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Membrane Systems Planning and Design 371
Combining Eqs. (1) and (7) demonstrates that the additional membrane area required is
directly proportional to the increase in water viscosity (for constant flow, TMP, and membrane
resistance), as shown in Eq. (30):
where
Qp
Am
Qp = filtrate flow, gpd
Am = membrane surface area, ft 2
TMP = trans-membrane pressure, psi
Rt = total membrane resistance, psi/gal/ft 2 /d/cp
mT = viscosity of water, cp
¼ TMP
; (30Þ
RtðmTÞ Membrane filtration systems are commonly designed to operate at a particular flux (e.g., as
determined via pilot testing or mandated by the state) to produce a specific flow (i.e., rated
system capacity) at a reference temperature of 20 C. Thus, the required membrane area at
20 C can be calculated using Eq. (1). The increased membrane area required to compensate
for cold weather flow can be determined by multiplying this area by the ratio of the viscosity
at the coldest anticipated temperature (e.g., the coldest average monthly temperature) to that
at the reference temperature of 20 C. Values for water viscosity can be found in the literature
or approximated using Eq. (8):
mT ¼ 1:784 0:0575 T þ 0:0011 T 2
10 5 T 3 ; (8Þ
where m T is the viscosity of water at temperature T, cp and T is the water temperature, C.
After the appropriate values for water viscosity have been determined for both the
reference temperature (commonly 20 C for MF/UF systems) and the coldest anticipated
temperature, then the design membrane area, as compensated for seasonal temperature
variation, can be calculated as shown in Eq. (31):
where
Ad ¼ A20
mT m20 Ad = design membrane area (as adjusted for temperature), ft 2
A20 = membrane area required at 20 C reference temperature, ft 2
mT = viscosity of water at temperature T C, cp
m20 = viscosity of water at temperature 20 C, cp
; (31Þ
Equation (30) can also be utilized to calculate the required membrane area using a less
conservative approach that accounts for seasonal fluctuations in demand. First, if the information
is available, the average daily flow and temperature over each calendar month can be
tabulated, and the temperature data converted into associated values for water viscosity using
Eq. (8). Then, the 12 sets of paired flow (Q p) and viscosity (m) data can be applied to Eq. (30)
to generate 12 values of membrane area. The largest of these values for the required