Cstr Performance Limitations Due to Cooling Jacket Dynamics - Open and Closed-loop Considerations

The classic two-state exothermic continuous stirred tank reactor (CSTR) is known to exhibit complex static and dynamic nonlinear behavior, which includes input and output multiplicities, hys-teresis (ignition/extinction behavior), parametric sensitivity, and nonlinear oscillations. An implicit assumption of the two-state CSTR model is that cooling jacket temperature is the manipulated input (for feedback control of reactor temperature). The theoretical and experimental focus during the past decade has been on the aaect of complex kinetics on steady-state multiplicity and dynamics. However, we show that adding a third state to account for the cooling jacket temperature dynamics has an important innuence on the steady-state multiplicity and the open and closed-loop dynamics of exothermic CSTR's. A stabilizing inner-loop cascade controller is implicitly assumed in the two-state model, because the three-state model may be open-loop unstable when the two-state model is open-loop stable. We use singularity theory to study the aaect of process parameters (such as the heat transfer coeecient and the cooling jacket feed temperature) on the steady-state multiplicity of the two and three-state models. A key point is that this multiplicity analysis provides practical guidance for process redesign to eliminate \diicult" operating regions associated with multiplicities. We show that when the CSTR is operated at an open-loop unstable (for the two-state model) operating point, there are inherent performance limitations in the closed-loop system due to the presence of unstable \zero dynamics" between the cooling jacket temperature and the cooling jacket owrate.