Steady-state multiplicity and dynamic behavior of premixed/unpremixed autocatalytic systems in an isothermal continuous stirred tank reactor: an analytical study

Abstract In this paper the dynamic behavior of autocatalytic reactions within an isothermal continuous stirred-tank reactor (CSTR) is investigated using Cholette’s model, comparing mixing condition effect and premixed/unpremixed feed configurations. The analysis reveals that the feed configuration significantly influences not only the presence of multiple steady states but also the selectivity and yield of the desired product due to altered reaction pathways. Phase plane simulations demonstrate that for both single and dual unpremixed feed scenarios exhibiting multiplicity, a high conversion (upper steady state) can be achieved by initiating the reaction with initial conditions above the separatrix corresponding to the middle steady state. Furthermore, nonideal mixing, a common occurrence in industrial CSTRs, alters the effective residence time. For instance, reduced residence time due to nonideal mixing expands the region above the middle steady state’s separatrix in the phase plane, increasing the likelihood of achieving high conversion. Given the practical challenges of perfect mixing and the prevalence of single premixed or dual unpremixed feed configurations in chemical processes, these findings provide valuable insights for the design and control of real-world CSTRs. Overall, this analytical study elucidates how steady-state multiplicity and dynamic stability in single premixed or dual unpremixed autocatalytic CSTRs are governed by mixing conditions, feed configuration, and initial states, thereby providing fundamental insight into the nonlinear behavior of autocatalytic reactor systems.