INDUSTRIAL AND ENGINEERIIVG CHEMISTRY
548
Vol. 23, No. 5
Solubilities of Gases in Liquids at High Pressure' Per K. Frolich,* E. J. Tauch, J. J. Hogan, and A. A. Peer DEPARTMENT O F CHSMlCAL ENGINEERING. MASSACHUSBTTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE. MASS.
HE application of high pressures to industrial processes
T
has led to engineering operations that frequently require a knowledge of solubilities of gases in liquids a t pressures higher than those for which such data ordinarily are available. Examples of this type are the separation of gases by preferential solution in a suitable scrubber liquid and the condensation of vapors in the presence of non-condensable gases. Occasionally also the rate of a chemical reaction in the liquid phase is controlled by the solubility of a gaseous reactant.
,
200
I
Experimental Procedure &.lost of the solubilities were determined by saturating the liquid with gas at suitable intervals of pressure and measuring the ratio of solute to solvent in a sample drawn off for analysis. To this end a small amount of solvent was introduced into an evacuated steel cylinder of 2 liters capacity. The gas was then forced in a t the highest pressure available and the cylinder agitated in a water bath maintained a t 25' C. After the pressure had become constant, the cylinder was taken from the bath and inverted in a vertical position for withdrawal of a sample of the solution. The liquid and the gas separating from it on release of the pressure were collected over mercury in one of three burets, so designed that the volumes could be measured with the same degree of accuracy a t any ratio of gas to liquid.
3 - I=-PROPANOL
9
e
I4O
IPO
II00
t
3 r3 b
BO
3
60
Since these data did not, permit of any generalization as to the behavior of other combinations of gases and liquids, a systematic study of the subject was undertaken. This work involved solubility determinations for a number of the common industrial gases in a variety of solvents, covering a wide range of pressure but limited to room temperature. Preliminary experiments by Simard and Sturznickle (7) on methane, nitrogen, and hydrogen in water and a series of alcohols gave results which showed in a qualitative way that the solubilities in such systems came close to being straightline functions of pressure.
40
20
0 0
20
40
60 80 ABSOLUTE PFZSSURC IN
100 I20 ATYOSPHERES
140
Figure 1-Solubility of Methane a t 25' C. Within experimental error the curve for isopropanol may also be considered as representing solubilities in methanol, normal propanol, isobutanol, and normal butanol.
The determinations of Larson and Black (3)on nitrogen and hydrogen in liquid ammonia, and those of Wroblewski (9), Sander (4), and Hachnel (5) on carbon dioxide in water and some organic solvents seem to be the only data on gas solubilities at real high pressures available in the literature. Finlayson @), in attempting to develop a method of separating oxygen and nitrogen in air, studied the behavior of these gases toward various solvents a t pressures not exceeding 160 pounds per square inch (10.9 atm.); and the solubilities of air and natural gas in kerosene, mineral seal oil, and various crudes have been determined by Dow and Calkin (1) a t pressures up to 350 pounds per square inch (23.8 atm.). Larson and Black's data show that the amount of nitrogen and hydrogen dissolved in liquid ammonia is roughly proportional to the pressure up to 150 atmospheres. I n the case of carbon dioxide, however, the linear relationship breaks down after the pressure has exceeded a few atmospheres, and thereafter the solubility is lower or higher than that calculated from the atmospheric data according to the solvent used (4)< 1 Received March 6, 1931. Presented before the Division of Industrial and Engineering Chemistry at the Slst Meeting of the American Chemical Society, Indianapolis, Ind., March 30 to April 3, 1931. * Present address, Standard Development Co., Elizabeth, N. J.
ABSOLUTE
PRESWRC IN
ATMOSPHERES
Figure 2-Solubility of Hydrogen a t 25' C. Wjthin experimental error the curve for isopropanol may also be considered as representing the solubilities in ethanol, normal propanol, isobutanol, normal butanol. and benzene.
When the solvent was liquid a t room temperature, as was usually the case, the two volumes were read directly and corrections made for the vapor pressure of the liquid and the atmospheric solubility of the gas. Since the liquid was atomized by the sudden release in pressure, complete separation of solute from solvent occurred without any sign of supersaturation, and it was only necessary to wait for drainage of the liquid before the volumes could be read. If the whole sample was in the gas phase, it was analyzed in an
INDUSTRIAL AND ENGINEERING CHEMISTRY
May, 1931
-PROPANE
LIQUID
Pressure range
0-7
Carbon tetrachloride
Pressure range
Equation
ALm.
Gas oil
PROPYLENE
y = 1 9 . 1 (z)
I
0-5
Equation
Y
=
HYDROGEN SULFIDE sure range
1 2 . 1 (z)
C-15
Equation
Y
a
4.17 (I -k 1 . 7 ) ~
Ethanol Heavy naphtha Water Formic acid Pentane
-
3-7
I
Y
=
15.1
(X
f 0.7)
0-9.0 Y = 5 . 5 ( x )
~~
1 1
54 9
ET€iYLENE Pressure range
Equation
-
Y =
0-32 32-60 0-33 33-60
Y 5 7 . 8 (x) y = 35.1 (x
y
2.84 (x) 1 2 . 1 (x 30)
-
-
0-70
y
-
0-70
y
0-70 0-70
y = 0.028 (x)
24.5) 2 . 8 (x) y 5 . 5 ( X - 15.6) y = 5.0 (x)
Y
Equation
Atm.
0-41 t:zO
0-6
OXYGEN Pressure range
0.154 ( x ) 0.31 ( x )
5 5
I
0-100
y = 0.047 x ) Y = 0 576ix)
Volume of gas at 25' C. and 1 atmosphere per vo'ume of liquid. x = Absolute pressure in atmospheres.
y
ordinary gas-analysis apparatus, or the solvent was frozen out with carbon dioxide snow. I n working with liquids of high vapor pressure, such as the lighter hydrocarbons, it was necessary also to determine the composition of the gas phase in the high-pressure cylinder. With less volatile solvents, however, the pressure of the vapor was usually an insignificant part of the total pressure in the cylinder. The sample taken for analysis was so small that the pressure drop in the steel cylinder was negligible. After che& runs had been made at one pressure, gas was bled from thae steel cylinder and further determinations were made at successively lower points. To make sure that no error due to supersaturat,ion in going from a higher to a lower pressure was introduced, the procedure was reversed in several experiments, but without any difference in the results. Another method, involving measurement of the gas dissolved in a measured amount of liquid by the pressure drop in a previously calibrated reservoir, was used successfully in checking some high solubilities determined by the other procedure. A carefully calibrated Bourdon gage was used for measuring all pressures.
Figure 3--Solubility of Nitrogen at 25' C . Within experimental ?mor the curve for isopropanol may also be considered as representing the solubilities in methanol, normal propanol, isobutanol, normal butanol, and benzene.
Inasmuch as the work was undertaken to obtain data for engineering use, a somewhat low accuracy, compared with that of ordinary physical measurements, was tolerated in order to simplify the procedure. Although the individual determinations were as a rule checked within 2 per cent, it
is believed that the total error of this method is such that the results should not be considered accurate to better than + 5 per cent. The materials used for the solubility measurements were in general of the highest purity available. The heavy naphtha had a specific gravity of 0.8003 with a vapor pressure of 80 mm. a t 25' C. For the gas oil the corresponding figu$&i were 0.8319 and 2 mm. The other hydrocarbons were from 98 to 99 per cent pure. Discussion of Results
The majority of solubilities determined were for hydrogen, nitrogen, and methane in various alcohols and hydrocarbons as well as water. Except for some of the alcohol curves, which fell so close together that it was impossible to include them all in the plots, Figures 1 to 3 give these results expressed as volumes of gas dissolved per volume of liquid as a function of absolute pressure. The gas volumes are measured a t 25" C. and 1 atmosphere. Within the experimental error the curves for isopropanol may be considered representative of a group of alcohols, as indicated under the individual diagrams. The solubilities of hydrogen and nitrogen in benzene also coincide with the isopropanol curves. The solubilities are not strictly linear functions of pressure, although the deviations from a straight line are hardly noticeable for hydrogen in any of the liquids studied or for nitrogen in the solvents other than heavy naphtha and gas oil. There is a general tendency, however, for the hydrogen and nitrogen solubilities to increase less rapidly with pressure than called for by a straight-line relationship. On methane pressure has the opposite effect, as shown by the curves in Figure 1. That this trend in curvature is due in part to deviations from the perfect gas law is brought out by Figure 4. Here the solubilities of the three gases in isopropanol are plotted against the pressure which the solute would have exerted had it obeyed the perfect gas law, and the resulting straight lines show that the solubilities in question follow Henry's law within the whole pressure range studied. This correction is not sufficient, however, to eliminate the more marked curvature in the case of some of the hydrocarbons. Regardless of whether the failure to straighten some of the curves is due to factors other than experimental errors, it is apparent that all the data in Figures 1 to 3 might for practical purposes have been obtained from the corresponding atmospheric solubilities. This is illustrated by the following examples chosen at random: Solubility of methane in methanol at 50 atm. abs. (49 atm. gage) : (2)
(3)
. . ..
. . . .. . . . .. . ..... .. ..
.. . ..... 24.8 Estimated from solubility at atmospheric pressure: 0.438 (6) X 50 = . . . . , .. .... . . . .... 22.0 Estimated from atmospheric solubility with correction of pressure: 23.7 Corrected pressure = 54 atm. ( 8 ) 0.438 X 54 =
(1) Read from Figure 1 (curve 3) the value i s . .
. . . .. . . . . . . .
.
INDUSTRIAL AND ENGINEERING CHEMISTRY
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The corresponding values for hydrogen in benzene a t 100 atm. abs. are: (1) 7 . 3
(2)
7.6
7.6
(3)
For nitrogen in gas oil at 100 atm. abs. the following solubilities
result:
(1) 9 . 7 351
,
(2)
I
I
11.3 I
(3) 11.1 I
I
I
1
,
i
i 30
b I - METHANE 2-NITROGEN 3-HYOROGEN
!
Vol. 23, No. 5
when there is a tendency for the solute to combine chemically with the solvent. An example is carbon dioxide dissolved in water. According to Hachnel’s data (6),represented by the solid line in Figure 5, the linear function breaks down a t about 5 atmospheres, and from then on the solubility increases less and less rapidly with rising pressure. Correcting the pressure of the carbon dioxide for its deviation from the perfect-gas law only increases the curvature, as shown by the dotted line. On the other hand, carbon dioxide behaves normally in many organic solvents. Thus, the data given by Sander (4) for carbon dioxide in ethanol, propanol, benzene, and some derivatives of benzene obey Henry’s law, since the solubility curves become straight lines when the pressure correction is applied. Figure 6 gives further aid to the estimation of solubilities in the hydrocarbons. Here the data for methane and hydrogen are plotted as functions of the hydrogen-carbon ratio of the solvent, and it will be noted that all the aliphatic hydrocarbons, as well as cyclohexane, fall on smooth curves. I n the alcohols, however, neither the num,20 ber nor the arrangement of the c a r b o n atoms affects the solv e n t power to any ~ I o Q appreciable e x t e n t . H y d r o g e n is somewhat more soluble in methanol than in the 3 o t h e r alcohols, a s would be e x p e c t e d $ 40 from the known soh- ’ bilities a t atmospheric pressure. The lower curves for n i t r o g e n RATIO A T W S H TO ATOMS C =VENT and e ane in Figure 6-Effect of Hydrogen-Carbon e t h a n o l m a y have Ratio of Solvent on Solubilities of Hydrobeen due to the pres- gen and Methane 140
AasoLurE
PRESSURE IN ATMOSPHERES
of Pressure Correction on Solubility Curves f o r Isopropanol
Figure 4-Effect
Judging from these examples, high-pressure solubilities of the three permanent gases, hydrogen, nitrogen, and methane, in other liquids may be estimated with engineering accuracy from Henry’s law. I n other words, the solubilities of these gases in any solvent may be predicted over a wide range of pressure from one experimentally determined point. That a knowledge of the solubility a t atmospheric pressure serves this purpose is borne out by the illustrations given above. This may be expressed by the relation v = k p , where u, the volume of gas dissolved, is measured a t atmospheric temperature and pressure. If p is the pressure in atmospheres absolute, k becomes equal to the atmospheric solubility. To obtain better accuracy, p should be corrected for the deviation from the perfect gas law.
)N
The hydrogen data are for 70 atm. abs. while
Of Some wat&r, methane solubilities are plotted for 48 atm. abs. since the solubilities should be in line with the other alcohols judged by the atmospheric values.
Conclusions
O
4
8 12 10 20 24 ABSOLUTE PRESSURE IN ATMOSPHERLS
1
I
28
32
Figure %Effect of Pressure Correction on Solubility Curve for Carbon Dioxide in Water
The data for oxygen in five solvents, given in the last two columns of Table I, show that this gas belongs to the same class as hydrogen, nitrogen, and methane. However, in dealing with gases of the vapor type, the linear solubility relationship holds only over a limited pressure range. This is illustrated by the data in Table I for propane, propylene, hydrogen sulfide, and ethylene. The approximate vapor pressures of these materials at 25” C. are, respectively, 10, 11, 20, and 65 atmospheres, and it will be noted that their aolubilities in various liquids obey Henry’s law only up to about one-half to two-thirds of the saturation point. The behavior of ethane is similar t o that of ethylene, as shown by qualitative experiments not recorded in the table. As would be expected, Henry‘s law cannot be applied
The solubility data presented here show that if a gas does not form a chemical compound with the solvent, i t follows Henry’s law over a wide pressure range within the limits of error allowed in engineering calculations. The solubilities of hydrogen, nitrogen, oxygen, and methane may for practical purposes be considered linear functions of the recorded absolute pressures, the validity of this assumption being largely dependent upon the extent to which the solute obeys the perfect gas law. However, the straight-line relationship still holds a t real high pressures provided corrections are applied for the deviations from the gas law. A practical rule is that the solubility of a gas of the vapor type is a linear function of pressure up to one-half t o two-thirds of its saturation point a t that temperature. Literature Cited (1) Dow and Calkin, Bur. Mines, Repts. of Investigations 2732 (Feb., 1926). (2) Finlayson, Trans. I n s f . Chem. Eng. (British), 1, 29 (1923). (3) Larson and Black, IND. ENG.CHEM.,17, 715 (1925). (4) Sander, Z . physik. Chem., 78, 513 (1911). ( 5 ) Seidell, “Solubilities,” p. 432, Van Nostrand, 1928. (6) Seidell, I b i d . , p. 1155. (7) Simard and Sturznickle, Undergraduate Thesis, M. I. T. Library, 1928. (8) Standards, Bur., Circ. 279, 18 (Dec., 1925). (9) Wroblewski, A n n . 9hys. chim., 18, 290 (1883).
