Parametric sensitivity for thermal runaway and its critical criterion in batch reactors with n-order reaction

According to the theory and mathematical features of parameter sensitivity in a batch reactor, the parametrically sensitive point of batch reactor with n-order reaction was proved to be the contact point of the operation curve and the locus of inflection points of operation curves. The upper limit of the safe operation temperature of n-order reaction system was derived. In order to avoid solving a quartic equation, a asymptotic solution for the upper limit of the safe operation temperature was obtained based on small parameter disturbance theory. A new general formula for safe operation criterion of the reaction system was obtained by taking advantage of the relationship between the maxima temperature point on the critical operation curve and the inflection point on the supercritical one. The new criterion was compared with the classic criteria which proposed by Adler and Enig, Wu et al. and it was found that the two classic criteria were conservative than the new one when B was smaller than some value, and vise verse, but the difference between the new criterion and the two classic criteria tended to the some value when B was big enough.