(171d) Practical Bounds on Reaction Selectivity

Knowledge of the maximum attainable selectivities for a given chemical reaction network would be very useful during process design and operation. However, until recently a methodology to obtain such information for chemistries with more than two or three reactions was not readily available. Horn first introduced the concept of attainable regions (AR) in 1964 in an attempt to find optimal process designs for a given chemistry [1]. Since then, much creativity and effort has resulted in methodologies to enumerate ARs using geometric arguments for systems involving reaction and mixing [2-8] as well as systems involving reactions, separations, and mixing [9]. Unfortunately, all of these geometric methods are limited to a small number of components and reactions, which limits their utility.

The Continuous Flow Stirred Tank Reactor (CFSTR) Equivalence Principle, developed by Feinberg and Ellison [10], abandons the geometric approach altogether. This principle allows one to decompose any and every reaction/mixing/separation process into an equivalent process comprising only R+1 CFSTRs and a perfect mixer-separator (a “Feinberg Decomposition”), where R is the number of linearly independent reactions. Feinberg and coworkers [10, 11] showed that one can use the CFSTR Equivalence Principle to find the maximum attainable production flowrate of some desired product from a given chemistry for a given feed and reaction volume. This is done by maximizing the flowrate of the Feinberg Decomposition (with a given feed and total reactor volume) specified by the CFSTR Equivalence Principle. The utility of this method results from the fact that one can optimize an objective function over the AR without having to first identify the AR or its boundary. Frumkin and Doherty [12] showed that one can use the CFSTR Equivalence Principle together with a global optimization routine to find the maximum selectivity of a chemistry entirely independent of process design using kinetic models. They also show that constraints on overall reaction conversion and molar flowrates on the Feinberg Decomposition can be enforced to obtain bounds on selectivity that are more practical than the unconstrained case.

In this work, the problem is reformulated as a mixed-integer nonlinear program to solve the optimization problem. The problem is nonlinear and non-convex, and we implement a more robust, deterministic global optimization using a spatial branch-and-bound algorithm (BARON). We use this optimization routine to investigate the selectivity limits of the production of acrolein, the chemistry for which has thirteen components ant seventeen reactions. We find upper bounds on selectivity that are less than the stoichiometric selectivity limit, and thus provide valuable process information which may otherwise be unknown. Although the Feinberg Decomposition given by the CFSTR Equivalence Principle may not be practical, the selectivity limits it yields provide a useful target or benchmark for process design and operation. Furthermore, an optimization of the Feinberg Decomposition can provide practical hints for improved process designs. Finally, by using the CFSTR Equivalence Principle to compare synthesis routes, we can gain insight into which reaction path amongst a number of options is superior. In conclusion, the CFSTR Equivalence Principle is a useful engineering tool that can be applied to obtain important and practical information about a chemistry of interest.

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[12] Frumkin, J. Doherty, M. Submitted to AIChE Journal. 2016.