Models of Mass Transport in Porous Media

Equations 3.15, 3.17 and 3.19 provide the flux relationships in the limiting regimes. There remains the problem of finding the flux relationships in intermediate situations, where the pore size is comparable to the mean free path and the mixture is a multicomponent one. At present, no quantitative kinetic theory exists for flow in the transition region where the dimensions of A and dt are comparable. Therefore different simplified models have been developed. 

The dusty gas model (DGM) [21] is used most frequently to describe multi component transport in between the two limiting cases of Knudsen and molecular diffusion. This theory treats the porous media as one component in the gas mixture, consisting of giant molecules held fixed in space. The most important aspect of the theory is the statement that gas transport through porous media (or tubes) can be divided into three independent modes or mechanisms  

This model assumes the diffusive flows combine by the additivity of momentum transfer, whereas the diffusive and viscous flows combine by the additivity of the fluxes. To the knowledge of the authors there has never been given a sound argument for the latter assumption. It has been shown that the assumption may result in errors for certain situations [22]. Nonetheless, the model is widely used with reasonably satisfactory results for most situations. Temperature gradients (thermal diffusion) and external forces (forced diffusion) are also considered in the general version of the model. The incorporation of surface diffusion into a model of transport in a porous medium is quite straightforward, since the surface diffusion fluxes can be added to the diffusion fluxes in the gaseous phase. 

The flux equation for species i in an n-component mixture can be written as 

Eliminating JB from Equations 3.21 and 3.22 and assuming DeAB=DeB/i, the flux of A is given by 

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