Kinetic Analysis of Nonisothermal Data

The above example deals with a simple isothermal situation. In Chapters 1 and 2 it was suggested to operate reactors for kinetic studies, whenever possible, in an isothermal way. There are cases, however, in which isothermal operation is impossible, in spite of all precautions, for example, a homogeneous reaction like thermal cracking of hydrocarbons. In such a case it is inevitable that part of the reactor is used to bring the feed to the desired temperature. In contrast with catalytic reactors there is no clear-cut separation between prdieat and reaction section in such a case. If the rate is to be determined at a reference temperature, say T, and if the reaction volume is counted from the point where T, is reached, then the conversion in the preheat section that cannot be avoided is not accounted for. Similarly 

Such a situation can be dealt with in two ways. The first way is to analyze the data as such. The temperature dependence of the rate parameters is then directly included into the continuity equation and the resulting equation is numerically integrated along the tube with estimates for the parameters. If the gas temperature profile itself is not available or insufiBciently defined, the energy equation has to be coupled to the continuity equation. To determine both the form of the rate equation and the temperature dependence of the parameters directly from nonisothermal data would require excessive computations. 

The strong correlation between Aq and necessitated a reparameterization. Setting 

The equivalent reactor volume concept, introduced by Hougen and Watson [1] allows for a second way of dealing with nonisothermal data it first reduces the data to isothermality and determines the temperature dependence of the rate parameters in the second stage only. The equivalent reactor volume has been defined as that volume, which, at the reference temperature T, and the reference total pressure p,i, would give the same conversion as the actual reactor, with its temperature and pressure profiles. It follows that 

Once Vp has been derived, the calculation of the rate is straightforward, as for isothermal experiments, and is based solely on the cmitinuity equation. Calculating Vp requires the knowledge of the temperature and pressure profiles along the tube and of the activation energy, . Note also that where several reactions are occurring simultaneously the dependence of Vp on leads to different Vp for each of the reactions considered. 

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