Diffusion in packed beds of porous particles

Abstract

The determination of the effective diffusivity for small porous particles (the intraparticle diffusion coefficient) by direct experimental methods is generally not possible. Because of this, one is forced to measure the overall effective diffusivity for packed beds of porous particles and subsequently extract the particle effective diffusivity by means of a theoretical analysis of the two-region diffusion process. In a recent study by Park et al. (1987), experiments using arrested-flow chromatography were described and a method of obtaining the particle effective diffusivity was presented. Based on solutions of the overall diffusion equation and experimental measurements, values of D, were determined for a variety of packed beds of porous particles. In order to calculate values of the particle effective diffusivity, semiempirical equations were developed on the basis of the classic works of Maxwell (1873), Rayleigh (1892), Burger (1919), andJeffrey (1973). All of these represent high void fraction theories for steady heat conduction in two-phase systems.Rather than modify special theories in order to extract particle effective diffusivities from measured values of D,, it would seem wise to make use of the general solution to the problem (Whitaker, 1983). The system under consideration is shown in Figure 1, where the @ phase represents the homogeneous gas phase and the u phase represents the porous particle phase. The diffusion equation for the gas phase contained within the porous particles must be volume-averaged and this is done in terms of the averaging volume ' v, indicated in Figure 1. An expanded view of the u phase averaging volume is shown in Figure 2 where the K phase represents the rigid solid and the y phase is used to identify the gas within the porous particles. A detailed analysis of diffusion in porous catalysts (Whitaker, 1987) leads to a governing equation for the u phase, and for dilute solutions or equi- (Gray, 1975) of the diffusing species in the u phase, and ce represents the point concentration of the diffusing species in the @ phase. One must keep in mind that a), represents an effective diffusivity for the porous particles.It is also important to keep in mind that a)# represents the molecular diffusivity of the diffusing species in the @ phase, and that the patching together of volume-averaged transport equations and point transport equations is not necessarily an obvious process. The details are given in the original paper. The structure of the boundary value problem given by Eqs. 2-5 is almost identical to a transient heat conduction problem, and it would be identical if it were not for the presence of the particle void fraction, cy, in the boundary condition given by Eq. 4. Clearly the steady state diffusion problem is analogous to the heat conduction problem, and this has important consequences for the solution of the closure problem (Crapiste et al., 1986).Since the position of the interface between the porous particles and the surrounding gas phase is unknown, one seeks a voiume-av...

Pore and surface diffusion in multicomponent adsorption and liquid chromatography systems

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Window effects in zeolite diffusion and brownian motion over potential barriers

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