(216e) Ultimate Bounds on Reaction Selectivity for Batch Reactors

Frumkin, J. A., University of California, Santa Barbara
Doherty, M. F., University of California
Targets and benchmarks are useful in chemical process design as they provide an objective, quantitative assessment of a proposed process flowsheet. However, targets for reaction selectivity are difficult to obtain using conventional design methods. Over the last several decades, there has been much work in the field of Attainable Region (AR) theory, which has the goal of defining an “attainable region” comprising all possible output states for a process operating a chemistry with a given input state. Once the entire AR for a chemistry is known, it can be investigated to find the optimal output state. Unfortunately, all of these methods fall short of guaranteeing that one can calculate the complete AR for a chemistry with an arbitrary number of reactions and components for a process involving reaction, mixing, and separation. Here, we present a methodology that allows us to obtain ultimate bounds on reaction selectivity for a chemistry, regardless if the chemistry is carried out batch-wise, at steady-state, or in a periodic or chaotic fashion.

In 2001, Feinberg and Ellison1 developed the Continuous Flow Stirred Tank Reactor (CFSTR) Equivalence Principle, providing a methodology to obtain ultimate bounds on steady-state productivity for a chemistry of interest entirely independent of process design. The CFSTR Equivalence Principle shows that any and every arbitrary, steady-state reactor-mixer-separator system can be exactly modeled by a fictitious process (which we call a “Feinberg Decomposition”) comprising R+1 CFSTRs and a perfect separator system, where R is equal to the number of linearly independent reactions in the chemistry of interest. While this methodology does not provide one a way to find the boundary of the AR, one can explore the AR by changing the operating conditions of the R+1 CFSTRs in the Feinberg Decomposition.

In previous articles2,3, we showed how the CFSTR Equivalence Principle can be used to obtain bounds on reaction selectivity independent of process design for steady-state processes while incorporating useful capacity constraints. In this article we prove that the CFSTR Equivalence Principle is also applicable to batch and semi-batch processes (as well as those operating in a periodic or chaotic fashion), thus providing a unifying framework to obtain an ultimate target for reaction selectivity that is applicable to all candidate processes for a chemistry of interest, not just those that occur at steady state.

We demonstrate the methodology for the production of lactic acid through the alkaline conversion of fructose. In doing so, we compare the ultimate attainable selectivity for this chemistry to a conventional batch reactor. We additionally show how this methodology can be used to help determine if one should focus on process improvement (e.g., designing a better reactor) or chemistry improvement (e.g., identifying a better catalyst). Finally, we show that the problem can be reformulated to determine the minimum batch time (for batch processes) or minimum reactor capacity (for continuous processes) required to achieve a desired selectivity. In summary, the CFSTR Equivalence Principle is an incredibly powerful design tool that can be used in a number of ways to assist in chemical engineering design. By proving its applicability to non-steady processes, we are able to significantly improve its utility.


  1. Feinberg, M., Ellison, P., 2001. General kinetic bounds on productivity and selectivity in reactor-separator systems of arbitrary design: Principles. Industrial & Engineering Chemistry Research. 40 (2001), 3181-3194.
  2. Frumkin, J.A., Doherty, M.F., 2018. Target bounds on reaction selectivity via Feinberg’s CFSTR Equivalence Principle. AIChE Journal 64, 926–939.
  3. Frumkin, J.A., Fleitmann, L. and Doherty, M.F., 2018. Ultimate Reaction Selectivity Limits for Intensified Reactor–Separators. Industrial & Engineering Chemistry Research. Article ASAP.