Tower Absorption Coefficients V.
Determination and Effect of Free Volume'
C. W. SIMMONS . ~ N DH. B. OSBORN, JR., Lehigh University, Bethlehem, Pa. QGATIOSS applied to countercurrent absorption processes contain an expression in some form which represents the free volume of the tower. This free volume, whether determined as dry or drained, has been considered as a constant. It seems more logical to assume that the free volume is a function of the extractor rate. It is the purpose of this paper to determine this free volume variation and to illustrate its use when applied to the equation of Bennetch and Simmons ( I ) .
The free volume variations are given in Table I and plotted in Figure 1. TABLEI. WATERSYSTEM WATERRATE Literslmin. ,Moles/ nain. Glass spheres, 1495 cc. 4.80 267 231 4.17 (av. water temp., 3.21 178 8.5' C . ) 2.67 148 121 2.18 1.86 103 96.8 1.745 91.5 1.65 1.45 80.4 1.3 72.0 1 16 64.2 1.06 59.0 51.2 0.924 0.77 42.7
1.0
1.5
2.0
2.5
r n C T O B UTE
3.0
3.5
4.0
4.5
ON
0.350 0.345 0.325 0.260 0.195 0.170 0.1275 0.1075
1.060 1.065 1.085 1.15 1.2150 1.2400 1.2825 1 3025
Coke, 1560 cc. (av. water temp., 8' C . )
4.90 4.75 3.61 2.69 2.32 1.60 1,345 0.95
273 260 200 150 129.6 89.0 75.0 53.0
0.514 0.420 0.410 0.340 0,325 0.260 0.240 0.210
1.046 1,100 1.150 1.220 1.235 1.300 1.320 1.350
FREE-VOLUME
FREEVoLunrESI. A FGNCTION OF EXTRACTOR RATE For the purpose of determining the free volume variat'ion, apparatus of the following specification was used : A Pyrex glass tower of 0.4801 sq. dm. total cross section and 8.14 dm. in filled height was set up and equipped for countercurrent absorption. A reservoir above the tower supplied a steady flow of extractor, at' a constant pressure, through a valve and spray. The carrier gas mas measured through wet test meters and constancy of flow was checked by a Venturi, the pressure being measured by a manometer. The filler, which was of varying specifications as listed below, rested upon a screen tray below which the carrier gas entered. A valve in the extractor outlet line made it possiblp to maintain the liquid at constant level.
A variation due to difference in character of extractor was studied using a light oil-air system to approximate the work of Bennetch and Simmons on the absorption of benzene. The oil used had the following specifications : Density a t 20," C gram per cc. Molecular aeight" Viscosity (S-21' C 1 , seconds
Glass spheres Clay spheres Coke
DESCRIPTION 1 . 8 5 cm. diam. 1 . 5 em. diam. 81% through 0.5 in. (1.27 cm.) on 0.25 in. (0.635 cm.)
DRAINED FREE VOL. Liters 1.495 1.410
0.808 168 34
1.
g 1
1.
8
1.
g 3
e
EXPERIMEXTAL PROCEDURE The drained free volunie of the tower was determined for each type of filler by measuring the amount of liquid that was held in the filled section of the tower. The operating free volume was measured by closing the inlet and outlet extractor valves simultaneously and then draining off the effluent liquid into a measuring cylinder and subtracting this amount froin the drained free volume. This was done at varying extractor rates and for the different; kinds of filler. The extractor rate was determined by collecting a definite quantity of extractor leaving the tower anti observing the time of flow with a stop watch. Checks were made within 9.1 second for each extractor rate. The fillers used for a water-air system and drained free volumes were : TYPEFILLER
VOL.
273 266 239 175 136 101 60.3 51.2
5.0
The literature on countercurrent absorption is rather deficient in experimental data applied to a variety of processes. Considerable experimental data are presented in sufficient detail that may be of general use to investigators in this field.
Liters 1.173 1,195 1.265 1.286 1.310 1.333 1.335 1.347 1.359 1,372 1.379 1.386 1.398 1.400
4.92 4.8 4.3 3.15 2.46 1.815 1.09 0.924
- LIrERs/uIw.
FIGURE 1. EFFECTO F EXTRACTOR RATE WATERSYSTEM
FREE
EFFLUENT WATER Liter 0.322 0.300 0.231 0,209 0.185 0.16% 0.160 0.148 0.136 0.123 0.116 0.109 0.097 0.095
Clay spheres, 1410 cc. (av. water temp., 8.0' C . )
0.5
ACTU.AL
TYPEFILLER AND FREEVOL. DRAIXED
1.
1.
1. 1.
1. 0.
D(TRACT0R F*TE-LITE+I/YII.
FIGURE 2 . EFFECTOF EXTRACTOR RATEON FREE-VOLUME KEROSENESYSTEM
The fillers used for the oil and the drained free volumes were: TYPBFILLER
DESCRIPTION
DRAINED VOL.FREE
Liters Coke Glass sphere Glass Raschig rings
81% through 0.5 in. (1.27 cm.) on 0.25 in. (0.635 cm.) 1 . 8 5 om. diam. See specifications of absolute data, Table V
1.630 1.510 2.00
The free volume variations are given in Table I1 and plotted in Figure 2.
1.560
1
529
For Parts I to IV, see literature citations 1 t o 3.
INDUSTRIAL AND ENGINEERING CHEMISTRY
530
TAB^ 11. KEROSENESYSTEM TYPEFILLERAND DRAINEDFREE VOL.
KEROSENE RATE Literr/min. Moles/min.
AcruaL EFFLUENT FREE K ~ R O R E N ~ VOL. Liter Liters
Coke filler, 1630 cc. (av. kerosene temp., 22.00 C.)
4.80 4.26 2.80 2.04 1,605 1.458 1.02 0.894
23.20 20.45 13.45 9.80 7.70 7.00 4.90 4.28
0.685 0.710 0.430 0.310 0.246 0.222 0.210 0.178
0.945 1.020 1.200 1.320 1.384 1.408 1.420 1.452
Raschig ring filler, 2000 cc. (av. keroBene temp., 24.0' C.)
4.75 4.28 3.23 0 97 3.80 2.95 1.90 1.40
22.60 20.51 15.5 4.66 18.25 14.18 9.12 6.72
0.800 0.720 0.590 0.300 0.670 0.340 0.420 0.370
1,200 1.280 1.410 1.700 1.330 1.460 1.580 1.630
3.30 2.75 2.06 1.03 1.26 0.89 0.56
15.85 13.25 9.9 4.95 6.05 4.275 2.69
0.420 0.360 0.275 0.140 0.180 0.150 0.105
1.09 1.15 1.235 1.370 1.33 1.36 1.405
Glass spheres, 1510 CC. (av. kerosene temp., 24.5O C.)
The free volume variations in the case of both the water and the oil systems show that the free volume is a linear function of the extractor rate. The slopes of the curves for each system individually are identical and independent of the type of filler.
Vol. 26, No. 5
For comparison, the data on glass sphere filler, for both the water and oil systems, is shown in Figure 3 where the free volume has been plotted against extractor rate in both moles per minute and liters per minute. When plotted with liters of extractor per minute as abscissa, the rate of diminution of free volume was approximately twice as great for oil as for water. With the extractor rate in moles per minute, we find that the free volume decrease becomes about 225 times as great for oil as water. The slopes of the curves given in Figures 1 to 3 are as follom~s: FIQURE1 A. 0.069 E. 0.070 C. 0.070
FIQURE2 A. 0.130 E. 0.130 C. 0.131
FIQCRE3 A. 0.0225 5. 0.130 c. 0.0001 D. 0.070
All of the data shown by the curves were obtained a t zero carrier rate. Several runs were made using a counterflow of air of about 1.84 liters per second. Since no appreciable change in free volume variation was noticed, the gas effect may be considered negligible. USE OF CORRECT FREEVOLUME
The results of the investigation on the free volume variation have shown it to be a function of extractor rate, being practically independent of the filler used and only dependent upon the extractor. From the data on water i t has been possible to determine the correct free volume at any extractor rate and thus substitute the correct value in the equation of Bennetch and Simmons for absorption data involving a carbon dioxidewater system. Similarly, the kerosene determinations have been applied to a benzene-oil system, believing that the kerosene closely approximates the characteristics of the extractor actually used. Considerable published data, as well as recent experimental FIQURE3. EFFECTOF EXTRACTOR RATEON FREE-VOLUME results were applied to the calculations of absorption coeffiGLASS-SPHERE FILLER TABLE111. CARBON DIOXIDE-WATER SYSTEM
Tmm
cos GAS
Inlet
Outlet
%
%
TEMPERATURE Av. Gas Water CARRIER WATER PRESSURE inlet outlet G . moles/ G. moles/ L./min. man. L./min. man. Mm. H e a C. ' C.
GAS
MOLE EFFECTIVE DRAINEDOPERATINQ ABS. GROSS FREE FREE COEFFIVOL. VOL. VOL. CIENT,K
FLOW
RATIO
Liters
Liters
Liters
GLASS SPHERE FILLER
1 2 3 4 5 6 7 8 9 10
18.8 16.6 17.8 15.5 16.7 15.9 16.0 13.5 13.6 12.3
16.5 14.2 15.5 13.0 14.4 13.6 13.0 9.4 8.2 6.3
5.664 6.664 5.664 2.450 7.485 6.715 5.755 4.595 1.613 8.314
0,1905 0.1955 0,1925 0,0849 0,2661 0,2450 0.2047 0.1684 0,0580 0,3025
0.905 0.905 0.905 2.866 1.318 1.303 1.338 1.334 1.064 2.724
50.25 50.25 50.25 159.2 73.2 72.4 74.3 74.1 59.2 151.2
11 12 13 14 15 16 17
18 19 20 21
23.6 25.6 20.8 25.4 21.6 17.8 13.6 11.8 15.2 14.6 11.9
10.4 13.4 10.6 18.0 12.0 12.4 7.8 7.2 8.2 7.5 5.2
3.85 4.05 3.91 4.02 3.88 3.38 3.57 3.46 3.40 2.10 1.95
0,1255 0.1296 0.1330 0.1282 0.1254 0.1174 0.1305 0,1260 0.1200 0.0750 0.0730
8.34 6.06 6.13 2.72 5.21 2.24 5.05 2.94 4.39 5.40 7.48
463 337 341 151 289 124.5 280 163.5 244 300 416
22 23 24 25 26 27 28 29 30 31 32 33 34 35
16.8 17.0 17.1 17.1 16.9 16.9 8.1 7.6 9.2 8.5 8.7 9.7 10.3 15.1
14.5 15.1 15.3 15.6 15.8 15.9 6.2 5.2 6.3 5.1 4.7 6.4 7.3 12.4
7.67 7.58 7.66 7.74 7.68 7.64 3.17 2.94 3.62 2.62 2.07 1.94 2.11 1.69
0.2710 0,2562 0,2610 0.2718 0.2694 0.2684 0,1225 0.1095 0.1341 0.1006 0.0802 0.0738 0.0763 0,0607
1.261 1.133 0.97 4.34 6.06 10.64 5.14 5.13 6.31 5.33 4.34 4.28 5.15 4.35
70.0 62.8 53.8 241 337 591 285 285 350 296 241 238 286 242
760.0 760.0 760.0 760.1 759.6 758.2 760.3 759.8 759.7 760.1
21.0 21.0 21.0 21.5 12.6 12.9 14.0 14.5 20.0 20.0
9.0 9.1 8.9 9.2 11.2 11.5 11.7 11.85 8.3 8.7
264 257 261 1875 275 301 362 440 1020 500
3.209 3.209 3.209 3.132 3.561 3.561 3.561 3.561 3.132 3.132
1.383 1.383 1.383 1.350 1.535 1.535 1.535 1.535 1.350 1.350
1.284 1.284 1.284 1.035 1.390 1.392 1.398 1.388 1.230 1.050
0.660 0.663 0.656 0.850 0.676 0.679 0.677 0.678 0.676 0.926
12.2 12.0 10.4 11.6 21.2 15.6 14.0 18.2 18.8 17.6 14.3
7.2 7.2 7.4 7.0 7.0 9.2 6.4 8.2 6.8 7.2 7.6
3690 2600 2566 1179 2301 1060 2162 1297 2030 4000 5700
5.588 5.588 5.588 5.588 5.588 5.588 5.588 5.588 2.082 2.082 2.082
3.515 3.515 3.515 3.515 3.515 3.515 3.515 3.515 1.310 1.310 1.310
2.598 2.949 2.841 3.216 2.942 3.269 2.950 3.152
0.72 0.59
1.027 0.923 0.976. 0.656 0.785 0.562 0.705 0.607 0.958 1.945 2.775
12.9 15.2 17.0
13.9 16.2 15.4 17.0 18.0 17.1 5.3 10.1 9.7 9.7 7.2 7.2 9.5 7.2
258 245 206 887 1250 2200 2325 2505 2610 2940 3010 3225 3750 3930
3.174 3.174 3.174 3.252 3.174 3.252 3.252 3.174 3.174 3.252 3.252 3.174 3.252 3.252
1.495 1.495 1.495 1.675 1.495 1.675 1.675 1.495 1.495 1.675 1.675 1.495 1.675 1.676
1.356 1.371 1.338 1.198 0.828 0.510 1.110 1.030 0.801 1.089 1.198 1,024 1.108 1.196
0.684 0.663 0.645 0.639 0.677 0.819 0.833 0.850 0.871 0.924 0.925 0.971 1.111 1.180.
RASCHIQ RINQ FILLER
760.0 763.0 755.2 756.0 755.6 758.3 755.0 759.0 755.3 760.3 743.1
0.830
COKE FILLER
759.7 759.7 759.9 759.3 759.3 760.0 760.0 760.0 759.1 760.1 760.3 760.0 758.9 759.7
14.7
16.1 15.2 16.7 18.2 17.1 17.1 14.2 14.6 15.1 12.0
INDUSTRIAL AND ENGINEERING CHEMISTRY
May, 1934
TAB- IV. CaHa GAS TEST
Inlet
Outlet
%
%
CARRIER C. moles/ LJmin. mzn.
EXTRACTOR
L./min.
G . moles/ rnm.
531
BENZENE-OIL SYSTEM T E M P E R A T U R ~ MOLE EFFBCTIVE DRAINEDOPERATINQ Ass. FREE COEFFIFREE Oil FLOW GROM VOL. VOL. CIENT. K outlet RATIO VOL.
Av. Gas PRESSURE inlet
Mm. Hg
C.
O
C.
Liters
Liters
Liters
RASCHIQ RINQ F I L L E R
1 2 3 4 5 6 7 8 9
6.00 4.38 3.64 4.38 3.73 3.80 4.01 3.89 6.01
1.10 0.78 0.67 0.78 1.42 1.67 0.92 0.52 1.09
5.38 5.95 5.95 5.96 6.53 6.81 5.66 5.25 3.38
0.221 0.242 0.243 0.244 0.266 0.276 0.226 0.212 0.1355
0.04 0.09 0.12 0.09 0.034 0.029 0.110 0.145 0.141
10 11 12 13 14 15 16 17 18 19 20
4.97 5.00 4.61 4.61 4.12 4.76 4.76 3.55 5.55 4.21 4.21
0.94 0.90 0.81 0.65 0.64 0.71 0.64 0.47 0.70 0.50 0.46
5.36 5.36 5.12 4.12 5.36 5.86 5.01 3.62 4.67 4.69 4.61
0.218 0.218 0.204 0.1685 0.218 0.239 0.204 0.1495 0.187 0.188 0.185
0.029 0.053 0.058 0.035 0.131 0.151 0.164 0.131 0.183 0.204 0.220
21 22 23 24 25 26 27 28 29 30 31 32
4.17 4.17 4.17 3.01 5.22 4.17 3.63 4.17 4.17 3.66 3.95 4.17
0.79 0.69 0.63 0.43 0.72 0.54 0.45 0.50 0.47 0.40 0.68 0.43
3.16 3.21 3.37 4.32 4.33 3.81 4.51 3.96 3.01 4.96 4.12 3.55
0.130 0.132 0.1385 0.178 0.175 0.155 0.1835 0.1614 0.1215 0.202 0.1664 0.144
0.019 0.059 0.084 0.130 0.136 0.139 0.182 0.167 0.137 0.234 0.066 0.185
24.0 23.5 26.4 27.0 26.0 27.0 27.0 24.3 30.0
29.0 28.7 30.0 28.7 33.5 33.0 29.5 28.3 29.1
0.608 1.249 1.669 1.240 0.430 0.354 1.638 2.30 3.50
2.917 2.917 2.917 3.025 3.025 3.025 2.917 3.025 3.025
1.765 1.765 1.765 1.830 1.830 1.830 1.765 1.830 1.830
1.760 1.754 1.750 1.819 1.826 1.826 1.751 1.811 1.812
5.70 5.82 5.67 5.83 5.70 5.71 4.68 5.93 5.83
28.1 27.3 33.8 25.2 21.6 26.1 26.2 23.1 32.4 31.7 31.0
0.448 0.805 0.970 1.70 2.02 2.12 2.70 2.95 3.29 3.63 4.00
4.935 4.775 4.775 4.935 3.205 3.205 4.775 4.935 3.205 3.205 4.935
2.065 1.975 1.975 2.045 1.325 1.325 1.975 2.045 1.325 1.325 2.045
2.041 1.968 1.968 2.034 1.308 1.306 1.954 2.028 1.302 1.299 2.019
5.72 5.66 6.84 5.75 6.00 5.81 5.96 5.68 5.88 5.95 5.80
24.5 24.9 24.3 24.5 28.1 28.1 28.7 28.1 29.3 27.6 30.1 24.6
0.49 1.51 2.04 2.46 2.61 3.02 3.34 3.4s 3.79 3.90 1.34 4.32
6.271 6.271 6.271 5.325 5.325 6.271 5.325 6.271 6.271 5.325 5.325 6.271
3.125 3.125 3.125 2,415 2.416 3.125 2.415 3.125 3.125 2.415 2.415 3.125
3,123 3.117 3.114 2.398 2.398 3.107 2.392 3.104 3.108 2.385 2.407 3.101
6.04 6.16 6.14 5.67 6.26 6.18 5.98 5.73 6.91 5.78 5.69 6.80
C O K l FILLER
0.0639 0.199 0.282 0.437 0.457 0.468 0.613 0.562 0.461 0.788 0.222 0.622
760.5 760.0 760.0 760.0 757.3 761.0 761.7 760.3 758.1 757.9 760.7 760.1
cients using the equation of Bennetch and Simmons (1). These data consisted of runs on various types of filler as given in Tables I11 and IV; the resulting coefficients have been plotted in Figure 4.
23.4 23.0 23.7 23.5 27.5 27.1 27.3 27.0 28.7 26.4 29.1 23.0
TABLIIV. TABLB
I11
IV
ii: 3
500
io00
1550
2000
2500
3000
SS0iI
4000
4500
SPECIFICATIONS
TEST 11-18 inclwive 19-21 inclusive 1, 2, 3 4, 9, 10 5, 6, 7, 8 22, 23, 24, 26, 29, 30, 33 25, 27, 28, 31, 32, 34, 35
1, 2, 3, 4, 5, 6, 10, 13, 11, 12, 14, 15, 21. 22, 24, 25,
FILLED DIMENSIONS Cm. 9 . 1 X 86.0
FILLERG
7 8, 9 17, 20 16 18, 19 23, 26, 28, 29, 32 27, 30, 31
Glass spheres Glass spheres 0.5-inch coke 0.75-inch coke
7.1 7.1 7.1 7.1 7.25 7.25
X 52.6 X 81.2 X 79.1 X 89.8
7.1 7.1 7.25 7.25 7.1 9.1 9.1
X
73.5
X X
80.8 95.2 81.8
Raschig rings Raschig rings Glass spheres Glass sDheres
Filler: Raschig rings, glass, 10 mm. length; 3 mm. 6 mm. outside diameter. glass spheres 1.85 om. average inch coke, 76 per cent through 0.75 inc’h (1.9 om.) on 0.5 0.5-inch coke, 81 per cent through 0.5 inch (1.27 om.) on om.).
X 76.8 X 78.8
X 75.8 X 119.4 X 115.5 X
inside diameter; diameter. 0.75inch J1.2? cm.); 0.25 inch (0.635
MOL PLoiy RATIO
LITERATURE CITED
FIGURE 4. ABSORPTION COEFFICIENTS
(1) Bennetch and Simmone, IND.ENQ.CHBM.,24, 301 (1932). (2) Cantelo, Simmons, Giles, and Brill, I b i d . , 19, 989 (1927). (3) Simmons and Long, I b i d . , 22, 718 (1930).
The description of the absorption towers and the methods of operation have been given in detail in previous articles (1-3). Table V shows the specifications of the tower packing used in each test of Tables I11 and IV, and the actual dimensions of the effective volume of packing in the tower.
RECEIVEDAugust 26, 1933.
CONCLUSION 1. For a given extractor the free volume is an inverse function of the extractor rate, this function being independent of the type of filler, tower size, or gas velocity. 2. This free volume variation is dependent upon the physical properties of a particular extractor. 3. The use of a constant free volume under all operating conditions is shown to be impossible in calculations involving design and operation of absorption systems. 4. The use of an operating free volume in the Bennetch and Simmons equation gives absorption coefficients which vary linearly with extractor rate.
CORRECTION.In the article on “Physical Factors Governing Cracking Operations” by B r o w n , Lewis, and Weber, in the March, 1934, issue, the drawing reproduced on page 327 as Figure 4 was published by mistake. I n s t e a d the gra h shown hereand taken from an article bv Watson
ACKNOWLEDGMENT This investigation was carried out under the Henry Marison Byllesby Memorial Research Fellowship in Engineering.
wit1
I
I L
I I
.
I
5
1
I
rm
FIGURE 4. HEATCONTENT CORRECTION FOR CHANGING PRESSURE OF HYDROCARBON VAPORS AH PR
TR M T
--
heat content a t atmospheric pressure minus heat content a t pressure P, B. t. u. per Ib. reduced pressure reduced temperature molecular weight absolute temperature, O Rankine
