Membrane and Desalination Technologies - TCE Moodle Website

358 N.K. Shammas and L.K. Wang
where mT is the viscosity of water at temperature T, cp, T is the water temperature, C.
Since water temperature can have a significant impact on flux, it is common practice to
“normalize” the flux to a reference temperature during operation for the purposes of monitoring
system productivity independent of changes in water temperature. For MF/UF and
MCF processes, a reference temperature of 20 C is typically used for convenience, since the
viscosity of water is approximately 1 cp at 20 C. For constant TMP and total membrane
resistance, Eq. (9) can be used to illustrate the relationship between the normalized flux and
viscosity at 20 C and the actual flux and viscosity at a given temperature of interest T:
J20ðm20Þ ¼JTðmTÞ; (9Þ
where
J20 = normalized flux at 20 C, gal/ft 2 /d
m 20 = viscosity of water at 20 C, cp
J T = actual flux at temperature T, gal/ft 2 /d
m T = viscosity of water at temperature T, cp
Substituting the value of 1 cp for the viscosity at 20 C(m20) and Eq. (8) for the viscosity of
water at temperature T (mT), yields an expression for normalized flux at 20 C as a function of
the actual flux and the temperature, as shown in Eq. (10):
J20 ¼ JTð1:784 0:0575 T þ 0:0011 T 2
10 5 T 3 Þ; (10Þ
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 T is the water temperature, C.
It is important to note that the normalized flux (J20) does not represent an actual operating
condition. This term simply represents what the flux would be at 20 C for a constant TMP and
total membrane resistance. Thus, changes in the value of J 20 during the course of normal
operation are indicative of changes in pressure and/or membrane resistance due to fouling. If
values for viscosity are known, the polynomial expression for viscosity as a function of
temperature in Eq. (10) may be simplified to a temperature correction factor (TCF). For a MF,
UF, or MCF process, the TCF is defined as the ratio of the viscosity at temperature T to the
viscosity at 20 C, as shown in Eq. (11):
TCF ¼ mT ; (11Þ
m20 where TCF is the temperature correction factor, dimensionless, mT is the viscosity of water at
temperature T, cp, and m 20 is the viscosity of water at 20 C, cp.
Note that the term TCF is often used generically to refer to any type correction factor used
to adjust a parameter for temperature. Thus, the specific equation for the TCF may vary
depending on the parameter to which it is applied. For example, in the context of membrane
filtration, the TCF applied to reference MF, UF, and MCF flux to a standard temperature, as
defined in Eq. (11), is different than that applied to NF and RO flux to a standard temperature,
as shall be shown in Eq. (15). Thus, it is important to always consider the context in which the
term TCF is used.