Slab catalyst

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... 

A linear relationship (not shown) is found between the calcn-lated surface d-band center for the studied slab catalysts and the binding energy of OOH, O, and OH, in agreement with many pre-... 

Catalyst deactivation in large-pore slab catalysts, where intrapaiticle convection, diffusion and first order reaction are the competing processes, is analyzed by uniform and shell-progressive models. Analytical solutions arc provid as well as plots of effectiveness factors as a function of model parameters as a basis for steady-state reactor design. 

The model equation is a mass balance for reactant species inside a volume element of the slab catalyst in terms of dimensionless concennation f=c/cs and dimensionless ace coordinate x=z/t we... 

The dimensionless concentration profile inside the slab catalyst is fp (sinh rj) - (sinh rj)... 

The slab catalyst has now layers of poison of thickness aton both sides. The mass balance in the unpoisoned section is ... 

Consider diffusion in a slab catalyst with a highly nonlinear Hinshelwood kinetics.[18] The governing equation and boundary conditions are ... 

The dimensionless concentration profile inside the slab catalyst is ... 

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

This expression arises when gas-phase A adsorbs onto the catalyst sur-Tace and the reaction is first order in the adsorbed A concentration. If we consider the slab catalyst geometry, the mass balance is... 

In terms of surface-averaged mass transfer across the external surface, the effectiveness factor for Hougen-Watson kinetics in flat-slab catalysts is... 

At relatively low pressures, what dimensionless differential equations must be solved to generate basic information for the effectiveness factor vs. the intrapellet Damkohler number when an isothermal irreversible chemical reaction occurs within the internal pores of flat slab catalysts. Single-site adsorption is reasonable for each component, and dual-site reaction on the catalytic surface is the rate-limiting step for A -h B C -h D. Use the molar density of reactant A near the external surface of the catalytic particles as a characteristic quantity to make all of the molar densities dimensionless. Be sure to define the intrapellet Damkohler number. Include all the boundary conditions required to obtain a unique solution to these ordinary differential equations. 

In this problem, we explore the dimensionless mass transfer correlation between the effectiveness factor and the intrapellet Damkohler number for one-dimensional diffusion and Langmuir-Hinshelwood surface-catalyzed chemical reactions within the internal pores of flat-slab catalysts under isothermal conditions. Perform simulations for vs. A which correspond to the following chemical reaction that occurs within the internal pores of catalysts that have rectangular symmetry. 

Flat-slab catalysts have the appearance of wafers, and a rectangular coordinate system is most appropriate to exploit the symmetry of the macroscopic boundary. The catalyst has a thickness of T in the thinnest dimension, which is the... 

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. 

We illustrate the above five variations of weighted residuals with the following example of diffusion and first order chemical reaction in a slab catalyst (Fig. 8.1). We choose the first order reaction here to illustrate the five methods of weighted residual. In principle, these techniques can apply equally well to nonlinear problems, however, with the exception of the collocation method, the integration of the form (8.7) may need to be done numerically. 

The diffusion-reaction problem for slab catalyst particles is a classic problem used to illustrate the orthogonal collocation method. We consider this problem next. 

The problem of a slab catalyst particle, sustaining linear reaction kinetics, was posed earlier and the dimensionless material balance equations were given in Eqs. 8.25. 

For the slab geometry, dV = Adr, where A is the cross-sectional area of the catalyst. Hence, Eq. 8.152a becomes for a slab catalyst... 

We illuminate these attractive features by considering the difficult problems of diffusion and reaction in a slab catalyst sustaining highly nonlinear Hinshelwood kinetics. The mass balance equations written in nondimensional form are taken to be... 

Harold, M.P., Watson, P. C., 1993. Bimolecular exothermic reaction with vaporization in the half-wetted slab catalyst. Chemical Engineering Science 48,981-1004. 

Figure 3.4 Asymptotic forms of the effectiveness factor (7) as a function of the Thiele modulus ( ) for a slab catalyst with a first-order exothermic reaction (0 = 1/3 and y = 27) for Bim/Bii, =6. Numerical values in the intermediate region are given in Ref [80].

Ocone and Astarita ° considered uniformly coupled reactions in an isothermal slab catalyst. All species are assumed to have the same difflisivity, which may correspond to a petroleum fraction of narrow boiling range. A significant result is that fj can be greater than unity at small Thiele moduli,... 

For a slab catalyst the concentration profile inside the pellet... 

Figure 7a - E versus (j) for first order irreversible reactions in isothermal slab catalysts.

For first order reactions (irreversible) in isothermal slab catalysts it is possible to get analytical solutions for the concentration profile inside the particle,i.e.,... 

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