Thermal conductivity of porous catalysts

A random pore model of catalytic pore structure is applied to the determination of the thermal conductivity of porous catalytic solids. The low thermal conductivities reported for such materials are explained by considering the microporous particles to consist of a packed bedlike assembly of smaller particles; heat transfer through the solid fraction occurs by conduction through individual small particles in contact with other particles. An expression for the effective thermal conductivity of a gas in the region between ordinary thermal conduction and free molecule conduction is used in determination of heat conduction through the void volume. Agreement of the theory with experimental data on alumina ond silver catolysts over a wide range of conditions is good. There has been a considerable interest in the recent literature on problems of estimation and measurement of transport properties within porous solids owing to the importance of such information in determination of catalytic effectiveness and selectivity. A majority of this work has concentrated on the question of diffusional mass transport within catalysts and thus on the measurement or estimation of effective diffusion coefficients within the porous matrix. Wakao and Smith (1) have presented a detailed model of catalytic pore structure which appears to explain the available data on diffusion through an important class of catalytic materials very well. In particular, their pore structure model refers to those solids exhibiting the bidisperse pore size distribution, commonly termed a macropore and micropore .structure, which is typical of catalyst pellets produced by compression of individual powder particles. More detailed descriptions of this concept are given in a number of sources. Simultaneous mass and heat transfer effects within porous catalysts have been analyzed by Carberry (2), Tinkler and Pigford (3), and Weisz and Hicks (4), among others. Catalytic effectiveness in such situations has been treated in terms of a nonisothermal effectiveness factor, defined analogously to the isothermal quantity; the problem of nonisothermal selectivity has not been discussed. The results of these studies indicate that considerable temperature gradients within catalyst particles can exist in the case of pronounced exothermic or endothermic reactions, as indicated theoretically by Wheeler (5) and Prater (6). The existence of these temperature gradients has recently been verified experimentally by Cunningham et al. (7). Relatively little information is available concerning thermal conductivities of porous catalysts, although the magnitude of nonisothermal effects is very strongly dependent on this property. The question of the thermal conductivity of packed beds, a system which is comparable in some respects, has been studied extensively (8), but information on catalytic thermal conductivity has been given only by Sehr (9) , Masamune and Smith (lo), and Mischke and Smith (11 ) . These studies have primarily been concerned with the experimental determination of thermal conductivity; analysis of the results in terms of the effect of the solid’s pore structure on the thermal transport property is not reported. Though small in number, the three studies (and particularly the latter two) include an extensive range of variables including temperature, pressure, and void fraction. An ordinary, low conductivity catalyst support (alumina) and an extremely high conductivity material (silver) have been used as the solids in these studies. The primary objectives of the present work are to investigate the mechanism of thermal conduction within such porous solids and to propose a method whereby this important property may be estimated which is in agreement with the available experimental data. CONDUCTION IN SOLIDS-MECHANISM