November, 1923
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1105
Some Factors Influencing t h e Design of Absorption Apparatus’ By R. T. Haslam, W. P. Ryan, and H. C. Weber MASSACHUSETTS INSTITUTB
OB
TECHNOLOGY, CAMBRIDGE, MASS.
N THE design of an to the driving force (distance The advisability of studying absorption by methods successfully absorption system we the system is from equilibused in the study of the similar and related field, flow of heat, is are. usually concerned rium), but it is also inversely pointed out. proportional to the resiswith the size of tower or The effect of the two resistances, the “gas film” and the “liquid tances in between the gas scrubber necessary to abfilm,” is shown by studying the e$ect of gas oelocity or the absorption and liquid-namely, as sorb a given amount of maof sulfur dioxide by water. The gas-film resistance appears to be shown by Whitman and terial per hour under fixed proportional to the gas oelocity to the 0.8 power. The liquid-film Keats,2the gas film and the terminal conditions-e. g., resistance appears to be practically independent of the gas oelocity. liquid film. These film reconcentration of entering The ooer-all coeficient of absorption rises rapidly with an increase sistances are not due to gas, temperature of scrubin gas aelocity reaching an asymptote due to the comparatioely actual stationary films bing liquid, per cent recovstationary liquid-film resistance. through which heat flows by ery, etc. Oftentimes, in The equations connecting the rate of absorption with gas oelocity conduction and material by addition, it is desirable to are gioen. diffusion, but in both cases know how a change in one a t present these resistances or mor(? of these terminal conditions will affect either the size unit required, the capac- are considered as equivalent to staiionary films of varying ity of % given unit, or the per cent of material lost in thickness. The similarity between the flow of heat and the transfer the exit gases. Both problems involve the rate a t which matter is transferred from a gas to a liquid or vice versa. of material from a gas to a liquid phase, or vice versa, does Here, as in the cases of the flow of electricity and the not end with the fact that each is proportional to a, driving flow of heat, the rate of transfer is proportional to a “driv- force and inversely proportional t o a resistance. It has been ing force.” I n the flow of heat this driving force is the shown also that the major resistances in both cases are equivtemperature difference between the hot and the cold body; alent to film resistances, gas and liquid films, and, in addiin electricity the driving force is the potential difference or tion, W. K. Lewis3 has shown that under certain limite. m. f. existing between the two points; in absorption it is ing conditions the coefficient of material transfer: is prothe distance the gas-liquid system is from equilibrium. I n portional to the coefficient of heat transfer. I n view of the case of the flow of electricity the resistance also influences this similarity it seems advisable to study the rate of abthe quantity of electricity that will flow in a given time. With sorption (or transfer of material from gas to liquid) in a the transfer of heat the same situation holds true-the amount manner similar to the study of the older science, the flow of of heat that flows from a hot body to a cold one in a unit time heat. Newton’s law on the flow of heat is as follows: is not only proportional to the temperature difference (driving force), but it is also inversely proportional to the resistance through which the heat must flow. So, too, with the transfer of material in absorption apparatus, the rate of flow of the where dQ/de is the quantity of heat flowing per unit of time material from one phase to the other is not only proportiopal through the area A of thickness, dl, when the driving force or temperature difference is dt. The constant h is the coeffi1 Received August 27, 1923. Revised from a paper presented at the meeting of the American Institute of Chemical Engineers, Richmond, Va., December 6 to 9, 1922.
2
8
THISJ O ~ R N A L ,14, 186 (1922). Mech. E n g . , 44, 445 (1922).
INDUSTRIAL A N D .ENGINEERING CHEMISTRY cient of heat conductivity. This,equation has the same form as Ohm's law, whyre Driving force (e. m. f.) Resistance where d&/de is the quantity factor, dt the driving force, and Quantity (current) =
dl/hA is the resistance. I n the transfer of heat l / h is the total or over-all coefficient of resistance, often composed of three resistances, the intervening wall, and the fluid film resistences on either side of the wall. An exact knowledge of
VOl. 15;No: 11
Turning now to material transfer or absorption, the rate of absorption of one material from a stream by another stream of material flowing countercurrent to the former may be expressed in a manner similar to the flow of heat (Equation 1).
where
dW
de
in pounds of material being absorbed per minute AP = driving force or distance from equilibrium, often expressed as pressure difference between the partial pressure 01 solute in gaseous and liquid phases, expressed in millimeters of mercury V = total interior volume of apparatus in cubic feet Ka = over-all absorption coefficient equivalent to the pounds of gas absorbed per minute per cubic foot of volume per millimeter mercury partial pressure difference when AP and Vare expressed as above = weight
This differential may be expressed as an average equation of rate W
5
= k u v (AP)By,
(4a)
When the gas obeys Henry's law and the temperature effects are small, the AP,,, is the logarithmic mean of the pressure differences between the partial pressure of the solute in the gaseous and liquid phases taken at the ends of the system. I n this equation the over-all coefficient of absorp tion, k, is coupled with the unknown area through which absorption takes place, u. The over-all coefficient, ka, is where R, is the resistance of the Ro -t R L ' gas film and R L is the resistance of the liquid film. The following experimental work absorbing sulfur dioxide from burner gas by water was carried out with the view of studying the effect of gas velocity and temperature on the rate of absorption, with the hope thereby to obtain more information regarding the nature of the film resistance and to see if the resultant over-all coefficient of absorption, ka, could be explained on the basis of two films, gaseous and liquid, in series each obeying a law similar to that governing the flow of heat through similar films. EXPERIMENTAL RESULTS Series I was made with an unpacked tower 8 inches in diameter by 30 inches high, through which water was fed down the inside wall at a rate equivalent to 16.8 pounds per square foot of cross-sectional area per minute a t a constant proportional to
0
a2 0.4 66 08 A0 1 the laws governing the flow of heat was brought about, not by investigating the over-all coefficient of resistance, l / h , but by determining the coefficients of resistance of the walls and the films separately and noting how such variables as materials, velocity, temperature, etc., changed each resistance. Knowing each of the resistances, one may easily calculate the over-all resistance. I n heat transfer the main problem is the determination of the two film coefficients. As shown by Weber4 the coefficient of heat transfer for gaseous films (forced convection) is as follows: 0.88 (V,)O.' (T)'.' (S)'.' ( C p ) (2) h, = MO.8 where hg = coefficient of heat transfer through the gaseous film V , = the mass velocity of the gas T = gas temperature in degrees centigrade absolute ~~
(se)
s
= surface factor
C,
= specific heat of gas a t constant pressure = molecular weight of gas
M McAdams and Frost5 have shown that the coefficient of heat transfer through a liquidfilm is as follows: hL =
where
hL
K D z
V
23.3 K (DVz)O.p
D
(3)
= coefficient of heat conduction = thermal conductivity of stationary liquid = = =
diameter of pipe through which liquid flows fluidity of film on pipe relative to water average mass velocity of liquid
From these two'equations it is seen that the resistance of the gaseous film, l/ho, is inversely proportional to the gas velocity to the 0.8 power, and that the resistance of the liquid film, l / h ~ , is inversely proportional to the 0.8 power of the liquid velocity and the 0.8 power of the fluidity. 4
6
M I. T. Thesis, 1919. THISJOURNAL, 14, 13, 1101 (19.22).
INDUSTRIAL AND ENGINEERING CHEMISTRY
November, 1923
temperature of approximately 58' F. The velocity of the gas was varied from 0.084 foot per second to 0.396 foot per second, and the rates of absorption, absorption coefficient,
1107
diameter coke, the water rate being 32.3 pounds per square foot of cross section per minute and the temperature approximately 56" F. The gas velocity was varied from 0.204 to 0.976 foot per second and the results are shown in Table I11 and in Fig. 3 the absorption coefficient, La,is plotted against gas velocity. OF LINEARGASVELOCITY O N ABSORPTION Lbs. of SO, Per cent Absorbed/Min. Per cent EquilbiGas Velocity d_w AP SO1 rium Mm. Hg Absorbed Reached Ft./Sec. ka X 108 de
TABLE11-EFFECT
0.204 0.282 0.389 0.484 0.578 0.684 0.785 0.976 0.113 0.223 0.352 0.449 0.565
and per cent absorption are given in Table I. The absorption coefficient is plotted vs. gas velocity in Fig. I. TABLEI-RATE
OF
ABSORPTION US.
GAS
VELOCITY
Lbs. SOz
Absorbed/Min. dW
Gas Velocity Ft./Sec.
ka X 108
0.084 0.125 0.166 0.213 0.256 0.294 0.339 0.396
0.39 0.44 0.55 0.59 0.61 0.66 0.71 0.78
0.088 0.167 0.254 0.341
0.63 0.77 0.85 0.Q5
d0
Series I 0.0134 0.0162 0.0204 0.0208 0.0221 0.0252 0.0270 0.0286 Series 2 0.0225 0.0304 0.0382 0.0438
Per cent of Total
1.41 1.81 1.84 2.06 2.02
0.0278 0.0398 0.0516 0.0614 0.0686 0.0770 0.0833 0.0933 Series 4 0.0256 0.0480 0.0627 0 0688 0.0694
21.8 22.2 24.0 26.2 29.1 31.4 30.1 33.2 20.8 30.3 39.0 38.1 39.4
92.0 77.7 61.1 50.5 47.7
15.8 28 4 35 0 40.5 40.2
Series 4 was made with a tower 8 inches in diameter, 30 inches high, packed with 3 x 3-inch spiral tile, the water rate being 32.1 and the temperature approximately 60' F. The gas velocity was varied from 0.1 foot per second to 0.565 foot per second. The results are given in Table 11, and in Fig. 4 the absorption coefficient, La, is plotted against gas velocity.
SOX
AP Mm. Hg
Absorbed
39.2 42.0 42.5 40.5 41.5 43.7 43.5 42.0
47.3 40.5 30.0 31.6 30.0 26.0 24.5 17.0
41.1 45.2 51.5 52.8
68 49 34 30
.
Series 2 was made in the same tower as Series 1, but the water was sprayed in a t the rate of 32.6 pounds per square foot of cross section per minute. The temperatures were approximately constant a t 55" F. The gas velocity was varied from 0.088 foot per second to 0.341 foot per second. The resultant data similar to that taken in Series 1 are shown in Tablo I, and in Fig. 2 La is plotted against gas velocity. Series 3 was made with the same tower packed with 1-inch
DISCUSSION OF RESULTS EFFECT OF GAS VELOCITY-In all cases (Series 1 to 4 and Figs. 1 to 4, inclusive) it will be seen that with an increase in gas velocity La increases probably from zero (or a point near to it) a t a rapid rate, the increase in k a growing less a t the high gas velocities. Fig. 5 shows how the rate of absorption (pounds sulfur dioxide absorbed per minute, Series 111) increases with gas velocity. This also is indicated in Fig. 6, which shows how the per cent equilibrium reached by the absorbing liquor increased from 15 to 52 per cent with an increase in gas velocity from 0.2 per second to 1.0 foot per second. However, the exit losses increase with gas velocity, as shown in Fig. 7, which gives the per cent absorbed vs. gas velocity. I n considering Equation 2 for the transfer of heat through gas films, it is seen that increased gas velocity increases the heat transfer through the gas film proportional to the mass velocity of the gas to the 0.8 power, or, in other words, the resistance to the flow of heat decreases inversely as the velocity to the 0.8 power. Now if the resistance l/ka to the transfer of sulfur dioxide from the gas to the liquid is composed of a gas film and a liquid film, then
,
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1108 1 ka = RQ
+ RL
Assuming that the gas resistance varies inversely as the gas velocity and that gas velocity has no effect on the liquid a m , we have 1
C
+
Vol. 15, No. 11
a t different velocities were computed and the results are shown in Table 111. A N D GAS FILMRESXSTANCSS AT GASVELOCITIES
TABLE111-RELATIVB L I Q U I D
GRSResistance R Liquid Gas Velocit; Series PACKING Resistance 0 . 1 Ft./Sec. 0 . 3 Ft./Sec. 1 Wall only 0.83 1.57 0.66 wetted 2 Spray 0 83 0.69 0.29 3 1-in. diam0.21 0.63 0.26 eter coke 4 Spiral tile 0.40 0.33 0.14
VARIOUS
at
08; 0 . 5 Ft./Sec.
(5) ka - v0.s RL 0.44 &a = absorptioncoefficient C = constant 0.19 ‘c‘ = gas velocity Ra = gas-film resistance 0.17 RL = liquid-film resistance 0.10 Whitman and Keats2 do not consider. the liquid film to be unaffected by gas velocity, while Robinson6 finds otherwise. The equations connecting the absorption coefficient, Ica, Fig. 8 shows l / k a plotted against 1/Vo.8 for Series 1 to 4, expressed in pounds per minute per cubic foot of volume per inclusive, the points falling close to straight lines as one would millimeter mercury partial pressure difference with gas veexpect if Equation 5 is correct. Based on these assumptions, locity, V , in feet per second are as follows: the relative liquid-film resistance and the gas-film resistance Series PACKING EQUATION 6
go 30
Mech. Eng., 46, 99 (1923).
1
1
0 25
1
0.11
iL;2 =
vo.8 f 0.83
2
Spray
E
3
1-inch coke
;a_ = _
4
Q
Wetted wall
3-inch spiral tile
1
=
- =
~ 0 -I. 0~. 8 3
;;:
f 0.21
0 0.52
VO8
40
The first term on the right-hand side of the equations is the gas resistance term, while the second refers to the water resistance. I n Series 2, 3, and 4 the water rate was constant a t approximately 32 pounds water per square foot per minute, while in Series 1 it was 17 pounds. It is to be noted that the liquid-film resistances follow the order of magnitude one would expect-namely, that it is least with the 1-inch coke-packed tower and greater with the spray and wetted-wall type of tower. The spiral-packed tower is intermediate in this respect between spray and the coke-filled towers. From an inspection of Table I11 and Figs. 1 to 4, inclusive, and Fig. 8, it can be said that the data show the effect of the two films, the effect of gas velocity at low gas velocities being great since the main resistance is the gas film, whereas a t high gas velocities the effect is due to the increasing importance of the fairly constant liquid film. Furthermore, these data indicate why increased gas velocity has such a small effect on the absorption coefficient of spray type of towers-namely, that the liquid-film resistance, which is fairly constant with increasing gas velocity, is the major resistance, in addition to the gas resistance being excessively high due to “slippage” between the gas and liquid. This treatment shows quickly the line of attack along which to improve any given type of absorption tower-that is to say, for example, whether the liquid-film resistance should be lowered by increased water velocity or the gas-film resistance lowered by increased air velocity. It is of importance ‘to note that Robinson6 finds the absorption coefficient ka of cooling towers to be linearly proportional to the air velocity, the line for ka versus air velocity passing through zero. As pointed out by Robinson6 and Whitman and Keats,2 during adiabatic humidification or air cooling the water temperature remains constant, with Dhe result that no liquid film exists, leaving only one film resistance, the gas film. Robinson’s6 data show that the gas-film resistance is inversely proportional to the gas velocity to the 0.8 power, and that the liquid-film resistance, in the case mentioned, is zero. ACKNOWLEDGMENT The authors wish to thank M. B. Donald and C. W. Tyson, students in the School of Chemical Engineering Practice, Massachusetts Institute of Technology, whose investigations are here discussed. Thanks are also due to the Merrimac Chemical Co., So. Wilmington, Mass., in whose plant this work was carried out.
