Membrane and Desalination Technologies - TCE Moodle Website

Membrane Technologies for Point-of-Use and Point-of-Entry Applications 631
Here, NDP = net driving pressure (psi), DP = transmembrane differential pressure (psi), and
Dp = transmembrane osmotic pressure differential (psi).
The performance of an RO system is defined by the feed flow to the membrane unit (Qf) and its salt passage. The feed flow through the RO is directly proportional to the wetted
surface area of the membrane (Am) multiplied by the NDP and the membrane permeability
coefficient (k). The water permeation equation can be described by the following equation:
Qf ¼ðAmÞðkÞðNDPÞ ¼ðAmÞðkÞðDP DpÞ (7Þ
Here, Qf = feed flow to the membrane unit (m 3 /h), Am = wetted surface area of membrane
(m 2 ), k = membrane permeability coefficient (psi 1 h 1 ), NDP = net driving pressure (psi),
DP = transmembrane differential pressure (psi), and Dp = transmembrane osmotic pressure
differential (psi).
In addition, salt passage has to be considered in an RO system, as the salt flux (SA) is
proportional to the salt concentration difference between both sides of the membrane. The
salt flux across the membrane can be explained by Eq. (8):
SA ¼ k 0 ðCfCPÞ; (8Þ
where SA = salt flux (mg/m 2 h), k0 = salt diffusion coefficient (m 2 h), Cf = concentration of
solid in feed (mg/L), and CP = concentration of solid in permeate (mg/L).
It is important to note that the flux associated with an RO system is typically referenced to
a temperature of 25 C (298 K). It is necessary to have the temperature correction factor
(dimensionless) for the purposes of assessing operational performance. The calculation of
temperature correction factor (TCF) for RO systems is shown in Eq. (9):
TCF ¼ exp U
1
T þ 273
1
298
; (9Þ
where TCF = temperature correction factor (dimensionless), T = water temperature ( C), and
U = membrane-specific manufacturer-supplied constant (1/K).
As the RO process is normally rated to produce purified water at 60 psi (or 4.1 bars), the
pressure correction factor (PCF, dimensionless) is necessary in some systems that operate at
any pressure other than 60 psi. PCF can be determined as follows:
PCF ¼ P=60; (10Þ
where PCF = pressure correction factor (dimensionless) and P = line pressure (psi).
Typically, the RO process produces the purified flow at 60 psi (4.1 bars) operating
pressure, 25 C (77 F) operating temperature, and 500 ppm TDS. Once the TCF and PCF
have been determined, the flux normalized to 25 C and 60 psi can be calculated according to
Eq. (14):
J25 ¼ JTðPCFÞðTCFÞ (11Þ
Here, J 25 = normalized flux at 25 C (gfd), J T = actual flux at temperature T (gfd), PCF =
pressure correction factor (dimensionless), and TCF = temperature correction factor
(dimensionless).