Kinetics disguised

If a kinetic study is carried out under conditions where the resistance to internal transport is high, the experimental data will be very misleading  

When 0 is greater than about 10, = 1/0. Substituting this relationship into Eqn. (9-2) 

The actual reaction rate is the rate that is measured experimentally in the laboratory. Let s consider an irreversible, nth-order reaction. The Thiele modulus is given by 

On a volumetric basis, the rate with no internal gradients is kyC. Combining these relationships gives 

suppose that the external transport resistance is neghgible, so that Ca,s = Ca,b-The above equation becomes 

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As all of the direct extraction rates were low relative to the hydrogenative HDS rates, even at low conversions, the fully saturated compound dimethyl-cyclohexylcyclohexane was observed in the product mixture. As discussed in later sections, this fact indicates that the major cause of rate reduction by adjoining alkyl substituents may not be due to lowering adsorption constants but could well be due to steric limitations in the oxidative addition of the C-S bond to the catalytic site, as discussed later. A more subtle explanation could be adsorption-disguised kinetics whereby the intermediate is not released from the catalyst surface but remains adsorbed so that further conversion proceeds. This was not observed for unsubstituted diben-zothiophenes, however. 

Hydrodemetallation reactions require the diffusion of multiringed aromatic molecules into the pore structure of the catalyst prior to initiation of the sequential conversion mechanism. The observed diffusion rate may be influenced by adsorption interactions with the surface and a contribution from surface diffusion. Experiments with nickel and vanadyl porphyrins at typical hydroprocessing conditions have shown that the reaction rates are independent of particle diameter only for catalysts on the order of 100 /im and smaller (R < 50/im). Thus the kinetic-controlled regime, that is, where the diffusion rate DeU/R2 is larger than the intrinsic reaction rate k, is limited to small particles. This necessitates an understanding of the molecular diffusion process in porous material to interpret the diffusion-disguised kinetics observed with full-size (i -in.) commercial catalysts. 

The chemist or engineer designing his experiments to establish quantitative kinetics of gas-phase reactions will do his best to look for constant-volume equipment. However, occasionally he may have to work with data obtained at constant pressure. The complication here is that a change in mole number affects the reaction volume and, thereby, the concentrations of the participants, distorting their histories from which reaction orders and rate coefficients are deduced Volume variation disguises kinetics and must be corrected for. 

In order to understand and modify the functions of a catalyst in a process, it is necessary to determine whether or not rates are determined by physical or chemical steps. Responses to process parameters and catalyst adjustments are different for the two regimes. Diffustonal resistance, in particular, causes unexpected complicrations. We have seen how low effectiveness factors decrease conversion and disguise kinetics, but selcc tivity also can be decreased. In addition, poisoning of pore mouth sites in conjunction with low diffusion results in a much more rapid activity decline than otherwise. 

If there is no mass-transfer hindrance at all, rate control is exclusively by the reaction, and the apparent order and activation energy are those of the reaction. If there is severe mass-transfer limitation, the apparent order is (n + l)/2 (n = true order of reaction), and the apparent activation energy is ( a,rx + a,ml)/2 s ViEi n (the activation energy of mass transfer, is typically very small compared with that of reaction, arx). In other words, both the order and the activation energy are the arithmetic means of those of reaction and mass transfer ("disguised kinetics"). 

With the meaningful title Sorption kinetics and intracrystalline diffusion of methanol in ferrierite an example of disguised kinetics , [71] exemplifies the pitfalls which, in cases like the given one, will necessarily lead the researcher to completely wrong conclusions if he is only able to base his reasoning on the overall uptake and release rather than on the processes of intracrystalline mass transfer. 

The kinetic model used is shown in Figure 6.15 (Chapter 6). It consists of five lumps and was previously reported in the literature (Sfinchez et al., 2005). The lumps are gases, naphtha (IBP— 204°C), middle distillates (204°C-343°C), VGO (343 C-538 C), and unconverted vacuum residue (538°C+). As mentioned earlier, experiments were performed under a disguised kinetic regime due to the presence of internal diffusion limitations this made necessary the introduction of the effectiveness factor (n) since internal gradients are indeed present. 

J.5.2 Implications of the Effectiveness Factor Concept for Kinetic Parameters Measured in the Laboratory. It is useful at this point to discuss the effects of intraparticle diffusion on the kinetic parameters that are observed experimentally. Unless we are aware that intraparticle diffusion may obscure or disguise the... 

Mass transfer can disguise the intrinsic kinetics severely [15]. For example, suppose the intrinsic kinetics is given by a power rate law ... 

When intraparticle diffusion is rate limiting, the kinetic behaviour of a chemically reacting system is generally different from that which would prevail if chemical reaction were rate limiting. It is therefore extremely important to develop criteria to assess whether intraparticle diffusion effects may be neglected and thus define the conditions of experiment which would reveal true chemical kinetics rather than overall kinetics disguised by intraparticle diffusion effects. 

Many industrial processes are mass-transfer limited so that reaction kinetics are irrelevant or at least thoroughly disguised by the effects of mass and heat transfer. Questions of catalyst poisons and promoters, activation and deactivation, and heat management dominate most industrial processes. 

After reactivity and selectivity, the next complication we encounter with all catalytic reactions is that there are essential transport steps of reactants and products to and from the catalyst. Therefore, in practice catalytic reaction rates can be thoroughly disguised by mass transfer rates. In fact, in many industrial reactors the kinetics of individual reactions are quite unknown, and some engineers would regard knowledge of their rates as unimportant compared to the need to prepare active, selective, and stable catalysts. The role of mass transfer in reactions is therefore essential in describing most reaction and reactor systems, and this will be a dominant subject in this chapter. 

With the goal of obtaining intrinsic catalyst properties (reaction kinetics and selectivities) from experimental data without being disguised by the above-mentioned phenomena, the following conditions should be fulfilled ... 

For a comparison of catalyst activities and in kinetic studies, one needs data that are not disguised by concentration gradients. For a 5% tolerance level the criterion for the effectiveness factor for the absence of internal diffusion limitations reads... 

In this chapter the aspects of model selection/discrimination and parameter estimation and the experimental acquisition of kinetic data are not dealt with, since they fall fell outside its scope. Moreover, in interpreting the observed temperature dependency of the rate coefficients in this chapter it was assumed that we are dealing with intrinsic kinetic data. As will be shown in a Chapter 7, other, parasitic, phenomena of mass and heat transfer may interfere, disguising the intrinsic kinetics. Criteria will be presented there, however, to avoid this experimental problem. 

This result implies that it is not the intrinsic kinetics that are observed, but the so-called disguised or false kinetics. This has as consequences that ... 

Heat or mass transfer effects, caused by intrareactor, interphase, or intraparticle gradients (see Figure 5), can disguise the results and lead to misinterpretations. Before accurate and intrinsic catalyst kinetic data can be established, these disguises must be eliminated by adjusting the experimental conditions. 

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