Runaway criteria critical temperature

In Section 2.5.2, the Semenov diagram was used to show the critical cooling medium temperature. In the same way it allows discrimination of a stable operation conditions from a runaway situation. A stable operation is achieved for a limit value of the Semenov criterion / (also called Semenov number) ... 

Still with reference to the temperature-concentration profile, van Welsenaere and Froment [13] proposed a criterion based on the locus of the temperature maxima that was originally derived for homogeneous tubular reactors but whose validity for batch reactors was also proved. The criterion is discussed here with reference to Fig. 4.8, where the temperature-concentration profiles in a batch reactor are reported for Se = 0.470, 2 = 40, Tro = 7j = 1, and different values of A in the range 0.2-1.16. The maxima of the %(C) curves (continuous lines) define a new curve (dashed line), which has itself a maximum with respect to %. According to the criterion of van Welsenaere and Froment, the latter maximum defines the critical conditions for runaway, i.e., it provides the maximum value of A that allows one to have an easily controlled temperature in the reactor for any given set of the remaining parameters. In Fig. 4.8, the critical point on curve 1 is found at Ac = 0.7. 

In Fig. 11.5.C-2 the locus of the partial pressure and temperature in the maximum of the temperature profile and the locus of the inflection points before the hot spot are shown as p and (pj), respectively. Two criteria were derived from this. The first criterion is based on the observation that extreme sensitivity is found for trajectories—the p-T relations in the reactor—intersecting the maxima curve p beyond its maximum. Therefore, the trajectory going through the maximum of the p -curve is considered as critical. This is a criterion for runaway based on an intrinsic property of the system, not on an arbitrarily limited temperature increase. The second criterion states that runaway will occur when a trajectory intersects (Pi)i, which is the locus of inflection points arising before the maximum. Therefore, the critical trajectory is tangent to the (pi)i-curve. A more convenient version of this criterion is based on an approximation for this locus represented by p in... 

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