Generalized parametric sensitivity: Application to a CSTR

Abstract

We have recently introduced a generalized condition for thermal runaway or parametric sensitivity. The condition defines criticality as the point in the parameter space at which the system's behavior exhibits maximum sensitivity to small, unstructured perturbations. Here we use the same concept to study the steady-state behavior of a single irreversible nth-order exothermic reaction occurring in a nonadiabatic CSTR. Although the new condition provides critical parameter values in good agreement with the results of earlier methods, it reveals that the notion of parametric sensitivity in steady-state models considerably differs from the notion of parametric sensitivity in dynamical systems. First, in the steady-state CSTR criticality is related to the near-singularity of the model equation. Second, unlike in dynamical systems, there exist no well-defined boundary between subcritical and supercritical behavior. The close connections between thermal runaway and steady-state multiplicity, as well as thermal runaway and self-similarity of the sensitivity functions are discussed.