Heerden steady-state stability criterion

The program REFRIG 1 calculates the steady-state heat generation and heat loss quantities, HG and HL, as functions of the reactor temperature, TR, over the range 320 to 410 K. It is shown that, according to the van Heerden steady-state stability criterion that the simple loop control response, KP=0 is unstable. 

Equation 10.4.a-7 is a necessary but not sufficient condition for stability. In Other words, if the criterion is satisfied, the reactor may be stable if it is violated, the reactor will be unstable. (Aris [1] prefers to use the reverse inequality as a sufficient condition for instability.) The reason is that in deriving Eq. 10.4.a-7, it was implicitly assumed that only the special perturbations in conversion and temperature related by the steady-state heat generation curve were allowed. To be a general criterion giving both necessary and sufficient conditions, arbitrary perturbations in both conversion and temperature must be considered. Van Heerden s reasoning actually implied a sense of time ( tends to move... ), and so the proper criteria can only be clarified and deduced by considering the complete transient mass and energy balances. 

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