Porous particles are described by a random capillary model predicting the frequency of pore intersections and the evolution of pore volume and surface area during reaction. The model is applied to char gasification at chemically controlled rates, and the results are compared with data from the literature. GEORGE R. GAVALAS Division of Chemistry ond Chemical EngineeringCalifornia Institute of Technology Pasadena, California 91 125 SCOPERandom capillary models have been used widely to describe catalytic and noncatalytic reactions in porous particles. In these applications, it has not been necessary to precisely elaborate the random nature of the capillary structure. In particular, the overlap volume and number of intersections between different capillaries was either ignored or treated in an ad hoc fashion. Overlap volume is the key concept for describing the changing pore volume and surface area in reactions such as char gasification. Likewise, the frequency of intersections is often required to describe mass transfer in coals and chars when an effective diffusivity is not applicable.In this paper, we develop a random capillary model in which number of intersections, length of pore segments and evolution of pore volume and surface area are exactly and consistently derived from a single probability-density function characterizing the porous solid. As an application of the model, we analyze the gasification of char by oxygen or other gases under conditions of chemical control of the reaction rate. An expression is obtained for the conversion-time curve which clearly displays the effects of surface reaction rate and porous structure. In addition to these model-specific results, we obtain some general model-independent results concerning char conversion. Both the model dependent and the general results are compared with experimental data from the literature.The random capillary model which is here applied and tested for chemically controlled reaction rates could be applied to char reactions involving diffisional limitations. However, the resulting equations would require numerical solution. In all applications, the assumption of constant reactivity of the, pore surface should be kept in mind. This assumption should be further tested experimentally. A simple application of the random model to coal pyrolysis was given recently by Gavalas and Wilks (1979). CONCLUSIONS AND SIGNIFICANCEA random capillary model has been developed describing the porous medium by a single density function A(@, related but not identical to the customary pore size distribution. Precise expressions are derived for the number of intersections between pores of different sizes, the lengths of the pore segments between intersections and the evolution of pore volume and surface area accompanying pore enlargement by reaction.An application to char gasification by oxygen (or carbon dioxide, water, hydrogen) is considered under two assumptions: no diffusional limitations and no dependence of the intrinsic surface reaction rate on conversion. First some ...
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