# (636f) Robust Optimization of Biomass and Natural Gas to Liquid Transportation Fuel Refineries: Process Synthesis Under Uncertainty in Feedstock and Product Prices

- Conference: AIChE Annual Meeting
- Year: 2016
- Proceeding: 2016 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Thursday, November 17, 2016 - 10:20am-10:42am

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.

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