NAT'L INST. OF STAND & TECH NBSIR 74-373

,11.0.

^^J^y^^^^pi^P NATURAL GAS RESEARCH

NIST REFERENCE

PUBLICATIONS

at the

NATIONAL BUREAU OF STANDARDS

PROGRESS REPORT FOR THE PERIOD

1 JAN - 30 JUNE. 1974

D. B. Mann, Editor

^. 7¥'3 73

/fry

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

NBSIR 74-373

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 Jan - 30 June, 1974

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent. Secretary

NATIONAL BUREAU OF STANDARDS. Richard W Roberts. Director

at the
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

General Services Administration

Motor Equipment Research & Technology Division

Washington, DC 20406

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

Aerospace Safety Research and Data Institute

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135
ABSTRACT

Seventeen cost centers supported by seven 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 $500,000,

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

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

annual report on the activities of their individual programs.

2) Inform all sponsoring agencies on related research being

conducted at the Cryogenics Division of NBS-IBS.

3) Provide a uniform reporting procedure which should maintain and improve communication while minimizing the

time, effort and paper work 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 con - sidered preliminary, subject to change and unpublished; and therefore

not for citation in the open literature .

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

properties; research.
CONTENTS

Reference Data

a) Refractive Index - Fluid Methane

(NBS-NRC Postdoctoral Research)

b) Fluid Transport Properties

(NBS-Office of Standard Reference Data)

c) LNG Fuels Safety

(NASA-Aerospace Safety and Data

Institute)

d) Properties of Cryogenic Fluids:

Hypersonic Velocity and Thermal

Diffusivity (NBS)

e) Properties of Cryogenic Fluid Mixtures:

Equilibrium Properties Data, Compilation and Evaluation, Prediction

Methods (NBS; NBS-Office of Standard

Reference Data)

f) Survey of Current Literature on LNG

and Methane (American Gas Association,

Inc. )

g) Thermophysical Properties Data for Pure

Components of LNG Mixtures (American

Gas Association, Inc.)

h) Densities of Liquefied Natural Gas (LNG

Density Consortium of 1 8 energy companies - AGA)

i) Low Temperature Material Behavior

(Maritime Administration)

j) Elastic Properties of Materials Intended

for use in LNG Applications (NBS)

Cost Center Page

2750122

2750124

2750427

2750141

2750142

and

2750145

2750362

2750364

2751364

and

2752364

2750430

2750131

55

12

12

16

19

28

28

32

35

II. Measurement Science

a) Heating Value of Flowing LNG

(Pipeline Research Committee - AGA)

b) LNG Density Reference System

(American Gas Association, Inc.)

2750361

2751361

36

40

iv
Contents (Continued) Cost Center Page

III. Technology Transfer

a) LNG Technology Transfer 2750401 43

(Maritime Administration)

b) Federal Power Commission Consultation 2750404 49

(FPC)

c) LNG - Dual Fuel Auto 2750590 52

(NBS; General Services Administration)

IV. Bibliography 54

V

1, Title. Refractive Index of Fluid Methane

Principle Investigator. James D. Olson

2. Cost Center Number. 2750122

3. Sponsor Project Identification. NBS-NRC Postdoctoral Research

Associate Program.

4. Introduction. This experimental program will provide accurate

measurements of the refractive index of liquid and gaseous methane.

The data can be related to the fluid density hy the Lorenz - Lor entz

electromagnetic equation of state and, as such, offers the possibility

of fluid density gauging by optical techniques. This pure fluid data

is essential to the possible study of mixture refractive index properties.

5. Objectives or Goals . The refractive index of liquid and vapor

methane will be measured along the two-phase saturation boundary.

In addition, gaseous isotherms will be obtained at 220 K, 250 K,

280 K, and 300 K at pressures to 200 atm. Low pressure isotherms

will be measured below the saturation boundary,

6. Background. The high precision interferometric technique used to

measure the refractive index was developed in this laboratory by

D. E. Diller (J, Chem. Phys. 49_, 3096 (1968)). An improved optical data gathering method was the principal modification of this

technique. Prior to this reporting period, a literature survey of

Lorenz - Lorentz and Clausius -Mos sotti virial equation data was conducted. A cryostat was constructed using the design of Diller. The

temperature measurement problems described in the previous report

were eliminated after modification of the apparatus in December and

January.

7. Program and Results . All of the essential measurements of the refractive index of fluid methane were completed during this reporting

period. These data include the saturated liquid and vapor and the

gas isotherms above the critical point. Table 1 lists the saturation

data. The measurements were made at the Hg''"^^ green line, X = 546. 22705 nm.

The refractive index data were combined with the experimental densities of Goodwin and Prydz"*^ to calculate the Lorenz -Lorentz function.
LL = n

2 n + ,Z

1 ^

P

9.

Figure 1 is a preliminary sketch of the trends exhibited by the LL

function. Aj. is the zero density limit of the LL function at 300 K.

The saturated vapor LL data may be about 0, 3%-0. 5% too small because uncertainties in the vapor densities. The saturated liquid LL

function decreases sharply at higher densities in contrast to the

Clausius -Mos sotti function previously obtained by Straty and Goodwin^. The LL data for all the gas isotherms are represented within

0. 05% by the fitted equation, LL 6. 6081 + (0. 00679)p - (0. 0003439)p'

The critical refractive index, n^, was obtained by use of the rectilinear diameter law on the saturated liquid and vapor refractive

index data (T^-, = 190. 555 K) . The critical refractive index was combined with an estimate of the critical LL function, indicated by the

diamond on Figure 1, to calculate an estimate of critical density;

= 10. ISg ± 0. 01 mole/l. The critical density uncertainty was

calculated from the error bounds on LLj, in Figure 1. This is a preliminary value and differs from that currently used. Further

analysis will be necessary to determine the best value for the critical

dens ity.

Problem Areas. There are no problems at this time.

Funding . January 1 - June 30, 1974

Labor

Other Costs

0. 5 MY

Total

Remaining

17. 0 K$

4. 0 K$

21.0 K$

8. 5 K$

10. Future Plans. The data will be reduced and a manuscript prepared

during the next two months. Some additional experimental data will

be taken as well. This is an NRC - Postdoctoral Appointment which

terminates near the end of September 1974 and thus, this effort will

be completed prior to that time.

Schedule July Aug. Sept.

Further Experiments

Data Analysis

Manuscript Preparation — —

)

)

2
6.68 1-

6.64

.60

6.56

——— Gas Isotherms — Saturated Liquid — Saturated Vapor

/

•"Ar /

V /

10 20

DENSITY, moles/liter

FIGURE 1. LL Function vs. Density
References .

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

2. G. C. Straty and R. D, Goodwin, Cryogenics 21, 712 (1973).

Table 1. Refractive Index of Methane at Saturation

Saturated Liquid Saturated Vapor

n i (K) n

yD , U U

U

1 9 Q 1 Q 9 c; QQ 9 on 7 7. cyv 1 nnnAi UUU'^l

inn n n n i u u . u u u1 9 Q 7 9 Q 1 1 1 /t zL n ^ 114:. 4U J i nU n 1 Q U 1 J 7

1 n c; nnn 1 9 Q 9 c; 1 Q i . Co CD I o

1 9 Q ft A 1 7 . ODD 1 nnUU J 7A(

1

1 1iun . nnn uuu 1 9 7 7A % Q 1 Q A A Q 1 J 7 . D ^ 7 1 n n A 9 9

lie: nnn 1 1 0 . UUU 1 9 7 9 A A A 1i D nU . nnn UUU 1 n 1 n 1 A U 1 U Id

1 7 n nnn 1 ZU . UUU 1 9 A 7 c: n C 1 A n nnn i oU . UUU 1 n 1 c 7/1 A U 1 b

(

4d

11 9 c:

. nnn UUU 1 9 A 9 9 n A 17 9 ^ Q A 1 1 C. , JOO 1 n9UcOyA Q7Ato

ion nnn 1 JU . UUU 1 9 C A 7 1 7 1 . Zbo / 1 /

1 7 A Q 9 Q 1 (o . yco 1 IOC n r\ r\ lib. UUU 1 . 251031 1 O A AAA 1 oU . uuu 1 A "2 O >1 A /I U D o4U4

1 A r\ AAA 1 4U . UUU 1 O /I C A O O

1 . 245083 1 O 9 AAA 1 o2 . UUU 1 A /I O C /I A U4Zb4U

1 /I C AHA 14b. UUU 1 o o o o c o

1 . 238853 1 O A AAA 1 oo . uuu 1

1 C A AAA 1 5U . UUU 1 O O O O '7 A

1 . 232279 1 A A AAA 1 9U . UUU 1 A O A C A U / o9b

9

ICC AAA 1 b b . UUU 1 O O C O "7 A

1 . 2252 /U

1 L r\ AAA 1 bU . uuu 1.21 1 / 3 9

1 L c nnn 1 D b . UUU 1 9 n O C "2 Q

i . ZUVb JO

1

1 7n1 u nnn

.

uuu 1 9 n n A c; I . <i U U4 J D 175. 000 1 . 190055

178. 000 1. 182914

180. 000 1 . 177615

181. 000 1. 174749

182. 000 1 . 171708

183. 000 1. 168460

184. 000 1. 164957

185. 000 1 . 161 138

186. 000 1.156889

187. 000 1. 152056

188. 000 1. 146359

189. 000 1 . 139107

189. 404 1. 135383

190. 555 1.10326^" 190. 555 1. 10326-^"

extrapolated n

4
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. Studies of mixtures have not received the attention or support that have been given to equivalent studies of pure fluids.

This is especially true for transport properties where the mixture

effort has been negligible. Yet from the standpoint of the liquefied

natural gas industry mixtures are more important than pure fluids.

At this time there is no adequate method in existence for predicting

the transport properties of fluid mixtures even in the dilute regions.

Properties cannot be measured for all possible mixtures, thus adequate predictions methods are needed in order to supply the necessary design data needed to increase efficiency and reduce costs.

5. Objectives or Goals. The long range or continuing goal of the program is to perform a systematic study of the theories and experimental measurements relating to transport properties, specifically

the viscosity and thermal conductivity coefficients, of simple mixtures over a wide range of experimental conditions. The specific

objectives of the program include: 1) the systematic correlation of

the transport properties of simple binary mixtures and the development of prediction techniques, 2) development of a mixture theory for

the dilute gas region and the dense gas and liquid regions, 3) extension of the theory and prediction techniques to multicomponent systems,

and 4) suggested guidelines for future areas of experimental work.

6. Background. A program was started in 1965 with the goal of producing tables of fluid transport properties through many approaches;

e.g. , data correlation and evaluation, statistical mechanics, kinetic

theory, thermodynamics and statistics. A theory was developed

based on a modification of the Enskog theory. In addition, a systematic study of new potential function, the M-6-8. The theoretical

studies along with data analysis results in prediction techniques for

the dilute gas region for monatomic and polyatomic fluids. These

techniques were then successfully extended to the dense gas and

liquid regions. To date tables of transport properties have been

prepared for argon, krypton, xenon, oxygen, nitrogen, fluorine and

hydrogen. In addition an analytical representation of the anomalous

behavior of the thermal conductivity coefficient in the "critical region"

5
has been developed. As a precursor to the study of fluid mixtures

we have started a task to apply numerical techniques such as molecular dynamics to transport properties. To this end the Principal Investigator is in Australia gaining experience in advanced theoretical

techniques. During the current reporting period a molecular dynamics

model has been modified and applied to methane. The program has

been run for a system of 108 methane molecules. The resulting output are, in effect, experimental data and will be compared with

methane data and equations of state from the Cryogenics Division.

8 . Problem Areas. There are no problem areas at this time.

9. Funding . January 1 - June 30, 1974

10, Future Plans. The mixture part of the program will begin after

August 1974. If the methane calculations prove successful, it may

be possible to make preliminary calculations on binary systems of

methane with ethane and nitrogen during the next year.

Allocation

Labor

Other Costs

5 3.5 K$

0, 5 MY

OSRD

20. 3 K$

0. 4 K$

20. 7 K$

5 3.5 K$

Total

Funding FY 75

6
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 5000 references in cryogenic fluid safety. In addition, ASRDI has published

approximately ten 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 safety- related information. In addition, NBS-Boulder has been

7
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 . This NASA-funded program is not due to

start until September 30, 1974, however, some preliminary work is

being done on the thesaurus as well as some literature searching.

We expect to locate some 400 safety- related papers which will be

processed during the succeeding year. We also plan to publish, under

a companion ASRDI Contract, a comprehensive thesaurus for Cryogenic Fluid Safety, This will include terminology pertinent to LNG

safety,

8, Problem Areas. None

9. Funding . September 30, 1974 - October 1, 1975

Allocation - FY 75 50 K$ - NASA/ASRDI

10, Future Plans. We will begin processing safety- related documents in

October and complete over 400 of them by October 1975. In addition,

we will process carefully selected LNG/Methane /Methane Mixtures

documents. Selection of these documents will be done in cooperation

with other LNG projects within NBS,

8
1. Title. Properties of Cryogenic Fluids: Hypersonic (GHz) Velocity

and Thermal Diffusivity Measurements

Principal Investigator. G, C. Straty

2. Cost Center Number . 2750141

3. Sponsor . NBS

4. Introduction. Laser light scattering spectroscopy techniques will be

used to obtain accurate thermophysical properties data for compressed

and liquefied pure methane. This work will complement related work

on the thermodynamic properties of the pure components of LNG mixtures (2750364). This work will provide data for the development of

LNG technology at NBS and throughout the fuel gas industry.

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

accurate sound velocity and thermal diffusivity data for pure methane

(90-300 K, 350 bars) 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 useful for calculating transport properties data

for LNG mixtures, required for performing 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 mechanisms, 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 in

9
inherent in more conventional methods. For example, laser light

scattering techniques permit measurements of sound velocities for

fluids and under conditions for which sound absorption is too large to

perform ultrasonic measurements; laser light scattering techniques

permit measurements of thermal diff usivities under conditions for

which convection interferes with measurements of thermal conduction.

The feasibility of light scattering experiments to obtain data on binarydiffusion coefficients has also recently been demonstrated.

We have assembled and performance tested apparatus for laser light

scattering spectroscopy measurements on compressed and liquefied

gases (76-300 K, 350 bars). The apparatus consists of a copper

optical cell with fused quartz windows, cryostat for refrigeration with

liquid nitrogen, an argon ion laser, pressure scanned Fabry-Perot

interferometer, and photon counting equipment.

Program and Results . Preliminary data on the hypersound velocities

in pure methane have been obtained at low densities (< 14 mol/ i) where

the large sound absorption in methane prohibits ultrasonic measurements. Data have been obtained along several isotherms from 210 K

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

measured ultrasonic velocities in the regions of overlapping data is

good. Agreement with values calculated directly from PVT data is

satisfactory.

Problem Areas. No significant problems have been encountered.

Progress on the light scattering experiment has been determined primarily by our assignment of priorities to other LNG related efforts.

The program to measure the hypersound velocities in pure methane

is, however, progressing satisfactorily and on schedule.

Funding . Man-years expended (Jan. -June 1974)

Equipment and/or Services Purchased

0. 3

1. 4 K$

Total Reporting Period Cost 15. 0 K$

Balance Remaining (June 30, 1974) 0. 0 K$

10
10. Future Plans.

year

Schedule: quarter

1974

3 4

Methane:

Measure hypersonic (GHz)

velocities in methane

Assemble and test apparatus

for Rayleigh line-width

(thermal diifusivity) measurements on methane

11
1. Title. Properties of Cryogenic Fluid Mixtures: Equilibrium

Properties Data, Compilation and Evaluation, Prediction Methods

Principal Investigators. M. J. Hiza, A. J. Kidnay (part time), and

R. C. Miller (part time).

2. Cost Center Numbers. 2750142; 2750145

3. Sponsors . NBS; NBS-OSRD

4. Introduction. This project provides new experimental measurements

on equilibrium properties and compilations of evaluated equilibrium

properties data which are suitable for direct technological use or for

the evaluation of prediction and calculation methods. This project

supports the development of LNG technology in the areas of separation,

purification, liquefaction and custody transfer by defining relationships

between the composition, temperature, pressure, and equilibrium state

properties for mixtures related to LNG.

5. Objectives or Goals. The overall objective of this project is to provide critically evaluated data, original and from other sources, on the

phase equilibria and thermodynamic properties of cryogenic fluid mixtures. The program has been divided into the following elements:

a) Preparation of a comprehensive bibliography on experimental

measurements of equilibrium properties for mixtures of selected

molecular species of principal interest in cryogenic technology.

b) Selection and/or development of methods for correlation, evaluation and prediction of equilibrium properties data.

c) Retrieval and evaluation of experimental data for specific mixture

systems selected on the basis of theoretical and/or technological

importance.

d) Preparation of guidelines for future research based on the deficiencies noted in (a), (b), and (c).

e) Performing experimental research to alleviate deficiencies and

provide a basis for improvement of prediction methods.

6. Background. A physical equilibria of mixtures research project was

established in the Cryogenics Division in 1959. The initial effort,

based on a bibliographic search and other considerations, was directed

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

liquid-vapor equilibria and physical adsorption properties for a limited

number of binary and ternary mixtures of components with widely

12
separated critical temperatures. Most of the systems studied included

one of the light hydrocarbon species -- methane, ethane, or ethylene

(ethene) -- with one of the quantum gases -- helium, hydrogen, or

neon. The data for these systems led to significant improvements in

the predictions of physical adsorption equilibrium and a correlation

for the prediction of deviations from the geometric mean rule for

combining characteristic energy parameters. In addition, significant

new information was obtained for interaction third virial coefficients

which was used in a correlation by one of our consultants, J, M,

Prausnitz. The approach taken in this work has been as fundamental

as possible with the intention of having an impact on a broad range of

mixture problems.

Recent efforts have been directed toward problems associated with

systems containing components with overlapping liquid temperature

ranges, such as the nitrogen + methane system.

Preceding this reporting period, an expanded bibliography was prepared to update NBS Technical Note 56, published in May I960 (objective a). Experimental liquid-vapor equilibria measurements were

also completed at selected temperatures on the argon + methane systems,

7. Program and Results . The recent progress of this program is summarized as follows:

a) A comprehensive bibliography of experimental data for ten equilibrium properties has been completed, reviewed, and revised.

The final manuscript has been sent to a publisher selected by

the OSRD, The bibliography includes sections on solid-liquid,

solid-vapor, solid-liquid vapor, liquid-liquid, liquid-vapor, and

gas -gas equilibria, as well as sections on liquid mixture densities,

Joule-Thomson coefficients, and calorimetric measurements.

The materials considered are hydrogen, helium-3, helium-4,

deuterium, neon, carbon monoxide, nitrogen, oxygen, hydrogen

sulfide, fluorine, argon, carbon dioxide, krypton, xenon, and

the staurated and unsaturated hydrocarbons through the C4's.

Because of its importance, the section on liquid-vapor equilibria

was published as a survey paper in Cryogenics J^, 575 (Oct,

1973). It is anticipated that the complete bibliography will be

published and available by late summer of this year.

b) Work is currently in progress on the retrieval and evaluation of

equilibria data for the methane + ethane system. Data for both

argon + methane systems have been retrieved and evaluated. To

13
maintain this phase of the program within reasonable bounds,

the only properties under study are liquid-vapor equilibria, liquid

mixture densities, and gas or vapor mixture densities. This effort also requires selection of the pure vapor pressure and saturation densities. The new vapor pressure measurements of

Wagner (Cryogenics J_3, 1973) for nitrogen and argon have been

programmed and compared with other data sets. As expected,

there are significant discrepancies between data sets for the

pure fluids which must be resolved,

c) Our most recent liquid-vapor equilibria measurements for the

nitrogen + methane system between 95 and 120 K are now being

extended above the critical point of nitrogen to approximately

180 K, Preparations for these experiments were started during

the last week of this reporting period.

Problem Areas. The major problem that may affect progress on the

evaluation of mixtures data is the lack of generally accepted, rigorous

methods for critically evaluating phase equilibria data. Each binary

system poses special problems of its own, and it may be necessary

to tailor the techniques employed.

Funding .

Man-years expended (Jan. -June 1974) 0. 6

Equipment and/or Services Purchased 3. 0 K$

Total Reporting Period Cost 38. 0 K$

Balance Remaining (June 30, 1974) 0. 0 K$

1 4
10, Future Plans,

Schedule:

year

quarter

1974

Retrieve phase equilibrium data

for methane -ethane mixtures

Select pure component ethane data

Calculate excess Gibbs energies

for methane -ethane mixtures

Compare calculated excess Gibbs

energies for different sets of

data

Compare calculated excess volume

TP V for different sets of data

Complete phase equilibria measurements for the nitrogen -methane

system between 120-180 K

Analysis of nitrogen-methane data,

comparisons, preparation of

paper

Prepare for new L-V equilibrium

measurements on methaneethane mixtures

Examine the prospects for new

experiments on heats of mixing

and virial coefficients of

selected binary mixtures

15
1. Title. Survey of Current Literature on LNG and Methane.

Principal Investigator. Neil A. Olien

2. Cost Center Number. 2750362

3. Sponsor Project Identification. American Gas Association Project

BR 50-10.

4. Introduction. It is important that all NBS personnel working in LNG,

as well as the AGA and others, keep up with what is going on throughout the world in the LNG field. This project is designed to provide

the Current Awareness and other information services to allow workers to keep abreast of new research and other developments.

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

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

patents relating to methane and LNG properties and technology. The

references will be listed under convenient subject headings. The

Quarterly will be distributed to all interested AGA member companies

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

In addition, LNG related information will be entered into the Cryogenic Data Center's Information System for quick retrieval. A continuing awareness of the current publication scene will be maintained

for any new periodicals to be reviewed cover -to- cover. Finally we

will update and make available comprehensive bibliographies on the

properties and technology of LNG. There are three bibliographies

involved: methane properties, methane mixtures properties, and

processes and equipment involving methane and LNG. These three

will be updated each October.

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

should be scanned cover-to-cover to adequately encompass the LNG

field. The result is that we now scan over 300 primary publications

and nearly 30 secondary publications. Of these approximately onethird 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 of this information is also pertinent to

LNG and as such is listed in our LNG-related publications. Our

Current Awareness Service has been published weekly since 1964 and

the Liquefied Natural Gas Survey has been published quarterly since

1970.

16
7. Program and Results . Two issues of the LNG Quarterly were prepared and distributed. There are now 118 subscriptions going to

AGA Member Companies and 191 to other subscribers. In September

and October we updated the three bibliographies covering methane

properties, methane mixtures properties and processes and equipment involving methane and LNG.

For some time we have realized that the above mentioned comprehensive bibliographies had grown to such a large size as to limit

their usefulness (e.g. , B-965 covering processes and equipment listed

over 1500 references). With this in mind we have reviewed the individual references in each bibliography and selected those which were

most useful either from the standpoint of accuracy of the data or the

appropriateness of the subject matter. These are now complete and

copies have been printed and are available for sale as listed below.

B-1055 THERMOPHYSICAL PROPERTIES OF METHANE - A

SELECTED BIBLIOGRAPHY, 61 pp. , indexed by property,

phase and author (Sept. 1973) $8. GO.

B-1056 PROPERTIES OF METHANE MIXTURES - A SELECTED

BIBLIOGRAPHY, 95 pp. , indexed by property, system and

author (Sept. 1973) $10,00.

B- 1075 PROCESSES AND EQUIPMENT INVOLVING LIQUEFIED

NATURAL GAS AND METHANE - A SELECTED BIBLIOGRAPHY,

52 pp. , indexed by subject and author (Oct. 1973) $5. 00.

During the period January through July 1974 we have distributed 32

copies of these and the comprehensive bibliographies.

8. Problem Areas. We have no problem areas at this time.

9. Funding . January 1 - June 30, 1974

Labor 7. 5 K$

Other Costs 2, 1 K$

Total 9. 6 K$

Remaining 8. 0 K$

10. Future Plans. Issue 74-2 of the LNG Quarterly was mailed to the

National Technical Information Service for printing and distribution

on June 19, 1974. Issue 74-3 will be published in late September or

early October. The three bibliographies discussed in Item 7 above

will be updated in October.

17
July Aug, Sept. Oct, Nov, Dec.

Preparation of Issue 74-3

Preparation of Issue 74-4

^

>

^

18
1 . Title . THERMOPHYSICAL PROPERTIES DATA FOR PURE

COMPONENTS OF LNG MIXTURES

Principal Investigators . R. D. Goodwin, G. C. Straty

2. Cost Center Number . 2750364

3. Sponsor . American Gas Association, Project BR50-10

4. Introduction. This cost center will provide comprehensive accurate the r mophysical properties data to support the development of

LNG technology at NBS and throughout the fuel gas industry.

5. Objectives or Goals. The objective of our work is the determination of comprehensive accurate the rmophysical properties data

for the major pure components (methane, ethane, propane,

butanes, and nitrogen) of liquefied natural gas mixtures at temperatures between 90 K and 300 K and at pressures up to 350 atm

(5000 psi). Our goal is to provide a ra.nge and quality of data

that will be recognized as definitive or standard for all foreseeable

low temperature engineering calculations.

Accurate phase equilibrium, compressibility, and thermodynamic properties data are needed to design and optimize gas

separation and liquefaction processes and equipment. Accurate

data for the pure components of LNG mixtures will permit developing calculation methods which take into accoimt the dependence

of the the rmophysical properties on the composition.

6. Background . Liquefied natural gas is expected to supply an increasing percentage of the United States' energy requirements. It is

likely that massive quantities of liquefied natural gas will be

imported during the years 1976-1990. Ships and importation

terminals are being built for transporting, storing, and vaporiz-

'ing liquefied natural gas for distribution. Accurate physical and

thermodynamic properties data for compressed and liquefied

19
natural gas mixtures are needed to support these projects. For

example, accurate compressibility and thermodynamic properties

data are needed to design and optimize liquefaction and transport

processes; accurate data for the heating value, which for liquefied

natural gas mixtures depends on the total volume, the density,

and the composition, are needed to provide a basis for equitable

custody transfer.

Accurate thermodynamic properties data for liquefied gas

mixtures must be based on precise compressibility and calorimetric

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

calorimetric data give the dependence of thermodynamic properties

on temperature (at fixed pressures and densities). It is impossible

however, to perform enough compressibility and calorimetric measurements directly on multicomponent mixtures to permit accurate

interpolation of the data to arbitrary compositions, temperatures

and pressures. Instead, thermodynamic properties data for multicomponent mixtures usually must be predicted (extrapolated) from

a limited number of measurements on the pure components and

their binary mixtures.

This project was initiated to provide the natural gas industry

with comprehensive accurate data for pure compressed and liquefied methane, the most abiindant 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, during this reporting period. This report contains the most comprehensive and

20
accurate tables available for the thermophy sical properties of

pure gaseous and liquid methane, and provides an accurate basis

for calculating thermophysical properties data for LNG mixtures.

We have also published comprehensive accurate dielectric

constant and Clausius -Mo ssotti function data for pure compressed

and liquefied methane (Cryogenics j_3, 712 (1973) ). This data will

provide a data base for mass and density gauging.

7 . Program and Results .

7.1 Ethane, Thermodynamic Properties Data--R. D. Goodwin

We have completed a voluminous manuscript, "Provisional

Values for the Thermodynamic Functions of Ethane, " comparable with our report on methane in NBS Technical Note 6 53, "The

Thermophysical Properties of Methane, From 90 to 500 K at

Pressures to 700 Bar. " The above ethane report covers the

entire range of fluid states at temperatures from 90 to 600 K,

and pressures to 700 bar. The purpose of this work has been

twofold: to indicate those physical properties for which experimental data are inadequate; and to provide the AGA with useful results at an early date.

In this work on ethane we have achieved a long -sought

goal, namely an equation of state for thermal computations of

such simplicity that it virtually ensures a correct qualitative

behavior of the P(p, T) surface and of the important derivatives,

especially about the critical point. It also gives qualitatively

acceptable extrapolation to pressures at least twice those of

P-p-T data used for adjusting constants in the equation of state.

A manuscript on the above vmique equation of state has been

21
prepared for open publication. It is our hope that complex computations on LNG mixtures may be simplified by use of this equation in identical form for each pure component.

In appendices to the present report we give copies of our

unpublished work on the physical properties of ethane, namely-

Appendix J R. D. Goodwin, The Vapor Pressure of Ethane,

Laboratory Note 73-3, July 9, 1973.

Appendix K R. D. Goodwin, Ethane Virial Coefficients and

Saturated Vapor Densities, Laboratory Note

73-4, Aug. 14, 1973.

Appendix L R. D. Goodwin, The Orthobaric Densities of

Ethane, Methane, Oxygen and Fluorine, Laboratory Note 73-5, Sept. 18, 1973.

Appendix M R. D, Goodwin, Liquid -Vapor Saturation Temperatures of Ethane and Methane, Laboratory

Note 73-6, Nov. 28, 1973.

22
7.2 Ethane, Compressibility (PVT)Data -- G. C. Straty

In the gas expansion technique used in this laboratory for

accurate, absolute, compressibility (PVT) determinations, the

molar volume V of a cryogenic fluid contained in a cell at temperature T and pressure P is determined by expanding the fluid from

the calibrated cell into large calibrated volumes maintained near

room temperature ( ~ 295 K). Using the near -ideal-ga s-like

behavior of the room temperature gas, the number of moles of gas

residing in the total system can be computed accurately. One of

the factors limiting the accuracy of this method is the ability to

assign correctly the appropriate proportions of the fluid to the cell

and to the various noxious volumes elsewhere in the system.

PVT measurements on ethane present an additional problem

not encountered with most cryogenic fluids such as methane,

oxygen, etc., because the critical temperature of ethane (305.33 K)

is well above room tempe rature . The consequence is that during

many of the density measurements on ethane, relatively high density fluid would reside in external parts of the system which could

not be a.ccurately accounted for in the present apparatus without

some modifications.

During this reporting period, appropriate portions

of the apparatus have been enclosed in ovens and/or provided with

heaters to maintain their temperatures well above the critical temperature of ethane, Thermometric sensors have been calibrated

and installed to these various portions of the apparatus to enable

the temperatures to be measured and accurate PVT data obtained.

Volume calibrations of several new system components have been

made. Preliminary testing of the apparatus has been performed

with satisfactory results.

23
7. 3 Methane, Sound Velocity Data - - G. C. Straty

The ultrasonic velocities of sound in pure saturated and compressed fluid methane have been measured at MHz frequencies. Data

have been obtained along the saturation boundary from near the triple

point to 186 K and along several isotherms from 100 K to 300 K at

pressures up to about 345 bar. The sound velocity data have been combined with the previously measured PVT data to calculate the isentropic

and isothermal compressibilities and the specific heat ratio C /C . p v Measurements along the compressed fluid isotherms at temperatures

of 210 K and above were limited to a minimum density ranging from

about 14 mol/t at 210 K to about 10 mol/^ at 300 K due to the large

sound attenuation in methane. A manuscript reporting the results of

the ultrasonic sound velocity measurements on methane has been published in Cryogenics, 14, 367 (1974), and is attached as an appendix to

this report.

A newly constructed light scattering spectroscopy apparatus has

been employed to obtain hypersonic (GHz) velocity data at the lower

densities where measurement by ultrasonic techniques were impossible.

Preliminary data have been obtained to densities as low as 1 mollt

along several isotherms. Measurements in the regions of overlap with

the ultrasonic data indicate excellent agreement,and overall agreement

with calculated sound velocity data is satisfactory.

7 . 4 Methane, Thermophysical Properties Data

AGA Project BR50-10 was initiated to provide the natural gas

industry with comprehensive accurate thermophysical properties data

for pure compressed and liquefied methane, the most abundant component in LNG mixtures. The final report of this work, "The Thermophysical Properties of Methane, From 90 to 50 K at Pressures to 700

Bar", was published as NBS Interagency Report (NBSIR) 73-342 in

24
October 1973, It has been reprinted as NBS Technical Note 653, by

R, D, Goodwin, in 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 accurate thermophysical properties data for LNG mixtures,

(For example, see references [1 ] in the section on Densities of LNG

Mixtures in this report. )

The NBS Cryogenics Division has suggested that the report should

become internationally accepted as "agreed on" standard reference data

by the American Gas Association, Inc. , and the natural gas industry.

This suggestion has received approval from the AGA Pipeline Research

LNG Supervisory Committee and the AGA Measurement Committee

and is currently under consideration by the AGA-LNG Committee,

E. L. Smith, Chairman. The report was recently brought to

the attention of the international LNG industry at the Fourth Internationl

Conference on LNG in Algiers, June 24-27, 1974 (see Paper VII- 1 by

L. A. Sarkes, AGA, Inc. , and D, B. Mann).

8. Problem Areas . For ethane, the computation of an accurate thermodynamic network in liquid states is more difficult that for methane.

Vapor pressure measurements of high accuracy are needed at low temperatures, where these pressures are so small that no accurate

experimental technique so far has been developed. Heats

25
of vaporization are so large at low temperatures (17, 000 J/mol)

that the experimental error of greater than 1% in these data

gives about 200 J/mol error in computations across the vapor

liquid "dome. " Densities of saturated liquid ethane in the midrange of temperatures (l60 to 250 K) apparently never have been

measured. The melting line is known only with very low accuracy. Comparison of our calculated speeds of sound for saturated

liquid ethane with experimental data suggests that derivatives of

the P(p, T) surface (via the equation of state) are not as accurate

at low temperature s as desired. All of these deficiencies suggest the need for new highly accurate compressibility (P-p-T)

measurements, sound velocity measurements in the homogeneous,

single-phase domain, and possibly additional specific heat measurements, e. g, C^(p,T), over a wide range of (p, T).

Some delays in the modifications of the PVT apparatus have

been encountered and are due almost entirely to delivery delays of

purchased components. This lost time however has largely been

made up and the PVT program is essentially on schedule.

9 . Funding , Man -years Expended, January- June 1974 0.9

Equipment and/or Services Purchased $ 9.1 K

Total Reporting Period Cost $ 58.9 K

Balance Remaining (June 30, 1974) $ 9.6 K

26
10. Plans for Future Work.

Schedule

1974

3 4

Ethane

:

Complete editorial work on

two major publications

Measure compressibilities

(PVT) of liquid ethane

>

27
Title . DENSITIES OF LIQUEFIED NATURAL GAS MIXTURES

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

Cost Center Numbers . 2751364, 2752364

Sponsor . LNG Density Project Steering Committee, American Gas

Association, Inc., Project BR 50-11.

Introduction. Accurate density data for liquefied natural gas mixtures are needed to provide a basis for custody transfer methods

and equitable custody transfer agreements. This project will provide a data base for developing accurate methods for mass and

density gauging at NBS and throughout the fuel gas industry.

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

accurate (0. 1%) measurements of the densities of saturated liquid

methane, ethane, propane, butanes, nitrogen and their mixtures,

mainly in the temperature range 90-150 K, at pressures to 10 bar;

and to test and optimize accurate methods for calculating the densities of LNG mixtures at arbitrary compositions and temperatures. 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.

Methods for calculating the heating value of liquefied natural gas

require knowing its density, which in turn depends on its composition and temperature. As the compositions of LNG mixtures vary

considerably depending on the source of the gas and the processing

conditions, methods are needed for calculating accurate densities

at arbitrary compositions and temperatures. The accuracy (0. 1%)

is important because of the extremely large volumes of liquid involved. Each 1% error in density is equivalent to an inequity of

$15-20 thousand dollars per shipload of LNG (72,000 class).

28
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.

A high precision (0.05%) magnetic densimeter (based on Archimedes

Principle) was designed and constructed prior to this reporting period.

7. Program and Results. Density measurements have been completed

for nitrogen from 95 to 120 K, for methane from 105 to l60 K, and for

ethane from 105 to 220 K. Some measurements on propane and on normal

and isobutane have also been made.

The scope of work for this project has been amended (January 15,

1974) to include testing and optimizing of computer programs for calculating accurate (0. 1%) density data for LNG at arbitrary compositions,

temperatures and pressures in the following ranges:

Composition: more than 70% methane, less than 10%

of each of the minor components,

temperature: 90-140 K.

pressures: below 10 bar

Funds for this work have been placed in cost center 2752364.

Calculation methods will be compared with accurate density measurements as they become available. Several available methods for

predicting the densities of LiNG mixtures have been programmed for

the NBS digital computer. These methods include a cell model [l], a hard sphere model [2] a corresponding states technique [3] and a computerized graphical interpolation scheme [4].

29
8. Problem Areas . A potential problem area is the delay in

delivery of accessory equipment for the mixture studies,

9 . Funding . 2751 364 (Measurements)

Man years expended, January- -June 1974 0.8

Equipment and/or Services Purchased $ 5.7 K

Total Reporting Period Cost $ 31.0 K

Balance Remaining (Jiine 30, 1974) $ 4.0 K

10,

2 752 364 (calculation methods)

Man years expended, January- June 1974

Equipment and/or Services Purchased

Total Reporting Period Cost

Balance Remaining (June 30, 1974)

Plans for Future Work.

0. 1

$ 0, 9 K

$ 5. 6 K

$ 14. 5 K

year

Schedule: quarter

1974

3 4

Measure densities of

binary mixtures containing methane, ethane,

propane and nitrogen

Test available calculation methods

30
fer ence s : Albright, M, A., Technical Publication No. 3, A Report to the Gas

Processors Assoc., 1812 First Place, Tulsa, Okla. 74103 (1973).

Rodosevich, J. B. and Miller, R. C, Paper No. K-5, Advances,

in Cryogenic Engineering, Vol 18, (in press, 1974).

Mollerup, J. and Rowlinson, J. S., Chemical Engineering

Science, 2% 1373 (1974).

Klosek, J, and McKinley, C., Proc. First Int. Conf. on LNG,

Paper 22, Chicago (1968).

31
Title. Low Temperature Material Behavior

Principal Investigators. R. P. Reed, R. L. Tobler, R. P. Mikesell,

and R. L. Durcholz.

Cost Center Number. 2750430

Sponsor Project Identification. Maritime Administration Project

55-300-15-011.

Introduction. Data on thermal and mechanical properties of structural

and insulation materials are essential to facilitate material selection

on the basis of cost and safety. Proper material choice and reliable

definition of material behavior using fracture mechanics is of major

economic importance for cryogenic containers in the sea transport

of LNG.

Objectives . The objective of this program is to obtain fracture

toughness and fatigue crack growth rate data in the temperature range

76-300 K. These measurements are being conducted on a series of

Fe-Ni alloys and Al alloys.

Background. To construct tanks for sea transport of LNG requires

between 500,000 and 7,000,000 pounds of expensive alloys, depending

on the type of tanker chosen. This large-scale consumption of costly

alloys demands very careful material selection to insure economical

but safe, storage tanks. Therefore, since MarAd's goal is to reduce

ship costs, it is in their interest to insure the availability of relevant

thermal and mechanical property data to enable the best possible

material selection and dependable, efficient design.

Program and Results . The materials effort in this program has concentrated on two areas, a general materials properties assessment

and the initiation of an experimental low temperature tensile, fatigue,

and fracture study of candidate materials. The materials properties

assessment has included a compilation of all fatigue and fracture data

on Fe-Ni steels and their weldments , a collection of ship design data

and an analysis of materials in use, an assessment of the current

production and/or research efforts of the materials suppliers, an

assessment of the current materials requirements for LNG containers

by the American Bureau of Shipping, U. S. Coast Guard, and the

ASME pressure vessel code, and the bibliography of literature containing data on aluminum alloys, non-metallics , and insulation

materials. For the experimental program the materials were procured
specimens were made for tensile, fatigue and fracture tests for

selected materials; a variable temperature cryostat was built; and

the experimental procedures proofed, and fracture data obtained on

selected Fe-Ni alloys.

Materials Properties Assessment

The literature data from some 60 references on the fatigue and fracture properties of the ferritic Fe-Ni steels (Ni < 18%) has been extracted, critically valuated, and compiled. The fracture data in the

compilation are the impact energy; nil ductility transition, crack

opening displacement, fracture toughness, and dynamic tear tests

and their dependencies on temperatures, composition, and heat treating or cold working. Fatigue data include fatigue lifetime and fatigue

crack growth rates at LNG temperatures. Also included are tensile

properties, hardness, impact energies , explosion bulge tests , and

other fracture data. The entire compilation will be sent as an interagency report and included in a review article on LNG materials in

the open literature.

The production and research capabilities of the major suppliers of

LNG structural alloys were also assessed. Direct contact was made

with the research personnel of all the major suppliers to assess what

work on these materials has been done or was in progress. These inhouse efforts indicated are generally low level. We have attended the

LNG Materials Conference at the British Welding Institute and visited

Technigaz, Det Norske Veritas, and the Welding Institute to provide

information about the foreign efforts in LNG materials research. We

also have a member of our staff on the Cryogenic Materials for LNG

Tank Applications Committee of the Metals Properties Council.

Experimental Program

Test materials of 1-1/2 inch thick plate have been obtained for the

3-1/2, 5, 6 and 9% Ni steels and Ai 5083, Fe-9Ni steel has been obtained from two sources,

A cryostat for variable temperature control near LNG temperatures

was designed and built. The experimental procedures, especially J

integral test techniques, were evaluated and proven satisfactory.

New methods were devised to monitor the crack growth and crack

opening.

Fracture toughness and fatigue crack growth rate tests at 300, 195,

111, 76, and 4 K have been completed. These alloys include Fe-6Ni

and Fe-5Ni in the QLT or austenitized, temperized, and reversion

annealed condition, and Fe-9Ni in the quenched and tempered condition.

33
Linear elastic fracture mechanics parameters (Kq, Kj(^) and Jintegral (Jjc) test data have been measured for identical 1.25 inch

thick compact tensile specimens. For the first time valid Kxc critical

stress intensity" data have been obtained for these Fe-Ni alloys. Also,

for the first time a decided temperature dependence of the fatigue

crack growth rate has been measured; the rate of crack propagation is

higher at 76 K compared to room temperature for all alloys.

Program Publications and Talks

One talk was presented at the ASTM Special Symposium on Properties

of Materials for LNG Tankage. This conference was held in Boston,

Mass, on May 21-22, 1974.

One paper will be included in the Special Technical Publication of that

ASTM conference, "Low Temperature Fracture Behavior of Ferritic

Fe-Ni Alloy Steels," by R. L, Tobler, et al. (see Appendix P).

8. Problem Areas. Testing has proceeded on schedule. There are no

delays,

9. Funding . During this reporting period, about $75,000 has been spent.

This leaves $40,000 for research during the next reporting period.

10. Future Plans. During the next three months the fatigue and fracture

toughness properties of Fe-3-l/2Ni (heat treated), steel and 5083 Al

will be measured at 300, 195, 111, and 76 K.

34
1. Title. Elastic Properties of Materials Intended for Use in Liquefied

Natural Gas Applications

Principle Investigators. H, M, Ledbetter, E. R. Naimon (NRC-NBS

Postdoctoral Research Associate, 1973- 74) and Vf. F. Weston (NRCNBS Postdoctoral Research Associate, 1973-74).

2 . Cost Center Number. 2 750131

3. Sponsor Project Identification. NBS

4. Introduction. The elastic properties of structural and insulation

materials must be known before such materials can be selected economically and safely. Proper material choice for cryogenic containers for the sea transport of LNG is a major economic problem.

5. Obj ectives

.

The objectives of this program were to determine the

elastic properties of structural materials in the temperature range

4 - 300 K. These properties include: Young's modulus, shear modulus, bulk modulus, and Poisson's ratio. Measurements were made

on a series of iron-nickel alloys and on some aluminum alloys,

6. Background. Depending on the type of tanker for \sea transport of

LNG. 500,000 to 7,000,000 pounds of expensive alloys are required.

This large-scale consumption of costly metals demands careful

material selection to insure economical, but safe, storage tanks.

Since the goal is to reduce ship costs, it is essential to have relevant

elastic property data for the best possible selection and design of

tankers

.

7. Program and Results . The program's general aspects, the experimental approach, the data analysis, and both tabulated and graphed

results are given in a manuscript "Low- temperature elastic properties of aluminum 5083-0 and four ferritic nickel steels" by W. F.

Weston, E, R, Naimon, and H. M. Ledbetter, This manuscript is

included as Appendix N.

8. Problem Areas, Currently, there are no problems with the program,

9. Funding . The program cost is estimated at $ 15 , 000,

10. Future Plans. Currently, no additional measurements are planned

in this program.

35
1. Title. Heating Value of Flowing LNG

Principal Investigators. J. A. Brennan and R. W. Stokes

2. Cost Center Number. 2750361

3. Sponsor Project Identification. Pipeline Research Committee

(American Gas Association) PR-50-48.

4. Introduction. This project will draw on information and facilities

generated by other sectors of the NBS LNG effort. Thus the calibration

of a densimeter used will be traceable to the NBS density reference

system being constructed by Younglove under cost center 2751361.

Mixture density data produced under 2751364 by Haynes and Hiza will

also provide a necessary input to the proper interpretation of results.

5. Obj ectives

.

The original objective of this program was to set up a LNG flow facility and to evaluate selected flowmeters in LNG service.

In November 1973 the objective was expanded to demonstrate the accuracy of measurement of the heating value of LNG flowing in a pipeline through integration of state-of-the-art instrumentation for flow,

density and heating value. The expanded project has been conceived

of in a three year time frame. In the first year individual components

will be calibrated and installed in the NBS LNG flow facility.

6. Background . The need for accurate flowmetering of LNG provided the

original impetus for the work in this program (unpublished NBS Report

[ 1972] , NBSIR 73-300). Since liquid natural gas may be sold on the

basis of heating value the program was broadened to include the necessary instrumentation for determining heating value of LNG, this

expanded program to commence early in 1974, The objectives are

based on scaling small flowmeters capable of laboratory testing up to

full line size components. Appropriate intermediate sizes are included with field tests scheduled as part of the overall project.

7. Results

.

A four-inch vortex shedding flowmeter was purchased and

calibrated in water at NBS-Gaithersburg over the flow range 50 to

600 gallons per minute. The results of the calibration agreed very

closely with the manufacturers predicted performance. A liquid

nitrogen calibration was run at NBS-Boulder over a reduced flow

range of 50-230 gallons per minute. Since it is not possible to test

the meter in the actual piping configuration that will be used later in

the LNG tests, a second liquid nitrogen test will be run with a different inlet piping configuration to determine what affect the piping may

36
have on meter performance. The results of both tests will be compared with the results reported earlier [NBSIR 74-358] on the 1-1/2

and 2-inch meters to see if the performance is similar.

A new sensor was supplied with the four-inch meter which did not re- quire changing when changing test fluids from water to liquid nitrogen.

It was still necessary to adjust the current through the sensor but

this adjustment is easily made.

A second four -inch vortex shedding flowmeter was obtained from a different manufacturer and calibrated in water at NBS-Gaithersburg,

This meter is now being tested in the liquid nitrogen flow facility at

NBS-Boulder, Results of the liquid nitrogen test are now being

analyzed.

Test results from both four-inch meters will be used in testing techniques for predicting meter performance in liquid nitrogen. Testing

of the second four-inch meter was not originally planned as part of

the test program but the availability of a meter using the same principle but with different sensing elements was thought to be a worthwhile addition to the program. The additional testing required will

add some expense to the program but the information available is

already proving very beneficial.

All the components are on hand to fabricate the test section necessary

for the LNG field tests on the four-inch meter. This section will be

fabricated and ready for installation in July 1974. No installation

date at the LNG facility has been determined at this time.

Static tests on the densitometer have been completed. Tests were run

in liquids methane, propane and nitrogen using the same densitometer

that had previously been tested in flowing liquid nitrogen on another

program. Some adjustments to the electronics were necessary before

testing in liquid methane but after the adjustment was made the densitometer worked properly in all three fluids.

It was decided to delay the purchase of new densitometers for this

phase of the program until some additional information from the LNG

Density Reference System is available. With that information selection of the most desirable densitometer should be easier. Since the

older densitometer was available no program delay or other adverse

affects will result from this decision.

The densitometer was intended to be used over small temperature

limits but was used in these tests over the range 78 K to 277 K, Results obtained on each fluid independently were consistent but when

all results were combined there was a definite degradation in overall

37
performance. This degradation appears to be caused by covering

such a broad temperature range with an instrument not designed for

that use. Discussions have been held with the manufacturer about

the performance and much of the above analysis came from that discussion. Since actual LNG measurements will not involve such wide

temperature limits this problem should not occur in actual usage.

A surplus calorimeter was obtained from one of the sponsoring companies and some preliminary tests run. As a result of these tests and

discussions with the manufacturer it was decided to have the manufacturer's service representative inspect the machine. The service

representative suggested what would be needed to put the machine in

good operating condition and the necessary parts have been ordered.

Approximately $700 will be expended to refurbish the calorimeter.

A surplus trailer has been obtained and will be installed at the LNG

flow facility for housing the calorimeter. After installation the trailer will require some renovation for proper calorimeter operation.

A gravitometer has been ordered and is scheduled for delivery the end

of July. This gravitometer will be installed in the trailer with the

calorimeter.

The two -inch flowmeter and the densitometer have been installed in

the LNG flow facility in preparation for system integration tests. Installation of the calorimeter must await the trailer installation and

refurbishing work.

In preparation for the system tests the electrical circuitry for the

load cell system has been modified in an effort to improve performance. The flow control valve has also been modified for better control

at low flow rates.

Problem Areas . No problems have been encountered that would have

an adverse affect on the project.

Funding . Man Years Expended 0. 75

Major Equipment Purchased $ 5,776

Total Reporting Period Costs $45, 000

Balance on Hand $31 , 000

38
10. Future Plans. Flowmeter tests at an LNG peak shaving plant are

planned late this calendar year. Actual test date depends on facility

availability. The calorimeter will be refurbished and installed at

the LNG flow facility after the necessary building arrangements have

been completed. After the calorimeter is running, system integration

tests will be started. It is planned to complete this phase of the program this calendar year.

39
1. Title and Principal Investigators. LNG Density Reference System - Ben Younglove.

2. Cost Center Number. 2751361

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

Project BR 50-10.

4. 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

2751364 will provide basic reference data on pure liquids and mixtures which will serve as density standards.

5. Objectives. This research will provide a system for evaluating

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 select one capable of performance as a transfer standard in order to provide traceability of accuracy to

field density measurement systems.

The first year will be devoted to construction and testing of the

density reference system. In the second year we will concentrate

on evaluation of commercial meters, while the fiAal year will Involve selection testing and application of the transfer standard.

6. Background. In early 1973 a proposal was made to the American

Gas Association for research in several areas of LNG technology

to be done at this installation. Part of this program was the

density reference system. Initial scheduling indicated for the

first year of work, starting in April to be design, fabrication, and

testing of a density system. Work actually commenced in August

as a result of staffing difficulties. Since this initiation, we have

conducted extensive study on the feasibility of various techniques

for such a system, deciding finally on an application of Archimede's

principle (see 7. below). Construction has begun on the various

components of the system, and the automatic weighing head plus a precision gas balance for mixture determination are on order.

40
7. Program and Results . Two sample containers were built, A

large one of approximately 8. 9" O. D. x 17" deep is intended to

house, at best, all of the densimeters that are anticipated.

Another of the same diameter, but 7" deep will be used for preliminary testing and can also be used to house all but the largest

of the densimeters. These vessels have been pressure tested to

200 psi at room temperature with water and the smaller has been

pressure tested in liquid nitrogen to 90 psi with He gas.

A vacuum jacket large enough to house the pressure vessels was

obtained.

A room temperature pressure vessel large enough to house the

weighing head has been built and pressure tested to 200 psi with

water. Various other items have been built such as vapor pressure bulbs and electrical feed throughs. The boule of single

crystal silicon, donated by Texas Instruments, was cut to provide

a buoy of approximately 127 grams and the ends polished. This

will be suspended from the weighing heat via fine tungsten wire.

Manufacturers of densimeters have indicated willingness to loan

working devices for test. One device is on hand and another is

expected in about two weeks. Others will arrive later, the latest

date mentioned for delivery was September this year.

8. Problem Areas. The weighing head being supplied by the manufacturer did not arrive during this reporting period. It is expected

that this will be integrated in the system within the next two months.

9. Funding.

Man Year Expended

Principal investigator 0, 85

Technician 0, 31

Equipment Purchased $ 8, 000

Total Cost $70, 300

Balance on Hand $ 9, 700

10. Future Plans, First three months. Continue assembly of density

reference system. Install weighing head. Check ability of density

monitor to measure water density at room temperature. Check

system ability to provide reduced temperatures. Check system

temperature regulation. Check density monitor performance with

liquid nitrogen.

41
We will develop a test plan which will determine the statistical

relevance of the experimental procedure.

Second three months. Install one or more test densimeters,

depending on availability etc. , and observe overall performance

of density reference system with densimeters. Observe preliminary behavior of test densimeters.

42
1. Title. Liquefied Natural Gas Technology Transfer

Principle Investigator. D. B. Mann

2. NBS Cost Center . 2750401

3. Sponsor Project Identification. Maritime Administration, Project

55-330-15-011.

4. Introduction. The NBS support of the Maritime Administration

(MarAd) LNG ship program is divided into two area

contract. These are an experimental program (NBS Cost Center

2750430) and the subject 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. Objectives . 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 13 of these complicated ships.

Various future projections indicate a total of from 25 to well over a 100 ships will be required to handle LNG importation within the next

10-15 years. 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 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.

43
Program and Results . (1 January to 30 June, 1974) In the initial

phases of the LNG Cryogenic Technology Transfer program emphasis

was placed on establishing the level and degree to which we could

interface with MarAd, MarAd research centers (NMRC), and MarAd

contractors. Progress therefore is measured as specific responses

to MarAd and MarAd contract requests and NBS generated output felt

necessary for the overall program.

7. 1. Data and Information - LNG. On March 5, 1975, N. A. Olien,

Acting Chief of the NBS Cryogenic Data Center visited the National

Maritime Research Center at Galveston, Texas for the purpose of

surveying the information and library needs of the center. It was his

purpose to provide NMRC aid and assistance in establishing a reference library for subjects dealing with liquefied natural gas, Mr. Olien

spent some time with Tom Burttschell, Superintendent of Docuaientation Services at NMRC discussing how best to accomplish the task.

Discussions were productive and upon returning to Boulder, Mr. Olien

sent the following items to Mr. Burttschell of NMRC:

1) Six bibliographies on the properties of construction materials,

2) A bibliography on LNG refrigeration utilization,

3) A bibliography on the properties of methane and one on methane

mixtures,

4) Two copies of the LNG technology bibliography,

5) A list of books on cryogenic subjects,

6) A list of LNG related periodicals with ordering information for

each.

7) A copy of Goodwin's NBSIR 73-242 "Thermophysical Properties

of Methane".

8) Two copies of the quarterly Hydrogen - Future Fuel,

It is believed that the necessary contacts have been made between NBS

Boulder and NMRC Galveston which should result in a continuing exchange of information on the general subject of LNG,

7. 2. LNG Custody Transfer Systems. NBS has been requested to

review a custody transfer system to be installed on one of the ships

constructed in U. S. shipyards and dedicated to LNG service. The

request for review came from the ship owner through the ship contractor, NBS notified the Maritime Administration of the request

with the recommendation that the review be performed under this

Maritime funded program. After several iterations, a work statement

44
was submitted to the ship contractor outlining a two -phase work

statement to accomplish the custody transfer review. The purpose

of phase 1 - System Design Review - is twofold:

1) To estimate the total uncertainty of the shipboard measurement

of LNG mass.

2) To suggest a possible testing program which would verify the

design review.

The scope of work of phase 1 will entail the definition of technical

areas which have direct bearing on the estimate of total uncertainty

in the shipboard measurement of LNG vmass. These areas will include, but not be limited tor

a) Physical dimension of system coTiponents

b) Changes in physical dimensions due to thermal contractions.

c) Tank strapping procedures.

d) Relationship between capacitance measurements, dielectric

constant, liquid level and density.

e) Range of LNG mixture fractions.

f) Heat transfer and system thermodynamics.

It is expected that technical evaluations by the instrumentation subcontractor have already been performed in many of these areas, in

these cases NBS will review the technical content of these valuations.

From the technical areas indicated above, it is expected that NBS

will define a set of parameters which can be used to give a measure

of the uncertainty in total mass. A mathematical relationship will

then be derived for the total mass uncertainty in terms of these

parameters. Limits on these parameters can then be set by NBS

(or other users) giving the best information available. In this format,

variations in system dimension from tank to tank can easily be incorporated in a total shipboard analysis.

Phase 2 - Physical Hardware Evaluation (Testing Program) - will not

be initiated until the completion of phase 1,

Approval of the NBS work statement by General Dynamics was received on June 11 and authorization by MarAd to commit funds to the

program was received on June 24. It is estimated that Phase 1 of the

program will require 4 months for completion with the results being

submitted to the sponsor in the form of an NBSIR.

45
7. 3. Fourth International Conference on Liquefied Natural Gas . Dr.

R. H, Kropschot and D. B. Mann of the Cryogenics Division of NBS

attended the above conference held in Algiers, Algeria (23 June to 27

June 1974). LNG 4 is the fourth in a series of conferences sponsored

by the International Gas Union (IGU), London; the International Insitute of Refrigeration (IIR), Paris; and the Institute for Gas Technology (IGT), Chicago, LNG 4 was held in Algeria by invitation of

the Algerian Gas Union and the Algerian Governoient, All conference

meetings were convened at the Palace of Nations, situated in the Club

des Pins just outside the capitol of Algiers. Technical tours to industrial areas containing LNG liquefaction sites were also provided.

Dr. Kropschot and Mr, Mann, in addition to attending all sessions of

the conference, toured the Skikdka industrial zone which includes

the 450 million cubic feet per day liquefaction plant and port facilities.

During the opening session an address "The Role of Liquefied Natural

Gas in U, S. Energy Policy" by Mr, John N. Nassikas, Chairman of

the Federal Power Commission, seemed at first to indicate an official

aloofness on the part of the U, S, in respect to large LNG programs

such as those involving Algeria and other Arab countries. A study of

Mr. Nassikas' press release of his address does not confirm this

impression. Although he does indicate energy self-sufficiency as

the U, S. policy and outlines the methods to be used in accomplishing

this goal, he nevertheless indicates imports of LNG are estimated to

be 3 trillion cubic feet by 1985 with an estimated investment of $5 to

10 million in LNG. This is consistent with the AGA prediction of

supplemental LNG import requirements of 2. 7 trillion cubic feet by

1985 and 3. 2 trillion cubic feet by 1990,

Mr. Louis A. Sarkes, Associate Director of the American Gas Assoc

ation. Incorporated and Douglas Mann of the NBS Cryogenics Division

co-authored a paper "A Survey of LNG Technological Needs in the U.S.

- 1974 to 2000". Mr, Sarkes made the presentation which described

the gas industry long range research plan and the current level of

LNG research at NBS, The paper was well received and comments

following the presentation indicated satisfaction on the part of delegates that the U. S. does have a structured plan for providing necessary research for continued U. S. participation in national and

international LNG programs. (See Appendix Q, ) Delegates (1900) from over 24 different countries, in addition to

Algeria, were present at the conference with the U. S. , France,

Germany, Japan, and the United Kingdom representing the largest

number of delegates in that order. This group of delegates assembled

to attend a conference on a high technology industry that has matured

46
over the past few years to a point where large expansion can and is

taking place. They, the delegates, want assurance that fixed expansion will take place, they wish to be part of this expansion, they

wish to identify who is responsible for the present program in Algeria,

and to assess the political climate of this first of the Arab states to

embark on a massive program of export of natural gas in liquid form.

The delegates found a demonstrated desire on the part of the government, both in policy and structure, to encourage input of foreign

technology for expansion of their program in LNG and a demonstrated

desire to show a stable political structure to accomplish this. The

Algerian operating personnel had a pride in their workmanship and

their progress and are working definitely towards technological selfsufficiency, independent of all foreign influences. It seems that their

position is rather strong in that they feel that they can dedicate over

100 trillion cubic feet of natural gas reserves for possible LNG export

projects. This should be compared with the north slope of Alaska

estimated reserves of 26 trillion cubic feet which could possibly enter

the LNG export trade.

Fifty-two papers were presented covering such subjects as world

trade in LNG, large-scale transportation projects, liquefaction and

processing, peak load plants and liquid handling, marine transportation, storage systems, new developments, and economic and legal

aspects. Papers were printed and distributed in a bound proceedings.

In spite of the tone of the subjects listed there did not seem to be a great deal of new technology, only improvements.

Problem Areas, Major problem areas under this program are the

definition of scope and content, MarAd has a number of separate current advisory studies, the results of which are necessary for defining

their position in LNG marine technology. Until these decisions by

MarAd are made, NBS will continue to provide information and assistance of the type outlined above.

Funding, January 1 - June 30, 1974,

Labor $67,000

Other Costs 3, 000

Total $70,000

Remaining $42,000

The major portion of the remaining funding will be expended during

the next 4 months on the custody transfer review, NBS will continue

47
to provide consultation and advisory services in the transfer of LNG

technology within the scope and present funding limitations.

48
1. Title. Federal Power Commission Consultation

Principle Investigators. D. B, Chelton and A. F. Schmidt

2. Cost Center Number. 2750404

3. Sponsor . Federal Power Commission - Bureau of Natural Gas -- letter agreement dated 4 June 1973,

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 results and 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 vaporizer and the liquefaction units (if any). These include,

but are not limited to the transfer lines, the storage tanks, the vaporizers and the process piping as it interacts with the storage tanks.

It is essential that the reviews cover the operation, maintenance and

emergency procedural philosophies for each terminal. Based upon

these studies, reports are submitted to the staff of the FPC setting

forth the technical evaluations and conclusions on each proposal. In

addition, NBS may provide expert witnesses on behalf of the staff of

the FPC in any hearings on the aforementioned applications.

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.

49
Funding . Total Funding FY 74 $57,000

Expenses July 1 - June 30, 1974 $57,000

Man Years of Effort 1. 0

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.

50
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51
1. Title. LNG - Dual Fuel Auto

Principle Investigator. J. M. Arvidson

2. Cost Center Number . 2750590 (Reimbursable)

3. Sponsor Identification. Joint NBS and General Services Administration

Requisition Number F4KE023, Case Number 66551.

4. Introduction. The work described relates to the general area of

transfer of technology based on Division experience in the handling

of liquefied combustible gases, instrumentation and systems analysis.

5. Objectives. To establish the degree of hazard to passengers and

auto on the release of liquefied natural gas in the trunk area of the

standard GSA dual fuel (natural gas and gasoline) sedan.

6. Background . The General Services Administration (GSA) dual fuel

automobiles are equipped to run on gasoline or natural gas. In the

initial GSA program the natural gas was compressed and carried in

high pressure cylinders, which in sedans were located in the trunk

space. To take care of accidental leakage, a large vent was installed

in the roof of the passenger compartments, with two small air vents

installed in the top of the trunk space. More recently, most of the

dual fuel installations have been installed with liquefied natural gas

(LNG) carried in an insulated tank at low pressure in the trunk compartment.

Natural gas has a density less than air and therefore is buoyant and

will rise at temperatures above about 151 K, It was anticipated that

vents provided would be adequate for dilution of explosive concentrations of methane gas in the trunk and passenger compartments

under conditions of operation. This was believed to be the case even

if very cold gas was vented (at a temperature of less than 157 K) as

the amount of the methane gas vented at this lower temperature would

be minimal, would be heated rapidly above 157 K and then vented

normally.

A recent explosion of a sedan, believed to be caused by migration of

methane gas from a trunk area to the passenger area, raised the

question of the functional adequacy of the high level vents. In other

words, can a combustible mixture of cold methane gas (at a temperature of less than 157 K) migrate from a leakage area in the trunk to

the passenger compartment, and if so, can additional venting, relocation of vents, or other methods be incorporated in the sedan to

eliminate this hazardous situation?

52
GSA has requested the Cryogenics Division of NBS to perform tests,

analyze data, and make recommendations for the modification (if any)

to be made in the vent system or any other aspect, method or design

that would minimize the concentration of methane gas (or LNG vapor)

in the trunk or passenger area to well below the lower explosion limit

(at least to 50% LEL).

A test program and results were described in the previous reporting

period (NBSIR 74-358), The potentially hazardous condition caused

by release of methane or vaporized LNG in the trunk area was re- ported to the co-sponsor in the form of a progress report.

7. Program and Results . Review of the test reports is in progress by

sponsor.

A decision by GSA is expected by September on the future course of

the program. Permission was requested of GSA and granted for NBS

to start hydrogen gas venting studies.

8, Problem Areas. None

9. Funding . No expenditures this reporting period,

10, Future Plans, NBS submitted a preliminary work statement to GSA

for further work designed to define the limits of venting capability of

the sedan (by minor structural changes) and aquire venting data of this

type of car body with hydrogen gas. In addition, a safety review of

LNG distribution stations (gas stations) was proposed.

53
Bibliography

Recent NBS reports and publications giving thermophysical properties data for fluids related to LNG mixtures (January 1, 1973--

June 30, 1974).

1, J, F. Ely, H. J. M. Hanley and G, C. Straty, Analysis of the

Pressure Virials and Clausius -Mos sotti Function for Polyatomic

Gases, J. Chem. Phys S% 842 (1973).

2, J, F. Ely and D, A, McQuarrie, Calculations of Dense Fluid

Transport Properties via Equilibrium Statistical Mechanical

Perturbation Theory, J. Chem. Phys. 60^, 4105 (1974).

3, W. M. Haynes, Viscosity of Gaseous and Liquid Argon, Physica 67,

440 (1973).

4: . W. M. Haynes, Viscosity of Saturated Liquid Methane, Physica 70,

410 (1973).

5. * D. E. Diller, The Clausius -Mos sotti Functions (Molar Polarizabilities) of Pure Compressed Gaseous and Liquid Methane, Ethane,

Propane, Butanes and Nitrogen, Cryogenics 14, 215 (1974).

6. * R. D. McCarty, A Modified Benedict-Webb-Rubin Equation of State

for Methane, Cryogenics 14, 276 (1974).

7. J. F. Ely and G. C. Straty, Dielectric Constants and Molar Polar

izabilities of Saturated and Compressed Fluid Nitrogen, J. Chem.

Phys. (in press, 1974).

8. R. D. Goodwin, The Thermophysical Properties of Methane from

90 to 500 K at Pressures to 700 Bar, NBSIR 73-342 (1973) and

Tech Note 653 (1974).

9. Thermophysical Properties of Nitrogen from the Fusion

Line to 3500 R (1944 K) for Pressures to 150.000 psia,

NBS Tech Note 648 (1973),

See attached appendices.

54
10. * D. E. Diller, Properties Data for LNG, Amer. Gas Assn.

Monthly, 55, 27 (1973).

11. * G. C. Straty and R. D. Goodwin, Dielectric Constant and Polarizability of Saturated and Compressed Fluid Methane, Cryogenics

13, 712 (1973).

12. G. C. Straty, Velocity of Sound in Dense Fluid Methane, Cryogenics

14, 367 (1974).

13. '•' B. A. Younglove, The Specific Heats, C^ and C , of Compressed

and Liquefied Methane, J. Res. NBS (in press, 1974).

14. * A. J. Kidnay, M. J. Hiza and R. C. Miller, Liquid -Vapor Equilibria Research on Systems of Interest in Cryogenics - -A Survey,

Cryogenics 1^, 575 (1973).

15. M. J. Hiza, A. J. Kidnay and R. C. Miller, A Bibliography of

Important Equilibria Properties for Fluid Mixtures of Cryogenic

Interest., NBS Special Publication (in press, 1974).

16. * W. R. Parrish and M. J. Hiza, Liquid-Vapor Equilibria with

Nitrogen-Methane System Between 95 and 120 K, Advances in

Cryogenic Engineering (in press 1974).

17. * R. D. Goodwin, The Vapor Pressures of Ethane, NBS Cryogenics

Division Laboratory Note 73-3, July 9, 1973.

18. * R. D. Goodwin, Ethane Virial Coefficients and Saturated Vapor

Densities, NBS Cryogenic s Division Laboratory Note 73-4,

August 14, 1973.

19. * R. D. Goodwin, The Orthobaric Densities of Ethane, Methane,

Oxygen and Fluorine, NBS Cryogenics Division Laboratory Note

73-5, September 18, 1973.

20. R. D, Goodwin, Liquid-Vapor Saturation (Orthobaric) Temperatures of Ethane and Methane, NBS Cryogenics Division Laboratory

Note 73-6, November 28, 1973,

55
21. - Weston, W. F. , E. R. Naimon, and H. M. Ledbetter, Low Temperature Elastic Properties of Aluminum 5083-0 and Four Ferritic

Nickel Steels (in press, 1974).

22. Sarkes, L. A, and D. B. Mann, A Survey of LNG Technological

Needs in the USA -- 1974 to Beyond 2000, Fourth International

Conference on Liquefied Natural Gas (Algiers, Algeria, June 1974).

23. Tobler, R. L. , R. P. Mikesell, R. L. Durcholz and R. P. Reed.

Low Temperature Fracture Behavior of Ferritic Fe-Ni AlloySteels, Sponsor report (1974),

56
A-1
Fhysica 70 (1973) 410-412 © North-Holland Publishing Co.

VISCOSITY OF SATURATED LIQUID METHANE*

W.M. HAYNES*

Cryogenics Division, Institute for Basic Standards, National Bureau of Standards,

Boulder, Colorado 80302, USA

Received 27 June 1973

Synopsis

The results of absolute measurements of the viscosity of saturated liquid methane using a

torsionally vibrating quartz crystal are reported for temperatures from 95 to 190 K. Comparisons are made with other data, all of which have been obtained with techniques different from that of the present work.

The viscosity of saturated liquid methane has been determined at temperatures

from 95 to 190 K, and at densities from 0.2 to 0.45 g/cm^ with a torsionally

oscillating quartz cylinder. The precision and accuracy of these measurements are estimated to be better than 0.5 and 2%, respectively. Details of the apparatus and

experimental techniques have been given in a previous publication-').

The sample gas was obtained from commercial, research-grade methane. Massspectral analysis of a representative sample by the supplier resulted in a specified

minimum purity of 99.97 mol percent. Its most probable impurities were nitrogen,

carbon dioxide, and ethane. The sample gas was further purified by passing it through a silica-gel trap immersed in an ice bath. Absolute measurements of the viscosity-density product were accomplished

using a quartz crystal of approximately 5 cm length and 0.5 cm diameter. (Its exact dimensions and mass have been reported in an earlier paper^).) Densities were obtained from measured temperatures and an equation developed by Goodwin and Prydz^) to represent their liquid densities along the saturation curve. In

general, the equation represented experimental density data within the 0.1 % uncertainty of their measurements, except within a few degrees of the critical temperature. At 190 K the density may be in error by as much as 0.5%.

The present results are presented in table I as a function of temperature and

density; in fig. 1 the experimental points are plotted as a function of temperature

along with independent measurements^"^) of other laboratories. The older and,

generally, less consistent data^~^) are included for the sake of completeness.

* Contribution of the National Bureau of Standards (USA), not subject to copyright. * NRC-NBS Postdoctoral Research Associate, 1970-72.

410

A-2
VISCOSITY OF SATURATED LIQUID METHANE 411

Table I

Viscosity of saturated liquid methane

Tempera.t ure Density Viscosity

(g/cm^) ([xg/cm s)*

U.44381 1 1QA lUU.UUU u.4o yuz 1 joy

U.4j zUo 1383

1 1 n Ann n >i'> ACS'! U.4Z 4y /1 T>C

U.41 /OO 1 AQA

1 ZV.Kjkjk) A /i 1 m "3 ymc73 125.000 0.40235 883

130.000 0.39429 810

135.000 0.38591 733

140.000 0.37715 673

145.000 0.36793 612

150.000 0.35819 557

155.000 0.34779 514

160.000 0.33659 465

165.000 0.32437 419

170.000 0.31077 376

175.000 0.29523 343

180.000 0.27658 309

185.000 0.25174 261

190.000 0.20020 198

* 1 !xg/cm s = 10"' Pa s.

It is particularly satisfying that the discrepancies between the values obtained

with four different techniques (this work; oscillating disk, ref. 3; capiliary flow,

ref. 4 ; falling cylinder, ref. 5) are generally within the estimated uncertainties of

the independent measurements. It should be noted that the results of refs. 4 and 5 were acquired on viscometers cahbrated with fluids of presumably known viscosity.

The agreement of the present saturated-liquid results for methane with those

of refs. 3 and 4 is consistent with comparisons of saturated-liquid data for

argon^'^'"^) and oxygen"^-^"-^^) obtained with the same apparatuses by the respective authors. However, it should be mentioned that, for compressed liquid argon

and oxygen, the results obtained with the present apparatus^ •^°) showed a consistently larger pressure dependence than those obtained with the oscillating-disk

viscometer of Hellemans et al.^'^^). (The discrepancies are most significant at ihe

higher hquid temperatures, e.g., approximately 20% at 10 MN/m^ at 140 K for argon^).) The above inconsistency is pointed out to illustrate that, although

viscosity measurements by different experimenters on the same fluid may agree

for the saturated liquid, it does not necessarily follow that this agreement would

carry over to the compressed liquid or other fluid regions.
412 W. M. HAYNES

90 100 no 120 130 140 150 160 170 180 190 TEMPERATURE. K

Fig. 1. Viscosity of saturated liquid methane; data from this work and refs. 3-9.

Acknowledgment. The author would like to acknowledge the National

Research Council, National Academy of Sciences - National Academy of

Engineering and the National Bureau of Standards for the Postdoctoral Research

Associateship during the tenure of which this research was performed.

REFERENCES

1) Haynes, W.M., Physica 67 (1973) 440.

2) Goodwin, R.D. and Prydz, R., J. Res. Nat. Bur. Stand. (U.S.) 76A (1972) 81.

3) Hellemans, J., Zink, H. and Van Paemel, O., Physica 46 (1970) 395.

4) Boon, J. P., Legros, J.C. and Thomaes, G., Physica 33 (1967) 547.

5) Huang, E.T.S., Swift, G.W. and Kurata, F., AIChE J. 12 (1966) 932.

6) Rudenko, N.S. and Schubnikov, L.W., Phys. Z. Sowjetunion 8 (1935) 179.

7) Rudenko, N.S., Soviet Physics-JETP 9 (1939) 1078.

8) Gerf, S.F. and Galkov, G.I., Zh. tekh. Fiz. 10 (1940) 725.

9) Gerf, S.F. and Galkov, G.I., Zh. tekh. Fiz. 11 (1941) 801.

10) Haynes, W. M., unpublished data.

11) Hellemans, J., Zink, H. and Van Paemel, O., Physica 47 (1970) 45.

A-4
APPENDIX B

B-1
This report gives accurate interpolation functions for the Clausius—ti/lossotti functions (molar polarizabilitiesj of pure compressed gaseous and liquid methane, ethane, propane, butanes and nitrogen; and suggests a method for calculating the dielectric constants or

the densities of their mixtures. The accuracy of calculated Clausius—Mossotti functions

for mixtures containing a high concentration of methane is expected to be better than 1% using only data for the pure components. Additional data for the dependence of the excess Clausius—Mossotti fuction on composition could reduce the uncertainty in Clausius—Mossotti functions for multicomponent mixtures to less than 0.2%.

The Clausius—Mossotti functions (molar polarizabilities)

of pure compressed gaseous and liquid methane, ethane,

propane, butanes, and nitrogen

D. E. Diller

Accurate thermophysical properties data for compressed and

liquefied gases and their mixtures are needed to design lique- faction, storage, and transportation processes and to provide

a basis for custody transfer agreements. For example,

accurate Qausius—Mossotti function data for compressed and liquefied natural gas mixtures are useful for practical densimetry applications; the density of a multicomponent

fluid mixture can be determined directly from a dielectric constant measurement (or vice versa). The compositions of

technically important gas mixtures are so variable however

that it is nearly impossible to obtain sufficiently comprehensive experimental data for many applications. Instead, accurate thermophysical properties data for multicomponent mixtures must usually be calculated from data for the pure components and selected binary mixtures.' - ^ The

purpose of this report is to give accurate interpolation functions for the dielectric constants and Clausius—Mossotti

functions of pure compressed and liquefied methane, ethane, propane, butanes, and nitrogen in a form useful for calcu- lating the dielectric constants or densities of their mixtures.

InterpKjIation functions for the Clausius—Mossotti

functions of pure compressed gaseous and liquid

methane, ethane, propane, butanes, and nitrogen

The Qausius—Mossotti function (molar polarizability),

C-M = '-^V (1) e + 2

gives a relationship between the dielectric constant e and

the molar volume K of a non-polar fluid. For low density

gases, the Oausius—Mossotti function is related to the molecular polarizability a by

An C-M=-Noa (2)

The author is with the Cryoqenics Division, Institute of Basic Standards, Nntional Bureau of Standards. Boulder Laboratories, Boulder, Colorado 80302, USA. Received 29 November 1973.

where Nq is Avogadro's number; therefore C—M depends

mainly on a fixed molecular property of the fluid. The

Clausius—Mossotti function for many non-polar gases and

liquids has been found to be nearly independent of temperature, pressure, density, and state ; varying less than 2% over

large density and temperature ranges. The Qausius—

Mossotti functions for compressed non-polar gases typically increase slightly with increasing density, reaching a maxi- mum in the vicinity of the critical density, and then

decreasing continually with further increasing density. The Qausius—Mossotti functions for most non-polar fluids decreases slightly with increasing temperature at fixed densities. Accurate empirical representation of the complete

dependence of the Qausius—Mossotti functions of compressed

gases and bquids on density and temperature is a difficult problem. An accurate 'equation of state' for the Qausius—

Mossotti function is not available, even for the simplest pure

gases. The dependence of C-M on density (neglecting the dependence on temperature) is given to good approximation however by

C-M ^Ae+B^p + Cep'^ + DgP^ + . . . (3)

The coefficient 5g is analogous to the second virial coefficient in the pressure virial expansion; the coefficients Q and ate purely empirical. The coefficients for (3) have been obtained for pure compressed and liquefied

methane, ethane, propane, butanes, and nitrogen from avail- able dielectric constant and density data. Further discus- sion of the data basis and the coefficients obtained for (3)

is gjven for each fluid.

Methane. Accurate data for the dielectric constants and

densities of pure compressed and liquefied methane are given in references 3 and 4. Data are available for temperatures between 91 and 373.4 K at pressures to 345 bars. The

data for the low density limit and the liquid- vapour

equilibrium curve have been fitted to (3). The coefficients obtained for (3) are given in Table 1. The uncertainty in the Qausius— Mossotti function for pure methane calcuhited with these coefficients is probably smaller than 0.2%.

Ethane. Accurate data for the dielectric constants and

densities of pure gaseous and liquid ethane at temperatures

CRYOGENICS APRIL 1974 Vol U, No. k B-2 215
Table 1 nitrogen

The Clausius—Mossotti functions for pure compressed and liquefied methane, ethane, propane, butanes, and

Methane

Ethane Propane

n-butane

/-butane Nitrogen

Coefficients for (3)

A,:, cm^ mole'^ flg, (cnn-^ mole'^ )2 Cf. (cm3 mole"'')^

6.541"^

11.225

15.935 20.656

20.885 4.3898

8.523 20.005

76.005 141.00'^

143.00*7

2

20a. 9

-4.26 X 102 3 -14.60 X 102 5 -58.40 X 102 5 -139.20 X 102* 7 -99.00 X 102' ^ -1.00 X 102 Q-io

Oe, {cm3 mole'M'* + 4.43 X 103 3

* Obtained from refractive Index measurements

f Reference numbers

between 283 and 305 K at densities up to twice the critical density axe given in reference 5. The Qausius—Mossotti

function for compressed fluid ethane changes less than 1%

with density and temperature in this range. Coefficients for

(3) are given in reference 5 and are reproduced in Table 1

.

It is expected that the Qausius—Mossotti function obtained by extrapolating (3) to densities up to 3pc at temperatures down to 90 K will be accurate to about 0.5%.

Propane. Accurate data for the dielectric constants and

densities of pure gaseous and Hquid propane at temperatures between 293 and 369.5 K at densities to 2pc are also given in reference 5. Coefficients obtained for (3) are given

in reference 5 and reproduced in Table 1. If (3) is extra- polated to densities up to 3pc and temperatures down to 90 K, the estimated uncertainty in C-M will be smaller than 1%. Normal and isobutane. Accurate data for the dielectric constants and densities of pure gaseous normal and iso- butane at temperatures above 400 K are given in reference

6. There are no dielectric constant data available for

liquefied butanes at low temperatures, but accurate data

for the refractive indices of gaseous and liquid normal and

isobutane along tlie liquid—vapour equilibrium curve are given in reference 7. The coefficients and C« obtained

for the dependence of Lorentz— Lorenz function, — 1/n^ + 2) X V, on density are given in Table 1. The

uncertainty in C-M obtained by using /Ig, and C« in (3) is probably smaller than 1%.

Nitrogen. Accurate data for the dielectric constants and

densities of compressed gaseous and liquid nitrogen at temperatures between 65 and 313 K are given in references

8, 9, 10. The Qausius-Mossotti function for gaseous and

liquid nitrogen changes less than 1% with density and

temperature in this range. Coefficients are given for (3)

for nitrogen in Table 1. The uncertainty in C-M calculated

for nitrogen using (3) with these coefficients is probably

smaller than 0.5%.

Suggested method for calculating the Clausius—

Mossotti functions (and dielectric constants or

densities) for mixtures of compressed and lique- fied gases

Ifllic Clausius -Mossitti function,

r \i = ^niixture - 1 . . '"mixture — r ''^mixture v*) ^mixture + 2

is known for a liquefied non-polar gas mixture, then the

dielectric constant can be determined from a density measurement, or the density p = 1/Fcan be determined from a dielectric constant measurement. The QausiusMossotti function can be calculated for a multicomponent

fluid mixture by using

C-A/mixture = ^ x/ C-M/ + C-M^(x/, T. P) (5)

I where thex/ and C-Mi are the mole fractions and

Qausius-Mossotti functions for the pure components and C-M^ is the excess Qausius-Mossotti function. The excess Qausius-Mossotti function is defined here as the change in C-M on mixing at fixed temperature and pressure. The

excess Qausius-Mossotti function is zero for non-polar gas mixtures at low densities. There are no data available for the Qausius-Mossotti functions of liquefied gas mixtures. The excess Qausius-Mossotti function C-Afi is expected

to be less than 1% of C-A/mixture for liquefied natural gas mixtures containing a high concentration of methane.

Therefore calculations of C-A/mixture for liquefied natural

gas mixtures are expected to be accurate to better tlian 1%

using pure component data only. Accurate data for the dependence of C-M^ on composition could probably

reduce the uncertainty in C-A/mlxture t^o less than 0.2%.

1 would like to thank G. C. Straty, R. D. Goodwin, and

J. F. Hy for the use of their data before publication, and

J. D. Olson for assistance with the calculations.

References

1 Rowiinson, J. S. Liquids and Liquid Mixtures (Plenum

Press, 1969)

2 Van Ness, H. C Qassical Thermodynamics of NonElectrolyte Solutions (MacmiUan, 1964)

3 Straty, G. C, Goodwin, R. D. Cryogenics 13 (1973) 712; Goodwin, R. D., Prydz, R. JResNBS 76A (1972) 81

4 Bose, T. K., Sochanski, J. S., Cole, J. H. / Chem Pliys 57

(1972) 3592

5 Sliwinski, P. Zeitschnft fitr Physikalische Cliemie 68 (1969)

91

6 Watson, H. E., Kane, G. P., Ramaswamy, K. L. Proc Roy

Soc (Loiidonj A156 (1936) 130, 144

7 Sliwinski, P. Zeitsclihft fur Physikalische Chemie 63 ( i 969)

263

8 Oudemans, G. J. PhD lliesis (University of Amsterdam,

1967)

9 Straty, G. C, Ely, J. F. (Unpublished data) 10 Jacobsen, R. T., Stewart, R. B., McCarty, R. D., Haiiley,

II. J. M. NBS Technical Note 648 (1973)

I M.dMH - ^-RI

216 B-3 CRYOGENICS . APRIL 1974

APPENDIX C

C-1
A 33 term modified Benedict— Webb—Rubin equation of state is presented for metfiane. The adjustable parameters in tfie equation of state have been estimated using recent experimental data and least squares techniques which include the thermodynamic equilib- rium conditions for the co-existing liquid and vapour phases. Comparisons of the new

equation of state and an older modified Benedict—Webb—Rubin equation of state to experimental data are given.

A modified Benedict—Webb—Rubin equation of state

for methane using recent experimental data

R. D. McCarty

There is currently an extensive worldwide interest in the

properties of liquefied natural gas (LNG). This laboratory

has recently completed an experimental programme on the thermodynamic properties of methane,"*- the principal constituent of LNG. These new data are believed to be more

accurate than those previously available and it therefore seemed worthwhile to use these new data to estimate the

coefficients to a modified Benedict—Webb—Rubin (MBWR)

type equation of state. The MBWR equation of state is es- pecially appropriate for the study of the properties of mixtures for two reasons; first, the mathematical form of the equation allows the inclusion of the thermodynamic conditions for phase equUibria '• ^ in the parameter estimation

process, and second, the MBWR is widely used throughout

the world for the calculation of the thermodynamic properties of other fluids. The particular form of the BWR

modification used here was developed by Jacobsen ^ for nitrogen. The development of this equation by Jacobsen

included a long and exhaustive study to determine an optimum functional form. The applicability of this form

of the BWR to other fluids has since been demonstrated for oxygen by Stewart et al and for hydrogen by this author.^ The only other modification of the BWR considered was

the form used by Bender' for a number of gases including

nitrogen and methane. Both the equations of state for nitrogen (Jacobsen and Bender) were constructed using the thermo-dynamic conditions for phase equUibria. The comparisons given later in this paper show that the form used by

Jacobsen reproduces the new experimental data better than

the form used by Bender. This result is not surprising as the form used by Jacobsen has 33 adjustable constants while

the form used by Bender has 20 adjustable constants.

Equation of state The parameters TV, N-^j for the equation of state, (1), were

estimated by least squares techniques using the data hsted in Table 1. The parameter y was chosen such that 7p^ ^ + 1 as suggested by Bender.'

The author is with the Cryogenics Division, National Bureau of Standards, Boulder, Colorado 80302, USA. Received 10 December

1973.

Table 1 Sunf^mary of data

Reference

No

ofpoints Temperature

range, K

Saturation data

Density

range, mole 1

Kind

ofdata

4 555 92-300 No 3-28.5 PVT

10 274 92-300 No 8-28 Cm

4 200 91-190 Yes 0.016-

28.12 Orthobaric densities

3 171 273-398 No 0.75-

12.5 PVT

4 96 140-270 No 0.5-

2.0 PVT

4 100 91-190 Yes 0.016-

28.12

Gibbs

function

The saturation data listed in Table 1 were calculated from

equations given by Goodwin,'* see appendix. The condition of equal Gibbs function for the saturated liquid and

saturated vapour in isothermal co-existence was included as data points at the 100 saturation temperatures referred to

in Table 1. The equation of state was also constrained at the

critical point loT^Tc = 190.555 K,Pc= 10.23 mole l"',

7^ = Pc = 45.387 atm, and (dF/dp) = (82/'/9p2) = 0. For a more detailed description of the techniques of simultaneous

data fitting, constraints, and weighting see Hust and McCarty ' or McCarty.^ The functional form of the equation of state is

P = pRT + p^ (7V,r + 7V27"'/2 +7V3 +NJT+Ns/T^)

+ p^{N^T + N^ +NJT + N^/T^)

+ pUN^oT + Nu ^Ni2/r)+p' (7Vi3) + pHN,JT + N,s/T^)+pUN,JT}

+ P^{N,,/T + NiJT^) + pUN,9/T^)

+ pHN2o/T^ +N^^/T^)exp(^yp^) (1) +

ps (N22/T^ +N23/T^}exp (-yp^)

276 C-2

CRYOGENICS . MAY 1974
+ pM^24/2^' +A^25/7^')exp (-7p2)

+ p9 {N^JT^ +^27/7^") exp (-7p2)

+ P" (VV28/7^' +Af29/7^')exp(-7p2)

+

pi3 (TVso/T-^ +A'3i/7'3 +yV32/r'')exp (-7p2)

where P is in atmospheres, p is in mole 1"' , and T is in kelvins. The coefficients {NO are given in Table 2.

Comparisons

The equation,

Gibbs (pi, 7) - Gibbs (py, T) = 0 (2)

was formulated using the equation of state (1). Equation

2 was then solved for the co-existing saturated liquid and

vapour densities (py and pi) at various temperatures {T). The resulting P- T locus is the vapour pressure curve given

by the equation of state. Fig.l compares the vapour pres- sures predicted by the equation of state to the vapour pres- sures given by Goodwin.''

Figs 2 and 3 show a comparison of the saturation densities using Goodwin's densities and values calculated by this equation of state and by Bender's equation of state, using

the coefficients reported by Bender.

0.3

50 200

Temperature , K

Fig.l Comparison of vapour pressure predicted by the equation

of state and those of Goodwin *

Saturated vapour

o This work

a Bender '

lOO ISO Temperature , K 200

Table 2 Coefficients to equation 1

A/i = — 1.o4jy4o6666 x 10"^

/V2 = 1 .Ubl Ul D^Ub4

A/3 = — 1 .dUo/ozUoUo X

1 r\

1

U

/V4 = c5.4<3H-*+Ui£/00^ X I u

/V5 = —^.z / oo^uy 1 UD X in4 1 u

/Ve = / .DOOO^loOZO't X 1 u

= 4. ft'^Rn79d1Q7 V 1 u Ns = in

/Vg = — 1 fiRn7A'^4791 V

/V10 = —0.? 7R9in7dR'^9 I Oc. l\J 1 H30t AV in-5 1 u N,, = in-2

/V12 =

/Vl3 = in-4 1 u

/Vl4 = —0.00 1 0/ 1 ooyy X in-3 1 u

/Vl5 =

N^e = Z.*+yODO-iOo/y X

in-5 1 u

0. /y /4bJ 1 4bo X

in-6 lU

/V18 = — /.Ib4oozyzy/ X

ir»-3 lU

/Vi9 = 1 .Zb/ /oDo/o4 X

1 n-4

/V20 = Z.ZZ4U iUz4bD X in4

/V21 = — 1 >ioriOc 10000 w

1 .4oUUbl zJzo X 1U° N22 = b.u*^yc5uo4oo/ X

1 n1

U

N23 = 1 .D'fzoo / oyyz x in6 1 u

/V24 = z. lozooo/ lyo x in-i

/V25 = 0.T 770197*5499 / / y 1 z / Ofzz VX in

A/26 = — 1 . 1 00 1 Do 1 0 A in-5

/V27 = 1 1fi'507fin7R7 V in

A/28 = 10-6

A/29 = 10-3

A/30 = 3.1512261532 x

10-9

A/31 = -2.1670774745 x 10-6

A/32 = 2.4000551079 x 10-5

7 + 0.0096 R 0.08205616 1 atm mole"' K"1

Fig.2 Comparison between saturated vapour densities of Goodwin ' and those predicted by this equation of state and the equation of

state by Bender '

The equation of state, (1), like other MBWR equations does

not have the proper theoretical behaviour at the critical point, that is, the derivative (d'^P/dT^)p at the critical point does not become very large. A comparison of experimental Cy with those calculated using (1) and those calculated by Bender's equation of state (coefficients from reference 1) is given in Fig.4. The large deviations between experimental Cy s and those calculated from Bender's equation were also noted in the case of O2-

CRYOGENICS . MAY 1974 C-3 277
Saturated liquid

o This work

o Bender '

-2 lOO 150 200

Temperature , K

Fig. 3 Comparison between saturated liquid densities of Goodwin ^ and the predictions of this equation of state and the equation of state by Bender '

A Experimental

o This work Bender

'

lOO

90

80

T\ 70

oE

>so

40-

30

90 95 lOO

Temperature , K

Fig.4 Comparison between experimental Cv data of Younglove ' and predictions by this equation of state and the equation of state by

Bender '

O This work Bender

'

200 250 300

Temperature, K

Fig.5 Comparison between experimental Cv data of Younglove ' and predictions by this equation of state and the equation of state by

Bender '

These large deviations between experimental Cy s and those

calculated by Bender's equation of state occur only at low

temperatures and high densities. Fig.5 gives a comparison of Cy s at moderate densities from the same three sources. As is the case with all equations of state which cover a large range of pressure and temperature, the deviations between

experimental and calculated densities become large in the

region of the critical point. Fig. 6 gives typical deviations between experimental and calculated densities from the same three sources. The data points illustrated in the first six figures were

chosen to show maximum deviations. A summary of

the rms deviations is given in Table 3. An attempt was made to use Bender's form of the modified BWR to represent the experimental data given in Table 1

.

Figs 7 and 8 compare the re-fitted Bender equation with

(1) and experimental data. A comparison of Figs 4 and 6

with Figs 7 and 8 show a definite improvement in Bender's equation but also that it still does not represent the data as well as (1) does.

i05

-0.5

o This work

o Bender

'

-I 21 2 mole I isochore

-o o—o Q o

ISO I60 I70 ISO I90 200 2IO

Temperature , K

Fig.6 Comparison between experimental PVT data of Goodwin

and predictions by this equation of state and the equation of state by Bender '

Table 3 rms deviations between equation 1 and input

data (Table 1)

rms

in density. rmsin pressure. Reference No of points mole !"'' atm

4 555 0.024 0.91

9 274 0.21 r

4 200 0.004

3 171 0.012 0.40

4 96 0.0023 0.023

4 100 0.01 r

* rms is in the Gibbs function difference of the saturated liquid and

vapour in the units of J mole"'

t rms is in Cv J mole ' K"'

278 C-4 CRYOGENICS . MAY 1974
a Experimental o This work

D Refit -Bender

equation

lOO

Temperature , K

Fig. 7 Comparison between experimental Cv data of Younglove ' and predictions of this equation of state and a refit of Bender's equation of state

o O S

5 O

-0.5

O

o This work Bender- Refit

21.2 mole I

' isochore

ISO I60 170 ISO I90 200 2IO

Temperature^ K

Flg.8 Comparison between experimental PVT data of Goodwin

and predictions of this equation of state and a refit of Bender's equation of state

Conclusion From experience of estimating the constants for (1) for methane, the region of greatest uncertainty for (1) was

found to be the densities of the saturated vapour boundary. More experimental data are needed before the uncertainty can be reduced. The 33 term equation of state given here will reproduce the experimental data with greater accuracy than the form

suggested by Bender, however, the 33 term equation requires double precision arithmetic on most digital computers and

a much greater exponent range than the twenty term

equation.

References

1 Bender, E. Proc 5th Symp on Thertnophysical Properties (ASME, NY, 1970) 227

Benedict, M., Webb, G. B., Rubin, L. C. J Chem Phys 8 (1940) 334

Douslin, R. D., Harrison, R. H., Moore, R. T., McCullough,

J. P. J Chem and Eng Data 9 (1964) 358 Goodwin, R. D. Internal Report No 73-342 (October 1973)

Hust, J. G., McCarty, R. D. Cryogenics 7 (1967) 200

Jacobsen, R. T. The thermodynamic properties of nitrogen from 65 K to 2 000 K with pressures to 10 000 atm', PhD

thesis, Washington State University (June 1972)

10

McCarty, R. D. Experimental Thermodynamics of NonReacting Fluids (Butterworths 1973) Chapter 10 McCarty, R. D. 'A modified Benedict-Webb-Rubin equation

of state for hydron' Internal Report No 74-357 (Feb 1974)

Stewart, R. B., Jacobsen, R. T., Meyers, A. F. 'The thermo- dynamic properties of oxygen and nitrogen. Part II -

Thermodynamic properties of oxygen from 100 R to 600 R

with pressures to 5 000 psia'. Final Report, NASA-Manned

Spacecraft Center, Houston, Texas (1972) Younglove, B. A. NBS J Res (1973) APPENDIX A

Supplemental equations To provide a useful minimum set of equations which will be

helpful to the reader who wishes to programme the equation of state for the calculation of thermodynamic

properties, the following equations from Goodwin '* are reprinted here. Vapour pressure equation

P

\o%e- =ax+bx^ +cx^ +dx{\ -xyi'^ (Al)

Equation for the saturated liquid densities

(P -Pc)

(Pt - Pc) = w^ exp [.4(1 -w^l^)+B{\ -H''*/3)

+ C(1 - w2)]

Equation for the saturated vapour densities

loge — = fli + ^2 w + ^3 H'''/3 -I- vv^'^ Pc + fl5 Uw

Equation for the ideal gas

C° 4 5 — =b^+-b2 Q^l^ +-b3 Q^l^ + 2b^Q

R. 3 3

(A2)

(A3)

+ bs exp e / I G[exp(iJ0-l]

J

(A4)

See Appendix B for the coefficients to equations Al, A2,

A3, and A4. APPENDIX B

Coefficients to equations

Table 4 Critical and triple point parameters for equations

(Al, A2, A3, and A4)*

190.55 K pc= 10.0 mole 1-1

Tt= 90.68 K pt = 28.147 mole 1-1

Pt = 0.117435675 bar

*The critical density for equations Al , A2, A3, and A4 is shghtly lower than the one used for the equation of state. The lower Pc is preferred by Goodwin,'' but did not work

well as a constraint for (1)

CRYOGENICS . MAY 1974 C-5 279
Tables Coefficients to equation A

1

a =4.77748580 c =-0.56788894

b = 1.76065363 d = 1.32786231 X =(1 -Tt/mi -TtlTc)

Table 6 Coefficients to equation A2

A =-0.178860165 C =-0.01848987

B = 0.04838475 E = 0.36 w ={Tc- HKTc -Tt)

Table 7 Coefficients to equation A3

a, =-2.7036003 ^4 = 5.2640362

02 = 3.1661552 a; = -3.5269034

flj = -8.6573409 fle = 0.46 w ={Tc- T)KTc - TO U = {TJT - 1 )l{TJTx - I

)

Table 8 Coefficients to equation A4

Q = 7/400 bs = 4.7207907 bi= 2.5998981 65 = 5.02288 ^2= 1.4449418 = 8.3143 J mole-' K-i

Z73 = -1.8472716 r =inK

^4= 0.8211218

APPENDIX C

Sample calculations and table of symbols

Table 9 Sample calculations from equations 1, A1, A2,

A3, and A4

For a temperature of 150 K and saturation pressure the equations 1 to A4 should give the following results.

(1) (Al) (A2) (A3) (A4)

Density, Pressure, Density, Density, C^lR,

mole r' atm mole T' mole l'' dimensionless

Liquid

pliase 22.3223 10.278 22.325 Vapour

phase 1.0187 10.278

3.0053

1.020

Table 10 List of symbols

a, b, c, and d parameters to vapour pressure equation

^ A, B, C, and D parameters to equation for saturated

liquid densities

fl] , fif2 • • ^6 parameters to equation for saturated vapour densities

by, b^ b(, parameters to equation for ideal gas P pressure

Pq, critical pressure

triple point pressure R gas constant T temperature

Tq critical temperature

T\ triple point temperature U reduced temperature in (A3) w reduced temperature in (Al) X reduced temperature in (A2)

7 parameter in (1)

p density

Pc critical density

Pt triple point density

280 C-6 CRYOGENICS . MAY 1974
APPENDIX D

D-1
R-787

Properties Data for LNG

By D. E. DILLER A.G.A.-supported research seeks cryogenics Division ~~ Institute for Basic Standards data essential to transport and exchange °" ^^^"'^^"'^ of this new energy source l. a. sarkes

Associate Director Research and Engineering American Gas Association

Thermophysical Properties of Pure Components of LNG Mixtures Research Plan: 1970-1978

1970-1973 Thermodynamic Properties of Methane

1973-1976 Thermodynamic Properties

of Ethane (Densities, compressibilities, enthalpies,

etc.) I

1976-1978 Thermodynamic Properties

of Propane

Other Thermophysical Prop)erties of Methane (Dielectric constants, sound velocities, viscosities)

Other Thermophys'cal Properties

of Ethane, Propane

Table 1

Thermophysical Properties of LNG (Pure Components)

Research Plan (April 1973-March 1976) Task 1Determine Densities, Compressibilities and Thermodynamic Properties of Ethane

• Analyze available data

• Measure vapor pressures and compressibilities (PVT)

• Measure specific heats, Csai

• Calculate thermodynamic properties

Task 2Determine Other Thermophysical Properties of Methane

• Measure dielectric constants

• Measure sound velocities

• Measure viscosities

Table 2 SEPTEMBER 1973 Amer . Gas Assoc. Monthly Vol 55, No. 9 D-2

Imported natural gas is supplying an

increasing percentage of the nation's energy requirements and new tech- nology is being developed to support

large importation projects. To take advantage of the large volume de- crease, about 600 to 1, which occurs when natural gas is liquefied, ships and importation terminals with cryo- genic tanks are being built for transporting, storing, and vaporizing large quantities of liquefied gas. To support these projects, extremely

accurate data on physical and thermo- dynamic properties for liquefied natural gas mixtures is needed. For example, accurate compressibility and

enthalpy data is essential to the design and optimization of liquefaction proc- esses. To provide an equitable basis

for transfer of custody, accurate data

is needed for heating value, which for liquefied natural gas mixtures depends

on the total volume, the density, and

the composition. There is little accurate data avail- able on thermodynamic properties of liquefied natural gas mixtures at low temperatures. (Typical natural gas

mixtures liquefy at temperatures below -120 degrees F, boil at temperatures

near —256 degrees F, and freeze at temperatures below -296 degrees F.) Nor is there much accurate data

available on thermodynamic properties

of the liquefied pure components

(methane, ethane, propane, etc.) in this temperature range. Moreover, the compositions of natural gas mixtures

vary considerably from one source to another, and change continuously dur27
ing transport and storage due to selective vaporization. The introduction of composition as an additional independent variable adds to the complexity of the task of providing an adequate data base. Accurate data on thermodynamic

properties of liquefied gases must be based on precise volumetric and calori- metric measurements. The dependence

of the thermodynamic properties on

pressure or density at fixed temperature is obtained from volumetric data. The dependence of these properties on temperature is determined by

calorimetric measurements.

It is impossible to perform enough

volumetric and calorimetric measure- ments directly on multicomponent

mixtures to permit accurate interpolation In composition, temperature, and

pressure. Instead, simple, accurate

calculation methods are needed to predict thermophysical properties data

for mixtures at arbitrary compositions,

temperatures, and pressures from a minimum of measured input data (Note 1). Several projects are underway currently at the Cryogenics Division of the National Bureau of Standards in Boulder, Colorado, to provide new

input data for calculating the thermophysical properties of LNG mixtures. One of these projects, supported

directly by the American Gas Association, is obtaining accurate physical and thermodynamic properties data for the major pure components of LNG

at temperatures down to 300 de- grees F (90 K) and at pressures to 5000 psi. This range encompasses the combinations of temperatures and

pressures most likely to be en- countered in low temperature processes.

R. D. Goodwin and B. A. Younglove

have developed accurate interpolation functions, computer programs, and

data tables for all of the thermody

namic properties of gaseous and liquid methane at temperatures down to 296 degrees F. Methane is the most

abundant major component of LNG

with concentrations ranging from 80

to 99% in typical mixtures. The NBS programs and data tables are based on precise measurements

of the vapor pressures, densities, compressibilities, and specific heats per- formed at NBS and in other laboratories. Dr. Goodwin has developed an

empirical equation of state for pure

methane which is consistent with all of the available volumetric and calori- metric measurements at temperatures between -296 degrees F and 400

degrees F at pressures to 10,000 psi. Extensive comparisons have been made between the NBS data and the volumetric and calorimetric data from

other laboratories. The NBS data will soon be available in both the InternaNote 1. Several methods are available for calculating thermodynamic properties data for multicomponent liquid mixtures.' For liquid mixtures at temperatures well below the critical temperature, the "ideal mixture" is a useful concept. The molar volume

and the molar enthalpy of an ideal

liquid mixture are linear functions

of the composition. The only data required to calculate the properties of an Ideal mixture are properties data for the pure components. To calculate the properties of real liquid mixtures, one must add the small changes in the properties which occur in mixing. The follow- ing expressions give the recipe for calculating the volume and the en- thalpy of a real liquid mixture:

real ideal mixture mixture where V =

ideal mixture

^X;V.

(1)

and H + H^ (2)

real mixture where H

ideal mixtjre ^x>H,

ideal i mixture

In these expressions the Xi, the

Vi, and the H, are the mole frac- tions, molar volumes, and molar

enthalpies of each of the components. The V''' and are the excess

properties representing the property changes on mixing. This calculation method separates

the required input data into meas- urements of the physical properties

of the pure components and meas- urements of the changes in the

physical properties on mixing. Most

of the information for the latter can

be obtained from data on binary mixtures, i.e., pure components

mixed two at a time.

1 J. S. Rowlinson, Liquids and

Liquid Mixtures, New York Plenum

Press, second edition (1969)

tional System of Units and British engineering units for the convenience

of a variety of users. The other project, supported by a consortium of natural gas companies

in cooperation with A.G.A., will obtain accurate input data for calculating the

densities of LNG mixtures. Accurate

density data is urgently needed to provide a basis for equitable custody

transfer. W. M. Haynes and M. J. Hiza are developing a magnetic densi- tometer, applying Archimedes principle, for precise density measurement

on liquid mixtures in equilibrium with

their saturated vapor. Measurements

will be performed at temperatures be- tween - 200 degrees F and —295

degrees F at pressures to 250 psi to include the conditions likely to be encountered in transporting and stor- ing LNG. The priorities for continuing sys- tematic work on these projects through

1975 have been tentatively established. Objectives of the work on pure components of LNG mixtures will be

to provide accurate data on dielectric constants, speed of sound and viscosity for compressed gaseous and liquid methane, and to provide accurate thermodynamic properties data for compressed liquid ethane and propane

at low temperatures. The LNG density

project will provide accurate density data for saturated liquid methane,

ethane, propane, butanes and nitro- gen, and for selected binary and multicomponent liquid mixtures. New

phase equilibrium data and low pre- cision estimates of the heats of mixing

will also be obtained. The density data

will be used to develop and test methods for calculating the change

in volume on mixing.

28 D-3A.Q.A. MONTHLY

ISOOHII EJU.

APPENDIX E

E-1
Accurate measurements of the dielectric constant of methane have been made on the saturated liquid from near the triple point to 188 K and on the compressed fluid along

selected isotherms from 100 K to 300 K and at pressures to 345 bar. The data are combined with accurate densities to obtain the molar polarizability and its dependence

on density and temperature. The density range examined extends to nearly three times

the critical density. The molar polarizability is found to increase initially with density

and then decrease in qualitative agreement with theoretical predictions and the behaviour of other fluids.

Dielectric constant and polarizability of saturated

and compressed fluid methane

G. C. Straty and R. D. Goodwin

In this paper, we present accurate, wide range measurements

of the dielectric constant of saturated liquid methane from

91 K to 188 K and of compressed fluid methane along

selected isotherms from 100 K to 300 K at pressures to 345 bar (1 bar = 10^ N m"^). The data have been combined

with accurate densities ^ to determine the molar polarizability and its dependence on density and temperature. The

density range examined extends to nearly three times the

critical density.

In the low density limit, the molar polarizability d is related to the dielectric constant e and density p via the Qausius—

Mossotti relation

e - I \ 47rjVQa p-l = —-

(1)

where A'^q is Avogadro's number and a is the average molecular polarizability. The molar polarizability has been found to be very nearly independent of density for most

non-polar fluids, often varying only a fraction of a percent

over wide density ranges. A knowledge of the polarizability can therefore be of practical value since it can provide

a simple and convenient method for density determination through a measurement of capacitance. With increasing transport and handling of natural gas in the hquid state (LNG) a knowledge of the molar polarizability of liquid methane, the principal constituent of LNG, can be of parti- cular importance since it offers a potentially useful method

of LNG density metering. As with other fluids,^"^ the molar polarizability of methane

shows small but significant deviations from (1). These

deviations are usually analysed by expressing the polarizability in a truncated virial type expansion, that is,

1 =Ag+B^p+CgP^ (2)

The authors are with the Cryogenics Division, Institute for Basic Standards. National Bureau of Standards, Boulder, Colorado 80302, USA. This work was sponsored by the American Gas Association. Received 16 July 1973.

where .4 g = 4TiNQaj3 and5g and Q are the second and third

dielectric virial coefficients. Existing theories ^ have yielded

analytical expressions for these coefficients and wide range measurements of the dependence of the polarizabihty on

density and temperature can be used to obtain information on molecular interactions.

Experimental

The dielectric constant was determined by measuring the capacitance C of a highly stable cylindrical capacitor ^ with

fluid contained between the plates. A subsequent measure- ment of the capacitance Cq of the evacuated capacitor then gives the dielectric constant directly as the ratio C

e = —

Co

The capacitances were measured using a commercial

three terminal capacitance bridge capable of six figure resolution. Uncertainty in the measured dielectric constants is estimated at less than 0.005%. The methane used was 99.99% pure research grade and was passed through a molecular sieve to ensure no H2O was present. Temperatures were measured on the IPTS 1968 usmg a platinum

resistance thermometer calibrated by the National Bureau

of Standards. Pressures were measured by reference to

oil pressures derived from an ofl dead weight gauge accurate

to within 0.01% through differential pressure transducers.^ The experimental apparatus and procedures were identical to those used previously for measurements on oxygen

and fluorine and have already been described in detail.'*'^

Results and discussion The dielectric constants obtained for the saturated liquid

are shown plotted against temperature in Fig. 1 and are tabulated along with the calculated polarizabilities in Table 1. Also shown for comparison are dielectric constants at the melting and boiling points obtained by

Amey and Cole.' The dielectric constant for the critical point was calculated from an extrapolated value of the

712 E-2 CRYOGENICS . DECEMBER 1973
I.70 Table 1. Dielectric constant and polarizability of saturated

liquid methane

200

Temperature, K

Fig.1 Dielectric constant as a function of temperature for saturated liquid methane

o this worl<; reference 9 Arrows indicate triple point, normal boiling point and critical point temperatures

polarizability of the saturated liquid from Fig. 2. The

polarizability at the critical density of 10. 10 ± 0. 1 mole 1'^ was taken as 6.585 ± 0.005 cm^ mole'^ resulting in a calculated dielectric constant of 1.2137 ± 0.0025 at the

critical point. The polarizabilities for the saturated and compressed

liquid are shown plotted against density in Fig. 2. The

polarizability increases initially with density and then

decreases in qualitative agreement with the behaviour of

other fluids and with theoretical prediction.^ Data

for the compressed fluid are tabulated in Table 2. The

densities were calculated from the measured temperatures and pressures and the Ppr data of Goodwin and Prydz ^

6.6IO

6.600 -

6.590 -

6.580

T, P, e, K mole 1"^ e crn^ mole''

91.000 28.121 1 67619 6.5410

95.000 27.789 1 66668 6.5428

100.000 27.367 1 65456 6.5448

105.000 26.934 1 64225 6.5468

110.000 26.491 1 62970 6.5488

1 1 5.000 26.035 1 61688 6.5509

120.000 25.566 1 60372 6.5527

125.000 25.081 1 59024 6.5549

130.000 24.578 1 57640 6.5574

135.000 24.055 1 56204 6.5595

130.000 24.578 1 57638 6.5572

135.000 24.055 1 56204 6.5594

140.000 23.508 1 54719 6.5621 145.000 22.933 1 53167 6.5645

150.000 22.326 1 51539 6.5669

155.000 21.678 1 49819 6.5695

160.000 20.980 1 47979 6.5718 165.000 20.219 1 45992 6.5744

170.000 19.372 1 43800 6.5766

175.000 18.401 1 41319 6.5789

180.000 17.232 1 38377 6.5816

184.000 16.036 1 35418 6.5846

186.000 15.269 1 33543 6.5864

188.000 14.260 1 31117 6.5903

150.000 22.326 1 51546 6.5677 175.000 18.401 1 41329 6.5804

180.000 17.232 1 38391 6.5838

184.000 16.036 1 35430 6.5867

190.53* 10.10 1 2137 6.585t

'Critical point; the dielectric constant is calculated from an extra- polated value of d tExtrapolated value of d, see Fig.

2

-I— IfM

6.570

6.560 -

6.550

6.540

6.530

Density , mole I

Fig.2 Molar polarizability (cm^ mole'' ) as a function of density (mole 1"'

) for saturated and compressed fluid methane o 220 K; X 250 K; A 280 K; Q 300 K; • saturated and compressed liquid as indicated. The broken line and its intercept are from reference 9 (see text). Extrapolated value of 6 at critical density

CRYOGENICS . DECEMBER 1973 E-3 713
Table 2. Dielectric constant and polarizability of compressed fluid methane

Pressure, bar

T, (1 bar =

P. e 6. K 10^ N m-2l1 mole crtY^ mole'^

100.000 228.079 28.314 1.68094 6.5336

100.000 153.203 28.031 1.67300 6.5366

100.000 97.1 10 27.801 1.66663 6.5396

100.000 51.839 27.598 1.661 17 6.5436

120.000 266.417 27.022 1.64387 6.5390

120.000 147.997 26.448 1.62795 6.5443

120.000 50.442 25.884 1.61252 6.5506

150.000 348.259 25.286 1.59475 6.5431 150.000 234.488 24.553 1.57517 6.5522

150.000 167.521 24.046 1.56140 6.5555

150.000 117.544 23.608 1.54951 6.5576

150.000 64.940 23.053 1.53473 6.5622

150.000 23.946 22.492 1.52074 6.5759

170.000 322.417 23.642 1.54996 6.5527 170.000 261.170 23.138 1.53653 6.5567 170.000 200.661 22.555 1.52099 6.5603

170.000 154.135 22.019 1.50678 6.5632

170.000 116.695 21.501 1.49316 6.5662

170.000 81.608 20.903 1.47759 6.5701 170.000 54.927 20.328 1.46270 6.5735 220.000 343.100 20.000 1.45331 6.5634 220.000 274.601 18.982 1.42716 6.5664 220.000 213.396 17.725 1.39549 6.5713 220.000 171.259 16.473 1.36454 6.5772 220.000 142.848 15.249 1.33469 6.5819 220.000 122.996 14.014 1.30494 6.5838 220.000 108.846 12.760 1.27507 6.5820 220.000 98.454 1 1 .494 1.24537 6.5782 220.000 90.162 10.192 1.21544 6.5737 220.000 82.842 8.853 1.18534 6.5720 220.000 75.722 7.512 1.15576 6.5703 220.000 67.738 6.133 1.12584 6.5644 220.000 58.009 4.728 1.09602 6.5595 220.000 45.581 3.301 1.06634 6.5541 220.000 28.747 1.842 1.03663 6.5500 250.000 345.558 17.729 1.39544 6.5692 250.000 284.251 16.512 1.36527 6.5735 250.000 238.340 15.295 1.33551 6.5764 250.000 203.208 14.059 1.30573 6.5783

250.000 176.512 12.831 1.27660 6.5790 250.000 154.248 1 1.523 1.24600 6.5770 250.000 136.108 10.211 1.21585 6.5736 250.000 120.569 8.906 1.18643 6.5698 250.000 105.714 7.550 1.15650 6.5668 250.000 90.896 6.181 1.12682 6.5618 250.000 74.891 4.780 1.09709 6.5580 250.000 56.522 3.343 1.06719 6.5534 250.000 34.727 1.884 1.03746 6.5472 280.000 333.164 15.299 1.33549 6.5743

280.000 290.178 14.249 1.31025 6.5775 280.000 250.396 13.053 1.28177 6.5777 280.000 215.396 11.749 1.25122 6.5767 280.000 186.296 10.430 1.22083 6.5735 280.000 161.737 9.130 1.19144 6.5704 280.000 139.635 7.827 1.16259 6.5688 280.000 117.974 6.474 1.13312 6.5634 280.000 95.475 5.057 1.10287 6.5561 280.000 71.641 3.616 1.07278 6.5511

Pressure, bar

T, (1 bar =

P. e e, K 105 N m-2 ) mole crn^ mole"^

280.000 45. 1 50 2.143 1.04275 6.5567 300.000 330.057 13.911 1.30214 6.5773 300.000 280.913 12.604 1.27122 6.5781 300.000 242.818 11.370 1.24249 6.5774 300.000 209.259 10.082 1.21299 6.5752 300.000 179.506 8.766 1.18342 6.5724 300.000 151.916 7.414 1.15359 6.5688 300.000 124.943 6.011 1.12321 6.5631 300.000 98.027 4.590 1.09310 6.5576 300.000 71.072 3.205 1.06438 6.5551

(see Appendix). The uncertainty in the calculated polariz^

abilities is estimated to be better than ±0.15% at low densities where e — 1 is small, decreasing to about ±0.1% at higher densities and is Limited by the accuracy of the

densities, estimated by Goodwin and Prydz ^ as ±0. 1%. The overall precision is better as reflected by the scatter of the data. Our experimental apparatus and procedures were

designed for making measurements over a wide pressure and density range and are not particularly suitable for making high precision measurements at low density where e — 1 becomes very small. As a result, attempts

to extract dielectric virial coefficients from these data must be approached with some caution. Bose et al have recently pubUshed the results of high precision measurements of the dielectric constant of methane at pressures below about 100 bar. They use an expansion

technique to obtain relative densities. The polarizability

for their 279.8 K isotherm calculated using their virial coefficients is shown in Fig.2 for comparison with our 280 K data. The value of A^, the zero density intercept,

is the most directly and accurately determined quantity

in their experiments. They obtained a slightly temperature dependent value for but select A^ = 6.541 cm^ mole"! ^ j^gsj value which is consistent with our data. Their value for Bp however appears to be somewhat large when compared to our higher density data.

Attempts to simply fit the polarizability data to (2) were unsatisfactory. For those isotherms which exhibit

a maximum in the polarizability however, an additional

constraint can be imposed, that is, Q = —•6e/2pmax where Pmax is the density at the maximum in the polarizability. Using the temperature dependent values of from

reference 9, a large number of one parameter {B^) fits with Pmax constrained to the limits 12.0 mole <

Pmax ^ 16.0 mole resulted in a best fit with the parameters in Table 3. These curves are shown together with the experimental data in Fig.3. Note that the curves do not fit the data weU at low densities. The vertical bars, however, indicate the variation in the polarizabihty which

could result from ±0. 1% variation in density. The slight oscillatory behaviour of the isothermal data is believed

to be the result of the polynomials used to represent the PpT data ' (see Appendix).

The scatter in our low density data for the various iso- therms does not permit us to resolve the temperature

714 E-4 CRYOGENICS . DECEMBER 1973
dependence of although the data do suggest that it is small. This is to be expected since the 1/T dependence

of 5g arises from dipole moments induced in one molecule by multipole moments in the other. The first nonvanishing multipole is the octopole in methane because

of its tetrahedral symmetry and octupole effects should be small.

APPENDIX

We discuss briefly the method of obtaining densities from

the PpT data of Goodwin and Prydz. ' They have measured

the density of methane from the triple point to 300 K at pressures up to about 340 bar. They chose to represent

their data by a unique, non-analytic equation of state capable of reproducing the experimental data to reasonable accuracy over the complete region of the state surface

investigated. Because of the importance of density in the calculation of the polarizability from dielectric constant measurements, severe demands are made on the representation of the PpT data and it was found that the equation of

state was not adequate for our analysis. The somewhat sparse experimental PpT data along isotherms were therefore fitted to polynomials of the form

-I a.

Density, mole I

Fig.3 Fit of the molar polarizability data (cm' mole"' ) as a function of density (mole l '

) for o 220 K; A 250 K; 280 K; 220 K; 250 K; 280 K

(see text) The vertical bars indicate the possible effect of the ±0.1% uncertainty in the densities of reference 1

Table 3. Dielectric virial coefficients of methane

P = pRT+y A„p"

n

and an iterative procedure was then used to calculate the density from the measured temperature and pressure.

Experimental saturated liquid densities were represented

by an equation, derived by Goodwin,^ of the form

=w«exp [b{\-oj^'^)

(Pt~Pc)

+ c(l -w4/3)-Hj(i_cj2)]

where to = (T^ - T)/(T^ - Tj), a = 0.36 consistent with

scaling theory, and the subscripts c and t refer to the values

at the critical and triple points respectively. This equation

reproduced the experimental saturated liquid densities to within the accuracy of the data.

The authors wish to express their appreciation to Dr J. F. Ely and Dr J. D. Olson for helpful discussions and assistance with the calculations.

T, Ae,* Be, , Pmax

K cm-^ mole"^ (cm-^ mole'^ )2 (cm-' mole"^ )^ mole V

220 6.534 7.10 -278.4 12.75 250 6.536 6.53 -266.5 12.25 280 6.538 6.07 -252.7 12.00

'Values of /Af calculated from reference 9

References

1 Goodwin, R. D., Vryiz, R. J Res NBS 76A (1972) 81

2 Younglove, B. A. 7 C/jem 48 (1968) 4181

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

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

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

6 See, for example, Kielich, S. Acta Phys Polonica 27 (1965) 305 ,4 eta Phys Potonica 28 (1965) 95 and McQuarrie, D. A., Levine, H. B. Physica 31 (1965) 749 and references cited 7 Younglove, B. A., Straty, G. C. Rev Sci Instr 4 1 (1970) 1087

8 The pressure system has been described in detail. See, for example, Stiaty, G. C, Prydz, R. Rev Sci Instr 41 (1970) 1087

9 Amey, L. A., Cole, R. H. J Chem Phys 40 (1964) 146

10 Bose, T. K., Sochanski, J. S., Cole, R. H. J Chem Phys 57

(1972) 3592

CRYOGENICS . DECEMBER 1973 E-5 715

APPENDIX F

F- 1
^'easu^ements of the velocity of sound in saturated and compressed fluid methane are reported. Measurements were made on the saturated liquid from 91 K to 186 K and on

the compressed fluid along selected isotherms from 100 K to 300 K at pressures to about 35 MN m'"^. Data were combined with newly available PpT data to obtain the isentropic

compressibility and the ratio of the specific heats. Measurements along the higher temperature isotherm were limited to densities greater than about 10 mole 1'^ at 300 K increas- ing to about 14 mole 1'^ at 210 K due to the large low pressure sound attenuation in methane.

Velocity of sound in dense fluid methane

G. C. Straty

The increased handling, storage, and transportation of fuel gases in the liquid state has created a need for wide range thermodynamic and transport properties data on these

fluids in engineering and development applications. The

properties of methane are particularly important since it is the principal constituent of liquefied natural gas (LNG).

Sound velocity measurements, when combined with newly

available pressure, density, temperature (PpT) data

offer a convenient and more accurate method of obtaining

certain thermodynamic quantities which cannot easily be

determined by other means, as well as providing a sensitive check on the PpT surface and its derivatives. The weU-known equations

relate the sound velocity W to the density p, the isentropic

compressibility k^, and the ratio of specific heats, 7. This

relation has been used together with FpT data '-^ to determine Kg and 7 from the measured sound velocities for saturated and compressed fluid methane. Measurements of the sound velocity for saturated liquid methane have been made from near the triple point to 186 K

and on compressed fluid methane along several isotherms from 100 K to 300 K at pressures to about 35 MN m'^. Measurements, in our apparatus, on the compressed fmid

were limited however to minimum pressures corresponding

to densities ranging from about 10 mole 1"' at 300 K to about 14 mole at 210 K because of the large sound

attenuation in low pressure gaseous methane.

Experimental

The pulse echo technique was used for the sound velocity measurements. The apparatus was identical 10 that used

previously in this laboratory for measurements on

hydrogen,-* oxygen," and fluorine ^ and has been described

in detail. Uncertainty in the measured velocities is estimated at about 0.05% at the higher densities increasing..

The author is with the Cryogenics Division, Institute for Basic S'andards, National Bureau of Standards. Boulder, Colorado 80302, USA. Received 1 April 1974.

'

somewhat in the regions of high attenuation. Measurements

were made at frequencies of 1 MHz and 10 MHz with no

observable dispersion. Temperatures were measured using

a platinum resistance thermometer calibrated by the National Bureau of Standards on the IFTS 1968. Uncertainty in temperature is estimated at 0.005 K at the lower temperatures increasing to 0.030 K at 300 K.^ Pres- sures were measured by referencing to oil pressures derived from an oil dead weight gauge, accurate to within 0.01%,

through differential pressure transducers.'' The methane

used was a commercially available, ultra high purity

(99.97%) grade.

Results The measured sound velocities for the saturated liquid are tabulated along with the density and the calculated compressibility and specific heat ratio in Table 1 . Also shown

in Table 1 , for comparison, are the sound velocities inter- polated from the data of Blagoi et al * and Van Dael at al ^ and the sound velocities calculated by Goodwin ^ directly from PpT and specific heat data. Sound velocities for the compressed fluid along several isotherms and for the saturated liquid are shown as a function of density in Fig.l and are tabulated along with

the measured pressures and temperatures and the derived

values of compressibility and specific heat ratio in Table 2. Van Itterbeek et al '° have also made measurements on the compressed liquid at 190 K and below but their data are not

directly comparable with the present data without multiple

interpolations. Their compressed liquid data however

were obtained on the same apparatus as the saturated liquid data of Van Dael et al and our agreement with these saturated liquid values is indicative of the overall agreement. No ultrasonic data are available for comparison at temperatures above 190 K.

Densities for the saturated liquid were obtained from the measured temperatures and a correlation for the saturated

liquid densities due to Goodwin.^ Densities for the compressed fiuid and the derivatives necessary for fhe calcula- tions were obtained from the measured temperatures and

pressures and an equation of state for methane also due to Goodwin.

2

The uncertainty in the derived isentropic compressibilities

is estimated at about + 0.2% due to the combined uncercainty

CRYOGENICS . JULY 1974 F-2 367
Table 1 Velocity of sound W and derived values of the isentropic compressibility ratio 7 of the heat capacities in saturated liquid methane at temperature T and density p

W, m s"'

Expt

Reference 9Reference

8

Calc Reference

2

p, mole 1

' (G (M m-2)-i 7

91.0 1538.1 1530.2 28.121 0.9369 1.525 92.0 1528.7 1522.0 1564 28.038 0.9514 1.530 96.0 1490.6 1491.5 1487.3 1523 27.703 1.013 1.551 100.0 1452.2 1451.4 1442.8 1480 27.364 1.080 1.575

104.0 1413.4 1413.2 1401.5 1437 27.020 1.155 1.601 108.0 1373.8 1374.6 1364.6 1393 26.669 1.238 1.629 112.0 1334.1 1334.7 1352.2 T351 26.310 1.331 1.660

116.0 1294.0 1294.1 1208.7 1308 25.943 1.435 1.693

120.0 1252.9 1253.6 1245.3 1266 25.567 1.553 1.726

124.0 1211.3 1212.6 1207.6 1224 25.181 1.687 1.763

128.0 1169.1 1170.0 1165.2 1181 24.783 1.840 1.801 132.0 1126.0 1227.0 1120.4 1138 24.372 2.017 1.842

136.0 1082.2 1083.0 1079.2 1093 23.947 2.222 1.886

140.0 1037.4 1038.0 1034.7 1047 23.507 2.464 1.933

144.0 991.7 992.4 987.2 999 23.050 2.750 1.986 148.0 944.8 945.3 946.5 951 22.572 3.094 2.045

150.0 921.0 921.4 921.4 927 22.324 3.292 2.079

152.0 896.6 897.2 896.3 902 22.071 3.513 2.114

156.0 846.9 847.8 850.2 852 21.524 4.034 2.195

160.0 795.5 796.0 796.4 802 20.981 4.695 2.295

164.0 742.2 742.5 746.0 749 20.379 5.552 2.423

168.0 686.3 686.7 684.6 695 19.724 6.709 2.590

170.0 657.5 657.5 657.5 667 19.373 7.444 2.698

172.0 627.5 628.2 632.2 637 19.001 8.331 2.824

176.0 564.1 564.8 568.0 570 18.183 10.77 3.168

178.0 530.5 530.8 536 17.725 12.50 3.413

180.0 495.0 495.5 500 17.222 14.77 3.736

182.0 457.7 458.0 462 16.662 17.86 4.195

184.0 417.2 415.8 421 16.022 22.35 4.882

186.0 370.9 371.7 377 15.263 29.68 6.012

Columns 3, 4 and 5 give values of IV from references 9 and 8 and those calculated from PpT <iata in reference 2

in the experimental densities of ± 0.1% '-^ and the equation of state correlation.2 The uncertainty in 7 is difficult to

assess, depending almost entirely on the accuracy of the

derivative (dP/dp)j- used to obtain 7 from the sound velocity. Goodwin,^ however, has shown that his equation of state can be used successfully for the calculation of wide range

self-consistent thermodynamic functions involving extensive use of both first and second derivatives of the Pp7" sur- face, which adds confidence to the accuracy of values of (dP/dp)T used here. Comparison of the measured sound

velocities with those calculated from the equation of state suggests that the uncertainty in 7 is probably less than

1 .0% at the higher temperatures increasing somewhat for the low temperature, high density Uquid where (dP/dp)j' is very large and most difficult to determine accurately from ?pr data. This work was sponsored by the American Gas Association

Inc.

References

1 Goodwin, R. D., Piydz, R. J Res NBS 76A (1972) 81

2 Goodwin, R. D. 'The thermophysical properties of methane

from 90 to 500 K at pressures to 700 bar', NBSIR 73-342

(1973); available from the Cryogenics Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Co

80302

3 Younglove, B. A. J Acoust Soc Am 38 (1965) 433

4 Straty, G. C, Younglove, B. A. J Chem Thermo 5 (1973) 305

5 Straty, G. C, Younglove, B. A. J Chem Phys 58 (1973) 2191

6 For a more complete discussion of thermometry and possible source of error, see for example, Piydz, R., Straty, G. C. NBS

Technical Note 392 (revised) 1973

7 The pressure system has been described in detail. See for example: Straty, G. C, Prydz, R. Rev Sci Inslr 41 (1970) 1223

8 Blagoi, Yu. P., Butko, A. E., MikhaUenko, S. A., Yakuba, V. V.

Zfi FizKhim 41 (1967) 1699

9 Van Dael, A-, Van Itfetbeek, A., Thoen, J., Cops, A.

Physica 31 (1965) 1643

1 0 Van Itterbeek, A., Thoen, J., Cops, A., Van Dael, W Physica 35 (1967) 162

1 1 A complete description of procedures for calculating various thermodynamic quantities from the methane /"pT data can be found in reference 2. An abbreviated discussion o!' cal- culating sound velocities from PpT data can be found in reference 4

368 F-3 CRYOGENICS . JULY 1974
lO 12 14 16 18 20 22

Density, mole I

'

Fig.l Velocity of sound plotted against density for saturated and compressed fluid methane

Table 2 Velocity of sound \N and derived values of the isentropic compressibility Ks and ratio 7 of heat capacities in compressed fluid methane at temperature T and

density p

30

W, m s"'' M N m-2

Expt

Calc Reference 2

p, mole I" Ks. (G N m-2)-i

33.385

26.077

19.123

13.088

7.244

1.661

1672.6

1630.7

1588.1 1548.5

1507.4

1465.1

T= 100.0 K

1610.3

1589.5 1566.0

1542.4

1516.5

1488.9

28.692 28.430

28.169

27.930

27.686

27.439

0.7766

0.8245

0.8774

0.9307 0.9908

1.058

1.576 1.565

1.561

1.561 1.565

1.572

31.161 26.233

19.980

15.149 9.258

4.367

1517.2

1482.8

1436.0

1397.0

1345.2 1290.5

T= 120.0 K

1475.3

1449.5 1413.4

1382.7 1341.3

1302.8

27.225 27.004

26.707 26.460

26.136

25.841

0.9947

1.050

1.132

1.207 1.318

1.448

1.611 1.620

1.635

1.651 1.675

1.681

34.530

28.845

23.669

18.433

1339.6

1290.0 1240.3

1184.6

r= 150.0 K

1303.6

1260.0

1216.1 1166.4

25.275

24.923

24.572 24.178

1.374

1.503

1.649

1.837

1.700

1.727 1.758

1.797

CRYOGENICS . JULY 1974 F-4 369
p,M N m-2

Expt

Calc Reference

2

p, mole r

'

!G N m-2)-i 7

1 Z.OO /

1 1 1 y1 C 1 1 no o

1 1 Uo.O oo coo z. 1 ly 1 oirir 7.263 1036.6 1032.5 23.132 2.508 1.931 3.020 962.1 964.4 22.609 2.979 2.021

T = 170.0 K

31.457 1 183.8 1169.0 23.584 1.886 1.778 26.994 1135.5 1124.7 23.213 2.082 1.813 20.773 1059.2 1053.8 22.619 2.456 1.877 17.538 1013.9 1011.2 22.263 2.724 1.922

1 o.u 1 z

Q"4 1 Q z 1 .uo4 T O/IQ o.z4y z.uuy 7.774 833.5 838.6 20.819 4.309 2.183

4.528 742.9 750.5 20.078 5.624 2.397

J = 184.0 K

34.254 1129.0 1119.8 22.751 2.150 1.794 27.883 1055.1 1050.5 22.145 2.528 1.850

22.511 982.8 981.6 21.538 2.996 1.919 17.863 909.0 910.3 20.903 3.609 2.007

13.839 831.9 834.9 20.221 4.454 2.126

10.436 751.2 754.2 19.475 5.672 2.301 7.722 666.6 669.4 18.661 7 C 1 7

/.b1 / 2.561 5.770 579.9 584.5 17.809 10.41 2.934 558.2 17.535 1 1 63 3.091

T = 210.0 K

34.074 987.0 988.0 20.741 3.085 1.843 27.598 898.0 901.2 19.885 3.887 1.929 22.264 809.8 813.7 18.981 5.007 2.045

17.486 71 1.5 714.8 17.885 6.884 2.228

14.832 643.9 646.2 17.053 8.817 2.405

12.703 577.5 579.5 16.159 11.56 2.635

10.944 51 1.5 512.1 15.124 15.76 2.988

in 1

1 U. 1 /o yi 77 n 1 O.oO o.zoy y.D4o 4b 1 .z

/I K 1 Q 1/1 14. nmuu 1 01z 1 .oo 'i AQ1

7"= 240.0 K

34.638 863.5 870.2 18.505 4.517 1.871 29.111 782.7 789.0 17.531 5.803 1.964 24.656 707.0 712.4 16.520 7.549 2.076 20.885 632.6 636.8 15.395 10.12 2.221 18.890 588.8 591.9 14.637 12.28 2.330

16.841 540.2 541 .7 13.673 1 5.62 2.A lo m 1 Rfi 498 4 498 8 1 2 697 19 77 2.617

1 4 07

1

470 0 1 1.907 23.72 2.698

7" = 270.0 K

34.769 771.5 775.8 16.311 6.420 1.867 30.486 71 1 .2 714.6 15.387 O.UlU 25.972 641 6 643 6 14.167 10.69 2.029 21.837 572.8 573.3 12.708 14.95 2.131

34.838 713.9 713.7 14.331 8.534 1.818 29.732 649.5 648.5 13.065 11.31 1.873 27.295 618.0 616.7 12.352 13.21 1.896 24.427 580.4 580. i 11.404 16.23 1.904 20.983 537.3 537.9 10.094 21.39 1.895

Column 3 gives the value of calculated from PpT data

370 F-5 CRYOGENICS . JULY 1974

APPENDIX G

G-1
JOURNAL OF RESEARCH of the National Bureau of Standards — A. Physics and Chemistry

Vol. 78A, No. 3, May-June 1974 The Specific Heats, C„, and Cy, of Compressed esn

Liquefied Methane*

B. A. Younglove**

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

(January 30, 1974)

The specific heats. Co-, of saturated lii|uid methane have been measured at 66 temperatures in the temperature range 9.5-187 K. The specific heats at constant volLime. Cv, have been measured at 20

densities ranging from 0.8 to 2.8 times the critical density, at temperatures between and 300 K, and

at pressures to 3.'50 bar (at 280 FJ T states in ail). T!ie uncertainly of most of the mcasurenicnis i- estimated to be less than 0.5 percent, except near the critical point. Tiiese measurements uere per- formed primarily to provide input data for accurate tliermotlynamic properties data calculations for

li(|uid methane. They are believed to be the must comprehensive specific heat measurements available

for pure compressed gaseous and liijuid methane.

Key words: Constant volume; heat capacity; hquid; saturated liquid; specific heat; methane.

*Thi? work was carried out jt the National Bureau of Standards under the sponso'ship

of The -American t/as .Assoriation. **l*rcsenl address; Cryogenics Division, National Bureau ^^f Standards. Boulder, CO

80302.

G-2
1. Introduction

For the calculation of fluid thermodynamic properties such as internal enerj:y, enthalpy, entropy, and

velocity of sound, at temperatures less than the critical point, one needs either the latent heat of vaporization

or specific heat alon^ a path traversin<i the temperatures of interest. Heat capacity measurements are much easier than latent heat measurements and the

specific heat measurements are not restricted to the

liquid-vapor curve but can be made coverinji temperatures and densities in the single phase fluid region as

well. For methane, specific heat of the saturated liquid,

Co-, was measured from 95 to 187 K, and specific heat

at constant volume, Cr, was measured on 20 isochores

with densities ranging from 8 mol/1 to 28 mol/1, temperatures from 90 to 300 K, and pressures to 330 bar

[1].' 2. Apparatus

The specific heats were obtained using a constant volume adiabatic calorimeter, as described previously

by Goodwin [2]. Basically, it consists of a thin spherical

stainless-steel sample holder bearing a heater and

platinum resistance thermometer and enclosed in an

adiabatic shield. The calorimeter and cryostat are shown in figure 1. The refrigerant was liquid nitrogen.

The versatihty of this instrument is demonstrated

in that it has been used with very minor modifications

for the Ci and C^r nieasurenients of h\drogen [3, 4], oxygen [5, 6]. fluorine [7, 8], and in this work on methane. These measurements cover temperatures

from 14 to 300 K and pressures to 330 bar. The thermometer was calibrated by the NBS Temperature Section. Temperatures are on the IPTS-68

scale. The temperature of the adiabatic shield and

guard ring are controlled to the sample temperature

with difference thermocouples and automatic power

regulation. Heat exchange to the sample holder is considered negligible.

The sample used was 99.99 percent methane. Impurities as analyzed by the supplier in ppm were

CO.. < 10; 0_>, 4; N-i, 12. A molecular sieve in an ice bath served to ensure removal of water vapor present

in the sample.

' f it:urf-> in braikcl.-* in<lii-:ttf \hf lilt- ruturt- rrfrrcncr^ at tlip rtul of paper.
3. Procedure

In essence, the specific lieat Ci is calculated from

the measured parameters as follows. The total heat

capacity is determined as the ratio of tlie heat input

AQ to the temperature increase AT brought about by

applying a very stable power source to a resistor

attached to the calorimeter sample holder, for an

elapsed time Af. The heat capacity of tlie empty

sample holder Co is then subtracted off. It, of course, was previously measured in exactly the same way

excei)t witli the samf)le space pumped to a vacuum. The difference of tliese two quantities is the heat

capacity of the methane sample. Tlie specific heat is obtained by dividin;^: the heat ca()acity by tlie amount

of methane. N.

Actually, several corrections are made to the above.

Since the sample holder is a thin stainless steel sphere

(— 0.16 mm wall thickness and 5 cm diam), it stretches as the pressure increases. This allows work to be done

by the methane due to the increase of the sample

volume. This correction [4. 5, 6]. developed by Walker

[9], ranges from 0.5 to 5 percent of the resulting Cy

value. However, it can be made accurately.

Of the three variables, pressure, temperature, and

density, only temperature is measured during the

measurement of an isochore. The pressure and

temperature are measured at filling and the density

calculated from the PVT surface [10]. The amount

of methane, N, is calculated from the volume V {T, P)

as previously determined [3. 5]. The density for each

Cy measurement is calculated from the filHng density

after correcting for sample holder expansion and the

amount compressed into the filling capillary [6J. In the case of the Co- measurement, the two phase

heat capacity (liquid and gas) is first determined as

the difference of the total heat capacity (DQjDT,

column 6 of table 1) and the empty heat capacity

(CO, column 7) and the result divided by the total amount of sample (C^-, column 8). Then the effects of

the latent heat of vaporization and heat absorbed by

the vapor are subtracted [3, 5. 7] to give (column 10). This type of correction is derived by Hoge [11]. The temperature increment, resulting from a constant power input over a time At, is evaluated at the

middle of the heating interval by extrapolating the

temperature drift rates evaluated just before heating

and after an equilibrating time has elapsed (about

20 min). Care was taken to reduce the effects of noise on drift rate by taking many (10 to 20) measurements

of time and temperature.

G-4
Table 1. Specific heat of satnnital luiiiiil methnne, L.„ or Cvrr,' specific heiit iit constimt rohtnie of satiiniletl liipiiil ciilcnhiteil, C^ ; specific heat of the tico phase (li .fuid-vapor) system, C-.; heat capacity of the calorimeter (empty) d, and heat capacity of the calorimeter {full)

AQ/^l L)Q/Dr, uilh temperatare, pressure, density, and temperature increment. D T

ID Press bur Deiis rn(>l/l DeltK DQIDTilK C(, J/K C2 J/inoI • K J/iiiol * FC (

'

, , I/riif >1

201 95.402 0.209 27.755 3,657 133.482 46.671 54.418 34.271- S1.240

401 95.846 .219 27.718 5.799 139.159 46.881 54.252 34.103 .5-1.131 202 99.021 .311 27.450 3.574 135,870 48.,348 54.864 34.169 .54.647 302 101.651 .409 27.224 6.638 141.300 49.520 55.058 .34.016 54.877 402 101.961 .422 27.198 6.420 143.111 49.656 54,943 33.883 54.790 203 102.574 .448 27.145 3.524 137.905 49.923 55.152 33.898 54-896 204 106.891 .673 26.767 5.110 140.924 51.750 55,899 33.941 55-602 303 108.219 .758 26.649 6.495 145.302 52.293 55.794 33.710 .55.533 403 108.800 .797 26.597 7.236 146.902 52.528 55.483 33.349 55.315 205 112.604 1.097 26.254 6.273 144.013 54.022 56.410 33.478 56.075 304 115.165 1.343 26.019 7.-386 149.404 54.988 56.638 33.391 56.4-34 206 119.117 1.802 25.649 6.702 147.576 56.412 57.144 33.041 56.310 305 122.474 2.278 25.327 7.194 153.257 57.561 57.404 32.862 57.287 405 123.367 2.419 25.240 7.498 154.829 57.8,58 57.008 32.389 .56.996 207 125.766 2.8.30 25.005 6.568 151.006 58.6,36 57.899 32.5.34 57.645 406 130.765 3.852 24.500 7.297 158.819 60.171 57.992 32.000 58.245 208 132.274 4.209 24.343 6.430 154.477 60.612 58.834 32.162 53.774

1001 132.751 4.326 24.293 5.117 122.552 60.750 62.894 32.148 58.879 902 135.455 5.038 24.007 4.538 137.072 61.512 60.813 31.499 58.930

1002 137.805 5.723 23.752 4.973 125.195 62.151 64.157 31.650 59.729 903 139.970 6.412 23.513 4.476 139.223 62.720 61.570 30.986 59.698

801 144 305 7.971 23.017 4.019 141.250 63.808 62.323 30.460 60.560 904 144.401 8.009 23.005 4.386 141.728 63.831 62.689 30.797 60.929 802 148.500 9.725 22.514 4.371 143.789 64.800 63.565 30.407 62.033 905 148.881 9.896 22.467 4.316 143.807 64.888 63.509 30.230 62.005 1003 150.824 10.807 22.224 4.332 133.134 65.326 68.994 31.449 64.014 803 152.809 11.798 21.969 4.247 146.566 65.763 65.022 30.468 63.898 906 153.157 11.978 21.924 4.229 146.775 65.838 65.129 30.4,59 64.048 1004 155.542 13.267 21.606 4.941 1,35.238 66.345 70.092 30.518 65.246 804 1.57.043 14.128 21.401 4.180 148.588 66.657 65.926 29.932 65.435 907 157.355 14.312 21.358 4.167 148.747 66.721 66.001 29.899 65.569 1005 159.127 15.383 21.107 4.035 137.307 67.080 71.446 30.244 66.905 805 161.181 16.707 20.808 4.095 151.123 67.486 67,294 29.823 67.733 908 161.483 16.908 20.763 4.088 151.234 67.5 1.5 67.375 29.7''.3 67.898

1006 163.136 18.036 20.512 3.982 138,917 67.864 72,280 29. 161 68-379

1402 163.782 18.492 20.412 5.441 153„354 67.987 68.702 30,257 69.936 806 165.249 19. .556 20.179 4.036 153.713 68,263 68.749 29. 7 16 70.53-1. 1407 165.128 19.467 20.199 5.131 154.144 68.240 69. 132 30,171 70.865 909 165.548 19.779 20.131 4.043 153.880 68.318 68.838 29.719 70.745

1007 166.549 20.536 19.967 2.738 141,994 68 ,,503 74.756 29.907 71.756 807 16Q.253 22.687 19.505 3.963 156.273 68.991 70.216 29.b09 73.960 910 169.565 22.945 19.450 3.949 156.6.56 69.047 70.480 29.743 74.41

1220 170.157 23.440 19.3-14 7.335 1.38.896 69.151 79.614 29.404 74.696

1008 170.197 23.474 19. .336 4.297 14-k726 69.159 76.862 30.033 75.369 1408 170.251 23.520 19. .327 5.020 157.666 69.168 71.213 30.181 1403 171.097 24.243 19.172 5.271 158.018 69.316 71.376 29.980 76.320 808 173.180 26.094 18.773 3.890 159.0,54 69.675 71.898 29.577 78.540 911 173. ^V80 26.369 18.714 3.873 159.572 69.727 72.273 29.813 79.194 701 173.505 26.392 18.709 5.002 141.928 69.731 81.284 29.262 73.678 1216 174.032 26.880 18.603 7.180 141.932 69.820 82.310 29.445 79.623 1009 174.429 27.252 18.522 4.167 148.478 69.887 79.930 30. .5,56 81. .334 1409 175.228 28.012 18.3.55 4.900 161.213 70.021 73.374 30.(,>69 82.128 1404 176.295 29.051 18.125 5.118 162.367 70.198 74.158 30.312 84.2,53 809 177.029 29.782 17.961 3,811 162.720 70.318 74.323 30.097 85.466

1221 177.420 30.177 17.872 6,963 146.364 70.382 86.720 3! .201 87. .382 702 177.902 30.670 17.760 3,7'>9 145.938 70,461 84,967 29.5.52 86.790

1010 178.557 31..349 17.603 4,090 151. .355 70..567 82,1.56 29.861 88.641 1200 180.613 33..553 17.078 5,694 148.814 70.895 83,923 30.420 95,067

1217 181.034 .34.018 16.963 6,825 149.125 70.961 89,202 30.254 96.349 703 181.645 34.702 16.790 3,688 150..564 71.057 89.-196 30.451 98.8 14 1011 182.572 35.7,59 16.516 3.9 10 1,56.745 71.201 86.983 31.025 103. U2

1222 184.222 37.703 15.976 6.616 154.219 71.4,54 94.-U5 31.451 113..330 704 185.271 38.932 15..588 3..549 1.56.464 71.613 95.503 31.421 121.7r.9 1201 186.127 40.0.50 15.2.36 5,320 1,53,456 71.742 98.9-18. 32.509 132.1.53 1012 187..577 41.915 14,530 6,026 151.278 71.957 80.630 lti.30f> 141.3.59 1218 187.633 41.988 14.49y 6,358 160.079 71.965 100..5-W 3U.0.50 156.489 G-5
4. Results

The specific heat of the saturated liquid was measured for 66 temperatures. The lowest was 05 K (triple

point, 90.68 K) and the highest 187 K (see fig. 2 and

table 1). The estimated uncertainty in the measured

vahie of Co- is about 0.5 percent generally but increasing to about 5 percent within a few Kelvin of the

critical point. The data of Weibe and Breevort [12] are shown for comparison as the closed circles. Tlieir measurements agree remarkably well with the new

data, considering the state of the art at that time.

Figure 3 and table 2 show Cy as a function of temperature for the various isochores. The dashed line

is the locus of Cr for saturated liquid as extrapolated

from the Cv measurements. The uncertainties in Cy

are the same as for Co-. Densities Q, R, S, and T have

uncertainties as large as 5 percent near critical temperature, indicated as Tc on figure 3. Density T is 22

percent less than critical density.

Figure 4 shows Cy at saturation. The circles are values extrapolated from the Cy data and the triangles

are computed from Co- data by adding the term T

These derivatives, evaluated analytically from a

representation of the PVT surface [2], introduce the

scatter and the lowering of the values from the extrapolated values which have essentially the same accuracy

as the measured Cy values. Comparison was made with the C,, data of Jones et

al. [17] on their 2000 lb/in- (136.7 bar) by interpolation

of the Cr data and adding the PVT contribution.

Figure 5 shows the close agreement of the two sets of

data. The other curve is calculated from spectroscopic

heat capacities togetlier with the PVT term above

critical temperature, (7",). Below the critical temperature, latent heats must also be used. The discontinuity is, of course, at T-.

dV

G-6
T/4BLE 2. Specific heat at constant volume, Cv, of methane; heat correction for calorimeter expansion C\,heat capacity of empty calorimeter, CO, total heat capacity of calorimeter (full) AQ/AT or DQ/DT, with temperature , pressure, density, and temperature increment, DT

ID Temp Press Deii DT DQIDT CO CI Ci K bar mol/1 K J/K J/K J/mol K J/riiol K

2209 200.342 56.917 7.991 7.542 94.477 73.734 0.166 35.351 2203 201.339 58.027 7.991 5.459 94.406 73.865 .167 35.004 2210 207.854 65.217 7.988 7.559 94.1.52 74.691 .170 33.1.53 2204 208.168 65.562 7.988 7.419 94.184 74.729 .170 33.141 2211 215.402 73.451 7.984 7.554 94.227 75.593 .175 31.732 2212 222.937 81.598 7.980 7.511 94.677 76.439 .182 31.0-16 2205 222.993 81.658 7.980 7.361 94.691 76.445 .182 31.059 2206 230.373 89.583 7.977 7.387 95.264 77.226 .189 30.698 2213 230.453 89.668 7.977 7.484 95.130 77.234 .189 30.455 2207 237..534 97.229 7.973 7.324 95.819 77.940 .195 30.419 2214 238.128 97.862 7.973 7.382 95.748 77.998 .196 30.193 2208 244.733 104.881 7.970 7.292 96.283 78.619 .202 30.045 2215 245.476 105.669 7.969 7.369 96.374 78.687 .203 30.034 2216 252.815 113.433 7.966 7.3.32 97.017 79.3.35 .210 30.067 2218 266.349 127.671 7.959 7.246 97.960 80.436 .222 29.785

1505 195.780 53.853 10.176 6.728 102.498 73.123 .185 39.325 1523 198.095 57.310 10.175 5.257 101.084 73.4.36 .189 36.999

1521 198.426 57.804 10.174 5.284 101.071 73.480 .189 36.921 1506 202.601 64.048 10.171 6.923 1 Afi A/' A 74.028 .194 34.818 lo02 203. 142 64.857 10.171 <C 1 7A 6.4/U 1 r\£^ AOA 74.098 .19o <U.0.32 1524 203.375 65.206 10.171 C OA 1 100.142 74. 128 1 A£ .196 34.793 1522 203.731 DO. lO^ 10.171 0.320 r\() on 1 99.K0I 74.173 .197 34.382

1 cor 1520 ZUO. /U4 16. Ivo 1 n 1 A7 IVAoi o.oo4 yy.ooo 7-1 70C /4. /9o OAO .203 33.078 1523 209.057 73.722 lU. 16/ o..ii6 00 OCA VV . boo i4.o3o .204 33.4-t7 1507 209.526 /4.426 iU. 166 6.V42 7 1 OA" /4.o9o .203 32.879 1503 209. oo3 7,1 ri 1 ~ 74.910 10. 166 6.900 99.636 7 .1 A 0 r /4.93o .204 33.020 1526 214.044 81.206 10.164 0.346 AA 70A 99. /06 7 C 10 1 /0.434 .211 32.476 1508 216.467 84.845 10.161 6.956 99.479 75.715 .213 31.750 1504 216.813 85.365 10.161 6.945 99.842 75.755 .214 32.185

1509 223.396 95.256 10.157 6.923 99.937 76.489 .223 31.318 1510 230. 1 90 106.373 10.151 6.920 100.066 77.268 .233 30.432

1511 237.756 116.844 10.147 6.901 100. 143 77.962 .242 29.998 1512 244.636 127.181 10.142 6.864 100.993 78.610 .251 29.857 1513 251.488 137.466 10.137 6.819 101.457 79.221 .261 29.650 1514 259.403 149..331 10.131 6.782 102.116 79.886 .271 29.632 1515 266.154 159.433 10.126 6.725 102.604 80. 121 .280 29.,560 low Zo^.r) 10 loo.o40 1 A 1 1 1 A AT 7 0.0 1 1 1U4.U0 / 0 1 . OVv .oul .>Q AOO

1518 289.146 193.696 10.110 6.625 104.5.38 82.032 .310 29. 9M

1519 295.822 203.596 10.105 6.556 105.109 82.4-14 .319 30.170

219 195.627 55.318 11.838 9.621 105.430 73.102 .204 37.165 223 196.581 57.055 11.839 7.285 104.709 73.232 .209 36.177 224 203.924 70.601 11.8.32 7.393 103.134 74. 198 .226 33.223 225 211.370 84.5.')() 11.826 7..394 102.930 75.118 .242 31.903

1 205 215.626 92.584 1 1 .822 8.023 102.779 75.618 .250 31.148

1 226 218.787 98,572 11.819 7.41

1

102.950 75.979 .2.56 30.922 206 223.653 107.819 11.815 8.022 103.224 76.517 .265 ?,().GfJ 227 226.191 112.653 11.813 7.374 103.274 76.789 .270 30.347

!

G-7
Table 2. Specific heat at constant volume, Cy . of methane; heat correction for calorimeter expansion OA. heat capacity of empty calorimeter, CO, total heal capacity of calorimeter {full) AQ/AT or DQ/DT, with temperature, pressure, density, and temperature increment, DT—

Continued

ID Temp Press Den DT DQIDT CO Cl Cl K bar mol/1 K J/K J/K J/inol K J/ni..l K

907 231.675 123.117 11.808 7.947 103 685 77 1=^0 0 970 OUin 1

. 1 -J-J 998 126.729 11.806 7.338 103 858 77.549 981 in 1 10

£.UO 9nft 138.319 11.801 7.906 104 383 78. 141 901 30 043 990 204.923 140 803 11.800 7.311 104.171 78.264 90ft 29 653 900 155.761 11.792 7.882 104.855 78.979 .Ov3' 100 29 604

91ft 172.4.59 11.784 9.556 105.552 79.726 191 90 ^11

91

1

190.643 11.775 9.438 106 408 80.482 110 Z90 . ft19 U- JZ 919 97fi ^"iS 90S 9'^4. 11.766 9.341 107.186 81.187 .ODD 1^^ 29 70'^ 91d 246.647 11.748 9.271 108.845 82.476 18R 30 098

0\JX 904 751 77.746 13.088 7.244 105.556 74.303 .264 32.393 109 919 016 93.924 13.080 7.229 105.596 75.195 .282 31 .485 303 219.265 110.242 13.073 7.214 105.859 76.033 ^299 30,868 304 226.524 126.697 13.065 7.179 106.293 76.824 .315 30,478

14.^ 8S1 13.057 7.166 106.784 77.600 • OO111X OU. 10 Ift'i 1 'J-J ouo 941 94^ 1^^0 9^6 13.050 7.146 107.321 78.295 .04 1171 9y 98,5 Ou< 9/lfl Z40.00^ft7

1

1 lf\ sSO 1^ 019 7.078 107.969 78.948 .ooz 1ft9 }{.) f)^^ 900 9A9 908 Zuo.VO087i 7.007 109.144 80.140 -O"101I Of) 0 1 ft z - > 1 o 97A 7ftn 9J.1 ^Q8 ^ oil 6 874 1 in hOS 81 90.1 110 10 ''110 97A Q,l/t 911 779 1 ^ 010 6.908 1 10 434 81 91ft .417 110 OU. 1 if

9R'l 7Q^ ZOO. too 9^7 ^18 1 ^ 00'^ ft a=il 1 1 0 017 81 ftfti .4oO 111 OV/. in 1 17 I 4 i 91 1 All zvu.oyi 979 7'^ft 19IZ. 00 ^

7

/o ftU.048171 111 ft17 R9OZ . 11 Z'r 91 llA Of10 I o 919 907 .197 988 91ft 12 987 6.788 112.344 R9 "iin -4^Jl/ ovy.'JO ;,1 6871

i^Ol OU J 101 cr^Q CO 998 11 188 7.056 ins =^Qt 79 9ft8 11 0.19 ^9R 10^ O'iQ Al 9'>ft 11 ^si 8.352 107.756 71 091 -ZO 981L 19 7ft^ O.- . 1 l)i> IVO.OoO 70 (i(19 14 379 7.127 107.453 71 =iOO .295 520 75.028 14.377 8.432 107. .534 711 O. 719 t OZ 900 OIt .^'fiO V , »,''Jv' 503 205.816 89.577 14.371 7.131 107.532 74 4.37 .O11 =i 1 .J 11 1 ~ O 1 1 . 1 I 1 521 97.366 14.366 8.358 107.655 74.799 .OZ1911 in 0 in 108 fiQfi 7i . 109 i vZ 107 801 7^ 10ft 11

1

.004 111 917 Ifl^ 1 1 0 881 14-. JOO a 110 107 990 7t1 O. 788 1 oo .04 117

1

OA •)Q9 ow,_V„ 990 Ofifi 1 97 001 11 7 07=; 108 187 7ft 1-'1 l^ft in 1 ^9 oy*. I OZ 199 99^ '01 119 '^ftO 11 lift 8 911^ O.Z40 108 ft^ft 7ft I O. 701 ( W4 .oov IftO 10 rr<9 997 ^f\~ 117 180 11 111 7 010 108 RS7 76 SO9 .O » •) in 11^7 524 234.287 lUU . O 1 -r 11 '^'^1 8.234 109.380 77.621 .o •;() Hvft 507 9^4. dl7 166.928 1114.0.30 '^^T 6.969 109.372 77.6-34 .O101./O 90 80^ 508 241.372 185.902 14.326 6.927 109.898 78.307 .411 29,647 525 242.493 188^962 14.324 8.159 109.9,39 78.412 .412 29..585 509 248.293 204.791 14.317 6.910 110..378 78.940 .428 29.485 510 255.197 223.622 14.308 6.870 111.009 79.538 .445 29,500 511 262.143 242.543 14.299 6.820 111.759 80.107 .461 29,656 514 265.537 251.779 14,294 7.970 112.059 80.373 .468 29.631 512 269.538 262.650 14.289 7.971 112.383 80.678 .478 29.689 515 273.495 273.386 14.284 7.928 112.890 80.969 .487 29,885 513 277.494 284.223 14.278 7.914 113.176 81.255 .497 29.877 516 281.439 294.892 14.273 7.875 113.651 81.527 .506 30.061 517 289.349 316.229 14.262 7.793 114.710 82.045 .524 30.557

G-8
Table 2. Specific heat at constant volume, Cy, of methane; heat correction for calorimeter expansion CI, heat capacity of empty calorimeter,

CO, total heat capacity of calorimeter (full) AQ/AT or DQ/DT, with temperature, pressure, density, and temperature increment, DT —

Continued

ID Temp Press Den DT DQIDT CO CI C, — K bar mol/1 K J/K J/K J/niol • K J/mol-K

701 187.947 51.088 16.104 7.172 110.110 72.012 0..350 32.038 707 188.669 53.498 16.103 6.9.57 110.16-1- 72.118 .353 31.990

721 191.577 63.245 16.098 6.895 110.072 72.537 .367 31.543 702 195.118 75.188 16.093 7.178 110.019 73.032 .378 31.066 708 195.637 76.94.3 16.092 6.947 110.062 73.103 .380 31.040 720 199.140 88.833 16.087 6.859 110.111 73.576 .390 30.670 703 202.277 99.525 16.082 7.135 110.530 73.987 .397 30.670 709 202.632 100.738 16.082 6.943 110.308 74.032 .399 30.441 704 209.408 123.943 16.071 7.112 110.909 74.881 .426 30.204 710 209.569 124.495 16.071 6.933 110.994 74.901 .427 30.2.58 711 216.494 148.306 16.060 6.873 111.429 75.718 .450 29.911 705 216.509 148.360 16.060 7.078 111..388 75.720 .4.50 29.875 712 223.3.52 171.937 16.049 6.816 112.095 76.484 .472 29.805 706 223.900 173.825 16.048 7.007 112.128 76.544 .473 29.780 713 230.437 196.359 16.038 6.824 112.675 77.232 .494 29.639 714 237.251 219.833 16.027 6.791 113.485 77.913 .515 29.729 715 244.048 243.213 16.016 6.758 113.994 78.556 .536 29.594 716 2.50.777 266.302 16.005 6.660 114.660 79.159 .557 29.627 717 257.424 289.044 15.994 6.627 115.322 79.724 .577 29.689 718 264.035 311.587 15.983 6.571 116.177 80.2.56 .597 29.944 719 270.623 333 970 15.972 6.544 116.590 80.7.59 .616 29.849

1601 185.501 42.477 16.0.38 2.172 110.226 71.648 .337 32.608

1602 187.587 49.323 16.035 2.006 110.069 71.959 .348 32.198- 1603 189.591 55.934 16.032 2.009 109.944 72.2.52 .358 31.832 1604 191. .595 62.582 16.029 2.004 110.119 72.539 .361 31.732

1618 192.871 66.824 16.024 6.135 109.928 72.719 .367 31.410

1603 193.605 69.272 16.026 2.010 109.753 72.822 .377 31.163

1606 195.615 75.989 16.023 2.012 109.895 73.100 .383 1607 197.622 82.719 16.020 2.003 110.31

73.373 .389 31.157

1603 199.628 89.464 16.917 2.005 110.203 73.640 .396 30.831 1619 200.031 90.821 16.011 8^252 110.152 73.693 .391 .30.746 1620 209.230 121.946 15.996 10.164 110.765 74.859 !419 30!246

1609 217.884 151.399 15.986 6.097 111.290 75.877 .452 29.793

1611 223.224 169.616 15.977 6.069 111.946 76.470 .469 29.830

1610 223.903 171.930 15.976 6.052 112.026 76.544 .471 29.8;'.4 1622 229.421 190.764 15.964 10.032 112.633 77.128 .484 29.842

1612 229.453 190.871 15.967 6.063 1 12..588 77.131 .488 29.795

1623 239.424 224.878 15.948 9.937 113.475 78.122 .515 29.681 1613 241.503 231.959 1.5.948 5.956 113.763 78.319 ..525 29,718 1614 247..521 252.433 15.939 5.898 114.293 78.871 .544 29.715 1615 253.443 272.535 15.929 5.912 1 14.H68 79.389 .562 29.712

1616 259.333 292.473 15.919 5.842 115.529 79.830 .579 29.R69

1617 265.198 312.270 15.910 5.849 116.001 80.347 .597 29.8.56

G-9
Table 2. Specific heat at constant volume, Cy, of methane; heat correction for calorimeter expansion C\,lieni capacity of empty calorimeter. CO, total heat capacity of calorimeter i/uil) AQ/AT or DQ/DT, with temperature, pressure, density, and temperature increment, DT —

Continaed

ID Temp Press Den DT DQjDT CO CI C, K bar mu!/l K J/K J/K J/mol • K J/mol • K

1309 184.764 45.449 16.723 5.354 110.741 71.537 0.381 31.721 1301 187.826 56.698 16.717 6.932 110.769 71.994 .394 31.357 1310 190.103 65.099 16.714 5.347 110.862 72.326 .406 31.150

1302 194.733 82.255 16.706 6.892 110.968 72.979 .423 30.685

1311 195.445 84.904 16.706 5.344 111.063 73.077 .427 30.679 1303 201.094 105.956 16.696 5.855 111.252 73.833 .446 30.196 1323 202.937 112.841 16.693 6.031 111.551 74.072 .453 30.2.39 1312 206.062 124.532 16.688 5.287 111.919 74.468 .465 30.204 1304 206.122 124.756 16.689 4.249 111.707 74.475 .466 30.023 1324 208.680 134.336 16.683 5.477 112.228 74.792 .473 30.184 1305 210.401 140.788 16.681 4.330 112.079 75.001 .481 29.882 1313 211.348 144.339 16.679 5.286 112.322 75.115 .483 29.987 1325 214.143 154.818 16.674 5.464 112.494 75.446 .492 29.847 1306 215.024 158.123 16.673 4.934 112.592 75.549 .496 29.840 1314 216.658 164.252 16.670 5.219 112.889 75.737 .501 29.924 1326 219.582 175.218 16.665 5.433 112.992 76.069 .511 29.727 1327 225.003 195.545 16.655 5.423 113.635 76.662 .530 29.749 1317 232.337 223.009 16.643 5.178 114.228 77.426 .555 29.585 1318 237.657 242.891 16.633 5.448 114.856 77.952 .572 29.651 1319 243.097 263.174 16.624 5.401 115.579 78. 168 .590 29.802 1320 248.519 283.339 16.614 5.387 115.951 78.960 .608 29.686

253.921 30? 370 16.604 5.359 1 16.619 7"' t.iO .626 1322 259.304 323.264 16.595 5.339 117.189 79.878 !644 29.913

411 187.325 58.469 17.007 8.019 1 1 1 .229 71.920 .416 31.221 401 193.924 83.993 16.997 6.900 111.328 72.867 .4-13 ,30.513 406 196..587 91..H7 16.992 7.437 111..563 73.233 .452 30.399 413 203.9.-).! 123.025 16.978 7.970 112.216 74.202 ,478 30.119 414 211.98vS 1,V;.39() 16.961 7.898 113.134 75.192 .507 30.033 415 219.901 185.282 16.9.50 7.850 113.769 76.101 .535 29.782 416 227.768 215.9.52 16.936 7.807 11 4..5.50 76.9.55 .562 29.698 417 235.598 246.397 16.922 7.735 1 15.4,35 77.751 .590 29.743 418 245.293 2a3.931 16.904 7.650 116.261 78.670 .623 29.635 419 252.926 313.338 16.890 7.598 117.007 79..345 .649 29.667

1801 178.581 37.972 18.086 3.069 112.W 70.571 .469 31.280 1802 181.649 51.8.36 18.080 3.085 112.625 71.0.57 .496 30.991 1803 186.224 72.545 18.068 6.089 1 12.813 71.756 .503 30.598

1804 192.299 100.083 13.056 6.060 113.4.^3 72.639 .530 30.377 1805 198.354 I27.,540 18.0-U 6.039 113.922 73.471 .5.54 30.000 1806 204.379 154.828 18.032 6.010 1 14..564 74.256 .578 29.958

1807 210.370 181.915 18.019 5.964 115.1.32 74.998 ,602 29.803 1808 216.641 210.187 18.006 5.923 115.821 75.7.35 .627 29.741 1809 222.620 237.053 17.994 5.886 116.615 76.404 .651 29.812 1810 228.488 263.318 17.982 5.8.54 117.179 77.031 .674 29.742

1811 234.304 289.242 17.970 5.825 117.723 77.623 .697 29.683 1812 240.990 318.901 17.955 5.797 118.614 78.271 .723 29.841

G-10
Table 2. Specific heat at constant volumtf, Cy, of methane: heat correction for calorimeter expansion VA.Iient capacily of empty calorinifCi^r. CO, total heat capacity of calorimeter {full) AQ/A'l' or DQ/DT, uilh temperature, pressure, density, and temperature increment. DT —

Continued

ID Temp Press Den DT DQjDT CU Cl C, K bar moi/1 K J/K J/K J/mol K J/mol • K

1709 172.603 40.302 19.500 6.087 114.035 69.577 0.596 30.637 1710 178.550 73.409 19.436 6.101 114.965 70.566 .608 30586

1701 181.613 90.419 19.479 6.082 115.092 71.052 .636 30.306

1711 184.637 107.182 19.472 6.065 115.515 71.517 .650 50.262 1702 187.628 123.725 19.465 6.054 115.740 71.965 .663 30.094 1712 190.680 140.564 19.457 6.039 116.187 72.408 .676 30.082 1703 193.640 156.857 19.450 6.008 116.537 72.827 .690 30.021 1713 196.693 173.622 19.443 5.997 116.917 73.247 .7a}- 29.980 1704 199.616 189.630 19.435 5.980 117.239 73.639 .717 29.918 1714 202.661 206.260 19.428 5.946 117.740 74.036 .731 29.976 1705 205.568 222.086 19.421 5.941 117.875 74.406 .745 29.798 1715 208.615 238.633 19.413 5.927 118.353 74.784 .759 29.854 1706 211.480 254.140 19.406 5.895 118.705 75.131 .772 29.844 1716 214.522 270.555 19.398 5.886 118.993 75.490 .787 29.733 1707 217.573 286.970 19.391 5.857 119.326 75.842 .801 29.7.52 1717 220.387 302.058 19.384 5.842 119.782 76.158 .814 29.837 1708 223.411 318.216 19.376 5.818 120.066 76.491 .829 29.789

807 161.140 39.441 21.313 5.723 116.134 67.478 .746 30.544

801 165.189 68.515 21.299 6.791 116.981 68.251 .772 30.565 808 166.828 80.226 21.296 5.647 117.232 68.5.54 .798 30.507 802 171.921 116.429 21.279 6.676 118.171 69.459 .8:33 30.495 809 172.488 120.139 21.279 5.633 118.018 69.557 .831 30.336 810 178.091 159.906 21.262 5.566 118.950 70.491 .859 30.307 803 178.582 163.345 21.258 6.640 118.980 70.571 .859 30.275

811 183.640 198-640 21.24-1 5.532 119.742 7] .365 .890 30.224 804 18.5.182 209.346 21.238 6.587 1 19.9,38 71.600 .896 30.193 812 189.1.53 236.787 21.227 5.487 120.631 72.188 .921 30.236 805 191.734 254..532 21.218 6.521 120.927 72.559 .933 30.175 813 194.626 274.322 21.210 5.456 121.445 806 198.229 298.849 21.197 6.467 121.824 73.454 .971 30.139 814 200.073 311.376 21.193 5.439 122.044 73.700 .985 30.109

2109 153.984 30.846 22.126 4.385 117.-120 66.016 .818 31.040

2101 157.876 62.103 22.113 4.327 118.099 66.827 .845 30.931 2102 162.200 96.526 22.098 4.314 118.875 67.684 .927 30.801) 2103 166.497 130.432 22.083 4.273 119.755 68.493 .910 30.832 2104 170.767 163.847 22.069 4.251 120..349 69.259 .951 .30.716 2105 175.011 196.789 22-054 4.233 120.874 69.985 .976 30.567 2106 179.314 229.914 22.040 4.211 121.698 70.688 1.003 30.615 2107 183.514 261.982 22.025 4.186 122.103 71.346 1.029 30.4.32 2108 187.701 293.689 22.011 4.164 122.834 71.976 1.0.56 30.468 1406 148.828 44.459 22.933 6.789 118.758 64.875 0.899 31.314

1407 155.536 104.131 22.907 6.633 120.057 66..344 1.015 31.098 1402 155.969 107.942 22.906 6.629 120.154 66.435 1.017 31.100

1401 156.936 116.449 22.900 7.882 120.264 66.635 1.020 31.0-12 1408 162.130 161.805 22.883 6.560 121.193 67.671 1.042 30.958 1403 162.555 165.498 22.881 6.,564 121.222 67.753 1.043 30.925 1409 168.648 217.963 22.8.58 6.496 122.400 68.883 1.075 30.923 1404 169.076 221.618 22.856 6.499 122.320 68.960 1.078 30.826 1410 175.122 272.905 22.834 6.45 J 123.385 70.003 1.120 30.798

1405 175.530 276.347 22.832 6.440 123.626 70.071 1.123 30.898

G-11
Table 2. Specific heat at constant volume, Cy, of methane: heat correction for calorimeter expansion Cl.henc capacity of empty calorimeter, CO, total heat capacity of calorimeter (full) AQ/AT or DQ/DT, icith temperature, pressure, density, and temperature increment, DT —

Continued

ID Teinp

K

Press bar Den

niol/l or

K

DQIDT

j/K

CU

J/K

CI

J/mol K J/ mo! K

2001 2002

2003

200-1 2005

2006

2007

901 909

904

902 910

903

911 906

912

907

913 908

139.073

143.270 147.448

151.599 155.908

160.011 164.072

130.508

131.693 132.694

134.136

137.159 139.337

142.547

143.713 147.886

149.124

153.185

154.473

45.399

88.569

130.924

172.491 215.104

255.209

294.445

34.766

48.379

59.842

76.278

110.410

134.756 170.300

183.112 228.554 241.915

285.371 299.029

24.008

23.990

23.972 23.954

23.935

23.917 23.900

24.785

24.772

2^1.767 24.761 24.746

24.735 24.720

24.715 24.695

24.689 24.670

24.664

1201 121.160 64.484 25.872 1202 124.223 104.694 25.855 1203 127.262 144.001 25.838 1204 130.274 182,414 25.822

1101 110.867 44.963 26.655 1106 111.917 60..514 26.649 1103 111.855 59.603 26.649

1102 116.030 120.523 26.624

1107 117.051 135.181 26.618

1104 122.089 206.386 26.588

1108 122.094 206.453 26.588

1109 127.100 275.451 26.5.59 1105 127.123 275.769 26.558

1004 102.424 48.414 27.388

1001 105.029 90.948 27.371 1005 107.466 129.912 27.3.55 1002 110.058 170.735 27.333

1006 112.446 207.806 27.322

1003 115.142 249.013 27.305

1007 117.361 282.491 27.290

1912 92.592 40.274 28.164

1901 92.609 40.540 28.164

1907 93.793 62.384 28.1.55 1902 95.465 92.859 28.143 1913 95.634 95.885 28.141 1908 96.675 114.525 28.134

1903 98.301 143.313 28.122

1909 99.505 164.435 28.114

1904 101.123 192.506 28.102 1910 102.319 213.085 28.093

1905 103.902 240.032 28.032

1911 105.104 260.314 28.074 1906 106.655 286.252 28.063

4.195 119.866 0.988 4.184 120.961 \JO.OO-ir 1.146 4.155 121.919 U-r.OO / 1.165 4.133 122.597 1.191 4.091 123.742 1.205 4.084 124.120 A7 1.236 4.052 124.977 1.263

2.255 121.056 60.095 1.097 5.484 121.045 0U.-i4o 1.106 5.557 i 1 . -too OU. / OHr 1.136

4.991 191 ^dft 01. 144 1.174

5.421 122.150 61.977 1.245 5.473 122.514 62.555 1.258 5.356 03.3(5 1.283 5.439 l^O. 1 9'^ "n 1 i VI 03. 063 1.287 5.336

1 .303 5.389 1.313 5.287 19^ ^A'^ Oil 1.348 5.310 Oo.lzU 1.359

3.070 199 nc\^ D/.llo 1.274 3.048 122.909 58.138 1.400 3.035 123..532 59.107 1.420 3.013 124.390 OU.UzD 1.455

5.194 121.731 CO O/IQ Oo.O-J-V 1.309 5.165 121.991 00. / 00 1.354 5.215 121.835 Do. i 04 1.351 5.136 123.377 oo.oUO 1.503 5.109 123.607 55.677 1.510 5.057 125.308 57.432 1.546

5.051 125.107 57.434 1.546

4.981 126.527 59.056 1.574 5.028 126.592 59.064 1.574

5.069 121.472 49.8.58 1.475 5.078 122.552 50.974 1.619 5.035 123.275 51.986 1.613 4.931 124,205 53.030 1.637 4.941 125.126 53.962 1.646 4.914 126.082 .54.979 1.6.52 4.903 126.695 55.789 1.673

3.061 2.871 2.873

2.842 3.022

2.824

2.807

2.821 2.793

2.791 2.749

2.766

2.751

120.491 120.603

121.008

122.072 122.178

122.424

123.144

123.531 124.316

124.573

125.401 125.533

126.307

45.311 45.319 45.899

46.701 46.780

47.269

48.020

48.566 49.288

49.812

50.495

51.005

51.653

1.351 1.313

1.458

1.769

1.765

1.769 1.740 1.745

1.708

1.767

1.755 1.766

1.781

31.796

31.6.55 31.612

31.4.37 31.5.50 31.258

31.267

32.662 32.454

32.479 32.166

32.080

31.949

31.911 31.964

31.785 31.732 31.728

31.839

33.145

32.958

32.757

32.691

33.910

.33.789 33.724

33.557 33.478

33.415

33.311 33.180

33.210

34.428

34.267 34.129

34.049

34.035 33.999

33.879

35.326

35.415

35.186

35.003

35.020

34.898

34.913 34.830 34.839

34.710

34.793

.34.600 34.644

G-12
Comparison of Cv/^methane^ extrapolated to saturation ,to several other liquids: /-i [8], Oj [6], KR [13J,

Ar [i4], and Ne [15] is sliownl'infii^ure 6. The density is reduced by the critical deirsity. The spectroscopic

heat capacity, C" is subtracted in each case. Molar

specific heats are independent of reducing parameters

[16]. All of the data except that for Ne correlate quite

well. Presumably this departure of Ne is a result of

its being more of a quantum fluid. H2 and He also depart markedly from this grouping as shown by Diller

[16].

I would like to acknowledge the support of the Ameri- can Gas Association. R. D. Goodwin's data of the PVT

of methane were essential and his computer programs

calculating the various functions and derivatives were

of great help. I thank D. E. Diller for his numerous

contributions. The data shuvm in fijjure 6 ' ctfe from his -

5. References

[1] The S. I. (international svstem) unit of pressure is the Pascal

(1 Pa 22 1 N7m-). The bar is 10'> Pa, also 1 atm = 1.01325 X 10'- Pa, 1 lb/in-' = 6894.757 Pa. 1 clyne/cm-= lO"' Pa. Alsoone mole methane = 16.0430 g, based on the '-C scale and the natural

isotopic abundance averages: see Remv. H.. Chem. Berichte 101,1(1968).

[2] Goodivin, R. D.. J. Res. Nat. Bur. Stand. (U.S.) 65C, (En?, and

Instr.), No. 4,231-243 (Oct.-Dec. 1961).

[3] Younglove, B. A. and Diller. D. E.. Cr)i>genics 2, 1 (1962).

14) Youii-love, B. A. and Diller. D. E., Cryoi:enics 6, 1 (1962).

[5] Goodwin, R. D. and Weber, L. A.. J. Res. .Nat. Bur. Stand. (U.S.), 7.SA, (Phys. and Chem.), No. 1, 1-13 (,lan.-Feb. 1969).

[61 Goodwin, R. D. and Weber. L. A.. J. Res. Nat. Bur. Stand. (U.S.), 7:iA, (Phvs. and Chem.). No. 1. 15-24 (Jan.-Feb. 1969).

[7] Goodwin. R. D. and Prvdz, R.. J. Res. Nat. Bur. Stand. (U.S.), 74A, (Phys. and Chem.), No. 4. 499-,50S (July-Auii. 1970).

[8] Prydz, K. and Goodwin, R. D.. J. Res. Nat. Bur. Stand. (U.S.). 74A, (Phys. and Chem.), .No. 5. 661-665 (Sept.-Oct. 1970).

[9] Walker, P. A.. Dissertation (University of London, 1956).

[10] Goodwin, R. D. and Prvdz, R.. J. Res. Nat. Bur. Stand. (U.S.), 76A,(Phvs. and Chem.). No. 2.81-101 (Mar.-Apr. 1972).

[11] Hoge,H. J...I. Res. Nat. Bur. Stand. (U.S.). 36, 1 1 1 (1946).

[12] W cibe. R. and Breevort,.M. J.. J. Am. Chem. Soc. 52, 622 ( 19.30). [131 Gladun.C. and .Menzel. F.. Crvo-enic^ 10, 210(1970).

[14| Gladun.C, Cryo-enics 1 1,205(1971).

[15| (iladun. C. Cryo-zenics 7, 78 ( 1967).

[16| Diller, D. E.-Crvoiienics 1 1,166(1971).

[17| Jones, .M. L., Jr.. .Ma-e. D. T.. Faulkner, R. C. Jr.. and Katz.

D. L.. Chem, Eng. J'rogress Symposium Series 59, 52 (1960).

G-13
54A

Figure 1. Calorimeter and cryostat.

55A

Figure 2. Specific heat of the saturated liquid for methane, this work, O, the measurements of IViebe and Breevort % [12J.

56A

Figure 3. Specific heat at constant volume of methane on isochores versus temperature.

Open and closed circles 'jn altercale is4-»chores are for clarity.

A-28.0 mol/l, B-27.4mol/l C-26.7 mol/l D-2.V8 E-21.7 F-24.0 G-23.0 H-22.1 1-21.3

J-l'J.5 K-18.0 I.- 17.0 .M-16.7 N-16.0 P-14.4 0-13.1 R-13.1 S-11.8 T-7.9

57A

Figure 4. Cv of liquid methane evaluated at the liquid-gas boundary.

Extrapolation of Cp(0). calculation from using FVT surface (A).

58A

Figure .5. Comparison of methane from Jones, et al. (-0-); to Cp calculated from Cy data, this work (A), and to Cp calculated from FV T tiam ( —). 57A

Figure 6. Reduced specific heats versus reduced density for CH,

t© ), F, ( 0 ), O, (A), Kr (). Ar (O), and Ne ( V

)'.

G-14
APPENDIX H

H-1
This survey provides a convenient summary of available data on liquid— vapour equilibria for systems of interest in cryogenics. An annotated bibliography of 392 references has been

compiled, current to January 1973. These references have been scanned individually with ^-ygg

few exceptions, and cross-indexed by system with notation of extent of data and other

significant features. The systems included are those made up of the possible combinations

of H2(D2. HD), N^. CO, H2S, He(He^), Ne, Ar, Kr, Xe, and the saturated and

unsaturated hydrocarbons through the C^s.

Liquid—vapour equilibria research on systems of

interest in cryogenics — A survey

A. J. Kidnay, M. J. Hiza, and R. C. Miller

This paper is intended as a survey of the available experi- mental data for the equilibria between the liquid and vapour

phases of fluid mixture systems of interest in cryogenics. These data are described in a number of different ways in the scientific literature, that is, dew- and bubble-points,

total vapour pressures of solutions, A'-values or equilibrium

distribution coefficients, solubility of gases in liquids, Henry's constants, liquid-gas equilibria, liquid—vapour, etc. Such terms are simply related to the type of data and method

of representation or are intended to clarify the relationship between critical temperatures of the included components.

In this paper, the term 'liquid-vapour equilibria' is used

collectively for all of the various descriptors.

This survey on liquid—vapour equilibria is only one part of an extensive compilation and evaluation effort on the important equilibrium and thermodynamic properties of low temperature mixtures. These include solid- liquid, solid—vapour, solid—liquid—vapour, liquid—liquid, liquidvapour, and gas—gas phase equilibria, liquid densities, gas

or vapour densities, enthalpies, and Joule—Thomson coefficients. A complete annotated bibliography of these properties will be pubhshed as a special NBS-Office of Standard

Reference Data publication. However, there is an immediate

interest in liquid—vapour equilibria data for a number of low

temperature systems, such as those related to liquefied natural gas technology. Thus, it seems warranted to make

this section available prior to publication of the complete

bibliography.

In an earlier paper,' a review of research associated with low temperature solid-vapour equilibria was given with emphasis on the fundamental value of such studies. The

present survey of low temperature liquid—vapour equihbria

is a logical sequel, and many of the fundamental aspects presented in the earlier paper apply here as well. The

same molecular species were considered in this survey of

liquid—vapour equilibria data; however, the number was expanded to include isotopes of helium and hydrogen,

additional hydrocarbon species, and hydrogen sulphide.

AJK is with the Colorado School of Mines, Golden, Colorado, USA, MJH is with the National Bureau of Standards, Institute for Basic Standards, Boulder, Colorado 80302, USA, and RCM is with the

University of Wyoming, Larannie, Wyoming, USA. Received 25 May

1973.

Thus, the information included here would be valuable

to the low temperature physicist as well as to the cryogenic

engineer, whose current interest may be in liquet^ied natural

gas technology.

Literature search

In the early phases of the fluid mixtures research programme

in the NBS Cryogenics Division, an indexed bibliography

of 681 references was prepared current to October 1959.^ Included were references to experimental and theoretical work on phenomena and properties of selected pure components and mixtures containing these species. The components of primary interest were: hydrogen, helium,

nitrogen, carbon dioxide, carbon monoxide, methane,

ethane, and propane. Oxygen, the remaining noble gas

species, and other hydrocarbons were considered only

when included in the primary systems. From experience

in using this early bibliography, it was apparent that the scope was too broad and the number of primary components was too limited. The scope of the present effort was reduced to experimental properties of fluid mixtures

only, but for an increased number of primary components. The components included here are: H2(D2, HD), N2, O2,

Fj, CO, CO2, H2S, He(He-3), Ne, Ar, Kr, Xe, and the saturated and unsaturated hydrocarbons through the C4S.

In addition, systems containing components other than

those of primary interest (for example, the methanebenzene system) were not included. References in the 1959 bibhography which met these new criteria contributed

significantly to the present effort. A search of the NBS-Cryogenic Data Center computer list- ing for citations on properties of mixtures containing the subject molecular species resulted in approximately 1 400

citations. These were also screened in accordance with the

criteria described above. Though the Cryogenic Data

Center personnel expend considerable effort to attain comprehensive coverage of the literature,^ all of the fluid species of interest here were not consistently subjects in their search of the literature. Specifically, the hydrocarbon

species other than methane were not adequately covered. On the other hand, since the Cryogenic Data Center operafion was begun just before Tech Note 56 ^ was completed,

the two sources provide comprehensive coverage for some

CRYOGENICS . OCTOBER 1973 Vol 13, No. 10 H-2 575
of the systems of interest. The deficient areas were the primary objects of the present search.

The following sources of references were used as cross- checks and to remedy the deficiency of coverage discussed above.

a The monograph of Hala, at al ^

b The handbook of Katz, et al ^

c The bibliography of Ruhemann and Harmens ^

d The bibUography of Gunn and Mainkar ^

e The bibliography of Mendelssohn et al ^

f Extensive bibliographies found in several dissertations and papers scanned

g The files of the NBS Cryogenics Division fluids mixtures

project, which have been maintained for the past 14

years h Lists of pubUcations of our colleagues who have been

actively engaged in fluid mixtures research for a number

of years The resulting list of references was finally updated by

searching Chemical Abstracts, section 68 — Phase equili- briums, chemical equilibriums, and solutions, and section 69 — Thermodynamics, and thermal properties, all of 1971 and 1972, and with an issue by issue search of the following periodicals for 1972.

a AIChEJ

b Can J Chem Eng

c Ind Eng Chem Fundam

d J Chem Eng Data

e J Chem Thermodyn

FinaUy, more current papers, of which we were aware', were included for the sake of completeness.

20 27 K

Ne %| 1 2709

HD 1^ Z9

6 1

N» 3 2 3 CO

CO 6 1

"2 IS 14 6 7

S 3 13

h 2 Ar 2 7 1 1 10 II COj °\ 8 3 4 10 6 3 1

Kr 1 3 2

X» 1 CH4 e 9 4 16 1 2 6 7 2

3 3 1 1 4 S". S 4 1 5 1 2 12 4

1 1 1 1 1 2 5 2 1 1 2 S". 3 2 3 5 4 4 10 1 4 s

n- C^H

1 6 1 3 7 1 3

2 Z 1 1 3 z\

Liquid-vapour equilibria for binary systems

Fig.l Summary of the number of references which report original liquid—vapour equilibria data for each binary system

CO

Nj^

Oz

^2

Ar

CO2

Kr

Xe

CH4

81.64 m

Triple point Critical point ]7735

^9019

"18728

194 69 (Subl

)

J 1694

1 1 84,5

0 ICQ 200 300 400 500 Temperature, K

Fig. 2 The saturated liquid phase temperature range of representative pure component species included in this survey

Availability of liquid—vapour equilibria data

The bibliography of references on liquid—vapour equilibria data and the tables in which the references are indexed by

system are the results of this effort. The references are indexed in the tables by system with

separate tables for binary systems, ternary systems, and

systems containing four or more components. For binary

systems, the lowest molecular weight component is listed

first. The systems are arranged in order of increasing molecular weiglit of the light component, with system.s having

non-hydrocarbon light components preceding those having

hydrocarbon liglit components. For ternary and higher systems, components within the mixture are listed in order of increasing molecular weight. The arrangement of the systems follows the same pattern as for binary systems. The bibliography of 392 references is arranged in alphabetical order by author.

Fig.l provides a superficial summary of the available data

for the binary systems. The numbers in the spaces indicate

the number of papers reporting data for each system.

Dissertations were not included in these totals if the included data were subsequently published in the periodical

literature. The one reference for the carbon dioxidecyclopropane system is included in the total for C^H^^ under CO2. Two references not included are those for the propane 1—butene and propane—isobutene systems.

Fig. 2, which portrays the normal liquid range of representative pure component species, is included as an aid to indicate the temperature regions in which liquid -vapour

equilibria can exist for given combinations.

576 H-3CRYOGENICS . OCTOBER 1973
Discussion

It is important to emphasize that this survey is intended

to include all references containing experimental data without judgement as to the reliability of the results given. Selection of best values for a given system is a complicated

process at best, but must begin with a common method of

data reduction which is most sensitive to discrepancies in the available data sets. A cursory discussion of the funda- mental relationships is given here only to indicate the

basis of data reduction or presentation methods. Examples

of two such methods of liquid phase data reduction are given which serve to indicate the potential ease or difficulty

in best value selection. The equilibria represented here fall into two distinct categories: (1) equilibria of close-boiling systems in which

the included components would be subcritical at the temperature of solution, and (2) equilibria of systems in which both subcritical and supercritical components are included. In either case, the equation of equilibrium is

/^(vapour) =7)(liquid) (1)

where is the fugacity of component ; in the mixture. The fugacity of / in the vapour is related to its mole frac- tion^,- and the pressure of solution tt by

7;-(vapour) = ^iyjTT (2)

where ^pj is the fugacity coefficient of / in the vapour mixture. The fugacity of /" in the liquid is related to its mole

fraction Xj and a standard state fugacity term Sj by

//(liquid) = yiXiSj (3)

where 7,- is the activity coefficient of / in the liquid mixture. The differences in the two categories of liquid—vapour

equUibria are manifested in (3) in the method of normalization of 7 and in the choice of the standard state term.

For close-boiling systems, 7 for each component is conventionally normalized in the sense of Raoult's law (symmetric convention) such that

7,- 1 as Xj -* I (4)

The standard state term is taken as the fugacity for the pure

fluid at the temperature and pressure of solution. Thus (3) becomes

/;(liquid) = yjXifj

where

dn = PjiPi exp I -—

' RT

Pi

n - J R

(5)

(6)

The terms pj and ipj are the pure component vapour pressure and fugacity coefficient, respectively.

It is also common practice to correct activity coefficients

at the conditions of the solution to a reference state pres- sure TT^) by the following relationship

7/ =7f exp f RT

(7)

The excess Gibbs energy, directly related to the activity coefficients by

g'' = i:xjRT\nyf^ (8)

is often reported in experimental papers, and in a number

of cases appears to have been the primary purpose of the

investigation.

For systems containing both subcritical and supercritical components, the activity coefficient of the subcritical component is still normalized in the sense of Raoult's law, but it is more convenient to normalize the activity coefficient of the supercritical component in the sense of Henry's law (unsymmetric convention) such that

1 as X 0

The standard state term is taken as the infinite dilution Henry's law coefficient. Equation 3 then becomes

fj{\iqmd) = y*XjHjwhere

(9)

(10)

Hj i = lim 0

(11)

Full details of these relations and their uses are given by

Prausnitz.^ The brief discussion given here, however, is adequate for an understanding of the data reduction that

is encountered in the literature on liquid-vapour equilibria of mixtures, and to some extent the significance of the

general relationships which apply. Typical examples of reduced hquid phase data for the two categories of equilibria, taken from the bibliography of references are given

in Figs 3 and 4.

Fig.3 is an example of the excess Gibbs energy for a close- boiling system, nH2—Ne, derived from the data of two

different investigations. Since this system also exhibits

liquid phase separation, the data were taken from the region of complete Uquid phase miscibility. This is also an example

of excellent agreement between two different sets of data, which unfortunately is not the general case. Fig. 4 is an example of a Henry's law reduction of data from two dif- ferent investigations for a system, nH2—Ar, containing

a supercritical component. This is also an example of

discordant results for which critical selection becomes

extremely difficult without additional information on this particular mixture. In this case pressure has been used

rather than fugacity, which is quite common. Though the data have not been reduced in tlie true sense of Henry's

law, the infinite dilution intercepts are for practical pur- poses the same as the Henry's constant.

Critical evaluation of the data for a given system also will require knowledge of the best available pure fluid properties which are an inherent part of the fundamental relations discussed above. The importance of thermodynamically

consistent vapour pressure data was specifically emphasized

CRYOGENICS .OCTOBER 1973 H-4 577
o

E75

I /)-Hydrogen-Neon

£iA Keck a Borrick ( 1 966) 0« Streetl a Jones (1965)

—O 08

2900 50 00 3100 32 Temperature, K

Fig.3 Excess Gibbs energy for the nH2—Ne system as determined by Duncan and Hiza (1972) from the data of the two investigations indicated

-I 1 1 1 1 1 I r

/)-Hydrogen-Argon

T r

A Mullins a Ziegler (1965) O Volk a Holsey (I960)

0 20 40 60 80 100 120 (7r-p|) ,atm

Fig. 4 Gas solubility data from two investigations for the nHj—Ar

system as reduced in the sense of Henry's law by Mullins and Ziegler (1965)

in the review of solid—vapour equilibria research,^ and

selected references were included. A similar list of vapour pressure references for the entire

liquid region of each fluid has not been included as part of this liquid—vapour equilibria survey. However, it

is worth noting several non-periodical sources of vapour

pressure values and citations which are quite useful. The

references to the work of W. T. Ziegler et al given in reference 1 include calculated values of vapour pressure up to the normal boiling point for most of the fluids of

interest here, as well as providing a review of the available properties of the substance considered. A brief survey of vapour pressure data for the hydrocarbons not included

in those references are given in an earlier NBS Technical Note of Ziegler.'*^ AJso, the bibUography of Olien and

Hall " is a valuable source of vapour pressure references

for methane and the non-hydrocarbon fluids. These may

still be the best available sources of vapour pressure values and citations for most of the fluids in the regions covered, but some have been definitely out-dated in part by new

precise experimental measurements. Notably, the new vapour

pressure measurements of Prydz and Goodwin on methane cover the entire Uquid range, and are considered by

the present authors to be the best values currently available

for this fluid. Nevertheless, in addition to the above sources, an examination of the literature from 1964 to the present would provide a fairly complete list of vapour pressure data references.

It is hoped that this survey of experimental Liquid—vapour

equilibria data for fluid mixtures of cryogenic interest includes all of the significant experimental research done

prior to January 1972 and most of that done between

January 1972 and January 1973. Literature searches, however, seem to approach the intended objective asymptotically. Therefore, we would welcome conespondence from

those who are aware of appropriate research papers which do not appear in this survey.

The authors wish to express thanks to H. J. White Jr for

his useful suggestions and discussions and to the Office of Standard Reference Data of the National Bureau of Standards

for financial support. The contribution of both past and

present staff members of the Cryogenic Data Center, and

especially that of N. A. OUen, is gratefully acknowledged.

A special acknowledgement is due to Mrs M. F. Birchfield

for her painstaking typing and assistance in editing of the bibHography and tables, without which this survey would

not have been possible.

References

1

10

11

12

Hiza, M. J. 'Solid-vapour equilibria research on systems

of interest in cryogenics", Cryogenics 10 (1970) 106

Flynn, T. M. 'A bibliography of the physical equilibria and related properties of some cryogenic systems', NBS

Tech Note No 56 (May 1960)

Olien, N. A. 'The Cryogenic Data Center, an information

source in the field of cryogenics". Cryogenics 11 (1971) 11 Hala, E., Pick, J., Fried, V., Vilim, O. Vapour-Liquid

Equilibrium (Pergamon Press, 1958) KaU, D. L., ComeU, D., Kobayashi, R., Poettmann, F. H., Vary, J. A., Elenbaas, J. R., Weinaug, C. F. Handboolc

of Natural Gas Engineering (McGraw-Hill, 1959

)

Ruhemann, M., Harmens, A. 'Review Series No 4'. Bibliography of vapour-liquid equilibrium of low boiling mixtures and notes on -value correlations", The Chetn EngiNov 1967) Gunn, R. D., Mainkar, S. V. 'Bibliography of data sources

for low temperature vapor-liquid equilibria in non-absorber

oil systems", Nat Gas Proc Assoc Res Rept RR- 1, Project No 692-A, Univ Texas, Austin (1971) Mendelssohn, K.. Scott, R. B., Weil, L. A Bibliography of Low Temperature Engineering and Research (a supple- ment to Cryogenics) 1944-1960 (Heywood-Temple, 1961)

Prausnitz, J. M. Molecular Thermodynamics of Fluid-Phase

Equilibria (Prentice-Hall, NJ, 1969)

Ziegler, W. T. 'The vapor pressures of some hydrocarbons

in the liquid and solid state at low temperatures", NBS

Tech Note No 4 (1959)

Olien, N. A., Hall, L. A. 'A bibliography of experimental

saturation properties of the cryogenic fluids", NBS Tech

Note No 309 (1965)

Piydz, R., Goodwin, R. D. 'Experimental melting and

vapor pressures of methane", 7 C/iem Thermodyn A (1972) 127

578 H-5 CRYOGENICS OCTOBER 1973
Liquid—vapour equilibria for binary systems

System

Temperature

range, K

Pressure

range, atm Reference Remarks

Hydrogen--helium 3 22-28 1-16 Hiza (1972)

Hydrogen--helium 3 17-24 0-9 Matyash, Mank, Starkov

(1966)

Pressures given as He-^

nrpQ^li 1 rp H \/H rnnpn--hydrogen deuteride 17-18 <1 Hoge, Arnold (1951)

Hydrogen--hydrogen deuteride 20 1 Karwat {I960)

Hydrogen--hydrogen deuteride 19-27 0-4 Newman (1954) Graphs only

Hydrogen--hydrogen deuteride 18-28 1-4 Newman, Jackson (1958)

Hydrogen--hydrogen deuteride 18-32 0.1-11 Trevino (1956) Graphs only

Hydrogen--helium 4 14-16 1-16 Greene ( 1966) Normal and para hydrogen,

bubble-point

Hydrogen--helium 4 14-16 1-16 Greene, Sonntag (1968) Normal and para hydrogen,

bubble-point, graphs only

Hydrogen--helium 4 20-28 1-20 Hiza (1972)

Hydrogen--helium 4 16-29 2-8 Roellig, Giese (1962) Pressures given are partial

Hydrogen--helium 4 17, 20, 22 2-58 Smith (1952)

Hydrogen--helium 4 15-30 26-102 Sneed (1966), Sneed, Sonntag, Van Wylen (1968)Both normal and para hydrogen, barotropic and

critical locus

Hydrogen--helium 4 15-33 2-34 Sonntag, Grain, Streett Both normal and para hydrogen, barotropic and

critical locus

Hydrogen-—helium 4 on "30 z—J4 Sonntag, Van Wylen, Grain (1964)

Equilibrium hydrogen

Hydrogen -helium 4 16-33 2-34 Streett (1963), Streett, Sonntag, Van Wylen (1964) Normal hydrogen

Hydrogen--deuterium 4 — Bulatova, Kogan, Lazarev (1960)

Qualitative data from

x-ray measurements

Hydrogen--deuterium 19-20 <1 Hoge, Arnold (1951)

Hydrogen--deuterium 19 <1 Lewis, Hanson (1934) Limited qualitative data

ijla|JMd L/iiiy

Hydrogen-— deu te r iu m 20—28 0—5 Npwm;in iwcuviiiaii \ 1 ^ f firanh<: uia^iio nnlv i_iiny H\/Hmnpn- 1 y 1 vjy c I 1 — rlpi kJ CU1 tpr LCI H1 U1 m1 1 1 18—28 1 —4 Mp\A/nnan INCVvMIOll, JdL'lxoUII lapl^cnn ) IQRft^ V iZ/\JOi n y u 1 uyc 1

1

UcUoi i'to r 1 1 1 rr^ Lc! lull) 1 o—ou n 1 R Xrevino (1956) Graphs only

Hydrogen--neon 26-43 0-26 Heck, Barrick (1966) Normal hydrogen

Hydrogen--neon 25 <1 Simon (1963b) Para hydrogen, graphs only

Hydrogen--neon 25-34 0-14 Streett, Jones (1965) Normal hydrogen

Hydrogen--carbon monoxide 83, 100, 122 21-238 Akers, Eubanks (1960) Graphs only

Hydrogen--carbon monoxide 32-70 1-50 Dokoupil, Van Soest, Swenker (1955)

Isobaric data, gas phase

only

Hydrogen--carbon monoxide 83, 100, 122 21-238 Eubanks (1956) Graphs only

Hydrogen--carbon monoxide 78, 83, 90 7-50 Ruhemann, Tsin (1937) Graphs only

Hydrogen--carbon monoxide 68-88 17-225 Verschoyle (1931)

H-6

CRYOGENICS . OCTOBER 1973 579
S y st6m

Temperature

range, K

Pressure

1 ol lyc, d LP 1

1

n c 1 c 1 c 1 1 uc R P m a r c It C 1 1 1 a 1 In 5

Hydrogen--carbon monoxide 77-123 10-150 Yorizane, Yoshimura,

Masuoka, Toyama (1968)

Hydrogen--nitrogen 83-122 0-170 Akers, Eubanks (1960) Graphs only

Hydrogen--nitrogen 63-113 0-200 Charlseworth, Ruhemann

(1965) Graphs only

Hydrogen--nitrogen - 25-70 1-50 Dokoupii, Van Soest, SwenKer ( 1955)Isobaric data, gas phase

only

Hydrogen--nitrogen oo inn 100 oo, 1 UU, 1 O 1 1 C "7 Z 1 — 1 0 / bubanks ( 19ob)

Hydrogen--nitrogen 79-109 13-175 Gonikberg, Fastovskii,

(jurvitsch (1939) Hydrogen--nitrogen 90, 95 3-45 Maimoni (1956) (1961) Hydrogen--nitrogen 77 0-8 Matyash, Mank, Starkov

(1966)

Graphs only

Hydrogen--nitrogen 63—75 5—45 Omar, Dokoupii (1962) Isobaric data, gas phase

only

Hydrogen--nitrogen 78, 83, 90 1 1—50 Ruhemann, Tsin (1937) Graphs only

Hydrogen--nitrogen 79-91 <1 Sister, Sokolov (1940) Hydrogen--nitrogen 88, 90, 108,

1 1

3

0-1 10 Stekkei, Tsin (1939a) Graphs only

Hydrogen--nitrogen 88, 90, 1 08, 113 0—1 10 Stekkel, Tsin ( 1939b) Graphs only

Hydrogen--nitrogen CO o o bo—oo 0—225 Verschoyle ( 1931

)

Hydrogen--nitrogen 77, 88 <188 Yorizane (1971) Hydrogen--nitrogen 77 5-150 Yorizane, Yoshimura,

IVlasuoka, Toyama (1968)

Hydrogen--argon 68—105 20— 1 20 Mulhns (1965), iviullins, Ziegler (1965) Hydrogen--argon 87-140 10-100 Volk, Halsey (1960) Hydrogen--carbon dioxide Abdulayev (1939a) Hydrogen--carbon dioxide 298 78—195 Abdulayev (1939b) Graphs only

Hydrogen--carbon dioxide 222, 273 39—242 Greco, Casale, Negri (1954) Hydrogen--carbon dioxide 233-298 50-197 Kaminishi, Toriumi (1966) Hydrogen--carbon dioxide 281, 288 56-106 Mills, Miller (1945) Hydrogen--carbon dioxide 220—290 1 1—200 Spano, Heck, Barrick (1968) Hydrogen--carbon dioxide 273 <370 Yorizane (1971) Hydrogen--carbon dioxide 273 60-370 Yorizane, Yoshimura, Masuoka (1970) Hydrogen--methane 117, 144, 172 34-272 Benham (1956), Benham,

Katz (1957) Hydrogen--methane 90-127 31-227 Fastovsky, Gonikberg

(1940a, 1940b)

Hydrogen--methane 91 17-205 Freeth, Verschoyle (1931) Hydrogen--methane 67-1 17 10-125

H-7

Kirk (1964), Kirk, Ziegler (1965)

580 CRYOGENICS . OCTOBER 1973
System

Temperature

range, K

Pressure

range, atm Reference Remarks

Hydrogen—methane Hydrogen— methane

Hydrogen— methane

Hydrogen— methane

Hydrogen-ethene

Hydrogen— ethene

Hydrogen-ethene

Hydrogen— ethane

Hydrogen-ethane

Hydrogen—ethane Hydrogen— ethane Hydrogen—ethane Hydrogen-propene

Hydrogen— propane

Hydrogen— propane

Hydrogen— propane Hydrogen—n— butane Hydrogen—n— butane Hydrogen— isobutane

Helium 3— hehum 4

Helium 3— helium 4

Helium 3—helium 4 Helium 3— helium 4

Helium 3—helium 4

Helium 3—helium 4

Helium 3—helium 4

Helium 3— helium 4

Helium 3—helium 4

Helium 3—helium 4

Helium 3— helium 4

Helium 3— helium 4

158-178 31-78 Levitskaya ( 1941

)

158-188 28-83 Likhter, Tikhovovich

(1940)

107 4-90 Steckel, Tsin (1939a, Graphs only

1939b)

103-163 10-150 Yorizane, Yoshimura,

Masuoka, Toyama (1968) 80-170 2-150 Hiza, Heck, Kidnay

(1968a) 158-188 1-80 Likhter, Tikhonovich (1939)

1 17-255 17-544 Williams, Katz ( 1954) 144-200 7-136 Cohen, Hipkin, Koppany

(1967) 80-190 3-154 Hiza, Heck, Kidnay

(1968b)

158-188 31-78 Levitskaya (1941) 139-149 1 Uehara(1932)

103-283 17-544 Williams, Katz (1954) 117-297 17-544 Williams, Katz ( 1954) 278-361 27-497 Burriss, Hsu, Reamer, Sage

(1953) 88- 348 10-204 Trust ( 1968), Trust, Kurata (1971) 89-297 17-544 Williams, Katz ( 1954) 144-297 20-544 Aroyan, Katz (1951) 297-389 22-106 Nelson, Bonnell ( 1943) 311-394 34-204 Dean, Tooke ( 1946) 1—2 — Abraham, Weinstock, Osbourne (1949) 1-3 - Daunt, Heer (1952)

1.5-2.5 <1 Daunt, Tseng (1955) 1-3 - Eselson (1954) 1-3 <1 Eselson, Berezryak (1954) 1-3 <1 Eselson, Berezryak (1956) 1-3 <1 Eselson, Berezryak (1955) 1— 2 — Eselson, Kaganov,

Lifshits (1957)

1 — Eselson, Lazarev, Alekseevskii (1950) 2—5 — Fairbank, Lane, Aldrich,

Nier (1947) 2—5 — Fairbank, Lane, Aldrich, Nier (1948) 1-4 - Fairbank et al (1948) Graphs only

He^-He'' liquid \

temperature only

Graphs only

Graphs only

Dew-point measurement

Extensive tabular data

Graphs only

2nd order phase transition

in He l-He II

CRYOGENICS . OCTOBER 1973 H-!

581
System

Temperature Pressure

range, K range, atm Reference Remarks

Helium 3—helium 4 1-2 <1 Oigorev, Eselson, Masimov et al (1968)

Data obtained

Helium 3-helium 4 1-2 <1 Nelson, Band (1952) Graphs only

Helium 3-helium 4 1-2 <1 Peshkov, Kachinskii (1957) Dew-point me;

Helium 3—helium 4 1-3 <1 Sreedhar, Daunt (1960)

Helium 3—helium 4 0-2 <1 Sydoriak, Roberts (1960)

Helium 3—helium 4 1-2 <1 Taconis, Bennakker, Nier, Aldrich (1949)

Helium 3—helium 4 1-2 <1 Wansink, Taconis, Staas (1956)

Helium 3—helium 4 1-3 <1 Weinstock, Osborne,

Abraham (1950)

Graphs only

Helium 3—deuterium 20-30 1-16 Hiza (1972)

Helium 4—deuterium 20-30 1-20 Hiza (1972) Helium—neon 27-42 3-200 Heck (1968), Heck, Barrick (1967) Helium—neon 25-27 6-51 Knorn (1967) Helium—carbon monoxide 77-128 17-136 Sinor, Kurata (1966) Helium— nitrogen 83, 113 5-50 Burch (1964) Helium—nitrogen 78-122 12-68 Buzyna, Macriss, Ellington (1963) Helium—nitrogen 77 14-68 Davis, Rodewald, Kurata

(1963) Helium—nitrogen 77-126 15-98 Davydov, Budnevich

(1971) Helium—nitrogen 77-120 14-136 Devaney, Dalton, Meeks

(1963) Helium—nitrogen 65-125 10-100 Forg, Wirtz (1970) Graphs only

Helium—nitrogen 78, 90, 109 1-295 Gonikberg, Fastovsky (1940a) Helium—nitrogen 68-112 1-215 Kharakhorin (1940) Helium—nitrogen 65, 69, 77 14-68 Rodewald (1963), Rodewald,

Davis, Kurata (1964) Helium—nitrogen 64-108 5-150 Ruhemann, Fedoritenko

(1937) Graphs only

Helium—nitrogen 67-90 6-26 Skripka, Dykhno (1964) Helium—nitrogen 78-122 66-816 Streett (1967) Helium—nitrogen 112-162 1 000

10 000

Streett, Erickson (1972)

Helium_—nitrogen 122-126 34-211 Tully, Devaney, Rhodes

(1971) Helium—oxygen 78-122 20, 48 Cannon, Robson,

English (1968)

Liquid phase oi

Helium—oxygen 70-150 10-200 Herring (1964), Herring, Barrick (1965)

H-9

582 CRYOGENICS . OCTOBER 1973
System

Temperature

range, K

Pressure

range, atm Reference Remarks

rie He

He

He

He

He

He

He!

HeHe

He

He

He

Hel He

He

He

HeHe

HeHe

He

He

He

He

Hei

He

Hei He

He

He

lum—oxygen ium—oxygen ium—oxygen ium—fluorine ium—fluorine

ium—argon

ium—argon

ium—argon lum—argon ium—argon ium—argon ium—argon ium—carbon dioxide

ium—carbon dioxide ium—carbon dioxide

ium— krypton

ium—methane

lum—methane ium—methane ium— methane ium—methane ium—methane

ium—methane

ium—methane

ium—methane

ium—ethene

ium—ethene ium—ethene ium—ethane

ium—ethane ium—ethane

77- 143 67-90 65-116

77. 120 78- 111

84-87

68- 108

93- 148

9190- 115 91- 148 98-160

253, 273, 293

200, 220 220-290

100-150

124-191

90, 106 95-185

9191-150

94- 192

93-188

95-290

91-124

144-228

<260

91-150

144-228

170-290

95-150

17-136

6-26

<216

0-35

20, 48

<1

20-120

17-136

6-26

196-235

14-680

218-4 080 20-139

80-144

10-200

3-121

3-68

30-160

5-203

13-102

5-170

68-259

0-136

136-10 000

0-67

20-48

<120

4- 130 20-48

9-200

4-130

Sinor, Kurata (1966)

Skripka, Dykhno (1964)

Skripka, Lobanova (1971)

Cannon, Crane (1968) Cannon, Robson,

English (1968)

Karasz (1958), Karasz, Halsey (1958)

Mullins (1965), Mullins,

Ziegler (1965)

Sinor, Kurata (1966)

Skripka, Dykhno (1964)

Skripka, Lobanova (1971)

Streett (1969)

Streett, Hill (1971a)

Burfield, Richardson, Guereca (1970)

Liu (1969)

MacKendrick, Heck,

Barrick (1968)

Kidney, Miller, Hiza

(1971)

Devaney, Rhodes, Tully (1971)

Gonikberg, Fastovsky (1940b)

Heck, Hiza (1967)

Hiza, Kidnay (1966)

Kharakhorin {1959a)

Rhodes, Devaney, Tully (1971)

Sinor (1965), Sinor, Schindler, Kurata (1966)

Streett, Erickson,

Hill (1972)

Tully, Devaney, Rhodes

(1971)

Liquid phase only

Graphs only

Gas phase only

Gas phase only

Cannon, Robson,

English (1968)

Garber (1971)

Hiza, Duncan (1969) Cannon, Robson,

English (1968) Heck (1968)

Hiza, Duncan (1969)

Liquid phase only

Gas phase only

Liquid phase only

Gas phase only

H-10

CRYOGENICS .OCTOBER 1973 583
Temperature Pressure System range, K range, atm Reference Remarks

Helium—ethane 113-273 5-120 Nikitina, Skripka, Gubkina

(1970) Helium—propene <260 <120 Garber (1971) Helium—propane 172-255 20-48 Cannon, Robson,

English (1968)

Liquid phase only

Helium—propane 123-348 0-204 Schindler, Swift, Kurata (1966) Helium—n—butane 330-426 10-71 Jones, Kay (1967) Graphs only

Deuterium— neon 25 <1 Simon (1962) Graphs only

Deuterium— neon 25 <1 Simon (1963a) Deuterium—neon 25-40 1-21 Streett (1968b)

Deuterium—nitrogen 90, 95 8-67 Maimoni (1961) Deuterium— argon 87-120 10-100 Volk, Halsey (1960) Neon— nitrogen 83, 113 5-50 Burch (1964) Neon— nitrogen 90 8-30 Skripka (1965) Liquid phase only Neon—nitrogen 67-90 6-26 Skripka, Dykhno (1964) Neon—nitrogen 65-101 85-123 Skripka, Lobanova (1971) Neon—nitrogen 66-121 4-70 Streett (1965) Neon—nitrogen 66-114 73-217 Streett (1968a) Neon—oxygen 67-90 6-26 Skripka, Dykhno (1964) Neon—oxygen 64-118 176-206 Skripka, Lobanova (1971) Neon—oxygen 63-152 2-340 Streett, Jones (1966) Neon—argon 80-104 0-10 Browning (1964) Phase boundary measure- ments, graphs only Neon—argon 84-88 <1 Karasz (1958), Karasz, Halsey (1958)

Graphs only

Neon—argon 91 6-26 Skripka, Dykhno (1964) Neon—argon 90-120 176-206 Skripka, Lobanova (1971) Neon—argon 84-130 4-71 Streett (1965) Neon—argon 96-130 74-613 Streett (1967) Neon—argon 87-94 63-1 020 Streett, Hill (1971b) Neon— krypton 100-150 3-106 Miller, Kidnay, Hiza

(1972) Neon—methane 95-181 20-4 300 Streett, Hill (1971c) Neon—ethene 102, 122 7-45 Hiza, Duncan (1969) Gas phase only Neon—ethane 112, 130 15-33 Hiza, Duncan (1969) Gas phase only Carbon monoxide- nitrogen 68 0.1-0.3 Duncan (1966), Duncan,

Staveley (1966)

Liquid phase only

Carbon monoxide-•nitrogen 84 1-2 Pool, Saville, Herrington,

Shields, Staveley (1962)

Liquid phase only

Carbon monoxide--nitrogen 84 1-2 Sprow, Prausnitz (1966a) Carbon monoxide-nitrogen 83-114 2-17 Steckel (1935) Carbon monoxide-nitrogen 70-122 0-28 Torocheshnikov (1937) H-11

584 CRYOGENICS . OCTOBER 197"<
System

Temperature Pressure

range, K range, atm Reference Remarks

Carbon monoxide— nitrogen 70—79

Carbon monoxide 70—122

Carbon monoxide—argon 84

Carbon monoxide—carbon dioxide 273—298

Carbon monoxide—carbon dioxide 273

Carbon monoxide—carbon dioxide 223—283

Carbon monoxide— carbon dioxide 223—283

Carbon monoxide—methane 91 — 124

Carbon monoxide— methane 91

Carbon monoxide— methane 91

Carbon monoxide— methane 114—186

Carbon monoxide—ethane 173—273

Carbon monoxide— propene 311

Carbon monoxide— propane 86—128

Carbon monoxide—propane 148—323

Carbon monoxide—propane 252—361

Nitrogen— oxygen 65, 70, 78

Nitrogen— oxygen 77—91

Nitrogen— oxygen 81—91

Nitrogen—oxygen 79—115

Nitrogen—oxygen 77—125

Nitrogen— oxygen 63

Nitrogen—oxygen 75, 79

Nitrogen-oxygen 132-153

Nitrogen—oxygen 84

Nitrogen— oxygen 77—90

Nitrogen— oxygen 88—90

Nitrogen—oxygen 78

Nitrogen—oxygen 78—134

0-1 Verschoyle (1931) 0—28 Yushkevich, Torocheshnikov

(1936) 0.7—1.3 Duncan ( 1966), Duncan, Liquid phase only

Staveley (1966) Abdulayev (1939a) 200 Abdulayev (1939b) Graphs only

24—129 Kaminishi, Arai, Saito,

iVlaeda (1968) 10—130 Kaminishi, Toriumi Graphs only

(1968) 0-5 Cheung, Wang (1964) 0— 2 Mathot, Staveley, Young, Liquid phase only Parsonage (1956) 1— 2 Sprow, Prausnitz (1966a) 7—48 Toyama, Chappelear, Leiand, Kobayashi (1962) 8- 116 Trust (1967), Trust, Kurata (1971) 17-41 WIddoes, Katz (1948) 0-6 Cheung, Wang (1964) 7-136 Trust (1967), Trust, Kurata (1971) 10-177 Widdoes, Katz (1948) 0— 1 Armstrong, Goldstein, Roberts (1955)

1 Baly(1900)

1 Cockett (1957) 1- 10 Din (1960) 0-30 Dodge, Dunbar (1927) 0.01-0.12 Duncan (1966), Duncan,

Staveley (1966) 0- 1 lnglis(1906)

28—56 Kuenen, Verschoyle, Van

Urk (1923) 1—2 Pool, Saville, Herrington, Liquid phase only

Shields, Staveley (1962) 1-2 Sagenkahn, Fink (1944)

1 Thorogood, Haselden

(1963)

Wilhelm, Schneider (1961)

Liquid phase compositions

only

Condensation measure- ments on two mixtures

Graph of excess Gibbs

free energy, graphs only

1—26 Wilson, Siiverberg, Zellner (1965)

H-12

CRYOGENICS . OCTOBER 1973 585
System

Temperature Pressure

range, K range, atm Reference Remarks

66—75 <1 RmvA/n inn lIQA^i riiabc UUUrlUaiy Lie tions, graphs only

Nitrogen—argon 78-103 1-4 Fastovsl<y, Petrovsky

(1956b)

Nitrogen—argon 74-95 0-2 Hoist, Hamburger (1916a)

Nitrogen—argon 74-95 0-2 Hoist, Hamburger (1916b)

Nitrogen— argon 112 8-15 Miller, Kidnay, Hiza (1973) N itrogen—argon 90— 1 20 1—24 Nannskii (1966)

Nitrogen—argon 84 1—2 Pool, Saville, Herrington,

Shields, Staveley (1962)

Liquid phase only

Nitrogen—argon 84 1-2 Sprow, Prausnitz (1966a)

Nitrogen— argon 80-115 1-11 Thorpe (1968) Graphs only

Nitrogen— argon 72-134 1-26 Wilson, Silverberg, Zellner (1965) Nitrogen—carbon dioxide 273-298 Abdulayev (1939a)

Nitrogen—carbon dioxide 273 0-181 Abdulayev (1939b) Graphs only

Nitrogen—carbon dioxide 233-298 50-125 Kaminishi, Toriumi (1966)

Nitrogen —carbon dioxide 00*3 OylT 07'3 /— lUU isuiiKov ( lyby) brapns only

Nitrogen—carbon dioxide AQ lie 'HJ— 1 Id Muirorook ( iyb4), Muirbrook, Prausnitz (1965)

Graphs only

Nitrogen—carbon dioxide 222, 273 41-155 Pollitzer, Strebel (1924)

Nitrogen—carbon dioxide o—^UU omitn \ lyboj

Nitrogen—carbon dioxide 273 34-117 Yorizane, Yoshimura, Masuoka ( ly /uj

Nitrogen—carbon dioxide 273 <1 17 Yorizane (1971)

Nitrogen—carbon dioxide 218—273 12—137 Zenner, Dana (1963) Nitrogen—methane 100—187 7—48 Bloomer, Eakin,

Ellington, Garni (1955)

Graphs only

Nitrogen— methane 91—191 1—48 Bloomer, Parent (1952), (1953) Nitrogen—methane 129-179 34 Brandt, Stroud (1958) Nitrogen—methane 122, 171 3-49 Chang, Lu (1967) Nitrogen— methane 92-124 0-4 Cheung, Wang (1964) Nitrogen—methane 100-172 1-44 Cines, Roach, Hogan, Roland (1953) Nitrogen— methane 79—187 1—48 Ellington, Eakin, Parent

et al (1959) N itrogen—meth ane 90-150 1-16 Fastovsky, Petrovsky

(1957) Nitrogen— methane 80-180 1-103 Forg, Wirtz (1970) Graphs only

Nitrogen— methane 84-89 0.9-2.4 Fuks, Bellemans (1967) Liquid phase only

Nitrogen— methane 77-109 1 McTaggart, Edwards (1919) Nitrogen— methane 112 2-13 Miller, Kidnay, Hiza (1973)

H-13

586 CRYOGENICS . OCTOBER 1973
System

Temperature

range, K

Pressure

range, atm Reference Remarks

Nitrogen— methane 113 Sl<ripka et al (1970)

Nitrogen— methane 91 0-4 Sprow, Prausnitz (1966a)

Nitrogen— methane 89-133 0-24 Torochesnikov, Levius (1939)

Graphs only

Nitrogen— methane 90 0-1 Vellinger, Pons (1943) Graphs only

Nitrogen— ethene 144-228 20-48 Cannon, Robson,

English (1968)

Liquid phase only

Nitrogen—ethane 144-228 20-48 Cannon, Robson,

English (1968)

Liquid phase only

Nitrogen—ethane 122, 171 3-34 Chang, Lu (1967)

Nitrogen—ethane 93 <1 Cheung, Wang (1964)

Nitrogen—ethane 101-302 7-126 Ellington, Eaking, Parent

et al (1959)

Nitrogen—ethane 114-133 18-40 Yu, Elshayal, Lu (1969)

Nitrogen— propene 78-91 0-3 Blagoi, Orobinskii (1965)

Nitrogen— propane 172-255 20-48 Cannon, Robson,

English (1968)

Liquid phase only

Nitrogen— propane 92-128 1-6 Cheung, Wang (1964)

Nitrogen— propane 312-365 41-149 Roof, Baron (1967) Critical locus measurements

Nitrogen— propane 103-353 0-136 Schindler, Swift, Kurata

(1966)

Nitrogen— propane 90 0-1 Vellinger, Pons (1943) Graphs only

Nitrogen—/7—butane 311-422 35-287 Akers, Atwell, Robinson

(1954)

Nitrogen—n—butane 311 137-284 Lehigh, McKetta (1966)

Nitrogen—n— butane 311-411 16-231 Roberts, McKetta (1961)

Nitrogen—n—butane 294-394 17-131 Sage, Budenholzer, Lacey

(1940) Nitrogen—n— butane 153-273 5-200 Skripka et al (1969)

Nitrogen—/?— butane 273, 283, 293 4, 6, 9, 11 Steinbach, Steinbrecher (1966)

Nitrogen— isobutane 248-323 0-100 Ryabtsev, Khuchua (1970)

Nitrogen— isobutane 273, 283, 293 4, 6, 9, 11 Steinbach, Steinbrecher (1966) Oxygen —argon 87 90 95 1—2 Riirho Isrhkin ( 19'?6)

Oxygen — argon 85—1 18 1 — 10 Burn Din (1962) Oxygen— argon 90-110 1-3 Clark, Din, Robb (1953) Oxygen—argon 87-110 1-7 Din (1953) Oxygen—argon 89-96 1-2 Fastovsky, Petrovsky

(1955) Oxygen—argon 82 <1 Inglis (1906) Oxygen—argon 90-120 1-12 Narinskii (1957) Oxygen—argon 84, 90 0-1 Pool, Saville, Herrington,

Shields, Staveley (1962)

Liquid phase only

H-14

CRYOGENICS . OCTOBER 1973 587
System

Temperature Pressure

range, K range, atm Reference Remarks

Oxygen—argon 87—97 1—2 Oxygen—argon 91, 95 1—2

Oxygen-argon 87-139 1-26

Oxygen—carbon dioxide 224 7—142

Oxygen-carbon dioxide 223-283 10-130

Oxygen-carbon dioxide 233-298 50-125

Oxygen-carbon dioxide 282-298 1-2

Oxygen—carbon dioxide 273 41-116

Oxygen-carbon dioxide 218-273 22-147

Oxygen-I<rypton 94-107 1—4

Oxygen-krypton 90-100 1-3

Oxygen-krypton 94-151 0-6

Oxygen-methane 93-107 1-4

Hydrogen sulphide-carbon 254-366 20-80

dioxide Hydrogen sulphide-carbon 225-364 7-82

dioxide Hydrogen sulphide-carbon 221,246,273 -

dioxide Hydrogen sulphide-methane 167-344 0-136

Hydrogen sulphide-methane 278-344 11-133

Hydrogen sulphide-ethane 267-355 17-82

Hydrogen sulphide-propene 243, 273, 288

Hydrogen sulphide—propane 217—344 1—27

Hydrogen sulphide-propane 324-367 27, 34, 41 Hydrogen sulphide-propane 272-370 1-79

Hydrogen sulphide-propane 243, 237, 288 -

Hydrogen sulphide-/7-butane 311-408 3-79

Argon-carbon dioxide 233-273 25-131

Argon-krypton 104,116 1-9

Argon-krypton 88 1 Argon-methane 116 1-9

Argon-methane 92-124 0-4

Argon-methane 105-126 2-16

Sagenkahn, Fink (1944) Wang (1960)

Wilson, Silverberg, Zellner (1965)

Fredenslund, Mollerup,

Persson (1972)

Fredenslund, Sather (1970)

Kamlnishi, Toriumi (1966) Keesom (1903)

Muirbrook (1964), Muirbrook, Prausnitz (1965)

Zenner, Dana (1963)

Burch (1966)

Fastovsky, Gurvich

(1939a, b)

Fastovsky, Petrovsky

(1956a)

Hodges, Burch (1967)

Bierlein, Kay (1953)

Sobocinski, Kurata (1959)

Steckel (1945)

Kohn, Kurata (1958)

Reamer, Sage, Lacey

(1951)

Kay, Brice (1953)

Steckel (1945)

Brewer, Rodewald, Kurata

(1961)

Gilliland, Scheeline (1940)

Kay, Rambosek (1953)

Steckel (1945)

Robinson, Hughes, Sondercock (1964)

Kaminishi, Arai, Saito, Maeda (1968)

Davies, Duncan, Saville, Staveley (1967), Duncan

(1966) Schmidt (1960)

Calado, Staveley (1972)

Cheung, Wang (1964)

Duncan, Hiza (1972)

Liquid phase only

Liquid phase only

588 H-15

CRYOGENICS. OCTOBER 1973
System

Temperature

range, K

Pressure

range, atm Reference Remarks

Methane—n— butane Methane—/7— butane

Methane-n— butane

^iethane—/?— butane

Methane—/7— butane Methane— isobutane

Methane— isobutane

Ethyne— propene Ethyne— propane

Ethene—ethane

Ethene—ethane

Ethene—ethane

Ethene—ethane

Ethene— propene

Ethane— propene

Ethane— propene

Ethane— propane

Ethane— propane

Ethane— propane

Ethane—propane Ethane—n— butane Ethane— isobutane Propene— propane

Propene— propane

Propene— propane Propene— propane

Propene— propane Propene— I— butene

Propene— isobutane

252-316 10-30 Nederbragt (1938)

311 65-130 Rigas, Mason, Thodos

(1958)

211-411 2-119 Roberts, Wang, Azarnoosh, McKetta (1962) 294-394 2-131 Sage, Hicks, Lacey

(1940)

177 5-31 Wang, McKetta (1964) 198-293 5 to critical Barsuk, Skripka,

values Benyaminovich (1970) 311-378 5-114 Olds, Sage, Lacey

(1942) 295-357 15-62 McCurdy, Katz ( 1954) 283-365 15-63 McCurdy, Katz (1945)

200, 233, 255 1-26 Hanson, Hogan, Ruchlen,

Cines (1953) 169-273 0-40 Kharakhorin (1941) 169-273 0-41 Kharakhorin (1959b)

149-196 0-2 Moran(1959)

303, 323 <40 Rozhnov, Dorochinskaya

(1969) 243-343 2-50 Lu, Newitt, Ruhemann

(1941) 261-344 4-49 McKay, Reamer, Sage, Lacey

(1951) 128-256 0-15 Djordjevich (1968),

Djordjevich, Budenholzer

(1970) 311-367 13-51 Matschke, Thodos (1962) 255-283 7-27 Price (1957), Price, Kobayashi (1959) 203-273 - Skripka etal (1970) 338,367,394 32-55 Mehra, Thodos (1965) 203-273 - Skripka et al (1970)

270, 298, 330 4-23 Hanson, Nelson, Hogan,

Cines (1952) — — Hirata, Hakuta, Onoda

(1967) — - Hirata, Hakuta (1968) — 22 Mann, Pardee, Smyth

(1963) 261-361 3-41 Reamer, Sage (1951) 278-411 1-46 Goff, Farrington, Sage

(1950) 315-397 13-41 Gilliland, Scheeline (1940)

Isobaric measurement,

temperature not measured

H-ll

CRYOGENICS . OCTOBER 1973 591
System

Temperature Pressure

range, K range, atm Reference Remarks

Propane- isobutene 338-402 13-41

Propane-/7-butane 333-419 15-42

Propane—n—butane 311—411 5—42

Propane—/7— butane 253, 263, 273 —

Propane- isobutane 267-394 1-39

Propane- isobutane 340 10-24

Propane— isobutane 253, 263, 273 —

n— Butane— isobutane — —

n— Butane—Isobutane 353,373 11 Hydrogen—hydrogen deuteride— 18—20 <1

deuterium Hydrogen—carbon monoxidenitrogen

Hydrogen—carbon monoxidenitrogen

Hydrogen—carbon monoxidenitrogen

Hydrogen—carbon monoxidenitrogen

Hydrogen-carbon monoxide- 78,83,90 12-50

nitrogen

Hydrogen—carbon monoxide— 68—88 30—150

nitrogen

Hydrogen-carbon monoxide- 233-283 50-200

carbon dioxide Hydrogen-carbon monoxide- 233-283 50-200

carbon dioxide

Hydrogen-nitrogen-carbon 273-293 51-203

dioxide Hydrogen—carbon monoxide— 87 32

propane Hydrogen—carbon monoxide— 88—348 to 204

propane Hydrogen—carbon monoxide— 88—348 to 204

propane

83, 100, 122 21-136

35-66 5-15

83, 100, 122 21-136

68-88 30-150

Scheeline, Gilliland (1939) Kay (1940) Nysewander et al (1940)

Skripica et al (1970)

Hipkin (1966)

Hirata, Suda, IVliyashita, Hoshino (1970)

Skripka et al (1970)

Hirata, Suda (1968) Yokoyama, Ohe (1971)

Arnold, Hoge (1950)

Akers, Eubanks (1960)

Dokoupil, Van Soest, Swenker (1955) Eubanks (1956)

Fischer (1938) Graphs only

Ruhemann, Tsin (1937) Graphs only

Verschoyle (1931) Graphsonly

Kaminlshi, Aral, Saito. Maeda (1968)

Kaminlshi, Toriumi (1968) Graphsonly

Abdulayev (1941)

Measurement of dew-point

pressures

Stein, Claitor, Gelst (1962)

Trust (1967)

Trust, Kurata (1971)

Graphs only

Hydrogen--nltrogen--methane 144 34, 68 Cosway (1958) Hydrogen--nltrogen--methane 144, 200 34, 68 Cosway, Katz (1959) Hydrogen--nitrogen--methane 90, 108 10-100 Steckel, Tsin (1939a) Hydrogen--nitrogen--methane 90, 108 10-100 Steckel, Tsin (1939b)

Hydrogen--methane--ethene 158-188 30-80 Likhter, Tikhonovich

(1940) Hydrogen--methane--ethane 115-255 2-136 Cohen, Hipkin,

Graphs only

Koppany (1967)

592

H-19

CRYOGENICS . OCTOBER 1973
System

Temperature

range, K

Pressure

range, atm Reference Remarks

Hydrogen—methane—ethane 144, ZUU J4, DO uosway ( lyoo)

Hydrogen—methane—ethane 144, ZUU o4, DO uosway, ivatz ( wo^)

Hydrogen—methane—ethane loo— loo on ACi on JU, 4U, OU LeviisKaya (ly^ij

Hydrogen—methane—propene *j4 Dennarn, isaiz \ lyo/

j

Hydrogen—methane—propane 144-255 34, 68 Benham, Katz (1957) Helium— neon— nitrogen 83, 113 5-50 Burch (1964) Helium— neon—nitrogen 68-78 7-48 Tompkins, Geist (1963) Graphs only

Helium— nitrogen— methane 76-130 14-136 Boone, Devaney, Stroud

(1963) Helium— nitrogen— methane 77-164 7-82 Rhodes, Stroud, Tully (1972) Helium— nitrogen— propane 273 34-204 Schindler, Swift, Kurata (1966)

Nitrogen—oxygen—argon 81-88 1 Fastovskii, Petrovskii

Nitrogen—oxygen—argon 90-120 1-23 Narinskii (1969)

Nitrogen—oxygen—argon 81-96 1-2 Sagenkahn, Fink (1944)

Nitrogen—oxygen—argon Weishaupt (1948) Graphs only

i>jiirogcn—oxygen—argon / o— 1 o / vviison, Oliver uci^, Zellner (1965) Graphs only

Nitrogen—oxygen—carbon

dioxide 273 51-104 Muirbrook (1964), Muirbrook, Prausnitz (1965) Nitronen-oxygen—carbon 218-273 52-129 Zenner, Dana (1963)

dioxide N itrogen—argon—methane

Nitrogen— argon— methane

Nitrogen—methane—ethane

Nitrogen— methane—ethane

Nitrogen—methane—ethane

Nitrogen— methane—ethane

Nitrogen— methane—ethane

Nitrogen—methane—n—butane

Nitrogen—methane—n— butane

Nitrogen—ethane—propane

Nitrogen—ethane—n— butane

N itrogen—propene—propane Hydrogen sulphide—carbon

dioxide—methane

Hydrogen sulphide—carbon

dioxide— methane

Hydrogen sulphide—carbon

dioxide—methane

112

91

122, 171

144, 200

144, 200

112 114-129

311-411

311-411

87311-411

77

222, 239

311

278, 344

3-13 Miller, Kidnay, Hiza (1973) 1-4 Sprow, Prausnitz (1966b)

2-28 Chang, Lu (1967) 34,68 Cosway(1958)

34,68 Cosway, Katz (1959)

14 Lu, Yu, Poon (1969) 15-35 Yu, Elshayal, Lu (1969) 34-204 Roberts (1963) 34-204 Roberts, McKetta (1963) 0-1 Cheung, Wang (1964) 34-272 Lehigh (1965), Lehigh, McKetta (1966) 0-1 Cheung, Wang (1964) 20-48 Hensel, Massoth (1964)Liquid— liquid—vapour

41, 82, 103 Robinson, Bailey (1957)

27-109

H-20

Robinson, Lorenzo, Macrygeorgos (1959)

CRYOGENICS . OCTOBER 1973 593
System

Temperature Pressure

range, K range, atm Reference Remarks

Hydrogen sulphide— methane-

/7— butane 244,269,311 27-82

Hydrogen sulphide-methane- 244, 278, 31 1 27, 54, 82 n—butane Argon—methane—ethane

Carbon dioxide—methane—

butane

116

Carbon dioxide— methane—n- butane 177-311

Methane—ethene—ethane 169—273

Methane—ethene—ethane 159 Methane—ethene— isobutane 311,344

Methane—ethane—propane 144—283

Methane—ethane—propane 144—283

Methane—ethane—propane 158—213

Methane—ethane—propane 1 1 5— 1 43

Methane—ethane—n— butane —

Methane—propane—n— butane 311

Methane—propane—^—butane Ethyne—ethene—ethane

Ethyne—ethene—ethane Hydrogen—carbon monoxidenitrogen—oxygen—methane Hydrogen—carbon monoxide—

nitrogen— methane Hydrogen—carbon monoxidecarbon dioxide—propane Hydrogen—carbon monoxidecarbon dioxide—n-butane Hydrogen—nitrogen— methaneethane Hydrogen—methane—ethene—

ethane— propene— propane

278, 289

78, 90

273

273

144, 200

200, 255

4-7

244,269,311 27-82

Carbon dioxide-methane-n- 244, 278, 311 27, 54, 82

butane

Robinson, Saxena (1966) Graphs only

Saxena, Robinson (1969)

Elshayal, Lu (1971)

Robinson, Saxena (1966) Graphs only

Saxena, Robinson (1969)

27-116 Wang, McKetta (1964)

Carbon dioxide—ethene—propane — —

Carbon dioxide—propene—propane 273, 293, 313 10—65

5-50

<22

34, 68

7-88

7-88

2-60

1

48-117

278-378 0-100

236,255,278 10-32

32-52

6-78

8-45

8-45

34, 68

34, 68

Shearn (1955)

Toyoshima, Yoshimura,

Masuoka (1971)

Guter, Newitt,

Ruhemann (1940)

Hsi, Lu (1971)

Benedict, Solomon,

Ruben (1945)

Price (1957)

Price, Kobayashi (1959)

Wichterle, Kobayashi

(1972c)

Watanabe, Kuroki, Oguro Graphs only

Saito (1969)

Cota, Thodos (1962)

Rigas, Mason, Thodos

(1959)

Wiese, Jacobs, Sage (1970)

Hogan, Nelson, Hanson,

Cines (1955) McCurdy, Katz (1944)

Torochesnikov, Gurevich

(1941)

Torochesnikov, Serenova

(1954)

Yorizane, Yoshimura, Masuoka (1972)

Yorizane, Yoshimura, Masuoka (1972) Cosway (1958), Cosway,

Katz (1949) Benham (1956), Benham,

Katz (1957)

Measurement of critical temperature and pressure

H-21

594 CRYOGENICS . OCTOBER 1973
System

Temperature

range, K

Pressure

range, atm Reference Remarks

Helium— nitrogen— methane—

,;thane— propane—butane 123-183 7 Stutzman, Brown (1949)

Nitrogen— methane—ethane—

i)ropane—n— butane 153-253 28-38 Banks, Haselden (1969)

iVlethane— ethane— propane—

/?-butane

222 14-20 De Priester (1953)

IVlethane— ethane— propane—

isobutane

244 14 De Priester (1953)

Natural gas system 1 uz

£.00 Drdnai, oTrouu, iviiiier (1961)

Natural gas system 229-300 34, 68, 101 Buckley, Lightfoot (1941)

Natural gas system Q 1 1 yi 1 "1 nouerts ( lyoJ)

Natural gas system 311-378 34-204 Roberts, McKetta (1963)

Natural gas system 102-200 7-34 Stroud, Miller, Brandt (1959)

Natural gas system 339-394 7-136 Stuckey (1966) Graphs only

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CRYOGENICS .OCTOBER 1973

H-26

599
ERRATA

LIQUID-VAPOUR EQUILIBRIA RESEARCH ON SYSTEMS OF

INTEREST IN CRYOGENICS A SURVEY

by

A, J. Kidnay, M. J, Hiza, and R. C. Miller

in Cryogenics Vol. 13, No. 10, 575-99 (Oct. 1973)

page 575; Last sentence of Abstract add CO^ after CO.

page 577: Change equations (7) and (10) as follows

^i = ^ -o ' (R) -r¥- f . n

1

f .(liquid) = Y. x. H. . (10)

J J J J.i

page 578: Ref. 4. Hala et al; change date to 1967.

page 579: (a) - 4th entry under Hydrogen-helium 4; Roellig,

Giese (1962); change remark to "Pressures

given are partial pressures of helium"

(b) - 7th entry under Hydrogen-helium 4; Sonntag,

Crain, Streett (1964); delete remark.

page 581: 2nd entry under Hydrogen-methane; change

Tikhovovich to Tikhonovich.

page 583: Entry under Helium-krypton; change Kidney

to Kidnay.

page 586: 5th entry under Nitrogen-carbon dioxide; Muirbroc

(1964), etc.; delete remark.

H-27
4th entry under Hydrogen sulphide -propane

;

Steckel (1945); change temperature from

237 to 273.

Entry under Ethyne -propene ; change reference

date to (1945).

After n- Butane -isobutane entries, insert new

table title: "Liquid-vapour equilibria for ternary

systems . "

After Ethyne -ethene -ethane entries, insert

new table title: "Liquid-vapour equilibria for

systems of four or more components. "

BIBLIOGRAPHY

(a) Abdulayev (1941); change Priki to Prikl

(b) Aerov et al. (1968); change Zalayaletoinova

to Zalyaletoinova.

(c) Benham, Katz, Williams (1957); change

AICHe J to AIChE J.

(d) Burn, Din (1962); change the page no. 1241 to 1341.

(a) Cines et al. (1953); add the page no. 1

- after (1953).

(b) Greene, Sonntag (1968); change )Plenum

(Plenum.

(c) Hirata, Hakuta (1968); change the page no. 594 to 1594.

(a) Kulikov (1969); change the page no. 8 to 18.

(b) Morlet (1963); change the page no. 27 to 127.

(c) Newman, Jackson (1958); change the page no. 481 to 1481.

H-28
Rodewald (1963); change An Arbor to Ann Arbor

.

Scheeline, Gilliland; change year and page

no. from (1969) 69 to (1939) 1050.

Watanabe et al. (1969); change the page no. 293 to 292.

Yokoyama, Ohe (1971); add the page no.

4 after (1971).

H-29

ISCOMM - ERL

APPENDIX I

I-l
LIQUID -VAPOR EQUILIBRIA IN THE NITROGEN- ME THANE

SYSTEM BETWEEN 95 and 120 K

W.R. Parrish and M. J. Hiza

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Paper K-9

Prepared for

The 1973 Cryogenic Engineering Conference

August 8, 9 and 10, 1973

Georgia Institute of Technology

Atleinta, Georgia

1-2
LIQUID- VAPOR EQUILIBRIA IN THE NITROGEN- METHANE

SYSTEM BETWEEN 95 and 120 KW.R. Parrish and M. J. Hiza

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

A study was undertaken to obtain liquid-vapor equilibria data for the

nitrogen- methane system at uniform temperature increments between the

triple point of methane and the critical point of nitrogen. The measured

liquid and vapor phase equilibria compositions and the derived excess Gibbs

energy values for six isotherms from 95 to 120 K are compared with the

corresponding values taken from other investigations. The excess Gibbs

energy for the equimolar mixture exhibits a zero to slightly positive temperature

dependence, in qualitative agreement with calculations based on the SniderHerrington hard sphere model. This temperature dependence of the excess

Gibbs energy also suggests that the excess enthalpy (heat of mixing) must be

equal to or slightly less than the excess Gibbs energy.

INTRODUCTION

The development and evaluation of liquid mixture (solution) theory depends

heavily on the availability of precise data for mixtures of simple molecules.

The most useful data are for binary mixtures at closely spaced temperatures

over as wide a temperature range as possible, both above and below the critical

temperature of the most volatile component. The nitrogen-methane mixture,

which is technologically important as one of the more important binary mixtures in liquefied natural gas, is an excellent compromise between theoretical

and practical considerations.

Key Words: Binary mixture, excess Gibbs energy, experimental phase equilibria

data, heat of mixing, liquid- vapor equilibria, nitrogen- methane

system.

Contribution of the National Bureau of Standards, not subject to copyright.

1-3
The interest in the phase equilibria properties of this particular

system is apparent by the large number of studies reported in the literature.

A number of experimental investigations have been conducted to determine

the liquid- vapor eqviilibria properties of nitrogen-methane mixtures [1-15].

In addition, several investigations have been conducted to determine the solidliquid equilibria and the three phase ( solid- liquid- vapor ) locus [16-19]. In the liquid-vapor region the data of Bloomer and Parent [l] and of Cines et al.

[3] cover most of the methane liqviid range, and consequently, one or the other

of these data sets frequently has been used in correlations and for testing

computation methods for the nitrogen- methane system [20-23]. Since the

data of Bloomer and Parent are isobaric and those of Cines et al. are isothermal, direct comparisons are not possible. However, from comparisons

made by Bloomer and Parent of isothermal crossplots of their data and those

of Cines et al. , these data sets appear to be in fairly good agreement at the

lower temperatures, but are in less satisfactory agreement at the higher

temperatures.

Of the remainder of the data reported prior to 19'72, most studies were too

limited to add independently to the description of the liquid-vapor equilibria behavior of this system. In addition, the method of investigation, i.e. isobaric

dew-point, bubble-point measurements versus isothermal vapor- recirculation

measurements, and the method of reporting data, i.e. graphical versus tabular,

further complicate evaluation and comparison of all of the data.

The recent investigations of Miller et al. [10] at 112.00 K and of

Stryjek et al. [13] from 113.72 K up to the methane critical temperature

add new isothermal data which readily can be compared with some of the

previous data sets. In the mutual liquid range ot the two components, with

which we are concerned in the present study, these newer data tend to highlight

the discordant aspects of some of the previous data more clearly.

1-4

2
In addition to phase equilibria data, density or more specifically

excess molar volumes are vital to the development of liquid mixture theory.

Liu and Miller [24] recently reported excess molar volumes for the nitrogenmethane system between 90 and IZO K. Subsequently, Massengill and Miller

[25] provided an interesting theoretical discussion of the effects of adjustments

to the combining rules and of predictions of excess molar volume and excess

Gibbs energy as a fvinction of temperature with a modified hard sphere equation

of state. Because of the lack of consistency of phase equilibria data for the

nitrogen-methane system in the same temperature region, it is difficult

to draw definitive conclusions from their treatise. Thus, the need for a consistent set of phase equilibria data for the nitrogen-methane system

between 90 and 1 20 K was clearly indicated.

The purpose of the present study was to obtain liquid-vapor equilibria

data for the nitrogen-methane system at 5 K increments of temperature between

the triple point of methane and the critical point of nitrogen, and from these

data to obtain the magnitude and temperature dependence of the excess Gibbs

energy. These values of excess Gibbs energy provide the basis of comparison

with the corresponding values derived from other data and with the qualitative

temperature dependence of the excess Gibbs energy predicted from the hard

sphere model by Massengill and Miller [25].

EXPERIMENTAL

The liquid- vapor equilibria measurements were made in a closed- loop

vapor- recirculating system described previously [26]. Thus, other than

some minor differences, discussion of experimental details need not be

included he re

.

The equilibrivim pressures were measured with a standard laboratory,

double- revolution, 0-20 bar Bourdon gage and a 0-100 psia spiral quartz

Bourdon gage. The 20 bar gage has a claimed accuracy of ± 0. 1% of full

1-5

3
scale and was found to be consistently better than these limits when compared

with the 100 psia gage. The latter instrument was calibrated against an

air dead-weight gage in this laboratory giving a maximum uncertainty of less

than ±0.1 psia over the full range. The pressure tap was a small tube connected

directly to the top of the equilibrium cell and was independent of the recirculation system.

Temperatures were controlled as described previously [26]. However,

the reported temperatures are those determined by vapor pressure measurements of pure methane and pure nitrogen as compared with the new methane

data of Prydz and Goodwin [27] and the nitrogen values from the equation of

Strobridge [28]. For our purposes, nitrogen vapor pressure values from

the equation of Strobridge are in excellant agreement with the newer data

of Weber [29]. Within experimental uncertainties of the present study, the

temperatures reported here are consistent with the IPTS-68 temperature

scale

.

Compositions were determined chromatographically with helium elution

gas and thermal conductivity detector. Calibration gas mixtures were prepared

on a pressure basis, corrected for nonideality, at 4. 94, 9. 90, and 49. 89

mole % methane in nitrogen. These calibration mixtures and pure methane

and pure nitrogen were analyzed at a number of different sample pressures

to determine analyzer response as a function of component partial pressure.

It was determined that a linear calibration based on the pure species at near

atmospheric pressure (60 cm Hg) satisfactorily reproduced compositions

over the entire composition range of interest, based on peak areas, within

0. 5"v) of the actual composition of the minor component. Since this difference

is approximately equivalent to the precision of analysis, the results reported

here are based entirely on pure component calibrations. The experimental

liquid and vapor compositions are thought to be accurate within ± 1 % of the

actual composition or within ±0.1 mole %, whichever is greater.

1-6

4
Liquid samples were withdrawn directly from the bottom of the equilibrium

cell through a stainless steel capillary tube, while the vapor samples were

isolated in a room temperature sample loop which included the pump free

volume. In all cases, compositions were determined by analysis of both

components in the mixture. The total sample pressure was taken as the sum

of the partial pressures determined in the analysis. Though total sample

pressure was measured, the sum of the partial pressures was used to compensate for slight variations in analyzer sensitivity and for any lack of sample

thermal equilibrium.

It is also worth noting that the apparatus and chr omatograph used in

this study were the same as those used in the study of Miller et al. [10].

However, there were significant differences. The more precise 100 psia

quartz Bourdon gage was acquired for the present study to improve the measurement of the lower pressures. The standard mixtures, except the pure

component species, were prepared separately for each study using different

methods. The calibration mixtures used in the earlier study were only

equimolar mixtures prepared by weight. However, it was determined in

both studies that assuming linear response based on calibration of the chromatograph with the pure fluid species represented the compositions of the

prepared standard mixtures within the precision of analysis. In addition,

temperatures reported in the earlier study were taken from the platinum thermometer readings, while in the present study the control point and thus the

experimental temperature were determined by the vapor pressures of the pure

component species. Thus, the two investigations are significantly different

to be considered as two independent investigations.

RESULTS AND DISCUSSION

Equilibrium liquid and vapor compositions were measured at 95.00,

100.00, 105.00, 110.00, 115.00, and 120.00 K. The results of these measurements, along with the vapor pressures of the pure components, are

given in Table 1

.

1-7
A negative departure from Raoult's law occurs on the nitrogen rich

end at the higher temperatures, consistent with the data of Bloomer and

Parent [l], Cines et al. [3], Stryjek et al. [13], and Miller et al. [10].

However, the isotherm of Chang and Lu [4] at 1Z2.0 5 K does not show this

negati\'e departure. Extrapolation of the data of Chang and Lu to the pure

nitrogen axis suggests a higher nitrogen vapor pressure than that for 122 K

and thus a slightly higher temperature than that reported, which could easily

account for the discrepancy.

In figure 1, the liquid and vapor phase compositions at 100.00 K

from the present investigation are compared with the smoothed values of

Cines, et al. [3] at 99. 8Z K. This is the only direct comparison that can be

made with the experimental data of other investigators. The significant point

worth noting is that, even though the data of Cines et al. are for a slightly

lower temperature, their vapor phase compositions are lower in nitrogen

content than the present data. From the temperature dependence of the

vapor phase compositions of the present study, the nitrogen content should

be higher at the lower temperature. This is significant since the activity

coefficient of methane is strongly affected by this inconsistency.

A sensitive method for comparing close-boiling liquid-vapor equilibria

data is through the derived excess Gibbs energy, G , as a function of tempera

ture and composition. This topic was discussed in some detail in an earlier

paper by Duncan and Hiza [30]. The composition dependence of G is obtained

from

E

. G = x^RT InYj + -^2^^ "^"^ 2

where x is the liquid phase mole fraction and y is the activity coefficient.

The equation selected here for calculating the activity coefficient for each

component is the one given in reference 30 and will not be repeated here.

This equation is based on the virial equation of state and includes third virial

coefficient effects. The activity coefficients thus calculated are corrected

to a reference pressure, which for our purposes has been taken as one bar.

1-8

6
Second virial coefficients for pure nitrogen and the interaction second

virial coefficients for nitrogen- methane were calculated from the corresponding

states equation of McGlashan and Potter [31]. The mixture characteristic

temperature was calculated from

T = (1 .- k^^) (T T )^/^ (2)

^12 12 ^1 "2

in which the value of °^ 0.03 was taken. The characteristic volume of

the mixture was calculated from the arithmetic mean rule

V = 1/8 (V^/^ + V^/^ )^ (3)

'^IZ "l "2

For pure methane, second virial coefficients were taken from Goodwin [32].

Molar volumes for pure liquid methane and for pure liquid nitrogen were taken

from Goodwin and Prydz [33] and from Strobridge [28], respectively. Isothermal

compressibility for the pure liquids were taken from Rowlinson [34], For

purposes of the present calculations, it was assumed that the molar volume

and compressibility of each component in the mixture are the same as those

of the pure fluid.

Values of the eqmmolar G for much of the previous data on the

nitrogen-methane system are shown in figure 2. The values given include

those obtained using both experimental liquid and vapor phase data (filled

symbols) and those obtained from the liquid phase data only by the method

attributed to Barker [35]. In both methods, the derived values of G were

fitted by the method of least squares to the following equation

.E , ,2. G = x^x^RT [A + B(x^-x^) + CCx^-x^) ] (4)

where 1 refers to nitrogen. The values shown in figure 2 were calculated

from the fit of equation (4) obtained by each method. The two values shown for

Fastovskii and Petrovskii [6], however, were calculated from the smoothed

equimolar liquid and vapor compositions tabulated in their paper, interpolated

from the original isobaric data.
The curve shown in figure 2 was calculated by Massengill [36] from

the hard sphere model applied by Snider and Herrington [37], This curve was

E

adjusted by Massengill to fit approximately the equimolar G value of Miller

et al. [10] at 112.00 K by including a k^^ correction for the "a" parameter

of 0.035, similar to the correction indicated in equation (2).

Though values of G obtained from the two methods are not expected

to be exactly equal, the results from both methods should exhibit the same

temperature dependence if the data were internally and mutually consistent.

It is not possible to conclude from the data presented in figure 2 that the

temperature dependence of the excess Gibbs energy predicted from the hard

sphere model is either reasonable or incorrect.

E

The values of G calculated from the present liquid and vapor phase

data are given in Table 1 also. The constants of equation (4) obtained from

these N'alues and from the Barker method are given in Table 2. The equimolar

G values from both methods are compared in figure 3 with those from the

previous data of Miller et al . [10] and the calculated curve taken from

E

Massengill [36]. The values of the equimolar G from the present study are

in excellent agreement with those from Miller et al . Furthermore, the results

obtained from both methods give the same temperature dependence, though

the absolute values differ by about 10%. It thus can be concluded that the

calculated curve is a reasonable representation of the temperature dependence

of G^.

E

The fact that the heat of mixing, H , is related to the excess Gibbs energy

and its temperature dependence by

= G^ - T(6G-^/B T)p (5)

also allows a conclusion about the heat of mixing for this system. From.

E

approximately 90 to 110 K, the value of G remains essentially constant. Thus,

F E

the temperature dependence is zero and H 'and G are equal. Above 110 K the

E

temperature dependence becomes slightly positi\'e; thus, the value of H

E

would become less than the value of G in this region. Unfortunately, there are no calorimetric heat of mixing data for this system to substantiate this

deduction.

I-IO
Additional comparisons are given in figures 4, 5, and 6 between the

isothermal G values from the liquid and vapor phase data of the present

study at 95.00, 115.00, and 120.00 K and the corresponding values from four

other investigations at approximately the same temperatures. It is apparent

that the G values from the present study are more symmetrical about the

equimolar value than those from the other investigations. The values from

Stryjek et al. and Cines et al. are in reasonably good agreement with the

present results at these temperatures. Those from Sprow and Prausnitz,

however, are significantly lower than the present results. With the exception

of two points, the G values from the data of Chang and Lu are in reasonable

agreement with values from the present study, which is surprising considering

the qualitative difference apparent in their data in the nitrogen rich end.

SUMMARY

The results of this investigation provide a single set of closely spaced

and consistent liquid-vapor equilibria data for the nitrogen-methane system

between the triple point temperature of methane and the critical point of

nitrogen. The derived excess Gibbs energy values substantiate the qualitative

temperature dependence of the equimolar Gibbs energy predicted by the hard

sphere model of Snider and Herrington as applied by Massengill. From the

temperature dependence of the excess Gibbs energy, it can be concluded that

the nitrogen-methane system closely approximates a regular solution over EE E much of the temperature range examined, i.e. H = G and S =0. These

conclusions strongly suggest the desireability of calorimetric heat of mixing

measurements for the nitrogen-methane system, at least in the lower temperature

region of this investigation.

ACKNOWLEDGEMENTS

The authors wish to express their thanks to R . C. Miller for providing

the calculated values of the equimolar Gibbs energy, given only graphically

in the thesis of one of his students, D. R. Massengill.

I-U

9
REFERENCES

1. O. T. Bloomer and J, T. Parent, Chem. Eng. Progr. Symp. Series

No. 6, Vol. 49, 1 1 (1953).

2. L. W. Brandt and L. Stroud. Ind . Eng. Chem. _50, 859 (1958).

3. M. R. Cines, J. T. Roach, R. J. Hogan, and C. H. Roland, Chem.

Eng. Progr. Symp. Series No. 6, Vol. 49, 1 (1953).

4. S.-D. Chang and B. C.-Y. Lu, Chem. Eng. Progr. Symp. Series

No. 81, Vol. 63, 18 (1967).

5. H. Cheung and D. I. -J. Wang, Ind. Eng. Chem. Fundam. \ No. 4,

355 (1964).

6. V. G. Fastovskii and Yu. V, Petrovskii, Zhur. Fiz. Khim. _M_, 2317

(1957).

7. W. Forg and P. Wirtz, Linde Rep. Sci. Technol. J_5, 46 (1970).

8. S. Fuks and A. Bellemans, Bull. Soc. Chim. Belg. _76, 290 (1967).

9. H. A. McTaggart and E. Edwards, Trans. Roy. Soc. Can. 1

3

, Sect. Ill, 57 (1919).

10. R. C, Miller, A. J. Kidnay, and M. J. Hiza, AIChE J. No. 1,

145 (1973).

11. V. G. Skripka, I. E. Nikitina, L. A. Zhdanovich, A, G. Sirotin, and

O. A. Benyaminovich, Gazov. Prom._l_5, No, 12, 35 (1970).

12. F. B. Sprow and J. M. Prausnitz, AIChE J. 11, No. 4, 780 (1966).

13. R. Stryjek, P. S. Chappelear, and R. Kobayashi, Low temperature

vapor-liquid equilibria of the nitrogen-methane, nitrogen- ethane,

and nitrogen-methane-ethane systems. Monograph, Rice Univ. Houston,

Texas (June 30, 1972) .

14. N. S. Tor ochesnikov and L. A. Levius, J. Chem. Ind. (USSR) 16,

No. 1, 19 (1939).

15. E. Vellinger and E . Pons, Compt. Rend. 2r7, 689 (1943).

16. V. G. Fastovskii and Yu. A. Krestinskii, J. Phys. Chem. (USSR)

15, 525 (1941).

1-12

10
17. M. F. Fedorova, J. Exptl. Theoret. Phys . (USSR) _8, 425 (1938).

18. D. W. Moran, Low temperature equilibria in binary systems, including

the solid phase, Ph.D. Thesis, Imperial College, Univ. of London (1959).

19. M. H. Omar, Z. Dokoupil, and H. G. M. Schroten, Physica 28,

No. 4. 309 (1962).

20. H. E, Barner and S. B. Adler, Hydrocarbon Proc e s sing _47 , No. 10,

1 50 (1968).

21. M.-S. Lin and L. M. Naphtali, AIChE J. 9, No. 5, 580 (1963).

22. H. H. Stotler and M. Benedict, Chem. Eng. Progr. Symp. Series

No. 6, Vol. 49, 25 (1953).

23. G. M. Wilson, Advances in Cryogenic Engineering, Vol. 9, p 168

[ed. K. D. Timmerhaus, Plenum Press, N.Y. 1964].

24. Y.-P. Liu and R. C. Miller, J. Chem. Thermodyn.4, 85(1972).

25. D. R. Massengill and R. C. Miller, J. Chem. Thermodyn. _5, 207 (1973).

26. A. G. Duncan and M. J. Hiza, Advances in Cryogenic Engineering,

Vol. 15, p 42 [ed. K. D. Timmerhaus, Plenum Press, N.Y. 1970].

27. R. Prydz and R. D. Goodwin, J. Chem. Thermodyn. 4, 127 (1972).

28. T. R. Strobridge, The thermodynamic properties of nitrogen from

64 to 300 K between 0.1 and 200 atmospheres, Nat. Bur. Stand. Tech.

Note No. 129 (1962).

29. L. A. Weber, J. Chem. Thermodyn. 2, 839 (1970).

30. A. G. Duncan and M. J. Hiza, Ind. Eng. Chem. Fundam. JJ_, No. 1, 38 (1972).

31. M. L. McGlashan and D. J. B. Potter, Proc. Roy. Soc. (London)

A 267 , 478 (1962).

32. R. D. Goodwin, J. Rei.. Nat. Bur. Stand. 74A , No. 5, 655 (1970).

33. R. D. Goodwin and R. Prydz, J. Res. Nat. Bur. Stand. 76

A

, No. 2,

81 (1972).

34. J. S. Rowlinson, Liquids and liquid mixtures, Butterworth and Co.,

London, 1969.

1-13

11
35. J. A. Barker, Austral. J. Chem. _6, Z70 (1953).

36. D. R. Massengill, Excess volumes of the argon-nitrogen and methane- argon

nitrogen systems, M.S. Thesis, Univ. of Wyoming, Laramie (197Z).

37. N. S. Snider and T. M. Herrington, J. Chem. Phys. 47, 2248 (1967).

1-14
TABLE 1. Experimental nitrogen-methane liquid-vapor equilibria properties.

T, K XN

P, bars G , J/m(

o.onoo 0.199 0.0000

0.2679 2.254 0.9216 1.5755 1.0950 148.67

0.3562 2.737 0.9374 1.4433 1 . 1790 186.99

0.42A9 3.018 0.9460 1.3355 1.2384 194.24

0.5271 3.431 0.9573 1 .2238 1.3271 189.77

0.5889 3.646 0.9618 1.1621 1 .4361 187.42

0.7495 4.247 0.9756 1 .0600 1.7038 139.92

0.8271 4.580 0.9823 1.0327 1.9007 108.73

1.0000 5.400 1 .0000

0.0000

0.1329

0.2397

0.3301

0.3831

100.00 0.^463

0.5069

0.5638

0.6671

0.8133

1 .0000

0.343

1 .988

2.960

3.621

3.989

4.396

4.706

5.032

5.598

6.451

7.778

0.0000

0.8336

0.8907

0.9168

0.9277

0.9372

0.9448

0.9508

0.9618

0.9764

1 .0000

1 .8662

1.6059

1.4436

1.3734

1.2987

1.2241

1 .1742

1. 1002

1 .0320

1.0275

1.0987

1. 1286

1. 1547

1.2099

1.2614

1.3398

1 .4799

1.8111

88.48

153.91

168. 15

174.8 7 184.71

180.44

181.37

161.46

113.52

l05.00

0.0000 0.565 0.0000

0.2101 3.649 0.8533 1.6242 1.0605 129.47

0.2869 4.512 0.8355 1.4960 1.0963 158. 15

0.4108 5.664 0.9149 1.3191 1. 1835 186.00

0.4836 6.298 0.9275 1 .2444 1 .2478 192. 13

0.6012 7.242 0.9440 1.1455 1.3831 184.21

0.7548 8.417 0.9626 1 .0511 1 .6684 142.43

0.8990 9.805 0.9829 1 .0148 2.0457 74. 64

1.0000 10.835 1 .OnoO

1-15

13
TABLE 1 . (continued)

T, K

O.OOOO

n.2093

0.2856

0.4061

0.4843

110.00 0.5008

0,6056

0.6948

0.7956

0.8978

1 . 0000

P, bars

0,844

4,8 10

5.916

7.450

8.366

8.479

9.603

10.580

1 1 .797

13.179

14.680

0,0000

0.8237

0.8615

0.8950

0.911?

0.9147

0,9319

0.04^^6

0.9612

0.9790

1 .0000

1 .6008

1 .4743

1.3129

1 .2342

1.2112

1.1278

1 ,0756

1 .0364

1.0131

1.0546

1,0850

1 , 1799

1.2477

1,2516

1,3765

1,5125

1 , 7208

1 .9841

G^, j/mol

128.53

154.66

190.96

197.60

190.24

181.88

161.82

127.47

74. 76

0 • 0000

0.1891

0.2868

0. 3989

115.00 0.5027

0.5789

0.7110

0.8043

0.9040

1 .0000

1.327

5,882

7,725

9,580

11,130

12.218

14,170

15.650

17.474

19,389

0, 0000

0,7782

0.8363

0.8739

0 ,8983

0.9129

0,9377

0,9538

0,9750

1 .0000

1,6384

1,4712

1.3218

1 .2148

1.1515

1.0736

1 .0344

1.0116

1,0465

1,0873

1 , 1606

1 ,2501

1,3398

1,5208

1 ,7540

2,0407

124,51

162,93

192.05

199.65

195.85

164. 16

131.17

75.40

0 .0000

0.0977

0. 1938

0.2990

120.00 0.3978

0. 4959

0.5938

0.7055

0.7877

1.0000

1.919

4,984

7,549

9,982

12,100

13 ,942

15,919

18,029

19,880

25.128

0 e 0000

0,6122

0,7458

0.8125

0.8512

0.8773

0.9000

0.9225

0.9414

1.0000

1 .8083

1 .6058

1 ,4348

1 .3177

1 ,2136

1 ,1444

1,0748

1 ,0459

1,0174

1 ,0490

1.0956

1, 1523

1,2381

1,3476

1,5323

1,6785

73,31

130,07

171.53

194.66

203. 17

200.81

176. 16

144. 97

1-16

14
>Q

-(->

00 00 IT) LTl LT) a- IT)

IT) 00 CO 00 00 00 r—

H

O 1—1

Ln ro

O 1—1 O 1—1

1—1

tn o (M sD o o

ro 1—( 1—1 o o O r—( o 1—( o O o o o o o o O O o o o ^ 1—1

00 00 LTl un 00 o

r~ fM 1—1 1—1

^, 00 00 1—I

LO 00 LD

fM

O o CM o r- CO r-H LTl o LTl vD O 00 00 00 in sD 00 ^ O i-H 00 ro LTl n£) LT) 00 O o O r-i o O o o o O O O O o o O o O o o o O o O

•XjuO

a!> >Q

ro a- 0 0 (M 0 ro

LTl 00 00 00 r-H i-H 00 00 00 (M

LO LO 00 0 ^ 0 r-- 0 (M 0

f—1

-X) f—(

00 0 r-- i-H 0 0 0

(M 0 0 0 0 1—1 0 I-H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(M 00 cn r- sO LO LT) 00

CO 0 r~ 1—1

LT) 00

00 0 00 1—100 sO

00 cr- (M 1—1 1—I

00

m .—1

00 0 r-H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 >Q

-t-> 0) Q ^

I-H 0 (N3 0 r- 00 00 in 1—1

00

00 I-H 00 1—t

r-- 00 t—1 0 1—1

OJ in 1—1 0 0 Ln 0 vO 0 0 0

CO 0 0 1—1 0 0 0 0 0

i-H 0 0 0 1—1 0 I-H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

-vO 0 ro ro 1—1

I-H Ln 1—1 1—1 0

ro 00 vO 1—100 in r-H in in ro 00 ro ro 1—1

in I-H CT- i-H sO ^ 00 00 00 ro 0^

Ln CO

m 00 r- ro in I-H 00 00 00 00 00 CO 00 0 0 0 0 0 0 0 0 0 0 0 0

a, 1 >^ Dh 1 >> a. 1 >> P. 1 >. a, 1 >^ 1 >> 1 X 1 X t

><! 1X 1 X 1X 1X

X

X

X 1X 1 X 0 0 0 0 0 0 0 0 0 0 0 0

Ln 0 Ln 0 in 0 0 1—1 1—t

00

I-H I-H i-H I—1

15 1-17
LIST OF FIGURES

1. Liquid and vapor equilibrium compositions for the nitrogen- methane

system at 100.00 K compared with those of Cines et al. (1953).

2. Values of equimolar G calculated from the literature data. The

value shown for Fuks and Bellemans (1967) is their reported \'alue.

3. Values of equimolar G from the data of this in\-estigation compared

with the values calculated from the data of Miller et al. (1973) at 11?.. GO K.

4. Values of G from the data at 95.00 K compared with the values

calculated from the data of Sprow and Prausnitz (19b7) at 90.67 K.

E

5. Values of G from the data at 115.00 K compared with the values

calculated from the data of Stryjek et al. (1972) at 113.72 K.

E

6. Values of G from the data at 120.00 K compared with the values calculated

from the data of Cines et al. (1953) and of Chang and Lu (l'^67) at 1 22.05 K.

1-18
CH^ 0.2 0.4 06 0.8 Ng

NITROGEN MOLE FRACTION

Figure 1

.

1-19

IB- Ui7>vj I
300

Calc. 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 Sfryjek, Chappelear, and Kobayashi(l972)

V Chang and Lu (1967) - Fastovskii and Petrovskii (1957)

o Fuks and Bellennans (1967)

(Open symbols from Barker's Method

)

200

o

£

IT

o

d

Ui 100

40

-40

100 110

TEMPERATURE, K

120

Figure 2.

1-20
Calc. from Snider - Herrington, k, 2= 0.035

• o This investigation

A A Miller, Kidnoy and Hizo (1973)

(Open symbols from Borker's Method)

300

200 - •

- JB —— ^

o o

O A

100

J \ L_L

90 100 110 120

TEMPERATURE, K

Figure 3

.

1-21
• 95.00 K*, This investigation

A 90.67 K; Sprow and Prausnitz (1966)

NITROGEN MOLE FRACTION

Figure 4.

1-22
• 1 1 5.00 K; This investigation ^ 113.72 k; Stryjek, Chappeiear,

and Kobayashi (1972)

CH4 0.2 0.4 0.6 0.8 N2

NITROGEN MOLE FRACTION

Figure 5.

16' iu7>a^ I

1-23
• 120.00 K', This investigation

1 22.05 K ; Cines, Roach, Hogan,

and Roland (1953)

A 122. 05K, Chang and Lu (1967)

CH4 0.2 0.4 0.6 0.8 Ng

NITROGEN MOLE FRACTION

Figure b.

1-24
APPENDIX J

J-1
Cryogenics Division - NBS Institirte for Bosic Stondards LABORATORY NOTE

PROJECT NO. 2750364FIIE NO. 73-3

PAGE

1 SUBJECT The Vapor Pressures of Ethane R. D. Goodwin

DATE Julv 9, 1973

This is the first of several reports planned on the physical properties of ethane.

Our ultimate purpose is to compute tables of thermodynamic functions over the entire

range of fluid states. We first will discover regions where data are inadequate or

lacking by attempting to compute provisional tables based on existing data.

Accurate vapor pre s sure s, and a proper analytical representation of these data, are essential for computing heats of vaporization via the Clapeyron equation.

In this note we give a limited bibliography. Not all of these references were

available at this writing. We compare several sets of data by use of our new, nonanalytic vapor pressure equation. We make a choice of the best for least squares, and we give deviations from this selected equation.

At the triple point near 90 K the vapor pressure of ethane is about 0.00001 atm

(10 u-atm). Experimental methods therefore differ for the range below one atm

(184. 5K) and for the range of higher pressures to 48 atm at T = 305 K.

c Data to about I960 are reviewed by Tester [19], who selected the representation of Barkelew et al. [3] for the entire range from triple- to critical point.

Below one atm the data to 1964 are reviewed by Ziegler et al. , who give their

own, high quality set of data computed for thermodynamic consistency with all related or derived data, in a work for the National Standard Reference Data Program [23].

More recently we have the measurements of Carruth, obtained by the gas saturation

flow technique, employing a flame ionization detector for analysis of the gas mixture [4j. See also J. J. Chen et al. (Rice University), paper G-1, 1972 Cryogenic

Engineering Conference, on the same technique.

For high pressures the only new data of which we presently are aware are those

of Pope (Table 25) [13], and those attributed to Dr. A. K. Pal by Pope [13] in Table 31 . For these latter data there is no description of experimental method.

After this note was written we received the new precise measurements of

Douslin and Harrison [24], and therefore have recomputed our results including these

data, Douslin and Harrison note especially the new, pr"':ise measurements of

Miniovich and Sorina [25], which were not available to us at this writing,

V 11342*
Cryogenics Division - NBS Institute for Basic Standards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

PAGE 2

SUBJECT The Vapor Pressures of Ethane R. D. Goodwin

July 9, 1973

Our vapor pressure equation [6] uses the reduced argument,

x(T) 2 (1-T /T)/(l-T /T ) , t t -C where subscripts t and c refer to triple- and critical points,

In (P/Pj.) = a.x + b«x^ + cx^ + d'X^ + e-x. (1-x)® (1)

and the exponent is e =1.5 for methane [15] and for oxygen [16]. Originally the term

4 d'X was absent. It has been added here to improve representation of the ethane data.

The following discoveries are found with the original equation of four terms.

Optimum exponents in the range 1. 1 ^ e ^ 1.9 are obtained merely by changing the

sets of data used for least squares. Hence we must rely on the more precise methane

and oxygen data to select e =1.5. Varying the critical-point temperature within

reasonable limits has no significant effect on the overall, rms relative pressure deviations.

By examining numerous results we have selected for least squares only the data

of Ziegler at P S 1 atm [23], and the data of Pope, Pal [13] and Douslin [24] at P> 1.9 atm.

Whereas the temperature scale of Ziegler may be thermodynamic (the report is not

clear), we nevertheless find that deviations (rms in relative P) are minimized by

converting both sets of data to T-1968 as if they had been on T-1948 [ 1]. All T used

in the following are T-68.

The triple-point temperature was reviewed by Ziegler et al. Their selection

of 89. » 9 K becomes 89. 899 on the 1968 scale. The critical -point temperature 305.4 2 K

of Pope has been changed to 305 . 33 K for consistency with the data of Douslin [ 24] . A

value T = 305.33 ± 0.005 K is given by P. Sliwinski, Zeit. Phys. Chem. 68_, 91

c (196 -)) based on analysis of dielectric constants. This was kindly pointed out by

D. E. Diller. We obtain pressures at these end points from the vapor pressure

equation:

T, K (1968) P, atm

Triple point 89.899 9.616.10"^

Critical point 305.33 48.07695

J-3
Cryogenics Division - NBS Institute for Bosic Standards LABORATORY NOTE

PROJECT NO. 27503b4FILE NO. 73-3

PAGE

3

SUBJECT NAME The Vapor Pressures of Ethane R. D. Goodwin

July q, 1973

The constants for eq (1) were obtained via the data of Ziegler, Pope, Pal and

Douslin. They include g = 1 , 6 as shown at the head of table 1.

a = 8.4549 8734

b = 12.4880 3978

c = -4. 1042 8155

d = -1.4138 6053

e = 8.5265 2253

In the following tables we give the authorfe ID, his temperature and as converted to T-68, and the published and calculated pressures. Next is the deviation of

his temperature from our calculated value.

DT T -T

xpt calc

and finally his relative pressure deviation,

P, PCT = 100- {P -P , )/P

xpt calc calc

At the bottom of each table we give the number of datum pairs, NP, and the rms of

relative pressure deviations in percent.

The source of data in each table is identified by the numerical code, ID, in the

first column--

Table No. I. D. Author s Reference

1 4 A. K. Pal [13]

7 Ziegler et al. [23]

9 G. A. Pope [13]

10 Douslin, Harrison [24]

2 1 Tickner, Los sing [20]

2 API Proj. 44 [2]

3 Carruth [4]

3 5 Loomis, Walters [11]

4 6 F. Porter [14]

8 Barkelew et al [3]

5 Calculated vapor pressures (this report)

6 Reduced v. p. functions (this report)

» l)3till J-4
Cryogenics Division - NBS Institute for Basic Standards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3PAGE 4

SUBJECT The Vapor Pressures of Ethane

NAME D. Goodwin

July 9, 1973

As additional data may be found, we reserve comment on the deviations of

individual authors, and omit the labor of preparing deviation plots.

Calculated pressures, slopes and curvatures are given at uniform temperatures

by Table 5.

For comparison with functions in our original vapor pressure publication [6],

we give these functions in Table 6, as computed via eq (1) namely

x(T) = (T-T /T)/(l-T /T ),

t t c

Y(P) - -tn(P/P )/-tn(P /P ). (2)

t c t These variables range from zero to unity. The equation

Y = X (3)

represents the basic vapor pressure equation

'f.n(P) = a - b/T (4)

when this is constrained to the end-points (triple and critical). Hence (Y-x) is the

deviation of data from (4).

Finally, we give the computer programs used in this work as a means to check

for errors, and to facilitate resumption of this research.

Addendum. Following work shows that the second virial coefficient used by Ziegler

et al. to obtain vapor pressures is not consistent with our selection. At 200°K his

B(T) = - 455 cc/mol, whereas our B(T) = - 417.5. We therefore have recomputed our vapor pressure constants using Ziegler's vapor pressure data from his Table IX for

"Curve B" of his Figure 1, for which B(T) = - 410 cc/mol at 200 K. The difference in

his vapor press ures at 90 K is (7.80-'i.33)/7.33 6.4 percent, the new value s be ing

the greater. Our new results for eq (1) are given in Table 7, (pages 20, 21) and tables

8,9 on pages 22, 23 of this report. We prefer these constants for future use.

V 11342

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Cryogenics Division - NBS Institute for Etosic Stondards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

PAGE

c

SUBJECT The Vapor Pressures of Ethane

NAME , R. D. Goodwin

July 9, 197 3

[1

[2

[3

[4

[5

V

[8

[9

[10

[11

[12

[13

[14

[15

\ 16

Bibliography

The International Practical Temperature Scale of 1968, Metrologia _5 ( 2), 35 (1969).

Amer. Petrol, Inst. Res. Proj. 44, Selected Values of Properties of Hydrocarbons and Related Compounds (loose-leaf), Table 20 k, (Part 1), p. 1, Dec. 31 (1952).

C. H. Barkelew, J. L. Valentine and C. O. Hurd, Thermodynamic properties

of ethane, Trans. Amer. Inst. Chem. Eng. 43, 25 (1947).

F. G. Carruth, Determination of the vapor pressure of n-paraffins and extension

of a corresponding states correlation to low reduced temperatures. Thesis,

Dept. Chemical Engineering, Rice University, Houston, Texas, (Nov. 1970).

N. M. Dykhno, M. V. Tsyrulnikova and M. V. Mochalova, Hydrocarbon vapor

pressures at low temperatures, Zh. Fiz, Khim. 42 (9), 2310-1 (1968).

R. D. Goodwin, Nonanalytic vapor pressure equation with data for nitrogen and

oxygen, J. Res. NBS 73A (5), 487(1969).

A. S. Holmes, W. G. Braun and M. R. Fenske, Bibliography of Vapor Pressure

Data for Hydrocarbons , Amer. Petrol. Inst., New York, Bibliog. No. 2, (1964).

E. E. Hughes and S. G. Lias, Vapor Pressures of Organic Compounds in the

Range Below one Millimeter of Mercury, NBS Tech. Note 70, Washington, D. C.

(Oct., 1960).

J. G. Hust, A compilation and historical review of temperature scale differences,

Cryogenics 2(6). 443 (Dec., 1969).

G. Klipping and F. Schmidt, Dampfdrucktabellen Tiefsiedender Gase (V),

Kaltetechnik J_8 (1 1), (Nov. 1966).

A. G. Loomis and J, E. Walters, The vapor pressure of ethane near the normal

boiling point, J. Amer. Chem. Soc. 48, 2051 (1926).

R. E. Perry and G. Thodos, Vapor pressures of the light normal saturated

hydrocarbons, Ind. Eng. Chem. 44(7), 1649 (1952).

G, A. Pope (quotes v. p. of Dr. A. K. Pal), Calculation of Argon, Methane, and

Ethane Virial Coefficients at Low Reduced Temperature Based on Data Obtained

by Isochorically Coupled Burnett Experiments, Thesis, Dept. Chemical Engineering, Rice University, Houston, Texas (July, 1971).

F". Porter, The vapor pressures and specific volumes of the saturated vapor of

ethane, J. Amer. Chem. Soc. 48_, 2055 (1926),

R. Prydz and R. D. Goodwin, Experimental melting and vapor pressures of

methane, J. Chem. Thermodynamics 4. 127 (1972).

Rolf Prydz, An improved oxygen vapor pre s sure representation, Metrologia 8^ ( 1 ),

1 (1972).

SP 1134; A J-6
Cryogenics Division - NBS Institute for Basic Standards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

PAGE 6

SUBJECT The Vapor Pressures of Ethane

NAME R. D. Goodwin

July 9, 1973

[17] C. T. Sciance, C. P. Colver and C. M. Sliepcevich, Bring your C^-C. up to date, Hydrocarbon Process. 4_6(9), 173 (1967).

[18] N. E. Sondak, and G. Thodos, Vapor pressures, the saturated aliphatic hydrocarbons, A.I.Ch.E. Journal 2, 347(1956).

[19] H, E. Tester, ETHANE, in Thermodynamic Functions of Gases, F. Din, Editor,

Butte rworths , London (1961).

[20] A. W. Tickner and F. P. Lossing, The measurement of low vapor pressures by

means of a mass spectrometer, J. Phys . Colloid Chem. 55, 733 (195 1).

[21] G. M. Wilson, R. G, Clark and F. L. Hyman, Thermodynamic properties of

cryogenic fluids, Ind . Eng. Chem, 6_0(6), 58 (1968).

[22] W . T. Ziegler, The Vapor Pressures of Some Hydrocarbons in the liquid and

solid state at low temperatures, NBS Tech. Note 4, (May, 1959).

[23] W. T. Ziegler, B. S, Kirk, J. C. MuUins and A . R. Berquist, Calculation of

the Vapor Pressure and Heats of Vaporization and Sublimation of Liquids and

Solids below One Atmosphere Pressure. VII Ethane, Tech. Rpt. No. 2 Proj.

A-764, Eng. Expt. Sta., Georgia Inst. Tech; Atlanta, Georgia, Dec., 1964.

[24] D.R. Douslin and R. H. Harrison, Pres sure- Volume -7"emperature Relations

of Ethane (manuscript for the Journal of Chemical Thermodynamics), 1973.

[25] V. M. Miniovich and G. A. Sorina, Russian J. Phys. Chem. 45_, 306 (1971).

U 11342

«

J-7
Cryogenics Hvision - NBS Institute for Bask Standards LABORATORY NOTE

PROJECT NO, 2750364FILE NO. 73-3

PAGE 7

SUBJECT The Vapor Pressures of Ethane

Table 1. Data of Pal (4), Ziegler (7) , Pope (9), and Douslin(lO).

NAME R. D. Goodwin

"^^^ July 9, 197 3 ETHANE VAPOR PRESSURES, E = 1.60

TTRP = 89.899, TCRT - 305.330

PTRP,MUATM = 9.61600, PCRT.ATM = 48.07695

Q »k5k3d7ikk 12.^+88039775 .1 j i+ 28 15 5

1

-1.'+1336j533 8 .526522526 0 . Q 0 0 u L : U 0 C

ID T ,XPTL r-68 P» A TM CALCC DEL T P,PCT

7 91+. 01 3 J. 0000271+ 0. GOiO 271+ -0. 00 1 0 .02

7 3 3 • w C C 98. 012 0.00 00693 0. QQC069it 0 . 30 2 -0 .05

7 IJ 2 . Q C 0 102. Ou 8 0. 00 cioie 0. 0 001619 0 . DO 2 -0 . 05

7 10 6. jO I. ICo. 002 0.0003526 C. 00G3522 -0.00 6 0 .11

7 11 u. jC C 109. 998 0. 0007207 0. 0 0L7 20 5 -0. 00 2 0.03

7 111*. ^OQ 113. 995 0. 00 1391+7 0. 001391+7 -0 . 00 0 0.3C

7 11 8. £00 117. 991 0. 00 25697 C. 0 0 25698 0 . 30 0 -0 . 00

7 122. 3Q0 121. 988 0. 00 1+53 0 3 C. 0^+5293 -Q . 00 2 0.02

7 1 2 6* u L u 125, 987 u. 00767 37 0 . 0076731+ -0 , 00 0 0.00

7 130. JOG 129, 987 0 .0 125 36 0 .ul25i+u 0 . CO 1 -0 ,01

7 1 3 i*. J i< G 133. 988 0 .t 193 3C 0 .019831+ 0.002 -0 . 02

7 1 3 8 . j 0 0 137, 99'j C .0 3Q1+1+7 0 . 0 301+6 0 0 . GC 1+ -0.01+

7 li* 2. G Q 0 litl. 993 0 .0 1+5501* 0 .Cit5527 0 . 005 -0.C5

7 l<+6, JOG 11+5. 996 G .C 66355 0 .066389 0. 0C6 -0 . 05

7 150. OuC 150. 0 J J C .091+606 0 .091+657 0 . 00 6 -0 .05

7 15 1*. J 0 Q 15<+. DC It a. 13215 G.1322C 0. 00 7 -C ,35

7 15 8. iOO 158. uO 8 0.18139 0.18117 0.005 -0 .01+ 7 162. JO Q 162. 012 0. 21+392 0.21+39 7 0 . CO 3 -u . 02

7 1 6 6 . u C 0 166. 015 0. 3233? 0 . 32 33 G -3 , 30 1 0 .01

7 1 7 C . 3 3 L 170. 019 0. 1+22 3C 0.1+2211+ -0.006 0 . 01+ 7 i7h..:oo 171+, 023 0. 51+1+09 0.51+371 -0.011 0 .07

7 173. iiQO 178. 026 0.69221+ C. 6911+5 -0. 02C 0.11

7 1 6 2 . u 0 u le 2. G28 0. 870 1+7 G .66905 -0. 329 0 .16

7 ISh. 520 161*. 550 1. 0 0 J 0 C 0 .9980 3 -0 . 036 Q . 20

9 19 6.181 193. 21

6

1 .97 37 1.9 75 8 0 . 02 3 -0.11

i+ 21 It. 3D 2 21'+. 33 ^ 3 .9209 3.9176 -0. 021 0 . 06

i+ 22't. 10 2 ZZk, 130 5.6367 5,61+29 u. 031 -0 .11

i^ 229. 755 229. 762 6.8569 6.8629 C . 02 6 -0 . 09

it 23^+. 556 231+. 581 8.0335 8,3 1+2 3 0 . 031+ -0 .11

9 23*+. t92 231+. 715 8.071+1 B.0772 0 . 312 -0.01+

10 233.150 238. 150 9.00 97 9.0 10 8 0 . 0Q1+ - 0 .01

9 23 3. 771 238. 792 9 .181+3 9.1935 0. 032 -0.10

U 239. B'+'t 239. 861+ 9.1+959 9.501+9 0. 030 -0 .09

i+ ZkZ.Slk 21+G. 531+ 9 .696C 9,7032 0 . 021+ -0.07

IC 2^+3. 150 21+3. 150 10 .5063 1C.5071 0 . 00 3 -0.01

2'+3. 359 21+3. 377 10 .5761 IC .579C J . GO 9 -0 .03

i+ 2't6. 31it 21+b. 830 11 .71 37 11.7183 5.011+ -0 . C1+ 21*7. 816 21+7. 831 12 .05 02 12.061+8 3. 01+2 -0 . 12

IC 2'+8. 150 21+8. 15u 12.1756 12.1766 0 . OC 3 -0 ,C1

2^9. 71*1 2iv9. 755 12.752G 12.7512 -0.030 Q . 08

i+ 250. Itb 250. 160 12.89 8 5 12.8991 3. 00 2 -0 . 01

i+ 251.567 251.6 00 13 .i+'+25 13.*+356 -0.018 0 . 05

i+ 252. 5i»i+ 252. 556 13.8065 13.800 6 -0. 015 0.01+

10 253. 150 253. 15 J 11+. 0 310 11+. d 31 C -0 . 00 0 o.ao

it 25^. 29u 251+. 3C 1 11+. 1+3 96 li+.i+85if -0. Oil 0 .03

257. 5'*3 257. 552 15 .6252 15.8261+ 0 . OC 3 -0 .01

IG 2 5 3. 15 0 258. 15 j 16 .08 3^ 16.0 323 -0 . CO 3 0.01

J-8
Cryogenics Division - NBS Institute for Basic Stondords LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

PAGE a

SUBJECT Table 1--

The Vapor Pressures

-continued

.

of Ethane NAME D. Good win

July 9, 1973

J.T nu T f KPTL T-68 P , A T M DEL T P» PCT

1 l'' 1 0 263,150 26 3. 15 0 X 0 , 0 *+ D H 1 A 7 ii.7 7 -0.007 u • u c H 2 6 3, i 8 G 263. 3 86 X 0 , H H 0

1 ft i. CC 7 1 0 . H Pt> 0 0.002 -0,01

J.*+ 26 7,536 267. 539 C U . 7 X X 0 -0 . 016 0.04

1 Ij 268, 150 268, 15 u cU ,0010 on Q 07 /. -0.00 9 0,02

271. 7<t9 271. 75 3 C C , f 0 O X C C • f OX C -Q . 00 8 0,02

9 272, 9't9 272. 949 ?3 . 45 1 ? 3 . U 34 7 -0.03 0 0 , 07

1 Ci 27 3, 15G 273. 150 23,55 49 ? 3 .5 4ft ft -0 . 01

1

0,03

2 7 5,922 275. 921 25 » 1 5 8 4 25 .1 64 6 0 . 01

1

-0 . C3

276. 363 276. 362 25 . 45 5 8 25,429 3 -0 . 044 0 . lu

276, 385 276. 384 25 . 44 91 25 ,442 5 -0 . 01

1

0.03

276.51*+ 276, 513 25 . 54 7 2 25 , 5 20 3 -0.04 4 0.11

u 277. 813 277, 811 C w • ^ X Q > C?60 .7177 e 0 X 0 0 -0.00 8 0.02

•1 . 278, 15C 278, 15 0 c 0 . P J 1. T cPADC> ? 7 7 , P c 0 0 -C . 01

2

0.03

/. 28 v . ^ 'I 280, 038 ? 7 7 1 Q ?7 7 1 ft 0.019 -0 . 04

28 2, Z't? 282,243 cP Q^ 1 Cift ft • X 5 0 0 0.008 -0 , 02

1 r X L 28 3.150 28 3. 15 0 C.V 9 f 1 DO P Q 7 Pvft 1

m 1 DO X - 0 . 012 0.03

28if. 635 284. 63 0 07 n1^ , 7f ft0 70 Pu 0 . 02 5 -0,06

g 284. 845 28 4. 6 4 0 3n . Q5 5

5

-0 . 037 0 , 08

287. 'i53 287. 64fi 32 , 92 8 9 3 ? . 9 34 fl 0 . 007 -0 . 02

1 0 26 8. 15C 28 8. 15 0 33.3110 33.3C3 0 -0. 211 0 . 02

28 8.263 268.257 33.38 9° 33.38?? -0*010 0 . 02

£+ 2 9 0 . 'J 4 0 290. 03 4 34 .6873 34,7148 0.036 -0 . 08

9 290.214 290. 20 8 34.8748 34,8474 -0 . 036 0 . 08

292.236 292, 229 07PiU ,

iiH 1X ft0 PC. -0.033 0 « C7

it 293. ;:96 293. 091 Or . U 0 X C Of7 7 1 n u it , X U H H 0,028 • 0 • D 6

iX cf' 293. 15D 29 3,15 0 3701 .. X1 5 ft0 0 77.1 Of , X

C-lX pc -3.00 8 0 • 02

c 293. 266 293. 25 9 Of77 9 C?r>\J 71 cP Of77 p 7Q ii • c 0 J t -0,03 5 0 . 07

296. 347 296. 339 7q 7c: q B 07Q^ , 7f ftii 0 H C? 0 , 029 -0 , 06

-1 r X I. 296. 15G 298. 15 0 ^X . 0 J *T i*1X •, 30 U5*T rc -0.00 5 0 , 31

299. d65 299. 65 7 42.6543 4? - 6 8? ? 0.031 -0 . 07

9 299, 3d3 299. 855 4? . 88 63 4? . 8 60 6 -3 . 02 8 0 . 06

k 3 C 0. 20 5 30 0. 196 43 . 16 5 C 43.1703 3 . C 0 6 -0 • 01

3 0 1.251 301. 2 42 44 .10 8 5 4H . 1 297 0 . 02 3 -0,05

X V 3 0 2. 15 0 30 2. 15 0 44 .98 n c 44 . Q 77 ft - 0 . CO 3 0.01

X 3Q 3. 15 0 30 3. 150 US . Q ?9 5 -0.00 3 0,01

/.H 30 3,471 30 3. 4f. 2 H D , c 'J 0 cf. c p 7 n ,"1 H D , c 0 u U 0,028 -C , 06

30 3. 477 3C 3. 46 8 Ho/. t P7 Q t. , c f y 0

/.HD^ p 7 c; p , c oP 0 -0,046 0.10

Q 3 0 4.012 304. CO 2 *+D , 71 7r 07 C

f, t 7 CC a H D , f PP 0 -0,018 0.04

/.T 30'+. u 4 9 304. 0 3 9 tip. 7f. Q R HD . f ^ c U 0.023 -0 . 05

1 r'l 3C 4, 15 0 30 H, 15 0 H D , ^ U X U -0 . 00 3 0.01

3 u 4 . 3 6 0 3 C 4 , 3 5 0 L.7 n Q 7 1 *+ r . U ^ 0 X

ii7 n Ci7 H f • U ^ f H 0.004 -0 . 01

3G 4. '»46 304. 435 u7 . ? 1 9 f 47.1 ft? ? -0 . 038 0 .08

30 H, 519 30 4. 50 8 47.2025 47 - ? 5U 4 0. 352 -0 . 11

3l 4. 734 30^-. 72 3 1+7 . u 3 1 f 47 ,4 67 7 0. 037 -0 . 08

u 3u4, 795 304. 785 47 . 5 1 A^^ 47 .5 ?Q 4 3. Oil -0 . 02

30 4. 324 3 0 4. 9^ 3 47 .6846 47.6572 -0. 027 0.06

k 30 4. 960 304. 969 47 .71 31 47.7132 0 . 30 0 -0 . 00

tf 3 0 5. 121 305. 110 h7 . 84 96. 47.8547 0. 00 5 -C . 01

i+ 50 5. 135 305. 124 +7 .8251 H7.8688 0. 04 3 -0 . 09

1

:

305. 15G 3C5. 15 0 47 .8992 47.8950 -0 . 03 4 0 . 01

305. 153 30 5, 142 47.8807 47.8869 0 . 006 -C .01

ic 30 5.250 305.250 47 .9994 47.9959 -0. 00 3 0.01

MP = 99, .RMS PCT = 0 ,061

Vt 11342

1

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Cryogenks Division - NBS Institule for Bosk Standards LABORATORY NOTE

PROJECT NO. 1 FILE 27503641 73NO. -3

PAGE 7

SUBJEaTable

The Vapor Pressures of Ethane

2. Data of Tickner (1), API (2), and Carruth (3).

NAME

^ j-j^ Goodwin

DATE T , r^ July 9, 1973

10 TtXPTL T -6 8 P , A T M

r* A I n UA Lb U DEL T P, PCT

1 91. 350 91. 36 1 0*0000132 u. ouLulHl 0. 26 5 -6. 86

1 9^. '63 0.00Cg263 t': * rt 0 "2 n t U. jULU .5ljC Q. 58 2 -13 . 98

1 98.550 98. 562 0. 00 00658 u. GCCO 783 0 . 73 0 -15.98

1 101. 35C 101. 858 0. 00 0 13 16 0. 00ol571 0 . 79 7 -16.23

1 105.350 105. 353 C. 0CC2632 0. 0003118 n a? U . 'jC o -15.60

1 110. 550 110. 5^8 u. 00 C6579 C . 0 CL79l'+ 0. 99 2 -16.87

1 111*. 650 lit*. 6'+'+ 0. 00 131 56 0. 00l5'+53 0 . 94 7 -14. 85

1 119. D50 119. Oi+U 0. 0026316 C. 00299U2 0.839 -12. 11

41 125.550 125. 537 3.00 65789 0. C072'+50 0 . 717 -9. 19

13Q.650 130.637 0.013158 G .013539 0 » 24 0 -2. 81

fir — 10, RMSPCT = 13.226

ID T,XPTL T-68 P, ATM CA LC D DEL T P, PCT

2 130. 270 130. 257 0 .0 131 56 0 . 0 129^+7 -0 . 13 8 1 .63

2 136. 'SO 136. kk9 0.0 26316 0 . y 25 90 9 -J . 14 8 1.57

2 li^O. <tlO 0 .0 39474 0 . C 38 925 -0 . 141 1.41

2 l'+3.370 li+3. 36i+ 0.052632 0 . 0 51 9i+5 -0 . 139 1. 32

2 l'+5.76C l't5. 756 0.065789 0 . C6'+9'+6 -0. 14 2 1

.

30

2 11+7.790 11+7. 78 8 0 .0789^*7 0 .078 01 8 -0. 134 1. 19

2 151. 120 151. 121 0.10526 U . 10 Hi 5 -0 . 127 1 . 07

2 153.620 153. 9,Zh 0. 131 58 C . 13 u 2 8 -0. 12 2 0 . 99

2 159. j30 159. G39 0. 197 37 0.19591 -0. 09 9 0 .74

2 162. 960 162. 973 0. 26316 C . 26 1^+ 0 -0. 094 0 . 67

2 156. 170 166. 185 J. 3239B 0.52708 -0 . C8 4 0 .57

2 168.900 168. 918 0. 39'+7i4 £ . 3928 ! -0. 074 0 . 48

2 I73.ifl0 173. '32 0. 52632 0.52'+22 -0 . 054 0 . 40

2 177. 100 177. 125 0. 657 89 0 « 6557^+ -0 . 05 6 0. 33

2 18 0.250 180. 277 0. 789i+7 C .78 74 3 • 0 . 04 6 0 .26

2 183. 010 183. 039 0. 921 0 5 0 .91908 -0 . 039 0 . 21

2 18'+.520 Ifii^. 550 1. CO J OL n G Q fi r, "7 U . ?y 0 Li 0 -0 . 03 6 0 . 20

2 185.i*80 185. 510 1.05 26 1. 050 9 -0 . 03 1 Q . 16

2 187.710 187. 7i+l l.lBi+2 1.1821 -0. 034 0 . 18

2 189. 770 189. 8C 2 1 .3156 1.3143 -0 . 023 0 . 11

c 193. khC 193. '73 1.5789 1 .5777 -0.017 0 . 08

198. 15C 198. 185 1.9737 1.972 9 -0 . 008 0 .04

MP — 22, RMSPCT = 3.857

I D T ,XPTL T-66 P, ATM LA LL D DEL T P, PCT

3 91. 3tf 0 91. 351 0. 0000152 0. C0c0141 -0 . 315 8. 14

S 93. 700 93. 712 G. Q0 00 27 C 0 . u 0 C 0 25 5 -0 . 237 5. 80 3 96.2tf0 96. 253 0. 00 00'+91 G . 0C:0 46 6 -0 . 235 5. (2

3 100.700 100. 710 0. 00 012 97 0. C0C1239 - 0 . 22 2 4.64

3 105.600 105. 60 3 0. 00 C3263 0 . 0 e C 3 26 8 0. Q09 -0 .16

3 im. ZkQ ili». 235 0.00 l'+'+61 0. G01'+487 0.012 -0 . 19

3 120.380 120. 369 0. 00 56J 66 0. C036185 0.023 -0 . 33

3 129. 310 129. 797 C .012312 0 .wl226C - 0 . 03 6 0 .42

3 135.770 135. 759 O.D2i+l97 0 .024065 -0. 051 0 .55

3 I'+O. 550 l^+O. 5^+2 0 .0 '0 211 0 .059472 -0 . 188 1.87

3 I'+i^. 135 0 .0 562 89 0 .055871 -0. 080 0 .75

NP = 11, RMS PCT = 3.759

J- 10
Cryogenics Division - NBS Institule for Basic Stondards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3PAGE 10

SUBJECT The Vapor Pressures of Ethane

Table 3. Data (5) of Loomis, Walters [ll].

NAME R. D. Goodwin

July 9, 1973

I D

T V D T 1 T _ A P ATM DEL T P» FCT

5 i 3 5. 73 b J.35. 72 5 0 , u 2 Ht? y w

rt r o Q7 7 -Q . 20 3

? • 1 ft 5 1^+3.267 ltt3. 261 n c o o r. 0.0522Uw U . u t?l '3 f -a

.

15 6 X * HO

1 1+ 7, 52^+ 1^+7. 321 -0 . 15 8

i L.7 X . Hil 5 15 i*. 5W6 15 5 5 u U. iH J 0 C

r 1 7 Ci •! c

U . 1 J 0 1 C -0. 16 6 X « OO

?3 15 6 » 38 5 15 3. 39 3 (J « 1 O 3 D Li r -1 ft p, c; 7 -0 . Ik 3 X . J 7

5 162.629 162. 6'tl 5 K 7

<" -0. 110 U . 1 7

1 D p . ^c: y Ids. 3h J . ox u U L u . O X o u u -0 . 13 9 0 . 96

r- i O * . 0 ^ D It r . O 5 J U . O D 7 0 v " J • 13 3 0 . 89

lb 9. 1 f y ley. 1 y -J J • H o 0 0 u f . i* n r. ;i 0 • ^ U U C V -0. 12 6 0 . 82

1 r 1 . / u L •17 1^1.1 7 ^> 1 f c 1

1 L 7 ti 7 J . H r H 0 0 U . M f u o *+ -0. 116 0.7'+

1 r U . ou 2

•17 1 o o ll J . ode 1 L. 7 ft Q Ti 0 . *+ 0 0 7 u -0 . 14+

5

5 17^. j 6 2 1 r U 8 p

1 c /. o o r 0 . !5H7 o b

n c> it 7 Q U . f H -> f 7 -0. 119

175, 7u tt 4 7 C 7 7 O 175 . 73 2

1 C. 1 7 7 r n [1 7 7 ft - j. 10 8

17 7.62 5 17 7.6^+9 Q . 6 8 J 0 n — 7 C 7 -1 li • c bo 1 -a

,

IC 3 u . ox

17 d. 621 17 8. 6^+7 J . 7 2 1 J b u t /

1

69 b -0 , 097 U . -50 c 1 7 '3 . 7 5 G 17 9. 77 7 0 . 769 6 Ll f 7 C C "7 C -0 . 099 J . 7 r 1 O 1 . D 1 o 1 . t><5 H

" ft ii. O Q

' -0 . 396 0.5'+

5 182. -tbS 182. ^+92 0. 8 96 3

C

L. 69172 -D . 39 3 0 .51

5 18 3. 77 c} 183. 8j 7 J. 9b3'+L L . 95 8b ci -3. C92 0.50

5 ISt*. 559 le'*. 569 1. OQi+au C. 99906 -0 . Q91 0 .'+9 135. 137 165. 167 1 . C366 l.Q 318 -3. J87 0 .'+7 185. ylt* 165. 9i+^ 1 ,06 3C 1,0 755 -0 . 078 0 . '+2 5 186. bC9 166, 64+0 1 .12ufc 1.1158 -0 . LBk

187. 30 2 187. 333 1 .1619 1.1572 -0. 37 7 0 . '+0 5 137.726 167, 757 1 . 1881 1.1831 -3. 081 Q .*+2 13 379 168, i*l. 1.22 89 1.2239 - G . 38 0 C . '+1

c: 18 9. n't 189. 1^46 1 .2757 1.271G -C . 072 0.37

5 18 9. 65 6 189. 69- 1 . 32 i+e 1.32Q 2 -0. 069 0 . 35

5 190. 791 19a, 823 1.33 85 1 .3839 - u . 357 0 . 33

191. '+5C 191, '+63 1 .'+33'+ l.i+286 -3 . 06'+ 0 , 32

192.266 192, 319 1 , ^+953 1.^+90 8 ~ j . 361 0 . 3lj

c; 192.777 192, 81o 1,5316 1.5273 -0 . C6G 0 . 29

196. Zhk 196, 27 8 1 , 80 86 1.80^+9 -0. QkS 0 .22

199. 9C 9 199. 9»+i* 2 . 1^+17 2.138'+ " u • 0 .15

MP = 3'+, RMSHCT = u .789

V 11342/1 J-11
Cryo9^K$ Division ~ NSS InstHvte for Bask Standards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

PAGE 11

^""^'^ The Vapor Pressures of Ethane

Table 4. Data of Porter (6), and Barkelew (8).

'^'^^ R. D. Goodwin

July 9, 1973

ID T,XPTL T-68 P , A T H CALCD DEL T P, POT

e IS**. 500 0 . 999 'tC C .99 53^+ -0.075 0 . Hi

6 23 3.49 0 20 3. 52k 2 . '9 60 2.5076 3 . 10 6 -0 . '+6 20 5. 62C 20 5. 653 2 . 7 3 3 C 2,7'+89 0.135 -0 . 58

5 21 1] . 960 210.99 2 3 .'t 30 8 0 . 12 1 -0 . '+9 5 216. 310 216. 3^+1 '*.225C ^+.2338 0 . 05 *+ -C * 21

5 ?C ?b. 1X .« 8vj ftLf uu 221.910 5,2370 5 . 2 IC 0 . 01 8 -0 • 06

225. 10 G 225. 12 8 5 . 83 8 C 5 , a z+S 6 3 . 03 7 -0.13

5 2W> 2 6.W V iiL 8 uW 226. 20 7 6 . 07 3G 6.0 70 9 -0.010 Q . 03

6 23'+. 580 ZZk, 6Q3 8 . Qi+i+C 8.0U81 0. 016 -0.05

6 238. 90a 238. 921 9.229L 9.2305 C, 00 5 -0 .02

6 2'+3,22C 2't3. 238 IC .5360 10 .535C -0 . 00 3 0.01

6 2'+8. fe5Q 2«+3, 665 12 . 35^+1 12,3586 0. 013 -0 . 0'+ 5 25 3. 0 3 C 253. 0U2 1*+ . 0 i+ 3 0 13.968 9 -0 . 13 9 U • 39

6 258. 3G0 25 8. 8C 9 16 .t*21C 16.3679 -0. 12 2 0 . 32

6 263. 26u 26 3. 28 6 18 81 18. '076 -0 . 085 0 . 22

6 26 3. 730 268. 732 21 .1850 21.1317 -0 . 10 1 0 . 25

6 27 3. u90 273. 09^ 23

.

5kkl 23,51i+7 -0 . 051 0 .12

6 278. ottS 273. 633 26 .837C 26.8276 -0. 015 0.0'+

6 283. 580 283. 576 30 .10 60 30 .0 575 -0 . 071 0.16

6 288.260 268. 25it 33.f*63L 33.380 G -3 . 119 0 .26

UP = 20. RMSPCT = 0.27i+

10 T ,XFTL T-68 P, A TM CALCD DEL T P, FCT

3 11 J . u U u lu9. 995 ij.L!G07&0w -0 . 31

9

5 . '+9 g 1 2 G . C G 0 119. 989 0.003 'S 0 C 0. CO 3'+ 29 5 — 0 . u 6 3 0 . 89

v.) 1 3 0 . U 0 0 129. 987 D . 0 1 27 2 L 0 . G 125'+ 0 -0 . 12 1 1 . '+'+ I'f 3. ^0 0 139. 992 0WVWv* .0 378 5 C fl . 0 37 359 -0 . 131 1 . 31

s I5t, jOG 150.

J

0 « 3 955 0 0 « C9'+657 -0 . 11

6

1.00

g 1 6 0 . <: C 0 16 0. QID 0 • 2 12 0 C 0 . 21 068 -0.08'+ 0 . 63

8 17 0.^^0 3 170. 019 U . ^+23 60 0 . '221 -0.05 3 0 . 35

g 1 8 0 . J C u 180. 027 Q . 7 7 7 8 0 £, . 7762 6 -0.03'+ 0 . 20

8 190. JOC 190. 032 1 .33 00 1.3297 -0. 00'+ 0 .02

8 20 0.^0 0 2au. 035 2.1i+62 2.1'*72 0 . 01

1

-0.05

8 21 u. b u G 210. 033 3 .297l 3.2 99 8 0 . 02C -0.08

e 22o.uOa 220. 03C '+.85 8 0 '+.8639 0. 03 3 -0 .12

6 230. JOQ 230. 025 6.912C 6.9196 0. G32 -0 . 11

8 2'+ C» «Q 0 2<+Q. 020 9.55 IC 9.550 8 -0. GO 1 0.00

8 25Q. u'OO 250. Oli* 12 .850c 12.8'+56 -U.C12 0.03

8 26 u . J u G 260. uO 8 16 .910 C 16.8973 -0. 028 0 . 08

.8 27 u. 'J QC 270. 0 0 1 21 . 83 a L 21.8066 0 . CI 2 -0.03

8 280. wQO 279. 997 27.65 0: 27.6895 3. 062 -0 . 1'+ 8 2 9 Q . 0 C 0 289. 99it 3'+ .65 0 0 3'+.68'+3 3 . 01+5 -O.IO

NP = 19, RMSPCT = 1.383

J-12
Cryogenics Division - NBS Institute for Elosic Stanbords LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

PAGE 12

^'^^''^^ The Vapor Pressures of Ethane

Table 5. Calculated Ethane Vapor Pressures.

R. D, Goodwin

DATE July 9, 1973

ETHANE VAPOR PRESSURES

T, K P , A T H OF/DT D2P/DT2

89, i99 C. GuCG096 0 . 00 0 3 0 26 G .G0033C63

9l .,jGC 0.0 33 0 099 0. 03 00 026 CI .0003 CC6V

95. J C'C CQQjZlk'i 0 • 0 'J 3 0 0 8 3 C .0 0 30 3 177

10 o , J C G 0 . U 3 J IG 67 ii . 33 0 0 226 G . 0 00 3 0 1+30 1Q5,.3 Ot C.0a0291c 0

.

03 OC 555 0 .0 GOC d9i+2

lie, oc 0.3037227 u * 03 Q 1239 0 .0 GOj 1881

115, 3 0C CO 016337 J . 00 02 5t+5 0 .0 00 0 31*75

12o .,3 0 0 0. 3 3343'i-7 0 . 30 0 1+868 c .0 0 03 5997

125, Q.O C&76ue 0. 00 067V9 0.3 GOO 9759

13 C .. 'K C 0. 312559 3,0 311+89 0 . C u 0 1 5C 8 135,> 1 ij C :. 322167 0 .3 0 2 vlV 0. CGj 2226

Iku ,,-0 3-: C . Q3 73 9C 0 3 0 3 7 53 0 . C 0 3 3 161+ 1^5. jO 0 0 . C D 0 5 7 C.0C5618 0. 003 V339

15 c , J GG 3. 39'»651 G .3 0 8 135 3. 003 5771

155,> J 0 c ; .l'+325 0. 01143 G . 0 3 3 ?i+7

16C , 300 J .2iL 5? 1. 0 1565 0 .03 C91+1+ 165 .2 D 0 0 . 3311+6 Q. 02091 0.0^ 1167

17c 1 'J G C 0 .'+2162 0. 02736 0 .03 liii5

175, J 2 C J . 5 7 7 2 £ 0. 03511 0 . Q3 168 8 18 ;

,

C J J. 0 .77507 0. 01+ 1+2

8

0 . 0 3 1 98 1+ 185 ( J b C 1. 0 2 2n 0 . 0 550 0 . 3 3 23 0 19G. U u 1.3276 3 .0673 0 . 0 0 26 3 195 . 0 fl

:

1. 696V 0 .0813 C. 3 0 29 8 2ao ,3 0D 2. 11+39 3 .0 972 C. 3 0 335

2^5 0 J 2.S731 3 .111+3 3 • 3 0 37 2 211 ,jCO 3. 295^- 3 .

1

Zkk C .0 01*11

215,.OOu 3 20 5 3 « 1 560 C . 3 0 1*5

1

2 2.:,.2CC H. 3585 3 .1795 G .3 Gi+92

225 . J 0 c 5.819'* 0 .2 352 C.3 u53 3 ZZi .iCt 6, 913 6 3 .2329 3 . 0 3 57 6 235 . JOQ 5. 1519 . 2 6 2 6 C. 3 0 619

Z^L 1 J J c 9. fWSO Q .2 91+8 G .3 0661+

2i+5 . j 0 G 1 1. lOi+C 0 .3 292 0 . 0 0710

25C ,. C< 0 -0 12. 81+C6 3 .3658 0. 3 3 757

2 5 5 ,jCC 1^+. 766^+ J . 1*31+9 0 « 0 0 60 6

26:,, JO b 16. *93b 3 . 1+1+65 '3 .0 0 85 8

2 65 1 J G G 19. 2357 0 .1+907 0.00913

27C J 0 0 21.60 56 : .5378 C . 3 3 97 2 275,1 0 C L 2 1+ . o 1 9 w 3.583 3 G .3 1C36

28 J . 3 c

:

27.t:91!T 3.61+16 0.0 1106

285 T .* > J I- L 31. -.VIC 3 .6990 0.3 119 2 29 J 1 3 0 D 3^. o59C 3 .7610 0 . 0 1291+

295 < !'

' > ^J w ^ 3 3. 6612 0 . 8289 G .3 11*2 9

3GG .330 ^+2. 99 2 2 3 .9w53 C . 3 161+9

3 J5 • 3 C G V7. 7VV2 1 . C C29 0 .3 2691+

335 .330 8 . J 7 7 j 1 . 0160 O.J 0 L 0 G
Cryogenics Division - NBS Institute for Basic Standards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

PAGE

. ^

The Vapor Pressures of Ethane

Table 6. Reduced Vapor Pressure Functions.

R. D. Goodwin

DATE July 9, 1973

ETHANE R£DUC£3 VAPOR PRESSURE FUNCTIONS

T f K X y (Y-X ) 3 9.399 0 . 0 u W * LV IjU 3 n Tj <<J U V 0W .9 Gw Cw 0W Q M 91.185 0.02 0 . G2199 0 . 00 199

9 2 . 5 1 (j 0.^4 0 . 04 39 2 0 . u 0 39 2 9 3.373 0.06 0 .06578 0 . 0 0 57 8 9^.277 0.08 C. 0675 9 0 . CO 759

96.723 0 .iL, 3.1C93 4 0 . CO 934

96.215 0.12 C . 13 10 2 0.01102

99.753 0 . 1

H

0 . 15264 0 . Q 1 26 4 101.339 0.1b 0.17419 0 . G 141 9

10 2.977 0.13 C . 1956 6 0.01568

10 k,bS9 G .2 J L) . 2171 0 0 . 0171

C

106. 'tis G .22 0.2384 5 0.01345

10 8.226 0.24 "j .25 97 2 0 . 01 97 2

1 1 C . G 96 G . 26 0 . 28093 0.02093

112. J 32 0.2 8 0 . 30 20 5 0 .02 20 5 114 . 0 37 C . 3 u 0 . 32 31

0

a. 0231G

116.116 0.32 C . 34 4b 6 0 . C-2 40 6

116.272 0 .34 U. 36495 0 .02 49 5 12C .509 C . 3 6 0 . 38574 0.02574

12 2.332 0 .3 S Q . 40 645 0 . 02 54 5 125.?'t7 0 .4i; I . 4270 6 0 . 0 2 70 6 127.759 0.42 0 . 4475 8 0 . 02 75 8 13 C . 37 3 0.44 Lw .• 46~ ^ 80\j y (Jw 13 3.397 0,46 C . 46832 Q . 02 83 2 13 5.937 0.4 3 0 .50 85 4 0 .C2 85 4

13 8.901 0 . 5 'J C . 52 86 6 0 . 02866

141.997 0.52 0 . 54866 0.02856

1 45 . 2 3 4 C .54 :j . 5685 5 0 . J2 35 5

1 4 8 . o2 2 0.56 G . 56 83 3 0 . 0 2 83 3 15 2.172 0.5 8 0 . 60 80 0 0.02800

15 5.596 0 . 6275 5 0.02755

15 9.307 C .62 L . 6469 8 Q .02698

15 3.919 0 . C . 66 62 9 0 . 0 2 52 9

16 8.248 0.66 L . 68 54 8 0 . 0 2 54 8

1 7 ? . 3 1 ? 0.53 J . 70 45 5 0 . 0245 5

1 7 7 . S 3 £ u . 72 35 u 0 . 02 35 Q 18 2.725 0.72 0 . 74 23 3 0 . 'w2 23 3 18 8.121 0.74 L, . 7610 5 0 . 0 2 10 5 19 3.345 0.76 C . 77 965 0 . 0 1 95 5 199.928 C .76 G . 79315 0 . u 1 31

5

? n 6 . 4 0 5 li . 31 65 5 0 . J 1 65 5 213.317 0 .82 C. 83 43 6 0 .01486

22C.707 0 .84 : . 8530 9 0.G1309

228.527 C .86 0.67126 0.01125

237.138 G .33 0 . 88936 0 . 0 0 93 8 246.306 0 .9G 0.9C749 0 . 00 749

256.212 0 .92 C . 92552 0 . 00 552

266.948 0 .94 0 . 94 381 0 . 00 381

278.623 0.9b C . 96216 0.0C216

291.366 0 .98 (..98 07 8 0.0C078

30 5.330 1.0 a 1. OCOO u 0 . 0 0 0 0 C

J-14
Cryogenics Division - NBS Institute for Basic Standards LABORATORY NOTE

PROJECT NO. FILE NO. PAGE

The Vapor Pressures of Ethane NAME Goodwin

July 9, 1973

PROGRAM PSATFIT

ETHANE VaPOR PRESSURES, X = ( 1- T T/ T ) / (1 - T T/ TC ) , LN(P/PTRP) = A1»X + A2*X2 + A3*X3 + A4*Xit + A5*X * ( 1-X) *£.

AUTH3RS 10 = (DTICKNER, (2)R0SSINI» {5)CARRUTH, (H)PAL/POPEt

(5)L00MIS, (6)P0RTt:R, (7)ZIEGL£R, ( 8 ) 8 ARKE LE W/ TE ST ER

(9)P0P!^, (1Q)D0USLIN,PREPRINT(19 73) . COMMON TTRP ,TCRT,PTRP, E,A(9), FZ,F1,F2» DL P DT , D2 LP0T2

COM'iOH/999/NFUN ,Y ,F (30)

DIMENSION TEMP(13]) ,0ELT(13J)

D IMENSION I 0(999) ,T (999 ) , TX (999) , P(9 99)

DIMENSIUN G (3 J)

1 FOR-HATdS, 2F10.C)

2 FOPMATdHl i7X *xTHANE VAPOR PRESSURES,

1 lex 6HTTRP =F7.3, 8H, TCRT =F8.3//

2 18< 12HPTRP, 'iUATM =F9.5, 12Ht PCRT,ATM

E = F5.2//

3 FCFMAK

1 5X3H0EL T FCRMATdHl

i 5>X3HDEL T 5 F0R^AT(i5X

FOR^AK 15X

FO^-IATdFX

FCRilAK l^X

FORMA T ( IHu

FORMAK^e. Q FC^^ iATdHl

C X 5 H DP / C T FGPMAT( ICX

FCRiAT{ IIX

F0R'-1AT( ICX

FOR-IA TdCX

FOPIAK IHl

i lit 3HT,K

17 FCF^ATdCX

15 F0t,iATd6X

19 F0R^AT(1CX

RE An- IN THfc

c:J 'F. A3 10,

21 TTPP=89.

6

789

10

11

1 12

13

l-* 15

16

15,

15,

15,

17X

Fi : , 3,

F 1 . 3 , Fl . .3,

ISX

7X IHX

f^lO.S,

2F12.7,

2F12.6,

2F12.5,

2F12.U,

lOH,

F10.3

F1C.3

FIG. 3 FiO.3

RMSPCT

FIO .2 ) FIO .2 ) FIO ,2 ) FIO .2)

=F7. 3)

VAPOR

)

IdX 2HID i+XbHT,XPTL

5X5HP ,PCT)

17X 2HI0 <fXbHT,XPTL

5X5HP,PCT)

15, 2F10.3,

2^ 1 u • 3 , 21^10 .3 , 2F1C .3

,

i+HNP =11+,

, F9. t , 63X)

16X *ETHANE

5X7HD? P/ DT2

F1..3, 2Fil.7,

2F11. 6 , 2F11. 5,

2F11. i+, THANE

9X1HY

F8. 2,

2Hi:P fcX2HSS)

2F10.<+)

Ti+'i - Tb8 TEMP. CONVERSION TABLE

( ( TEMP ( J ) ,OFLT ( J) ) , J = l ,13 0)

699 5 TCKT = 305. 33 $ PTR P= 9 . 6 3 8E-6

= F9.5// 2 (15X 3Fi6. 9/)

6Xi*HT-e8 7X5HP,ATM 7X5HCALC0

ex^+HT-fce 7X5HP,ATM 7X5HCALCD

PRESSURES* // 17X3HT,K 6X5HP,ATM

Fi2.8)

F12.7)

F12.6)

F12.5)

REOUCEO VAPOR

5X5H(Y-X) ) 2 FIO .5)

PRESSURE FUNCTIONS* //

E = i.5 $ N=0

IF(IDO) 23,25

$ TX(N)=TT

\l 11342 A

REAP (7)ZIEGLtR, KELVIN, MM HG.

22 DC >^ J = l,99 f; READ 1, IDD,TT,PP $

23 N = N + 1 f ID(N)=IDD $ P(N) = PP/76u

T<N) = Tfe6(TT,D£LT, TEMP)

25 NI-1 = N READ MIXED (i^)PAL, {9)P0PF, (IDO^USuIN DATA,

(U ) KElVI'>!,PSIA, ( 9) K£LV IN , ATmos , ( i 0 ) CEN T I G . , A TM OS . 26 DC 35 J=1,2Gj $ READ 1, IDD,TT,FP S IF(IDC) 27,36

27 N = N + 1 I IO(N) = 100 ? If^(IDO-i+) 28, 3C

29 IF(IDD-9) 3'+,j2

30 P(N) = PP/li+.b9595 % T(N) = T68 ( TT , C£ LT , T EMF

)

31 TX (N) = TT S GOTO 35

3? ?(N) - PF ? T(N) = Td8 (TT,OLLT, TEMP)

^3 Ty(N) - TT t GD TO 35

J-15
Cryogenics Division - NBS Institute for Basic Standords LABORATORY NOTE

SUBJECT The Vapor Pressures of Ethane

PROJECT NO. 2751364FILE NO. 73-3

PAG^ /5

R. D. Goodwin

Tnlv 9. 1973

PSATFIT 07/23/7 3

Zk P(N) = PP T(N) = TX (N) = TT 273.15

35 CONTINUE

36 NF = N t Hf = 5 READ (1) DATA, OENTIGRADt, MH HG.

3a DO 'Q J=l,99 i READ 1, IOO,TT,PP $ 1^

39 N = N+1 $ IO(N) = ID3 $ P(N) = PP/76Q $

ifO T(N> = T68 ( TX (N) , OELT ,TEMP)

hi NP2 = N READ (2) DATA, CENTIGRADE, HM HG

.

kZ DO '^k J = l,99 $ READ 1, IOD,TT,PP S IF(IDD)

k3 H - N+1 $ I3{N) = IDD $ P(N) = PP/760 $

hi* T(N) = T68 (TX (N) , D£LT,T£MP)

it5 NP3 = N READ <3) DATA, KELVIN, MM HG. -

46 DO 48 J=l,99 S READ 1, IDD,TT,PP

it7 N = N + 1 S IO(N) = IDD $ P(N) = kd T(N) = TeS ( TT,0£LT, TEMPJ

i*9 NP4 = N READ (5) DATA, KELVIN, ATMOS.

50 DO 52 J=l,99 $ READ 1, IOO,TT,PP

51 N = N+1 $ IO(N) = IDD t P«N) = 52 T(N» = T68(TT, OELT, TEMP)

53 NP5 = N READ (6) DATA, KELVIN, ATMOS.

DO 56 J=l,99 f READ 1, IOD,TT,PP

55 N = N+1 $ IO(N» = IDD S P(N) = 56 T«N) = Tee (TT.DELT, TEMP)

57 NP6 = N READ (8)0ATA, KELVIN, ATMOS.

6Q DO S2 J=l,99 S READ 1, IDD,TT,PP

N = N+1 f IO(N)=IDD S P(N)=PP J TX

T (N) = Te8(TT,DELT,TEMP)

NPP = NP7 = N

(100) 39,itl

$ TX(N) = 273.15 + TT

U3 ,k5

TX(N) = 273.15

$ IF(IDD) '+7,'+9

PP/763 $ TX(N) = TT

+ TT

PP

PP

IF (IDD)

$ TX(N)

51 ,53

= TT

IFdDD) 55,57

$ TX(N) = TT

61

62

63

S IF(IDD)

( N) =TT

61 ,63

EXPLORE VALUES FOR

79

80

51

82

83

8h

85

86

87

88

89

90

91

92

93

9t+ 95

SSK = I.CE+OIG

PTPP.

£ = 1.6 $ PRINT 18 5 XK = 1 - TTRP/TCRT

DO 92 IP=1,25 5 PTP = 9.600 + NFUN = NF S DO 85 J=1,NP % X F(1)=X $ F(2)=X»»2 $ F(3)=X»*3 S

Y = LOGF (P{ J) /PTt'P)

CALL FIT $ CALL COEFF S SS = 0 A (K) = F (K)

DO 58 J=1,NP $ PC = PSATF (T( J) ) $

CONTINUE S SS = 10G»SQRTF (SS/NP) % SSK=SS S EK=E $ TCK=TCRT $ TTK=TTRP

DO 31 K=l,9

G (K) = F (K)

PRIMT 19, PTR, SS

£ = E< 5 TCRT = TCK % TTRP=TTK $ PTRP=PTK $ DO 94 K = l,9

A(K) = ii(K) 5 FCRT = P T RP*EXP F ( A ( 1 ) +A (2 ) + A ( 3) + A (4 ) ) PTR = 1,CE6*PTRP

J-16

O.0ul*IP S PTRP PTR»1. OE-6

= ( 1-TTRP/ T(J) )/XK

F(4)=X*»4 $ F(5) =X*(1-X)

S D3 8 6 K=l,9

SS = SS+ (P{ J) /FC-1) **Z

IF (SS. LT.SSK ) 89,92

S PTK=PTRP
Cryogenics Division - MBS Institute for Bosk Stondords LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3PAGE 16

SUBJECT The Vapor Pressures of Ethane R. D. Goodwin

July 9, 1973

PRINT

1Q5 L = 9 :ncluding dt = -dp/(cp/ot)

1G6

107

lae

112

113

11^

117

118

119

120

121

122

123

125

126

VIATIQNS,

% SS = a PRINT 2, EjTT-^P^TCRTtPTRtPCRT, (A(K),K=1,6) ? 00 125 J = 1,NP I L = L*l $ IF(L-57) 112»106

L - Q S PRINT

PC = PSATF(T(J)) $ DPDT = PC*OLPOT

OP = P(J)-PC S OT = -OP/OPCT

PCT = i:0»DP/'PC I SS = SS + PCT*»2

01) 123,118,118

1) 121,119,119

0) 122, 123, 123

ID ( J) , TX ( J) , T( J) ,P( J)

T( J) ,P( J)

T( J) ,P( J)

T( J) ,P( J)

PPINT 3

IF (3C-0

IF (pc-a

I F (PC-l

P=INT 5 PFINT 6

PRINT 7 PFINT 3 CONTINUE

SS = SqRTF(SS/NP}

ID (J) , TX ( J) , 10 ( J» , TX ( J) , ID (J) ,TX (J) ,

, PC , OT

, PC ,DT

, PC

,PC

,0T

,DT

, PCT

, PCT

,PCT

,PCT

GOTO

GOTO

GOTO

125

125

125

PRINT 9, NP,SS

PRINT OTHER OATft DEVIATIONS.

IfC

141

lk2

1^3

14U

1 i+5 lk6

lk7

Iki

150

151

152

153

155

156

157

15^

K = NP+1 ? SS = N = 0 S PRINT i+ DC 157 J=K,NPP f IF(J-NPP) l'+3,l'*2

SS = SQPTr(SS/N) S PRINT 9, N,SS $ N = N + i ?; PC = PSATF(T( J) ) ? DPDT = OF = P(J)-PC B DT = -DP/OPOT

GO TO 15 8 PC*DLPDT

PCT = 1,

IF (?»C-J , IF (PC-0 . IF(3C-1.

PRINT 5,

PRINT 6. PRINT 7 PPINT i.

C*DP/fC SS = CI) 153 , l'*7 ,1^+7

1) 15i,lt^5,md

C) 152,155,153

IO(J),TX(J),T( J) ,P(J)

ID ( J) , TX ( J) , T( J) ID (J) , TX (J) ,T( J)

ID (J) , TK ( J) , T( J)

IF (10 (J<-1)-I0{ J) ) 156,157

SS = SQ=^TF(SS/N) S PRINT

CONTINUE

CONT IN'JE

SS + PCT**2

,P( J)

,P( J)

,P( J)

, PC ,0T , PCT

,PC ,DT , PCT

, PC ,DT , FCT

, PC ,0T , PCT

GO

GO

GO

TO

TO

TO

155

155

155

N ,SS SS=N = i $ PRINT k

TABLE s^^OR PUBLICATION

2Cu

2L1

2G2

203

Z-jk

2 05

2u7

2 U<5 2C9

210

211

212

213

21't 215

2 2:

%r 11342 «

PRINTOUT UNIFORM

P^INT 11 5 no 22j 0=1,46

TT=TT-P 5 GO TO 2 05

IF(J-'46) 20 4, 2C3

TT = TC'vT S GO TO 2Q5

TT = 80 + 5*J

PS = PSATF(TT) DPOT = PS» DLPDT

IF(as-9.Cl) 2lu,2Jd,2G8

IF(PS-j.l) 211,2c9,209

IF(3S-1.C) 212,215,213

P=INT 12, TT,PS,DPDT,02PDT2

PRINT 13, TT,PS,GPDT,02PDT2

PPINT Hr, TT,PS,DP0T,02PDT2

IF(J-u6) 215,214

0 2P3T2 = 0 Pf^rU 13, TT,PS,rPDT, D2PDT2

CONTINUE

J-17

$ IF(J-l) 202, 201

I D2PDT2=PS» {0LP0T**2 + D2LPDT2)

GOTO

GOTO

GOTO

22 C 22G

22 0
Cryo9^tcs Division - NBS Institute tor Ekisic Stanckirds LABORATORY NOTE

PROJECT NO. Z750364FILE NO. 73-3

PAGE 11

SUBJECT The Vapor Pressures of Ethane

NAME R. D. Goodwin

July 9, 1973

P5ATFIT 07/23/73

C PRINT UNIFORM REDUCED TABLE.

C Y = LN (P/FTRP) /YN, YN = LN ( PCRT/ PTR P )

.

C YC = (A(1)*X + . , . + A (5)»X»(l-X)»*E)/YfM.

250 XN = 1-TTRP/TCRT $ YN = Ad) + A{2) + A (3 ) + AC**)

251 PRINT 16 S 00 270 J=l,51 $ X = 0.l2*(J-1)

252 IF(J-l) 25'»,253

253 TT = TTRP $ GOTO 257

25^+ IF(J-51) 256,255

255 TT = TCRT $ GOTO 257

256 TT = TTRF/(1-X»XN)

257 IF(J-5H 259,256

258 Z = 0 $ GO TO 260

259 Z = X»( 1-X) **£

260 YC = A(5)*Z « DO 261 K = l,'t

261 YC = YC + A{<)*X**K

262 YC = YC/YN 5 YX = YC - X 270 PRINT 17, TT, X, YC, YX 999 CONTINUE % STOP % END

SINGLE-BANK COMPILATION.

FUNCTION PSATF{T)

C LN(P/PTRP) = Al»X + A2*X2 + A3*X3 + Ai+*Xif + A5*X* ( 1-X) **E.

C ARGUMENT, X = { 1- TT/T ) / ( 1 -TT/TC )

.

C fliiLDS ALSO OLPDT = <CP/OT)/P, AND D2LPT = (D2P/0T2)/P.

COMMON TTRP ,TCRT,PTRP , E,A(9), FZ , Fl , F2 , DL PDT , 02 LP 0T2

1 F0R1AT(1H: 9X »FSATF = 0, T EXCEEDS TCRT. / ) 2 XN = 1-TTRP/TCRT $ X= (1-TTRP/T)/XN J X2=X*»2 $ X3=X»*3 $ Xi+=X*»'+

3 OXDT = TTRP/XN/T**2 $ D2XDT2 = -2*DX0T/T

Q = 1-X $ IF(Q) 5,5,7

5 PSATF = DLPDT = C2LPDT2 = 0 S PRINT 1 $ RETURN

5Z = 71 = Z2 = U S GOTO 9

7 W = Q**£ 5 Wl : -E*W/Q $ W2 = {1-L)*W1/Q

8 Z = X*v< $ Zl = X*W1 + W S Z2 = X»K2 + 2»W1

9 FZ = A(1)»X + A(2>»X2 * A(3)*X3 + + A(5)*Z

10 PSATF = PTRP»EXPF (FZ)

11 Fl = A(i) + 2*A(?)*X + 3*A{3)*X2 + 'A(4)*X3 + A{5)*Z1

12 OlPDT = Fl'OXOT

13 F2 = 2*A(2) 6»A(3>*X + 12*A('+)»X2 + A(5)*Z2

15 02LPDT2 = F1»02XDT2 + F2*DXDT*»2 $ RETURN $ END

J-18

ISCOMM -
Cryogenics Division - NBS Institute for Basic Stondards LAbUKAIUKY NUIt

PROJECT NO. FILE NO. 73 -J

PAGE 18

SUBJECT The Vapor Pressures of Ethane NAME Goodwin

July 9, 1973

FUNCTION T68(X,YMAT, XiiAT)

THIS PROGRAM HAS 3EEN CHANGED SO THAT THE OSCILLATING NATURE OF

THE MATRIX TO BE INTERPOLATED EXISTS ONLY AT THE UPPER END OF THE

TA3LE

THIS ROUTINE WILL TAKE INPUT MATRICES OF UP TO 999 ELEMENTS EACH,

ARRANGED SO THAT THE X MATRIX(XMAT) IS IN EITHER ASCENDING OR

DESCENDING ORDER, SELECT NMAX OF THESE PO I NT S , CH OSFN SO THAT

SUCESSIVE X VALUES OSOILATE ABOUT THE VALUE OF THE ARGUMENT X UNLESS THE ENDS OF THE XMATRIX INTERFERE (IN THIS CASE THE

OSCILATORY NATURE IS LOST BUT THE PROGRAM WILL STILL PERFORM AN

INTERPOLATION), INTERPOLATE ON THESE NMAX PAIRS OF DATA BY

AN OSCILATING VARIABLE POINT AITKEN INTERPOLATION ALGORITHM

EITHER UNTIL THE PERCENTAGE CHANGE IN THE INTFRPOLANT IS LESS

THAN THE ftCRCY A RGU-iEN T ( THE ARGUMENT NESSY INDICATES THE

NUMBER OF THE POINT JUST BEFORE THE LAST ONE CHECKED) OR UNTIL

THE NMAX POINTS ARE ALL USED. IT IS SUGGESTED THAT NMAX

3E LESS THAN 10, AND OF COURSE LESS THAN NELMTS. NELMTS

INDICATES THE NUMBER OF ELEMENTS IN XMAT OR YMAT.

IF NESSY IS ZERO IT INDICATES THAT THE INTERPOLATION REQUIREMENT

HAS NOT BEEN SATISFIED IF NESSY IS 1 IT MEANS THAT THE VALUE OF

X LIES OUT SIDE THE RANGE OF XMAT.

DIMENSION YMAT(999), X MAT (999) , A ( 21 , 2 Q

)

ILU F0RMAT(tf2HINTERP0LATI0N REQUIREMENT NOT S AT I SFI E D (X= , E 16 . 8 , 1 H ) / 33 H 1LA3T 2 APPROXIMATIONS OF Y A RE ( Y= , E 1 6 . 8 , 1 H, , E 16 . 6 , IH )

)

2C0 F0RMAT(35HTHIS REPRESENTS AN EXTRAPOLATION OF THE XMAT MATRIX(X=,

lEio. 3,lH)/3 3HN0 CALCULATION HAS BEEN PERFORMED)

3DJ FORMAK i^+HNELMTS IS LESS THAN NMAX)

^GC FORHAK 22HNMAX IS LARGER THAN 23)

NELMTS=13G S NMAX=9 S ACRCY=D.01

IF (N~1AX-2C ) 71 ,7 1 ,o9

69 WRITE OUTPUT TAPE 6 , J 0 Tbd = X $ RtTURN

71 IF(N.'^AX-NELMTS) 75,73 3 73 WRITE OUTPUT TAPE 6 , 3 J & T6S = X $ RETURN

75 CONTINUE

FIRST TWO SUCCESSIVE VALUES OF THE XMATRIX THAT STRADDLE THE

VALUE X WILL BE SOUGHT

JJ1=NELMTS1

DO 2J 1=1, JJl

DIF1 = X-XMAT(I)

DIF2=X1AT(I +1 )-X

IF(OIFl) 16, 15,16

15 T&8 = X + YHAT(I)

NESSY =NMAX

RETURN

16 IF (0IF2 ) 18, 17 ,16

17 T6S = X + YMAT(I+1)

NESSY =NMAX

KcTURN

18 RATI0=0IF1/ DIF2

IF(RATIO)2(3 ,20, 19

19 IMID=I

GO TO 32

CONTINUE

J-19
PROJECT NO. FILE NO. PAGE 73-3 19

SUBJECT NAME R. D. Goodwin The Vapor Pressures of Ethane

DATE July Q. 1973

AT THIS POINT ONE COULD P>^INT THE FOLLOWING STATEMENT

WRITE OUTPUT TAPE 6,2]0,X

N£SSY=1

Tb8 = X $ RETURN

32 CONTINUE

NOTE THAT RATIO IS POSITIVE IF THE TWO POINTS STRADDLE X REGARDLESS WHICH IS LARGER

JJJ=Ii'^IO

JUP = IMIO

JDN=IMIO

IF( JJJf NMAX-NELMTS+1) 98,9S,102

98 DO 2J1 J=1,NMAX

JJJ = IMIO+J-i

A (1 , J)=XMAT ( J JJ

)

201 A (2, J)=YMAT (JJJ)

GO TO 20 3 1£2 DO Hi J=i,NMAX

JJ=J/2

J0E=J-2*JJ

JOE IS 1 IF J IS EVEN AND 1 IF J IS ODD

IF ( J-i) 33, it j , 33

33 IF(J0N-l)3i+,3o,3it

3*+ IF ( JUP- NELMTS )35 , 37 , 35

35 IF (JOE) 37,36, 37

36 JUP=JUP+1

GO TO ifj ^ ^ ) 37 JON=JD^^-l P^/f JryJ-i.

JJJ=JDN f GO TO i+j

i+J A(l, J)=XMAT (JJJ)

A (2, J) = YMAT (JJJ)

itl CONTINJE

2C3 NNN=NMAX+1

DO D J=3,NMN

L = J-1

DO 5 K=L,NMAX

J IS THE COLUMN NUM3ER

K IS THE ROW NUMBER

CA(J,K)=(A(J-1,K)-A(J-1,J-2))*(X-A (1, J-2) ) / ( A ( 1 , K

) -A ( 1 , J-2 )

)

1 +A(J-l,J-2)

IF (K-L) 3,2,3

2 if (a3sf ( (a( j,l) -a (j-1,l-1) ) / a ( j , l )

) - acrc y /i c 0 . 0 ) 7 ,7 ,

3

3 continue

5 continue

6 continje

n£ssy=o

at this point one could print out the following statement,

write output tape 6 , ij 0 , x , a ( nnn , nmax ) , a ( nnn - 1 ,n m ax-1

)

T6d = X + A (NNN,NMAX)

RETURN

7 NES3Y=J-1

To3 = X + A(J,L) S RETURN % END

JJJ= JUP

J-20
Cryogenics Division - NBS Institute for Elask Stan<kirds LABORATORY NOTE

The Vapor Pressures of Ethane

ETHANE VAPOR PRESSURES, E = 1.50

TTRP = 89.899, TCRT = 305.330

PTRP,MUATM = 9.96700, PORT, ATM = 48.07723

10. 806922651

-0 .6i»2995191

8.1^1*715336

6. 059966098

-3.119603823

0.0 00 0000 00

PROJECT NO. 2750364

FILE NO. 73-3

PAGE

R. D. Goodwin

July 9, 1973

ID T,XPrL T-68 P, ATM CALCO DEL T P,PCT

7 90.000 90.010 0.00 00103 0. 0000 103 0,000 -0.01

7 100.000 100.010 0. 0001096 0. 0001098 -0,001 0.01

7 110.000 109.998 0. 0007364* 0. 0007363 -0,001 0.02

7 120. 000 119.989 0. 00 3'*93it 0. 0031*939 0,001 -0.01

7 130.000 129.987 0.012726 0 .012732 0,00 3 -0.01*

7 lifO.OOQ 139,992 0.037792 0 .037 80 3 0.003 -0.03

7 15 0.000 15Q.000 0 .095it7«t 0 ,0951*76 0.000 -0. 00

7 160. 000 160,010 0. 21196 0,21192 -0.003 0 . 02

7 170. 000 170,019 0. '2387 0,1*2 369 -0.007 O.Of*

7 180.000 180,027 0. 77821* 0,77783 -0.009 0.05

7 18't.520 18i*,550 1.00000 0,999i*i* -0.010 0.06

9 198.181 198,216 1.9737 1.9761 0.027 -0.12

t* 21i+.3D2 2ik,33i* 3.9209 3.9159 -0.032 0.13

t* 22t».102 221*, 130 5,6367 5.61*02 0.017 -0 .06

k 229.756 229,782 6.8569 6.8598 0.012 -0.01*

k 23't.558 23'*, 581 8.0335 8.0392 0.022 -0 .07

9 23'*.692 23tt,715 8.07U1 8.071*1 -0.000 0. 00

10 238.150 238.150 9.0097 9.0077 -0.007 0.02

9 238. 771 238,792 9.18U3 9.1905 0. 021 -0.07

*f 239. at*t* 239,86«i 9.t*959 9.5019 0.020 -0.06

t* 2i*Q,53k 9.6960 9.700 3 0.011* -0.01*

10 2£»3.150 2k3,15Q 10 .5063 10 ,501*5 -0.006 0.02

<* 2'»3. 359 2hZ,Z77 10 ,5760 10.5761* 0.001 -0.00

k 2%6,830 11.7137 11.7162 0.007 -0.02

21*7, 816 2^+7.831 12.0502 12.0628 0. 036 -0. 10

10 2't8.150 2t*8,150 12.1756 12.171*7 -0.003 0.01

k 2'»9. 7t»l 2t»9, 755 12.7620 12.71*96 -0,031* 0. 10

I* 250. I!t6 250,160 12.8985 12.8976 -0,002 0. 01

t* 251.587 251,600 lZ,hk25 13.1*31+1* -0.022 0. 06

252.5£»it 252,556 13.8065 13.7997 -0.018 0. 05

10 253. 150 253,150 l<f .0310 lif.O 30 1 -0.002 0.01

CO uH ? a n t aii c V H , <J U i. 1. H . H O ^ O J. H • H O H O — U . U i c

n IT?

i* 25 7. 5!»3 257,552 15.8252 15.8266 0.003 -0.01

10 258. 150 258,150 16.0835 16.0827 -0.002 0.00

10 263. 150 263.150 18.3tt6*» 18.31*52 -0.00 3 0.01

t* 263,360 263,366 18.*»5U3 18.1*573 0.006 -0.02

k 267.536 267,539 20 .5197 20.511*5 -0.010 0 .03

10 268. 150 268.150 20 ,8318 20,8308 -0.002 0. 00

271, 7tf9 271,750 22.7661 22,7662 0.000 -0.00

9 272. 9tf 9 272,9'»9 23.4*515 23,i*39i* -0.021 0.05

10 273. 150 273. 150 23.55t»9 23.5536 -0.002 0. 01

i» 275.922 275.921 25.158*+ 25,1702 0.020 -0.05

276.363 276. 362 25.«»558 25 ,1*31*7 -0.035 0 .08

1* 276.385 276. 38'* 25.itii91 25,1*1*79 -0.002 0.00

276.51£» 276,513 25.5«*72 25,5257 -0.036 0 . 08

277.313 277.811 26.3185 26,3189 0.001 -0. 00

10 278. 150 278, 150 26.5309 26,5290 -0,003 0. 01

Sf II342A J-21
Cryogenics Division - NBS Institute for Bosic Standards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

PACE 7/

SUBJECT The Vapor Pressure of Ethane NAME

July P, 1Q73

10 T,KPTL T-68 P, ATM CALCD DEL T P,PCT

2d0.0i»l 280.038 27.7039 27.7217 0.028 -0. 06

k 282,2«»7 282.243 29.1537 29.1647 0.016 -0.04

10 283. 150 283.150 29.7763 29.7739 -0.003 0.01

* 28't.b35 284.630 30 .7664 30,7893 0.033 -0 .07

9 28'*.8«»5 284.840 30 .9555 30,9353 -0.029 0. 07

287, 653 287.648 32.9289 32,9392 0.014 -0.03

10 288. 150 288.150 33.3110 33,3080 -0,004 0.01

k 288.263 288.257 33.3899 33.3872 -0.004 0.01

290.0«fO 290.034 34.6873 34.7192 0.042 -0.09

9 290.21it 290.20 8 34. 8748 34.8518 -0.030 0.07

1* 292.236 292.229 36 .4440 36.4216 -0.028 0.06

I* 293.098 293.091 37,0816 37,1074 0.032 -0.07

10 293.150 293.150 37.1583 37.1547 -0.005 0.01

9 293.266 293.259 37.2672 37.2422 -0,031 0.07

tf 296. 3t»7 296.339 39.7598 39.7852 0.030 -0. 06

10 298. 150 298. 150 41 .3494 41.3446 -0.005 0. 01

k 299.665 299.657 42.6543 42.6808 0.030 -0.06

9 299.863 299.855 42.8863 42.8591 -0.030 0.06

1* 300.205 300.196 43.1650 43.1686 0.004 -0. 01

< 301. 251 301.242 44.1085 44.1274 0.020 -0 . 04

10 302. 150 302.150 44.9809 44.9751 -0.006 0.01

10 303. 150 303. 150 45 .9327 45.9268 -0.006 0.01

303.«»71 303.462 46.2032 46.2273 0.025 -0.05

I* 303. '77 303,468 46,2798 46.2331 -0.048 0.10

9 304.012 304.002 46.7736 46.7533 -0.021 0 . 04

I* 304. 049 304.039 46.7696 46.7896 0.020 -0 . 04

10 304. 150 304. 150 46,9040 46.8987 -0,005 0.01

k 304. 360 304.350 47,0931 47.0953 0,002 -0. 00

304. 446 304.435 47.2198 47.1802 -0,040 0.08

304.519 304,508 47,2025 47.2525 0. 050 -0.11

304. 734 304,723 47.4310 47.4661 0.035 -0.07

304.796 304,785 47.5185 47.5280 0.009 -0.02

k 304.924 304,913 47.6846 47,6560 -0.028 0.06

I* 304.980 304,969 47.7131 47,7122 -0.001 0.00

305.121 305,110 47,8496 47.8541 0.004 -0.01

10 305.150 305.150 47.8992 47.8945 -0.005 0.01

305, 153 305.142 47,8807 47.8864 0.006 -0.01

305.250 305.250 47.9994 47.9958 -0.004 0*01

NP = 85, RMSPCT = 0.050

Sr 11342 « J-22
Cryogenics Division - NBS Institute for Basic Starxkirds LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3PAGE

SUBJECT The Vapor Pressures of Etnane

NAWE „ ^ ^ ,

. R. D. Goodwin

July 9, 1973

ETHANE VAPOR PRESSURES

T * K P, ATM OP/DT D2P/DT2

89.399 0.0000100 0. 0000 027 0. 0 000 0064*

9 0.000 0.0 00 0102 0. 0000027 0. 0 000 0 066

9 5.00 0 0. 0000358 0.0000085 0 . 000 0 0181

10 0.000 0.0 0010 95 0. 0000232 0 . 0 0 00 04*39

1 0 5. 0 0 0 0. 0002985 0. 0000 567 0.00000 96 0 110.000 0 • 0 007365 0. 000126'* 0.00001915

115.000 0.0 016670 0. 0002592 0. 0000 3529

12 0.0 00 0.003«»991 0. 00049<i8 0.00006077

12 5.00 0 0.0068762 0. 0008875 0.00009864*

13 0.000 0. 012752 0 . 001507 0. 0001521

135.00 0 0. 022'»68 0. 002't39 0. 00 0 224*2

lU 0 .0 0 0 0.037B3ti 0. 003785 0. 000 3177

l'+5.00 0 0. 061192 0 .005656 0. 0004+350

15 0.000 0. 095«t78 0. 008177 0. 0005776

155.00 0 0 .lif«*26 O.OlltfS 0 . 00 0 74*7 160.000 0 .21176 0.01569 0 . 0 0 094*2

165.000 0.30288 0. 02095 0 .001165

170.0 0 0 0.«»2317 0.02738 0 .0014*12

175.000 0.57882 0 .03511 0 .00 1684*

180.000 0.77662 0 . 0<t'«26 0 . 00 1979

18 5.00 0 1.0239 0.05£»9 0. 0 0229

190.0 0 0 1. 3287 0. 0 672 0. 0 0263

195.00 0 1. 6991 0, 0812 0. 0 0298

200.000 0. 0970 0. 0 0334*

205.00 0 2. 6726 0. ll'*7 0. 00372

210.000 3.29<t3 0. 1 3'+3 0 . 0 0 4*1 1 215.000 <«.Q188 0. 1558 0 . 0 04*51

220.000 '. 8561 0. 179i» 0. 0 04*92

225.00 0 5.8165 0.2051 0, 0 0534*

230.000 6. 9105 0 . 2 329 0. 0 0 577

235.00 0 8. 1W87 0 .2628 0.00620

2'f 0 . 0 0 0 9. 5!»20 0.29'»9 0. 00665

2'+5.00 0 11.1016 0 .3293 0. 0 0711

250.000 12. 8390 0. 3660 0 . 0 0 75 8

255.000 li+.7659 0. '+052 0.00807

260.00 0 0.'t«+68 0. 0 0 858

265.00 0 19.2381 0.4*910 0. 0 0 913

270.00 0 21.8098 0. 5381 0 . 0 0971

275.000 0.5882 0.01034*

280.000 27.6972 0.64*16 0.01105

285.000 31. 0it67 0.6989 0.01187

29 0.000 3'+.693«» 0. 7607 0.01288

295. DO 0 38.6630 0,8283 0. 014*25

300.000 42.9905 0. 904*6 0.01657

305.000 k7, 7k33 1. 0 055 0.03283

305.330 1*8. 0772 1.0228 0. 00000

it 11342

«

J-23
Cryogenics Division - NBS institute foi Basic Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-3

PAGE J 3

^"''^'^ The Vapor Pressures of Ethane NAME R. D. Goodwin

July 9, 197 3 ETHANE REDUCED VAPOR PRESSURE FUNCTIONS

T,K X y (Y-X ) 89,899 0.00 0.00000 0.00000

91.186 0.02 0. 02190 0.00190

92.510 0.0t» 0. 0*»376 0,00376

93.873 0.06 0.06558 0.00558

95.277 0.03 0.0873«» 0.00 734

96.723 0.10 0.10906 0.00906

98.215 0.12 0. 13073 0.01073

99.753 0.1<> 0. 1523'* 0.01234

101.339 0.16 0.17389 0.01389

102.977 0.18 0. 19538 0.01538

10 '.669 0.20 0.21680 0.01680

106.«»18 0.22 0 .23816 0.01816

108.226 0.2«* 0.25945 0.01945

110.096 0.26 0.28066 0,02066

112.032 0.28 0.30180 0,02180

n't. 037 0.30 0. 32285 0,02285

116,116 0.32 0. 34382 0,02382

118.272 O.Si* 0, 36471 0.02471

120.509 0.36 0.38551 0,02551

122.832 0.38 0.40621 0.02621

125.247 0.i»0 0.42682 0 .02682

127,759 0.i#2 0.44733 0.02733

130.373 Q,kk 0. 46774 0.02774

133.097 0.(*6 0. 48805 0,02805

135.937 0.<»8 0.50825 0,02825

138.901 0.50 0.52835 0.02835

l«tl.997 0.52 0.54833 0,02833

lt»5.23't 0.5£» 0.56820 0,02820

li*8.622 0.56 0.58796 0.02796

152.172 0.58 0. 60760 0.02760

155.896 0.60 0.62713 0.02713

159,807 0.62 0.64654 0.02654

163.919 Q,bh 0.66583 0 . 0 2 58 3

168 .2«»8 0.66 u, 68501 0.0 2 501

172.812 0.63 0. 70406 0.02406

17 7.630 0.70 0.72301 0,02301

182.725 0.72 0. 74184 0.02184

188.121 Q,7k 0.76056 0.02056

193.8'*5 0.76 0.77917 0,01917

199.928 0.78 0.79769 0,01769

206.tf05 0.30 0.81611 0,01611

213.317 0.82 0.63445 0.01445

220.707 0.8<» 0.85272 0.01272

228.627 0.86 0.87093 0.01093

237.138 0.83 0 .68910 0.00910

2t»6.306 0.90 0.90726 0,00726

256.212 0.92 0.92544 0,00 544

266.9'+8 O.gif 0.94369 0,00369

278.623 0.96 0.96208 0 ,00 208

291.366 o.9e 0,98074 0,00074

305.330 l.QO 1.00000 0.00000

J-24
APPENDIX K

K-1
Cryo^anks Division - NBS Inslitule for Basic Standards PKOjeO NO, 2750364

FIIE NO. 73-4

PAOC

1 SUBJECTEthane Virial Coefficients and Saturated Vapor Densities

R. D. Goodwin

DATE . Aueust 14. 1973

1 . Introduction

The virial equation of state for low densities is needed for thermal computations

to generate P-Q-T data, and to obtain saturated vapor densities via the vapor pressure

equation.

In this report we develop analytical representations for the virial coefficients

of ethane and obtain the corresponding saturated vapor densities.

In the truncated virial equation,

2 3 Z(T,d) = P/(R.T.d) = 1 + B(x)-a + C(K).a +D(x)-a, (1)

P is pressure, R the gas constant, T the absolute temperature, d the density, and

G^d/d^ is reduced density. The second, third, and fourth coefficients B(x), C(x),

D(x) are d irr ensionle s s functions of reduced temperature x ^ T/T . We use T

c c ^ 305 . 33 K , and V ^ 1/d = 145.56cc /mol from Douslin [21 . In the table s we use

c c symbols B", C and D"' for the coefficients of (1).

2. The Second Virial Coefficient

Data for B(x) through about I960 are reviewed by Tester [16]. Since then we

have data from Gunn [8], Hoover [9], Pope [15], McGlashan [12], and Douslin [2].

Data of Gunn and of Douslin extend from 273 K upwards to 623 K. McGlasham gives

outstanding experimental work on the hydrocarbon series (but not on ethane) down to T/T = 0.5. From his formulations he concludes that the low-temperature data of

c Eucken and Parts [ 4] are wrong. This suspicion also was expressed by Ziegler et

al. [17],

For least squares we have selected for low temperatures only the data from

McGlashan' s formula because all other data diverge widely therefrom (Table 2), For

high temperatures we have selected Douslin' s recent data because the experimental

work [2] was executed with great care. Table 2 shows that Michels (1D = 3) and Gunn

(1D=8) are in substantial agreement with Douslin. For consistency with Douslin,

we have increased the absolute values of McGlashan's data by one percent, well within

the luicertainty of his V - 148 cc/mol.

K-2
Oyoganics Divnion - N6S Kistihfte for Boaic Standards LABORATORY NOTE

MOJeCT NO. 2750364nu NO. 73-4 2

SUUECTEthane Virial Coefficients and Saturated Vapor Densities

R, D. Goodwin

"^^August 14, 1973

Our formula for B(x), selected from many variations, finally is similar to that

developed for methane [6],

1/4

B(x) = IB, + B^/x^' ^ + B /x +B /x +B /x^]-[l-(T /T)^^^],

J 4 5 J u o J

(2)

T = 740.0 K,

o B^ = 7,99 3156,

= -10,67 2497,

9. 21 7322,

B^ = -2.48 1668,

4

B 0.84 23 28.

Table 1 gives results for (2) with the data used for least squares: (6 ) McGlashan;

(lO)Douslin. Data not used for -t. s. are compared with ( 2) in Table 2: (l)Eucken;

(2) Lambert; (3) Michels: (4) Hoover; (5) Pope; (8) Gunn.

3^ The Third Virial Coefficient

F or C(x) relatively few data are known to us. The data of Michels [ 13] and

Hoover [9] were generalized in 1967 by Chueh [1], using a formula similar to that developed by Goodwin [5]. In 1971 Pope [15] gave five low-temperature values from 210

to 306 K. For temperatures above 273 K we are fortunate to have the recent, carefullyderived data of Douslin [2].

A comparison of Chueh's generalized function with Douslin's data at T/T =2

shows C" = 0.20 (Chueh), and C* = 0. 15 (Douslin). Whereas the Chueh formula gives

nearly constant values at high temperatures, the Douslin data are trending asymptotically toward zero.

For least squares we have selected the data of Douslin at high temperature s , and

data generated by Chueh's formula at low temperatures. For consistency we have

diminished these latter values by two percent. (Chueh fails to give his critical densities.)

A.t low temperatures the third virial coefficient is not important in the computation of

q (1) because the maximum possible density (saturated vapor) is diminishing exponenbially with temperature, e , (see Table 4).

9 nwt K-3
Oyogenki Divtiion - N6S Institute for Botk StandorcH LABORATORY NOTE

rHOJECT NO. 2750364PILE NO. 73-4

PAOt

3

SUBJECT Ethane Virial Coefficients and Saturated Vapor Densities

R . D. Goodwin

August 14, 1973

Our formula for C(x) is much simpler than that of Chueh, and is similar to that

developed for methane [6],

C(x) [C /x + C^/J + C /x^l . (l-T /t) , (3) l1 2 3J\o/

T = 217. 80 K, C = 0. 865 299,

o ^

= 0.253 773, = 0.556 075.

Least squares results are in the upper part of Table 3: (7) Chueh; (10) Douslin.

Other data in the lower part are: (4) Hoover; (5) Pope.

4. The Fourth Virial Coefficient

Recent data of Douslin [2] are plotted in Figure 1. The general behavior expected for D' is shown in the book by Mason and Spurling [11]. As present data exist

only at T > T . we use the simple formula,

100- D* =x"^^^ ' expra-b/(x-l)] , (4)

where x

~ T / T , and a = 4.00, b = 1.84 from Figure 1

.

c

5. Examination of the Virial Equation

It is valuable to know the relative importance of the terms of eq (1). In Table 4

we compute these for the saturated vapor, using densities from the formula of Plank

and Kambeitz quoted by Tester [16]. We have increased the P.K. densities by 0.088%

to agree with the virial equation at 90 K. Pressures are from our vapor pressure

equation [ 7]

.

In the fourth column of Table 4 we give the ratio DI/DN of ideal gas density to 2 the P.K calculated densities. Fifth and sixth colunons give B(x).a and C(x).a . If all

data were accurate, we should expect Z(T,d) in the last column to be the same as DI/DN.

The vapor pressures of Ziegler [17] were based on second virial coefficients

of Eucken and Parts [4], the accuracy of which Ziegler questioned. Our selection for

also disagrees with Eucken and Parts. We therefore have recomputed our vapor

V IIMl K-4
Cryoganics Division - NBS Instiluto for Basic Standards LABORATORY NOTE

WtOiKT NO. 2750364

FILE NO. 73-4 4

SUBJECT Ethane Virial Coefficients and Saturated Vapor Densities

R. D. Goodwin

August 14, 1973

pressure constants using alternate vapor pressure data of Ziegler, as shown in the

addendum to our Laboratory Note [7]. This revised vapor pressure equation is used

in the following to obtain the densities of saturated vapor.

6. Derivation of the Saturated Vapor Densities

For a given temperature we iterate density in the virial equation to obtain a pressure therefrom which is the same as the vapor pressure. Results are in Table 5.

In previous work we have found that this method gives acceptable results at densities

up to about D /3, which for ethane occurs near T = 286 K. We see that data from the

c Plank-Kambeitz formula diverge increasingly from our results on approach to T . c The highest temperature at which our results are accurate remains to be seen by comparison with data from other sources. Figure 2 shows ,howeve r , that in the region of

overlap with Douslin's vapor densities [2], our results (the filled circles) appear

reasonable.

Figure 3 r^hows the results at lower temperatures. We see that powers of

(1/T) greater an the first will be needed to describe these data.

7. Discussion of Uncertainties

Experimental uncertainties for virial coefficients vary inversely as the signifi- cance of these coefficients in giving departure from ideal gas behavior, see Table 4.

For the second coefficient only, for example,

6R/R 5Z Z 6B/B - — .-^ .

where 6B and 6Z are small variations in B and Z. Assume a tolerable error of 0.01

percent in Z. From Table 4 we compute the approximate tolerable uncertainty in B,

neglecting the effect of C(T),

K-5
Cryogenics Division - l>(AS btsriluto for tcnic Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-4

PAoe 5

SUBJECTEthane Virial Coefficients and Saturated Vapor DensitiesNA**^ R. D. Goodwin

DATE August 14. 1973

T, K mol/-t- &B/B, %

100 0.000013 357. 0

1 20 0, 000349 21.6

140 0.00327 3.37

160 0.01626 0.915

180 0.05434 ^ 0.352

200 0. 1401 0. 170

220 0. 3035 0.096

240 0. 5864 0. 060

260 1.057 0.040

Not all authors give estimates of uncertainty for experimental virial coefficients,

Hoover et al, however, give these estimates for ethane,

T,K 6B/B, % 6C/C, %

215 1.0 10.0

240 0.4 4.0

273 0.1 1.0

and we believe these to be reasonable estimates for very careful work. In Table 2,

however, we see that Hoover's data, ID=4, differ from our selection by up to five percent at low temperatures (215 and 240 K).

Our derived densities depend on the vapor pressure equation. This we estimate

to be uncertain by several percent at the lowest temperatures approaching the triple

point. The virial equation, on the other hand, approaches ideal gas behavior at these

low temperatures. At the higher temperatures above 270 K, we believe the virial coefficients and vapor pressures of Douslin to be accurate as can be derived from the best

of PVT measurements.

» ttMIl K-6
Cryc-ijenks Dtvmon - NBS Institute for Bosk Stondordt LABORATORY NOTE

noitci NO. 2750364nu NO. 73-4PAOC 6

SUBJECTEthane Virial Coefficients and Saturated Vapor Densities

R. D. Goodwin

DATE Aueust 14. 1973

8. Bibliography

1] P, L, Chueh and J. M. Prausnitz, Third virial coefficients of non polar gases

and their mixtures, AIChE Journal (5) 896 (1967).

2] D. R. Douslin and R. H. Harrison, Pressure-volume-temperature relations

of ethane, (U.S. Bureau of Mines, Bartle sville , Okla. 74003). Manuscript for

J. Chem. Thermodynamics, July, 1973.

3] J. H. Dymond and E. B. Smith, The Virial Coefficients of Gases, Oxford

Science Research Papers 2, Clarendon Pres s , Oxford, England, (1969).

4] A. Eucken and A. Parts, Z. Phys. Chem. B20, 184 (1933).

5] R. D. Goodwin, D. E. Diller, H. M. Roder, L. A, Weber, Second and third

virial coefficients for hydrogen, J, Res. NBS 68A ( 1), 121 (1964).

6] R. D. Goodwin, Thermophysical Properties of Methane from 90 to 500 K at Pressures to 700 Bar, NBS Tech. Note, manuscript, April, 1973.

7] The Vapor Pressures of Ethane, Laboratory Note 73-3, July 9, 1973.

8] R. D. Gunn, M. S. Thesis, University. Calif. (Berkeley), 1958, quoted by

J. A. Huff and T. M, Reed, J. Chem. Eng. Data 8, 306 (1963).

9] A. E. Hoover, I. Nagata, T, W. Leland, R. Kobayashi, Virial coefficients

of methane, ethane, and their mixtures at low temperatures, J, Chem.

Phys. 48 (6), 2633 (1968).

10] J, D. Lambert, G. A. H. Roberts, J. S. Rowlinson, V. J. Wilkinson, Proc.

Roy. Soc. (London) A 196 , 113(1949).

11] E. A. Mason and T. H. Spurling, The Virial Equation of State, Pergamon Frees,

Oxford (England), 1969.

12] M. L. McGlashan and D. J. B. Potter, An apparatus for the measurement of

the second virial coefficients of some n-alkanes and of some mixtures of

n-alkanes, Proc. Roy. Soc. (London) A267 , 478 (1962).

13] A. Michels, W. van Straaten and J. Dawson, Physica 20, 17(1954).

14] Plank and Kambeitz, Z. Ges. Kalte Ind. 10, 209 (1936), quoted by Tester.

15] G. A. Pope, Calculation of Argon, Methane and Ethane Virial Coefficients, etc.,

Thesis, Rice Univ., July 1971.

16] H. E. Tester, ETHANE, in Thermodynamic Functions of Gases, F. Din,

Editor, vol. 3, Butterworths, London, 1961.

» inai K-7
Cryogenics Ovision - NSS InsMvto for Boiac Standards LABORATORY NOTE

SUBJECTEthane >/;rial Coefficients and Saturated Vapor Densities

PROjea NO. 2750364nu NO. 73-4

PAOI7

NAME R n. r.nndwin

August 14, 1973

fl7] Ziegier, Kirk, Mullins, Berquist, Calculation of the vapor pressures, etc.,

VII Ethane, Eng. Expt. Sta. , Georgia Inst. Tech ., Atlanta, Ga. , Dec. 1964.

[18] F. Porter, J. Am. Chem. Soc. 48, 2055 (1926),

[19J P. Sliwinski, Z. Phys. Chem. 6_3 263 (1969).

[20] K. R. Hall and P. T. Eubank, Experimental technique for direct measurement

of interaction second virial coefficients, J. Chem. Phys. 59(2), 709 (1973).

[21] R. D. Goodwin, Estimation of critical constants , Dq from the p(T) and T(p)

relations at coexistence, J. Res. NBS 74A(2), 221 1970).

Table Captions

Table 1. Second virial data of (6) McGlashan, (10) Douslin.

Table 2. Second virial, (1) Eucken, (2) Lambert, (3) Michels, (4) Hoover, (5) Pope,

(8) Gunn.

Table 3. Third virial, (7) Chueh, (10) Douslin, (4) Hoover, (5) Pope.

Table 4. Terms of the virial equation for saturated vapor.

Table 5. Saturated vapor densities derived via V.P. and virial equations.

W IIMII K-8
Oyogcnks Omuon - NtS Institute for Basic Standords LABORATORY NOTE

PtOMCT NO. 2750364

nu NO. 73-4

PAOI 8

SUBJECT Ethane Virial Coefficients and Saturated Vapor DensitiesNAME R. D. Goodwin

August 14, 1973

Figure 1. Ethane fourth virial coefficients of Douslin [2],

100. D* = x"-^^^.exp[4.0 - 1.84/(x-l)].

K-9
Lab. Note 73-4- p. 9
gure 3. Ethane saturated vapor densities from Table 5, this report, K-11
j Oycigwfk>Di«n<on-r4BSImliMafi>rBo>kStarKlards LABORATORY NOTE

ntojecT NO. 2750364nu NO. 73-4 11

SUBJECT Ethane Virial Coefficients and Saturated Vapor Densities R. D. Goodwin

August 14. 1973

Table 1. Second virial data of (6) McGlashan, (10) Douslin.

ETHANE SECOND VIRIAL COEFFICIENT

EB = 0.25a, TZ = 71*0.0

7.993156 -ia.672«»97 9.217322 -2.'»81668 0.8<*2328

T n 1 T IN T/ TC B» CALC OIFF PENT

c.o ^ 7 U . U w il 0 • '9 13 -5. 309 -5.310 0. 001 0.01

6 15G.O0O 0 •52<*0 -«*.598 -i*.597 -0.001 -0.01

6 L70.0QO 0.5568 'h, 031 -i*.3 30 -0. 001 -0.02

6 180.000 C.5895 -3.56 9 -3.5 69 -0. 000 -0.01

6 190.000 0.6223 -3. 188 -3.188 0.000 0.01

6 200. QOO 0.6550 -2. 868 -2.869 0.001 0.02

6 210.000 0.6378 -2.597 -2.597 0. 001 0.03

6 220.000 0.7205 -2. 353 -2.36** 0. 001 0.03

6 230. 3Q0 0. 7533 -2.161 -2.162 0.000 0.02

6 2i»Q. uOO 0.7360 -1. 981* -1.98^* -0. 000 -0.00

6 250. 000 0.8188 -1.828 -1.828 •0.001 -0.0<»

6 2S0.0aQ 0.8515 -1.690 -1.688 -0. 002 -0.09

113 273. 150 0.89<*6 -1. 527 -1.527 0. 001 0.06

10 298.150 0.9765 -1.276 -1.275 -0. 001 -0.08

10 303. 150 0.9929 -1.232 -1.232 -0. 001 -0. 05

IQ 323.150 1.058^* -1. 077 -1.076 -0. 001 •0.06

10 31*8.151] l.li»02 -0. 91'* -0.911* 0. 001 0.08

IC 373.150 1.2221 -0.780 -0.781 0. 001 0.10

10 398. 150 1.3a<frO -0.668 -0.670 0. 001 0. 16

10 i*Z3. 150 1.3859 -0.57'* -0.575 0. 000 0. 06

10 '*<*8.150 l.'*o78 -0. '*93 -0.«»93 0. 000 0. 10

10 (73.150 1.5i»96 -0. '*2 3 -0.<*22 -0. 000 -0.08

10 W98. 150 1.6315 -0. 360 -0.360 -0. 000 -0.01

10 523. 150 1.7l3i* -0. 306 -0.305 -0. 001 -0.27

10 51*8.150 1.7953 -0.256 -0.256 -0.000 -0. 19

10 573.150 1.8771 -0.212 -0.212 -0.001 •0.30

10 598.150 1.9590 -0.172 -0.172 -0. 000 •0.02

10 623.150 2.01*09 -0.135 -0.135 0. 001 0.53

NP = 28» MEAMPCT = 0.088

K-12
Oyogenks Dnwon - NftS tnilttuMi for Sonic Standords LABORATORY NOTE

PROJECT NO. 2750364nu NO. 73-4fAOt 12

SUBJECT Ethane Virial Coefficients and Saturated Vapor Densities

R. D. Goodwin

"^^^ August 14, 1973

Table 2. Second Virial, (1) Eucken, (2) Lambert, (3) Michels, (4) Hoover

(5) Pope, (8) Gunn.

ID T,K T<TC B*

1 20U.OCG 0.6550 -3. 112

2 200. 000 C.6550 -3. 119

5 209.53I* 0.6363 -2.533

1 210. aoo 0.68 76 -2.817

2 210.000 0.6378 -2.817

<* 215. uOO 0.701*2 -2. 31*0 1 220.000 0.7205 -2.5«*2

2 220.000 0. 7205 -2.576

1 230.000 0.7533 -2.288

2 230.1jOO 0.7533 -2.31*3

5 238.769 0.7520 -1.972

1 0.7860 -2.095

2 aito.ooQ 0.7360 -2. 116

« 21*0. 000 0.73 60 -1.90 0 1 230.030 0.8188 -1.921*

2 250.000 0.8188 -1.91*1*

5 25'*.8Q7 0.831*5 -1.733

1 250. uO 0 0.8515 -1.759

2 260.000 0.8515 -1.786

1 270. JCO 0.83<*3 -1.611*

2 270.00 0 0.88W3 -1. 61*9

3 273.150 0.89<*6 -1.521

273.150 a.69<*& -1. 535

5 273. 150 0.d9<*6 -1.507

8 273.200 Q.89<*d -1.527

1 280. 000 0.9170 -1.1*70

2 280.000 0.9170 -1.511

2 290.000 \i,9k9& -1.1*08

3 298. 138 0.9764 -1.275

8 298.200 3.9766 -1.281*

2 30 0.000 0.9825 -1. 305

5 336. ii&2 1. 03 21* -1.201*

3 322.7«»8 1.0570 -1. 078

8 323.200 1.0585 -1.032

3 3'»7.652 1.1386 -U.916

3 372.522 1.2201 -0.781*

6 377.600 1.2367 -0.752

3 397.8!»i* 1. 3030 -0.671

8 1*10. 900 1.3W58 -0.616

3 (22.730 1.381*1* -0.576

6 (»(»<*. 300 1.4*551 -0.508

8 <»77. 600 1.561*2 -0.1*23

6 510.900 1.6733 -0. 350

CALC 0 IFF Id T -2.869 -0. 21*3 • 8» ^8

-2.869 - 0. 250

-2.609 0. 076 2. 93

-2.597 -0. 219 - 8. •»• -2.597 -0 . 219

-2.<*77 0. 137 C CO

-2.361* -0. 178 -7. 52

-2.361* -0. 212 a OTP - 8. 9r

-2.162 -0. 126 -5. 81* -2.162 -0. 181 - 8. 38

-2.005 0. 033 1. 63

-1.981* -0. Ill - 5. 61

-1.981* -0. 132 -6. 65

-1.981* 0* 085 1*. 26

-1.828 -0. 096 -5. 2o

-1.828 -0 . 117 •o. 39

-1.7 59 0. 026 1. 1*5 -1.688 - 0. 070 -1*. 17

-1.688 -0. 098 -5. 80

-1.561* -0. 051 -3. 23

-1.561* -0.085 -5. 1*3 -1.527 0. 006 0. 39

-1.527 -0. 007 -0. 1*8 -1.527 0. 020 1.33

-1.527 0. 000 0.02

-l.«*52 -0. 018 -1.25

-1.1*52 -0. 059 -1*. 09

-1.351 -0. 058 -i*.26

-1.275 0.000 0.03

-1.275 -0. 009 -0.71

-1.259 -0. 01*6 -3.68

-1.207 0. 003 0.27

-1.079 0. 001 0. 07

-1.076 -0.006 -0.60

-0.917 0. 002 0. 19

-0.781* 0. 001 0.09

-0.760 0. 008 1. 10

-0.671 •0. 001 -0.08

-0.619 0.001* 0.61

-0.576 -0.000 -O.Qi*

-0.505 -0.003 •0.69

-0.1*11 -0. 013 -3.09

-0.331 -0. 019 -5. 83

9 iim;* K- 13
1 Cryagww3[XvHion'NtSln«itwto for fciik Standards roojea mo. nu NO. PAM

LABORATORY NOTE 2750364 73-4 11

SUBJECT Ethane Virial Coefficients and Saturated Vapor Densities R. D. Goodwin

August 14. 1973

Table 1. Second virial data of (6) McGlashan, (10) Douslin.

ETHANE SECOND VIRIAL COEFFICIENT

E8 = 0. 250, TZ = 7i»0.i]

7.993156 -10.672'»97 9.217322 -2. '81668 0.8<f2328

PC NT

0.01

-0.01

-0.02

-0.01

0.01

a.02

0.03

0.03

0.02

•0.00

•0.0<»

-0.09

0.06

-0.08

-0.05

-0.06

0.08

0.10

0.16

0. 06

0. 10

-0. 08

-0.01

-0.27

-0. 19

-0.30

-0.02

0.53

T n T/ TC B* CALC OIFF

D X 7 U . U U U -5. 309 -5.310 0.001

co 1^ SV Ju .• Qu Qu Qu 0 .52 *£ -'•598 -'.597 -0.001

170.000 0.5568 -<. 031 -If. 3 30 -0. 001

6 180.000 C.5895 -3.56 9 -3.569 -0.000

6 190.000 0.6223 -3. 188 -3.188 0. 000

6 200.000 0.6550 -2. 868 -2.869 0.001

6 210.000 0.6S78 -2.597 -2.597 0. 001

6 220.000 0.7205 -2.353 -2.36'f 0.001

6 230.000 0. 7533 -2.161 -2.162 0.000

6 awo.uoo 0.7360 -1. 98'+ -i.gsif -0. 000

6 250.000 0.8183 -1.828 -1.828 -0.001

6 2&o.oao 0.8515 -1.690 -1.688 -0.002

10 273. 150 0.89'^6 -1. 527 -1.527 0. 001

10 298.150 0.9765 -1.276 -1.275 -0. 001

10 303. 150 0.9929 -1.232 -1.232 -0. 001

10 323. 150 1.058*^ -1.077 -1.076 -0. 001

10 3^8.150 1. 1!^02 -0. 91'* -0.91'^ 0. 001

IC 373.150 1.2221 -0.780 -0.781 0. 001

10 398. 150 1.33<^0 -0.668 -0.670 0. 001

10 if23.l50 1.3359 -0.57'^ -0.575 0. 000

10 kkd, 150 l.'^o78 -0.'^9 3 -0.'^93 0.000

10 W73.150 1.5i^96 -0.'^2 3 -0.i^22 -0.000

10 W98. 150 1.6315 -0.360 -0.360 -0.000

10 523. 150 1.7134 -0.30 6 -0.305 •0.001

10 5(*8.150 1.7953 -0.256 -0.256 -0. 000

10 573.150 1.8771 -0.212 -0.212 -0.001

10 598.150 1.9590 -0.172 -0.172 -0. 000

10 623.150 2.0!^09 -0. 135 -0.135 0. 001

NP = 29, MEASPCT = 0. 088

K-14
CiyogMiks Divition - hWS Institute tor Boac Stondordi LABORATORY NOTE

PIOJtCT MO. 2750364

nu NO. 73-4

PAOC 12

SUBJECT Ethane Virial Coefficients and Saturated Vapor Densities

R. D. Goodwin

August 14, 1973

Table 2. Second Virial, (1) Eucken, (2) Lambert, (3) Michels, (4) Hoover

(5) Pope, (8) Gunn.

PC NT

20 0. aCC 0.6550 -3. 112 -2.869 -0. 2<»3 -S.'tS

200.000 C.6550 -3.119 -2.869 -0.250 -8.72

2a9.53t» 0.6363 -2. 533 -2.609 0. 076 2.93

210.000 0.6878 -2. 817 -2.597 -0. 219 -d.<»'»

210.000 0.6378 -2. 817 -2.597 -0.219 -8.'»'»

10 T,K

125

1

2* 215. GOO

1 220.000 0.7205 -2.5«»2 -2.36*» -0.178 '"^'H

220.00 0 0. 7205 -2. 576 -Z.Zbt* -0.212 -8.97

230.000 0.7533 -2.288 -2.162 -0.126 -5.8^

230.ii00 0.7533 -2.3i»3 -2.162 -0.181 -8.38

238.769 0.7320 -1.972 -2.005 0.033 1.63

2

1

2

51 ZkQ.iiQQ

2 2i»0.000

I* 2<*o.oao

1 250.030

2 230.000

5 25'+.&07

1 250. uQO

2 260. jOO

1 27J.aOO

2 270.000

3 273,150

k 273.150

5 273.150

8 273.200

1 230.000

2 280. UOO

2 290.000

3 298. 138

8 298.200

2 300.000

5 336.ti62

3 322.7«»8

8 323.200

3 3'»7.652

3 372.522

8 377.600

3 397.8tti*

8 (»10.90U

3 '22.700

8 i*(»<f.30Q

8 «»77. 600

8 510.900

T / T P CA LC DIFF

0 . 6550 -i . lie —C .0 07 - 0 . 2<*3

r c C C n » 7 1 1 Q C . D 0 7 - 0. 250

r. c a £. 7 — C . P«> <5 t . 0 u ^ 0. 076

Q • Dt5 r o —c . 01 » -? .5 97 -0.219

— c . 01

>

-2 .5 97 -0 . 219

0 . 7 0 *<: — c . o** u -? .U77 0 , 137

u . 7205 — <: . 5** t - 0 • 178

— 5 (;7 P. C . *J V "T -0. 212

0. 7533 -2 . 28 0 _9 1 ft? —C .

X

U . A fc. v# 0. 75 33 -2. 3«*

3

—C . lOC U . X Q

0.7320 -1. 97 2 «5 n n K —c . u u 9 y • u «^

0 . 7860 -2 . oy 5 —i . 7 0 H - fl - 1 1

1

0. 7360 -2. lie — X . 7 O"* - fl . 132

0 • 7360 4 on n -1 . yo U 0I—X Q Alv . 7 0*» fl. Q65

0.8188 -1

.

•— X1 . A0 7ACO - 0 . 096

0 . 81 88 -1. y**"* ——X1 - A 7 ft . 0 c 0 - 0 . 117

0 . 83 <»5 _-1.4 7 7 1 f 0 0 —X .177 0.026

0.8515 4 7 C 0 -1. f^y ..1 —X .000 ft A A •0.070

C . 85 15 _-14 7 A C> . f 0 D 0IX .

ft A0 A0 - 0 . 098

0 . 8343 4 c 4 /> -1. 61 ** —X • 3 OH •0.051

0 . 88't3 - 1 . 6** 9 — 1 .5 0** - n . 0/15

0.89'*6 -1.521 —-1•1 R 57 . 5 fc f 0 .83i»6 d CYC -1. 535 ——1I . K9 t97f - n - 00 7

0 . 0'9'f b — 1 t>fl 7 -1.527 0. 020

Q.89<»8 -1.527 -1.527 0. 000

0.9170 -l.'*70 -l.<*52 -0.018

0.9170 -1.511 -l.«*52 -0.059

0.91*98 -l.'*08 -1.351 -0. 058

0.976** -1.275 -1.275 0. 000

3.9766 -1.28'* -1.275 -0. 009

0.9325 -1. 305 -1.259 -0. 0'*6 1. 03 2** -1.20** -1.207 0. 003

1.0570 -1. 078 -1.079 0. 001

1.0585 -1.082 -1.076 -0.006

1.1386 -0.916 -0.917 0. 002

1.2201 -0.78<* -0.78** 0.001

1.2367 -0.752 -0.760 0.00a

1.3030 -0.671 -O.o7l -0. 001

1.31*58 -0.616 -0 .519 0.00**

1.33'*** -0.576 -0.576 -0.000

l.'*551 -0.508 -0.505 -0.003

1.561*2 -0.**23 -0.«*11 -0. 013

1.6733 -0. 350 -0.331 -0.019

5.52

-5. 61

-6.65

**. 26

-5. 26

-6. 39

l.**5 -<. 17

-5.80

-3.23

-5. 1*3 0. 39

-0.<*8

1.33

0.02

-1.25

-*». 09

-**.26

0. 03

-0.71

-3. 68

0.27

0. 07

-0. 60

0. 19

0. 09

1. 10

-0.08

0.61

-0.0**

-0.69

-3.09

-5. 83

V nio* K-15
Oyoganics Divnion - NBS Instilufe lor Bo<k Stondards LABORATORY NOTE

PROitCT NO. 2750364

FILE NO. 73-4

PAOf

1 3

SUBJECT Ethane Virial Coefficients and Saturated Vapor DensitiesNAME R . D. Goodwin

August 14, 1973

Table 3. Third virial, (7) Chueh, (10) Douslin, (4) Hoover, (5) Pope.

THIRD y/IRIAL.

217.800 0.253773 0.865299 C. 556075 0.000000

ID T»K T/TCRT C* CA LCD DIP F

7 210. QQ 0 0.3878 0. 251 "0 . 247 -0.004

7 220.000 0.720 5 0.055 0 « 055 0.000

7 230.000 0.7 533 0* 2'*9 0 . 247 0.002

7 2(»D.uO 0 0.7860 0. 367 0 c 366 A A A 4 0.001

7 250. :i[tO 0.8188 0. 436 0.438 -0.002

7 260. ODD 0.3515 0. '72 0. 477 -0.006

10 273. 15D 0.39'*6 0 • <*o9 n OQ 0 • 4yy - U . U 1 U 10 298. 150 0 .9765 0. 500 0.489 0.011

10 30 3.150 0.9929 0. 491 0. 483 0.008

1 U 323.150 1.058** U . **> 3 U . *.70 U . II II >J 1 u 3(t3.l50 1.1<*02 u • **u ? U . *t X W U • W If A

1 n 373.150 1.2 221 0. 364 0 . 369 -0.004

1 n 398. 15D 1.30<*0 0 . 328 0 . 332 -0.003

1 n W23. 150 1.3859 Q. 295 0 . 299 -0.004

i n (»if8.l50 l.'*678 n « 268 0 . 271 -0.003

z.1 nu 1*73. 150 1.51*96 3. 250 0 e 247 0.002

1 u 1*98.150 1.3315 U . o a . ?27 U W W b

1 U 523.150 1.713<+ u . u 7 0.001* y • u II ^

1 U 5<f 8. 150 1.7953 n 1 QCi U . X 7? U . X 7 w 0U .. GU 0II ?^

1

0

573. 150 1.8771 u . xou nu .. 0u 0u c? lu 598. 150 1.9590 U a IDr u . Iw

O

U • U U X 10 623.150 2.3<»09 U. 19'* U • X7 f „ n . n fl »

U . H II •* NP -= 22* MEANOIFF = 0.00«*

ID T.< T/TCRT c* CALCD OIFF

5 209.531* 0.5863 2.770 -0.264 -2.505

k 215. 000 0.7042 3.356 -0. 079 -3.277

5 238.769 0.7820 0. 175 0. 354 -0.180

2(»0.000 0.7860 0. 121 0. 366 -0.487

5 25V. 807 0.33t*5 0. 401 0. 460 -0.059

5 273.150 0.69'*6 0. 489 0.499 -0.010

i* 273.150 0.89'*6 0.501 0.499 0.002

k 273. 150 0 .89i*6 0. 537 0.499 0.038

k 298. 138 0.976** 0. 507 0.489 0.017

5 306,062 1.102** 0. 473 0.479 -0.006

322. 7i»8 1.0570 0. 456 0. 453 0.0Q3

31*7.652 1.1386 0. 405 0.411 -0.006

372.522 1.2201 0. 364 0. 370 -0.006

397. 81*1* 1.3Q30 0. 330 0. 332 -0.002

1*22.700 1.38'*'* 0. 301 0. 300 0.001
Oyogank^ Oivnton- NK Inflitvte for Bcnk Stonclards LABORATORY NOTE

PROJECT NO. '750364FIIE NO. 73-4

PAoe

SUBJECT Ethane Virial Coefficients and Saturated Vapor Densities

NAME R. D. Goodv^in

"^^^ August 14, 1973

Table 4. Terins of the virial equation for saturated vapor.

TERMS OF THE tflRIAL EQUATION FOR SATURATED VAPOR

I » N

O ATM nuL / L U X /UN B*S C»S2 7 # T n 1 Q n fi n n ii n n Q Q n A n ii R n -1 7 U U U U u X •9 -0 .0C0Q0<i -0 .000 000 n QQQQQC. U . 777770

n •

(1

«

nU flU .1U n n U U ^3 n QqQQAT -0 .000011 -0 .000 000 n

U . QQQQAQ 7 77 7 07

1L 0V flV fii» U U U w X o u -0 .000028 -a .000000 nU . QQQQ7? 777 3 f C

1 n t> I U ^ ij • u

jii unu nu o7 ^7Ro

n QQ Q Q9 n • 0 .oCiO06<* -0 .000 000 U . 7 77 7 jD

L1 1 n Jl U U*UUU' CtJ< u •

fl n fi n 7 QQ H QQ Q A7 i -Q .000133 -0 .000 000 nU . QQaA(«7 7 77 O Of

.1 fiU nw flu X

I 7r O7?Ct1 QQ Q ^7

n

U . 77 7 Or u -0 .000 256 -0 .000000 n QOQ7^t<. U . 7 77 f Wa fl n T 7 1. Q ft ft QQ Q 7Q 12 U . 77 7 070 -0 .000'»62 -0 .000 000 n Q QQ C 7fl U . 7773

L c 7

n ii n 7 c n A u

JUOrouo U • n *i n £^ £^ Q o U • 77 0 7b 7 -0 .000787 -0 .000 00 0

(% Q QQ O 4 7

U . 777£ lO

L >J U

nU t n tl i 4 7 Q 7 U U 11 r ?d n QQ Q 7

0 . 77 8 OC 3 -fl .001276 -0 .000001 n Q Q A ^ 7 7. 778 1 CO

L O 7

n f\ o i z*. 7 a U* UccLoru JTl n ri O n fl £. 7 ft QQ 7 70*7

0 . 77 ( iHl -0 .Oul982 -0.000 002 ^\ Q Q a 11 4 C

U . 778 0 lb

i Ia Ci 1 1 U U «fl n 7 o c U U 3£bf

H

rt Qd C 4 4 Q 0 . 7^ O 11 7 -0.002961 -0.000005 rt Q Q7 n 7 /. fl . 77f U 34

n .T £L P C 7 7 fl U « 0 U 7l

1

rfl Q Q '3 n 3.77 **<: u -0 .0^^276 -0.000 009 fl QQC T 4 C Q . 773 r l7

1 7 U U • U7'>D97£. nu •

ii n 7 7 K fl A fi QQ 7 79 <l U « 7 7 C o »o «005991 u 9 u u u u X on QO 7QQi;i U . 77 J 7

flU a n 4 ! 7D n Q U X X <3 O U ^nU . Q70A Qli7 7Hf Q7 -0 .008171 -0 .000026 n Q ft n 7

1. D U U • U X O u o

n Qa fk < 7 U .700Xx>3 -0 .010682 -0 .000042 ft Q flQ n 77

LOW 4 * n ? 7 A 7 9 1 U C £0/ CX ini Q A 7 r A 7 -0 .01^185 -0 .000063 n a AC% 7 K7 U » 7 07 / 3C

U • X O C t O

n

u a A 7 1"! Q O C )C n Q 7 7 71. 7

U • 7f f -8 •0131^1 -0 .000 090 .1 Q A 4 7 & Q

U*9f r cccX 'I U a

fl 4 7 n 7 (1 Q7 1 A<k U . 7 f 1 OD D -0 .022806 -0 .000124 fl Q77 n 7n U .7» fUfU

I 0 U 0 a 0 « 9o Po2 5 -0 .028233 -0 .000164 0 . 9 f lb03

185 !• 022557 3 Oa 07 02692 0 .958606 -0 .03<»'»70 -0 .000 20 6

#1 <c e 0 #. 0 . 965324

1 • 32 f 9903 U a 0 8 9557 3 0 . 95 0 796 -0 ,041563 -0 .000246

Oa 11 2o577 0

•

9h 2 186 -0 .0<t9 554 -0 .OQ0251 0 . 790 1 b4

•* rt n

£ 0 0 2* 1>»38735 Qa l<*005u3 0 .932771 -0 .0 581*8 5 -0 .0 30 29 9 0 . 941 2 17

? f) c Clio 2 • br SQ9r 3 Oa 1722'*9'* 0 • 92 25h1 -0 .066 395 -0 .000287 A Q 7 4 7 4 0 U . 9 31 318

c 1

U

. tU < •3 .1 Q Q fl O 7 2u you 0 . 91 1 »*8 H -0 .079325 -0 .000230 ft Q 7n ii /aC

i. X 3 U a £9 C:3 a<3 77 7a

4 Q X

7

n AQ a RA 7 U . 0 7 7 PO J -fl .091321 -0 .000107 nU.7U03rX Q n ft R 71 £20 0. 303«»770 0 .886826 -0 .104432 0 .000108 0 .895676

225 5. 8193516 Oa 3609763 0 .873177 -0 .118715 0 .000 448 fl .881732

23U 6. 91361C 8 a< <»266509 0 .858605 -0 .134238 0 .000952 0 .866714

235 8. 1518573 0, 501*»34»7 0 e8<»3069 -0 .151085 0 .001671 0 .650586

2kQ 9. 5 '•9551 586<»036 3 .826523 -0 .169358 0 .002667 0.833309

ikS 11. 10<»0336 a, 0 .808912 -0 .189185 0 .004017 0 .814632

250 12. 8<*05&ii3 0. 7921552 0 .79017'* -0 .210 72 5 0 .005816 0 .795093

255 I'*. 76635S8 Oa 9162120 0 .77Cl2'»0 -0 .234180 0 .008194 0.774014

260 16. 89375!t2 1. 0571595 0 .7'»9Q33 -0 .259604 0 .011305 0 .751500

265 19. 2356771 1. 2176851 0 •726'i66 -0 .287 92 5 0 .015361 0.727436

270 2l.8056i»75 1. <*0116<»1 0 .702'«<*0 -0 .318 963 0 .020642 0.701679

275 2<*. 619a2(»9 1. 6119133 S .676839 -0 .353469 0 .027531 0 .674063

280 27,6913739 li 8555713 0 .6<i9528 -0 .392177 0 .036563 0 .644386

285 31.0l»102S3 2..1396901 0.620339 -0 .436086 0 .048505 0.612418

290 3t».68903i»5 2. «»7^7097 3 .589059 -0 .486600 0 .064498 0.577898

295 38.6511522 2. 8756823 0 .555393 -0 .545771 0 .086320 0.540549

300 '2.9921502 3. 3657'»09 0 .518891 -0 .616 618 0 .116916 0.500098

30 5 '7.7<»itl963 3,.985933<» 0 .'*78608 -0 .705645 0 .161805 0.456160

vt 1134; I K-17
! Cryogenics Oivnion - NBS InsHlvte tor Btnic Standards

' LABORATORY NOTE

I nx>xcr NO. 2750364

nu NO. 73-4

PAOt 15

SUBJECTEthane Virial Coefficients and Saturated Vapor Densities

NAME ^ , . K. D. Goodwin

August 14, 1973

Table 5. Saturated vapor densities derived via V. P. and virial equations.

ETHANE SATD. VAPOR DENSITIES VIA V.P. AND VIRIAL EQNS.

ID

11

1111

1

11

1

111

1

11

11

1

11

1

11

1

11

11

1

11

111

1

11

11

1

1

as. b99

30,000

95.003

100.000

105.000

110.000

115.000

120.000

125. 000

130.000

135.000

lt*0. 000

IffS. 000

150. 000

155.000

160.000

165.000

170.000

175, 000

180.000

1S5, 000

190,000

195, 000

20 0,000

205, 000

210,000

215.003

220, 000

225.000

230,00 0 235,000

2W0, 000

2k5, 000

250,000

255,000

260, 000

265.000

270,000

275,000

280.000

285.000

290. 000

P, ATM

9.9670-006

1. 0236-005

3.5806-005

1.0952-00t»

z.gdsi-oot*

7.365i»-00U

6670-003

'991-003

8762-003

2752-002

2^+68-002

763'+-002

6, 1192-002

9.5'*7d-002

1 .''26- 001

2. 1176-001

3.0 288-001

4+. 2317-001

5.7882-001

7662-001

0239+000

3287+000

6991+000

l'»'»0 + 000

6726+000

29'^3 + 000

0186+000

8561+000

5.6165+000

6.9105+000

8.1'+87 + 000

5'^20 + 000

1102+001

2839+001

'766 + 001

6695+001

9238+001

1310+001

2. '+62'^ + 001

2.7697+001

3.10t^7+001

3. '693 + 001

PLANK/KAMB

1 .3511-006

1 .3863-006

«. 5936-006

1.33«^7-005

3.'^6*^9-005

8.1615-0 0 5 l,7671-00'^

3,5558-D0'+

6.7110-00'^

1 . 197'+-003

2.0336-003

3.306'^-003

5.1721-003

7 ,818'^-003

1,1'^6'^-002

1.6358-002

2.2781-002

3.10'»2-002

',l'^79-002

5. * '57-002

7,0369-002

8.9635-002

1 .1271-001

1 .'006-001

1,7222-001

2,0973-001

2,5321-001

3,0331-001

3,6077-001

'.26'^2-001

5,0120-001

5.8618-001

6.8262-001

7.9203-001

9.1618-001

1.0572+000

1 .2179 + 000

1. '016 + 000

1.6125+000

1 . 8563+000

2.1'^0'+ + 000

2. '^75'+ + 000

MOL/L

1,3511-006

1 ,3663-006

'.593 6-006

1 .33'+7-005

3 ,'^6'^8-005

8,1612-005

1 .7670-00'+

3.5552-00'^

6 ,7093-00'^

1 .197 0-003

2.032 3-003

3,3033-003

5.165 3-003

7 ,80'^3-003

1 .l'^36-002

1 .6308-002

2 .269'^-002

3 .0899-002

'.1252-002

5 .'11 1-002

6.966 0-002

8 .891 1-00 2

1 .1171-001

1 .3672-001

1 .70'^ 7-001

2.075 0-001

2,50'^3-001

2,999 3-001

3.567'^-001

.2173-001

,9585-001

5.8025-001

6,762 6-001

7,8551-001

9.0997-001

1.0522+000

l,215'^+000

1 ,'01^1+000

1 .62'+5+000

1.8861+000

2.20'^7+000

2.6108+000

PCT

0.00

0.00

0.00

0.00

0.00

0.00

0.01

0.01

0.02

O.QJ^

0.06

0.09

0.13

0.18

0 .2(»

0.31

0.38

0.(f6

0.55

0.6'*

0.73

0.81

0.89

0.97

1.03

1.08

1.11

1.13

1.13

1.11

1.08

1.02

Q,9i*

0.83

0.68

0 .'S

0.21

-0.18

-0.7'^

-1.58

-2.91

-5.19

V 1114? I K-18
CryoQefiics Divisfon — NftS Ifistituto for Bosk S^orKiofcis LABORATORY NOTE

PROJECT NO. 275036^

FILE NO. 73-4PAOf 16

SUBJECT Ethane ^-'irial Coefficients and Saturated Vapor DensitiesNAME R. D. Goodwin

August 14, 1973

PROSRAM VIRUS

£THflvJE VIRIAL COEFFICIENTS, X = T/TCRT, Q = X»»l/2,

3V = (31 + 32/X*»£B B3/X B5/X3 ) • ( 1- ( TZ/T ) )

.

:v = (C1/X»*EC C2/X3 * C3/X5)* (1-TZ/T) . ID, (DEUGKEN, t2)„AMBERT, (3)MICHELS, («*)HOOVeR, (5)P0PE,

(6)M:GLASHftN, (7)3HUEH, (8)GUNN, ( 10 ) OOUSL IN , PREPR INT.

>/CRT,CC/MOL, R0SSINI(1953) /MCGLASHAM=1'»8, EU 8ANK/P0PE=1«*6. 2«

T£STER( 1961) =1^1.7, DOUSL IN (1 97 3 ) =1 <»5 .56.

COMiON/l/*1,£B,EC,TZB,TZC, BVS,CVS, B(5),C(«»)

COM^ON/3/ OPSOT

C0M10N/999/NP,SF, H(15) ,Y( 200), 5(200, 15)

DIMENSION 10(200) ,T{203) ,BV(200)»CV(2Cfl)tX(20G) ,XQ(200)

1 F0RiAT{I5, 2F1U.J)

2 FOR^ATdHl 13X IHM 5X5H£(BC) 8X2HTZ 8X2HSS)

3 FORHATdOX 15, 2F10.3, FlO.**)

k F0R-1AT(1H1 17X ^ETHANE SECOND VIRIAL COEF F I CIENT* //

1 leX'+HEB =F6.i, 5H, TZ =F6.1// 15 X 5F12.6//

2 18X2HI0 7X3HT,< SX^HT/TC 7X2HB* 5X<+HCALC 5X<»HDIFF 5X<*HPCNT)

5 F0RiAT(l5X 15, Flu. 3, -g.'*, 3F9.3, F9.2)

6 F0R*1AT(1H117X»THIR0 VIRIAL, M =»I2, 6H, EC =F6.3// 16X FlO.3,

t 'Fll.6// 16X2HIJ 7X3HT,K 'X6HT/TCRT eX2HC» 5X5HCALCD 6Xf»H0IFF ) 7 F0RiAT(l5K 15, F1j.3, ~10.'», 3F10.3)

8 F0RiAT(18X i*HH? =13, 12H, MEANDIFF = F7.3)

9 F0RiAT(18X kHHP =13, IIH, MEANPCT =F6.3)

10 FORiATdHl l3X»TERMS OF THE VIRIAL EQUATION FOR SATURATED VAPOR*//

1 17<3HT,K 7X5HP,ATM 7X5HMOL/L 5X5HDI/DN

2 7X3HB»S bX*+HC»S2 ^X6HZ(T,0) ) 11 FORMATdOX Fia.O, 2F12.7, 'F10.6)

12 FORiATdHl 17X 2iID 7X3HT,K 5Xi»HT/TC 7X2HB* 5X<»HCALC

L 5X!»HDIFF 5XitHPCNT)

13 FORiAT(lH117X2HI0 7X3HT,K «»X6HT/TCRT 6X2HC* 5X5HCALCD 6Xi»H0IFF)

15 TTR' = 89.899 5 TCRT=305.33 $ DCRT= 1 . 0 / l'*5. 56

GENERATE MC3LASHAH DATA FOR BV(T), C3/M0L.

INCREASE A8S (MC&LASHAM) BY ONE PERCENT d'»8/l'*5.56 = 1.017).

16 N = 0 $ DO 19 J = l,i2 B N = N + 1 $ TT = T (N) = l«f0 10»J

17 X(N)=TT/TCRT $ X 3 ( N ) = S^RT F ( X ( N) ) $ IO(N) = 6

18 3V(M) = 1.01»GLA3F(TT) $ Y (N) = 8V(N>»0CRT

19 CONTINUE

READ OOUSLIN (1973) DATA, CC/MOL.

20 DO 23 J = l,99 $ READ 1, ID0,TT,3B $ IFdDO) 21,2'*

21 N = N+1 B IO(N)=IDD $ T(N)=TT S BV(N)=BB

22 X{N)=TT/TaRT $ X 3 ( N ) =SaRT F ( X ( N) ) $ Y{N)=3B»0CRT

23 CONTINUE

2'» NP = N $ NF = 5 $ SSK = l.OE+010

READ SECOND VIRIAL DATA.

25 DO 28 J=l,99 B READ 1, IDD,TT,BB $ IF(IOD) 26,29

26 N = N+1 B IO(N)=IOD B T(N)=TT $ BV(N)=BB

27 X(N»=TT/TCRT { X 3 ( N) = SSRT F ( X ( N) ) $ Y(N)=3B»DCRT

28 CONTINUE

29 NPP = N B H - Q ^ EXPLORE VALUES FOR EB AND FOR TZB.

MCGLASHAM TZB NEAR 2.7»TCRT = 82** K. 30 EB = 0.25 $ TZ = TZB = 7<»0 $ PRINT 2 31 DO IE=1,3 B EB = 3.25»IE

32 DO IT = 1,17 S TZ = 6^0 1Q*IT

K-19
Cryogsnks Dnoaon - NIS bulitvle for Bcnic Standards LABORATORY NOTE

rtoxci NO. 2750364FILE NO. 73-4PAOE 17

SUIJECT Ethane Virial Coefficients and Saturated Vapor Densities

NAME „ ^ ^ , . R. D. Goodwin

August 14, 1973

SS = 0 00 38 K=1,NF

$ SS = 100»SS/NP

33 DO 36 J = 1*NP $ U = X(J) $ Q=XQ<J) $ H = 1-(TZ/T(J)1

31* G(J,1) = M $ G( Jt 2» =W/U^»EB $ G(J,3)=W/U $ G ( J.^t) =W/U**2

35 G (J,5)=H/U*»3

36 CONTINUE 5 CALL EGENFT I 37 00 39 J=1,NP i YC = a $

38 YC = YC H (K) »G( J»K)

39 SS = SS + ABSFtYt J)/YC-1)

<*0 IF(SS.LT.SSK) <*i^ki*

<! SSK=SS i EK=£9 $ TK = TZ $ 00 K=l,5

kZ 8(K) = H(K)

t*k PRIHI 3, M,£B,TZ,SS $ EB=EK $ TZ = TZB=TK $ SS = fl C JSE SAVED CONSTANTS FOR DEVIATIONS.

k5 PRINT E8, TZ, (B(K),K=1,5)

kb 00 51 J=1,NPP { U=X(J> $ Q=XQ(J) $ W = 1-(TZ/T{J))»»0.25

k7 YC = W»(B(l) B(2)/U*»EB B(3)/U * B(<*)/U»*2 B(5)/U»»3)

kQ OIF = Y{J)-YC $ PCT = -1&0»DIF/YC $ SS=S S+ABSF ( PCT)

1*9 PRI^<T 5, 10 (J> ,T ( J) ,X (J) , Y(J) ,YC, OIF , POT $ IF(J-NP) 51,^50

50 SS = SS/NP $ PRINT 9» NP,SS $ PRINT 12

51 CONTINUE $ N = U C SENE^ATE THIRD VIRIAL DATA VIA CHUEH(1967), 10 = 7.

C DIMimSH CHUEH DATA BY 2 PERCENT.

52 DO 55 J=lt6 i H - N+1 $ TT = T(N) = 200 + 10*J

53 X (N> =TT/TCRT $ XQ (N) = SaRTF(X (N) ) $ ID(N) = 7

5<» CV(M) = 0.98»GHUCF(TT) $ Y (N) = CV ( N) 0CRT»*2

55 CONTINUE $ K = N + 1 C READ D0USLIN(19r3> DATA, (CC/M0L)»*2.

56 00 58 J = K,99 $ READ 1, 10 ( J) t T{ J) , GV( J» $ IF(IO(J)) 57,59

57 X { J) =T( J»/TCRT $ XQ ( J ) = SQRTF (X ( J) » $ Y ( J) =C V ( J) 0CRT»»2

58 CONTINUE

59 NP = J-1 $ NF = 3 $ SSK = l.OE+010

C ^EAO THIRD VIRIAL DATA. TZC NEAR 220 K.

60 K = NP+1 $ DO 63 J=K, 99

61 REA3 1, IQ(J) ,T(J) »CV(J) $ IF(ID(J)) 62,6'»

62 X(JI = T(J)/TC?T $ xa(J)=SQRTF(X«jn 8 Y ( Jl =C V ( J) OCR T» 2

63 CONTINUE

6i» NPP = J-1 S EC = 1.0 $ PRINT 2

C EXPLORE VALUES FO? EC AMD FOR TZ.

C 65 DO rb lE = li'* t EC = 3.5»IE

$ TZ = 217.60 + a.05»IT

U = X{J) $ M = 1-TZ/TCJ)

$ G(J,2) =W/U*»3 $ G(J,3) =H/U»»5

$ SS = 0 $ 00 71 K=1»NF

$ SS = SS/NP

66 DO 76 IT=ltll

67 DO 39 J=1,MP

68 G ( J,1)=W/U**EC

69 CONTINUE $ CALL EGENFT

70 DO rz J=1»NP $ YC = 0 71 YC = YC H(K)»G(J,K)

72 SS = SS ABSF <Y ( J) -YC)

73 IF (SS.LT.SSK) 7!*, 76

7k SSK=SS $ TK-TZ $ £K = EC $ MK=M B 00 75 < = ! f < 75 C (K) = H (K)

76 PRIMT 3, M,EC,TZ,SS $

77 TZC = TZ = TK $ EC = EK

USE SAVED CONSTANTS FOR DEVIATIONS.

79 PRIf^T 6« H,EC,TZ, ( C ( K) , K = l

,

80 DO 85 J=1,NPP S U = X(J) $ W = 1-TZ/TCJ)

81 YC s W»(CC1)/U»»EC C(2)/U*»3 + CC3J/U»»5>

82 PCT = YCJ)-YC « SS = S5; * ABSF(PCT)

7/26/75

M = MK

$ SS = Q

K-20
Cryogenics Drmion - lf»fitu+e for Bo»ic !0on6or6i LABORATORY NOTE

MfOJtCT HO 2750364wie NO. 73-4 18

SU EJECT Ethane Virial Coefficients and Saturated Vapor Densities R. D. Goodwin

Aufeust 14, 1973

VIRUS ' 37/26/73

83 PRINT 7, ID ( J) t T ( J) ,X ( J) , Y( J) , YC» PCT $ IF(J-NP) bS^dk

8i+ SS = SS/NP S PRINT 3, NP.SS $ PRINT 13

85 CONTINUE

Z ^OW iXA'ilNE Tcl^S OF THE VIRIAL EQUATION AT SATURATION.

C THE IDEAL 5AS DENSITY IS DI = P/ (R»T)

i

90 PRI'^T 10 S 00 95 J = ljkk $ TT = 35 5»J

91 PS=^SATF(TT) $ DN=DN&SF(TT) $ Z = ZIPF(TT,DN)

92 01 = PS/TT/Q. u323 56156 $ DR = DI/ON

95 PRI^^T 11, TT,PS»DN, DR, BVS,CVS, Z 99 ST03 S ENID

SINGLE-BAnJK GOHPILATIO?^ .

fun:tion 3hucf(T)

z etha'^e third virihl via chueh form ul a ( 1967 ) » (cc/m0l)**2.

c :v (t) /vcrt»»2 = fa*fb + fc , fa = a/cj + b/x5,

c -b = 1 - exp (1-al*x2) , fc = exp(-c + d»x - e*x2), x = t/tcrt.

DAT4 (TCRT=30 5. 33 ) , ( V CR T = lif 5 . 56 ) , (AL = 1.89)

DATA (A = C.2 32) , ( 8 = C .'63 ) , (C = 2.'t9) , (0 = 2.30 ) (E=2.7 0)

1 X=T/TCRT $ Q=SaRTF{SQRTF(X)) $ X2=X**2 $ X5=X»^5

2 FA = A/a + B/X? S FB = 1 - EXPF (1- AL»X2

)

3 FC = EXPF(-C D*X - £»X2)

k CHU:f = (FA»FBfFC ) *VCRT»»2 $ RETURN $ END

FUNCTION DNGSF(T)

C 3LAN</KAMBEITZ VIA TESTER (P.171)/DIN. VALID 17 0 TO 305 K.

C V = l*J/P - Ci/X»^A - C2*P»»2/X»*B, X = T/IOC,

C a IN CC/GRAM, T IN KEH/INSt P IN KG/CM»»2,

: 1 ATI = 1,03323 K5/CM»»2, R=2.322, Cl=69.0, C2=27.9, A=2.W, Bs9.0

DATA (R = 2. 322), (31 = 39. 3) ,(02=27.9), (A =2.'*), (B=9.0 ) , (HM=3 0 .0 7)

1 P = PSATF(T) 5 P = 1.03323*P $ P2 = P»»2

2 X = T/lOO $ XA = X*»A S XB = X»*

B

3 V = R»T/P - :i/XA - C2*P2/XB

it DNGSF = lOOO.dS/V/WM $ RETURN $ END

9 nici K-21
Cryogenics Division - NBS Inslilute for totk Stondordt

! LABORATORY NOTE

nrojtCT NO. 275036'^PttI NO. 73-4 19

SUBJECTEthane Virial Coefficients and Saturated Vapor Densities

^^'^ R. D. Goodwin

August 14, 1973

fun:tion glabf(T)

C ethane second tflRIAL COEFF. VIA MC GLASHAM FORMULA (1962).

C G. BELIEVES EUCKEN/P4RTS ARE WRONS.

3 3V{T)/VCRT = 31 - B2/X - B3/X2 - Bi*/>l**h,St X = T/TCRT,

DAT4 (TCRT = 30 5.'»» (VCRr = l'f8.0)

DAT* (B 1 = 0. ifSfl) ,(82 = 0.886 >* (B3=0.69«») , (B'» = 0 .0375)

1 XsTiCTCRT $ X2 = K»»2 $ X^ = X**k»5

2 F = 31 - B2/X - 93/X2 - Bi»/XN

9 &LA3F = VCRT'F $ RETURN $ END

07/26/73

FUNCTION PSATF(T)

C LN(P/PTRP) = A*K * B»X2 C*X3 0»X*» + E» X* (1-X ) £?.

COMHON/3/ DPSOT

DATA (TTRP=89.8 99) , ( TCR T= 305 . 33 ) , ( PT RP=9. 61 6E-6) , (EP*1.6)

DATA (A = 8.'»5'»98 73^'+) . (B = 12.'»880 39 775 ) , (C=-'» . lO'* 28 1551 ) ,

L ( 0=-l. '13860533 ) , (£=8.52 6522526)

1 FORiATdHa 9X »PSATF = 0, T EXCEEDS TCRT. / ) 2 XN = l-TTRP/TCRr $ X= (l-T TRP/T) /XN $ X2=X»»2 $ X3*X»»3 $ Xk-X****

3 OXOT = TTRP/XN^T»*2 $ Q = 1-X $ IF<Q) ',5,6

k PSATF = DPSOT = 3 $ ^RINT 1 $ RETURN

5 Z = Zl = 0 $ G3 TO 7 6 W = Q»»£P $ Wl = -EP*H/Q $ Z = X»W $ Zl = W X»H1

7 F = A*X B»X2 C*X3 O^Xi^ + E*2

8 Fl = A 2»B»X 3*C»X2 + 'D*X3 E Zl

9 PSATF=PTRP»EXPF(P) $ OP SO T=F1»PSA TF» OXOT $ RETURN $ END

07/26/73

FUNCTION ZIPF(T,D)

C Z(T,3) = 1 * BV(T)*S :V(T)»S»»2, S = 0/OCRT, X = T/TCRT,

C BV = (Bl B2/X»»EB B3/X B'*/X2 B5/X3 ) (1- ( TZ/T) •!/') • C :V = (C1/X»»£C f 32/X3 C3/X5) (1-TZ/T) . C0Mf10N/l/i,EB,EC,TZB,TZC, BVS,CVS, B(5),C('^)

DATA (TCRT = 305. 33) , (VCRT = 0.1'+556)

1 S=D»VCRT S X=T/TCRT $ Q=SQRTF(X) $ R=X»»EC

2 X2 = X»»2 $ X3=X»»3 $ X'*=X*»'^ $ X5=X»»5

3 ZB = 1 - (TZB/T) •0.25 $ ZC = 1 - TZC/T

k 3>J = ZB»(B(1) B{2)/X»»EB 6(3) /X B(i^)/X2 B(5)/X3)

5 CV = ZC»(C{1>/R C(2)/X3 C(3)/X5)

6 BVS = BV*S $ CVS = CV»S»*2

7 ZIP- = 1 BVS CVS $ RETURN $ END

K-22
Cryogxws Divnion - N8S InctHuto (or fiotic Siondordt LABORATORY NOTE

PtOJfCT NO. 2750364nu HO. 73-4 20

SUBJEa R. D. Goodwin

Ethane Virial Coefficients and Saturated Vapor Densities August 14. 1973

07/26/73

C F.THAN: SATy/at3Qi<0EN VIA V.P, AND \/IRIAL EQNS.

C Ori ISJTHcRMS, IThKATt OEN IN VIRIAL EQN. TO MINIMIZE (P-PSAT).

C3IM:;J/3/ DPSuT

1 (- J-<.^;r(liX ^ETHf.NE SATO, 7AP0i? DENSITIES VIA V.P. AND VIRIAL EQNS.

1 *//LtiKdHID 7X3hT,K 7X5HP,ArM 2 X 1 OHPL ANK/KA MB 7X5HM0L/L 7X3HPCT)

2 F0<MAl(i5X 15, FlQ.3, 3Ei2.it, F10.2)

3 FJ-4MAT(I5, FIG. 3, 2£15.5)

1^ ID = 1 i TT-^3 = 39. 393 $ PRINT 1 2G 00 3J J=l,42 i IF{J-1) 23,22

22 T - rr<P i GD TO 2'+ 23 T = .iU + 5»J

2^ JI = JNGSF(T) * P = PSATF(T) f DEN = FI NOF ( T , P, 01

)

2b PUNCH 3, 1D,T,JEN,P

27 Uir = DI-DEN I PCT = iOO*OIF/OEN

2d F<i.JT 2, 10, T,P, 01, JEN, PCT

30 C)--ITlr-iJJ ?; i,TDP S END

SihJG-E- 3AN< COMPILATION.

FU>lCTiOW FI'nIDF( r ,P,'JI)

C ON ISOTHERM T, ITERATE DEN TO MINIMIZE (P-PCALC).

CJ-iMJN JZDS

OaT; (3K = 0, 062056156), {VC^T = 0,lit556)

1 rO-<-^AT(lH0 S)X *FINDF = Q, FAILS TO CONVERGE.* / ) 2 J = JI i GT = GK»T S 00 9 J=l,50

3 Z = ZIPK(T,0) PC = O'-GT^Z J DP = P-PC J AP = AeSF(OP)

^ v4 = AP/P-l.OE-6 t If IV 10,10,5

5 UPJO = GT*(Z + 0*0Z3S*VCRT) t ADP = ABSF(DPOD)

6 u = AP/ADP/O-i. Ox-6 I Ir{Q) 10,10,7

7 0 - 0 ¥ OP/JPOO S IF(0) 8,8,9

6 D - P/r/GK

i OONTiNJE S FINDF = 0 J PRINT 1 $ RETURN

10 FIJJF =0 * RETJRN S END

IT IllOt K-23
1 Oya0M)ks Divnion - NSS ImMwta tor Bonk Stondordt

1 LABORATORY NOTE

nOJfCT NO. 2750364nu Na

73-4 21

SUBJECT Ethane \ irial Coefficients and Saturated Vapor Densities R. D. Goodwin

August 14. 1973

FU''(CTIO-J O^J&SF(T)

C Pu AiU/K^ ^flEI rZ \/IA TZSrtR.

DATA (^ = 2.52^),('^l = i9.0),(C2 = 27.9),(A = 2.^), (I8=9),(WM = 30. 07)

1 P = 1.03J23*PS4TF(T) S ^2 = P*»2

= 1/100 T. XA = X«-*A i X3 = X**IB

.Si/ - ^*T/P - Sl/xa - C?»P2/XB

1+ DNGSF = 10 0 0 . 88/ V/W.'l « RCTURN S FND

08/01/73

FUNCTION PSATF(T)

Z lN(P/PTRP) = ft»X * 8»X2 C»X3 0*K(* + E»X» (1-X ) COMMON/3/ OPSOT

C :ONSTANTS VIA ZliGLER TYPE B V.P. OATA«

DATA (TTRP=a9.a99)»(TCRT=305.33), ( PT RP=9e 96 7E-6 ) , (EPsl.5)

DATA (A = 10. 806922651) , ( B= 8. 3'*<+7 1593 8) , <C=-3 . 11960 3823)

DATA (0 = -O.6l^995191^ , (E = 6. 0 59966 098 )

1 FORMATdHO 9X »PSATF = 0, T EXCEEDS TCRT. / ) 2 XN=l-TTRP/TCRT B X = ( 1 - TTRP/T ) / X N S X2=X**Z $ X3=X»»3 $

3 OXDT = TTRP/XN/T»*2 $ Q = 1-X $ IFCQ) '»5t6

PSATF = DPSDT = 0 $ PRINT 1 $ RETURN

5 Z = Zl = 0 S GD TO 7 6 W = Q*»EP 5 = -EP»W/Q $ Z = X»W $ Zl = W X»H1

7 F = A»X B»X2 C*X3 0*Xi» < £»Z

8 Fl = A 2»B»X * 3»C*X2 'X3 E*Z1

9 PSATF=PTRP»£XPF(F> S DPS D T=F 1 ^P SA TF» DXD T $ RETURN $ END

FU >ICT13.^ ZIPF (T , D)

7(7, J) = 1 * UV(X)»S + C\/(<)*S**2.

ii\J - (Lil t 32/J i3/X + B'+/X2 + B5/X3)* ( 1- ( TZB/T) »*1/'*) . - (Cl/x f :2/Xj + C3/X5) * ( l-TZC/T) . Coi.-IJN i3/0S IJAIA (ro.vT-?0^j.J3),{\/:RT = ').l'+'j5b),(TZB=7'+0.C),(TZC=217.8),

1 ( 11^ z'. '9 J31 56) , (82 = - 10 .6 72'49 7) , (8 3 = 9. 217 322) , (B i4=-2 . 8 1 66 8) , 2 (J 5=0. 3i4232tt),(Cl = 0, 253773), (02=0.865299) , (C3= 0 . 5560 75 )

1 l. = J»\/Gr<T y X^l/TG-^T J Q = X»*0.25 S X2 = X»*2 I X3=X**3 J X5=X»»5

2 Zj ^ 1 - (TZ3/r)"0.25 J ZC = 1 - TZC/T

i L.v/ - ZJ»(M1 f JZ/U « U/X + Ui+/X2 + 85/X3)

ol/ = Z3»(C1/X * C2/X3 + C?/X5)

o ZIPF = 1 + B\/»S + Cy»S»*2 i DZDS = 8V + 2*Cv/»S

K-24 USOOMI ' UU.
APPENDIX L

L-1
Cryogenks Division - NBS Institute for Basic Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5

PAGE

1 SUBJEa The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R. D. Goodwin

Sept. 18, 1973

1. Introduction.

These densities, and accurate analytical descriptions thereof, are essential

for the computation of thermodynamic functions, in particular to obtain heats of

vaporization via the Clapeyron equation, and to formulate the equation of state which

originates on this locus [4].

We have had difficulties in representing the available ethane data, and therefore have returned to fundamentals. For comparison we shall include oxygen [18],

fluorine [13], and methane [4]. Previous formulations occur in [4, 7], We start with

the saturated liquid densities because their representation is much simpler than that

of the saturated vapor densities.

2. The Saturated Liquids.

It is well known that these densities are described near the critical point by the

form

p = p + a • (T - T) + b . (T - T)^ (1) c c c

wherein the first two terms are the rectilinear diameter, and the exponent is near

e =0.35.

Let us constrain (1) at the boundaries by use of the variables,

x(T) H (T^ - T)/(T^ - T^), (2)

W(p) = (p - p etc )/(p^ - p ), (3)

where subscripts c and t refer to critical and triple points. Equation (1) now

becomes,

W(p) = a • X + b . x*^, (4)

and the constraint requires that a + b = 1. If we solve this for the constant b, we may

expect to obtain a function Y(p,x) which is nearly constant over the entire range

0 < X < 1,

Y(p,x) = [W(p) - x]/(x" - x). (5)

This sensitive function is useful for examining data.

In past work we found that three arbitrary coefficients are required to describe

saturated liquid densities. We now find the following results via many exploratory

computations. For the smoothed data used here for oxygen and fluorine, the use of

five arbitrary coefficients gives an improvement in the "fit". For the rough experinaental data used here for methane and ethane, the use of five arbitrary coefficients

gives virtually no improvement in the "fit" as compared with only three coefficients.

With only three, the first equation used was,

U 11342 « L-2
OryoQcnics Division — NBS Institute for Bosic Stondords LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5PAGE 2

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME K . D, Goodwin

Sept. 18, 1973

Y(p,x) = A^ + A^ . X + A^ . X , (6)

and we found exponent cc = 4/3 for oxygen, fluorine and methane, but a = 8/3 for

ethane. After much exploration we have selected the following representation,

2/3 Y(p,x) = A^ + A^ . X + A^ • x (7)

Table 1 gives the fixed-point constants. Table 2A gives the exponent e found

by trial, the least- square s coefficients, the rms of relative density deviations in

percent, and the number of datum pairs, NP.

Tables 3, 4, 5, 6 compare calculated with experimental densities. No

temperature- scale adjustments have been made in present work. Column YX gives

the experimental value of Y(P,x) via (5), whereas column YC gives the value calculated

by the right side of (7). Table 7 compares ethane data not used for least squares.

Tables 8, 9, 10, 11 give saturated liquid densities computed by (7) at uniform

temperatures, and also their slopes and curvatures.

The small deviations for oxygen and fluorine necessarily are systematic because the data were smoothed by the authors. The overall methane deviation is large

be cause experimental data from various sources are included in the critical region.

The low-temperature ethane data of Miller were used to estimate the triplepoint liquid density. Other data are from Canfield et al. , and from Klosek/McKinley

.

The high-temperature "data" of Eubank are a correlation of available experimental

data down to the boiling point 184.5 K, (x -- 0.561). We estimate uncertainty in our

calculation of these densities to be about 0. 1 percent over the entire range.

Concerning assignment of critical densities, we at first found both and

exponent simultaneously by trial to minimize the overall deviation. The results are rough because these two parameters are mutually compensating for data in the critical

region. Hence we have adjusted >: one step at a time for both saturated liquid and

saturated vapor, examining the values of s found by trial. We select that value of p (- which yields reasonable exponents for both liquid and vapor. For methane it thus

is necessary to select ^= 10. 2 mol/-f , at the upper limit of uncertainty in the experimental values [4].

3. The Saturated Vapors

^6 Densities of the ethane vapors range thru a factor of about 10". We have given reasons for using the logarithm of vapor densities, with arguments in powers of

(1/T), [7]. Define the normalized variables

z(T) = (T /T-1)/(T /T - 1), c c t W(p) = In (p /p)/'tn(p /P J.

c c t

(8)

(9)

L-3
Cryogenics Dimion - NBS Institute for Basic Slondords LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5

PAGE 3

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

R . D . Goodwin

Sept. 18, 1973

We write the vapor densities equation for the critical region as follows,

-W(p) = (b-1) . z - b . z*" (10)

whe rein the minus sign on the left arises inerely from our definition of W^(p). Solving

(10) for b yields the dependent variable,

Y(p,z) = [Wii^ - z]/(z 11)

For the present work we have explored all kinds of representations, finally

selecting the expression,

5 Y(p,z) = + A. • z'^^. (12)

Table 2B gives results for (12), analagous to table 2A for the liquid. Tables

12, 13, 14, 15 compare calculated with experimental vapor densities. Column YX is the experimental value of Y(p,z) via (11), whereas YC is calculated by the right side

of (12). Table 16 compares ethane data not used for least squares. Tables 17, 18, 19

20 give uniformly computed densities and derivatives via (12).

Computer programs used in this work are attached as an appendix.

L-4
Cryogenics Diviston - NBS Institute for Bask Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5PACE 4

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME „ „ R . D

Sept

. Goodwin

. 18, 1973

4. Bibliography

I] C.H. Chui and F. B, Canfield, Trans. Faraday Soc. 67, 2933 (1971).

2] D. R. Douslin and R. H. Harrison, Pres sure -volume -temperature relations

for ethane, (U.S.Bureau of Mines, Bartle sville , Okla. 74003, Manuscript for

J. Chem. Thermodynamics, 1973),

3] P. T. Eubank, Thermodynamic properties of ethane: vapor-liquid coexistence.

Advances in Cryogenic Engineering 17, 270 (Plenum Pub. Corp. , New York,

N.Y. 10011, 1971).

4] R. D. Goodwin, The The rmophy sical Properties of Methane from 90 to 500 K

at Pressures to 700 Bar, NBS IR 73-342, October, 1973. Also, NBSIR

73-300, February, 1973.

5] R. D. Goodwin, The Vapor Pressures of Ethane, Laboratory Note 73-3,

July 9, 1973.

6] R, D. Goodwin, Ethane Virial Coefficients and Saturated Vapor Densities,

Lab. Note 73-4, Aug. 15, 1973.

7] R, D. Goodwin, Estimation of critical constants T^, \j ^ from the ^^T) and T(p)

relations at coexistence, J. Res. NBS 74A (2), 221 (1970),

8] A. Harmens, Orthobaric densities of liquefied light hydrocarbons, Chem,

Engrng. Science^, 813 (1965); 2J_, 725 (1966),

9] J. Klosek and C. McKinley, Densities of liquefied natural gas and of low

molecular weight hydrocarbons, paper 22, Session 5, Proc. First Internat.

Conf. on LNG, Chicago, April (1968).

10] O. Maass and C. H. Wright, J. Am. Chem. Soc. 43, 1098 (1921).

II] Reid C. Miller, Ann, Rpt, to AGA, "Experimental Liquid Mixture Densities

for Testing and Improving Correlations of LNG," Proj, BR-76-1, Univ.

Wyoming, July 1, 1972,

12] Frank Porter, The vapor pressures and specific volumes of the saturated

vapor of ethane, J. Am, Chem, Soc, 48, 2055 (1926).

13] Rolf Prydz and G, C, Straty, The Thermodynamic Properties of Compressed

Gaseous and Liquid Fluorine, NBS Tech. Note 392, October, 1970.

14] M. J. Shana'a and F. B. Canfield, Trans. Faraday Soc. 64, 2281 (1968).

Sr 1)342 « L-5
Cryogenics Division NBS Ins1i1u>e for Bosk Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5PAGE 5

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R . D. Goodwin

Sept. 18, 1973

[15] P. Sliwinski, The Lorenz-Lorenz function of gaseous and liquid ethane, propane

and butane, Zeit. Phys. Chem. Neue Folge 63, 263 (1969).

[16]

[17]

[18]

[19]

H. E. Tester, ETHANE, in Thermodynamic Functions of Gases , voL. 3,

F. Din, Editor (Butte rworths , London, 1961).

J. R, Tomlinson (Gulf Res. and Devel. Co., Pittsburgh, Pa.), Liquid

Densities of Ethane, Propane, and Ethane -Propane Mixtures, Tech. Pub.

TP-1, Nat, Gas Processors Assoc. (808 Home Federal Bldg. , Tulsa, Okla.

74103, Feb. 1971).

Lloyd A. Weber, P-V-T, thermodynamic and related properties of oxygen

from the triple point to 300 K at pressures to 33 MN/m^, NBS J. Res. 74A

(1), 93 (1970).

David Zudkevitch (Esso Res. &: Engrng. Co. , Florham Park, N. J. ), The

importance of accuracy in physical and thermodynamic data to chemical

plant design, October, 1972. (Offered for publication in the Proceedings

of the NBS. )

L-6
Cryogenics Division - NBS Instrtote for Bask Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5PAGE 6

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

T^l nr-ir inf

R.D.Goodwin

"^'^ Sept. 18, 1973

List of Tables

Table 1

.

The fixed-point constants.

Table 2A. Constants for liquid equation (7),

Table 2B. Constants for vapor equation (12).

Table 3. Comparison of oxygen liquid densities.

Table 4. Comparison of fluorine liquid densities.

Table 5. Comparison of methane liquid densities.

Table 6. Comparison of ethane liquid densities.

Table 7, Ethane liquid data not used for least squares

Table 8. Calculated oxygen liquid densities.

Table 9. Calculated fluorine liquid densities.

Table 10. Calculated methane liquid densities.

Table 11. Calculated ethane liquid densities.

Table 12. Comparison of oxygen vapor densities.

Table 13. Comparison of fluorine vapor densities.

Table 14, Comparison of methane vapor densities.

Table 15. Comparison of ethane vapor densities.

Table 16. Ethane vapor data not used for least squares

Table 17. Calculated oxygen vapor densities.

Table 18. Calculated, fluorine vapor densities.

Table 19. Calculated methane vapor densities.

Table 20. Calculated ethane vapor densities.

SP 11342 A L-7
Cryogenics Division - NBS Institute for Basic Standards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-5

PAGE 7

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R . D. Goodwin

Sept. 18, 1973

List of Authors for Computer Tables

ID''' Author(s) Reference

1 Goodwin ( Virial 4- V . P . ) [6]

6 Porter [12]

9 Te ster [16]

10 Douslm [2]

1

1

oliwmski [15]

12 Canfield et al. ri 141 13 Klosek [9]

14 Miller [11]

15 Eubank [3]

16 Tomlinson [17]

98 Prydz [13]

99 Weber [18]

For METHANE, see references in [4],

it 113421 L-8
Cryogenic Division - NBS Institvne for Basic Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5PAGE 8

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

R . D. Goodwin

"^'^ Sept. 18, 1973

Table 1. The fixed -point constants.

Oxygen

T^, K

T , K

c

p , mol/l

c

P^, liquid

p^, vapor

54. 3507

154. 576

13. 63

40. 830

3. 36122- lO"

Fluorine

53. 4811

144. 310

15. 15

44. 8623

5. 670- lO"'^

Methane

90. 680

190. 555

10. 20

28. 147

1. 567865- lO"

Table 2A. Constants for liquid equation (7)

Oxygen Fluorine Methane

^2

rms, %

NP

0. 349

0. 758 8805

0. 228 3200

• 0. 230 4342

0. 014

50

0. 354

0.791 3438

0.112 9132

0. 100 6980

0.010

46

0, 361

0. 837 0910

0. 084 1613

-0. 074 7858

0. 084

49

Ethane

89. 899

305. 330

6. 87

21. 680

1.35114- lO"

Ethane

0, 350

0. 761 7350

0. 298 6535

-0. 327 6239

0. 142

29

Table 2B . Constants for vapor equation (12)

Oxygen Fluorine Methane Ethane

0,382 0,362 0. 382 0, 362

\ 0. 277 3707 0. 257 1572 0, 374 1014 0, 192 7743

^2 -0. 338 6621 -0, 227 0644 -0. 261 5 731 0, 041 5501

^3 0. 769 0708 0, 605 3864 0. 675 3322 -0. 789 2263

\ -1. 5 76 1185 -1.391 6332 -1. 012 2063 0, 357 6675

0. 939 8713 0. 792 5719 0. 439 8834 0. 124 5438

rms, % 0.052 0, 134 0, 148 0, 104

NP 50 46 96 29

» 11342 A L-9
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-5PAGE 9

SUBJECT -pj^g Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAJAE _ _ K . D . Goodwin

DATE SpDt. 1«. 1973

Table 3. Comparison of oxygen liquid densities.

TCRT = iSi^.STb, TTRP = Sk.3BQ7

OCRT = 13.63C, OTRP = <«0 .830 0 Q ,

7. 5868052-001 2.2632003-001 -2 . 30 3'*1 5 -0 0 1 0.0 00 0000^ 000 0. 000 0000 + 000 0 . 00 0000 04-000

ID T,K MOL/L CALC PCNT X YX YC YOIF

99 56. 000 '0.601 '0.603 -COO 0 .9e35'4 0.75202 0 . 75805 -0.0 0603

99 58.000 '40.323 140.326 -0.01 c . 96359 0. 75397 0 . 75958 -0.00561

99 60. 000 'C.0'*9 -0.00 0 . 914363 0.76038 0 . 76109 -0.000 72 99 6^.o 00 39.777 39.770 0. C2 0 .92368 0. 76779 0 . 76258 0.0 0520

99 6'*. 000 39. '9'* 39. '91 C. 01 c .90372 0 . 76630 0 . 761405 0.0 0225

99 66.000 39.216 39.210 0.01 0 .88377 0 . 768'^0 0. 76550 0.0 0291

99 68. JUO 38.926 38.928 -0.00 0 . 86381 0 . 76610 0. 76692 -0.00081

99 70.300 38.655 38. 6'^'^ 0.03 0 .8'4366 0.772'43 0. 76831 0.00'4ll 99 72.000 38.358 38.358 -0.00 0 . 82390 0.76966 0. 76969 -0. 0 00.02 99 7i». 000 38.081 36.071 0.03 0 . 80395 0 0 77392 0. 771C3 0.00289

99 76.000 37.779 3 7.7 82 -0.01 c . 78399 0 . 771'^5 0 . 77235 -0.00090

99 78.000 3 7 .'95 37. '91 9.01 0 . 76140 < 0 . 77'+82 0 . 7736'* 0.0 0118

99 b 0 . J 0 J 3 7.202 37.197 0.01 0 . 7'*i^ 0 8 0. 7761'^ 0 . 77^90 0. 0 012'^ 99 fi 2 . 0 00 36.900 36.901 -0.00 0 . 72'+l 3 0 . 77599 0 . 77613 -0 . 0 00 1'^ 99 8i» . 000 36.6 0 3 36.602 0.00 0 . 70'+l 7 0 . 77750 0 . 77733 0.0 00 17 99 8 6.000 36.298 36.3C1 - 0 . CI c . 68'+22 0.77788 0 . 77350 -0.0 0061

99 86.000 35.997 35. 996 0.00 0 . 66'426 0 . 77979 0 . 77963 0. 0 00 16 99 9 0.000 35 . 6c9 35.6rt6 0.00 0 . 6<^'^31 0.78081 0 . 78073 0.0 00 07 99 92.000 ib.57 3 35.377 -0.01 0 . 62'^3 5 0.78113 0 . 78 180 -0. 0 CO 61 99 9 1* . 0 00 3 5.063 35.062 0.00 0 .6014 'C 0.78335 0 . 78 282 0.00023

99 9 6.000 3 . 73't 3'^. 7'^2 -0.02 0 ,58'4'4'^ 0.78261 0

.

78 381 -0.00120

99 98.0 00 3 ' .

i* 12 3'^.'^18 -0.02 0 . 56'*'^9 0.7 8376 0 . 781475 -0.00099

99 1 U 0 • J U 0 3 < . 0 8 3 3 . 0 90 -0.02 0 . 5'^'+5

3

0 . 78i^72 0 . 78 565 -0 . 0 C 0 93 99 1 J 2 . J 0 0 3 3.750 3 3.756 - u . 0 2 c . 52'^5 8 0 . 78563 0 . 78651 -0 . 0 C 0 68 99 1 L) . 0 0 0 3 3 . ' 1

1

3 3 . ' 1

7

-0.02 0 . 50 '6 2 0.7865 9 0 . 78 732 -0.00072

99 10 6.000 3 3 . 0 d9 3 3.072 -0.01 0 . '8'^6 7 0 . 7877 2 0 . 78 80 7 -0.00035

99 1 C 8 . 0 Ou i 2.7 12 32.720 -0.02 0 .'6'^71 0. 78783 0 . 78878 -3.00098

99 1 1 U . OOJ 32.362 32.361 COO 0 . '''76 0.78960 0. 789'^3 0.0C017

99 112.000 31.990 51.995 -0.02 0 . '2'^8 0 0 . 789146 0. 7 9 J 0

1

-0.00056

99 ll'^.OOO 3 1 . 6 1 o 31.620 -0.01 0 . '40<485 0 .79005 0. 7995'^ -o.oooi^g

99 llD.UuO 3 1.234; 31 .236 -C 02 0 . 381489 0.79038 0. 79100 -0.00062

99 116. OOO 30.6'45 3C .6i42 3 . CI 0 . 36'49'4 0.79169 0. 79138 0.00031

99 120.000 30 .''I 30 .' 38 0.01 0 . 3'4'+98 0. 79208 0. 79169 0.00039

99 122.000 30.021 3 0.021 -0.00 0 . 3250 3 0 . 79190 0. 79192 -0.00001

99 1 2 . 0 0 3 29.595 29.591 0. CI 0 .3050 7 0. 79239 0. 79205 0. 0 00 3'^ 99 12 6.000 29. 1 'u 29.1'*7 -0.00 0 .28512 0 . 7920 3 0. 79209 -0.00006

99 12 1.000 2 6 . 6 H (, 2e.6rt5 0.00 0 .26516 0.79210 0. 79201 0.00008

99 1 50.000 28.2l9 28.205 0.01 . 0 . 2'4521 0 . 79216 0 . 79182 0.0 00 33 99 13 2.000 2 7 . 7 L' 9 2 7. 7^4 0.0 2 c .22525 0 . 79192 0. 79150 0 .0 00'42 99 i i . J Cu 2 7.161 27.179 0.01 0 .20530 0. 79129 0. 79103 0.00026

99 1 3 o . J 0 0 26.b31 2 6.625 0.02 0 . 1853'^ 0.791J 3 0 . 79039 0.0 0063

99 1 J . 0 0 U 2 b . J 2 2t . 0 37 0.02 c .16539 0 .78999 0 . 78956 0. 00043

99 1 4 o . 0 U b S . I. 1 5 2': .'IC 0.01 0 .1^51*3 0 .78883 0. 78851 0.0CC32

99 1 2 • J u 0 2 . 7 J <- . 7 J 0 0.01 0 . 12548 0.76733 0. 78719 0. 0 00 1'^ 99 1 ^ •. . 0 00 2 3.992 2 3.<i-rl3 -J. 00 c .10552 0 . 785149 0 . 78555 -0.00006

19 1 O . J J 2 3.16'* 23.170 - 0 . C 2 0 .08557 0.78237 0. 78350 -0.00063

99 1 •. 8 . 0 u J 2 2.227 22 .2 30 -O.Cl c . 06561 0.78057 0 . 78090 -0.0C033

99 1 5 0 . J 00 21.1U6 21.108 -0.01 0 . 01^566 0 . 777214 0. 77753 -0.00029

99 132. OUO 1 9 . 6 '. b 19.6'.7 -0.00 0 . 0257C 0 . 77280 0. 772e'+ -0. 0 00 0'^ 99 1 S ^ . J J J 1 7 . 1 C b i7.i:'4 0.01 0 . 00575 0. 76528 0 . 76i^e8 0. 000<»0 NP = 5J, FcMSPCT = C.C14

oaiLvic pncss. imc. anooKLYN it. n. y. stock no. *bo L-10
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING UBORATORY LABORATORY NOTE

PKuJECT NO. 73-5

PAGE

in

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R .D i Goodwin

DATE

Table 4. Comparison of fluorine liquid densities.

E =

TCRT = !<<. 31L, TTRP = 53.'»811

CRT = 15.150, DTRP = *tit. 8623

7.913i«383-001 1.1291315-001 -1 . 0 0 698 0 14- 0 0 1 0.0000000^000 0.0000000+000 0.0000000+000

T n 1 UT W 1 , K MOL /L 1/ B L L r C N 1 9 6 5 . 0 0 0 ''.761 '+'•781

9 8 5 6.000 ''.' 6 5 ''+•' 6*+ O.CO

9 8 5 8.000 ' ' • 1 * 6 k k 9 1 '6 O.CO

98 6 0.000 '3.825 '(3.825 0.00

98 6 2 . j 00 '3.501 '3.501 0.00

98 6 . 0 0 J ' 3 . 1 7'+ '3.17'+ -0.00

96 6 6 • J 0 0 ' 2 . 8 ' 5 ' 2 . 8 '5 -0.00

98 6 8 . 3 G 0 * 2 . 5 1

2

"2.513 -O.CO

Q a y 0 7 G • 0 0 0 2 . 1 76 H ^ . 1 / 1 -0.00

y 0

7 ? n n n / c . u u u H 1 • 0 ^ D '1.838 —- n n 1 u . u 1 Q a 7^.000 ' 1 . * 9 3 ' 1 • 't.9 6 — 0.01

y 0

7 c .inn / 0 . u U U ' 1 . 1 ' 6 '1.1 '9 - U . U 1 Q A y 0

7 H n fi n f 0 . u u u H u . f y ^I. r, 7 G Q H u . f y y - U . U 1 98 J . 0 0 0 * 0 . ' * C 't 0 . ' '' -O.Cl

Q ft y 0 8 2.300 I.e. n ft 1 H U . U 0 1 H u . U 0 ^ - U . 0 1 y 0 8^.000 3 9.717 3 9 . 7 2 L -0.01

9 8 8 b . J 0 0 3 9 . 3 < 7 3 9.351 -0.01

98 •i 8 . 0 Q 0 3 8.973 3 8.976 -0.01

98 9 J . J 0 J 38.592 3 6.596 -0.01

98 9 2.000 38.206 36.2C9 -0.01

98 9 . 0 0 0 37.813 3 7.815 -0.01

98 96.000 37. '13 37. '15 -0.00

98 9d . JCO 37.005 3 7.006 -u.CO

98 1 J u . 3 JJ 36.590 36.590 O.CO

98 10 2.000 3b. 165 36. 161+ b. 00 98 1 J 1* . 0 0 0 35.731 35.729 0.01

98 1 0 0 . J 0 0 35.286 3'^.2p3 C . CI 98 I b 3 . J 00 3'4.«29 3'*. 826 0.01

9a 110.000 3'4.3bl 3'.. 356 0.01

98 112.000 33.878 3 3.673 G. 01 98 1 1 H. J 00 i3.37y 33.37k 0. C2 98 lib. JOO 32.86i^ 32.856 0. C2 98 lid. JGO 32.330 32. 32'. 0. C2 98 1 2 J . J UO 31. 77'. 3 1 . 7be 0. C2 98 1 2 2 . J 0 0 31.19 3 3 1 . 1 £6 u . 02 93 1214. JOJ 30.56'* 30.579 0.02

96 120.000 2 . y 2 29.939 0.01

9d 1 2 i . J 0 0 2 9 . 2 0 2 2 9.2oG O.Cl

98 1 3 j . J U u 20.535 28. 53'+ b • C 3 y 8 1 3 2 . J : 0 2 7 . 7 0 2 7.751 - J . 0 0 98 13-.. JOJ 2M,e91 26. 89'. - c . c 1 98 1 3 0 . J J J 2 . . 9 3 5 25.9^9 - c . : 1 98 1 3 d. JOu 2 ' . 6 3 9 2 '.6 '3 - . c 2 9b It ) . u Ou 2 5.521 2 3 . 5 2w -O.Cl

98 1 4 2 . J u u 21. /d9 2 1.7 7C -G. CO 98 li*^ . J 00 10.327 16.326 - 0 . 0 G NP -. "o, kMSPCT C .CIC

X YX TO T U i r

0 .99'+29 0 .80556 n • 0 u 0 r u u • u u 1 0 D

0 .9722 7 0 .8052't n A n f. 0 c . 0 U 't: P

n n p n qq

0 .95025 Q .30550 nU A n /. 7 Q • 0 u H / y

n n n n 7 4 U • U U U 1 1

C .92823 0 .8057'^ 0 .60532 n n n n 1. 0 0.90621 0 .80603 0 •60 563 n A n n 0 ii 0.00021

0 .88'+19 0 . 80632 0 .60633 n n n n n r>

0 .8621

7

0 .80662 0 • 8 0 6 6

1

n ft n n 4 Q u . u u u ly

0 0 .80693 0 . 8 C 7 2 8 _ n n n n 1 i. 0 .61813 0 .80728 u

A n 7 7 "? — n n n n c:

0 .79611 0 .30760 nu . A0 n A 1 7 u 0 1 r 0 .77'+09 0 .80796 u • A0

n A c Q V 0 — y • n ft n n A 7

0 . 752C 7 0 .30331 u . A0 nu A0 0 Q T y — n n n n A

0 .73005 0 .80363 U

A n Q 7 A • 0 u y J 0

— n n n n (kQ 0 . 7080 3 0 .30903 U An 0 7 1. • 0 U 9 r —. n n n n 7 i

0 .66602 0 .809'4l u • A0 1 n r Q 1 u u y

— ft n n ft A A

c .66'+uO 0 .30977 nU A 1 n r 0 — ft n ft ft c

0 .6'+198 0 .31011 rtU A 1 1I 7 7 . 0 1 U r d — ft n n ft ft 1 0 .61996 0 .313'«7 U A 1 1 n 1 . 0 1 1 U 1 — ft n p ft c;

0 .5979'+ 0 .31080 0 .81127 -0.0 00<»7

0 .57592 0 .31112 0 .81151 -0. 0 00 39

0 .55390 0.'jll'43 0 .61172 -0.00029

c .53188 0 .31171 0 .81191 -0.0 0019

0 .50986 0 .31197 0 . 812C6 -0.00009

0 .'878'» 0 .81220 0 .61219 0.00001

G . '6582 0 .312'(0 0 .81229 0.00012

0 .''36C 0 .31256 0 .61235 0.00021

0 .'2178 0 .31268 0 .61238 0.00030

0 .39976 0 .3127'^ 0 .81236 0.00036

0 . 3777'+ 0 .31276 0 .81231 0. 0 00'»5

0 .35572 0 .31272 0 .61221 3.00050

G .33370 0.81261 0 . 612C6 0.00055

0 .31166 0 .dl2'^3 0 .81166 0.00056

c .26967 0 .31218 0 , 81 161 0.00057

G . 26765 0 .31183 0 .61129 0.00055

0 .2'+563 0 .31139 0 .81090 0.0 0 0'»9

0 .22361 0 .31066 0 .810'+2 0. 0 00'43

C .20159 0 .81320 0 .80966 0. 0 00 3'+ C .17957 3 . 3 09'«2 0 .80920 0.0C022

C .15755 0 .30350 0 .60 3'»2 0.00309

C .13553 0 . 307'+2 0 .60 74+9 -0.00007

0 .11351 Q .30617 0 . 80638 -3.00022

c .39l'+9 0 .dCi+70 0 .80506 -0.00036

c . C.69'+7 0 .30333 0 .80 3'+3 -0. 0 00'»3

0 . U'+7'.5 3 .30 396 0 . 80 137 -0. OOO'^O

0 . 025'+3 0 .7g8i^3 0 .79855 -0.00012

0. 0C3'^1 0 . 793'4a 0 . 79356 -0.00016

OSILViC PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 4SO L- 1

1
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING UBORATORY LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5

PAGE 11

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

r luorine

NAME R .D .Goodwin

DAH a£.pt_L5_LQi3

Table 5. Comparison of methane liquid densities.

0.361

TCRT =-190.555, TTRP = 90.6800

OCRT = 10.200 , DTRP = 28.1'»70 8.37091C3-0C1 d . ^.l 61267- 0 02 -7 .<»785753-002

O.OOOOQOO«'000 J. 000 0000-^000 O.OOOQOOO'fOOO

ID T,K MOL/L CALC PCNT

1 93.512 27.910 27.912 -0. CI

1 97.173 27.605 27.605 0. CO

1 10 l.',3'. 27.2'«0 0.01

1 10 5.165 26.916 26.916 0.00

1 109.611 26.527 26.521 0. 02

1 11 3. 772 26.1',6 26. l'*'* 0. 01

1 11 7. 7<«6 25.782 25.775 0.03

1 121.893 25.388 25.380 3. C3

1 125.825 2'».999 2'*. 995 0. C2

1 129.657 2'».611 2'*. 610 0.01

101 13 3.000 2'«.558 2'*. 575 -0.07

1 13 i. 773 2'+. 186 2'.. 182 0. 01

1 133.878 2',.176 2'*. 1 71 0.02

102 135.000 2i». 0*41 2'*. 052 -0.05

1 1 39. 352 2 3.578 23.579 -0 . CO

IC 3 1 0 . 0 0 0 23.500 23.507 -0. C3

1014 l'*5.000 22.932 22.931* -0.01

1 l'*5. i+ifS 22.8t3b 22.881 -0.00

105 1 5 ] . 0 00 22.329 22.328 0.01

60 1 15 J. JOO 22.332 22. 328 0.02

1 15 1. 3 53 22.130 22.132 -0.01

106 155. JCO 21.686 2 1.682 0.02

1 157.199 21.379 21.363 -0.02

10 7 1 o J . J 0 a 20 . 991 2 G . 9o6 0 . C2

1 16 i. 659 20 .<»28 2 0.'*38 -0.05

10 8 1 b5. J 00 20 .23'* 20.227 0.03

1 16 ^ . 326 19. '92 19.502 -0.05

109 1 ('0. JCO 19.3K7 19.3o2 0.03

110 1 75. JOO 18. '17 1 8. '*1'* 0.01

6C2 1 75 . JuO ia.<*2c It.'+l'* 0.03

1 17 5.053 18.390 18.1*03 -0.07

111 Id J . J uO 17.2'*9 17.250 -0.00

60 3 IdJ .000 17.251* 17.250 0. C2 112 Idi*. juO 16.05'* 16.061 -b. Ci* bO'* lai.. JOO 16.060 It . 061 -0.00

6 1 8 3. J 30 15.71U 1 5 . 6 d 8 0. I't 113 186. JCO 15.286 15.299 -Q.08

t> ld6.03J 15.3C2 15.2d6 0.11

6 1 d 7 . J 31 l'».d36 11*. 826 0.07

5 l't.582 11*. 589 -0. 05

ll*. Id d . 000 l**. 26'* 1 '..298 -C . 10

6 1 d d . 0 31 1 . 2 6 5 1'*.279 0. Oi* 6 18 9.032 13.57^1 1 3. 57e 0. CO

5 189. 331 1 3 . 3 C o 13.31S -I. . 11

5 ld9. 7C7 12.879 12.920 -C . 31

6 190.332 12.',7'« 12.1.77 -0.02

5 190. J68 12.397 12.'*ie -0.17

7 19 0.070 12.','.C 12. '.15 0 . 20

7 190. 17J 12.27C 12.235 0.28

NP = "9, RMSPCT 0.08'*

X YX YC

0 . 9716'* 0 . 81*05 0 0. 8'*699

0 .931*99 0 . 31*830 0 • 8'*76i*

0 . 89233 0.8501*3 0. 81*336

0 .QS'*97 0 . 31*90 J 0 • SI* 396

0 . 3101*5 0.85231 0 • 81* 961*

0 . 76679 0.85112 0. 85023

0 . 7290 0 0.3532 7 0. 850 7'* 0 . 68 71* 8 0.85373 0.85123

0 . 6 ' 8 1

1

0.85272 D . 8 5 1 6^

0 .60971* 0.85236 0.85201

0 .60 631 0 . 81*80 3 0 . 85 2 D 1* 0 . 56653 0.35313 U • 0 7 C. I.' 0

0 . 56 71* 6 0 . 35338 0 . 8 5 2 3U 0.5562 5 0U .• fl"?^ Q<J aU 2Ci 0

•

$S ?k?

0 .51267 0 . 8521*9 U • V > (_ 0 u

P . ^061 Pi 0.35132 il ft ^ 7 P Q

0 • **56 1 2 0.85255 n M ? ft U • 0 V t D I? 0 e ^5 1 6 3 0.85272 u • 0 7 c 0 0

U . O O L ^ n A c; ? fl 7 U • 0 5 c 0 r r /i n f» ji L • H U D U D n A c 7 cr 7 U . O J t> # n Q c 0 a 7 u m Oz> c. 0 f U • O T U -7 X 0.85255 U • 0 7 ^ 0 V 0.35599 nU . O |^ O 1* X1 n A ^ 7 7Zi U • 0 7 c / H

C • U J J u 0.852 01 n A c; ? A ^ u • 0 V ^ C 0

C . 30593 0.35311 0 .8521*2 0.26930 0.8501*8 0.852C5

0.25587 0.85289 0.85188

0 .21256 0.31*962 0.85117

0.20581 0.85180 0.85101*

0 . 15571* 0.85022 0.81*981

C . 15571* 0.85080 0.81*961

0 . 15521 0 . 81*777 0.81*979 0.10568 0 . 8i»786 a. 61*800 0.10568 0.31*867 0.81*800

C . C6563 0 .31*1*66 0 . 81.588

0 . 06563 0 .31*575 0.81*588 0.05532 0 . 81*922 0 .81*517

0 .01*561 0.81.203 0 .81* 1*1.2 C .01*530 0. 31*765 0 . 8'* 1*1*0 0 . 03528 0.di*572 0.81*351

0 . Q3070 0.31*153 0.8'*305

0 .02558 0 .33922 0 .84*21*8 0.02527 0.31*388 0.81*21.5

0 .01525 0 . di*ll'* 0.81*113

0 .01226 0 .3361*3 0.81*065

0 . 0061*9 0.32667 0 . 83996

0 . 00521. 0. 33812 0. 83921*

0. 001*68 0.33082 0. 83915

0 . 001*66 0 . d'*908 0 .83911* 0.00385 0.35369 0.83867

YDIF

-0.0 061*9 0.00066

0.00207

0.00003

0.00267

0.00089

0.00252

0.0 021*9 0.00107

0.00035

-0.001*00 O.OCOSO

O.OQlQi*

-0.0 021*0 -0.00017

-0.00137

-0.00030

-0.00013

0.00027

0.00070

-0.00030

0.00067

-0.00062

0.00069

-0.00157

0.00102

-0.00155

0.00076

O.OCOi*2

0.00100

-0.00203

-0 lOOOli* 0.00067

-0.00121

-0.00013

G.O 01*05 -0.0021*0

0.00325

0.00221

-0.0 011*7 -0.0 0327

O.OOlttS 0.00002

-0.001*25

-0.01329

-0.00111

-0.00833

0.00991.

0.011*82

oaiLvic i>REas. inc., Brooklyn it. n. t. stock ho. 4«o L-12
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5PAGE 12

SUBJECT fi^Q Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

R.D.Goodwin

DATE „Sept. 18. 1973

Table 6. Comparison of ethane liquid densities.

CM a> vD o J- (T ro J- cvj o u\ CO J- eg vO « ro tVJ (\J (Ji (VI K UN PO

-H K. fT) <T> oo J' (T> UN ro K vO «\J CP •H vO T-t <M P^ o

o (NJ IfN -H J- O CJ (\J -r-S J- N. <T> CO «M ^^ <o in o O -H to CO > tH o o o o o o o o o O O o o a o o o o o a o o o o o o o

O o o o o o a o o o o o o O C3 o o o o o o o o o o o o o o

ooooooooooaaoooooooocsaooacsaoo I ( tit " « t I I I I I

iv5aoforo^r^'^oo-rH^r^''-tro^Dofoint^«ooaovi)fON.'.Hj-f\io>J'

poroj-j-j-j-.^^ir\tf>irioo«oco<r<r<r><r(T><ro>(T'<roooof^NvOio

ooaoooooooooocaooaooooaocsoaooa

><T-»-*'-*--»H-*oi^iri'7^f^o^'o<^ooijo<or~vfi(TiN.c3j'(T'ooroc3vi5r>-J'

>-^o(T>^-^o^J^•••H.H^o~J^-<t>ooc3r^^Doc^>(^JC^j^w^»^i3lf^o^•r-(•^-^<^J(^J •i-»fMJ-<OP>-a3aOinCJeoJ-o>HJ-irivDt^J-tO.^O>aOl^rO'.-ILnj-CVJ(\j tvjfoj-j-roj'J'j-iriinvocr»<r(r>o>(ra>a»cr<T>ooooooooaDN-N.t^N.

oocsoooooocsooooooooooooooooooo

X J- (\J <o <y> m 1-1 l_D tH fO T-l in ro T-l cr 1^ in ro th cr vO -a- ro gj CM CO -3- o CO o CVJ ro CJ cr vO <o o CM CD ro (y in CD \0 CM CO CM fO cr in ro pw 1-1 -J- CO

in J- ro m in CVJ ro cr> \D CD in <r tH in CO CM \0 (y> ro \0 CM in cr CM ro J- O in CD

1*5 cr> in o CO N- in CM ro 00 J- <r J- o in J- o in ro T-t T-t o O

• CJ> (T> OO <X) CO CO CO N. m in J- J- ro ro ro CM CM T-l T-t T-t CD a O O o o

o ^ o

o a o o O CD CD o CD C3 o o CD CD O o CD o o o a o a O a o o a o

II CD

1 a

•• UJ J- o

(T> o

ro o

(/I «M o

LU o a \C o

t-l cr> o p^ o

(T> to CVJ o CD •H rg ro o O CVJ T-t ro O <r> OO in T-t in CO CO vO ro ro J- in T-l tH in ro

t-l iJ3 • • z O O O u o O o o o o CM T-l tH tH T-l o o T-t CM ro ro CM T-l o o CD o T-t 00 • • o

z 1 Q. o CD a CD o o O o o o o o o O o o o a o O o CD o o CD CD O o o

UJ <o {\J 1 1 1 1 1 1 1 s 1 • t 1 D r-t

II II o o CM O o o -3- a. Q. 1 + O o in J- CVJ CVJ CVJ vO 1-1 cr g} CM CO CD in CM t^ in r«» J- CM vO gD cr J- CO ro o o T-t Z3 a: QC r-» d _l -3- <\J CVJ cvi J- CVJ »-« 1-t T-l ro H CO -i- r«- CO in CO iT ro CO T-t <r J- cr ro CM • Cf >- t- in C3 <x <i> ro o o CJ> r^ N. in ro T-( tH <T> J- o in o in cr N- T-t to ro -3- in th r-^ 00 o

n »- a PO o o

-J in o T-l tH Ti T-) CD O o CD CD OS N- N. vO in J- -J- ro CM T-t a cr (T CO f«~

>£> o (\J CVJ CVJ CVJ CVI CVJ CVJ CVJ CVJ CM CM T-l t4 tH T-t tH T-l tH T-l T-t tH T-l T-l T-l tH II a i_i o CO CJ

UJ tr> s. ft- CO • • O

<t • • Q. a: in _l CT in >x> in T-l N. T-t ro « in -s- vD CO in ro in 1^ ro o> CM CO r*. cr -3- T-t o CO a fO «-( eg CVJ T-» -J- T^ CVI CM CM r^ J- T-l cr cr in in CO J' in cr cr J- ro fO s;

ro H -1 o C3 o> N. r«» m ro T-l t4 cr in o in o in cr CD ro J- CM J- in (M to a:

C3 o

lA II II O o :c T-l T-( T-t CD o o o a o C3 CO rw N. yJO <o in J- J- <t ro CM T-l CD <r cr CO »

1 4- (M OkJ (VJ CVJ CVJ CVJ CVJ CM CVJ CM CM cr U t— ro o CVI Z QC Q^ o o

1 O o in o II T o o

t— CD V o o o OO o o ro cr> O CD o o a CD C3 CD CD CD CD o O O o CD o o CL U O T^ (\i tH in CVI in CO ro C7> in o CD CD O CD a a in in in in in in in in in in z O 1— --1 T-t <T> J- C5 in T-l J- CD C3 CD o O C3 C3

•

T-l '—

)

CO ro o in in CM r^ ro J- o O O .-3 O O ro ro ro fO ro « CM ro -J- in crnooT-iTHT-tT-icgcMroajcroT-ifMroj'iningjf^'Ocrcrooocs

T-liHT-lT^T-tT-ti-lT-ti-tT-lT-li-ICMCMCMCMCMCMCMCMCMCMCMCMrOrororO

Qj-^j-cMro^cMrorororoLninininininininooooooocaoo

OOILVIE PRESS, INC.. BROOKLYN 17, N. Y. STOCK NO. >tSO
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO.

i. /bL)i64

FIlE NO.

7 3 - S

PAGE

SUBJECT -pj^g Orthobaric Densities of Ethane, Methane, Oxygen

Fluorine

and NAJAE R .D . Goodwin

DATE Sent. . 197^

Table 7. Ethane liquid data not used for least squares.

ao J- in r^ CVJ ^£> ro cn a O iH 1-4 CM CM ro 00 CM (M lH vO r- OO in ho vC 1-1 in (M -s- CVJ OO rw in (M J- J- OO <o ^ in o vO o o N- ho iH O c:> ro in in iH 1-1 CP CO o v-4 so CO -3- uv vO CVJ rvj -* i-» CP r» 1-4 o « <o in in CM o C3 1-4 vO vO in o CP ro CVJ 1-4 1-4 y~ («o fo "H o (VJ ro J- in OO O tH iH iH O o a o O o o C3 o (M in ro o o O o O CD •>rl o o o a o o o a o o iH O O O O CP o o o o o O o e1 o 1-4 o o O o o O O

O o o o o o o o o o CD o o o o o o o o o o CD CD o c» o o o o CD CD o O CD

1 1 1 1 t 1 0 1 1 » 1 1 1 1 ( 1 1 1 u (VJ rr> J- J- vO o cr in <T> (J> CM CO J- CM in m vi3 (M ro 1-4 (VJ 1-4 in CP CM OO J- CM tn in

>• J- CVJ cr o •H J- so (X> iH in <T> •rt 00 <D ro (M T-l iH 00 ro m CP 1-4 ro CO CO o o o CJ> vD ro CO J- 00 ro ro c5 N. J- 1-4 r>~ J- CM (P rw J- 1-4 CO in ro CD 1^ J- J- in N. CO (Ti CT* (T> CO 0% CO OO 00 K. N. vD \D <£ J fO ro CP (P CO CO CO N. ro

N. N- N. r^ rs. r«. K N. N. N. s- r^ r>o r- N.. N. 1^ r>o ro ho r^ K. ro r«- o a o O o o o o o o o o o o a o o O o o o O O o C» O o CD o o o o o o

X N. CM 00 V0 flO (T> iD rs. in PO CO iJ3 CJ» 1-4 (VJ a 1-4 CM CP J- in (M OO J- in (M CM ro ro CP

vO (T ro J- •H uv vC (T> (y> T^ iH J- (J< r>. in vO 1-1 CO in O' (M 1-1 N CO iJ3 o ro CO vD vO CP vO

vfi CM tH J- CVJ <r (T> CD CT» 1-4 aO a 1-1 O CO vO vD CM CM 1-4 CP CO o in CM -I- J- ro ro CVJ ro -t vO

(M UN O 1-t (VI ro in vD r«- 00 CO CO CO ho N. r^ r*. r- vO vO N. 1-4 OO vjO <o CO CO CO CO CO

CO N. IV. r- 00 CO OO <o OO r>. f<- r*. r». r^ 1^ N. r^ ro fo. iD in ro r^ ro N. N. r>o |o o o o O o o o o o o o o o o C3 a o o o c> O o o C3 o o a o

X tH CO J- o \0 ro CJ> in (VJ CO vC N- CM vO C3 J" o 1-1 r*. CO \D J- CO v£) in CVJ vO o -s- J- CO 1-1

CVJ J- N. C3 CVJ J- in 1-4 r^ ro in ^ OO CM o -J- iH CO 4 CP r>o ro in 00 (M vO s. o J- CO \0 ro o r«. i-» -t o CM (T vO ro 1-4 J- o in ro CD CC> ro CP CM CP vO J- ro iH Jv£) <o CO (r> o T-t iH r»- CVJ o o r». in ro CM »-4 1-4 o o o CM in ro o N. in J- ro CM H

<r> CO vO UV J- ro to CVJ iH a o i-» C3 O o CD o O O o a o CP CP cn iH CD o CD o O o

o o o o o o a cs o o CD O o a a o o o C9 C9 o o o c:1 o <=> cn O O o o o

vO H ••-1 a> o ro in o in in o CVJ ro ^ CM iH CO (M (M ro CP CO 1-4 in CP 1-t 00 ro in (P z OJ C>J J- CVJ o J- a o ro O CM J- J- ro ro (M 1-1 O O o o o C» 1-4 iH ro fO 1-4 u o CM ro oQl o o o o o 1-t (VJ ro ro o a c3 o o O o o o o a a c1 O CD o o CD CD o a o

1 t 1 1 • 1 1 • • t 1 1 » 1 t 1 f

o ro IT o uv iH CVJ cr> (VJ ro J- vO cr> J- J- in o (M a in o (M ro ro vO (T J- J- in o

_t o (VJ 00 N. tn LfV (r> (VI 1-1 CO <0 ^ a ro (P in J- a> ro CP CM (M (VJ CM ao J- O ro CP in J 4 lf> OO H ro in in ro N- 1-4 in cr ro (J> J- (P in 1-4 IS. ro 00 1-4 ro in CP ro CP -3- (P in O

•H (y> <o uv J- cvi 1-4 CM 1-4 1-) o o cr> cr> c7> 00 CO f«o 1-4 iH 1-4 CM iH 1-1 Ci C3

CvJ C\J H •H ri 1-1 1-4 iH 1-4 1-1 iH »H 1-4 1-4 1-4 (M CM CM 1-4 1-4 1-4 1-1 1-4

-i •H CP rs. in m (VJ CO ro (VJ o ro in o a> CVJ N. J- o (M ro in <x> a -3" CP O J- CM o CO N. in ro (T> in OO ro CO CVJ iH O CM (jv r^ r* ro ro a> ro (M c» (P <p ro a CX» CM o CO fo _J N. o ro in N. r«- >£) 1-1 •H in kO •d* CO (VJ CO <p in 1-4 N. ro CO 1"4 (M J- ^ (P CM «T> in CP in o

X ^ o <J> cr CO vC in J- ro (\| o r«- CM »-4 »-4 o a (ji CP (T « CO ro 1-1 1-1 1-4 CVJ 1-1 o o CP H H iH iH iH 1-1 iH 1-4 1-4 1-4 1-4 •r-4 1-4 (M (M CM 1-1 T-4 1-4 1-4 iH

V o a O o a o a o O o o C9 O o a O o o o es a r-» a CM ro 1-4 a C3 O o CD o a» » a o C3 a o o o a o o o o in O CT» OO r^ vO vO in in in N 1-4 vD C3 CP <X5 to. vO CJ o O o o o o o a o o O CM CM 1-4 1-4 vO H vi3 1-1 1-4 1-4 vO 1-4 ro OO CM CM 1-1 H vO 1-4 vD 1-1

CD o o o o a o o o o c3 in fo GO ro in OO <VJ ro J- J- in in (T> -s- ro OO ro in CO CD CM o J- vC CO o CVJ J- ^0 CO a* o o CO OO CP o o o cn o a> CP (P CO CO CP CP O c: •H 1-4 •H CVJ (VJ (VJ CVJ (VJ CVJ ro ro CM CM CM CM (M ro ro ro ro ro ro 1^1 CM CM CM CVJ (VJ ro ro

O o> cr> <y> <3> cn 0^ 0*' 0^ ^ o ro ro ro vO vO vO vO M 1-4

OaiLVIE PMS*. INC.. BROOKLYN 17. N. Y. STOCK NO. 4SO
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING UBORATORY LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5PAGE 14

SUBJECT -pj^g Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

R . D . Goodwin

DATE

, , 5.gj.t, ig. im

Table 8. Calculated oxygen liquid densities

T,K

56.aoo

58,000

60.000

62.000

6^^.000

66.000

66.000

70.000

72.000

7i*.000

76.000

73.000

80.000

82.000

Stt.OOO

86.000

88. 000

90.000

92.000

9^.000

96.000

98.000

10 0.000

102.000

10^.000

106.000

108.000

110.000

112.000

11<4.000

116.000

118.000

120.000

122.000

12<i.000

126.000

128.000

130.000

132.000

13^. 000

136.000

138.000

l^u. 000

1<*2.000

I'^'i.OOO

l't6.000

l'+8. 000

150.000

152.000

15f+.000

15i».5 76

R,MOL/L

<«0.830

<»0.603

U0.326

^0.0^+9

39.770

39. 'gi

39.21C

38.928

38.356

38.071

37.782

37.k91

37.197

36.901

36.602

36.301

35.996

35.688

35.377

35.062

3't.7tt2

3i».<»18

3'+.C90

33.756

33. '17

33.072

32.720

32.361

31.995

31.620

31.236

30.8U2

30.'f38

30.021

29.591

29.1'«7

26.685

28.205

27.70i*

27.179

26.625

26.037

25.«tlO

2«*.733

23.993

23.170

22.23C

21.108

19.6't7

17.10t»

13.630

OR/DT

-0.1377

-0.1380

-0 .1385

-0 .1390

-0.1395

-O.lttOl

-D .l'+C6

-0 .l'+15

-0.1'»23

-0.1^*32

-0

-0 .l*t51

-0 .l'»62

-0 .l'*7t» -0 .l'»87

-0 . 1500

-0.1515

-0 .1531

-0 .ISi^e

-0 .1567

-0 .1586

-0 .1608

-0.1631

-0 .1655

-0 .1682

-0.1711

-0 .17^*2

-C .1776

-0 .1813

-0 .1852

-C .1696

-C . 19^*3

-0 .1995

-0 .2052

-0 .2115

-0 .2165

-0 .2263

-0 .2351

-0 .2'*50

-0 .2561*

-0 .2695

-0 .26'»8

-0.3031

-0 .3253

-0.3529

-0 .3686

-C .'370

-C .5079

-0 .6253

-0 .67'f9

-2.1732

C .0000

D2R/DT2

-0.00019

-0.00021

-0.00023

-0.00026

-0.00029

-0.00032

-0.00035

-0.00038

-0 .000i»l

-0 .000't5

-0 .000<»9

-0.00053

-0.00057

-0.00061

-0.00066

-0.00071

-0.00077

-0.00083

-0.00089

-0.00096

-0.00103

-0.00111

-0.00119

-0.00129

-0.00139

-0.00150

-0.00162

-0.00176

-0.00191

-0.00207

-0.00226

-0.002't6

-0.00272

-0.00300

-0.00332

-0.00369

-0.00'tl3

-0.00'*66

-0.00530

-0.00606

-0.00707

-0 .00633

-0.01000

-0.01229

-0.01555

-0.02051

-0 .02869

-0.0if396

-0 .07893

-0.2006't

-2.3<+«»79

0.00000

oeiLVIC PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. ASO L-15
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING UBORATORY LABORATORY NOTE

PROJECT NO. FILE NO. 73-5PAGE

1 K

SUBJECT ^Yie Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME jQ Goodwin

DATE Sept. 18. 1973

Table 9. Calculated fluorine liquid densities.

T,K

53. '81

56.00G

58.000

60.000

62.000

6^.000

66.000

68.000

70.000

72.000

7<+.000

76.000

78.000

80.000

82.000

8<t.000

86.000

88.000

90.000

92.000

9k,Q00

96.000

98.000

10 0.000

102.000

10^.000

106.000

108.000

110.000

112.300

n't. 000

116.000

118.000

120-000

122.000

12'*. 000

126. 000

128.000

130.000

132.000

13tf.0Q0

136.000

138.000

lUO.OOO

l<t2.000

I't't.OOO

l't'*.310

R,HOL/L

t*k.7Ql

1*3. Q25

'3.501

'*3.i7k

'2.513

'2.177

'1.838

'l.t»96

'0.799

'O. <<< '0.085

39.720

39.351

38.976

38.596

38.209

37.815

37. '15

37.006

36.590

36.16'^

35.729

35.283

3'^.826

3i^.356

33.873

33.37'+

32.858

32. 32'*

31.768

31.188

30.579

29.939

29.260

28.53'+

27.751

26.89'+

25.939

2'+.8'+3

23. 52'*

21.770

18.328

15.150

DR/DT

-0.1573

-0 .1576

-C .1587

-0 .1599

-0.1612

-0 .1625

-0 .1639

-0 .165'f

-0 .1670

-0 .1686

-0 .170'+

-0 .1722

-0.17'*2

-0 .1763

-0 .1785

-C.18C6

-0 .1833

-0 .1860

-0 .1888

-0 .1918

-0 .1951

-0 .1985

-0 .2022

-0 .2062

-C.2105

-0 .2151

-0 .2202

-C .2257

-0.2316

-0 .2382

-0.2'+5'+

-C.253<+

-0.262'+

-0 .272'+

-0.2838

-0 .2967

-0.3118

-0 .329'f

-0 .3505

-0 .3762

-0 .'08'*

-0 .'50'+

-0.5081

-0 .5939

-0.7'+00

-1.0696

-3.689'+

0 .0000

D2R/DT2

-0.0005'+

-0.00055

-0.00058

-0.00061

-0.00065

-0.00068

-0.00072

-0.00076

-0.00081

-0.00085

-0.00090

-0.00095

-0.00101

-0.00107

-COOllt*

-0 .00121

-0.00129

-0.00137

-O.OC1'*6

-0.00156

-0.00167

-0.00179

-0.0C192

-0.00207

-0.00223

-0.002'+2

-0.00262

-0.00286

-0.00313

-0.003'+'+

-0.00380

-0.00'+22

-0.00'»72

-0.00533

-0.00606

-0.00696

-0.00811

-0.00959

-0.01156

-0.01'+28

-0.01821

-0.02426

-0 .OSift+O

-0.05377

-0.09999

-0.2770'+

-7.'»979'+

0.00000

OOILVIE PRESS. INC.. BROOKLYN 17, N. Y. STOCK NO. 480 L-16
NATIONAL BURcAU Or 5TANDARDb« CRYOGENIC ENGINtcKlNG LABORATORT LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5

PAGE 16

SUBJECT ^j^^ Orthobaric Densities of Ethane , Methane, Oxygen and

Fluorine

NAME D QQQjJ^ij-j

Sept. 18, 1973

Table 10. Calculated methane liquid densities

T,K

90.680

92.300

96.000

98.300

100.000

102.000

lO'+.OOO

106.000

108.000

IIJ.OOO

112.000

11^.000

116.000

118. OQO

12 0.300

122.000

12't.OOO

126.000

128.000

130.000

132.000

13i». JflO 136.000

138.000

li(0.300

m2.000

l^tf .300

1<46.000

I'td. 000

150.300

152.300

15U.000

156.000

158.000

16 3.3 00

162.000

16'*. 000

166.000

168.300

170.000

172. 000

17'*.000

176.000

178. 000

180.000

182.000

la^+.GCO

186.000

188.000

193.000

190 .555

R,MOL/L

28.1<»7

28.036

27.871

27.70**

27 ,53k

27.36't

27.192

27.018

26.8<*3

26.665

26. '86

26.306

26.123

25.938

25.751

25.561

25.369

25.175

2'f.978

2t».778

21*. 575

2i».368

24.158

23.9't5

23,728

23.507

23.281

23.051

22.815

22.57«*

22.328

22.C75

21.815

21.5'*7

21.271

20.986

20.691

20.385

20.066

19.732

19.382

19.012

18.620

18.200

1.7,71*7

17.250

16.696

16.061

15.299

l't.298

12.527

10.200

DR/DT

-0 .0825

-0 .0829

-0 .0836

-0'.08i*9

-0 .0857

-0 .0865

-0 .0873

-0 .0881

-0 .0890

-C.0899

-0 .0909

-0 .0919

-0 .0930

-0 .Og'fl

-0 .0953

-0 .0966

-0 .0979

-0 .0993

-0 olOCS

-0.1023

-0 .10i*0

-0 .1057

-0 .1076

-0 .1096

-0 .1117

-0 .11^+0

-0 .116U

-0 .1190

-0 .1219

-0 ,12k9

-0 .1282

-0 .1318

-0 .1358

-0 .I'tOl

-0. 1503

-0 .1562

-C .1630

-0.1707

-0 .1797

-0 .1901

-0 .2026

-0 .2177

-0 .2367

-0 .2612

-C .29t*7

-0 .3'»'*0 -0 .'261

-U .6021

-1 .5385

0 .OOOG

D2R/DT2

-0.00031

-0.00032

-0.00033

-0.00035

-0.00036

-0.00038

-0.000'»0

-COOOifl

-0.000'*3

-0 .000'*5

-0 .000'*8

-0,00050

-0.00052

-0.00055

-0.00058

-0.00061

-0.0006'*

-0.00068

-0.00072

-0.00076

-0.00080

-0.00085

-0.00090

-0.00096

-0.00103

-0.00110

-0.00117

-0.00126

-0.00136

-0.001'»7

-0.00159

-0.00173

-0.00188

-0 .00207

-0.00228

-0.00253

-0.00282

-0.00318

-0.00361

-0.001*14

-0.00481

-C. 00568

-0.00683

-0.00841

-0.01068

-0.01415

-0 .01988

-0.03064

-0.05538

-0.14217

-1.72796

0.00000

OaiLVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 450 L- 17
NATIONAL BUREAU OT STANDARDS, CRYOGENIC ENGINEERING UBORATORY LADvJKAHJKT iNvJIC

PROJECT NO. 0 7 C A "2 /IFILE NO.

( 6 -b

PAGE

1 1 SUBJECT Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME _ ^ „ , R .D .Goodwin

DATE SeDt. 18. 1973

Table 11. Calculated ethane liquid densities.

ETHANE SATURATED LIQUID DENSITIES

T,K

89.899

90. 000

95.000

100.000

105.000

110.000

115.000

120.000

125.000

130.000

135.000

lit 3. 0 00

l'*5.000

150.000

155.000

160.000

165.000

170.000

175.000

IdO.OOO

185.000

190.000

195.000

200.000

205.000

210.000

215.000

220.000

225.000

230.000

235.000

2<t0.a00

2'»5.000

250.000

255.000

260.000

265.000

270.000

275.000

280.000

285.000

290.000

295.000

300.000

305.000

305.330

R,MOL/L

21.660

21.676

21.<»96

21.316

21.136

20.955

ZQ, 77k

20.593

20.*fll

20.228

19.859

19.673

i9.«»85

19.296

19.105

18.912

18.717

18.520

18.320

18.116

17.910

17.700

17.'f85

17.266

17,0'*2

16.813

16.577

16.335

16.085

15.826

15.557

15.277

Ik. 96k

ltt.676

l'*.35i

lif .005

13.635

13.233

12.792

12.299

11.729

11.0'tO

1C.112

d.Qkb

6.870

DR/DT

-0 .0360

-0 .0360

-0 .0360

-0 .0360

-0.0361

-0 .0362

-0 .0363

-0 .036*+

-0.0365

-0 .0367

-0 .0369

-0 .0371

-0 .037'*

-0 .0377

-0 .0380

-0 .Q36k

-0 .0388

-0 .0392

-0 .0398

-0 .0^03

-0 .O'+IO

-0 .0<tl7

-O.QkZk

-0.0't33

-O.OttUS

-0.0'+53

-0 . 0^*65

-C .0't78

-0 .Ot»93

-0 .0509

-0 .0527

-0.05tt8

-0.0572

-0.0600

-0 .0632

-0 .0669

-0 .0715

-0 .0770

-0 .0839

-0 .0929

-0 .1053

-0 .1238

-0.155'*

-G .2288

-1 .2696

0.0000

D2R/DT2

0.00000

0.00000

-o.ocooo

-0.00001

-0.00001

-0.00002

-0.0C002

-0.00003

-0.00003

-0 .0000'*

-0 .0000**

-0.00005

-0.00006

-0.00006

-0.00007

-0.00008

-0.00009

-0.00010

-0.00011

-0.00012

-0.00013

-0.00015

-0.00016

-0.00018

-0.00020

-0.00022

-0.00025

-0.00028

-0.00031

-0.00035

-0.00039

-0.D00'*5

-0.00051

-0.00059

-0.00069

-0.00082

-0.00099

-0.00123

-C.0C156

-0.00208

-0.00295

-0.004*63

-0 .00871

-0.02539

-2.'*<*167

0.00000

QOILVIE PRESS. INC.. BROOKLYN 17. N. T. STOCK NO. 4SO L-18
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE 2750364 73-5 18

SUBJECT Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

R.D .Goodv^in

"'"'^ Sept. 18, 1973

Table 12. Comparison of oxygen vapor densities.

E. - c, .3o2

TCRT = 15i».57b, TTRP = 5i*. 350 7 OCRT.= 13.630, DTRF = 3. 36122-00'*

2.7737C66-0C1 -3.3666205-001 7.6907075-001 -1 . 5 7 611 85 0 0

0

9.3987130-Cul 0 . 0 C C 0 0 G C + 0 0 0 0 . 0 0 0 0 0 0 0 + 00 0 G . C 0 0 0 0 0 0 0 0

0

10 T,< MGL/L CAlCD PCNT z YX YC YDIF

99 5o. JOO 5. 330 C-3C'4 c 3288-0 0'* :.02 0 .951+53 •; .07082 0.07159 -0.00C77

99 58.000 6 . 993 C-uC* 8 . 99'4l-00'» -3.01 0 .90 296 0 .07289 3.07270 0.00019

99 6 0.000 1. <+6'tu-0C3 1

.

'6'+'+- 0 0 3 -9.0 3 G . 85'+79 3 . 0750 5 0 .07'+7i+ 0.00031

99 6 2.000 2.3057-003 2. 3C68-C33 -0.0 5 0 .80972 .07792 0 . 07752 0 . 0 0 01+3 99 d1«.000 3.5233-303 3. 5251-003 -0.05 0 . 767(+7 0 .08123 0.08089 O.C0 031+ 99 66.0 00 5.2367-003 5. 2386-003 -0.01+ 0 . 72778 3 .081+97 0.08'»73 0 . 000214 99 68.000 7.58eC-3D3 7. 5899-C03 -0.C2 0 . 690'*2 0 .08906 0 .08893 0.00013

99 7 0.000 1. 07i42-OC2 1

.

-7^2-C 32 -0.03 0 .65520 0 . 0931+3 3.C93'+1 3.00001

99 72.000 1 . 1+665-002 1. '633- 0 02 0.01 0 .6219'+ 0 . 09801+ 0.09811 -0.00006

99 71.. 000 2. 0227- 302 2. 0220-002 0.01+ 0 0 .10281 0.10296 -0.00015

99 76.3 03 2. 6996-332 2 . 6983-Cu2 0.0 5 0 .56067 0 .10773 0 . 10 792 -0 . cocig

99 73.300 3 . 5it'il-:C2 3. 5't21-0G2 0.06 0 .53239 0 .11275 3.11296 -C . 03 C2 1 99 80.000 1*. 5631-002 k. 5802-002 0.06 G .50552 3 .11781 0.11801+ -0 . CO 02 3 99 o2. 000 5 . a^* '9-002 5. 8i»12-002 0.06 0 . 1+7996 0 . 12292 0 .12311+ -0.00022

99 Si*. 300 7 . 3595-002 7 . 3552-0 32 C . 0 6 0 . '5562 0 . 1280 ' 0.12823 -0.CCC19

99 86.3 00 9 . 1589-002 9. 151+2-CC2 Q.C5 c . <+32i+2 0 .13313 0.13330 -0.00017

99 88.000 1 . 1276-00

1

1. 1271-001 0 . C It 0 . '1026 0 .13821 0.13633 -0 . 00 01 2 99 93.000 1. 37i»5-001 37'+l-C01 0.0 3 0 .38910 0 . l'+323 3 .1'4331 -0.OOC03

99 92 . 0 CO 1.6603-001 1

.

6601-COl 0.0 1 0 .35865 0 . l'+820 3 . l'+62i+ -0 . 00001+ 99 9<«. JOO 1 . 968 7-3C

1

1

.

9887-COl - 0 . 0 C 0 . 3'+9'+6 0 .15311 0 .15 310 0.00003

99 96.000 2 . 363 7-001 2. 361.1- 0 01 -0.01 c . 33068 0 . 15791+ 3.15 7 90 0 . 00 00 1+ 99 98.000 2. 789^-001 2 . 7902-001 -3.0 3 0 .31306 0 .16270 3 . 16262 0.00009

99 10 3.300 3.27C2-3C1 3. 2 71d- 0 0

1

0 . 29596 0 .16738 0 .16726 0 . 00 01 2 99 1 u . J 0 0 3. dlCe-3G

1

3 . 6127-001 -0.05 0 .27952 0 . 17196 0.17182 0 . 0 0 01 -4 99 IC*. JOO '162-00 1 !. '186-001 -0.05 0 . 26372 0 . 1761+5 0 . 17630 0.00015

99 10 6.000 S.Ogiii-GOl 5 . G 9'+3- 0 0 1 -0.06 0 . 2'+851 3 .18086 0 . 18 C 73 0 . C 0 0 1 6 99 lu8.uQ0 5.8'.21-00l 5. 6I+55-CC1 -0.06 0 .23387 . 18518 0 .185C2 O.OGQlc

99 11 3 . JC3 6. b?!* 7-001 6 • d763- C 01 -3.05 c .21975 0 . 189'+0 0.18925 0.00015

99 112. JUU 7 . 5953-001 7. 5992-0 31 -0.05 0 .20615 0 . 1-935 5 3.193'+1 0 . 0 0 01-+ 99 1114. 30 j 8.6121-03 1 8. 6155-0 01 -3 .0 c .19 3 3 2 0 .19759 0.1971+3 3.00011

99 lib. JOO 9. 7325-001 9 . 7353-031 -3.C3 0 . 13 031* 0 .20156 3.2011+8 0.00003

99 118.000 1 . 0965+300 1. 0 9 6 7+030 -3.02 c .16 8 0 9 0 . 205'+5 0 .20 5'+0 0.00005

99 12 0.000 1.2321tJ0O 1. 2322+000 -0.00 0 .15625 0 .20926 0 . 20 925 0.00000

99 12?. JOG 1. 3612+30 0 1. 3610+0 30 0.01 0 . l'+i«80 3 .21299 3 .21 303 -3 .CO CO 1+ 99 1J'«.3Q0 1 . 5'45G + 3Gu 1

.

5'+ 1+5+0 JC 3.03 0 .13372 3 .21666 0.2167'+ -3 . 0 0 00 3 99 126. JOO 1 . 725C +00 3 1

.

72'+3*CuO 0.0'+ 0 . 12299 0 .22027 3.22039 -0.00 012

99 12 J. 003 1.923C+300 1- 922 3+ CoO 3.05 0 .11259 0 .22383 0 .22 398 -0.03015

99 1 i . . J

:

2.1'*11 + 30G 2. 1399+03C 0.06 c .13252 •J .22735 0 .22751 -0.00017

99 1 .5 J . : : 0 2. 301-3 + 3 3

C

2. 5eos+c JG 0.06 0 .09275 0 .23033 0.23130 -0.00 017

9 -i 1 3 -4 . J u J 2.b'»63 + 33 0 c • oU 70+OOC 0.05 0 .08327 0 . 23'+29 0 . 23'+'+'+ -0.00016

99 1 0 '1 . J G u 2. 9'4'*'.+ 300 2 , 33 + 0 00 ij. 0<+ 0 . 0 71+07 0 .23773 0 .23 786 -J.C0C12

99 1 5i. jo3 3.271'1,+jOu 3. :7<+5+C 30 0.01 L . 0 6511+ D . 2'+119 0 . 2'+12'+ -0.00005

9:1 1-4 > . J u' 3 3. 6'*b6+3C3 7 t'.7'»+CCC - : . c 2 0 . 0 56'46 3 . 2'+ 1+68 J .21+ '62 0.00006

S -) 1 j 0 J Cb92 + '300 u . 0 712+000 -C.05 0 . 04803 0 .2kbl9 0 .2'+8 01 0.00018

99 JJj i*. 5552 + OOLi ^592+000 -0.09 0 . 0 3983 3 .25176 0.2511+3 0.00033

99 1 D . J 03 5 . 1261 + 0: 5. 13 16+ 0 C C -0.11 c . C 3185 3 .25536 0 .25i»93 0 .COCi+3

9 9 1 -• -1 . 3 C J 5.6177+030 5

.

c225+CjL -0.C3 c . 021+10 0 .25892 3 .25857 0.00035

-i -> 1 ' J > J J J o . 7.564-33d t . O967+0C0 0.13 0 . 0 1651+ 0 . 26132 0 .262147 -0.00065

99 1 J . 3 C 3 7 . 9239 + 03 0 7. 91 3 3+03 0 0 .13 c .00919 0 .26616 3 .26692 -0.00075

99 1 > . 3 3 C I.t225+G31 1

.

0230+031 -3.05 n . C 3 20 3 0 .27367 0 .27313 0 .000514

NP - 53, RmSPCT --- u .052

OGILVIE PRESS. ]NC.. BROOKLYN 17, N. Y, STOCK NO. 450 L-19
NATIONAL BUREAU OF STANDARDS CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-5

PAGE 19

SUBJECT -pj^g Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R .D .Goodwin

DATE Seot. 18. 1973

Table 13. Comparison of fluorine vapor densities.

E = 0.362

TCRT = l'*i».310, TTRP = 53.i»811

OCRT = 15.150, OTRP = 5.67000-00'*

2.5715721-OCl - 2 . 270 6'»4» 3- 0 0

1

7.9257188-001 0.0000000+000

10 T,K MOL/L CALCD

98 Sk.SOO 6.600C-00'* 6. 6001-00'*

98 56.000 1.1500-003 1. 1518-003

98 5 8.000 1 . 930 0-00 3 1 • >yc f c— u U o 98 6 0.000 3.1100-00 3 3 »

^ n 7 Q ft n "7 ID ott- 0 0 s5 98 62.0 00 '.8'«00-003 *

.

Q o rt 4 m n t 98 6 '« . 0 00 7.2900-003 7. o o < n n 7 98 66.0 00 1 . 0680-002 1

.

n c 7 c rt A T 0675-002

98 68.0 00 1 . 5250-00 2 1

.

t>2 5 3- U U 2 98 7 0.300 2. 128C-002 2. 1293-C u2 98 7 2.000 2.9070-002 2 . 910 5-002

98 7 4 , 0 00 3.8970-002 3

.

90 29-0 02 98 76.0 00 5. 1350-002 5. l<+3'4-0 02 98 78.000 6. 6600-002 6. 6713-0 02 98 80.000 8. 5150-002 8. 5291-002

98 62.000 1 . 0 7'»5-00 1 1. 0761-001

98 dif-ooo 1. 3397-001 1 . 3'+16-001

98 86.000 1 . 6523-001 1. 65'*1-001

98 8 8.0 00 2. 017'.-001 2. 0191-001

98 90.000 2.** '07-00 1 2. ''20-001

98 9^.0 00 2.9280-001 2. 9286-001

98 gi*. uoo 3. '857-00 1 3. '852-001

98 96.000 k. 1203-001 '. 118'+-001

98 93. 300 '. 8389-00 1 I*. 8352-001

98 10 J. 000 5.6'*91-001 5. 6'^32-OCl

98 1 0 2 . 0 C 0 6. 5591-001 6. 5507-001

98 lOU.OOO 7.5776-001 7. 5667-001

98 106.000 8.7151-001 8. 7012-COl

98 1U8.000 9.9617-001 9. 9651-001

98 113.000 1. 139L;t300 1. 1371+000

98 1 12. JOO 1 . 2':.53 + 000 1. 2932+000

96 n't. 000 l.'+b87<-000 1. '666+CCO

98 116. 3C0 1. 6610+000 1. 659C+0CC

98 118.300 1.67'*3+000 1. 6725+000

98 120.300 2. 1111 + 000 2. 1099+000

9d 2. 37'^ i^ + OO 0 2. 37141 + 000

9« 12<«. 300 2. 6680 + 0OC 2. 6690+000

98 12O.300 2.9965+000 2. 9992+000

98 128.000 3. 3b61+Q0u 3. 5709+000

96 1 3 : . 0 0 3 3 . 7d'^ 8 + 00 0 3

.

7921+OOC

98 1 o 2 . 0 b 0 '.26'*l + 300 '. 2739+OuO

98 13i*. 000 '• 8207 + 000 k. 8319+000

98 13b. 000 5. '616 + 000 5. '905+ 000 96 138.000 6. 291C+0C0 6. 2909+COO

98 1 '* 0 . J Gu 7 . 3226+OOC 7. 31 53+ 0 L C 98 l'+2. OOO 6. 765'^ + 000 6. 76'^'^+000 98 IttH. 000 1 . 1868 + 00 1 1. 1893+001

HP := 'b, RMSPCT = 0 .13'*

6 .05386U'*-001

0.00 00000+000

PCNT

-0.00

-0.16

0.1'* 0.20

0.23

0.11

0.05

-0.02

-0.06

-0.12

-0.15

-0.16

-0.17

-0.17

-0.15

-O.l'* -0.11

-0.08

-0.05

-0.02

0.01

0.05

0.08

0.10

0.13

0.15

-1.3916332+000

0.0000000+000

16

17 0.17

0.16

0.15

0.12

0.09

0.06

0.01

-O.Oi* -0.09

-0.1'* -0.19

-0.23

-0.23

-0.16

O.CO 0.13

0.2'+ -CO'*

z Y X YC YDIF

0 .9a'»73 0.03779 0 . 03 768 0.00013

0 .92853 0 . 0'*6'»5 0 .0*»297 0 . 00 31*3

0 .87621 0 . 0'f&9 3 0 . 0'»877 -0 . 00 ISi*

0 .82738 0.05309 0 • 05 '93 -0 . 00 18 <» 0 .78169 U • 05968 3 .06135 -0 .00167

0 .73887 0 . 0672 5 0 . 06 792 -0.00067

0 .69863 0 • 07'*3'« 0 .07'»59 -0.00Q26

0.66077 0 . 08139 0.08130 0.0000 9

0 .62507 0 . 0 882 7 0.08 799 0.00028

0 .59135 0. 09515 0 . 09*«6'» 0.00 051

0 .559'*5 0.10131 0.10121 0.00 063

0 .52923 0 . 10829 3 . 10 769 0 .C0G63

0 . 50357 0 . Il't66 0.11'*06 0.00060

0 . '7333 0. 12086 0.12030 0.00056

0 .ttkThZ 0. 12691 Q . 126'*1 0.00053

0 . '2275 0.13281 0.13238 3 . 00 0'*'* 0 . 39923 0.13620 0 .00 03'*

0 . 37677 0. l'^'*13 0.m388 0.00025

0 . 35532 0 .l'*956 0 .l't9'^0 0.00015

0 . 33'*79 0 . 15'^8<* 0 .15'478 0.00006

0 . 3151'» 0. 15997 0 .16001 -0.0000 4 0 .29631 0. 16'*96 0.16509 -0.00013

0 . 2782'^ 0 . 16931 0.17003 -0.00021

0 .26090 3.17'*53 0 .17«^62 -0 .C0C29

0 . 2'*i«2'^ 0 . 17912 0.179'*7 -0.00035

0 .22822 0.18356 0.16398 -0 .OOOf+O

0 .21281 0 . 18792 0.13836 .00 0'*'* c .19796 0. 1921

5

0 .19261 -0 .00 0'*6

0 . 18 366 0 .19627 0 .19673 -0 . 000'*6

0 . 16986 0.20028 0.20072 -0 .00 0'* I* 0 .15655 0 .20'»19 0 .20U60 -0 . 03 0'tl

0 . l'^370 0 .23801 0 .20836 -0.00035

0 .13129 0.2117't 3.21200 -0.00027

0 .11928 0.21538 0.2155't -0.00015

0 .10768 0.2189'» 0 .21893 -0 .C0C9'*

0 . C 9o'^i+ 0 .222'*3 0 .22232 3.00011

0 .08556 0.2258'^ 0.22556 0.00027

0 .07503 0.22917 0.22873 0 .G00'*5

0 . C &'*81 0. 232'+3 0 .23181 3.00062

G .05'i91 0.23560 0 .23'^8'* 0.00076

0 . 0 '530 0.23862 0 .23782 3.00081

0 .03598 0.2'^138 0 .2'*0 77 0 .00061

0 . C2692 0.2'+37i» 0 .2'»375 -3.00003

0 . 01813 0.2'^625 0.2<^683 -0.00058

0 . 00958 0 . 2'*889 3.25 0 23 -0.00133

0 .00127 Q. 25552 0.25509 0. 000'*'*

OOILVIE PRESS. INC.. BIIOOKLYN 17. N. Y. STOCK NO. 4SO L-20
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING UBORATORY LABORATORY NOTE

PROJECT NO. FILE NO. 73-5

PACE

SUBJECT Orthobaj-ic Densities of Ethane, Methane, Oxygen and

Fluorine

R . D . Goodwin

DATE Seot. 18. 1973

Table 14. Comparison of methane vapor densities.

E = 0.382

TCRT = 190.555, TTRP = 90.6800

OCRT = 10.200, DTRP = 1.56787-002

3.7ifUl«»3-Q01 -2. 6157309-001 6.7533217-001 -1. 0122063*000

1*. 3988336-001 0 . 0 G 0 C 0 0 0 ^ 0 0 3 0.0000000*000 0 .0300000*000

T n T . K MOL/L CALCD PCN T z Y X YC YDI

F

c Q^3 c7 • nu nnu u 1 . 8280-002 1. 8280-002 n n n 'J . u u 0 .97263 u . C X 0 7 J

n ?i A 7t. — n n n fi p 1 c Q /. inn 2 .2860-002 2. 2858-002 n n 1 0 .93261 u . c c 0 c ^ — nU .UUnn n?UCP? 2 9 6.000 2 .8290-002 2. 829't-002 -0.01 0 . 89'^27 u . c c 0 0 ^ 0 . 22 6 2 8

n n n ni P« 2

o a . n DO 3 . '690-002 3. '691-002 -0.00 0 . 8571*9 Q . ? 3 30 1 0.23295 Q . 0 0 GO 6

c J.in,-, U U . Jinnu u <* .2160-002 2159-002 0.00 0 .62 218 0.2375 2 0.23755 - n n n n n ^ c 1 n p "inn 1 U C • J u u 5 .0810-002 5. C813-002 -0.01 0 . 78 826 n ?i*?i ?

U . t ** C X J 0 . 21* 2 0 7 nU •• pL nU nU nU 7f 3c X u . U U U 6 .0770-002 6. 0772-002 "0.00 0 . 7556'» 0 . 2'«65 3 n ?(. f, K

n

U . C*. D 7 U n n n n n 7 C inc. n n n 7 .2160-002 7. 2161-002 — n fi n 0 .72 1*25 n p ^ n A f\ n n A I* U . c V u 0 ** n n n n n ? u . u u U U c C

1 ii A linn 8 .5110-002 8. 5110-002 — n n n 0 . 69i»02 n p CI1 n U . c !> VX un p c; 1 n n n n n fl 1 U • U VI U V J C 11 U . U U U 9 . 9750-002 9.9753-002 —— n n n u . u u 0 . 66'«90 U . c P y 11 0 n n fi n n p u . u u u u c 2 112.000 1 . 1623-001 1. 1623-001 0.00 .63661 n 0 c "7 ^ •> U . c b 0 J c

n pt T 7 7 — n n n n n n ~U . UU U U 0 2

11/. n n n

1 1 H . U U U 1 . 3'*68-001 1. 3't68-001 _— n n n U • U U 0 . 6 0 971 U . c b / J c

n PC 7 7 n

U . CD / 0 u

n n n n n p

U • U U U U c 2 1 1 6 . J 00 1 . 5527-CO

1

1. 5527-001 3.00 0 . 58 351* n 0 7 14 7

0 .27119 n n n ft n 0 2 1 1 d • 3 0 0 1 . 781«»-001 1. 7813-001 n n n 0 . 55826 n p 7 /i Q c M • £L 1 1*^ P

n P7 I. Q A U . c f ** p 0 _— n n n n n p u . u U UU c o

c

1 » n n n n 1 c u . J u u 2 . 03<*6- 00 1 2. 031^5-001 n n 1 0 .53383 n ? 7 Af» /i U . c f OD H n p 7 A ft U . C 1 0 D D — nU.UUUUH n n n n £a oc. IP"? n n n

1 c c • 'J U U 2 .3139-001 2. 3138-001 n n n u . u u 0 .51019 n p A ?P f. U . c OCC D n p A p p A u . c 0 c c 0 n n n n n 1 U .UUUU.J

c

1 /. inn 1 c ^ . J U U 2 .6212-301 2. 6211-001 n n n U . U U 0 . 1.8 732 T ? A 7 7 n p A A n u . c 0 p 0 u «— n n n n n U .UUUU J z 1 2 6 . J 00 2 .9583-001 2. 9582-OGl 0.00 0 . 1*6 5 17 U . c: 8 yc 1

n p Q Q p 7

U . CO p c 0 —— nU.UUUUc n n n n p 2 12^.000 3 .3272-001 3. 3271-001 0.00 0 .1*1*372 n 0 0 0 c c 0.29257 rt n n ft n 7 2 liU.OOO 3. 7299-00 1 3. 7299-CGl 0.0 0 0 . 1*2292 0.29582 0 .29583 -0.00031

2 132. JQO '4 .1686-001 1687-001 -0.00 0 . 1*0 276 0.29902 0 .29900 0.0000 2 2 13'+. JOO I4 .6'*57-00 1 61*61-001 -0.01 0 , 38320 0. 30213 0.30209 0 . 00001*

2 I3r>. JOO 5 .1638-00 1 5. 16'4'4-001 -0.0 1 0 . 361*21 0.30515 0.30510 0.00006

2 138.300 5 . 7255-00 1 5. 726'*-0Gl -1.02 0 .31*577 0.30811 0.30803 0.00008

2 li^O .000 6 . 3337-001 6. 3351-OCl -0 .C 2 0 . 32786 0 .31099 0 .310 68 0.00011

2 1'42. JOO 6 .9916-001 6. 9937-001 -3.03 0 . 3101*6 0. 31380 0.31366 0 . 00011*

2 l-ti*. JOO 7 . 7028-00 1 7. 7055-001 -O.Oi* 0 .29353 0. 31651* 0.31637 0.00016

2 l'«o.OGO 8 . 7 1 1 - J C 1 6 . '7^5-oa^ -0.0 < 0 .27708 0. 31920 0 .31901 0 .00C19

2 1 US . 0 0 0 9 . 3C0 7-CG 1 9. 30'49- 0 0 1 -3.05 0 .26106 0.32179 0.32153 0.00021

2 15 J .000 1 . Cl9b+uOO 1. G201»- 000 -0.05 0 . 21*51*8 0. 321*31 0 .321*09 0.C0022

2 152.000 1 . lloi^^OOO 1. 1169*000 -0.05 0 . 23 030 0 . 32675 0.32653 0.00022

2 I5i». JOO 1 . 2 1:' 0 9 + 1 : G 1. 221'«+CGG -0.05 0 .21552 0.32912 0.32691 0.00021

2 15 6.000 1 . 3 i38*00 C 1

.

33'43 + 0 jL -0.OI+ 0 .20111 0. 3311*0 0.33123 0 .00 017

2 155.000 1 . '«560*OOL) 1. 1*563*000 -0.02 0 .19 707 0. 33361 0.33350 0.00011

2 160.000 1 . 538'»tOO0 1. 586'«* OGG -0.00 c .17339 3 . 35571 0. 33571 0.00003

2 162.000 1 , 7j22+0J0 1

.

7 3 1 6 + 0 . G G .0 3 0 . 16001* 0.33772 0 .33788 -0.00016

2 1 b < . J 0 J 1 . 3 tt rt 6 J G 1. b67C+0uC J. 06 0 .11*701 0.33961 0.31*000 -0.00039

2 1 b b . 0 0 0 2 .0593*00 0 2. G5bl+0G0 0.16 c . 1 31*30 0 . 31*135 0.31*208 -0.00073

Ibd . Ju

J

2 . 2 •« t. 5 .K O 2. 2'*06+ 000 :.26 0 .12190 0 . 31*291 0.31*1*12 -3.00 121 Iblo 1 b 9 • J 67 2 . 3'i8e + JJ J C • j'loj* OOG 0.11 0 .1151*0 3 . 3<*i*69 0.31*520 -0.00051

Id 3. 2 70 2 . 3be7*CC G 3b70+CvL : .c 7 0 .111*17 0.31*506 0 .31*51*0 -0.00035

^12 169. I? £. . 3 n 5 a 0 0 0 2. j821fOCO 0.16 0 . 1 1 328 0 . 31*1*80 0.31*555 -0.00075

1612 169. ^bS 2 .3dtilv0C0 2. 3e73*CuO 0.03 c . 1 1 297 0. 3t*5i*5 0 .31*560 -0.00015

910 1 b9 .oOl 2 . u i . 5 ii + j 0 G 2 . hC11*CuC 0.18 c .11217 0. 31*1*83 0.31*573 -0 .00085

^cd lo9. J'ih . H ^ 3 6 : 0 0 2. ii215*C3 0 j.lO c .11101 0 . 3i*5i* 7 0.31*593 -0 .0001*6 1716 17^.099 2 . 7972 + 00 0 79611 * 0 G . 0 3 0 . C9162 0. 31*905 0.31*920 -0.00015

17 i. 2 00 2 .6203*000 0 8215+COO -O.O"* 0 . 0901*6 0 .31*961 0 .31*91*3 3.00021

OSILVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. «80 L - 2 I
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY

1LMD\JKM AR<^DATOPY 1 \_/K T KJOTP iNl^lC

PROJECT NO. 2750364FILE NO.

1 «J TM _J

PAGE 21

SUBJECT The Orthobaric Densities of Ethane , Methane, Oxygen and

Fluorine

R . D . Goodwin

DATE Seot. 18. 1973

Table 14- (Continued) . Methane vapor densities.

ID T ,K MOL/L CftLCD PCNT z YX YC YOIF

1712 173.1489 2.8i*57-»-000 2. 81*65+000 -0.03 0 .08931 0 . 3'»973 0.3'^959 0 .OOOl'^ 1012 1 73.'»73 2 . 81*60 +000 2.8'* '5 + 000 0.12 0 .089'*0 0 . 31*896 0 .si^gsa -0 .00062

1010 173.675 2.870C+000 pc . Or Ui.>UUU -0.00 0 .0382'* 0 . 31*980 0 .3'»978 0.00002

1006 173.857 2 . 8935*00 0 c . aqT^ 4. n n n 0.0 0 0 .08720 0 . 3'*995 0 . 3'^996 -O.ODOO

1

1616 17 7. 09'* 3.3501+00 0 3 . 7c: * ?+ n n

0

-0.03 0.06901 0 . 35 33 3 0 . 35 3 1

5

0 .0001 a iai<» 1 7 7.2 92 3 . 3801+00 0 3 . -0.06 0 .06792 0 . 35369 0 . 35335 0.0003'^

ill** 177.328 3.3663+00 0

•»o . J Q 1 J~UUU -0.05 0 .06772 0 . ZSZf>i* 0 .35 3 39 0.00025

1812 1 77.i»85 3. '108 + 000 3 . •ACO'UUU 7ft*nnn -0.06 0 .06686 0. 35386 0 .35351* 0.00031

1112 177.509 3.i»209+000 3

.

ill 'AOO~UUU f^Fii-nnn 0.12 0.06673 0.35290 0 .35357 -0.00067

1110 177.700 3.1*602 + 000 7o . 0.37 u

n c; A A . U 0 vbo 0.35175 0.35376 -0.00200

1916 181.105 1*. 0663 + 000 H .

r, c, Q c, * r n n -0.06 n

U

n 7 7 A 0.35755 0.35722 0.00033

181.30'* «*. 1077 + 000 1* . llUl+UuU -0.06 U

p /. (1 7 7 . U H 0 J 0 0.35778 0 .3571*3 0.00031* 1213 181.389 1*. 1269 + 000 /.H .

*icOl+UUU ^ai^nnn -0,03 nU

n f. c; A A . U H 5 0 0 0 .35769 0 .35752 0.00017

1912 181.506 11*96 + 00 0 1* . IPJU+UUU -0.08 U 0. 35813 0 . 35765 0 .0001*8 1211 181 .589 t*. 1656 + OOU L, If uo+uuu -0.12 0 . 0 ''83 0. 356'^8 0.35771* 0.00071* 1209 18 1 . 763 1*. 201*2 + 000 1,H • cU^f c> n Q 7 i p .1 fi + LI1JU -0.13 0 . 0 '* 389 0.35870 0 .35793 0.00078

1516 163.117 '.5212 + 000 1* . c /. n i n n r -0.06 0 .0 3 663 0. 35978 0 .3591*0 0.00038

151<» 18 3. 322 '.570<* + 000 1* . -0.11 0 .0 3 582 0 . 36032 0 .35963 0 .00069

1512 18 3.51'* '.6189 + 000 1* . bdi^b+UUU -0.12 0 . 03'«e'* 0. 36063 0 . 35965 0 .00078

1316 18 <*. 125 '. 7B22+000 * . 7Aftn*finn fOOUTUUU -0.12 0 . 0 3171 0 . 3613'^ 0.36055 0.00079

2106 181*. J87 1*. 7825 + 00 0 1* . 7775+000 0.10 0 .03190 0 . 35982 0 .36051 -0.00068

210 7 181*. 285 '*. 8263 + O0C 1* . 8>52(+0Gb -0.13 0 .03089 0. 36161 0 . 36071* 0.00087

131(» 181*. 370 t*. 8'*62 + 000 1* . OPbf+UUU QC£L7ifinn -0.22 0 . 0 30'*6 0 . 36228 0 .36061* 0.0011*1* 2106 181*. 1*71 '.8797 + 000 1* . e85'+DUU -0.12 0 .02991* 0. 36177 0.36096 0.00081

1312 iei*.51J 1*. 3676 + 000 1* . 8969+000 -0.19 0 .02975 0.36228 0,36101 0.00127

6 185.030 5. J360 + 00O 5. 052i*+00C -0.28 0 .02711 0. 36359 0 .3616'* 0.00195

6 1 86. 030 5 . 381*0 + 000 5. 3838+000 0.00 0 .02208 0.36290 0.36292 -0.00002

2206 186.103 5. 1*077 + 000 5. 1*0 98+ 0 00 -0.01* 0 .02172 0. 36331 0.36302 0.00029

1W16 186.129 5.1*096 + 030 5. 1*192 + 000 -0.18 0 .02159 0. 36'^36 0.36305 0.00131

li^l** 186.319 5. 1*795 + 000 5. 1*691+0 0 0 -C.17 0 . 02061* 0.36<^61 0.36331 0.00130

220 7 1 86. 301* 5 . 1*827 + 000 5. 1*6 35+ 000 -0.01 0 .02072 0. 36339 0.36329 O.OOOIQ

220b 186.501 5. 5571+000 5. 5581+000 -0.02 0 . 0 1971* 0. 36369 0.36356 0.00013

l'»12 1 36.518 5.5591+000 5. 561*6+000 -0.10 0 . C 1965 C . 36i^3'* 0.36359 0.00075

6 18 7 . 0 31 5. 7860+000 5. 7723+OUU 0.21* 0 .0 1711 0. 362i*'^ 0 .36i*33 -0.00 189

6 18d.031 6. 2750+000 6. 2'*7i*+000 0.1*1* 0 . 0 1219 0. 36201 0.36592 -0.00392

2308 188. 11*0 6. 2930+000 6. 306i*+000 -0.21 0 .01165 0 . 3680'^ 0 .36612 0.00193

230 7 183.31*3 6. <*o67 + 000 6. '.216+000 -0.21* 0 . 0 1066 0. 36868 3 .366i^8 0 .00 219

2306 188.51*5 6.5276+000 6. 51*1*1 + 000 -0.25 0 .00956 0, 36926 0.36686 0 .00239

6 189.032 6.9180+000 6. 8777+000 0.59 0 .00732 0. 36167 0.36787 -0.00620

5 189. 765 7.5510+000 7. 5576+OCO -0.09 0 . 0 0 378 0. 37093 0.36975 0 .00117

6 193 .J32 7.9600+000 7. 9153+OOC 0.56 0 .00250 0 . 36186 0.37065 -0,00879

5 19 J. 0 4*6 7 . 9350 +0 00 7. 9371+000 -0.03 0 . 0 0 21*3 0.37113 0.37070 0 . 0001*3

7 190. J70 6.0000+030 7. y756+000 0.31 0 .0 3232 0.36588 0.37079 -0 .001*91

7 193. 17J 6.170C+0G0 8. 1506+000 0.21* 0 . C 0 181* 0.3670 9 0 .37120 -0 . 001^1 2

7 190 .270 8. 36oc+oac 6. 3595+OOC O.Cl 0 .00 136 0 . 3715'^ 0 .37166 -0.00013

5 19 0 .279 8 . 392 u + 0 0 0 8. 3605+000 0.11* 0 . 0 3 132 0.36899 0 .37171 -0,00272

7 1 i J. 370 8.6200+300 6. 621*2+ 000 -0.05 0 .00088 0. 37333 3.37221 0,00112

7 19 3.1*70 9. OuOO+OOC 9. 0116+000 -0 .13 0 . 0 0 01*1 0.37689 3.37291 0,00397

5 190 .500 9. 1610+000 9. 1667+000 -0.26 c . C 0 026 0. 38333 3 .37319 0.01011*

NP :: 96, RMSPCT :: 0 .11*6

oaiLVIE PRESS. INC.. BROOKLYN 17. N. T. STOCK NO. 480 L-22
r4AIIV./nAL DUKCAU KJT OlAriUAKUd, L.KTV,/\7CNIC tNVjlNttKlH(> LABORATOKY LABORATORY NOTE 2750364

fllE NO. 73-5PAGE 22

SUBJECT rr^u r\ 4.U \^ 1 he Orthobaric

Fluorine

Densities of Ethane , Methane, Oxygen and hJAME R.D ,Gooc3win

DATE

Cj

f iq73

T able 11 Compari son of e thane vapor c3en sitie s

.

1

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•1-4 -H •H T-l •H H •H CVJ CVJ CVJ CVJ CVJ CM (VJ CVJ CVJ CV CVJ CVI CVJ ro ro ro ro ro

ID a o o a o (3 a a o a o

OQILVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. -ISO T _ 7
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING UBORATORY LABORATORY KIOTF

PROJECT NO. 0 7 C 0 /I

FILE NO.

1 J — -J

PAGE 23

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R .D .Goodwin

DATE

Table 16. Ethane vapor data not used for least squares.

Li. vO (\J CO ro oo lf\ ID (T> ir\ tr> k£> -3> J- fM vC ITi in to J- 03 o n? M Q o H CM u> <T» 00 O tvj OS K> J- 09 o CO CO CS 0^ cr •»-( OO ^ -* ^ <T> PO IPI 1*) Q O a o a o o H J- CVJ CM »H o C3 a o H C3 o H o o tH a o o a a O i-t OJ J- o

>- o o a o o o o CJ a O o O o o O O o o o C3 o o a o o O o o o o *-l o o o o o o o o o o o o <3 o o C3 O o o o o o o a o o

• • • » • o • • • 9 « • • • • « • o e o » • • • • « « • • • • • o

« 1 cs

1 CD

t o

1 o

1 o

1 o

t o

1 o

1 o

I 1 o1 o

1 o

t o

I o1 O

• e o o o o o o a O o o o

o o cr in fVJ H in CM o CO ao in J- CM in -r ro CM r^ in in ro a J- J- in

J- o in o J- N. (T o vO J- ro in o o> 1^ m vO t m vD in f*. J- T-t o in c> ^ 00 OJ iH o J- J- « ro oo CM vC 1-) m in (r> ro in K <r o CM CM (M

in in in f«- CO <M rr> ro J- J- in in V0 >X) N. N. f>>. t>~ 00 « a> oo o> IT> cy CJ»

1-1 •«-! 1-* »H •H ^ H a %H H <r-t iH »H •H T-t H -<-«

C3 o O o o O o o o o o O C5 O o O o o o o o O o o o o CJ a o a C3 o a

>i3 CM vD r>- CT" ro J- iH cr ro C3 ro ro <D oo 1-t CM i-« vO in <s CM CP CM N- (M 00 0> ro

-» o J- r^ 00 K a O CM CM i-« o» vO OO 1-1 iH r>s. vO «0 in m ^ 63 i-« o in a «0 in 1-4 o m <j> ro r«. 1-t in N. a ro <e fO CM S- CM in o vC iH in o ^ (jO oo O CM CM vO ro in in in vo ro N 1^ CM ro ro J- J- in in vO vO r^ CO r>* CO oo 00 oo CP ff* <T> cr <j> o

i-» »H i-« o iH 1^ 1-1 iH 1-t •»-( 1^ 1-1 H 1^ 1-1 i-« T-l 1^ 1-1 1-t 1^ 1-4 1-1 iH 1-t CM o a o a o o o o o » o o o a O o o O o o o o O o o o O O C3 o o o o

OS in 1-4 O CM in P«» >o CP iH CM CT" ro 1-« ro i-« CM CM cr> ro CM OO OO <J» CM ro in

ro r>- in vo o r«. o CM OO cr> m O CM a oo CM C vO 00 CM o ^ ro cr vO cr CM

CM CM ro 4- \D cr CM ro in in in vO in in vO <£) o" cy CM J- CM r^ ro O vD ^ CM 1-1 03 a

oo r>- in J" ro CM CM r^ 1-1 ea CT^ SO r^ m J- ro ro CM ro CM 1-) 1-) o o a CD a o

o o o o o o o CM i-« 1-* v-t 1-1 o o o o o o o a o c3 a o a a o C9 o a

• • • • 9 « * « « • 0 9 « o o C3 O C3 o o O o O C3 a a o a o o C3 O o o a a a o o o o o C9 o o

t— ro i-« >£> to ro 1-t ro J- CM 1-4 N. 00 ro in CM 1-t vO 03 iH in -9- CM ro CP ro o OO z o (9 H CM 1-4 fO 1-4 CM J- in J- ro ro ro o ro 1-t 1-4 1-1 CM CM CM ro m

u • • • • a • e o « • e « • • • « » • » • • • • • • • • • • • » • 0. a

I Q O o O O 1-4 1-t iH o o o o o o o o o o a

1 o1 o1 a

1 C3

) a

t o1 oI o

1 a

1 1 o

1

a H o a o o O o O CM i-« 1-t 1-1 1-t 1-4 1-4 O o C3 O o O o O o C9 o o a O o O

u o o o o o o o o o o o a O o o o O o o o a O a o O o o o o o

-i o o o o o o o o a a o o o o a o a o o o O a a o o o o

<i ! + 4- + * ) t t I » \ « 4- + + 4- •s> + + + • + + * + + + o in 1-4 ro r>. J- •Si ro CM ro CM v£) J- vO J- iH CM CP CO in CO CP in CP rv. x> J- CM SM CM o OO CO ro -J- iH CM h- *o J- vO CM ro ro ro 00 CP f) in oo J- CP 05 in 00 -t CM o in 1-4 o CM 00 1-1 CM O 1-4 1-i in CP 1-4 m in ro o 0^ CM 03 CM in o J- o 1-t fO in iH

1-t CM J- OO 1-4 in CO r^ cr J- in in O 1-4 ro in 00 C3 -i- o J- oo 1-4 in <p ro ro CP

• « « • « • e e 9

1-t 1-4 1-) iH iH CM CM vO ro J- in vO r^ oo 1-1 1-t iH 1-4 iH CM CM CO CM CM ro ro ro J- J- in in in

1-t a O o O O o C9 CM iH 1-1 1^ f-l 1-4 1-t O a o a a a a O o o o o o o o o o

o o a o o o o C3 a o o C3 C3 a o o o C3 o o o o o C3 o o a o o o o o o

_J CJ o a o o o O o C3 O C3 o o o o o a C3 o O CJ C3 a o o o CJ o

o 1

•4- + •¥ + + 1 « 1 1 % 1 1 + + * + + + + »• + 4- •f + + + + + 4- 3l r>- CM -a- 1-1 in 1-t r^ a m ro N. O CP 1-t ro oo (M in in o 05 ro CM ro ro ro ro CP CM in J- J' 1-1 m ro 00 1-4 iH 1-1 r* a 1-4 00 05 •H o O J- in o r«- vO in 1-1 o CM oo o <y> N. ro J- CM ro CM vO in -a- iM « 1-t vD 1-1 in o -s- CP CM CM 05 a a CM J- vD OO CM oo CP vD J' in O H fO in oo o J- o J- OO 1-4 in CP CM o ro CO

<p 1^ 1-1 1-1 i-( 1-1 CM CM vO ro J- in 00 1-1 1-4 H 1-t 1-4 CM CM CM CM CM ro ro ro J- J" in in in

^ac3oaooooor».rOi-tooincM0^05CMaoov0^c3ooooc3oc3C3oa •.ooooooooooacMrovOj-ooorocpror>>-ino(Poof>^i^»X)vOiOininin

I— aaOOOOOainCMvOCPCM^DOcOCMrs.o05intMCM'Hi-10)i-lvi)i-ti-li-t>X)i-t

incjinoinoinoj-oJJ-aorofloroooroaorooorocorocorointoocMroj-j-in

invOoiN-h-oooooicocMroro-^j-ininuDosr^tv-coeoaofloo^cPO^ocaoooo

CMCMCMCMCMCMCMCUi-tCMCMCMCMCNJCMCOCMCMCMCMCMCMCMCMCMCMCMrorOrorororO

Q i'4i-ti^i-4i-li-4'Hi-4O303O3vDvDvOvOve\O05ij0vOvjDvO

t-4

oaiLvie PRESS, inc., Brooklyn )7. n. y. stock ho. 4so L-24
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE 2750364 73-5 24

SUBJECT r^Yie Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

^**^^ R.D.Goodwin

DATE Sent. 18. 1973

Table 17. Calculated oxygen vapor densities.

R,MOL/L DR/DT D2R/DT2

7 H • O V X 3. 3612-00i» J . O f CI nU nU 7 2.'»35'»-•005

5 &u .• Qu 00u w 5. 3288-00'* X • "T"T ^ t nU nL. U H 3.i»007-005

5 8.000 8.99<»l-00<f ? . ?70 9- 0U 0U u" it. 9253- 005

60. 000 l.<»6*»<t-0 03 *J • *T *T ^ 0 flu 6.8929-005

62.0 00 2. 3066-003 5. 0609- 0w ouu *t 9. 3527- 0 0 5

V ~ V WWW 3.5251-003 7. ?? 1 3- 0 Ql* 1.23'*2- 0 0'* 6w 6.000 W • W u u 5. 2388-003 1X . nU nU >J 7 n n 3 X • ^ V %J *T fi n u

6 8.000 7. 5899-003 X . O O X o nu nu o3 1 . QQQ n

L • ^ u 0U nU uH

7f 0.000 u • u u u 1. 07<»2-002 X . O U w o n n 3 u u o t . ^ vl ^ 0w 0u u** 7f ?c .• nu nu nu 1. t»883-002 c • X X

n n 3 u u o 9 QA Aft- fl fl fl^ u u ** 2. 0220-002 nn c;n> o . U U 7 u

n n 7 u u on n L. u u *

7 6.000 2. 6983-002 O . « » O D n n 3 U U rj (i* . 1 A ti n o • X o * u — U U H 7m (inn 3. 5't21-002 H . OO X » — n n 7 u u o /iH ac;l.3- . O P H O n n ii u U ** MO n n

n

o u . u u u i*. 5802-002 O » 1 c s5 J — n n "7 0 U 0 9 . PO O H n n i» u u ** 0 c . u u u 5. 8'*12-002 b . ?! 1 O- n n 7 u U 0 6.32 3Q- nu nu u*

t . U U U 7. 3552-002 6 . c t) PH — ft n 7 U U <i 7.11 f . X X ftu 5- 0U 0U (iH

0 O . u U U 9. 15<»2-002 y . / D 1 f

n n "3 U U o 7f • Q5 10- X u u u •* A A n n n 0 0 . u u u 1. 1271-001 X . XH oO — n n ? u u c 8.8208- u • u ^ w u

7 J . u u u 1. 37'tl-OOl X . y o — n n 9 u u c ~ • ( coo not* u u *t Q 7 (inn 1. 6601-001 X . -? o o c— nu

nU c? i • U v3 f D nu nu 3o 4u . 0 no 1. 9887-001 X 9 f 7 O D n n 9 u U c X • X W V V 0W 0U 3w Q A ii n n 2. 36^*1-001 c? .

fiunu nu c?— n n 9 u U c 1.2703- 0u 0u o3 Q A (inn 2. 7902-001 c . ^ D ? X

n fi 9 1 . 37Q 3- %i \f X V U . V U U 3. 2716-001 C « 7Z> £. O n n 9 w U c. 1 , 1^9 t^if 0 0 3

1J. nu ^? «. nu nnu u 3. 8127-001 C . OO «J o fiu nu c? 1 . 61 6't- 0 0 3

1 3 U . 0 Qfl I*. '186-001 1 99i*- nU nU 2c. 1 . 7't 66- 0 0 3 10^ V 6.000 V V W W 5. O9'»3-001 3.5626- 0u 02w c 1.8865- 003

5. e^tSS-OOl 3. 95U8- 0u 02u c 2,0377- 003

110.000 X .X u • w u u 6. 6783-001 1*. 37 ft5- 0u 02u c 2. 2023- 003

X1 1X 2k. .• QUl 00u u 7. 5992-001 0u 0u 2c 2.3830- 0 0 3

1X X1 uH -. nU 0U nu 8.6155-001 V . O O »J u n n 9 u u c C . 1/ O £. 7 0U 0U 3«J X1 X1 ^ .. nu n n u u 9. 7353-001 s; A 7

1

nun 9 U c 9 An (;q— c . O U 9 ^ n n 7 u u o

X1 1X Ao . n n n u u u 1. 0967+000 O . ( C— n n 9 u U c 1O . n(> ^^Q— U 9 O ^ n n 3 U U J

1X c? n ii n n u . u u u 1. 2322*000 n n 9 u u c

7 7 li 9 9 — n n 7 u U X1 c? c? .

fiu nu nu 1. 3610*000 n fi 9 u U c 3.6695- 003

1X C? iiH . un unnu 1.5'+i»5 + 00Q AO . 50 7f O—A — n n 9 U U c '.0'»93- 003

1 ^ n n n 1 c o . U U U 1. 72<*3+00fl y • 1 u — n n U U £ '.'951- 003

1 O . U uU 1. 9220+000 1. 0371- 0 01 5.025'*- C03

1 "J 1 inn 2. 1399+000 l.lt»38- 001 5.6657-003

1 "7 o n n n 1 J <^ • 0 UU 2. 3805+000 1. 26'*7- 001 6.'*520- 003

13<«.0QQ 2. 6'»70 + 000 l.'*032- 001 7.'*368- 003

136.000 2. 9't33 + 000 1. 56i»l- 001 8.6997- 003

133. J03 3. 27'»5 + 000 1.7539- 001 1.0366-002

1^0.000 3. 6'»7i» + 000 1.9828- 001 1.26'*'*- 002

l<t2.000 <i. 0712+000 2.2661- 001 1.5903- 002

m<».ooo t*. 5592+000 2.63 0 0- 001 2.085'*- 002

l<f 6.000 5. 1316+000 3. lei^*- 001 2.9031- 002

1(*8.000 5. 8225+000 3.6373- 001 '*.'*33'*- 002

150.000 6. 6967+000 5.020'+- cai 7.9575- 002

152.000 7. 9136+000 7. 5't20- 001 2.03'*6- 001

15it.vJ00 1. 0230+001 2. 0822+000 2. 4*109 + 000

15 '.5 76 1. 3630+001 0.0000+000 0.0000+000

OSILVIE PRESS. INC., BROOKLYN 17. N. Y. STOCK NO. 4SO Lj-Z5
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING UBORATORY LABORATORY NOTE

PROJECT NO. FILE NO. 73-5PAGE

0 c SUBJECT fYie Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R .D .Goodwin

DATE Sppt. ^R 1Q7^

Table 18. Calculated fluorine vapor densitie s

.

T,K R,MOL/L DR/DT D2R/DT2

53.^81 5. 6700-00'* 1.6771- 001* (.2852- 005

5^.00Q 6. 6001-00^ 1.9119- QQk '+.7718- 005

56.000 1, 1518-003 3.0617- 00<* 7.0323- 005

58.000 1

.

9272-003 k. 7699- OQk 9.9683- 005

60 . G QQ 3 . 1038-003 7.1188- Q0<4 1.3650- 001*

62.000 8291-003 1.0283- 003 1.8127- 001* W . U U U 7 , 2821-003 003 2.34*26- 001* 1

.

0675-002 1.9709- 003 2.955'*- 001*

68.0 00 1

.

5253-002 2.6301- 003 3.6'*99- 001*

7 0.000 2. 1293-002 3.'+361- 003 '.1*236- 001*

72.000 2

.

9105-002 '.'0't6- 003 5.2731- 001*

7'*. 000 3. 9029-002 5.5501- 003 6.191*5- 001*

76. 000 5. l**3t»-002 6.8869- 003 7.181*1*- 001*

78.000 6. 6713-002 8.it282- 003 8.2395- 001*

80 .000 8. 5291-002 1.018 7- 002 9.3580- 001*

82.000 1. 0761-001 1. 2176- 0 02 1.0539- 003

8<«.000 1. 3i*16-001 1. ''07- 002 1.1783- 003

86.0 00 1. 65'*1-001 1. 6893- 002 1 . 3091*- 003

88.000 2. 0191-001 1.96'»9- 002 1.1*1*75- 003

9 0.000 2. ''20-001 2.2689- 002 1.5935- 003

92.000 2. 9286-001 2.6029- 002 1.71*82- 003

9'f.OOO 3. <»852-001 2.9638- 002 1.9129- 003

96.0 00 <». llSif-OOl 3 . •)& 88— 0Q2 2.0893- 003

98.000 (». 8352-001 3. 805it- 002 2.2793- 003

10^ V 0.000 V V www 5. 6'+32-001 '.2816- 002 2. 1*85'*- 003

A U Cs S W w u 6.5507-001 t».8009- 002 2.7105- 003

^ U ^ V U W v 7. 5667-001 5. 367't- 002 2.9585- 003

X U • W W w 8. 7012-001 5.9861- 002 3.2339- 003

A1 0u Au .• Qw QQu w 9. 9651-001 6.6631- 002 3. 51+26- 003

11 0 . a Q 0 1. 1371+000 7.4+058- 002 3.8918- 003

1 1 ? • n no 1. 2932+000 8.2232- 002 i*.2910- 003

X1 X1 £*T .• Qu DOu u 1. <t666*000 9.126«+- 002 t*.7523- 003

116.000 1.6590+000 1. 0129- 001 5.2919- 003

118.000 1. 8725+000 1.1250- 001 5.9315- 003

12 0.000 2. 1099+000 1.2511- 001 6.7C13- 003

122.000 2. 37«»1 + 000 1.39'*2- 001 7.61*3 7- 003

.Ap 1 2b. ^ • 0W 00W W 2. 6690+000 1. 558<*- 001 8.8210- 003

126.000 X U V W V v 2. 9992+000 1.7i»92- 001 1.0328- 002

126.000 3. 3709+000 1.97if6- OGl 1.2313- C02

130.000 3 • 7921+000 2.2't65- 001 1.5026- 002

132.000 2739+000 2.583'*- 001 1.8913- 002

13^^.000 h. 8319+000 3. 0165- 001 2.i»8i*l- 002

136.000 5. '9C5 + 000 3.6028- 001 3.1*720- 002

138.000 6.2909+000 tf.'+628- 001 5.3532- 002

li»0.000 7. 3133+000 5.9079- 001 9.81*76- 002

1^2.000 8. 76^ ' + 000 9. l'*69- 001 2.7251- 001

I't'i.OOO 1. 1893+001 3.5620+COO 7.7289+COO

1<»'».310 1. 5150+001 0.0000+000 0.0000+000

oeiLvie PRESS, inc., Brooklyn it. h. y. stock no. 4so L-26
NAilUNAL klATI/*tklAt DIIDCAII dUKcAU KJr olANDARUo, CTA kjr\ A Dr\C /*DV^\^ CRYC/OcNIL CkJ 1 CkJ^ cNtjlNccRiNl^ IkJCCDI 1 A D^B A T^BV LAoOKATORY LABORATORY NOTE

PtOJECT NO. 2750364

FILE NO. •73-5

PAGE 26

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R .D .OnnHwin

DATE

.c;«pt 1R 1Q7-?

Table 19. Calculated methane vapor densities.

T .K R,MOL/L DR/DT D2R/Dt2

90*660 1. 5679-002 1. 8523- 003 1.7385- QQi*

92.000 1. 6260-002 2.0919- 003 1.8937- 001*

9't.aoo 2. 2856-002 2.**952- 003 2.11*09- 001*

96.000 2. 629*t-002 2.9'»92- 003 2.1*020- 001* 98.000 3. 1*691-002 3.1*569- 003 2.6763- 001*

100 .000 k. 2159-002 <».0206- 003 2.9631*- 001*

102.000 5. 0813-002 1*. 61*30- 003 3.2628- 001*

10<f.00Q 6. 0772-002 5.3265- 003 3. 571*1*- 001*

106.000 7.2161-002 6.0736- 003 3.8980- 001*

106.000 8.5110-002 6.6666- 003 i*.2339- OQi*

110.000 9.9753-002 7.768 0- 003 i*.5823- 001*

112.000 1. 1623-001 8.7201*- 003 1*. 91*39- OQi*

ii<i.aoo 1. 3<*68-001 9. 71*65- 003 5.3195- OQi*

116.000 1. 5527-001 1.081*9- 002 5.7100- 001*

118.000 1. 7813-001 1.2032- 002 6.1170- OQI*

120.000 2. O3'»5-001 1.3297- 002 6.51*20- COi*

122.000 2. 3138-001 1.1*650- 002 6.9870- 001+

i2'«.aoo 2. 6211-001 1.6093- 002 7.1*51*5- 001*

126.000 2.9582-001 1. 7633- 002 7.91*71- 001*

128.000 3. 3271-001 1.9271*- 002 6.1*681- 001*

130.000 3. 7299-001 2.1023- 002 9.0211*- 001+

132.000 1*, 1687-001 2.2885- 002 9.6113- 0Q1+

13'».000 li. 6't61-001 2. 1*870- 002 1.021+3- 003

136.000 5. 16'»'»-001 2.6986- 0C2 1.0922- 003

138 .000 5. 7264-001 2.921*2- 002 1.1657- 003

ItfO.OOO 6. 3351-001 3.1652- 002 1.21*51*- 003

I'f 2.000 6. 9937-001 3.1+229- 002 1.3325- 003

lt»<f . 000 7. 7055-001 3.6968- 002 1.1*280- 003

1^6.000 6. U7'»5-001 3.991*8- 002 1.5335- 003

l<t8.000 9.30i»9-001 1*. 3130- 002 1.6506- 003

150.000 1. 0201+000 i*.6559- 002 1.7615- 003

152.000 1. 1169+000 5.0267- 002 1.9288- 003

15'».000 1. 221i» + 000 5.1*288- 002 2.0957- 003

156.000 1. 33'»3 + 000 5.8665- 002 2.2865- 003

158.000 1. '563 + 000 6.31*53- 002 2.5065- 003

160.000 1.588it + 000 6.8715- 002 2.7627- 003

162.000 1. 7316+000 7.1*531*- 002 3.061*3- 003

16^.000 1. 8870+000 8.1011- 002 3.i*2'*0- 003

166.000 2. 0561+000 8.6260- 002 3.6592- 003

168.000 2. 2ii08+fl00 9.6511*- 002 i+. 391*5- 003

170.000 2. tf'f30 + 000 1.0595- 001 5.0661- 003

172.000 2. 6656+000 1.1691- 001 5.9269- 003

17i*.000 2. 9119+000 1.2965- 001 7.0695- 003

176.000 3. 1867+000 1.1*51*6- 001 8.6322- 003

178.000 3.1*963 + 000 1.61*62- OCl 1.0673- 002

180.000 3. 6'»97+000 1.8973- 001 1.1*288- 002

182.000 2610 + 000 2.231+1*- 001 1.991*9- 002

18^.000 it. 7537+000 2.7271*- 001 3.0592- 002

186.000 5. 3730+000 3.51*61*- OGl 5.5251- 002

188.000 6. 2307+000 5.3071- 001 1.1*281- 001

190.000 7. 8666+000 1.1*866+000 1.7833+000

190.555 1. 02CC+001 0.0000+000 0.0000+000

OSILVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. A30 L-27
National bureau of standards, cryogenic engineering laboratory

LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-5

PAGE 27

SUBJECT rpj^^ Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

^^^^ T~\ T-v 1 K . D . Goodwin

DATE Sent. 18. 1973

Table 20. Calculated ethane vapor densities.

ETHANE SATURATED VAPOR DENSITIES

T,K

89.699

9Q.000

95.000

100.000

105.000

110.000

115.000

120.000

125.000

130.000

135.000

I'tO.OOO

l<t5.000

150.000

155.000

160.000

165.000

170.000

175.000

160.000

165.000

190.000

195.000

200.000

205.000

21 3.000

215.000

220.000

225.000

230.000

235.000

2<»0.000

2<»5.000

250.000

255.000

260.000

265.000

270.000

275.000

260.000

285.000

290.000

295.000

30 0.000

305.000

305.330

R,MOL/L

1.3511-006

1.3863-006

'.59*f<»-006

1.3356-005

3.t»683-005

8. 1696-005

1.768<*-00'*

3,5568-00'»

6.7091-00't

1.1963-003

2.030'»-003

3.2990-003

5.1575-003

7.7918-003

1. l'*18-002

1.628'»-002

2.2666-002

3.0869-002

'.1225-002

5.'»09'»-002

6. 9862-002

8.89i»'»-002

1.1178-001

1. 3885-001

1. 7066-001

2.0777-001

2.5078-001

3.0036-001

3.5725-001

t». 2230-001

'f.96«»7-001

5.8068-001

6. 7685-001

7.8599-001

9.1025-001

1.0521+000

1.21t»7+000

l.(»0234-000

1.6207+000

1.878(» + 000

2.1886+000

2.5736+000

3.0777+000

3.8180+000

5.6669+000

6.8700+000

DR/DT

3. '18-007

3.5229-007

1.0376-006

2.692'^-006

6.26i^8-006

1.3276-005

2.5955-005

it. 7323-005

6.1216-005

1.3223-00'^

2.0559-00<^

3.0703-00*^

'.'25 7-0 0'^ 6.1835-00'^

6.^C51-00<^

1.1151-003

l.<^ '78-003

1. e^^ '3-003

2. 3101-003

2.850'^-003

3. '707-003

'.1767-003

'.97'^2-003

5.6703-003

6.8727-003

7.9907-003

9.2355-003

1. 0621-002

1. 216*^-002

1.3887-002

1. 5817-002

1.7990-002

2.0'+53-002

2.3267-002

2.6519-002

3.0325-002

3. '858-002

'.C373-002

'.7273-002

5.6239-002

6.8532-002

8.6820-002

1.1813-001

1.9083-001

1. 2377+000

0.0000+000

D2R/DT2

7.9'^22-008

8.1081-008

2.1037-007

'.8256-007

9.9665-007

1.8818-006

3.2903-006

5.3851-006

8.3256-006

1.225'^-005

1.7283-005

2.3'^93-005

3.0926-005

3.9592-005

'.9'^7'^-0 0 5

6.0539-005

7.27'^i^-005

8.6050-C05

1.00'^3-00'^

1.1588-00'^

1.32'^3-00'^

1.501'^-00'^

1.6912-00'^

1.8956-00'^

2.1170-00'^

2.3567-00'^

2.6252-00'^

2.922'^-00'^

3.2581-00'^

3.6'^25-00'^

'.08 9'^-0 0'^ '.6176-00'^

5.2532-00'^

6.0330-00'^

7.0116-00'^

6.2712-00'^

9.9'»30-00«^

1.22'^6-003

1.5572-003

2.0691-003

2.9298-003

'.5876-003

8.62<^l-003

2.5135-002

2. '827 + 000

0.0000+000

OOILVIB PRESS. INC.. BROOKLYN 17. H. Y. STOCK NO. *V> L-28
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LAftOitATORY LABORATORY NOTE

PROJECT NO, 2750364

FIIE NO. 73-5

PAGE 28

SUBJECT jy^Q Orthobaric Densities of Ethane, Methane, Oxygen and

r luoi int:

NA^AE _ R .D .Goodwin

DATE Sent. 18.1973

10/10/73

PROGRAM LICKFIT

C REPRESENT ETHANE SATURATED LIQUID DENSITIES.

C DEFINE X = (TC-T)/TC-TT) , Q = X»»l/3, XE = X»»E, AND -

C DEFINE YY = (0-DC) / (DT-OC) , WHEN THE EQN. IS -

C (YY-X)/ (XE-X) = Al A2*Q2 + A3»Q3 . . . C DCRT = 6.86, 6.87 POSSIBLY VIA MY VAPORDEN EQN.

C DTRP = 21.68 ESTIM. VIA REID C. MILLER.

C ID, (9)TESTER, (lO)DOUSLIN, ( 1 1 ) SLIWINSKI , (12)CANFIEL0 ET AL.,

C ID, (13)KL0SEK, (li»)hILLER, (15)EUBANK, ( 16) TOMLI NSON

COMMON E,AZ, TTRP,TCRT , DTRP, DCRT, DRDT,D2RDT2, A(6)

C0MM0N/999/NP,NF,H(15) ,Y < 2 0 0 ) , G C 200 , 15)

DIMENSION ID(99) ,T(99) ,DEN(99) , U (99) ,W ( 99) , XQ (99)

1 F0RMAT(I5, 2F10.0)

2 FORMAT (IHl 13X IHE 8X2HAZ 6X<»HDCRT 8X2HSS)

3 F0RMAT(5X i*F10.3)

t* FORMAT (IHl 17X ETHANE SATURATED LIQUID DENSITIES, E = F6.3//

1 20X 6HTCRT =F8.3, 8H , TTRP =F6,k//

2 20X 6HDCRT =F6.3, BH, DTRP =F6.k// 2(13X 3E15.7/) /

3 8X2HID 7X3HT,K 5X5HM0L/L 6Xi»HCALC 'XtfHPCNT

li»X IHX 8X2HYX 8X2HYC 6XUHYDIF ) 5 F0RMAT(5X 15, 3F10.3, F8.2, F15.5, 3F10.5)

6 FORMATdHl 16X ETHANE SATURATED LIQUID DENSITIES^ //

1 17X 3HT,K 3X7HR,M0L/L 5X5HDR/DT 3X7HD2R/DT2 ) 7 FORMATdOX 2F1C.3, F10.*», F10.5)

9 F0RMAT(18X i»HNP =13, lOH, RMSPCT =F7.3/)

C

C DO ALL FOUR, OXYGEN, FLUORINE, METHANE, AND ETHANE.

10 DO 99 IG=1,<* $ GOTO (11,13,15,17) ,IG

C CONSTANTS FOR OXYGEN.

11 TTRP=5U.3507 $ TCRT = 1 5«». 576 $ TZ=52 J DT = 2 $ NZ=52

12 DTRP=ii0.83 $ DCRT=13.63 S DZ=13.58 $ EZ = 0.3«*0 $ GOTO 19

C CONSTANTS FOR FLUORINE.

13 TTRP=53.<*811 I TCRT = 1 31 $ TZ=50 S DT=2 « tiZ=t*B

Ik 0TRP='*i+.6623 $ DCRT = 15.15 $ OZ = 15.10 $ EZ = Q.3<»2 $ GOTO 19

C CONSTANTS FOR METHANE.

15 TTRP=90.680 $ TCRT=19C.555 $ TZ=88 $ DT=2 $ NZ=52

16 DTRP=28.1U7 S DCRT=10.20 $ DZ=10.05 J EZ=0.350 $ GOTO 19

C CONSTANTS FOR ETHANE.

17 TTRP=89.899 $ TCRT=305.33 $ TZ=80 % DT=5 t NZ='»6

18 DTRP=21.68 $ DCRT= 6.67 $ 0Z= 6.82 $ EZ = 0.3'*9

19 XN = TCRT-TTRP « YN = DTRP-DCRT

C READ NP DATA FOR LEAST SQUARES.

C READ L.A.WE3ER S OXYGEN VOLUMES, CC/MOL

.

20 00 27 J = l,99 J READ 1, I D ( J ) , T ( J) , DEN ( J ) $ IF(ID(J)) 21,28

21 IF(ID(J)-15) 23,22

22 CONTINUE

23 IF(ID(J)-99) 25, 2^* Zk DEN(J) = 10CG/DEN(J)

25 U(J) = X = {TCRT-T( J) ) /XN $ Q = CUBERTF(X) $ 00 26 K=2,6

26 G(J,K) = Q+^K J G(J,i) = 1 27 W(J) = (DEN (J) -DCRT) /YN

28 NPP = NP = J-1 $ NF = 3 $ E = 0.36

C EXPLORE E, AZ, AND DCRT.

29 AZ = NF S SSK = l.CE+010

30 DO i»9 IE=1,21 $ £ = EZ + O.OOl^IE

OGrLVIE PRESS, INC., BROOKLYN 17, N. Y. STOCK NO. ABO L-29
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. FILE NO. PAGE 2750364 73-5 29

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R D . Goodwin

DATE IS- 1^73

LICKFIT 10/10/73

C SET UP THE LEAST SQUARES ARRAYS.

36 DO ^0 J=1,NP $ X = U(J) $ XQ(J) = XE = X**E

37 \r(J) = (HC J>-X) / (XE-X)

kQ CONTINUE $ CALL EGENFT S SS = 0 $ 00 1*3 J = 1,NP $ YC = 0 $ DO kl K=1,NF

hi YC = yC H(K)*G(J,K) $ X = U(J) $ XE = XQ(J)

kZ DC = DCRT (X + {XE-X)»YC>»YN

^3 SS = SS {DEN(J)/DC-1)»»2 $ SS = 100»SQRTF(SS/NP)

IF(SS.LT.SSK) kSfitQ

1*5 SSK=SS $ EK=E $ AZK = AZ $ DK = DCRT

^6 00 k7 K=l,6

k7 A(K> = H(K)

k6 CONTINUE

<*9 CONTINUE

50 E=EK $ AZ=AZK t DCRT=OK $ YN = DTRP - DCRT

C USE SAVED CONSTANTS FOR DEVIATIONS.

60 PRINT k, E, TCRT,TTRP, DCRTjDTRP, (A(K) ,K=1,6) f SS = 0 61 DO 70 J=1,NPP $ X = U(J) J XE s X»»E $ XEX = XE-X

62 YC = 0 $ DO 63 K=1,NF

63 YC = YC ACK)»GCJ,K)

&< YS = X + XEX'YC $ DC = DCRT YN»YS

65 YX = (W(J)-X)/XEX $ YD = YX-YC

66 PCT = 100» (0EN(J)/0C-1> $ SS = SS PCT»»2

67 PRINT 5, ID (J) ,T(J) ,DEN( J) , DC,PCT, X,YX,YC,YD

68 IF(J-NP) 70,69

69 SS = SQRTF{SS/NP} $ PRINT 9, NP, SS

70 CONTINUE

C PRINT UNIFORM TABLE FOR PUBLICATION.

71 PRINT 6 $ DO 80 J=1,NZ t IF(J-l) 73,72

72 TT = TTRP $ GO TO 76

73 IF(J-NZ) 75,7%

7k TT = TCRT I GO TO 76

75 TT = TZ DT»J

76 R = DENLIQF(TT)

80 PRINT 7, TT,R,DROT,D2RDT2

99 CONTINUE

C DO OTHER ETHANE DATA WITH EXISTING COEFFICIENTS.

100 PRINT t*t E, TCRT, TTRP, DCRT, DTRP, (A(K) ,K = 1, 6) $ SS = 0 101 DO 110 J=l,99 $ READ 1, IDD,TT,ON S IF(IDD) 102,999

102 X=(TCRT-TT) /XN $ Q=CUBERTF(X) $ XEsX**E $ XEX=XE-X

103 YC = A(l) S DO 10k K=2,NF

IQk YC = YC A(K)»Q»*K

105 DC = DCRT + YN* (X+XEX*YC) I PCT = 100 ( DN/DC-1

)

106 YY = (DN-DCRT)/YN $ YX = (YY-X)/XEX $ YD = YX-YC

110 PRINT 5, IOD,TT,DN, DC, PCT, X,YX,YC,YD

999 STOP $ END

OOlLVIe PRESS. INC.. BNOOKLYN 17. N. V. STOCK HO. 4SO L-30
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-5PAGE 30

SUBJECT rj,^^ Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

R . D . Goodwin

OAn Sent. 18. 1973

10/10/73

PROGRAM VAPORFIT

C REPRESENT ETHANE SATURATED VAPOR DENSITIES.

C THIS FORM IS CONSTRAINED AT THE TRIPLE POINT, AND

C DEFINE X(T) AS FOR THE VAPOR PRESSURE EQUATION -

C Z = (1-X) = (TC/T-1)/{TC/TT-1) , ZE = Z»»E, Q = Z*»l/3, AND -

C DEFINE YY = LN ( OC/D) /L N ( DC/ D T) , AND THE DEPENDENT VARIABLE -

C Y(Z,YY) = (YY-Z)/{ZE-Z) , WHEN THE L.S. EQN. IS -

C Y(Z,YY) = Ai A2»Q2 + A3*Q3 + ^t^'^C^k + . . . C ID., (1) VIRIAL/V.P. , (6)P0RTER, (lO)DOUSLIN, (11 ) SL IWINSKI

.

COMMON E,AL, TTRP,TCRT, OTRP,DCRT, DRDT,D2RDT2, A(9>

C0MM0N/999/NP,NF,H(15) , Y ( 2 0 0 ) , G ( 20 0 , 15)

DIMENSION ID(99) ,T(99) ,DEN(99) , U(99),W(99), ZQ(99)

1 F0RMAT(I5, FIO.O, E15.5)

2 FORMATdHl 18X IHE 6X2HAL SX^fHOCRT 8X2HSS)

3 FORMATdCX 'F1G.3)

i* FORMATdHl 17X ETHANE SATURATED VAPOR DENSITIES, E = F6.3//

1 20X 6HTCRT =F8.3, 8H, TTRP =F6.k/

2 20X 6HDCRT =Fd.3, 8H, DTRP =E12.5// 2d3X *»E15.7/) /

2 8X2HID 7X3HT,K 8X5HM0L/L 8X5HCALCD i^X^^HPGNT

3 12X IHZ 8X2HYX 3X2HYC 6XtfHY0IF ) 5 F0RMAT(5X 15, F10.3, 2E13.t», F8.2, F13.5, 3F10.5)

6 F0RMAT{I5, 2F10.0)

7 FORMATdHl 16X *ETHANE SATURATED VAPOR DENSITIES* //

1 17X 3HT,K 6X7HR,M0L/L 8X5HDR/DT 6X7HD2R/DT2 ) 8 FORMATdOX F10.3, SElS.'t)

9 FORMATdSX <tHNP =13, lOH, RMSPCT =F7.3/)

61 FORMATdHl 7X2HID 7X3HT,K 8X5HM0L/L 8X5HGALCD *»XitHPCNT

1 12X IHZ 6X2HYX 8X2HYC 6Xi»HYDIF ) C

C DO ALL FOUR, OXYGEN, FLUORINE, METHANE, ETHANE.

10 DO 81 IG = 1,'+ $ GOTO (11,13,15,17) ,IG

C CONSTANTS FOR OXYGEN.

11 TTRP=5i*.3507 $ TCRT = 1 5tf . 576 $ TZ = 52 $ DT = 2 $ NZ=52

12 DTRP=3.36122E-«t I 0CRT = 13.63 f DZ = 13.58 J EZ=0.360 S GOTO 19

C CONSTANTS FOR FLUORINE.

13 TTRP=53.'+811 $ TCRT = 1 t+i*. 31 $ TZ = 50 $ DT = 2 $ NZ=48

Ik OTRP=5.670E-it S DCRT = 15.15 J DZ = 15.10 $ EZ = 0.3ttO I GOTO 19

C CONSTANTS FOR METHANE.

15 TTRP=90.660 $ TCRT=190.555 $ TZ=88 $ DT=2 $ NZ=52

16 OTRPsQ. 01567865 S OCRT=1C.20 J DZ=iO.G5 S EZ=0.360 $ GOTO 19

C CONSTANTS FOR ETHANE.

C OMIT Zkt AND FIX DTRP.

17 TTRP=89.899 $ TCRT = 305.33 S TZ = 80 $ 0T=5 $ NZ='»6

18 DTRP= L,35LlkE-b $ DCRT = 6.e7 S DZ = 6.8'» $ EZ=0.3ifO

19 ZN = TCRT/TTRP-1 $ YN = LOGF (DCRT/OTRP)

C READ OUR IDd) DATA MIXED WITH DOUSLIN.

C INCREASE OUR DEN BY 0.15 PCT TO AGREE WITH DOUSLIN.

20 00 27 J = 1,20C $ IF(IG-i») 22,21

21 READ 1, ID(J) ,T{J) ,DEN(J) $ IF(ID(J)) 23,28

22 READ 6, ID ( J) , T ( J) ,DEN ( J) $ IF(ID(J)) 25,28

23 IF(ID(J)-1) 25, 2'*

2<» CONTINUE

25 U(J) = Z = (TCRT/T(J) -1)/ZN f Q = CUBERTF(Z) f DO 26 K = 2,7

26 6 (J,K) = Q»»K $ G(J,1) = 1 27 W(J) = LOGF (DCRT/OEN ( J) ) /YN

OeiLVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. *BO L-31
NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. FILE NO. PAGE

SUBJECT -j^j^g Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R .D .GnoHwin

DATE Sent 18

VAPORFIT 10/10/73

28 NP = J-1 J AL=NF=5 $ E= 0.360

EXPLORE DCRT, AND EXPONENT E.

33 SSK = I.OE+OIC

3«t 00 kB IE = 1,21 I E = EZ 0.002»IE

SET UP THE ARRAYS FOR LEAST SQUARES.

36 DO 39 J=1,NP $ Z = U(J) S ZQ(J> = ZE = Z^^E

37 Y(J) = (W(J)-Z>/(ZE-Z)

39 CONTINUE I CALL EGENFT I SS = 0 NOW GET THE RMS DEVIATION.

'O DO kk J=1,NP $ YC = 0 $ 00 1*1 K=1,NF

kl YC = VC + H(K)»&(J,K)

'2 Z = U(J) $ YS = Z {ZGl(J)-Z)»YC

'»3 DC = OGRT*EXPF(-YN*YS)

1*1* SS = SS + (DC/DEN( J)-l)»*2 $ SS = 100 SQRTF (SS/NP)

1*5 IF(SS.LT.SSK) '6,«t6

46 SSK=SS $ EK=E I ALK = AL J DK=OCRT « 00 t*7 K = l,9

1*7 A(K) ' H(K)

kb CONTINUE

1*9 E=EK $ AL = ALK J OCRT = DK « YN = LOGF (DK/OTRP)

USE SAVED CONSTANTS FOR DEVIATIONS.

50 PRINT i*t E,TCRT,TTRP,DCRT,OTRP, (A(K) ,K=1,8) $ SS = 0 51 DO 59 J=1,NP $ Z = U(J> $ ZE = Z»*E $ ZEZ = ZE - Z 52 YC = 0 $ DO 53 K=1,NF

53 YC = YC ACK)*G(J,K)

5U YS = Z ZEZ»YC S DC = DCRT»EXPF ( -YN» YS)

55 YX = (W{J)-Z)/ZEZ $ YD = YX - YC

56 PCT = 100* (OEN( J>/0C-1) J SS = SS + PCT»»2

57 IF(IG.EQ.3.AND. J.EQ.t»8) 58,59

58 PRINT 61

59 PRINT 5, ID(J) ,T(J) ,DEN(J) , DC, PCT, Z,YX,YC,YO

60 SS = SQRTF (SS/NP) $ PRINT 9, NP, SS

PRINT UNIFORM TABLE FOR PUBLICATION.

71 PRINT 7 $ DO 80 J=1,NZ S IF(J-l) 73,72

72 TT = TTRP $ GO TO 76

73 IF(J-NZ) 75, 7'* 7i* TT = TCRT $ GO TO 76

75 TT = TZ DT^J

76 R = DENGASF(TT)

80 PRINT 8, TT,R, DRDT, D2RDT2

81 CONTINUE % PRINT 61

DO OTHER ETHANE DATA WITH EXISTING COEFFICIENTS.

82 00 88 J=l,99 $ READ 6, IDO,TT,0N J IF(IDO) 83,99

83 Z = (TCRT/TT-1)/ZN $ ZE = Z**E $ ZEZ = ZE - Z

a** Q = CU3ERTF{Z) $ YC = A(l) $ DO 85 K=2,NF

85 YC = YC A(K)»Q»»K

86 YY = LOGF (DCRT/DN)/YN $ YX = (YY-Z)/ZEZ $ YD = YX-YC

87 DC = DCRT»EXPF(-YN»(Z+ZEZ»YC) ) t PCT = 10 0 (DN/OC-1

)

88 PRINT 5, IDD,TT,DN, DC, PCT, Z,YX,YC,YD

99 STOP $ END

oeiLvia pREsa. inc , Brooklyn t7. N. t. stock no. 4so L-32
NAT10>4AL BUREAU Of STANHAPD^ rPYrv^FKIir PKi^lKIPPBIkJi^ 1 aR('\daT('%ov LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-5PAGE 32

SUBJECT The Orthobaric Densities of Ethane , >.Iethane, Oxygen and

Fluorine

NAME _ ^ „ , R . D . Goodwin

DATE Sent. 18. 1973

10/10/73

FUNCTION DENLiaF(T)

C ETHANE SATURATED LIQUID DENSITIES, MOL/L.

C Y - Al + A2+Q2 + A3*Q3 + . . . , YN = DTRP-DCRT,

C DEN = DCRT + YN*(X + (XE-X)*Y).

COMMON E, AZ,TTRP, TORT ,DTRP, DCRT, DRDT,D2RDT2, A(6)

1 FORMATdHO 9X DENLIQF = 0, T EXCEEDS TCRT. / ) 2 IF(TCRT-T) 3,t».,5

3 PRINT 1 J STOP

k DENLiaF=DCRT $ DRDT=D2RDT2= 0 $ RETURN

5 XN=TGRT-TTRP $ YN=DTRF-DCRT J X= (TCRT-T ) /XN $ DXDT=-1/XN

6 XE = X**E S XEl = E»XE/X S XE2 = (E- 1) XEl/X

7 W = CUBERTF(X) $ Wi = W/3/X $ W2 s - 2»Hl/3/X

8 Q = XE-X $ Ql = XEl - 1 $ Q2 = XE2

9 NF = AZ $ Y = Ad) $ Yl = Y2 = 0 J DO 11 K=2,NF

IC Y = Y + A (K) W^^K S Yl = Yi + K»A(K)*W (K-1)

11 Y2 = Y2 + K* (K-1) A (K) (K- 2)

12 Y2 = Y1»H2 + Y2*Wi»»2 S Yl = Y1*H1

13 OENLISF = DCRT + (X + Q»Y)*YN

lU DRDT =(14- Q»Yi + Q1*Y> YN+ DXDT

15 D2RDT2 = {a*Y2 + 2»Q1*Y1 + a2 * Y

) YN» DXO T*»2 $ RETURN $ END

10/10/73

FUNCTION DENGASF(T)

C ETHANE SATURATED i/APCR DENSITIES, MOL/L,

C Y = Al + A2*Q2 A3»C3 + . . , NF = AL, YN = L N ( D CRT/OTRP )

,

C U = Z + (ZE-ZJ*Y, DEN = DCRT*EXP (-YN*U )

.

C NOTE THAT Z = 0 ONLY AT T = TCRT, WHICH IS EXCLUDED.

COMMOS E,AL, TTRP,TCRT, DTRP,DCRT, DRDT,D2R0T2, A(9)

1 FORMATdHO 9X OENGASF = 0, T EXCEEDS TCRT. / ) 2 IF(TCRT-T) 3, it,

5

3 PRINT 1 S STOP

k OENGASF = DCRT i CRDT = D2RDT2 = 0 $ RETURN

5 ZN=TCRT/TTRP-1 $ YN=LOGF ( DCRT/ DTRP) S Z= ( TCRT / T-1) / ZN

6 OZDT = -TCRT/ZN/T»*2 S D2ZDT2 = -2*DZDT/T

7 Z£ = Z*»E $ ZEi = E*ZE/Z S ZE2 = (E-i)»ZEl/Z

8 X = ZE-Z $ Xi = ZFl - 1 $ X2 = ZE2

9 Q = CU3ERTF(Z) $ Ql = Q/3/Z $ a2 = -2*Ql/3/Z

10 NF = AL $ Y = Ad) $ Yl = Y2 = 0 $ DO 13 K = 2,NF

11 Y = Y + A(<)*a**<

12 Yi = Yi K»A (K) Q*' (K-1)

13 Y2 = Y2 + K*{K-l)*A(K)»Q»*(K-2)

ik Y2 = Yi»G2 Y2*Q1**2 $ Yl = Y1*Q1

15 U = Z * X»Y $ UA = 1 + X*Y1 X1*Y 5 Ul = UA*DZDT

16 U2 = UA»D2ZDT2 + (X»Y2 + 2*X1*Y1 + X2*Y ) DZDT»*2

17 XP = EXPF(-YN»U) S DENGASF = F = DCRT*XP S YU = -YN»U1

18 DRDT = YU*F J D2RDT2 = ( YU* Y U- YN* U2 ) F $ RETURN $ END

OGILVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 4SO L-33

APPENDIX M

M-1
Cryogenics Division-NBS Institute for Basic Standards LABORATORY NOTE

COST CENTER 2750364

FILE NO 73-6

PAGE

SUBJECT Liquid-Vapor Saturation (Orthobaric) Temperatures of

Ethane and Methane

NAME Goodwin

Nov. 28, 1973

1, Introduction,

The present, new investigation has been necessary to accommodate the

extreme range of ethane saturated vapor densities (a factor of 10 ). Our previous

work on ethane appears in Lab, Notes 73-2,3,4,5.

Analytical description of the two-phase, liquid-vapor equilibrium (temperature-density relationship) is needed for our new equation of state which originates on this locus (NBS IR 73-342). In particular, the forms used below give the important

property that all derivatives are zero at the critical point.

In the following we split the range, using different functions according

P ^ Pc . In each case the dependent variable is

Y(T) (Tc /T-l)/(Tc /Tt-1) (1)

The symbols used here appear in a LIST,

2, The Saturated Vapor Temperatures . The analytical formulation is

where

and

Y(T)

U(a)

"W(rT)

U(a) 1 + Ao • -f.n (a/ag ) + W(cr )]

exp[a . (ug - u)], n

i = ]

The notation is q = a

1/3

qi).

1/3

(2)

(2-a)

(2-b)

, and lOg - 1 / I CTg - 1

This equation is constrained at the vapor triple point.

Fixed-point constants are given by table 1, and coefficients by table 2. The comparisons of results for ethane and for methane are in tables 3,5. Deviations

necessarily are systematic because the "data" are smoothed analytically (Lab. Note

73-5). We believe all deviations to be well within the real accuracy of the data.

3. The Saturated Liquid Temperatures . The analytical formulation is

where

^.n(Y)

W(o;

n

ut - u) + W(n )

(x' -xi).

(3)

(3-a)

SP 11342 A M-2 li- U S Government Printing Office 1973- ^ 7&0-339
Crvogemcs Divlsion-NBS Institute lor Basic Stanilards LABORATORY NOTE

SUBJECT Liiquid-Vapor Saturation (Orthobaric) Temperatures of

Ethane and Methane

COST CENTER 2750364

FILE NO 73-6PAGE 2 NAMEj^^p^ Goodwin

Nov. 28, 1973

The notation is = j - 1 j , u^ = 1 /xt .

This equation is constrained at the liquid triple point.

The comparisons of results for ethane and for methane are in tables 4,6.

Computer programs are attached.

LIST OF SYMBOLS

d, density, mol/-t, DEN

do , critical -point density, DCRT

dg , vapor triple -point density, DGAT

dt , liquid triple-point density, DTRP

1/3 1/3

q. ^ . qg = "^g

p, d/dt , density reduced at liquid triple point

a, d/d<; , density reduced at the critical point

(Jg , dg /dc 5 reduced triple-point vapor density

CTt , dt /dc , reduced triple-point liquid density

T, Ts(p), the saturation temperature

To, critical-point temperature, TCRT

Tt , triple-point temperature, TTRP

U, 1/x, Ug = 1/Xg , Ut = 1/xt

X, la - ll , Xg lag - ll , Xt = jat - ll

Table 1. The fixed -point constants

Ethane Methane

89.899 90. 680

To, K 305. 330 190. 555

do , mol/'t- 6. 87 10. 20

dt , liquid 21.68 28. 147

dg , vapor 1. 35114. 10"^ . 1.567 865

SP 11342 A M-3 U.S. Government Printing Office: 1973- § 780-3 3 9
Cryogenics Division-NBS Institute lor Basic Standards LABORATORY NOTE

COST CENTER 2750364

FILE NO 73-6

PAGE 3

SUBJECT Liquid-Vapor Saturation (Orthobaric) Temperatures of

Ethane and Methane

NAME R^D^ Goodwin

Nov. 28, 1973

Table 2. Coefficients for the equations

Ethane Methane

a 3/2 1/2

Ao -0.0610 6983 -0. 1596 5159

Ai -0.5510 7806 -0.6669 5380

Aa 1.8906 0757 1.0242 2995

Ae -4.8476 0684 -0,5885 7993

A4 8.5887 8625 0. 2042 8358

A5 -8.3103 1296

As 3.3001 3887

d 0.111 0. 043

T 0.009 0.004

Liquid 8 1/3 1/3

Bi 9.10717170 8.5837 7917

Bg -7.9603 9387 -7.0525 4699

B3 4.8472 6284 4.1610 2443

B4 -1.5919 0104 -1,36919291

Bg 0.2253 7899 0,2067 1342

SP 11342 A M-4 si- U S Government Printing Office, 1973- ^f 780-339
Cryogenics Division-NBS Institute lor Basic Standarits LABORATORY NOTE

COST CENTER 2750364

EILE NO 73 6PAGE 4

SUbJ-' Table 3. Ethane Saturated Vapor Temperatures

NAME r- ] R. J. Goodwin

°*"Nov, 28 1973

NF = 7, AL r 1. 500 , FE = G . 0 0 j , DGAT = LiSlli^-JO^

TTRP = P9.599, TCRT = 305.330, OTRP = 21. 680, DCRT 6, £70

-0 . 061 06983 -0 . 5 51:7806 1 .890 6C' 757 4+. 8^760 654+

8 . 58673625 -8. 3ir 31 296 3.30013387 c

,

0 0 0 0 0 0 0 0 0 . J C G 0 0 0 0 0 C . 0 c I C 0 0 u c 0.0 00 00000 0

.

OGOGOOOO

MOL/L CALC PCNT T ,K G ALC PCNT OTS/CC

1. 3? 11 (+-0^6 1. 3511 '+-C 06 0 . QC 39.899 39. 899 COG 2.915+006

1.38 5 31-0 06 1 . 3861 9-0 06 -0.01 90.000 90 . GOO 0.00 2 . 8 4« 3 + r C 6

it . 59'+«t3-0 06 ^ . 5813 1+-0 06 -0.28 95.000 95. 013 0.01 9.651+0C5

1 . 33361-005 1. 33129-005 -0 . 32 1 0 G . 0 0 0 100. G 16 0.02 3 . 7 144 + 0 0 5

3 ,kt5Zb-b(iS 3.'+6C67-0U5 -0 . 22 105.000 135 . 012 C . 0 1 1 .59'++0C5

8.16960-005 3. 16'+5h-005 -0.06 110.000 1 1 0 . 0 0 4+ G . G 0 7 . 5 18+ 0 0 4+ 1 . 768'+ 0^+ 1 . 7695 7-00'+ 0 . 0 e 115.003 114+, 995 -0.00 3.34+6 + 0C4+

3 . 5 5 6 3 1 - ! UT+ 3. 56292-00't 0.17 120 . C C 0 119.937 -0.01 2 .111 + 004+ 6.70 9 0 3-00^ 6 . 7225 g-OC* 0 .20 125 .0 0 0 124+ . 933 -0.01 1 .231 + 0G4+ 1. 1963'+-JC3 1. 198'+5-0C3 0 .18 130.000 129. 934+ -C . 01 7.567+003

2. 030^+1-0 0 3 2.0 3275-C03 0 .12 135.000 134+. 969 -0 . CI 4+ . 5 7 0 + 0 0 3 3.2990 3-0 0 3 3.30029-003 0 .04+ 14+0.0 0 0 1 39. 996 -0 . 0 c 3.262+C0 3 5. 1575it-u03 5. 1556 8-0 03 -0 . 14+5.009 14+5. 0 Q4+ 0.00 2 .263-^003

7.79177-0 0 3 7. 78'+'*9-003 -0 .09 15 0 . 0 0 0 150. C12 C . 01 1 .61<= + 0&3

l.l'+1 33-0 02 1. lit Oi* 0-002 -0.13 L55 . 0 0 0 155.017 C . 01 1.191+005

1.6? = '2-002 1 . 6262 8-002 -0.13 L60 . 0 G 0 160 . 019 0.01 8 .969 + 00 2

2 .26o60 -002 2. 26'+r; 2-0 02 -0.il 165 . 0 00 165 . C 18 0.01 6 . 903 + 00 2 3.0663 6-0 02 3 . oaf+ft 6-C 02 - 0 . 08 170 . 0 00 17G. C13 0.01 5. '+15 + 002

'.1224+7-0 02 '+. 1211'+-0G2 -0.03 175 .000 175 . 006 0.00 '+ .322+00 2 5. i+O 93 9-002 5.4+1016-002 0.01 180.000 179.997 -0.00 3.502+00 2 5.9£b23-0G2 6. 99 003-0 0

2

0.05 185 . 0 0 0 184+. 939 -C . 0 1 2,377+002

8 .Bgu 3^-0 02 6.90172-002 G . 08 190.0 00 189. 932 -G . 01 2.392+0 0 2 1.117 32-001 1 . 11 85 8 -0 01 0.10 195.000 194+. 979 - 0 . G 1 2.0C°+0G2

1.3t'^ 50-001 1. 33 97 8-001 0.09 200.000 199. 978 -0.01 1 .70'+ + 00 2 1.7C662-001 1 . 7 0 76 7- 0 01 0.07 235 .000 2 04+. 95 2 -0.01 l.'+57 + Q02

2 . 0777 0-0 01 2 . 0735 2-0 01 0.04+ 210.000 2 0 9.938 -0 . C 1 1.253+00 2 2.5L7BG-001 2.50 803-001 0.01 215.0 00 214+. 997 -0.00 1 .085 + 0 0 2 3.0G 559-001 3. 0 0 280-001 -0.03 220 . 0 0 0 220. 007 C . 0 0 9.'+3'+ + 001

3.572 53-0 01 3 . 5705 0 -0 01 -0.06 225. OOG 225. 017 0.01 3 .23'++001

4+. 223 0 1-001 '+. 2197 7-COl -0.08 230 .000 230. 023 0.01 7 .2 08 + 00 1 '+.96'+69-rjjl '+.96Q61-0 01 -0.03 235. 0 00 235. C2& 0.01 6 . 322 + 0 C

1

-0.07 2'+G.0 QO 2'+0. 023 C . 0 1 5.553+001

&.76'^5?-GQ1 6 . 765'+ 1 -0 Q 1 -0.05 24+5 . 0 0 0 24+5 . 015 0.01 H . 379 + 0 0 1 7.85990-001 7. 85922-001 -0 .01 250.000 250. 003 0.00 4+. 286+0C1

9.10251-0 01 9 . 1055 3-0 01 0 .03 2 55.0 00 254+. 989 -0.00 3.760+001

1 . 05210 + 0 0 J 1. 0525 3+OOC 0 .07 260.000 259. 976 -C . 01 3.291+OCl

1 .2i'+71 + G00 1. 21579+000 0 .09 265.000 264+. 969 -e .01 2 . 367 + 00 1 i.'+C231+C00 1 . '+0 34+3 + 0 0 0 0.08 2 7 0.000 269. 972 -0.01 2.'+82 + G01

1.62073+000 1. 6213 1 +0 0

G

a .04+ 275. 000 274+. 988 -G . 00 2.124*+0C1

1 . 37=)'+5 + 00D 1. 87773+000 -0.0'+ 2 3 0.000 2 3 0 . G 1

3

0 . 0 c 1 .788 + 00

1

2.18360+uOG 2.18616+OOf -0 .11 285.000 285 . 0 35 0.01 1 . 4463 *- 0 0 1 2.57 557+uOO 2 .57Gol+00C - 0 . 1

J

290 . 0 0 0 290. 0 32 G . 01 1.14+6+OGl

3.07/73+000 3. 0301 1+OGO 0.08 295 . 0.0 0 29'+. 980 -0.01 8.351+OOC

3 . 3 1 0 3 + u G G 3. 82168+000 U . 10 3 0 0.000 299. 980 -0 . 01 5. '+26+ 00 C

NP = hk, DNRMS^CT = 0.111, TSPMrPCT = 0.009

M-5
Cryogenics Oivision-NBS Institute tor Basic Standards LABORATORY NOTE

COST CENTER 2750364

FILE NO 73-6

PAGE 5

iUBJtui Liquid-Vapor Saturation (Orthobaric) 1 emperatures oi Ethane and Methane

R. D. Goodwin

"'^^^ Nov, 28, 1973

Table 4. Ethane Saturated Liquid Temperatures

NF = 5, AL = O.OCO, BE = 0. 333, OGAT = 1.3511it-006

TT^P = 89.899, TCRT = 305.330, DTRP = 21.f80, DCRT = 5.370

9.10717170

0.22537699

0.00000000

-7. 96039387

0 . 00 0 00 000

O.OOOCOOOO

0.00000000

0 . 0 0 0 000 00

0.00000000

0.00000000

MOL/L CALC PCNT T,K CALC PCNT OTS/00

2 . 1580 0 + 0 01 2 .16B00+001 0.00 39.899 89.899 0.00 -2.753+001

2. i676m-oai 2 . 16763 + 00 1 -0 .00 90.00 0 89.999 -0.00 -2. 753+001

2. 1H963 + 0Q1 2 . 14951+001 -0.01 95.000 94.967 -0.04 -2.764+001

2. 13162 + 001 2 .13145+001 -0.01 100.000 99.952 -C.05 -2.771+001

2. 11359+001 2 . 11341 + 001 -0.01 105.000 104.951 -0.05 -2.773+001

2. 09553 + 0 01 2 . 09538+00

1

-0 .01 110.000 109.958 -0.04 -2.771+001

2.07743+0 01 2 . 07732 + 00 1 -0 .01 115.000 114.969 -0.03 -2.766+001

2.05926+001 2 . 05921+00

1

-0.00 120.000 119.983 -0.01 -2.758+001

2.0'*106 + 0ai 2 . 041 05 + 0 0 1 -0,03 125.000 124.997 -0.00 -2.746+001

2.02276+001 2 . 0228 0 + 00 1 0.00 13 0.000 130.010 0.01 -2.733+001

2.00436+001 2 . 00445 + C 0

1

0 .00 135.00 0 135.020 0,01 -2.7i:' + 001

1.965;56 + 001 1 .98598+00

1

0 .01 140.000 140. 027 0.02 -2.698+001

1.96727+001 1 .9d739+001 0.01 145.000 145.0 31 0.02 -2,673+001

1.94852+001 1 . 94S64 + 0 0

1

0.01 150.000 150.0 32 0.02 -2. 655+001

1 .92961+001 1 .92972 + 0 0 1 0 .01 155.00 0 155.0 31 0.02 -2.631+001

1.91052+001 1 . 91062+00

1

0.01 160 .00 0 160.027 0.02 -2.604+001

1. 89123 + 001 1 . 89132 + 00 1 0.00 165.000 165.021 0.01 -2. 575+001

1. 871 73+ 0 01 1 . 37178 + 00 1 0 .00 170.000 170.014 0.01 -2.544+001

1.85198+001 1 . 85201+001 0.00 175.000 175.006 0.00 -2.511+001

1.83196+0 01 1 .83195+001 -0.00 180.00 0 179.999 -0.00 -2.476*001

1.61164+001 1 . 81160+001 -0.00 185.00 0 134.992 -0.00 -2.438+001

1.79 0 9 8+001 1 .790 92+0 0

1

-0.00 190.00 0 1S9.906 -0.01 -2.397+001

1.76996+001 1 . 76987+001 -0.00 195.000 194.981 -0.01 -2.354+001

1 . 7't652 + 0 01 1 . 74843+001 -0.01 200.000 199.978 -0.01 -2.308+001

1. 72664+001 1 .72653 + 001 -0.01 205.000 204.977 -0.01 -2.260+001

1.70425+001 1 .70415+001 -0 .31 210.00 0 209.973 -0.01 -2.208+001

1.68130+0 01 1 . 68121+001 -0 .01 215.000 214.981 -0.01 -2.153+001

1.65774+001 1 . 65767+00

1

-0.00 220 .00 0 219.985 -0.01 -2. 094+001

l.b3348+001 1 . 63344 + 0 0 1 -0.00 225.000 224.990 -0.00 -2.033+001

1.60845+001 1 .60843+001 -0 .00 230.000 229.996 -0.00 -1.967+00

1

1. 53255+001 1 .58256+001 0 . GO 235.000 235.002 0.00 -1.898+001

1.55567+001 1 .55571+001 0.00 240.00 0 24 0 .0 0 7 0.00 -1.825+001

1 . 52767 + 0 01 4

jL .52773+001 0 .30 245.000 245.011 0.00 -1. 749+001

1 .49638 + 0 01 1 . 49846+001 0 .01 250.000 250. 0 13 0.01 -1.663+031

1.4o 761+0 01 1 . 4677 0 + 0 0 1 0.01 255.000 255.014 0.01 -1. 582+001

1.43511+001 1 . 43518+00

1

0 .01 260.000 260.012 0.00 -1. 493 + 00 1 1.40054+001 1 . 40059+001 0.00 265.00 0 265.003 0.00 -1.393+001

1,36348+001 1 .36350+001 0.00 270 .00 0 270.002 0.00 -1. 298 + 001

1. 32 3 3 3 + 0 J 1 1 . 32331 + 0 01 -COG 275.000 274.997 -0.00 -1.191+001

1.27923+001 1 . 27917+001 -coo 280.00 0 279.994 -0.00 -1. 076+001

1.22965+001 1 .22978+001 -0.01 285.000 284.993 -0.00 -9.500+000

1 . 172 93 + 0 01 1 .17290+001 -0. 00 290 . 00 0 2S9.997 -0.00 -8. 090+000

1.10398+001 1 . 104 03 + 0 0 1 coo 295. 00 0 295.0 03 O.OQ -6.441+000

1.01117+001 1 . Oil 17 + 0 0

1

coo 300.000 300.000 -0.00 -4. 358+000

= 44, DNRMSPGT = 0.DO4, TSRMSPCT = 0.016 M-6
File No. 73-6

Table 5. Methane Saturated Vapor Temperatures

Nr = 5, AL = 0.500. BE = 0 , 0 00 , CGAT = 1. 56767 -002

TTcp - 90.6^0, TC^J = 190. 555 , DTRP = 28 . Itt7, D^RT =10. 200

-0.1596F159 -0.6n 695380 1.02£+22995 0 .59857993

o.20^?8353 o.ooooooon 0. 00000000 0 .000 OOOOO

n .n 0 000000 0.00000000 0 . 0 00 0 0 000 0.000 00 000

MOL/L CALC T , K CALC PGNT DTS/DO

1 ,5t=^7a 6-10? 1.567P6-002 0. 00 90.660 90 .630 0,00 5. 391+00 2

1 « 6?79 l-in2 1.5 28 3 0-002 0.0 2 92.000 91 . 9 33 -0 .0 0 £+. 775+002

2. ? •"57 9-00 2 ?,?ti6 6'*-002 0 . 0 £* 9^.000 93 .9 96 -o.no £+. 005 + 002

2. 829tf 3-nn? 2..':' 306 6- 002 0 . 0 96.0 0 0 95 .9 36 -0.0 0 3. 390 + 00 2 3,£*ft926-!)Q2 3.i«70 6i--002 0. 0 i+ 98.000 97 . 9 36 -0.00 2.893+002

it. 2162 5-002 i*. 2 175 6 - 002 0,0 3 10 0.000 99.9 37 -0.0 0 2. £+88 + 00 2 5.0816 e-no2 5,0 52 66-002 0.0 2 102.000 101.993 -0 .0 0 2, 15<+ + 0O2

6.0 7dO 3-00? 6 . 0 7fi5''-002 0,01 10'+. 000 1 03 .9 39 -0.00 1. 878<-002

7.21719-002 7 . ?170?-00? -0. 00 106. 000 106. 010 0 .OG 1. 61+7+002

B.5122U-m2 ''.5112 3-002 -0.01 1 0 .3 . 0 0 0 108,001 0.00 1. £+53 + 002

9.9 765 6-0 0 2 9.971+66 -002 -0.0 2 110.000 110.002 0.00 1.288+002

1 . i^^2if i-oni l.lo213-0Cl -0,02 112.000 112 .0 13 0.0 0 1. l£+7 + 002

1.3i*692-n01 1 . 3 i+65 V -0 01 -0,03 1 iH. 0 0 0 1 1£+ . 0 0 i+ 0.00 1. 026+002

1. 53269-noi 1.5522o-001 -0,0 3 116.000 116 . 0 T+ 0.00 9. 221+001

1,7;<12 «-n01 1.7-S06O-001 -0,0 3 113,000 1 19 . 0 0 £+ 0.0 0 8, 31£++001

2. n 3h3 1 -no 1 2.0 3 363-001 -0,0 2 120.000 120 , 0 0 £+ 0.00 7. 522+1101

2.31 3i»h-n01 2.313 0^-001 -0,02 122. 000 122 .00 3 0,00 6. 827+001

2.6205 ft-!101 2,62022-001 -0.01 12'+. 0 0 0 12£+.0 02 0,00 6.215+001

2.957^+ ^<-n01 2.9572'^-001 -0, 0 1 126. 000 126 . 0 0

1

0.0 0 5,672+001

3, 3261 6-001 3.3 261 1-001 -0.00 128.0 00 128.0 00 0.00 5. 189+001

3, T-^dzo-nni 3 .7 ?et^ 9-001 0. n 1 130.000 129,999 -0.0-0 i+. 757+^)01

^. lf.73 3-Q0 1 t, 1675 0-001 0. 0 1 132,000 131,9 38 -0.0 3 £+. 370+001

i+.6a(+£tf+-noi '+.'3 4 52n-001 0.0? 1 3i+. 0 0 0 133.997 -0 ,00 £+. 021 + 001

5 .1625 :r-no 1 5. Io362-0 01 0.0 2 1 36, 0 0 0 1 35 . 9 36 -0.0 0 3. 70 6+00 1 5 . 7?i»!+ 1-Oni 5.7257^-001 0,02 135,000 1 37 .935 -0.0 0 3. £+20+001

6. 3329 7-301 6 , 3 346 ?- 0 0 1 0.0 3 I'+0 . 0 00 1 39. 9 35 -0.00 3. 159 + 001

S,991't'*-noi b. 9 9 331-001 0.0 3 1 £+2 . 0 0 0 1 £+1 9 35 -0,0 0 2.921+001

7. 7 0 33 i*-0 0 1 7.70 5 31,-001 0,03 1 i+u , 0 0 0 1 £+ 3 , 9 3 5 -0.00 2. 70£+ + 00i

6.i»725 i-nm o.-*7^+5 1-Qni 0,0? 1 £+6 . 0 0 0 1 £+5 , 9 35 -0.0 0 2. 503+001

9 .3032 0-nOl '^. 3 050'*-001 0,0? 1 £+6 . 0 0 0 1 '+7 , 9 36 -0.0 0 2. 319+001

i.n?G0 1 + 000 1,02016+000 0.01 15 0.000 l£+9, 9 37 -0,00 2, 1^6 + 001

i.iiear+Doo 1.1159<- + 000 0.0 1 152.000 151 . 9 36 -0.0 0 1.989+001

1.2^1i+ 3 + 00 0 1.2 21'+H+0 0C 0,00 15£+, 000 1 5 '+ . 0 0 0 -0,00 1. 8£+2-^001

I, 3 3t+u 1 + COn 1.3 3 £+33+000 -0,01 1 56 , 0 00 156 . 0 0 1 0,0 0 1.705+001

1 . '+565 6 + 0 0 0 l.'*5&3 6 + 000 -0,01 156.000 158 » 0 03 O.OQ 1. 576+001

1,5^87 7+000 1.5^)^'+3+000 -0,0? 16 0,000 160 , 0 0 5 0,00 1. £+55 + 001

1 .7320 u + noo 1.73156+000 -0.0 3 lo2, 000 162,007 0.00 1. 31+1 + 001

1.^375^^ + 00 0 l.c 369^ + 00 0 -3.03 16£+.000 16£+. 0 0 6 0.0 0 1. 231+ + 001

2. 0 5 66 f' + OeO 2 , 0561 n + OQ 0 -0, 01* 166, 0 00 166.006 0 .01 1, 132+001

2. 2i*15^ + 00n 2.?i+07^ + 000 -0. Ot, 163.0 00 168.006 0,0 1 1. 036+001

2.i»C35l + 00n 2,4^^300+0 00 -0.03 170, 000 170. 0 06 0 ,00 9.1+33+O00

2 .666 3 1 + 000 ?.6656i- + 00n -0.0 3 172,000 172.006 0,00 6 . 5£+8 + 00 0 2.912i+9 + 1Q0 2.9121«- + 000 -0, 0 1 17£+. 000 l^'+.003 0,00 7.696+000

3. 15 69 1 + 0 0 0 3,13711+000 0. 01 176, 000 1^5.9 39 -0,00 6. 671 + 00 0 3.^953 1+00

n

3. i+ 968 5 + 0 0 0 0.0 3 178,000 177.9 3£+ -0.00 6. 066 + 00 0

3 . flit -^2 3 + 0 0 n 3.'^503 :' + 000 0,0 6 18 0.000 179.9 39 -0 .01 5. 275 + 00 0 i+.P^d 0 6 + 0 0 0 '+.?61'+3 + 00 0 0,08 13 2,000 131.9 35 -0.0 1 i+. 1+86+00 0 ^ . 7'+'i6 7 + O 0 0 U, 75265 +000 0.06 13i+. 000 133,935 -0.0 1 3. 690+000

5. 365? 6 + 0 0 0 ^.3 667 '^+0 0 0 0.0 3 186. 000 135.9 36 -0.0 0 2. 858+000

6. 22000+ 0 00 6.2057^+000 -0.23 18 3,000 138.0 ?8 0.01 1.935+00 0

= -.0, D-jPf-'S ^^CT = 0.0 £+3, T3' M SPOT = O.OOh M-7
Table 6. Methane Saturated

NF = 5, AL = 0.000

T7RP = 90.680, TCRT = 190.55

8.5^377917 -7. 05251+399

0.206713'*2 0. 00 0 000 00

1 MOL/L CALC P3NT

2.8m7 0 + QOl 2.61'+70 + 001 0. 00

2.80376+001 2.80375+001 -0. 00

2.7871 i++001 2.78706+001 -0. 00

2.77036+001 2,77026+001 -0, 00

2.753'»'++001 2.75332+001 -0. 00

2. 7363 e + 001 2 .73625 + 001 -0. 00

2 .7191 6+GOl 2.7igO't + 001 -0.00

2.70179+001 2.70167+001 -0. 00

2.68'*25 + Q01 2.68'+15 + 001 -0. 00

2.6665^+001 2 .6661+5 + 001 -0.00

2.6U865+001 2.6^857+001 -0,00

2. 6305 6 + 001 2.63051+001 -0, 00

2.61226+001 2.6122'+ + 001 -0. 00

2.59379+001 2.59377+001 -0.00

2.57507+001 2.57507+-001 0, 00

2 .5561 2+001 2.55615+001 0.00

2.53693+001 2.53697+001 0.00

2.517^+9 + 001 2. 517514 + 001 0. 00

2.. '9777 + 001 2.'+978'» + 001 0.00

2.U7776+001 2 .i+776'. + OOl 0.00

2. '+57'+ 5 + 0 01 2.'*575'+ + 001 0, on 2.'+3682 + 001 2.1+3692 + 001 0. 00

2^'tl535 + 001 2.'+159? + 001 0. 00

2.39'+52 + 001 2.391+62 + 001 0.00

2.372d 0 + 001 2 .37290 + 001 0.00

2.35067+001 2.35076+001 0.00

2.3281 0+001 2.32815+001 0. 00

2.3050 6 + 001 2.30513+001 0.00

2 .28152+901 2.28155+001 0.00

2. 257'+i++001 2.2 57i+f' + 0 01 0.00

2*2327 6 + 001 2.23276+001 0.00

2.207'+6 + 001 2.2071+5 + 001 -0, 00

2.i81'+6 + 001 2.1811+3 + 001 -0. 00

2.15'+7 1 + 001 2.151+66 + 001 -0.00

2. 1271 3+001 2.12705+001 -0.0 0 2.09863+aoi 2.0 98 5 3+001 -0. 00

2.06912+901 2.06901+001 -0.01

2. 0381+9 + 001 2.03835+001 -0.01

2.00656+001 2.006<+3 + 001 -0.01

1.97322+001 1.97307+001 -0.0 1 1.93320+001 1.93607+001 -O.OJ

1.90125+001 1.90111+ + 001 -0. 01

1.8620-1 + 001 1.66195+001 -0, 00

1.8200 ii + OOl 1 .82001+ + 001 0, 00

1 .77'+d7 + 001 1.771+75 + 001 0.00

1.72'+9 9 + 001 1.72516+001 0.01

1.6695 8 + 001 1 .66963 + 001 0.01

1.60606+001 1.60632+001 0.02

1. 52986+001 1.52997+001 0.01

l.'+297 8 + 00l 1. '2937 + 001 -0. 03

1 . 25270 + 001 1.25276+001 0.00

NP - 51, DNRMSPCT = O.OOd, TS^MSPCT = 0.

File No. 73-6

Liquid Temperatures

333, DGAT = 1. 56767-002

DTRP = 28.11+7, O'ORT =10.200

i+. 161021+1+3 -1 .369 19291

0.00000000 0.00000000

I T,K cal: PCNT OTS/DD

9 0.680 90.630 0,0 0 -1.208+001

92.000 91.936 -0 .0 0 -1.203+001

91+. 000 93.9 U -0.01 -1. 191+ + 001

96. 000 95.986 -0.0 1 -1.186+001

95.000 97.986 -0.01 -1.176+001

100.000 99.9 35 -0.01 - 1. 167+001

102.00 0 101 .936 -0.01 -1. 157+001

lOif. 000 103.987 -0,01 -1. 11+7 + 001

106.000 105.938 -0,01 -1. 136+001

108.000 107.990 -0.01 -1. 125+001

110.000 109.932 -0.01 -1. 113+001

112.000 111.9 31+ -0.01 -1,10 1+001

111+. 000 113.936 -0.0 0 -1,069+001

116.000 115.938 -0.00 -1, 076+001

118.000 118. 000 0.0 0 - 1, 063 + 001

120.000 120.002 0.0 0 - 1, 05 0 + 001

122.000 122.0 11+ 0.00 -1, 036 + 001

121+. 000 121+.006 0.0 0 -1,022+001

126.000 125.007 0.01 -1, 008+001

128. 000 128.0 ]

6

0.01 -9, 928+000

130.000 130.009 0.01 -9, 775+000

132.000 1 32. 0 3 9 0.01 -9, 616+000

131+. 0 00 131+.0Q9 0.0 1 -9,1+57 + 000

136. 000 1 36 . 0 0 9 0.01 -9,292+000

1 33 , 0 00 138.009 0.01 -9,122+000

11+0.000 11+0,008 0.01 -8, 91+8+000

11+2.000 11+2,007 0.0 1 -8, 768+000

11+1+. 00 0 11+1+, 036 0.00 -8, 581+ + 000

1 1+6 . 0 0 0 m6,0 35 0.0 0 -8, 395+000

11+8.000 11+8.003 0.0 0 -8,200+000

150.000 150.002 0.0 0 -7, 999+000

152. 0 00 152. 0 i] 0 -0.00 -7, 793+000

151+, 0 00 153. 9 33 -0.0 0 -7, 579+000

156. 000 155.9 36 -0.0 0 -7, 359 + 000

158.000 157.935 -0,0 0 -7.132+000

160.000 159.9 33 -0,0 0 -6.896+000

162. 0 00 161 .9 32 -0,00 -6.652+000

1 61+ . 0 00 163.9 31 -0,01 -6. 399+000

165, 000 165.9 31 -0,0 1 -6. 135+00 0 168,000 167.9 32 -0,00 -5. 859 + 000

170,000 169.9 33 -0,00 -5. 570 + 000

172,000 171.931+ -0,00 -5. 265 + 000

171+, 000 173.937 -0.00 -»+. 91+3+000

176.000 176.0 DO -0.00 -1+. 60 0+000

178. 000 173.003 0.0 0 -i+. 232+000

180.000 180.0 36 0.00 -3. 833 + 000

182.00 0 182.0 38 0.0 0 -3. sgi^+ooo

1 81+. 00 0 18I+.008 0 ,0 0 -2.903+000

186.000 136.0 03 0.0 0 -2.336+000

188.000 187.933 -0.00 -1. 652+000

190.000 190.000 0.0 0 -6. 700-001

006 M-8
Cryogentcs Division~N6S Institute for Basic Standards LABORATORY NOTE

COST CENTER 2750364fILE NO 73-6

PAGE 8

SUBJECT Liquid-Vapor Saturation (Orthobaric) Temperatures

of Ethane and Methane

NAME ^ ^ , , R. D. Goodwin

Nov. 28, 1973

11/28/73

Appendix I. The Computer Programs

!3R0GPAM TSATFIT

C "JESCRIbE ETHANL SATN. TEMFS., TSAKOEN).

C .DEFINE l! = D/DTRP, S-O/DCRT, S T = D TRP/DCR T , ANO -

C YY(TSAT) = (TGRT/T-1)/ (TCFT/TTRP-l) , ANO -

C COHfOh NG, AL,aE, TTRP, TCRl , OGAT , DTRP , QCRT , DTSDR» A(15),B(15)

COMMOiM/9 99/NP,NF , H (15 ) , Y (20 0 ) , G (20 0 , 15)

01 MENS I ON T(99) ,nEN(99),YY(99) ,F(15)

HI ME MS I ON UK 99)

2 FORMAT (IHl jOX ETHANE SfTURATION TEMPERATURES* //

1 16X'+HNF =r.^, 6H , AL =F7.3, 6H , BE =F7.3, 8H, DGAT =E13.5//

1 lex oHTTF?' =F7.3, SH, TCPT =F8.3, 8H, DTRP =F7.3,

2 8H, OCRT =F6.3// 3(1?X t,F16.8/ ) /

3i5X5HMCL/L IIX'+HCALC 5XttFPCNT 8X3HT,K 6XifhCALG 5 XitHPCNT6X6H0TS/CD)

3 FORMAT (IHl l^tX 5HM0L/L 13X4HCALG SXt^HPCHJ

3 SX3HT,K eXitHCALC 5X'H^C^'T 6X6HDTS/DD ) k F0R^.AT(5X 2tl5.5, F9.2, F11.3, FlC.3, F9.2t E12.3)

5 F0KriAT(13X 2HNF 13X2HAL 13X2HBF eX2HS3)

6 FORMATdOX 15, 2Ei5.5, FK.3)

9 FOFMATdHC bX kHUP -13, j2H, CNRMSPGT =F6.3, 12H , TSRMSPCT =F6.3)

11 TTRP:^59.fi99 i TCRT=3L^5.33 $ YN - TCRT/TTRP-1

12 9TRP = 21.6.?. $ -1CRT = 6.e7 $ OGAT= 1. 351 1^ E-6

13 ST-HGAT/OCRT ? VT=1/(1-ST) % 0T=CU3ERTF ( S T) G

C 5ATn. \/APOF TEHPS. CONSTRAINED AT T.P. BY SUBTRACTION -

C "Q'JATION, YY = U (S) * ( 1 +W (S) ) T U = E XP ( A L* ( V T- V ) ) » C V/ = 1/ABS(S-1), 0 = 5** (1/3), AND - C i-l = A1»LN(S/ST) A2»(a-QT) + A3*(Q2-QT2) + . . . C GENLvATE THE SATD. VAPOR EfTA.

25 DO 29 J-iy^h '5 IF(J-l) 27,26

26 T ( J) = TTRP J GO TO 26

27 T(J) = clj + 5^ J 2" OEN (J) - OErJGASF (T( J) ) 29 YY(J) - (TCRT/T( J}-1) /YN Z NP = t^k G Jt-nK'T FOR NF, GF T AL BY TRIAL.

3 C A L = 1 . 5 i'' 31 DO n9 NF = i^,i:] f \iG - NF $ SEK = I.OE + IQC

32 DO i+Q J^1,NP ^ S = PEN ( J) / DGRT $ Q = CUBERTF(S) S V = l/{1-S)

33 U - EXr^F ( AL* ( VT- ) % G(J,1) = U»L0GF(5/ST)

-j5> do 3b K=2 ,:^jF 5 N = K-1

3r- r,(J,K> = U'^(Q»*M - OT«*N)

i+ C Y ( J ) - > Y { J ) - u 49 CALL EGE IFT r DO 50 K = 1,NF

5 r A ( K ) = H ( K ) f S 0 = S E = 0 51 DO 52 J=l,NiP I TC = T 3 f T F ( DE N ( J ) ) 52 - S:> + (TC/T( J)-l) **2 $ 3S = 1 0 0 #5 QR TF ( 3S/N P ) 53 IF (3S.LT.ESK) 5tt , 5E

5i, S3K-3S i NGK-NG 3 ALK=AL ? 3EK = BE 5 00 55 K = 1,NF

55 F" ( K) - I (K)

5f COh'TINUF

57 CONTINUE T NG-NGK f AL = ALK % B'^=BEK $ DC 58 K=1,NF

5 1 A ( '<) - F i K' ) ^ S 3 = S C - 0

SP 11342 A M-9 U S Government Printing Office 1973- ^ 790-339
Cryogenics Division-NBS Institute toi Basic Standards LABORATORY NOTE

COST CENTER 2750364

FILE NO 73-6

PAGE 9

SUBJECT Liquid-Vapor Saturation (Orthobaric) Temperatures of

Ethane and Methane

NAME

-p^ Goodwin

Nov. 28, 1973

Appendix I. (continued)

C PRINT CONSTANTS AND DEVIATIONS.

6C PRiriT 2, NG,AL,BE,nr,AT, TTRd , TCRT ,OTRP, DCRT , ( A ( K ) , K = l , 12 ) 61 00 67 J=1,NP $ D=nFN(J) $ X = T(J) $ DC=F I NO S AT F ( 0 , X ,)

TSATFIT ll/^8/73

62 OPCT = 10C»(OC/D-1) $ SD = SD + DPCT*OPCT

6*+ TC ^ TSATF(D) $ OTSDD = DTSOR/DTRP

6? TPCT = 10G*<TC/X-i> $ = SS + TPCT*TPCT

67 PRINT it, D, DC, OPCT, X,TC,TPCT, DTSDD

68 SD=SQRTF (SO/NP) $ SS=SORTF ( SS/NP ) $ PRINT 9, NP, SD, SS

69 CONTINUC $ AL = 0 C

C SATO. LIQUIO TEMPS. CONSTRAINED AT THE T.P. 3Y SUBTRACTION, -

C EON., LN{YY) = K(S), KHFRE X=ABSiS-l), XT=ABS { ST-1) , AND -

C W(3) = BE» {i/XT-l/X) + BIMX-XT) + 82''(X2-XT2) + . . . C GENERATE LIQUID DATA.

7r DO 7k J=Likk $ IF(J-l) 72,71

71 T(J) = TTRP S GO TO 73

72 T(J) = 30 + 5*J

73 DEN ( J> = DENLIQF { T ( J)

)

7k YY{J) = LOGF ( (TCRT/T( J)-l) /YN)

75 NP = kk $ NG = NF = 5 $ XT - DTRP/DCRT - 1 C SET UP FIXED LEAST SQUARES FUNCTIONS.

30 DO 85 J=1,NP $ S - nEN(J)/DCRT $ X = AB3F{S-1)

81 UL(J) = i/XT - i/X $ DO 82 K=1,NF $ N = K 3? G ( J ,K) = X**N - XT*»N

35 CONTINUE

C FIND NF, BE BY TRIAL.

9C 3E = 1.D/3.Q $ DO 91 J=1,NP

91 Y(J) = YY(J) - BE*UL(J) $ CALL FGENFT $ DO 92 K=ltNF

92 B(K) = H(K) 5 30 = SS = 0 C PRINT LIQUID DEVIATIONS.

IQD PRINT 2, NG, AL,BE,DGAT , T T RP , T C RT ,D TRP , DC RT , ( B ( K ) , K=l , 12

)

IQl DO 1G5 J=1,NP $ D=DFN(J) $ X=T(J) $ DC = F I ND S AT F ( 1 , X)

1D2 OPCT = 100*(DC/C-1) $ SD = SD + DPCT»*2

103 TC = TSATF(D) J DTSDD = DTSOR/DTRP

10^+ TPCT = 1G0*(TC/X-1) $ SS = SS + TPCT**2

lj5 PRINT k, D, DC, OPCT, X,TC,TPCT, CTSDD

136 3J = 30RTF(S0/NP) S SS = SQRTF(SS/NP)

107 PRINT 9, NP, S0,3S

llL CONTINUE

99^ST0P $ END

SP 11342 A M- 10 b u s Government Printing Office, 1973- 0 780-339
Cryogenics Dtviston-NBS Institute lor Basic Standards LABORATORY i\!OTE

COST CENTER 2750364FILE NO 73-6PAGE

1 0

SUBJECT Liquid-Vapor Saturation (Orthobaric) Temperatures

of Ethane and Methane

NAME R. D, Goodwin

DATE Nov. 28. 1973

Appendix I. (continued) 11/23/73

Ik

15

17

2l

22

K

FUNCTION TSATF(DEN)

COMFON NG,AL ,3E,TTRP,TCRT , DGA T , DTRP , DC RT , DTSDR, A(15),B(15)

R=DEN/DTRP S S=DEN/DCRT T QS = S-1 $ OS OR =OTRP/D CRT $ IFtOS) 2,30

X = AOSFJQSJ $ XI = DSrR*OS/X $ YN = TCRT/TTRP - i

\/ = 1/X J Vi = -nSOR/Q?/X $ IF(QS) ^+,30,15

SATC. VAPOR TEMPS. CONSTRAINED AT T.P. BY SU3TRACTI0N - EQUATIOiM. YY = U ( S) * ( 1 + W IS ) ) , U = E XP ( A L» ( VT- V ) ) , J = 1/AES(S-1), U = S**(l/3), AND -

W = A1^LN(S/ST) * A2*(n"QT) + A3*(Q2-QT2) + . . . D&AT/DCRT 3 VT=1/(1-ST) $ 0 T= CUBER TF ( S T

)

EXPF(AL» (VT-V)) ? L'l = -AL*V1*U

CUBhRTFtS) $ Ql = C*DS0R/3/S

1 + A (1) *LOGF (S/ST ) £ Wl = A<1)*DSDR/S

10 K=2,MG S N = K-1

W + A (K) *(Q* M - OT**N)

= Wl + N*A(K) *ai*Q** (r -1)

U*W I Fl - 'J*W1 + U1*W $ Q = 1 + YN»F

TSAir = TCRT/Q $ DTSDR = -YN»F1*TSATF/Q $ RETURN

;ATu. LIQUin TEMPS. CONSTFAINED AT THE T.P, BY SUETRACTICN, - :QN., LN(YY) = W(S), WHF.RE X = ABS(S-1J, XT = ABS ( ST-1) , AND - MS) = BE* (l/XT-l/X) 4- B1*(X-XT) + 32*(X2-XT2) + . . . XT = DSDR-1 £ W = BF*(l/XT-V) $ Wl = -BE*V1

DO 19 K^l^NlG $ H - K

W = W + 3iK) *(X*-*rJ - XT»*N)

Wl = Wl + B (K)*N*X1*X'? " (f -1)

F = EXPFiW) 5 Fi = W1*F $ 0=1+ YN*F

T3ATF - TCRT/i^ S GT^C'R = - YN *F 1* TS A TF /Q $ RETURN

TSATF = TC^T 5 DTSCR = C S RETURN $ END

3T

IJ 6 Q

7

8 30

o W 10 Wl

IZ F

FUNCTION OENGASF (T)

G ETHANF UATURAFED VAPOR DE^SITIES, MOL/L.

C r = Al + A2*Q2 + A3*Q3 + . . , NF = AL, YN = LN ( TCRT/CTRP)

»

C U = Z f (ZE-Z)*Y, DEN = DC RT* E XF (-YN»U J

.

QIMtN:jION A 15)

DATA (TTRP=a9.899) ,(TCRT=305.53),(E=0.362)

QATA (nCRT:^6.37) , (P TR P = 1 . 3 5 i lit E- 6

)

OATA(A = G.12d77kSli 0. 0^+155009, -0.73922629,

1 0 . 35? f-75 Q , 0 .3 2^+5^+376)

1 FORMAT (IHG 9X *DENGASF - D, T EXCEEDS TCRT. / ) ? IF(TCRT-T) 3,4,5

3 PRINT 1 f. STOP

k nEf;GAZF r OCRT S OPDT = D2kDT2 = 0 B RETURN

5 ZN^TCr^T/TTRP-l S YN=LUC F { OCRT/DTRP) $ Z= ( TCR T / T- 1 ) /Z N OZCT = -TC-^T/ZN/T/T ? Zf = Z^*E $ ZEl = E*ZE/Z

6 X = Zt-Z 5 XI = ZEl-1 $ Q = CU3ERTF(Z) $ Ql = C/3/Z

1CY=A(1) 5 yi = o $ r0 13i< = 2,5

11 Y = y + A ( K) 'Q*» K 12 Yl = Yl + <»A(K) *0-^* (<-l)

13 CONTJ-jUE :> Y1 = Y1*Q1

15 J = Z + X^Y ^ UA = 1 + X*Y1 + X1*Y 5 Ul = UA»DZOT

lb XP = EXPF(-YN^U) $ DENCASF = F = OCRT*XP

17 ^ROT = -VN"-U1*F I FFTURN $ END

SP 11342 A M-U iir U 5. Government Printing Office; 1973- # 7S0-339
Cryogenics Oivision-NBS Institute lor Basic Standards

1 ARnRATORY IMflTC

COST CENTER 2750364

FILE NO 73-6

PAGE

1 1 SUBJECT Liquid-Vapor Saturation (Orthobaric) Temperatures R.D. Goodwin

of Ethane and Methane Nov. 28, 1973

Appendix I. (continued) 11/28/73

FAILS TO CONVERGE.* / ) T EXCEEDS TCRT.» / )

IF (ABSF(OT/T)-1.0c-6) 21,21

FUNCTION UNDSATF (M,T)

THIS FINOSATF ADJUSTED FOP ETHANE.

ITERATE DEN TO MINIMIZE (T-TS) VIA TSATF(DEN).

1 = 0 FOR VAPOR, M = 1 FCR LIQUID.

COMMON NG,AL,i3E, TTPP,TCRT , OGA T , D TRP , OC RT , DTSOR,

DATA {DGT=1. 0E-&) , (DLT = 23. a ) 1 FORMATdHO 9X FINCSATF ~ Q,

2 FORMATdHO 9X FINCSATF - 0,

3 IF (T-TCRT) t+ ,22, 23

IF(M.EC.U) 5,6

5 0= OENGASF(T) $ GO TO 7 6 D ^ DENLIQF(T)

7 00 2a J=l,5u $ DT=T-TSATF (0)

6 QTDD = DTSDR/DTRP $ I F (D T DC . E Q . 0 . 0 ) 2 2 ,

"5 9 DD = nT/DTDD $ IF ( A BS F ( C D /D ) - 1 . 0 E-6 ) 21,21,10

IL D = 0 + DL $ IF(M.EQ.iJ) 11,15

11 IF(D.GT.OGT) 13,12

12 0 = DGT $ GO TO 20

13 IF (C.LT.UCRT) 2G,1^

l^t D = OCRT - 0.02 $ GO Tf 2 0 15 IF(D.GT.OLTJ 16,17

16 0 = OLT $ GO TO 20

17 IF (D.GT.OCRT) 2C , 18

18 0 = DCRT + 0.02

2C CONTINUE $ FINOSATF - C 5 C'RINT 1 $ RETUR

21 FINCSATF =0 $ '^ETURf

22 FINOSATF = OCRT S RETURN

23 FINOSATF = Z $ PRINT 2 $ Rf TURN $ END

AU5) ,B(15)

11/28/73

FUNCTION DENLIQF (T)

C ETHANE SATURATED LIQUID DENSITIES, MOL/L.

C Y = Al + A2»Q2 * A3*03 + . . . , YN = OTRP-DCRT,

C 3EN = DCRT + YN»{X + (XE-X)*Y).

DATA (TCRT=3G5.33),(TTPP=e9.899),(DCRT=6.87),{DTRP:

DATA (A=0 .7617 35 0 3) , (8 = 0.29 865 3 51) , (C = -G . 3276 239^)

FORMATdHC 9X *DENLIGF = D, T EXCEEDS TCRT. * / ) IFtTCRT-T) 3,i+,5

21.68) , (E=0 . 35)

12

3

56

fiQ

IC

11

13

Ik

PRINT 1 $

DENLiaF=DCRT

XN=TCRT-TTRP

XE = X**E S Q = XE-X $

WW = W*W $

Yi = 2*B*W + Yi = ri»wi

DENLIQF = DCRT t DRDT = (1 *• Q»Y1

STOP

S DRDT=D2FDT2=U $ RETURN

S YN=DTRP-DCPT $ X = ( TCRT -T ) / XN $

XEl = E*XE/X $ W = CUQERTF(X)

01 = XFl-1

Y = A + B*WV + C*X

3*C*WW

DXDT=-1/XN

$ Wl = W/5/X

(X + Q*Y)»YN

Q1*Y) *YN*DXDT RETURN END

SP 11342 A M-12 •tr u s. Government Printing Office 1973- ^ 790-339
Cryogenics Division-NBS Institute for Basic Standards LABORATORY NOTE

COST CENTER 2750364

FILE NO 73-6

PAGE 12

SUBJECT Liquid- Vapor Saturation (Orthobaric) Temperatures

of Ethane and Methane

NAMEj^

-|^^ Goodwin

Nov. 28, 1973

Appendix I. (continued) 11/28/73

FUNCTION OENGASF(T)

C METHANE SAT. VAPOP DEN, MOL/L, VIA VAPORFIT, 11/19/73.

C Y = Al + A2*Q2 + A3*Q3 + . . , NF = AL, YN = L N ( 33 RT /O TRP)

C U = Z + (Z£-Z)*Y, DEN = DCRT*E XP ( -Y N" U ) . DIMENSION A(5)

DATa (TTRP=90 .63)

,

(TCkT= 190. 555) , (E=0. 386)

DATA (DCRT=10.2),(OTPP=Q.0156 73 65)

3ATA(A = 0. 3925579, -0. '+976886, 1 .3200516,

1 -1.6617790 , 0. 68^+860 9) 1 FORHATdHO 9X DENGASF = 0, T EXCEEDS TCRT. * / ) 2 IF(TCRT-T) 3,;+,

5

3 PRINT 1 $ STOP

DENGASF = DCRT 5 ORDT = 02R0T2 = 0 $ RETURN

5 ZN=TCRT/TTRP-1 » Y N = LO G F ( OCR T/ D TPP ) S Z= (TCRT/T-1) /ZN

6 OZOT = -TCRT/ZN/T/T 5 ZE = Z*»E S ZEl = E»ZE/Z

8 X = ZE-Z $ XI = ZEl-1 S Q = CU9ERTF(Z) $ Ql = Q/3/Z

10 Y = Ad) J Yl = 0 S DO 13 < = 2,5

11 Y = Y + A(K)*Q»*K

1? Yl = Yl + t<*A{K)»Q**{K-l)

13 CONTINUE $ Yl = Yl*ai

15 U = Z + X*Y 5 UA = 1 < X»Y1 f X1»Y B Ul = UA»DZOT

16 KP = EXPF(-YN»U) $ DENGASF = F = OC=^T*XP

17 DPDT = -YN*U1*F B RETURN $ END

FUNCTION OENLIQFCT)

C METHANE SATO. LIQUID DEN, MOL/L, VIA LAB, NOTE 73-5.

C Y = Al + A2*Q2 *- A3»Q3 + . . . , YN = OTRP-DCRT,

C DEN = DC'^T + YN*(X + (XE-X)»Y).

DATA {TTRF=90 .68) , (TCRT = 190. 555 ) , (E= 0.361)

DATA (DCRT=10 .2) , (DTRP=28 .l£+7)

DATA ( A = 0 .8 37 0910 3) , ( 3= 0 . 0 3^ 1 61 2 7 ) , ( C = - 0 . 0 7 i+7 35 75 ) 1 FORMATCIHQ 9X DFNLIQF = 0, T EXCEEDS TCRT. * / ) ? IF(TCRT-T) 3,i+,5

3 PRIIJT 1 f STOP

k DtNLiaF=DCRT % 0^DT=02 ROT2=0 $ RETURN

5 XN=TCoT-TTRP 5 YN=DTRp-OCRT % K = ( TCRT- T ) / X N $ DXDT=-1/XN

6 XE = X**E 5 XEl = E*XE/X B W = CUBERTF(X) $ t) 1 = W/3/X

8 Q = XE-X S 01 = Xcl-1

9 WW - U* M B Y = A + 3*WW C*X

to Yl = 2»3*W -»• 3»C*WW

11 ri = Yi*wi

13 DENLIQF = OCRT + (X + Gl*Y)»YN

11* DROT = (1 + Q*Y1 + 01»Y) YN^DXDT B RETURN B END

SP 11342 A M- 13 Ct U S. Government Printing Office. i973- ^ 7*0-339

USCOHM - EiU.

APPENDIX N

N-1
LOW -TEMPERATURE ELASTIC PROPERTIES OF ALUMINUM 5083-0

AND FOUR FERRITIC NICKEL STEELS

W. F. WestonT E. R. Naimon/'' and H. M. Ledbetter

Cryogenics Division, Institute for Basic Standards

National Bureau of Standards, Boulder, Colorado 80302

ABSTRACT

The low-temperature elastic properties have been determined for five

commercial alloys that have possible structural applications at cryogenic

temperatures. The alloys are 5083-0 aluminum and four ferritic steels: 3.5,

5, 6, and 9 percent nickel. An ultrasonic (10 MHz) pulse-superposition

method was used to measure longitudinal and transverse wave velocities.

Using the velocities and the mass density as input, the following moduli were

calculated: longitudinal modulus , Young's (tensile) modulus , shear (rigidity)

modulus, bulk modulus (reciprocal compressibility), and Poisson's ratio.

Measurements were made semi-continuously from 300 K to 4K. The composition dependence of iron-nickel alloys is reviewed comprehensively up to 1 Z percent nickel. Debye temperatures were calculated from the elastic constants.

A discussion is given of the temperature dependences of the elastic constants,

differential relationships among the elastic constants, and the possible

relationships between elastic and plastic properties.

i Key Words: Aluminum alloy; bulk modulus; compressibility; Debye temperature;

elastic consfant; nickel steels; Poisson's ratio; shear modulus; sound velocity;

Young's modulus.

- NRC-NBS Postdoctoral Research Associate, 1973-4.

t Contribution of NBS, not subject to copyright.

N-2
LOW-TEMPERATURE ELASTIC PROPERTIES OF ALUMINUM 5083-0

AND FOUR FERRITIC NICKEL STEELS

W. F. Weston'-, E.R. Naimon-, and H. M. Ledbetter

Cryogenics Division, Institute for Basic Standards

National Bureau of Standards , Boulder, Colorado 80302

INTRODUCTION

The recent expansion of cryogenic technology to extensive use of

liquefied gases has created new materials problems. In particular, detailed

knowledge and understanding of the mechanical properties of common m^etals

and alloys are required. The temperature range of interest is from room

temperature to near absolute zero. For engineering, the most important

mechanical properties in cryogenic applications are strength (sometimes

strength -to -density ratio) and toughness (resistance to low -temperature

embrittlement). In this paper, the elastic properties of several common

alloys are reported between 300 and 4 K. These properties--Young's modulus,

shear modulus, etc. --are essential engineering design parameters, are useful parameters in alloy development, are fundamental data for fracture

analysis and theories of solid -solution strengthening, figure prominently in

dislocation-model descriptions of mechanical properties, and can be related

empirically to a variety of phenomena associated with plastic deformation.

Oilman has maintained that "the most important mechanical characteristic

of a crystal is its elastic modulus. " The elastic moduli of polycrystalline

aggregates are also paramount.

2

It is well known that the major contributions of the addition of small

amounts of nickel to steel are: (1) hardening of the ferritic alpha phase;

(2) retarding the bainite and pearlite transformations; (3) lowering the Y -Ck' transition temperature, which enables nickel steels to be hardened by quenching at lower temperatures; and (4) resistance to embrittlement at low

temperatures. Thus, nickel steels are well suited for cryogenic applications.

Three and one -half percent nickel steel is a weldable low-carbon steel

NRC-NBS Postdoctoral Research Associate, 1973-4.

N-3
useful at temperatures down to about -100°C. Its possible applications

include the containment at atmospheric pressure of liquid ethylene and other

liquefied gases of higher boiling points, such as ethane, acetylene, carbon

dioxide, and propane. Five percent nickel steel is useful at temperatures

down to about -120°C in its quenched-and-tempered state and down to lower

temperatures in its austenitized, temperized, reversion-annealed state; and

nine percent nickel steel is useful down to liquid nitrogen temperatures

(-196°C). This alloy may contain as much as 15 percent austenite

and could be used for the containment of liquefied oxygen, argon, and nitrogen.

Aluminum alloys also are particularly useful for low-temperature

applications, since at cryogenic temperatures their strength increases without loss of ductility. In particular, the 5000 series alloys contain magnesium

as the major alloying constituent; magnesium is very effective as a hardener.

Alloys in this series possess good welding characteristics and good resistance

to corrosion in marine atmosphere.

The low-temperature elastic properties are reported here for five

commercial alloys that have possible structural applications at cryogenic

temperatures. These alloys are 5083 aluminum and four ferritic steels:

3. 5, 5, 6, and 9 percent nickel. An ultrasonic (10 MHz) pulse -superposition

method was used to measure longitudinal and transverse wave velocities.

Using the velocities and the mass density as input, the following moduli were

calculated: longitudinal modulus , Young's (tensile) modulus, shear (rigidity)

modulus, bulk modulus (reciprocal compressibility), andPoisson's ratio.

Measurements were made semi-continuously from 300 K to 4 K.

These data have been compared to previously reported results and used

to calculate the elastic Debye temperatures. Also, the elastic moduli

have been used to deduce information on some of the plastic properties of the

materials

.

Most engineering alloys selected for cryogenic use have close-packed

crystal structures; these include austenitic steels and alloys of aluminum,

copper, nickel, and titanium. Commercial purity body-centered cubic alloys

2

N-4
tend to have high ductile-to-brittle transition temperatures, that is, a high

notch sensitivity. The nickel steels reported on here are a notable exception

to the general exclusion of body-centered alloys frora cryogenic structures.

EXPERIiVIENTAL

The alloy specimens were obtained from commercial sources in the

form of plates. The nickel steels were used as -received (quenched and

tempered in the cases of the 3.5 and 9.0 percent nickel specimens, and

austenitized, temperized, and reversion annealed in the cases of the 5 and

6 percent nickel specimens). The 5083 aluminum was annealed at 413°C

for 30 min. at a pressure of 5 X 10"^ torr and cooled in the furnace.

Cylindrical specimens 5/8-in, (1.6 -cm) in diameter and 3/8 -in. (1.0-

cm) long were prepared by grinding. Opposite faces were flat and parallel

within 100 X 10"^ in. (2.5 [X m). Chemical compositions (obtained from mill

analyses), hardness numbers, and mass densities are given in Table 1. Hardness was determined by standard metallurgical methods. Mass density

was determined by Archimedes ' method using distilled water as a standard.

Quartz transducers (10 MHz) were bonded to the specimens with phenyl

salicylate for room -temperature measurements and with a stopcock grease for

lower temperatures. The specimen holder is shown in Fig. 1. The holder was

placed in the ullage of a helium dewar and lowered stepwise to achieve cooling.

Temperatures were monitored with a chromel-constantan thermocouple

contacting the specimen.

Ultrasonic sound-wave velocities, both longitudinal and transverse, were

3-5 determined by a pulse-superposition technique. High-frequency pulses

(nominally 10 MHz) were gated from a continuous carrier in such a way that

they were all phase coherent. Each pulse, when applied to the quartz transducer, generated an echo train in the specimen. The repetition rate of the

pulses was adjusted so that each pulse was superposed on the second echo of

each preceding pulse. Thus, the transit time of a sound wave in the specimen

is directly related to the repetition rate of the pulses. Denoting the carrier

N-5

3
frequency by f, the repetition rate is then f/n, where n is an integer. Typical

values of n, which are deternained from the frequency-divider setting, were

70-200 for these experiments. It follows that the round -trip transit time t in

the specimen is simply

t = n/(2f) . (1)

Ultrasonic velocities v are given by

V = 211 t, ^ (2)

where J^is the specimen length, A block diagram of the experimental apparatus

is shown in Fig. 2,

In practice the pulse-superposition method proceeded as follows. The

carrier frequency f was adjusted as closely as possible to the resonant frequency

of the quartz transducer (nominally 10 MHz). The frequency-divider setting n was then varied until each pulse was approximately superposed on the second

echo from each preceding pulse. The carrier frequency was then readjusted

until a maximum constructive interference condition was obtained. A change

in the environmental conditions of the specimen caused a change in the transit

time, and thus in the interference condition. As the environment changed,

superposition was maintained by adjusting the carrier frequency. The divider

setting was kept constant for a given experiment. Thus, the experimentally

measured quantity was Af/f. It is easily shown that

At/t = -Af/f, (3)

and that ? Av/v = Af/f + hlli. (4)

Since an elastic modulus C is related to the velocity v and mass density

0 by

C = Dv^ ,

' (5)

it follows that

AC/C = Ap/p + 2Av/v. (6)

4

N-6
Since Ap/p = -3AJJ/^, one then obtains

AC/C = 2Af/f - Ml I. (7)

Changes of elastic moduli due to temperature effects were

determined. The measured quantities were thus j- , where T is

absolute temperature.. Since the thermal expansion coefficient a is defined as

_ 1 A£ . ^ ~ AT ' ^

it follows that

At room temperature, elastic moduli typically change linearly with temperature.

the relative modulus change with temperature. Room-temperature values of

the temperature coefficients are reported in this paper.

It is usually found that the thermal-expansion contribution to (l/C) (dC/dT)

is less than 10% of the velocity contribution, that is,,] a j < • 2l(l/f) (df/dT)|.

Thus, errors in the thermal expansion coefficient will not lead to significant

errors in the temperature coefficients of the elastic moduli.

Except for determining room-temperature values of (l/C) (dC/dT), effects

of thermal expansion are neglected in this paper. Typically an elastic modulus

changes by only 5-10% over the temperature range 4-300K, and neglect of

thermal expansion leads to an error of at most 0. 5% in the low-temperature

value of the elastic modulus. Such errors are well within experimental

accuracy. Thus, when elastic -moduli — temperature curves were fit to a semi -theoretical function, as discussed below, thermal expansion was neglected.

Relative velocity changes as small as 10"^ could be detected; however,

absolute errors in the measured moduli are estimated to be about 1-2 percent.

Thus, since the individual data points are normalized to the room-temperature

value, the overall curve could be shifted by 1 or 2 percent because of

systematic error.

Of. (9)

The temperature coefficient (l/C) (dC/dT) is then significant, since it gives

N-7

5
RESULTS

From the longitudinal and transverse ultrasonic velocities, v and v , the respective elastic moduli are given by:

= Pv| . (10)

and = pv^ , (11)

where p is the mass density.

While polycrystalline aggregates (quasi-isotropic solids) have only two

independent elastic constants, several constants are commonly used for

various applications. The four most common are the bulk modulus B, Young's

modulus E, the shear modulus G, and Poisson's ratio v . These constants can

be calculated from C and C by the relationships

= = - I

/

- C,), (12)

B = C^-|C^, (13)

V = i (C^ - 2C^) / (C^ - C^), (14)

and ^ = ^t'

^^^^

Rather than calculate the temperature dependence of these four elastic

constants point by point from the experimental moduli, C« and C, can be fit to a

6

s emi -theoretical relationship suggested by Varshni : C = C° - s/(e*^^ - 1), (16)

where C°, s, and t are adjustable parameters and T is the temperature. The

value of C at T = O K is C°, and -s/t is the high -temperature limit of dC/?iT.

By invoking an Einstein oscillator model of solids, it can be shown (in the

absence of electronic effects) that t is the Einstein characteristic temperature.

The elastic constants can then be calculated from the moduli using Eqs. 12-15.

A. 5083 Aluminum

Longitudinal (C ) and transverse (C = G) moduli are shown in Figs. 3

and 4. Room-temperature values of the elastic constants are given in

Table 2 and room-temperature values of the temperature coefficients of the

elastic constants are given in Table 3. Values of commercially pure aluminum

(1100 aluminum) are included for comparison.

N-8

6.
Carves in Figs. 3 and 4 are plots of Eq. 16 determined by an unweighted

least-squares fit of the data. Average percentage differences between naeasured

and curve values are 0. 03% and 0. 10% for the longitudinal and transverse

moduli, respectively. Parameters C°, s, and t are given in Table 4. The elastic constants were calculated from the moduli shown in Figs.

3 and 4 by Eqs. 12-14. The constants E, B, and v are shown in Figs. 5-7.

Ferritic Nickel Steels

Longitudinal and transverse moduli for the four nickel steels are shown

in Figs, 8 and 9. Two of the nickel steels, 5 and 6 percent nickel, exhibit

maxima at low temperatures. These maxima may be caused by magnetic

transitions. The occurrence of these maxima, however, necessitated fitting

the low-temperature data to a different function. The Varshni function (Eq, 16)

was fit to the data from room temperature to the maximum. The dashed curve

represents a continuation of the Varshni function. From O K to the maximum,

a polynomial of the form

2 3 4

C = C + A1^ + BT + Df (17) o

was used to fit the data, where C , A, B, and D are adjustable parameters and

o f = T/T , where T is the temperature and T is the temperature at which

max max

the maximum occurs. Since this function has no physical significance, the

parameters are not reported. However, the function does satify the requirement that the slope go to zero as T approaches zero. Also it was required that

the slope go to zero as T approaches T

max

Room-temperature values of the elastic constants are given in Table 2,

and room-temperature values of the temperature coefficients of the elastic

constants are given in Table 3, Average percentage differences between

measured and curve values vary between 0. 01% and 0. 04% for the longitudinal

moduli and 0, 02% to 0. 04% for the transverse moduli. The constants E, B,

and V are shown in Figs, 10-12.

7

N-9
C, Elastic Debye Temperatures

It is of interest to calculate the elastic Debye temperature 9 for the

alloys. This fundamental parameter is important in the lattice properties of

7

solids and is related to the elastic wave velocities by

e = K <v> , (18)

Here his Planck's constant, k is Boltzmann's constant, N is Avogadro'

s

constant, p is the mass density, and A is the atomic weight. The average

velocity is given by

V ^ + 2v

' (20)

The Debye temperatures for the nickel steels and 5083 aluminum at T = O K

are given in Table 5. The Debye temperatures of iron and commercially pure

aluminum are included for comparison.

DISCUSSION

The elastic properties of 5083 aluminum behave regularly with respect

to temperature. The elastic moduli (C , C = G, B, E) decrease with increasing

temperature, show a relative flatness at low temperatures , achieve zero slope

at T = OK, and approach linear behavior at high temperatures, Poisson's

ratio also behaves regularly, having a positive temperature coefficient.

As mentioned earlier, however, the moduli of two of the nickel steels

(5 and 6 percent nickel) behave anomalously at low temperatures. The moduli

first increase with increasing temperature, then decrease approaching linear

behavior. Both Cp, and exhibit a maximum at approximately the same temperature. The 6 percent alloy was checked on both heating and cooling, and no

hysteresis seemed to be associated with the anomaly. This behavior is similar to

g that of some stainless steels, which undergo paramagnetic to antiferromagnetic

transitions at low temperatures. Possibly, the anomalies are caused by some

magnetic transition.

N-10

8
It is emphasized that the data reported here are dynamic (adiabatic)

rather than static (isothermal) and apply to rapid, rather than slow loading.

In most cases the differences between adiabatic and isothermal elastic

constants are small, less than one percent. Conversion formulas are given by

9 Landau and Lifshitz, for example.

Of the many possible engineering elastic constants (five - C , E, G,

B, and v - are discussed herein), only two are independent. Both isotropic

and quasi-isotropic solids are characterized elastically by two constants.

Thus, n-2 independent relationships must exist among n variables. By

differentiation, several quite useful relationships can be obtained. These

include:

dC_A ^ L_ (dB+jdG), (21)

i B+jG — = G . dB 3B . dG

E G+3B B G + 3B G ^ ^

dB dE 2 ^

dG = dB 3

G B ' (l+v)(l-2v)

dv, (24)

and dv E . / dE dG \

^25)

V E-2G \E G /

1 If V « —, which is a typical value for most metals and alloys, then these

equations simplify to

9

N-11
dE _ dB 8 dG

E 9B ^ 9 ° G ' ^^'^^ ^ - ^ + 2

^ , (28, B E V ^

'

dG _ dB 9 dv

G ~ B ' 4

' V

and

^ « - ^) . 1 - ^) V \E G / 9 \B G /

(29)

(30)

These relationships contain some surprising and useful information.

For example: Young's modulus is eight times more sensitive to shear than

to dilatation; Pois son's ratio depends equally, but oppositely, on shear and

dilatation, and only on the B/G ratio; the longitudinal modulus is twice as sensitive to dilatation as to shear, etc.

Furthermore, these relationships can be used to predict a wide variety

of effects when only partial information is available. Equations (26)-- (30) can be

expressed generally as

dX dY , dZ « a + b -— , (31 X Y Z ^

'

where X, Y, and Z are elastic constants and a and b are numerical coeffi clients.

Much more powerful relationships result by introducing another variable V:

X dV Y dV Z dV ' ^

'

where V represents any independent variable such as temperature, pressure,

or composition. As a useful example, these relationships will now be used to

discuss the effects of nickel on the elastic properties of iron.

10-28 The existing data on the room-temperature elastic constants of

nickel-steels are presented in Figs. 13-16. Data for pure iron, obtained by a N-12

10
Voigt -Reus s -Hill -arithmetic average of single-crystal data are also included.

The data were least-squares fitted to a straight line, the slope of which is

included in the figures. The data of Speich, Schwoeble, and Leslie was omitted

from the least-squares fit for the bulk modulus and Poisson's ratio.

If, in Eq. (32), V represents composition, the change with composition

in one elastic constant can be found from the measured changes with composition

in two others. For example, considerably more data exists for Young's modulus

and the shear modulus of nickel steels than for Poisson's ratio. Using Eq. (21),

however, the compositional dependence of v can be foTind from E and G data:

1^-4/1.^ 1 dG

V dV ^ \E dV G dV

or

dy_ _ 4 A dE 1 dG

dV ^ 3 \2 dV " .8 dV

since v ^ ^

, E ^ Z {x 10^^ N/m^) and G «.8 (x 10^^ N/m^) for iron. Using the

slopes given in Figs. 13 and 14 as values for dE/dV and dG/dV, dv/dV«6. 7x10-4.

The slope given in Fig. 16 is ~7 x 10"'^. Similarly, if the G and B data are used

in Eq. 27 (with B « 1. 6 x 10^^ N/m^), then dE/dV « -2. 19 x 10^ N/m^, in very

good agreement with the measured value of -2. 22 x 10''9/2 N/m . In fact, using

the E and G data to calculate the compositional dependence of B and V justifies

excluding the Speich et al. data from the linear least-squares fit for the

compositional dependence of B and v. The Debye temperatures of the nickel steels are lower than the Debye

24 29

temperatures of either iron or nickel ' This is expected since the ela^stic

constants, and thus the sound velocities, decrease drastically with the addition

of nickel to iron. In fact, the largest known alloying effects on elastic constants

28

may occur for iron-nickel alloys. This effect is not completely understood,

but may in part be caused by magnetic interactions.

Finally, the relationship between elastic and plastic properties is discussed

briefly, and the possible use of elastic data for predicting plastic properties is

indicated. The importance of this is two-fold. First, for cryogenic engineering

applications the most important properties of metals are strength and toughness.

Second, the possible relationships between elastic and plastic properties seem to

be generally unappreciated,

N-13

1

1

(33)

(34)
Usually, elastic and plastic behavior are considered separately. For

example, in a typical stres s -strain experiment the elastic and plastic regions

can be separated by an elastic limit, a proportional limit, or sometimes a

yield point. While these concepts differ from each other and are not always

well-defined and reproducible experimentally, they serve to define a stress

level that if exceeded results in permanent, plastic, irreversible mechanical

deformation.

The most obvious link between elastic and plastic properties is provided

by a dislocation model of microplastic mechanical behavior. All students of

dislocation theory know that the mathematical equations describing phenomena

such as slip, yielding, bending, cleavage, etc, from a dislocation viewpoint

almost always contain elastic constants as material parameters. In an isotropic

elasticity model these constants are Young's modulus, the shear modulus, and

Poisson's ratio. Isotropy is, of course, an idealization since all real materials

are anisotropic in some way.

Despite its potentially high impact, surprisingly little work on elastic

plastic relationships has been published. The advantages that might accrue

from such work include: (a) the ability to relate plasticity more intimately to

interatomic forces; (b) the possibility of correlating plastic properties with other

parameters via the elastic constants — for example atomic number, melting

temperature, or Debye theta; and (c) a possibly higher degree of correlation

among plastic properties themselves. Some correlations — for example,

between Young's modulus and yield stress, or between microhardness and the

shear modulus — are already well known.

The most thorough study of the elastic-plastic relationship was made by

32 33

Pugh. Other studies have been made by Hasselman and by Crutchley and

34 Reid Pugh made the following suggestions: (1) at temperatures less than

one third of its melting point, a material's resistance to plastic deformation

12

N-14
is proportional to Gb, where G is the shear modulus, and b is the magnitude

of the Burgers vector; (2) fracture strength is proportional to Ba, where B

is the bulk modulus, and a is the lattice parameter; (3) ductility increases

with B/G, the ratio of the bulk modulus to the shear modulus. Since Poisson's

ratio V is an increasing monotonic function of B/G, ductility should also

increase with Poisson's ratio; most data support his suggestion lead

( V = 0. 40), aluminum ( v = 0.37), copper ( v - 0. 34), chromium ( v = 0.25),

beryllium (v = 0.04) as examples. Since Poisson's ratio changes only very

slowly with alloying, mechanical deformation, etc. , it does not provide as

sensitive an index of ductility as would be desired. On the other hand, small

changes in Poisson's ratio may correspond to large changes in ductility. A

possible large influence of v on the plastic anisotropy of b.c.c. metals was

35 discussed by Crutchley, Reid, and Webster. In terms of the iron-nickel

alloys reported on here, the following inferences would be drawn from the

room-temperature elastic data: (1) the plastic resistance decreases with

increasing nickel content; (2) the fracture strength decreases slightly with

increasing nickel content; and (3) the ductility, as measured by B/G increases

3 6 slightly with increasing nickel content. The experimental study by JoUey

contradicts the first two assertions while affirming the third. The poor

correlation in this case between elastic and plastic properties suggests either

32

that the particular dislocation models used by Pugh are too simple or that

alloying nickel into iron changes somehow the behavior of dislocations in the

alloy. For example, atomic ordering could cause localized effects on dislocations that would not be revealed by macroscopic elastic constants.

This leads naturally to another topic, which is especially important in

the cryogenic application of iron-nickel alloys -- the ductile - brittle transition.

The elastic data in Figs. 8-12 show no irregularities near temperatures where

the ductile -brittle transitions occur. This is expected since acoustic waves

sample a macroscopic volume of a specimen, and the modulus defect due to

dislocations is quite small. Assuming the ductile-brittle transition results

from immobilizing dislocations, then measurement of ultrasonic attenuation

would be a better approach than measurement of ultrasonic velocities, if in

these alloys dislocations contribute significantly to the attenuation.

N-15

13
Acknowledgment

Specimens of nickel steels were graciously supplied by Armco

Steel Corporation and by Nippon Steel Corporation.

14

N-16
References

1. Gilman, J. J., Austr. J. Phys. , Vol, 13, I960, pp. 327-46.

2. Rosenberg, S, J., Nickel and Its Alloys , Nat, Bur. Stand. (U.S.),

Monogr. 106 (May 1968).

3. McSkimin, H, J., J, Acoust. Soc. Amer. , Vol. 33, 1961, pp. 12-6.

4. McSkimin H, J. , and Andreatch, P, , J. Acoast. Soc. Amer. , Vol, 34,

1962, pp, 609- 15..

5. McSkii-nin, H. J., J. Acoust. Soc. Amer. , Vol. 37, 1965, pp. 864-71.

6. Varshni, Y. P, , Phys. Rev, , B, Vol. 2, 1970, pp, 3952-8.

7. Debye, P., Ann. Phys. (Leipz) , Vol, 39, 1912, pp, 789-839.

8. Weston-, W, F, , Ledbetter, H. M. , and Naimon, E. R. , to be published,

9. Landau, L. D, and Lifshitz, E. M, , Theory of Elasticity, Pergamon,

London, 195 9, p. 17,

10. Guillaume, Ch. -Ed, , C. R. Acad, Sci. , VoL 124, 1897, pp. 752-5.

11. Carpenter, H, C. H. , Hadfield, R, A, , and Longmuir, P, , Proc, Inst.

Mech. Engrs. , Parts 3-4, 1905, pp. 857-87,

12. Honda, K. , Sci, Rep. Tohoku Univ. , Vol, 8, 1919, pp. 59-71,

13. Miiller, W. , in For schungsarbeiten auf dem gebiete des Ingenieurwesens , Part 247, J. Springer, Berlin, 1922, pp. 5-38.

14. Carrington, H, , Engineering, Vol, 117, 1924, pp. 69-71.

15. Honda, K. and Tanaka, T. , Sci. Rep. Tohoku Univ. , Vol. 15, 1926,

pp. 1-37.

16. Chevenard, P., Trav. Mem, Bur. Int. Poids Meas . , Vol. 27, 1927,

pp, 115-9.

17. Nishiyama, Z, , Sci, Rep. Tohoku Univ. , Vol. 18, 1929, pp. 359-400,

18. Nakamura, K. , Sci. Rep. Tohoku Univ. , Vol. 25, 1935, p. 303; Z^. Physik, Vol, 94, 1935, pp, 707-16.

N-17
19. Ebert. H. and Kussmann, A., Physik. Zeitschr. , Vol. 38, 1937,

pp. 437-45.

20. Chevenard, P. and Crussard, C. , C. R. Acad. Sci. , Vol. 215, 1942,

pp. 58-61.

21. Koster, W. , Z. Metallk. , Vol. 35, 1943, pp. 194-9.

22. Scheil, E. and Reinacher, G. , Z. Metallk. , Vol. 36, 1944, pp. 63-9.

23. Markham, M. F. , Brit. J. Appl. Phys . , Suppl. 6, 1957, S56-63.

24. Rayne, J. A, and Chandra sekhar, B. S. , Phys. Rev. , Vol. 122, 196l,

pp. 1714-6.

25. Smith, R. T. , Stern, R. , and Stephens, R. W. B, , J. Acoust. Soc.

Amer. , Vol, 40, 1966, pp. 1002-8,

26. Roberts, M, J., and Owen, W, S. , Trans. ASM, Vol, 60, 1967,

pp. 687-92.

27. Takahashi, T, , Bassett, W. A. , and Mao, H, -K, , J. Geophys. Res. , Vol. 73, 1968, pp. 4717-25.

28. Speich, G. R. , Schwoeble, A, J. , and Leslie, W. C, , Met. Trans. , Vol. 3, 1972, pp. 2031-7,

29- Weston, W. F. , Naimon, E. R. , and Ledbetter, H. M. , unpublished results.

30. Dixon, M. , Hoare, F. E. , Holden, T. M. , and Moody, D. E. , Proc.

Roy. Soc . , Vol. 285, 1965, pp. 561-80.

31. Ledbetter, H. M. and Reed, R. P., J. Phys. Chem. Ref. Data , Vol- 2,

No. 3, 1973, pp. 531-617.

32. Pugh, S. F. , Phil. Mag., Vol. 45, 1954, pp. 823-43.

33. Hasselman, D, P. H. , in Anisotropy in Single-Crystal Compounds (F, W,

Vahldiek, S. A. Mersol, Eds.), Plenum, New York, 1968, pp. 247-65.

34. Crutchley, D. E. and Reid, C. N. , High Temperature Materials (Plansee

Seminar, F, Benesovsky, Ed.), Springer-Verlag, Vienna, 1969, pp. 57-66.

35. Crutchely, D, E. , Reid, C. N. , and V/ebster, T, H. , personal communication.

36. JoIIey, W., Trans. Met. Soc. AIME, Vol. 242, 1968, pp. 306-14.

N- 18
List of Tables

1. Compositions and properties of alloys.

2. Room-temperature values of elastic constants, units of 10 N/m^

except V (dimensionless ).

3. Logarithmic temperature derivatives of elastic constants at room

temperature (10"^ K"^).

4. Parameters in equation 16.

5. Elastic Deb ye temperatures at T = O K.

List of Figures

1. Schematic diagram of specimen holder.

2. Block diagram of pulse -superposition system.

2

3. Temperature variation of longitudinal modulus Cjj = Pvj^ of 5083

aluminum.

4. Temperature variation of transverse or shear modulus C - p = G of 5083 aluminum.

5. Temperature variation of Young's modulus of 5083 aluminum.

6. Temperature variation of bulk modulus (reciprocal compressibility) of

5083 aluminum.

7. Temperature variation of Poisson's ratio of 5083 aluminum.

8. Temperature variation of longitudinal modulus = Pv^ of four

nickel steels

.

9. Temperature variation of transverse or shear modulus = Pv^ = G

of four nickel steels. '

10. Temperature variation of Young's modulus of four nickel steels.

11. Temperature variation of bulk modulus (reciprocal compressibility) of

four nickel steels.

12. Temperature variation of Poisson's ratio of four nickel steels.

13. Compositional variation of Young's modulus of iron-nickel alloys.

14. Compositional variation of shear modulus of iron-nickel alloys.

15. Compositional variation of bulk modulus of iron-nickel alloys.

16. Compositional variation of Poisson's ratio of iron-nickel alloys.

N-19
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Table 2. Room Temperature Values of Elastic Constants

(lO-'-^ N/m^ except v (dimensionless))

Alloy E G B V

A.i 5083 0.716 0. 269 0.716 0. 333

Aj^ 1100* 0. 695 0.259 0. 724 0. 340

Fe-3. 5 Ni 2. 038 0. 791 1. 600 0. 288

Fe-5 Ni 1. 984 0. 770 1. 559 0. 288

Fe-6 Ni 2. 024 0. 790 1. 543 0. 281

Fe-9 Ni 1. 951 0. 754 1. 562 0. 292

2. 05 0. 81 1. 664 0.282

'' Calculated from data taken by the autbors.

Reference 3 1.

N-21
Table 3. Logarithmic Temperature Derivatives of Elastic Constants

at Room Temperature (10-4 K"^)

Alloy

1 dB

rlT U. -L

1 dE

F dT

1 dG

G dT

1 dv

V U. J.

A;^ 5083 -2 . 15 -6.29 -6.81 2. 08

AjillOO- -2 . 24 -5.25 -5. 60 1.41

Fe -3.5 Ni -1 . 56 -2. 82 -3. 02 0. 93

Fe - 5 Ni -1 . 53 -3. 32 -3.61 1. 32

Fe - 6 Ni -1 . 42 -3. 21 -3.52 1. 40

Fe - 9 Ni -1 . 25 -2. 77 -3. 01 1. 08

Fe -0 . 90 -2. 11 -2.31 0. 95

Calculated from data taken by the authors.

Calculated from data in Reference 24 using a Voigt -Reus s -Hill average.

N-22
Table 4. Parameters in Equation 3

Alloy Mode C°

(10^^ N/m'' )

s (10^^ N/m^)

t (K)

Ai5083 1 . 151 0. 093 235. 3

Pv^^ 0 . 307 0. 038 206. 7

Fe - 3. 5 Ni 2 . 763 0. 140 246. 7

pv/ 0 . 840 0. 053 218. 7

Fe - 5 Ni Pv.^ 2 . 687 0. 230 353. 8

^: 0 . 819 0. 104 345. 8

Fe - 6 Ni 2 . 692 0. 244 380. 5

^\ 0 . 835 0. 125 398. 7

Fe - 9 Ni 2 . 663 0. 126 252. 7

pv/ 0 . 799 0. 057 246. 0

N-23
Table 5. Elastic Debye Temperatures at T = O K

Alloy e(K)

AJi 5083

- 414. 8

Aj^ 1100 405. 4

X t; O » D J-N J. 4^"^ 7

Fe - 5 Ni

\ 459. 0

Fe - 6 Ni 463.4

Fe - 9 Ni 453.0

Fe * 477

* Reference 24.

N-24
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<> Nishiyama (1929)

A Honda, Tanaka (1926)

V Nakamura (1935)

<3> Koster (1943)

s$> Scheil, Reinacher ( 1944)

® Rayne, Chandrasekhar (1951)

O Speich, Schwoeble, Leslie (1972)

Q Present Results

Slope - -2.22x10^ M/m^

1.8

76

4 6 8

NICKEL (wt. pet.)

10 1 2

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0.86

()

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A Honda, Tanaka (1926)

® Chevenard (1927)

m Markham (1957)

® Rayne, Chandrasekhar (1961)

^ Smith, Stern, Stephens (1966)

O Roberts, Owen (1967)

O Speich, Schwoeble, Leslie (1972)

Present Results

Slope=-9. 28x10^ N/m^

4 6 8

NICKEL (wt. pet.)

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0.35

V Honda (1919)

B Carrington (1924)

A Honda, Tanaka (1926)

0 Cold Worked

J Chevenard,

S Annealed } Crussard (1924)

® Rayne, Chandrasekhar (1961)

O Speich, Schwoeble, Leslie (1972) • Present Results

on

0.25

4 6 8

NICKEL (wt. pet.)

10

N-40
APPENDIX O

O-l
A SURVEY OF LNG TECHNOLOGICAL NEEDS IN THE

U.S.A. -- 1974 TO BEYOND 2000

L. A. Sarkes

American Gas Association, Incorporated

1515 Wilson Boulevard

Arlington, Virginia 22209

and

D, B, Mann

Cryogenics Division

National Bureau of Standards, Institute for Basic Standards

Boulder, Colorado 80302

ABSTRACT

A comprehensive analysis of near and long term research needs has

been conducted by the U. S. Gas Industry covering operational areas of

Production and Exploration, Synthetic Supply, Transmission, Distribution,

Utilization and LNG,

Identifiable research needs are reported for the area of LNG encompassing time frames of:1974 - 1978 (In detail, year by year)

1979 - 1985 (In 5 year period)

19 86 - 2000 (As specific as possible)

Beyond 2000 (As believed necessary),

A year by year examination of LNG research priorities for the first

five years are considered vital to overcome the potential suppression of

growth in the LNG industry that could result from lack of available technology.

Assessments of technical LNG needs beyond 1978 cannot, of course, be too

well defined and must be examined annually for purposes of updating.

The National Bureau of Standards Cryogenics Division has become the

governmental focal point for LNG research. A survey of NBS LNG research

and how these relate to the future technological growth of the LNG industry

are di scus s ed.

Paper presented at Fourth i nternat i ona ] Conference on Liquefied

Natural Gas (Algiers, Algeria, June 24-27, 197^)

0-2
UN EXAMEN DES BESOINS TECHNOLOGIQUES DU GAZ NATUREL

LIQUEFIE AUX U.S.A. -- DE 1974 JUSQU' AU-DELA DE 2000

L. A. Sarkes

American Gas Association, Incorporated

1515 Wilson Boulevard

Arlington, Virginia 22209

and

D. B. Mann

Cryogenics Division

National Bureau of Standards, Institute for Basic Standards

Boulder, Colorado 80302

RESUME

Une analyse complete des besoins d'etudes, a court et a long terme,

est menee par I'industrie du Gaz des U.S.A. (U. S. Gas Industry) concernant

les secteurs operationnels de la Production et de l' Ebcploitation , de la Production Synthetique, de I'Acheminement, de la Distribution, de l' Utilisation et du

Gaz Naturel Liquefie (G.N. L. ). Les besoins de recherche daus le domaine du G. N. L. sout passes en revue pour les periodes suivantes:

1974 - 1978 (En detail, annee par annee)

1979 - 1985 (Pour la periode de 5 ans)

1986 - 2000 (Aussi precisement que possible)

Au-dela de 2000 (Ainsi que cela semble necessaire).

Un examen, annee par annee, des priorites de la recherche en ce qui

concerne le G. N, L. , est considere comme vital pour les cing premieres

annees, afin de surmonter la stagnation potentielle de I'industrie du G. N. L.

qui pourrait resulter d'un manque de disponibilite technologique. La repartition

des besoins techniques du G.N. L. au-dela de 1978 re peut evidemment pas etre

parfaitement bien definie et doit etre examinee annuellement en vue d'une mise

a jour.

La Division Cryogenic du Bureau National des Etalons (National Bureau

of Standards Cryogenic Division) est devenue le centre official d'etudes du G. N. L,

Un examen des etudes du Bureau National des Etalons ainsi que leur relation

avec la future croissance technologique de I'industrie du G. N. L, sont discutes.

2 0-3
A SURVEY OF LNG TECHNOLOGICAL NEEDS IN THE

U,S.A„ 1974 TO BEYOND 2000

The total energy needs of the United States are enormous and are continuously increasing. The nation's growing demand coupled with increasing

concern for the environment, difficulties in meeting increased demand from

traditional sources and current import uncertainties have led to shortages of

all types of energy resources within the U. Between 1965 to 1970, the total

U, S, domestic energy supply grew at a rate of 5% per year. Many energy

economists now are foreseeing energy growth rates in the range of 4. 1% to

4. 8% per year during the 1970's [ i] , The total energy consumed was 44, 8 X lO^^btu in I960, 54, 0 X 10-^^ in

1965 and 68, 8 X 10^ in 1970 (Figure 1), As suming a total energy demand increase of 4-^% per year, 96 X 10''''^btu will be required during 1980 and 122 X

10''"^btu by 1985, Natural gas, coal and oil were the primary resources of the

energy consumed in residential, commercial, industrial and transportation

sectors of the economy during 1973-74 (Figure 2).

The goal of the gas industry in the United States is to continue to provide

a major portion of these future energy needs through the use of untapped natural

resources, Canadian imports, s ynthesized f uel gas production from coal, oil

shale, solid wastes, biomass, other natural resources and through the importation of LNG, The options and alternatives in support of this goal have been

well defined what remains to assure future gas supply is the technological

capability to find, produce and deliver this gas to the consumer by new or improved techniques and procedures.

The U. S. gas industry has the incentive and resources to meet this goal.

It currently provides about one -third of the nation's total energy requirements.

At the end of 1973, it served 43,700,000 residential, commercial and industrial

customers through a 981,000 mile underground network of transmission and

and distribution lines. The gas industry has grown nearly twelvefold in terms

of the book value of total assets since 1945, expanding from a 5 billion dollar

industry to more than 59 billion dollars at the end of 1973, Preliminary figures

for 1973 show a total consumption of 22-|- trillion cubic feet (637 billion cubic

meters). The total annual gas requirements in the U. S. are expected to increase to 46, 7 trillion cubic feet (1, 32 trillion cubic meters) by 1990 as shown

in Figure 3,

In the U, S, , as in every industrialized nation of the world, the demand

for natural gas is increasing. The growing intensity of the worldwide shortages

over the past year has touched off a global scramble to obtain supply agreements

with producing nations and arrange for construction of related facilities. In the

U. S, alone some 10 LNG import terminals [2] are under construction or planned

at a cost of almost 1 billion dollars per facility. Each liquefaction complex

3 0-4
120

100

80

ENERGY

(lO^^BTU)

60

40

ACTUAL

PROJECTED

TOTAL ENERGY

20

01 —J I i I960 62 64 66

GAS

68 70 72 74 76 78

YEAR

80

Figure 1. Energy consumption in the United States

4- 0-5
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CO

Si

CO

CO

LU

CO

CO

UJ

CJ

COo

CO

COud

>-

3=

0-6 5

accounts for approximately $300 million with the remainder of the $1 billion

going for ships, pipelines, receiving terminals and storage facilities.

Supplemental gas supply projections for the period 1972-1990 prepared

by A. G. A, forecast an LNG importation of 3. 2 trillion cubic feet (91 billion

cubic meters) by 1990, This projection (Table 1) represents 20% of the total

estimated supplemental supply. This thousand-fold increase over the two billion

cubic feet (57 million cubic meters) imported during 1972 demonstrates the

massive dimension of the rapidly emerging LNG market in the U. S, alone,

LNG technology has created a truly international gas industry.

It is axiomatic that this growing section of international gas operations

be supported by a comprehensive, continuing research effort to assure energy

conservation and safety of all elements, liquefaction, transportation, transfer,

storage and plant operation.

Over the past year, the Natural Gas Industry has placed an accelerated

emphasis on viewing its supply in relation to projected demand, the reasons for

that demand and identification of future technological needs required to balance

supply and demand.

Based on an awareness of the role played by Research and Development

in furnishing the required advanced technology to assure continued supply and

growth, the U, S. Natural Gas Industry undertook a comprehensive study to

define the requirements for future research and development and formulated an R&D plan that would assist the gas industry to help satisfy the nation's future

energy needs. This study [4] was structured to examine in detail the needs for

research and development in each of six major areas, namely

e Exploration and Production

® Synthesized Natural Gas (SNG)

© Transmission

• Distribution

« LIQUEFIED NATURAL GAS

© Utilization

The basic technology required to import LNG exists today (no major

technology "breakthrough" required). However, to respond to the rapidly

changing demands for energy in all forms, a major research activity has been

identified for the gas industry as necessary at this time to accelerate development of this market. The technology involved in ship transportation and largescale liquefaction is being pursued aggressively and adequately by groups of

companies with large financial commitments. We recognize, however, that

many items of the research plan program we have recommended will impact on

the development programs being conducted by companies outside the gas industry.

Coordination between these various R&D programs is essential, therefore, particularly in such areas as LNG ship design and the configuration and construction

of marine terminals.

7 0-8
w<

««3

5s

C5

«^

c:

CO ^ O to

c; Co ^ I

Co « 0-9
Seven critical research needs were selected for immediate study. These

items generally cover the metrology and the safety aspects of liquefied natural

gas transport, transfer and storage.

This plan also recommends an additional allocation of research funding on an unassigned basis; the rapid changes occurring in the overall LNG picture

will undoubtedly create new demands for research. Total cost of the R&D

program to meet the essential needs is estimated to be almost $13 million

(Figures 4 and 5).

The LNG research plan includes the results of an industry-wide poll of

LNG research needs, both foreign and domestic. Based on the responses to

this poll, an original group of some forty-two research needs were defined and

identified. It was obvious that many of these research needs were being, or should be undertaken by manufacturers, perhaps with the cooperation of the gas

industry. Many of these topics are listed in Table 2,

The LNG plan identified four research projects that could properly be

categorized as long-range research (beyond 1980) needs; long distance LNG

transfer lines, novel LNG transport methods, improved concepts of LNG

storage, and utilization of LNG refrigeration.

These tasks were suggested to provide a more definitive answer to constantly recurring questions such as: are long-range LNG pipelines really

feasible and economic? ; are there really any new concepts for LNG storage

or transportation? ; can the refrigeration available from LNG be utilized

practically and economically?

It is recognized that specific LNG research is being sponsored by many

segments of the International LNG Industry. These efforts are applauded and

are expected to continue as the LNG market continues to grow. It is our purpose, however, to recognize and identify those research areas that can impact

upon and re-enforce the many individual LNG research efforts underway or planned by the various elements of the LNG industry. Communication internationally between the various programs as exemplified by LNG-4 is deemed

essential to assure an orderly and effective worldwide growth in LNG trade.

The National Bureau of Standards, having played a vital role in past

LNG research in support of the gas industry plan, has a number of programs

underway that are of importance to the future of the LNG industry.

LNG RESEARCH AT NBS

As the LNG industry has matured from concept through demonstration

projects to full scale peak shaving, satellite and base load operations, the

requirements for information necessary for implementation of current and

future LNG application have been significant. This required information

exists in many forms, including data for equipment design, decision making

9O-IO
Therm-Meter Development

Quantity Gage for

Static LNG (2%)

Control of Vapor

Dispersion

from LNG Spills:

Land (19%)

Water (10%)

LNG Fire Control

(10%)

Technical Manual LNG

System (8%)

Fire Control Manual (2%)

Thermophysical Properties (8%)

gure 4. Allocation of LNG research and development costs - first

five years [ 4] .

10 O-ll
1 THERM METER DEVELOPMENT

2 QUANTITY GAGE FOR STATIC LNG

Thousdiids

of Dollars

1000

Figure 5. Annual LNG research and development funding [4]

0-12

1 1
TABLE 2.

SECONDARY LNG R

GAS RESEi

LNG Facility Siting Criteria

Definition of standards and

codes

Risk analysis

Analysis of hazards to LNG

from adjacent facilities

Environmental impact of LNG

(cold, vapor and fire)

Flame detection systems

Properties of Materials Used

in LNG Service

Insulation research

Structural materials

Other materials

LNG Transportation Systems

Research

Development of new ship unloading

concepts

Reliquefiers for ships

Risk analysis re: storage, tanks,

equipment

Purge of LNG transfer systems

Develop effective, quick shutdown systems (e. g. , water

hammer)

New concepts in moorings

Supertanker port

Supmarine pipeline

Economics of long distance

transport

Ship construction and strength

during collision

EARCH TASKS -- AGA

CH PLAN [4]

Processing Improvements

Improved liquefiers , vaporizers,

etc.

Limits of water, CO2 and other

trace contaminents as a function

of onstream time without deriming

Thermal and chlorine pollution

of cooling water

Long Range Research Area

Short Distance LNG Pipelines

Review existing files and literature

to search for new technology

Other

LNG conservation research

Effect of SNG and imported LNG on peak shaving LNG operations

Static electricity in plants and

ships: sources, effects, methods

of preventative design

Earthquake design

Effects of LNG spill on outer, noncryogenic hull plate of tanker

Tanker disturbance of shore and

bottom life in shallow canals

Contingency plans for LNG industry

12 0-13
(which process to choose), commodity transfer (providing equity in trade),

data for safety applications as well as information for local, state, federal

and international codes and standards, preparation of environmental impact

statements and data for establishing insurance rates and financial considerations.

Certain well defined areas of required information fall within NBS

traditional roles in this specialized field of c ryoengineering and cryophysics.

It was believed that NBS could combine both leadership and supportive roles

to other government agencies and industry by (1) providing physical data of

national importance not previously available in sufficient accuracy, (2) measurement methods, test methods and instrumentation, (3) standard assistance

to voluntary and regulatory standardizing bodies, and (4) innovative technological leadership in methods and systems to reduce losses in transport and

storage and to provide necessary expertise to facilitate and reduce the time

required for program implementation.

Historically, NBS, through its Cryogenics Division in Boulder, Colorado,

has supported government and industrial programs in cryoengineering and

cryophysics since 1952, Concerted efforts in the general field of liquefied

natural gas were begun in 1968, Currently, our program (having 14 elements

or parts) provides the content of liquefied natural gas technology at NBS and is

supported by a group of government agencies and industrial organizations

(Table 3) which have a broad range of requirements. For purposes of explanation the 14 programs can be categorized into three more or less traditional

NBS areas -- reference data, measurement science, and technology transfer.

Reference Data

By 1965 programs involving liquefied natural gas had demonstrated its

viability as a peak shaving, satellite and supplemental fuel. Requirements

for property data included PVT relationships, enthalpy, entropy, internal

energy, dielectric properties, specific heats, heats of vaporization, speed of

sound and the transport properties of viscosity, thermal conductivity and

thermal diffusivity. Properties data were available from a number or sources

and, where useful for certain purposes, were found to be insufficient for future

planning, inadequate for many process designs and of either undefined or of

inadequate precision and accuracy. What was needed therefore were accurate

precise reference data over a broad range of pressures and temperatures

generally extending from near the triple point of methane to well above ambient conditions. LNG presented an additional challenge since it is a nonideal mixture of five or more hydrocarbon fluids and nitrogen, and the

LNG mixture fraction will vary with source, time and storage treatment. The

reference data must be of such quality as to classify it as basic reference values

where foreseeable advances in measurement technology would not materially

affect the listed values.

13 0-14
TABLE 3. LIST OF AGENCIES AND COMPANIES CURRENTLY SUPPORTING

LNG RESEARCH AT NBS

U. S. Department of Commerce

National Bureau of Standards

Maritime Administration

American Gas Association, Incorporated

Pipeline Research Committee (AGA)

U. S. General Services Administration

U. S, Federal Power Commission

LNG Density Committee consisting of: El Paso Natural Gas

Tennessee Gas Pipeline

Distrigas Corporation

Columbia Gas Service Corp,

Gaz de France

Natural Gas pipeline Company

Easco Gas LNG, Incorporated

Transcontinental Gas Pipe

Line Corporation

Chicago Bridge & Iron Company

Shell International Gas, Ltd.

Sonatrach

Southern California Gas Company

Phillips Petroleum Company

Texas Eastern Pipeline Company

Marathon Oil Company

Mobil R&D Company

Tokyo Gas Company, Ltd.

14 0-15
A comprehensive program including both interim and long term objectives is currently in progress. The interim program involves the definition

of densities of LNG as a function of pressure, temperature and mixture fraction. A 17 company committee is participating in the development of these

accurate data of liquefied natural gas mixtures to provide a basis for custody

transfer methods and equitable custody transfer agreements. The program

will provide a data base for mass and density gauging. The objective of this

LNG density measurement program is to provide accurate (0. 1%) measurements of the densities of saturated liquid methane, ethane, propane, butanes,

nitrogen and their mixtures, mainly in the temperature range 90-150 K. at

pressures to 10 atmospheres. Measurements are in progress and will include

six pure components, about 60 binary mixture compositions, and about 13

multicomponent mixture compositions. A high precision (0. 05%) magnetic

densitometer (based on Archimedes Principle) has been designed and constructed and is in the final stage of proving. The program is in its second year

of operation with anticipated completion in 1975.

The long term fluids program involves a wide range of properties in

addition to density. In general, the pure components of LNG are being studied

and analyzed extensively over broad ranges of pressure and temperature, and

then mixture laws applied or developed and confirmed with experimental verification. An example of this approach is the recently completed program on pure methane. Prior to 1970, interest in methane was general and was primarily directed to pure methane considered as a cryogenic fluid [5-17], Several

progress reports were published by Goodwin [ 18, 19] and the final report is now

available [20], This latter report includes extensive physical properties data

for methane such as fixed point constants, melting line, vapor pressure, orthobaric densities, virial equations, equation of state, specific heats, heats of

vaporization and speed of sound. In addition, derived properties of entropy,

enthalpy, and internal energy are included along with detailed explanations of

computational methods including computer programs. Tabular data in both SI

and British Units are also provided with estimates of uncertainties of all data.

Figure 6 shows pressure and temperature boundaries of properties described

by Goodwin.

It is acknowledged that this publication of the thermophysical properties

data is not necessarily in the form most useful for engineering applications.

Various charts and graphs will be required as well as other data forms of lessor

or greater detail. This major three-year program has produced what we believe

to be "best value" reference data on the major component of LNG,

The work on methane has also resulted in publication of accurate dielectric constants data for pure, compressed and liquefied methane [21], This data

should prove useful in providing a data base for mass and density gauging.

15 0-16
oCD

en oo s oo o CDo I UJ

anos oCD

CNI

0)uco

(I) o

(J COo

tooo

00 (i

-t-> ci c t; %ooO > co

ted 1 o

niu

WiV 'd

16

0-17
Current work in the long term LNG properties program is directed to

the second most important constituent of LNG -- ethane. It is the intention of

the program to methodically consider each of the pure constituents of LNG in a similar manner as previously described for methane. Current status of the

ethane work involves establishing a firm foundation for computing tables of

provisional values of thermodynamic functions. The activity has two purposes:

to indicate those physical properties for which experimental data are lacking or inadequate and to provide useful results at an early date. These properties

include vapor pressure, virial state equation, orthobaric densities, and formulations of the melting line of the ideal gas thermofunctions. Under the present

level of effort the work on ethane should be completed in April 1975; propane,

the butane and LNG mixtures will follow with a completion date for the entire

program by 1980.

Measurements of the liquid vapor equilibria of cryogenic fluids [22] , refractive index of liquid and vapor methane and direct measurement of sound

velocity and thermal diffusivity are well underway. A program on transport

properties -- viscosity, thermal conductivity - -is in the initial state of development.

Reference data on thermal and mechanical properties of structural and

insulation materials are essential to facilitate material selection on the basis

of cost and safety. Proper material choice is of major economic importance

for cryogenic containers, particularly in sea transport of LNG. Studies to define fracture toughness and fatigue crack growth rate in the temperature

range 76-300 K are currently being conducted on a series of iron-nickel alloys

and aluminum alloys. This materials properties assessment has included the

compilation of all the fatigue and fracture data on iron-nickel steels and their

weldments; a collection of ship design data and analysis of materials and use;

an assessment of the current materials requirements for LNG containers by

the American Bureau of Shipping, the U. S. Coast Guard and ASME Pressure

Vessel Code. In addition, a bibliography of literature containing data on aluminum alloys, non -metallic s and insulation materials is in progress. Results

and data for this program should be available after 1 July 1974.

Measurement Science and Methodology

Instrumentation and instrumentation methods are essential to process

control, safety and custody transfer of liquefied natural gas. The NBS LNG

program contains two examples of application of field type measurements.

The objective is to define the ability of the instrument to determine and maintain a known accuracy and precision of the parameter of interest, such as density or flow rate.

A density reference system consists of a volume of LNG of adequate

size and dimension to accept the measurement element of candidate densitometers. This volume will be filled with LNG of known density traceable to the

0-18 1'7
reference data established under the mixtures program referred to in the

previous section. Density, pressure, temperature and constituent fraction

will be varied over a range of controlled conditions .and the performance of the

densitometer will be evaluated. Long term stability of calibration will be of

interest as a logical extension of this work would be the development of a transfe

standard for field type densitometer certification. The LNG density reference

system is currently in the second year of a three year planned program. The

reference system is under construction and proving, with the completion date

of the program scheduled for 1975.

The demonstration of an instrumentation method which would measure

the heating value of liquefied natural gas flowing in a pipeline is the subject of

the second example of measurement science in our LNG program. The project approach combines existing and evolving measurement technology with

industry standard practices. The experience gained on a previous cryogenic

flowmetering program [ 23-26] will provide necessary scaling information for

the flowmetering portion of this three eleme;nt measurement system. The

second element of the heating value measurement system is a densitometer

evaluated and calibrated as described previously. The third element of the

heating value measurement involves an industry compatible flow calorimeter

which will provide heating value per unit mass. A combination of these three

measurement elements should provide a time -based rate for heating value of

liquefied natural gas flowing in a pipeline. The objective of this three- year

program will be to demonstrate the precision and accuracy of such a measurement system and to provide necessary supportive data for scaling to large pipe

sizes. The program is scheduled for completion in 1976.

Technology Transfer

It is the objective of this portion of the LNG program to provide a broad

dissemination of information on general cryogenic subjects. An LNG Quarterly

[27] is published and distributed each April, July, October and January listing

all significant papers, reports, and patents relating to LNG, LNG properties

and technology. LNG related information has been entered into the NBS Cryogenic Data Center's information system for quick retrieval and comprehensive

bibliographies on the properties and technology of LNG are available. There

are presently three bibliographies involved; methane properties, methane

mixture properties and processes and equipment involving methane and LNG.

These three are updated each October [28-30].

A second example of technology transfer is a program concerned with

safety of large LNG storage tanks. This program is primarily a consultation

and advisory type service to a regulatory agency charged with the responsibility

of approval for the location and safe operation of such storage containers.

These examples are of a short term transitory type but indicate the

approach in providing this type of information where it is needed and where

NBS can provide a proven capability.
FUTURE PLANS

The ongoing program of providing reference data, measurement science

methodology and technology transfer can be projected into the early 1980' s. An outline of such research topics is suggested by Table 2, The definition of

priorities for these secondary tasks will certainly provide the framework for

LNG research in the period 1980-1990 and beyond.

In the long-range future, there may be a number of possibilities for

pipeline distribution of energy or development of new sources of energy that

will impinge upon gas utility operations, and require continuing definition of

research objectives and goals. Several of these possibilities are listed below.

Methanol, distributed as Clathrates, hydrates,

vapor or liquid and hydrides

Low-btu gas Hydrogen

Coa-1 slurries Ammonia-hydrazine

Solar energy supplementation Geothermal energy

Many of these opportunities will require new facilities and new concepts

of business strategy by the gas utilities, but offer important opportunities either

on a general basis or in specific localities. A research planning system to

monitor and review these alternatives will be the most effective way for the

gas utilities to understand and posture themselves to capitalize upon these

shifts in a timely fashion.

19

O-20
REFERENCES CITED

[ 1] "Energy Folic/ Issues for the United States During the Seventies,"

A. D. Little, Inc. Report 1-2650,

[2] Oil and Gas Journal (1973) October 22.

[3] Gas Review (revised) 4 (1974) Jan. 15.

[4] Gas Industry Research Plan 1974-2000, A. G. A. Publication M-20274

(1974) January,

[5] Armstrong, G. T. , Brickwedde, E.G. and Scott, R. B. , "The Vapor

Pressures of the Deuteromethanes , " J. Chem. Phys, 21, No. 7,

1297-8 (1953) July.

[6] Armstrong, G. T. , Brickwedde, F, G. and Scott, R. B. , "Vapor

Pressures of the Methanes," J. Res. Nat. Bur, Stand. (U. S. ) 55

No. 1, 39-52 (1955) July.

[7] Hall, L. A. , "A Bibliography of Thermophysical Properties of Methane

from 0 to 300°K," Nat. Bur. Stand. (U.S.) Tech. Note 367, 121 pages

(1968) May.

[8] Mann, D. B. and Roder, H. M, , "Liquefied Natural Gas as a Cryogenic

Fluid - Instrumentation and Properties," (a) Proceedings Transmission

Conference of A. G. A. Operating Section (New Orleans, La. , May 26-27,

1969) T-98--T-106, American Gas Association, Arlington, Va. (1970);

(b) Cryogenic Ind. Gases 5_, No, 7, 23-9 (1970) July-August (out of print),

[9] Johnson, V. J, (General Editor), "A Compendium of the Properties of

Materials at Low Temperature - Phase I," Wright Air Development Div, , Wright- Patterson AFB , Ohio, Tech, Rept, No. WADD 60-56 (Prepared

at National Bureau of Standards, Boulder, Colo, , Cryogenics Div. , under Contr, No. AF 3 3(6 16) 58 -4) . Parti. Properties of Fluids , 489

pages (I960) July. Part II, Properties of Solids, 333 pages (I960) October.

Part III, Bibliography of References, 165 pages (I960) October,

[10] Ziegler, W, T, , Mullin s , J, C. and Kirk, B, S. , "Calculation of the Vapor

Pressure and Heats of Vaporization and Sublimation of Liquids and

Solids, Especially below one Atmosphere Pressure, III. Methane,"

Georgia Inst, of Tech, , Atlanta, Engineering Experiment Station, Tech.

Rept, No. 3 (Prepared under NBS Contr. No. CST-7238), 60 pages

(1962) August.

[11] Ziegler, W, T, and MuUins , J, C, , "Calculation of the Vapor Pressure

and Heats of Vaporization and Sublimation of Liquids and Solids, Especially below one Atmosphere. IV, Nitrogen and Fluorine," Georgia

Inst, of Tech, , Atlanta, Engineering Experiment Station, Tech. Rept.

No. 1 (Prepared under NBS Contr, No. CST-7404), 59 pages (1963) April.

20 0-21
[ 12] Hilsenrath, J, , Beckett, C. W. , Benedict, W. S. , Fano, L. , et al, , "Tables of Thermal Properties of Gases," Nat, Bur. Stand. (U.S.)

Circ. No. 564, 488 pages (1955) November.

[13] Ziegler, W. T. , Kirk, B. S. , MuUins, J. C. and Berquist, A. R. , "Calculation of the Vapor Pressure and Heats of Vaporization and Sublimation of Liquids and Solids below one Atmosphere Pressure. VII.

Ethane," Georgia Inst, of Tech. , Atlanta, Engineering Experiment

Station, Tech. Kept. No. 2 (Prepared under NBS Contr, No. CST-1154),

65 pages (1964) December.

[14] Stewart, R. B. and Johnson, V. J. (General Editors), Compressibility

Factor Chart for Methane; Z vs P (122 to 273°K; 1 to 600 atm. ). From:

"A Compendium of the Properties of Materials at Low Temperature - Phase II. " Wright Air Development Div. , Wright-Patterson AFB, Ohio,

Tech. Rept. No. WADD 60 - 56 ( 196 1)

[ 15] Pressure-Enthalpy Diagram of Methane (90 to 480°K; 1 to 300 atm.),

Leiden Univ. , Netherlands, Kamerlingh Onnes Lab. (1940).

[ 16] Ziegler, W. T. , "The Vapor Pressures of Some Hydrocarbons in the

Liquid and Solid State at Low Temperatures," Nat. Bur, Stand. (U.S.)

Tech. Note No. 4, 17 pages (1959) May.

[ 17] Flynn, T. M. , "A Bibliography of the Physical Equilibria and Related

Properties of Some Cryogenic Systems," Nat. Bur. Stand, (U. S, ) Tech.

Note 56, 123 pages (I960) May.

[18] Goodwin, R. D. , " The rmophysical Properties of Methane: Virial

Coefficients, Vapor, and Melting Pressures," J. Res. Nat. Bur, Stand.

(U,S.), Sect. A, 74, No. 5, 655-60 (1970) Sept. -Oct.

[19] Goodwin, R. D. , "Thermophysical Properties of Methane: Orthobaric

Densities and Some Thermal Properties," J. Res. Nat. Bur. Stand,

(U.S.), Sect. A, 75, No. 1, 15-21 ( 1 97 1 ) Jan. -Feb.

[20] Goodwin, R. D, , "The Thermophysical Properties of Methane from 90

to 500 K at Pressures to 700 Bar, " NBSIR 73-342, 274 pages (1973)

October.

[21] Straty, G. C. , and Goodwin, R, D. , "Dielectric Constant and Polarizability of Saturated and Compressed Fluid Methane," Cryogenics 13(12),

712-15 (1973) December.

[22] Kidnay, A. J. , Hiza, M. J. and Miller, R. C. , "Liquid- Vapor Equilibria

Research on Systems of Interest in Cryogenics - - A Survey," Cryogenics

13(10), 575-99 (1973) October.

21 0-22
Dean, J. W. , Brennan, J. A. , Mann, D. B. , and Kneebone, C, H. , "Cryogenic Flow Research Facility Provisional Accuracy Statement,"

Nat. Bur. Stand. (U.S.) Tech. Note No. 606, 40 pages (1971) July,

Brennan, J. A. , Dean, J. W. , Mann, D. B. , and Kneebone, C. H, , "An Evaluation of Positive Displacement Cryogenic Volumetric Flowmeters," Nat. Bur. Stand. (U.S.) Tech. Note No. 605, 134 pages

(1971) July.

Brennan, J. A. , Stokes, R. W. , Mann, D, B. and Kneebone, C. H. , "An Evaluation of Several Cryogenic Turbine Flowmeters," Nat. Bur.

Stand. (U.S.) Tech. Note No. 624, 90 pages (1972) October.

"Specifications, Tolerances, and Other Technical Requirements for

Comme rcial Weighing and Measuring Devices , " Nat, Bur. Stand. (U.S.)

Handbook 44 - 4th Ed. (1971).

LNG Quarterly, A publication of the NBS Cryogenic Data Center,

Boulder, Colo. 80302.

NBS Cryogenic Data Center, "The Ther mophy sical Properties of

Methane -- A Selected Bibliography," B-1055, 55 pages (NBS, Boulder,

Colo. ) (1973) Sept.

NBS Cryogenic Data Center, "The Properties of Methane Mixtures -- A

Selected Bibliography, " B- 1056, 75 pages (NBS, Boulder, Colo.) (1973)

Sept.

NBS Cryogenic Data Center, "Liquefied Natural Gas Technology," B- 1075,

44 pages (NBS, Boulder, Colo.) (1973) October.

Doslin, D. R. , Harrison, R. H. , Moore, R. T. , and McCullough, J. P. , "PVT Relations for Methan^', J. Chem. Eng. Data _9, No. 3, 358 (1964).

0-23 ISCOMM [JU.

!

APPENDIX P

P-1
LOW TEMPERATURE FRACTURE BEHAVIOR OF FERRITIC Fe-Ni ALLOY STEELS

R. L. Tobler, R. P. Mikesell. R. L. Durcholz and R. P. Reed

Cryogenics Division

Institute for Basic Standards, National Bureau

of Standards, Boulder, Colorado 80302

Fracture toughness tests over the interval Z98-4K and fatigue crack growth

rate tests at 298, 111, and 76K are reported on selected Fe -Ni alloys which are

commerically available for potential use in storage or transportation of LNG.

These alloys include Fe-6Ni and Fe-5Ni in the QLT or austenitized, temperized,

and reversion annealed condition, and Fe-9Ni in the quenched and tempered

condition. Linear elastic fracture mechanics parameters (K , K ) and

J-integral (J^,.,) test data are presented for 1.25 inch thick compact tensile

specimens. Discussion includes comparisons of fatigue crack growth rate and

f racture data between alloys.

Key words; Crack propagation, cryogenics, fracture toughness, iron alloys,

mechanical properties, nickel alloys, steels.

This work was conducted at the National Bureau of Standards under the sponsorship of the Maritime Administration, U. S, Department of Commerce.
INTRODUCTION

The increasing role of natural gas as a source of energy has pronnpted

recent research into the mechanical and physical properties of nnaterials

related to LNG technology. Considerable effort has been devoted to

characterizing the mechanical behavior of materials for use in LNG storage

and transportation. The basic design considerations for tankage materials are

low temperature strength, fracture toughness, and fatigue properties. Recent

research has concentrated on providing such design data for 5083 aluminum

alloy and the ferritic 5, 6, and 9Ni steels.

The most important characteristic of the low temperature mechanical

behavior of ferritic steels is the ductile-to-brittle transition. The transition

occurs over a narrow temperature interval and is marked by an abrupt change

in the fracture behavior of sharply notched or cracked specimens. At higher

temperatures these materials are ductile and fail by fibrous or dimpled

rupture. At temperatures below the transition regime, failure occurs

predominantly by cleavage, a brittle fracture mode.

To reduce the probability of brittle fracture in service, the structural

applications of ferritic materials are limited to environments where the

service temperatures remain above the ductile to brittle transition temperature.

A mild steel may be brittle at temperatures near the ice point but, for

similarly heat treated steels, the transition can be lowered progressively by

increasing nickel concentration^'

1 P-3
Nine percent nickel steel is a weldable ferritic naaterial which was

1, 3 developed in the 1940's for cryogenic applications , Because it has

relatively high strength and retains toughness down to liquid nitrogen temperatures

(77 K, - 320 °F), it has been used extensively for LNG containment (111 K,

260 °F). Nickel is an expensive alloying element, however, and for economic

reasons it has become desirable to optimize the nickel content of ferritic steels

intended for LNG tankage.

Five and 6 percent nickel steels were recently developed having reduced

nickel concentration while retaining high toughness at 111 K. In these steels

the effect of decreased nickel is compensated by the application of a special

three step hea,t treatment. The heat treatment of 5 percent Ni steel has been

4 termed the austenitized, temperized, and reversion annealed condition . The

2

heat treatment of 6 percent Ni steel has been referred to as the QLT condition .

Such treatments are departures from the double normalized and tempered or

quenched and tempered heat treatments which are applied to 9 percent nickel

steel. The details and benefits of the three step heat treatment are described

4 5 elsewhere '

The high toughness levels achieved with nickel steels have created

difficulties in measuring valid fracture toughness design data. The transition

temperatures are easy to determine by a number of mechanical tests^, including

Charpy impact; but these tests do not provide data on allowable stress levels for

materials in service. Linear eleastic fracture mechanics tests are capable of

providing a useful design parameter, Kj^; but K testing of nickel steels has

2 P-4
not proven very successful because large and impractical specimen sizes are

required for valid test results.

The recently developed J-integral technique is an important tool for

evaluating tough materials such as the nickel steels. The theory of the

7 J-integral was originated by Rice. Subsequent experiments by Begley and

8 10 Landes verified that J can be used as a fracture criterion in cases where

the specimen exhibits elastic, elastic-plastic, or fully plastic load-deflection

behavior

A practical consideration is that the specimen size required for J-integral

testing is not as large as that for linear elastic K testing. A tentative size

I c

criterion for the J-integral test is that^^:

B, b, a > Z5 (J/a^, ) flow

where B is specimen thickness, b is ligament length, a is crack length, and

a„ is the average value of the 0.2 percent offset yield stress and the ultimate

flow

flow stress. B is typically an order of magnitude smaller than the val ue required

for linear elastic behavior as calculated from the size criterion of the ASTM Test

for Plan Strain Fracture Toughness of Metallic Materials (E-399-72):

ys

This paper describes fatigue crack growth rate and fracture toughness tests

on 5, 6, and 9 percent Ni steels. J-integral tests are applied to these materials

and the fracture parameter J is reported over a wide range of temperatures.

J measurements are converted to K values, thus providing useful design

IC iC

data at LNG temperat ures and other te.nperatures of interest.

3 P-5
EXPERIMENTAL PROCEDURES AND APPARATUS

Materials

Five, 6 and 9 percent nickel steels were obtained in the form of 1.25 inch

thick plates. All materials were commerically heat treated. The 5 percent

Ni steel was austenitized , temperized and reversion annealed according to

the ASTM Specification for Pressure Vessels Plates, Five Percent Nickel

Alloy Steel, Specially Heat Treated (A - 645 - 72a). The 9 percent nickel

steel was quenched and tempered according to the ASTM Specification for

Pressure Vessel Plates, Alloy Steel, Quenched and Tempered 8 and 9 Percent

2 Nickel (A 553-72a). The 6%Ni steel was in the QLT condition ; at present,

there is no specification on the heat treatment of this material.

Chemical compositions and mechanical property data are presented

in Tables 1 and 2. All tensile properties referred to in this investigation were

t he average values of two tests performed in accordance with the ASTM Methods

of Tension Testing of Metallic Materials (E 8-69).

All fatigue and fracture experiments were performed on 1.25 inch

(3,17 cm) thick compact tensile specimens having the geometry illustrated in

Figure I. The width of thickness ratio (W/B) was 2.4, and the planar dimensions

were equal to those of a I. 50 inch (3. 81 cm) thick specimen proportioned according

to ASTM E-399-72. The notch was machined parallel to the rolling direction.

P-6 4
producing a TL orientation. Leadline displacement was measured by means

of a modified notch configuration as shown in Figure 1. Roberts' K calibration

was used .

Test Procedures

The majority of tests were conducted at 298 K (70T), 195 K (-108'F),

ill K (-260°F) and 76 K (-3Z0°F). Two fracture tests were performed in liquid

helium at 4 K (-459 °F). The temperature of 76 K was obtained by immersion

in liquid nitrogen; 195 K was obtained by immersion in a mixture of alcohol

and dry ice; and 111 K was obtained by testing in nitrogen vapor. Before testing

s pecimens were allowed between thirty and sixty minutes to reach thermal

equilibrium.

A temperature control system with a chromel- constantan thermocouple

sensor was used to maintain a temperature of 111 K ± 3K. The control thermocouple was located on the specimen at the level of the fatigue crack. Vapor from

a pressurized liquid nitrogen dewar was introduced to the cryostat through a

solenoid valve. The solenoid valve permitted the flow of cold vapor as required

by opening and closing automatically in response to the electrical signal from

a commercial temperature recorder.

Fatigue testing was conducted on a 20, 000 lbs. (100 kN) capacity MTS

servo-hydraulic mechanical test system^'-'. This was a "cryogenic" model

'l-'Tradenames of equipment and materials are used for clarity and to conform

with standard usage in the literature. Their use does not imply recommendation

or endorsement by the National Bureau of Standards, nor does it imply that the

equipment or matsrials are necessarily the best available for the purpose.

P-7

5
with the accaator positioned above the level of the specimen to accomnnodate

the cryostat and to allow access from below for assembling dewars. The

testing machine and associated equipment are illustrated in Figure 2.

A 20, 000 lb. (100 kN) cryostat was used for fatigue tests. The load

carrying frame consists of two tubular stand-off compression members linked

at the lower ends with a maraging steel bridge. Fiberglass reinforced plastic

was used in construction of the stand-off columns to minimize heat conduction.

The lower specimen grip was pinned in place in the center of the bridge, and

the upper grip was threaded to the end of the pull rod. A cylindrical fiberglass

reinforced plastic dewar was used to enclose the load frame, specimen, and

clip gage for cryogenic tests. A similar cryostat was employed in fracture

testing, except that the stand-off columns were stainless stell and load

carrying capacity was 60, 000 lbs. (267 MN).

ASTM type clip gages were used at all testing temperatures.

Commercially available foil resistance strain gage films were bonded to the

clip gage beams using an adhesive suitable for low temperature applications.

The clip gages were calibrated at temperatures from 298 K to 76 K, but

there was not a large change in sensitivity. Clip gage linearity met the

requirements of ASTM E-399-72 over the maximum operating range of up to

0.090 inches (0.229 cm) displacement.

Crack Growth Rate Tests

Fatigue tests were pt-rformed using load control at a frequency of 24 Hz.

The load cycle was sinusoidal at a constant stress ratio (minimum/maximum

load) of 0.1. Dynamic fatigue loads were measured and controlled to within

1-2 percent by means of a digital peak recording device.

P-8

6
The change in crack length during crack growth rate tests was

monitored by compliance measurements. Direct measurement of crack

lengths at the specimen surface was not possible during cryogenic tests.

The compliance technique is based on the fact that for a given load, the

specimen compliance (reciprocal of stiffness) increases with increasing

IZ , 1 3 . crack length. Compliance methods are discussed in detail elsewhere

Experimental crack length- compliance correlations were obtained for

each material and temperature. An X-Y recorder was used to measure the

compliance for a number of specimens of varying crack lengths. Fatigue

striations were generated by load changes during precracking and crack

growth rate tests so that several crack length- compliance measurements

were obtained from each specimen. The data were plotted as a function

of crack length which was measured as an average of three readings at

the center and quarter points of specimen thickness.

Theoretical crack length- compliance curves were calculated from the

generalized solution given by Roberts^^ but these were not in complete agreement

with the experimental correlations. Comparison showed that the calculated

curves consistently under estimated the true crack lengths by 2-4%. The

difference between the calculated and the experimental curves may result

from crack front curvature effects, but it can not be attributed to uncertainty

in calculations since Young's moduli were known to within 1% at all temperatures

from tests on the same stock materials

The procedure for determining crack growth rates involved plotting the

static compliance at intervals during the tests. Using the experimental

crack length - exompliance correlation, crack length could then be obtained.

7 P-9
to within ±1.5 percent. Crack length (a) was plotted versus the total number

(N) of fatigue cycles and the crack growth rate (da/dN) was determined bygraphical differentiation of the a vs . N curve.

It is well known that the rate of crack growth may be retarded by

changing from a higher to a lower stress intensity range. Crack growth

rates may also be influenced by abrupt temperature changes. Whenever these

kinds of changes were made the crack growth rate was allowed to stabilize

before data were accepted as valid. Crack growth data under the new

conditions were ignored until the crack had advanced an increment equal to

15 or greater than the plastic zone size as calculated from Irwin's formula

Fracture Toughness Tests

Fracture tests were conducted using a 60, 000 lb. (267 kN) capacity

hydraulic testing machine. The loading rate was constant, corresponding

-1 -4 -1 to a crosshead displacement of 0.02 in min (8.5 x 10 cm * sec ),

Most specimens were precracked at the temperature of subsequent

fracture testing; the few exceptions are noted in the text. The final crack

length was deep, corresponding to a ratio a/W of between 0. 60 and 0. 62.

Precracking was performed at fatigue loads always less than half of the

specimen limit load and at stress intensities never exceeding a value of

1/2 0.002 in V Young's modulus. was measured according to the method

described in E-399, using the same J-integral test specimens.

For the deeply cracked compact tensile specimens described in this

report, J was calculated from the eq uation''' ^

' ^ ^:

J -'-^ Bb

where A is the area under the load deflection curve to a particular value

P-10
of displacement. The critical value J^^ is the value of J just prior to

crack extension. For specimens which exhibited unstable crack extension

(pop-in), J was calculated usi ng the load at the first pop-in. When crack

J. V> extension took place by stable ductile tearing the J value was obtained by

extrapolation of the J versus crack extension curve.

The extrapolation technique was based on a method outlined by

Landes and Begley^*^, According to the procedure, 3-5 nearly identical

specimens with average crack lengths agreeing to approximately 3 percent

were tested at each temperature. A series of load-deflection curves were

obtained by loading each specimen to a level sufficient to cause decreasing

amounts of crack extension. The specimens were then unloaded and heat

tinted 20 minutes at 538 K (1000 °F) to oxidize the surfaces where crack

extension had taken place. The samples were subsequently pulled apart at

298 K, The average value of Aa was measured and plotted versus the

corresponding value of J.

It was observed in these tests that deformation at the crack tip

preceded material separation. Apparent crack extension therefore included

a contribution due to deformation in addition to actual material separation.

The deformation was visible on the fractured samples as a zone between the

fatigue cracked region and the torn ligament. The material in the stretch

zone had been deformed out of the plane of the fatigue crack surface.

The length of the stretch zone was measured with a traveling microscope. An average value of several measurements from each specimen was

P-1 1

9
plotted as a vertical line on the J vs . graphs. The intersection of

the J vs. Aa curve with the stretch zone line was taken to represent the

initial point of material separation, and J was obtained as the value

of J at the point of intersection.

Landes and Begley^^ recommend construction of the J/2ct-, line

flow

to establish the J resistance curve over the stretch zone interval.

For 9% Ni steel, construction of the Z I Zo line resulted in a flow

triple intersection with the vertical stretch zone line and the J vs . Aa curve.

For the other materials, the J/2ct line intersection point was less

flow

compatible with the data. In some cases, material separation was

observed at values of Aa less than those predicted by the J/2ct intersection

flow

point and it appeared that a J / 3a ^, line would have resulted in better

flow

agreement. The intersection point defined by the vertical stretch zone

line was chosen for consistency. The attempt to measure the extension

of the stretch zone directly is a technique which may not be generally

applicable; it depends on the ease of identifying the stretch zone visually.

When the J versus Aa graphs appeared to be linear, J was

J. determined by a "best" si raight line extrapolation. In other cases a linear

trend was not clearly defined. Scatter in the data was accounted for by

examining a number of reasonable extrapolations and a range of possible

J values were determined.

K values were calculated from the J measurements according

IC IC

8 9- to the relation '

E a/2

10

P-12
where E is Young's modulus and v is Poisson's ratio. Data on the elastic

constants at all temperatures were available from the work of Weston

et al.

RESULTS

Fatigue Crack Growth Rate

Figures 3-5 summarize the fatigue crack growth rate results

17

for all three materials. The data conform to the relation

da/dN = C(AK)"

where da/dN is the change in crack length per cycle, AK is the range of

stress intensity and C and n are empirical constants.

Figure 3 illustrates that the crack growth rate behavior of 5 percent

Ni steel appears to be temperature independent for stress intensity ranges

1/2 -22 1/2 1/2 from 20-25 ksi • in (22 - 27 MNm ' m ). Above AK = ksi • in

-2 1/2

(33 MNm • m ) growth rates at 76 K are definitely higher than at room

temperature or 111 K,

Superimposed on the data of Figure 3 are straight line approximations

18

of the data reported by Bucci, et al, , The straight line approximations

are used for clarity in illustrating data trends, but do not indicate the degree

of scatter in their results. The present results are in good agreement with

the data from this source.

Fatigue crack growth rate data for 6 percent and 9 percent Ni steel

followed the same trend observed for 5 percent Ni steel. As shown in

Figures 4 and 5, the crack growth rat es were somewhat higher at 76 K than

1/2 -2 1/2

at 298 K for stress intensity ranges above 25 ksi • in (27,5 MNm • m ).

P-13

11
Figure 4 shows that the crack growth rate results for 6 percent Ni

steel at 111 K agreed well with room temperature data over the entire range

of AK. The increase in growth rates occurred between 111 and 76 K. This

effect may be related to the fact that 6 percent Ni alloy begins its ductileto-brittle transition near liquid nitrogen temperatures. There is no

published data in the literature with which to compare the present results

for 6 percent Ni steel. ^

18 The results of Bucci, et al. for 9 percent Ni steel are represented

in Figure 5. The present results reveal a somewhat higher growth rate at

76 K, but the general agreement is good.

The fatigue crack growth rate behavior of 5, 6, and 9 percent Ni

steels appears to be similar. If all data from this report are superimposed

on a single graph, it appears that the fatigue crack growth rates of the

three materials are nearly equivalent for AK values ranging from 20 - 60 ksi

1/2 -2 1/2

in (22 - 66 Nm • m ),

Fracture Toughness

Representative load-deflection curves for 5 percent Ni steel are

illustrated in Figure 6. The arrows terminating the curves at 298 K and

195 K indicate that ductile tearing continued to larger deflections without

the occurrence of pop-in. At 111 K an appreciable amount of plastic

deformation occurred, followed by a single pop-in. Multiple pop-ins

occurred at temperatures below 111 K where linear elastic behavior was

approached. At 76 K, the load continued to increase significantly after the

first pop-in. The deviation from linearity at the upper end of the 4 K loaddefection curve was due to a series of faint but audible pop-ins.

P-14

12
The load-deflection cuves for 6 percent and 9 percent Ni steels are

illustrated in Figures 7 and 8. In connparison, it is significant to note that

pop-in did not occur in tests of 6 percent Ni at 111 K.

The fracture surfaces of 6 percent and 9 percent Ni steel specimens

exhibited 40 - 50 percent slant fracture at 298 K. Shear lips took the form

of hugh cusps rising 0.4 inch (1 cm) above the plane of the fatigue crack.

There was also a large lateral contraction in the thickness direction,

amounting to 12 percent. As temperature decreased to 76 K, the proportion

of slant fracture descreased to about 15 percent, and the percentage of

lateral contraction decreased to approximately 5 percent.

For 5 percent Ni steel, a lateral contraction of 18 percent was

measured at room temperature, but the fracture surface was relatively flat

compared to the other materials. The proporticn of slant fracture decreased

from about 25 percent at room temperature to zero at 5 K. At 4 K the

fracture surface exhibited reflective cleavage facets.

For 6 percent and 9 percent Ni steels the degree of cia ck front

curvature bordered on, but did not exceed, the limits established for fatigue

crack uniformity (ASTM E-399-72). In the case of 5 percent Ni steel

crack front straightness requirements were occasionally violated when the

crack length at the specimen edge was found to be less than 90 percent of

the average crack length. The difference in edge cia ck and average cia ck

lengths ranged from 87-88 percent for the four specimens which did not

meet this requirement. The degree of crack front curvature appears to

depend on loading history. Crack growth rate specimens tested at higher

stress intensities had less curvature; the specimens with excessive curvature

P-15

13
were those used in low temperature fracture tests where the maximum

stress intensities (K^) were lowered to comply with the ^ .

criterion of ASTM E-399-72.

Graphs of J versus ar e shown in Figures 9-11. Tabulations

of the data used in determining the parameters J and K„ are

^ ^ IC IC Q

presented in Tables 3-8, and Table 9 presents an evaluation of the size

criteria for valid testing.

The results are summarized in Figure 12, which illustrates the

temperature dependence of the parameters and Kj^. For all three

materials, increased with decreasing temperature over the interval

298 K - 76 K. At these temperat ures does not represent a valid

fracture parameter for 1, 25 inch thick specimens - the ASTM E-399-72

thickness requirement is not satisfied. The K_ values measured under

Q

non-linear elastic conditions have no practical significance and are

included merely for comparison. Over the interval 298-76 K, it was

obs erved that:

1. The disagreement between and values was largest

at ambient temperatures;

2. The effect of temperature on was oppoa te to the general

trend displayed by K values; and

IC

3. The values did not provide an indication of the relative

toughness of the materials. For example, 9 percent Ni steel exhibited the

highest values but not the highest values.

14

P-16
Only in tests of 5 percent Ni steel at 76 K and 4 K did the Kq

values agree with the K values converted from J-integral measurements.

I

Nevertheless, these K values did not qualify as valid K according to Q ^ / IC ^ ASTM E-299-7Z, This point is amplified in the discussion.

1/2 For 5 percent Ni steel, K values decreased frcjm 200 ksi • in

-2 1/2 1/2 -2

(220 MNm • m ) at room temperature to 50 ksi" in (55 iMNm

1/2

rn ) at 4 K . The datum point at 195 K was determined by extrapolation

of only two fracture tests and should not be heavily weighted. The fracture

toughness remained nearly equivalent to that of 9 percent Ni steel at

temperatures as low as 111 K. Below 111 K the K values decreased

abruptly.

The 9 percent Ni steel was tested at 298 K and 76 K. K

decreased from 210 ksi • in^''^ (230 MNm'^ * m^'^^) at 298 K to 167 ksi •

in^*^^ (184 MNm ^ " m^'^^) at 76 K, a reduction of 15 percent. A more

drastic reduction in toughness over this temperature interval was not

expected, Charpy impact data from the mill analysis of this material

indicate that the ductile -to-brittle transition is just beginning at 76 K.

Additional testing at temperatures lower than 76 K vro uld be necessary

to define the ductile -to -brittle transition temperature regime in terms

o f K values . IC

The fracture toughness of the 6 percent Ni alloy exceeded that of

the other materials tested. K values indicated that the upper shelf

J. V-> 1/2 , -2

toughness tended to increase from about 240 ksi • in (2 63 MNm

m^^^) to 268 ksi ' in'''^^ (294 MNm"^ ' m^^^) over the interval 298 - 111 K.

However, a rather sharp drop in the data occurs between HI and 76 K,

15

P-17
indicating the beginning of the ductile-to-brittle transition. The value

1/2 -2 1/2

of K declined to 195 ksi • in (214 MNm • m ), slightly higher

J. than the value obtained for 9 percent Ni steel.

It was observed in a few tests on 6 percent Ni steel that a small

amount of stable crack extension preceded pop-in at 76 K. For testing

convenience, this effect was neglected and J values were calculated

IC

at the point of pop-in. A rigorously determined J measurement

would be slightly lower than the value calculated at pop-in; but the

error introduced in determinations was estimated to be less than

5 percent which is less than the degree of scatter observed in replicate

tests. It is probable that some amount of stable crack extension preceded

pop-in tests of 5 percent Ni steel at 111 K, but observations were

inconclusive.

DISCUSSION

19-23 Previous authors have not reported valid data for 5,

6, or 9 percent nickel base metal steels. The J-integral test procedures

used in this investigation appeared to provide valid K data. Several

I

factors must be considered in assessing the validity of the present results

The J-integral test results indicated ambient temperature K

values as high as 200-240 ksi • in^^^ (220-263 MNm"^ * m^^^). These

values are quite reasonable. The size criterion was satisfied at all

temperatures. Confidence in the data stems from the fact that thifc

8 10

size criterion was established from tests on steels equivalent in

-2

fracture toughness (,T^^ 1000-2000 in- lb • in or 0.175 - 0.350 MJ •

-2 m ) to the nickel steels tested in this report.

P-18

16
Serious problems regarding test validity arose only in tests of 5 percent

Ni steel at 76 K and 4 K. At 4 K the linear elastic size criterion was satisfied

but precracking stress intensities could not be lowered successfully to comply

with the criterion that < . 6 . At 4 K the K was relatively low and crack

f Q U

^

f ront curvature increased significantly at the lower fatigue stress intensities.

To keep the crack front curvature within reasonable limits, one specimen was

precracked at 298 K (K^ ^ 0. 6 ^q) a second specimen was precracked at

76 K (K^ ^ . 75 Kq). The first specimen satisfied crack front curvature requirements but was 10 ksi • in^^^ higher than the specimen precracked at 76 K.

It is probable that precracking at 298 K introduced disparities in plastic zone

size and crack sharpness. The specimen precracked at 76 K fell 2 percent short

of the requirement that the edge crack length be 90% or more of the average crack

1/2

length. For this specimen, the measured value of 50 ksi • in is probably

closer to the true value of fracture toughness; however, neither of the tests at

4 K can be considered valid.

For 5 percent Ni steel at 76 K, the ASTM Method E-399-72 requires a

specimen thickness of 1. 5 - 1.6 inches 4 cm). In two tests at 76 K, was

maintained < 0. 6 but the edge crack lengths were 87-88 percent of the average

crack lengths; 90 percent or more is required. Therefore the data are invalid

according to a strict interpretation of ASTM E-399-82. On the other hand, the

size criterion for J-integral testing is amply satisfied. The magnitude of the

effect of a minor transgression in crack front curvature is not known, but it

appears that there could be only a small error in the data for 5 pf;rcent Ni steel

at 76 K.

17

P-19
Agreement of values with values converted from J^^

measurements implies that the linear elastic fracture mechanics test is valid

from the standpoint of size considerations. J-integral results can then be

used to evaluate the linear elastic thickness requirement. For 5 percent Ni

steel at 76 K, the mean value of K was 87 ksi ' in^''^ (95 MNm ^ • m^^^)

1 -2

and the 0. 2 percent offset yield strength was ~ 110 ksi (76 Nm ). These

data suggest that the ASTM size criterion factor of 2 . 5 is slightly conservative

in the case of 5 percent Ni steel. The factor could be reduced to 2. 0, since a

calculation shows that:

B = 1.25 inch- 2.0 (—^)

'^ys 76 K

The 6 percent Ni steel contained low levels of sulfur and phosphorous,

a relatively high percentage of manganese, and some chrome (Table 1). Sulfur

and phosphorous are tramp elements, usually deleterious in their effects on

mechanical properties, whereas manganese is beneficial with respect to

2 microstructural refinement . Thus, compositional variations may account for

the somewhat higher fracture toughness observed for 6 percent Ni steel.

The present results confirm that 5 percent and 6 percent Ni steels are

promising materials for potential use in LNG tankage applications. At ill K,

the fracture properties of these newly developed steels are comparable to

those of 9 percent Ni steel. Further evaluation is needed to determine the

properties of weldments and their heat affected zones (HAZ). It is probable

that the fracture toughness of these materials will be lowered somewhat by the

deleterious effects of heat inputs from welding. Therefore, the ultimate

18

P-20
suitability of 5 percent and 6 percent Ni steels must be determined byfracture toughness comparisons of both the base metals, the weld, and the

HAZ.

SUMMARY

1. The fatigue crack growth rates of 5, 6, and 9 percent Ni steels were

nearly equivalent at AK from 20-60 ksi • in^'^^ (22-66 MNm ^ • m^*^^).

1/2 -2

2. AtAK>25ksi* in (27.6 MNm ) the fatigue crack growth rates

of 5 and 6 Ni steels were higher at 76 K than at 111 K or 298 K.

3. The J- integral test procedures used in this investigation appeared

to yield valid K data for the 5, 6, and 9 Ni steels.

4. For 9 Ni steel there was only a small decrease in fracture toughness

over the interval 298 - 76 K; the fracture toughness of 5 and 6 Ni steels decreas

abruptly over the interval 111 - 76 K.

5. At 111 K, the fracture toughness of these materials ranged from

160 ksi • in^^^ to 270 ksi in^'^^ (180 - 300 MNm"^ • m^^^).

ACKNOW r.E DOME NTS

The authors would like to thank Steve Keefer who assisted in data

reduction.

P-21

19
REFERENCES

1. Anonymoas, Final Results from Operation Cryogenics , International

Nickel, CBI, and US Steel Corp. (1961), p. 10.

2. Nagashima, S. , Ooka, T. , Sekino, S. , Mimura, H. , Fujishima, T. ,

Yano, S. , and Sakurai, H. , Trans. Iron and Steel Institute of Japan

n., (1971) p. 402.

3. Yeo, R. B. G. , and Miller, O. O. , "A History of Nickel Steels, "

Presented at the Sorby Centennial Symposium on History of Metallurgy,

Cleveland, Ohio (1963).

4. Sarno, D. A. , Havens, F. E. , and Bowley, D. L. , ASM Technical

Report No. C70-39-2 ASM (1970).

5. Yano, S. , Sakurai, H. , Mimura, H. , Wakita, N. , Ozawa, T. , and

Aoki, K. , Trans. Iron and Steel Institute of Japan 13 (1973) p. 133.

6. Wessel, E. I. , Clark, W. G, , and Wilson, W. K. , Westinghouse

Res. Labs. , Final Tech. Report Contract No. DA-30-069-AMC 602 (T)

(June 1966).

7. Rice, J. R. , J. Appl. Mechs. 35_(1968)p. 379.

8. Begley, J. A. , and Landes, J. D. , Fracture Toughness , Proc. of

the 1971 Nat. Symposium on Fracture Mechs. , Part II ASTM STP 514

(1972) p. 1-20.

9. Landes, J. D. , and Begley, J. A. , Fracture Toughness , Proc. of

the 1971 Nat. Symposium on Fracture Mechs. , Part II ASTM STP 514

(1972) p. 24-39.

P-22
10. Landes, J. D. , and Begley, J. A. , "Test Results from J-Integral

Studies — An Attempt to Establish a J Testing Procedure,"

Private Communication from J, A. Begley to R. P. Reed, Cryogenics

Division, NBS, Boulder, CO (1973).

11. Roberts, E. , Jr., Mat. Res. Standards 9 (1969) p- 27.

12. Bubsey, R. T. , Fischer, D. M. , Jones, M. H. , and Srawley, J. E. ,

"Compliance Measurements" Experimental Techniques in Fracture

Mechanics , (A. S. Kobayashi, Editor) Society Experimental Stress

Analysis and Iowa State Univ. Press (1973) p. 76-93.

13. Brown, W. F. , and Srawley, J. E. , Plane Strain Crack Toughness

Testing of High Strength Metallic Materials , ASTM STP 410 (1966).

14. Weston, W. F. , Naimon, E. R. , and Ledbetter, H. M. , Properties

of Materials for LNG Tankage , ASTM STP (1974).

15. Irwin, G. R. , "Fracture" Handbuch der Physik 6 (1958) p. 551-590.

16. Rice, J. R. , Paris, P. C. , and Merkle, J. G. , Progress in Flaw

Growth and Fracture Toughness Testing , ASTM STP 536 (1973) p. 231.

17. Paris, P. C. , and Erdogan, F. , Jnl. Basic Engrg. , Trans. ASME

Series D 85 (1963) p. 528.

18. Bucci, R. J. , Greene, B. N. , and Paris, P. C. , Progress in Flaw

Growth and Fracture Toughness Testing , ASTM STP 536 (1973)

p. 206-228.

p-23

21
19. Sarno, D. A. , Bruner, J. P. , and Kamps chafer, G. E. , Fracture

Toughness of Armco Cryonic 5 Steel Weldments , presented at the

Welding Institute International Conference "Welding Low Temperature

Containment Plant" London, England, Nov. 20-22, 1973,

20. Sarno, D. A. , McCabe, D. E. , Sr. , and Heberling, T. G. , Jnl.

Engrg. Industry 95 , No. 4 (1973) p. 1069-75.

21. Tenge, P. , and Solli, O. , Norwegian Maritime Res . ]_, No. 2

(1973) p. 1-18.

22. Vishnevsky, C. , and Steigerwald, E. A. , Fracture Toughness

Testing at Cryogenic Temperatures , ASTM STP 496 (1971) p. 3-26.

23. Lehigh University, Dept. of Metallurgy and Materials Science, The

Static and Dynamic Fracture Toughness of 5% and 9% Nickel Steels ,

Quarterly Report Nos. 1-7, University Research Projects Task Group,

Pressure Vessel Steels Subcommittee, Materials Division, Pressure

Vessel Research Committee (1973).

P-24

22
Table 1. Chemical Composition

Alloy Mill Analyses (wt. pet. ) Fe C Mn PS Si Ni Cr Mo Al N

Fe-5Ni Bal 0.13 0.45 0.025 0.025 0.275 5.00 - 0.275 0.085 0.020

Fe-6Ni Bal 0.06 1.12 0.005 0.004 0.24 5.66 0,63 0.18

Fe-9Ni Bal 0.06 0.56 0.007 0.003 0. 27 9. 25 -

Table 2. Mechanical Properties

0. 2% Offset Tensile Elongation Reduction Hardness C (longitudinal)

Yield Strength Strength of Area

(ksi) (ksi) (%) (%) (RcJ 76 K (ft - lbs)

Fe-5% Ni 77.5 97.9 34 79 20 38

Fe-6% Ni 82.0 106.6 30 81 23 166

Fe-9% Ni 99.9 109-1 27 78 25 130

NOTE: 1 ksi = 0. 689 Nm

2 3 P-25
Temp

(K)

Spec aW

Q

(lb) (ksi Jin)

298

298

298

298

195

195

195

111

111

111

76

76

4

4

Notes:

16

3

11

A

21^

23'

24

29

32

25

27

t 28

26

tt

0. 597

0. 60

0. 60

0. 597

0. 607

0. 611

0. 617

0. 621

0. 654

0. 623

0. 599

0. 612

0. 624

0. 606

10, 200

9, 150

9, 900

14, 100

Avg

13, 100

11, 450

13, 400

Avg

13, 400

11, 700

17, 200

Avg

12, 950

13, 200

Avg

8, 550

7, 950

Avg

1 lb = 4. 448 N

A 7

1 ksi Jin = 1. 098 X 10 Nm' Jm

B = 1. 228 in (3. 119 cm) + 0. 5%,

W = 3. 034 in (7. 706 cm) ± 0. 9%

t precracked at 298 K

tt precraclced at 76 K

24

62

56. 4

60. 8

86. 8

66. 5

83. 7

74. 4

89. 5

82. 5

90. 7

92. 7

117

100

82. 0

86. 1

84. 0

60. 1

50. 2

55. 2

P-26
Table 4. J-Integral and Converted K of Fe -5% Ni

Temp

(K)

Spec b

(in)

J

( 2

\ 1 n

Aa

V ave

j

(in)

Stretch

Zone

A .3in-lb\

r )

^IC

(ksi ^in)

298 16 1. 240 3. 42 VJ , U V/ TT

298 3 1. 214 2.47 n 0?? n 006

298 11 1. 216 1. 76 0. oil 0. 003

298 A 1. 204 U 34 n 004

- 0. 004 1. 27 ± 0.19 200 ± 15

195

+

1. 191 4, 16 0. 046 0. 005

195 lo 179 2. 58 n n 04 ^vg - 0. 0045 1. 41 210

111 24 1. 146 n/a N / A N / A 1. 05 L85

111 29 1. 053 1

1

1. 09 189

111 32 1. 145 1

11

A \Tcr —

0. 774

0. 972

159

178

76 25 1. 217 1

11

0. 178 76. 5

76 27 1. 180 1

1

Avg =

0. 287

0. 232

97. 1

86. 8

4 28^ 1. 138 1

•t 1 1

0. 102 58

4 1. 193 1

1! 1

Avg =

0.074

0. 088

49. 4

53. 7

Notes: 1 in = 2. 54 cm

in-lb

in

2 -2

1. 75 X 10 Jm

1 ksi Tin = 1. 098 X lO^Nm'^Tni

t precracked at 298 K

tt precracked at 76 K

25 P-27
Temp

(K)

Spec aW

(lb) si a/it

7 0V ft \J X1 4TT 12 snn 0 J

1

J. 0 ('i 1 7 12 Q5n ft7

7 O

c; CiWe AU X1 Q7

1 ^ 700 Q27 ^

trf /O 3 0 fi2 0 1 ^1 ^00 XXX 1 1 1

*-» 7 t> 2 0 ^1 1 s 1411-, QSO 7 J u 1 00

? Q8 n A

U , U X 12 n ft4

\ Ave = Q3

1 7:? 11 ^0 0 An? 14. ? 1=, f) ftQ 0 7

1 7 J 1 7 V_/ , L> *-/ J 1 3 "^nn ft3

X16u 0 S Q 1 14 500 0 VJ

X 7 J 1-1 Q7 DVJ , JSQ?7 1-. 14 5 00 0 w

Ave i i V = g 86

1 1 1 2 n 0 . AV X1 4t 17 2^0 X1 X1 4

1 1 1 2 T C# X 0 A 1 A X1 1X 71

1XXX1 1 22 0 A 1 4 X1 R0 , 3-J 00w U 1X 2^ 0w

111 X 12 0 A 1 ^ 1 A 7^

1X X1 J^

Avp = 1X 1X Au

1 0 1 2 0 AO? 2 0 3 00 1 28

1 0

1 1 X X 0 A 07 1ft "^00 X1 1X R

1 0

Q0 0 A 1 7 X1 Q A 0 7 , U -J w 1 30

1 0 X1 nu 0 A 1 7 2 1 OR 0 X1 3fi -J u AVP = X1 27£J 1

Notes: 1 lb = 4. 448 N

X In. 0 X fJin= 1. 098 Y^\ 1XV/0^ XNmN I i 1

I j_> — 1. 250 in (3. X/O 1 7R f-m\ —f 0u. 4%

w = 3. 046 in (7 . 737 cm) ± 0 .6%.

26 P-28
Table 6. J-Integral and Converted K of Fe-6% Ni

Temp

(K)

Spec b

(in)

J Aa ave

(in)

Stretch

Zone

(in)

298 7 1. 159 6. 14 0. 052 0. 006

298 1 1. 167 4. 57 0. 033 0. 008

298 5 1. 159 2. 07 0. 008 0. 005

298 15 1. 174 2. 58 0. 013 0. 005

Avg = 0. 006

195 18 1. 208 2. 90 0. 015 0. 006

195 17 1. 205 6. 99 0. 061 0. 007

195 16 1. 247 5. 18 0„ 034 0. 007

195 19 1. 243 4. 12 0. 028 0. 006

Avg =

0. 006

111 20 1. 172 5. 86 0. 040 0. 004

111 21 1. 168 4. 54 0. 030 0. 005

111 22 1. 176 2. 74 0. on 0. 005

111 23 1. 177 3. 65 0. 018 0. 006

Avg - 0. 005

76 12 1. 194 N/A N/A

76 11 1. 195 1

1

76 8 1, 165 1

1

76 10 1. 180 1

1

^IC ^IC

(, ^3 in-lb\ . -—

10 —\ (ksi ^)

Notes: 1 in = 2. 54 cm

, in-lb , „ 2-2 1 Y~

= 1. 75 X 10 Jm

in

1 ksi ^= 1. 098 X 10 Nm"^

^

27

1. 75 ± 0. 14 236 ± 9

2. 25 ± 0. 15 272 ± 9

2. 15 ± 0. 13 268 ± 9

1. 30 208

1. 30 208

0. 944 177

1. 14 195

Avg ^ 1.17 197

p-29
Table 7. of Fe-9% Ni

Temp Spec _a_ P K

K (lb) (ksivln)

6 0. 594 19, 200 116

9 0. 606 19, 200 121

12 0. 601 18, 900 117

4 0. 599 19, 050 116

18 0. 617 17, 400 114

Avg = 117

19 0. 615 21 , 150 137

20 0. 609 22, 700 142

21 0. 614 22, 250 144

Avg = 141

Notes: 1 lb = 4. 448 N

6 -2 , 1 ksiVin ^ 1 . 098 X 10 Nm v m

=^ B = 1 . 25 3 in ( 3. 182 cm) ±.2%,

W = 3.036 in (7.711 cm) ± .5%.

P-30

28
Table 8. J - Integral and Converted K of Fe-9% Ni

Temp

(K)

Spec

(in)

J ave

(in)

Stretch

Zone

(in)

10

IC

3 in-lb

fksi Vin)

298

298

298

298

298

76

76

76

6

9

12

4

18

19

20

21

1 .236

1.20

1.213

1.219

1. 168

1. 159

1. 185

1. 172

2. 70

4. 02

4. 92

6. 80

1.22

n/a

0. 021

0. 028

0. 044

0. 054

Avg = N/A

0. 007

0. 007

0. 006

0. 007

0. 007

0. 007

N/A

1. 14 ± 23

0. 810

0. 935

0. 846

210 ± 3

162

174

165

Av£ 0. 864 167

1 in = 2.54 cm

, in-lb , , ^2 m - N ^ -2

1 . 75 X 10 7— Jm m

1 ksi Vin = 1. 098 X 10^

^

Vm Nm'^^m

m*-

P-31

29
Table 9. Dimensional Criteria for Valid K and J

X C I c

Alloy Temp B ..,(^) .4^ .,c^) .•(^^)

ys ys . flow flow

(K) (in) (in) (in) (in) (in) (in) (in)

Fe-5% Ni 298 1 . 80 1.23 1 . 22 1 . 84 16. 1 0. 36 0. 72

195 K85 1.23 1. 18 3. 3 20. 9 0. 36 0. 72

111 1.92 1, 23 1 . 12 2.4 9. 1 0. 20 0. 40

76 1,81 1.23 1 . 20 1.47 1. 60 0. 04 0. 08

4 1 . 84 1. 22 1. 19 0.25 0. 25 0. 01 0. 02

Fe-6% Ni 298 1. 88 1.25 1.16 3.2 20. 7 0. 46 0. 93

195 1 . 82 1.25 1.23 2.5 24. 9 0. 53 1. 07

111 1 . 86 1.25 1.17 2. 6 14.1 0. 40 0. 81

76 1.86 1.25 1. 18 2. 6 6. 2 0. 20 0. 40

Fe-9% Ni 298 1.83 1.22 1.21 3. 3 • 10. 8 0. 27 0. 54

76 1. 85 1.25 1.17 2.5 3. 5 0. 14 0. 29

K value obtained from J-integral results

P-32

30
P-33

31
Figure 2 Cryogenic Fatigue Testing ApparatusP-34
STRESS INTENSITY FACTOR RANGE, AK (N/m^/m )

10^ 10^ 10^

I

1 1 1—

I—I I I I

I

r

1 1—I I I I M

I

Figure 3. Fatigue Crack Growth Rate of Fe-5 Ni

P-35

33
10'

"u -4

>> 10

c

to a

zo

<

CL£

10-^

o

CD

!5

10

STRESS INTENSITY FACTOR RANGE, AK (N/m^/F )

^8 10' T 1 1

1

1 I I I I I r

10"

I I

• '"I

-

1 1 1 1 1 I 1 1

1

I 1

1 j

1 1 1 1

-

— •

- • o

— f

• 00

- • o

• o

- •1 o

6%\J fO Ni111 STEEL

- O 298 K 111 K • 76 K

• A

A A

• ^A

• d»A

\*

o •

1 • r 1 1 1 i 1 1 1

1 1

1 1 1

1 1 1

- 10

-3

10

10

-5

10 50 100 500

STRESS INTENSITY FACTOR RANGE, AK (ksi/Tn)

1000

Figure 4, Fatigue Crack Growth Rate of Fe-6 Ni

P-36

34
STRESS INTENSITY FACTOR RANGE, AK (N/mVnT)

10

5

u^ 10^

10

-5

10

10

8

1—I I I I T

1

1 I

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NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

, NBSIR 74-373

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 Jan 1 - Tune 30 1 Q74

6. Performing Organization Code

7. AUTHOR(S)

D. B, Mann (ii^aitor)

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. 2750401

n. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as Item 9.

13. Type of Report & Period Covered

Progress Report

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.) Seventeen cost centers supported by seven 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 $500,000. This integrated progress report to be

issued in January and July is designed to:

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

the activities of their individual programs.

2) Inform all sponsoring agencies on related research being conducted at

the Cryogenics Division of NBS-IBS,

3) Provide a uniform reporting procedure which should maintain and improve communication while minimizing the time, effort and paper work

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 un - published; 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 |

' Unlimited

1 X' For Official Distribution. Do Not Release to NTIS

1

' Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402. SD Cat. No. C13

1

! Order FrdrrTNational Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

21. NO. OF PAGES

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

22. Price

USCOMM-DC 29042-P74