Page 267 - gas transport in porous media

264
100
100 Šolcová and Schneider
p (kPa) 50 Cherox A5 50 p (kPa)

0 0
0 500 1000 0 100 200 300
t (s) t (s)

Figure 14.13. Dynamic permeation cell; argon pressure change in the lower cell compartment for dif-
ferent starting pressures and porous solids with different pore-size distribution. Only part of experimental
points is shown for clarity

The time change of pressure in the bottom compartment, P(t), obtained by
integration of the compartment mass balance (14.42)

dP S p
= N R g T (14.42)
dt V L

together with Eq. (14.41) in the form
U
U
o
U
EP − (a + bP )(P − P )
P(t) = (14.43)
o
U
E + b(P − P )
where

S
U
o
E(t) =[a + b(P + P )] exp a + 2bP U t (14.44)
V L L
and
r ψK
a = r ψK b = (14.45)
16η
Of course, integration of the system (14.41), (14.42) can be also performed
numerically, together with parameter fitting, by any suitable commercial software.

Dynamic cell – full solution. The gas material balance in porous pellets under
dynamic conditions reads

p
∂p(t, x)/R g T ∂N (t, x)
ε =− (14.46)
∂t ∂x