summary · web viewq ip = volumetric flow rate of species i in the permeate in m3/minρ =density of...

Air Membrane Separation University of Illinois

Membrane Air Separation

In this lab two membranes are used to separate oxygen from nitrogen in air. The two separators are used in series and in parallel to see which set-up will

result in the best separation.

1Unit Operations ChE 382 Group 5 Spring 2011 5/7/2023Damo, Duffy, Guerrero, Hsu, Kosak, Qamar, Tyska


Final Lab Report

Unit Operations II Lab 6

May 7, 2023

Group 5

Andrew Duffy

Daniyal Qamar

Jeff Tyska

Bernard Hsu

Ryan Kosak

Tomi Damo

Alex Guerrero



Contents1. Summary.............................................................................................................................................4

2. Results.................................................................................................................................................5

3. Discussion..........................................................................................................................................11

4. Conclusion.........................................................................................................................................14

5. References.........................................................................................................................................14

6. Appendix I: Data Tabulation/Graphs.................................................................................................15

7. Appendix II: Error Analysis.................................................................................................................21

8. Appendix III: Sample Calculations......................................................................................................24

9. Appendix IV: Individual Team Contributions.....................................................................................27



1. Summary

In this lab the goal was to find the effect of pressure and different configurations of membranes on

the separation of air into its constituent components. For the configurations, two membranes were set

up in parallel and in series. The air was approximated as a mixture of only nitrogen and oxygen. From

the data in this lab, it can be concluded that increasing the pressure increases the amount of separation

in the cylinders, and that a series configuration works better than a parallel one.

For both the parallel and series trials, the concentration of oxygen in the air through the membrane

increased in each trial (as can be seen in table 1). This makes sense since there shouldn’t be a high

enough of an oxygen concentration to create a boundary layer on the membrane. Since there is no

boundary layer, the diffusion of oxygen through the layer increases when pressure is increases. This

trend occurs in both configurations because the exact configuration of the membrane does not matter;

only the concentration of oxygen at the surface does (concentration at the boundary layer).

The series configuration was found to separate the oxygen from the nitrogen better than the parallel

configuration, which also makes sense. In the parallel configuration, all of the air only sees one

membrane, and thus is only separated once. With the series configuration, the air is separated twice,

and thus there is a better separation. This can be seen in table 1, where the concentration of oxygen in

the concentrated stream is, on average 0.5% higher. Similarly, the concentration of oxygen in the

retentate stream is about 1.4% higher (on average) in the parallel configuration.

These conclusions are also backed by our other data and calculated values. The density of oxygen

and nitrogen different (oxygen is heavier), and the trends in concentration with configuration and

pressure can also be seen in the pressure data. Similarly, the flow rates of oxygen in the permeate were



also calculated. As expected, the flow rates of oxygen in the permeate increased when pressure was

increased, and they were higher in the series configuration than the parallel configuration.

Overall this lab went very well, and the data consistently supported the conclusion that the series

configuration separated the oxygen from the nitrogen better than the parallel configuration, and the

higher pressures resulted in higher oxygen concentrations in the permeate.

2. Results

The solubility of the particular gas being separated from air depends on its solubility in the

separating membrane. Calculations were made to determine the flux of the air through the membranes,

the diffusivity of Oxygen through the membrane, the solubility of Oxygen in the membrane, the

permeability of the membrane, the separation factors, the recoveries, and the stage cuts.

Most of these properties increase as the pressure of the incoming air increases. An increase in

pressure also dictates to an increase in the amount of oxygen and nitrogen coming through the

membranes. As pressure increases, the flux, diffusivity, permeability, and separation factors all increase

as well. The following graphs and data help visualize these properties better:



Flux vs Pressure

0.600

0.650

0.700

0.750

0.800

0.850

0.900

0.950

1.000

90 95 100 105 110 115 120 125

Pressure (psi)

Flux

(g/m

2-m

in)

Parallel

Series

Figure 1: Flux vs. Pressure

Figure 1 makes it clear that as the inlet pressure of the gas increases the flux increases as well.

As pressure was increased from 100 to 122 psi the flux increased from 0.718 to 0.955 g/m2min for

parallel configuration and from 0.741 to 0.965 g/m2min for series configuration. The errors were

relatively low for the flux ranging in ±0.01 g/m2min to 0.001. These errors were relatively low for the flux

ranging in ±0.01 g/m2min. The flux for the parallel configuration is lower since the force is divided into

two separators instead of a single pass. The flux was obtained from the inlet flow of the air and the area

of the membrane, the appendix I and III have detailed calculations on flux.



Diffusivity vs Pressure

0.00150

0.00170

0.00190

0.00210

0.00230

0.00250

0.00270

0.00290

90 100 110 120 130

Pressure (psi)

Diffu

sivity

(m2/

min

)

Parallel

Series

Figure 2: Diffusivity vs. pressure

Diffusivity is the area per time the component (oxygen in this case) covers, as pressure increases

there is a bigger driving force and more area is covered in less time. Figure 2 shows the graph of

diffusivity of oxygen vs pressure. As the pressure increases the driving force of oxygen through the

membrane also increases and thus there is a higher diffusivity. Since the concentration of oxygen is

lower in the series configuration (more membrane area to go through) the diffusivity in the series

configuration is lower. The error was in the ±10-4 m2/min range which is low for the given diffusivities.

The diffusivity was obtained from the oxygen flux and concentrations from the inlet and outlet flows.



Solubility Constant vs Pressure

4.00E-05

4.20E-05

4.40E-05

4.60E-05

4.80E-05

5.00E-05

5.20E-05

5.40E-05

70 80 90 100 110 120 130

Pressure (psi)

Solu

bilit

y (m

ol/P

a-m

3)

Parallel

Series

Figure 3: Solubility vs. Pressure

At first glance figure 3 seems unusual since solubility of gasses increase as pressure increases

according to Henry’s law. But if the units are looked at more closely the solubility is expressed in

mol/m3Pa. As the pressure increases it has a decreasing affect on the solubility. If the same data is

expressed in mol/m3 units, then solubility decreases as the pressure increases. The parallel and series

configuration have the similar solubilities of oxygen since pressure and concentration have very little

affect on solubility. The material has a certain affinity towards oxygen and that stays constant for each

configuration. The errors were in the ranges of ±10-6 mol/Pa m3, this number seems pretty high but it is

acceptable.



Permeability per thickness vs Pressure

1.020E-07

1.040E-07

1.060E-07

1.080E-07

1.100E-07

1.120E-07

1.140E-07

1.160E-07

1.180E-07

95 100 105 110 115 120 125

Pressure (psi)

Perm

eabi

lity

(mol

/Pa-

min

-m4)

Parallel

Series

Figure 4: Permeability vs. Pressure

The permeability also increases with increasing pressure as figure 4 shows. Permeability is the

amount of gas that passes through the membrane. As the driving force (pressure) increases the

permeability increases as well since more oxygen goes through the membrane. Since Permeability =

Diffusivity X Solubility, and the solubility is inversely proportional with pressure. Since the pressure in

the parallel configuration is lower, a higher permeability is observed. The values increase from 1.101E-

07 to 1.169E-07 for the parallel configuration and from 1.049E-07 to 1.111E-07 for the series

configuration as the pressure is increased from 100 to 122 psi. The permeability was obtained from the

solubility and the diffusivity both of which were obtained using the concentrations and the flow rates of

oxygen and air. Appendices I and III provide details over these calculations



Separation Factor vs Pressure

1.000

2.000

3.000

4.000

5.000

6.000

7.000

8.000

9.000

95 100 105 110 115 120 125

Pressure (psi)

Parellel alpha prime

Parallel alpha double prime

Series alpha prime

Series alpha double prime

Figure 5: Separation Factors vs. Pressure

Figure 5 shows the separation factors vs. pressure, this is the ratio of the amounts of oxygen in

the permeate and the retentates. Since the final concentration of oxygen is lower in the series

configuration (double pass) the separation factors are higher (higher separations). The series prime data

is the ration of the oxygen concentrations in the permeate and feed streams. Most of the errors were in

the ±0.1 range for alpha prime and ±0.01 for alpha double prime.



Recovery and Stage Cut vs Pressure

0.400

0.500

0.600

0.700

0.800

0.900

1.000

70 80 90 100 110 120 130

Pressure (psi)

O2 Rec. Parallel

N2 Rec. Parallel

Stage Cut Parallel

O2 Rec. Series

N2 Rec. Series

Stage Cut Series

Figure 6: Recovery/Stage Cuts vs. Pressure

Figure 6 shows the recoveries and stage cuts of oxygen in both the configurations of membrane

separators. As the pressure is increased the recovery increases as well, more of the oxygen is driven

through the membrane. The stage cuts are also shown in the graph and they increase as pressure

increases as well. The recovery is the amount of oxygen separated from the feed stream and the cut is

the amount of permeate per the amount of air fed. The errors for recovery were in the ±0.01 range

while the error for cuts were in the ±1 range which is relatively high.

3. Discussion

As can be seen in Figure 1 the flux vs. pressure is linear for both configurations, yet the fluxes for the

series configuration are larger than those in the parallel configuration. As stated before in the

anticipated results, this outcome was expected. It was a reliable assumption, because in the series

configuration the air will be passing through two different membranes, one after the other resulting in a

lower pressure drop (higher separation). This differs in the parallel configuration, where the air stream



will be split into two and each stream will pass through the membranes only once, thus leading to a

higher pressure drop (less separation). So the flux for the parallel configuration is lower since the

pressure is divided into two separators instead of a single two pass.

The solubilities were also calculated for each component. With the units of solubility expressed

in mol/m3Pa it can be seen that as the pressure increases, there is a decreasing affect on the solubility.

Given the fact that the solubility constants are inversely related to the pressure drop, it was reasonably

assumed that the solubility constants for both components would be higher in the parallel configuration

compared to the series configuration. This is because as stated before, the pressure drop is higher for

the parallel configuration as opposed to the series. The parallel and series configuration have the similar

solubilities of oxygen since pressure and concentration have very little affect on solubility. *Note that

since the change in pressure was kept the same for both configurations in which Figure 3 depicts the

solubilities being the same for both configurations. Although, if the change in pressures were varied the

new figure would depict the solubility being lower for the parallel configuration than in series, for the

reasons stated above.

With this information it was reasonably assumed that the diffusivity for each component would

be higher in the parallel configuration as opposed to the series since it was confirmed the solubility is

lower for the parallel configuration. In addition, as the pressure increases the driving force of oxygen

through the membrane also increases and thus there is a higher diffusivity. Since the concentration of

oxygen is lower in the series configuration – due to more membrane area – the diffusivity in the series

configuration is lower. As can be seen in Figure 2 these reasonable assumptions were confirmed.

Lastly, the permeability of each component was calculated. Permeability is the product of

diffusivity and solubility, with the solubility being inversely proportional with pressure. As stated

previously, since the pressure in the parallel configuration is lower, a higher permeability was observed.



The compiled results show that permeability also increases with increasing pressure as seen in Figure 4.

Since permeability is a measurement of the amount of gas that is passed through the membrane it was a

reasonable assumption that as the pressure (driving force) increases, the permeability will increase as

well since more oxygen will permeate through the membrane.

Given the fact that the measuring devices in this lab were extremely accurate the errors in the

measured values were very minimal. The most probable source of experimental error involved the

oxygen analyzers. After calibrating the two sensors, they still differed by around 0.3 from each other

despite them measuring the same air. With this error propagating throughout the rest of the lab there

were a few areas where this experimental error affected the ability to draw conclusions. This was

notable with the solubility constant for oxygen, which had a big error (57.5%) associated with it. This can

be attributed to the fact that the solubility constant for oxygen is directly proportional to the

concentration of oxygen inside the membrane wall, which was measured with the oxygen analyzers that

were not reading the same values. Due to the differing oxygen readings, the pressure of oxygen per

thickness, α'O2, N2, and α''O2, N2 yielded high average errors. This is again because these values were

defined in terms of mole fractions – which were calculated from the oxygen analyzers that measured

concentrations in mole percent. These errors would have significantly been reduced if both oxygen

analyzers were calibrated to both read the same exact volume percent of oxygen and not starting the

lab until this occurred. This way the values measured with the oxygen analyzers would have fewer

experimental error associated it.

Definitive conclusions that could be made are that the values for flux, diffusivity, and

permeability will increase as pressure increases, and solubility constants will decrease as pressure

increases. For all these values the permeability and diffusivity for the parallel configuration should be

higher than the series configuration. This is due to the fact the solubility constant will be lower as



pressure increases, and also because in the series configuration the air will be passing through two

different membranes, one after the other resulting in a lower pressure drop, rather than in the parallel

configuration, where the air stream will be split into two and each stream will pass through the

membranes only once, thus leading to a higher pressure drop.

4. Conclusion

In this lab the goal was to find the effect of pressure and different configurations of membranes on

the separation of air into its constituent components. For the configurations, two membranes were set

up in parallel and in series. The air was approximated as a mixture of only nitrogen and oxygen. From

the data in this lab, it can be concluded that increasing the pressure increases the amount of separation

in the cylinders, and that a series configuration works better than a parallel one.

For both the parallel and series trials, the concentration of oxygen in the air through the membrane

increased in each trial (as can be seen in table 1). This makes sense since there shouldn’t be a high

enough of an oxygen concentration to create a boundary layer on the membrane. Since there is no

boundary layer, the diffusion of oxygen through the layer increases when pressure is increases. This

trend occurs in both configurations because the exact configuration of the membrane does not matter;

only the concentration of oxygen at the surface does (concentration at the boundary layer).

The series configuration was found to separate the oxygen from the nitrogen better than the parallel

configuration, which also makes sense. In the parallel configuration, all of the air only sees one

membrane, and thus is only separated once. With the series configuration, the air is separated twice,

and thus there is a better separation. This can be seen in table 1, where the concentration of oxygen in



the concentrated stream is, on average 0.5% higher. Similarly, the concentration of oxygen in the

retentate stream is about 1.4% higher (on average) in the parallel configuration.

These conclusions are also backed by our other data and calculated values. The density of oxygen

and nitrogen different (oxygen is heavier), and the trends in concentration with configuration and

pressure can also be seen in the pressure data. Similarly, the flow rates of oxygen in the permeate were

also calculated. As expected, the flow rates of oxygen in the permeate increased when pressure was

increased, and they were higher in the series configuration than the parallel configuration.

Overall this lab went very well, and the data consistently supported the conclusion that the series

configuration separated the oxygen from the nitrogen better than the parallel configuration, and the

higher pressures resulted in higher oxygen concentrations in the permeate.

5. References

W.E. McCabe, J.C. Smith, and P. Harriott 2001. Unit Operations of Chemical Engineering, McGraw Hill, New York.



6. Appendix I: Data Tabulation/Graphs

Membrane Separation

RunTank Outlet

(psig)Gauge Outlet

(psig)FM1

(SLPM)FM2

(SLPM)O2 Sensor

1O2 Sensor

2Run 1 || 140 122 6.13 11.4 7.4 34.5Run 2 || 140 110 5.47 9.95 7.2 33.7Run 3 || 140 100 5 8.98 7.2 33

Run 4 -- 140 122 6.06 11.41 6 34.8Run 5 -- 140 110 5.46 10.05 5.7 34.1Run 6 -- 140 100 4.95 9 6 33.9

tube side 1 = Nonpermeate

shell side 2= Permeate

|| = parallel

-- = seriesslpm=standard liters per minute

Table 1

RunΔP

(psi)Jo2 (g/m2-

min)DO2/L

(m2/min) ΔP (psi)SO2 (mol/Pa-

m3) PO2/L (mol/Pa-min-m4)Run 1 || 122 0.955 0.00265 122 4.41E-05 1.169E-07Run 2 || 110 0.814 0.00231 110 4.84E-05 1.116E-07Run 3 || 100 0.718 0.00209 100 5.26E-05 1.101E-07

Run 4 -- 122 0.965 0.00252 122 4.41E-05 1.111E-07Run 5 -- 110 0.832 0.00220 110 4.84E-05 1.065E-07Run 6 -- 100 0.741 0.00199 100 5.26E-05 1.049E-07

Table 2



Run α'O2,N2 α''O2,N2

ΔP (psi)

O2 Recovery

N2 Recovery

Stage cut

Run 1 || 6.591 1.981 122 1.068 0.410 0.650Run 2 || 6.551 1.912 110 1.035 0.417 0.645Run 3 || 6.348 1.853 100 1.009 0.420 0.642

Run 4 -- 8.362 2.008 122 1.082 0.413 0.653Run 5 -- 8.561 1.947 110 1.052 0.420 0.648Run 6 -- 8.035 1.929 100 1.041 0.422 0.645

Table 3

Flux vs Pressure Drop

0.600

0.650

0.700

0.750

0.800

0.850

0.900

0.950

1.000

70 80 90 100 110 120 130

Pressure Drop (psi)

Flux

(g/m

2-m

in)

Parallel

Series

Figure 7



Diffusivity per thickness vs Pressure Drop

0.00150

0.00170

0.00190

0.00210

0.00230

0.00250

0.00270

0.00290

70 80 90 100 110 120 130

Pressure Drop (psi)

Diffu

sivity

(m2/

min

)

Parallel

Series

Figure 8

Solubility Constant vs Pressure Drop

4.00E-05

4.20E-05

4.40E-05

4.60E-05

4.80E-05

5.00E-05

5.20E-05

5.40E-05

70 80 90 100 110 120 130

Pressure Drop (psi)

Solu

bilit

y (m

ol/P

a-m

3)

Parallel

Series

Figure 9



Permeability per thickness vs Pressure Drop

1.020E-07

1.040E-07

1.060E-07

1.080E-07

1.100E-07

1.120E-07

1.140E-07

1.160E-07

1.180E-07

70 80 90 100 110 120 130

Pressure Drop (psi)

Perm

eabi

lity

(mol

/Pa-

min

-m4)

Parallel

Series

Figure 10

Separation Factor vs Pressure Drop

1.000

2.000

3.000

4.000

5.000

6.000

7.000

8.000

9.000

70 80 90 100 110 120 130

Pressure Drop (psi)

Parellel alpha prime

Parallel alpha double prime

Series alpha prime

Series alpha double prime

Figure 11



Recovery and Stage Cut vs Pressure Drop

0.400

0.500

0.600

0.700

0.800

0.900

1.000

70 80 90 100 110 120 130

Pressure Drop (psi)

O2 Rec. Parallel

N2 Rec. Parallel

Stage Cut Parallel

O2 Rec. Series

N2 Rec. Series

Stage Cut Series

Figure 12



7. Appendix II: Error Analysis

Measuring Device Uncertainty in MeasurementPressure Sensor ± 1 PSIGDigital Oxygen Sensor ± 0.1 PercentFlow meter ± 0.1 SLPM

Three main sources of instrumental error were present for this experiment. The pressure

sensors, digital oxygen sensor, and flowmeters were used to measure the values needed in

determining calculations. These instruments are both accurate and easy to read. The Digital

Oxygen Sensor was calibrated before use however; there was some error present in the

calibration. After exposing the sensors to the ambient air they both read about 21% oxygen but

the two sensors differed by around 0.3 from each other despite them measuring the same air. The

pressure sensors and flow meters did not need calibration. As always there was also the

possibility of human error present caused my misreading the indicators or by calculation error.

Other than those sources of error this lab was done relatively accurately. This was mostly due to

the fact that there were few measurements needed and the instruments used were accurate and

easy to operate.

Error Analysis Table IRun Jo2 (g/m2-min) QO2 (SLPM) QO2 (NLPM) QO2 ([N]-m3)/min ρP (kg/m3)

Run 1 ||

0.012516 0.005085 0.010170 0.000086 0.012430

Run 2 ||

0.008210 0.003342 0.006685 0.000048 0.008161

Run 3 ||

0.102772 0.041909 0.083818 0.000533 0.102239

Run 4 --

0.011820 0.004800 0.009599 0.000082 0.011738

Run 5 --

0.008814 0.003586 0.007172 0.000053 0.008762



Run 6 --

0.105955 0.043148 0.086295 0.000565 0.105390

Analysis of error from Table I: The diffusive flux calculated using Fick’s Law produced an

average error of 4.98%. The volumetric flow rate of oxygen exiting the oxygen rich stream

produced an average error of 4.9%. The density of the permeate produced an average error of

3.39%

Overall the error present in this experiment is very low. There are relatively few numbers

of measurements taken during this lab and the equipment used is accurate. The density of the

permeate stream depends only on the measurement obtained from O2 sensor 2. This sensor was

calibrated before the lab was conducted and has an error of ± 0.1% associated with it. The

volumetric flow rate of oxygen depends on O2 Sensor 2 and Flow Rate 2. Flow Meter 2 had an

error of ± 0.1 SLPM .The diffusive flux depends on the previous two calculations and the

thickness of the membrane (provided by the manufacture) therefore the only measurable point of

error would be O2 Sensor 2.

Error Analysis Table IIRun Cin,1 (mol/m3) FM1

(NLPM)Cin,2 (mol/m3) FM2

(NLPM)DO2/L (m2/min) pO2 (Pa) SO2 (mol/Pa-

m3)Run 1

||N/A N/A N/A N/A 5.35579E-05 0.888004207 5.1047E-06

Run 2 ||

N/A N/A N/A N/A 4.0375E-05 0.72 3.8809E-06

Run 3 ||

N/A N/A N/A N/A 0.001759024 7.200473405 7.4394E-05

N/A N/A N/A N/A N/A N/A N/A N/A

Run 4 --

N/A N/A N/A N/A 4.82228E-05 0.720011675 6.2882E-06

Run 5 --

N/A N/A N/A N/A 2.1328E-05 0.570012272 2.9753E-06

Run 6 --

N/A N/A N/A N/A 0.001721844 6.000394505 7.4394E-05



Analysis of error for Table II: The pressure of oxygen in the nitrogen rich stream produced an

average error of only 0.005%. The Solubility Constant for oxygen had an average error 57.5%

associated with it. The Diffusivity of oxygen per thickness of the membrane yielded an error of

26.5%.

Both the pressure of oxygen in the nitrogen rich stream and the Solubility Constants of

oxygen were dependent of the measurements taken from O2 Sensor 1 and the outlet pressure

gauge. These two pieces of equipment have errors of ± 0.1% and ± 1 PSIG respectively. The

Diffusivity of oxygen per thickness of the membrane depends on O2 Sensor 1, O2 Sensor 2, and

Flow Meter 2. The error in these instruments is stated above.

Error Analysis Table IIIRun PO2/L (mol/Pa-min-

m4)α'O2,N2 α''O2,N2 O2

RecoveryCN2,r

(mol/m3)N2

RecoveryStage Cut

Run 1 ||

1.8824E-08 0.24854628 0.05193083 0.21596665 N/A 0.07749319 0.13059018

Run 2 ||

1.42401E-08 0.15265225 0.04455491 0.13290789 N/A 0.04916656 0.08172921

Run 3 ||

1.5564E-07 9.5194518 2.06543431 8.30990503 N/A 3.45872448 5.24896362

Run 4 --

1.75806E-08 0.46029265 0.04578146 0.19672683 N/A 0.06936061 0.1179853

Run 5 --

1.36579E-08 0.45490829 0.01285494 0.14820561 N/A 0.05578717 0.09119116

Run 6 --

1.48361E-07 12.0979024 2.16826296 8.58095947 N/A 3.47871539 5.27634161

Analysis of error for Table III: The error calculated from the values in Table III was much

higher than that of the previous two tables. Pressure of Oxygen per thickness, α'O2, N2, and

α''O2, N2 produced average errors of 55.7%, 51.6%, and 37.7% respectively. The other three

values in the table yielded errors of over 100%.



8. Appendix III: Sample Calculations

All sample calculation values are sampled from trial 1 of the parallel separation, the rest are identical.

Known Values:A 2.7 m2

ρO2 1.331 kg/m3

ρN2 1.165 kg/m3

MW-O2 32 g/molMW-N2 28 g/mol

Total Flux:

Jo2=Qo2 ρnA

Where:Qip = Volumetric flow rate of species i in the permeate in m3/minρ =Density of permeate in kg/m3

A = Area of membrane, (in this case 2.7m2 per module)n = Number of modules used, (in this case 2)

0.955 ( g/m2 min) = 0.00422 ( m3/min) * 1.22 (kg/m3) * 1000 (g/kg) / 2 * 2.7 (m2)

Diffusivity Flux:Di

L=

J i(C¿ 1−C¿ 2)

Where:Ji = Flux of component i in grams/m2 minDi = Diffusivity of component i in m2/minL = Thickness of membrane in metersCin1 = Concentration of component i inside membrane wall on feed side in mol/m3

Cin2 = Concentration of component i outside the membrane wall on permeate side in mol/m3

0.00264 ( m2/min) = 0.955 ( g/m2 min) / 32 ( g/mol) * ( 14.34 – 3.07 ) (mol/m3)

Henry’s Law:Cℑ=Si p i

Where:Cim = Concentration of component i inside the membrane wall in mol/m3 Si = Solubility constant for component i in the membrane in mol/m3Papi = Partial pressure of component i in the gas phase in Pa



3.07 ( mol/m3) = 4.41X10^-5 ( mol/Pa m3) * 69736.19 ( Pa)

Permeation:Pi=DiS i

Where:Pi = Component i membrane permeability in mol/m3sPaDi = Diffusivity of component i in m2/sSi = Solubility constant for component i in the membrane in mol/m3Pa

1.11X10^-7 (mol/Pa min m4) = 0.00264 ( m2/min) * 4.41X10^-5 ( mol/Pa m3)

Separation Efficiency:

α ij=PiP j

Where: αij = Separation factor Pi = Component i membrane permeability in mol/m3sPa

Based on feed composition

1.98 = ( 34.5 / 65.5 ) * ( 0.79/0.21 )

Recovery:

O2Recovery=Q pCO2 p

Qf CO2 f

Qp = Volumetric flow rate of permeate in m3/sQf = Volumetric flow rate of feed in m3/sCO2f = Molar concentration of oxygen in feed in mol/m3

CO2p = Molar concentration of oxygen in permeate in mol/m3

CN2f = Molar concentration of nitrogen in feed in mol/m3

CN2r = Molar concentration of oxygen in permeate in mol/m3

1.06 = ( 12.23 / 6.57 + 12.23) * ( 14.35 * 32 / 0.21 * 1.33 * 1000)

Stage Cut:

STAGECUT=Qp

Qp+Qf

Where: Qp = Volumetric flow rate of permeate in m3/sQf = Volumetric flow rate of feed in m3/s



0.65 = 12.23 / ( 6.57 + 12.23)

Error Sample:

Relationship between Z and (A,B)

Relationship between errors ΔZ and (ΔA,ΔB)

ΔZ

Z=A+BZ = A-B

(ΔZ)2 = (ΔA)2 + (ΔB)2 ∆ Z=√(ΔA )2+(ΔB)2

Z=A*BZ= A/B

(ΔZ/Z)2 = (ΔA/A)2 + (ΔB/B)2

∆ Z=(√( Δ AA )2

+( ΔBB )2)×Z

Z=An ΔZ/Z = n * ΔA/A ∆ Z=n×∆ AZ × A

Z= Ln(A) ΔZ = ΔA/A ∆ Z=∆ AA

Z= exp(A) ΔZ/Z = ΔA ∆ Z=Z×∆ A

An example of error is given using trial 1 parallel for finding the error in the oxygen flux , JO2.

E JO2 = E QO2 + E ρO2

0.012 = 0.000086 + 0.0124



9. Appendix IV: Individual Team Contributions

Name: Andrew DuffyTime (Hours) Description

Operator (Both Lab Days) 7 Operated lab with groupPre-Lab Editing 0Final Lab Editing 0Summary 0Introduction 1 Wrote SectionLiterature Review / Theory 0Apparatus 0Materials and Supplies 0Procedure 0Anticipated Results 0Results 0Discussion 0Conclusion 0References 0Data Tabulation / Graphs 0Error Analysis 2 Wrote SectionSample Calculations 0Job Safety Analysis 0.5 Wrote SectionPower Point Presentation 0Total 10.5

Name: Bernard HsuTime (Hours) Description

Operator (Both Lab Days) 7 Operated lab with groupPre-Lab Editing 0Final Lab Editing 0Summary 0Introduction 0Literature Review / Theory 0Apparatus 0Materials and Supplies 0Procedure 0Anticipated Results 1 Wrote SectionResults 0Discussion 0Conclusion 0References 0



Data Tabulation / Graphs 2.5 Compiled DataError Analysis 0Sample Calculations 0Job Safety Analysis 0Power Point Presentation 0Total 10.5

Name: Ryan KosakTime (Hours) Description

Operator (Both Lab Days) 7 Operated lab with groupPre-Lab Editing 0.5Final Lab Editing 1.5 Compiled Summary 0Introduction 0Literature Review / Theory 1.5 Wrote SectionApparatus 0Materials and Supplies 0Procedure 0Anticipated Results 0Results 0Discussion 0Conclusion 0References 0Data Tabulation / Graphs 0Error Analysis 0Sample Calculations 0Job Safety Analysis 0Power Point Presentation 0Total 10.5

Name: Daniyal QamarTime (Hours) Description

Operator (Both Lab Days) 7 Operated lab with groupPre-Lab Editing 0Final Lab Editing 0Summary 0Introduction 0Literature Review / Theory 0Apparatus 0.5 Wrote SectionMaterials and Supplies 1.5 Wrote SectionProcedure 0Anticipated Results 0Results 2



Discussion 0Conclusion 0References 0Data Tabulation / Graphs 0Error Analysis 0Sample Calculations 0Job Safety Analysis 0Power Point Presentation 0Total 11

Name: Tomi DamoTime (Hours) Description

Operator (Both Lab Days) 7 Operated lab with groupPre-Lab Editing 0Final Lab Editing 0Summary 0Introduction 0Literature Review / Theory 1.5 Wrote SectionApparatus 0Materials and Supplies 0Procedure 0Anticipated Results 0Results 0Discussion 0Conclusion 0References 0Data Tabulation / Graphs 0Error Analysis 0Sample Calculations 2 Wrote SectionJob Safety Analysis 0Power Point Presentation 0Total 10.5

Name: Alex GuerreroTime (Hours) Description

Operator (Both Lab Days) 7 Operated lab with groupPre-Lab Editing 0Final Lab Editing 0Summary 0Introduction 0Literature Review / Theory 0Apparatus 0Materials and Supplies 0



Procedure 1.5 Wrote SectionAnticipated Results 0Results 0Discussion 2 Wrote SectionConclusion 0References 0Data Tabulation / Graphs 0Error Analysis 0Sample Calculations 0Job Safety Analysis 0Power Point Presentation 0Total 10.5

Name: Jeff Tyska Time (Hours) Description

Operator (Both Lab Days) 7 Operated lab with groupPre-Lab Editing 1.5 CompiledFinal Lab Editing 0Summary 2 Wrote SectionIntroduction 0Literature Review / Theory 0Apparatus 0Materials and Supplies 0Procedure 0Anticipated Results 0Results 0Discussion 0Conclusion 0References 0Data Tabulation / Graphs 0Error Analysis 0Sample Calculations 0Job Safety Analysis 0Power Point Presentation 0Total 10.5


summary · web viewq ip = volumetric flow rate of species i in the permeate in m3/minρ =density of...

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