Environmental Engineering Reference
In-Depth Information
At this point it is important to mention that in our derivation above we
made several assumptions (ideal gas law, Henry regime, ideal mixing,
and a diffusion coeffi cient that is independent of the concentration). If
these assumptions hold, we can express the permeance of a material for
a given gas as a simple product of the
Henry coeffi cient
and the
diffu-
sion coeffi cient
:
P
′=
H
The more general case is more complex, as both the adsorption and
diffusion depend on the concentration. The most important conclusion —
that the experimental permeance of a material is a combination of diffusion
and adsorption — is independent of these details.
That was the easy part, now the tricky part — units. The above equa-
tions have been derived using a particular selection of units. We have
used for the fl ux mol/m
2
s, but it is equally possible to write the equation
in terms of kg/m
2
s or m
3
/m
2
s, similarly for the Henry coeffi cient, we use
((moles gas)/mole material atm), but the Henry coeffi cient can also be
expressed in moles of gas per kg material per atm. Finally, for the diffu-
sion coeffi cient we have
D
in m
2
/s.
If we combine the terms, we can get the units for the permeance:
2
(
)
(
)
moles of gas
unit of length
×
(
)
(
)
(
)
volume of membrane
×
unitpressure
unit time
(
)
(
)
moles of gas
×
unit of length
=
(
)
(
)
(
)
unit area
×
unit time
×
unitpressure
Note that we use moles per second as the fl ux. In most of the engineering
literature, the fl ux is defi ned in volume per second.
At the time when the fi eld of membrane separations was developing,
people were naturally determining the permeance of materials that were
readily available at that time. As with many other fi elds, researchers intro-
duced a unit (which was later named a “
Barrer
” after one of the pioneers
in the fi eld, Richard Barrer) that took a value on the order of one for most
of the available materials. Here is the defi nition of 1 Barrer:
−
10
3
(
)
10
(cm
gas STP) cm thickness
1 Barrer
=
2
(
)
(cm membrane area) sec cm Hg pressure
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