The cooled isothermal CSTR

In most exothermic processes carried out in a stirred tank reactor the bulk of the heat of reaction is carried away by external cooling, either via the wall of the reactor, or by means of an internal or extenal heat exchanger. Internal heat exchangers are usually vertical tube bundles or coils (spirals), mounted coaxially with the impeller shaft. When external heat exchangers are used, the reactor contents are pumped through it and back into the reactor. We consider here the CSTR the semi-batch reactor is treated in section 8.4.4. The steady-state heat balance for a first order reactor in a cooled CSTR can be written as follows  

The logarithmic-mean temperature difference between the reactor and the cooling 

The temperature throughout the reaction medium is T. The entrance and exit temperatures of the cooling liquid are 7 and 7, respectively. 

For a first order reaction, the heat balance can be simplified by substituting eq. (3.38) and putting V/F = x. The unsteady state heat balance can be written as 

When most of the heat is transferred through the walls, the second term is much greater than the first one. From a comparison with eq. (8.6) one can see immediately that the stability of the reactor has become much greater (dTIdt is smaller), thanks to the heat transfer term. 

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