Multiplicity, Stability, and Dynamic Accessibility of Steady States in Continuous Stirred Tank Reactors with Free and Immobilized Enzymes Subject to Substrate Inhibition

This work investigates the occurrence, stability, and dynamic accessibility of steady states in isothermal continuous stirred-tank reactors (CSTRs) containing free or immobilized enzymes subject to substrate inhibition. For homogeneous systems, a dimensionless reactor model was employed to identify operating conditions leading to multiplicity and hysteresis. For immobilized enzymes, the reactor mass balance was coupled with an intraparticle diffusion–reaction model to determine substrate concentration profiles and effectiveness factors. Steady-state solutions were obtained using complementary stationary and transient numerical approaches, while stability was assessed through eigenvalue analysis of the Jacobian matrix referring to the linearized system of governing equations. The results show that substrate inhibition may generate multiple steady states at both the reactor and particle scales. For immobilized enzymes, multiple concentration profiles and effectiveness factors may coexist for specific combinations of kinetic and transport parameters. Stability analysis showed that the multiple steady states identified at both the reactor and particle scales are organized into stable lower and upper branches separated by an unstable intermediate branch. Dynamic simulations showed that, in regions where multiple stable states coexist, the steady state attained by the system depends on the initial intraparticle concentration profile and operating trajectory. Moderate intraparticle diffusion limitations were found to alleviate substrate inhibition and substantially improve reactor performance. By combining multiplicity, stability, and dynamic accessibility analyses, this work provides a framework for identifying physically attainable operating states and predicting reactor performance under different reaction–diffusion conditions, thereby supporting the design, start-up, and operation of continuous reactors employing immobilized enzymes under substrate inhibition.