Stability criteria, summary

In summary, at the subcritical pressure operation during the pressurization phase, thermal criteria are more limiting due to dryout. The startup scheme prior to line switching is mainly determined by thermal criteria. The thermal-hydraulic stability criterion is satisfied by applying a sufficient orifice pressure drop coefficient. The coupled neutronic and thermal-hydraulic stability is also satisfied, since the power to flow rate ratio is low during this phase. 

Other stability conditions are obtained from the negativity of second derivatives with respect to V or N. (More generally, determinants of such second derivatives must also be negative in order to guarantee stability with respect to arbitrary combinations of energy, volume, and mass changes.) In summary, we can say that the Gibbs criterion of equilibrium for a closed system is equivalent to conditions of uniform intensive properties 7, P,... 

This criterion is a so-called sliding criterion, since it is established for time 0, but may be applied for any time (sliding). It also represents a summary of the stability diagrams presented in Section 5.2.3.2. The exponent 1.2 of B introduces a safety margin. This criterion uses a comprehensive knowledge of the reaction kinetics. 

The data comparison described above in Figs. 13.2 and 13.3 may be performed statistically in several ways. The statistical approach takes data variability into account when setting limits. Therefore, a single acceptance criterion for OOT identification can be set for different types of assays. Three such procedures for normally distributed data are described in a review by the PhRMA CMC Statistics and Stability Expert Teams [3]. Each of these approaches has its own advantages and disadvantages, a summary of which is provided in the paragraphs below. 

Over a three-decade period, Feinberg [83] developed the criteria for answering chemical network stability questions, given any reaction with any given number of reactants. The basis for the so-called deficiency theorems is rooted in topology (structure), but in short summary, one takes each reactimi with each set of inputs and outputs and defines new quantities called complexes. After summing over all individual reactions, aU reactants and all complexes, one obtains the criterion. 

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