Catalyst activity decay functions

The Aree catalyst activity decay functions evaluated (exponential decay, power law decay and a Froment-Bischoff type decay) showed that no one particular function predicted the experimental data better than the others for the range of experimental conditions used. It is concluded that for short reaction times (below 10 seconds) the simple exponential decay law may be used to effectively predict the data. It was also observed that the deactivation constant (kj or a) was not... 

The deposition of coke on the catalyst results in rapid activity decay and hence a catalyst decay function is multiplied by the intrinsic rate to give the actual rate. It is normally assumed that the same active sites will crack both gas oil and gasoline molecules, therefore the activity decay functions and 2 are assumed equal (Weekman, 1968). In general, the catalyst activity is dependent on the carbon laid down and is thus related to the time the catalyst is exposed to hydrocarbons. Then, to completely describe the kinetics of cracking according to the three lump model involves the determination of the parameters k, ki, kj and the deactivation function. ... 

A deactivation function is needed to account for the catalyst activity decay due to coke deposition on the catalyst. The various forms of this function were discussed in Chapter 2 where can be a function of catalyst time-on-stream or more appropriately as a function of coke content on the catalyst. The kinetic constant, k, is the overall gas oil cracking rate constant which is the sum of ki and kj from the 3-lump scheme. Substituting this value for rA in equation (3.1) results in ... 

It can also be shown (Kraemer et al.,1991) that the activity decay function described equation 1.5b, which relates the catalyst activity to the amount of coke on the catalyst, has the following... 

Mi Molecular weight of component i (g/gmol) n Order of catalyst activity decay N Function of the order of decay ( = l/(n-l))... 

Shah et al.46 also carried out a dynamic analysis of the commercial HDS reactor similar to the one described above, assuming the activity functions to be dependent upon the coke content of the catalyst. Exponentially decaying catalyst activity functions similar to the ones described by Szepe55 were used. This analysis gave results qualitatively similar to the ones described above. 

Although this section is not a prerequisite to the remaiiting sections, the internal-age distribution is introduced here because of its close analogy to the external-age distribution. We shall let a represent the-age of a molecule inside the reactor. The internal-age distribution function I (a) is a function such that /(a) Aa is the fi action of material inside the reactor that has been inside the reactor for a period of time between a and a + Aa. It may be contrasted with E(oi) Aa, which is used to represent the material Eeaving the reactor that has spent a time between a and a Aa m the reaction zone /(a) characterizes the time the material has been (and still is) in the reactor at a particular time. The function (a) is viewed outside the reactor and /(a) is viewed inside the reactor. In unsteady-state problems it can be important to know what the particular state of a reaction mixture is, and /(a) supplies this information. For example, in a catalytic reaction using a catalyst whose activity decays with time, the age distribution of the catalyst in the reactor is of importance and the intemal-age distribution can be of use in modeling the reactor. 

The approach proposed by FROMENT and BISCHOFF [4,5], that considers activity decay as a function of the coke on catalyst was used. 

The optimal catalyst distribution problem was studied in an adiabatic reactor (Ogunye and Ray, 197la,b). The optimal initial distribution of catalyst activity along the axis of a tubular fixed-bed reactor was examined for a class of reactivation-deactivation problems by Gryaert and Crowe (1976). A general set of simultaneous reactions was considered, quasi steady state approximation was used, and the decay of the catalyst expressed as a function of temperature, concentration and catalyst activity. The influence of various initial catalyst activity distributions upon the reactor performance was also considered. 

To account for these different time scales, different activity functions are used for the formation of coke and for the formation of the other products the activity for coke formation is described by an exponentially decaying function of the residence time (characteristic time of about 0.02 s) the conversion and formation of the other products are described by one activity function that decreases exponentially as function of the catalyst coke content. This model describes the conversion obtained with the regenerated catalyst according to the curve that was drawn in Figure 2. 

Table 8.4 contains the deactivation parameters estimated from the long-term catalyst stability test and the feedstock evaluation with HCO. d and d are the parameters of the hyperbolic function that describes the initial activity decay caused by coke formation, whereas 3 is the exponent of the power-type function that represents the slow deactivation process by metal deposition (see Equation 8.21). Each set of... 

When the amount of coke formed as a function of time on stream is compared to the decrease in catalytic activity (see Fig. 3), two regimes of deactivation can be noticed for the strongly deactivating catalysts, i e, a slow initial deactivation which is followed by a rapid loss of activity This first phase is characteristic of a slow transformation of the reactive carbon into less reactive coke. The second phase is attributed to carbon formed on the support which accumulates there and rapidly covers the Pt particles when its amount reaches a critical value causing the sudden decay of catalytic activity. 

For all four alcohols in the zeolitic catalysts with small enough crystallite sizes—when diffusion limitations also disappear—dehydration kinetics are well approximated by the exponental function, a fact that is explicable in terms of the unimolecular decay of molecules of butyl alcohol adsorbed on identical active sites. With isobutyl alcohol, for example, the rate coefficient k may be written... 

Because of the catalyst decay, the activity decreases with time and a typical curve of the activity as a function of time is shown in Figure 10-18. 

The activity, as before, is a function of the time the catalyst has been in contact with the reacting gas stream. The decay rate law is... 

Some other catalysts, such as Cr /aluminophosphate, exhibit polymerization rates that do decay with time. In these systems, at least, polymer accumulation over time might cause the declining activity, because of increasing resistance to mass transport. However, this interpretation would mean that the polymerization rate would be a function, not of time itself, but of the amount of polymer accumulation. Investigation of the kinetics variables makes it clear that the rate is dependent not on polymer build up but on the reaction time. Similar rate-decay kinetics can be obtained with a high or a low polymer yield, by variation of ethylene concentration and other variables. In one experiment, the ethylene in the reactor was removed just as the peak reaction rate was reached, and not... 

Damkohler number, primary bubble size (m) secondary bubble size (m) catalyst decay constant (1/s) particle diameter (m) tube diameter (m) activation energy (kcal/kmol) energy input rate (W) function (-) feed rate (mol/s) feed rate of i (kmol/s) solids circulation rate (kg/s) flow rate in a single tube (kmol/s) total feed rate (kmol/s)... 

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