General model of a gas transport
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I.
INTRODUCTION
R E C E N T L Y , the author has reported a general model of transport of gases in porous m e m b r a n e s ) ~] The model was developed based on the Dusty Gas Model (DGM) and solution diffusion. The model was used to predict the transport of a HE-CO 2 mixture under different transport conditions. In the present work, an extended version of the obtained model ]q of transport of gases in porous membranes is reported. The extended model incorporates the DGM, solution diffusion, and surface diffusion. Consequently, different solutions of the extended model are derived and given for various transport conditions.
The contribution of both NO and Nr V components is described in the DGM, tz] where the diffusive flux in one dimension is given as n
Nr~ -F E Dr e
X s N O - X r N D -- - - 1 d P
s~r
Drs e
RT dZ
S=I
and the viscous flux in one dimension is given as
x
[4]
N~v = - ~
where [5]
Dr e = KoVr
II.
and
THEORETICAL ANALYSIS
8
Derivation of an overall flux equation of gases in a porous solid membrane is developed based on the following assumptions: (1) membranes properties are time independent (steady state condition); (2) all flux processes take place at an isothermal condition; and (3) the solid membranes are homogeneously porous with an average pore diameter = a and a membrane thickness = Z. The total flux of gases in a porous solid membrane comprises a flux in the gas phase, a flux in the solid phase, and a flux on the solid surface. Therefore, the total flux of a component r can be described as follows: N, = N ~ + N f
+ Nr s + Nr z
[l]
where flux of r in pores; flux of r in gas pores; in solid phase (membrane); and on the surface.
[6]
In DGM, the structural parameters K~, K0, and B0 are defined as follows: EG
Kl = - -
[7]
r~
EG a 2
K0 -
[8]
to3 EG a 2
Bo
=
--
--
[9]
~-G8
Usually ~G = 1/e c if the value of r c is not available.
Addition of Eqs. [3] to [4] yields the general form of D G M in one dimension:
Dr ~
" X, N f r~'s
1 dPr
- X,Nf
RT dZ
D rf
s=|
[101
It is obvious that the flux in the gas phase consists of diffusive and viscous components and can be described as
g ~ = NOr + N v
RT / 1/2
Vr = \ ~ ' M r ]
Nr ~
N~ = diffusion N v = viscuous N s = flux of r Nr~ = flux of r
The flux of gases in solid phase is based on Fick's law, the solution diffusion model. The model is given as
[2]
s derS Nr s = --Ore
dZ K. HABIB, Research Scientist, is with the Materials Application Department, Kuwait Institute for Scientific Research, Safat, 13109 Kuwait. Manuscript submitted November 23, 1992. METALLURGICAL TRANSACTIONS A
[3]
[11]
Assume Cr S = K | S f r G
[12]
VOLUME 24A, JULY 1993-- 1527
since
nr V
C rG -
SO Dre = KoSr and since
Pr RT
[13]
De, = Kp' o rs o
therefore, therefore
Pr CrS = K1s - RT
[141
By substituting Eq. [14] into [11], this becomes
KSdpr NrS = --Ores ! RT dZ
D2e =
[23]
K oS 2
[24]
P
[16]
= DrSK1 s
where Qres is the permeability of gas r in solid. By substituting Eq. [16] into [15], this yields
Q,-es dPr
U,.s -
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