Diffusion and Heat Conduction in Catalysts

The work of Thiele (1939) and Zeldovich (1939) called attention to the fact that reaction rates can be influenced by diffusion in the pores of particulate catalysts. For industrial, high-performance catalysts, where reaction rates are high, the pore diffusion limitation can reduce both productivity and selectivity. The latter problem emerges because 80% of the processes for the production of basic intermediates are oxidations and hydrogenations. In these processes the reactive intermediates are the valuable products, but because of their reactivity are subject to secondary degradations. In addition both oxidations and hydrogenation are exothermic processes and inside temperature gradients further complicate secondary processes inside the pores. 

Many authors contributed to the field of diffusion and chemical reaction. Crank (1975) dealt with the mathematics of diffusion, as did Frank-Kamenetskii (1961), and Aris (1975). The book of Sherwood and Satterfield (1963) and later Satterfield (1970) discussed the theme in detail. Most of the published papers deal with a single reaction case, but this has limited practical significance. In the 1960s, when the subject was in vogue, hundreds of papers were presented on this subject. A fraction of the presented papers dealt with the selectivity problem as influenced by diffitsion. This field was reviewed by Carberry (1976). Mears (1971) developed criteria for important practical cases. Most books on reaction engineering give a good summary of the literature and the important aspects of the interaction of diffusion and reaction. 

The effectiveness of a porous catalyst T] is defined as the actual diffusion-limited reaction rate divided by the reaction rate that could have been achieved if all the internal surface had been at bulk concentration conditions. 

For the effective diffusivity in pores, De = (0/t)D, the void fraction 0 can be measured by a static method to be between 0.2 and 0.7 (Satterfield 1970). The tortuosity factor is more difficult to measure and its value is usually between 3 and 8. Although a preliminary estimate for pore diffusion limitations is always worthwhile, the final check must be made experimentally. Major results of the mathematical treatment involved in pore diffusion limitations with reaction is briefly reviewed next. 

For the simplest one-dimensional or flat-plate geometry, a simple statement of the material balance for diffusion and catalytic reactions in the pore at steady-state can be made that which diffuses in and does not come out has been converted. The depth of the pore for a flat plate is the half width L, for long, cylindrical pellets is L = dp/2 and for spherical particles L = dp/3. The varying coordinate along the pore length is x  

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