Gas Absorption in a Packed Tower Unit Operations Laboratory - Sarkeys E111

April 15th & 22nd, 2015

ChE 3432 - Section 3

Eric Henderson

Eddie Rich

Xiaorong Zhang

Mikey Zhou

1

2

ABSTRACT

Gas absorption in a packed tower was the focal point of this experiment, and the tower was used

to evaluate the properties of pressure drop and mass transfer across separate sections of structured

and dumped packing. The loading and flooding point of each section was found by using the

pressure drop data of a dry run in combination with multiple air and liquid flow rates. Counter-

current flow was used to maximize the diffusion of CO2 gas into water in order to achieve the

optimal operating conditions for conversion of CO2 to sodium bicarbonate. During the initial

experimental testing, water flow rate was varied from 9.03 to 2.10 gpm to determine the effect of

liquid flow rate on pressure drop and the overall mass transfer. For the second part of the

experiment a CO2 flow rate was introduced at 0.40 SCFM as water flow rate varied from 8.64 to

2.16 gpm. An increase in flow rate led to an increased pressure drop. Our experimental data

resulted in a packing coefficient value of 569 for dumped packing and 542 for structured packing.

For high water flow rates dumped packing had a higher gas adsorption rate than structured packing.

However, for low water flow rates dumped packing had a lower gas adsorption rate than structured

packing.

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INTRODUCTION AND THEORY (Mikey Zhou):

The objectives of the Packed Tower experiment were to study the pressure drop through

the column and to determine the mass transfer coefficient for absorption of CO2 from air. These

factors were studied for two different types of column packings: dumped and structured (figure

1). The purpose of column packings is to

mass transfer efficiency by maximizing

the surface area per unit volume, which

maximizes the vapor-liquid contact area,

by evenly spreading the surface area, and

by maximizing void space per unit volume to minimize resistance to the vapor upflow (Perry 14-

53). Dumped packings are usually irregularly shaped and hollow, and are literally dumped into the

tower. As a result, the packings’ locations in the tower are random, hence why dumped packings

are sometimes called “random” packings. Many are made of cheap materials such as various types

of plastics. Structured packings, on the other hand, are made of sheets of perforated corrugated

metal; adjacent metal sheets are placed so that liquid can flow on the surfaces and vapor can flow

through the void spaces made by the corrugations. Structured packing is more efficient for mass

transfer than is dumped packing, but is also generally more expensive and is susceptible to

corrosion due to it being metal (McCabe 689). Industrially, packed towers are often used in

absorption processes, in which certain components of a gas are transferred to a liquid – e.g.,

minimizing CO2 emissions by gas absorption. In this experiment in particular, the absorptive

capabilities of two kinds of packings, dumped and structured, were compared. The ideal operating

conditions for the tower were determined in the first week, when the column was run with only

water and air. In the second week, the absorption of CO2 by water was then studied.

Figure 1 Left: structured packing. Right: Dumped packing.

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In the packed column, the gas and liquid streams are counter-currently run, with liquid

running down between the packings and gas flowing up through the wetted packings, making

contact with the liquid along the way. The gas contains the

solute, the component to be absorbed by the liquid, the

absorbent. One phenomena that may occur in tall towers is

called channeling, in which liquid flows down closer to the

walls and gas flows up through the center. This reduces the

efficiency of mass transfer because there is less contact

between the two phases. (Seader 209). Under the assumptions

that diffusion controls the mass transfer and that there is no

resistance to diffusion across the liquid-gas interface, the two-

resistance theory describes how mass transfer occurs in the column. The transfer of CO2 to water

occurs in three steps: 1) from air to the air-water interfacial surface, 2) across the interfacial surface

into the liquid phase, and finally 3) into the bulk liquid phase, as figure 2 depicts (Welty 554).

As mentioned, the optimal operating conditions for the tower had to be determined before

the absorption of CO2 could be studied. To do this, the loading zone had to be found. The loading

zone is the region between the loading and flooding points. As water flows down a column, at a

certain air flow rate, water will begin to accumulate in the packings. This is called the loading

point. As air velocity is increased, more water will be accumulated. At the flooding point, the air

velocity will be high enough such that entire liquid is entrained, causing the whole column to be

filled with water. Column operation in the loading zone is unstable, and thus it is recommended to

operate at below the loading point in the preloading region (Seader 237). The two critical

aforementioned points can be determined both physically and graphically. Physically, the loading

Figure 2 Absorption of gas solute A by the

liquid phase

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point can be observed when surges of air can be seen moving up the column. The flooding point

can be seen when water has been pushed out of the top of the column by the air. Graphically, these

points can be determined from a log-log plot of the following equation, which expresses pressure

drop as a function of gas velocity (lab manual):

Δ𝑃 = 𝑎𝑉𝑔𝑏 (𝐸𝑞′𝑛 1)

where Δ𝑃 is the pressure drop per unit height of packing, 𝑎 and 𝑏 are constants, and 𝑉𝑔 is the

superficial gas velocity. In a log-log plot, 𝑎 would be the y-intercept and 𝑏 would be the slope.

During a dry run, the slope of the line on the plot should be approximately 1.8 (McCabe 691).

When there is water flowing in the system, the slope of the curve will initially also be 1.8. At the

loading point, as the air begins to slow the downflowing liquid causing increased water

accumulation, the pressure drop will rise suddenly due to there being less available space through

which gas can flow. This will increase the slope, thereby causing the curve to break from linearity.

An even more drastic rise in pressure drop, and thus slope, occurs at the flooding point. According

to McCabe, the operational gas velocity is sometimes chosen to be one half the flooding velocity

(McCabe 692).

With the optimal operating conditions determined, the absorption of CO2 by water can now

be studied. As stated previously, the two-resistance theory claims that mass transfer is controlled

by a concentration gradient. Equation 2 relates the overall mass transfer coefficient, 𝐾𝐿 , to the

individual phase coefficients:

1

𝐾𝐿=

1

𝑚𝑘𝐺+

1

𝑘𝐿 (𝐸𝑞′𝑛 2)

where 𝑘𝐺 and 𝑘𝐿 are the individual phase coefficients. However, because CO2 has a low solubility

in water, the system is said to be liquid-phase controlled and 𝐾𝐿 is essentially equal to 𝑘𝐿 (Welty

560). Correlated values of 𝐾𝐿 are found using equation 3 (Welty 587):

6

𝐾𝐿 = 𝛼𝐷𝐴𝐵 (𝐿

𝜇)1−𝑛

(𝜇

𝜌𝐷𝐴𝐵)

1

2 (𝐸𝑞′𝑛 3)

where 𝛼 is the packing coefficient, 𝐷𝐴𝐵 is the diffusivity coefficient of CO2 in water, 𝐿 is the liquid

flow rate, and 𝜇 and 𝜌 are the viscosity and density of water, respectively. The packing

exponent,1 − 𝑛, should be equal to 0.72. This correlation assumes that the Schmidt

number, (𝜇

𝜌𝐷𝐴𝐵)

1

2, is constant. A plot of

1

𝐾𝐿𝑣𝑠.

1

𝐷𝐴𝐵(𝐿

𝜇)1−𝑛

(𝜇

𝜌𝐷𝐴𝐵)

12

should yield a straight line with

slope 1

𝛼 that passes through the origin. If a straight line through the origin is not observed, then the

coefficient 0.72 is not valid (lab manual). In order to verify the above correlation, experimental

values of 𝐾𝐿 were plotted versus 𝐿

𝜇 on a logarithmic scale. In this log-log plot, the slope will be

equal to 1 − 𝑛, and if the slope is equal to 0.72, then the correlation is valid for this experiment.

Experimental values of the overall mass transfer coefficient are estimated using equation 4 (lab

manual):

𝐾𝐿exp

=𝑁𝐶𝑂2

ℎ𝐴𝑐Δ𝑥𝑙𝑚 (𝐸𝑞′𝑛 4)

where 𝑁𝐶𝑂2is the number of moles of CO2 transferred per hour, ℎ is the height of the packing in

ft., 𝐴𝑐 is the tower cross-sectional area, and Δ𝑥𝑙𝑚 is the logarithmic mean composition difference,

given by equation 5 (lab manual):

Δ𝑥𝑙𝑚 =(𝑥∗ − 𝑥)2 − (𝑥

∗ − 𝑥)1

ln {(𝑥∗ − 𝑥)2(𝑥∗ − 𝑥)1

} (𝐸𝑞′𝑛 5)

where 𝑥∗ is the liquid phase mole fraction of CO2 in equilibrium with the bulk phase mole fraction

of CO2, 𝑥 is the mole fraction of CO2 in water, and the subscripts 1 and 2 refer to the top and

bottom of the column, respectively.

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APPARATUS AND PROCEDURES (Eddie Rich):

The packed tower shown in Figure 3 consisted of a

six inch inner diameter glass pipe that was twelve feet tall.

The vertical pipe was split in two six foot sections housing

5/8 inch polypropylene Flexiring dumped packing in the

bottom section, and Flexipac Type X corrugated metal

structured packing in the top section. Each six foot section

of the packed tower contained five and one half feet of each

type of packing. A redistributor plate and a support plate

divided the two sections. The column also contained a

liquid distributor at the top, and a support plate at the

bottom.

At the bottom of the column, there was an

Oberdorfer Model 109 MB centrifugal pump that fed water

from the 200 gallon steel water tank shown in Figure 4, to the top of the packed tower. Water

flowed down through the packed tower and exited from a U shaped bend in the pipe into the smaller

surge tank also shown in Figure 4. A red valve controlled the amount of water flowing from the

bottom of the packed tower into the surge tank, where excess water was automatically pumped

back into the 200 gallon water tank with another centrifugal pump when the surge tank filled to a

certain level.

Figure 3 Packed tower apparatus

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The operating panel shown

in Figure 5 housed the measuring

devices and operating valves and

switches. There were three

rotameters on the panel. The two on

the left measured the volumetric

flow rate of air and carbon dioxide

in cubic feet per minute, and the one

on the right measured the

volumetric flow rate of water in gallons per minute. The air was fed from the compressed air

system in the building, and carbon dioxide was fed from compressed cylinders next to the operating

panel. Air, carbon dioxide, and water flow rates were controlled using the valves underneath each

of the respective rotameters. The pressure differences across the two sections of the packed tower

were measured by connecting the yellow tubes attached to the pressure taps from top and middle

of the column, or the pressure taps from the middle and bottom of the column to one of three

pressure gauges. These three pressure gauges from left to right measured ranges of pressures from

0-3 inches of water, 0-15 inches of water, and 0-50 inches of water respectively. The pressure

gauge above the yellow tubes measured the pressure drop across the entire column in pounds per

square inch. A Drager Polytron 5700/57X0 gas chromatograph that measured the percent volume

of carbon dioxide was located on the panel above the yellow tubes as well. Above the gas

chromatograph was a water sensor that alerted if there was excessive buildup of water in the

column. At the bottom of the panel, there was a row of switches. The function of the switches from

Figure 4 Back of packed tower apparatus

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left to right were to turn on the recovery pump, zero the meters, turn on carbon dioxide heaters,

and turn on the feed pump and sample pump.

Initially for the first part of the experiment, the drain valve exiting from the 200 gallon

water tank was closed, and the tank was filled with water. The system was first operated with only

air running through the packed tower to find the pressure difference for the dry column. This was

accomplished by slowly increasing the air feed by an interval of 5 cubic feet per minute up to 45

cubic feet per minute by turning the air valve counter-clockwise. The pressure differences across

the top section, bottom section, and entire column were recorded for the various air flow rates used

during the dry run. As the pressure difference increased, the pressure gauges of higher ranges were

used. Once the pressure differences across the entire column, top section, and bottom section were

recorded for various air flow rates through the dry column, the feed and recovery pump switches

were turned on. The water control valve was then opened until the feed reached ten percent of the

Figure 5 Packed tower apparatus operating panel

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pumps maximum flow rate of thirty gallons per minute. With water flowing through the system,

excess water will build up at the bottom of the column. The red valve in Figure 3 allows the excess

water to flow into the recovery tank. An ideal level that is marked on the tube at the bottom of the

column is maintained by opening or closing the red valve to control the buildup of water. Before

each pressure difference was measured, the meters were zeroed using the designated switch at the

bottom of the operating panel. Once the water flow rates increased to twenty percent and above,

loading and flooding was observed at higher air flow rates. Loading began when air can visually

be seen rising and pushing froth up the column. It can also be observed by a rapidly increasing

pressure difference across the top section, bottom section, and entire column. Flooding was

reached when the log-log plot of change in pressure to the gas velocity broke linearity. Care should

be taken when increasing the air flow rate to ensure excessive flooding doesn’t occur. After the

loading and flooding zones were identified for the different water and air flow rates, the system

was shut down. This was done by closing the water and air valves, turning off the feed pump,

opening the drain valve for the water tank, and purging the recovery tank.

During the second part of the experiment, the apparatus was operated in a similar way as

the first part of the experiment, except that the 200 gallon tank is filled with a 0.2 N water and soda

ash mixture, and carbon dioxide was fed into the system along with air. To start the process, the

water tank was filled with a soda ash and water mixture, the recovery pump and feed pump was

turned on, and the drain valve exiting the surge tank was closed. The water flow rate was then set

at 40% while the air flow rate was set at a constant 13 SCFM. The carbon dioxide heaters were

then turned on to keep the lines from freezing. A manifold regulator for carbon dioxide was then

set between 40 and 50 pounds per square inch, and carbon dioxide was introduced to the system.

The sample pump was then tuned on so that the volume percent of carbon dioxide could be

11

measured. The carbon dioxide flow rate was set at 0.4 SCFM to ensure that the percent volume of

carbon dioxide did not exceed the maximum measureable value of the gas chromatograph. Gas

chromatograph measurements were then recorded at the entrance, middle, and exit of the column,

after two minutes of the column reaching operating conditions. This was then repeated at constant

air and carbon dioxide flow rates, while taking pressure drop and carbon dioxide volume percent

data for different water flow rates ranging between 10-40%. After all of the data was obtained,

the system was shut down. This was accomplished by first completely closing the water flow rate

valve, and turning off the feed pump, sample pump, and carbon dioxide heaters. The air and carbon

dioxide control valves were then closed, followed by closing the carbon dioxide tank valves. The

column was then allowed to drain. The drain valves were then opened for the water and recovery

tanks.

Safety precautions were taken during the setup and operation of the packed tower unit, to

ensure no harm occurred during the laboratory. High voltage centrifugal pumps were utilized in

the experiment, so care was taken to avoid electric shock. Safety glasses were always worn

throughout the experiment. Soda ash is a skin and lung irritant, so the teacher assistant for the lab

wore the necessary safety equipment while making the soda ash and water mixture.

RESULTS AND DISCUSSION (Xiaorong Zhang):

The result of this experiment is separated into two parts according to two weeks of the

experiment. The first week’s experiment is to find the effective loading region of the packed

column for use in mass transfer, which will be done during the second week. Figures 6 and 7 show

the log-log plot of pressure drop to superficial gas velocity for structured packing and dumped

packing, respectively. Both figures show good linear trend without flooding point at different

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percentages of max water flow rates. The flooding point is defined as the point which departs from

the linear trend in the figures. In addition, the loading point is defined as the point before the

flooding point. From both figures, flooding occurred at higher gas velocities for each run, and it

occurred at a relatively lower gas velocities as the percent max water flow rate increased.

Comparing the figures for structured and dumped packing, structured packing obtained a lower

pressure with different water flows, since the data points were more concentrated than in the

dumped packing from the figures.

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Figures 8 and 9 show the pressure drop versus gas mass velocity for structured and dumped

packing. The loading and flooding lines were indicated as orange and blue on the graph for both

structured and dumped packing. Since not enough data after loading was obtained, the flooding

line might not be accurate, however, the trend can be seen easily on the graph. The flooding

occurred at high gas mass velocity with low percent max water flow and at low gas mass velocity

with high percent max water flow. The pressure drop at the loading line is below 0.2 in inches of

water for structured packing, while for dumped packing it is below 0.1, each of which are varied

with different water flows and air flows. These values increase as water flow rate increases. A

change in the water flow rate causes a significant difference on the graph. It is safe to conclude

that water flow was the main factor to determine loading and flooding points. Comparing the two

figures, it is easy to flood at low pressure drop for dumped packing. Figure 10 shows the L versus

G plots for structured and dumped packing which is used to determine which type of packing is

more efficient. The points are determined by calculating each L/G value at flooding point for each

percent max flow rate. The operating line is drawn by connect origin with highest flooding point

which gains maximum L and G value. The blue area below operating line and flooding points refer

to the optimal area for operation. The area beyond optimal area with high possibility of flooding.

Figure 10 Comparison of G vs L plots for Structured packing (left) and dumped packing (right)

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The optimal area for structured packing obtains larger area due to its larger base. It can be inferred

from this graph that structured packing is more efficient than dumped packing. It also confirms the

conclusion we made previously.

.

y = 0.001756652xR² = 0.941100993

y = 0.001844930xR² = 0.922722441

0

0.001

0.002

0.003

0.004

0.005

0.006

0 0.5 1 1.5 2 2.5

1/K

La

1/(DAB(L/μ)0.72(Sc)0.5)

Structured

Dumped

y = 0.705x + 0.0193R² = 0.9599

y = 0.7645x - 0.2066R² = 0.9484

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.3 3.4 3.5 3.6 3.7 3.8 3.9 4

log(

KLa

)

log(L/μ)

log-log

Structured

Dumped

Figure 11 Sherwood and Holloway correlation for structured and dumped packing

Figure 12 log-log plot of KLa to L/μ for structured and dumped packing.

15

Figure 11 gives slope of 0.001756 and 0.001844 for structured and dumped packing respectively.

The correlation is good for our data because both trend lines for structured and dumped packing

go through the origin. In this circumstances, it can be assumed that the Schmidt number is constant.

The slopes in the graph represent values of 1/α which is the inverse of specific area of packing.

We got α values of 542 and 569 for structured and dumped packing respectively. These α values

were used to find the experimental exponent 1-n for L/µ in equation 3. 𝐾𝐿𝑎 value was estimated by

using equation 4. Then we made a log-log plot of 𝐾𝐿𝑎 to L/µ shown in figure 12. The slopes indicate

the 1-n values which are 0.705 and 0.765 for structured and dumped packing respectively. Those

values are very close to 0.72 which was given in equation 3

CONCLUSIONS

Experiment data was accurate since all the plots followed expected trend and values are

close to theoretical values.

Flooding and loading regions with different water flow rate and air flow rate were found

during first week experiment

Structured packing is more efficient than dumped packing due to less pressure drop was

found in the plots.

Mass transfer coefficient and packing coefficient were determined during second week

experiment

RECOMMENDATIONS

Re-run experiment with columns of various heights and diameters to study how these

parameters affect pressure drop and mass transfer characteristics

Consider using columns with liquid redistributors for more uniform water flow to avoid

excessive channeling

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For more accurate determination of flooding velocity, increase water flow rate by smaller

intervals during the first week of experiment

REFERENCES

Lab Manual, Exp VI Packed Tower. (n.d.). Retrieved from learn.ou.edu

McCabe, W., Smith, J., & Harriott, P. (1993). Unit Operations of Chemical Engineering.

(5th ed.) McGraw-Hill Book Co.

Perry, Robert. (2008). Perry’s Chemical Engineers’ Handbook, (8th ed.) McGraw-Hill

Professional.

Seader, J. D., & Henley, E. J. (2005). Separation Process Principles. Chichester: John Wiley.

Welty, J., Wicks, C., Rorrer, G., & Wilson, R. (2008). Fundamentals of Momentum, Heat, and

Mass Transfer. (5th ed.) John Wiley and Sons, Inc.

17

APPENDIX (Eric Henderson):

% Max water flow rate, Air FR, Top-Mid ΔP, Mid-Bottom ΔP, and Column Gas pressure are

measured experimentally. [Flow Rate: FR]

Calculations are carried out for 40% max water flow-rate:

Water FR = % 𝑀𝑎𝑥 𝑊𝑎𝑡𝑒𝑟 𝐹𝑅

𝑀𝑎𝑥 𝑊𝑎𝑡𝑒𝑟 𝐹𝑅∗ 100 =

40

21∗ 100 = 8.4 𝑔𝑝𝑚

Top-Mid ΔP/h = 𝑇𝑜𝑝−𝑀𝑖𝑑 ΔP

𝑃𝑎𝑐𝑘𝑖𝑛𝑔 ℎ𝑒𝑖𝑔ℎ𝑡=0.3 𝑖𝑛 𝐻2𝑂

5.5𝑓𝑡∗12𝑖𝑛

𝑓𝑡

=0.3 𝑖𝑛 𝐻2𝑂

66 𝑖𝑛= 0.005

Mid-Bottom ΔP/h = 0.28 𝑖𝑛 𝐻2𝑂

66 𝑖𝑛= 0.004

1 ft3 = 7.48 gal

Liquid FR = 𝑊𝑎𝑡𝑒𝑟 𝐹𝑅 [𝑔𝑝𝑚]

7.48 𝑔𝑎𝑙∗60𝑠

𝑚𝑖𝑛

=8.4 𝑔𝑝𝑚

7.48 𝑔𝑎𝑙∗60𝑠

𝑚𝑖𝑛

= 0.019𝑓𝑡3

𝑠

Cross-Sectional Area = 𝜋∗0.52

4 = 0.196 𝑓𝑡2 where 0.5 ft is the column diameter

Air FR = 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝐴𝑖𝑟 𝐹𝑅

𝑈𝑛𝑖𝑡 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛=

5𝑓𝑡3

𝑚𝑖𝑛

60𝑠

𝑚𝑖𝑛

= 0.083𝑓𝑡3

𝑠

Air velocity = Vg = 𝐴𝑖𝑟 𝐹𝑅

𝐶𝑜𝑙𝑢𝑚𝑛 𝐴𝑟𝑒𝑎=0.083

𝑓𝑡3

𝑠

0.20 𝑓𝑡2= 0.424

𝑓𝑡

𝑠

Liquid Molar FR = L = 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑊𝑎𝑡𝑒𝑟∗𝐿𝑖𝑞𝑢𝑖𝑑 𝐹𝑅

𝐶𝑜𝑙𝑢𝑚𝑛 𝐴𝑟𝑒𝑎=62.3

𝑙𝑏𝑚𝑓𝑡3

∗0.019𝑓𝑡3

𝑠

0.20 𝑓𝑡2∗ 3600

𝑠

ℎ𝑟= 21378.99

𝑙𝑏𝑚

ℎ∗𝑓𝑡2

Air Molar FR = G = 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝐴𝑖𝑟∗𝐴𝑖𝑟 𝐹𝑅

𝐶𝑜𝑙𝑢𝑚𝑛 𝐴𝑟𝑒𝑎=0.075

𝑙𝑏𝑚𝑓𝑡3

∗0.083𝑓𝑡3

𝑠

0.20 𝑓𝑡2∗ 3600

𝑠

ℎ𝑟= 114.52

𝑙𝑏𝑚

ℎ∗𝑓𝑡2

Top-Mid log (ΔP/h) = log10 (Top-Mid ΔP) = log10 (0.3) = -0.523

Mid-Bottom log ΔP/h = log10 (Mid-Bottom ΔP) = log10 (0.28) = -0.553

log10 (Air Velocity) = log10 (Vg) = log10 (0.424) = -0.372

18

CO2 Incorporation

𝐺𝐶𝑂2 = 𝑉𝑔𝐶𝑂2 ∗ 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝐶𝑂2 = 0.042𝑓𝑡

𝑠∗ 0.1144

𝑙𝑏𝑚𝑓𝑡3

∗ 3600𝑠

ℎ𝑟= 364.9

𝑙𝑏𝑚ℎ𝑟 ∗ 𝑓𝑡2

𝐺𝐶𝑂2′ =

𝐺𝐶𝑂2 (𝑙𝑏

ℎ𝑟 ∗ 𝑓𝑡2) ∗ 𝐴𝑐𝑠(𝑓𝑡

2)

𝑀𝑊𝐶𝑂2 (𝑙𝑏𝑚𝑙𝑏𝑚𝑜𝑙

)=(364.9

𝑙𝑏ℎ𝑟 ∗ 𝑓𝑡2

) ∗ (0.196 𝑓𝑡2)

(44𝑙𝑏𝑚𝑙𝑏𝑚𝑜𝑙

)= 1.628 (

𝑙𝑏𝑚𝑜𝑙

ℎ𝑟)

𝐺𝑇𝑜𝑡𝑎𝑙′ = 𝐺𝐴𝑖𝑟

′ + 𝐺𝐶𝑂2′ = (1.619

𝑙𝑏𝑚𝑜𝑙

ℎ𝑟) + (1.628

𝑙𝑏𝑚𝑜𝑙

ℎ𝑟) = 𝟑. 𝟐𝟓 (

𝒍𝒃𝒎𝒐𝒍

𝒉𝒓)

Correction Factors

𝑓𝑇 = 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝐹𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 = √𝑇(℉) + 460

530= √

75℉ + 460

530= 1.00

𝑓𝑃 = 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝐹𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = √14.7

𝑝𝑠𝑖𝑔 + 14.7= √

14.7

0 + 14.7= 1.00

𝑓𝑀𝑊𝑔 = √𝑀𝑊𝑔

𝑀𝑊𝐴𝑖𝑟= √

29 (𝑙𝑏𝑚𝑙𝑏𝑚𝑜𝑙

)

29 (𝑙𝑏𝑚𝑙𝑏𝑚𝑜𝑙

)= 1.00

𝑓𝑀𝑊𝐶𝑂2= 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝐹𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑀𝑊 = √

𝑀𝑊𝐶𝑂2𝑀𝑊𝐴𝑖𝑟

= √44 (

𝑙𝑏𝑚𝑙𝑏𝑚𝑜𝑙

)

29 (𝑙𝑏𝑚𝑙𝑏𝑚𝑜𝑙

)= 1.238

𝐒𝐭𝐫𝐮𝐜𝐭𝐮𝐫𝐞𝐝 𝐍𝐂𝐎𝟐 = 𝐺𝑇𝑜𝑡𝑎𝑙′ ∗ ((𝑌𝐶𝑂2)𝑀𝑖𝑑𝑑𝑙𝑒 − (𝑌𝐶𝑂2)𝑇𝑜𝑝) = 3.25 ∗ (0.0209 − 0.02262)

= 0.00570𝑙𝑏𝑚𝑜𝑙

ℎ𝑟

𝐃𝐮𝐦𝐩𝐞𝐝 𝐍𝐂𝐎𝟐 = 𝐺𝑇𝑜𝑡𝑎𝑙′ ∗ ((𝑌𝐶𝑂2)𝐵𝑜𝑡𝑡𝑜𝑚 − (𝑌𝐶𝑂2)𝑀𝑖𝑑𝑑𝑙𝑒) = 3.25 ∗ (0.02262 − 0.02411)

= 0.00484𝑙𝑏𝑚𝑜𝑙

ℎ𝑟

19

𝑺𝒕𝒓𝒖𝒄𝒕𝒖𝒓𝒆𝒅 𝜟𝑿𝒍𝒎 =(𝑥∗ − 𝑥)𝑡𝑜𝑝 − (𝑥

∗ − 𝑥)𝑚𝑖𝑑𝑑𝑙𝑒

ln {(𝑥∗ − 𝑥)𝑡𝑜𝑝(𝑥∗ − 𝑥)𝑚𝑖𝑑𝑑𝑙𝑒

}

=(1.93 ∗ 10−5 − 0) − (2.1 ∗ 10−5 − 0)

ln (1.93 ∗ 10−5 − 02.1 ∗ 10−5 − 0

)

= 𝟐. 𝟎𝟏𝟏 ∗ 𝟏𝟎−𝟓

𝑫𝒖𝒎𝒑𝒆𝒅 𝜟𝑿𝒍𝒎 =(𝑥∗ − 𝑥)𝑀𝑖𝑑𝑑𝑙𝑒 − (𝑥

∗ − 𝑥) 𝐵𝑜𝑡𝑜𝑚

ln {(𝑥∗ − 𝑥)𝑀𝑖𝑑𝑑𝑙𝑒(𝑥∗ − 𝑥)𝐵𝑜𝑡𝑡𝑜𝑚

}=(2.1 − 0) − (2.237 ∗ 10−5 − 0)

ln (2.1 ∗ 10−5 − 02.237 ∗ 10−5 − 0

)

= 𝟐. 𝟏𝟔𝟔 ∗ 𝟏𝟎−𝟓

𝟏/𝑲𝑳𝒂 =1

𝑁 (𝑙𝑏𝑚𝑜𝑙ℎ𝑟

)

∆𝑋𝑙𝑚 ∗ ℎ(𝑓𝑡) ∗ 𝐴𝑐𝑠(𝑓𝑡2)

=1

(0.0057)𝑙𝑏𝑚𝑜𝑙ℎ𝑟

(4.83 ∗ 10−5) ∗ (5.5𝑓𝑡) ∗ (0.196𝑓𝑡2)

= 0.0038 (𝑙𝑏𝑚𝑜𝑙

ℎ𝑟 ∗ 𝑓𝑡2)−1

1

𝐷𝐴𝐵 (𝑓𝑡2

ℎ𝑟) ∗ (

𝐿 (𝑙𝑏𝑚

ℎ𝑟 ∗ 𝑓𝑡2)

𝜇 (𝑙𝑏

ℎ𝑟 ∗ 𝑓𝑡))

0.72

∗

(

𝜇 (

𝑙𝑏ℎ𝑟 ∗ 𝑓𝑡

)

𝜌 (𝑙𝑏𝑚𝑓𝑡3

)∗ 𝐷𝐴𝐵 (

𝑓𝑡2

ℎ𝑟)

)

0.5

=1

(6.855 ∗ 10−5𝑓𝑡2

ℎ𝑟) ∗ (

(5497.09𝑙𝑏𝑚

ℎ𝑟 ∗ 𝑓𝑡2)

(0.000669 ∗ 3600𝑙𝑏

ℎ𝑟 ∗ 𝑓𝑡))

0.72

∗

(

(0.000669 ∗ 3600

𝑙𝑏ℎ𝑟 ∗ 𝑓𝑡

)

(62.261𝑙𝑏𝑚𝑓𝑡3

)∗ (6.855 ∗ 10−5

𝑓𝑡2

ℎ𝑟)

)

0.5

= 2.3453

o 𝐷𝐴𝐵 = 𝐷𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝐶𝑎𝑟𝑏𝑜𝑛 𝐷𝑖𝑜𝑥𝑖𝑑𝑒 𝑖𝑛 𝑊𝑎𝑡𝑒𝑟

o 𝜇 = 𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 𝑜𝑓 𝑊𝑎𝑡𝑒𝑟

20

Supplementary Equations:

Middle of Tower:

L

GyGyLxxGyLxGyLx outinin

outoutoutinin

xin=0 because no CO2 enters with liquid phase

Equation becomes

G

L

yyx outin

out

o xout = Middle mole fraction of CO2 in liquid phase

o yin = Middle mole fraction of CO2 in vapor phase

o yout = Top mole fraction of CO2 in vapor phase

Bottom of Tower:

G

L

yyG

Lx

xinoutin

out

*

o xin = Middle mole fraction of CO2 in liquid phase

o xout = Bottom mole fraction of CO2 in liquid phase

o yin = Bottom mole fraction of CO2 in vapor phase

o yout = Middle mole fraction of CO2 in vapor phase

Mole Fraction of CO2 at equilibrium = x*= PCO2/HCO2

o H=Henry’s Law Constant (inches of H2O)

o P=Partial Pressure of CO2

21

o x*=mole fraction of CO2 at equilibrium

Lb Moles Transferred Per Hour = 𝑁 = (1

𝑅𝑇) ∗ ( 𝑦𝐶𝑂2, 𝑡𝑜𝑝 ∗ 𝑃𝑡𝑜𝑝 – 𝑦𝐶𝑂2, 𝑏𝑜𝑡𝑡𝑜𝑚 ∗

𝑃𝑏𝑜𝑡𝑡𝑜𝑚) ∗ (𝑎𝑖𝑟 𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒)

o yCO2,top =mole fraction of CO2 in top

o yCO2, bottom =mole fraction of CO2 in bottom

o Ptop = Pressure at top of tower

o Pbottom = Pressure at bottom of tower

Overall Mass Transfer Coefficient for the Packed Tower =lm

LXAH

NaK

**

o Moles Transferred per hour = RT

VPPN

g

COCO ww 12

o H = Henry’s Law Constant

o A = Cross-Sectional Area of Tower

Where N given by:

RT

VPPN

g

COCO ww 12

Also:

2/172.0 )*

(*)/(**AB

ABL DuLDaK

o DAB= Mass diffusivity of CO2 through water

o L= Liquid/water flow rate

o μ = liquid viscosity

o u = superficial gas velocity

o ρ = liquid density

22

Log-Mean Difference for Mole Fraction of CO2 =

1

2

12

)*(

)*(ln

)*()*(

xx

xx

xxxxX lm

o x* = equilibrium mole fraction of CO2

o x = liquid phase mole fraction of CO2

o 1 corresponds to the top of the tower

o 2 corresponds to the bottom of the tower

23

% o

f

Max

Wate

r

FR

Wate

r FR

(gpm

)

Air FR

(ft3/m

in)

Top

-Mid

ΔP

(in. o

f H20)

Mid

-

Bo

ttom

ΔP

(in. o

f

H20

Co

lum

n

Gas (p

si)

Top

-Mid

ΔP

/h

Mid

-Bo

ttom

ΔP

/h

Liqu

id FR

(ft3/s)

Air FR

(ft3/s)

Vg (ft/s)

L (lbm

/h*ft

2)G

(lbm

/h*ft

2)

Top

-Mid

log

(ΔP

/h)

Mid

-

Bo

ttom

log

(ΔP

/h)

log (V

g)

50.3

0.30.4

0.0050.005

0.0830.424

114.515-0.523

-0.523-0.372

100.9

0.80.5

0.0140.012

0.1670.849

229.030-0.046

-0.097-0.071

152.2

1.80.7

0.0330.027

0.2501.273

343.5450.342

0.2550.105

Load

164.8

51

0.0730.076

0.2671.358

366.4490.681

0.6990.133

Floo

d17

4222

2.80.636

0.3330.283

1.443389.352

1.6231.342

0.159

439.03

0.02022982.410

% o

f

Max

Wate

r

FR

Wate

r FR

(gpm

)

Air FR

(ft 3/min

)

Top

-Mid

ΔP

(in. o

f H20)

Mid

-

Bo

ttom

ΔP

(in. o

f

H20

Co

lum

n

Gas (p

si)

Top

-Mid

ΔP

/h

Mid

-Bo

ttom

ΔP

/h

Liqu

id FR

(ft 3/s)

Air FR

(ft 3/s)V

g (ft/s)L (lb

m/h

*ft2)

G

(lbm

/h*ft

2)

Top

-Mid

log

(ΔP

/h)

Mid

-

Bo

ttom

log

(ΔP

/h)

log (V

g)

50.3

0.280.4

0.0050.004

0.0830.424

114.515-0.523

-0.553-0.372

100.95

0.850.6

0.0140.013

0.1670.849

229.030-0.022

-0.071-0.071

152

1.80.7

0.0300.027

0.2501.273

343.5450.301

0.2550.105

Load

203.5

3.250.9

0.0530.049

0.3331.698

458.0610.544

0.5120.230

Floo

d26

4020

2.60.606

0.3030.433

2.207595.479

1.6021.301

0.344

408.4

0.01921378.986

50.2

0.180.5

0.0030.003

0.0830.424

114.515-0.699

-0.745-0.372

100.8

0.60.5

0.0120.009

0.1670.849

229.030-0.097

-0.222-0.071

151.7

1.250.7

0.0260.019

0.2501.273

343.5450.230

0.0970.105

203.6

2.10.8

0.0550.032

0.3331.698

458.0610.556

0.3220.230

254.5

3.51

0.0680.053

0.4172.122

572.5760.653

0.5440.327

3018

152.1

0.2730.227

0.5002.546

687.0911.255

1.1760.406

Load

3238

192.8

0.5760.288

0.5332.716

732.8971.580

1.2790.434

3050

13.83.4

0.7580.209

0.5002.546

687.0911.699

1.1400.406

Floo

d31

5014

3.30.758

0.2120.517

2.631709.994

1.6991.146

0.420

306.3

0.01416034.239

Raw

Data D

ay 1

24

% o

f

Max

Wate

r

FR

Wate

r FR

(gpm

)

Air FR

(ft3/m

in)

Top

-Mid

ΔP

(in. o

f H20)

Mid

-

Bo

ttom

ΔP

(in. o

f

H20

Co

lum

n

Gas (p

si)

Top

-Mid

ΔP

/h

Mid

-Bo

ttom

ΔP

/h

Liqu

id FR

(ft3/s)

Air FR

(ft3/s)

Vg (ft/s)

L (lbm

/h*ft

2)G

(lbm

/h*ft

2)

Top

-Mid

log

(ΔP

/h)

Mid

-

Bo

ttom

log

(ΔP

/h)

log (V

g)

50.2

0.120.4

0.0030.002

0.0830.424

114.515-0.699

-0.921-0.372

100.72

0.50.5

0.0110.008

0.1670.849

229.030-0.143

-0.301-0.071

151.5

10.5

0.0230.015

0.2501.273

343.5450.176

0.0000.105

202.6

1.680.7

0.0390.025

0.3331.698

458.0610.415

0.2250.230

254

2.51

0.0610.038

0.4172.122

572.5760.602

0.3980.327

306

31.2

0.0910.045

0.5002.546

687.0910.778

0.4770.406

Floo

d35

215.8

1.50.318

0.0880.583

2.971801.606

1.3220.763

0.473

3635

152.75

0.5300.227

0.6003.056

824.5091.544

1.1760.485

204.2

0.00910689.493

50.2

0.140.45

0.0030.002

0.0830.424

114.515-0.699

-0.854-0.372

100.7

0.40.5

0.0110.006

0.1670.849

229.030-0.155

-0.398-0.071

151.5

0.80.5

0.0230.012

0.2501.273

343.5450.176

-0.0970.105

202.5

1.50.75

0.0380.023

0.3331.698

458.0610.398

0.1760.230

253.5

20.9

0.0530.030

0.4172.122

572.5760.544

0.3010.327

305.3

31.1

0.0800.045

0.5002.546

687.0910.724

0.4770.406

357.5

41.4

0.1140.061

0.5832.971

801.6060.875

0.6020.473

4010.6

5.41.75

0.1610.082

0.6673.395

916.1211.025

0.7320.531

4514.4

7.32.1

0.2180.111

0.7503.820

1030.6361.158

0.8630.582

102.1

0.0055344.746

50.19

0.090.4

0.0030.001

0.0830.424

114.515-0.721

-1.046-0.372

100.6

0.310.45

0.0090.005

0.1670.849

229.030-0.222

-0.509-0.071

151.25

0.690.5

0.0190.010

0.2501.273

343.5450.097

-0.1610.105

202.1

1.10.6

0.0320.017

0.3331.698

458.0610.322

0.0410.230

253.3

1.670.75

0.0500.025

0.4172.122

572.5760.519

0.2230.327

304.9

2.41

0.0740.036

0.5002.546

687.0910.690

0.3800.406

356.5

3.21.4

0.0980.048

0.5832.971

801.6060.813

0.5050.473

409

4.31.6

0.1360.065

0.6673.395

916.1210.954

0.6330.531

4511.5

5.52

0.1740.083

0.7503.820

1030.6361.061

0.7400.582

00

0.0000.000

25

Raw Data Day 2

Air Properties Water Properties CO2 Properties mo heat Column Specs

density 0.074887 lbm/ft^3 density 62.3 lbm/ft^3 density 0.1145 lbm/ft^3 Diameter 0.5 ft

viscosity viscosity viscosity 9.83E-06 lbm/fts Top h 5.5 ft

MW MW 18.016 MW 44.01 bottom h 5.5 ft

T 70 F T 70 F T

Packed TowerAir Flowrate

[SCFM]

Air

Flowrate

[ft3/s]

CO2

flowrate

[SCFM]

CO2

flowrate

[ft3/s]

GCO2

[lbm/h*ft2]

Gair

[lbm/h*ft2]VgCO2 [ft/s] Vgair [ft/s]

0.008250.173974Day 2 13 0.4 0.88604030.042034364.9068 238.87043

% of Max

Water FR

QWater

[gpm]QWater [ft

3/s]

Top-Mid

ΔP

[in H2O]

Mid-

Bottom ΔP

[in H2O]

Column P

[psi]

Top CO2

Vol%

Middle CO2

Vol%

Bottom CO2

Vol%

10 2.16 0.004813 1.2 0.5 0.4 3.12 3.38 3.6

15 3.24 0.007219 1.4 1.5 0.5 3.04 3.32 3.72

20 4.32 0.009625 1.5 2.1 0.5 2.92 3.28 3.68

25 5.4 0.012031 2.9 4 0.6 2.78 3.22 3.7

30 6.48 0.014438 3.6 4.8 0.75 2.64 3.12 3.7

35 7.56 0.016844 4.3 5.7 0.85 2.54 3.08 3.68

40 8.64 0.01925 4.5 7 0.9 2.52 3.04 3.72

P_top [atm]P_mid

[atm]

P_bottom

[atm]

CO2 Molarity

Tpo(mol/ft3)

CO2

Molarity

middle

CO2

Molarity

Bottom

air Molarity

Top

(mol/ft3)

air Molarity

middle

air Molarity

Bottom

1 1.002947 1.004175 0.0369882 0.040071 0.042679 1.7359015 1.731243 1.727301

1 1.003438 1.007122 0.0360398 0.039359 0.044101 1.7373349 1.732318 1.725151

1 1.003684 1.008841 0.0346172 0.038885 0.043627 1.7394851 1.733035 1.725867

1 1.007122 1.016945 0.0329574 0.038174 0.043864 1.7419936 1.73411 1.725509

1 1.008841 1.020629 0.0312977 0.036988 0.043864 1.7445021 1.735901 1.725509

1 1.01056 1.024558 0.0301122 0.036514 0.043627 1.7462939 1.736618 1.725867

1 1.011051 1.028241 0.0298751 0.03604 0.044101 1.7466523 1.737335 1.725151

26

Y CO2 Top Y CO2

middle

Y CO2

Bottom x_top x_mid x_bottom

0.020863 0.022622 0.024113 1.93E-05 2.1E-05 2.23745E-05

0.020323 0.022216 0.024927 1.88E-05 2.06E-05 2.31977E-05

0.019512 0.021945 0.024655 1.8E-05 2.04E-05 2.29843E-05

0.018568 0.021539 0.024791 1.72E-05 2E-05 2.32964E-05

0.017625 0.020863 0.024791 1.63E-05 1.94E-05 2.33808E-05

0.016951 0.020593 0.024655 1.57E-05 1.92E-05 2.33423E-05

0.016817 0.020323 0.024927 1.55E-05 1.9E-05 2.36841E-05

G'CO2

[lbm/hr]

G'air

[lbm/hr]

G'total

[lbm/hr]

structured

NCO2

[lbmol/hr]

Dumped

NCO2

[lbmol/hr]

structured

NCO3

[g/mol]

Dumped

NCO3

[g/mol]

0.00571221 0.00484135 2.591 2.195989

0.00614866 0.00880427 2.788971 3.993529

0.0079011 0.00880186 3.583859 3.992435

0.0096503 0.01056079 4.377279 4.790267

0.01051897 0.01275659 4.771299 5.78626

0.01182818 0.01319376 5.365145 5.984557

0.01138777 0.01495293 5.165377 6.7825

1.619548 3.247941.628393

structured

Δxlm

dumped

Δxlm

structured

1/KLa

dumped

1/KLaSc

L

[lbm/h*ft2]1/(DAB(L/μ)0.72(Sc)0.5) log(L/μ)

structured

Log(Kla)

dumped

log(Kla)

2.011E-05 2.166E-05 0.003802 0.004832 563.6308 5497.09 2.345339603 3.358404 2.419989 2.315867

1.968E-05 2.187E-05 0.003456 0.002683 563.6308 8245.635 1.751539882 3.534495 2.461465 2.571397

1.917E-05 2.164E-05 0.00262 0.002655 563.6308 10994.18 1.423849674 3.659434 2.581705 2.575881

1.856E-05 2.163E-05 0.002077 0.002212 563.6308 13742.72 1.212520056 3.756344 2.68247 2.655244

1.782E-05 2.135E-05 0.00183 0.001808 563.6308 16491.27 1.063355382 3.835525 2.737649 2.742847

1.739E-05 2.122E-05 0.001587 0.001737 563.6308 19239.81 0.95164889 3.902472 2.799324 2.760234

1.721E-05 2.125E-05 0.001632 0.001535 563.6308 21988.36 0.864415495 3.960464 2.787373 2.813994

F1 F2 F3 Corr.

Air 1 0.802955 1 0.802955

Water 1 1 1 1

CO2 1.238 1 1 1.238

CO2 Vg

(ft/s) air Vg (ft/s)

CO2 G

[lbm/h*ft2

]

air G

[lbm/h*ft2]

0.0420339 0.8860403 17.402 0.000

27

100% QWater

[gpm] QAir [pisg] Tower Across [ft

2]HCO2 [atm]

@ 70FDAB (cm2/s)

ρwater

(lbm/ft3)

ρair

(lbm/ft3)

ρCO2

(lbm/ft3)

Packing

Height [ft]

μwater

(lbm/ft-s)

21.6 8.1 0.196349541 1082.18 1.77E-05 62.3 0.074887 0.1144 5.5 0.000669

DAB (ft2/hr)

6.86E-05 0.66248

0.115

MW air (g/mol) 28.96

MW CO2 (g/mol) 44

0.00076

ρsoda ash (lbm/ft3)1

529.67

0.7302413

P atm

Air Temp (Rankine)

R (ft3*atm/R*lb-mol)