The experiment investigated the characteristics of a reverse osmosis membrane system with one, two, and three membranes. A calibration curve was generated to relate conductivity to salt concentration. For a single membrane, the water permeability was found to be 0.245 g/s-psi-m2 and the salt rejection coefficient was 0.879 on average. The salt mass transfer coefficient was 15.248 m/s. For two membranes, the second membrane had a lower rejection coefficient due to its more concentrated feed. The third membrane in a three membrane system had an even lower rejection coefficient. Overall, the rejection coefficient decreased as more membranes were added due to increasing feed concentration.

1. 3 March, 2015
TO: Professor A. Drews, PhD
FROM: Group B4: Brandon Sanchez, Saman Hadavand, Janet Mok, Liliana Busanez
SUBJECT: Reverse Osmosis, Final Report
Attached is the final report and our recommendations concerning the Reverse Osmosis Lab. This
report includes a study on the effect of flow rate, pressure, and change in concentration of the feed on
the permeate flow. Whereby changing parameters such as pressure and flow rate enables change of
concentration for the feed/retentate, ROM1 and ROM2 (as well as ROM3) in series can be tested for
recovery technology in optimized design and parameters. We hope this report will satisfy the desired
expectations. If you have any questions or concerns, please contact us.
Sincerely,
Group B-4
Janet Mok: Theory and Background
Saman Hadavand: Results and Discussion
Liliana Busanez: Letter of Transmittal, Abstract, Introduction, Methods, Conclusion
Brandon Sanchez: Presentation and Tech Memo

2. 2
Reverse Osmosis
Janet Mok, Saman Hadavand, Liliana Busanez, Brandon Sanchez
The goal of the experiment was to understand the characteristics and design of a
Reverse Osmosis Membrane (ROM), and in series test the system which
included three membranes: ROM1, ROM2, and ROM3. Investigation on the
effect of pressure and feed concentration of reverse membrane water purifying
system included applying a single, double, and triple membrane system where a
rejection coefficient for NaCl was found. The rejection coefficient found is 0.88,
compared to the manufacturer's rejection coefficient of 0.96. The performance of
the system was characterized by the flux of water, where the water permeability
was 0.245 (g/s-psi-m²). The membrane’s salt mass transfer coefficient was found
to be 15.249 m/s.
Advisor: Professor Aaron Drews
3 March, 2015

3. 1
1 Introduction
Reverse Osmosis Membrane (ROM) technology is used to treat industrial wastewater or to treat
contaminated water for processes that require high-quality purified water. Semiconductor processing or
biochemical applications use reverse osmosis to optimize system performances and reduce quantity of
dissolved solids in solution.1
Other Pressure driven membrane filtration systems include microfiltration,
ultrafiltration, and nanofiltration. These systems’ application depend on pores size, and charge of solutes;
furthermore, RO membranes exclude particles such as salt ions, organics compounds, etc.1
Reverse
Osmosis as a feasible process that is implemented for a variety of solute separation techniques including
nanofiltration (NF), where separation characteristics between these two technologies are referred to as NF
membranes and are being used commercially.2
For nanofiltration applications, membranes also usually
have good rejections of organic compounds with molecular weights above 200 to 500 g/mol.2
The most
important membranes are composite membranes made by interfacial polymerization; thin film composite
of aromatic polypiperazine is an example of a widely-used nanofiltration membrane for water treatment.2
RO and nanofiltration applications include the treatment of organic containing wastewater from
electroplating and metal finishing, wood pulping to food processing industries, as well as municipal and
radioactive wastewater. Treatment of such operations utilize reverse osmosis to reject particles from
contaminated water and to reuse product water.1
Early industrial development for desalination purposes, via dual role of membrane support and
pressure applied with process pump systems, have been applied since 1961 by industrial firms developing
potential designs studying membrane modification, and feed water additives in favorable economic
projections for seawater.3
In reverse osmosis salt water is forced against membranes under high pressure
where fresh water passes through. The performance of RO membranes is the usually the measurement of
water flux and solute (NaCl) rejection for the membrane, which indicate the suitability of the membrane
for the application.1
To ensure good performance, membrane type, flow control, feed water quality,
temperature and pressure are factors that enable maximising output of water.3

4. 2
2 Background & Theory
Osmosis is a process in which a weaker saline solution tends to migrate to a stronger saline
solution, which means reverse osmosis (RO) is essentially the process of osmosis in reverse. A RO
membrane is a semi-permeable membrane that allows the passage of water molecules, but not the
majority of dissolved salts.4
The water needs to be pushed through the reverse osmosis membrane by
applying a pressure that is greater than the osmotic pressure in order to desalinate the water in the process,
allowing pure water through while holding back a majority of the contaminants.4
Figure 1 shows a
diagram of the Reverse Osmosis process when pressure is applied on one end, the water molecules are
pushed through the semi-permeable membrane while the contaminants are not allowed through.
Figure 1: Outline of Reverse Osmosis process showing how when pressure is applied to the semi-permeable
membrane, mostly only water molecules are pushed through
Reverse Osmosis works by using a high pressure pump to increase the pressure on the salt side of
the RO and force the water across the semi-permeable RO membrane, leaving almost all of the dissolved
salts behind in the reject stream. The more concentrated the feed water, the more pressure is required to
overcome the osmotic pressure.4
The desalinated water is called the permeate or product water, and the
stream that carries the concentrated contaminants that did not pass through the RO membrane is called the
retentate or reject stream. The retentate stream goes to drain or can be fed back into the feed water supply

5. 3
in some circumstances to be recycled through the RO system to save water. This process is shown in
Figure 2 below.
Figure 2: Diagram of a Reverse Osmosis process with labeled streams
Since the flow rates and the concentrations of the permeate and retentate were seen to remain
constant, only the feed concentration varied with time.5
The two mass conservation equations that were
then used for the feed reservoir were:
Overall Mass Balance:
𝑑!
𝑑𝑡
= 𝑄! − 𝑄! (1)
Salt Mass Balance:
𝑑
𝑑𝑡
( 𝑉𝐶 𝑓) = 𝑄𝑟 𝐶𝑟 − 𝑄 𝑓 𝐶 𝑓 (2)
where V is the volume of the solution in the reservoir, Qr is the volumetric flow rate of the retentate being
recycled, and Qf is the outlet flow rate, which is also the feed flow rate to the RO membrane module. Cr
and Cf are the salt concentrations in the streams Qr and Qf , respectively.
In regards to the RO membrane at quasi-steady state, since all variable are assumed to be constant
except for Cf
5
:
Overall Mass Balance:
𝑄 𝑓 = 𝑄𝑟 + 𝑄 𝑝 (3)
Salt Mass Balance:
𝑄 𝑓 𝐶 𝑓 = 𝑄𝑟 𝐶𝑟 + 𝑄 𝑝 𝐶 𝑝 (4)
where Cp is the salt concentration in the permeate.

6. 4
The rejection coefficient is expressed as the following:
𝑟 = 1 −
𝐶 𝑝
𝐶 𝑓
(5)
The closer the rejection coefficient is to 1, the more the permeability percentage decreased. The closer it
is to 0, the more the permeability percentage increased. RO membranes have a higher rejection coefficient
after longer periods of use, which shows the stabilized rejection.4
The water flux across the RO membrane is a pressure-driven flow, and thus the water flux can be
defined as5
:
𝐽 𝑤 = 𝐴 𝑤(∆ 𝑃 − ∆𝜋) (6)
where ∆P is the transmembrane hydraulic pressure difference, ∆ is the osmotic pressure difference, and
Aw is the membrane water permeability. Aw was found by removing the osmotic pressure difference from
the equation and running the system with fresh water. Aw is found by this equation:
𝐴 𝑤 = 𝐽 𝑤/∆ 𝑃 (7)
The following equation was then used to solve the water flux through the membrane:
𝐽 𝑤 = ( 𝑄 𝑝 𝐶 𝑤)/ 𝑆 𝑎 (8)
where Qp is the permeate flow rate, Cw is the density of water, and Sa is the active surface area of the
membrane obtained from the manufacturer.
The salt transport across the membrane is predominantly due to diffusion, and the flux of salt can
be based on the concentration gradient:
𝐽𝑠 = 𝐾𝑠( 𝐶 𝑓 − 𝐶 𝑝) (9)
where Ks is the salt mass transfer coefficient related to the salt permeability in the membrane. This model
ignores the axial gradients and is applied to average values along the membrane.5
To determine the salt concentration in the permeate, Cp, the salt mass flux and the total permeate
flow rate was used to determine the following equation:
𝐶 𝑝 = ( 𝐽𝑠 𝑆 𝑎)/ 𝑄 𝑝 (10)

7. 5
where Sa is the membrane surface area. It is then assumed that the permeate is a very dilute solution. As a
dilution solution, the salt passage rate, Js , can then be evaluated by the equation:
𝐶 𝑝 = ( 𝐽𝑠 𝐶 𝑤)/ 𝐽 𝑤 (11)
Finally, by rearranging equation (6) and writing it as 𝛥 𝑃 − ( 𝐽 𝑤/ 𝐴 𝑤) = 𝜑( 𝐶 𝑓 − 𝐶 𝑝), the
osmotic pressure can be expressed as5
:
𝛥𝜋 = 𝜑( 𝐶 𝑓 − 𝐶 𝑝) (12)
3 Methods
The valve to the pump that equalizes the pressure of the inlet and outlet pressure pumps is
initially open, but closed when operating the pump. Also, f water pump for the Reverse Osmosis is dry
then the inside chamber should be filled using salt water reservoir water, and the bolt loosened then
adjusted into the pump so that it is closed tight so the pressure inside the inlet pipe is adjusted with an
appropriate water level above the inlet pipe. For the piping system the valves are slightly opened so that
liquid can flow through the system. To fill the reservoir with fresh water use the valve located against the
wall. The volume increments are noted on the reservoir for calculating the concentration.
The conductivity meter will measure the conductivity in Siemens per cm, or using the option to
change units to PPM which is done with a reference line. Constructing a calibration curve, from the
measured conductivity and PPM values using 2 grams of salt from initially 30 mL water, then diluted by
20 mL of water where conductivity is checked. The known range of PPM values from this serial dilutions
are used to convert from conductivity measurements to PPM for trial analysis. For a single membrane set-
up, the three streams include the inlet that carries the water from the feed into ROM1, second stream is
the first retentate or in a 2 membrane system the second inlet. This stream can be recycled into the
primary reservoir for a non-steady state solution. The third stream is the permeate or the “clean water”
from the RO. This will be at lower pressure and flow rate indicating less permeate than retentate, and is
drained into a clean beaker. As for the 2 or 3 ROM system, a second or third permeate, and retentate out
of the last membrane will result as a consequence. A dual membrane system is illustrated in figure 3.

8. 6
Figure 3: Diagram of RO Membrane System showing a two membrane system in series.
4 Results and Discussion
Before starting the reverse osmosis lab, a calibration curve was generated to test the accuracy of
the measuring device by graphing a relationship between a range of concentrations of salt in a water
solvent and its conductivity measurements. Figure 4 displays the calibration curve. The equation of the
conductivity versus concentration is expressed as y= 0.0186x + 36209. This equation is useful when
wanting to convert known values of conductivity or concentration. Conversions of conductivity and
concentration were necessary in order to perform calculations later in the lab. Its useful to note that the
higher of concentration of salt in the solutions, the higher the conductivity. There could have been error in
the readings due to the mixing not being completely uniform.

9. 7
Figure 4: Calibration curve using salt and water dilutions (PPM) for conductivity measurement
For the first part of the experiment, the water permeability (Aw) of the system was found to be
245(g/s-psi-m^2). The water permeability was found by generating a graph that showed the relationship
between a range of pressures (dP) and the water flux (Jw) through membrane 1. Figure 5 illustrates this
graph. The water flux (Jw) was calculated using equation 8 and its values are illustrated in Table-A1.
Variables that were incorporated are the surface area of the membrane (Sa) which stayed constant at
0.096m^2 and the density of water Cw= 0.988 g/ml. Ideally fresh water was suppose to be ran through the
system because water permeability is being analyzed and not the purification of water. There was error in
the system because the initial feed was not fresh or clean. This concentration of impurities in the water
could have interfered with the flow rates and pressures through the membrane giving inaccurate results.

10. 8
Figure 5: Water Flux (Jw) vs Change in Pressure (dP); Slope of Water Permeability (Aw)
A one-membrane system was used in the next part of the experiment. The salt rejection
coefficient, r, was determined for this membrane using equation 5. The average salt rejection coefficient
was determined to be 0.879, which was lower than the manufacturers given value of 0.96. This could
have been due to damage in the laboratory equipment, minimal trials, and inaccurate recordings. The
values of the salt rejection coefficients for each trial are illustrated in Table A2. Also from the one
membrane system, the salt mass transfer coefficient, Ks, was found by generating a graph that showed the
relationship between the flux of salt across membrane 1 (Js) and the concentration difference of the
permeate and feed (Cf-Cp). The value of Ks was determined to be 15.248m/s. As analyzed in the tables,
the higher the dP, the more permeate exited from the product stream. Also the same concept works vice-
versa; the lower the dP the less permeate will exit. Pressure is a crucial factor for the salt mass transfer
coefficient. Pressure has a higher magnitude effect on the system versus the flux because Cf-Cp is smaller
in magnitude, thus has more sensitive changes. The graph is illustrated in Figure 6. This directly affects
the rejection coefficients because r= 1-(Cp/Cf). The higher the permeate, the smaller the rejection which
is dependent on pressure. Finally for the one membrane system, the osmotic pressure difference, dπ, was
determined by equation 12. The constant, Ψ , was used to calculate dπ and was determined by the plot
shown in figure 6. The value for constant, Ψ, was determined to be -0.06 ((psi-m^3)/g). The osmotic
pressure difference values are illustrated in Table A3.

11. 9
Figure 6: Flux of Salt (Js) vs Change of Concentration; Slope of Salt Mass Transfer coefficient Ks
Figure 7: Slope of osmotic pressure constant Ψ
A two-membrane system was used next in the experiment. The rejection coefficient, r, was
determined in both system as illustrated in Table A4. Because of errors made in the lab, the system did
not run to well. This could have been to the damaged device or the broken flow meter that did not allow
accurate adjustments. The second membrane had much lower rejection than the first membrane due to
retentate being its feed. For a few trials no permeate would exit, this was due to a low pressure and flow
rate. The system was simply too weak. A three-membrane system was also observed. The third membrane
had an even smaller rejection coefficient than the second membrane observed. This was due to the even
more concentrated feed, its a similar trend. The more membranes that are added, the higher the
concentration in the feed, the lower the rejection, the less permeate will exit. The rejection coefficient for

12. 10
the third membrane is illustrated in Table A5. Finally a single membrane system with a recycle stream
was observed. The rejection coefficient for this system is illustrated in Table A6. The feed reservoir was
so large that the results stayed relatively constant. The prediction was that the rejection coefficient would
decrease as time increased because the feed would become saltier thus increases Cf. More trials were
needed to prove this point.
5 Conclusion
The concept proved in the lab was the higher the water flux the higher the permeate. Higher
pressure enabled a higher permeate flow rate. This is illustrated in figure 6. The goal of the lab was to get
a high quantity of permeate to exit, not necessarily the quality of the permeate stream. Adding second and
third membranes to the system allowed permeate to flow out, but due to systematic errors in lab setup, the
permeate did not flow out well in the second and third membranes. The rejection coefficient for the first
membrane was the highest and decreased heavily in the second and third membranes. This was due to the
retentate being higher in salt concentration, thus creating less permeate. These values are illustrated in
tables 2,4,5, and 6. The salt mass transfer coefficient (Ks) was generated from figure 6; the pressure and
permeate streams were the most sensitive variables. Lastly, the rejection of salt concentration for the
Reverse Osmosis setup was relatively high in the membrane system indicating good performance of the
system in removing salt.

13. 11
6 References
[1] J. Kucera. Properly Apply Reverse Osmosis. Chemical Engineering Progress. 54, 1997.
[2] EET Corporation and Williams Engineering Services Company, Inc. A Brief Review of Reverse
Osmosis Membrane Technology. 2003
[3] J. Glater. Desalination. 297-309. 1998
[4] What is Reverse Osmosis?
http://puretecwater.com/what-is-reverse-osmosis.html#salt-rejection (Accessed March 1, 2015)
[5] Chau, P.C. Reverse Osmosis with Retentate Recycle. UCSD. 1-6
https://ted.ucsd.edu/bbcswebdav/pid-520234-dt-content-rid-
10306897_1/courses/CENG176A_WI15_Zhang/Lab%20attachments%282%29/RO-recycle.pdf
(Accessed March 1, 2015)
7 Appendices
Table A1: Water Flux ( Jw) vs Pressure Change (dP)
Trials
Qp
(ml/s) dP
(psi) Jw
(g/s-­‐m^2)
1 3.5 50 36.20412298
2 4.93 75 50.99609322
3 4.17 94.3 43.13462652
4 3 50 31.03210541
5 4.17 75 43.13462652
6 5.83 94.3 60.30572484
7 3.83 94.3 39.61765457
8 3.67 94.3 37.96260895

14. 12
Table A2: Flux of salt (Js), Rejection Coefficient of a Single Membrane
Trial Cf
(ppm) Cp
(ppm) Cf-­‐Cp
(ppm)
Qp
(ml/s)
Jw
(g/s-­‐
m^2)
Js (g/s-
m^2)
Rejection
Coefficient
2 3546 325 3221 1.9 19.6477
6062
3 3546 498 3048 0.84 8.68637
8378
6398.318
838
0.908347434
4 4666 608 4058 3.1 32.0568
7259
4334.485
403
0.859560068
Average
19529.63
781
0.869695671
0.879201057
Table A3: Osmotic Pressure Difference
Trial Cf-­‐Cp
(ppm) dπ
(psi)
2 3221 -­‐193.26
3 3048 -­‐182.88
4 4058 -­‐243.48

15. 13
Table A4: Rejection Coefficients of a Two System Membrane
Trial
dP
(psi) Cf(ppm) Cp1(ppm
)
Cr(ppm) Cp2(ppm) rejection
coefficient
1
rejection
coefficient
2
1 25 4666 363 5218 1402 0.9222031
72
0.7313146
8
2 25 4560 265 4820 0 0.9418859
65
1
3 25 4560 245 4786 2084 0.9462719
3
0.5645633
1
4 26 4570 185 4712 0 0.9595186 1
5 18 9022 960 9130 0 0.8935934
38
1
Table A5: Rejection Coefficient of a Three System Membrane
Trial Cf1
(ppm)
Cf3
(ppm)
Cp1(p
pm)
Cp2
(ppm)
Cp3
(ppm)
Cr
(ppm)
rejection
coefficie
nt 1
reject
ion
coeffi
cient
3
1 9135 7545 3567 4717 4080 6508 0.609523
81
0.459
2445
33
Table A6: Rejection Coefficient of a One System Recycled System
Trial 1 Cf (ppm) Cp1 (ppm) rejection coefficient 1
9152 2704 0.704545455

16. 14
3 March, 2015
TO: Professor A. Drews, PhD
FROM: Group B-4: Brandon Sanchez, Saman Hadavand, Janet Mok, Liliana Busanez
SUBJECT: Technical memorandum regarding Cooling Tower
The purpose of the cooling tower is to apply simultaneous mass & heat transfer in order to construct a
design model for the cooling tower. We will configure the temperature set point of the cooling tower
water reservoir and let the system run until it reaches steady state. After it reaches steady state, we will
record parameters such as the temperatures of the: water inlet and outlet, inlet and outlet air dry bulb, inlet
air wet bulb, water flow rate and humidity at the bottom and top of the tower. Furthermore, we will adjust
the water and air flow rate and water inlet temperature in order to further analyze the effects of reservoir
temperature on the cooling tower. We expect to see the enthalpy of the humid air to increase as the mass
of water to air ratio increases. We also expect an increasing mass flux if the concentration difference
between the absolute humidity and mass ratio at the air-water interface is increasing. If you have any
concerns, please contact us.
Sincerely,
Brandon Sanchez