June 1951
. f
INDUSTRIAL AND ENGINEERING CHEMISTRY‘
D‘ = diffusivity of reagent in solution d = thickness of liquid layer on packing or other solid surface H = Henry’s law constant k = generalized mass-transfer coefficient kr, = liquid-film mass-transfer coefficient kc = gas-film mass-transfer coefficient (partial-pressure units) ks = mass-transfer coefficient for surface resistance (concentration units) kE = mass-transfer coefficient for eddy diffusion I = distance traveled in time e by element of surface of moving liquid R = mean rate of absorption per unit area of nonstagnant liquid r = velocity constant for first-order reaction between absorbed gas and liquid $”’ velocity constant for second-order reaction between absorbed gas and reagent in solution s = fractional rate of renewal of surface of liquid so = value of s for area a volume of liquid per unit volume of packing X L = “effective thickness of liquid film” x = distance beneath surface of liquid B = quantity defined by Equation 16 e = time for which a liquid surface has been exposed to gas, “age” of surface * = rate of absorption into unit area of surface of stagnant liquid
1467
4 = surface-age distribution function M = viscosity of liquid p = densityofliquid erf(z) =
1 - erfc(z)
=
e -Pdy (numerical values may
be found in tables) LITERATURE CITED
(1) Carslaw, H. S., and Jaeger, J. C., “Conduction of Heat in
Solids,” p. 43, Oxford University Press, 1947. (2)Ibid., p. 53. ( 3 ) Ibid., p. 240. (4) Danokwerts, P. V., Research, 2, 494 (1949). (5) Danokwerts, P. Trans. Faraday Soc., 46,300 (1950). (6)Ibid., p. 701. (7) Higbie, R., Trans. Am. Inst. Chem. Engrs., 31, 65 (1935). (8) Perry, J. H., “Chemical Engineer’s Handbook,” pp. 1179. 1184, New York, MoGraw-Hill Book Co., 1941. (9) Sherwood,T. K., “Absorption and Extraction,” p. 61, New York,
v.,
v =
McGraw-Hill Book Co., 1937. (10) Ibid., p. 196. (11) Ibid., p. 202. RECEIVED August 8,1950.
Air-Water Contact Operations in a Packed Column
Engrnyring Process development I
FUMITAKE YOSHIDA
AND
TATSUO TANAKA
DEPARTMENT OF CHEMICAL ENGINEERING, KYOTO UNIVERSITY, KYOTO, J A P A N
S
1
1MULTANEOUS interphase transfer of heat and water vapor between air and water flowing countercurrently in packed columns is of considerable engineering importance in humidifiers, dehumidifiers, and water coolers. T h e performance of this equipment used to be expressed in terms of the over-all coefficient of heat or mass transfer, or in the over-all height of transfer unit (H.T.U.), the bulk-water temperature usually being assumed equal to the interfacial temperature. However, this assumption is indisputably valid only in the case of constant water temperature humidification, in which the heat given up by air is wholly consumed for evaporating water and hence no heat transfer takes place across the water film. T h e present work was intended (I) to study the effects of the gas and water rates on the true gas-film coefficients of heat and mass transfer from the constant water temperature data; (2) to investigate how the water-film resistance, if any, was affected by the gas and water rates from the water-cooling data; (3) to study whether the correlations for the film coefficients obtained from the above tw8 operations were applicable to the dehumidification data. This work was undertaken before the similar study by McAdams and coworkers ( a ) was published. Some discrepancies exist between the results of the two investigations. EXPERIMENTAL
T h e schematic diagram of the apparatus is shown in Figure 1. The column (Figure 2) was 10 inches (25 om.) in inside diameter and was dumped-packed with 15-, 25-, or 35-mm. ceramic Rasohig rings to a depth of 12.5 inches. It was necessary to
The work was undertaken to study the film coefficients of mass and heat transfer in the three kinds of air-water contact operations-i.e., constant water temperature humidification, water cooling, and dehumidification, in columns packed with ceramic Raschig rings. The results showed that liquid-film resistance was not negligible as compared with gas-film resistance and that the same empirical equations for gas- and liquid-film coefficients could practically correlate the performance of a packed column throughout the three operations. The gasfilm coefficients of heat and mass transfer were proportional to gas rate and to the 0.2 power of water rate, while the liquid-film coefficient of heat transfer was proportional to the 0.8 power of water rate. The ratio of eas-film coefficient of heat transfer to that of mass transfer nearly equaled the humid heat of air in the column. The correlations obtained should make it possible to design packed column-type air-water contact apparatus on a sounder basis.
make the packed section relatively short in order to obtain substantial driving potential at the top of t h e packin . Due care was taken in the column design to minimize the e n 3 effects owing to the sprays above apd below the packed section. As shown in Figure 2, nineteen overflow pipes from t h e waterdistributing tray were extended down to t h e top of the packing, thus eliminating the air-water contact above the packed section. Below the packing, there were a tray with air risers and an overflow ipe through which water was drawn out of the column. The c h a n c e between the water level on the tray and the bottom
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1463
packing was about 0.5 inch. The air could then be blown through the risers directly into the packing with little contact with Rater spray. ~h~ column and the piping were insulated with diatomaceous earth 2 inches thick. The air was sup lied by a rotary blower. From the blower the air passed througf a n oil separator and a calming section to an orifice and then through an electrical preheater into the column Of
Voi. 43, No. 6
exit air determined at the exit pipe and the temperature of thc recirculating water, which was practically equal to the netbulb temperature there at steady conditions. In water-cooling and dehumidification runs it was necessary ollly to determine the wet-bulb temperatures, or the adiabatic saturation temprlratures, above and below the packing. Such a temperature just abovr the packing was obtained by the wet-bulb thermometer, Tu,,inserted there. Strictly speaking, because of Gonstaltt relatively low velocit? of air in the column, there might be a slight difference between thc adiabatic saturation temperature and the teinperature shown by the wet-bulb thermometer However, because the air was near to saturation a t this point, the difference was considered negligible. The adiabatic saturation tempeiature just below the packing was computed ab stated before. 911 the thermometers were rnlibrated accurately to 0.1 C. t h c 3
Wet- andDry-bulb Thermometers
B A S I S OF INTERPRETATION
Blower
--
Water
ReSeTUOiT
Figure 1.
Schematic Diagram of Apparatus
Pump
The sensible heat transfer between bulk of gas and interface in the differential height of the packing, dZ, per unit of gross cross-sectional area of the column is -Gocsdt
=
haa(t
-
Ti)dZ
(1) where Go represerit,s the mass velocity (JC dry
bottom. In constant water temperature and ~ater-coolingruns water was recirculated through the system by means of a pump. From the pump the water passed through a flow-controlling valve and a calibrated orifice to the column top. The water from the column bottom flowed through a U-tube into a reservoir equipped with electrical immersion heaters. From the reservoir the water returned to the pump. I n dehumidification runs fresh city water was supplied from a constant head tank to the column top without recirculation.
-E,
I n runs a t constant water temperature air was preheated to 70" to 150" C., so that it would not be substantially saturated a t the column top. Water was heated only a t the beginning of operation. However, after a steady condition had been reached, the water temperatures above and below the packing showed close agreement with maximum difference of 0.3 C. and were within 1" C. of the adiabatic saturation temperature just belolv the packing, which was computed from the air temperature measured at that point and the absolute humidity determined at the air inlet pipe. This indicated that operations at substantially constant water temperature were achieved, although the insulation was not perfect. Probably the heat losses were compensated by the slight heating in the pump. I n water-cooling runs air was not preheated, the heat lost by water in the column being made up by the heat supplied by the heater in the water reservoir. I n dehumidification runs air was preheated by a supplementary heater and then humidified by injecting steam at a constant rate from an atomizing nozzle before it entrred the orifice. Humidities of the inlet and the exit air were determined by means of couples of wet- and dry-bulb thermometers located a t the inlet and the outlet pipes, respectively. The air velocity through the outlet pipe, E1 (Figure 2), was controlled by means of the adjustable blast gate installed a t the vent pipe, Ez, as an excessive air velocity might wet the dry-bulb thermometer in the outlet pipe with water spray. The air temperature just below the packing was measured by the thermometer, TI,which was surrounded by the shield, SI,in order to prevent errors due to radiation. To obtain data on constant water temperature humidification it was necessary to know the air temperature just above the packing, and it was computed from the absolute humidity of the
H Figure 2. A . Air i n l e t B . B o t t o m tray C. Air risers D . Packing E l . Air o u t l e t E*. V e n t F . Water i n l e t
Packed Column 6. Wa)er-distributing PIPS
H . Water outlet R . Water-reaeiving cup SI,SI. R a d i a t i o n shields TI-Ta. T h e r m o m e t e r s T m , T m . Wet-bulb thermometers
1469
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1951
WATERTEMPERATURE TABLEI. RUNSAT CONSTANT
water
Exit Air
G~~
Inlet Air (before Preheater) Rate, L, Rate 0, DryWetAbS: Lb./ Lb.) bulb bulb (Hr.) (Hr.) t:mz., tyy:, humidity, Ib./lb. (Sq. Ft.) (Sq.Ft.)
3;-
&-:; t%mz.,,
t$rnZ:,
Abs. humidity, lb./lb.
Water Air Temperature Temperature Below Above Below Above packpackin p,ack- pack(calcd.?, ;ne. O
hGa,
B.t.u./
kLa,
Lb./
c.
hsa/k&
av. B.t.u.1 (Lb.) (" F.)
DATAFOR 15-MM. RASCHIQ RINGB
b
4160 3890 4160 3890
227 321 365 420
35.5 34.7 38.7 36.2
22.0 20.6 23.2 21.3
0.01070 0.00903 0.01100 0.00934
40.5 31.7 39.6 31.4
40.1 31.6 39.1 31.3
0.0489 0.0298 0.0460 0.0293
137.0 87.0 llW.5 82.0
48.6 37.1 48.6 35.7
41.5 32.7 40.6 32.5
41.3 32.7 40.5 32.2
134 181 218 261
510 723 763 1005
0.262 0.250 0.286 0.260
0,264 0.248 0.253 0,248
2460 2460 2460 2500
190 279 445 447
33.1 36.2 37.4 39.6
22.5 22.3 24.4 23.5
0.01243 0,01080 0.01350 0.01110
39.4 39.8 38.6 32.5
38 9 39.5 38.2 32.4
0.0455 0.0473 0.0438 0.0313
134.5 133.0 114.0 82.0
46.4 49.0 47.4 37.5
40.3 41.0 39.8 33.2
40.0 40.9 39.6 33.4
102 157 242 269
417 588 905 1020
0.244 0.267 0.268 0.263
0.254 0.254 0.2530.250
1530 1465 1495
251 331 475
31.9 35.2 39.1
21.9 23.3 24.4
0.01210 0.01270 0.01272
33.6 34.1 32.7
33.3 33.9 32.4
0,0329 0.0342 0.0312
89.4 93.0 82.5
39.8 40.5 39.7
34.5 35.1 33.8
34.5 35.1 33.8
132 172 234
516 701 902
0.257 0.246 0.260
0.251 0,252 0.251
840 838 840 828 833 835
233 300 351 370 481 481
32.4 34.3 35.5 36.4 39.0 39.1
23.0 25.1 23.7 25.7 24.4 25.6
0.01350 0.01600 0.01322 0.01610 0.01275 0,01470
33.8 33.2 32.4 33.9 32.5 33.5
33.6 33.1 32.4 33.6 32.2 33.2
0.0336 0.0326 0.0313 0,0336 0.0308 0.0327
93.0 77.5 83.5 90.0 82.3 82.5
41.2 43.1 41.5 41.8 41.5 42.3
35.0 85.0 34.2 35.1 34.0 35.0
35.0 35.0 34.2 35.1 34.0 34.9
108 127 155 152 214 209
451 465 590 652 802 789
0,240 0.277 0.263 0.233 0.267 0,265
0.251 0.251 0.250 0.251 0.250 0.251
408 420 412 418
295 39 1 416 484
32.8 28.4 36.2 37.4
22.1 18.9 23.0 24.2
0.01220 0.00950 0.01180 0.01317
31.0 30.4 32.2 33.0
31.0 30.0 31.9 32.7
0.0288 0,0270 0.0303 0.0317
77.0 82.0 86.5 92.2
40.2 40.2 43.2 40.1
32.8 32.1 34.1 34.1
82.9 32.1 34.1 34.1
130 159 168 210
492 630 650 908
0.264 0.253 0.258 0.233
0.250 0.248 0.250 0.251
258 259 260
237 379 486
35.4 37.7 41.7
21 .o 21.7 23.8
0.00926 0.00926 0.01062
34.6 33.9 34.3
33.1 31.6 31.4
0.0319 0.0288 0,0283
105.0 90.0 84.3
45.6 45.3 47.6
35.2 33.9 34.1
35.2 33.9 34.1
93 142 164
375 542 602
0.247 0.262 0.273
0.250 0.249 0.249
0.01125 0.01166 0.01104
39.6 40.2 40.4
39.4 39.8 40.1
0.0470 0.0480 0,0489
134.5 138.2 137.5
46.1 48.1 47.8
40.6 41 .O 41.3
40.4 41.0 41.2
104 126 225
406 497 860
0.257 0.254 0.262
0.254 0.254 0.254
0,0526 0,0495 0.0486
143.0 145.3 136.0
51.0 50.2 49.1
42.7 41.7 41.5
42.7 41.7 41.3
120 165 259
439 645 1038
0,273 0.256 0.250
0.255 0.254 0.254
152.8 65.0 96.0 138,O 131.0 80.7
52.1 29.6 37.7 50.6 49.6 35.6
43.3 a6.o 31.9 41.1 40.8 29.8
43.1 26.1 32.0 41.1 40.8 29.8
125 166 181 187 245 244
465 656 716 725 922 981
0.269 0.253 0.253 0.259 0.266 0.249
0.255 0.246 0.248 0.254 0.253 0.252
61
D A T AFOR 25-Mx.
RASCHIG
RINGS
3660 3660 3560
172 223 375
34.5 34.9 36.3
22.1 22.5 22.5
2360 2360 2440
203 300 458
35.3 37.6 38.8
22.5 22.4 23.5
0.01150 0.01030 0.01145
41.8 40.7 40.4
41.4 40.3 40.0
1640 1640 1720 1670 1680 1720
223 311 345 359 447 510
39.2 22.7 24.7 39.4 40.4 26.7
23.6 14.2 14.6 23.0 23.4 15.2
0.01141 0,00642 0.00600 0.01040 0.01060 0.00580
42.1 25.0 30.7 40.0 39.8 28.7
41.7 24.8 30.5 39.5 39.3 28.2
730 760 750 809
137 188 269 513
20.4 19.3 18.1 24.7
13.5 11.9 11.3 16.4
0.00667 0.00550 0.00542 0.00805
30.0 27.3 25.2 28.5
29.9 27.0 25.1 27.9
0.0270 0,0225 0,0202 0,0237
86.5 74.2 66.5 72.0
41.2 37.8 33.7 37.5
32.4 29.6 27.4 30.2
32.3 29.5 27.3 30.0
120 218
81
227 296 442 820
0.267 0.273 0.271 0.266
0.248 0.247 0.246 0.248
238 238 256 238
156 225 375 586
23.2 21.4 36.6 22.2
14.4 13.0 24.3 13.4
0.00642 0.00535 0.01360 0.00578
30.9 34.5 35.9 38.7
29.0 30.6 34.7 30.9
0.0247 0,0263 0,0352 0,0250
91.7 104.5 101.0 93.0
41.7 47.4 47.6 46.7
31.4 33.3 36.8 32,6
31.4 33.3 36.8 32.6
55 73 144 192
230 298 574 745
0.239 0.224 0.252 0.258
0.247 0.247 0.251 0.248
3560 3520 3600 3630
217 264 320 418
33.3 37.4 38.2 39.8
22.0 23.5 24.1 24 6
0.01160 0.01205 0.01265 0.01275
39.4 41.2 40.7 40.7
38.9 40.3 39.8 39.3
0,0456 0,0492 0.0477 0.0461
131.5 141.0 131 2 123.0
46.4 49.3 48.1 46 5
40.2 41.6 41.0 40.3
40.0 41.5 40.9 40.2
123 145 181 261
482 574 686 952
0.254 0.252 0.265 0.264
0.253 0,254 0.254 0.254
2440 2610 2545
256 301 373
34.8 37.7 38.4
22.5 23.7 24.0
0.01168 0.01230 0.01240
41.0 41.6 40.7
40.1 40.5 39.4
0.0486 0,0496 0.0465
145.5 141.0 127.8
49.1 49.8 47.9
41.5 41.8 40.4
41.3 41.7 40.5
135 164 208
532 638 810
0.254 0.257 0.258
0.254 0,255 0.254
1525 1530 1515 1510
188 235 316 394
26.9 29.7 31.2. 33.2
17.7 19.2 18.9 20.4
0.00866 0.00936 0.00829 0.00942
29.5 31.7 31,5 32.0
29.4 31.5 31.0 31.2
0.0261 0.0296 0.0286 0.0288
74.0 90.0 85.0 $1.0
34.0 36.5 37.2 38.7
30.4 32.5 32.2 32.6
30.4 32.5 32.1 32.6
94 128 171 201
364 530 662 752
0.258 0,242 0.259 0.268
0.248 0.247 0,249 0.249
780 830 800 780 817 772 823 830 772
158 171 229 256 292 385 395 465 492
28.6 22.5 24.2 28.6 24.2 32.1 26.6 28.4 34.3
18.4 14.1 15.1 17.8 14.0 19.4 15.8 16.9 21.4
0.00878 0.00641 0.00678 0.00804 0.00557 0,00856 0.00653 0.00704 0.01032
29.5 28.2 29.3 29.9 30.0 33.1 33.6 33.1 32.1
30.7 30:l 30.4 30.9 31.0 33.1 32.6 32.4 32.0
30.7 29.9 30.3 30.8 31.0 33.1 32.6 32.4 32.0
74 70 91 120 114 169 159 189 219
292 296 398 449 450 632 702 845 826
0.252 0.237 0.229 0.268 0.253 0.267 0.227 0.235 0,266
0.248 0,247 0.247 0.248 0.247 0.248 0.248 0.248 0.241)
440 376 414 440 404 424
209 223 260 294 368 376
27.6 24.9 27.3 29.4 31.0 31.6
21.4 14.8 17.6 21.4 21.4 20.8
0.01330 0.00613 0.00834 0.01248 0.01 175 0.01065
32.5 29.6 32.0 33.7 33.8 34.8
31.6 28.0 30.5 32.3 31.6 32.6
0 0295 0.0234 0,0273 0.0305 0.0289 0.0307
82.5 88.0 90.0 85.5 81.0 90.0
41.3 38.2 41.5 41.2 43.6 43.4
33.4 30.0 32.5 33.8 33.6 34.3
33.4 30.0 32.5 33.8 33.6 34.3
81 83 102 125 142 158
324 366 385 500 522 606
0.249 0.226 0.264 0.250 0.273 0.260
0.250 0.247 0,249 0.250 0.249 0.250
201 201 206
170 256 478
26.6 27.7 31.4
17.4 17.4 18.9
0.00843 0.00795 0,00821
29.3 30.4 33.6
28 1 27 6 28 9
0 0237 0 0222 0 0233
80 7 75 0 76 0
38.8 42 9 44 4
30.3 30.5 31.3
30.3 30.5 31.3
59 79 151
253 300 563
0.235 0.263 0,269
0.248 0.247 0.248
DATABOR 35-MM. RASCHIG RINGS
. 1
INDUSTRIAL AND ENGINEERING CHEMISTRY
1470
Vol. 43, No. 6
Go(Hz - H I ) ~AuZ(AH)I.,. (5) where ( A H ) I , is ~ the logarithmic mean of ( H i - H I ) and ( H , - H z ) . Thus, k& was computed from the data on constant water temperature humidification with the use of Equation 5 . From Equation 4 one obtains
which defines (Ht)G -Le., the height of a gas-film transfer unit. The mass velocity, G, used in correlation was that of air plus water vapor. In practice, however, Go may be considered as approximately equal to G. Hence, ( H t ) a is substantially equal to G divided by &a. I n correlating the data on water-cooling and dehumidification runs, the enthalpy potential method is simple and convenient. As the principle of this method was treated in detail by McAdams and others ( 1 , a), it is only briefly summarized here. Equations I and 4 hold good also for water cooling and dehumidification without fog formation, although Hi varies with Z. Assuming the ratio of haa to &a equal to cs, as was confirmed by the present experiment, the following relation can be derived: Godi = k & ~ ( i i i)dZ
, LB.XSQ.FTXHR.) Figure 3.
Logarithmic Plot of haa us. G for 25-Mm. Raschig Rings
air, cs the mean humid heat of air, t the bulk-air temperature, T i the interfacial temperature, and hGa the gas-film coefficient of heat transfer in appropriate units. In the case of constant water temperature humidification, T , attains a constant temperature which equals the bulk-water temperature. Hence, regarding T,, hca, and cs as constants, integration of Equation 1 over the entire height of the packing gives
LcLdT = Godi (8) in which L is the water mass velocity and its change due to vaporization is negligible; CL is the heat capacity of liquid water which substantially equals 1.0; and 1 ' is the bulk-water temperature. The heat transfer through the water film is LcLdT = hr,a(T
-
Tt)dZ
GoCs(ti -
t.) =
hGaZ(At)l.m.
(24
where ( A ~ ) I .is~ the . logarithmic mean of ( t l - T,) and ( t a - Ti). Furthermore, neglecting the enthalpy change of water, heat balance gives Gocsi(ti
- tz)
= XGo(H2
- HI)
(3)
in which csl is the humid heat of the inlet air, A is the latent heat of vaporization of water a t the water temperature, and HI and H 2 are the absolute humidities of the inlet and the exit air, respectively. Both sides of Equation 3 calculated from the data on constant water temperature humidification showed agreement within a few per cent. I n computing hca from the data, the right-hand sides of Equation 3 and Equation 2a were equated. The water vapor transfer from interface to bulk of gas for the differential height of packing, d Z , per unit of gross cross-sectional area is GodH
=
?&(Hi
- H)dZ
(4)
where H i and H are the absolute huyidities a t the interface and of the bulk-air, respectively, and kGa is the gas-film coefficient of water vapor transfer. For constant water temperature humidification, Hi is considered constant, and integration of Equation 4 gives
(9)
where hLa is the water-film coefficient of heat transfer. Equations 7 , 8, and 9 one obtains -hLa/kAa = (i, - i ) / ( T i
where tI and t 2 are the temperatures of the inlet and the exit air, respectively. Rearrangement gives
(71
where i, and i are the enthalpies of air plus water vapor a t the interface and of the main stream, respectively. Furthermore, enthalpy balance gives
-
T)
From
(10)
I n the graph of the enthalpy of saturated air as ordinate us. the water temperature as abscissa, Equation 10 represents tie lines connecting the points on the operating line with the corresponding points on the saturation curve. The position of the operating line can be fixed if the water temperatures a t the top and bottom and the adiabatir saturation temperature of air at the top and that a t the bottom are obtained. The values of h ~ a were computed from the water-cooling data as follows : Estimating &a by means of the empirical equation obtained from the data on constant water temperature humidification, and assuming a value of h ~ a tie , lines having a slope of -hLa/kba were drawn from several points on the operating line to the saturation curve. Thus, trial-and-error procedures were repeated until the following relation was satisfied.
which is the integrated form of Equation 7 . The use of the over-all coefficient of enthalpy transfer, K&, for water-cooling and dehumidification operations is not theorebically sound, except when the water-film resistance is zero, but one can define Kha by the folloiving relation:
INDUSTRIAL AND ENGINEERING CHEMISTRY
1472
Vol. 43, No. 6
(Ht)cr as defined by Equatiori 6 should b e prwticallj. in(25-mm. Raschig rings) dependent of G :tiid inverselv Wet-Bulb Water kd.a hLa, proportionttl to the 0.2 power Gas Water Inlet Air Temperature Temperature (Calod.), &a ~ . t . ~ . Rate, G , Rate L. DryWetBelow Above Below Above Lb./ Lb./' (Hr.) oi L , since /& can be correLb./ Lb.) bulb bulb humidity, Abs. packing packpack(Hr.) (Hr.) (Cu. Iated by Equatiou 14. The (Hr.) (Hr.) t;rnZ,., temp., (calcd.), packing, in& in& (Cu. (Cu. Ft.) (Sq.Ft.) (Sq. Ft.) C. lb./lb. C. C. Ft.)(H) F t . ) ( H ) ( a F.) viilues of (. H t. h calcula.ted 37.0 27.0 460 1625 0.01810 26 8 36.6 36.6 40.1 909 froin tlie dat,a ranged i'rom 38.4 2 7 . 5 0.02340 27 4 470 1333 38.2 38.9 897 43.8 0.44 to 1.0 foot itccording to 37 38.4 .. ..A 457 932 36.9 2 7 . 3 0.01800 27 1 44.0 812 36.5 34.7 473 679 0,01830 26 7 36.3 27.0 45.7 787 the rnagriitude of L. 457 34.2 0.01830 27 3 35.7 38.4 27.5 44.6 659 759 39.0 27.2 461 35.3 364 0,01765 27 0 35.6 678 49.9 W A T m R- C o o L, I N G I1 u N s . 34.0 37.9 27.0 461 33.7 253 0.01770 26 8 631 51.0 Table 11 gives the principal 26 5 0.01760 39.9 362 26.7 44.9 data, together with the more 39.1 26 4 361 0.01730 26.4 35.0 20 9 360 0.01123 20.9 iinport:irit calculated results, 21 5 36.2 355 0.01157 21.6 on the water-cooling runs with 24 7 0.01654 34.0 40.4 350 24.7 21 5 21.6 0.01165 33.7 43.7 346 25-mni. ceramic Iliischig rings. 356 0.01125 2 0 . 8 33.4 20 8 45.3 25 8 0,01710 2 5 . 8 355 36.6 49.7 In t,liese runs G ranged from 34.6 27 3 45.0 372 0.01920 27.2 204 to 473 pounds per hour 27.2 34.5 371 0.01960 26.8 32.3 44.9 per square foot 0 1 gross cross 268 1180 32.0 2 3 . 4 0.01430 2 3 . 6 39.0 39.9 43.5 481 340 2400 261 606 28.3 19.7 0.01060 19.9 33.6 35.9 40.7 425 249 1017 sectiori of the column; I, 268 394 27.7 1 9 . 0 0.00992 19.0 32.1 32.5 41.1 402 240 961 261 344 34.5 25.7 0.01780 25.8 38.0 38.7 51.3 380 179 760 rmged froin 189 to 1825 266 200 33.0 25.7 0.01760 2 5 . 6 33.9 32.5 48.7 348 170 566 pourids per 11our per square 204 321 30.8 2 5 . 0 0,01740 25.3 38.4 37.8 49.4 286 174 937 foot. The w ~ ~ l etemperature r 205 189 28.4 23.6 0.01625 2 3 . 9 34.5 33.4 47.5 265 151 594 above ttic pacltirig was 40" to 51" C. The water-film TABLE 111. DEHCUIDIFICATIOS RUKd coefficient, h a , was computed (25-mm. Raschig rings) by the iiietliocl outlined behLa Wet-Bulb Water fore, using tile value of /&a Inlet Air (after Preheater) Temperature water Temperature &a, &a G~~ estimated with the use of WetBelow Above Below Above (Hr.) Lb./ Lb./' Rate 0 , Rate, L , Drybulb Lb.) Lb./ bulb Abs. packing packpackp,ack(Cu. (Hr.) (Hr.) Equation 14. Such a procetemp., temp., humidity, (calcd.), ing, (Hr.1 ing, ing, Ft.) (Cu. (Cu. (Hr.) dure nuiy be soinewhat dis(Sq. Ft.) (Sq.Ft.) ' c. c. Ib./lb. c. c. O c. (O F.) Ft.)(H) Ft.)(H) c. ,. putable, Ijecwise the gas-film 33.6 22.6 0 01240 12.8 11 7 466 8.5 1685 674 592 0 01422 22.7 14.5 29.8 12.8 458 7 1250 736 450 temperature lor tlie water25.5 16.4 0 01231 14.8 7 .. 46 808 477 422 449 23.0 13.1 11.3 0 01570 420a 7.2 1550 673 503 coolirig t'uiis was riot equal to 13.4 12 2 416 2 0 . 5 0 01077 8.5 942 497 438 18.8 9.8 1410 830 596 that for t,lie ~ U I I Sat conetant 0 01644 19.5 36.6 385 21.3 29.5 22.3 0 02000 379 517 398 273 water teinper:Lhue. However, 15.2 79 ..63 942 450 425 13.4 2 5 . 0 0 01950 370a 12.6 14.2 29.6 0 02060 342" 26.5 7.3 1350 587 457 this ett'ect, if :my, may be 0 O178Zb 13.8 25.4 12.9 24.6 342' 7.3 1170 615 443 13.8 7.0 1573 606 492 neglected, so i'ar as the prw. 12.2 43.1 2 9 . 3 0 01965 330 18.1 0 02100 92.2 19.3 318 39.2 97 .. 0 6 1462 730 599 ent datit w e coricerued. 13.7 0 02090 30.5 11.5 26.9 1305 467 431 307a 17.9 14.4 44.2 305 3 0 . 5 0 02160 7.6 942 337 322 Calcu1:tted results showed 16.3 0 02290 18.9 37.4 29.6 301a 8.0 797 362 288 8.5 942 472 358 that ~ L Uwaq :tfiected main11 16.8 15.7 29.2 0 01988 42.3 297 14.6 27.1 15.5 2 6 . 5 0 02035b 222Q 651 382 322 by the water velocit,y. No 10.3 78 .. 65 687 287 267 30.6 10.2 19.3 0 00911 178 definite trend with gas veloca Runs in which exit air was saturated. ity was iiot,icealh, although Saturation humidity a t air temperature below packing. G was varied considerably. I n Figure 7 calculated values of h ~ aare plotted against L on logarithmic coordinates, with a resulting single straight linr 300 I represented by the equation:
Rum TABLE11. WATER-COOLING
O
O
g:kd)*
O
O
I
hLU
200
5
b
.yo
IO0 80 I
/
200
400
I
600 800
G Figure 6.
Logarithmic Plot of kLa/Lo.l cs. G
=
8.OLO.8
(1 53
wherein hLa is in B.t.u./(hour)(cubic foot)(' I('.), I, i n pounds/ (hour)(square foot). This correlation was obtained froni the data for 25-mm. rings only. However, the effect of the packing size on h ~ uis considered negligible as in the cases of hca and kAa. The effect, of water temperature was not studied, but is also considered very small. In Figure i broken lines show the correlat,ion by McAdaim ef al. ( d ) , accord. ing to which h ~ isa proportional t o Go.' and Lo.;,for two values of G Xow, it is obvious that the procedure of evaluatirig the per. formance of packed cooling t,owers in terms of the over-all eo. efficient or over-all H.T.U. is not theoreticall>*sound, although it may be sometimes convenient in practice. For comparison. calculated values of the over-all coefficient' of enthalpy transfer, defined by Equation 12 Cali KAa, are given in Table 11. (H~)oG practically be obtained by diyiding G by Khu. Values of Kba were 40 to 70yoof those of k,a, mid consequently ( H t ) c was 40. to 70% of (Ht)oc, which ranged from 0.75 t o 2 feet. It has been
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1951
.=$*KT
4 3
T,
0 457-473
LLi
t ?
E
z 2 2
k 3
.I
r! c ai 1000 -
8
a
11
r
'
1473
-T
(94
Values of &a thus obtained for each run were divided by the corresponding values of G and were .plotted against L on logarithmic coordinates as shown in Figure 8. The points scatter somewhat, but are roughly correlated by the straight line representing Equation If, which was obtained from data on the constant water temperature run. T h e points include rune in which the exit air was saturated-i.e., runs in which, as is generally supposed, fog formation was possible. This indicates that Ic& for dehumidification can practically be correlated by the same equation, whether or not the exit air was saturated. For definite conclusions, however, more exact experimental studies are desirable. It seems urobable that in case the temuera2 ture of water is considerably lower than that of air, formation of fog or mist leads to a different situation. I n resume, the same equations for the gas- arid liquid-film coefficients can practically correlate the performance of a packed column, throughout three kinds of air-water contact operations-constant water temperature humidification, water cooling, and dehumidification
.
6 r;
"I50 2
4 6 8 1000 , LB/(SQ.FTXHR)
3
L Figure 7.
3.0
Logarithmic Plot of hLa us. L
I
I
ACKNOWLEDGMENT
The authors wiqh to express their sincere appreciation to 8. Kamei for his guidance and encouragement, and also to T. J. Walsh and M.Ma3ders for their kindness in reviewing the original manuscript. Acknowledgment is made to T. Koyanagi, who assisted with the experimental work and calculations.
tu I.o
o
0
o I
NOMENCLATURE
0 EXITAIR SATURATED
8
j
-
nx I I "'750 200
+
Z
Figure 8.
. (4
H
CL
I
I
t
i
600 8001000
400
L
a
-
kla for Dehumidification a s Compared with Equation 14
shown that the water film offers considerable resistance as compared with the gas film., DEHUMIDIFICATION RUNS. Data and principal calculated results for the dehumidification runs with 25-mm. ceramic Raschig rings are listed in Table 111. Although the water-film temperatures for these runs were lower than those for watercooling runs, the water-film heat transfer coefficient for dehumidification is considered to be approximately correlated b~ Equation 15 obtained from water-cooling data. There was some doubt, however, whether the gas-film coefficient, kAa, for dehumidification is also correlated by Equation 14 obtained from the data on the runs a t constant water temperature, since the dehumidification data involved runs in which the exit air was saturated. I n order to study this point, a comparison was made between the values of k;u calculated with the use of Equation 14 and those obtained from the dehumidification data assuming that hLa for dehumidification can also be correlated by Equation 15. The values of khu were computed from the data as follows: Estimating hLa by means of Equation 15 and assuming a value of k&, several tie lines having a slope of -haL/khu were drawn between the operating line and the saturation curve, and trialand-error procedures were repeated until the following relation was satisfied.
cs
G
Go
H Ht h
i Kd. k6
L 2' t
2 A
area of contact per unit of packed volume, square feet/ cubic foot = heat ea acity of liquid water, B.t.u./(pound)(" I?.) = humid [eat, B.t.u./(" F.) (pound of dry air) = mass velocity of air plus water vapor, pound/(hour) (square foot of gross cross section of column) = mass velocity of dry air, pound/(hour)(square foot of gross cross section of column) = absolute humidity of air, pounds of water vapor/pound of . . dry air = H.T.U., height of a transfer unit, feet; subscripts G and OG refer to gas film and over-all value in gas units, respectively = individual coefficient of heat transfer, B.t.u./(hour) (square foot)(' F.); hc for gas film, h~ for liquid film = enthalpy of humid air, B.t.u./pound of dry air; i* denotes enthalpy of air saturated a t the bulk-water temperature = over-all. coefficient of enthalpy transfer, B.t.u./(hour) (square foot)(i* - i) = gas-film coefficient of enthalpy or mass transfer, B.t.u./ (hour)(square foot)(& - i) or pound/(hour)(square foot)(Hi H) = superficial water mass velocity, pound/(hour) (square foot of gross cross section of column) = water temperaturoe, O F. (except where noted) = air temperature, F. (except where noted) = packed height, feet = latent heat of vaporization of water, R.t.u. /pound =
-
General Subscripts 1, 2 = to inlet and exit air, respectively i = to interface LITERATURE CITED
(1) MoAdams, IT. H., "Heat Transmission," 2nd ed., S e w York. McGraw-Hill Book Co., 1942. (2) McAdams. M-.H., Pohlenz, J. B., and St. John. R. C., Chem. Eng. Progress, 45, 241 (1949). RECEIVED March 25, 1950.
