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Membrane Systems Planning and Design 359
Because the TCF is a dimensionless ratio, the values for viscosity can be expressed in any
convenient and consistent units. Thus, the temperature-normalized flux can be expressed in
simplified terms, as shown in Eq. (12):
J20 ¼ JTðTCFÞ; (12Þ
where J20 is the normalized flux at 20 C, gal/ft 2 /d, JT is the actual flux at temperature T,gal/ft 2 /d,
and TCF is the temperature correction factor, dimensionless.
Generally, in order to identify changes in productivity (as measured by flux) that are
specifically attributable to membrane fouling, it is desirable to normalize the flux for pressure
as well as temperature, as shown in Eq. (13). Note that the temperature- and pressurenormalized
flux is often referred to as either the specific flux or permeability.
M ¼ J20
; (13Þ
TMP
where M is the temperature- and pressure-normalized flux, gal/ft 2 /d/psi, J20 is the normalized
flux at 20 C, gal/ft 2 /d, and TMP is the trans-membrane pressure, psi.
4.3. NF and RO Processes
As with the microporous MF, UF, and MCF membranes, the driving force for the transport
of water across a semi-permeable membrane – such as that utilized by NF and RO processes –
is a pressure gradient across the membrane. However, because NF and RO processes reject
dissolved salts, the resulting osmotic pressure gradient, which acts against the transport of
water from the feed to the filtrate side of the membrane, must also be taken into account.
Typically, the osmotic pressure gradient is approximated from the concentration of total
dissolved solids (TDS) on the feed and filtrate sides of the membrane. The corrected driving
force across semi-permeable membrane is termed the net driving pressure (NDP) and can be
calculated using Eq. (14) (5):
where:
NDP ¼ Pf þ Pc
2
0:01
NDP = net driving pressure, psi
P f = feed pressure, psi
Pc = concentrate pressure, psi
TDSf = feed TDS concentration, mg/L
TDSc = concentrate TDS concentration, mg/L
TDSp = filtrate TDS concentration, mg/L
Pp = filtrate pressure (i.e., backpressure), psi
TDS þ TDSc
2
TDSp Pp; (14Þ
Equation (14) can be considered as three distinct components. The first term represents the
average pressure on the feed side of the membrane; the second term represents the average
osmotic backpressure; and the third term represents the filtrate backpressure. The conversion
factor of 0.01 in the osmotic pressure term comes from a widely used rule of thumb for fresh