Page 251 - gas transport in porous media

248
p
The DGM permeation molar flux density of component i, N , is described by
i
Darcy law Šolcová and Schneider
p dc T
N =−y i B i = 1, ... , n (14.13)
i
dx
with identical effective permeability coefficients, B, for all gas mixture components:
B = B o p/η i = 1, ... , n (14.14)
B o is the third DGM transport parameter that can be, formally, replaced by
2
r ψ/8.
Description of the combined diffusion and permeation gas transport is obtained
by applying Eq. (14.1) to diffusion and permeation constitutive Equations (14.3) and
(14.10) (for MTPM) or Equations (14.3) and (14.13) (for DGM). In both cases the
combined transport can be expressed in a vector form

dc
− = FN (14.15)
dx
T
with the (n ∗ 1) vector of component molar concentrations, c =[c 1 , c 2 , ... , c n ] ,
T
(n ∗ 1) vector of combined molar flux densities, N =[N 1 , N 2 , ... , N n ] anda(n ∗ n)
matrix F ={f ij } with elements
c i c i α i
f ij =− m + i = j; i = 1, ... , n; j = 1, ... , n (14.16)
c T D D k
ij i
n
1 1 c j c i α i
f ii = k + m + k i = 1, ... , n (14.17)
D i c T j = 1 D ij D i
j = i

Parameter α i is different for MTPM and DGM. For MTPM it is defined as:
n
B i 1 6 c j (B j − B i )
1 − + m
D k c T D ij
i
j = 1
j = i
α i = i = 1, ... , n (14.18)
n
6 c j B j
D k
j=1 j
For DGM:
B/D i k
α i =− i = 1, ... , n (14.19)
n
6 k
1 + B c j /D j
j=1