(23e) Integrated Biorefinery Design Under Multi-Scale Uncertainties

With the increasing awareness to reduce the carbon oxide emission in the chemical industry, using biomass as the feedstock for chemical production has gained significant interest in recent years. Promising processes have been designed to produce p-xylene from cellulose¹, furfural² and other value-added products³ from hemicellulose, as well as phenols from lignin⁴. The concept of the biorefinery is developed to enable efficient utilization of all components in the biomass feedstock to increase the revenue and thus the process economic viability. The challenge of biorefinery design lies in rationally choosing different feedstocks, potential products and technology alternatives under different demand and supply constraints. Consequently, a superstructure optimization framework is often utilized to solve this problem. Yuan and Eden applied superstructure optimization to an integrated fast pyrolysis and gasification biorefinery to compare different conversion routes.⁵ Superstructure model is also developed by Gong and You for an algal biorefinery to determine the optimal configuration and operating conditions.⁶

Many parameters used in the biorefinery design come with considerable uncertainties. For instance, experimental yields and separation efficiencies are often utilized for industrial-scale plant design. However, there are inevitably subject to intrinsic variations and inaccurate measurement. Moreover, the performance of scaled-up processes may differ from its bench-scale counterpart.⁷ The feedstock supply and composition provide another source of uncertainties to be considered in process design. Meanwhile, the prices of chemicals are volatile and unpredictable, affecting the plant's profitability.⁸ Incorporating uncertainties in optimization has gained growing attention over recent years.⁹ Currently, the number of uncertain parameters considered in the process design is limited by computational complexity. Two commonly used optimization methods under uncertainty are robust optimization and stochastic programming. Stochastic programming uses probability distributions of uncertain parameters to build the scenario tree and calculate the expected values as objective functions. Proper sampling and scenario reduction techniques are crucial to its implementation.¹⁰ When ensuring process feasibility is the top priority, or only ranges of parameters are known, the robust optimization problem should be adopted to provide a conservative process design that is feasible even in the worst case.¹¹

In practice, uncertainties from various sources may have different impacts on the process outcome.¹² In the multistage optimizations under uncertainty, wait-and-see decisions are taken after the uncertainty’s realization, which are captured by the affine decision rule in the adaptive robust optimization.¹³ On the other hand, decisions may affect the endogenous uncertainty’s distribution or the time it realizes.¹⁴ Furthermore, uncertainties associated with process operation or product quality need to be treated with more care to ensure the process's feasibility in all scenarios. Other uncertainties, including market prices, are less restricted, for which optimizing expected profit is more appropriate.¹² Yue and You also formulated a stochastic robust optimization that distinguishes uncertainties associated with strategic and operational decisions.⁷

In this work, we consider a unified framework to include different levels of uncertainties in the biorefinery design. Various feedstocks, including lignocellulosic biomass, food waste and technical lignin, introduce the flexibility for supply but also composition uncertainty. Based on experimental data, processing block flowsheets are developed in Aspen Plus to synthesize a variety of chemicals from biomass.¹⁵ The input, output, operating and capital cost information of each block is extracted and scaled to formulate the optimization problem’s objective functions and constraints. Both the profitability and environmental benefits are main driven forces for biorefinery development. Thus, a multi-objective optimization problem is formulated to simultaneously minimize the greenhouse gas emissions based on life cycle assessment (LCA) and maximize profit. We first identify the primary sources of uncertainties and classify them based on their main effects of various decision making including process design, operation and LCA. The LCA calculation is independent of the previous stages, meaning that its uncertainty analysis could be performed after finalizing the plant configuration. Its uncertainty provides a reference for the accuracy of our objective values obtained from the optimization problem. Next, uncertainties on the prices and demands are considered in the strategic decisions that maximize the expected profit, while those associated with feedstock and operating conditions are more restrictive so that the feasibility is satisfied throughout the entire uncertainty range. This biorefinery design problem is solved by a combination of robust optimization and stochastic programming techniques.

Reference

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