Transport effects intraparticle

If intraparticle diffusion effects are important and an effectiveness factor ij is employed (as in equation 3.8) to correct the chemical kinetics observed in the absence of transport effects, then it is necessary to adopt a stepwise procedure for solution. First the pellet equations (such as 3.10) are solved in order to calculate t) for the entrance to the reactor and then the reactor equation (3.87) may be solved in finite difference form, thus providing a new value of Y at the next increment along the reactor. The whole procedure may then be repeated at successive increments along the reactor. 

Figures 13 and 14 refer to the situation where only intraparticlc transport effects influence the observable reaction rate. However, a similar behavior is observed if, besides intraparticle heat and mass transport processes, the heat and mass transfer between the catalyst pellet and the bulk fluid phase is also considered. More information about this situation can be found, for example, in the works of Cresswell [26], McGreavy and...

Table 2. Experimental diagnostic criteria for the absence of intraparticle transport effects in simple, irreversible reactions (power law kinetics only).

At this point, it should be mentioned that there may be some doubt about how successful the nonisothermal criteria are at involving observable quantities only. This concerns the fact that in the nonisothermal case one has to specify the Arrhenius number which contains the true activation energy of the catalyzed reaction. The above statement would obviously define the true activation energy as a directly observable quantity in the nonisothermal criteria. However, this would presumably be an experimental value derived from studies in which intraparticle transport effects were absent, which is precisely what one is attempting to define [12]. 

Table 4 summarizes a number of well-known theoretical diagnostic criteria for the estimation of intraparticle transport effects on the observable reaction rate. Tabic 5 gives a survey of the respective criteria for interphase transport effects. It is quite obvious that these are more difficult to use than the simple experimental criteria given in Tables 2 and 3. In general, the intrinsic rate expression has to be specified and, additionally, either the first derivative of the intrinsic rate with respect to concentration (and temperature) at surface... 

Table 4. Theoretical diagnostic criteria for the absence or intraparticle transport effects (simple reactions with arbitrary kinetics).

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 evaluation of catalyst effectiveness requires a knowledge of the intrinsic chemical reaction rates at various reaction conditions and compositions. These data have to be used for catalyst improvement and for the design and operation of many reactors. The determination of the real reaction rates presents many problems because of the speed, complexity and high exo- or endothermicity of the reactions involved. The measured conversion rate may not represent the true reaction kinetics due to interface and intraparticle heat and mass transfer resistances and nonuniformities in the temperature and concentration profiles in the fluid and catalyst phases in the experimental reactor. Therefore, for the interpretation of experimental data the experiments should preferably be done under reaction conditions, where transport effects can be either eliminated or easily taken into account. In particular, the concentration and temperature distributions in the experimental reactor should preferably be described by plug flow or ideal mixing models. 

A disturbing question may be just how successful these criteria are in utilizing only observable quantities. For example, if we follow the letter of the statements above, the true activation energy is apparently defined as an experimentally observable quantity in the nonisothermal criteria. This would presumably be an experimental value resulting from studies in which intraparticle transport effects were absent, but this is precisely what one is trying to determine. What can we say Sometimes an active imagination plus iteration is the best course. 

The procedure is quite simple in the case of intraparticle effects, since the diffusional modulus is directly proportional to the characteristic particle dimension. Thus the very practical idea of chop em up and run em again is very sound. If there is any influence of intraparticle transport, it should be manifested by a change (normally an increase) in the rate or conversion observed, with all other factors being the same. In principle, one should always be able to minimize intraparticle transport effects by working with catalyst particles of sufficiently small size. There are, however, practical limits associated with doing this, such as high pressure drops in fixed beds or elution in slurry or fluid beds that employ very fine particles (as we will see later). 

The first set of preliminary experiments in a kinetic study carried out in laboratory PBRs should establish the flow conditions at which external transport effects are negligible. The second set of diagnostic experiments conducted should verify the particle size requirements under which intraparticle transport effects are eliminated. A study of intrinsic kinetics must make use of the flow rates and particle sizes that exclude both external and internal transport limitations, respectively. 

The phrase effective considers that the rate within the particle may be diminished by intraparticle transport effects, if the rate of diffusion into the pores is small compared to the rate of reactant consumption by the reaction at the surface of the pores. This leads to a concentration profile within a porous particle and therefore... 

As pointed out earlier, the major external resistance is that of mass transfer, and therefore, the effect of external heat transfer can be neglected. Furthermore, internal (intraparticle) transport effects can be neglected in slurry reactors except under some unusual reaction conditions since the size of the catalyst particles is of the order of 100 microns. In trickle-beds, however, both the internal heat and mass transport effects can be important. 

Intraparticle mass transport resistance can lead to disguises in selectivity. If a series reaction A — B — C takes place in a porous catalyst particle with a small effectiveness factor, the observed conversion to the intermediate B is less than what would be observed in the absence of a significant mass transport influence. This happens because as the resistance to transport of B in the pores increases, B is more likely to be converted to C rather than to be transported from the catalyst interior to the external surface. This result has important consequences in processes such as selective oxidations, in which the desired product is an intermediate and not the total oxidation product CO2. 

This involves knowledge of chemistry, by the factors distinguishing the micro-kinetics of chemical reactions and macro-kinetics used to describe the physical transport phenomena. The complexity of the chemical system and insufficient knowledge of the details requires that reactions are lumped, and kinetics expressed with the aid of empirical rate constants. Physical effects in chemical reactors are difficult to eliminate from the chemical rate processes. Non-uniformities in the velocity, and temperature profiles, with interphase, intraparticle heat, and mass transfer tend to distort the kinetic data. These make the analyses and scale-up of a reactor more difficult. Reaction rate data obtained from laboratory studies without a proper account of the physical effects can produce erroneous rate expressions. Here, chemical reactor flow models using matliematical expressions show how physical... 

The ratio of the observed reaction rate to the rate in the absence of intraparticle mass and heat transfer resistance is defined as the elFectiveness factor. When the effectiveness factor is ignored, simulation results for catalytic reactors can be inaccurate. Since it is used extensively for simulation of large reaction systems, its fast computation is required to accelerate the simulation time and enhance the simulation accuracy. This problem is to solve the dimensionless equation describing the mass transport of the key component in a porous catalyst[l,2]... 

Application of the Balzhinimaev model requires assumptions about the reactor and its operation so that the necessary heat and material balances can be constructed and the initial and boundary conditions formulated. Intraparticle dynamics are usually neglected by introducing a mean effectiveness factor however, transport between the particle and the gas phase is considered. This means that two heat balances are required. A material balance is needed for each reactive species (S02, 02) and the product (SO3), but only in the gas phase. Kinetic expressions for the Balzhinimaev model are given in Table IV. 

In this equation the entire exterior surface of the catalyst is assumed to be uniformly accessible. Because equimolar counterdiffusion takes place for stoichiometry of the form of equation 12.4.18, there is no net molar transport normal to the surface. Hence there is no convective transport contribution to equation 12.4.21. Let us now consider two limiting conditions for steady-state operation. First, suppose that the intrinsic reaction as modified by intraparticle diffusion effects is extremely rapid. In this case PA ES will approach zero, and equation 12.4.21 indicates that the observed rate per unit mass of catalyst becomes... 

Spacer chain catalysts 3, 4, and 19 have been investigated under carefully controlled conditions in which mass transfer is unimportant (Table 5)80). Activity increased as chain length increased. Fig. 7 shows that catalysts 3 and 4 were more active with 17-19% RS than with 7-9% RS for cyanide reaction with 1-bromooctane (Eq. (3)) but not for the slower cyanide reaction with 1-chlorooctane (Eq. (1)). The unusual behavior in the 1-bromooctane reactions must have been due to intraparticle diffusional effects, not to intrinsic reactivity effects. The aliphatic spacer chains made the catalyst more lipophilic, and caused ion transport to become a limiting factor in the case of the 7-9 % RS catalysts. At > 30 % RS organic reactant transport was a rate limiting factor in the 1-bromooctane reations80), In contrast, the rate constants for the 1 -chlorooctane reactions were so small that they were likely limited only by intrinsic reactivity. (The rate constants were even smaller than those for the analogous reactions of 1-bromooctane and of benzyl chloride catalyzed by polystyrene-bound benzyl-... 

In this study the ratio of the particle sizes was set to two based on the average value for the two samples. As a result, if the diffusion is entirely controlled by secondary pore structure (interparticle diffusion) the ratio of the effective diffusion time constants (Defl/R2) will be four. In contrast, if the mass transport process is entirely controlled by intraparticle (platelet) diffusion, the ratio will become equal to unity (diffusion independent of the composite particle size). For transient situations (in which both resistances are important) the values of the ratio will be in the one to four range. Diffusional time constants for different sorbates in the Si-MCM-41 sample were obtained from experimental ZLC response curves according to the analysis discussed in the experimental section. Experiments using different purge flow rates, as well as different purge gases... 

The effects of physical transport processes on the overall adsorption on porous solids are discussed. Quantitative models are presented by which these effects can be taken into account in designing adsorption equipment or in interpreting observed data. Intraparticle processes are often of major importance in adsorption kinetics, particularly for liquid systems. The diffusivities which describe intraparticle transfer are complex, even for gaseous adsorbates. More than a single rate coefficient is commonly necessary to represent correctly the mass transfer in the interior of the adsorbent. 

Even better yields of C result if components X and Y are incorporated in the same catalyst particle, rather than if they exist as separate particles. In effect, the intermediate product B no longer has to be desorbed from particles of the X type catalyst, transported through the gas phase and thence readsorbed on Y type particles prior to reaction. Resistance to intraparticle mass transfer is therefore reduced or eliminated by bringing X type catalyst sites into close proximity to Y type catalyst sites. Curve 4 in Fig. 3.10 illustrates this point and shows that for such a composite catalyst, containing both X and Y in the same particle, the yield of C for reaction 3 is higher than it would have been had discrete particles of X and Y been used (curve 3). 

Several quantitative analyses of the effect of intraparticle heat and mass transport have been carried out for parallel, irreversible reactions [1]. Roberts and Lamb [2] have worked on the effect of reversibility on the selectivity of parallel reactions in a porous catalyst. The reaction selectivity of a kinetic model of two parallel, first order, irreversible reactions with a second order inhibition kinetic term in one of them has also been investigated [3]. 

Based on the studies on the KD306-type sulfur-resisting methanation catalyst, the non-isothermal one-dimensional and two-dimensional reaction-diffusion models for the key-components have been established, which were solved using an orthogonal collocation method. The simulation values of the effectiveness factors for the methanation reaction ch4 and the shift reaction fco2are in fair agreement with the experimental values, which indicates that both models are able to predict intraparticle transport and reaction processes within catalyst pellets. 

FCC catalyst development to reduce the effect of vanadium has been aimed at reduction of vanadium mobility the application of special ingredients in the catalyst which function as metal scavengers or metal catchers. In the past (2, 10) transport experiments were used to show that during steam-aging, intraparticle transfer of vanadium occurs and that migrating vanadium can be irreversibly sorbed by a metal trap such as sepiolite (2) in the form of a heat stable vanadate. 

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