General Kinetic Bounds on Productivity and Selectivity in Reactor−Separator Systems of Arbitrary Design:  Principles

Abstract

For a specified set of feed streams and a specified network of chemical reactions, there is an almost limitless variety of reactor−separator designs that might be employed in enhancing the production rates of certain desired molecules while suppressing the production rates of undesired ones. Of special significance is the vast spectrum of very different reactor configurations available to the designer. Here we seek to determine sharp kinetic bounds on what can be achieved in steady-state reactor−separator systems of arbitrary design, subject perhaps to certain natural physical constraints. A primary conceptual tool is the continuous flow stirred tank reactor (CFSTR) equivalence principle, proven here, which asserts that the effluent of any steady-state reactor−separator design can be achieved arbitrarily closely by another steady-state design involving perhaps arbitrarily sharp separations but in which the only reactor components are s + 1 ideal CFSTRs, where s is the rank of the underlying network of chemical reactions. Thus, for the sole purpose of assessing bounds on the set of attainable effluents, it suffices to consider a surprisingly narrow and simple class of reactor configurations.

A unifying framework for optimization-based design of integrated reaction–separation processes

“…In particular, shortcut methods can be used to determine performance bounds, which can be used to robustify subsequent rigorous optimization. For reaction-separation processes such bounds can be predicted by a steady-state design of a process only involving sharp separations and ideal CSTRs (Feinberg and Ellison, 2001;Feinberg, 2002). Alternatively, bounds can be predicted by optimizing a species-dependent residence time distribution function (Balakrishna and Biegler, 1993;Freund and Sundmacher, 2008), which is similar to the concept of elementary process functions for reactor networks.…”

“…Section 2.1 and Feinberg and Ellison, 2001). The exponential growth of the number of variables and equations of the LP problem introduced by Kauchali et al (2002) can be avoided, if the problem is formulated without discretization of the concentration space as suggested by Recker and Marquardt (2012) and summarized in Appendix A.…”

“…The number of equations describing this shortcut model for reactor networks scales linearly with the number of components and the number of reaction devices. As only few reaction devices are needed to approximate most reactor networks (Feinberg and Ellison, 2001), the NLP embedding this model is capable to approximate the optimal operating point for industrially relevant reactor networks. This way, a synthesis method can be devised at the expense of replacing the LP problem of Kauchali et al (2002) by an NLP problem.…”

“…It scales linearly with the number of components n c and the number of reaction devices n i . As only few reaction devices are needed to approximate most reactor systems (Feinberg and Ellison, 2001), the NLP embedding this reactor model is capable to approximate the optimal operating point for industrially reactor networks. Therefore, this novel reactor shortcut can be combined with shortcut models for separation to optimize integrated reaction-separation processes.…”

Attainable regions of reactive distillation—Part III. Complex reaction scheme: Van de Vusse reaction

“…Fienberg and co-workers found attainable region for a reactor-separator system with arbitrary separation efficiency but with constraints on operating temperature, pressure, production of unwanted products, etc. They solved the problem by a constrainted optimization technique (Feinberg and Ellison, 2001;Tang and Feinberg, 2007). The AR approach is further extended by others to reactive distillation systems for some specific cases (Nisoli et al, 1997;Gadewar et al 2002;Agarwal et al, 2008a), which provided momentum for setting ideal performance targets, and gave insight into the synthesis problem by means of graphical visualization.…”