Empirical deactivation functions

Notice that coking rate equations were derived, so that there was no real need to resort to empirical deactivation functions. That was done because it was not investigated if the deactivation was caused by site coverage or pore blockage or by both mechanisms ... 

Butene dehydrogenation into butadiene on chromia-alumina A- Empirical deactivation functions ... 

So far these processes have been modeled in terms of lumps. In catalytic cracking the 3-lump -and the 10-lump model [Nace et al, 1971 Jacob et al, 1976] are still widely used although the lumps are based on boiling ranges rather than on chemical nature. These models contain in general only one deactivation function of an empirical nature for the reactions of the various lumps, b their study of the catalytic cracking of n-hexane on a US-Y-zeolite in an electrobalance with recycle Beimaert et al, [1994] derived an empirical deactivation function of the type (2) for the various reactions, but with different a-values, as illustrated in Table 2 for the isomerizations. 

The catalyst activity factor (aj) is time-dependent. Several models have been proposed in the literature, depending on the origin of catalyst deactivation, i.e. sintering, fouling or poisoning (8). The following differential equation can represent semi-empirically different kinds of separable deactivation functions. 

The influence of the coke on the kinetics of the main reaction can be accounted empirically by multiplying the kinetic coefficient of eq. (4) by a deactivation function coke content of the catalyst, Cc ... 

Deactivation functions hexane isomers 3-Me-pentane, 2,3-di-Me-butane and 2,2-di-Me-butane, The parameters of the empirical exponential deactivation functions are shown in Table 4. 

This simple analysis is semi empirical it is not a description of the diffusion limited reaction within the crystals but allows one to take into account both phenomena, in order to provide kinetic models for FCC reactor description [11]. Experimental results on the three feedstocks are shown in figure 1, with the deactivation function determined according to the method described in [10]. Curves are calculated from equation (3) after fitting E and F. These values are reported in table 2. 

Now the rate expression for the reaction A —> B together with (26) indicates that the deactivation depends on the composition of the reaction mixture and may vary along the length of the reactor. Under integral reactor conditions this leads to a nonuniform catalyst deactivation in a packed bed. So differential conditions are to be preferred to study this phenomenon. Various empirical activity functions have been proposed [15] whereby using Oc = f(t) instead of = /(cc) has the advantage of being independent of... 

These deactivation functions do not contain the gas phase composition It Is clear from (2) and (3) that the coke content is a local value. Consequently, in an integral reactor coke is deposited according to a profile, leading to non uniform deactivation Such a situation cannot be predicted when (1) is multiplied by an empirical function of time only Conversely, it is clear from (2) and (9) e.g. that, when a deactivation function like exp(-at) is used to fit experimental data on deactivation, a cannot be a true constant [ref. 5]. 

Figure 4.35 shows the time-on-stream behavior for a single CSTR at three levels of holding time according to the exponential decay function. It can be seen that the reactor performance is very sensitive to the relative magnitudes of the decay constant a and the residence time i. Use of the empirical time-on-stream correlation of equation (4-157) amounts to disregarding the kinetics expressed in equation (4-156). Just as a reminder we will repeat that the nature of the deactivation function—exponential, linear, hyperbolic, etc.—will not change the qualitative nature of the results... 

To evaluate the exact variation of 0 with time is to measure the rate of deposition of KX and the other parameters directly or to apply an empirical correlation relating to the effect of the decrease in C rOK he overall reaction. The expression of the deactivation function and the kinetic data would determine the form of (j>, such as... 

The approach followed in deactivation studies is often different from the one outlined here. The alternate approach does not consider a coking rate equation and uses an empirical time-related deactivation function for the particle or bed O = /( called activity [Szepe and Levenspiel, 1971 Wojchiechowski, 1968]. Linear, hyperbolic or exponential functions of time were used. Deriving the activity O with respect to time gives the corresponding rates of change of the activity and defines a so-called order of deactivation, from which it has been attempted to get some insight into the mechanism of deactivation—an attempt... 

The deactivation function is expressed in terms of the coke content of the catalyst, not in terms of time as has been done frequently. Indeed, time is not the true variable for the deactivation, as discussed earlier. The deactivation functions for the coking used here are still empirical in the sense that they do not explicit the mechanism of the deactivation-site coverage or blocking or both, as will be attempted in Example 5.3.3.B. 

Figures 11.5.6-6, 11.5.6-7, and 11.5.6-8 compare experimental data with results obtained from a simulation on the basis of the above equations and the best set of parameters. The agreement is quite satisfactory, and the approach appears to be valuable despite the empirical nature of the deactivation functions which do not explicitly reflect the mechanism of the deactivation.

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 ... 

Empirical Methods. The grcphical deactivation plot is a very useful empirical method for prediction of the catalyst performance and for estimation of catalyst lifetime (18,19). The deactivation plot shows the length of the reaction front as a function of time. This illustrates the movement of the temperature profile caused by the progressive deactivation of the catalyst. The method is illustrated in Figure 3. The temperature increase over the catalyst bed is calculated as AT = Texii - Twet and a certain percentage hereof, e.g. 90% (AT90) is calculated. The axial distance in the... 

Figure 1 illustrates the extent of n-heptane conversion over those catalysts as a function of time-on-stream, working under deactivation conditions. The catalyst deactivation was modeled by the well-known Voorhies equation C= Af [6], where C denotes percentage conversion, t denotes time-on-stream (min), and A and B are empirical parameters. Even though the Voorhies equation was originally used to correlate the coke content with time, the use of the equation for correlating activity and time was also confirmed by Magnoux et. al. [7]. 

It is necessary to determine rj(e) under reaction conditions, and a life test should be included in any catalyst development effort. The data from this test will allow r] to be fitted as a function of time on stream, 6. Equations 10.35 and 10.36 can obviously be used to model deactivation processes other than site sintering, and ko can be regarded as an empirical constant with units of reciprocal time. 

A general equation (8.183 and 8.184) is thus obtained from which the many empirical forms used in describing deactivation can be derived. Often the deactivation is considered to be irreversible, a = 0 and the initial activity is set to unity, ao = 1. Then by varying the order (n) of deactivation the different forms of the empirical functions can be obtained as special cases. 

Since neither Cq or C, can be measured, some empirical correlation for Ca/C, has to be substituted into Eq. 5.3.b-7 to express the decline of o in terms of the deactivation. The ratio CaJC, could be replaced by some function of a measurable quantity. 

Since neither Ca nor Q can be measured, some empirical relation for Cc/Ci has to be substituted into (5.3.2.2-S) to express the decline of The ratio CcJCi could be replaced by some function of a measurable quantity (e.g., coke) or of less direct factors such as the ratio of total amount of A fed to the amount of catalyst or even process time. This approach was followed in the early work of Johanson and Watson [1946] and Rudershausen and Watson [1954]. In the terminology of Szepe and Levenspiel [1971] it corresponds to non separable deactivation . 

From equation (1.8) it is apparent that two parameters, k and n, are required to describe the decay kinetics. TTius, authors such as Nace et al.(1971) and Corella et al.(1985) who used the decay function of the form = Df did not evaluate k but instead included it in their overall kinetic constant, a combined cracking and decay constant. This is certainly sufficient from an empirical stand point but to adequately describe the deactivation kinetics the value of k must be assessed. As well, the activation energy from these studies represents the combination of the energy of activation of gas oil cracking and the activation energy for the loss of active sites. 

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