Membrane and Desalination Technologies - TCE Moodle Website

356 N.K. Shammas and L.K. Wang
The recovery of a membrane unit is defined as the amount of feed flow that is converted to
filtrate flow, expressed as a decimal percent, as shown in Eq. (2):
R ¼ Qp
; (2Þ
Qf
where R is the recovery of the membrane unit, decimal percent, Qp is the filtrate flow
produced by the membrane unit, gpd, and Qf is the feed flow to the membrane unit, gpd.
The recovery does not account for the use of filtrate for routine maintenance purposes
(such as chemical cleaning or backwashing) or lost production during these maintenance
operations. Because the definition of recovery is not necessarily consistent throughout the
water treatment industry, it is important to identify how recovery is defined in any particular
discussion. However, the use of the term recovery as defined in this discussion by Eq. (2) is
consistent with the applicable US EPA regulations and the Membrane Filtration Guidance
Manual (1). Note that for some types of membrane systems, particularly those that operate in
suspension mode that can be modeled as plug flow reactors (PFRs), recovery can also be
defined as a function of position within a membrane unit. This is simply a variation of Eq. (2)
for systems in which the filtrate flow increases in the direction of feed flow through the
membrane unit, thus increasing the recovery in direct proportion. The limit of this recovery in
the direction of flow (i.e., the recovery at the furthest position in the unit) is equivalent to the
overall membrane unit recovery, as defined in Eq. (2).
A general flow balance that can be applied to all membrane filtration systems is shown in
Eq. (3):
Qf ¼ Qc þ Qp; (3Þ
where Q f is the feed flow to the membrane unit, gpd, Q c is the concentrate flow from the
membrane unit, gpd, and Qp is the filtrate flow from the membrane unit, gpd.
Note that the concentrate (i.e., bleed or reject) flow, Qc, is zero for systems operating in
deposition (i.e., dead-end) mode. For the purpose of sizing a membrane filtration system, it
may be desirable to account for the additional filtered water used for both backwashing and
chemical cleaning in the determination of the filtrate flow, Qp. Similarly, an estimate of the
total required feed flow Qf to the system should incorporate any raw water that may be used in
these processes.
4.2. MF, UF, and MCF Processes
The driving force for the transport of water across a microporous membrane – that utilized
by MF, UF, and MCF processes – is a pressure gradient across the membrane, or the TMP.
The TMP is defined by the pressure on the feed side of the membrane minus the filtrate
pressure, commonly called the backpressure, as shown in Eq. (4):
TMP ¼ Pf Pp; (4Þ
where TMP is the trans-membrane pressure, psi, Pf is the feed pressure, psi, and Pp is the
filtrate pressure (i.e., backpressure), psi.