(537a) Addressing Uncertainty in Large-Scale Bioconversion Product and Process Networks with Two-Stage Adaptive Robust Optimization

Daniel J. Garcia^a, Jian Gong^b,Fengqi You^b*

1. Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL, 60626
2. Department of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York, 14853

*Email: Fengqi.you@cornell.edu

Submitted for consideration in session 10A01 Design and Operations Under Uncertainty

While enthusiasm towards production of biofuels and bioproducts has fallen somewhat out of favor in recent years, these products could be a renewable alternative to petroleum fuels and chemicals in the future. There are many questions on which biofuels to produce, which feedstocks to use, and if the net life cycle CO₂ emissions of biofuels even are lower than their petroleum counterparts.¹ Biofuel production is fraught with a host of uncertainties. If biofuels or bioproducts are to be economically and environmentally feasible, then identifying optimal production pathways from feedstock to fuels and chemicals is crucial.^2-5 However, previous works that aim to optimize biofuel production both for cost and environmental impacts typically treat the input parameters as deterministic rather than uncertain. In reality, there are many parameters of the bioconversion processes that are uncertain. For example, feedstock price and product demand often vary significantly over time. If bioconversion pathways are optimized without considering these uncertainties, then it is possible that the identified designs might be infeasible for certain realizations of the uncertainties.⁶ This uncertainty and others throughout the bioconversion process must be considered if optimal bioconversion pathways are to be identified.⁷

Thus, in this work, we construct a two-stage adaptive robust mixed integer nonlinear programming (MINLP) problem to identify optimal bioconversion pathways from a large-scale bioconversion product and process network of alternatives. Feedstock price and final product demand are considered uncertain and are modeled with uncertainty sets. The network we consider has 194 different technologies and 139 feedstocks, intermediates, byproducts, and final products.² We choose an adaptive robust approach rather than a conventional robust optimization approach to identify less conservative solutions that could be more practical.^8-10 Stochastic programming could be another modeling alternative, but this method requires knowledge of the probability distribution of values the uncertain parameter can take, which is often difficult to obtain.^11,12 After formulating a two-stage adaptive robust MINLP model, we propose a solution method that combines a column-and-constraint generation algorithm and a branch-and-refine algorithm. We compare results from the two-stage adaptive robust model, a deterministic model with no consideration of uncertainty, and results from a conventional static robust version of the model. Decisions to be made in the model include technology selection, capacity sizing of each chosen technology, operating level of each technology, CAPEX and OPEX, and quantities of feedstocks to purchase and products to produce. Nominal values for biomass feedstock prices and product demands were taken from previous works, and readily available statistical reports or official government reports were used to determine the ratio of the largest deviation of the uncertain parameters from their nominal values.^1,2,13,14

Adaptive robust optimization provides optimal solutions for each uncertainty level of each uncertain parameter. The minimum total annualized cost of the deterministic version of the model (uncertainty budgets of 0 for all uncertain parameters) is the lowest at $17.9M/y, and the most conservative two-stage adaptive robust optimal solution has the highest cost at $22.5M/y. As the uncertainty budgets decrease, the overall annualized cost decreases, but the risk of being unable to meet demand at the lowest possible cost increases. Soybeans and softwood are used in all solutions in varying amounts to produce ethanol, gasoline, biodiesel, and polyhydroxybutyrate (PHB). In the adaptive robust solutions, more softwood is purchased and more gasoline is produced via gasification, syngas reforming, methanol synthesis, and the methanol to gasoline process than in the deterministic solution. Increasing the feedstock price or product demand uncertainty budgets increase the total annualized cost in all cases. However, if the feedstock price uncertainty budget is higher than 2, the uncertainty budget of product demand does not influence the minimum annualized cost much. Therefore, the final solutions are more sensitive to product demand uncertainty than feedstock price uncertainty, an important result for the biofuels industry. The range of results provided from the two-stage adaptive robust approach in this work provide decision-makers with more information, allowing for more tailored decisions.

References

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