August, 1934
I N D U'ST R EA L A N D E N G I N E E R I N G C H E M I S T R Y
(4) Carles, Compt. rend., 144, 37,201 (1907). (5) Churchill, IXD. EXG.CHEM.,23, 996 (1931). (6) Dean, J. Am. Dental Assoc., 20, 319 (1933). (7) Eager, U . S. Public Health Rept., 16, 2576 (1901). (8) $airchild, J. Wash. Acad. Sci., 20,141 (1930). (9) Foster, IND.ESG. CHEM.,Anal. Ed., 5, 234 (1933). (10) Gautier and Clausmann, Compt. rend., 154, 1469, 1670, 1763 (1912); 158, 1389, 1631 (1914). (11) Kempf and McKay, U . S. Public Health Rept., 45, 2923 (1930). (12) McKav. Dental Cosmos. 68. 847 11925). i13j McKay; J. Am. Dental Assoc., 20,1137 (1933). (14) McKee, U. S. Patent 1,133,049(1915).
85 1
(15) Papish, IND. ENG.CHEM.,Anal. Ed., 2, 263 (1930). (16) Smith, M.C.,and Lantz, E. L., Ariz. Agr. Expt. Sta., Tech. Bull. 45 (1932). (17) Smith, M. C.,Lantz, E. L., and Smith, H. V., Ibid., 32 (1931). (18) Smith, M. C.,Lantz, E. L., and Smith, H. V., Science, 74, 244 (1931). (19) Smith, M. C.,and Smith, H. V., Ariz. Agr. Expt. Sta., Tech. Bull. 45 (1932). (20) Smith, 0.M.,and Dutcher, H. A., IND. ENG.CHEM.,Anal. Ed., 6. 61 11934). (21) Thompson and Taylor, Ibid., 5, 87 (1933) RECEIVED April 7, 1934.
Formation of Gas Hydrates in Natural Gas Transmission Lines E. G. HAMMERSCHMIDT, Texoma Natural Gas Company, Fritch, Texas
T
HE p r e s e n c e of w a t e r
temperatures above the normal Solid compounds, resembling snow or ice in f r e e z i n g p o i n t of water is a vapor in natural gas has appearance, are formed with methane, ethane, phenomenon that has not been always been a source of propane, and isobutane in the presence of water at generally recognized by the gas trouble to the n a t u r a l g a s inelecated pressures and temperatures. The meltindustry. dustry in the m e a s u r e m e n t ing point of these mixed hydrates in a natural gas S c h r o e d e r (7) has reviewed and transportation of the gas. the history of t h e d i s c o v e r y One of the chief difficulties has mixture depends upon the pressure and Daries of g a s hydrates: H u m p h r e y been the interruptions of serfrom about 34" F. at 110 pounds per square inch Davy, in 1810, discovered the vice due to the liquefaction and absolute to about 60' at 800 pounds. first known gas hydrate, a cryss u b s e q u e n t f r e e z i n g of t h e The formation of gas hydrates in natural gas talline c o m p o u n d f o r m e d b y water within the system. The pipe lines depends primarily upon the pressure, solid matter which collects in chlorine and water. Wroblewski, in 1882, reported a carbon the pipe line usually resembles temperature, and composition of the gas-water dioxide hydrate. Cailletet, in ordinary snow in appearance. vapor mixture. After these primary conditions 1878, reported a c e t y l e n e hyThe movement of thegas through are fuljilled, the formation of the hydrates is acthe pipe line tends to collect and drate and was the first to discelerated by high velocities of the gas stream, prescover that a sudden decrease in compress the snow a t low spots sure pulsations, or inoculation with a small cryspressure aided in the formauntil the line may become ention of these crystalline comtirely plugged. The snow is tal of the hydrate. honeycombed with small p o u n d s , W o e h l e r , i n 1840, At equilibrium conditions the hydrates, bechannels through which the gas reported hydrogen sulfide hycause of their lower vapor pressure, cause more passes before the flow is entirely drate. Villard and de Forcrand water to be removed from the vapor phase than in stopped. T h e c a u s e of t h i s have worked for m o r e t h a n the case of liquid water at the same temperature freezing has usually been attrib40 years on this class of comuted to subzero ground tempounds. Villard (6, 9) reported and pressure. peratures or to a combination of hydrates of methane, ethane, low temueratures with Dressure acetylene, and ethylene. fluctuations; the latter causes intermittent liquefaction and Schutzenberger reported the first double h y d r a t e h y d r o g e n vaporization of the more volatile hydrocarbons, such as pro- sulfide and carbon disulfide. Double hydrates are definite compounds having a definite melting point and are by no pane and the butanes. However, it was discovered, during a series of experiments means a mixture of the single hydrates, since the decompowhere natural gas and water vapor were compressed to 800 sition temperature of the double hydrate may be entirely pounds per square inch, that freezing occurred a t higher different from the decomposition temperature of either single temperatures than would ordinarily be expected. Later hydrate. De Forcrand characterized that product, which the same observation was made on a commercial scale where was obtained from hydrogen sulfide and aqueous alcohol the natural gas was compressed to about 600 pounds per (Woehler, 1840) as a mixed hydrate of hydrogen sulfide and square inch and cooled to 40" F. in a refrigeration unit (1, 2) alcohol, and in addition discovered the great family of "sulfwhich was designed to remove the excess moisture and oil hydrierten" hydrates whereby hydrogen sulfide could be from the compressed gas. united with a great number of halogen-substitution derivaThese observations suggested the possibility of another tives of the aliphatic series, in hydrate form. Cailletet and and probably more general cause of freezing in natural gas Bordet, in 1882, discovered the double hydrate of carbon systems than had heretofore been recognized. Therefore, dioxide and phosphine. De Forcrand and Sully Thomas, in the object of this investigation was to determine the causes 1897, found that acetylene and carbon tetrachloride form a of freezing a t elevated temperatures and pressures together double hydrate. They also reported double hydrates of with such other factors as might affect the operation of a acetylene, ethylene, sulfur dioxide, and carbon dioxide with natural gas transportation system. the following: ethylene chloride, ethylene bromide, methyl The combination of certain gases with water to form crys- iodide, methyl bromide, methylene chloride, and methylene talline compounds (hydrates) a t elevated pressures and a t iodide. Hempel and Seidel also reported similar compounds
INDUSTRIAL AND ENGINEERING
852
FIGURE 1. DIAGR.4M 1. 2. 3 4.
Gas inlet 40 feet of I/r-inch 0 . d. copper precooling coil Water sup ly reservoir Copper tug,, 1/16 inoh i. d. soldered t o inlet wate; valve at one end and discharging into Pyrex glasa tube at oppoaite end
OF
APPARATUS
5.
Pyrex glass tube, 5/32 inch i. d. and 13/39 inch 0. d. Constant-temperature baths Thermocouple junction Millivolt meter Drip Preasure gage Pressure-reducing valve Meter
6.
7. 8. 9. 10. 11. 12.
g., carbon dioxide and ether. A gas hydrate of ammonia also appears to exist. Methyl mercaptan forms a crystalline hydrate with water (8).
-e.
APPARATUS
A diagram of the experimental apparatus is shown in Figure 1: The compressed gas was passed through a length of copper tubing, 2, which was immersed in a water bath, 6, at the same temperature as the water bath which contained the Pyrex glass tube. This precooling bath allowed the passage of gas through the apparatus a t velocities which were comparable to actual operating conditions in pipe lines, and a t any desired temperatures. Water was injected from 3 by gravity flow through the internal copper tube, 4, at the inlet of the Pyrex glass tube, 5. The temperature of the gas was measured by means of an ironconstantan thermocouple, 7, which was inserted in the glass tube through a stuffing box arrangement. The gas was vented to atmospheric pressure at 11 through the positive meter, 12. The pressure was measured with a Bourdon tube gage, 10, which had been calibrated by means of a piston gage. The natural gas that was used for these experiments was taken directly from the pipe line after the gas had passed through (a) an oil absorption plant and ( b ) a refrigeration system where the gas was cooled to about 38' F. in order to remove the excess water and oil vapors. For pressures above 600 pounds per square inch, the gas was passed through a small motor-driven compressor, the discharge gas from this compressor being filtered through a plug of cotton in order to prevent the entrainment of lubricating oil. The composition of this pipe line gas does not vary greatly, as shown by frequent analyses over a 2-year period. Typical analyses are given in Table I. TABLEI. ANALYSESOF GASES GAS FROM
PIPELINE
NATURAL GAB Date samded Carbon dibxide Nitrogen residue Methane Ethane Propane Isobutane n-Butane Pentanes, plus Tota
PIPEL I N ~ SNOW
%
%
%
6-8-33
8-28-32 0.00 5.11 82.70
1-3-33
0.20 7.19 82.50 5.99 3.26 0.30 0.49 0.07
100.00
6.68 4.46 0.40
0.57 0.08 100.00
-
0.44 6.46 56.95 5.66
24.97
4.69 0.83
0.00
loo.o0
RELATIONSHIP BETWEEN PRESSURE AND MELTING POINT OF GAS HYDRATE The formation or decomposition of the natural gas hydrate could be observed in glass tube 5 (Figure 1). The appearance of the hydrate usually resembled ordinary snow although a t
CHEMISTRY
Vol. 26. No. 8
times transparent crystals resembling ice were separated, The transparent crystals formed only when there was no agitation of the melt. In order to observe the melting point of the hydrate at various pressures, the flow of gas through the tube was stopped, and the gas was vented from the system until the desired pressure was obtained. The temperature of the bath was then slowly increased until the hydrate began to melt. The melting point was fairly sharp (within 1" F.) and duplicate results could be obtained. The temperature as recorded by the thermocouple could be checked during the melting point determinations (i. e., when there was no gas flow through the glass tube) by means of a mercury thermometer placed in the bath, 6. The following relationship between pressure and melting point of the natural gas hydrate was determined from the experimental data (Figure 2): y g.9X0.286 where Y = temp., ' F. X = abs. pressure, lb./sq. in.
PRIMARY CAUSESOF HYDRATE FORMATION The formation of natural gas hydrates depends primarily upon the temperature, pressure, and composition of the gas. As shown by the melting point diagram (Figure 2), both high pressures and low temperatures are favorable to the formation of hydrates. In regard to the composition of the gas, water vapor is the only component that can be controlled on a practical basis. However, the removal of the moisture in the gas will of course eliminate the possibility of any hydrate formation. It is not necessary that the gas be entirely free from water vapor since these hydratks cannot form until the dew point of the gas is reached. As a matter of fact, if the partial pressure of the water vapor in the gas is less than the vapor pressure of the gas hydrate, the hydrate will lose water and decompose. This fact was demonstrated by passing some relatively dry gas over some gas hydrate in the glass tube (Figure I): The inlet gas had a dew point of approximately 30' F. at a pressure of 600 pounds per square inch. The temperature of the tube was maintained several degrees below the decomposition point of the hydrate or about 47' F. at 600 pounds per s q u a r e inch. The t e s t was continued for 5 days. A small amount of moisture + which was present in the glass tube with the hydrate was removedfirst. T h e n '? the h y d r a t e w a s $ slowly removed from the walls of the tube. The removal of the hydrate began at the inlet end of the tube, FIGURE2. MELTINGPOINTDIAGRAM and there was a sharp line of separation (between the dry tube and the hydrate-coated portion) which marked the progress of the evaporating hydrate along the tube as the gas was passed through.
*
S E C O ~ X D CAUSES ~ R Y O F HYDRATE FORMATION As stated above, a definite temperature, pressure, and composition are necessary before the gas hydrate is formed. However, even if these conditions are established, it is by no means certain that the hydrate will crystallize out. For example, there was no hydrate formationeduringa test which was conducted over a 40-hour period while a low flow of gas was passed through the glass tube which contained droplets
August, 1934
I N D U S T R I A L A N D E N G I N E E R I S G C H E JI I S T R Y
853
REFRIGERATION UNITS Propane ia employed as refrigerant i n t h e vertical oolumns; t h e horizontal tubes a r e h e a t exchangers.
of water. The temperature was maintained between 32" and 40" F. and the pressure was 600 pounds per square inch absolute; i. e., the conditions were such that the existence of a hydrate was entirely possible. There are, then, certain other secondary factors which influence the formation of hydrates. For example, it has been found that high velocities of the gas stream, pressure pulsations of the gas stream (due to compressors), or the introduction of a small crystal of the hydrate all hasten the formation of the hydrate. It has been demonstrated under actual operating conditions that the high velocity of the gas in the pipe line furnishes almost ideal conditions for the formation of hydrates, once the proper conditions of pressure, temperature, and composition are established. These secondary causes of hydrate formation appear to be adequately explained by the general behavior of crystal formation as described by Eucken ( 3 ) : "The formation of a crystal generally requires a certain arrangement and, above all, a definite adjustment of the molecules with respect to each other, the lack of which is characteristic of the liquid phase, and which can'not always be established a t once. In general, a certain time elapses before the essential number, of molecules come together into correct positions by purely accidental influences. Only after the formation of a small elementary crystal or crystallization nucleus, which then exercises a certain directing force on the neighboring liquid molecules and forces them to join together, does the crystallization proceed smoothly." From this, i t appears that hydrate formation should be promoted by any force which tends to mix or stir the melt, because any such agitation increases the probability of bringing the essential number of molecules into the correct position required for crystallization. Both high velocities and pressure pulsations impart a mixing action to the droplets of condensed moisture.
unit was maintained a t 38" F., the dew point of the exit gas was 25"; i. e., it was 13" lower than would ordinarily be expected. That this depression of the dew point was caused by the formation of the gas hydrate was proved by raising the temperature of the same unit from 38" to 60" F.-i. e., t o a temperature where the gas hydrate could not exist a t the operating pressure of 525 pounds per square inch (Figure 2 ) . In this case the dew point of the exit gas was 60" or exactly the same as the minimum temperature to which the unit had been cooled. The explanation of this apparently abnormal depression of the dew point lies in the fact that the vapor pressure of the gas hydrate is less than the vapor pressure of liquid water a t the same temperature. When the water vapor in the gas mixture is in equilibrium with the gas hydrates, the partial pressure of the water vapor is less t'han it would be if the water vapor were in equilibrium with liquid mater. In other words, less water in the vapor phase is required for equilibrium between hydrate and vapor than for equilibrium between liquid water and vapor. While this depression of den- point increases the efficiency of a refrigeration plant whose purpose it is to remove water vapor from the gas, it is apparent that the same procedure in the pipe line will hasten clogging. The fugacity of the natural gas hydrate may be calculated from the following observed data that were taken during the normal operation of the refrigeration plant (1): Slin. temp. t o which gas is cooled, ' F. Dew point of outlet gas-i. e., gas t h a t is in equilibrium with gas hydrate, F. Operating pressure, Ib./sq. in. abs.
38 25
523
/ The following relationship has been shown ( 5 ):
DEPRESSION OF DEWPOINT ASD C-ALCULATION OF FUGACITY P = total or operating pressure, lb./aq. in. abs. OF SATURAL Gas HYDRATE fh = fugacity of hydrate at pressure P , lb./sq. in. fw = fugacity of water at pressure P, lb./sq. in. The presence of the gas hydrates in pipe lines causes a v = molal vol. of liquid (mater) definite lowering of the dew point of the gas. This was p = normal vapor pressure of water, lb./sq. in. proved by making a series of dew point determinations upon From the above data the fugacity of the natural gas hythe ex$gas-from the refrigeration plant ( 2 ) . The results of this dew point survey are &own in Figure 3 and include the drate a t 38" F. is calculated to be fh = 0.0685 pound per time that the refrigeration unit was first placed in operation square inch. Likewise, the fugacity of mater a t the same until the accumulation of gas hydrate had caused sufficient temperature and under the same total gas pressure is fw = pressure drop across the unit to require a "defrosting" pe- 0.1157 pound per square inch. In Figure 4 the fugacity of water which is under a total riod, When the minimum temperature of the refrigeration
Vol. 26, No. 8
INDUSTRIAL AND ENGINEERING CHEMISTRY
854
Ethane and water formed a hydrate which melted at 57" F. and 460 pounds per square inch absolute, or 6" higher than the natural gas hydrate a t the same pressure. TABLE 11. COMPOSITION OF PUREHYDROCARBON GASES METHANE
7l-BUTANE
Methane Ethane f propane
99.9
0.1 1oo.00
IBOBUTANE Isobutane 100.00
ETHANE
%
% Isobutane n-Butane Isopentane
%
0.18 99.21 0.61
Methane Ethane Propane
1oo.00
1.0 97.0 __ 2.0
100.0
HYDROQEN SULFIDE Hydrogen sulfide 99.7 Water 0.3 100.0
PROPANE Ethane Trace Propane 100 00 Isobutane Ni 100.0
Propane was mixed with nitrogen gas in order that the total pressure on the apparatus could be increased to conditions approaching actual pipe line operation-. g., 600 pounds per square inch. The mixture of propane, nitrogen, and water formed a hydrate. The following melting point data were obtained: PRESSURE Lb./sq. in. 620 405 a
I
I III
/'
L
*A06
C\?
'
I
I":RoP,"bo'
NDS
PL I sq.afir
I1
2
dI
p r e s s u r e over the snow during the collection of the sample probably altered its composition somewhat, the results of the analysis of the evolved vapors gave . some interesting information regarding t h e c o m Dosition of the snow. The
gether with typical analyses of t h e original gas f r o m t h e p i p e line are shown in Table I. Both propane and isobutane are highly concentrated in the sample of pipe line snow. A study was next made with pure hydrocarbon gases and water. The composition of these gases is shown in Table 11. Methane and water formed a hydrate which melted a t 54.5' F. and 591 pounds per square inch absolute. This compares with 54.8" on the natural gas hydrate curve (Figure 2 ) . Solid line, fugacity of water at a total pressure of 500 pounds per square inch absolute Broken line, fugacity of natural gas hydrate
M. P. OF PROPANE HYDRATE F. 54.5 50.0
hf. P. OF NATURAL Gas HYDRATEa O
F.
55.5
49.2
From Figure 2.
The nitrogen gas was now purged from the system so that the propane hydrate was in equilibrium with pure propane vapor and water vapor. The melting point of the hydrate under these conditions was determined to be 45" F. a t 163 pounds per square inch absolute. (While the vapor pressure of propane a t 45" is approximately only 85 pounds per square inch, a total pressure of 163 pounds was possible because the inlet end of the glass tube was in communication with propane that was a t room temperature or about 90" F. This condition necessitated the presence of some liquid propane in the glass tube.) This melting point is 7" higher than a t the same pressure on the natural gas curve (Figure 2). This increase in melting point might be explained as follows: The hydrate exerts a definite vapor pressure. If an inert gas (nitrogen in this case) is mixed with the propane-water vapor over the hydrate, the same effect is produced as by reducing the pressure in a n ordinary distilling flask, and in this way the partial pressure of the hydrate vapor will be reduced so that the hydrate will melt a t a lower temperature than if the pure hydrate vapor is in contact with the solid hydrate. Isobutane and water were also mixed with nitrogen gas in the same manner as propane. It was more difficult to obtain a solid hydrate with isobutane than in the case of methane, ethane, or propane, The following melting point data were obtained: , PRESSURE L b . / s q . in. 833 617
bf. P . O F ISOBUTANE HYDRATE
F. 58
53.3
M. P . O F NATCRAL GAS HYDRATE
F. 60 55.5
The difficulty in the formation of the isobutane hydrate in this case may be due to the relatively low vapor pressure of isobutane. For example, a t 40" F. the vapor pressure of isobutane is roughly one-third as great as propane. Hence at any constant total pressure of a gaseous mixture in which propane and isobutane are constituents, the partial pressure of propane will be about three times greater than isobutanei. e., the concentration of propane will be approximately three times greater than isobutane, provided there is excess liquid hydrocarbon in contact with the gaseous mixture. Therefore, the probability of bringing the essential number of
August, 1934
f
INDUSTRIAL AND ENGINEERING CHEMISTRY
855
n=- Q ' - Q molecules together into the correct position required for or (3) 1.430 crvstallization of the +DroDane hydrate would be about three where times as great as in the case of isobutane. &' = heat of formation of hydrate (gaseous mol. and liquid Normal butane and water were mixed with nitrogen in water), Cal. the same manner as with propane and isobutane. A hydrate Q = heat of formation of hydrate (gaseous mol. and solid water), Cal. could not be obtained with normal butane, although the total n = no. of mol. of pressure was varied water in hyf r o m 500 t o 800 drat@ p o u n d s p e r square 1.430 = heat of fusion of 1 mol. of inch a t 32" F. and a t liquid water, various velocities of Cal. the gas stream. The T' = m. p. of hyreason offered for the drate at atm. difficulty with which pressure, absolute the isobutane hydrate T = normal b. p., w a s f o r m e d would ' absolute also explain the nonP , = v a p o r pressure at T I formation of a normal P, = v a p o r p r e s butane hydrate. sure at T , Likewise i t might be reasonably assumed From T r o u t o n ' s t h a t a l l heavier hyratio : d r o c a r b o n s of t h e REFRIGERATION P L 4 Y T WITH CONTROL BUILDING I N FOREGROUND paraffin series do not Q / T ' = K = 0.030 Gasoline absorbing columns in right rear. form hydrates, at (4) least under the conditions to which they would be subjected in pipe line operations. For a value of K = 0.030, de Forcrand claimed an accuracy Ntrogen and water, or oxygen gas and water, did not form of 1/15. If the observed points on the melting point-pressure diaa hydrate a t pressures as high as 900 pounds per square inch gram (Figure 2) are plotted on logarithmic paper, a straight and temperatures as low as 32' F. line results. If lines are then drawn through the experimenTABLE 111. DATAON GASHYDRATES tally determined points for methane, ethane, and propane, CALCD. PROBABLE T T' Q' Q FORMULA F~~~~~~~ parallel to the curve for natural gas hydrate and extended F R O M D E F O R C R 4 N D (7) to a Dressure of one atmomhere. the value of T' mav be read A CHI 109 86 244 **9.2 i;:: ;;1$ c~: direc'tly and the value of calculated from Equatiln 4. COS 194.8 251.8 16.16 7.55 6 6 &' may be calculated from known vapor pressure data by 6 6 16.29 7.61 185 253.7 NrO of the Clausius-Clapeyron equation which has been means 5.7 15.92 7.73 188 257.6 CzH2 6$ C2H6 185 257.2 17.71 7.71 I integrated by Findlay (4) as follows:
+'
169 188 211 C P H O F 241 SO? 263 CHjCl 250 CL 238.4 Br? 332 HrSe 231 CzHi PHI
HnS
CHI CrHs C3Hs
... ...
...
259.6 266.6 273.35 276.7 280 250.5 282.6 >273 28 1
18.34 16.44 16.34 20.12 19.83 18.83 18.36
7.76 8.00
16.82
8.'43
1
8.20 8.30 8.40 8.41
8.148
7.4 5.: 5. 8.27 #
s, . 2
6.91 10 5.87
6
6 8 8 7 7
lo 6
CALCULATED F R O M D A T A O F THIS R E P O R T
265.6 266.9 267.7
16.73 16.92 18.19
7.97 8.01 8.03
6.1 6.2 7.1
6 6 7
When hydrogen sulfide and mater were admitted to the apparatus, the glass tube immediately became fouled, and it was impossible to determine visually whether a solid had formed. However a sudden pressure drop of 100 pounds per square inch across the apparatus was fairly conclusive evidence that a hydrate had formed. COMPLEXITY O F THE GAS H Y D R A T E LIOLECULE
Wroblewski ( 7 ) determined the complexity of a number of gas hydrates in an indirect manner by meansofgasvolumetric measurements where he introduced a small chop of water of known weight into an eudiometer tube which contained the compressed gas a t a definite pressure. After reading the volume of the eudiometer tube, the small drop of water was converted to the gas hydrate in which case the same volume of gas exerted a smaller pressure. While this investigation did not include a study of the composition of gas hydrates, some data mere obtained that permit the calculation of several of them according to the method employed by de Forcrand (7') who obtained the results, shown in Table 111, by means of the following relationships: (2'
=
Q
+ 1.430 n
(2)
Q' = 4.572 log
P,(Ti T d Pl(T, - TI)
(5)
Values of Q' were calculated from data in the International Critical Tables. The results of these calculations are shown in Table I11 where it may be seen that the formula for methane hydrate is the same as that calculated bv de Forcrand while ethane hydrate contains one less molecule of water. Since propane hydrate has apparently never been reported, no comparisons can be made in this case. Cnfortunately the melting point data for isobutane hydrate cannot be used in the above manner because it was mixed with an indefinite quantity of nitrogen gas prior to the formation of the hvdrate.
LITERATURE CITED ( 1 ) Anonymous, Oil Gas J . , 30, S o . 19, 34, 8:3 (1931).
(2) Burnham. C. H. M.. paper read hefore meeting of Am. Gas Assoc., May IO, 1932. (3) Eucken, "Fundamentals of Physical Che,mistry," McGraw-Hill Book Co., S . T., 1925. (43 Findlay, Alexander, "The Phase Rule and Its Applications," Longmans, Green &- C o . , London and h-.Y . , 1931. ( 5 ) Hamnierschmidt, E. G., Western Gas, 9, S o . 12, 9 (1933). (6) International Critical Tables. Vol. VII, p. 244. McGraw-Hill Book Co., X , T., 1926. (7) Schroeder, Ti., in Ahren's "Sammlung chemischer und chemischtechnischer YortrLiige," pp. 21-71 (1926-28). (8) Thorpe, Edward, Dictionary of Applied Chemistry, Vol. IV, p. 316, Longmans, Green & Co., London and iY.Y., 1928. (9) Kllard, C o m p t . rend., 107, 395-7 (1888). RECEIVED March 15, 1934.
