The choice between cooled tubular reactor models: analysis of the hot spot

Abstract

Abstract-The applicability of the one-dimensional pseudo-homogeneous model of the cooled tubular reactor is studied. Using the two-dimensional model as the more accurate one we compared both models by studying the influence of the design and operating variables on the conditions in the hot spot of the reactor. The effects were studied on an analytical basis, and a relation is derived that describes the radial temperature profile in the hot spot of the reactor. In the first section we present the model equations and discuss the results obtained from a numerical evaluation. In the second section we compare mean and maximum radial temperatures and reaction rates in case a single exothermic reaction is carried out. We conclude that-for reactors operating in the steady state-in the hot spot the one-dimensional model predicts the proper temperature when it is compared with the average temperature calculated by the twodimensional model, although large differences may arise between maximum and mean radial temperature. A new method is presented to obtain the maximum radial temperature in the hot spot directly from the results of the one-dimensional model. It was found that there can be large differences between the actual average reaction rate and the reaction rate at mean temperature as obtained from the one-dimensional INTBODUflIONIn the literature many studies have been published dealing with the proper design of tubular reactors for exotherrnic reactions. These studies are either based on the prevention of runaway or the preservation of a certain a priori desired selectivity. Well known is the paper by Barkelew (1959), who showed that in a plot of the conversion vs the hot spot temperature two regions can be distinguished. One region-that of the low parametric sensitivity-has the property that a small change in the operating conditions also leads to a small change in the hot spot temperature. In the second region-that of high parametric sensitivity-a small change in operating conditions causes a large increase in the temperature profile along the reactor axis.Westerterp er al. (1984), Westerterp and Overtoom (1985), and Westerlnk and Westerterp (1988) present a series of papers dealing with the design and operation of cooled tubular reactors for reaction systems consisting of two or more exothermic reactions and relate the design and operating parameters to the desired selectivity.Both Barkelew and Westerterp used the pseudo-homogeneous one-dimensional modelto arrive at their results. Morbidelli and Varma (1988, 1989) presented a series of papers in which they study parametric sensitivity in a cooled tubular reactor. They conclude that the reactor becomes sensitive to all the operating conditions and physicochemical parameters simultaneously.'Author to whom correspondence should be addressed. Several investigatorspresented papers that deal with the applicability of the ODM. Froment (1967Froment ( , 1974 studied the difference between the ODM and the pseudo-homogeneous two-dimensional model (TDM).He concluded that fo...

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