Reaction, exothermic, single stirred tank reactor

Example 1.9.1. The concepts of the present section can be illustrated by the simple example of a single irreversible exothermic reaction in a stirred tank reactor with no heat exchange (6 = 0). 

This analysis is limited, since it is based on a steady-state criterion. The linearisation approach, outlined above, also fails in that its analysis is restricted to variations, which are very close to the steady state. While this provides excellent information on the dynamic stability, it cannot predict the actual trajectory of the reaction, once this departs from the near steady state. A full dynamic analysis is, therefore, best considered in terms of the full dynamic model equations and this is easily effected, using digital simulation. The above case of the single CSTR, with a single exothermic reaction, is covered by the simulation examples, THERMPLOT and THERM. Other simulation examples, covering aspects of stirred-tank reactor stability are COOL, OSCIL, REFRIG and STABIL. 

Consider a simple first-order exothermic reaction, A -> B, carried out in a single, constant-volume, continuous stirred-tank reactor (Fig. 3.10), with constant jacket coolant temperature, where rA=kCA. 

The classical problem of multiple solutions and undamped oscillations occurring in a continuous stirred-tank reactor, dealt with in the papers by Aris and Amundson (39), involved a single homogeneous exothermic reaction. Their theoretical analysis was extended in a number of subsequent theoretical papers (40, 41, 42). The present paragraph does not intend to report the theoretical work on multiplicity and oscillatory activity developed from analysis of governing equations, for a detailed review the reader is referred to the excellent text by Schmitz (3). To understand the problem of oscillations and multiplicity in a continuous stirred-tank reactor the necessary and sufficient conditions for existence of these phenomena will be presented. For a detailed development of these conditions the papers by Aris and Amundson (39) and others (40) should be consulted. 

Let us now consider some of the problems that can arise in the design of a stirred tank reactor with a single reaction. We shall speak in terms of an exothermic reaction, but most remarks will apply, mutatis mutandis, to the endothermic case. 

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