Anisotropic Catalyst Pellets

Cylindrical catalyst pellets, whether hollow or not, are often given shape by extrusion of a paste of wet catalyst (Chapter 3). During this process the diameter of pores in the radial direction will become smaller, whereas for pores in the longitudinal direction the length will decrease. This can result in a radial effective diffusivity being smaller than the longitudinal one. Thus cylindrical catalyst pellets can be anistropic. 

This anisotropy can be accounted for in the Aris numbers. Considering a ring-shaped catalyst pellet, the material balance on a micro scale, for simple reactions, reads as (Appendix C) 

Differential equation 7.120 describes the concentration profile in an isotropic ring-shaped catalyst pellet with an effective diffusion coefficient DeAH, a height H, and an inner radius 

TTius the following formulae for the Aris numbers for simple reactions are obtained  

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Rather than accounting for anisotropy by modifying both the characteristic dimension and effective diffusion coefficient, this is achieved by modifying the effective diffusion coefficient only. Thus, for anisotropic catalyst pellets a modified effective diffusion coefficient D is defined, which accounts for the anisotropy. Hence, for anisotropic catalyst pellets and simple reactions the Aris numbers can be calculated from... 

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. 

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. 

It is assumed that component A is the component not in excess, thus /3g < 1, )8C < 1,... and that the numbersPb, 0. a do not depend on the temperature. They do not depend on the gas composition inside the catalyst pellet either, since the gas diluted. Notice the superscript + of the effective diffusion coefficient, which denotes that the catalyst pellet may be anisotropic. 

Assume the catalyst pellet to be anisotropic. The radial effective diffusion coefficient is De R = 5x10 m2 s 1 the longitudinal effective diffusion coefficient equals DeAH = 1.8xl0 6 m2 s 1. Then, if the effective diffusion coefficient is determined from measurements of the effectiveness factor, this gives... 

The catalyst may not be completely homogeneous on a pellet scale due to the method of manufacture. Furthermore, the extrusion or pelleting processes may render the material anisotropic, so that properties such as the effective diffusivity are not the same in every direction. Thus, the effective diffusivity may be substantially different in the axial and radial directions for cylindrical particles [4]. This should be accounted for in the balance equations. 

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