Dynamic analysis of viscous flow and diffusion in porous solids

Abstract

In case of nonisobaric diffusion, the total flux of a gas through a porous solid is expressed in terms of the summation of diffusion and viscous flow terms. The diffusion flux is generally considered to be inversely proportional to the series combination of molecular and Knudsen resistances. On the other hand, viscous flow is expressed by the Darcy equation.In some applications with porous catalysts, diffusion with a pressure gradient is of interest. A detailed review of diffusion and flow of gases in porous solids was reported by Youngquist (1970). Evans et al. (1961), following a dusty gas model, have shown the flux relationships. Scott and Dullien (1 962) used the simple kinetic theory of gases to derive the flow equation in a well as adsorption parameters. Moffat (1978), Baiker et al. (1982), and Wang and Smith (1983) used this technique for evaluation of effective diffusivities and tortuosities. Dogu (1984) and Dogu et al. (1986) illustrated the use of single-pellet moment technique for the measurement of surface reaction rate constants for catalytic and noncatalytic gas-solid reactions. In this work, a method was introduced for the study of relative significance of diffusion and viscous flow in porous catalysts using the single-pellet moment approach. The method allows the measurement of Darcy coefficient together with effective diffusion coefficient in a porous solid.capillary. Wakao et al. (1965) and Otani et al. (1965) derived the governing equations of diffusion and flow in fine capillaries in the presence of significant pressure gradients.The theory of mass transport in porous materials under cornbined gradients of composit~on and pressure was developed by G~~~ and ~i~~ (1969). M~~~~ et al. (1967) and G~~~ and ~i~~ ( 1969) considered the viscous flow term to be independent of the diffusive flux and wrote down the total flux as the summation of diffusive and D~~~~ fluxes. This assumption, which is implicit in the use of the classical convective diffusion equation, was later verified by Allawi and Gunn (1987). Asaeda et al. (1981) and Nakano et al. (1986) also reported Some diffusion rate data at nonisobaric conditions.Single-Pellet moment technique is one of the fastest and Method and TheoryIn the single-pellet moment method used in this study, dynamic version of the Wicke-Kallenbach type of a diffusion cell was used for the evaluation of relative significance of diffusion and viscous flow terms. The schematic diagram of the diffusion cell was shown in Figure 1. A pulse of an inert tracer was injected into the carrier gas flowing past the upper face of the single pellet, and the response was detected at the outlet of the lower stream carrier gas by a T C detector. These experiments were repeated a t different pressure differences between the upper and lower faces of the pellet (Figure 1). The experimental values of the zeroth and first absolute moments were determined from the observed response peaks using the equations, dependable methods for the measurement of intraparticle rate parameters. The me...