Page 250 - gas transport in porous media

Chapter 14: Experimental Determination of Transport Parameters
with the Knudsen coefficient K i 247

2 8R g T
K i = (14.6)
3 πM i
The driving force term (df ) i differs for MTPM and DGM:
dy i
MTPM (df ) i =−c T (14.7)
dx
d (c T y i )
DGM (df ) i =− (14.8)
dx i
c T is the total molar concentration of the gas mixture and x is the length coordinate
in the transport direction. For pure (isobaric) diffusion, where dc T /dx = 0, both
driving forces (14.7), (14.8) are identical: −d(c T y i )/dx =−c T dy i /dx. The (rather
small) difference starts to appear in combined diffusion and permeation cases.
By summing modified Maxwell-Stefan isobaric diffusion equations (14.3) for all
gas mixture components the generalized Graham’s law appears
n
d 9
N M i = 0 (14.9)
i
i=1
which is the condition that must be fulfilled in order to have pure diffusion mass
transport.
p
The MTPM permeation molar flux density of gas mixture component i, N ,in
i
porous solids is described by the Darcy equation:
p dc T
N =−y i B i i = 1, ... , n (14.10)
i
dx
B i is the effective permeability coefficient of mixture component i (Schneider, 1978):
2
+ ,
ων i + Kn i r ψp
B i = r ψK i + i = 1, ... , n (14.11)
1 + Kn i 8η
2
which includes the MTPM transport parameters, ψ, r , r . The numerical coeffi-
cient ω depends on the details of the wall-slip description (ω = 0.9, π/4, 3π/16, etc.,
see, Schneider, 1978); ν i is the square root of the relative molecular weight of the gas
mixture component i:

;
<
nj
<

<
ν i = =M i / y j M j (14.12)
j=1
η is the gas mixture viscosity and Kn i is the Knudsen number of component i (Kn i ≡
λ i /2 r ) based on mean free-path length of component i in the gas mixture.