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giving rise to the formation of free layers of discontinuity and eddies. If any accelerating or retarding pressure differences exist in the outer fluid which adjoins the boundary layer, these differences in pressure affect the fluid in the boundary layer also. Hence in a double-liquid system the drag of the core on the wall liquid can be expected to have an effect on the motion prevailing in the wall liquid. The present investigation shows that the point a t which turbulence sets up in one fluid is apparently also dependent upon the physical properties and motion of the other fluid in contact with it, resulting in the development of turbulence a t a lower value of the Reynolds number than for flow in full circular or annular pipes.
6
VOL. 29, NO. 3
Literature Cited (1) GIaaasen, Centr. Zuckerind., 26, 497 (1gl8).
(2) Cooper, Drew, and McAdams, IND.EXG. CSEM.,26,428 (1934). (3) Ewald, Poschl, and Prandtl, “Physics of Solids and Fluids,” p. 283 (1930). (4) Fallah, Hunter, and Nash, J. Soc. Chem. Ind., 53, 369T (1934). physik, 32,777 (1910), ( 5 ) Hopf, (6) Kirkbride, Trans. Am. Inst. C h e m . Engrs., 30, 170-93 (1933-34). (7) Prandtl, Phwik. z., 11, 1072 (1910). Reynoldsi Oshorne? Trans. (London)*1883. (9) Schoklitsch, A k a d . Wiss. Wien, Math.-naturw. Klasse, 129,IIA, 895 (1920). (io) Stanton, Proc. Roy. SOC.(London), A85, 366 (1911); Stanton, Marshall, and Bryant, Ibid., A97,413(1920).
.
RECEIVED October 19, 1936.
Desorption of Carbon Dioxide from Water in a Packed Tower T. K. SHERWOOD, F. C. DRAEMEL, AND N. E. RUCKMAN Massachusetts Institute of Technology, Cambridge, Mass.
A
LTHOUGH the theoretical basis for a general correla-
tion of data on gas absorption has been laid by Lewis and Whitman (e), little progress has been made towards the collection of sufficient basic data to enable general prediction of the performance of various types of absorption towers. Individual gas and liquid film resistances are additive, and the reciprocal of the sum is the over-all coefficient of absorption or mass transfer. After the manner of treating heat transfer data, it should be possible to obtain separate correlations of gas and liquid film resistances and to combine estimated values of each with appropriate solubility data in predicting the over-all coefficient. This addition employs one of the two equations (IO): 1 1 H Ka=G+=
-1 = - + -1
Koa
koa
(1)
1 HkLa
Before this procedure can be put on a sound basis, it will be necessary to have thoroughly tested correlations indicating
FIGURE 1. DIAGRAM OF APPARATUS
.
Data are reported on the desorption of carbon dioxide from water by air in a tower packed with 1-inch carbon Raschig rings. Gas rate was found to have no effect on KLa over the range of 57 to 314 pounds per hour per square foot. The effect of water rate is indicated by the empirical relation, KLa = 0.021 Lo.’*. L was varied from 770 to 9120. Slight variations in water temperature were found to have a marked effect on RLa. The estimation of
those factors affectingkLa and kGa,as well as adequate data on both a highly soluble and a relatively insoluble gas in various packings. Gilliland and Sherwood (6)have presented a correlation of gas film resistances in wetted-wall towers, showing kG to be proportional to the 0.56 power of the diffusivity, D. The same relation between ka and D presumably applies in packed towers but has not been thoroughly tested. No general correlation of kL as a function of the nature of the solute has been presented, although the problem is now being studied in these laboratories. Considerable data on the absorption and desorption of ammonia by water are available, and serve as a valuable basis for the prediction of kGa. I n many cases, however, the packing size or the ratio of tower diameter to packing size was too small to make the data of great value for design purposes. Data on absorption with liquid &n controlling are particularly scarce. Considerable data on the absorption of sulfur dioxide by water are available (Z), but no good method of analyzing the data to determine the film coefficients kLaand kola has been developed.
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283
The present paper attempts to fill one of the gaps in the missing data by reporting experimental results on the desorption of carbon dioxide from water in a tower packed with one-inch carbon Raschig rings. It was shown previously (7) that the coefficient k,a for ammonia and water is the same for either absorption or desorption, and it may be assumed that the same rule applies to kLa for the carbon dioxide- water system.
Apparatus The principal apparatus consisted of a packed absorption tower and a packed stripper fitted with necessary auxiliaries so that carbon dioxide might be absorbed in water in the absorber and continuously stripped of carbon dioxide by a current of air in the stripper. In Figure 1, A represents the absorber, which consisted of an 18-inch i. d. galvanized iron tower packed for 51 inches of its height with 3-inch spiral tile. Pure carbon dioxide from a commercial cylinder was fed continuously through an electrically heated valve to the bottom of the absorber at such a rate that a slight positive pressure was maintained within this apparatus. The packing rested on a heavy metal grid through which the solution drained to a reservoir below, and thence to a head box, E. The stripper, B , consisted of a 7-foot tower 10 inches in diameter constructed of 22-gage galvanized iron cemented tight and painted inside. This was packed for 54-56 inches of its height with 1-inch carbon Raschig rings.l The solution fed to the stripper was distributed over the packing by means of a distributing device designed to minimize any spray effect. Thirtytwo copper tubes were soldered into holes in a heavy brass pipe through which the solution entered the top of the stripper. These were bent down and cut off a t the same horizontal plane just above the top of the packing. The ends of these tubes were
over-all absorption resistances for design purposes by the addition of individual film resistances is impracticable at present because of the lack of basic data on typical packing materials. The data and correlations needed to put absorption tower design on a satisfactory basis are discussed. It is suggested that KLa or K,a may go through a maximum as packing size is increased from a very small to a large size, at any given liquor rate. adjusted so that the same quantity of solution issued through each, and bent into each position so that each supplied solution to approximately the same fraction of the total cross section of the stripper. The solution leaving the stripper collected in a reservoir, G, from which it was pumped continuously to the spray head at the top of absorber A . A small amount of fresh water was fed continuously into this transfer line to make up for leakage from the system. Centrifugal pumps were used to deliver the solution from head box E to the top of the stripper, and from reservoir G to the top of the absorber. A 50-gallon storage drum, C, D, was placed in each line to smooth out minor fluctuations in the carbon dioxide concentrations of the solutions pumped. The rate of flow of solution tsothe stripper was measured by means of a sharp-edged orifice calibrated with water by means of weighing tanks. Air was supplied to the stripper by the centrifugal fan, F, entering above the level of solution in reservoir G through a conical distributor head. The gas leaving the stripper was metered after passing through a horizontal straight section of 3-inch duct, 20 feet long. A 0.6875-inch sharp-edged orifice was used, and, since no means of calibration were available, the orifice coefficients of Spitzglass (9) were employed in the calculations. 1 One inch 0. d.. 0.75 inch i. d., 1 inch long; 1325 rings per cubic foot; 57 square feet per cubic foot of dry packing; 74 per cent free space (manufacturer’s data).
FIGURE2. GAS ANALYSIS APPARATUS In making a run, the two liquid pumps were started simultaneously. That supplying the stripper was adjusted t o give the desired flow rate to the column, and the other then adjusted to maintain a constant level in reservoir G . The pumps were regulated by means of valves in short by-passes. The blower was then started and its speed adjusted to give the desired air flow. Carbon dioxide from the cylinder was supplied to the absorber at such a rate that a small amount was purged continuously at the to . After approximately a half-hour, conditions reached a steaty state, as indicated by the constancy of the analysis of the gas leaving the stripper. The test was then continued for at least another half-hour, and observations were made of the gas and liquid flowmeter manometers and of the temperatures of gas and liquid entering and leaving the stripper. A small amount of the gas leaving the stripper was withdrawn continuously during the run, the sampling point being located about a foot above the top of the stripper in the outlet gas duct. Since the top 18 inches of the stripper were not packed and formed a natural entrainment eliminator, there was little chance of solution being withdrawn with the gas sample. The air entering the stripper was sampled occasionally to be analyzed for carbon dioxide. Liquid samples were withdrawn from reservoir G and from the liquid line feeding the top of the stripper. The small sampling lines were kept running continuously to ensure fresh samples, and liquid samples were taken every 10 minutes during the run.
Methods of Analysis Since the carbon dioxide-air mixtures to be analyzed were very dilute, a special gas analysis apparatus was constructed to give high accuracy with little difficulty in manipulation. This consisted of a modified Orsat apparatus (Figure 2). The volume of the calibrated measuring buret was 98.39 cc., 10 cc. of which were contained in a tube about 1.0 meter long and graduated every 0.01 cc. (graduations about 1mm. apart). Connected to the gas system by a three-way stopcock was a compensating bulb similar in size and shape to the measuring buret and immersed in the same water bath. Buret readings were made after balancing the water levels in the small-bore manometer connecting the compensating bulb to the system. Since the pressures in the two bulbs were made equal and the volume of gas in the compensating bulb could not change, the ~7olumeof gas in the buret could not be influenced by temperature changes between readings made before and after carbon dioxide absorption. With this arrangement it was possible to analyze dilute gas with a n absolute error of less than 0.01 per cent (for example, 1.13 * 0.01 per cent carbon dioxide). The carbon dioxide was absorbed in caustic in an absorption pipet as in an ordinary Orsat apparatus. The confining liquid in the buret was mercury, kept covered with 0.10 cc. of water. The time required for each analysis was from 10 to 15 minutes.
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INDUSTRIAL AND ENGINEERING CHEMISTRY
284
TABLEI. DATAAND CALCULATIONS _R_ _I _I
0 10 11 15 16 17 18 19 20 21 22 23
~
Liquor Temp. Inlet Outlet
F. 75.0 74.6 75.0 71.5 69.0 70.8 72.8 70.9 74.0 78.0 74.7 74.7 75.4 76.7 76.5 77.3 79.0
O
F.
76.0 73.9 74.0 70.5 66.0 70.2 72.5 70.4 73.2 77.0 74.2 73.8 75.1 76.2 76.0 77.5 78.0
COZin Outlet Outlet Gas Gas. Temn. - Drv- Basi.' O
F.
76.5 74.7 75.0 71.5 69.0 70.8 72.7 70.5 73.9 78.0 75.4 74.6 75.6 77.2 77.0 78.0 78.8
% 1.44 1.42 1.19 0.68 0.43 2.08 2.84 2.64 0,555 1.81 3.60 0.92 1.23 3.60 2.74 3.05 0.685
Liquor Rate
Outlet Gas Rate
Lb./(hr.) ( S q . ft.) 3160 2810 2230 1.510 770 2820 3620 3220 1500 1450 2680 2700 3410 9120 6460 7600 2700
Lb./(hr.) (Ea.
ft.)
154 154 153 157 155 92.3 92.4 92.4 206 56.5 56.5 204 205 153 154 157 313
I n taking the liquid samples, the measuring pipet was connected to the sampling line and flushed for a short while with the liquid. It was then quickly removed, allowed to run aomn to the mark, and emptied into a measured volume of standard sodium carbonate solution. The flask containing the sample was kept stoppered until subsequently analyzed. This was done by adding an excess of standard hydrochloric acid and back-titrating with standard sodium carbonate to the carbonate-bicarbonate end point, using phenolphthalein as an indicator. The end point was indistinct because of the dilution and because of the presence of small traces of iron. It was found that titrations to the first faintly perceptible change in color could be reproduced, with practice, to 0.1 cc., and this change was taken as the end point in all titrations. The same method was employed in standardizing the sodium carbonate solution, and in the analysis of solutions for the determination of the carbon dioxide-water equilibrium data.
Equilibrium Data
Lb.
Lb.
0.1111
0.0083 0.0149 0.0123 0.0098 0.0112 0.0131 0.0134 0.0130 0.0057 0.0090 0.0082 0.0084 0.0084 0.0118 0.0104 0.0117 0.0093
0.1269 0.1224 0.1178 0.1240 0.1187 0.1224 0.1233 0,1191 0.1085 0,1212 0.1173 0,1202 0.0942 0.1078 0.1075 0.1137
Equivalent Conon. Corresponding to Outlet Gas
COz Transferred From From gas liquor data data
Lb. COa/lOO lb. aoln. 0,00289 0.00290 0.00239 0.00144 0.00098 0.00453 0.00596 0.00574 0.00114 0,00340 0.00717 0.00188 0.00250 0.00706 0.00536 0.00594 0.00129
3.22 3.12 2.58 1,50 0.882 2.77 3.78 3.51 1.55 1.46 2 93 2.66 3.58 7.93 6.08 6.92 2.94
KLa Lb. ?nolea/(hr.) (cu. ft.)(Zb.
Lb./(hr.)(sq. ft.) mole/cu. ft.) 3.25 29.0 3.15 21.1 2.46 18.5 1.63 12.6 0.865 6.5 2.98 21.4 3.95 29.3 3.55 26.8 1.70 15.9 1.44 13.8 3.03 26.8 2.96 24.8 3.81 32.3 7.51 74.0 6.39 55.9 7.28 61.6 2.82 25.1
the particular water used, the results are not given in detail.
Calculations The partial pressure of carbon dioxide in the gas leaving was calculated from the gas analyses, assuming the gas to be saturated with water a t the temperature of the solution fed to the stripper. The carbon dioxide picked up by the gas was calculated from the carbon dioxide content of inlet and outlet gas and the measured flow rate of the gas leaving. This value was compared with the corresponding quantity calculated from the liquid feed rate and the analyses of the
-e
100 80
. 5
U
60 40
20
Because ordinary city water was used in the present work, it seemed inadvisable to use the values reported in the literature for the solubility of carbon dioxide in water. Accordingly, solubility data were obtained over the range of carbon dioxide pressures from 1 to 760 mm. of mercury. This was done by bringing boiled samples of the water from the system into contact with prepared mixtures of carbon dioxide and air, and analyaing the solution after a thorough shaking of the container. These tests were run a t room temperature, and the temperatures of the water were observed though not controlled. The measured solubility was corrected to 20" C. by muItiplying by the ratio of solubilities of carbon dioxide in distilled water a t the two temperatures, using the values of the International Critical Tables for distilled water. This method of temperature correction was also employed in the calculation of the equilibrium values for computation of the experimental results on desorption. The solubility curve obtained paralleled that for pure water over the range of carbon dioxide pressures from 40 to 760 mm. of mercury. The partial pressure of carbon dioxide was some 14-18 mm. of mercury less over this range than for the same carbon dioxide concentrations in pure water. In the low range from 0-40 mm. of mercury, the results could be represented by the equation (for 20" C.) pcoz = 4.4c
COa/100 Lb. S o h . Inlet Outlet
10 0 6
41 4M)
I
I IIIII 600
1000
L
-
I I I 1 IIII
2000 4000 0000 10000 LE /[HR.)(SQ. FT.)
I
20000
FIGURE 3
solution entering and leaving. This comparison was poor in six of the twenty-three runs, and these runs were discarded. The material balances checked within 10 per cent for the seventeen runs reported. The equilibrium liquor concentrations corresponding to the gas entering and leaving were obtained from the equilibrium data, and the driving forces a t the top and bottom of the stripper were calculated. The logarithmic mean of these two values was used to obtain values of the absorption coefficient, KLa, which is reported in English units as pound moles per (hour) (cubic foot) (pound mole per cubic foot of solution). I n calculating these values, the carbon dioxide transferred was taken as the arithmetic mean of the two values obtained from gas and liquor data. KLa in these units is numerically the same as pounds per (hour) (cubic foot) (pound per cubic foot).
(3)
This equation holds over the range involved in the calculations of the experimental desorption data. Because the equilibrium data were doubtless peculiar to
Results The results are given in Table I, which gives the basic data and the calculated values of KLu. The liquor rate wa8
MARCH, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
varied from 770 to 9120 pounds per (hour) (square foot), and the gas rate (outlet gas) from 57 to 313 pounds per (hour) (square foot). The inlet liquor temperature was varied from 69” to 79” F. The values of KLu (plotted against liquor rate in Figure 3) varied from 6.5 to 74.0. The importance of obtaining special equilibrium data for the water used was not as great as was first thought when the work was undertaken, since the equilibrium concentration corresponding to the gas analysis was never more than 8 per cent of the actual liquor concentration. The driving force a t the bottom was usually about 10 per cent of that at the top of the stripper. As indicated by Figure 3, the results are well correlated in terms of liquor rate alone. No appreciable trend of KLu with gas velocity is evidenced although there is a definite effect of liquor temperature indicated. The points corresponding to the high liquid feed temperatures all fall above the line, and the points corresponding to the low feed temperatures all fall below the line shown. The lack of any effect of gas rate and the marked effect of slight temperature changes point strongly to the conclusion that. the liquid film is the controlling resistance to interphase diffusion, and that HkL is small compared to koa. The equation of the line shown is KLa = 0.021 Lo.=
(4)
which applies a t 75” F. over the range of liquor rates, L, from 800 to 9000 pounds per (hour) (square foot). The temperature was not varied sufficiently to indicate the quantitative effect of this variable, although it is apparent that its effect is quite marked. Equation 4 is suggested for use in estimating kLa for similar packing, not only ,for carbon dioxide but for other solutes. The use Of Equation to combine these data with the of Kowalke, Hougen, and Watson (6) for kGa makes possible the estimation of KLa for sulfur dioxide absorption in 3-inch spiral tile which check the experimental results of Adams within about 20 per cent. The present results contradict the conclusions of Drane (S), who absorbed carbon dioxide in water in a tower packed with 4-inch “propeller” units. Drane reports a large effect of gas velocity and no effect of water rate. This discrepancy is difficult to explain, particularly as Drane does not report his experimental data. The data of Cantelo, Simmons, Giles, and Brill ( 2 ) on absorption of carbon dioxide in a small toTver packed with 0.4 x 0.25 inch hollow glass cylinders fall considerably below the present data, as indicated by line AB, Figure 3. At L=lO,OOO, KLa is 27, and the line has a s l o p e of a b o u t 0.6. The scattered data of Simmons a,nd Osborn (8) on absorption of carbon dioxide in a tower packed with 0.73-inch glass spheres are represented by line CD. It would appear from these three sets of experimental data that a t hiffh liquor rates KLa increases with increase in packing size. I n the discussion of absorption coefficients, two fallacies
285
are prevalent which are worth mentioning. The first is that gas rate can have no effect if the liquid film offers the controlling resistance. Actually, there is reason to expect that variations in gas rate in some types of packings will affect the interphase surface, a, and so cause variations in kLa or KLu. The existence of such an effect in the absorption of sulfur dioxide in 3-inch spiral is reported by Adams (1). The lack of any effect of gas velocity indicates s€rongly that the liquid film is controlling, but the existence of a large effect of gas velocity in a packed tower is no proof that the gas film is controlling. The other fallacy lies in the association of the variable, a, with the surface per cubic foot of dry packing. That the two quantities are neither equal nor proportional should be evident from a consideration of the operation of a packing over which liquid is circulating. At the usual liquor rates it seems probable that the coefficient expressed on a volume basis may go through a maximum as the packing is varied from a very small to a very large size. Investigations of the location of such optimum sizes for various liquor rates should prove interesting.
Nomenclature a = active interphase surface, sq. ft./cu. ft. of packing = COZ concentration in solution, grams/100 grams water,
C
or lb./100 lb. water D = diffusion coefficient of solute gas through carrier gas H = Henry’s law constant, lb. moles/(cu. ft.) (atm.) k~ = gas film coefficient, lb. moles/(hr.) (sq. ft.) (atm.) koa = gas film coefficient, lb. moles/(hr.) (cu. ft.) (atm.) Koa = over-al~coefficient, Ib. moles/(hr.) (cU. ft.) (atm.) k~ = liquid film coefficient, lb. moles/(hr.) (sq. ft.) (lb. mole/ cu. ft.) = liquid film coefficient, 1b. moles/(hr.) (cu. ft.1 (1b. mole/cu. ft.) KLa = over-all coefficient,lb. moles/(hr.) (cu. ft.) (lb. mole/cu. ft.) L = liquor flow over packing, lb./(hr.) (sq. ft. total cross section) p c o 2 = partial pressure of COZ over an aqueous solution, atm.
Literature Cited (1) Adams, F. W., Trans. Am. Inst. Chem. Engrs., 28, 162 (1932); IND.ENQ.CHEM.,25, 424 (1933). (2) Cantelo, R . c., Simmons, C . W., Giles, E . M., and Brill, F. A., IND. E m . CHEM.,19, 989 (1927). (3) Drane, H. S., J. SOC.Chem. Ind., 43, 329T (1924). (4) Gilliland, E . R.,and Sherwood, T. K., IND.ENQ. CHEM.,26, 516 (1934). (5) Kowalke, H ~ and watson, ~ ~ ~ ~ l~univ. l . ~ vis. , ~ ~ Sta., 68 (1925). (6) Lewis, W. K., and Whitman, W. G., IND.ENG.CHEM.,16, 1215 (1924). (7) Sherwood, T. K. and Kilgore, A. J., Ibid., 18, 744 (1926). (8) Simmons, C. W., and Osborn, H. B., Jr., Ibid., 26, 529 (1934). (9) Spitzglass, Trans. Am. SOC. Mech. Engrs., 44, 919 (1922). (10) Walker, W. H., Lewis, W. K., and McAdams, W. H., “Principles of Chemical Engineering,” 2nd ed., New York, McGraw-Hill Book Co. RECEIVED November 30, 1936.
ram Banka T i n
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