INDUSTRIAL AND ENGINEERING CHEMISTRY
December, 1924
1215
ABSORPTION SYMPOSIUM Papers presented before the Division of Industrial and Engineering Chemistry a t the 68th Meeting of the American Chemical Society, Ithaca, September 8 to 13, 1924
Principles of Gas Absorption By W. K.Lewis and W. G. Whitman MASSACHUSETTS I N S T I T U T E OF
TECHNOLOGY, CAMBRIDGE, ?.IASS
XGINEERIPU’G information on the operation of gas absorption equipment is a t present quite inadequate to permit proper estimates and designs for new operations. Further progress in this field can be made most effectively through SI study of the mechanism of absorption phenomena and of the factors which control them. When the basic principles have been definitely established, they can then be applied to specific problems by the engineer in the same manner as he now employs heat transfer coefficients, friction factors, and the like. The object of this paper is to outline certain of the more fundamental conceptions which have been developed from the available data and from the general laws of reactions between two phases. The basis of all processes involving the absorption or the escape of gas lies in the fact that a liquid-gas system which is not in equilibrium tends to approach equilibrium conditions. Thus, if the liquid is not saturated with gas under the existing conditions, absorption occurs, whereas if it is supersaturated the reverse is true. The escape of gas, as applied in this case, is merely negative absorption, and for simplicity the discussion will be confined to absorption alone. Equilibrium or saturation represents the ultimate state which the system tends to assume, and is the first of the primary characteristics of absorption phenomena to be considered. The other fundamental is the rate at which the system approaches equilibrium, and in many cases the rate is more important than the equilibrium itself. These two factors are not independent of each other and, in general, the rate is greater the further the system is from equilibrium.
E
NATURE OF ABSORPTION PROCESSES Existing data clearly indicate that in almost all the cases so far investigated the rate of absorption of a solute from a gas by a liquid is limited by processes of diffusion. Any other reactions which may take place are so rapid relative to the speed of diffusion that they have no appreciable effect upon the absorption rate. It is now becoming generally recognized that wherever a liquid and a gas come into contact there exists on the gas side of the interface a layer of gas in which motion by convection is slight compared to that in the main body of the gas, and that similarly on the liquid side of the interface there is a surface layer of liquid which is practically free from mixing by convection. This phenomenon is frequently expressed by assuming the existence of stationary films of gas and liquid respectively on the two sides of the interface. This phraseology will be employed because of its simplicity, although one should not infer that there is a sharp line of demarcation between stationary liquid or gas films on the surfaces and the major bodies of the fluids. In the main body of either liquid or gas, except under special conditions which will not be considered here, mixing by convection is so rapid that the concentration of solute in the
AT.
Y.,
fluid is essentially uniform a t all points. (The exception is illustrated in Becker’s paper, p. 1220 this issue, in experiments with quiescent liquids. Differences in gas or liquor concentration due to “channeling” in absorption apparatus are not involved in this concept.) On the other hand, the surface films are practically free from convection currents and consequently any transfer of solute through these films must be effected by the relatively slow process of diffusion. These films, therefore, offer the controlling resistances to transfer of a material from one phase to another. Diffusion through the gas film proceeds at a rate that is proportional to the difference between solute concentrations in the gas on the outside and inside of the gas film. (Resistance to diffusion due to a gas film is, of course, nonexistent in the special case where an absolutely pure gas is being absorbed. This problem is very rarely encountered in practice, however, since the presence of very small amounts of inert gas, which will concentrate a t the liquid surface, is sufficient to create an effective gas film.) Diffusion through the liquid film, on the other hand, is controlled by the difference between the concentration of solute in the liquid a t the interface and its concentration on the other side of the liquid film-i. e., in the main body of the liquid.’.* Since the surface films are very thin, the actual amount of solute contained in them a t any one time is usually negligible compared to the amount diffusing through them. It follows, therefore, that all the solute which passes through one film must also pass through the other, and the two films may be considered as two diffusional resistances in series. Under certain circumstances the importance of one of the films may be so much greater than that of the other that the second film may be neglected and the problem treated as if only one film existed. The concentration difference through either of these films represents the potential or driving force that is causing diffusion to take place. If the concentration differences be expressed in identical units-e. g., gram mols per liter-it is readily seen that the specific conductivity of the gas film will be much greater than that of the liquid. The only resistance encountered by the diffusing molecules is due to their collisions with the interfering molecules of the gas or liquid through which diffusion is taking place. Because of the greater density of the liquid the collisions in the liquid are much more frequent and the diffusional resistance is correspondingly greater than in the gas. However, the resistances to absorption are dependent also upon the film thicknesses. It is to be expected that the gas film would be somewhat thicker than the liquid, because under comparable conditions of disturbance the major factor in determining film thickness is probably the ratio of viscosity to density and this ratio is greater for gases than for liquids. Despite this fact, the greater specific conductivity of the gas film far more than overbalances the greater film thickness, so that the actual diffusional resistance encountered in the liquid film is much greater than that in the gas. The amount of solute absorbed per unit time by diffusion through the two films is
de.
(See table of nomencla-
* Numbers in text refer to bibliography a t end of article.
IND UXTRIAL AND ENGINEERING CHEMISTRY
1216
ture for resume of all symbols.) The amount of diffusion is obviously proportional to the surface of the interface, A , and it is therefore convenient to refer to the diffusional current density, A dW dThis e. quantity is equal to the diffusion coefficient per unit area ( k , for a gas film or k , for a liquid film) multiplied by the concentration difference available as a driving force-i. e.,
Vol. 16, No. 12
EFFECTOF SOLUBILITY
Certain simplifications of the general equation (1) are permissible when the conditions become such as to make one of the two films negligible in importance as compared with the other. Since these conditions are primarily determined by the solubility of the solute, it is desirable to consider as three separate cases the very soluble gases, the slightly soluble gases, and those of intermediate solubility. dW CASEI. VERYSOLUBLE GASES-The absorption of hydro= kL(Ci - CL) (1) Ade = K,(P, gen chloride in water is typical for the very soluble gases. where P = gas concentration In dilute solutions this gas is so soluble that even a 20 per C = liquid concentration cent solution (0.18 gram per cubic centimeter) exerts a and the subscripts g, i, and L refer respectively to conditions at the outside of the gas fiIm, at the interface, and at the inside of vapor pressure of hydrogen chloride of less than 0.2 mm. Hg (0.00026 atmosphere) at 30" C. In this case the solubility the liquid film. of the gas makes it possible to build up high concentration It is clear that the numerical values of the diffusion coeffi- gradients through the liquid film, although the concentration cients k , and kL will depend upon the units in which the gas in the gas at the interface may be very small. In other words, and liquor concentrations are expressed. The choice of these once it reaches the interface, the hydrogen chloride is rapidly units is purely arbitrary. I n this paper solute concentration sucked through the liquid film and the gaseous concentration in the gas is expressed as its partial pressure in fractions of Pi is maintained at a very low figure. The absorption rate for an atmosphere and concentration in the liquid as grams per this extreme case will be determined almost solely by the rate cubic centimeter because of the convenience of these units. of diffusion through the gas film under a difference in gaseous This makes the separate values of k , and kL of the same concentration substantially equal to P, since the value of order of magnitude for many cases and offers a good working Pi is negligibly small in comparison with P,. The general basis which will be employed throughout the paper. formula can therefore be simplified for very soluble gases to the form TABLSOF NOYRNCLATURB (4)
W = weight of solute, in grams 8 = time, in hours
E de
=
rate of absorption, in grams per hour
A = area of liquid-gas interface, in square centimeters
k, = diffusion coefficient through gas film kL = diffusion coefficient through liquid film P = concentration of solute in gas, in atmospheres C = concentration of solute in liquid, in grams per cubic centimeter Subscript g applies to conditions in main body of gas Subscript i applies t o conditions at liquid-gas interface
Subscript L applies to conditions in main body of liquid H = solubility coefficient = liquid concentration in grams per cubic centimeter divided by equilibrium gas concentration in atmospheres K O = over-all diffusion coefficient, based on gas concentration K L = over-all diffusion coefficient, based on liquid concentration M = molecular weight of solute
The data at present available indicate that at the true interface between liquid and gas the two phases are at substantial equilibrium (Pi in equilibrium with Ci), even though there may be rapid diffusion and therefore high concentration gradients through the films on the two sides of that interface. This fact puts us in a position to visualize clearly what takes place in an absorption process. (Figs. 1 and 2) Conditions at the outside of the gas film and at the inside of the liquor film are the same as those in the main bodies of gas and liquid, respectively. Conditions at the interface are determined by two factors: first, the equilibrium between gas and liquor concentrations; and second, the fact that all the solute diffusing through the gas film must also diffuse through the liquid film. Thus, this function being the solubility relationship; Equation 1 k,(P,
- Pi)
=
k ~ ( C i- CL)
and from
and the problem treated purely as a case of gas film diffusion. The same result can be reached by a more mathematical treatment. Consider the absorption of hydrogen chloride by water from an air mixture in which the partial pressure of hydrogen chloride is 0.1 atmosphere. The gas at this pressure would be in equilibrium with a saturated solution containing 0.39 gram hydrogen chloride per cubic ;'-b l centimeter at 30' C. The liquid concentration at the interface, Ci, would t h e r e f o r e be somewhere between the limits of zero (that of the main body of liquid) and 0.39 (that of a saturated solution). This L /ow0 concentration would be definitely fixed by Equations 2 and 3. For example, if the absorption c o n d i t i o n s were such that k , = kL, the equations would be satisfied by C< = 0.1 and Pr = 4-0 0.000021; if k o = 2 k ~ , I Ci = 0.2 and Pi = G#ES 0 H/Cn JOLVB/L/TY 0.00037; and if k , = fNc,l 0.5 k ~ Ci , = 0.05 and FIQ.1 Pi = 0.0000054. It will be observed that in the three examples the value of P I is so low compared to P, that it can be neglected in the expression, from (1)
(3)
If the values of k , and of k L are known, the values of Pr and Ci, the interfacial concentrations, are at once determined by these two considerations. If, for example, k , should be just equal to kL, (Pa - Pi) would have to equal (Cs - C,) to satisfy Equation 3.
and we may substitute the simpler form of Equation 4. Fig. 1 shows the film conditions diagrammatically, with the concentrations prevailing at the interface when k , = k ~ . The sudden rise in concentration at the interface is due to the
solubility characteristics of this solute-i. e., a low partial pressure in the gas is in equilibrium with a high liquid concentration because the solute has a great affinity for the water phase. It will be noted that the concentration gradient through the gas film is essentially the same as it would be if no liquid film existed. CASE11. GASESOF Low SoLuBILmY-with gases of low solubility the rate of absorption is low because only very small concentration differences can be established across the liquid film. The solute diffuses so slowly through the liquid film that only a small concentration difference is required across the gas film. As a result the liquid at the interface is substantially saturated with solute at the pressure P, and it is unnecessary to consider the gas film in the calculataons. This may be shown mathematically for the absorption of oxygen at 0.1 atmosphere by oxygen-free water at 30" C. Saturation under these conditions corresponds to only 0.0000037 gram per cubic centimeter, and the value of Ci must therefore be between this saturation value and the zero concentration of the main liquid. As in the earlier example, Ci is determined by Equations 2 and 3. If k , = k ~Ci, = 0.0000037 and PC= 0.0999963; if IC, = 2 k ~ CC , = 0.0000037 and Pi = 0.0999981; and if k , = 0.5 k t , Ci = 0.0000037 and Pi = 0.0999926. It is evident that in all cases Pi is essentially the same as Po-i. e., the interfacial conditions are practically the same as those existing in the main body of the gas. The value of Ci is therefore the same as that of a liquid saturated with oxygen at P,, and may be expressed as C,. It then becomes possible to express the rate equation as (5)
and eliminate any consideration of the gas film. The film conditions for oxygen are represented in Fig. 2, with the concentrations prevailing when k g = IC,. The sudden drop in concentration at the interface is due to the low solubility of this solute-i. e., its slight affinity for the water phase. It should be noted that the relative slopes of the gas and liquid gradients are the same as in Fig. 1,since p , - pi ( = 1 for both figures) Ci
-
w7
INDUSTRIAL AND ENGIiVEERIiVG CHEMISTRY
December, 1924
CL
kp
I n the diagram it is necessary to magnify the slopes of the gradients, since they would appear as horizontal lines if drawn to scale. CASE 111. GASESOF INTERMEDIATE SoLuBILITY-There are many important cases where the gas is too soluble to permit one to neglect the gas film (Equation 5 ) ) but is nevertheless not soluble enough to allow the liquid film to be disregarded (Equation 4). General Equation 1 must be used as the basis of calculation for such gases. Fortunately, however, an over-all coefficient, combining the two film coefficients, may be used whenever Henry's law holds over the concentration range in question. The concentration difference to be used with this over-all coefficient is the total difference between gas and liquid, expressed in comparable units. Thus, if gaseous concentration is expressed as partial pressure, Po, the corresponding liquid concentration must be given as the partial pressure, P,, in equilibrium with the liquid concentration, CL. Correspondingly, the gaseous concentrations must be expressed as C, (the liquid in equilibrium with Po)if the liquid concentration, CL,is sed.^.^.^ If the Henry's law relation is shown as C = HP
(6)
the absorption equation becomes (7)
or dW = K L ( G - CL) (8) Ade and the over-all coefficients, K gand KL,can be obtained from the individual film coefficients, k , and k ~ by , algebra, using Equations 1,6, w d 7 or 8. Thus , a
=
Hk&, Hk, k,
+
(9)
- HkLk L +"k k,
(10)
and KL =
Kg -
From the nature of the over-all coefficients it will be seen that the over-all coefficient KI, can never be greater than the liquid film coefficient k ~ and , similarly, that K, can never be greater than k,. C; 099996 It should be noted that theoretically the over-all *Equations 7 and 8 can be applied only to isothermal a b s o r p t i o n s , since the coefficient of Henry's law changes with temperature. I n practice, however, it is permissible to employ this method over narrow GrN L lQYl0 ranges of temperature. The t r e a t m e n t f o r soluble gases which do not approximatbly obey Henry's law over the range being studied, and y e t a r e n o t soluble enough to be treated under Case I, may bec,= 0 come quite complicated. CC = 0.0000037 I n such cases, one must Gases of Low Solubilify resort to the original (Oxygen) equation and work out Fro. 2 a method of integration which is determined by the character of the solubility curve. The absorption of hydrogen chloride in solutions of strong hydrochloric acid (which exert a vapor pressure of HC1) represents this type of problem. Fortunately, most industrial problems can be classified under one of the three simplified treatments.
-
0
OTHERVARIABLES The discussion has so far considered only the effect of solubility of the gas as affecting absorption rate per unit area. The other important valuables are the diffusion coefficients k , and k ~which , can be varied considerably by the character of the absorption process. Any factors which tend to cut down the thickness of the surface films should increase the coefficients and correspondingly speed up the absorption rate. Thus, agitation of the liquid increases diffusion through the liquid film, while higher gas velocities past the surface cause more rapid diffusionthrough the gas film. The effect of such factors will be somewhat dependent upon whether the process is controlled by gas film or liquid film diffusion. Thus, a change that decreased the thickness of the gas film but did not affectthe liquid film would increase the absorption of hydrogen chloride but would not affect the rate of oxygen absorption. Changes in temperature affect several factors, and it is necessary to distinguish clearly between the effect of temperature on the equilibrium and its effect on the coeffioients of
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1218
diffusion. Increase in temperature makes the gas less soluble, thus tending to lower the rate of absorption. The diffusion coefficients themselves may, however, be either raised or lowered by temperature, depending upon changes in film thickness and in specific diffusivity. Liquid film coefficients, l c ~ , rise rapidly with increasing temperature, both because of decreased film thickness due to lowered viscosity and because of greater diffusivities. On the other hand, Haslam, Hershey, and KeanKshow that the gas film coefficients, k,, decrease somewhat as the temperature rises because the ratio of density to viscosity for the gas decreases and therefore the gas film becomes thicker. Although little is known regarding the effect of temperature on specific diffusivities through gas films, it seems evident that this effect is less than that due to an increase in the film thickness. A type of apparatus in which gas bubbles up through a liquid would represent vitally different conditions from one where liquid drops are sprayed through a gas. I n the first instance, a rising gas bubble would continuously expose fresh liquid surface and the conductivity of the liquid film would be high, whereas the gas film would be relatively undisturbed. Such a device should therefore be most satisfactory for absorbing the less soluble gases where liquid film diffusion is controlling. In the other case, a falling drop might be expected to have only a very thin gas film but a fairly thick liquor film. Apparatus of a spray type might therefore be well suited for absorbing very soluble gases. From these suggestions it is evident that the ratio of film conductivities
(2)-. varies with the type of apparatus and ,
with the conditions of operation. It is therefore quite possible that the absorption of a gas of intermediate solubility might be controlled primarily by liquid film diffusion in one piece of equipment and by gas film diffusion in another. This point is illustrated later by the case of sulfur dioxide, which is almost entirely governed by the liquid film when passed over a free surface of liquid, but which is largely affected by the gas film when absorbed by bubbling through water. It is possible to predict comparative performances of different solutes in the same equipment on the basis of this general concept. Under similar operating conditions the effective film thicknesses will in most cases be independent of the solute that is being absorbed. It has been shown6 that for low concentrations of the diffusing component there is a definite relationship between the coefficient of diffusion of material through a gas film and the coefficient of diffusion of heat through the same film. In the units here employed this relationship requires that the gas film coefficient be proportional to the molecular weight of the diffusing substance. The total gas pressure and character of the inert gas are also involved in such a way that the coefficient varies inversely with the product of the molecular weight of the inert gas and the total pressure. This relationship is based upon a thermodynamic analysis, which is believed to be valid so long as the concentration of the diffusing component relative to that of the interfering gas is low. I n other words, we have dependable information as to the change of the gas film coefficient with changes in solute, inert gas, and total pressure. Furthermore, the influence of such other variables as velocity, temperature, and the like must be identical for different diffusing substances. Our knowledge as to liquid film coefficients is incomplete. It is known that as the molecular weight of the diffusing material becomes high its diffusivity decreases, but the data show clearly that the change in diffusivity is small compared with that in molecular weight. In the absence of more definite information the authors have elected to assume
Vol. 16, No. 12
that the liquid film coefficient follows the same rule as that just given for the gas film. In the units here employed this means that the liquid film coefficient, k ~ under , conditions of equal film thickness, is the same for all substances. This approximation is somewhat justified by the fact that diffusivity data given in the literature show a surprisingly small variation for various weak electrolytes and other aqueous solutions of low molecular weight.
CORRELATION OF DATA Certain of the published data on absorption rates illustrate the applicability of these principles and the effects of certain factors and types of apparatus. The experimental methods employed may be grouped in two general classes-those in which the gas was bubbled through the liquid, and those in which the gas was passed above the liquid surface. Since there is a marked difference in the absorption characteristics under these conditions, the discussion will consider each one separately. For purposes of comparison, wherever possible, results are expressed, not only as diffusion coefficients, but also (for liquid film processes) in terms of effectivefilm thicknesses. The calculation of fllm thickness is based on Hufner's data for the specific rate of diffusion of oxygen through water. Hufner's figures show that 0.067 gram of oxygen diffuse per hour through an area of 1 sq. cm. when the diffusion layer is 1 cm. thick and the concentration difference between the ends of this layer is 1 gram per cubic centimeter. The effective film thickness in centimeters for an absorption layer is then calculated by dividing Hufner's figure of 0.067 by the value of k ~ . GAS BUBBLEDTHROUGH LIQUID-Adeney and Becker' studied the absorption of oxygen, nitrogen, and air by water from gas bubbles. The solubilities of these gases are so low that they may be classed under Case I1 as examples of liquid film diffusion. The absorption rates in these experiments were very rapid, giving values of k~ as high as 60 (Equation 5 ) expressed as grams abaorbed per hour per square centimeter when the concentration difference is 1 gram per cubic centimeter. This k~ of 60, obtained a t 20' C. with an elongated bubble about 15 cm. long, offering 20.5 sq. cm. of surface area, corresponds to a film thickness of 0.0011 cm. The largest bubble used in their work had about three times the surface area of the one noted above and gave a coefficient of 43 corresponding to a film thickness of 0.0016 cm. The effect of increasing temperature was to increase the coefficient almost linearly owing to greater fluidity; thus the value of ki, doubled in going from 0" to 35" C. Ledig and Weaver,s absorbing a bubble of carbon dioxide in water, report results from which the calculated value of k~ is about 80, corresponding to a film 0.0008 cm. thick. This coefficient is greater than the maximum obtained by Adeney and Becker, but the carbon dioxide bubble was much smaller and was nearly spherical. As Adeney and Becker intimated, the coefficient should be greater under these conditions. Permang studied rate of escape by bubbling air through solutions of ammonia, chlorine, bromine, sulfur dioxide, and hydrogen sulfide in similar experiments. The data are too incomplete to permit a calculation of specific absorption rates, as the rate of air flow and size of bubbles were not recorded. His work, however, allows a comparison of rates between gases which vary widely in solubility. Perman's data are shown in Fig. 3, in which the logarithm of the liquor concentration is plotted against the time of bubbling air. The significance of these data may be analyzed by computing the over-all diffusion coefficients for the whole apparatus, AKL and A K , (Equations 8 and 7 ) . If the values of A K L should be constant for the five gases it would mean that the process is substantially liquid film diffusion alone for all of
INDUSTRIAL AND ENGINEERING CHEMISTRY
December, 1924
them and hence that the over-all coefficient KL is practically identical with the film coefficient kL. On the other hand, if the values of A K , were nearly constant, varying only with the molecular weight as previously noted, it would indicate that gas film diffusion controls in all five cases, the over-all coefficient Kg being equal t o the film coefficient k,. The values of AKL in the second column of Table I were determined directly from the slopes of Fig. 3, with the addiI
the most soluble gas, ammonia, the process is largely controlled by the gas film. The validity of this reasoning may be checked in a semiquantitative way by assuming that the chlorine and hydrogen sulfide diffusions are entirely liquid film ( A K , = Ak,) and that the ammonia diffusion is entirely gas film ( A K , = Ak,). The values of Ak, and Ak, may be taken in round numbers as 1170 and 2.1 X M , respectively, and used in Equation 10 to predict the over-all coefficients A K , for the other gases.
1
I
1219
1170 X 2.1M AkLkl7 = A K L = Hk, ko H X 1170 2.1M
+
+
The coefficients figured from this formula are given in the sixth column of Table I and show a reasonable agreement with the experimental values of A K , in the secohd column. GASPASSED OVER LIQUIDSURFACE-Adeney and Beckerlo studied the aeration of quiet columns of pure and salt water. They found coefficients, IC, for the relatively insoluble atmospheric gas of about 0.4for pure water and 0.5 for salt water a t 15" C., corresponding to film thicknesses of 0.17 and 0.13 cm., respectively. These rates obtained with quiet liquid surfaces are about one-hundredth of those realized with gas bubbles. When the liquid is stirred the rate, of course, is greatly increased. Thus Reeker" obtained coefficients of 5 a t 150 r. p. m. of his stirrer and of 15 at 1000 r. p. m. in another set of experiments with air. Bohr2studied both absorptionandescape of carbon dioxide by passing gas over a liquid surface, and the coefficients calculated from his data give a value of about 7.5 a t 250 r. p. m. He also found that the coefficients for absorption approximately checked those for escape. Davisx2 passed oxygen gas over water and obtained a value of k , of about 3.3 a t 60 r. p. m. The effect of velocity on the liquid film is shown in a qualitative way by the table of results by different investigators. TABLEI1 R . p . m. A t rest
60 150 250 1000
tioiial information that 50 cc. of liquid were employed in each experiment. The third column gives the solubility coefficient H under the experimental conditions. Values of A K , were calculated by multiplying A K , by H (Equation lo), and these values are divided by M in the fifth column to compensate for the effert of molecular weight on the gaseous coefficient. TABLEI
c 1 2
HzS Brz
so1
NH?
AKL 1340 1000 490 380 19
H
0 0096 0 0048 0 238 0 199 1 90
A Kg
12 9 4.8 117 76 36
A4
A K L calcd a s below
0 18 0 14 0 73 1 2 2.1
1090 1090 640 430 19
K, are conSince neither the values of A K , nor those of A 7 stant, it is evident that neither gas nor liquid film alone controls the diffusion for all five gases. The coefficients AKL decrease with increasing solubility, showing that the least soluble gases (chlorine and hydrogen sulfide) most nearly approach purely liquid film diffusion. For example, ammonia could escape much more rapidly than it actually does if only the liquid film had to be considered, since the value of AKL for ammonia would be a t least as high as 1000. The AK values of increase with solubility, indicating that with
xg
INVESTIGATOR Adeney and Becker Davis Becker Bohr Becker
Gas 03, 0 2 0 2 ,
Nz
02,
Nz
Nz
coz
kL 0.4 3.3 5 7.5 15
Film thickness Cm. 0.17 0.020 0.013 0.009 0.0045
It is somewhat fortuitous that the order of absorption rates so closely follows that of the rates of stirring when different types of vessel and stirrer were employed by the various experimenters. Becker's own data on rates of stirring, however, show in a more quantitative way that the coefficient increases almost proportionally to the 0.8 power of the velocity of rotation. Davis also absorbed more soluble gases under conditions similar to those of his oxygen runs. He found the following over-all rate coefficients KL and K O :
Oz in water SO2 in water
NHa in water HCI in water NHs in 2.3 N HCI
TABLE IIr KL 3.3 3.8 1.6 0.29
..
Ko 0.00014 0.47 1.5 4.0 2.4
Just as was shown with Perman's data, the values of K , decrease and those of K , increase with increasing solubility. Assuming that the absorption of ammonia in hydrochloric acid solution is controlled entirely by gaseous diffusion in this case ( K O= IC,), and that oxygen absorption is a purely liquid film phenomenon (KL = k, for OZ), one may calculate how rapidly sulfur dioxide, ammonia, and hydrogen chloride, which are between these two in solubility, should be absorbed by water. In a more complete discussion of this work, t o
1220
INDUSTRIAL A N D ENGINEERING CHEMISTRY
be given in a later paper, it is shown that the predicted absorption rates check the experimental rates within 15 per cent for all three gases. It is of interest to note that the ratio of liquid to gas film coefficients
2 is roughly about 15-30 to 1 in the case of gas
bubbles (estimated from Perman’s data) ; whereas the ratio
is only about 1to 1 for gas passed over a liquid surface (using Davis’ data). This difference can probably be attributed more to the exceedingly thin liquid films obtained around gas bubbles than to any marked change in gas film thickness.
CONCLUSIONS Rate of absorption is controlled by rate of diffusion of solute through the surfade films of gas and liquid a t the gasliquid boundary. The relative importance of the two films is determined primarily by the gas solubility and to a lesser degree by the conditions of operation. Gas bubbles give very thin liquid films and are therefore particularly adapted to the absorption of the less soluble ga$es. On the other hand, the rates for the more soluble gases are limited by slow diffusion through the gas, and this effect becomes increasingly evident with gases above sulfur dioxide in solubility. Absorption through free liquid surfaces is enormously increased by stirring the liquid. The same general considerations hold as for gas bubbles, but the liquid film is thicker relative to the gas flm. For this reason the effect of the gas film is less noticeable with sulfur dioxide, although with more soluble gases it comes into prominence.
BIBLIOGRAPHY ‘1-Whitman, Chem. Met. Eng., 29, 146 (1923). %Bohr, A n n . Phys. Chem., 68, 500 (1899). 3--lewis, J . Ind. Eng. Chem.. 8, 825 (1916). 4-Donnan and Masson, J SOC.Chem. I n d . , 89,236 (1920). 5--Haslam, Hershey, and Kean, I n d . Eng. Chem., 16, 1224 (1924). 6--lewis, Much. Eng.,44,445 (1922). 7-Adeneyand Becker, Phil. Mag.,88,317 (1919); S9,385 (1920). 8-Ledigand Weaver, J . A m . Chem. SOC.,46, 650 (1924). g-Perman, J . Chem. SOC.( L o n d o n ) , 67,868 (1895). 10-Adeneyand Becker, Phil. Mag., 42,87 (1921). 11-Becker, I b i d . , 46, 581 (1923). 12-Whitman and Davis, I n d . Eng. Chem., 16, 1233 (1924).
.......... DISCUSSION
In the discussion following this paper, R. E. Wilson suggested that the general absorption equation could be expressed using partial pressures multiplied by the solubility coefficient in place of liquid concentrations for diffusion through the liquid film. Dr. Lewis pointed out that, although this was quite permissible in those cases where the solubility followed Henry’s law, it did not really simplify the problem and could not be used when the solubility relationship was not linear. The chairman noted that this method of presentation waq employed in a later paper (by Professor Haslam) and that the choice between the two systems of expressing liquid concentration would be primarily determined by convenience in using the equations. Dr. Becker communicated $he following discussion: It should be pointed out that the film theory can apply only when the liquid is mixed and in fact that it will have its most precise application when the conditions on both sides of the interface are distinctly turbulent. When the gas and the liquid are not kept in motion other factors appear to become of greater importance and the values of the absorption rates are not then always proportional to the solubility of the gas. The conclusion that for the absorption of less soluble gases a bubble rising through the liquid is the most efficient device is t)orne out by my experiments on stirring. When the liquid was
Vol. 16, No. 12
stirred as rapidly as possible without causing splashing, the value of the rate of solution was only about half the value obtained when the absorption took place from a bubble rising through the liquid. A further important point is the form of the bubble, as this determines the area i t exposes for a given volume, and also the rapidity with which the film surroundingit is renewed as it rises in the liquid. From previous experiments i t has been found that the most effective form is that of a cylindrical bubble ascending a fairly narrow tube, as this gives the maximum of mixing of the liquid for a given speed of rise. The remarkable effect of very slow stirring of the liquid in reducing the effective thickness of the film is of great importance when circumstances are such that a relatively insoluble gas has to be absorbed without bubbling the gas through the liquid, as by this means it is possible to obtain a very large increase in the rate of solution with the expenditure of very little power. Thus a stirrer running a t only 60 r. p. m. increases the value of k~ for oxygen about twenty-five times, as compared with stationary water.
Mechanism of Absorption of Moderately Soluble Gases in Water . By H.G . Becker STANDARD OIL
COMPANY O F NEW JERSEY,
ELIZABETH,
16.J.
WHENTHE LIQUIDIs MIXED
vv
HEN a liquid and a moderately soluble gas are allowed to come in contact and the liquid is kept thoroughly mixed so that it may be regarded as of
uniform composition a t all points, the rate of solution of the gas varies directly as the degree of unsaturation of the liquid. This has been shown experimentally by following the course of the absorption of oxygen and nitrogen in air-free water by a method which allowed the liquid surface to remain unbroken although the liquid was vigorously mixed.’ The method used consisted in allowing a large, cylindrical bubble of the gas to pass up through a tube full of water which was initially airfree, and measuring the reduction in pressure which resulted in the bubble, due to the absorption of a portion of the gas. After each traverse of the bubble, the pressure could be restored to its original value by connecting the gas space with an air reservoir by means of a special tap. The process of absorption could thus be followed step by step from zero concentration of dissolved gas to saturation. The curves shown in Fig. 1 which are for oxygen, show the regular way in which the percentage saturation of the liquid with the gas increases with time, and it is found that when the rate of solution a t various points on the curve is plotted against the corresponding gas content of the liquid a straight line results. The rate of solution can therefore be expressed in the form
-- a dw dt
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Integrating, w
- bw
- a / b = ce-bt
For the experiments with air-free water, Whent = 0 , w = 0 , c = - a / b Therefore w = a / b (1 - e-b8) and when t = infinity, a / b = w = w8,the saturation value Hence, w = w, (1 e-bt) where w = weight of gas per cubic centimeter of liquid a t time, t w. = weight of gas per cubic centimeter of liquid a t equilibrium
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When the initial gas content wt is not zero, this expression becomes 1
Adeney and Becker, Phil. Mag., 88, 317 (191s); 89, 385 (1920).
