HE absorption of a
T
s o l u b l e gas from a mixture of insoluble gases and the extraction of a solute from a liquid are both processes involving the transfer of molecules from a region of high conc e n t r a t i o n to a gas-liquid or liquid-liquid i n t e r f a c e where the equilibrium conc e n t r a t i o n is low. Such processes are similar to that of heat transfer where a temperature gradient causes heat to flow from a region of high temperature to one of low temperature. Prandtl (7) postulated as follows for the mechanism of heat transfer in a solidfluid i n t e r f a c i a l system where the fluid is in turbulent flow: (a) The e x i s t e n c e of a liquid layer in laminar flow next to the solid boundary in which the liquid velocity is zero at the solid-liquid interface itself, with velocity and temperature gradients prevailing across this liquid layer ( b ) The existence of a turbulent liquid core with a mean t e m p e r a t u r e and velocity ( c ) The transference of heat through the turbulent core by c o n v e c t i o n and through the boundary film by conduction only
Conditions at a Liquid-Liquid Interface L. C. STRANG, T. G. HUNTER,
AND A. W. NASH University of Birmingham, England
I n a system consisting of a liquid flowing between a solid and a fluid boundary, the point where turbulence of the liquid sets in does not occur at a fixed value of the Reynolds number but is affected by the nature of the fluid forming the fluid boundary. The appearance of waves at the interface furnishes a visual indication of the change from streamline to turbulent flow. For a liquid in streamline flow between a solid and a liquid boundary, the ratio of the velocity at the liquid-liquid interface to the average velocity of the flowing liquid decreased with increasing viscosity of the liquid forming the liquid boundary.
by fluid-solid interfaces, as exemplified b y flow in circular pipes o r a n n u l a r s p a c e s , the change from viscous to turbulent flow occurs a t a critical value of about 2100 for the Reynolds is, the dinumber-that mensionless function pVD/p where p, V , p are the density, a v e r a g e v e locity, and viscosity of the fluid, and D is the diameter of the pipe. For flow in the annular space between two concentric pipes the diameter, D, is replaced by 4m where m is the hydraulic depth-namely, the ratio of the cross-sectional area of the stream to the wetted perimeter. In mass transfer the int e r f a c e i n q u e s t i o n is n o r m a l l y fluid-fluid, and actual knowledge about the interfacial conditions and the factors c o n t r o l l i n g t u r b u l e n c e is lacking, especially in the case of liquid-liquid interfaces.
Previous Investigations
A considerable amount of work h a s , h o w e v e r , been done on the s y s t e m bounded a t one side by a solid-liquid interface and a t the other by a liquidgas i n t e r f a c e . The flow of water along a n inclined plane or trough has been Investigated b y H o p f (6) and Schoklitsch (9), and the flow of water and oil on a flat glass plate by Chwang ( 2 ) . The flow in single-liquid, vertical wetted-wall systems was examined by Claassen (1) for water down the outside of a steel tube, by Warden (2) for water in both glass and brass tubes, and by Willey and Cooper (2) for dilute sulfuric acid inside glass tubes. These results were correlated by Cooper, Drew, and McAdams ( 2 ) . Fallah, Hunter, and Nash (4) re-correlated the same data together with new measurements of their own for water inside glass tubes. Kirkbride (6) has also examined the flow of water and hydrocarbon oils down the outside of a vertical tube. For all these cases measurements were taken of the film thickness, m, of the liquid which is flowing in contact with a solid and with air. Correlation of these results was obtained by plotting the friction factor,
Similarly, the mechanism of mass transfer from a fluid in turbulent flow will be by convection or eddv motion from a turbulent “fluid core to a boundary film and then by diffusion across a viscous or laminar film to the fluid interface. Similarly, if the sccond fluid, to which transference is taking place, is in turbulent flow, transfer will take place by diffusion across the viscous film of the second fluid and then by convection into the second turbulent core. Recent work has shown that the total resistance to mass transfer between two fluids in turbulent flow may be visualized thus in terms of siniple laminar films of such effective thicknesses as to offer the same resistance as that actually encountered a t the boundary in question. It is clear, therefore, that both heat transfer and mass transfer processes require some knowledge of the conditions a t the interface and the factors controlling turbulence. In heat transfer work the fluid-solid interface is almost entirely involved, and the conditions of flow existing a t such an interface have long been known. The velocity distribution for fluids flowing in a full circular pipe was determined experimentally by several investigators (IO); velocity distribution curves for turbulent flow were obtained which showed that eddy motion begins to decrease at a certain distance from the solid-liquid interface, and that very close to this interface flow is apparently laminar, the velocity decreasing to zero a t the solid surface. For a system bounded
f = 2 gmspp,2sin a/W2
against the Reynolds number, where pf,
278
p,
Re = 4mVpflp = d W / p V = density, viscosity, and av. velocity of film liquid W = mass rate of flow per unit width of surface a = angle of inclination to the horizontal
MARCH, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
Such correlation shows that, up to a value of Re of about 1500, the points lie on the line f = 24/Re, which is the theoretical equation for viscous flow derived on the assumption that the liquid velocity at the gas-liquid interface is a maximum, and that no traction is exerted by the gas on the liquid. At a Reynolds number of about 1500 to 2000, turbulence has set in as indicated by the departure of the points from the theoretical line representing viscous flow. The change from streamline to turbulent flow in this system at a Reynolds number of about 1500 to 2000 agrees well with the change of flow in circular pipes which occurs a t the same Reynolds number. Maximum liquid velocity occurs at the interface when the liquid is in streamline flow, and similar conditions must be expected to prevail when the liquid flow is turbulent, since no appreciable traction is exerted by the gas on the liquid. If this is true, then the existence of a laminar film on the liquid side of the liquid-gas interface becomes doubtful since the velocity is a maximum a t this interface. The only known work on conditions a t the liquid-liquid interface is that of Fallah, Hunter, and Nash (4) who have investigated a system bounded by a solid-liquid and a liquidliquid interface obtained in an apparatus of the wetted-wall type with a water film flowing down the walls of a vertical tower and completely surrounding a stationary or slowly moving oil core. Most of the results obtained appeared to be in the turbulent range of flow and the conclusions drawn were as follows: (a) With viscous flow of the wall liquid the velocity u at the liquid-liqyid interface between the wall liquid and a stationary core is a maximum. ( b ) For the system employing a stationary or lowvelocity core of kerosene, the change from viscous to turbulent flow of the wall liquid occurred at a modified Reynolds number1 (Re’ = 4W (p, - pJ/p,p) of about 27, and at about 10 when a stationary core of medicinal paraffin mas employed. ( c ) A core, stationary with respect to the walls of the tube, is agitated by local currents set up by the traction of the wall liquid on the core liquid.
279 1
,
CONSTANT
LEVEL
t--
U It
LlqUlD WALL
WATlR
v
,, r,
10 DRAIN
FIGURE 1. DIAGRAM OF
THE
APPLRATUS
Experimental Procedure The apparatus and method of procedure were the same as those used by Fallah, Hunter, and Nash (4),and consisted in measuring the thickness of a layer of water on the wall, m, in a double-liquid wetted-wall tower with a stationary oil core. The apparatus is illustrated in Figure 1.
A vertical glass tower of average internal diameter (2.280 cm.) was fitted with inlet and exit liquid connections and with a scale attached to the outside. The inlet water flowed from an overThe magnitude of the Reynolds number a t which the head, constant-level tank through an inclined-gage glass flowliquid flow changed from streamline to turbulent appears meter to the top of the tower where it flowed over the upper from these results to be determined to some extent by the inner edge and produced a falling water film down the inside of the tower. A constant water level was maintained at the bottom nature of the liquid-liquid interface. The investigation of the tower just below the top of the inlet oil line. described in the following pages is an attempt to extend Before use, the tower was thoroughly cleaned by filling with these observations further and to determine, as far as posstrong caustic soda solution; after draining out the caustic solusible, the effect of different liquid-liquid interfaces on turtion, it was thoroughly washed with running water for about half an hour. A steady water rate bulence and interfacial conwas then set, and the exit water m ditions. -* valve adjusted so that the botI n a double-liquid wetted’! tom water level was maintained wall system the wall liquid just below the top of the inlet INLET oil line. The oil was then allowed may be in either viscous or WATCl to enter slowly until the height turbulent flow; the core liquid of the oil core was about 70 cm. may be stationary or, if flowThe appearance of the system at ing, i t may be co-current with this stage is that shown in Figure 2A. The height of the oil or countercurrent to the wall column was then measured on liquid and in either streamline the scale attached t o the side of or turbulent flow. I n the presthe tower. This measurement e n t i n v e s t i g a t i o n the simwas repeated at varying water rates, previously a d j u s t e d b y plest case was chosen-i. e., means of the flowmeter. The with the c o r e s t a t i o n a r y . highest possible water rate at Water was used as the wall which measurements could be EX,T liquid, and v a r i o u s l i a u i d s obtained was just below that at r a n g i n g from kerosene to a WATE which the core liquid tended to rupture, and the lowest water hiahlv viscous 1u b ri c a t i np: rate that at which the film liauid (A) - , o c ;-ere u s e d as the core FIGURE 2. APPEARANCE OF THE SYSTEM AT Two STAGES liquid. ~ ~ $ a ~ ~~ m ~~ ~/ t ~ A series of results was obtained for as many water rates as possible between these two limits. The 1 Strictly speaking, this is the produot of t w o dimensionless groups, the inlet and exit water were then shut off SO that the system settled For t h e flow of water Reynolds number 4 W / p and the ratio (p, - pc)/p,. down into the position shown in Figure 2B. Knowing the averagainst air this latter ratio is substantially unity. Y
280
lNDUSTRIAL AND ENGINEERING CHEMISTRY
VOL. 29, NO. 3
These results are shown in Table I and Figure 3 in which are also drawn the lines f = 24/Re’ (the theoretical line for viscous flow with maximum interfacial velocity) and f = 96/Re’ (the theoretical line for zero velocity a t the interface). Figure 3 shows that in all cases the lines representing viscous flow of the wall liquid using varying liquid cores are parallel to and in between the lines f = 24/Re’ a n d f = 06/Re’. The general t h e o r e t i c a l e q u a t i o n (3) representing viscous flow on the doubleliquid system employed is given by the equation:
- PJI’/~
m = [12wrW{1 - ~ / 2 V l / g p h f
(1)
where
PI, pf,
V
density, viscosity, av. velocity of fiIm liquid p o = density of core liquid u = interfacial velocity =
From the position of the lines in Figure 3 the value of u/V from this equation can be calculated as follows: Any one of the straight lines in Figure 3 can be represented by an equation of the form, j = C/Re’
(2)
where C has some value between 24 and 96. Replacing f and Re’ by their equivalents already given, Equation 2 becomes
FIGURE 3. DATAON SIXLIQUIDS age diameter, 2R, of the portion of the tower in use, the volume
of oil in the column was obtained from the height of this oil column, H . If His the height of the oil column when the water is not flowing, and h the height of t h e oil column when the water is flowing, then the film thickness, m, is:
m
-
R[1
-
Kerosene Tetralin Lubricating oil:
A B C D
Density of Film ,Liquid Minus Density of Density of Core Liquid, Core Liquid, Temp.
therefore
(4)
(H/h)”21
The nature of the core liquid was varied from kerosene to a very heavy lubricating oil. In all cases the water rate was varied over the greatest possible range so as to obtain, as far as possible, both viscous and turbulent flow. The density and viscosity of the core liquids were determined at the temperature at which they were used in the tower and are as follows:
Core Fluid
(3)
Pf
- PO
c.
PO Qram/cc.
19.4 17.3
0.7912 0.9733
0.2071 0.0255
19.2 24.0 16.5 15.9
0.8709 0.9089 0.9292 0.9390
0.1279 0.0884 0.0693 0.0696
Combining Equations 1 and 4: 1
Viscosity of Core Liquid, PO
Poiees 0,0108 0.0243 0.0825 1.198 12.50 43.00
Calculations In each case the water layer thickness, m, was calculated from the radius of the tower, R, and the radius of the core, T , for a given water rate, W (in grams per second per cm. of tower perimeter). From these values of m and JJ’ the friction factor .
f = 2 gmSp,2/W2 was calculated and plotted against the modified Reynolds number,
PJ/P/P
= C/96
(5)
The values of C for the various core liquids were easily obtained from Figure 3, and hence u/V was calculated giving the results shown in the following table:
Core Fluid
Air
Kerosene Tetralin Lubricating oil:
A R C
D
Re’ = 4 W(P/-
- u/2V
a
C
E
//Re‘
u/V
24
1.P
20
32
1.458 1.333
41 62 78 91
1.156 0.710 0.375 0.106
Ratio Viscosit bore Viscosity of Liquid/&cosity Core Liquid, of Film, PC
Poises 0.00019 0.011 0.024
0.083 1.20 12.60 43.00
PC/Pf
0.019 1.07 2.26 8.05 130 1140 3860
Theoretical value, neglecting drag caused by air.
This table shows that u/V decreases as pc/pf increases. As might be expected, the interfacial velocity, u, decreases with increasing viscosity of the core liquid, although it is never actually zero even with very viscous liquid cores. Since it has now been shown that the interface between the two liquids is moving, it follows that there must be a drag on the layers of core liquid adjacent to the interface, causing them to move in the direction of the film liquid. In order to keep the core as a whole stationary with respect to the walls of the tube, there must be a flow up the center of
MARCH, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
281
TABL ,EI. REBTJLTS OF EXPERIMENTS ON SEVERAL LIQUIDS W G./sec./ em.
m Cm.
x
102
0.126 0,1435 0.1675 0.173 0.184 0.198 0 212 0.230 0.245 0.256 0.270 0.286 0.306 0.3165 0.3355
2.7 2.8 2.9 3.0 3.1 3.1 3.2 3.4 3.3 3.5 3.5 3.6 4.0 3.9 4.1
0.065 0.0742 0.079 0.094 0.107 0.1182 0.121 0.1268 0.1352 0.1398 0.144 0.1512 0.154 0.1606 0.1702 0.1815
5.0 5.1 5.2 5.5 5.7 5.7 5.7 6.0 6.1 6.2 6.3 6.5 6.5 6.7 6.9 7.0
0.1038 0.1212 0.129 0.143 0.147 0.159 0.1595 0.173 0.177 0,188 0.191
3.5 3.7 3.7 3.9 3.9 4.1 4.1 4.3 4.3 4.4 4.4
f
W
Re’
Q./rec./ em. Kerosene 2.42 10.5 0.350 2.09 11.9 0.368 1.935 13.1 0.398 1.77 14.35 0.420 1.635 15.7 0,443 1.49 16.4 0.478 1.43 17.6 0.475 1.45 19.1 0.640 1.17 20.3 0.596 1.285 21.2 0.661 1.15 22.4 0.731 1 . 1 5 23.7 0.830 1.34 25.4 0,902 1.16 2 6 . 5 1,030 1.20 27.8 Tetralin 57.9 0.61 0.1955 47.0 0.70 0.207 44.1 0.75 0.221 36.8 0.89 0.247 1.01 0.261 31.6 1.12 0.284 25.9 24.8 1.14 0.300 26.4 1.20 0.315 24.2 1.28 0.327 24.0 1.325 0.341 1.365 0.360 23.25 1.43 0.384 23.6 22.7 1.46 0.409 22.9 1.52 0.430 22.0 1.615 0.451 1.72 20.4 Lubricating Oil A 7.81 5.21 0.196 6.85 6.10 0.204 6.48 0.212 6.00 5.65 7.18 0.24 5.37 7.49 0.27 5.30 7.99 0.315 5.30 8.00 0.342 5.20 8.68 0.376 4.50 8.89 0.415 4.81 9.44 0.461 4.52 9.60 0.485
m
f
Re’
Cm.
x
102
4.2 4.2 4.4 4.2 4.3 4.6 4.6 6.0 5.1 5.3 5.5 5.8 6.1 6.4
1.186 1.075 1.045 0.82 0.79 0,835 0,906 0.84 0.73 0.66 0.61 0.555 0.545 0.486
29.1 30.6 33.1 34.9 36.8 39.7 36.8 42.0 46.3 51.4 56.8 64.8 70.0 80.0
7.6 7.8 7.9 8.3 8.4 8.7 9.1 9.0 9.4 9.2 9.7 9.9 10.2 10.7 10.6
22.5 21.7 19.8 18.3 17.1 16.0 16.4 14.4 15.2 13.2 13.8 12.9 12.45 12.95 11.52
1.85 1.96 2.09 2.34 2.47 2.69 2.84 2.98 3.10 3.23 3.41 3.64 3.87 4.06 4.27
4.7 4.5 5.0 5.2 5.4 5.7 6.0 6.2 6.5 6.8 7.0
5.30 4.30 5.90 4.80 4.24 3.66 3.62 3.32 3.14 2.90 2.86
9.84 10.25 10.65 12.05 13.55 15.8 17.2 18.8 20.8 23.2 24.4
the core liquid to counteract the downward flow a t the interface. The direction of flow of the layers of core liquid next to the interface is the same as that of the wall liquid; this direction is reversed a t the center of the core. Between these layers a stationary region of core liquid presumably exists. It would appear, therefore, that on either side of a gas-liquid or liquid-liquid interface the direction of flow of the two fluids immediately adjacent to such interface is the same. The direction in which both these layers move would, of course, be determined by the direction of flow of one of the main streams in a countercurrent system. On increasing the water rate, the motion of the wall film changes from viscous to turbulent flow, as shown in Figure 3 by the breaking away of the points from the straight lines representing viscous flow. The point a t which turbulence starts does not appear to be a t any fixed value of either the Reynolds number or the modified Reynolds number as shown in the following table but seems to be affected by nature of the core liquid:
Core Fluid Air Kerosene Tetralin Lubricating oil: A B C D
Viscosity of Core Fluid Poises 0.00019 0.011 0.024 0.083 1.20 12.5 43.0
Critical R e
Critical Re‘
Critical m
1500-2000 111 54
1500-2000 23 1.4
5 . 0 X 10-2 3 . 7 X 10-2 6 . 4 X 10-2
69 192 157 86
9 18 12 5.5
4 . 4 x 10-2 7 . 2 X 10-2 8.8 X 10-2 8 . 0 x 10-2
Cm.
I n all cases the critical value of the Reynolds number is very much less than the value for the flow between
W
m
ff./sec./
Cm.
f
cm.
xi02
0.192 0.204 0.214 0.235 0.265 0.333 0.364 0.398 0.424
5.4 5.6 5.6 5.8 5.9 6.5 6.7 7.0 7.0
0.134 0.139 0.1515 0.1645 0.184 0.202 0.212 0.231 0.247 0.280 0.299 0.314 0.335 0.349
23.6 23.0 21.4 19.8 6.7 17.3 6 . 8 15.1 7 . 0 14.9 7.2 13.7 7.3 12.5 7.5 10.6 7 . 7 10.0 9.75 7.9 8.1 9 . 3 0 8.2 8.85
0.0816 0.094 0.109 0.125 0.144 0.165 0.187 0.190 0.204 0.217 0.233
5.6 5.9 6.2 6.5 6.7 7.0 7.4 7.3 7.5 7.7 8.0
8.35 8.25 7.60 6.90 5.71 4.85 4.46 4.25 3.76
6.0 6.1 6.3 6.5
51.5 45.4 39.0 34.5 28.4 24.8 22.8 21.1 19.9 19.0 ISi 6
Re’
W
Q./sec./ cm. Lubricating Oil B 7.40 0.452 7.86 0.484 8.25 0.610 9.06 0.698 10.25 0.780 0.920 12.85 14.05 1.065 15.40 1.26 16.35 1.50 Lubricating Oil C 3.38 0.373 3.61 0.389 3.83 0.397 4.16 0.414 4.65 0.431 5.10 0.45 5.36 0.468 5.84 0.475 6.24 0,484 7.07 0.619 7.55 0.731 7.94 0.884 8.46 0.985 8.81 Lubricating Oil D 1.74 0.270 2.01 0.296 2.33 0.326 2.67 0.349 3.08 0 373 3.53 0,400 4.00 0.417 4.06 0.438 4.36 0.466 4.64 0,481 4.98 0.494
f
Re‘
7.2 7.6 7.6 8.5 8.8 9.9 10.7 11.6 13.0
3.58 3.68 2.30 2.46 2.20 2.25 2.12 1.92 1.91
17.5 18.7 23.5 27.0 30.5 35.5 41.0 48.6 57.8
8.2 8.5 8.4 8.6 8.7 9.0 9.1 9.1 9.3 10.3 11.6 13.4 16.1
7.95 7.95 7.40 7.30 6.95 7.05 6.74 6.55 6.74 5.60 5.74 6.01 8.45
9.43 9.83 10.05 10.48 10.90 11.4 11.86 12.0 12.2 15.7 18.5 22.3 24.9
m Cm. xi02
8 . 4 15.9 8 . 9 15.9 9 . 5 15.8 9.9 15.6 10.4 15.3 10.9 1 5 . 9 11.4 16.7 12.4 19.5 12.8 18.9 14.0 23.1 15.6 30.4
5.76 6.32 6.96 7.45 7.97 8.54 8.90 9.35 10.00 10.30 10.58
liquid and air, and for the flow in full circular or annular pipes.
Effect of Turbulent Flow The change from viscous to turbulent flow in the system can be observed visually by the appearance of waves a t the interface between the two liquids; it is particularly pronounced in the case of a core liquid of high viscosity. With lubricating oil I) as the core liquid, very large, slowly moving waves were set up, resulting in a large increase in the average thickness of the wall liquid; with the less viscous kerosene, the waves were much smaller and more rapidly moving. In experiments with water or oils flowing down the outside of a vertical tube in contact with air, Kirkbride (6) observed the formation of ripples a t a certain velocity, producing a deviation from the viscous flow equations. The production of these ripples rendered it impossible to measure the average film thickness by the use of a micrometer. The formation of waves at a liquid-liquid interface has been observed by Reynolds (8) who examined the flow a t a water-carbon disulfide interface. On tilting a horizontal tube, half full of water and half full of carbon disulfide, the liquids flowed in opposite directions. When the inclination was small, there were no signs of eddies, but a t a certain definite inclination waves appeared a t the interface. These waves were nearly stationary and had all the appearance of wind waves. Reynolds concluded that there was a critical velocity in the case of opposite flow a t which direct motion became unstable, and that this critical velocity was many times smaller than the critical velocity in a tube of the same size when the motion was in one direction only. Ewald, Poschl, and Prandtl (3) state that the retarded boundary layers formed a t a surface have the property of
INDUSTRIAL AND ENGINEERING CHEMISTRY
282
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.
