Voorhies relation

It further follows from Froment and Bischoff s study that, for a given bed length, both the point and the average carbon content increase with increasing space time (or decrease with space velocity) for the consecutive reaction mechanism, but decrease for the parallel mechanism (increase in terms of space velocity). Eberly s data [142] also indicate that the power in the Voorhies relation depends on the space time or on the liquid hourly space velocity. Another consequence of this analysis is shown in Fig. 11.5.f-5 for a parallel reaction. In the absence of fouling, and for isothermal conditions, the maximum rate of reaction A - / is always at the reactor entrance. This is not necessarily true when the catalyst is foul ... 

In other time-on-stream models, mostly used for coking, the decay rate is assumed to be independent of the current activity. An old but still widely used empirical equation by Voorhies [67] relates the coke content, qmke, of a catalyst in hydrocarbon processing to temperature and time ... 

The third class of theories is based on the time on stream concept proposed by Maxted (1951) and used in various forms by Weekman (1968a,b), Crowe and Lee (1971) and many others (Eley and Rideal, 1941 Ogunye and Ray, 1970 Szepe and Levenspiel, 1968 Voorhies, 1945). All of these authors and others used the time on stream concept in formulating various empirical functions which were then used to account for the decay of the catalyst. The success of these functions in the various specific instances where they were applied, is well founded in the kinetic relation of catalyst decay and can be understood when we consider the theoretical basis of the time on stream theory-proposed by Wojciechowski (1968, 1974). 

An alternative approach to the correlation of catalyst deactivation kinetics has been widely employed for coking mechanisms. Here the precise reactions that cause deactivation may be more complex or difficult to identify than in chemical poisoning, and one may not write such precise expressions as equation (3-94) for (—r ). The practice generally has been to relate activity to the time of utilization or time-on-stream , and a number of mathematical forms have been employed. The best known is the Voorhies correlation [A. Voorhies, Jr., Ind. Eng. Chem., 37, 318 (1945)], which relates the weight of coke on the catalyst to a power of time on stream. 

First studies on the influence of intraparticle diffusional mass transfer on catalytic reactions, and about deactivation of cracking catalysts by coke deposition, started with Thiele [1] and Voorhies [2], respectively. To-date, Thiele s analysis remains valid, however the approach followed by Voorhies in which coke formation is expressed as a function of time on stream (fos), although still used in many studies [3], is not adequate. It has been stated that deactivation, due to the coverage of active sites by coke deposition and to pore blockage by coke growth [3, 4], should be directly related to coke itself emd not to tos [5]. In this way, coke formation is linked to the operating conditions, the nature of the feedstock and the type of catalyst. 

It follows from the preceding that equations that try to relate the activity of the bed with time (Voorhies formula) can only be approximate. The Voorhies formula can at best be valid only for a given bed length. By plotting the average carbon content of the bed versus time in a double-logarithmic plot — the way Voorhies and others did (Chapter 5) — Froment and Bischoff obtained a power... 

Froment and Bischoff (1961, 1962) examined the effect of catalyst decay and reactor performance when coke is produced from both products and reactants. TTiey showed a Voorhies type law holds over certain operating ranges and defined a deactivation function as the fraction of active sites remaining active on the catalyst. They related this function, to the coke content, Cc, by the following two empirical relationships which are equivalent at low coke concentrations ... 

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