Gas Absorption in a Packed Tower Unit Operations Laboratory - Sarkeys E111 April 15 th & 22 nd, 2015 ChE 3432 - Section 3 Eric Henderson Eddie Rich Xiaorong Zhang Mikey Zhou
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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. Countercurrent 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. 2
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 Figure 1 Left: structured packing. Right: Dumped packing. 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. 3
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 Figure 2 Absorption of gas solute A by the liquid phase resistance to diffusion across the liquid-gas interface, the tworesistance 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 4
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 = av g b (Eq n 1) where ΔP is the pressure drop per unit height of packing, a and b are constants, and V g 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, K L, to the individual phase coefficients: 1 = 1 + 1 (Eq n 2) K L mk G k L where k G and k L are the individual phase coefficients. However, because CO2 has a low solubility in water, the system is said to be liquid-phase controlled and K L is essentially equal to k L (Welty 560). Correlated values of K L are found using equation 3 (Welty 587): 5
K L = αd AB ( L μ )1 n ( 1 μ 2 ) ρd AB (Eq n 3) where α is the packing coefficient, D AB 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, ( 1 μ ) ρd AB 2, is constant. A plot of 1 K L vs. 1 1 D AB ( L μ )1 n ( μ 2 ) ρd AB should yield a straight line with slope 1 that passes through the origin. If a straight line through the origin is not observed, then the α coefficient 0.72 is not valid (lab manual). In order to verify the above correlation, experimental values of K L 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): K L exp = N CO 2 ha c Δx lm (Eq n 4) where N CO2 is the number of moles of CO2 transferred per hour, h is the height of the packing in ft., A c is the tower cross-sectional area, and Δx lm is the logarithmic mean composition difference, given by equation 5 (lab manual): Δx lm = (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. 6
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 Figure 3 Packed tower apparatus 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. 7
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 Figure 4 Back of packed tower apparatus 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 8
Figure 5 Packed tower apparatus operating panel 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 9
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 10
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 11
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. 12
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 Figure 10 Comparison of G vs L plots for Structured packing (left) and dumped packing (right) 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. 13
log(k L a) 1/K L a 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. 0.006 0.005 Structured Dumped y = 0.001756652x R² = 0.941100993 0.004 y = 0.001844930x R² = 0.922722441 0.003 0.002 0.001. 0 0 0.5 1 1.5 2 2.5 1/(D AB (L/μ) 0.72 (Sc) 0.5 ) Figure 11 Sherwood and Holloway correlation for structured and dumped packing 2.9 2.8 Structured Dumped y = 0.705x + 0.0193 R² = 0.9599 log-log 2.7 y = 0.7645x - 0.2066 R² = 0.9484 2.6 2.5 2.4 2.3 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 log(l/μ) Figure 12 log-log plot of KLa to L/μ for structured and dumped packing. 14
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 a were used to find the experimental exponent 1-n for L/µ in equation 3. K L value was estimated by a using equation 4. Then we made a log-log plot of K L 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 15
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, (8 th 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. 16
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 = Top-Mid ΔP/h = % Max Water FR Max Water FR Mid-Bottom ΔP/h = 1 ft 3 = 7.48 gal Liquid FR = Top Mid ΔP Packing height 0.28 in H2O 66 in Water FR [gpm] 7.48 gal 60 s min 40 100 = 100 = 8.4 gpm 21 = Cross-Sectional Area = π 0.52 4 Air FR = Experimental Air FR Unit Conversion Air velocity = Vg = 0.3 in H2O 0.3 in H2O = = = 0.005 5.5ft 12 in 66 in ft = 0.004 8.4 gpm 7.48 gal 60 s = 0.019 ft3 s min = 0.196 ft 2 where 0.5 ft is the column diameter = 5 ft3 min 60 s = 0.083 ft3 s min Air FR = 0.083 ft 3 s Column Area 0.20 ft 2 = 0.424 ft s Liquid Molar FR = L = Density of Water Liquid FR Column Area = 62.3lbm ft 3 0.019ft3 s 3600 s = 21378.99 lb m 0.20 ft 2 hr h ft 2 Air Molar FR = G = Density of Air Air FR Column Area = 0.075lbm ft 3 0.083ft3 s 3600 s = 114.52 lb m 0.20 ft 2 hr h ft 2 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 17
CO2 Incorporation G CO2 = Vg CO2 Density CO 2 = 0.042 ft s 0.1144 lb m s 3600 ft3 hr = 364.9 lb m hr ft 2 lb G CO2 ( hr ft G CO2 = 2) A cs(ft 2 lb ) (364.9 hr ft MW CO2 ( lbm = 2) (0.196 ft2 ) lbmol lbmol ) (44 lbm = 1.628 ( lbmol ) hr ) G Total = G Air + G CO2 = (1.619 lbmol lbmol ) + (1.628 ) = 3. 25 (lbmol hr hr hr ) Correction Factors T( ) + 460 75 + 460 f T = Correction Factor for Temperature = = = 1.00 530 530 14.7 f P = Correction Factor for Pressure = psig + 14.7 = 14.7 0 + 14.7 = 1.00 f MWg = MW 29 ( lb m ) g lb = mol MW Air 29 ( lb = 1.00 m ) lb mol f MWCO2 = Correction Factor for MW = MW CO 2 = 44 ( lbm lbmol ) MW Air 29 ( lbm = 1.238 lbmol ) Structured N CO2 = G Total ((Y CO2 ) Middle (Y CO2 ) Top ) = 3.25 (0.0209 0.02262) = 0.00570 lbmol hr Dumped N CO2 = G Total ((Y CO2 ) Bottom (Y CO2 ) Middle ) = 3.25 (0.02262 0.02411) = 0.00484 lbmol hr 18
Structured ΔX lm = (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 0 2.1 10 5 0 ) = 2. 011 10 5 Dumped ΔX lm = (x x) Middle (x x) Botom = 2. 166 10 5 ln { (x x) Middle (x x) Bottom } = (2.1 0) (2.237 10 5 0) ln ( 2.1 10 5 0 2.237 10 5 0 ) 1/K L a = 1 N ( lbmol hr ) X lm h(ft) A cs (ft 2 ) = = 0.0038 ( lbmol hr ft 2) 1 1 (0.0057) lbmol hr (4.83 10 5 ) (5.5ft) (0.196ft 2 ) lbm L ( D AB ( ft2 hr ) ( hr ft 2) lb ) μ ( hr ft ) = 0.72 1 ( lb μ ( hr ft ) lbm (5497.09 (6.855 10 5 ft2 hr ) ( hr ft 2) ) lb (0.000669 3600 hr ft ) = 2.3453 ρ ( lbm ft 3 ) D AB ( 0.72 1 ( ft 2 hr ) ) 0.5 lb hr ft ) (62.261 lbm ft 3 ) (0.000669 3600 (6.855 10 5 ft2 hr ) ) 0.5 o D AB = Diffusivity of Carbon Dioxide in Water o μ = Viscosity of Water 19
Supplementary Equations: Middle of Tower: x in L y in G x out L y out G x out x in L y in G y L out G xin=0 because no CO2 enters with liquid phase Equation becomes x out yin y L G 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: x out x in * L G y L G out y in 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 20
o x*=mole fraction of CO2 at equilibrium Lb Moles Transferred Per Hour = N = ( 1 ) ( yco2, top Ptop yco2, bottom Pbottom) (air flow rate) RT 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 = K a L N H * A* X lm o Moles Transferred per hour = N P P o H = Henry s Law Constant o A = Cross-Sectional Area of Tower CO 2 CO w w 1 Vg RT Where N given by: Also: K a * D L AB N P P CO *( L / ) 2 CO w w 1 0.72 *( u * D Vg RT AB ) 1/ 2 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 21
Log-Mean Difference for Mole Fraction of CO2 = X lm ( x * x) 2 ( x * x) 1 ( x * x) 2 ln ( x * x) 1 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 22
Load 32 38 19 2.8 0.576 0.288 0.533 2.716 732.897 1.580 1.279 0.434 30 50 13.8 3.4 0.758 0.209 0.500 2.546 687.091 1.699 1.140 0.406 Flood 31 50 14 3.3 0.758 0.212 0.517 2.631 709.994 1.699 1.146 0.420 5 0.2 0.18 0.5 0.003 0.003 0.083 0.424 114.515-0.699-0.745-0.372 10 0.8 0.6 0.5 0.012 0.009 0.167 0.849 229.030-0.097-0.222-0.071 15 1.7 1.25 0.7 0.026 0.019 0.250 1.273 343.545 0.230 0.097 0.105 20 3.6 2.1 0.8 0.055 0.032 0.333 1.698 458.061 0.556 0.322 0.230 30 6.3 25 4.5 3.5 1 0.068 0.053 0.014 0.417 2.122 16034.239 572.576 0.653 0.544 0.327 30 18 15 2.1 0.273 0.227 0.500 2.546 687.091 1.255 1.176 0.406 Load 20 3.5 3.25 0.9 0.053 0.049 0.333 1.698 458.061 0.544 0.512 0.230 Flood 26 40 20 2.6 0.606 0.303 0.433 2.207 595.479 1.602 1.301 0.344 5 0.3 0.28 0.4 0.005 0.004 0.083 0.424 114.515-0.523-0.553-0.372 10 0.95 0.85 0.6 0.014 0.013 0.167 0.849 229.030-0.022-0.071-0.071 40 8.4 15 2 1.8 0.7 0.030 0.027 0.019 0.250 1.273 21378.986 343.545 0.301 0.255 0.105 Load Water FR 16 Air FR Top-Mid 4.8 ΔP 5 Column 1 0.073 Top-Mid Mid-Bottom 0.076 Liquid FR 0.267 Air FR 1.358 366.449 G 0.681 0.699 0.133 Flood (gpm) (ft 17 3 /min) (in. 42 of H20) 22 Gas 2.8 (psi) 0.636 ΔP/h 0.333 ΔP/h (ft 3 /s) 0.283 (ft 3 Vg 1.443 (ft/s) L (lb m /h*ft 2 ) /s) (lb 389.352 m /h*ft 2 1.623 1.342 log ) 0.159 (Vg) Max Water FR 43 % of 9.03 0.020 22982.410 Mid- Bottom ΔP (in. of H20 Top-Mid log (ΔP/h) Mid- Bottom log (ΔP/h) 5 0.3 0.3 0.4 0.005 0.005 0.083 0.424 114.515-0.523-0.523-0.372 10 0.9 0.8 0.5 0.014 0.012 0.167 0.849 229.030-0.046-0.097-0.071 15 2.2 1.8 0.7 0.033 0.027 0.250 1.273 343.545 0.342 0.255 0.105 % of Max Water FR Water FR (gpm) (ft 3 /min) Air FR Top-Mid ΔP (in. of H20) Mid- Bottom ΔP (in. of H20 Column Gas (psi) Top-Mid Mid-Bottom Liquid FR ΔP/h ΔP/h (ft 3 /s) (ft 3 /s) (lb m /h*ft 2 ) Vg (ft/s) L (lb m /h*ft 2 ) Air FR G Top-Mid log (ΔP/h) Mid- Bottom log (ΔP/h) log (Vg) 23 Raw Data Day 1
% of Max Water FR Water FR (gpm) Air FR (ft 3 /min) Top-Mid ΔP (in. of H20) Mid- Bottom ΔP (in. of H20 Column Gas (psi) Top-Mid Mid-Bottom Liquid FR ΔP/h ΔP/h (ft 3 /s) Air FR (ft 3 /s) Vg (ft/s) L (lb m /h*ft 2 ) G (lb m /h*ft 2 ) Top-Mid log (ΔP/h) Mid- Bottom log (ΔP/h) 5 0.2 0.12 0.4 0.003 0.002 0.083 0.424 114.515-0.699-0.921-0.372 10 0.72 0.5 0.5 0.011 0.008 0.167 0.849 229.030-0.143-0.301-0.071 15 1.5 1 0.5 0.023 0.015 0.250 1.273 343.545 0.176 0.000 0.105 20 2.6 1.68 0.7 0.039 0.025 0.333 1.698 458.061 0.415 0.225 0.230 20 4.2 0.009 10689.493 25 4 2.5 1 0.061 0.038 0.417 2.122 572.576 0.602 0.398 0.327 30 6 3 1.2 0.091 0.045 0.500 2.546 687.091 0.778 0.477 0.406 Flood 35 21 5.8 1.5 0.318 0.088 0.583 2.971 801.606 1.322 0.763 0.473 36 35 15 2.75 0.530 0.227 0.600 3.056 824.509 1.544 1.176 0.485 log (Vg) 5 0.2 0.14 0.45 0.003 0.002 0.083 0.424 114.515-0.699-0.854-0.372 10 0.7 0.4 0.5 0.011 0.006 0.167 0.849 229.030-0.155-0.398-0.071 15 1.5 0.8 0.5 0.023 0.012 0.250 1.273 343.545 0.176-0.097 0.105 20 2.5 1.5 0.75 0.038 0.023 0.333 1.698 458.061 0.398 0.176 0.230 10 2.1 25 3.5 2 0.9 0.053 0.030 0.005 0.417 2.122 5344.746 572.576 0.544 0.301 0.327 30 5.3 3 1.1 0.080 0.045 0.500 2.546 687.091 0.724 0.477 0.406 35 7.5 4 1.4 0.114 0.061 0.583 2.971 801.606 0.875 0.602 0.473 40 10.6 5.4 1.75 0.161 0.082 0.667 3.395 916.121 1.025 0.732 0.531 45 14.4 7.3 2.1 0.218 0.111 0.750 3.820 1030.636 1.158 0.863 0.582 5 0.19 0.09 0.4 0.003 0.001 0.083 0.424 114.515-0.721-1.046-0.372 10 0.6 0.31 0.45 0.009 0.005 0.167 0.849 229.030-0.222-0.509-0.071 15 1.25 0.69 0.5 0.019 0.010 0.250 1.273 343.545 0.097-0.161 0.105 20 2.1 1.1 0.6 0.032 0.017 0.333 1.698 458.061 0.322 0.041 0.230 0 0 25 3.3 1.67 0.75 0.050 0.025 0.000 0.417 2.122 0.000 572.576 0.519 0.223 0.327 30 4.9 2.4 1 0.074 0.036 0.500 2.546 687.091 0.690 0.380 0.406 35 6.5 3.2 1.4 0.098 0.048 0.583 2.971 801.606 0.813 0.505 0.473 40 9 4.3 1.6 0.136 0.065 0.667 3.395 916.121 0.954 0.633 0.531 45 11.5 5.5 2 0.174 0.083 0.750 3.820 1030.636 1.061 0.740 0.582 24
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 Tower Air Flowrate [SCFM] Air Flowrate [ft 3 /s] CO2 flowrate [SCFM] CO2 flowrate [ft 3 /s] G CO2 [lbm/h*ft2] G air [lbm/h*ft2] Vg CO2 [ft/s] Vg air [ft/s] Day 2 13 0.173974 0.4 0.00825 364.9068 238.87043 0.042034 0.8860403 % of Max Water FR Q Water [gpm] Q Water [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 25
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] 1.628393 1.619548 3.24794 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 structured Δx lm dumped Δx lm structured 1/K L a dumped 1/K L a Sc L [lb m /h*ft 2 ] 1/(D AB (L/μ) 0.72 (Sc) 0.5 ) log(l/μ) structured Log(K l a) dumped log(k l a) 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 F 1 F 2 F 3 Corr. Air 1 0.802955 1 0.802955 Water 1 1 1 1 CO2 Vg (ft/s) CO 2 1.238 1 1 1.238 air Vg (ft/s) CO2 G [lbm/h*ft2 ] air G [lbm/h*ft2] 0.0420339 0.8860403 17.402 0.000 26
100% Q Water [gpm] Q Air [pisg] Tower A cross [ft 2 ] H CO2 [atm] @ 70F D AB (cm 2 /s) ρ water (lb m /ft 3 ) ρ air (lb m /ft 3 ) ρ CO2 (lb m /ft 3 ) Packing Height [ft] μ water (lb m /ft-s) 21.6 8.1 0.196349541 1082.18 1.77E-05 62.3 0.074887 0.1144 5.5 0.000669 P atm Air Temp (Rankine) R (ft3*atm/r*lb-mol) 1 529.67 0.7302413 D AB (ft 2 /hr) 6.86E-05 ρ soda ash (lb m /ft 3 ) 0.66248 0.115 MW air (g/mol) 28.96 MW CO 2 (g/mol) 44 0.00076 27