Neil T. Van Dresar and Gregory A. Zimmerli

Glenn Research Center, Cleveland, Ohio

Correlation of Helium Solubility in Liquid Nitrogen

NASA/TM—2012-217716

October 2012
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Neil T. Van Dresar and Gregory A. Zimmerli

Glenn Research Center, Cleveland, Ohio

Correlation of Helium Solubility in Liquid Nitrogen

NASA/TM—2012-217716

October 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

We thank E.W. Lemmon at National Institute of Standards and Technology (NIST) for providing the solubility data and references 

used to develop the correlation. This work was supported by NASA through the Cryogenic Propellant Storage and Transfer 

Technology Maturation Program.

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Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2012-217716 1 

Correlation of Helium Solubility in Liquid Nitrogen

Neil T. Van Dresar and Gregory A. Zimmerli

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

A correlation has been developed for the equilibrium mole fraction of soluble gaseous helium in 

liquid nitrogen as a function of temperature and pressure. Experimental solubility data was compiled and 

provided by National Institute of Standards and Technology (NIST). Data from six sources was used to 

develop a correlation within the range of 0.5 to 9.9 MPa and 72.0 to 119.6 K. The relative standard 

deviation of the correlation is 6.9 percent.

Introduction

Although liquid nitrogen (LN2) is not a propellant, it is often used for ground-based testing of 

cryogenic propulsion systems. It is a safer and less costly alternative test fluid for liquid oxygen (LO2) or 

liquid methane (LCH4). Often LN2 is substituted for other cryogenic propellants in the early stages of 

testing, and it is typically used in preparing test hardware for follow-on testing with the actual propellants 

of interest, such as LO2, LCH4, or liquid hydrogen (LH2). Since LN2 systems pressurized with helium are 

commonly tested, a convenient method of accurately estimating the amount of helium dissolved in the 

LN2 would be useful. In a previous publication (Ref. 1), correlations for helium solubility in LO2, LCH4, 

and LH2 were reported. In this report, we present a similar correlation for helium in LN2. 

Data Analysis and Correlation

As was the case for the previous work, the solubility data was provided by Lemmon at the National 

Institute of Standards and Technology (NIST), who compiled the data from various published sources and 

corrected the data to conform to the latest ITS-90 temperature scale (Ref. 2). The data was provided in 

tabular form consisting of total pressure (P, in MPa), temperature (T, in K), helium mole fraction in LN2

(x), and the original data source. 

Our correlation for helium-nitrogen is of the form

( *pbTaa*px ) 010 exp ++⋅= (1) 

where x is the mole fraction of helium in liquid nitrogen, p* is a dimensionless pressure defined as 

( ) 0 ref −= /PPP*p , where P is the total pressure (sum of liquid nitrogen vapor pressure plus the partial 

pressure of the helium pressurant gas), P0 is the saturated vapor pressure of pure LN2 at temperature T, 

Pref is a reference pressure defined as 1 MPa, and a0, a1, and b0 are empirically determined coefficients.

The value of P0 was determined using NIST’s Standard Reference Database 23 software program 

REFPROP (Ref. 3). The coefficients a0, a1, and b0 were obtained via multiple linear regression fitting of 

the data. The goodness of fit was evaluated by use of the relative standard deviation calculated as

N

)xx(

R

∑ − =σ

2

fit (2) 

where xfit is the fitted mole fraction value, x is the reported value, and N is the number of reported values.
NASA/TM—2012-217716 2 

As done previously for LCH4 and LO2, we limited the pressure to 0 to 10 MPa and did not include 

data very close to nitrogen’s critical temperature (126.2 K). Data below the normal boiling point (77.3 K) 

did not fit the correlation as well as higher temperature data, so data at temperatures significantly lower 

than the NBP were also excluded. Data from each individual source was first analyzed separately. Some 

of the data was deemed to be of lesser quality and was excluded. Reasons for exclusion were a large σR

for data from an individual source or an insufficient number of reported significant digits in values of x. 

Data from six sources (Refs. 4 to 9) were used to develop the correlation. One of the data sets (DeVaney

et al. (Ref. 6)) was substantially larger than the others due to a high number of repeated measurements (as 

many as six) at each individual pair of P and T. For this source, average values of x were computed for 

each (P,T) pair. Another source (Davis et al. (Ref. 5)) reported two measurements of x at each (P,T) pair; 

these were averaged as well. In some of the remaining data sets, there were occasional repeated tests with 

close values of pressure for the same temperature; these pairs were then averaged for P and x. Only two of 

the data sources (DeVaney et al. (Ref. 6) and Kharakhorin (Ref. 7)) contained data points for p* greater 

than 7. However, these sources showed substantial scatter at low p*, so only data from mid-to-high p* 

was used. The low p* data (with high scatter) from these two sources was omitted as other sources were 

available to provide data for the low p* region.

The best-fit correlation for helium mole fraction in liquid nitrogen for the set of data described above 

is





 



 ⋅−⋅+−⋅= *p.T K

. .*px 0250 04720

exp 7279 (3) 

Data in the range 0.5 to 9.9 MPa and 72.0 to 119.6 K were used to obtain this correlation. The percent 

relative standard deviation of fitted values from the data considered is 6.9 percent (N = 102).

In Figures 1 to 3, the data is plotted as ln(x/p*) versus p*. In each figure, the solid lines representing 

fixed temperatures were generated from Equation (3). Each figure shows the temperature dependence of 

the solubility as well as the linear pressure dependence of ln(x/p*). Figure 1 shows data that fits the 

correlation very well. Figure 2 shows data sets where the pressure dependence is slightly less than the 

correlation prediction and also shows the correlation over-predicts the solubility for two of the sources 

(DeVaney et al. (Ref. 6) and Skripka (Ref. 8)) at low temperatures. Opposite trends are shown in Figure

3, where the pressure dependence is greater than the correlation prediction and the correlation underpredicts the solubility for two different sources (Burch (Ref. 4) and Davis et al. (Ref. 5)) at low 

temperature.

The temperature dependence of helium solubility in LN2 is shown in Figure 4. The correlation fits the 

data very well at higher temperatures, while at the low end of the temperature range, small differences are 

apparent, depending on the source of the data.

As an example calculation, consider LN2 at its NBP (77.3 K) pressurized with helium to a total 

pressure of 1.72 MPa. Therefore, p* = 1.62 and the equilibrium solubility mole fraction calculated from 

Equation (3) is x = 0.36 ± 0.025 percent. Similar example calculations were given in Reference 1 for 

helium solubility in LO2 and LCH4 at the same pressure (1.72 MPa) and the respective NBP for each 

liquid. For both LO2 and LCH4 at these conditions, the helium mole fraction was x = 0.13 percent, thus 

indicating, on a mole fraction basis, that helium is almost three times as soluble in LN2 as in LO2 or LCH4

for the example conditions.

Summary

Solubility data for the mole fraction of gaseous helium in liquid nitrogen from various sources has 

been correlated as a function of temperature and pressure. The correlation is valid over a broad range of 

temperature and pressure and should be valuable in the testing and analysis of cryogenic propulsion test 

systems when liquid nitrogen is utilized.
NASA/TM—2012-217716 3 

References

1. Zimmerli, G.A., Asipauskus, M., Van Dresar, N.T., Cryogenics, 2010;50:556-560.

2. Lemmon, E.W., Private communication.

3. Lemmon, E.W., Huber, M.L., McLinden, M.O., NIST standard reference database 23: reference fluid 

thermodynamic and transport properties-REFPROP, Version 8.0. National Institute of Stands and 

Technology, Standard Reference Data Program, Gaithersburg: 2007.

4. Burch, R.J., “Low Temperature Phase Equilibria of the Gas-Liquid System Helium-Neon-Nitrogen,” 

J. Chem. Eng. Data, Volume 9, Number 1, pp. 19-24, 1964.

5. Davis, J.A., Rodewald, N. and Kurata, F., “An Apparatus for Phase Studies between 20 K and 300 

K,” Ind. Eng. Chem., Volume 55, Number 11, pp. 36-42, 1963.

6. DeVaney, W.E., Dalton, B.J. and Meeks, J.C. Jr., “Vapor-Liquid Equilibria of the Helium-Nitrogen 

System,” J. Chem. Eng. Data, Volume 8, Number 4, pp. 473-478, 1963.

7. Kharakhorin, F.F., “The Phase Relations in Systems of Liquefied Gases. The Binary Mixture 

Nitrogen - Helium,” Foreign Pet. Technol., Volume 9, Number 11/12, pp. 397-410, 1941; transl. of 

Zh. Tekh. Fiz., Volume 10, Number 18, pp. 1533-40, 1940.

8. Skripka, V.G., “Virial Coefficients of Inert and Associated Gases in the Low Temperature Region. 

Second Viral Coefficients of Oxygen, Nitrogen, Argon, Helium, Neon, Hydrogen, Deuterium and 

Krypton at Temperatures below 150 K,” Tr., Vses. Nauchno-Issled. Inst. Kislorodn. Mashinostr., 

Volume 10, pp. 163-183, 1965.

9. Streett, W.B., “Gas-Liquid and Fluid-Fluid Phase Separation in the System Helium-Nitrogen Near the 

Critical Temperature of Nitrogen,” Chem. Eng. Prog., Symp. Ser., Volume 63, Number 81, pp. 37-42, 

1967.
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14. ABSTRACT

A correlation has been developed for the equilibrium mole fraction of soluble gaseous helium in liquid nitrogen as a function of temperature 

and pressure. Experimental solubility data was compiled and provided by National Institute of Standards and Technology (NIST). Data from 

six sources was used to develop a correlation within the range of 0.5 to 9.9 MPa and 72.0 to 119.6 K. The relative standard deviation of the 

correlation is 6.9 percent. 

15. SUBJECT TERMS

Helium; Liquid nitrogen; Solubility 

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