Fischer–Tropsch synthesis (FTS) has emerged as a promising pathway for the sustainable production of liquid hydrocarbons from syngas derived from natural gas or biomass [1]. Nonetheless, the intrinsically broad product distribution over a wide range of carbon numbers in the FTS mixture poses substantial challenges in the design of efficient separation processes, which are crucial for ensuring the commercial viability of FTS systems.
The inherent uncertainty of the FTS process, particularly in product composition caused by fluctuations in key parameters, further complicates the design of effective separation systems. Specifically, the hydrocarbon chain growth probability, represented by the alpha (α) value, and the olefin-to-paraffin (O/P) molar ratio directly determine the mass fractions of products with specific carbon numbers [2]. These uncertainties hinder the application of conventional process design methodologies in achieving efficient separations.
Conventional process design typically does not explicitly incorporate uncertainty at the design stage but rather addresses it during the operation stage. Such designs are usually optimized at a nominal point of uncertainty, focusing primarily on minimizing the total annualized cost (TAC). A potential approach to mitigate the effects of uncertainty is to introduce design factors or safety margins. However, this approach has inherent limitations, often leading to unnecessary capital investment [3]. Therefore, conventional approaches exhibit limitations when applied to systems like FTS mixture separations, which are highly sensitive to intrinsic uncertainties.
While flexibility analysis for existing process designs has gained attention as a means of addressing uncertainty, its direct integration into the early design stage remains relatively unexplored. Although some studies have applied flexibility analysis to modularized processes at the design stage, application to more complex systems has not yet been reported [4]. Therefore, in this work, we propose a flexible process design methodology which explicitly incorporates uncertainty at the design stage by defining an expected uncertainty space. This approach not only evaluates the expected TAC within the defined uncertainty space but also employs a flexibility index to quantitatively assess design feasibility across the entire uncertainty space [5].
To demonstrate the applicability of the proposed methodology, it is applied to the design of a linear alpha olefins production process that refines C6-C8 hydrocarbons derived from the FTS process, which is characterized by its inherent uncertainties. Once the uncertainties are explicitly defined within a specified range, corresponding feasibility data are extracted using a commercial process simulator. Based on these data, a surrogate model of the feasibility function is developed using a machine learning–based classification technique and subsequently employed to calculate the flexibility index [6]. Finally, the process is designed by simultaneously optimizing both the flexibility index and TAC as key performance indicators, thereby ensuring operational feasibility under uncertainty while contributing to a more economical process design.
Reference
[1] Z. Tian et al., “Product Distributions of Fischer‐Tropsch Synthesis over Core‐Shell Catalysts: The Effects of Diverse Shell Thickness,” ChemistrySelect, vol. 3, no. 44, pp. 12415–12423, Nov. 2018.
[2] V. R. R. Pendyala et al., “Fischer–Tropsch Synthesis: Effect of Activation Gas After Varying Cu Promoter Loading Over K-Promoted Fe-Based Catalyst,” Catalysis Letters, vol. 144, no. 9, pp. 1624–1635, Jul. 2014.
[3] R. Sinnott and G. Towler, Chemical Engineering Design. Oxford: Butterworth-Heinemann, 2009.
[4] A. Bhosekar and M. Ierapetritou, “Modular Design Optimization using Machine Learning-based Flexibility Analysis,” Journal of Process Control, vol. 90, pp. 18–34, Jun. 2020.
[5] R. E. Swaney and I. E. Grossmann, “An index for operational flexibility in chemical process design. Part I: Formulation and theory,” AIChE Journal, vol. 31, no. 4, pp. 621–630, Apr. 1985.
[6] F. Boukouvala and M. G. Ierapetritou, “Feasibility analysis of black-box processes using an adaptive sampling Kriging-based method,” Computers & Chemical Engineering, vol. 36, pp. 358–368, Jan. 2012.
