Diffusion and Pseudo-Homogeneous Chemical Reactions in Isothermal Catalytic Pellets

15-2 DIFFUSION AND PSEUDO-HOMOGENEOUS CHEMICAL REACTIONS IN ISOTHERMAL CATALYTIC PELLETS 

The rigorous description of diffusion and heterogeneous surface-catalyzed chemical reactions in porous catalytic pellets is almost never solved in practice because the partial differential mass balance and the supporting boundary conditions are extremely complex. The approximate solution overlooks intricate details of the pore structure, exploits the symmetry of the macroscopic boundary of one catalytic pellet instead of one of the pores, and invokes the concept of homogeneous diffusion that is not influenced by the orientation of the internal pores. 

Most important, heterogeneous surface-catalyzed chemical reaction rates are written in pseudo-homogeneous (i.e., volumetric) form and they are included in the mass transfer equation instead of the boundary conditions. Details of the porosity and tortuosity of a catalytic pellet are included in the effective diffusion coefficient used to calculate the intrapellet Damkohler number. The parameters (i.e., internal surface area per unit mass of catalyst) and Papp (i.e., apparent pellet density, which includes the internal void volume), whose product has units of inverse length, allow one to express the kinetic rate laws in pseudo-volumetric form, as required by the mass transfer equation. Hence, the mass balance for homogeneous diffusion and multiple pseudo-volumetric chemical reactions in one catalytic pellet is 

The Hougen-Watson rate law lEinw, with units of moles per area per time, is written on a pseudo-volumetric basis using the internal surface area per mass of catalyst S , and the apparent mass density of the pellet Papp. k is the nth-order kinetic rate constant with units of (volume/mole) per time when the rate law is expressed on a volumetric basis using molar densities. 

15-3 PSEUDO-FIRST-ORDER KINETIC RATE EXPRESSIONS THAT CAN REPLACE HOUGEN-WATSON MODELS AND GENERATE LINEARIZED ORDINARY DIFFERENTIAL EQUATIONS FOR THE MASS BALANCE 

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