NBSIR 76-831 (V S

LIQUEFIED NATURAL GAS RESEARCH

at the

NATIONAL BUREAU OF STANDARDS

CRYOGENICS DIVISION • N BS— INSTITUTE FOR BASIC STANDARDS • BOULDER, COLORADO

NBSIR 76-831

LIQUEFIED NATURAL GAS RESEARCH

NATIONAL BUREAU OF STANDARDS

D. B. Mann, Editor

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Progress Report for the Period

1 July - 31 December, 1975

U.S. DEPARTMENT OF COMMERCE, Rogers C. B. Morton, Secretary

James A. Baker, III, Under Secretary

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

at the

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

American Gas Association, Incorporated - 1515 Wilson Boulevard

Arlington, Virginia 22209

LNG Density Project Steering Committee

(in cooperation with the American Gas Association)

Pipeline Research Committee

(American Gas Association)

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 Energy Conservation

Washington, DC 20234

Aerospace Safety Research and Data Institute

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135
ABSTRACT

Nineteen 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 at

a 20 man-year level with funding expenditures of over $600, COO. 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 con- ducted 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: Cryogenic; liquefied natural gas; measurement; methane;

properties; research.

iii

CONTENTS

Cost Center Page

REFERENCE DATA

a) SURVEY OF CURRENT LITERATURE ON LNG 2759574 1 AND METHANE (American Gas Association,

Inc. )

b) LNG FUELS SAFETY 2750427 3 (NASA-Aerospace Safety and Data Institute)

c) THERMOPHYS ICAL PROPERTIES DATA FOR PURE 2750574 5 COMPONENTS OF LNG MIXTURES (American

Gas Association, Inc.)

d) FLUID TRANSPORT PROPERTIES 2750124 9 (NBS-Office of Standard Reference Data)

e) PROPERTIES OF CRYOGENIC FLUIDS 2750141 11

(NBS)

f) PROPERTIES OF CRYOGENIC FLUID MIXTURES 2750142, 13

(NBS; NBS-Office of Standard Reference 2750145 and

Data; NASA) 2750548

g) DENSITIES OF LIQUEFIED NATURAL GAS MIX- 2751574 15

TURES (LNG Density Project Steering and

Committee - AGA) 2752574

h) LOW TEMPERTURE MATERIAL BEHAVIOR 2750430 17

(Maritime Administration)

i) PROGRAM FOR REDUCING THE COST OF LNG 2751430 19

SHIP HULL CONSTRUCTION — PHASE II 2752430

SHIP STEEL IMPROVEMENT PROGRAM (Mari- 2753430

time Administration)

II. MEASUREMENT SCIENCE

a) CUSTODY TRANSFER - LNG SHIPS 2750460 21

(Maritime Administration)

b) HEATING VALUE OF FLOWING LNG (Pipeline 2756579 25

Research Committee - AGA)

c) LNG DENSITY REFERENCE SYSTEM 2757574 29

(American Gas Association, Inc.)

III. TECHNOLOGY TRANSFER

a) LIQUEFIED NATURAL GAS TECHNOLOGY 2750401 31

TRANSFER (Maritime Administration)

b) FEDERAL POWER COMMISSION CONSULTATION 2750404 37

(FPC)

IV. BIBLIOGRAPHY 3 9

v
ents (continued)

APPENDICES

A. Phase transition and melting pressures of solid

ethane, G. C. Straty and R. Tsumura

B. PVT and Vapor Pressure Measurements on Ethane,

G. C. Straty and R. Tsumura

C. Hypersonic velocities in saturated and com- pressed fluid methane, G. C. Straty

D. Dielectric constant data and the derived ClausiusMosotti function for compressed gaseous and liquid

ethane, L. A. Weber

E. Equation of state for thermodynamic properties

of fluids, Robert D. Goodwin

F. Orthobaric liquid densities of normal butane

from 135 to 300 K as determined with a magnetic

suspension densimeter, W. M. Haynes and M. J. Hiza

G. On the consistency of liquid-vapor equilibria data

for binary mixtures of methane with the light

paraffin hydrocarbons, W. R. Parrish and M. J. Hiza

H. Liquid-vapour phase equilibria in the N--CH. system

from 130 to 180 K, A. J. Kidnay, R. C. Miller, W. R.

Parrish and M. J. Hiza

I. Fracture mechanics and its application to cryogenic

structures, H. I. McHenry

J. Ship steel weldments for low temperature service,

Harry I. McHenry

K. The refractive index and Lorenz-Lorentz function

of fluid methane, James D. Olson

L. Thermophysical properties data research on compressed and liquefied gases at the NBS

Cryogenics Division, Dwain E. Diller

M. Equations for the viscosity and thermal conductivity coefficients of methane, H. J. M. Hanley,

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

N. Evaluation of capacitance densitometry by examination of the relationships between density,

dielectric constant, pressure and temperature

for LNG mixtures, PJ. Giarratano and R. S. Collier

vi
:. n-ie . SURVEY OF :_ :: ENT LITERATURE ON LN3 ANC ''ETHANE

Principal :-vest:ra-cr Neil A. Ilier

2. lost Center Member . 2~595~4

4. Introduction It is ir.pcr-iar.-c char all MBS perscr.r.el working ir. LMG,

as veil as ere AG.-, arc others , keep up with what is going cn throughout

the world in the TNG field. Ihis prefect is designed cc provide che

Current Awareness and other information services to allow workers to

references will he listed "under convenient subject headings. The

Quarterly will he distributed to all interested AGA member cor.panies arc :e race available tc the general public on a subscription basis.

In addition, IMG related information will be entered into the Cryogenic

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

awareness cf the current publication scene will be ~air.tair.ed for any new periodicals tc be reviewed cover- to-oover . Finally we will update

lclllc properties, r.ethane r.ixtures properties, and processes and equipment

involving r.ethane and IMG. These three will be updated each October.

result is that we now scan ever 300 primary publications and nearly 30

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

related to LNG. In addition, within the past year we have increased

our coverage of the energy field to include hydrogen as a future fuel

.

Much cf this information is also pertinent tc IMG 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 bequarterly since 1970.

Frcgam and Results . Four issues cf the 1.NG Quarterly are prepared each

year and distributed. There are now 120 subscriptions going to AGA

reviewed and shortened, and mere selective bibliographies have resulted.

The latest versions were completed as of January 1, 197 6. THE THERMOPHYSICAL PROPERTIES OF METHANE AND DEDTERO-METHANE

IN THE SOLID, LIQUID AND GASEOUS PHASES - A SELECTED BIBLI-

(Jan 1976). ($8.00?.

P

SZ1ZCTZI F III 1 1 GRAF FT . Indexed by crctertv, svstem arc author, 140 pages (Jan 1976). ($10.00").

B-1264 IF:1F=5F5 AMI FQTIFMZNT IM.'OIYING 1IITFFIFI MATTRAT GAS AXI

METHANE - A SELECTED BIBLIOGRAPHY. Indexed by subject and

author, 76 pages (Feb 1975). ($8.00).
B-1367 Supplement to B-1264, indexed by subject and author, 40 pages

(Jan 1976) . ($5.00)

These are being updated now and will be available in January 1976. Over

the past five years we have distributed over 400 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.

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

10. Future Plans . Issue 75-4 was mailed to the National Technical Information Service (NTIS) for printing and distribution on January 8, 1976.

That will be the last issue which NTIS will handle. Beginning in 1976

all functions, including subscription fulfillment and distribution, will

be returned to the Cryogenic Data Center. We feel that this will give

us closer and more positive control over the entire operation.

Labor

Other Costs

Total

2.8K$

1.1K$

3.9K$

Remaining 6. 1K$

2
1. Title . LNG FUELS SAFETY

Principal Investigators . Neil A. Olien and A. F. Schmidt

2. Cost Center Number . 2750427

3. Sponsor Project Identification . National Aeronautics and Space

Administration, Cleveland, Ohio, Aerospace Safety Research and Data

Institute. Order No. C-39327-C.

4. Introduction . The NASA-Aerospace Safety Research and Data Institute

(ASRDI) was established to provide a focal point for information and

research in aerospace safety. One of the areas of concern for ASRDI is

Cryogenic Fluid Safety. In fact, this was the first area of effort for

ASRDI. The thrust of the program is two-fold: first, to provide an automated information bank for retrieving references, and second, to

publish series of state-of-the-art reviews. The information system is

now operational and contains over 7000 references in cryogenic fluid

safety. In addition, ASRDI has published approximately twenty reviews.

Until this time, ASRDI has focused its attention and efforts on the two

primary cryogenic propellants, hydrogen and oxygen. The oxygen work

was started at NBS-Boulder in 1970 and the hydrogen work in 1972. With

the coming possibility of methane or LNG fueled aircraft and the close

affinity of LNG safety and cryogenic safety, ASRDI felt that it was timely to begin work in that area.

5. Objectives or Goals . The following objectives are to be achieved:

a) Review and modify an existing Cryogenic Fluids Safety Grid and

thesaurus to include and adequately cover LNG safety.

b) Make a thorough search of over eleven information sources for

LNG information. This will include published and unpublished

material

.

c) Catalog, index, abstract and put into machine readable form all

available documents located in b) above. The indexing will be

done by technical personnel with demonstrated competence in

cryogenic safety and related fields.

6. Background . This program was started at NBS-Boulder by ASRDI in 1970.

Since then considerable skill and experience has been gained in locating,

processing and, most important, detailed subject indexing of safetyrelated information. In addition, NBS-Boulder has been providing detailed coverage of the LNG field for the American Gas Association since

early 1970. The present program, then, provides an opportunity for

industry, government and the public to capitalize on the accumulated

past efforts of two seemingly unrelated programs.

7. Program and Results . Under this and another ASRDI-funded program we

have started a major review of the indexing and retrieval terminology

which will be used in the Cryogenic fuels safety information system.

This review will result in a thesaurus to be published by NASA. The

review is complete and we are now in the process of editing and preparing the thesaurus in its final form. Publication has been delayed

awaiting a decision as to publishing the thesaurus separately or com- bined with one in fire safety and one in the mechanics of structural

failure. Most of the terminology unique to LNG safety is now incorporated into this thesaurus. Approximately 500 papers, reports, etc.,

have been carefully indexed, abstracted, cataloged and transmitted to

ASRDI.

3
8. Problem Areas. None.

9. Funding . July 1 - December 31, 1975

Allocation (9/30/74 - 10/1/75) - 50K$ NASA/ASRDI

Labor 0.2 MY 8.1K$

Other Costs . 8K$

Total 8.9K$

Remaining —

10. Future Plans . The work on this project has been completed and there

are no current plans to continue the effort.

4
1. THERMOPHYSICAL PROPERTIES DATA FOR PURE COMPONENTS OF LNG

MIXTURES

reeded ~z supper- tr.es e projects. - or example, a::;raliquef actic- and transport processes; a:cura-e data fc:

value, which for liquefied natural gas mixtures depend;

volume, tie density, ar.d tie ccrpcsi.icr. , are needed tc for eceitaile custody transfer.

Accurate thermodynamic properties data for liquefied gi

pressures and densities) . It is impossible, however, i enough compressibility and calorimetric measurements d: :ctpcr.er.- fixtures tc ;er- :: accurate interpolation of

arbitrary ccr.pc sitiens , temperatures and pressures. Zz dynamic properties data fcr mclticcmpcnent mixtures us;

* Conssjo -Tacicnal de Ciencia y _ecnologia ZZV.kZZ . Mexico City. Currently

a cuest worker with the Crvcterics division, National Bureau cf Standards,

5
This project was initiated to provide the natural gas 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). This report contains the most comprehensive and

accurate tables available for the thermophysical properties of pure

gaseous and liquid methane, and provides an accurate basis for calculating thermophysical properties data for LNG mixtures. Similar data

is now being obtained for compressed and liquefied ethane.

7 . Program and Results . 7.1. Melting Pressures, Vapor Pressures and Equation of State (PVT)

Data — G. C. Straty and R. Tsumura

Comprehensive, accurate measurements of the melting pressures, vapor

pressures and equation of state (PVT) for compressed and liquefied

ethane, 90-320 K, to 35 MPa (5000 psi) , have been completed. Two re- ports have been completed and submitted for publication:

a) G. C. Straty and R. Tsumura, "Phase Transition and Melting

Pressures of Solid Ethane." J. Chem. Phys. (in press, 1976).

b) G. C. Straty and R. Tsumura, "PVT and Vapor Pressure Measurements on Ethane." J. Res. Nat. Bur. Stand, (in press, 1976).

Both reports are reprinted in the appendices (see Appendices A and B)

7.2. Methane, Sound Velocity Data — G. C. Straty

A light scattering spectroscopy apparatus has been employed to obtain

hypersonic (GHz) velocity data at the lower densities where measurement by ultrasonic techniques were impossible. Data have been obtained

to densities as low as 1 mol/l along several isotherms. Measurements

in the regions of overlap agreement with calculated sound velocity data

is satisfactory. The data have been combined with previously measured

PVT data to obtain the isentropic compressibility and specific heat

ratio Cp/C

v

- A manuscript reporting the results of the hypersound

velocity measurements has been published in Cryogenics 15_, 729 (1975)

and is reprinted in the appendices (Appendix C)

7.3. Ethane, Dielectric Constant Data — L. A. Weber

Dielectric constant measurements have been completed over a temperature

range of 95-323 K, including the saturated liquid from triple point to near the critical point and compressed liquid and fluid states at pressures up to 390 bar. The dielectric constant data have been combined

with available accurate density data to form the Clausius-Mosotti

function [ 1/p ( e-1 ) / ( e+2 ) ] , which has been expressed analytically as a function of density and temperature over a wide range, with an overall

estimated accuracy of 0.1%. This function has been used to examine the

consistency of the various sources of density and PVT data for ethane.

A manuscript reporting the results has been completed, and is preprinted in the appendices (Appendix D)

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

Specific heat data (Cv

) are required to accurately define the derivatives of the equation of state (PVT) , which in turn are used to calculate other thermodynamic functions such as enthalpy. Measured values

of Cv are particularly valuable to cross-check thermodynamic calculations for the compressed liquid states. We have prepared for a series

of C and C„ 7

. m measurements on ethane similar to those completed on

v SAT c

6
methane under this program. Measurements of the heat capacity of the

empty calorimeter have been extended from 300 to 330 K to permit Cv measurements of compressed gaseous ethane at temperatures above critical.

Since the critical temperature of ethane (305.3 K) is well above room

temperature, fluid of relatively high density will reside in the filling

capillary part of the system, and will have to be accounted for accurately.

During the reporting period, we completed the measurements on the heat

capacity of the empty calorimeter, and measured 32 Cv points for methane.

Deviations between present and previous measurements on methane vary

from several tenths of a percent to 0.8 percent.

We have converted the data reduction programs for methane to ethane, and

have measured a total of about 200 points on 9 different isochores for

ethane. Since we had planned for about 350 points, data taking is about

60% complete. Measurements of C and C have been combined; that is

o/\ J. V

both are made for a single filling of the cell. Since we have measured

only liquid phase isochores to date, the measurements on C--^ are nearly

complete. Deviations for Cg

flT from the values calculated in NBSIR 74-398 are on the order of 0.j%. . Deviations from values of other authors run

up to 2% because the earlier papers do not account accurately for the

amount of fluid vaporized or condensed during the measurement. Present

values of Cv usually differ from NBSIR 74-398 by 1% or less, with larger

deviations, i.e., up to 3%, occurring very close to the saturation

boundary. We have yet to determine if this latter effect is real, or if

it occurs because we have not accurately accounted for the amount of

sample in the capillary.

7.5. Ethane, Sound Velocity Data — R. Tsumura

New ultrasonic measurements of the velocity of sound in compressed and

liquefied ethane (90-320 K, 35 MPa (5000 psi)) are in progress. The

ultrasonic velocities of sound in pure saturated liquid ethane have

been measured at MHz frequencies. Data have been obtained along the

saturation boundary from near the triple point (90.35 K) to 280 K, using

the pulse-echo technique, in which the imprecision is estimated to be

less than 0.05%. In the temperature interval 150 K to 280 K these data

appear to be consistent with other available data within the experimental

error. There is, however, a systematically increasing disagreement as the triple point is approached, reaching a maximum of 0.4% near this

point.

7.6. Ethane, Thermodynamic Properties Data — R. D. Goodwin

In a previous report, NBSIR 74-398 (June 1974) , "Provisional Values for

the Thermodynamic Functions of Ethane," we made use of available physical properties data to derive provisional thermofunctions at the earliest

possible date, including results never before available for the com- pressed liquid at temperatures from the normal boiling point (185 K)

down to the triple point (90 K)

.

Our purpose during both the previous and forthcoming six months is to

utilize newly available accurate physical properties data to improve

the accuracy of the derived thermofunctions and to produce a final re- port giving these results.

7
For the computation of consistent and accurate thermodynamic functions,

it is essential to have an accurate equation of state, describing the

P(p,T) surface in three dimensions, which is much more than merely

accurate in reproducing experimental PVT data. The derivatives of this

surface must be regular in their behavior and must be consistent with

the known behavior of specific heats and other thermodynamic properties.

See for example "Equation of State for Thermodynamic Properties of

Fluids," by R. D. Goodwin, J. Res. NBS 79A (1), 71 (1975) (Appendix E)

New experimental data have become available for the vapor pressure, the

orthobaric densities near the critical point, the saturated liquid densities at low temperatures, and for PVT data at densities from the

critical density to the liquid triple point density. Forthcoming new

dielectric constants, specific heats, and speeds of sound will permit

further indirect checks on thermodynamic computations via the equation

of state.

Our new form of equation of state is so highly constrained for selfconsistency (e.g., between orthobaric densities and the PVT surface)

and for consistency with the behavior of specific heats, that the use

of experimental PVT data from different sources, which are not consistent with each other, yields deviations which are quite disturbing when

compared with the "good" fit of PVT data to which the reader may be

accustomed. This problem has occupied much of our efforts during the

past reporting period.

8. Problem Areas. None.

Funding . July 1 - December 31, 1975.

Man-years expended 1.0

Equipment and/or Services Purchased 4.7K$

Total Reporting Period Cost 69.0K$

Balance Remaining 71.0K$

10 . Future Plans . Year

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

specific heat (CgAT and

data for ethane.

Measure, analyze and report

ultrasonic velocity data

for ethane.

Calculate and report accurate

thermodynamic properties

data for ethane.

*

5

>

8
1. Title . FLUID TRANSPORT PROPERTIES

Principal Investigator . Howard J. M. Hanley

2. Cost Center Number . 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 mea- surements 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 fcr 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 , 02, F2, He,

H

2

/ CH^. Recent work has extended this approach to ethane. It is felt

that a successful mixture program will 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 . Statistical mechanics has been applied to predict

and correlate the dilute and moderately dense thermophysical properties

of carbon dioxide. 1 Carbon dioxide was selected as a typical polyatomic

molecule. The self-diffusion coefficients of methane have been correlated and tabulated. 2 Results for the dilute gas transport properties

of oxygen and nitrogen have been published. 3 The well-known critical

point anomaly in the thermal conductivity can now be predicted to within

experimental error.

14 An equation to calculate the dense gas and liquid

transport properties of several simple fluids has been reported. 5 Preliminary work on the transport properties of mixtures has been very

promising. Theoretical studies on transport theory have been reported. 6

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

for comparison purposes is the main problem.

9. Funding . July 1 - December 31, 1975.

Allocation 59.0K$ OSRD

Labor 0 . 5 MY 31.1K?

Other Costs 3. 0K$

Total 34. IKS

9
10. Future Plans . The transport properties of methane and ethane have been

tabulated and will be published. Propane is being investigated. A preliminary procedure to calculate the transport properties of mixtures will

be reported.

References

1. J. F. Ely and H. J. M. Hanley, Mol. Phys. 30, 565 (1975).

2. K. R. Harris, H. J. M. Hanley, et al., "The Self-Diffusion of Simple

Fluids," Australian National Univ. Press., DRU-RR 2 (1974).

3. H. J. M. Hanley and J. F. Ely, J. Chem. Phys. Ref. Data 2, 735 (1973).

4. H. J. M. Hanley, J. V. Sengers and J. F. Ely, Proc . 14th Int. Conf.

Thermal Conductivity (Pergamon Press, 1975)

.

5. H. J. M. Hanley, W. M. Haynes and R. D. McCarty, Cryogenics 15^, 413

(1975); J. Chem. Phys. Ref. Data 3, 979 (1974).

6. For example, H. J. M. Hanley and W. M. Haynes, J. Chem. Phys. 6_3, 358

(1975); H. J. M. Hanley and R. 0. Watts, Physica 79A, 351 (1975).

10
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 consumer 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 com- pressed 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 for fluids under

conditions for which sound absorption is too large to perform ultrasonic

measurements; laser light scattering techniques permit measurements of

thermal dif f usivities 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.

11
7. Program and Results . An apparatus has been assembled for laser light

scattering spectroscopy on compressed and liquefied gases (76-300 K,

350 bars) . 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 pressure scanned Fabry Perot

interferometer for the measurement of the Doppler frequency shifts

associated with the scattering from propagating density (pressure)

fluctuations (Brillouin scattering)

.

Data on the hypersound velocities in pure methane have been obtained by

Brillouin scattering techniques at low densities (< 14 mol/£) where the

large sound absorption in methane prohibits more conventional ultrasonic

measurements. Data have been obtained along several isotherms from

210 K to 300 K at densities down to 1 mol/£. Agreement with previously

measured ultrasonic velocities in the regions of overlapping data is

good. The data have been combined with previously measured PVT data to

obtain the isentropic compressibility and ratio of the specific heats.

A manuscript reporting the results of these measurements has been published in Cryogenics 15, 729 (1975) and is reprinted in the appendices

(Appendix C)

.

Equipment modifications have been made which should permit the determination of the thermal diffusivity, X/pC , of pure methane. The most

accurate method of doing this is to use photon-counting and digital

autocorrelation techniques to measure the temporal behavior of the

spontaneous temperature fluctuations occurring in the fluid which is

governed by the bulk fluid thermal diffusivity. This is equivalent to

measuring the very narrow Rayleigh line width and requires a resolution

12 of about one part in 10

Preliminary checks of the modified apparatus on a well-characterized

test fluid appear to have been satisfactory. Further testing with

methane is planned.

Current work involves the interfacing of mini-computer systems with the

scattering apparatus to permit more rapid data accumulation and accurate

on-line computer analysis of the data.

8. Problem Areas. None.

Funding . July 1 - December 31, 1975

Man-years expended 0.3

Equipment and/or Services Purchased 3.9K$

Total Reporting Period Cost 20.0K$

Balance Remaining 17.5K$

10. Future Plans.

Objectives and Schedule Quarter

Year

Measure, analyze and report

thermal diffusivity coefficient

data for methane.

12
1. Title . PROPERTIES OF CRYOGENIC FLUID MIXTURES

Principal Investoragors . M. J. Hiza, A. J. Kidnay (part-time) , R. C.

Miller (part-time), and W. R. Parrish (part-time).

2. Cost Center Numbers . 2750142, 2750145 and 2750548

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

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 com- pilations 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 mea- surements 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 gasses — 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.

13
7. Program and Results . The recent progress of this program is summarized

as follows:

a) The comprehensive bibliography of fluid mixtures data entitled

"Equilibrium Properties of Fluid Mixtures: A Bibliography of

Cryogenic Data" has been published (IFI/Plenum Press, 1975).

b) Work is continuing on the compilation of liquid-vapor equilibrium

data and derivation of the excess Gibbs functions and Henry's

constants for binary systems containing methane with the light

hydrocarbons, argon and nitrogen. A paper, "On the Consistency of

Liquid-Vapor Equilibria Data for Binary Mixtures of Methane with

the Light Paraffin Hydrocarbons," which covers a portion of this

work, was presented at the 1975 Cryogenic Engineering Conference.

This paper is reprinted in the appendices (Appendix G)

c) A paper entitled "Liquid-Vapor Phase Equilibria in the System

N

2 + CH

4 from 130.00 K to 180.00 K," has been published, Cryogenics

15 , 531 (1975) . This paper includes an evaluation of available

data for this system, as discussed in (b) , as well as the new

measurements. This paper is reprinted in the appendices (Appendix

H) . d) New liquid-vapor equilibrium composition measurements at selected

conditions for the methane + ethane system have been obtained and

are being analyzed.

e) Funds have been received to initiate research on PVTx (equation of

state) data for mixtures of compressed and liquefied gases.

8. Problem Areas . None.

9. Funding . July 1 - December 31, 1975

Man-years expended 0.7

Equipment and/or Services Purchased 2.6K$

Total Reporting Period Cost 37.1K$

Balance Remaining 83.8K$

10, Future Plans.

Year

Objectives and Schedule: Quarter

Compile, evaluate, correlate

and report liquid-vapor

equilibrium data for methaneethane mixtures.

Initiate evaluation of promising

predictive equation of state

calculation methods using

available data.

Measure, analyze and report

liquid-vapor equilibrium

data for methane-ethane

mixtures

14
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, 2752574

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.

Prior to this reporting period 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 repeatability and estimated precision of measurement are better than 0.02% while the accuracy is better

than 0.1%.

7. Program and Results . Density measurements on mixtures of LNG components are in progress. Saturated liquid density measurements have been

carried out for the following mixtures:

a) 0. 30 N

2 + 0. 70 CH4 (105 -130 K)

b) 0. 67 C

2 H

6 + 0. 33 nC4 H

1Q (110-140 K)

c) 0. 65 C

2 H6 + 0. 35 nC4 H1Q (115, 120 K)

d) 0. 47 iC

4 H10

+ 0.53 nC

4 H1Q (125-140 K)

e) 0. 49 C

3

H

8 + 0. 51 iC

4 H 1Q (105-130 K)

f) 0. 50 C

3 H8 + 0. 50 iC4 H1Q (125, 130 K)

g) 0. 72 C

2 H

6 + 0. 28 iC4 H1Q (105-130 K)

h) 0. 69 C

2 H

6 + 0. 31 iC4 H1Q (115, 120 K)

15
i) 0. 68 CH

4 + 0. 32 C2 H

6 (105-130 K)

j) 0. 35 CH

4 + 0. 65 C2 H

6 (105-130 K)

k) 0

.

75 CH

4 + 0

.

25 C

3 H

8 (105-130 K)

1) 0. 90 CH

4 + 0. 10 C

3 H

9 (105-140 K)

m) 0. 34 CH

4 + 0. 31 C

2 H

6 + 0.34 C

3 Hg (110-125 K)

n) 0. 85 CH

4 + 0. 05 C2 H6 + 0.04 C

3 Hg + 0.03 iC4 H

1Q

(105, 110 K)

o) 0.34 N

2 + 0.34 CH

4 + 0.32 C^E^ (105-115 K)

The new experimental data for the binary mixtures have been used as input data to several equations of state, which have been then used to

predict the densities of the multicomponent systems. Most of these

predictions agree with direct measurements to about 0.05% in density.

A paper "Orthobaric Liquid Densities of Normal Butane from 135 to 300 K as Determined with a Magnetic Suspension Densitometer," was presented

at the 1975 Cryogenic Engineering Conference. This paper is included

in the appendices (Appendix F)

.

8. Problem Areas . None

9. Funding . July 1 - December 31, 1975

2751574 (measurements)

Man-years expended 0 .

8

Equipment and/or Services Purchased 3.0K$

Total Reporting Period Cost 52.2K$

Balance Remaining 68.2K$

2752574 (calculation methods)

Man-years expended 0.25

Equipment and/or Services Purchased 0.5K$

Total Reporting Period Cost 8 . 3K$

Balance Remaining 25.6K$

10 . Future Plans . Year

Objectives and Schedule: Quarter 1 2 Measure orthobaric liquid

densities of mixtures

containing methane,

ethane, propane, butanes

and nitrogen.

Evaluate and optimize several

available accurate density

calculation methods.

>

16
1. Title . LOW TEMPERATURE MATERIAL BEHAVIOR

Principal Investigators . H. I. McHenry and R. P. Reed

2. Cost Center Number . 2750430

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

#400-58074.

4. Introduction . For cryogenic applications, the ASME Boiler and Pressure

Vessel Code and the API Standard 620 Appendix Q Code specify the same design allowable stress level for 5Ni steel as for 9Ni steel. Since

5Ni steel costs approximately 20% less than 9Ni steel, significant cost

savings could be achieved by using this material for LNG applications.

At the present time, 5Ni steel cannot be used in place of 9Ni steel for

marine applications because the U. S. Coast Guard has not approved it.

The principal reasons that the USCG has delayed approval are lack of

service experience in land based tankage and concern that the fracture

resistance of the weld heat affected-zone (HAZ) is inadequate.

5. Ob j ectives . This program is being conducted to evaluate the fracture

resistance of the heat affected zone of 5Ni steel weldments at room

temperature, 111 K and 7 6 K.

6. Background . This program is a continuation of the program conducted by

Reed, et al. to determine the mechanical properties of candidate materials for LNG tankage. The work demonstrated that 5Ni steel plate has

adequate mechanical properties for LNG applications. Further work was recommended to verify that the plate properties would be retained in the

weld heat affected zone.

7. Program and Results . The program to evaluate 5% Ni steel weldments

consists of evaluating the weldment toughness in accordance with the

USCG requirements for weld procedure qualification and determining the

fatigue crack growth and fracture toughness properties of the weldment.

Weld procedure qualification involves testing three Charpy impact specimens at five locations within the weld zone: at the weld centerline,

the fusion line, and the heat affect zone at 1 , 3 and 5 mm beyond the

fusion line. The tests were conducted in accordance with ASTM Standard

Method E-23 at 76 K. The results exceeded the USCG requirements in all

weldment locations.

Fatigue crack growth tests are being conducted using three-thickness

bend specimens to enable definition of the part of the HAZ most susceptible to crack growth. To date, tests have been conducted on the base

metal at room temperature and 7 6 K and on the HAZ at room temperature.

The base metal results are essentially the same as those obtained previously using compact specimens. In the HAZ test, the crack was started

in the fusion line, but proceeded to propagate into the base metal —

in the direction perpendicular to maximum stress. Thus, at room temperature, HAZ embrittlement is not apparent in the crack growth tests.

Fracture toughness tests have been conducted on the base metal and the

HAZ at 111 K. The results indicate that the base metal toughness is

approximately 150 ksi/Tn. No crack extension could be detected prior to

failure despite repeated efforts using heat-tinting procedures. The HAZ

toughness ranged from 94 to 102 ksi/Tn on the three specimens that ex- hibited crack extension (pop-in) prior to fracture and from 106 to 133

ksi/Tn on the three specimens that failed prior to any detectable crack

extension

.

17
A paper entitled "Fracture Mechanics and its Application to Cryogenic

Structures" was prepared and presented at the International Cryogenic

Materials Conference in Kingston, Ontario (see Appendix I).

8. Problem Areas . The test schedule has been extended to March 31, 1976

(from December 31, 1975) and no additional problems are anticipated to

completion

.

9. Funding . July 1 - December 31, 1975

Expended

Remaining

30K$

20K$

10. Future Plans . All testing will be completed by March 31, 1976.

18
Title. PROGRAM FOR REDUCING THE COST OF LNG SHIP HULL CONSTRUCTION -- PHASE II SHIP STEEL IMPROVEMENT PROGRAM

Principal lr.ves~igat.ors . H. I. McKer.ry, 3. Kasen, and R. P. Reed

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

2751430 - LNG Ship Construction Materials (Metallurgical Evaluation)

2752430 - LNG Ship Hull Materials (Fracture Properties)

Sponsor Project ler.-rzica 4 Maritime Administration Mi so 0 400-58073

I-.r::::-::" . Cons-ruction of INC 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 C F. Several

AES 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 encoun- tered 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 irias

gram described below

:his tro _ ect eading to the Phase II prolb; ective . Che objectives of the Phase II program are 1) to have the

four major place 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

.

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

Corm.i~.tee recommended that a program be conducted to reduce the cost of

ship hull construction. NHS 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 1 s recommended program, i.e., to survey the problem and the technology available for ics solution. In the oasis of this survey ant as the result of a meeting of the Welding Panel in March, 1975, a coordinated program 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.

Program and Results . Contracts have been awarded to the three shipyards currently building INC- cankers: Avondale Shipyard, Inc.; General

Dynamics "uincy Shipbuilding Division; and Newport News Shipbuilding.

Each of these vards has Placed orders for steel as follows:

Shipyard

Avondale rmco General U.S. Steel

Dynamics Bethlehem

Newport News Bethlehem

* The steel grades V-062, V-051 and CS

(ABS) grades

** SSC - Sulfide Shape control employed.

Steel Grade * V-062

V-062 (SSC) ** CS (SSC)

ASTM A53 7A-Mod.

and -50°F V-051 (SSC) are American Bureau of Shipping

_est lemoerature

-25=F

-50°F

-25=F

-60°F

-25

19
Upon receipt of material, each participating shipyard will evaluate the

steel plates by qualifying optimum weld procedures in accordance with

USCG requirements. The welding processes being qualified are submerged

arc, gas metal arc, and shielded metal arc. The test weldments will

also be subjected to a metallurgical evaluation to determine the effect

of microalloying and sulfide shape control on heat affected zone toughness. A paper entitled "Ship Steel Weldments for Low Temperature Service" was prepared and presented at the Fourth Materials Technology Conference in

Boston, MA (see Appendix J)

8. Problem Areas . The development work has been delayed because more time

was required for contract negotiation and steel procurement than was originally anticipated.

9. Funding . July 1 - December 31, 1975

Cost Center Cost to 12/21/75 Balance

*Includes phase I costs.

10. Future Plans . The steels should be delivered and the shipyard and

metallurgical evaluations should be started during the next reporting

2753430

2751430

2752430

$105 K

$ 57 K*

$ 26 K

$105 K (obligated)

$ 18 K

$ 14 K

period.

20
1. Title . CUSTODY TRANSFER - LNG SHIPS

Principal Investigators . R. S. Collier, P. J. Giarratano, and J. D. Siegwarth

2. Cost Center Number . 2750460

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

#400-58074.

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.

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

shipbuilders have been established. 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

a) thermal effects

b) loading factors

c) measurement techniques

3. Convection (Non-Unifarm 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

B. We have reviewed in detail the capacitance densitometer both from

theoretical and experimental point of view. The theoretical analysis

has shown two major effects for LNG near the saturation temperature

21
and pressure nominally close to atmospheric pressure (or slightly above)

These two effects are:

1. The heavy hydrocarbons in the absence of nitrogen tend to partially

compensate for their density as a function of molecular weight to

the extent that, at saturation, the density versus dielectric con- stant is approximately single valued relationship (within a certain

error which, for a typical range of LNG mixtures, is approximately

0.3 percent). This is a new result which is independent of the

Clausius-Mosotti relationship. The Clausius-Mosotti function does

not delineate the saturation curve of the LNG mixtures and includes

subcooled fluids; but when the saturation curve is delineated, the

unique one to one relationship between density and dielectric con- stant very nearly exists.

2. Nitrogen has a very pronounced effect on the density versus dielectric constant. Mole fractions of nitrogen on the order of 1 percent of the total composition can cause about 1% increase in the

density for the same dielectric constant. This nitrogen effect

tends to negate the usefulness of dielectric properties for density

measurement except for the fact that the saturation temperatures of

LNG mixtures containing nitrogen are somewhat lower. Consequently,

we have found that it is possible to temperature compensate the

capacitance densitometer using a bilinear relationship between

density, dielectric constant, and temperature; curves for this

bilinear relationship and the coefficients that go in this relationship have been obtained by the use of least squares computer programs together with the correlations using 1) the law of corresponding states as proposed by JcJrgen Mollerup and as modified by Bob

McCarty at NBS and 2) the Clausius-Mosotti relationships as proposed

by Pan, et al. 2

. The details of this analysis are contained in the

appendices of this report (see Appendix N)

C. As part of the testing program in the area of capacitance densitometers we have obtained dielectric constant data for methane binary mixtures with hydrocarbons and also some typical LNG mixtures with and

without nitrogen. These measurements confirm the theoretical analysis

described above to within about 3/10 of one percent. This experimental

program together with the theoretical analysis gives positive and con- clusive indication of the capability of the capacitance densitometers

as their anticipated end use onboard ship custody transfer systems.

D. In connection with the program on the density reference systems

(Cost Center 2757574) we have conducted a prototype capacitance densitometer system which although not temperature compensated for nitrogen,

performs within theoretical uncertainties for the hydrocarbon mixtures

and is capable of the suggested temperature compensation for nitrogen.

Further testing is in progress.

E. We have calculated the difference between the corresponding states

theory and the Klosek-McKinley relationship for the temperature and

pressure and composition ranges envisioned by the LNG industry and

found that these two agree to within 2/10 of a percent. If a temperature is measured accurately, and also composition, the density can then

be obtained using the Klosek-McKinley relationship to about the same certainty as using the densitometer approach. (The Klosek-McKinley

approach is to be used by the industry in the absence of a more precise

correlation or an adequate densitometer.)

F. We have investigated the heating value of LNG as a function of

density and dielectric constant for the saturated LNG mixtures. We find

again that for mixtures without nitrogen the heating value versus saturation density is very close to unique functions and the heating value

versus dielectric constant is a unique function to the same order of

22
magnitude that the density is a unique function of dielectric constant.

Here again, however, the effect of nitrogen is pronounced. The heating

value versus density and dielectric constant changes markedly with the

addition of nitrogen. Further work needs to be done in the area of

direct therm-metering for mixtures containing nitrogen.

G. We have begun to review in detail the ability of the ship companies

to measure fluid volume which together with the density will give them

a total mass. The fluid volume is a function of both the tank strapping

and the liquid level measurement:

1. There are two basic techniques for tank strapping: a) the stereophotogrammetric method of measuring the inside dimension of the tank

and b) tape measurements on selected circumferences of the tank.

Both of these methods are under consideration by the ship companies

and we are presently discussing, with the industry, possible NBS

involvement concerning verification of the accuracies of either or both of these methods.

2. We have begun preliminary design (consistent with manufacturers

specifications) concerning a test facility for stratification

research and level testing. This facility would be capable of

testing prototype level gauges on the order of 10 meters in length

which seems to be adequate for observing thermogradient effects,

LNG stratification effects, and also possible effects caused by con- densation of heavy hydrocarbon vapor on the sensing elements. A

preliminary test plan has been drawn up and distributed to MarAd,

the engineering departments of the major shipyards, and some of

the manufacturers. It is likely that industry will participate in

these tests which would involve consignment of equipment and some financial commitment on their part to complete the tests.

H. We have been involved in pursuing advanced gauging techniques including therm-metering and RF gauging techniques. We have modeled the

spherical LNG ship tanks in the laboratory, including a model of the

measurement stillwell (which in the ship is a cylindrical tube 8 feet

in diameter running along a 120 foot spherical diameter from the top to

the bottom of the tank) . We have found for the laboratory model that

it is feasible to use the measurement stillwell as an RF antenna with

the electrical connection being made directly to the stTllwell at mid

point. In this configuration the model can be resonated as an electromagnetic resonant cavity and the resonant modes have been identified;

as the tank if filled with LNG the resonant frequencies decrease as the

LNG fills the tank. The scaling laws for the RF cavity are under investigation and experiments are in progress for testing the scaling laws

in tanks that range between the laboratory model which is 18 inches in

diameter and the actual spherical LNG tank which is 12 0 feet in diameter.

I. We have conducted preliminary studies into the possibility of a direct reading therm-meter for LNG custody transfer. It seems worthwhile, at this point, to conduct some feasibility studies involving the

electromagnetic spectroscopic properties of LNG as well as some of the

thermodynamic physical properties for possible use in a direct reading

therm-meter

.

8. Problem Areas . One of the most difficult estimates to make is the

degree of density or composition stratification within the tank; this

could also include the effect of stillwells and remote access areas within the tank. It will probably not be possible to estimate these

effects to the desired accuracy. It is therefore recommended that

some of these ship tanks be fitted experimentally to measure density,

temperature and composition at various locations within the tank during

the normal course of checkout of these systems.

23
9. Funding . July 1 - December 1, 1975

Man-years expended 0.5

Total Cost 33.4K$

Balance Remaining 11.7KS

10 . Future Plans . 1. Complete the rangeability test of the capacitance type densitometer.

2. Continue a program of exchange of information with the U.S. shipbuilding companies.

3. Develop and update procedures for calculating weathering and boiloff rates for tanks containing LNG mixtures.

4. Initiate studies of stratification and detection in large systems

consistent with solving problem areas as in paragraph 8 above.

5. Conduct further experiments on RF gauging in large tanks.

References

1. J. Mollerup and J. S. Rowlinson, Chemical Engineering Science 29 , 1373 (1974).

2. W. P. Pan, M. H. Mady , and R. C. Miller, Dielectric constants and

Clausius-Mosotti functions for simple liquid mixtures: systems

containing nitrogen, argon and light hydrocarbons, AIChE Journal

21, No. 2 (March 1975)

24
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 are 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. Work in this area did progress

during this reporting period when a short field test at the peak shaving

facility was completed. If additional testing can be completed during

the current send-out season additional delays in the project will be

prevented

.

7. Results . Field testing of the four-inch flowmeter at the LNG peak shaving facility was completed December 16, 1975. The actual test period

available was approximately 3-1/2 hours which was shorter than desirable

but long enough to obtain some very useful data.

A preliminary analysis of the data indicates agreement between the liquid

and gas flow measurements within about one percent. Data analysis is

still proceeding and the final results must await receipt of the final

gas phase measurements from the peak shaving facility. Therefore, re- sults from this test will not be reported until the next semi-annual

report

.

In the last semi-annual report it was stated that a new LNG peak shaving facility had been selected for testing the eight-inch flowmeter

since this new facility had a high probability of send-out during the

current season. To reduce the possibility of additional delays in this

phase of the program plans were made to move the flowmeter tests. These

plans had to be dropped, however, because the cost involved was too high.

Therefore, the eight-inch flowmeter has been installed in the same location as the four-inch meter and the smaller meter has been removed

from the line.

25
Some component testing on the NBS flow facility was also completed during

this reporting period. As previously stated it was necessary to assemble

a natural gas condenser for making LNG. This condenser uses liquid

nitrogen to condense low pressure natural gas and was used as the source

of the LNG for the testing in the flow facility.

Figure 1 is a schematic of the NBS flow facility in which the various

elements of the measuring station are being tested. During the most

recent tests data were obtained on all the individual elements and cross checks are being calculated. The individual signals will be integrated into a single indication of heating value during the next years

test program.

8. Problem Areas . None.

9. Funding . July 1 - December 31, 1975

Man-years Expended 0.2

Total Reporting Period Costs 7 0K$

Balance Remaining . 5K$

10. Future Plans . Flowmeter tests on the eight-inch meter will be run whenever there is a send-out. The current send-out season ends in March

1976. Additional tests on the NBS flow facility will be run after the

instrumentation integration has been completed.

26
27

utie . LNG DENSITY REFERENCE SYSTEM

Principal Investigator . Ben Younglove

Cost Center Number . 2757574

Sponsor Project Identification . American Gas Association, Inc.,

Project BR-50-10

Introduction . The emphasis of the LNG effort of NBS is in providing

technical support to industry in meeting the energy needs of our economy with natural gas.

The density reference system will evaluate the ability of commercially

available instruments to measure densities of LNG. Density is an essential measurement in performing total energy content determinations of

natural gas reservoirs. While this effort is oriented towards metrology,

the output from cost center 2751574 will provide basic reference data

on pure liquids and mixtures which will serve as density standards.

Ob j ectives . This research will provide a system for evaluating the

density measurement capability of commercially available meters. We

will evolve a density reference system capable of generating accurate

densities for this evaluation. From the commercial meters we will

attempt to selecte one capable of performance as a transfer standard in

order to provide traceability of accuracy to field density measurement

systems

.

Background . The density reference system was initiated in 1973 with a proposal to the AGA for research on LNG technology. Since that time

the reference system has been selected, designed, constructed, and is

now in operation, evaluating density metering systems.

Program and Results . Data have been accumulated on performance of the

vibrating cylinder, vibrating plate, and the capacitance meter in liquid

methane, methane + ethane, methane + propane, methane + butane, methane

+ nitrogen, and two LNG type mixtures.

Pure methane runs are incorporated on a regular basis in an attempt to

establish reliability limits of the density reference system over an extended time.

A second series of tests is underway to evaluate the commercial displacement type (or Archimedes type) meter. The other devices were left in the

system in order to accumulate more data on them as well. We have accu- mulated data on pure methane and methane + nitrogen in this configuration.

John Labrecque of the NBS Statistical Engineering Laboratory has analyzed

the pure methane runs of the first series. Using the model

S=u+ap+n+e

where £ is density deviation from NBS densities for pure methane from

vapor pressure, is the bias independent of density, temperature, or pressure; r, error constant within an occasion (or data taken on a given

run) ; and z is an error changing randomly from occasion to occasion, he

finds these results, where z is an estimate of "one sigma" deviation:

3 3 Accuracy Affected by Density a kg/m a kg/m

NBS DRS

Cylinder

Plate

Dielectric Cell

Not Significant 0.2 0 Significant 0.49

Significant 1.55

Significant 0.41

0. 30

0.57

1.16

0.07

These results will be given in more detail in the final report.
Results taken so far for the displacement type meter show roughly a

3 constant bias of -1 kg/m and a random scatter of about half that.

This latter observation is very preliminary.

Problem Areas . Deviations of the meters for the mixtures data show

roughly the same behavior as the above with the notable exception of

the capacitance (or dielectric cell) densimeter, which showed marked

deviations with nitrogen composition. Two binary mixtures of nitrogen

were taken, showing approximately a 1 to 1 or greater deviation of

density indication to nitrogen composition (mol %).

Funding . July 1 - Decmeber 31, 1975

Man-years expended 0.75

Equipment and/or Services Purchased 3.0K$

Total Project Cost 43.0K$

Balance Remaining 2.0K$

Future Plans . To complete measurements and write summary of results.

30
i. Title . LIQUEFIED NATURAL GAS TECHNOLOGY TRANSFER

Principal Investigator . D. B. Mann

2. Cost Center Number . 2750401

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

400-58074.

4. Introduction . The NBS support of the Maritime Administration (MarAd)

LNG ship program is divided into three areas. These are a materials

experimental program, LNG ship custody transfer, and cryogenic technology transfer. In addition to those objectives listed below this

program provides a cohesive structure for the coordination of the NBS

LNG program.

5. Obj ectives . Cryogenic Technology Transfer is designed to provide

cryogenic technical information, data, and advice to the Maritime

Administration (MarAd) , its contractors and other agencies performing

work of interest to, or for, MarAd in the design, development, testing,

construction, and operation of LNG ships and ship components.

6. Background . The Merchant Marine Act of 1970 restructured federal

maritime policies to make bulk carrier vessels, such as tankers and

LNG ships, eligible for construction and operating subsidies. In

December 1973 the keel was laid for a 926 foot long LNG vessel carrier

at Quincy, Mass. The keel laying initiated the construction of the

first LNG tanker to be built in the United States. American ship

builders have orders for a total of 15 of these complicated ships.

Various future projections indicate a total of from 25 to well over

a 100 ships will be required to handle the LNG importation within the

next 10-15 years. Recent proposals to liquefy and transport Alaskan

gas to the U.S. only reinforced the importance of this new technology

to providing a measure of energy self-sufficiency to the U.S.

LNG marine technology is presently foreign dominated. As a matter of

fact, many of the ships being constructed in U. S. shipyards are using

designs under license from foreign industrial groups or governments.

LNG is a cryogenic fluid and the massive technology developed over the

past 15-20 years in cryogenics, as applied to industrial gases and the

aerospace effort, provides a resource which could be applied profitably

to improving the U. S. competitive position in the construction and

operation of LNG shipping. Because of its historical association with

broad based cryogenic technology over a period of some 20 years, the NBS

Cryogenics Division was requested to provide support to the MarAd LNG

ships program in order to aid in the transfer of cryogenic technology

where it could enhance the effectiveness of maritime LNG shipping.

Therefore, on April 17, 1973 we submitted a work statement which was confirmed by the establishment of a program in May of that year.

7. Program and Results . As a result of extensive assessments of user requirements, it was found that a most effective mode for technology

transfer would be a LNG Materials and Fluids Data Book. The purpose,

scope, format, content and schedule were developed over a period of 10

months and involved LNG interests in the gas industry, Maritime Administration, NASA and other Division of NBS in addition to the staff of

the Cryogenics Division

A description of the Data Book is as follows:

31
LIQUEFIED NATURAL GAS MATERIALS AND FLUIDS DATA BOOK

Purpose . To provide a method of quick dissemination of property data and re- lated 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 purposes of this

data book, Liquefied Natural Gas is defined as a cryogenic mixture (at less

than ^150 K) of hydrocarbons, predominantly methane, with less than a total

of twenty percent of the minor components ethane, propane, iso and normal

butane, and nitrogen as an inert contaminant.

Scope . 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 the scientific and engineering literature.

Data is classified into three groups by NBS Cryogenics Division.

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

been assessed, evaluated, and experimentally verified by NBS.

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

Group III . Data available in the scientific and 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 for the LNG Data Book will be from Groups I and

II. No new assessments or correlations are anticipated or required for this

work

Format. 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 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. Content . Part 1. LNG Materials - Primarily those materials used directly or indirectly

in the liquefaction, storage, transport, and measurement of LNG. This will

include primary and secondary containment structure, weldments, insulations,

etc. A proposed table of contents is as follows:

Section Description

1.1. Introduction

1.1.1. Objective of Data Book

1.1.2. Overview of temperature effect on materials

1.1.3. Nomenclature

32
Section Description

1.2. Structural Metals and Alloys

1.2.1. Alloy steels

1.2.2. Nickel steels

1.2.3. Stainless steels

1.2.4. Aluminum alloys

1.2.5. Copper alloys

1.2.6. Nickel alloys

1.2.7. Miscellaneous metals

1.3. Thermal Insulations

1.3.1. Wood products

1.3.2. Inorganics

1.3.3. Fiberglass

1.3.4. Foams

1.3.5. Mineral wools

1.3.6. Vapor barrier systems

1.4. Joining Materials

1.4.1. Welding rod, filler materials

1.4.2. Brazing consumables

1.4.3. Soldering consumables

1.4.4. Mechanical fasteners

1.4.5. Adhesives

1.5. Structural Composite Materials and Aggregates

1.5.1. Glass reinforced plastics

1.5.2. Concrete

1.5.3. Reinforced concrete

1.5.4. Wood

1.5.5. Advance composites

1.6. Polymeric Materials

1.6.1. Thermalsetting plastics

1.6.2. Thermoplastics

1.6.3. Elastomers

1.6.4. Silicones

1.7. Miscellaneous Non-structural Materials

1.7.1. Lubricants

1.7.2. Sealants

1.7.3. Threading compounds

1.7.4. Gaskets and packings

1.7.5. Paints and coatings

Data for each material or class of materials will include a general description and its primary LNG usage, availability, and chemical composition.

Mechanical properties as a function of temperature (76-300 K) will be presented

in graphical form. These will include:

Tension Modulus Static fatigue

Compression Poisson's Ratio Thermal fatigue

Shear Fracture toughness Wear resistance

Bearing Dynamic fatigue Impact

Design allowable performance specifications (ASME & API) will be provided

for various product forms including restrictions.

Physical properties as a function of temperature (76-300 K) will be provided in graphical form including:

Thermal conductivity

Thermal expansion

Density

Magnetic properties

Specific heat

33
Compatibility of the materials with LNG will be presented where possible

as to

Flammability

Solubility

Adsorption and swelling

Corrosion/Erosion

Permeability

Aging and effects of thermal cycling

Specifications for fabrication will be defined for:

Welding and brazing

Thermal treatment

Forming

Machining

Forging and casting

Environmental considerations

Handling characteristics

Finally, the data on all materials will be extensively documented with

references

Part 2. Fluids - Primarily those fluids which compose LNG which is defined

here as at least 80% methane with minor components of ethane, propane, iso

and normal butane, and nitrogen.

A proposed table of contents is as follows:

Section Description

2.1. Introduction

2.1.1. Objective of Data Book

2.1.2. Overview of non-ideal behavior of pure fluids and

mixtures

2.1.3. Nomenclature

2.2. Pure Fluids: Methane, ethane, propane, iso and normal butane,

nitrogen

2.2.1. Physical

2.2.1.1. Compressibility - Z = f(P,T,p)

2.2.1.2. Pressure - P = f(T,p)

2.2.1.3. Temperature - T = f(P,p)

2.2.1.4. Density - p = f(P,T)

2.2.1.5. Sound Velocity - W - f(T,P)

2.2.1.6. Surface Tension - a = f(T,P)

2.2.1.7. Vapor Pressures = f(T,ln P)

2.2.2. Thermophysical

2.2.2.1. Density, temperature, entropy as functions

of pressure and enthalpy (Mollier chart)

2.2.2.2. Pressure, density, enthalpy as functions of

temperature and entropy (T-S chart)

2.2.2.3. Pressure, density, temperature as functions

of enthalpy and entropy (H-S chart)

2.2.2.4. Specific heats at constant pressure as a function of temperature and pressure.

2.2.3. Electromagnetic Properties

2.2.3.1. Dielectric constant - e = f(T,P)

2.2.3.2. Dielectric constant - e = f(T,p)

2.2.3.3. Refractive index - n = f"(T,P)

2.2.3.4. Refractive index - n = f(T,p)

2.2.3.. 5. Clausius-Mosotti - CM = f(T,p)

2.2.3.6. Lorentz-Lorenz - L-L = f(T,p)

2.2.4. Transport Properties

2.2.4.1. Viscosity - n = f(P,T)

2.2.4.2. Thermal conductivity - k = f(P,T)

34
2.3. Fluid Mixtures - Binary mixtures of methane with ethane, propane, iso and normal butane, nitrogen.

2.3.1. Liquid Vapor Equilibrium

2.3.1.1. K values

2.3.1.2. Vapor pressures

2.3.1.3. Pressure-composition

2.3.2. Saturated Liquid Densities

2.3.2.1. Density-temperature

2.3.2.2. Excess volumes-temperature

Ternary and higher order mixtures will be considered for graphical presentation if data and methods of graphical display are practical.

Schedule . Data now available or which, as a logical output of existing

funded programs, will be available within the next 18 months can be considered in the first edition of the data book. Therefore, during calendar years

1976 and 1977, the following sections can be completed and the data book

binder and data sheets printed and issued.

Calendar Year

OCL '

:

1 - 1 J-1 97fi J f \J 1977 1 Q7P 4. 1.1 X - - 1.2 X - - 1.3 - X X

1.4 - - X

1.5 X

1.6 X

1.7 X

2.1 X

2.2.1 methane

,

ethane propane

,

nitrogen butanes

2.2.2 methane

,

ethane propane

,

nitrogen butanes

2.2.3. 1, methane

,

ethane, propane,

2.2.3. 2 nitrogen butanes

2.2.3. 3, methane ethane, propane,

2.2.3. 4 butanes, nitrogen

2.2.3. 5 methane

,

ethane, propane,

nitrogen butanes, nitrogen

2.2.3. 6 methane ethane, propane,

butanes, nitrogen

2.2.4 methane

,

ethane propane, butanes

nitrogen

2.3.1. 1, 2.3.1.2, methane-nitrogen methane , propane

2.3.1. 3 methane- ethane methane-butanes

2.3.2. 1, methane-nitrogen methane -propane

2.3.2. 2 methane- ethane methane -butanes

It is estimated that this should result in the production of ^ 220 charts

in CY 1976 and ^ 250 charts in 1977. The balance of charts would be issued

after the end of 1977 based on need and assessment of the value of the data

book to the user.

It is anticipated that the binder and up to 70 charts could be issued

within six months with the additional charts sent to subscribers in six

month intervals thereafter. A yearly review of the program as to content

and form by sponsors and users would guide NBS in the management of the long

range program. Data exists now in a quantity and quality to define the two

year program at a two man year per year level. The table of contents and

current interest levels within the industry indicate that this level could

be maintained to late 1979. A one man year per year level thereafter would

provide the necessary support until such time as the original content is

completed or active NBS participation is no longer necessary.

35
8. Problem Areas . The data book as described above is an extremely ambitious proposal. The first year effort should involve only a conversion

of existing LNG Program output to graphical format. However, the con- tinuing support will depend on the utility of this first year effort.

9. Funding . Funding for this cost center has been exhausted and future

support will be directed to the generation and distribution of the data

10. Future Plans . Four potential sponsors of the data book have been

identified. A description of the first year effort is included in

section 7. A slight slippage in the schedule may occur, caused by

funding transfer delay.

book.

Labor

Cost to 31 December 1975

0.2 MY

8K$

36
1. Title . FEDERAL POWER COMMISSION CONSULTATION

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

Strobridge.

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 several 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 landbased 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 emer- gency 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.

FY 76

July 1 - December 31, 1975

Anticipated Man-years of Effort FY 76

35K$

15K$

0.5

37
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BIBLIOGRAPHY

NBS reports and publications related to LNG technology.

1. R. D. Goodwin, "Provisional values for the thermodynamic functions of

ethane," NBSIR 74-398 (1974).

2. J. F. Ely and G. C. Straty, "Dielectric constants and molar polarizabilities of saturated and compressed fluid nitrogen," J. Chem. Phys.

61, 1480 (1974).

3. G. C. Straty, "Velocity of sound in dense fluid methane," Cryogenics

14, 367 (1974).

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

thermal conductivity coefficients for dense gaseous and liquid argon,

krypton, zenon, nitrogen, and oxygen," J. Phys. Chem. Ref. Data _3, 979

(1974).

5. * R. D. Goodwin, "Equation of state for thermodynamic properties of

fluids," J. Res. NBS 79A, 71 (1975).

6. * J. D. Olson, "The refractive index and Lorenz-Lorentz function of fluid

methane," J. Chem. Phys. 6_3, 474 (1975).

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

and liquefied gases at the NBS Cryogenics Division," talk prepared for

the 1975 Cryogenic Engineering Conference, Kingston, Ontario, Canada.

8. * G. C. Straty, "Hypersonic sound velocities in saturated and compressed

fluid methane," Cryogenics 15, 727 (1975).

9. H. J. M. Hanley and W. M. Haynes, "The density expansion of the viscosity coefficient," J. Chem. Phys. 6_3, 358 (1975).

10. * H. J. M. Hanley, R. D. McCarty and W. M. Haynes, "Equations for the

viscosity and thermal conductivity coefficients of methane," Cryogenics

15, 413 (1975)

.

11. B. A. Younglove, "The specific heats, C_ and C , of compressed and

liquefied methane," J. Res. NBS 78A , 401 (1974Y.

12. J. F. Ely and D. A. McQuarrie, "Calculation of dense fluid transport

properties via equilibrium statistical mechanical perturbation theory,"

J. Chem. Phys. 60^ 4105 (1974).

13. * 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," talk prepared for 1975 Cryogenic Engineering Conference,

Kingston, Ontario, Canada.

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

of solid ethane," J. Chem. Phys. (in press, 1976).

15. * G. C. Straty and R. Tsumura, "PVT and vapor pressure measurements on ethane," J. Res. NBS (in press, 1976).

16. * L. A. Weber, "Dielectric constant and derived Clausius-Mosotti function

data for ethane," Physica (to be published, 1976).

* See attached preprints or reprints in appendices.

39
17. H. J. M. Hanley and R. 0. Watts, "Molecular dynamics of an m-6-8 fluid,"

Physica 79A, 351 (1975).

18. H. J. M. Hanley and R. 0. Watts, "Molecular dynamics calculation of the

thermodynamic properties of methane," Aust. J. Phys. 2_8, 315 (1975).

19. H. J. M. Hanley and R. 0. Watts, "The self diffusion coefficient of

liquid methane," Mol. Phys. 2_9, 1907 (1975).

20. J. F. Ely and H. J. M. Hanley, "The statistical mechanics of non-spherical polyatomic molecules," Mol. Phys. 30^, 565 (1975).

21. Max Klein, F. J. Smith, H. J. M. Hanley, and P. M. Holland, "Tables of

collision integrals and second virial coefficients for the m-6-8

potential," NBS-NSRDS Monograph 47 (1974).

22. R. D. McCarty, "Correlation of the equilibrium and transport properties

of fluids," Proc. of Eighth Int. Conf. on Properties of Steam, Giens,

France (1975).

23. W. R. Parrish and M. J. Hiza, "Liquid-vapor equilibria in the nitrogenmethane system between 95 and 120 K," Advances in Cryogenic Engineering

19 , 300 (Plenum Press, 1974).

24. * A. J. Kidnay, R. C. Miller, W. R. Parrish, and M. J. Hiza, "Liquidvapor phase equilibria in the nitrogen-methane system from 130.0 K to

180.0 K," Cryogenics 15, 531 (1975).

25. M. J. Hiza, A. J. Kidnay and R. C. Miller, "Equilibrium properties of

fluid mixtures; a bibliography of data on fluids of cryogenic interest,"

(IFI, Plenum, 1975).

26. * W. R. Parrish and M. J. Hiza, "On the consistency of liquid-vapor equilibria data for binary mixtures of methane with the light paraffin

hydrocarbons," talk prepared for 1975 Cryogenic Engineering Conference,

Kingston, Ontario, Canada.

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

structures," Presented at International Cryogenic Materials Conference,

Kingston, Ontario, Canada (August 1975)

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

Army Materials Technology Conf., Boston, MA (Sept. 1975).

* See attached preprints or reprints in appendices.

40
APPENDIX ---
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, 1-4 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 Weigand1 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, 2-4 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. 1 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'"t. This purity was

verified by chromatographic analysis. Temperatures

were measured with a platinum resistance thermometer calibrated by the National Bureau of Standards on

the EPTS-1968. Pressures were determined by refer- encing, through differential pressure transducers, to

oil pressures derived from a precision oil dead-weight

gauge accurate to within the greater of 500 Pa or 0. 015 7. The apparatus and instrumentation was similar to that used previously in this laboratory5 with small modifications to be discussed. Measurements of the pressure as a function of temperature along the melting line of other fluids such as H2 , Oj, F2 , and CH4 6-9 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 re- duced. 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, 2 "4 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 Copyright © 1976 American Institute of Physics 859 A-2
860 G. C. Straty and R. Tsumura: Phase transition of solid ethane

«89.8 T. K 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 cm3 while the volume of the external portions of the system were minimized to less than 1 cm3

. 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 + P0 {(T/T,)e -1] , (1) where the subscript t refers to the triple point, and P

and T are the pressure and temperature. The value of Pt - 1. 2 Pa was taken from a vapor pressure correlation

for ethane by Goodwin10 at the triple point temperature

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

the following:

P, = 1.2 Pa (Ref. 10) , P0 = 255.97 MPa , rt = 90.348 K ,

£ =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.

Si 92 93 94 95

T. K A-3

J. Chem. Phys . Vol. 64, No 2, 15 January 1976
G. C. Straty and R. Tsumura: Phase transition of solid ethane 861

TABLE I. Ethane melting pressures and

deviations from Kq. (11.

T (K) P I MPa) P

F

1 LKJ

eitp

yu. "tu Q 3231 — 0 189

Q 6181 — 2. 345

90. ;")0 94 96 -, o 810

ani7W , 0( 1 338 _ a 804

90. 60 1

1 , - - aO-io — 0 182

yu. 0*4 1

c, q ^ 549

90. 74 a 4y.j 2 551

90 . 80 o 795 — 0 219

yu, "o qj , .0/0 2 690

yu. y-.) j

o. DiJ" 2 41

Q1 C\f\ y i . uu A AO ~ UoO — 0 247

91 03a A 266 o 801

91 50 1 82 o 1 96

y i , ou 7 1 45 — 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 1 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. 1

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

2-' while those of Clusius and Weigand, 1 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 AJ. Chem. Phys., Vol. 64,

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 11 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 solid-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. Eggers12 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. 13 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).

3 R. K. Witt and J, D. Kemp, J. Am. Chem. Soc. 59, 273

(1 937).

4 L. J. Burnett and B. H. Muller, J. Chem. Eng. Data 15, 154 (1970).

5 See for example G. C. Straty, and R. Prydz, Rev. Sci. lu- strum. 41, 1223 (1970).

6 R. D. Goodwin, J. Res. Nat. Bur. Stand. C 65, 231 (1961).

7 L. A. Weber, J. Res. Nat. Bur. Stand. A 74, 1 (1970).

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

Note 392 (Revised 1973).

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

(1974).

Kl R. D. Goodwin, Natl. Bur. Stand. (U. S. ) Interim Report, NBSIR 74-398 (1974). U

D. S. Webster and M. J. R. Hoch, J. Phys. Chem Solids

32, 2663 (1971).

12 D. F. Eggers, Jr., J. Phys. Chem. 79, 2116 (1975).

13 For an example of metastable behavior, see for example, W.

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

(1 960).

lo. 2, 15 January 1976
APPENDIX B

B-l
PVT AND VAPOR PRESSURE MEASUREMENTS ON ETHANE

G. C. Straty and R. Tsumura*

Cryogenics Division

National Bureau of Standards

Institute for Basic Standards

Boulder, Colorado 80302

Abstract

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.

This work was carried out at the National Bureau of Standards under the

sponsorship of the American Gas Association, Inc.; and it is not subject

to copyright.

*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.

B-2
PVT AND VAPOR PRESSURE MEASUREMENTS ON ETHANE

G. C. Straty and R. Tsumura

Introduction

Liquefied tuel gases, such as LNG, are expected to play an increasing role

in satisfying future energy requirements. Accurate thermo physical 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 experimenta] 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. PVT 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)

.

B-3
Experimental

To measure £«.ngle-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 calibrated volume.

When either the maximum pressure or maximum temperature is reached, the fluid

is expanded, 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 research grade with specified

minimum purity of 99.98%. This purity was verified by chromatographic

analysis. Temperatures were measured on the IPTS (1968) with a platinum

resistance thermometer calibrated by the National Bureau of Standards. Pressures

above about 3 MPa were measured by referencing to oil pressures derived from

an oil dead weight gage accurate to within 0.015%. 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%.

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], Slight 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 relatively density of the fluid residing in these parts, permitting a

more accurate adjusted density to be computed.

2

B-4
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/&. 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.

Although comparison with data from other sources is, in general, impossible

without multiple interpolations, the agreement has been deduced by examining the

density deviations of the various data sets [9,10] from densities calculated

from an equation of state for ethane due to Goodwin [11] . The agreement is

found to be, in general, within the combined experimental error. Maximum

differences 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% at the lowest

temperatures, increasing to + 0.2% at higher temperatures and lower densities,

becoming as much as + 1.0% 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 removed from the cell

between measurements . Identical pressure observations indicated that the

two-phase condition existed in the cell.

3

3-5
A vapor pressure equaLiou of the form

£n (P/P

t

) = AX ^BX

2

+ CX

3

+ DX

* + EX (1-X)

3/2

(1)

was fit to all available data for ethane [12], Here, X= (1-T /T)/(l-T /T ),

P and T are the pressure and temperature and t and c refer to the triple and

critical points. Coefficients giving the best fit were found to be the

following:

A = 10.67324

B = 8.33782

C = -3.08489

D = -0.65857

E - 6.04955

g - 1.14 x 10"5 bar

T.= 90.348 K [Ref 1]

T

c

= 305. 330 K [Ref 10]

Deviations of the experimental vapor pressures from those calculated from this

equation for the various data sets [9, 10, 13] are shown in Fig. 1.

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 liquefied

natural (fuel) gas properties being studied in this and other laboratories.

4

B-6
References

1. G. C. Straty and R. Tsumura, J. Chem. Phys., to be published.

2. L. A. Weber, J. Res. Nat. Bur. Stand. 74A, 93 (1970).

3. R. Prydz and G. C. Straty, NBS Tech. Note 392 (Revised, 1973).

4. R. D. Goodwin, NBS Tech. Note 653 (1974).

5. L. A. Weber, NASA SP-3088/NBSIR 74-374 (1975).

6. R. D. Goodwin. J. Res. Nat. Bur. Stand. J35C, 231 (1961).

7. G. C. Straty and R. Prydz, Rev. Sci. Inst. 41, 1223 (1970).

8. R. D. Goodwin and R. Prydz, J. Res. NBS 76A, 81 (1972).

9. G. A. Pope (also reports vapor pressure and PVT data of A. K. Pal).

Ph.D. Thesis, Dept. of Chemical Engineering, Rice University,

Houston, Texas (July 1971)

.

10. D. R. Douslin and R. H. Harrison, J. Chem. Thermo _5, 491 (1973).

11. R. D. Goodwin, NBS IR 74-398 (1974). Goodwin has used a non-analytic

equation of state to correlate previously available data on ethane

and to calculate provisional thermodynamic functions. Experimental

data from this work are being used to fill in gaps in previously

published data and to -refine the equation of state 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 included in the

final report. See also reference 8.

B-7
13. W. T. Ziegler, B. S. Kirk, J. C. Mullins and A. R. Berquest,

Tech. Rept. No. 2, Project A-764, Eng. Expt . Sta. Georgia

Inst. Tech.; Atlanta, Georgia, December 1964.

6

B-8
Table 1

P

(MPa)

P

(mol/1)

P

(MPa)

P

(mol/1)

T= 92.0 0 K

.7928 21.629

T= 93.00 K

8.7 37 0 21.682

T= 9^.00 K

3.5870 21.599

10.^980 21.66**

T= 96. 0C K

6.3091 21.555

1^.6217 21.6^1

T= 98.0 C K

8.1853 21.503

19.1732 21.625

T=100.00 K

1.7991 21.3*»8

11.3755 21.^68

23.8694- 21.613

T=1Q2,C0 K

4.7964 21.315

15.4890 21.448

28.5382 21.603

T=104.GG K

1.1828 21.198

6.9534 21.269

19.9C98 21.434

33.1959 21.594

T=10 6.a0 K

9.0567 21.221

24.4329 21.422

T=108.0Q K

1.8227 21.065

6.4514

12.4806

29. 0045

21. 125

21.193

21. 412

T=110.C0 K

4.7101 21.034

16.4766 21.176

33.5B10 21.403

T=112.00 K

1.19 20.911

6.84 20.990

11.2851 21.01*1

20.6898 21.163

T=114.00 K

3.8739 20.882

8.8149 20.9^2

24.9715 21.152

T=116.00 K

1.9636 20.776

6.3156 20.841

12.0035 20,913

19.0660 21.009

29.2820 21.143

T=118 .00 K

8.0478 20.791

15.7492 20. 896

23.2017 20.997

T=120 .00 K

1.2747 20.621

6.8130 20.702

10.8020 20.757

19.6919 20. 883

27.3594 20.988

T=122 • 0 0 K

3.866** 20.592

1^.2998 20.737

23.7193 20.873

B-9
Table 1 ("cont'd)

(MPa)«

P

(mol/1)

P

(MPa)

P

(mol/1)

31.5310 20.979

T=124.00 K

6.2436

11.6827

18.0492

27.7606

20. 553

20. 627

20. 724

20.863

T=126.00 K

7.9236

21.9553

31.8410

20.505

20.712

20. 855

T=128-00 K

.6715

10.4737

18.8911

25.8617

35.9026

20.312

20.470

20.597

20.703

2 0. 847

T=130.00 K

2.9285

13.7499

29.7809

20.287

20.450

20.694

T=132.00 K

5.4980

17.2765

26.4639

33.6963

20.254

2 0.436

20.577

20. 687

T=134.C0 K

7.2368

20. 8906

20. 209

20. 425

T=136.0 0 K

1.3639

9.2^90

24.5518

34. 0682

20. 030

20. 167

20. 416

20. 561

T=138.00 K

3.7831

12.1243

28.2309

20.003

20.14*t

20. i+07

T=140 .00 K

6.0574

15.3375

31.9091

19.972

20. 129

20. 400

T=142,00 K

7.6559

18.7024

35.5822

19. 92 6

20, 117

20. 392

T=144.00 K

.9387

9.8460

22.1094

19.722

19. 890

20.107

T=148 .0 0 K

5.4489

15.7717

28.9678

19.667

19. 856

20. 091

T=152.0C K

1.2079

8.9240

22.1746

35. 8308

19.424

19. 584

19. 836

20. 077

T=156.00 K

5.5978

14.2846

28,6589

19.369

19.545

19.820

T=160. 0G K

.»*675

8.9636

20.2324

35.1^68

19.091

19. 238

19.524

19. 806

B-10
Table 1 ( cont'd)

P

(MPa)

P

(mol/1)

r

(MPa)

P

(mol/1)

T=164.0C V

4.258Q

14.0474

26.2855

19.043

19. 250

19.50 8

T=168 .0 0 K

1.7297

7.6437

19.6507

32,3436

18. 817

18.969

19. 230

19.1*95

T=172.C0K

1.2449

5.7607

11.8776

25.3400

38.3722

18.650

18.768

18.916

19.214

19.482

T=176.0 0K

1.1073

5. 2091

8.8759

16.9907

31.0365

18.488

18.602

18.691

18.892

19. 201

T=180.0CK

.5247

9583

8.2782

13.3001

22.2633

36.7C92

18.295

18.442

18.525

18.655

18. 87 6

19.18 9

T=184.00K

3.9725

7.9795

12.4806

18.2646

27.51-82

18. 253

18. 368

18. *»8 3

18. 63 5

18.862

11. 9718

17.2C59

23.3273

32.831*0

18.323

18. 463

18, 62 0

18. 850

T-192.G0 K

.9865

5.5964

10.6669

16.5186

22.0330

28.3464

17.815

17.977

18.128

18. 302

18. 447

18.607

T=196.00 K

,4943

4.4533

8. 1*330

14,9662

21.1586

26.8669

33.3 677

17.619

17.775

17.90 3

18.101*

18.286

18.«*3i*

18.595

T=200.00 K

• 6801

3.5738

7.3933

12.2367

19.4175

25.8517

31.691+5

17.445

17.581

17.709

17.866

18. 087

18. 273

18. 423

T=2Ci*.0G K

3.7760

6.71*20

10.6983

16.4076

23.9051

30.2305

36.4896

17. til

17.524

17.653

17. 846

18. 074

18.262

18. 1*12

T=2 08 .0 0 K

T=l 88.00

K

1.9317

7, 2058

18. 021

18. 186

.5697

6, 8033

9. 6616

14.6253

17. 079

17. 354

17.1*61

17. 63^

B-11
Table 1 (cont'd)

P H P p

(MPa) (mol/1) (MPa) (mol/1)

20. 6552 17. 831 T=,1 32. GO K

28.3791 18. 062

35.0371 18. 251 1.2667 15, 950

4.5325 16.167

T=212.GC K 9.4583 16. 428

13.6904 16.633

3.4269 17.048 19.2025 16.874

9.6570 17.293 28.2402 17.215

13.3583 17. 434 32.7523 17. 37 2

18.6673 17.619

24. 9088 17. 819 T=;?36.00 K

32.8419 18.051

3. 850.8 15.92 0

T=216.00 K 7;0049 16. 114

12.4747 16. 403

2.1043 16.793 16.9765 16.618

6.4050 16. 998 22.6904 16. 862

13.2349 17.267 31.9811 17.205

17.2225 17.417

22.7370 17.606 T-240.0C K

29.1542 17. 808

i.2548 15.515

T=220.00 K 2. 2021 15.586

6.3368 15.87 7

1.4301 16.567 9.4209 16.062

5.1249 16.761 15.5972 16.387

8.9985 16.934 20.2787 16.606

16.9669 17.25 0 26.1772 16.852

21. 1113 17. 404 35.7C46 17.196

26.8053 17. 594

33.3^71 17.798 T=244.0 0 K

T=224.00 K 3.6366 15.487

4.6703 15. 556

4.3322 16.536 8.5355 15.817

7.6124 16.699 12.2246 16. 039

12.2714 16.904 18.7424 16.375

20.7255 17.237 23.5 869 16. 59 5

25.0127 17. 392 29.6476 16.842

30.8565 17. 584

T=2 48 .0 0 K

T=228 .00 K

1.7380 15.078

1. 5552 16.198 5.9925 15.449

6.9228 16. 483 6.8903 15.503

10. 4762 16. 654 11.1353 15.788

15.7164 16. 887 15. 1129 16. 023

24.4895 17. 225 21. 8905 16. 364

28. 89^6 17. 332 26.8798 16. 536

34. 8859 17. 574 33.1044 16. 833

B-12
Table 1 (cont'd) Bp P p"

[HPa) (nol/1) (i'?a) C^ol/1)

T=252.0 0 K

1.593G 14*811

3,9745 15.055

8.0325 15. 392

9. 0 553 15. 457

15.771

18. 0 295 16. Gil

25. 0 39V 16 . 35V

30 .1617 16. 577

T=256.00 K

3.7062 14.790

6.1397 15, CIS

10 . 374G 15. 358

11. 532V 15. 43 3

16. 6249 15.758

20 .9491 16. GO 0 28.1716 16.345

33.V255 16,568

T=2 60 .CO K

2. 6853 14.414

5.7990 14.757

8.0637 14. 963

12. 8526 15.340

14. 0783 15. 417

19.39^7 15.747

23. 8662 15, 990

31.2936 16. 336

T=264 .00 E

2.^038 14.085

4.6766 14.389

7, 6561 14. 70 5

10 . 2294 14.931

15,3689 15.327

16.6 £-65 15.405

22.1619 15.737

26.7721 15. 981

34,3936 16.328

T=2 6 8.0 0 K

3. 05^5 13. 884

4. 2654 14. C6 2 6.5471 14. 352

9 . 66 8 0 1^.569

12, 5C33 14. 914

17. 89-3 1 5. 316

19.230

5

15. 395

2V, 9263 15.728

29.663^ 1 5. 973

T = 272 .00 K

2 , 0 84^ 1. 243

3.6257 1 3. 67 0 4. 8506 13. 559

6 , 0 67 9 14,032

8. 2942 14. 302

11. 8077 14, 65 0 14, 8065 14.90 1

20, 4232 15. 306

21.8C42 15.33 5 27.6730 15.719

32, 5542 15* 964

1=276.00 K

2.1376 1. 242

3.2634 13, 256

5,3267 13. 644

6. 5457 13. 824

7.7197 13. 983

10.2212 14. 275

13. 9836 14, 63 6

17.1196 14, 890

22.9^62 15, 297

24.3837 15, 377

20. 4166 15.711

35.4306 15.957

T = 280 .00 K

2. 1904 1. 241

2.9753 12.737

4. 8428 13.234

6. 9195 13. 60 4

8.1525 13. 77 3 9.4390 13. 951

12. 2137 1 4. 259

16. 1653 1 4. 625

19.4375 1^.330

25.4635 15.233

26.9473 15.363

33.1520 1 5. 7C3

3-13
Table ! (cort'd)

P Q P p

(MPa) (mol/1) (MPa) (mol/lj

T=284.00 K 3. 8806 2. 88o

4.3963 11.212

2.2^28 1. 240 4. 8686 11.505

4.3982 12.768 6.4389 12. 146

6.3596 13. 203 8.4817 12. 672

8-4885 13.563 10,8697 13. 115

9.8840 13.751 13.6040 13.514

11.3395 13.933 15.2773 J.3.713

14.2261. 14.247 16.9735 13. 900

18.3557 14.615 20. 2346 1 <r. 21

21.7505 14. 87 2 24.8761 591

27.9731 15.280 28.6«t75 14.848

29.4971 15.360 35.4484 15.258

35.8724 15.696

T=300 .00 K

T=2 88.QC K

2.4492 1.237

2.2951 1.239 4.0309 2. 87 5

3.0547 1.955 4.6932 10.611

3.9706 12. 19** 5.3970 lic!96

5.8026 12.745 5.9^85 11,485

7.7971 13.160 7.6275 12.109

10.1657 13.540 9.8845 12.652

11.6682 13.735 12.4490 13. 10 2

13.2063 13.920 12.4489 13.102

16.2439 14.237 15,3377 13.504

20.5477 14.607 17.0906 1 3. 70 4

24.0580 14.86 3 18.8621 13.592

30.4719 15. 273 22.3018 14. 211

32.0446 15.353 27.0931 14.583

30.9501 14.841

T=292.0 0 K

T=3 04.C0 K

2.3466 1.239

3.8113 11. 522 2.4997 1.237

5.2158 12.173 3.4158 1.950

7.1396 12.707 4.1784 2.873

9.3105 13.131 4.6828 4.325

11.8771 13.525 4.7721 9. 097

13.4688 13.723 £.9674 9.788

15. 0863 13.910 5.393 0 10.298

18.2640 14.228 5.5668 10.596

22.7394 14.598 6.3948 11.173

26.3645 14. 855 6.9986 11.455

32.9673 15.265 8. 847«* 12. 082

11.3086 12. 63 3

T=2 96 .00 R 14. 0362 13. 092

17.0942 13.^95

2.3987 1.238 18.9013 13.696

3.2373 1.95 2 20.7454 13. 884

B-14
p p (X?a) (col/1)

Table 1 (cont'd)

P (MPa)

P

(nol/1)

24. 3137 14. 2022.5240 13.631

29 . 2629 14. 576 24.5119 13. 869

33.2309 1^. 333 28.3286 14. 189

33*5824 14. 562

T=3C6 .0 0 K

T=316 . 00 K

4. 8094 4.323

4.9441 6.533 2, 6491 1.235

5.0757 9. D92 4.6083 2. 366

5. 3014 10. 290 5.4200 4. 312

5.9353 6. 5i3

T=3 0 8.0 0 K 6.6610 9. 05 4 7.1729- 9.732

2.5499 1. 236 7. 3532 10. 22 9

4. 3236 2. 871 8. 1936 10.522

4,9341 4.321 9.3878 11. 099

5. 1434 6.530 10.1932 11. 390

5.3872 9. 086 12. 6240 12. 044

5.6969 9.775 18. 8045 13. 068

6.2111 10. 280 22.3CC4 13. 472

6.4452 10. 57 it 24.3313 13.673

7.3779 11. 142 26.3890 13. 862

8.0 352 11. 424 30.3236 14. 183

10 . 0940 12. 066

12.7418 12.623 T=320 . 0 0 K

15.6 25 8 13. 083

18.8310 13. itS7 2.6983 1.234

20.7132 13. 683 3.7629 1.945

22.6295 13. 87 6 4.7483 2. 864

26.3246 14.195 5. 6574 4.307

31.4-261 14.56.9 6.3309 6. 503

35.5024 14. 826 7. 3G64 9. 032

7.9172 9.710

T=312.0G K 8.6869 10. 211

9, 0937 10.50 6

2.5996 1. 235 10.4137 11. 037

3.59C3 1. 847 11.2486 11.38 0 4. 4653 2. 869 13.9CG7 12. 036

5.1793 it. 316 17. G663 12.602

5.5401 6. 522 20.4014 13. 060

6. G2Q6 9.072 24. 0313 13.466

6.4330 9.756 26.1304 13.667

7. 0307 10. 25 ^t 23.2533 13. 35 5

7.3179 10. 545 32.3174 14.176

8.3744 11. 116

9. lllh 11. 404.

11.3574 12. 05 4

14.1819 12. 613

17. 2177 13. 075

2C . 5666 13. i-30

B-15
Table 2

T T P

(K) kPa (K) kPa

160.00 21.502 230.00 700.48

165.00 30.670 235.00 825.96

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

185.00 103.84 250.00 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 1710.3

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

B-16
ZD

<

DC

LU

LU

B-17

APPENDIX C

I

C-l
Brillouin scattering techniques have been used to measure the velocity of hypersonic waves in gaseous and liquid methane. Measurements were made on the saturated liquid

and vapour and along selected isotherms to a maximum pressure of about 17.5 MPa. The

data, which agree well with previously measured ultrasonic velocities, have been combined

with PVT data to obtain the isentropic compressibility and the ratio of specific heats.

Hypersonic velocities in saturated and compressed

fluid methane

G. C. Straty

Sound velocity measurements, when combined with PVT

data, offer a convenient way of determining certain thermo- dynamic quantities as well as providing a sensitive check on

the equation of state and its derivatives. In a recent paper 1 we reported new measurements of the ultrasonic sound vel- ocities in dense fluid methane. These ultrasonic measure- ments were limited to densities greater than about 10-14

mol f

1 due to a large sound attenuation at lower densities.

In this paper we report the results of hypersonic sound vel- ocity measurements using Brillouin scattering techniques. Measurements were made along three supercritical isotherms and on the saturated liquid and vapour to densities as low as

1 mole l"

1

. The data have been combined with the pre- viously measured PFJdata 2 to obtain the isentropic compressibility Ks

, and the ratio of the specific heats 7 = Cp /Cv , using the well-known thermodynamic relation ^ = (pA

' s )-i =y(^)

where W, p, P, and Tare the sound velocity, density, pressure, and temperature, respectively.

Experimental details The sample of high purity (99.99%) methane was placed in a high pressure cell and was illuminated with an argon-ion

laser operating in a single mode at 488.0 nm with an output power of typically 20—50 mW. The frequency shifts Av of

the Brillouin components at a scattering angle of 90° were

determined using a pressure scanned Fabry-Perot interfero- meter with a finesse of about 20, as determined from the apparent width of the naturally very narrow central Rayleigh

line. Interferometer spacers were chosen which avoided cor- rections for shrinkage effects due to neighbouring components. The light was detected with an S-20 photomultiplier and recorded on a chart recorder. Uncertainty in the measured frequency shifts and derived sound velocities is about 0.5% as estimated from the stand- ard deviation of replicate measurements. This uncertainty

is due largely to frequency drifts of the laser and to small

The author is with the Cryogenics Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302, USA. Received 13 June 1975.

thermal effects on the interferometer. The scattering angle was determined by triangulation over distances of a few

metres and is not considered a significant source of error. Temperatures were measured with a platinum resistance thermometer calibrated by the National Bureau of Standards on the IPTS 1968. Pressures were determined to within 0.02 MPa using a temperature compensated bourdon

tube gauge. This gauge had been previously calibrated

against a high precision commercial dead weight gauge whose uncertainty is estimated to be whichever is greater, 200 Pa or 0.015%. The experimental arrangement is similar

to that used by Fleury and Boon 3 for argon and neon; however, chopping the beam and phase sensitive detection of

the photomultiplier output was found to be unncessary.

Results and discussion

The Brillouin scattering data and the derived sound vel- ocities, along with the density and derived values of isen- tropic compressibility and the specific heat ratio, are tabulated for the saturated fluid in Table 1 and for the compressed fluid along isotherms in Table 2. Some previously measured ultrasonic velocities 1 for the saturated liquid and

for the compressed gas in the regions of overlap are also included for comparison. The velocity data are plotted as a function of density in Fig.l together with the ultrasonic

data, which are included for completeness.

Densities and the derivatives necessary for the calculations were obtained from pressure and temperature observations and the PVT data and equation of state of Goodwin. 2 The

hypersonic velocities Fwere determined from the observed

Brillouin frequency shift Av in the usual way, using the equation

2nV 6 Au = sin -

X 2

where n is the index of refraction for the wavelength, A of

the incident radiation, and 6 is the scattering angle. The

index of refraction was calculated at a given density using data for the Lorentz-Lorenz function

n

2 - 1 1 R =

n

2 + 2 p

CRYOGENICS . DECEMBER 1975 C-2 729
Table 1. Brillouin scattering data, velocity of sound W, and derived values of isentropic compressibility Ks and specific heat

ratio 7 of saturated vapour and liquid methane at temperature T and density p

W. m s'

1 T An Angle, ncl Density, I n I

S

Ultrssonic is

IX IVInZ degrees i ndex moi i work / Do-f 1 \ \ n eT i ) (ura) ' 7

184.0 786.3 90.22 1.04800 4.751 258.4 197.1 5.052

170.0 821.2 90.22 1 .02449 2.437 276.1 335.5 2.280

150.0 834.8 90.22 1.01020 1.019 284.7 756.0 1.630

170.0 2283.8 90.22 1.20153 19.356 654.7 657.7 7.528 2.675

160.0 2812.6 90.22 1.21895 20.971 794.7 795.5 4.717 2.290

112.0 4939.5 90.22 1.27698 26.310 1332.4 1334.1 1.338 1.655

Table 2. Brillouin scattering data, velocity of sound W, and derived values of isentropic compressibility Ks and specific heat

ratio 7 in compressed fluid methane at temperature T, pressure P, and density p

W, m s'

1 Au, Angle, Ref Density, This Ultrasonic Ks MPa MHz degrees index moll' 1 work (Ref1) (GPa)" 1 7 T= 300.0 K

17.59 1602.0 on 99 11 .Uo / 3D 0.000 ou / M 9R OA

12.57 1428.2 Qfl ziU. 99Z Z

1

1 flfil T9 D.UH / HOO.O 40. I 1 I .OZvJ 7.80 1339.9 Qfl 99 1

1 nicoc UJJOJ o.OO I ou.oo 1

I .0RinIU 2.46 1312.3 90.22 1 .01031 1.029 447.7 302.9 1.401 T= 240.0 K

14.47 1569.5 90.10 1 .12541 12.20 480.8 480.5 22.15 2.683

12.54 1394.7 90.22 1 .10907 10.63 433.1 31.34 2.729

12.50 1387.6 90.10 1 .10868 10.60 431.5 31.68 2.720

10.18 1219.4 90.22 1 .08361 8.226 387.6 50.58 2.688

9.778 1194.0 90.10 1 .07890 7.772 381.6 55.24 2.621 8.106 1140.5 90.22 1 .06001 5.940 370.6 76.62 2.311 7.640 1126.8 90.10 1 .055T1 5.459 368.2 84.44 2.199

6.232 1115.9 90.22 1 .04156 4.126 369.0 111.2 1.926

5.451 1116.2 90.10 1 .03487 3.465 371.9 130.4 1.804 3.530 1126.6 90.22 1 .02051 2.045 380.3 211.3 1.561 3.415 1124.6 90.10 1 .01973 1.968 380.3 219.6 1.545 2.118 1144.0 90.22 1 .01154 1.153 389.7 357.0 1.445

1.824 1151.8 90.10 1 .00981 0.981 393.5 411.6 1.436 T= 210.0 K

9.869 1540.8 90.22 1 .14654 14.22 462.9 462.7 20.50 3.376

8.724 1315.3 90.22 1 .13156 12.80 400.4 30.47 4.127

7.954 1158.5 90.22 1 .11626 11.29 357.5 43.33 4.771 6.809 985.0 90.22 1 .08342 8.177 313.1 77.95 4.573

5.806 957.0 90.22 1 .05778 5.725 311.6 112.4 3.088

4.417 980.3 90.22 1 .03589 3.574 326.0 164.6 2.087 2.300 1038.0 90.22 1 .01529 1.528 352.2 329.7 1.554

Fig.1 Velocity of sound as a function of density for saturated and compressed fluid methane X — this work; 0 — ultrasonic velocities from reference 1 ; dashed line — qualitative estimate for the critical region

CRYOGENICS . DECEMBER 1975
obtained by Olson 4 for a wavelength of 546.2 nm. Adjust- ment to the laser wavelength was made by means of a trun- cated dispersion relation 5 of the form

A

X

2

where R x

is the value of the Lorentz-Lorenz function for wavelength X, and the constants = 5.15 x 10'6 cm 5 mol' 1 was evaluated from the low pressure gas data of Cuthbertson

and Cuthbertson. 6 The index of refraction calculated in

this way is rather insensitive to the exact value of R used and does not contribute significantly to the experimental

error. For comparison with ultrasonic velocity data, the experi- mental velocities in Table 1 have been adjusted for a pre- dicted slight negative dispersion in accordance with the cal- culations of Mountain. 7 At most, this correction amounts

to 0.08% at the highest temperature and lowest density, decreasing rapidly by more than an order of magnitude at higher densities. The adjusted velocities are found to be in good agreement with the previously measured ultrasonic data in the regions of overlap. The data also appear to

agree quite well with the data of Longequeve and Lallemand 8 after taking into account temperature differ- ences; however, these authors report their data in graphical form only. The measurements of Cardamone et al 9 are in substantial disagreement with the present measurements,

being about 5% too low. More recent determinations 10 at

low densities from the same laboratory, however, appear to be in better agreement with this work. The accuracy of the density data used in the analysis is esti- mated by Goodwin 2 at ±0.1%, resulting in a combined uncertainty in the derived isentropic compressibility, due

largely to the uncertainty in the velocities, of about ±1.0%. The uncertainty in 7 is more difficult to assess depending to

a large extent on the accuracy of (dP/dp)T used to obtain it from the velocity data. Our experience with similar analysis of more accurate ultrasonic data suggests that this derivative is probably accurate to about ±1 .0% 11 in the region of interest here, resulting in a combined uncertainty for 7

of about ±2.0%.

References

1 Straty, G. C. Cryogenics 14 (1974) 367

2 Goodwin, R. D. NBS Tech Note 653 (1974), available from

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

3 Fleury, P. A., Boon, J. P. Phys Rev 186 (1969) 186

4 Olsen, J. D. J Chem Phys 63 (1975) 474

5 Corruccini, R. J. NBS Tech Note 323 (1965)

6 Cuthbertson, C, Cuthbertson, M. Proc Roy Soc (London) A97 (1920) 152

7 Mountain, R. D. Rev Mod Phys 38 (1966) 205

8 Longequeve, A. M., Lalleman, M. P. Comptes Rendus 269B

(1969) 1173

9 Cardamone, M. J., Saito, T. T., Eastman, D. P. R., Rank,

D. H. J Opt Soc of Am 60 (1910) 1264

10 Wiggins, T. A. Private communication

1 1 Straty, G. C, Younglove, B. A. J Chem Thermo 5 (1973)

305

Sixth International Cryogenic Engineering Conference

11 - 14 May 1976

Alpes Congres, Grenoble, France

ICEC6 will cover all areas of current interest in cryogenic engineering. The main topics to be covered will be refrigeration; technology; superconductivity and its applications, including power generation and transmission, magnetic levitation, motors, MHD, storage; insulation; handling; properties of materials; instrumentation; and cryobiology.

Hotel accommodation in Grenoble is limited, so early registration is advisable. The deadline for registration is 1 April 1976

but early notification would enable the organizers to secure hotel bookings.

The registration fee is estimated as 500 francs. This will include pre-print of papers, refreshments, and conference

dinner. Special day and student rates will be available.

A series of visits to various European laboratories will be organized, the week before or after the conference.

An exhibition is to be held in conjunction with the 6onference. 500 m of exhibition area are available. Further details can be obtained from the Conference Secretary.

The deadline for the submission of abstracts of prospective papers is 15 November. All abstracts should be sent to the Conference Secretary J. Mazeur, 1CEC6 Secretary, Centre de Recherches sur les Tres Basses Temperatures, BP 166

Centre de Tri, 38042 Grenoble, France.

CRYOGENICS. DECEMBER 1975 C-4 731
APPENDIX D

D-1
DIELECTRIC CONSTANT DATA AND THE DERIVED CLAUSIUS-MOSSOTTI

FUNCTION FOR COMPRESSED GASEOUS AND LIQUID ETHANE

by

L. A. Weber

National Bureau of Standards

Institute for Basic Standards

Cryogenics Division

Boulder, Colorado 80302

USA

January 1976

D-2
DIELECTRIC CONSTANT DATA AND THE DERIVED CLAUSIUS-MOSSOTTI

FUNCTION FOR COMPRESSED GASEOUS AND LIQUID ETHANE

Abstract

Comprehensive, accurate 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 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 function is given, and the

consistency of the available density data is discussed.

D-3
DIELECTRIC CONSTANT DATA AND THE DERIVED CLAUSIUS-MOSSOTTI

FUNCTION FOR COMPRESSED GASEOUS AND LIQUID ETHANE*

I

L. A. Weber

National Bureau of Standards

Institute for Basic Standards

Cryogenics Division

Boulder, Colorado 80302

1 . Introduction

Measurements of the dielectric constant, combined with accurate density

data for compressed gases and liquids, can provide useful information about

1 molecular polarizabilities and molecular interactions . Such measurements

are generally combined to form the Clausius-Mossotti (CM) function, l/p(e-l)/

(e+2) , where £ is the dielectric constant and p is the density. The CM

function 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. Applications of this technique vary from the determination of the average density

in a large tank to the use of very small density probes for study of the

2 behavior of fluids in the vicinity of the critical point . In addition,

dielectric constant data may be combined with different sets of PVT data to

provide a convenient and sensitive test of agreement between the densities

*This work was carried out at the National Bureau of Standards under the

Sponsorship of the American Gas Association.

D-4
of different laboratories. This technique is useful even in situations where

two sets of density data do not overlap.

3 4 Such measurements have been made in this laboratory on hydrogen , oxygen ,

fluorine"*, nitrogen^, and methane^. This paper presents new dielectric

constant measurements and the derived Clausius-Mossotti function for ethane

for the saturated liquid and 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.

2 . Experimental

Measurements were made with the highly stable cylindrical capacitor

g 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 £ is given

by the ratio C/C

q

, where C is the capacitance with fluid between the plates

and is the vacuum capacitance at the same temperature. The capacitance

was measured with a three-terminal a-c 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 K at the lowest temperatures to 0.03 K for the room temperature

measurements . Presssures were measured with an oil dead weight gage having

an accuracy of about 0.01 percent. The sample holder and cryostat are similar

59

to those described elsewhere '

. The sample used was 99.99% pure ethane

which was passed through a molecular sieve trap to remove any water.

D-5
3 . Results

The dielectric constant of the saturated liquid was measured at 34

temperatures between 95 and 295 K. The results are given in Table 1.

Measurements were also made along seven isotherms between 120 K and 323.15 K

at pressures up to 390 bar. The results are shown in Table 2.

Because the cylindrical capacitor was mounted vertically, measurements at

temperatures closer to the critical point (approximately 305.3 K) were not

attempted. Due to the configuration of the sample holder it was also not

possible to make measurements in the saturated vapor.

The results for the saturated liquid were combined with available

densities to produce the Glausius-Mossotti function^ and are shown in Figure

For temperatures up to 270 K the densities of Haynes and Hiza^^ 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

12

the independent density-dielectric constant data of Sliwinski for the

saturated liquid and vapor near the critical point and the liquid CM data

13

of Pan, Mady and Miller near the triple point. Three points derived from

14

the saturated liquid density curve of Burton and Balzarini are shown. The

error bars indicate the uncertainty involved in estimating densities from the

figure given in their publication.

In Figure 2 are plotted the single phase isothermal CM function data.

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

1

datum of Watson, Rao and Ramaswamy at a pressure of one atmosphere at 298 K

D-6
The isothermal density data were fitted with polynomials of the form,

P = RTp + £ A

1 p

1

, (1)

i

for the purpose of smoothing and interpolation. At temperatures below the

critical, the polynomials were constrained at the saturation boundary to the

densities from references 10 and 12. The density was then calculated by an

iterative procedure for a given pressure.

4 . Accuracy and Comparisons

The calculated CM function is extremely useful for intercomparing sets

of PVT data. In Figure 1 the saturated 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 to be 0.2 - 0.3% higher than the others. The results of Burton and

Balzarini agree with those of Sliwinski within the uncertainty with which we

could estimate the former. The densities of Miller et al. are in agreement

with Haynes and Hiza near the triple point to within about 0.1%. The data

of Canfield et al.^ lie between those of Miller et al . and Haynes and Hiza

at 108 and 115 K and agree very well with Haynes and Hiza at 161 K.

In Figure 2 the isothermal CM data are compared with the best estimate

of the saturation curve from Figure 1. The isotherms between 120 K 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 observed for other fluids and is believed to be real.

D-7
Their density data at 320 K may be compared direccxy with the density data of

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. The newer data are in good agreement with the point of Watson, Rao

and Ramaswamy"^

.

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

measurements are also smaller than those of Miller et al. by about 0.018%.

The dielectric constant measurements presented here, in combination with

the saturated liquid densities of Haynes and Hiza and the PVT data of Straty

and Tsumura, along with the independent measurements of Sliwinski, have been

fitted with the equation,

CM = ^

= A + Bp + CP

2

+ DTp (2)

to provide an analytical expression for the results. The very precise PVT

data of Douslin and Harrison were not included because of their large

systematic deviation from the others. The coefficients given in Table 3 are

estimated to reproduce the Clausius-Mossotti function of ethane to within

0.1%.

In Table 3 the parameter A, which is generally equated with the molar

polarizability , is much larger than the corresponding parameter for methane and

for the diatomic gases previously measured in this laboratory. This is to be

expected based on considerations of molecular size. The dielectric second

D-8
virial coefficient, B, is also considerably larger than the coefficient found

for the smaller molecules. Had the data of Dousiin and Harrison been included

in the fit, B would be somewhat smaller. 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 3. 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.

D-9
6. References

1. See for example, Kielich, S. Acta Phys . Polonica 27_ (1975) 305;

Acta Phys. Polonica 28 (1965) 95 and McQuarrie, D. A., Levine, H. B.,

Physica 31 (1965) 749 and references cited.

2. Weber, L. A., Phys. Rev. 2 (1970) 2379.

3. Stewart, J. W. , J. Chem. Phys. 40 (1964) 3297.

4. Younglove, B. A., J. Res. NBS 76A (1972) 37.

5. Straty, G. C, Younglove, B. A., J. Chem. Phys. 57_ (1972) 2255 i

6. Ely, J. F., Straty, G. C., J. Chem. Phys. 61 (1974) 1480.

7. Straty, G. C, Goodwin, R. D., Cryogenics 13_ (1973) 712.

8. Younglove, B. A., Straty, G. C, Rev. Sci. Instr. 41 (1970) 1087.

9. Diller, D. E. , J. Chem. Phys. 47 (1968) 3096.

10. Haynes, W. M. , Hiza, M. J., unpublished data.

11. Douslin, D. R. , Harrison, R. H. , J. Chem. Therm. _5 (1973) 491.

12. Sliwinski, P., Zeit fur Phys. Chem. 68 (1969) 91.

13. Pan, W. P., Mady, M. H., Miller, R. C, AICHE J. 21 (1975) 283.

14. Burton, M. , Balzarini, D., Can. J. Phys. 52 (1974) 2011.

15. Straty, G. C, Tsumura, R. , to be published.

16. Watson, H. E., Rao, G. G., Ramaswamy, K. L., Proc. Roy. Soc.

Lond. A143 (1934) 558.

17. Chui, C, Canfield, F. B., Trans. Far. Soc. 67 (1971) 2933, and

Shanaa, M. J., Canfield, F. B. , Trans. Far. Soc. 64 (1968) 2281.

D-10
Table 1. Dielectric constant of saturated liquid ethane.

CM

(cm /mol)

T

(K)

95. CO

100. GO

10 5.00

110. CO

115.00

120. oe 125. 00

13 0 . C 0 135. CO

14 3. GO

145. 00

150.00

155. 00

16 0. 00

16 5. 0 0

170. 00

175. 00

180.00

185. CO

190. GC

20 0. 00

210. CO

220. CO

230. 00

240. 00

250. 00

260. 00

270. GO

275. 00

28 j. 00

285. 0C

290. 00

295. 00

p x 10

(mol/ cm )

21. 520

21. 341

21. 159

20. 975

20.793

20. 63 2

20. 419

20. 232

20.046

19. 85 7

19. 667

19. 47 5

19. 281

19. C86

18. 887

18.68 7

18. 434

18.279

13. 070

17. 861

17. 429

16. 971

16.499

15. 99 7

15. 464

14. 89G

14. 261

13. 549

12. 747

12. 258

11. 699

11. G24

1.93563

1.92576

1.91590

1.90606

1.89612

1.88952

1.87661

1.86637

1.85700

1.34713

1.83721

1.82729

1.81729

1.60725

1 . 7 97 1

4

1.78695

1.77669

1.76628

1.75576

1.74516

1.72349

1.70104

1.67786

1.65352

1.62730

1.600 36

1.57076

1.53773

1.51962

1.49994

1.47309

1.45318

1.42343

11. 047

11. 050

11. 054

11. 059

11. C62

11.101

11. 074

11.080

11.034

11. 039

11, G94

11. 099

11.1Q4

11. 10 9

11.115

11. 121

11.126

11. 131

11. 136

11.143

11. 143

11. 161

11. 171

11. 131

11. 191

11.199

11.203

11. 220

11. 196

11.20 6

11. 214

11. 218

11. 220

J;Densities from ref. 10

**Densities from ref. 11

D-11
Table 2. Dielectric constant of compressed liquid and gaseous ethane.

rp1 P

3

p X 1U CM

(K) (.bar) (mol/ cm ) (cm /mol

12 0. CO 304.927 1.90928 21. 026 11.062

12 0. CO 171.351 1.89966 2 0. 84 8 11.0 66

12 0.00 66.985 1.89165 20.70 5 11.066

16 0. 0 0 360 • ^54 1 • 84490 19. 827 11 .0 83

160. 00 358 .376 1.84471 19.824 11.083

160. 00 36.520 1.81160 19.171 11.107

16 0. CO 36.628 1.81161 19.171 11.1C7

20 0. 0 0 377.816 1.78020 18. 564 11.118

2G0. 00 256.633 1.76482 18. 266 11.122

20 0.00 151.137 1 . 74954 17. 965 11 .127

200.0 0 69.172 1.73601 17. 639 11.137

200. 00 13.071 1.72560 17.472 11.147

24 0. 00 392 .0 29 1.71687 17. 305 11.145

240. 00 294.735 1.70044 16.975 11.151

24 0. t0 211 . 1 48 1.63411 16. 645 11 . 156

240. 00 115.755 1.66165 16. 18 6 11.164

24 0. 0 0 62.930 1.64649 15. 869 11.172

240. 00 30.356 1.63563 15. 637 11.181

280. CO 376.142 1.64357 15. 919 11.166

230. 00 253.274 1.61794 15.274 11.182

28 0. CO 165.058 1.58855 14. 653 11.193

280. CO 100.002 1.55358 14. CIS 11.199

280. 00 54.692 1.52795 13. 355 11.205

32 0. CO 380 .835 1.58441 14.579 11.183

320. GO 196.092 1.510 88 12. 962 11*226

32 0. CO 113.562 1.44096 11.402 11.239

32 0. 0 0 79.1^6 1.36772 9.711 11.244

32 0. 0 0 67.649 1.29621 7. 894 11,256

320. CO 62.595 1.22571 6. 220 11.249

320. 00 56.26C 1.15041 4.235 11.274

320. 00 40 .699 1. 07576 2. 194 11.227

Densities from ref. 15

0-12
Table 2. Continued

T

(K)

323. 15

323. 15

32 3. 15

323.15

323. 15

323. 15

32 3.15

323. 15

323. 15

323.15

32 3. 15

323.15

323.15

323. 15

323. 15

323.15

32 3. 15

323. 15

323. 15

32 3. 15

323.15

32 3. 15

323. 15

323.15

323.15

323. 15

P

(bar)

313.351

243.358

205.702

134.<f35

163.787

132. 02C

109 .0 32

9^.055

84.177

77.255

72.719

69.510

66.909

64.i»**8

61.725

53.073

52.652

44.559

3*f.222

62.010

54.090

38.0 2*+ 24.6QI*

16.106

10.202

6. 027

1.55939

1.52894

1.509^0

l.i+9630

1.^8155

1,452<»3

1.42223

1.39319

1.36464

1.33429

i.3Q<+33

1.27426

1.24358

1.21258

1.18186

1.15018

1.11762

1.08526

1.05686

1.13^69

1.12503

1.06621

1.G3699

1.022^9

1.01362

1. 00732

p x 10

3 (mol/cm )

1<». C51

13.389

12. 959

12. 663

12. 339

11. 684

10.993

10.321

9.650

8. 92^

8. 195

7. 455

6.636

5. 893

5.039

4. 246

3.362

2.466

1. 662

5.166

3. 566

1.929

1.089

0. 6660

0. *fQ46

0 . 2326

CM

3

(cm /mpl)

11 .185

11 .195

11.201

11.205

11.210

11.216

11.223

11.227

11.230

11.235

11.238

11.236

11.231

11.229

11.231

11.227

11.221

11.207

11.191

11.225

11.220

11.196

11 .185

11.174

11 .170

11 .171

Densities from ref . 11

D-13
3 Table 3. Parameters for equation (2); density in mol/cra , temperature in K.

A 11.180 + 0.005

B 30.7 + 2.1

C -1627 + 77

D -0.021 + 0.003

D-14
Figure Captions

Figure 1. Clausius-Mossotti function for the saturated liquid and

vapor.

Figure 2. Clausius-Mossotti function for the single phase fluid.

The curve is for saturation conditions, from Figure 1.

D-15
D-16
D-17

APPENDIX E

i

I

E-l
JOURNAL OF RESEARCH of the National Bureau of Standards-A. Physics and Chemistry

Vol. 79A, No. 1. January-February 1975 Equation of State for Thermodynamic Properties of Fluids*

Robert D. Goodwin**

Institute for Basic Standards, National Bureau of Standards, Boulder, Colo. 80302

September 6, 1974

This equation of state was developed from PVT compressibility data on methane and ethane. The

highly -constrained form originates on a given liquid-vapor coexistence boundary (described by equations

for the vapor pressures and the orthobaric densities). It then requires only five least-squares coeffi- cients, and ensures a qualitatively correct behavior of the P (p, T) surface and of its derivatives, especially about the critical point. This nonanalytic equation yields a maximum in the specific heats C, (p, T)

at the critical point.

Key words: Coexistence boundary: critical point; ethane: equation of state: fluids: methane: orthobaric

densities; specific heats; vapor pressures. Symbols and Units

Subscripts c and _t refer to critical and liquid triple

points

Subscript cr refers to liquid-vapor coexistence

a, b, 8 nonlinear constants in the equationxof state B(p), density-dependent coefficients in the equa- C(p) tion of state Ccr ( T) , molal heat capacity for saturated liquid

C°{T) , molal heat capacity for ideal gas states Cv {p,T) , molal heat capacity at constant density

C,)(p,T) , molal heat capacity at constant pressure

<f, density, mol/1

7, the Joule, 1 N-m

/, the liter, 10" 3 m3 mol, 16.043 g of CH 4 ; 30.070 g of C 2H6 , (C 12 scale) P, pressure in bars, 1 bar = 10 5 N/m 2

. (1 atm = 1.01325 bar)

Pcr(p) , the vapor pressure, bar

R, the gas constant, 8.31434 (J/mol)/K

p, d/di, density reduced at the liquid triple

point

cr, d/dr * density reduced at the critical point

T, temperautre,K,(IPTS-1968)

7V(p), temperature at liquid-vapor coexistence

6{p). defined locus of temperatures, figure 3 u(p, T) , T/T„ (p), temperature reduced at coexistence

v, l/<i, molal volume, 1/mol

W(p,T), the speed of sound

x(T), T/Tc , temperature reduced at the critical point x tT (p) , Ta (p)ITc^ reduced temperature at coexistence

Z(P,p,T) Pv/RT, the "compressibility factor"

*This work at the National Bureau of Standards was supported by The American Gas

Association, 1515 Wilson Boulevard. Arlington. Va. 22209. **Cryogenics Division. National Bureau of Standards. Boulder. Colo. 80302.

71

1 . Introduction

A problem of importance for the natural gas in- dustry is the prediction of thermodynamic properties

of liquefied, multicomponent mixtures. For the wide

range of compositions encountered, it may be necessary to utilize accurate properties of the pure components. We therefore believe that it will be helpful

to have a relatively simple and rational equation of

state of identical form for each component, such as the equation of state described below.

This equation originates on a given, liquid-vapor

coexistence boundary, thus eliminating the longstanding problem of consistency between equations

of state and this independently-derived envelope

[26]. It ensures a maximum in the specific heats C,(p,T) approaching the critical point, qualitatively consistent with experimental behavior near, but

not necessarily exactly at this pole [16J, and it has

only five arbitrary, least-squares coefficients. Experimental compressibility data for methane and ethane

have been used at densities to the triple-point liquid

density, temperatures to twice the critical, and

pressures to 350 bar or greater.

Our objective in the present report is to give a concise description of this new type of equation of state which, with full documentation, has been presented

in previous publications [14, 15J. For methane we have shown in [14J that an equation

similar to that described below yields calculated

specific heats, C„(T), Cv (p,T), C,j(p,T), and speeds

of sound in acceptable agreement with experimental

data, without any weighting of the equation of state

to those data. In a current report on ethane [15

J

we compute provisional thermodynamic and related properties by means of the simpler equation of state

(1) described herein. Symbols and units used here are given in a List. Fixed-point values from [14, 15] are given in table 1.

E-2
For equation of state (1) the gas constant is R =(0.0831434)- (d,) bar/K, consistent with use of the dimensionless density, p = d/dt

.

Table 1. Fixed-point values from [14, 15]

Triple point Methane Ethane

Density mol/1..

Vapor 1.567 865-10" 2 1.3511410- 6 Liquid 28.147 21.68 Temperature K.. 90.680 89.899

bar 3.. 0.1174 35675 1.009 906 10" 5

Critical point

Density mol/1.. 10.0 6.74 Temperature K.. 190.555 305.37 45.988 48.755

a Precision required for vapor-pressure equation.

Various methods for utilizing the equations of state of pure components to derive properties of mixtures

are described in a number of recent publications, e.g.,

[1, 4a, 17, 18, 19, 20, 21, 21a, 22, 23, 24, 271.

FIGURE 1. The locus of isochore inflection points.

2. The Equation of State

The P(p, T) surface and equations of state are described in several reports, e.g., [6, 7, 10, 12, 14, 15, 20, 24, 28]. Figure 1 shows the qualitative behavior of isochores as indicated by Rowlinson [20], needed to give a calculated maximum in CV (p, T) at the critical point via the isothermal computation —

AC, = -TJ*

(d 2PldT2 )-dplp2

. (a)

Figure 2 shows the well-known zero slope and

curvature of the critical isotherm at the critical point.

This monotonic behavior (nonnegative slopes) is difficult to achieve from equations of state, yet is very important for such computations as —

Cp (p, T)=Cv(p, T)+T-(dPldT)*l(dPldp)lp 2

, (b) w(P,T) = [cp -(dPidP)icv yi*.

( C )

FIGURE 2. Behavior of the critical isotherm. The liquid-vapor envelope, Ta (p), figure 3, is an

important boundary of the P(p, T) surface for the equation of state. We constrain the equation to this bound-

\ /

> B

C D

i

//

A

TEMPERATURE

FIGURE 3. Behavior of the locus 6(p).

Point C is the critical point, and T„ [p) is the Liquid-vapor coexistence envelope.

72
ary as follows, by use of the vapor pressures and the coexistence temperatures Tir (p) formulated in the appendix. For any density (isochore), obtain the coexistence

temperature from the function TIT {p). Use this to obtain the vapor pressure P(J [7

,

,r (p)] as a function of density, thus defining the equation of state at coexist- ence. By subtraction one then obtains an equation of the type of eq (1). The melting line is not a part of this equation of state P

PAp ) = PR [T- TAP)] + p

zRTr F (p, T),

where,

F(p, T) -fi(p)-0(P , T)+C(p)-V(P , T). (1)

The functions B(p) and C)p) are polynomial coeffi- cients to be found by least squares. The temperaturedependent functions <I>(p, T) and 9 (p, T) must be

defined to be zero on the coexistence boundary at T=Ta (p) , as shown by figures 4 and 5.

0

t<tIM t —

FIGURE 4. Behavior of the function <t>(p, T).

i

©(/>] Up) rp_

FIGURE 5. Behavior of the function ^(p, T).

Equation (1) has, in addition to pRT, only two temperature-dependent functions, which is the minimum

number of functions (monotonic in T) needed to

describe the sigmoid shape of isochores in the density range pc < p < 2-pf , figure 1. The first of these functions is —

<&(p, T) s( x»/».ln[tt'(p, T)], (2)

where u(p, T) = T/TA]p)- It is linear (d 2<&ldT 2 = 0)

everywhere on the coexistence boundary at u= 1, figure 4. It therefore gives a critical isochore which is linear at the critical point because C(p) — 0 by defini- tion along this isochore, eq (6). The second of these functions, ^(p,T), is defined

such that eq (1) will yield a maximum in the specific heats C v (p,T) at the critical point via eq (a). We

first define the arguments —

a>(p,T) - 8 • [TI0(p) -1].

coAp) - 8- [TAp)lO(p) - 1]

,

where 8 is an arbitrary constant, and 6(p) is our

locus of temperatures inside the coexistence en- velope, figure 3,

9(p) =TAp) -exp [-a-f(a)]. (3)

The function /(cr) here is normalized to unity at the

liquid triple-point density —

/(o-) Ho--l | 3/(o-,-l) 3

,

where <7t

'•- dtldc is a constant. Function ^(p, T) now is defined as the difference,

f(pj) = ^(p,n-i(p), (4)

such that ^ = 0 at coexistence, T= T,r (p). Component

functions, i//(p, T), are designed to give infinite curvature (d 2 ^j/dT2

) at the origin, u> = 0,

<\si(p,T) =[l-a>- ln(l + l/to)]/*, (4-a)

i//, r (p) = [1 - w,r• ln(l + l/oj,r )]/x,r . (4-b)

Figure 5 shows behavior of ty{p,T). Sufficiently far away from the critical point it behaves roughly like l/r2

, found in the well-known, Beattie-Bridgeman

equation of state. Behavior of the coefficients B(p) and C(p) in eq

(1) is shown by figure 6 for methane. The following

polynomial representations have been developed

tediously by trial,

B(p) = B„ + fl, p + B2 p

2 /(l + b p2

) , (5)

C(p) = (o--l) • (o--C„) • (C,+C2 -p). (6)

The sign of the curvature of isochores {H 2Pji)T2

) at the coexistence boundary is determined uniquely

by the sign of C(p), figure 6, because <t>(p,T) is linear

E-4
FIGURE 6. Behavior of the coefficients B(p), Qp) for methane.

on this boundary. The root in C(p) at a= 1.9 was found

by least squares for methane and for ethane. It then was introduced as the constant Co in eq (6). This constraint is valuable because, under various conditions, we often have failed to obtain any such root from

PVT data by least squares.

3 0

H2

I 0 P/Pl—

Figure 7 shows the presumed behavior of C(p) for hydrogen, needed to give the observed positive curvature of isochores in compressed liquid states at the lowest temperatures [3, 7). The behavior of figure 7

is described by a double root at C0, e.g.,

C(p) = C, • (cr-1) (o--C„) 2

,

or without a root by —

C(p) = (o- - 1) (C, + C2

• p + C, p

2

)

.

Table 2 presents constants of eq (1) for methane and

ethane. Individual deviations of experimental PVT

data from eq (1) are given for ethane in [15 1. For methane with eq (1) they are comparable with those

obtained in [14| using nine least-squares coefficients. Complete computer programs are reported in [15

1

for adjusting the vapor-pressure equation, the ortho- baric-densities equations, the coexistence-temperatures equations, and the equation of state (1).

TABLE 2. Constants for equation of state (I

)

Methane Ethane

a 2 2

b 1 1 8 1/2 1/2 C„ 1.9 1.9

Bo 1.5082 12989 1.8481 67996

s, 0.6544 90304 1.5697 04511

4.1320 82291 5.5601 86452

c, -0.7654 09076 -1.0428 42462

c, -0.0590 88717 + 0.2249 78299 N 756 562

l^P/P, % 0.42 0.57

Figure 7. Presumed behavior of C(p) for hydrogen, reflecting observed positive isochore curvatures in compressed liquid states at the lowest temperatures [7|.

3. Comments on the Equation

Behavior of the critical isotherm from eq (1) at the

critical point is deduced as follows. The functions

P,r [Ta(p)] and <J> (p, T) depend directly upon T,r (p),

which gives the overpowering factor exp [— yj \ cr — 1 | ] for derivatives with respect to density at the critical point, (j=l. The function ^(p, T) has a finite third derivative because it depends also on 0(p), eq (3). Its coefficient, C(p), however, is zero at the critical density, eq (6). The first, second, and third derivatives

of eq (1) therefore are zero at the critical point.

Detailed examinations of this isotherm from eq (1) show, however, that small variations in the assigned

(pc Tr) critical point give small irregularities (negative slopes) nearby at <x§l. We find that, given an

accurate value of Tr , eq (1) serves to find the critical density which yields a well-behaved critical isotherm

[15). For methane and ethane the value of the critical density obtained by this method is roughly 1 percent

lower than estimated by the conventional procedure

of extrapolating the rectilinear diameter to the critical

74

E-5
temperature [14, 15, 20|, but in each case falls within

bounds of uncertainty in published works.

Ioschore inflection points figure 1, calculated from

eq (1), are obtained as the difference of second derivatives (versus T) from the functions composing

F(p, T). We therefore expect high sensitivity to the

analytical forms of $(p, T) and ^(p, T). Variations

of these forms might improve accuracy in representing

PVT data. In the following we describe two alternative functions for ^(p, T) from among many different functions investigated both for 4>(p, T) and for ^(p, T). We then compare computed specific heats obtained via these two forms in the modified equation

of state described below. Each of the following component functions must be differenced, as indicated by

eq (4), to obtain ^(p, T) for the equation of state. The

argument for each of the following functions is changed

to —

o(p, T) - [i-o(P )ir\.

In (7) the adjustable exponent is 1 < e«<2, and the adjustable coefficient was selected by trial to be 8= 1/e, iMp, T) = l-(<u-8-a)«)/(l-8). (7)

This function approaches zero at high temperatures

in proportion to 1/jT2

, as seen by expanding co

(

. By

trial with methane and ethane PVT data, we found

e = 3/2, and hence r) 2

i// 2 /r)P behaves like (l/co) 1/2 on approach to the origin, a>=0.

In (8) we use the arbitrary constant 0 =£ 8 =S 1 to give

relative weighting to two terms behaving, respectively,

like 1/T and 1/T2 at high temperatures,

!/»3 (p, T) = 8-(6IT) + (l-8)-[l-u) + cj-\n (to)].

(8)

The last term in (8) was explored for hydrogen [10].

Equation (8) can be simplified for computations. This

function gives r) 2

\jj3 /r)T2 ~ (1/oj) on approach to the

origin, oj^O, similar to definition (4-a) above.

With above functions, we find that coefficients B\

and C-i of eq (l) become nonsignificant for methane,

leaving an equation of state with only three arbitrary,

least-squares coefficients. For computations on mixtures, the simplest possible

equation of state is desirable. We have modified (1) such that it is suitable for corresponding-states adaptations, by specifying that densities shall be reduced at the critical point (hence R = 0.0831434 • dc , bar/K),

and by introducing the critical pressure. The functions

$(p, T) and ^(p, T) remain unchanged — P-PAp) = aR-[T-T,Ap)] +Pc-<T2 -F(p, T),

(1-A)

B(<t) =Bo + B2 -a*l(l + b-o- 2 ), (5-A)

C(o-) =Ci-(cr- l)-(o— Co). (6-A)

Table 3 for methane gives the rms of relative density

deviations for authors in [14], corresponding to each

function i//(p, T) described above and, on the bottom

line, the mean of combined pressure deviations. Tables 4 and 5 give the constants for eq (1-A), so that

it will be possible to compute specific heats.

TABLE 3. Methane density deviations, rms percent

Equation of state

Function \\i(p, T)

eq (1) eq (1-A)

<b\, eq (4-a) i/<2. eq (7) 1//3, eq (8)

Authors TV

Virial eq, [14] 46 0.06 0.12 0.16 Douslin et al. [4| 171 .06 .13 .10 NBS [14] 539 .51 .60 .50 Mean AP/P, %... 756 .42 .46 .45

Table 4. Constants for equation of state il-A), using i|/ 2 (p,T),

eq (7)

Methane Ethane

b 1/8 1/8 a 1/2 1/2 8 2/3 2/3

e 3/2 3/2

Bo 1.9894 21671 2.2373 56347 B2 0.7924 35706 0.9304 97491

C„ 1.9 1.9 c, -0.8309 40825 -1.0494 11810 N 756 562 APIP,% 0.46 0.79

Table 5. Constants for equation of state (1-A), using i//.-i(p,T), eg (8)

Meth dne Ethane

6 1/8 1/8 a 1/2 2/3 S 1/3 1/2

Bo 1.9794 55787 2.1805 54662 B2 0.8017 24817 0.9814 53571

C„ 1.9 1.9 Ci -0.9465 70360 -1.3543 33999 N 756 562 &P/P, % 0.45 0.75

The interaction specific heats (Cv — C°) for methane

have been compared along the critical isochore, as computed by equations (a) and (1-A), using the functions

i//2 (p, T) and faip, T). Experimental behavior of specific heats suggests that these data should be described

very near the critical temperature by —

(C„-C°)~(7/Tc -!)-», (9)

75
where exponent 0 < n < 1, and usually, 0.05 =£ n =s 0.15,

[16].

Figure 8 shows the computed results via 4jo(p, T),

eq (7). Their qualitative behavior is correct, but they cannot be represented by (9). Instead, they are described accurately to 210 K by—

(CP -C») = 15.1 - 18.0(r/rc - 1) 1/3

, J/mol/K,

suggesting that they might become finite at the critical temperature.

Using i//3(p, T), eq (8), on the other hand, yields

results on the logarithmic plot of figure 9. The slope, n ~ 1/3, is close to that observed for our experimental

oxygen specific heats [8]. We conclude that i//2(p, T) gives too weak a curvature to isochores from (1-A) approaching coexistence,

and that the forms i//i(p, T) and t//3 (p, T) may be preferable, despite the logarithmic infinity in their first derivatives versus T at the origin, w = 0.

210 TEMPERATURE , K

FIGURE 8. Computed interaction specific heats (Cv — C) ofmethane

along the critical isochore, via eq (1-A) and tjj 2 (p. T).

*n[T/T

c

-l]

FIGURE 9. Computed interaction specific heats (C v — C°) methane along the critical isochore, via eq (1— A) and 4>s (p, O

of

4. Conclusions

As argued above, the present equation of state

(1) is rational because we understand the purpose of most of its component parts. Inclusion of the vapor

pressures and orthobaric densities in this equation

merely incorporates these physical properties which

almost invariably must be used for a consistent net- work of thermodynamic functions, and eliminates

the long-standing problem of continuity at the co- existence boundary [26]. We believe eq (1) to be valuable for thermal computations because it ensures an inherently correct be- havior of the P(p, T) surface, giving a maximum in the

specific heats Cv (p,T) at the critical poirt. The very- small number of arbitrary least-squares coefficients

(five, and possibly only three) facilitates comparisons of the equation of state for different substances,

and may be attractive for work on mixtures.

We cannot expect eq (1) to represent some highprecision PVT data as well as equations with a much

greater number of arbitrary constants. As the preci- sion of "good" PVT data probably is often much bet76

E-7
ter than absolute accuracy, especially in the critical region, it would appear to be a self-defeating exercise

to strive for the ultimate "representation" while ignoring essential features of the P(p,T) surface. Any in- accuracies in the given, liquid-vapor, P—p

T

boundary for eq (1), however, will be propagated along

calculated isochores because eq (1) originates on this boundary.

Equation (1) almost certainly cannot be integrated,

analytically to express derived properties in closed

form. It therefore would not be convenient for multi- property analysis [2]. Equations amenable to in- tegration, however, probably are not accurate in the

critical region, which influences a large fraction of the P(p,T) surface. To some extent, this must create

a need for multiproperty analysis. For methane with an equation of state similar to eq (1), on the other hand, we have used a minimum of

specific heat data only to compute around the critical point for high densities near the critical temperature

(fig. 3). In all other regions we computed specific heats and speeds of sound "a priori" via ideal gas specific heats and the equation of state, finding acceptable

agreement with experimental data. We concluded

that if such data do not exist experimentally, they could

be estimated via the present type of equation of state

for many but probably not all regions of the P(p,T)

surface [14].

5. Appendices

5.1. The Vapor Pressure Equation

The original form of our vapor pressure function [9]

is satisfactory for methane [14], but for ethane it has

been necessary to add the term d-x 4 [15]. Define the argument —

x(T) - (\-Tt IT)!(\-T,ITc ), when the function is —

In (PIP, ) = a-x + b-x2 + c-x3 + d-x4 + e-x- (1 - x) 312

. (5.1)

Table 6 presents the coefficients.

T.ABI.E 6. Constants for vapor-pressure equation (5.1)

and polynomials are selected to represent small deviations. For the saturated liquid, define the variables,

x(T) - (Tc -T)I(TC -Tt ),

yip) = (p-pc)l(pt-pc),

Y(p, T) = (y-x)l(x<-x),

Methane Ethane

a 4.7774 8580 10.7954 9166

b 1.7606 5363 8.3589 9001

c -0.5678 8894 -3.1149 0770 d 0.0 -0.6496 9799

e 1.3278 6231 6.0734 9549

5.2. The Orthobaric Densities The following expressions are constrained to the boundaries, the triple- and critical points [15]. In each

case the basic behavior is described by —

Y (p, T) = const.,

when the function is — Y= a + b-x 2l3 + c-x. For the saturated vapor, define the variables,

x(T) = (TcIT- \)I(TCIT, — 1)

,

y{p) -- ln(p c/p)/ln(p c/p,)

Yip J) - (y -*)/(*<-*),

when the function is —

(5.2)

Y = A, + J A t x*

i = 2

(5.3)

Table 7 presents constants for (5.2) and (5.3). TABLE 7. Constants for orthobaric densities equations

Methane Ethane

Saturated liquid densities, eq (5.2)

6 0.36 0.33 a .8595 3758 .7219 0944

b .0243 6448 .2965 7790

c -.0268 5285 -.3003 6548

Saturated vapor densities, eq (5.3)

€ 0.41 0.39 A, .4171 4211 .2158 7515 A 2 -.5194 9762 -.0852 2342 A, 1.2077 7553 -.6152 3457 A 4 -1.4613 0509 .2545 2490 A-n 0.5765 8540 .1517 7230

5.3. The Coexistence Envelope, J„ (p)

This envelope is shown by figure 3. For the equation

of state (1) we obtain the coexistence temperature for any density from the following analytical descriptions. If the coexistence density must be found at a given temperature, it is obtained (for consistency in the equation of state) from the following expressions

by iteration, using eqs (5.2) and (5.3) only to estimate an initial density.

An important feature of the present formulations

[15] is that derivatives —

d"Tcrldp"

of all orders, n, are zero at cr= 1, the critical point.

We describe T,r ip) in two parts, according as cr§ 1.

77
This simplifies constraint to the boundaries (liquid and

vapor triple points). For each range the dependent

variable is —

Y[Tir (p)] = (TCIT,T -1)I(TCIT,-1),

and we use the following function, infinite at the critical density

U(a) =-y[l/|o— l|-l/|o-,-l|]

where (T t = dtldc is a constant, and d, refers to vapor

or liquid at the triple point according as a Ss 1.

For the liquid range at <j 2= 1 the equation is —

ln(F) = U(a) + J) Ai {a* - tr$ . (5.4) != 1

For extremely low densities in the vapor range at

o~ =£ 1 we modify the above expression as follows. Define the variable

W(cr) =ln(l + s/o-)/ln(l + s/o- r ) ,

where s is an arbitrary constant. Our equation for the vapor range now is —

ln(y) = f/(o-)+fi 0 -ln(r)+51

• (o- 13 -o-f 1,3

) + B2 (O- 2 3 - Of3

) + 2 Bi: (O"

1'- 2 - <T>- 2

) .

i = 3 (5.5) Table 8 presents constants for (5.4) and (5.5)

Table 8. Constants for the Tcr(p) equations

Metha Ethane

Saturated liquid, eq (5.4)

y 1/2 1/2 A, 11.4317 7230 23.7245 1840 Az -3.8765 9480 -14.8860 5161 A 3 0.5378 8326 5.4317 7443 A, .0 -1.0715 0566

A-, .0 0.0913 5183

Saturated vapor, eq (5.5)

s 1/4 1/4 S„ 0.9034 9557 0.8681 0517

B. .0 .0151 6978 B2 .0 -.7296 0432 s3 -.38.34 4338 1.0096 5493

B< -3.9210 8638 -8.7340 2710 Bs 6.2600 3837 21.1071 2823 B6 -9.3296 0083 -31.4499 4087 B7 5.6060 2816 17.8637 0397

Anneke L. Sengers emphasized to us some time ago

the importance of the critical region for the entire equation of state, thus motivating present develop- ments. In this laboratory, R. D. McCarty provided the

essential least-squares program, and we are indebted

to D. E. Diller and L. A. Weber for discussions and

valuable suggestions. The American Gas Association very kindly has supported this work.

6. References

[1| Baziia. E. R.. and Prausnitz. J. M., Vapor-liquid equilibria for crvogenic mixtures. Cryogenics 11. No. 2. 114 (April. 1971).

[2 1 Cox,' K. W., Bono. J. L., Kwok. Y. C, and Starling. K, E.. Multiproperty analysis. Modified BWR equation for methane

from PVT and enthalpv data. Ind. Eng. Chem. Fundam. 10,

No. 5, 245(1971).

(3 1 Diller. D. E., The specific heats (C,) of dense simple fluids. Cryogenics 11, No. 3. 186 (June. 1971).

[4] Dous'lin. D. R.. Harrison. R. H., Moore. R. T., and McCullough.

J. P., P-V-T relations for methane. J. Chem. Eng. Data 9, No. 3.358(1964).

[4a] Fisher. G. D. and Leland. T. W.. Jr.. Corresponding states principle using shape factors. Ind. Eng. Chem. Fundam.

9, No. 4. 537 (1970).

[5] Furtado, Andre W.. The measurement and prediction of thermal properties of selected mixtures of methane, ethane, and propane. (Ph. D. Thesis, Dept. of Chemical Engineering, Univ. of Michigan. Ann Arbor. Mich.. Dec. 1973.)

[fc] Goodwin, R. D., Approximate Wide-Range Equation of State

for Parahydrogen. Advances in Cryogenic Engineering 6, 450 (Plenum Press, New York, 1961).

[7) Goodwin. R. D., An equation of state for fluid parahydrogen from the triple point to 100 °K at pressures to 350

atmospheres, J. Res. Nat. Bur. Stand. (U.S.) 71A (Phys. and

Chem.), No. 3, 203-212 (May-June 1967).

[8] Goodwin. R. D. and Weber. L. A., Specific heats C, of fluid oxygen from the triple point to 300 K at pressures to 350

atmospheres, J. Res. Nat. Bur. Stand. (U.S.). 73A(Phys. and

Chem.). No. 1, 15-24 (Jan.-Feb. 1969).

[9] Goodwin. R. D., Nonanalytic vapor pressure equation with data

for nitrogen and oxygen, J. Res. Nat. Bur. Stand. (U.S.) 73 A (Phys. and Chem.), No. 5. 487-491 (Sept. -Oct. 1969).

[10] Goodwin. R. D.. Formulation of a nonanalytic equation of

state for parahydrogen, J. Res. Nat. Bur. Stand. (U.S.) 73A (Phys. and Chem.), No. 6, 585-591 (Sept.-Oct. 1969).

[11] Goodwin. R. D., Estimation of critical constants Tc . p c. from

the p(T) and T(p) relations at coexistence, J. Res. Nat. Bur. Stand. (U.S.) 74A (Phys. and Chem.). No. 2. 221-227 (MarApr. 1970).

[12] Goodwin. R. D. and Prydz. R.. Densities of compressed liquid methane, and the equation of state. J. Res. Nat. Bur. Stand.

(U.S.), (Phys. and Chem.), No. 2, 81-101 (Mar-Apr.

1972).

[13] Goodwin. R. D., Nonanalytic equation of state for methane,

constrained to the vapor-liquid P-p-T boundary, unpublished NBSIR.

[14] Goodwin, R. D., The thermophysical properties of methane

from 90 to 500 K at pressures to 700 bar, Nat. Bur. Stand.

(U.S.), Tech. Note 653. 280 pages (Apr. 1974).

[15] Goodwin. R. D., Provisional values for the thermodynamic

functions of ethane, unpublished manuscript. June. 1974.

[16] Green, M. S., and Sengers, J. V., Editors, Critical phenomena.

Nat. Bur. Stand. (U.S.), Misc. Publ. 273, 256 pages (Dec.

1966).

[17] Kirk. B. S., Ziegler, W. T., and Mullins. J. C, A comparison

of methods of predicting equilibrium gas phase compositions

in pressurized binary systems containing an essentially pure condensed phase. Advances in Cryogenic Engineering 6,

413(1961).

[18] Mollerup, J., and Rowlinson. J. S., The prediction of the densities of liquefied natural gas and of lower molecular weight

hydrocarbons. Chem. Eng. Sci. 29, 1373 (1974).

78
[19| Rowlinson, J. S., Molecular theories of liquids and mixtures,

Ind. Eng. Chem. 59, No. 12. 28 ( 1967). [20 ] Rowlinson, J. S., Liquids and Liquid Mixtures, p. 98, (Butter- worths Scientific Publications, London, 1959). See also sec- ond edition (1969).

[2 1 J Smith, G. E., Sonntag, R. E., and Van Wylen, G. J., Analysis of the solid-vapor equilibrium system carbon dioxide-nitrogen. Advances in Cryogenic Engineering 8, 162 (1963).

[21a] Smith, W. R., Perturbation theory and one fluid corresponding

states theories for fluid mixtures. The Can. J. Chem. Eng. 50,271 (1972).

[22] Sood, S. K. and Haselden. G. G., Prediction methods for vaporliquid equilibria in multicomponent cryogenic mixtures. Cryogenics 10, No. 3, 199 (June, 1970).

[23 1 Starling, K. E.. Fluid Thermodynamic Properties for Light Hydrocarbon Systems (Gulf Publishing Co., Houston, Texas.

1973).

[24] Tsonopoulos, C. and Prausnitz, J. M., Equations of state: a review for engineering applications. Cryogenics 9, No. 5,315

(Oct., 1969).

[25) Verbeke, O.B., Representation of P-V-T data by means of a "universal" state equation for simple fluids. Paper F-6, Advances in Cryogenic Engineering 18, 256 (1972).

[26] Wagner. W., A method to establish equations of state exactly representing all saturated state variables applied to nitrogen. Cryogenics 12, No. 3, 214 (June, 1972).

[27] Zellner, M. G., Claitor, L. C, and Prausnitz, J. M., Prediction of vapor-liquid equilibria and enthalpies of mixtures at low

temperatures, Ind. Eng. Chem. Fundam. 9, No. 4, 549 (1970). [28 J Zemansky, M. W., Heat and Thermodynamics (McGraw-Hill Book Co., Inc., New York, 1957).

(Paper 79A 1-844)

E-10
APPENDIX F

F-l
ORTHOBARIC LIQUID DENSITIES OF NORMAL. BUTANE

FROM 135 to 300 K AS DETERMINED WITH A

MAGNETIC SUSPENSION DENSIMETER

W. Mo Haynes and M. J. Hiza

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Paper E-6

Preprinted for the

Cryogenic Engineering Conference

Kingston, Ontario, Canada

July 22-25, 1975

F-2
ORTHOBARIC LIQUID DENSITIES OF NORMAL BUTANE

FROM 135 to 300 K AS DETERMINED WITH A

MAGNETIC SUSPENSION DENSIMETER*

W. M. Haynes and M. J. Hiza

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Abstract

A magnetic suspension densimeter, developed for absolute density

measurements of the principal components of liquefied natural gas and their

mixtures, has been used to determine the orthobaric (saturated) liquid

densities of normal butane from 135 to 300 K. These measurements provide

the first set of density data for liquid n -butane that spans the range of

temperatures from near ambient to just above the triple point, 134.8 K.

These new data have been fitted to a simple analytical expression to provide

a convenient and precise interpolation method. This equation has also been

used to calculate densities for the subcooled liquid region at temperatures

normally associated with liquefied natural gas. The precision and repeatability of measurement is within two parts in 10, 000 or better. The absolute

error in the densities is estimated to be less than ±0.1 percent.

This work was carried out at the National Bureau of Standards under the

sponsorship of the LNG Density Project Steering Committee , through

a grant administered by the American Gas Association, Inc.

F-3
Introduction

Of the principal constituents of natural gas, normal butane is the

first in the series of paraffin hydrocarbons that has a triple-point

temperature significantly higher than the normal boiling point (112 - 115 K)

of methane-rich LNG (liquefied natural gas). Unlike isobutane, with a

triple-point temperature (113.6 K) near the normal boiling point of methanerich LNG, normal butane freezes at the relatively high temperature of

134.8 K. Thus any estimate of the contribution of n-butane content to the

molar volume (or molar density) of LNG requires a relatively long extrapolation into the subcooled liquid region of n-butane. It is also known that

n-butane is the first in the series of paraffin hydrocarbons exhibiting

geometrical isomerism, with nearly instantaneous equilibrium, which

contributes to the temperature dependence of the molar density [1-5]. It follows that an analytical expression that provides the most reliable

means of extrapolating n-butane densities into the subcooled liquid region

cannot be based on correspondence alone, but must be based on extensive

and accurate data above the triple-point temperature.

Other than a few references [6, 7] that report results of saturated

liquid density measurements near room temperature, no references were

found that report experimental orthobaric liquid densities of n-butane

below 283 K. (The results given by Klosek and McKinley [8] at temperatures

below the triple -point temperature are probably based on their own data at

somewhat higher temperatures.) The purposes of the present study were to

obtain orthobaric liquid densities for n-butane that cover a relatively

large temperature range at low temperatures, as well as some measurements

up to ambient temperature, and to provide an analytical representation of these

data that is used for extrapolation into the subcooled liquid region to compare

with the results of reference [8].

F-4
A relatively new technique for determining absolute densities of

cryogenic fluids [9] was used in the present work. It is simple in principle

and is based on a straightforward application of Archimedes' principle.

Using a magnetic suspension technique, a cylinder of magnetic material of

known mass and volume is freely suspended by air-core solenoids in a

stable configuration in the fluid whose density is to be determined. At such

a stable equilibrium position, the upward magnetic force is added to the

buoyancy force to balance the gravitational force. Densities of the fluid

can be determined directly from the measured currents in the coils necessary

to support the magnetic "float" at the same position in vacuum and in the

fluid at constant temperature. The vertical position of the float is controlled

by the automatic regulation of a servo -circuit, which includes a linear

differential transformer for sensing inductively the position of the float.

The horizontal position of the float is determined and maintained by the

divergence of the magnetic field intensity.

Expe rimental

A complete description of the apparatus and a detailed discussion

of the performance characteristics are beyond the scope of this paper and

will be published elsewhere [10]. Only those essentials of the experiment

necessary for clarity are included here.

The feasibility of using a magnetic suspension densimeter for

measurements on cryogenic fluids had been demonstrated earlier with an

absolute density measurement on liquid nitrogen at the normal boiling

point [9]. The development of the present apparatus, shown in Fig. 1,

was based on experience with that apparatus and incorporates a cryostat

with continuous wide-range temperature control, a windowed equilibrium

cell suitable for studies of the liquids and liquid mixtures of interest here,

a new servo-circuit for vertical position control of the magnetic buoy, and

a high-powered (125 X) microscope for monitoring the position of the

magnetic buoy.

F-5

2
The magnetic buoy is a barium ferrite (Ba Fe O ) ceramic

1 z 19

magnet in the shape of a right circular cylinder, approximately 5 mm in

diameter and 6 mm in length. It has been plated with approximately

0.07 mm of copper over its entire surface to prevent fluid from penetrating

into the porous ceramic. Gold was flashed over the copper surface. The

mass of the buoy was determined to better than 0. 002% with an analytical

balance. The volume of the buoy was determined within 0. 02% at room

temperature by using distilled water as a reference fluid of known density.

At temperatures below ambient, the change in volume was calculated using

the recent thermal expansion data obtained for barium ferrite [11].

Evaluation of the experimental parameters involved in this method

and extensive performance tests indicate that the uncertainty in the density

measurements depends primarily on the uncertainty in the determination of

the position of the buoy, relative to the main coil, from vacuum to liquid

-3

measurements. The position of the float was determined to less than 10 mm

with a 125 X microscope. The position of the main coil was maintained from

vacuum to liquid measurements by supporting the coil at its midplane with

quartz rods and by controlling the temperature of the coil with water.

The total uncertainty in the density measurements was estimated

to be less than 0. 1% at the lower temperatures; near room temperature

the absolute error should be less than 0. 05%. The imprecision of the

density measurements was less than 0. 02% over the complete temperature

range.

A platinum resistance thermometer calibrated on the IPTS (1968)

was used for the temperature measurements. The uncertainty of the

calibration was approximately 0. 002 K. Due to the specifications of the

potentiometric measuring system, uncertainties in the temperature

amounted to a maximum of 0. 0135 K at 135 K, increasing to 0. 030 K at

300 K. The temperature of the sample holder was controlled to better

than 0. 005 K, approximately the same as the reproducibility of the

temperature measurements.

3 F-6
The purity of the n-butane used in these experiments was determined

by chromatographic analysis with thermal conductivity detection. A 7. 5-

meter liquid partition column was used, capable of separating air (or N.,)

from methane in small concentrations and the paraffinic from olefinic

hydrocarbons. The only detectable impurity in this sample was air (or N-

)

at approximately 2 5 ppm. The limits of detectability of the analyzer were

approximately 20 ppm of air (or N

2

) and methane and approximately 10 ppm

of ethane and the higher hydrocarbons.

Results

The experimental densities for n-butane are given in Table 1 with

the corresponding experimental temperatures. These data were fitted by

the method of least squares to an equation of the following form:

T ,0,35 T.n ,

.

p-Pc =a(l-— ) + I ) (1)

c i=l c where p - density in mol/t

;

p = a characteristic density in mol/-L,

approximately the critical density;

T = a characteristic temperature in kelvin, approximately

the critical temperature;

n = 1 +

1

; and

a, b. are coefficients determined by least squares.

The parameters of equation (1) also are given in Table 1, as well

as the standard deviation and the molecular weight.

In Fig. 2 the deviations of other experimental results [6, 7] and

frequently used literature values [12-14] from the values calculated from

equation (1) are plotted as a function of temperature. The accuracy with

which equation (1), with parameters as given in Table 1, can be extrapolated

above 300 K has not been investigated, but from the comparisons with

Sliwinski [6] and Kahre [7 J it appears that the equation gives reasonably

accurate values up to 370 K.

4

F-7
In Fig. 3 two different methods of extrapolation to temperatures below

135 K are presented. First the present data from 135 to 170 K were fitted

to equation (1) using two coefficients (a = 7. 3182177712 and b

{ = 3.4895578558),

and then densities were calculated for temperatures below the triple point

and compared with the values of Klosek and McKinley [8]. Next the present

data from 135 to 300 K were fitted using equation (1) with four coefficients,

and again comparisons were made with Klosek and McKinley. The graph

demonstrates the significant differences obtained for the two extrapolation

methods and also provides comparisons with the only other published

density values for normal butane at temperatures below 283 K. It should be

noted that no effort has been expended in the present work to produce a "best" method for extrapolation into the subcooled liquid region.

Conclusions

The results of this study provide the first set of experimental

density data for the orthobaric liquid phase of n-butane at temperatures

between 135 and 300 K. The absolute error is estimated to be less than

± 0. 1%. The analytical expression selected represents these data with a standard deviation less than the estimated imprecision of measurement,

i.e. ± 0.02%. It is felt that the analytical expression given here provides

a reasonable means of extrapolation of n-butane densities into the subcooled

region for liquefied natural gas applications.

Acknowledgments

The authors wish to acknowledge the contributions of the LNG

Density Project Steering Committee and the financial support of the

companies they represent.

5

F-8
E References

1. P.. A. Bonham and L. S. Bartell, J. Am. Chem. Soc. 81_, 3491

(1959).

2. R. A. Bonham, L. S. Barlell, and D. A. Kohl, J. Am. CLem.

Soc. 81* 4765 (1959).

3. A. L. Verma, W. F. Murphy, and H. J. Bernatein, J. Chem.

Phys. 60, 1540 (1974).

4. M. R. Cines, Phillips Petroleum Co . , private communication

(Jan 1974).

5. T. W. Schmidt, Phillips Petroleum Co., private communication

(May 1974).

6. P. Sliwinski, Z. Phys. Chem. (Frankfurt) 63, 263(1969).

7. L. C. Kahre, J. Chem. Eng. Data 18, 267 (1973).

8. J. Klosek and C. McKinley, Paper 22, Session 5, Proceedings

of the First International Conference on LNG, Chicago, 111. (1968).

9. W. M. Haynes and J. W. Stewart, Rev. Sci. Instr. 42_, 1142 (1971).

10. W. M. Haynes, N. V. Frederick, and M. J. Hiza, manuscript in

preparation.

11. A. F. Clark, W. M. Haynes, V. A. Deason, andR. J. Trapani,

submitted to J. Amer. Ceramic Soc.

12. A. W. Francis, Ind. Eng. Chem. 49, 1779 (1957).

13. Natural Gas Processors Supplies Association, Engineering Data Book,

Ninth Edition, NGPA, Tulsa, Oklahoma (1 972).

14. American Petroleum Institute, Project 44, "Selected Values of

Physical and The rmodynamic Properties of Hydrocarbons and

Related Compounds, " Carnegie Press, Pittsburgh, Pa. (1953).

F-9

6
Table 1. Densities of Saturated Liquid Normal

Butane and Parameters of Equation (1)

exp

(mol/£)

12.6584

12. 5772

12.4984

12.4153

12. 3362

12.2544

12. 1694

12. 0898

1 1. 0955

10. 0099

9.8135

T

(K)

135.075

140. 075

145.075

150.075

155.075

160.075

165. 075

170.075

230.000

290.000

300.000

calc

(mol/*,)

12. 6590

12. 5779

12.4968

12.4157

12. 3345

12.2532

12. 1719

12. 0904

11. 0950

10. 0106

9. 8130

100 (p -p

exp calc ) ^calc

0.005

•0.006

0.013

0.003

0.014

0.010

•0.020

•0.005

0.005

•0.006

0.005

Standard Deviation = 0.013%

a = 7.4784309557

b

i =11. 182486252

b

2

= -18.803855715

b

3 =11. 170674620

T

c

= 425.0 K

P c

= 3.876 mol/t

Molecular Weight = 58. 12430

7

F-10
Figure Captions

Figure 1. A magnetic suspension densimeter for cryogenic fluids.

Figure 2. Deviation plot of densities of saturated liquid normal butane

compared with values calculated from equation (1); data from

this work and references 6, 7, 12-14. (Note that results

from references 12-14 are not experimental data. ) Figure 3. Deviations plot of densities of liquid normal butane of Klosek

and McKinley [8] below the triple -point temperature compared

with the extrapolated values calculated from equation (1)

for two cases; (a) a least squares fit of the data from the

present work from 135 - 170 K using two coefficients and

(b) a least squares fit of the data from the present work from

135 - 300 K using four coefficients. (Note that the baseline

represents two sets of extrapolated results obtained from the

present data and that both curves with designated points

represent a single set of values from reference [8]. )

F-n

8
Figure 1

F-12

ITSX 3242 I
F-13

APPENDIX G

G-l
ON THE CONSISTENCY OF LIQUID-VAPOR EQUILIBRIA DATA

FOR BINARY MIXTURES OF METHANE WITH THE

LIGHT PARAFFIN HYDROCARBONS

W. R. Parrish and M. J. Hiza

Cryogenics Division

National Bureau of Standards

Institute for Basic Standards

Boulder, Colorado 80302

Paper E-2

Preprinted for the

Cryogenic Engineering Conference

Kingston, Ontario, Canada

July 22-25, 1975

G-2
ON THE CONSISTENCY OF LIQUID-VAPOR EQUILIBRIA DATA

FOR BINARY MIXTURES OF METHANE WITH THE

LIGHT PARAFFIN HYDROCARBONS*

W. R. Parrish and M. J. Hiza

Cryogenics Division

National Bureau of Standards

Institute for Basic Standards

Boulder, Colorado 80302

Abstract

Published experimental liquid-vapor equilibria data for the binary systems

of methane with ethane, propane, isobutane, and normal butane have been compiled and evaluated for internal and mutual consistency. Equimolar excess

Gibbs energies and infinite dilution Henry's constants are obtained by a

method which uses only P - x data. The derived equimolar excess Gibbs energies

are compared with those calculated from a modified hard-sphere model for the

equimolar mixtures. Critical loci (P c , T

c

, x ) are also examined where

available. Discrepancies in the data are enumerated which suggest the desirability of more precise and accurate measurements.

Contribution of the National Bureau of Standards, not subject to copyright.
ON THE CONSISTENCY OF LIQUID-VAPOR EQUILIBRIA DATA

FOR BINARY MIXTURES OF METHANE WITH THE

LIGHT PARAFFIN HYDROCARBONS

W. R. Parrish and M. J. Hiza

Introduction

The process design engineer usually relies upon correlations for predicting

the liquid-vapor equilibria of multicomponent systems. These correlations

require accurate binary data—both as a test and as a source of binary

interaction parameters. With this problem in mind, we have compiled and

evaluated liquid-vapor equilibria data for four binary systems of interest in

LNG technology. The systems considered are methane with ethane, propane,

n-butane and isobutane.

This paper gives qualitative results of the evaluation and points out the

current status of each of the systems. A more detailed quantitative evaluation

of these data along with volumetric and calorimetric data will be published

later.

The primary source of reference for these systems (as well as other

systems of cryogenic interest) is the bibliography by Kidnay et al. [1],

updated through December, 1974.

Method of Evaluation

In this paper we consider only the mutual consistency between the isotherms

of different Investigators; the three best indicators of mutual consistency are

equimolar excess Gibbs energies, G

E

(x - 0.5), infinite dilution Henry's

constants and critical loci. To calculate the first two quantities we use the

G-4
numerical technique proposed by Christiansen and Fredenslund [2]. Their method

uses only total vapor pressure and liquid composition data and calculates thermodynamically consistent vapor phase values along with G

E and Henry's constants.

It does not require an analytical expression to represent the liquid phase activity

coefficients; vapor phase non-ideality corrections are made using the Redlich-Kwong

F E equation of state. To find the equimolar G we least squares fitted the G values from

their program to the Redlich-Kister expansion, i.e.,

G

E /RT = Xl x2 [A + B ( Xl - x 2

) + C( X1 ~ x 2 ) 2

]

where R is the gas constant, T is the absolute temperature, x^ and X2 are the liqu id

phase mole fractions and A, B, and C are fitted coefficients. It was found that the

E value of the equimolar G can depend upon the number of interpolated points used in

the numerical technique.

E The equimolar G gives an indication of the overall shape of the P - x

curve for each isotherm below the critical temperature of methane (190.56 K)

.

(It does not, in this case, give any indication of the quality of the vapor

phase data. The vapor phase data are evaluated by comparing them with the

calculated vapor phase values; this part of the evaluation is omitted here.)

E Graphical representation of equimolar G versus temperature provides an indication

E of consistency between the various isotherms. These values of G are compared

with the values calculated using a modified hard-sphere equation of state with

the parameters given by Rodosevich and Miller [3]. This equation of state seems

to reliably predict the correct temperature dependence of equimolar G [4,5] for

systems of simple molecules. Therefore, it is used as a guide for qualitatively

E determining which values of equimolar G seem to be the most reasonable. To

estimate how sensitive the equimolar G is to systematic errors in pressure

E

and composition, the equimolar G

T s for the liquid phase methane-propane data of

Calado et al. [16] were recalculated twice,; with a systematic increase of one

2 G-5
percent in pressure, the equimolar G increased about 5 J/mol; with a systematic

increase in composition of one percent, the equimolar G decreased about 5 J/mol

(*Vi 3 percent change) .

Henry's constants indicate the behavior of the P - x curve in the methanelean region; they are especially useful in analyzing the data above the critical

temperature of the more volatile component (methane in this case). The methanepropane data of Calado et al. [16] were used to determine the dependence of the

Henry's constant on pressure and liquid phase composition errors. For a

systematic one percent increase in pressure or composition the Henry's constant

increased one percent.

The critical loci (P

c , T

c , xc

) are fairly difficult to determine. However,

when they are reported they provide an excellent check on the consistency of the

high pressure portion of the data.

Data Evaluation

Figures 1, 2 and 3 show the equimolar G , Henry's constants and critical

loci, respectively, for the methane-ethane system. In the critical loci figures

the curves were drawn to show trends in the data; no analytical model was used.

Despite the many investigators, this system is clearly not well defined,

especially below the critical temperature of methane. In fact, if the predicted

E equimolar G curve is qualitatively correct, one-half of the low temperature

data are in error. Based on Henry's constants, the higher temperature data are

in better agreement as are the critical loci. Clearly this system needs to be

studied further, especially in the 90 to 190 K temperature range.

As can be seen by Figures 4, 5 and 6, the methane-propane system appears

to be better defined. Based on the Henry's constants, the region above 200 K

G-6

3
is still not completely understood. There is good agreement in the critical

loci, especially in the critical compositions. Based on these results, the

methane-propane system is probably the best understood of the four systems

considered here. Even so, more work is needed on this system.

Figures 7, 8 and 9 consider the methane-n-butane system. Relatively

little work has been done on this system and there are no data reported below

144 K. Whereas the critical loci show good agreement, the Henry's constants

show discrepancies of up to 15 percent in the 190 to 260 K range. This indicates

that the data are more scattered in the low pressure and low methane concentration region. In summary, this system needs to be studied further, especially

in the 100 to 150 and 190 to 260 K range.

Figures 10 and 11 show the available data for the methane-isobutane system.

There are only two reported investigations of this system. The lowest temperature investigated is 190 K; there are no data in the open literature in

temperature ranges of LNG applications.

Conclusions

For the four binary systems considered here, there are over 130 isotherms

reported in the open literature. Even so, these systems are not as well

defined as one would expect or desire. The discordant nature clearly indicates

the necessity of assessing the reliability of liquid-vapor equilibria data.

The preliminary evaluation given here indicates the need for more accurate

liquid-vapor equilibria data, especially the methane-ethane system. Of these

four systems, the methane-propane system appears to be the best defined.

G-7

4
Acknowledgment

The authors are grateful to L. J. Christiansen and A. Fredenslund for

their computer program used in this work and to the Office of Standard

Reference Data of the National Bureau of Standards for financial support.

References

1. A. J. Kidnay, M. J. Hiza, and R. C. Miller, Cryogenics 13_, 575 (1973).

2. L. S. Christiansen and A. Fredenslund, A.I.Ch.E. J. 2^, 49 (1975).

3. J. B. Rodosevich and R. C. Miller, Advances in Cryogenic Engineering,

Vol. 19, Plenum Press, N. Y. (1974) p. 339.

4. W. R. Parrish and M. J. Hiza, ibid, p. 300.

5. A. Blinowska, T. M. Herrington, and L. A. K. Staveley, Cryogenics 13 ,

85 (1973).

Methane-Ethane System

6. 0. T. Bloomer, D. C. Garni and J. D. Parent, Inst, of Gas Technol. Res.

Bull., No. 22 (1953).

7. Shinn-der Chang and B. C.-Y. Lu, Chem. Eng. Progr. Symp. Ser. 63_ (81),

18 (1967).

8. M. Guter, D. M. Newitt and M. Ruhemann, Proc. Roy. Soc. (London) 176A,

140 (1940).

9. C. Hsi and B. C.-Y. Lu, Can. J. Chem. Eng. 49_, 140 (1971).

10. D. W. Moran, Ph.D. Dissertation, Imperial College, University of London,

London (1959).

11. A. R. Price and R. Kobayashi, J. Chem. Eng. Data 4_, 40 (1959).

12. M. Ruhemann, Proc. Roy. Soc. (London) 171A , 121 (1939).

G-8

5
13. V. G. Skripka, I. E. Nikitina, L. A. Zhdanovich, A. G. Sirotin and

0. A. Benyaminovich, Gazov. Prom. 15 (12), 35 (1970).

14. I. Wichterle and R. Kobayashi, J. Chem. Eng. Data 17, 9 (1972).

Methane-Propane System

15. W. W. Akers, J. F. Burns and W. R. Falrchild, Ind. Eng. Chem. 46, 2531

(1954).

16. J. C. G. Calado, G. A. Garcia, and L. A. K. Staveley, J. Chem. Soc,

Faraday Trans. 1 Vol. 70, Part 8, 1445 (1974).

17. A. J. B. Cutler and J. A. Morrison, Trans. Faraday Soc. 6^, 429 (1965).

18. D. P. L. Poon and B. C.-Y. Lu, Advances in Cryogenic Engineering, Vol. 19,

Plenum Press, New York (1964), p. 292.

19. A. R. Price and R. Kobayashi, J. Chem. Eng. Data 4_, 40 (1959).

20. J. G. Roof and J. D. Baron, ibid 12, 292 (1967).

21. H. H. Reamer, B. H. Sage and W. N. Lacey, Ind. Eng. Chem. 42, 534 (1950).

22. B. H. Sage, W. N. Lacey, and J. G. Schaafsma, ibid 26, 214 (1934).

23. V. G. Skripka, I. E. Kikitina, L. A. Zhdanovich, A. G. Sirotin and

0. A. Benyaminovich, Gazov. Prom. 15 (12), 35 (1970).

24. H. F. Stoeckli and L. A. K. Staveley, Helv. Chim. Acta. 53_ (8), 1961

(1970).

25. I. Wichterle and R. Kobayashi, J. Chem. Eng. Data 17_, 4 (1972).

Methane-n-Butane System

26. D. G. Elliot, R. J. J. Chen, P. S. Chappelear and R. Kobayashi, J. Chem.

Eng. Data _19, 71 (1974) .

27. L. C. Kahre, ibid 67, (1974).

6G-9
28. K. L. Mulholland, Ph.D. Dissertation, University of Kansas, Manhattan (1970).

29. T. J. Rigas, D. F. Mason and G. Thodos, Ind. Eng. Chem. 50, 1297 (1958).

30. L. R. Roberts, R. H. Wang, A. Azarnoosh, and J. J. McKetta, J. Chem. Eng.

Data 484 (1962).

31. B. H. Sage, B. L. Hicks and W. N. Lacey, Ind. Eng. Chem. 32^, 1085 (1940).

32. R. H. Wang and J. J. McKetta, J. Chem. Eng. Data 9_, 30 (1964).

Methane-isobutane System

33. S. D. Barsuk, V. G. Skripka and 0. A. Benyaminovich, Gazov. Prom. 15_

(9), 38 (1970).

34. R. H. Olds, B. H. Sage and W. N. Lacey, Ind. Eng. Chem. 34, 1008 (1942).

6-10

7
List of Figures

E Equimolar G as a function of temperature for the methaneethane system. The solid line was calculated using a

modified hard-sphere equation of state [3].

Infinite dilution Henry's constants as a function of

temperature for the methane-ethane system.

Critical pressure and composition as a function of

temperature for the methane-ethane system.

Equimclar G as a function of temperature for the

methane-propane system. The solid line was calculated

using a modified hard-sphere equation of state [3]

.

Infinite dilution Henry's constants as a function of

temperature for the methane-propane system.

Critical pressure and composition as a function of

temperature for the methane-propane system.

Equimolar G as a function of temperature for the

methane-n-butane system. The solid line was calculated

using a modified hard-sphere equation of state [3].

Infinite dilution Henry's constants as a function of

temperature for the methane-n-butane system.

Critical pressure and composition as a function of

temperature for the methane-n-butane system.

Infinite dilution Henry's constants as a function of

temperature for the methane-isobutane system.

Critical pressure and composition as a function of

temperature for the methane-isobutane system.

G-11
o

E

260

240

220

200

80

IT) w>< 160

140

120

100

80

o

A

V

O

Bloomer et.al. (1953)

Chang and Lu (1967)

Hsi and Lu (1971) CH 4 +C2 H 6

Moran(l959)

Skripka et.al. (1970)

Wichterle and Kobayashi (1972a)

Calculated o

100 120 195 140 160

TEMPERATURE, K

180 200

Figure 1. Equimolar G as a function of temperature for the methaneethane system. The solid line was calculated using a modified hard-sphere equation of state [3]

.

G-12
K)

N ^ m tf> o ^

0> o

0)E oco — o

o» v. 8 1 1

CDO

O o <

T3CO

(/) X

inco

\_o

0>

inoCouC

Q_ ccoE

0) JZ3

cr o

CM

0)

10ooocD

ft. G> .9- 2 oo

It

CO X

CM O+Xo 4 o —

CMo

<oCMo

CMo

CM

CMo

GO

cr<

UJa. 8 i5 o

sro

CM

Oo

CM oO om o ^n o

00

4-1ocoH

4-1 uCa E

cd oi 4J

CO CO

ed

CO

CO 4Jc c

03 CO 4J Xi

CO 4J C CL O I CJ CJC

co cc - XI

>. 4J u cu

(3 E

CD S3 aj C

ai3

4-) CO

5-i <yaE

cu U

CU

(-1 D

00
oc

ri

4-> o—I3 cx t L , u>

CU

4-J CO

CO CO

fO

r-*

t-t o CCj •H X.

4-1 4-1 •H CO

CO 1 O cu a. c B CO o 4= u 4-1 0) T3 e c

C3 cu

0) 4-1 H3 1-1 cn o

to U—1

cu3

iH 4-1 CO o3 u 14 •H <u

4-1 cx

•H

a

M cu U 4-1

CO

CUu3

00

T-l

6-14
350

300

o

E

250

m

c>

ti uj x

CD 200

150 —

100

T

v Poon and Lu (1974) CH4+C3H8

O Skripka et al. (1970)

o Wichterle and Kobayashi (1972b)

Stoeckli and Staveley (1970)

* Cutler and Morrison (1965) • Caladoet al (1974)

' I n

1 J

_ —Calculated

J I L J I L

80 100 120 140 160

TEMPERATURE, K

180 200

Figure A. Equimolar G as a function of temperature for the methane

propane system. The solid line was calculated using a modified hard-sphere equation of state [3].

G-15
400

100

50

j> 10

8- 5

CM

C H4 + C3 Hq

OA A

O • • • •

o o

O V

Calado et al (1974)

Akers et al. (1954)

Cutler and Morrison (1965)

Poon and Lu (1974)

Price and Kobayashi (1959)

Reamer et al. (1950)

Sage et al (1934)

Skripka et al. (1970)

Stoeckli and Staveley (I970T

Wichterle and Kobayashi

(l972bTl

l I l I 1

60 100 140 180 220 260 300

TEMPERATURE,

K

340 380

Figure 5. Infinite dilution Henry's constants as a function of

temperature for the methane-propane system.

G-16
*H0

G-17
450

425

400

375

350

o

E

- 325

in

a

w X

e> 300

275

250

225

o Kahre (1974)

a Elliot et al. (1974)

v Wang and McKetta (1964) — Calculated

200

100 110 120 130 140 150 160

TEMPERATURE,

K

170 180 190

Figure 7. Equimolar G as a function of temperature for the

methane-n-butane system. The solid line was calculated

using a modified hard-sphere equation of state [3].

G-18
o

CM

v3- •3

o« o

*3 o+Xo

CD

0>

CM

— ^CD -~- CO

(J)

O - N ^ 3 ^

CT> 2 C7>

>3- oco

4-

V

O

LU

O ° <w o

4> i2

— t « — O D

or cr

0> acoco O < O > O<

<? < 0« o

CO

rOO

ro8

rO8

cr

hcm <

<rLU o 5

cm H-1 o

COo M i l 8 8 8

CM CM

O o

GO o

CD

O o

ro

O

CM

G-19
HO

oo CD CVJ o 0o

CMo

00

roO

roOo

roO

CD

CJO

CVJ

CVJ o

00

LU<

LU

moGO

•H

•U • O S C CD

>4-4 CO

co co

co cy

cfl

C

cfl 3I cI CD (X C e co O J=

CJ 4J

CD T) B C

CO 0)

CDW 3 U

cn o

CO M-l CD

V-i CD a- >-i 3

CO CO o ^

•H CD 4J Pu •H S M CD CJ ^

CD3

00

G-20
I03

o Olds et al. (1942)

a Barsuk et al. (1970)

o

t a

o

^io2

8 oj

CH4 + i C4H10

10' 1

180

Figure 10.

220 260 300 340

TEMPERATURE, K

380

Infinite dilution Henry's constants as a function of

temperature for the methane-isobutane system.

R-21
O (O ^ N Oo

6-22
APPENDIX H

H-l
Isothermal composition measurements for both the equilibrium liquid and vapour phases R-917

have been determined for the nitrogen + methane system at eight temperatures between

1 12. 00 and 180. 00 K, and at pressures from 1 to 49 atm (1 to 50 bar). The internal consistency of these data is checked by comparing experimental and calculated thermo- dynamically consistent vapour phase compositions. Derived Henry's constants are used

to provide a comparison between these data and those of other investigators.

Liquid—vapour phase equilibria in the N2—CH4 system

from 130 to 180 K

A. J. Kidnay, R. C. Miller, W. R. Parrish, and M. J. Hiza

Nomenclature

./ fugacity

6/' excess (lilihs energy

Henry's constant forN 2 in CH4 K equilibrium constant, y/x P total system pressure

P° vapour pressure T absolute temperature X liquid phase mole fraction y vapour phase mole fraction

critical pressure

Substantial quantities of nitrogen are present in most natural

gases as they come from the well, and thus the design and

operation of low temperature processes involving natural

gas requires a knowledge of the nitrogen— methane phase

equilibria over extensive ranges of pressure and temperature. There have been two previous sets of measurements of

liquid-vapour equilibria on the nitrogen-methane system

at this laboratory : the work of Miller, Kidnay, and Hiza 1

at 1 12 K, and the work of Parrish and Hiza 2 at 95, 100,

105, 110, 115, and 120 K. The objective of the present re- search is to extend these measurements from temperatures above the critical point of nitrogen to near the critical point of methane, and thus provide an internally consistent data

set over the methane liquid region. Six isotherms (130, 140,

150, 160, 170, and 180 K) have been measured over the

entire liquid- vapour pressure region, and additional measurements made at 1 12 K and 120 K to tie in the pres- ent work with the earlier data from this laboratory. Because of the growing interest in this system, the results of this work have been compared with existing data of

other investigators, and a discussion of all liquid— vapour

data for nitrogen-methane in the region above the critical point of nitrogen is given.

The authors are with the Cryogenics Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302, USA. AJK is an Associate Professor at the Colorado School of Mines and RCM is an Associate Professor at the University of Wyoming. Received 2 May 1975.

Experimental procedure

The measurements were made in a closed-loop vapourrecirculation system. The general flow scheme is shown in Fig. I and the cryostat is shown in Fig.2. The recirculation pump and the cryostat have been discussed in detail else- where 3 ' 4 and thus only a general description of the equip- ment and procedure will be given here. The procedure followed was to cool (with liquid nitrogen) and evacuate the system, fill with pure methane, warm to

the preselected operating temperature, and then measure

the vapoui pressure or me condensed methane. Measuring

the vapour pressure ensures that the temperature and pres- sure measuring systems are functioning properly, and

establishes the purity of the methane. Nitrogen gas was then introduced into the system, and recirculation of the vapour was initiated. The cold vapour from the top of the cell was

heated to room temperature by exchange with the warm

vapour stream returning to the cryostat. The vapour then

passed through a large room temperature sample loop and was pumped back to the cell through the heat exchanger.

The return vapour entered the cell near the bottom and

bubbled through the liquid. When equilibrium was estabFig. 1 Experimental apparatus

CRYOGENICS . SEPTEMBER 1975 Vol 15, No . 6 H-2 531
liquid ievei indcaior

ce'' oe'~~' 1 venl (me

Fill Ine for

Refrigerant liquid

Fig.2 Plan of cryostat

lished in the system, as determined by the constancy of the temperature and pressure measurements, the gas sample was

isolated in the sample loop, and liquid samples were with- drawn through a capillary sample line, vaporized, and

analysed in the gas chromotograph. Upon completion of

the liquid analysis, the gas samples were withdrawn from

the sample loop and analysed. The system was then re- pressurized with nitrogen to a new pressure, and the sequence repeated to establish another point on the isotherm.

All samples were analysed with a gas chromatography using a thermal conductivity analyser, a 1 cm3 sample loop, helium

carrier gas. and a 5 m column packed with 60 '80 mesh

molecular sieve 5A. The chromatograph was calibrated

using samples of pure nitrogen and pure methane introduced

into the chromatograph at varying pressures. When analysing samples from the equilibrium cell, the compositions of both components were determined chromatographically. and the sum of the compositions thus determined was

normalized to 100%. The temperature in the system was controlled and measured

with an accuracy of ±0.02 K using a calibrated (IPTS-68)

platinum resistance thermometer. The pressures were measured with two bourdon tube gauges previously calibrated with an air piston gauge. The gauges had ranges of 0—20 bar and 0—50 atm (0-51 bar). In the range of 0 to 20 bars, the accuracy of the pressure measurements is ±0.02 bar. while

in the region above 20 bar, the accuracy is ±0.05 bar.

The composition measurements are. in general, reproducible

(o 0.0005 in the mole fraction. The accuracy ol llic. impositions is believed to be ±l'% of the reported \alue or 0.00! in the mole fraction, whichever is the greater.

Results The experimental results arc presented in Table I and in Figs 3 and 4. The isotherms ai 140.00 K and 160.00 K have

been omitted to avoid cluttering the graphs. The methane

vapour pressures of Table 1 were obtained from Goodwin.5

i 1 I I I I I I I n

0 0 1 0.2 Q3 04 05 06. 07 08 09 10

Mole fraction nitrogen

Fig.3 Liquid and vapour compositions

P, but

P, aim

Fig. 4 K factors for nitrogen—methane

532 H-3 CRYOGENICS . SEPTEMBER 1975
.\n exccllcnl indication of the internal consistency of low

j'l.'v.mv experimental (.lata can be obtained by examination

i ! pressure-composition and enhancement factor graphs for

ll 10 liquid and vapour phases, respectively. For t he liquid phase, a plot of (P p°) against must extrapolate

smoothly to I he origin .is the N2 mole fraction approaches

/cio. Additionally, in the region of very low N : concentration the relation between pressure and N 2 mole fraction

must be linear. Fig. 5 is a typical graph foi this invesiigjiion and it clearly shows the excellent consistency ol the low

pressure liquid phase data. The points at 130.00 K and

150.00 K lie on a straight line, while pomls .it 170 00 k

exhibit slight curvature. Another method for examining the

liquid phase is to examine (P />°)/.v N , . ms ;i function of (P - p°) as shown in Fig. 6. A plot ot this type provides a severe test of the internal consistency of the experimental

Table 1. Experimental liquid—vapour equilibrium data for the nitrogen— methane system

P. bnr P atm *CH 4 Vn 2 Kch 4 KCH4

r 1 12.00 K,pCH<1 = 1.0443 bar - 1.0306 atm

1.965 1.939 0.0376 0.9624 0.4720 0.5280

4.332 4.275 0. 1 504 0.8496 0.7654 0.2346

10 538 10.400 0.5876 0.4124 0.9249 0.0751

T 120.00 K,n°CMA

- 1.9190 bar = 1.8939 atm

5 234 5.166 0.1048 0.8952 0.6327 0.3673

10.058 9.926 0.3012 0.6988 0.8182 0.1818

f= 130.00 K,p° H4 = 3.681 bar = 3.633 atm

4.155 4.101 0.0097 0.9903 U. 1 U30 n Aon? 11 "31QR 4.552 4.492 0.0186 0.9814 0.1862 0.8138 10.0108 0.8292

5.025 4.959 0.0292 0.9708 0.2640 0.7360 9.041

1

0.7581 6.594 6.508 0.0641 0.9359 0.4339 0.5661 6.7691 0.6049

7.797 7.695 0.0926 0.9074 0.5201 0.4799 5.6166 0.5289

10.203 10.070 0.1547 0.8453 0.6316 0.3684 4.0827 0.4358

12.579 12.415 0.2188 0.7812 0.7018 0.2982 3.2075 0.3817

15.038 14.841 0.2941 0.7059 0.7508 0.2492 2.5529 0.3530

17.847 17.614 0.3822 0.6178 0.7932 0.2068 2.0754 0.3347

19.923 19.662 0.4512 0.5488 0.8166 0.1834 1.8098 0.3342

22.85 22.55 0.5516 0.4484 0.8463 0.1537 1.5343 0.3428

27.73 27.37 0.7077 0.2923 0.8860 0.1140 1.2519 0.3900

30.31 29.91 0.7828 0.2172 0.9054 0.0946 1.1566 0.4355

33.58 33.14 0.8676 0.1324 0.9285 0.0715 1.0702 0.5400

34.82 34.36 0.9017 0.0983 0.9393 0.0607 1.0417 0.6175

f= 140.00 K,p CH4 = 6.422 bar = 6.338 atm

7.221 7.127 0.0132 0.9868 0.1051 0.8949 7.9621 0.9069

8.298 8.189 0.0316 0.9684 0.2166 0.7834 6.8544 0.8090

9.258 9.137 0.0485 0.9515 0.2952 0.7048 6.0866 0.7407

10.108 9.976 0.0637 0.9363 0.3498 0.6502 5.4914 0.6944

14.056 13.872 0.1372 0.8628 0.5228 0.4772 3.8105 0.5531

18.047 17.811 0.2165 0.7835 0.6214 0.3786 2.8702 0.4832

21.94 21.65 0.3008 0.6992 0.6850 0.3150 2.2773 0.4505

26.59 26.24 0.4063 0.5937 0.7383 0.2617 1.8171 0.4408

30.76 30.36 0.5026 0.4974 0.7726 0.2274 1.5372 0.4572

32.69 32.26 0.5512 0.4488 0.7849 0.2151 1.4240 0.4793

36.33 35.85 0.6304 0.3696 0.8038 0.1962 1.2751 0.5308

37.86 37.36 0.6662 0.3338 0.8107 0.1893 1.2169 0.5671 40.39 39.86 0.7267 0.2733 0.8128 0.1872 1.1185 0.6850

42.00 41.45 0.7788 0.2212 0.8032 0.1968 1.0313 0.8897

T= 150.00 K,pg H4 = 10.414 bar = 10.278 atm

10.673 10.533 0.0038 0.9962 0.0224 0.9776 5.8947 0.9813

11.213 11.066 0.0106 0.9894 0.0675 0.9325 6.3679 0.9425

12.908 12.739 0.0333 0.9667 0.1776 0.8224 5.3333 0.8507

14.228 14.042 0.0518 0.9482 0.2479 0.7521 4.7857 0.7932

18.088 17.851 0.1082 0.8918 0.3938 0.6062 3.6396 0.6797

22.55 22.26 0.1788 0.8212 0.5026 0.4974 2.8110 0.6057

CRYOGENICS . SEPTEMBER 1975 H-4 533
Table 1. Experimental liquid-vapor equilibrium data for the nitrogen—methane system (Cont'd)

P. bar P, atm X N2 X CH 4 Kn 2 Kch4 KCH 4

27.21 2b. Bb U.^b I

U

n ~ia on Z.Zo/o U.bbob

32.36 31.94 0.3377 0.6623 0.6288 0.3712 1.8620 0.5605

37.30 36.81 0.4231 0.5769 0.6630 0.3370 1.5670 0.5842

41.39 40.85 0.4951 0.5049 0.6812 0.3188 1 .3759 0.6314

45.20 44.61 0.5763 0.4237 0.6813 0.3187 1.1822 0.7522

45.86 45.26 0.6042 0.3958 0.6712 0.3288 1.1 109 0.8307

T= 160.00 K,p£h 4 = 15.939 bar = 15.731 atm

16.813 16.593 0.0095 0.9905 0.0438 0.9562 4.61

1

0.9654

17.968 17.733 0.0223 0.9777 0.0979 0.9021 4.3901 0.9227

18.988 18.740 0.0334 0.9666 0.1394 0.8606 4.1737 0.8903

19.913 19.653 0.0448 0.9552 0.1742 0.8258 3.8884 0.8645

21.94 21.65 0.0684 0.9316 0.2406 0.7594 3.5175 0.8152

22.10 21.81 0.0714 0.9286 0.2458 0.7542 3.4426 0.8122

26.19 25.85 0.1205 0.8795 0.3442 0.6558 2.8564 0.7457

30.38 29.98 0.1756 0.8244 0.4184 0.5816 2.3827 0.7055

33.95 33.51 0.2243 0.7757 0.4657 0.5343 2.0762 0. boots 38.46 37.96 0.2820 0.7180 0.5051 0.4949 1.791

1

0.6893

42.29 41.74 0.3333 0.6667 0.5289 0.4711 1.5869 0.7066

46.15 45.55 0.3937 0.6063 0.5422 0.4578 1.3772 0.7551 47.86 47.23 0.4246 0.5754 0.5360 0.4640 1.262 0.8064

48.38 47.75 0.4310 0.5690 0.5315 0.4685 1.233 0.8234

T= 170.00 K,pgH4 = 23.308 bar = 23.003 atm

24.27 23.95 0.0082 0.9918 0.0291 0.9709 3.5488 0.9789

25.39 25.06 0.0189 0.9811 0.0652 0.9348 3.4497 0.9538

26.20 25.86 0.0276 0.9724 0.0889 0.9111 3.2210 0.9370

27.47 27.11 0.0399 0.9601 0.1219 0.8781 3.0551 0.9146

28.43 28.06 0.0495 0.9505 0.1458 0.8542 2.9455 0.8987

30.36 29.96 0.0688 0.9312 0.1875 0.8125 2.7253 0.8725

34.43 33.98 0.1115 0.8885 0.2593 0.7407 2.3256 0.8337

38.58 38.08 0.1562 0.8438 n o i oc U. J 1 OO U.OOOO Z.UU /u n Qi oc U.O I OD

42.52 41.96 0.2001 0.7999 0.3519 0.6481 1.7586 0.8102

46.31 45.70 0.2466 0.7534 0.3743 0.6257 1.5178 0.8305

48.33 47.70 0.2729 0.7271 0.3784 0.6216 1.3866 0.8549

48.95 48.31 0.2915 0.7085 0.3798 0.6202 1.3029 0.8754

49.39 48.74 0.3066 0.6934 0.3801 0.6199 1.240 0.894

r= 180.00 K,pgH4 = 32.883 bar = 32.453 atm

34.11 33.56 0.0089 0.9911 0.0230 0.9770 2.58 0.986

35.40 34.94 0.0202 0.9798 0.0494 0.9506 2.45 0.970

36.72 36.24 0.0327 0.9673 0.0738 0.9262 2.26 0.958

37.87 37.37 0.0434 0.9567 0.0936 0.9064 2.16 0.947

39.45 38.93 0.0588 0.9412 0.1192 0.8808 2.03 0.936

40.24 39.71 0.0632 0.9368 0.1260 0.8740 1.99 0.933

42.72 42.16 0.0863 0.9137 0.1572 0.8428 1.82 0.922

44.75 44.16 0.1083 0.8917 0.1786 0.8214 1.65 0.921 46.56 45.95 0.1254 0.8746 0.1919 0.8081 1.53 0.924

48.70 48.06 0.1567 0.8433 0.1992 0.8008 1.27 0.950

data, since very small deviations in the low concentration

region are greatly magnified. Graphs of the type shown in Fig.5, on the other hand, provide some information on the thermodynamic consistency of the data, since it is necessary that the data points be linear through the origin. For

comparison, the nitrogen-methane data of Stryjek,

Chappelear, and Kobayashi 6 are shown in Fig.7. The

amount of scatter exhibited by both data sets is not excessive for high quality data, and the deviation from linearity of

the isotherms as the critical temperature of the solvent is approached is also typical. The enhancement factor, defined as>, C H 4 ^

)/PcH4

. provides

valuable insight into the vapour phase behaviour, since a plot of enhancement factor versus total pressure must form a smooth curve extrapolating to a value of unity at the vapour

pressure of methane. Typical enhancement curves, shown

in Fig.8, demonstrate the high degree of consistency generally realized. Two of the isotherms measured by Stryjek,

534 H-5 CRYOGENICS . SEPTEMBER 1975
. ._. L 1 i . I J 002 OOT .".01 005 006 007 OOB

Faj.r) Luiuiri phase compositions tor Ni --CH4

Chappelear. and kobayashi are within 1 K of isotherms re- ported here, and in Figs l > and 10 enhancement factors for these isotherms are compared. The agreement between the two seis 11I data is satisfactory. The data of Tabic 1 at 1 I 2.00 K and 1 20.00 K are in excellent agreement with the earlier data from this laboratory. 1 ' 2

Discussion

There have been nineteen previous experimental sets of measurements of liquid-vapour equilibrium in the nitrogen- methane system. Table 2 summarizes all of the previous work. However, of the studies listed in Table 2, only those of Bloomer and Parent; Chang and Lu; Cines et al; Torochesnikov and Levius; Stryjek, Chappelear, and

Kobayashi: and Yu and Lu are in the temperature region 130 to 180 K and present sufficient tabular data to attempt

a meaningful comparison with the results of the present

study. The data reported by Bloomer, Eakin, Ellington, and

Garni as well as that reported by Ellington, Eakin, Parent et

al for nitrogen— methane is the same data reported earlier by Bloomer and Parent. Brandt and Stroud, and

Fastovskii and Petrovskii have very little data above 1 30 K

and the results of Forg and Wii tz are presented only as graphs, so that comparison with our work is not worthwhile.

It is also not clear whether data reported by Forg and Wirtz

are original or a composite of the work of others. Two methods are used to compare the available experi- mental data sets in the temperature region between the

critical points of nitrogen and methane (126.20 to 100.50 K). First, a numerical method is used with the P-x data for each isotherm to calculate y values which are then compared to the experimental y values, and second, Henry's law constants are calculated from the data and

plotted as a function of temperature.

bar 4 8 ,i *

,1 1 I 1

I I I I 0 2 4 6 8 10 12 14 16

(P-p° ), aim

Fig. 6 Liquid phase compositions for N2—CH4

( P-p ), otm

Fig. 7 Liquid phase compositions of Stryjek, Chappelear, and

Kobayashi

CRYOGENICS . SEPTEMBER 1975 H-6 535
<P-p° ), bar

4 S 12 16 20

Fig. 8 Enhancement factor for nitrogen— methane

Numerical method

It has been appreciated for quite some time that, in principle, the measurement of P-x-y data at a constant temperature is redundant (see for example, Redlich and

Kister 26 and Barker 27

). since it is possible in principle to calculate the third variable if two are known. Van Ness,

Byer, and Gibbs 28 have recently discussed this type of

calculation in some detail, and Won and Prausnitz 29

as well

as Christiansen and Fredenslund 30 have presented computational methods for determining y from constant temperature P-x data in high pressure binary systems containing one supercritical component. The work of

Christiansen and Fredenslund is the basis for the comparisons presented here, and a brief description of their method

follows.

Christiansen and Fredenslund use the orthogonal collocation technique to solve the non-linear differential equations re- lating the excess Gibbs energy to the activity coefficients

that are used to calculate the mixture total pressure. The

liquid phase compositions used in the calculation are roots of Legendre polynomials rather than experimentally determined x values. To determine the total pressures at the collocation points (that is, the interpolated x value at which the computations are made) the experimental P-x

curve is interpolated with a cubic spline fitting procedure.

The technique uses the interpolated P-x values to calculate the excess Gibbs energy, the activity coefficients, and

finally the vapour phase composition at each collocation

point. The calculated x versus;' curve can then be inter- polated to determine the.y values for the experimental

values of x. A modified Redlich-Kwong equation of state

is used to calculate the necessary vapour phase thermo- dynamic properties. Since one component is supercritical the unsymmetric convention for activity coefficients is applied and the Henry's constant is required. This is obtained by extrapolating the curve o{(J/x) versus x to

infinite dilution using Lagrangian extrapolation. The

P-x-y calculations involve a doubly iterative precedure;

however, the outer iterative loop (which calculates^ values)

usually takes less than ten iterations and the inner loop

(which calculates the excess Gibbs energy) normally takes

less than five iterations. For each isotherm, the programme

is repeated seven times, using eight to fourteen collocation

points. Generally, the variation in \Ay\ and the Henry's

constant depend somewhat on the number of collocation

points used, so at all isotherms studied the Av and Henry's

constants selected correspond to the number of collocation

points yielding the minimum \Ay\.

The advantages of this technique arc that it applies both above and below the solute critical temperature, provides a good estimate of the I lenry's constant , and does not

require an analytical expression for (?'' as a function of .v.

[P-P° ), twr

), otm

Fig. 9 Comparison of enhancement factors at approximately 150 K

), bar CH 0 4 8

4 12 16 20

I I6| 1 1 1 1 r

Fig.10 Comparison of enhancement factors at approximately 160 K

536 H-7 CRYOGENICS . SEPTEMBER 1975
Table 2

Approximate Approximate pressure Reference temp region region covered,

1 nve c t irjal nrs No Year covered K atm R pmark ^

Bloomer, Eakin, Ellington, Graphs only, data at Ljami 1 incc l ybb 1 r\r> 1 0"7

1 UU— 1 o

/

7/—AQ4o constant composition

Bloomer, Parent Q Q o, y iyoz, i yoj 0 1 1 Q 1 y i — i y i 1 AQ Data at constant composition

Brandt, Stroud 1 nI u

1 QCQ i zy— i /y *3A J4

Chant), Lu 1 1 1 9o / 1 11, 1/1 3—49

Chflunfj, Wang 1 o I yon OO 1 ^iA yz— i z4 n a U—

4

Cmes, Roach, Hogan, Roland 1 6 I UU— I /z 1 A A I —44

Ellington, Eakin, Parent et al 1 A 1 Q&Q 7Q/y— 1 Q7 1 0 / Data at constant composition

Fastovskii, Petrovskii 15 1957 90-150 1-16

Forg, Wirtz 16 1970 80-180 1-103 Graphs only

Fuks, Bellemans 17 1967 84-89 1-2 Liquid phase only

McTaggert, Edwards 18 1919 77-109 1

Miller, Kidnay, Hiza 1 1973 112 2-13

Parrish, Hiza 2 Forthcoming 95-120 0-25

Skripa, et al 19 1970 113 1-18

Sprow, Prausnitz 20 1966 91 0-4

Stryjek, Chappelear, Kobayashi 6 1972 114-183 1-50

Torochesnikov, Levius 21 1939 89-133 0-24 Graphs only

Vellinger, Pons 22 1943 90 0-1 Graphs only Yu, Lu 23 Forthcoming 130 4-34

'Essentially the same data

The collocation technique also has several drawbacks, the major one being that it must interpolate values from the P-x curve instead of using the experimental points. This

is not a serious problem if the P-x data are smooth and

there are enough data points to allow a reliable inter- polation, but if the data are not smooth then the method may

not yield meaningful results. However, in this case the experimental data must be considered to be of questionable

value. A second disadvantage is the lack of an analytical or graphical method for eliminating the scatter in the liquid phase

compositions. This failure to smooth the data means that a single bad data point on an isotherm can significantly affect the calculated results, and it also prevents the weighting of

data points or the use of duplicate measurements.

Table 3 contains the Henry's constants and the average

absolute deviation between experimental and calculated y

values (IAy|) calculated with the procedure of Christiansen and Fredenslund. Fig. 1 1 is a graphical comparison of the

calculated y values, represented by the solid line, and the experimental measurements of this work at 170.00 K. The

table also lists the number of experimental points where Ay is less than or greater than 1%. Predicting the critical region of a mixture is very difficult; therefore, the number

of points where I Ay I exceeds 1% is divided into two

categories: those where the total pressure is less than 90%

of the critical pressure and those where the total pressure

is within 10% of the critical pressure. If most of the points where I Ay I exceed 1% are near the mixture critical point it

is more than likely that the fault lies with the calculational procedure rather than the experimental data. The failure of the 1 83. 1 5 K isotherm of Stryjek et al to

give consistent results is probably due to a failure in the equation of state, since the temperature is very near the

critical temperature of methane (190.56 K). The 171.43 K

isotherm of Chang and Lu and the 130.1 K isotherm of Yu

and Lu could not be evaluated with the computer pro- gramme; this is probably due to excessive scatter in the experimental data. Bloomer and Parent report only dew point and bubble point

data. To convert their measurements into isotherms it was

necessary to fit their bubble point pressures to the equation

B C

\oge P = A + - + —

T T2 (I)

where A, B, and C are the least squares constants for each

mixture. Bubble point pressures were then calculated at various temperatures. No attempt was made to interpolate

y values from their dew point data. The comparison of calculated and experimental .y values shown in Table 3 indicates a high degree of internal consistency in the data of this investigation, the data of

CRYOGENICS . SEPTEMBER 1975

H-8

537
Table 3

Average Number of data points \Ay\ > V/, deviation

Investigator T, K ^N 2 . CH 4 bars

in Ay,

% IAkI < 1% P < 0.9PC P > 0.9PC Remarks

Tn is work 1 "?n nn ap, nn nU. 5RDO 1

1

1 o

oo nu 57 7n n 47 1 9 1

1 u 150.00 68.77 0.66 9 0 3 160.00 79.30 0.80 10 0 4 170.00 98.98 0.42 12 1 0 180.00 102.70 0.88 9 0 1 Bloomer, 127.59 42.84 Interpolated Inipi . .. .

: Parent 138.71 55.28 — _ _ _ point datH • !•.•>.; 150.00 66.27 - - — for details of 160.93 88.43 - — lation

v_.ir.es e i oi jj. i *j 4P, Q7 1 nn o

:Di

i 144 9fi 72.00 0.63 1

1

J n

1 55jj. j77/ Q1J7 I . 4P, HO n 74 q 1 n

172.04 1 12.83 2.23 0 6 0

Stryjek et al 127.59 3 C DC Oj.uj nU.ODRfi 1I oT qo u 138.44 n 7*5 D 1

nu 149.82 65.74 1.64 5 1 3 160.93 65.02 1.70 7 1 4

172.04 60.75 1.32 7 0 3 177.59 112.11 0.72 8 0 3 183.15 Computation method failed Torochesnikov 1 29.87 78.60 4.80 2 3 0

and Levius 132.92 175.23 11.37 0 6 0

50

45

40

E

o

30

25

I7000 K/

50

-45

40

• Liquid o Vapour

201 I I I I I L_

35 =

-30

25

0 1 0 2 0.3 0 4 0 5

Mole fraction nitrogen

Fig. 1 1 Comparison of calculated and experimental y values

Stryjek, Chappelear, and Kobayashi, and the data of Cines

et al, with the exception of their isotherm at 172.04 K. The data of Torocheshnikov and Levius exhibit unacceptably high scatter, and, as noted previously, the isotherms of Chang and Lu, and Yu and Lu could not be processed with

the computer programme.

Henry's constants Henry's constant, defined by the equation

_ limit #n2 ,ch4 =*

n

-:o

/n2 *N2

(2)

is a valuable thermodynamic constant for two reasons.

First, some of the procedures for calculating liquid- vapour

equilibria of systems containing a supercritical component

require the Henry's constant,24 the second, it proves useful

in testing the internal consistency of a set of experimental

data and in comparing data sets from different investigations. There are two basic approaches to the evaluation of Henry's

constant from experimental data. In the first method, the vapour phase fugacity of the supercritical component is evaluated with a suitable equation of state, and (2) is directly applied to the data by preparing graphs of/N2

versus xN or (/n2 An2

) versus *n2 and evaluating the

slope of the curve at infinite dilution or the intercept, res- pectively. The disadvantage of this method is that it uses only the data in the region of very low nitrogen concen538 H-9

CRYOGENICS . SEPTEMBER 1975
I50r

I30I--

I20 :

N

2 + CH 4 Orthogonal collocotion programme with all experimental

data

Orthogonal collocotion programme omitting the two data

points of lowest concentration

Gunn . Yamodo.and Whitman eguation

Slope of f versus X

,. lOOt200

Fig. 12 Henry's constants

50

45-

40

35

30

N„+CH„ -50

• This investigation

Stryjek , Chappeleor, Kobayashi

* Cines , Roach, Hogan, Roland

45

40

-35

05 06 07 08

30

Fig. 13 Comparison of Henry's constants

tration, which is a difficult region to measure experimentallv

.

The second approach makes use of an integrated form of

(2), such as the Krichevsky-Kasarnovsky equation, 24 the Krichevsky-Ilinskaya equation, 24

or the equation proposed

recently by Gunn, Yamada, and Whitman.25 These equations have the advantage of utilizing data in the mid-range

of nitrogen concentrations, but have the drawback of

requiring assumptions regarding the liquid-phase behaviour

of the system. All of the methods for evaluating Henry's

constant require the use of an equation-of-state for the vapour phase.

In Fig. 12. Henry's constants determined by several different methods from the data of this investigation are shown. The

isotherms at 1 70 and 180 K (Fig. I 2) were treated with the orthogonal collocation programme in two ways; first, using all of the experimental data, and second, omitting for each isotherm the two data points of lowest nitrogen concentration. Using all the data, the Henry's constants are in serious disagreement with values obtained from the other methods, while elimination of the two data points on each isotherm results in reasonably satisfactory agreement (5T#) among the Henry's constants. The difficulty encountered with the orthogonal collocation programme is due primarily to the particular extrapolation

method used in obtaining the Henry's constants. With the method employed, very small errors in x^ 2 at the lowest concentration level of N 2 can significantly alter the value of

the Henry's constant. The effect of analytical imprecision in the liquid phase concentration measurements is shown by

the vertical lines in Fig.6 for 130, 170, and 180 K. To compare the Henry's constants from this work with

those of previous investigations, the method of Gunn,

Yamada, and Whitman was selected, and the comparison is made in Fig. 1 3 . The Henry's constants of this work and

that of Stryjek, Chappelear, and Kobayashi are in excellent agreement over the entire temperature region studied. The

data of Cines et al are in good agreement at the lower

temperatures, but show marked deviations at the higher temperatures. The smooth behaviour of the data in Fig. 13

indicates good internal consistency for all the data.

Conclusions

The 'enhancement factor' graphs (Figs 8, 9, and 10), the pressure-composition graphs (Fig. 5), and the Henry's constant graphs (Figs 12 and 13), as well as the results of the orthogonal collocation programme (Table 3, Fig.l 1) all demonstrate the high degree of internal consistency and the probable thermodynamic consistency of the data reported

here. Unfortunately, there exists no technique for establishing beyond doubt the thermodynamic consistency of any high pressure liquid—vapour equilibria data. The data of Stryjek, Chappelear, and Kobayashi are in good

agreement with this study, as are the lower temperature

data of Cines et al. The isotherm of Cines et al at 172.04

disagrees markedly with this study (Fig. 13), and shows considerable internal scatter (Table 3). The reliability of the

data reported by Chang and Lu, Yu and Lu, and Torocheslmikov and Levius is questionable. Since Bloomer

and Parent did not measure isothermal data, as was the case

in all of the other studies, it is difficult to make a meaningful comparison with their results. However, the Henry's

constants obtained from their data with the numerical

orthogonal collocation programme appear to be in subCRYOGENICS . SEPTEMBER 1975 H-10

539
statiti;il agreement with those of Stryjek, Chappelear, and

Kohayashi. and with this study.

Summari/ing. it appears that highly reliable data for the -N2 CH4 system are now available over the temperature

region neai the nitrogen critical point to approximately the methane critical point.

The authors aic grateful to L. J. Christiansen and

A. [-"reilenshnul lor the orthogonal collocation computer programme used in this work, to R. D. Gunn for calculating

the I leim 's constants of Fig. I 3. and to the Office of Standard Reference Data of the National Bureau of Standards for partial financial support.

References

1 Miller. K. C. Kidnay. A. .1.. Hi/a. M. I. MClih. .1 19 i 1973) 145

2 Parrish, W. R.. and Ili/.a. M. J. Advances in Crvogcnic Engineer- mg 19 tPlenuni Press. New \ ork. 1974) 300

3 lliza. M. .1.. Duncan. A. (i. Rev Sci Inan 40 1 1 969) 5 1 3 4 Duncan. \. G.. lliza. M. J. Advances in Cryogenic Engineering

15 (Plenum Press. Now s. ork. 1970) 42

5 Goodwin, R. D. "The thermophysical properties of methane, from 90 to 500 k at pressures to 700 bar." US Dept of Commerce. NBS Tech Note 65 3 6 Stryjek. R.. Chappelear. P., Kobayashi. R. J Chem Eng Data 19 (1974) 334

7 Bloomer, O. T., Eakin, B. E., Ellington, R. T., Garni, D. C. 'Thermodynamic properties of methane-nitrogen mixtures', Inst Gas Techn Res Bull No 21 (1955).

8 Bloomer, O. T., Parent, J. D., 'Physical-chemical properties of methane-nitrogen mixtures'. Inst of Gas Techn Res Bull No 17 (1952)

9 Bloomer, O. T.. Parent, J. D. Chem En? Progr St'mp Scr 49 No f (1953) 1 1

1 0 Brandt, L. W., Stroud. L. Ind Eng Chem 50(1958) 849

1 1 Chang, Shinn-der, Lu, B. C.-Y. Chem Eng Progr Svmp Sci 63. No 81 (1967) 18

12 Cheung, H., Wang, D. I. -J. Ind Eng Chem Fundam 3 No 4 1 1 "64i 355

1 3 Cines, M. R., Roach, J. T.. Hogan. R. J., Roland. ( II. < 'In m

Eng Progr Symp Scr 49 No 6 ( 1 95 3 ) 1 14 Ellington, R. T., Eakin, B. E.. Parent. J. D.. Garni. I). ( .. and Bloomer, O. T. Thermodynamic and Transport Properties 01 Gases. Liquids, and Solids, Am Soc Mech Eru:rs. Ileal Transl'i-i Div (McGraw-Hill, New York. 1959) 180

15 Eastovskii, V. G., Petrovskii. Yu. //; Eiz Khun 31 1 1 957) 23

1

n

I 6 Eorg, W., Wirtz, P. Linde Rep Sci Techno! 15 ( 197m 4<-

1 7 Fuks, S., Bellemans. A. Bui! Soc Chim Beiges 76 ( 196" i N. s 6 290

1 8 McTaggart. II. A.. Edwards, E. Tram Riv Six Can 13 1 1 9-1 9

1

47

19 Skripka. V. G., Nikitina, I. E., Zhdanovich. L. A., Siroliu. \. Bcnyaminovich. O. A. Gasov Prom 15, No 12 ( 1970i "5 20 Sprow, F. B., Prausnitz, J. M. Cryogenics 6 (1966) 338

21 Torocheshnikov. N. S., I.evius, L. A. /.h Khim Prom 16 i |93«>

19. This data appears in graphical form in Ruhemann. St. Pin- Separation of Gases (Oxford Umv Press. 1 949 1 54

22 Vellinger, E., Pons, E. Compt Rend 217 ( 1 943) 689

23 Yu, P., Lu, B. C.-Y. Advances in Cryogenic Engineering 20 1 1975)

24 Prausnitz, J. M. Molecular Thermodynamics of fluid-Phase

Equilibria, (Prentice-Hall, Englewood-Cliffs, NJ. 1969)

25 Gunn, R. D., Yamada, T., Whitman, D. AlChE J 20 ( 1 974) 906

26 Redlich, O., Kister, A. T. J Am Chem Soc 71 (1949) 505

27 Barker, J. A. Australian Jour of Chem 6 (1953) 207

28 Van Ness, H. C, Byer, S. M., Gibbs, R. E. AlChEJ 19 (1973) 238

29 Won, K. W„ Prausnitz, J. M. Ind Eng Chem Fund 12(1973)

459

30 Christiansen, L. J., Fredenslund, Aa. AlChE J 21 (1975) 49

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POLICY.

540 H-n CRYOGENICS . SEPTEMBER 1975

ISCOXM - EJU.

APPENDIX I

I-l
FRACTURE MECHANICS AND ITS APPLICATION TO CRYOGENIC STRUCTURES*

H. I . McHenry

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

A tutorial review of fracture mechanics is presented with emphasis

on the application of this technology to cryogenic structures. The concepts

of linear-elastic and elastic-plastic fracture mechanics are briefly reviewed. Test methods and representative data for fatigue crack growth

and fracture toughness of structural alloys at cryogenic temperatures

are summarized. The elements of a fracture control plan are presented and

applications of fracture mechanics to cryogenic structures are described.

Key Words: Crack propagation; cryogenics; fracture mechanics; fracture

toughness; material properties; structures.

Contribution of NBS —not subject to copyright.

1-2
FRACTURE MECHANICS AND ITS APPLICATION TO CRYOGENIC STRUCTURES*

H . I . McHenry

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

The hazardous nature of many cryogenic fluids requires the use of conservative design procedures to assure adequate structural safety. The prevention

of brittle fracture is an important consideration because of the sudden and un- controlled nature of such failures. Experience gained from service failures of

many engineering structures indicates that most brittle fractures are initiated

by small flaws that grow, as cracks, to a critical size during operation. Accordingly, there are three elements to the fracture problem: 1) the initial flaw,

2) crack growth and 3) crack tolerance. To account for these factors, a new

design approach, based on fracture mechanics, is being developed 12and applied

3 in varying degrees to the design of nuclear pressure vessels, bridges, aircraft

and missiles^

Fracture mechanics is the study of the influence of loading, crack size

and structural geometry on the fracture resistance of materials containing

cracks. When applied to design the objective of the fracture mechanics analysis

is to limit operating stresses such that a pre-existing flaw of assumed initial

size will not grow to critical size during the desired service life of the

structure. Service life is calculated on the basis of probable initial flaw

sizes limited by inspection, a stress analysis of the structure and experimental data relating crack growth and fracture to fracture mechanics parameters.

In this paper, the concepts of fracture mechanics and their application

to the design of cryogenic structures are reviewed. Emphasis is placed on

imparting an understanding of the technology, a review of the information

available and an appreciation of the many factors contributing to the fracture

problem.

Contribution of NBS —not subject to copyright.

1-3
LINEAR ELASTIC FRACTURE MECHANICS

The physical basis of fracture mechanics stems from the work of Griffith"*

who demonstrated that the strain energy released upon crack extension is

the driving force for fracture. The strain energy, V, is the work done

by load, P, causing a displacement, A:

v - f - si (i)

where, C = ^ = elastic compliance.

The loss of elastic energy upon crack extension of unit area, A, is defined as the strain energy release rate, G:

r = dV | _ dC = dV| dA ' A

2 dA dA 1 K }

Irwin and Kies^ used this relationship to determine the fracture resistance of

structural materials, G , by measuring the critical load, P , in a specimen

c c with a known compliance function, dC/dA.

The Stress Intensity Factor

Irwin? who determined the stress distribution near the tip of a crack

located in a linear elastic body, developed a stress analysis basis for fracture

mechanics. The magnitude of the crack tip stress field, , was found to be

proportional to a single parameter, K, the stress intensity factor:

a,. = f. . (9) = K • f (position) (3)

ij

/2iTr ±3

where, r and 9 are cylindrical position coordinates; r = 0 at the crack

tip and 9 = 0 in the crack plane. K is a function of the applied stress,

a, crack length, a, and a factor dependent on structural geometry, Y(a):

K = Y(a)a/rra . (A)

8 9 r Tada, Paris and Irwin and Sih have published handbooks of K formulae for

various geometries and boundary conditions.

2

1-4
Irwin demonstrated that the strain energy-release rate and stress

intensity approaches are related:

K

2 = E'G (5)

where, for plane stress, E' = E, the elastic modulus; and for plane strain,

2

E' = E/ (1-V ), where V is Poisson's ratio. Thus, it is equivalent to attribute

the driving force for fracture to the crack tip stress field, which is proportional to K, or to the elastic strain energy release rate, G. The stress

intensity, K, is used more commonly than G because K can be computed for different

structural geometries using stress analysis techniques.

Fracture Toughness

Fracture occurs when the crack tip stress field reaches a critical magnitude, i.e., when K reaches K , the fracture toughness of the material. K is a

c c mechanical property that is a function of temperature, loading rate and microstructure, much the same as yield strength is; however, is also a function

of the extent of crack tip plasticity relative to the other specimen (or

structural) dimensions. If the plasticity is small compared to the specimen

dimensions and the crack size, then approaches a constant minimum value defined as K , the plane strain fracture toughness.

Measurements of fracture toughness based on linear elastic theory are

limited to the case of plane strain testing in accordance with ASTM E 399.

The dimensional criteria in this specification are:

K 2 B, a, W-a > 2.5 ) (6)

ys

where, B, a and W are defined in Figure 1. The specimens are precracked by

fatigue cycling to an initial crack length of a/W =0.5 and subsequently loaded

to failure. K is calculated from the critical load, P , the measured crack

a length, the specimen dimensions and the specimen calibration function, Y (y)» as follows:

K

0

= ^- Y(|) . (7)

Q B/W W

1-5
K = K if all the conditions of ASTM E 399 are met, i.e., precracking

procedures, load-displaceinent record, specimen dimensions, etc. At cryogenic

temperatures, the test procedures are similar to those employed at room

11

temperature. A cryostat, such as the one shown in Figure 2, is used to

contain the cryogen for obtaining the desired test temperature.

Crack. Tip Plasticity

Applicability of the linear elastic analysis has been extended to conditions

approaching net section yielding by correcting for the zone of plasticity that

12 exists at the crack tip. The idea is that the plastic material at the crack

tip strains without carrying the incremental load; therefore, in the elastic

sense, the crack behaves as if it were slightly longer. The adjustment is

made by adding the radius of the plastic zone, r , to the apparent crack length:

K = Y(a+r ) a/a+r (8)

y y

1 K

2

where, o is the yield strength at the crack tip.

The r correction modifies the crack tip stress field to account for the

y

elastic stress redistribution due to the localized plasticity.

The extent of crack tip plasticity is influenced by specimen dimensions.

This is particularly true for thickness. As specimen thickness increases,

a,, increases from 0 to /3 O due to through-the-thickness elastic constraint.

Y ys ys

The maximum value of a is reached when the plastic zone size is limited to

y

about 5 percent of the thickness. Thus, in a given material, the plastic

zone size as computed by Equation 9 can vary with thickness by a factor of

three—leading to a strong dependence of on thickness as shown in Figure 3. The inflection point of the curve in Figure 3 occurs at approximately

2 (K rrJo ) ; thus, for maximum toughness:

IC ys °

K 2 B < (— ) or KTr > a /B. (10) a IC ys

ys

14 Equation 8 is often useful in material selection.

13

4

1-6
Summary Comments

The crack tip stress field is the driving force for fracture and the

magnitude of this stress field is proportional to the stress intensity

factor, K. K is a function of crack size, applied stress and structural

geometry and can be computed using stress analysis methods. The resistance

to fracture is a material property defined as the fracture toughness,

K

c

; fracture occurs when K = K . Thus, for a given structural geometry

and material, critical crack sizes can be determined as a function of

applied stress and vice-versa:

K

c 2

The approach is applicable to conditions of localized crack tip plasticity,

i.e., where c < .8a or r < 0.3a, when the r correction is used to account

ys

15y ~ y

for crack tip plasticity.

ELASTIC PLASTIC FRACTURE MECHANICS

Many of the high toughness structural materials used for cryogenic structures

undergo extensive plastic deformation prior to fracture. Thus, the concepts

of linear elastic fracture mechanics are being extended to account for elasticplastic behavior. Three approaches currently under development include: the

crack opening displacement (COD) , the J integral and the R-curve.

The Crack Opening Displacement

The crack opening displacement concept is a crack tip strain criterion

for fracture stemming primarily from the work of Wellsl^ For a crack in an elastic body, the crack opening displacement, v, at a distance r from the

crack tip is given by Westergaard 1 s"^ displacement equation:

v = fr to* . (12)

Under conditions of small scale yielding, the displacement at the crack tip, 6, can be calculated by assuming the effective crack tip (a cc 3 6 r

' = a + r ) effective y

is at a distance r from the actual crack tip:

y

2

6 = 2v = /27ir = I %— • (13)

7T E y TT E CL

5 1-7
Theoretically, fracture occurs when 6 = 6^, the critical COD. In practice, a characteristic value for 5 exists only for the crack initiation event; significantly more scatter exists for 6 measured at maximum load or final fracture.

The COD approach is limited by the analytical and experimental uncertainties

of the crack tip region. Analytically, 6 is defined as the COD at the interface of the elastic plastic boundry and the crack surface. Experimentally, 6 is

calculated from displacement measurements taken remotely from the crack tip; direct

physical measurements of 5 have been abandoned due to lack of precision. Further

uncertainty is introduced by the term in Equation 13, which may vary

by 75 percent depending upon the degree of elastic constraint—a crack

tip characteristic that cannot be measured directly.

Despite these shortcomings, the COD approach is being widely used,

particularly in Great Britain, because it offers a significant improvement

over linear elastic methods in the plastic range. Several useful empirical

correlations have been developed relating COD, crack size and applied

18 strain for specific structure/material combinations. Test methods for

19 measuring 6 have been standardized and found to be useful as a comparative measure of material toughness.

J-Integral

20 The J-integral is a characterization developed by Rice of the elastic-plastic

field in the vicinity of the crack tip. The use of the J-integral as a fracture

21

criterion was suggested and experimentally demonstrated by Begley and Landes.

J is defined as the line integral:

J = / fwdy - T (|£)ds] (14)

p ox

where, T is any contour surrounding the crack tip, w is the strain-energy density,

->T is the stress vector normal to T,

->u is the displacement vector and

s is the arc length along T.

6

1-8
20 The J-integral is path independent for linear and non-linear elastic materials

22 and nearly so for most structural materials under monotonic loading conditions.

Thus, J can be computed using numerical methods by analyzing along a contour

avay from the crack tip, i.e., in a region where the analysis methods are quite

accurate. This relieves the uncertainties of the crack tip region—a problem

that seriously limits the usefulness of the COD method.

An equivalent interpretation is that J is equal to the change of

potential energy, U, upon an increment of crack extension of unit area, A:

I - - f . (15,

For the linear elastic case the potential energy equals the strain energy

D = V) and, therefore, Equation 15 is the same as Equation 2 and J = G.

Thus, J appears to be a logical extension of linear elastic fracture mechanics

into the elastic-plastic range. Due to the irreversibility of plastic deformation, the energy interpretation of the J-integral does not apply to the

process of crack extension, and J is not equal to the energy available

for crack extension in elastic-plastic materials —as G is for elastic

materials. J is simply an analytically convenient, measurable parameter

that is a characteristic of the elastic-plastic field at the crack tip. The

21 contribution of Begley and Landes was to demonstrate that crack initiation

under elastic-plastic conditions occurs at a characteristic value of J, called

J , that is related to K in the same way G is related to K in Equation

5. Thus, J integral methods can be used to determine K in specimens

significantly smaller than the size requirements of Equation 6.

Methods of measuring J are not yet standardized; however, the method

23

or:o:sec by ler.des and Begley is receiving widespread use. A deeply notched

soeci-er. or ASTM I 399 design is precracked to aAi * 0.6 and loaded

to a predetermined J-level in the region where crack extension is anticipated.

The load-displacement curve is recorded on an X-Y plotter. Displacement is

measured along the load line. Subsequently, the specimen is unloaded and heat

tinted to mark the region of crack extension. The specimen is fractured and

the crack extension, la, is measured from the exposed fracture surface. J is

calculated from the load displacement record and specimen dimensions using the

24 approximation of Rice, Paris and Merkle.

7 1-9
(16)

where, A is the area under the loctd displacement record and B is the ligament

(W-a)

.

The results of a test series are plotted as J vs. Aa, and the J is defined

-L v> as the extrapolation of the best-fit curve to Aa = 0. Data for ASTM A453

25 stainless steel at 4 K are shown in Figure 4. K is related to J as follows

:

K

IC

(J) " /E ' J

ic • (17)

The principal limitation of the J-integral concept is that it is only

applicable to crack initiation. In most of the materials that fail in the

elastic-plastic range, significant fracture resistance exists after crack

initiation. Thus, in some cases the J-integral may be unduly conservative

as a fracture criterion. Another factor currently limiting the routine

application of J is the analytical complexity in determining J. The

stress-strain characteristics of the material must be properly accounted

for in the analysis. Thus, for a given structural configuration, J

solutions art required for each distinct material instead of the single

solution needed for K analyses.

R-Curves

26

The R-curve concept, introduced by Krafft, Sullivan and Boyle , is a characterization of the increase in fracture resistance accompanying the

slow crack extension that precedes unstable fracture. The R-curve is

determined by measuring crack extension, Aa, as a function of the driving

force for fracture expressed in terms of G, K, J or 6. The level of

driving force required to extend the crack is defined as the resistance,

R, of the material. An R-curve is a plot of R vs Aa as shown in Figure

5, where R is expressed in terms of K and is denoted by K^. The R-curve

may be used as a fracture criterion when crack driving force curves,

expressed in terms of K vs a at constant load in Figure 5, are shown on

the same plot. Fracture is predicted when the following conditions are met

:

8

I -1 0
(18)

and K are computed for the test specimen and structure respectively using

the appropriate value of Y(a) in Equation 8.

In applying the R-curve concept as a fracture criterion, it is assumed

that: 1) the R-curve is a property of the material for a given thickness and

temperature and 2) the influence of planar geometry on the predicted instability

point is accounted for in the calculation of K for the driving force curves.

The first assumption implies that the R-curve is independent of specimen size

and configuration and the initial crack size. This assumption has not been

28 29 clearly established because results which both agree and disagree with this

hypothesis have been reported. The validity of the second assumption is limited

to the case of small scale yielding where the K-analysis is appropriate. These

30 uncertainties, coupled with the complexity of the proposed test method, have

limited the applicability of the R-curve approach.

The R-curve approach is used as a measure of fracture toughness for plate

thicknesses where valid K data cannot be obtained because of the size

requirement of Equation 9. For example, the nickel steels have been evaluated

31

at temperatures down to 76 K using the R-curve approach. The results can be

misleading if one compares materials on the basis of fracture toughness, i.e., an initiation criterion such as K indicates a substantially lower toughness

It

than an instability criterion such as the R-curve.

Summary Comments

The COD and J-integral concepts are efforts to define single parameter

characterizations of the fracture process that are applicable to linear

elastic and general yielding fracture. In the COD concept, attention is

focused at the crack tip; fracture theoretically occurs when a critical

displacement develops at the crack tip. The J-integral concept examines

the stress-strain conditions along an arbitrary contour away from the crack

tip; fracture theoretically occurs when the potential energy available for

crack extension reaches a critical value defined by J. For the linear elastic

case, 6 and J T „ are consistant with the linear elastic fracture criteria:

c IC

9 1-11
1

1/ ~ G -

c E

The principal limitation in extending these criteria to general yielding

tracture is that both 6 and J,,, are only applicable to the onset of crack

c TC ' rr extension. Only the R-curve approach accounts for the significant increase

Lb fracture LiuisLaace that accompanies the slow crack growth preceding unstable

tracture. The application of the CUD, J-integral and R-curve approaches to the

design of cryogenic structures has been limited to characterizing the fracture

toughness of the materials.

SUBCRITICAL CRACK GROWTH

In linear elastic fracture mechanics, the crack tip stress field represented

by K is the driving fctcvi lor fracture. It is logical then that K would also

describe the conditions tor incremental extension of the crack due to fatigue

cycling, stress corrosion and hydrogen embrittleiiierit . Extensive experimental

evidence indicates that this is indeed the case.

Fatigue Crack Crowch

Fracture mechanics concepts have been applied to the study of fatigue

32 crack propagation. In reviews of extensive crack propagation data, Paris

observed that a log-log plot of the crack growth rate, da/dN, versus the stress

intensity range, AK, is a straight line of the form:

LC ' °Y V (19)

§ = c(AK)

n

(20)

where, c and n are empirical constants; and AK = -

Kkjtn' where and

K^^ are the maximum and minimum stress intensity factors of the fatigue cycle,

respectively. This relation implies that the cyclic crack tip stress

field described by AK is the driving force for fatigue crack extension.

Cyclic profile and frequency, mean load and stress state are of secondary

importance. The principal limitation of the Paris equation is the

33

failure to account for environmental-enhanced fatigue crack growth.

Environmental factors, including temperature, increase the importance of

the secondary variables; however, Equation (20) still provides a useful

basis for the empirical analysis of crack growth data. Accordingly, most

data are presented as log-log plots of da/dN vs. AK.

10

1-12
Equation (20) is frequently used to estimate the life of a cracked

structure subject to fatigue. A crack is assumed to exist at a selected

location in the structure. For this location, the relationship between

K and crack length is determined by stress analysis or by handbook

values. Experimental data for the material of construction relate the

fatigue crack growth rate and the critical crack size to AK and K , c respectively. Life is calculated by integrating Equation (20) between

the limits set by the initial flaw size and the final size based on

fracture toughness data:

N = A = -i f

C -*5 . (21) a

± c(AK) n

c(Aa) n

a. Tf(a)] n

For complex load histories, Aa takes on many values as a function of time, and

Equation (21) must be integrated sequentially using numerical methods. Several

computerized techniques have been developed to evaluate Equation (21), including

34 35 some to account for load interaction effects. ' These latter methods attempt

to account for the beneficial effect of peak loads on subsequent low load

growth rates, i.e., da/dN is frequently reduced below expected values during

low stress amplitude cycles that follow high stress amplitude cycles.

Stress Corrosion Cracking

Stress corrosion cracking is a type of crack extension that occurs in

susceptible materials under the combined action of corrosion and static tensile

36

stress. Experimental studies indicate that for a given material and environment, a threshold stress intensity (K _) exists below which crack extension

does not occur. K has been shown to be independent of specimen configuration and thus may be regarded as a material property for a given environment.

Kinetic studies also indicate that the crack tip stress field is the driving

force for stress corrosion cracking, i.e., the crack growth rate, da/dt, is

38

a repeatable function of K.

Stress corrosion cracking is an important consideration for many engineering

structures because of the wide range of susceptible materials and aggressive

environments. To date, however, stress corrosion cracking has not been reported

to occur at cryogenic temperatures. It is likely that stress corrosion cracking

is less a problem in cryogenic structures because the low temperatures

preclude the existence of an aggressive environment.

11

1-13
Hydrogen Embrittlement

Sustained load cracking may occur in a high pressure hydrogen

39 environment in a manner analogous to stress corrosion cracking; i.e.,

the time to initiate cracking is a function of K and a threshold K exists

below which cracking will not occur. Cracking may also occur due to

hydrogen reaction embrittlement, e.g., cracking of copper alloys due to

the formation of high pressure water vapor in voids; or due to internal

hydrogen embrittlement, where the hydrogen is introduced by electrolytic

charging. At cryogenic temperatures, cracking due to hydrogen embrittlement

has not been observed. However, in liquid hydrogen vessels, materials

in the ullage space that are near ambient temperature may be susceptible

to hydrogen environment cracking.

FRACTURE PROPERTIES OF MATERIALS AT CRYOGENIC TEMPERATURES

In applying fracture mechanics to design, the material properties of

interest are the fracture toughness, which is used to compute critical crack

sizes, and the fatigue crack growth rate, which is used to estimate the

cycle life expectancy of a cracked structure. At cryogenic temperatures,

sustained load flaw growth is presumed negligible; however, caution

should be taken for components of the cryogenic system subjected to

ambient temperature conditions.

When comparing alloys of different base-metal systems, it is important to

recall how critical flaw sizes are influenced by fracture toughness and by

stress level as shown in Equation (11). In most design codes, the design

allowable stress levels are related to the strength of the material. Since

2 critical flaw sizes are proportional to the ratio (K^/a) , high strength

materials need greater fracture toughness than low strength materials. For

comparable fracture resistance, a steel alloy with an allowable stress of

30 ksi must have a fracture toughness 9 times greater than an aluminum

alloy with an allowable stress of 10 ksi. Similarly, the fatigue crack

growth rates are strongly related to operating stress levels as shown

in Equation (20). Thus, in comparing growth rates of different alloys,

the AK ordinate of the da/dN-AK curve should be normalized for operating

stress, i.e., AK/Aa.

1-14

12
Mechanical property tests have been conducted at cryogenic temperatures

on most of the metals and alloys of practical interest. Extensive

reviews and compilations of these data are given in References 40, 41, 42.

The fracture test methods most generally employed were the Charpy and

Izod impact tests, notched tensile tests and tear tests. Although these

data are not suitable for a fracture mechanics analysis, they are indicative

of relative toughness. These data indicate that the fracture properties

of metals at cryogenic temperatures are primarily controlled by yield

strength within a given base metal system and by crystalline structure

when comparing different systems. As yield strength increases, fracture

toughness generally decreases due to diminishing plastic strain energy

dissipation upon fracture-a trend that is apparent in the data in aluminum

43-48

alloys at 76 K shown in Figure 6. Fracture toughness tends to be

high for face-centered cubic (FCC) metals, e.g., Al, Cu, Ni and austenitic

stainless steels, and low for body-centered cubic (BCC) metals, e.g., most

steels and refractory metals. Metals with a hexagonal close packed (HCP)

structure exhibit mixed behavior at cryogenic temperatures; HCP titanium

alloys are reasonably tough, but magnesium and beryllium alloys are brittle.

Fracture mechanics test methods have been used to determine fracture

toughness and fatigue crack growth on materials for aerospace pressure vessels,

LNG tankers and superconducting machinery. Several reviews of fracture toughness

49

data at cryogenic temperatures have been prepared recently; Matthews

compiled K data for aerospace materials at temperatures ranging from

50

20 to 300 K, Campbell reviewed the fracture toughness of high strength

alloys at low temperatures, and Pense and Stout"'"'" included extensive

fracture data in their review of cryogenic nickel steels. The available

52

fatigue crack growth data at 4 K have been reviewed by Tobler and Reed.

The fatigue crack growth rates tend to decrease at low temperature except

for steels at temperatures below their ductile-to-brittle transition temperature. The data for materials being used for LNG applications are summarized

. 7 53,54 in Figure 7.

FRACTURE CONTROL PLANS

Many factors contribute to brittle fracture and its prevention. Consider,

for example, Equations 11 and 21 for determining critical crack size and

13

1-15
cycle life, respectively. These relations require an understanding of the

material properties, the service load history, probable initial flaw sizes and

the functionality of K vs. a for the locations of interest. A complete understanding of all these aspects is obviously not possible for a complex structure.

Thus, to assure safety, it is necessary to devise a plan to limit the uncertainties. Such a plan, referred to as a fracture control plan, consists

of the following elements:

1. Establish design criteria and analysis assumptions

2. Design for damage tolerance

3. Implement the controls necessary to assure the validity of the

design assumptions.

Design Criteria and Analysis Assumptions

The design criteria and analysis assumptions need to be clearly defined

in the procurement specification or agreed upon early in the design phase.

Criteria relevant to fracture control include the design service life, the

anticipated service load history and the thermal and chemical environment.

The principal analysis assumptions are the initial flaw size and location,

the fracture criterion (plane strain or plane stress) and the load for use in

critical flaw size calculations.

The U.S. Air Force has recently developed a rigorous set of damage

Lolerance- requirements to augment the standard strength and fatigue requirements for military aircraft?^ Primary structure must be designed such that

assumed initial flaws cf prescribed size and location do not grow to critical

size within either a specified inspection interval or the entire service

life depending upon the inspectability of the structure. Damage tolerance

requirements are also specified for nuclear reactor^ and spacecraft pressure

vessels^ These requirements, although currently of limited applicability,

may be the precursors of requirements for cryogenic structures where public

safety is a prominent consideration.

Design for Damage Tolerance

The role of the design function is to integrate materials and structures

technology into the design of a safe, functional and economical structure.

The design should incorporate the results of the structural analyses for

14

1-16
strength, rigidity, fatigue life and fracture resistance. Careful attention

to design detail is essential because fatigue cracks initiating at stress

concentrations are perhaps the most likely source of failures.

The two principal design options for providing damage tolerance are the

fail safe and the safe life approaches. In the fail safe approach, fracture

safety is provided by structural redundancy. Inspectability is essential to

fail safe design to assure detection of the initial failure before the damage

spreads beyond control. In the safe life approach, the stress levels are limited such that a flaw will not grow to critical size during the life of the

structure. When sufficient inspectability exists, this latter approach can be

modified to provide for a safe inspection interval —at which tine the structure

is inspected and certified for another interval of safe operation.

Fracture mechanics analyses are complex and costly and thus must be con- ducted judiciously on the parts and locations deemed most susceptible to

fracture. These parts, identified as fracture critical parts, are also subjected to more stringent controls during material procurement and fabrication

as outlined in the next section.

Specifications and Controls

A variety of controls are necessary to assure that the fabricated

structure is adequately represented by the design and analyses. Material

procurement and processing are controlled by specifications that are sufficient to preclude use of materials in the structure that have fracture

properties inferior to those assumed in design. Inspection of the raw material

and the final assembly should be sufficient to assure that the flaws in the

fabricated structure are smaller than those assumed in the crack growth

analysis. For fracture critical parts, records are needed to provide traceability of product quality from the raw material heat identification, through all

manufacturing operations, to final assembly. These records are needed to

limit the scope of a retrofit program in case of service failure due to

inferior material quality.

The engineering drawing is a convenient vehicle for transmitting the

requirements of a fracture control plan. Drawing notes can be used to identify

the part as fracture critical, to invoke material and process specifications

and to specify inspection and corrosion protection requirements.

15

1-17
The control measures discussed above are sufficient to provide the

customer with a safe structure. It is the responsibility of the user to

exercise control over usage of the structure such that service operations

do not exceed the design limits.

APPLICATIONS

Structural safety has always been a primary consideration in the design

of cryogenic structures. Thus, it is not surprising to find the essential

fracture control implemented in their design and fabrication. However, as cryogenic technology advances, there is an increased tendency to use higher

strength materials, higher operating stresses and/or thick sections to build

larger and more complex structures. These trends increase the hazard of

brittle fracture and sometimes justify the use of fracture mechanics methods.

In this section the potential uses of fracture mechanics in conventional

structures are proposed and sophisticated applications of fracture mechanics

to the design of LNG ships and aerospace pressure vessels are reviewed.

Storage Tanks and Piping System

For cryogenic structures such as storage tanks and piping systems,

tiiere exists a considerable body of favorable service experience. Thus, the

design practices, the fabrication methods and the type and extent of inspection

have proven satisfactory, and there is little need for a fracture mechanics

analysis. The existing design codes published by ASME^ API~^ and ANSI^ fulfil]

the need for a fracture control plan. There is, however, a trend in engineering

design toward increased structural efficiency through the rational determination

of structural loads, working stresses and material properties. This trend has

created pressure for changing certain aspects of the design codes in the

Interest of cost reduction. Fracture mechanics is a useful tool for assessing

the impact of these changes on structural safety.

In most cases, the design allowable stress level for a material used

at cryogenic structures is based on the strength of that material at room

temperature. Generally, the strength increases at cryogenic temperatures

and thus a higher allowable might be appropriate. Fracture mechanics can provide a quantitative assessment of the effect of increased stress levels

on the flaw tolerance of the material at low temperatures and, therefore,

can provide a rational basis for modifying stress allowables.

16

1-18
The qualification of materials and welding procedures for fabricating

58 cryogenic structures in accordance with the ASME Pressure Vessel Code of

6 0 the ANSI Piping Code is difficult. Charpy impact tests are not appropriate

at temperatures below 76 K because of testing difficulties and adiabatic

heating of the test specimen. Standards have not been established for alternative tests such as the notched tension test. Fracture mechanics tests are

a bit cumbersome for qualification testing, but may provide a useful basis

for comparison with other tests. The correlations of unit propogation energy

in the tear test for aluminum alloys^ and impact energy in Charpy tests for

62 steel alloys as functions of fracture toughness are good examples of this

approach.

Shipboard LNG Tanks

Several types of containment systems have been devised for the marine

6 3 transport of liquefied natural gas (LNG) . In general, the containment

system consists of a primary barrier to contain the cargo for the life of

the ship, and a secondary barrier to contain the cargo for 15 days in case

the primary barrier fails. Spherical free standing tank designs do not

require a secondary barrier if fracture mechanics analysis indicates

64 satisfactory leak-before-break behavior.

The leak-before-break criterion requires demonstration by test and

analysis that a subcritical crack will grow through the thickness of the

tank wall and cause a detectable amount of cargo leakage for a safe period

of operation prior to failure. The minimum period of safe operation is

defined as 15 days at sea under storm conditions. Fracture mechanics analysis

is used to compute the minimum flaw size that will allow leakage of sufficient

3 3

gas to be sensed by the gas detectors. The period of safe operation is

determined by integrating Equation 21 between the limits set by this minimum

flaw size and the critical flaw size determined from fracture toughness

measurements; crack growth data for the tank material and the appropriate

cyclic stress history for storm conditions are used.

Aerospace Pressure Vessels

Cryogenic vessels used by NASA for launch vehicles and spacecraft gas

containers are designed, fabricated and tested in accordance with an overall

17

1-19
fracture control plaru ^ One of the principal elements of this plan is the

proof pressure test. The proof test concept is shown schematically in

Figure 8. The proof test is conducted at a pressure (and stress level,

a ^) which exceeds the maximum service pressure (and stress level, 0

g

)

;

thus, the critical crack size during proof test, a

p t

» is smaller than the critical

crack size during service, a

g

. The flaw size that could exist in the pressure

vessel following proof test is conservatively estimated to be equal to a , i.e., any flaw larger than a would have caused failure during proof test.

During service, this initial flaw is stable until it grows to critical size,

a

g

, and thus a period of safe operation exists. This period of safe operation

is determined using empirical data (or Equation 21) relating crack length

to service time, t, where all the appropriate loads and environments are simulated in the test and/or analysis.

Future Applications

In the coming years, many applications of fracture mechanics will be

directed toward the establishment of a more rational basis for design codes

and improved standards for material acceptance, welding procedure qualification and nondestructive inspection. In addition, many new design ideas will

be developed for constructing superconducting devices and hydrogen fuel

equipment. Superconducting systems for energy storage and for fusion magnets

will involve enormous structures and capital investment considerations may

justify the use of fracture mechanics methods. Public safety considerations

will probably lead to the application of fracture mechanics to the design of

equipment for storing, handling and transporting cryogenic hydrogen fuel.

SOURCES OF INFORMATION

An abundance of information is available for those interested in further

65 66

study of fracture mechanics. Textbooks have been written by Knott, Brock and

Lawn and Wilshaw^ Extensive surveys on specific applications have been

prepared for aircraft structures^ and for space vehicles^ Analysis handbooks

which include compilations of stress intensity factor solutions have been

8 9 written by Tada et al. and by Sih. Material property handbooks are generally

beginning to include fracture mechanics test data and one handbook^ is

specifically for the compilation of fracture mechanics data on aerospace

18

1-20
materials. Experimental methods in fracture mechanics are reviewed in a training manual written by Hickerson ^ and in a monograph edited by

72 Kobyashi. Fracture mechanics concepts are applied to failure analysis

73 in a book by Colangelo and Heiser.

Current research in fracture mechanics is published quarterly by

two journals: Engineering Fracture Mechanics and International Journal

of Fracture. The American Society for Testing Materials (ASTM) regularly

publishes the proceedings of symposia on topics in fracture mechanics

including the papers presented at the annual National Symposium on Fracture Mechanics. Work in progress is presented at the semi-annual

meetings of ASTM committee E-24 on Fracture Testing of Metals.

SUMMARY

Fracture mechanics has made significant contributions to our understanding of the fracture process. Yet, much remains to be learned

particularly in the area of elastic-plastic fracture. The design methodology limits stress levels throughout the structure such that initial

flaws will not grow to critical size during the desired service life.

Further progress in fracture mechanics should lead to acceptance of this

approach to structural safety by those responsible for the design,

operation and regulation of cryogenic structures.

19

1-21
aA

a

Pt

B

b

c

C

COD

da/dN

da/dt

E

E»f(a)

f ij(

e)

G

J IC

K

K

K

c SlAX

tllN

K

IC

K

IC

(J)

K

ISCC n

N

P

P

NOMENCLATURE

crack length

crack surface area critical crack size

initial crack size

critical crack size at maximum stress in service

critical crack size at maximum stress in proof test

thickness

ligament , b = W-a

empirical coefficient in crack growth rate equation

elastic compliance

crack opening displacement

crack growth per load cycle in fatigue

crack growth per unit time

elastic modulus

2 reduced modulus, E/ (1-V ) function of crack length

generalized distribution function

strain energy release rate

strain energy release rate at fracture

the line integral of Equation 14 or the potential energy

difference of Equation 15

the critical value of J for crack initiation

degrees kelvin

stress intensity factor

fracture toughness

maximum K is fatigue cycle

minimum K in fatigue cycle

plane strain fracture toughness

K computed from J

XL* ±\j

crack growth resistance

stress corrosion cracking threshold

empirical exponent in crack growth rate equation

number of load cycles in fatigue

applied load

critical load

20

1-22
Pq candidate critical load per ASTM 399

r radial coordinate from a crack tip

r radius of the plastic zone at the crack tip

y

v

s arc length along the contour V

t time

T stress vector normal to T T temperature

-»- u displacement vector

U potential energy per unit thickness v displacement in the Y direction

V elastic strain energy w strain energy density

W width

x coordinate in the plane of the crack

Y(a) geometry correction factor

Y(—) specimen calibration function

A displacement

6 crack opening displacement at the crack tip

6 6 at the onset of fracture

c Aa increment of crack extension

AK stress intensity factor range during fatigue cycling

Aa stress range during fatigue cycling

T any contour surrounding the crack tip

9 angular coordinate measure from the crack plane

V Poisson's ratio

a applied stress

a.. tensor notation for the crack tip stress field

0 maximum stress in service

s a ^ maximum stress in proof test

Pt

a critical stress

c yield stress of the material local to the crack tip

a 0.2% offset yield strength

ys

21

1-23
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23

1-25
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24

1-26
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25

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176, 1974.

69. A. F. Liu, R. M. Ehret and E. J. Malcahy, Fracture Control Methods

for Space Vehicles, NASA, CR-134596 (Vol. 1), CR-134597 (Vol. 2) and

CR-134598 (Vol. 3), 1974.

70. Anon., Damage Tolerant Design Handbook, Metals and Ceramics Information

Center, MCIC HB-01, 1972, and MCIC HB-01S, 1973, Columbus.

71. J. P. Hickerson, Elements of Experimental Fracture Mechanics, Sandia

Laboratories, SLA-73-0424, Albuquerque, 1973.

72. A. S. Kobayashi, Editor, Experimental Techniques in Fracture Mechanics , Society for Experimental Stress Analysis, SESA Monograph No. 1, 1973.

73. V. J. Colangelo and F. A. Heiser, Analysis of Metallurgical Failures , John Wiley and Sons, New lork, 1974.

26

1-28
LIST OF FIGURES

Fig. 1. ASTM E399 Compact Specimen for Fracture Toughness Testing [10]

.

Fig. 2. Cryostat for Fracture Testing in Liquid Helium [11].

Fig. 3. Fracture Toughness Transition in Structural Alloys.

Fig. 4. J-Integral Crack Growth Resistance Curves for an Fe-Ni-Cr Superalloy [25].

Fig. 5. Crack Growth Resistance Curve and Crack Driving Force Curves

in R-Curve Format [28].

Fig. 6. Fracture Toughness of Aluminum Alloys at 76 K.

Fig. 7. Fatigue Crack Growth Behavior of 5083-0 Aluminum and 9% Ni Steel

at LNG Temperature (111 K)

.

Fig. 8. The Proof Test Concept [57].

1-29

-Pull Rod

Stand Offs

C 2 4

I i 1 L_J

SCALE, inches

0 5 10

I I I SCALE, cm

FRP Insulators

Grip

ASTM

Clip Gage^

Bridge

CT Fracture Specimen

FRP Helium Dewar, vacuum insulated

FRP Nitrogen Dewar,

foam insulated

Cryostat for Fracture Testing in Liquid Helium [11].

29

'" 31

31

1-33
32

1-34
,31

ui/NW ' » SS3NH0R0i 3MI13VIIJ NIVH1S 3NVld

LIS CO

LTD

CO

r—

r-— • LTD CO

Cfi

1

1 r—

r-— r—

CO

G-sl CNJ

CVI

C-vl

r—

m r—

.

LT5 CO 1

LPS 1 CVI CO

r— CVI

1 mr—

p—

in

co

I CO

CO

CO

LTD

CO

CO

LPS

CO

C">l

coo

o

toCO

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ctj M

Pe,

00 H

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. 31

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33

1-35
STRESS INTENSITY RANGE, AK (MN/m^j

1 10 100 1000

STRESS INTENSITY RANGE, AK, ksi/in

Fig. 7. Fatigue Crack Growth Behavior of 5083-0 Aluminum and 9% Ni Steel

at LNG Temperature (111 K)

.

34

1-36
-O'SSJHIS 0])1ddV

35

1-37

APPENDIX J

J-l
SHIP STEEL WELDMENTS FOR LOW TEMPERATURE SERVICE *

by

Harry I. McHenry

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Preprint of paper prepared for presentation at the Fourth Army Materials

Technology Conference, Advances in Joining Technology, Boston, MA,

September 16-19, 1975.

J-2
SHIP STEEL WELDMENTS FOR LOW TEMPERATURE SERVICE*

H. I. McHenry

National Bureau of Standards

Cryogenics Division

Boulder, Colorado

ABSTRACT

The ship steels, welding practices and weldment toughness requirements

applicable to low temperature (to -46°C) regions of liquefied-natural-gas

(LNG) tankers are reviewed. In the construction of LNG ships, the principal

welding productivity problem is the low deposition rate associated with

the low heat input welding practices required to provide sufficient toughness

in the weld heat-affected-zone (HAZ). A potential solution to this problem

is to use improved steels which can be welded using efficient procedures

and still provide satisfactory HAZ toughness. The steelmaking practices

that contribute to low temperature toughness are reviewed with respect

to economic limitations associated with ship steels and to their potential

for improving HAZ toughness.

* Contribution of NBS -- not subject to copyright.

J-3
INTRODUCTION

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,

1 2

the U.S. Coast Guard (USCG), the American Bureau of Shipping (ABS) and

comparable regulatory agencies around the world have established strict

requirements on the ship steels and weld procedure qualifications for weldments

subjected to low temperatures. To meet these requirements, shipyards

generally employ low-heat-input, multipass welding practices for welds in the

low temperature regions of the hull. 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 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 technology 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 transverse bulkheads

3 dividing the ship into several cargo bays as shown in Figure 1. The

cryogenic containment system fitted within each cargo bay consists of

the cargo tank, the insulation and a secondary barrier to contain the
LNG in case of tank failure. Thomas and Schwendtner have described

eight types of containment systems in use or under consideration worldwide.

In the U.S., three designs are under construction: The Conch freestanding 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 - 1 62 0 C and

atmospheric pressure with boil-off rates less than .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

3 C . The inner hull, the transverse bulkheads and the tank support structure

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 water! ine and parts of the tank support

structure.

STEEL SELECTION

The chemistry, processing and testing requirements of steels used in

LNG ships being made in the U.S. are summarized in Table I. These steel

selections are generally in accordance with the proposed (1975) regulations

of the International Maritime Consultive Organization (IMCO) as outlined

in Tables II and III. For temperatures below -10°C, fully-killed, aluminum

treated, fine grain, C-Mn-Si steels are used. For temperatures below -25°C,

the steel must also be either normalized or quenched and tempered.

The most commonly used steels are the ABS ordinary strength grades; CN

is used for temperatures to -23°C, CS for temperatures to -34°C and V051 for temperatures to -46°C. For high strength applications, ABS grade

EH steel is commonly used for temperatures to -34 C C and ASTM grade A537

Modified is used for temperatures to -46 C C.

Approximately 28,000 metric tons of steel are required 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

IV. These data are indicative of the total usage of low temperature

2

J-5
steels and include significant tonnage selected for improved toughness

and used in parts of the ship not exposed to temperatures below 0°C.

WELD 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, wire and flux combination and must be

established for each welding process and position. The joint preparation,

preheat and interpass temperatures, root coping and other aspects of the

procedure must be representative of the procedures used in production.

Generally, two qualifications are required to cover the range of plate thicknesses: 9.5 < t <_ 19 mm and t > 19mm. Test plates for these qualifications

are usually 19 mm thick for the lower thickness range and the maximum thickness used in production 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 Charpy 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 fusion 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

Figure 2. The average Charpy value must equal or exceed 2.8 kgm (20 ft lb);

the minimum value for one specimen is 1.9 kgm (13.3 ft lb).

WELDING PROCESSES 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 pro- cesses are submerged arc (SA), shielded metal arc (SMA) and gas metal arc (GMA).

For flat position welds and horizontal fillet welds, SA is the most efficient

and reliable process, and therefore is widely used on automated panel-lines.

3

J-6
Both SMA and GMA are used for most of the other welding; the selection of one process over the other varies widely from yard to yard. Variations of these

processes such as one-sided welding, gravity welding, tandem arc and 3 o'clock

sub-arc welding are used in specific instances depending on the capabilities

of the shipyard. High-heat-input processes such as the electro-slag and

electro-gas processes are not approved by ABS for use on low temperature steels.

A wide range of wires, rods and fluxes are used to weld ship steels for

low temperature service. For submerged arc welding, two approaches have been

taken: 1) use a mild steel wire and an alloy flux, or 2) use an alloy wire

and a neutral flux. The mild steel wires conform to AWS specification

AS. 17-69 Class EM12K, and the alloy fluxes are of a proprietary nature.

The alloy wires, which contain 1 to 2% Mn, .1 to .5% Mo and .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 electrodes, 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- core wires are used for GMA welding. The solid wires are alloyed with

Mn, Mo and Ni for low temperature toughness and the cored wire 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 significant productivity problem to the LNG shipyards because

deposition rate is proportional to heat input, and their welding equipment is

capable of far greater deposition rates than are possible using the low-heatinput practices. Consider, for example, the welding procedures that are representative for welding 19mm plate. For X-ray quality welds in steels such

5 as ABS grade B, the following conditions are recommended:

Joint preparation: double V groove with an 8 mm land

Backing weld: 850 amps, 33 volts, 16 in/min (.68 cm/sec), 105 kJ/in.

(267 kJ/cm)

Finishing weld: 1150 amps, 35 volts, 13 in/min (.55 cm/sec),

186 kJ/in. (472 kJ/cm)

4

J-7
In contrast, 19 mm ship plate for low temperature service must be multipass

welded with the heat input limits ranging from about 40 to 80 kJ/in.

(102 to 203 kJ/cm) 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, because strict requirements

are appropriate for hazardous cargo such as LNG. In addition, the

requirements have recently been adapted by IMCO as standards 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 alternative

solution would be to make available an economical steel which, when

welded using efficient procedures, provides the required level of toughness.

This potential solution is attractive because it is based on steelmaking

technology and shipyard economics instead 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 increment added to the

price of the steel and the extent of the improvement. Because of the large

tonnages involved, the added cost of an improved ship steel will likely be

limited to a maximum of $20 to $60 per ton, depending on the specific

appl ication.

5 J-8
ALLOYING

The use of additional alloying to improve ship steels is severely con- strained 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^

The chemistry specification for ABS EH 36 shown in Table I is typical of

the degree of alloying permissible in carbon steels. Notice that there

are no minimum requirements 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 ship steels can be reduced by alloy adjustments within the AISI limits for carbon steels. As shown in Figure 3,

the transition temperature is reduced by increasing the Mn content and

by lowering C, Si and N?

Microal loying with Cb or V is an economical approach 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

provided by a combination of reduced grain size and precipitation hardening.

The low temperature toughness is improved because of the small grain

size—an improvement that is only partially offset by the precipitation

hardening effect shown in Figure 3. However, the HAZ toughness near the

fusion line is adversely affected by grain coarsening and further reduced

8 9 by the strengthening effect of carbonitride precipitation.'" This

embrittlement is almost always observed in simulated HAZ specimens, but

is frequently not evident in Charpy specimens taken from weldments. The

absence of embrittlement in high-heat-input weldments such as shown in

Figure 4 suggests that the high toughness material surrounding the

6J-9
embrittled region substantially reduces the embrittlement. 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

8 9 as significant in real weldments as suggested by some investigators '

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 solidifying metal due to decreased

solubility of oxygen and sulfur upon cooling, and 2) the exogenous inclusions

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 dominate oxide is

A^Og, 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)^

The process generally consists of lowering the sulfur content of the heat

below .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

7 J-10
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; 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

1

2

and REM additions on toughness are shown in Figure 5.

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 require 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

13

nature of the transformation products. It involves a schedule of re- ductions 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 normally employed. As shown in Figure 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

8

j-n
grades, and the lack of facilities for producing 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 toughness

of ship plate.

HEAT TREATMENT

Nearly all of the ship steels used for low temperature (to -46°C)

applications are normalized. The typical normalizing heat treatment involves

heating the as-rolled plate to 925 + 25°C and air cooling to room temperature. As shown in Figure 7, the low temperature toughness of

these steels could be improved by a quench and temper (Q and T) heat

14

treatment. For C-Mn 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-treatment 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/metric ton)

is not considered a cost effective means of improving heat affected zone

toughness.

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

9

J-12
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-1976, 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-of-the-art steelmaking technology

can substantially improve 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.

ACKNOWLEDGEMENTS

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 collaborated on all aspects of the program

described herein. The author also expresses appreciation to R. W. Schaffran

of the U.S. Maritime Administration and W. C. Brayton of Bethlehem Steel

Corporation who were responsible for initiating the program.

10

J-T3
REFERENCES

1. Anon., U.S. Coast Guard Marine Engineering Regulations, Subchapter F,

CG-115, July 1970.

2. Anon., 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 Liauefaction

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 Reference 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 HT

Steels," Welding Journal, 54, No. 5 (1975) 1625-1685.

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 N.Y., November 1974.

12. Kozasu, I. and Osuka, T. , "Processing Conditions and Properties of

Control -Rolled Steel Plates," in 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 Grain Refiner in Hot Rolled

Steels," in Processing and Properties of Low Carbon 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.

11 J-14
J-15
Table II. IMCO Requirements for LNG Hull Steels

Minimum Design Plate Thickness, t Approved ABS

Temperature, T, °C mm Steel Grades

T > 0 -- Normal Practice

0 > T > - 10 t < 12.5 B 12.5 < t < 25.5 D

t > 25.5

-10 > T > -25 t < 12.5 D

t > 12.5 E

-25 > T > -55 — See Table III

J-16
Table III. IMCO Requirements for LNG Hull Steels for

Design Temperatures of -25 to -55°C

Chemical Composition

C Mn Si S P .16% max 0.70-1.60% 0.10-0.50% 0.035% max 0.035% max

Optional additions:

Ni Cr Mo Cu Cb V 0.80% max 0.25% max 0.08% max 0.35% max 0.05% max 0.10% max

Heat Treatment

Normalized or quenched and tempered.

Deoxidation

Fully killed, aluminum treated, fine grain practice.

Toughness Requirements

Temperature: 5°C below design temperature

Specimens: Charpy V-notch-transverse

Energy, min. avg.: 2.8 kg m

No. of Tests: 3 from each plate

J-17
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Figure 1. Structural Arrangement of an LNG Ship Hull [3].

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Figure 3. Strength Toughness Vectors for Structural Steels [7].*

Figure 4. Charpy Toughness Traverse for Cb-Treated EH-36 Weldment [10].

Figure 5. The Effect of Rare Earth Metal Treatments on the Transverse Shelf

Energy of Low Sulfur C-Mn Steel [12].**

Figure 6. The Effect of Rolling Reduction Below 900°C on the Fracture

Appearance Transition Temperature [13].**

Figure 7. Charpy Impact Transition Curves for Normalized and for Quenched

and Tempered CS Steel [14].

* Reprinted with permission of the Welding Research Council.

** Reprinted with permission of the Metallurgical Society of AIME.

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USCOMM • ERL
APPENDIX K

K-l
The refractive index and Lorenz-Lorentz function of fluid

methane*

James D. Olsorr*

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

(Received 13 February 1975)

The refractive index of gaseous and liquid methane was measured between 95 and 300 K and to pressures of 225 bar (1 bar = 105 Pa). The measurements were performed at the "8 Hg vapor green

line, X = 546.2 nm, with a Fabry-Perot interferometer referred to vacuum. The refractive index data were combined with the previously measured densities of methane to calculate the Lorenz-Lorentz (LL) function. Refractometric virial coefficients were obtained from analysis of the small (~0.5%)

maximum exhibited by the (LL) function with increasing density. B R , the second refractometric

virial coefficient, is estimated to be ~6.0 (cm3 /mol)2 and is almost independent of temperature between 220 and 300 K. The critical point refractive index, n c = 1.10333, was extrapolated from a

rectilinear diameter treatment of the saturated liquid and vapor results. The critical point refractive index was combined with an estimate of the critical point (LL) function to yield a critical density of methane, pc = 10. 16 ±0.01 mol/1.

I. INTRODUCTION

The refractive index n and the molar density p are

related by the Lorenz-Lorentz (LL) electromagnetic

equation of state:

(LL)

n

z -\ \ n

z + 2 p

477JV. 0 (1)

where iVA is Avogadro's number and a° is the isolated molecular electronic polarizability. For real nondipolar

gases, the (LL) function shows small (=* 1%) deviations from the rhs of Eq. (1). These deviations may be rep- resented by a density expansion analogous to the ther- modynamic virial equation of state,

(LL) = AR + BRp+CRp

z + (2) where ARj BR , CR are the refractometric virial coefficients. Similarly, the dielectric constant € is related

to the molar density by the Clausius-Mossotti (CM)

equation and the dielectric virial coefficients,

(CM) = ^

= ylD + £Dp + CDp

2 + . (3)

This article reports the experimental determination

of the refractive indices of methane at temperatures be- tween 95 and 300 K and at pressures to 220 bar. The

(LL) function was calculated by combining these data

with the experimental densities of Goodwin and Prydz. 1 The purposes of this study are twofold: (i) To provide

data with which to test the (LL) relation and estimate

the magnitude of the refractometric virial coefficients. This type of study is useful in assessing the details of the intermolecular potential function and in the correlation of the macroscopic properties of nondipolar fluids. 2

(ii) To provide additional thermophysical properties

data for methane whose other macroscopic properties have been measured in this laboratory. In particular,

this study will suggest refinements in the PVT surface

of methane near the critical point, similar to a recent

analysis on hydrogen. 3

The microscopic expressions for the refractometric

and dielectric virial coefficients have been derived in

many forms. 4" 8 Careful experiments are required to provide data sufficiently precise to obtain refractometric virial coefficients and to test molecular theories of refractive index. Unlike the more abundant studies of the CM function and the dielectric virial coefficients, 8 there have been few experimental determinations which

provide data over large ranges of density and temperature. Michels and co-workers measured the refractive index of carbon dioxide, 9 nitrogen, 10 ethylene, 11 and argon 12 interferometrically to high pressures (2. 5 kbar)

at room temperature and above. As the precision of these measurements decreased rapidly at lower densities, their chief achievement was to determine the behavior of the (LL) function at densities above the critical density. Teague and Pings 13 measured the refractive in- dex of argon from temperatures near the triple point

temperature to temperatures above the critical point and

to pressures of 100 bar. Diller 14 of this laboratory per- formed precise interferometric measurements of the refractive index of hydrogen at temperatures from 15 to 300 K and at pressures to 230 bar. This work indicated

significant deviations from Eq. (1) in qualitative agree- ment with molecular theory. Buckingham and Graham 15 recently measured the first and second refractometric

virial coefficients, AR and BR , for several gases at room temperature using a differential interferometric

expansion technique.

II. EXPERIMENTAL METHOD AND APPARATUS

The refractive index was measured with a FabryPerot interferometer immersed in the fluid methane.

The absolute index was obtained by monitoring the change in interference order while venting the fluid to vacuum. This reference to vacuum is necessary be- cause interferometric measurements record only

changes in refractive index. In this particular experimental arrangement, a change of one order in the inter- ference pattern (passage of one fringe) corresponded to a change in refractive index of about 5x 10'5

. Fractional order changes of about ± 0. 025 could be detected, indi- cating a uncertainty of about ± lx 10" 6 in refractive in- dex. This is about 100 times more sensitive than nonThe Journal of Chemical Physics, Vol. 63, No. 1, 1 July 1975 K-2

Copyright © 1975 American Institute of Physics
James D. Olson: Refractive index of fluid methane 475

To Recorder

Interferometer —.

Hg Lamp LI

Spectrograph FIG. 1. Schematic diagram of optical arrangement, top view. Arrows indicate optical path.

interferometric methods of refractive index measurement. This procedure also has the advantage of not requiring a calibration experiment with a fluid of known

refractive index. The sample holder and cryostat were built from the original plans of Diller 14 based on a general cryostat ar- rangement for hydrogen studies suggested by Goodwin. 16 Complete details of this and other aspects of the experimental arrangement are discussed in the paper by Diller. 14 Liquid nitrogen was used as the refrigerant except at 300 K. The high pressure sample holder is sus- pended from the refrigerant tanks by a reflux tube. Low

temperature shields from these tanks attenuate radiation heat leaks. This assembly is contained in an evacuated

cryostat equipped with windows to accommodate optical measurements. Temperatures were measured on the IPTS-68 scale

with a platinum resistance thermometer calibrated by

the NBS Temperature Section. The sample holder temperature was proportionally controlled by electrical heating in a feedback loop from the output of the potentiometer used for the thermometer measurements. A

guard ring and adiabatic shield were controlled to the sample temperature by differential thermocouples. This

arrangement typically controlled the steady state temperature of the sample holder to ± 1. 5 mK.

Fluid pressures were referenced from the sample

holder system through a null pressure detector to an oil dead weight piston gauge. Equilibrium pressures derived in this manner are accurate to 0. 04% or 0.007 bar

whichever is greater.

The Fabry-Perot interferometer consisted of two

fused- silica cylinders 1. 1 cm in length which were

wrung to a 0. 5 cm tungsten spacer. The cylinders were vacuum coated with aluminum to about 50% transmission. The spacer is spacer #2 from the hydrogen

work. 14 A

198 Hg vapor lamp was used as the light source because the vacuum wavelength of the green line is precisely known to be 546. 22705 ± 10"5 nm. 17 The interferometer was entirely immersed in the fluid methane

which allowed an unambiguous calculation of the pressure correction to the spacer length.

The sample was 99. 99 mol% methane from a commercial supplier (1 mol CH4= 16.0430 g).

18 Any residual water vapor was removed by passage of the methane

through a molecular sieve trap immersed in an ice bath.

III. EXPERIMENTAL PROCEDURE

Absolute refractive indices were calculated from lab- oratory measurements by means of the data reduction formula,

K^m . p_

2i7ac 3S[ 2ty (4)

where AN = total fringe count to vacuum, X vac = vacuum

wavelength of light, t ne = vacuum spacer length at the temperature of the fluid, P = pressure of the fluid, and B= bulk modulus of tungsten, taken to be 3. 14± 0. 03

x 10s bar. The spacer length was determined by observation of the coincidence of the vacuum fringe patterns

for the different wave lengths of 198 Hg light by means of the method of exact fractions. 19 The fractional part of

the total fringe count was calculated from photographs

of the ring diameters of the initial and final interference

patterns. 20 The application of those techniques and the derivation of Eq. (4) is discussed in detail by Diller. 14 A major difficulty is the unambiguous determination

of the total fringe count between an initial point in the

fluid and vacuum. A decrease in the interference order, which is caused by a decrease in the spacer length or a decrease in the refractive index of the fluid, is in- dicated by the collapse of the concentric Fabry-Perot

rings toward the center of the fringe pattern. The re- verse direction of fringe travel indicates an increase in the spacer length or refractive index of the fluid. The

integral interference order change (fringe count) may

be recorded by focusing the center of the ring pattern upon a photoelectric device, A strip chart record of the periodic intensity changes of the interference pattern allows one to count the total number of fringes. However, temporary reversals in the fringe direction may oc- cur while venting the fluid to vacuum, particularly while making pressure measurements at intermediate points

between the highest pressure and vacuum. This problem was overcome by monitoring the output of two photomultipliers which were positioned to observe slightly different parts of the ring pattern. The two strip chart

fringe records were, therefore, slightly out of phase

and reversals in the fringe count could be unambiguously

determined.

The dual fringe patterns were monitored in the optical

arrangement shown in top view by Fig. 1. These optical components were aligned with a small He-Ne laser. Light from the extended 19a Hg lamp source is focused by

lens LI into the interferometer through the vacuum window of the cryostat and the high pressure window of the sample holder. The ring pattern produced by the inter- ferometer is imaged by lens L2 on the slit of a spectrograph after passage through a beamsplitter Bl. The

other branch of the optical train passes through a green

J. Chem. Phys., Vol. 63, No. 1, 1 July 1975 K-3
476 James D. Olson: Refracti

150 -

225 TEMPERATURE ,

K

FIG. 2. Pressure-temperature phase diagram of methane. Arrows indicate fringe count path for measurement of saturated

liquid refractive index.

filter F and second beamsplitter B2. These two images

are focused on adjustable pinhole targets, SI and S2. The pinhole targets admit light from slightly different parts of the ring pattern to two photomultiplier tubes,

PM1 and PM2, whose output is recorded on a dual channel stripchart recorder. In addition, the output from

the pinhole aligned exactly with ring pattern center is fed into a digital counter. This eliminates the tedious procedure of counting several thousand fringes from the

strip chart record. However, the strip chart provided

a permanent record of the fringe count that could be

checked for discrepancies indicated by the (LL) function. The experimental procedure for gas isotherms above

the critical point was as follows: The sample holder was filled to the highest pressure for the particular run. After steady- state conditions were attained (about 30

min), the pressure was measured with the dead weight

piston gauge and a photograph of the ring pattern was

taken. The pressure gauge was then isolated from the sample system by a needle valve and an amount of gas was slowly vented from the pressure bomb. The inte- ger fringe count was monitored during this attenuation

of the fluid pressure. The sample system was again

equilibrated at a lower pressure, after which another photograph and pressure measurement were taken. This process continued to vacuum. The cumulative fringe count could then be added up for each pressure measurement and the refractive index calculated from Eq. (4). Determinations of the refractive index of saturated vapor methane were carried out along isotherms. Methane was admitted to the evacuated sample holder at a

subcritical temperature and the fringe count increase was recorded. When the increasing gas pressure

reached the vapor pressure, the fringe pattern ceased

changing as liquid condensed in the sample holder. The

intersection with the two phase boundary was also indi- cated by a sudden increase in sample holder temperature as the liquid condensed. The fractional fringe count was estimated directly from the strip chart record to ±0. 1 fringe. This was necessary because of the poor

quality of the equilibrium fringe pattern photographed

on the saturation boundary. The vapor pressure was

index of fluid methane

either measured or calculated from the experimental

results of Goodwin. 21 In either case, these data were

then substituted into Eq. (4) to yield the refractive in- dex.Nonisothermal measurements along the coexistence

boundary were complicated because t nc must be known

or calculated for each temperature, and the presence

of the vapor-liquid meniscus prevented the direct fringe count from a point in the liquid to vacuum. To overcome

these difficulties, the fringe count was measured from a

point on the coexistence boundary to vacuum at a refer- ence temperature above the critical point. Two adjust- ments were made on the data before using Eq. (4): (i) The vacuum spacer length was calculated from an equation derived from the experimental measurements of the temperature dependence of the length of the spacer,

(ii) The total fringe count was adjusted to correspond to the fringe count from the point on the coexistence boundary to vacuum at the same temperature. This correction is illustrated for the saturated liquid data by the methane phase diagram, Fig. 2. Because the refractive index is a thermodynamic state function, a measure- ment of A« depends only on the initial and final states. The absolute index of the saturated liquid point labeled

(1) on the phase diagram is obtained from the fringe count between (1) and (2) which is vacuum at the same

temperature. The dotted line shows the actual temperature-pressure path used to measure the different parts

of the fringe count. Part (I), an isochoric fringe count, and Part (II), an isothermal fringe count, are measured

directly by counting the fringe count decrease to vacuum

at the reference temperature (200 K) above the critical

point. Part (HI), from vacuum at the reference temperature to vacuum at the initial temperature, is cal- culated from the change in the vacuum spacer length:

*yaetfvac= 2*vao , (5)

AATUIX » = NZ° - = 2(C1> " WAvac • (6) The change in £ vac is calculated from experimental measurements as described above. AJV

<nI)

is added to the

total fringe count from Sees. (I) and (II) and this total

is substituted into Eq. (4) as usual. The effect of the adjustment on the spacer length had

a relatively small effect on (LL), typically a few parts

in 100 000. However, the adjustment to the fringe count, AN(III>

, was relatively large for the low temperature

liquid. For methane at 95 K, AWOII) was about 0. 13%

of the fringe count which increased the (LL) function by

about 0. 1%. A nonisothermal fringe count path from a

point in the saturated vapor passed beneath the critical

point; hence a reference temperature less than the critical point temperature could be used in this case. Because the fringe counts were small for low temperature

saturated vapor data, the amount of the correction,

AAT(III)

, was similar in magnitude to the total fringe

count. Consequently, the saturated vapor refractive in- dex data below 160 K decreases rapidly in accuracy. The tables of experimental results for the coexistence

boundary nonisothermal runs include the calculated spacer length and fringe count adjustment for each temperature.

J. Chem. Phys., Vol. 63. No. 1, 1 July 1975 K-4
James D. Olson: Refractive index of fluid methane 477

TABLE L Experimental results for methane at 300 K.

p p (LL) Fringe ID (bar) (mol/1) (count)

615 1. 2 /8 1. 000508 Q OA y. o-± 615 1. 701 1 AAAC7Q l. ouuo /y 1i O iQ — , 4y

614 2. 116 1 . 000844 13. 613 2. 523 1 AA1 AAQ lb. 3o 612 2. 937 1 . 0011 i 4 21. 58

512 2. 99S 1 AA1 1QQ l. uunyy OO AO 526 Q AAA o. vvv 1 AA1 1 QQ 0 0 525 O AAA 1

l AA1 1 QQ . uuii yy 00— A. AAU-i 524 3. 003 1 AAIOAO OO 1 1 S2a 11 523 o. ou3 1. L'L'i-L'j 00 1

1

, 11 Dlo 3 0^° 1 001 "'09 99 23

CIOil1 3 ^90

511 3 3° 8 1 001331 24 46 319 o. /UO 1 AA1 Aft A 1. UUl-io-i 97 9Q 610 Q 7AO 0. • 1 AA1 ^AA 1. UHJ13UU 07 k7 510 3. /44 i Am ioa 27. 54 609 -2. lit) 1 AA1 tt**A 1. UU1 034 OA A1 o09 4. 150 1 AA1 CCO 1. UUlDDi 30. 56 514 4. 3/5 1 . 001 3 55 OO 9C 608 4. 543 1. 001 825 33. 55

d08 a. 33o 1 AA1 fiOC OO ^7 CA7 Ov / 4. 34y

1 Am QQA Ofi ^7 o07 4. ybj 1 AA9AA1 36. 78 306 5. 329 1. 002141 39. 35 606 5. 360 1. 002155 39. 61 DUO - 7< Q O. #41? 1 AA9 01 1 42. 47

505 ^ 77A 42.64

517 £ 1 9Q i aaoacc 45. 3v 604 6. 162 i AA9 4CA 45, 58 d04 O. Ibb 1. uu_-*oo 45. i 2 603 6. 370 1. lrU.£04b 46. 64 303 c ifli o. oyj 1. 002655 A D fi A 4b, bo 602 6. 927 1 AA97Q9 51 . 33

502 6. 988 1. 002 SI

5

51 . 74

521 7. 418 1 flAO Q Q O

l. iKJi yy^ 54, 99 382 i . 418 1 AA9QQ0 54. 99

-

7 A99 1 AAOQQO r - im 33, 519 / a -_C 1 AAOQQO i. uu^yy o 55. 02 501 7. 429 1 AAOQQ7 l. oojyy / 55, 08 31b 7/. 4 i O

T AAQAT 0 1. OUoUlo 33, oo

/ . 4 <g 1 AAOA1 O 1. WoUIj =.Z. OR

. . . 7 A~Q 1 AA O AO A 33. 31 OOnr £&U3 1 #. 1 34 1 AA7A4Q 1. OU / l>4o 1 OQ A i^y , 43 2804 32. 150 1. 013562 249. 23 2803 46. 433 i. UiUuyi QCQ OA ooy. OV

2 m .2 60. 092 1 A9CCOO ~z ~ r . : - 201 65. 927 1. 029497 Q BIO 6. 6340 542. 20

103 65. 983 1, 029525 o Q^9 6. 6341 542, 71 307 68. 965 1. 031011 O

J, t1VUfin 6. 6334 570, 03 407 co n o c by. 03b T AOI AA O

1. 0.3104b 1 04 6. 6334 570. 70

2801 73. 195 1 . O33I30 o

"a oi o

6. 6319 boy. oy 406 75. 924 1. 034524 qo. -±-ty 6. 6322 634. 61

: . z 76. 180 1 . 034653 Q

3. 463 6. 6319 C 1C QC bob. yb 305 B2. 705 1, 03S005 o

3, / y3 6. 6319 698. 59 40o 82. 884 1. 038098 3, fi AA 6. 6321 700. 31

10j 85. 211 1 AOQOAA OJ, 9°-i 6. 6311 722. 39 304 89, 053 1. 041309 4, 1 00 C C OO A 759. 32 404 89. 812 1. 041705 110—CO 6. 6319 766, 61 303 96. 923 1 . 045455 -qo 0 j: 6. 6324 835. 53 403 96. 946 1. 045469 534 6. DOZO 635. 79 402 104. 118 1. 0492S6 4. 910 6. 6331 905, 96 302 105. 113 1. 049820 4# 963 6. 6335 915. 78 106 105. 638 1. 050101 4. 990 6. 6335 920. 94 401 113. 950 1. 054566 5. 430 6.6346 1003.02

301 114.430 1.054824 5. 455 6.6346 1007.76

105 124.534 1.060275 5 990 6.6364 1107.95

104 144. 848 1.071146 052 6.6389 1307.79

103 163. 592 1.080883 8. 000 6.6405 1486.77

102 184. 859 1.091353 9 015 6.6413 1679.22

101 214.779 1. 104755 10 : ; • 6. 6417 1925. 57

The optical path of the light undergoing multiple reflections in the etalon was distorted whenever large

density gradients were present in the fluid. This caused

a degradation of the ring pattern that reduced the amplitude of the recorded interference fringes and destroyed

the continuous fringe count. To prevent this, data were

taken by slowly %'enting the fluid or slowly heating along

the coexistence boundary in order to maintain nearequilibrium conditions. The absolute fringe count to vacuum was measured

for only one point in the saturated liquid, 183 K. The

refractive indices at the other temperatures were de- termined by measuring the fringe count difference be- tween those temperatures and 183 K. This was necessary because the entire coexistence boundary (91-190 K) could not be covered with one filling of the pressure bomb as Diller had previously done for hydrogen. 14 The

fluid methane passed into the saturated vapor or compressed liquid after a large enough temperature change.

Also, the time required to count fringes along the path above the critical point (see Fig. 2) was prohibitive because the sample holder was heated very slowly to prevent density gradients that could destroy the fringe pattern.

IV. EXPERIMENTAL RESULTS

The results for 255 determinations of the refractive index of methane are displayed in Tables I- VII. The

experimental ID numbers indicated the chronological order in which the data were taken. A change in the

first two digits of the ED number indicates a new filling of the sample holder. Table Vm contains the vacuum

spacer length measurements for the gas isotherm results. These data were combined with previous measurements on the same spacer

14 to produce a correlation from which the spacer length could be calculated for measurements on the coexistence boundary as described

in Sec. m.

The densities used to calculate the (LL) function for

the gas isotherms were obtained in exactly the same

manner as those used by Straty22 for Clausius-Mossotti

(CM) experiments on methane. Experimental gas densities : were interpolated along an isotherm with a polynomial equation. However, these experimental data had

a lower bound of about 3 mol/1; hence extrapolation to lower densities was not valid and the LL function was

not evaluated. The low pressure data (3-7 bar) at 300 K

were used to estimate the zero density limit, AR , of the LL function as discussed in Sec. V.

The densities for saturated liquid methane were also calculated as described by Straty. 22 At temperatures

above 175 K, these numbers are obtained from an extrapolation2

' which is highly sensitive to the form of the fit- ting equation. This problem will be discussed further

in Sec. V. The ED numbers for different temperature

regions indicate the data were taken in several overlapping segments. The junction points between these runs were reproduced to 0. 15 fringe.

Accurate densities for saturated vapor methane are

especially difficult to measure. The LL function for

J Chem. Phys., Vol. 63, No. 1, 1 July 1975

\±h
478 James D. Olson: Refractive index of fluid methane

TABLE II. Experimental results for methane at 280 K.

P P (LL) Fringe

ID (bar) n (mol/1) (cmVmol) (count)

9Q1 fl flO^I UUOOIOft 60. 98

14 905 120. 94

21 936 ftflQft44 180. 94 9Q07 28 742 \ 013110 240. 96

32 373 273. 77

JO, jtJ. 300. 99

U J. 13 C O E7 360. 98 2904 47 970 421. 16 2903 54 007 \ 026173 481. 07 7m/ vo 55 778 027143 498. 89 2902 59 901 099439 2. 944 6. 6323 541. 09

701 62 476 030893 3. 089 6. 6319 567. 83 702 62 476 1. 030893 3 089 6. 6319 567. 83

OVJU 62 703 1. 031021 3 102 6, 6317 570. 18 2901 1. 032733 3 272 6 6311 601. 64

7n c; / uo 77 783 1. 039842 3 978 fi fi3f)3 732 30 out 78 314 1. 040161 4 010 738. 18 803 95 770 1. 050957 5 075 6 6328 936. 61 706 1. 051356 5. 115 6 6331 943. 95 708 107 RQ^ 1. 058704 5. 836 6. 6352 1079. 02 707 108 797 1. 059287 5. 893 fi 6355 1089 73 802 111. 339 1. 060924 6. 054 6. 6356 1119. 81 906 125. 805 1. 070278 6.968 6. 6385 1291.76

801 128.082 1. 071738 7.111 6.6383 1318.58

905 142. 739 1. 081039 8.016 6.6399 1489. 56 904 159.312 1.091102 8.992 6.6401 1674. 50 903 178.249 1. 101772 10.023 6.6402 1870.62

902 200.126 1.112835 11.086 6.6403 2073.96

901 222. 740 1. 122864 12.046 6. 6400 2258.29

the saturated vapor was calculated using the densities obtained by Goodwin24 from intersection of his virial equation densities with the vapor pressure curve. These

TABLE III. Experimental results for methane at 250 K.

P P (LL) Fringe

ID (bar) n (mol/1) (cmVmol) (count)

3010 6. 174 1. 003012 55.35

3009 12.598 1. 006282 115.45

3008 18. 722 1. 009537 175.27

3007 24. 600 1. 012805 235.34

3006 30.233 1. 016078 295.48

3005 35. 942 1. 019541 359.13

3004 41. 107 1. 022817 419.34

3003 46.058 1.026084 479. 39

3002 50. 804 1. 029344 2. 935 6. 6306 539.30

1008 52.940 1.030858 3. 085 6. 6316 567.11

1001 54. 677 1. 032102 3. 209 6. 6311 589.98

3001 55. 362 1. 032598 3 259 6. 6311 599.11 1007 66. 726 1. 041260 4. 117 6. 6329 758.31

1006 78. 391 1. 050972 5. 076 6. 6342 936. 80 1005 90. 025 1.061420 6. 102 6. 6365 1128.83

1004 100.300 1.071081 7. 047 6. 6377 1306.40

1003 109.979 1. 080309 7. 946 6. 6392 1476.01

1107 122. 379 1. 091852 9. 065 6. 6400 1688.17

1002 123.304 1. 092684 9. 146 6. 6398 1703.45

1106 134.331 1.102257 10 069 6. 6405 1879.39

1105 146. 728 1. 112018 11 008 6. 6405 2058.79

1104 162. 000 1.122518 12. 013 6. 6399 2251.77

1103 180. 747 1.133356 13. 048 6. 6386 2450. 94 1102 201. 627 1. 143297 13. 994 6. 6361 2633.62

1101 222. 795 1.151671 14 790 6. 6334 2787. 51

vapor (LL) results should not be considered comparable

in accuracy with the more accurate values obtained for

the supercritical isotherms.

Figure 3 shows a plot of refractive index vs temperature for the two phase region. The critical refractive index nc was obtained by extrapolation from a rectilinear diameter treatment13 ' 25 of the saturated liquid and vapor

results. The more abundant liquid refractive index data were used to interpolate values for sparse refractive index vapor points above 160 K. These data were fit to a straight line: »(T) = £[ra(T) + n(T)] = AT + B . (1) mean liquid vapor An ordinary least squares fit to the nine data pairs

yields these results for A, B, nc

, and their standard

deviation estimates: A= -4.423 xlO"4

, S.D. (A)=1.5X10-6

, 5= 1. 187615, S.D.(B)= 3x 10-4

, nc = 1.10333, S.D.(W(.)=2xl0-5

. The refractive index at the triple point, 90.680 K, was

TABLE IV. Experimental results for methane at 220 K. P P (LL) Fringe

ID (bar) n (mol/1) (cm'/mol) (count) 3110 6 187 1 003465 63. 68 3109 11 669 1. 006723 123. 54 3108 16 837 1. 009991 183. 61 3107 21. 709 1. 013263 243. 73 3106 26 267 1. 016522 303.61

3105 30 569 1. 019790 363.68 3104 34 606 1. 023054 423.67

3103 38. 401 1. 026319 483. 66 3102 41. 950 1. 029572 2. 958 6. 6307 543.45

1210 43. 632 1. 031188 3.119 6.6308 573. 14

1201 44. 447 1. 031982 3.198 6.6293 587.72

3101 45. 315 1. 032855 3.284 6.6309 603.78

1209 52. 806 1. 040980 4.091 6.6308 753. 09 1208 61 290 1. 051908 5.168 6.6338 953. 93 1207 67. 935 1. 062057 6.164 6.6365 1140. 44

1206 74. 042 1. 072713 7.206 6. 6378 1336.29

1205 79. 797 1. 083718 8.275 6.6410 1538.55

1204 84. 324 1. 092565 9.133 6.6405 1701. 14 1203 89. 922 1. 103091 10.151 6.6399 1894.59

1202 95. 669 1. 112834 11.087 6.6399 2073.65

1308 95. 730 1. 112944 11.096 6.6407 2075.67

3210 98. 966 1. 117832 11.565 6. 6403 2165.52

1307 102. 714 1. 122997 12.058 6.6406 2260.43

3209 106. 914 1. 128180 12.552 6.6406 2355.69

1306 111. 034 1. 132727 12.984 6. 6405 2439.25

3208 116. 854 1. 138388 13.522 6.6400 2543.30

1305 122. 856 1. 143457 14.004 6.6388 2636.43

3207 130. 205 1. 148850 14.516 6.6373 2735.55

1304 138.604 1. 154149 15.020 6.6348 2832.91

3206 144. 959 1. 157695 15.357 6.6332 2898. 07 3205 151.826 1. 161162 15.686 6.6314 2961.78

1303 159.298 1. 164578 16. 011 6.6293 3024. 54 3204 167. 767 1.168095 16.345 6.6274 3089. 17 3203 176.997 1. 171557 16.674 6.6251 3152.79

1302 186.786 1. 174899 16. 990 6.6231 3214.16

3202 198.015 1. 178378 17.320 6.6208 3278.10

3201 210.288 1.181825 17.647 6.6183 3341.43

1301 222.462 1. 184964 17. 943 6.6167 3399.08

J. Chem. Phys., Vol. 63, No. 1, 1 July 1975 K-6
James D. Olson: Refractive index of fluid methane 479

TABLE V. Experimental results for methane at 200 K and

subcritical isotherms.

T P Fringe

ID (K) (bar) n (count) 49.37

55.48

60.42 65.47

70.48 75.49

80.46 85.38 90.40

95.43 100.54

106.15

56.87

78.78

100.86

122.91

144. 83 166.54

188.80 210.78

232. 72 254.73

276.43

64.27

124.26

184.25

244. 63 305.23

365.10

425.22 484.87

544.71

605.01 62.04

122. 01 182.14 242.13

302.08

362. 18

422. 02 482.14

542. 14 602.30

calculated from a second order Lagrange interpolating

polynomial fit to the refractive index data at 95, 100, and 105 K. The Lorenz-Lorentz function for fluid methane is plotted vs density in Fig. 4. Several replicate isother- mal results are not included in the figure. Note the in- crease in the (LL) function as the lower limit of accurate

gas densities is approached. Also, the oscillatory behavior of the 220 K results in an artifact of the polynomial interpolating function. The accuracy of the (LL)

values is limited by the accuracy of the PVT surface be- cause the refractive index is known much more precisely than the pressure-density relationship. Uncertainties as large as 0. 1% could exist in the experimental

densities of Ref. 1. The precision of the experimental data is best indi- cated by replicates of experimental measurements. Replicate determinations starting from the same initial density and pressure generally agreed within 0. 05% in the derived (LL) function, as indicated by Fig. 4 and Tables I- VII. The two replicates of the 183 K saturated

liquid reference point agreed within 0. 003% in («- 1). The evaluation of the accuracy of experimental measurements in the absence of exactly known reference

values is a difficult and ill-defined process. 26 An esti- mate of the accuracy of the quantity (n - 1) may be cal- culated from the upper bounds of the possible systematic errors in the quantities appearing in Eq. (4). Not surprisingly, this number is most directly influenced by the percentage of uncertainty in the total fringe count. This

suggests that accuracy of the measurements is on the same order as the precision described above. The percentage uncertainty varies from 0. 1% at small fringe counts to 0.002% at the largest fringe counts. Additional uncertainty due to the calculated fringe count adjust- ment has been discussed in Sec. Ill for the results on

the coexistence boundary.

V. DISCUSSION

A. Comparisons with other work

The refractive index of methane has been previously

measured at room temperature and low pressure by

several workers, 27-29 and by Abbiss et al.

30 for the sat- urated liquid at 588. 3 nm. None of these results can be

directly compared with the present experiments because

of differences in pressure, temperature, and wavelength of light used. The widely referenced work by Ramaswamy and Watson

27 was performed with a Rayleigh interferometer designed for determinations at pressure near or below

1 bar. Also, the temperature of their apparatus was

not closely controlled. However, extrapolation of the low pressure 300 K results of Table I to a pressure of

1 atm and temperature of 298. 15 K agrees within ex- perimental error with the 25 °C (n - l)i|tm number of Ramaswamy and Watson.

Pings and co-workers30 used a minimum deviation angle refractometer that required a room temperature

calibration with water. The uncertainty in the refractive indices was estimated to be ±0. 0001. Unfortunately, their results are at 588. 3 nm and no dispersion

data exists for liquid methane. However, these refractive index results at 588.3 nm are about 0.8% lower

than our results at 546. 2 nm at the common temperatures. This is in qualitative agreement with the normal

wavelength dependence of refractive index observed for other cryogenic fluids. The (LL) vs density behavior shown in Fig. 4 is similar to the (CM) and (LL) density behavior observed for other nondipolar fluids. This behavior is in qualitative

agreement with the predictions of theoretical calculations, 31 that is, a slight increase with density to the

critical density, then a decreasing (LL) or (CM) function

at higher densities. No temperature dependence among

the gas isotherm results is distinguishable at densities below 12. 0 mol/1 . At higher densities, the 220 K data are higher than the 250 K data in qualitative agreement

3612 140. 000 2. 974 1.002687

3611 140. 000 3. 314 1.003020

3610 140. 000 3. 594 1. 003288

3609 140. 000 3.866 1. 003563

3608 140. 000 4.137 1. 003836 3607 140. 000 4.405 1.004109

3606 140.000 4.664 1.004379

3605 140. 000 4. 921 1. 004647

3604 140. 000 5.181 1. 004920

3603 140. 000 5.437 1. 005194

3602 140.000 5. 689 1. 005472

3601 140.000 5. 959 1. 005777

3511 160. 000 3.944 1. 003095

3510 160. 000 5.355 1. 004288 3509 160.000 6. 704 1.005489

3508 160.000 8. 002 1. 006689

3507 160.000 9.232 1. 007882

3506 160. 000 10.392 1. 009063

3505 160.000 11. 521 1. 010275

3504 160. 000 12. 579 1. 011471

3503 160.000 13.589 1.012665

3502 160.000 14. 530 1.013863

3501 160. 000 15.409 1.015044

3410 180.000 5.030 1. 003498

3409 180.000 9.307 1.006763

3408 180. 000 13.194 1. 010027

3407 180.000 16. 724 1.013313

3406 180.000 19. 901 1. 016611

3405 180. 000 22. 697 1. 019869

3404 180. 000 25. 172 1.023141

3403 180.000 27.323 1. 026387

3402 180.000 29. 187 1. 029643

3401 180.000 30. 785 1. 032925

3310 200.000 5.451 1. 003376

3309 200.000 10.351 1. 006640

3308 200.000 14.900 1.009912

3307 200.000 19.107 1.013177

3306 200.000 22.983 1.016439

3305 200.000 26. 572 1.019710

3304 200.000 29.846 1. 022966

3303 200.000 32.868 1. 026238

3302 200. 000 35.618 1.029503

3301 200.000 38.133 1. 032776

J. Chem. Phys., Vol. 63, No. 1, 1 July 1975

K-7
480 James D. Olson: Refractive index of fluid methane

TABLE VI. Experimental results for saturated liquid methane.

T jP* P Fringe15 'vac ID (K) (bar) (mol/1) n (cm3 / mol) (count) (cm)

c 90.680 28.15 1. 29581 6.5580

2501 95.000 0.199 27.789 1 291899 6. 5615 5362.83(6.23) 0. 501770

2502 100.000 0.345 27.367 1 287255 6. 5650 5277. 58(5.97) 0.501777

2503 105.000 0. 566 26.934 1 282490 6.5680 5190.12(5.72) 0.501784

2504 110.000 0.884 26.491 1. 277612 6.5711 5100.56(5.46) 0.501791

2505 115.000 1.326 26.035 1. 272619 6.5745 5008.89(5.19) 0.501798

2506 120. 000 1.919 25.566 1. 267479 6.5779 4914.52(4. 92) 0. 501806 2507 125. 000 2.694 25.081 1. 262181 6.5814 4817.25(4.65) 0. 501813

2508 130.000 3.681 24. 578 1 256692 6. 5848 4716.47(4. 37) 0. 501821 2509 135.000 4.912 24.055 1 251007 6.5887 4612.08(4.08) 0.501828

2401 140. 000 6.422 23.508 1 245061 6.5924 4502.89(3.79) 0.501836

2402 145.000 8.244 22.933 1 238832 6.5962 4388.50(3.50) 0. 501844

2403 150.000 10. 414 22.325 1 232260 6.6003 4267.81(3.21) 0.501852

2404 155. 000 12.966 21.678 1 225253 6.6041 4139.11(2.91) 0.501861

2405 160. 000 15. 939 20.980 1 217723 6.6079 4000.80(2.60) 0.501869

2301 165. 000 19.372 20.219 1 209524 6.6119 3850.19(2.29) 0.501877

2302 170. 000 23.308 19.371 1. 200443 6.6168 3683.38(1.98) 0.501886

2303 175.000 27. 794 18.401 1 190045 6.6212 3492.36(1.66) 0. 501895

2304 178.000 30. 771 17.731 1. 182905 6.6244 3361.17(1.46) 0. 501900

2203 180.000 32.884 17.232 1 177607 6.6271 3263.83(1.33) 0.501903

2204 181.000 33. 980 16.962 1 174741 6.6284 3211.17(1.27) 0.501905

2205 182.000 35. 104 16.675 1. 171701 6.6298 3155.31(1.20) 0. 501907

2001 183.000 36.256 16.368 1, 168454 6. 6315 3095.64(1.14) 0.501909

2201 184.000 37.437 16.036 1 164951 6.6334 3031.27(1. 07) 0. 501911

2202 185.000 38.648 15.673 1. 161132 6.6358 2961.11(1.01) 0. 501912

2101 186.000 39.890 15.269 1. 156884 6.6384 2883.04(0.94) 0. 501914

2102 187. 000 41.165 14.808 1. 152051 6.6417 2794.23(0.88) 0. 501916

2103 188.000 42.473 14.260 1. 146355 6.6469 2689.56(0.81) 0.501918

2104 189.000 43.818 13.561 1. 139103 6.6539 2556.29(0.74) 0. 501920

2105 189.404 44. 372 13.201 1 135379 6.6582 2487.87(0.72) 0. 501920

d 190.555 10.16 1. 10333 6.6475

•Calculated from vapor pressure equation (Ref. 21).

bC ale ulated fringe count correction in parenthesis.

eTriple point extrapolation.

"Critical point extrapolation.

with a negative temperature dependence of refractometric virial coefficients. In addition, an isochoric comparison of the saturated liquid results with the gas iso- therms indicates the same trend. An interesting comparison may be made between the present (LL) results and the earlier (CM) results deter- mined by Straty. 22 Figure 6 is a plot of the (LL) and

(CM) results for methane, with the zero density limit, AR or AD , subtracted to illustrate the relative change

in polarization as a function of density. The sharper

decrease in the (LL) function at higher (liquid) densities was also noted in the case of the carbon dioxide. 5 However, experiments on argon32 exhibited the same relative behavior for both the (CM) and (LL) functions. There is presently no theoretical explanation for this difference

in behavior at high densities. However, the importance

of three-body interactions on the induced dipole forces

at high densities may explain the relatively higher polarization in the (CM) case.

B. Refractometric virial coefficients Estimates of second and third refractometric virial coefficients. BR and CR , were obtained from a least squares fit of Eq. (2) to the gas isotherm data. Several

assumptions are implicit in this type of analysis33

: (i) The truncated form of the virial equation, Eq. (2), is truly representative of the (LL) function over the density range Osp< 18 mol/1. If a real fourth term, DR

p*, is

in fact neglected, then the adjusted values of BR and CR are in error, (ii) Systematic deviations from Eq. (2) due to the form of density interpolating functions are small compared to the overall (LL) trend with density,

(iii) The temperature dependence of the (LL) function

is small so that the 220 K isotherm, which includes data over the largest density range, may be combined with an estimate of AR

at 300 K. (iv) An independent method

of determining AR , the zero density limit, is available. The results of the least squares fit are extremely sensitive to a choice of AR . Moreover, a fit of only the 3-18

mol/1 data cannot be attempted because the value of AR obtained in this case was found to be heavily influenced by meaningless random variations in the data.

The low pressure refractive index data at 300 K may

be used to estimate AR , the zero density limit of the LL

function, with the use of the thermodynamic virial equation of state: P/RT=p + B^pz + Cp p

3 + .-' . (8)

J. Chem. Phys., Vol. 63, No. 1, 1 July 1975

K-8
James D. Olson: Refractive index of fluid methane 481

TABLE VII. Experimental results for saturated vapor methane.

T P (LL) Fringe11

rr> (K) (bar) (mol/1) n (cmVmol) (count) (cm) 1905 99. 290 0. 320 1. 000403 • 7. 41(3.41) 0. 501797

1904 114. 403 1. 266 1 001378 • 25 32(2.62) 0. 501S19

1903 129. 865 3. 651 -1. 003738 • 68 67(1.77) 0. 501842

2601 138. 000 5. 783 ... 1 005704 • 104 80(0. 00) 0.501833

1902 139. 649 6. 307 1 006216 • 114. 21(1.21) 0.501857

1901 150. 000 10. 414 ... 1. 010161 •• 186. 71(0. 61) 0. 510874

1406 158. 411 14. 946 ... 1, 014804 • 272. 00(2.70) 0. 501866

2701 160. 000 15. 939 1. 589 1. 015772 6. 6010 289 80(0. 00) 0. 501891

1803 160. 000 15. 927 1. 589 1. 015739 6. 5875 289. 20(1.39) 0. 501875

1405 166. 136 20. 221 2. 069 1. 020622 6. 6210 378. 92(2.22) 0. 501879

1404 171. 307 24. 426 2. 588 1. 025774 6. 6112 473. 59(1.89) 0. 501888

1802 172. 386 25. 358 2. 713 1. 026973 6. 5977 495. 62 (0.62) 0. 501897

1403 175. 711 28. 479 3. 146 1..031356 6. 6076 576. 16(1. 61) 0. 501S96

1801 176. 928 22. 773 3. 327 1. 033132 6. 6016 608. 83(0.33) 0. 501904

1402 179. 077 31. 896 3. 680 1. 036723 6. 6095 674. 80(1.39) 0. 501902

1501 180. 000 32. 865 3. 849 1. 038404 6. 6072 705. 70(0. 00) 0. 501915

1401 181.560 34.606 4.162 1. 041568 6. 6095 763. 83(1.23) 0. 501906

1703 182.000 35.104 4.258 1. 042540 6. 6105 781 70(0. 00) 0. 501913

1702 184.000 37. 415 4.747 1. 047515 6. 6164 873. 13(0.13) 0. 501915

1701 186.000 39.870 5.362 1. 053738 6. 6171 987. 50(0. 00) 0. 501919

1601 190. 000 45.192 7.829 1. 078959 6. 6262 1451. 00(0. 00) 0. 501925

c 190. 555 10.16 1. 10333 6. 6475

"Calculated from vapor pressure equation (Ref. 21). Calculated fringe count correction in parenthesis. Zero correction indicates isothermal

determination.

•Critical point extrapolation.

Upon elimination of density between Eq. (2) and Eq. (8), a "pseudo" (LL) function expansion is obtained:

Figure 5 is a plot of Eq. (9) for the low pressure (3-7

bar) data of Table I. Note the dramatic increase in the scatter of replicates at low pressure. The percentage amount of the fringe fraction error compared to the total fringe count has increased from 0. 06 to 0. 12a

c . The

interferometer was originally designed for use atmoderTABLE Vm. Experimental vacuum spacer lengths.

T

ID (K) (cm) 100-400 300. 000 0. 502146 500-600 300. 000 0. 502145

2800 300. 000 0. 502150 700-900 280. 000 0. 502101 2900 280.000 0. 502106 1000-1100 250. 000 0. 502036

3000 250. 000 0. 502041 1200-1300 220. 000 0. 501976

3100 220.000 0. 501977

3200 220. 000 0. 501978

3300 200. 000 0. 501938

3400 180. 000 0. 501906

3500 160. 000 0. 501892

3600 140. 000 0. 501874

a 100. 000 0.501756

a 80. 000 0. 501729

"Experimental measurement on same spacer from Ref. 14.

ate and high densities. To restore its optimal sensitivity for the low pressure experiment, the spacer

length would have to increase from 0. 5 cm to, say 10 cm. Moreover, these low pressure results are very

sensitive to the determination of the fractional order

measured at vacuum because this number enters the calculation of [n - 1) for each point in the run.

An ordinary least squares fit to Eq. (9) gave these values for Bt and AR

at 300 K (assuming BR 5. 0 to 7.

0

1 35 1 1 ill

1.30

1.25

• 1.20

•

• •

1.15 \ 110

0

1.05

1 00 - e e

90 I 10 130 150 170 190 TEMPERATURE,

K

FIG. 3. The refractive index of saturated liquid and saturated vapor methane as a function of temperature: •, saturated

liquid; o, saturated vapor; is rectilinear diameter line ® indicates extrapolated ciritcal point refractive index.

J. Chem. Phys., Vol. 63, No. 1, 1 July 1975
482 James D. Olson: Refractive index of fluid methane

666

6.64

£c

<^

i CM+ c

CNJc

6.58

6.56

-i—i—i—i—|—i—i—i—I—|—i—I—i—i—|—i—I—I—I—|—I—i—i—i—|—i—i—i—

r

?&> ******** A\

Ar (300 K)

ff

Saturated Vapor

_i i i i I i i

' i

AS

1

0.1 % .

Saturated Liquid -

i i I i

i i i I i i i i L

5.0 100 15.0 200 25.0 DENSITY, mol/l

300

FIG. 4. The density depen- dence of the Lorenz-Lorentz

function of fluid methane; o, 300 K; , 280 K; 250 K;

a , 220 K; •, saturated liquid; a, saturated vapor. AR

is the zero density limit at 300 K. Ois estimated value

of critical point (LL) function with error bar.

(cmVmol)2

): AR

= 6. 6143 (cm/mol), S. D. (AR ) = 0. 002 (cm3/mol),

Bp = - 44. 0 (cmVmol), S. D. (Bp

) = 3.0 (cm3 /mol).

The second pressure virial coefficient agrees within

the experimental error with the 300 K value from the correlation of Goodwin. 24 AR should be weakly temperature dependent, decreasing slightly with decreasing

temperature. Direct determination of ARat low tem-

_EL , mol/l

RT

FIG. 5. Ideal gas Lorenz- Lorentz function for methane low- pressure (3-7 bar) data at 300 K; is least- squares-fit

to Eq. (9).

peratures was not attempted because Bp becomes more

negative as temperature decreases. The slope of the

fitted line in Fig. 5 increases as Bp becomes more negative and the large scatter in the data owing to the fractional fringe uncertainty would vitiate any attempt to es- timate an intercept.

Buckingham and Graham15 reported a value of 6. 600 (cm3/mol) for AR measured at 299 K and X = 632. 8 nm.

Their measurement required previous knowledge of the second pressure virial coefficient Bp

. There are no

other direct determinations of AR for methane. However, the low pressure measurements of (n- l)

27-29 may

be combined with the STP density to estimate AR . Val- ues pf 6. 584, 6.608, and 6.615 (cm3/mol) were calculated from this analysis for AR

at X = 546. 2 nm.

The results of an ordinary least squares fit to Eq. (2) of the gas isotherm data and AR , the zero density limit, are shown in Table DC. Two fits were performed; first, a fit of all the gas isotherm data in the (3-18) mol/l

range, and second, a fit of the 220 K gas isotherm. The

uncertainty in BR

is about 1 (cm°/mol)2 in both cases. Buckingham and Graham 15 obtained a value of 7. 15 ±0. 35 (cmVmol)2 for BR from their differential inter- ferometric expansion experiments. Our value is in substantial agreement with theirs when the limitations of the curve fitting procedure discussed above are considered.

TABLE IX. Refractometric virial coefficients of methane at X = 546.2 nm.

Data used

for fit (cmVmol) (cmVmol)2 cR(cmVmol)3

All isotherms 6.615 5. 5 -290

220 K isotherm 6.613 6.1 -320

J. Chem. Phys., Vol. 63. No. 1, 1 July 1975
James D. Olson: Refractive index of fluid methane 483

0.06

004

n

S 0.02

a -002 5

o- -0.04 h

-0.06

i 1 1 r

° - o g 4 * <a 5

o

4

J I I I _J l_ 0 12 16 20 24 28 32 DENSITY (mol/l)

FIG. 6. The density dependence of the reduced Lorenz-Lorentz

and Clausius-Mossotti functions of fluid methane: A,(LL-.Afi ); O, (CM-i4fl ).

C. Octopole moment of methane

The first nonvanishing molecular moment of methane

is the octopole moment because of the Td symmetry.

Attempts to determine the magnitude of this moment in- clude analyses of the second pressure virial coefficient

data,

34-36 but these analyses were hampered by the lack

of a suitable reference intermolecular potential function. For example, it is common practice to fit the viscosity coefficients assuming spherical intermolecular interactions. However, proper fits of this type have

only recently been possible. 37

Alternatively, analysis7 of experimental dielectric

virial coefficients may also indicate the magnitude of the octopole moment. BD is separated into two parts:

Bn - B, Bd + Ba (10) where BiBi results from the dipolar induced polarization of the external field and B0r results from octopolar

interaction with induced dipoles. It is B0r that is used

to estimate the octopole moment from the experimental measurements. Unfortunately, it is difficult to esti- mate B0r, for example, Bose, Sochanski, and Cole38 measured BD to be 6.75 (cm3 /mol)2 at 373.4 K and

8. 14 (cm3/mol)2 at 279. 8 K. They estimate a value of

•Bind- 2. 5 (cm3/ mol)2 on the basis of this temperature

dependence. However, both our results and those of Buckingham and Graham15 suggest that if BR

-BlBd (Bose et al. suggest this approach at the end of their paper), then .Blnd is on the order of 5.5-7.5 (cm3/mol)2

. Further work is necessary here to show exactly how

BR and Biai are related and how a more significant value

of B0r may be estimated from BD before a definitive value of the octopole moment may be determined from

electromagnetic virial coefficients. Furthermore, it may be that an analysis of the temperature and higher

density dependence of (CM) and (LL) taken together, as shown in Fig. 6, would indicate the octopolar contribution to the molecular polarization.

D. The critical density and PVT surface of methane

Electromagnetic equation of state data provide a sensitive test of the P-p-T relationship, especially near

the vapor-liquid critical point. This section will be concluded with some comments on the thermodynamic

implications of the methane refractive index and (LL)

function data. It is expected that the saturated vapor

(LL) function would be as large or larger than the gas isotherm values. Hence, our data suggests the calculated vapor densities24 may be 0. 3%-0. 5% too large.

Adsorption of a film of liquid methane on the interferometer optical surfaces during the saturated vapor measurements would increase the apparent refractive index

and, therefore, raise, not lower, the calculated (LL)

values.

The low pressure refractive index data at the eight

temperatures between 140 and 300 K provide a basis for examination of the virial equation of state representation for methane. This type of procedure was recently

applied to dielectric constant measurements on nitro- gen.

39

The behavior of the saturated liquid (LL) function near

the critical point (see Fig. 4) does not represent the

real (LL) behavior, but rather indicates inaccuracy in the liquid density determinations. Experimental data1 were not available above 175 K so that densities at higher temperatures were essentiaUy obtained from an

extrapolation that is very sensitive to the choice of criti- cal parameters in the fitting equation. Previous workers

13 ' 14 also observed anomalous deviations in the (LL)

function of simple fluids as the critical point was ap- proached.

The diamond in Fig. 4 represents a "reasonable" extrapolation of the critical Lorenz—Lorentz function,

(LL)C, from the saturated liquid values. This value of (LL) C was combined with nc, the critical point refractive index, to calculate a value of the critical density of methane,

pe =10.16±0.01 mol/l . The uncertainty in the critical density was calculated from the error bounds on the extrapolated value of (LL)C

. All methods of determining the critical density

depend on some form of extrapolation, 40 usually with a

rectilinear diameter analysis. The high precision of interferometric refractive index measurements coupled

with the relative constancy of the (LL) function suggests

that the method described in our work is the most accurate technique currently available for determination

of the critical density.

ACKNOWLEDGMENTS

The author expresses his appreciation to B. A. Younglove, G. C. Straty, and W. M. Haynes for their advice on cryogenic instrumentation and experimental

technique. D. E. Diller suggested the project and provided valuable comments on all aspects of the work.

Finally, the author gratefully acknowledges the encour- agement and perceptive guidance of H. J. M. Hanley.

J. Chem. Phys., Vol. 63. No. 1. 1 July 1975 K-ll
484 James D. Olson: Refractive index of fluid methane

Contribution of the National Bureau of Standards, not subject

to copyright.

tNRC-NBS Postdoctoral Research Associate, 1972-74.

'R. D. Goodwin and R. Prydz, J. Res. Natl. Bur. Stand. (U.S.) A 76, 81 (1972).

2 J. F. Ely, H. J. M. Hanley, and G. C. Straty, J. Chem. Phys.

59, 842 (1973).

3 R. D. McCarty, NBSIR 74-357 (1974); Available from the National Bureau of Standards, Cryogenic Data Center, Boulder, CO 80302.

4 J. G. Kirkwood, J. Chem. Phys. 4, 592 (1936).

5 A. D. Buckingham, Trans. Faraday Soc. 52, 747 (1956). B. Levine and D. A. McQuarrie, J. Chem. Phys. 44, 3500

(1966).

7C. J. F. Bottcher, Theory of Electric Polarization, revised by O. C. Van Belle, P. Bordewijk, and A. Rip [Elsevier, New York, 1973), 2nd ed. , Vol. I, Chap. VI.

8 H. Sutter, "Dielectric Polarization in Gases," in Dielectric and Related Molecular Process, Specialist Periodical Report,

edited by M. Davies (The Chemical Society, London, 1972).

9 A. Michels and J. Hamers, Physica (Utr. ) 4, 995 (1937).

I0 A. Michels, H. Lebesque, L. Lebesque, and S. R. De Groot, Physica (Utr.) 13, 337 (1947). UA. Michels, A. Brotzen, and S. R. De Groot, Physica (Utr.)

13, 343 (1947).

12 A. Michels and A. Brotzen, Physica (Utr. ) 15, 769 (1949).

13R. K. Teague andC. J. Pings, J. Chem. Phys. 48, 4973

(1968).

,4 D. E. Diller, J. Chem. Phys. 49, 3096 (1968).

15 A. D. Buckingham and C. Graham, Proc. R. Soc. A 336, 275 (1974).

,6R. D. Goodwin, J. Res. Natl. Bur. Stand. (U.S.) C 65, 231

(1961).

17 B. Edlon, Rep. Int. Astron. Union 12, 138 (1964).

,8H. Remy, Chem. Ber. 101, 1 (1968). C. Candler, Modern Interferometers (Hilger, London, 1951),

p. 218.

20 F. H. Rolt and H. Barrell, Proc. R. Soc. A 122, 122 (1929).

21 R. Prydz and R. D. Goodwin, J. Chem. Thermodyn. 4, 127

(1972).

2 -G. C. Straty and R. D. Goodwin, Cryogenics 13, 712 (1973).

23 R. D. Goodwin, J. Res. Natl. Bur. Stand. (U.S. ) A 75, 15

(1971).

24R. D. Goodwin, Tech. Note U. S. Natl. Bur. Stand. 653,

(1974); Available from Superintendent of Documents, U. S. Govt. Printing Office, Washington, D.C., Order No. C13.46 :653, $2.25.

25J. R. Partington, Treatise on Physical Chemistry (Longmans,

Green, London, 1949), Vol. 1, p. 639.

26J. Mandel, The Statistical Analysis of Experimental Data (In- terscience, New York, 1964), p. 125.

27H. E. Watson and K. L. Ramaswamy, Proc. R. Soc. A 156, 144 (1936).

28C. Cuthbertson and M. Cuthbertson, Proc. R. Soc. A 97, 152 (1920).

29 Landolt-Bornstein (Springer-Verlag, Berlin, 1962), Band II, Teil 8.

30C. P. Abliss, C. M. Knobler, R. K. Teague, and C. J. Pings, J. Chem. Phys. 42, 4145 (1965).

31 G. Stell and G. S. Rushbrooke, Chem. Phys. Lett. 24, 531

(1974).

32 J. de Boer, F. van der Maeson, and C. A. ten Seldam,

Physica (Utr.) 19, 265 (1953).

33 H. J. M. Hanley, R. D. McCarty, and J. V. Sengers, J. Chem. Phys. 50, 857 (1969).

34S. Kielich, Acta Phys. Pol. 27, 475 (1965).

35T. H. Spurling, A. G. DeRocco, and T. S. Storvich, J. Chem. Phys. 48, 1006 (1968).

36K. K. Datta and Y. Singh, J. Chem. Phys. 55, 3541 (1971).

37J. F. Ely and H. J. M. Hanley, Mol. Phys. 24, 683 (1972).

38T. K. Bose, J. S. Sochanski, and R. H. Cole, J. Chem.

Phys. 57, 3592 (1972).

39 J. F. Ely and G. C. Straty, J. Chem. Phys. 61, 1480 (1974).

40M. R. Moldover, J. Chem. Phys. 61, 1766 (1974).

J. Chem. Phys., Vol. 63, No. 1, 1 July 1975 K-12
APPENDIX L

|
THERMOPHYS I CAL PROPERTIES DATA RESEARCH

ON COMPRESSED AND LIQUEFIED GASES

AT THE NBS CRYOGENICS DIVISION

Dwain E. Di Her

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado

Paper E-4

Preprinted for the

Cryogenic Engineering Conference

Kingston, Ontario, Canada

July 22-25, 1975
THERMOPHYSICAL PROPERTIES DATA RESEARCH

ON COMPRESSED AND EIQUEFIED GASES

AT THE NBS CRYOGENICS DIVISION*

Dwain E. Diller

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado

Abstract

This report summarizes important NBS contributions to accurate thermophysical properties data for compressed and liquefied gases (helium, hydrogen,

nitrogen, oxygen, fluorine and argon), and discusses research on liquefied

hydrocarbon gases (methane, ethane, ethylene etc.) and their mixtures.

Representative results of research on the thermophysical properties of methane

and mixtures containing methane are presented. Additional contributions

expected through 1977 are summarized.

Contribution of the National Bureau of Standards, not subject to copyright

L-3
THERMOPHYSICAL PROPERTIES DATA RESEARCH

ON COMPRESSED AND LIQUEFIED GASES

AT THE NBS CRYOGENICS DIVISION

Dwain E. Diller

Introduction

The Cryogenics Division of the National Bureau of Standards, with support

from the NBS Office of Standard Reference Data, the National Aeronautics and

Space Administration, the American Gas Association, Inc., and the LNG Density

Project Steering Committee*, is engaged in a program of thermophysical properties

data research on compressed and liquefied gases and their mixtures in support of

advanced cryogenic technology. New technologies are continually being developed

to promote efficient, economical and safe utilization of the country's material

and energy resources. Important cryogenic processes, such as the separation,

liquefaction, storage, transport and custody transfer of gases, are being used

in much larger projects than ever before, and will benefit greatly from

comprehensive accurate thermophysical properties data. The purpose of the NBS

program is to provide critically evaluated data and calculation methods, original

experimental measurements, new measurement technology, and data awareness and

dissemination services in support of these projects. Our technical goal is to

provide a range and quality of data which will be recognized as definitive or

standard for all foreseeable low temperature engineering calculations. Our

*The LNG Density Project Steering Committee is a consortium of national and

international energy companies which includes representatives from British

Gas Corporation, 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 Oil Corp., Natural Gas Pipeline Co., Phillips

Petroleum Co., Shell International Gas Ltd., Sonatrach, Southern Calif. Gas

Co., Tennessee Gas Pipeline, Texas Eastern Pipeline Co., Tokyo Gas, Ltd.,

and Transcontinental Gas Pipeline Corp.

L-4
scientific goal is to understand the relationships between molecular structure,

dense fluid structure, and the behavior of simple molecular fluids, which are

the basis for developing accurate predictive calculation methods. The purpose

of this report is to summarize important NBS contributions to thermophysical

properties data research on the monalomic and diatomic gases (helium, hydrogen,

nitrogen, oxygen, fluorine and argon), and to discuss NBS research on the hydrocarbon gases (methane, ethane, ethylene, etc.) and their mixtures. Table 1 gives

references to selected NBS publications on the equation of state, thermodynamic,

electromagnetic and transport properties of the monatomic and diatomic gases.

Accurate equations of state and thermodynamic property data tables for these

substances are among the most important NBS contributions to cryogenic technology.

NBS Research on Compressed and Liquefied Hydrocarbon Gases

In 1970 the American Gas Association, Inc. initiated a project at the NBS

Cryogenics Division on the thermophysical properties of compressed and liquefied

hydrocarbon gases (methane, ethane, propane etc.) in support of liquefied natural

gas (LNG) technology. There are few accurate Lhermophysical properties data

available, even for the simplest pure hydi. carbon gases and liquids, at temperatures below 200 K. Table 2 shows the hydrocarbon gases having freezing and

normal boiling temperatures in this range. We expect that the demand for

accurate data for these fluids and their mixtures will continue to increase with

the necessity for efficient distribution and utilization of energy and chemical

feed stock supplies.

The most important NBS contribution to liquefied hydrocarbon gas technology

to date is comprehensive accurate thermophysical properties data for pure compressed and liquefied methane, the most abundant constituent in natural gas.

2

L-5
Table 3 summarizes selected NBS publications of this data [29-40]. The most

useful publication for engineering calculations is NBS Technical Note 653, "The

Thermophysical Properties of Methane, from 90 to 500 K at Pressures to 700 Bar"

[36], This publication contains a critical evaluation and correlation of all of

the accurate equation of state (PVT) and thermodynamic properties data available

for methane through April 1974, and reports original NBS measurements and

interpolation functions for the vapor pressures, melting pressures, orthobaric

densities, equation of state (PVT) and specific heats. The thermodynamic property

tables were calculated using an isochoric equation of state, which typically

differs from the experimental PVT data by less than 0.2% in density, except in

the critical region. The calculated calorimetric and sound velocity data,

obtained without recourse to multiproperty analysis, typically differ less than

3% from their measured values. The data, equations, and computer programs

given in this report have already found important applications in recent

calculations of the phase equilibria, orthobaric densities and thermodynamic

properties of LNG mixtures [50]

.

A similar project on the thermophysical properties of compressed and

liquefied ethane is underway. An isochoric equation of state has been used to

analyze all of the volumetric and calori ;etric data available for ethane, and

to compute provisional thermodynamic property tables covering the temperature

range 90 - 600 K at pressures to 70 MPa (10,000 psia) [51]. New measurements

of the vapor pressures, melting pressures, orthobaric densities, equation of

state, dielectric constants and specific heats are being performed to extend

the experimental data down to the triple point temperature, 89.9 K. A revision

of the provisional thermodynamic tables, incorporating all available new

measurements is planned. A project on the thermophysical properties of propane

will be initiated in 1976.

3

L-6
The Cryogenics Division is also participating in a joint industrygovernment project on the thermophysical properties of ethylene. This project

was initiated in 1974 by the NBS Office of Standard Reference Data and a

consortium of seven industrial firms to provide accurate equation of state and

thermodynamic properties data for ethylene for improved plant design and custody

transfer operations. New measurements are being carried out at NBS-Washington

,

NBS-Boulder , the ERDA Energy Center at Bartlesville , Oklahoma and at the

University of Michigan. Evaluation and correlation of the data are now

underway at NBS Boulder with completion scheduled for 1979.

Properties of Methane: Represent a cive Results

High priority has been given to obtaining comprehensive accurate thermophysical properties data for compressed and liquefied pure methane, the most

abundant constituent in natural gas. Methane air o brs the simplest structure

of any of the hydrocarbon gases and is therefore a useful model for theoretical

calculations of dense fluid structure and properties. Representative results

of thermophysical properties data resear h ov. methane are given in Figures 1-4.

Figure 1 shows the dependences of the Clausius-Mossotti function, V(e-l) / (e+2)

,

on density and temperature [37]. The behavior of the Clausius-Mossotti function,

C-M, for methane is typical of the behavior of other non-polar fluids; the dependence on density is less than 1% at fixed temperatures, and the dependence on

temperature is less than 0.5% at fixed densities. Figure 1 demonstrates the

utility of the Clausius-Mossotti function for evaluating the consistency and

accuracy of equation of state measurements. As the quantity (e-1) can easily

The NES-Industry Project on the Thermophysical Properties of Ethylene is

jointly supported by the NBS Office of Standard Reference Data and seven industrial firms including Celanese Ch2mical Co., Cities Service Oil Co.,

Continental Oil Co., Gulf Research and Development Co., Mobil Chemical Co.,

Monsanto Polymers and Petrochemicals Co., and Union Carbide Corp.

4 L-7
be measured with an accuracy better than 0.1%, equation of state inconsistencies

of this magnitude are readily visible. The figure also demons urates the utility

of accurate Clausius-Mossotti function data for density gauging. Once the

Clausius-Mossotti function has been determined for a particular fluid, the

density can easily be obtained from a capacitance gauge measuring the dielectric

constant

.

7 2 Figure 2 shows Lorentz-Lorenz function, V(n^ - l)/(n^ -I- 2), data for

methane, recently obtained from precise refractive index n^ measurements

[38] and the equation of state. The dependences of the Lorentz-Lorenz function,

L-L, for methane on density and temperature are typical of other non-polar fluids,

and are similar to the behavior of the Clausius-Mossotti function. There are

subtle differences between the behavior oi the L-L and C-M functions at ~igh

densities which have not been satisfactorily expl.< ied, even for the simplest

gases and liquids. Figure 2 shows inconsistencies in the orthobaric density

data used to compute L-L near the critical temperature. Unlike many other

physical properties, the C-M and L-L fur ct ions appear to be well-behaved near

the critical point ; this fact has been uj_ iliseii to obtain very precise equation

of state data near the critical point from :ise oi ' '-. trie constant and

refractive index measurements [64].

Figure 3 shows the dependences of the sound velocities in gaseous and

liquid methane on density and temperature- The circles indicate conventional

ultrasonic measurements [34] and the crosses indicate light scattering

spectroscopy measurements [35] obtained in this laboratory. The light scattering

measurements were made in a density range inaccessible to conventional ultrasonic

measurements on methane. Accurate sound velocity measurements give a valuable

5

L-8
check on the consistency of the equation of state derivatives and calorimetric

2 data using the thermodynamic relationship = Y(3p /3p)

T

, where W

g is the sound

velocity and y = C /C is the specific heat ratio. Both sets of measurements

p v

are consistent with each other and with the thermodynamic sound velocities

within their combined uncertainties.

New equations have been developed to calculate the dependences of the

transport properties of gaseous and liquid methane on density and temperature

[40] . The behavior of the thermal conductivity coefficients for methane can

be calculated to good approximation with

A(p,T) = A Q

(T) +°A

1 (T)p + AX'(p.T) + AAJp.T) , (1)

where Xq is the dilute gas coefficient, A^ is the first density correction

coefficient, AA 1 is a remainder term and AA gives the enhancement of the thermal

c conductivity coefficient near the critical point. The enhancement occurs at

densities within about 50% of the critical density and at temperatures within

about 20% of the critical temperature. Detailed equations for each term are

given in reference [40], In the absence >£ systematic measurements for methane,

the last term AA has been estimated from pealing law relations [53], mode-mode

coupling theory [54] and by corresponding states with data for CO^ [55].

Figure 4 shows the predicted dependences of the excess thermal conductivity,

(A.p + AA ' + AA )

, on the density and temperature as these parameters approach

1 c their critical values. The estimated accuracy of equation (1) is better than

5% outside the critical region, and about 20% in the region of the predicted

enhancement. Preparations are underway for systematic light scattering

measurements of the thermal diffusivity coefficients, x - ^/P c

p

> to provide

additional information on the behavior in the critical region.

6

L-9
NBS Research on Compressed and Liquefied Gas Mixtures

The National Bureau of Standards has supported thermophysical properties

data research on cryogenic fluid mixtures since 1959. The purpose of this

research is to provide critically evaluated physical and thermodynamic

properties data and accurate original measurements needed to evaluate and

optimize predictive calculation methods. One of the most valuable NBS contributions to date is a comprehensive bibliography of experimental phase equilibrium

data [56] . This report has been revised and expanded and now gives references

to all experimental phase equilibrium, volumetric and calorimetric data available

for fluid mixtures through 1974 [41]. Information is given on the composition,

temperature and pressure ranges investigated for mixtures (mostly binary) ->f

26 molecular species, consisting mainly of the monatomic, diatomic and hydrocarbon

gases. Because of the vast scope of this subject it is extremely important that

additional research be carried out primarily on carefully selected simple

representative systems, which have most of the features of technically important

multicomponent mixtures. We have therefore given high priority to experimental

and analytical research on binary mixtures of the simplest molecular gases. We

are evaluating the available phase equilibrium and volumetric data for carefully

selected binary mixtures, and performing precise liquid-vapor equilibrium and

orthobaric density measurements to fill important data gaps and reconcile

inconsistencies

.

Properties of Mixtures Containing Methane : Representative Results

The evaluation of available phase equilibrium data for compressed and

liquefied gas mixtures has been hampered by the lack of generally accepted

rigorous analytical methods. Several approaches have been explored. One

approach involves the comparison of excess thermodynamic properties data derived

7 L-10
from different kinds of measurements. For example, direct calorimetric

E measurements of the enthalpies of mixing H can be compared with the estimates

E E of H derived from the temperature dependence of the excess Gibbs energies G

(obtained from precise phase equilibrium measurements) and the thermodynamic

relationship

H

E = G

E

- T (dG

E /8T)

p

. (2)

There are, however, very few sets of sufficiently comprehensive and accurate

data, obtained for the same mixtures in similar composition, temperature and

pressure ranges, to make this type of comparison possible. We have analvzed the

available phase equilibrium data for several carefully selected mixtures

containing methane, with typical results shows for methane-nitrogen mixtures

in Figure 5

.

This figure indicates relatively good agreement at temperatures above

110 K and relatively poor agreement below 110 K among data from different

laboratories. There is considerable uncertainty in estimating the temperature

dependence of the excess Gibbs energy fro1? the.ie data. As a result of this

analysis we have performed new high precision liquid-vapor equilibrium composition measurements for this mixture in the temperature range 95 - 120 K [43]

.

Figure 6 shows the excess Gibbs energies derived for equimolar methane-nitrogen

mixtures in this range. The results give an improved estimate of the temperature

E dependence of G , which is in satisfactory agreement with direct calorimetric

measurements [44] . Similar analyses of the data available for other mixtures

containing methane are underway. Paper E-2 at this conference gives additional

details of this work [57]

.

8

L-11
The evaluation of phase equilibrium data is even more difficult at

temperatures above the critical temperature of one of the components, where

direct comparison of the excess thermodynamic functions is not possible. In

this case it is useful to compare Henry's constants, derived from the data

using the definition

H

2 1 = lim (f

2 /x

2 ), (3)

' x

2-M)

where is the vapor phase fugacity of the supercritical component. Figure 7

shows the dependence of the Henry's constants, derived from phase-equilibrium

data for methane-nitrogen mixtures, on temperature in the range 130 - 180 K

[45]. It appears that there are now highly consistent phase equilibrium data

available for methane-nitrogen mixtures throughout the entire temperature

range 95 - 180 K.

The LNG Density Project Steering Committee, a consortium of 13 U.S. and

5 international energy companies initiated a project at the Cryogenics

Division in 1972 on the orthobaric densities of liquefied hydrocarbon gases

and their mixtures. The goal of this project is to obtain accurate (0.1%)

measurements and evaluated calculation methods for the orthobaric densities

of LNG mixtures having arbitrary compositions for custody transfer operations.

Several promising calculation methods of varying complexity are being evaluated

and optimized for this purpose [46, 47, 48]. A magnetic suspension densimeter,

based on Archimedes' principle, has been constructed and thoroughly performance

tested to obtain accurate absolute density measurements on liquefied gases at

temperatures down to 90 K and pressures to 5 MPa. The densities measured

typically range from 0.3 to 1.3 g/cm . Accurate orthobaric density data have

9

L-12
been obtained for liquefied methane, ethane, propane, butanes and nitrogen,

mainly at temperatures between 100 and 150 K, with a typical repeatability of

0.02% and an estimated accuracy better than 0.1%. Preliminary comparisons with

measurements from other laboratories show differences smaller than 0.2% in most

cases. Paper E-6 at this conference gives additional information on the

apparatus and presents results for liquefied normal butane [49] , which are

typical of data for the other components.

Extensive measurements are now being performed on carefully selected and

gravimetrically prepared mixtures of LNG components. The scope of this project

is shown in Table 4. High priority has been given to equimolar binary i -'.xtures

containing methane. Data for the dependences of the densities of the binary

mixtures on both composition and temperature will be obtained to test several

mathematical models and optimize the adjustable coefficients. Data for multicomponent mixtures will be obtained to evaluate the accuracy of the optimized

calculation methods and to discriminate between the models.

Discussion

Thermophysical properties data research at the NBS Cryogenics Division is

currently concentrated on obtaining comprehensive accurate data and predictive

calculation methods for compressed and liquefied hydrocarbon gases and their

mixtures. This report summarizes important NBS contribution on the thermophysical properties of methane and binary mixtures containing methane, and

discusses typical current and planned projects. Table 5 summarizes some

additional NBS contributions expected through 1977, and suggests that emphasis

on liquefied hydrocarbon gases will likely continue through the rest of the

10

L-13
seventies. It is hoped that the systematic approach being taken to the phase

equilibrium properties and the orthobaric liquid densities will soon be extended

to include the equation of state, thermodynamic and transport properties of

several carefully selected simple representative liquefied gas mixtures.

Acknowledgments

The contributions of all members of the Properties of Cryogenic Fluids

Section, the Cryogenic Data Center, and of various university groups, especially

at Rice University and the University of Michigan, are gratefully acknowledged.

L-14

11
References

R. D. McCarty, J. Phys . and Chem. Ref Data 2_, 923 (1973).

R. D. McCarty, "Thermophysical Properties of Helium-4 from 2 to 1500 K

with Pressures to 1000 Atmospheres," NBS Tech. Note 631 (1972).

H. J. M. Hanley and G . E. Childs, Cryogenics 9_, 106 (1969).

W. G. Steward and G. H. Wallace, unpublished data (1971).

R. D. Goodwin, J. Res. NBS 73A, 585 (1969).

H. M. Roder, L. A. Weber, and R. D. Goodwin, "Thermodynamic and Related

Properties of Parahydrogen from the Triple Point to 100 K at Pressures

to 340 Atm," NBS Monograph 74 (1965).

H. M. Roder and R. D. McCarty, "Modified Benedict-Webb-Rubin Equation of

State for Parahydrogen II," NBSIR 75- 814(1975).

R. D. McCarty and L. A. Weber, "Thermophysical Properties of Hydrogen from

the Freezing Liquid Line to 5000 R for Pressures to 10,000 PSIA,"

NBS Tech. Note 617 (1972).

L. A. Weber, "Thermodynamic and Related Properties of Parahydrogen from

the Triple Point to 300 K at Pressures to 1000 Bar," NBSIR 74-374/

NASA SP-3088 (1974)

.

10. R. D. McCarty,

Properties

"ASRDI

, NASA

Hydrogen Technology Survey

SP-3089 (1975).

, Volume I:

11. J. W. Stewart, , J. Chem. Phys. 40,3297 (1964)

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13. D. E. Diller, J . Chem. Phys. 42_, 2089 (1965)

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.

15. R. T. Jacobsen, R. B. Stewart, R. D. McCarty , H. J. M. Hanley

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H. J. M. Hanley, R. D. McCarty and W. M. Haynes , J. Phys. Chem. Ref. Data _3- 979 (1974).

12

L-15
18. L.

19. R.

20. H.

21. B.

22. W.

23. A

24. w.

25. R.

i.\3 . c

U1 1 •

zo

.

T.T

JU . K.

ji . K.

**9 K.

JJ . nD .

34. G.

35. G.

36. R.

37. G.

38. J.

L. A. Weber, J. Res. NBS 74A, 93 (1970)

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.

W. M. Haynes, Physica 67, 440 (1973).

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and Liquid Fluorine," NBS Tech. Note 392 (revised), (1973).

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13

L-16
39. W. M. Haynes, Physica 70_, 410 (1973).

40. H. J. M. Hanley, R. D. McCarty and W. M. Haynes, Cryogenics (in press, 1975).

41. M. J. Hiza, A. J. Kidnay and R. C. Miller, Equilibrium Properties of Fluid

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42. A. G. Duncan and M. J. Hiza, Ind. and Eng. Chem. Fund. 11_, 38 (1972).

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46. M. A. Albright, Technical Publication No. 3, A Report to the GPA , Tulsa, OK (1973)

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48. J. Mollerup and J. S. Rowlinson, Chemical Engineering Science 29_, 1373 (1974).

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,

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14

L-17
58. R. L. Amey and R. H. Cole, J. Chem. Phys . 40, 146 (1964).

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.

62. R. Stryjek, P. Chappelear and R. Kobayashi, J. Chem. Eng. Data

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15

L-18
List of Symbols

C Specific heat at fixed volume, J/mol • K

v

Cp Specific heat at fixed pressure, J/mol • K

3

C-M Clausius-Mossotti function, V(e-l) / (e+2) , cm /mol

2 X Thermal diffusivity coefficient, X/p C^, cm /s

£ Dielectric constant

f_^ Fugacity of component i, Pa

Excess Gibbs energy, J/mol

Specific heat ratio, C /C

p v Excess enthalpy (heat of mixing), J/mol

H„

1 Henry's constant, Pa

z , J. 2 2 3

L-L Lorentz-Lorenz function V(n^-l) / (n^+2) , cm /mol

X Thermal conductivity coefficient, W/m K

n^ Refractive index at wave length X

p Density, mol/£

p^ Critical density, mol/£

T Temperature, K

T Triple point temperature, K

T, Normal boiling point temperature, K

bp

T^ Critical temperature, K

3

V Specific volume, cm /mol

W

g

Sound velocity, m/s

x. Mole fraction of component i

16

L-19
Table 1. Selected NBS Publications on the Thermophysical Properties of Compressed

and Liquefied Monatomic and Diatomic Gases.

HELIUM HYDROGEN NITROGEN OXYGEN FLUORINE ARGON

Equation of state (PVT) 1 5,7 15 18 25 23

Thermodynamic properties 2 6,8,9 15 18,19,20 25 23

Electromagnetic properties 2 8,11,12 16 19,20,21 26

Transport properties 3,4 13,14 17 19,20,22 27,28 24

The numbers refer to the reports and publications given in References

.

L-20

• 17
m co <t sO in

• • • • • • • • o CM m o os co m os o OS 00 o sO rH o CM sO H rH CM CO cn CO St St st st

a

Xi

st

PCo

sO OS

SO

CMst

coCO

OS

CO

CMCO

I--- st m iH OS St o • • • • • rH os st m rH sO rH CM OS

rH sO oo CM CO sO sO o rH i-t rH CM CM CM CM CM CO

OS. OS OS m 00 sO 00 st

A • • • • • • • • 4J o CO OS m CO st CO H OS orH 00 00 00 00 iH

iH CO

rH 3

CO St o rH 00 st St rH st m 00 OS o CM CM uo o o o o o rH rH rH rH

• • • • • • • SO 00 d CM st sO ao oo CM

rH CM CO st st m m m

o o CM

st so sO 00 00 rH rH rH

as 33 S3 33 S3 S3 S3 S3 CM CM CO CO st st st m

U CJ u u u U O CJ

01

cu C3 0)

CU c 0) CU

C3 cu cu rH c s

03 rH c >s cd u

.C >s CO O. o. 0

4J J3 O o x>

a) 4J 4J M u 1 e 0> 01 a Cu rH

cd9

Xio

0) 3

CU%U

c

atcu

ic

18

L-21
Table 3. Selected NBS Publications on the Thermophysical Properties of Methane.

^ Equation of State

R. D. Goodwin, J. Res. NBS 79A , 71 (1975)

R. D. McCarty, Cryogenics 14, 276 (1974)

Specific Heats

B. A. Younglove, J. Res. NBS 78A, 401 (1974)

Sound Velocities

G. C. Straty, Cryogenics 14, 367 (1974)

M Thermodynamic Functions

R. D. Goodwin et al. , NBS Tech. Note 653 (1974)

"¥ Dielectric Constants

G. C. Straty & R. D. Goodwin, Cryogenics 13, 712 (1973)

Refractive Indices

J. D. Olson, J.Chero. Phys . (in press, 1975)

Transport Properties

H. J. M. Hanley et al., Cryogenics (in press, 1975)

W. M. Haynes, Physica 70, 410 (1973)

19

L-22
Table 4. LNG Density Project: Scope of Work

•^t Pure Components

methane isobutane

ethane n-butane

propane nitrogen

Binary Mixtures

methane-ethane

methane-propane

methane- isobutane

methane-n-butane

methane-nitrogen

^f 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

ethane-propane

ethane- isobutane

ethane-n-butane

ethane-nitrogen

propane-isobutane

propane-n-butane

propane-nitrogen

20

L-23
Table 5. Expected NBS Publications on the Thermophysical Properties of

Compressed and Liquefied Hydrocarbon Gases and Their Mixtures

Refractive Indices of Methane (1975)

Hypersonic Velocities in Methane (1975)

Thermal Diffusivity Coefficients for Methane (1977)

+t Equation of State (PVT) for Ethane (1976)

Dielectric Constants of Ethane (1976)

Specific Heats of Ethane (1977)

Thermodynamic Properties of Ethane (1977)

Bibliography - Equilibrium Properties Data for Fluid

Mixtures (1975)

Liquid-Vapor Equilibrium Data for Methane-Nitrogen

Mixtures (1975)

Liquid-Vapor Equilibrium Data for Methane-Ethane

Mixtures (1977)

Magnetic Densimeter for Liquefied Gases and Their

Mixtures (1976)

•fc Densities of LNG Components (1976)

•^t Densities of Mixtures of LNG Components (1976)

«{( Accurate Calculation Methods for LNG Densities (1977)

21

L-24
Figure Captions

Figure 1. Clausius-Mossotti function for saturated and compressed fluid

methane

.

O 220 K; X 250 K; A 280 K; 300 K; • saturated and compressed

liquid as indicated; and - - - from reference [58];

O estimated C-M at the critical density.

Figure 2 . Lorentz-Lorenz function for saturated and compressed fluid

methane

.

O 300 K; 280 K; V 250 K; A 220 K; • saturated liquid;

saturated vapor; Ar is the estimated zero density

limit at 300 K; O estimated L-L at the critical density.

Figure 3. Sound velocities in saturated and compressed fluid methane.

X - hypersonic (light scattering velocities; • O ultrasonic velocities;

- - - estimated thermodynamic sound velocities.

T Figure 4. Excess thermal conductivity coefficient (AX = X^p + AX' + AX

c

) for compressed gaseous methane.

• 235 K [59]; O 200 K [59]; 200 K [60]; calculated [40].

Figure 5. Excess Gibbs energies for equimolar methane-nitrogen mixtures

obtained in different laboratories. The key to the symbols is

given on the figure.

Figure 6. Excess Gibbs energies for equimolar methane-nitrogen mixtures. • O [43]; A A [61]; — calculated from modified hard-sphere

equation of state with >i.035.

Figure 7. Henry's constants for methane-nitrogen mixtures in the

temperature range 130 - 180 K.

O [45]; [62]; A [63].

L-25
L-26
L-27
s/w 4 A±I0013A ONHOS

L-28
L-29
300

Cole, from Snider- Herrington, k )2 = 0.035

• o Miller, Kidnay, and Hiza(l973)

Cines, Roach, Hogan, and Roland (1953)

a a Sprow and Prausnitz (1966)

O Stryjek, Chappelear, and K'bayashi (1972)

v Chang and Lu (1967)

* Fastovskii and Petrovskii (1957)

o Fuks and Bellemans (1967)

(Open symbols from Barker's Method

)

200

o

E o

3

9

b

nx

UJ 100

40

•40 L

100 110

TEMPERATURE, K

120

Figure 5

Ifl- 1U7S92

L-30
Calc. from Snider - Herrington, k )2 = 0.035

• o This investigation

a a Miller, Kidnay and Hiza (1973)

(Open symbols from Barker's Method)

300

2001 - . — - - o

100

90 100 110 120

TEMPERATURE, K

Figure 6

L-31
N

2 CH

4

5.0 5.0

4.5 o 4.5

5<0

Xo

CM a

4.0 4.0

O This Investigation

Stryjek, Chappelear, Kobayashi

A Cines, Roach, Hogan, Roland

3.5 3.5

3.0

0.5 0.6 0.7

(10°), K

-i

0.8

3.0

Figure 7

L-32

\7iX lt.S> J
APPENDIX M

I

!

M-l
An equation is proposed to calculate the viscosity and thermal conductivity coefficients of methane from the dilute gas to the dense liquid. The range of validity of the equation

is approximately 95—400 K for pressures up to 50 MPa (~*500 atm). The reliabilities of

the coefficients calculated are estimated at approximately 2% and 5% for the viscosity

and thermal conductivity coefficients, respectively. The equation includes a contribution

for the thermal conductivity enhancement in the critical region.

Equations for the viscosity and thermal conductivity

coefficients of methane

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

This laboratory has reported results for the thermodynamic

properties. 1 the equation of state, 1,2 and the viscosity coefficient 3 of methane. In this paper we extend this work

by discussing briefly a correlation of the viscosity and ther- mal conductivity coefficient from the dilute gas to the dense liquid. Some details of the correlation are presented

here but a discussion of the critical evaluation of the data with extensive tables will be published elsewhere.4 Interest

in methane both as a pure fluid and as the major component of liquefied natural gas is extensive and it seemed worthwhile to summarize our results at this time.

In a previous paper 5 we presented an evaluation and correlation of the transport properties of several simple fluids - argon, krypton, xenon, nitrogen and oxygen — and this work is a straightforward extension of that study to methane. Several points, in particular, were discussed in our pre- vious publication. For example: (a) the general behaviour

of the viscosity and thermal conductivity coefficients as a function of density and temperature was outlined 6

; (b) criteria for the evaluation and selection of data were

established; (c) the behaviour of the thermal conductivity

coefficient in the critical region was discussed; and (d) an

equation was proposed to represent both viscosity and

thermal conductivity data over a wide range of experimental

conditions. It appears that this equation is general, that is, the form is independent of the structure of the fluid considered.

It was further emphasized in our previous paper that a proper correlation of the transport coefficients appears possible only in terms of density-temperature coordinates

even though the practical variables are temperature and

pressure. An accurate equation of state, therefore, is central to our programme. The equation of state used here is the BWR of McCarty, described in reference 2.

Correlating equations

We consider the viscosity coefficient, 77, for methane to be

given by the expression found suitable for other simple

fluids, 5

7?(p, T) = vQ(T) + t?, (T)p + At)'( P, T) 0)

The authors are with the Cryogenics Division, National Bureau of Standards, Boulder, Colorado 80302, USA. HJMH is supported by

the Office of Standard Reference Data (US). Received 10 March

1975.

where p is the density and T is the temperature. Similarly,

for the thermal conductivity coefficient, A

Up, T) = A0 (7) + A,(r)p + AX'(p, T) + AAt (p, T) (2)

In these equations, tj 0 and A0are dilute gas coefficients;

17] and A] represent first density correction terms 7

; while

At?' and AA' are remainders. Note that (2) differs from (1

)

only by the inclusion of the term AAc (p, T) to take into account the known enhancement of the thermal conductivity coefficient in the region of the critical point (see Appendix C). The dilute gas coefficients for methane were calculated from kinetic theory 8 (Appendix B). The terms tj, and

A, were represented by an empirical relation 5

(

f - ,o4) 77, (7*) or A] (71 = A +B[ C - log,

and At? and AA were also represented empirically 5

po-ij h +

and

1.0

(3)

Ar?'(p, T) = t e\p [/, +/4/T] < exp h_

f3/2

If, h

+ Op 05

is + ~ + T T

2

AA'(p, T) = D exp [A:, + kjT] C exp

k6 ; kn

p°> k 2 +

+ 0p°' 5 ^ 5 + T T

2

(4)

7-3/2

(5)

The parameter 9 is included to account specifically for the high density behaviour of the transport coefficients and is a function of the critical density, pc

_(P ~Pc)

(6)

CRYOGENICS . JULY 1975 M-2 413
The parameters in (3)—(5) were estimated for methane by

the least squares analysis procedure discussed in our pre- vious paper, using selected data listed in Table 1 . Values of

the parameters determined are listed in Table 2. As noted. 5 however, thermal conductivity data close to the critical point was excluded from the fit: rather the contribution to

Table 1 . Data sources

Estimated Experimental range accuracy

Viscosity

Haynes3

Kestin and

Leidenfrost9

Giddings et al 10

Barua et al 11

Saturated liquid 95-190 K -296 K

Pressures to 1 5 MPa

283-410 K

Pressures to 54 MPa 223^23 K

Pressures to 17 MPa

Thermal conductivity Le Neindre 12 298-723 K

Pressures to 100 MPa

Mani 13 139-400 K

Pressures to 60 VPa

Ikenberry and

Rice 14 98 - 235 KPressures to 50 MPa

2

:

:

1%

2%

2%

4%

3%

5

1

:

Table 2. Parameters for equations 3—5

Viscosity

Equation 3

Equation 4

A 1.696985927

8 = -0.133372346

C 1.4 F = 168.0 E 1.0 h = -1.035060586 x 101 h 1.7571599671 x 101 h = -3.0193918656 x 103 u 1.887301 1594 x 102

is 4.2903609488x 10-2

ie 1.4529023444 x 102

:- 6.1276818706 x 103

Thermal conductivity

Equation 3 A = B

C

F

Z

*4

k-,

-0.25276292

0.33432859

1.12 168.0

1.0 -7.0403639907

12.319512908

-8.8525979933 x 102 72.835897919

0.74421462902

-2.9706914540

2.22097585G1 x 103

fhe units are as follows: density in g cm , temperature in K, viscosity

the enhancement. A\., was obtained by the calculation outlined in Appendix C.

Comparisons and discussion

Representative comparisons between experimental data and

equivalent values calculated from (1) or (2) are given in Figs l^k

These figures illustrate that we have been able to fit the data to within their estimated experimental accuracies. We

observed only one instance where we feel our equation

deviates systematically from experiment, namely the cal- culated viscosity coefficient appears too low close to the

critical point. Although it is possible that experimental

error and/or incorrect density values contribute to the

deviation, it is also possible that the deviation is the result of a small enhancement in the viscosity close to the critical point 19 which is not included in the correlating equation. This feature was also observed in our previous work.

Use of the equations. The equations should not be used to

calculate transport coefficients beyond the range of the

fitted data which is (viscosity) between 95 and 423 K for pressures up to 54 MPa and (thermal conductivity) between

99 and 725 K for pressures up to 100 MPa with the additional restriction that the density under consideration should not exceed about 2.7 pc

. Within these limits, we

Saturated liquid viscosity

• =e ; 3

020 030 035

Densrty,g cm"3

Fig.1 Deviations between calculated and experimental viscosities of the saturated liquid; data from Haynes.3 % is defined as

( "exp - icalc' x 100 ^exp

1 -

in tig cm' 1 s , thermal conductivity in MW m"' K"

OIO Q15

Density, g cm~3

Fig. 2 Deviations between calculated viscosities at 344 K and

experimental values from reference 10

025

414 v_ 3 CRYOGENICS . JULY 1975
4

-

2 -

Thermol conductivity, 160 K

•(Ref 13)

034 036 038 040

Density, gcm~3 042

Fig.3 Deviations between calculated thermal conductivities and

experimental values from reference 13 at 160 K

2 -„

Thermal conductivity, 725 5 K

• (Ref 12)

0 05 0I0 0I5 020 025

Density, g cm"3

Fig.4 Deviations between calculated thermal conductivities at 725.5 K and experimental values from reference 12

Table 3. Calculated transport properties for the saturated

liquid

Thermal

estimate that the calculated viscosity coefficient has an

uncertainty of ±2% and the thermal conductivity an uncertainty of 5%, except in the critical region where the uncertainty is ±20%.

Saturated liquid values. For convenience, we drew up

Table 3 which presents calculated values at the saturated

liquid boundary.

Conclusion

An equation to represent selected viscosity and thermal

conductivity data of methane from the dilute gas to the dense liquid has been proposed. We note that the equation

is identical in form for both transport coefficients (excluding the critical point enhancement for the thermal conductivity coefficient). We also note that the equation

appears to be general in that it was used in our previous

work with other simple fluids. 20 It is apparent that additional accurate data are required before the correlation can be improved significantly. Regions for which additional data are required include the dilute gas and vicinity of the

critical point for the thermal conductivity coefficient, and

the low temperature, high pressure region for the viscosity coefficient.

References

Temperature, Density, Viscosity, conductivity,

10 K mole I' 1 /ig cm' 1 s'

1 MW nrf 1 K" 1

95 27.789 1792 215

1

1

100 27.367 1563 206 12 105 26.934 1377 197 110 26.491 1223 189 115 26.035 1094 181 120 25.566 984 173

125 25.081 889 165 13 130 24.578 807 158

135 24.055 734 150

14 140 23.508 669 143 15 145 22.932 611 136

150 22.322 558 129 16 155 21.672 509 122 17 160 20.971 464 115 18 165 20.206 421 108 19 170 19.356 380 101

20 175 18.386 340 94

180 17.226 300 88

185 15.690 256 84

190 12.485 187 89

21

Goodwin, R. D. NBS Tech Note No 653 (1974) and

references therein: Straty, G. C. Cryogenics 14 (1974) 367

McCarty, R. D. Cryogenics 14 (1974) 276

Haynes, W. M. Physica 70 (1973) 410

Haynes, W. M., McCarty R. D., Hartley, H. J. M. J Phys Chem

Ref Data (in preparation); detailed tables are available from

the Cryogenics Division, NBS, Boulder, Colorado

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

Chem Ref Data 3 (1974) 979

Diller, D. E., Hanley, H. J. M., Roder, H. M. Cryogenics 4 (1970) 286

Hanley, H. J. M., McCarty, R. D., Sengers, J. V. J Chem Phys

50(1969) 858

Hanley, H. J. M., Klein, M. J Phys Chem 76 (1972) 1743

Kestin, J., Leidenfrost, W. Thermodynamic and Transport

Properties of Gases, Liquids and Solids ( ASME, McGraw-Hill, NY, (1959) 321

Giddings, J. G., Kao, J. T. F., Kobayashi, R. J Chem Phys 45 (1966) 758

Barua, A. K., Afzal, M., Flynn, G. P., Ross, J. J Chem Phys

41 (1964) 374

Le Neindre, B. 'Contribution a I'etude Experimentale de la Conductivite Thermique de Queleques f luides a Haute Temperature et a Haute Pression' Ph D Thesis, Paris (1969): Le Neindre, B., Tufeu, R., Bury, P. Thermal Conductivity

(Proc 8th Conf, Lafayette, Ind) (Plenum Press, New York, 1969) 229

Mani, N. 'Precise determination of the thermal conducticity

of fluids using the absolute transient hot-wire technique', Ph D thesis, Univ of Calgary (19-71) Ikenberry, L. D., Rice, S. A. J Chem Phys 39 ( 1 963) 1 561

Hanley, H. J. M., McCarty, R. D., Sengers, J. V. NASA

Contractor Rept NASA CR-2440 ( 1974)

Vincentini-Missoni, M., Levelt Sengers, J. M. H., Green, M. S. J Res NBS 73A (1969) 563 Widom, B. J Chem Pin s 43 (1965) 3898

Sengers, J. V. NASA Contractor Rept NASA CR-21 12 (1972) Strumpf, H. J., Collings, A. F., Pings, C. i. J Chem Phvs 60

(1974) 3109 Our equation for the thermal conductivity in reference 5 did not include terms proportional to 0, unlike (5) in this paper. Such a contribution appeared unnecessary since the scatter

in the data used in reference 5 did not allow us to return

significance in more than 3 of the k\ coefficients Olson, J. D. J Chem Pin s (in press, 1975)

CRYOGENICS. JULY 1975 „ . 415

M-4
Appendix A

Fixed point parameters for methane 1

• 2 - 21 Tc = 190.55 K pc = 10.15 mole l"

1 Pc = 45.387 aim (4.5988 MPa)

7", = 90.68 K p, = 28.147 mole l"

1

/>

t = 0.1 1590 atm (0.11744 MPa)

Molecular weight = 16.043 The subscripts c and t refer to the critical point and triple point respectively.

Appendix B

Dilute gas transport coefficients The dilute gas transport coefficients were calculated using

the standard kinetic theory expressions with the m-6-&

potential function of Hanley and Klein 8

Table 4. Dilute gas parameters

1 1 [6 + 2y] (d/r*y»

m — 6 m — 6

-T{m - 8)] (d/r*r - y(d/r*)* (7)

where d = rm/o and r* = r/o. The distance parameters a

and rm , and the energy parameter, e, are defined by the

relationships 4Krrn) = — e and ®(o) = 0 while 7 is a par- ameter representing inverse eighth attraction in the potential. We have previously reported 8 that for methane

GV[\\ == -2.090975 X 105 GV(2) = 2.647269 X 10 5 GV(3) =: -1.472818 X 10 5 GV(4) = 4.716740 X 10 4 —y .^y 1

0

1

1

X 1I n3u GV{6) = 1.219979 x 10 3 GV[7) = -9.627993 x 10 1 GV(8] = 4.274152 GV{9] = -8.141531 x 10 -2

G7"(1) = -2.147621 X 10 s

G7"(2) = 2.190461 X 105

G7~(3) = -8.618097 X 1 o

4

G7"(4) = 1.496099 X 104

G7"(5) = -4.730660 X 10 2 G7(6) = -2.331178 X 10 2

G7"(7) = 3.778439 X 10 1 GT{8) = -2.320481

Groi = 5.31 1764 x 10" 2

The units are: temperature in K, viscosity in Mg cm s , and

thermal conductivity in MW m K~

where -^.-(p, T) is the enhancement as a function of

density and temperature. According to Hanley. McCarty, and Senaers s> 1S

- = 168.0 K; a = 3.68 x 10" 10 m: k

rm =4.101 x 10" 10 m:7 = 3.0:m = 11 (8)

where k is Boltzman"s constant. For computational convenience we fitted the calculated

Tj 0 and Xq to a polynomial in temperature

T? 0 =GK(l)r' +GK(2)r2 / 3 +GK(3)r 1 / 3

+ GK(4) + GV{S)T 1 ' 2 + GV(6)T2 V + GV(1)T

+ GF(8)7"4/3 + G V(9)T5 /3 (9

)

and similarly for Xq but with coefficients G1\i) (/" = 1 . 9)

replacing GV(i) in (9). Values of the coefficients for (9)

are listed in Table 4.

AMp, 7*) / -V/ pXkT

kT2 f'dP^ 1

6-rR 1 37"

in

x exp y- 18.66 ST2 j

exp ^-4.25 Ap4

where Kt=\T- Tc \/Tc ;Ap = lp - pc|/pc

(10)

(11)

with Tc and pc the critical temperature and density, re- spectively. In (10). k is Boltzmann*s constant. A is Avogadro's number. A' T = p" 1 [bp dP) T (the compressibility ). and R is a length parameter (cm) given b> the relation 1

5

for methane

1/2

- - - I '-

I x 10" 6 (12)

Appendix C

Calculation of the thermal conductivity enhancement in the critical region

It is convenient to treat the enhancement of the thermal

conductivity coefficient in the region of the critical point

separately and we have written already

X(p, T) = Xo(f) + X, (7> + AX'fp, T)

+ AXc (p, T) (2)

given p in g cm' 3 and Tin kelvin. With the viscosity of (1) and values of (bP dT) 2 and A' T from the equation of state, one could determine AXt but. unfortunately, the calculation would not necessarily be

sufficient: it is known that an analytical equation of state, such as the equation used here, cannot accurately repre- sent the PpT surface very close to the critical point. It is felt, in particular, that the value of Ay from the equation

of state is too small. Hanley, McCarty. and Haynes, 5 however, proposed a procedure to partially resolve this problem: for methane AXC

is calculated from (10) using

416 M-5 CRYOGENICS . JULY 1975
and

Fig. 5 Plot of the thermal conductivity, less the dilute gas value, A\T , versus density for two isotherms. We define A\T by the

relation

A\T = Mp, T) - \0 [T)

where Mp, 7") is given by (2). The critical point contribution from

(2) is indicated by the dashed curves

• — reference 14 at 235 K; o — reference 14 at 200 K; — reference 13 at 200 K

A' Tvalues from reference 2 unless AT < 0.025; Ap < 0.25 (13)

If these conditions are encountered, KT is calculated from

the scaling law equation proposed by Vicentini-Missoni,

Levelt Sengers, and Green 16 and by Widom. 17 - 18 Their equation is

[p*2 A'f]" 1 = |Ap| 6-1 8h(x) -

x dh(x) dx

where

p* = p/pc ; X = AT/Ap 1 /*3

; Kj = PC KT

h(x) = Ei X + Xr

1 + E- x + x

(14)

(15)

2/3-1 (V-D/20

(16)

dh(x) _EX dx x0 y'-l

1 +EX +Xr

X + Xr x0

2/3'

2(3

(V-l)/2(3

1 +En

X + X

*0

2/3 "I (7 - 1 - 2/3)/2|3 (17)

values for Tc and Pc are listed in Appendix A. We chose

(based on our work with oxygen) the following values for the other parameters of (14)—( 17)

*o = 0.1892;j3 = 0.35;5 =4.30;£'1 = 2.058;

E2 =0.30; -y' = 1.155

Since data in the critical region are scarce for methane, we

cannot present any extensive comparisons between experi- ment and calculated conductivities from (10) but the total thermal conductivity, less the corresponding dilute gas

value, is plotted as a function of density for two isotherms

in Fig.5. The solid curve represents the conductivity in the absence of any critical point enhancement while the dotted

curves are obtained by adding the values for AXc (p, T) from (10). Data in the figure were extracted from Mani 13 and from Ikenberry and Rice. 14

Appendix D

Conversion factors

T, K to T, °F: multiply by (9/5) then subtract 459.67

T, K to T,°C: subtract 273.15

T, K to T, °R: multiply by (9/5)

P, MPa to P, bars; multiply by 10

P, MPa to P, atm: multiply by (1 0/1 .01 325)

P, MPa to P, lb in" 2

: multiply by (146.9595/

1.01325)

to 7?, Pa s: multiply by 10"'

to rj, lb ft

-1 s"

1

: multiply by 0.0671969

A, Win" 1 K" 1 to Veal cm"1 s"

1 K" 1

: multiply by 1/418.4

A, Win" 1 K" 1 to A, Btu ft' 1 h" 1 °R"' : multiply by 0.5781 76

77, g cm" 1 s"

1

tj, g cm" 1 s"

1

CRYOGENICS . JULY 1975

M-6

417
APPENDIX N

N-l
EVALUATION OF CAPACITANCE DENSITOMETRY BY EXAMINATION OF THE RELATIONSHIPS

BETWEEN DENSITY, DIELECTRIC CONSTANT, PRESSURE AND TEMPERATURE FOR LNG MIXTURES

P. J. Giarratano and R. S. Collier

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Prepared for

The Maritime Administration

Washington, DC 20236

January 1 , 1976

N-2
EVALUATION OF CAPACITANCE DENSITOMETRY BY EXAMINATION OF THE RELATIONSHIPS

BETWEEN DENSITY, DIELECTRIC CONSTANT, PRESSURE AND TEMPERATURE FOR LNG MIXTURES

P. J. Giarratano and R. S. Collier

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

Densities of typical LNG mixtures under saturation and subcooled

conditions were calculated by means of the MSllerup equation of state;

the corresponding density-dielectric constant relationship was determined from the CI ausius-Mosotti relationship for the mixture using

ideal mixing rules for the 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, it is

shown that the linear relationship is not a segment of the Clausiusmosotti function, but results from the more fundamental thermodynamic

properties of the mixture. Also, the nitrogen composition of the

mixture is predicted to have a pronounced effect on the saturation

density versus dielectric constant, the increase in nitrogen causes

an increase in saturation density for the same dielectric constant.

There is also a substantial decrease in the saturation temperature

with an increasing nitrogen content. For the normal range of mixtures, it is possible to determine the density to + 0.3% independent

of a knowledge of the composition from an exact measurement of

dielectric constant and temperature. Further improvements can be

made if the exact composition of the mixture is known.

Keywords: Clausius-Mosotti ; densitometer (capacitance); density;

dielectric constant; LNG; mixture(s).

N-3
1. Introduction

In response to a request from the U. S. shipbuilding industry, NBS is con- ducting an independent design review of the shipboard liquefied natural gas (LNG)

custody transfer systems under the sponsorship of the Maritime Administration

(MARAD) and in cooperation with the major U. S. shipbuilding companies.

Since the basis for sale of LNG is the total energy content of the LNG

delivered, the ability for accurate determination of the total mass is of con- siderable importance because the specific heating value is usually measured

independently. The total mass may be obtained from a measurement of density of

the LNG and the volume of liquid in the storage tank, thus the need for accurate

and reliable determination of these quantities.

Two possible alternatives for obtaining density are:

(a) Prediction from measurements of temperature, pressure, and

composition using an equation of state for LNG mixtures,

e.g., reference [1]. Accuracies of approximately + 0.1% may

be expected from such predictions if measurements of temperature, pressure, and composition are known exactly. [1] Inaccuracies in the measurement of temperature and composition cause increased inaccuracies in the determination of the density.

(b) Direct measurement of a physical property such as dielectric

constant or refractive index which is related to the density

(e.g., the Clausius-Mosotti function or Lorentz-Lorenz function

respectively)

.

The custody transfer system design under review incorporates a densitometer

utilizing the measurement of dielectric constant and the Clausius-Mosotti

relation as the primary input for determination of density. This relation is:

£-1

P, (2) mix CM. e+2 mix

where

e = dielectric constant

CMmix

= Clausius-Mosotti function for the mixture.

N-4
Therefore, in this report we have investigated the relationship between density

and dielectric constant for a range of LNG mixtures and the resulting possible

uncertainties in the density determination due to variation in composition.

At this stage we have not considered any heat transfer effects on density,

any of the variables affecting the determination of total volume, nor electronic

signal conditioning of the measured quantities.

2. Definitions and Range of Variables

2.1 Range of composition

In this report normal composition vange is defined as follows:

Table 1. Normal LNG composition

Component Mole Fraction x.

Methane (CH

4

) 0.8577 - 0.97

Ethane (C

2 H

6

) 0.03 - 0.09

Propane (C

3

Hg) 0.0 - 0.03

Butanes (iC

4

H ]0

+ nC

4

H 1Q ) 0.0 - 0.01

Pentane (C

5

H 12 ) 0.0 - 0.0023

Nitrogen (N

2

) 0.0 - 0.014

These are typical of the composition make-up found in LNG from the Algerian

fields. 336 different mixtures within the range given by table 1 were calculated. The various mixtures were obtained by the following procedure.

Each component was assumed to have the possible mole fraction values of:

Mole Fraction

Component Possible Values x. No. of Values

C

2

H 6 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09 7

C 3Hg

0.0, 0.01, 0.02, 0.03 4

C4H 1Q

0.0, 0.01 2

C

5 H 12 0.0, 0.0023 2

N

2 0.0, 0.007, 0.014 3

2

N-5
Then x rH = 1 . - (x r

„ + x

r

„ + x r u + x r u + xM ).

For x M

= 0.0, 0.007, and 0.014 all possible combinations of the above were

n

2

determined, (i .e. , 7 x 4 x 2 x 2 = 1 12 different mixtures for each of x^ = 0.0,

0.007, and 0.014).

2

The assumed limits for LNG containing more of the heavier hydrocarbons are:

Table 2. Typical Libyan LNG compositions

Component Mole Fraction x.

Methane (CHj 0.62 - 0.87

Ethane (C

2 H6

) 0.08 - 0.24

Propane (C

3

Hg

) 0.04 - 0.10

Butanes (iC

4

H

1

Q

+ nC

4

H 1Q ) 0.01 - 0.02

Pentane (C

5 H 12 ) 0.0 - 0.01

Nitrogen (nJ 0.0 - 0.01

The above limits on composition are somewhat arbitrary but typify

Libyan composition LNG as given in reference [2].

Various mixtures within the Libyan composition limits were obtained by

the same procedure given for the normal composition. The assumed values were:

Mole Fraction

Component Possible Values x^ No. of Values

C

2 H

6 0.08, 0.12, 0.16, 0.20, 0.24 5

C

3 Hg 0.04, 0.06, 0.08, 0.10 4

C

4

H 1Q 0.01, 0.02 2

C

5 H ]2 0.0, 0.01 2

N

2 0.0, 0.01 2

i.e., 80 different mixtures for each of x^ =0.0 and x^ ~ 0.01.

3

N-6
2.2 Clausius-Mosotti Functions

The Clausius-Mosotti function for a mixture of LNG is given rigorously by:

CMmix

=

I

x

i CMi + CM

E (xi'

T ' P) (3)

where

1

CM^ = Clausius-Mosotti function for each of the

pure components

CM^ = Excess CM function, which is the change in CM

on mixing at fixed temperature and pressure.

Diller [3] estimates CM

£ to be less than +1% of CMmix for ordinary mixtures

of LNG with high concentrations of methane. Pan, et al . [4] experimentally

determined values of CM^ less than + 0.1% of the mixture CM values for the binary

and ternary mixtures of their investigation. Therefore in this study we define

CM_mix

=

I x

i CM

i (4)

with the CM. values used given in table 3. These values were taken from

Pan, et al. reference [4] and assumed to be constant since the CM^ are nearly

independent of temperature and pressure [3 and 4].

Table 3. CM^ values for LNG components

Component CM^ (cm /mole)

CH

4

6.548

C

2 Hg

11.072

C

3H8

16.406

C4H 1Q

* 20.88

C

5 H ]2 ** 25.25

N

2 4.394

***

Average of nC^H-jg and iC^H^

Determined by extrapolation of the remaining hydrocarbons CM

i

4

M-7
It is apparent that within the normal composition limits a maximum density

exists when the maximum amount of the heavier components are present and a minimum density exists when a minimum amount of the heavier components are present,

The corresponding CMmax density

and CMmin den$ity are (in units of m

3 /kg):

Ex. CM.

CMmax density Ex^ MW^

where MW^ = molecular weight of component i.

CM = max density

(N

2 =0%)

"

( 0 . 8677 ) ( 6 . 548 )+ ( 0 . 09 ) ( 11 . 072 )+ ( 0 . 03 ) ( 1 6 .406.)+ ( 0.01) (20 .88 }+ ( 0

.

0023) (25.25 ) (0.8677)(16.04)+(0.09)(30.07)+(0.03)(44.09)+(0.01 )(58.12)+(0.0023)(72.15)

- 0.398 cm

3 /g = 3.98 x 10" 4 m

3

/kg.

Similarly,

CM = mm density

(N

2 =0%)

*

(0. 97) (6. 548)+( . 03) (1 1 .072) n . n

, 3, _ A nc w ln -4 3,.

(.97)(l6.04)+(.03)(30.07) " °' 406 Cm /g ~ 4 ' 06 X 10 m /kg '

Further, if we know only the range of N

2 composition, i.e., 0-1.4% then:

CMmax density

(0.8534)(6.548)+(.09)(11.072)+(.03)(16.406)+(.01 )(20.88)+(.0023)(25.25)+(.014)(4.394)

(0.8537)(16.04)+(.09)(30.07)+(.03)(44.09)+(.01 )(58.12)+(.0023)(72.15)+(.014)(28.01)

7 407 3 -4 3

= 13 3626

= °- 393 cm '9 = 3.93 x 10

4

rn /kg

CM - (•97)(6.548) + (.03)(n.072) _ - nfi 1Q

-4 3,. CMmin density "

( . 97) (1 6. 04)+( . 03) (30. 07 ) " 4 ' 06 X 10 m /kg '

5

M-8
2.3 Method used for prediction of density from equation of state

The scheme used for the prediction of density of LNG for a given composition,

temperature, and pressure is that of Mollerup [1].

We have selected this method instead of the commonly used method of Klosek

and McKinley [5] and other correlation methods for the following reasons:

(1) The method of Mollerup is more versatile in its usage. Densities

may be calculated for a given temperature, pressure, and composition

(off the saturation surface) or saturation densities may be calculated

for a given composition and pressure or a given composition and temperature. With the method of Klosek and McKinley densities may be

calculated only for a specified temperature and composition. Thus,

the results shown in the following sections would not have been

possible using the Klosek and McKinley method.

(2) Mollerup output includes phase equilibria data including densities

of the equilibrium vapor phase of the LNG mixture.

(3) In figures 1 and 2 we have compared the normal composition

densities as calculated by Mollerup with the densities as calculated

by Klosek and McKinley. For 1 atm pressure the saturation densities and

saturation temperatures were determined for the various LNG

mixtures by the method of Mollerup and the resulting saturation

temperatures and corresponding mixture fractions were used

to calculate densities by the K-M method. The relative deviations

in the densities calculated by the two methods are thus plotted

in figures 1 and 2 for N2 composition of 0 and 1%, respectively.

The maximum deviation in density calculation between the two

methods is 0.13% for N

2

= 0% and 0.18% for N

2

= 1%. This is

consistent with the claimed accuracies of + 0.1% for MbllerupDl

and + 0.3% for Klosek and McKinley[5].

6

N-9
I I I

I 1 I 1 I t

* N

2 = 0%

Normal Composition

428 ' Ag

1 iu ' A2 Ao * Ae *:s

MOLLERUP DENSITY (kg/m3

) Figure L Comparison of density calculation methods for No=0%

7

N-10
:.2:

cr

2=XLQI _JO

2ZQ

N2

= It

Normal Composition

H2 as 472 KOLLER'JP DENSITY (kg/nf

Figure 2. Comparison of density calculation methods for H2=l%

8

N-n
3. Results and Discussion

We have examined the relationship between density and dielectric constant

for liquefied natural gas mixtures of normal composition via the Clausius-Mosotti

relation and Mbllerup's equation of state. We have also examined the improvement in density determination by measurement of temperature in addition- to

dielectric constant.

Four general cases or effects are considered:

Case 1 - The range of composition of the mixture is known but it is

not known if the liquid is subcooled or at saturation.

Case 2 - The range of composition of the mixture is known and further- more the fluid is known to be saturated and at constant pressure. For

purposes of this study the pressure is taken to be 1 atm or 2.6 atm which

is the head pressure of the bottom of a 37 meter (120 ft) deep storage container

Case 3 - The range of the composition is known and the temperature of

the fluid is uniform but the fluid is subject to varying pressure (e.g., the

pressure difference between the top and bottom of a storage tank due to the

weight of the liquid).

Case 4 - The range of composition of the mixture is known and further- more the fluid is known to be saturated over a pressure range 0.5-8 atm.

and at constant temperature. The range of saturation temperatures considered

is 105-145 K. Cases la , 2a, 3a, & 4a - As a subset of the above, the effect of nitrogen

composition on the mixture density.

Case 2 is also examined for typical Libyan composition mixtures for possible

evidence of deviation of results for higher density mixtures.

When applicable (cases 2 through 4) least squares fitting techniques were

used to determine the probable intrinsic uncertainties in density determination

(due to variation in composition) from measurement of dielectric constant only or measurement of dielectric constant and temperature. The equations are given in

the Appendix. Since the equilibrium temperature of the mixture varies roughly

as the inverse of the nitrogen composition (Fig. 3) and, as will be seen below,

the nitrogen composition has significant influence on the density of the mixture,

the effect of temperature measurement was included in the investigation. The

stated intrinsic uncertainties do not include possible systematic uncertainties

in the use of Mbllerup's equation of state (claimed to be accurate to within

9

N-T2
w.irt

\ ^— 1

1 1 \ \ NORMAL COMPOSITION

P=l atm

« 0.2 x 10

c \ \ { \\ \

\

' $i ftj

T,at«>

Figure 3. N£ mole fraction vs. saturation temperature

10

N-13
+ 0.1% [1]) or systematic uncertainties in the determination of dielectric con- stant (~+ 0.1%) due to neglect of CM^. Uncertainties due to instrumentation

must also be included in addition to the intrinsic and systematic uncertainties

in order to obtain a total uncertainty for the system.

3.1 Case 1

As noted earlier, if a capacitance densitometer is used to measure p . r , mix

the defining equation is:

. 1 e-1

mix CM.mix e+2

This relationship is plotted in figure 4 for the range of CM^. corresponding to the maximum and minimum densities possible plus three intermediate

mixtures within the composition limits described in section 2.1.

The uncertainty in p . (due to variation in composition) may be expressed

III I A as: dCM_.„

(5)

mix

= 2.0% as shown in

dp 3de

+ dCMmix

P U+2)(e-l)

Assuming no error in dielectric constant measurement, i.e., de = 0, dC,

(4.06 - 3.98K10-

4

), and Cmix

= < 4 - 06

\

3 ' 98) (10" 4

) then

figure 4 for N

2

= 0%.

3.1.1 Case la

Extending the above calculation to the situation where the ^ composition

is not known but only the range of the composition (0 - 1.4%) we have:

dp

dCM,mix

CM.mix

(4.06 - 3.93) x 10

" 4 - 06 {

3 - 93

x 10

-4

- 3.3%.

3.2 Case 2

Using the method of Mbllerup the saturation densities at 1 atm and 2.6 atm were calculated for the different mixtures described in section 2.1 and the

dielectric constant for each mixture was calculated through the C-M relation

(eq. 1). The corresponding p r3+p vs e are shown in figure 5 at P = 1 atm for

sa is

the normal composition and ^ = 0%. It can be seen that there is a substantial

improvement in due to variation in composition if it is known that the mixture

11 N-T4
176 i 1 I i I

1.64 1755 1.68 DIELECTRIC CONSTANT

:i/:i/:4

Figure 4. LNG density vs. dielectric constant with CM mi

-

as parameter

12

N-15
47G

4S8-

4SC--

COE\cn

_^>-I—

*—

4

2:UJo

452-

444 -

43S"

428

1 e-1

p = CM

CM = Clausius-Mossotti Function

CMmax density

= 3.98 x 10" 4m

3

/kg.

Dots:

p . for N 9 h = 0%

sat 2 and various CM

(Normal Composition)

CM . . = 4.06 x 10" 4m

3

/kg mm density 3

1.64 1.66 t.68 DIELECTRIC CONSTANT

Figure 5. LNG saturation density vs. dielectric constant

13

N-16
of LNG is at saturation conditions since is approximately 0.4% for this case compared to ~2% for case 1 where the thermodynamic state of the fluid was not

presumed to be known. The Clausius-Mosotti relationship does not delineate the

thermodynamic state of the LNG mixture but when the saturation curve is delineated

through the equation of state the unique one to one relationship (within a + 0.2%

error) between density and dielectric constant very nearly exists.

Figure 6 shows a plot of p $at vs e for three different nitrogen compositions

(0%, 0.7%, and 1.4%). The three linear equations which best represent the data

are given in the appendix. We note through calculation that a change in density

of about 1.4% maximum results when the nitrogen composition changes from 0 to 1.4%.

3.2.1 Case 2a

Fitting all the normal composition data with one equation (range of composition known) results in a density variation of about + 0.8% as shown in Table 4.

We conclude that a single calibration curve for a capacitance type densitometer could not be used to predict densities to better than about + 0.8% for normal

composition of LNG which may have a nitrogen content between 0-1.4%.

3.2.2 Measurement of temperature as well as dielectric constant for cases

2 and 2a.

For an assumed functional relationship of the form p . = A + B(e-l) + CT,

where pm ^ x and T were determined from the Mollerup equation of state for each

mixture at the given saturation pressure, and e determined through the C-M

relationship, the constants A, B, and C were determined by least squares fitting

techniques. As can be seen by comparison of tables 4 and 5, addition of temperature measurement when the nitrogen composition is not known exactly (only the

range 0-1.4%) improves the density determination from + 0.8% to + 0.3%. There

is no improvement due to the additional temperature measurement for the case where the nitrogen composition and pressure are fixed.

3.3 Cases 3 and 3a

In figures 7a, 7b, and 7c we have plotted for a fixed composition, density

versus dielectric constant for three different conditions:

(1) Saturation conditions at P = 2.6 atm (the pressure which approximates

the absolute pressure at the bottom of a 37 meter (120 ft) deep LNG

storage tank).

14

N-17
15

N-18
C/l +-

g— ^5 O "O co ^ O

Q -Q | | + 1 f ^- 1 % O "^3 03 *E QJ CO

03 QJ

O "O O C

Z3 03 o ) ^

03 ZZ3 CO

(J QJ I/) CL O") QJ

£E

C C/0 1 1 ^ iSi *tj QJ 01

QJ

V (_) >«-» to 1—' w Q

^C? -__|

T 1 w

Q

QJ— (/) n ) Q

5^. Q_

Cvl c:—

co

O

»v? c (_)

g r~

QJO "—s ' r- i*0 4. 1 CO

+-> +-> C\J +j Q to

Q

Q (/) CO c O O O 03 03 Q_— t~

II CSJO ^7 to T rv

QJ 4—) (/> | ) fTJ QJ f

QJO

—

4-) j _ T

Q

03 # 00 CD * ^

QJ 03 jj

jTM CD 5^

<o 03 " rr c

III LJ 0 1 Q +J

•r—

C/l ^ 03 O S/ Q.E • ~n O i f—

w w u

•r- 1 < (Tj c 03 1 ) 1 ) i e—Q 0 <4- O QJ 03 0 ) > j_ — ITS <u Q QJ 03 O i- C71 Cl CD C —

K O E C

01 >> -3 M- <TJ CM

O (O S. Z O

jQ

O + 1 to

05 E CD >1 1— S- C

cu •r~ "O 0 1— 03

CD

"3

~o = E QJ *0 4J

00 * >>

00 00

to QJ

OJ 4-> 00 X) 4-1 E E O) 4- E 0 c 4J 01 r" S- E 01 3 3 O 00 00

•T- O) -O re 4J ^: 01 QJ <o E E

=5cr E Oi

QJ •rTM E -E 0 +-> cl-o 0

C5 Oi i. QJ 0

QJ *+- QJ +J >)

!o E 00 -M

03 s: 3 E * 1rTM E r~ E CJ +-> re ^r JC O E M

CJ +J E O S-

'1

0) E O) +-> 0

•r~ S- A3 E

ro 3 3 O 00 4-> 0J 0) •r- 1 1 4—

S- 00 re

u +j

(T3 T3 +-> 0 0 S- a; E +j c C! O QJ w O O E re 0 -O (J S- QJ (O Cl 5- E

03 E 3 f- . to W7 E 00 re O O O <T3 +-> Q O •1— QJ 4J +J E O w to

03 a) nD

O

n 3 4->

O -0U E e>= •r- S- "O f0 QJ >i +j a -a X3

-C E QJ S- &9 a> J- O

4— </> E O 0) ns 3 E _ s_ +J O

Cl 00 E

s- E r- 00 0 +J O QJ 03 re O QJ p-

-Q 4-> -a 5^ O E

0) CO •O •r- 1 X 0 S- re w d 3 +-> O LU O u O t- + a» 3 QJ _

tl

O

'a; +-> E

r— re 3

-O

00 4-J

U

<D QJ r~

"i~ ^ 00 +J +J -M s- re c C 0 E 0 • r- E s_ QJ •r— (O •r" s- +-> 0 +J +J QJ 00

•r— f- S- 00 >»

+-> 00 01 QJ E 00

"l~

O 0 r~O

00 Cl c O f a O E 3 ro +-> E

CL CM

O i. re re E O O 3 +j O •r- (J E u O -M QJ • r~ f0 E 00 CM E E 3 E

o> 1TM S_ M +-> S_ 00 QJ 00 4-> >^JC E E

CO +-> 1—1 • rN16

19
"O E

at +- c cu

s. •o * ra +-> 3 CM to

+-> 3 • cu • >>

(0 cu +-> to 00 S- s- U_ + 1 ro S- CU

O) 3 +-> a> -•-> O. +-> -a ro to J2 4-> SZ E ro CU CO E CU

cu S- to i

<+- 3 -C E +-> at c on o c -p ai CL o o e •i— S- "O E •i— (j (O C <U 3 3

sz cu +-> _Q

O to 00

ra 1

i— 3 ro •i— CU "O ra "O CO +-> -C cu cu

+-> £ e to ro +-> c E

s_

O Cn CU 3 •!- ro o o c to U C XI (U 4_ •i— ra +- D t- E -C

to "O o S3

O +-> e 3 —

CO O. "O o o rD •""0 • 3 CU S- o (J O o S.H o o e CU 3 4_ o h—4 + 1 r— i

— • I— U +-» >>

S- e :o c to +-> -M 3 1— 5- "i- 3 C o o • E •>- cu e cu c CU CU 4-> ro > 1— 3 -C O E +-> CD -Q O +J E O i-

•1

£ ro ro •i— CU "O o r— r— E CU +-> O

•r— •r- S- ro E

4— +-> i- J- ro 3 3 O •r- CU o CU to +-> ^ v to CL I

Q- CU CU -r- i

+-> -—N £ +-

O +-> •i- S- to ro e E -M S3 Q_ — O 3 -M

O) * CM E to r0 T3 4->O E to rO • O o S- CU E +-> ai —* V£J o c_> CL 3 O CU S- o + 1 E O O E ro +j c\J ro to o O S- CU to 4_) rQ 11 C\J c o ro Q. S- E

r0 to II o E 3 tcu E to Q_ "O -Q C C to c: •r- E to ra E e O • CL. C S- o O o O O ro +-> o {_) r^j n ro ro -Q r~* o -Q •r" O "i— CU -Q E <_) 0 " (J i- +-> -Q S- 4-> 4-> +-> E O O ii S— ro o c\i O ro i

S- ro "1

ro

S- -TJ o i

SU 00 rOO 00 CU i— ro

O

4- CD +j i— c\i to "O

O o CU

O

O o CU 3 3 +->

-|_> ro E 1 — CU >i s_ Q- CT) o S- Q- cn "O (J E

>> rO tO I 1 t"^, | (/) JZ "O i- T3 E c i— • i

-l-> i_ r\ ro CD i— ro >->

O ro T3 >>O ro ^-^ ra CU

•r" i— r\j c_> 4- C_) Qi >> a: C_3 4->

U X!

to +J +- o ^ e ai s. c ro . CU +-> S- o

O) co * CO cu 4- to E S- "O • cn O • CU ro 3 E j o c '

S_ +->O •!- e ro CU Q. 00 E + 1

S- cn E •!— to o +J O CU

to "O ro ro

U CU t-

<1J c S- X3 4-> •r~ ro "O O E

+-> • >> cu • CO "I— "O 'I- C E r— X o • S- r— ro r— o 1 C r" O +-> 3 +J

ra •iO o Li_ o . (J

O S-

+-> to +- 4-> + 1 CU 3 CU

S- e •r— +-> r—

O

ai o * (XI to 3 (1 CU +J E u "e" 'ro • O -Q 1- ra 3 C 4-> 4-> —« 4J o Q- T3 -E

•r- to ro E C to +J

U o c -a + 1 o 3 CU CU •!— e O LD CO C u o •t— 00 +->

O o O «* 1 (0 +-> +-> S- ro

•i

C_) i— LO CNJ c E O E

to II 1 . z: o o •r- E S- CU e -o LO O •I— c *l

ro S- +->

•r- cu +->

O to CU M- -M o +-> 4-> CU to

S- +-> ro r— j) CU r— o "n~ •r- •r— s- to -M fa to — to to +-> to CU CU E to

to S- 1— D. ro ro CU

O CU •io O -rO e 3 -— O

1— cn Q. CD to Q- e o •!- -a

+J e i

Sz: o cz^- eg 4_) CO •4- S_ ro CM O ro Q- CM O S- ro ra co O S- O a: E O O 3 +-> * cn M— O •r- O E (J to "3 o +-> U CU "i- o CD r— ro ra E to

a>CC CM E C 3 E + 1 •r- O CU -I- S_ -i- !a "O 4-> 4-J S- ro ro oo CU 00 +-J t— d) >,-E E E

00 4-> l—l •!- * -D +-

17

N-20
in

UJ

4»«

NORMAL COMPOSITION

L-0.6%

P=l atm (saturation conditions) T:112-113 K

& P=2.6 atm (subcooled con- ditions-! corresponding to T

gat

@ 1 atm

for each mixture)

P=2.6 atm (saturation conditions)

T: 125-126 K

N

2

=0%

1.C2 1.54 i.CC

DIELECTRIC CONSTANT

LCI I.T3

Figure 7a. Effect of pressure on LNG density vs. dielectric constant {^2=0%)

18

N-21
a:

>:

It'

fr - **•

» * to

ui

c >

42: •

A"

NORMAL COMPOSITION

P=l atm (saturation conditions)

& P=2.6 atm (subcooled conditionsT corresponding to T

sat

@

1 atm for each mixture)

P=2.6 atm (saturation conditions)

N o =0.7%

5.64

CIELECTRIC CO MS TAN"

SI

Figure 7b. Effect of pressure on LNG density vs. dielectric constant (N2= 0.7%)

19

N-22
NORMAL COMPOSITION

:.'2

.i 1.

1

••a

Figure 7c. Effect of pressure on LNG density vs. dielectric

constant (PL- 1.4*)

20

N-23
Uniform temperature conditions:

(2) Saturation conditions at P = 1.0 atm.

(3) Subcooled conditions at P = 2.6 atm and T corresponding to the T . sar at 1.0 atm for each mixture.

As shown in the graphs for fixed ^ composition and dielectric constant and as determined by the least-squares-fitting there is not a significant change in the

range of density (0.6%) when the subcooled data at 2.6 atm is included with the

saturation data at 1 atm. This illustrates the predominant dependence of density

on the mixture temperature as might be expected for an incompressible fluid.

The range of density for a change from saturation conditions at 1 atm. to saturation

conditions at 2.6 atm is approximately 1.9%, again for fixed ^ composition and

dielectric constant.

For a range of composition of 0-1.4% and the uniform temperature conditions

described above the density variation is 1.8% (+ 0.9%) as shown in table 4.

3.3.1 Measurement of temperature as well as dielectric constant for cases

3 and 3a (uniform temperature-varying pressure 1-2.6 atm).

Table 5 shows the improvement in possible error in density measurement if

temperature is measured along with dielectric constant. If the nitrogen composition

is not known exactly (0-1.4%) the improvement is from + 0.9% to + 0.3%. For fixed

nitrogen composition there is still slight improvement (from + 0.3% to + 0.2%) by

the additional measurement of temperature.

The above results illustrate the potential usefulness of a temperature com- pensated capacitance densitometer for measuring densities of LNG in a large

storage tank if it's at uniform temperature but where the pressure varies from

1 atm at the top to approximately 2.6 atm at the bottom due to the weight of the

1 iquid.

3.4 Cases 4 and 4a

A similar linear relationship between saturation density and dielectric

constant exists for isotherms (P'sat

and mixture varies along the isotherm) just

as for isobars (T . and mixture varies along the isobar). This is shown in

sat

figures 8a, 8b, and 8c for saturation temperatures from 105-145 K. A bilinear

relationship between density, dielectric constant and temperature is clearly

21

N-24
NORMAL COMPOSITION

105 K

DIELECTRIC CONSTANT

Figure 8a. Saturation density vs. dielectric constant for

various isotherms for N o =0%

22

N-25
cr

in

"?/:»/. »*&£ !

:.5S

DIELECTRIC CONSTANT

Figure 8b. Saturation density vs. dielectric constant for

various isotherms for 1^2=0-7%

23

N-26
50C

41 £

E *CC

to

UJo

Ut

§ 42C

I/)

1" (

5«:

:.52

*/it/::

»4|( I

NORMAL COMPOSITION

U2 1.4!

l.SO i.u

DIELECTRIC CONSTANT

!.(• I.?

Figure 8c. Saturation density vs. dielectric constant for

various isotherms for N2=1.4%

24

N-27
suggested by these graphs. Fitting the data for this range of temperatures

resulted in a + 0.2% range of density for a given dielectric constant if the

N

2 composition is fixed and + 0.9% range of density if only the range of N

2 composition (0-1.4%) is known. Thus for an anticipated use of a capacitance

meter in saturated liquids which may range from 105-145 K in temperature, a single calibration may be obtained for predicting densities within the above

noted limits.

3.5 Libyan Composition Results

Results similar to those noted for normal composition mixtures were

obtained for Libyan composition mixtures. Figures 9 and 10 show the apparent

linear relationship between p satand e and the approximate 2.6% difference in

slopes of the two curves for the two nitrogen compositions. In figure 11 it can be seen that at the higher densities the effect of nitrogen composition

is qualitatively the same as for normal composition, a 1% increase in nitrogen

resulting in approximately 1.3% (max) increase in density. Further even if

the nitrogen composition is known the uncertainty in p for a given e is

approximately + 0.4% compared to + 0.2% for the normal composition mixtures.

We have plotted the results for all of the data (normal plus Libyan

composition mixtures) in figures 12, 13 and 14. There is no significant

difference in results when all data are considered together.

4. Summary of Results and Observations (see also tables 4 and 5)

(1) The Clausius-Mosotti relationship shows a wide range of densities for a particular dielectric constant as one varies the mixture of LNG. A range

of "~3.3% ( + 1.7%) is possible for the normal LNG mixtures of this study.

(2) However, if the mixture is saturated then a unique linear relationship

between density and dielectric constant very nearly exists for a constant

pressure (or temperature) and fixed nitrogen mole fraction. For the normal

range of LNG mixtures the saturation density can be determined to within

approximately 0.2% at constant pressure or temperature if the nitrogen

composition is known.

(3) Nitrogen has a very pronounced effect on the density versus dielectric constant. For example, at saturation conditions and 1 atm pressure a change of

nitrogen mole fraction from 0 to 1.4% of the total composition results in

25

N-28
55;

sr.-

CD >

t—tn 52:

•z. UJ

•z. o

to

is;"

N

2 = 0%

LIBYAN COMPOSITION

pH

.= 720.074s - 746.985

sat

7^3 , U 1—

DIELECTRIC CONSTANT

»»« :

Figure 9. LNG saturation density vs. dielectric constant

for Libyan composition with N2=0*

26

N-29
DIELECTRIC CONSTANT

air*?

Figure 10. LNG saturation density vs. dielectric constant

for Libyan composition with N2=l%

27

N-30
DIELECTRIC CONSTANT

Figure 11. Effect of nitrogen composition on saturation density

vs. dielectric constant for Libyan composition mixtures

28

N-31
DIELECTRIC CONSTANT

ur.'.r.i

Figure 12. LNG saturation density vs. dielectric constant for

normal & Libyan composition mixtures with N2=0%

29

N-32
:.S2

w.'.r.i »»« :

N

2 = 1%

NORMAL + LIBYAN COMPOSITION

P C3+ = 703.6i4e - 715.963

Sat

:.ss \% 1.74 DIELECTRIC CONSTANT

:.82

Figure 13. LNG saturation density vs. dielectric constant for

normal & Libyan composition mixtures with N2 = l%

30

N-33
580

CO

540-

C7>

I—CO

ZLLUQ

§ 50C

a:

<:CO

:.S2

v.-.ri

ALL DATA

NORMAL + LIBYAN COMPOSITION

N

2

= 1%

:.ss l^TO" 1.74 1 DIELECTRIC CONSTANT

N

2

= 0%

!.82

Figure 14. Effect of nitrogen composition on saturation density

vs. dielectric constant for normal & Libyan composition mixtures

31

N-34
about a 1.4',- increase in the density for the same dielectric constant.

However, since the nitrogen composition significantly affects the saturation

temperature it is possible to partially compensate for these changes by an independent measurement of the temperature.

For the normal range of mixtures considered the density of the mixture is

predominantly dependent on the temperature. This result plus the approximate bilinear relationship between density and dielectric constant and

temperature suggests a temperature compensation for a capacitance meter

which allows density to be determined to + 0.3 ;

: over a wide range of temperatures and subcooled conditions. For all such cases considered there

is substantial improvement in the density measurement when temperature as well as dielectric constant is measured. (See tables 4 and 5.)

The results of calculations for the libyan composition indicate that the

intrinsic uncertainties increase as the anticipated range of composition

increases

.

The results of the study tend to give positive and conclusive indication

of the capability of capacitance densitometry for anticipated end use onboard ship custody transfer systems.

Topics for Future Research

(1) The systematic uncertainties due to state equations and the excess

CM function need to be better defined and determined. This is being done

currently at NBS for the state equation by a systematic acquisition of

PVT data for well defined mixtures. Improvement in the excess CM function,

however, will have to rely on future experimental relations between

dielectric constant and density for well defined mixtures.

(2) More work should be done explicitly on subcooled fluids although un- certainties for a given subcooled condition can be estimated from interpolations and extrapolations from the 2.6 atm results (at the corresponding

1 atm saturation temperature) given in this report.

(3) Systematic methods need to be developed for determining intrinsic un- certainties for composition ranges other than those given in this report;

Particularly to define techniques for internally calibrating the densitometer

for a narrow range of mixtures or equivalently, when the approximate com- position of the fluid is known.

32

N.-35
References

1. MSllerup, J., Correlated and predicted thermodynamic properties of LNG and

related mixtures in the normal and critical regions, Advances in Cryogenic

Engineering 2£ (Plenum Press, NY, 1975).

2. Sarsten, J. A., LNG stratification and rollover, Pipeline Gas J. 199, No. 11,

37-39 (Sept. 1972).

3. Diller, D. E., The Clausius-Mosotti functions (molar polarizabilities) of

pure compressed gaseous and liquid methane, ethane, propoane, butanes, and

nitrogen, Cryogenics 14^ No. 4 (April 1974).

4. Pan, W. P., Mady, M. H., and Miller, R. C. , Dielectric constants and ClausiusMosotti functions for simple liquid mixtures: systems containing nitrogen,

argon and light hydrocarbons, AIChE Journal 21^ No. 2 (March 1975).

5. Klosek, J. and McKinley, C, Densities of liquefied natural gas and of

low molecular weight hydrocarbons, Proceedings First International Conference,

IGT, Chicago, Illinois (1968), paper 22.

33

N-36
APPENDIX

Equations determined by least squares fitting techniques for the cases described in the text. (Normal Compositions)

Notation

3

p . = density of mixture, kg/m

e = dielectric constant

T = temperature of mixture, K

3 CM . = Clausius-Mosotti function for the mixture, m /kg mix | CM. = Clausius-Mosotti function for each component, m /kg.

Cases 1 and la (not least squares determination, see Sec. 2.2, 3.1, and 3.1.1)

_J e£L 1 e-1

pmix CMmix e+2 ZCM. £+2

p vs (e-1) equations (Table 4)

Case 2 Saturated Conditions, P ^

= const

N

2 = 0%

mix

P

• mix

0.7%

mix

mix

N

2

= 1.4%

mix

P • mix

29.076 + 723. 5(e-l

23.602 + 723.6(e-l

20.749 + 714.6(£-1

13.419 + 710.9(e-l

13.58 + 707.68(e-1

4.726 + 700.98U-1

sat

sat

sat

sat

sat

sat

1 atm

2.6 atm

1 atm

2.6 atm

1 atm

2.6 atm

34

N-37
N

2

= 0-1.4%

pmix

=

" 51 - 630 + 760.8(e-l)

mix 42.051 + 756.1 (e-1)

P sat

= 1 atm

Psat

= 2.6 atm

Case 3 Uniform Temperature Conditions, P = 1-2.6 atm

N

2 =

"mix

N

2

= 0.7%

•27.947 + 721. 7 (e-1)

"mix

N

2

= 1.4%

•17.924 + 710.15(e-l)

mix -9.035 + 700.62(e-l)

Case 3a

N

2

= 0-1.4%

mix

-807.377 + 757.68(e) = -49.702 + 757.68(e-l)

p vs e-1, T equations (Table 5)

Case 2 Saturated Conditions, P sat

= const

N

2

= 0%

^mix

N

2

= 0.7%

•275.568 + 667.06(e-l) + 2.521 (T)

mix

N

2

= 1.4%

-286.721 + 701 .27(e-l ) + 2.499(T) P sat

= 1 atm

mix -301.885 + 730.33(e-l) + 2.539(T)

35

N-38
N

2 = 0%

p . = -281.40 + 639.6(e-l) + 2.464(T) mix

N

2

= 0.7%

pmix

=

" 287 - 76 + 675.9(e-1) + 2.393(T)

N

2

= 1.4%

pmix

=

" 278 - 91 + 706.6(e-l) + 2.2295(T)

Case 2a

N

2

= 0-1.4%

pmix

= 78,71 + 720 - 98 ( £

- 1

) " 0.9422(T)

pmix

= 90,19 + 725 - 16 ( £

- 1

) " 0.9102(T)

Case 3 Uniform Temperature Conditions, P = 1-2.6 atm

N

2

= 0%

pmix

=

" 281 - 18 + 664.67(e-l) + 2.5845(T)

N

2

- 0.7%

pmix

=

" 292 - 49 + 598.87(e-l) + 2.5768(T)

N

2

= 1 .4%

pmix

=

~ 269 - 39 + 720.10(e-l) + 2.2987(T)

Case 3a

N

2

= 0-1.4%

pmix

= 78,99 + 716 -"12 ( £

- 1

) " 0.9164(T)

36

N-39
Case 4 Saturation Conditions, T t

= const (Range of applicability 105-145 K)

N

2 " 0%

P

• mi x

N

2

- 0.7%

P

• mix

N

2

- 1.4%

pmix

-62.03 + 709.4(e-l) + 0.3747(T)

-52.94 + 704.5(e-l ) + 0.3518(T)

46.87 + 702.8(e-l) + 0.3369(T)

If mole fraction is included as parameter

pmix

= " 56 - 97 + 705.4(e-l) + 0.3543(T) + 448. 3N

2

,

Case 4a

N

2

= 0-1.4%

pmix

= -47.94 + 699.2(e-l) + 0.3379(T)

37

M0
NBS-J14A (REV. 7-73)

U.S. DEPT. 0* COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 76-831

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

1 July-31 December, 197E

6. Performing Organization Code

7. AUTHOR* Si D. B. Mann, Editor

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. 2750141

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 - July 1 - December 31, 1975

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) Nineteen 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 at a 20 man-year level with funding

expenditures of over $600,000. 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 con- ducted 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 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)

Cryogenic; liquefied natural gas; measurement; methane; properties; research.

18. AVAILABILITY Q Unlimited

1 X 1 r°r 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. C13

| Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

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'THIS REPORT)

UNCL ASSIFIED

21. NO. OF PAGES

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(THIS PAGE)

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