Transcript
Ryerson University
Department of Chemical Engineering
CHE 415 Unit Operations II
Lab Report
Lab #6
Reverse Osmosis
Experiment Performed on: Tuesday, September 26th, 2006
Report Submitted to:
Dr.
By Group # 4 Section # 011
Members
(Leader)
(Inspector)
(Data Reporter)
Date Report Submitted: Monday, October 2nd, 2006
Marking Scheme
Formatting Answer to all 6 questions in each Report Section / 10
General Appearance; Grammar and Spelling / 5
Complete and Informative Tables and Graphs / 15
Contents Accuracy and Precision of Results / 20
Comparison with Literature Data / 10
Influence of Procedural Design on Results / 10
Logic of Arguments / 20
Sample Calculations / 10
_____
Total: / 100
Table of Contents
Abstract…………………………………………………………………….……3
Objective…………………………………………………………………….4
Introduction..........................................................................................4
Theoretical Background………………………………………….….…...5
Technical Procedure and Schematic Diagram.………………….…...7
Technical Procedure………………………………………….…...7
Schematic Diagram…………………………………………..……8
Results and Discussion………………………………………….….……9
Results………………………………………………………….……9
Discussion……………………………………………………..…...11
6.0 Error Analysis……………………………………………………..….…....13
7.0 Conclusions and Recommendations…….……………………….…...14
Appendix A ? Experimental Observations…………………….…..……..15
Appendix B ? Sample Calculations…………………………………......…16
Appendix C ? Safety Concerns………………………………………….….19
Appendix D ? Sample Information Gathering……………………….……20
Appendix E ? Bibliography…………………….………..…………………...21
Abstract
In this experiment, the performance of a Filtration Concepts Inc. Commercial Tap-Water Reverse Osmosis System Model #TW 1 – 1 / 2 – 120 – 60 was measured, to see if it was in agreement with basic theory of Reverse Osmosis. Basic membrane theory predicts that when permeate mass flow-rate is plotted against (?P-??)*, a straight line passing through the origin is obtained. In this experiment, experimental permeate mass flow rate, nA, and experimental (?P-??) values were plotted to see if it matched the theory predicted trend. The secondary objective of the experiment was to calculate the proportionality constant (KmAmembrane) relating nA and (?P-??). The experimental results reveal that that there are two regions in the chart. In the first region nA is directly proportional to (?P-??); however, in the second region, this proportionality is no longer valid. This unexpected observation can be explained based on the concentration polarization of the solute on the membrane, and will be discussed in greater detail in the report. The proportionality constant (KmAmembrane) was calculated to be 0.0013 kg/s-psi.
* where ?P is the hydraulic pressure difference between the feed and permeate sides of the RO membrane, and ?? is the osmotic pressure difference between the feed and permeate sides of the RO membrane.
1.0 Objective
Membrane theory suggests that when permeate (solvent) mass flow-rate is plotted against (?P-??)*, a straight line passing through the origin is obtained. The objective of this experiment was to use regression analysis to correlate experimental permeate mass flow-rates versus experimental (?P-??) values, using the Filtration Concepts Inc. Commercial Tap-Water Reverse Osmosis System Model #TW 1 – 1 / 2 – 120 – 60, to confirm theoretical expectations. Feed and recycle flow rates were used to control t
A secondary objective of this experiment was to determine the proportionality constant (KmAmembrane) relating permeate mass flow-rate and (?P-??).
* where ?P is the hydraulic pressure difference between the feed and permeate sides of the RO membrane, and ?? is the osmotic pressure difference between the feed and permeate sides of the RO membrane.
2.0 Introduction
Reverse osmosis is a unit operation used to filter and purify liquids, typically drinking water. Reverse osmosis refers to the passage of a solvent, such as water, through a membrane that is permeable to the solvent, but not for the solute (Seader, 1998, pg 755). The purified solvent has a natural tendency to flow to the solute-rich solvent on the opposing side of the membrane by osmosis. This natural flow can be reversed by applying a sufficiently large pressure drop across the membrane so that the flow occurs in a direction opposite to that expected for osmosis (Long, 1995, pg 237). Hence, a reversing of the solvent flow under sufficient pressure allows for the production of a purified liquid through a semi-permeable membrane. Fouling can be reduced by having cross-flow filtration, where the solvent feed is parallel to the membrane. Reverse osmosis with cross flow is the is method used in this experiment.
3.0 Theoretical Background
The mass flux of the solvent on the product-side of the membrane is given by the following equation:
3.1
where Pmembrane is the permeability of the membrane, lmembrane is the thickness of the membrane, ?P is the total pressure drop across the membrane and ?? is the osmotic pressure drop across the membrane (Seader, 1998, pg 758). The ?P must be greater than the ?? for reverse osmosis to occur, and it is this difference in pressures that represents the driving force of reverse osmosis filtration systems.
As mentioned in Equation 3.1, Nsolvent represents the mass flux of the solvent. However, the mass flux of the solvent could also be described as the solvent mass flow rate over the area of the membrane:
3.2
Substituting Equation 3.2 into Equation 3.1 and re-arranging for the nsolvent term yields Equation (3) given as:
3.3
Equation 3.3 can be simplified by introducing the permeance of the membrane, which can be stated mathematically as:
3.4
where the Km is the permeance of the membrane, Pmembrane is the permeability of the membrane and lmembrane is the thickness of the membrane. The permeance (Km), along with the area of the membrane, (Amembrane), are constant values and are dependent on the type of membrane used in the reverse osmosis filtration system (Long, 1995, pg 239).
Substituting Equation 3.4 into Equation (3) and solving for KmAmembrane, Equation 3.5 is as follows:
3.5
Since the permeance and the area of the membrane are not known for the particular semi-permeable membrane used in the experiment, it is possible to theoretically calculate Km Amembrane by graphical plotting nsolvent against (?P-??).
The van’t Hoff’s approximation of osmotic pressure can determine the osmotic pressure for low concentration reverse osmosis operations. The van’t Hoff equation is:
3.6
where vns is the total ion concentration in kmol/m3, R is equal to 8.313 kPa-m3 / (kmol-K) and T is the temperature of the product stream in Kelvins (Perry et al., 1997, pg 22-49).
Using the stated metal concentrations in effluent water from the North Toronto filtration plant from the 2004 Toronto Water Annual Report, the ion concentration in the municipal water source into the reverse osmosis system is approximately 9.613E-06 kmol/ m3. It is assumed that the average effluent water concentration from the North Toronto plant in 2004 is the same as the municipal water ion concentrations used in the experiment in the laboratory. It is also assumed that the municipal water source used as the feed source to the reverse osmosis filtration system is 23oC (or 296K), and that the product stream after filtration contains no ion concentrations. Based on these assumptions, the osmotic pressure difference (??) would be constant at approximately 3.432E-03 psi (see Sample Calculations).
Therefore, plotting nsolvent against (?P-??) should theoretically produce a slope, and that slope on the plot would be the Km Amembrane constant value of the semi-permeable membrane used in the reverse osmosis filtration system in the experiment.
4.0 Technical Procedure & Schematic Diagram
4.1 Technical Procedure
* Before proceeding with the procedure, please read the Ryerson University Laboratory Safety Manual and the Operations Manual from Filtration Concepts Inc.
** Some of the most important technical aspects of the Reverse Osmosis equipment which should be addressed are:
Do NOT close the Inlet Shut-Off Valve while the system is running
Do NOT close the High Pressure Valve completely
Do NOT allow the High Pressure Pump to run dry
Verify that the Reject and Product tubes are connected to the water collection tank.
Verify that the water collection tank is empty to ensure that there is enough space for water collected from the Reject and Product tubes during the experiment.
Open the Inlet Shut-Off Valve all the way counter-clockwise.
Open the High Pressure Valve all the way counter-clockwise.
Turn on the Reveres Osmosis electrical equipment.
Open the municipal water source (the feed source).
Once there is water in the system (check Reject Flow Meter), turn on Pump.
Close the Recycle Valve all the way.
Adjust the High Pressure Valve until reading is 65 psi. Record reading.
Record High Pressure Gauge and Low Pressure Gauge readings. Also record Product Flow Meter reading and Reject Flow Meter reading.
Try to move the High Pressure Valve slightly clockwise for a pressure increase of 10 psi in the High Pressure Gauge reading. If necessary, open the Recycle Valve and set to a variable opening to modulate the High Pressure Gauge reading for a uniform increase of 10 psi.
Repeat steps 10 and 11 until High Pressure Gauge reads 115 psi.
Open the High Pressure Valve all the way counter-clockwise to prevent over-pressurization.
Turn off Pump.
Shut off municipal water source completely.
Turn off Reverse Osmosis electrical equipment.
Drain water collection tank; also keep Reject and Product tubes in tank for any dripping of water.
4.2 Schematic Diagram
Figure 4.1: The below diagram illustrates the flow diagram of the reverse osmosis equipment used in this particular experiment only.
Water tank
Pressure gauge for municipal water source Purple Line - Water Source
Valve for municipal water Green Line – Feed Stream
Motor Red Line – Product Stream
High Pressure Pump Blue Line- Reject Stream
Inlet Shut-Off Valve Dashed Line – Recycle Stream
Pre-Filter
Semi-permeable membrane
Recycle Valve
High Pressure Gauge
High Pressure Valve
Low Pressure Gauge
Product Flow Meter
Water collection tank
5.0 Results and Discussion
5.1 Results
In this section, all experimental results and findings are outlined. All calculation techniques used to obtain results are also described.
In order to satisfy the objectives two major steps were necessary,
Plot the mass flow rate of solvent through the membrane (nsolvent), against the difference between the hydraulic pressure differential and the osmotic pressure differential; denoted as (?P-??) or net driving pressure differential.
Use linear regression with the plot to determine if nsolvent (?P-??) for some particular region. This is based on rearranging Equation 3.5 from the theory section seen bellow in terms of nsolvent:
3.5
According to theory the is a proportionality constant for the particular membrane system. Therefore nsolvent should be proportional to (?P-??) according to this equation.
To calculate the nsolvent the volumetric flow rates given in table __ in appendix X, was converted to a mass flow rate by assuming a density of 1000kg/m3 and using the necessary conversion factors to obtain values in kg/s. A sample calculation is included in appendix.
Sample calculation 3 in appendix Y explains how the (?P-??) is calculated. The same sample calculation calculates the proportionality constant for reading #2.
The summary of the calculated data is given below in Table 5.1. The data given in the first line of the table is predicted by equation 3.5, that is, the nsolvent is “0” when ?P-?? is “0”. See equation 3.5 for clarification.
Table 5.1: Calculated (?P-??) and nsolvent
Figure 5.1 below is a plot of the data from Table 5.1 where the nsolvent is plotted against the (?P-??). The data is separated into two regions to aid in the discussion section.
Figure 5.1: Solvent flow rate versus net driving pressure differential
5.2 Discussion
Figure 5.2 below expands region 1, and models the data by regression to get an equation of the line
Figure 5.2: Linear regression of Figure 5.1. Solvent flow rate versus net driving pressure differential
As can be seen the data in figure 5.2 is represented well by a linear regression having a R2 value of 0.9983. The equation of the line was found to be nsolvent = 0.0013(?P-??).
As can be seen in figure 5.1 in the results section the data in region 1 including the theoretical data point at (nsolvent , ?P-??) = (0,0) follows the general trend predicted by equation 3.5 where nsolvent (?P-??). Figure 5.2 further expands upon this theory by using a linear regression to obtain the equation of the line. The equation of the line was given as nsolvent = 0.0013(?P-??) which is analogous to equation 3.5. Comparing terms in equation 3.5 to the equation of the line it can be seen that for this data in region 1 the proportionality constant is 0.0013 (kg•s-1•psi-1). This constant is specific for this system and can be used to calculate the solvent flow rate for the domain of (?P-??) from 0 to 50psi; anything higher than 50psi will not necessarily follow this equation.
The experimental value of which was found to be 0.0013 (kg•s-1•psi-1) is the product of membrane permeability and area. This value is a function of the membrane properties, the particular solvent passing through the membrane, and the specific solutes fed to the system.
The data in region 2 represents data that deviates from the predicted theory and represents a condition where nsolvent is not proportional to the (?P-??). This may be explained by a phenomenon common to reverse osmosis membranes called concentration polarization.
Concentration polarization occurs as permeate flux and therefore flow rate of solvent through the membrane increases and there is an increased rate of salt depositing at the membrane. The salt forms a boundary layer along the feed side of the membrane; thus, the salt concentration on the feed side of the membrane is higher then the bulk concentration in the feed. This has two effects which directly pertain to the observed deviation of the data. The first is that the net driving pressure denoted as (?P-??) decreases because the osmotic pressure differential term increases; since the osmotic pressure is dependent on the concentration of salt at the membrane surface. Second the net driving pressure decrease results in a reduced solvent flow rate; according to equation 3.5. (www.membranes.com)
6.0 Error Analysis
Aside from the original assumption regarding the origin of the TDS in Toronto water; the osmotic pressure assumption used in this experiment is only valid if there is perfect mixing between the feed and reject streams and no concentration gradient is exists across the length of the membrane tube. This is especially important because the recycle was needed to obtain the necessary hydraulic pressures on the feed side. If the recycled reject stream had a higher TDS then the feed stream then the osmotic pressure would not be the constant for any changes made to the recycle valve during the experiment. Unfortunately there is no way to measure the entering concentration.
The flow meter used in the experiment for the product stream had graduations every 3.0 LPM, where as most flow changes that occurred where observed to be on the order of 0.1-0.3 LPM. This meant that the flow rates were estimated between these graduations. A higher precision flow meter with more divisions to the graduations is necessary for the expected changes in product flow rate.
7.0 Conclusions and Recommendations
It was found by use of linear regression that for the domain of (?P-??) 0 to 50psi the solvent flow rate through the membrane is proportional to the net driving pressure; that is, nsolvent = 0.0013(?P-??). The equation of the line was deemed to be reasonable given and R2 value of 0.9913. It was observed that for pressure readings above 50 psi that nsolvent (?P-??) was not valid. This was explained by use of concentration polarization theory, which predicts that a boundary layer of high concentrated salt will form along the membrane at ever increasing solvent flow rates through the membrane.
To prevent concentration polarization the most common solution is to increase the feed rate. Unfortunately the feed rate could not be increased much further for this experiment; future experiments may add a larger variable feed line to decrease the rate of concentration polarization. The increased feed rate increase the turbulence in the feed side region of the membrane preventing the build up of the boundary layer; net effect being an increase in the range for which solvent flow rate is proportional to the net driving pressure.
Main sources of error included; having to use the recycle with an unknown TDS concentration, and secondly measurement error associated with inadequate flow meters. The first can be address by adding a larger variable feed this way the pressure may be brought higher on the feed side without the recycle. The second error source would be addressed by replacing the flow meter gauge with a higher precision device.
Appendix A
Appendix B
Sample Calculations
1. Osmotic pressure calculation for feed side
Using van’t Hoff approximation for osmotic pressure,
(6)
(Perry et al., 1997, pg 22-49)
From table of concentrations (source below), the total is 9.61329E-06 kmol/m3
T(oC) = 23oC
T(K) = (23 + 273)K = 296K
R = 8.313 kPa-m3 / (kmol-K)
Therefore,
Table 1: Concentrations of common ions in Toronto Water
Metal mg/L* MW (g/mol) kmol/m3
Arsenic 0.001 74.92159 1.33473E-08
Cadmium 0.0001 112.411 8.89593E-10
Chromium 0.003 51.9961 5.76966E-08
Copper 0.016 63.546 2.51786E-07
Iron 0.47 55.847 8.41585E-06
Mercury 0.00001 200.59 4.98529E-11
Nickel 0.003 58.6934 5.11131E-08
Lead 0.012 207.2 5.79151E-08
Zinc 0.05 65.39 7.64643E-07
Total (mg/L or ppm) 0.5551 Total conc. of ions (kmol/m3) 9.61329E-06
(*Toronto Water, Toronto Water Annual Report 2004, City of Toronto, 2004, Canada: pg 48)
2. Conversion of volumetric flow rate of solvent to mass flow rate (data from reading # 2)
, where is the volumetric flow rate.
, assumed to be water since TDS is assumed to be small
=0.06kg/s
3. Product of permeance and area (Using data from reading # 2)
*See Theory in Inspector’s Pre-Lab for the development of equations in more detail.
(1)
(Seader, 1998, pg 758)
Since,
Substitution and rearranging yields
,
Since, (5)
(Long, 1995, pg 239)
Therefore substitution and rearranging yields,
, (concentration low in product at 96-98% salt rejection according to manual)
Lastly,
Appendix C
Safety Concerns
Inspect the floor for any water spills/leakage before and during the experiment.
Wear protective eye gear when reading gauges and flow meters.
Do NOT close the High Pressure Valve completely; over-pressurization can damage the system and could cause a safety concern.
Always monitor the High Pressure Gauge and do not allow it to exceed 130 psi.
In case of a fire alarm:
Turn-off the Pump
Turn-off the electrical control equipment
Shut-off the municipal water source using the valve
6. At least two people should be present to attend to the equipment at any moment of the experiment.
Environmental Concerns
No dangerous chemicals are used in this experiment.
Appendix D
Appendix E
Bibliography
Long, R.B., Separation Processes in Waste Minimization, Marcel Dekker, New York, N.Y., USA, 1995.
Perry, R.H., Green, D.W., Perry’s Chemical Engineer’s Handbook (7th Edition), McGraw-Hill,
United States, 1997.
Seader, J.D., Separation Process Principles, J. Wiley, New York, N.Y., USA, 1998.
Toronto Water (Agency), Toronto Water Annual Report 2004, City of Toronto, Canada, 2004.
_www.membranes.com_ (see attached PDF)
2
2
