Steady States and Local Stability in CSTR

Multiple Steady States and Local Stability in CSTR.—In the two decades since the seminal work of van Heerden and Amimdson, there has been vast output of papers conoemed with the dynamic behaviour of stirred-tank reactors. Bilous and Amundson put the van He den analysis of local stability of the equilibrium state on a rigorous basis by use of linear stability theory. Their method is similar to the phase-plane treatments of thermokinetic ignitions and oscillations discussed here in Sections 4 and 3 (and preceded them dironologically). The mass and energy balance for the CSTR having a single reactant as feedstock may be expressed as  

Let us assume a simple first-order deceleratory reaction in the CSTR with kinetic rate constant k = The overall rate of reaction at the steady state 

An analysis of the local stability of (c.,7. ) in the phase plane provides the necessary and sufficient conditions for stability as 

Since the paper of Bilous and Amundson in 19SS, it has been a straightforward matter to determine the stability of the steady states via these two relationships. Although the paper also included phase-plane concentration-temperature plots, the first really extensive numerical calculations were first reported by Aris and Amundson. These results promoted many further theoretical and numerical studies of CSTR, both to elucidate the variety of phenomena which can 

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