Catalytic Pellets with Rectangular Symmetry

Homogeneous one-dimensional diffusion accompanied by chemical reaction in porous catalysts with rectangular symmetry is described by the following dimensionless mass balance  

Under isothermal conditions, the kinetic rate constant is truly constant and the dimensionless rate law is 

DIFFUSION AND ZEROTH-ORDER REACTIONS IN CATALYTIC PELLETS 

This second-order ordinary differential equation given by (16-4), which represents the mass balance for one-dimensional diffusion and chemical reaction, is very simple to integrate. The reactant molar density is a quadratic function of the spatial coordinate rj. Conceptual difficulty arises for zeroth-order kinetics because it is necessary to introduce a critical dimensionless spatial coordinate, ilcriticai. which has the following physically realistic definition. When jcriticai which is a function of the intrapellet Damkohler number, takes on values between 0 and 1, regions within the central core of the catalyst are inaccessible to reactants because the rate of chemical reaction is much faster than the rate of intrapellet diffusion. The thickness of the dimensionless mass transfer boundary layer for reactant A, measured inward from the external surface of the catalyst, 

The quantitative definition of this critical spatial coordinate is I a = 0 at = criticai- Two Constants of integration appear when the mass balance is solved for the basic information, I a = fiv)- These two integration constants, together with ncriticah represent three unknowns that are determined from two boundary conditions and the mathematical definition of the critical spatial coordinate. Hence, the three conditions are  

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In this chapter we present a pseudo-homogeneous model of diffusion and heterogeneous surface-catalyzed chemical reaction within the internal pores of catalytic pellets with rectangular symmetry. 

The catalytic volume Vcataiyst and the external surface 5 extemai that bounds this volume are calculated explicitly for pellets with rectangular, cylindrical, and spherical symmetry in Section 20-2. The quantity... 

However, the void area fraction is equivalent to the void volume fraction, based on equation (21-76) and the definition of intrapellet porosity Sp at the bottom of p. 555. Effectiveness factor calculations in catalytic pellets require an analysis of one-dimensional pseudo-homogeneous diffusion and chemical reaction in a coordinate system that exploits the symmetry of the macroscopic boundary of a single pellet. For catalysts with rectangular symmetry as described above, one needs an expression for the average diffusional flux of reactants in the thinnest dimension, which corresponds to the x direction. Hence, the quantity of interest at the local level of description is which represents the local... 

Two coupled ODEs must be solved to calculate temperature and reactant concentration profiles within a catalytic pellet that exhibits rectangular symmetry. The primary contribution to diffusion occurs in the thinnest dimension of the catalyst (i.e., the x direction). Hence, the mass ttansfer equation with one-dimensional diffusion and nth-order irreversible chemical reaction reduces to... 

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