Page 18 - gas transport in porous media

Chapter 2: Gas Transport Mechanisms
The term β is defined as
β = φ S g τ 11

where D ∗ is the effective diffusion coefficient for the AB gas system in a porous
AB
media, D AB,CF is the effective diffusion coefficient of the AB gas system in a clear
fluid, φ is the porosity, S g is the gas saturation (equal to 1.0 for all-gas conditions),
and τ is the tortuosity. The tortuosity factor is discussed in further detail below.
Similar to the clear fluid equation, the mole flux through a porous media relative
to stationary coordinates is given by

F A − ω A (F A + F B ) =−βρ g D AB,CF ∇ω A
=−ρ g D ∗ AB ∇ω A

Inclusion of the β term takes into account the effective area for gas flow in the
pores (φ S g ) and the porous media tortuosity (τ). The diffusion coefficient D AB,CF
can be estimated from correlations as discussed by Reid et al. (1987). The diffusion
coefficient for gases is inversely proportional to the absolute pressure and directly
proportional to the absolute temperature to the 1.75 power as given by the Fuller et al.
correlation discussed in Reid et al. (1987).
The tortuosity factor, τ, as defined in this application as the ratio of the length of
the “tortuous” path in a porous media divided by a straight line value. The tortuosity
factor is evaluated for diffusion, not advection. For clear fluids, the tortuosity is
equal to 1.0. Note that sometimes other definitions of the tortuosity factor are used
(Dullien, 1992, pg. 311). There are a number of models for the tortuosity factor. The
most widely used correlation is that of Millington and Quirk (1961). The tortuosity
correlation of Millington and Quirk (1961) is given by

S
τ = φ 1/3 7/3
g
which can be rewritten as

1/3 7/3
= φ S
g
τ = τ o τ S g
is the
where τ o is the tortuosity due to the structure of the porous medium and τ S g
tortuosity due to the partial saturation. For all-gas conditions as discussed in this
chapter, the tortuosity factor reduces to the porous medium value, or

τ(S g = 1.0) = τ o = φ 1/3

Costanza-Robinson and Brusseau (Chapter 7 of this book) discuss porous media
tortuosity.