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Membrane Technologies for Oil–Water Separation 661
where SCR solute concentration ratio, R observed rejection coefficient, CF concentration
factor, C0 initial solute concentration in the feed (mg/L), Cr the retained bulk solute concentration
(mg/L).
This equation allows the calculation of rejection using only retentive data.
5.1. Example 1
Membrane technology is used to remove oil particles from industrial wastewater. The
initial feed tank volume is 8,640 m 3 /day and after treatment, the retained volume is required
to be 50% of the initial volume entering to the basin. If the observed rejected coefficient is
0.02, find solute concentration ratio.
Solution:
1. Find concentration factor
Concentration factor ¼ CF ¼ V0
Vr
V0 8; 640 m 3 =day; Vr 50% V0 0:5 V0
CF ¼ V0
¼ 2
0:5 V0
Concentration factor 2
2. Find solute concentration ratio
Solute concentration ratio, SCR, could be find from
Solute concentration ratio is 1.15.
5.2. Example 2
logðSCRÞ ¼R logðCFÞ
logðSCRÞ ¼0:02 logð2Þ ¼0:06
SCR 1.15
The permeate flux of the membrane is 20 L/h m 2 . Calculate the required surface area for
the membrane if the volume of permeate are 10 L, 20 L, and 50 L, consequently. Let the
membrane operating time is 3 h.
Solution: Find the surface area of membrane using the following equation:
J ¼ V
F t
1. If volume of permeate is 10 L, the surface area can be calculated as follow:
F ¼ V
J t
(1Þ