Operation Limited by the Maximum Allowable Temperature

In many practical cases, the conditions for criticality described in the previous sections are only necessary to ensure safe operation. Such conditions do not guarantee, indeed, that the maximum allowable temperature in the reactor, Tma, is not exceeded. For instance, this upper temperature limit can be imposed, in liquid systems, by the bubble point of the reacting solution or by the decomposition temperature of some compounds in it, or, in gaseous systems, by the maximum internal pressure the vessel can comply with. 

To deal with the modifications to the runaway criteria determined by the existence of an upper temperature limit, let us denote by 9ma the value of the generic parameter 9 that generates a temperature profile with a maximum equal to Tma. In the same way, let us denote by 9C the critical value of the parameter corresponding to the runaway boundaries obtained with any of the criteria discussed in the previous sections and generating a temperature profile with maximum value Tc. Two possible cases can be distinguished, namely 

When condition (4.44) is satisfied, the existence of a maximum allowable temperature does not affect the critical parameter value 9C obtained with any of the classical runaway criteria. On the contrary, when condition (4.45) is satisfied, the actual limit value of the parameter to define safe operation must be replaced by 9ma. 

Regardless of which one of the previous conditions is met, when 9 has a mono-tonically positive effect on the maximum reactor temperature Tma, as is the case of A, Q, and %o, the following scenarios can be encountered [7]  

If 9 has a monotonically negative effect on Tma, as for and P, all previous inequalities must be inverted. 

---