Page 16 - gas transport in porous media

Chapter 2: Gas Transport Mechanisms
9
As discussed later on in Section 2.2.2, the Klinkenberg coefficient for a given
porous media is different for each gas and is dependent on the local temperature. The
Klinkenberg factor can be corrected for different conditions as follows
1/2 1/2

µ i m ref T i
b i = b ref
µ ref (T ref ) m i T ref
where ref refers to the reference gas, which is usually air, and m is the molecular
weight. The temperature is in absolute units.
As the permeability of the medium gets even lower, the pore dimensions approach
those of a single molecule. At this point, the flow mechanisms change, and con-
figurational diffusion (Cunningham and Williams, 1980) becomes important. As
discussed in Section 2.2.2, the transition from Knudsen diffusion (Klinkenberg effect)
to configurational diffusion is estimated to be at a permeability of approximately
2
10 −21 m .

2.2 GAS-PHASE DIFFUSION
Diffusion in porous media consists of continuum, or ordinary, diffusion and free-
molecule diffusion. Continuum diffusion refers to the relative motion of different gas
species. Free-molecule diffusion, or Knudsen diffusion, refers to an individual gas
and occurs when the mean-free path of the gas molecules is of the same order as
the pore diameter of the porous media. As the pore size decreases further, configura-
tional diffusion is encountered where the gas molecule size is comparable to the pore
diameter. Configurational diffusion is briefly discussed in the free-molecule diffusion
section.
Anumber of different models have been used to quantify gas diffusion processes in
porous media, some of which will be discussed in the next section. Many of the models
are simply models derived for a clear fluid (no porous media) that were simply adapted
for a porous media. The clear fluid diffusion models only consider molecular diffusion
and do not include Knudsen diffusion. Other models are specifically derived for
porous media applications. Molecular diffusion and Knudsen diffusion are included
in their formulation.

2.2.1 Ordinary (Continuum) Diffusion
Fick’s law is the most popular approach to calculating gas diffusion in clear fluids
(no porous media) due to its simplicity. While it is only strictly applicable to clear
fluids, it has been extensively applied to porous media situations through introduction
of a porous media factor. Another approach often employed is the Stefan-Maxwell
equations. This equation set is simply an extension to Fick’s law for a multicomponent
mixture as discussed by Bird, Stewart, and Lightfoot (1960, pg. 569) (hereafter BSL).
While attempts have been made to define effective diffusion parameters to account
for the presence of the porous medium, the basic transport equations are not altered.