Pore Diffusion Control

For a linear isotherm tij = KjCj), this equation is identical to the con-seiwation equation for sohd diffusion, except that the solid diffusivity D,i is replaced by the equivalent diffusivity = pDj,i/ p + Ppi< ). Thus, Eqs. (16-96) and (16-99) can be used for pore diffusion control with infinite and finite fluid volumes simply by replacing D,j with D. When the adsorption isotherm is nonhnear, a numerical solution is... 

FIG. 16-18 Constant separation factor batch adsorption curves for pore diffusion control with an infinite fluid volume. X is defined in the text. 

Finally, one must know the effect of catalyst particle size on Kw. For a pore diffusion-controlled reaction, activity should be inversely proportional to catalyst particle diameter, that is directly proportional to external catalyst surface area. 

Cooper, R.S. and Liberman, D.A. (1970) Fixed-bed adsorption kinetics with pore diffusion control. Ind. Chem. Eng. Fund., 9, 620. 

Finally, two models based on nonlinear driving forces will be presented. The first one covers the case of a pore diffusion control and the second one the case of solid diffusion control. Both models hold for the Langmuir-type isotherm. For the case of... 

Figure 4. Silylation of porous silica beads. The fractional extent of completion of the reaction at the external surface and on the internal surface is shown on the ordinate and abscissa, respectively. The straight diagonal line shows expectation for reactivity control. The TFSA data show a high degree of pore diffusion control. (From [33], with permission from Gordon and Breach, Science Publishers S.A.)...

Figure 9 The grain model for a solid undergoing reaction under conditions of pore diffusion control.

For reactions that are pore diffusion controlled, it is advisable to locate the active catalytic species close to the fluid-solid interface in order to decrease the diffusion path of reactants and products. This applies to all forms... 

Fig. 7.2. Conversion of a reactant vs. temperature.The concentration of reactants [R] within the porous catalyst structure. Concentration of R is (a) uniform for kinetic control, (b) decreasing within the catalyst for pore diffusion control, and (c) zero immediately at the surface of the catalyst for bulk mass transfer.

Variation of catalyst area. The catalytic rate is proportional to the total surface area, A, external and internal, for reactions controlled by surface kinetics. In the case of internal or pore diffusion control, the rate is proportional to A1,2 and is also a function of the catalyst shape and size [49, 53]. Under an external diffusion regime, the catalytic rate is proportional to the external surface area of the catalyst, Aex. 

Cases of internal or pore diffusion control make up the third category. As shown in eqn. (41), the observed rate constant under such conditions is proportional to yJkD where k is the rate constant of the surface reaction. 

The interest in the properties of the chars derived from cellulosic or biomass solid.s extends beyond those associated with thermal transport in the char. Insofar as the char residue from a pyrolysis process must typically be burned, gasified, or put to use as an activated carbon product, there is also a need to examine the porous nature of the char, bi acbvated carbons, the pore structure is key to adsorption performance. In combustion or gasification, the porosity can play a role in determining conversion kinetics in the intrinsic rate controlled or pore diffusion controlled regimes. 

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