Porous pore diffusional limitations

Characterisation of porous texture of solids is of relevance because their properties are determined, or at least, influenced by this characteristic [1-3]. A number of techniques exist to characterise the porous texture of solids. Among them, physical adsorption of gases is the most widely used due to its simplicity [1-11], N2 adsorption at 77K [3] is, undoubtedly, the most used. One of its main advantages is that it covers reduced pressures from 10 to 1, being sensitive to the whole range of porosity. However, N2 adsorption at 77K has some limitations when used to characterise solids containing ultramicroporosity (i.e., pore sizes lower than 0.7 nm). It can be influenced by diffusional limitations in this range of porosity [4]. 

The influence of diffusional limitations in gas phase reactions has been extensively treated by Wheeler and from a chemical engineering viewpoint by Hougen and Watson More recently a monograph by Satterfield and Sherwood has appeared. The problem of diffusion can be separated into two parts, the first is diffusion or mass transfer to the external surface of the catalyst and second, for those catalysts which are porous, diffusion within the catalyst pores. When diffusion is the rate limiting process, reaction rate, selectivity and activation energy are affected. 

Therefore, within the scope of this treatment, only the critical condition for diffusional limitation will be given attention. An order of magnitude value of the effective diffusivity in a porous medium is readily available when the diffusing species is a gas and when the mean free path of the gas is large in comparison to the average diameter h of the pores. Then, the analog of the approximate gas kinetic formula ... 

The integral product yield as function of conversion for different values of the Thiele modulus is shown in Figure 2.28 for k = k /k = 1/4. It is obvious that internal diffusional resistance leads to a drastic decrease of the target product selectivity and yield. In the domain of practical interest with k <1, the maximum obtainable yield for strong diffusion resistance ( 3, Equation 2.194) drops roughly to 50% of the value reached in the kinetic regime (Equation 2.187). At the same time the efficiency factor in the porous catalyst drops to r p<0.2 as indicated. This demonstrates the dramatic impact of pore diffusion limitation on the overall productivity of the catalytic process. 

Internal surface of porous particles also has limitations. Diffusional resistances of participants may be such that only a fraction of the pore surfaces is accessed, resulting in a waste of expensive catalyst, or undersizing of equipment that is designed for full utilization of the catalytic surface. Appraising the effectiveness of internal surface is the main thesis of this chapter. 

---