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ON THESOLUBILITIES AND

RATES OF SOLUTION OF

GASES I N LIQUID METHANE

...

NATIONALAERONAUTICSAND SPACE A D M I N I S T R A T I O N W A S H I N G T O N , D. C. 0 AUGUST 1 9 6 8

TECH LIBRARY KAFB.NU

ON THE SOLUBILITIES AND RATES OF SOLUTION

O F GASES IN LIQUID METHANE

By Robert R. Hibbard and Albert Evans, Jr.

Lewis Research Center

Cleveland, Ohio

NATIONAL AERONAUTICS ANDSPACE ADMINISTRATION

I

For sole by the Clearinghouse for Federal Scientific and Technicol Information Springfield, Virginia 22151 - CFSTI price $3.

O N THE SOLUBILITIES AND RATES OF SOLUTION OF GASES IN LIQUID METHANE

by Robert R. HibbardandAlbert Evans, Jr.

Lewis Research Center

SUMMARY

Hildebrand’s methods were modified and used to estimate the solubilities of oxygen, argon, carbon monoxide, nitrogen, neon,hydrogen,andheliuminliquidmethane (or liquefied natural gas) at temperatures between 90 and 112 K. This is the temperature range of interest in the possible use of liquid methane in aircraft. Curves are presented which permit the easy calculation of the equilibrium solubilities of these gases. Solubili- ties for the seven gases decrease in the order in which they are listed above. It is prob- able that the solubilities of oxygen, argon, carbon monoxide, nitrogen, and air in liquid methane are too high to permit their use as a pressurant in aircraft fuel systems. It was also found by experiment that the rates of solution of gases in liquefied natural gas are very high. This is confirmed by similar experiments in the literature and by considerations based on kinetic theory. Therefore, it appears that only neon, hydrogen, and helium can be used as pressur- ants if liquefied natural gas is to be used in aircraft unless the gases andliquid fuel are separated by a barrier.

INTRODUCTION

Liquid methane promises to give higher performance in supersonic aircraft than can be obtained with conventional liquid hydrocarbon fuels (ref. 1). This is because liquid methane has a much greater capacity as a heat sink and has a higher heat of combustion than the conventional fuels. Liquid methane also promises lower, direct operating costs per seat mile and greater payloads in commercial supersonic transport aircraft because of this better performance and because, as liquefied natural gas, it may cost less per Btu (ref. 2). However, one of the technical problems that must be resolved before liquid methane or liquefied natural gas finds widespread use inaircraft is that of boiloff losses during climb. In a typical supersonic transport mission these losses may amount to 9.6 percent

of the total fuel load unless pumps are installed to recover the boiloff (ref. 2). Even with these pumps some 2000 pounds, or over 1 percent of the fuel load, will be lost during that portion of the climb when the external pressure is being most rapidly reduced (ref. 2). The loss is prohibitive without boiloff recovery pumps and is undesirable even with pumps. Besides, these pumps represent a weight penalty and added cost and complexity. Therefore, it would be desirable to eliminate both pumps and boiloff losses through changes in the fuel system or fuel. This can be done, in theory, by making the fuel tanks strong enough to withstand the difference between the vapor pressure of the fuel as loaded (1 atm) and the ambient pressure at cruise altitude (about 0.04 atm). Such tanks may be practical although they will be more complex and heavier than tanks that do not have to withstand this pressure difference (ref. 3). Alternately, the fuel could be cooled to below its normal (1 atm) boiling temperature and thereby reduce the vapor pressure to a level that could be contained in conventional (although insulated) tanks at cruise ambient pres- snres. Subcooling the fuel presents a new problem. The vapor pressure will be lower than the external pressure when the aircraft is on the ground or at low altitudes and the tanks may collapse unless a pressurant gas is used. This pressurant is air in normal fuel systems but preliminary estimates indicated that air is quite soluble in subcooled meth- ane. Air might dissolve to the extent of about 10 weight percent and this is not acceptable because of the added weight (ref. 3). There are other approaches to this gas solubility problem but none are ideal. The use of less soluble gases or the separation of gas and fuel by some sort of barrier have been considered (ref. 3). However, the above estimated solubility of air in liquid methane is only an estimate, and, in general, little has been published on the solubilities of gases in this liquid. There are some data, to be discussed later, on the solubilities of helium, hydrogen, and nitro- gen in liquid methane as the results from phase studies at high pressure. W e know of no published data on some of the other gases that might be considered, and none of the solu- bility data are for the conditions contemplated in the use of methane in aircraft. There is also a need to know the rates of solution of gases in liquid methane. Tanks containing subcooled methane could be opened to the air if the rates of solution were low even though the equilibrium solubility might be prohibitively high. Again, we know of no data in this regard. Therefore, an analysis has been made of the equilibrium solubilities of several gases in liquid methane under conditions that might be encountered in the use of this fuel in air- craft. These results are compared with literature data where available. Some experi- mental measurements, in rather simple apparatus, were also made of the rates of solu- tion of gases in subcooled methane. These analytical and experimental results are re- ported herein.

x2molefraction of thesolutegas in solution ppartialpressure of thesolutegas,atm

p2 saturation pressure (vapor pressure) of the solute gas at the temperature of the solution,atm The pressure p2 as a function of temperature can be determined from standard vapor pressure data up to the critical temperature. And, as Hildebrand shows on pages 241- 242 of reference 5, a fair estimate of solubilities above the critical temperature can be made by using pressures obtained by extrapolation on a log saturation pressure against reciprocal temperature plot. These plots for the seven gases and for methane are given in figures l(a) and (b), using data from reference 4. The extrapolated portions above the critical temperatures are shown as dashed lines in figure l(b). The oxygen curve is shown as a dashed line in figure l(a) to distinguish it from the adjacent curve for argon.

methane at a temperature of 100 K (-279.7' F) and a solvent-solute system pressure of 1.0 atmosphere. From figure 1 the vapor pressures of methane and nitrogen are 0. and 7.95 atmospheres, respectively. At 1 atmosphere system pressure, the partial pressure of the nitrogen will be 1.00 - 0.35 = 0.65 atmosphere and the solubility in mole fraction would be

A s an example of the use of equation (l), consider the solubility of nitrogen in liquid

x2=--7.95 65 -^ 0.

This is equal to 13.6 weight percent nitrogen in the subcooled methane. These values are for an ideal solution and represent the upperbound; the actual solubilities will al- ways be less in the absence of chemical reaction o r hydrogen bonding.

Solubilities in Real (Nonideal) Solutions

Lower, and presumably better, values for solubilities than those obtained from equa- tion (1) can be calculated by correcting for the nonideality of the solutions. Hildebrand (ref. 5) has introduced a solubility parameter 6 anddifferences in the 6 value of sol- vent and solute a r e a measure of this nonideality. At pressures of 1 atmosphere and for dilute solutions, solubilities can be calculated from the following equation taken from page 244 of reference 5.

where

v2 molar volume of the solute gas^ as^ a^ liquid, m l

61, &i2, solubility parameters for the solvent and solute

absoluteT temperature of thesystem, K

At pressures other than 1 atmosphere the equation shouldbe

V2(61 - 62) 2 -log x2 = log p2 + - logP 4.58 T

It can be seen that any differences in the solubility parameters of solute and solvent in- troduce a term that reduces the solubility and thatthe solubility becomes less as these differences increase. For ideal solutions, 61 = 62 and the third term in equation (2b) drops out to leave an expression that reduces to the logarithmic form of equation (1). The solubility parameter is a term based on the latent heat of evaporation per unit volume. Appendix I in reference 5 gives both these values and also the molar volumes for all the compounds considered herein at their normal boiling temperatures. These values are listed in the following table.

7" --- - Compound

Helium Hydrogen Neon Nitrogen Carbon monoxide Argon Oxygen Methane

P a r a m e t e r , 6

**0.

6.**

Molar volume,

v,

m l 32 28 17 35 34 28 28 38

T e m p e r a t u r e , K

**4.

27 77 82 87 90 112**

The solubility parameters decrease in value with increasing temperatureand Hildebrand

(p. 434 of ref. 5) recommends the following equation for this temperature correction

d l n 6 d l n V

• S -1.

The helium data are from reference 7 and, at temperatures of 90.3 and 106.0 K

gave extrapolated solubility values at 1 atmosphere of 5. 5 ~ 1 0 - ~ and 8. 5 ~ 1 0 ~ ~ mole frac- tion,respectively.

The hydrogen data at 116.5 K are from reference 8 and extrapolates to a 1-

atmosphere solubility of 1 0. 5 ~ 1 0 - ~ mole fraction. The data at 90.7 K are from refer-

ence 9 and are quite scattered (see fig. 4); extrapolation gives a solubility of about mole fraction at 1 atmosphere. The nitrogen solubility data are from reference 10. These are plotted in figure 4 over a much lower range of pressures than are the helium and hydrogen data. Reason- able extrapolations can be made to 7. 7X10-2 and 4. 3X10-2 mole fraction for 99.83 and 110.9 K, respectively.

Calculated Solubilities and Comparison with Literature Data

The solubilities of the various gases in liquid methane can be easily calculated from equation (2) using the vapor pressures, molar volumes, and solubility parameters from figures 1 to 3. A s previously mentioned, constant (temperature independent) values for V and 6 must be used for hydrogen,helium,and neon. These calculations were made for the six points (two for each gas) extrapolated from the literature and listed above. The results are shown in the following table along with the calculated values for ideal solutions using equation (1).

-. ~ ...I Solute gas

Helium Helium Hydrogen Hydrogen Nitrogen Hydrogen

-~ T e m p e r a t u r e , K

-~.. **106

90.**

99. 8 110.

" Solubility, mole fraction ~. ~ L i t e r a t u r e extrapolation **8.

5. 5 ~ 1 0 - ~ 1 0. 5 ~ 1 0 - ~ 2 ~ 1 0 - ~**

**7. 7X10-

4. 3X10-**

Nonideal solution 1. 9 ~ 1 0 - ~

3. 5 x 1 0 - ~

. 2 5 x 1 0 - ~

1. 1 ~ 1 0 - ~

2.9x10-

6. Ox10-

Ideal solution

It can be seen that, in all six cases, the nonideal calculation using equation (2) gives val- ues that are less than the literature indicates they should be. These range from 0. (nitrogen at 99.8 K) to 0.045 (helium at 90.3 K) of those estimated by extrapolating the literature data. Nevertheless, the values calculated from equation (2) are very much

closer than those obtained from the ideal equation (1). The latter very seriously over- estimates the gas solubilities and especially for helium where the predicted solubilities are over 100 times too high. It appears that the Hildebrand correction for nonideality is too large. Considerably better agreement with the data canbe achieved by multiplying this term by a factor less than 1.0. The factors required to fit the data are:

Helium Helium Hydrogen Hydrogen Nitrogen Nitrogen

T e m p e r a t u r e ,

116.

**90. 7

110.**

F a c t o r

0. . . . . .

However, the use of adjustable constants for each gas and temperature o r even for just each gas is obviously of little value. There would be no way of predicting solubilities in the absence of data and no need to predict solubilities if data are available. Neverthe- less, the above comparison does indicate that much better results canbe obtained by ap- plying a single correction factor to Hildebrand's last term. This factor is about 0. based on the data presented herein. Therefore, the following equation is recommended for the prediction of the solubility of any gas in liquid methane over the temperature range of 90 to 112 K.

0.65 Vz(61 - 62) 2 -logx2 = log p2 + - P log 4. 5 8 T

The constants can be combined and rounded off to give

-logx2 = log p2 + - log P 7.0 T

Equation (5a) was used to predict the solubilities, at 1 atmosphere solute gas pressure, shown in figure 5(a) and (b). Figure 5(a) presents the curves for oxygen, argon, carbon monoxide, and nitrogen. Also shown are the two experimental values for nitrogen. Agreement is excellent at

RATES OF SOLUTION

Reference 3 suggests that liquefied natural gas (LNG) might be subcooled 25' R (13.9 K) for aircraft use but that the solubilitiesof air or nitrogen would be excessive; the solution of about 10 weight percent nitrogen would be expected. For this amount of subcooling, calculations from figure 5(a) gives the nitrogen and air solubilities as 11. and 21.8 weight percent. This study confirms the earlier estimates that equilibrium solubilities are high but does not prove that the rates of solution are so great that equi- librium is likely to be approached. Therefore, some relatively simple experiments were run to get an indication of the rates of solution of gas into LNG.

Apparatus

This is shown in figure 6. The Dewar flask had a capacity of 1.74 liters and was connected, through the use of a silicone-greased rubber stopper to a 1/4-inch outside diameter steel tubing manifold, a Heise 0 to 1.0 atmosphere absolute pressure gage, a vacuum pump, and to either of two sources of solute gas. One w a s a 19.7-liter glass carboy that was filled to 1 atmosphere. The other w a s a 16.27-liter steel tank that had its own gage and could be filled to higher pressures. Two copper-constantan bare junc- tion thermocouples were led through the stopper. One had its junction in the liquid and the other measured the temperatureof the ullage space in the neck of the flask. A preliminary experiment on the boiloff rate of LNG showed the heat leak rate into the Dewar to be 232 calories per hour. This heat leak would raise the temperature of confined LNG less than 0.4' C per hour when the flask is full. This small heat leak was included in subsequent calculations. The volumes of all lines, vessels, and the gage were determined for use in the cal- culations.

Procedure

The gas reservoirs werepumped down to less than 1 t o r r and then filled with the solute gas under investigation. The natural gas w a s condensed from the laboratory supply lines. A mass spectro- metric analysis of the condensed liquid gave

I

Component

Methane Ethane Propane Carbon dioxide Nitrogen Oxygen Total

Concentration, mole percent

3. 1.

. 9 2. 7 . 6 100.

The nitrogen, oxygen, and carbon dioxide were probably contaminants introduced during liquefaction. There were also trace amounts of less volatile components that showed up as a residue when a flask of LNG had evaporated nearly to dryness. The Dewar flask w a s weighed prior to each experiment to get the weight of LNG. The flask w a s connected to the system and the LNG subcooled by pumping off a part of the charge. There were some slugging losses in preliminary experiments. These were avoided later by adding a few porous ceramic chipsas boiling aids and by throttling the pump inlet during the early part of the pump down. The LNG was so subcooled about 15' C (27' F) in 30 to 45 minutes and then closed off for about 1/2 hour to come to tem- perature equilibrium and to insure that there were no leaks. The liquid temperature as measured by the thermocouple always corresponded to that calculated from the measured system pressure within the accuracyof the temperature measurement (about 2' C) using pure methane vapor pressure data. After subcooling and when the 19. 7-liter, l-atmosphere reservoir (supply system A in fig. 6) w a s used, the connecting stopcock w a s fully opened so that all parts of the sys- tem were at the same pressure. This resulted in an initial increase in system pressure to near 1 atmosphere followed by a decrease in pressure as the gas dissolved in the LNG. System pressure was recordedas a function of time. When the pressurized tank gas supply (system B in fig. 6) w a s used, the valve on this tank w a s manually controlled to keep the Dewar at near 1 atmosphere pressure. The pressure in this supply tank w a s then recorded as a function of time. With either system the rates of solution were observed for 5 to 35 minutes with the LNG flask undisturbed. These rates were quite high initially but slowed down very much by the end of this time. The experiment w a s continued by gently swirling the LNG flask by hand. There was sufficient flexibility in the connecting line to allow a swirling motion, in the horizontal plane, with an amplitude of 1 to 2 centimeters and a rate of 2 to 4 cycles per second. This is a very mild agitation but the rate of solution increased markedly and then again became very slow after another 5 to 15 minutes. At the end of this time, the

Mass transfer and thermal conduction are certainly the rate-limiting processes in the quiescent experiments. When a solute gas is admitted over a liquid, the very upper- most surface must quickly become both saturated by the gas and heatedby the enthalpy -contribution of this gas. Concentration and temperature gradients are set up which limit the rate for further gas additions. These gradients and subsequent rates would be amen- able to purely analytic solutions for a completely quiet liquid. However, natural convec- tive mixing would complicate the analysis. The results would be of little practical im- portance anyway since any aircraft application would have liquid motion in the fuel tanks. These experiments showed only that the rate of solution is quite fast and that appre- ciable amounts of nitrogen are dissolved in 2 to 3 minutes in a system where the motion of the liquid is much less than that in any sort of a mobile fuel system. Therefore, LNG cannot be exposed to gases with high equilibrium solubilities with the hope that little will dissolve because the rate of solution might be low. This conclusion from simple experiments is confirmed by a study of the rates of solution and evolution of air into vigorously shaken petroleum fluids (ref. 12). Rates were determined for fluids ranging fromheavy lubricating oil to aviation gasoline andit w a s found that the rate of solution increased with decreasing fluid viscosity. The gaso- line was least viscous (0.635 centistoke) and, in two experiments, had a half-life solution time of only 1.21 and 1.34 seconds with strong shaking. Liquid methane has an even lower viscosity (0.33 centistoke at its normal boiling temperature) so it can be assumed that the rate of solution of gases into LNG would be even higher. This suggests that LNG would be substantially saturated in a few seconds if a liquid-gas system were agitated strongly. This same conclusion can be reached from arguments based on kinetic theory when mass and heat transfer are not limiting. There would be no concentration or tempera- ture gradients in a well-stirred system and the solution rate would be controlled by the arrival rate of gas at the gas-liquid interface. This arrival rate per unit area, W , is given by

W = - n C^1 4

where n is the number density and 3 the mean molecular velocity. At 100 K and 1.0 atmosphere, the arrival rate for nitrogen is 0.84 gram mole per second per square centimeter. In the experiments with the quiet liquid there were about 40 gram moles of LNG, about 50 square centimeters of liquid to gas surface, and about 2/3 atmosphere nitrogen pressure. The arrival rate of nitrogen would then be 0.84 X 50/40 X 2/3 = 0. mole nitrogen per second per mole of LNG. Since the equilibrium solubility is of the order of 0.04 mole per mole, saturation should be achieved in less than 0.1 second in

the absence of concentration and temperature gradients. The rate would be even higher if the area of the surface to gas interfacewere increased by shaking.

Rates of Gas Evolution

There is the related question as to how easily a gas contaminated solution ofLNG could be degassed. Nothing was done in this regard except the observation that oxygen and nitrogen were still present in LNG that had been subcooled about 15' C by evacuation; 8 to 10 percent of the LNG was so removed. This should have been expected since the removal of the more volatile components (oxygen and nitrogen) from an only moderately less volatile liquid (LNG) cannot be accomplished by a simple flash evaporation. An effi- cient separation of these components would require a fractional distillation. Considera- tion of this aspect is beyond the scope of this report.

CONCLUDING REMARKS

A study of the equilibrium solubilities and the rates of solution of gases into sub- cooled liquid methane (or liquefied natural gas) was prompted by an interest in this hydro-

carbon as a possible fuel for the Supersonic Transport o r other supersonic aircraft.

Calculations were based on Hildebrand's treatment of nonideal (real gas) solutions. These showed that the solubilities of nitrogen, carbon monoxide, argon, and oxygen would all be quite high in subcooled methane. For example, when subcooled 25' F

(13.9 K) below its normal boiling point, this calculated value was 1 1. 3 weight percent for

nitrogen.Carbonmonoxide,argon,and oxygen would be even more soluble. On the other hand,neon, hydrogen,andhelium a r e much less soluble. Calculations for these three gases are probably less exact. Nevertheless, it appears that the solubilities of

neon, hydrogen, and helium in 25' F (13.9 K) subcooled methane will be about

5 ~ 1 0 - ~ , and molefraction,respectively. Curves are presented which allow the easy calculation of the solubilities of all these

gases in methane or LNG between 90 and 112 K.

A few experiments were run on the rates of solution of gas into LNG. These showed that the rates were quite high in completely quiet LNG with an indication that equilibrium solubility would be approached in a few minutes with only modest agitation. Other evi- dence suggests that equilibrium solubility would be attained in the order of a second if the liquid-gas system were shaken vigorously.

10. Cines, M. R. ; Roach, J. T. ; Hogan, R. J. ; and Roland,C. H. : Nitrogen-Methane

Vapor-LiquidEquilibria. Chem.Eng. Progr. Symp. Ser., vol. 49, no. 6, 1953, pp. 1-10.

11. McKinley,C. ; and Wang, E. S. J. : Hydrocarbon-OxygenSystemsSolubility. Ad- vancesinCryogenicEngineering. Vol. 4. K. D. Timmerhaus,ed.,Plenum Press, 1960, pp. 11-25.

12. Schweitzer, P. H. ; andSzebehely, V. G. : Gas Evolution in LiquidsandCavitation.

J. Appl. Phys. - 21, no. 12, Dec. 1950, pp. 1218-1225.

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Reciprocal temperature, UK

(a)Methane, oxygen, argon, carbon monoxide, andnitrogen.

6.2 -

5. 8 r

5.4 r

5.0 -

4.6-

-3 -;I3.0 3.

. 8 . 4

0

-. 4

-. 8

-1.

-1.

-2.0 (^020 10) 30 40 50 60 70 8 0 ~ l O - ~ Reciprocal temperature for neon and hydrqlen, UK

0 u 50 100 150250 200 300 3 5 0 ~ 1 0 - ~ Reciprocal temperature for helium, UK (b) Neon, hydrogen, and helium.. Figure I. -Vapor pressure as function of temperature.