Bosnjakovic, F., Springe, W., Knoche, K. F., Pyrodynarnics 1, 283-97 (1964). Chater, W. J. B., Harrison, J . L., “Recent Advances with Oxygen in Iron and Steel Making,” p. 301, Butterworths. Washington, 1964. Elliott, J. F., Gleiser, M., “Thermochemistry for Steelmaking,” Vol. 1 , Addison-Wesley, London, 1960. Elliott, J . F., Gleiser, M., Ramakrishna, V., “Thermochemistry for Steelmaking,” Vol. 2, p. 406, AddisonWesley: London, 1963. Gilles, H. L., “Reduction of Iron Ore with Hydrogen in a Direct Current Plasma Jet,” Ph.D. dissertation, Lehigh University, Bethlehem, Pa., 1968. Graves, R. D., Kawa, W.,Hiteshue, R. W., IND. ENG. CHEM.PROCESS DESIGNDEVELOP. 5, 59-62 (1966). Grieveson, P., Turkdogan, E. T., Trans. Met. SOC.AZME 250, 1609-14 (1964). Grosse, A. V., Stokes, C. S.. Cahill, J . A., Correa, J. J . , “Plasma Jet Chemistry,” Final Report, U. S. Dept. Comm., AD-630.549 (December 1965). Hamilton, D. R., Chu, T. L., Chang, H . C., Barrett, D., Goldberg, C., Kroko, L., “Research in Preparation of Hyperpure Single Crystal Silicon Carbide,” Final Report, U.S. Dept. Commerce, PB 154308 (1960). Huska, P. A., “Characteristics of Induction-Coupled Argon Plasmas and Their Use for Direct Production of Molybdenum by Thermal Decomposition of Molybdenum Disulfide,” Ph.D. dissertation, Lehigh University, Bethlehem, Pa., 1965. Huska, P.A., Clump, C. W., IND. ENG. CHEM.PROCESS DESIGNDEVELOP. 6, 238-44 (1967). Kubanek, G. R., Gauvin, W. H., Can. J . Chem. Eng. 45, 251-7 (1967).
Landler, P. F. J., Komarek, K. L., Trans. Met. SOC. AZME 236, 138-49 (1966). Morris, J. P., Riott, J. P., Illig, E. G., J . Metals 18, 803-10 (1966). Olsson, R. G., McKewan, W. M., Trans. Met. SOC.AZME 236, 1518-22 (1966). Seth, B. B. L., Ross, H. U., Trans. Met. SOC. AZME 233, 180-85 (1965). Spitzer, R. H., Manning, F. S., Philbrook, W’. O., Trans. Met. Soc. AZME 236, 726-42 (1966a). Spitzer, R. H., Manning, F. S., Philbrook, W. O., Trans. Met. SOC.AZME 236, 1715-24 (196613). Stokes, C. S., Cahill, J. A., Correa, J. J., Grosse, A. TJ., “Plasma Jet Chemistry,” Final Report, U. S. Dept. Commerce, AD-625591 (December 1964). Stokes, C. S., Knipe, W. W., Ind. Eng. Chem. 52, 2878 (1960). Themelis, N . J., Gauvin, W. H., Can. Mining Met. Bull. 55, 444-56 (1962). Till, P. H., Jr., Turkevich, J., “Electron Microscopic Study of Thermal Decomposition of Iron Pentacarbonyl,” Princeton University, AEC Rept. NYO-3430 (May 1, 1953). Touloukian, Y. S., “Recommended Values of Thermophysical Properties of Eight Alloys, Major Constituents and Their Oxides,” Thermophysical Properties Research Center, Purdue University, U. S. Dept. Commerce N6623802 (February 1966). RECEIVED for review September 9, 1968 ACCEPTED January 6, 1970 Work financially supported by the Bethlehem Steel Corp. and conducted a t the Homer Research Laboratories.
EVAPORATION OF WATER IN AIR, HUMID AIR, AND SUPERHEATED STEAM TETSUO
Y O S H I D A
A N D
TSUTOMU
H Y O D O
Faculty o f Engineering, Osaka City University, Osaka, Japan
The rate of evaporation of water into air, humid air, was estimated. When the mass velocity is constant, the evaporation rate is the same for different degrees point, it decreases as the humidity increases; above it,
and superheated vapor a t one inversion point of humidity. Up to this this relation is reversed.
These relations were confirmed experimentally by a wetted-wall column with countercurrent water and air, after which the heat and mass transfer coefficients were calculated. O n the basis of these studies, modern dryers might be modified and extended to a completely closed circuit. Heat and mass transfer terms obtained were: J H = (h,/C,G,) Pr2 = 0.029 Re-’* and J D = (kGpB.wMm/Gm) Sc13 = 0.022 Re-“.
’
evaporation of water in air is important in heat and mass transfer and in applications such as drying and air conditioning. For this reason, many experiments in water evaporation have used flat pans (Lurie and Michailoff, 1936; Shepherd et al., 1938), wetted-wall columns (Barnet and Kobe, 1941; Gilliland and Sherwood, 1934), and water droplets (Rantz and Marshall, 1952). The study of the evaporation of water in superheated
THE
vapor instead of air is comparatively recent. For example, experiments carried on by Wenzel and White (1951) and Chu, Lane, and Conklin (1953) have shown that more water evaporates in superheated vapor than in air. These applications to drying have been reported by several authors (Base1 et al., 1962; Yoshida and Hydd6, 1963, 1966). Furthermore, studies of evaporation of water in highly Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 2, 1970 207
humid air by Cairns and Roper (1954), using a wettedwall column, confirmed the effect of P B M on the J factor of heat and mass transfer. Chu, Finelt, Hoerrner, and Lin (1959) studied the evaporation of water using a pan in air, humid air, and superheated steam. Tdei, Okazaki, and coworkers (1966) reported a study of evaporation from water droplets into air, superheated steam, and a mixture of the two. These simultaneous heat and mass transfer data are usually correlated by the J factor, and recent studies have shown how the mass transfer coefficient is affected by P B M . Some confusion and disagreement exist concerning the results of these studies. T o clarify the results and conclusions, the authors believe that research should be done as a series on air and superheated vapor. Superheated steam and dry air may be considered extreme conditions of these two gas mixtures, and between them the humidity of air varies. Then it is most important to make clear the rate of water evaporation into air, humid air, and superheated steam under various conditions of temperature, flow rate, and humidity. This report first considers the evaporation rate itself and estimates the evaporation curve in the range from air to superheated steam. I t s purpose is to confirm these evaporation curves by experiments using a wetted-wall column, in which case convection heat can be more easily measured and undesirable effects of other forms of heat considerably lessened. The conditions are extremely important, because convection heat should play the leading role in our experiments. Estimation of Evaporation Curves
When the mass velocity is constant, the rates of evaporation of water into air, steam, and their mixtures are shown in Equation 1,
k!
a
CONSTANT M A S S VELOCITY
z
g
( I atm.)
Ly
0
n
s W
PAINT \
DEW FOR tiz
loo-
TEMPERATURE
FORH,
Figure 1. Effect of change of temperature on evaporation rate in air, humid air, a n d superheated vapor
more rapidly in humid air and superheated steam than in air. How can this contradictory relation of evaporation rate in humid air or an air-stream mixture be explained? These evaporation curves, a t constant humidity, starting a t the dew point of air, would intersect a t the same point as the curve of air and steam intersected, the “inversion point.” All evaporation curves in air, steam, and humid air would pass this inversion point; if the concentration of steam in air increased above this point, the evaporation rate would increase. But below this inversion point, as steam concentration increased the evaporation rate would decrease. The empirical fact that the evaporation rate in humid air is less than in dry air is true only in the temperature range below this inversion point. Chu and other investigators obtained a higher evaporation rate in steam than in air a t a temperature above the inversion point. T o confirm the existence of the inversion point is an important purpose of this experiment. Experimental Apparatus and Procedure
where, if the variations of the ratio h c / r uare small compared with the variations of temperature, the evaporation rate, W,, is in proportion to the temperature difference,
(t - t,). In the case of air, the surface water temperature, t,,, is nearly equal to the wet-bulb temperature; so the evaporation curve rises slightly a t lower temperatures, and is approximately straight a t higher temperatures. In the case of superheated vapor, the temperature of the evaporation surface is equal to 100°C. independent of the temperature of vapor a t atmospheric pressure, and the evaporation rate is zero a t 100”C., so the evaporation line becomes approximately straight starting from this zero point. According to the studies of Chu et al. (1953), Wenzel and White (1951). and the authors, water evaporates more rapidly into superheated vapor than into air. The curves for evaporation of air and steam would intersect at one point, as shown in Figure 1. Then, where would the curves of the evaporation rate in humid air or in an air-stream mixture be located on Figure l ? When the humidity in air increases, the rate of evaporation of water into air decreases; furthermore, the evaporation rate becomes zero a t the dew point temperature of humid air. According to Chu, Finelt, Hoerrner, and Lin (1959) water evaporates 208
Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 2, 1970
The equipment was the same as the countercurrent wetted-wall column of other investigators, but varied in detail because the boiling point of 100°C. water had to be supplied when superheated steam was used and the temperature of air and steam was raised to 400°C. An outline of the apparatus is shown in Figure 2. Air from a blower, measured by orifice, was put through an electric preheater (superheater) involving five 1-kw. heaters, and led to the wetted-wall column. The steam was generated in the boiler, then put through the same electric heater, and led to the wetted-wall column. I n this case, the rate of flow of steam from the boiler was measured by the boiler level gage. When the air-steam mixture was used, the boiler and the blower were used a t the same time, and the flow rate was measured separately, the total being the assumed flow rate of the mixture. The temperature of the steam, air, or their mixture was controlled by a Slidac connected to a heater, and a t the inlet of the column ranged from 50” to 400°C. The mass velocity was from 9100 to 27,300 kg. per sq. meter per hour. The boiler having a 50-liter capacity was heated by four 2-kw. immersion heaters and lagged with a 5 c m . diatom. One of the four heaters was connected to the Slidac. The wetted-wall column was made of a gun metal tube 2.9 cm. in inside diameter and 1 meter 1,ong. The inside
measured to check the wall radiation effect, to calibrate the temperature. The humidity of the air and steam mixture entering and leaving the column was measured by the wet- and dry-bulb thermometer of the thermistor. Manometers were used at the upper and lower parts of the column to determine the pressure in the column. To examine the rate of fluid evaporation, liquid rates of 16.1, 18.0, 34.0, and 67.0 kg. per hour in air were used; the maximum difference was 10°C. But only 18.0 kg. per hour were used in all runs. Calculations BLOWER
The evaporation rates were obtained by measuring the difference of the rate of flow of water at the inlet and outlet of the column and calculating heat and mass balances. These three methods agreed within 5 5 . In the case of low temperature and low mass velocity, measurement of flow rate was difficult, because the difference of the flow at the top and bottom was very little. At high temperature, wet-bulb temperature included the radiation error, so this affected the mass balance. Therefore, during all runs, the evaporation rate obtained from a heat balance was adopted and Equation 2 was used;
wt =
Figure 2 . Experimental wetted-wall column apparatus
of this tube was polished carefully. The column was enclosed in another gun metal tube 6 cm. in inside diameter, lagged with 3 cm. of asbestos. Between these two tubes heated oil was circulated to check the leakage of heat by conduction. The upper and lower parts of this column were equipped with peep windows which allowed the water film to be seen a t all times, to ascertain whether complete wetting occurred during all runs. The water leaving the column was recirculated by a small polypropylene centrifugal Pump. The temperature of the water entering the column was adjusted to the wet-bulb temperature of gas in an upper large vessel and a small vessel attached to the entrance of the column, by using electric immersion heaters. The upper large vessel had a small overflow tank, so that the water level in it was maintained constant. The oil and water temperatures were automatically controlled by thermistor temperature regulators having a sensitivity of 0.2" c. Distilled water was supplied to the lower vessel at regular intervals. The evaporation rate was determined by measuring the water flow at the inlet and outlet of the column with a measuring cylinder and stop watch. A constant flow rate of water to the column was required. When high temperature water was recirculated, the generation of bubbles in the pipe disturbed the accurate measurement of flow rate, so several small nozzles of various diameters were used instead of valves a t the inlet of the column to regulate the flow rate. The temperature of the gas was measured a t the inlet and outlet of the column with the copper-constantan thermocouples and the millivoltmeter, and the wall temperatures a t the inlet and outlet of the column were
c,(ti - t?) G' r, + c,(t? - t u )
(2)
where t l and t2 represent the temperature of gas a t the inlet and outlet of the column, calibrated in the study of the wall radiation effect by McAdams (1954). The principal experimental data and calculation results are shown in Tables I and 11. A sample calculation for run AS-10 is given in the Appendix. Results
The evaporation curves obtained in air, humid air, and superheated vapor a t inlet mass velocities of 9100 and 18,200 kg./sq. meter hour are shown in Figure 3. The evaporation curves initially assumed agree with this experimental result, and the inverse point exists a t 176" C. for mass velocity 9100 and a t 170°C. for 18,200 kg./ sq. meter hour. The relation of the inverse point and mass velocity is shown in Figure 4. The temperature for the inversion point decreased slightly as mass velocity increased, because the evaporation curves of steam slope gradually as the mass velocity is increased and evaporation curves of air move up as the mass velocity increases. This inversion point is important to decide the temperature of the operation of a closed circuit dryer. However, this inversion point would also change according to surface conditions of evaporating liquid and be different for different materials. The change in evaporation rate when the steam in the air was changed from 0 to 100% at 120", 170", 200", 250", and 300'C. and the mass velocity was 18,200 kg./ sq. meter hour, is shown in Figure 5. This figure shows clearly that at the temperature of the inversion point, the evaporation rate was the same in spite of the increase in steam. Above this point, at 200", 250", and 300°C., the evaporation rate increased as the percentage of steam increased, and inversely, below the inversion point a t 120°C. the evaporation rate decreased as the percentage of steam increased. The evaporation curves in this figure are almost linear and differ from Chu and Finelt's result Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 2, 1970
209
Table 1. Data and Calculated Results MaSS
Velocity (Inlet), G, Kg. Hr. Sg. M
Run No.
Humidity (Inlet), H, Kg Kg.
In
out
Water Temp (Mean) "C
Wt > Kg Hr
Kg Hr
Gas Temp , O C ~
WC,
Stl, O
C
pnwIPt
1 2 3 4 5
9100 9100 9100 9100 9100
0.012 0.012 0.012 0.012 0.012
110.0 156.9 202.4 228.0 269.8
66.0 86.0 102.8 112.0 129.6
37.9 45.7 49.0 50.5 55.0
0.108 0.176 0.242 0.286 0.344
0.108 0.176 0.242 0.286 0.344
46.6 70.2 94.9 109.2 132.5
0.955 0.935 0.923 0.912 0.906
A- 6 A- 7 A- 8 A- 9 A 10
9100 9100 18200 18200 18200
0.012 0.012 0.009 0.009 0.009
349.4 416.7 98.0 125.5 163.6
156.5 177.6 62.0 74.5 96.8
61.1 62.5 35.6 40.5 45.0
0.476 0.590 0.176 0.249 0.326
0.476 0.590 0.176 0.249 0.326
174.1 212.9 41.9 55.7 75.6
0.860 0.844 0.959 0.946 0.929
A-11 A-12 A-13 A-14 A-15
18200 18200 18200 18200 18200
0.009 0.016 0.016 0.010 0.016
193.8 217.6 237.3 260.7 259.4
110.1 121.5 141.0 137.0 139.4
48.0 51.5 53.5 54.0 54.8
0.412 0.469 0.520 0.603 0.589
0.412 0.469 0.520 0.603 0.589
98.3 111.1 123.0 135.3 135.8
0.923 0.906 0.907 0.905 0.890
A- 16 A-17 A-18 A-19
18200 18200 27300 27300
0.016 0.017 0.018 0.018
329.3 401.6 189.9 228.9
170.8 198.1 113.1 130.3
59.0 63.3 49.5 53.0
0.771 0.986 0.565 0.725
0.771 0.986 0.565 0.725
179.2 221.0 97.0 120.0
0.850 0.845 0.915 0.900
s- 1 s- 2 s- 3 s--4 s- 5
9100 9100 9100 9100 9100
... ... ... ...
135.8 171.8 208.8 240.4 313.0
113.8 130.2 146.2 161.9 192.2
100.0 100.0 100.0 100.0 100.0
0.114 0.216 0.317 0.396 0.598
0.105 0.198 0.284 0.354 0.527
23.1 46.8 73.1 94.7 144.3
... ... ... ... ...
S- 6
9100 18200 18200 18200 18200 18200 18200
...
220.8 113.4 127.5 144.3 166.0 197.5 232.2
100.0 100.0 100.0 100.0 100.0 100.0 100.0
0.780 0.131 0.294 0.450 0.687 1.003 1.310
0.680 0.126 0.279 0.425 0.656 0.935 1.215
189.6 19.8 40.1 63.9 96.3 142.9 190.5
...
... ...
380.1 128.0 156.0 188.7 234.7 299.3 367.3
2 3 4 5
9100 9100 9100 9100 9100
1.o 1.0 1.o 1.0 1.0
168.2 215.1 249.8 254.7 332.0
118.1 137.2 149.7 152.9 180.3
87.7 87.9 88.6 88.6 89.2
0.192 0.300 0.376 0.383 0.564
0.177 0.276 0.342 0.350 0.509
51.4 78.6 101.1 107.2 154.5
0.368 0.358 0.353 0.354 0.342
AS- 6 AS- 7 AS- 8 AS- 9 AS-10
9100 18200 18200 18200 18200
1.o 1.0 1.o 1.0
398.6 132.2 156.4 201.6 242.4
205.7 106.7 119.5 138.6 157.0
89.8 87.1 87.4 87.8 88.6
0.711 0.193 0.279 0.470 0.627
0.624 0.184 0.256 0.449 0.590
196.5 30.6 48.2 78.2 105.4
0.332 0.375 0.370 0.371 0.356
AS-11 AS- 12 AS-13 AS-14 AS-15
18200 18200 18200 18200 18200
1.o 1.o 0.333 0.333 0.333
310.6 376.5 138.6 253.7 315.0
190.2 221.4 102.7 147.5 183.0
89.2 89.8 74.7 78.4 80.0
0.890 1.131 0.226 0.646 0.814
0.840 1.045 0.219 0.621 0.787
153.2 199.2 43.4 114.1 160.6
0.345 0.336 0.632 0.595 0.581
AS 16 AS-I 7 AS-18 AS-19 AS-20
18200 18200 18200 18200 27300
0.333 3.0 3.0 3.0 1.o
387.8 237.1 303.8 371.1 169.3
212.1 163.9 196.0 222.8 129.9
80.5 95.3 95.5 95.7 87.8
1.060 0.641 0.929 1.210 0.448
1.010 0.604 0.864 1.120 0.431
206.5 100.8 147.5 195.5 59.7
0.566 0.156 0.155 0.147 0.369
AS-21
27300
1.o
209.4
148.3
88.3
0.693
0.665
87.2
0.356
AAAAA-
s- 7 S- 8 s- 9 s-10
s-11 s-12 ASASASASAS-
1
... ...
... ...
...
1.o
(Chu et a1 , 1959), which is not linear. The rate of evaporation in their study is comparatively large up to 50Cr of steam, but does not change above 5OCc. From the experimental result, the heat and mass transfer coefficientsof gas film and Colburn type J Hand J D factors were calculated, and Equations 3 and 4 were written.
J H= (h,/c,G,) Pr' ' = 0.029 Re 210
"'
Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 2, 1970
(3)
J , = ( h c , p x M M m / GSc' m ) ' = 0.022 Re-"
...
...
...
... ... ...
(4)
These J factors do not include the term ( p ~ v / P t "r ) for J H , and (pR,,/Pr)-"' for J,,, as do the results of Cairns and Roper (1954) in their study of highly humid air. The gas film coefficient of mass transfer in Equation 3 was inversely proportional to pHv, as is assumed in the film theory. Recently this has been confirmed theoretically
Table II. Data and Calculated Results
Run No.
G,
S,
Pr
J"
Re
Apim
kb
sc
JD
1 2 3 4 5
9190 9240 9290 9300 9380
0.00662 0.00698 0.00705 0.00716 0.00699
0.734 0.722 0.721 0.730 0.723
0.00539 0.00565 0.00567 0.00581 0.00563
3187 3643 3550 3492 3362
23.64 41.16 47.98 49.86 69.70
0.0501 0.0470 0.0554 0.0629 0.0542
0.624 0.623 0.604 0.604 0.599
0.00458 0.00412 0.00471 0.00471 0.00435
A- 6 A- 7 A- 8 A- 9 A-10
9460 9550 18380 18420 18950
0.00711 0.00709 0.00610 0.00636 0.00587
0.754 0.762 0.712 0.719 0.724
0.00593 0.00591 0.00487 0.00505 0.00452
3270 3180 7690 7478 7431
95.12 94.05 22.95 32.20 44.33
0.0550 0.0689 0.0841 0.0849 0.0808
0.598 0.599 0.615 0.639 0.619
0.00407 0.00494 0.00380 0.00385 0.00341
A-11 A-12 A-13 A-14 A-15
18550 18600 18600 18700 18700
0.00605 0.00580 0.005P6 0.00601 0.00572
0.731 0.736 0.735 0.734 0.741
0.00489 0.00472 0.00474 0.00489 0.00468
7098 6975 6863 6817 6800
50.59 56.60 66.90 69.40 67.47
0.0896 0.0906 0.0854 0.0954 0.0960
0.605 0.604 0.600 0.598 0.599
0.00377 0.00350 0.00348 0.00405 0.00378
A-16 A-17 A-18 A-19
18820 19000 27800 27900
0.00570 0.00573 0.00516 0.00548
0.750 0.762 0.736 0.737
0.00470 0.00477 0.00421 0.00447
6541 6236 10624 10384
83.90 105.10 49.85 60.88
0.1010 0.0953 0.1245 0.1308
0.598 0.603 0.605 0.601
0.00372 0.00343 0.00346 0.00352
s- 1 s- 2 s- 3 s- 4 s- 5
9210 9280 9360 9400 9540
0.00610 0.00570 0.00519 0.00495 0.00472
1.039 1.044 1.048 1.045 1.023
0.00625 0.00586 0.00535 0.00510 0.00497
5879 5647 5484 5321 5129
S- 6
s-10
9700 18350 18470 18600 18700
0.00450 0.00435 0.00471 0.00418 0.00450
1.012 1.044 1.050 1.049 1.043
0.00453 0.00447 0.00487 0.00433 0.00462
4932 11713 11401 11050 10636
s-11 $12
19050 19250
0.00424 0.00401
1.041 1.032
0.00431 0.00409
10115 9625
1 2 3 4 5
9240 9340 9400 9410 9550
0.00629 0.00625 0.00602 0.00575 0.00566
0.870 0.871 0.886 0.870 0.888
0.00574 0.00570 0.00555 0.00524 0.00523
4589 4483 4399 4384 4226
10.70 19.34 23.05 22.06 29.10
0.1845 0.1565 0.1628 0.1741 0.1920
0.599 0.562 0.565 0.564 0.573
0.00449 0.00374 0.00382 0.00406 0.00426
AS- 6 AS- 7 AS- 8 AS- 9 AS-10
9670 19750 18460 18600 18700
0.00534 0.00531 0.00483 0.00501 0.00497
0.879 0.893 0.890 0.898 0.878
0.00490 0.00494 0.00447 0.00467 0.00456
4092 10059 9230 8986 8766
36.90 7.32 10.40 19.00 22.00
0.1825 0.2820 0.2700 0.2595 0.2950
0.572 0.561 0.556 0.561 0.564
0.00394 0.00345 0.00338 0.00321 0.00352
AS-11 AS-12 AS-13 AS-14 AS 15 AS-16 AS- 17 AS-18 AS-19 AS-20
18900 19100 18420 18750 18870 19050 18750 18920 19180 27700
0.00517 0.00501 0.00557 0.00577 0.00513 0.00500 0.00454 0.00436 0.00416 0.00437
0.887 0.874 0.790 0.766 0.774 0.782 0.957 0.954 0.949 0.872
0.00477 0.00458 0.00497 0.00484 0.00434 0.00432 0.00441 0.00442 0.00402 0.00399
8400 8116 8702 8132 7800 7342 9783 9260 8935 13645
26.70 38.30 15.07 47.40 56.70 68.27 9.00 13.18 15.74 11.73
0.3450 0.3020 0.1585 0.1438 0.1527 0.1625 0.7366 0.7184 0.7831 0.0895
0.575 0.577 0.548 0.545 0.551 0.564 0.571 0.588 0.581 0.560
0.00402 0.00335 0.00374 0.00317 0.00324 0.00343 0.00371 0.00350 0.00351 0.00338
AS-21
27900
0.00456
0.869
0.00415
13349
18.53
0.0850
0.563
0.00322
AAAAA-
s- 7 S- 8 s- 9
ASASASASAS-
and experimentally by Wasan and Wilke (1968) and Vivian and Behrmann (1965). These data are compared with results of other investigators in Figures 6 and 7. The J H factor is about 30% higher than the JD factor. This difference might be considered due to the difference in film thickness (Barnet and Kobe, 1941). The effects of ( ~ B M / on P ~the ) J factors are shown in Figures 8 and 9.
Application to a Completely Closed Circuit Dryer
The experimental results of this study permit prediction of the completely closed circuit dryer. Xowadays, the rate of recirculation of the exhaust humid air in the usual dryer is limited because the drying rate decreases as air humidity increases. However, a t high temperatures this limit would not be an essential factor. If humid air is used as a drying gas at temperatures Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 2, 1970
21 1
-
0007
STEAM
-0-
.-L.AI
-+
~
R
0004
I ai sa003
-
u
A
AIR
STEAM A I R M I X T U R E
100
60
140
180
220
ME A N TEMP E R A T U R E
260
300
0002 2000
,
4000
3000
,
,
I , , , ,
1
1 I
,
,
,
15000
6000 e000 10000
Re
'C
Figure 3. Rate of water evaporation in air, superheated steam, a n d 50% mixture Mass velocity. 9100 and 18,200 kg./sq. meter hour
Figure 7. Comparison of mass transfer d a t a with results o f other investigators
c
' H
170
[
> 5
160
e
c
00161 0.I
W
0.2
os
a4
0.8 10 .
0.6 P s d Pt
$ 150
Figure 8. Effect of P B M / f f on heat transfer d a t a
z
Yk
/T
140
0.041 MASS VELOCITY
I
I
"
j
kg/n?hr
Figure 4. Variation o f inverse point temperatures with mass velocity 1
1
MASS VELOCITY
I
I
I
i
18200 k g / d n r !
I
0. I
0.2
0.3
0.4
0.6
0.8 1.0
P e d Pt
Figure 9. Effect of pm4/ft on mass transfer d a t a
!
0
50 IO0 WEIQHT PERCENT S T E A M
Figure 5. Effect of percentage of steam in air on evaporation rate
-O
I
F
"I",
a
a
s
\
.c
' 0.002 2000
STEAM AIR MIXTURE
3000
4ooo
6OOO
eo00 10000
Is000
Re
Figure 6. Comparison of heat transfer d a t a with results of other investigators
212
Ind. Eng. Chem. Process Des. Develop., Vol. 9,No. 2, 1970
above the inverse point, the drying rate will be higher than if dry air is used. When a dryer is operated in a completely closed circuit, air inside changes to humid air, then highly humid air, and finally superheated steam almost completely replaces the air. Consequently, air drying may change to a superheated vapor drying, which has many merits (Yoshida and Hyddd, 1963, 1966). Figure 10 shows the outline of this dryer. At first, it is filled with atmospheric air. Then the air is circulated by the blower. The amount of steam in the dryer increases as time goes on, because the steam is evaporated from the drying material. To keep the pressure inside the chamber a t 1 atm. a regulating valve is mounted on the chamber. Therefore the mixture of evaporating steam and air over 1 atm. is exhausted from this valve. The change of steam content in the air of the completely closed circuit dryer was examined. If the volume of the dryer, including the heating chamber and the pipeline, is V cu. meters and the amount of evaporated steam from drying material is L' cu. meters per hour, the amount of steam, x, in the chamber a t time T i s shown as Equation 5,
x = V ( 1 - e - l ' 1'
(5)
Then, the following assumptions were made: the tem-
:i ti
46
'~APORATINQ
Xml
SURFACE
D)
1.0
0
0.5
1.0
T hr.
1.5
20
Figure 10. Closed circuit dryer a n d relation of steam content t o time
perature of the chamber was 300" C., and the evaporation rate was 0.25 to 5.0 kg. per hour (constant drying). Thereafter, Equation 5 was calculated. Figure 10 shows the relation of cubic meters of steam in the drying chamber, x , and time, T . I n the case of an evaporation rate of 5 kg. per hour, this chamber will be almost entirely filled with steam in about 20 minutes. Conclusions
The statement that the rate of water evaporation decreases as the humidity of air increases should be revised. The rate of evaporation of water has a limit point (inversion point) with respect to air temperature. The above statement holds below this point, but at higher temperature the rate of water evaporation increases as the humidity of air increases. Since water evaporates more rapidly into superheated vapor than into air at temperatures above this point, an ideal closed-circuit dryer should be operated a t a temperature above the inversion point. Further investigation of the inversion point is necessary to make clear theoretically the reasons for its existence. Appendix
Sample Calculation for Run AS-10. Total pressure of column, Pi= 756.1 mm. Hg Inlet temperature of gas, tl = 242.4"C. Outlet temperature of gas, t? = 157.0"C. Evaporation rate by heat balance = 0.627 kg.1 hour (Equation 2) Mean temperature of water t = 88.6"C. Flow rate, G' = 1 2 kg.ihour Evaporation rate by gas radiation, W , = 0.036 kg./ hour (by method of Perry, 1963) Evaporation rate, eliminating gas radiation effect W , = W, - W, = 0.591 kg./hour Logarithmic mean temperature difference Atlm = [ ( t i - t u ) - (tl - t,)]i[ln ( t l - t , ) / ( t z - t u ) ] = 105.4" C.
Convective heat transfer coefficient of gas film h, = Wcr,/Atl,A = 33.6 kcal./sq. meter hr. 'C. A = evaporation surface area = 9.11 x IO-* sq. meter Inlet humidity of gas, H1= 1 kg./kg. dry air Outlet humidity of gas, H2 = HI + W t / [ G ' ( l / l + HI)] = 1.105 kg./(kg. dry air) Inlet partial pressure of air p l = P t / ( l+ 1.61 H I ) = 272 mm. Hg Outlet partial pressure of air p 2 = P t / ( l+ 1.61 HJ = 272 mm. Hg Vapor pressure for t, p a = 498.4 mm. Hg Logarithmic mean partial pressure of air Inlet gas film p B M l = [PI - (Pt - p&)]/[lnp l / ( P t pu)]= 273.2 mm. Hg Outlet gas film p B M 2 = [P? - (Pt - p d l / [ l n p s / ( P t - p,)] = 264.8 mm. H g Logarithmic mean partial pressure of gas film in column p B M= (pBM1 + pBM2)/2= 269.0 mm. H g Ratio of ~ B and M total pressure, p B u / P t = 0.356 Mean temperature of gas film t, = [ ( t l + t 2 ) / 2 + t u ] / 2 = 144.2"C. Specific heat of air a t t , c, = 0.2432 kcal./kg. OC. Specific heat of steam at t, c, = 0.4725 kcal./kg. 'C. Mean molecular weight M , = [29 pB,v + 18 (Pt - p ~ v ) ] / P = t 21.9 Mean specific heat of gas film C, = [29 c,pBAv + 18 C, (Pt - p a u ) ] i P t Mm = 0.365 kcal./ kg. C. Mean mass velocity G, = ( l / S ) ( G ' + Wti2) = 18700 kg./sq. meter hour S = sectional area of column = 6.52 x sq. meter St = h,/c,G, = 0.00497 Viscosity of gas film, p = 0.064 kg./meter hour by method of Bromley and Wilke (1951) Thermal conductivity of gas film = 0.064 kg./meter hr. C. by the method of Lindsay and Bromley (Wassiljewa, 1904) P r = cmpL/X= 0.878 J H= St Pr2 = (h,/c,G,) [ ~ , ( p / h ) ] ~= 0.00456 Reynolds number Re = DGmip = 8766 1) = inside diameter of column = 0.029 meter Logarithmic mean driving force Appim = [ ( p i L- Pt + p l ) - (psi - Pt + p 2 ) ] / [ l n ( p k - Pt + p , ) / ( p , - Pt + p ~ )=] 22.0 mm. Hg Mass transfer coefficient h t = W,/Jpl,A = 0.295 kg./(sq. meter hour mm. Hg) hc = 0.0164 kg. moleisq. meter hour mm. Hg J D= (kGpRnM,/G,) SC' = 0.00352 D, = 0.067 sq. meterihour SC = p / p D , = 0.564 Acknowledgment
A. Sumi, T. Nishioka, K. Nakamura, F . Ikeda, and H. Tamura were very helpful in the experimental work and calculations. Nomenclature
A = evaporation surface, sq. meters c, = specific heat of air, kcal./ kg. C. c, = specific heat of steam, kcal.ikg. 'C. c, = specific heat of air and steam mixture gas, kca1.i kg. C. D, = diffusion coefficient, meters/hour Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 2, 1970
213
D G’ G, G h,
= inside diameter of column, meters = mass rate, kg./hour = mean mass velocity, kg./sq. meter hour = inlet mass velocity, kg./sq. meter hour = corlvective heat transfer coefficient of gas film, kcal./sq. meter hr. C. H = humidity of gas, kg./kg. dry air J H = (h,/c,G,) Pr2 < J D = (kcp,,Mm/Gm) SC* kb = mass transfer coefficient of gas film, kg./sq. meter hr. mm. Hg k , = mass transfer coefficient of gas film, kg. mole/ sq. meter hr. mm. Hg M , = mean molecular weight of gas Pf = total pressure in column, mm. Hg P = partial pressure of gas, mm. Hg P B M = logarithmic. mean partial pressure of air in gas film, mm. Hg P r = Prandtl number = c , p / x r, = latent heat at t,, kcal./kg. Re = Reynolds number = DG,/p s = sectional area of column, sq. meters s c = Schmidnumber =p/pDL t = temperature of gas, C. t, = temperature of water surface, C. T = time, hours v = volume of evaporation steam, cu. meters/ hour volume of dryer, cu. meters = evaporation rate, kg./hour w, = evaporation rate eliminated radiation effect, kg./ hour x = volume of steam in dryer, cu. meters F = viscosity of gas film, kg./hour meter A = thermal conductivity of gas film, kcal./ meter hr.
Literature Cited
Barnet, W. I., Kobe, K. A., Ind. Eng. Chem. 33, 436 (1941). Basel, L., Conn, S., Gray, E., Chem. Eng. Progr. 58, 67 (1962). Bromley, L. A., Wilke, C. R., Ind. Eng. Chem. 43, 1641 (1951). Cairns, R. C., Roper, G. H., Chem. Eng. Sei. 3, 97 (1954). Chu, J. C., Finelt, S., Hoerrner, W., Lin, M. M., Ind. Eng. Chem. 51, 275 (1959). Chu, J. C., Lane, A. M., Conklin, D., Ind. Eng. Chem. 45, 1586 (1953). Gilliland, E . R., Sherwood, T. K., Znd. Eng. Chem. 26, 516 (1934). Lurie, M., Michailoff, N., Ind. Eng. Chem. 28, 345 (1936). McAdams, W. H., “Heat Transmission,” 3rd ed., p. 262, McGraw-Hill, New York, 1954. Perry, J. H., “Chemical Engineers’ Handbook,” 4th ed., p. 10-40, McGraw-Hill, New York, 1963. Rantz, W. E., Marshall, W. R., Chem. Eng. Progr. 48, 141, 173 (1952). Shepherd, C. B., Handlock, C., Brewer, R. C., I d . Eng. Chem. 30, 338 (1938). Tdei, R., Okazaki, M., Kubota, K., Ohashi, K., Kataoka, K., Mizuta, K., J . Chem. Eng. Japan 30, 43 (1966). Vivian, J. E., Behrmann, W. C., A.I.Ch.E. J . 11, 656 (1965). Wasan, D. T., Wilke, C. R., A.I.Ch.E. J . 14, 577 (1968). Wassiljewa, A., Physik. 2. 5, 737 (1904). Wenzel, L., White, R. R., Ind. Eng. Chem. 43, 1829 (1951). Yoshida, T., Hydd6, T., Food Eng. 38, 86 (1966). DESIGN Yoshida, T., Hyddd, T., IND.ENG.CHEM.PROCESS DEVELOP. 2, 52 (1963).
O
v= w,
O C .
3pim = logarithmic mean driving force, mm. Hg P = density of gas film, Kg./cu. meter SUBSCRIPTS RECEIVED for review October 7, 1968 ACCEPTED September 29, 1969
1 = inlet 2 = outlet
RADIAT ION-INIT IAT E D SIDE-CHA IN C H LOR INATION 0F TO L UE NE Kinetic Investigations J .
Y .
Y A N G
A N D
C .
C .
T H O M A S ,
J R .
Western New York Nuclear Research Center, Inc., Power Drive, Buffalo, N . Y . 14214 H .
T .
C U L L I N A N
Department of Chemical Engineering, State University of New York at Buffalo, Buffalo,N . Y . 14214
ALTHOUGH there have been significant advances toward the peaceful utilization of atomic energy in many areas of industrial applications, the extent of developments within the chemical industry has been rather disappointing. Silverman (1968) and Ballantine (1968) recently reviewed the problems as well as achievements in the field of radiation chemical processing. The application of radiation energy for the initiation of chemical synthesis 214
Ind. Eng. Chem. Process Des. Develop.,Vol. 9, No. 2, 1970
has made particularly slow progress and more efforts directed toward the development of such applications are definitely needed. The side-chain chlorination of toluene is expected to proceed by free radical chain reactions, resulting in a large number of molecules reacted for a given amount of energy absorbed. A recent report (Collins et al., 1967) based on a literature survey and economic evaluations
