimization framework. Energy Environ. Sci. 2013, 6 (1), 267-287.

[3] Baliban, R. C.; Elia, J. A.; Floudas, C. A. Biomass and Natural Gas to Liquid Transportation Fuels: Process Synthesis, Global Optimization, and Topology Analysis. Industrial & Engineering Chemistry Research 2013, 52 (9), 3381-3406.

[4] Baliban, R. C.; Elia, J. A.; Floudas, C. A.; Gurau, B.; Weingarten, M. B.; Klotz, S. D. Hardwood Biomass to Gasoline, Diesel, and Jet Fuel: 1. Process Synthesis and Global Optimization of a Thermochemical Refinery. Energy & Fuels 2013, 27 (8), 4302-4324.

[5] Onel, O.; Niziolek, A. M.; Elia, J. A.; Baliban, R. C.; Floudas, C. A. Biomass and Natural Gas to Liquid Transportation Fuels and Olefins (BGTL+C2_C4): Process Synthesis and Global Optimization. Industrial & Engineering Chemistry Research 2015, 54 (1), 359-385.

[6] Niziolek, A. M; Onel, O.; Hasan, M. M. F.; Floudas, C. A Municipal solid waste to liquid transportation fuels - Part II: Process synthesis and global optimization strategies. Computers & Chemical Engineering 2015, 74 (0), 184-203.

[7] Matthews, L. R; Niziolek, A. M; Onel, O.; Pinnaduwage, N.; Floudas, C. A Biomass to Liquid Transportation Fuels via Biological and Thermochemical Conversion: Process Synthesis and Global Optimization Strategies. Industrial & Engineering Chemistry Research 2016, 55 (12), 3203-3225.

[8] 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.

[9] 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.

[10] 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.

[11] 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.

[12] 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.

[13] 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.

[14] 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.

**Extended Abstract:**File Not Uploaded

See more of this Group/Topical: Computing and Systems Technology Division