Catalyst geometries

Similar approaches are applicable in the chemical industry. For example, maleic anhydride is manufactured by partial oxidation of benzene in a fixed catalyst bed tubular reactor. There is a potential for extremely high temperatures due to thermal runaway if feed ratios are not maintained within safe limits. Catalyst geometry, heat capacity, and partial catalyst deactivation have been used to create a self-regulatory mechanism to prevent excessive temperature (Raghaven, 1992). 

This section is concerned with analyses of simultaneous reaction and mass transfer within porous catalysts under isothermal conditions. Several factors that influence the final equation for the catalyst effectiveness factor are discussed in the various subsections. The factors considered include different mathematical models of the catalyst pore structure, the gross catalyst geometry (i.e., its apparent shape), and the rate expression for the surface reaction. 

The Effectiveness Factor Analysis in Terms of Effective Diffusivities Extension to Reactions Other than First-Order and Various Catalyst Geometries. The analysis developed in Section 12.3.1.3 may be extended in relatively simple straightforward fashion to other integer-order rate expressions and to other catalyst geometries such as flat plates and cylinders. Some of the key results from such extensions are treated briefly below. 

Analyses have been carried out for a variety of other catalyst geometries including among others, porous rods of infinite length (or with sealed ends), a porous rod with open ends, and... 

To assess whether a reaction is influenced by intraparticle diffusion effects, Weisz and Prater [11] developed a criterion for isothermal reactions based upon the observation that the effectiveness factor approaches unity when the generalised Thiele modulus is of the order of unity. It has been shown that the effectiveness factor for all catalyst geometries and reaction orders (except zero order) tends to unity when... 

Thus we have expressions for the effectiveness factor for different catalyst geometries. The Thiele modulus can be computed from catalyst geometry and surface area parameters. The characteristic size is 21 for a porous slab and 2R for a cylinder or sphere. While the expressions for r)(0) appear quite different, they are in fact very similar when scaled appropriately, and they have the same asymptotic behavior,... 

From these experiments, one can see that the direct partial oxidation of CH4 to synthesis gas over catalytic monoliths is governed by a combination of transport and luetic effects, with the transport of gas phase species governed by the catalyst geometry and flow velocity and the lanetics determined by the nature of the catalyst and the reactor temperature. Under the conditions utilized here, the direct oxidation... 

In addition to importance of the catalyst composition and temperature, we have shown that methane partial oxidation selectivity is strongly affected by the mass transfer rate. Our experiments show that increasing the linear velocity of the gases or choosing a catalyst geometry that gives thinner boundary layers enhances the selectivity of formation of H2 and CO. Since H2 and CO are essentially intermediate... 

Conventional Ni-based catalysts still dominate in SR applications however, ceria-supported noble metal catalysts have also attracted interest reeently. The study of Rh for both POX and ATR has increased sinee Rh is in general more active for reforming and is less prone to form carbon. H2 and CO selectivities in Rh-based catalysts have been shown to be affected by catalyst geometry. This indicates that feed mixing and mass transfer can play an important role. 

In assessing whether a reactor is influenced by intraparticle mass transfer effects WeiSZ and Prater 24 developed a criterion for isothermal reactions based upon the observation that the effectiveness factor approaches unity when the generalised Thiele modulus is of the order of unity. It has been showneffectiveness factor for all catalyst geometries and reaction orders (except zero order) tends to unity when the generalised Thiele modulus falls below a value of one. Since tj is about unity when 0 < ll for zero-order reactions, a quite general criterion for diffusion control of simple isothermal reactions not affected by product inhibition is < 1. Since the Thiele modulus (see equation 3.19) contains the specific rate constant for chemical reaction, which is often unknown, a more useful criterion is obtained by substituting l v/CAm (for a first-order reaction) for k to give ... 

F(c,/cb) denotes the dimensionless form of an arbitrary rate expression, n = 0,1 or 2 for slab, cylinder or spherical catalyst geometry ... 

Figure 12 shows the effectiveness factor as a function of the Wheeler-Weisz modulus for different reaction orders, indicating that criterion (33) holds for the generalized Thiele modulus. Due to the definition of L it is fairly independent of the catalyst geometry. 

The literature contains a number of correlation equations for the mean gas-catalyst mass transfer and heat transfer as a function of gas properties, catalyst geometry, and flow conditions [7, 8]. In practice they play only a minor role for catalyst packings since design and simulation calculations are frequently performed with a model that is quasihomogcncous, at least with regard to temperature. The reason lies in the above-mentioned strong local fluctuations, which make experimental differentiation between the gas temperature and catalyst temperature difficult. 

This last item is important because it leads to an easy way to accommodate the molar contraction of the gas as the reaction proceeds. The program calculates steady-state profiles of each of these down the length of the tubular reactor, given the reaction kinetics models, a description of the reactor and catalyst geometries, and suitable inlet gas flow-rate, pressure and composition information. Reactor performance is calculated from the flow-rate and composition data at the reactor outlet. Other data, such as the calculated pressure drop across the reactor and the heat of reaction recovered as steam, are used in economic calculations. The methods of Dixon and Cresswell (7) are recommended for heat-transfer calculations. 

From this formula it follows that the shape generalization that was introduced by Aris for first-order kinetics holds for arbitrary kinetics. The generalized Equation 6.11 given by Bischoff [10] for an infinite slab holds for arbitrary catalyst geometries, provided that the dimension R is replaced by the characteristic dimension VpMp introduced by Aris. For nth order kinetics Equation 6.30 yields... 

From Equation 6.30 we find that the proper modified Thiele modulus for arbitrary catalyst geometries, for this case, is given by... 

This holds for arbitrary reaction kinetics and arbitrary catalyst geometries. For example, for n-th order kinetics this yields... 

The dimensionless number T is a geometry factor. Its value depends on the catalyst geometry only. This is illustrated in Thble 6.3 where T is given for an infinitely long slab,... 

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 ... 

Finally, 1 and A tie down the catalyst geometry of the ring-shaped catalyst pellet (Figure 6.9) ... 

Figure 6.11 holds for a slab. Similar figures can be obtained for other catalyst geometries. This is illustrated in Figure 6.13 where the effectiveness factor is plotted versus 8 for zeroth-order kinetics in an infinite slab, infinite cylinder and a sphere. Figure 6.13 has been constructed on the basis of the formulae given in Table 6.6. Hence, the discussion that follows is not restricted to a slab, but holds for any arbitrary catalyst geometry. 

Several formulae have been given for the calculation of the effectiveness factor as a function of one of the Aris numbers An or An, or as a function of a Thiele modulus. These formulae can become very complex and, for most kinetic expressions and catalyst geometries, it is impossible to derive analytical solutions for the effectiveness factor, so... 

Up till now the discussion has been restricted to first-order kinetics in a slab. However, if A is plotted versus tj for other forms of kinetics or other catalyst geometries, curves similar to Figure 6.16 are obtained. For each individual case a different value of A K will be obtained. This is illustrated in Table 6.8 where Aw is given for several forms of kinet-... 

From Equation 7.13 it then follows that the error <5 i0 does not depend on the catalyst geometry or a Thiele modulus like <5 J it only depends on the value of and the reaction kinetics. This is illustrated in Figure 7.3 where <5W is plotted versus for zeroth-, first- and second-order kinetics and for exothermic reactions ( > 0). The curves were obtained from the formulae given in Table 7.2, which were calculated with the aid of Equations 7.13 and 7.26. 

From this discussion it follows that all conclusions drawn for isotropic catalyst pellets hold for anisotropic catalyst pellets as well. In fact, with a single catalyst geometry, it is not possible to distinguish between isotropic and anisotropic pellets. The effect of anisotropy is lumped in with the effective diffusion coefficient. If the catalyst pellet is isotropic, then from Equation 7.128 it follows that we measure the effective diffusion coefficient D / = D J = D. For anisotropic pellets, we measure for pellets with a large height (0 large) and D H for flat pellets (0 small). For intermediate values of 0 the value of DeA is between De/iR and D H. 

Hie only situation where anisotropy can give rise to errors, is when the catalyst geometry is changed (and thus 0) and if the value of the effective diffusion coefficient which was determined for another catalyst geometry is used. This is illustrated in Example 9.22. 

The procedure given above can be extended for other catalyst geometries. For example, for an anisotropic parallelepiped with the dimensions width length height = W L H, the Aris numbers can still be calculated from the Equation 7.126 and 7.127. However, the modified effective diffusion coefficient DtAnow becomes ... 

Modified effective diffusion coefficients for other catalyst geometries can easily be obtained. 

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