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Membrane Technologies for Oil–Water Separation 659
5. DESIGN EXAMPLES
Three terms usually used in designing of membrane unit include permeate flux, rejection,
and volume recovery. The description of each term is defined as follows.
Permeate flux, L/h m 2 : Permeate flux is the volume of permeate generated from a
membrane surface area within a given time as shown in Eq. (1):
J ¼ V
(1Þ
F t
where J = permeate flux, L/h m 2 , V = volume of permeate, L, F surface area, m 2 , t = time, h.
Rejection, %: Rejection (R) is a fraction of the total contaminant mass/concentration
rejected by the membrane. It is also determined by the following Eq. (2):
R ¼ 1 ðCp=CrÞ (2Þ
where R = observed rejection coefficient, Cp = bulk solute concentration in the permeate,
mg/L, Cr the retained bulk solute concentration, mg/L.
Volume recovery, %: Volume recovery (R) is the fraction of the total feed volume of the
test water that can be recovered as the clean permeate:
Rv ¼ VP=VF
(3Þ
where Rv volume recovery, VF = volume of feed, L, Vp volume of permeate, L.
The concentration polarization ratio (Cmembrane/Cbulk) depends on the flux, rejection, and
mass transfer coefficient and is estimated from the following equation:
Cmembrane exp
¼
Cbulk
J
k
RO þð1 ROÞ exp J
(4Þ
k
where RO observed rejection which becomes equal to 1 when the solute is completely retained
by the membrane, k = the mass transfer coefficient, J permeate flux, L/hm 2 .
The value of mass transfer coefficient, k, is determined by using RO and J data taken at
different pressures, but constant feed concentration and feed rate to plot a straight line of best
fit between ln((1 RO)J/RO) versus J of slope 1/k and intercept ln(Dk/d) where D is diffusion
coefficient and d represents boundary layer thickness.
Some design information of the widely used ultrafiltration for oil and water separation are
provided in this section. The permeate flux (J) is an important parameter in the design and
economic feasibility analysis of the UF separation process. Hydrodynamics of membrane
modules have an important effect on the mass transfer, separation, and fouling behavior of
membrane systems.
Generally, the pure solvent transporting through porous ultrafiltration membranes is
directly proportional to the applied transmembrane pressure (DP). The Kozeny–Carman
and Hagen–Poiseuille equations describe the convection flow (J0) as follows (109):
J0 ¼ DP
(5Þ
Rm