Target bounds on reaction selectivity via Feinberg's CFSTR equivalence principle

Abstract

In this work, we show that the continuous flow stirred tank reactor (CFSTR) equivalence principle, developed by Feinberg and Ellison, can be used to obtain practical upper bounds on reaction selectivity for any chemistry of interest. The CFSTR equivalence principle allows one to explore the attainable reaction region by decomposing any arbitrary, steady‐state reactor‐mixer‐separator system with total reaction volume V > 0 into a new system comprising R+1 CFSTRs (where scriptR is the number of linearly independent chemical reactions) with the same total reaction volume and a perfect separator system. This work further refines the allowable selectivities by incorporating capacity constraints into the CFSTR equivalence principle to prevent arbitrarily large recycle streams between the CFSTRs and the separators and infinitesimally small CFSTR conversions. These constraints provide practical upper bounds on reaction selectivities of chemistries completely independent of reactor design. We present the methodology and the results for a selection of realistic chemistries. © 2017 American Institute of Chemical Engineers AIChE J, 64: 926–939, 2018

Operability and control in process intensification and modular design: Challenges and opportunities

“…Two key questions result from the above framework which also open up more opportunities toward a holistic framework for process intensification and operation: Definition of driving forces to define the optimal operation trajectory — Various driving forces have been defined pertaining to specific types of processes. For example, the previously mentioned elementary process function for reactors, 69 attainable region theory to determine ultimate performance bounds in reaction/separation systems, 70,71 reactive driving force for (reactive) distillation systems, 72,73 Gibbs free energy‐based driving force constraints for reaction/separation systems, 74 and so on. Given the large scope of PI and modular designs, a well‐defined driving force formulation is clearly needed, which may not suggest directly the type of equipment but can rapidly screen the design space and provide preliminary design and operation information (including temporal and spatial profiles). Mathematical formulations — While dynamic modeling and optimization provide accurate descriptions of process systems in both temporal and spatial domains, it is highly demanding (and currently limited) in solution algorithms, problem scales, and computational complexity.…”

Ultimate Reaction Selectivity Limits for Intensified Reactor–Separators

“…The effluent flow rates from each CFSTR are calculated using eq , and eqs and allow for calculation of the inlet concentrations associated with the given ( ) state, volume, and feed flow rate of each CFSTR. As shown by Frumkin and Doherty, constraining the feed flow rates to a CFSTR may make certain composition–temperature–pressure ( ) states infeasible for a given volume (concentrations become less than zero or greater than the component molar densities). Therefore, we must calculate the inlet concentrations to ensure that only feasible ( ) states are permitted.…”

“…For example, in one chemistry that we optimized, the upper bound on selectivity was found to be on the order of 10 5 . There is, in fact, a stoichiometric upper bound on reaction selectivity that is independent of the kinetics and is of order O(1), as discussed by Frumkin and Doherty . In this section, we outline how we can reformulate the problem to obtain tighter bounds that match the stoichiometric selectivity limit, increase the efficiency of the algorithm, and preserve the physical nature of the constraints.…”

“…The utility of this method results from the fact that an objective function can be optimized over the AR without having to first identify the AR or its boundary. Frumkin and Doherty showed that the CFSTR Equivalence Principle, together with the chemical kinetics and a global optimization routine, can be used to find the maximum selectivity of a chemistry entirely independent of process design. They also show that constraints on the overall reaction conversion per pass and molar flow rates within the FD can be enforced to obtain bounds on selectivity that may be more practical than the unconstrained case for certain classes of chemistries.…”

Toward an Envelope of Design Solutions for Combined/Intensified Reaction/Separation Systems

“…Hereafter, we will refer to this approach as “Feinberg Decomposition (FD)”. Frumkin and Doherty − further extended the FD approach to characterize selectivity bounds in RMS systems. Despite the indispensable boundary information given by the CFSTR principle, this approach cannot generate correspondingly candidate process alternatives at, or within, the derived bounds.…”