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