Deactivation functions

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. 

Haynes apd Leung (1983) formulated a similar configurational diffusion model combining the effects of active site poisoning as well as pore plugging on the HDM reaction. In this case the reaction form in the conservation equation is multiplied by a deactivation function which accounts for the loss of intrinsic activity, (1 - ) is frequently chosen, where x is the fractional coverage of the sites. Other forms of the site deactivation function have been discussed by Froment and Bischoff (1979). The deactivation was found to depend on a dimensionless parameter given by... 

For the optimal strategy of maintaining operational stability, Lee et al. have calculated the optimal profile of addition of fresh, non-deactivated enzyme into a CSTR under different deactivation kinetics. If a CSTR is charged initially with an amount of enzyme of initial activity N0, at time t under deactivation, the amount remaining is given by Eq. (5.83), where k(t) denotes an arbitrary deactivation function (J. Y. Lee, 1990). 

However, several assumptions are inherent in this interpretation of the data. First, it is assumed that the change in the observed effect (such as conversion of 850°F+, percentage denitrogenation, etc.) is linear with respect to time. Thus a linear delta-effect per period of time could be established and intermediate data could be adjusted to a MfreshM activity corresponding to that observed at the reference period and at any desired temperature. Second, it is assumed that the intermediate process parameter variations had no adverse effect on the catalyst deactivation function. For example, operation at constant temperature for a given interval of time would produce the same catalyst deactivation as varying temperatures (within limits) over the same interval of time. 

Figure 3 A schematic representation of catalyst deactivation functions for REY and USY catalysts.

All the previously cited models and works also consider, and some explicitly cite, this assumption—that the catalyst activity varies with time-on-stream (or with coke concentration [12]) in the same manner or with the same deactivation function (VO for all reactions in the network. That is, a nonselective deactivation model is always used. Corella et al. (16) have recently demonstrated that in the FCC process this assumption is not true and that it would be better to use a selective deactivation model. Another work (17) also shows how this consideration, when applied to catalytic cracking, influences the yield-conversion curves. Nevertheless, to avoid an additional complication, we will use in this chapter a nonselective deactivation model with the same a—t kinetic equation and deactivation function (VO for all the cracking reactions of the network. 

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 ... 

Equations for the kinetic mechanisms of coke formation with the exponential form of the deactivation function are obtained by integrating eqs. (6)—(8) ... 

This form of the deactivation function is very similar to forms used in the time-on-stream approach to cracking catalyst activity... 

Further, from its definition, a deactivation function is connected to one reaction only, not to the net rate of formation of a certain product, which may involve rates of formation and... 

To quantify the deactivation effect of coke on the various reaction rates, a deactivation function (Cc) was defined as the ratio of the reaction rate at a given coke content to the... 

The resulting reaction rate (r° ) at 9% n-hexane conversion is shown in Figure 6. The deactivation function for the 2-Me-pentane formation, fczMp(Cc), is plotted in Figure 8. It is independent of conversion, as required by its definition. 

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. 

Table 4 Estimated a-values of the exponential deactivation functions for some reactions leading to products of hexane cracking.

Since the coking reaction is not deactivated by coke formation, its deactivation function equals one. 

The deactivation functions for the isomerisation reactions of n-hexane were shown to be exponential functions of the coke content. The deactivation constant, the parameter of these functions, did not differ significantly for the various isomerisation reactions leading to tertiary carbenium ions. The deactivation constant for the isomerisation to 2,2-di-Me-butane, formed out of a secondary carbenium ion, was larger. 

The deactivation of cracking catalysts by coking with vacuum gas oils (VGO) is studied in relation to the chemical deactivation due to site coverage, and with the increase of diffusional limitations. These two phenomena are taken into account by a simple deactivation function versus catalyst coke content. The parameters of this function arc discussed in relation to feedstock analysis and change of effective diffiisivity with catalyst coke content. 

The experimental studies using industrial feedstock are carried out in a modified MA.T. (micro activity test) [10], The reaction conditions are presented in table 1, The catalyst is NOVA D equilibrium catalyst from Grace Davison Co, The equilibrium catalysts are previously coked under the same reaction conditions to get partially deactivated samples. The method using the conversion versus initial coke content from experiments to determine the deactivation function, is described in [10]. Three different feedstocks are used (table l). 

At low coke content, pore plugging is still negligible and decay is mainly due to site coverage. Consequently, the variation of deactivation function with coke content is only due to chemical deactivation, and it is proportional to the remaining activity ... 

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. 

Parameters of the deactivation function at 803°K with Nova D catalyst... 

Figure 1. Deactivation function versus initial coke content (O) Aramco, (A) Montmirail and (D)Nigeria.

We assume that the deactivation function is the same for each reaction. So, only the simple cracking reaction of a feedstock lump, to a product lump, was considered. Such a reaction occurring with the molar expansion (m) may be represented as... 

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