Intraparticle gradient effects gradients

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. 

Changing catalyst particle sizes can be used to test intraparticle effects (Figure 7). If there is no change of catalyst activity with change in particle size (assuming the exposed surface area of active catalyst is constant), the catalyst is considered to be free of intraparticle gradients. 

The intraparticle transport effects, both isothermal and nonisothermal, have been analyzed for a multitude of kinetic rate equations and particle geometries. It has been shown that the concentration gradients within the porous particle are usually much more serious than the temperature gradients. Hudgins [17] points out that intraparticle heat effects may not always be negligible in hydrogen-rich reaction systems. The classical experimental test to check for internal resistances in a porous particle is to measure the dependence of the reaction rate on the particle size. Intraparticle effects are absent if no dependence exists. In most cases a porous particle can be considered isothermal, but the absence of internal concentration gradients has to be proven experimentally or by calculation (Chapter 6). 

The importance of the intraparticle heat transfer resistance is evident for particles with relatively short contact time in the bed or for particles with large Biot numbers. Thus, for a shallow spouted bed, the overall heat transfer rate and thermal efficiency are controlled by the intraparticle temperature gradient. This gradient effect is most likely to be important when particles enter the lowest part of the spout and come in contact with the gas at high temperature, while it is negligible when the particles are slowly flowing through the annulus. Thus, in the annulus, unlike the spout, thermal equilibrium between gas and particles can usually be achieved even in a shallow bed, where the particle contact time is relatively short. 

For working in absence of intraparticle gradients the criterium generally utilised is to decrease the catalyst particle size until no effect in the rate of reaction is obtained. 

The presence of pores, for which the observed reaction rate is lower than the kineti-cally controlled intrinsic one, in the particles or pellets affects the reaction rate due to diffusion limitations. This intraparticle diffusion effect causes a concentration gradient within the pores. If diffusion is fast, then the concentration gradient is negligible. 

The effect of intraparticle gradients was assumed to have been included in the estimated parameters, i.e. the reaction rates at the whole catalyst particle was calculated with the surface conditions. The intr article gradients were not calculated, because a commercial FCC catalyst was used in the experiments. The bulk gas temperature was assumed to remain constant along the reactor length due to the surrounding heating oven. 

The Consequences of Intraparticle Temperature Gradients For Catalyst Effectiveness Factors... 

An extension of this one-dimensional heterogeneous model is to consider intraparticle diffusion and temperature gradients, for which the lumped equations for the solid are replaced by second-order diffu-sion/conduction differential equations. Effectiveness factors can be used as applicable and discussed in previous parts of this section and in Sec. 7 of this Handbook (see also Froment and Bischoff, Chemical Reactor Analysis and Design, Wiley, 1990). 

The film diffusion process assumes that reactive surface groups are exposed directly to the aqueous-solution phase and that the transport barrier to adsorption involves only the healing of a uniform concentration gradient across a quiescent adsorbent surface boundary layer. If instead the adsorbent exhibits significant microporosity at its periphery, such that aqueous solution can effectively enter and adsorptives must therefore traverse sinuous microgrottos in order to reach reactive adsorbent surface sites, then the transport control of adsorption involves intraparticle diffusion.3538 A simple mathematical description of this process based on the Fick rate law can be developed by generalizing Eq. 4.62 to the partial differential expression36... 

Table 2 lists most of the available experimental criteria for intraparticle heat and mass transfer. These criteria apply to single reactions only, where it is additionally supposed that the kinetics may be described by a simple nth order power rate law. The most general of the criteria, 5 and 8 in Table 2, ensure the absence of any net effects (combined) of intraparticle temperature and concentration gradients on the observable reaction rate. However, these criteria do not guarantee that this may not be due to a compensation of heat and mass transfer effects (this point has been discussed in the previous section). In fact, this happens when y/J n [12]. 

Small catalyst particles are also effective in avoiding intraparticle concentration gradients. 

The intraparticle concentration and temperature gradients in a porous particle can always be neglected, when the pore effectiveness factor rj is close to 1. Assuming that rj... 

Another aspect concerns catalyst particles with intraparticle temperature gradients. In general the temperature inside a catalyst pellet will not be uniform, due to the heat effects of the reaction occurring inside the catalyst pellet. The temperature inside the catalyst can be related to the concentration with (see for example [4]) ... 

Volume changes due to the reaction may become considerable. This may lead to intraparticle pressure gradients, which will influence the effectiveness factor because ... 

Using the dusty gas model [5] analytical solutions are derived to describe the internal pressure gradients and the dependence of the effective diffusion coefficient on the gas composition. Use of the binary flow model (BFM, Chapter 3) would also have yielded almost similar results to those discussed below. After discussion of the dusty gas model, results are then implemented in the Aris numbers. Finally, negligibility criteria are derived, this time for intraparticle pressure gradients. Calculations are given in appendices here we focus on the results. 

Now that we have derived the intraparticle pressure gradients, we can also determine the effective diffusion coefficient as a function of the gas composition. 

Many complex situations have not been addressed, such as simultaneous intraparticle temperature and pressure gradients and nondiluted gases with anisotropic catalyst pellets. Calculations for these and other complex situations proceed along the same line as demonstrated for bimolecular reactions and nondiluted gases. A framework that can be used to investigate the effect of complex situations on the effectiveness factor is given. Also presented are criteria that can be used for a quick estimate as to whether or not certain phenomena are important. 

The intraparticle temperature gradients result in an increase in the effectiveness factor. This is obvious since the reaction is strongly exothermic. The increase, however, is only 2 % relative. Thus in this case intraparticle temperature gradients can be neglected. 

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