Effect of the Residence Time Distribution on the Dynamical Behavior of Isothermal Continuous Stirred Tank Reactors: A Nonlocal Modeling Approach

Residence time distribution (RTD) plays a crucial role in the performance of chemical reacting systems. Although numerous techniques and results have been published on RTD estimation, only a limited number of studies have focused on mathematical modeling of chemical reactors incorporating RTD. The segregated fluid assumption and maximum mixedness modeling have achieved some success in modeling nondynamic continuously stirred tank reactors (CSTRs), but dynamic models remain lacking. Our work provides an approach for modeling isothermal CSTRs by considering that RTD induces a set of reactors with differential concentrations. We show that the interaction of reactants with different residence times is represented as an integral equation with partial derivatives, where time and residence time become independent variables. The modeling framework is motivated by first-order kinetics and subsequently applied to more complex chemical kinetics schemes. Numerical simulations were used to illustrate our findings. An example based on computational fluid dynamics for first-order kinetics was used to contrast predictions generated by local and nonlocal modeling frameworks.