INDUSTRIAL A N D ENGINEERING CHEMISTRY
1224
water. Thus certain gases, such as carbon dioxide, hydrogen, and hydrogen sulfide, tend to saturate the surface layers of the water fairly readily, and the layers so formed are of considerable permanency and not easily dislodged. On the other hand, gases such as nitrous oxide, nitric oxide, and chlorine show no tendency to form such saturated surface layers and are absorbed at a correspondingly higher rate. Since in most cases the effect of dissolved gas on the density of the water is to increase it, we may form a picture of the process by assuming that the first action is to form a saturated layer which is heavier than the rest of the liquid and tends to sink. At the same time the surface tension and the viscosity of the liquid tend to maintain the surface in its original condition. Whether the layer will sink and a t what rate is then determined by the relative magnitude of these opposing agencies, which also determine whether the layer will be stable or unstable-i. e., whether the rate of solution will be greatly affected by slight disturbances of the liquid or not. The effect of dissolved gas in the surface tension and viscosity of the liquid is of importance even when the liquid is used in a scrubbing tower, as it has been pointed out by Hurtersand also by Donnan6 that these properties may affect the effective interface of the gas and liquid owing to their effect on the formation of drops, splashing, and the wetting of the packing material of the tower. The matter is therefore of considerable importance and worthy of further study.
Vol. 16, No. 12
with single bubbles of known area, and that the chief difficulty in estimating absorption rates for this case would come in determining the actual area of the many bubbles formed by such means. Mr. Wilson remarked that experiments on absorption from bubbles by oil indicated that the type of nozzle used to deliver the bubbles had very little effect upon the rate of absorption, since the bubbles aggregated to a definite size a t a point just above the nozzle. I n this connection T. A. Boyd stated that the type of nozzle was very important in experiments where gas was bubbled through water. He had noted a certain amount of aggregation of bubbles through water, but in dilute sodium chloride solution there was no such effect. W. H. McAdams noted the similarity between Dr. Becker’s curve showing the effect of velocity on the rate of absorption coefficient and the curves obtained in studies on the effect of velocity on the coefficient of heat transfer. This point further emphasized the parallelism between the two processes of absorption and heat transfer.
Effect of Gas Velocity and Temperature on Rate of Absorption’ By R. T. Haslam, R. L. Hershey, and R. H. Keen
..........
MASSACHUSETTS INSTITUTE OR TGCHNOLOGY, CAMBRIDGE, MASS.
DISCUSSION
I n discussing the first halfof Dr. Becker’s paper, R. P. Russell pointed out the similarity between Dr. Becker’s results with stirred solutions and the theory presented by Dr. Lewis. Since the atmospheric gases are only slightly soluble, the absorption of these gases is determined by liquid diffusion. Although Dr. Becker had developed his equation with a different nomenclature and had finally expressed it in integrated form, the basic principle was the same in both treatments. In fact, the coefficientf,when multiplied by 60, was the same as Dr. Lewis’ coefficient kL, the factor 60 being necessary to convert from minutes to hours. The results obtained when the liquid was free from agitation could not be interpreted so readily, since it was evident that stratification effects were pronounced. Such results could not be subject to the formula proposed by Dr. Lewis, which assumed uniformity of composition in the main bodies both of the liquid and of the gas. However, it was possible that the initial absorption rates tabulated by Dr. Becker would conform to the theory, provided the influence of stratification was unimportant a t the start. Mr. Russell had therefore calculated absorption coefficients from these initial rates, assuming that the rate was controlled entirely by liquid film diffusion. He believed that it was permissible to neglect any gas film because Dr. Becker worked with pure gases. These calculations gave values of k L varying from 1.1 to 15-4. e., a 1Cfold range for the pure gases in water, whereas the initial rates themselves varied over 200,000 fold on a weight basis. Admitting that the agreement of the coefficients was only qualitative, the results, nevertheless, seemed to check reasonably with his assumptions. Mr. Russell asked if Dr. Becker believed that stratification was evident a t the start, which might explain the discrepancies in the coefficients, and Dr. Becker replied that it probably did affect the initial rate. Mr. Melligan asked whether Dr. Becker had any data on absorption rates when air was bubbled up through a porous plate. Dr. Becker replied that his work had been carried out
T
HE research herein reported was conducted in an effort
to discover whether the two-film theory of absorption of a gas in a liquid would quantitatively describe the rate of absorption in a given system under varying conditions. Accordingly, it was proposed to operate a definite systemthat is, a system of a given gas absorbed in a given liquid in a standard apparatus-first, under conditions such that the liquid film offered the major resistance; and second, under conditions such that the gas film offered the major resistance. Furthermore, two such systems, one having very soluble solute gas and the other having a less soluble solute gas, were to be employed. Thus the effect of solute gases of widely different properties was to be studied. The similarity between the rate of transfer of heat by conduction and the rate of transfer of material by diffusion has already been indicated. This investigation has as the second object the further extension of this relationship.
EXPERIMENTAL METHOD APPARATUS-The apparatus used is shown diagrammatically in Fig. 1. The tower was a Pyrex- glass tube 3 inches in diameter and 3 feet long, lagged with magnesia pipe covering. The liquid was introduced into the tower through a distributor a t the top. The tower was of the wetted wall type, without packing. The gas was blown up through the tower. T h e solute gases were drawn from cylinders; the air, which was used as a “carrier” gas, was forced through the tower by means of a pressure blower. Flowmeters and an orifice were used to measure the gas. The liquid, which was water in all cases, was heated where necessary by blowing steam into it. The final adjustment of water temperature was made by leading the water through a coil in a constant temperature water bath. The gas temperature was adjusted by leading the gas through a coil in the same bath. Thermometers were inserted in the water and gas lines both before and after the tower. Presented under the title “A Study of the Mechanism of Absorption.” A. E. Marshall, Consultiag Engineer, Corning Glass Company. 1
6
J. SOC.Chem. I n d . , 4, 641 (1885). Ibid , 39, 236T (1920).
* Obtained through courtesy of
December, 1924
INDUXTRIAL A N D ENGINEERING CHEMISTRY
METHoD-8UlfUr dioxide was fist used as the solute gas and runs were made a t temperatures varying a t 10 degree intervals, from 10' to 5OoC.,andat gasvelocitiesvaryingfrom0.03 to 1.5 feet per second. Similar data were obtained using ammonia.
1225
A p and Ac for these equations were determined by making the log mean of the terminal differences. Table I gives the values of K , and KL obtained. Figs. 2 and 3 show these coefficients plotted against gas velocity.
FIG.I-DIAGRAMO F APPARATUS
Runs were made a t a constant gas velocity, the temperature being varied. When this series of runs was complete the velocity was adjusted to a new value and runs were made a t this new velocity, varying the temperature. The procedure for an individual run was essentially as follows: The gas velocity was first set at the desired value; then the water rate, which was constant for all runs a t 1800 cc. per minute, was adjusted. Meanwhile, the temperatures of gas and liquid were being adjusted. When all conditions were constant a t the desired values, they were so maintained until equilibrium was reached within the tower, when samples of the effluent liquid were taken for analysis. Analyses were made of the gas entering the tower. The composition of this gas was kept as near 10 per cent solute gas and 90 per cent air as possible.
CALCULATIONS
EQUILIBRIUM DATA-In order to calculate these coefficients from the original data it was necessary to extrapolate accurately the results 'I2J3t found in the literature on equilibrium solubilities of sulfur dioxide and ammonia in water. The method of extrapolation of the sulfur dioxide (suggested by W. K. Lewis) was as follows: Let p = partial pressure of Son, mm. Hg c
= total concentration
of solution, grams per cubic
centimeter H = Henry's constant
K = dissociation constant K = (H+) (HSOs-) HzSOo
y
Then
c
(
= fraction H&03 dissociated = YC HD
+
RESULTS p From the original data over-all absorption coefficients for these runs were calculated by means of the following equations : W / e = K I A 49 (1) W/e = K L A 4 6 (2) where W/e = grams OP material absorbed per hour
A KI
KL Ap
Ac
= area of transfer surface, in square centimeters = over-all gas film coefficient, in
grams hour X sq. cm. X atmosphere = over-all liquid film coefficient, in grams hour X sa. cm. X gram/cc. . = pressure difference between partial pressure of solute gas in gas phase and vapor pressure of solute gas in equilibrium with the liquid phase, in atmospheres = concentration difference between concentration in equilibrium with gas phase and concentration in liquid phase, in grams per cubic centimeter
whence y c = c
= Hp+
d K 3
A plot of 4; vs. c / d c should therefore be a straight line of slope H and intercept d K T . These functions of the original solubility data's2 were plotted and the slopes and intercepts read off. These, in turn, were plotted against temperature and the values for the desired temperatures secured from this plot. The straight lines fixed by the slopes and intercepts thus obtained were and c/ read from them, and these drawn, values of values used to calculate c and p , the plot of which is shown in Fig. 4. This treatment could not be applied to the vapor pressure data of ammonia as given in the literatures as the plots of t Numbers in text refer to bibliography at end of article.
4;
46
/
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1226
6and c/ .\/;
were not straight lines, so it was necessary to use a purely empirical method. It was found that plots of c vs. c / p gave straight lines, so these functions were used. The general equation for these lines is c / p = a - bc. Values of a and b were plotted against temperature, and the rest of the process was carried through exactly as in the case of the sulfur dioxide data. The final plot is shown in Fig. 5.
Vol. 10, No. 12
By exactly analogous reasoning the equation for the over-all liquid film coefficient may be deduced. (5)
where KL is in
grams hour X sq. cm. X gram/cc.
T A B ~I-OBSERVED E
VALUES OF THB OVER-ALL ABSORPTION COEFFICIENTS K OA N 0 K L Sulfur Dioxide vs. Gas Velocity and Temperature Grams KO= Hour X sq. cm. X atmosphere
Velocity Feet/second 1.48 1.26 1.12 1.01 0.867 0,698 0.498 0.257 0.152 0.102 0.0298
10°C. 3.46
...
...
... ...
2.97
2.18 1.67 1.09 0.896 0.495
KL 1.48 1.26 1.12 1.01 0.867 0.698 0.498 0.267 0.152 0.102 0.0298
2OoC. 3.01 2.88 2.86 2.60 2.47 2.31 1.93 1.57 1.03 0.842 0.491
18.6
=
23.9 22.8 22.0 20.4
...
1i.i
11.3 8.37 5.65 4.38 2.25
3.0
1.91
1.69
2.0
1,52 1.27 1.01 0.760 0.480
1.38 1.21 0.97 0,722 0.401
4OoC. 2.34
2.21
1.69 1.44 1.02 0.805 0.473
...
... ...
... ...
... ... ... ,..
Grams Hour X sq. cm. X gram/cc.
... ... ...
16.0
500 c. 2.08
30OC. 2.74
... ... ...
31.8
... ... ...
E.2 14.8 11.6 7.50 6.18 3.32
35 8
... ... ,..
44.7
... ...
29.8
36.2
18.4 15.0 10.8 8.22 4.43
24.3 18.7 14.7 10.9 5.93
2i:i 25.0 18.4 14.4 7.51
...
tO
I
01
I
I a2
0
...
25.2
...
4.0
I
ao
I
I
as
a6
I. 2
1.0
1.4
These equations are exactly similar to those given by Lewis and Whitman,4 derived in a different manner. The identity may be made evident by clearing fractions. For instance: =
H k , kL HkL k,
+
which is the equation as given by Lewis and Whitman. It is desired to determine values for the individual film IC, and k , , and to determine how these coefficoefficients, 2.25 2.49 2.82 2 64 2.94 1.42 cients are dependentupon temperature, gas velocity, and solute 1.80 1.87 2.06 1.92 2.17 0.947 0.897 1 03 0.972 1.04 1.06 0.489 gas. In calculating these effects, conditions have, in general, 0 228 0.278 0 337 0 321 0.344 0.146 0 114 0.109 0.123 0 111 0.140 0.0301 been so chosen that the resistance of one film is either negliGrams gible or calculable, and the effect of one of the operating KL = Hour X sq. cm. X gram/cc. variables, temperature or gas velocity, upon the individual 6.70 3.47 5 20 1.70 2.87 1.42 film in question can be calculated from its effect upon the over5.32 2.69 3.88 1.23 1.81 0.947 2.675 1.402 1.975 0.922 0.605 0.459 all coefficient, KO. 0,833 0 435 0 591 0.276 0.192 0.146 0.328 0.164 0 242 0.110 0.0804 0.0301 If the individual firm coefficients are considered as expoGESERAL METHODO F CALCULATING EFFECTO F GAS nential functions of gas velocity and temperature, k , and k L may be written as: VELOCITY AND TEMPERATURE O S FILMCOEFFICIENTS-The k , = a T/n T" (6) over-all coefficients, K , and K,, are conductances and hence kL = b V r T" (7) the reciprocals of resistances. Let us consider only one of them, K,, for purposes of discussion. Assuming the two- where T is centigrade absolute temperature and Vis gas velocity (feet per second). film theory to be valid, we may write Ammonia vs. Gas V e l o c i t y and Temperature Grams ' KO = Hour X sq. cm. X atmosphere
I
where R, and R L are the individual gas and liquid film resistances to absorption, respectively; and where IC, and I C L are the individual film conductances, respectively, expressed as grams grams and hour X sq.cm. X gram/cc. hour X sq.cm. X atmosphere The over-all coefficient, K,, is in terms of grams hour X sq. cm. X atmosphere It is a t once evident that the units of the individual liquid film coefficient, k,, are incompatible with the units of the gas film coefficient, since kL differs from k , in its expression of driving potential. To establish a sound equation the liquid coefficient, kL, must be multiplied by the Henry's law constant, grams/cc. H' atmosphere'
I
I
I
I
I
I
I
I
I
I
I
4.0
3.0
~
.
K, =
1
1
1
& +HkL
(4)
2,o
a.! GUJ Velpclty- I!. per sccond
0 0
a2
a4
0.6
0.8
1.0
1.2
1.4
EFFECTOF VELOCITY O N LIQUIDFILMCOEFFICIENT Whitman, Naess, and Moyes6 have studied t% absorption of carbon dioxide in water in the apparatus used in these experiments and under conditions exactly like those existing
INDUSTRIAL A N D ENGINEERING CHEMISTRY
December, 1924
in these experiments. Since carbon dioxide is very insoluble in water, the gas film resistance to absorption may be considered as negligible,4 that is, the resistance to absorption is due almost wholly to liquid film. These investigators found that over a range of gas velocity from 0.03 to 1.5 feet per second the value of the over-all coefficient, KL, increased only very slightly with velocity, and hence we may conclude that the individual liquid film coefficient, ICL, is independent of gas velocity, so that Equation 7 becomes: k L = b Ts (8)
1227
0.86, and for ammonia 0.82. Since the data do not justify using more than the first place in such an exponent, the value of n will be called 0.8. EFFECT OF TEMPERATURE O N LIQUIDFILM COEFFICIENTWhen the gas film resistance is very small compared with the liquid film resistance, changes in the former may be neglected in calculating the effect of changes in the latter upon the overall coefficient. For sulfur dioxide, a relatively insoluble gas, a t high gas velocities the gas film resistance is small compared with the liquid film resistance. Hence if we know the value
ilG.4
fIG.5
soumirr OF RH,
IN HO, Calculated from data of
20 I8 I6 14 12
IO
8 6 4 2 - -.0 ..
0
\
10
20
90
40
50
60
70
80
90
Lewis and Whitman4 show that the value of the individual liquid film coefficient, k,, in the units here employed, for a given soIvent and a t a definite temperature, is the same for all solutes. At 20" C., Whitman, Naess, and Moyes found the average value of the over-all liquid film coefficient, K,, for carbon dioxide over a gas velocity range from 0.03 to 1.5feet grams per second to be 36.5 . Since hour X sq. cm. X gram/cc. for this case kL = K,, the value of the individual liquid film coefficient, k L , may be taken as 36.5 a t 20" C. for all solutes in witter .when the concentration of the solute in the gas is fairly low (in this case about 10 per cent). EFFECT OF GAS VELOCITY O N GAS FILMCOEFFICIENTThe value of k , for these conditions being known, by means of Equation 4 values of the individual gas film coefficient, Lo,for both sulfur dioxide and ammonia, were calculated a t 20" C. and a t various velocities from the values of K Oas read from Figs. 2 and 3 and the values of N as determined from Figs. 4 and 5. The values of k , thus calculated are given in Table 11. If the logarithms of both sides of Equation 6 are taken, since T is kept constant we have, log k, = log ( a Tm) n log V which is the equation of a straight line of slope n. Fig. 6 is a plot of these logarithms. The value of n for sulfur dioxide is
+
of the individual gas film coefficient, Lo,for sulfur dioxide at a high gas velocity and for a certain temperature, we may assume that its change with temperature has a negligibly small effect on the over-all coefficient, KO. Then for purposes of calculating the temperature effect on the liquid film coefficient, k,, we may assume the known value of the gas film coefficient, le,, to be practically constant. OF THE INDIVIDUAL GAS FILMCOEFFICIENT, ko, AND O* THE OVER-ALL COEFFICI&NT, Kg,FOR SULFUR DIOXIDE AND AMMONIA vs. GAS VELOCITY AT 20° C.
TABLE 11-VALUES
Grams Hour X sq. cm. X atmosphere -Sulfur dioxide-Ammonia-
Both Kg and kp = Velocity Feet/second
0.05 0.25 0.60 1.00 1.30
KO 0.58 1.52 2.17 2.61 2.94
k9
0.673 2.37 4.45 6.82 9.61
K9 0.17 0.70 1.36 2.18 2.69
kn 0.171 0.713 0.41 2.31 2.89
Thus, values of the individual liquid jilm coefficients for temperatures of lo", 20", 30", 40", and 50" C., a t a gas velocity of 1.3 feet per second were calculated by Equation 4. The values of K , were read from Fig. 2, the value of k , was taken from Fig. 6 as 9.00, and the value of H was determined from Fig. 4. The values of k L thus calculated are given. in Table 111.
I
Vol. 16, No. 12
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1228 TABLE 111-VALUES
OF THE INDIVIDUAL LIQUIDFILMCOEFSICIENTkL,FOR A GASVELOCITY O F 1.3 US. TEMPERATUdE
DIOXIDEAT Temperature
SULFUR
c.
'L =
our x
Grams sq. cm. x gram/cc.
31.5 37.5 43.0 48.3 55.6
10
20 30 40 50
kL
+
.O(I
ai
0.2
a3
CY
(10)
T4.0
These equations show that the gas film coefficient increases as the gas velocity to the 0.8 power, whereas gas velocity has no appreciable effect on the liquid film coefficient.
By taking the logarithms of Equation 8, we have log KL = log b s log T which is the equation of a straight line whose slope is s. Fig. 7 is a plot of these logarithms and s has the value of 4.0. .oq.os.06
cients may be noted from the following equations which summarize the effects as calculated above: ko CY vO.8 T-1.4 (9)
0.4 o.so.6 0.8 1.0
2.0
TABLE IV-VALUES OF THE INDIVIDUAL GASFILMCOEFFICIEST, k, AND OF THE OVER-ALLCOEFFICIENT, KO,FOR AMMONIA AT A VELOCITY OF 0.2 FOOT PER SECOND 8s. TEMPERATURE Temperature
c.
10 20 30 40 50
J.0 8.0 9.0
6.0 5.0 4.0
3.0 2.0
I.0
0.6 0.5 0.4
K"
kn
0.i15 0.495 0.466 0.447 0.430
0.51 0.49 0.46 0.44 0.42
Temperature apparently has a very marked and divergent effect on the coefficients, causing, as it does, the gas film coefficient to decrease as the 1.4 power of the absolute, temperature; whereas the liquid film coefficient increases as the 4.0 power of the absolute temperature. Temperature apparently affects th&%wo-film coefficients differently, increasing the one and deBeasing the other. The remarkable effect of temperature is. easily appraised by noting that the power function of temperature is -1.4 in the case of the gas film coefficient and 4.0 in the case of the liquid film coefficient.
0,J
DISCUSSION OF RESULTS
0.2
0.1
EFFECT OF TEMPERATURE O N GAS FILMCOEFFICIENTI n calculating the effect of temperature on the gas $lm we use the ammonia data a t low gas velocities. Under such conditions the absorption is almost entirely controlled by the gas film,ammonia being a very soluble gas. Equation 4 is again used, the values of K , for the various temperatures a t a velocity of 0.2 foot per second are read from Fig. 3, values of H are determined from Fig. 5, and the values of kL have already been calculated. The values of Lo for a gas velocity of 0.2 foot per second thus calculated are given in Table IV. When logarithms of IC, are plotted against logarithms of T for a constant velocity, a straight line whose equation is log K , = log (a V") m log T
+
VELOCITY E F F E C T - I t is interesting to note that the coefficient of heat transfer varies with the 0.8 power of the gas velocity, as does also the coefficient of material transfer (absorption) through the gas film. The similarity of this relationship is evident. TENIPERATURE EFFECT-Lewis and Whitman4 state that the ratio of viscosity to density of the film fluid is probably the controlling factor in determining film thickness. Then, if film resistance is directly proportional to film thickness, we can say the film conductivity is a function of the inverse of the foregoing ratio-that is, the individual film coefficients are functions of the ratio of density to viscosity. The effect of temperature on the density of a gas is great, but temperature affects the density of water only slightly. Furthermore, an increase in temperature causes an increase in the viscosity of a gas, but the same increase in temperature greatly lowers the viscosity of water. Consequently, tem-
GAJ VELOCITY 1.3 fT. PER SC 1.70
1.60
1.x)
I .40 2.45
2.46
2.47
2.48
2.49
2.50
231
2.52
is obtained. Fig. 8 is such a plot, and the value of m, which is the slope of the line, is found to be -1.4. Thus the gas film coefficient decreases with an increase in temperature whereas the liquid film coefficient increases. DIRECTEFFECT OF TEMPERATURE AND GASVELOCITY ON THE GASAND LIQUIDFILM COEFFICIENTS-The direct effect of temperature and gas velocity on gas and liquid film coeffi-
2.45
2.46
2&7
218
2.49
220
2.51
2.52
perature has a marked influence on the ratio of density to viscosity. Furthermore, an increase in temperature decreases this ratio for gases but increases it for liquids. Based on Lewis and Whitman4 one would expect the main effect of temperature to be on this ratio. Therefore, we may write in place of Equations 6 and 7 the following, where the ratio of density to viscosity is substituted for temperature:
1229
INDUSTRIAL A N D ENGINEERING CHEMISTRY
December, 1924
k, = c V" ( S / Z ) ~ (11) KL = d ( s / z ) ~ (12) where s is the density of the film and z is its viscosity. If we plot the log of k L against the log of s / z for the liquid film we get a straight line whose equation is log kL = log d p log S / Z Fig. 9 is such a plot and p , the slope of the line, equals 2/3.
+
and CSOZ C -N c H~
Molecular weight weight of of SO2 Molecular NH3
The actual data satisfy this relationship remarkably well, as the following comparison shows: 1 . 7 4 x 104 5.31 X loa
am2
- =
3'3
. _ ,
Molecular weight of SO2 = s_4 = 3.76 Molecular weight of NHp 17
1.8
COMPARISON OF OBSERVED AND CALCULATED OVER-ALL ABSORPTION COEFFICIENTS-The equations for the individual film coefficients now become
1.7
1.6
For SO2 k , = 1.74 X IO4 Vas T-1.4 k, = 43 Vo.8 (s/z)'/s k L = 5.1 X lo-' T4 K L = 37.5 ( S / Z ) % I
1.5
(134
U3b) (14a) u4b)
For a".
1.4 -0.2
-0.1
0
0.1
0.3
0.2
5.31 X loa Vo'ST-1.4 k y = 13 Vo."8 (S/Z)~/S k L = 5.1 X 10-7 T4 k~ = 37.5 (s/.z)Va
k,
In the same way Fig. 10 shows a plot of log k , against the log of the ratio, s/z, for air. The slope of this line is also 2/3. Equations 11 and 12 then become k , = c VO"*s/zz/a k L = d s/z2/a
(11) (12)
Thus, the widely divergent effect of temperature on the film coefficients is shown to be due to the effect of temperature$ on the ratio s / ~ which, , in turn, affects the gas and liquid film coefficients in the same manner: namely. k , is proDor- density of gas and k L is proportional to tional to viscosity of gas -
)
(
I
I
9
(-viscosity of liquid
=
(154 (15b) (164 (16b)
Values of the over-all coefficients, K , and KL, for both sulfur dioxide and ammonia, have been calculated by substituting the equations for k, and k L in Equations 4 and 5, respectively. Table V shows the comparison between the calculated and the observed values of K , and K L over a gas velocityrange of from 0.03 foot per second to 1.5 feet per second and a t lo", 30", and 50" C. Figs. 11 and 12, give a graphical comparison of the calculated and observed values. The agreement over the whole range is very good, the discrepancy being, in most cases, less than 10 per cent; the very worst cases are in disagreement by about 15 per cent. When it is remembered how many calculations the original data have undergone, and that some of these data themselves, including the equilibrium solubility data, are probably not more accurate than 10 per cent, the agreement between calculated and observed values is remarkably close. TABLE V-CALCULATED
AND O B S E R V E D V A L U E S OF T H E TION COEFFICIENTS, K , AND K L
-IOo
Velocity Feet/second
Calcd.
C.-
Obsd.
OVER-ALLABSORP-
--30' C.Calcd. Obsd.
-50' C . 7 Calcd. Obsd.
Sulfur Dioxide vs. Gas Velocity and Temperature Grams = Hour X sq. cm. X atmosphere
1.4 1.0 0.6 0.2 0.05
EFFECT OF SOLUTEGAS-The principal effect of changing the solute gas film sulfur dioxide to ammonia should be in changing the diffusion of these gases through the gas film. Lewis and Whitman4 state that the molecular diffusivities of all solutes, under similar conditions, are the same. This means that, in the units here employed, the diffusion coefficients of any two gases through the gas film should bear the ratio to each other of their respective molecular weights. Thus, the following should be true: a802
-=
aNHp
Molecular weight of SOZ Molecular weight of NHp
t The effect of temperature on diffusivities is incIuded as a function of no reliable data are available and it Is believed that the effect of temperature on S/I is the greater. S/S, since
1.4 1.0 0.6 0.2 0.05
3.49 3.14 2.55 1.44 0.544
'
3.46 3.00 2.45 1.42 0.600
2.60 2.65 1.87 2.38 1.74 2.32 2.01 1.93 1.52 1.21 1.21 0.98 0.482 0.550 0.417 Grams KL Hour X sq. cm. X aram/cc. . 20.5 18.7 30.9 31 42.9 18.4 16.8 28.3 26 8 39.9 15.0 13.2 23.9 21.5 34.9 8.46 6.8 14.4 13.0 22.5 3.20 2.8 5.73 5.5 9.56 Ammonia YS. Gas Velocity and Temperature Grams K Hour X sq. cm. X atmosphere 2 92 2.54 2.63 2.24 2.88 2.27 1.96 2.05 1.74 2.20 1.17 1.42 1.31 1.28 1.45 0.52 0.56 0.46 0.49 0.59 0.15 0.18 0.17 0.17 0.18 Grams KL = Hour X sq. cm. X gram/cc. 6.94 1.88 1.83 3.58 3.70 5.39 1.44 1.30 2.76 2.80 3.62 0.80 1.85 1.80 0.95 1.52 0.30 0.79 0.70 0.39 0.46 0.10 0.24 0.21 0.12
1.97 1.75 1.50 1.05 0.500
43.7 38.2 32.0 21.3 9.5
-
1.4 1.0 0.6 0.2 0.05
1.4 1.0 0.6
0.2 0.06
2.26 1.82 1.15 0.43 0.15
6.80 5.27 3.40 1.30 0.42
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1230
Vol. 16, No. 12
k, = 290 MV"'*T-1.4
SUMMARY The values of the over-all absorption coefficients, K Oand KL, have been experimentally determined for sulfur dioxide and for ammonia over a temperature range of from 10" to 50" C., and over a gas velocity range of from 0.03 to 1.5 feet per second. These coefficients have been investigated by means of the two-film theory, as developed by Lewis and Whitman.
k, = 0.72 MVO.8 kL
= 5.1 X
kL
=
(s/~)"~
lo-' T4
37.5 ( s / z ) " ~
Agreement is excellent between the observed values of the over-all coefficients ( K , and K L ) and those calculated by substituting the values of k , and k L for the foregoing equations in the general equations:
K, =
1 ~
1
E
and
1
KL =
1 1
+ HKL
BIBLIOGRAPHY t Obmved 0
1-Sims, J . Chem. SOC.(London), 14, 1 (1862). 2-Lindner (1912) in Seidell's, "Solubilities of Inorganic and Organic Compounds," 2nd ed., 1919, p. 706. a-Perman, J . Chcm. SOC.(London), 89, 2, 1186 (1903). 4-Lewis and Whitman, I n d . Eng. Chem., p. 1215, current issue. 5-Naess and Moyes, M. I. T.Thesis, 1944, not yet published.
b'4lwS
Calculated Vakrc
.......... DISCUSSION 0
0.2
0.4
0.6
a6
1.0
1.2
1.4
The dependence of the individual film coefficients upon gas -velocity, temperature, and solute gas has been calculated. Gas velocity is without appreciable effect on the liquid film in this apparatus, while the gas film coefficient is proportional to the gas velocity to the 0.8 power. Absolute temperature has a vastly different effect upon the two individual film coefficients. The gas film coefficient decreases as the 1.4power of absolute temperature, whereas the liquid film coefficient increases as the fourth power of temperature. This wide differepce in temperature effect is explained on the basis of the dependence of the gas and liquid film coefficients upon the ratio of density (s) to viscosity (2) of the film fluid. This ratio increases with temperature for the liquid film, and decreases with temperature for the gas film. Both individual film coefficients are proportional to the two-thirds power of the ratio s / x . These data also support Lewis and Whitman's statement that the molecular diffusivities of all solutes are identical. The calculations are made on the assumption that this is true for the liquid film and the ratio of the calculated diffusion coefficients through the gas films, which should, according 3.0
Referring to the decrease in the gas film coefficient, k,, with increasing temperature, Mr. Wilson was surprised that the increase in specific diffusion rate with temperature did not cause k, to increase. Was the gas saturated with water vapor before entering the tower to avoid complications due to evaporation and resultant cooling effects? Professor Haslam replied that the gas was saturated prior to absorption. He then pointed out that the ratio of density to viscosity of the gas decreases from 1 to about 0.6 as the temperature increases from 0" to 65" C., and suggested that the effect of an increase in the specific rate of diffusion per unit thickness of gas film was evidently much less than the increase in thickness of gas film due to the effect of decreased density and increased viscosity.
Constant Water-Level Devices' By Robert E. Jefferson 70 LINWOODROAD,HANDSWORTH, BIRMINGHAM, ENGLAND
An apparatus similar' to one of those described by Wilde2 was made by the writer in 1905, but was not reliable as air collected at the top of the siphon. To overcome this difficulty the apparatus shown in Fig. 1 was finally devised.
WLCULATLD AND OBSERMD
1
2.0
i P
1.0
FIG.1
0 0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
to the theory, equal the ratio of the molecular weights,is within 16 per cent of agreement with this ratio. The molecular weight ratio is 3.76 and the specific diffusivity ratio 3.3. The general equations for the individual film coefficientsfor this tower are
FIG.2
A is the water supply, B the overflow. The flask C is filled with water a t the start. D is the bath. If the flask C is not desired, the modification shown in Fig. 2 may be substituted, but the apparatus will not function so long without attention. 1 Received 9
September 26, 1924.
THISJOURNAL, 16, 904 (1924).
