Slab catalyst pellets

By using Fick s and Fourier s laws in one-dimensional transport in a slab catalyst pellet (Figure 9.1) with, equimolar counter-diffusion under mechanical equilibrium, Eqs. (9.14) and (9.15) become... 

Cross-sectional area of slab catalyst pellet (m ) Refractory surface area (m )... 

The catalyst pellets are 6 mm X 6 mm semi-infinite slabs, with all faces permeable. (Problems 21-16 and 21-17 are based on data provided by Rase, 1977, pp. 44-60.)... 

Hollow cylindrical catalyst pellets are sometimes employed in commercial chemical reactors in order to avoid excessive pressure drops across a packed bed of catalyst. A more complex expression for the effectiveness factor is obtained for such geometry. This case was first discussed by Gunn [4]. Figure 2 illustrates the effectiveness factor curves obtained for the slab, sphere and cylinder. 

The simplest boundary conditions for the catalyst pellet are those for which the concentration and temperature at the edges of the slab are specified as being equal to the respective reservoir values. These Dirichlet boundary conditions then give... 

A fraction ( of the active surface of some porous slab-shaped catalyst pellets becomes poisoned. The pellets are used to catalyse a first-order isothermal chemical reaction. Find an expression for the ratio of the activity of the poisoned catalyst to the original activity of the unpoisoned catalyst when (a) homogeneous poisoning occurs, (b) selective poisoning occurs. 

The characteristic length is the thickness of the equivalent slab used in the single catalyst pellet equation and it is defined as the thickness lc of the catalyst slab that gives the same external surface to volume ratio as the original pellet. For Raschig16 rings this is given by... 

The catalyst packing of the reactor consists of an iron oxide Fe20s, promoted with potassium carbonate K COo, and chromium oxide Cr O-s,. The catalyst pellets are extrudates of a cylindrical shape. Since at steady state the problem of simultaneous diffusion and reaction are independent of the particle shape, an equivalent slab geometry is used for the catalyst pellet, with a characteristic length making the surface to volume ratio of the slab equal to that of the original shape of the pellet. 

The conditions are substantially more favorable for the microporous catalytic membrane reactor concept. In this case the membrane wall consists of catalyti-cally active, microporous material. If a simple reaction A -> B takes place and no permeate is withdrawn, the concentration profiles are identical to those in a catalyst slab (Fig. 29a). By purging the permeate side with an inert gas or by applying a small total pressure difference, a permeate with a composition similar to that in the center of the catalyst pellet can be obtained (Fig. 29b). In this case almost 100% conversion over a reaction length of only a few millimeters is possible. The advantages are even more pronounced, if a selectivity-limited reaction is considered. This is shown with the simple consecutive reaction A- B- C where B is the desired product. Pore diffusion reduces the yield of B since in a catalyst slab B has to diffuse backwards from the place where it was formed, thereby being partly converted to C (Fig. 29c). This is the reason why in practice rapid consecutive reactions like partial oxidations are often run in pellets composed of a thin shell of active catalyst on an inert support [30],... 

Consider, by way of example, an irreversible first-order reaction, A B, occurring in a pellet with slab geometry. As a result of the concentration profile, the reaction rate depends on the position within the catalyst pellet. Hence, a mass balance for the reactant has to be taken over an infinitesimal slice of the slab. At the steady state this leads to ... 

Without any prove it is stated here that the geometry factor T falls between the two extremes of 2/3 for the infinitely long slab and of 6/s for the sphere for almost all practical cases. Thus T is almost always close to unity. This holds for any catalyst geometry, hence also for catalyst geometry s commonly found in industry, for example ring-shaped or cylindrical catalyst pellets. For this type of pellet it can be shown (Appendix C) that the geometry factor T equals ... 

For an infinite slab, analytical solutions can be derived for the effectiveness factor. If r/ is plotted versus Ahq two branches occur (Figure 7.3). For the low Ahq branch, concentration profiles inside the catalyst pellet are as given in Figure 6.12a. For this branch the effectiveness factor can be calculated from... 

Now consider several ideal geometries of porous catalyst pellets shown in Figure 6.3.5. The first pellet is an infinite slab with thickness 2xp. However, since... 

Schematic representations of ideal catalyst pellet geometries, (a) Infinite slab, (b) Infinite right cylinder, (c) Sphere.

To evaluate the effectiveness factor for a first-order, isobaric, nonisothermal, flat plate catalyst pellet, the material and energy balances must be solved simultaneously. As shown previously, the mole balance in a slab is given by ... 

Metal deposition occurs with sharp gradients within a catalyst pellet, usually concentrated on the outside of catalyst pellets forming a U-shaped distribution. Sato et at [3] related this metal deposition with simultaneous diffusion and reaction, and suggested a value of 8 for the Thiele modulus in a slab geometry, Tamm [4] suggested that this distribution can be characterized by a theta factor defined in a ( Undricat geometry as... 

First, SOMC was applied to Co promotion of M0/AI2O3 sulfide. As shown in Fig. 1, the choice of complex was important for uniform distribution of Co over catalyst pellets. Probably due to its too high reactivity, bis(2,4-pentanedionato)cobalt(II) (Co(CsH702)2) resulted in over-concentration of Co in oirter region of the pellets (Fig. la), while bis(cyclopentadienyl)cobalt (Co(CioHio)2) led to a uniform distribution over the entire catalyst pellets at the same concentration of Co (Fig. lb). Selective reaction between Co-containing complexes and Mo sulfide edge sites should give more efficient Co-promotion. More local analyses like EDS and IR(CO) should be done to verify if, by use of Co(CioHio)2, closer association was really achieved between sulfide slabs and incorporated Co. 

A differential mass balance on the consumed /-th component in a catalyst pellet of slab geometry (Figure 5.59) gives the following equations ... 

Figure 7,33 Catalyst pellet with slab geometry.

Generate expressions for the effective intrapellet diffusion coefficient of component A in catalytic pellets when (a) all pores have radii below 50 A, and (b) aU pores have radii that are larger than 1 (im (i.e., 10 A). All pores can be described by straight cylindrical tubes at an angle of inclination of 45° with respect to the thinnest dimension of flat-slab catalysts. The gas mixture contains two components, A and B. 

Suppose further that the process proceeds in a fixed-bed catalytic reactor the conditions for steady-state are fulfilled the process is non isothermal and the catalyst pellet is symmetrical (infinite slab, semi-infinite cylinder, sphere). 

Fig. 3. Dimensionless concentration as a function of the dimensionless position in a catalyst pellet during simultaneous reaction and diffusion for first-order kinetics and slab...

Internal Pore Diffusion and Reaction in a Slab-Shaped Catalyst Pellet... 

Consider a porous catalyst pellet (Figure 4.18) in the shape of a slab in contact with a gas stream containing reactant A at concentration CAg- A is transferred from the bulk gas to the surface of the slab and is the concentration of A on the slab surface. 

The plots of q versus O in the log-log scale for a slab-shaped pellet, a cylindrical pellet and a spherical catalyst pellet are shown in Figure 4.22. At larger values of O, q versus O plots are asymptotic to q = I/O, q = 2/0, q = 3/0, respectively, for a slab-shaped pellet, a cylindrical pellet and a spherical pellet. We can merge these three plots into a single plot... 

Plots of T versus 4> for slab, cylinder and spherical-shaped catalyst pellets. 

---