(341h) Impact of Spatial Segregation in Coupled Reactors with Catalytic and Autocatalytic Reactions

The effect of spatial segregation in catalytic reactors is mimicked by considering two well-mixed reactors with one-way and two-way coupling. The reactors in the two-reactor system are identical only in terms of feed composition and reactor space time and need not have identical volumes and volumetric feed, effluent, and exchange rates. A comprehensive analysis of static and dynamic behavior of autocatalytic reaction and a catalytic reaction exhibiting inhibition kinetics with respect to a reactant occurring in the two-reactor system is presented. Enzyme-catalyzed reactions subject to substrate inhibition belong to the latter class of reactions. A single well-mixed reactor may operate at up to three steady states. A two-reactor system may admit up to nine steady states, due to emergence of six additional steady states, at least at very low interaction rates. Three of these steady states, symmetric steady states, correspond to identical composition in the two reactors. The remaining steady states, the asymmetric steady states, correspond to different composition in the two reactors and are admissible over a range of interaction rates. Three different types of interaction are considered: (1) equal interaction, (2) unequal interaction, and (3) one-way interaction (series reactors). The six asymmetric steady states exhibit four different pairing sets with two or more limit points. When the interaction rates are equal, the asymmetric steady states are comprised of sets of steady state counterparts, each set admissible over the same range of interaction rate. In terms of merges at limit points, the asymmetric steady states exhibit two pairing sets in the operating parameter space. A switching in steady state pairs is caused through emergence of up to four additional steady states, which are admissible over the same range of interaction rate. When the interaction rates are not equal, three pairs of asymmetric steady states are admissible over different ranges of interaction rates. In terms of merges at limit points, the asymmetric steady states exhibit three pairing sets in the operating parameter space, two inherited from the equal interaction rate case. The additional pairing set corresponds to the unique pairing set for one-way interaction between the two reactors. Two such pairing sets are possible depending on which of the two interaction rates is higher. The two switches in steady state pairs are caused through emergence of four additional steady states, which are admissible over two different ranges of interaction rates. The additional pairing set is admissible over a broader region of the operating parameter space as the inequity between the interaction rates is increased. The limiting case of this inequity corresponds to two reactors in series, where there is only pairing set of the asymmetric steady states and no additional steady states emerge. Numerical illustrations reveal the rich steady state structure of the reaction schemes in coupled reactors. The steady states are tracked systematically as the interaction rate is varied. A catalytic reaction exhibiting inhibition kinetics or an autocatalytic reaction without autocatalyst decay does not lead to periodic states in two-reactor systems. The two-reactor system is operationally more flexible and more robust vis-a-vis single reactor. Emergence of additional steady states at low and intermediate values of interaction rates reveals that the two-reactor systems are examples of a complex system.