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MEMBRANE PROCESSES 13.11

Solute rejection (removal): solute rejection or removal SR (or for TDS, salt rejection
or removal) is the fraction of solute in membrane feedwater that remains in the con-
centrate (retentate) stream and does not enter the product stream, expressed as a per-
cent. For ED/EDR systems, removal is the term used instead of rejection.
c,- cp cp
SR- - - x 100= 1 - -- x 100 = 100- SP
cl cl
where SR = solute (salt) rejection or removal, %
SP = solute (salt) passage, %
Cp = concentration of solute in permeate or filtrate stream, mg/L
Cf = concentration of solute in feed stream, mg/L
Transmembrane osmoticpressure ~rtm: feed stream (average feed/concentrate) osmotic
pressure of a pressure-driven membrane minus permeate osmotic pressure, mathemat-
ically expressed as

~f+ ~rc
"B'tm 2 ~'P
where '/rtm = transmembrane osmotic pressure, psi
~-f = feed osmotic pressure, psi
~'c = concentrate osmotic pressure, psi
¢rp = permeate osmotic pressure, psi
Transmembrane pressure Ptm: feed stream (average feed/concentrate) pressure (cross-
flow operating mode) or feed pressure (dead-end operating mode) minus the perme-
ate (product) pressure, mathematically expressed as
P, + Pc Ap
Ptm 2 PP = PJ 2 PP

where Ptm = transmembrane pressure, psi
Pf = feed pressure, psi
Pc = concentrate pressure, psi
Pp = permeate pressure, psi
Ap = feed/concentrate pressure differential Pf- Pc, psi

Membrane System Components
A simplified membrane system flow schematic is shown in Figure 13.9. Membrane sys-
tems typically include pretreatment, the membrane unit(s), product (permeate or filtrate)
posttreatment, and possibly concentrate (or retentate) waste stream posttreatment. Mem-
brane systems are commonly designed with multiple parallel process "trains" to give
greater flexibility in production output rates and to allow cost-effective incremental ex-
pansions. The flow schematic also shows that in some cases it is possible to bypass a por-
tion of source or pretreated water around the membranes and blend it with the product to
produce finished water, before disinfection (i.e., split-flow treatment). In some applica-
tions, two membrane units may be placed in series such as in the dual-membrane system,
with MF or UF as pretreatment for NF or RO (Figure 13.10), or two-pass RO desalting
(Figure 13.11). In the two-pass seawater desalting process, the second-stage concentrate
is typically less saline than the raw seawater and commonly is recycled to lower the TDS
of the membrane feed.