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Spherical catalyst pellets effective diffusivity

One must understand the physical mechanisms by which mass transfer takes place in catalyst pores to comprehend the development of mathematical models that can be used in engineering design calculations to estimate what fraction of the catalyst surface is effective in promoting reaction. There are several factors that complicate efforts to analyze mass transfer within such systems. They include the facts that (1) the pore geometry is extremely complex, and not subject to realistic modeling in terms of a small number of parameters, and that (2) different molecular phenomena are responsible for the mass transfer. Consequently, it is often useful to characterize the mass transfer process in terms of an effective diffusivity, i.e., a transport coefficient that pertains to a porous material in which the calculations are based on total area (void plus solid) normal to the direction of transport. For example, in a spherical catalyst pellet, the appropriate area to use in characterizing diffusion in the radial direction is 47ir2. [Pg.432]

Consider the spherical catalyst pellet of radius R shown in Figure 12.4. The effective diffusivity approach presumes that diffusion of all types can be represented in terms of Fick s first law and an overall effective diffusion coefficient that can be taken as a constant. That is, the appropriate flux representation is... [Pg.447]

The well known Thiele modulus of the reaction. This is defined as the ratio of the intrinsic chemical rate, calculated at bulk fluid phase conditions, to the maximum rate of effective diffusion at the external pellet surface. For spherical catalyst pellets, the Thiele modulus is given by... [Pg.331]

A reaction of the order Vi is carried out in a spherical catalyst pellet. For the given surface temperature and concentration the product ksCAjmii equals 0.2 s 1. The effective diffusion coefficient has been determined as 2 x Iff7 m2 s"1. The diameter of the sphere is 6 mm. Fur-... [Pg.217]

A lack of significant intraphase diffusion effects (i.e., 17 > 0.95) on an irreversible, isothermal, first-order reaction in a spherical catalyst pellet can be assessed by the Weisz-Prater criterion [P. B. Weisz and C. D. Prater, Adv. Catal., 6 (1954) 143] ... [Pg.228]

Tn the remainder of the text the term effective is used to indicate that a transport coefScient applies to a porous material, as distinguished from a homogeneous region. Effective diffusivities Dg and thermal conductivities kg are based on a unit of total area (void plus nonvoid) perpendicular to the direction of transport. For example, for diffusion in a spherical catalyst pellet at radius r, Dg is based on the area Anr. ... [Pg.400]

The effect of pore-mouth poisoning can be obtained by equating the rate of diffusion through the outer, deactivated layer to the rate of reaction on the inner fully active part of the pellet. Figure 11-12 depicts a spherical catalyst pellet at a time when the radius of the unpoisoned central portion is r, corresponding to a thickness of completely poisoned catalyst — r. Consider a first-order reaction where the concentration of reactant at the outer surface is C. The rate of diffusion into one pellet will be... [Pg.460]

Figure 12.6 Effectiveness factor plot for spherical catalyst pellets based on the effective diffusivity model for a first-order reaction. Figure 12.6 Effectiveness factor plot for spherical catalyst pellets based on the effective diffusivity model for a first-order reaction.
This relation is plotted as curve B in Figure 12.11. Smith (68) has shown that the same limiting forms for T are observed using the concept of effective diffusivities and spherical catalyst pellets. Examination of curve B indicates that for fast reactions on catalyst surfaces where the poisoned sites are uniformly distributed over the pore surface, the apparent activity of the catalyst declines much less rapidly than for the case where catalyst effectiveness factors approach unity. Under these circumstances, the catalyst effectiveness factors are considerably less than unity, and the effects of the portion of the poison adsorbed near the closed end of the pore are not as apparent as in the earlier case for small values of hj. With poisoning, the Thiele modulus hp decreases, and the reaction merely penetrates deeper into the pore. [Pg.401]

Charles and Thomas (1963) in their paper considered firstly a spherical catalyst pellet of radius R and focus attention on a spherical shell of thickness dr and radius, as shown in Fig. 9. He assumes isothermal condition and that the complicated diffusion phenomena within the porous structure can be represented by a single overall effective diffusion coefficient, D ff. In the catalyst pellet, reactants are transported to the shell by diffusion and consumed... [Pg.371]

Consider the case of a nonisothermal reaction A B occurring in the interior of a spherical catalyst pellet of radius R (Figure 6.4). We wish to compute the effect of internal heat and mass transfer resistance upon the reaction rate and the concentration and temperature profiles within the pellet. If Z)a is the effective binary diffusivity of A within the pellet, and we have first-order kinetics, the concentration profile CA(f) is governed by the mole balance... [Pg.265]

Diffusion effects can be expected in reactions that are very rapid. A great deal of effort has been made to shorten the diffusion path, which increases the efficiency of the catalysts. Pellets are made with all the active ingredients concentrated on a thin peripheral shell and monoliths are made with very thin washcoats containing the noble metals. In order to convert 90% of the CO from the inlet stream at a residence time of no more than 0.01 sec, one needs a first-order kinetic rate constant of about 230 sec-1. When the catalytic activity is distributed uniformly through a porous pellet of 0.15 cm radius with a diffusion coefficient of 0.01 cm2/sec, one obtains a Thiele modulus y> = 22.7. This would yield an effectiveness factor of 0.132 for a spherical geometry, and an apparent kinetic rate constant of 30.3 sec-1 (106). [Pg.100]

A hydrocarbon is cracked using a silica-alumina catalyst in the form of spherical pellets of mean diameter 2.0 mm. When the reactant concentration is 0.011 kmol/m3, the reaction rate is 8.2 x 10"2 kmol/(m3 catalyst) s. If the reaction is of first-order and the effective diffusivity De is 7.5 x 10 s m2/s, calculate the value of the effectiveness factor r). It may be assumed that the effect of mass transfer resistance in the. fluid external Lo the particles may be neglected. [Pg.645]

The Effectiveness Factor Analysis in Terms of Effective Diffusivities First-Order Reactions on Spherical Pellets. Useful expressions for catalyst effectiveness factors may also be developed in terms of the concept of effective diffusivities. This approach permits one to write an expression for the mass transfer within the pellet in terms of a form of Fick s first law based on the superficial cross-sectional area of a porous medium. We thereby circumvent the necessity of developing a detailed mathematical model of the pore geometry and size distribution. This subsection is devoted to an analysis of simultaneous mass transfer and chemical reaction in porous catalyst pellets in terms of the effective diffusivity. In order to use the analysis with confidence, the effective diffusivity should be determined experimentally, since it is difficult to obtain accurate estimates of this parameter on an a priori basis. [Pg.447]

This study was carried out to simulate the 3D temperature field in and around the large steam reforming catalyst particles at the wall of a reformer tube, under various conditions (Dixon et al., 2003). We wanted to use this study with spherical catalyst particles to find an approach to incorporate thermal effects into the pellets, within reasonable constraints of computational effort and realism. This was our first look at the problem of bringing together CFD and heterogeneously catalyzed reactions. To have included species transport in the particles would have required a 3D diffusion-reaction model for each particle to be included in the flow simulation. The computational burden of this approach would have been very large. For the purposes of this first study, therefore, species transport was not incorporated in the model, and diffusion and mass transfer limitations were not directly represented. [Pg.374]

Effectiveness factors for a first-order reaction in a spherical, nonisothermal catalysts pellet. (Reprinted from R B. Weisz and J. S. Hicks, The Behavior of Porous Catalyst Particles in View of Internal Mass and Heat Diffusion Effects, Chem. Eng. Sci., 17 (1962) 265, copyright 1962, with permission from Elsevier Science.)... [Pg.216]

Intraparticle Diffusion and External Mass-Transfer Resistance For typical industrial conditions, external mass transfer is important only if there is substantial intraparticle diffusion resistance. This subject has been discussed by Luss, Diffusion-Reaction Interactions in Catalyst Pellets, in Carberry and Varma (eds.), Chemical Reaction and Reactor Engineering, Dekker, 1987. This, however, may not be the case for laboratory conditions, and care must be exerted in including the proper data interpretation. For instance, for a spherical particle with both external and internal mass-transfer limitations and first-order reaction, an overall effectiveness factor r, can be derived, indicating the series-of-resistances nature of external mass transfer followed by intraparticle diffusion-reaction ... [Pg.22]

When the rate is measured for a catalyst pellet and for small particles, and the diffusivity is also measured or predicted, it is possible to obtain both an experimental and a calculated result for rj. For example, for a first-order reaction Eq. (11-67) gives directly. Then the rate measured for the small particles can be used in Eq. (11-66) to obtain k. Provided is known, d) can be evaluated from Eq. (11-50) for a spherical pellet or from Eq. (11-56) for a fiat plate of.catalyst. Then 7caic is obtained from the proper curve in Fig. 11-7. Comparison of the experimental and calculated values is an overall measure of the accuracy of the rate data, effective diffusivity, and the assumption that the intrinsic rate of reaction (or catalyst activity) is the same for the pellet and the small particles. Example 11-8 illustrates the calculations and results for a flat-plate pellet of NiO catalyst, on an alumina carrier, used for the ortho-para-hydrogen conversion. [Pg.439]

In reality, a typical catalyst pellet will be a porous solid that may be quite complicated or even irregular in shape with a large number of catalytic reaction sites distributed throughout. However, to simplify the problem for present purposes, the catalyst pellet will be approximated as being spherical in shape. Furthermore, we will assume that the catalyst pellet is uniform in constitution. Thus we assume that it can be characterized by an effective reaction-rate constant kef that has the same value at every point inside the pellet. In addition, we assume that the transport of reactant within the pellet can be modeled as pure diffusion with a spatially uniform effective diffusivity To Author simplify the problem, we assume that the transport of product out of the pellet is decoupled from the transport of reactant into the pellet. Finally, the concentration of reactant in the bulk-phase fluid (usually... [Pg.242]

The current catalyst has reached the end of its useful lifetime and needs to be replaced. Your project is to make a design change with the new catalyst to improve the reactor efficiency. In particular you are considering changing the catalyst size. The catalyst vendor has told you that they easily can make spherical pellets with diameters of 0-075 cm, 0.15 cm, and 0.30 cm. You also have been assured that the effective diffusivity, bed density, and reaction rate constant do not vary among the catalysts in this size range. One of your team members wants to use the smallest diameter catalyst to minimize the total mass of catalyst required. Another team member wants to use the largest diameter catalyst to miminize the pressure drop. [Pg.545]

Suppose that the reaction in Problem 12.1 is carried out in an adiabatic trickle-bed. What is the catalyst volume required for the desired conversion Assume that the effective diffusivities are the same at 10 cm Vs and the spherical pellet diameter is 1 cm. Use the following data ... [Pg.232]


See other pages where Spherical catalyst pellets effective diffusivity is mentioned: [Pg.801]    [Pg.433]    [Pg.442]    [Pg.1094]    [Pg.131]    [Pg.518]    [Pg.546]    [Pg.376]    [Pg.327]    [Pg.421]    [Pg.452]    [Pg.327]    [Pg.421]    [Pg.424]    [Pg.198]    [Pg.299]    [Pg.904]    [Pg.391]    [Pg.327]    [Pg.378]    [Pg.518]    [Pg.573]   
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