# (112g) Simultaneous Synthesis and Design of Reaction-Separation-Recycle Processes Using Rigorous Models

- Conference: AIChE Annual Meeting
- Year: 2019
- Proceeding: 2019 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Monday, November 11, 2019 - 2:24pm-2:43pm

Many efforts have been made for either obtaining optimal reaction-separation process routes based on simplified or surrogate models, and/or optimizing all unit parameters of a fixed reaction-separation flowsheet using rigorous models (Recker et al., 2015). Very few efforts have been made for simultaneous synthesis and design of reaction-separation processes using rigorous models (Zhang et al., 2018). Zhang et al. (2018) proposed a superstructure-based optimization approach for such simultaneous synthesis and design of integrated reaction-separation process using rigorous models. The superstructure was modelled using generalized disjunctive programming (GDP)(Grossmann & Trespalacios, 2013), which was then reformulated into a mixed-integer nonlinear programming (MINLP) model using the big-M approach, leading to worse MILP relaxation and high computational expense. In addition, the feasibility of their approach largely depends on the initial points. How to systematically generate such good initial points is not given.

In this work, we first use the superstructure proposed by Lakshmanan and Biegler (1996) to represent the reactor network, which is more efficient than that in Zhang et al. (2018). In the superstructure, the outlet stream from a reactor can be fed into downstream reactors. Therefore, it can represent all possible reactor configurations in serial, parallel or hybrid with fewer number of reactors. The separation network only involves distillation columns, which is represented by using the state-task network (STN) (Yeomans & Grossmann, 2000) as it can lead to smaller scale model. The superstructure for the integrated reaction-separation system is modelled using the generalized disjunction programming (GDP) approach (Grossmann & Trespalacios, 2013) and then reformulated into a mixed-integer nonlinear programming (MINLP) model using the convex hull approach (Grossmann & Trespalacios, 2013), leading to much tighter MILP relaxation compared to that of Zhang et al. (2018). When modelling the activeness and inactiveness of a tray in a distillation column, we use the bypass efficiency method proposed by (Dowling & Biegler, 2014) in which a 0-1 continuous variable is introduced to denote the bypass efficiency of a stage which often tends to be 0 or 1 only in the optimal solution (global optimality). By doing this, the number of integer variables are significantly reduced. To solve the proposed MINLP model, we propose a computationally-efficient solution approach in which a systematical approach is proposed to generate a good starting point for the MINLP model. We first solve the reactor network using the SBB/GAMS solver and employ the robust pseudo-transient continuation (PTC) model proposed by Ma et al. (2017) to do simulation of distillation columns in Aspen Custom Modeler and generate a good starting point for the MINLP model. This systematical approach is implemented in Excel VBA, which could connect GAMS and Aspen Custom Modeler. Then, the MINLP model is solved using the SBB/GAMS solver (reference) to local optimality where the bypass efficiency variables may be values between 0 and 1. Finally, we enforce those bypass efficiency variables to be 0 or 1 only by solving the original MINLP model with the additional complementary slackness. Two examples from the literature are used to illustrate the capability of the proposed optimization framework. While the first example is related to synthesis of cyclohexane oxidation process, the other is related to the synthesis of hydrodealkylation of toluene (HDA) process involving three distillation columns. The computational results demonstrate that our proposed model and solution approach solved these two examples to local optimality within several minutes. Furthermore, we can achieve significant reduction in computational expense by 89% and decrease in total annualized cost by 5%, compared to those of Zhang et al. (2018).

**References**

Chen, Q., & Grossmann, I. E. (2017). Recent Developments and Challenges in Optimization-Based Process Synthesis. Annual Review of Chemical and Biomolecular Engineering*, *8, 249-283.

Daichendt, M. M., & Grossmann, I. E. (1998). Integration of hierarchical decomposition and mathematical programming for the synthesis of process flowsheets. Computers & Chemical Engineering*, *22, 147-175.

Dowling, A. W., & Biegler, L. T. (2014). Rigorous Optimization-based Synthesis of Distillation Cascades without Integer Variables. In P. S. V. JiÅ™Ã JaromÃr KlemeÅ¡ & L. Peng Yen (Eds.), Computer Aided Chemical Engineering (Vol. Volume 33, pp. 55-60): Elsevier.

Grossmann, I. E., & Trespalacios, F. (2013). Systematic modeling of discrete-continuous optimization models through generalized disjunctive programming. AIChE Journal*, *59, 3276-3295.

Hentschel, B., Peschel, A., Freund, H., & Sundmacher, K. (2014). Simultaneous design of the optimal reaction and process concept for multiphase systems. Chemical Engineering Science*, *115, 69-87.

Recker, S., Skiborowski, M., Redepenning, C., & Marquardt, W. (2015). A unifying framework for optimization-based design of integrated reactionâ€“separation processes. Computers & Chemical Engineering*, *81, 260-271.

Yeomans, H., & Grossmann, I. E. (2000). Disjunctive Programming Models for the Optimal Design of Distillation Columns and Separation Sequences. Industrial & Engineering Chemistry Research*, *39, 1637-1648.

Zhang, X., Song, Z., & Zhou, T. (2018). Rigorous design of reaction-separation processes using disjunctive programming models. Computers & Chemical Engineering*, *111, 16-26.