Page 256 - gas transport in porous media

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Chapter 14: Experimental Determination of Transport Parameters
with gas B (gas system (A + B) vs. B) or with another gas C (gas system (A + C) vs.
B) in order to increase the confidence of evaluated transport parameters. Equations
corresponding to the use of more than two gases can be found elsewhere (Šolcová
et al., 2001).
With boundary conditions
L
U
L
U
y = y = 1 y = y = 0
A B A B
the integration of differential Equation (14.21) with the Graham’s law (14.23) on
application of Eqs. (14.4) and (14.5) yields
m

d d d c T m 1 + D / r K A
AB
N = N + N = ψD ln (14.25)
A B AB m
L 1 − α + D / r K A
AB
d
If net diffusion flux densities, N , are experimentally determined for different gas
pairs A − B, then by comparison with Eq. (14.25) it is possible to obtain the corre-
sponding bulk- and Knudsen-effective diffusion coefficients. These coefficients are
connected with transport parameter via Eqs. (14.4) and (14.5). Figure 14.4 shows 95%
confidence regions of transport parameters for several commercial and laboratory-
prepared porous catalyst pellets evaluated from Eq. (14.25) with three-component
gas systems ((A + B) vs. B and (A + C) vs. B). The optimum parameter sets are
marked as circles. It is interesting that the shape of the confidence region is inti-
mately connected with region in which the diffusion process takes place. There are
two limiting diffusion mechanisms: the Knudsen diffusion, which appears only in
narrow pores and the bulk diffusion mechanisms, which takes place in wide pores.

0.3
0.3
c

h
0.2
0.2
c
g
0.1 a
0.1
f
e
b
d
0.0
0.0
100
30
200
0 0 0 5 5 5 100 200 300 0
<r> c (nm)
Figure 14.4. 95% confidence regions of transport parameters for porous catalyst samples a–g