Recovery of Sulfur Dioxide H. F. JOHNSTONE AND A. D. SINGH University of Illinois, Urbana, Ill.
Measurements of the rates of absorption and heat transfer and of the resistance to gas flow were made for a number of arrangements of (a) vertical smooth plates, ( b ) vertical corrugated plates, with horizontal corrugations, set at various spacings and with different depths and frequencies of corrugations, (c) grid surfaces with various channel dimensions and arrangements, and, for comparison, ( d ) ordinary tower packing such as Raschig rings, spiral rings, and wire helices. The absorption data on sulfur dioxide by alkaline solutions, and on ammonia by acid solutions were found to be accurately correlated with heat transfer data by the Chilton-Colburn equation. Taking all factors into consideration, the most desirable packing of those studied for handling large quantities of flue gases is composed of grids with 1.5inch channels and with individual sections from 4 to 6 inches high.
use in the scrubbing of combustion gases. These characteristics are : 1. Minimum pressure drop 2. Minimum uantity of solution for maintaining wetness 3. Low cost o? material which must withstand any corrosive action of the absorbent 4. Minimum cross section to reduce floor space 5 . Open channels to prevent clogging by flue dust 6. Low weight
7. Resistance to crystal growth in order to prevent scaling
Many of these items are not important in treating smaller quantities of gases. For large volumes, however, they seriously enter into the choice of contact surfaces, and the final design cannot be made without a proper balance of the cost contribution of each. As an important part of the present investigation, a consideration of the types of scrubber surfaces available was imperative. Measurements of the rates of absorptioh and of draft losses were made for a number of arrangements of (a) vertical smooth plates, (b) vertical corru-
T
HE treatment of large quantities of gases to remove a
dilute constituent is a relatively new engineering problem. The chemical industries have developed scrubbers for handling gas volumes of the order of a million cubic feet per hour, such as in the absorption of gasoline from natural gas. I n air conditioning, even larger volumes of gas are treated to accomplish the relatively easy processes of humidification and cooling, The scrubbing of waste gases to remove sulfur dioxide, however, such as those from the combustion of coal, is a different problem. The quantity of gas may readily amount to a million and a half or two million cubic feet a minute. The gases are hot and dust-laden and the concentration of sulfur dioxide is of the order of 0.2 to 0.3 per cent by volume. At best, therefore, the rate of absorption is none too great. Unless the scrubber is properly designed, it will be highly inefficient and its bulk out of proportion to the job it is doing. Furthermore, the operating costs, which include power for fans and pumps, will be excessive if the draft loss is much over one inch of water, if the quantity of liquid required for wetting the surfaces is large, or if the height of the scrubber is great. In the three installations that have been reported (IO,I7), some sort of contact surface was found highly superior to simple spray washers. This has also been found true in a pilot plant operated in the present investigation. I n one foreign installation a simple network of channel irons is used; in another, small wooden grids, closely spaced, have been found highly efficient. The usual form of tower packing was designed to give the maximum rate of gas absorption without giving much consideration to the other characteristics which are essential for
BOX
HEATER
FfGURE
286
VENTURI
METER
1. ABSORPTION TOWER ASSEMBLY
from Waste Gases Design of Scrubbers for Large Quantities of Gases' gated plates, with horizontal corrugations, set a t various spacings and with different depths and frequencies of corrugations, ( c ) grid surfaces of various depths, spacings, and arrangements, and, for comparison, (d) ordinary tower packing such as Raschig rings, spiral rings, and wire helices. Surprisingly, absorption data on the latter do not appear to have been published, and, therefore, the results presented should be useful to many chemical engineers interested in the absorption operation. As far as possible, the data for each type of surface have been correlated both in respect to the dimensions of the packing and to the gas absorbed. The correlated results therefore form a contribution to the flow of fluids and mass transfer through tortuous channels. The final equations have been used in the design of a scrubber for a pilot plant removing sulfur dioxide from flue gases by a cyclic process employing chemical regeneration.
IRON
II
DETAILS OF GRIDS
HERMOMETER MOL
1
S P A C l N O BETWEE METAL WALLS
13
O R l P P A N T
48'
i
"
Method of Investigation THERMOMETER
HOLE I'PIPE I n some preliminary work (6) it was NIPPLE \u;1 TOWER @ ascertained that the liquid film resistTOWER @ TOWER @ ance in the absorption of sulfur diFIGURH 2. DETAILS OF ABSORPTIONTOWERS oxide is reduced to a negligible quantity when the gas is absorbed by the application of heat transfer data to absorption design, or alkaline solutions, or by solutions containing appreciable vice versa. quantities of buffer ions, regardless of the alkalinity, of pH. Since these solutions are the ones of most interest as solvents Experimental Procedure for the gas, it is possible to neglect the liquid film and to study The assembly of the absorption towers is shown in detail the gas film only. Further evidence of the absence of the in Figures 1 and 2: liquid film resistance will be found in Figure 3 in which the extrapolation of the over-all film coefficient for several of A measured quantity of air was forced through an insulated the absorption surfaces to infinite velocity passes through the duct comprising, or containing, the wetted surfaces. Temperature measurements, or gas analyses, and pressure determinazero of the reciprocal plot. This is the accepted method of tions were made at two oints in the gas stream. For the corrudetermining the absence of the liquid film (23). Partly in gated and smooth sur&ces (Figures 1 and 2C, respectively), order to make the results applicable to all gases and partly for ordinary black iron sheets were used. These were thoroughly convenience, it was decided to determine the film coefficients cleaned with an acid sulfite solution which was found to remove effectively the oxide scale and grease so that a uniform film of of the various surfaces by measuring rates of evaporation of water could be obtained. With these towers only one wall was water as determined by wet- and dry-bulb observations. wetted. The stoneware, wire, and grid packings were placed in These data were then to be used for predicting sulfur dioxide larger rectangular ducts, the size of which was chosen to suit the absorption coefficients by means of the Chilton-Colburn dimensions of the packing and the capacity of the fan available (Figures 2A and B , respectively). analogy (4). Sufficient data were taken on the rates of abThe Venturi meter was calibrated by weighing the quantity sorption of sulfur dioxide by alkaline solutions and of amof air flowing through it from a large tank. The equipment used monia by dilute acetic acid solutions to confirm the predicted is a part of that assembled in the EngineeringExperiment Station values of the coefficient. Since the humidity data are acfor studying flowmeters (18). Pressure measurements were made at points sufficiently retually heat transfer measurements, the work, therefore, esmoved from the entrance t o avoid the effect of the baffles at the tablishes the accuracy of the suggested analogy and confirms lower end of the tower. For draft losses below 0.5 inch of water, a Wahlen micromanometer (88)capable of reading to 0.0001 inch 1 For previous articles in this series see literature oitstions 28 and IS.
287
288
INDUSTRIAL AND ENGINEERING CHEMISTRY
of water was used. For greater pressure differences an inclined gage was sufficiently accurate. Temperature measurements were made with thermometers graduated t o 0.1 F. and calibrated against a Bureau of Standards thermometer. The usual technic was used in determining the wet-bulb temperature. The thermometer with the wick wetted with distilled water was inserted into the gas stream and the temperature read at 1-minute intervals for 5 minutes. Simultaneous readings were made on both the wet and dry thermometers at the two points in order t o avoid errors due t o fluctuations of air temperatures. With this precaution, the data for the 1-minute intervals often agreed within 0.02' F. The wetand dry-bulb observations were used only t o measure heat transfer and were not converted t o humidity values. This was done t o avoid the uncertainty of any conversion factors and, furthermore, to eliminate the double dependence of the data on the wet-bulb observations. The wet bulb was used only t o determine the temperature of the water interface, and it should have done this accurately since precaution was taken t o introduce the water at the top within 1" F. of the wet-bulb tem erature at the highest sampling point. dsorption measurements were made by introducing a small amount of sulfur dioxide, or ammonia, in front of the fan intake and analyzing the gas at two sampling oints simultaneously. In order to avoid a liquid &m resistance and also to prevent a finite equilibrium vapor pressure over the solution, a dilute solution of sodium hydroxide or acetic acid was used, respectively, for the two gases. Analyses of the gas for sulfur dioxide, or ammonia, were made by drawing samples, respectively, through a standard solution of sodium hydroxide c on t a i n i n g hydrogen peroxide, or through P standard solution of hydrochloric acid. The volume of the inert gas was determined by wet test meters placed in series after the absorption bottles and the exhauster . Simultaneous samples were drawn from tE%% sampling points in order t o avoid errors due to fluctuations of gas compositions. The measurements covered a range of actual gas velocities from 4 to 18 feet per second. At the highest velocities some spray was blown from the surfaces even in the case of the vertical smooth sheets. The data were taken over a period of about 8 months during which time the wet-bulb temperature of the entering air varied from 55" to 65" F. and the dry bulb from 70" to 95'. Some measurements were taken with heated air in which the lower dry bulb reached 195" F. The data on these runs agreed with those on cold air after making suitable modifications of the constants a s i n d i c a t e d below.
Correlation of Heat Transfer and Absorption Data The analogy between t h e p r o c e s s e s of momentum transfer and heat transfer was first recognized by Reynolds. The possibility of correlating fluid friction data with heat transfer data has been useful as a means of predicting heat transfer in tubular heaters. Colburn (6) showed that a modified Reynolds analogy, into which the Prandtl group is introduced, holds for turbulent flow parallel to plane surfaces as well as for flow inside tubes, but does not apply to viscous flow in tubes nor to flow across tubes and tube banks. This equation reads :
TABLE1. HEATTRANSFER DATAON VERTICAL CORRUGATED AND SMOOTH SHEETS Air Entering Air Leavine Air - I _ Run Flow, Dry Wet Dry Wet No. Go bulb bulb bulb bulb
Lb./(hr.) (8g.A.)
O
F.
P.
A.
F.
Transfer Factor, H. T. U. j for SO,
leg
dsGa fi
YO
F.
-
VERTICAL CORRUGATED SHEETS;WAVELENQTH= l'/f IN.; TOWERLENGTH= 8 FT.; DISTANCE BBTWEEN SAMPLING POINTS= 7.6 FT A = 11.93 Sa. FT.; WETTEDPERIMETER 1.47 FT.: WATERR A T i ' = 37 LB.//HR.)fFT.) ,. Channel Width, da = 1 In.: S = 0.122 Sa. Ft. l a 1950 76.21 56.32 65.88 58.67 0.00977 7 . 9 5 0.57 7 025 0.00134 lam 1950 76.47 56.58 65.04 58.77 0.00997 7.95 0.58 7:025 0.00136 0.00126 2" 2130 75.05 56.00 65.60 58.12 0.00905 8 . 5 8 0.58 7 660 2aa 2130 75.47 56. 08 65.92 58.21 0.00890 8.73 0.57 7:660 0.00124 3 2380 81.48 70.57 74.82 71.29 0.00862 9 . 0 1 0.61 8,560 0.00122 3a 2380 81.39 70.68 74.84 71.37 0.00862 9.01 0.61 8,560 0.00122 4a 2670 74.97 55.48 65.40 57.41 0.00879 8 . 8 4 0.67 9,600 0.00122 4aa 2670 75.18 55.53 65.55 57.44 0.00874 8.89 0.67 9 600 0.00122 5 2740 80.94 68.32 73.55 69.52 0,00829 9.38 0.68 9:840 0.00121 Sa 2740 80.77 68.36 73.46 69.68 0.00840 9 . 2 4 0.68 9 840 0.00121 6 3060 81.70 70.11 74.76 70.83 0.00840 9.24 0.76 11:ooo 0.00123 6a 3060 81.61 70.26 74.86 70.94 0.00815 9.53 0.74 11,000 0,00120 7a 3120 74.51 55.22 65.16 66.75 0.00850 9.14 0.79 11.220 0.00127 7aa 3120 74.96 55.29 65.30 56,44 0.00863 9.00 0.81 11,220 0.00130 8 3450 80.79 68.18 73.46 69.16 0.00803 9.68 0.80 12 400 0.00118 Sa 3450 80.25 68.17 73.36 69.15 0.00776 10.00 0.83 12,'400 0,00122 3520 80.90 68.03 73.30 68.94 0.00815 9 9.53 0.86 12 650 0.00124 Sa 3520 80.66 68.20 73.41 69.07 0.00795 9 . 7 7 0.84 12:650 0.00122 l o a 3690 74.21 54.80 65.16 56.16 0.00790 9.84 0.88 13,300 0.00123 lOaa 3690 74.08 54.88 64.97 56.14 0.00807 0.86 9.62 13,300 0.00120 11 3980 79.84 68.02 73.09 68.85 0.00771 10.06 0.92 14,300 0.00120 l l a 3980 79.91 68.00 73.19 68.83 0.00760 10.22 0.90 14,300 0.00118 12 4550 79.46 67.61 72.55 68.38 0.00796 0.00784 1.08 9.76 16,360 0.00127 12a 4550 79.72 67.81 72.82 68.53 9.92 1.06 16,360 0.00125 I
~
~
Av. 0,00124
-
VERTICALC O R R U Q A TSHEETS; ~D WAVELENQTH= 25/8 IN.; TOWERLENGTH 8 FT.; WETTEDPERIMETER = 1.34 FT.; WATERRATE= 20 TO 50 LB./(HR.)(FT.) Channel Width, de = 1 In.; S = 0.110 Sq. Ft.; Distance between Sampling Points, 6.9 Ft.; A = 9.72 Sa. Ft. 1 1940 73.28 63.36 66.84 64.59 O.OlO68 7.32 0.61 6,950 0.00143 l a 1940 73.23 63.19 66.82 64.50 0,01068 7.32 0.61 6,950 0.00143 2 2130 79.58 69.64 73.61 70.87 0,00986 7.92 0.63 7 630 0.00137 2a 2130 79.58 69.77 73.71 70.99 0.00994 7.86 0.63 7:630 0.00137 3 2160 72.82 61.96 66.15 63.08 0.00971 0.01008 0.65 7.75 7 800 0.00140 3a 2160 72.66 61.77 66.17 63.01 8.04 0.62 7:800 0.00133 4 2760 73.00 62.15 66.65 63.19 0.00921 8.48 0.76 9,880 0.00134 4a 2760 72.84 62.50 66.72 63.25 0.00833 9.38 0.69 0 880 0.00122 5 2805 79.55 70.44 72.10 69.25 0.01293 6.03 0.80 10:050 0.00139 6 2830 79.68 69.95 73.96 70.84 0.00924 0.00922 8.47 0.78 10 120 0.00134 6, 2830 79.60 69.97 73.86 70.78 8.46 0.78 10:120 0.00134 7 3385 72.89 62.35 66.79 66.03 0.00868 9.00 0.88 12,110 0.00132 0.00135 7a 3385 72.65 62.13 66.57 62.99 0.00885 8.83 0.90 12,110 8 3815 71.00 61.20 65.79 62.06 0.00774 1.01 0.88 13,660 0.00125 Sa 3816 71.36 61.35 65.84 62.13 0.00814 9.60 0.92 13,660 0.00120 9 4220 79.90 69.92 74.14 70.48 0.00857 9.13 1.08 15 100 0.00135 9a 4220 80.29 69.95 74.28 70.65 0.00869 8.99 1.09 15:lOO 0.00136 10 5485 71.50 61.09 66.11 61.70 0.00725 1.19 10.76 19,600 0.00122 10a 5485 71.48 61.18 66.10 61 78 0.00730 IO.68 1 . 1 9 19,600 0.00122
B.
Av. Channel Width, dr
1 2 3 3a 4 4a 5 5a 6 7 8 8s
1606 1650 2310 2310 3120 3100 3920 3920 3990 4030 4485 4485
81.42 SO. 56 81.57 81.50 79.99 81.34 81.62 81.33 77.54 76.96 76.43 75.88
2 In.; S = 6.9 71.33 77.28 71.46 76.71 70.34 77.26 70.54 77.28 67.76 76.26 70.19 77.18 70.78 77.84 71.34 77.91 64.46 73.31 62.96 72.85 63.77 72.31 62.04 71.82 =
0.220 Sq. Ft.; Distanoe between Sampling Ft.; A = 9.80 Sq. Ft. 71.61 0.00994 15.57 0.48 10 840 71.52 0.01210 12.80 0.51 11:lSO 70.54 0.00906 17.08 0.62 15 600 70.61 0.00900 17.20 0.62 l5:600 70.05 0.00775 20.00 0.72 21,200 70.44 0.00876 17.66 0.81 20,950 71.20 0.00815 19.00 0.95 26,500 71.51 0.00782 19.80 0.92 26,500 64.84 0.00735 21.07 0.87 26,950 63.84 0.00668 23.18 0.80 27 230 63.83 0.00709 21.86 0.95 30:250 62.76 0.00700 22.12 0.94 30,250 AV.
-
Channel W idth, dr = 3 In.; S = 0.33 Sq F t DistanoeI between A = ls.1Sq. Ft. 36.3 1 2080 78.10 65.75 75.43 66.07 0.00664 37.0 l a 2080 78.31 65.75 75.65 66.07 0.00651 38.3 2 2430 78.75 66.00 76.13 66.31 0.00628 38.3 2a 2430 78.76 66.10 76.16 66.38 0.00628 39.4 3b 2900 80.95 61.63 77.26 62.11 0.00611 42.4 46 3190 82.24 61.44 78.51 61.75 0.00568 40.2 5 3470 78.12 65.60 75.64 65.74 0.00699 41.3 Sa 3470 78.23 65.42 75.50 65.58 0.00582 30.6 6b 3720 81.99 61.32 78.07 61.62 0.00608 46.8 7 4010 76.17 64.41 74.15 64.68 0.00614 38.7 7a 4010 75.94 64.55 73.59 64.68 0.00623 40.8 8b 4160 82.05 60.86 78.05 61.14 0.00590 41.2 9 4580 76.80 64.37 74.38 64.52 0.00588
0.00133 Points
=
0.00132 0.00132 0.00140 0.00132 0.00115 0.00131 0.00126 0.00122 0.00114 0.00104 0.00113 0.00112 0.00123
Samplinig Points = 7.3 Ft.; 0.43 0.42 0.45 0.45 0.53 0.55 0.62 0.61 0.67 0.61 0.74 0.73 0.81
20,100 0.00096 20,100 0.00093 23,470 0.00089 23,470 0.00089 28,000 0.00085 30,800 0.00086 33,500 0.00091 33,500 0.00090 35,900 0.00093 38,800 0.00079 38,800 0.00096 0.00092 40,200 0.00094 44,200 Av.
A = 8.48 89. ft.; L = 5.4 ft. b A = 9.56 sq. ft.; L = 6.9 ft.
0
The quantity on the left will be recognieed as
VOL. 29, NO. 3
0.00090
~
I
MARCH, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY TABLEI (Continued)
Air Run Flow, No. Go
-------Air Entering
Air Leaving
7 -
Dry bulb
Dry bulb
Wet bulb
Wet bulb
Transfer
Faotor, H. T. U. 3
for SO1
kg
YO
P
Lb. moles SOa/(hr.) Lb./(hr.)
(84.
ft.)
F. F. F. F. Ft. (atm.) VERTICAL SMOOTH SHEETS.TOWER LENQTH= 8 FT.; DISTANCE BETWEEN SAMPLINQ POINTS= 5.0 FT A ' = 6.63 So. FT.; WETTED PERIMETER = 1.33 FT.; ~ ~ T RATE E B = 28 T O 42 LB./(HR.)(FT.) Channel Width, d s = 1.1 In.; S = 0.127 Sq. Ft. 22.3 0.29 5,360 0.00084 1500 8 0 , 8 4 69.14 78.12 69.83 0.00430 21.3 0.35 5,360 0.00101 1500 81.08 6 9 . 2 8 77.72 69.86 0.00450 13.6 0.32 5,711 0.00088 1600 90.00 8 0 . 4 8 8 6 . 6 3 8 0 . 9 3 0.00707 23.2 6,900 0.00087 0.37 1930 8 4 , 0 8 70.67 81.04 71.18 0.00413 6,900 0.00090 22.4 0.38 1930 8 4 , 2 1 71.14 81.15 71.60 0.00427 8,670 0.00083 15.7 0.42 2420 9 2 . 0 1 7 9 . 2 8 8 8 . 0 3 79.89 0.00610 17.4 0.60 13,900 0.00080 3880 9 2 , 5 4 77.58 8 8 . 2 3 78.22 0.00550 25.7 15,000 0.00085 0.68 4180 8 3 . 9 5 70.90 8 1 . 2 3 71.39 0.00373 21.2 15,000 0.00082 0.65 4180 84.07 7 0 . 4 5 8 1 . 5 8 7 0 , 7 7 0.00451 18.0 0.78 19,000 0.00082 5300 92.44 76.56 87.95 7 7 . 0 9 0.00532
(5Q.ft)
C.
1 la 2 3 3a 4 5 6 6a 7
1 la 2 2a 3 4 4a
.
1300 1300 2640 2640 3130 3840 3840
Channel Width, da = 83.89 69.54 8 1 . 1 3 69.58 83.99 6 9 . 7 4 80.78 69.83 8 5 . 0 1 7 0 . 4 8 8 2 . 2 7 70.65 8 4 . 9 1 70 20 8 2 . 5 1 70.37 85 08 70.22 82.80 70.36 8 4 . 9 3 70.13 8 2 . 8 7 7 0 . 1 9 84.99 70.47 82.67 70.61
2 In.; S 0.00584 0.00695 0.00574 0.00490 0.00458 0.00411 0.00477
=
0.221 Sq. Ft. 28.6 0.23 23.9 0.27 29.1 0.45 34.0 0.39 36.4 0.43 40.6 0.48 35.0 0.55
Av.
0.00086
8,800 8,800 17,830 17830 21:200 26,280 26,280
0.00075 0 00088 0,00083 0,00072 0.00069 0,00065 0.00074
Av. a b
-4 = 8.48 sq. ft.; L A = 9.55 sq. ft.; L
= =
0.00075
5.4 ft. 6.9 ft.
289
At first it was expected that the wet- and drybulb observations could be expressed in terms of the partial pressure of water, using the usual psychrometric equation ( I I ) , and the differences a t the two sampling points could be used to calculate k, for sulfur dioxide. It was found, however, that these calculated values were uniformly about 20 to 30 per cent higher than those observed from the actual absorption data. However, if Equation 4 were used instead of the usual psychrometric equation, the data were found to agree much better. This agreement is shown in Figure 4 where the j factors calculated from heat transfer by the wet- and dry-bulb readings are seen to agree fairly well with those from absorption measurements on both sulfur dioxide and ammonia. The discrepancy mentioned above might be said t o indicate that the constant in the psychrometric equation is in error. As a matter of fact the value, which is empirical, does differ considerably from that found by substitution of the constants for water and air in Equation 4. Sherwood and Comings (go), however, in a n attempt to correlate wet- and dry-bulb measurements on various substances, noted a tendency for water vapor to differ from organic vapors, so that there may be other factors entering into the countertransfer of heat and water molecules through the film surrounding a wet bulb. At present,
equal to the familiar Fanning friction factor, f/Z; that on the right has been designated by Colburn as a heat transfer factor, j . Recently Chilton and Colburn (4) called attention to the fact that the transfer of material by diffusion is closely related to heat transfer, since the latter can be considered merely as diffusion of hot molecules into a region of cold ones and a corresponding diffusion of cold molecules in the reverse direction. In humidification, both mass transfer and heat transfer take place simultaneously. The analogy leads to the expectation that the group,
( ~ ) ( ~ ) ( ~= j ) z ' 8 will be the same function of the Reynolds number as the corresponding heat transfer factor and will equal the friction factor under the same conditions as it does. Although the two-thirds exponent on the Prandtl group has been fairly well established from heat transfer data on several substances, the power function of ( p / p k d ) was chosen mainly by analogy, owing to the almost complete absence of uniform absorption data. Isolated measurements on the absorption and evaporation of water in falling film towers and on evaporation from plane surfaces of reservoirs, however, were found to agree fairlv well with the value Dredicted from the fricGon factor, although thk data of Gilliland N k a, and Sherwood (8) for the mass transfer factors of a number of organic vapors as well as for water in a falling film tower were somewhat higher than the predicted values. When the diffusing vapor is relatively dilute, as is the case in all of the present measurements, the relation between the individual gas film coefficient k, and the factor j is given by
4~
3%
k,
-.:-"(?/&) At, rrM,
z /a
pkd
(4)
FIGURE3. ABSENCEOF LIQUIDFILMIN THE ABSORPTION OF SULFUR DIOXIDE BY ALKALINE SOLUTIONS
--
A
-
a
HEAT TRANSFER
A
302 ABSORPTION BY 0.5N NaOH NH~ABSORPTION BY 0.3 N cn6oon
o
-+
I
. I /JJ
0
y\
0
A0 1
FIGUREI 4. CORRELATION OF HEAT TRANSFER WITH ABSORPTION DATAON GRID-PACKED TOWERS USINGTHE CHILTON-COLBURN ANALOGY
INDUSTRIAL AND ENGINEERING CHEMISTRY
290
however, i t is sufficient to conclude that for practical purposes the heat transfer measurements reported here, on the basis of the single assumption that the temperature of the wet bulb is the same as that of the water surface, agree with the absorption measurements on the basis of the Chilton-Colburn equation. The actual experimental data on heat and mass transfer, together with the more important calculated quantities, are given for all of the measureme@ in Tables I to IV. All of the data from the temperature measurements and those for ammonia absorption have been converted to the absorption coefficient k, for sulfur dioxide by means of Equation 4. The values used for the constants (in C. G. S. units) in the various groups were those for 25" C. as follows : c = 0.237 p = 1.154 X p
IC
= 0.00018
0.0000568
k d for so2 = 0.116 kd for NHa = 0.196
Since the effect of temperature on the groups themselves is negligible, the use of these values for all the measurements, except those few a t high temperatures, is justified. For the latter, suitable corrections were made according to the accepted equations for the effect of temperature. The values of A , the area of contact, for the wetted walls were taken as the actual wetted area. For the grids the area was estimated from the dimensions of the sections, excluding the horizontal surfaces on the edges. The general equation for the effect of velocity on the absorption coefficient is expected to be Lo = YO GO)".^ (5)
As a matter of fact, the slopes of the lines on the logarithmic plots show that the exponent varies somewhat. It seems to be greatest for Raschig rings and the grid packing with smallest pitch, or spacing, an effect which might be ascribed to change in effective surface with gas velocity, The values, however, with the exception of that for the rings and occasional deviations of single experiments, do not differ from 0.8 by more than 10 per cent. For engineering purposes, with the one exception noted, it is convenient and sufficiently accurate to assume this constant value of the exponent. Values of the coefficient yo for all of the wetted walls and grids are given in the tables. Since the exact surface area of the loose packing is unknown, the transfer coefficient is expressed as koa, where a is the interfacial area per unit volume of the packing. I n this case the effect of gas velocity agrees closely with the equation koa =
yo'(G0)O.S
--
TABLE 11. HEATTRANSFER DATAON GRIDS Run No.
Air Flow, GO
Air Entering vDry Wet bulb bulb
Air Leaving
Dry
bulb
Wet bulb
Transfer Fa$or, H. T.U. 3 for SO1
dsGo lip
*Fa
YO
Lb. moles
A.
Experimental Results
VOL. 29, NO. 3
1
la
2 2a 3 3a 4 4a 5 5a
6
t"7a 8
Sa
GRIDS,da = 0.625 IN.; de = 1.15 IN.; 8 0 5 3 8 SO FT.; Fa 0.666. W E T T E D PERIMETER, 15.05 FT.; WATERRATE = 40 LB.)(HR.)(FT. WETTEDPE& BTER) Grida stanaered: do 1 In.: Death of 1Paoking = 1.67 Ft.; A = 25.04 Sq. Ft.
-
1070 1070 1160 1160 1710 1710 1815 1815 2175 2175 2220 2220 2490 2490 2540 2540
0.0294 1 . 0 0 0.0287 1.02 0.0295 0.99 0.0304 0.96 0.0308 0.95 0.0285 1.02 0.0269 1 . 0 9 0.0272 1 . 0 8 0.0266 1 . 1 0 0.0266 1.10 0.0269 1.09 0.0268 1.07 0.0256 1.14 0.0258 1.14 0.0251 1.17 0.0253 1.16
Grids Nonstaggered; do = 1 In.; Depth of Paoking = 1.67 1 1070 1.02 la 1070 0.96 2 1530 1.05 1.05 1530 1.10 1840 1.12 3a 1840 1.18 2110 4 1.14 2110 4a 1.16 5 2520 2520 1.18 1.18 2680 6a 1.21 2680
5"
1.36 1.32 1.44 1.48 2.21 2.11 2.11 2.12 2.49 2.49 2.49 2.49 2.68 2.69 2.75 2.76
3,520 3,520 3,820 3,820 5,620 5,620 5,960 5,960 7150 7:150 7,280 7,280 8,195 8,195 8,350 8,350
Av. 0,00525 Ft.; A = 25.04 Sq. Ft. 1.35 3,520 0.00511 1.39 3,520 0.00525 1.83 5,025 0.00523 1.83 5,025 0.00523 2.08 6,050 0.00511 2.06 6,050 0.00505 2.24 6,990 0.00492 2.34 6,990 0.00515 2.71 8,300 0.00519 2.66 8,300 0.00510 2.85 8,820 0.00516 2.78 8,820 0.00504 Av.
Grids Nonstaggered; 1 1130 1130 la 1860 2 2a 1860 3 2150 3a 2150 4 2530 2530 4a 2690 5 2690 5a
dp =
0.00514 0.00498 0.00510 0.00525 0.00575 0.00550 0.00522 0.00525 0.00532 0.00532 0.00523 0.00523 0.00518 0.00520 0.00522 0.00525
0.00513
2 In.; Depth of Packing = 1.67 Ft.; A = 25.04 Sq. Ft.
1.16 1.10 1.31 1.31 1.31 1.30 1.34 1.32 1.37 1.35
1.24 -1.30 1.81 1.82 2.09 2.11 2.40 2.42 2.51 2.54
3,110 0.00450 3,110 0.00471 5,120 0.00438 5,120 0.00440 7.110 0.00451 7,110 0.00455 8,351 0.00458 8,351 0.00462 8,880 0.00452 8,880 0.00457 Av.
0,00453 Sq. Ft. 0.00366 0.00343 0.00370 0.00368 0.00368 0.00374 0.00367 0.00372 0.00372 0.00362 0.00369 0.00358
Av.
0,00366
Grids Nona 1 1070 la 1070 2 1510 2a 1510 3 1820 3a 1820 4 2120 4a 2120 5 2540 5a 2540 6 2750 6a 2750
GRIDS,ds = 1.25 IN.; de = 1.98 IN.; S = 0.556 SQ. FT.; F a = 0.763; WETTED PERIMETER = 10.28 FT.; WATERRATE= 58.4 LB./(HR.)(FT.) Grids Nonstaggered; d p = 4 In.; Depth of Packing = 3.33 Ft.; A = 34.3 Sq. Ft. 0.65 1010 4,990 0.00259 1 0.68 1010 4,990 0.00271 la
B.
2 2a 3 3a 4 4a 5 5a 6 6a 7 7a
0.78 0.78 0.91 0.90 1.05 1.02 1.12 1.12 1.31 1.31 1.45 1.46
1380 1380 1500 1500 1850 1850 2110 2110 2460 2460 2850 2850
6,825 6,825 7,375 7,375 9,140 9,140 10,400 10,400 12,170 12,170 14,090 14,090
0.00242 0.00242 0.00264 0.00261 0.00254 0.00245 0.00246 0.00246 0.00255 0.00255 0.00248 0.00250
Av.
0.00262
(5-4)
for the spiral rings and Bregeat coils are also Values of given in Table 111. The line for Raschig rings is best represented by the equation: k,a = 0.107 GO)^-^^
transfer unit for sulfur dioxide absorption (H. T. U.) has been calculated from the equation:
As another means of comparison of the efficiency of the various surfaces for absorption, the value of the height of a
(The factor j' differs from j of Equations 1 and 2 in that it refers to the free area of the tower rather than the total cross-
H. T. U. =
(dpkd)
j'a
o '3Fa - k,a GnM,
MARCH, 1937
Run
No.
Air Flow, Go
INDUSTRIAL AND ENGINEERING CHEMISTRY
Air EnterinaDry bulb
TABLE I1 (Continued) Air Leaving
-A< Transfer Dry Wet Factpr,H.
Wet bulb
bulb
bulb
Lb./(hr.) (sq. ft.)
F. 'F . F. Fa C. GRIDS,ds = 1.75 IN.; de = 2..68 IN: PERIMETER, 8.27 FT.; WAT& Grids No nstaggered; do = 4 In.; Depth 76.39 64.83 68.49 66.03 1 930 76.39 67.78 68.50 6 6 . 0 1 la 930 82.13 66.85 70.73 66.61 2 1310 82.09 66.79 70.39 66.57 2s 1310 76.68 65.02 68.76 65.91 3 1350 76.88 65.00 68.67 65.86 3a 1350 82.13 66.32 71.11 6 6 . 4 1 4 1690 75.64 65.09 68.76 65.87 4a 1700 75.51 65.12 68.94 65.78 5 2360 75.88 65.13 69.06 65.75 5a 2360 7 5 . 3 1 65.10 69.15 65.73 6 2610 6a 2610 75.82 65.14 6 9 . 0 5 65.74 75.10 64.98 68.80 65.58 7 2840 Grids Staggered; d, = 1 1310 125.95 74.70 la 1310 125.05 73.39 2 1650 80.46 66.93 3 1720 124.68 74.18 3a 1720 124.30 73.39 2030 123.40 73.54 4 2030 123.40 73.54 4a 81.06 67.22 5 2040 81.07 67.14 5& 2040 2380 80.78 67.62 6 80.82 67.35 6a 2380 80.60 67.42 7 2800 7a 2800 80.62 67.51 2810 122.16 73.05 8
4 In.; Depth of 85.97 75.01 87.56 74.62 59.98 60.88 87.31 74.56 87.56 74.62 88.13 74.27 87.77 74.19 59.85 60.65 59.74 60.56 59.26 60.08 59.13 60.36 59.29 60.42 59.55 60.55 88.12 73.85
j
T. U. for SO2 kg Lb. moles XOz/(hr.)
d e lrFa
( 8 s . It.) Ft. (aim.) S = 0.556 Sa. FT.; Fa = 0.807; RATE = 72.6 LB./(HR.)(FT.) of Packing = 4.0 Ft.; A = 33.1 0.52 0.0151 4.40 5,675 0.51 0.0150 4 . 4 3 5,675 0.73 0.0151 4 . 4 0 7,950 0.0159 4.18 7,950 0.76 0.72 0.0142 4 . 6 7 8,200 0.71 0.0146 4 . 5 5 8,200 0.86 0.0135 4 . 9 1 10 310 0.0130 5 . 1 3 10:390 0.81 0.0122 6 . 4 5 14,400 1.05 0.0122 5 . 4 5 14,400 1.05 15,900 1.07 0.0111 5 . 9 8 15 900 1.16 0.0121 5 . 4 8 1.23 0.0117 5 . 6 8 17:300
Packing 0.0165 0.0169 0.0154 0.0149 0.0148 0.0141 0.0143 0.0149 0.0150 0.0138 0.0132 0.0138 0.0138 0.0135
= 4.0 Ft.;
4.02 3.92 4.31 4.45 4.4s 4.71 4.64 4.46 4.44 4.81 4.85 4.81 4.81 4.93
A
0.78 0.78 0.89 0.94 0.94 1.05 1.07 1.07 1.07 1.11 1.13 1.36 1.36 1.40
1 la 2 2a 3 3& 4 4a 5 5a
dn 58-.90 59.10 58.60 58.85 57.50 57.74 57.96 57.72 57.81 57.21
Grids Nonstaggered; do = 1 960 77.89 58.15 960 77.50 58.12 la 2 1710 76.67 5 7 . 9 8 2a 1710 76.20 57.96 3 2240 75.90 67.60 2240 3a 75.86 57.62 4 2410 75.06 57.34 4a 2410 75.11 57.19 5 2750 74.83 57.23 74.55 67.19 6& 2750
Sq. F t . 0.00219 0.0021 1 0.00236 0.00245 0.00227 0.00224 0.00226 0,00213 0.00210 0.00210 0,00198 0.00214 0.00212
0.00239
8 In.: Depth of Paokina = 3.33 Ft.: A = 27.6 Sa. F t . 63.73 63.75 64.18 64.20 64.29 64.13 64.46 64.09 64.18 63.93 8 In.; 63.60 63.57 64.08 64.04 64.15 64.21 64.05 63.94 63.86 63.78
59.74 58.82 59.29 59.42 58.64 58.74 58.85 58.55 68.69 58.29
0.0203 0.0203 0,0174 0.0174 0.0153 0.0157 0.0151 0.0155 0.0154 0.0151
3.27 3.27 3.82 3.82 4.35 4.24 4.40 4.28 4.31 4.40
Depth of Packing = 3.33 59.64 0.0192 3.46 59.64 0.0190 3 . 5 0 58.94 0.0158 4.20 58.93 0.0155 4.28 58.51 0.0144 4.61 58.52 0.0143 4.64 58.36 0.0137 4.85 58.23 0.0137 4 . 8 5 58.27 0.0138 4.80 58.26 0.0138 4.80
0176 0.76 1.09 1.08 1.25 1.28 1.37 1.41 1.47 1.45
6,290 0.00296 6,290 0.00296 10 570 0.00281 10:570 0.00278 13 800 0.00258 13:800 0.00264 15,390 0.00260 15 390 0.00268 16'200 0.00268 l6:200 0.00256
Av. Ft.; A = 27.6 0.66 5,820 0.65 5,820 0.97 10,400 0.96 10,400 1.16 13,600 1.15 13600 1.19 14:700 1.19 14,700 1.38 19,750 1.37 16,750
-
Av.
GRIDS, ds = 2.25 IN.: da = 3.25 IN.; S = 0.556 SQ. FT.; Fa 0.815; PERIMETER, 6.33 FT.;WATERRATE = 95.0 Lb./(HR.)(FT.) Grids Nonstaguered; do = 4 In.: Depth of Packing = 3.33 Ft.: A = 21.1 1 1025 4.50 0.74 7,790 1025 la 4.01 0.83 7,790 1060 2 0.81 4.32 8,090 1060 2a 4.20 0.83 8 090 1345 1.05 3 4.14 10:210 1345 3a 4.48 0.98 10 210 1800 4 4.60 1.27 13:600 1800 4a 4.55 1.28 13,600 2100 4.73 1.44 15 910 5s 2100 4.90 1.38 15'910 2410 6 4.87 1.62 18'300 2410 6a 4.76 1.64 18:300 2450 4.78 1.69 18,590 2870 4.87 1.90 21,620 2870 Sa 4.90 1.89 21,620 2880 9 4.87 1.94 21.810 2880 Sa 4.83 1.94 21;s10
D.
WETTED
Av. 0.00219 33.1 Ss. Ft. 7 950- 0.00253 7'950 0.00253 10:080 0.00238 10 450 0.00244 10:450 0.00244 12,320 0.00238 12,320 0.00242 12,400 0.00241 12,400 0.00241 14,500 0.00221 14 500 0.00225 17'090 0.00237 17:OQO 0.00237 17,110 0.00242 Av.
Grids Staggered; 1035 79.16 1035 78.88 1735 78.12 1735 77.85 2270 77.48 2270 77.11 77.12 2530 2530 77.13 2660 77.00 2660 76.73
YO
i
Av.
section area. Further significance will be discussed later.) This length has been suggested by Chilton (3) as a convenient comparative measurement of the efficiency of a packing. The literature contains only a few data on absorption coefficients obtained under the same conditions as those reported here so that the opportunity for comparison of the ex-
0.00273
Sa. Ft. 0.-00272 0.00268 0.00263 0.00251 0.00242 0,00240 0.00236 0,00236 0,00245 0.00243
291
perimental data is limited. Many qualitative statements have been made, however, concerning the relative efficiency of various types of packings. Kowalke, Hougen, and Watson (14) measured the rate of absorption of ammonia by water on a number of surfaces including 3 x 3 inch spiral stoneware packing and x 3 inch paraffined wood grids spaced on one-inch pitch (d, = 0.5 inch). Their data have been recalculated to the present units by means of the equation:
(7) The value of a for their grids was 32.2 square feet per cubic foot. The corresponding values of y o and 70' are: For grids, y o For spiral packing,
= 0.00284 YO' = 0.087
These are in excellent agreement with the data for similar packings given in Tables I1 and 111, the value for the spiral rings falling between those for the staggered a n d n o n s t a g g e r e d arrangements of these surfaces. Considering the fact that Kowalke, Hougen, and Watson's data were obtained on an entirely different system and a t gas velocities about one-tenth of those used here, it is felt that the agreement offers excellent substantiation for the proposed correlation of absorption data. No data have been found for corrugated steel surfaces, Raschig rings, or wire coils which can be used for comparison.
Effect of Liquid Velocity
Besides the effect of gas velocity, Kowalke, Hougen, and Watson found that the absorption coefficient for the various packings was a function of the liquid velocity. Above a liquid rate of 480 pounds per hour per square foot, their values were fairly constant for the grid and spiral packing for a given gas velocity. It is 0.00249 important in the design of scrubbers for large WETT~D quantities of gases to determine the minimum Sa. Ft. quantity of liquid required to wet the surface, 0.00290 since the power required for circulating the 0.00326 0.00308 solvent often exceeds that required for moving 0.00316 the gas through the scrubber. By means of 0.00330 0.00308 celluloid windows in the towers the flow of water 0.00318 0.00320 over the surfaces was observed. It was found 0.00317 that the minimum rate a t which a uniform 0.00304 0.00321 film could be maintained was approximately 0.00325 22.5 pounds per hour per foot of wetted perime0.00331 0.00323 ter. The actual rate used was, in general, 0.00321 0.00327 about three times this quantity. 0.00327 I n making the tests on grid packings, the 0.00318 water rate was maintained a t 1100 pounds per hour per square foot of cross section, which corresponded to 40-95 pounds per hour per foot of wetted perimeter according to the dimensions of the grids. Within this range the liquid rate was found to have little effect on the absorption coefficient. This conclusion is in substantial agreement with that of Rosebaugh ( I @ , who measured over-all heat transfer coefficients from hot gases to cold water flowing over similar grids with d, = 4 inches, ~~
INDUSTRIAL AND ENGINEERING CHEMISTRY
292
-
locity.2 The data are best represented by the equation:
TABLE 111. HEATTRANSFER DATAON LOOSEPACKING Air
R u n Flow, No. Go
--
Lb./(hr.) (sq. j t . )
A.
1 la 2 2a 3 3a 4 4a 5 5a 6 6a 7 7a 8 8a 9 9a
Air Entering
Dry bulb
* F.
Wet bulb
O
Air Leaving
Dry bulb
F.
F.
Wet bulb
a
Transfer H. T. U. Factor, for ja Son
F,
Ft.
2
-=
ba Lb. moles SOd(hr.) (SP. ft.) (atm.)
0.555 SQ. FT.; DEPTHOF BREQEATCOILS, 1.25 X 1.25 IN.; DUMPED;8 0.5 FT.; WATERRATE = 1080 LB./(HR.)(SQ.FT.) 4.52 920 87.07 67.77 69.18 4.59 69.27 87.10 67.74 920 4.09 1390 86.76 67.28 69.48 4.00 69.45 1390 86.85 67.48 3.79 69.48 1700 86.11 67.42 3.69 1700 69.54 85.96 67.11 3.87 1710 68.64 85.14 66.57 3.96 1710 68.59 85.16 66.86 3.48 2020 70.09 87.40 67.32 3.49 2020. 87.43 67.58 70.24 3.40 2040 69.25 84.69 66.56 3.56 2040 69.10 84.78 66.80 3.43 68.38 83.98 65.80 2370 3.39 2370 68.76 84.03 65.87 3.38 2610 68.49 83.78 65.97 3.36 2610 68.42 83.88 66.12 3.28 2810 68.80 83.63 66.21 3.23 83.54 66.05 2810 68.79
RASCHIQ RINQB,1 X 1 IN.: DUMPB :D; S = 0.556 SQ. FT: WATERRATE = loso LB./(HR.)(s& 2.61 1 625 75.19 59.26 64.66 62.71 2.56 la 625 75.00 59.04 64.57 62.56 2.58 2 943 75.43 59.22 64.36 62.09 2a 943 75.15 59.28 64.32 62.07 2.56 3 1347 75.78 58.73 64.00 61.52 2.58 2.54 3a 1347 75.09 58.96 64.07 61.72 4 1713 74.70 58.65 63.92 61.52 2.48 4a 1713 75.12 58.70 63.93 61.53 2.52 5 2090 74.89 58.35 64.01 61.72 2.49 Sa 2090 74.77 58.23 64.06 61.84 2.48 6 2410 74.68 58.16 63.78 62.20 2.83 2.76 6a 2410 74.52 58.27 63.85 6 2 . 2 1
FT.)
0.469 0.478 0.475 0.478 0.475 0.482 0.493 0.486 0.492 0.493 0.433 0.443
47.0 46.1 70.3 69.6 100.0 98.5 122.5 124.5 149.5 149.0 196.5 190.3 Av.
0.494
0.104 0.102 0.106 0.105 0.106 0.104 0.104 0.106 0.106 0.105 0.120 0.116 0.1070.
C. SPIRALRINQE,3 X 3 IN.: S 1 la 2 2a 3 3a 4 4a 5 5% 6
6a 7 7a
1 la 2 2a 3 3a 4 4a 5 5a 6
800 800 1.190 1190 1440 1440 1740 1740 2030 2030 2210 2210 2380 2380
830 830 1215 1215 1450 1450 1720 1720 2075 2075 2240
Pa 2400 Et:
7a
* koa = Q
=
0.510 0.515 0.506 0.492 0.488 0.475 0.495 0.506 0.460 0.460 0.475 0.455 0.488 0.494 0.505 0.508 0.523 0.532
DEPTHOF PACKINQ = 0.5 FT.; I.
0.654 SQ.FT.; WATERRATE = 918 LB./(HR.)(SO.FT.) Packing Staggered; Depth of Packing = 2.58 Ft. 88.00 71.93 73.16 72.75 1.23 0.99 0.136 1.13 1.08 73.26 72.69 0.125 87.98 71.89 1.06 1.16 73.20 72.50 0.126 88.05 71.81 1.06 1.16 73.22 72.53 0.126 88.09 71.75 1.24 73.36 72.51 0.123 87.91 71.76 0.99 1.16 1,05 88.00 7 2 . 0 5 7 3 . 4 1 72.70 0.130 1.25 0.98 73.84 72.93 0.126 88.18 72.50 1.25 73.85 72.95 0.98 88.09 72.49 0.126 1.29 0.95 8 8 . 3 1 72.42 73.86 72.85 0.126 1.30 0.94 0.124 87.89 72.52 73.86 7 2 . 8 5 1.29 0.95 89.19 73.01 73.91 7 2 . 7 8 0.128 1.32 0.93 74.01 72.82 0.125 89.29 72.87 1.41 0.87 73.74 7 2 . 5 5 0.119 87.55 72.23 1.39 0.88 87.74 72.00 73.61 72.40 0.121
Av. Paoking Nonstaggered: Depth of Packing = 2.33 Ft. 83.58 70.80 72.14 70.54 0.76 1.61 18.2 1.64 83.66 70.68 0.75 18.0 72.13 7 0 . 6 4 83.60 70.56 0.68 1.80 23.8 72.57 7 0 . 7 1 83.65 70.68 0.68 1.80 23.8 72.54 70.73 83.49 70.80 0.66 1.86 27.6 72.70 70.76 83.22 7 0 . 8 4 0.67 1.83 28.1 72.62 70.71 83.55 7 1 . 0 1 7 2 . 3 5 70.26 0.68 1.80 33.7 83.29 70.84 0.64 1.92 72.76 70.64 31.7 0.62 1.98 37.0 83.16 7 0 , 8 2 72.89 70.70 2.04 35.8 0.60 83.14 7 0 , 5 2 72.92 70.64 2.08 38.1 83.02 70.59 72.91 70.57 0.59 2.08 0.59 72.77 70.43 82.93 70.41 38.1 2.11 0.58 72.60 70.19 40.1 82.76 70.13 2.11 82.53 69.90 0.58 72.34 6 9 . 9 0 40.1 Av.
ro'Go0.8.
For Raschig rings, kpa
= 0.107
GoO.86.
d. = 1 inch, dt = 0.5 inch. The heat transfer coefficient increased as the flow increased from 40 pounds per hour per foot of perimeter to 75 pounds and then decreased slightly until flooding took place a t 300 pounds per hour per foot.
Pressure Losses The draft loss through the various towers is represented in inches of water per foot of height. In order to conserve space, the complete data are not recorded here but the values are shown in Figure 6 plotted against the apparent mass ve-
&(GO)'.*
(8)
YO'*
PACKINQ
Av.
B.
VOL. 29, NO. 3
Deviations from the given exponent were, in general, less than 5 per cent and did not show any definite trend. Values of 60 are given in Table V. As in the case of the absorption coefficient, comparative data on draft losses are scarce. Zeisberg (ad), Blake (a)and Arnould (1) measured the resistance of various tower packings including Raschig rings and spiral rings similar to those used in the present study. For comparison the values interpolated from their data for a mass velocity of 900 pounds of air per hour per square foot are as follows: Packing, In. 1 X 1 Raschig rings 3 X 3 spiral rings, stacked
Obsvd. Value Zeisberg 0.35 1.48 0.056
0.26
Blake 0.23
Arnould 0.35
..
..
The observed pressure losses are much below those found by Zeisberg but agree with those of Blake and of Arnould for Raschig rings. Zeisberg found that for small packing the resistance was greater when the surface was wet than when it was dry. This effect was noticed for the loose packing in the present study but the difference was negligible for the grids and vertical walls.
Discussion of Results
For practical considerations the question of interest in comparing the data on rate of absorption and draft loss is how much of the energy loss is converted into a useful form by decreasing the apparent film thickness. It is expected that increased turbulence of the gas would result in increased friction and, for similar causes, in a decreased resistance to the transfer of matter or heat. If an increased pressure loss due to turbulence were accom0.126 panied by a proportional gain in the absorp0.0835 tion coefficient, the net result would be in favor 0.0825 0.0815 of the greater turbulence. For example, if 0.0815 both pressure loss per foot and the film coeffi0,0822 0.0837 cient were doubled, for the same mass velocity 0.0871 0.0820 the tower would be half as high and the total 0.0805 pressure drop would be the same, resulting in a 0.0780 0.0794 smaller investment with the same operating 0.0794 0.0795 charges. 0.0795 It is expected, however, that with some pack0.0815 ings the pressure loss may increase more rapidly than the film coefficient, because of the loss of kinetic energy in entrance and exit effects, or of the so-called form drag. The increased turbulence in this case mav or may not be advantageous, depending on which effect prkdominites. It was a t first expected that the turbulence of flow between corrugated sheets would be the most desirable type because of the smooth sinuous nature of the gas flow without sudden changes in direction or in velocity. This expectation was not fulfilled. Comparison of the data in Figures 5 and 6 shows that the smooth sheets have the lowest pressure loss and film coefficients. A spacing of 1 inch would be desirable to one of 2 inches because the surface area per cubic foot would be doubled and the 'I
Copies of the aomplete data m a y be obtained from the authors.
101
I I
FIGURE5 (Above). ABSORPTIONCOEFFICIENTS FOR SULFUR DIOXIDE FOR V A R I O U S C H A N N E L S A N D P A C K I N G S FIGURE 6 (Right). PRESSURE DROPTHROUGH VARIOUSCHANNELS AND PACKINGS Table V gives identification of curves.
INDUSTRIAL AND ENGINEERING CHEMISTRY
294
rate of absorption per square foot would be increased by about 15 per cent, resulting in a smaller tower to offset the 70 per cent increase in pressure loss per foot of height. The introduction of turbulence due to the corrugations, however, does not materially increase the film coefficient but it increases the resistance nearly tenfold. This effect is evidently due to the manner in which the gas flows around the corrugations. If the corrugations are too small, or if the spacing is too great, the path becomes more of an exaggerated roughness rather than a curved smooth surface and there are probably pockets in which there is scarcely any movement of gas; consequently, the resistance increases and the absorption may actually decrease. This is seen in the case of the shallow ll/d-inch corrugations as compared with the deeper 2S/8-inch corrugations (both set with 1-inch spacing). The former has the largest pressure loss of any of the vertical sheets studied but the rate of absorption is actually less than that for the deeper corrugations.
Correlation of Data o n Smooth Vertical Plates and on Grids The friction factor, f/2, for the turbulent flow of gases through rectangular ducts is generally assumed to be the same function of the Reynolds number as that for circular ducts when the equivalent diameter of the channel is used in the Fanning equation. Thus (9)
The pressure drop data for the two spacings of the vertical smooth sheets are shown to be accurately correlated on this basis in Figure 7. The equation for the friction factor is: f/2 = 0.04
(?)-””
TABLE IV. Run
Air Flow,
No.
Go
VOL. 29, NO. 3
MASSTRANSFER DATAON GRIDS
-Val. o/ Inlet 8 Z gas gas
Transfer H. T. U. factor, for j’
so2
bo Lb. moles SOz/(hr.) (sq.
d J uFa
Y O
A.)
Ft. (atm.) A. ABSORPTION OF SO2 BY NaOH SOLNS.;GRIDS,da = 0.625 IN.; de = 1.15 IN.; S = 0.538 SQ. FT.; F a = 0.666; WETTED PERIMETER = 15.05 FT.; WATER RATE= 40 LB./(HR.)(FT.) Grids Nonstaggered; do = 4 In.; Depth of Packina. Ft. -. 2.0 Ft.: A = 30.00 Sa. ._ 1 1080 0.190 0.0447 0.0218 1.34 1.02 3,540 0.00382 1080 0.196 0.0472 la 0.0214 1.37 1.00 3,540 0.00375 1570 0.0454 2 0.171 0.0200 1.36 1.46 5,160 0 00381 1570 0.174 0.0460 2a 1.36 1.46 0.0200 5,160 0.00381 1835 0.180 0.0518 3 1.49 1.56 0.0188 6,040 0.00368 1835 3a 0.186 0.0530 0.0189 1.50 1.55 6,040 0,00370 2130 0.0536 4 0.188 0.0188 1.73 1.56 7,000 0.00376 2130 0.190 0.0548 4a 0.0187 1.73 1.57 7,000 0.00376 2520 0.184 0.0538 5 1.58 0.0185 2.02 8.280 0.00388 2520 0.193 0.0582 5a 1.62 0.0181 1.97 8,380 0.00378 2720 0.0597 0.198 0.0181 6 2.13 1.62 2720 0.203 0.0631 6a 0.0176 2.07 1.67 8,910 0.00378 0.00368 Av.
B.
1
la
2 2a 3 3a 4 4a 5 5a 6 6a
-
I
c. PLBSORPTION OF NHs BY ACETICACIDSOLNS.;GRIDS,ds = 0.625 s 0.538 SQ. FT.; Fa 0.666‘ WETTED P1RIMETER = WATERRATE=’ 40 LB./(HR.)(FT.) la
2
;a
3a 4 4a 5 5s
6 6s.
-
..
Av.
1
0,00377
ABSORPTION OF 802 BY NaOH SOLNS.;GRIDS, d a = 1.75 IN.; de = 2.58 IN.; S 0.556 SQ. FT.; Fa = 0.807; WETTED PERIMETER = 8.27 FT.; WATER RATE = 72.6 LB./(HR.)(FT.) Grids Nonstaggered; do 8 In.; Depth of Paokinn. .. _. 3.33 Ft.: A = 27.6 Sa. -Bt. 890 0.124 0.0473 0.0189 0.60 3.50 5,410 0.00263 890 0.114 0.0437 0.0188 3.53 0.60 5,410 1500 0.0166 0.207 0.0883 0.89 9,110 3.99 0.00258 1500 0.202 O.OS64 0.0166 0.90 3.99 9,110 0.00261 1820 0.184 0.0162 0.0808 1.06 4.10 11,050 0.00262 1820 0.0161 0.181 0.0789 1.05 4.12 0.00260 11,050 2100 0.188 0.0844 0.0157 1.18 4.22 12,810 0.00260 2100 0.175 0.0155 0.0794 1.18 4.27 12,810 0.00260 2470 0.202 0.0143 0.0980 1.26 4.64 15,090 0 00246 2470 0.199 0.0143 0.0969 1.26 4.64 15,090 0.00244 0.00246 2730 0.205 0.0140 0.1006 1.37 4.74 16,640 2730 0.0996 0.204 0.0140 4.74 1.38 16,640 0.00246 0.00256
IN 15.b5 ’ dsFT.; = 1.15 IN.;
Grids Nonstaggered; do = 4 In.; Depth of Packing, 2 Ft.; A = 30 Sq. Ft. 1180 0.343 0.0444 0.0209 1.48 1.07 3880 0.00375 1180 0.345 0.0462 0.0206 1.05 1.51 5’100 3’880 1550 0.291 0.0417 0.0199 1.33 1.56 0.00368 0.00375 1550 0.291 0.0423 0.0193 1.61 1.30 5’100 0.00366 1650 0.336 0.0551 1.32 0.0185 1.67 6:lOO 0.00353 1650 0.335 0.0546 1.33 0.0186 1.68 6,100 0.00356 2170 0.385 0.0658 1.70 0.0181 1.70 7,150 0.00364 2170 0.384 0.0668 0.0175 1.64 1.72 7 150 0.00351 2560 0.0575 0.389 0.0196 2.17 1.58 8:400 0.00410 2560 0.385 0.0623 0.0187 2.07 1.64 8,400 0,00390 2780 0.374 0.0536 0,0199 2.39 1.56 9,150 0.00418 2780 0.365 0.0531 0.0198 2.38 1.56 9,150 0.00417 Av.
(10)
The value of the coefficient, 0.04, is about 75 per cent greater than that given by Colburn (6) as the best value for smooth circular pipes. This difference is undoubtedly due to irregularities of the rectangular channels caused by the presence of the celluloid windows and the difficulty of pulling the plates together uniformly. The excellent agreement of the heat transfer data on the smooth vertical plates with the Colburn analogy is also shown in Figure 7, in which the factor j is plotted against the Reynolds number. Heat and mass transfer coefficients for such towers may readily be estimated, therefore, by adaptation of Equation 10. Correlation of the data on the grid ~.packing must be based on a consideration of the dimensions and arrangements of the grids as well as on the gas velocity as included in the Reynolds group. The final equation was developed as follows: The resistance to the flow through the grids is considered as arising from (a)the frictional resistance of the walls of the channels and (b) the contraction and expansion losses due to the flow through the orifices formed between each layer. The former is given by Equation 10. For grid towers in which each successive grid layer is placed a t right angles to the adjacent sections, the restriction at the plane of contact is given by the ratio of the free area of the channels to that of the orifices formed by the contact.
+
0.00379
+
The reciprocal of the term (d, d,)/(dw d J represents the number of orifices formed by the contact of one section on another. Since dt is small compared to d,, the velocity increase a t each intersection is: uo
- u = u (2 - 1)
=u
(2)
The velocity, u, is the actual linear velocity through the channels while uodenotes the velocity through the orifices. The pressure loss due to flow through the contact planes then is:
The term L/d,represents the total number of planes of contact. The function $
(2) is known for sharp-edge orifices
and for certain types of entrance and exit pieces, but for the present purposes it is best found by empirical methods. The total pressure drop through the grids then is represented by a modified friction factor:
INDUSTRIAL AND ENGINEERIKG CHEMISTRY
MARCH, 1937
TABLE V.
DROPDATAFOR
(T)
Rasohig rings
1
2 3 4
Bregeat coils Spiral tile
(2) (‘7)
5
Bregeat coils Wood grids
Corrugated sheets
In.
fi
:$:
0 11/4X11/4
0
3x3 3x3
6 7 8 9 10 11 12 13 14 15 16
0 I1/4X11/4 0 dr = I/( A d t = 1/4 A dt = 0 dt = 1/4
17
A -
18 19 20 21 22 23 24
O
0
80
(15)
In these plots it was noted that the effect of arrangement of the alternate grid sections-i. e., whether in a staggered or nonstaggered fashionwas inconsequential. This c o n d i t i o n prev a i l e d don7n to g r i d h e i g h t s of one inch. Whether or not it is valid for smaller grids is not known, but a t some point the grid height is expected to enter to some extent a t least into the coefficients of the equations. It may be noted that for large grid towers, so that f’ - = 0.035
2
Corrugated sheets Wood grids
Corrugated sheets
(16)
(9 -”’ ) +
Smooth sheets
0.43___ dt’.5 dB . d,O. 76 (17)
I n this case also the effect of staggering and nonstaggering was negligible. For large t>owers: =
0.035
(%)-”’+
HEAT TRANSFER’ 0 2 IN.SflOOTH R A T E
.g.cloz 4
I
I
s
6
I
I
A
~
I
I
0.053 -LLdo8
(19)
(ds.d,)0.4
-t-i
. P ~ E S S U R E DROP A 2 IN. SMalTH R A T E A I IN. *I I
I
I
I
I
7 e e i o REYNOLDS NUMBER XI^'^
”
fi P
I
1
20
30
FIGURE7 . FRICTION AND HEAT TRANSFER FACTORS FOR SMOOTH VERTICAL PLATES
35 36
.. .. .. ., .. ..
... . .. ... .. .. ..
1
1
dt = ‘/a
4
*/4
j: I :(: E Wave length, 11/4 Wave length, 26/a dt dt dt dr
= = = = dt = dt =
I
-
Wave length, 25/a
0
dt = ‘/a d t = 1/4
i
0
dt dt dt dt
A
dt =
at = 1/4
= l/k
= =
J/&
l/g
= l/r at = ‘/a l/a
0
Wave length,
0
1 5 . 9 wide 1 5 . 9 wide
60
Arrangement
=
Ahw -
L p o )1.8
(Equation 8)
Dumpedwet 32.8X10-7 Dumped’dry 16.3 Dumped’ wet 3.40 Staggereh, wet 2.78 Nonstaggered, wet 2 . 7 6 .. Dumped, dry 2.64 0.625 Staggered 2.14 0.625 Nonstaggered 1.89 0 . 6 2 5 Staggered 1.46 0 . 6 2 5 Nonstaggered 1.36 0.625 Staggered 1.01 0.625 Nonstaggered 0.82 0.64 !?%%~~ered 0.67 1.25 X‘onstaggered 0.237
.
8ft. 1 . 0
l/q 1/4 J/4 1/4 ‘/4 l/4
A
A
In.
l/4
dt = dt =
26/8
= 2 d.
Although the experimental data include only one value of d,, it is believed from dimensional considerations that the value of the exponent 1.5 is probably valid for grids of any thickness. Similar treatment of the data for heat and mass transfer on grid surfaces leads to the following formula for the modified transfer factor:
J”
25 26 27 28 29 30 31 32 33 34
0 0 0
In.
2 2 4 4
~
Wood grids
a,
VARIOUS CHaNNELS AND PACKINGS
-Dimensions of PackingChannel Channel Figs. 5 and 6 Curve Symheight, width, Type of Packing No. bol Size do ds
The value of f/2 is given by Equation 10. Although the grid height do enters into Equation 14 as the inverse first power, actually it was d,Up -0.2 found, by plotting f’/2 - 0.04 against d, for each value of d, studied, that the exponent should be -0.75 rather than -1. The value of the function # expressed as a n exponential power was then determined by ”“ - 0.04 against plotting d,/d, for the various grids. The points for the four values of d, studied feIl closely to a straight line on the logarithmic scale for which the final equation is :
(2) [g
PRESSURE
295
Parallel
0.211
8ft. I . 0 8 1.25 4 1.75 4 1.75 12 1.25 1.25 16 8 1.75
Parallel Nonstaggered Staggered Nonstaggered Nonstaggered Nonstaggered Nonstaggered
0.179 0.176 0.174 0.120 0.116 0.116
8ft. 2 . 0 8 1.75 12 1.75 12 1.75 16 1.75 4 2.25 16 1.75 2.25 8 12 2.26 16 2.25
Parallel Staggered Staggered Nonstaggered Nonstaggered Nonstaggered Staggered Nonstaggered Wonstaggered Nonstagaered
0.107
Parallel Parallel Parallel
0.056 0.021 0.0125
8ft. 3 . 0 8ft. 1 . 0 8ft. 2 . 0
0.187 ..
~~
Since the equations are developed for flow through the individual grid channels, the heat and mass transfer factor is now defined on the basis of actual velocity through the grids-i. e., by introducing the fractional free area into the denominator, so that
The final evidence of the validity of Equations 15 and 18 is shown in Figure 8 in which the corrected factors minus the Reynolds number term are plotted against the respective functions of the grid dimensions. The agreement is excellent, with the exception of the single heat transfer measurement on the grids for which d, = 2l/4 inches, It is interesting to note that the grid dimensions do and d, enter into the effect on heat and mass transfer to approximately one-half the exponential power to which they affect the pressure loss. This indicates that the turbulence caused by the shape of the grids is only partially useful in decreasing the thickness of the apparent stagnant film. Greenewalt (9) has already noticed a similar relation, and for different types of entrances and baffles has found the gas-film coefficient to be approximately proportional to the 0.4 power of the pressure loss.
Optimum Grid Dimensions Equations 15 and 19 can be used as the basis of design of grid-packed towers when consideration is given to the other characteristics desired for handling large quantities of gases. I n order to show the efficiency of these towers for sulfur di-
INDUSTRIAL AND ENGINEERING CHEMISTRY
296
VOL. 29, NO. 3
FIGURE 8. MODIFIED FRICTION AND ABSORPTION FACTORS FOR GRIDPACKING 1
I
I
I
I
I
I
I
FIGURE9. DIMENSIONS OF GRID TOWERS FOR REMOVING 0.3 PER CENTSULFURDIOXIDEFROM 100,000 CUBICFEETPER MINUTE(300" F.) OF FLUEGASES
spacing of 2.5 inches. The linear velocity also will be much greater than used in towers packed with ordinary stoneware. Actual linear velocities of 10 feet per second have been used without excessive spray formation. The total time of contact is of the order of 1 to 2 seconds. Because of the small ratio of height to cross-sectional area, attention must be given to methods for securing uniform distribution of the solvent liquid in order to avoid channeling. This may be accomplished by the use of banks of coarse sprays, or by special distributing devices. The power requirements for circulating the solvent and for moving the gases through the grids is shown in Figure 10. Since the pump requirements are large for low gas velocities and the pressure loss is greatest for high velocities, there is a minimum in the power curves. These values for the operating costs should be combined with capital charges of construction, including the cost of the packing and shell and the value of the floor space. I n such a case the final cost sheet shows an even more decided minimum at a mass velocity between 1800 and 2200 pounds per hour per square foot. The effect
oxide absorption, the dimensions and power requirements have been calculated for a tower removing 96.7 per cent of the sulfur dioxide from 100,000 cubic feet of flue gases a t 300" F. containing 0.3 per cent sulfur dioxide. The quantities involved in the calculation are as follows: SO2 absorbed/min Ib. Mean partial pres&re difference, mm. Wet-bulb temp. of gas, F. Vol. of gas in scrubber, cu. ft./min. Av. density of gases lb./cu. ft. Liquid rate, lbJ(hr.5 (ft.)
34.6 0.66
126
77,000 0.0666 675
The effect of varying the spacing and height of the individual grid sections on the size of the tower is shown in Figure 9. It is evident that, for small pitch, the height of the sections has little effect on the absorption efficiency. For wide spacing, however, the total tower height increases as the height of the individual sections increases. It is interesting to note that an absorption tower for handling large quantities of gases does not follow the usual ratio of height to cross-sectional area used for ordinary packed towers. In fact, the height may be reduced to a mere 5 feet of packing for small grids and will not exceed 50 feet for grid
FIGURE10. POWERREQUIREMENTS FOR FANAND PUMPFOR GRIDTOWERS FOR REMOVINQ 0.3 PER CENTSULFUR DIOXIDE FROM 100,000 CUBICFEET PER MINUTE(300" F.) OF FLUE GAREB
MARCH, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
of grid spacing disappears above d, = 1.5 inches, and there is little choice in the height of individual sections. For secondary reasons, however, such as keeping the total height as low as possible, a channel width of 1.5 inches and channel height of 4 inches are chosen as optimum. These grid dimensions are in substantial agreement with those given in a recent patent issued to Learmonth (16). Other descriptions of packing of this type are given by Meade ( I B ) , Tymstra ( d l ) , Rosebaugh ( I @ , and Furnas and Newton (7). The final dimensions of the most economical tower for treating 100,000 cubic feet of the hot gas per minute then becomes 12 X 12 x 18 feet. The pressure loss through the packing is estimated to be only 0.26 inch of water. For uniform operation it is necessary to circulate 260 gallons of solution through the tower per minute. It is interesting to note that a tower designed on these principles having d, = 1 inch and d, = 4 inches and a total height of only 9 feet is now removing 90 per cent of the sulfur dioxide from combustion gases in a pilot plant operating on a sulfite-bisulfite cycle utilizing chemical regeneration. Further details of this work will be published in a later paper.
Acknowledgment The authors acknowledge with pleasure the help of H. C. Cooper, K. F. Krebs, H. C. Blankmeyer, and Raymond Largent in the experimehtal work and calculations.
Nomenclature Consistent units are used except where designated in the text: A = surface area a = interfacial area per unit volume c = sp. heat of gas mixture at constant pressure d. = equivalent diam. of channel between grid members d, = height of individual grid members d, = clearance between grid members d, = thickness of grid members d,,, = length of grid channel F, = fractional free area of tower f = friction factor in Fanning equation g = acceleration of gravity Go = apparent mass velocity, lb./(hr)(sq. ft.) yo, yo’, 60 = proportionality constants Ah,,, = pressure loss, in. of water j = heat and mass transfer factor for gross cross section = factor for free area = thermal conductivity kd = diffusion coefficient of absorbed gas k, = mass transfer coefficient, Ib. moles/(hr.)(sq. ft.)(atm.)
$
L
297
total height of packing mean mol. weight of gas viscosity of gas P = partial pressure of absorbed gas P APm = mean partial pressure difference across film AP = pressure loss 7r = total pressure = density of gas stream = cross-sectional area of tower = cross-sectional area of grid channels = free area of section through plane of contact between grids = temp. of gas stream = mean temp. difference across gas film = actual linear gas velocity M m
= = =
Literature Cited (1) Arnould, Chimie et industrie, 21, 479 (1929). (2) Blake, Trans. Am. I n s t . Chem. Engrs., 14, 415 (1921-22). (3) Chilton, IND. ENG.CHEM.,27, 255 (1935). (4) Chilton and Colburn, I b i d . , 26, 1183 (1934). (5) Colburn, Trans. Am. I n s l . Chem. Engrs., 29, 174 (1933).
(6) Dobry, L. F., and Krebs, R. W., unpublished Ph.D. theses, Univ. of Ill., 1935 and 1937. (7) Furnas and Newton, Chem. & Met. Eng., 40, 301 (1933). (8) Gilliland and Sherwood, IND.ENG. CHEM.,26, 516 (1934). (9) Greenewalt, I b i d . , 18, 1291 (1926). (10) Hewson, Pearoe, Pollitt, and Rees, J. Sac. Chem. I n d . , Preprint, 1933. (11) International Critical Tables, Vol. I, p. 71, New York, McGrawHill Book Co., 1926. ENG.CHEM.,27, 587 (12) Johnstone, Combustion, 5 , 19 (1933) ; IND. (1935). (13) Johnstone and Keyes, Ibid., 27, 659 (1935). (14) Kowalke, Hougen, and Watson, Univ. Wis. Eng. Expt. Sta., Bull. 68 (1925). (15) Learmonth (to Imp. Chem. Ind.), U. S. Patent 2,056,429 (Oct. 6 , 1936). (16) Meade, “Modern Gasworks Practice,” p. 524, 2nd ed., London, Benn Bros., 1921. (17) Pearson, Nonhebel, and Ulander, J . I n s t . Fuel, 8 , 119 (1935). (18) Polson, Lowther, and Wilson, Univ. Ill. Eng. Expt. Sta., Bull. 207 (1930). (19) Rosebaugh, Chem. & Met. Eng., 35, 144 (1928). (20) Sherwood and Comings, Tyans. Am. I n s t . Chem. Engrs., 28, 88 (1932). (21) Tymstra, Univ. Wash. Eng. Expt. Sta., Bull. 67 (1932). (22) Wahlen, in Univ. Ill. Eng. Expt. Sta., BUZZ. 120 (1921). (23) Walker, Lewis, and McAdams, “Principles of Chemical Engineering,” 2nd ed., p. 706, New York, McGraw-Hill Book Co., 1927. (24) Zeisberg, Trans. Am. Inst. Chem. Engrs., 12, 231 (1919). RECEIVED November 20, 1936. Published by permission of the Director of the Engineering Experiment Station, University of Illinois. Thia paper contains a part of the results obtained on the oooperative research project, Case 34, with the Utilities Research Commission of Chioago.
