Reverse Osmosis Performance & Design
Calculations
There are a handful of calculations that
are used to judge the performance of an RO system and also for design
considerations. An RO system has instrumentation that displays quality, flow,
pressure and sometimes other data like temperature or hours of operation. In
order to accurately measure the performance of an RO system you need the
following operation parameters at a minimum:
·
Feed pressure
·
Permeate pressure
·
Concentrate pressure
·
Feed conductivity
·
Permeate conductivity
·
Feed flow
·
Permeate flow
·
Temperature
SALT REJECTION %
This equation tells you how effective the
RO membranes are removing contaminants. It does not tell you how each
individual membrane is performing, but rather how the system overall on average
is performing. A well-designed RO system with properly functioning RO membranes
will reject 95% to 99% of most feed water contaminants (that are of a certain
size and charge). You can determine how effective the RO membranes are
removing contaminants by using the following equation:
Salt Rejection % =
|
Conductivity of Feed
Water – Conductivity of Permeate Water
|
× 100
|
Conductivity of Feed
|
The higher the salt rejection, the better
the system is performing. A low salt rejection can mean that the membranes
require cleaning or replacement.
SALT PASSAGE %
This is simply the inverse of salt
rejection described in the previous equation. This is the amount of salts
expressed as a percentage that are passing through the RO system. The lower the
salt passage, the better the system is performing. A high salt passage can mean
that the membranes require cleaning or replacement.
Salt Passage % = (1 –
Salt Rejection %)
|
RECOVERY %
Percent Recovery is the amount of water
that is being 'recovered' as good permeate water. Another way to think of
Percent Recovery is the amount of water that is not sent to drain as
concentrate, but rather collected as permeate or product water. The higher the
recovery % means that you are sending less water to drain as concentrate and
saving more permeate water. However, if the recovery % is too high for the RO
design then it can lead to larger problems due to scaling and fouling. The %
Recovery for an RO system is established with the help of design software
taking into consideration numerous factors such as feed water chemistry and RO pre-treatment
before the RO system. Therefore, the proper % Recovery at which an RO should
operate at depends on what it was designed for. By calculating the % Recovery
you can quickly determine if the system is operating outside of the intended
design. The calculation for % Recovery is below:
% Recovery =
|
Permeate Flow Rate
(gpm)
|
× 100
|
Feed Flow Rate (gpm)
|
For example, if the recovery rate is 75%
then this means that for every 100 gallons of feed water that enter the RO
system, you are recovering 75 gallons as usable permeate water and 25 gallons
are going to drain as concentrate. Industrial RO systems typically run anywhere
from 50% to 85% recovery depending the feed water characteristics and other
design considerations.
CONCENTRATION FACTOR
The concentration factor is related to the
RO system recovery and is an important equation for RO system design. The more
water you recover as permeate (the higher the % recovery), the more
concentrated salts and contaminants you collect in the concentrate stream. This
can lead to higher potential for scaling on the surface of the RO membrane when
the concentration factor is too high for the system design and feed water
composition.
Concentration Factor =
|
1
|
1 – Recovery %
|
The concept is no different than that of a
boiler or cooling tower. They both have purified water exiting the system
(steam) and end up leaving a concentrated solution behind. As the degree of
concentration increases, the solubility limits may be exceeded and precipitate
on the surface of the equipment as scale.
For example, if your feed flow is 100 gpm and your permeate flow is 75 gpm,
then the recovery is (75/100) x 100 = 75%. To find the concentration factor,
the formula would be 1 ÷ (1-75%) = 4.
A concentration factor of 4 means that the water going to the concentrate
stream will be 4 times more concentrated than the feed water is. If the feed
water in this example was 500 ppm, then the concentrate stream would be 500 x 4
= 2,000 ppm.
FLUX
Gfd =
|
gpm of permeate ×
1,440 min/day
|
# of RO elements in
system × square footage of each RO element
|
For example, you have the following:
The RO system is producing 75 gallons per
minute (gpm) of permeate. You have 3 RO vessels and each vessel holds 6 RO
membranes. Therefore you have a total of 3 x 6 = 18 membranes. The type of
membrane you have in the RO system is a Dow Filmtec BW30-365. This type of RO
membrane (or element) has 365 square feet of surface area.
To find the flux (Gfd):
Gfd =
|
75 gpm × 1,440 min/day
|
=
|
108,000
|
18 elements × 365 sq
ft
|
6,570
|
The flux is 16 Gfd.
This means that 16 gallons of water is passed through each square foot of each
RO membrane per day. This number could be good or bad depending on the type of
feed water chemistry and system design. Below is a general rule of thumb for
flux ranges for different source waters and can be better determined with the
help of RO design software. If you had used Dow Filmtec LE-440i RO membranes in
the above example, then the flux would have been 14. So it is important to
factor in what type of membrane is used and to try and keep the type of
membrane consistent throughout the system.
Feed
Water Source
|
Gfd
|
Sewage Effluent
|
5-10
|
Sea Water
|
8-12
|
Brackish Surface Water
|
10-14
|
Brackish Well Water
|
14-18
|
RO Permeate Water
|
20-30
|
MASS BALANCE
A Mass Balance equation is used to help
determine if your flow and quality instrumentation is reading properly or
requires calibration. If your instrumentation is not reading correctly, then
the performance data trending that you are collecting is useless. You will need
to collect the following data from an RO system to perform a Mass Balance
calculation:
1. Feed
Flow (gpm)
2. Permeate
Flow (gpm)
3. Concentrate
Flow (gpm)
4. Feed
Conductivity (µS)
5. Permeate
Conductivity (µS)
6. Concentrate
Conductivity (µS)
The
mass balance equation is:
(Feed flow1 x Feed Conductivity) = (Permeate Flow
x Permeate Conductivity)
+ (Concentrate Flow x Concentrate Conductivity)
1Feed
Flow equals Permeate Flow + Concentrate Flow
For example, if you collected the following
data from an RO system:
Permeate Flow
|
5 gpm
|
Feed Conductivity
|
500 µS
|
Permeate Conductivity
|
10 µS
|
Concentrate Flow
|
2 gpm
|
Concentrate Conductivity
|
1200 µS
|
Then
the Mass Balance Equation would be:
(7 x 500) = (5 x 10) + (2 x 1200)
3,500 ≠ 2,450
Then
find the difference
(Difference / Sum) x 100
((3,500 - 2,450) / (3,500 + 2,450)) x 100
=
18%
A difference of +/- 5% is ok. A difference
of +/- 5% to 10% is generally adequate. A difference of > +/- 10% is
unacceptable and calibration of the RO instrumentation is required to ensure
that you are collecting useful data. In the example above, the RO mass balance
equation falls out of range and requires attention.
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