(60i) Accounting for Economics in Attainable-Region-Based Reactor–Separation Network Synthesis: Models, Tradeoffs, and Insights

In reaction engineering, the attainable region defines the set of all possible states (e.g., concentrations or molar flow rates) attainable in the outlet stream of any steady-state reactor network, given specified feed and reaction kinetics. Geometric and optimization-based methods have been proposed to build the attainable region and propose targets for the productivity of chemicals in reactor–separation networks. However, costs are often neglected in this approach, which results in targets that require uneconomical processes (e.g., targets requiring the use of expensive separation units and large recycle streams). In this work, we propose modeling methods that allow us to account for costs in reactor–separator synthesis while preserving the ability to generate the attainable region. Our goal is to holistically (1) analyze trade-offs between costs and attainability, (2) compare relative costs of reactor and separation networks, and (3) provide a method to obtain practical targets to be used as benchmarks to evaluate new and existing designs.

To generate the attainable region, we use the CSTR equivalence principle [1] and cost models for separations [2]. The CSTR equivalence principle states that, for the purpose of determining the set of outlet molar flow rates attainable by any reactor–separation network, it suffices to consider a network containing only a relatively small number of CSTRs connected to an idealized separator capable of arbitrary sharp separations solely constrained by mass balance. The separation model determines the costs associated with carrying out the required separations to generate (1) the streams that are recycled to the reactors and (2) the product stream. We use a separation energy target model [2] to determine the minimum energy required to purify a stream of variable composition into multiple outlet streams based on the vapor molar flow rate required to operate a fully thermally coupled distillation network. The CSTRs and the separators are embedded into a rich superstructure. We generate the attainable region by minimizing the total cost of the system over a wide range of attainable outlet molar flows.

We develop a system-wide descriptor of how hard (or expensive) it is to carry out a given set of separations based on the relative volatility of all components in the system. The proposed descriptor is used to understand how the separations affect the costs within the attainable region. Furthermore, we study the effect of the feed flow rate on the costs to attain a desired production target, where solutions with low or high feed conversions are obtained depending on the relative price of feed and difficulty of separations.

The attainable region obtained by our approach is equivalent to the one obtained by the CSTR equivalence principle, but we discuss how some subregions are expensive to operate despite being attainable. These expensive subregions are typically close to the attainable region boundary. Finally, we show how the proposed approach enhances our understanding of the tradeoffs between costs and attainability, therefore providing guidelines for evaluating chemical process designs.

References

[1] Feinberg, M., Ellison, P. (2001). General Kinetic Bounds on Productivity and Selectivity in Reactor–Separation Systems of Arbitrary Design: Principles. Industrial & Engineering Chemistry Research, 40, 3181-3194.

[2] Ryu, J., Maravelias, C.T. (2020). Computationally efficient optimization models for preliminary distillation column design and separation energy targeting. Computers and Chemical Engineering, 143, 107072.