Page 366 - Water and wastewater engineering

REVERSE OSMOSIS AND NANOFILTRATION 9-5

Flux
3
2
Several models have been developed to describe the flux of water (m /d · m of membrane sur-
2
face area) and solutes (kg/m · d) through the RO membrane. Because there is some controversy
about the mechanics of permeation, these are presented in summary here. For more details see
MWH (2005). The models are:
• Solution-diffusion model: Permeation occurs through a dense membrane where the active
layer is permeable but nonporous. Water and solutes dissolve into the solid membrane mate-
rial, diffuse through the solid, and reliquefy on the permeate side of the membrane. Separa-
tion occurs when the flux of the water is different from the flux of the solutes.
• Pore flow model: This model assumes the RO membranes have void spaces (pores) through
which the liquid water travels. It considers the water and solute fluxes to be coupled. Rejec-
tion occurs because the solute molecules are “strained” at the entrance to the pores. Because
the solute and water molecules are similar in size, the rejection mechanism is not a physical
sieving but rather a chemical effect such as electrostatic repulsion.
• Preferential sorption-capillary flow model: This model assumes the membrane has pores.
Separation occurs when one component of the feed solution (either solute or water) is pref-
erentially adsorbed on the pore walls and is transported through the membrane by surface
diffusion.

Ultimately, these models express flux as the product of a mass transfer coefficient and a driv-
ing force. The water flux is
J k ( P ) (9-5)
w
w
3 2

where J w volumetric flux of water, m /d · m
3 2
k w mass transfer coefficient for water flux, m /d · m · kPa

P net transmembrane pressure, kPa
difference in osmotic pressure between the feed and the permeate, kPa
The driving force for the solute flux is the concentration gradient. The solute flux is
ks(
Js C) (9-6)
2
where J s mass flux of solute, kg/d · m
2
3
k s mass transfer coefficient for solute flux, m /d · m
3
C concentration gradient across the membrane, kg/m
The flux of solutes through the membrane is
J C J
s p w (9-7)
3

where C p solute concentration in the permeate, kg/m .
The recovery ( r ) is the ratio of permeate flow to feed water flow:
Q
r P (9-8)
Q F