Membranes - Introduction to Carbon Capture and Sequestration - page 292

relatively small compared to the fl ux through membranes that have larger
pores. This implies that one would need a relatively large membrane area.
The main advantage of molecular sieving is that we can completely
remove one of the components, as the cartoon in Figure 7.2.4 suggests.
For some separations a 100% removal is not required, and one can
use a membrane in which both components can pass but with differing
permeabilities. The advantage of such a membrane is that the fl uxes tend
to be larger and hence require a smaller total membrane area. In the lit-
erature we can fi nd two different mechanisms to explain the differences
in permeation of multiple components: Knudsen diffusion and diffusion
solubility .
Knudsen diffusion
Let us consider the model of a membrane (shown in Figure 7.2.4(b) ). We
assume that the membrane consists of an array of parallel cylinders
imbedded in an inaccessible matrix. For convenience we assume that the
solubility of the molecules in the pores is identical for all components,
meaning that the difference in permeabilities is caused by a difference in
diffusion coeffi cients only. If we assume that the density of the gas mol-
ecules is very low, the molecules will collide with the walls of the cylin-
ders more often than they will collide with other molecules. We further
assume that with every wall collision the molecules bounce back with a
velocity taken from a Maxwell distribution, determined by the tempera-
ture of the membrane. As the kinetic energy of the gas molecules is
related to this temperature, we see that molecules with a large mass will
have a lower average velocity. Hence, the diffusion coeffi cient will
depend on the (square root of) the mass of the particles. In Knudsen dif-
fusion, the diffusion coeffi cient will also depend on the pore diameter,
and this is the only membrane material property that plays a role.
Diffusion solubility
If we are not in one of the extreme cases that either one of the molecules
does not adsorb (molecular sieving) or that Knudsen diffusion holds (low
pressures), we have a material in which all the components dissolve and
diffuse, see Figure 7.2.4(c) . The resulting permeability is then the prod-
uct of the solubility and the diffusivity, and a separation process can be