Environmental Engineering Reference
In-Depth Information
Table 9.4
Osmotic pressures.
Concentration
Osmotic pressure (atm, at 25
◦
C)
Compound
(g
/
L)
(Total moles in solution
/
L)
Sucrose
1
0.003
0.07
NaCl
58
2
49
NaCl
1
0.02
0.5
NaHCO
3
1
0.02
0.6
CaCl
2
1
0.03
0.7
C
=
total ionic concentration
R
=
universal gas constant
T
=
absolute temperature.
We can see from the flux equation that we have reverse osmosis if
.
The osmotic pressure depends on the type of solution as well as the concentration in
which it is present. Thus, 1 mole of NaCl dissolved in 1 L of water will double the osmotic
pressure compared to 1 mole of glycerin added in the same amount of water, since the
former yields two ions as opposed to only one molecule produced by glycerin. Similarly,
1 mole of ferric chloride (FeCl
3
), by yielding four ions, will double the osmotic pressure
of 1 mole of NaCl. Some typical osmotic pressures are given in Table 9.4.
As the pressure difference across the membrane is increased, the rate of solvent mass
transfer is also increased. Typical feed pressures are between 17 and 55 atm (1.7-
5.5 MPa).
Remember that the pressure difference must be greater than the osmotic pres-
sure for reverse osmosis to occur, and that the osmotic pressure varies for different types
of solutions and for the same solutions in different concentrations
.
As temperature varies, the diffusivity and viscosity vary also, and this in turn causes the
flux to vary. Membrane area corrections (
A
T
/
P
>
A
25
◦
C
) due to the respective temperatures
are as follows [11]:
Temperature (
◦
C):
10
15
20
25
30
Area correction:
1.58
1.34
1.15
1.00
0.84
Example 9.3: reverse osmosis
Problem:
A reverse osmosis unit is to demineralize 750,000 L
/
day treated effluent. Pertinent
(m
2
kPa) at 25
◦
C, pressure difference
data are: permeability coefficient
=
0.2 L
/
·
day
·
between the feed and product water
=
2500 kPa, osmotic pressure difference between
10
◦
C.
the feed and product water
=
300 kPa, lowest operating temperature
=
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