(371q) From Flexibility Evaluation to Economic Optimization: An Iterative Multi-Objective Framework for Process Design Under Uncertainty

Conventional process design methodologies have primarily focused on optimization at nominal operating points, often neglecting both exogenous and endogenous perturbation of the uncertain parameters, such as fluctuating feedstocks and market conditions or operational disturbances. This approach, while straightforward, often leads to designs that require the application of empirical overdesign factors to accommodate uncertainties. The reliance on nominal points and subsequent empirical overdesign leads to economically suboptimal design. Therefore, it is of importance to incorporate flexibility assessment early in the process design, allowing for a better understanding of operational feasibility and economic viability within a space of uncertainties. Especially for distillation process design, numerous design options exist depending on the sequence and the size of units. Uncertainties also exist particularly in the feed composition due to the reactor upstream processes.

Accordingly, flexibility which is defined as the ability of a process to accommodate a set of uncertain parameters was proposed to handle uncertainties in the design stage [1]. A flexibility index quantifies the degree of flexibility of the process, specifically, it represents the determination of largest hyperrectangle inscribed within the feasible space of the design. This concept is well established by pioneering work by Swaney and Grossmann through the mathematical formulation of the flexibility test problem which underscore the importance of a systematic approach to flexibility analysis [2]. Flexibility assessment through mathematical formulation of feasibility functions is considered difficult in their application due to the complexity of process systems which leads to the evaluation of feasibility by utilizing process simulating programs. Existing literature highlights that even for a constrained set of design candidates, conducting comprehensive feasibility analysis by process simulator requires time-consuming evaluations across a vast grid of uncertain parameters [3].

Even though significant efforts have been devoted in the literature to mathematically quantify accurate process flexibility, the feasible region is prone to being underestimated due to the use of a fixed shape, such as a hyperrectangle, for estimation and the specific convexity assumptions. Aiming to address this limitation, research has introduced a more accurate method to determine a non-convex feasible region by employing simplicial approximation. [4]. Further research has explored the potential of feasibility analysis using black-box methods such as a high dimensional model representation methodology or a surrogate-based method where only simple case studies are illustrated [5].

While previous studies have extensively focused on the evaluation of flexibility, direct application of theses evaluation in the process design remains unexplored. This paper proposes an iterative process design methodology that utilizes a surrogate based feasibility evaluation for assessing flexibility index. The process design is iteratively revised based on the flexibility index value, ensuring that the updated design modification aligns with the improvements in flexibility. An overall framework is constructed upon the foundation of gradient descent-based algorithms within a multi-objective optimization. Initially, the emphasis is on enhancing flexibility, and once the desired threshold of flexibility is achieved, focus shifts toward minimizing economic costs. The application of proposed method is demonstrated in the Fischer-Tropsch distillation process as a case study. Further research hopes to extend the methodology to consider not only simple configuration but also superstructure process synthesis.

Reference

[1] P. M. Hoch and A. M. Eliceche, “Flexibility analysis leads to a sizing strategy in distillation columns,” Computers & Chemical Engineering, vol. 20, pp. S139–S144, Jan. 1996.
[2] 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.
[3] Alessandro Di Pretoro, Ludovic Montastruc, Flavio Manenti, and X. Joulia, “Flexibility assessment of a biorefinery distillation train: Optimal design under uncertain conditions,” Computers & Chemical Engineering, vol. 138, pp. 106831–106831, Jul. 2020.
[4] V. Goyal and M. G. Ierapetritou, “Framework for evaluating the feasibility/operability of nonconvex processes,” AIChE Journal, vol. 49, no. 5, pp. 1233–1240, May 2003.
[5] 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.