Membranes - Principles of Chemical Separations with Environmental Applications - page 262

The driving force for the process is generated by the low pressure on the permeate side of
the membrane, through cooling and condensing the permeate vapor.
Because of the phase change associated with the process and the non-ideal liquid-phase
solutions (i.e., organic/water), the modeling of pervaporation cannot be accomplished
using a solution-diffusion approach. Wijmans and Baker [14] express the driving force
for permeation in terms of a vapor partial pressure difference. Because pressures on the
both sides of the membrane are low, the gas phase follows the ideal gas law. The liquid
on the feed side of the membrane is generally non-ideal.
The permeant flux of compound i is

γ i x i P i

y i P p

Q

N i = − (9.20)

γ i (activity coefficient) and x i refer to the feed-side liquid, P i is the vapor pressure
at the feed-side temperature, y i is the mole fraction in the permeant vapor, and P p is the
total permeant pressure.
The feed stream is usually heated to raise the equivalent vapor pressure on the feed
side of the membrane. This results in a flux increase. The flux is also a strong function
of permeate pressure. Maintaining a very low permeate pressure is important to maintain
sufficient driving force.
The permeability for pervaporation depends on the concentrations of permeants in the
polymer, which can cause swelling and solute-interaction effects in polymers. Inorganic
membranes have recently been used in this application to overcome some of these limita-
tions. Because of these non-ideal effects, the selectivity can be a strong function of feed
concentration and permeate pressure, causing inversion of selectivity in some cases.
The separation selectivity can also be described by a separation factor,

where

β pervap , defined

as:

β pervap = P i P j permeate C i C j feed

(9.21)

where C i and C j are the concentrations of components i and j on the feed (liquid) side and
P i and P j are the vapor pressures of the two components i and j on the permeate (vapor)
side of the membrane.
The separation factor

β pervap can be easily shown to be the product of two other separation

factors, β evap , given by:

β mem = P i P j permeate P i P j feed

β mem and

(9.22)

P i P j
C i C j

β evap =

feed .

(9.23)

It follows from equations above that:

β pervap = β evap · β mem . (9.24)