Membrane Separation Properties
Permeation Flux
The membrane permeation flux is defined as the volume flowing through the membrane per unit area per unit time. The SI unit used is m3/m2.s although other are often used as well.
For the case of transport of gases and vapors, the volume is strongly dependent on pressure and temperature. As such, gas fluxes are often given in terms of a "standard condition" which is defined as 0 oC and 1 atmosphere (1.0013 bar).
Permeability Coefficient
The permeability coefficient, P (or simply the permeability) is defined as the transport flux of material through the membrane per unit driving force per unit membrane thickness. It's value must be experimentally determined. The barrer is the commonly used unit for gas separation and it is defined as:
The term cm3 @STP / cm2.s refers to the volumetric trans-membrane flux of the diffusing species in terms of standard conditions of 0oC and 1 atm, the term cm refers to the membrane thickness, and cm-Hg refers to the trans-membrane partial pressure driving force for the diffusing species.
Other commonly used units include: kmol.m.m-2.s-1.kPa-1,
or m3.m.m-2.s-1.kPa-1,
or kg. m.m-2.s-1.kPa-1.
Note here that the driving force is the pressure difference across the membrane.
In general, permeability of a polymer for a gas mixture increases with decreasing size and increasing solubility (or condensability) of the gas. The relative permeability of a gas is given below in order of decreasing gas permeability as:
H2 > He > H2S > CO2 > O2 > Ar > CO > CH4 > N2
The permeability of component-i is a product of 2 terms:
where Ki is the sorption (or partition) coefficient and Di is the permeate diffusion coefficient.
The sorption coefficient is an equilibrium term linking the concentration of a permeating component in a fluid phase with its concentration in the membrane polymer phase. It accounts for the solubility of the component in the membrane.
The diffusion coefficient is a kinetic term that reflects the effect of the surrounding environment on the molecular motion of the permeating component. It accounts for the diffusion of the component through the membrane.
Permeabilities (in Barrer) of several pure gases in widely used polymers are shown in the Table.
From: Table 8.1, "Membrane Technology and Applications",
R.W. Baker, p.295
Permeance
The permeance PM is defined as the ratio of the permeability coefficient (P) to the membrane thickness (L). The permeance for a given component diffusing through a membrane of a given thickness is analogous to a mass transfer coefficient.
Membrane Selectivity
In gas separation, the membrane selectivity is used to compare
the separating capacity of a membrane for 2 (or more) species. The membrane
selectivity, a (also known as the permselectivity)
for one component (A) over another component (B) is given by the ratio of their
permeabilities:
Replacing for PA and PB, and re-arrange, we have:
The ratio DA/DB is the ratio of the diffusion coefficients of the 2 gases and can be viewed as the mobility selectivity, reflecting the different sizes of the 2 molecules. The ratio KA/KB is the ratio of the sorption coefficients of the 2 gases and can be viewed as the sorption or solubility selectivity, reflecting the relative condensabilities of the 2 gases.
In all polymer materials, the diffusion coefficient decreases with increasing molecular size, because large molecules interact with more segments of the polymer chain than small molecules do. Hence the mobility selectivity always favour the passage of small molecules over large ones.
However, the magnitude of the mobility selectivity depends greatly on whether the membrane material is above or below its glass transition temperature, Tg. The polymer is glassy below Tg and its structure is tough and rigid. The polymer is rubbery above Tg and there is flexibility in its structure.
Diffusion coefficients in glassy polymers decrease much more rapidly with increasing permeate size than diffusion coefficients in rubbers.
The sorption coefficient of gases and vapours increase with increasing condensability of the permeant. This dependence on condensability means that the sorption coefficient also increases also increases with molecular size. Thus sorption selectivity favours large, more condensable molecules such as hydrocarbon vapour, over permanent gases such as O2 and N2. However, the difference between the sorption coefficients and permeabilities in rubber and glassy polymers is far less marked than the difference in diffusion coefficients.
Thus, the balance between the mobility term and the sorption selectivity term is different for glassy and rubbery polymers.
In glassy polymers the mobility term is usually dominant,
thus small molecules permeate preferentially. When used to segregate organic
vapour from N2, glassy polymer preferentially
permeates nitrogen. In rubbery polymers the sorption term is usually dominant,
so larger molecules permeate preferentially. When used to separate organic vapour
from N2, rubbery polymer preferentially permeates
the organic vapour.
Selectivity obtained from ratio of pure gas permeabilities is called the ideal membrane selectivity or the ideal permselectivity. This is an intrinsic property of the membrane material.
If a membrane had holes or pores which were all exactly the same diameter, then those molecules or particles whose diameters were smaller than the pore diameter would pass through the membrane, and those molecules or particles with larger diameters than the pore diameter would be totally rejected. Such a membrane would show an infinite selectivity.
The selectivities of actual membranes are less than infinite due to several factors. First, seldom will all pores in a membrane be exactly the same size. Thus smaller pores might exclude one component while larger pores permit it to pass. In such a case, the selectivity would be a function of the relative populations of various pore sizes.
Second, molecules may be able to deform to some extent and may actually enter pores slightly smaller than their original diameter.
Third, molecules of one type may adsorb on the walls of the pores and reduce the effective diameters of these pores. In this case a pore's effective diameter might vary with the feed/retentate and permeate compositions, depending on how much of the adsorbing component is in each of the streams.
It is also important to note that practical gas separation
processes are performed with gas mixtures rather than pure gases. If the gases
in a mixture do not interact strongly with the membrane material, the pure gas
intrinsic selectivity and the gas mixture selectivity will be equal. This is
usually the case for mixtures of O2 and N2.
Gas mixtures are also usually non-ideal, especially under high pressure, and
thus the actual selectivity may be quite different from the ideal value. In
many cases, such as the mixture of CO2 and CH4,
the CO2 is sufficiently sorbed by the membrane
that permeability of CH4 is affected. The selectivity
for such a gas mixture will deviate from the calculated selectivity from pure
gas measurements.
Nonetheless, selectivities are usually reported under ideal conditions because pure gas permeabilities are more frequently available.
Separation Factor
Similarly, in liquid separation, the selectivity for component A over B in a binary liquid mixture may be expressed by the separation factor as: