INDUSTRIAL AND ENGINEERING CHEMISTRY
1112
= individual liquid film coefficient, Ib. moles/(hour')(cu. =
= = = =
= = * = =
Vol. 42, No. 0
(9) Gilliland, Ibid., 26, 681 (1934). (IO) Gilliland and Sherwood, Ibid., 26, 516 (1934). (11) Hutchings, Stuteman, and Koch, Chem. Eng. Propress, 45, 253
foot)(lb. mole/cu. foot) liquid rate, Ib. water/(hour)(sq. foot) logarithm, base e logarithm, base 10 molality of solute, Ib. moles/1000 Ib. solution solute partial pressure in air, atm. temperature, R. mole fraction of solute in water density, Ib./cu. foot viscosity, Ib./(hour)(foot) viscosity, centipoises
(1949). ENG.CHEM.,ANAL.ED.,6,459 (1934). (12) Iddles and Jackson, IND. (13) International Critical Tables, Vol. 5, New York, McGraw-Hill Book Go., 1929. (14) Kowaike, Hougen, and Watson, Univ. Vis. Eng. E@. Sta., 68 (June 1925). (15) Ma and Zuazaga, IND. ENG.CHEM.,ANAL.ED., 14, 280 (1942). (16) Molatad, McKinney, and Abbey, Trans. Am. Inst. C h . Engrs., 39, 605 (1943). (17) Othmer, Kollman, and White, IND. ENG.CHEM.,36, 965 (1944). (18) Othmer and Scheibel, Trano. Am. Inst. Chem. Enprs., 40, 611 (1944).
LITERATURE CITED
(1) Arnold, Sc.D. thesis, Massachusetts Institute of Technology,
),!j:;
1931. (2) Baller, Thomson, and MaoLennan, J. Chem. Soc., 1933, 674. (3) Brinsmade and Bliss, Trans. Am. Inst. Chem. Engrs., 39, 679 (1944). (4) Chalov, N. V., and Tsvetaeva, J. Applied Chem. (U.S.S.R.), 19,945 (1946). (6) Chilton and Colburn. IND. ENG.CHEM.,26,1183 (1934). (6) Dobson, J. Chem. Soc., 127,2871 (1925). (7) Dwyer and Dodge, IND. ENG.CEEM.,33,485 (1941). (8) Elgin and W e b , Ibid., 31, 435 (1939).
:kw$,F&: ~ ~ ~ ~ ~ . ~ ~~ ~ ~ ~f ~ ~ . ' ~ ~ ~ ) i
(21) Sherwood and
Holloway, Ibid., 36, 21, 39 (1940).
,E ::t B , l d ~ ~ , P " , p , ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ [ii; $ ,: ~ ~ ~ ~ ~ ~ ~ ~ f ; , 21923), ~ ~ 6 ( ~ ~ ~ ~ ) ) 2 3 (26) Wilke, Chem. Eng. Progress, 45, 218 (1949).
$!&f::zl:
R E C E I V ~November D 80,1949. Based on a diwertation pmented by R. W. Houeton in June 1950 to the faculty of the School of Engineering of Yale University, in candidaoy for the degree of doctor of engineering.
Effect of Diffusivity on Gas-Film Absorption Coefficients in Packed Towers ALAN E. S U R O S K Y '
AND
BARNETT F. DODGE
YALE UNIVERSITY. N E W HAVEN. CONN.
T h e molecular diffusivity in the gas phase is one of the variables commonly used in correlating the results of gas rbsorptlon experiments, but l i t t l e quantitative informa. t l o n on i t s effect has been available, especially In packed towers. The main objective of t h e present investigation wasto studytheeffect of diffusivity in a packed tower by as direct a method as possible. To eliminate the possibility of any liquid-phase resistance t o mass transfer, the method of vaporizing pure liquids i n t o an air stream was adopted. Three organic liquids and water were used, giving a 3.7-fold range of diffusivities. A special effort was expended in the design of gas and liquid distributors t o minimize end effects. Experiments were conducted a t Substantially atmospheric pressure and temperature in an &inch diameter tower packed w i t h 1-inch rings. Resist-
ance t o heat transfer in t h e liquid phase was assumed t o be negligible on the basis of previous work. Packed height was varied f r o m 4 t o 12 inches, liquor rate from 435 t o 5OOO pounds per hour per square foot, w i t h the bulk of t h e runs a t 1600, and the gas rate from 140 t o 500 pounds per hour per square foot. The main results of t h e Investigation may be summarized as follows: End effects were equlvalent t o 2.2 inches of packing. Gas-film coefficient koa was independent of liquor rate above a liquor rate of about 1OOO. koa varied as the 0.72 power of the gas-flow rate. koa varied as diffusivity t o the 0.15 power. The small effect of diffusivity in a packed tower indicates t h a t the main resistance is due t o eddy diffusion in t h e t u r b u l e n t core. This result is in close agreement w i t h t h e only other published data on the subject.
A
Similar equations have been proposed for packed towers, the one of Van Krevelen and Hoftijier (16)being aa follows:
SATISFACTORY correlation of gas film absorption coefficients in packed towers, comparable to that available for liquid film coefficients, has not yet been made. Some years ago, Gilliland and Sherwood (6) proposed the following correlation for their results on the evaporation of liquids into gas streams in a wetted-wall tower
;- c (4)" ($)"
(1)
where the values of the constants were C = 0.023, n = 0.83, and m = 0.44. From the relation between ka, D,and z,this equation may be modified to
D kad I
C'
i
r;)'
($)%
Preaent address, 126 Market St., Patereon, N. J .
(2)
kod D
c (")"'($)'" ad#
(3)
Chilton and Colburn (9)extended the Reynolds analogy between fluid friEtion and heat transfer to include mass transfer in diffusionalprocesses and arrived at an equation for the mass tramfer coefficient involving the group, &, to the o.67 power. PD When comparing the performance of a given absorption tower in which gas film is controlling, with different gas system, the diffusivity is assumed to be the main correlating variable. With B reliable correlation for the effdct of diffusivity and data on the diffusivities of various solute gases in a variety of inert or carrier
June 1950
INDUSTRIAL A N D ENGINEERING CHEMISTRY
A- LIQUOR PUMP
8- LIQUOR ORIFICE METER
--
C -EXIT GAS SAMPLING LINE D STATIC PRESSURE MANOMETER E PACKED VAPORIZATION TOWER F- GAS PLATE BURNER G DEW POINT CELL H MAIN LIQUOR RESERVOIR J CALIBRATED RESERVOIR K GAS HEATER HOOD
--
-
-
L GAS ORIFICE METER M- WATER TRAP 8 COLLECTOR N HEAT EXCHANGER P-DRYING TOWER R- 50 FT. OF $2 IN. CONNECTING PIPE s SURGE a COOLING TANK U -SAFETY VALVE W-OIL flLTER X -HIGH PRESSURE GAS BLOWER Y -GAS EXHAUST LINE 2 -LIQUID PRECOOLING SYSTEM
CA CWOR
COMPRESSED AIR COOLING WATER DRAIN LINES 71-7 THERMOMETER WELLS VI -z ATMOSPHERIC VENT LINES DQ I---VALVES 83o.toSTOPCOCKS
-
Figure 1.
1113
--
Flow Sheet of Apparatus
gases, the engineer should be in a position to predict the perform-
ance of a tower for one gas system from the known performance with another system. In this discussion the term “diffusivity” is used to mean the molecular diffusivity as differentiated from “eddy diffusivity.” The actual transfer process involves molecular and eddy diffusion processes operating in series. In the usual treatment, i t is assumed that the entire transfer resistance is in a boundary layer in laminar flow, across which molecular diffusion occurs. The effect of flow rates, type of contact apparatus, and other variables on the relative resistance to transfer by these two processes is not known, so that few predictions can be made, but it is probably reasonable to conclude that the effect of molecular diffusivity on the absorption coefficient cannot be adequately represented for all cases by an equation such as Equation 2 with a single value of exponent m. Up to the present time there have been very few data published which were obtained for the specific purpose of investigating the effect of diffusivity on absorption in a packed tower. The equation of Van Krevelen and Hoftijzer, which predicts that IC0 is proportional to Dn/s, was based on a wide variety of previously published data with so many other variables involved that the effect of D alone would be completely obscured. This is evident when one realizes that the value of C in their equation varied as much as 14-fold. Unpublished results of Mehta and Parekh ( 9 ) referred to by Sherwood and Holloway (ZS), which were obtained from an experimental investigation specifically designed to study the effect of diffuuivity in a packed tower, were correlated on the basis of DJ.17. Four different liquids were vaporized into an air stream in their experiments and the maximum variation of D was %fold. Scheibel and Othmer (IO),on the other hand, concluded from their investigation of the absorption of four different methyl.
ketones from air by water that the exponent on D should lie somewhere between 0.5 and 1.0. In their final correlating equationa they use the latter value. Their range of diffusivities was too small to establish a more definite value of the exponent, and furthermore in the case of two of the ketones the gas-film resistance was far from being controlling. If the total resistance to transfer is made up of the sum of the resistance of the film and the core, equations such as 1, 2, and 3 are not of the correct form to represent the effect of D. As pointed out by Gilliland ( 4 ) , the results of Gilliland and Sherwood (6) could also be correlated by the equation 1 = 903 +[ 9 1 m-1 ko
(4)
The relative resistances of the two diffusional processes are independent of Reynolds number according to this equation. In a packed tower it seems reasonable to expect that eddies would be suppressed and that the resistance of the turbulent core would be greater than in a wetted-wall tower. This would point to a smaller exponent on D if an equation of the type of Equation 2 were used. It may be concluded that the effect of diffusivity has not been satisfactorily established and that further experimental work ia desirable. The main objective of the work reported in this paper was to obtain additional data on the effect of diffusivity by as direct a method as possible and one in which there could be no question about all the resistance being in the gas film. To accomplish this, the method originally used by Gilliland and Sherwood-namely, the evaporation of pure liquids into flowing gas streams-was selected. The method has one serious disadvantage-the approach to saturation is so close in a packed column of only 1- to 2-foot length that the determination of the
1114
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 42, No. 6
The drying agent yrxisirted of 130 pounds of 4- to 14i n s h nctivnted alumina. I'liwc n~xtcr-cooline coils were w i t inwit.
Figure 2. Gsr Dlstrlbutor and Packing Support
driving ioree becomes very inticcurate. The obvious remedy is to shorten the packed COIUIIIII, h i t this increases the uneertnint) from stid eKocts. Caught it, thid dilcmma tlie authors' choice was to use very short packed columns (4 to 12 inches) and to take very speoial preesutions to ininirnize end eKects. There is also B problem involved iii obtaining much of a range of diiTwiuities. Sherwood and Gilliland (28) lirted the diffusivities of 18 suhstances in air a t 30" C. and 1 atmosphere and the total range W&F 3.6-fold. By varying also the enrrier or incrt g a , B variation io diffusivitiesof ahout 10-fold can be achieved. .4 still greater variation can he obtained by operating under pmss a , since D a l l p . In the work reported in this paper the suthors have ohosen to vary only tlie solute gas a t constant pressure, temperature, and inert gas. In a subsequent paper some rasulta with previure us the variable will be presented. The scope of the work reported may he outlined &J follows:
& distributor deuevihed helor.
The onokinz. conisiatine of I-inch carbon ltaechiu rinm. w w
tween the-distributors and wits accurate aithin 0.25 inch. The number of rinm in the tmvcr by this method u-as in excellent. agreement with the yacking dmsity tabulated hy Slierrvood (11).
1. Carrier gss. Air 2. Solute VBDO~S. Water. methanol. benzene. and ethvl nl"",.""" 3. Pressure. 1 atmosphere 4. Liquid temperature. 5' to 24' C. (not purposely varied) 5. Tower. &inch inside diameter packed with l i n c h oarbon
APPARATUS
A N D PROCEDURE
General Outline of Method. Air, dried hy alumina, WYM p w e d up through the vsporization tower counter to tho liquid end exhausted to the atmosphere. The liquid, on the other hsnd, wy&9oontinuously reeiroulated between the tower and a storege reservoir. Means were provided for heating the sir so that thc entoring water would be at tho wet-bulb temperature in some of the ruw, but the heater wus subsequently found to have insufficient cspwity for this purpose. I n all cases tho concentration of solute in the entering air wag negligible. Concentration in the leaving gases in the cave of water vapor was determined in two ways: (1) from the amountofliquidevaparatedduringtherunas determined by the drop in level in B calibrated reservoir and (2) by adsorption of the water vapor from B sample of gas on wtivatcd alumina, followed by wlume measurement of the gsij and weighing of the adsorbent tubes. Method I wus used in aubatantidly all runs, hut in the runs with water both methods wem used and the average agreement wus within 4%. Both B liquid and a gss distributor were used in order to introduce esch stream uniformly over the tower area and us dose to the packiog ss possible. Inlet and outlet temperature8 and flow r a h of both streams were meusured. Gus-flow rate was ohthined from B standard orifice and liquid flow rate from B Calibrated orifice.
Figure 3. Photograph of Setup
INDUSTRIAL A N D ENGINEERING CHEMISTRY
June 1950
111s
Table I. Experimental Data for Runs with Air and Water a t Constant Gas Rate
Run 1
5
Packed Hei ht, Incies 12 12 12 12 12 12 12 12 12 6 6 6
2 3 4 5 6 7 8 9 10 11 12 6 13 14 6 15 6 6 16 17 6 18 4 4 19 20 4 21 4 4 22 23 4 24 4 25 4 26 4 27 4 28 4 29 4 30 4 31 4 32 4 4 33 4 34 35 4 36 4 4 37 Corrected for
Inlet Gas Rate. Lb./ Hour/
Inlet Liquor Rate Lb./'
nour/
tl,
liquor sa. pas gas .s, out in out Foot Foot 20 16.9 20.5 201 1035 17.3 24.5 21.5 200 1800 20 16.9 22.5 202 2000 17.6 20 24 200 2040 17.1 20 24 199 2260 16.5 20 22 200 2360 16.9 21.5 23 200 3515 16.9 19.5 22 202 4040 16.6 20.5 22.5 202 5050 21 19.2 23 201 682 18.8 21.5 23 1067 203 22 18.8 23 202 1077 19.0 199 21.5 24.5 1525 19.4 21.5 24.5 2180 202 19.6 21.5 24.5 200 2640 19.1 201 20.5 23.5 3184 19.4 21 24 199 5148 22 19.5 23.5 200 435 21.8 24.5 27.5 199 580 22 19.7 24 200 725 21.9 199 25 27 870 22 19.7 25 200 1180 19.8 25 200 22 1360 19.2 199 21.5 26 1910 19.1 21 25 2000 199 198 21 18.8 24 3480 21.5 18.6 24 198 4820 17.6 20 22 1220 201 200 21 18.9 24 1740 199 21 18.6 24 2260 21.5 18.7 25 3410 199 200 23 20.8 40 1180 22 21.0 40 200 1525 20.7 24 41 201 1870 24 20.8 40 201 2260 21.1 41 23 3300 199 24 21.3 42 199 4780 end effect equivalent to 2.2 inches of packing.
in 18.6 18.9 18.4 19.1 18.8 18.4 18.6 18.9 17.9 20.0 19.8 20.0 20.0 20.2 20.4 20.2 20.5 22.4 23.7 22.8 23.8 21.5 21.7 20.5 20.5 20 7 20:'4 19.1 20.9 20.6 20.7 21.7 21.6 21.6 21.5 21.8 21.9
I n order to reduce end effects to a minimum, both fluids were introduced through distributors. The liquid distributor was a 25-point, manifold-type distributor. with the. liquid being dischar ed immediately above the packing to avoid splashing. The gas &tributor, which also formed the packing sup ore, is Fhown in Figure 2. It consisted of a 1.5-inch brass pipe fjody with six radial 0.75-inch brass distributor arms. Nineteen upright drilled brass nip les were silver-soldered into the distributor arms. A six-armex cover late, drilled to reduce disturbance to flow, served both to seafthe top nipple openings and to act as a base for a coarse wire-mesh paclung sup ort. The gas flowed into the distributor body, into the manifok arms, through the side ports of the nipples, and u between the arms or throu h the holes of the cover plate. No Piquid entered the completefy submerged dwtributor a t gas rates of 75 pounds per hour per square foot or reater based on the tower cross-sectional area. Both these &tributors operated very satisfactorily and reduced end effects to the equivalent of about 2 inches of packin A photograph of the setup is shown in hgure 3. Operating Procedures. The liquid to be vaporized was pumped from reservoirs H and J by pump A through tower E , and back to the reservoirs. Reservoir H was then isolated from the sysltem, and all flow of li uid was from J t h o u h the tower and back to J. The rate o f vaporization of liquid was determined by measuring the rate of fall of the liquid in the sight glass attached to the calibrated reservoir J. In the case of the vaporization of water, the rate was checked by gravimetric analysis of the exit gas. The gas stream flowed from blower X through the surge and cooling tank, S, through the oil filters, U,through the drying tower, P,through the heat exchanger, N , and into the bottom of the vaporization tower, E , where it was passed countercurrently to the liquid, and exhausted to the atmos here. The regeneration of the drying tower toot place as follows: Hot gases and excess air from the plate burner, F , were drawn through the hood, K , through the drying tower, P, through the water cooler, N through the water trap, M ,and through the long cooling line, k, and were exhausted to the atmosphere through the gas blower, X . The liquid flows were determined by a gravimetrically calibrated sharp-edged orifice in the case of variable liquor-rate runs, and by means of a Flowrator for constant liquor-rate runs. Gas flows were calculated from the readings of a sharp-edged orifice installed according to A.S.M.E. specifications, and checked a t lower flow rates by a dry-test gas meter.
reservoir 0.0205 0.0214 0.0207 0.0218 0.0207 0.0212
0.0206 0.0212 0.0204 0.0226 0.0190 0.0222 0.0209 0.0211 0.0201 0.0195 0.0189 0.0205 0.0200 0.02~15 0.0200 0.0216 0.0213 0,0206 0.0208 0.0203 0.0211 0.0213 0.0191 0.0181 0.0218 0.0215 0.0204 0.0204 0.0223 0.0213 0.0204 0.0176 0.0206 0.0195 0.0184 0.0182 0.0195 0.0202 0.0176 0.0201 0.0175 0.0159 0.0195 0.0172 0.0185 0.0189 0 I0200 0.0207 0.0199 0.0213 0.0196 0.0211 0.0205 0.0217 0.0204 0.0210 0.0217
++ +
Deviation 0.5 1.0 - 1.4 2 3.7 - 3.9 4.7
-
+ $3.2
-
+++
2.5 2.4 1.4 1.0
++
-%.2 1.4 - 0.0 4.5 -13.7 - 5.3 1.1
-
++ +
-$.l -11.8 2.2 -3.9 - 7.5 2.9 6.0
-+
t
+
Bottom 0 0195 0,0197 0.0193 0.0201 0.0195 0.0189 0.0194 0.0191 0.0187 0.0223 0.0218 0.0216 0.0220 0.0223 0.0229 0.0221 0.0226 0.0230 0.0264 0.0232 0.0269 0.0232 0.0283 0.0224 0.0223 0.0222 0,0220 0.0201 0.0219 0.0216 0.0218 0.0246 0.0249 0.0244 0.0245 0.0254 0.0257
Top
Uncor- -Corrected rected'
TREATMENT OF RESULTS
This starts with the assumption that there is no liquid phase resistance to mass transfer and that the true driving force acrom the gas film is a partial pressure difference. This leads to the following equation for any differential tower length: dni = GpdY = kmS ( p i {
- P A ) dZ
(5)
On the bask of the assumptions that ka and a are constant throughout the tower, temperature is constant, and 1 Y = 1is a good approximation, Equation 5 can be integrated to give
+
(In the worst owe, Y was about 0.10 and in many cases was of the order of 0.02 to 0.03. The added complexity introduced by integrating Equation 5 in a more rigorous manner did not appear justified.) Although the temperature of the liquid did not change very much in its passage through the tower (about 5" C. in the worst case), nevertheless the assumption of a constant temperature was inadmissible because i t would lead to erroneous and even negative driving forces at the top of the tower where there was a relatively close approach to equilibrium. T o get around this difficulty the assumption was made that the temperature of the liquid at any point varies in a linear manner with the amount of liquid evaporated. Then assuming a linear vapor pressure curve over the very short ranges involved, one can readily derive
dY
AYa y2 - AY, " d (AY)
(7)
Substitution of Equation 7 in 5 and integration yield an equation of exactly the same form as Equation 6, but the AYim instead of being based on a constant average temperature is based on the actual measured temperaturea at the two ends of the tower. Gas film vaporization coefficients were calculated from the
1116
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1
IO
Figure 4. rected), VI.
G :197- 203 LSS/HR.FT.' PACKED HEIGHT 12 IN.
Absorption Cbefficlent, koa (UncorLiquor Rate for Packed Height of 12 Inches
experimental &ta by this equation. It is also assumed that, such vaporization coefficients are identical with gaa film absorp tjon coefficients. In the use of Equation 6 the tlssumption is made that the temperature gradient across the liquid is negligible or that p i , the partial pressure a t the interface, is equal t o the vapor pressure of the liquid at the mean bulk temperature. The validity of this assumption is substantiated by some of the results of previous workers. Chambers and Sherwood (8), in their runs on the vaporization of water in B wetted-wall tower, took precautions to minimize the temperature gradient in the water film by introducing the air at such a temperature that the water was at its adiabatic saturation temperature. Their results agreed well with the previous results of Gilliland and Sherwood (6)) who took no such precautions. Barnet and Kobe ( 1 ) investigated heat and mass transfer in a wetted-wall tower and concluded that resistance to heat transfer in the liquid film waa negligible. EXPERIMENTAL DATA AND CALCULATED RESULTS
The data on 37 runs with the air-water system at a constant gas rate of about 200 pounds per hour per square foot and with various liquid rates and packed heights are given in Table I. The results for the 9 runs at a 12-inch height of packing are plotted in Figure 4 as kaa (uncorrected) versus the liquor rate. There is considerable spattering of these data, which can be attributed largely to the fact that the approach to equilibrium a t the top of the packing is so close that slight errors in determina-
50
40
I
30
c
.
20
=
9 -
PACKED HEIGHT 61N.
00
IO00
SOW
2000
4ooo
@COO
10
e; 30
AIR- W A T E R IO Q ~ l S 7 - 2 0 3 L B S l H R . F b '
-
STANOARO R U N S
0 PACKING REOUMPED t SEMI WET BULB
PACKED HElQHT4 IN,
0
1000
2000
3000
4OW
!$OW
LLb./(Hr.)(Sq. Ft.)
Figure 5. Absorption Coefficient, koa (Uncorrected), vs. Liquor Rate for Packed Heights of 6 and 4 Inches
Vol. 42, No. 6
tioa of the vapor concentration make a great difference in the driving force. The runs serve chiefly to prove that 12 inches is too great a packing depth, but they also tend to confirm the independence of koa of liquor rate, indicating that the packing is completely wetted at liquor rates of 1000 and above. The values of koa (uncorrected) obtained with &inch and 4 inch packed heights are plotted in Figure 5. These show somewhat lese spattering than was the case for 12 inches of packing and confirm again the fact that koa is independent of liquor rate above IO00 pounds per hour per square foot. To test the reproducibility oi packing a section as short aa 4 inches, the packing waa removed and redumped. The resulta (Figure 5 ) are In good agreement with those on the packing before removal. In the same figure are shown the results (labeled "semi wet-bulb") obtained when the inlet air was preheated in an attempt t o eliminate temperature drop of the water by having it enter a t the wet-bulb temperature. This attempt waa not entirely successful, because of limitations of the air heater, but the temperature drop of the water in its psssage through the tower waa reduced from about 1.8' to 0.8" C. The resulting koa values were in agreement with those obtained without air preheating. This serves to confirm still further the assumption that temperature drop through the water film is negligible.
2 $lz
50 40
¶
30
7
&
20
-D f
lo
4
0
\
d
-2
o
1000
2060
3000
L Lb./(Hr.)(Sa.
400)
5000
Ft.)
Figure 6. Absorption Coefflcient, koa (Corrected for End Effects), vs. Liquor Rate a t Packed Heights of 4, 6, and 12 Inches
By a trial process it was determined that an end-effect correction of 2.2 inches to be added to the packed height brought the results on the three heights into the best agreement. The corrected coefficients for the 37 runs on the air-water system a t constant gas rate are plotted in Figure 6. The same end-effect correction was assumed to apply in the c@e of the runs made with organic liquids. All subsequent runs were made a t a constant liquor rate of 1600 pounds per hour per square foot and a packed height of 4 inches. This is well above the rate a t which the coefficients begin to decrease because of incomplete wetting and yet well below the rate a t which fluctuations in the liquid level in the reservoir rendered uncertain the measurement of amount of liquid evaporated. Where rates above 2400 were used in some of the runs with water, the concentration of water vapor in the exit gas waa obtained from a gravimetric analysis of gas samples. Runs on the air-water system at constant liquor rate and variable gas rate are presented in Table I1 and plotted in Figure 7. The data are considerably more consistent than those for variable liquor rate. The slope of the line is 0.72, which is in accord with what one is led to expect for a case of gas-film controlling. Results of runs on the air-methanol system a t variable gas rate and constant liquor rate of 1600 are given in Table 111and plotted in Figure 8. Similar results for the systems air-benzene and airethyl a-butyrate are given in Tables IV and V and plotted in Figure 9. The lines were drawn with a slope of 0.72 and it can be seen they represent the data well. Vapor pressure data, needed for the calculation of the vapor concentration at the interface,
June 1950
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1117
IL
@ POINT ESTABLISHED IO
.
BY RUNS 1-37 AT CONSTANT QAS RATE
IO00 LBS/ HR FT?
IO 100
I00
900
250 800
G Lb./(Hr.)(Ss.
400 500
Ft.)
Fisure 8. Absorption Coefficient, kda (Corrected), vs. Gas Rate for System Air-Methanol
The diffusivity values used were those given (7) for 1atmosphere and 0" c., corrected to a temperature which W W the average of the four measured temperatures by the equations given in International Critical Tables.
were obtained from International Critical Tables (7) and (for the the case of ethyl butyrate) from the paper by Stull(14). To show the effect of vapor diffusivity, the coefficientsfor the four svstems are dotted in Figure 10 versus EM rate. The koa values increase Bs' the diffusi&y increases, b i t the effect is not vervnreat for a 8.7-fold chanze in diffusivitv. A d o t of koca/Db.lS v e i & G (Figure 11) brings the results on all four systems into a narrow band with the order no longer related to the diffusivity.
DISCUSSION OF RESULTS
The most important conclusion from this investigation is that the effectof vapor diffusivity is very small. This is in agreement
-
Table II. Experimental Data for Runs with Air and Water a t Constant Liquor Rate (Packed height
4 inohes)
Absorption Coefficient,
0.0236 0.0237 0.0174 0.0169 0.0197 0.0182 0.0176 0.0172 0.0164 0.0144 0.0143 0.0141 0.0141
Table 111.
0.0270 0.0264 0.0203 0.0196 0.0233 0.0224 0.0210 0.0209 0.0193 0.0186 0.0185 0.0180 0.0183
0.0289 0.0288 0.0224 0.0217 0.0267 0.0248 0.0235 0,0236 0.0210 0.0202 0.0202 0.0195 0.0201
16.7 18.6 24.4 29.3 30.0 28.0 31.8 32.6 39.3 36.6 38.3 41.2 40.2
24 26 26 24 29 27 26 26 24 24 27 24 27
23 24.5 23.5 21 26 25 23.5 24 20 19.5 23.5 19 23
22.1 22.0 17.9 17.2 20.0 19.4 18.3 18.2 16.9 16.3 16.4 15.9 16.2
23.2 23.4 19.4 18.8 21.6 21.0 20.0 20.0 18.2 17.6 17.8 17.1 17.7
Experimental Data for Runs with Air and Methanol a t Constant Liquor Rate (Packed height = 4 inohes)
Run 51 62 63 54 65 56 67 68 69
60
61 62 63 64 66
Inlet Inlet Gw Liquor Rate Rate Lb./' Lb./ Hour/ Hour/ Sq. Foot 89. Foot 143 170 197 219 241 276 294 322 345 369 415 445 456 472 484
Concn. of Vapor in Gas YY Yii Ycl
Absorption Coeflicient kQo, Lb. ~ ~ Hour)l ~ Tempersturee, / ' C. (Cu. Qoot) Ti, T:, ti h, (Atm,) liqdor liquor Correcteh out in
h %
16.3 19 *v 20.9 23.4 25.7 25.8 27.0 29.7 33.5 32.7 37.6 38.0 38.6 39.9 39.0
18.5 17 17.6 16 14 16 15.5 16 14 14 13.5 13 13.5 12.5 13
9.9 9.1 8.6 6.8 5.7 5.1 6.3 6.0 5.8 5.1 5.0 4.8 4.4 4.7 4.6
14.8 14.6 13.4 11.1 10.5 9.8 9.7 9.1 9.4 8.6 8.4 8.6 7.4 7.9 8.0
1118
INDUSTRIAL A N D ENGINEERING CHEMISTRY 10
40
x)
25
-
AIR BENZENE EQUIVALENT PACKED HEIOHT 8.2IN. L
'
I
O
j
100
2 3 - so f
40
2
30
4
* I600 LBS/
nR.FT.*
I I50
2lX
2W 300
400
Vol. 42, No. 6
and a liquor rate of 2300. At higher or lower liquor rates the relative values of film and turbulent core resistances might change end this would alter the exponent. The authors have no way of predicting even the direction of the effect. Houston and Walker ( 6 )found the effect of molecular diffusivity to be a function of the liquor rate ranging from an exponent on D of 1.0 at low liquor rates to zero at a rate of 3000 pounds per hour per square foot. Further work is indicated, particularly at other liquor rates, with other liquids, and with other carrier gases. A comparison of the magnitude of the authors' vaporization coefficients with those obtained in previous work on both absorp tion and vaporization was considered, but in the present state of knowledge of true gas-film coefficients it would have little value.
500
A few examples will suffice to illustrate this point. In the equation of Van Krevelen and Hoftijzer (the authors' No. 3) the value of constant C was given as 0.02, but if one examines the individual values calculated by these investigators from the results in the literature, one finds that they vary over a 14-fold range. The data of Mehta and Parekh (obtained from 13) show a value of koa of 60 for vaporization of methanol on 6/*-inch rin s at a liquor rate of 2300 and a gas rate of 400. The authors' vafue for 1-inch rings at a somewhat lower liquor rate is 34 and the value based on the absorption results of Houston and Walker (6) for 1inch rings and an L of 1500 is 18. In other words, there is a 3.3fold range in values of koa obtained by different investigators for nearly identical conditions.
25 20
16
HEIGHT 6.21N.
IO 100
IS0
XK)
250 300
G Lb./(Hr.)(Sq.
400 moo Ft.)
Figure 9. Absorption Coefficient, koa (Corrected), vs. Gas Rate for Systems Air-Benzene and Air-Ethyl Butyrate
with the results of Mehta and Parekh (9),who found an exponent on the diffusivity of 0.17 for '/*-inch rings. The practical importance of this result is considerable, because it means that, to a first approximation, the gas-film absorption coefficient is independent of the gas system being used. Consequently, the designer of an absorption tower can predict the gas-film absorption coefficient for any case in which he is interested without having any diffusivity data, and the result should be a good approximation. The exponent of 0.15 on D is limited to the authors' particular conditions-namely, 1-inch ring packing and a liquor rate of 1600 pounds per hour per square foot. On the other hand, Mehta and Parekh ( 9 )found substantially the same result with '/pinch rings
RicAdams, Pohlenz, and St. John (8) vaporized water into air in a tower packed for short depths with 1-inch rings under adiabatic-isothermal conditions (water enteringat the adiabatic saturation temperature) and also under water-cooling conditions. The runs at constant water temperature enabled them to calculate gas-film vaporizztion coefficients. The results spatter badly and they were unable to correlate them, but the agreement with those of the present authors is fair-for example, at L = 1600 and U = 350, the limiting values of koa obtained from their Figure 11 and corrected to the authors' units are 17 and 28, whereas the authors' value is 32. McAdams, Pohlenz, and St. John used their water-cooling data to calculate the liquid-film heat transfer coefficient, hLa, and concluded that there was a considerable resistance to enthalpy transfer in the liquid film. This is contrary to the assumption the authors have made, which was based on the previously reported results in wetted-wall towers. Hence some discussion of this point is in order. The values of hLa reported by these investigators were based, not on their experimentally determined values of koa but on the assumption that ho/ka = os, an assumption which their own experimental data do not support. In fart, they state
?
I
dr; 50 a
u_
40
230
-
325
HEIOHT 8.21N.
3 120
L.1600 LISlHR.FT.'
4
15
r
i
SLOPE 0.72 EQUIVALENT PACKED HEIGHT 6.2 IN.
G Lb./(Hr.)(Sq. Ft.)
G Lb./(Hr.)(Sq. Ft.)
Figure 10. Absorption Coefficient, koa (Corrected), VI. Gas Rate for Four Systems
Figure 11. VI.
Absorption Coefficient, kaa/lW", Gas Rate for Four Systems
INDUSTRIAL A N D ENGINEERING CHEMISTRY
lune 1950
1119
that because of this assumption Table IV. Experimental Data for Runs with Air and Benzene a t Constant Liquor Rate their values of hLa clues- (tare (Packed height = 4 inches) tionable and the error involved Absorption is unknown.,’ Their experiCoefficient, Inlet Inlet koa, Lb. Liquor mental mass-transfer data indiGas Temperatures, C. Moles/( Hour) Rate Rnte cate that hLa is considerably (Cu. Foot) Ti? II, TI, tn. Lb./ Lb./ Concn. of Vapor in Gaa pas gas liquor liquor Hor1r/ Hour/ (Atm.), greater than the values based in in out Corrected out Y¶ Yi, Yi, Run sq. Foot Sq. Foot on the abovestated assump19.8 28 23 15.6 17.4 0.0839 0,1080 152 1600 66 tion and, within the experi16.0 28 22 12.9 20.9 0,0910 1600 0.0722 175 67 15.7 28 10.5 11.8 0.0869 20.3 0.0645 197 1600 68 mental accuracy, could just as 14.9 28 17 11.0 21.1 0.0829 216 1600 0.om 69 14.0 29 16.5 11.2 24.0 0.0794 1600 0,0580 250 70 well be infinite as finite. It 15.1 29 17 10.7 26.8 0.0834 0 .OS90 1600 286 71 15.3 appears, therefore, that i t is far 30 18 10.0 0.0840 30.3 0.0590 1600 319 72 14.2 29.2 30 16.5 10.2 0.0793 0.0548 1600 336 73 from being proved that there 15,l 9.9 0.0832 31.7 30 16 0.0559 1600 365 74 14.0 32.7 31 16 9.4 0,0785 0.05ao 1600 380 75 is a significant temperature 14.8 32.4 30 17 9.6 0.0814 1600 0,0527 402 76 gradient across the liquid film 14.1 31.3 30 15.5 8.9 0.0785 0.0478 1600 430 77 14.4 29.5 16 8.7 0.0797 33.7 0.0500 440 1600 78 in the vaporization of liquids 13.9 29.5 17 9.1 36.2 0.0775 0.0503 462 1600 79 13.2 8.6 0.0746 40.7 30 16 1600 0.0494 495 80 in a packed tower and until more conclusive proof is forthcoming the authors’ asTable V. Experimental Data for Runs with Air and Ethyl n-Butyrate a t Constant Liquor Rate sumption seems to be a logical (Packed height I 4 inohes) one. When good data on hLa Absorption ate available for packed towers, Coefficient. Inlet Inlet it will be possible to make the kQa. Lb. Liquor 088 Temperatures, C. Moles/( Hour) Rate Rate appropriate corrections. (CU. Foot) TI, Ta, L, k, Lb./ Lb./ Concn. of Vapor in Gas g;i (Atm.) gas liquor Liquor Hour/ Hour/ All mass and heat transfer out out in Correct$ Sq. Foot Sq. Foot Run Y; Yi, Yl¶ coefficients for packed towers 23.7 0.0163 156 1600 81 contain the factor a, the 23.7 0.0166 1600 170 .82 23.6 0.0162 1600 208 83 effective area per unit volume. 23.5 0,0164 1600 231 84 23.0 The present authors, in com0.0145 262 1600 85 22.8 0.0144 286 1600 86 mon with other investigators, 22.5 0.0185 1600 810 87 22.4 0.0136 1600 328 88 have made the tacit assump22.6 0.0190 1600 348 89 22.0 tion that the area factor does 0.0128 1600 867 90 23.3 0.0135 1600 375 91 not change as the liquid is 23.0 0.0130 1600 408 92 22.5 0.0130 1600 439 93 varied, If it does vary appre22.4 0.0126 1600 466 94 22.9 ciablv from one liquid to an0.0123 1600 488 95 other, the effect o i diffusivity may be masked. Because the organic liquids with their lower SubSCfiPts surface tension might be expected to wet the surface more readily Im refers to logarithmic mean and hence give a greater effective area than water, the effect of A refers to a component diffusivity itself might be greater than that corresponding to the 0 to inert or carriergas i refers to the interface o! refers to gas phase exponent 0.15 as between water and an organic liquid; still i t does not explain the small effect of diffusivity as between the The units given after a symbol are those used when giving numerical values. The general equations such as 1,2, and 3 may, various organic liquids. of course, use other Units. Much more work needs to be done before the effect of these factors can be properly sorted out. Studies on absorption and on LITERATURE CITED vaporization with a given system but with pressure as a variable (1) Barnet w, I,, and Kobe, K, A., cHEM., 33, 436 (1941). and studies on a given liquid with varying carrier gases would be (2) Chambers, F. S., Jr., and Sherwood, T. K., Ibid., 29, 1415 very desirable. ’
:$tFt&!F
NOMENCLATURE
effectivesurface area of packing per unit volume of packed space surface area of packing per unit volume of packed ad space C,c’ = constants d = diameter of tower D molecular diffusivity, G = mass velocity of gas, Ib./(hour)(sq. foot) = gas film absorption coefficient,Ib. moles/(hour)(sq. foot) ko (atm.) L mass velocity of liquid, Ib./(hour)(sq. foot) rn exponent = exponent and rate of absorption n P = total pressure p = artial or vapor pressure Re = ~eynoldsnumber S = cross-sectional area of tower, sq. feet Y = concentration in gas phase, Ib. moles of solute gas per Ib. mole of carrier gas AY Yi Y = driving force at any level in tower 2 = height of packing in a tower p = density p viscosity z = filmthickness
a
=
5
-
-
5
(1937). (3) Chilton, T. H., and Colburn, A. P., Ibid., 26, 1183-7 (1934). (4) Gilliland, E. R., Ibid., 30, 506 (1938). (9) Gilliland, E. R.,and Sherwood, T. K., Ibid., 26, 516-23 (1934). (6) Houston, R. W., and Walker, C. A,, Zbid., 42, 1105 (1950). (7) International Critical Tables, New York, McGraw-Hill Book Co., 1928. (8) MoAdams, W. H., Pohlenz, J. B., and St. John, R. C., Chem. Eng. Progress, 45, 241-52 (1949). (9) Mehta, J. J., and Parekh, R. H., M.S. thesis in chemical enpineering, Massachusetts Institute of Technology, 1939. (10) Scheibd, E. G., and OOhmer, D. F., Trans. Am. Inst. Chem. E W ~ . , 40, 611-53 (1944). (11) Sherwood, T. K., “Absorption and Extraction,” New York, McGraw-Hill Book Co., 1937. (12) . . Sherwood, T. K., and Gilliland, E. R., IND. ENG.CHEM.,26, 1093-6 (1934). (131 Sherwood, T. K.,and Holloway, F. A. L., Trans. Am. 1 ~ 1 . Chm. EngTs., 36, 21-36 (1940). (14) Stull, D. R., IND. ENQ.CHEM.,39, 517 (1947). (15) Van Krevelen, D. M., and Hoftijzer, P. J., Chem. Eng. Progress, 44, 529-36 (1948). REosIvsD February 1, 1950. Based on work done by Alan E. Surosky in partial fulfillment of the requirements for the degree of doctor of engineering at Yale University.
