Wheelers semi-empirical pore model

Wheeler [16] proposed that the mean radius, r, and length, L, of pores in a catalyst pellet (of, for that matter, a porous solid reactant) are determined in such a way that the sum of the surface areas of all the pores constituting the honeycomb of pores is equal to the BET (Brunauer, Emmett and Teller [17]) surface area and that the sum of the pore volume is equed to the experimental pore volume. If represents the external surface area of the porous particle (e.g. as determined for cracking catalysts be sedimentation [18]) and there are n pores per unit external area, the pore volume contained by nSx cylindrically shaped pores is nSx nr L. The total extent of the experimentally measured pore volume will be equal to the product of the pellet volume, Vp, the pellet density, Pp, and the specific pore volume, v. Equating the experimental pore volume to the pore volume of the model 

Similarly, the experimental surface area may be equated to the surface area of pores as given by the model. Now, the mass of the catalyst pellet is the product of the pellet volume, Vp, and its density, Pp, so the experimentally determined surface area is Pp VpSg where Sg is the BET 

In terms of the pellet size, dp, the ratio Vp/Sx is dp/6 for spheres and cubes Thus, for most practical catalyst pellets, the average pore length is 2 dp/6 according to Wheeler s model. The roughness factor rappearing in eqn. (27) is assumed to be 2 for practical purposes. 

The Wheeler model thus provides an average pore radius, r and pore length, L, in terms of the experimentally determinable parameters v, and fj. The only adjustable parameter is the roughness factor, r. The usefulness of this model was demonstrated by Wheeler, who successfully predicted the reaction rates of several catalytic reactions of industrial importance. 

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