NBSIR 77-854

N!ST

PUBUCATIONS

LIQUEFIED NATURAL GAS RESEARCH

at the

NATIONAL BUREAU OF STANDARDS

PROGRESS REPORT FOR THE PERIOD

1 JULY - 31 DECEMBER 1976

D.E. Oilier, Editor

€?CL

/oo

^- 77-

CRYOGENICS DIVISION • NBS-INSTITUTE FOR BASIC STANDARDS • BOULDER, COLORADO

NBSIR 77-854

LIQUEFIED NATURAL GAS RESEARCH

at the

NATIONAL BUREAU OF STANDARDS

D.E. Diller, Editor

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Progress Report for the Period

1 July-31 December, 1976

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Betsy Ancker-Jotinson , Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director
Prepared for:

Americarx Gas Association, Inc.

1515 Wilson Boulevard

Arlington, Virginia 22209

LNG Density Project Steering Committee

(in cooperation with the American Gas Association, Inc.

Pipeline Research Committee

(American Gas Association, Inc.)

Federal Power Commission

Bureau of Natural Gas

Washington, DC 20426

U. S. Department of Commerce

Maritime Administration

Washington, DC 20235

U. S. Department of Commerce

National Bureau of Standards

Institute for Basic Standards

Boulder, Colorado 80302

U. S. Department of Commerce

National Bureau of Standards

Office of Standard Reference Data

Washington, DC 20234

U. S. Department of Commerce

National Bureau of Standards

Office of International Standards

Washington, DC 20234

LNG Sampling Measurements Supervisory Committee

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135

American Bureau of Shipping

45 Broad Street

New York, NY 10004

ii
ABSTRACT

Twenty-five cost centers, supported by six other agency sponsors in

addition to NBS, provide the basis for liquefied natural gas (LNG) research

at NBS. During this six-month reporting period the level of effort was

20 man-years/year with funding expenditures of over $500,000. This

integrated progress report to be issued in January and July is designed to:

1) Provide all sponsoring agencies with a semi-annual and an annual

report on the activities of their individual programs.

2) Inform all sponsoring agencies on related research being conducted at the Cryogenics Division of NBS-IBS.

3) Provide a uniform reporting procedure which should maintain

and improve communication while minimizing the time, effort

and paperwork at the cost center level.

The contents of this report will augment the quarterly progress meetings of some sponsors, but will not necessarily replace such meetings.

Distribution of this document is limited and intended primarily for the

supporting agencies. Data or other information must be considered pre- liminary, subject to change and unpublished; and therefore not for citation

in the open literature .

Key words: Cryogenics; liquefied natural gas; measurement; methane;

properties; research.

iii
CONTENTS

Cost Center Page

REFERENCE DATA

a) THERMOPHYSICAL PROPERTIES DATA FOR PURE

COMPONENTS AND MIXTURES OF LNG COMPONENTS (American Gas Association,

Inc.; NASA Lewis Research Center)

b) FLUID TRANSPORT PROPERTIES

(NBS-Office of Standard Reference Data)

C) PROPERTIES OF CRYOGENIC FLUIDS (NBS)

d) PROPERTIES OF CRYOGENIC FLUID MIXTURES

(NBS: NBS-Office of Standard Reference

Data; AGA)

e) . DENSITIES OF LIQUEFIED NATURAL GAS

MIXTURES (LNG Density Project Steering

Committee - AGA)

f) PROGRAM FOR REDUCING THE COST OF LNG SHIP

HULL CONSTRUCTION — PHASE II SHIP STEEL

IMPROVEMENT PROGRAM (Maritime Administration)

II. MEASUREMENT SCIENCE

a) CUSTODY TRANSFER - LNG SHIPS

(Maritime Administration)

b) HEATING VALUE OF FLOWING LNG (Pipeline

Research Committee - AGA)

c) LNG DENSITY REFERENCE SYSTEM

(American Gas Association, Inc.;

National Bureau of Standards)

d) . LNG SAMPLING MEASUREMENT STUDY (LNG

Sampling Measurements Supervisory

Committee

)

III. TECHNOLOGY TRANSFER

a) SURVEY OF CURRENT LITERATURE ON LNG

AND METHANE (American Gas Association,

Inc. )

b) LIQUEFIED NATURAL GAS TECHNOLOGY TRANSFER

(Maritime Administration; American Gas

Association, Inc.; American Bureau of

Shipping

)

C) OIML JOINT SECRETARIAT ON LNG MEASUREMENTS (American Gas Association, Inc.;

NBS-Office of International Standards;

NBS-Cryogenics Division)

2750574 and 1

2750548

2750124

2750141 6

2750142, 9

2750145 and

2754574

2751574 12

2751430, 14

2752430 and

2753430

2750460 16

2756579 19

2757574 and 22

2750161

2750575

2759574

2750403,

2751403,

2752403,

2750570,

2754574 and

2758574

2750104

23

25

27

29

IV
Contents (continued)

III. TECHNOLOGY TRANSFER (continued)

Page

d) FEDERAL POWER COMMISSION CONSULTATION (FPC) 2750404 31

IV. BIBLIOGRAPHY 34

V. APPENDICES

A. Straty, G.C., and Tsumura, R. , "Phase transition and A-1

melting pressures of solid ethane," J. Chem. Phys.

64, 859 (1976).

B. Straty, G.C., and Tsumura, R. , "PVT and vapor pres- B-1

sure measurements on ethane," J. Res. Natl. Bur. Stds.

80A , 35 (1976).

C. Weber, L.A. , "Dielectric constant and the derived C-1

Clausius-Mossotti function for compressed gaseous

and liquid ethane," J. Chem. Phys. £5, 446 (1976).

D. Roder, H.M. , "The heats of transition of solid D-1

ethane," J. Chem. Phys. 65, 1371 (1976).

E. Roder, H.M. , "Measurements of the specific heats, E-1

Cq and C^/ of dense gaseous and liquid ethane," J.

Res. Natl. Bur. Stds. 8 OA, 739 (1976).

F. Diller, D.E., "LNG densities for custody transfer," F-1

Proceedings, International School for Hydrocarbon

Measurement, University of Oklahoma, April 12-14, 1977.

G. Haynes, W.M. , Hiza, M.J., and Frederick, N.V. , "Mag- G-1

netic suspension densimeter for measurements on fluids of cryogenic interest," Rev. Sci. Instrum. 47 , 1237 (1976).

H. Haynes, W.M., "A simplified magnetic suspension

densimeter for absolute density measurements,"

Rev. Sci. Instrum. 48^, 39 (1977).

I. Haynes, W.M. , and Hiza, M.J., "Measurements of the

orthobaric liquid densities of methane, ethane,

propane, isobutane and normal butane," J. Chem.

Thermodynamics (in press, 1977).

J. Hanley, H. J.M. , Haynes, W.M. , and McCarty, R.D.,

"The viscosity and thermal conductivity coefficients

for dense gaseous and liquid methane," J. Phys.

Chem. Ref. Data (in press, 1977).

K. Hanley, H.J.M., "Prediction of the viscosity and

thermal conductivity coefficients of mixtures,"

Cryogenics 16, 643 (1976).

L. Tobler, R.L., and Reed, R.P., "Fracture mechanics

parameters for a 5083-0 aluminum alloy at low

temperatures," Journal of Materials for Engineering

and Technology (submitted, 1977).

M. McHenry, H.I., "Ship steel weldments for low temperature service," Welding Journal 55^, 387 (1976).

N. Younglove, B.A. , and Siegwarth, J.D., "Cryogenic

fluids density reference system: provisional accuracy

statement," NBSIR 77-852 (January 1977).

0. Mann. D. B., "What's new in LNG measurement and 0-1

instrxamentation" Pipeline Industry 4_5, 21 (1976).

V

H-1

I-l

J-1

K-1

L-1

M-1

N-1

1. Title . THERFIOPHYSICAL PROPERTIES DATA FOR PURE COMPONENTS AND

MIXTURES OF LNG COMPONENTS

Principal Investigators . R. D. Goodwin, H. M. Roder, G. C. Straty,

R. Tsumura*, W. M. Haynes, and R. D. McCarty

2. Cost Center Number . 2750574, 2750548

3. Sponsor Project Identification . American Gas Association, Inc.,

Project BR-50-10. National Aeronautics and Space Administration,

Lewis Research Center, Purchase Order C-78014-C.

4. Introduction . Accurate phase equilibrium, equation of state (PVT) , and

thermodynamic properties data are needed to design and optimize gas

separation and liquefaction processes and equipment as well as heat

transfer calculations. Accurate data for the pure components and

selected mixtures of hydrocarbon systems will permit developing

comprehensive accurate predictive calculation methods which take into

account the dependence of the thermophysical properties of mixtures on

the composition, temperature, and density.

This project will provide comprehensive accurate thermophysical

properties data and predictive calculation methods for compressed and

liquefied hydrocarbon gases and their mixtures to support the development of LNG technology at NBS and throughout the fuel gas industry. It

will also serve as the base for a comprehensive mixtures prediction

methodology.

5. Objectives or Goals . The objectives of our work are the determination

of comprehensive accurate thermophysical properties data and predictive

calculation methods for the major pure components and selected mixtures

(methane, ethane, propane, butanes, and nitrogen) of liquefied natural

gas and hydrocarbon mixtures at temperatures between 90 K and 300 K and

at pressures up to 350 MPa (5000 psi) . Our goal is to provide a range

and quality of data that will be recognized as definitive or standard

for all foreseeable low temperature engineering calculations.

6. Background . Liquefied natural gas is expected to supply an increasing

percentage of the United States' future energy requirements. It is

likely that massive quantities of liquefied natural gas will be

imported during the years 1976 - 1990. Ships and importation terminals

are being built for transporting, storing, and vaporizing liquefied

natural gas for distribution. Accurate physical and thermodynamic

properties data for compressed and liquefied natural gas and hydrocarbon

mixtures are needed to support these projects. For example, accurate

compressibility and thermodynamic properties data are needed to design

and optimize liquefaction and transport processes; accurate data for the

heating value, which for liquefied natural gas mixtures depends on the

total volume, the density, and the composition, are needed to provide a basis for equitable custody transfer. Accurate mixtures prediction

methods are needed for use in automated heat transfer calculations.

Accurate thermodynamic properties data for liquefied gas mixtures must

be based on precise compressibility and calorimetric measurements;

compressibility data give the dependence of thermodynamic properties on pressure and density (at fixed temperatures) ; calorimetric data give

Consejo Nacional de Ciencia y Tecnologia (CONACYT) Mexico City. Currently

a guest worker with the Cryogenics Division, National Bureau of Standards,

Institute for Basic Standards in Boulder, Colorado.
the dependence of thermodynamic properties on temperature (at fixed

pressures and densities). It is impossible, however, to perform

enough compressibility and calorimetric measurements directly on multicomponent mixtures to permit accurate interpolation of the data to

arbitrary composition, temperatures and pressure. Instead, thermodynamic

properties data for multicomponent mixtures usually must be predicted

(extrapolated) from a limited number of measurements on the pure

components and their binary mixtures. This project was initiated to

provide the natural gas and aerospace industry with comprehensive

accurate data for pure compressed and liquefied methane, the most

abundant component in LNG mixtures. We have published National Bureau

of Standards Technical Note 653, "Thermophysical Properties of Methane,

From 90 to 500 K at Pressures to 700 Bar," by Robert D. Goodwin (April

1974) , and National Bureau of Standards Technical Note 684, "Thermophysical Properties of Ethane, From 90 to 600 K at Pressures to

700 Bar," by Robert D. Goodwin, H. M. Roder, and G. C. Straty (August

1976) . These reports contain the most comprehensive and accurate tables

available for the thermophysical properties of pure gaseous and liquid

methane and ethane, and provide accurate basis for calculating

thermophysical properties data for LNG and hydrocarbon mixtures.

7 . Program and Results .

7.1 Ethane, Specific Heat Data — H. M. Roder

This phase of the program is complete. Two manuscripts describing

the results of the research have been published:

H. M. Roder, Measurements of the Specific Heats, and of Dense

Gaseous and Liquid Ethane, J. Res. Nat. Bur. Stand. (U.S.), Vol 80A,

No. 5, 739-59 (Sep-Oct 1976).

H. M. Roder, The Heats of Transition of Solid Ethane, J. Chem. Phys.

Vol 65, No. 4, 1371-3 (Aug 1976).

7.2 Ethane, Sound Velocity Data — R. Tsumura, G. C. Straty

Sound speed measurements on ethane have been completed. Measurements

were made on both the saturated and compressed fluid in a temperature

range from near the triple point 91 K) to 320 K and to pressures of

35 MPa. A systematically increasing disagreement between data for the

saturated liquid obtained at 1 MHz and 10 MHz as the triple point

temperature is approached has been explained as a wave-guide effect due

to experimental geometry.

A manuscript entitled "Speed of Sound in Saturated and Compressed Fluid

Ethane," by R. Tsumura and G. C. Straty has been prepared and submitted

to CRYOGENICS for publication.

7.3 Ethane, Thermophysical Properties Data — R. D. Goodwin

The manuscript. National Bureau of Standards Technical Note 684,

"Thermophysical Properties of Ethane, From 90 to 600 K at Pressures to

700 Bar," by R. D. Goodwin, H. M. Roder, and G. C. Straty (August 1976)

has been published and distributed.

7.4 Propane, Thermophysical Properties Data — R. D. Goodwin

Available, published physical properties data, acquired through our Cryogenic Data Center, have been evaluated and formulated as required

for thermal computations. These numerous properties now have been used

to compute a complete set of Provisional tables of thermodynamic functions.

2
The manuscript, "Provisional Thermodynamic Functions of Propane, From

85 to 700 K at Pressures to 700 Bar," is 50% complete. Present plans

are to publish these provisional tables as a National Bureau of Standards

Internal Report by mid-1977.

7.5 Propane, Experimental Measurements — W. M. Haynes

A magnetic suspension densimeter, which has been used previously (Rev.

Sci. Instr. 47_, 1237 (1976)) for measurements on liquids (including

mixtures) at temperatures between 95 and 300 K and at pressures to

3.5 MPa (500 psi) , is being modified for PVT measurements on liquid

propane at pressures to 35 MPa (5000 psi) . Significant differences

between the two apparatus are noted here. A capacitor with slotted

concentric cylinders will be located just above the density sensor in

the high pressure cell for simultaneous dielectric constant measurements on liquid propane. Major modifications have been carried out on

an existing cryostat so that it is compatible with the high-pressure

magnetic suspension densimeter.

A copper equilibrium cell with a prototype window assembly for use at

pressures to 35 MPa (5000 psi) has been fabricated. This type of

window assembly has been tested at pressures to 6,2 50 psi at room

temperature and liquid nitrogen temperature. The assembly was cycled

between these temperature limits four times and no leaks were detected.

A new differential capacitance sensor, designed to be minimally sensitive

to changes in the dielectric constant of the test fluid, is being

evaluated as a detector of the motion of the magnetic buoy that serves

as the density sensor. It has at least the sensitivity to changes in

the position of the buoy as the linear differential transformer used

in the previous work.

The auxiliary systems for handling of the test fluids including those

for pressure measurements have been assembled and tested. An oil dead

weight gauge will be used for most pressure measurements. Two spiral

quartz Bourdon gauges and a double revolution Bourdon gauge have been

calibrated against an air dead weight gauge and will be used to measure

the vapor pressure of the liquid propane in the cell and the vapor

pressure of liquids in vapor bulbs that are used to monitor temperature

gradients along the length of the cell.

Major tasks to be completed before PVT data for propane are obtained are

as follows:

a) Performance tests on magnetic suspension densimeter circuitry

including servo system, differential capacitance sensor, support

coil, etc.

b) Final assembly of capacitor and differential capacitor sensor

inside the sample holder.

c) Installation of sample cell and associated components (guard ring,

shields, capillary tubes, vapor bulbs, thermocouples, platinum

resistance thermometer, etc.) inside cryostat.

d) Wiring of cryostat, sample cell, and sensors for measuring density,

dielectric constant, and temperature.

e) Alignment of cryostat, sample cell, support coil, microscope, and

buoy for control and determination of buoy-coil separation distance.

f) Capabilities for simultaneous measurements of density, temperature,

pressure, and dielectric constant. These tests will include

measurements on well-characterized fluids.

3
7.6 Calculational Methods — R. D. McCarty

Four available calculation methods have been evaluated and optimized

under another project (2752574) from the standpoint of predicting

orthobaric liquid densities of LNG-like mixtures at pressures below

about 2 MPa (290 psi). These methods are now being examined for

predicting the thermophysical properties of mixtures over a wide range

of temperatures and pressures. Available data in the literature for the

methane-nitrogen system have been compiled for use in evaluating the

extended corresponding states method. Thus far, efforts have

concentrated on mapping PVT properties as a logical first step prior to

examining the utility of the method in calculating other thermodynamic

properties.

8. Problem Areas. None.

9. Funding . July 1 - December 31, 1976.

Man-years expended 1.8

Equipment and/or Services Purchased 14 . 3K$

Total Reporting Period Cost 109. 8K$

Balance Remaining 75.2K$

10. Future Plans.

Objectives and Schedule: Quarter

Measure, analyze and report

ultrasonic velocity data

for ethane.

Analyze and report available

physical properties data for

propane.

Prepare and performance test PVT

and dielectric constant

properties apparatus for propane,

Perform PVT and dielectric

constant measurements on propane

and on methane-nitrogen mixtures,

Evaluate and optimize promising

calculation methods for the

thermodynamic properties of

mixtures of LNG components.

4
1. Title . FLUID TRANSPORT PROPERTIES

Principal Investigator . Howard J. M. Hanley

2. Cost Center Ntimber. 2750124

3. Sponsor Project Identification . NBS-Office of Standard Reference Data

4. Introduction . Methods for predicting the transport properties of fluid

mixtures are unreliable and data are scarce. Prediction methods are needed, however, to supply the necessary design data needed to increase

efficiency and reduce costs.

5. Objectives or Goals . The long range or continuing goal of the program

is to perform a systematic study of the theories and experimental measurements relating to transport properties, specifically the viscosity

and thermal conductivity coefficients, of simple mixtures over a wide

range of experimental conditions. The specific objectives of the program include: 1) the systematic correlation of the transport properties

of simple binary mixtures and the development of prediction techniques,

2) development of a mixture theory for the dilute gas region and the

dense gas and liquid regions, 3) extension of the theory and prediction

techniques >to multicomponent systems, and 4) suggested guidelines for

future areas of experimental work.

6. Background . A continuing program has successfully expanded the stateof-the-art of transport phenomena for pure fluids. Information for pure

fluids is required as a prerequisite for mixture studies. The theory

of transport phenomena has been developed and applied to produce practical

numerical tables of the viscosity, thermal conductivity and diffusion

coefficients of simple fluids: Ar, Kr, Xe, N2 , ©2 , He, H2, CH^

.

Recent work has extended this approach to ethane. It has been shown

that a successful mixture program can emerge from combining the results

for pure fluids with equation of state studies. The equation of state

work is being carried out by other investigators in this laboratory.

7. Program and Results . A procedure to predict the transport properties of

mixtures has been developed via corresponding states. (i) The method has

been shown to be satisfactory. The program has been expanded by the

addition of James C. Rainwater, a NBS/NRC Postdoctoral Research Fellow

who will investigate the theoretical background. Progress has already

been made in this direction. A paper reporting the transport properties

of ethane has been submitted to the Journal of Physical and Chemical

Reference Data for publication.

8. Problem Areas . The lack of suitable experimental mixture transport

properties data for comparison purposes is the main problem. Also

equation of state (PVT) data for mixtures are needed.

9. Funding . July 1 - December 31, 1976.

10. Future Plans . The transport properties of propane and ethylene will be

investigated. The corresponding states predictive procedure for mixtures

will be expanded in line with the concurrent equation of state studies.

References

1. H. J. M. Hanley, Cryogenics 16, 643 (1976)

.

Allocation

Labor

Other Costs

60. 0K$

0,4 MY

OSRD

22.8K$

7.3K$

Total 30.1K$

5
1. Title . PROPERTIES OF CRYOGENIC FLUIDS

Principal Investigators . G. C. Straty, B. J. Ackerson, and D. E. Diller

2. Cost Center Number . 2750141

3. Sponsor Project Identification . NBS

4. Introduction . Accurate thermophysical properties data and predictive

calculation methods for cryogenic fluids are needed to support advanced

cryogenic technology projects. For example, liquefied natural gas is

expected to supply an increasing percentage of the United States'

energy requirements through 1990. Liquefaction plants, ships and

receiving terminals are being constructed to transport and store natural

gas in the liquid state (LNG) . Accurate thermophysical properties data

for LNG are needed to design low temperature processes and equipment.

Accurate data will benefit the energy industries and the consiamer by

providing for safe and efficient operations and reduced costs.

5. Objectives or Goals . The objectives of this project are to provide

comprehensive accurate thermodynamic, electromagnetic and transport

properties data and calculation methods for technically important

compressed and liquefied gases (helium, hydrogen, oxygen, nitrogen,

methane, ethane, etc.) at low temperatures. Precise compressibility,

calorimetric and other physical property measurements will be performed

to fill gaps and reconcile inconsistencies. Definitive interpolation

functions, computer programs and tables will be prepared for engineering

calculations. The immediate goals of this work are to obtain accurate

sound velocity and thermal diffusivity data for compressed and liquefied

gases by using laser light scattering spectroscopy techniques. Sound

velocity data are useful for testing the consistency of volumetric,

calorimetric and thermodynamic properties data, and are potentially

useful for density gauging applications. Thermal diffusivity data are required for performing thermodynamic and heat transfer calculations.

6. Background . When light is incident on a perfectly homogeneous fluid,

the reradiated (scattered) light field sums to zero in all but the exact

forward direction. For a "real" fluid, however, fluctuations, arising

through various mechanism, destroy the perfect homogeneity and results

in the scattering of light in other directions as well. For example,

thermally activated density fluctuations (phonons) , propagating with

the characteristic velocity of sound, give rise to scattered light which

is Doppler shifted in frequency from the incident light frequency and

whose spectrum contains information on the sound velocity and attenuation. Local non-propagating temperature fluctuations, which decay

diffusively, give rise to scattered light in a narrow frequency band

about the incident light frequency and whose spectrum contains

information on the lifetime of the fluctuations (thermal diffusivity)

.

Since the frequency shifts are generally very small, it was not until

the advent of the lasers with their extremely well defined frequency,

that practical experiments using these phenomena were possible.

The application of laser light scattering techniques to obtaining

thermophysical properties data was initiated to complement and check

other measurement methods and to solve measurement problems inherent

in more conventional methods. For example, laser light scattering

techniques permit measurements of sound velocities foj: fluids under

conditions for which sound absorption is too large to perform ultrasonic

measurements; laser light scattering techniques permit measurements of

thermal dif fusivities under conditions for which convection interferes

with measurements of thermal conduction. The feasibility of light

scattering experiments to obtain data on binary diffusion coefficients

has also been demonstrated.

6
7. Program and Results . An apparatus has been assembled for laser light

scattering spectroscopy measurements on compressed and liquefied gases

(76-300 K, 35 MPa) . The apparatus consists of a high pressure optical

cell, a cryostat refrigerated by means of liquid nitrogen, an argon ion

laser and low-level light detection equipment.

The light scattered from fluctuations in the fluid can be analyzed with

either digital autocorrelation techniques for the examination of the

very narrow lines associated with scattering from temperature

fluctuations (Rayleigh scattering) or with a scanned Fabry Perot

interferometer for the measurement of the Doppler frequency shifts

associated with the scattering from propagating density (pressure)

fluctuations (Brillouin scattering)

.

Apparatus for photon-counting and digital autocorrelation has been

assembled, interfaced with computer facilities and programmed to

enable on-line data acciamulation and analysis. Initial problems

associated with signal modulations from excessive building vibrations

have been solved by levitating the apparatus on an air suspension

system. A small, highly stable capacitor has also been designed,

constructed and installed inside the scattering cell to permit the

dielectric constant of the scattering fluid to be determined, which

should allow more accurate fluid densities to be obtained for use in

the data analysis. Apparatus tests on well characterized, strongly

scattering, test fluids have been made to verify data analysis

programs

.

Extensive thermal diffusivity data have been obtained for methane,

primarily along the critical isochore, over the temperature interval

of 190 K to 220 K. Replicate measurements indicating accuracies

approaching about 5 percent are now being achieved in this region. — The range of measurements in the critical region is expected to be

substantially increased with the use of the aforementioned capacitor

method of density determination which will negate the necessity for

measurements along an isochore (i.e., the critical isochore). Some

measurements in regions more removed from the critical point have also

been made.

8. Problem Areas . Light scattering has proven to be a valuable tool for

obtaining thermal diffusivity data on fluids. This is particularly

true in a broad temperature and density range around the critical

point, where more conventional experimental methods fail or are severely limited. The intensity of the scattered light however

decreases drastically as one moves away from the critical region.

Data accuracy in this region becomes limited by the statistical nature

of the scattering process and the ability to maintain stability and

precise experimental parameters over the extended periods of time

necessary for data accumlation.

We are currently investigating other experimental techniques, which

could be used to complement the light scattering measurements, in

order to provide sufficiently accurate data in regions where light

scattering methods are expected to be unsatisfactory, and which could

be used for mutual confirmation of data in the regions of overlap.

Preliminary investigations have suggested that the recently refined (1)

transient hot wire measurement method of thermal conductivity

determinations may be well suited for measurements on fluids in the

liquid state at low temperatures. This possibility is being

investigated and considered further.

7
9. Funding . July 1 - December 31, 1976

Man-years expended

Equipment and/or Services Purchased

Total Reporting Period Cost

Balance Remaining

0.5

10. 8K$

47.8K$

61.7K$

10. Future Plans.

Objectives and Schedule: Quarter 1 2 Measure, analyze and report

thermal diffusivity

coefficient data for >

methane in the critical region.

References

1. J. J. De Groot, J. Kestin and H. Sookiazian, Physica 75, 454 (1974)

.

8
1. Title . PROPERTIES OF CRYOGENIC FLUID MIXTURES

Principal Investigators . M. J. Hiza, W. M. Haynes, A. J. Kidnay (parttime) , and R. C. Miller (part-time)

.

2. Cost Center Numbers . 2750142, 2750145 and 2754574

3. Sponsor Project Identification . NBS, NBS (OSRD) , AGA

4. Introduction . Accurate thermodynamic properties data and predictive

calculation methods for mixtures of cryogenic fluids are needed to

design and optimize low temperature processes and equipment. This

project provides new experimental measurements on equilibrium properties

and compilations of evaluated equilibrium properties data which are suitable for direct technological use or for the evaluation of

predictive calculation methods.

5. Objectives or Goals . The overall objectives of this project are to

provide critically evaluated data, original and from other sources, on the phase equilibria and thermodynamic properties of cryogenic fluid

mixtures. The program has been divided into the following elements:

a) Preparation of a comprehensive bibliography on experimental

measurements of equilibrium properties for mixtures of selected

molecular species of principal interest in cryogenic technology.

b) Selection and/or development of methods for correlation, evaluation

and prediction of equilibrium properties data.

c) Retrieval and evaluation of experimental data for specific mixture

systems selected on the basis of theoretical and/or technological

importance.

d) Preparation of guidelines for future research based on the

deficiencies noted in (a) , (b) , and (c)

.

e) Performing experimental research to alleviate deficiencies and

provide a basis for improvement of prediction methods.

6. Background . A physical equilibria of mixtures research project was established in the Cryogenics Division in 1959. The initial effort,

based on a bibliographic search and other considerations, was directed

toward the acquisition of new experimental data on the solid-vapor and

liquid-vapor equilibria and physical adsorption properties for a limited

number of binary and ternary mixtures of components with widely separated

critical temperatures. Most of the systems studied included one of the

light hydrocarbon species -- methane, ethane, or ethylene (ethene) -- with one of the quantum gases — helium, hydrogen, or neon. The data

for these systems led to significant improvements in the predictions of

physical adsorption equilibrium and a correlation for the prediction of

deviations from the geometric mean rule for combining characteristic

energy parameters. In addition, significant new information was obtained

for interaction third virial coefficients which was used in a correlation by one of our consultants, J. M. Prausnitz . The approach taken

in this work has been as fundamental as possible with the intention of

having an impact on a broad range of mixture problems.

Recent efforts have been directed toward problems associated with

systems containing components with overlapping liquid temperature

ranges, such as the nitrogen + methane system.

9
7. Program and Results . The recent progress is summarized as follows:

a) A paper reporting new liquid-vapor equilibria measurements for

the methane + ethane and the methane + ethylene systems is in

press in the Journal of Chemical Thermodynamics.

b) Data on the liquid-vapor equilibria, Henry's constants, excess

Gibbs functions, liquid phase heats of mixing and excess volumes

have been compiled, evaluated, and correlated for the methane + ethane system. A paper discussing this work is now in editorial

review. When released, this paper will be submitted to the

Journal of Physical and Chemical Reference Data.

c) An equation of state, recently proposed by Peng and Robinson, has

been optimized to represent the phase equilibria data for the

nitrogen + methane and methane + ethane systems. The optimized

equation has now been used to generate the nitrogen + methane

K-values and liquid and vapor equilibrium compositions for

inclusion in the LNG Materials and Fluids Data Handbook.

d) An empirical excess volume model has been developed based on orthobaric liquid density measurements for the pure components

and binary mixtures completed in the LNG density project. This

model has been tested on multicomponent LNG mixtures data and

appears to be a simple and reliable method for predicting LNG

densities from 105 to 120 K. A short paper discussing the

development of this model is in preparation.

8. Problem Areas. None.

Funding

,

July 1 - December 31, 197 6

10,

Man-years expended

Equipment and/or Services Purchased

Total Reporting Period Cost

Balance Remaining

Future Plans.

0.7

1.2K$

55.6K$

83. 0K$

Objectives and Schedule; Quarter

Evaluate, correlate and report

liquid-vapor equilibrium

properties data for methaneethane mixtures.

Evaluate promising calculation

methods for LVE and PVTx

properties of methane-nitrogen

mixtures

.

Prepare and report graphs of

liquid-vapor equilibrium

properties data for methanenitrogen mixtures.

Analyze and report total vapor

pressure data and orthobaric

liquid densities for methaneethane mixtures.

10
Objectives and Schedule: Quarter 1 2 Prepare and performance test

phase equilibria apparatus

for total vapor pressure

measurements of methaneisobutane mixtures.

11
1. Title . DENSITIES OF LIQUEFIED NATURAL GAS MIXTURES

Principal Investigators . M. J. Hiza, W. M. Haynes, R. D. McCarty and

W. R. Parrish

2. Cost Center Numbers . 2751574

3. Sponsor Project Identification . LNG Density Project Steering

Committee; American Gas Association, Inc., Project BR-50-11.

4. Introduction . Accurate density measurements and calculation methods

for liquefied natural gas mixtures are needed to provide a basis for

custody transfer agreements and for mass,, density, and heating value

gauging throughout the fuel gas industry.

The basis for the custody transfer of natural gas is its heating value.

It is difficult to determine and agree on the heating value of extremely

large volumes of natural gas in the liquid state. For example, methods

for calculating the heating value of a liquefied natural gas mixture

require knowing its density, which in turn depends on its composition,

temperature, and pressure. As the compositions of LNG mixtures vary

considerably, depending on the sources of the gas and the processing

conditions, accurate methods are needed for calculating liquid densities

at arbitrary compositions, temperatures and pressures. The accuracy is

important because of the extremely large volumes of liquid involved.

5. Objectives or Goals . The objectives of this work are to perform

accurate (0.1%) and precise (0.02%) measurements of the densities of

saturated liquid methane, ethane, propane, butanes, nitrogen and their

mixtures mainly in the temperature range 105-140 K, and to test and

optimize methods for calculating the densities of LNG mixtures at

arbitrary compositions and temperatures.

6. Background . This project is being carried out at NBS because of the

realization that equitable custody transfer agreements could be reached

more readily if the density measurements and the evaluation and development of calculation methods were performed by independent professionals

of established reputation.

An apparatus incorporating a magnetic suspension technique has been

developed for absolute density measurements on liquids and liquid

mixtures, particularly at saturation, for temperatures between 90 and

300 K. The estimated imprecision of measurement is less than 0.02%

and the estimated inaccuracy is less than 0.1%.

7 . Program and Results . 7.1 Measurements . All measurements on pure fluids as well as binary

and multicomponent mixtures have now been completed. Three papers have

been prepared reporting the results of the pure component measurements .( 1 ' 2 , 4 ) paper on the binary mixture results is in the final

stages of review. (3;

A paper on the multicomponent mixture results is in the final stages of

preparation. In addition, two papers on the magnetic suspension

densimeter have been published. (4 , 5)

7.2 Calculational Methods . Four promising methods of calculating the

densities of liquid mixtures have been tested, modified and optimized

utilizing the pure component and binary mixture data reported above.

The four methods are a corresponding states method, a cell model, a hard-sphere model and a graphical method. Computer programs have been

written for all four methods and these have been used to calculate

densities for comparison with the data for the mixtures measured. The

calculated results agree with the experimental data to within 0.1% for

12
all multicomponent mixtures except those containing methane and butanes

but no nitrogen. If nitrogen is present the inaccuracies reduce to

0.1% or less.

A report has been prepared on the calculational methods work and is

currently in the review process. A summary report of the entire

project is also in preparation and a two-part paper has been submitted

to the LNG-5 Conference in Dusseldorf, Germany, August 1977.

8. Problem Areas . At this time, a definite answer cannot be given as to

why there is an inconsistency between calculated and measured data for

multicomponent mixtures containing butanes. Further work is being done

on the calculational methods under another project (2750548). In

addition, it is hoped that new measurements can be made at a later date

on the butane-containing mixtures.

9.

10,

Funding . July 1 - December 31, 1976

2751574 (measurements)

Man-years expended

Equipment and/or Services Purchased

Total Reporting Period Cost

Balance Remaining

2752574 (calculation methods)

Man-years expended

Equipment and/or Services Purchased

Total Reporting Period Cost

Balance Remaining

Future Plans . Objectives and Schedule: Quarter

0.3

1.1K$

21.4K$

0.2K$

0.1

0.8K$

3. 2K$

0.0K$

Prepare multicomponent mixtures

data paper.

Prepare project summary report.

Prepare paper for presentation at

LNG-5 Conference.

References

1. W. M. Haynes and M. J. Hiza, Orthobaric Liquid Densities of Normal

Butane from 135 to 300 K as Determined with a Magnetic Suspension

Densimeter, Advan. Cryog. Eng. 2_1, 516-21 (Plenum Press, New York, 1976)

2. W. M. Haynes and M. J. Hiza, Measurements of the Orthobaric Liquid

Densities of Methane, Ethane, Propane, Isobutane, and Normal Butane,

J. Chem. Thermodynamics (Feb 1977).

3. M. J. Hiza, W. M. Haynes and W. R. Parrish, Orthobaric Liquid Densities

and Excess Volumes for Binary Mixtures of Low Molecular Weight Alkanes

and Nitrogen Between 105 and 140 K, J. Chem. Thermodynamics (to be

submitted)

.

4. W. M. Haynes, M. J. Hiza and N. V. Frederick, Magnetic Suspension

Densimeter for Measurements on Fluids of Cryogenic Interest, Rev. Sci.

Instrum. 47, No. 10, 1237-50 (Oct 1976).

5. W. M. Haynes, A Simplified Magnetic Suspension Densimeter for Absolute

Density Measurements, Rev. Sci. Instrum. 48, 39 (1977).

13
1. Title . PROGRAM FOR REDUCING THE COST OF LN6 SHIP HULL CONSTRUCTION -- PHASE II SHIP STEEL IMPROVEMENT PROGRAM

Principal Investigators . H. I. McHenry, M. B. Kasen, and R. P. Reed

2 . Cost Center Number . 2753430 - LNG Ship Hull Materials (Shipyard Contracts)

2751430 - LNG Ship Construction Materials (Metallurgical Evaluation)

2752430 - LNG Ship Hull Materials (Fracture Properties)

3. Sponsor Project Identification . Maritime Administration Misc. P. 0.

400-58073.

4. Introduction . Construction of LNG tankers requires the use of fine

grain normalized steels for the part of the hull structure that is

cooled by the cargo to temperatures in the range of 0 to -50°F. Several

ABS steels have satisfactory base plate properties but extreme care must

be exercised during welding to avoid degradation of the steel adjacent

to weld (the heat affected zone) to a level of toughness below U. S.

Coast Guard requirements. Significant cost problems are being encountered by U. S. shipyards due to the resulting inefficient low-heat-input

welding procedures that must be employed to meet the fracture requirements in the heat affected zone. The feasibility of reducing the cost of LNG ship hull construction was investigated in Phase I of this project, leading to the Phase II program described below.

5. Objective . The objectives of the Phase II program are 1) to have the

four major plate producers supply three LNG shipyards with production

heats of ABS steels modified to possess improved transverse fracture

properties at low temperatures, 2) to have the LNG shipyards evaluate

these plates by qualifying optimum welding procedures in accordance with

the USCG requirements, and 3) to provide' a metallurgical evaluation of

factors that influence heat affected zone toughness in the improved

steels.

6. Background . Early in 1974, the Welding Panel of MarAd's Ship Production

Committee recommended that a program be conducted to reduce the cost of

ship hull construction. NBS was requested by MarAd to propose such a program to the LNG subcommittee of the Welding Panel at a meeting in

Boulder in August. In mid-October, MarAd approved the initial phase of

NBS ' s recommended program, i.e., to survey the problem and the technology available for its solution. On the basis of this survey and as the result of a meeting of the Welding Panel in March, 1975, a coordinatedprogram involving the LNG shipyards, the steel suppliers, and NBS

was recommended to MarAd and to the Welding Panel. This program was approved and work started in May 1975. Cost-sharing contracts for the

evaluation of the improved steels were awarded in 197 5 to the three

participating shipyards: Avondale Shipyards, Inc., Newport News Shipbuilding and Drydock Co. and General Dynamics-Quincy Shipbuilding Division.

7. Program and Results . Steel deliveries to the three LNG shipyards were

completed in August 1976, The properties of the steels delivered in

this reporting period are summarized below:

14
steel ''^rade Steel Co. Plate

Transverse Charpy

Energy (ft-lb)

ASTM A537A-Mod (SSC)

V-062 (SSC)

V-062 (low sulfur)

Armco

Armco

Bethlehem

1/2-in-thick

1-in-thick

1/2-in-thick

1-in-thick

1/2-in-thick

1-in-thick

62 ft lb @ -80°F

43 ft lb (§ -SOT

66 ft lb (a -SOT

129 ft lb (? -80°F

76 ft lb @ -60°F

61 ft lb (? -60°F

Each of the shipyards started the weld evaluation test program during

this reporting period. A status meeting was held at Newport News Shipyard on November 3, 1976. The 17 attendees included representatives of

four shipyards (Newport News, General Dynamics/Quincy , Avondale and

Bethlehem Sparrows Point) , four steel producers (Bethlehem, Armco,

Lukens and U.S. Steel), ABS, MarAd and NBS . The initial results indicate

that T^S grades V-051, V-062 and CS are significantly improved by sulfide

shape control and that this improvement is reflected in the Charpyimpact toughness of the heat affected zone (HAZ) . In the case of ASTM

A537A-Mod steel, the base plate properties are significantly improved,

but the HAZ toughness at -60°F is worse than the HAZ toughness in con- ventional A537A-Mod.

A contract was signed with Lukens Steel Company to evaluate Cb-treated

V-051 steel with and without sulfide shape control. Lukens will provide

the steel and perform the weld evaluation. It was originally intended

that a shipyard would conduct the weld evaluation, but the shipyards

contacted did not want to participate on a cost-sharing basis.

8. Problem Areas . The A5 37A-Mod steel procured by General Dynamics for

this program does not meet the requirements for -60"'F applications. It

may be necessary to downgrade this steel to grade CS for use to -30°F.

The cost of downgrading is a potential program expense of nearly $6000.

9. Funding . July 1 - December 31, 1976.

10. Future Plans . The shipyard evaluation should be completed by June 30,

1977 and work should start on the comparative testing program (Phase II

of the Ship Steel Improvement Program)

.

Cost Center Cost to 12/31/76 Balance

1 K$

19 K$

17 K$

2753430

2751430

2752430

144 K$

61 K$

43 K$

15
1. Title . CUSTODY TRANSFER - LNG SHIPS

Principal Investigators . R. S. Collier and J. D. Siegwarth

2. Cost Center Niomber . 2750460

3. Sponsor Project Identification . Maritime Administration, Misc. P.O.

#400-58074, #400-69012.

4. Introduction . In response to a request from the U.S. shipbuilding

industry, NBS is conducting an independent design review of the shipboard custody transfer systems under the sponsorship of the Maritime

Administration and in cooperation with the major U.S. shipbuilding

companies

.

5. Objectives . The objectives of this program are to 1) Identify the

major technical areas relating to uncertainties in the measurement of

total mass and total heating value, 2) Estimate uncertainties in the

total mass and total heating value due to these identified factors,

3) Develop a proposed testing program for custody transfer system com- ponents, and 4) Investigate improved gauging techniques.

6. Background . Calendar year 1974 funding provided for the initial re- view of ships designated by MA Design LG8-S-102a MA Hulls 289, 290, 291.

The current funding provides for an extension of this program to include

ships of other designs which are being built by the major U.S. shipbuilding companies and also to verify tank survey and gauging methods

for LNG custody transfer.

7. Program and Results . A. Working relationships with four major U. S.

shipbuilders have been initiated. Most of the problem areas which

are common to custody transfer systems of all types have been identified

and are listed as follows:

1. Density

a) accuracy

b) rangeability

c) stability

2. Tank Strapping (Tank Surveys)

a) thermal effects

b) loading factors

c) measurement techniques

3. Convection (Non-Uniform Density)

a) density or composition stratification

b) possible isolation of measurement stillwells

4. Tank Weathering

a) time changes in composition, stratification, etc.

b) composition measurement

c) sampling

5. Liquid Level/Total Volume Measurement

6. Pressure and Temperature Measurements (gradients included).

7. Electronic Signal Conditioning, Data Reduction, Analysis and

Readout

16
B. Progress - The procedures for NBS involvement in evaluating the

multiple station photogrammetry were established with representatives of

the ship owners, the shipyard and tank fabrication facility, and the

survey contractors. Considerations of production schedules and physical

accessability to the inner tank surfaces have been reasonable constraints

to NBS activity at the tank construction site.

Gauge rods were manufactured and two prototype rods were tested during an actual photogrammetric survey. As a result of this test only minor

problems were encountered and it is felt the entire complement of ten

gauge rods may be deployed during one of the next two surveys without

interference with the survey procedure. Nominal length measurements were

taken between targets on the ends of these rods and arrangements were

made with the NBS Dimensional Metrology Section in Gaithersburg , MD for

more precise measurements at the conclusion of the program.

At NBS' request, twelve extra targets were painted on the inner tank

surface for use as redundant surface coordinate data. This is part of a program to determine whether as many as 100 extra targets per tank will

be necessary or whether the present number of targets is sufficient. The

extra targets will be used to evaluate the closeness of fit to a tank

surface calculated from the original set of targets.

Surveys were obtained between targets located in the mid, and upper

regions of the tank using a solid aluminum rod held to the tank surface

with positive vacuum suction cups. These measurements were taken with

the use of construction scaffolding in the later stages of tank construction. Surface temperatures were recorded.

Photographic plates were examined with an x-y plotting microscope using

equipment of the NBS Dimensional Metrology Section. It was determined

that the 3a uncertainty for an inexperienced operator to find the center

of the target was approximately 2 ym; and with care could be improved by a factor of 2 to the order of 1 um. This corresponds in

actual coordinate dimensions to well within the + 1.2 mm for specifying

the coordinate location. Of course, this is just one aspect of the

coordinate determinations but probably the most important one. Arrangements were made for obtaining the target coordinate data on com- puter cards in a form where programs for calculating the model for the

tank surface may be utilized.

The program of RF gauging was continued with measurement on a 35 ft

diameter aluminum LNG container in cooperation with the Cincinnati Gas

and Electric Company. This is part of a program to establish scaling

laws between the resonance modes for extremely large tanks and their

laboratory size models. (If these laws are obtained, calibration curves

for the large tanks can be obtained from data taken on the models). The

primary frequencies of the 35 ft dicuneter tank were, within experimental

error, exactly those calculated from measurements of the tank size.

Extra modes were obtained which were thought to be due to guy wires

stretched across the tank diameter; this was confirmed by similar rigging

of the laboratory model. It appears now, at least for aluminum tanks,

that the scaling laws for the empty tanks are completely predictable.

It also appears that RF resonance measurement may be useful in measuring

some of the major dimensions of a large tank independently of other

measurement methods.

17
Problem Areas . A long baseline measurement in a horizontal direction

is deemed necessary in order to minimize the estimated uncertainties in

coordinate location. This may be difficult to do within the desired

accuracy. Tape or wire measurements and microwave methods have been

considered along with RF resonance methods.

Funding . July 1 - December 31, 1976

Man-years expended 0.5

Total Cost 36.7K$

Balance Remaining 4.0K$

Future Plans .

1. NBS will install a sufficient number of gauge rods on one of the

next two photogrammetric surveys in order to complete the assessment

of the photogrammetric technique to measure coordinate differences

in the lower and upper portions of the tank.

2. We will continue to assess the ability of RF resonance measurements

to give major dimensions of the empty tank and also to evaluate its

potential as a method of gauging LNG.

3. We will continue to work with the shipbuilders to assess the effects

of loading and stresses due to thermal contractions on the projected

tank capacity.

4. Depending on the continued funding of this program, we will analyze

the coordinate data as it comes from the photogrammetric procedure

and evaluate results using independent data from the gauge rods and

the redundant coordinates in order to complete the assessment of the

empty tank survey accuracy.

18
1. Title . HEATING VALUE OF FLOWING LNG

Principal Investigators. J. A. Brennan and J. M. Arvidson

2. Cost Center Number . 2756579

3. Sponsor Project Identification . Pipeline Research Committee (American

Gas Association) PR-50-48.

4. Introduction . This project will test instrumentation for making heating

value measurements in actual applications of flowing LNG. Information

from projects currently underway by Younglove (cost center 2757574) on densimeters and by Haynes and Hiza (cost center 2751574) on mixture

densities will be utilized where appropriate to provide state of the

art information.

5. Objectives . The objective of this program is to measure total heating

value of LNG flowing in a pipeline by the integration of individual

measurements of flow, density and specific heating value. Flow measurement requires determination of flowmeter performance in line sizes

larger than presently available calibration facilities. Therefore, a secondary objective is to establish appropriate flowmeter scaling laws.

6. Background . The LNG flow facility at NBS will be utilized to evaluate

the response of the individual elements in the heating value measurement. Different compositions of LNG will be prepared to provide a range

of densities and temperatures sufficient to determine any dependencies.

A limited amount of sampling work is included to determine the relative

importance of this parameter to the overall measurement.

Flowmeter scaling is being done utilizing the cryogenic and the water

flow facilities at NBS and private LNG peak shaving facilities. This

portion of the program is behind schedule because of scheduling problems at the private LNG facilities.

7. Results. A. Tests at NBS.

Three separate densitometer tests were run in liquid nitrogen on the NBS

liquid nitrogen flow facility. The shift in performance referred to in

the last report continued to occur each time the densitometer was thermally

cycled between room temperature and liquid nitrogen temperature. There

were seven such cycles during these nitrogen tests but the densitometer

had been cycled many more times during tests on other instrumentation.

The magnitude of the densitometer performance shifts did decrease during

the last series of tests and the shifts were bi-directional. This

probably indicates the performance is stabilizing but not yet stable.

No similar performance characteristics were detected in the first densitometer so nothing can be said about how typical this performance might

be. The performance will continue to be closely monitored and additional

data on other densitometers obtained whenever possible.

The densitometer was reinstalled in the LNG facility so that tests could

be run on the integrated system. System integration was done by monitoring the individual elements of the measurement station with a mini-computer system and appropriate computations made to indicate heating value

on a rate basis. Some problems were experienced in obtaining a suitable

signal from the calorimeter but subsequent discussions with the manufacturer have indicated possible solutions. These solutions will be

tried during the next test. In the interim, heating value measurements

were entered into the computer manually. Since the heating value cannot

change rapidly this procedure was not difficult to do for these tests,

but it is not a satisfactory solution to the problem.

19
Shortly after starting the tests some of the computer peripheral equipment

started to malfunction. This problem finally resulted in the loss of the

computer altogether, so the major purpose of the test could not be completed. The test was not terminated, however, since there was other information that could be obtained that would be useful in future tests.

Of significant importance was the ability to get additional data on the

densitometer. This was done by extending the test over several days and

allowing the composition to change due to boil off from one day to the

next. Density changes within the day were obtained primarily by changes

in the LNG temperature. LNG density was calculated from an analysis of a sample withdrawn from the LNG. A check on the analysis was also made by

calculating the heating value based on the analysis and comparing it with

the heating value measured with the calorimeter.

Initially the comparisons between the two heating values were pretty

good — usually within the experimental error. As the LNG weathered, the

comparisons became worse. The weathering observed in these tests was much worse than in any normal LNG facility because we were looking for wide

variations in the compositions and density. Therefore, the discrepancies

observed in the heating value may never occur in a normal LNG installation

but are of sufficient importance to warrant further investigation.

Additional testing on the NBS LNG flow facility will be done in conjunction with some testing required on a LNG sampling project (cost center

2750575). In that way more timely control can be exercised since the

gas analysis will be conducted on a more timely basis. During this series

of tests the computer will also be used to integrate the signals from the

individual components of the measurement system. The turbine flowmeter

will be removed from the flow loop during these tests to facilitate the

installation of the sampling probes required for the other project. This

change will not affect the test on the measurement station since the turbine flowmeter is not used for that purpose.

Results of all the tests will be published in a separate report after the

tests are completed.

B. Tests at Transco.

The new instrumentation on the gas phase flow measurements was installed

at the Transco peak shaving facility in Carlstadt, NJ in October. This

instrumentation includes measurements on orifice AP, line pressure, gas

temperature, ambient temperature and elapsed time. Both a 16 inch and

the 12 inch meter runs were instrumented. Recordings of these data will

be on magnetic tape which will be returned to NBS for processing.

Recording of the data from the liquid flow measurements vras expanded

to include the data from the sonic flowmeter as well as the second sensor

on the vortex shedding flowmeter. These data plus the output from the

first sensor on the vortex shedding flowmeter, the liquid temperature and

pressure and the elapsed time are also recorded on magnetic tape for processing at NBS.

Recording of the liquid and gas phase measurements are on separate recorders

but they are synchronized so that each recording is started at the same

time. Data is recorded on all measurements every ten seconds.

The system was checked out during vaporizer tests on December 1 and 2,

1976. Everything appeared to work normally during these tests and the

preliminary data reduction looks good. Data will continue to be recorded during any send out for the remainder of the season and the results

should be available for the next report.

C. Installation at Southern Energy.

A twelve inch vortex shedding flowmeter has been ordered for installation

at the Southern Energy Company's Elba Island import terminal. This flowmeter will be installed between the storage tanks and the vaporizers and

20
will measure the flow of LNG to the vaporizers. This measurement will

be compared to the vaporized gas measurement in the same way that the

measurements are compared at the Transco facility.

At the import terminal not only will data on a larger flowmeter be

available but, in addition, much more data will be available. Since the

import terminal will operate continuously, data will be available as re- quired for as long as desired.

In addition to the flowmeter the installation at Southern will include a densitometer and temperature and pressure instrumentation. All of the

instrumentation will be installed during the construction phase of the

terminal and ready for use when the terminal becomes operational.

8. Problem Areas . None.

9. Funding. July 1 - December 31, 1976.

10. Future Plans . Additional component integration tests on the NBS LNG

facility will be run in conjunction with tests on another LNG project.

Flowmeter field tests at the peak shaving facility will continue whenever

possible for the remainder of this send out season. Flowmeter installation

at Southern Energy will be completed as soon as possible.

Man-years Expended

Total Reporting Period Costs

Balance Remaining

1.0

86. 0K$

40.0K$

21
1. Title . LN6 DENSITY REFERENCE SYSTEM

Principal Investigators . Ben Younglove, John Arvidson and J. D. Siegwarth.

2. Cost Center Number . 2757574, 2750161

3. Sponsor Project Identification . American Gas Association, Inc.,

Project BR-50-10; National Bureau of Standards

4. Introduction » A density reference system has been developed to evaluate

the ability of commercially available instruments to measure densities

of LNG directly. Density is an essential measurement in determining the

total energy content of natural gas reservoirs. This effort is oriented

towards metrology, whereas the output from cost center 2751574 will provide basic reference data on pure liquids and mixtures, to evaluate

methods for calculating the density indirectly.

5. Obj ectives . The objective of this research is to provide a system for

evaluating the density measurement capability of commercially available

meters. From the commercial meters we will attempt to select one or two capable of performance as transfer standards, in order to provide

traceability of accuracy to field density measurement systems.

6. Background . The density reference system project was initiated in 1973.

Since that time the reference system has been designed, constructed, and

is now in operation, evaluating commercial density metering systems.

7. Program and Results . Additional methane density data were acquired and

the provisional accuracy report for the LNG density reference system has

been completed, reviewed and approved for publication as an NBSIR report.

The accuracy of a future density measurement has been established as

+ 0.21%. A second densimeter test has been planned for the same set of

densimeters and most of the densimeters have been remounted, recalibrated

by the vendor, readjusted or whatever else was required to obtain the

best results. Modifications to the density reference system include:

the crystal disconnect is now in the liquid so no mass and bouyancy cor- rections are required for the suspension, and the stirrer speed has been

increased and the stirrer converted to turbine pump to shorten sample

equilibrium time. The balance will be monitored in the future to ascertain that the measured weights lie within the balance range.

8. Problem Areas . The cause of the small occasion-to-occasion shift in

density measurement has not been located yet. Perhaps the change in

the crystal suspension arrangement will have eliminated this problem.

Monitoring the absolute weight may help locate it.

9. - Funding . July 1 - December 31, 1976

Man-years Expended 0.2

Total Project Cost 11.0K$

10. Future Plans . The four commercial densimeters previously tested will be

retested after the Archimedes type has been recalibrated and the vibrating plate type has been remounted to the cryostat. The readout parameter

has been changed in the capacitance type. The results of this retest

will be reported in the next period.

22
1. Title . LNG SAMPLING MEASUREMENT STUDY

Principal Investigator . W. R. Parrish

2. Cost Center Number . 2750575

3. Sponsor Project Identification . LNG-Sampling Measurements Supervisory

Committee

.

4. Introduction . Composition is used to determine both the heating value

and the quantity (through density) of LNG shipments. Thus, any error

in composition doubles when calculating the total heating value and

dollar value of a LNG tanker cargo. Compositions are determined by

sampling LNG, on either a batch or continuous basis, and analyzing the

vaporized mixture. Although several sampling techniques exist, none

have received widespread acceptance in the LNG industry. Also, a standard technique has not been established for analyzing the vaporized

sample

.

5. Objectives or Goals . The objectives of this work are to evaluate existing sampling techniques appropriate to LNG systems and to recommend the

most accurate analytical technique. Only sampling devices applicable

to pipelines are being considered. The sampling techniques are judged

on

a) representativeness of sample,

b) insensitivity of results to composition, temperature, pressure,

degree of liquid subcooling, flow rate and operator, and

c) simplicity.

Initial evaluations will be made in a laboratory-scale apparatus; final

evaluation of the most promising sampling techniques will be performed

in the LNG flow facility.

6. Background . This work is being performed at NBS because there is a need

to determine the best means for obtaining the composition of LNG shipments. Current LNG buying contracts include specifications on when and

how many liquid samples are to be taken but omit the sampling technique

to be used. The evaluation of sampling techniques by impartial professionals will lead to the acceptance of the most accurate composition

determination method by all parties involved in LNG custody transfer.

7. Program and Results . An evaluation of techniques for analyzing LNG type

mixtures has been completed. Gas mixtures, prepared gravimetrically in

this laboratory were analyzed by mass spectrometry (MS) and by gas

chromatography (GC) . The standard deviation in the heating values com- puted from the compositions obtained by MS ranged between 1.5 to 2 percent. By comparison the standard deviation in the heating values calculated from the GC analysis was 0.06 percent; the average error in com- puted heating values was 0.03 percent. The evaluation of the GC technique

failed to show any composition, operator or day-to-day biases for mixtures

comparable to Algerian LNG.

Construction of the laboratory apparatus was completed and two sampling

probes, a pitot tube and a side tap, have been evaluated. Although the

data have not been thoroughly evaluated, it appears that both probes can

be used to collect a representative sample from a flowing LNG stream.

The apparatus is being modified to accommodate several different kinds of

sample collecting and conditioning devices. Evaluation of these devices

will begin shortly. We expect to begin evaluating the most promising

sampling systems in the LNG flow facility in February 1977.

23
8. Problem Areas. None.

9. Funding . July 1 - December 31, 1976.

Man-years expended 0.8

Total reporting period cost 60.0K$

Balance remaining 27.0K$

10. Future Plans . Objectives and Schedule: Quarter 1 2

Evaluate sampling techniques in laboratory

scale apparatus

Evaluate most promising sampling techniques

in the LNG flow facility

)

>

24
1. Title . SURVEY OF CURRENT LITERATURE ON LN6 AND METHANE

Principal Investigator . Neil A. Olien

2. Cost Center Number . 2759574

3. Sponsor Project Identification . American Gas Association, Inc.,

Project BR-50-10.

4. Introduction . It is important that all NBS personnel working in LNG, as well as the AGA and others, keep up with what is going on throughout the

world in the LNG field. This project is designed to provide the Current

Awareness and other information services to allow workers to keep

abreast of new research and other developments.

5. Objectives or Goals . We will publish and distribute each April, July,

October, and January a listing of all significant papers, reports, and

patents relating to methane and LNG properties and technology. The

references will be listed under convenient subject headings. The

Quarterly will be distributed to all interested AGA member companies and

be made available to the general public on a subscription basis. In

addition, LNG related information will be entered into the Cryogenic

Data Center's Information System for quick retrieval. A continuing

awareness of the current publication scene is maintained for any new

periodicals to be reviewed cover-to-cover. Finally we will update and

make available comprehensive bibliographies on the properties and

technology of LNG. There are three bibliographies involved: methane

properties, methane mixtures properties, and processes and equipment

involving methane and LNG. These three will be updated annually.

6. Background . In 1969 we made a thorough review of the world's publications to determine which periodicals and abstracting services should be

scanned cover-to-cover to adequately encompass the LNG field. The

result is that we now scan over 330 primary publications and nearly 25

secondary publications. Of these, approximately one-third are directly

related to LNG. In addition, we have increased our coverage of the

energy field to include hydrogen as a future fuel. Much of this

information is also pertinent to LNG and as such is listed in our LNG-related publications. Our Current Awareness Service has been

published weekly since 1964 (beginning in 1975 the publication became

biweekly) and the Liquefied Natural Gas Survey has been published

quarterly since 1970.

7. Program and Results . Four issues of the LNG Quarterly are prepared each

year and distributed. There are now 126 subscriptions going to AGA

Member Companies and 16 3 to other subscribers.

The three comprehensive bibliographies mentioned in section 5 have been

reviewed and shortened, and more selective bibliographies have resulted.

The latest versions were completed as of January 1, 1976.

B-1371 THE THERMOPHYSICAL PROPERTIES OF METHANE AND DEUTERO-METHANE

IN THE SOLID, LIQUID AND GASEOUS PHASES - A SELECTED BIBLIOGRAPHY. Indexed by property, phase and author, 80 pages

(Jan 1976) . ($8.00).

B-1372 THE THERMOPHYSICAL PROPERTIES OF METHANE MIXTURES - A

SELECTED BIBLIOGRAPHY. Indexed by property, system and

author, 140 pages (Jan 1976). ($10.00).

B-1264 PROCESSES AND EQUIPMENT INVOLVING LIQUEFIED NATURAL GAS AND

METHANE - A SELECTED BIBLIOGRAPHY. Indexed by subject and

author, 76 pages (Feb 1975). ($8.00).

25
B-1367 Supplement to B-1264, indexed by subject and author, 40 pages

(Jan 1976) . ($5. 00)

.

Over the past five years we have distributed over 430 copies of these

and the comprehensive bibliographies. A bibliography on LNG Patents

was supplied to AGA in May, 1975. Two supplements to this were also

completed, one in July 1975 and one in January 1976.

8. Problem Areas. None.

Funding . July 1 - December 31, 1976.

Labor 5.5K$

Other Costs 1.4K$

Total 6. 9K$

Remaining 1.2K$

10. Future Plans . Issue 76-4 was delivered to the printer on January 7,

1977 . In January 1977 we will update the three LNG bibliographies

mentioned above (B-1371, B-1372, B-1367). In addition we will prepare

a new bibliography on LNG related patents which will replace the one prepared in May 1976 as well as the two supplements.

26
1. Title . LIQUEFIED NATURAL GAS TECHNOLOGY TRANSFER

Principal Investigator . D. B. Mann

2. Cost Centers . 2750403, 2751403, 2752403, 2750570, 2754574 and 2758574.

3. Sponsor Project Identification . Maritime Administration Miscellaneous

Purchase Order No. 400-69012; American Gas Association, Inc. Project

BR 50-10; American Bureau of Shipping, letter dated 21 November 1975.

4. Introduction . The liquefied natural gas program at the Cryogenics

Division of NBS-IBS/Boulder represents an investment by industry and

Government agencies of over $5 million over the past six years. This

investment was designed to develop reference quality properties data for

both fluids and materials, instrumentation and measurement technology

for the use of the LNG and related industries. Information developed

under this program must be transmitted to the ultimate user in a timely

and useful format. The classical publication methods of NBS most

certainly provide the scientist and research engineer information in a form most useful to the academic or near academic community. However,

as a result of extensive assessments of user requirements, it was found

that an additional effective mode for technology transfer would be an LNG Materials and Fluids Data Book. A complete outline and planned table

of contents has appeared in previous semi-annual reports. The Maritime

Administration of the Department of Commerce and the American Bureau of

Shipping have agreed to sponsor the first year's efforts on the materials

section and the American Gas Association, Inc. has agreed to sponsor the

section on fluids and fluid mixtures. The project was begun on April 1,

1976.

5. Objectives . The Liquefied Natural Gas Materials and Fluids Data Book

will provide a method of quick dissemination of property data and related

information for the effective generation, utilization and transportation

of LNG. The object is to improve technology transfer from the current

NBS Cryogenics Division LNG physical measurements program to the users,

including federal agencies, the states and industry. For the purpose of

this data book, liquefied natural gas is defined as a cryogenic mixture

(at less than approximately 150 K) of hydrocarbons, predominantly methane,

with less than a total of 20% of the minor components ethane, propane,

iso and normal butane, and nitrogen as an inert contaminant. LNG materials

will be those associated with the liquefaction, transport and storage of

liquefied natural gas.

6. Background . The Data Book is only one of a number of information dissemination methods used to provide workers in the liquefied natural gas

(LNG) industry with properties data of known quality in a format consistent with the requirements of the intended user. In the case of the

LNG Data Book, the intended audience is the field engineer, plant

manager, ship designer or process engineer interested in a ready reference

of assessed quality for data to be used in conceptual design, process

monitoring, process analysis, and intercomparisons where precision and

accuracy are secondary to specific problem solutions. The hierarchy of

accuracy and precision will be defined and traceable through reference

to scientific and engineering literature.

Data is classified into three groups by the NBS Cryogenics Division.

Group 1 . Data which has been generated experimentally by NBS or has been

assessed, evaluated or experimentally verified by NBS.

Group 2 . Data which has been assessed and evaluated by NBS.

27
Group 3 . Data available in the scientific engineering literature

through the NBS Cryogenic Data Center or elsewhere. No NBS evaluation

or assessment has been made at this date.

In general, all data included in the LNG Data Book will be from groups 1 and 2. No new assessments or correlations are anticipated or required

for this work.

Data will be presented primarily in graphical form. Tables and analytical

expressions will be used only where absolutely necessary. Graphs and

charts will be in loose-leaf form for ease of updating and additions.

This form will also allow immediate implementation for data already

available under the NBS LNG program and will provide a convenient form

for the output of data from existing projects. The data book will not

be a substitute for traditional publications in the scientific literature

where measurement science, technique, precision and accuracy are paramount,

but will provide the data and references for the necessary assessment by

the user. The publication of both graphical and tabular data will be in a dual

system of physical units. These units will be the traditional LNG industry British System of BTU, pound, degree Fahrenheit and the SI system

of joule, kilogram and kelvin. It is the intent to give equal weight to

each system of units.

Nine structural metals have been selected with additions possible upon

consultation with the sponsors. Primary emphasis in the liquid section

will be data on pure methane, pure nitrogen, and methane-nitrogen mixtures.

7. Program and Results . A three-post expandable post binder and special

graphics have been selected, purchased and delivered. Over 80% of the

graphic material has been completed, which includes three of the six

wall size multi-property diagrams on nitrogen and methane.

8. Problem Areas . None.

9. Funding . July 1 - December 31, 1976.

Labor - Man years expended 1.0

Funds expended 77.0K$

Balance remaining 43.0K$

10. Future Plans . The first edition of the Data Book should be completed

and distributed by April with the first printing of 750 copies. A

second edition of the Data Book or an extended supplement seems to be

assured by the anticipated continuing support of existing sponsors and

the addition in sponsorship by the NBS Office of Standard Reference Data.

Supplementary data will include properties on non-structural materials,

insulations, pure ethane and mixtures of methane, nitrogen and ethane.

28
1. Title . OIML JOINT SECRETARIAT ON LNG MEASUREMENTS

Principal Investigator . Douglas Mann

2. Cost Center Number . 2750104

3. Sponsor Project Identification . American Gas Association, Inc.;

NBS-Office of International Standards; and NBS-Cryogenics Division.

4. Introduction . The liquefied natural gas program of the National Bureau

of Standards Cryogenics Division has, over the past five years, provided

the gas industry and interested Government agencies with properties data

on materials and fluids, instrumentation, and measurement assistance in

the support of commerce in this significant and growing segment of the

supplementary fossil energy supply. Support of this program by the

American Gas Association, Inc. and Federal Government agencies such as the Maritime Administration (MarAd) , NASA, GSA, Federal Power Commission

and the NBS-Office of Standard Reference Data has provided a basis for

the national acceptance of the results of the NBS LNG program. Through

the U.S. membership in the International Organization of Legal Metrology

there exists, at the present time, an opportunity to extend, internationally, the utility of data and measurement practice developed under

our joint Government/industry program. We have been requested (by OIML

membership) to establish an LNG Measurement Secretariat within OIML which,

if implemented, would provide a significant international forum for the

results of our joint work. It is believed that a joint Secretariat with

the LNG industry would provide the most effective means of accomplishing

these objectives.

5. Objectives or Goals . Our objective is to accomplish the following goals

within the next three years.

a) To establish U.S. (NBS) thermophysical properties data for LNG as the standard data in international usage.

b) To establish U.S. (NBS) materials property data used in fabrication

and construction of LNG facilities (liquefiers, storage, transport) as the standard data in international usage.

c) To establish U.S. (NBS) approved measurement technology and

instrumentation as related to LNG (pressure, temperature, density, liquid

level, flow) as the standard in international LNG trade. The precedent

has been established with the successful completion of the joint NBS-CGA

cryogenic flow measurement program which has resulted in the adoption of

a cryogenic flow measurement code by the National Conference on Weights

and Measures. We wish to extend this code on an international basis.

d) To establish and maintain the leadership of U.S. science, engineering,

and industry in the research, technology, manufacture and marketing of

instruments and measurement systems for liquefied natural gas.

6. Background . OIML was founded in 19 5 5 to promote intergovernmental

cooperation in the field of legal metrology which relates to the com- patibility of standards of measurement and the legislation and government

regulations which may affect such standards of measurement. OIML

recommends uniform international requirements for scientific and measurement instruments used in industry and commerce and works out model laws

and regulations for consideration by member nations; and, in addition,

serves as a center of documentation and information exchange in legal

metrology. At present 4 3 nations are members of this intergovernmental

organization.

The United States joined OIML in 1972 (the Senate by resolution of

August 11, 1972 gave its advice and consent to the accession of the U.S.

to the convention establishing OIML) . The responsibility for managing

U.S. participation in OIML was assigned to the Department of Commerce

29
and has since been delegated by the Department to the National Bureau of

Standards (NBS) . Under the general guidance of the Department of State

and the Secretary of Commerce, NBS is directly responsible for formulating and implementing U.S. policy towards OIML. U. S. participation in

the organization is deemed important for two reasons: First, to protect

and enhance some $1 billion worth of scientific and measurement instruments

exported each year by U. S. firms and to insure equity in the trade of

commodities measured by these instruments; and second, to maintain the

U.S. as the world leader in the field of metrology.

In the spring of 1975 at a meeting in Paris of the International Committee

of Legal Metrology, the French and U.S. representatives discussed the

possibility of creating a new Reporting Secretariat No. 13 on "Liquefied

Natural Gas (LNG) Measurement." The U. S. representative, W. E. Andrus

,

Jr. of NBS, agreed to explore the possibility with U. S. industry and

interested government agencies. These discussions resulted in a decision

to propose a joint Secretariat with the American Gas Association and

NBS-Cryogenics Division in order to best accomplish the tasks. These

conclusions were reached during several meetings extending through the

latter part of 1975 and early 1976.

7. Program and Results . The final organizational meeting was held at NBS

Boulder in August 1976 attended by representatives of the American Gas

Association, the American Petroleum Institute and the NBS Office of

International Standards Program. At this meeting Mr. Lee Hillburn, an employee of the Phillips Petroleum Company was selected as the A.G.A.

CO- technical advisor for the Secretariat on LNG Measurements. Mr.

Douglas Mann has been designated as the NBS co-technical advisor.

Mr. D. E. Edgerly, NBS Special Assistant for International Standards

Program, indicated that the Secretariat for LNG Measurements will be

proposed to the International Committee in October and will be assigned

to the Pilot Secretariat No. 5 "Measurements of Volumes of Liquids."

The Pilot Secretariat has not been assigned to a country but currently

the U.S., West Germany and France are involved in assuming this Secretariat . The first task of the Working Secretariat on LNG Measurements will be to

provide a definition of the scope of the Secretariat on LNG Measurements.

Consideration will be given to both static and dynamic measurement

methods

.

8. Problem Areas . None.

9. Funding . July 1 - December 31, 1976.

Labor - Man years expended

Funds expended

Balance remaining

10. Future Plans . A draft scope for the LNG Measurements Secretariat will

be generated and circulated to interested industry and government agencies prior to submission to the NBS Office of International Standards.

0.1

11. 0K$

22. 0K$

30
1. Title. FEDERAL POWER COmiSSION CONSULTATION

Principal Investigators . D, B. Chelton, T. R. Strobridge and A. F.

Schmidt.

2. Cost Center Number . 2750404

3. Sponsor . Federal Power Commission - Bureau of Natural Gas -- letter

agreement dated 4 June 197 3.

4. Goals . The Cryogenics Division will provide consultation and advisory

services to the Federal Power Commission on the cryogenic safety and

the design aspects of current applications before the FPC for authorization of LNG terminal and storage facilities. These services cover

properties of cryogenic environments, insulation systems, cryogenic

safety, thermodynamics, heat transfer, instrumentation, and cryogenic

processes such as refrigeration and liquefaction.

5. Background . Cost Center initiated July 7, 1973.

6. Program and Results . The status of those facilities presently under

the jurisdiction of the Federal Power Commission and subject to our review are outlined in the following table.

Elements of the facilities that are subject to review are the land-based

cryogenic storage tank components, bounded by the tanker or barge, the

inlet and distribution pipelines. These include, but are not limited

to the transfer lines, the storage tanks, the vaporizers and the process

piping as it interacts with the storage tanks. It is essential that the

reviews cover the operation, maintenance and emergency procedural

philosophies for each terminal. Based upon these studies, reports are submitted to the staff of the FPC setting forth the technical evaluations

and conclusions on each proposal.

Emphasis is placed on the safety aspects of the facilities including

their possible interactions with the surrounding areas. The impact of

engineering design such as appropriate use of existing technology and

material selection for structural integrity must be assessed. The

basis of review includes various codes and standards, prior experience,

precedent and engineering knowledge. Vapor cloud generation and plume

dispersion is considered a subject beyond our area of expertise.

7 . Funding .

8. Future Plans . At the present time there are several pending

applications , but detailed information is not yet available. It is

anticipated that additional facilities will be reviewed as applications

are made to the Federal Power Commission.

June 30 - December 31, 1976

Anticipated Man-years of Effort FY 77

FY 77

40K$

0.8

50K$

31
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33
BIBLIOGRAPHY

NBS Reports and Publications Related to LNG Technology

Goodwin, R.D., "An equation of state for thermodynamic properties of

fluids," Proceedings, Fifth International CODATA Conference, University

of Colorado, June 28-July 1, 1976.

Goodwin, R.D,, Roder, H.M. , and Straty, G.C., "Thermophysical properties

of ethane from 90 to 600 K at pressures to 700 bar," NBS Technical

Note 684 (August 1976).

Straty, G.C., and Tsumura, R. , "Phase transition and melting pressures

of solid ethane," J. Chem. Phys. 64_, 859 (1976).

Straty, G.C., and Tsumura, R. , "PVT and vapor pressure measurements on ethane," J. Res. Natl. Bur. Stds. 80A, 35 (1976).

Tsumura, R. , and Straty G.C., "Speed of sound in saturated and com- pressed fluid ethane," Cryogenics (in press, 1977).

Weber, L.A. , "Dielectric constant and the derived Clausius-Mossotti

function for compressed gaseous and liquid ethane," J. Chem. Phys. 65 , 446 (1976).

Roder, H.M. , "The heats of transition of solid ethane," J. Chem. Phys.

65^, 1371 (1976 ).

Roder, H.M. , "Measurements of the specific heats, C and C , of dense

gaseous and liquid ethane," J. Res. Natl. Bur. Stds. 80A , Y39 (1976).

Roder, H.M. , "The PVT surface of simple liquids at densities near melting," Proceedings of the Fifth International CODATA Conference,

University of Colorado, June 28-July 1, 1976.

Diller, D.E., "Thermophysical properties data research on compressed

and liquefied gases at the NBS Cryogenics Division," Advan. Cryog.

Eng. 21, 522 (1976).

Diller, D.E., "LNG densities for custody transfer," Proceedings,

International School for Hydrocarbon Measurement, University of

Oklahoir.a, April 12-14, 1977.

Haynes, W.M., and Hiza, M.J., "Orthobaric liquid densities of normal

butane from 135 to 300 K as determined with a magnetic suspension

densimeter," Advan. Cryog. Eng. 2]^, 516 (1976).

Haynes, W.M., Hiza, M.J., and Frederick, N.V. , "Magnetic suspension

densimeter for measurements on fluids of cryogenic interest," Rev.

Sci. Instrum. 47/ 1237 (1976).

Haynes, W.M. , "A simplified magnetic suspension densimeter for absolute density measurements," Rev. Sci. Instrum. 4_8, 39 (1977).

Haynes, W.M. , and Hiza, M.J., "Measurements of the orthobaric liquid

densities of methane, ethane, propane, isobutane and normal butane,"

J. Chem. Thermodynamics (in press, 1977).

See attached reprints or preprints in appendices.

34
16. Hiza, M.J., Haynes, W.M.,and Parrish, W.R., "Orthobaric liquid densities

and excess volumes for binary mixtures of low molecular weight alkanes

and nitrogen between 105 and 140 K," J. Chem. Thermodynamics (submitted

1977) .

17. Parrish, W.R., and Hiza, M.J., "On the consistency of liquid-vapor

equilibria data for binary mixtures of methane with the light paraffin

hydrocarbons," Adv. Cryog. Eng. 21, 485 (1976).

18. Miller, R.C., Kidnay, A.J., and Hiza, M.J., "Liquid + vapor equilibria

in the methane + ethene and methane + ethane systems from 150 to 190

K, " J. Chem. Thermodynamics (in press, 1977).

* 19. Hanley, H. J.M. , Haynes, W.M. , and McCarty, R.D., "The viscosity and

thermal conductivity coefficients for dense gaseous and liquid methane,"

J. Phys. Chem. Ref. Data (in press, 1977).

20. Hanley, H. J.M. , Gubbins, K.E., and Murad, S., "A correlation of the

existing viscosity and thermal conductivity coefficients of gaseous

and liquid ethane," J. Phys. Chem. Ref. Data (in press, 1977).

21. Hanley, H. J.M. , and Cohen, E.G.D., "Analysis of the transport coefficients of simple dense fluids: the diffusion and bulk viscosity coefficients," Physica 83A, 215 (1976).

22. Hanley, H.J.M., Sengers, J.V. , and Ely, J.F., "On estimating thermal

conductivity coefficients in the critical region of gases," Thermal

Conductivity 14 , Proc. 14th Int. Conf . , Storrs, Conn. June 2-4, 1975,

(Plenum Press, New York, 1976).

* 23. Hanley, H.J.M., "Prediction of the viscosity and thermal conductivity

coefficients of mixtures," Cryogenics 16, 643 (1976).

* 24. Tobler, R.L., and Reed, R.P., "Fracture mechanics parameters for a 5083-0 aluminum alloy at low temperatures," Journal of Materials for

Engineering and Technology (submitted, 1977).

* 25. McHenry, H.I., "Ship steel weldments for low temperature service,"

Welding Journal 55, 387 (1976).

26. McHenry, H.I., and Reed, R.P., "Fracture behavior of the heat affected

zone in 5 % Ni steel weldments," Welding Journal (in press, 1977).

27. McHenry, R.I., "Fracture mechanics and its application to cryogenic

structures," Advances in Cryogenic Engineering, 22^, (in press, 1977).

28. Clark, A.F., Haynes, W.M. , Deason, V.A. , and Trapani, R.J., "Low

temperature thermal expansion of barium ferrite." Cryogenics 16^, 267

(1976).

* 29. Younglove, B.A. , and Siegwarth, J.D., "Cryogenic fluids density

reference system: provisional accuracy statement," NBSIR 77-852

(January 1977 )

.

* 30. Mann, D. B. , "What's new in LNG measurement and instriimentation"

Pipeline Industry 45, 21 (1976).

35

APPENDICES

A through 0

Phase transition and melting pressures of solid ethane*

G. C. Straty and R. Tsumura^

National Bureau of Standards, Institute for Basic Standards, Cryogenics Division, Boulder, Colorado 80302

(Received 29 September 1975)

The melting pressures of ethane at 14 temperatures from near the triple point to 95.50 K and pressures to 32.0 MPa are reported. A triple point temperature of 90.348±0.005 K is obtained from the data which is in agreement with the determination of Clusius and Weigand (1940) but in substantial disagreement with

other determinations. Qualitative evidence has been obtained which indicates the existence of a previously unrecognized solid phase transition along a boundary roughly parallel to the melting line at a temperature about 0.5 K below the melting temperature, suggesting that some previous melting point determinations may have been influenced by a misinterpretation of the effects of this transition.

INTRODUCTION

Although a number of melting point determinations have been reported for ethane,'-^ there still exists considerable disagreement on the correct triple-point temperature. Furthermore, no accurate data for the melting pressures above about 4. 3 MPa exist. Clusius and Weigand^ in 1940 reported the measurement of the melting line of ethane to a maximum pressure of 4.27 MPa

and obtained a triple-point temperature of 90.35 K. Other determinations of the melting temperature,^"*

however, yielded values in the vicinity of 89. 9 K.

In this paper we report new measurements of the melting pressures of ethane at 14 different temperatures

to a maximum pressure of 32. 8 MPa at 95. 5 K. The

data have been represented by a Simon equation which

has been used to obtain the triple-point temperature of

90. 348 ±0. 005 K in excellent agreement with the earlier data of Clusius and Weigand. ' Qualitative evidence has been obtained which indicates the existence of a solid- phase transition along a (P, T) boundary roughly parallel to the melting line at a temperature about 0. 5 K below the melting temperature, suggesting that some previous determinations of the melting point may have been

influenced by a misinterpretation of the effects of this transition. EXPERIMENTAL PROCEDURES

The ethane used in these experiments was commercially available research grade with minimum purity

certified by the supplier at 99.98%. This purity was

verified by chromatographic analysis. Temperatures were measured with a platinum resistance thermometer calibrated by the National Bureau of Standards on

the IPTS-1968. Pressures were determined by referencing, through differential pressure transducers, to

oil pressures derived from a precision oil dead-weight

gauge ac c urate towithinthegreaterof500Paor0.015%.

The apparatus and instrumentation was similar to that used previously in this laboratory^ with small modifications to be discussed. Measurements of the pressure as a function of temperature along the melting line of other fluids such as

Ha, Oj, Fj, and CH4*~* have been performed routinely

in this laboratory as part of programs to accurately

characterize technically important cryogenic fluids. For such measurements, it has only been necessary

to fill the cell with compressed liquid to the maximum

pressure, at a temperature slightly above the freezing

temperature corresponding to that pressure, and to then measure the pressure as the temperature is reduced. The slope of the pressure-temperature locus changes dramatically as the liquid begins to freeze

indicating that the two-phase condition exists in the

cell. Measurements along the freezing line can then be made. The normal temperature gradient along the

filling capillary and the small solid fraction in the cell during these measurements have been sufficient to prevent solid from plugging the capillary. Furthermore,

upon solidification there is usually a sufficient change

in density so that the solid-liquid boundary can be tra- versed over a considerable pressure range from near

the filling pressure to low pressures near the triple

point

.

Initial attempts to use these procedures for ethane were unsuccessful because of experimental difficulties associated with the somewhat unusual properties of ethane. In attempting to obtain samples in the two-phase

region by filling at higher pressures and cooling to the melting line, considerable subcooling was observed before the onset of freezing. When freezing began, a

solid plug would apparently form in the filling capillary,

isolating the pressure measurement system from the

cell. To remedy this, the capillary was brought into the cell through a reentrant cavity machined into the stainless steel cell closure and was provided with a

heater. In this configuration, a considerable temperature difference could be maintained between the massive

copper cell body and the filling capillary.

Several attempts were made to obtain data with this modification. The samples were prepared by filling

at moderate pressure, cooling to well below the expected triple point to ensure solidification and then

taking data while warming. Data obtained in this way

clustered about a line as indicated by • in Fig. 1, These

data suggested a triple point temperature of about 89. 9 K, consistent with some earlier determinations, and were initially interpreted incorrectly as representing the melting line. Attempts to make measurements

above about 4 MPa by warming were found to be impossible, however, since this pressure corresponds to the vapor pressure of ethane at the ambient laboratory

temperature and when this pressure was exceeded, considerable mass transfer out of the cell was associated

with the condensation of liquid into the external portions

The Journal of Chemical Physics, Vol. 64, No. 2, 15 January 1976 .A-1

859
860 G. C. Straty and R. Tsumura: Phase transition of solid ethane

FIG. 1. Schematic phase diagram in the PT plane for ethane. The solid-solid boundary above 100.0 MPa was observed by Webster and Hoch (Ref. 11). The solid-solid boundary below

4.0 MPa from this work. Path of typical data before apparatus

modifications: • data obtained by warming, X data obtained by

cooling. For a more complete explanation, see text.

of the system. Attempts to obtain data by cooling from

high pressure and temperature were also unsatisfactory since the data then clustered about a second curve in- dicated in Fig. 1 by X. In either case, it was impossible to cross the pressure of about 4. 0 MPa because

of the mass transfer problem. Both sets of measurements were also unsatisfactory because of large scatter and lack of adequate reproducibility. The indi- cations of what appeared to be segments of two separate

melting curves were also difficult to explain at first.

The behavior was, however, understood upon closer examination. For measurements below the pressure

of 4.0 MPa, almost all of the ethane in the system resided in the cell, resulting in a sample almost entirely

in the solid phase. Heat applied to the capillary was

sufficient to ensure that pressure communication with

the cell was always maintained, and the data obtained were, in fact, a manifestation of a solid transition along a boundary ('Fig. 1) roughly parallel to the true melting curve but about 0. 5 K lower. The higher pressure line (X, Fig. 1) traversed a portion of the true melting line. The lack of reproducibility and large scatter were found to be associated with large cell temperature gradients imposed by an unnecessarily

high power input to the capillary heater. To verify this interpretation of the results, additional modification to the apparatus was made. The cell vol- ume was increased to over 50 cm^ while the volume of the external portions of the system were minimized to less than 1 cm^. In addition, these external portions were heated to about 330 K, well above the ethane criti- cal temperatures of 305 K. With these modifications it was then found possible to

fill the cell with liquid at the highest pressure of in- terest, to cool sufficiently to initiate solidification, and

to then traverse the melting line in either direction without encountering the difficulty at 4 MPa as found

previously. Under these conditions, the solid fraction

in the cell was always small. The heat input to the capillary necessary to prevent plugging was also found

to be very small or zero, consistent with the experi- ence with other fluids. Data were highly reproducible

with minimum scatter, and were found to coincide roughly with the high pressure portion of the curve ob- served previously and its extension to lower pressures. THE MELTING LINE

The results of the melting line measurements were

fitted to the Simon melting pressure equation,

P=Pt+Po[{T/Tt)'-l] , (1) where the subscript t refers to the triple point, and P

and T are the pressure and temperature. The value of P, = 1. 2 Pa was taken from a vapor pressure correlation

for ethane by Goodwin'" at the triple point temperature

of 90. 35 K. The parameters yielding the best fit were

the following:

P, = 1.2 Pa (Ref. 10) , Po = 255.97 MPa ,

Tt = 90. 348 K ,

e =2.179 .

FIG. 2. Deviations of experi- mental melting pressures from

the Simon equation, • , this work, X, Ref. 1. The solid line corresponds to the range of pressure resulting from a dif- ference of ±0.005 K in temperature.

91 92 93 94 95

T. K

J. Chem. Phys., Vol. 64, "j. '', 15 January 1976 A-2
G. C. Straty and R. Tsumura: Phase transition of solid ethane 861

TABLE I. Ethane melting pressures and

deviations from Eq. (1).

T (K) P (MPa)

90. 40 0. 3231 -0.189

90. 45* 0. 6181 -2.345

90. 50 0. 9496 + 0. 810

90. 57* 1. 338 -2.804

90. 60 1. 558 -0. 182

90. 64* 1. 895 4. 549

90. 74» 2. 493 2.551

90. 80 2. 795 -0.219

90. 83* 3. 070 2. 690

90. 93* 3. 698 2.411

91. 00 4. 035 -0.247

91. 03* 4. 266 0.801

91. 50 7. 182 0.196

91. 50 7. 145 -0.317

92. 00 10. 30 — 0. 095

92. 50 13. 49 0. 081

93. 00 16..66 0. 008

93. 00 16. 67 0.091

93. 50 19.,89 0.117

94. 00 23. 09 0.024

94.,50 26.,35 0. 064

95. 00 29.,59 -0.026

95. 50 32.,85 -0.107

"Reference 1.

The experimental results and their deviations from the equation are given in Table I. These deviations are

plotted in Fig. 2 along with the data of Clusius and

Weigand' for comparison. The derived triple point

temperature of 90. 348 ±0.005 K is in excellent agree- ment with 90.35±0.03 K obtained by Clusius and Weigand.

It is interesting to note that experiments performed

by completely freezing a solid sample and then warming

through the melting transition resulted in values for

the triple point of about 89.9 K*~* while those of Clusius and Weigand, * made by cooling the liquid until freezing, resulted in a higher melting temperature . This

suggests that the measurements performed by warming the solid from low temperature may have been misinterpreted and that the effect of the solid transition has been responsible for obtaining such low melting points.

This would, of course, be the situation for specific heat type experiments if the heat of transition was in- correctly interpreted as a large pre-melting effect or

as the heat of fusion,

SOLID-SOLID TRANSITION

When measurements were made with a small solid fraction in the cell and with very low heater power to the capillary, as was necessary for the melting line measurements, it was, of course, impossible to ob- serve the solid transition due tO the unavoidable plugging of the capillary. However, if the cell were filled

to a large solid fraction, and by using fairly large heat- er power to the capillary, pressure communication with

the cell could be maintained and the solid transition could be detected. The necessary large gradients imposed on the cell, however, introduces considerable

uncertainty in the temperature determinations and the observations can only be considered qualitative.

An additional check on the existence of the solid transition was made by observing the temperature as a function of time as the cell, filled with solid, was

slowly warmed. A number of runs using various constant input powers to the cell were made and in each

case distinct changes in the warming rate were ob- served at about 89, 8 K associated with the solid trans- formation and at about 90, 3 K corresponding to melting.

Based on these qualitative results, it appears that the solid-solid boundary is roughly parallel to the melting

line at a temperature about 0. 5 K lower. This is not inconsistent with the measurements of Webster and

Hoch'' who detected a definite solid transformation

above about 100.0 MPa, Experimental difficulties prevented them from making measurements below 100.0 MPa but from their data and from certain theoretical considerations, they predicted a sol id- solid- liquid tri- ple point for ethane at lower pressure. No evidence for such a triple point below our maximum pressure of

32, 8 MPa was observed in this work, and the solidsolid boundary, in fact, appears to continue to low

pressure.

Note : After the completion of this work, we learned

of some visual observations and dilatometric measurements on solid ethane by Professor D, Eggers'^ who

confirms the existence of a plastic-crystalline phase

in a temperature range extending to about 0. 45 K below

the melting temperature. He has found this isotropic

phase to be thermodynamically stable and not a metastable phase formed only under certain special conditions. We thank Dr, Eggers for discussing his work

with us prior to publication,

*This work was carried out at the National Bureau of Standards under the sponsorship of the American Gas Association, Inc. tConsejo Nacional De Ciencia Y Tecnologia (CONACYT) Mexico City. Currently a guest worker with the Cryogenics

Division, National Bureau of Standards, Institute for Basic

Standards,

'k. Clusius and K. Weigand, Z. Phys. Chem. B 46, 1 (1940). ^R. Wiebe, K. H. Hubbard, and M. J. Brevoort, J. Am.

Chem. Soc. 52, 611 (1930). 'R. K. Witt and J. D. Kemp, J. Am, Chem, Soc. 59, 273

(1937). ^L. J. Burnett and B. H. Muller, J. Chem. Eng. Data 15, 154 (1970), 'See for example G, C, Straty, and R, Prydz, Rev. Sci. In- strum. 41, 1223 (1970).

^R. D. Goodwin, J. Res. Nat. Bur, Stand, C 65, 231 (1961), 'L, A. Weber, J. Res. Nat. Bur. Stand, A 74, 1 (1970),

°R. Prydz and G. C. Straty, Nat, Bur, Stand, (U.S.) Tech.

Note 392 (Revised 1973).

'R. D. Goodwin, Nat. Bur. Stand, (U. S. ) Tech. Note 653

(1974).

'"R. D. Goodwin, Natl. Bur, Stand. (U. S. ) Interim Report, NBSIR 74-398 (1974). "d. S. Webster and M. J. R. Hoch, J. Phys. Chem Solids

32, 2663 (1971).

'^D. F. Eggers, Jr., J, Phys, Chem, 79, 2116 (1975). "For an example of metastable behavior, see for example, W,

F, Giauque and J. B. Ott, J. Am. Chem. Soc. 82, 2689

(1960),

J. Chem. Phys., Vol. 64, No. 2, 15 January 1976 A-3

JOURNAL OF RESEARCH of the National Bureau of Standards — A. Physics and Chemistry

Vol. 80A, No. 1, January-February 1976 PVT and Vapor Pressure Measurements on Ethane*

G. C. Straty and R. Tsumura**

Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302

(October 15, 1975)

New measurements of the vapor pressures and PVT properties of ethane are reported. PVT

determinations have been made from near the triple point to 320 K at pressures to 33 MPa. The

density range investigated extends to more than three times the critical density. The new measurements

of the vapor pressures of ethane extend from 160 K to near the critical point.

Key words: Density; ethane: vapor pressure: PVT.

1 . Introduction

Liquefied fuel gases, such as LNG, are expected to play an increasing role in satisfying future energy

requirements. Accurate thermophysical properties

data for these liquefied gas mixtures are necessary for the design of liquefaction plants, transport equipment,

shipping and receiving terminals, and for custody

transfer. The near infinite variations in mixture compositions encountered with these fuel gases rule out completely experimental or strictly computational

approaches for determining these properties. Calculation methods, based on accurate, wide range pure

component data and selected mixtures data are being

developed in a number of laboratories, and appear

to offer the only reliable and economical approach

for the generation of the necessary thermophysical

properties.

This paper reports new measurements of vapor

pressures and PVT properties of pure ethane. The

measurements have been made as part of a comprehensive program to provide the required experimental

data and to develop suitable calculation techniques for mixture properties determinations. PFT" measurements

have been made from near the triple point (90.348 K)

[1]' to 320 K at pressures up to 33 MPa. The density

range extends to more than three times the critical density. The new measurements of the vapor pressures

extend from 160 K to near the critical temperature

(305 K).

*This wr)rk was carried out at the National Bureau of Standards under the sponsorship

of the .-\merican (ias .Association, Inc. •*Cnnsein Naci'.nal De (jencia Y Tecnolopia (CONACYT) Mexico City. Currently a

tiuest worker with tlie ('ryogenics Division. National Bureau of Standards, Institute for Basic Standards.

' Figures in brackets indicate the literature references at the end of this paper.

2. Experimental Detail

To measure single-phase densities, the gas expansion

technique was used. A series of pressure-temperature

observations are made on a nearly constant density

sample of fluid confined in a cell of accurately cali- brated volume. When either the maximum pressure or maximum temperature is reached, the fluid is ex- panded, to low pressure, into large calibrated volumes

maintained at an accurately known temperature

above room temperature. The density can then be

determined from the cell volume and the compressibility factor (PV/RT) of the ethane at the conditions

of the expansion volumes.

The ethane used was commercially available re- search grade with specified minimum purity of 99.98

percent. This purity was verified by chromatographic

analysis. Temperatures were measured on the IPTS

(1968) with a platinum resistance thermometer cahbrated by the National Bureau of Standards. Pressures

above about 3 MPa were measured by referencing to

oil pressures derived from an oil dead weight gauge

accurate to within 0.015 percent. Lower pressures were measured with a precision fused quartz bourdon

tube gauge which had been previously calibrated

against an air dead weight gauge accurate to within

0.01 percent. The apparatus and procedures were

similar to those used previously in this laboratory for measurements on several other cryogenic fluids [2-5]

and have been described in detail [6-8]. SHght

modification to existing apparatus was necessary

because of the higher critical temperature of ethane.

Those external parts of the system which contained

fluid during a measurement were heated to well above

the critical temperature (typically 330 K) in order to reduce the relative density of the fluid residing in these parts, permitting a more accurate adjusted density to be computed.

B-1
3. Results

With the techniques used here, each experimental

PVT "run" consists of a number of pressure-temperature observations lying along a near-isochoric path.

About 50 such runs were made covering a density

range of from about 1.5 to over 21.5 mol/1. Each run

consisted of from 5 to 16 PVT points, depending on the

density. Measurements were always made at fixed temperatures to permit direct analysis in terms of isotherms. A total of over 450 PVT data points was

determined. These data are tabulated along isotherms

in table 1.

Table 1. PVT data for ethane

p P PP

P P P (MPa) (mol/1) (MPa) (MPa) \ IllUi/ 1

;

T= 92.00 K T= 112 00 K T= 130.00 K

0.7928 21.629 1.1911 20.911 2.9285 20.287 6.8417 20.990 13.7499 20.450 T= 93.00 K 11.2851 20.6898

21.041 21.163 29.7809 20.694

8.7870 21.682 T= 114 00 K T= 132.00K

T = 94.00 K 5.4980 20.254

3.8739 20.882 17.2765 20.436 3.5870 21.599 8.8149 20.942 26.4639 20.577

10.4980 21.664 24.9715 21.152 33.6963 20.687

T= 96 00 K T= 116 00 K T= 134.00 K

6.3091 14.6217 21.555

21.641

1.9636 20.776 7.2368 20.209 6.3156

12.0035

20.841 20.913 20.8906 20.425

no fill k 19.0660 21.009 T = 136.00 K

T —I — 29.2820 21.143

8.1853 21.503

1.3689 20.030 T= 118 00 K 9.2490 20.167

19.1732 21.625 24.5518 20.416 8.0478 20.791 34.0682 20.561 T = 100.00 K 15.7492 20.896 23.2017 20.997 T = 138.00 K

1.7991 21. .348 11.3755 21.468 r= 120 00 K 3.7831 20.008 23.8694 21.613 12.1243 20.144

1.2747 20.621 28.2309 20.407

102.00 K

6.8130 20.702

1 U . oUZU 20.757 T = 140.00 K

4.7964 21.315 19.6919 20.883

15.4890 21.448 20.988 6.0574 IV.V/Z 28.5382 21.603 15.3375 20.129 T = 122.00 K 31.9091 20.400 f — 104 00 k 3.8664 20.592 T — 14,0 00 w

1.1828 6.9584

19.9098

21.198

21.269 21.434

1 A 9QQfl 23.7193

O 1 C 0 1 A

20.737

20.873 20.979

7.6559

18.7024

19.926 20.117 33.1959 21.594 T"

/ — 124 00 K

35.5822 20.392

T= 106.00 K 0. Z4'00 20.553 T = 144.00 K

9.0567 21.221 11.6827 20.627 0.9387 19.722 18.0492 20.724 9.8460 19.890 24.4329 21.422 27.7606 20.863 22.1094 20.107 T = 108.00 K r= 126 00 K T= 14«.00 K

1.8227 21.065 7.9236 20.505

5.4489 19.667 6.4514 21.125 21.9553 20.712

15.7717 28.9678

19.856 20.091 12.4806 21.193 31.8410 20.855 29.0045 21.412 T= 128.00 K

110.00 K 7= 152.00 K T= 0.6715 20.312

10.4787 20.470 1.2079 19.424

4.7101 21.034 18.8911 20.597 8.9240 19.584

16.4766 21.176 25.8617 20.703 22.1746 19.836 33.5810 21.403 35.9026 20.847 35.8308 20.077

p

(MPa) P(mol/1) T= 156.00 K

5.5978 19.369 14.2846 19.545 28.6589 19.820 T= 160.00 K

0.4675 19.091

10 9Rfl 1 7 . /oo

IQ

or 1 A£.Q 1 0 ftOA 1 y . OUO T= 164.00 K

4.2580 19.043 14.0474 19.250 26.2885 19.508

T = 168.00 K

1.7297 18.817

7 A/1 17 1 o . yo7 19.6507 19.230 32.3436 19.495 T= 172.00 K

1.2449 18.650 5.7607 18.768 11.8776 18.916 25.3400 19.214 38.372? 19 482

/ — 1 7A CU\ k'

1.1073 18.488

5.2091 18.602 8.8759 18.691 16.9907 18.892 31.0365 19.201

r= 180.00 K

0.5247 18.295 4.9583 18.442 8.2782 18.525

13.3001 18.655 22.2633 18.876 36.7092 19.189

T= 184.00 K

3.9725 18.253 7.9795 18.368 12.4806 18.483 18.2646 18.635 27.54S2 18.862 B-2
Table 1. PWT data for ethane — Continued

P P p

MI'ai IIMil/ll (MPa) (mol/1) T= 18H.0I1 K T = 216.00 k

1.9817 18.021 2.1043 16.798 7.2058 18.186 6.4050 16.998

1 1.9718 18.323 13.2349 17.267 17.2059 18.463 17.2225 17.417

£-tJ > \J 1 \J 18.620 22.7370 17.606 32.8340 18.850 29.1542 17.808

T= 192.00 K ^= 220.00 K

0.9865 17.815 1.4301 16.567

5 5964 17.977 5.1249 16.761

in 6669 18. 128 8.9985 16.934

16 5186 18.302 16.9669 17.250 22 0^30 18.447 21.1113 17.404 28.3464 18.607 26.8053 17.594 33.3471 17.798 T= 196.00 K T= 224.00 K

0.4943 17.619 4.4533 17.775 4.3322 16.536 8.4330 17.903 7.6124 16.699 14.9662 18.104 12.2714 16.904 21.1586 18.286 20.7255 17.237 26 R669 18.434 25.0127 17.392

18.595 30.8565 17.584

T= 200.00 K T= 228.00 K

0.6801 17.445 1.8552 16.198 3.5738 17.581 U.VZZO 10. "+00 7.3933 17.709 1U.4 /OZ 10.OD4 12.2367 17.866 la. / 104 10. Oo / 19.4175 18.087

1 7 99^^

25.8517 18.273

1 1 QOO 1 / .OOZ 31.6945 18.423

1 7 Q7/1

1 ( .0/4 T= 232.00 K T= 204.00 K

1.2667 15.950 3.7760 17.411 4.5825 16.167 6.7420 17.524 9.4583 16.428

10.6983 17.658 13.6904 16.633 16.4076 17.846 19.2025 16.874

23.9051 18.074 28.2402 17.215 30.2305 18.262 32.7523 17.372 36.4«96 18.412 T= 236.00 K T= 208.00 k

3.8508 15.920 0.5897 17.079 7.0049 16.114

17.354 12 4747 16.403

9 6616 17 461 16 9765 16.618

1 7 h'lA 1 t .uo^ 16.862 20 6552 17.831 ^1 QH 1

1

17.205 28.3791 18.062 35.0871 18.251 T= 240.00 k

T= 212.00 k 1.2548 15.515

2 2021 15.586 3.4269 17.048 6.3368 15.877 9.6570 17.293 9.4209 16.062 13.3583 17.434 15.5972 16.387 18.6673 17.619 20.2787 16.606 24.9088 17.819 26.1772 16.852 32.8419 18.051 35.7046 17.196

7=244.00 k

3.6366

4.6703

8.5355

12.2246

18.7424 23.5869

29.6476

15.487 15.556

15.817 16.039

16.375 16.595

16.842

r= 248.00 K

1.7380 15.078 5.9925 15.449 6.8908 15.508 11.1353 15.788 15.1129 16.023 21.8905 16.364 26.8798 16.586 33.1044 16.833

7"= 252.00 K

1.5930 14.811 3.9746 15.056 8.0325 15.392 9.0553 15.457 13.8649 15.771 18.0296 16.011 25.0394 16.354 30.1617 16.577

T= 256.00 K

3.7062 14.790 6.1397 15.018 10.3740 15.358 11.5324 15.433 16.6249 15.758 20.9491 16.000 28.1716 16.345 33.4255 16.568

T= 260.00 K

2.6858 14.414 5.7990 14.757

8.0637 14.963 12.8526 15.340

14.0783 15.417 19.3947 15.747 23.8662 15.990 31.2936 16.336

T= 264.00 K

2.4038 14.085 4.6766 14.389

7.6561 14.705 10.2294 14.931 15.3689 15.327 16.6466 15.405 22.1619 15.737 26.7721 15.981 34.3986 16.328

p p (MPa) (mol/l) 7=268.00 k

3.0548 13.884 4.2654 14.062

6.5471 14.352 9.6680 14 669

12.5033 14.914 17.8943 15.316 19.2306 15.395 24.9268 15.728 29.6684 15.973 T= 979 no k

2.0844 1.243 3^6257 13.670 4.8506 13.859 6.0679 14.032 8.2942 14.302 11.8077 14.650 14.8065 14.901 20.4232 15.306 21.8042 15.385 27.6780 15.719 32.5542 15.964 T= 276.00 K

2.1376 1.242 3.2684 13.256 5.3267 13.644 6.5457 13.824

7.7197 13.983 10.2212 14.275 13.9836 14.636 17.1196 14.890 22.9462 15.297 24.3837 15.377 30.4166 15.711 35.4306 15.957 T= 280.00 K

2.1904 1.241 2.9758 12.787 4.8428 13.234 6.9195 13.604 8.1526 13.778 9.4890 13.951 12.2137 14.259

16.1653 14.625 19.4376 14.880 25.4635 15.288 26.9473 15.368 33.1520 15.703 T= 284.00 k

2.2428 1.240 4.3982 12.768 6.3596 13.203 8.4885 13.563 9.8840 13.751 11.3395 13.933

14.2261 14.247 18.3557 14.615 21.7505 14.872 27.9731 15.280 29.4971 15.360 35.8724 15.696

B-3
Table 1. \'\ T <tcit<i for (th<ine — ( .iti\['muft\

I' iMI' I rnol 7=288.00 K

2.2951 3.0547 3.9706

5.8026

7.7971 10.1657 11.6682

13.2063 16.2439

20..5477 24.0580

30.4719

32.0446

1.239

1.955 12.194

12.745 13.160

13.540

13.7.35 13.920

14.237

14.607 14.863 15.273

15.3.53 r= 292.00 K

2..3466

3.8113

5.2158

7.1396 9.3105

11.8771 13.4688

15.0863 18.2640 22.7394

26.3645

32.9673

1.239 11.522

12.173

12.707

13.131 13.525

13.723

13.910 14.228

14.598

14.855

15.265

7=296.00 K

2..3987 3.2373

3.8806 4.3963 4.8686

6.4389

8.4817

10.8697 13.6040

15.2773

16.97.35 20.2846

24.8761 28.6475 35.4484

1.238

1.952 2.880

11.212

II..505

12.146

12.672

13.115 13.514

13.713 13.900

14.219

14. .59

1

14.848

15.258

H

(MI'a) 1 IMol/l 1 T= 300.00 K

2.4492 1.237 4.0309 2.875 4.6932 10.611 5.3970 11.196 5.9485 11.485 7.6275 12.109 9.8845 12.652 12.4490 13.102 12.4489 13.102

17.0906 13.704

18.8621 13.892 22.3018 14.211 27.0931 14.583 30.9501 14.841

T = 304.00 K

2. mi 1.237 3.4158 1.950 4.1784 2.873 4.6828 4.325

4.7721 9.097 4.9674 9.788 5.3930 10.298 5.5668 10.596 6.3948 11.173 6.9986 11.455 8.8474 12.082 11.3086 12.638 14.0362 13.092 17.0942 13.495 18.9013 13.696 20.7454 1 "X QUA

24.3137 14.204 29.2629 14.576

'JO O'jno 0.3 . zoUV

r= .306.00 K

4.8094 4.323

4.9441 6.,533 5.0757 9.092 5.8014 10.290

iMFai llllol/ll f

iMI'ai P

I moll r= 308.00 K

2.5499 1.236 4.3236 2.871 4.9341 4.321 5.1434 6.530 5.3872 9.086

5.6969 9.775

6.2111 10.280 6.4452 10.574 7.3779 11.142 8.0352 1 1.424 10.0940 12.066

19 74.1ft 1 91 Z.O^IO

1 J.DZDo 1 0 . Uoo

1 ft /^"^ 1 n 1 0 . 'to i 90ZU. 71/ ^9 lOZ 1 0

.

000

99 A9Q#^ ZZ.OZVu 1 Hlfx lo.O /o

9^» iOAA ZO.0Z4O 1/1 1 QA 14. IVO

0 1 .'+Z0 1

1I't.oOV A QAO

DC c:n9/l OO.OUZ4 1 A QOA 14.OZ0

r=3i2 00 K

2.5996 1.235 3.5908 1.947 4.4668 2.869 5.1793 4.316

5.5401 6.522 6.0206 9.072 6.4330 9.756

7.0307 10.254 7.3179 10.546 8.3744 11.116 9.1114 11.404

11.,3574 12.054 14.1819 12.618 17.2177 13.075 20.5666 13.4«0 22.5240 13.681 24.5119 13.869 28.3286 14.189 33.5824 14.562

7-= 316.00 K

2.6491 1.235 4.6083 2.866 5.4200 4.312 5.9358 6.513 6.6610 9.054

7.1729 9.732 7.8532 10.229 8.1986 10.522 9.3878 11.099 10.1982 11.390 12.6240 12.044 18.8045 13.068 22.3004 13.472 24.3313 13.673 26.3890 13.862 30.3236 14.183

7"= 320.00 K

2.6983 1 234

3.7629 1 945

4.7483 2 864

5.6574 4 307

6.3309 6 503

7.3064 9 032

7.9172 9 710

8.6869 10 211 9.0937 10 506

10.4137 11 087

11.2486 11 380

13.9007 12 036

17.0663 12 602

20.4014 13 060

24.0318 13 466

26.1304 13 667

28.2588 13 855

32.3174 14 176

Altlioufih comparisdn with data from other sources

is, in jienerai, impossible without multiple interpolations, the afireement has been deduced l)y examining

the density deviations of the various data sets [9, 10]

(rom densities calculated from an equation of state

for ethane due to (ioodwin [11]. The agreement is found to bt', in general, within the combined experimental error. Maximum difference occur in the critical region where the equation of state representation is expected to be less satisfactory and where the experimental densities are subject to increasing uncertainty.

Estimated uncertainty in the experimental densities

in this work is typically ±0.1 percent at the lowest

temperatures, increasing to ±0.2 percent at higher

temperatures and lower densities, becoming as much

as ±1.0 percent in the critical region.

New vapor pressure measurements also have been

made at 5 K intervals from 160 to 300 K and are given

in table 2. At each temperature, the pressure was

measured at least twice with some ethane being re- moved from the cell between measurements. Identical

pressure observations indicated that the two-phase

:ondition existed in the cell. A vapor pressure equation of the form

IniPIP,) x + Bx' + C^^ + Dx' + EA l - x)

'"' (1)

was fit to all available data for ethane [12]. Here,

X = {\-T,IT)l{\-T,ITr). and P and T are the pres- sure and temperature and t and c refer to the triple and

critical points. Coefficients giving the best fit were

found to be ihe following:

B-4
A = 10.67324

B = 8.33782

C -3.08489

D =-0.65857

E =6.04955

P, = 1.14 X 10-3 bar

T, = 90.348 /v[Refl]

Tr = 305.330 K [Ref 10]

Table 2

TI p T p

1 k 1 Kid L Pa

lOU.UU 91 ^09 9^n nn 7nn Aft

1lOD.UUnn OU.O / u ZoO.UU R9^ ozo.yoQA

170.00 42.870 240.00 966.60

175.00 58.636 245.00 1124.4 180.00 78.734 245.00 1124.8

180.00 78.706 250.00 1300.0

18.5.00 103.84 250.00 1301.9 190.00 134.63 250.00 1302.1 190.00 134.72 250.00 1301.8 195.00 172.21 255.00 1495.0

195.00 172.26 260.00 1670.3 200.00 217.26 265.00 1947.9 200.00 217.32 270.00 2208.0

205.00 270.93 275.00 2493.1 205.00 271.00 275.00 2493.2 210.00 334.13 280.00 2804.6

210.00 334.17 280.00 2806.2 210.00 333.98 285.00 3144.3 210.00 333.99 290.00 3513.5 215.00 407.34 298.15 4190.9

220.00 492.16 298.15 4188.9

225.00 589.73 300.00 4353.5

Deviations of the experimental vapor pressures from

those calculated from this equation for the various

data sets [9, 10, 13] are shown in figure 1.

010| ,

0 051-

o|—o "-o-

-0 05- ,

A ^

• • •

200 225 250 TEMPERATURE. K

300

HK-UKE I. Deviations of vapor pressures from eq. 1. • I his v»„rk: /,i.-(;l,T ,-t al. iKcl. I'al lKi-l.|Vil; . : l'„pr iKrl. V Douslin and

Harris. .n iK.-f. |10|).

4. Summary

We have made new wide-range measurements of

the vapor pressures and PVT properties of ethane.

These are the only data currently available which cover

the entire temperature range from the triple point to 320 K. In addition, these data are the only accurate PVT data available for the compressed liquid below

about 190 K. The data are being used along with other

available data to refine the calculation of thermodynamic functions for ethane and as input to. and as a check upon, new calculation methods for predicting

Hquefied natural (fuel) gas properties being studied

in this and other laboratories.

5. References and Notes

[l| Straty, C. C, and Tsumura, R.,,). Chem. Phys.. 64,859(1976).

[2] Weber, L. A.. J. Res. Nat. Bur. Stand. (U.S.), 74A (Phys. and

Chem.). No. 1, 93-129 (.Ian. -Feb. 1970).

[3] Prydz R., and Straty, G. C. Nat. Bur. Stand. (L'.S.), Tech. Note

392, 197 pages (Revised 1973).

[4] Goodwin, R. D., Nat. Bur. Stand. (U.S.) Tech. Note 653, 280

pages (April 1974).

[5] Weber, L. A., NASA SP-3088/NBSIR 74-374(1975).

|6] Goodwin, R. D., .1. Res. Nat. Bur. Stand. (U.S.), 65C,(Eng. and

Instr.), No. 4, 231-243, (Oct.-Dec. 1961).

[7J Straty, G. C, and Prydz, R., Rev. Sci. Inst. 41, 1223(1970).

[8] (;oodwin and Prydz, R., ,|. Res. Nat. Bur. Stand. (U.S.). 76A

(Phys. and Chem.), No. 2. 81-101 (Mar.-Apr. 1972).

[9] Pope G. A., (also reports vapor pressure and Pf Tdata of A. K.

Pal). Pli.D. Thesis, Dept. of Chemical Engineering, Ric University, Houston, Texas (,|uly 1971).

[10] Douslin. D. R., and Harrison, R. H., J. Chem. Thermo 5, 491

(1973).

[11] Goodwin, R. D., NBSIR 74-398 (1974). Goodwin has used a nonanalytic equation of state to correlate previously available data on ethane and to calculate provisional thermodynamic

functions. Experimental data from this w(»rk are being used

to till in gaps in previously published data and to refine the equation of slate to permit more accurate calculations of thermodynamic properties to be made. We defer extensive comparisons between data sets and a more elaborate analysis

for inclusion in a final report in preparation.

(12] Further refinements in the correlation are expected which will probably alter slightly the final values of the constants. The

deviation plot, however, is representative of the agreement among data sets. Coefficients for this equation will be in- cluded in the final report. See also reference |8]. [13] Ziegler, W. T., Kirk, B. S.. Mullins, J. C, and Berquest, A. R., Tech. Rept. No. 2. Project A-764, Eng. Expt. Sta. (ieorgia

Inst. Tech.: Atlanta, Georgia, December 1964.

(Paper 80A 1-878)

B-5

Dielectric constant data and the derived Clausius-Mossotti

function for compressed gaseous and liquid ethane*

L. A. Weber

National Bureau of Standards. Institute for Basic Standards, Cryogenics Division, Boulder, Colorado 80302

(Received 25 March 1976)

Measurements are presented for the dielectric constant of ethane in the saturated liquid and compressed

fluid states at temperatures between 95 and 323 K. Pressures ranged up to 390 bar. The data, which have an estimated uncertainty of 0.01%, are combined with accurate density data from several sources to produce the Clausius-Mossotti function over a wide range of temperature and density. An analytical expression of the Clausius-Mossotti fiinction is given, and the consistency of the available density data is discussed.

I. INTRODUCTION

This paper presents dielectric constant measurements

and the derived Clausius-Mossotti function for ethane. Measurements were made on the saturated liquid from

the triple point to near the critical point and on seven compressed fluid isotherms in the range 95-323.15 K. The data range in pressure up to 390 bar and in density

from 0.036 to 3, 16 times the critical density. This

work is part of a series which previously has included

data on hydrogen/ oxygen/ fluorine/ nitrogen/ and

methane.

Measurements of the dielectric constant, combined

with accurate density data for gases and liquids, provide useful information about molecular polarizabillties and molecular interactions.* Such measurements

are generally combined to form the Clausius-Mossotti

(CM) function, (l/p)(e - l)/(e +2), where e is the di- electric constant and p is the density. The CM ftmction has the property of being nearly a constant, generally varying only about one percent over a wide range

of density and temperature for nonpolar molecules. A

knowledge of the CM function provides a convenient and

sensitive way of determining density from accurate dielectric constant measurements. ' In addition, dielectric constant data can provide a convenient and sensitive intercomparison between independent PVT measurements, even in situations where the PVT data are

widely separated in temperature,

II. EXPERIMENTAL

The dielectric constant measurements were made

with the highly stable cylindrical capacitor developed

by Younglove and Straty,® which has a vacuum capacitance of about 33 pF. The curve of its vacuum capacitance versus temperature has proven to be stable to within one part in 10^. The dielectric constant e is given by the ratio C/ Cq, where C is the capacitance

with fluid between the plates and Co is the vacuum

capacitance at the same temperature. The capacitance was measured with a three-terminal ac bridge. Uncertainty in the determination of the dielectric constant

is estimated to be less than 0. 01%. Temperatures were measured with a platinum resistance thermometer

calibrated on the IPTS 1968 scale and were reproducible to 0. 001 K. The overall accuracy varied from

0.005 at the lowest temperatures to 0.03 K for the

room temperature measurements. Pressures were

measured with an oil dead weight gauge having an accuracy of about 0.01 percent. The sample holder and

cryostat are described elsewhere.'** The sample used was 99.99% pure ethane which was passed through a molecular sieve trap to remove any water.

III. RESULTS

The dielectric constant of the saturated liquid was

measured at 34 temperatures between 95 and 295 K.

TABLE I. Dielectric constant and calculated Clausius-Mossotti

values of saturated liquid ethane.

T px 10' CM

(K) (mol/cm') e (cmVmol)

95.00 21. 520* 1. 93563 11. 047 100.00 21. 341 1. 92576 11. 050 105.00 21. 159 1. 91590 11. 054 110.00 20. 975 1. 90606 11. 059 115.00 20. 793 1. 89612 11. 062 120.00 20. 602 1. 88952 11. 101 125.00 20. 419 1. 87661 11. 074 130.00 20. 232 1. 86687 11. 080 135.00 20. 046 1. 85700 11. 084 140.00 19. 857 1. 84713 11. 089 145.00 19. 667 1.,83721 11. 094 150.00 19. 475 1. 82729 11. 099 155.00 19. 281 1., 81729 11. 104 160.00 19. 086 1. 80725 11. 109 165.00 18. 887 1.,79714 11. 115 170.00 18.,687 1.,78696 11. 121 175.00 18.,484 1,,77669 11. 126 180.00 18. 279 1,,76628 11. 131 185.00 18.,070 1.,75576 11. 136 190.00 17.,861 1,,74516 11. 140 200.00 17.,429 1., 72349 11. 148 210.00 16,,971 1,,70104 11.,161 220.00 16,,499 1,.67786 11,,171 230.00 15,,997 1,,65352 11. 181

240. 00 15,.464 1,.62780 11, 191

250. 00 14,,890 1,,60036 11,,199

260. 00 14.,261 1,, 57076 11,,208 270.00 13,,549 1,. 53778 11,,220

275.00 13,,186" 1,,51962 11,,196 280.00 12,.747 1,.49994 11.,206 285.00 12,,258 1,.47809 11., 214 290.00 11,,699 1,.45318 11., 218 295.00 11,,024 1,. 42343 11,, 220

^Densities from Ref. 10. "Densities from Ref. 11.

446 The Journal of Chemical Physics, Vol. 65, No. 1, 1 July 1976 C-1
L. A. Weber: Dielectric data for ethane 447

TABLE n. Dielectric constant and calculated Clausius-Mossotti values of compressed liquid and gaseous ethane.

T

(K) P

(bar)

pxio'

(mol/cm') CM(cm' /mol)

120. 00 304. 927 1.90928 21. 026* 11. 062

120. 00 171. 351 1. 89966 20. 848 11. 066

120. 00 66. 985 1.89165 20.705 11.066

160. 00 360.454 1.84490 19. 827 11. 083

160. 00 358.376 1. 84471 19. 824 11. 083

160. 00 36. 520 1. 81160 19. 171 11. 107

160. 00 36.628 1. 81161 19. 171 11. 107

200 00 377. 816 1 78020 18. 564 11. 118

200. 00 256. 633 1.76482 18. 266 11. 122 200.00 151. 137 1.74954 17. 965 11. 127

200. 00 69. 172 1. 73601 17. 689 11. 137

200. 00 13. 071 1 72'i60 17. 472 11. 147

240. 00 392. 029 1. 71687 17. 305 11. 145 240.00 294.735 1.70044 16. 975 11. 151

240. 00 211. 148 1.68411 16. 645 11. 156 240.00 115.755 1.66165 16. 186 11. 164 240.00 62. 930 1.64649 15. 869 11 172 240.00 30. 356 1.63563 15. 637 11. 181

280. 00 376 142 1. 64857 15 919 11 166 280.00 253. 274 1.61794 15 274 11 182 280.00 165 058 1. 58855 14 653 1

1

1 yo 280.00 100. 002 1.55858 14 016 1

1

199

280. 00 54.692 1. 52795 13 355 11 205

320. 00 380. 835 1. 58441 14. 579 11 183 320.00 196. 092 1.51088 12. 962 11 226 320.00 113. 562 1.44096 11. 402 11 239

320. 00 79. 146 1.36772 9. 711 11 244 320.00 67.649 1.29621 7. 894 11. 256 320.00 62. 595 1.22571 6. 220 U. 249

320.00 56.260 1.15041 4. 235 11. 274

320.00 40. 699 1.07576 2. 194 11. 227

323. 15 318. 351 1. 55939 14. 051" 11 185

323. 15 243. 358 1. 52894 13. 389 11 195 323 15 204. 702 1. 50940 12. 959 11 201 323 15 184. 435 1. 49630 12. 668 11 205

323 15 163. 787 1 . 48155 12. 339 11 210

323 15 132. 020 1 . 45243 11. 684 11 216

1 1^ O^O . 1

o

109. 032 1 42223 10. 993 11 223

OOO 1 c O^O . X tJ 94. 055 10. 321 11 227

323 15 84. 177 1 . 36464 9. 650 11 230

77. 255 1 33429 8. 924 11 235

TP*? 1 ^ 72. 719 1 . Ov*±00 8. 195 11 238

69. 510 1 27426 7. 455 11 236

oZo. 1

0

66 909 1 . ^looo 6. 686 11 231

o^-o, 1 O 64. 448 1 919t^ft L , £i L £iO O 5. 893 11 229

ooo 1 c o^o . 10 61 725 1 18186 5 089 11 231 323.15 58. 073 1.15018 4 246 11 227

323. 15 52. 652 1.11762 3. 362 11 221

323. 15 44 559 1 . voo^o 2. 466 11 207 323.15 34. 222 1 . Ut)DoD 1 662 11 191

323. 15 62 010 1.18469 5 166 11 225

323. 15 54. 090 1.12503 3. 566 11 220

323. 15 38 024 1.06621 1 929 11 196 323.15 24 604 1.03699 1 089 11 185 323.15 16 106 1.02249 0. 6660 11 174

323. 15 10 202 1.01362 0. 4046 11 170 323.15 6 027 1.00782 0. 2326 11 171

^Densities from Ref. 15. ""Densities from Ref. 11.

11.3

_ 11.2

-'-11.1 -

11.1

, 0 005 fit 0.015 0.020 P\ />(Hl/»') FIG. 1. Clausius-Mossotti function for the saturated liquid and vapor derived from our e measurements combined with

densities from the references cited. References 12 and 13 are independent e — p measurements. The curve represents the

fit of Eq. (2).

The results are given in Table I. Measurements were

also made along seven isotherms between 120 and

323. 15 K at pressures up to 390 bar. The results are shown in Table II. Because the cylindrical capacitor was mounted vertically, measurements in the vicinity

of the critical point {approximately 305.3 K) were not attempted. Due to the configuration of the sample hold- er it was also not possible to make measurements in the saturated vapor. The dielectric constant data for the saturated liquid were combined with available deiisities to produce

the Clausius-Mossotti function, shown in Fig. 1. For

temperatures up to 270 K the densities of Haynes

and Hlza'" and of Canfield et al. " were used. At temperatures above 270 K the density data of Douslin and Harrison/' represented by their smooth curve, were

used. Also shown in the figure are the independent

density-dielectric constant data of Sliwinski'^ for the saturated liquid and vapor near the critical point and

the liquid CM data of Pan, Mady, and Miller" near the

triple point. Three points derived from the saturated

liquid density curve given by Burton and Balzarini'^ are shown. The error bars on these points indicate

the uncertainty Involved in estimating densities from

the figure given in their publication.

The single phase isothermal CM function data are

plotted in Fig. 2. The Isotherms at temperatures from

120 to 320 K made use of the PVT data of Straty and Tsumura," and the CM data at 323. 15 K made use of the densities of Douslin and Harrison" at that temperature. Also shown Is the single CM datum of Watson,

Rao, and Ramaswamy" at a pressure of one atmosphere at 298 K. The isothermal density data were fit- ted with polynomials of the form,

P= RTp + (1)

for the purpose of smoothing and interpolation. At temperatures below the critical, the polynomials were

J. Chem. Phys., Vol. 65, No. 1, 1 July 1976 C-2
448 L. A. Weber: Dielectric data for ethane

constrained at the saturation boundary to the densities from Fef. 10 and 12. The density was then calculated by an iterative procedure for a given pressure.

IV. ACCURACY AND COMPARISONS

The calculated CM function is extremely useful for intercomparing sets of PVT data. In Fig. 1 the saturat- ed liquid densities of Sliwinski are seen to be highly consistent with those of Haynes and Hiza. Sliwinski's estimated uncertainty in CM of 0. 1% increasing to 0. 4%

nearest the critical point is shown in the figure. In the range 270-295 K Douslin's densities are seen-tobe 0. 2%-

0. 3% higher than the others. The Burton and Balzarini results agree with those of Sliwinski within the uncertainty with which we could estimate the former. The Miller

ef al. densities are in agreement with those of Haynes

and Hiza near the triple point to within about 0. 1%. The data of Canfield et al.^'' lie between those of Miller

ef al. and those of Haynes and Hiza at 108 and 115 K

and agree very well with those of Haynes and Hiza at 161 K.

In Fig. 2 the isothermal CM data are compared with

the best estimate of the saturation curve from Fig. 1. The isotherms between 120 and 280 K, using the densities of Straty and Tsumura, are seen to be in good

agreement with the saturation curve. The small variation with temperature at a given density has been ob- served for other fluids and is believed to be real. Their density data at 320 K may be compared directly with the density data given by Douslin and Harrison at 323,15 K (assuming negligible dependence of CM on

temperature over this small range), and it is seen that the latter 's densities are again systematically higher

by about 0, 2%. The error bars indicate the deviations which would be introduced by a 0,01% uncertainty to the dielectric constant. All of the newer data are in good agreement with the datum of Watson, Rao, and

Ramaswamy,'* reported in 1934. Our dielectric constants are consistently smaller

than those of Sliwinski by about 0.014%, which is about

equivalent to the precision of his data. Our measuren.3

11.2

I*? 11.1

11.1

£ 323.15-^§°'^,

32011

210

ItflKI

a> 1111 OA»vo 1151

I 0.2%

o.oK n 0 010 0 01S />(Ml/ea3)

V'"

12011—<^

_L

0 020 n

FIG. 2. Clausius-Mossottl function for the single phase fluid making use of densities from the references cited. The curve

is for saturation conditions, from Fig. 1.

TABLE III. Parameters for Eq. (2); density in mol/cm'', temperature in kelvln.

11.180±0.005

30. 7 ±2.1 -1627 ±77 -0.021 ±0.003

ments are also smaller by about 0,018% than those of Miller et al. , who used a capacitor similar to ours.

Since, in each case, the agreement is within the combined uncertainty of the authors, these differences are

not considered significant.

The dielectric constant measurements presented

here, in combination with the saturated liquid densities recorded by Haynes and Hiza and the PVT data re- corded by Straty and Tsumura, along with the independent measurements recorded by Sliwinski have been

fitted with the equation.

CM €-1 1 € + 2 p A + Bp + Cf^ +DTP (2)

to provide an analytical expression for the results. The

very precise PVT data recorded by Douslin and Harrison were not included because of their large systematic deviation from the others. The coefficients given

in Table in are estimated to reproduce the ClausiusMossotti function of ethane to within 0. 1%.

In Table HI, the parameter A, which is related to the molecular polarizability, is much larger than the corresponding parameter for methane and for the di- atomic gases previously measured in this laboratory.

This is to be expected based on considerations of molecular size. The molecular polarizability is calculated to be 4. 43 x 10^* cm^. The dielectric second virial coefficient, B, is also considerably larger than the

coefficient found for the smaller molecules. Sliwinski found 11. 22, 20, and - 1460 for the values of A, B, and

C from an analysis of his data alone. His value for B

should be compared with the quantity (B + DT) from Table in. At room temperature this quantity has a value

of about 24, However, little reliance should be placed

on the significance of the value of B given here as it is based upon only one supercritical isotherm.

V. CONCLUSIONS

We have used a highly stable cylindrical capacitor

to measure the dielectric constant of ethane over a wide

range of density and temperature. The derived CM

function has been used to intercompare the available PVT data for ethane, and an analytical expression has been given to relate density, temperature, and the di- electric constant.

This work was carried out at the National Bureau of Standards under the sponsorship of the American Gas Association, Inc.

J. W. Stewart, J. Chem. Phys. 40, 3297 (1964). B. A. Younglove, J. Res. Natl. Bur. Stand. See. A 76, 37

(1972).

••g. C. Straty and B. A. Younglove, J. Chem. Phys. 57, 2255

J. Chem. Phys., Vol. 65, No. 1, 1 July 1976 C-3
L. A. Weber: Dielectric data for ethane 449

(1972).

^J. F. Ely and G. C. Straty, J. Chem. Phys. 61, 1480 (1974). *G. C. Straty and R. D. Goodwin, Cryogenics 13, 712 (1973). ^C. J. F. Bbttcher, Theory of Electric Polarization (Elsevier, New York, 1973), Vol. 1, and references cited therein.

'L. a. Weber, Phys. Rev. A 2, 2379 (1970). 'b. a. YoungloveandG. C. Straty, Rev. Sci. Instrum. 41, 1087 (1970). 'd. E. Diller, J. Chem. Phys. 47, 3096 (1968). '"W. M. Haynes and M. J. Hiza (unpublished data). 'd. R. Dousiin and R. H. Harrison, J. Chem. Thermodyn.

5, 491 (1973).

'^P. Sliwinski, Z. Phys. Chem. 68, 91 (1969). '^W. P. Pan, M. H. Mady, and R. C. Miller, AIChE J. 21, 283 (1975). '^M. Burton and D. Balzarinl, Can. J. Phys. 52, 2011 (1974).

'^0. C. Straty and R. Tsumura (to be published).

""H. E. Watson, G. G. Rao, and K. L. Ramaswamy, Proc. R.

Soc. London Ser. A 143, 558 (1934). "C. Chui and F. B. Canfield, Trans. Faraday Soc. 67, 2933

(1971); M. J. Shanaa and F. B. Canfield, Trans. Faraday

Soc. 64, 2281 (1968).

J. Chem. Phys., Vol. 65, No. 1, 1 July 1976 C-4
The heats of transition of solid ethane*

Hans M. Roder

Cryogenics Division. Sational Bureau of Standards. Institute for Basic Standards. Boulder. Colorado 80302

(Received 3 May 1976)

The existence of a solid-solid transition in ethane is now generally accepted. A value for the heat of

transition, 2437±35 J/mol at 89.774 K, together with a new value for the heat of fusion, 279±6 J/mol at 90.337 K, is reported in this work. The suin of the new values is in excellent agreement with the earlier measurements, provided that the heat required to raise the temperature of the solid between transitions is included. The transition temperatures are in agreement with the most recent determinations of other

authors.

I. INTRODUCTION

Several recent papers address the question of a solidsolid phase transition in ethane at temperatures close

to the triple point. Webster and Hoch' detected a definite transition at high pressures, above about 100 MPa.

However, these authors predicted that a solid- solid transition does not occur at zero pressure, Eggers^

showed that two different solid phases existed down to zero pressure and identified the new phase as a plasticcrystalline form. At the same time Straty and Tsumura, ^ while attempting to remeasure the melting pres- sures of ethane, found evidence of a solid phase transition along a pressure- temperature boundary roughly

parallel to the ordinary melting curve but approximately

0. 5 K lower.

In connection with ongoing measurements of the specific heats of liquid ethane, * it appeared possible and worthwhile to measure the heats of transition of ethane. We have determined new enthalpy differences for the solid- solid transition and for the heat of fusion. In addition, values for the specific heat of solid and liquid ethane were obtained from the experiment, as well as

an estimate for the specific heat of the solid at temperatures between the two transitions. The sum of enthalpy for the solid- solid transition, the new heat of fusion, and the heat required to change temperatures

between the two solid phases is in excellent agreement

with earlier measurements by Witt and Kemp^ who apparently identified the total as the "heat of fusion.

"

II. APPARATUS

The apparatus used is a constant volume adiabatic calorimeter fully described by Goodwin,^ The essential features are a spherical sample holder, a filling capillary, a heating/cooling interceptor ring, an adiabatic

shield, and a platinum resistance thermometer mounted

externally on the sample holder. The instrument has been used to measure the specific heats of hydrogen,

oxygen, fluorine, '^''^ and methane. Measurements

of C^, and Cjj, for liquid ethane are in progress.

* While not specifically designed for solidified gases the system has been used to intercompare the heat capacity

of solid argon' with excellent results. Minor modifications to the original system have been described by

Goodwin and Weber. ' The only change made for the present experiment was to connect the heater voltage leads to the same potentiometer as the heater current

leads. This left the other potentiometer available for a

continuous display of temperature. The new connection degrades the accuracy of the power measurement to about 0. 2%. However, in view of other effects the in- accuracy in the power measurement is not a limiting

restriction.

III. PROCEDURE

The experiment consisted of running a cooling curve from several K above the triple point to several K be- low on one day, and a heating curve covering the same

temperature range on the following day. A continuous

display of temperature vs time was obtained on a re- corder for each run. Temperatures were measured

with a platinum resistance thermometer calibrated by

the National Bureau of Standards on the IPTS-1968.

The sample holder had been filled during a regular

specific heat run with 1.432 moles of ethane. The

ethane used in these experiments was commercially

available research grade with minimum purity certified by the supplier at 99. 98%. This purity was verified by chromatographic analysis. Nominal volume of the sample holder is about 73 cm^. Thus, near the triple

point the sample holder was about 90% full. With the very low vapor pressure of ethane, a negligible amount of sample

resides in the filling capillary. Using liquid nitrogen

as refrigerant, cooling was applied by placing helium

gas in the space around the sample holder. This space

is normally under vacuum. Using the known specific heat of saturated liquid ethane* the cooling applied to sample and holder was estimated to be somewhat over

1. 1 W. Of course, as the temperature difference be- tween sample holder and nitrogen bath decreased, the applied refrigeration decreased also. Total cooling

time was about l| h. For the heating curve the pertinent events taken from

the recorder charts are summarized in Table I, The

applied power was chosen to be approximately j that of the cooling, namely 0. 2764 W, in order to reduce thermometer offsets as much as possible. Total heating time was 5 h with power readings taken every 10 min. For a period of 30 min in the middle of the run

the power was turned off to observe thermometer equilibration. A similar observation was made at the end

of heating after all of the sample had melted. The final drift of the thermometer is quite in keeping with the normal specific heat runs on the liquid where equilibration times of up to 30 min are common. During the heating period both the interceptor ring heater and the

The Journal of Chemical Physics, Vol. 65, No. 4, 15 August 1976 D-1

1371
1372 Hans M. Roder: Heats of transition of solid ethane

TABLE I. Events during heating. TABLE n. Temperatures and heats of transition of ethane.

137. 174.75

347.

377.

415. 3±3

427. 12 451.25

Onset of solid-solid

transition Power off Power on

Check thermometer

equilibration

86.466 K at start

Temperature lower

by 0.315 K

End of solid— solid transition Onset of melting End of melting

Check thermometer

equilibration

Final thermometer drift 0.46 K

Final temperature

94.505 K

adiabatic shield heater were under automatic control, as they normally are during a specific heat run.

IV. RESULTS

The initial portion of the cooling curve is shown in Fig. 1, Any lingering doubts about one vs two transitions are resolved. The two transitions, liquid to solid and solid to solid, are clearly in evidence. A schematic

representation of what would be expected under ideal conditions is shown in the upper portion of Fig. 1. It is obvious that the thermometer is not in equilibrium

with the sample in this portion of the experiment. At

the onset of each transition the thermometer recovers

to a value quite close to the transition temperature but

still offset from it. Maximum amount of thermometer

offset in the cooling experiment is about 100 ^xV, or

approximately 0. 5 K. Most of the results are, therefore

calculated from the heating curve with information from

the cooling curve being used to estimate errors in the measurements.

The temperature and heats of transition are given in Table n. The temperatures are taken from the heating curve at the point where the slope changes at the onset

Transition temperatures Heats of transition Transition (K) (j/mol) Liquid—solid This experiment 90. 333 i 0.05 279 ±6

Eggers 90.27

Straty and Tsumura 90.348

Solid-solid This experiment 89.774±0.13 2437. 5 ±35

Eggers 89.82

Straty and Tsumura 89.8

of each transition. This is also the point where the temperature curve stays flat for the longest period of time. The heats of transition are calculated from the elapsed time between phase changes, the applied power,

and the amount of sample. The only time which cannot be established with any degree of precision is the end

of the solid-solid transition, as indicated in Table I. It is the uncertainty in the end of this transition which

leads directly to the rather large uncertainty in the heat

of the solid- solid transition. The uncertainty in the new heat of fusion 279± 6 J/mol is estimated from the uncertainty in the power measurement 0. 2% and a maximum uncertainty of 0. 5 min in the time that this power

is applied. The uncertainty can be confirmed from the cooling curve. We had estimated the amount of cooling

applied to be 1. 1 W from the known heat cjqjacity of saturated liquid ethane and the heat capacity of the empty calorimeter. This value together with the elapsed

time yields a value of 285 J/mol for the heat of fusion on cooling.

To calculate values of specific heat one needs, in addition to the elements above, the heat capacity of the empty calorimeter. These values are available. * Values for the specific heat of solid and liquid ethane

calculated from the heating curve are given in Table HI. The agreement between this experiment and others*'^ for liquid ethane is excellent, 0. 3%. The specific heat

of solid ethane below the lower transition is in very

good agreement with the earlier measurements by Witt and Kemp. ^ The agreement found here, and the fact

FIG. 1. The Initial portion

of the cooling curve.

[LAPSED TIME, min

J. Chem. Phys., Vol. 65, No. 4, 15 August 1976

- D-2
Hans M. Roder: Heats of transition of solid ethane 1373

TABLE III. Specific heats of ethane.

Phase Temperature range(K)

Specific heats (J/mol-K)

This exper iment Others Ref.

Liquid 90.3-94 68.5± 1 68.3 4 68.3 5

Solid 89.7-90.3 214±70'

Solid 86.4-89.7 91.5±7 87.1" 5 ^he heat capacity of the empty calorimeter is 43.95 J/K for

this interval. "At 86.73 K.

that a highly purified sample was used, suggests that the rise in heat capacity is an intrinsic property of pure

ethane. It also suggests that the impurity content of Witt and Kemp^ was probably much lower than the 0. 5%

that they estimated from "premelting. " The uncertainty of the specific heat of the solid between the two

transitions is quite large. There is a definite indication

of the end of the solid-solid transition on the heating

trace, however; the time associated with the end of ti e transition is smeared out over an interval of about 6 min.

V. DISCUSSION

We note that our system is not especially appropriate

for these measurements. An instrument specifically

designed to measure heats of fusion should be thin walled, should provide a:^ isothermal sample space,

i. e. , have Internal vanes and the thermometer should be mounted inside the san.ple holder in Intimate contact with the sample being tested. As a result, the lack of precise knowledge of the sample temperature was dis- concerting, but not unexpected. In both cooling and

heating experiments the thermometer indication is running ahead of the true sample temperature. In Fig. 1 the thermometer recovers toward the proper temperature at the onset of each phase change but does not quite reach the actual values of the sample temperature. With the much lower power used for the heating

experiment, the offset experienced at the onset of a phase change is expected to be the minimum possible, hence the transition temperatures were taken at the very beginning of each phase change. To provide an estimate of the temperature error we averaged the temperatures from both heating and cooling curves at the

fixed points obtaining 90. 29 K for the triple point and

89. 65 K for the lower transition. The difference be- tween these values and the ones given in Table II are

taken as an indication of the temperature errors at the fixed points, namely 0. 05 and 0. 13 K. The imprecision in sample temperature, however,

does not carry over into the heat measurements. The

indications of a phase change given by the thermometer

trace are very sharp, and with the exception noted in Table I, the phase changes can be determined to better than 0. 5 min. Earlier measurements of the heat of fusion of ethane^' were made before the existence of two solid phases was known. We can compare the earlier measurements to the sum of the heat of solid- solid transition, the heat required to raise the temperature

of the solid between transitions, and the new heat of fusion. The values are 2858^ and 2854 J/mol for the present experiment. The agreement 0, 14% is excellent. The higher temperature solid has been identified as

a plastic crystal'*^ and is thus associated with a change

in positional order only. The solid- solid transition is associated with a change in the long-range orientational order. The entropy or enthalpy change for the melting

transition is, therefore, expected to be much less than

that of the solid- solid transition. Our experiment

confirms this, the ratio of the heat of fusion to the heat

of transition being nearly 1 to 9.

*Thi8 work was carried out at the National Bureau of Standards under the sponsorship of the American Gas Association, Inc. 'D. S. Webster and M. J. R. Hoch, J. Phys. Chem. Solids 32, 2663 (1971). ^D. F. Eggers, Jr., J. Phys. Chem. 79, 2116 (1975). ^G. C. Straty and R. Tsumura, J. Chem. Phys. 64, 859

(1976). ^H. M. Roder, J. Res. Natl. Bur. Stand. U.S. (to be published).

*R. K. Witt and J. D. Kemp, J. Am. Chem. Soc. 59, 273

(1937).

^R. D. Goodwin, J. Res. Natl. Bur. Stand. U.S. Sect. 0 65, 231 (1961).

'B. a. Younglove and D. E. Diller, Cryogenics 2, 283 (1962). 'b. a. Younglove and D. E. Diller, Cryogenics 2, 348 (1962). ^R. D. Goodwin and L. A. Weber, J. Res. Natl. Bur. stand. U.S. Sect. A 73, 1 (1969).

'"r. D. Goodwin and L. A. Weber, J. Res. Natl. Bur. Stand. U. S. Sec. A 73, 15 (1969). "R. D. Goodwin and R. Prydz, J. Res. Natl. Bur. Stand U.S.

Sect. A 74, 499 (1970).

'^R. Prydz and R. D. Goodwin, J. Res. Natl. Bur. Stand. (U.S.) Sect. A 74, 661 (1970). "B. A. Younglove, J. Res, Natl. Bur, Stand. (U.S.) Sect. A

78, 401 (1974).

'^R. Wiebe, K. H. Hubbard, and M. J. Brevoort, J. Am.

Chem. Soc. 52, 611 (1930),

J. Chem. Phys., Vol. 65, No. 4, 15 August 1976 D-3

JOURNAL OF RESEARCH of the National Bureau of Standards—A. Physics and Chemistry

Vol. 80A, Nos. 5 and 6, September-December 1976

Measurements of the Specific Heats, Ca, and Cv, of Dense

Gaseous and Liquid Ethane

Hans M. Roder

Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302

(August 20, 1976) The specific heats of saturated lic|uid ethane, C,, have been measured at 106 temperatures in the temperature ranp;e 93 tu 301 K. The specific heats at constant volume, C,., ha%'e been measured at 19 densities ranging fruni 0.2 to 3.1 times the critical densitv, at temperatures between 91 and 330 K, with pressures to 33 MPa, at 200 PVT states in all. The uncertainty of most of the measurements is estimated to l)e less than 2.0 percent. As the critical point is a])proached the uncertainty rises to about 5.0 percent. The measurements were

performed to prox'ide input data for accurate calculations of the thermodynamic properties

for ethanr. They are belie\ed to be thr most comprehensi\'e specific heat measurements

avaiialile for the lic|uid and \'ai)or states of ethane. Key words: Constant volume: ethane; heat capacity; lic[uid; saturated liquid; specific heat;

vajxir.

1 . Introduction

For tlie calculation of the tlieiinodynamic properties of a fluid, ])roperties .such as internal energy,

enthal]\v, entropy, and velocity of soinul, especially

at temperatures less than critii al, one needs either

the latent heat of vaporization or a specific heat

along a |)ath traversing the teniperatiu'c- of interest. Heat cai)acity measinenients are nuich easier to nnike than latent heat inea>ureinents, and they are not restricted to the liquid-vapor curve hut can be

made at temperatures and densities in the single

phase fluid region as well. For ethane, the specific iieat of the saturated

licpiid, Ca, was meastu-ed fi'om 9.^ to 301 K, and

specific heats at constant volume, (\, were measured on 19 isociiores with densities ranging from 1.5 mol/1

to 21 mol 1 with tem])eiat\ues from 91 to 330 K and

])ressures uj) to 33 MPa [1].' In a forthcoming publication Goodwin [2] uses the

present results together with extensive PVT data

to construct a complete thermodynamic network

for ethane fi'om the trii)le ])oint to 600 K with

])ressures up to 70 MPa.

2. Experimental Method

The basics of the s]iecific heat ex])eriment are

dece])tively sim])le. The heat capacity of a sample

of fluid is determined in princi])le as follows. A

sam|)le holder is filled witli a known amount of

•This work was carried out at tlie Nalional Bureau of Standards under the sponsorship of 1 he .American tias Association.

' Figures in brackets indicate tlie lileralure references at the end of this paper.

sam])lc, .V, and is placed in an adiabatic environment. If we now a]i])ly a carefully measured amount

of heat, Q, to the sample holder, then the temperature

of sample and holder will rise to a new value, from

an initial temperature, T,, to a final temperature,

To, the change in temperature being AT. To obtain

the heat cai)acity of the sample we must accoimt

for the heat absorbed by the container. This is accomplished by conducting a second exj^eriment

with the sam])ie holder emi)ty to find the heat

capacity of the emi)ty container, Co- With

^0 = A7\ (1)

the desired specific heat of the sample can be

calculated from

Q-CVAT

C- atn (2)

Thus, the parameters we mtist measure in the

experiment are Co, Q, AT, and A''.

3. Apparatus and Procedures

The apparatus used is a constant volume adiabatic

calorimeter fully described by Goodwin [3]. The

essential feattn-es are a sjjherical sample holder, a

filling ca])illary, a heating/cooling interce])tor guard

ring, an adiabatic shield, and a ])latinum resistance

tliermometer mounted on the sample holder. Calorimeter and cryostat are shown in figure 1. The

refrigerants used were liquid nitrogen, ice, and cold

E-1
water. The instrument has been used to measiu-e

the s])ecific heats, C\ and C,, of hydrogen [4, 5], oxygen [6, 7], fluorine [8, 9], and ' metliane [10]. Measurements of the heat of fusion and of the solid- solid transition in ethane with this apparatus have

been reported elsewhere [11]. Minor modifications

to the system have been described by Goodwin and

Weber [6].

^Calorimeter

I'li.im: I.

< 'alonmctrr mid rri/ostat

.

The major experimental ])arameters are AT,

and A''. These are measuied as follows. We obtain

the calorimetric heating rate from nearly .simulta- neous i-eadings of the potential and current applied

to the calorimeter heater. The time of the heating

interval is measured by an electronic counter triggered by the potential across the calorimeter heater.

Tein])eratures are measured with the platinum

resistance thermometer. The thermometer was cali- brated l)y the NBS Temi)erature Section. Temperatures are on the IPTS-68 scale. The temj^erature of the adiabatic shield and guard ring are controlled to the sample temperature with difference thermocouples and automatic power regulation. The amount

of sample is determined from an observed temperature 7' and pressure F in the single-phase domain,

from the bomb volume at this T, P, and from the

fluid density derived from an equation of state [2]. The ethane used in these experiments was commercially available research grade with minimum

purity certified by the supplier at 99.98 ])ercent.

This purity was verified by chromatographic analysis.

The procedures used for measurement of the empty

caloi'imeter, for loading of the sample, and for the

specific heat measurements are the same as those

used previously [4-10] except for filling the sample

holder at low densities, and in the sequence of measurements. Differences in the filling of the calo- rimeter arise because the critical tempei'ature of ethane is above room temperature. The ethane

suppl}' tank is normality at room temperature, about

296 K and the cones|)onding supply pressure, vapor pressure, is about 4 MPa. Fillings with liquid

densities down to 12 mol/1 are determined by select- ing the temperature of the calorimeter, as before.

However, different techniques had to be used to achieve densities below 12 mol/1. One was to raise the filling ])ressurc by ])lacing the ethane sup])ly

tank in a liot water bath, uj) to 40 °C. The other was

to fill the sample holder around 12 mol/1, heat it to a temperature above critical, and then bleed it in small increments down to the desired density.

The .secjuence of measurements adopted was to conduct the C\ and C,. measurements with a single

filling rather than with different fillings as was the

l)ractice before. In this scheme the sample holder is filled to a known density in the single ])hasc I'cgion

and is then cooled to a temperature where both

liquid and vapor are ])resent in the calorimeter.

Heating intervals are applied to the two phase

sample, the data reduction yields values of C\.

Duiing these measurements both liquid and vapor

densities are changing, graduall}^ filling the samjile

holder. From that ])oint on the data reduction is carried out to yield values of C,.. The heating interval

in which the sample holder contains both two ])hase

and single jihase fluid is called the "breakthrough"

])oint. A sharp change in rate of temperature rise can be .seen on u recorder trace of calorimeter

tem])erature, and both guaid ring and shield heaters

show a slight "bump" on the recorder traces of the

differential thermocouples corresponding to a change

in power requirement.

4. Calculations and Adjustments

The data reduction a|)plical)le to this experiment

has been described in detail by Goodwin and Weber

[6, 7]. However, for ethane the se|)arate programs of and C,. were combined ai\(l a phasefinder developed

that would pinpoint the "breakthrough" point of each filling. The |)hasefinder, the filling conditions,

and the FVT conditions at which each point was

measured are based on the equation of state by

Goodwin [2]. One of the primary exi)erimental parameters is the total amount of samjile in the system, A''. The

pressure and temperature at filling are measured,

the corresponding density is calculated from the

PFr surface, and A'' is evaluated from a knowledge

of the calorimeter volume, and the various ancillary

volumes such as capillary, connector, and valve

volumes. As mentioned before, the critical point of ethane, at 305.33 K, is above room temperature.

A number of fillings and experimental measurements

E-2
wol'o iniulo botwooii 305 and 3-'^0 K. For these runs

the poi'tion of the sample in tlie cuijillary is not

nojili!i'il)le, and lia> to be accounted for accurately.

All of tlie "nuisance" volumes were revised, in particulai' tlie valve volume which, nominally at room teinperatui'c, wa^ lai'ii'ei- than previously esti- mate(l. '|\) pailially alleviate the problem the valve was tliermo-tated at 40 °(', and a variable valve

temperature was included in the data I'cduction

I'outines. 'J'he amount in the capillary is determined

by a-sumiiiii' a tem))erature (li>tiibution along the

capillaiy. 'J'hi> disti-ihution was changed to accom- modate a variable tempei'ature at the valve end.

Several othei' corrections made in the programs

are icviewed hiiefly. 'J'he calorimeter volume depends

both on temperature, thei'mal expansion, and on pre—ure [4, ()]. Siiu-e the sample holder is a thin

-taiides- steel sphere it stretches as the |)ressure

inci'cases. 'J'hu-, in a <", measurement work is done

by tlH> sam])le due to the increase in sample volume.

Thi-- coirection develo|)ed by Walker [12] ranges

from 0.5 to 5 percent of the resulting (',. value.

Jlowc\('i', it can be nuule accurately. The density

foi- each (', measurement is calculated fi'om the

filling (leii-ity after cori'ecting foi' >ample holder

expansion and the amount compressed into the

filling c!i|)illary [7]. In the ca>e of a ('„ measurement

the eil'ects of tlie latent heat of vaporization and

heat ab-orbed by the vapor must be subti'acted

|4, (), s]. This t\'pe of correction ha> been derived by

Jloge \ \:\\. It is worthwhile to mention that of the three

state variables, pressure, temperatui'e, and density,

only tempeiature is measuicd duiing the measure- menl of a .-pecilic heat point. The amount of sample

in the calorimeter is used to establish the density and

|)ressure at the mean tem|)erature of tlie exp(M-iment.

While the total amount of samj)le jcnuiins constant,

the di-t lihution between caloiimeter and ca|)illary

changes from point to i)oint l)ecause the calori- meter volume changes with tem|)erature and pressure. Thus, while the results for (', are corrected to he a true (',, the measurements of a given run are nuide a( slightly changing mean densities. ('ur\ature adjustments have l)een made foi' the

(

'„ values at temperatures above 101.5 K. Ad justmeiils to the experimental gross heat capacitylicpiid and vapor-range from 0.002 .)/mol-K to

().:)()() .1 iiiol-K, or up to 0.10 percent of the total value of ('„. ( 'urvature adjustments for the values

of (', were not significant, and were, therefore,

omitted.

5. Heat Capacity of the Empty Calorimeter

Early cslimatcs revealed that under the hest of

cii cunislances 50 percent of the applied heat is i-e(juired for the calorimeter; for tlie very low

densities at the highest temperatures u|) to 9.'-! percent

of the heating goes to raise the temperature of the

calorimeter. Since the critical temperature of ethane

is :^U5. .').) K it appeared desii-able to make at least some of the C\, measurements at temjieratures above

critical. An up])er limit of .'-i.SS K is im|)ose(l by the

fact that the platinum I'esistance thermometer is mounted with Wood's metal, which melts at 05 °( Measurements on the other fluids had been carried

out to only 300 K, therefore, an extension of tin' measurements on the em])ty calorimeter were

indicated.

Remeasuring the heat capacity of the calorimeter

Co provided an opportunity to conduct additional

checks of the system with regard to .systematic

errors, and to see if the precision of the measurements

could be improved. The measurements of the li(>at ca])acity of the empty calorimeter included huge

and small AT"s from S to 0.5 Iv; large and small

ai)|)lied powers, from 1.0 to 0.2.3 W; I'uns with deliberate temperature offsets in both guard ring and

shield tem|)ei'atures, 3 K (100 jN) hot and cold; as well as different coolants in the refrigerant tank, runs

2, 3, 4, with ice and runs 5, 6, 7 witli licpiid nitrogen.

The results of these measurements, some 92 points, are shown in tabh^ 1. The applied temperature dif- ferences are small enough so that a curvature cor- rection is not re(piired. Intercomparison of the data

is achieved by using the functional I'cpresentation

develo|)ed by Goodwin and Weber [6].

Log, (ro/50)---i: (\-{miTy~K (3)

(=1

Values of the coefficients, are given in the heading

of table 1. Points 208 through 304 are included in table 1 to show the most extreme variation in ^.T. They were

not used to obtain the coefricients, because

during these runs one of the d.c. ani])lifiers had a large bias which was not corrected until the start of run 4. The analytical curve represents the heat

capacities of the empty calorimeter with an im-

])recision of 0.07 percent. To the level of 0.1 percent

in ('„ there ai-e no discernible systematic errors that can t)e related to the size of the AT, the size or rate

of th(> applied heating, the temperature gradient of the capillary, or to temperature ei'rors in shield or guard ring systems. The agreement of the present

values with those measured by Goodwin and Wel)er

[G] is well within the imprecision of the sej)arate

measurements. In the temperature range 87 to 320 K

the uncertainty in the quantity {Q ~ t\,^T) ji\T will range from 0.04 to 0.08 -I/K due to the uncertainties

in C\, aloiie.

6. Results

'J'he results to be presented include values for the

specific heat of saturated liquid ethane, values for the specific heat of single phase ethane, both in

compressed liciuid and in gaseous states, and a limited

set of measurements on methane, macle for purposes

of comparison. As mentioned above, both C„_ and

C,. measurements were made during a single filling.

Table 2 gives the loading conditions for all exjjerimental runs; the runs are shown in density-temperature coordinates in figure 2. Temperature and presE-3
Pi,

1- CD O OC

I - CD

CO in in cf)

II I! Cl CD CO

Cl cd" lO CO

CD ^

CO CO ,-.

.2^ II II

o

o

o

o

c

c c c c c c

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E-5
Tahi.i, 2. Cahirim(i( r loading condilinns far Ihc nit asur( inriit runs

Breakthroug h coiiciitions

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1

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22

20

18

Run No 2

__

r

rrzzi37

14

i 12

the two phase boundary

measurements resulting in Cqmeasurements resulting in Cy

—

X

\

- 9

10

11

16

14

17

12

13

IS

T P =90 348K r

CP

19

= 305 33K

_L_] 90 100 150 200 250 TEMPERATURE. K

280 300 330

FiGunio 2. The locus of experimental runs in the density-temperature plane.

the two phase boundary

measurements resulting in C,

. measurements resulting in C, F-6
>\m\ obtained by computation from laboratory

observations, arc in effect diiect measiu'cnients.

The vohnne of the calorimeter is computed, tlie density is obtained from tlie eciuation of state [2]. Tlie total number of moles, ;V, includes the amount

in capillary and valve with the upper stem tempei-ature e([ual to the indicated valve temperatui'c.

Breakthiouch density and temperature define the

point on the saturation boimdary applicable to the run in ({uestion. The values are calculated from the

equation of state, the loading; conditions and the

vapor piessuic 1)V consideiing the variation of cal- orimeter volume with temperature and pressure.

6.1. Performance Tests: The Specific Heats

C„ and C, of Methane

Prior to making measurements on ethane we matle

a limited set of measurements on methane. The

])urj)osc was to check on the operation of the instrument by com|)arison to the values ])reviously

measured by Younglove [10]. Several values of and 29 values of (\. were measured at three dift'erent

filling densities and at widely differing temperatures.

Results and comjiarisons are shown in table 3. Two

coiu'lusions can be drawn from the measurements on

methane. One is rather surprising, namely that the

values of the specific heats calculated from the raw

(lata will differ, if slightl}' different /^rJ" surfaces are used in the data reduction process. The other is oxj)ected, namely that the values of the s])ecific heats

depend directly on the values measured foi' the heat

capacity of the empty calorimeter.

To calculate the present results, which are shown

in colilnm 5 of table 'A, we used Goodwin's most re- cent foinnilation of the I'VT suiTace of methane

[14]. Since Vounglove used a different, eaiiier fornudation [15], a s(>con(l calculation of our results using the eai liei- l'\ '7' surface is shown in column G of table ()iu' of the most impoitant differences l)e- tween tlic-^c two /'I '7' surfaces is the assignment of

eritieal density, 10.0 mol 'I for reference [14], and

10.1.") mol I for reference [I.')]. 'I'he intercom])aiison

of the two calculations is given in colunm 7. Clearly,

both <

'„ and (', aic sensitive to the l'\'T surface

u>ed in the data reduction ])rocess. Furtherniore,

the (li^feI•<'nce^ vary from ])oint to point on the I'VT

siu'face. Recomputing all of Voungiove's results with the (wo diffei-ent /M '7' surfaces leads to ma.ximum differences of .OS ])ercent in both ('„ and (',. Accoi'dingly, the most consistent way to compare

the ])i-eseiit results with those of Vounglove [10] is to us(> the same /'\ '7' surface. This comparison in- volves coliunns t; and 10 of table with differences

given in colunui 11. The disagrecMuent between the

two e,\|)eiiments runs from ~1 to -f 1 percent. Several explanations weie considered, only one of which

is displayed in table ''>. 'i'here (>.\ists a consistent

ofl'set, 0.4 ])eicent, between the (\^ measured in the course of this experiment and that measured by

oungiove [10]. in column <S we have calculated our

pr(>sent I'csidts on methane using "^'ounglove's [10] values for ('^ and Goodwin's earlier formulation of

the /'resurface [15]. Cohunn 9 shows the departure

of the values in colunm S from those in colunm 6. Fimdiy, a comparison of columns 9 and 11 suggests

if not (piantitatively, then at least (pialitatively,

that indeed the diffei'ence in the values of the (\'^

is the explanation for the difference between the

])resent measurements and those of "^'oungiove [10].

6.2. The Specific Heats, C, of Saturated Liquid

Ethane

'J'he specific heat of satm-ated li(pnd ethane was

measured for 106 tcmjx-ratures. 'i'lie lowest was

93.7 K, the triple point is 90.34S K, the highest

temperature was 301.5 K, the critical point is 305.33

K. Values of C\ along with the experimental conditions, expeiimental parameters, and the various

correction terms are given in table 4. A plot of (\ is shown in figure 3. "^I'lie measurements for C\ were made with A 7' between 3 and 5 kelvin, and with

loadings such that at each temperature TV is defined

by at least two diffei'ent fillings (see column 11,

table 4). Gui'vatui'e corrections were necessary only

at tiMnperatures above 101 Iv. The i-esults for (\

are represented with an analytical ecjuation as follows:

( \ = (\ + C, T+ (\ ri{T-T)'- rvr+ (\IT' (4) where 7'^ is the critical temperature, 305.33 K and

values of the coefficients ai-e given in the heading

of table 4. Values calculated fi'om eq. (4) and diffei'- ences between experimental and calculated values

expressed, in percent ai'e also given in table 4. The

standard deviation of the entire fit is 0.3 J/mol-K.

Foi' tempei'atures below 260 Iv the imprecision in the experiment is ±0.1 percent, not much larger

than that expei'ienced for measurements of the

empty calorimeter. GonsidcMing all sources the esti- mated uncertainty in the measured value of ('^ is about 0.5 ])ercent generally, increasing to about

5 i)ercent within a few kelvin of the critical point.

(\)m|)arison with the earlier measurements of

Wiebe et al. [16], and Witt and Kemp [17] is made

using eq (4) for interpolation. Differences in C„ are shown in table 5. They are negligible at low temperatures but increase gradually to 5 ])ercent at the

highest temperatures of comparison. The explanation of the differences lies in the different PVT

surfaces used to evaluate the experimental data and

correction terms, in i)articular the rather large

difference in assignment of the critical density, G.SO mol/1 this experiment and 6.99 mol/1 for the

other authors.

6.3. The Specific Heats, C, of Dense Gaseous

and Liquid Ethane

The specific heats at constant volume were measured at 19 densities ranging from 0.2 to 3.1 times the critical density, at tem])eratures between

91 and 330 K, and with pressures to 33 MPa. As

shown in figure 2, a given density is limited either

by the maximmn allowable system pressure, about

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35 MPa, which in turn leads to a maximum pressure

of ?>'^ MPa at tlic mean temi^craturc of the ex])erim<'nt, or by the upper limit in temperature, 330 K.

Values of C, along with the ex]jerimental eonditions,

the major experimental parameters, and the correction term are given in table 6. The tem]:)erature

and density dependence of C,. is illustrated in figure

4. For a wide range of densities to either side of the

critical density the specific heat increases sharply

as the coexistence enevelope is approached. At

liquid densities far removed from critical the temperature dependence is relativel}' weak.

T.MJLi; .-). Comparison of the calculated C\ with results of others

TcmiJcra- C-calculatcd Co from the Difference

turc K this i)apcr literature in 0/0 J/mol-K J/mol-K

Reference [16]

!M). / / ()!S. 2.1 68. 46 — 0. 3

Mb. nj. t)». z8 68. 76 — . 7 no f\(' 08. )) — . 3

101. .")4 68. 44 68. 71 — . 4

1 07. 08 68. 00 68. 03 — . 0

1 08. 6.-) 68. ti4 68. 55 • .1

1 1 .-). 74 68. 81 68. 67 ; . 2

1 10. 19 68. 82 68. 45 • 0.

1 22. 70 69. 00 69. 13 —. 2

1 2?t. 00 69. 02 69. 17 —. 2

1 28. 08 69. 16 69. 55 —. 6

1 28. 49 69. 17 69. 51 — . 5

i:i2. ().") 69. 32 69. 84 — . 8

138. 00 69. .-)3 69. 89 — . 5

138. 18 69. ."i4 70. 01 —. 7

138. 31 69. .').) 69. 84 -. 4

142. 43 69. 73 70. 10 —. 5

iKJ. U-) A

l.-)l. 7.-) 70. 24 69. 97 . 4

1.V2. 00 70. 30 70. 14 . 2

l.-)4. 99 70. 4.') 70. 26 . 3

1 .')0. 98 70. :>H 70. 26 . 0

l.")7. 42 70. 61 70. 10 . 7

100. 10 70. 80 71. 10 -. 4

102. 0.-) 70. 99 71. 18 -. 3

104. 49 71. 14 71. 73 -. 8

1

(•>.-). 93 71. 26 71. 31 -. 1

1 68. 09 71. 44 71. 60 -. 2

170. 18 71. (i2 71. 77 -. 2

172. ().-) 71. 79 71. 77 . 0

172. 09 71. 8.-) 72. 15 -. 4

178. 17 72. 39 72. 82 -. 6

181. .-)0 72. 7.') 73. 07 4

182. 03 72. 81 73. 32 -. 7

190. 00 73. ?.) 73. 53 . 3

199. 80 71 1

1

74. 37 1. 0

208. 88 76. .')6 75. 66 1. 2

212. SO 77. 26 75. 96 1. 7

220. 48 78. 78 ,

, 77. 80 1 1. 2

22s. 7t) 80. 67 ! 80. 61 . 1 230. 21 82. 6.-) 82. 32 ' . 4

244. 01 81 28 83. 90 i 1. 6

2.-)2. .-)3 88. 29 87. 14 1. 3

2.')8. 22 90. 89 88. 44 1 2. 7 20.1 2.-) 94. 80 92. 33 2. 6

273. 0() 1 00. .')3

i 98. 11 ! 2. 4

278. 07 101 41 i 101. 33 ! 3. 9

284. 07 113. 41 109. 12 1 3. 8

291. 27 129. 25 122. 69 i 5. 1 294. 8.') 142. 89 131 79

1

5. 0

T.\HLi; 5. Compari.soii of the calculated C„ with results of others—

Continued

Tempera- C,-calculatcd Co from the Difference

ture A' this jKipcr literature in 0/0 J/mol-K J/mol-K

Reference [17]

91. 59 68. 03 68. 30 — 0. 4

92. 97 68. 10 68. 46 — . 5

94. 94 68. 20 68. 38 —. 3

96. 60 68. 27 68. 25 . 0

98. 23 68. 33 68. 88 -. 8

98. 89 68. 35 68. 38 — . 0

100. 49 68. 41 68. 34 . 1 104. 05 68. 51 68. 59 — . 1 106. 67 68. 59 68. 88 — . 4

109. 24 68. 65 68. 92 -. 4

111. 67 68. 71 69. 13 -.6

114. 20 68. 77 69. 01 -. 3

116. 24 68. 82 69. 17 — . 5

119. 33 69. 90 69. 30 6

122. 72 69. 00 69. 43 -. 6 121 96 09. 09 69. 59 7

129. 47 69. 20 69. 55 —. 5

134. 49 69. 39 69. 64 4

138. 72 69. 56 69. 76 ^ 3

142. 83 69. 75 69. 89 ~ 2 141 97 69. 91 70. 05 - 2

149. 80 70. 13 70. 31 -. 3

1.53. 58 70. 36 70. 77 -. 6

1.57. 95 70.- 65 70. 77 -. 2

162. 82 71. 01 71. 02 0

167. 43 71. 38 71. .52 2

172. 02 71. 79 71. 56 . 3

176. 54 72. 23 72. 06 . 2

180. 88 72. 68 72. 1

1

. 8

Representation of the specific lieats has been

achieved by Goodwin [2] who correlates the available

data, the specific heats of the ideal gas, the

specific heat of the saturated licpiid from this experiment, and selected vahies of (',. from runs 1, 8, and 9. Values of (', calculated from his equation of state and diflferences between experimental and calculated

values expressed in percent are given in table 6. A scan of colunm 7 in table 6 reveals that the agree- ment between experimental and calculated values

is excellent over much of the P]^T surface, i.e., a nominal 2 p(>rcent or less. It is oidy in tiie region near the critical i)()int where th(> experim(>ntal heat

capacities increase drastically that the representation

is not able to match the experimental surface of

( ',; departures reach values of up to .18 percent. The

agreement for the very lowest density, run 19, is particulaiiy gratifying since for this run the experimental uiu ertainty in C',. is about 2 percent, whereas

the calculation of (',. from ideal gas and a very

small /-TT" contribution should have very little error attached to it. Experimental measurements of specific' heats

have been made by other authors [18,19], however

these jneasurements are measurements of the specific

heat at constant pressure, (\. The vahies can be

compared only indirectly to the present measureE-12
220

160

140

100

Run No.

> - 1

I - 2

- 3

- 4

- 5

- 6

- 7

- 8

- 9

- 10

- 11

- 14

- 16

- 17

- U

T P -90 348K

see i»o« » o»o» a o i: C P =305.33K

90 100 120 140 180 200 220 240 260 280 TEMPERATURE. K

300 320

Figurt; 3. The specific heats, C,, of saturated liquid ethane.

Run No! I ^

14,6 mol/Z

211619.6

19

18

1715

14

13

1 ^ \

^ [

50

1 -

2

-

3

-

4

-

5

-

6

-

7

-

8

-

9

-

10

40

90 100 120

Rui No' ' r

12 mol/1

5 9

4 6

9 2 3.3

11

7 9 20 3

11 -

12 -

13 -

14

1516-

17 -

18 -

19 - 158

C P =305 33K J 'AI I I 180 200 220 240

TEMPERATURE, K 260 300

FiGURK 4. The specific heats, C,, of dense gaseous and liquid ethane.

iiioiits tlir()u,<2;li tlio use of a PVT surface. Since

iiioasuroinoiits arc iiormallv made alon^ isobars

while (',. ineasureineiits are made along isocliores,

the most ajjpropriate 1*VT states for comparisons

arc at those values of pressure and density common

to both sets of data. For the results of Furtado

[IS] and the present measurements this intercomparison is given in table 7. The pressures are taken

220-208 0 - 77 -4 E-13
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lOiOiOiOiOiOiO COCOCOCOCOCOOCDCOCOCO t^t^t^t-^ot^-t-^t^

E-17
to i c ' " C2 cc X cc CO o —I — — —, « _ „ , ^ — —

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^ ^ 5 ^ 'S* io

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— CO o CM od CM Ci * ci

~'

<x> o ci C: o o — — CM

CM CM CM CM

C50-«tiC5T*<cn ic>;o";:ic:T}<TfcococMCM Xt^iOCOCMO XXXXXOCXCCXX

CM Ol CM CM CM CM lO lO lO lO lO lO lO it lO lO c CO c o o o

—' —' — ' CM CM C^l CM CM CM

CO o 00

CM C2 CM Tf O O — O X

•^X—<OCOt^—'CMCO-* T}<or^oOcoxcot^-^o — t--CMC>QC;OiOCOCMO t^t^XOOCsO'-'CMCOTti

Oi CM cm' cm" CM CO CO CO CO CO

c O CM CO O

X X 00 X X X

^CMCO'^iOCOt^XOJO OOOOOOOOO'— C; C". ~ C". ~ C: O ~ C:
T.uiij: 7. I Htrrcoinparison of C„ and Cp

rcf. (IS]

l)ciisit\*

llKll/l This ]);il)iT

Ten 1 [jcra t u re K

from CH(. rcf III. 121 L^j

C\

,J 'iiuil-K intcrpol.

tlii-s paper

Pl'T Contr

J/mol-JC

calc.

rof 121

-

(' J/iudl-K

calc.

. , )

('„

,J/ni(il'-K interpiil. ref [18]

Ditf pet

'.i. 4474 14. G47 2.")7. 677 47. 19 44. 44 !)1. 04 !)(). 43 "1.3

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13. 7S<).-, 17. !)4.") !9<). 373 44. 38 2s! 38 72. 7(; 72. 07 -. 1

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."). 7() 1 1 3. .")7 - 1. !) 10. 3421 1 1. !M() 30!). !)!)!) 52. 47 .-)S. 3!( 110. SO 10!). 53 - 1. 2

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0

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(i. 8948 7. 880 320. 009 00. 00 217. 10 277. 77 273. 85 1. 4

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*S(iiii(' of [•"urtado's values [18] may he in ( rrcir b.v as mui'h as 10 percent, sec text.

E-19
from reference [18], the densities from the present

measurements. A temperature corresponding to the

P and p of an intersection is obtained from the

equation of state [Goodwin, 2], and experimental

values of C\ and Cp are interpolated from the two

sets of data. The comparison is completed by

calculating a value of C\ from

The second term in equation 5 is the contribution

from the Prr surface. It is clear from table 7 that in almost all cases the PVT contribution to 6V-ealculated is as large or larger than the value of C'„. The mean deviation between calculated and experimental f\ for the 50 intersections is just under 2 percent. This implies that the thermod3aiamic

consistency' between experimental (\ and Cp measure- ments is indeed excellent, i.e., at least as good as 2 percent, but quite probably much better than that

foi' two reasons. First, a large part of the total discrepancy must be assigned to errors in the PVT

surface derivatives. Second, some of the values

presented b}- Furtado [18] may be in error by as much as 10 percent. A detailed example is as follows. In our table 7 a comparison is made at 6.8948 MPa

(1000 psia) and 298.929 K (78.40°F). Furtado's

closest smoothed value of Cp taken from his table

VJn-5 at 6.8948 MPa (1000 psia) and 299.817 K

(80°F) is 111.84 J/mol-K (0.889 BTU/lb-°F).

'I'liis value changes to 124.06 J/mol-K if interpolated

from his table VI 1 1-3, a table of smoothed enthalpies, or to 122.4 J/mol-K if interpolated from his figure

VlII-6, a plot of Cp versus temperature for the 1000

psia isobai-. Thus the inconsistencies in Furtado's

values, depending on how they are obtained, are at times as large at 10 percent.

7. Discussion

it is readily apparent that accurate values of C^

ai(^ essential if we wisli to obtain accurate values of

eithei- or (\,. A change of 0.1 percent in Cq, for example, will result in a change of 1 ])ercent in the

values of C,. calculated for run 19. The temperature

increment, AT, is evaluated at the middle of the

heating interval by extrapolating the temperature

drift rates just before heating and after an equilibrating time has elapsed. Since the drift is linear the

statistics of the extrapolation can be used to estimate

an uncertainty in the AT. For the first 14 points of

('n the average slope imcertainty was 0.19X10"'

K/min, since the average elapsed time to the center

of the measurement interval is about 20 min, the

average uncertainty in AT" turns out to be ±0.004 K.

'J'his in turn implies that if we seek 0.1 percent

precision in the specific heats the ^T must be 4 K

or larger. The choice of ^T, as shown in tables 4 and

6, was based on this consideration and on the idea

that there ought to be at least 5 points per experimental run. The imprecision in the temperature time

data is attributed to the exact setting or resetting

of the platinum thermometer current rather than

potentiometer inaccuracy. Potentiometer inaccuracy was actually reduced from values given by Goodwin

and Weber [6] to a maximum of 0.003 K by consideration of a potentiometer calibration. Heat leak

to and from the sample is estimated to be less than

0.1 percent by considering the difference in drift rates before heating and after equilibration has been

reached. Shield temperatures lag at the start of the

heating interval by about 0.02 K. They lag again at the end of the heating interval after the power is turned off. The two lags compensate to produce a

nearl}^ adiabatic environment during the entire

heating interval. Deliberate changes of temperatm-e

along the capillary were introduced to see if the

applied heat, and therefore the results could be

changed. In run 14 points 1401-1413 were obtained

with liquid nitrogen in the refrigerant tank. These

points were duplicated for 1414-1425 using cold

water as coolant. The results, as shown in tables 4 and 6, are virtually identical. However, when we

applied deliberate heating to the capillary, actually

quite drastic heating 100 ma to a 140 n heater,

the results changed. Points 508-517 differ from those

obtained in a duplicate run 520-527 without heating

the capillary by 1 percent at the lowest temperature.

The difference disappears entirely^ at the highest

temperature of the run. However, rather than

changing the applied heat, heating the capillary ap- parently changes the distribution of sample between

calorimeter and stem. The same ])roblem, distribution of samj^le between

calorimeter and stem, is thought to give rise to the

curvature of the runs. Runs 18, 4, 5, 6, and 7 show

a definite curvature as to two phase boundary is a])proached, see figure 4, if compared to the values

calculated by Goodwin [2]. The curvature seems to abate at ]iressures above the critical pressure, or at a

])oint where mass change between calorimeter and

stem has stabilized. It is ]iossible that a heat of

vapoiization correction to Q should be included for the Ci- calculation as long as sam])le is being transferred from calorimeter to stem. It should l)e noted

that the correction term, cohunn 13 of table 6, is irregular for the first few ])oints of the runs in question.

Sample distribution is also thought to explain the

(le])ai ture of point 208 from the rest of run 2. The

])Ossibiity exists that for run 208 the ca])illary was

frozen, because if point 208 is recalculated with

zero stem volume the value of (7„ is increased by

about 2.5 peicent.

We had hoped to employ the breakthrough points

to resolve the jiroblem of samjile distribution.

Ex|)erimental breakthrough temi)eratures agree well

with calculated values; densities and total sample

agree to a ])oint where we are confident that the

calorimeter volume has not changed. However, to calculate C„ and C, values from a breakthrough

l)oint requires that we know the time of breakthrough

E-20
exactly in order to jiroportioii tlio ujiplied lieat Q.

TluM'o is simply tof) mucii lag in the i'es])oiise of tlic I'ecorders to pei'init an accui'ate (letermiiiation of the

breakthrouoji time.

The impieei^ioii in the expeiiment depends

primai'ily on tiie imprecision of Cq and on the amount

of sample since in most cases the AT" is aroimd 4 K.

For liqnid densities the im|)recision from ])oint to

])oint alono- an isochoie is about 0.1 ])ercent with

occasional difTei-ences as lai'ge as 0.3 ])ei'cent. For

densities le-^-^ than critical the imprecision, the

variation of point to point from a smooth ciu've,

increases to al)out 1 ])ercent. The inaccuracy or

un.certainty of the |)resent measurements is estimated

from the comparison to the ex|)eriments of otheis aiul from the comparison to values calculated from the

l*VT coi relation. We consider the excellent agree- ment between the present results and the experiments

of otheis [10, 10, 17, IS], in particular tlie agreement

with experiiueiital values of Cp, and we consider the

results of deliberately introducing changes in the ])re- sent expei'iment. It is difficult to see how systematic

ei-roi's laiger than about 2 percent for licpiid densities or larger tiuni 5 percent for vapoi' densities close to

critical could remain undetected in the |)resent

experiment.

8. References

[1] Tile S. I. ( intcrnatidnal system) unit of pressure is the

Pascal (1 Pa=l N/m^). The bar is 1()> Pa, also 1 atin= l.()i:]2:)X KP Pa, 1 li>/iii2 = GS!)4.7.")7 Pa, I dviic'cni-'= 10 ' Pa: see Page, C". H. and Vigourcux,

P., Xat. Bur. Stand. (U.S.), Spec. Publ. ii.'iO, (Jan.

I'.)7I). .\l>o one mole ethane = ;5().()7 g, l)ased on the

'-(' scale .and the natural isutopic abundance axcrages:

sec Remy, II., Chem. Perichte 101, 1 fl!»(iS).

[2] (ioodwin, R. 1)., Roder, II. M., and Stratv, Vx. C,

Nat. Bur. Stand. (I'.S.), Teeh. Note (iN4 (in pre.<s), for pro\-isional data see (ioodwin, H. 1)., Nat. Bur. Stand. (I'.S.), NBSIR, 74-,S(>,S (1 Jiuie 1974). (Avail- able as COM 74-11717 from the Nation;il Technical

Inf(jrmation Ser\ices, Springlield, \'A 221(11.) Goodwin, R. D., J. Res. Nat. Bur. Stand. (U.S.) 65C

(I'Jig. and Instr.), No. 4, 231-243 (Oct.-Doc. 1961).

[4] Younglovc, B. A., and Diller, 1). E., Cryogenics 2, 283 (1962).

[•"i] Younglove, B. A., and Diller, D. E., Cryogenics 2, 348 (1962).

[6] C.oodwin, R. D., and Weber, L. A., J. Res. Nat. Bur. Stand, (U.S.) 73A, (Phys. and Chein.), No. 1, 1-13

(Jan.-Feb. 1969).

[7] (ioodwin, R. D., and Weber, L. A., J. Res. Nat. B\ir. Stand. (U.S.) 73A, (Phys. and Chem.), No. 1, l.-)-24 (Jan.-Feb. 1969).

[S] (ioodwin, R. I)., and Prydz, R., J. Res. Bur. Stand.

(U.S.) 74A, (Phys. and Chem.), No. 4, 499-.-)().-) (Juiy-Aug. 1970).

[9] Prydz, R., and Coodwin, R. I)., J. Res. Nat. Bur. Stand. (U.S.) 74A, (Phvs. and Chem.), No. 5, 661-66.') (Sept.-Oct. 1970).

[10] Younglove, B. A., J. Res. Nat. Bur. Stand. (U.S.) 78A,

(Phys. and Chem.) No. 3, 401-420 (Mav-June 1974J.

[Ill Roder, II. .M., J. Ch(>ni. Phys. 65, 1371 iVMW).

112] Walker, P. A., Dissertation (llniversitv of London, 19,')6). [13] lloge, 11. J., J. Res. Nat. Bur. Stand. '( U.S.) 36, 111-118,

(1946) RP1693.

[14] Coodwin, R. D., Nat. Bur. Stand. (U.S.), Tech. Note

6r)3 208 ])ages (April 1974).

[1.",] Coodwin, R. I)., and Prydz, R., J. Res. Nat. Bur. Stand. (U.S.) 76A, (Phvs. and Chem.), No. 2, 81-102

(Mar.-Ai)r. 1972).

[16] Wiebe, R., Ilubb.ard, K. II., and Bre\<iort, AI. J., J. Am. Chem. Soc. 52, 611 (1930).

[17] Witt, II. K., and Kemp, J. D., J. Am. Chem. Soc. 59, 273 (1937).

[IS] Furtado, A., Ph.D. Thesis, 1 )ei;artmcnt of Chem.

Ivngineering, University of Michigan (Dec. 1973).

[19] Bier, K., Kunze, J., and Maurer, (i., to be published,

.1. Chem. Thermodynamics 8, S.")7 (1976).

(Paper 80A5-915)

E-21

LNG DENSITIES FOR CUSTODY TRANSFER*^

Dwain E. Diller

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

Accurate LNG densities are required for equitable custody transfer

contracts and operations. Mathematical models and direct reading

densimeters for use on LNG type mixtures are being evaluated at the

National Bureau of Standards. Accurate (0.1%) orthobaric liquid density

data have been obtained for LNG components and their mixtures and are being used to optimize and evaluate four published mathematical models.

A density reference system has been constructed and is being used to

evaluate commercially available densimeters. Recent progress on these

tasks is summarized and discussed.

Key words: Custody transfer; densimeter; density; liquefied natural gas;

mathematical model.

* This work was carried out at the National Bureau of Standards under the

sponsorship of British Gas Corp., Chicago Bridge and Iron Co., Columbia Gas

Service Corp., Distrigas Corp., Easco Gas LNG, Inc., El Paso Natural Gas., Gaz

de France, Marathon Oil Co., Mobil R&D Corp., Natural Gas Pipeline Co., Phillips

Petroleum Co., Shell International Gas, Ltd., Sonatrach, Southern California

Gas Co., Tennessee Gas Pipeline, Texas Eastern Transmission Co., Tokyo Gas Co.,

Ltd., and Transcontinental Gas Pipe Line Corp., through a grant administered by

the American Gas Association, Inc.

t This work was carried out at the National Bureau of Standards under the

sponsorship of the American Gas Association, Inc.

F-1
LNG DENSITIES FOR CUSTODY TRANSFER

Dwain E. Diller

INTRODUCTION

LNG is typically bought and sold on the basis of its heating value. Important

elements in calculations of the heating value of LNG in tanks and pipelines

include tank volume and liquid level, flow rate, density, composition, temperature, pressure and specific heating value of the vaporized liquid. The density

of the liquid is required in all heating value calculations. The basis for

determining the density is usually agreed to in custody transfer contracts,

which may involve several companies and countries. LNG densities can be either

calculated from a mathematical model, as a function of composition and

temperature (or pressure) , or measured directly in a tank or pipeline. During

the course of a typical contract the density will be determined many times with

systematic errors benefiting one of the contractual parties. An inaccuracy of

3

1% in the density of a 125,000 m LNG cargo is currently worth approximately

$40,000. An inaccuracy of less than 0.1% in the density has been selected as

a reasonable goal for this calculation or measurement.

CALCULATION OF THE DENSITIES OF LNG TYPE MIXTURES*

Calculation of the densities of LNG with a mathematical model has several

advantages and disadvantages. An advantage is that the model can be based on

the most accurate available density measurements performed under ideal laboratory

conditions. A disadvantage is that use of the model depends on knowledge of the

mixture composition, which may be difficult or inconvenient to obtain with

sufficient accuracy. Another disadvantage is that accurate mathematical models,

which cover a large range of mixture compositions, temperatures and pressures, are fairly difficult to use.

F-2
The molar volume V of a fluid mixture can be written mix

V = Z X. V. +

mix 1 1 (1)

,E where x.,11V, and V are conventionally the mole fractions, molar volumes of

the constituents, and the excess volume respectively, all at the temperature

and pressure of the mixture. For LNG type mixtures V is typically negative

E and 1-2% of V . . Therefore an accurate mathematical model for V . (or V ) mix mix

is required to achieve an inaccuracy of less than 0.1% in the density. Several

promising models for calculating accurate densities of LNG type mixtures have

been published. They include the Klosek and McKinley excess volume correlation [1]

,

the modified cell model [2], the modified corresponding states model [3], and

the modified hard sphere equation of state model [4] . The details of these models

are given in the references. The mathematical models must be based on and tested

against accurate density measurements for LNG components and their mixtures. For

contractual purposes it is desirable that the measurements and evaluation be

carried out by an independent third party.

Until recently there have been few accurate (0.1%) density measurements

available for liquefied LNG components and their mixtures in the normal boiling

temperature range (110-115 K) of LNG type mixtures. To obtain the additional

data needed a magnetic suspension densimeter has been constructed and performance

tested for measurements in the temperature range 90-300 K at pressures to 5 MPa

(725 psi) [5] , and a comprehensive program of orthobaric liquid density

measurements has been carried out on six LNG components (methane, ethane, propane,

isobutane, normal butane and nitrogen) [5,6], on 29 compositions of 13 binary

mixtures [7], and on 13 multicomponent mixture compositions [8], including

several LNG type mixtures. This work has been carried out by W. M. Haynes,

M. J. Hiza, and others at the National Bureau of Standards. The measurements

F-3
on the pure components, at temperatures mainly between 95 and 160 K, have an estimated imprecision less than 0.02% and an estimated inaccuracy of approximately

0.1%. The estimated imprecision is primarily based on the standard deviation

obtained for 123 measurements on liquid methane. The estimated inaccuracy of

a single density measurement on liquid methane was taken as the square root of

the sum of the squares of the systematic error plus an allowance of three times

the standard deviation for random error. The measurements on the binary and

multicomponent mixtures, at temperatures mainly between 105 and 140 K, have a typical estimated inaccuracy of approximately 0.1% and a maximum estimated

inaccuracy of 0.16%. The derived excess volumes V of the binary mixtures can be

classified into several quantitatively distinguishable groups: in the temperature

range of these measurements the alkane mixtures without methane have excess volumes which are less than 0.1% of V . , the alkane mixtures containing methane mix

have excess volumes up to 3% of V . , and the nitrogen-alkane mixtures have mix

excess volumes up to 10% of V . . mix > . .

The modified Klosek and McKinley correlation, the modified corresponding^

states model and the modified hard sphere equation of state model are being . optimized and evaluated by R. D. McCarty at the National Bureau of Standards.

The modified cell model is being optimized and evaluated by M. A. Albright at the

Phillips Petroleum Company. Within various composition range limitations these

models have correlated most of the NBS data within their estimated inaccuracies.

The results are now being prepared for publication.

t

DIRECT READING DENSIMETERS FOR LNG TYPE MIXTURES

Direct reading densimeters for use on LNG type mixtures also have several

advantages and disadvantages. Advantages include the relative simplicity of use (knowledge of the mixture composition is not required) and the possibility

of continuously monitoring the density. Disadvantages include the need for,

calibration of densimeters now commercially available and the difficulty of

obtaining sufficient information on the calibration and performance of a

F-4
particular densimeter. For contractual purposes it is desirable that the

performance of types of available densimeters be evaluated by an independent

third party. Accordingly, an apparatus [9] for evaluating the performance of

types of commercially available densimeters on LNG components and their mixtures

has been constructed and tested at the National Bureau of Standards. This work

has been carried out by B. A. Younglove and others. The direct reading

densimeters to be evaluated are placed in a density reference system (DRS)

containing carefully characterized liquefied gases and are compared against an accurate absolute densimeter based on Archimedes' principle. The accessible

temperature range of the DRS is 80 to 300 K and the pressure limit is 7 bars

('^ 100 psi). The estimated inaccuracy of the reference densimeter is less

than 0.21%. The estimated inaccuracy was based on the sum of the known sources

of systematic error, + 0.026%, plus three times the standard deviation, + 0.062%,

based on 71 independent measurements using eight different samples of liquid

methane (99.97% pure). The direct reading densimeters can also be compared with

densities calculated from measurements of the composition and temperature and a mathematical density model. Tests have been performed on commercially available

densimeters based on Archimedes' principle, on dielectric property measurements,

and on the frequency response of several vibrating elements. The results are now being prepared for publication.

SUMMARY AND CONCLUSIONS

Comprehensive accurate orthobaric liquid density data have been obtained

for six LNG components and their mixtures and are being used to optimize and

evaluate four promising calculation methods. Within various composition

limitations these models have correlated most of the data within their estimated

inaccuracies. Several significant differences between the measured and calculated

densities still remain, and efforts to resolve these differences are continuing.

A density reference system has been constructed and is being used to

evaluate the performance of commercially available densimeters for use on LNG

type mixtures. Several types of densimeters look promising for obtaining direct

density measurements on LNG in tanks and pipelines within the estimated inaccuracy

of the reference densimeter.

F-5
REFERENCES

1. J. Klosek and C. McKinley, Densities of Liquefied Natural Gas and of Low

Molecular Weight Hydrocarbons, Proc. First Int. Conf . on LNG, IGT, Chicago

(1968), Session 5, paper 22.

2. M. A. Albright, A Model for the Precise Calculation of Liquefied Natural

Gas Densities, NGPA Technical Publication TP-3 (1973).

3. J. Mollerup and J. S. Rowlinson, The Prediction of Densities of Liquefied

Natural Gas and of Lower Molecular Weight Hydrocarbons, Chem. Eng. Sci.

2_9, 1373 (1974).

4. J. B. Rodosevich and R. C. Miller, Calculation of LNG Excess Volumes by a Modified Hard-Sphere Model, Adv. Cryog. Eng. 19, 339 (1974).

5. W. M. Haynes, M. J. Hiza and N. V. Frederick, A Magnetic Suspension

Densimeter for Measurements on Fluids of Cryogenic Interest, Rev. Sci.

Instr. 47, 1237 (1976).

6. W. M. Haynes and M. J. Hiza, Measurements of the Orthobaric Liquid Densities

of Methane, Ethane, Propane, Isobutane and Normal Butane, J. Chem. Thermo,

(in press) (1976).

7. M. J. Hiza, W. M. Haynes and W. R. Parrish, Orthobaric Liquid Densities

and Excess Volumes for Binary Mixtures of Low Molecular Weight Alkanes

and Nitrogen Between 105 and 140 K, to be submitted to J. Chem. Thermo.

8. M. J. Hiza and W. M. Haynes, unpublished data.

9. B. A. Younglove and J. D. Siegwarth, Cryogenic Fluids Density Reference

System Provisional Accuracy Statement, unpublished data.

F-6
Magnetic suspension densimeter for measurements on fluids

of cryogenic Interest*

W. M. Haynes, M. J. Hiza, and N. V. Frederick

National Bureau of Standards. Institute for Basic Standards, Cryogenics Division, Boulder, Colorado 80302

(Received 24 June 1976) An apparatus incorporating a magnetic suspension technique has been

developed for density measurements on Uquids and Hquid mixtures, particularly

at saturation, at temperatures between 90 and 300 K and at pressures to 5 MPa

(approximately 50 atm). The feasibility of adapting this method, previously used

at room temperature, for low temperature use had been demonstrated in an

earlier study with a density measurement on saturated liquid nitrogen near its normal boiling point. The present apparatus, which is significantly improved,

and in most respects different from the earlier model, is described in detail. It includes a cryostat for continuous wide-range temperature control, a windowed

equilibrium cell particularly suited for studies of liquid mixtures, and a new

electronic servocircuit with a linear differential transformer for position control of the magnetic buoy. Extensive tests and density measurements have been

carried out to evaluate the performance of this apparatus. Densities of saturated

liquid nitrogen between 95 and 120 K and saturated liquid methane between 105 and 160 K are reported. The estimated standard deviation of a single density measurement is less than 0.02%. The total systematic error in the measurement

process from known sources is approximately 0.05%. The total uncertainty of a

single density measurement, which is taken as three times the standard deviation

plus the systematic error, is approximately 0.1%. Comprehensive comparisons of

the present results with previous experimental data are presented.

I. INTRODUCTION

With the advent of large-scale liquefaction and global

transport of natural gas, accurate equilibrium liquidphase densities have become important for custody

transfer. The density data for liquefied natural gas mixtures and their components have been generally characterized by the existence of large discrepancies (approximately 0.5%) between different sets of data for the pure components and by a limited amount of mixture

data. Hence, an apparatus has been developed to pro- vide accurate, consistent, and comprehensive density data for liquefied natural gas mixtures and their pre- dominant pure components at saturation conditions. These measurements will serve as a data base for test- ing and optimizing selected mathematical models (correlations) useful in predicting the densities of liquefied natural gas. In the present paper the apparatus and

experimental procedures are described in detail and

representative measurements for two components of

liquefied natural gas are presented.

A magnetic suspension densimeter, which is based on an application of Archimedes' principle, has been

selected for the present measurements primarily be- cause this instrument is suitable for an independent,

direct determination of the density of a saturated

liquid over wide ranges of temperature and pressure

within the precision and accuracy required for antici- pated technical applications. In an earlier study,' the

feasibility of adapting the magnetic suspension tech- nique for density measurements at low temperature was

demonstrated with a measurement on saturated liquid

nitrogen near its normal boiling point. The present

apparatus (see Fig. 1 for a scaled assembly drawing),

which is a much improved version of the earlier model, incorporates a three-coil support system,^ a cryostat for temperature control at any temperature

between 90 and 300 K, a windowed equilibrium cell suitable for projected studies on liquid mixtures at pressures to 5 MPa, and a new electronic servocircuit with a linear differential transformer that serves

as a position sensor for a barium ferrite magnetic buoy.

The present work has included an extensive evaluation of the use of a magnetic suspension densimeter

for absolute density measurements. (Here the term

"absolute density" is used to indicate that cryogenic

fluids were not used to calibrate the instrument.) Results of performance tests along with densities

for saturated liquid nitrogen between 95 and 120 K and

saturated liquid methane between 105 and 160 K are presented in this paper to demonstrate the low temperature performance of this new apparatus. The estimated

standard deviation of a single density measurement is less than 0.02%. The total uncertainty of a single

measurement, which is taken as the sum of the systematic error and three times the standard deviation,

is approximately 0.1%.

In Sec. II the general principles of a magnetic

1237 Rev. Sci. Instrum., Vol. 47, No. 10, October 1976 1237 G-1
CELL VERTICAL

POSITION CONTROL

I -y, COAXIAL LEADS ^ TO SERVO-CIRCUIT

LNt FILL 4 VENT VACUUM

Fig. 1. Assembly drawing (approximately to scale) of a magnetic suspension densimeter for cryogenic fluids.

suspension densimeter are outlined. Section III is mental procedures and measurements is given in Sec. devoted to a detailed description of the experimental IV. In Sec. V a summary of performance tests carried apparatus. A comprehensive discussion of the experi- out in evaluating the instrument is presented. This sec1238 Rev. Scl. Instrum., Vol. 47, No. 10, October 1976 Densimeter 1238 G-2
tion also deals with the uncertainties in the density measurements. Finally, the experimental data for saturated liquid nitrogen and methane, along with comparisons with independent measurements, are re- ported in Sec. VI.

II. PRINCIPLES OF OPERATION

A piece of magnetic material is magnetically sus- pended in a fluid at a stable equilibrium position

through the use of a closed-loop servosystem. When

the float (or buoy) is in free support, there are three forces acting on it. In the present system the magnetic float is more dense than the fluid in which it is suspended; thus, an upward magnetic force is added to the buoyancy force to balance the downward gravitational force. In the present work a three-coil (air-core) system^ is used to supply the magnetic force. The three coils are aligned coaxially. Each coil is symmetric about an

axis in common with the cylindrical axis of the magnetic buoy. The three coils consist of a main coil, which supplies the major part of the field necessary

to lift the float, and a pair of gradient coils. The

horizontal position of the float, which is in the shape

of a right circular cylinder (length/diameter > 1) magnetized along its cylindrical axis, is maintained by

the axially symmetrical, diverging field of the main coil. The magnetic force on the ferromagnetic buoy is given

by

M

dH

(1)

where M is the total magnetic moment of the buoy

and dH/dZ is the variation of the external field intensity along the common cylindrical axis of the coils. For the present system the float is a permanent

magnet for which the total magnetic moment (excluding

temperature dependence) can be represented by

M = M„ + M,(H), (2) where M,, is the permanent moment, and M,(H) is the induced moment resulting from an applied field. At a fixed position along the cylindrical axis of an air- core solenoid. H = kl and

dH

~dZ

(3)

(4)

where / is the solenoid current and k and k' are constants dependent upon the number of turns and

dimensions of the coil. As mentioned earlier, the float is supported at a position relative to the main coil such that its horizontal

position is fixed. This results in the float being sup- ported at a distance below the main coil slightly larger than the inside radius of this coil. The float is supported approximately midway between the gradient

coils. These coils are connected in series such that their magnetic field intensity contributions cancel at the float position. (For a Helmholtz coil arrangement the magnetic fields would add at the midpoint.) Thus, the magnetic field intensity at the float position is due

solely to the main coil contribution. Similarly, the magnetic field gradients of the gradient coils add at the float position. For this three-coil arrangement and with a constant main coil current (/,,/) (and subsequently the magnetic

moment of the float does not change), the density of the

fluid (p) is related to the gradient coil current (I,-) by the following relation:

P = A + BIf;. (5) where A and B are constants to be determined by

calibration with fluids of known density. This relation- ship is valid whether the float is magnetically hard or

soft. Knowledge of the mass and volume of the float is not required to obtain relative density results using Eq.

(5). However, since the magnetic moment of the float

is temperature dependent, the constants A and B would

have to be determined at each temperature of interest. At low temperatures at least two fluids of known

density, one of which may be "vacuum," are needed

for calibrating the instrument for use in performing rela- tive density measurements. However, the densities of low temperature fluids are not known to sufficient accuracy to permit them to be used as calibration

fluids and, in fact, this had been one of the major

motivations for developing an independent technique for density measurements on cryogenic fluids. In the previous work by Haynes and Stewart,' a new method was demonstrated for determining absolute

densities using the same three-coil arrangement, but which is dependent upon the magnetic properties of

the buoy material. If one uses a permanent magnetic

material for the float and its induced moment is zero

or, at least, very small compared to the permanent

moment, then the magnetic force on the float is given

by the relation.

^mag — C'Jxi + D' Iq, (6) where C and D' are constants depending on the rela- tive position of the coils and float, the magnetic moment

of the float, and the dimensions and number of turns of the support coils. One should note that for Eq. (6) the main coil current {1^) is not held constant. Now

the density of the fluid is given by the expression,

p = {m- CIj,- DIaVV, (7) where m and V are the mass and volume of the float. The acceleration of gravity has been included in the constants C and D. (The mass and volume of the float must be determined by independent measurements.)

The validity of this equation can be tested experimentally. For measurements in a vacuum, Eq. (7) re- duces to the following relation:

1239 Rev. Sci. Instrum., Vol. 47, No. 10, October 1976 Densimeter 1239 G-3
m = C/,„ + Die- (8)

It should be emphasized that the critical assumption

in deriving Eq. (7) is that there is no induced moment

in the buoy resulting from changes in the magnetic

field intensity over the range of magnetic fields needed

for the density measurements. (For the present

measurements this includes fields between 0.006 and

0.016 T.)

The current in the gradient coils has been measured

as a function of the current in the main coil while

the float was suspended at a constant height in a given

fluid, usually vacuum, at constant temperature. The

currents were fitted by the method of least squares to either Eq. (6) or Eq. (8). The quality of this fit indicated the validity of the assumption concerning

the dependence of the magnetic moment upon the magnetic field. (Results will be presented in a later section.) For the present measurements the main coil current, and thus the magnetic field, could be varied over a range amounting to 25% of its maximum value. The minimum ratio of /„//(, was determined by the

loss of horizontal stability of the float. From the above discussion it should be apparent

that relative density measurements using Eq. (5)

(/,; constant) can be carried out to complement the

results of absolute measurements using Eq. (7) with the same three-coil arrangement. In performing measure- ments using Eq. (7) for which the main coil current

is varied over a considerable range, it is experimentally difficult to fix or determine the position of

the main coil from vacuum to liquid measurements

within the desired precision. This problem does not

arise when making relative density measurements for which the main coil current is held constant. In principle, both procedures should give identical density

ratios for the same fluids at constant temperature.

In practice, the relative density measurements can be

carried out to deduce the systematic error in the absolute density measurements that depends on the magnitude of the main coil current. These tests have

been performed in the present work and will be dis- cussed in a later section.

III. APPARATUS

A. General considerations and cryostat

An assembly drawing (approximately to scale) of the major components of the apparatus is shown in Fig. 1. The general dimensions and configuration of the cryostat

and equilibrium cell were determined by the dimensions

and configuration of the main coil and the two gradient

coils. (See Table I for coil dimensions.)

Criteria considered essential, and which have been

satisfied, in the design of the apparatus are as follows:

(a) all materials of construction in ciose proximity to the magnetic suspension assembly are nonmagnetic; (b) the entire assembly is rigidly supported so that the rela- tive position of the buoy, microscope, and support coils

Table I. Parameters of support coils.

Main coil Gradient coils

Length 6.0 cm 6.2 cm

Inside diameter 7.4 cm 25.4 cm

Outside diameter 20.24 cm 38.6 cm

Number of turns 5000 5000

can be maintained; (c) the magnetic buoy and the liquid level are visible within a windowed cell capable of withstanding working pressures up to 5 MPa; (d) the volume occupied by the liquid sample within the cell

is sufficiently large to render the unavoidable vapor volume of the access tubing, etc., insignificant within

the accuracy goals of experiments involving liquid

mixtures; (e) temperature gradients along the length

of the working space of the cell are monitored and

reduced to a practical minimum, i.e., less than a total of 10 mK; (f) the rate of refrigeration of the equilibrium

cell is adjustable and continuous; and (g) the temperature of the cell can be controlled at any temperature

between 90 and 300 K. A concrete block structure provides a stable support for the cryostat, the coils, and the microscope.

The cryostat assembly is suspended from an aluminum

plate that spans the top of the concrete structure. The stainless steel central support tube of the cryostat is attached to this aluminum plate with a brass

collar (not shown in Fig. I). The lower end of the

stainless steel tube is soldered to a copper tube to which a heat exchanger is soldered.

Refrigeration is provided by continuous transfer of

liquid nitrogen from the cryostat reservoir through the heat exchanger. Regulation of the refrigeration rate is accomplished by controlling the nitrogen vent rate to the atmosphere.

Refrigeration is supplied to the bottom of the equilibrium cell through the copper radiation shield and

to the top of the cell through two copper braided

straps. The radiation shield, which contains a slit aperture in a position corresponding to the ceil window,

is attached to a copper plate at the top of the shield with Wood's metal to facilitate removal of the shield and alignment of the shield within the glass tail section. The glass tail is connected to the stainless steel vacuum

jacket through a stainless steel-to-glass transition joint.

B. Equilibrium cell The equilibrium cell, made of electrolytic tough

pitch copper, has an overall length of approximately

30 cm, including the copper-plated bellows at the bot- tom. The cell closure is a compression fitting with a

silver-plated, solid copper 0-ring. The closure plug,

threaded backing ring, and compression screws are

stainless steel. The top of the cell is held in alignment by a stainless steel tube, which is brazed to the closure plug and extends through the uppermost

cryostat plate. The upper end of the cell support tube

1240 Rev. Sci. Instrum., Vol. 47, No. 10, October 1976 GDenslmeter 4

1240
is threaded through a nut and bearing assembly to al- low small adjustments in the vertical position of the cell and thus the vertical position of the magnetic buoy.

The bottom of the cell is thermally anchored to the

radiation shield by mechanical attachment of a flanged bellows section. A thin coat of commercially avail- able conducting grease is used to enhance thermal

contact between the bellows flange and the shield. Two thermal links of copper braid are also mechanically

attached to the top of the cell from the top plate of

the radiation shield using thin coats of conducting

grease between the contact surfaces. The outside diameter of the main part of the cell is 4.13 cm and that of the closure section is 7.60 cm. The internal working space is 1.99 cm in diameter

and approximately 20 cm long. More than half of the

internal volume, however, is occupied by the magnetic buoy-sensor coils assembly (—10 cm^) and the vapor bulb ( — 35 cm'). The vapor bulb is a slip fit in the top section of the cell and is attached directly to the closure plug. The internal free volume of the cell is approximately 20.5 cm'. Anticipating measurements on

mixtures, the volume (—0.3 cm^) in the annulus be- tween the vapor bulb and the cell wall has been made as small as possible, since this is normally part of the vapor volume.

The electrical lead-throughs for the sensor coils consist of three No. 32 coated copper wires encapsulated

with an epoxy adhesive in a copper capillary tube. This tube extends through the closure plug to the bot- tom of the vapor bulb. The epoxy adhesive, an

alumina-filled resin with elevated temperature curing

agent, was selected based on an earlier study' of low temperature properties of epoxy adhesives. By

pressurizing with helium gas while the adhesive was

hot, the entire length of the capillary tube was filled with

adhesive to minimize the available vapor volume in the equilibrium cell. The cell window was designed to allow viewing the

liquid sample from the base of the vapor bulb down

to 2 cm from the bottom of the liquid space. The

viewing slit is 0.6 cm wide x 7.5 cm long. The window

consists of a piece of tempered Pyrex^ glass of 0.32-cm

thickness with semicircular ends and chamfered edges.

The seal between the glass and the cell is made with

indium wire compressed in a racetrack groove machined in a flat surface on the cell. The glass is compressed against the indium seal with a hardened

beryllium copper plate secured by stainless steel screws. A rubber asbestos pad is placed between the beryllium copper plate and the glass to relieve thermal and

mechanical strains. The maximum working pressure of

the equilibrium cell is limited by the maximum working

pressure of the window.

C. Magnetic buoy

The buoy is a barium ferrite (BaFejjOig) magnet in the shape of a right circular cylinder magnetized

along its cylindrical axis. Its length and diameter are approximately 0.64 and 0.51 cm, respectively.

Barium ferrite is a magnetically hard, ceramic material with a density of approximately 5 x lO'' kg/m''. It

is somewhat porous and has a high electrical resistivity.

The buoy used in the present work has been permanently magnetized in a saturation field of 1 T. After

initial cycling over maximum ranges of temperature

(90-300 K) and magnetic field intensity (0-1.3 x 10* A/m) the barium ferrite magnet exhibited no hysteresis over the ranges of currents and temperatures needed

in the density measurements. The magnet is operating

in a very small segment (5- 13 x lO'' A/m) of a broad

hysteresis loop. The slope of the B-\s-H curve is small and constant. The change in the magnetic moment of the

float with temperature varies from 0.2%/K at 300 K to

0. 1%/K at 100 K, as determined from the present meas- urements in vacuum. This variation in the magnetic

moment with temperature results in a random error in the density of approximately 0.002% at 100 K, increasing

to 0.004% at 300 K. This estimate is based on a

reproducibility in the temperature of 2 mK from vacuum

to liquid measurements.

Since the barium ferrite magnet is porous, it must

be coated with a material which does not allow fluid to penetrate into the buoy. Copper was found suitable for this purpose. After a piece of barium ferrite was ground into the shape of a right circular cylinder

with chamfered edges (0.25 mm deep), a conducting

layer of copper was uniformly plated onto the ceramic

magnet by chemical reduction. On top of this conducting layer, copper was electroplated to a thickness of approximately 0.25-0.50 mm; a much thicker coating

resulted at the edges. Then most of the copper was

removed with a diamond tool until the copperplated barium ferrite magnet was in the shape of a right circular cylinder without chamfered edges. The final buoy had a minimum of 0.06 mm of copper over the

cylindrical surface and the end faces and at least 0.25 mm

on the edges where the magnet had been chamfered.

The edges were built up to a thicker coating since

the plating strength would be weakest at these

locations. (For density measurements it is not necessary that the plating be symmetric about the center of mass of the buoy.) Gold was flashed (lO"'' mm) over

the entire copper surface as a protective coating.

0. Electromagnetic support coiis Each of the coils is composed of two separate

coils of 2500 turns of epoxy-coated aluminum foil of approximately 0.025-mm thickness. The foil for the main coil has a width of 2.5 cm while that for the gradient coils is 3.0 cm. Selected coil parameters

are given in Table I. Each of the gradient coils is rigidly supported by three aluminum rods resting on the concrete structure. The

gradient coils have a separation distance of approximately 23 cm. No effort has been made to control the

1241 Rev. Scl. Instrum., Vol. 47, No. 10, October 1976 GDenslmeter 5

1241
12V 12V 12V 12V 1^4-44-4-4

1.35V

Hg CELL

(TEMP & LOAD STABILIZED)

J MAIN J COIL

POWER SUPPLY

( 100 VOLTS)

f MR1123

DIFFERENTIAL

VOLTMETER

THERMAL LAGGING

ENCLOSURE

Fig. 2. Current control circuit for main coil.

position of the gradient coils except through the control of the laboratory temperature. The dH/dZ of the gradient coils changes very slowly (2.5 x 10~^/cm)

from a maximum at the float position. Since the change

in dH/dZ with position for the main coil is two orders of magnitude larger than that for the gradient coils, special care has been taken to minimize changes in the position of the main coil. First, the main coil is supported at its midplane so that thermal expansion effects inside the coil are minimized.

A circular copper plate has been soldered to the brass tube on which the main coil is wound. A coil of aluminum

foil (2500 turns) is clamped tightly to each side of the copper plate with a thin layer of vacuum grease be- tween the aluminum foil and copper for maximum

thermal contact. The copper plate (and thus the coil)

is supported by quartz rods extending to the concrete

structure. Thus, any changes in the position of the midplane of the coil due to room temperature changes

would be negligible. Copper plates with cooling water have been placed on the outside faces of each section of the main coil such that the average temperature of the main coil is below room temperature

for maximum current (I A). However, for absolute

density measurements, the temperature of the main coil changes from vacuum to liquid measurements (1.2 K

for nitrogen at 100 K) since a larger current is required

to support the float in vacuum than in the liquid for

a given gradient coil current.

E. Support system electronics

The current in the main coil, which contributes the major portion of the magnetic force necessary to lift the buoy, is provided by the circuit of Fig. 2. The circuit

functions as follows: The main coil current flows through

a stable resistor Rstd (0.1 H) in the emitter of Q2 (the

current-controlling transistor). The voltage developed

across R^td is compared with a reference voltage from

a Kelvin-Varley voltage divider by amplifier A,. The

output of A, drives the base of Q2 and controls the current through Rstd and the main coil. Since the loop

gain of this circuit is exceedingly high (>I0*') and the thermal drifts are very low, the long-term stability of

the main coil current is of the order of 0.001%. This

current controller has a temperature coefficient of the order of 5 ppm/K and a sensitivity to power supply variations of less than 2 x 10"^ A/V. A slow drift of

the coil current of 2.5 x 10"* A/h has negligible ef- fect on the density measurements since the main coil current is measured each time that the gradient coil current is determined. (It should be noted that the precision and accuracy of the density results depend on

the short-term stability and not the absolute accuracy of

the standard resistor.) The gradient coils are included in a control circuit (Figs. 3 and 4) that senses and maintains the vertical position of the buoy. The requirements for stability of a magnetic support or levitation system are dis- cussed in detail in Refs. 5 and 6 and will not be repeated

here. Suffice it to say that the characteristic equation

for a magnetic levitation system has a root with a positive

real part, and for system stability the plot of the frequency response of the characteristic equation (the Nyquist plot) must encircle the origin once in the counterclockwise sense. This is accomplished by the dual-lead network composed of R,, R2, Ci, and C2 in Fig. 4. A dual-lead network is required for this system

since minimization of the steady state offset or buoy

position change requires at least a first-order integrator

1242 Rev. Scl. Instrum., Vol. 47, Na 10, October 1976 Dantlmeter 1242 G-6
POWER SUPPLY

(250 VOLTS)

Fig. 3. Current control circuit for gradient coils.

in the control loop. This integrator consists of amplifier

and R, and C2. The additional resistor R-, is re- quired to stabilize the combined integrator and dual-lead network. A block diagram of the electronics is presented

in Fig. 5 to complement the detailed circuit diagrams in Figs. 2-4. The circuit diagrams are presented in detail since this circuit is considerably different from

any found in the literature. It should be noted that the

1243 Rev. Sci. Instrum., Vol. 47, No. 10, October 1976 Densimeter G-7

1243
current control amplifier for the main-coil constant- current source is the same as that for the gradient

coils. Perhaps the most interesting part of the support

system is the position sensor. In the past, position

sensing has been accomplished by either opticaP-**

(light beam-photomultiplier tube arrangement) or

electronic' ""'^ (inductance pickup coil or differential transformer) means. The requirements of small size, low

power dissipation, high sensitivity, the ability to with- stand high pressure and low temperatures, and exceptional dimensional integrity resulted in the use of a linear

differential transformer (LDT) wound on a machinable

glass ceramic form. The LDT consists of a pair of coils equally spaced about a transverse rectangular opening

in the ceramic form inside which the buoy is suspended.

Each coil is wound with 34 turns of double silk- wrapped 50/44 Litz wire in circumferential grooves of 2.8-mm width and 6.1-mm depth. The outside diameter

of the coils and the ceramic holder is 17.3 mm. The

complete transformer assembly has been potted with a

low-viscosity epoxy resin to prevent intrusion of the pressurized fluid into the windings.

The sensitivity of the LDT as measured at the phasesensitive detector (synchronous detector) is of the order

of ! V/mm. The noise voltage at the sensor amplifier

input is less than 10 * V/Hz"^. The operational

amplifiers in the compensation circuit have very low off- set drifts and are thermally lagged to a large copper

block in the amplifier chassis. Consequently, the vertical movement of the buoy due to operational amplifier

drifts and rf amplifier noise is less than 10~^ mm.

The LDT is the major component of a ratio-trans- former-type bridge. Part of the bridge is located at the top of the cryostat and is connected to the LDT through

long coaxial lines. The bridge is constructed so as to re- move proximity effects of the outer conductors of the coaxial lines. The neutral position of the buoy is controlled by a small variable capacitor between the center

lead and one side of the LDT. Conductance balance

is achieved with a resistor connected across the capacitor. Unbalance in the LDT due to the inductance

of the long leads is minimized by tuning the two halves of the LDT to resonance with matched capacitors

(as large as possible for the 0.5-MHz exciting signal).

These capacitors are connected near the LDT outside

the sample cell but inside the vacuum space.

IV. EXPERIMENTAL MEASUREMENTS AND

PROCEDURES

A. Temperature and pressure

The techniques and instrumentation for the measure- ment and control of the temperature and pressure are standard. The primary temperature sensor, calibrated on the IPTS 1968, is a platinum resistance thermometer

secured in a well at the base of the equilibrium cell with Wood's metal. The calibration of the thermometer

Miisurini

Circuits fifmf—

G,

Voltiii Cintrollid

Cirriat Sourci

Pticisi Voltaic

Control

Niik Friooncr

Osclllitor

Hiik Fri^micif Iransfornor

Irl^ie

Hilt

tmrliflon

Pkiso

Dotoctor

latiintor t

CtMMiisotlon

CIrcolts

Gj

Vtltiie Contrilloi Cvrront Siorco

Miisirlii

CIrcalts

Fig. 5. Block diagram of a magnetic suspension densimeter:

G|, Gj —gradient coils; M —main coil; S,, Sj —sensing coils; B —

magnetic buoy.

has been checked against vapor pressure measurements

on liquid methane and nitrogen.

The uncertainty of the calibration is approximately

0.002 K. Due to the specifications of the potentiometric

measuring system, uncertainties in the temperature

amount to a maximum of 0.010 K at 1 10 K, increasing to 0.030 K at 300 K. The temperature of the sample

holder is controlled to better than 0.005 K, approximately the same as the reproducibility of the temperature measurements. A current of I mA for the thermometer is supplied

by an electronic constant current source. The voltage

drop across a 100 fi calibrated standard resistor in series with the thermometer is monitored continuously with a

six-digit differential voltmeter. With this setup the uncertainty and repeatability of the current is approximately 0.002%. The voltmeter is checked periodically

against a microvolt potentiometer using a calibrated standard cell. The total uncertainty in the reported temperatures in Sec. VI is believed to be less than 0.03 K. (At room

temperature it would be less than 0.04 K.) The 0.03-K

total uncertainty consists of approximately 0.025-K

systematic error and 0.(X)5-K random error. The syste- matic error was determined from the uncertainties in the calibration of the thermometer and in the potentiometric measuring system.

The temperature of the cell is regulated by balancing

coarsely variable cooling with precisely controlled

electric heating. A control heater near the bottom of the

cell is connected to a dc power regulator, which is part of a measuring/regulation system that also includes a

six-dial microvolt potentiometer and a microvolt

amplifier. A second heater at the top of the cell is con- nected to a matiual power supply. Independent heaters

at the top and bottom of the cell are used to minimize

temperature gradients along the length of the cell.

1244 Rev. Scl. Instrum., Vol. 47, No. 10, October 1976 Densimeter 1244 G-8
Temperature gradients are detected by monitoring the vapor pressure of the liquid in the vapor bulb. Pressures below 7 bars are measured with a 0- to 7-bar spiral quartz Bourdon gauge. This gauge has a resolution of less than 3.5 x 10~' bar. It has been cali- brated against an air dead-weight gauge giving an uncertainty of approximately 0.1% over the full range. For

pressures above 7 bars, a double-revolution 0- to 20-bar Bourdon gauge is used. It has also been calibrated against the air dead-weight gauge and can be read to the nearest 0.005 bar. Vapor pressure measurements have been used in the present work primarily as a means of monitoring

temperature gradients. They have also been used as a check against the calibration of the platinum resistance thermometer. In general, the vapor pressures for methane have been consistently lower than those of Prydz and Goodwin.''* This pressure difference cor- responds to a temperature difference of 0.01-0.02 K. The discrepancies between the nitrogen vapor pressures of the present work and those of Wagner'^ correspond

to an average temperature difference of less than 0.015 K. with no particular trend observed.

B. Position of buoy

The accuracy and precision of the density measure- ments depend on being able to suspend the float at the same position relative to the support coils in vacuum

and in the test liquid at the same temperature. A

I25x filar micrometer microscope is used to determine

the position of the float. It has a resolution of ap- proximately 5 X 10"* mm. The maximum error in the

position determination is 2 x 10"^ mm, which cor- responds to an error in density of less than 0.03%.

This error includes approximately equal contributions from the alignment of the microscope, so that the "apparent" position of the float is independent of the index of refraction of the fluid inside the sample cell, and from the repositioning of the float for vacuum and

liquid measurements. The first contribution would be a systematic error while the second is random. The preci- sion of the density measurements depends primarily on

the reproducibility of the position of the buoy from vacuum to liquid measurements. As mentioned above, the microscope must be aligned so that the "apparent"" position of the float does not depend on the index of refraction of the fluid inside the sample cell. In viewing the float inside the cell one must

look through the glass tail of the cryostat and the sample holder window. The "apparent" position of the

float would be dependent on the refractive index of the

fluid inside the cell unless the light rays are perpendicular

to the interface between the test liquid and the inside surface of the sample holder window.

The procedure for adjusting or aligning the micro- scope is as follows. First, the float is positioned at rest on the ceramic holder at the same horizontal

position as when in support. Then a fiducial mark on the

float is observed under two experimental conditions,

i.e., with the float first immersed in gas and then im- mersed in liquid. Both methane and nitrogen were used

to carry out this procedure. During this procedure

the microscope tilt is adjusted so that the "apparent"

position of the float does not depend on the refractive index of the fluid inside the cell within the resolution of the microscope. The temperature of the cell is controlled to better than 0.01 K during these observations. Care is taken to ascertain that the float is ob- served through the same parts of the windows as during

the density measurements. Necessarily a different part of the float is observed. This presents no special problem

since there are diamond tool marks the entire length of

the float that can be used as reference lines. This

procedure has been repeated frequently during the course of the reported measurements. It has been found

that a readjustment of the microscope tilt is necessary

only if the apparatus is perturbed by disassembly.

C. Volume of buoy

Absolute density measurements [Eq. (7)] with a magnetic suspension densimeter require a determination of

the volume of the magnetic buoy. In the past this has been accomplished either by using distilled water as a reference fluid of known density''' or by making direct length and diameter measurements on a uniformly constructed float.' Here the volume has been determined

by the first method.

The volume (0.13485 cm' at 300 K) of the magnetic

buoy was determined within 0.02%. The distilled water was vacuum distilled to remove air. Any problems with

bubbles inside the cell were rectified by pressurizing the water with helium gas. The volume of the buoy has been measured three times at 300 K and once at 290 K. These four measurements gave a standard deviation of 0.005% using thermal expansion data for barium ferrite to calculate the volume change from 290 to 300 K.

This resulted in a 99% confidence interval of ±0.015%.

The systematic error in the volume determination de- pends on the uncertainty in the density of water. This should be less than 0.005%.

The present paper reports density data for cryogenic

fluids. Thermal expansion data for barium ferrite were

used to calculate the volume of the float at low

temperatures. Recently the linear thermal expansion

of polycrystalline barium ferrite was measured at this laboratory at temperatures from 76 to 293 K with a quartz tube dilatometer." The volume of the float at 100 K is approximately 0.4% less than the room temperature value. Barium ferrite is somewhat anisotropic and its thermal expansion was measured both parallel and perpendicular

to the magnetization direction. An anisotropy of 15-20%

was observed. The estimated overall uncertainty of the thermal expansion measurements would correspond to an error of 6% in the adjustment to the volume.

This would produce an uncertainty of approximately

1245 Rev. Sci. Instrum., Vol. 47, No. 10, October 1976 Densimeter G-9

1245
0.02% in the volume at 120 K. The uncertainty in the adjustment to the volume due to the contraction of

the copper plating is negligible.

The effect of pressure on the volume of the float

is negligible at the highest pressures encountered in the present work. The bulk modulus for barium ferrite should be less than that for copper, which is 1.35 X 10" Pa.'" This value would correspond to a volume

correction of approximately 0.001% at 2.5 MPa, the vapor pressure of nitrogen at 120 K.

D. Mass of buoy

The mass of the magnetic buoy was determined with

a 10-g capacity equal-arm microbalance. A calibrated

class M weight set was used in the weighings. Pre- cautions were taken to assure that the copper plating

and gold protective coating provided an impervious

barrier to liquids under pressure. The buoy was rapidly

cycled between room temperature and 76 K. It was then immersed in liquid ethanol at 5-atm pressure and room

temperature for 4 h. The buoy was weighed twice after removal from the ethanol bath. The average of these weighings was 9 ixg higher than the mean of the initial four weighings. A significantly larger increase in the mass was expected if the plating on the float contained a

pinhole that allowed ethanol to penetrate into the porous

ceramic. Thus, at room temperature, the metallic coating appeared to be impervious after thermal cycling.

The reproducibility of liquid methane density measure- ments (see experimental results) after many cycles be- tween room temperature and 100- 140 K is further evidence of the resistance of the metallic coatings to damage from thermal cycling.

The final mass of the magnetic buoy (0.73706 g) was taken as the mean of all weighings, including the weighings after immersion in ethanol, corrected for air buoyancy. A confidence interval for the six weighings, based on a standard deviation of 6 fig, was ±10

ixg. The systematic error in the mass determination,

lesulting primarily from the weight set calibration, is believed to be less than 5 fig.

V. EVALUATION OF PERFORMANCE OF

MAGNETIC SUSPENSION DENSIMETER

A. Performance tests

The use of Eq. (7) for obtaining absolute densities has again been verified experimentally'. The gradient

coil current has been measured as a function of the main coil current over a range of approximately 20%

of the maximum main coil current. These measurements

were carried out while supporting the float in a given

fluid (including vacuum) at constant height at a fixed temperature. The various pairs of /v/ and Iq were

fitted by the method of least squares to Eq. (7). The

residual standard deviation, with the gradient coil current as the dependent variable, was less than 10~^ A. Examination of the residuals showed that they were

random and well approximated by a normal probability

distribution. These results demonstrated that within the precision of the current measurements the magnetic

moment of the barium ferrite float is independent of the magnetic field intensity over the range of fields (0.006- 0.016 T) considered in the present work.

Other coil configurations have been tried that gave re- sults that substantiated the observations given above.

First the bottom gradient coil was disconnected re- sulting in a two-coil system. The values of the constant

(C) in Eq. (7) for the two- and three-coil arrange- ments under otherwise identical experimental conditions were in agreement within the experimental uncertainty.

In other words, the magnetic moment of the float (contained in C) remains constant for significantly differ- ent magnetic field intensities. Next the pair of approximately identical (gradient)

coils were connected to the constant current source in a Helmholtz arrangement. The main coil was connected

into the servosystem. The float was first supported at a constant height at fixed temperature by the force supplied by only the main coil. The float was located

at the midpoint of the Helmholtz coils while the current in the Helmholtz coils was increased to 0.6 A. There was an insignificant change in the main coil current

(10"* A) for this relatively enormous change in the magnetic field intensity (about an order of magnitude more than for the typical data point). The results of these

tests demonstrated that this technique could be used for absolute density measurements.

In carrying out density measurements with this tech- nique, the position of the main coil must remain fixed over a wide range of currents for the vacuum and liquid measurements. This means that the "constant" k' in Eq. (4) and the constants, C and D, in Eq. (7) must

be independent of the current in the coil. It was hoped

that the measures exercised in controlling the temperature and position of the main coil (see Sec. Ill D)

would result in such behavior. It was experimentally

impracticable to determine if k' was a constant by

monitoring the position of the coil. However, the effect of a change in the current in the main coil on the density measurements could be obtained in another manner. As shown in Sec. II the fluid density is linearly

proportional to the current in the gradient coils if the main coil current is held constant. Not only is the posi- tion of the main coil fixed, but also the magnetic field intensity at the midpoint of the gradient coils (float position) is constant. Relative measurements [Eq. (5)] carried out with vacuum, nitrogen, methane, and

propane at 1 10 K were not consistent with the density

ratios computed from absolute measurements [Eq. (7)] for the same fluids. These results showed that the "constants" (k', C, and D) vary slightly with the main

coil current. This variation produces a density error

relative to the difference between main coil currents

for vacuum and liquid measurements (constant Ig) of

approximately 1.4%/A. This corresponds to a density

adjustment of O.l-0.2%/(g/cm*) to the results from Eq.

1246 Rev. Sci. Instrum., Vol. 47, No. 10, October 1976 D>n»IWWlW 1246 G-10
Table II. Estimated uncertainties in density measuremenls.

Percent error in density

Methane Nitrogen Normal butane

Systematic errors 105 K 160 K 95 K 120 K 135 K 300 K

Mass of float (Sec. IV D) ±0.002 ±0.002 ±0.002 ±0.002 ±0.002 ±0.002 Volume of float at 300 K (Sec. IV C) ±0.02 ±0.02 ±0.02 ±0.02 ±0.02 ±0.02 Thermal expansion coefficient ofbariumferrite (Sec. IV C) ±0.022 ±0.017 ±0.023 ±0.021 ±0.020 ±0.001

Position of float (Sec. IV B) ±0.015 ±0.018 ±0.010 ±0.012 ±0.009 ±0.009

Position of main coil, determined from relative measurements. Eq. (5) (Sec. V A) ±0.02 ±0.02 ±0.02 ±0.02 ±0.02 ±0.02 Temperature of sample fluid (Sec. IV A) ±0.010 ±0.021 ±0.023 ±0.076 ±0.004 ±0.008

Three times standard deviation ±0.045 ±0.054 ±0.030 ±0.036 ±0.027 ±0.027

Total uncertainty' ±0.09 ±0.10 ±0.07 ±0.12 ±0.06 ±0.06

" The total uncertainty was determined from the square root of the sum of the squares of the systematic errors added to three times the standard deviation.

(7). Since all measurements are based on the volume de- termination using distilled water as a reference fluid of known density, the adjustment must be applied relative to this point.

A further check on this density-dependent adjustment was accomplished by measuring the densities of two other fluids of known density at room temperature.

The densities of liquid samples of normal pentane

and ethanol were determined by the Mass and Volume

Section of the Mechanics Division of the National Bureau of Standards in Washington, DC, to an estimated

inaccuracy of less than 0.01%. Measurements on these

fluids at 300 K with the present apparatus using Eq.

(7), combined with the adjustment based on the relative density measurements at low temperature, gave

densities that agreed with the reference values to better than 0.027c. Thus, the densities presented in this paper

based on absolute measurements [Eq. (7)] have been

adjusted slightly to be consistent with the results of

Tabi.i III. E\perimental results for saturated liquid nitrogen (molecular weight = 28.0134).

T Am. 100(p,.,„ - p,,;,i,

)

(K) (mol.'ll (mol/1)

95.000 25.6731 25.6755 -0.009

loo.ooo 24.6400 24.6391 0.004

105.000 23.4998 23.4988 0.005

1 10.000 22.2079 22.2071 0.004

1 15.000 20.6719 20.6748 -0.014

120.000 18.6818 18.6856 -0.020

100.000 24.6361 24.6391 -0.012

105.000 23.4963 23.4988 -0.011

1 10.000 22.2044 22.2071 -0.012

1 15.000 20.6787 20.6748 0.019

120.010 18.6800 18.6808 -0.004

95.075 25.6624 25.6605 0.007

100.075 24.6207 24.6229 -0.009

100.075 24.6279 24.6229 0.020

105.075 23.4841 23.4807 0.015

110.075 22.1840 22.1862 -0.010

115.075 20.6490 20.6492 -0.001

1 17.575 19.7356 19.7326 0.015

1 20.075 18.6525 18.6497 0.015

relative measurements [Eq. (5)]. The density difference between the relative and absolute measurements, ex- pressed in terms of the difference in main coil currents between the vacuum and liquid points (/, - If) for a constant gradient coil current, is independent of temperature. The temperature dependence of the magnetic

moment of the float must be included if the difference

is expressed in terms of density.

The relative measurements were carried out using the same experimental setup and parameters (mass, volume,

and position) as the absolute measurements. Thus the

total uncertainty in the adjustment determination should

only include the random error in the measurement

process. Thus an estimated uncertainty of ±0.02% in the adjustment is based on the comparisons with the refer- ence fluids since this density difference was larger than a 99% confidence interval from a fit of the differences between relative and absolute measurements.

B. Error analysis

Evaluation of the experimental parameters involved in the present work showed that the uncertainty in the density measurements depends primarily on the uncertainties in the determination of the volume of the

float, the relative position of the float and the main

coil, and the temperature of the sample fluid. The

precision of the density measurements is inversely

proportional to the difference between the density of the

fluid and the density of the float. This variation with

density cannot be observed for the measurements re- ported in this paper because of the density range covered.

The precision also varies with temperature, corresponding to the change in the magnetic moment of the float with temperature.

Table II summarizes the uncertainties in the density measurements for the nitrogen and methane results presented in this paper. Normal butane is also included

in this table, primarily to show the performance of the instrument at higher temperatures. Normal butane

densities, determined with this instrument at tempera1247 Rev. Scl. Instrum., Vol. 47, No. 10, October 1976 G

Densimeter -11

1247
tures between 135 and 300 K, will be presented in a forthcoming paper. The standard deviation given in the table for methane

at 105 K was based on twelve measurements. The

other standard deviations were computed relative to the density and temperature of this point. Standard deviations at the other temperatures and densities could not be estimated from statistical analysis since sufficient repetitive measurements were not taken for these points.

Measurements on more dense fluids, such as argon and

krypton, have demonstrated the expected variation of

the precision with density. Measurements near room

temperature, especially those on distilled water, have

exhibited the expected improvement in the precision as the temperature is increased. The total uncertainty of a single density measure- ment was taken as the square root of the sum of the squares of the systematic errors plus an allowance of

three times the standard deviation for random error.

VI. EXPERIMENTAL RESULTS

A. Nitrogen

The experimental saturated liquid densities for nitrogen are presented as a function of temperature

(IPTS 1968) in Table III. The explanation for some of

the nitrogen points not being at integral temperatures

involves the presence of a temperature gradient along

the length of the cell in some of the initial measure- ments with this apparatus. Each of the data points was

taken from a new charge of nitrogen. For each

datum point the vacuum measurements were carried out immediately before or after the liquid measurements. The same procedure was used for methane. The three data sets for nitrogen over the temperature range of 95- or 100-120 K were obtained at approximately

six-month intervals. Of the two data sets at integral

lemperatures. one was taken with methane, and the other with nitrogen, in the vapor bulb. The third set was taken with no liquid in the vapor bulb. (For the

I2().()l(l-K point a slight temperature gradient was applied to remove bubbles from the sample liquid inside the

cell. I The nitrogen samples were taken from commercially

available, research grade gas. A purity specification of 99.99 mofr was given by the supplier. The gas has been analyzed chromatographically with a thermal conductivity detector and found to be within the specified

purity. The nitrogen gas was passed thrt)ugh a room

temperature molecular sieve trap, primarily for re- moval of water. The saturated liquid densities (p) of nitrogen have

been fitted as a function of temperature (T) by the method of least squares to an equation of the following form:

p - p,. = (l - - ) + V (l - - I

. (9)

Table IV. Parameters of Eq. (9) for nitrogen.

a = 19..1921?' (0.11)" /,, = ->l •<"'977 (4.8) p, = 1 1.21 mol/1

/>, = 26.01408 (2.5) T, = 126.20 K (T = O.OI6':r

/,,, = -39.49759 (6.5)

" These coefficients Ui. h,. h,, Z?.,) and those in Table VI were obtained from a least-squares program in which the experimental densities in g/cm' to five digits were converted to molar densities within the program.

Standard errors of coefficients in parentheses.

Pr and are selected values of the critical density

and temperature and «, are coefficients determined by

least squares. Equation (9) consists of a scaling law

modification'" to a generalized Guggenheim equation.'"

The parameters of Eq. (9) for nitrogen, along with the

residual standard deviation (cr) of the fit and the standard

errors of the coefficients, are given in Table IV. The

standard errors of the calculated densities in Table III are not presented since they are significantly smaller than the standard deviation. The main purpose of the above expression is to facilitate comparisons with in- dependent measurements. The choice of the critical point parameters is arbitrary in the sense that the critical point density can be varied by as much as 5'7c and the

critical point temperature by 0.2% without changing the

fit of the data within the estimated precision of the present measurements. For nitrogen the critical point values were obtained from the PVT data compilation

of Jacobsen^'.

In Fig. 6 independent experimental data available

in the literature are compared with the expression

representing the present nitrogen data over the temperature range of the present measurements. The present

data are also shown. The experimental temperatures

0.6

(D

0.5 NITROGEN

0 4

0 3

g 02

0 1 o A

a! 1

° §--- 9 »

a

01 a.

a.-0 1

-0 2

» » » »

•

-0 3

-0 4

•

. ,

(D <D

•

• •

•

•

-0 5

-0.6 1 1 1

1 1 95 100 105 110 115 TEMPERATURE, K

Fig. 6. Deviation plot of experimental densities of saturated liquid nitrogen compared with values calculated from Eq. (9) using parameters from Table IV: O present data. <3 Brauns," C Weber.^' A Rodosevich and Miller," • Goldman and Scrase,^'' Terry ci <//..-" CD Street! and Staveley." Mathias ci al.-'

1248 Rev. Sci. Instrum., Vol. 47, No. 10, October 1976 GDenslmeter 12

1248
Table V. Results for saturated liquid methane (molecular weight = 16.04303).

Standard Temperature Mean density deviation Number of (K) (mol/i) (%) data points

105.000 26.9458 0.015 12 110.000 26.4985 0.019 It 115.000 26.0443 0.014 12 120.000 25.5721 0.016 17 125.000 25.0845 0.016 18 130.000 24.5775 0.017 16 135.000 24.0540 0.016 23 140.000 23.5067 0.018 5 145.000 22.9312 0.014 5 150.000 22.3218 2 160.000 20.9876 2

of other measurements have not been adjusted to the temperature scale of the present results.

' The data of Brauns,^^ Weber.^^ and Rodosevich and

Miller,^* each obtained with a technique different from

that used here, fall within 0.15% of the present results. The densities of Goldman and Scrase^^ and Terry et

al.^^ are consistently lower than the present results by

approximately 0.3-0.4%. This pattern is also followed

for methane by Terry et al., and preliminary analysis of recent results for argon and krypton obtained with

the magnetic suspension densimeter indicate comparisons with Terry et al.. for these fluids exhibit the same

behavior.

B. Methane

Methane has been used as a control fluid throughout the entirety of a project that has included

density measurements on six pure fluids and, at least, thirty mixtures of these components. As a result, well over one hundred data points have been accumulated

for saturated liquid methane, primarily in the temperature range 105-150 K. Although these experimental

data are not presented in this paper, the results of an

analysis of the methane data are helpful in evaluating

the performance of the magnetic suspension densimeter

used in the present work. More than ten data points were obtained at each 5-K interval between 105 and

135 K. The mean of the experimental densities, along

with the standard deviation and the number of points

at each temperature, are given in Table V. (The

standard deviations are not given at 150 and 160 K since

there are only two data points at each of these temperatures.) Each of the data points represents a new

methane sample. The vapor bulb contained liquid

methane for all points.

Table VI. Parameters of Eq. (9) for methane.

a - 18.65812 (0.035^ Tc = 190.555 K

h, = 6.712030 (0.21) Pc = 10.16 mol/1

b2 = -0.9472020 (0.20) a = 0.016%

" Standard errors of coefficients in parentheses.

The liquid samples were obtained from either of two

cylinders of different batches of commercial, research grade methane. The purity for each cylinder as specified

by the supplier is 99.99 moI% minimum. Analyses in this laboratory substantiated these specifications. As with

nitrogen the methane gas was passed through a room

temperature molecular sieve trap to remove moisture

and any heavy contaminants not detected by analysis.

The 123 experimental data points have been fitted by

the method of least squares to Eq. (9). Only three

coefficients were needed to fit the methane data within

the precision of the measurements. The fourth term in the equation was not statistically significant. The coefficients of Eq. (9), the standard errors of the coefficients, the residual standard deviation (a) of the fit, and a selected critical density^* and temperature^" are given in Table VI for methane. Equation (9), with the

coefficients for methane, has been used to compare the present results with experimental data from independent

investigators. The methane data from the present work

are not shown on the deviation plot because of the large

number of points. All of the experimental densities of methane obtained in the present work will be pre- sented in tabular form in a future publication.

For saturated liquid methane there have been considerably more measurements than for saturated liquid

nitrogen. All of the other measurements were obtained

with techniques different from that of the present work.

Some of the older, less precise data have been included

in Fig. 7 for the sake of completeness. It is satisfying

that the relatively recent data of Orrit and Olives,^'

McClune,'^ Goodwin and Prydz,^^ and Shana'a and

1.4r MITHANE

-LO - e

.] 2U I I I i I 1 100 no 120 130 140 150 160 TEMfERATURE, K

Fig. 7. Deviation plot of experimental densities of saturated liquid methane compared with values calculated from Eq. (9) using parameters from Table VI: Terry et al..'" Q Orrit and Olives. A McClune,^ C Goodwin and Prydz,'^ igi Shana'a and Canfield,** Vennix," ® Grigor,^ V Davenport et al..'''' Klosek and McKinley ,^ 0 Sinor and Kurata," A Jensen and Kurata," A Bloomer

and Parent,'" 9 Fuks et al.," • Keyes et al.," Moran," O Van

Itterbcek et al."

1249 Rev. Scl. Instrum., Vol. 47, No. 10, October 1976 GDenMiwtar

13

1249
Canfield" agree with the present results within 0.1%.

However, as mentioned earlier, the densities of Terry

et al.'^'^ are systematically lower than the present results by 0.3-0.4%. The extrapolated densities of Vennix'*' at approximately 150 and 160 K are 0.4% larger than the present results although the discrepancy at 140 K is ap- proximately 0.01%.

C. Other fluids To demonstrate the performance of the magnetic

suspension densimeter at low temperature, this paper

presents only a representative cross section of the data

that have been taken in the present work. Data have

recently been obtained for other pure fluids (ethane, propane, isobutane, normal butane, argon, and krypton) over a density range extending to 2.3 g/cm'' (krypton)

and over a temperature range extending to 300 K (iso- butane and normal butane). These data will be published

in the near future. ACKNOWLEDGMENTS

The authors would like to express their appreciation

to the following individuals who have made significant

contributions to the development of this apparatus.

M. R. Cines of Phillips Petroleum Co., Chairman of the LNG Density Project Steering Committee, was instru- mental in the development of support for this project.

W. G. Layne, D. L. Smith, and A. N. DiSalvo as- sisted in the design and fabrication of the apparatus.

J. E. Cruz designed some of the electronics associated

with the refrigeration and temperature control systems.

J. R. Whetstone determined the densities of liquid

samples of normal pentane and ethanol. which were used

as reference fluids. P. V. Tryon assisted with the

statistical analysis of the data.

* This work was carried out at the National Bureau of Standards under the sponsorship of British Gas Coi p.. Chicago Bridge and

lion Co.. Columbia Gas Service Corp.. Distrigas Corp., Hasco Gas l.NG. Inc.. El Paso Natural Gas, Gaz de France.

.Marathon Oil Co.. Mobil R and D Corp.. Natural Gas Pipeline Co..

Phillips Petroleum Co.. Shell International Gas. Ltd.. Sonatrach, Southern California Gas Co., Tennessee Gas Pipeline. Texas

Hastcrn Transmission Co.. Tokyo Gas Co., i^td.. and Transcontinental Gas Pipe Line Corp.. through a grant administei ed by the American Cias Association. Inc.

' W. M. Havnes and J. W. Stewart. Rev. Sci. Instrum. 42,

1 142 ( 1971).

- J. W. Beams. Rev. Sci, Instrum, 40. 167 (l%9).

' R. M. McClintock and M, J. Hiza, Mod. Plast. 35, 172 (1958).

' The use of a trade name for clarity and completeness does not

signify an endorsement or recommendation by the National Bureau of Standards,

' J. B. Breazeale, Ph,D, thesis. University of Virginia (1955),

" H. S. Morton. Jr.. Ph.D. thesis. University of Virginia (1953).

J. P. Senter. Rev. Sci. Instrum, 40, 334 (1969),

" J, W, Beams. C, W, Hulburt. W, E, Lotz, Jr,, and R, M,

Montague, Jr., Rev, Sci. Instrum. 26, 1181 (1955).

" S, P, Almeida and T. H, Crouch, Rev. Sci, Instrum,

42, 1344 (1971).

"* M. G, Hodgins and J. W. Beams, Rev, Sci, Instrum.

42, 1455 (1971), " J, L. Hales. J. Phys. E 3, 855 (1970),

S. C, Greer, M, R, Moldover. and R, Hocken, Rev, Sci, Instrum. 45, 1462 (1974). " R, Prydz and R, D, Goodwin, J. Chem, Thermodyn, 4, 127

(1972), W. Wagner, Cryogenics 13, 470 (1973).

J. W. Beams and A. M, Clarke, Rev, Sci, Instrum, 33, 750 (1962), M, Menache and G. Girard, Metrologia 9, 62 (1973), " A, F, Clark, W, M. Haynes, V, A, Deason. and R, J, Trapani, Cryogenics 16, 267 (1976),

'" G. Simmons and H, Wang. Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook (MIT

Press, Cambridge. MA, 1971), p. 181.

'' R, D. McCarty, Natl, Bur, Stand, (U.S.) Intern. Rept. 74-357

(1974).

2" Y, C. Hou and J, J. Martin, AIChE J, 5, 125 (1959),

^' R, T. Jacobsen, Ph,D. thesis, Washington State University

(1972). " P. Brauns (private communication. 1973). L. A. Weber, J. Chem. Thermodyn, 2, 839 (1970).

J. B, Rodosevich and R, C, Miller. AlChE J, 19, 729(1973).

K. Goldman and N. G, Scrase. Physica 44, 555 (1969), M, J, Terry, J, T, Lynch, M, Bunclark, K. R. Mancell, and L, A, K, Staveley. J, Chem, Thermodyn. 1, 413 (1969). W. B, Streett and L. A, K, Staveley, Adv, Cryog, Eng. 13, 363(1968),

E. Mathias, H, K. Onnes, and C. A, Crommelin, Commun,

Leiden 145C, 19 (1914),

2" J, D, Olson, J, Chem, Phys. 63, 474 (1975). R, D. Goodwin, Natl, Bur, Stand, (U,S,) Tech, Note No,

653 (1974).

" J. Orrit and J. Olives, distributed at 4th International Conference on Liquefied Natural Gas, Algeria (1974),

'- C, R, McCIune, Cryogenics 16, 289 (1976), R. D, Goodwin and R, Prydz, J, Res. Natl, Bur, Std, (U.S.) 76A, 81 (1972),

" M. Y. Shana'a and F, B, Canfield. Trans. Faraday Soc. 64, 2281 (1968), A, J. Vennix, Ph,D, thesis. Rice University (1965). A. F. Grigor, Ph,D, thesis, Pennsylvania State University (1966).

'" A. J. Davenport. J, S. Rowlinson, and G, Saville. Trans. Faraday Soc. 62, 322 (1966),

J, Klosek and C, McKinley, Proce;edings of the First International Conference on LNG. Chicago ( 1968), Paper 22, •"J. E, Sinorand F. Kurata, J. Chem, Eng, Data II. I (1966). R. H, Jensen and F. Kurata. J. Petrol, Technol. 21, 68.^ (1969), " O, T. Bloomer and J. D, Parent, Chem. Eng, Progr. Symp,

Ser, 49, II (1952),

S, Fuks. J. C, Legros, and A, Bellemans. Physica 31, 606

(1965).

F. G. Keyes. R. S, Taylor, and L, B, Smith. J. Math. Phys.

1, 21 1 (1922). D, W, Moran, Ph.D. thesis. Imperial College, University of London (19.59). A, Van Itterbeek, O, Verbeke. and K. Staes, Physica 29, 742 (1963).

1250 Rev. Sci. Instrum., Vol. 47, No. 10, October 1976 Densimeter G-14

1250
Simplified magnetic suspension densimeter for absolute

density measurements*

W. M. Haynes

National Bureau of Standards, Institute for Basic Standards, Boulder, Colorado 80302

(Received 24 September 1976) A magnetic suspension densimeter, incorporating three support coils, has been reduced to a system using only one coil. This simplifies considerably the design of the apparatus and

the procedures involved in the measurements. This instrument can be used for absolute

density measurements; i.e., it does not have to be calibrated with reference fluids of known

density.

During the past two decades the magnetic suspension

densimeter'"" has evolved into a versatile research instrument that has been used routinely for liquid density measurements to a precision of ten parts per million. (Reference 14 presents a detailed review of the principles, applications, and development of the magnetic

densimeter.) In the original design (Fig. 1) of the instru- ment a piece of soft ferromagnetic material is suspended

in a fluid of unknown density by the magnetic force produced by a single solenoid. The magnetic force on

the buoy is given by the relation

F^ mag = M

Hz

(1)

where M is the magnetic moment of the buoy, H is the

axial magnetic field intensity of the air core solenoid,

and Z is the distance along the vertical. The density

(p) of the fluid is related to the current (I) in the support

coil by

p = A+ BP, (2) where A and B are constants to be determined by cali- bration of the instrument with reference fluids of known

density. The above relation is based on the assumption

that the magnetic moment of the buoy is linearly proportional to the magnetic field intensity.

It is not unusual for the magnetic susceptibility of the magnetically soft material of the buoy to vary slowly

with H. Thus a relatively large number of reference

fluids are required to calibrate a one-coil instrument to maintain a given precision over its entire operating

range. The precision is inversely proportional to the difference between the density of the fluid and the density of the buoy. To cover an extended density range

it is necessary to construct and calibrate buoys of dif- ferent densities. The calibration of the instrument must

be checked periodically to test the buoy material for

hysteresis.

These procedural tasks were reduced considerably

with the development of a three-coil support system^

(Fig. 2) which allows variations indHldZ while// is held

constant. The three-coil arrangement consists of a main

coil , which supplies the major part of the force necessary

to support the buoy, and a pair of gradient coils con- nected in such a way that at the buoy position their magnetic fields cancel and their magnetic field gradients add. The magnetic moment of the buoy is held constant;

it depends only on the stability of the constant current source that supplies the main coil current. In the first applications of the three-coil arrangement (with a magnetically soft buoy) the instrument still had to be cali- brated but now the density range for a given buoy was

increased significantly over that for a single-coil system.

Also the calibration was simplified since the density was

linearly proportional to the current in the gradient coils for a constant main coil current. The buoy may be

either magnetically soft or hard for the three-coil system.

Recently, in the adaptation of the magnetic suspension

densimeter for use at low temperatures,'' " the same

three-coil arrangement (Fig. 2) was employed to deter- mine the force on a magnetic material in a nonuniform

field; i.e., it was used to determine the variation of the magnetic susceptibility of the buoy material with H over

the range of magnetic fields needed for the density measurements. It was found that the magnetic

force on a barium ferrite buoy could be represented by

the expression

dH^ ^dHo

F' mag = M

dZ dZ

CI,, + Die, (3)

where the subscripts denote the main and gradient coils.

SUPPORT

COIL

[flMICROSCOPE"]j 4^

SENSOR

COILS

MAGNETIC

BUOY

CONTROL

CIRCUIT

Fig. 1. Schematic diagram ofa magnetic suspension densimeter with one support coil.

39 Rev. Sci. Instrum., Vol. 48, No. 1, January 1977 H- 1

39
This result demonstrated that, over the range of magnetic fields considered (0.006-0.016 T), there was no in- duced moment in the barium ferrite buoy (a magnetically

hard material with a permanent moment). Therefore, it was possible to determine fluid densities without the use

of calibration fluids. The instrument constants [C, D in Eq. (3)] could be determined from measurements of the gradient coil current as a function of the main coil current

while the buoy was supported at a fixed position at constant temperature in vacuum. The mass and volume of

the buoy must be determined from independent measurements. Now that it had been determined with the three-coil arrangement (Fig. 2) that the magnetic moment of the barium ferrite buoy was independent of the magnetic

field strength over the range of magnetic fields needed

for the desired density measurements, the instrument

could be simplified considerably by reducing to a onecoil system (Fig. 1). The magnetic force on the buoy de- pended only on the magnetic field gradient (dH/dZ) and

not on the magnetic field intensity {H). Thus the single

(main) coil was connected into the servosystem and the

gradient coils were eliminated.

It should be noted that a one-coil system can be used

for absolute density measurements as long as the varia- tion in the magnetic moment of the buoy with magnetic

field intensity is known. This information could be obtained by techniques other than that used in the present

work, e.g., a vibrating sample magnetometer. This is mentioned to emphasize that, with a knowledge of M(H)

of the magnetic buoy material, the initial apparatus

design could be simplified significantly with the use of only one coil. To carry out density measurements with the one-coil system with a barium ferrite buoy, first the current necessary to support the buoy in vacuum (Iv) at a given

position and temperature must be determined. Then the current necessary to support the buoy in a liquid (//) of unknown density at the same position and temperature is measured. The density of the fluid is related to

this current ratio by

(4)

where m and V are the mass and volume of the buoy.

It should be emphasized that no reference fluids are required for calibration of the one-coil system (or the

three-coil system) used in the present work. However,

the volume of the float may best be determined near room temperature using distilled water as a reference

fluid of known density and, in fact, this procedure was

used in the present work.'^ There are several obvious advantages of the onecoil system over one using three coils; most are in- volved with the experimental design and procedures.

With elimination of the two gradient coils and the alignment problems associated with them, the design and

construction of the apparatus are much simpler. The

constant current source is no longer needed. The

CONSTANT

CURRENT SOURCE

CONTROL

CIRCUIT

Fig. 2. Schematic diagram of a magnetic suspension densimeter with

three support coils.

vacuum points for a single-coil system require only a

single current measurement, while those for a three-coil system require a series of measurements of and /c while holding the buoy at a fixed position. Then the currents must be fitted by the method of least squares to Eq. (3) to obtain the instrument constants. Also the error analysis is less complicated with a one-coil system.

There is one inherent disadvantage in the method for obtaining absolute densities with either the one-coil or

three-coil systems where the magnetic force depends

only on dH/dZ. The change in dH/dZ with position is significantly larger than the change in the product of H and dH/dZ with position. Thus a very precise deter- mination ( 10"^ mm) of the separation distance of the main

coil and buoy was required in the present work and has been described in Ref. 17. Experimental densities have been determined for saturated liquid argon and methane at temperatures be- tween 100 and 120 K with both the three-coil and one-coil systems. The results agreed within the imprecision of

the measurements, which was approximately 0.015%

for methane and 0.005% for argon. Thus the simpler

one-coil system is now utilized for all density measure- ments with the present instrument.

The servosystem that is used with the single coil was

originally connected to the gradient coils in the threecoil system. No modifications to the servosystem as described in Ref. 17 were required for its use with the

single coil. The present series of density measurements in this laboratory with the magnetic suspension densimeter

represented a nontypical use of the instrument. In

the past the instrument has been used for highly precise

(usually less than 0.001%) measurements over a short density range at a single temperature. Here a relatively

modest precision (less than 0.02%) was the result of

40 Rev. Scl. Instrum., Vol. 48, No. 1, January 1977 Magnatic auapanalon donalmatar 40 H-2
measurements over large density (0.3-2.3 g/cm^) and

temperature (95-300 K) ranges with a single buoy.

The total uncertainty of the present measurements was

approximately 0.1%.

In order to obtain the highest precision and accuracy

with the present instrument it was necessary to perform vacuum measurements immediately before or after the

liquid measurements. The possible use of the instrument

without repeating the vacuum measurements for each

datum point has been investigated. In other words the precision and accuracy of the instrument has been

estimated, based on a single series of vacuum measure- ments as a function of temperature at the beginning

(and/or end) of a set of density measurements without

regard to the temperature and magnetic field cycling of

the buoy. The separation distance of the coil and the buoy must be maintained throughout the set of measurements.

In the present setup the position of the main coil was

fixed as described in Ref. 17. The position of the float was determined with a 125x microscope and the buoy

could be returned to a desired position either elec- tronically or mechanically. Over a period of several months during the course of density measurements at low temperatures on several different fluids, the sample

cell was cycled between approximately 100 to 130 K

and 3(X) K more than twenty times. The standard deviation of the vacuum measurements at low temperatures was of the order of 0.05% with no systematic trend observed. This was a measure of the thermal hysteresis of the magnetic moment of the barium ferrite buoy over

rather large temperature cycles. This result demonstrated that densities with a total uncertainty of approximately 0.2% could be expected without repeating

vacuum measurements for each datum point. Thus, for density data in which the highest precision and accuracy

are not required, the use of a one-coil system and a barium ferrite buoy would result in a relatively simple

and efficient measurement process that requires few vacuum measurements.

* This work was carried out at the National Bureau of Standards under the sponsorship of British Gas Corp., Chicago Bridge and

Iron Co., Columbia Gas Service Corp., Distrigas Corp., Easco Gas LNG, Inc., El Paso Natural Gas, Gaz de France. Marathon

Oil Co., Mobil R and D Corp., Natural Gas Pipeline Co., Phillips Petroleum Co., Shell International Gas, Ltd., Sonatrach, Southern

California Gas Co., Tennessee Gas Pipeline, Texas Eastern Transmission Co., Tokyo Gas Co., Ltd., and Transcontinental Gas Pipe Line Corp., through a grant administered by the American Gas Association, Inc.

' J. W. Beams, C. W. Hulburt, W. E. Lotz, Jr., and R. M. Montague,

Jr., Rev. Sci. Instrum. 26, 1181 (1955).

2 J. W. Beams and A. M. Clarke, Rev. Sci. Instrum. 33, 750 (1962).

^ A. M. Clarke, D. W. Kupke, and J. W. Beams, J. Phys. Chem. 67, 929 (1963).

* D. V. Ulrich, D. W. Kupke, and J. W. Beams, Proc. Nat. Acad.

Sci. U.S.A. 52, 349(1964).

" J. W. Beams, Rev. Sci. Instrum. 40, 167 (1%9).

« J. P. Senter, Rev. Sci. Instrum. 40, 334 (1%9).

' P. P. Fahey, D. W. Kupke, and J. W. Beams, Proc. Nat. Acad. Sci. U.S.A. 63, 548 (1969).

' A. M. Wims, D. Mclntyre, and F. Hynne, J. Chem. Phys. 50, 616 (1%9).

" R. Goodrich, D. F. Swinehart, M. J. Kelly, and F. J. Reithel, Anal. Biochem. 28, 25 (1%9).

'» J. L. Hales, J. Phys. E 3, 855 (1970). " W. M. Haynes and J. W. Stewart, Rev. Sci. Instrum. 42, 1 142 ( 1971). " S. P. Almeida and T. H. Crouch, Rev. Sci. Instrum. 42, 1344 ( 1971). " M.G. HodginsandJ. W. Beams, Rev. Sci. Instrum. 42, 1455(1971). D. W. Kupke and J. W. Beams, Methods Enzymol. 26, 74 (1973). " S. C. Greer. M. R. Moldover, and R. Hocken, Rev. Sci. Instrum.

45, 1462 (1974). " S. C. Greer, T. E. Block, and C. M. Knobler, Phys. Rev. Lett. 34, 250 (1975). " W. M. Haynes, M. J. Hiza, and N. V. Frederick, Rev. Sci. Instrum.

47, 1237 (1976).

41 Rev. Sci. Inatrum., Vol. 48, No. 1, January 1977 Magnetic auapenalon denalmetar H-3

41

MEASUREMENTS OF THE ORTHOBARIC LIQUID DENSITIES

OF METHANE, ETHANE, PROPANE, ISOBUTANE, AND

NORMAL BUTANE^

by

W. M. Haynes and M. J, Hiza

Cryogenics Division

National Bureau of Standards

Institute for Basic Standards

Boulder, Colorado 80302

Send proofs to: W. M. Haynes

Cryogenics Division, 275.02

National Bureau of Standards

Boulder, Colorado 80302

Short Title: Liquid Densities of CH, , C„H,, C^H^,

iC^H^Q, and nC^H^Q

This work was carried out at the Nataonal Bureau of Standards under

the sponsorhip of British Gas Corp., Chicago Bridge and Iron Co.,

Columbia Gas Service Corp., Distrigas Corp., Easco Gas LNG, Inc.,

El Paso Natural Gas., Gaz de France, Marathon Oil Co., Mobil R6<D Corp.,

Natural Gas Pipeline Co., Phillips Petroleum Co., Shell International

Gas, Ltd., Sonatrach, Southern California Gas Co., Tennessee Gas

Pipeline, Texas Eastern Transmission Co., Tokyo Gas Co., Ltd., and

Transcont in^uital Gas Pipe Line Corp., through a grant administered by

the American Gas Association, Inc.

I-l
ABSTRACT

The orthobaric liquid densities of the major components of natural

gas have been determined with a magnetic suspension densimeter.

This paper reports results for methane (105 to 160 K) , ethane

(100 to 270 K) , propane (100 to 288 K) , isobutane (115 to 300 K)

,

and normal butane (135 to 300 K) , The imprecision of the measured

densities is approximately 0.015 percent; the estimated overall

uncertainty is 0.1 percent at low temperatures and decreases to

0.06 percent at 300 K. A simple expression has been used to

represent the densities as a function of temperature. Comprehensive

comparisons with the experimental results of other investigators

are presented.

1-2
1. Introduction

Liquefied natural gas (LNG) is expected to become an increasingly

important commodity on the world energy market. The basis for

sale of LNG is its total heating value, which requires a knowledge

of both density and composition. A project was initiated at this

laboratory to provide orthobaric (saturated) liquid densities for

the major components of LNG, and for mixtures of these components.

The density data will be used to develop a mathematical model or

correlation that predicts the density of LNG type mixtures with an

inaccuracy of 0.1 percent, given a knowledge of the composition

and temperature of the liquid. In the development of an accurate

mather^atical model (correlation) , it is important to have both an

accurate and an internally consistent set of density data.

Before this project was started there were significant temperature ranges for which saturated (orthobaric) liquid density

data did not exist for some of the major components of LNG. For

nitrogen and methane there were discrepancies as large as 0.5 per

cent between different sets of data. Not only was it important to

fill in gaps, but also to provide new independent measurements of

sufficient accuracy to help resolve inconsistencies.

In this paper orthobaric liquid densities for methane, ethane,

propane, isobutane, and normal butane are reported. Data for

nitrogen were presented in an earlier paper^"^\ Major emphasis has

been placed on the low temperature region of ].05 to 140 K; however,

measurements have been carried out to 160 K for methane, to 270 K

1-3
for ethane, to 288.7 K for propane, and to 300 K for isobutane

and normal butane. The densities have been represented as a

function of temperature with an expression that is used to facilitate comparisons with other measurements.

The present measurements were carried out with a magnetic

(1)

suspension densimeter. In this method a magnetic buoy is freelysuspended in the liquid of interest by the force generated from

the axial magnetic fields of air-core solenoids. The motion of

the buoy is controlled by the automatic regulation of a servocircuit. The magnetic force necessary to maintain the buoy at a

given position is inversely proportional to the buoyant force on

the buoy. Thus, using Archemedes ' principle, along with measurements

of the mass and volume of the buoy, the density of the liquid is

obtained.

2, Experimental

The experimental apparatus and its operation have been described

in detail elsewhere^"'' . At low temperatures the experimental

procedures for the measurements on the hydrocarbons other than

methane differed significantly from those for nitrogen and methane.

The density of a given fluid is determined from measurements of

the magnetic force necessary to support a barium ferrLte buoy in

a vacuum and in the fluid at the same position and temperature.

For nitrogen and methane the vacuum measurements were performed

immediately before or after the liquid measureinents . At low

temperatures it has been found impossible to evacuate tlie sample

cell within a reasonable length of time after it has been filled

with one of the heavier hydrocarbons. Most of the liquid can be

1-4
removed by pressurizing with helium gas; however, a liquid film

is left on the surfaces, including those of the buoy, inside the

cell. The buoy cannot be brought into suport until the film is

removed. Thus, for the heavy hydrocarbons at low temperatures,

the vacuum points must be obtained before the liquid measurements.

So that more than one data point could be obtained in a given

day for a heavy hydrocarbon at low temperatures, vacuum points were

obtainr.-J at two temperatures separated by 5 K before liquid was

condensed into the cell. Then the liquid measurements were performed

at each of these temperatures. Performance tests had demonstrated

that the barium ferrite buoy does not exhibit any detectable

hysteresis at low temperatures within the precision of the current

measurem.ents for a temperature range of, at least, 20 K. After

the vacuum and liquid measurements were performed for one of the

heavy hydrocarbons at low temperatures the cell was warmed to a

temperature above the normal boiling point of the test fluid for

evacuation.

Methane was used as a control fluid during the heavy hydrocarbon measurements at low temperatures. Each day a new methane

data point was taken to insure that the warm-up and cool-down of

the apparatus did not affect the apparent position of the buoy

from liquid-to-vacuum measurements. The position of the buoy was

determined with a high-powered microscope that had been adjusted

initially so that the apparent position of the buoy did not depend

on the index of refraction of the fluid inside the cell. It was

found that the temperature cycling of the cell had no detectable

effect on the apparent buoy position.

1-5
Some of the data presented in this paper were taken with a

one-coil system instead of the three-coil arrangement described

in the apparatus paper^'^\ The evolution to the use of only one

coil is discussed in reference 2.

All of the gases were of research grade quality. The minimum

purities as specified by the suppliers were 99.9 mol percent for

isobutane and normal butane and 99.99 mol percent for methane, ethane,

and propane. The gases were analyzed chromatographically with a

thermal conductivity detector and found to be within the specified

purities except for isobutane. It was found that the isobutane

contained approximately 0.15 percent normal butane. This relatively

large amount of normal butane impurity has a negligible effect

(< 0.01 percent) on the density results.

The methane gas was passed through a room temperature molecular

sieve trap to remove moisture and any heavy contaminants not

detected by analysis. The other hydrocarbon gases were normally not

passed through a molecular sieve trap.

3. Results

The experimental orthobaric liquid densities of methane, ethane,

propane, isobutane, and normal butane are presented as a function

of temperature (International Practical Temperature Scale-1968) in

tables 1-5. The relatively large number of data points for methane

at any given temperature resulted from the use of methane as a

control fluid throughout the entirety of this project. Although the

mean experimental densities of methane have been given in an earlier

paper

^'^^ they are presented again here, along with other information

1-6
(calculated densities, etc.)j so that the orthobarlc liquid densities

of all the low molecular weight alkanes investigated in the present

work are included in a single paper. All of the experimental points

(3) for methane will be presented in a future report . Each methane

point was taken from a new filling of the cell. For the other

hydrocarbons no more than two data points were taken from a single

filling.

The experimental densities (p) have been fitted as a function

of temperature (T) to the following expression,

P-P, - a(l-f)«-35^ I K a-f)'l^¥> (1)

c i=l c

(A) which incorporates a scaling law modification to a generalized

Guggenheim equation^"^\ The coefficients (a, b^) , determined by

least squares, and selected values of the critical temperature (T^)

and density (p ) for each fluid are given in table 6^^ Only

three coefficients were needed to fit the methane data, which covered

a relatively small temperature range compared to that for the other

fluids

.

The residual standard deviations of the fit to equation (1) for

each fluid are given in table 6. These values substantiate the

estimate of the imprecision of the density measurements, which is

approximately 0.015 percent. The estimated inaccuracy in the

densities is 0.1 percent at low temperatures and decreases to

0.06 percent at 300 K. The total uncertainty in the reported

1-7
temperatures is estimated to be less than 30 mK at 100 K and less

than 40 inK at 300 K. These uncertainty limits in the temperature

correspond to a maximum uncertainty of 0.02% in the density for the

data reported in this paper. A detailed error analysis of the

magnetic suspension densimeter used in the present work has been

given elsewhere ^^^

Equation (1), along with the parameters given in table 6, has

been used for comparisons of the present results with independent

, ^ (8, 12-25) ^ . . experxmental data . Deviation plots for ethane, propane,

isobutane, and normal butane are presented in figures 1 through 4.

The deviation plot for methane was presented in an earlier paper^"''^;

thus, it is not included here.

In comparing the results of other investigators with equation (1)

some general trends are observed. Below 140 K the densities of

Shana'a and Canf ield Chui and Canf ield ^"^"^"^

, Orrit and Olives^"'"^^

Rodosevich and Miller^"^^\ McClune and Klosek and McKinley ^''"^^

are generally lower than the present results by 0.05 to 0.1 percent.

Exceptions to this trend are as follows: for isobutane the densities

of Rodosevich and Miller ''"'"^^ between 114 and 120 K are larger (maximum

of 0.1 percent) than the present results and exhibit a significantly

different temperature dependence; and for ethane the change in density

with temperature reported by Klosek and McKinley ^"'"^^ is appreciably

larger than that observed in the present work.

(13) Above 140 K the data of Chui and Canfield^ , Orrit and

Olives ^ '"'^^ and McClune^^^"^ differ from the present results by less

than 0.05 percent. At higher temperatures (above 280 K) the data of

1-8
Sliwinski for propane, Isobutane, and normal butane generally

differ from the present results by less than 0.05 percent. The

/ 1 Q \ orthobaric liquid densities reported by Douslin and Harrison

for ethane at temperatures between 248 and 263 K were systematically

larger than the present results by 0,3 to 0.35 percent. Some of the

older, less precise (but frequently used) data have been Included

on the deviation plots for the sake of completeness.

(17) Although Klosek and McKinley give densities for isobutane

and normal butane at temperatures between 105 and 133 K, these

densities are not experimental, and therefore, are not plotted on

figures 3 and 4. A few comments on the reliability of the omitted

values are appropriate. Their densities were obtained from the

Francis equation . For normal butane at temperatures below its

triple point temperature, the Lr results were systematically higher

by less than 0.2 percent than the densities obtained through extra-

(27) polation of the present data . However, their isobutane densities

at temperatures between 116 and 133 K were 1.5 percent higher than

those of the present work.

4. Summary

This research has provided accurate and self-consistent measurements

of the orthobaric liquid densities of methane, ethane, propane,

isobutane, and normal butane at temperatures down to 100 K. Most of

the measurements recently reported by other workers differ from the

present data by less than 0.1 percent. In subsequent papers, density

measurements on liquefied mixtures of the major components of

liquefied natural gas will be reported.

1-9
Acknowledgment

The authors would like to acknowledge R. D. McCarty and M. J. Brown

for assistance with the correlation and reduction of the data.

I-IO
References

1. Haynes, W. M. ; Hiza, M. J.; Frederick, N. V. Rev. Sci.

Instrum. (to be published)

.

2. Haynes, W. M. Rev. Sci. Instrum. (submitted for publication),

3. Methane data are available from authors upon request and

will be published in a Nat. Bur. Stand. (U.S.) report.

4. McCarty, R. D. Nat. Bur. Stand. (U.S.), Internal Rept.

74-357, 1974 .

5. Hou, Y.C.; Martin, J. J. A.I.Ch.E. J. 1959 , 5, 125.

6. Goodwin, R. D. Nat. Bur. Stand. (U.S.), Tech. Note 653,

1974 .

7. Olson, J. D. J. Chem. Phys. 1975 , 63, 474.

8. Sliwinski, P. Z. Phys. Chem. (Frankfurt) 1969, 63, 263.

9. Das, T. R. ; Eubank, P. T. Advances in Cryogenic Engineering

1973 , 1, 208.

10. Das, T. R.; Reed, Jr., C. 0.; Eubank, P. T. J. Chem. Eng.

Data 1973, 18, 253.

11. Das, T. R.; Reed, Jr., C. 0.; Eubank, P. T. J. Chem. Eng.

Data 1973, 18, 244.

12. Shana'a, M. Y.; Canfield, F. B. Trans. Faraday Soc. 1968 ,

64, 2281.

13. Chui, C. H.; Canfield, F. B. Trans. Faraday Soc. 1971 , 67,

2933.

14. Orrit, J.; Olives, J. distributed at 4th International

Conference on Liquefied Natural Gas, Algeria, 1974 .

I-ll
15. Rodosevich, J. B.; Miller, R. C. A.I.Ch.E. J. 1973 , 19, 729.

16. McClune, C. R. Cryogenics 1976 , 16, 289.

17. Klosek, J.; McKinley, C. Proc. First International Conference

on LNG, Paper 22, Chicago, 1968 .

18. Douslin, D. R. ; Harrison, R. H. J. Chem. Thermodynamics

1973 , 5, 491.

19. Maass, 0.; Wright, C. H. J. Am. Chem. Soc. 1921 , 43, 1098.

20. Jensen, R. H. ; Kurata, F. J. Petrol. Technol. 1969 , 21, 683.

21. Kahre, L. C. J. Chem. Eng. Data 1973 , 18, 267.

22. Tomlinson, J. R. Natural Gas Processors Assoc. Tech, Publ.

TP-1, Tulsa, Oklahoma, 1971.

23. Seeman, F.-W.; Urban, M. Erdol und Kohle Erdgas Petrochemie

1963 , 16, 117.

24. Tech. Comm., Natl. Gas. Assoc. Am. Ind. Eng. Chem. 1942,

34, 1240.

25. Van der Vet, A. P. Congress Modial du Petrol., Paris, Vol. II,

p. 515, 1937 .

26. Francis, A. W. Ind. Eng. Chem. 1957 , 49, 1779.

27. Haynes, W. M. ; Hiza, M. J. Advances in Cryogenic Engineering,

Vol. 21. Timmerhaus, K, D. and Weitzel, D. H. , editors.

Plenum Press, New York, 1976 , p. 516.

1-12
Table 1. Orthobaric liquid densities of methane, where T is the

temperature (IPTS-1968) , ^ is the mean experimental density

for n density calculated from equation (1)

.

observations at a given temperature, and P^^-j^^ is the

T/K

105.000

110.000

115.000

120.000

125.000

130.000

135.000

140.000

145.000

150.000

160.000

) /mol I exp

26.9458

26.4985

26.0443

25.5721

25.0845

24.5775

24.0540

23.5067

22.9312

22.3218

20.9876

-1

12

11

12

17

18

16

23

5

5

2

2

p^^^^/mol I

26.9456

26.5005

26.0429

25.5712

25.0839

24.5790

24.0540

23.5060

22.9311

22.3243

20.9857

Maximum

value of

"*"*^^^^exp '^calc'^

'^calc

0.030

0.035

0.028

0.036

0.037

0.036

0.031

0.024

0.024

0.014

0.037

1-13
Table 2. Orthobaric liquid densities of ethane, where T is the temperature

(IPTS-1968) , p is the experimental density, and p ^ is the

exp calc

density calculated from equation (1).

100(p -p ^ ) exp cal c_

T/K

p /mol I

^ exp

0-1

p /mol ^ calc

^calc

100.000 21.3408 21 . 3388 0.009

105.000 21.1585 21.1568 0.008

110.000 20.9746 20.9742 0.002

115.000 20.7927 20.7907 0.010

120.000 20.6022 20.6063 -0.020

125.000 20.4186 20.4208 -0.011

130. 000 20.2317 20.2343 -0.013

135. 000 20.0461 20.0466 -0.002

140.000 19 .8566 19.8575 -0.005

150.000 19.4751 19.4748 0.002

160.000 19 .0857 19.0850 0.004

170.000 18.6867 18.6869 -0.001

180.000 18.2793 18.2787 0.003

190.000 17.8612 17.8586 0.015

200.000 17.4289

' 17.4240 0.028

210. 000 16 .9713 16.9720 -0.004

220.000 16.4988 16.4989 -0.001

230.000 15.9973 15.9994 -0.013

240.000 15.4642 15.4670 -0.018

250.000 14.8899 14.8919 -0.013

260.000 14.2610 14.2598 0.008

270.000 13.5493 13.5477 0.012

T-] 4
Table 3. Orthobaric liquid densities of propane, v^/here T is the temperature

(IPTS-1968) , p is the experimental density, and p , is the

exp ^calc

T/K

density calculated from

p /mol l

exp

equcition (1) •

p ^ /mol £ calc

100(p -p

exp 1

'^calc

100.075 16.3065 16.3048 0.011

105.075 16.1872 16.1885 -0.008

110.075 16.0718 16.0723 -0.003

115.075 ' 15.9557 15.9562 -0.003

120.075 15.8411 15.8401 0.006

125.075 15.7250 15.7241 0.006

130.075 15.6085 15.6080 0.003

135.075 15.4910 15.4918 -0.005

140.075 15.3751 15.3755 -0.002

145.075 15.2588 15.2590 -0.002

150.075 15.1400 15.1424 -0.016

200.000 13.9560 13.9524 0.026

240.000 12.9271 12.9285 -0.010

270.000 12.0733 12,0742 -0.008

280.000 11.7622 11.7631 -0.008

288.706 11.4790 11.4775 0.013

1-15
Table 4. Orthobaric liquid densities of isobutane, where T is the temperature

(IPTS-1968) , p is the experimental density, and p ^ is the

exp calc

density calculated from equation (1)

100(p -p . ) e xp calc

-1 -1 Pi

T/K p /mol Z _ p ^ /mol i ^^^^

exp calc

115.075 12.7305 12.7313 -0.006

120.075 12.6489 12.6491 -0.001

125.075 12.5687 12.5669 0.015

130.075 12.4850 12.4846 0.003

135.075 12.4015 12.4022 -0.005

140.075 12.3215 12.3197 0.014

145.075 12.2353 12.2372 -0.015

150.075 12.1534 12.1544 -0.008

228.000 10.8273 10.8263 0.009

288.706 9.6676 9.6687 -0.012

290.000 9.6411 9.6417 -0.007

300.000 9.4300 9.4287 0.014

1-16
Table 5. Orthobaric liquid densities of normal butane, where T is the

T/K

temperature (IPTS-1968) , p is the experimental density, and

exp

p ^ is the density calculated from equation (1)

calc

p /mol Z exp

-1

p -, /mol I calc

100(p -p . ) exp calc

'^calc

135.075

140.075

145.075

150.075

155.075

160.075

165.075

170.075

230.000

288.706

290.000

300.000

12.6517

12.5706

12.4920

12.4089

12.3299

12.2484

12.1634

12.0839

11.0911

10.0325

10.0067

9 . 8103

12.6524

12.5714

12.4904

12 .4093

12 .3283

12.2471

12 .1659

12.0846

11.0905

10.0324

10.0073

9.8099

-0.005

-0.006

0.013

-0.003

0.014

0.010

-0.020

-0.005

0.005

0.001

-0.007

0.004

1-17
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1-18
List of Figure Legends

Deviation plot of experimental orthobaric liquid densities of

ethane compared with values calculated from equation (1) using

parameters from table. 6; O present data, # Shana'a and

Canf ield^"'"^'' , O Chui and Canf ield , ® Orrit and Olives^"'"^^

A Rodosevich and Miller^''"^\ McClune^"^^\ Klosek

and McKinley A Douslin and Harrison © Maass and

. ^ (19) „ , , (20) _ ^ (21) Wright , V Jensen and Kurata , ^ Kahre

Deviation plot of experimental orthobaric liquid densities of

propane compared with values calculated from equation (1) using

(8) parameters from table 6; O present data, ^ Sliwinski , • Shana'a and Canf ield ^"""^^ 0 Orrit and 01ives^'^^\ A

Rodosevi ch and Miller ^'^^'^

, McClune^"''^\ CI Klosek and

McKinley © Maass and Wright ^'^^'^

, V Jensen and Kurata^^^\

Kahre^^"""-* , © Tomlinson Seeman and Urban^^~^\ <8l mkA^~^\ © Van der Vet^^"^-^.

Deviation plot of experimental orthobaric liquid densities of

isobutane compared with values calculated from equation (1) using

(8) parameters from table 6; O present data, ^ Sliwinski ,

CD Orrit and 01ives^'''^\ A Rodosevich and Miller^"^^\

McClune^-^^\ Kahre^^^\ ® NGAA^^^-^ , © Van der Vet*^^^^

Deviation plot of experimental orthobaric liquid densities of

normal butane compared with values calculated from equation (1)

(8) using parameters from table 6; O present data, Sliwinski , 0 Orrit and Olives^''"^^ McClune , Kahre , ®

NGAA (24)

, © Van der Vet^^^-*

1-19
1-20
001 X

3\B3 (1X3

1-21
1-22
1-23

THE VISCOSITY AiND THER>IAL CONDUCTIVITY COErFICIENTS FOR

DENSE GASEOUS iVN'D LIQUID METHANe"

H. J. M. Hartley, W. M. Haynos and R. D. McCarty

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

AfiSTPvACT

Data for the viscosity and thermal conductivity coefficients of

dense gaseous and liquid methane have been evaluated. Selected data

were fitted to a function derived in our previous work and tables of

values were generated for temperatures from 95 to 500 K and for

pressures up to 50 MPa 500 atm) . The uncertainties of the tabular

values are estimated to be approximately 3% and 5% for the viscosity

and thermal conductivity coefficients, respectively. The contribution

for the thermal conductivity enhancement in the critical region is

included in the tables. Care has been taken to ensure that the

calculated values are consistent with reliable equation-of-state data

and also with dilute gas transport coefficients determined previously.

Key words: Correlation; critical point anomaly; methane; tabJ.es; thermal

conductivity coefficient; viscosity coefficient.

Publication of the National Bureau of Standards, not subject to copyright.

J-1
.1 . INTROiJUCTTOM

Th^ vLycosity coefficient (ri) aad the thermal coriduc tivit>- coef f icir^a t

(' ) of several fluids — argon, krypton, xenon, oxygen and nitrogen — have been

correlated over a wide range of experimental conditions [1] . The correl^ition

was recently extended to methane [2]. The object of this paper is to expand

on reference [2] by presenting tables and to give some further details of the

correlation. We will follow closely the outline of reference [11 in which

criteria for evaluating systematically literature data were discussed and in

which an equation for the viscosity and thermal conductivity coefficients was

proposed. The criteria and equations will be used here with only minimal

comments. '

2. CORRELATING EQUATIONS

The correlations are based cm the behavior of the transport coefficients

with respect to temperature (T) and density (p) according to the equations

n(p,T) = n (T) + n. (T)p + An' (p,T) '

' (D

o 1

>(o,T) - A^(T) + A^(T)o + AX'(p,T) + AA^(p,T) (2)

for the viscosity and thermal conductivity coefficients, respectively. In these

eqviations, ri (T) and A (T) are the dilute gas values, (T) and A (T) represent

Numbers in brackets refer to references.

.1-2
- densicy corrections for the. modertitely dense gas, i^/hile /ri'(p,T) and

T) are reaialnders. The term ri^(T) is given by the empirical expression

(T) = A + B [C - £n (T/F)]" (3)

and similarly for A^(T). The coefficients A, B, C and F can be found from

a fit of data but we set F = e/k where e is the energy parameter of the methane

pair potential function and k is Boltzmann's constant. See section 3.

The terms Ar|'(p,T) and AX'(p,T) are expressed empirically by the relations

Ari'(p,T) = Ejexp [j^ + j^/T] exp

+ 6P°-' (13 + j,/T + j/T^)]

(4)

- 1.0

and

A/'(p,T) = Djexp [k^ + k^/T] exp

+ 9p°-^ ^k^ + k^/T + k^/T^)

(5)

1.0

Tlie parameter 0 is included to account specifically for the high density behavior

of the transport coefficients and is a function of the density with respect to

the critical density, p :

<~ = (0-0 )/p (6)

c c

J3
ihe CO - f L icients , E, D, j ^

. . . j , kj^...k-^, are all to be detorrainad from

cxpe r inien tial data.

One sees that equation (!) and (?.) are of the same structure except that

equation (2) includes the term AX (g,T) . This is included to take into account

c the known enhancement of the thermal conductivity coefficient in the neighborhood

of the critical point [3]. [The viscosity coefficient also shows anomalous

behavior close td the critical point [4]. The anomaly is small, however, and is

not included in the calculated values.]

We have remarked in reference [1] that the form of equations (4) and (5) was

independent of the nature of the fluids considered. The behavior of methane [2]

is consistent with this characteristic. This apparent generality is a useful

feature of the equations but, since they are empirical, each fluid should be

treated on its merits without prior prejudice.

Equation of State . The majority of transport coefficient data in the literature

is repotted in temperature-pressure coordinates but we emphasized [1] that a

correlation of the coefficients should be preferably in terms of density rather

than pressure. An accurate equation of state is, therefore, essential to our

procedure. The equation of state used here for methane is a modified BenedictV.'ebb-Rubin (BWR), which was introduced and discussed in reference [5]. The equation

is, in turn, based on the m.ethane correlation of Goodwin [6]. The form of the

BivR and values for its parameters are given in the Appendix of the present paper.

4; Equation (5) here includes a contribution proportional to 9, unlike the corresponding equation [equation (9) J in reference [1]. In our earlier work with

oxygen, nitrogen, and the rare gases, however, the data were either not

:-:uf f iciently precise, or extensive to justify seven k coefficients.

J-4
3. THE DILUTE GAS :

The dilute gas coefficients appear separately in equations (1) and (2) . .

rt'e have discussed the calculation of these quantities from statistical mechanics

[7,8,9] and have sho\m, in particular, that statistical mechanics can give a con- !

sistent representation of the transport properties and the thermodynamic properties

for a given simple gas.

Dilute gas transport coefficient data for methane have been listed and

evaluated in reference [10]. Calculated values were obtained via the standard

kinetic theory equations [9] using the m-6-8 pair potential function of Klein and

Hanley [10]. This potential has the form ;

«r) - ^

[6.2,.] (>) [_,.(.-8)l (^) (7)

where r is the intermolecular separation, e the maximum well-depth of the

potential, and r is defined according to the relation 4)(r ) = -£ . Repulsive

m m

forces between molecules are represented by a 1/r^ contribution, while attractive

6 8 forces are represented by -1/r and -1/r contributions; y' depicts the strength

of the latter. Since we have discussed the application of kinetic theory to

methane in reference [10], details of the calculation procedure are omitted here.

m-6-8 methane parameters are given in table 1. The dilute gas data were fitted

to within their estimated accuracy (approximately + 2% for the viscosity coefficient and approximately + 5% for the thermal conductivity coefficient) . Recent

work [53] has suggested, however, that the m-6-8 potential can lead to small systematic

differences between theory and experiment at very lov/ temperatures [T/ (c/k) < 0.8]

and at very high temperatures [T/(e/k) > 20]. Accordingly we revise our estimate

of accuracy for the dilute gas transport coefficients of methane for temperatures

J-5
- -"ss than 150 K to 3% and 6% for the viscosity and thermal conductivity

coeff icient , respectively. Ely and Hanley have further discussed [9 J the

approximations introduced when a nonspherical molecule, such as methane, is

regarded as spherical from the viewpoint of the pair potential. For methane, w

have verified that this assumption does not effect the correlation of a single

property (e.g., the viscosity) but effects slightly the consistency between

calculated values of different properties.

For computational convenience we fitted the calculated n and A to a

o o polynomial in temperature

-1 -2/3 -1/3 1/3

= GV(1)T + GV(2)T ' + GV(3)T ' + GV(4) + GV(5)T^

+ GV(6)T^^"^ + GV(7)T + GV(8)T^^~^ + GV(9)T^''^

(8)

and similarly for A^, but with coefficients GT(i)(i = 1,..9) replacing GV(i) in

equation (8). Values of the coefficients are listed in table 2.

4. CALCULATION OF THE THERi>lAL CONDUCTIVITY COEFFICIENT IN THE

CRITICAL REGION

The quantity AA^ appears as a separate term in equation (2) and represents

the anomalous behavior of the thermal conductivity coefficient in the neighborhood

of the critical point [3]. There is no doubt that AA^ can contribute significantly

to the value of the thermal conductivity coefficient and has to be included in a

correlation [1]. Conductivity data, however, in the critical region for methane

arc scarce and we prefer to obtain A^^ by calculation.

The calculation follows a procedure suggested by Sengers [3] and expanded

hy Hanley, Sengers and McCarty [11]. Details are given in reference [11], in

J-6
:;--'Ction 3.2 of reference [1], and in reference [2], Our application to methane

^ivea in appendix C of reference [2].

5. DATA SELECTION AND CORRELATION

Since the dilute gas coefficients, and , have been calculated previously

[10] , we considered here data for the dense gas and liquid regions only . A

comprehensive search of the world's literature through 1975 turned up references

[12] - [37] for the viscosity coefficient and references [38] - [49] for the

thermal conductivity. Much of the data prior to 1970 are summarized in

references [50] - [52]. The data reported in these papers were examined according

to the criteria set out in section 2 of reference [1]. The data used for

correlation purposes were chosen on the basis of the procedure described in

section 2.3 of reference [1] and table 3 gives the final choices with our accuracy

assessments

We have shown that it is essential to have reliable data close to the

saturated liquid boundary and for at least one high temperature (about 2 T^)

isotherm if equations (1) to (5) are to give a reliable correlation. Such data

are available for methane. [Conversely, if data are available for the saturated

liquid boundary and for one high temperature isotherm only , equations (1) to (5)

are excellent interpolation functions.]

The experimental coverage for the thermal conductivity coefficient of

methane is perhaps the most extensive of any fluid due to the measurements of

Mani [39], using a transient hot wire technique, and to those of Le Neindre [38],

using a concentric cylinder apparatus. In the region of overlap, data from these

two authors differ systematically by about two percent, which is within their

estimated uncertainties.

J-7
5.1 Parameters for Equa t ions (3)-(5)

The parameters for equations (3)-(5) were estimated by the least squares

procedure outlined in section 3.1 of reference [1], using the selected data from

table 3, and are given in table 4. As remarked, however, thermal conductivity

data close to the critical point (from references [39] and [40]) were excluded

from the fit; rather AA^ was obtained by calculation [2].

5.2 Deviation Curves

Representative deviation curves are shown as figures 1-4. In every example

the percent deviation has been defined as

"

percent deviation = (expt

.

—^^1*^ • ) ^ -^qq /g\

expt.

The figures are self-explanatory and show that we have been able to fit the data

to within the estimated experimental uncertainties with one possible exception:

namely, the calculated viscosity coefficient appears too low close to the critical

point, see figure 1. Although it is possible that experimental error and/or

incorrect density values contribute to the deviation, it is more likely that the

deviation is the result of a small enhancement in the viscosity close to the

critical point [4], which is excluded in the correlating equation. This feature

was also observed in our previous work [1]

.

6. CONSTRUCTION OF TABLES

Wo constructed tables of values for the viscosity coefficient (table 5) and

Che thermal conductivity coefficient (table 6) from equations (l)-(5) with the

parameters of table 4 using the equation of state in the appendix. The temperature

range Is 95 to 500 K. The pressures extend to 50 ^tPa for temperatures less than

J-8
i:".: K, and to 75 MPa for temperatures between 205 and 500 K. These ranges so:netiuies correspond to a slight extrapolat xon of the data. The correlations, howo.ver,

are based on the temperature-density behavior of the transport coefficients.

Density is the limiting variable. We therefore assured that a P-T entry in the

3 table did not correspond to a density exceeding 0.4A5 g/cm [27.8 mole/l], which

was the upper experimental limit.

For convenience we constructed table 7 which presents values for the

saturated liquid.

6.1 Uncertainty of the Tables and Extrapolation

Our assessment of the correlating procedure of reference [1] led to the

conclusion that the correlation does not give rise to significant systematic

deviations between calculated and experimental values of the transport coefficients. This conclusion is reinforced from this work with methane. Hence, an

estimate of the uncertainty of the tabulated values is essentially the estimate

of the uncertainty of the input data. [We note that the percentage of uncertainty

given in table 3 and meiitioned here is an assessment of inaccuracy.] For

temperatures below 200 K, we assign an uncertainty of + 3% to the tabulated viscosity

values, + 5% to the tabulated thermal conductivity values. For temperatures above

200 K, the uncertainties are felt to be slightly less: + 2% and + 4%,

respectively. Close to the critical point, our viscosity values are probably too

low by about 5% and our values for the thermal conductivity have an uncertainty

of 15%. Extrapolation of the tables is not recommended.

7. CONCLUSION

A general equation, identical in form for both transport coefficients

(excluding the critical point enhancement for the thermal conductivity coefficient)

has been used to represent selected viscosity and thermal conductivity data of

J-9
methane from the dilute gas to the dense liquid. Parameters tor the equation

Wire determined by fitting experimental data. Comprehensive tables of the

transport coefficients are presented.

8. ACKNOWLEDGEMENTS

We are most grateful for the information given us by many of the authors of

« the experimental papers. We are also grateful to D. E. Diller, H. M. Roder and

J. V. Sengers for comments on the data in the literature. The work was supported

in part by the Office of Standard Reference Data.

J-10
REFERENCES

Hanley, H. J. M. , McCarty, R. D., and Haynes , W. M, , J. Phys. Chen, Ref.

Data 2. 979 (1974) .

2. Hanley, H. J. M. , McCarty, R. D. , and Haynes, W. M. , Cryogenics 1_5, 413

(1975).

3. Sengers, J. V., in Transport Phenomena - 1973 (AIP, New York) Kestin, J., Ed.

(1973) p. 229.

4. Strumpf, H. J., Collings, A. F. , and Pings, C. J., J. Chem. Phys. 60^, 3109

(1974) .

5. McCarty, R. D. , Cryogenics 14, 276 (1974).

6. Goodwin, R. D. , Nat. Bur. Stand. (U.S.), Tech. Note 653 (1974).

7. Hanley, H. J. M. , J. Phys. Chem. Ref. Data 2, 619 (1973).

8. Hanley, H. J. M. , and Ely, J. F., J. Phys. Chem. Ref. Data 2. 735 (1973).

9. Ely, J. F., and Hanley, H. J. M. , Mol. Phys. 30, 565 (1975).

10. Hanley, H. J. M. , and Klein, Max, J. Phys. Chem. 7^, 1743 (1972).

11. Hanley, H. J. M. , Sengers, J. V., and Ely, J. F. , Proc. 14th Int. Conference

Therm. Cond. (Pergammon Press, 1976).

12. Haynes, W. M. , Physica 70, 410 (1973).

13. Giddings, J. G. , Kao, J. T. F., and Kobayashi, R. , J. Chem. Phys. 45_, 578

(1966)

14. Barua, A. K. , Afzal, M. , Flynn, G. , and Ross, J., J. Chem. Phys. 41, 374

(1964).
.15. Kestin, J., and Leidenfrost, W. , Thermodynamics and Transport Properties

of Gases, Liquids and Solids, ASME Heat Transfer Division, Publ. by

McGraw-Hill, N. Y. (1959), p. 321-38.

16. Boon, J. P., and Thomaes, G., Physica 29, 208 (1963); Boon, J. P., Legros,

J. C., and Thomaes, G., Physica 33., 547 (1967).

17. Carmxchael, L. T. , Berry, V., and Sage, B. H. , J. Chem. Eng. Data 10, 57

(1965).

18. Sage, B. H. , and Lacey, W. , Trans. Am. Inst. Mining. Met. Eng. 127 , 118

(1938).

19. Bicher, L. , and Katz, D. , Ind . Eng. Chem. 3_5, 754 (1943).

20. Baron, J. D. , Roof, J. G. , and Wells, F. W. , J. Chem. Eng. Data ^, 283

(1959).

21. Ross, J. F., and Broira, G. M. , Ind. Eng. Chem. 49, 2026 (1957).

22. Hellemans, J., Zink, H. , and Van Paemel, 0., Physica 46^, 395 (1970); 47,

45 (1970).

23. Galkov, G. I., and Gerf, S. F. , Zhur. Tekh. Fiz. 11, 613 (1941).

24. Gerf, S. F. , and Galkov, G. I., Zhur. Tekh. Fiz. JLO, 725 (1940).

25. Rudenko, N. S., and Shubnikov, L. N., Physik. Z. Sowjetunion 6^, 470 (1934).

26. Rudenko, N. S., Soviet-Physics-JETP 9^, 1078 (1939).

27. Huang, E. T. S., Swift, G. W. , and Kurata, F. , AIChE J. 12^, 932 (1966).

28. Swift, G. W., Lohrenz, J., and Kurata, F. , AIChE J. 6, 415 (1960).

29. Carr, N. L. , Inst. Gas Tech. Res. Bull. 23^ (1953).

30. Comings, E. W. , Mayland, R. J., and Egly, R. S., Univ. Illinois, Eng. Exp.

Sta. Bull. Serial 354 (1944).

31. Gnezdidov, N. E. , and Golubev, I. F., Gazov. Prom. 1_3, 46 (1968).

32. Iwasakl, H. , J. Chem. Soc. Japan 62^, 918 (1959).

J-12
, Vj. Makita, T. , J. Chem. Soc. Japan 23^, 367 (1959).

34. Pavlovich, N. V. and Timrot, D. L. , Teploenergetika ^, 61 (1958).

35. Kuss, E., Z. Agnew. Phys. A, 203 (1952).

36. Meshcheryakov, N. V., and Golubev, I. F. , Trudy GlAP (1954).

37. Timrot, D. L., Serednitskaya, M. A., and Bespalov, M. S., Soviet Physis-Dokl.

20, 107 (1975).

38. Le Neindre, B. , "Contribution a I'etude Experimentale de la Conductivite

Thermique de Quelques Fluides a haute Temperature et a haute Pression,"

Ph.D. Thesis, Univ. of Paris (1969); Le Neindre, B., Tufeu, R. , and Bury, P.,

Proc. 8th Conf. Thermal Conductivity, Plenum Press, New York, 1969, Eds.

Ho, C. Y., et al. , page 75; Le Neindre, B. , Int. J. Heat Mass Transfer 15 ,

1 (1972).

39. Mani, N., Ph.D. Thesis, University of Calgary (1971).

40. Ikenberry, L., and Rice, S. A., J. Chem. Phys. 39^, 1561 (1963).

41. Pavlovich, N. V., Gaz. Prom. _5, (1959).

42. Sokalova, V., and Golubev, I., Tephoenergetika 4_ (1967).

43. Lenoir, J., Junk, W. , and Comings, E. , Chem. Eng. Progr. 49^, 539 (1953);

Lenoir, J. M. , Ph.D. Thesis, Univ. of Illinois (1943); Lenoir, J. M. , and

Comings, E. W. , Chem. Eng. Prog. 47, 223 (1951).

44. Misic, D., and Thodos, G., Physica 32^, 885 (1966).

45. Keys, F. G. , Trans. Am. Soc. Mech. Eng. 76, 809 (1954); 77, 1395 (1955).

46. Golubev, I. F. , Teploenergetika 10, 78 (1963).

47. Carmichael, L. T. , Reamer, H. H. , and Sage, B. H. , J. Chem. Eng. Data 11,

52 (1966).

48. Borovick, E. S., Manveev, A., and Panina, Y. E. , Zhur. Tekh. Fiz. 10, 988

(1940)

J-13
49. Stoliarov, E. A., Ipatev, V. V,, and Teodorovich, V. P., Zhur. Fiz. Khim.

24, 166 (1950).

50. Golubev, I. F., Viscosity of Gases and Gas Mixtures, Israel Program for

Scientific Translations, Jerusalem, 1970. Available from the U. S.

Department of Commerce.

51. Zagoruchenko , V. A., and Zhuravlev, A. M. , Thermophysical Properties of

Gaseous and Liquid Methane, Israel Program for Scientific Translations,

Jersulem, 1970. Available from the U. S. Department of Commerce.

52. Vargaftik, N. B., Filippov, L. P., Tarzimanov, A. A., and Yuchak, R. P.,

Thermal Conductivity of Gases and Liquids (Moscow, 1970)

.

53. Kestin, J. and Mason, E. A., Reference [3], p 137.

J-14
FIGURE CAPTIONS

Deviations between experiment and calculation for the viscosity

of saturated liquid methane.

Viscosity deviations at several representive temperatures.

Thermal conductivity deviations at low temperature.

Thermal conductivity deviations at representive temperatures

above 300 K.

J-15
6r4

0

-2

viscosity: saturated Liquid

[16]

1

.2 .3 .4 .5

DENSITY, g/cm^

1

J-16
0

viscosity: 223K [14]

^2r-H \ 1 b—

•3

O

I I I I I '0 .1 .2

283 K O

2t- 294 KD

0

13]

[15]

r-r.- -5

J I 1

2

0 .1 .2 .3

344 K [13]

0

'

I II I "0 .1 .2 .3

DENSITY, g/cm^

J-17
THERMAL CO.NDUCTlViTY:

I20K O [39]

4

° P 0

-4

125 K [40]

°

I . I J

.40 .42 44

' 140 K [39]

0

-4

0

38 40 42 44

175 K [40]

180 K O [39]

-4

.25 .30 .35 .40 45

DEMSITY, g/m^

J-18
o

h-

<

>

LiJ Q

I2:

UJo

cr

111

THERMAL CONDUCTIVITY:

4r- ^'25K [38]

0

4

0

4r0

J2L

0

-4

Q ^ O

I

340 K [39]

O

J

.2 .3 .4

300 K [39]

^5 b qO^sI I? '

.2 ; DENSITY, g/cm

0

J-19
TABLE 1. Potential Function Parameters [Equation (7)] and

Critical Point Parameters for Methane

m = 11

Y' = 3.0

r = m4.101 X lO'-^^m (a = 3.68 x

e/k = 168.0 K

T

c 190.55 K

P

c 4.5988 MPa (45.387 atm)

0.1628 g/cm^ (10.15 mole/i)

molecular weight = 16.043

J-20
TABLE 2. Parameters for the Dilute Gas Equation (8) . The units

are: Temperature in K, viscosity in yg/(cm's), and

thermal conductivity in mW/(m'K).

GV(1) - -2.090975 X 10= GT(1) = -2.147621 X 105

GV(2) = 2.647269 X GT(2) 2.190461 X 10=

GV(3) = -1.472818 X 10= GT(3) = -8.618097 X 10*

GV(A) = 4.716740 X lo'' GT(4) 1.496099 X 10*

GV(5) = -9.491872 X 10^ GT(5) = -4.730660 X 10^

GV(6) = 1.219979 X 10^ GT(6) = -2.331178 X 10^

GV(7) - -9.627993 X iqI GT(7) 3.778439 X 10^

GV(8) = 4.274152 GT(8) = -2.320481

GV(9) = -8.141531 X 10-2 GT(9) 5.311764 X

10" 2

J-21
TABLE 3. Selected References for Methane

Authors

Viscosity

Haynes [12]

Giddings, et al. [13]

Barua, et al. [14]

Kestin and Leidenfrost [15]

Boon and Thomaes [16]

Approximate

experimental range

Saturated liquid

95-190 K

283-410 K

Pressures to 54 MPa

223-423 K

Pressures to 17 MPa

'\'296 K

Pressures to 15 MPa

Saturated liquid

91-114 K

Estimated

accuracy + %

2%

2%

2%

1%

3%

Thermal conductivity

Le Neindre [38] 298-723 K 4%

Pressures to 100 MPa

Mani [39] 139-400 K

* 3.5%

Pressures to 60 MPa

Ikenberry and Rice [40] 98-235 K 5%

Pressures to 50 MPa

J-22
TABLE A. Parameters for Equations (3) - (5). The units

3 are: Density in g/cm , temperature in K,

viscosity in yg/(cm*s), thermal conductivity in

mW/(m'K).

Viscos ity

Equation (3)

Equation (4)

Thermal conductivity

Equation (3)

Equation (5)

A

B

C

F

E

A

B

C

F

D

h

1.696985927

-0.133372346

1.4

168.0

1.0

-1. 035060586 x 10^

1. 7571599671 X

-3. 0193918656 X

3

10

1. 8873011594 X

4. 2903609488 X

10~

1. 4529023444 X 102

6. 1276818706 X

-0. 25276292

0. 33432859

1. 12

168.0

1.0

-7.0403639907

12.319512908

-8.8525979933 x lO'

72.835897919

0.74421462902

-2.9706914540

2.2209758501 x 10"

J-23
TABLE 5. Tabulated values for the viscosity coefficient of methane. The

units for the viscosity are yg/(cm*s).

TABLE 6i Tabulated values for the thermal conductivity coefficient of methane.

The units aremW/(m'K).

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J-32
TABLE 7. Transport Coefficients of Saturated Liquid Mothane

Thermal

Ten^.perature , Density, Viscosity, conductivity,

K mol/Z yg/(cm*s) in"'.,V(m*K)

95 27.789 1792 215

100 27.367 1563 206

105 26.934 1377 197

110 26.491 1223 189

115 26.035 1094 181

120 25.566 984 173

125 25.081 889 165

130 24.578 807 158

135 24.055 734 150

140 23.508 669 143

145 22.932 611 136

150 22.322 '558 129

155 21.672 509 122

160 20.971 464 115

165 20.206 421 108

170 19.356 380 101

175 18.386 340 94

180 17.226 300 88

185 15.690 256 84

190 12.485 187 89

J-33
APPENDIX

METHANE EQUATION OF STATE

The equation of state used in the work is that reported by McCarty in

reference [5]. The form of the equation, and its parameters are reproduced in

this appendix.

The equation of state is given by the following functional form:

2 1/2 2 P = pRT + p (N,T + N^T + N^ + N,/T + N,/T ) 1 z J 4 J + p^ (N^T + N^ + Ng/T + Ng/T^)

+ p^ (N^qT + N^^ + N^^/T) + (^^3) + p^ + N^5/T^) + 9 (N^e/T) + p^ (N_^^/T + N^g/T^) + p^ (N^g/T^)

+ p^ (N^q/T^ + N^-^/T^) exp (-YP^)

+ p^ (N22/T^ + N23/T^) exp (-YP^)

+ Q (N2^/T^ + N23/T^) exp (-YP^)

+ p^ (N2^/T^ + N2^/T^) exp (-YP^)

+ p-^^ (N2g/T^ + N2g/T^) exp (-yp^)

+

p-*-^ (N3q/T^ + ^31^^^ ^32^^^^ (-TP^)

where, to be consistent with reference [5], P is in atmospheres, p is in mo

and T is in kelvins.

J-34
The coefficients (N^ , Y and R) are

"2

"3

\

"5

\

"7

^11

"12

he

hi

\&

"20

''21

'^23

'^24 ^25

'^26

«27

''28 "29

^'30

«31

^^32 Y

R

-1. 8439-86666 X 10-2

1, 0510162064

-1. 6057S20303 X 10

8. 484^027562 X 10^

-4. 273S-09106 X 10*

7. 6565285254 X 10-*

-4. 8360724197 X 10-

8. 5195-73835 X 10

-1. 6607434721 X 10*

-3. 7521074532 X 10-5

:- 2. 8616309259 X 10-2

-2. 8685285973

1. 1906973942 X 10-*

-8. 5315715699 X 10-3

3. 8365063841

—

2. 4986328379 X 10-5

5. 797A531455 X

10"**

= -7. 1648329297 X 10-3

1. 2577353784 X 10-*

2. 2240102466 X 10*

- -1. 4800512328 X

10*^

5. 0498054887 X 10

— 1. 6428375992 X 10^

2. 1325337196 X 10-1

3. 7791273422 X 10

-1. 1857016815 X 10-5

-3. 1630780767 X 10

-4. 1006732941 X

10-*^

- 1. 48700^3284 X 10-3

= 3. 1512261532 X 10-5

-2. 1670774745 X

10-'^

2. 4000551079 X

10-5

-0. 0096

0. 082G5616

J-35

A corresponding states procedure to predict the viscosity and t/iermal conductivity

coefficients of a pure fluid or mixture is discussed. We stiow the transport properties of a

fluid or mixture can be calculated to within experimental error given only corresponding

values for a reference fluid and equation of state data. With methane, as the reference

fluid, we consider nitrogen, ethane, propane, butane, carbon dioxide, and mixtures of

these fluids. LNG is also included. It is shown that the conventional corresponding

states approach is not sufficient to predict correctly the transport properties. The

effect of internal degrees of freedom on the thermal conductivity coefficient and the enhancement in the critical region for this coefficient is discussed briefly.

Prediction of the viscosity and thermal

conductivity coefficients of mixtures

H.J.M. Hanley

The task of measuring the transport properties for all mixtures of possible practical interest is out of the question, even for simple fluids. Any method, then, which could

predict the properties to within the experimental error would be both interesting and useful. Unfortunately, the

lack of suitable data, on the one hand, and the theoretical problems that can be encountered in the study of transport phenomena in general, on the other hand, are obstacles which

have only been overcome for special cases. SimUar problems come up when one considers the thermo- dynamic (or PVT) properties of mixtures. In this case, however, the principle of corresponding states has been used

widely as a prediction too! and, in particular, the principle has been extended systematically to multicomponent

mixtures of polyatomic molecules. It is thus logical to in- vestigate how the corresponding states approach can be broadened to include transport properties and the object of

this paper is to do this. Specifically, we discuss an ad hoc

procedure, based on the principle of corresponding states, to predict the viscosity coefficient (7?) and the thermal conductivity coefficient (A) of fiuid mixtures given thermo- dynamic data. We will show that the procedure appears to work (data for comparison are scarce) for a variety of mixtures over a wide range of experimental conditions.

Background

Some introductory material is summarized in this section.

Simple two-parameter corresponding states The basic criterion for two pure fluids to obey the principle of corresponding states, or to 'conform' or 'correspond' is that a given intermolecular potential form, such as

(1)

The author is with the National Bureau of Standards, Cryogenics

Division, Boulder, Colorado 80302, USA. Received 7 July 1976.

(where r is the intermolecular separation) is appropriate for both. Each fluid can thus be characterized by an energy

parameter, e, and a distance parameter, a. If the two fluids do correspond, then the transport coefficients of the one

fluid, a, at a particular temperature (7^ and density (p) can

be expressed in terms of the coefficients of the other fluid,

0. For example, for the viscosity and thermal conductivity

coefficients we have'

andK [P, T] = Xo

Mr

Co

/ Mr,] \ a„

(2)

(3) The coefficients, tjq and Xq , which can be taken as refer- ence values, have to be evaluated at the proper density and

temperature as indicated. M is the molecular weight.

Since one can write 7"^ ~ e//c, p"^ ~ a"^, where the superscript, c, refers to the critical point value and k is Boltz- mann's constant, alternative expressions for 77^ and Xq are

T?q(P. T) = T?o

Xa(p, T) = Xo

'M. Mo

Mo

M,

Pa

Pi

P'o

V3

(4)

\'/2

(5) Equations (4) and (5) are the basis for many of the corre- lation techniques of transport properties discussed in the

literature,^ both for pure fluids and for mixtures. However,

results can be very inconsistent if the equations are used as predictive tools, and clear-cut procedures have not been

proposed. This is particularly true for mixtures for which

one needs mixing rules (for the critical parameters, for

CRYOGENICS . NOVEMBER 1976 K-1 643
example). Several mixing rules have been suggested, but on

essentially intuitive grounds.^

Recently, however, the relationship between corresponding states and transport properties of mixtures has been

clarified considerably by Mo and Gubbins." These authors

considered a conformal fluid mixture [that is, a mixture^

in which each component obeys the universal potential of

equation (1)] in the Van der Waals one-fluid approximation.

The one-fluid approximation allows the mixture to be equated to an equivalent pure fluid so (4), for example,

becomes for mixture x.

T?x(P. T)

Mo

(6) with a similar expression for the thermal conductivity coefficient. Mo and Gubbins derive (6) under well-defined assumptions and show that one possible set of mixing rules for the density and temperature of a binary mixture are (using the notation of Gubbins et al) 2 '^XaXpipgp)'^

a 0 and 2 ^-^a-^g^ggCPag)

a (i

(7)

(8)

where x^ is the mole fraction of a. It is also argued that a mixing rule is needed for the molecular mass, namely for rjx

a /3

(9) and for X,

M;''(nf{p%)i^ = yyx^x0M-^'{n0f{pgp)%

a ^ (10) The cross parameters of (9) and (10) can be estimated from

the relations

and

1

(11) (12)

(13)

where ^"d ^ap ^re binary interaction parameters, which

are best obtained from experiment.

The mixing rules, (7) and (8), are consistent with the mixing rules derived for thermodynamic properties using

the one-fluid approximation. If, therefore, the binary inter- action parameters are assumed to be those valid for thermo- dynamic properties, one has a procedure to predict the

viscosity and thermal conductivity coefficients of mixture x, given the equivalent coefficients of the reference fluid.

not valid for polyatomic fluids, or for mixtures containing

polyatomic molecules. The situation is, of course, paralleled with respect to the thermodynamic properties and has been

discussed extensively in this context. A particularly convenient extension of corresponding states has been developed

by Leiand* and Rowlinson' and appears relevant to the transport properties of interest here. According to the Leland approach, a third parameter, co, which can be taken as the Pitzer acentric factor,^ is intro- duced, but the framework of simple corresponding states

is preserved, if one works with the relations

faa, o _ I ^ aa h. Pi

C PacL (14)

for fluid a with respect to o. The terms 6aa,o ^nd ^aa.o

called shape factors and are weakly varying functions of

temperature and density

^aa, o = 1 + i^acc - <-^o)f(Z p)

Paa, o = 1 + i<^aa " <^o)giT, p) (15)

where (jj^j^^ and cjq are acentric factors for fluids a and o, respectively. [The form of the functions f{T, p) and^(r, p)

are given in reference 6. A set of numerical values for the parameters of /and g, and for to, are also given. However

these parameters are subject to revision depending on the

state-of-the-art of the appropriate equation of state data. The set used by us are preliminary but are available from

the Cryogenics Division.] Using the shape factors, the compressibility factor (for example) of a. would be given by the

relation Zq(p. 7) = Zo{phaa,o' Vfaa,o)- With the appropriate' expression for the Helmholtz free energy, the thermodynamic properties of a are completely defined in terms of the properties of o. Let us introduce shape factors into the expressions for the

viscosity and thermal conductivity coefficients.' We then

obtain for fluid a

Wo/ (16)

^a(Pi ^ [P^'aa, c '^/faa, ol I | ^^aa, ofaa, o(IV) and for the transport properties of the mixture x.

T?x(P. T) = Vo[ph.,o, T/f,,o]\^] ^K'oKU (18)

K(P. T) = Xo[p/2x.o, Wx,o](^)"/'x;o/^o

where mixing rules for x are

''x, o ~ y^ y^^a^phap,o

a p

(19)

(20)

(21)

Extension to polyatomic fluids and non-conformal mixtures Equations (2)-(6) are not general since the assumption of

the simple two-parameter corresponding states theory are

with

fap,o ~ ^apifaa, ofpp, o)^' (22)

644 K-2 CRYOGENICS . NOVEMBER 1976
and

Following Gubbins.'a mixing rule for is

= V ^M\f'^' h-''!^ (24)

a li

for the viscosity coefficient, and an equivalent rule for the thermal conductivity coefficient follows from (10).

Evaluation of the extended corresponding states equations

One might hope that (16)-(24), which we designate as the extended corresponding state equations, could predict the transport properties of non-conformal fluids given a reference transport property and appropriate thermodynamic

data. It was decided to test this assumption. Initially we

considered the calculation of the viscosity coefficient for the pure fluids (a) nitrogen, ethane, propane, and carbon

dioxide. Methane was chosen as the reference fluid (o): methane viscosity data have been analysed and correlated

as a function of temperature and density, '° and the methane

equation of state of Goodwin" was used'^ as the basis for the shape factor calculations.

Results for nitrogen are shown in Fig. 1 in which the ratio 7?(exp)/T}(calc) has been plotted as a function of temperature for several reduced densities (p/Pc): i?(calc) refers to

values from (16), while values for r?(exp) were obtained from our previous correlation of the transport properties of nitrogen.'^

It is seen that (16) gives a reasonable prediction if p/p'^ £ 1 (that is, the viscosity ratio is close to unity) but there is a strong density dependence in the deviation pattern above

the critical density. As a contrast, the temperature depen- dence is relatively weak for all densities. As a matter of interest we include Fig. 2 which illustrates the variation of the shape factors 6 and 0 used to obtain

i7(calc). The density dependence of these variables is very weak.

Results similar to those shown in Fig. 1 were observed

for the other fluids. Thus it appears that (16), with shape

factors obtained from thermodynamic data, cannot represent adequately at high densities the viscosity coefficients of

fluids which do not correspond with methane. These results for the pure fluids further suggest that (18) will also be unsatisfactory for non-conformal mixtures — with the added

complication of mixing rules and binary interaction parameters - and, in fact, this turned out to be the case.

Modified equation for the viscosity coefficient

The relationship between the experimental viscosity coefficient and values calculated from (16) for the fluids studied in this work suggests that an equation of the form

T?.(P. T) = T?o(p', 7-')Wa, o ^(P. T) (25)

might be successful where (16) is re-written as Vjp. T) Vo( P'. T')FH^^^ o (16a) where

P' = P^aa, o; T' = T/faa, o (26)

2 4 r 2 2

i

09I I I I I I I I 100 200 300 400

Temperature, K

Fig. 1 Ratio of i?{exp)/T)(calc) for nitrogen plotted schematically

as a function of temperature at several densities. Values of 7i(exp) were extracted from reference 13 while values of rjlcalc) were

obtained from the extended corresponding states equation (16). The figure indicates (16) is not satisfactory if p/p'' ^ 1. p"- is the

critical density

I 02 I

100 20c 3C0 400

Temperature , K

Fig. 2 Plot of the shape factors for nitrogen with resfject to methane, d and 0, ((14) and (15)] based on a fit of thermo- dynamic data. The density dependence is small and can essentially be ignored

and

FHS.,, ={^^Jh-2%f^ko (27)

The correction factor, X{ p, T), should be unity if fluids a

and o follow simple corresponding states, but should be a strong function of density and a weak function of temperature otherwise. However, X should approach unity as the density approaches zero in this latter example (see Fig. 1). Furthermore, if X can be expressed in terms of thermo- dynamic (PVT) data alone, (25) would have the predictive

capability of (5) for fluids in addition to those which obey

simple corresponding states. A suggestion for a convenient form for X(p, T) is now

discussed.

The modified Enskog theory

We have shown in references 14, 15, and 16 that an ad hoc

modification of the Enskog theory for the hard sphere fluid.

CRYOGENICS . NOVEMBER 1976 K-3 645
called the modified Enskog theory (MET), can represent the transport properties of real fluids given only PVT data. The

MET expressions for the viscosity and thermal conductivity

coefficients of fluid a, are,

T?a = r?e,(o)6p(— + 0.8 + 0.716ipx| C

\bpx I

i

= \'o,io)bpi— + 1.2 + 0.755Z7px| + K(o)

\bpx I

8)

where

X;,'(o) = pZ)„(o)c;'(o)

(29)

(30)

In the above equations, 77^(0) is the dilute gas viscosity of

fluid a, which can be obtained from experiment or calcu- lated from kinetic theory; Xa(o) and Xa'(o) are contributions

to the dilute gas thermal conductivity due to translational and internal degrees of freedom, respectively; Dq(o) is the

dilute gas self-diffusion coefficient; c'l(o) is the constant volume dilute gas specific heat per unit mass due to internal degrees of freedom. The term bpx is obtained from the equation of state written

in the form

(31)

which introduces the thermal pressure, T(dP/dT\, of the

fluid Q. b ha second virial term. A particular choice for

b, selected to ensure that (28) and (29) approach the dilute gas limit as the density tends to zero is

b = B + T-dT

where B is the second virial coefficient of fluid a.

(32)

The MET is discussed at length in reference 14-1 6 so details are unnecessary here but, generally, the MET can predict and

represent the transport properties of simple fluids to within about 10-15% for densities not exceeding about twice the

critical density.

One particular feature of the MET can be deduced from

our previous work, viz, that a pair of fluids (say a and o) do not necessarily correspond if t?^ and X^- are reduced

according to simple corresponding states. In other words,

in the context of this paper, suppose we calculate the MET

viscosity for fluid a, t?^, at a given density and temperature, but also calculate the MET viscosity for o, r?t:, at the equivalent density and temperature: p{p%lp%) and

T( To/Ta), respectively. According to simple corresponding states one then has,

I '/z / c /tc\ '/2 ^a(l

and

7?^-(l)

(33)

(34) But the results of references 14 to 16 show that (34) is not always upheld and, moreover, we showed that the lack of correspondence according to the MET arose from the lack of correspondence in the PVT terms of (28), that is, in

bp and [l/bpx + 0.8 + 0.755 bpx] This being the case,

a relationship

T?^ = V^{2) (35) cannot be expected to hold, where r?^(2) is calculated from

extended corresponding states, that is, from the relation

r?f (2) = T?^(p', T')FH2^ (36)

That TjJ was not equal to t?|-(2) was in fact, verified. However, as a matter of interest, we repeated, with the MET

viscosity coefficients, the procedure which led to the conclusions depicted in Fig. 1 for nitrogen, and to similar conclusions for the other fluids. Hence, the ratio v^lriai^) was examined as a function of temperature and density

for the fluids of interest. The results turned out to be significant. We observed that the temperature and density behaviour of the MET ratio was

very similar to the corresponding ratio i7(i(exp)/Tjc(calc), and actually indicated a relationship, namely

vi(2) T7tt(calc) (37)

Here 7?^(exp) is the experimental viscosity and T?o((calc) is the

value from (16) as before. The significance of (37) is that it leads to an expression for the correction factor X(p. T) of (25) since, if one accepts (37) as an apparently empirical fact

7?o(exp) 77(j(calc)^£,^ qGJq, o (38)

where we have used that 17^(0) = Vo(o)^^aa, ofor the

dilute gas. q^a ois the ratio {bp)J{bp)o and GJq o

is the

ratio [ ]J[ ]„' where [ ] = [l/Z^px + 0.8 + 0.755 dpx]

from (28). Note that both {bp)^ and [ ] q for fluid q can

be determined from the equivalent terms for fluid o using the shape factor approach. For example, for bg^iT)

b^{T) = h B^ + rd(^gg, o ^o)

dr

(39)

[The shape factors do not necessarily cancel if one takes the ratio of bp since 9 and 0 are, in general, functions of

temperature and density.]

Since 7?tt(calc) is given by (16) or (16a), 7?a(p, T) can be

redefined from (38)

RociP. T) = T?o(p', T')FH2c,oQaa,oG2a.o (40)

Comparison with (25) indicates that

X{p. T) = qaa.oG2a,o (41) We examined the experimental behaviour of X{p,T). The

result was that X turned out to be a strong function of temperature and density if fluid q did not correspond with o. However, it was observed that the temperature dependence was due largely to q^a, th^t is, the ratio of the bp terms. This feature suggested a refinement to (41) according to the following reasoning. In the MET, b is defined in a way

to ensure that the viscosity coefficient approach the correct zero density limit. Further, q^a, o^aa, o ^ i i" this dilute gas limit. We thus argue that q^a. o imposes an incorrect temperature dependence to the product qaa,oG2a.o for the dense gas and liquid. Since it is not clear how to redefine b.

646 K-4 CRYOGENICS . NOVEMBER 1976
we replace t7c,c«,o by Qaa.o where Q - fll ' - l/exp(p'^/p)M (42)

In this way Qaa,o ^aa, o

3t low densities and the MET

format is preserved, but the temperature dependence of Qaa o becomes insignificant at high densities since

Qaot, o ^

• Our modified equation for the viscosity coefficient of fluid a is thus

T?„(p, r) = Vo(p\T')FH2a,oQaa.oG2a,o (43)

This equation predicts tj^ from t?o and /'FT' information.

Test of (43)

Initially we tested (43) for nitrogen (a) given, as before, the viscosity of methane (o) as a reference. The procedure

is summarized as follows: from a fit of the thermodynamic

properties of nitrogen using the equation of state for methane, one determines the shape factors and h^co

faa,o 2nd faa.o defined by (14). Hence one has p', T' and FH2a.o and VoiP'^ T'). (hpX and [ \aQacc,o andCo^.o

follow from (30) and (31).

Selected results for nitrogen are given in Tables 1 and 2. Results predicted from (16) are included for comparison.

The improvement of (43) over (16) as a representation of

the data is significant. Since both the experimental nitrogen

viscosities and the reference methane viscosities are judged

accurate to about 2%, the agreement between experimental and calculated nitrogen values is considered satisfactory.

Similar agreement between calculation and experiment was observed for the other fluids of interest here; ethane, propane, and carbon dioxide.

Viscosity equation for mixtures

For mixtures, one modifies (43) to become

T?x(P. T) = r/„(p',r')F//2,oCx,oG?.o (44)

If (44) is to have the predictive capability of the equation

for pure fluids, then the shape factor terms and mixing rules

,, and/, o, have to be defined by (20) and (21) which,

in turn, incorporate the equilihrium binary interaction parameters, '^^0 and i/z^jj of (22) and (23). Thus 0x, o- ^x.o'

^u^, and ija0 can be found from thermodynamic data alone.

[It is not clear what mixing rule to use for the molecular

weight. Although (24) has been proposed, the mixing rule that arises naturally from thermodynamics is

a We prefer this rule because we have modified (16) on the

basis of the fFr behaviour of the mixtures.]

Comparison between experiments and the viscosity

equation for mixtures

Viscosity data for non-conforming mixtures, apart from

the dilute gas, are scarce and their reliability are often

difficult to assess. Further, the choice of mixture data

suitable for comparisons is somewhat restricted by our

previous work on the equation of state. In principle, the shape factors and binary interaction parameters can be

estimated for many fluids and their mixtures but, in pracTable 1. Nitrogen viscosity: saturated liquid Deviations between the experimental viscosity coefficients and values calculated from (43) for saturated liquid nitro- gen. Deviations between experiment and the extended

corresponding states equation, (16) are also given.

^exp — VcaU: X 1 UU

Tj(exp),

'icatc T,K p/p^ juq cm' s"' (43) (16)

75 2.61 1658 -8.1 20.1 80 2.54 1377 -3.5 18.4 85 2.46 1160 3.0 17.1 90 2.38 988 3.0 95 2.29 846 4.6 15.3 100 2.19 726 5.0 14.4 115 1.84 447 2.6 10.6 120 1.67 365 2.0 8.6 125 1.37 259 1.5 8.0

Table 2. Nitrogen viscosity: 220 K isotherm

Deviations between the experimental viscosity coefficients'^

for nitrogen at 220 K and values calculated from (43) as a function of reduced density. Deviations between experiment

and values from (16) are also given.

^exp ^calc ^ 100

(43) (16)

0.1 0.5 0.8 0.3 -2.8 -1.1

1.0 -7.0 -4.3

1.6 -4.0 4.0

1.9 -4.8 12.0

2.1 -5.8 18.6

2.5 -6.9 24.0

tice at this time, our work is limited to methane, ethane, propane, n-butane, i-butane, pentane, nitrogen, carbon

dioxide, nitrous oxide, and mixtures thereof Equation

(44), however, was checked with data for several representive mixtures over a wide range of experimental conditions.

Table 3 gives typical and representative results for the methane-propane system. The data, perhaps the most

extensive and reliable viscosity mixture data available, are those of Huang, Swift, and Kurata.'^ Approximate critical temperatures and densities of the given mixture" are included in the tables as a measure of the reduced temperature and density involved. Values from extended corres- ponding states are given in parentheses. The data are judged accurate to within about 3% so our equation (44)

is very satisfactory.

Table 4 illustrates typical results for the methane-n-butane

system. The data are those from reference 19. Agreement

is excellent between the predicted values from (44) and

experiment. The experimental accuracy is about 6%.

Data for liquid mixtures which contain components other than hydrocarbons are scarce and the majority are repro- duced in the monograph by Gobubev.^° We investigated

CRYOGENICS . NOVEMBER 1976 K-5

647
Table 3a. Methane-propane viscosity

Comparison between viscosity data" for a methane (22.1%)- propane (77.9%) mixture at 193.15 K and the results predic- ted from (44): T" ^ 350 K, p'^ 6.25 mole 1"

n (exol 7^ (calc)

,

p,mole r' jug cm"' s"'

15.39 2390 2412 (2086)*

15.63 2676 2610 (2300)

15.79 2846 2750 (2441) 15.92 3020 2900 (2580) 16.06 3184 3040 (2717)

* Values obtained from extended corresponding states.

Table 3b. Methane-propane viscosity

Comparison between viscosity data'^ for a methane (50%)-

propane (50%) mixture at 153.15 K and the results predicted

for (44): 7^ 319 K, p" 7.7 mole I"'.

I \ I I l_

80 100 120 140 160

Temperature, K

Fig. 3 Saturated liquid viscosity of a N,/CH4 equimolar mixture. Data (filled circles) from reference 21, curve from (44). The insert gives a plot of the saturated liquid viscosity of pure methane. It can

be argued that the data from reference 21 are unreliable (see text)

Tj(exp), V (calc). p

mole r' Hg cm"' s"'

18.69 2780 2614 (2286)*

18.78 2860 2710 (2360) 18.96 3030 2878 (2509) 19.12 32000 3002 (2659) 19.28 3380 3232 (2807) 19.42 3550 3407 (2952)

* Values obtained from extended corresponding states.

Table 3c. Methane-propane viscosity

Comparison between viscosity data'^for a methane (75.3%) propane 24.7%) mixture at 173.15 K and the results pre- dieted from (44): T"^ ^ 276 K, ^ 9.1i mole r'.

r?{exp). T?(calc), P,mole r

pg cm^' s"'

19.52 975 943 (889)* 13.76 1020 988 (933) 20.17 1090 1075 (1013) 20.53 1170 1156 (1090) 20.84 1250 1233 (1162) 21.12 1320 1308 (1232)

* Values obtained from extended corresponding states.

the N2/CH4 system discussed in that work and Fig. 3

illustrates our prediction from (44) for the equimolar

mixture. The data are those of Gerf and Galkov^' for the saturated liquid. Our values are generally lower than experiment; the discrepancy increases as the temperature

increases. Superficially the prediction appears poor but we

can argue that the data are unreliable on the following

Table 4. Methane-n-butane viscosity

Comparison between viscosity data for a methane (50%)- n-butane (50%) mixture at 31 1 K and the results predicted

from equation (44): T'^ ^ 375 K, p^ ^ 7.1 mole 1"'.

Tj(exp), T?(calc), p,mole r' jug cm"' s"'

11.58 645 675 (730)*

12.21 772 730 (836) 12.66 835 854 (922) 13.03 920 927 (1000)

13.34 993 995 (1070)

13.61 1070 1056 (1136) 13.85 1115 1144 (1200)

14.07 1230 1172 (1258)

* Values obtained from extended corresponding states.

grounds. First, it is surprising that the discrepancy increases with temperature since the density decreases. The evidence from pure fluids indicates that the extended corresponding states treatment is reasonable if p/p*^ < 1, and the

factor Qx,o(^\,o approaches unity as the density approaches

the critical density. Second, the insert in Fig. 3 gives a schematic plot of pure methane saturated liquid viscosity. The lower curve is based on the data of Haynes,^^ which we believe to be accurate to within ± 2%, while the upper

curve is based on the data of Gerf and Galkov;^' the authors of the N2/CH4 data. The similarity between the methane and

nitrogen/methane plots is obvious. We suggest, therefore,

that the mixture data of reference 21 are systematically

in error.

Table 5 compares our prediction with Golubev and Petrov's data^° for a 62% N2-38% CO2 gaseous mixture at 289 K. Note that the mixture does not contain the reference

fluid (methane) as a component.

648

K- 6

CRYOGENICS . NOVEMBER 1976
Finally we include Table 6 which gives a comparison bet- ween predicted and experimental values for an LNG

gaseous mixture^" at 273 K. The mixtures have the following

composition: CH4 - 91.5%; CjHg- 1.8%; CsHg- 0.8%; C4H10 - 0.6%; N2 - 5%; others - 0.3%. We cannot evaluate

the accuracy of the data but the prediction appears reasonable. Although, in fact, the viscosity values for this mixture

are very close to those for pure methane under equivalent

conditions. Table 6 does illustrate that our procedure can

adapt to a six-component mixture without difficulty.

Thermal conductivity equation for mixtures

We have investigated the prediction of the thermal

conductivity coefficient for a pure fluid and for a non- conformal mixture. At this stage our results are to be considered preliminary. There are two principle reasons for this caution: it is not clear how to treat the contribution of

internal degrees of freedom to the conductivity (these contributions are icnown not to follow the corresponding

states principle), and the data for thermal conductivity of liquid mixtures are very limited. Based on the procedure discussed for the viscosity coefficient, we considered the equations [see (17) and (19)]

Up. n = Xoip'.T')-^

and

(45)

(46)

for a pure fluid and mixture, respectively. , etc, are the MET expressions from (29). If we substitute from (29) we

obtain from (45)

Ota, o

X ^1 + j:[(X';(o),A;(o)]} (47)

where the terms Xa{o)/x and Xo(o)/x are assumed to give only small contributions to X^- and X^, respectively. This

has been verified experimentally.'" FH^^.o' analogous to FH^a.o^ is defined from (17)

fh: "Q!Q, oJaa, o (48)

We introduced FH^cx, o '"to (46) by assuming

that X'aio) = X'„(o)FHaa,o is valid for the translafional contributions in the dilute gas. G^q, o

is the ratio of the MET terms

[\lbpx + 1.2 + OJ55bpx]a

(49) [llbpx + 1.2 + OJ55bpx]o

Ignoring the function,'2jClXj;^(o), Xo(o)] , and introducing the correction for the bp ratio, q^^.o' (47) becomes

K(P,T) = Xo(p', r')F//aa,oeaa,oGL,o (50)

Similarly for a mixture

Kip, T) = Xo(p' T')FHloQ..oGio

Internal degrees of freedom enter into (50) and (51)

through Xo(p',. T').

(51)

Table 5. Nitrogen-carbon dioxide viscosity

Comparison between predicted viscosity coefficients for a nitrogen (62%)-carbon dioxide (38%) mixture at 289 K. Data from Golubev.'°

Ti (pvn\ n / 1 r\ p P, atm mole r' fig cm"' s"'

20 0.9 167.0 167.0 60 2.8 179.5 186.5 100 4.9 200.5 213.6 120 7.0 212.5 229.1

Table 6. Viscosity of LNG

Comparison between predicted viscosity coefficients of an LNG mixture at 273 K. Data from Golubev.^"

7j(exp), T?(calc),

p. P. atm mole r' /jg cm s

20 0.9 109.3 110.0 60 3.1 132.2 123.6 100 5.8 160.2 145.8 200 11.8 244.5 227.7 300 15.0 313.7 298.8 400 17.0 372.3 345.0

Table 7. Nitrogen thermal conductivity: saturated liquid Comparison between experimental data'^ and values predictf from (50) for the thermal conductivity of nitrogen at the saturated liquid.

X (exp). X (calc), T,K mW m-' K"'

75 137.0 142.1 (122.2)* 80 129.9 128.1 (114.2) 85 122.3 116.4 (106.5) 90 114.4 106.4 (99.1) 100 98.1 89.9 (84.9) 115 72.5 67.2 (63.7) 120 64.6 60.1 (56.3)

* Values from extended corresponding states.

Comparison between experiment and the thermal

conductivity equations As remarked earlier, limited data restricts a comparison of

(50) and (51) with experiment, but we followed the procedure discussed with respect to the viscosity coefficient

as far as possible. That is, (50) was first used to predict

values for the pure fluid, (51) was then used to predict

values for a mixture.

Results for nitrogen are reported in Tables 7 and 8 for the

saturated liquid boundary and for the 220 K isotherm;

data from reference 13. Also included in parentheses are the results from the extended corresponding states equation

(17), that is, without an MET correction. We estimate'^

CRYOGENICS . NOVEMBER 1976

K-7

649
Table 8. Nitrogen thermal conductivity: 220 K isotherm Comparison between experimental data'^and values pre- dicted from (50) for the thermal conductivity of nitrogen at 220 K.

p,mole r' pip"

X(exp), X(calc), mW m"' K''

1 n 1 .U Ci no 21.47 22.00 \/./ .yu; 5.0 0.45 28.01 28.72 (33.5)

9.1 0.82 35.74 36.90 (40.14)

12.1 1.09 43.17 44.06 (46.4) 18.37 1.65 65.89 64.00 (65.52) 22.6 2.04 90.33 88.66 (92.37) 25.7 2.32 115.8 118.2 (106.9) 27.7 2.50 137.1 145.2 (124.0)

* Values from extended corresponding states.

Table 9. Ethane thermal conductivity: 310 K isotherm Comparison between experimental data^^ and values pre- dicted from (50) for the thermal conductivity of ethane at 310 K.

X(exp), A(calc),

P,mole!'' p/p'= mWm''K"'

1.0 0.15 29.37 27.36 (19.08)*

4.0 0.60 49.94 48.90 (35.69) 7.0t 1.05 79.26 74.61 (60.6) 10.0 1.49 77.90 71.03 (58.4) 14.0 2.09 105.5 93.8 (83.8) 17.0 2.53 145.4 137.8 (125.7)

* Values from extended corresponding states.

t Note the anomalously large value of A. This arises from the critical point enhancement.'*

the nitrogen data to be accurate to within about ± 4 and

our predictions are generally within this error band.

Table 9 displays the results for ethane. The data are from

a recent correlation^^ and are accurate to within about

i 10% only, which is the agreement between experiment and prediction. There are two remarks on the results in Tables 8 and 9. The

first is that the predictions at low densities are surprisingly

good since, as remarked, the internal degrees of freedom

enter the calculation through Xo only: the internal degrees of freedom are known to contribute up to 50% of the value of the dilute gas thermal conductivity. The second remark

is that Table 9 indicates, for the plp'^ = 1 .05 data point,

the critical point enhancement in the thermal conductivity

coefficient.'^'' Our prediction will also include the enhance- ment through the reference thermal conductivity for methane.'" The topic is under further investigation, however, and will be discussed in detail separately.

Results similar to those of Tables 7-9 were observed for propane and carbon dioxide.

Two mixtures were selected for study: a liquid methane

(39.4%)-n-butane (60.6%) mixture discussed by Car- michael, Jacobs and Sage^* and a gaseous nitrogen-ethane mixture discussed by Gilmore and Comings.^* Tables 10 and 1 1 give typical comparisons between the data and our

predictions from (51). The mixing rules and binary inter- action parameters were again determined from thermo- dynamic information, as for the viscosity. We estimate the data to be accurate to 5-10%. The agree- ment, therefore, between experiment and prediction is excellent.

Discussion and conclusions

A corresponding states procedure to predict the viscosity and thermal conductivity coefficients of a pure fluid or mixture has been presented.

In developing our procedure, we first considered modifying the two-parameter {T'^ and p*^ in this work) conformal

fluid corresponding states equations to include non-confor- mal fluids by introducing the concepts of the extended

corresponding state approach of Leland and Rowlinson, We

had, however, only, partial success with this approach, which

is essentially a technique to include a third parameter, if the necessary parameters were obtained from thermodynamic

(PVT) data. We observed, in particular, that deviations between calculated and experimental transport coefficients

for the pure fluid could be as much as 20% at high densities

(see Fig. 1, for example). The deviations did suggest, however, a possible modification of the basic corresponding

states relationships, (15)-(16), by the inclusion of a term X(p, T). The form of X was deduced by observing the behaviour of the transport coefficients according to the modified Enskog theory (MET). Our final equations for a pure fluid, a, and for a mixture, x, are (43) and (44), and

(50) and (51) for the viscosity coefficient and thermal conductivity coefficient, respectively. Note that the calculation of the transport coefficients for a given fluid require corre- sponding values for a reference fluid and thermodynamic

data only. Hence out method is predictive in the sense that transport data of the given fluid are not needed.

With methane as a reference fluid, we calculated the vis- cosity and thermal conductivity coefficients of nitrogen,

ethane, propane, butane, and carbon dioxide and for mixtures of these fluids. Typical results are given in Tables 3—11. Although transport data for mixtures are limited, the results show we have tested our method over a wide

range of experimental conditions, including the dense

liquid, and we have predicted consistently the data to within the experimental error.

We are very grateful to R.D. McCarty for his considerable help with the equation of state calculations needed in this study. The work was supported by the Office of Standard Reference Data.

References

1 Hitschfelder, J.O., Curtiss, C.F., Biid, R.B. Molecular Theory

of Gases and Liquids, 2nd edn (Wiley, NY, 1964) 617

2 See, for example, Reid, R.C., Sherwood, T.K. The Properties of Gases and Liquids (McGraw-Hill, NY, 1966) Ch 9 and 10, and references therein

650

K-8

CRYOGENICS . NOVEMBER 1976
Table 10. Thermal conductivity of a methane-n-butane

mixture Comparisons between thermal conductivity data from

reference 25 and the predictions from (51) for a CH4

{39.4%)-n-C4Hio(60.6%) mixture at 277.6 K. For this mixture'^ T" ^ 390 K, p"^ ^ 6.25 mole 1"',

X(exp), X(calc),

P.mole r' mW m"' K"'

12.26 99.00 95.33 (92.50)* 12.49 101.46 99.63 (96.61)

13.01 113.39 109.99 (106.5) 13.25 114.90 115.05 (111.3)

* From extended corresponding states.

Table 11 Thermal conductivity of a nitrogen-ethane mixture Comparison between thermal conductivity data from ref- erence 26 and the predictions from (51 for a nitrogen

(59.8%)-ethane (40.2%) mixture at 348.16 K. For this mixture. * 7^ ^ 260 K, p'^ - 12.0 mole r'.

X(exp), X(calc), P

mole r' mW m"' K"'

7.34 46.0 46.11 (61.5)* 10.16 55.2 54.69 (72.65) 13.75 70.3 69.47 (92.4) 16.43 85.4 84.44 (113.0)

* From extended corresponding states.

3 Preston, G.T., Chapman, T.W., Prausnitz, J.M. Cryogenics 7 (1967) 274

4 Mo, K.C., Gubbins, K.E. Chem Eng Commun 1 ( 1 974) 281

Molecular Physics (forthcoming)

5 Longuet-Higgins, H.C. Proc Roy Sac (London) A205 (1951) 247

6 Leiand, T.W., Chappelear, P.S., Gamson, B.W. AlChE J 8

( 1962) 482; Leach, J.W., Chappelear, P.S., Leiand, T.W.

Proc Am Petrol Inst 46 (1966) 223

7 MoUerup,J., Rowlinson, J.S. Chem Eng Sc 29 (1974) 1373

8 Pitzer, K.S., Curl, R.F. Thermodynamic and Transport

Properties of Fluids, (Inst of Mech Eng, London, 1958) 1 9 Haile, J.M., Mo, K.C., Gubbins, ICE. Cryogenic Eng Conf

(1975); Gubbins, K.E. private communication

10 Hanley, H.J.M., McCarty, R.D., Haynes,W.M. Cryogenics

15 (1975) 413

11 Goodwin, R.D. NBS Tech Note (US) No 653 (1974)

12 Mollerup, J. Advances in Cryogenic Engineering 20

(Plenum Press, NY) 172

1 3 Hanley, H.J.M., McCarty, R.D., Haynes, W.M. J Phys Chem

RefData 3 (1974) 979

14 Hanley, H.J.M., McCarty, R.D., Cohen, E.G.D. Physica 60

(1972) 322

15 Hanley, HJ.M.,Prydz,R. 7 C/jem^e/flafa 1 (1972) 1101

1 6 Hanley, H.J.M., Cohen, E.G.D. Physica 83 A ( 1 975^ 2 1

17 Huang, E.T.S., Swift, G.W., Kuiata, F. AIChE J \i (1967) 846

18 Hicks, CP., Young, C.L.C;jemi?ev 75 (1975) 119

1 9 Dolan, J.P., Ellington, R.T., Lee, A.L. J Chem Eng Data 9

(1964) 484; 'Monograph on API Research Project 65, Viscosity of light hydrocarbons', [Lee, A.L. (ed)] 20 Golubev, LF. Viscosity of Gases and Gas Mixtures, (Israel Programme for Scientific Translations, Jerusalem. 1970)

2 1 Gerf, S.F., Galkov, G.I. Zhur Tekh F/z 11 ( 1 94 1 ) 80

22 Haynes, W.M. Physica 70 (1973) 410

23 Hanley, H.J.M., Gubbins, K.E. (forthcoming); data available from the Cryogenics Division, NBS, Boulder 24 Sengers, J.V., Hanley, HJ.M., Ely, J.F. Proc 14th Int Conf

Thermal Conductivity (Pergamon Press, NY, 1976)

25 Carmichael, L.T., Jacobs, J., Sage, B.H. J Chem Eng Data 1

(1968) 489

26 Gilmore, T.F., Comings, W.E. AIChE 712(1 966)1172

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CRYOGENICS . NOVEMBER 1976 K-9

651

FRACTURE MECHANICS PARAMETERS FOR A 5083-0

ALUMINUM ALLOY AT LOW TEMPERATURES

R. L. Tobler and R. P. Reed

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

The fatigue crack growth and fracture resistance of a 5083-0

aluminum alloy plate were investigated at four temperatures in the

ambient-to-cryogenic range -- 295, 111, 76, and 4 K. J-integral test

methods were applied using compact specimens 3.17 cm thick, and the

value of J required to initiate crack extension (Jj^) is reported as

an index of fracture toughness. The fracture toughness was orientation

dependent, with anisotropy accounting for Jj^ variations of up to a

factor of 2. For specimens having fracture planes parallel to the

rolling direction, Jj^ increases progressively from 9 to 25 kJm as

temperature decreases between 295 and 4 K. In contrast, the fatigue

crack growth rates (da/dN) are insensitive to specimen orientation.

The fatigue crack growth rates at cryogenic temperatures are up to 10

times lower than in air at room temperature, but are virtually constant

between 111 and 4 K. These results should be useful in fracture

mechanics analyses of cryogenic structures, including liquified natural

gas tankers.

Key words: Aluminum alloys; cryogenics; crack propagation; fatigue;

fracture; low temperature tests; mechanical properties.

tContribution of NBS, not subject to copyright.

L-1
INTRODUCTION

The aluminum alloy designated 5083-0 is strengthened by solid

solution additions of magnesium and used in the annealed condition.

Excellent formability, weldability, toughness, and relatively low cost

are some advantages that make this alloy an attractive low temperature

structural material. Applications include storage and transport tanks

for cryogenic fluids. Currently, thousands of tons of 5083-0 alloy are

destined for use in liquefied natural gas (LNG) tankers at service temperatures as low as 111 K. Emerging applications may include structural

components for superconducting machinery. These structures are costly,

and in the case of LNG tankers, the transported cryogen is flammable.

Design engineers and regulatory agencies therefore require efficient

and fail-safe design.

Extensive mechanical property data exist for 5083-0 aluminum [1-7].

Between room and liquid helium temperatures (295 to 4 K), the yield and

ultimate strengths increase by 25% and 70%, respectively, with most of

the improvement occurring at lower temperatures [2]. Ductility also

improves at low temperatures, and precracked specimens retain the ability

to deform prior to fracture. Nevertheless, quantitative fracture toughness data for this alloy are lacking. Several attempts to measure the

critical stress intensity factor, Kj^, have been unsuccessful. As defined

by the ASTM testing method for plane strain fracture toughness of metallic

materials (ASTM E 399-74), the parameter Kj^ applies to linear-elastic

loading behavior. Kaufman, Nelson, and Wygonik [3] showed that 5083-0

alloys in section thicknesses up 20 cm remain sufficiently plastic to

invalidate direct K.^ measurements.
This study employs an alternative approach to fracture toughness

characterization. The method is based on Rice's formulation of the

J-integral [8], which is the rate of change of potential energy with

respect to crack area. In applications of the J-integral, Begley and

Landes identify a parameter denoted Jj^ which, unlike Kj^, can be measured under nonlinear-elastic conditions [9,10]. Since experimental

results for aluminum alloys support the hypothesis that Jj^ is a material constant [11,12], the J-resistance curve test method [10] was

applied here to a 5083-0 aluminum plate. The Jj^ values and fatigue

crack growth rates reported in this study should assist fracture

mechanics analyses of 5083-0 structures at temperatures in the ambientto-cryogenic range.

PROCEDURES

Material and Specimens

A 4.32 cm thick 5083-0 aluminum alloy plate was obtained from a

commercial source and tested in the as-received condition. The microstructure is shown in Figure 1. The ASTM specification B 209-66 gives

the chemical composition of this alloy in wt% as: 4.0-4.9 Mg, 0.3-1.0

Mn, 0.05-0.25 Cr, 0.4 max. Si, 0.4 max. Fe, 0.10 max. Cu, 0.25 max. Zn,

0.15 max. Ti , and 0.15 max. of other impurities.

After machining 0.44 cm of metal from each surface of the stock

plate, 3.17 cm thick compact specimens were fabricated with the geometry

shown in Figure 2. The specimen width, W, was 7.62 cm. The width-tothickness ratio, W/B, was 2.4. Knife edges were machined integral to

the notch to enable clip gage attachment and deflection measurements at

the loadline. Most of the specimens were machined in the TL orientation (fracture plane normal to the long transverse direction), but

L-3
several specimens of the LT orientation (fracture plane normal to the

longitudinal or rolling direction) were also tested.

Tensile tests of unnotched, longitudinally-oriented specimens

were performed at room and liquid nitrogen temperatures, following

ASTM Method E 8-69. Two tests were performed at each temperature. The

yield and ultimate strengths, elongation, and reduction of area results,

shown in Table 1, agree with other data for similar 5083-0 products [13]

Fatigue Crack Growth

A 100 kN servo-hydraulic test machine adaptable for cryogenic

service was used in all fatigue and fracture tests. Room temperature

tests were conducted in unconditioned air at a relative humidity, H, of

approximately 30%. Low temperatures were achieved by enclosing the load

frame, specimen, and clip gage in a dewar of liquid helium (4 K), liquid

nitrogen (76 K), or nitrogen gas (111 + 4 K) . The low temperature

apparatus and techniques were previously described [14,15]. The clip

gage satisfied ASTM Method E 399-74 linearity requirements, and its

sensitivity changed by no more than 5% over the temperature range

investigated.

The compact specimens were precracked at their test temperatures

1 II using maximum fatigue stress intensity factors of from 10 to 22 MPa^m

The minimum- to-maximum load ratio, R, was 0.1. Some fatigue crack

growth rates were measured during precracking, but additional rates at

relatively high stress intensity factors or R values were measured

using specimens not intended for J-tests. All precracking and fatigue

crack growth tests used sinusoidal ly-varying loads at a frequency of

20 Hz.

A correlation between crack length (a) and specimen compliance

L-4
(deflection per unit load, 6/P) was established using measurements

from fractured specimens. Crack length was defined as the average of

three measurements at the middle and quarter points of specimen thickness. The fatigue tests were then interrupted periodically to record

compliance, and the inferred crack length was plotted as a function of

load cycles, N. The fatigue crack growth rates, da/dN, were calculated

by graphical differentiation of a-versus-N curves, while the corresponding stress intensity factor ranges, AK, were calculated from the maximum

and minimum fatigue loads:

According to ASTM Method E 399-74,

f(a/W)=29.6(a/W)^/2.^85.5(a/W)3/2+655.7(a/W)^/2-1017.0(a/W)^/^638.9(a/W)^/^ (2)

The uncertainty in crack growth rates is estimated at less than + 25%.

Fracture Toughness

At each test temperature, a series of specimens having similar precrack lengths were loaded to selected deflections at the stroke rate of

0.05 mms ^. These loadings were sufficient to cause stable crack extensions of up to 0.25 cm. Each specimen was then unloaded and refatigued

using cyclic loads no greater than 70% of the maximum static load. After

the refatigue crack was propagated several millimeters, the specimens

were fractured into halves by a single loading.

The fracture surfaces showed, in succession: (1) a precrack zone,

(2) a crack extension increment due to static loading, and (3) a refatigue

L-5
crack zone. The relatively coarse and less reflective increment of static

crack extension was measured to the nearest 0.003 cm with a traveling

microscope at the center and quarter points of specimen thickness,

the three-point average being defined as Aa. The corresponding values

of J were calculated for each test, using the approximate solution for

deeply cracked compact specimens [16]:

J

= 2A/Bb. (3)

Here, A is the total area (energy) under the test record up to the point

of unloading, and b is the original ligament depth (b = W - a). The

uncertainty in J measurements was not greater than + 2%.

To obtain critical J values, the resistance curves of J-versus-Aa

were back-extrapolated to Aa = 0.005 cm. In tests of a 2219-T6 aluminum

alloy. Read and Reed [12] suggested that defining Jj^ at 0.005 cm crack

extension leads to reproducible results. The uncertainty in the Jj^

values obtained in this way for 5083-0 aluminum is estimated at + 15%.

RESULTS AND DISCUSSION

Fatigue Crack Growth

Fatigue crack growth data at 4, 76, 111, and 295 K for 5083-0

aluminum specimens of the TL orientation at R = 0.1 are shown in Figure 3.

The results span two orders of magnitude from 5 X 10'^ mm/cycle to 2.5 X _3

10 mm/cycle. For a given AK value, the rates of crack growth at 111,

76, and 4 K are equivalent within the degree of scatter among replicate

tests. However, the rates at room temperature are up to 10 times faster

than the rates at cryogenic temperatures.

L-6
As plotted on logarithmic coordinates, the low temperature fatigue

crack growth data describe an approximately linear trend over the entire

AK range, whereas the room temperature data do not. The linear approximation to the data at 111, 76 and 4 K, shown in Figure 3, is consistent

with a Paris equation of the form:

1 /2

Here da/dN (mm/cycle) is a power law function of AK (MPa^m ' ). The

constants C and n correspond to the ordinate intercept at AK = 1, and

the slope, respectively. A graphical solution for the equation of the

line drawn through the 111, 76 and 4 K data yields:

^ = 1.3 X 10"''°(AK)^'2.

The room temperature data fail to conform to a single power-law

equation, due to the appearance of a "shoulder" on the da/dN-versus-AK

1 /2

plot at AK values between 10 and 15 MPa^m '

. This shoulder brings the

room and low temperature crack growth rates into closer agreement at

higher AK values. Consequently, the room temperature fatigue crack

growth resistance is only slightly inferior at stress intensity factor

1 /2

ranges greater than 15 MPa^m

Figure 4 shows additional crack growth data for the TL orientation

at 295 and 111 K (R = 0.3), as well as data on specimens of the LT

orientation at 111 K (R = 0.1). Scatterbands representing the data of

Figure 3 are superimposed on Figure 4 for comparison. This comparison

indicates that the change in R from 0.1 to 0.3 had no effect on the
room temperature fatigue crack growth rates, whereas, at 111 K, this

change increased the rates by nearly a factor of 2. Also the data

obtained for specimens of the LT orientation at 111 K fall within the

band for TL orientations for the same stress ratio, R = 0.1. Thus,

specimen orientation has no measureable effect on fatigue crack growth

rates. Kaufman and Kelsey [17] also noted relatively isotropic fatigue

crack growth in their tests of a 5083-0 aluminum alloy.

Comparisons of fatigue crack growth data reported in the literature

for compact specimens of 5083-0 aluminum are shown in Figures 5 and 6.

Although these data show considerable variance, most results can be

rationalized in terms of the different test variables and procedures.

Usually, higher R values lead to increased fatigue crack growth rates.

Other significant factors to be considered include the procedure used

to obtain a-versus-N data, and the relative humidity at room temperature

In reference to Figures 5 and 6 note first that the present study

yielded somewhat lower rates at a given AK value as compared with other

investigations ['^,17-19]. In our study, the crack length was defined as

an average of rreasurements at the center and quarter points of thickness

Other studies used measurements of the crack at specimen edges. In our

study the edge crack lengths were typically 5 to 8% shorter than the

average crack lengths. If edge crack lengths had been used, the f(a/W)

values of Eq. (1) would have been reduced, and the AK value for a given

growth rate would have been 10 to 17% lower than actually reported.

This would shift the bands of Figures 5 and 6 into good agreement with

the bulk of previously published results.

As shown in Figure 5, at least three other laboratories report a

shoulder in roor temperature fatigue crack growth rates [17-19]. This

L-8
shoulder occurs at rates near 3 X 10" mm/cycle, for tests conducted

in air with appreciable moisture contents. Kelsey, Nordmark and

Clark's [4] room temperature results at 90% relative humidity and

R = 0.33 are nearly in agreement with Argy, Paris, and Shaw's [18]

results at 50% relative humidity and R = 0.4. However, as the relative humidity is decreased to less than 10%, the shoulder is eliminated

and fatigue crack propagation resistance at low AK is improved. Note

in Figure 5 that the overall agreement of data is better at high AK

values where differences in relative humidity are less influential.

Deleterious effects on the fatigue crack growth resistance of this

alloy due to moisture are not surprising in view of the trends exhibited

by other aluminum alloys [20]. Hartman and Schijve's [21] data for a

7075-T6 alloy derr.onstrate trends analogous to the behavior indicated in

Figure 5. In dry air, their logarithmic plots of da/dN-versus-AK display

-5 -3

a linear trend for growth rates in the range 10 to 10 mm/cycle; in

moist air (relative humidity = 45%), a shoulder appears in the data

1 /2

at AK - 15 MPaTn , and the rates at lower AK are accelerated by up

to a factor of 10. Again, the rates at high AK are not sensitive to

moisture.

Thus, the effects of moisture on the room temperature fatigue crack

growth behavior of 5083-0 and 7075-T6 alloys are remarkably similar.

The trend of the Kelsey et al . [4] data for 5083-0 aluminum in a dry

air environment probably represents the true trend of room temperature

results when moisture effects are practically eliminated. Note from

Figures 5 and 6 that the rates reported by Kelsey et al . [18] for tests

in dry air at 295 K are nearly equivalent to but slightly faster than

their rates at 76 K. Based on these observations, it may be concluded

L-9
that moisture effects at 295 K are predominant, and temperature variations between 295 K and 4 K intrinsically have little effect on the

fatigue crack propagation resistance of 5083-0 aluminum. This is consistent with results for other face-centered cubic alloys which show

only modest improvements of fatigue crack growth resistance at low

temperatures [22].

Fracture Toughness

Plasticity and stable crack extension caused nonlinearity in the

fracture test records at all temperatures, and unstable cracking was

never observed. As expected, the linearity requirements of sections

9.1.2 and 9.1.5 of ASTM Method E 399-74 could not be satisfied using

our specimens of aluminum alloy 5083-0, so it was appropriate to conduct J-integral tests. Table 2 lists the J-integral test results for

both the LT and TL specimen orientations.

Resistance curves (J-versus-Aa graphs) for the TL orientation are

shown in Figure 7. The results at 295, 111, 76, and 4 K show that

higher J values are required for a given crack extension as temperature

decreases. The Jj^ values obtained at Aa = 0.005 cm progressively

_2 increase from 9 to 25 kJm between 295 and 4 K. Moreover, the rate

of increase of J with respect to Aa is greater at 111, 76, and 4 K

than at room temperature. Thus, greater energy is expended in fracture

initiation and propagation at cryogenic temperatures. Kahn-type tear

and dynamic tear tests render a similar conclusion [5-7, 23].

Figure 8 compares the J-resi stance curves for the TL and LT orientations at 111 K, demonstrating the anisotropy of fracture toughness

for this alloy. Based on these curves, Jj^ for the LT orientation is

_2 approximately 39 kJm at 111 K, or twice the value for the TL orientation. The superiority of the LT orientation in comparison with the TL

L-10
orientation is typical of many alloys, and the tear test results

and projected Kj^ values reported by Kaufman et al. [3,5,6] indicate

a similar orientation dependence for 5083-0 aluminum.

The fracture anisotropy is also evident in Figure 9, which shows

TL and LT specimens that were tested at 111 K. The LT specimen was

fatigue cracked and fractured in a single loading. The TL specimen

was used in a J-test, and it shows an increment of crack extension, Aa,

located between two fatigue cracks. The LT specimen displays shear fracture portions ar.ounting to 30% of specimen thickness; delaminations are

also visible at mid-thickness. In comparison, the TL specimen exhibits

a flat fracture mode requiring less energy for crack extension. The

fracture surface appearance of the TL orientation was not significantly

influenced by test temperature.

The Jj^ data listed in Table 2 can be used to estimate Kj^ values

by using the equation:

2

1 - V

In this equation, E is Young's modulus of elasticity and v is Poisson's

ratio. The values of E and v at temperatures between 295 and 4 K are

known from Naimon, Weston, and Ledbetter's study [24]. The Kj^ estimates

based on these data at 295, 111, 76 and 4 K are plotted in Figure 10,

along with the corresponding Jj^ values.

As shown in Figure 10, the Kj^ estimates converted from Jj^ data

1 /2

range from 27.0 to 60.2 MPa*m ' , depending on temperature and specimen

orientation. For the TL orientation, the Kj^ estimates at 295 and 76 K

1 /2 are 27.0 and 43.4 MPa*m '

, respectively. These are lower than Kaufman

L-11
and Kelsey's [17] projected Kj^ estimates of 49.5 MPa-m ' at 295 K

1 II

and 55 MPaTn at 77 K. Kaufman and Kelsey's Kj^ estimates also pertain to specimens of the TL orientation, but their K calculations are

based on the maximum load observed in fracture tests. Their procedure

does not account for the fact that crack extension occurs prior to

maximum load.

Finally, it should be noted that Merkle and Corten's method [25]

of J calculation could have been used in this study. When applied to

the 5083-0 aluminum experiments described in the text, that method

amounts to replacing the coefficient 2 in Eq. (3) by higher factors

from 2.2 to 2.3. The Jj^ values would have been increased by about

10%; the Kj^ estir.ates, by 5%. Read and Reed [12] found from measuring

both Kt and J. at 76 K for the aluminum alloy 221^-T87 that Jr as

Ic Ic ^ Ic

calculated from the measured Kj^ was about 40% greater than the measured Jj^. Thus, the Jj^ data and Kj^ estimates reported here for

5083-0 may be considered conservative.

SUMMARY AND CONCLUSIONS

The fatigue crack growth behavior and J-integral fracture toughness

of a 5083-0 aluminum alloy have been investigated at 295, 111, 76 and

4 K, a wider range of temperatures than previously studied. Specifically

1. Fatigue crack growth resistance at 111 K was insensitive to

specimen orientation, but improves at decreasing R ratios.

2. Although the fatigue crack growth rates in ambient air at room

temperature exceed the rates at cryogenic temperatures by up to a factor of 10, the rates between 111 and 4 K are nearly equivalent. The

high rates in ambient air can be attributed to the presence of moisture,

rather than temperature effects per se.

L-12
3. Results for the TL orientation at decreasing temperatures

between 295 K and 4 K indicate nearly a three-fold increase of J, •' Ic

from 9 to 25 kJm"^.

4. Anisotropy in rolled plate caused a Jj^ variation of a least

2:1 at the LNG temperature of 111 K.

5. In view of the favorable low temperature effects on tensile,

fatigue, and fracture properties, it is apparent that the structural

reliability of flawed or unflawed 5083-0 alloy components will not be

decreased by cryogenic temperatures.

ACKNOWLEDGMENTS

This work was sponsored by the Maritime Administration and the

Advanced Research Projects Agency of the U.S. Department of Defense.

The authors gratefully acknowledge the assistance of R. L. Durcholz

and Dr. R. P. Mikesell in conducting the tensile tests. We also wish

to thank Dr. R. A. Kelsey of the Alcoa Technical Center for reviewing

the manuscript.

L-13
REFERENCES

1. Properties of Materials for Liquefied Natural Gas Tankage, ASTM STP

579, Amer. Soc. Test. Mater., Philadelphia, 1975, pp. 1-204.

2. Rice, L. P., Campbell, J. E., and Simmons, W. F., in Advances in

Cryogenic Engineering, Vol. 8, 1963, pp. 671-677.

3. Kaufman, J. 6., Nelson, F. G., and Wygonik, R. H., in Fatigue and

Fracture Toughness -- Cryogenic Behavior, ASTM STP 556, Amer. Soc.

Test. Mater., 1974, pp. 125-158.

4. Kelsey, R. A., Nordmark, G. E., and Clark, J. W., in Fatigue and

Fracture Toughness -- Cryogenic Behavior, ASTM STP 556, Amer. Soc.

Test. Mater., 1974, pp. 159-185.

5. Kaufman, J. G. , Nelson, F. G., and Wanderer, E. T., Mechanical Properties and Fracture Characteristics of 5083-0 Products and 5183

Welds in 5083 Products, Proceedings of the International Congress

of Refrigeration, Washington, D.C., Vol. 1, 1971, pp. 651-658.

6. Nelson, F. G., Kaufman, J. G., and Wanderer, E. T., Tear Tests of

5083 Plate and of 5183 Welds in 5083 Plate and Extrusions, Paper D-1

in Adv. in Cryo. Eng., K. D. Timmerhaus, Ed., pp. 91-101.

7. Judy, R. J., Jr., and Goode, R. J., Fracture Resistance of Thick

Plate 5083-0 Alloy, Report of NRL Progress, December 1974, pp. 36-38

8. Rice, J. R., J. Appl . Mechs., Trans. ASME, Vol. 35, 1968, pp. 379-386

9. Begley, J. A. and Landes, J. D. , in Fracture Toughness, ASTM STP 514,

Amer. Soc. Test. Mater., 1972, pp. 1-39.

10. Landes, J. D. and Begley, J. A., in Fracture Analysis, ASTM STP 560,

Amer. Soc. Test. Mater., 1975, pp. 170-186.

L-14
11. Griffis, C. A. and Yoder, G. R. , Application of the J-Integral to

Crack Initiation in a 2024-T351 Aluminum Alloy, Naval Research

Report 7676, 1974, pp. 1-25.

12. Read, D. T. and Reed, R. P., Effects of Specimen Thickness on Fracture Toughness of Some Aluminum Alloys, submitted to Int. J. Fract.

(1976).

13. Bogardus, K. 0. and Malcolm, R. C, in Ref. 1, pp. 190-204.

14. Fowlkes, C. W. and Tobler, R. L., Fracture Testing and Results for

a Ti-6A1-4V Alloy, Eng. Fract. Mechs., to be published.

15. Tobler, R. L., Mikesell, R. P., Durcholz, R. L., and Reed, R. P.,

in Ref. 1, pp. 261-287.

16. Rice, J. R. , Paris, P. C, and Merkle, J. G., in Progress in Flaw

Growth and Fracture Toughness Testing, ASTM STP 536, Amer. Soc.

Test. Mater., 1973, pp. 231-244.

17. Kaufman, J. G. and Kelsey, R. A., in Ref. 1, pp. 138-158.

18. Argy, R., Paris, P. C, and Shaw, F., in Ref. 1, pp. 96-137.

19. Person, N. L. and Wolfer, G. C, in Ref. 1, pp. 80-95.

20. Wei, R. P., Eng. Fract. Mechs., Vol. 4, 1970, pp. 633-651.

21. Hartman, A. and Schijve, NLR Tech Note No. MP 68001 U, 1968; see

also Fig. 11 of Reference 17.

22. Materials Research in Support of Superconducting Machinery, Vols.

Ill, IV, and V, Reed, R. P., Clark, A. F., and van Reuth, E. C.

,

Eds., National Bureau of Standards, Boulder, CO.

23. Zinkham, R. E. and Ashton, R. F., in ASTM STP 579, Ref. 1, pp. 159-175.

24. Weston, W. F., Naimon, E. R., and Ledbetter, H. M. , in Ref. 1,

pp. 397-420.

25. Merkle, J. G. and Corten, H. T., "A J-Integral Analysis for the Compact

Specimen, Considering Axial Force as Well as Bending Effects," presented at the Pressure Vessels and Piping Conference with Nuclear

Engineering and Mechanical Divisions, American Society of Mechanical

Engineers, Paper No. 74-PVP-33, 1974.

L-15
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OJ CO CM

CO (O 00 s- O OJ C3V—» -—. -—

ID > c •>- CM If) fO OJ fco S- s- ^ 00 00 o -t-J «

ID <X)

»+- oo

«/> c OJ -M O -M r— • r~" 3 +-> E in ^ CM

to ra •1- Q_ o O CU -M *-> S ro

s- c

O) +J ss- o

a>Q.r- O fO

s_ c -M Q.T- C7) C

QJ O) -i- UD 1^ o 1— -M S- (/I «-> ^ O (/I cn CO CM CM c c

OJ o -o 1— 1—

>- r3 CM

O V£) tn CO

(U CM !a o *o

OJ

i-

—

O ro CO

13 Ll. CM

-(-> c ro

ro 1 S-OJ^ LD <£)

cr> 1— CM
Table 2. J-integral test results.

Temperature KTmax Specimen Orientation a/W Aa J

_

1 /9 cm cm , , -2

295 13 TL

28 TL

9 TL

8 TL

31 TL

7 TL

14 TL

111 2 LT

3 LT

4 LT

5 LT

111 30 TL

20 TL

22 TL

10 TL

11 TL

76 20 TL

17 TL

19 TL

16 TL

14 TL

9 TL

4 15 TL

11 TL

10 TL

17 TL

16 TL

18 TL

14 .642 .010 10.3

21 .647 .020 15.8

1 ^ fid? . y on 1 91 . OCKJ . UoD cc . y

1 <j . fid! OH 1 nt; Q 97 C C./ .0

1 ^ . OHH

22 .611 .109 41.6

16 DD . D 18 fil ? ^0. DH 9. C 18 . U J vJ fin Q

18 fil Q 7A n

19 .622 .010 23.6

13 .630 .023 36.4

14 fil 7 . UJO 1 20 / 0 . D 20 fil 7 199 /I

1 5 . fi?Q u c 7 . mU 1 nu 97 Q

Id fi?? m Q "^l 9

16 .631 .026 40.5

14 .633 .039 54.7

17 .628 .083 72.5

21 .632 .093 77.3

19 .602 .003 13.7

18 .597 .003 17.6

20 .608 .010 30.2

19 .602 .019 38.3

18 .602 .030 47.3

18 .597 .056 61 .4

L-17
St

L-longitudinal or roiling direction

T-long transverse direction

S-short transverse or plate thickness direction

Figure 1. Microstructure of 5083-0 after rolling and annealing, lOOX.

L-18
Figure 2. Compact specimen used in fatigue and fracture tests (thickness,

B = 3.17 cm; dimensions are in cm).

L-19
2 5 10 20 50 100

STRESS INTENSITY RANGE, AK, MPa m'^

Figure 3. Fatigue crack growth rate results for TL orientations at

295, m, 76 and 4 K.L-20
2 5 10 20 50 100

STRESS INTENSITY RANGE, AK, MPa m!^

Figure 4. Fatigue crack growth rate results at 295 and 111 K, showing

the effects of orientation and R ratio variations.

L-21
Kaufman [l7j

R=0.33

H=90%

H=10%-

Person [19]

R=0, H=?

Argy [is]

Hs50%

R=0.4

" R=0.05

Kelsey [4]

R=0.33, H= 10%

This Study

5083-0 ALLOY

Room Temperature

2 5 10 20 50 100

STRESS INTENSITY RANGE, AK, MPa m'/'

ure 5. Comparison of fatigue crack growth data at 295 K.

L-22
2 5 10 20 50 100

STRESS INTENSITY RANGE, AK, MPa m'/'

Figure 6. Comparison of fatigue crack growth data at low temperatures.

L-23
.02 .04 .06 .08 .10 .12

AVERAGE CRACK EXTENSION, Aa, cm

Figure 7. J-integral resistance curves for 5083-0 aluminum, showing

the effect of temperature.

L-P4
.02 .04 .OS .03 .10 .12

AVERAGE CRACK EXTENSION, Aa, cm

Figure 8. J-integral resistance curves for 5083-0 aluminum at

111 K, showing the effect of orientation.

L-25
Fracture appearance of LT (left) and TL (right) specimens

tested at 111 K.

L-26
__l i L i I 100 200 300

TEMPERATURE, K

Figure 10. Temperature dependences of Jj^ data and Kj^ estimates.

L-27

Ship Steel Weldments for

Low Temperature Service

Cooperation among shipyards, regulatory agencies and

steelmal<ers may lead the way to higher welding productivity

BY H. I. MCHENRY

A large fleet of tankers is under construction for the marine transport of liquefied natural gas (LNG). In LNG

ships, significant portions of the hull are cooled by the cryogenic cargo to temperatures ranging from 0 to -46 C. At these temperatures many ship steels exhibit

brittle behavior. Consequently, the U.S. Coast Guard

(Ref. 1), the American Bureau of Shipping (Ref. 2) and

comparable regulatory agencies around the world have

established strict requirements on the ship steels and

weld procedure qualifications for weldments subjected

H. I. MCHENRY is associated with the Cryogenics Division, National Bureau of Standards, U.S. Department of Commerce, Boulder Colorado 80302.

to low temperatures. To meet these requirements, shipyards generally employ low heat input, multipass

welding practices. As a result, welding productivity is being limited to a level far below the capability of the equipment and facilities. The Maritime Administration (MarAd) was advised of the increased costs of welding LNG ship hulls by the Welding Panel of the Ship Production Committee, a group of industry experts organized by the Society of Naval Architects and Marine Engineers to advise

MarAd on how to improve shipyard productivity. In their efforts to reduce the cost of ship construction, MarAd

requested the National Bureau of Standards to conduct a survey to establish the feasibility of improving

6 5 4 3

Engine Room Cargo Tanlis

Double Hull

Fig. 1 — Structural arrangement of an LNG ship hull (Ref. 3)

Reprinted from WELDING JOI RNAL, May 1976

M-1
the efficiency of welding ship steels for low temperature service. The survey included visits to the shipyards involved in LNG construction, to the appropriate

regulatory agencies, to the steel plate producers and to other companies engaged in fabricating structures for low temperature service. These visits clarified the problem and the rules, and provided a review of the tech- nology available for improving welding efficiency. The

survey has been completed and the results are presented herein.

Shipyard Practice

The LNG ships under construction in the United

States are approximately 280 m long, 42 m wide and 30

m deep and have a cargo capacity of 125,000 cubic

meters. The ships are double-hull vessels with trans- verse bulkheads dividing the ship into several cargo

bays as shown in Fig. 1 (Ref. 3). The cryogenic containment system fitted within each cargo bay consists of the cargo tank, the insulation and generally a secondary barrier to contain the LNG in case of tank failure. Thomas and Schwendtner (Ref. 4) have described

eight types of containment systems in use or under

consideration worldwide. In the U.S., three designs are under construction: The Conch free-standing prismatic tank, the Gazocean membrane prismatic tank

and the Kvaerner-Moss free-standing spherical tank. For each system, the insulation Is sufficient to permit

transport of the LNG at approximately -162 C and

atmospheric pressure with boil-off rates less than

0.25% per day.

The temperature environment within the hull is a

function of the ambient air and water conditions, the

effectiveness of the insulation system and the proximity of the cargo. For North Atlantic routes, the USCG

specifies that the design temperatures be based on

assumed ambient conditions of -18 C air, a 5 mph

(2.33 m/s) wind and still water at 0 C. The inner hull, the transverse bulkheads and the tank support struc- ture are the principal areas cooled by proximity to the cargo. Minimum design temperatures in these areas range from 0 C to -46 C. The coldest locations are the

inner side-shell above waterline and parts of the tank

support structure.

SImI S«l«ctlon

The chemistry, processing and testing requirements

of steels used in LNG ships being made in the U.S. are summarized in Table 1. These steel selections are generally in accordance with the proposed (1975) regulations of the International Maritime Consultive Organization (IMCO) as outlined in Tables 2 and 3. For temperatures below -10 C, fully killed, aluminum

treated, fine grain, C-Mn-Si steels are used. For temperatures below -25 G, the steel must also be

either normalized or quenched and tempered. The

most commonly used steels are the ABS ordinary

strength grades; ON is used for temperatures to -23 C, CS for temperatures to -34 C and V-051 for temperatures to -46 C. For high strength applications, ABS grade EH steel is commonly used for temperatures to -34 C and ASTM grade A537 Modified is used for temperatures to -46 0. Approximately 28,000 metric tons of steel are re- quired for the hull of a 125,000 cubic meters LNG ship.

The tonnage requirements for all grades of hull steel and for low temperature steels are summarized in Table

4. These data are indicative df the total usage of low

temperature steels and include significant tonnage

selected for improved toughness and used in parts of the ship not exposed to temperatures below 0 C.

Table 1 — Sp*clllcatlon« for StMl Platat Uaad In LNQ Ship Hulla(•)

Min. design temp, C

Composition, %

C, max Mn

Si

P, max

S, max

Al

Ni, max

Cr, max

Mo, max

Cu, max

Cb, max

V, max

Mech. properties;

Tensile, MPa (ksl) Yield, MPa (ksl) Elong. In 50 mm

Charpy impact: Test temp., C

Energy, mIn avg. J (ft-lb) Specimens

CN

-23

ABS 1972 Rules

0.23

0.6-0.9 0.1-0.35 0.05

0.05 0.02-0.06

Ordinary strength grades

CS V-051 -34 -46

ABS 1974 Rules

402-490(58-71)

24%

0.16

1.00-1.35 0.10-0.35

0.04

0.04 0.02-0.06

402-490(58-71)

235(34), min

24%, mIn

0.16

1.15-1.50 0.10-0.35

0.04

0.04

402 (58), min

245(35), mIn 24%, mIn

-51

27.5(20)transv.

3/plate

Higher strength grades

EH-36 A537-A,Mod.

-34 -46

ABS 1974 Rules ASTM 1970 Std

0.18 0.90-1.60

0.10-0.50

0.04

0.04

0.06 max

0.40

0.25

0.08

0.35 0.05

0.10

490-618 (71-90) 353 (51), mIn 22%, min

-40

34.3 (24) longit. 3/plat3

0.16

1.15-1.50 0.15-0.50

0.04 0.04

0.25

0.25

0.08

0.35

0.08

451 (65), min

314 (47), min

22%, min

-51

41.2 (30) longit. 3/plate

(a) Heat Treatment: all grades normalized. Deoxidatlon: all grades aluminum killed, line grain practice

M-2
W«ld Procedure Qualification

For service temperatures less than -18 C, the welding procedures must be qualified in accordance

with USCG and ABS requirements. Procedures are

specific for each base metal, filler metal and flux combination and must be established for each welding pro- cess and position. The joint edge preparation, preheat

and interpass temperatures, and other aspects of the procedure must be representative of the procedures

used in production. Generally, two qualifications are re- quired to cover the range of plate thicknesses: 9.5 < t < 19 mm and t > 19 mm. Test plates for these qualifications are usually 19 mm thick for the lower thick- ness range and the maximum thickness used in pro- duction for thicknesses greater than 19 mm. The test plates are oriented such that the weld axis is parallel to the rolling direction. The qualification requirements include the room

temperature tensile and guided bend tests specified by

ABS for all weld procedure qualifications plus a series

of Gharpy V-notch impact tests. The Charpy tests are conducted at 5.5 C below the minimum service temperature in accordance with ASTM A 370, using type A

specimens. The specimens are cut transverse to the weld axis with the notches normal to the plate surface. Three specimens are tested for each of the following

notch locations: centered in the weld metal; on the fu- sion line; and in the heat-affected zone (HAZ) 1, 3 and

5 mm from the fusion line. The impact specimen location requirements are summarized in Fig. 2. The averTabl* 2 — IMCO Raqulramanta for LNG Hull StMlt

Minimum design Plate thickness, Approved ABS

temp., T, C t, mm steel grades

T ^ 0 — Normal Practice 0>T^-10 . t<12.5 B 12.5<t<25.5 D

t>25.5 E -10>T>-25 t<12.5 D

t>12.5 E -25 > T > -55 — See table 3

age Charpy value must equal or exceed 27.5 J (20 ft- Ib); the minimum value for one specimen is 18.6 J (13.3

ft-lb).

Welding Proceesee and Consumables

Conventional shipyard welding practices are generally being used to fabricate low temperature steels; however, the heat inputs are restricted in order to meet

the Charpy impact requirements. Consequently, the deposition rates are far below the equipment capabilities. The principal welding processes are submerged

arc (SA), shielded metal-arc (SMA) and gas metal-arc

(GMA) welding. For flat position welds and horizontal

fillet welds, SA welding is the most efficient and reli- able process, and therefore is widely used on auto- mated panel lines. Both SMA and GMA welding are used for most of the other applications; the selection of one process over the other varies widely from yard to yard. Variations of these processes such as one-side

welding, gravity welding, tandem arc and 3 o'clock SA

welding are used in specific instances depending on

the capabilities of the shipyard. High heat input

processes such as the electroslag and electrogas pro- cesses are not approved by ABS for use on low temperature steels. A wide range of electrodes and fluxes are used to weld ship steels for low temperature service. For submerged arc welding, two approaches have been taken:

(1) use of a mild steel electrode and an alloy flux, or (2) use of an alloy electrode and a neutral flux. The mild

steel electrodes conform to AWS specification A5. 17-69

Class EM12K, and the alloy fluxes are of a proprietary

nature. The alloy electrodes, which contain 1 to 2% Mn,

0.1 to 0.5% Mo and 0.5 to 2.0% Ni, are welded with a

neutral flux suitable for multipass welding. For SMA

welding, the most common electrode is AWS E 8018-

C3 which contains 1% Ni. In some cases, E 7018 elec- trodes, which contain 0.5% Mo, are used for moderately low temperatures and E 8018-C1 electrodes,

which contain 2 to 2.75% Ni, are used for the lowest temperatures. Both solid and flux-cored electrodes are used for GMA welding. The solid electrodes are alloyed

with Mn, Mo and Ni for low temperature toughness and

Table 3 — IMCO Requirements for LNQ Hull Steels for Design Temperatures of -25 to -55C

Chemical CjOfWf^sition

C Mn SI S P

.16% 0.70- 0.10- 0.035% 0.035% max 1 .60% 0.50% max max

Optional additions:

Ni Cr Mo Cu Cb V 0.80% 0.25% 0.08% 0.35% 0.05% 0.10% max max max max max max

Heat Treatment: normalized or quenched and tempered

Deoxidatlon:

fully killed, aluminum treated, fine grain practice

Toughness requirements:

Temperature: 5 C below design temperature

Specimens: Charpy V-notch-transverse

Energy, min. avg: 27.5 J (20 ft-lb) No. of Tests: 3 from each plate

Centerline Of Weld

Fision Line HAZ, iRifli From Fusion Line HAZ, Sum From Fusion Line

HAZ, SMi Ftiin Fusion line

\ \ \ \ \

\ \ N \

si

T>12.7mni

/#f--;^

Fir T<t2.7niRi , Specimen Centerline At T/2

Fig. 2 — Charpy V-notch specimen locations for weld pro- cedure qualification (Ref. 1)

M-3
Table 4 — Usage of Low Temperature Steele In LNG Ship Hull*

Ship

design Gazocean Membrane

Prismatic Conch

Free standing

Prismatic

Kvaerner-Moss

Free standing

Spherical

Steel

All grades

ABSCS

ABS V-051

All grades

ABSCN

ABSCS

ASTM A678-A

All grades

ABSCN

ABSCS

ABS EH-36

ASTM A537{Mod)

Weldment

test temp., C

-34

-43

-23

-21 to -32

-45

-23

-33

-29

-51

Tonnage,

long tons Applications

29,573 Total hull plus scrap and spare

9,666 Inner bottom, web frames, gunwale, bilge

2,695 Inner side shell, transverse deck box

17,810 Midbody (hull less bow and stern) 6,058 Trans. Bulkhead, inner side shell, deck

4,602 Inner bottom, gunwale, bilge 418 Roll key

17,393 Midbody

1,408 Inner hull 1,602 Transverse bulkheads

1,515 Deck girders

1,185 Cylindrical tank support

the flux cored generally has a mild steel sheath and a

proprietary flux. Low heat input welding practices are necessary to meet the USCG impact requirements in the HAZ of low

temperature ship plate weldments. This poses a signif- icant productivity problem to the LNG shipyards be- cause deposition rate is proportional to heat input, and

their welding equipment is capable of far greater

deposition rates than are possible using the low heat in- put practices. Consider, for example, the welding pro- cedures that are representative for welding 19 mm

plate. For x-ray quality welds in steels such as ABS

grade B, the following conditions are recommended

(Ref. 5): Joint preparation: double V-groove with an 8 mm

root face

Backing weld: 850 A, 33 V, 16 in./min (6.8 mm/s),

105 kJ/in.

Finishing weld: 1150 A, 35 V, 13 in./min (5.5 mm/s),

186 kJ/in.

In contrast, 19 mm ship plate for low temperature ser- vice must be multipass welded with the heat input limits ranging from about 40 to 80 kJ/in. %0C to eoS'KJj'e iTi depending on the particular combination of steel grade

and service temperature. At heat input levels within this range, anywhere from 4 to 14 passes may be required

to weld 19 mm plate.

Two approaches to solving the productivity problem

are apparent: either change the weldment toughness

requirements or improve the tolerance of the base

metal to higher heat input welding practices. Changing

the rules is not a viable solution to the problem, be- cause strict requirements are appropriate for haz- ardous cargo such as LNG. In addition, the requirements have recently been adopted by IMCO as stan- dards acceptable to all major shipping countries. Thus,

any change in the existing requirements would probably be contingent upon agreement by both the USCG

and IMCO, certainly a long term proposition. The alter- native solution would be to make available an economical steel which, when welded using efficient pro- cedures, provides the required level of toughness. This

potential solution is attractive because it is based on

steelmaking technology and shipyard economics in- stead of international agreements. The feasibility of this solution is addressed in the next section.

Steelmaking Technology

Current steelmaking technology offers several methods for providing improved toughness at low

temperatures. The methods include alloying, rolling

practice, sulfide shape control and heat treating. The

extent to which the improvements are reflected in HAZ

toughness of high heat input welds is not well documented. Nevertheless, there exists reason to believe

that one or a combination of the available metallurgical treatments will permit higher heat inputs than currently

being used. Whether or not the improvement will be

economically justifiable depends on the cost incre- ment added to the price of the steel and the extent of the improvement. Because of the large tonnages in- volved, the added cost of an improved ship steel will likely be limited to a maximum of $20 to $60 per metric

ton (Mg), depending on the specific application.

Alloying

The use of additional alloying to improve ship steels

is severely constrained by steel pricing practices. Steel prices are comprised of a base price and extras for the

specification, plate dimensions and quantity. There are two base prices; the carbon steel base and the alloy

steel base, the latter of which is about 40% higher. The

carbon steel base price is applicable to all the steels used in LNG ship hulls. The American Iron and Steel

Institute (AISI) considers a steel to be an alloy steel when either (1) the maximum of the range given for the content of alloying elements exceeds one or more of the following limits: Mn, 1.65%; Si, 0.60%; Cu, 0.60%; or

(2) a definite range or a definite minimum quantity of any other element is specified to obtain a desired

alloyed effect (Ref. 6). The chemistry specification for ABS EH 36 shown in Table 1 is typical of the degree of alloying permissible in carbon steels. Notice that there are no minimum re- quirements on alloying elements such as Cr, Mo, Ni, V

and Cb. Thus, the steelmaker has flexibility on how best

to achieve the required tensile and impact properties.

These pricing practices preclude the use of 0.4 to 0.8%

Ni additions that are frequently specified for low

temperature applications by Japanese and European

shipbuilders. However, the transition temperature of

M-4
YIELD STRENGTH , MPa

10 20

CHANGE IN

TRANSITION TEMPERATURE, 1

C, N |8-1SF/ksi|

Si (6F/lisil

recipitates |Cb. V|

3-6F/lisil

Mn h4F/ksi|

Al (-22F/ksir , ^ VGrain Size (-8F/lisi)

+ 5

CHANGE IN

0 TRANSITION TEMPERATURE, C

Fig. 3 — Strength toughness vectors for structural steels (Ret. 7)

1 2 3

YIELD STRENGTH, ksi

ABS Grade EH36 Steel (.036% Cb]

Ail Tests At - 40°C

5k

oSMA, "Sff kJ/cnt

A SA, m kJ/cm

1 1 1 1 31

1 1 1 1 Weld Fusion 1 3 5 7 9 Base

Metal Line

DISTANCE FROM FUSION LINE, mm

60 S

40 «

C0

20 =

0 "

fig. 4 — Charpy toughness traverse tor Cb-treated EH-36 weldment (Ret. 10)

ship steels can be reduced by alloy adjustments within the AISI limits for carbon steels. As shown in Fig. 3, the

transition temperature is reduced by increasing the Mn

content and by lowering C, Si and N (Ref. 7). Microalloying with Cb or V is an economical ap- proach to providing strength and good low temperature properties in the base plate, and is currently used

in EH 36 and A537 Modified steels. Strengthening is pro- vided by a combination of reduced grain size and

precipitation hardening. The low temperature tough- ness is improved because of the small grain size — an improvement that is only partially offset by the precipitation hardening effect shown in Fig. 3. However, the HAZ toughness near the fusion line is adversely affect- ed by grain coarsening and further reduced by the strengthening effect of carbonitride precipitation (Refs.

8, 9). This embrittlement is almost always observed in simulated HAZ specimens, but is frequently not evi- dent in Charpy specimens taken from weldments. The

absence of embrittlement in high heat input weldments

such as shown in Fig. 4 suggests that the high tough- ness material surrounding the embrittled region substantially reduces the embrlttlenient (Ref. 10). It is not

clear at this time whether this can be attributed to an

averaging effect, i.e., the Charpy impact specimen

samples a composite of high and low toughness

material, or to a reduction of constraint provided by the

ductile material surrounding the embrittled region. In either case, it appears that the problem of Cb or V embrittlement in the HAZ may not be as significant in real weldments as suggested by some investigators (Refs.

8, 9) on the basis of simulated HAZ studies.

Inclusion Control Nonmetallic inclusions are an intrinsic constituent of

all steels. There are two main types of inclusions: (1) the indigenous inclusions which precipitate in the molten or

M-5
REM Frie

1 1 I \ \ \ I.M2 O.OOE 0.010

SULFUR GONTENT, wt. %

Fig. 5 — The effect of rare eartii metal treatments on the transverse shelf energy of low sulfur C-Mn steel (Ref. 12)'

solidifying metal due to decreased solubility of oxygen

and sulfur upon cooling, and (2) the exogenous inclu- sions which are introduced into the steel from materials such as the refractories which come in contact with the molten steel. The indigenous inclusions are far more numerous and predictable in their behavior than

the exogenous types, which occur sporadically. The

principal types of indigenous inclusions are oxides and

sulfides. In Al killed steels, the dominant oxide is AI2O3,

which precipitates as small refractory crystals that do

not agglomerate and do not change shape appreciably

during rolling operations.

The principal sulfide inclusion In C-Mn steels is MnS.

In low oxygen steels (e.g., Al killed), the MnS inclusions are quite plastic and tend to elongate during rolling.

These stringer shaped inclusions separate readily from

the steel matrix, and have a higher surface-to-volume

ratio and a shorter interparticle spacing than globular

inclusions. Consequently, the MnS stringers serve as

initiation sites for low energy fracture when the steel is loaded transverse to the direction of rolling. Sulfide shape control is rapidly emerging as a practical tool for eliminating stringers and thereby improving the transverse toughness of structural steels

(Ref. 11). The process generally consists of lowering

the sulfur content of the heat below 0.015% and then

adding elements to the melt which form refractory sulfides. The refractory sulfides take on a spherical shape

in the liquid steel and tend to retain this shape upon

solidification and during the rolling process. Several

elements, including Ti, Zr, Ca, Mg and the rare earth

metals, form refractory sulfides. Although practices vary widely, sulfide shape control by the ladle addition

of rare earth metal (REM) in the form of mischmetal, a mixture of rare earths containing about 50% Ce,

appears to be gaining favor. The rare earths are preferred over Ti and Zr because, in addition to shape control, an appreciable reduction in sulfur content occurs due to the solution of rare earth sulfides and oxysulfides in the slag. Calcium and magnesium are effective

for both sulfide shape control and sulfur reduction;

'Reprinted with permission of the Metallurgical Society of AIME.

however, Mg is difficult to introduce into molten steel because of its high vapor pressure; and Ca, which is not soluble in liquid iron, does not mix readily enough to assure complete sulfide shape control. The influences

of sulfur content and REM additions on toughness are shown in Fig. 5 (Ref. 12),

Rolling Practice

Significant toughness improvements can be obtained by altering the rolling practice. Cross rolling can improve transverse properties at a moderate increase

in steel cost; however, substantial improvements re- quire rolling ratios that approach unity. Steel specifications rarely include cross rolling requirements;

however, a guaranteed transverse Charpy requirement generally implies that cross rolling will be used. Thus, the principal use for cross rolling is to make

moderate improvements in transverse properties to assure conformance to a transverse toughness guarantee. Controlled rolling can improve strength and low

temperature toughness by substantially reducing the austenite grain size and the fineness and nature of the transformation products (Ref. 13). It involves a schedule of reductions at specified temperatures,

sometimes coupled with controlled cooling between

passes and after the final pass. Most commonly, controlled rolling is limited to performing the final reduction at a specified temperature which is lower than nor- mally employed. As shown in Fig. 6, the reduction

below 900 C causes a significant decrease in transition temperature. It is particularly useful for the production

of line pipe, where the large tonnage involved permits

optimization of the rolling schedules on an economical

basis. For ship steels, the large variety of plate sizes,

thickness and grades, and the lack of facilities for pro- ducing controlled-rolled plates greater than 16 mm

thick, limit the practicability of controlled rolling. In addition, the large variety of rolling schedules can lead

to more scatter In the material properties than is associated with more easily controlled procedures such as

normalizing. Due to these limitations, controlled rolling

is not considered practical for Improving the tough- ness of ship plate.

H«at Tr«atm*nt

Nearly all the ship steels used for low temperature (to -46 C) applications are normalized. The typical nor- malizing heat treatment involves heating the as-rolled

plate to 925 ± 25 C and air cooling to room temperature. As shown in Fig 7, the low temperature tough- ness of these steels could be improved by a quench

and temper (Q and T) heat treatment (Ref. 14). For CMn steels such as ship plate, Q and T involves heating

to 925 ± 25 C, quenching in water and subsequently

tempering at 650 ± 50 C. This heat treatment is nearly

twice as expensive as normalizing. Although Q and T

improves base plate toughness, it is not clear whether

this benefit will be apparent in the heat-affected zone of weldments. It is considered likely that the reheat treat- ment caused by the weld thermal cycle will impart the same toughness to the heat-affected zone regardless of prior heat treatment. Thus, the extra cost of Q and T

over normalizing, $30 to $40/metrlc ton (Mg), Is not considered a cost effective means of improving heataffected zone toughness.

M-6
Work In Progress

On the basis of the shipbuilding and steel industry survey. MarAd requested NBS to conduct a follow-on program in cooperation with the LNG shipbuilders to evaluate improved ship steels for low temperature service. In this program, the major steel companies are

providing the LNG shipyards with production heats of ABS steels, modified to possess improved transverse

fracture properties at the appropriate test temperatures. The shipyards will evaluate these steels by qualifying optimum weld procedures in accordance with the USCG requirements. A comparison of the optimized

procedures with those currently employed will be indicative of the cost reduction possible through the use of improved steels. As a result, each participating shipyard will be in a position to make a rational decision

regarding the cost effectiveness of premium quality

steels. The program, currently in the formative stages,

will be completed in mid-1977, and the results will be

published shortly thereafter.

Summary

A survey of the U.S. shipyards engaged in LNG ship

construction, the major steel plate producers and the maritime regulatory agencies has been conducted to establish the feasibility of improving the efficiency of welding ship steels for low temperature service. The results of this survey suggest that application of state-ofthe-art steelmaking technology can substantially im- prove the low temperature toughness of ship steels. A

program is being conducted to determine if steels with improved toughness retain satisfactory toughness in the HAZ when higher heat input welding practices are

used.

Acknowledgments

This work was sponsored by the U S Maritime Administration The author wishes to acknowledge the many contributions of M B. Kasen and R P Reed of NBS who collab- orated on all aspects of the program described herein The

author also expresses appreciation to R W Schaflran of the U S Maritime Administration and W C Brayton of Bethle- hem Steel Corporation who were responsible lor initiating the program.

References

TOTAL REDUCTION BELOW 900 C. \

Fig 6 — The effect of rolling reduction below 900 C on the fracture appearance transition temperature (Ret 13i'

TEMPERKTURE,

Fig 7 — Charpy impact transition curves for normalized and

for quenched and tempered CS steel (Ret 14)

1 USCG. U.S. Coast Guard Marine Engineering

Regulations. Subchapter F, CG-115. July 1970

2 ABS. Rules for Building and Classing Steel Vessels. American Bureau of Shipping. New York, 1974.

3. Emery II. W B.. Sterrett. E. L and Moore. C. S.. "Alaskan

Liquefaction Plant to Supply Gas for Japanese Use.' Oil and

Gas Journal. 66(1). 55-59.

4 Thomas. W D and Schwendtner. A. H.. 'LNG Carriers: The Current State of the Art." 1971 Annual New York Meeting,

The Society of Naval Architects and Marine Engineers. 1971

5. Anon. Submerged Arc Welding Handbook. Linde Refer- ence Library. Union Carbide Corp., New York. 1974

6 Anon., Alloy Steel Plates," American Iron and Steel

Institute. New York. April 1970

7. Cordea. J. N "Niobium-and Vanadium-Containing Steels

for Pressure Vessel Service," Welding Research Council

Bulletin No. 203, February 1975.

8. Hannerz. N. E.. "Effect of Cb on HAZ Ductility in Constructional HI Steels," Welding Journal. 54, (5) May 1975, Res.

Suppl., pp 162-s to 168-s.

9. Hannerz, N. E. and Jonsson-Holmquist, B. M., "Influence of V on the HAZ Properties of Mild Steel.' Metal Science

8 (1974) 228-233

10 Alia. B. L., Stern, I L. and Null. C . Toughness Evaluation of Electrogas and Electroslag Weldments. Project Report. The National Shipbuilding Research Program, U S

Maritime Administration. March 1975

11. Korchynsky, M.. The Relationships Between Sulfide Composition Morphology and Distribution on Mechanical

Properties of HSLA Steels, presented at the International Symposium on Sulfide Inclusions in Steel, American Society

for Metals, Port Chester, NY, November 1974

12 Kozasu, I and Osuka. T , 'Processing Conditions and

Properties of Control-Rolled Steel Plates, m Processing and

Properties of Low Carbon Steel. Gray, J M. (editor). The

Metallurgical Society of AIME. New York. 1973

13. Gray, J M.. "Columbium (Niobium) as a Gram Refiner in Hot Rolled Steels, " in Process/r7g and Properties of Low Car- bon Steel. Gray, J. M (editor). The Metallurgical Society of AIME, New York, 1973.

14. Anon . "N-Tuf, Low Temperature Steels,' Nippon Steel Corp , Tokyo, 1972

M-7

NBSIR 77-852

CRYOGENIC FLUIDS DENSITY REFERENCE SYSTEM:

PROVISIONAL ACCURACY STATEMENT

B.A. Youngiove

J.D. Siegwarth

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder , Colorado 80302

January 1977

Prepared for:

American Gas Association, Inc. 1515 Wilson Boulevard

Arlington, Virginia 22209

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Edward 0. Vetter, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

N-l
CONTENTS

Page

1. INTRODUCTION 1 1.1. Symbols 2

2. DESCRIPTION OF THE BASIC MEASUREMENT PROCESS 4 2.1. Density 4 2.2. Pressure 10

2.3. Temperature 10

2.4. Composition 11

3. MEASUREMENT PROCESS PARAMETERS 12

3.1. Bounds for Systematic Errors 12

3.2. Random Error from Measurements on Methane 15

3.3. Uncertainty Statement 16

4. MEASUREMENT PROCESS CONTROL 16

5. SUMMARY 19

6. ACKNOWLEDGEMENTS 19

7. REFERENCES 20

8. Appendices 21

8.1. The Change in Volume of the Silicon Crystal from

Hydrostatic Compression and Temperature 22

8.2. Silicon Crystal Weighings in Air 23

8.3. Densities of Single-Crystal Silicon 24

8.4. Weight Certificate 25

8.5. Linearity Check of the Balance 27

N-2
CRYOGENIC FLUIDS DENSITY REFERENCE SYSTEM: PROVISIONAL ACCURACY STATEMENT

B. A. Younglove and J. D. Siegwarth

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

The measurement capability of the density reference system

(DRS) of the National Bureau of Standards, Cryogenics Division, is

described. This system measures density, pressure, and temperature

of LNG mixtures for the purpose of testing densimeters which are contained in the liquid sample. Sample composition is determined

by weighing the gas samples separately before condensing them into

the sample. The DRS measures density by weighing a single-crystal

of silicon immersed in the LNG mixture. This process is described

and the equations used in the computation of density are discussed.

At this time the estimate of sample standard deviation for

a single density measurement made on this system is + 0.062% (at

0.4 g/cc) . Using three times this standard deviation as a limit

for random error and adding + 0.026% as an upper bound for known

sources of possible systematic error, the uncertainty of a single

determination by this system is + 0.21%. This statement of accuracy applies for the density range 380 to 430 kg/m^ and 1200 to

1400 kg/m^, pressures to 7 bar, and temperatures from 80 K to 140 K. This statement is expected to be correct in the intermediate density

range and for all temperatures up to 300 K. Measurement uncertainties for temperature, pressure, and composition are discussed. Comparison of measurements for liquid argon

densities with the results of other laboratories is given.

Key words: Densimeters; density reference system; liquid methane;

LNG .

1. INTRODUCTION

The density reference system (DRS) was evolved to determine the uncertainty of measurements made by several field type densimeters capable of

operating at cryogenic temperatures in liquefied natural gas (LNG) . The

project was performed under a grant from the American Gas Association, Inc.

(A.G.A.) on behalf of its membership.

This system has the capability at present of operating from room temperature to near the boiling point of liquid nitrogen (300 K to 80 K) , and

at pressures of 7 bar (100 psi) to vacuum. In this work we covered densities

3 of 390-500 kg/m , a range normally found in LNG work. Some additional density measurements were made on liquid argon. Only methane density measurements were used in the determination of the system uncertainty.

At this time the value of the sample standard deviation for a single

density measurement made on this system is + 0.062% (at 0.4 g/cc), based on measurements made using samples of liquid methane (99.97%). Using three

N-3
times the standard deviation as a limit for the random error, and adding 0.026%

as an upper bound for known sources of possible systematic error, the uncertainty of a single determination by this system is + 0.21%.

Density is determined in the DRS by weighing an extremely pure (semiconduc

tor grade) single-crystal of silicon in the liquid whose density is to be deter

mined. The density of the liquid is calculated from the apparent weight of the

silicon submerged in the liquid using Archimedes principle.

It is appropriate that silicon was used in this work as its density has

been recommended by Bowman [1] of NBS as the primary standard for solid densities. His work which uses Archimedes principle discusses the several

advantages that this type of silicon has for accurate measurements of liquid

densities: relatively low density (compared to other solids), high thermal

conductivity, reasonably low electrical resistance, and low compressibility.

Of course Bowman's work and others [2] provide accurate values for silicon

density

.

1.1, Symbols

g acceleration of a freely falling body

k compressibility factor

L length

^2^S length at reference temperature 298 K

length at absolute temperature T

apparent mass

M^j^ apparent mass as read by balance during calibration

M^^ apparent mass as read by balance for zero mass load

Mj_^ buoy mass, silicon crystal + tungsten wire + stainless steel wire

immersed in liquid

Mj_^g apparent mass of buoy in gas

Mj^j apparent mass of buoy in liquid

counterweight mass apparent mass of counterweight in gas

hanger mass

Mj_^g apparent mass of hanger in gas

M, calibration mass k

Mj^g , apparent mass of calibration mass in gas

range mass apparent mass of range mass in gas

N-4
M silicon crystal mass

s

^ M replacement mass standard used to evaluate zero of balance

apparent mass of replacement mass in gas

hanger mass, brass part

M2 hanger mass, stainless steel wire part

hanger mass, stainless steel wire, that part of M2 located in liquid

hanger mass , tungsten wire part

P system pressure

T system temperature

V volume of buoy

V volume of silicon

s AMa apparent mass less zero mass reading of DRS balance

6 density difference between DRS density and a reference density

e density variation in 6 from the average value of 6, for a methane

sample

n density variation in 6 from a methane sample to an average methane

sample

p density of liquid sample

Pg density of gas (vapor phase in equilibrium with sample liquid)

Pj^ density of reference methane liquid

Pg density of silicon

P-^ density of brass

p2 density of stainless steel

density of tungsten

a standard deviation

a standard deviation of e

e a standard deviation of n

n

M density difference bias

N-5
2. DESCRIPTION OF THE BASIC MEASUREMENT PROCESS

2.1. Density

The density reference system determines density via the Archimedes principle, which is that a body submerged wholly or partially in a liquid is buoyed

by a force equal to the weight of the fluid displaced. The net force on the

object is the difference between its weight and the buoyant force.

The basic arrangement of the silicon crystal, the weighing balance, and

sample holder can be seen in figure 1. Figures 2 and 3 are photographs of the

partially disassembled reference system. A silicon crystal, is weighed immersed in the test liquid. Its apparent weight is the difference in its true

weight and the buoyant force exerted by the liquid.

M^g = (Mg - pVg)g. (1)

In the following relations we have removed the factor, g, as it is common in

all terms. Solving for density

p = (M^ - M^) ^. (2) s Using the measured value for the silicon mass and the value for single-crystal

pure silicon density, p^, we have

M = p V . (3) s s s Combining equations (2) and (3) to eliminate ,

p = (1 - M^/M^) . (4) o as

This is the basic form of the measurement equation. The one actually used is more elaborate and is developed in the following sections.

Density from actual readings using a balance .

In practice we measure density using an automatic balance. This balance

uses magnetic force to achieve balance. It has the advantage of speed and

convenience of operation. On one side of the balance we have a movable counterweight which can be initially adjusted to put the system in balance. Ordinarily one would adjust its moment arm to precisely balance the system. Here

we leave a slight unbalance so that the automatic system will always react in one direction initially. For purpose of clarity we take the small initial

unbalance of the system as being M^, however this will subtract out subsequently

as seen below. The force generated by the magnetic balancing system is con- sidered to be an equivalent mass M^

the automatic balance. Here we have

sidered to be an equivalent mass M (or apparent mass), and is the reading of

a M+M = M+M, +M,„. (5) a eg rg hg oi

N-6
N-7
Figure 2. Density Reference System showing small sample holder.

N-8
Figure 3. Partially disassembled Density Reference System.

N-9
Notice that is now M^g» we have a buoyant effect of the gas pushing

upwards on the masses in the gas.

The value of M was chosen for a given M, and M to be large enough to

r h s give a reading on-scale (0 to 20 grams) for the automatic balance for the

range of densities of LNG under consideration. When more dense liquids were

measured, for example liquid argon, a heavier range weight was used.

Zeroing the balance . Experience with the balance showed that the zero would change although the

calibration did not. In order to zero the balance the silicon crystal and its

wire hanger and brass support piece were lifted off manually via a mechanical

contrivance that could be operated outside the enclosure through a sliding vacuum seal.

This decrease in weight was compensated for by placing the weight on

the balance pan, again with a mechanical device such that

M+M=M+M (6) ao eg rg wg

where M^^ is the zero reading of the balance. Here the range weight is still

on the pan as before. Since this measurement occurs just before the measurement described by equation (5) then we may subtract out M and M giving

M - M = M, + M, „ - M

a ao hg bJc wg

or

Calibration of the balance,

AM = M, + M, „ - M , (7) a hg bJl wg

The linearity was verified using a procedure recommmended by the Statistical Engineering Laboratory of NBS . See appendix 8.5. A continual check

of the calibration was performed using a 10 gram weight. Provision was made

for lowering this calibration weight onto the balance pan by a thermally

actuated bi-metallic strip. This allowed a very gentle and precise method of

placing this weight onto the balance pan.

The calibration was checked under the zero check procedure. Immediately

after checking the zero, as described by equation (6), the calibration weight,

Mj^, was placed on the balance pan so that the apparent mass (the M^^ in

equation (6)) is now M , , M,+M = M+M+M, . (Va) ak eg rg wg kg

Subtracting equation (6) from (7a),

M , - M = M, . (7b) ak ao kg

N-10
As long as equation (7b) holds, no adjustment was needed for the balance.

In practice it was found that adjustment of the balance was rarely needed.

The measurement equation .

As in equation (4), the final measurement equation can be put in the form

p = Pg(l - f (M^,M2, . . .p-,^,p2. . . ) ) (8)

where the independent variables are all known. In actual practice the hanger

M^, consisted of a brass part (M^,p^) and a stainless steel wire suspended from

this brass hanger (M2/P2)> However, part of the stainless steel wire was immersed in the liquid. The part in the gas is M2 - and the part in the liquid

is M^. Therefore,

h 12 3 (9)

and

,

hg L Z 3 g

M M - M — + —= (10)

Also the mass M, breaks down into b

b s 3 4 where is a short length of tungsten wire (M^,p^) wrapped around the silicon

crystal (^^^'Pg^ ^° have

Mv,r, = M + M^ + M.-p hi s 3 4 + -1 + ^

Ps P2 P4

(11)

Putting these relations into equation (7)

AM = M, + - - p a 1 2 3 g

+ M + M-, + M. - p s 3 4

^ ^ ^2 - ^3

Pi ^ P2

M M

^ + ^ + -J. Ps P2 P4- M + p w

w g p. (12)

M + M + M + M. - M - AM - p [ (M - M )/p, + (M - M )/p„]

S J. ^ T W 3 J

2» i ^ " (Mg/p^ + M3/P2 + M^/p^) (13)

the form of equation (8) may be obtained by factoring out p^ and Mj_^ to obtain

P = P,

M + M- + M - M - AM p 1 + ^- ^ - ^ [(M^ - M^)/p^ + (M2 - M3)/P2]

s s M -, p M p 1 + ^ + ^ -i

M, p„ M, p J

(14)

N-11
The following are the measured values of the masses used in equation (13)

Literature values of the densities were used, the possible effect this could

have on measurement accuracy is discussed below.

M = 127.4330 g, p = 2. 33078 g/cm"^ the silicon crystal.

s -^''^s

^14 " ------ ^2

= 4. 2441 g, Pt = 8.5 g/cm"^ the brass hanger.

3 = 0.2121 g, p^ = 7.9 g/cm the stainless steel suspension wire.

= 0.026 g stainless steel suspension

wire submerged in liquid.

3 = 0.055 g, P^ = 18.8 g/cm the tungsten wire tied about

the silicon crystal.

= 100.9296 g the brass replacement weight

The denominator of equation (13), ^^g/Pg '^3/'p2 ^ '^4'^'^4 """^ total volume of

the submerged material. From the above it is

V = 54.674 + 0.00329 + 0.00293 cm^

V = 54.680 cm^.

The total equation (13) becomes

31.0146 - AM + p (11.351)

a g ,3 P = 54. 6802 5/^"^ •

The value for the silicon mass is an average of several weighings in air,

corrected to weight in vacuum. (See appendix 8.2, page 23).

The density of silicon of 2. 33078 g/cm"^ has been corrected for thermal

contraction to LNG temperatures (appendix 8.3) from the literature values

(appendix 8.1). Pressure dependence of p^ is negligible (appendix 8.1).

2.2. Pressure

The system pressure was measured using a quartz-spiral bourdon

tube. During the first series of measurements (data taken before December

1975), the system used a 500 psi* gage, the data after that used a 200 psi

gage. The calibration of all pressure gages used was checked at this laboratory using an air-dead weight gage, which is accurate to 0.015%, with

the accuracy traceable to NBS . Pressure uncertainty was found to be within

the 0.015% of full scale pressure specified by the manufacturer.

2.3. Temperature

Temperature was measured using vapor pressure thermometers. One thermometer bulb was located at the bottom of the sample volume and the other near

3 . . the top. Each thermometer contains about 5 cm of liquid methane. Pressure

1 psi = 6.895 k Pa,

N-12
communicates from the thermometers to a quartz-spiral bourdon tube (100 psi

maximum) via 1/16" O.D. stainless capillary tubing. The temperature range

was 100 K to 140 K. Sensitivity and precision of this device is the same as specified for the gages in section 2.2. This pressure uncertainty is equivalent to 0.03 K at 100 K and 0.003 K at 140 K for the 100 psi gage used to measure vapor pressure.

Temperature gradients as measured by the vapor pressure thermometers were generally 0.030 K and on rare occasions approached 0.3 K. The density difference

resulting from this temperature difference can be calculated by using methane

properties [3,4]. Here we can use the dimensionless derivative dilnp/dJlnT at

saturation

Average System Ap at = 0 0^ K Temperature dilnp/dilnT p ° ^ ^'^^

110 K 0.38 0.0038%

140 K 0.26 0,0026%

In the worst instance the difference was only 0.04%. The densimeters under

test were actually physically closer to the DRS density probe (the silicon

crystal) than were the two vapor pressure thermometers, implying a lower density

difference.

2.4. Composition

When mixtures were used for the density measurements, the compositions

(mole fractions) were determined by accurate measurement of the mass of the

separate constituents and subsequently applying corrections for the effect of

gas phase to the total system composition to obtain liquid phase compositions.

The samples were weighed in metal cylinders. After transfer to the DRS

cryostat, the cylinders were again weighed and the amount transferred computed

from the difference.

The balance used for this purpose is a high-resolution and high-capacity

balance (resolution better than 0.01 g, with maximum capacity of 20 kg).

Class S weights were used (see appendix 8.4).

Upon condensation in the cryostat the sample separates into a liquid

and gas phase. The volume of the gas phase was two to four times the volume

of the liquid. The large volume of the gas phase was required to house the

automatic balance used in weighing the silicon crystal which measured the

liquid density.

The composition of the liquid phase was calculated from the total composition by subtracting the amount of the vapor phase. The total composition is

that computed from the amounts of sample gas transferred into the system. If

the composition of the gas and liquid phase were the same, then the liquid

composition would be the same as the total composition.

N-13
For mixtures of methane with ethane, propane and butane the vapor phase

was assumed to be methane. The vapor phase densities in the balance volume

sample chamber and interconnecting tube are computed from a virial equation

of state [3] using the system pressure and temperatures. The calculated

quantities of methane are then subtracted from the total amount of methane

in the system and the result is used to compute the liquid phase composition.

For mixtures with nitrogen, the vapor phase is assumed to be methane and

nitrogen. The densities of the vapor phase were computed from a mixture virial

equation which included terms to the second virial coefficient. Since this

equation used the mixture second virial coefficient, it was computed from the

second virial coefficients of the pure components and the interaction second

virial coefficient for the mixture, as well as the vapor phase compositions.

The vapor phase compositions were estimated from phase-equilibria data for

methane-nitrogen of this laboratory [5] using enhancement factors. The re- sulting computation of vapor densities allows a first estimate of the amount

of nitrogen and methane in the vapor phase. From this, a corresponding first

estimate of the liquid phase composition is made. The estimate is improved by

iterating the computation using the results of the preceding evaluation.

In the instance of a binary mixture the composition could be computed

from another approach. Dielectric constant density measurements of the liquid

and with the assumption that the polarizability of the methane-nitrogen mixture could be computed from ideal mixing, allows one to compute the mole fraction

of the binary mixture. Agreement between the calculation described in the

above paragraphs and the dielectric constant calculation was found to be about

0.2 to 0,4 mole percent when the nitrogen composition was less than 2 mole

percent.

Because of the additional uncertainties of mixtures discussed above, only

pure methane results were used in the random error determination.

3. MEASUREMENT PROCESS PARAMETERS

3.1. Bounds for Systematic Errors

A listing of the primary sources of uncertainty in density measurement

can be obtained from examination of the measurement equation. If one has

knowledge of the basic uncertainties of the separately measured quantities

such as the masses and densities, then these can be combined to give an estimate of the systematic errors in the density as measured by the density

reference system.

However, until experimental evidence of the actual effect is obtained

by introducing an offset in these factors, both singly and jointly, this

analysis is just that, an estimate of undemonstrated validity.

N-14
Equation (13) , the measurement equation, has the density p as a function

of several independent variables.

p = p (M^,M^,M2,M3,M^,M^,AM^,Pg,p^,P2,p4) . dS;

The uncertainty in p, arising from uncertainty in p^, for example, can be

evaluated from

or as a dimensionless ratio.

6p = 6p^ (16)

(Sp _ dlnp s

p ~ 8£npg Pg

(17)

which has the advantage of expressing the independent and dependent variables

as dimensionless ratios. The total uncertainty in density is the square root

of the sum of the squares of the various contributions.

p

^

^ „ 6x

9ilnx. x.

1 1

2 1/2

(18)

This is the propagation of error relationship for systematic error [6] when the

variables are independent and the magnitudes of the relative errors are small

so that second order terms are negligible.

Table 1 is a summary of the most significant contributions to the total

systematic uncertainty in density as estimated from the various contributing

sources. The first column, labelled x identifies the variable for which the

uncertainty is calculated. The second column is the total logarithmic partial

derivative of the liquid density with respect to the variable of the first

column. The column labelled 6x/x is the ratio of the estimated worst possible

uncertainty of that variable.

The systematic error, 6x/x, due to mass determinations is estimated from

the uncertainty generated by the balance and weights used to determine the masses. The estimate of the systematic error of the apparent mass is the

uncertainty of the electronic balance reading as specified by the manufacturer.

Linearity measurements (appendix 8.5) indicate this number is conservative.

The error estimate of the silicon crystal density covers uncertainties due to

the temperature and pressure effects (appendix 8.1) as well as uncertainties

in published densities (appendix 8.3). The metal density uncertainties of

which is the dominant term are estimated from volume and weight. The gas

density is required for bouyancy corrections, contains all gas pressure,

temperature and composition uncertainties and is the leading systematic error

for mixtures containing LN2. The uncertainties due to temperature gradients

is discussed in section 2.3. An additional systematic error results from the

uncertainty in the absolute value of T. This is not included in the table

since it makes no contribution to the systematic error when densimeters are

N-15
being compared. When density measurements are being compared with those of

other workers, however, there is an 0.01% maximum contribution to the systematic

error at the lowest temperature th^t decreases to less than 0.001% at the

highest temperatures.

Variable, x

temperature

gradient

Table 1. Systematic errors.

silicon crystal (P3 - mass brass hanger

1 mass

steel wire mass io, -

steel wire mass (p - p in liquid

tungsten wire (P4 - mass apparent mass AM /pV

a silicon density M /p V

s S metal densities (M^ -

gas density Pg((M^

- p)Mg/pPgV 3.9

- p )M^/pp^V. .1.8 X 10

- Pg)M2/PP2V. 8.9 X 10

6.0 X 10

- Pg)M^/pp^V. .5.4 X 10

-1

-4

-5

-5

- M ) p /Pt pV. . 2 . 0 X 10 w g 1

- M^)/p^)/pV. .2.2 X 10

d«.np/d£nT 3.8 x 10

-3

-3

-1

Total, from equation (18) + 0.026%,

6x/x

1.6 X 10

2.4 X 10

4.7 X 10

3.8 X 10

1.8 X 10

-5

-4

-3

-4

-2

1.0 X 10

1.0 X 10

-1'

-4

6p/p in %

+ 0.0062

+ 0.0043

+ 0.00042

1. 0 X 10 + 0. 010

1. 6 X 10-5 + 0.0016

2. 3 X 10-2 + 0.0046

+ 0.022

+ 0.0038

The. large uncertainty for gas density results from the large uncertainty of

the methane-nitrogen vapor densities. The uncertainty due to gas density is

only 0.002% for methane and the total from equation (18) is + 0.014%.

Some of the systematic errors listed above will be eliminated in

future measurements. By moving the point the silicon float disconnects

from the balance down into the liquid such that the float disconnects from

all suspension hardware, all systematic errors associated with the brass

hanger and the steel and tungsten hanger wires will be eliminated. The un- certainty of the silicon mass was determined from the uncertainty of the

measuring weights and the density uncertainty comes from literature values

of the density. The uncertainty in apparent mass is due to the balance and

has been determined experimentally (see appendix 8.2). The temperature

gradient was measured to determine that uncertainty. Only the uncertainty

due to the density of the replacement weight and the gas density correction

has yet to be examined experimentally. This can be done by using a more

dense mass for the replacement weight. However, any effect due to changing

N-16
this weight should be very small compared to the random error. If any change

in the estimated systematic error is warranted after experimentally checking

for replacement weight buoyancy effects, this correction will be made in

the updated uncertainty statements.

3.2. Random Error from Measurements on Methane

The random error of the density reference system was determined experimentally by measurements on liquid methane.

Density measurements on pure methane were compared to densities computed

from the Haynes-Hiza relation for density versus temperature for saturated

liquid methane [4]. The vapor pressure measurements were converted to temperature [3] and the resulting temperature converted to densities as described.

The present estimates of the precision for density determinations made

using the DRS are based on measurements of the density of eight different

samples (fillings) of liquid methane. For the eight samples there was a total

of seventy-one density measurements of saturated methane in the temperature

range 100 K to 140 K — for the last four samples the temperatures were 110 K,

125 K, and 140 K,

The model used to analyze the methane data is

^(T)ij - ^T) = Nt) ^ «i ^ ^ij

where Y^-p^j^j is the jth density determination by the DRS on the ith methane

sample for temperature T; H^^^ is the corresponding density value derived

from the Haynes-Hiza relationship, M ^rpj represents the long term relative

bias, is the random contribution to all measurements made using the ith

sample, and e^^ is the random contribution to the jth measurement made on

the ith sample. The standard deviation (SD) for the is called the between

sample SD, and the SD for the e^^ is called the within sample SD. The SD of

measurements Y^-pjj^j is the square root of the sum of the squares of these

two SD

There were seventy-one least squares estimates of the e^^ for the

liquid methane measurements. The variability among the estimate samples -- the last twenty-two, e.g. — is less than among the preceeding forty-nine.

The point estimate for the within SD for the first six samples is + 0.074%

3 (using 400 kg/m as reference) and that for the last two is + 0.034%. The

corresponding 99% confidence intervals are (0.057, 0.101) and (0.024, 0.055).

This change in variability is attributed to the cleaning of the knife edges

on the DRS ' s balance. The point estimate for the between samples SD for

the eight samples is + 0.052%, a 99% confidence interval is (0.029, 0.13).

The cleaning of the knife edges has not effected this component of the

variability. The estimated SD for a single measurement made on the DRS

N-17
previous to the cleaning of the balance is + 0.090%. For measurements made

after that time the SD is estimated to be-+ 0.062%.

Only the within SD ' s after the knife edges were cleaned are taken to

correctly reflect the precision of the within sample density measurements.

A comparison of these data with the Haynes-Hiza densities is shown in Figure

4 as well as a comparison to the work of Goodwin [3].

For the methane data the DRS measurements of density shows a bias with

the Haynes-Hiza relationship which is a linear function of density. For

a density of 0.38 g/cc the bias is -0.062% with an estimated SD of 0.021%;

a 99% confidence interval is (-0.12%, -0.006%). For a density of 0.43 g/cc

the bias is -0.11% with an estimated SD of 0.018%; a 99% confidence interval

is (-0.16%, -0.062%)

.

Figure 5 shows a comparison of densities for two samples of liquid argon

as measured by the density reference system to those measured by the HaynesHiza apparatus, as well as other laboratories as indicated in the caption.

As can be seen in this figure, the agreement with Haynes and Hiza is generally

within 0.1%. .

3.3. Uncertainty Statement

While the use of three times the estimated SD is commonly used in re- porting the limits of random error, because of the small number of observations (eight) relating to the sample-to-sample error, the limits using

3 X 0.062% will provide a 98% confidence interval rather than one of 99%.

When the samples of liquid methane measured by the DRS exceed fifteen, the

use of the factor 3 will give confidence intervals of better than 99%. The

limit. of possible sources of systematic error has been judged to be + 0.026%

(see section 3). This systematic limit of 0.026% plus 3 x 0.062% gives the

present estimated limit of total uncertainty for a single density measurement made on the DRS as + 0.21%.

4. MEASUREMENT PROCESS CONTROL

As future measurements are made, the random errors will be continually

checked and the systematic error estimates will be confirmed experimentally or the error source eliminated where possible as described below.

Each time a set of density reference measurements are made using the

system, measurements on at least two separate fillings of pure liquid methane

will be included in the tests. Density measurements will be made at temperatures around 110 K, 125 K, 130 K and 140 K. Three measurements will be made

at each temperature in random order. The remeasured methane densities can

be compared to the Haynes-Hiza results and to the earlier reference system

measurements to determine whether the system has shifted. This reliability

of the system will be checked only in conjunction with density comparison

N-18
LUO

Haynes and Hiza

DRS

Goodwin

0.38 0.39 0.40 0.41 0.42

DENSITY, g/cm3

Figure 4. Liquid methane density results of this work relative to the work

of Haynes, et al.[4]. The data are the 22 points taken after the

knife edges were cleaned.

N-19
90 95 100 105 110 lis TEMPERATURE, K

Figure 5. Liquid argon densities of other

fit to this work.

O Younglove, this work.

O Haynes and Hiza [9]. e Chui and Canfield [10].

•• Van Itterbeek and Verbeke

[11].

A Terry, et al. [12]. — Gosman, et al. [13].

workers compared to a least squares

Pan, et al. [14].

V Goldman and Serase [15].

« Saji and Kobayashi [16].

D Mathias, et al. [17]. • Street and Staveley [18].

Dobrovolskii and Golubev [19].

N-20
work rather than periodically because of the expense of making density measurements.

For these occasions the within SD's will be compared statistically to

those of previous occasions for any change in this measure of precision,

and the occasion-to-occasion shifts, (see 3.2), will be tested for any

change in their variability or for signs of non-random behavior (e.g., drifting). If there is no apparent change, the data from previous occasions will

be combined with the new data to obtain updated estimates. Any statistically

verifiable changes in the DRS process will call for corrective action with

respect to the process. A revised uncertainty statement will be presented

as further calibration measurements are completed.

5 . SUMMARY

The density reference system of the National Bureau of Standards, Cryogenics

Division is described. Since the density determination by the DRS is basically

a weighing process, the details of calculation of this process are described in

detail. The procedure for determining the density from weighing, zeroing and

calibrating the balance is discussed.

The uncertainty of the density reference system is + 0.21%. The contribution

from the estimated systematic error in density was + 0.026%. The estimated un- certainty caused by random error is three times the standard deviation of

+ 0.062% and is based on the measurements of the densities [4] of liquid

methane taken on eight samples and on 22 independent measurements. The total

density uncertainty was taken to be the sum of the systematic and random errors.

6. ACKNOWLEDGEMENTS

Special acknowledgement is given to John LaBrecque of the NBS Statistical

Engineering Laboratory for the considerable help and advice given this project

during its various phases. Acknowledgement is also given to Janet Donaldson

of the same group for her recommendations on the method of acquiring data from

the automatic balance.

Jim Holste contributed very heavily in the construction and start up phase

of this project. He designed and built several important features of the DRS.

N-21
7. REFERENCES

[I] Bowman, H. A., Schoonover, R. M. , and Jones, M. V., Procedure for high

precision density determinations by hydrostatic weighing, J. of Research,

NBS C, TIC, 178 (1967)

.

[2] Henins, I., and Bearden, J. A., Silicon crystal determination of the absolute

scale of x-ray wavelengths, Phys. Rev. 135 , A890 (1964)

.

[3] Goodwin, R. D., The thermophysical properties of methane, from 90 to 500 K

at pressures to 700 bar, NBS Tech. Note 653, Apr. 1974.

[4] Haynes , W. M. , Hiza, M. J., and Frederick, N. V., A magnetic suspension

densimeter for measurements on fluids of cryogenic interest, to be submitted to Review of Scientific Instruments.

[5] Parrish, W. R. and Hiza, M. J., Liquid-vapor equilibria in the nitrogenmethane system between 95 and 120 K, Advances in Cryogenic Engineering

(Proc. 1973 CEC) , Vol. 19 (Plenum Press, NY, 1974).

[6] Cook, N. H. and Rabinowicz, E., Physical Measurement and Analysis, AddisonWesley Publishing Co., Inc., 1963.

[7] McSkimmin, H. J., J. Appl . Phys. 24_, 988 (1953).

[8] Corruccini, R. J. and Gniewek, J. J., Thermal expansion of technical

solids at low temperatures, Nat. Bur. of Stand. (U.S.) Monograph 27,

May 1961.

[9] Private communication.

[10] Chui, C. and Canfield, F. B., Trans. Faraday Soc. 61_, 2933 (1971).

[II] Van Itterbeek, A., Verbeke, 0., and Staes, K. , Physica 2_9/ 742 (1963).

[12] Terry, M. J., Lynch, J. T. , Bunclark, M. , Mansell, K. R. , and Stavely,

L. A. K., J. Chem. Thermodyn. 1, 413 (1969).

[13] Gosman, A. L., McCarty, R. D., and Hust, J. G., Thermodynamic properties

of argon from the triple point to 300 K at pressures to 1000 atmospheres.

NSRDS-NBS 27 ( 1969 )

.

[14] Pan, W. P., Mady, M. H. and Miller, R. C, AIChE J. 2A, 283 (1975).

[15] Goldman, K. and Scrase, N. G., Physica 45^, 1 (1969).

[16] Saji, Y. and Kobayashi, S., Cryogenics 4, 136 (1964).

[17] Mathias, E., Onnes, H. K., and Crommelin, C. A., Ann. Phys. 1/7 , 442 (1922).

[18] Street, W. B. and Staveley, L. A. K., J. Chem. Phys. 50, 2302 (1969).

[19] Dobrovolskii , 0. A., and Golubev, I, F., Tr. Nauch . -Issled . Proekt. Inst.

Azion. Prom. Prod. Org. Sin. 8^, 14 (1971).

N-22
8. APPENDICES

N-23
8.1. The Change in Volume of the Silicon Crystal from Hydrostatic

Compression and Temperature

The buoyant force of the liquid on the silicon crystal will be reduced by

the effect of its volume being decreased by hydrostatic compression. This is

described by

V = V^(l - kP)

where V is the volume at the reference pressure, in this case about one ato mosphere or one bar. P would be the pressure in excess of this and k the

compressibility;

k - - 1 ~ V 9P

This correction was found to be negligible since k = 1.01 x 10 ^ bar ^ and at

110 K and P - 6 bar, ^ = 6 x 10 ^. In this case k was computed from silicon

data on velocity of sound by McSkimmin [7] using the usual relations for bulk

modulus and elastic constants as evaluated from sound velocities.

The change in volume was computed from the thermal contraction of silicon

values from Corruccini and Gniewek [8]. We have

^298 " —=

-""T =

„^ ^ 25.5 X 10

298

for the change from 298 K to 100 K. This value is essentially unchanged over

the temperature interval 100 K to 140 K.

Av _ , AL

V~ ~ L

'

= 232.90 (1.000765) kg/m^

Pg = 233.08 kg/m^.

N-24
8.2. Silicon Crystal Weighings in Air

Date

Silicon Weight

in Air

gram

Temperature

Celsius

Pressure

mm Hg

Silicon Weight

in Vacuum

gram

01-10-74 127. 3947 21 633 127.4335

01-15-74 127. 3950 20 631 127.4339

01-27-74 127. 3941 20 625 127. 4335

02-28-74 127. 3945 21 620 127.4334

04-02-74 127. 3926 21 628 127 . 4320

04-05-74 127. 3941 20 630 127.4338

10-27-74 127. 3930 23 625 127. 4319

10-28-75 127, 3927 21 620 127.4316

Average 127.4330 + 0.0003

std. dev.

N-25
8.3. Densities of Single-Crystal Silicon

Densities of Silicon

2. 328932*

Temperature

22-27°C

Preparation

Grown in Vacuum

Std. Deviation, la

1 ppm

2. 329021* 22-27°C Grown in Argon 1 ppm

2. 32904** 25°C Not known + 9 ppm

* Each are average of 12 measurements, Bowman, Schoonover, and Jones [1].

** An average of about 75 measurements, Henins and Bearden [2]. Reference

density for silicon was taken to be 2.3290 at 25°C.

A 14 g portion of the same crystal was weighed in water and in air. Using

averages of four weighings in air and water the density computed at 30 °C was

p = 2. 3291 g/cm"^ , as compared to p = 2 . 3289 from the above after correction

for thermal expansion. This is a difference of about 0.009%.

N-26
8.4 Weight certificate

Her V TROEMNER, Inc.

MANUFACTURERS OF PRECISION BALANCES AND WEIGHTS and LABORATORY APPARATUS

6825 GREENWAY AVENUE, PHILADELPHIA, PA. 19142 PHONE 215 SA 4-0800 TRACEABLE CERTIFICATE

Voland Corporation

27 Centre Ave. New Rochelle, N. Y. 10802

Attn: Robert C. Luce

Order 1695

This is to certify that the weights furnished on your referenced order

have been calibrated to Class S of the National Bureau of Standards

tolerances under our N.B.S. Certificate No. as follows:

Weight Set 5 kg - 1 g N.B.S. Certificate No.

5 Kg. 2 kg. 2 kg. 1 kg 232.09/209275 Set A

500 g, 200 g, 200 g, 100 g 232.09/209275 Set A

50 g, 20 g, 20 g, 10 g 232.09/209275 Set A

5 g, 2 g, 2 g, 1 g 232.09/209275 Set A

Dated: March 28, 1974 By:

Wilbert D. Abele

Vice President and General Manager

N-27
Richard D. Lamm

Gnver-or

Hov R. Romer

C ("tvyn s SI oner

Donnid L. Svedman

DrDutv Commissiune

COLORADO DEPARTMENT OF AGRICULTURE

406 STATE SERVICES BUILDING

1525 SHERMAN STREET

DENVER, COLORADO 80203

June 9, 1976

REPORT OF TEST

AGRICULTURAL COMMISSION

Clarence Stone, Center Chairman

William A. Stephens, Gypsum

VI ce-C hai rman

Ben Eastman, Hotchkiss John L. Mallov, Denver

M. C. McCormick. Holly

Elton Miller, Fort Lupton

Kay D. Morison, Fleming

William H. Webster, Greeley

Kenneth G, Wilmore, Denver

OWNER: National Bureau of Standards

Cryogenic Laboratory

Boulder, Colorado

Certification No. 3087

DESCRIPTION: Seven weights from NBS Kit No. 1^3922

The standards described below have been tested and compared with the

standards of the State of Colorado, and have been found to be within the

tolerances as prescribed by the National Bureau of Standards for Class S weights. The effect of air bouyancy has been considered negligible.

ITEM APPARENT MASS CORRECTION UNCERTAINTY CLASS S AmUSTMENT TOLERANCE

20 . gra m 20. . 10

5

2.

2.

.

1

-0.0080

HtO.Ol6

-fO.009 -0.0403

^0.0216

+0.0431

H^0.0229

.022 mg

.022

.020

.0134

.0134

.0134

.0093

0.074 mg 0.074

0.074

0.054

0.054

0.054

0.054

The uncertainty figure is an expression of the overall uncertainty usin^

three standard deviations as a limit to the effect of random errors of

measurement, the magnitude of systematic errors from known sources being

negligible

.

F H Brzfotidy l/Metrologist

Test completed June 9, I976

Colorado Department of Agriculture

Metrology Laboratory

3125 Wyandot Street

D-nver, Colorado 80211

Baro. Press. Temp.

Rel. Hum.

627.0mm

23.4°C

45.5^

THESE CERTIFICATIONS ARE TRACEABLE TO THE

NATIONAL BUREAU OF STANDARDS.

ALL CERTIFICATION CERTIFICATES ISSUED BY THE COLORADO DEPARTMENT OF AGRICULTL'Rl WlIC^ I > AND MEASURES-FOR STANDARDS HCrL LIS.hA

EXPIRE AS INDICATED BELOW:

(a) PRIMARY STANDARDS Fi> i! Teari Alter Date ot c :r;i r .tlon

(b) OFFICE (CH SECCND,\Ry) SrANJA:(Di CNE Yc-.R MF..! D>lt

OF CtnTIFICATI'"'!.

(t) Working (or Field) Standards - One Tear Alter Dale of Geillf cilioil

N-28
8.5. Linearity Check of the Balance

The linearity of the balance was verified by weighing 1, 2, 2, 5, 10, and

20 g class S weights (see weight certificate in appendix 8.4) in combinations

to produce weights of 1, 2, 3, 4, 5, 6, ... 20 g in a random order. These

weighings were analyzed by the Statistical Engineering Laboratory of NBS.

Their interpretation was that the residual standard deviation is 0.0008 g

based on 37 degrees of freedom. The linearity coefficient was 0.99960.

A summary of these measurements are shown below.

Independent Dependent Predicted Standard Dev

Variable Variable Values of Predicted

4 . 000 4 .000 4 .001 . 20E-03

15.998 15.998 15.998 . 19E-03

10.999 10 .997 11. 000 . 12E-03

2.000 2 .001 2 . 001 . 24E-03

6 . 999 7.000 7. 000 . 16E-03

1. 000 1 . 002 1 .001 . 26E-03

8 . 999 9 . 000 9 . 000 .14E-03

17.998 17 . 998 17 . 999 . 22E-03

8.999 9 . 000 9.000 . 14E-03

18 . 998 18.999 18.998 . 24E-03

10.999 11. 000 11.000 . 13E-03

11. 999 11 . 999 12 . 000 . 14E-03

14.998 14 . 999 14 . 999 . 17E-03

19.998 18.998 19. 998 . 26E-03

4.000 4.000 4 . 000 . 20E-03

12 .999 12 . 997 12.999 . 15E-03

4 . 999 5.000 5.001 . 19E-03

12 . 999 12 . 999 12.999 . 15E-03

1.000 1 . 002 1. 001 . 26E-03

11.999 12 . 000 12 . 000 . 14E-03

18 . 998 18 . 999 18.998 .24E-03

13.998 14 . 000 13.999 . 16E-03

19. 998 19.999 19.998 . 26E-03

17. 998 17 . 999 17. 999 .22E-03

7 .999 8.000 8. 000 . 15E-03

15.998 15.999 15.999 . 19E-03

1.999 2 . 002 2.001 . 24E-03

5.999 6.001 6. 000 . 17E-03

9.998 10.000 10.000 . 13E-03

14.998 15. 000 14.999 . 17E-03

6.999 7. 001 7.000 . 16E-03

3.000 3.001 3.000 . 22E-03

16. 998 17.000 16.999 . 20E-03

5.999 6.002 6.000 . 17E-03

3.000 3.001 3.001 . 22E-03

9.999 10.000 10.000 .13E-03

16.998 16.999 16.999 . 20E-03

7.999 8. 001 8.000 . 15E-03

13.998 13.998 13.999 . 16E-03

4 .999 5.000 5.001 . 19E-03

N-29 USCOMM - KRL
NBS-IHA (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUhLIC A 1 ION OR RKPORT NO. NBSIR 77-852

Uov t Accession

No.

3, Recipient's Accession No.

A T" 1 "T~ I AM r~\ Clin t" 1 1" i i

4. lliLr. AND SUBTITLb.

CRYOGENIC FLUIDS DENSITY REFERENCE SYSTEM: PROVISIONAL

ACCURACY STATEMENT

5. Publication Date January 1977

6. Performing Organization Code

275.08

7. AUTHOR{S)

B. A. Younglove and J. D. Slegwarth

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2750161

11. Contract/Grant No.

I i. Sponsoring Organization Name and Complete Address (jtreet, i^tty, Jtate, ZIP)

American Gas Association, Inc.

1515 Wilson Boulevard

Arlington, Virginia 22209

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less (actual summary of most sigpificaryt information. If document includes a significant

bibliography or literature survey, mention it here.) The measurement capability of the density reference system (DRS) of the National

Bureau of Standards, Cryogenics Division, is described. This system measures density,

pressure, and temperature of LNG mixtures for the purpose of testing densimeters

which are contained in the liquid sample. Sample composition is determined by weighing the gas samples separately before condensing them into the sample. The DRS measures density by weighing a single-crystal of silicon immersed in the LNG mixture.

This process is described and the equations used in the computation of density are discussed

.

At this time the estimate of sample standard deviation for a single density

measurement made on this system is + 0.062% (at 0.4 g/cc) . Using three times this

standard deviation as a limit for random error and adding + 0.026% as an upper bound

for known sources of possible systematic error, the uncertainty of a single determination by this system is + 0.21%. This statement of accuracy applies for the density

range 380 to 430 kg/m^ and 1200 to 1400 kg/m\ pressures to 7 bar, and temperatures

from 80K to 140 K. This statement is expected to be correct in the intermediate

density range and for all temperatures up to 300 K. Measurement uncertainties for temperature, pressure, and composition are discussed. Comparison of measurements for liquid argon densities with the results of

other laboratories is given.

17. KHY WORDS (six Io twelve entries; alphabetical order; capitalize only the first letter of the fir.'st key word unless a proper name; separated by semicolons

)

Densimeters; density reference system; liquid methane; LNG

18. AVAILABILITY [X Unlimited

[ ^ For Official Distribution. Do Not Release to NTIS

[

~^ Order From Sup. of Doc, U.S. Government Printing Office Washineton. D.C. 20/102. SD Cat. No. CI 3 [K] Order From National Technical Information Service (NTIS)

Springfield, Virginia 22I5I

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

21. NO. OF PAGES

30

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

22. Price

$4.00

USCOMM-DC 29042-P74

USCOMM - tKL
What's new in LNG measurement

methods and instrumentation

Industry supported research programs at National Bureau

of Standards provide data on cryogenic metering devices

D. B. Mann, Coordinator of LNG

Programs, Cryogenics Division, Insti- tute for Basic Standards, National

Bureau of Standards, Boulder, Colo.

Characterization, instrumentation and measurement of liquefied natural gas are the primary objectives of the LNG Program at the National Bureau

of Standards (NBS).

Characterization involves the deter- mination of accurate PVT, thermodynamic, electromagnetic and transport

properties data for multi-component

mixtures of liquefied hydrocarbon

gases. Instrumentation and measure- ment are essential to the safe and eco- nomic liquefaction, transport storage and custody transfer of this form of

fossil fuel. Although the main purpose of this article is to report on current progress

in instrumentation and measurements,

it should be emphasized that basic reference quality property data are fundamental to accurate, precise field measurements for pressure, temperature, density, liquid level and flow.

Data development. The NBS ap- proach to development of thermophysical properties data for LNG has been

to concentrate initially on providing

accurate wide range data and calculation methods for the pure components.

These include methane, ethane, pro- pane, iso and normal butane and

nitrogen.

The range of interest is from the

triple p>oint conditions to temperatures above ambient at pressures to at least 34,500 kPa (5,000 psi). This work is being carried out primarily in the

Properties of Cryogenic Fluids Section under the supervision of D. E. Diller. Accomplishments to date under an

.American Gas Association (AGA)

funded grant include published reports on comprehensive thermophysical

properties data for methane, dielectric constant and polarizability of methane,

velocity of sound in methane, specific heats of methane, provisional thermo- dynamic functions for ethane, dielectric constant of ethane, PVT and va- por pressure measurements on ethane,

phase transitions of ethane and a comprehensive accurate equation of state

for the thermodynamic properties of

fluids. Related accomplishments funded by

NBS and other agencies include publications on refractive index data for methane, viscosity and thermal conductivity equations for methane and

saturation densities of liquefied nor- mal butane. Additional publications influenced by the quality of the data are available and are classic illustrations of the dif- fusion and widespread use of accurate and precise property data generated

as a result of an original AGA grant. Another NBS project is concerned

with prediction of densities of LNG,

at or near saturation as a function of

pressure, temperature and mixture

composition. This project is funded by

the LNG Density Project Steering

Committee, through a grant administered by the AGA.

Objectives of the project are to meaTABLE 1—Densities of liquefied natural gas mixtures

Scope of work on project

• Pure Components Methane

Ethane Propane

Isobutane n-butane Nitrogen

Binary Mixtures Methane-Ethane Methane-Propane

Methane-Isobutane Methane-n-butane Methane-Nitrogen

Ethane-Propane

Ethane-Isobutane Ethane-n-butane

Ethane-Nitrogen

• Multicomponent Mixtures Methane-Ethane- Propane

Methane-Ethane-Nitrogen

Methane-Ethane-Propane-n-butane

Methane-Ethane-Propane-Nitrogen

Methane-Ethane-Propane-n-butane-Nitrogen

Typical LNG Mixtures

Propane- Isobutane Propane-n-butane

Ethane-Nitrogen

0-1

Circle 72 on Reader Service Card 21
FLOW, mVs

3

1 1 1 1 1 1 ^^^^^^^^^^^^^^^^^^^^^^^^^^M TURBINE ^^^^^^^^^^^^^^H HEAD ^^^^^^^^^H VENTURI. NOZZLE ^^^mm^^^l MOMENTUM

HH VORTEX SHEDDING

POSITIVE DISPLACEMENT—

ROTATING VANE

POSITIVE DISPLACEMENT- IB OSCILLATING PISTON

POSITIVE DISPLACEMENT— SCREW IMPELLER II i i 200 400 600 FLOW, gpm

600 1000

Fig. 1 —Flow range of cryogenic flowmeters confirmed by experiment.

POSITIVE DISPLACEMENT- SCREW IMPELLER VORTEX SHEDDING

MOMENTUM

TURBINE

POSITIVE DISPLACEMENTOSCILLATING PISTON

POSITIVE DISPLACEMENT

ROTATING VANE

HEAD TYPE-ORIFICE, VENTURI, NOZZLE

0 100 200 300 400 PRECISION (3ff)-0NE PART IN 100 -400

Fig. 2—Precision of flowmeters for cryogenic service based on experimental data.

sure the saturated liquid densities of LNG type mixtures with an inaccuracy

and imprecision of less than 0.1 per- cent and to evaluate and optimize

three existing density calculation

methods using this experimental data

as the measurement base. Table 1 outlines the content and scope of the ex- perimental program. The approach involves precise measurements of the pure fluid and binary

mixture densities throughout a temperature range of 110 to 140 K. Optimization of the correlation methods

are then evaluated by comparing cal- culated densities with precise density measurements for selected multi-component (including LNG type) mixtures. The project is nearing completion, and several reports will be issued describing the methods and results. The basic properties data required

for assessing and proving field-type

LNG measurements are becoming

available. The following projects deal- ing with field instruments and measurements are also underway at NBS

and rely heavily on these properties data measurements and correlations.

Flow measurements. Within general advances in the state-of-the-art, in- strumentation for LNG flow measurements can draw on a well-developed

research and field experience of cryo- genic industrial gases (liquid nitrogen, argon, oxygen, hydrogen), specifically

in the area of small diameter, truck

mounted, custody transfer meters. An

8-year joint NBS-industry efi'ort has provided extensive data on the perfor- mance of volumetric and mass flow

devices, both under well controlled laboratory conditions and in the field. The program was begun in 1968 as a cooperati\e effort involving NBS

and members of the Compressed Gas

.Association. Accomplishments include: • An evaluation of generic classes of flowmetering devices over a broad

range of expected operating conditions • Initial work on establishment of

specifications, tolerances and recom- mended practices for flow devices used

in commerce

• Promulgation of transfer stan- dards traceable to NBS for field certi- fication of new meters to be put in service or recertification of in-service meters. More than 60 meters, based on five different generic types, were included

in the program. A summary of experi- mental cryogenic performance of these meters is shown in Fig. 1. Documented

performance for various cryogenic volumetric flow ranges is shown in Fig. 2, which includes experimental

results from the literature in addition

to that developed under the NBSCGA program.

Active work under this program is drawing to a close with the develop- ment of a model code (NBS, 1972)

and conclusion of field tests of transfer standards to be used for field certification. The model code will be sub- mitted to the National Conference on Weights and Measures this year for approval as a permanent code. Members of the LNG industry, particularly those interested in road trailer operation involving custody transfer, could take advantage of the results of

this work. Actual code and recom- mended practices specifically exclude LNG, primarily because the industrial cryogenic fluids—hydrogen, oxygen,

argon and nitrogen—are more adequately characterized than LNG mixtures. As mentioned above, this situation is changing and most other as- pects of the flow metering program

could prove useful.

Densimeter evaluation. Prediction

of LNG densities by using a computer program which relates pressure, temperature and mixture fraction to pre22 0-2 PIPE LINE INDUSTRY • DecBmber 1976
rise accurate density measurements is most probably the method which provides the least possibility of error. However, accomplishing this inferred density calculation will require metic- ulous attention to detail in the sample

extraction, gas analysis and temperature and pressure measurments. These activities, in most cases, can

be handled best in a well equipped

laboratory environment where all ele- ments are under careful control. If such measurements are made in the

lield where sampling, gas analysis, etc. are made under varying or severe conditions, then uncertainties associated

witli sampling and analysis may be unacceptable.

An alternative to this approach

would be to use, in the field, a direct reading densimeter evaluated and cal- ibrated under the most accurate and

jjrecise laboratory conditions. The

densimeter could be placed in the LNG directly, avoiding sampling errors, and the calibration would be

based on accurate, precise measure- ments needed for correlations of density with pressure, temperature and

mixture fraction. A direct reading

densimeter would also eliminate the need for field gas analysis for density determination. A program designed to evaluate per- formance of several different types of commercial densimeters has recently been completed at NBS. This work is being carried out primarily in the Metrology Section under the supervision of R. S. Collier. Funded under an AGA grant, the program provided a reference system

of such size as to allow installation of several densimeters. The measurement

f>f the performance of each densimeter under various pressure, temperature

and LNG mixture composition conditions was made with a comparison to an accurate Archimedes principle den-

-mieter and continuously monitored

and referenced to precise laboratory

ilensity measurements.

Three types. Three generic types of (Irnsimeters were investigated. Changes

"f dielectric pro])erties with density were incorporated in a capacitance

densimeter and in a microwave reso- nant cavity. Changes in damping of a vibrating element with density pro- vided a second generic type densimeter and the changes in the forces acting on an element submerged in LNG pro- vided the third type. The work at NR.S will be reported

in two parts. The first will be a detailed description of the density refer- ence system with particular attention

to accuracy and precision of the sys- tem. The second part will be perfor- mance data for the three generic types

of densimeters. A number of summary statements can be made which provide a preview

of the program results (in general, the density ranged from 390 to 490 kg/m^

for the densimeters under test) :

1 ) Dielectric Cell Densimeter. Analysis of the data for density differ- ence versus density computed from

vapor pressure measurements for pure methane, using

(pf — Pn-bs) = a + BpxBS' shows an over-all standard deviation

of about 1 percent. From the mixture data other than

the butane and nitrogen mixtures, the data all lie in a band ±0.24 percent

with butane mixture data below the median line by about 0.4 percent. The

nitrogen mixtures are outside this range and further work needs to be done on mixtures containing nitrogen.

2) Vibrating Element Densimeter.

The performance of the two types of densimeters when fitted to the relation

in ( 1

) above varied over a range of

0.2 percent to 1.6 percent for pure

fluids and mixtures.

3) Displacement or Archimedes

Densimeter. All of the data taken for

this device lie in a band ±0.2 percent

wide. From a median line the data have a standard deviation of about ±0.1 percent. The measurements

taken on this device are less extensive than for the others but include pure methane, a methane-nitrogen mixture

and a five component hydrocarbon

mixture. A detailed analysis of the dielectric constant densimeter will be published.

Under this Maritime Administration funded program, densities of LNG

type mixtures under saturation and

subcooled conditions were calculated by means of the Mollerup [Mollerup,

1975] computer program; the corre- sponding density-dielectric constant re- lationship was determined from the Clausius-Mosotti relationship for the mixture using ideal mixing rules for

tlic CM function. The results show that a nearly

unique and linear relationship between

saturation density and dielectric constant exists for both constant pressure and constant temperature conditions independent of mixture. Furthermore.

About the author

DotJGLAs B. Mann is coordinator of LNG

Programs nt the Cryogenics Division, NBS

Institute for Basic

Standards, Boulder,

Colo. A mechanical

engineer (B.S. and

M.S., Colorado University), he has more than 20 years

experience in the field of cryogenic engineering. He led the joint NBS-Compressed Gas Association program at NBS which assessed the performance of cryogenic flowmeters in commercial service, developed the model code for their use in commerce and aided in the acceptance of this type of measurement in the U.S. and Europe. His interests are pri- marily in measurement and instrumentation for determining density, pressure, temperature, liquid level and flow of cryogenic fluids. Since 1908, he has been

involved with the application of these cryogenic measurement techniques to liquefied natural gas. He holds three patents on cryogenics devices and has authored or co-authored more than 45 papers on cryogenic subjects.

it is shown that the linear relationship

is not a segment of the Clausius- Mosotti function, but results from the more fundamental thermodynamic

properties of the mixture.

Also, the nitrogen composition of

the mixture is predicted to have a pro- nounced effect on the saturation density versus dielectric constant, the in- crease in nitrogen causes an increase

in saturation density for the same di- electric constant. There is also a substantial decrease in the saturation temperature with an increasing nitrogen

content. This allows a temperature

compensation for the nitrogen content.For the normal range of LXCJ type mixtures, it is possible to determine the density to ±0.3 percent independent

of a knowledge of the composition

from an e.xact measurement of dielectric constant and temperature. Further improvements can be made if the exact composition of the mixture is known.

Therm meter. A current program

for therm meter for flowing LNfi. funded by the Pipeline Research Committee of .\G.\, is an illustration of objectives from one measurement's re- quirement being met by output from

other ongoing measurements and activities. The thenn meter jjrogram

goals are to demonstrate and assess the accuracy and precision of a three- element measurement system for preDecember 1976 • PIPE LINE INDUSTRY

0-3

23
290,000 BBL

CALORIMETER

TO

PIPELINE ^

PRESS

VORTEX

SHEDDING ^"^^fl ULTRASONIC FLOWMETER PUMP roJ FLOWMETER PRESS | TEMP MM— —^^HCI>^<—D-H}LrU- 6X8 8X4

GRAVITOMETER

4X8 8x6 VAPORIZER

I

PRESS EMP

J

r KM!

-Lni APPROX

400 PSI 12X 16

Fig. 4—Flow schematic of Transco field tests in New Jersey.

dieting the gross heating value of I-\C; flowing in a pipe line. This is a minimum risk approach

combining existing performance data

of \olumctrir flowmeters (NBS-CGA

Program), performance and calibration data for a direct reading densi- tometer (density reference system)

and the industry compatible combustion calorimeter. Therefore the volumetric How may

be measured in cubic meters per hour —combined with measured density

and kilograms per cubic meter to give mass flow rates in kilograms per hour. This rate is then combined with the output of the combustion calorimeter

(fitted with a gra\ itometer to provide data in joules per kilogram) to give

the required measurement of joules per hour.

Fig. 3 shows the NBS Liquefied

N'atural Gas Flow Facility at Boulder,

Colo. The facility, made available

through a grant from PRC, is cur- renth testing the individual measurement components under flow conditions with LNG. Conditions of pressure, temperature, flow and mixture

fraction can be controlled, and the re- cently installed calorimeter with gravi- tomcter provides the complete "breadboard"' of the therm flow measurement

system. The wide application and use of

this measurement system for LNG

must consider scaling to large pipe diameters (0.6 to 0.9 m). It is believed that for single phase fully de- veloped turbulent flow, the densitometer and combustion calorimeter will not be affected by line size. However, the performance of cryo- genic flowmeters is generally docu- mented only at diameters less than about 0.1 m. Therefore, a second goal

of the NBS-PRC program is directed

at defining the scaling laws when in- creasing the meter diameters to the

0.6 to 0.9 m size. Demonstration of the methods used

to scale the flowmeters is complicated

by not having cryogenic flow reference systems of a size or capacity required.

The NBS facility is limited by a maximum line size of 0.1 m and a flow rate of 45 m^ per hour. Larger capacity

LNG flow rates are available at industrial LNG peak shaving plants, and

gas flow measurement after LNG vaporization could provide a reference system for the liquid flow. A three-step program to define the scaling laws was selected. A volumetric vortex flowmeter was chosen based on the performance on this meter type under the NBS-CGA flowmetering program and the potential for scaling

to larger sizes. Water and liquid nitro- gen calibrations were used for both

the LNG and gas flowmeters where

applicable. In this cooperative effort, Transcontinental Gas Pipeline Corp. allowed

the installation of a 0.1 and 0.2 m di- ameter flowmeter (4 and 8-in. diameter) at its New Jersey peak shaving

facility and testing of these two meters was conducted last winter. A flow schematic of the installation is shown

in Fig. 4. Data from these tests are currently

being analyzed but indicate an agree- ment of near ±1.5 percent with the gas flow measurements. Current plans

under this program include the selec- tion of a large capacity LNG site for the installation and testing of meters

of greater than 0.4 m in diameter. •

24 0-4
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR Rivl^ORT NO.

NBSIR 77-854

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

LIQUEFIED NATURAL GAS RESEARCH AT THE NATIONAL

BUREAU OF STANDARDS

5. Publication Date March 19 77

6. Performing Organization (~odc

7. AUTHOR(S)

D. E. Diller FHii-or

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. ?75Q1Q4

11. Contract /Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as Item #9.

13. Type of Report & Period Covered

Semi-Annual —

1 JiJly-31 npcpmher 1976

14. Sponsoring Agency (^odc

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less (actual summary of most si^ificant information. If document includes a significant

bibliography or literature survey, mention it here.)

Twenty-five cost centers, supported by six other agency sponsors in addition to

NBS, provide the basis for liquefied natural gas (LNG) research at NBS. During this

six-month reporting period the level of effort was 20 man-years/year with funding

expenditures of over $500,000. This integrated progress report to be issued in

January and July is designed to:

1) Provide all sponsoring agencies with a semi-annual and annual report on the activities of their individual programs.

2) Inform all sponsoring agencies on related research being conducted at the

Cryogenics Division of NBS-IBS.

3) Provide a uniform reporting procedure which should maintain and improve

communication while minimizing the time, effort and paperwork at the

cost center level

The contents of this report will augment the quarterly progress meetings of some sponsors, but will not necessarily replace such meetings. Distribution of this docuTient is limited and intended primarily for the supporting agencies. Data or other

information must be considered preliminary, subject to change and unpublished; and

therefore not for citation in the open literature .

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Cryogenics; liquefied natural gas; measurement; methane; properties; research.

18. AVAILABILITY f Unlimited

1 For Official Distribution. Do Not Release to NTIS

1

' Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402. SD Cat. No. CH

1 Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

21. NO. OF PAGES

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

22. Price

USCOMM - tRL USCOMM-DC 29042-P74