NBSIR 73-300

Survey of Current Information on LNG and

Methane, the Thermophysicai Properties

of Methane, and Metrology

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

February 1973

Third Annual Progress Report

prepared for

The American Gas Association, Inc.

and the

Pipeline Research Committee (AGA)
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards^ was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and

technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measure- ment system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Center for Computer Sciences and

Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consistent system of physical measurement; coordinates

that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of a Center for Radiation Research, an Office of Measurement Services and the following divisions: Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics —

Linac Radiation - — Nuclear Radiation - — Applied Radiation '- — Quantum

Electronics — Electromagnetics ' — Time and Frequency ' — Laboratory

Astrophysics — Cryogenics

THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research lead- ing to improved methods of measurement, standards, and data on the properties of

well-characterized materials needed by industry, commerce, educational institutions, and Government; provides advisory and research services to other Government agencies;

and develops, produces, and distributes standard reference materials. The Institute consists of the Office of Standard Reference Materials and the following divisions: Analytical Chemistry—Polymers—Metallurgy—Inorganic Materials—Reactor

Radiation—Physical Chemistry.

THE INSTITUTE FOR APPLIED TECHNOLOGY provides technical services to pro- mote the use of available technology and to facilitate technological innovation in industry and Government; cooperates with public and private organizations leading to the development of technological standards (including mandatory safety standards), codes and methods of test; and provides technical advice and services to Government agencies

upon request. The Institute also monitors NBS engineering standards activities and

provides liaison between NBS and national and international engineering standards

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divisions and offices: Engineering and Product Standards—Weights and Measures—Invention and

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THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts re- search and provides technical services designed to aid Government agencies in improving cost effectiveness in the conduct of their programs through the selection, acquisition,

and effective utilization of automatic data processing equipment; and serves as the principal focus within the executive branch for the development of Federal standards for automatic data processing equipment, techniques, and computer languages. The Center

consists of the following offices and divisions: Information Processing Standards—Computer Information—Computer Services —Systems Development—Information Processing Technology.

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and accessibility of scientific information generated within NBS and other agencies of

the Federal Government; promotes the development of the National Standard Reference Data System and a system of information analysis centers dealing with the broader

aspects of the National Measurement System; provides appropriate services to ensure

that the NBS staff has optimum accessibility to the scientific information of the world,

and directs the public information activities of the Bureau. The Office consists of the following organizational units: Office of Standard Reference Data—Office of Technical Information and

Publications—Library—Office of International Relations.

1 Headquarters and Laboratories at Gaithersburg, Marj'land, unless otherwise noted ; mailing address Washington, D.C. 20234. Part of the Center for Radiation Research.

^ Located at Boulder, Colorado 80.302.

» Fart of the Center for Building Technolog.v.
NBSIR 73-300

SURVEY OF CURRENT INFORMATION ON LNG AND METHANE,

THE THERMOPHYSICAL PROPERTIES OF METHANE,

AND METROLOGY

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

February 1973

Third Annual Progress Report

prepared for

The American Gas Association, Inc.

and the

Pipeline Research Committee (AGA)

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

NATIONAL BUREAU OF STANDARDS, Richard W, Roberts, Director

CONTENTS

Page

PART 1. SURVEY OF CURRENT INFORMATION ON LNG

AND METHANE . 2

PART 2. THE THERMOPHYSICAL PROPERTIES OF METHANE 6

PART 3. METROLOGY l6

Appendix A. Densities of Compressed Liquid Methane and the

Equation of State A-1

Appendix B. Orthobaric Densities of Methane Near the Critical

Point . . . , B -

1

Appendix C. Dielectric Constants and Orthobaric Densities of

Methane C-1

Appendix D. Thermophy sical P ropertie s of Methane D-1

Appendix E. The rmophy sical Properties of Methane . . . . . E-1

Appendix F. Non-analytic Equation of State for Methane,

Constrained to the Vapor-Liquid P-P-T Boundary . . F-1

Appendix G. The Specific Heats, Cg^-p and Cy, of Compressed

and Liquefied Methane G-1

iii
ABSTRACT

This report suramarizes the third year of progress on a liquefied natural gas program supported by the Araerican Gas Association, Incorporated, The report is in three parts and reflects the areas

of interest defined by the sponsor. Part 1 sumraarizes the work done

by the Cryogenic Data Center in acquiring and disseminating published

information on liquefied natural gas. Part 2 summarizes the work done

by the Properties of Cryogenic Fluids Section on the experimental

determination of the thermophysical properties of compressed fluid

methane. Part 3 summarizes the work done by the Cryogenic Metrology

Section on liquid level and flow rate metrology on liquefied natural gas.

Key words: Densities; equation of state; flow mete ring; liquefied natural

gas; liquid level; methane; metrology; specific heats; stratification,

thermophysical properties.

i V
PART 1
SURVEY OF CURRENT INFORMATION ON LNG AND METHANE

by

Neil A. Olien

We have now completed three years of publication of the

Liquefied Natural Gas Quarterly Survey (the twelfth issue, No. 72-4,

is at the printer). During that period we have listed a total of 1967

references, papers, reports and patents in the field of liquefied natural

gas. Each of these references, when it appears on a given quarterly

issue, is listed under one or more of the 23 subject headings which have

been designed to separate the LNG field into manageable subsets. The

printing and distribution of the LNG quarterly is currently being handled

by the National Technical Information Service (NTIS) in Springfield,

Virginia. We prepare the camera-ready copy during the first week after

the close of a quarter and send it to NTIS; where about one month is re- quired for printing and distribution. Complimentary copies (all approved

first by AGA Headquarters) are currently being distributed to AGA

member firms. We also send ten copies of each issue to AGA Headquarters. There are, in addition, 101 paid subscriptions to the

quarterly.

The LNG Quarterly is prepared through the use of the CryDgenic Data

Center's automated Information Storage and Retrieval System, Approximately 8000 references are added to this system each year covering all

of cryogenics. The total number of references currently in the system

stands at over 80,000. Each quarter LNG references are selected from

the system and provide the bulk of the references for each issue. The

new references, in turn, are found by a review of over 300 primary

journals and 26 secondary or abstracting publications. We try to cover

2
the entire field including published articles, government and industrial

reports and United States Patents. We also publish a weekly Current

Awareness Service which covers the entire field of cryogenics. Each

weekly issue contains 100-200 new references. In the past six weeks we

have added a new heading to the subject index accompanying each issue.

This heading is 'Energy' and is designed to give our readers notice of

new developments in the application of cryogenic technology to the solution of our energy crisis. This includes electrical generation (superconductivity), transmission and other applications as well as items of

interest to the Natural Gas Industry. AGA Headquarter s receives

complimentary subscriptions and about 25 AGA affiliates subscribe as well

.

For the past three years we have updated, on an annual basis,

three comprehensive bibliographies covering the LNG/methane field.

We have again updated these and they are in the process of being reproduced. On completion, two copies of each will be sent to AGA

Headquarters and additional copies will be made available as follows:

B-963 THE THERMOPHYSICAL PROPERTIES OF METHANE

AND DEUTERO-METHANES IN THE SOLID, LIQUID

AND GASEOUS PHASES. 341 pages, indexed

by property, phase and author (Jan 1973). $25.00

B-964 THE THERMOPHYSICAL PROPERTIES OF METHANE

MIXTURES. 228 pages, indexed by property,

system and author (Jan 1973). $20.00

B-965 PROCESSES AND EQUIPMENT INVOLVING

LIQUEFIED NATURAL GAS (LNG) AND METHANE.

308 pages, indexed by subject and author

(Jan 1973), $25. 00

3
Orders for the above bibliographies should be sent to:

National Bureau of Standards, Cryogenic Data Center, Boulder,

Colorado 80302. Checks should be raade payable to: NBS- Department

of Comme rce

4
PART 2

I

II:

5
THE THERMOPHYSICAL PROPERTIES OF METHANE

by

R, D, Goodwin, B. A. Younglove, and G. C. Straty

, 1. Introduction

Accurate, comprehensive the rmophy sical properties data on

liquefied natural gas mixtures are needed to design liquefaction, storage

and transportation equipment and processes. The compositions of

liquefied natural gas mixtures are so variable that it is impossible to

obtain sufficiently comprehensive experimental data on all typical mixtures for these applications. Instead, thermophy sical properties data

for the mixtures must be calculated from the properties of the pure

components and the most important binary mixtures. For example, the

density, p = 1/V, and enthalpy, H, of a liquefied gas mixture may be

calculated from

. =X ^- + P, X.) Mixture *-r^ i i i 1

and

^AA- . "X) ^- H° + H^ (T, P, X.) Mixture *^ i i i i

o o where and H^ are the molar volumes and enthalpies of the pure comF TT ponents, and V and H-^ are the excess volume and excess enthalpy of

the mixture. For liquefied natural gas mixtures, the excess volume and

excess enthalpy are usually small percentages of the totals. Therefore,

the most important ingredients in the calculations are accurate thermophysical properties data for the major pure components, methane,

ethane, propane, etc.

6
The objective of our current work is to produce accurate

tables, interpolation functions, computer programs, etc, for the

densities, compressibilities, and thermodynamic properties of pure

gaseous and liquid methane.

lated them for use in thermal property computations. We noted

extensive gaps in the necessary data. By the end of 1971 we had completed most of our experimental PVT measurements. We then provided

AGA with tables of provisional values for the thermodynamic functions

of methane (NBS Report 10 715).

precision specific heat measurements on gaseous and liquid methane,

and to complete the mathematical formulations of density and compressibility data necessary for calculating accurate thermodynamic properties

data. All reports and publications completed for this project to date are

listed at the end of the present report. All reports and publications

completed during 1972 are reproduced in Appendices A through G.

completion of extensive high precision (0,5%) specific heat measurements

on compressed gaseous and liquid methane. Wide range, high precision

specific heat measurements are required to calculate accurate thermodynamic properties data, particularly at liquid densities and temperatures

below the critical temperature. Specific heat measurements also provide

a valuable check on the quality of the thermodynamic property calculations

through the thermodynamic relationship

In 1970 we surveyed available experimental data and formuDuring 1972 our main objectives were to complete new high

2, New Experimental Results

Our most important experimental achievement in 1972 was the

7
We have completed new high precision specific heat, Cg^-p , measurements on saturated liquid methane at temperatures between 95 K

and 187 K. The results are given in Table 1, Appendix G and in Figure 1 (attached).

We have also completed new wide-range high precision constant volume specific heat, , measurements on compressed gaseous

and liquid methane at 20 densities ranging from 0.8 to 2.8 times the

critical density, at temperatures down to the triple point (90,68K), and

at pressures up to 350 atm. The results are given in Table 2, Appendix G

and in Figure 2 (attached).

These results represent the most comprehensive specific heat,

C^, measurements ever performed on pure methane.

Orthobaric densities, for saturated vapor and liquid, are

critically important for thermal property computations. Dielectric

constant measurements may be used to find these densities indirectly.

Near the critical point this method is especially valuable because the

densities are notoriously difficult to find by conventional methods. We

have used this method to determine the densities of saturated liquid and

vapor methane at temperatures between 170 K and the critical temperature (190. 5 K). This work is reported in our Laboratory Notes 72-3 and

72-4, Appendices B and C. Many of the results for orthobaric densities

are to be seen in the tables of our manuscript on the equation of state,

Appendix F,

3. Mathematical Formulation of PVT Data

The analytical representation of physical properties data is

essential for their examination, for smoothing, for interpolation, for

the computation of derivative s and, in some cases, for extrapolation.

8
We have formulated all of our high precision PVT data by a unique, new

equation of state which has its origin on the vapor-liquid coexistence

boundary, thus eliminating the long-standing problem of consistency

with this boundary.

All of our recent work on the equation of state of methane is

summarized in one place in the attached manuscript, see Appendix F.

In the above manuscript are given analytical formulations and,

in most cases, the experimental data for the vapor pressures; the saturated vapor densities; the saturated liquid densities; the orthobaric

temperatures, Tg(p); the melting line, P(T); the freezing liquid densities,

p(T); the virial equation of state for low-density gas; the new, wide-range

equation of state constrained to the vapor-liquid boundary; and for the

thermodynamic functions in ideal gas states of zero pressure.

In preparation for the next step of our work, the computation

of thermodynamic functions, we give also in the above manuscript, for

the purpose of validating the equations, computations of the Joule

Thomson inversion locus in P-P-T coordinates, and of the specific heats

^SAT "^^^ saturated liquid.

During the first half of the coming year the emphasis will be

on the calculation of accurate thermodynamic properties data using the

measurements and analytical methods we have developed.

9

OCDCoi^tom^rocM — o(7^

>"'o ^

E

11
AGA-NBS FLUID PROPERTIES DATA PROGRAM

Research Highlights of 1972

measured specific heats of methane (AGA)

measured densities of saturated vapor methane (AGA)

developed accurate equation of state for methane (AGA)

measured some dielectric constants of methane (AGA)

measured liquid-vapor equilibria of methane - nitrogen-argon mixture s (NBS)

measured some viscosities of methane (NBS-NRC)

initiated LNG density project (AGA-gas industry)

initiated refractive index project on methane (NBS-NRC)

12
MEASUREMENTS OF THE THERMOPHYSICAL PROPERTIES OF

COMPRESSED FLUID METHANE

Reports and Publications Completed for This Project to Date

(April 1, 1970 - December 31, 1972)

1. R. D. Goodwin, Thermophy sical Properties of Methane: Virial

Coefficients, Vapor and Melting Pressures, J. Res. Natl.

Bur. Stds. 74A , 655 (1970).

2. R. D. Goodwin, Thermophysical Properties of Methane: Orthobaric Densities and Some Thermal Properties, J. Res. Natl.

Bur. Stds. 75A, 15 (1971).

3. R, D. Goodwin, Methane Equation of State and Outline of Thermodynamic Functions, unpublished.

4. First Annual Progress Report to the American Gas Association,

NBS Report 9781, February 1, 1971.

5. R. Prydz and R. D. Goodwin, Experimental Melting and Vapor

Pressures of Methane , J. Chemical Thermodynamics, 4, 127

(1972).

6. R. D. Goodwin, Densities of Liquid Methane Along the Solid-Liquid

and Liquid-Vapor Equilibrium Boundaries, Cryogenics

Division Laboratory Note 71-5, April 30, 1971,

7. R. D. Goodwin, Smoothed Tabulation of the PVT Properties of

Methane, Cryogenics Division Laboratory Note 71-8, July 6,

1971.

8. R. D. Goodwin and R. Prydz, Densities of Compressed Liquid

Methane and the Equation of State, J. Res. Natl, Bur. Stds.

76A , 81 (1972).

9. R, D. Goodwin, Tables of Provisional Values of Thermodynamic

Functions for Methane, NBS Report 10715, September 30, 1971

13
10. D. E. Diller and H. M. Roder, Correlation of Thermal Conduc

tivity Measurements on Compressed Gaseous and Liquid

Methane, Cryogenics Division Laboratory Note 70-5, August

13, 1970.

11. H. M. Roder, Correlation of Thermal Conductivity Measurements

on Compressed Gaseous and Liquid Methane. Part II. , Cryogenics Division Laboratory Note 71-10, December 30,

1971.

12. D. E. Diller, The Dielectric Constant and Refractive Index of

Gaseous and Liquid Methane, Cryogenics Division Laboratory

Note 71-7, June 17, 1971

13. Second Annual Progress Report to the American Gas Association,

NBS Report 10729, February 1, 1972,

14. R. D. Goodwin, Qrthobaric Densities of Methane Near the Critical

Point, Cryogenics Division Laboratory Note 72-3, February

26, 1972.

15. R. D. Goodwin, Dielectric Constants and Qrthobaric Densities of

Methane, Cryogenics Division Laboratory Note 72-4, June 2,

1972.

16. R. D. Goodwin, The rmophy sical Properties of Methane, paper 2,

Session V, Proc. 2nd Conf. Natural Gas Research and Technology, Atlanta, GA, June 5, 1972.

17. R. D. Goodwin, Thermophysical Properties of Methane, paper 10,

Session II, Proc. 3rd International Conf. on Liquefied Natural

Gas, Washington, DC, September 24, 1972.

18. R. D. Goodwin, Nonanalytic Equation of State for Methane, Constrained to the Vapor-Liquid P-P-T Boundary, December 7,

1972. Manuscript in present report.

19. B, A. Younglove, The Specific Heats, Cg^-j and Cy, of Compressed

and Liquefied Methane, to be published.

14
PART 3

15

I
METROLOGY

by

D. B. Mann and R. J. Richards

This part of the program is sponsored jointly by AGA Headquarters and by the Pipeline Research Committee (AGA).

Flow measurement runs and stratification tests were made

with liquid nitrogen, liquid methane, and liquefied natural gas.

Forty- seven flow measurement runs were made with liquid

nitrogen during January 1972, Forty-five of these measurements are

within the range of 20 to 220 gallons per minute. On a mass basis, flow

rates varied between 2.5 lbs /sec and 25 lbs /sec. In the range of 2.5

lbs/sec to 7.5 lbs/sec, the deviation between the gravimetric weigh

system and the turbine flowmeter is of the order of + 2 percent and

between 7.5 and 25 lbs/sec, deviations lie within ± 1 percent. This

indicated procedural problems in the measurement of small flow rates.

More flow data were taken with liquid nitrog- at 25 different

flow rates over a two-day period. Flows ranged from 21 to 205 gpm and

the mean value of deviation of the LNG facility mass measurements from

the calibration of the turbine flowmeter was + 0.09 percent. This is

excellent agreement between the two gravimetric weigh systems (LN2

Flow Facility) (LNG Flow Facility) and indicates good control over

systematic errors. All data were converted to volume flow for

16
comparison with the flow standard and fitted to a polynomial expression.

With the stated bias of + 0,09 percent, the standard deviation of all

data from the above cited equation was ± 0.47 percent.

Liquid methane was purchased from a commercial supplier in

February 1972 and flow runs were made with this liquid which were

similar to the runs made with liquid nitrogen. Flows varied from 20 to

211 gpm and over 40 data points were accumulated.

The mean value of the deviations indicated a bias shift in a positive sense of about 1.6 percent. All the data were again converted

to volume flow for comparison with the flow standard and fitted to a polynomial expression. The standard deviation from this fitted expression was ±1.3 percent. The difference in precision was greater than

expected from the difference in density between and LNG (a factor

of 1.9). Analysis of the data did not explain the imprecision so the

turbine flowmeter was removed and returned to the supplier for

inspection.

Stratification data were taken with liquid methane in the weigh

tank and all vent valves closed. There is little or no stratification when

the tank was one -third or half-full, however, some stratification did

occur near the surface of the liquid when the tank was three -fourths full.

Temperature differences were 3 to 4 degrees for methane compared to

7 degrees for nitrogen, with the largest temperature differences occurring

within less than two inches of the surface of the liquid.

During the summer of 1972, all of the pressure transducers

and signal conditioners, the power supply, and recording equipment

associated with the pressure transducers were removed from the flow

loop and calibrated on a precision pressure calibration stand covering
the full range of use and determining an inplace calibration check point.

A differential type pressure transducer was ordered to be used to

measure the pressure drop across the test flowmeters.

A flowmeter test box was made available as surplus from a separate flow program and has been installed in the LNG Flow Facility

(Figure 1), This box is 2 by 3 by 4 feet and has removable sides which

will simplify installation of test meters as well as centralize instrumentation used in evaluation of the flowmeters. The flowmeter

environment can be controlled within this test box from high vacuum

insulation conditions to dry nitrogen or high ambient humidity conditions.

In September 1972 a 1-1/2 inch diameter vortex shedding

meter was installed in the test box and the turbine flowmeter was

returned from the supplier and installed. The supplier found a small

piece of wire wound around the shaft of the turbine, which tends to explain the erratic performance of the turbine meter on liquid methane,

Recalibration of the turbine meter will be necessary to determine if damage was caused by the presence of the wire. In the interim, all

fluid will be passed through an in-line filter prior to flow through the

te st meter s . A series of tests were conducted in November and December

1972 to determine the relative performance of the vortex shedding meter

and the turbine flowmeter. The turbine meter was a commercially

available type previously tested on liquid nitrogen and liquid methane.

The turbine meter was located immediately upstream of the test box.

The vortex shedding device was purchased from a commercial

supplier under specifications requiring maximum resolution. Previous

evaluation of this vortex shedding device at the NBS Cryogenics Division

18

has shown that the meter suffers a reduction in rangeability when used

on cryogenic fluids. For instance, a manufacturer's specification of

linearity over range of ten to one has been shown to be restricted to a range of approximately five to one or less in liquid nitrogen service.

The vortex shedding meter was installed in the meter test box

immediately downstream of the turbine flowmeter (Figure 1). A platinum

resistance thermometer and pressure taps were installed to measure

temperatures and pressures at both instruments.

The first series of tests involved performance on liquid

nitrogen and covered a flow range of from 40 to 200 gallon per minute, or on a mass basis from about 4 to 20 lbs/sec of liquid nitrogen. It was

assumed that the turbine flowmeter had a predictable response over a flow range of 20 to 200 gallons per minute, A comparison of the performance of the vortex shedding meter and the turbine meter indicated

that the vortex shedding meter had a linear response range from about 7

to 18 lbs /sec. Over this flow range of linearity, the vortex shedding

meter exhibited a negative bias of 4. 6 percent. The presence of this

negative bias was unexpected and must be confirmed by recalibration of

both the turbine flowmeter and the vortex shedding flowmeter on the

precision liquid nitrogen flow stand.

The comparison of the vortex shedding device precision in

respect to the turbine meter was very encouraging. Over the flow range

of 7 to 18 lbs /sec, using the turbine meter as the flow transfer standard,

the vortex shedding device showed a 3a precision of ± 0. 54 percent based

on 20 flows distributed over the flow range. Cavitation was not observed

in either meter with overpressures equivalent to approximately 10

degrees subcooling.

20
Liquefied natural gas from a commercial supplier was then

ordered and tests were planned which were designed to confirm the

information accumulated with liquid nitrogen. Testing with LNG was not

completely successful due to equipment malfunction (burned out power

supply in gas chromatograph) and severe cold weather with ambient

temperatures to -l6°F. Flow tests involving the gravimetric weigh

system were meaningless as the load cells are uncompensated for this

temperature level. Flow data comparing the vortex shedding meter and

the turbine meter were conducted over a flow range from 80 to 180 gal/

min. Using the turbine meter as the transfer standard, the vortex

shedder exhibited a positive bias shift of about 0.5 percent with the prec ision remaining approximately the same as that found for liquid nitrogen.

Cavitation was indicated in the vortex shedding meter at flow rates less

than 120 gal/min. The tentative conclusion on the basis of the LNG flow

tests is that the turbine and vortex shedding meters exhibit approximately the same performance on liquid nitrogen as on liquefied natural

gas except that higher overpressures will be required for LNG to

eliminate cavitation. Further testing will be required to establish the

degree of overpressure needed.

During the above flow tests the time domain reflectometry

liquid level device has been used extensively. This device was described

in the Second Annual Progress Report, Two of these liquid level

measuring devices are installed on the LNG flow facility. They have

been shown to be an accurate and dependable method of determining

liquid level in the test tanks.

Additional testing and evaluation will be conducted on flow

measurement devices and liquid level indicators prior to completion of

the grant on April 1, 1973. A series of flow tests will be made using

21
liquid methane as a process fluid in order to determine with more

a,ccuracy and precision the relative performance of the turbine flowmeter

and the vortex shedding device. A laboratory test facility will be constructed and data taken to establish the precision of the TDR liquid level

indicator as a function of its performance on liquid nitrogen, liquid

methane, and commercial liquefied natural gas.

22
APPENDIX A

APPENDIX A

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

Vol. 76A, No. 2, March-April 1972 Densities of Compressed Liquid Methane,

and the Equation of State

Robert D. Goodwin and Rolf Prydz"^*

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

(September 30, 1971)

Experimental PVT data for liquid methane are reported at densities from 1.8 times critical up to the freezing liquid, at temperatures from 91 to 245 K and pressures to 350 bar. A nonanalytic equation

of state is adjusted to these and other PVT data from ideal gas states to the freezing liquid, at temperatures from the triple point to 400 K.

Key words: Compressed liquid; densities; equation of state; methane; orthobaric densities.

Symbols, Units and Constants

(Subscripts c and t refer to critical and liquid triple

points.)

(Subscripts g and 1 refer to saturated vapor and liquid.)

a, b, j8, 8 constants in eq (4). A, B, C, D, density-dependent coefficients of eq (4). d, density, <ic= 10.15, c?,- 28. 1472 mol/1.

1, the liter, 1000 cm^.

mol, 16.043 grams of methane (carbon 12

scale).

P, pressure, 1 bar=10^N/m2, j atm =

1.01325 bar. Pt= 0.1159 atm = 0.117 4356 bar,

Pc= 45.9566 bar. R, the gas constant, 8.31434 J/mol-K

(carbon 12 scale), 0.0831434 barliter/ mol K. p = didt, density reduced at the liquid triple

point.

0"= didc, density reduced at the critical point.

T, temperature, kelvin on IPTS—1968,

r, = 90.680,rc= 190.53.

Tsip), liquid. vapor coexistence temperature.

6{p) , a locus of temperatures.

v = \ld, molal volume.

o)(_p,r)= iT-d)li8-Tc).

X = TITc, temperature reduced at the critical point.

Z = PvIRT, the "compressibility factor".

1. Introduction

This report gives experimental data and analytical

formulations which are needed for the computation of

tables of thermodynamic functions. Reviews of thermophysical properties [1, 2]> show that densities avail- able for the compressed liquid at low temperatures

[3, 4] are not of the precision desired for thermal

computations. Quite recently we have formulated

available coexistence data [5, 6], and we have measured the melting- and vapor-pressures of methane [7]. We now report experimental PVT data for the compressed liquid at densities from 1.8 • pc up to the

melting line, at pressures to 350 bar. We obtain densities of freezing liquid and of saturated liquid from

these data by intersection with the PiT) melting line and with the P{T) vapor pressure line respectively.

Densities of saturated vapor are obtained at intersections of the virial equation of state with the P{T) vapor

pressure line. The corresponding vapor-liquid saturation temperatures, Ts{p) , then are represented

analytically.

Finally, we develop an equation of state for the entire

P(p, T) surface by use oiPVT data of several authors,

which data cover most of the domain at Tt < T < 400 K,

P ^ 350 bar. Temperatures are on the kelvin scale of IPTS—1968

[8]. Pressures are related to the International System

by use of the bar, 1 bar= 10^ Newtons per square

meter {Nlm'^).

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

of the American Gas Association. **Present address: Norsk Hydro, Inc., Bygd0y alle 2, Oslo 2, Norway. ' Figures in brackets indicate the literature references at the end of this paper. 81

A-1
2. Densities of the Compressed Liquid

Methane from a commercial supplier is the same

lot used for PiT) measurements on the two-phase

boundaries [7]. It was specified to be 99.99 percent

pure, the principal impurities being N2, CO2, and

C2H6. Independent mass-spectral analysis yields the

report of table A. The apparatus is that developed for hydrogen [9], as modified for oxygen [10] and for fluorine [11]. We

have used volumetric calibrations of the latter work

Table A. Analysis of the methane sample

Ethane 65 ppm*

Oxygen 22-60 ppm

Nitrogen 120-175 ppm

Minimum methane 99.97 percent

* Parts per million.

[12]. For methane, the virial equation and a preliminary

equation of state are used to find amounts in the

gasometer and in nuisance volumes.

Uncertainty in the determination of density is at most 0.1 percent, as noted in [9]. This figure is an accumulation of errors for the total amount of sample,

for the amount in capillary tube and null diaphragm,

and for the temperature- and pressure-dependent

volume of the pipet.

Our PVT data for compressed liquid methane are given in table 1 along experimental pseudo-isochores,

arranged in the order of increasing densities. The

first column gives our experimental sequence; the

second gives density in mol/1; the third is temperature;

and the fourth is observed pressure. Additional col- umns in this and following tables (2, 3, and 4) are dis- cussed below. These data overlap those of Vennix

[13] at 1.8 < pipe < 2.2, and extend up to the melting

line.

Table 1. NBS densities for compressed liquid methane

ID MOL/L T. K P, BAR P. CALC P. PCT D, PCT

1 10.150 190.530 45.957 45.957 -0.00

2601 18.384 176.000 32.172 31.403 2.45 -0.22

2602 18.357 180.000 50.437 49.912 1.05 -0.13

2603 18.332 184.000 68.691 68.387 0.44 -0.07

2604 18.307 188.000 86.906 86.781 0.14 -0.03

2605 18.281 192.000 105.089 105.058 0.03 -0.01

2606 18.256 196.000 123.227 123.266 -0.03 0.01 2607 18.232 200.000 141.311 141.405 -0.07 0.02 2608 18.203 205.000 163.860 163.972 -0.07 0.02 2609 lo. 1 /o 1 OA A 1 Q —U.UO U.Ul 2610 18.150 215.000 208.687 208.828 -0.07 0.02 2611 18.127 220.000 231.002 231.177 -0.08 0.02 2612 18.106 225.000 253.237 253.478 -0.10 0.03 2613 18.086 230.000 275.393 275.691 -0.11 0.03 2614 18.068 235.000 297.479 297.875 -0.13 0.04 2615 18.052 240.000 319.488 320.043 -0.17 0.05 2616 18.036 245.000 341.402 342.090 -0.20 0.06 2501 19.487 170.000 26.367 25.435 3.66 -0.17

2502 19.456 174.000 47.743 47.023 1.53 -0.12

2503 19.427 178.000 69.007 68.507 0.73 -0.08

2504 19.398 182.000 90.117 89.829 0.32 -0.04

2505 19.369 186.000 111.128 110.984 0.13 -0.02

2506 19.340 190.000 132.061 131.970 0.07 -0.01

2507 19.313 194.000 152.913 152.873 0.03 -0.00

2508 19.288 198.000 173.668 173.707 -0.02 0.00 2509 19.264' 202.000 194.349 194.436 -0.04 0.01 2510 19.247 205.000 209.838 209.936 -0.05 0.01 2511 19.221 210.000 235.576 235.715 -0.06 0.01 2512 19.197 215.000 261.206 261.396 -0.07 0.02 2513 19.176 220.000 286.762 287.057 -0.10 0.03 2514 19.156 225.000 312.214 312.594 -0.12 0.03 2515 19.138 230.000 337.542 338.084 -0.16 0.04 2401 20.425 164.000 20.288 19.657 3.21 -0.08

2402 20.389 168.000 44.689 44.077 1.39 -0.07

2403 20.357 172.000 68.823 68.407 0.61 -0.05

2404 20.324 176.000 92.700 92.447 0.27 -0.03

82

A-2
Table 1. NBS densities for compressed liquid methane — Continued

ID MOL/L T. K P, BAR P. CALC P, PCT D, PCT

2405 20.292 180.000 116.390 116.290 0.09 -0.01

2406 20.260 184.000 139.966 139.892 0.05 -0.01

2407 20.231 188.000 163.418 163.421 -0.00 0.00 2408 20.206 192.000 186.776 186.963 -0.10 0.02 2409 20.178 196.000 210.084 210.122 -0.02 0.00 2410 20.155 200.000 233.321 233.387 -0.03 0.01 2411 20.134 204.000 256.494 256.599 -0.04 0.01 2412 20.115 208.000 279.599 279.775 -0.06 0.01 2413 20.097 212.000 302.629 302.860 -0.08 0.02 2414 20.080 216.000 325.569 325.862 -0.09 0.02 2415 20.065 220.000 348.434 348.867 -0.12 0.03 2301 21.371 158.000 19.836 19.616 1.12 -0.02

2302 21.332 162.000 47.537 47.203 0.71 —0.03

2303 21.294 166.000 74.747 74.479 0.36 -0.02

2304 21.258 170.000 101.595 101.522 0.07 -0.01

2305 21.223 174.000 128.287 128.293 -0.00 0.00 2306 21.189 178.000 154.807 154.806 0.00 -0.00

2307 21.158 182.000 181.216 181.214 0.00 -0.00

2308 21.129 186.000 207.556 207.477 0.04 -0.01

2309 21.103 190.000 233.818 233.691 0.05 -0.01

2310 21.080 194.000 260.026 259.888 0.05 —0.01

2311 21.059 198.000 286.118 286.015 0.04 —0.01

2312 21.040 202.000 312.140 312.093 0.02 —0.00

2313 21.022 206.000 338.043 338.053 -0.00 0.00 2201 22.125 152.000 14.593 15.002 -2.73 0.03 2202 22.080 156.000 45.088 45.142 -0.12 0.00 2203 22.040 160.000 74.923 75.141 -0.29 0.01 2204 22.001 164.000 104.403 104.772 -0.35 0.02 2205 21.962 168.000 133.692 133.981 -0.22 0.02 2206 21.929 172.000 162.772 163.249 -0.29 0.03 2207 21.892 176.000 191.756 191.825 -0.04 0.00 2208 21.862 180.000 220.648 220.612 0.02 -0.00

2209 21.836 184.000 249.520 249.420 0.04 -0.01

2210 21.812 188.000 278.308 278.109 0.07 -0.01

2211 21.791 192.000 307.015 306.799 0.07 -0.01

2212 21.772 196.000 335.575 335.425 0.04 -0.01

2101 22.873 146.000 13.127 14.032 -6.45 0.05 2102 22.824 150.000 46.703 46.959 -0.55 0.01 2103 22.782 154.000 79.462 79.859 -0.50 0.02 2104 22.739 158.000 111.736 112.134 -0.36 0.02 2105 22.698 162.000 143.810 144.060 -0.17 0.01 2106 22.660 166.000 175.712 175.764 -0.03 0.00 2107 22.626 170.000 207.555 207.387 0.08 -0.01

2108 22.596 174.000 239.330 238.979 0.15 -0.02

2109 22.570 178.000 271.112 270.591 0.19 -0.02

2110 22.546 182.000 302.767 302.060 0.23 -0.03

2111 22.525 186.000 334.282 333.523 0.23 -0.03

2001 23.570 140.000 12.262 13.567 -9.62 0.06 2002 23.518 144.000 48.910 49.337 -0.87 0.02 2003 23.472 148.000 84.500 84.959 -0.54 0.02 2004 23.426 152.000 119.526 119.919 -0.33 0.02 2005 23.383 156.000 154.350 154.555 -0.13 0.01 2006 23.343 160.000 189.067 188.918 0.08 -0.01

2007 23.308 164.000 223.762 223.280 0.22 -0.02

2008 23.278 168.000 258.440 257.710 0.28 -0.03

2009 23.252 172.000 293.040 292.156 0.30 -0.03

2010 23.228 176.000 327.578 326.431 0.35 -0.04

1901 24. 183 134.000 6.861 8.975 -23.55 0.08 1902 24. 125 138.000 46.383 47.136 -1.60 0.03 83

453-425 OL - 72 - 2 A-3
Table 1. NBS densities for compressed liquid methdne— Continued

ID MOL/L T. K P. BAR P, CALC P, PCT D, PCT

1903 24.076 142.000 84.630 85.409 -0.91 0.03 1904 24.027 146.000 122.240 122.896 -0.53 0.02 1905 23.981 150.000 159.656 159.984 -0.20 0.01 1906 23.940 154.000 197.040 196.975 0.03 -0.00

1801 24.174 134.000 5.841 8.040 -27.35 0.09 1802 24.141 136.000 25.770 26.798 -3.84 0.04

1803 24.115 138.000 45.258 46.066 -1.75 0.03 1804 24.090 140.000 64.512 65.231 -1.10 0.03 1805 24.066 142.000 83.348 84.303 -1.13 0.04 1806 24.042 144.000 102.134 103.182 -1.02 0.04 1807 24.017 146.000 120.944 121.757 -0.67 0.03 1808 23.994 148.000 139.702 140.373 -0.48 0.02 1809 23.971 150.000 158.374 158.811 -0.28 0.02 1810 23.950 152.000 177.053 177.312 -0.15 0.01 1811 23.931 154.000 195.747 195.889 -0.07 0.00 1812 23.912 156.000 214.417 214.311 0.05 -0.00

1813 23.893 158.000 232.888 232.581 0.13 -0.01

1814 23.877 160.000 251.636 251.080 0.22 -0.02

1815 23.862 162.000 270.317 269.571 0.28 -0.02

1816 23.849 164.000 288.962 288.191 0.27 -0.02

1817 23.836 166.000 307.694 306.691 0.33 -0.03

1818 23.824 168.000 326.391 325.205 0.36 -0.04

1819 23.812 170.000 344.986 343.606 0.40 -0.04

1701 24.605 130.000 7.286 9.055 -19.54 0.06 1702 24.572 132.000 28.230 28.867 -2.21 0.02

1703 24.546 134.000 48.781 49.241 -0.93 0.02 1704 24.519 136.000 68.894 69.262 -0.53 0.01 1705 24.494 138.000 88.639 89.295 -0.74 0.02 1706 24.469 140.000 108.425 109.110 -0.63 0.02 1707 24.443 142.000 128.176 128.587 -0.32 0.01 1708 24.419 144.000 147.856 148.106 -0.17 0.01 1709 24.396 146.000 167.516 167.554 -0.02 0.00 1710 24.374 148.000 187.222 186.939 0.15 -0.01

1711 24.354 150.000 206.921 206.403 0.25 -0.02

1712 24.335 152.000 226.644 225.827 0.36 -0.03

1713 24.317 154.000 246.119 245.219 0.37 -0.03

1714 24.301 156.000 265.906 264.725 0.45 -0.04

1715 24.286 158.000 285.671 284.221 0.51 -0.04

1716 24.273 160.000 305.459 303.856 0.53 -0.05

1717 24.260 162.000 325.155 323.358 0.56 -0.05

1718 24.248 164.000 344.921 342.874 0.60 -0.06

1601 24.996 126.000 4.795 7.075 -32.23 0.07 1602 24.960 128.000 26.740 27.553 -2.95 0.03 1603 24.933 130.000 48.275 48.887 -1.25 0.02 1604 24.905 132.000 69.442 69.831 -0.56 0.01 1605 24.879 134.000 90.206 90.781 -0.63 0.02 1606 24.852 136.000 110.901 111.354 -0.41 0.01 1607 24.826 138.000 131.487 131.823 -0.25 0.01 1608 24.801 140.000 152.046 152.198 -0.10 0.00 1609 24.777 142.000 172.619 172.489 0.08 -0.00

1610 24.754 144.000 193.223 192.707 0.27 -0.01

1611 24.734 146.000 213.859 213.146 0.33 -0.02

1612 24.715 148.000 234.593 233.538 0.45 -0.03

1613 24.714 148.000 234.564 233.395 0.50 -0.03

1614 24.697 150.000 255.294 253.895 0.55 -0.04

1615 24.681 152.000 276.024 274.371 0.60 -0.05

1616 24.666 154.000 296.684 294.833 0.63 -0.05

1617 24.652 156.000 317.346 315.290 0.65 -0.06

1618 24.639 158.000 338.030 335.751 0.68 -0.06

84

A-4
Table 1. NBS densities for compressed liquid methane — Continued

ID MOL/L T, K p BAR p CALC p PCX D, PCX

1 "^01 IDXJ L 199 nno 3.482 6.324 —44.94 0.08

1 "in? 25.348 1J. ^24r . 000 \J\J\J 26.168 27.592 —5. 16 0.04

1 iJKJO 2S 320 126 000 48.814 49.922 —2.22 0.03 1504 25.293 128 000 70.363 72. 103 —2.41 0.05 2S 266 1 30 000 92.218 94.005 —1.90 0.05 25.239 1 32 000 114.039 115.637 — 1.38 0.04 25.212 1 34 000 135 786 137 X\J i . 005 \J\J*J —0.89 0.03

91 1 1 't4 nno 135.814 1 OW. 3ft 850 OiJ7 —0.76 0.03

9"^ 1H4 1 't^> nno 1 "^7 1 7'^ 157.971 —0w . ow'kO 0.02

Til fl 9=^ \ f\f\ 1 38 nno 178.801 179.281 —0.27 0.01

131

1

9"^ 1 XI 140 000 90n 430 9nO 510 —0.04 0.00 IDIZ 9"^ 1 l^i 149 000 222. 144 991 822 0. 15 —0.01

1310 9^; nQ7 144.000 243 865 243 231 0.26 —0.02

IDl'r 9'; fiRfi 14ft 000 9ft4 7t;c

i.OT*. 1 tJJ 0.34 —0.02

11010"i 148 000 987 46? 286 251 0.42 —0.03

lOlO 9"^ 040 1 ^0 nnn 309 282 307 728 0.50 —0.04

Til 101 7/ 9"^ (VVk 1 'i9 000 330 987 329. 197 0.54 —0.04

lOlo 9"^ 099 1 54 000 352 726 350 667 0.59 —0.05

i/ini 14U1 ZO. oc 777 / 1 / 111lO.Ul/U fl 000 4T". 740 i '-r\J 7.269 —34.80 0.07 14UZ ZD. / oV 1 90 non 9ft 4ft7 90 ft'?4 —0 . 870 4 0.03

1 Wo ocZO. 7in / lu 1izz.uuu 99 nno ^1 ftl4 00'i'^ . 009 vw^ —2.24 0.03 IIU* oc /;o9 ZO.OoZ 1 94 oon 74 ^0^ 7ft i W. 100 17 7 —2.49 0.05

I'rUO oc /iC/l ZO.OO'* 1 9ft nno 07 106 99.086 — 1.91 0.05 25 625 128 000 120 010 121.516 — 1.24 0.04

14(17 25.598 130 000 142.846 143.967 —0.78 0.03

14'UO 25.574 1 32 000 165 554 166.619 —0.64 0.03

l'*U!7 95 550 1 34 000 188 390 189 X 0 7 . 008 V/V/O —nw. ow^ft n n9

1I^IU ill fl 95 594 1 36 000 91 1 069 ^910X w. ftl6 0 lo n 1

9

w . 1 ^ —n ni

lill 1 l^-l 1 9'^'^ 10^^ nW. 9fl ZO —n 09

1419 95 503 1 "^8 000 OQ-i 44c; 9'^^ 10^ n 1

1

w. 1

1

—0w. 01Wl

141 It* 1 ^

0

25.484 140 000 256 331 955 fi78 0.26 —0.02

1414 9"^ 4fifi 14.9 000 970 '^'^n 978 ^ 1 1 1 4 0. ill 0W. 44't' —0 n^

1 4Ti 9"^ 4'iO Idd 000 "^09 900 ^00 ft77 0u.oi —0u. 04w^

141fi 25.435 Mfi 000 ^9"^ 997 '^9^ 991 0U.wZft9 —

n

u.uo

141 7 25.422 148 000 ^48 148 ^4"^ 09ft 0w. ft4 —

n

w. uo

1301 26.142 114.000 4. 106 5.811 —29.34 0.04 1302 26. 103 1 16 000 28.896 29. 135 —0.82 0.01 1303 26.072 1 1 a 000 52.968 53.369 —0 7"^ W. 4 0 nw. 01w 1 1304 26.044 1 90 000 7ft '^'^8 774 f . T\7 4 0 4 — 11.4477 w. wo

1305 26.014 122 000 inn ift9 ini 1 W 1 . 4^n 'TOW —1 9^; 0w. n^wo

1306 25.985 124 000 123.929 124.955 —0.82 0.02 1307 25.956 1 26 000 147.655 148. 158 —0.34 0.01 1308 25.929 128 000 171.338 171.393 —0.03 nW. nnWW 1309 25.904 1 30 000 195.123 194.677 nw. ^093 —nw. 01w 1 1310 25.881 1 32 000 918 055 ^9181 0. n'^0 wow nW. 49T"^ —0w. 09w^

1311 25 880 1 39 000 918 ^"Ki. 91^ J. 74 . 8'i'i 000 0w. 0"lli —0w. 01w 1 1312 25.859 1 34 000 242.441 941 90^ 0.48 —0.03

1313 25.840 1 36 000 966 44n ^U^. 964 837 0<J 1 0.61 —0.03

1314 25 822 1 38 000 9Qn ^7W. 474 ^ 1 T" 288 323 0.75 —0w.woO'i 1315 25.807 140 000 314.577 312 1 30 0.78 —0.05

1316 25.792 142 000 338 50n 335 726 0.85 —0.06

1201 26.519 1 10 000 5.935 7.782 —23.73 0.04 1202 26.480 112 000 31.839 32 288 —1.39 0.01 1203 26.449 114.000 56.444 57.777 —2.31 0.03 1204 26.419 116.000 81.054 83.045 -2.40 0.04 1205 26.388 118.000 105.870 107.750 -1.74 0.04 1206 26.357 120.000 130.659 132.083 -1.08 0.03 1207 26.327 122.000 155.400 156.241 -0.54 0.02 1208 26.299 124.000 180.154 180.425 -0.15 0.01

85

A-5
Table 1. NBS densities for compressed liquid methane— Continued

ID MOL/L T, K P, BAR P. CALC P, PCX D. PCT

1209 26.274 126.000 204.975 204.840 0.07 -0.00

1210 26.251 128.000 229.892 229.325 0.25 -0.01

1211 26.230 130.000 254.906 253.899 0.40 -0.02

1212 26.211 132.000 280.025 278.581 0.52 -0.03

1213 26. 193 134.000 305.214 303.196 0.67 -0.04

1214 26.192 134.000 304.967 303.002 0.65 -0.04

1215 26.176 136.000 330.185 327.759 0.74 -0.05

1101 26.901 106.000 12.022 12.593 -4.54 0.01 1102 26.864 108.000 38.986 38.731 0.66 -0.00

1103 26.833 110.000 64.591 65.550 -1.46 0.02 1104 26.801 112.000 90.300 91.734 -1.56 0.03 1105 26.768 114.000 116.122 117.294 -1.00 0.02 1106 26.736 116.000 141.871 142.638 -0.54 0.01 1107 26.706 118.000 167.653 167.983 -0.20 0.01 1108 26.679 120.000 193.539 193.550 -0.01 0.00 1109 26.653 122.000 219.542 218.964 0.26 -0.01

1110 26.630 124.000 245.820 244.647 0.48 -0.02

1111 26.631 124.000 245.678 244.851 0.34 -0.02

1112 26.610 126.000 272.049 270.626 0.53 -0.03

1113 26.592 128.000 298.510 296.721 0.60 —0.03

1114 26.574 130.000 325.020 322.534 0.77 -0.04

1115 26.559 132.000 351.423 348.707 0.78 —0.05

1001 27.232 102.000 8.474 9.235 -8.24 0.01 1002 27.192 104.000 36.489 36.050 1.22 -0.01

1003 27.160 106.000 63.034 63.985 -1.49 0.02 1004 27.127 108.000 89.515 91.224 -1.87 0.03 1005 27.093 110.000 116.218 117.781 -1.33 0.03 1006 27.060 112.000 142.937 144.093 -0.80 0.02

1007 27.029 114.000 169.612 170.392 -0.46 0.01 1008 27.001 116.000 196.480 196.915 -0.22 0.01 1009 27.001 116.000 196.471 196.915 -0.23 0.01 1010 26.976 118.000 223.568 223.689 -0.05 0.00

1011 26.952 120.000 250.862 250.311 0.22 -0.01

1012 26.931 122.000 278.278 277.234 0.38 -0.02

1013 26.912 124.000 305.898 304.267 0.54 -0.03

1014 26.895 126.000 333.424 331.430 0.60 -0.03

901 27.588 98.000 12.437 12.343 0.76 -0.00

902 27.548 100.000 41.407 40.503 2.23 -0.01

903 27.516 102.000 68.696 69.861 -1.67 0.02 904 27.481 104.000 96.270 98.007 -1.77 0.03 905 27.447 106.000 124.002 125.853 -1.47 0.03 906 27.413 108.000 151.755 153.199 -0.94 0.02 907 27.382 110.000 179.649 180.747 -0.61 0.02 908 27.353 112.000 207.794 208.298 -0.24 0.01 909 27.328 114.000 236.148 236.336 -0.08 0.00 910 27.305 116.000 264.752 264.435 0.12 -0.01

911 27.305 116.000 264.894 264.435 0.17 -0.01

912 27.285 118.000 293.612 292.851 0.26 -0.01

913 27.266 120.000 322.446 321.144 0.41 -0.02

801 27.900 94.000 7.513 6.980 7.64 -0.01

802 27.858 96.000 37.517 36.064 4.03 -0.02

803 27.825 98.000 65.517 66.637 -1.68 0.02 804 27.789 100.000 94.061 95.894 -1.91 0.03 805 27.753 102.000 122.725 124.572 -1.48 0.03 806 27.719 104.000 151.383 153.178 -1.17 0.03 807 27.686 106.000 180.222 181.498 -0.70 0.02 808 27.657 108.000 209.351 210.286 -0.44 0.01 809 27.630 110.000 238.728 239.088 -0.15 0.01 810 27.607 112.000 268.394 268.423 -0.01 0.00 86

A-6
Table 1. NBS densities for compressed liquid methane — Conlinued

IDin Mrti /T T K P BAR P. CALC P PCT D. PCT

Oil ^ i , oo\j 11 1It". 4 non V/WVf 9q« Of.] 9Q7 .671. S^9 OO^ nO. 14It" —nV/. niW 1

ftl 9 ^ i . ou f ^97 ^4^ nO. O111 —n ni

28. 147 90.680 0. 1 17 0.117 n no 0.00 601 28.209 92.000 44.123 42.754 3.20 —0.02

28.175 94.000 72.852 74.640 —2.40 0.02

28. 137 96.000 in? S4'^ 104 ft3n —2. 18 0 ni

28. 101 98.000 134.893 —1.88 0.04 QUO zo.uoo 9H C\f\f, inn nnn 1^1,9 iftn lfi4 1 Ot" . f\(\l \>\J t — 1 47 n ni Duo zo. 9ft f\fif> uoo inn nnn i^i9 iQn 1 Ot". OU 1 — 11 . 474" ( n ni UU / Zo. 9ft 004" in9 nnn 1Q9 9d1 1Q4 1 7*T. OHft1 O — 11.111 7 n ni

9ft nfid. ind nnn 999 ^ift7 994 4ni n n9

97 07ft infi nnn ^oo . 1 ^Ot". 91^4 ftnft 0\/0 —n\/. 404'7 n n9

oil/ 97 Q'l'; inft nnn 9R4 fid.1 ^OO 98"^ '^1

. O X o —n 11 nV . niW 1 Oil 97 Q'i'\ 1 in nnn iifi nift O^1^lO. OOO —n 1

7

U. 1 1 n m

97 Q^f\ 1 1 9 nnn ^d.7 '^91 04- / . JZ i 147 490 n ni —n nn

7ni 9ft tOI Qd. 74". nnn UUU 1 9ft 1 ^"l 111 7ft'^ 1 O 1 . 1 OO —9 77

9ft ^1^4. Oft nnn 1 '^H ftQI 1^9 lo^. ooo VK'K —9^ . 11 9^ n n4

9ft '191 Qft nnn IftQ iKfKf\ 1 07. ooo loa aQ7 1 70 . oo < —11 . 7ft ( o nO. n4U4

IK)'* OQ 9Qn 1 nn nnn 991 ZZ "lift 1 .ooo 994 9ft^i ZZ'*. ZOO —11 .Ol11 n0.04" n4

/Ud 9Q 9A/I Z0.Z04 1 r»9 Ann 9CO 999 zoo. 04*1 — 1 . lU A AA

IVO 9Q 9/in 1 nA nnn ZoO.'t'+U 9ft7 Zo ( .Ol'* ftl 4 A ft9 u. oz A m

lu I

1 AAA lUO.UUU lift A/IQ Ol 0 01/1 O 1 7. 7 1 1- U.OO nu.uzA9 mnlUo 9ft 9nn 1 nft nnn oou. ooo OO^ •^^9 . noo 1/7 7 —nV/. 4444" n n9

28 SS2 96.500 994 Q^R 99ft 91^i — I1 .44 44 AU.U4' n4

515 28.545 97.000 9'^'t 19H oo 1 — 1 1ft 1 . OO n n4 516 28.531 98.000 249.643 252.596 -1.17 0.04

•il 7 9ft ZO. OO<in7( inn nnn ZOO. / ^-O 1 AO A AQ U.Uo 518 28.507 100.000 282.935 285.748 -0.98 0.03 519 28.486 102.000 316.433 319.221 -0.87 0.03 520 28.466 104.000 350.093 352.461 -0.67 0.03

87

A-7
Table 2. Methane densities via the virial equation o/[5]

MOL/L T, K P. BAR P, CALC P. PCX D. PCX

0.500 140.000 5.213 5.221 -0.14 0.16 0.500 145.000 5.443 5.448 -0.09 0.10 0.500 150.000 5.670 5.673 -0.05 0.06 0.500 155.000 5.896 5.898 -0.03 0.03 0.500 160.000 6.120 6.121 -0.01 0.01 0.500 165.000 6.344 6.344 -0.00 0.00 0.500 170.000 6.566 6.566 0.00 -0.00

0.500 175.000 6.788 6.787 0.01 -0.01

0.500 180.000 7.009 7.008 0.01 -0.01

0.500 185.000 7.229 7.228 0.01 -0.01

0.500 190.000 7.448 7.448 0.01 -0.01

0.500 195.000 7.668 7.667 0.01 -0.01

0.500 200.000 7.887 7.886 0.00 -0.00

0.500 205.000 8.105 8.105 0.00 -0.00

0.500 210.000 8.323 8.323 -0.00 0.00 0.500 215.000 8.541 8.541 -0.00 0.00 0.500 220.000 8.758 8.759 -0.00 0.00 0.500 225.000 8.976 8.976 -0.01 0.01 0.500 230.000 9.193 9.193 -0.01 0.01 0.500 235.000 9.409 9.410 -0.01 0.01 0.500 240.000 9.626 9.627 -0.01 0.01 0.500 245.000 9.842 9.844 -0.01 0.01 0.500 250.000 10.059 10.060 -0.01 0.01 0.500 255.000 10.275 10.276 -0.01 0.01 0.500 260.000 10.491 10.492 -0.01 0.01 0.500 265.000 10.707 10.708 -0.01 0.01 0.500 270.000 10.923 10.924 -0.01 0.01 1.000 150.000 10.230 10.247 -0.16 0.21 1.000 155.000 10.723 10.731 -0.08 0.09

1.000 160.000 11.209 11.211 -0.02 0.02

1.000 165.000 11.689 11.687 0.02 -0.02

1.000 170.000 12.165 12.160 0.04 -0.05

1.000 175.000 12.636 12.630 0.05 -0.06

1.000 180.000 13.105 13.097 0.06 -0.07

1.000 185.000 13.570 13.563 0.06 -0.06

1.000 190.000 14.033 14.026 0.05 -0.06

1.000 195.000 14.494 14.488 0.05 -0.05

1.000 200.000 14.954 14.948 0.04 -0.04

1.000 205.000 15.411 15.406 0.03 -0.04

1.000 210.000 15.867 15.864 0.02 -0.03

1.000 215.000 16.322 16.320 0.02 -0.02

1.000 220.000 16.776 16.774 0.01 -0.01

1.000 225.000 17.229 17.228 0.00 -0.01

1.000 230.000 17.681 17.681 -0.00 0.00

1.000 235.000 18.132 18.133 -0.01 0.01 1.000 240.000 18.583 18.585 -0.01 0.01 1.000 245.000 19.032 19.035 -0.01 0.02

1.000 250.000 19.481 19.485 -0.02 0.02

1.000 255.000 19.930 19.934 -0.02 0.02

1.000 260.000 20.378 20.382 -0.02 0.03 1.000 265.000 20.825 20.830 -0.03 0.03 1.000 270.000 21.272 21.278 -0.03 0.03 1.500 160.000 15.310 15.319 -0.06 0.09

1.500 165.000 16.084 10.081 0.02 -0.03

1.500 170.000 16.847 16.834 0.08 -0.10

1.500 175.000 17.599 17.580 0.11 -0.14

1.500 180.000 18.343 18.321 0.12 -0.15

1.500 185.000 19.079 19.056 0.12 -0.15

1.500 190.000 19.809 19.787 0.11 -0.14

88

A-8
Table 2. Methane densities via the virial equation o/[5| — Continued

MOL/L T, K P. BAR P. CALC P. PCX D. PC T

1.500 195.000 20 535 20 514 0.10 -0.12

1.500 200.000 21 256 21 237 0.09 -0.11

1.500 205.000 21 973 21 956 0.08 -0.09

1.500 210.000 22 686 22 672 0.06 -0.07

1.500 215.000 23 397 23 386 0.05 -0.06

1.500 220.000 24 106 24 097 0.03 -0.04

1.500 225.000 24 812 24 806 0.02 -0.02

1.500 230.000 25 516 25 513 0.01 -0.01

1.500 235.000 26 218 26 218 0.00 -0.00

1.500 240.000 26 919 26 921 -0.01 0.01 1.500 245.000 27 618 27 622 -0.02 0.02

1.500 250.000 28 315 28 322 -0.02 0.03 1.500 255.000 29 012 29 021 -0.03 0.03

1.500 260.000 29 707 29 718 -0.04 0.04

1.500 265.000 30 401 30 414 -0.04 0.04

1.500 270.000 31 094 31 108 -0.04 0.05 2.000 170.000 20 664 20 639 0.12 -0.19

2.000 175.000 21 729 21 691 0.18 -0.26

2.000 180.000 22 776 22 731 0.20 -0.28

2.000 185.000 23 810 23 761 0.21 -0.28

2.000 190.000 24 831 24 782 0.20 -0.26

2.000 195.000 25 843 25 796 0.18 -0.24

2.000 200.000 26 847 26 803 0.16 -0.21

2.000 205.000 27 843 27 804 0.14 -0.18

2.000 210.000 28 833 28 800 0.12 -0.14

2.000 215.000 29 818 29 790 0.09 -0.11

2.000 220.000 30 798 30 777 0.07 -0.09

2.000 225.000 31 775 31 759 0.05 -0.06

2.000 230.000 32 747 32 737 0.03 -0.04

2.000 235.000 33 717 33 712 0.01 -0.02

2.000 240.000 34 683 34 684 -0.00 0.00 2.000 245.000 35 647 35 653 -0.02 0.02 2.000 250.000 36 609 36 619 -0.03 0.03 2.000 255.000 37 568 37 583 -0.04 0.04 2.000 260i)00 38 526 38 544 -0.05 0.05 2.000 265.000 39 482 39 504 -0.06 0.06 2.000 270.000 40 436 40 461 -0.06 0.07

89
Table 3. Methane densities ofVennix [loj

MOL/L T, K P. BAR P, CALC P. PCT D, PCT

2.560 172.527 24.660 24.653 0.03 -0.06

2.560 174.691 25.283 25.269 0.05 -0.09

2.559 177.203 25.994 25.976 0.07 -0.12

2.559 183.176 27.666 27.642 0.09 -0.14

2.559 190.532 29.676 29.664 0.04 -0.06

2.558 191.849 30.038 30.016 0.07 -0.10

2.556 203.084 33.048 33.036 0.04 -0.05

2.555 213.041 35.672 35.668 0.01 -0.02

2.555 217.864 36.931 36.930 0.00 -0.00

2.554 223.831 38.481 38.483 -0.00 0.00

2.553 233.546 40.990 40.989 0.00 -0.00

2.552 239.797 42.590 42.593 -0.01 0.01 2.551 252.833 45.897 45.910 -0.03 0.03 2.550 263.399 48.559 48.575 -0.03 0.04 2.548 273.380 51.058 51.074 -0.03 0.04 6.469 190.429 44.720 44.545 0.39 -2.53

6.471 190.532 44.814 44.641 0.39 -2.47

6.464 208.574 60.270 60.264 0.01 -0.02

6.459 223.234 72.346 72.419 -0.10 0.17 6.456 234.440 81.433 81.539 -0.13 0.20 6.453 243.733 88.913 89.016 -0.12 0.16 6.453 243.773 88.939 89.048 -0.12 0.17

6.451 251.376 95.018 95.119 -0.11 0.14 6.447 262.190 103.601 103.700 -0.10 0.12 6.444 272.155 111.478 111.550 -0.06 0.08 6.444 272.185 111.494 111.573 -0.07 0.08 7.235 190.052 44.989 44.798 0.43 -5.39

7.237 190.532 45.493 45.304 0.42 -4.35

7.235 190.750 45.710 45.532 0.39 -3.80

7.237 191.032 46.001 45.827 0.38 -3.40

7.234 193.325 48.336 48.192 0.30 -1.76

7.233 197.737 52.722 52.644 0.15 -0.57

7.231 202.753 57.627 57.604 0.04 -0.11

7.229 208.224 62.909 62.934 -0.04 0.10 7.228 212.165 66.689 66.736 -0.07 0.15 7.226 217.136 71.421 71.494 -0.10 0.20 7.224 222.926 76.909 76.995 -0.11 0.20 7.222 230.050 83.614 83.713 -0.12 0.19 7.219 237.336 90.432 90.536 -0.11 0.17

7.217 242.709 95.434 95.540 -0.11 0.15

7.215 248.444 100.757 100.861 -0.10 0.14

7.215 250.194 102.376 102.481 -0.10 0.13 7.214 253.445 105.378 105.483 -0.10 0.13 7.212 258.642 110.172 110.270 -0.09 0.11 7.210 263.050 114.229 114.323 -0.08 0.10 7.209 268.301 119.049 119.134 -0.07 0.09 7.207 273.171 123.504 123.581 -0.06 0.07 9.844 190.532 45.870 45.958 -0.19 12.43 9.844 191.032 46.579 46.685 -0.23 9.45 9.840 191.551 47.318 47.434 -0.25 7.18 9.840 192.938 49.282 49.431 -0.30 4.43 9.839 195.243 52.563 52.742 -0.34 2.62 9.838 197.562 55.870 56.069 -0.36 1.87 9.837 200.411 59.977 60.154 -0.29 1.13 9.835 202.829 63.417 63.620 -0.32 1.01 9.834 206.370 68.503 68.695 -0.28 0.72 9.830 213.503 78.771 78.921 -0.19 0.37 9.825 223.647 93.389 93.464 -0.08 0.12 9.819 236.398 111.767 111.738 0.03 -0.03

90

A-10
Table 3. Methane densities ofVennix [13] — Continued

MOL/L T, K p BAR P CALC p prx n PPT

Q Hid. Z4'0. 94R 147 XT' / 19H XZO.Of\7±/ T" 19ft xZo.oo'^ft7/ U.Uo A AO

0 fli 1 zoo. XOO 1100. "tft 740 / ^7 1 1H t^Oft I0O.O7O u. 1

1

—A 1 9 U. Iz 0 809 97^ lfi7 164 '=;n4 lft4 104-. ZO7 9ftO oil U. XO —A 1 1 u. 10 in 990 iQn '^'^9

X 7W. oo^ 4=1 *tO.OKT^/ 0 'tO. 7OO n 1 ft u. 10 1 ^ 19 lo.oz

10 910 IQl X 7 X . 0^9 \JOZ. 4ft ft07 4ft 40. 7n'^ / 00 nU. 91Z 1

1 1 7n 1 1 . /U in 91A IQO X 7U.OO7 R^Q 4ft '^49 4ft 4-0. 417 4'X / —U. XO 1 1 QQ 1 1.00 in 9ifi 101 1 7 1 . n4n u^-u 4ft ft! fl 4ft 4*0. 717 / 1 / —U.zx 1 1 79 1 1. /Z 101 171.ZZ7 990 4ft 4-0. ono 7UU 4ft OQQ —U.Zl y.ytj in 9ifi 101 1 71 .4'ZO 49R 474- / . 1XooHH 474- 90ft / .Z7O A 90 u.zo Q A7

in 9i^i 101 1 7 1 . R9n ozu 474- / . 7ft9 / OZ 474- ftftl / .00

1

n 9"^ u.zo 7 1/1

/ .0* in 9i^i lU. Z lO 1 09 n7^i 1 7Z.U /o 4ft 'to. 1101^1 4R 9ft4 4'0.ZO4' —AU.Z97/ A 7A 0. /O 10 91 1^ 11/. z xo 10'? =^99 X 70. o^z. 00. ^n zoo 9ft "? 00.4'Z ^(\ 497/ n0. oz19 44'.UU on

10.214 195. 158 52.700 52.877 —n\j ,0011 9z.ooftO 10 91 "K 197.926 5ft 57.030 —0U. 04* 14 1 ft4 1 .04' 10.212 200 575 60.814 61.011 —0.32 1X . 17X / in 9in 904 Ct%7 ftft DO. n^ft 000 ftft 00. 991 zz

1

A 90 U.ZO 0 7ft U. /o inlU. 90ft Zl/O 9n7 R^i^ 71/ 1 . 700 / 7 7 7/ 11.7/0 07fl A 9C 0. ZO n "^ft u. 00

10 90R 907 R55 71/ X . ft^^ 000 71/ X . 07R 7 / 0 —00. 9nZO 00.4'0 4ft lo 9nfi 910 C\AA 70 ftOl / 7.O7

1

7Q/ 7.0X4' HI 4 —A 1 C U. 10 nu.zy90 900 QOi: 1 1 n ftHH 1 lU.OOO 11

1iU.DX'J n ftl 4 A (\7 u.u / A AO —U.Uo

in 1 ftA lu. Loo ZOZ.Oo / 14n %9.7 114'U. 4n 171 I/O 011^ 0.10 A 1 — f. u. 10

lU. 1/0 970 CWfy 1 70 091; 1 /u. 7Z0 1 7n ftl 1 /U.Olo 0 1 R u. 10 A 1

7

—u. 1 / 10 1 7fi 97^ (V\9K 1X 70/ U. 0R7 70 / 1X 7n ft7Q / O.D / 7 n 1

R

0. 10 A 1

7

0. 1 / 11 Ifi^ 1 1 . IDO ion ^"^9 ^O.OO^ 4ft 4-0.000 nnft A 07 0.0/ 0U.Z7 in 90

11 lfi9 1 1 . IDZ 101 n^9 4ft ft4^ 4'0.04?O 4ft 4'O.OUo HnH A qc U.oo 1 ft ftft 10. 00

11 1 t^H 1 1 . IDo IQl ft Aft 474* Oft^ / .700 4H 1 1ft 'to. loo —

A 09 U.OZ ^ A9 o.oz

11 1 "nR 1 1 . lOO 1011 .09n%* 0 4ft 4'0. noo UO7 4H4-0. 11 77/ / A qc 0.00 fto.oz19

1111.11 DO"^ft 10*^ 9d.ft ou. ^(\ Z4*0 94ft 00.4f4'Z i=;n 449 —n0.0710 1 4ft

X X . 1 1 IQC 110 ^'K ^4n OO.Ot-O t^l '^4n —n0.017/ z.o 9 n?/

X X . X D\J 107 ^nn 00. ^ift 009 77Z 0•^7 91 1/ .Z X X —n0. 00iR 11.00"^n

1 1

.

IDO 100 91f^ ftn OU.ZZO 99ft ftn 00. 441 ^^-l A qc 0.00 11 . 19IZ

11 1 "^d. X 1 . 1 J'* 900 001 (\%. 00.U7Z no9 ftl OO.Z74' 904 Ao.ozq9 nU.oH7/ 11XI. 1li/O 90^ O^^d ftft 00. 7ft9 / oz ftft 00. QftR 7OO —no.zo9R n ftc; 0.00

11 1 "^0 1 X. XOv 907 ^f\A. 74 1ft / 4'.0 XO 74 ft'^n / 4'.000 —00. IRXO n0.0011

11XX. 1471 ^91^10. 107 1-7 1 ft4 9ftft 04". zoo R404'.0ZZ 199 A0.007/ n0. in10

11X X . 147 X ^ 1 91 ^ 904. R404<. ZOZ 9R9 R4Ot". OO** 114 —00.00Oft n0. in10

11XX. 1Xl"471 Z

91ItJ. Q 919 Z IZ H4 90^ H4 14ft A A7 u.u / nU. inxU

11IX. 141 1*t1 99*1 IftJ. ini lUX.DOU ftftn ini XU '^7ft X . 0 /

0

n nft 0. 00 A 1 A U. XU

11XX. ^'^f, xou zoo. 9^^ 1/^1 XQX 110 X X 7. 1xzz99 1X1Xft0. on4 70Hr n0. ift XO —n0. 9nZO

11. 131 9d^ 1 "^7 1lOO.OUl "tft ftOl 1xoo.z 1ft 979/ z n 94 —n0. 94zt

11. 126 9^^ 1 ^'^ zoo. 100 1104-. "^4 19^ XZO 1xoo. "^1 710 / 07 no.zo9=^ —n0. 91ZO

11X X . 190 L^\J zoo. 9^i1 1XZt- 9d 171 '^'^4

X / X . 004- 171 X / X . 19n XZO n 9=^ o.zo —n0. zz99

11 1

1

XX. X X o Z97^( O.U7Z 009 1XOO. RR 077 7 / / IRR XOO.47O 401 00. ZO9ft —n0. zz99

11XI. 11^ X XiJ 97*^ 1 "^0 z 1 0. xou IRR xoo. 097 7Z / IRR "^04 xoo. 074 00. IRXO —00. 1XO

1X 1X . 771 1 1 X 100 "^^9 X 71/ . 00^ R9'? 4ft 1 11^ T-U. XOO —0U. ftR UO 00. IR i,0 91

1X 1X . 771 1 fx 101 X 7 X . 0^9 \/OZ 4ft . 701 / V/ X 4ft T-U. 009 7 7^ —0 ft9 1X ft X1 7/

1XI.1 7fi7 i\J t 109 dOft 404'7. Z7O 901^ 40T"". 00'^I'^lX —n "^9 \J. 0£d 0,1 70i\j

1X11 . 7f>^ i oo 1 0"^ ftdO 00. ZOO 9'^ft 00.0 '^'^ '^Ift XO A0.447/ 1 ft'; X . 00

1X1X . 7^i4 ( KJHf 1 Oft 1 ft9 1 70 . X oz 07. 1^0 0

'^1 1 X X O7. •^0 7'^ft / 00 —n0. 414- X

1X . inXO

1XX./ 1 7^0ou ZUO.4'04' 90^ d^d ftO D7. 11 097Z ftO 07. 017R/ 0 —00. z97/ 0 =^0 0. 00

1 1 Z919XZ.UOt" O'^d ft"^ oo.ouo '^Oft R'; 11=19 —0 0"^ 0.00 n0.007/

1 1 7'^'^ XX./ Do 919 Z IZ.UOo 0^^ fti^ OD.o11lUn 00.004 A ACL 0.00 n0.007/

1XI./ 1 74Q4'7 999 ^^^9 in'^ 100.4-0 4n7/ in'i X00.Z04* 9ft4 0\J. 14XT' —0yj. 1LO^

111./ 1 744^irr ZOO.HiUZ 9*1^ d09 1IZO. 91^ 0'^ft 7OO 1XZO. 91^ ft'iR 000 n 94 —no.zo91

1IX./ 1 7444^ ZOO.'twO 9*^^ dO^ 1IZO. 9=^ 071 7 / 0 1IZO.UOO 9^^ ftftn n 95 —0I/. ^4' 94

11.741 237.033 132.922 132.549 0.28 -0.26

11.741 237.034 132.920 132.551 0.28 -0.26

11.737 243.378 145.053 144.614 0.30 -0.27

11.737 243.381 1 145.050 144.620 0.30 -0.27

91

A-ll
Table 3. Methane densities of Vennix [13] — Continued

MOL/L T, K P, BAR P, CALC P. PCT D, PCT

11.732 253.284 163.987 163.492 0.30 -0.25

11.726 263.449 183.402 182.854 0.30 -0.24

11.724 268.300 192.683 192.101 0.30 -0.24

11.724 268.300 192.678 192.101 0.30 -0.24

11.721 272.694 201.050 200.469 0.29 -0.23

11.721 272.695 201.049 200.471 0.29 -0.22

11.721 272.698 201.046 200.476 0.28 -0.22

12.873 190.032 45.236 45.783 -1.20 11.00

12.872 191.032 47.247 47.773 -1.10 5.03

12.873 190.532 46.239 46.774 -1.15 6.77

12.868 190.703 46.599 47.111 -1.09 5.71 12.868 191.454 48.097 48.616 -1.07 4.21 12.868 192.397 49.969 50.523 -l.iO 3.45

12.865 196.505 58.521 58.995 -0.80 1.47 12.861 203.573 73.642 73.948 -0.41 0.51 12.857 209.295 86.110 86.266 -0.18 0.19

12.851 218.622 106.682 106.607 0.07 -0.06

12.845 228.103 127.755 127.493 0.21 -0.17

12.839 238.550 151.093 150.664 0.28 -0.21

12.834 245.920 167.546 167.060 0.29 -0.21

12.829 252.972 183.347 182.778 0.31 -0.22

12.825 260.108 199.300 198.695 0.30 -0.21

12.821 267.312 215.373 214.767 0.28 -0.19

12.816 274.151 230.576 230.010 0.25 -0.16

13.756 188.969 43.856 44.457 -1.35 4.64

13.756 189.258 44.502 45.108 -1.34 4.05

13.756 189.767 45.639 46.262 -1.35 3.43

13.759 190.032 46.240 46.872 -1.35 3.19

13.755 190.172 46.549 47.183 -1.35 3.09

13.759 191.032 48.523 49.161 -1.30 2.50

13.755 190.447 47.177 47.812 -1.33 2.87 13.759 190.532 47.379 48.014 -1.32 2.80

13.755 190.738 47.840 48.478 -1.32 2.68 13.755 191.075 48.615 49.251 -1.29 2.48 13.753 192.892 52.817 53.453 -1.19 1.80 13.752 195.048 57.893 58.501 -1.04 1.31 13.752 195.065 57.928 58.542 -1.05 1.32 13.751 197.100 62.787 63.356 -0.90 1.00 13.749 200.010 69.812 70.306 -0.70 0.69

13.746 203.322 77.904 78.293 -0.50 0.44

13.744 207.197 87.439 87.726 -0.33 0.27 13.740 213.323 102.706 102.776 -0.07 0.05 13.733 222.792 126.432 126.292 0.11 -0.08

13.730 227.846 139.174 138.931 0.17 -0.12

13.727 233.272 152.884 152.544 0.22 -0.14

13.723 238.508 166.109 165.711 0.24 -0.15

13.720 242.985 177.429 176.987 0.25 -0.16

13.716 248.766 192.026 191.574 0.24 -0.15

13.713 253.111 203.005 202.554 0.22 -0.14

13.710 258.314 216.145 215.688 0.21 -0.13

13.707 262.932 227.811 227.350 0.20 -0.12

13.703 267.819 240.117 239.690 0.18 -0.11

13.703 267.886 240.288 239.861 0.18 -0.11

13.700 273.153 253.551 253.145 0.16 -0.09

14.976 187.649 43.274 43.891 -1.41 1.34 14.975 188.927 46.771 47.426 —1.38 1.18 14.978 190.532 51.216 51.918 -1.35 1.05 14.973 191.453 53.786 54.477 -1.27 0.94

14.971 194.804 63.256 63.941 -1.07 0.71 92

A-12
Table 3. Methane densities ofVennix [13J— Coniinued

MOL/L T. K P, BAR P. CALC P. PCX D, PCT

14.967 199.611 77.104 77.688 —0.75 0 4"^ W. T'O

14. OfiS 90"^ 0^4 87. 135 87.635 —0.57 0w. 0033

14.961 207 627 100.574 100 948 —0.37 0.20

14It?. O'^R 700 919 O"?"! 1 16 265 1 16.512 —0.21 0 1

1

\j , 1

1

14 9S1 921 360 141.310 141.395 —0.06 0.03

Id. It". Odft ^t'U 998 637 163 016 163 X KJyJ . 004 \J\J'-r 0.01 —0.00

'?'^f\ ^QQ 18ft 801 iOO. ( 07 0 0^ —0 09

Id. O^d, Zi'-rO VJOU 212. 140 919 Oft9 0.03 —0.01

Id. 14.. Q9H 7ZO 935 068 9^"^ 094 0 09 —0 01

Id. 099 959 036 259. 131 —0.04 0.02

Id. 01 7 9AQ Q94 989 716 282 976 —0.09 0.05

1 d. 01 9 •^01 479 t>u ^011 .0^ 8911 —0 1

9

U. IZ 0 Oft lOQ OCT 00 oco do. zoz 00 ftQQ 1i .yjKj on 0 Q97 1loO.ZO9^7/ 44. 884 — 1 99 U.oo

1ft CO/1 lOQ OCQ ^8 070 O7. iO 71ft 1 lU — 1 9=^ 1 . zo 0 41

Ifi lU. '^9R IQO ^"^2 63.513 64LIT". tJ<J«J 353 — 1.31 0.43

Ifi =190 194.419 77.509 78.329 — 1.05 0.35

16.517 198.420 91.963 92.864 —0.97 0.33

Ifi '^14 201.044 101 638 102.427 —0.77 0.27

lO. 907 770 11 9ft . 173 1 to 11^1. 97 O'ift wou —0 70 0.25

1ft =ind. 91 3 ftft8 147 It" 1 . 889 00^ 148 744 —0.58 0.21

1ft d.Oft 999 803 181.824 182.777 —0.52 0.20

1ft d.Rft 932 812 918 350 219.431 —0.49 0.19

1ft d.81 241.295 240 578 950 780 —0.48 0.19

1ft d.71 9'^4, "^31 ^70. 90ft 0971 909 605 —0.53 0.21

1ft d.ftd 9ftl 89ft '^94 "^04 ^9^ 491 —0.56 0.23

1ft A.'^Q 9ft7 883 '^46 Sft4. 'iAtt 640 —0.59 0.24

16 4SS 272.981 364.997 367 288 —0.62 0.26

17 "^70 179. 140 33.044 32 888 0.48 —0.07

17 "^70 179.830 35.849 35.772 0.22 —0.03

17 =^68 181 101. 008 \J\jO 40.651 40.700 —0.12 0.02

17 '^ft'^ Ifld. 44.1 ^4 773 55.111 —0.61 0.12

11. JUU 100 S^9 80.090 80.938 —1.05 0.24

17.555 196.384 104 601 105 638 —0.98 0.25

17.551 900 537 122.244 123 X ^0 . 296 ^ 7U —0.85 0.23

17 =;dA 908 899 157.426 158.617 —0.75 0.22

17 '^'^7 If. OO

I

217.044 192.276 193.684 —0.73 0.22 17.530 995 099 995 074 227.709 —0.76 0.24 17.522 233 079 259 963 261.996 —0.78 0.25

17.515 240.996 293 223 295 632 —0.81 0.27 17.507 250 735 333 924 336 853 —0.87 0.30 17.500 ^tJKj 958,\j'-r\j 646 366 598 370.211 —0.98 0.35 17.493 966 ^LFU. 750 1 \J\J 400 '-r\J\J 009^ 404 263 —1.03 0.37 17.486 974 303 431 t?lJ X . 136 X tJ\J 435 827 —1.08 0.39 18.495 182 834 65.518 66.743 —1.84 0.27 18.495 182 834 65.491 66.743 —1.87 0.28

18.502 175.629 31.376 31.857 —1.51 0.13

IR "^00 lO. 0\J\J 11 78( 0. 081 wo 1 49 035 43.709 —1.77 0.20

iR d.on 188 909 91.648 93.246 —1.71 0.30

Ifi lO. dOd. ^"74? IQO ^^9 102.401 104.296 —1.82 0.34

18lO. XSV^ rrOcI 1 7»J. UOW 1 17.303 119.193 —1.59 0.32

18lO. 480 T'OW 10ft 1 70. 6^t7 Uv> 1 141 XT' X . 000 558 143 673 —1.47 0.32 18.476 90^ 1 S6 163.181 165 489 —1.39 0.32

18lO. 479 T? 1 ^ 9nft 914 187.51

1

100 X 7V/ . 068 XJVJO —1.35 0.33

18lO. d.fi7 T'U I 212.424 207.694 210.472 —1.32 0.34

18.462 218.758 238.049 241.163 -1.29 0.35

18.457 223.742 261.867 265.231 -1.27 0.35

18.452 229.135 287.485 291.240 -1.29 0.37

18.448 233.395 307.683 311.741 -1.30 0.38 93

A-13
Table 3. Methane densities ofVennix [13] — Continued

MOL/L T. K P. BAR P. CALC P. PCT D, PCT

18.444 237.607 327.596 331.970 —1.32 0.39

18.439 243.055 353.252 358.014 —1.33 0.40

18.434 248.039 376.587 381.812 -1.37 0.42

18.429 253.126 400.348 405.992 -1.39 0.44

18.420 263.283 447.525 454.082 -1.44 0.47

18.411 272.927 498.737 499.450 —0.14 0.05 20 003 172.566 55.009 57.430 —4.21 0.32

19.997 178.480 90.082 93. 134 —3.28 0.36 19.988 186.850 139.761 143.501 —2.61 0.38

19.991 190.532 161.544 165.925 -2.64 0.42 19.979 196.089 194.310 198.830 -2.27 0.40

19.970 204.181 241.785 246.973 -2.10 0.41 19.963 211.525 284.629 290.457 -2.01 0.43 19.955 219.063 328.253 334.799 -1.95 0.44

19.946 227.105 374.341 381.848 -1.97 0.47

19.938 235.300 421.001 429.484 -1.98 0.50

19.929 244.174 470.891 480.637 -2.03 0.53

19.919 253.828 524.859 535.856 -2.05 0.56

19.913 259.343 555.441 567.200 -2.07 0.58

19.905 267.733 601.053 614.570 -2.20 0.63

19.898 274.489 638.125 652.480 —2.20 0.65 21.221 172.766 113.831 119.246 —4.54 0.42 21.216 176.889 142.805 148.646 -3.93 0.42

21.211 181.669 176.336 182.542 —3.40 0.42 21.201 189.783 232.523 239.707 -3.00 0.44 21.207 190.532 237.772 245.506 —3.15 0.47 21.193 197.315 284.387 292.377 —2.73 0.45 21.186 204.169 331.269 339.933 -2.55 0.46 21.176 212.644 388.576 398.246 -2.43 0.48 21.158 228.430 493.464 505.405 -2.36 0.52 21.150 235.778 541.550 554.696 -2.37 0.55 21.138 247.380 616.528 631.777 -2.41 0.59 21.131 252.992 652.311 668.704 -2.45 0.61 22.419 168.753 169.422 177.589 -4.60 0.42 22.405 180.116 262.685 271.707 —3.32 0.41 22.395 188.528 330.450 340.419 -2.93 0.42 22.400 190.532 346.440 357.440 -3.08 0.45 22.385 196.791 396.392 407.118 -2.63 0.42 22.376 204.366 455.919 467.593 -2.50 0.43 22.368 211.255 509.403 522. 106 —2.43 0.45 22.360 218.293 563.516 577.319 -2.39 0.46 22.350 226.285 624.075 639.303 -2.38 0.49 22.340 234.420 685.032 701.878 -2.40 0.51

94

A-14
Table 4. Methane densities of Douslin et al. [22]

MOL/L T, K P. BAR • P, CALC P, PCT D, PCT

0.750 273.150 16.376 16.377 -0.00 0.01 0.750 298.142 18.020 18.020 0.00 0.00 0.750 303.143 18.347 18.348 -0.00 0.00 0.750 323.140 19.656 19.658 -0.01 0.01 0.750 348.143 21.292 21.292 0.00 -0.00

0.750 373.150 22.925 22.923 O.OI -0.01

0.750 398.160 24.557 24.551 0.03 -0.03

1.000 273.150 21.558 21.559 -0.01 0.01 1.000 298.142 23.786 23.787 -0.01 0.01 1.000 303.143 24.232 24.232 0.00 -0.00

1.000 323.140 26.006 26.007 -0.00 0.00

1.000 348.143 28.221 28.219 0.01 -0.01

1.000 373.150 30.431 30.425 0.02 -0.02

1.000 398.160 32.637 32.627 0.03 -0.03

1.500 273.150 31.539 31.545 -0.02 0.02

1.500 298.142 34.993 34.999 -0.02 0.02

1.500 303.143 35.685 35.688 -0.01 0.01 1.500 323.140 38.427 38.434 -0.02 0.02

1.500 348.143 41.852 41.853 -0.00 0.00

1.500 373.150 45.267 45.260 0.02 -0.02

1.500 398.160 48.676 48.656 0.04 -0.04

2.000 273.150 41.053 41.063 -0.03 0.03 2.000 298.142 45.804 45.817 -0.03 0.03 2.000 303.143 46.753 46.764 -0.02 0.03 2.000 323.140 50.530 50.538 -0.01 0.02 2.000 348.143 55.222 55.232 -0.02 0.02 2.000 373.150 59.920 59.905 0.02 -0.03

2.000 398.160 64.582 64.561 0.03 -0.03

2.500 273.150 50.139 50.158 -0.04 0.04 2.500 298.142 56.263 56.286 -0.04 0.04 2.500 303.143 57.485 57.506 -0.04 0.04 2.500 323.140 62.343 62.364 -0.03 0.04

2.500 348.143 68.390 68.403 -0.02 0.02 2.500 373.150 74.424 74.411 0.02 -0.02

2.500 398.160 80.411 80.392 0.02 -0.02

3.000 273.150 58.842 58.875 -0.06 0.06 3.000 298.142 66.415 66.451 -0.05 0.06 3.000 303. 143 67.940 67.958 -0.03 0.03 3.000 323.140 73.926 73.958 -0.04 0.05 3.000 348.143 81.391 81.413 -0.03 0.03 3.000 373.150 88.835 88.825 0.01 -0.01

3.000 398.160 96.229 96.201 0.03 -0.03

3.500 273.150 67.222 67.258 -0.05 0.06 3.500 298.142 76.307 76.356 -0.06 0.07 3.500 303.143 78.146 78.166 -0.02 0.03 3.500 323.140 85.324 85.367 -0.05 0.05 3.500 348.143 94.279 94.310 -0.03 0.03 3.500 373.150 103.203 103.198 0.00 -0.00

3.500 398.160 112.073 112.039 0.03 -0.03

4.000 273.150 75.307 75.354 -0.06 0.07 4.000 298.142 85.992 86.049 -0.07 0.07 4.000 303.143 88.142 88.175 -0.04 0.04 4.000 323.140 96.585 96.638 -0.06 0.06 4.000 348.143 107.094 107.143 -0.05 0.05 4.000 373.150 117.577 117.581 -0.00 0.00 4.000 398.160 127.993 127.961 0.02 -0.02

4.500 273.150 83.156 83.208 -0.06 0.07 4.500 298.142 95.511 95.577 -0.07 0.08 4.500 303.143 98.002 98.035 -0.03 0.04 95

A-15
Table 4. Methane densities of Douslin et al. [22] — Continued

MOT /T T, K P. BAR P CALC P. PCT D PCT

^9^ i4.n 107.779 107 890 —

A/1 U4 nU. ndUt*

4. ^ifln Ot'O. ItTiJ 119.920 119.965 —

A/1 U4 0.04

4. ^inn ^75 1 c:a 1 39 013 139 L yj . 030 \JyJ\J —

AlUl 0.01 398.160 144 083 144.026 u

A/1 U4 —nU. ndUt* o. nnn uuu 273.150 on Hn9 on7U.0U0 8ft8 —

vl nU.U7no

298.142 1 nd 01

ind 1 Wt. oftfi 70U —

A'7 U/ nu.uon8

J. nnn uuu 303.143 in? 7d'^ in? lyj i , 709 1 7Z1 —0 A/1 U4 nu.uo o.uuu ^ nnn 323. 140 1 IR 01 9 1110. 1 8 0ft9 7UZ —0 A/1 U4 nu. uo

o.uuu nnn 348.143 1 "^9 781 11 OZ19 . 897 OZ

—

AQUo nU.U4' nd

o.uuu nnn 373.150 iT-u . 000 idfi finn —

AlUl 0u. niu 1 o.uuu '^ nnn 398.160 IfiO I 'Kd.f, \J\J, o^u 160 1 yjyj . 903 Ldjyj U AQUo —0.03

'^nn o. ouu 273.150 08 "^T^ 98.381 —

A'7 U/ 0.08

t^nn o. ouu 298.142 1 14.261 114.327 —

AAUO 0.06

t^nn o. ouu 303.143 1III, 1 7 ddO T'T'

1 17.498 —

A/1 U4 0.05

cinn

o. ouu 323.140 1 ^n n'ln 130. 1 19 —

A7U / 0.07 O.oUU 348.143 14-0. 7d8 1 4'0 Id"! i^-o . 787 / 0 / —

AQUo nu.uoni

O.OUU 373.150 IQ 1 . OZ

lAl I'^l —

AOUz nu.uzn9

O.OUU 398.160 11 7f> i u . 887 00 i i 1 U. OZ i 0 AQUo —0 ni

Ao.uuu nnn 273.150 in'^ lUO.OOU fific\ 105 703 —0 1 1 nu. 1310 A Ann o.uuu 298.142 19"^ IZO.OoO '^8'i 1I ZO91 . f\^(\ uou —0 AC05 nu. n^uu

A nnn O.uuu 303.143 197 iZ / . i^>n lUU 197 1 Z ( . 9n9 zuz —

AQUo nU. ndUt" O.UUU 323.140 Idl 9A1 Idl 1d9 —0 A/: 06 nU. nAUD

O.UUU 348.143 IO0.07O 1100. on9 7UZ -0 00 nu. nnuu

A AAA O.UUU 373.150 1 7f\ ^na 1 7A 1d8 -0 02 nu. n9uz

/: HAA O.UUU 398.160 IQO 7AI I70. /Ui 101 1 70.074' AOd 0 00 —nu.uunn

O.OUU 273.150 1110. 1 ^ n'^i uo

111 1 ^ll i 10. 100 -0 08 nU. inlU

0. OUU 298.142 1 ^9 Odl 1100. 13 007* -0 05 0.05 A "^nn O. OUU 303.143 1iOU. Ifi 091 7Z 1 1100. 16 058 700 -0 03 0.03

A C^AA 0. ouu 323.140 110Z.U7Z =^9 fi09 11 0^'^9 . fiOl U7 1 0.00 —0.00

A c^AA O.oUU 348.143 179 IQ'^ 172.234 -0.02 0.02

A c:nn 0. ouu 373.150 101 1 7 1 . 000 585 191.655 -0.04 0.03

f\O.OUU "^nn 398.160 z911i 1 .UniX 0 9Z 11 nU. OAA 7OO 0 02 —nu. n9uz

7i . nnn UUU 273. 150 1i ZU9n . dod ^74" 1 9n '^i

i ZU. 0 1 u -0 01 nu. n9uz

7/ .uuu nnn 298. 142 1 d9 dl 1 1 d9 d'^1 -0 03 nu.uoni

7 AAA / .uuu 303. 143 IdA Hno 114-O.ozz dA 899 -0 01 nU.Ulm

7 AAA i .uuu 323. 140 lAd 104-. 9n8 zUo lAd 104-. ZZO 99R -0 01 nU.Ulni

7 AAA ( .UUU 348. 143 loO.oOO IOC OCA loO.oOU 0 01 AU.Ulni

7 AAA ( .UUU 373. 150 ZU9A7 %A.7 / . 0^ I 907 ZU / .o4'0 IdA 0 00 —nu.uunn

7 AAA ( .UUU 398. 160 998 ZZo. 7nA / UO 998 ZZo. 799 1 ZZ -0 01 nU.Ulni 7 CAA ( .OUU 273 150 1 97 ai^d IZ ( .oO^- 1IZ97/ .7I0 Oil -0 05 n n"^ u. uo

/.OUU 298 142 1loz.u^-u ^0 ndn 110z.U4'4' CL9 ndd -0 00 nu. nnuu

7 CAA < .OUU 303 143 1100. RA 7P^ too 100. oOl -0 04 nU.U4' nd

71 . ouu inn 323 140 17 c; AAA 1 i 0 . 700 11 7A/ D.UUnn?t -0 02 nu.uzn9

7 t^AA

/ .ouu 348 143 lOQ 1 77. Hn? oU 1 100 1 77.0Z8911 -0 01 nU.Ulni

7 tinn

/ .ouu 373 150 991 ZZO.^I'U ddn ZZo. 991 d07 47 1 -0 03 nu.uzn9

7 tinA /.ouu 398 160 9d7 ni^i Z'* / .UOO Z^9d7 nd'i / .U40 0 00 —nu.uuno

Q AAA H.UUU 273 150 11O0.4-1U din IQC 100. /II 4*1 7/ -0 01 nU.Ulni H.UUU Q AAA 298 142 lAl 101.0871to lAi 101 .044 add 0 02 —nu.uzn9

Ho. nnn uuu 303 143 1 A7 1 1'^ 10 1 . 100 110A71 . ill 1 1

0 01 —nU.Ulni o.uuu H nnn 323 140 1loo. 88 1i^-Z d9 188 loo. ino IU7 0 02 —nu. 09uz

O.UUU Q AAA 348 143 91Z14-.Z10 d 918 91Z 14.d 999 ZZZ -0 00 0u. 00uu

Ho.uuu nnn 373 150 9dn Z^-U.Un78/ 0 9dn Z^U. 109 I7Z -0 05 0yj . ndu^

Q AAA o.uuu 398 160 9AA zOO.Uzo n91 9AA ZOO.UZO n91 -0 00 nu.uunn

n cinn O.OUU 273 150 1140. dl non uvu Idl 140.U0U nan 0 01 —nU.Ul01 8.500 298 142 171.979 171.918 0 04 —0.04

8.500 303 143 177.736 177.669 0 04 -0.04

8.500 323 140 200.673 200.604 0 03 -0.03

8.500 348 143 229.193 229.139 0 02 -0.02

8.500 373 150 257.427 257.522 -0 04 0.03

A- 16
Table 4. Methane densities of Douslin et al. [22] — Continued

MUL/L P R A R r , r 1 D, PCT

8.500 398.160 285.758 285.756 0.00 -0.00

9.000 273.150 151.095 150.964 0.09 -0.09

9.000 298. 142 182.470 182.341 0.07 -0.07

9.000 303.143 188.733 188.602 0.07 -0.07

9.000 323.140 213.759 213.577 0.09 -0.08

9.000 348.143 244.766 244.660 0.04 -0.04

9.000 373.150 275.434 275.585 -0.05 0.05 9.000 398.160 306.209 306.349 -0.05 0.04 9.500 273.150 159.307 159.142 0.10 -0.10

9.500 298.142 193.423 193.194 0.12 -0.11

9.500 303. 143 200.116 199.993 0.06 -0.06

9.500 323.140 227.366 227.118 0.11 -0.09

9.500 348. 143 261.024 260.888 0.05 -0.04

9.500 373.150 294.478 294.490 -0.00 0.00 9.500 398.160 327.865 327.918 -0.02 0.01 10.000 273.150 167.979 167.694 0.17 -0.16

10.000 298.142 204.825 204.570 0.12 -0.11

10.000 303.143 212.100 211.935 0.08 -0.07

10.000 323.140 241.534 241.329 0.09 -0.07

10.000 348. 143 278.048 277.931 0.04 -0.03

10.000 373.150 314.250 314.355 -0.03 0.03

10.000 398. 160 350.494 350.589 -0.03 0.02 10.500 273.150 177.002 176.711 0.16 -0.15

10.500 298.142 216.938 216.570 0.17 -0.14

10.500 303.143 224.805 224.534 0.12 -0.10

10.500 323.140 256.572 256.321 0.10 -0.08

10.500 348.143 296.014 295.912 0.03 -0.03

10.500 373.150 335.101 335.310 —0.06 0.05

10.500 398. 160 374.301 374.500 —0.05 0.04

11.000 273.150 186.780 186.294 0.26 —0.22

11.000 298. 142 zzy. OOO OOA OAT 229.30/ A 1 "7 0. 1 / —0. 13

1 1 AAA 11.000 303.143 238.292 237.903 0.16 —0.13

1 1 AAA 11.000 323.140

0*70 cork 272.539 272.219 0.12 —0.09

1 1 AAA ll.OOU 348.143 315.031 314.962 0.02 —0.02

1 1 AAA ll.OUU 373.150 ^JCT OAT

357.495 —0.06 0.04

1 1 AAA ll.OOU 398.160 Of\f\ COO 399.523 399.798 —0.07 0.05

1 1 CAA 11.500 273.150 197.051 196.557 0.25 —0.20

1 1 CAA 11.500 298.142 243.451 242.905 0.22 —0.17

1 1 CAA 11.500 303.143 252.507 252.170 0.13 ^ 1 A —0.10

1 1 CAA 11.500 323.140 289.542 289.157 0.13 Y\ 1 A —0.10

1 1 CAA 11.500 348.143

OO C 1 i\A 335.104 335.226 —0.04 A AO 0.03

1 1 CAA 11.500 373.150 OOA Oiiii 380.OOO 381.064 —0.05 A A/fl 0.04

1 O AAA iz.oou 273.150 OAO Oil 208.211 207.621 0.28 —AO! U.zl

1 O AAA 12.000 298.142 OC7 f\Cf\ 257.950 257.501 0.17 A 1 O —0.12

1 O AAA 12.000 303.143 0£T OOO 267. 883 267.472 0.15 —0.11

1 O AAA 12.000 323.140 307.555 307.281 0.09 —0.06

1 O AAA 12.000 348.143 356.651 356.860 —0.06 0.04

1 O AAA 12.000 373.150 ylAC AOO 405.932 406.182 —0.06 f\ f\A 0.04 12.500 273.150 220.275 219.620 0.30 -0.21

12.500 298.142 273.788 273.241 0.20 -0.13

12.500 303.143 284.252 283.960 0.10 -0.07

12.500 323.140 326.974 326.751 0.07 -0.04

12.500 348.143 379.993 380.035 -0.01 0.01

A-17
3. The Coexistence Densities The argument (o is defined

To obtain densities of freezing and of saturated

liquid, we represent initial points of each experimental pseudo-isochore from table 1 by

P=A + B T+CIT+DIT^ (1)

used for extrapolation to the P{T) melting- and vapor- pressure hnes of [7] respectively. Adjustment is made for the negligible change of density over the

range of extrapolation. On the melting line, we obtain

three densities to a maximum pressure of 220 bar. On the vapor pressure Hne, we obtain 19 densities to a maximum temperature of 175 K. Vapor densities are obtained by use of the virial equation of [5] and

vapor pressures of [7] to a maximum temperature

of 175 K. The analytical functions used to represent these

densities are given in the appendix. The singlevalued function Tgip) for coexisting vapor and liquid

then was adjusted to data from the above functions.

We omit details of aU this tedious work because they

are not essential to development of the equation of

state. They will be given in later reports. For the

saturated liquid, however, we give in Appendix

table 1 the derived and calculated densities because

these are of especial technological importance.

4. The Equation of State

On the notorious problem of the equation of state

[14, 14a], we have investigated further a form which is nonanalytic at the critical point [15], rectifying one

defect and making simplifications. For background, it was found with hydrogen that an excellent isochoric

equation is of the form

(Z-l) xlp=A + B-T+CIT-\- DIT\ (2)

provided we avoid the neighborhood of saturation and

that we modify the second term on the right for consistency with high-temperature behavior of the second

virial coefficient. We then modified the last term on the

right to obtain Cv—*'^ on approach to the critical point, as computed along the critical isotherm by means of the thermodynamic relation

CAp,T) = C%{T)-T- j\d^PldT^)odplp^. (3)

We now have developed the following isochoric

equation of state for methane via many exploratory

computations

(Z-l) - xlp = A + B ^{T) + Clx + D • ^ip,T). (4)

The temperature-dependent functions are

^{T) =x- [l-expi-b-pix)], (4a)

^(p,r) = [1 -co- In (1 + 1/0)) ]/jc. (4b)

<o{p,T)^ {T-d)l{8-Tc) (4c)

by use of the locus of temperatures

dip) ^ n(p) • exp [-u(o-)/2], (4d)

where «(o") is defined

uicT)^a^-[\<T-l\^-{(T-m

+ a,-[|o— l|3+(cr-l)3].

The saturation temperatures Ts{p) are given in the

appendix.

Density-dependent coefficients of (4) are formulated

as power series,

3 2 A{p)^yAi-p\ B{p)^\Bi-p\

dp) - i Cr pi. Dip) ^ia-D-^Di- p'.

!=1 i=0 An essential modification from [15] is the above

formulation of dip). The quadratic (cr — 1)^, formerly

used in the exponential, gives a logarithmic infinity

in d^P/dp^ at the critical point.

Coefficients of (4) are found by least squares after multiplying each polynomial throughout by its temperature-dependent factor. Via the least squares program

[16], we impose four constraints: the pressure shall be

our assigned values at the triple- and critical-points;

and we shall have dPjdp = d^P/dp^ = 0 at the critical point.

Experimental PVT data from four sources cover

virtually the entire domain of interest here, namely

Tt<T < 4:00 K and P ^ 350 bar. Table 5 gives these sources and the range of their data in T, P, and d. We then give the number of data, N, selected for present work. The last two columns give the mean of

relative pressure deviations AP/P and the rms of

relative density deviations Adjd, each from eq (4) with constants given below.

The constants of eq (4) for methane are given in the

last column of table 6. Behavior of the coefficients A(p) . . . D(p) is quite similar to plots given in [15].

A calculated table of P and of dPIdp along the critical isotherm shows that dPldp=0 at the critical point,

and dPIdp > 0 at all adjacent densities. Higher

derivatives through d^Pldp"^ also should be zero

at the critical point according to a recent scaUng-law

equation of state [17], but we have not investigated

these for eq (4). Complete PVT data and deviations are given by

tables 1 through 4 in response to readers' requests.

The source of data is given by the heading for each

table. Columns give the density in mol/1, the temperature, the pressure, the calculated pressure, and, in the last two columns, the relative deviations of pres- 98

A-18
Table 5. Data used for the equation of state

Source Range of the data A, %

T, K P, bar d, mol/1 N P d

140-270 5-46 0.5-2.0 96 0.05 0.09 172-273 25-400 2.5-17.5 133 0.22 0.26 This report 94-245 20-350 18-28.5 279 0.66 0.03 Douslin [22] 273-398 16-400 0.75-12.5 171 0.05 0.06

sure and of density from eq (4), respectively, expressed

in percent.

The reader should note that the derivative (dPI

dph approaches zero at the critical point. Density

deviations in this region (Vennix data) therefore should

be ignored. This derivative becomes extremely large, on the other hand, for compressed liquid at low temperatures, and here the pressure deviations (NBS

data) should be ignored.

5. Comments on the Equation of State

Equation (4) yields the perfect gas law^ Z = 1 in the limit of low density. In the hmit of high temperature it approximates the perfect gas, and yields Z = 1 for the special case b = 0. Due to its structure and

relatively small number of least-squares coefficients,

iit tends to preserve important qualitative characteristics of the P{p,T) surface. Among. these are consistency with the known behavior of some specific

heats [18]. For methane, we have examined the

shape of isochores from eq (4), finding that they have

monotonically negative curvature, d^P/dT^, at p < pc; a sigmoid shape in the range 1 < p/pc < 2; and (unlike

hydrogen) negative curvature again at higher densities.

The critical isochore has a very small, positive curvaTable 6. Constants of equation (4) for H2. O2, and CVU

Corjstant Hydrogen Oxygen Methane

Tu K 13.800 54.3507 90.680

Tc, K 32.962 154.52 190.53 d„ mol/1 38.203 40.83 28.1472

dc. mol/1 15.59 13.52 10.15 Pu * 0.0695 0.0015 0.1174

Pc, * 12.704 49.650 45.957

"b 0.3 0.4 0.5

«! .1 .4 .5 b .8 1 .8 7 3 4

8 1 1 1.2 Ao -3.6990 3501 -4.7457 9188 -4.1545 2847

A, -1.5630 8113 -3.6883 8499 -4.7739 0186

A2 5.0231 6164 -1.1695 4201 3.5199 9044

A3 -0.7443 2571 8.2956 4587 4.2573 7412

Bo 1.2426 3871 2.0447 2804 1.7474 4656

fi. 0.6032 6565 2.5732 0035 2.5767 9569

B, .0692 4977 2.1530 4750 0.4653 8980

c, 3.9354 2987 5.3321 8510 5.1033 5931

C2 -9.9450 4679 -13.4213 9863 -12.4202 2748

C3 5.7268 9781 7.6933 8807 6.3612 4273 Do 1.0188 2911 1.7942 7732 1.8838 3919 -2.1414 4245 -3.1707 7491 -3.5471 3477

1.2924 7888 1.2788 3788 1.8740 8815

*For H2 and O2 the equation of state is in atmospheres; for CH*. in bars.

ture at the critical point, similar to results for hydrogen

[15].

The nonanalytic function ^{p,T}, eq (4b), is de- signed to give a large increase of Cv upon close

approach to the critical point. It is similar to that used

for hydrogen [15], through transformation of variables.

Via the definition (4c) for w(p, T), however, we now

have the fact that ^(p,T) exists in the Hmit B^Q,

whereas formerly it vanished. This function ^ behaves

like 1/T^ at high temperatures. At low temperatures,

it terminates with a value of 1/x on the locus of temperatures d{p) inside the coexistence envelope,

at which point it gives infinite curvature d'^PIdT^. As density increases through the critical point, the sign

of this curvature is reversed by means of the root

(cr — 1 ) in the formula for coefficient D{p).

Temperature dependence in eq (4) is similar to that of the well-known Beattie-Bridgeman equation,

(Z-l) xlp = A+B x + DlxK (5)

in domains away from saturation. In particular, the

absence of a constant term in our formula for C(p) means that a term in l/T- is missing from description

of the second virial coefficient, consistent with (5). We have used eq (4) for extrapolation at pressures

up to 700 bar (10,000 psi) along isochores at T ^ 400

K, finding that the pressure increases monotonically

and that the derivatives dP/dT and dPjdp are well- behaved. This is noteworthy for the compressed liquid

at low temperatures because few if any of the well- known equations of state can pass this test and at the same time represent PVT data over the enormous

range of the entire P{p, T) surface, from ideal gas

states up to compressed liquid states near the melting

line at low temperatures.

The number of temperature-dependent terms in equation (4) appears to exceed the number needed for quahtative description of isochores. The second term

on the right gives weak negative curvature at high

temperatures, and the last term may give curvature of

either sign at low temperatures. We have, indeed,

formulated an equation like eq (4) for methane,

omitting the term C{p)lx [19]. This was prior to our PVT measurements on the compressed Hquid. As

with hydrogen, we have found a term in 1/x necessary on the right of eq (4) to obtain a reasonably precise

representation of PVT data when these include the

compressed Hquid states. We have applied the present equation of state to hydrogen and to oxygen without any special difficulties, indicating therefore that it is not unique for 99

-19

453-425 OL - 72 - 3
methane. Densities for these other gases also ranged

up to the melting line. Saturation temperatures

Tsip) are given in [21]. In some cases the coefficients

A3 and ^2 for eq (4) show a low significance, sug- gesting that the corresponding terms of eq (4) might

be omitted when PVT data extend to densities no

higher than about 2-pc. In table 6 we see that coefficients for all three substances are similar and

mostly of the same sign.

(3) The saturated vapor densities are described mere simply than in [6] by

5 \n{dJdc)=Ai W + A2 - w'l^ + ^Ai • u'-2,

where

u^iTc-T)liTc

i = 3

T,), w^{TclT-l)l{TclT,-l),

The authors are indebted to R. D. McCarty for use

of the least squares program open to constraints

[16], and to O. E. Diller and L. A. Weber for many

discussions and important suggestions.

6. Appendix

6.1. Functions for Densities on the

Coexistence Boundaries

(1) The freezing liquid densities are described by

dld,^{TIT,)^i\

a form developed for hydrogen [20].

(2) The saturated liquid densities are described

as in [6] by

dildc=l + a- z+b- z'^-^^' + c- exp[-€-x^lz],

where x = TI Tc , z ={1 — x) , and

G = 0.539 403

fc= 1.896 635

c = -0.018387.

e= 0.88. The triple point liquid density from this equation is

(if = 28. 1472 mol/1. Derived and calculated values

are given in Appendix table 1 below.

Table A1. Derived and calculated densities of saturated

liquid methane

T, K Mol/1 Calculated Percent

175.053 18.390 18.392 -0.01

169.326 19.492 19.492 0.00 163.699 20.428 20.425 0.02 157.199 21.379 21.379 -0.00

151.555 22.130 22.131 -0.00

145.448 22.880 22.882 -0.01

139.352 23.578 23.581 -0.01

133.773 24.186 24.186 0.00 133.878 24.176 24.175 0.01 129.657 24.611 24.613 -0.01

125.825 24.999 24.999 0.00 121.893 25.388 25.383 0.02 117.746 25.782 25.778 0.01 113.772 26.146 26.147 -0.00

109.611 26.527 26.525 0.01 105.165 26.916 26.919 -0.01

101.434 27.243 27.243 0.00 97.173 27.605 27.606 -0.01

93.512 27.910 27.913 -0.01

^,=-6.815 239,

^2 = -2.012 860,

^3= 1.203 942,

^4 = 0.736 090,

^5 = 0.416 449.

(4) The saturation temperature Tsip) for coexisting

vapor and liquid are described here by a function

which is constrained to the triple point, in contrast with our earlier form [21]. Define the variables.

YiTs)^ {TclTs-l)l{TclTt-l),

U{p) - (o--l)/(o-,-l),

i=2

where cxt is the constant, dijdc. The function now is K ( ) = . [1 + ^ ,

. In (p ) + (p - 1 )

. F (p ) ], ^,=-0.814 6680,

^..= 2.482 4192,

^3 = -6.872 7440,

^4= 43.037 4662,

^5 = -142.308 6536,

A6= 240.076 9868,

^7 = -195.876 1459,

As= 63.3001385.

7. References

[1] Tester, H. E., Methane, in Thermodynamic Functions of Gases, Vol. 3, F. Din, Editor (Butterworths, London, 1961).

[2] Zagoruchenko, V. A., and Zhuravlev, A. M., Thermophysical

Properties of Gaseous and Liquid Methane, (Moscow, 1969). National Technical Information Service, Springfield, Va.

22151.

[3] van Itterbeek, A., Verbeke, O., and Staes, K., Measurements

on the equation of state of liquid argon and methane up to 300 kg/cm- at low temperatures, Physica 29, 742 (1963).

[4] Dobrovol'skii, O. A., Belyaeve, T. N., and Golubev, 1. F., Gazovaya Promyshlennost' 11:47 (1964).

[5] Goodwin, R. D., Thermophysical properties of methane: virial coefficients, vapor and melting pressures, J. Res. Nat. Bur. Stand. (U.S.), 74A (Phys. and Chem.), No. 5, 655 (Sept.- Oct. 1970).

[6] Goodwin, R. D., Thermophysical properties of methane:

orthobaric densities and some thermal properties, J. Res.

Nat. Bur. Stand. (U.S.) 75A (Phys. and Chem.), No. 1, 15 (Jan.-Feb. 1971).

[7] Prydz, R.. and Goodwin, R. D., Experimental melting and vapor

pressures of methane, submitted to J. Chem. Thermodynamics, 1971.

[8] The international practical temperature scale of 1968, Metrologia 5{2),35-49(1969).

[9] Goodwin, R. D., Apparatus for determination of PVT relations and specific heats of hydrogen to 350 atm at temperatures above 14 K, J. Res. Nat. Bur. Stand. (U.S.) 650 (Phys. and

Chem.), No. 4, 231 (July-Aug. 1961). 100

A-20
[10] Weber, L. A., P-V-T, thermodynamic and related properties of oxvsen from the triple point to 300 K 'it pressures to 33 MN/m^ J. Res. Nat. Bur. Stand. (U.S.) 74A (Phy^. and Chem.),No. 1,93 (Jan.-Feb. 1970).

[11] Straty, G. C, and Prydz, R., Fluorine-compatible apparatus

for accurate PVT measurements. Rev. Sci. Instruments 41 (8), 1223(1970).

[12] Prydz, R., and Straty, G. C., The thermodynamic properties

of compressed gaseous and liquid fluorine, Nat. Bur. Stand.

(U.S.), Tech. Note 392, 182 pages (Oct. 1970).

[13] Vennix, A. J., Low temperature volumetric properties and development of an equation of state for methane. Thesis, Dept. of Chem. Engineering, Rice Univ., Houston, Texas,

April 1965.

[14] Tsonopoulos, C., and Prausnitz, J. M., Equations of state: a review for engineering applications. Cryogenics 9 (5), 315

(Oct. 1969).

[14a] Macdonald, J. R., Review of some experimental and analytical equations of state. Rev. Mod. Phys. 41,316-349 (1969).

[15] Goodwin, R. D., Formulation of a nonanalytic equation of state

for parahydrogen, J. Res. Nat. Bur. Stand. (U.S.), 73A

(Phys. and Chem.). No. 6, 585 (Nov.-Dec. 1969).

[16] Hust, J. G., and McCarty, R. D., Curve-fitting techniques and

applications to thermodynamics. Cryogenics 7 (4), 200

(Aug. 1967).

[17| Jansoone, V., Gielen, H., de Boelpaep, J., and Verbeke, O. B., The pressure-temperature-volume relationship of methane

near the critical point, Physica 46, 213 (1970).

[18| Diller, D. E., The specific heats C, of dense simple fluids. Cryogenics 1 1 (3), 186 (June 1971).

[19| Private communication 9781 (methane), this laboratory, Feb. 1, (1971).

[20] Goodwin, R. D., Density-temperature formulae for coexisting

liquid and vapor and for freezing liquid parahydrogen, J Res. Nat. Bur. Stand. (U.S.), 70A (Phys. and Chem.), No. 6, 541 (Nov.-Dec. 1966).

[21] Goodwin, R. D., Estimation of critical constants, Tc, pc from

the p{T) and Tip) relations at coexistence, J. Res. Nat.

Bur. Stand. (U.S.), 74A (Phys. and Chems), No. 2, 221 (Mar.-

April 1970).

[22] Douslin, R. D.. Harrison, R. H., Moore, R. T., and McCullough,

J. P., P-V-T relations for methane, J. Chem. and Eng. Data

9(3)358(1964).

(Paper 76A2-702)

101

A-21

APPENDIX B

APPENDIX B

Cryogenics Division - NBS Institute for Bosic S4anckirds LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 72-3

PAGE

1

SUBJECT Orthobaric Dejisities of Methajie Near the Critical Point

NAME R. D. Goodwin

February 26, 1972

These densities are important for computing the heat of vaporization via the

Clapeyron equation, and hence thermodynamic functions for the compressed liquid

states

.

We use recent values for the critical constants, communicated by Prof. Olav

B. Verbeke: = 190. 53 on the IPTS-1968, and = 10. 20 mol/i. These are from

his preliminary analysis of his dielectric constants obtained here in the summer of

1971 with the apparatus of L. A. Weber [l].

We have derived some densities from a formula given by Ricci and Scafe in

1969 [2], based on dielectric constants at 185 ^ T < T^:

A (1 - T/T)' (1)

= 10. 35 ± 0.13 mol/i,

A = 1. 89 ± 0. 09,

Tc = 190. 57 ± . 05 (1948),

B = 0. 367 + 0. 1 .

To obtain densities from (1), we formulate the rectilinear diameter from our

densities [3] at 175 K:

R. D. = (p^ + pg)/2 = p^ + 6 • z,

where z = (1 - T/T ), to obtain in mol/i,

(2)

p^ = R. D. + 19. 56 •

, (3a)

p = R. D. - 19. 56 • z^ . (3b)

Uncertainty in the coefficient, 19. 56, is 6%, corresponding, for example, to an

uncertainty of 0. 32 mol/i at 185 K. For the vapor, this is six percent. Results

are given in Table 1.

In 1970 Jansoone et al gave intersections of PVT isochores with the vapor

pressure curve [4]. In table 2 we make selections from their data, convert the

T-scale, and convert volumes to densities.

In a private communication from Professor Verbeke, we have a graph of his

preliminary results of last summer. From this we have read the results given here

in Table 3. For comparison, Table 4 gives vapor and liquid densities taken from

Report 10 715.

Figure 1 is a plot of some of these data. Filled circles are from Table 1; open circles from Table 2. Two values from Table 3 are shown by x; and four values

from Table 4 by circles with tails.

B-1
Cryogenics Division - NBS Institute for Basic Stondords LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 72-3

PAGE 2

SUBJECT Orthobaric Densities of Methane Near the Critical Point

'^^'^^R. D. G.oodwin

°*^^February 26, 1972

We see from this figure that data of Jansoone et al and the recent preliminarydata of Verbeke are in good agreement at 190 < T < T^,, and that they agree with

results derived from Ricci and Scafe in this range.

We see that liquid densities from Report 10 715 agree with above data, but

that vapor densities are roughly 3% low.

Currently we are obtaining dielectric constants with the apparatus of

Younglove and Straty [5] in order to derive densities over the wider range

170 < T < Tc.

We are indebted to the American Gas Association for generous support of this

work.

REFERENCES

[1] L. A. Weber, Advances in Cryogenic Engineering , vol. 15, p 50 (Plenum Press,

N. Y. , 1970).

[2] F. P. Ricci and E. Scafe, Physics Letters 29A (11), 650 (1969).

[3] R. D. Goodwin, NBS Report 10 715 , this lab., Sept., 1971.

[4] V. Jansoone et al. Physic a 46, 213 (1970).

[5] B. A. Younglove and G. C. Straty, Rev. Sci. Instruments 41(7) , 1087 (1970).

Table 1. Orthobaric densities via Ricci and Scafe

T, K Density, mol/i

(1948) (1968) Vapor Liquid Mean

185 185.030 5.038 15.710 10.374

186 186. O3O5 5.384 15.302 10. 343

187 187.031 5.786 14.836 10.311

188 I88.O3I4 6.275 14.285 10.280

189 189.031g 6.918 13.578 10.248

190 190.032 7.960 12.474 10. 217

V 1l)4?« B-2
Cryogenics Division - NBS Institute (or Basic Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 72-3

PAGE

3

SUBJECT Orthobaric Densities of Methane Near the Critical Point

NAMEj^^ D. Goodwin

''^^^ February 2 6, 19 72

Table 2 Orthobaric densities of Jansoone et al

T K Density

ID mol/i

5 187. 437 187. 469 14 582

9 189. 279 189. 311 13. 300

1 3 189. 675 189. 707 1 2 87Q

17 190.016 190. 048 12. 397

21 190. 284 190. 316 11. 824

25 190. 410 190. 442 11. 367

36 190. 483 190.515 in 7Q

A

37 190.498 190. 530 10. 059

50 190. 492 190. 524 9. 686

55 190. 448 190. 480 9. 161

D 1 190. 247 190. 279 Q '2 Q 9 o. jy C. Ort 190. 014 190. 046 1 Q n 1 . y JD

7 1

1 1 189. 733 189. 765 1 , DDI

Table 3. Preliminary densities of O. B. Verbeke

T, K Density, mol/i

(1948) vapor liquid

inn n c n

8. 00 12. 44

190. 150 8. 17 12. 27

190. 250 8. 36 12. 07

190. 350 8. 62 11. 79

190. 450 9. 00 11.41

Table 4. Calculated densities from Report 10 715

Density, mol/i

T,K (1968) vapor liquid

171.962 2. 647 19. 009

177. 245 3. 346 17. 912

181. 909 4. 190 16. 714

186. 087 5. 322 15. 253

189. 856 7. 555 12. 693

B-3
Cryogenics Division - NBS Institute for Basic Stondords LABORATORY NOTE

ppniprT NO 2750364

FILE NO. 72-3

PAGE

SUBJECT Orthobaric Densities of Methane Near the Critical Point

NAMEj^^ D. Goodwin

^"^^ February 2 6, 1972

185 186 187 188 189 TEMPERATURE, K

Figure 1. Orthobaric densities of methane near the critical point.

Filled circles are derived from Ricci and Scafe [z]. Open circles are from Jansoone et al [4]. Circles with tails are from NBS Report

10 715 [3]. The crosses are recent, preliminary results communicated

by O. B. Verbeke.

if 11342 A B-4 USCOMM • ERL
APPENDIX C

APPENDIX C

Cryogenics Division - NBS Institute for Basic Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 72-4PAGE

1 SUBJECT Dielectric Constants and Orthobaric Densities of Methane

NAME Goodwin

""'^ June 2, 1972

Introduction:

For the computation of methane thermodynamic functions in [1] we interpolated

orthobaric densities over the range from 175 K to 190.53 (the critical point). In [2] we

examined some data from other sources in the range 185 < 190.53 K, concluding

that some of our interpolated vapor densities were up to 2.5% too small, but that our

interpolated liquid densities were in good agreement with these other data.

We now have performed dielectric constant measurements on isotherms with

the purpose of obtaining the p(e) relationship, for use in determining saturated vapor

densities from observations of their dielectric constants alone. Critical constants used

here are T = 190. 53K, d :r 10. 20 mol/-t.

c c

Dielectric Constants on Isotherms.

We used a commercial hi^ precision capacitance bridge with the cryostat and

capacitor of [3]. Table 1 gives results taken along isotherms by releasing portions

of the sample stepwise, and waiting for restoration of isothermal conditions. The first

column gives our experimental sequence. The 100- and 600 - series are for saturated

liquid. They were measured by Gerald C. Straty. The dielectric constant is given in

column E. Densities mol /t were calculated from. T and P by an equation of state.

Densities "CALCD" are from the formula based on dielectric constants, as given in

the table heading, and discussed below.

Figure 1 is a plot of the Clausius-Mosotti function (e - 1 ) /(e + 2) /p vs. density.

The data fall within the 0. 1% range of uncertainty of the experimental densities. Figure

2 is a plot of the function ( 1 / 4tt p ) (e-l)/e recommended by J. F. Ely. As derived for

simplified theory, this function should be a constant over a range of low densities.

To simplify the computation of densities we have devised the formula

2 3 p=a-f + b.f +c-f

where p = '^^^^ density reduced at the liquid triple point d^ = 28. 1472 mol/liter, and

f(e) is defined as (1000 /4tt • d^) (e-l)/e,

a = 0.645 9274, b = 0.114 2290, c = 0.074 9169

C-1
Cryogenics Division - NBS Institute for Basic Stondords LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 72-4

PAGE 2

SUBJECT Dielectric Constants and Orthobaric Densities of Methane

NAME R. D. Goodwin

June 2, 1972

Dielectric Constants for Saturated Vapor

Table 2 gives observations obtained by slowly cooling the borab and capacitor

in steps of 0 . 1 K and waiting for restoration of equilibrium. The first several points are for the single vapor phase, as seen by the constant value of E. When E begins to drop along with teimperature , we are condensing liquid at the bottom of the bomb.

The first column is our experimental sequence; the second is temperature via

the platinum resistance thermometer (IPTS 1968); the third is pressure observed via

the dead weight gauge and the fourth is pressure from our vapor pressure equation [4],

Slope of the vapor pressure equation is DP/DT. In general, the observed pressures

are greater than the corresponding vapor pressures. Column TT gives temperatures

based on the observed pressure (via the v. p. equation). Column E is the dielectric

constant. Column mol/-t is density of saturated vapor via a formula from [1], whereas

CALCD densities are derived from the above formula for p(e).

Representation of Saturation Temperatures.

In table 3 we bring together all of the orthobaric densities, and represent

them by the TSATF(DEN) formula given in [ Ij . Identification ID = 1 at low densities

refers to data from intersections of our virial equation [5] with our vapor pressure

equation [4]; ID = 1 at high densities refers to intersections of our PVT isochores [1] with the vapor pressure equation. ID = 5 refers to Jansoon et al. ; ID = 6 refers to Ricci and Scafe, while ID = 7 refers to preliminary results by O. B. Verbeke. These

latter references are given in Lab Note 72-3 [2J. Identifications above 100 are for

data obtained via the dielectric constant. We propose to use this formula (table 3) in

future work on methane thermodynamic computations. By trial we found for these data

the exDonent 8/3 [ 1] , T = 190.53 K, d =10.2mol/^.

c c For the computation of thermodynamic properties, we often must find the

density from the formula for table 3. The initial density, needed for iteration, may

be estimated from the vapor and liquid formulas given below.

OOlLVie PRESS. INC.. BROOKLYN 17, N. Y. STOCK NO. 450 C-2
Cryogenics Division - NBS Institute for Basic Stanckirds LABORATORY NOTE

PROJECT NO. 2750364

fILE NO. 72-4

PAGE 3

SUBJECTDielectric Constants and Orthobaric Densities of Methane

NAME Q_ Goodwin

"^'^ June 2, 197 2

Vapor Densities

The vapor densities of table 4 are represented as a function of temperature by- use of the variables

u H (T /T-1)/(T /T -1), c c t

in the equation

ln(d/d

to = (T -T)/(T -T ] c c t

6 4/3 ^5/3^2

By trial we find g =0,35, Coefficients are given at the head of table 4.

Liquid Densities.

The formula developed for oxygen [6] is inadequate for methane data of table 5, Define

x= T/T and z= (1-x). The formula for table 5 is

c

B 2 3 d/d -1 =A.z +B-Z + C.Z +D.Z . c By trial we find 3 =0.36. Coefficients are given at the head of table 5, The triple point

density from this equation at T = 90 . 68 K is d^ = 28 . 1444 molZ-L,

REFERENCES

[ ij R, D, Goodwin, Tables of Provisional Values of Thermodynamic Functions for

Methane, NBS Report 10 715, September 1971,

2] R. D. Goodwin, Orthobaric Densities of Methane Near the Critical Point. Lab.

Note 72-3, February, 1972.

3] B, A, Younglove, Dielectric Constant of Compressed Gaseous and Liquid Oxygen,

J, Res, NBS, 76A (1), 37 (1972).

[4] R. Prydz and R. D. Goodwin, Experimental Melting and Vapor Pressures of

Methane, J. Chem. Thermodynamics 4, 127 (1972),

[5] R. D, Goodwin, The rmophy sical Properties of Methane; Virial Coefficients, Vapor

and Melting Pressures, J. Res. NBS 74A (5), 655 (1970).

[6] R. D. Goodwin, Estimation of Critical Constants, J. Res. NBS 74A (2), 221 (1970)

SP I1M2A C-3
Cryogenics Division- NBS Institute for Basic Standards

LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 72-4

PAGE 4

SUBJEa Dielectric Constants and Orthobaric Densities of Methane

NAME R. D. Goodwin

DATE June 2, 1972

C

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OOILVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 450 C-4
Cryogenics Division-NBS Institute for Basic Standards

LABORATORY NOTE

PROJECT NO. 2750364-

FILE NO. 72-4PAGE

SUBJECT Dielectric Constants and Orthobaric Densities of Methane

NAME ^, ^ „ R. D. Goodwin

J^jjie 2, 1972

PIni

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OGILVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 450 iao2 C-5
Lryogenics Division-iNJDo institute lor oasic otdiiudi u

LABORATORY NOTE 2750364-

FILE NO. 72-4

PAGP

SUBJECT ^'^^R. D. Goodwin

"^^ Jime 2, 1972

Table 1. Experimental Dielectric Constants

METHANE DIELECTRIC CONSTANTS

F(E) = ( 100 0/U/PI) (£-!) /E/DTRP

R = A»F 3*F2 * C»F3, R=D£N/DTRP

r 6.'t5927397-a01 1.142 289 76-0 0 1 7 . '9 1 6 85 9'*-a 02

10 E T ,K P,BAR MOL/L CALCO PCNT

2801 1.37611 225. 00 205. 160 16. 9%8 16.9%il 0.0%

2802 1.32037 225. 00 1!»6 .997 1%.675 1%.6730 0.01

2803 1.26500 225. 00 115.3<»8 12.3%% 12 .3339 0.08

280i* 1.211'*0 225. 00 96.5%5 10.016 10.0060 0.10

2805 1.15710 225. 00 31. 082 7.576 7.5717 0.06

2806 1.10269 225. 00 53.359 5.0%% 5 .0%31 -0.08

2807 1.0'*909 225. 00 37.592 2.%55 2 .%6b3 -0.%6

3001 1.3820i« 225. GO 213 . 76% 17. 187 17.1792 0.05

3 002 1.332bl 225.00 156.726 15.173 15.1708 0.01

3003 1.2839'* 225. 00 12%. 193 13. 1%6 13.1397 0.05

3 00% 1.23505 225. 00 10%. 030 11. 056 11.0%15 0.13

3005 1.18793 225.00 89. 773 8. 969 8.9626 0.07

3 006 1.139«*6 225. 00 75.8%6 6.766 6.76%0 0.03

3 007 1.09221 225. 00 59. 190 %. 5%% %.5511 -0.16

3 008 1.0'»'*il 225.00 3% .638 2.220 2.2308 -0.%8

2601 1.32010 250. 00 219.030 1%.650 1%.6538 -0.03

2602 1.27285 250. 00 173.558 12.672 12.6693 0.02

2603 1.22565 250. GO 1%1 . 690 IQ.6%3 10 .6321 0.10

260'* 1.17 869 250. 00 lib. 663 8.560 8.5%95 0.12

2605 1.13278 250. 00 93 .92% 6.%57 6.%5%9 0.03

2 606 1.08598 250.00 63.37% %.2%6 %.2539 -0.19

2607 1.03958 250. 00 36.387 1. 987 1.9973 -0.52

2702 1.27103 250.00 172.079 12.5 92 12 .5913 0.01

2703 1.22521 250. 00 1+1.380 10.620 10 .6130 0.07

270'* 1. 1800 '* 250. 00 117.309 8. 618 8.6097 0.10

2705 1.13532 250. 00 95.16% 6.573 6.5728 0.00

2706 1.09022 250.00 70 .895 %.%%9 %.%561 -0. 16

2707 1.0<t618 250.00 %1 . 5%0 2.313 2 .3227 -0.%2

2901 1.252'*3 2 75.00 206 . 969 1 1 . 798 11 . 79%5 0.0 3 2902 1. 2 15^*5 275.0 0 17 3 . 955 10.187 10 . 1852 0.02

2903 1.17835 2 75. 00 1%5 .680 8.533 8 .5337 -0.01

2 90** 1.1^183 275.00 12 0.022 6. 369 6.8 72 5 -0.05

29 05 1.10 5'«8 2 75.00 9% . %61 5.17% 5 . 1 80 2 -0.12

2906 1.0 6965 275. 00 57.202 3.%60 3.%691 -0.26

2907 1,03367 275.00 35 .563 1.69% 1 .7026 -0.50

101 1.57638 130.00 3. 683 2%. 578 2%. 5581 0.08

102 1.562l)«« 135.00 % . 918 2%. 0 55 2%.0%1% 0.06

103 1.5'»719 140. 00 6. %26 23.509 23. %999 0.0%

10** 1.53167 1<»5. 00 8 .2%8 22.935 22.9320 0.01

105 1.51539 150. 00 10 . %18 22.327 22 .3292 -0.01

106 i.k9dl9 155.00 12 .972 21.679 21.6858 -0.03

107 l.'*7979 160. 00 15 . 9%6 20.981 20.99U5 -0.05

108 l.'»5992 165. 00 19.380 20.219 20 .2335 -0.07

109 i.t^sauo 170.00 23.320 19. 372 19.3869 -0.08

110 l.i*13l9 175. 00 27.806 18.%03 18.%157 -0.07

111 1.38377 180. 00 32 .898 17.2%1 17.2%91 -0.05

112 1.35itl8 181*. 00 37.%59 16. 053 16.0539 -0.01

113 1.335'*3 186. 00 J9.916 15.290 15 .286% 0.G2

11<» 1.31117 188. 00 %2 .50% 1%.285 1%.2837 0.01

601 1.515it6 150. 00 10 . %12 22.327 22.3316 -0.02

602 l.t»1329 175. 00 27 .796 18.%03 18.%20% -0.09

603 1.38391 180.00 32. 891 17.2%1 17.25%0 -0.08

sat* 1.35«»30 13%. 00 37 . %53 16. 053 16.0599 -0.0%

HP = 53, RMSPCT = 0.166

OaiLVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. ASO
Cryogenics Division-NBS Institute for Basic Standards

LABORATORY NOTE

PROJECT NO. 2750364-

FILE NO. PAGE 7

SUBJECT Dielectric Constants and Orthobaric Densities of Methane

NAME , r, r- T• Ro D. Goodwin

DATE June 2. 1972

Table 2. Dielectric Constants for Saturated Vapor

IDOl

lODZ

10 03

lOOit 1005 1006

1007

lOOS

lOOS

1010 1011

1012

1102

1103

tlOit 1105 1106

1107

1202

1203

120't 1205

1206

izoe

1209

1210

1211 1212

121J

1J03

130<. 1305

X J0&

130() 1309

1310

1311 1312

1313

I31ii

IdOtl ItO'S

l^ilO

1502 1503

153t> 1505 1506

1511

1512 1513 15Ht

1&02

1603

160>> 1605

161J

leii) 1615 1616

1616

1705

1706

1707

1708

1709

1710

1711

1712

OF CALCULATED DINSITIES

250.00

170.50 170.35

170.25 170.15

170. US 169.95

169.35 169.75

169.65

169.55

169. >»5

17a. 10 17S.J0

177. ]U

l»2.lO

132.30 ld2.20

173,70

173.60

17 j.5U

30.901

30.d6<« 30.817 30.777

35.2<»t

3!>.192

35.ili3 35.091

35.031

3»..9<t2

..71.1

38.602

38.533

3a.<*76 38.390

38.261 38.172

38. J5t

37.

. 188

l.fSl

1.276

23.295 23,269

23.2<.9

22.778

22.701

22.620

26.ai<> 26.733

26.&3b

Z6.S52

26.>463 2(1.377 26.286

31..S76

3'..76j

}<«.ci^l

23.392

'3.31.8 23^22i<

1.833 169.71

1.831 169.6

i.9tit 17<t.J

173.675

173. 5b8

173. ".73

182.202

182.16f> 182. 12<«

187. 318 107.263

187.205

18 3. 9&

183.926

183.871

. 0't78<t .0<t765

. 0'*7it6

.05818

..05B17 .05816

.05816

.05616

.05816

.06991

.06985

. 069(>6

. O690(i .06665

. 06827

.0679'.

.0856(1 .06560

.06560

.06560 .08560

.06560 .06528

. 06<iS3

.11677

.1167'! .11671.

.1167'.

. 1167<.

. llb;<.

. Ilfe7t. .11573

. 0 9*1 III .093b2

. U931J

. 0<i790

.0<.751

.05813

.05613

. 05013

.05612

.05781

.05757

.05732

.05708

.05683 .05656

.05632

2.9't5 2.932

2 .919 2.906

3.370

3.35'. 3.339

'..12'.

1.. 103 .032

5.062

5.031 5.O01

'..970

CALCO

'..5076

2.1.361

2.<>36e

2.1.358 2.1.363

2. '•236

2. '.05'.

2.9123

2.9116

2.9112

3.1.32 7 3.1.013

3.'.813 3.1.782

3.1.602

•..2386

•..2359

>.9761

..97'>(.

..97'.ij i.97'.8 1.4759

..9751

5.7038

5. '064 5.7067 6.7063

5.70911

'..7039 ..7030

1.. 7031

'.. 70 39

1..7&2..

2.'.3>.9

2. (.177 2.1.033

2.9110

2.9096

2.9098

2.9097

2.6203

Z .7972

OOILVIE PRESS. INC., BROOKLYN 17, N. Y. STOCK NO. 4SO 1602 C~7
Cryogenics Division-NBS Institute for Basic Standards

LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 72-4

PAGE 8

SUBJEa Dielectric Constants and Orthobaric Densities of Methane

NAME R. D. Goodwin

DATE June 2, 1972

Table 2. Dielectric Constants for Saturated Vapor (continued)

ISOI

ISOi. isa«

isab

laoT isaa

1809

isio lAIt

tSl£

1811

1815

ltlL6

19D3

l^Oti 1905 190b

1907

1900 1909

1910 1911

1912

1)13

191i< 1915

1916

2101

2102 ZtOJ

210*> 2iai

21Db

2107 2100

2^05 220b

2207

2208

2301

2 J02 liOS

ZJUS 2306

2307

2J08

2^01

2S02

2503

Z5d<< 2505

2506

2<<01 2H02

2«0<> 2t05

2<«06

2H12

2<il]

2><1<> 2<*1S

177. -lO 177.80

177.70

177. t.0 177.50

177. JO

182.9(1

141.90

181.70

181.50

2311. Ji

2JL.J

22^. JO 225. Ji, 225. JO

250. JL. 250. JO 250.00 250.00

25(,.J0

D.522

0.4 Jb

0.<<3S

59.70.1 S/.617

>5.j'"2o

Jl.081

10. 7^

3a.b68

)0.5(>5 I0.J61 30.259

30 .157

31. 05b

177.897 177.85b

177.771

177.675

. 005 177. a9<.

.112 181. S9I

185. li'a ta5.02J

ia>>.d53

18<>. >.7l 18>>.2d5

ld<..O07

O.QOJ

O.OJO

Jb7ai

0B597 08597

08593

08591

08593

0959J

08510

09i.b7

0 8(.2i 08380

0a3J>.

I0ii7

00000

UUOOl. ODLOO

31(.87 270d7

22bl9

is2aj

1 Jb75

J9l'i9

020 J"}

•2581 I95J2

3bit32 J3353 27207

2011.8 21L7b

ld02S

l<.9'>a

38983

J390I. 28855

23738

13875

09853

0i>910

2^797

25^>25 21158

28272 20197

lbtS7 13221 087Sb

0<>02b 02001

I.. 321 ^.29S

"..275

22.935

21 .o79 20.219

12.b7J

5 .85b 2.952

17 .'tH') 15. (.29 13.129

l.iib59 S.kbbl

3.>i655

3.i>b58

3.3952

3. ISO 1 1.3659

3.35J1 J.lb27

••.25I.1 (•.2518

<<.2517

It. 2519

"..2519

•..2517

'..2<.J9

'..9K.7 <..8737

i..82b3

'..7825 5.709J 5.7051

5.7D>.1 5.6977

b.8729

b.S7J2

b.e7l>.

O.DOOi)

0. OOOb

lb.2t>lJ

1<>.(>372 12.58»b

ia.b6«2

17.b9b 17.

'.655 15.2095

13.9283

l2.bi^»

11.3207 9.97a0 8.5205

7.2236 5.8309

2.9falb

l.l".3 7 8.971b b.7302

15.2359

11.9150

b.><2d8

•..1102 2.0307

l.aid2 12.208U

8.i>5<>2 b.9&<«I 1.8751

2.2568

1.1227

OOILVIE PRESS. INC.. BROOKLYN 17, N. Y. STOCK NO. 4SO leoa C-8
Cryogenics Division-NBS Institute for Basic Standards

LABORATORY NOTE

PROJECT NO. 275036^FILE NO. -72-^

PAGE 9

SUBJECT Dielectric Constants and Orthobaric Densities of Methane R. D. Goodwin

DATE June 2, 1972

TABLE 3

TSATFtDEN), DTRP - 28.11*50

-0.79615729 2.<»*»003079 -6.1936735<f 31*. 08005320

105.82317071 I7<f .55135393 -li»l . 3807<t875 13385389

ID MOL/L T,K CALC PCNT DTS/OD D,PCT

1 0.0163 91.000 91.002 -0.00 525.262 0.02

1 0.0255 95.000 95.011 -0.01 367.689 0.12

1 0.038i* 99.000 99.021 -0.02 266.571 0.21

1 0.0557 103.000 102.991 0.01 199.8'^3 -0.08

1 0.0786 107.000 106.983 0.02 153.570 -0. 1'^ 1 0.1081 111.000 110.982 0.02 120. 67'^ -0.1'^

1 0.1«f52 115.000 11'*.976 0.02 96.711 -0.17

1 0.1912 119.000 118.978 0.02 78. 7'^'^ -O.l*^

1 0.2«»73 123.000 122.981 0.02 6'^.983 -0.12

1 0.3151 127.000 126.996 0.00 5'^.188 -0.03

1 0.3961 131.000 131.013 -0.01 '5.575 0.07

,1 0.ff920 135.000 135.029 -0.02 38.592 0.15

1 0.60<»9 139.000 139.0'^2 -0.03 32.8'»2 0.21

1 0.7370 l<f3.Q00 l'f3.0'^7 -0.03 28.053 0.23

1 0.8911 l't7.000 l'*7.0'*2 -0.03 2<^.020 0.20

1 1.070*» 151.000 151.026 -0.02 20.592 0.12

1 1.2790 155.000 155.000 0.00 17.652 -0.00

1.5221 159.000 158.966 0.02 15.106 -0.15

1.8063 163.000 162.927 O.O'^ 12.876 -0.31

1616 2.3<»88 169.067 169.0'*7 0.01 9.895 -0.08

Iblk 2.3687 169.270 169.2'^3 0.02 9.807 -0.11

912 2.3856 169.^*17 169. 'lO 0.00 9.732 -0.03

1612 2.3881 169. '68 169. '33 0.02 9.722 -0.15

910 2. '05V 169.601 169.600 0.00 9.6'^7 -0.00

908 2.*»236 169.79'» 169.775 0.01 9.569 -0.08

1716 2.7972 173.088 173. 07'^ 0.01 8.1'*5 -0.06

171^t 2.8203 173.290 173.262 0.02 8.066 -0.12

1712 173. '89 173. '66 0.01 7.981 -0.10

1012 2.8<»60 173. '73 173. '8'^ -0.01 7.973 0.05

1010 2.8700 173.675 173.658 0.01 7.900 -0.07

1008 2.8935 173.857 173.8i^3 0.01 7.823 -0.06

1816 3.3501 177. og** 177.100 -0.00 6. '88 0.03

181'* 3.3801 177.292 177.293 -0.00 6. '09 0.00

111<» 3.3863 177.328 177.333 -0.00 6.393 0.02

1812 3.«»108 177. '85 177. '88 -0.00 6.330 0.02

1112 177.509 177.552 -0.02 6.30'^ 0.20

1916 V.0663 181.105 181.133 -0.02 '.852 0.1'^

191«t <».1077 181. 30'^ 181.332 -0.02 '.770 Q.Ik

OOILVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 450
Cryogenics Division-NBS Institute for Basic Standards

LABORATORY NOTE

PROJECT NO. 2750364.FILE NO. 72-4

PAGE 10

SUBJECTDielectric Constants and Orthobaric Densities of Methane '^'*^R. D. Goodwin

DATE June 2, 1972

TABLE 3 (continued)

X C X o *r • X c O 3 181 X O X .. O3 AQO 3 1X AO X1 . 42tc 3o u . U t flU a 17X 1 X 3 X c XH 3D 1X A1O tin« X . 7 U D X1 A1ox . c>7 70 nU — u . U 1

L.H . AAQ OO 7 n 19

X1 ?C 1X 1X *T • X O 7 U 181 X w X .. 58Q 7 O 7 181 X O X ..Aim w U 7 • n . n 1 u . U X 4H . Ai« D7 AO n fl A

X C U J 181 X O X .76^ . f WW X181.783 W X . r O O — fl . n 1 U . U X 4.H . fifm 70 7 nu . nu A0

1516 X 1^ X W 4«5?12 *T • C X ^ 183-117 X U w • X X > 183.1 45 -0 - fl? 4. n?fl nU ..

1X A0

1514 X183. V w • 322 w C C 183. X U w . 341 w *T X '•nU .. nU 1X 3 .Q37 flU .• X1 X1 ^151^ ^ ?^ U. 61 8<3 18 3.514 183.53 0 -0.01 U . U X 3. 858 0.u . 0u Q7

1316 i*.7822 ~ • f vJ C C X184. V ~ • X125c ^ 1 84. 1 39 -0.01 U . U X 3 . 5QQ 0 . n A

210 k w 8v 4.7825 184. 087 184. X V ^ • 140 X ~ U -0.03 3.599 0-31 U . w X C X u * b. 8263 X184. V H . 2C 85O ^ 1X 840*T .. 2Q6 C 70 — flU . fl 1 . U X 3.0 . ^3? 7 0 c flu ..

flu A0

X O X *T •r • Ab62 O HO C 1 84. 37(1 1X 8i*. O H . 3O AO AO n . n n 03 . *>n 7 u c? — fl fl 9

C X u o ••Of J t 1X A4O • .. 471r X 1X 84O .

. 48? HOC. — fl n 1 U • U X 3 4f>? 0 . H7 C fl n7

X w X c U. 8876 1X 84V .. 151 7 X nu 1X 84OH ..

*57 1X nU n fl n 03 44 fl . HH U — flu fl fl • u u

e.O

c n 7 A n 7 • U O O U

1 A c: n n X O 7 . U o ui

i. AKO 7 . nil U X

n n i U . U X • n 19

o X1 A6O C . nU 30O u X1 AOOA n bit. . U HH u . U X c? . 7r A0 07 flU .

flU.7Q

ecu o *; ii.n 77 X O u . X U o 1X AAOO 1 1 n . X X u — n n n 7 77 7 nu . n uU H

X t xo 5 • t U ^D 1XOOA6 1 7CI • X C 7 1 AA 1 1 c; X OO . X X7 n n 1 U . U X 9 7 7 1 • fl 1 f) U . X U

X*t X *T 1 A6 3 1

Q

X O D . O X 7 1X AAo o . o3nu o3 nu n 1 . U X C . OH 7 — fl 1 1 U . X X £ c tl f 7 • H O C f 1X A6O O .. 3O n4U "T X1 AAOO 31 1 • O X X — nu .

flu nu 9c AL. 1 . OH X n fl c« u . u 7

C C U D 7 • 77 ( X 1 A A n 1 X O D . 7 U X 1X AO AO . finu 7 U H — n n n u . u u 9C . 77RCi 07 nu . n ? U c

1X*rU1X ?C 7 • 7 7 3 X 1 A6 1 a X O u • 7 X O X1 AO AO .

Ci7 nU Q7 n n n 9 n c . 77 U — nu . un A0

O 7 • f oOU 1 A7 fl "71 X u r • u o X

1 A7 flRQ X O f • U 7 7 — u . U 1 9 9Q 7 C . c 70 n 9 1 U . c X D O • c f 7 U -too n "7

xO o . U o

1100. A ft nU70CC^ — U . U 1

4 on 7 1 . OU c

n 99 U « c c D* ^tOU 'too 4 i. n 10 0. IHU 4 o o n o a loo. U 07 n n 7

U . 0 o

4 7 a c 1 . / ob _— ft li c U . 4b

1 0 0 f b« *f Ub f

•1 O O 7 i. 7 loo. OHO 4 O O O fi C loo . coo n ft 7 4 C Q Mm 1. bo4 -0.73 n c 7

2306 6.5278 188.545 188.484 0.03 1.579 -0.60

6 6.9180 189.032 189.038 -0.00 1.272 0.07

5 7.5510 189.765 189.706 0.03 0.855 -0.91

5 7.9350 190.046 189.993 0.03 0.646 -1.03

6 7.9600 190. 032 190.009 0.01 0.633 -0.45

7 8.0000 190.050 190.034 0.01 0.613 -0.32

7 8.1700 190.150 190.132 0.01 0.533 -0.42

7 8.3600 190.250 190.225 0.01 0.449 -0.67

5 8.3920 190.279 190.239 0.02 0.435 -1. 10

7 8.6200 190.350 190.328 0.01 0.345 -0.75

7 9.0000 190.450 190.433 0.01 0.216 -0.85

5 9.1610 190.480 190.464 0.01 0.169 -1.01

5 9.6660 190.524 190.520 0.00 0.052 -0.79

5 10.0590 190.530 190.530 0.00 0.006 -0.53

5 10.7960 190.515 190.515 -0.00 -0.066 -0.03

7 11.4100 190.450 190.432 0.01 -0.215 0.72

5 11.3670 190.442 190.441 0.00 -0.203 0.03

OOfLVIE PRESS. INC., BROOKLYN 17. N. Y. STOCK NO. 450 C-10
Cryogenics Division-NBS Institute for Basic Standards

LABORATORY NOTE

PROJECT NO. 2750364-

FILE NO. PAGE 11

SUBJECTDielectric Constants and Orthobaric Densities of Methane

R. D. Goodwin

DATE June 2, 1972

TilBLE 3 (continued)

7 11,7900 190.350 190 .328 0.01 -0 . 340 0.56

5 11. 8240 190.316 190 .316 0.00 -0 . 352 0,01

7 12. 0700 190.250 190 .218 0.02 -0 . 446 0*60

7 12*2700 190 • 150 190 .120 0.02 -0.529 0* 46

7 12*4400 190 A W •V 050 W W 190 .024 0.01 -0 .604 0.35

5 12* 3970 190 . 048 190.050 -0.00 -0 . 584 -0.02

6 12*4740 190. 032 190. 003 0.02 -Q .619 0.37

5 12*8790 189.707 189.714 •0 . 00 -Q . 814 •0.06

6 13*5780 189. 032 189. 014 0.01 -1. 198 0.11

5 13*3000 189.311 189. 324 -0.01 -1*039 -0.10

6 14*2850 188.031 188.014 0.01 -1*638 0.07

14*2837 188.000 188. 016 -0.01 -1 *637 -0.07

5 14*5620 187.469 187.498 -0.02 -1.836 -0.11

6 14*8360 187. 031 187. 010 0.01 -2.011 0.07

6 15*3020 186. 030 185.995 0.02 -2.344 0.10

113 15*2864 186. A V W V 0w 00w \J 186. X V 9 0U 32V/ w -0.02 -2.333 -0*0 9

6 15.7100 185. 030 184. 978 0.03 -2.646 0.13

112 16* 0539 184. 000 184.023 -0 . 01 -2.906 -0*05

604 16*0599 184. 000 184. 006 -0.00 -2*911 -0,01

111 17*2491 180.0 A V W V w 00w w 179. 994 0.00 -3*844 0*01

603 17*2540 180.0 00 179.975 0.01 -3* 848 0*04

18* 3900 175. 053 175. 084 -0.02 -4*766 -0*03

1 19.4920 169.326 169.336 -0.01 -5*667 -0*01

20*4280 163.659 163.673 -0.01 -6*434 -0*01

\ 21*3790 157.199 157.183 0.01 -7*212 0*01

22*1300 151.553 151.538 0.01 -7,822 0*01

22*8800 145.448 145.445 0.00 -8.424 0*00

23.5780 139.352 139.372 -0.01 -8*976 -0.01

24.1760 133.878 133.865 0.01 -9.441 0*01

24.1860 133.773 133.770 0.00 -9.449 0.00

24.6110 129.657 129.685 -0.02 -9.775 -0.01

24.9990 125.825 125.835 -0.01 -10.068 -0.00

25.3880 121.893 121.862 0.0 3 -10.359 0.01

25.7820 117.746 117.724 0.02 -10.647 0.01

26.1460 113.772 113.800 -0.02 -10.909 -0.01

26.5270 109.611 109.593 0.02 -11.175 0.01

26.9160 105.165 105.195 -0.03 -11.437 -0.01

27.2430 101.434 101.421 0.01 -11.646 0.00

27.6050 97.173 97.165 0.01 -11.863 0.00

27.9100 93.512 93.521 -0.01 -12.030 -0.00

NP = 120, SS = 0.015, SO = 0.300

OaiLVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 4SO C-1
Cryogenics Division-NBS Institute for Basic Standards

LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 72-4

PAGE 12

SUBJECTDielectric Constants and Orthobaric Densities of Methane ^**^R. D. Goodwin

June 2, 1972

TABLE 4

VAPOR DENSITIES, E = 0.350

-7. 07<t81328+000 -l.^tZ/ZOSeS + OOO -1.89269525+000 9.79362700 + 000

-1.21337730+001 6.30822607+000 0.00000000+000 0.00000000+000

T n Mm /I rCNT

O 4 C H ft ^1 • u U U u . U 1 bo 0 . U 163 A A f. 0.04

y?. U U U

n n 9 c c: ft n o c c 0.0 255 n AO -0.02

Q Q n n n

• U 0 U U . 0 O OH 0.0 364 A AD 0.08

luo. uOU n n c c 7 0 . 0557 0.0558 -0.12

1 U r • U U U U . 0 r ob 0.0 787 A A A -0.08

4 A 4 n n n 11 1 . UU 0 0 . 1 0 81 0.1081 A A A -0.00

4 4 C AAA 115. 000 0 . I*f52 0 . 1452 0.00

119.00 0 0.1912 0.1911 0.03

123.00 0 0

2h73 0 . 2473 0.01

127. 000 0.3151 0.3150 0.04

131.00 0 0 • 3961 0. 3959 0 . 06

135.000 0 .4920 0.4917 0.06

139.000 0 .6049 0.6045 0 .06

1<»3.000 0 .7370 0.7367 0.04

1^»7.000 0.8911 0.8910 0.01

151.000 1.0704 1.0707 -0.03

155.000 1.2790 1.2802 -0.09

159.000 1.5221 1.5246 -0.16

163.000 1.8063 1.8110 -0.26

1616 169.067 2.3488 2.3483 0.02

161*» 169.270 2.3687 2.3689 -0.01

912 169.*fl7 2.3858 2.3840 0.08

1612 169.lf68 2.3881 2.3892 -0.05

910 169.601 2.4054 2.4030 0.10

908 169.79*t 2.4236 2.4230 0.02

1716 173.088 2.7972 2.7967 0.02

1714 173.290 2.8203 2.8217 -0.05

1712 173.«t89 2.8457 2.8466 -0.03

1012 173.1*73 2.8480 2.8446 0.12

1010 173.675 2.8700 2.8701 -0.00

1008 173.857 2.8935 2.8933 0.01

1816 177.09** 3.3501 3.3491 0.03

1811* 177.292 3.3801 3.3799 0.00

llli» 177.328 3.3863 3.3856 0.02

1812 177.*»85 3.4108 3.4104 0.01

1112 177.509 3.4209 3.4142 0.20

OOILVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 4SO C - 1 2
Cryogenics Division-NBS Institute for Basic Standards

LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 72-4

PAGE 13

SUBJEaDielectric Constants and Orthobaric Densities of Methane

NAME-, n -i i^. D. uoodv.an

'''^^^June 2, 1972

TABLE 4 (continued)

1916 181. 1C5 ^.0663 '.06'^0 0.06

181.30** '.1077 '.105'^ 0.05

1213 181.389 ^.1269 '.123'^ 0.09

1912 181.506 '.l'^82 0.03

1211 181.589 ^.1656 '.1660 -0.01

1209 181.768 «. 201^9 -0.02

1516 183.117 '.5212 '.5190 0.05

151^t 183.322 '.570i^ '.570'^ -0.00

1512 183.51<» '.6189 '.6196 -0.02

1316 18't.l25 '.7822 '.7833 -0.02

2108 18i».087 '.7825 '.7728 0.20

2107 18«».285 '.8263 '.8280 -O.O'^

131i* 18<».370 '.8'*62 '.8522 -0.12

2106 18*t.**7l '.8797 '.8811 -0.03

1312 18'*.510 '.8876 '.892'^ -0.10

6 185.030 5.0380 5.0'^83 -0.20

6 186.030 5.38*^0 5.381'^ 0.05

2208 186.103 5. '077 5.^^075 0.00

l'*16 186.129 5. '096 5. '169 -O.l'*

186.319 5. '795 5. '872 -0.1*^

2207 186. 30** 5. '827 5. '816 0.02

2206 186.501 5.5571 5.5566 0.01

186.518 5.5591 5.5632 -0.07

6 187 • 031 5.7860 5. 772*^ 0 . 2'* 6 188.031 6.2750 6.2517 0.37

2308 188. 1<*0 6.2930 6.3113 -0.29

2307 188.3*»3 6. '067 6. '278 -0.33

2306 188.5it5 6.5278 6.5512 -0.36

6 189.032 6.9180 6.8883 0.43

5 189.765 7.5510 7.5757 -0.33

5 190.0^6 7.9350 7.9607 -0.32

6 190. G32 7.96 0 0 7.9385 0.27

7 190.050 8.0000 7.9671 O.i^l

7 190.150 8.1700 8.1'*07 0.36

7 190.250 8.3600 8.3'^72 0.15

5 190.279 8.3920 8. '160 -0.28

7 190.350 8.6200 8.6096 0.12

7 190.U50 9.0000 8,9975 0.03

5 190. '80 9.1610 9.1772 -0.18

5 19Q.52<» 9.6860 9.7072 -0.22

NP = 76, SS = 0.157, SD - 0.000

OaiLVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 4SO
Cryogenics Division-NBS Institute for Basic Standards

LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 72-4

PAGE 14

SUBJECTDielectric Constants and Orthobaric Densities of Methane

NAME R. D. Goodwin

DATE Jujie 2, 1972

TABLE

LIQUID DENSITIES, BE = 0.360, E = 0.000

l.if7920372+000

O.OOOOOOOO-i-OOO

3.1^f771601-001

O.OOOOOOOO-i-OOO

-6.0195781it-002

O.OOOOOOOO-t-OOO

2.5t»7263it3-002

O-OOOOOOOO-i-OOO

ID T,K MOL/L CALC PCNT DD/DT

5 190.515 10.7960 10.8347 -0.36 -15.2540

7 190.*t50 ll.ttlOO 11.3613 0.43 -5.2463

5 11.3670 11.4020 -0.31 -4.9378

7 190.350 11.7900 11.7573 0.26 -3.1352

5 190.316 11.82*»0 11.8581 -0.29 -2.8099

7 190.250 12.0700 12.0280 0.35 -2.3709

7 190.150 12.2700 12.2426 0.22 -1.9557

7 190.050 12.^t'f00 12.4240 0.13 -1.6885

5 190.0«»8 12.3970 12.4274 -0.24 -1.6841

6 190.032 12.«^7*fO 12.4540 0.16 -1.6499

5 189.707 12.8790 12.9081 -0.23 -1.2051

6 189.032 13.5780 13.5752 0.02 -0.8314

5 189.311 13.3000 13.3282 -0.21 -0.9443

6 188,031 lt».2850 14.2797 0.04 -0.6081

lik 186.000 1'».2837 14.2987 -0.11 -0.6035

5 187.«t69 l't.5820 14.6009 -0.13 -0.5379

6 187.031 l«t.6360 14.6270 0.06 -0.4963

6 186.030 15.3020 15.2866 0.10 -0.4271

113 186.000 15.286Xf 15.2996 -0.09 -0.4254

6 185.030 15.7100 15.6887 0.14 -0.3793

112 18^.000 16.0539 16.0598 -0.04 -0.3430

SOk 18*f.000 16.0599 16.0598 0.00 -0.3430

111 180.000 17.2«f91 17.2454 0.02 -0.2605

603 180.000 17.25i»0 17.2454 0.05 -0.2605

1 175.053 18,3900 18.3956 -0.03 -0.2098

1 169.326 19.4920 19.4938 -0.01 -0.1765

1 163.659 20.4280 20.4306 -0.01 -0.1554

1 157,199 21,3790 21.3776 0.01 -0.1387

1 151.553 22.1300 22.1288 0.01 -0 .1279

1 oo A A n n 9 9 A A n 7 — U • U U _ ft — 'I 1 A7 U • 1 lo f 1 139.352 23.5780 23.5806 -0.01 -0.1113

1 133.876 24.1760 24.1747 0.01 -0.1059

1 133,773 24.1860 24.1858 0.00 -0.1058

1 129,657 24.6110 24.6137 -0.01 -0.1022

1 125.825 24.9990 24.9997 -0.00 -0.0993

1 121,893 25.3880 25.3846 0.01 -0.0965

1 117»7kb 25.7820 25.7794 0.01 -0.0939

1 113,772 26.1460 26.1482 -0.01 -0.0917

1 109.611 26.5270 26.5252 0.01 -0.0895

1 105.165 26.9160 26.9186 -0.01 -0.0875

1 101.<t3*f 27.2430 27.2420 0.00 -0.0859

1 97.173 27.6050 27.6046 0.00 -0.0843

1 93.512 27.9100 27.9107 -0.00 -0.0830

NP = <t3, SS = 0.153, SD ' 0.000

DTRP = 28.14437

OOILVIE PRESS, INC.. BROOKLYN 17. N. Y. STOCK NO. 450 USCOMM ERL
APPENDIX D
I

i;
APPENDIX D

R-720

EROM: Natural Gas Research and Technology,

Proc . 2nd Conf., Atlanta, Ga., June 5-7^

1972. Institute of Gas Technology, Chicago,

111. (1972)

Session V

Paper 2

THERMOPHYSICAL PROPERTIES OF METHANE *

Robert D. Goodwin, Ph.D.

Physical Chemist

National Bureau of Standards

Institute for Basic Standards

Boulder, Colorado 80302

ABSTRACT

This report describes briefly the rather direct methods recently

used at this laboratory to prepare tables of provisional values of thermodynamic functions for methane. The basic data are spectroscopic

specific heats for ideal gas states; the vapor pressure and melting

curves; available virial coefficients for low density gas; and density

(PVT) measurements over the domain from the triple point (90.68 K)

to 400 K at pressures to 350 bar (1 atm = 1.01325 bar). References

are given for the principal sources of PVT data.

The analytical descriptions of the PVT physical properties are emphasized in this report because they are needed for smoothing, for

interpolation, and for the computation of derivatives. These have been

developed here in recent years to be at least qualitatively consistent

with known behavior about the critical point. The nonanalytic equation

of state used here is qualitatively consistent with the experimental

observation that specific heats C^ increase beyond measure upon close

approach to the critical point.

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

the sponsorship of the American Gas Association.

Copyright, 1972 by Robert D. Goodwin

D-1
Session V

Paper 2

THERMOPHYSICAL PROPERTIES OF METHANE

INTRODUCTION

The computation of thermodynamic functions of fluids over the

wide range which includes vapor and compressed liquid at subcritical

temperatures (Figures 1 and 2) always is difficult and often demands

improvisation to supply missing or inadequate knowledge of some

physical properties.

In the following we first report some of the sources of physical

properties data for methane, and give for each property the analytical

description used for thermal computations. We then describe the

rather direct computational procedure which has been used, and we

comment upon its difficulties. We conclude with an illustrative table

of derived thermal properties of saturated liquid methane. Symbols

used in the text are given in the List of Symbols, below.

INTERPOLATION OF PHYSICAL PROPERTIES DATA

Thermophysical propertie s of methane have been reviewed [7,17,20]. In particular, the thermodynamic functions for ideal gas states have

been represented analytically as a function of temperature [8]. Recently we have measured the melting and vapor pressures [14], as represented in the present appendix by equations (A-1) and (A-2). The

latter is our new form, nonanalytic at the critical point [4].

Densities of freezing liquid up to P = 220 bar, and of the saturated

liquid up to T = 175°K have been obtained at intersections of our new

PVT isochores [9] with the melting and vapor pressure lines respectively. They are represented by equations (A-3) and(A-4) respectively.

Densities of the saturated vapor up to T = 175°K (p = p^/3) have been

obtained at intersections of the virial equation of state [7] with the

vapor pressure line, as represented by equation (A-5). For the equation of state we require the single -valued function T^(p) for the vapor

liquid coexistence (saturation) temperatures, equation (A-6). This

function is modified from our original form [6] to be constrained to the

liquid triple point.

Equations (A-4), (A-5) and (A-6) have been developed to be qualitatively consistent with known behavior near the critical point [11]. They

thus permit interpolation up to the critical point [7], in the range where

accurate saturation densities are most difficult to obtain.

Experimental PVT data for the homogeneous domain have been used

from four sources to find the least squares coefficients of the equation

of state. The locus of these data is shown by Figure 1. At low densities they are generated by the virial equation [7]. At 0.2 < p/p^ < 1.8 the data are from [19]. At high densities we use our new measurements [9].

2 D-2
Session V

Paper 2

At high temperatures they are from [2]. The combined data cover most of the domain from 90 . 68 °K to 400 °K at pre s sure s up to 3 50 bar

The new equation of state [9] is (A-7) of the appendix. It has been

designed to be qualitatively consistent with the known behavior of P(T)

isochores [3, 15] and with the experimental observation that specific

heats increase beyond measure upon close approach to the critical

point [11]. It therefore is nonanalytic at the critical point. As a con- sequence of this form, we obtain a reasonable representation of the

entire PVT surface (up to the freezing liquid) with only thirteen least

squares coefficients (plus four non-linear constants). The equation

has been constrained to the liquid triple point, to the critical point,

and to 5P/5p = 5^P/5p^ = 0 at the critical point, A calculated table

of P and of 5P/bp along the critical isotherm shows that 6P/5p = 0 at the critical point and 5P/5p > 0 at all adjacent densities. Tables of

calculated isochores and their derivatives bP/bT, 5^P/bT^ show consistency with [ 1 , 11, 15].

Experimental specific heats C^{T) for saturated liquid methane

have a low precision [8], We therefore have represented our derived

entropies for the saturated liquid by equation (A-8), obtaining the

specific heats from

C (T) = T- (dS /dT) . a a

COMPUTATIONAL METHODS

Given values of thermofunctions corresponding to zero density at every temperature [8], the density dependence is given by the thermodynamic relations (along isotherms. Figure 2),

AE = J[P - T-(bP/5T)p] -dp/p^ , (1)

AC = - T- r (b^P/bT^) -dp/p^ , (2) v J p

AS = R.'tn[p°/(pRT)]+ J[R-(bP/bT)p/p] -dp/p . (3)

Equation (3) is for use with initial entropies in hypothetical ideal gas

states at P° = 1 atm [8]. In the compressed liquid at T < T^ we use

AS = - [(bP/bT) -dp/p^ . (4)

«J P

In each (T,p) state, reached by above integrations, we compute [15],

H = E + P- V ,

' (5)

3D-3
Session V

Paper 2

C =C + T- (bP/6T)^/(bP/5p)^/p^ , (6)

p V p T

= C • (5P/5p)^/C , (7)

p T V

At T < T , path A of Figure 2, we cross the vapor -to-liquid "dome"

by use of the Clapeyron equation,

AH = T. (dP/dT). (V -V ) , (8)

AE = AH - P- (v„ -V ) , (9)

AS = AH/T , (10)

where (dP/dT) is slope of the vapor -pres sure curve. For the saturated liquid we then obtain

C (T) = T- (dS /dT) . o o

The values of C^(T) on the saturated liquid boundary may be estimated from the following difference [15] ,

C (T) = C (T) + T.(5P/bT) -(dp /dT)/pf , (11) V a p t t

where (dp^/dT) is the negative slope of saturated liquid density vs. T.

Each term on the right of (11) approaches infinity at the critical point:

hence cannot be estimated reliably in this region. This difficulty

may be avoided by carrying the computations around the dome; first

along path B of Figure 2, and then to lower temperatures entering the

compressed liquid region, along an isobar or an isochore by use of

experimental specific heat data, C or C . ^ ^ ' p V

Table 1 for saturated liquid methane is taken from [10] as an illustration of derived results for thermophysical properties obtained by

this procedure. Under the heading Q are given the heats of vaporization.

DISCUSSION

The above equations involve derivatives of experimental or derived

PVT data and hence a loss of roughly one order of magnitude from ac- curacy in the data for a first derivative alone. Some expressions then

involve a difference. The tables of thermodynamic functions then are used for engineering purposes by again taking differences. This awesome situation led Professor Michels to the conclusion that PVT data are needed with an accuracy of 1/30,000 [13]. With pre sent methods

we obtain densities with absolute accuracy little better than 1/1,000,

4

D-4
Session V

Paper 2

while some improvement has been achieved by others [12, l6]. We conclude that with the present methods it is difficult to obtain thermodynamic functions with the reliability and accuracy desired for engineering design applications. The results must be considered an heroic

effort to provide guidance where no better information exists.

In view of the above difficulties, it becomes extremely important

that analytical descriptions of the PVT properties have a proper form,

related to accepted behavior, so that the derivatives will be at least

qualitatively correct. The indiscriminate use of power series places

upon the data a need for high accuracy and density of points which

usually do not exist. It is for this reason that we have, over the past

several years, concentrated upon the development of formulas given

here in the appendix.

ACKNOWLEDGMENTS

We are indebted to the American Gas Association for generous

support of this work, to Robert D. McCarty and Rolf Prydz for the

least squares programs, and to Dwain E. Diller and Lloyd A. Weber

for important suggestions.

LIST OF SYMBOLS

Subscripts c and t refer to critical and to liquid triple points

Subscripts g and t refer to saturated vapor and liquid

Subscript a refers to vapor-liquid equilibrium (saturation)

cv, b, 3, 6, non-linear constants in the equation of state A, B, C, D, density-dependent coefficients of the equation of state C^(p, T), molal heat capacity at constant v

Cp(p , T)^ molal heat capacity at constant P

C^(T), molal heat capacity for saturated liquid

d, molal density, dc = 10. 15, d^ = 28. 1472 mol/-t

E(p , T) , the internal energy

H(p , T) , the enthalpy

J, the joule, 1 N-m

I, the liter, lO'-^m^

12 mol, 16.043 grams of methane (C COscale)

P, pressure in bars, 1 bar = 10 N/m , 1 atm = 1.01325 bar

Pc = 45. 9566, Pt = 0. 117436 bar

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

p, d/d^, density reduced at the liquid triple point

a, d/d(-., density reduced at the critical point

S(p,T)^ the entropy

T, temperature, K, on the IPTS (1968)

T^ = 190. 53, T^ = 90. 68

v, 1/d, molal volume

5 D-5
Session V

Paper 2

W(p,T), the speed of sound

X, T/T^, temperature reduced at the critical point

Z, Pv/RT, the "Compressibility factor"

APPENDIX. ANALYTICAL DESCRIPTION

OF PHYSICAL PROPERTIES DATA

Fixed -point constants are given in the List of Symbols.

I) The Simon equation for melting pressure is

P = P^+ P^-[(T/T^)^ - l] , (A-1)

P = 1909. 40 bar, e = 1.85.

o

2) The nonanalytic vapor pressure equation uses the argument

X = (1-T /T)/(l-T /T ) , t t c

2 3 3/2

'Ln(P/P^) = a-x + b-x +c-x +d-x-{l-x) , (A-2)

. a = 4.773 2553, c = -0 . 5 70 28 1 2

b = 1.766 5879, d = 1.331 1873.

3) Densities of the freezing liquid are described by

1 /4

d/d^ = (T/T^) . (A-3)

4) Densities of the saturated liquid are described by use of the

arguments x = T/T , zh (1-x),

c

B 2 d/d^ = 1 + a. z + b- z + c- exp(-e -x /z), (A-4)

a = 0.539 403, c = -0.018 387,

b = 1 . 896 635, e=0.88, 3=0.36.

5) Densities of the saturated vapor are described by use of the

arguments u = (T -T)/(T -T), w= (T /T-1)/(T /T-1),

c c t c c t

5 'tn(d/d ) =a-w^^'^ + a^-w + "V^ a. - u^"^ (A- 5) c I Z 1 i=3

6

D-6
Session V

Paper 2

= -2.012 860, a^ = 0.736 090,

a^ = -6.815 239, a^ = 0.416 449.

a.^ = 1.203 942,

6) Saturation temperatures Tjj(p) for coexisting vapor and liquid are described by use of the variables

Y(T ) = (T /T -1)/(T /T -1) , a CO c t

U(a) = (a-\)l{o^-l)

where a = d /d is a constant. The function now is

t t c

Y(T^) = U^^^-[l + a^.-tn(p) + (P " l)-2^a. • p'"^] , (A-6)

i=2

a, = -0. 814 2449, as =- 133 . 444 9230,

a2 = 2.479 4529, a^= 223.495 5973,

a3 = -6.759 8384, a^ = -181.826 7154,

a^ = 41.056 0011, ag = 58.835 9684.

7) The isochoric, nonanalytic equation of state was described in [9]

Symbols are from our list above,

(Z-l)-x/p = A + B- $(T) + C/x + D- Y (p, T) , (A-7)

where

$(T) = x.[l-exp(-b-3/x)] ,

Y(p, T) = j^l-o) .^n(l + 1 /uj )]/x ,

aj(p,T)= (T-e)/(6.T ), c

e(p) = T^(p)-exp[-u(a)/2],

u(a) H a^.[la-ll ^ - (a-l)^]+ ff^-[|a-l| ^ + (a-1)^] ,

3 . 3 A(p) =y^A.-p' C(p) =2 C.-p' , i=0 i=l

B(p) = ^B.-p^, D(p) = (a-1).^ D.-p'

i=0
Session V

Paper 2

a =Q'=0.5, b=0.8, P=4, 6=1.2,

g ^

- J\Q - 4 1 ^4^ 7 847

^1 = -4. 7739 0186, Ci = 5 1033 5931,

^2 = 3. 5199 9044, C2 = -12 4202 2748,

A3 = 4. 2573 7412, C3 = 6 3612 4273,

^0 = 1. 7474 4656, Do = 1. 8838 3919,

Bl = 2. 5767 9569, Di = -3. 5471 3477,

^2 = 0. 4653 8980, ^2 = 1 8740 8815.

8) Entropies of the saturated liquid in J/(mol-K) are described by- use of the argument x = T/T , c

2 3 2/5

S (T) = A^ + AXn(x) + A^-x + A -x + A -x +A-(l-x) (A-8)

a 0 1 c 5 4 5

Aq = 68.44 781, A3 = -61.44 465,

Aj = 21.91 114, A4 = 11.57 187,

A2 = 100.93 346, A5 = -25. 34 264.

REFERENCES CITED

[1] Diller, D. E. , "The Specific Heats (Cv) of Dense Simple Fluids,"

Cryogenics 11 (3) 186-191 (1971) June.

[2] Douslin, R. D. , Harrison, R. H, , Moore, R. T. , and Mc Cullough,

J. P. , "P-V-T Relations for Methane, " J. Chem. and Eng. Data 9

(3) 358-363 (1964) July.

[3] Goodwin, R. D. , "An Equation of State for Fluid Parahydrogen

From the Triple-Point to 100°K at pressures to 350 Atmospheres, " J. Res. NBS, 71A (3) 203-212 (1967).

[4] Goodwin, R. D. , "Nonanalytic Vapor Pressure Equation with

Data for Nitrogen and Oxygen," J. Res. NBS 73A (5) 487-491

(1969).

[5] Goodwin, R. D. , "Formulation of a Nonanalytic Equation of State

for Parahydrogen, " J. Res. NBS 73A (6) 585-591 (1969).

[6] Goodwin, R. D. , "Estimation of Critical Constants, T^,

From the p(T) and T(p) Relations at Coexistence," J. Res. NBS

74A (2) 221-227 (1970).

[7] Goodwin, R. D. , " Thermophy sical Properties of Methane:

Virial Coefficients, Vapor and Melting Pressures," J. Res. NBS

74A (5) 655-659 (1970).

8 D-8
Session V

Paper 2

[8] Goodwin, R. D. , "The rmophysical Pr opertie s of Methane:

Orthobaric Densities and Some Thermal Properties," J. Res.

NBS 75A (1)15-21(1971).

[9] Goodwin, R. D. and Prydz, Rolf, "Densities of Compressed

Liquid Methane, and the Equation of State, "J. Res. NBS 76A

(2) March-April (1972).

[10] Goodwin, R. D. , Tables of Provisional Values of Thermodynamic

Functions for Methane, (a report to the American Gas Association): Private communication 10 715, this laboratory, September,

1971.

[11] Green, M. S. and Sengers, J. V., Editors, Critical Phenomena,

NBS Miscellaneous Publication 273, U. S. Gov't. Printing Office,

Washington, D. C. (1966),

[12] Haynes, W. M. and Stewart, J. W. , "A Magnetic Densitometer

for Low Temperatures and High Pressures, " Rev. Sci. Instruments 42 (8) 1142-1150 (1971).

[13] Michels, A., "High Pressure Research, " Research 9, 99-103

(1956) March.

[14] Prydz, Rolf and Goodwin, R. D., "Experimental Melting and

Vapor Pressures of Methane," J. Chem. Thermodynamics

_4(1) 123-33 (1972) Jan.

[15] Rowlinson, J. S. , Liquids and Liquid Mixtures, London:

Butterworths Scientific Publications, 1959.

[16] Street, W. B. and Staveley, L. A. K. , "Experimental Study of

the Equation of State of Liquid Krypton," J. Chem. Phys. 55 (5)

2495-2506 (1971) Sept. 1.

[17] Tester, H. E., "Methane," in Thermodynamic Functions of

Gase

Vol. 3, F. Din, Editor, London: Butterworths Scientific

Publications, 1961.

[18] van Itterbeek, A. , Verbeke, O. , and Staes, K. , "Measurements

on the Equation of State of Liquid Argon and Methane up to

• 300 kg/cm^ at Low Temperatures," Physica 29 , 742-754(1963).

[19] Vennix, A. J. , Low Temperature Volumetric Properties and

Development of an Equation of State for Methane , Thesis, Dept.

of Chem. Engineering, Rice Univ., Houston, Texas, April, 1965.

[20] Zagoruchenko, V.A. and Zhuravlev, A. M. , The rmophysical

Properties of Gaseous and Liquid Methane, (Moscow, 1969),

Available in translation from Clearinghouse for Federal Scientific

and Technical Information, Springfield, Virginia 22151.

9

D-9
Session V

Paper 2

Table 1. Properties of Saturated Liquid Methane

T TEG K 90.68

9? . Q C 9'«.00 96.00 99.00 100.00

.00

,00

10 2.00

lOit.OO 106.00

10"?. 00 113.00

11?. 00

111*. 00 116.00

118

120 122.00

12't. JO 126 .00

12<5.3Q 130.00

132. 00 13i».a0 136.00

133.00

li^J. 00 l'»2.00

11*1*. 00

11*6 . 0 0 1<*8. 00 150 ,00 152.0 0 151*. 00 156.00

15'i.OO 160.0 0 162.00

164.00

166.0 0 16H.0O

17 J. 00 172.00

17'.. 00 176.00

178.00

180.no 132.00

184.00 186.00

188.00

190 .53

DEN »OL/l

28.1't7 28.038

27. 873

27 . 7C5

27. 536 27.366

2 7. 194

27. 021 26. 846 26.669

26.490

26.309

26. 126 25.942

25. 754 25.565

25 .373 25.179

24.981

?4. 781 24.578

24. 372

2 4. 162 23.948

23.731

23. 509 23.283

23. 052 22. 810 22.575

22.327

22. 074

21 . 813

21. 544 21.267

2 0 .981 20.685

20 . 378 20. 057 19.723

19. 372 19.002

18.609

18. 190 17.737

17. 241 16.667

1 6. 053

15. 290 14.285

10.150

p Q

c H S csaT CV C=> W J/MOL J/MOL J/MOL J/MOL -K J/MOL -K J/MOL -< J/MOL-K M/SEC

0.117 8710 3450 3450 67. 98 52. 96 33.64 53. 08 1574 0.139 8681 3520 3521 68. 74 53.17 33.67 53. 29 1557 0.177 8636 3627 3628 69. 89 53. 49 33.71 53.61 1533 0.223 8590 3734 3735 71. 02 53. 79 J3.74 53. 92 1509 0.279 8543 3842 3843 72. 13 54.08 33.75 54. 23 1485 n.345 8494 3951 3952 73. 23 54. 37 33. 75 54. 52 1462 0.423 8444 406] 4062 74. 31 54.65 33. 74 54. 81 1439 0.515 8393 4170 4172 75. 37 54. 92 33 .71 55.10 1417

0.621 8339 4280 4283 76. 42 55.19 33. 67 55. 38 1395 0.743 8284 43^1 4394 77.45 55.45 33. 62 55. 65 1373 0.884 R227 4502 4506 78. 47 55.71 33.55 55. 92 1351 1.044 8169 4614 4618 79.48 55.97 33.43 56. 19 1330 1.226 8108 4727 4732 80 . 47 56.23 33.39 56. 46 1308 1.431 8046 4840 4845 81 . 45 56.48 33. 29 56. 73 1287

1 .662 7981 4953 4960 82. 42 56.74 33. 18 57. 01 1266 1.919 7915 5067 5075 83.38 57.00 33. 06 57. 28 1246 2.205 7846 51 82 5190 84.32 57.26 32.93 57. 56 1225 2.523 7775 5296 5307 85.25 57.52 32. 78 57. 85 1204 2.873 7701 5412 5423 86. 18 57.79 32.63 58. 15 1184 3.253 7625 5528 5541 87. 09 58.07 32. 47 58. 46 1164 3.681 7547 5544 5659 87. 99 58.36 32.30 58. 78 1143

4. 142 7466 5762 5779 88. 86 58 .66 32.11 59. 12 1123 4.645 7382 5879 5898 89. 77 58.97 31. 92 59. 48 1102 5.191 7295 5997 60 19 90.64 59. 30 31. 72 59. 87 1082 5.733 7204 6116 6141 91 . 51 59.65 31. 51 60. 28 1061 6.422 7111 6236 6263 92. 37 60.02 31.29 60. 73 1041 7.112 7014 6356 6387 93. 23 60 .41 31. 07 61. 22 1020 7.853 6914 6478 6512 94. 07 60.84 30.84 61. 76 999 8.649 6810 6599 6637 94.92 61.30 30.61 62. 35 97 8 9.502 6701 6722 6764 95. 75 61.80 30.37 63. 01 957 10.414 6589 6846 6893 96. 59 62.35 30 . 12 63. 74 935 11.337 6472 6971 7023 97. 42 62.95 29. 88 64.57 913 12.423 6350 7097 7154 98. 24 63. 61 29. 63 65. 51 891 13.526 6222 7224 7287 99. 07 64.35 29. 39 66. 58 868 14.697 6089 7353 7422 99. 89 65.18 29. 16 67. 81 845 15.939 5950 7483 7559 100 . 72 66.11 2 8.93 69. 23 821 17.255 5804 7616 7699 101. 55 67. 16 28. 72 70. 89 796

18 .647 5650 7750 7841 102.38 68. 36 28.52 72. 84 771 '0.118 5488 7886 7987 103. 22 69.74 26.35 75. 15 745 21.671 5317 8025 8135 104.06 71. 34 28. 21 77. 93 718

23.30 8 6135 8163 8288 104. 92 73.23 28.10 81. 31 690

25. 0"13 4941 8314 8446 105. 78 75.46 28. 04 85. 47 661 26.850 4732 8464 8609 106. 67 78.17 28.04 90. 70 630

28. 761 4506 8620 8778 107.58 81.51 28 .11 97. 43 598 30.771 4259 8783 8956 108. 53 85. 74 28.23 106.35 564 32.883 3986 39'^4 91 44 109. 52 91 .27 28.57 118. 65 527

35. 103 3679 9136 9347 110.56 98. 89 29.04 136. 60 488 37.437 3323 9335 9568 111. 70 110.14 29. 76 164. 91 445

3 9.890 2892 9559 9820 112. 98 128.91 3 J . 82 215.44 398 42.473 2322 9831 10128 114. 54 168. 93 32.06 328. 39 347 45.957 0 10733 11185 119.51

10

D-10

B- 95764 "1
Ses sion

Paper 2

VISd d

' ' 1 r

c V < CO

oo

bj

c^ z

Vl Ml Ml

_]

^il SI Ml O 'n Q N 0

3Nn 9NI1-13W

o

o —

8

UiV d

11 D-11
Session V

Paper 2

Liquid -''^^

t \ 1 >- \l

1-

\l

C/)

UJ —Pc A

Q B

Vapor

n

TEMPERATURE —

Figure 2. Phase diagram showing isothermal paths of computation.

Starting with ideal gas values at p= 0, path A at T < T crosses

the "dome", whereas path B at T > does not. Two isobars are shown, at P > P^, and at P < P^,. The critical point is at C. P. On isobars at P > P^, some discontinuities may be

expected at T = T^, point X.

12

D-12

USCOMM - ERL
APPENDIX E

APPENDIX E

FROM: International Conference and Exhibition on R-719

Liquefied Natural Gas, 3rd, Washington, D. C, Session II Sept. 2h-28, 1972. Institute of Gas Technology, Paper 10

Chicago, 111. (1972)

THERMOPHYSICAL PROPERTIES OF METHANE*

Robert D. Goodwin, Ph.D.

Physical Chemist

National Bureau of Standards

Institute for Basic Standards

Boulder, Colorado, U.S.A. 80302

ABSTRACT

This report describes briefly the methods recently used at this

laboratory to prepare tables of provisional values of thermodynamic

functions for methane. References are given for the principal sources

of PVT data. Emphasis is placed on analytical descriptions of physical

properties because these are needed for smoothing, for interpolation,

and for the computation of derivatives.

PROPRIETES THERMOPHYSIQUES DU METHANE

RESUME

Ce rapport decrit brievement les methods utilesees recement a ce laboratoire pour preparer des tables de values provisiones de functions

thermodynamique s du methane. Des references sont donnes pour le plupart des sources du data de compressibilite (PVT). L'interet principal se trouve dans les descriptions analytiques des proprietes

physiques, car on a besoin de celles-ci pour le lissage et pour interpoler et computer les derivatifs.

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

the sponsorship of The American Gas Association.

E-1
Session II Paper 10

THERMOPHYSICAL PROPERTIES OF METHANE

INTRODUCTION

This report is an outline of work on the thermophysical properties

of methane conducted at the NBS Cryogenics Division. Most of it has

been sponsored by the American Gas Association (A.G. A.). Previously

available data are given in surveys and compendia [8,9, 17, 21]. We

recently have measured many of the PVT properties needed for thermal property computations [10, 14]. Tables of provisional thermodynamic functions have been reported to the A.G. A. in the range

90 < T < 500 K, P < 700 bar (7. lo'^N/m^), at densities up to freezing

liquid on the melting line [11].

To obtain further data needed for these computations, measurements are in progress on specific heats and on dielectric constants

(useful to interpolate densities).

Concerning transport properties, the viscosities have been measured for saturated liquid methane, and thermal conductivity measurements from other sources have been combined with densities from an

equation of state to give a highly useful, simple correlation for the

entire (p , T) range of data

Looking ahead, we plan to obtain densities of some liquefied

natural gases by techniques different from our present method for

obtaining PVT data, again in cooperation with the A.G. A.

THERMODYNAMIC FUNCTIONS

Basic data for the computation of tables of the rmofunctions are

specific heats as a function of temperature [9] and accurate PVT

measurements. Figure 1 gives the P-T locus of data we have used

and identifies the sources. In addition, we must have PVT data for

the coexistence boundaries, solid -liquid and liquid -vapor . We have

measured pressures P(T) on these boundaries [14], and have derived

some densities along these lines. Table 1 gives densities of freezing

and of saturated liquid obtained at intersections of our experimental

PVT isochores with the P(T) boundaries. This table also gives saturated vapor densities obtained similarly by use of the virial equation

of state [8].

Analytical descriptions of the PVT data are essential for smoothing, for interpolation, and for the computation of derivatives. To

obtain derivatives which, in some regions, are even qualitatively

correct, the analytical formulas should be simple, and be consistent

with known behavior, especially about the critical point. The following forms [excepting (1)] have been developed here in recent years.

Symbols are given in the List, below.

2 E-2
Session II Paper 10

1) The Simon equation [16] for melting pressure is

P = P + P {{T/Tf -l1 . (1)

t o i_ t J

2) The nonanalytic vapor pressure equation [6] uses the argument

X = (1-T /T)/(l-T /T ) , t t c

2 3 3/2

-tnlP/P^) = a-x + b-x +c-x +d-x-(l-x) . (2)

3) Densities of the freezing liquid are described [11] by

d/d = (T/T )^/^ (3)

t t »

4) Densities of the saturated liquid are described [7] by use of the

arguments x = T/T^, z = (1-x) ,

d/d = 1 + a- z + b- + c- exp(-e -x^/z) . (4) c

5) Densities of the saturated vapor are described [10] by use of

the reduced arguments u= ( T^ / T- 1 ) /( T,, / T^- 1 )

, w= (T(,-T) /(T^-Tt),

5 ^n(d/d^) =a^-u-^^^ + a^-u +^ a.-w'"^. (5)

i=3

6) Saturation temperatures T^lp) for coexisting vapor and liquid are described [11] by use of the variables

Y(T^) = (Tc/T(j-1)/(T^/Tt-1), U(a) = (a- 1 ) /(Qf 1 ), where = d^/d^ is a constant,

8 . Y(T^) = U^^^.[l + a^tn(p) + (p-1)-^ ^'p'"

J

• (6)

i = 2

7) The heats of vaporization are described [9] quite well by use

of the reduced argument w = (T -T)/(T -T,),

6

AH = \ ^ a. w (7) vap / J 1 ^ '

i = l

8) Entropies of the saturated liquid are described [11] with high

precision by use of x = T /T^,

S^(T) = a^ + aj-tn(x) + a2-x + a3-x^ + a^-x^ + ag- (1-x)^^^ . (8)

3 E-3
Ses sion II Paper 10

Equations (2,4, 5) are nonanalytic at the critical point, consistent

with well-known behavior. The exponent in (3) must be adjusted for

individual substances. Equation (6) in effect replaces (4) and (5)

by a function which is single -valued over the entire range of vapor and

liquid densities. It can be used to estimate and without the need

for data in the approximate range 0.7< p/p^< 1.3 [7]. From (8) we

may obtain specific heats of the saturated liquid via Cq(T) = T-dS(j/dT.

Formulation of the specific heats for ideal gas states has been re- ported [9]

The saturated liquid methane densities are of especial technological importance. Constants for (4) are d^ = 10. 15 mol/-t,, T^, = 190.53 K

(IPTS-1968), P = 0.36, e = 0.88, a = 0.539 403, b = 1.896 635,

c = -0.018 387.

The isochoric equation of state P(p , T), used for our computations,

has been reported in three places [10, 11, 12]. It is nonanalytic at the

critical point, consistent with the experimental behavior of specific

heats C^. It gives a reasonable description of the entire PVT surface

by use of only thirteen least-squares coefficients (plus four non-linear

constants).

Illustrative of computational results for thermodynamic functions

obtained in [11] are the speeds of sound for saturated liquid. Figure 2,

and the Joule -Thomson inversion locus in P-T coordinates, Figure 3.

SPECIFIC HEATS

Specific heats, e.g., C^(p,T), are needed to compute temperaturedependence of thermofunctions . In [11] we used data for ideal gas states

(p=0) such that our computations with PVT data along isotherms at T< T^ must cross the vapor-liquid coexistence "dome". Both as primary

data, and for closed- Loop checks on internal consistency, we need specific heat data for the saturated liquid and throughout the homogeneous

domain.

Measurements in progress here on methane utilize our technique

developed for hydrogen and applied most recently to fluorine [5]. It is

important to note that "experimental" data for liquid along the saturation path, C^(T), are indirect, depending upon an accurate knowledge of

physical properties of the sample -holder , the vapor pressure equation,

and the saturated liquid densities [4]. Figure 4 gives a comparison of

older data with some current measurements of Cg.(T) by B. A. Younglove

at NBS. The line is from [11]. Measurements of C^(p , T) are in progress.

Over the homogeneous domain for the present we have good agreement for Cp(p, T) between [11] and the excellent flow-calorimetry

results of Jones et al. [ 13]

4

E.4
Session II Paper 10

DIELECTRIC CONSTANTS

Dielectric constants, e(p),are useful for interpolating densities

because they are virtually independent of temperature in our range of

interest [2]. Having established the e(p) relation, a measurement of e yields the density, useful especially for saturated liquid and vapor

near the critical point where accurate densities are notoriously difficult to obtain. We give preliminary results of work in progress on isotherms from 200 through 275 K with the apparatus of [20]. Define

the function of e x = -l^. cm^/mol,

4TTd^ e

where d^ = 28, 1472 mol/-t is the triple point liquid density. The re- duced density p = d/d^ then is given by

2 3 p=a'X + b.x+c-x ,

with a current uncertainty of about 0.5% at low densities, by use of a = 0. 645 133, b= 0.114 910, c= 0. 075 0 24. Figure 5 is a correlation plot of the available data.

VISCOSITIES

Viscosities, Tl(p,T), are needed for engineering design computations.

As part of the NBS contribution to methane properties, W. M. Haynes

obtained data for the saturated liquid, as shown in Figure 6, by the technique of the torsionally oscillating quartz crystal [1]. Methane is the

only substance for which these data, obtained by several different ex- perimental techniques, are in good agreement. Extensive data currently

obtained by W. M. Haynes on fluorine for the homogeneous domain might serve as a model for estimating methane data over the wide range of the

Tl(p , T) surface.

THERMAL CONDUCTIVITIES

Thermal conductivities, k(p,T), are needed for engineering design

computations. At this laboratory, data from other sources have been

correlated [15] by use of densities from an equation of state. At very low

densities, k is a function F(T) of the temperature only. For higher densities, a residual f (p ) may be added which is a function only of density.

k(p, T) = F(T) + f(p) ,

F(T) = a-T +b-[e'" -l] , f(p) = a-p + ^•[e'^'^ - 1] .

For methane T is in kelvins, p is in g/cm , and k is in mW/(cm-K):

a = 0.001 0384, b = 0.002 3608, c = 0.0085, o- = 0.989 9346,

e = 0. 037 9684, y =8.5.

5 E-5
Session II Paper 10

DISCUSSION

We have made significant progress in determining thermodynamic

properties of pure methane. There remains a need for accurate saturated vapor and liquid densities near the critical point, for specific

heats Cv over a wide range, and for a comprehensive smoothing of

PVT data via cross-formulating isochores and isotherms. The final

results should be directly useful for those natural gases which are nearly pure methane. For mixtures, the present work is an important first step because properties of the pure components are essential

for computations on any multi- component system.

ACKNOWLEDGMENTS

We are indebted to the American Gas Association for generous

support of this work, to R. D. McCarty for the least squares program,

and to D. E. Diller and L. A. Weber for valuable suggestions.

LIST OF SYMBOLS

Subscripts c and t refer to critical and liquid triple points

Subscripts g and t refer to saturated vapor and liquid

Subscript a refers to vapor-liquid equilibrium (saturation)

a, b, c , ck* , 3 , Y constant coefficients

Cp(p, T) molal heat capacity at constant P

C^(p , T) molal heat capacity at constant v

Cq-(T) molal heat capacity for saturated liquid

d molal density

e exponent in various expressions

e (p ) dielectric constant

T| (p , T) viscosity

E(p,T) the internal energy

H(p , T) the enthalpy

J the joule . 1 N-m

k(p , T) thermal conductivity

I the liter, lO'^m^

1 2 mol 16.043 grams of methane (C scale)

P pressure, 1 bar s IQ^N/m^ , 1 atm = 1.01325 bar

R the gas constcuit, 8.31434 J/(mol-K)

p d/d^, density reduced at the liquid triple point

CT d/d(,, density reduced at the critical point

S(p , T) the entropy

T temperature, K, (IPTS-1968) v 1/d, molal volume

W(p,T) the speed of sound x T/T^, temperature reduced at the critical point

e16
Session II Paper 10

REFERENCES CITED

[1] Diller, D. E., "Measurements of the Viscosity of Parahydrogen, " J. Chem. Phys. 42 (6), 2089-2100 (1965).

[2] Diller, D. E. , "The Dielectric Constant and Refractive Index of

Gaseous and Liquid Methane." Private communication L.N. 71-7,

NBS Cryogenics Division, June 17, 1971

[3] Douslin, D. R., Harrison, R. H. , Moore, R. T., and McCullough , J. P. , "PVT Relations for Methane, " J. Chem. Eng. Data 9 (3), 358-363 (1964).

[4] Goodwin, R. D. and Weber, L. A. , "Specific Heats of Oxygen at Coexistence," J. Res. NBS, 73A (1), 1-24 (1969).

[5] Goodwin, R. D. and Prydz, R. , "Specific Heats of Fluorine at Coexistence, " J. Res. NBS, 74 A (4), 499-505 (1970); 74A (5)

661-65 (1970) ,

[6] Goodwin, R. D. , "Nonanalytic Vapor Pressure Equation with

Data for Nitrogen and Oxygen, " J. Res. NBS, 73A (5), 487-491

(1969).

[7] Goodwin, R. D. , "Estimation of Critical Constants Tq,P^ From

the p(T) and T(p) Relations at Coexistence," J. Res. NBS , 74A (2),

221-227 (1970).

[8] Goodwin, R. D., "Thermophysical Properties of Methane:

Virial Coefficients, Vapor and Melting Pressures," J. Res. NBS,

74A (5), 655-660 (1970).

'

[9] Goodwin, R. D., "Thermophysical Properties of Methane:

Orthobaric Densities and Some Thermal Properties, " J. Res.

NBS,75A (1), 15-21 (1971).

[10] Goodwin, R. D. and Prydz, R., "Densities of Compressed

Liquid Methane, and the Equation of State," J. Res. NBS, 76A (2),

(1972).

[11] Goodwin, R. D. , Tables of Provisional Values of Thermodynamic

Functions for Methane, private communication 10 715, NBS Cryogenics Division, Sept. 30, 1971.

[12] Goodwin, R. D. , "Thermophysical Properties of Methane, " in

Proceedings of the 1972 Conf. on Natural Gas Research &

Technology, Atlanta, Ga. , June 5, 1972.

7 E-7
Session II Paper 10

[13] Jones, M. L. , Jr., Mage, D. T. , Faulkner, R. C. , Jr., and

Katz, D. L. , "Measurement of the Thermodynamic Properties

of Gases at Low Temperatures and High Pre s sure s - -Methane , " Chem. Engineering Progress Symposium Series 50 (44), 52-60

(1963).

[14] Prydz, R. and Goodwin, R. D. , "Experimental Melting and

Vapor Pressures of Methane," J. Chem. Thermodynamics 4(1),

127-133 (1972).

[15] Roder, H. M. and Diller, D. E., "Correlation of Thermal

Conductivity Measurements on Compressed Gaseous and Liquid

Methane, Part II, " private communication L.N. 71-10, NBS

Cryogenics Division, Dec. 30, 1971.

[16] Simon, F. , "On the Range of Stability of the Fluid State,"

Trans. Faraday Soc . 33, 65-69 (1937).

[17] Tester, H. E., "Methane," in Thermodynamic Functions of

Gases, Vol. 3, F. Din, Editor, London: Butterworths Scientific Publications, 196l.

[18] van Itterbeek, A., Verbeke, O., and Staes, K. , "Measurements

on the Equation of State of Liquid Argon and Methane up to 300

kg cm-2 at Low Temperatures, " Physica 29, 742-754 (1963).

[19] Vennix, A. J., Low Temperature Volumetric Properties and

the Development of an Equation of State for Methane , Thesis,

Rice Univ., Houston, Texas, 1965.

[20] Younglove, B. A., "Dielectric Constant of Compressed Gaseous

and Liquid Oxygen," J. Res. NBS , 76A (1), 37-40 (1972).

[21] Zagoruchenko , V. A. and Zhuravlev, A. M. , The rmophy sical

Properties of Gaseous and Liquid Methane , Moscow: 1969.

Available in translation from Clearing House for Federal

Scientific and Technical Information, Springfield, Va. 22151.

8

E-8
Session II Paper 10

Table 1. Methane Densities at Coexistence

T, K d, mol/'t Saturated Vapor

Freezing Liquid T, K d, mol/-L

90 680''^ 28 1472 175 3 0199

91 695 28 214 171 2 5388

93 866 28 393 167 2 1408

96 172 28 557 163 1 8063

159 1 5221

Saturated Liquid 155 1 2790

151 1 0704

175 053 18 390 147 0 891 1 169 326 19. 492 143 0 7370

163 699 20 428 139 0 6049

157 199 21. 379 135 0 4920

151 555 22. 130 131 0 3961

145. 448 22. 880 127 0. 3151

139 352 23. 578 123 0. 2473

133 773 24. 185 119 0. 1912

133. 878 24. 176 115 0. 1452

129. 657 24. 611 111 0. 1081

125. 825 24. 999 107 0. 0786

121. 893 25. 388 103 0. 0557

117. 746 25. 782 99 0. 0384

113. 772 26. 146 95 0. 0255

109. 611 26. 527 91 0. 0163

105. 165 26. 916

101. 434 27. 243

97. 173 27. 605

93. 512 27. 910

"'Triple point.

E-9
Session II Paper 10

T, °RDOUSlin et al.

27J < r ^ 398 l<

/6 Y- 4-00 at,n

T KFigure 1. The locus of NBS PVT data is shown by solid lines. Iso- therms of [18] fall between vertical dashed lines, and isochores of

[19] between long-dashed lines. Data above 273 K are from [3].

1600

1400

1200

1000

E

800

600

400

200

SPEED of SOUND in SATURATED LIQUID METHANE

Calculation, Goodwin (1971)

Measurements of Von Dael et ai (l965)-

100 120 140 T, K

160 180

Figure 2. Comparison of experimental and calculated [11] speeds of

sound for saturated liquid methane.

10

E-10
Ses sion II Paper 10

90 no 130 150 170 190

T.K

11 E-11
Session 11 Paper 10

E 1.4

roE

1.3

1.2

1 i

s>

1 11

METHANE DIELECTRIC

1 1 1 1

CONSTANTS

9

9

i

-

' 4

• Saturated Liquid

9 6 > 200 K O - 225 K

-

' 250 K

A - 275 K

9

9

-o

•?

-o

- \

m

•

9 Figure 5

1 1 1 1 1

9

<f m

1 II 1 •

180x10

r5

140

E

>^

^ 100

c7) OO

CO

> 60

20

10 15 DENSITY, mol/f

20 25

VISCOSITY OF SATURATED

^ LIQUID METHANE

^ • W.M.Haynes (NBS-1972)

Huang,Swift, Kurata ^

Rossini et al. \ O Boon et al. A Swift et al. O Hellemans et al.

Aft

Figure 6

1 1 1 1 1 1 1 1 1^

90 110 130 150 170

TEMPERATURE, K

ISO

12 E-12

USCOMM - ERl.
APPENDIX F
1
APPENDIX F

CONTENTS

List of Symbols ........ ii List of Tables . ... iii

1. Introduction 2

2. Experimental P-p-T Data ..... 3

3. The Equation of State . . , 7

4. The Computer Package ..... . 10

5. Adjustments and Tests for Methane . 11

6, Discussion . 12

7. Notes to the Tables ....... . 13

8. Bibliography ........ . 15

i F-1
List of Symbols

(Subscripts c and t refer to critical and triple points.)

(Subscripts g and refer to saturated vapor and liquid.)

a, 3, constants in the equation of state

B, C,D,E, density-dependent coefficients of the equation of state

d, - density, mol/l: d^ = 10.00, d^ = 28 . 1 47 raolA

e, an exponent in various expressions

J, the joule, 1 N-m

I, the liter, 10"^

mol, ' 16.043 grams of methane (C"""^ - scale)

P, pressure, bar: 1 atm = 1.01325 bar,

Pt = 0.117 436 bar, P^ = 46.0555 bar

R, the gas constant, 8.31434 j/(raol-K),

0.0831434 bar-^ /(mol-K)

p, . d/dt , density reduced at the liquid triple point

a, d/dc , density reduced at the critical point

T, temperature, kelvin (IPTS- 1 968),

Tt = 90. 68 K, To = 190. 60 K

u(p,T), T/e(p)

V, l/d, molal volume

a)(p, T), (u-l)

X, T/Tq , temperature reduced at the critical point

Y(P,p,T), (Z-l)-x/p, dependent variable for equation of state

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

ii F-2
List of Table

Table 1. Sources of single-phase P-p-T data.

Table 2, Sources of orthobaric densities.

Table 3. Methane second virial coefficient.

Table 4. Methane third virial coefficient.

Table 5. Methane orthobaric densities.

Table 6. Computer programs for the equation of state.

Table 7. Methane vapor pressures.

Table 8. Methane vapor densities.

Table 9. Methane liquid densities.

Table 10. Methane saturation temperatures.

Table 11. Coefficients for the equation of state, methane.

Table 12. Calculated derivatives in density, methane.

Table 13. Calculated critical isotherm, methane.

Table 14. Comparison of experimental P-p-T data for methane

with the equation of state.

Table 15. Calculated P(T) isochores for methane.

Table 16. Calculated P(p) isotherms for m.ethane.

Table 17. Calculated P-p-T locus of the Joule- Thomson inversion

for methane.

Table 18. Calculated entropies and specific heats of saturated liquid

methane .

iii F-3
APPENDIX F

NONANALYTIC EQUATION OF STATE FOR METHANE,

CONSTRAINED TO THE VAPOR- LIQUID P-p-T BOUNDARY

Robert D. Goodwin

Institute for Basic Standards

^. National Bureau of Standards

Boulder, Colorado 80302

December 7, 1972

ABSTRACT

For use in thermal computations there is described a novel

equation of state which is nonanalytic at the critical point, consistent

with the behavior of specific heats, C^ . The equation has its origin on

the analytically described vapor-liquid saturation boundary in P-p-T

coordinates. It utilizes only eleven least- squares coefficients.

A computer program is given for establishing coefficients of

equations for the vapor-pressures, the orthobaric densities, the

orthobaric (saturation) temperatures, and the constrained equation

of state. The program is applied to methane, with copious tables

useful to check the analytical formulations and derivatives for errors,

to examine behavior of the calculated P-p-T surface, and to compare

experimental P-p-T data.

F-4
1 . Introduction

The need for an improved equation of state for thermal computations is well-known, and we recently contributed a non- analytic form

for methane, giving references to the previous art [8],

In the present report we overcome the long-standing problem

of consistency with the vapor-liquid boundary by devising a formulation

which is tied to this boundary in the P-p-T coordinates. The problem

of consistency therefore cannot arise.

More important in an equation of state than mere precision in

reproducing experimental P-p-T data (often of indeterminate accuracy),

is the need for a functional form which will give some confidence that

derivatives (used for thermal computations) may be at least qualitatively

correct. In the following we examine the critical isotherm and print

other calculated isotherms in order to examine their behavior. We

also print isochores, their slopes and curvatures for similar examination. As a preliminary quantitative test, we compute the Joule- Thomson

P-p-T inversion locus, and the entropies and specific heats for saturated

liquid methane.

When functions in the equation of state have fixed or singular

points, as at the triple- and c ritical -points , it becomes necessary to

redetermine their coefficients whenever values for the fixed-point

constants are changed. For this reason we have prepared a complete,

equation- of - state program which, for any given fixed-point constants,

will adjust the vapor-pressure equation, the orthobaric equations, and

finally the equation of state. This program should be useful in future

work. The computer programs therefore are given below.

2

F-5
2. Experimental P-p-T Data

For the virial equation of state,

Pv/RT = 1 + B(T)-a + C(T)-a^ + ,

several sources of coefficients are available. For the second coefficient,

B(T), table 3 uses the following identifications: IDl - Douslin [5];

ID2 = Hoover [10]; IDS = Byrne [2]; ID4 = Pope [15]; ID5 = Sengers [6, 18].

The data are represented by use of d^ = 0.01017 raol/cm^ , = 190. 56 K,

' 6

B*^B(T).d, = Y

Bi .(Te/T)^^*'"^^/^

i=l

with constants at the head of table 3. Only data above the blank line

were used for least squares.

The third coefficient, C(T), using the same identifications, is

given in table 4. The data are represented by use of X = T/Tc , e = 1 . 86,

1/2 C* = C(T)-d| = [A/x / + B/x + C/x^ + D/x^ ]• f(T),

f(T) = 1 - exp(l - e -x^),

with constants at the head of table 4.

This virial equation, upon intersection with our vapor-pressure

equation [16], gives saturated vapor densities identified by ID=2 in

table 5.

The use of this virial equation to generate P-p-T data for the

equation of state was abandoned in favor of the virial equation of [6],

upon examination of deviations from the equation of state.

3

F-6
For the homogeneous domain, our sources of P-p-T data for

methane are summarized by table 1 . From the data of Cheng [3] we

have selected points of pressures thru 1000 bar. Coefficients of the

equation of state are based only on data of the first three lines of table 1,

i.e. through Douslin et al. Individual deviations from the equation of

state are given in table 14. Identifications given by three or four digits

refer to our NBS measurements [8], and this report.

For the vapor-liquid coexistence boundary, our sources of

orthobaric (p , T) data are summarized by table 2. Individual data

are given in table 5, which compares them with the calculated saturation temperatures used in the equation of state (d^ = 10.00 mol/-5,

Tc = 190.60 K) . At the suggestion of Prof. O. B. Verbeke we have

added 0.02 K to temperatures of Jansoone et al [12]. Some points

(ID=5) obtained by O. B. Verbeke at this laboratory in the summer of

19*71 are assigned two temperatures, differing by 0.02 K, to permit

an examination of the temperature- s ensitivity . Identifications given

by three or four digits are for our unpublished results from dielectric

constant measurements in the spring of 1972 [9], with densities based

on our P-p-T data of table 14 below.

4

F-7
HI Q_I

COI (U

Cud oooH

rX2 o>Q

CJ I—

i-i >

(U

+-> mO

<Va o2

^1O

-(-> Hi <Q

LTl o O o O LT) o o O o O 1—1 o 00 o in CO

.—1 o o (M o o o o o 1—

o 00

LTl LT)

LT) CO 1—

o O o o

IT) o IT) o o t—

1 ' 1 ' 1—1 1—

1 o :—

o 1—

1—

CM o O 00 OO ro r- O o

(M CO CO (M ro 1 O 1 (Nl 1 ro 1 ro 1 ro 1 r-H o

CO o oo LTl ro ro

00 oo (M un

(M .—

00 00 I I o o

r-H ro O

•r-l

03

0) 1—

ni •Hu• 1-1 >

00

00

CP

00o 00

00

CO0OQ >

roO

0) 1—

>

00

bjo u

=tfc

COO

ft

<U

CO •HH

00

CO • H

!^ CO

CO 5 F-8
I.D

Table 2. Sources of orthobaric densities

(The data are printed in table 5)

Authors

Density range,

molA

1

1

2

5

6

7

XXX

Virial equation, v . p . eqn,

Isochore intersections

Virial eqn,, this report

Jansoone et al

Ricci et al

Verbeke

NBS, (Dielectric consts.

[6, 16] 0.016 - 3.0

[8, 16] 18.4 - 27.

0.016 - 2. 3

[12] 7.6 - 14.6

[17] 5.0 - 15.7

[24] 8.0 - 12.4

[9] 2.3 - 24.6

6

F-9
3. The Equation of State

Following our previous report [8] we discovered that a significant

improvement was obtained in reproducing P-p-T data by the addition of

another temperature- dependent term in the following form (symbols

of this report),

. (Z-l)-x/p = A + B-$(T) + C/x + D/x^ + E-Y(p, T)/x^, (1)

where

$(T) = x.[l - exp(-3/x)],

/ Y(p, T) = 1 - uj ln{l + l/w),

. -'"'^ uu(p, T) [T - e(p)]/Te ,

and the density- dependent coefficients are

2 1 3

A(p)=^Al.p^ B(p)H ^ Bi-p\ C(p)= Y

Ci-p',

0 i=0 i=l

3 2

^ D(p) = ^ •p^ E(p) = (p-1). ^ El •p^

i = 0 i=0

for a total of 1 5 least- squares constants.

We now wish to have the equation of state tied to the vapor-liquid

coexistence boundary. This already has been done, via a different

approach, by O. B. Verbeke [22, 23]. Let us condense eqn. (1) to the

form

Y(P,p, T) = F(p, T). (1-a)

7

F-10
Consider that our equation describes P(T) along any isochore; i.e. the

density p is a parameter. For every density there exists a coexistence,

vapor-liquid (or a solid-liquid)temperature, Tg (p ) . The vapor pressure

now may be expressed as a function of density, Ps[Ts(p)]. Placing

these variables in (1-a) gives the equation of state at coexistence. We

shift the origin to this boundary by subtraction --

(Y-Yg.t) = (F-Fg.t), (1-b)

to obtain an equation of state with origin on the coexistence boundary.

With reference to eqn. (1), we see that the term A(p ) drops out upon

taking (F-Fgat)- Further exploratory work has modified the functions

Tg (p), uu(p, T), and D(p), as seen below.

The new, constrained equation of state may be written by use

of Xg (p) = T3 (p )/To , etc .

,

(Y-Yg ) = B-Xb + CX, + D-Xd + E-Xe, (2)

where

Y(P,p, T) = (Z-l).x/p, Y3 (p) = (Z3 -l)-x,/p,

Xb (p, T) = x-[l-exp(-3/x)] - X3 •[l-exp(-3/x3 )],

Xc (p. T) H (1/x - I/X3 ), X, (p, T) = (l/x^ - 1/x^),

Xe (p, T) = [l-aj-^n(l + l/uu)]/u2 - [l-uus^nd + l/uug )]/uf ,

and,

u(p, T) = T/e(p), U3 (p) = T3 (p)/0(p),

aj(p, T) = (u-1), ^3 (p) = (U3 -1),

e(p) = T3 (p)-exp[-a- |a-lP].

8

F-11
The saturation (orthobaric) temperatures Tg (p ) are described

with modifications from [8], in particular by use of an exponential

form about the critical density. Define the variables,

y(T3 ) = (Te/Tg -1)/(T,/Tt -1),

U(a) = exp[e.a.(a-at)/|a-l|],

9

W(p) H A3 + As-p^^^ + V A, .p'"^

i=4

where Qt = dt /do is a constant, and e = l/Z. The function is

y(T3 ) = U{ct)-[1 + Ai -Inip) + (p-1)- W(p)].

The density-dependent coefficients of eqn. (2) now have only

eleven constaxits --

1 3

B(p) ^ Y

' ^^P^ ^ I

i=0 i=l

P^

D(p) =^1^1 -P' > E(p) H (ct-D- ^ El

i=0 i=0

•P^

All of the above forms may be seen in the computer programs of

table 6

9

F-12
4. The Computer Package

Table 6 gives our computational package for adjusting the

equation of state. We may hope that it will be useful for substances

other than methane, with minor changes of characteristic constants

and ranges of the variables. The experimental data required for its

application are a virial equation for low density gas, the vapor pressures,

the orthobaric densities, estimates for the triple and critical points,

and P-p-T compressibility data over a sufficiently wide range. Not

used in this equation is the melting line, which must be combined

independently.

This program permits exploration of non-linear constants,

including the fixed-points. It saves coefficients of the equation of

state corresponding to a minimum in the mean pressure deviation.

The following is an example of statements which should be added to

the main program to explore the critical point temperature and density,

48 SSK = 1 . OE+010 $ DO60MT=l,3 $ TCRT = 1 90 . 50 + 0 . 03'';=MT

49 CALL PSATFIT $ PCRT = PSATF(TCRT)

50DO60MD = l,3 $ DCRT = 10 . 0 + 0 . 1-(MD- 1

)

51 CALL DSATFIT $ CALL TSATFIT

61 GK = DTRP-GKK $ CALL PSATFIT $ PCRT = PSATF(TCRT)

64 CALL DSATFIT $ CALL TSATFIT

10

F-13
5. Adjustments and Tests for Methane

Behavior of eqn. (Z) on the critical isotherm is found by

differentiating both sides with respect to density. For the first and

second derivatives we obtain 0 = 0 at the critical point, hence no constraints on these derivatives are possible via the least squares

program of [11]. Calculated results for the critical isotherm of

methane, however, often show an inflection near the critical point

when using the cubic form of Tg (p), function TSATXF(DEN). Nonnegative slopes are obtained by selecting dc = 10.00 m.o\/t,

Tc = 190.60 K. To obtain an acceptable critical isotherm for all

reasonable values of (d^ , T^, ) we have been forced to the exponential

form of Ts (p), function TSATF(DEN). With this form of T^ (p) we

find improving representation of the P-p-T data as dc diminishes

below the former value of 10.15 mol/l, and Te increases above the

former value of 190.53 K. We arbitrarily have selected the values

dg =10.00 mol/^, Tc = 190.60 K for the present equation of state.

The orthobaric densities of table 5 have been reduced in number

for use in the equation of state program, to obtain improved selfconsistency. When the critical point (pc , T^, ) has been selected, there

is little use for data near p^ because the form of the fitting function,

Tg (p), is relatively inflexible about Pc . The selected data are shown

by tables 8, 9, 10.

Coefficients of the equation of state for methane, and their

density-dependence, are given by table 11. Experimental P-p-T data

are compared with the equation in table 14, using identifications of

authors from table 1 . Tests of the equation are given by tables

12, 13, 15, 16, which serve to show that analytically derived functions

for the derivatives are giving correct values.

11

F-14
Preliminary, quantitative tests of the equation for methane are

given by table 17 for the Joule- Thomson inversion locus, and by table

18 for the entropies and specific heats of saturated liquid. These

results are numerically similar to values obtained earlier [8-a].

6. Discussion

Table 18 shows that the heat capacity for saturated liquid

(CSAT) probably is too small at the lowest temperatures, approaching

the triple point. This effect could arise (1) from the virial equation

used to find the saturated vapor densities (by intersection with the

vapor pressure equation; (2) from the fitting function Tg (p ) used to

represent the orthobaric (saturation) temperatures, or; (3) from the

fitting function used to represent entropies of the saturated liquid.

By means of the following steps we have succeeded in raising

the triple-point value of Cgat from 47.01 to 52.31 j/(mol-K). First,

we used the virial equation of this report, based heavily on virial

coefficients of Pope [15], to obtain the vapor densities below 2.25 mol/t,

as seen in table 5, ID=2.

Secondly, we have modified the Tg (p ) function, already described

in section 3 above, by use of the forms,

y(T, ) = U(a)-[1 + (P-I)-W(p)],

10

W(p) = Ai + As • 'tn(p) +- A^'iO^^ +A4/(l+£ •P^^^)+ ^

A^-p'"^,

i=5

where e=8 by trial. This gives a highly accurate representation of

the vapor densities.

12

F-15
Finally, we have modified the function for the entropies, which

has not been reported above. Define the variables

y(S) ^ (S-SJ/(S, -St), x(T) = (T, -T)/(Te -TJ,

when the function has the forra,

y(S) = (1-x) . exp[f(x)],

with,

7

£ . ^ . i-1

f(x) = Ai -x-^n (x)+A2 -x^

Z

X

i=3

This formula is constrained at the end-points (triple and critical) for

consistency in the derived thermodynamic tables. It represents the 52

derived, saturated liquid entropies with an rms deviation of O.OOl

percent by use of e = 0.15.

7. Notes to the Tables

Units or dimensions of the variables are not given in some

tables, although they are uniformly consistent with the List of Symbols.

Energies are expressed in joules, J.

The virial coefficients B(T), C(T) in tables 3, 4 are dimensionless, having been reduced as defined by the particular critical density

given in section 2 above.

For table 5, the heading DTS/DD represents the derivative of

Tg (p ) with respect to density, K'-t/mol. For table 12, the derivatives

m the form DFF/DD al so are relative to density in mo\/l . In table

13

F-16
13, however, the derivative DPR/DDR represents pc • (S P/9p )x /Po , and

the remaining derivatives, DFF/DR, are relative to the density

p = d/dt reduced at the liquid triple point.

Isochores and isotherms of tables 15, 16 give the derivative

DP/DD relative to density in molA.

In table 18 the volumes V, GAS, V, LIQ are in l/mol; the heat

of vaporization Q, VAP is in j/mol; the entropy S, and saturated liquid

heat capacity CSAT, are in j/(mol.K).

14

F-17
8 . Bibliography

[ l] Brewer, Jerome, Determination of mixed virial coefficients,

Mic3west Research Center, Kansas City, Mo. 64110 (Dec. 1967).

Defense Documentation Center No. AD 663 448. (Incl. methane,

-150 to + 50 deg. C. ).

[ 2] Byrne, M. A., Jones, M. R. and Staveley, L. A. K., Second

virial coefficients of argon, krypton and methane and their

binary mixtures at low temperatures. Trans. Faraday Soc .

_64 (7), 1747-56 (1968).

[ 3] Cheng, Vic M., Thesis, School of Engineering and Applied

Science, Princeton University, 14 April, 1972.

[ 4] Davenport, A. J., Rowlinson, J. S. and Saville, G. , Solutions

of three hydrocarbons in liquid methane, Trans. Faraday Soc.

62, 322-27(1966). (Densities of sat'd . liq. CH4 , 1 1 5 to 1 54 K) .

[ 5] Douslin, R. D., Har rison, R. H. , Moore, R. T. and McCollough,

J. P., P-V-T relations for methane, J. Chem. and Eng. Data

9(3), 358 (1964).

[ 6] Goodwin, R. D., Thermophysical properties of methane:

virial coefficients, vapor and melting pressures, J. Res.

NBS 74A (5), 655-60 (1970).

[ 7] Goodwin, R. D., Thermophysical properties of methane:

orthobaric densities and some thermal properties, J. Res.

NBS 75A(1), 15-21 (1971).

[ 8] Goodwin, R. D., Densities of compressed liquid -methane,

and the equation of state, J. Res. NBS 76A(2), 81-101 (1972).

[8a] Goodwin, R. D., Tables of provisional values of thermodynamic

functions for methane. Private communication 10 715, this

laboratory, 30 September, 1971.

15

F-18
Goodwin, R. D., Dielectric constants and orthobaric densities

of methane, private communication L.N. 72-4, this laboratory,

2 June, 1972.

Hoover, A. E., Nagata, I., Leland, T. W. Jr. and Kobayashi,

R., Virial coefficients of methane, ethane, and their mixtures

at low temperatures, J. Chem. Phys. 48(6), 2633-47(1968).

Hust, J. G. and McCarty, R. D., Curve-fitting techniques

and applications to thermodynamics. Cryogenics _7(4), 200

(Aug., 1967).

Jansoone, V., Gielen, H. and deBoelpaep, J., The pressuretemperature- volume relationship of methane near the critical

point, Physica 46, 213-21 (1970).

Kvalnes, H. M. and G addy, V. L., The compressibility isotherms

of methane at pressures to 1000 atmospheres and at temperatures

from -70 to 200°C., J. Am. Chem. Soc. _53, 394-99 (1931).

Michels, A. and Nederbragt, G. W .

, Isotherms of methane

between 0 and 150°C for densities up to 225 amagat, Physica

111(7), 569-77 (1936).

Pope, Gary A., Calculation of argon, methane, and ethane

virial coefficients. Thesis, Dept. of Chem. Engineering,

Rice University, Houston, Texas (July, 1971).

Prydz, R. and Goodwin, R. D., Experimental melting and

vapor pres sures of methane, J. Chem. Thermodynamics 4,

127-33 (1972).

Ricci, F. P. and Scafe, E., Orthobaric density of CH4 in the

critical region. Physics Letters 29A(11), 650 (1969).

16

F-19
Sengers, J. M. H. Levelt, Klein, M. and Gallagher, J. S.,

Pressure- volume-temperature relationships of gases: virial

coefficients, to appear in a forthcoming edition of the American

Inst, of Physics Handbook.

Terry, M. J., Lynch, J. T., Bunclark, M., Mansell, K. R.

and Staveley, L. A. K., The densities of liquid argon, krypton,

xenon, oxygen, nitrogen, carbon monoxide, methane, and

carbon tetrafluoride along the orthobaric liquid curve, J.

Chem. Thermodynamics J. (4), 413-24(1969).

van Itterbeek, A., Verbeke, O. B., and Staes, K., Measurements on the equation of state of liquid argon and methane up

-2

to 300 kg cm at low temperatures, Physica^9, 742-54 (1963).

Vennix, Alan J., Low temperature volumetric properties and

development of an equation of state for methane, Thesis, Dept.

Chem. Engineering, Rice Univ., Houston, Texas (April, 1965).

Verbeke, O. B., An improved state equation in the vicinity of

the critical point, J. Res. NBS 76A(3), 207-11 (1972).

Verbeke, O. B., Representation of P-V-T data by means of

a "universal" state equation for simple, pure fluids. Cryogenic

Engineering Conference, Boulder, Colo., 9 August, 1972.

Verbeke, Olav B., private communication, 1972.

17

F-20
Table 3. Methane second virial coefficient.

6. -+26978863- 00 1 1 . 262298136+000 -7 . 052537501 + 00 0 8. 31956996 0+ 000 -5 . 6732'+983 3+ 00 0 1 . 32 6tt 32 79 9 + 0 0 0 ID T,K T/TC B» CALC PCNT

k 126.571 0.66 '21 -2. '+639 -2. '+678 -0.16

k 135.98'* 0.71360 -2.1886 -2.178'+ 0.'+7

k l'*7.53l 0 .77'+'*6 -1.881'+ -1.8850 -0.19

h 158.916 0 . 6339'+ -1. 61+26 -1.6'*97 -0 .''+

I* 173.507 0.91051 -1.3997 -1 . '+033 -0.26

5 176.00 0 0 .92359 -1.3719 -1. 366'+ 0 .'1

5 IStt.OO 0 0 .96558 -1.2590 -1 . 256'+ 0.21

191.129 1.00299 -1.1623 -1 .1680 -0 .'9

5 192.00 0 1 . 00 756 -1.158'+ -1 . 1578 0.05

5 200.000 1 . 0'^95'+ -1.0689 -1.0692 -0.03

3 202.520 1 . 06276 -1.0 515 -1.01+31 0.81

5 210.000 1.10202 -0.9692 -0.9702 -0.11

5 220.000 1.15'+ 4*9 -0.8807 -0.8825 -0.20

3 221.130 1 . 160'+2 -0.8726 -0 . 8732 -0.07

5 230.000 1.20697 -0 . 8 02'+ -0 .8042 -0.22

5 2^*0.00 0 1 . 259'+5 -0.7 32 2 -0 .731*0 -0.2'*

2 2ii0.020 1. 25955 -0.7396 -0.7338 0.78

3 2'+3.«2 0 1.279'*9 -0.7150 -0.7090 0.83

5 260 .00 0 1. 36'+'+0 -0 .6122 -0 -0.19

1 27 3. 15 0 1 . '33'+l -0.5i+26 -0 . 5'+58 -0.59

2 27 3.150 l.'+33'+l -0.5'+19 -0 . 5'*58 -0.73

3 273.170 1. '33 51 -0.5'+61 -0 . 5'+57 0.08

5 28 0 . 00 0 1.46935 -0.5136 -0.5137 -0.02

1 298.1'»2 1 . 56'»56 -0.'+355 -0.'+373 -0 .i+l 5 300.000 1.57'+31 -O.'+302 -0.'»301 0.03

1 30 3. 1i»l 1 .59079 -0 .'+161 -0 . '+182 -0.50

5 32 0 . 00 0 1.67926 -0 .3 60 0 -0. 3590 0.28

1 32 3.1'+0 1.6957/+ -o.si+ai -0.3'+88 -0.20

5 3it0.00 0 1. 78'*21 -0.2990 -0 .2980 0 .35

1 3<+8.1it3 1.82695 -0 .2752 -0.2755 -0.12

5 36 0 . 00 0 1 . 88917 -0.2 '61 -0.21+50 0 .'+5 Of O . 1 7 u i. • o i. o U • c 1 0 " U • l P

5 38 0 . 00 0 1.99'+ 12 - 0 .2 00 3 -0 .1987 0.83

1 398.150 2 . 089'+2 -0.161'. -0.1611+ -0.02

5 'fOO.OOO 2. 09908 -0.1597 -0 . 1579 1.13

1 ^23. 17 0 2. 22067 -0.1159 -0. 1163 -0.32

1 '+'+8.182 2.35192 -0.0769 -0 .0771 -0.32

5 t+SO.GO 0 2. 361 '6 -0.0753 -0. 07'*5 1.03

1 '+73.193 2 . '8 3 1 7 -0.0 '2 3 -0. 0'+29 -1.30

1 '98.20 3 2.61'+'+2 -0.0118 -0.0127 -6.85

3 110.830 0.58160 -3.3571 -3. 0931 8.5'+

3 112.^+3 0 0.59000 -3.253'+ -3. 0196 7.7k

3 n't. 1+0 0.60055 -3.1303 -2.9308 6.81

3 116.780 0.61283 -3.0052 -2. 8321 6.11

3 121. 21+0 0.63623 -2.7917 -2.6570 5.07

3 1^8.830 0 . 67606 -2. '8'+

-2. 393'* 3.81

2 131.920 0 .69223 -2.2781 -2.2970 -0.82

3 136.7'+0 0.71757 -2.2262 -2. 1571+ 3.19

3 l'+8.28 0 0.77813 -1.9089 -1.8691 2.13

5 160.000 0 . 83963 -1.6 1+6 5 -1 .6291+ 1.05

3 162.30 0 0.85170 -1.6109 -1 . 5875 l.'+7

5 168.00 0 0 . 88161 -1.5001 -1.1+899 0.68

3 178. « 1+0 0 .936'+0 -1. 3 ''5 -1.3315 0.97

2 191.090 1.00273 -1.1829 -1.1685 1.23

2 200.030 1. 0'+970 -i.oe'+9 -1. 0689 1.50

2 215.030 1 . 1281+1 -0.91+16 -0.921+8 1.82

NP = 1+0, RMSPCT = 1.192

18

F-21
Table 4. Methane third virial coefficient.

1.86G 0. 26539993 -0 . 062*^6387 0 .1'42l3238 0. 39329^*10

ID T , K T/TC C* CALC PCNT

I* 0.71360 -C. 15^4 8 -0 . 1^+88 k.[iZ

lt+7. ^61 0,2017 0 .2116

I5d.91b 0. 8339^+ 0.3703 C . 3553 1.37

173.5.C7 0.91051 0 .it531 0.^+29'+ 5.52

191. 129 1 . G 0 2 9 9 0 . ii 1 2 7 0.^+251 -2.93

1 273. 15G i. ^433'+l 0 .2710 0 . 27^fl -1.13

1 298. 1^+2 1. 5b^+t 6 0.2i*51 0.2^*1+2 0.3 8

i 3Q3.1i+l 1.59079 0.2itOb C .2391 0.3^+

1 323 ,litG 1. 6957^+ 0 . 222i+ 0 . 221^ 0.4b

1 3^+8 , m3 1. 82695 0 . 2G'+3 C.2038 0.25

1 373. 15G 1.95818 0.1897 C. 1900 - C . 1 6

1 598. 160 2. 0 89^+2 0 .178b C . 1791 -C.28

1 i+23. 17G 2 . 2 2 0 b 7 0 . ie9b G . 17 03 -0.39

1 it£*8. 182 2.35192 0 .1639 C . 163C G .t?8

1 i+73.193 2.^+8317 0 .1566 0. 1568 -0.15

1 i498. 2C3 2.61t+'42 0 .1515 0.1515 -0.01

126.571 0. b o if 2 1 -2.1203

2 191.090 1. C 027 8 0.'490'+

2 2 0 0.030 1. Oi+9 7 0 0.^+50 0 2 215. 0 3C 1. 128i+l O.i+312

2 2^+0.020 1. 25955 0.3626

2 273 . 15 G l.<+3 3i*l 0.2761

NP = 16, f^MSPCT = 3.6aO

19

F-22

-0.7387 187.02

0.4252 15.33

C.itlCl 9.7'+

0.379C 13.77

C. 3278 10 . d8

v,2rm

1

I

i

I

'i

.1

1

J
Table 5. Methane orthobaric densities.

ID MOL/L CALC PCNT TS ,K CALC PCNT OTS/00

2 0 .0 157 u . 0157 u . 21 90. 660 90.662 0.02 542. 1+808

1 C .0163 b' . 0 1 6 3 0.C8 91.0 00 9Q .991+ 0.01 525. 8733

2 0 . 0183 C . C183 u. 1'+ 92. COD 91. 988 0.01 1+79. 8070

2 C.G229 0.0229 0. r7 91*. 0 OC 93.991+ 0.01 i+C 1.6 0 58

1 i .C255 c . C25 5 -0.09 95.0 00 95. CO 9 -0.01 368. 3178

2 (j .0283 3. 0263 3. C6 96. C 00 95. 995 0.01 339.3451

2 L . J 3 -+ 7 G. 0 3 1+7 0,01+ 98. 0 30 97 . 996 0.00 289. 1316

2 0.01+22 0 . J 2 2 n. C6 100. CGQ 99. 991+ 0.01 248. 3255

2 3.0509 3.10 102. OOQ 101. 989 0. 31 214. 8756

1 C . J 557 J . 0557 -3.G3 1C3. COC 103.003 -0. 00 200. 1658

2 C . UbC8 J . 0 6 0 ° 3 . 11+ 1 0 1+ . 0 0 0 103.981+ 0.3 2 167.1873

2 0 . j722 J. 0723 0.19 1 06. 0 00 105.978 0. 0? 164. 0973

1 CO 78 6 J. 0736 - 3 . C 1 137. OOC 107.001 -0.00 153.7315

2 C . i;051 J. 0853 '.23 108.0 00 107.971 0.03 144.6937

2 L. .0997 j.lOOC J. ?8 1 1 C . C 0 0 109.961+ 0.0 3 128. 2743

1 0 . 1 Ij 3

3.1081 - 0 . G 2 111.000 111. CO 3 -0. OC 120. 7063

2 0 .1 162 0. 1166 0. 32 112. COO 111.957 0.01+ 114.2751

2 C .13^7 J. 1352 G. 36 111+. 0 00 113. 950 0. 04 102. 2719

1 u . 1^*52 3.11+5? I. . I 3 115.00: 111*. 996 0.00 96.6507

2 b .lb53 0 .1559 3. 79 116.0 03 115. 91+5 0. 05 91. 9054

2 C . 1761 3 .1769 3.1+1 118.003 117. 939 0. 05 82.9075

1 L .1912 3 . 1913 0 . rji+ 1 19. r 3r. 118. 991+ 0. 01 78.6271

2 0 .2 .'3 5 J.2C1+3 :.'+2 1 2 0 . C 0 119.935 0. 05 75. 0507

7 C .231i+ J . 232'+ .i+3 12 2.003 121.932 0.C6 68.1551

1 D .2h7 3 0.21+75 3. t7 1 23. 0

0-^ 122. 989 0. 01 64. 6422

2 (i .2b21 3.2633 0 . 1.1+ 121+. 003 123.929 0. oe 62. C723

2 L .2958 u. 2971 : . 1+3 126. COO 125.928 0.06 56.6792

1 C . 3 151 . 3152 0 .01+ 127.0 00 126.991+ 0.00 54. 0492

2 0 . 3 327 0.331+1 126. COC 127. 927 0. 06 51.6760

2 C .3 73C 3.371+5 0.1+1 13 0.000 129. 927 0. 06 47. 5604

1 t .3 9d1 C . 3961 - 3 . C 1 1 3 1 . C 0 r 131. 001 -G. 00 45.4571

-) c Q .1+169 Q. 1+185 3.1+0 132. OCO 131.927 0. 06 43.7226

2 0 . Hebi* 0.39 131+. 0

0"^ 133.927 0. 05 40.2441

1 L .'+92C j.^91« -3.01. 1 3 5 . 0 0 G 135.007 -0.01 38.5070

2 L .516'+ j . 5 1 8 3

-

. 38 136. COG 135.928 C. 05 37. 0956

2 C .5 725 3 .571+6 : . 36 1 3 8 . C C 0 137.929 0. 05 74.2363

1 u .e c^+g J.bOi+F -0.07 13 9. C GO 139. 013 -0.01 32. 7956

2 0.b33-+ U . 6356 0. 35 11+0.000 139.930 0. 05 31.6312

2 0 .e 992 L. 7015 J. 31+ 11+2. C CO 11+1 . 930 0. 05 29. 2502

1 C .7370 0.7 365 -3.C7 11+3. 0 00 11+3.011+ -0. 01 28. 0445

2 c .77G3 : . 7 7 2 8 n . 33 11+1+. 0 0 0 11+3.931 0. 05 27. 0671

2 li .0 '71 3.8i+99 G. 32 11+6. OOC 11+5. 931 0. 05 25. 0599

1 0 .8911 3.3906 -0.C5 l'+7. 0 00 11+7. Oil -0.01 24. 0428

2 C.93C1 J . 9 3 3 0 e. 32 11+8. C Eu 11+7.932 0. 05 23.2C95

2 1 . L, 196 1.0228 J. 21 15 0. C 0 3 11+9.932 0.05 21.4989

1 1 .U70'+ 1.0703 -0.00 151. OOu 151. 001 -0. 00 20. 6369

20

F-23
Table 5. Methane orthobaric densities - continued.

I

MOL/L CALC PCNT PP WT U 1 o / u u

2 1 1 1 IS^t 1 . 1197 0.30 X V c. • u o u 1X ft 1X . Q7^ o o7 U . U H i Q Q 1 7

X ^ « 7X01

2 1 « 2 20 9 1 . 2 2 44 M . ?q X 3 H # U U J 1 ft 7 Q 7 ft n n L 1XT.ft LH 7O Q ? T C 1.2 790 1 . 2 798 C . C 7 X > ^ • U U iJ 1 ft U . Q ft ft nu n 1 . U X 17If 7 P ftft • r u o o

2 1.3338 X . O O f J . P7 1X c-? D

c. n 0 n • U L U 1 ft ft Q 7 A u . U H 17X f . nU

ftO ft? pc 2 X . *T ^ ^ U fi . ?c; J % C J ICQ X V O • nU n'J 0J 1 ft 7 Qij. 7 U . U H 1ft 7 ft n ft X ~ . f 0 u ^

J. X • V C ^ 1. 1X

c: ? ii . V C H H icq p n p 1 ft A Q ft ft X 5 O . ^ O !? n n 9 •J a u c

1ft 1 C 7 7

oc X . ;? T X o J • d X X D u • L u u

•1 ft Q Qft -1 n fi 7 414.1. C 7 C 7 P f P s5 2 X . ' o c c X.I O V 'J <. • X D X D C • U Lf u 1 ft 1 Qft 7 nu .

fiU c? 17 /«. £a nft 1 « 3 1 6 3 1X •

ftO 1X X1 rL X Q O t u J J 1ft? Q 7 Q P PL. 1 ? 01 7ft X c . ^ J. 0 >

2 X . U (J Q 1.8903 n • rq 1X D uH • rL nU nU 1 ft ^ Q7 Q nU . PiU X 1 ? 7 ft 7ft X c . O D f O

2 2 . 0 593 ?t- .. nU q^ ?c - li . 0 1

1 p. (; r n n 1X

ftft D O «fiU nU ?c. - n n p XX. 11 7O L*t fto Q^

?C .• X1 U^ 1 ft J o u . X H C -.. 7qo ^ 1X ftO 71 p 0 n • U J u1X ftO ftO Q n ft . ^ U Q p n ft in Q n Q

1 U . u ^ u

£- C . C H O ^ d • C H J H - • X *+ 1X ftO ft0 n n r • u u u 1 ft ft P ? 7 — p n ? IP 7 7ft n X U . 0 f 0 u lb 1

2 « 3 'tS 8 2.3486 -0.01 1 ft Q - n ft? 1XOftQ7 . nU ftD Q7 - nu . pu nu q A Q ft 7 1514 c? .• o^ t^i U HO 7f C • O C J c

1 ft Q ? 7 n 1 ft Q ? ft ft n n p q a p ft 7

^ X £_ 2.3858 7 7 ft ii ? - ' r 7 1X

ftD Q" • LH 1X 7f 1Xfto Q^ • LHOC7 P — fU

1 * PIu X Q^ • 7f 07 07J f X U X c 4. . O U O X C . O O T > . . . D 1X ftD Q^ • H ftO ^J 1XOft '3 L ft ft 3 . H V V n n 1 Q 7 P T ft 4 1.1 J 1 u 2 • ^ L ^ ^ X k n 7 ? - r q 1 ft Q f ViA X D ^ • O U X

1 ft 3 ft ? ? — fi n 1 u . U 1 Q ft /x /a ft Q ') ft ?c ^

/. p 7 1, c J D 7 u P 7 "J c • H c 0 ^ J . c X

i Q 7 Q i* xO1 ft CJ 7 Q 7 ^ • / T r — n n p O ft C ft

1 ;j :r ? c . P O A0 Ao > C C 7 f C . P ^ ^ Li J . 7 D

17-1 r P 0 17 1 ft 7

X f J . D f 1

n n ft Q*3 n A ^ n • U 0 o U

1X 7 1 Pi ( X u

•7 7 qpi ft . (- X iX 7f 0

7

• pU OA M0 17 7 P Q

X 1 J . L ^ J. — n n p A 1 7 Pft 0 . X c c 7

X1 7» 1X U*T 2 . 3 2 G 3 ? ft ? 1 ft 17 7 7 Q n 17 7 ? 7 ft X f J . c f 0 p n 1 A0 . n L. 7 n U H J U 1712 2 , a c 5 7 ? • 846 7 n r 7 iX 7f 7J • uH ft(1 Q" 17X 7 ft 1 * J . H O X n no 7f • Qft ^ 5 fto 7f X J X d ? H ll A Tl ^ . O H 1 - u; .

1X d? 17 7 L. 7 7 17 7 ii.Q Q U . U c 7f • QL.H AQ0 ^

X J X u ? A 7

' '] ?£- . HO 7f nU ?C - . >. X 17 7 ft 7 ft 17 7 ft 7 ti n p r 7f . A0 7f

ftV 9c

X J J O c * 0 ^ o 7 ? A C 7 z. c • O ^ 0 H « • L U 17 7 ft 7 i 7 7 ft ft fl X / J . 0 V 0 — n n p 7f 7Q 7£a . f f X o • U X J ^ 0 . J H H f n A 9 1 7 ft n n r 1 7 P 1 A J f . C i 0

nU IP . X u 7 7 Q/i 7 f . C f X 0 X u

7 7 c, ri 1 0 . _> V U X7 7 Q 9 0 . 0 H ^ £1 — 1 f, 7 J • t' 0 17 7 P Q 17If 7f inn . X U U — n n n C /, C 7 C • H 5 J 5

X O X H O7 7 H 'i 1 . 0 O J X 7 7 ft ' 0 ; 1 . 0 O J X L' . U J 17 7 P Q ? 17 7 ?Q 7 — n p n ft 7 7 ft n

X X X H V7 .0000 7 u<l 7 ? 7 ft 7 J • 0 0 P 1 — " (7 1 7 7 7 P ft X r f • 0 c 0 17 7 7 7 o — n OP ft 7 ft ft Q

XO X c

7 ii 1 n A 0 . H X U 0 0 . H- X u "

u . u X 17 7 ft ft 17 7 ft 7 X f f . H 0 f — p n p u • u u

ft 5 Qft 7

1X1 1 P X X c O7 •ij. H d? ,1 Q D ^7 1 /a "J 0 . H X H — f' 1 q 17 7 ft f' G 17 7 C c n X f f • V !? U — n n p ft 9 ft OQ

X1111 X X J 0 . *T D U c

70 . H uH fxH q^ 17 7 7 0 0 1If77 7Q ft f . f J V

— n n ft ft 1 7 P ft 1916 if . C b 6 3 4.0649 181.105 181. 11? -0.00 4.8326

igi^t . 1 l77 4. 1C64 -:.U3 161. 3Ci+ 181.310 -0.00 4. 7530

1213 it. 1269 H. 1243 -'-J. C6 lai. 369 181.401 -0.01 4. 7165

1912 if. 1^-96 4. 1492 -G.Cl IQl. 506 181. 508 -0.00 4.6738

1211 i+.lbSb 4.167C G.L3 181. 589 181.582 G. 00 4.6439

12 J9 if .2i;i»2 4. 2G59 181.768 181.760 0.00 4.5725

1516 i+ .5212 4.5201 - G • [' 2 183.117 183. 121 -0.00 4. 0265

151^4 '.570'+ +.5716 J. 0 3 183. 32? 183.317 0.00 3.9477

1512 '+.6189 4.6207 ecu 183. 514+ 183.507 0. 00 3. 8716

1316 '+.7«22 4. 7839 C3 184. 125 184. 119 0. GC 3.6258

21J3 4.7825 4. 7734 -Q.19 184. 087 184.120 -0.02 3.6254

21Q7 '. 6263 4.8284 C. Ci* 184. 285 18'*. 277 0.00 3.5621

1314 < .8462 4.8524 0.13 184. 37G 184. 348 0. 01 3. 5337

210 6 '.3 797 4.8812 0 . : 3 184.471 184.466 0. oc 3.4864

21

F-24
Table 5. Methane orthobaric densities - continued.

10 MOL/L C ALC FCNT TS , K CflL C PCNT DTS/DO

1312 '.8 875 '.8925 0.10 184.510 164. 493 0. 01 3.4753

6 5 • G 38 3 5 . 0't7

0 • 16 185.0 30 185 . 00 0 0. 02 3 . 2711

6 5 • 3 a** J 5 • 3 7'+9 -3.17 166. 0 30 186. 0 5 7 0. 01 2.6438

22 3 8 5 . < 0 7 7 5 . 'fC 0 - 0 . 1^+ 186. 103 186 .124 0. 01 2.6165

I'+lb 5 . 1+ 396 5 . C 96 0.00 186. 129 186 .12 9 0. 00 2 . 814 3

I'tl 5 • <*795 5.4781 - G . C 3 186. 319 186 . 32 3 0. 00 2.7354

22 3 7 5 . it 827 5.^726 - G • 16 186. 3 04 166 .332 0. 31 2 . 7 318

2206 5.5571 5 • 5 5 5 -0.21 136.501 166 . 5 3 2 0. 02 7 c CI n n 2 . b a 0 u 1412 5.5 591 5.5519 •0.13 186. 518 186. 537 0. 01 ? . 6479

6 5.7860 C 7 C 7 5 • 7 5 3 1 -0.57 187. 0 31 18 7.111 0. 04 7 /. 4 4 C 2 . 4 1 lb

6

7 c n b . t: u c: 1 -1.1b 18 8. 031 188.176 0. 08 4 Q C 7 ft 23 3 8 5.2930 6 . 2565 -0.58 188. 140 183.212 0. 04 4 d / 7 O 23 3 7 6 j67 6.3617 - 3 » 7 0 18 8. 3 43 18 3.427 0.04 1.8455

23 J 6 6.5 276 6.4717 -0.86 18 8. 545 18 8.644 0. 05 1.7449

6 6 .9180 6 . 7627 - 2 . 24 1 8 9 . C 3 2 189.264 0.12 1 . 4328

5 7 . 5 b 1 0 7.3096 -3.19 18 9. 765 19 0. 014 0. 13 0 . 9345

5 7 .5510 7. Z217 -2.96 13 9. 7 85 1 9 0 . U 1 4 0. 12 n o 7 /. c

U . y J 43

5 7.9350 7.586 3 -4.39 19 0. 046 190 . 313 0. 14 0 . 6270

t? 7 .9350 7.6086 -h ,11 19 0. 066 19 0. 313 0. 13 0.6270

6

7 3 £1 " I' r . a b . I 7 C 7 -1 n -4 . A a n n 7 7 190 . 32 9 0. 16 n t n 7 4 U . 6 0 r 1

7 0 . 0 U 0 U 7 C 4 7 4 -4.84 A n c\ n 7 r 1 y 0 . U / C 19 0. 35 2 0. 15 n c 7 c c0 . 5 7i55

-91 8.1700 7 7 7 O CT -5.35 C 7 C 19 0. 170 19 0. 439 0. 14 0 • 4 4 39

7I 0 • o b J J / .0005 — 5.00 4 Q n 7 7 0 1 y U . C. f \. 1 y U . 5 1 u 0. 13 U . 0 L bo

8.3920 7 a 0 Q 1

f . D 0 i: U - 6 . L 0 Ann 7 7 n 1 y 0 . 2 r y 19 3.520 0. 17 n 7 D C 7 5 6.3920 7.9125 -5.71 IT 7 4 19U . 2y9 Ann con 0. 12 0 . 2653

"71 o • b £ U U 0 • U ol

- D • C 0 ion 7 7 n 1 y U . i ( U ion a c ci 1 y u . 5 b y c. 10 n 4 c n 7

-f

1 9 « J J 0 0 6 . 2 41+3 -3.40 19 3. 470 A CI n C Q 7 ly u • ri y f 0. 07 0 . 0 2 34

y • 1 D 1 U 0 • 11 f 1 u _- Q 7 + y . f 1 ly u . 4 0 u

4 Q n c n n 1 y u . b u J 0. 06 n n n c fl U . U u t? 0

y . 1 D 1 U

Q 7 O Q 1 0 . o c 0 1 _ Q7 no . U 7 1 y u . 5 u u

i Q n c n n

1 y u • t u u 0.05 n 0 r c fl

c:O y • o OO u

J '.nan 0 • 4 U 3 U - 1 J » 1 y ion c 9 1 y U . r c 44 Q T c n n

1 y J . r u u 0. 04 n n n n n U . U U U U c

t> 1 U • J 5 y J

H -1 7 7 n fl 1 1 • f o u 0 1 c . be 4 Q P C 7 P 1 y L • 5 o 1

• + Q n c n n 1 y J .cur c. 04 _— n p r n n U . L U U U

C: 1 1 . 1 3D U

1-1 7 Q 7 C 7 » C 4 1 y J . t> 1

1 y J . b u L

r' 04 _— n n r 1 A U . U L 1 o

c

1 1 . 0 b ( u 1 C . U ^Pl •ion 1. 1. o 1 y U . 4 4c Ann c 0 1. 1 y J « 5 0 4 0. 07 _— n n fl 4 Q u . u 0 1 y

5 11 .3670 11.970C 5.30 190. 462 193.584 0. 06 -0. 0819

7 11.410 0 11.9i»66 4. 70 190. 470 193 . 580 0. 36 -0. 0951

7 11.79CC 12.19't3 3.43 190. 37r 193.516 0. 08 -0.2531

5 11.8240 12. 3CC6 4. C3 190.316 190.507 0. 10 -0.2702

5 11.8 24u 12.2627 3.71 190. 336 193.507 0. 09 -0.2732

7 12.0700 12. 3822 2.59 190. 270 193. 424 0. 08 -0. 4C33

7 12.2700 12.539'+ 2.20 19 0. 17 C 190. 332 0. 09 -0.5204

5 12 .3970 12.7C52 2.49 193. C 48 190 . 261 0. 11 -0.5971

5 12 .3970 12.6796 2.28 190. C68 190.261 0. 10 -0. 5971

7 12 .itt+OG 12.6770 1.90 190. 070 193.235 0.09 -0. 6234

6 12 .4740 12. 725i+ 2. 12 190. C 32 190.213 0. IC -0.6442

5 12.8790 13. 0825 1. 58 169. 707 139.902 0. 10 - 0 . 8949

5 13.3 300 13.it331 1. CO 189. 311 189. 470 0. 08 -1.1555

5 13.3 uOO 13.1+168 C .88 189.331 139.473 0. 07 -1.1555

22

F-25
Table 5, Methane orthobaric densities - continued.

ID MOL/L CALC PCNT TS ,K CftLC PCNT DTS/OD

6 13.5780 13.6'+73 C . 51 189.0 32 189.125 -0. C5 -1, 3265

n't li* .2837 IW. 3C42 J . l** 188. C 0 0 188.036 -0. 02 -1 . 7636

6 lU . 285 0 li+. 266'+ 0 . CI 188. 031 183.03'+ -0. cc -1 . 7615

5 1<+ . 5 82 0 1 '+ . 589'+ 0 . C5 187. '69 187 . 1+83 -0. 01 - 1 ,"gi»67

l'+. 582C Ik. 5792 - 0 . t2 187. '89 167 . 4+83 0. CO -1 . 9'f67

6 l«t .8 360 lit. 8 062 -0.20 187. 0 31 186 . 968 0. 03 -2. 1C75

113 15 . 2 86'+ 15 . 2671 -0.13 186. 0 00 185.95'+ 0. 02 - 2 . 3991+

6 15 .3 C20 15. 25^+3 - C . 31 186. G 30 185. 91

0. 06 -2. '+097

6 15 . 7 lu 0 15.6528 - j . 36 185.0 30 l&k. 878 3. 08 -2. 6837

112 16 . 0 539 16.0 2'+? -0.18 ISf*. 0 0 0 183. 91*+ 0. 05 -2.9221

6 Ji* 16 . C 599 16.0 2^+3 - : . 22 18'+. 0 00 183 . 696 0. 06 -2. 9263

111 17 . 2'*91 17.2231 -3.15 180. 0 0 0 179.901 0. 05 - 3. 8067

6 J 3 17.25^0 17.2231 -0.18 18 3. 000 179. 883 Q. 07 -3.8105

1 18.390 0 18.3876 - C . C 1 175.0 53 175 . C'+2 0. 01 -'.7212

110 18 . H 167 18.3939 - C . 10 17 5. 0 C Q 17'+ . 916 0. 05 -1+ , 71+32

6 J 2 16 . 20 <+ 18.3989 -0.12 175. 0 0'!' 171+ , 698 Q. 06 -'+. 7'+63 IJ 9 19 .3869 l-j. 3728 - 0 . C7 170.0 00 169. 922 0. 05 -5. 5541

1 19 . '+92 0 19. '9?3 0. ("l 169. 3 26 169 . 333 -0. 00 -5.6«+27

1 J 8 2C .2 335 2 1 . 22 C 3 - C.b7 165. COO 16'+. 917 0. 05 -6. 2680

1 2 0 . < 2 3 C 20 . '3 16 0.02 16 3.659 163. 682 -0. 01 -6. 4314

10 7 20.9906 20.9605 - 0. 05 169.0 00 159.932 0. 01+ -6. 90 17

1 21.3790 21.3 776 - 0 . C

157. 199 157 . 189 0. 01 -7.2210

106 21 . 5 858 21.6771 - C. 0 <+ 155. DOG 151+ . 935 0. 01+ -7 . 4716

1 22.1300 22.1279 - 0 . C 1 151.553 151 . 536 0. 01 -7. 83G5

1 u 5 22 . 3 292 22. 32^+? -0.02 1 5 0 . C 0 G 149. 961 0. 03 -7.9899

6 01 22 . 3316 22. 32'+3 - C . 0 3 1 5 0 . C 0 G l'+9. 9'f2 0. -7. 9918

1 22.8800 22.8790 - C . CO l'+5. ''8 l'+5 . '+39 0. 01 -8 . 4263

1 u <* 22 .9 520 2 2.9320 0 . C 0 145. 0 00 lk500 0 -0. 00 -8 . 4672

103 23 ."+999 23. 5D72 C. C3 l<+i. 0 00 I'+O. 065 -0. 05 -8.9110

1 2 3.5780 23.5797 J. 01 139. 352 139. 367 -0. 01 -6. 9717

lu2 2'+. 05'+9 0. r6 135. 0 00 135. 126 -0. 09 -9.3303

1 2^+. 1760 2.:+. 17'+5 - ; . ci 133.878 133. 86'+ 0. 01 -9.4341

1 2'+ .1 860 24.1856 - e . 0 0 133. 773 133. 769 0. 00 -9.4418

131 2^.5581 2H.5789 G . 08 130. 000 130.203 -0. 16 -9. 7278

1 2'+. 6110 2'+. Sli+l J. [1 129.657 129.687 -0. 02 -9.7684

1 2'+.9990 25. CCC'* J . C 1 125. 8 25 125.839 - 0. 01 -10. C646

1 25 .3880 25.3855 -O.Cl 121.893 121 . 867 0. 02 -10. 3589

1 25.7n2u 25.7eP3 -C. CI 117.74+6 117.727 0. 02 -10.6524

1 26.1'+6C 26. l<+86 C. CI 113. 772 113. 802 -0. 03 -10.9171

1 26.5270 26.5252 -0.01 109. 611 109. 591 0. 02 -11. 1839

1 26 .9160 26.9182 u. f 1 105. 165 105. 190 -0. 02 -11.4409

1 27 .2h30 27 . 2til'+ - 0 . 0 1 101. kZk 101. '+15 0. 02 -11.6406

1 27 .6 :5G 27. 60i+3 -0 . CO 97. 173 97. 165 0. 01 -11. 8388

1 27.9100 27.9116 0.01 93.512 93.531 -0. 02 -11. 9829

23

F-2 6
Table 6

Computer programs for the equation of state.

The following 16 pages give a complete package for establishing

coefficients of the vapor-pressure equation, the orthobaric densities

equations, and the equation of state which is tied to the vapor- liquid

coexistence boundary in P-p-T coordinates. Statements to be added

to the main program, for exploration of values of the fixed-point

constants, are given in section 4, above.

24

F-27
®

FTN5.<»I 11/30/72

PROGRAM EQNSTATE

C METHANE EQN. STATE CONSTRAINED TO VAPOR-LIQUID BOUNDARY,

C EQN. (Y-YSAT) = F(R,T), WHERE Y « (Z-1)*X/R, AND - C F(R,T) = B»XBF C»XCF 0»XOF * E'XEF, WHERE -

C XBF = XB-XBSAT XEF = XE-XESAT,

C B = Bl 82»R, C a C1»R C2»R2 C3»R3,

C D = Dl D2»R 03»R2, E = (S-1)»(E1 + E2»R E3»R2), NF = 11.

C LET GAS CONSTANT GK = 0. 0831'»3<»»OTRP, PN = R»GK»T.

C NOTE, PRESSURE IN BARS, 1.01325 BAR/ATM.

C AUTHORS ID, NBS SATN(l), VIRIAL (2) , VENNIX(3), ITTERBEEK (<») , C JANS00NE(5), D0USLIN(6), OOBROVOLSKII (7) , KVALNES(8), CHENG(IO).

C COMMON B1,B2, C1,C2,C3, Dl,D2,03,D't, El,E2,E3

COMMON/ 1/ AG, AL,BE,GK,TCRT,PCRT,DCRT,TTRP,PTRP,DTRP

COMMON /2/NP,NF, 10(1300) ,T(1300),P(13 00) , DEN ( 130 0 ) , WT (130 0) COMMON /3/DPDT,D2PDT 2, DPSDT,OPDR,DTSOR,DTHOR

C0MN0N/'»/XBl,XB2,XCl,XC2,X01,XD2,XEl,XE2

COMMON /5/TSAT, DXBDR , DXCDR , DXDOR , DXE DR COMNON/6/ PSAT,THETA,XB,XC,XO,XE

COMMON/8/NPP,Pl,P2,P3,P'»,IDP(120) , TPS ( 120 ) , PPS (1 20

)

C0MM0N/9/NPS,ALl,AL2,AL3,CG(5) ,A(10) , IDS (20 0 ) , TSS ( 20 0) , DNS (200)

COMMON/999/ NFUN,Y,F(30)

DIMENSION TQ(9> ,PQ(9) ,G(30) , PV(9)

1 FORMAT (15, 3F10.0)

2 FORMATdlO, 3F10.0)

3 FORMAT(1H09X 'EON. OF STATE, DTRP =»F7.3, 8H, DCRT =F7,3,

1 8H, TCRT =F8.3// 10X<tHAG =F5.2, 6H, AL =F5.2, 6H, BE =F5.2//

2 lOX WHHP lOH, PAVPCT =F6.3)

I* FORMAT (IHl IkX 'EQUATION OF STATE, COEFFICIENTS* //

1 15X 6HDTRP =F7.3, 8H, OCRT =F7.3, 8H, TCRT =F8.3//

2 15X <»HAG =F5.2, 6H, AL =F5.2, 6H, BE =F5. 2//

3 12X 2F15.9/ 3(12X 3F15.g/) ) 5 FORMAT (15X 5HH0L/L eXitHTSAT 5X5HTHETA BXt^HPSAT

1 9X1HB 9X1HC 9X1HD 9X1HE)

6 FORMATdOX FlO.l, 7F10.3)

7 FORMAT (IHl ItfX 'DERIVATIVES IN DENSITY»//15 X5HM0L/L 6X4HTSAT

1 WXenOTS/DD 5X5HTHETA 'XeHOTH/DO 6XifHPSAT i»X6H0PS/0T <»X6HDPS/D0)

8 FORMATdOX FlO.l, 5F10.3, 2F10.'»)

9 FORMAT (IHl IkX 'METHANE CRITICAL ISOTHERM* //

1 lOX 'HTC =F8.3, 6H, DC =F7.3, 6H, PC =F8.'»//

2 IIX l»HD/OC exi^HP/PC 5X7H0PR/DDR 'X6HDTS/DR 'X6HDTH/DR

3 «fX6H0PS/DR <»X6HDXB/DR itXeHOXC/DR 'X6HDXD/DR <tX6HDXE/DR)

10 F0RMAT(5X F10.3, 2F12.8, 7F10.5)

11 FORMAT (IHl 7X 'METHANE EQUATION OF STATE' //

1 8X 2HID 7X3HT,K 5X5HM0L/L 5X5HCALCD 'X5HD,PCT

2 6X5HP,BAR 5X5H0ALCD l*X5HP,PCT)

12 FORMAT (5X 15, F10.3, 2F10.'», F9.2, F11.3, F10.3, F9.2)

13 FORMAT (IHO 8X i»HNP =!'», 12H, DNRMSPCT =F6.3, 12H, PMEANPCT =F6.3)

15 FORMAT (8X 9F8.0)

16 FORMAT (F5.0, F15.0, 6F10.'0)

17 FORMAT (10F8. 0) 18 FORMAT (IHl 16X 'METHANE ISOCHORE' F5.1, ' MOL/L' //

1 17X 3HT,K 5X5HP,BAR 5X5HDP/DD 5X5H0P/0T X 7HD2P/DT2

)

19 FORMATdOX FlO.l, 2F10.3, F10.«», F11.5)

20 FORMAT (IHl lifX 'METHANE ISOTHERM' F6.1, DEG. K' //

25

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®

FTN5.'»I EQNSTATE 11/30/72

1 10X5HMOL/L 5X5HP,BAR 5X5H0P/DD 8X2HXB 'X6H0XB/DD 8X2HXC

2 'X6HDXC/DD 8X2HX0 «tX6HDX0/QD 8X2HXE (tXeHOXE/DD)

21 FORMAT (5X FlO.l, 10F10.3)

22 TTRP=90.68 $ 0TRP=28.1<»7 S PTRP=0. 117«»35675 t 0=1.01325

23 GKK=0. OaSlWi* S GK = DTRP»GKK S AG=AL=0.1 S BE=7 f NF = 11

CC READ OUR PSAT(T) VAPOR PRESSURE DATA, P IN ATMOS.

2<» 00 25 J=l,120 S READ 1, IDP ( J) , TPS ( J) , PPS ( J) f IF ( IDP ( J) ) 25 , 26

25 CONTINUE

26 NPP = J-1

C READ OUR TSAT(DEN> DATA FOR ORTHOBARIC DENSITIES.

27 00 28 J=l, 200 $ READ 1, IDS ( J) , TSS ( J) , DNS ( J) $ IFdDSCJ)) 28,29

28 CONTINUE

29 NPS = J-1

C GENERATE VIRIAL PVT DATA.

30 N = 0 $ DO 3<» 1=1,2 $ ON = I S TS = TSATXF(DN)

31 DO Zk J = l,36 « TM = 90*5»J $ IF(TM-TS) 3'»,3<»,32

32 N=N*1 $ ID(N)=2 $ T(N)=TM S DEN(N)=DN

33 P(N) = DN»GKK»TM»ZIPF(TM,DN) t HT(N) = 1 CONTINUE $ NPl = N C READ OUR NBS PVT DATA.

35 00 37 J=l,900 t READ 2, IDD,DN,TT,PP t IF(IDD) 36,38

36 N=N*1 $ T(N)=TT t P(N)=PP $ DEN{N)=DN S IO(N)=IDO

37 HT(N) = 1 C READ THE DOUSLIN PVT DATA, P IN ATMOS.

38 NP2 = N $ READ 15, <TQ'< J) , J=l,7)

39 CO '3 1 = 1,25 « READ 16, DN, (PQ ( J) , J=l ,7

)

'O 00 1*2 K=l,7 t IF(PQ(K)) <»l,i»3

1*1 N=N + 1 t T(N)=TQ(K) « P(N)=Q»PQ(K) t OEN(N)=DN t MT(N) = 1 kZ ID(N) = 6

i*Z CONTINUE $ NP = NP3 = N

C READ VENNIX PVT DATA, <IPTS-68), P IN ATM.

'If CO ke J = l,900 t READ 1, ID0,TT,PP,DN t IF(IDD) «»5,<»7 k5 N=N+1 S T(N)=TT f P(N)=ff»PP t 0EN(N)=0N t HT{N)=1

<»6 IO(N) = IDD

1*7 HPi* = N

C READ KV ALNES/6A0DY AMAGAT PV DATA, ID = 8. 500 READ 15, ( TQ ( J) , J= 1 ,9)

501 00 505 1=1,25 $ READ 17, PP, (PV ( J) , J=l, 9

)

502 00 505 J=l,9 $ IF(PV(J1) 503,505

503 N=Ntl $ T(N)=TQ(J) t P<N)=Q*PP t ID(N)=8

50«» OEN(N) = PP/PV< J)/22.360<» $ HT(N)=1

505 CONTINUE S NPS = N

C READ CHENG PVT ISOTHERMS (ID = 10), (PRINCETON, THESIS)

507 CO 509 J=l,500 t READ 2, IOD,TT,PP,VV $ IF(IDO) 508,510

508 N=N*1 t IO(N) = IDD $ T(N)=TT $ P(N)=1000»PP S DEN (N) =1000/VV

509 WT(N) = 1 510 NP6 = N

C

C EXPLORE NONLINEAR PARAMETERS OTRP,DCRT, TCRT , AG, AL ,8E.

'8 SSK = l.OE+010 S DCRT = 10.00 « TCRT = 190.60

50 CALL PSATFIT t PCRT = PSATF(TCRT)

51 CALL OSATFIT t CALL TSATFIT

52 CALL SETUP f SS = 0 S DO 53 J=1,NP

53 SS » SS ABSF(1-PVTF(T(J),DEN(J))/P(J)) t SS = 100*SS/NP

26

F-29
®

FTN5.UI EQNSTATE 11/30/72

55 PRINT 3, DTRP,DCRT,TCRT,AG,AL,eE, NP,SS

. 56 IF(SS-SSK) 57,60,60

57 SSK = SS S DT=OTRP S OCsDCRT « TC = TCRT f GA=AG S AK=AL S BK = BE 58 DO 59 K=1,NF

59 G(K) = F<K)

60 CONTINUE $ DTRP=OT $ DCRT=DC $ TCRT=TC $ AG=GA $ AL=AK f BE=8K

61 GK = GKK»OTRP

62 B1=G(1) $ B2=G(2) t C1 = G(3) t C2 = G{'») « C3=G(5)

63 0l=G(6) S D2=G(7) t D3=G(e) S E1=G(9) I E2=G(10) $ E3=G(11)

CC EXAMINE BEHAVIOR OF THE COEFFICIENTS.

65 PRINT kt OTRP,OCRT, TCRT, AG, AL,BE, (G (K) , K=l ,NF)

66 PRINT 5 f 00 72 J=l,60 $ ON = 0.5»J S S = DN/OCRT

67 R=ON/DTRP S R2=R»*2 S R3sR»»3

68 8 = Bl + B2»R S C = C1»R C2»R2 C3»R3

69 D = 01 D2»R 03»R2 S E = (S-1)»(E1 E2»R E3»R2)

71 TS=TSAT=TSATF(DN) $ TH=THET AF ( ON) « PS=PSATF(TS)

72 PRINT 6, DN,TS,TH,PS, B,C,D,E

CC EXAMINE DERIVATIVES OF PURELY DENSITY-DEPENDENT FUNCTIONS.

73 PRINT 7 S DO 77 J=l,60 S DN = 0.5»J

7U TS = TSAT = TSATF(DN) « DTSDO = DTSDR/OTRP

75 TH = THETAF(DN) S DTHDD = DTHDR/DTRP

76 PS = PSATF(TS) t DPSOO = OPSDT»OTS0R/OTRP

77 PRINT 8, ON, TS, DTSDD,TH,OTHDD, PS, DPSDT ,DPSDD

C

C PRINTOUT THE CRITICAL ISOTHERM.

78 PRINT 9, TCRT,DCRT,PCRT f 00 82 J=1,<»1

79 OR = 0.9 0.005»<J-1) f DN = DCRT'DR

80 PC ' DPDRF(TCRT,DN) « PR = PC/PCRT

81 OPROOR = OPDR»DCRT/DTRP/PCRT S DPSDR = DPSOT»DTSOR

82 PRINT 10, OR,PR,DPRDOR, CTSDR , DTHDR , DPSDR, DXBOR , DX COR, DXOOR , DXE DR

CC GET DEVIATIONS FOR INDIVIDUAL AUTHORS.

83 DO 98 IG0=1,6 S G OTO ( 8* , 85 , 86 , 87 , 8 8 , 89 ) , I GO

8'» M = l t N=NP1 $ GO TO 90

85 MsN«-l t N=NP2 S GO TO 90

86 M=N+1 t N=NP3 f GO TO 90

87 M=N*-1 $ N=NP^ S GO TO 90

88 M=N+1 S N=NP5 $ GO TO 90

89 M=N*1 f N=NP6 t GO TO 90

90 PRINT 11 t SO = SS = K = L = 0 91 00 96 J=M,N t K=K*1 S L=L*1 J IF(L-53) 93,92

92 L = 0 $ PRINT 11 93 PC = PVTF(T( J) ,DEN (J) ) f DC = FI NOENF ( T ( J ) , P ( J ) , DEN { J)

qi^ PPCT s 100»( 1-PC/P ( J) > f SS = SS ABSF(PPCT)

95 OPCT = 100»(1-DC/DEN(J) ) S SO = SO 0PCT»»2

96 PRINT 12, ID(J) ,T< J) ,OEN (J) ,OC,DPCT, P(J),PC,PPCT

97 SS = SS/K $ SD = SQRTF(SD/K) t PRINT 13, K,SO,SS

98 CONTINUE

CC PRINTOUT ISOCHORES, SLOPES, AND CURVATURES.

135 K = 0 S 00 160 1=1,31 « IF(I-27) 136,136,137

136 DN = I $ GO TO 138

137 K = K-»-l t DN=I - 0.5'K

27

F-30
©

FlH5,i*l EQNSTATE 11/30/72

138 PRINT 18, ON f IF(DN-OTRP) ItiO jlifl ,141

IkO TS = TSATF(DN) S GO TO li»2

l**! TS = TTRP»(DN/OTRP)»»'«

I'iZ IF(I-<») lifS, l'»3,l'»'« 11*3 IT = 8 f GO TO 150

l**** IF(I-20) l'»5,l'i5,l<»6

lk5 IT = $ GO TO 150

1«»6 IF(I-26) l<»7,l«»7,l<f8

lif7 IT = 2 S GO TO 150

l'»8 IT = 1 150 DO 159 J=90,'»00,IT $ TT = J J IF(TT-TS) 159,159,151

151 PP=PVTF(TT,DN) $ PX=OPORF (TT ,DN) $ OPDD=OPDR/DTRP

153 IF(PP-700.0) 155,155,160

155 PRINT 19, TT,PP,DP0D,0PDT,D2PDT2

159 CONTINUE

160 CONTINUE

CC PRINT ISOTHERMS AND SLOPES, DP/DR, UP TO 700 BAR.

C USE OENGASF AND DENLIQF TO LOCATE BOUNDARIES.

20'* 00 230 IG0=1,'» $ GOTO(205, 206, 207, 208) ,IGO

205 J= 90 t K=1<»0 t L=10 t DS=0.1 f GOTO 210

206 J=150 J K=170 f L=10 £ DS=0.2 $ GOTO 210

207 J=180 i K=210 S L=10 $ DS=0.5 « GOTO 210

206 J = 220 $ K='»00 $ L=20 S DS=0.5 t GOTO 210

210 DO 230 I=J,K,L t TT = I S PRINT 20, TT 211 IF(TT-TCRT) 212,212,213

212 CG = OENGASF (TT) $ OL = OENLIQF(TT)

213 DO 220 N=l,300 t ON = N'OS f IF(TT-TCRT) Zl**, 215, 215

21if IF(ON.LT.OG.OR.DN.GT.DL) 215,220

215 PP = DPDRF(TT,DN) t IF<PP-700.0) 216,216,230

216 OPOO = DPOR/DTRP t DXBCD = DXBCR/DTRP

217 DXCQO = OXCDR/OTRP S OXDOD = DXDDR/DTRP t DXEOD = DXEDR/DTRP

219 PRINT 21, ON,PP,DPDO,XB,DXBDO,XC,OXCOO,XD,OXODD,XE,DXEDD

220 CONTINUE

230 CONTINUE

999 CONTINUE S STOP S END

• SINGLE-BANK COMPILATION.

28

F-31
©

FTNS.'tl 11/30/72

SUBROUTINE DSATFIT

C GET COEFFS. FOR OENGASF(TI, DENLIQF(T).

C DATA ARRANGED IN ORDER OF INCREASING DENSITIES.

COflMON/l/AG, AL.BE.GK, TCRT , PORT , OCRT , TTRP, PTRP, OTRP

C0MM0N/9/NPS,ALl,AL2,AL3,CG(5) ,A(10) , IDS (2 0 0 ) , TSS (2 0 0 ) , DNS (2 00)

CONMOM/999/ NFUN,Y,F(30)

1 FORMAT (IHl 9X •SATURATED VAPOR DENSITIES* // lOX 6HTTRP =F7.3,

1 8H, TCRT =F8.3, 8H, OCRT =F7.3// 9X 5F12.8//

2 iaX2HID 7X3HT,K 5X5HM0L/L 5X5HCALCD 5X5HPRCNT)

2 F0RMAT(15X 15, F10.3, 2F10.U, F10.2)

3 FORMAT (IHl 9X 'SATURATED LIQUID DENSITIES* // lOX 6HTTRP =F7.3,

1 3H, TCRT =F8.3, 8H, DTRP =F7.3, 8H, DCRT =F7.3// 8X 3F1'».9//

2 18X2HID 7X3HT,K 5X5HM0L/L 5X5HCALCD 5X5HPRCNT)

t* F0RMAT(15X 15, 3F10.3, F10.2)

5 FORMAT (IHO 15X UHNP =13, lOH, RMSPCT =F6.3)

C FOR THE SATURATED VAPOR -

C LN(D/DC) = A1*W**E A2*W + A3*Q«t + Ak*05 * A5*U»W,

C U = (TC/T-1)/ (TC/TT-1) , W = ( TC-T) / ( TC-TT) , 0 = W**(l/3).

2't NFUN = 5 S E = 0,i*e S UN = TCRT/TTRP-1 f WN = TCRT-TTRP

25 00 30 J=l,200 $ IF (DNS < J) -OCRT) 26,31,31

26 U = (TCRT/TSS(J)-1 ) /UN f W = ( TCRT-TSS ( J ) ) /HN S Q = CUBERTF(H)

27 F(1)=H**E $ F(2)=W S F(3)=Q**'» t F(h) = Q**5 $ F(5)=U*H

28 Y = L0GF(0NS(J) /OCRT) f CALL FIT

30 CONTINUE

31 NP = J-1 S CALL COEFF $ CALL STAT S DO 32 K=l,5

32 CG(K) = F(K> f PRINT 1, TTRP , TCRT , DCRT ,( CG (K) , K=l , 5)

33 SS = 0 J DO 35 J=1,NP S DC = OENGflSF (TSS ( J)

)

31* PCT = 100» (DNS( J)/DC-1» t SS = SS PCT»*2

35 PRINT 2, lOS(J) ,TSS(J) ,DNS(J) ,DC,PCT

36 SS = SQRTF(SS/NP) J PRINT 5, NP, SS

C FOR THE SATURATED LIQUID, (D-DC) / (OT-DC) = F(T),

C F(T) = (1 A*(l-Z) + B*(l-Qit) C* (1-W2) )*H**E.

NFUN = 3 « M = NP+l S DK = DTRP-DCRT $ E = 0.36 $ N = 0 <! DO '6 J=H,NPS « N = N-»-l « T = TSS(J) « ON = DNS(J)

<»3 H = (TCRT-T)/WN % Q = CUBERTF(N) J X = $ Z = W/X

kt* F{l)=l-Z f F{2) = l-Q**«» « F(3) = l-H»*2

1*5 y = (DN-DCRT)/DK/X - 1 S CALL FIT

kt CONTINUE S CALL COEFF f CALL STAT t AL1=F(1) f AL2=F(2) « AL3=F(3)

i»8 PRINT 3, TTRP, TCRT, DTRP, DCRT, AL1,AL2,AL3

W9 SS = 0 S DO 51 J=M,NPS J DC = DE NL I QF ( T SS ( J )

)

50 PCT = 100* (DNS( J)/DC-1) t SS = SS PCT»*2

51 PRINT IDS (J) ,TSS( J) ,DNS( J) ,DC,PCT « SS = SQRTF(SS/N)

52 PRINT 5, N, SS S RETURN t END

• SINGLE-BANK COMPILATION.

29

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®

FTN5.'»I 11/30/72

SUBROUTINE TSATFIT

C FIT TSAT(DEN) DATA WITH EXPF FORMULA, NF = 9- C (TC/T-1) /(TC/TT-1) = U(S)»Z(R), WHERE -

C U(S) = EXP(E»FS), FS = S» (S-ST» /ABS (S-1) , E = 1/2.

C Z(R) = 1 A1»LN(R) {R-1)»W(R),

C H(R) = A2 A3»Q Ai»»R * ... A9*R6.

COMMON /1/AG, AL,BE, GK, TCRT, PCRT , OCRT , TTRP ,PT RP, DTRP

COMM0N/9/NPS,ALl,AL2,AL3,CG(5) ,A(10) , IDS (2 0 0> , TSS ( 2 0 0 ) ,DNS(200)

COMMON/999/ NFUN,Y,F(30)

1 FORMAT (IHl 30X 'SATURATION TEMPERATURES')

2 FORMAT (IHO 9X 6HTTRP =F7.3, 8H, TCRT =F8.3, 8H, DTRP =F7.3,

1 8H, DCRT =F7.3// 6X 5Flk,8/ 6X 5F1W.8)

3 FORMAT (IHO 12X 2HID 5X5HM0L/L 6X«»HCALC SXitHPCNT

1 8X3HT,K 6XI*HCALC SX^tHPCNT)

k FORMATdOX 15, 2F10.««, F9.2, Fli.3, F10.3, F9.2)

5 FORMAT (IHO 13X *»HNP =13, 12H, DNRMSPCT =F6.3, 12H, TSRMSPCT =F6.3)

6 NFUN = 9 $ YN=TCRT/TTRP-1 t ST=DTRP/DCRT S DO 11 J=1,NPS

7 D=DNS(J) % R=D/DTRP f S=D/OCRT « Q=CUBERTF(R)

8 FS = S»(S-ST)/ABSF (S-1) J U = EXPF(FS/2) $ X = U''(R-1)

9 F(1»=U'L0GF(R) $ F(2)=X S F(3)=Q»X t DO 10 K = <f,9

10 F(K) = X»R»»(K-3) $ Y = ( TCRT/TSS ( J) -1 ) / YN - U 11 CALL FIT t CALL COEFF « CALL STAT « DO 12 K=l,9

12 A(K)=F(K) S PRINT 1 I PRINT 2 , TTRP, TCRT , DTRP,DCRT, ( A f K )

, K= 1 , 10

)

13 PRINT 3 $ SO=SS=L»0 S DO 22 J=1,NPS S L=L*1 « TC=TSATF(DNS( J)

)

Ik TPCT=100»(TSS(J>/TC-1» $ SS=SS*TPCT»»2 t IF (DNS (J) -DCRT) 15,16,17

15 DC = DENGASF (TSS(J) ) % GO TO 18

16 DC = OCRT S GO TO 19

17 DC = DENLIQF (TSS(J)

)

18 DC = FINDSATF(TSS( J) ,DC)

19 DPCT X 100»(ONS (J) /DC-1) t SD = SO DPCT»»2

20 IF(L-3'») 22,21

21 L = 0 J PRINT 1 t PRINT 3 22 PRINT IDS(J) ,ONS(J) ,DC,DPCT, TSS ( J) , TC, T PCT

23 SO = SQRTF (SO/NPS) $ SS = SQRTF (SS/NPS)

Zk PRINT 5, NPS,SD,SS f RETURN « END

SINGLE-BANK COMPILATION.

30

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FTNS.itI

©

11/30/72

SUBROUTINE PSftTFIT

C FIT GOODWIN FORMULA TO OUR PSflT(T) DATA. CONVERT ATM TO BAR.

C LO&IP/PTRP) = A»X Q*X2 C»X3 0»X* (1-X)

COMMON /I/ AG, AL,BE,GK,TCRT,PCRT,DCRT,TTRP,PTRP,OTRP

COMMON /8/NPP, PI ,P2,P3,Pi», IOP( 120) , TPS (120) ,PPS(120»

COMMON/999/ NFUN,Y,F(30)

DATA (CF = 1.01325)

1 FORMAT (IHl li»X 'VAPOR PRESSURES, TTRP =*F7.3, 8H, TCRT =F8.3)

2 FORMAT (IHO 12X *»F12.8)

3 FORMAT (IHO 17X 2HI D 7X3HT,K 5X5HP,BAR 6X<»HCALC 6X4»HPCNT)

FORMAT (15X 15, ifFlO. 3) 5 FORMAT (IHO 16X ifHNP =I'«, lOH, RMSPCT =F6.3)

6 NFUN=i» t XK=1-TTRP/TCRT $ DO 10 J=1,NPP S P = CF»PPS(J)

7 X=(1-TTRP/TPS(J))/XK f Q = 1-X « QS = Q»SQRTF(Q)

8 F(1)=X S F(2) = X»»2 S F(3)=X»»3 S F(*»)=X*QS

9 Y = LOGF{P/PTRP> S CALL FIT

10 CONTINUE t CALL COEFF t CALL STAT

11 P1=F(1) I P2=F(2) S P3=F(3) t PU=F(W) $ SS = L = 0 12 PRINT 1, TTRP, TCRT $ PRINT 2, Pl,P2,P3,Pl» $ PRINT 3 13 CO 17 J=1,NPP f P = CF»PPS(J) f PC = PSATFCTPS(J))

I'* L = Lfl « PCT = 100»(P/PC-1) ? SS = SS PCT»»2

15 IFIL-Sk) 17,16

16 L = 0 I PRINT 1, TTRP, TCRT t PRINT 3 17 PRINT <, IDP(J) ,TPS{J) ,P,PC,PCT S SS = SQRTF ( SS/NPP)

18 PRINT 5, NPP, SS f RETURN t END

12

3

<*5

fe 11

13

i.U 20

30

31

32

SUBROUTINE SETUP

SET UP THE ARRAYS FOR LEAST SQUARES.

COMMON B1,B2, C1,C2,C3, 01, D2, D3,D'», E1,E2,E3

COMMON /1/AG, AL, BE, GK, TCRT, PCRT,DCRT, TTRP, PTRP.DTPP

C0MM0N/2/NP,NF, ID( 1300), T (1300), P(1300), DEN ( 1300), HT(1 30 0)

COMMON /5/TSAT, 0X8 OR , DXCDR , DXDDR , DXEDR

COMMON/999/ NFUN,Y,F(30)

NFUN=NF $ 00 30 J=1,NP S H = HT(J)

TT = T(J) t X = TT/TCRT « D = DEN(J)

R=0/DTRP $ R2=R»»2 S R3=R*»3

S XS = TS/TCRT J; XC = W»XCF(TT,D)

XE = W» (S-1)»XEF(TT,0)

S F(3)=R»XC « F(lf)=R2»XC

t S = D/DCRT

TS = TSAT = TSATF(D) PS = PSATF(TS)

XB = W»X8F (TT,D) t XD = W»XDF(TT,0) S F(1)=XB t F(2)=R»XB S F(3)=R»XC « F(lf)=R2»XC f F(5)=R3»XC

F(6)=X0 t F(7)=R»XD t F(8)=R2»XD

F(9)=XE $ F(10)=R»XE $ F(11)=R2»XE

Y = (P {J)/R/GK/TT-1) 'X/R - (PS/R/GK/TS-1)»XS/R * CALL FIT

CONTINUE S CALL COEFF S CALL STAT

B1 = F(1) J B2=F(2) t C1=F(3) t C2 = F (<) f C3=F(5)

D1=F(6) $ D2=F{7) S D3=F(e) S E1=F(9) t E2=F(10) f E3=F(11)

99 RETURN S END

SINGLE-BANK COMPILATION.

31

F-34
11/30/72

FUNCTION FINDENF(T,P,OI>

C ON ISOTHERM T, ITERATE OEN TO MINIMIZE (P-PCALO

C NEWTON-RAPHSON ITERATION. INITIAL OEN » 01.

C0MM0N/1/AG,AL,BE,GK,TCRT,PCRT,0CRT,TTRP,PTRP,0TRP

COMMON /3/0PDT,D2P0T2,DPSTDT,DP0R,DTSDR,0THDR

1 FORMAT (IHO 9X •FINDENF = 0, FAILS TO CONWERGE*/)

2 C = 01 t DO 8 J=l,50 t PC = DPORF(T,0)

3 PO = P-PC S APD 3 A8SF(PD) t DPDD « DPDR/DTRP

4 IF(APD/P-1.0E-6) 9,9,5

5 IF(APO/DPOO/D-1.0E-6) 9,9,6

6 0=0* PD/OPDO $ IF(D> 7,7,8

7 0=0. 00001

8 CONTINUE t FINOENF = 0 S PRINT 1 $ RETURN

9 FINOENF = D t RETURN t END

FTN5.<»I 11/30/72

FUNCTION FINOSATF(T,OI)

C ITERATE DEN TO MINIMIZE (T-TS) VIA TSATF(DEN).

COMMON/l/AG, AL,BE,GK, TCRT , PORT , OCRT , T TRP , PTRP , OTRP

COMMON /3/DPDT,D2P0T2,DPSDT,0PDR,DTSDR,DTHDR

1 FORMAT (IHO 9X •FINOSATF = 0, FAILS TO CONVERGE.* / ) 2 FORMAT (IHO 9X 'FINDSATF = 0, T EXCEEDS TCRT.» / ) 3 IF(T-TCRT) '»,18,19

i» D = 01 $ DO 16 J = l,50 S TS = TSATF(O) S OT = T-TS

5 DTDO = DTSOR/DTRP t IF(DTOO) 6,18

6 00 = OT/OTOD $ IF(ABSF<D0/O)-1.0E-5) 17,17,8

8 IF(ABSF(DT/T)-1.0E-6) 17,17,9

9 0= D*DD t IF(DI-DCRT) 10,18,1*»

10 IF(D) 11,11,12

11 C = 0. 00001 S GO TO 16

12 IF(O-DCRT) 16,13,13

13 C = XRT-0.05 t GO TO 16

l** IF(D-DCRT) 15,15,16

15 0 = OCRT 0.05

16 CONTINUE J FINOSATF=0 f PRINT 1 t RETURN

17 FINOSATF = D f RETURN

18 FINOSATF = OCRT $ RETURN

19 FINOSATF = 0 $ PRINT 2 $ RETURN S END

32

F-35
FTN5.i»I 11/30/72

FUNCTION PVTF(T,DEN)

C YIELDS P,BAR, ALSO OP/DT, 02P/0T2.

COMMON B1,B2, CltC2,C3, 01*02, Q3,0<*, E1,E2,E3

COMMON/l/AG, AL, BE,GK,TCRT,PCRT,DCRT,TTRP,PTRP,DTRP

COMMON /3/DPDT,D2PDT2,DPSET,0P0R,DTS0R,0TH0R

COMMON /'/XBl.XB 2, XC1,XC2,X01,XD2,XE1,XE2

COMMON /5/TSAT, DXBDR, DXCOR, DXDDR,OXECR

1 S=OEN/DCRT t R=DEN/OTRP t R2=R»»2 S R3=R»»3

2 TS = TSAT = TSATF(DEN) $ PS = PSATF(TS)

3 XB = XBF(T,OEN) S XC = XCF(T,DEN)

« XO = XDF(T,OEN) $ XE = XEF(T,DEN)

5 B = Bl + 62*R $ C = Cl'R C2»R2 C3»R3

7 C = 01 + 02*R * 03*R2 $ E = (S-1)»(E1 E2*R E3*R2)

g F = B*XB + CXC + D'XD + E'XE J Fl = B»X81 C'XCl D*XDl E'XEl

11 F2 = B»XB2 + C»XC2 D»XD2 + E*XE2 S YS = ( PS/R/GK/TS-1> *TS/TCRT/R

15 PVTF = (T*R» (F«-YS) •TCRT) 'R^GK $ DPDT = ( 1 R'Fl ) •R'GK

17 D2PaT2 = R2»GK»F2/TCRT $ RETURN « END

flU5.t*I 11/30/72

FUNCTION DPDRF(T,DEN)

C DPORF = P,BAR, DP/DR IS IN COMMON. GK = 0 . 0831 3<»»DTRP

,

C DEFINE Y = (Z-1)»X/R, WHEN EON. STATE IS -

C Y = YSAT F(R,T), WHERE - C F(R,T) = B'XB C»XC + D'XD E'XE, YIELDS DERIV, -

C OP/DR = 2»P/R - GK'T R2»GK»TCRT* (Fl YSl).

COMMON B1,B2, C1,C2,C3, 01 ,02 , D3 tOi* , E1,E2,E3

COMMON/l/AG, AL,BE, GK,TCRT,PCRT,DCRT,TTRP,PTRP,OTRP

C0MM0N/3/DPDT,D2PDT2,DPSDT,DPDR,DTS0R,DTHDR

C0MM0N/5/TSAT, DXBDR, DXCOR, DXDDR,OXEOR

COMMON/6/ PSAT,THETA,XB,XC,XO,XE

1 X = T/TCRT S S=OEN/DCRT $ OSOR = OTRP/DCRT

2 R = OEN/DTRP S R2=R»»2 « R3 = R"3

3 TS=TSftTxTSATF(DEN) « XS=TS/TCRT f PS=PS ATs PSATF ( TS)

t* XBsXBF (T,DEN) S XC = XCF (T,DEN> « XO = XDF (T,DEN) t XE = XEF (T,DEN)

5 B = 81 B2»R t BD = 82

6 C = C1*R + C2»R2 C3*R3 S CO = CI Z*C2*9 * 3»C3»R2

7 D = Dl >• D2»R 03*R2 t 00 = 02 + 2»D3»R

8 U = S-1 t V = El + E2»R E3»R2 $ VI = E2 2»E3''R

9 E = U»V $ ED = U»V1 V'DSDR t F = B^XB C*XC D»XD E»XE

11 Fl = B»0XBDR BD»xa C'DXCOR CD'XC

1 D»aXD0R OD*XD E»DXEOR * ED»XE

15 YS = < PS/R/GK/TS-1 ) 'XS/R

16 YSl = <TS - R'DTSDR + (DPSOT'DTSDR - 2» PS/ R ) /GK ) /TCRT

20 Q = R»(F+YS)/X t OPDRF = R»GK»T»(1+Q)

21 DPDR = &K»T»(1 2»Q * (R2»F1+YS1) /X) t RETURN f END

33

F-36
FINS.**! 11/30/72

®

FUNCTION PSftTF(T)

C METHANE VAPOR PRESSURE VIA PRYDZ/GOODWIN DATA, NOV., 1970.

C NOTE, PRESSURE IN BARS, 1.01325 BAR/ATM.

COMMON /1/AG,AL, BE, GK,TCRT, PORT, DCRT,TTRP,PTRP,DTRP

COMMON/3/OP0T,O2POT2,0PSDT,0POR,OTSDR,0THDR

COMMON/8/NPP,Pl,P2,P3,P'»,IOP(120) ,TPS(120) ,PPS<120)

1 FORMAT (IHO 9X •PSATF = 0, T EXCEEDS TCRT.*/)

2 XK=1-TTRP/TCRT $ X = ( 1-TTRP/T) /XK t Q = l-X « IF(0) 3, ',5

3 PSATF = OPSDT = 0 J PRINT 1 S RETURN

l» W = HI = 0 S GO TO 6 5 U=SQRTF(Q) $ H=Q»U t Wl=-3»U/2

6 CX0T=TTRP/XK/T»»2 S Z = X»W t Zl = X»H1 W 7 F = Pl'X P2*X**2 + P3»X»*3 P^'Z

8 Fl = PI + 2»P2»X 3*PZ*X**2 * PU^Zl

9 PSATF=PTRP»EXPF (F) t 0PS0T=F1»PSATF»DXDT t RETURN t END

FUNCTION DENGASF(T)

C LN(D/DC> = A1»W»»E A2»W A3*Qk A^t'QS * A5»U'W,

C U = (TC/T-1)/ (TC/TT-1) , W = ( TC-T ) / (TC-TT ) . C0MM0N/1/AG,AL,BE,GK, TCRT , PCRT , DCRT , T TRP , PTRP , OTRP

COMMON/9/NPS,ALl,AL2,AL3,CG(5),A(10) , IDS (2 0 0) , TSS ( 2 0 0 ) , DNS (200)

DATA (E = Q-kb)

1 FORMAT (IHO 9X •DENGASF = 0, T EXCEEDS TCRT.'/)

3 U=(TCRT/T-l)/aCRT/TTRP-l) S W= (TCRT-T) / (TCRT-TTRP) J Q=CUBERTF(W)

5 F = CG(1)»H»»E CG(2)*W + CG(3)»Q»"» * CG('t)»Q»»5 * CG(5)»U'W

6 DENGASF = DCRT»EXPF(F) J RETURN

7 DENGASF = DCRT S RETURN

e DENGASF = 0 S PRINT 1 $ RETURN J END

FUNCTION DENLIQF(T)

C (D-OC)/ (DT-OC) = (1 + A»(l-Z) + B»(l-Q'») C ( 1- W 2) ) • W» . C W = (TC-T)/ (TC-TT) , Q = CUBERT(M), Z = H'^d-E).

COMMON/l/AG, AL,BE,GK, TCRT , PCRT , DCRT , TTRP , PTRP , DTRP

C0MM0N/9/NPS,ALl, AL2,AL3,CG(5) ,A{10),IDS(2 00),TSS{200) ,DNS(200 ) 1 FORMAT (IHQ 9X •OENLIQF =0, T EXCEEDS TCRT.'/)

2 IF(T-TCRT) 3,7,8

3 W=(TCRT-T) /(TCRT-TTRPy S Q=CUBERTF(W) t X=W'»0.36 t Z=W/X

5 F = AL1»(1-Z) + AL2*(1-Q*»'f) AL3»(1-W*»2)

6 DENLIQF = DCRT ••• ( DTRP-OCRT ) • (1 + F ) 'X « RETURN

7 OENLIQF = DCRT $ RETURN

8 CENLIQF = 0 « PRINT 1 J RETURN t END

34

F-37
FTN5.WI 11/30/72

FUNCTION TSaTF(DEN)

C NOTE EXPONENTIAL U(S). EON., (TC/T-1) / (TC/TT-1) - U(S)»Z(R).

C U(S) = EXPF(E»FS), FS = S» (S-ST ) / ABS (S-1) , E = 1/2.

C 2(R) = 1 + A1»LN(R) (R-1)»H(R),

C W(R) = A2 + A3»Q * ... A9»R6.

COMMON/l/AG, AL.BE, GK, TCRT , PORT , OCRT , TTRP ,PT RP, DTRP

COMMON /3/0P0T,D2PDT 2, DPSCT,OPDR,OTSDR,DTHOR

C0MM0N/9/NPS,ALl,AL2,AL3,CG(5) , A (10 ) , IDS (20 0 ) , TSS (20 0 ) , DNS ( 200

)

1 R=DEN/OTRP S S=DEN/DCRT f QS = S-1 f IF(QS» 2,30

2 AS = ABSF(QS) $ ST = DSDR = DTRP/OCRT $ YN = TCRT/TTRP - 1

3 X = S»(S-ST) S XI = 2*S - ST f V = 1/AS t

«» FS = X*V I FSl = (X'Vl + X1*V)»DSDR

5 U=EXPF(FS/2> S Ul=U*FSl/2 « Q=CUBERTF(R) J 7 H = A(2) A(3)»q $ Wl = A{3)/3/Q2

8 DO 10 K=U,9 $ W = W A (K) 'R^* (K-3)

9 HI = Ml A(K) • (K-3) 'R** (K-i*)

10 CONTINUE S Z = 1 A(1)»L0GF(R) (R-1)»W

11 Zl = A(l)/R > (R-1)»W1 W S F = U*Z S Fl = 12 X = 14-YN»F $ TSATF=TCRT/X J DTSDR = -YN»F1»TSATF/X

30 TSATF = TCRT $ DTSDR =0 f RETURN t END

VI = -1/AS/QS

Q2 = (i**Z

U*Z1 U1»Z

$ RETURN

FUNCTION TSATXF (DEN)

C CONSTS. FOR CUBIC VIA TSATFIT, 10/6/72.

DIMENSION A(10)

OATA(A = -0. 87«»2'»368, 1.62092018, 6. 212'f7296, -20.95U78<»78,

1 20.98003520, - 25. 0 2998<«87, 38.07190012, - 8 . itl 89370 5

,

2 -26.60696105, 17. <»77715I0

)

DATA (TTRP=90.68) , ( TCRT = 190 . 56) , (DCRT=1 0 . 17 ) , (OTRP= 28 . I<f7)

1 R=OEN/OTRP t S=OEN/DCRT t Q=CUBERTF(R) t Q2=Q»»2 t IF(S-l) 2,20

2 YN = TCRT/TTRP-1 J SI = DTRP/DCRT S E = 1/(S1-1)»»3

3 X = ABSF(S-l) $ U = E*X»»3

5 W = A(2) A(3)»Q A(t»)»02

8 DO 10 K = 5,10 S H = W A (K) »R»» (K-ti)

10 CONTINUE S Z = 1 A(1)»L0GF(R) * (R-1)»W

15 TSATXF = TCRT/( 1+YN»U»Z) S RETURN

20 TSATXF = TCRT t RETURN S END

FUNCTION THETAF (DEN)

C THETA = TSAT»EXP(U(S)).

C IF S < 1, U = AG»(S-1)»»3. IF S > 1, U = - AL» (S-1) ••S

,C YIELDS ALSO THE FIRST DERIVATIVE RSP. TO RHO=DEN/DTRP.

COMMQN/l/AG, AL, BE,GK,TCR7,PCRT,DCRT,TTRP,PTRP,DTRP

COMMON /3/DPDT,D2PDT 2, DPSDT,DPOR, DTSDR, DTHDR

COMMON /5/TSAT, DXBDR,DXCDR,DXDOR,DXEDR

1 S = DEN/DCRT t DSDR = DTRP/DCRT

2 Q = S-1 $ Q2=Q"2 S Q3=Q»»3 $ IF(Q) 3,e,U

3 U = AG»Q3 « Ul = 3»AG»Q2*DSDR « GO TO 5 < U = -AL»Q3 I Ul = -3'AL»Q2»DSDR

5 XP = EXPF(U) $ THETAF = TSAT»XP

7 DTHDR = (TSAT»U1 + DTSDR)»XP $ RETURN

8 THETAF = TCRT $ DTHDR =0 t RETURN S END

35

F-38
FUNCTION XBF(T,0)

xe = X» (1-EXP {-BE/X ) ) - XS*(1-EXP(-BE/XS) ).

COMMON /I/ AG, AL , BE , GK , TCRT , PCRT , DCRT , TTRP , PTRP, DTRP

COMMON /3/0PDT,02PDT 2, OPSTJT,DPDR,OTSDR,DTHDR

COMMON /it/XBl ,XB2,XC1,XC2,XD1,X02,XE1,XE2

COMMON /5/TSAT, DXB OR , OXC OR , DXDDR , DXEDR

1 X=T/TCRT t XS=TSAT/TCRT $ OXSDR= DTSDR/TCRT

2 U = BE/X S Ul = -U/X f U2 = -2*U1/X

3 US = BE/XS S USl = -US/XS

h XP=EXPF(-U) $ Z = 1-XP S Z1=U1»XP t Z2= (U2-U1»»2 )*XP

5 PHI = X'Z t XBl = Z+X»Z1 % X62 = X»Z2 2»Z1

6 XPS=EXPF (-US) S ZS = 1-XPS t ZSl = USl'XPS

7 PHS = XS'ZS t DXBDR =- ( XS ZS 1 + ZS ) • DXSDR

8 XBF = PHI - PHS t RETURN t END

FUNCTION XCF (T,D)

XCF = 1/X - 1/XS, X = T/TC.

COMMON /I/ AG, AL, BE, GK, TCRT, PCRT, DCRT, TTRP, PTRP, DTRP

COMMON/ 3/0PDT,02P0T 2, DPSOT,DPDR,DTS0R,0THDR

C0MM0N/i»/XBl,XB2,XCl,XC2,XDl,X02,XEl,XE2

COMMON /5/TSAT, DXBDR , DXCDR , DXDDR , OXEDR

1 X = T/TCRT $ XS = TSAT/TCRT

2 XCF = 1/X-l/XS S XCl = -1/X*»2 t XC2 = -2»XC1/X

3 DXCDR = DTSDR/TCRT/XS**2 S RETURN S END

FUNCTION XDF(T,D)

XD = 1/X»»2 - 1/XS»»2, X = T/TC.

COMMON /I/ AG, AL, BE, G<, TCRT, PCRT, DCRT, TTRP, PTRP, DTRP

COMMON /3/DPDT, D2PDT2 , DPSDT, DPDR , CTSDR, DTHDR

COMMON /'/XBl ,XB2,XC1, XC2, XDl, X0 2, XE1,XE2

COMMON /5/TSAT, DXB OR , D XCCR , D XOOR , 0 XEOR

1 X = T/TCRT S XS = TSAT/TCRT

2 XOF = 1/X»»2 - 1/XS»»2

3 XOl = -2/X»»3 S XD2 - -3»XD1/X

< CXDOR = 2»DTSDR/TCRT/XS»»3 t RETURN S END

36

F-39
FUNCTION X£F(T,D)

C PSI = (1-W»LN(1+1/H) )/U2, XEF = PSI - PSISAT,

C U=T/TH, H=U-1, V=TS/TH, Z=V-1, XEF = PW/U2 - PZ/V2.

COMMON/l/AG, AL.BE, GK,TCRT,PCRT,DCRT,TTRP,PTRP,DTRP

COMMON /3/DPDT,02P0T 2, DPSDT,DPDR,DTSOR,DTHDR

C0MM0N/'f/XBl,XB2,XCl,XC2,X01,XD2,XEl,XE2

C0MM0N/5/TSAT, DXB DR , DXCDR , DX DDR , DXEDR

COMMON/6/ PSAT, THETA,XB,XC,XD,XE

1 TS=TSAT J TH=THETA=THETAF(D)

2 U = T/TH J U2=U"2 t U3 = U»»3 t U't = U»»J»

3 UiX=TCRT/TH S U 1R= - U'DTHOR/ TH

V = TS/TH f V2=V»»2 « V3 = \/"3 ? VI = (DTSOR-V»DTHOR) /TH

6 H = U-1 S WIX = UIX t WIR = UlR

7 Z = V-1 f Zl = VI I IF(W) 9,9,10

9 W=GW=GW1=GH2=0 J GO TO 11

10 G=LOGF (l+l/H) t GW=W»G t GW1=G-1/U S GW2=-1/W/U2

11 PW=1-GW t PH1X=-GW1»M1X f PW1R=-GW1*W1R t PW2X=-GW2»W1X»»2

12 IF(Z) 13,13, lit 13 Z=GZ=GZ1=0 S GO TO 15

It* G = L0GF(1>1/Z) S GZ = 7*0 % GZl = G-l/V

15 PZ = 1-GZ t PZl = -GZl'Zl

20 XEF = PH/U2 - PZ/V2 % XEl = PW1X/U2 - 2»PW»U1X/U3

22 XE2 = PW2X/U2 - i»» PW1X»U1X/U3 6»PW»U1X»» 2/U<»

23 CXEOR = PW1R/U2 - 2»PH»U1R/U3 - PZ1/V2 2»PZ»V1/V3

30 RETURN $ END

FUNCTION ZIPF(T,0)

C METHANE VIRIAL EQN. OF STATE FOR Z(T,D).

C Z(T,0) = 1 B(X)»S + C{X)»S»»2, X=T/TCRT, S=0/DCRT.

DIMENSION B(6)

DATA < TORT =190, 5 3) , (DCRT = 10.15) , (C 1= 0 . 2 38'»'» ) , ( C2 = 0 . 562'»3 ) , (03

DATA (B = 2. 1099H*, -7.268397, 13. 088869, - 16. 022<»0<»,

1 9.'t50if285, -2.5322231)

1 X=T/TCRT % S=D/OCRT- % Q=SQRTF(1/X) « QQ=SQRTF(0)

2 BV I 0.0 J DO 3 K=l,6

3 BV = BV B(K) •QQ»» (2»K-1)

CV = (Cl'Q + C2/X»»5)»(1-EXPF(1-C3»X»»2> ) 6 ZIPF = 1 + BV'S * CV»S»»2 S RETURN f END

37

F-40
FTN5.'»I 11/30/72

SUBROUTINE FITTER

COHMON/999/ NCOF,Y,G(30)

DIMENSION A(30,31) ,B(30,31)

COMMON /777/ *,SY,SYY,RES

TYPE DOUBLE SY, SYY , RES , A ,

ATA ( NTR=-1 ) , (NOIM=30)

EQUIVALENCE (A,B)

37 FORMAT ('ITHE COEFFICIENTS AND THEIR ESTIMATED ERRORS AREO'//)

38 FORMAT (0»/*0*/»OESTIMATtD RESIDUAL SUM OF SQUARES =»E17.9/

1 ESTIMATED REGRESSION SUM OF SQUARES =»E17.9/

2 ESTIMATED TOTAL SUM OF SQUARES =»E17.9/

3* VARIANCE OF FIT =»E17.9/» DETERMINANT OF THE MATRIX =»E17.9/

k* CORRELATION COEFFICIENT =»E17.9/» NUMBER OF POINTS =»I5)

kS FORMAT CITHE ARRAYS IN THE FITTING PROGRAM ARE TOO SMALL TO HOLD T IHE NUMBER OF CONSTRAINTS AND FUNCTIONS ASKED FOR IN THE CALLING PR 20GRAM*

)

371 FORMAT (£19.10, •0R-»E9.2)

C ENTER HERE TO FIT THE DATA

ENTRY FIT

IFCNTR) 1,3,3

1 NP=0

NF=NCOF

IF(NF. GT.NDIM) GO TO

NCON=0

SY=0.

SYY = 0. NY = NF«-1 DO 2 1=1, NY

00 2 J=1,NF

2 A{J,I) =0.

IF(NTR.EQ.O» GO TO 11

NTR=0

3 SY=Y+SY

SYY=SY Y*Y»Y

DO i* J=1,NF

A(J,NY)=A(J,NY) +Y*G(J)

DO k 1=1, NF

A (I, J) =A(I,J)+G (I) *G{J)

NP=NP*1

RETURN

C ENTER HERE TO CONSTRAIN THE EQUATION

ENTRY CONSTR

IF(NTR) 10,11,11

10 NTR=0

GO TO 1 11 N=NY-1

IF( (NY+NCON+2) . GT. NOIM) GO TO

CO 12 1=1,

A (I ,NY+1)=A{I,NY)

fl (NOIM-NCON, I)=G(I)

A(NY,I)=G(I)

12 A(I,NY)=G(I)

NC0N=NC0N+1

DO 13 I=NF,N

A {NY,I*1)=0. 0

38

F-41
FTN5.'»I FITTER

®

11/30/72

13 fl (I + l, NY) = 0. 0 NY=NY*1

/» (NY-1 ,NY) =Y RETURN

C ENTER HERE TO INVERT MATRIX AND GET COEFFICIENTS

ENTRY COEFF

N=NY-1

CO 20 1=1, NF 2C G(I)=A(I,NY)

DO 22 1=2,

00 21 J= I, NY 21 A(I-1, J)=A(I-1, J)/fl(I-l,I-l)

DO 22 J=I,N

DO 22 K=I,NY

22 A (J,K) =A(J,K)-A (J, I-l) •A(I-1,K)

A(N,NY)=A(N,NY) /A(N,N)

DO 21* 1 = 2,

L = N-I«- 2 DO 2t» J=L,N

2'+ A (L-1, NY)=A(L-1 ,NY) -A (L-1, J) "A (J,NY)

RES = SY Y CO 25 1=1, NF RES = RES-A(I', NY) G(I)

25 G(I)=A(I,NY)

0F = NP-NF«-NCON

Y=NCON

NTR=-1

RETURN

C ENTER HERE FOR STATISTICS OF COEFFICIENTS

ENTRY STAT

DO 27 I=1,NC0N

CO 27 J=1,NF

27 RES = RES-A(NDIM-H-1, J)»A(J,NY)»A(NF+I,NY)

TOT=SY Y-SY»SY/NP

REG = TOT-RES

SYY=RES/OF

ST=1.96-»-2.72/0F*8. Oi^/DF^^S

DET=1.

DO 30 1=1, NF DET=DET»B (1,1)

30 A(I,I) =1.0/A<I,I)

DO 32 1=2, NF

DO 32 J=2,I

SY=0.

DO 31 K = .J,I 31 SY = SY- A (I,K-1)»A(K-1, J-1)

32 A (I,J-1)=SY»A(I,I)

PRINT 37

DO 36 1=1, NF L=NF-I

00 33 J=1,L

K=NF-J

00 33 M=1,J

N=NF-M+1

33 A (K, I) =A (K,I )-A (K, N)»A (N,I)

39

F-42
FITTER 11/30/72

DO Zi* J=2,I

3<» fl(J-l,I)=A(I,J-i)»SYY

DO 35 J=1,I

35 fl(I,J) =A(I,J)»SYY

eB=a(I ,1) C B8 IS THE VARIANCE OF THE COEFFICIENTS

IF(BB.LT.O.O)BB=-BB

FF=ST»SQRT (BB)

BBB=B( I,NY)

36 PRINT 371,BBB,FF

IF(SYY.LT. 0. 0) SYY=-SYY

CORR=REG/TOT

PRINT 38,RES,REG,T0T,SYY,DET,C0RR,NP

Y=SQRT (RES/DF>

RETURN

ki* PRINT <»5 STOP

END

SINGLE-BANK COMPILATION.

40

F-43
Table 7. Methane vapor pressures

VAPOR PRESSURES, TTRP = 90-680, TCRT = 190.600

1.. 770 06989 1.77'.5'4l73 -0. 57292079 1. 33631826

10 T, K P , BAR CALC PCNT

3 01 91.000 0.122 0.122 -0 . 3 02 92 . 00 0 0.139 0.139 0 . 037 303 93 . 00 0 0.157 0.157 0 . 033

30', 9i».00 0 0 . 177 0.177 -0 . OttO 305 95 . 00 0 0 . 199 0 .199 0 . 002

3 06 96.00 0 0.223 0.223 0 . OOi* 307 97 .00 0 0 .250 0. 250 0

018

308 98.000 0. 279 0.279 0 . 000

3 09 99 .00 0 0.311 0.311 0

008

310 100.000 0 . 3'»5 0 . 3U5 -0

013

311 1 01 .00 0 0.383 0.383 -0

0 07 312 102.000 0 . '23 0.U23 0 . 008

313 103.000 0 . '67 0 .'.67 0 . 006

31i» lOit.OO 0 0 .Slf, 0.515 -0. 031

315 105.000 0 .566 0 .566 -0

021

316 106.000 0.621 0.621 -0 . 019

317 1 07 . 00 0 0.660 0.680 -0. 001

318 108 .00 0 0. 71(3 0 . 7i» 3 -0

016

319 109 .00 0 0.811 0.811 0 . 002

3 20 110.000 0. SB'* -0. 001* 321 111.000 0 .961 0.962 -0. Oil* 322 111.000 0.962 0.962 0. 00<» 323 112.00 0 1 . Off? 0. Ottl 32i» 113.000 1.133 1.132 0. 031

3 25 n't. 000 1 .226 1 . 226 0. 021*

2 01 115.000 1 .325 1.326 -0. 020 326 115.000 1. 326 1.326 0 . 0 36

2'»7 1 16 .00 0 l.'«31 l.'»31 -0. 015

327 116.000 1 . < 32 1 . 't 3

0. 026

2 02 117.000 1.5«t3 1.5l»3 0. 012

203 lis. 000 1.662 1.662 -0. 002

20<* 119.000 1.787 1.787 0 . Oil, 112 120.000 1.919 1.919 0. 001, 205 121 .00 0 2. 058 2.058 -0. 016 113 122.000 2.206 2.205 -0. 001, 2 06 123.000 2. 360 2.360 -0. 007

llf* 12<«.00 0 2.523 2.523 0. 006

2 07 125 .000 2.693 2.691. -0. 008

115 126.00 0 2.873 2.873 0 . 001, 208 127.000 3. 061 3.061 -0. 009

116 128.00 0 3.258 3.258 -0. 008

2 09 129.00 0 3.i»6', 3.1.65 -0. 008

117 130.00 0 3.680 3.681 -0. 010 210 131.000 3. 906 3. 906 -O.OOI. 118 132.000 '».1<«2 <«.1'42 -0. 007 211 133.000 U. 388 <..388 -0 . 001, 119 13(i.00 0 i«.6<t5 i..6<,5 -0 . 001, 212 135.000 <». 913 '4.912 0. 003

120 136 .00 0 5. 191 5.191 -0. 006

213 137.00 0 5.i»81 5.1«81 -0. 003

121 138.0 0 0 5.783 5.783 0. 009

21<» 139.00 0 6. 096 6.097 -0. 001

122 lUO.OOO 6.'»22 6.1*22 -0 . 007

41

F-44
Table 7. Methane vapor pressures - continued

ID T t K P, BAR

215 li«l .00 0 6. 761

1 23 1 '«2 . 0 0 0 7.112

Z 16 1 <<3 • 0 D 0 7 . '76

1 Zi* 1 1*"* • 0 0 0 7.853

2 IT 1 . 0 0 0 6. Zifh 125 1 (t6 . 0 0 0 8.6'»9 218 1 It? . 00 0 9.068

1 2b 1 itS . 00 0 9.502

2 19 1 . 0 0 0 9. 950

1 27 150 • 0 0 0 1 0 - l"* 220 151.000 1 0 . 8° 2 128 152 . 00 0 11.386

221 1 53 • 0 0 0 11.898

129 15't.OO 0 12. '»2'« 222 155 .00 0 12.967

130 1 56 . 0 0 0 13.526

223 157 . 0 0 0 l"* . lO"* ZZk 1 58 . 00 0 Ih. 698

225 159 . 00 0 15.310

1 31 160 .00 0 15. 9'»1 226 161 .00 0 16. 588

1 32 162 . 00 0 17 . 257

227 163.00 0 17 . 9't2 133 16<«.00 0 18.6'<e 228 165.000 19. 373

13'» 166 • 0 0 0 20-120

229 167.000 20.883

135 168 .00 0 21.67*. 230 169.00 0 22. l»81 136 170.000 23.310

231 171.000 2it.l60 137 172.00 0 25. 033

232 173.000 25.929

138 17't.OOO 26.81.9

2 33 175.000 27.791

139 176.00 0 28.761

2 3i» 177.000 29. 750

I'tO 178.000 30.769

2 35 179.000 31.809

l*.! 180.000 32.882

2 36 180.000 32. 88<» 2 37 181.000 33.977 l^ 182.000 35.098

238 182.000 35.100

239 183.000 36.256

2'«a 18<<.00 0 37. '.35

2'»l 185.000 38.61.7

2<»2 186.00 0 39. 989

2'»3 187.00 0 l.!. 166

2V» 188.000 1.2. '.71. 2i»5 189.000 1.3. 821.

2'«6 190 .000 1.5.210

NP = 105, RMSPCT = 0.011.

CALC PCNT 6.761 -0 . 0 02 7.112 -0. 00 3

7 . 1. 76 -0 . 002 7.653 -0 . oil

8.2'.'. -0 . 006

8.61.9 -000'. 9. 069 -0 . 006 9.5 02 0 . 000 9.950 -0. 0 02

1 0 . ' 1'. 0 • 0 c

10.892 -0003 11.3 87 -0 . 002 11.897 0 . 0 07 12 . '.23 0 003 12.966 0 . 0 05 13.526 0 . 0 02

11.. 1 0 3 0 . 006

1'«.697 0 . 009 15.309 0 . 0 09 15.939 0 . 009 16.588 0 . 003 17.255 0. 013

17.91.1 0

002

18.61.7 0

008 19.372 0 . 0 02 20.118 0. 009

20.881. -0. 005 21.671 0. 017

22.1.79 0. 009 23.308 0. 009

2'.. 160 0. 001

25.03'. -0. 00<t 25.930 -0. 003 26.850 -0. 005

27.79'. -0. 010 28.761 -0. 002

29.75'. -0. 012 30.771 -0. 005

31.811. -0 . 017

32.881. -0. 003

32.881. 0. 003

33. 980 -0. 010

35.101. -0. 016

35.101. -0. Oil 36.256 0. 001

37.1.37 -0. 005

38.61.8 -0 . 002 39.890 -0. 003

1.1. 165 0. 003

'.2. '.73 0. 003

'.3.818 0. 01'. 1.5.202 0. 017

42

F-45
Table 8. Methane vapor densities.

TTRP = 90.680, TCRT = 190.600, OCRT = 10.000 -2.6383760 3 2.5366625<» -7 . i»22<t7 197 '..5<»960972 -3. <,e20<.388

ID T, K MOL/L CALCD PRCNT

91 .000 0.0163 0.0163 -0.02

I 95.00 0 0. 0255 0.0255 0.03 103.000 0. 0557 0.0557 -0.03

107.000 0.0786 0. 0786 -0.01

I 111.000 0.1081 0.1081 0 .01. I 115.000 0. 11.52 0. 11.52 0.01

I 119.000 0. 1912 0. 1912 0.00

I 123.000 0.21.73 0. 21.71. -0.01.

I 127.000 0.3151 0.3152 -0 .02 131.000 0. 3961 0. 3961 -0.01

I 135.00 0 0.1.920 0. 1.920 0.01

I 139.000 0.601.9 0.601.7 0.03

li«3.00 0 0.7370 0.7368 0.03

I l'«7.00 0 0.6911 0.8908 0.03 151-000 1. 0701. 1.0703 0.01

1 155.000 1.2790 1.2795 -0. 01. 159.00 0 1.5221 1.5237 -0.10

1616 169.067 2. 31.88 2.31.81 0.03

161it 169.270 2. 3687 2. 3687 -0.00

912 169.1.17 2.3858 2. 3838 0 . 08 1612 169 .1.68 2.3881 2.3890 -0 .01. 910 169.601 2. 1.051. 2.1.028 0.11

908 169.791. 2. 1.236 2. 1.229 0.03

1716 173.0 88 2. 7972 2.7972 -0.00

1712 173.1.89 2. 81.57 2.81.72 -0.05

1010 173.675 2.8700 2.8708 -0.03

10 08 173.857 2. 8935 2.891.1 -0.02

1816 177 .091. 3.3501 3.3505 -0.01

1811* 177.292 3.3801 3.3811. -0 . 01. llll» 177.328 3.3863 3. 3871 -0.02

1812 177.1.85 3.1.108 3.1.119 -0.03

1916 181 .105 1.. C663 1.. 0652 0.C3

191i» 181 .301. 1..1077 I.. 1065 0.03

1213 181.389 1.. 1269 1.. 121.1. 0.06

1912 181.506 1.. 11.96 1.. 11.92 0.01

1211 181.589 1.. 1656 1.. 1670 -0.03

1209 181 .768 1.. 201.2 1.. 2057 -0 . 01. 1516 183.117 '..5212 '..5187 0.05

151<. 183.322 1..5701. 1..5700 0.01

1512 183 .511. 1..6189 1..6190 -0.00

1316 181. .125 I..7822 1.. 7618 0 . 01 2107 181.. 285 1..8263 '..8263 -0.00

2106 18".. 1.71 "..8797 '..8791 0.01

1312 181.. 510 1.. 8876 (.. 8903 -0.06

1<»16 186.129 5.1.096 5. '.113 -C. 03

I'.li, 186.319 5.1.795 5.1.810 -0.03

li»12 186.518 5.5591 5.5565 0 . 05

NP = 1.7, RMSPCT = 0.038

43

F-46
Table 9. Methane liquid densities.

TTRP = 90. 680, TCRT = 190.600, DTRP = 28.11.7, DCRT = 10.000

-0. 158253889 0.033175683 -0 • 0 17 1.<»16 83

10 T,K MOL/L CALCD PRCNT

1 175.053 18.390 18.389 0.00

1 169.326 19. '92 19. '92 -0.00

1 163.659 20. '28 20.1*21 -0.01

1 157.199 21.379 21.378 0.00

1 151.553 22.130 22.129 0.00

1 l'.5.'^i^8 22.880 22.880 -0 .00

1 139.352 23.578 23.580 -0.01

1 133.878 21,. 176 2i..l7'^ 0.01

1 133.773 2i^.l86 21^.185 0 .00

1 129.657 2'^.611 2't.613 -0.01

1 125.825 2I..999 2'.. 999 -0.00

1 121.893 25.388 25.381^ 0.02

1 117.71.6 25.782 25.779 0. 01

1 113.772 26.1it6 26.1<.9 -0.01

1 109.611 26.527 26.526 0.00

1 105.165 26.916 26.920 -0.02

1 101.1*3'* 27.21*3 27.2'*'* -0.00

1 97.173 27.605 27.607 -0.01

1 93.512 27.910 27.913 -0.01

MP = 19, RMSPCT = 0.008

44

F-47
Table 10. Methane saturation temperatures.

TTRP = 90. 680, TCRT = 190.600, DTRP = 28.1<t7, DCRT = 10.000

22977 1. 292361'.9 0. 138091.28 -0.2022'.ll.7 7. 51562869

• IfSl 96676 51.. 35860it8i« -56. 83'.69<.36 21.. 3266787<. 0. 00000000

I c MOL/L CftLC PCNT T,K CfiLC PCNT

0 .0163 0.0163 -0.08 91.000 90.991. 0.01

0 .0255 0.0255 0. 09 95.000 95. 009 -0.01

0 . 0557 0. 0557 0.03 103. 000 103. 003 -0.00

0 .0786 0.0786 0.01 107.000 107. COl -0.00

0 .1081 0.1081 0.02 111.000 111. 003 -0.00

0 . li«52 0.1i»52 -0.03 115.000 111.. 996 0.00 0.1912 0.1913 -0. Qk 119. 000 118. 991. 0. 01

0 .2'»73 0.2'»75 -0. 07 123.000 122. 989 0.01

0 .3151 0.3152 •0,01* 127.000 126. 99<» 0.00

0 . 3961 0.3961 0.01 131.000 131. 001 -0. 00

0 . <«920 0.<»918 0.01. 135. 000 135.007 -0. 01

0 .60<»9 0.60<,5 0. 07 139.000 139. 013 -0.01

0 .737 0 0.7365 0. 07 11.3.000 11.3. cm -0.01

0 .8911 0.8906 0 . 05 11.7.000 11.7. Oil -0.01

1 . 070'* 1.0703 O.OC 151.000 151. 001 -0.00

1 .2790 1.2798 -0. 07 155.000 151.. 965 0.01

1 .5221 1.52'«i» -0.15 159.000 158. 965 0.02 1616 2.3«»88 2.3'»86 0.01 169.067 169. 069 -0.00

161<t 2.3687 2.3692 -0.02 169.270 169. 265 0.00 912 2 .3858 2.381.2 0,07 169.1.17 169.1.32 -0.01

1612 2.3881 2.3895 -0.06 169.1.68 169.1.55 0.01

910 2.',05i» 2.'.032 0. 09 169.601 169. 622 -0. 01 908 2.1*236 2. 1.233 0.01 169.791. 169. 797 -0.00

1716 2.7972 2.7968 0.01 173.088 173. 091 -0.00

1712 2.8i.57 2.8<.67 -0.03 173.1.89 173.1.81 0.00 1010 2 . 8700 2. 8702 -0.01 173.675 173.671, 0. 00 looa 2 .8935 2.893'. 0.00 173.857 173. 858 -0.00

1816 3.3501 3.3<.92 0.03 177.091. 177. 100 -0. 00

181<. 3.3801 3.3801 0.00 177.292 177.292 -0.00 iim 3. 3863 3.3857 0. 02 177.328 177. 332 -0.00

1812 3.<»108 3.1.105 0.01 177.1.85 177.1.87 -0.00

1916 ',.0663 <..06<«9 0.03 181. 105 181. 112 -0.00

igif* If .1077 0.03 181.301. 181. 310 -0.00

ID 1213 1912

1211 1209

1516

151". 1512

1316 2107

2106

1312

11.16

11.11. 11.12

1

11

11

11

1

1

1

1

1

1

111

1

1

1

NP

MOL/L

,1269

.11.96 .1656

,201.2 .5212

.5701.

i» .6189

1. .7822

t>.8263

I.. 8797

<..8876

5 .1.096 5.1.795 5.5591

18 .3900

19.1.92 0 20 .1.280

21 .379 0 22.1300

22.880 0 23 .5780

21.. 1760

21.. 1860

21..6110

21.. 999 0 25 .3880 25.762 0 26 . 11.60 26.527 0 26.9160

27.21.30 27.6050

27 .9100

CALC

1.. 121.3

I.. 11.92 1..1670 1..2059

1..5201 1..5716

'..6207 1..7839

i..8 2ei» 1..8612

1..8925 5.1.096

5.1.781 5.5519 18.3876

19.1.933

20.1.316 21.3776 22.1279

22.8790 23.5797

21.. 171.5

21.. 1856

21.. 611.1 25. 0001. 25.3855 25.7803

26.11.86 26.5252

26.9182

27.21.11. 27.601.3 27.9116

PCNT

0.06

0.01

-0.03

-0.01. 0.02

-0.03

-O.Oi. -0. 03

-0.01. -0.03

-0.10

-0.00 0.03 0.13

0.01

-0. 01 -0.02

0.01

0. 01 0.00 -0.01

0.01

0.00

-0. 01 -0.01 0.01

0.01

-0.01 0.01

-0.01 0.01

0. 00 -0.01

T,K 181.389 181.506

181.589

181.768 183.117

183.322

183.511.

181.. 125

181.. 285

181.. 1.71 181.. 510 186.129

186. 319 186.518 175.053 169.326

163.659

157.199 151.553

11.5.1.1.8 139.352 133.878

133.773

129.657 125.825

121.693

117.71.6 113.772

109.611

105.165

101.1.31. 97.173

93.512

CALC

181.1.01 181.508

181.582

161.760

183. 121 183. 317 183.507

181.. 119

181.. 277

181.. 1.66 181.. 1.93 186. 129

186. 323 186.537

175. 01.2 169. 333 163.682

157. 189 151.536

11.5. 1.39 139. 367 133. 861. 133.769

129.687

125. 839 121.867

117.727

113. 802 109.591

105. 190

101.1.15 97. 165 93.531

PCNT -0.01

-0.00

0.00

0.00 -0.00

0.00

0.00 0.00

0.00

0.00 0.01

0.00 -0.00

-0.01

0.01 -0.00 -0.01

0.01

0.01 0.01 -0.01

0.01 0.00

-0. 02

-0.03

0.02 -0.02

0.02

0.01 -0.02

= 66, ONRHSPCT = 0.01.1., TSRMSPCT = 0, 010

45

F-48
Table 11. Coefficients for the equation of state, methane.

DTRP = 28. l**/, DCRT = 10. 000, TCRT = 190.600

AG = 0.10, AL = 0.10, BE = 7.00 1.770590163

3.<«&12256e8 -0.551*793076

0.5988696(»6

1.726197827

-13.9711.38178 2.878663686

-0. 511137332

7.8332«»9113

-1. 8711.26210 -0.503713816

MOL/L TSAT

0.5 135.313

1.0 11.9.506 1.5 158.628

2.0 165.318

2.5 170,515

3.0 171.. 670

3.5 178.038

i*.0 180 .787

1..5 183.036

5.0 181.. 875

5.5 186.379

6.0 187.605

6.5 188.595

7.0 189.379

7.5 189.965

8.0 190.352

8.5 190.51.7 9.0 190.597

9.5 190.600

10.0 190.600

10.5 190.600

11.0 190.599

11.5 190.570

12.0 190.1.51 12.5 190.196

13.0 189.789

13.5 189.227

II. .0 188.511

III. 5 187.61.1 15.0 186.611. 15.5 185.1.26 16.0 181.. 070 16.5 182.539

17.0 180.626

17.5 178.922

18.0 176.821

18.5 171.. 518

19.0 172.008

19.5 169.286

20.0 166.358

20.5 163.217

21.0 159.867

21.5 156.309

22.0 152.51.8 22.5 11.8.581.

2 3.0 11.1..1.2 3 23.5 11.0.065 24.0 135.512

21.. 5 130.767

25.0 125.829

25.5 120.702

26.0 115.388

26.5 109.893

27.0 101.. 226

27.5 98.1.05 28.0 92.1.51 28.5 86.396

29.0 80.279

29.5 71.. 11.9 30.0 68.061

THETA PSAT

12l».ig5 1..998 138.995 10.183

11.9.179 15.079

157.067 19.607

163.1.71 23.71.1. 168.780 27.1.79 173.215 30.810

176.921. 33.71.1. 180.015 36.297 182.579 38.1.95

181.. 686 1.0.369 186.1.08 1.1.951 187.789 1.3.269 168.668 1.1.. 337 189.666 1.5.152 190.200 1.5.700 190.1.82 1.5.978 190.578 1.6.052 190.596 1.6.055 190.680 1.6.055 190.598 1.6.055 190.580 1.6.051. 190.586 1.6.012 190.299 1.5.81.2 189.900 1.5.1.79 189.277 1.1.. 906

188.1.17 1.1.. 128 187.306 1.3.155 185.939 1.1.999

181.. 296 1.0.669 182.367 39.171. 180.137 37.521 177.595 35.722

171.. 728 33.787

171.530 31.731 167.995 29.571.

161.. 122 27.335

159.911. 25.01.0 155.379 22.715

150.527 20.390

11.5.375 16.093

139.9I.". 15.651.

131.. 256 13.702 128.339 11.661. 122.222 9.762

115.937 8.017 109.515 6.1.1.1. 102.993 5.051.

96.1.01. 3.653 89.786 2.81.2 83.171. 2.016

76.608 1.366 70.126 0.876 63.769 0.526 57.579 0.291 51.596 0.11.7 1.5.869 0.066

1.0. 1.32 0. 026 35.325 0.008 30.582 0.002

B C 1.801 0.057

1.832 0.106

1. 863 0.11.6 1.893 0.178

1. 921. 0. 203 1.955 0.220 1.985 0.229 2.016 0.232

2. 01.7 0.226 2.077 0.218 2.106 0.201 2.139 0.179

2. 169 0.151 2.200 0.117 2.231 0.078 2.261 0.035 2.292 -0.013

2.323 -0.066

2.353 -0.122

2.381. -0.183

2.1.15 -0.21.6

2.1.1.5 -0.311.

2.1.76 -0.384

2.507 -0.1.57 2.537 -0.532

2.568 -0.610

2.599 -0.690

2.629 -0.771

2.660 -0.851. 2.691 -0.938

2.721 -1.023

2.752 -1.108

2. 783 -1.191. 2.813 -1.280

2.81.1. -1.366

2.871. -1.1.52 2.905 -1.537

2.936 -1.620 2.966 -1.703

2. 997 -1.781.

3. 026 -1.861.

3. 058 -1.91.2 3.089 -2.017

3.120 -2.090

3.150 -2.160

3.181 -2.227

3.212 -2.290

3.21.2 -2.351

3. 273 -2.1.07

3.301. -2.1.59

3. 331. -2.507

3.365 -2.550 3.396 -2.588

3.1.26 -2.622

3.1.57 -2.61.9

3.1.88 -2.672

3.518 -2.686

3.51.9 -2.696

3.580 -2.701

3.610 -2.698

0 E -0.5 01. -0.56 0 -0 . 1.55 -0.5 22

-0 . 1. 07 -0.485

-0.360 -0.446

-0 . 311. -0.412

-0 • 269 -0.377

-0 . 226 -0.343

-0.183 -0.310

-0 . 1 1.2 -0.277

-0 . 102 -0.246

— 0 . 061. —0.216

-0.0 26 -0.187

0.010 -0.159

0.045 - 0 . 132 0.079 -0.107

0.112 -0.083

0.144 -0.060

0.174 -0.036

0.204 -0.016

0.232 0.000 0.259 0.017 0.284 0.032

0.309 0 . 0 46 0.332 0.056

0 . 355 0.068

0.376 0.077

0.395 0.083

0.414 0.088

0.432 0.091 0.448 0.092

0.463 0.091 0.477 0.087

0 • 490 0.082

0.501 0.075

0.512 0.065

0.521 0.053

0 • 529 0.039 0.536 0.022

0.541 0.003 0.546 -0.019

0.549 -0.043

0.551 -0.069

0.552 -0.098

0.552 -0.130

0.550 -0.164

0.548 -0.202

0. 544 -0.242

0.539 -0.284

0.533 -0.3 30 0.526 -0.379

0.517 -0.430

0.507 -0.485

0.497 -0.543

0.485 -0.603

0.471 -0.667 0.457 -0.734

0.441 -0.805

0.425 -0.879

0.407 -0.956

0.387 -1.036

46

F-49
Table 12. Calculated derivatives in density, methane

MOL/L

0.5

1.0 1.5

2.0 2.5

3.0

3.5

i*.0 k.S

5.0

5.5

6.0

6.5

7.0 7.5

S.O

8.5 9.0 9.5 10.0 10.5 11.0

11.5

12.0 12.5

13.0 13.5

I't.O li«.5 15.0

15.5

16.0 16.5 17.0

17.5

18.0 18.5 19.0

19.5 20.0

20.5

21.0 21.5

22.0 22.5

23.0 23.5

2't.O 2i».5 25.0 25.5

26.0

26.5

27.0 27.5

2S.0 28.5

29.0 29.5

30.0

TSAT 135.313

l'.9.506 158.626

165.318 170.515

17I..670 178.038

180.787 183.036

18i».875 186.379

187.605

188.595

189.379

189.965

190.352

190 .5'.7 190.597

190.600

19C .60 0 190.600 190.599

190.570

190.1*51 190.196 189.789

189.227 188.511

187,6'»1 186.611) 185.1*26

181.. 070 182.539

180.826

178.922

176.821

171.. 518 172.008

169.288 166.358

163.217 159.867

156.309

152.51.8

11.8.581*

11.1.. 1*23 11.0.065 135.512

130.767

125.829

120.702

115.388

109.893

101.. 226

98.1*05

92.1*51 86.396 80.279

71*. 11*9 68.061

OTS/DD

38. 031 21.852

15.361

11.687

9. 21*1* 7.1.56 6.072

1..963

1.. 061 3.322 2.713

2.2tJ5 1.768

1. 368 0.975

0.575 0.217

0. 023

0 . GOO 0.000 -0.000 -0.012

-0. 126

-0. 361. -0.660

-0.970 -1.279

-1.586 -1.895

-2.213

-2.51.1 -2. 881. -3. 21.2 -3.615

-1*. 003

-'..1.02

-1.- 812 -5.229

-5.61.9 -6.071

-6.1.92 -6.908

-7. 320 -7.726

-8.126

-8.521 -8.911

-9.298

-9.683

-10. 065

-10. 1.1.3 -10.812

-11.165

-11.1.91. -11.761. -12. 021

-12. 167

-12.261. -12.238

-12. 095

THETA

121.. 195 138.995

11.9.179 157. 067

163.1.71 168.780 173.215

176.921. 180.015

182.579

181.. 688

186.1.08 187.789 188.868

1 89.668 190.200

190.1.82 190.578

190.598 190.600

190.598

190.580 190.506

190.299

189.900 189.277

188.1.17 187.308 185.939

181.. 296 182.367

180. 137 177.595

171.. 728 171.530 167.995

161.. 122

159.911. 155.379

150.527

11.5.375

139.91.1.

131.. 256 128.339

122.222

115.937

109.515

102.993

96.1.01. 89.786

83.171. 76.608 70.126

63. 769 57.579

51.598

1.5.869

1.0.1.32 35.325

30.582

DTH/OD

38. 269 23.693

17.679

II.. 120 11.620

9. 686

8. 103

6. 768 5.628

I.. 650

3. 810

3. 086

2. 1.50 1. 875

1. 329

0. 803

31.6 081

Oil. 000 -0. Oil. -0. 070

-0. 255

-0. 592

-1. 015

, 1.78

, 966

-2. 1.75 -3. 008

-3. 567

-1.. 155

-1.. 768

-5. 1.05 -6. 062

-6. 732

-7. 1.08 -8. 083

-8. 71.7 -9. 392

-10. 009

-10. 590 -11. 127 -11. 611. -12. 01.1. -12. 1.13 -12. 718 -12.955

-13. 123

-13. 219

-13. 21.3 -13. 191 -13. 062

-12. 853

-12. 561

-12. 185

-11. 721. -11. 180 -10. 555

-9. 860

-9. 105

PSAT

I.. 998 10.183 15.079

19.607

23.71.1. 27.1.79 30.810

33.71.1. 36.297

38.1.95 1*0.369

1.1.951 1*3.269

1*1*. 337

1*5. 152

1*5.700

1*5.978

I. 6.052

1*6.055

1*6.055

1*6.055

1*6.051. 1*6.012

1*5.81*2 1*5.1*79

1*1*. 906

1*1*. 128

1*3.155

1*1. 999

1*0.669

39.171. 37.521 35.722

33.787

31.731

29.571. 27. 335

25.01*0 22.715

20. 390 18.093

15.851. 13.70?

II. 661. 9. 762 8.017

6.1.1.1. 5. 051. 3.853

2.81.2 2.016

1.366

0.876

0.526

0.291

0.11.7

0. 0 66 0.026

0.008

0.002

DPS/OT

0.2765

0.i*63(t 0.611*3 0.71*18 0.8518

0. 91*76

1. 0312

1. 101*1 1.1675

1.2226

1. 2701. 1.3119

1.31.79

1. 3768

1. 1*01*7 1.1*250

1.1*388

1. 1*1.58 1. 1.1.71. 1.1* 1.71* 1. 1*1*71* 1.1*1*62

1.1*1*12 1.1*313

1.1*162

1. 3965

1. 3725

1. 31.1*7 1. 3132 1.2782

1.2398

1. 1981 1.1532

1. 1051

1. 051.1 1.0003

0. 91.39 0.8651.

0. 821.9

0. 7630 0.7002

0.6368

0.5736 0.5109

0.1.1.95 0. 3900

0. 3329

0. 2788

0.2281. 0.1822

0. 11.09

0. 101.9 0.071.6 0.0501

0.0311. 0.0181

0. 0091.

0. 001.3 0.0017 0.0005

DPS/DD

10.517«* 10.1266

9.1*366 8.6700

7.871*0 .0656 .2609

.1*796 ,71*12 .0610

. 1*1*61 .8925 2.3628 1.8869

. 3696

.8200

.3123

. 0338

,0000 .0000

.0000 -0.0179

-0.1819

-0.5209

-0.9350

-1. 351*6 -1.751*9 -2.1321

-2. 1*889 -2.8262

-3.1509

-3.1*557 -3.7389

-3.9955

-i*.2193

-I*. 1*037

-I*. 51*23

-I*. 6293

-i*.6603

-i*.6326

-1*. 51*52 -i*.3995

-1*. 1985

-3.91*75 -3.6530 -3.3229

-2.9661

-2.5923

-2.2111* -1.831*2

-1.1*715 -1. 131*2 -0.8327 -0.5759

-0.3702

-0.2171* -0.111*2 -0.0523

-0.0203

-0.0065

47

F-50
Table 13. Calculated critical isotherm, methane.

TC = 190.600, DC = 10. 0 00 , PC = '«6.0555

D/OC P/PC DPR/DOR OTS/DR DTH/OR OPS/DR DXB/DR OXC/DR DXD/OR DXE/OR

0.900 0.99999325 Q.O 00696i«9 0. 65728 2. 2661.8 r. 95028 - 0

00 31.2 0. 0 0 31.5 0. 00690 0. 03369 0.905 0.99999607 0. 0 0 0<« 14653 0. 1.5151 1.90386 0.65291. -0. 00235 0 . 00237 0. 001*71* Q. 02361 0.910 0.99999781. 0. 0 0 027201. 0. 29581 1 . 59931. 0.1.2797 - 0 . 00151. 0. 00155 0. 00310 0.01578

0.915 0.99999889 0.00015606 0. 18321* 1.31.597 0. 26509 -0 . 00095 0. 00 096 0. 00192 0. 00998

0. 920 0.999999'«7 0.000OS333 0. 10611. 1. 13613 0. 15358 -0. 00055 0. 00 056 0. 00111 0 .00590 0.925 0.99999977 0. 0 0 0 0i»032 0. 05670 0. 96197 0.08205 -0. 0003 0 0. 00030 0. 00059 0. 00322

0.930 0 .99999991 0.00001800 0. 0271.1. 0 .81601. 0.03971 -0. 00011. 0. OOOIU 0. 00029 0. 00159 0.935 0.99999997 0. 0 0 000697 0. 01171. 0.69172 0.01700 -0 . 00006 0

00006 0. 000 12 0.00070

0. 9<«a 0.99999999 0.00000230 0. 001.31 0. 58370 0. 00621. -0. 00002 0. 00002 0. 000 05 0. 00026

1.0 000000 0 0.00000061 a. 00130 0.1*8815 0.00188 - 0

0000 1 0. 00001 0 . 00001 0. 00Q08 0.950 i.oooooaoo 0.00000013 0 . 00030 0 .1*0266 0. 0001*1* -0. 00000 0. 00000 0. OOOOO 0. 00002 0.955 1.00000000 0.00000002 0. 00005 0 . 32596 0.00007 - 0

0000 0 0. 00 000 0. OOOOO 0. OOOOO 0.960 1. 0 0000 000 0.00000000 0 . 00001 0. 25751 0. 0000 1 -0

0000 0 0 . ooooo 0. OOOOO 0.00 000 0.965 I.oooooaoo 0.00000000 0. OQOOO 0.19716 C. 0000 0 -0. 0000 0 0. 00300 0. ooooo 0.00000

0.970 1.0 000000 0 0.00000000 0. 00000 0.11.1.85 0.00000 -0. 0000 0 0. ooooo 0. OOOOO 0. ooooo 0.975 1.0 0000000 -o.oooooooo 0. 00000 0. 10059 0. 0000 0 -0. 0000 0 0. ooooo 0. ooooo 0. ooooo

0. 980 1.0 0000 000 0.00000000 0. 00000 0.061.38 0.00000 -0. 0000 0 0. ooooo 0. OOOOO -0. ooooo 0.985 1.0 0000000 0.00000000 0. 0000 0 0.03621 C. 0000 0 -0. 0 0 00 0 0. ooooo 0. ooooo 0.00000

0.990 1.0 000000 0 -0.00000000 Q. 00000 0.01609 0.00000 -0. 0000 0 0. ooooo 0. OOOOO -0. ooooo 0.995 1.00000000 0.00000000 0. 00000 0.001*02 C. 0000 0 -0. 00 00 0 0. ooooo 0. ooooo -0.00000

1. 000 1.00000000 0. 00000000 0. coooo 0.00000 0.00000 -0. 0000 0 0. ooooo 0. OOOOO 0. ooooo 1.005 1.0 0000 00 0 -0.00000000 -c. 00000 -0. 001*02 - C. 00000 0. 0000 0 -0. ooooo -0. ooooo 0.00000

1.010 1.00000000 o.oooooooo -0. OOGOO -0. 01609 -0.00000 0. 0000 0 -0. 0000 0 -0. ooooo 0.00000

1.015 1.0 000000 0 -0.00000000 -0. 0000 0 -0.03621 -0. 00000 0. 0000 0 -0. ooooo -0. ooooo -0.00000

1.020 1.00000000 o.oooooooo -0. 00000 -0.061.38 -0.00000 3 . 0000 0 -0. ooooo -0. OQOOO -0. ooooo 1.025 1.00000000 0.00000000 -0. 0 00 0 0 -0. 10059 -0.00000 a. 0000 0 -0. ooooo -0 . ooooo -0.00000

1.030 1.0 0000 00 0 - 0. 0 OOOOOOtl -0. 00000 -0. 11*1*85 -0. 00000 a. 00000 -0. ooooo -0. ooooo -0.00000

1.035 1.0 0000 000 O.OOOOOOOtI -0. 00000 -0. 19716 -0.00000 0. 0000 0 -0. ooooo -0. ooooo -0. ooooo

1. 0<*0 1.0 0000 00 0 0.00000000 -0. 0000 0 -0.25751 -0.00000 0 . 00000 -0. ooooo -0. ooooo -0. ooooo

1.0<.5 1.00000000 0.00000001 -0. 00 0 0 2 -0 . 32593 -0.00003 0. 0000 0 -0. ooooo -0. ooooo -0. ooooo

1. 050 1.00000000 o.oooooooe -0. 0 00 15 -0 .1*0250 -0.00021 0. 0000 0 -0. ooooo -0. ooooo -0.00001

1.055 1.00000000 0.000000 31! -0. 00063 -0.1*871*8 - 0. 00092 0. 0000 0 -0. ooooo -0. 00001 -0. 00001. 1.060 1.00000000 0. 0 0 00011i< -0. 00 212 -0 .58151 -0.00307 0. 0000 1 -0. 00001 -0. 0 0 0 02 -0. 00013 1.065 1.00000001 0. 0 0000352 -0 . 00581* -0 .68581 -0. 0081*5 0. 0000 3 -0. 00003 -0. 00006 -0. 00035

1.070 1.0 00O0OOi» 0.00000922 -0. 01376 -0.80236 -0.01992 0. 00007 -0. 00007 -0. 000 11* -0.00080

1.075 1.00000012 0.00002122 -0. 02871 -0. 93398 -C. 01.151* a. 00015 -0. 00015 -0. 00030 -0. 00163

1.080 1.00000027 0. 0 0001.399 -0. 051.21* -1.081.23 -0. 0781*9 0. 00028 -0. 00028 -0 . 00057 -0. 00302

1. 0S5 1 .0 0000 059 0. 0 0008370 -0. 091.52 -1.25726 -0.13676 0. 0001.9 -0. 00050 -0. 00099 -0. 00516

1.090 1.00000115 o.oooi'>e2e -0. 151.02 -1.1.5756 -0.22282 0. 00080 -0. 00081 -0. 00162 -0. 00821*

1. C95 1.00000213 0. 0 002i«7i.5 -0. 23729 -1.63967 -0.31.325 0. 00121. -0. 00121. -0. 0021.9 -0. 0121*6

1. 100 1.00000370 0.00039252 -0. 31.869 -1.95792 -C. 501.29 0. 00182 -0. 00183 -0.00366 -0.01797
Table 14

Comparison of experimental P-p-T data

for methane with the equation of state

The following 24 pages give experimental data of authors

identified in the first column. These ZD's are listed in table 1, above.

Calculated densities are found by iterating the P(p, T) equation of state.

Near the critical point, (BP/Sp)]- approaches zero, hence the densitydeviations should be ignored. For the compressed liquid at low temperatures, (SP/Bp)-]- becomes extremely large, hence the pressure

deviations should be ignored. The equation of state was adjusted only

to data thru Douslin (1D=6).

49

F-52
METHfiNE EQUATION OF STATE

ID T,K MOL/L CALCD O.PCT P,BAR CALCD P.PCT

2 150.000 1.0000 0.9998 0.02 10.230 10.232 -0.02

2 155.000 1. 0000 0.9998 0.02 10.723 10.721. -0.01

2 160.000 l.OOGO 0.9999 0.01 11.209 11.209 -0.00

2 165.000 1.0000 l.OQOO -0.00 11.689 11.689 0.00

2 170. 000 1. 0000 1.0001 -0.01 12. 165 12.16'« 0.01

2 175.000 1.0000 1.0001 -0.01 12.636 12.635 0.01

2 180.000 1.0000 l.OOQl -0.01 13.105 13.103 0.01

2 185.000 l.DOOO 1.0001 -0.01 13.570 13.569 0.01

2 190.000 1. 0000 1.0001 -0.01 1<». 033 lit. 032 0.01

2 195. 000 1. 0000 1. 0001 -0. 01 1<«.<»91« 1<<.(«93 0.01

2 200. 000 1. 0000 l.OOei -0.01 li».95i< 1<».953 0.01

2 205. 000 1. 0000 1. 0000 -0 .00 15. 1.11 15. ".ll 0.00

2 210.000 1.0000 1.0000 -0.00 15.868 15.867 0.00

2 215.000 1.0000 1.0000 0.00 16.322 16.322 0.00

2 220.000 1.0000 1.0000 0.00 16.776 16.777 -0.00

2 225. 000 1. 0000 1.0000 0.00 17. 229 17.230 -0.00

2 230.000 1.0000 0.9999 0.01 17.681 17.682 -0.01

2 235. 000 1. 0000 0.9999 0.01 18. 132 18.131. -0.01

2 21.0. 000 1. 0000 0. 9999 0 .01 18. 583 18.581. -0.01

2 21.5. 000 1. 0000 0.9999 0.01 19. 032 19.031. -0.01

2 250. 000 1. 0000 0.9999 0.01 19.1.81 19.1.81. -0.01

2 255.000 1.0000 0.9998 0.02 19.930 19.933 -0.01

2 260.000 1.0000 0.9998 0.02 20.378 20.381 -0.02

2 265.000 1.0000 0.9998 0.02 20.825 20.829 -0.02

2 270.000 1.0000 0.9998 0.02 21.272 21.276 -0.02

2 170.000 2. 0000 2. 0059 -0.29 20.661. 20.625 0.19

2 175.000 2.0000 2.0053 -0.27 21.729 21.689 0.18

2 180. 000 2. 0000 2. 001.9 -0.25 22. 776 22.737 0.17

2 185. 000 2. 0000 2. 001.5 -0 .22 23. 810 23.771 0.16

2 190. 000 2. 0000 2. 00til -0.20 21.. 832 21.. 791. 0.15

2 195. 000 2. 0000 2. 0036 -0.18 25. 81.3 25.808 0.1i«

2 200. 000 2. 0000 2.0032 -0.16 26. 81.7 26.811. 0.12

2 205. 000 2. 0000 2. 0028 -O.li. 27. 81.3 27.813 0.11

2 210.000 2.0000 2.0023 -0.12 28.833 28.806 0.09

2 215.000 2. 0000 2.0020 -0.10 29.818 29.791. 0.08

2 220.000 2.0000 2.0016 -0.08 30.798 30.778 0.07

2 225.000 2.0000 2.0013 -0.06 31.775 31.758 0.05

Z 230. 000 2. 0000 2. 0010 -0.05 32. 71.7 32.731. o.04

2 235.000 2.0000 2.0007 -0.03 33.717 33.707 0.03

2 21.0. 000 2. 0000 2. 0001. -0.02 31.. 683 31..677 0.02

2 21.5.000 2. 0000 2. 0002 -0.01 35.61.7 35.61.I. 0.01

2 250.000 2.0000 2.00DO -0.00 36.609 36.609 0.00

2 255.000 2.0000 1.9998 0.01 37.569 37.572 -0.01

2 260.000 2.0000 1.9996 0.02 38.526 38.532 -0.02

2 265.000 2.0000 1.9995 0.03 39.1.82 39.1.91 -0.02

2 270.000 2. 0000 1.9993 0.03 1.0.1.36 I.0.I.1.8 -0.03

NP = 1.6, ONRMSPCT = 0. 097, PMEANPCT = 0.01.2

50

F-53
METHANE EQUATION OF STATE

10 T,K

'«101 176. 000 180. 000

'»103 18<.. 000

%10i» 186. 000

i»105 192. 000

<»106 196. 000

<»107 200. 000

20'.. 000

i»109 208. 000 212. 000

'»111 216.000

220. 000 225.000

230. DOO

2'.0. 000

<»116 253. 000

<»117 260. 000

'»118 270. 000

'.119 280. 000

ttlZO 290. 000

l»121 300. 000

itDOl ISi.. 000

1*002 188. 000 '003 192. 000

'•OQ't 196. 000

'«005 200. 000

<«00& 201.. 000

l»007 203. 000

1*006 212. 000

ifoog 216. 000

'•010 220. 000

<»011 225. 000

if012 230. 000

'»013 2110. 000

'tOl't 250. 000

'»015 26 0. 000

'•016 270. 000

ffOl? 26 0. 000

ifOie 290. 000

'•019 30 0. 0 00 3901 168. 000 3902 192. 0 00 3903 196. 000

390'. 20 0. 000 3905 201.. 000 3906 203. 000 3907 212.000

3906 216. 000 3909 220.000

3910 225. 000 3911 230. 000 3912 21.0. 000

MOL/L CALCO

2. 995'. 3. 0023 2.9936 2.9978

2.9918 2.991.6 2.9901 2.9915

2.9883 2.9889

2.9665 2.9366

2.96<»6 2.96'.3 2.9831 2.9820 2.9613 2.9600 2.9796 2.9778 2.9779 2.9760

2.9761 2.971.2 2.9739 2.9718

2.9717 2.9695

2.9675 2.9651. 2.9630 2.9608

2.9585 2.9563

2.951.0 2.9517

2.91.95 2.91.72

2.9'.50 2.9'.23

2.91.02 2.9381. 3.9782 3.91.67 3.9756 3.9528

3.9730 3.95'.8

3. 9705 3.961.5 3.9683 3.9658

3.965'. 3.9628

3.9629 3.9606

3.960'. 3.9581

3.9579 3.9555

3.955'. 3.9528

3. 9522 3.9'.96

3.91.90 3.91.60 3.91.27 3.9391

3.9363 3.9322

3. 9300 3. 9255

3. 9235 3.9185

3.9170 3.9111.

3.9101. 3.901.8 3.9038 3.8982

1..9301. '..8951

"..9269 (.. 90 02 1..9236 '..901.2 '..9202 '..9076

'..9169 '..9103

'..9135 '..9121. 1..9102 1..9108

I.. 9069 '..9078

'..9035 '..9030

I.. 699'. '..90B0

'.. 8952 '..8958

'.. 8668 <..8866

O.PCT P,BAR

-0.23 27.962

-0.1'. 29. 335 -0.09 30.663

-0.05 32.008

-0.02 33.316

-0 .00 3'.. 610 0.02 35.890

0.0'. 37.158

0.0'. 38. '.17 0.06 39.665

0.06 1.0. 907 0.06 '.2.1'.2 0.07 '.3.673 0.07 1.5.196 0.07 1.6.219 0.07 51.203

0.07 51.. 160 0.08 57.089

0.08 59.996

0.09 62.672

0.06 65. 71.8 0.79 35.156

0.57 37.096

0 .1.6 38. 989 0.15 1.0.900 0.06 1.2. 750

0. 06 1.1.. 556 0.06 l.6.3<.9 0.06 1.6.121. 0.06 1.9. 885 0.06 51.632

0.07 53.600

0.08 55. 91.9 0.09 60. 201. 0.11 61.. '.07 0.11 66.568

0.13 72.682

0.1'. 76.758

0.1'. 80. 805

0.11. 81.. 819 0.71 '.0.276

0.5'. '.2.770 0.39 (.5. 221 0.26 '.7.6'.l 0.13 50.036

0 .02 52. '.09 -0.01 5'.. 7'.'. -0.02 57.052

0.01 59.330

-0.01 62.176

-0.01 61.. 995 0.00 70. 563

CALCD P.PCT

27.930 0.11 29.313 0.08 30.667 0.C5 31.999 0.03 33.312 0.01

3'.. 610 0.00

35.89'. -0.01 37.167 -0.02

38. '.29 -0.03 39.682 -0.01. 1.0.926 -0.05

1.2.162 -0.05

1.3.697 -0.06

1.5.222 -0.06

1.8.21.6 -0.06 51.235 -0. 06

51.. 191. -0.06 57.126 -0.07 60.036 -0.07

62.92'. -0.08 65.765 -0.06 35.269 -0. 32 37.193 -0.26 39.077 -0.23

1.0.932 -0.08

1.2. 765 -0.03

'.1..573 -0.01. 1.6.365 -0.03

1.8.11.2 -0.01.

1.9.901. -0. 01. 51.651. -0.01. 53.825 -0.05 55.980 -0.06

60.21.6 -0.07

61.. 1.61 -0.08 68.631 -0.09 72.760 -0.11 76.651 -0.12 80.906 -0.13

81.. 928 -0.13

'.0.366 -0.22

'.2.856 -0.20

1.5.295 -0.16

'.7.697 -0.12 50.069 -0.07

52. '.15 -0.01

5'..7'.0 Q.Ol

57.01.5 0.01

59.331. -0.01 62.172 0.01

61.. 989 0.01 70.565 -0.00

51

F-54
METHANE EQUftTION OF STATE

ID 3913

3915

3916

3917

3918 3801

3802

3803

3aoi> 3805

3806

3807

3808 3809

3810 3811

3812

3813

381lt 3815

3816

3817

3701

3702

3703

3701. 3705 3706

3707 3708

3709

3710

3711 3712 3713

371i» 3715

3716

3717

3601

3602

3603

360i« 3605

36 06 3607 3608

3609

3610 3611

3612

3613

T,K 250. 000 260. 000 270. 000 280. 000 290. 000 300. 000 192. 000 196. 000 200. 000

201*. 000 208. 900 212. 000

216. 000 220. 000 225. 000 230. 000

2<<0. 000 250. 000 260. 000 270. 000 280. 000 290. 000

30 0. 0 00 192.000

196.000

2Q0. 000

20'*. 000 208. 000 212.000

216. 000 220. 000 225. 000 230. 000

2'«0. 000 250. 000 260. 000 270. 000 280.000

290. 000

3 0 0. 000 192. 000 196. 000 200. 000

20i». 000 208. 000 212. 000 216. 000 220. 000 225. 000 230.000

2'tO. 000 250. 000 260. 000

MOL/L

k. 8781.

1.. 8699

i<. 8&li<

k. 8527

8^l•0 8353

5. 9<»78

5. <ik35

5. 9392 5.9350 5.9307

5. 9261.

5. 9222

5. 9179

5. 9126

5. 9072

5. 8965

5. 8857

5. 871.9

5. 86<.0 5.8531

5. 8<.22

5. 8312

6. 9618 6.9765 6.9712

6. 9659

6. 9607 6.9555

6.950 2 6. 91.50

6. 938<.

6. 9317

6. 9186

6. 9053

6. 8920

6. 8786

6. 8653 6.8521

6. 8389 7.9789

7. 9726

7. 9661. 7.9601

7. 9539

7. 91.76 7.91.13

7. 9350 7.9271 7.9192

7.9031.

7. 8876

7. 6718

CALCO

ii. 8773

<.. 8676

U. 6581

<. 81.86

1.. 8391.

<.. 8301 5.9293

5. 9393

5.9'.ll 5.91.16

5.91.15

5. 9385

5. 93^5

5. 9291

5.9231,

5. 9171 5.9035

5. 8903

5. 8772

5.861.1. 5.8515

5.8391.

5. 8275 6.9521 6.9797

6. 9866 6.9876

6.981.9

6. 9811. 6.9756

.9691 .9607

.9511. .9326

.9153

,8978 .8823

O.PCT

0.02

0.05

0.07

0.08

0.10

6.8665

6.8511. 6.8370

7.6888

7.9751 7.9833

7. 9821. 7.9799

7.9776

7.9710

7. 9636 7.9530

7.91.32 7.9213 7.9085

7.8805

-0.03

-0.11 -0.18

-0.20

-0.21 -0.19

-0.18

-0.17 -0.12

-0.08

-0.0". -0.01

0.03

0.05

0.06

0.1.3 -0.05 -0.22

-0.31 -0.35

-0.37 -0.36

-0.35

-0.32

-0.28

-0.20 -0.15

-0.08

-0.05 -0.02

0.01 0.03

1.13 -0.03

-0.21

-0.28 -0.33

-0.38

-0.37 -0.36

-0.33 -0.30

-0.23 -0.16

-0.11

P, BAR

76. 060

81 . 1.91 86. 867

92. 190

97. 1.69 102.699

1.5. 371

1.8. 1.93 51 . 555

51.. 580

57. 577

60 . 538

63.1.71 66. 376

69. 986

73. 565

80. 61.1 87.631

91.. 51.2 101. 381. 108. 156

111.. 873

121.531.

1.6. 81.5 50.661

51.. 1.08 58. 110

61. 771. 65.1.10 69. 013 72.591

77. 032

81. 1.37 90 . 158 98. 789

107. 322

115. 791

121.. 171, 132.1.89

11.0 . 737

1.7. 528

52. Oil

56.1.16 60.781

65. 120

69. 1.1.2 73. 730

77. 995

83. 292

88. 565

99. 012 109. 360 119. 611.

CALCD

76.073

81.522

86.915 92.256

97.550 102.798

1.5.1.06

1.8. 501. 51.51.9

51.. 555 57.529

60.1.76

63.1.01 66.301. 69.909

73.1.87

80.571. 87.580

91.. 513

101. 379 108.180

111.. 921 121.603

1.6. 875 50.656

51.. 372

58.01.6

61 .686 65.298 68.887

72.1.51. 76.887

81. 292 90.031

98.681

107.21.9 115. 71.0 121.. 155 132.500

11.0.771. 1.7.569 52.008 56.386

60.726

65. 038 69.327

73.591.

77.81.1. 83.132

88.395 98.852

109. 221

119.501.

P.PCT -0.02

-0. 01. -0.06 -0.07

-0.08 -0.10

-0.08

-0.02

0.01 0.05

0.08

0.10 0.11

0.11

-0.02

-0.01. -0.06

-0.06

0.01 0.07

0.11

0.11. 0.17 0.18

0.19

0. 19 0.18

0.11. 0.11 0.07

0.01. 0.02 -0.01 -0.03

-0.09

0.01

0.05 0.09

0.13

0.17

0.18

0.19 0.19

0.19

0.16

0.13

0.09

52

F-55
METHANE EQUftTION OF STATE

ID

3615 3616

3617 3501 3502

3503

350<» 3505

3506

3507 3508

3509

3510

3511 3512

3513

351"* 3515 3516

3517

3it01 3'*02

3l»03

3i«0<* 3'»05 31.06

31.07 31.06

31.09

31.10

31.11 31.12

31.13

31.11. 31.15 31.16

31.17 3301

3302 3303

3301. 3305 3306

3307

3308

3309

3310

3311 3312

3313

3311. 3315

T,K 270.000

280. 000 290. 000

30 0. 000 192. 000 196. 000 200. 000

201.. 300 208.000

212.000

216. 000 220. 000 225. 000 230. 000

21.0.000 250. 000 260. 000 270. 000 280. 000 290. 000 300. 000 192. 000 196. 000 200.000

201.. 000 208. 000 212. 000 216. 000 220. 000 225. 000 230. 000

21.0.000 250. 000 260. 000 270.000

280. 000 290. 000 300. 000 192.000

196. 000

20 0. 000

201.. 000 203. 000 212. 000 216. 000 220. 000 225. 000 230. 000

21.0. 000 250. 000 260. 000 270. 000 280. 000

MOL/L

7.8561

7.81.05

7. 8251

7. 8100

9. 0890

9. 0817

9. 071.3

9. 0669

9. 0595

9. 0520

9. 0'.i.5 9. 0369

9. 0275

9. 0180

8. 9990

3. 9801

8. 9611.

8. 91.29

3. 921.9 8.9072

8. 8900 10.2380 10.2296

10. 2210 10.2123

10. 2035

10. 191.7 10. 1858

10. 1769

10. 1657

10. 151.5 10. 1320

10. 1100 10.0882

10. 0671

10. 01.66 10. 0270

10. 0081

11. 1113

11. 1019

11. 0923

11. 0825

11. 0725

11. 0625 11.0523

11. 01.22 11. 0291. 11. 0167

10. 9911. 10.9667

10. 91.28 10. 9198

10. 8978

CALCD

7.8612

7.81.27

7, 821.8

7. 8077 9.1069

9.1090 9.0996

9. 0872

9. 0853 9.0780

9.0691.

9. 0621

9. 0503 9.0391

9.011.6 6.9982

8.9667

8.91.1.8 8.9235

3.9031.

8.881.8

10. 0931. 10.1357

10.1530

10. 1629

10. 1680 10.1692

10.1673

10.161.3 10.1561

10. 11.73 10.1250 10.1012

10.0780

10. 051.1. 10. 0326

10. 0117 9.9920

11. 02'.1 10.9732

10.991.3

11. 0122 11.0193

11. 01<>0 11. 0198 11.0158

11.0075 10.9976

10.9758

10.9502

10.9253 10.9012

10.8777

O.PCT -0.07

-0.03

0.00 0.03 -0.20

-0.30 -0.28 -0.22

-0.29

-0.29

-0.28

-0.28

-0.25 -0.23

-0.17

-0.11 -0.06

-0.02

0.02

0.01. 0.06

1.1.1 0.92

0.67

0.1.8 0.35

0.25

0.18 0.12

0.09

0.07

0.07 0.09

0.10 0.13

0.11. 0.15 0.16

0.78

1.16

0.86

0.63

0.1.8

0.1.1. 0.29

0.21. 0.20 0.17

0.11. 0.15 0.16

0.17

0.18

P, BAR

129. 779

139. 858

11.9. 353 159. 769

1.7.891 53.032

53. 237

63. 361. 68.502

73.615

78.711

63.800

90. 129

96. 1.39 108.970

121. 393 133.727

11.5. 970

158. 111. 170. 170 182. 11.9

1.8. 101.

51.. 0 20 59.983

65. 977 71.990

78. 012

81.. 035

90. 060

97. 568 105. 066

119. 985

131.. 809

11.9. 51.1. 161.. 165 178.700

193. 133 207. 1.71. 1.8. 322

51.. 855 61.513

68. 21.9 75. 017

81. 773

83. 609

95. 1.15 103. 913

112.1.02 129. 31.1 11.6. 170 162.909

179. 51.8 196. 070

CALCD

129.701. 139.822

11.9.856 159.815

1.7.887 53.058

5 3.197 63.317

68.1.23 73.515

78.596

83.661. 89.983

96.233

108.823 121.282 133.656

11.5.91.1 158.139

170.21.5 182.261

1.8. 136

51.. 110 60.101 66.103

72.111

78. 121

31.. 130 90.136

97.636 105.125

120.059

131.. 921

11.9.698

161.. 335 173.975

193.1.70 207. 861.

1.8.31.1. 51.. 992 61.702

68.1.1.8 75.217

82.001

88.793 95.589

101.. 035 112.576 129.522

11.6.1.02 163.199

179.902

196.503

P.PCT

0.06 0.03

-0.00 -0.03

0.01

0.05 0.07

0.07

0.12

0.11. 0.15

0.16

0.16 0.16

0.13

0.10 0.05

-0.01. -0.06

-0.C7

-0.17

-0.20 -0.19

-0.17

-0.11. -0.11 -0.08

-0.07

-0.06

-0.06

-0.08 -0.10

-0.13

-0.15

-0.17 -0.19

-0.05 -0.25

-0.31 -0.29

-0.27 -0.28

-0.21

-0.18 -0.17

-0.15

-0.11. -0. 16 -0.18

-0.20 -0.22

53

F-56
METHSNE EQUftTION OF STftTE

ID 3316

3317

3201 3202

3203

320i» 3205

3206

3207 3208 3209

3210 3211

3212

3213

321l» 3215

3216 3217

31Q1

3102

3103

310'* 3105 3106

3107

3108 3109

3110 3111

3112

3113 311^

3115

3116 3117

3001

3002

3003

3005 3006

3007 3008

3009

3010

3011

3012

3013

301'* 3015

3016

3017

290.000

30 0. 000 192. 000 196. 000 200. 000

2Q'«. 000 208. 000 212. 000 216. 000 220. 000 225. 000

23 0. 000

2(iO. 000 250. 000 260. 000 270. 000 280. 000 290. 000

30 0. 000 192. 000 196. 000 200. 000

20><. 000 208. 000 212. 000 216. 000 220. 000 225.000

230. 000

2'40. 000 250. 000 260. 000 270. 000 280. 000

29 0. 000 300. 000 192. 0 00 196. 000

20 0. 0 00

20i«. 000 208. 000 212. 000 216. 000 220. 000 225. 000

2 3 0 . 0 00

2i<0. 000

25 0. 0 00 260. 000 270. 0 00 280. 000

29 0. 0 00 300. 000

HOL/L

10. 8769

10. 8570

12. 0697

12. 0591

12. 0<i81 12. 0370

12. 0256

12. 01l»2

1 2. 0026 11.9912

11.9767

1 1. 962'.

1 1. 931.2 11. 9068 11.8808

11. 8562

11. 8330

11. 8112

11. 7906

12. 9815

12. 9695

1?. 9570

12. 9'.<»2 12. 931

12. 918<» 12. 9053

12. 8923

12. 8761

12. 860 0 12. 8286

12. 7988

12. 770 8 12. 7i*i*& 12.7205

12. 6980

12. 6767

11*. 2336

lU. 2188

lit. 2038

li*. 1886

!<.. 1733

l".. 158 0 11.. 1'.27

11.. 1275

li». 1088

l"!. 0906

l"*. 0557

!<.. 0233

1 3. 9939

1 3. 9669

13. 91.21 13.9190

13. 8972

CALCD

10.8559

10.8357

12. 071.2 11.9626

11.9677

11.9750

11.9770 11.9769

11.9754

11.9695 11.9569

11.9<.68

11 . 9206

11. 892". 11.8660

11. 8389

11. eiui. 11. 7919 11.7709

12.9871 12.9263

12.9171

12.9165

12. 9134 12.9076

12.9007 12.8915

12. 8766 12.8616

12. 8298 12.7980

12. 7679

12. 7399 12.7136 12.6896

12. 6677 14.1857 14.2022

14. 1979 14.1912

14. 1625

14. 1726 14.1599

14. 1464

14. 1286 14.1102

14.0743

14. 0396

14. 0072 13.9775

13. 9505 13.9253

13.9032

D.PCT

0.19

0.20 -0.04

0.80

0.67

0.51

0.40

0.31

0.23 0.18

0.15 0.13

0.11

0.12 0.13

0.15 0.16

0.16 0.17 -0.04

0.33 0.31

-0.01

-0.01

0.01 0.02

0 . 04

0 .05 0.07

0.07

,34

.12

,04 -0.02

-0.07

-0.10 -Q.12 -0.13

-0.14

-0.14

-0.13

-Q.12

-0.09

-0.08 -0.06

-0.05

-0.04

P, BAR 212.497

228. 828 48.685

56. 033

63. 574

71. 216

78 .913

86. 654 94.428

102. 201

111. 912

121. 617

140. 985

160. 255 179. 425 198. 490 217. 442 236. 293 255. 031

49. 455

57 . 790

66. 328

74. 993

83. 726

92. 499

101. 304 110. 116

121. 116 132. 115 154. 057 176.900

197. 638

219. 261

240 . 753

262. 130 283. 387

52. 052

62. 209

72. 451

82. 785

93 . 177 103. 608

114. 040 124. 478 137. 516

150 . 534

176. 506

202. 352

228 . 062 253. 635

279. 069

304. 333 329. 483

CALCD

213. 003 229.392

48.683

56.172

63.770

71.431 79.133

86.862

94.610 102.369

112.075

121.780 141.166

160.486 179.722

198.862

217.894

236. 816 255.616 49.448

57.893 66.469

75.125

83.832 92.576

101.342

110.124 121.109

132.095

154.038

175.916 197.700

219.383 240.946

262.388

283.690 52.213

62.290 72.489

82.765

93. 092 103.451

113. 831 124.221 137.212

150.197

176. 121 201.959

227.695 253.303

278.777

304. 095 329.236

P.PCT

-0.24

-0.25

0.00 -0.25

-0. 31 -0.30 -0.28

-0. 24 -0.19

-0.16

-0.15

-0.13 -0.13

-0.14 -0.17

-0.19

-0.21

-0. 22 -0.23

0.01 -0.18

-0.21 -0.18

-0.13

-0. 08 -0.04

-0.01

0.00

0.02

0.01 -0.01 -0.03

-0.06

-0.08 -0.10

-0.11

-0.31 -0.13 -0.05

0.02 0.09

0.15

0.18

0.21 0.22

0.22

0.22

54

F-57
METHftNE EQUATION OF STATE

10 2901 2902

2903

290'f 2905

2906

2907 2908

2909

2910

2911 2912

2913

291<» 2915 2801

2802 2803

280i» 2805

2806 2807

2808 2809

2810 2811

2812

2813 28H»

2701 2702

2703

270<t 2705

2706

2707 2708

2709

2710

2711 2712

2713

271<f 2601

2602

2603

260<« 2605

2606 2607

2608 2609

2610

T,K

190. 000

igi». 000 198. 000 202. 000 206. 000 210. 000 215. 000 220. 000 230. 000

2<iO. 000 250. 000 260. 000 270. 300 230. 000 290. 000 186. 000 190. 000

19i«. 000 198. 000 202. 000 206.000

210.000

215. 000 220.000

230. 000

2(<0. 000 250. 000

26 0. 000 270. 000 182. 000 186. 000 190. 000

1'}'*. 000 198. 000 202. 000 206. 000 210. 000 215. 000 220. 000 230. 000

2i<0. 000 250. 000 260. 000 176. 000 180.000

18'<. 000 188. 000 192. 000 196. 000 200. 000 205. 000 210. 000 215.000

MOL/L

15. 3796

15. 3621

15. 31*1*1* 15. 3267

15. 3088

15- 291

15. 2692

15. 2'.78 15.2071

15. 1701

15. 1369

15. 1069

15. 0797

15. 05'»6 15. 0313

16. 2733

16. 25l»3 16. 231(8 16. 2151

16. 1953

16. 1755

16. 1562

16. 1328

16. 1096

16. 0677

16. 0302 15.9971

15. 9676

15. 91*06 17. 2858

17. 2636

17. 2<«16 17. 219'« 17. 1973

17. 175't 17. 1539

17. 1331

17. loei* 17. 08i»8 17. OkZl* 17. 0056

16. 9731

16.9i»l.l 18. 36<»0 18. 3570

18. 3320

18. 3070

18. 2810

18. 2560

18. 2320

18. 2030

18. 1750

18. 150 0

CALCD

15. 3<»<t2 15. 31.33 15.3'f09

15. 334.8 15. 3256 15.3123

15.2939

15.271.2 15.2355

15. 1970 15.1620

15. 1300

15. 1006

15. 071.5 15.01.93 16.2551

16.21.22 16.2307

16.2188 16.2036

16.1881

16. 1723

16. 11.51 16.1306

16. 0911

16. 0531. 16. 0205

15. 9891. 15. 9612 17.2752

17.2572

17. 21.15 17. 2210

17. 2038 17.1853

17. 1677

17.11.68 17.1276

17.1060 17.0659

17.0301 16,9988

16.9689

18.3807

18. 3521. 18.3262

18. 3011

18. 2777 18.2555

18.231.2

18. 2091. 18.1857

18.1636

D.PCT

0.23 0.12 0.02

-0.05 -0.11

-0.11. -0.16

-0.17

-0.19

-0.18

-0.17 -0.15

-0.11. -0.13

-0.12

0.11

0.07 0.03 -0.02

-0.05 -0.08

-0.10

-0.08 -0.13 -0.15

-0.11. -0.15

-0.11. -0.13

0.06

0.01. 0.00 -0.01

-0.01. -0.06 -0.08 -0.09

-0.11 -0.12

-0.11.

-0.11. -0.15

-0.01

-0.01. -0.06

-0.08

P, BAR

51. 866

63. 787 75.861

88. 012

100. 201 112. 378 127.596

11.2. 792

173. 125 203. 287 233. 313 263. 178 292. 661 322. 396

351. 677

1.5.617 59. 078

72. 680

86. 363 100. 01.8 113. 751 127. 1.51. Ii«i4. 1.01. 161. 607

195. 626

229.1.38 263. 111. 296. 539

329. 757

1.1. 322

56. 91.8 72.675

88. 31.6 101.. 080 119. 771. 135. ^62

151. 080 170.602

190. 033 228. 723

267 . 186 305. I.I.2 31.3. 357

32. 172

50.1.37 68.691

86. 906

105. 089

123. 227 lUl. 311 163. 860 186. 312 208. 687

CALCD

52.082 63.936

75.895

87.918 99.979

112.061 127.175

11.2.287

172.1.66 202.551. 232.529

262.367

292.01.6 321.51.3

350.81.0

1.5. 767 59.203

72.731

86. 309 99.912

113. 520 127.126

11.1.. 127

161. 089

191.. 938 228.651

262.217 295.612

328. 80l»

1.1.1.51. 57. 01.1. 72.677

88.313

103.938 119.535

135.100

150.631. 170. 006 189. 32C 227.815

266.116

301.. 199

31.2. 036 32.232 50.535

68.831

87.062 105.185

123.21.1. 11.1.238 163.623

185.863 208.102

P.PCT

-0.1.2 -0.23

-0.01. 0.11

,22 28 0.33 0.35

0.38 0.36

0.31. 0.31

0.28 0.26

0.21. -0.33

-0.21 -0.07 0.06

0.11. 0.20

0. 26 0.19

0.32

0. 35

0.31. 0.31. 0.31 0.29

-0.32

-0.17

-0.00

0.01.

0.30

0.35

0.36

0. 1.0 0.1.0 0.1.1 0.38

-0.19

-0.20

-0.20 -0.18

-0.09

-0.01 0.05

0.11. 0.23

0.28

55

F-58
METHANE EQUATION OF STATE

ID 2611

2612

2613

261'* 2615

2616 2501

2502

2503

250<» 2505

2506

2507

2508

2509

2510

2511

2512 2513

251'* 2515

2'»01 2<*02

2<»03

2'«0<» 2i»05

2<»06

2it07

2'»08 2'»09

2i>10 2'»11

2'»12

2i»13

2l»li» 21*15 2301 2302

2303

230'» 2305 2306

2307

2308 2309

2310

2311

2312

2313

2201 2202

2203

220'»

T,K

220. 000 225. 000 230. 000 235. 000

2ii0.000

2't5. 000 170. 000

17i». 000 179. 000 182. 000 186. 000 190. 000

igi*. 000 198. 000 202. 000 205. 000 210. 000 215. 000 220. 000 225. 000 230. 000 164. 000 168. 000 172. 000 176. 000 180. 000

ISi*. 000 188. 000 192. 000 196. 000 200.000

zak. 000 208. 000 212. 000 216. 000 220.000

158. 000 162. 000 166. 000 170. 000

17<». 000 178. 000 182. 000 186. 000 190.000

198.000

202. 000 206. 000 152.000

156. 000 160. 000

16<<. 000

MOL/L

18. 1270

18. 1060

18. 0860

18. 0680

18. 0520

18. 0360

19. 5060

19. '750

19. i4i*bO 19. '170

19. 3880

19. 359 0 19. 3320

19. 3070

19. 2830

19. 2660

19. 21*0 0 19. 2160

19. 1950

19. 1750

19. 1570

20. ".250 20. 3890

20. 3570

20. 321*0 20. 2920

20. 260 0 20. 2310

20. 2060

20. 1780

20. 1550

20. 13U0

20. 1150

20. 0970

20. 0800

20. 0650

21. 371

21. 3320

21. 291*0 21. 2580

21. 2230

21. 1890

21. 1580

21. 1290

21. 1030

21. 0800

21. 0590

21. 01*00 21. 0220

22. 1250

22. 0800

22. 01*00 22. 001 0

CALCD

18. 11*31. 18. 121.3 18.1065

18. 0899

18. 071.1. 18. 0595

19.1.873

19.1.522 19.1.199 19-3886

19.3597 19.3332

19. 3087 19.2856

19. 261.1 19. 21.91* 19. 2268 19.2060 19.1873

19.1700

19.1537

20.1.227

20. 381.3 20.31*75 20.3117

20.2783

20. 21.79 20. 2200

20. 191.7 20. 1721 20.1517

20. 1333

20.1161. 20.1010

20. 0865 20.0731 21.3695 21.3276

21.2853

21.21.1.1* 21. 2079

21.17I.5

21. 11.^7 21.1181.

21. 0951

21. 071.5 21.0557

21. 0388

21. 0232

22. 1221. 22. 0762

22. 0290

21. 981.9

O.PCT -0.09

-0.10

-0.11 -0.12 -0.12

-0.13

0.10

.12 .13

,15

.15 .13 12

.11 0.10 0.09

0.07 0.05

0.01. 0.03

0.02

0.01

.02

.05

.06

.07 0.06

0.05

0.06 0.03

0.02

0.00

-0.01

-0.01* 0.01 0.02

0.01* 0.06

0.07

0.07

0.06

0.05

0.01* 0.03

0.02

0.01 -0.01

0.01 0.02

0.05

0.07

P.BAR

231. 002 253. 237

275. 393 297. 1*79 319. 1*88

31.1 . 1.02 26. 367

I. 7 . 71.3 69. 007

90. 117 111. 128 132. 061 152. 913 173. 668

191*. 31*9 209. 838 235. 576 261. 206 286. 762

312. 211. 337.51*2

20. 288

1*1*. 689

68. 823

92. 700 116. 390 139. 966

163. 1*18 186.776

210 .081* 233. 321 256. 1.91. 279. 599

302. 629

325. 569

31*8. 1*31* 19. 836

1*7.537

71*. 71*7 101. 595 126. 287

151*. 807 181.216

207. 556

233. 818

260. 026 286. 118 312. 11*0 338. 01*3

II. . 593

1*5. 088

71*. 923

101*. 1*03

CALCD 230.253

252.31*6

27i*.3i*C 296.292

318.215

31*0.001 26.885

1*8.1*1*5 69.888

91. 156

112.21*3 133. 11*8 153.959

171*. 688 195.300 210.703 236.307

261.792

287.237

312.537

337.768 20.376

1*1*. 879

69. 21*2 93.275 117.075

11*0.603

161*. 029

187.1*1.1 210.1* 1*5 233.532

256.51.1. 279.1.98 302. 31.0 325.079

31*7.801

19.911* 1*7.776

75.21*7 102.1*15 129.250 155.773

182.11*1* 208.326

231*. 1,19 260.1*58 286.391

312.21.1

337.91*2

11*. 753

1*5.31*0 75.683 105.569

P.PCT

0.32

0.35

0.38

0.1.0 0.1.0

0.1.1 -1.96

-1.1*7 -1.28 -1.15

-1.00 -0.82

-0.68 -0.59

-0.1*9 -0.1.1 -0.31

-0.22 -0.17

-0.10 -0.07

-0.1.3 -0.1.3 -0.61 -0.62

-0.59

-0.1.5 -0.37

-0.36 -0.17

-0.09

-0.02

0.01. 0.10

0.15

0.18 -0.39 -0.50

-0.67

.81 .75

.62

.51

.37

.26 -0.17

.10 -0.03

0.03 -1.10

-0.56

-1.01 -1.12

-0.

-0.

-0.

-0.

-0.

56

F-59
METHANE EQUHTION OF STATE

ID 2205

2206

2207

2206 2209

2210 2211 2212

2101

2001 2102

2103

210'f 2105

2106

2107

2108 2109

2110

2111 2002

2003

200<« 2005

2006

2007

2008

2009

2010 1901

1902 1903

190'» 1905 1906

1801

1802 1803

180<< 1805

1806 1807

1808 1809

1810 1811 1812

1813

1811. 1815

1816 1817 1818

T,K 168. 000 172. 000 176. 000

18 0. 000

iei«. 000 188. 000 192. 000 196. 000

l'<6. 000

IttO. 0 00 150. 000

151.. 000 158. 000 162. 000 166.000

170. 000

17i«. 000 178. 000 182. 000 186. 000

l<4i«. 000

1<<8. 000 152. 000 156. 000 leo. 000

161.. 000 168. 000 172. 000 176.000

13i«. 000

138. 000

11.2. 000

11*6. 000 150. 000

15>«. 000

13't. 000 136.000 138.000

litO. 000

11.2. 000

l<«i«. 000

11.6. 000

11.8. 000 150. 000 152. 000

15i<. 000 156. 000 158. 000 160. 000 162. 000

16(*. 000 166. 000 168. 000

MOL/L

21.9620

21.9290

21. 8920

21. 8620

21. 8360

21. 8120

21. 7910 21.7720

22. 8730 23.5700

22.821.0

22. 7820

22. 7390

22. 6980 22.6600

22. 6260

22. 5960

22. 5700

22.5<»6 0 22. 5250

23. 5180

23. 1.720 23.1.260 23.3630

23. 31.30 23. 3080

23. 2780

23. 2520 23.2280

2<.. 1830

21.. 1250

21.. 0760

21.. 0270

23. 9810

2 3. 91.0 0

21.. 171.0

21.. 11.10

2it. 1150

21.. 0900

21.. 0660

2k. 01.20

21.. 0170

23.991.0

23. 9710

23. 950 0 23.9310 23.9120

23. 8930

23. 8770

23. 6620

23. 81.90 23. 8360

23. 821.0

CALCD

21.91.53 21.9092

21. 8775

21.81.95 21.8255

21.801.3 21.7855

21.7682

22.8725

23.5719

22.821.2

22.771.7 22.7276

22.6855

22.61.79 22.6153

22.5870

22.5631

22.51.18 22.5226 23.5218

23.1.691.

23.1.191. 23. 371.7 23.3356

23. 3019 23.2731

23. 21.82 23.2266

21.. 1827

21.. 1303

21.. 0750

21.. 0222 23.9752

23. 931. 1. 2i». 1730

21.. 11.71. 21.. 1199

21*. 0926

21..0675

21.. 0361

21.. 0109 23.9871

23.961.3

23. 91.32 23.9237

23.9056

23. 8872

23. 8723 23.6581

23. 61. 1.8 23.8332

23.8221.

D.PCT

0.08 0.09

0.07

0.06

0.05

0.01. 0.03 0.02

0.00 -0.01 -0.00

0.03

0.05

0.06

0.05

0.05

0.01. 0.03

0.02

0.01 -0.02

0.01

0.03

0.01. 0.03

0.03

0.02

0.02

0.01

0.00 -0.02

0.00 0.02

0.02

0.02

0.00 -0.03 -0.02

-0.01

0.01 0.02

0.03

0.03 0.03

0.03 0.03

0.03

0.02

0.02

0.02 0.02

0.01 0.01

P, BAR 133.692

162.772

191. 756

220.61.8

21.9. 520 278. 308 307. 015 335.575

13. 127

12. 262

1.6. 703

79.1.62 111.736

11.3. 810 175. 712 207. 555 239. 330 271. 112 302. 767

331.. 282

1.8.910

81*. 500

119. 526

151.. 350 189. 067 223.762

258.1.1.0 293. 01.0 327.578

6. 861

1.6. 383

81.. 630

122.21.0 159. 656

197. 01.0 5. 81.1 25. 770

1.5. 258

61.. 512

83. 31.8 102. 131. 120. 91.1. 139.702

158. 371. 177. 053 195. 71.7 211.. 1.17 232. 888 251.636

270.317

288. 962

307. 691. 326. 391

CALCO

131*. 953

161.. 327

192.91.2 221.712

250.1.1.9 279.017

307.539

335.951

13.168 12.085

1.6.686 80.066 112.717

11.1.. 927 176.833

208.580

21.0.225 271.821. 303.217

331.. 51.5 1.8.51.8

81.. 751. 120.193

155.212

189.868

221.. 1.39 258.996

293.1.93

327.71.6 6.897

1.5.805

81.. 737 122.787

160.31.6 197.719

5.951

25. 091

1.1.. 721.

61.. 231 83.623 102.796

121.61.0

11.0.501. 159.167

177.870

196.628 215.209

233.616

252.230 270.816

289.510 308.062

326.609

P.PCT

-0.91. -0.96

-0.62

-0.1.8 -0.37 -0.25

-0.17

-0.11

-0.31

1.1.5

0.01. -0.76

-0.88 -0.78

-0.61.

-0.1.9 -0.37 -0.26

-0.15

-0.08

0.71. -0.30 -0.56

-0.56

-0.1.2 -0.30 -0.22

-0.15

-0. 05 -0.52

1.25 -0.13

-0.1.5

-0.1.3

-0.31. -1.88 2.63

1.18

0.1.1. -0.33

-0.65

-0.58

-0.57

-0.50

-0.1.6

-0.1.5 -0.37

-0.31

-0. 21. -0.18 -0.19

-0.12

-0.07

57

F-60
METHftNE EQUATION OF STATE

ID T,K 1819 170. 000 1701 130. 300 1702 132. 000 1703 13<«. 000

170<» 136. 000 1705 138. 000 1706 11(0. 000 1707 ii<2.oao 1708 litit. 000 1709 l'<6. 000 1710 liiS. 000 1711 150. 000 1712 152.000

1713 154. 000

171if 156. 000 1715 158. 000 1716 160. 000 1717 162. 000 1718

1601 126. 000 1602 128. 000 1603 130. 000

160't 132.000

1605 13i«. 000 1606 136. 000 1607 138. 000 1608 litO. 000 1609 li«2. 000 1610 li4i«. 000 1611 1<»6. 000 1612 11(8. 000 1613 1<«8. 000

161<» 150. 000 1615 152. 000 1616 ISU. 000 1617 156. 000 1618 158. 000 1501 122. 000 1502 12't. 000 1503 126. 000

150'. 128. 000 1505 130. 000 1506 132. 000 1507 isit. aoQ 1508 13<<. 000 1509 136. 000 1510 138. 000 1511 litO. 000 1512 l<i2.000 1513 mif. ooo

151<« 1<*6. 000 1515 1<<8. 000 1516 150. 000

HOL/L CALCD

23.8120 23.8117

2(1. 6050 2it.6100

2'». 5720 2'».583'»

2<».5<»60 2'».5556 2<..5190 2<».526i»

2'«.'»9'»0 2i». 1*963

2'<.if690 2i*.i*&85

2i«.i«i«30 2i<.i<i«2'< 2i». 1.190 2".. 1.175

21.. 3960 21.. 391.3

21.. 371.0 21.. 3730

21.. 351.0 21.. 3533

2i.o 3350 21.. 3351

21.. 3170 21.. 3165

21.. 3010 21.. 3015

21.. 2860 21.. 2876

21.. 2730 21». 271.9

21.. 2600 21..2627

21.. 21.80 21.. 2520

21.. 9960 21.. 9982

21.. 9600 21.. 9709

21.. 9330 2i». 91.25

21.. 9050 21.. 9135

21.. 8790 21.. 8835

24. 8520 21.. 8550

21.. 8260 21.. 6276 24.8010 24.8018 24.7770 24.7779

24.7540 24.7558

24.7340 24.7355 24.7150 24.7174 24.7140 24.7172

24.6970 24.7004

24.6810 24.6849 24.6660 24.6702

24.6520 24.6566

24.6390 24.6443

25. 3860 25.3844 25.3480 25.3543

25.3200 25.3262 25.2930 25.2924 25.2660 25.2628 25.2390 25.2349

25.2120 25.2084

25.2110 25.2086

25. 1840 25.1813

25.1600 25.1575

25.1370 25.1354

25.1160 25.1154

25.0970 25.0968

25.0800 25.0800 25.0640 25.0648 25.0490 25.0508

O.PCT P,BAR

0.00 344.966

-0.02 7.286

-0.05 28.230 -0.04 48.781 -0.03 68.894

-0.01 88.639

0.00 108. 425 0.00 128.176

0.01 147.856

0.01 167.516

0.00 187.222

0.00 206.921

-0.00 226.644

0.00 246.119

-0.00 265.906

-0.01 285.671

-0.01 305.459

-0.01 325.155 -0.02 344.921

-0.01 4.795

-0.04 26.740 -0.04 48.275

-0.03 69.442

-0.02 90.206

-0.01 110.901 -0.01 131.487

-0.00 152.046

-0.00 172.619

-0.01 193.223

-0.01 213.859

-0.01 234.593 -0.01 234.564

-0.01 255.294

-0.02 276.024

-0.02 296.684

-0.02 317.346

-0.02 338.030

0.01 3.482

-0.03 26.168

-0.02 48.814

0.00 70.363

0.01 92.218

0.02 114.039

0.01 135.786

0.01 135.614

0.01 157.173

0.01 178.801

0.01 200.430

0.00 222.144

0.00 243.865

-0.00 265.643

-0-00 287.462

-0.01 309.282

CALCD P.PCT 345.023 -0.01 6.700 8.04 26.888 4.75 47.630 2.36 67.999 1.30 88.363 0.31 108.488 -0.06 126.253 -0. 06 148. 041 -0.12 167.736 -0. 13 187.349 -0.07 207.019 -0.05 226.628 0.01 246.184 -0.03 265.833 0.03 285.451 0.06 305.185 0.09 324.765 0.12 344.339 0.17 4.517 5.81 25.346 5.21 47.038 2.56 66.327 1.61 89.612 0.66 110.504 0.36 131.276 0.16 151.937 0.07 172.497 0.07 192.966 0.13 213.636 0.10 234.244 0.15 234.099 0.20

254. 792 0. 20 275.441 0.21 296.054 0.21 316.641 0.22 337.218 0.24 3.707 -6.46 25.282 3. 39 47.943 1.79 70.455 -0.13 92.684 -0.51

114. 635 -0.52 136.313 -0.39 136.165 -0.26 157.574 -0.25

179.171 -0.21 200.672 -0.12

222.241 -0.04 243.891 -0.01 265.638 0.00 287.337 0.04 306.996 0.09

58

F-61
METHANE EQUATION OF STATE

ID 1517 1518

ll«01 11*02

li»03 IttOU

li»05

1<<06

1<»07 luoa

Ht09

1<.10 liill

litlZ

l'»13

1<»1I4 li«15 luie

11.17 1301

1302

1303

130'* 1305 1306

1307

1308 1309

1310 1311 1312

1313

131'* 1315

1316

1201

1202 1203

120<« 1205

1206

1207 1208

1209

1210

1211 1212

1213

IZlit 1215 1101

1102 1103

T,K

152. 000

151t.000 113. 000 120. 000 122. 000

12<4. 000 126. 000 128. 000

1 30. 000 132. 000

13'*. 000 136. 000 138. 000 138. 000

litO. 000

l't2. 000

l'<'<. 000

l'i6. 000

litS. 000

11'4. 000 116. 000 118. 000 120. 000 122. 000

12'«. 000 126. 000 128. 000 130. 000 132. 000 132. 000

13i<. 000 136. 000 138. 000

l<t0. 000

l'<2. 000 110-000

112. 000

lilt. 000 116. 000

118. 0 00 120. 000 122. 000

12't. OOP 126. 000 128. 000 130. 000 132.000

13<«. 000

13<<. 000

136. 000 106. 000 103. 000 110. OOO

MOL/L

25. 0350

25. 0220

25. 7770 25.7390 25.7100

25. 6820

25. 65i»0 25. 6250

25. 5960

25.571.0

25. 550 0 25. 521.0 25. 5030

25. 5030

25. 1.8I.0 25. 1.660 25. 1.50 0 25. 1.350 25. ^220

26. 11.20 26. 1030

26. 0720

26. OI.I4O 26. 011.0 25.9850

25.9560

25. 9290

25. 901.0 25. 8310

25. 880 0 25. 859C

25. 81.00 25. 8220

25. 8070

25. 7920

26. 5190

26. 1.800 26. 1.1.90 26. 1.190 26. 3880

26. 3570

26. 3270

26. 2990

26. 271.0 26. 2510

26. 230 0 26. 2110

26. 1930

26. 1920

26. 1760 26.9010

26. 861.0 26.8330

CALCD

25. 0372

25.021.9 25.7768

25. 71.63 25.7151 25.6806

25.6507

25.6222

25.5957 25.5701

25.51.66

25. 521.6 25. 501.1. 25.5019

25. 1.837 25.1.676

25. 1.520 25.1.38*.

25.1.251. 26. 11.55 26. 111.1. 26. 0810

26. 01.55 26.011.6 25.9853

25.9575 25.9313

25. 9071. 25.8853 25.8829

25. 8628

25. 81.1.6 25.8279

25.8130

25. 7987

26. 5191

26.1.876 26.1.509

26.1.161

26. 331.5 26. 351.5 26. 3261

26. 2995

26. 271.9 26. 2521. 26. 2319

26.2131.

26. 1966

26. 1953

26. 1300

26. 9051 26.8726

26.8351

O.PCT -0.01

-0.03

-0.02

0.01

0.01

0.01 0.01

0.02

0.01 -0.00

-0.01

0.00

0.00 -0.01 -0.01

-0.01

-0.01

-0.01

-0.01. -0.03

-Q.Ol

-0.00 -0.00

-0.01

-0.01 -0.01

-0.02

-0.01 -0.01

-0.02

-0.02

-0.02

-0.03

-0.00 -0.03

-0.01

0.01

-0.00

-0.00

-0.01 -0.01

-0.01 -0.01 -0.01

-0.02

P, BAR 330. 987

352. 726

1.. 71.0 28. 1.87 51. 811.

71.. 303

97 . 196 120. 010

11.2. 81.6 165.551. 188. 320 211. 062 233. 855 233. 1.1.5 256. 331 279. 330 302.209

325 . 227

31.8 . 11.8

1.. 106 28.896

52. 968

76. 358 100. 162 123. 929

11.7. 655

171 . 338 195. 123 218. 955

218 . 531. 21.2.1.1.1 266. 1.1.0 290. 1.71. 311.. 577

338. 590

5. 935 31.839

56. 1.1.1. 81 . 051. 105. 870

130 . 659

155 . 1.00 180 . 151. 201.. 975

229. 892

251.. 906

280 . 025 305. 211. 301.. 967

330. 185

12. 022

38. 986

61.. 591

CALCD 330.629

352.21.0

1..761. 27. 371. 51.026

71.. 523 97.717

120.1.55

11.3. 217 166.179

188.870 210.965 233.626

233.626

256. 378 279. 065 301.869

321.. 632

31.7.539 3.536

27. 022

51.1.75 76. 099

100. 066

123.881.

11.7. 389

170.931.

191.. 532 218.197

218.020

21.1.767 265.612

289. 389

313.1.75 337. 33*. 5.920

30.1.83 56. 110 81.572

106.512

131.111 155.561 180.056

201.. 799 229.620

251.. 531. 279. 556

301.. 505

301.. 308

329. 391

11.21.5 37.320

61.. 131.

P.PCT

0.11

0.11. -0.51

-0.30

-0.51. -0.37 -0.26

-0. 33 -0.29

0.05

0.10 -0.08 -0.02

0.10

0.11

0.18 0.17

13.87

6.1.9 2.82

0.28 0.31

0.37

0. 35 0.37

0.25

1..26 0.59

-0.61. -0.61 -0.35 -0.10

05

0912

15

1723

22

21.

1.6 2763

59

F-62
METHftNE EQUATION OF STATE

ID

110'» 1105

1106

1107 1106

1109

1110

1111 1112

1113

111<» 1115

1001 1002

1003

loot* 1005

1006

1007

1008 1009

1010 1011

1012 1013

lOlit 901 902

903

90i» 905 906

907 908

9 09 910

911

912 913

801 802

803

80<» 805 806

807 808 809

810

811

812

601 602

T,K

112. 000 n't. 000 116. 000 118. 000 120. 000 122. 000

12'«. 000

i2<».aoo 126. 000 128. 000 130. 000 132. 000 102. 000

1D<«. 000 106. 000 108. 000 110. 000 112. 000

11<«. 000 116. 000 116. 000 118.000

120. 000 122. 0 00

12<<. 000 126. 000

98. 000 100. 000 102. 000

lOi). 000 106. 000

10 8. 0 00 110. 000 112. 000

11<«. 000 116. 000 116. 000 118. 000 120. 000

gi*. 000

96. 000

98. 900 100. 000 102. 000

IQit. 000

106. 000 108. 000 110. 000 112. 000 n't. 000

116. 000

92. 000

91*. 000

MOL/L

26. 8010

26. 7680

26. 7360

26. 7060

26. 6790

26. 6530

26. 6300 26.6310

26. 610 0 26.5920

26. 571.0 26. 5590

27. 2320

27. 1920

27. 1600

27. 1270

27. 0930 27.0600

27. 0290 27.0010

27. 0010

26. 9760

26. 9520 26.9310

26. 9120

26. 8950 27.5880

27. 5I»80 27.5160

27.i.810

27.1»<*70 27. 4130

27. 3820

27. 353 0 27. 328C

27. 3050

27. 3050

27. 2850

27. 2660

27. 900 0 27. 8580

27. 8250

27. 7890

27. 7530

27. 7190

27. 6860

27. 6570

27. 6300

27. 6070

27. 5860

27. 5670

28. 2090

28. 1750

CflLCD 26. eooo

26.7671.

26. 7362 26.7070

26. 6799

26. 6551

26. 6332 26.6325 26.6125

26. 59'.«t 26. 5778 26.5620

27. 2321. 27. 1991. 27.1610

27. 121.2 27. 0903

27. 0583

27. 0278 26.9999

26. 9999

26.971.7

26. 9519 26.9312

26.9129

26.8951. 27.5905

27.5559 27.5155

27.1.782

27. i.i.3'i 27.1.101. 27. 3798

27. 3519 27.3265

27. 3037

27. 301.3 27. 2835

27.261.6 27.9029

27.8675

27. 8252

27. 7869 27.7510

27. 7166

27. 6846

27. 6558

27.6291. 27.6057

27. 581.3 27.5652

28. 2200

28. 1755

O.PCT

0.00

-0.00

-0.00 -0.01 -0.01

-0.01

-0.01

-0.01 -0.00 -0.03

-0.00

0.01 0.01

0.01

0.00

0.00

0.00

0.00

0.00 -0.00

-0.00

-0.00

-0.01

-0.03

0.00 0.01

0.01

0.01

0.01

0.00

0.01 0.00

-0.03

-0.00

0.00

0.01

0.01

-0.01. -0.00

P,B«R

90 . 300 116. 122

11.1. 871 167.653

193.539

219. 51.2 21.5. 820

21.5.678 272. 01.9 296. 510 325. 020 351. 1.23 8.1.71. 36. 1.89 63. 031. 89. 515 116. 218

11.2.937 169.612

196.1.80 196. 1.71 223.568

250. 862

278. 276 305. 896 333. 1.21. 12. 1.37

1.1. 1.07 68. 696

96. 270 124. 002

151. 755

179. 649

207. 794

236. 148 264. 752

264. 894

293. 612

322. 446 7.513

37. 517

65. 517

94. 061 122. 725

151 . 383 180. 222 209. 351 238.728

268. 394 296. 261

326. 347

44. 123

72. 852

CeLCO 90.492

116.241 141-627

167.458

193. 346 219.109

245. 161 245. 367

271 .526

296. 015 324.218 350.765

8.385 34.977 62.829

90.100

116.784

143.301 169.868

196.714 196.714

223.856 250.677

278.227

305.704

333. 326 11.900

39.667 66.807

96.896

124.816

152. 342

180. 156 206.050

236.495

265. 049

265. 049 293.964

322.763

6.854

35.315 65.476 94.545

123.211

151.946 180.514

209.648

238.660

268.716 298.685

328.601 41.421 72.722

P.PCT

-0 .21

0.27

0.13

0.19 0.17

0.25

-0.65 -0.49

-0.25 -0.15

-0.12

-0.12 -0.13

-0.01

0.02

0. 06 0.03 4.32

4.20 -0.16 -0.65

-0.66

-0.39

-0.28

-0.12

-0.15 -0.11

-0.06

-0.12 -0.10

8.77

5.87

0. 06 -0.51

-0.40 -0.37

-0.16

-0.14

-0. 06 -0.12

-0.14

-0.14

6.12

0.16

60

F-63
METHANE EQUATION OF STATE

ID 603

&0i« 605

606

607

608 609

610 611

612

701 702

703

lai* 705

706

707

708

Sli. 515

516

517 518

519

520

NP

T,K

96. QOO

98. OQQ

10 0. 0 00 100. 000 102. 000

10(t. 000 106. 000 108. 000 110. 000 112. 000

9<«. 000

96. 000

98. 000 100. 000 102. 000

IQit. 000 106. 000 108. 000 96.500

97. 000

98. 000 100. 000 100. 000 102. 0 00 lOU. 000

MOL/L

28. 1370

28. 1010

28. 0660

28. 0660

28. 03<»0 28. 00<>0 27.9780

27.9550 27.9350

27.9160

28. 3910

28. 35itO 28.3210

28. 290 0 28. 26<»0 28. 2<i0 0 28.2190

28. 2000

28- 5520

28. 5<«50 28. 5310 28.5070

28.5070

28. l»860 28. 4.660

CALCD

28.1366 28.0999

28. 06<>8 28.06<>9

28. 032<» 28.0030

27. 9768

27.9530 27.9317

27.912i»

28. 3909

28. 351.5 28. 3205 28.2896

28. 2623 28.2375

28.2156

28.191.8

28. 5578

28.550'.

28.536'. 28.5100 28.5103

28. '.86'. 28. <.61.6

D.PCT

0.00 0.00

0.00

0.00

0.01

0.00

0.00 0.01

0.01 0.01

0.00 -0.00

0.00

0.00

0.01

0.01

0.01 0.02 -0.02

-0.02

-0.02

-0.01 -0.01

-0.00

0.01

P.BAR

102. 51.3 132. 353 162. 180 162. 190

192. 21.3 222.687

253. 551

28'.. 6'.! 316. 018

3'.7.527 128. 133

158. 893

189. 886 221. 338 253.222

285. '.'.0 318. eg

350.566

22'.. 938 233. 128

21.9. 6'.3 282. 8'.3 282. 935

316. '.33 350.093

CALCD

102. 63<. 132.637

162.1.75 162. '.75 192.660

222.91.5 253.861 285.169

316. 890

31.8.500 128.159

158.770

190 . 020 221.382 253.683

286.121. 318.996

352.038 223.293

231.593

2'.8.11i. 281.983

281.983

316.306

350.517

P.PCT -0.09

-0.21 -Q.ie

-0.18

-0.22 -0.12

-0.12

-0.19

-0.28

-0.07

-0.02

-0.18

-0.21. -0.30

-0.1.2 0.73

0.66

0.61

0.30

0.31.

0.01. -0.12

= 551., DNRMSPCT = 0.182, PMEANPCT = 0.'.'.3

61

F-64
HETHANE EQU4 TION OF STATE

ID

6

66

6

6

66

6

6

6

6

6

66

6

6

6

6

6

6

6

6

66

6

66

6

6

6

66

66

6

66

6

6

6

6

6

66

6

66

6

6

6

6

6

T,K

273. 150 298. 1<.2 303.1<t3 323. li»0 31(8. 1«t3 373.150

398. 160 273. 150 298. 1<*2 30 3. 11.3 323. 11.0 31.8. 11.3 373.150

398. 160 273. 150 298. 11.2 303. 11.3 323. 11.0 31.8. 11.3 373. 150 398. 160 273. 150 298. 11.2 303. 11.3 323. 11.0 31.8. 11.3 373. 150 398. 160 273. 150 298.11.2

30 3. 11.3 323. 11.0 3i<8. 11.3 373. 150 398. 160 273. 150 298. 11.2 303. 11.3 323. 11.0 3'*8. 11.3 373. 150 398. 160 273. 150 298. 11.2 303. 11.3 323. mo

31.8. 11.3 373. 150 398.160

273. ISO 298. 11.2 303.11.3

MOL/L

0. 7500

0.75 0 0 0. 750 0 D.7500 0.7500

0.7500

0. 750 0 1. 000 0 1. 000 0 000 0 000 0

. 0000

, 0000

. 000 0

. 5000

1. 500 0 1. 500 0 1. 500 0 1. 5000 1.5000

1. 500 0 2. 000 0 2. 000 0 2. 000 0 2. 000 0 2. 0000

2. 000 0 2. 0000

2. 500 0 2. 5000

2. 5000

2. 5000 2.5000

2. 500 0 2.5000

3. 0000

3. 000 0 3. 000 0 3. 000 0 3. 000 0 3. 000 0 3. 000 0 3. 500 0 3. 500 0 3. 5000

3. 5000 3.5000

3. 5000

3. 5000

1.. 00 0 0

1.. 000 0

1.. 0000

CALCD

0.7500

0.7500

0.75B0

0. 71.99 0.7500

0.7500

0.7501

1.0000

1.0000 1.0001

1.0000

1.0000 1.0001

1.0001

1.5001

1.5000

1.5001

1.1.999 1.5000 1.5001

1.5003

2.0002

1.9999

2.0000

1.9999 1.9996 2.0002

2.0002

2. 1.996

2. 1.995 2.1.995

2.1.992 2.1.992

2. 1.998 2.1.998 2.9991 2.9989

2.9997

2.9987

2.9986

2.9991. 2.9996

3.1.995

3.1.986 3.50B0

3.1.981. 3.1.983

3.1.992 3.5000

1.. 0003 3.9993

I.. 00S3

D.PCT

-0.00 -0.01

-0.00

0.01

0.00 -0.00

-0.01 -0.00

0.00 -0.01

0.00 -0.00 -0.01

-0.01

-0.00

-0.00 -0.02

-0.01

0.00 coo

0.00 0.02 -0.01

-0.01

0.01 0.02

0.02

0.03

0.03

0.01

0.01 0.03

0.01. 0.01

0.01. 0.05

0.02

0.01

0.01

0.01. -0.00

,05

.05

,02 0.00 -0.01

0.02 -0.01

P, 8AR

16. 376

18. 020 18. 31.7 19.656

21. 292 22.925

21.. 557 21.558 23.786

21.. 232

26. 006

28 . 221

30 . 1.31 32. 637

31. 539

31.. 993

35. 685

38. 1.27

1.1 . 652

1.5. 267

1.8 • 676

1.1. 053

1.5. 801. 1.6.753

50. 530

55. 222

59. 920

61.. 582

50. 139

56. 263

57. 1.85 62. 31.3 68. 390

71.. 1.21. 80 . 1.11 56. 81.2 66.1.15 67. gi.0 73.926

81. 391

88. 835

96. 229

67. 222

76. 307 78. 11.6 85. 321.

91.. 279

103. 203 112. 073

75. 307

85. 992

68. 11.2

CALCD

16.375

18.019

18.31.7 19.657

21.293

22.925

21.. 551. 21.558

23.786

21.. 231

26. 007 28.221

30.1.30 32.633

31.537

31.. 992 35.681

38.1.30

1.1.651. 1.5.265 1.8.665

1.1. 050

1.5.806

1.6.751. 50.532

55.231.

59.911.

61.. 575

50.11.3 56.271.

57.1.95 62.361

68.1.11

71.. 1.28 80.1.17 58.657

66.1.37 67.91.6 73.957

81.1.26

88. 851

96.231. 67.230

76.331.

78.11.6 85.360

91.. 322 103.225

112.073 75.303

86.006

68. 135

P.PCT

0.00

0.01

0.00 -0.01

-0.00

0.00

0.01 0.00 -0.00

0.01 -0.00

0.00

-0.00

0.00 0.02

0.01 -0.00

-0.00 -0.00 -0.02

-0.01

-0.02

-0.02 -0.03 -0.03

-0.01

-0.01 -0.03

-0.03

-0.01

-0.01.

-0.01. -0.02

-0.00 -0.01 -0.03

0.00

-0.01. -0.05 -0.02

-0.00

0.01 -0.02

0.01

62

F-65
METHANE EQUATION OF STATE

ID

6

66

66

6

66

6

66

6

6

6

66

66

6

6

6

6

6

66

66

66

6

6

66

6

6

666

6

66

6

6

66

6

6

66

6

6

66

T,K

323. 1<»0 3i»8. litZ 373. 150 398. 160 273. 150 298. 1W2

30 3. 1<.3 323. li.0 31(8. 11.3 373. 150 398.160

273. 150 298. 14.2 303. 1<»3 323. 11.0 31)8. ll«3 373. 150 398. 160 273. 150 298. ll»2 303. 1i»3 323. li«0 31(8. li«3 373. 150 398.160

273. 150 298. 11.2 303. 11.3 323. 11.0 31.8. 143 373. 150 398. 160 273.150

298. 11.2 303. 11.3 323. 11.0 31.8. 11.3 373. 150 398. 160 273. 150

298.11.2 303. 11.3 323. 11.0 31.8. 11.3 373. 150 398. 160 273. 150 298. 11.2 303. 11.3 323. 11.0 31.8. 11.3 373. 150 398. 160

MOL/L

1.. 0000

1.. 000 0

1.. 000 0

1.. 000 0

1.. 5OO0

'.. 5000

1..500 0 1..5000

1.. 5000

1.. 5000

1.. 500 0 5. 0000

5. 0000

5. 0000

5. 0000

5. 0000

5. 0000

5. 000 0 5. 5000

5. 500 0 5.5000

5. 500 0 5. 5000

5. 5000 5.5000

6. 0000

6. 0000

6. 0000

6. 0000

6. 0000

6. 0000

6. 0000 6.5000

6.5000

6. 500 0 6. 500 0 6. 500 0 6.5000

6. 5000

7. 000 0 7. 0000

7. 0000

7. 000 0 7. 0000

7. 000 0 7. 0000 7.5000

7. 5000

7. 5000 7.5000

7. 5000 7.5000

7.5000

CALCO

3.9967

3. 9981 3.9992

<.. 0003

1..5022

1..5005

1..5020 1..5005

1.. 1.992

I.. 1.996 1..5018

5. 001.2 5.0021 5.0032

5.0011. 5.0OO2 5.0005

5.0027

5.5071.

5.501.7 5.5050 5.5011

5.5011. 5.5009 5.5039

6.0070 6.0063

6.0067

6.0023

6. 0032 6.0011 6.0031

6.5103

6.5071

6.5077

6.5061 6.5020

6.5001.

6. 501.9

7. 0169 7.0083

7. 0087

7.001.8

7. 0031. 7. 0025

7. 0031. 7.511.3

7. 5095 7.5050 7.5027

7.5016

7.5001.

7.501.5

O.PCT

0.03

0.05

0.02 -0.01

0.01

-0.01. -0.08

-0.01. -0.06 -0.03

-0.00

-0.01

-0.05 -0.13

-0.08

-0.09

-0.02

-0.03 -0.02

-0.07

-0.12

-0.10 -0.11

-0.01. -0.05 -0.02 -0.05

-0.16

-0.11 -0.12

-0.09 -0.03

-0.01 -0.08

-0.21. -0.12

-0.12

-0.07

-0.05

-0.01. -0.05 -0.19

-0.13

-0.07

-0.01. -0.02

-0.01

-0.06

P, BAR 96.585

107. 091. 117.577

127. 993

83. 156 95.511

98. 002

107. 779

119. 920

132. 013

11.1.. 083 90.802

101.. 911

107. 71.5 118.912

132. 781

II. 6. 583

160.31.6 98. 315

III. . 261

117.1.1.9 130. 030

11.5. 71.8 161. 321 176. 887 105.680

123. 585

127. 160

11.1. 261 158. 896 176. 308 193. 701 113. 057

132.91.1 136.921

152. 692

172. 195 191.585

211. 015

120. 1.91. 11.2.1.11

11.6. 809

161.. 208

185. 865 207. 31.7 228.706

127. 851. 152. 01.0 156.783

175. 966

199. 807

223.1.1.0

21.7. 053

CALCO 96.615

107. 11.3 117.598

127.981. 83.122

95.501

97.961. 107.769

119- 91.2 13 2. 0 26

11.1.. 021. 90.738

101.. 872

107.681. 118.880

132.777

II. 6.569 160.259 98.205

III. . 175 117.353 130.006

11.5. 711 161.295 176.758

105.577

123.1.68 127.029

11.1. 21C 158.811 176.273 193.595

112.907

132.809

136.771 152.553

172.11.2

191.571. 210. 81.5 120.21.5

11.2.253

11.6.636

161.. 096 185.770

207.266 228.582

127.61.2 151.856

156.681 175.901 199.762

223.1.27

21.6. 865

P.PCT

-0.03 -0.05

-0.02

0.01

0-01. 0.01

0.01. 0.01 -0.02

-0.01

0.01 0.05

0.11 0.08

0.06

0.02

0.09

0.10

0.01. 0.05

0.02

0.05

0.03

0.01 0.06

0.21

0.11 0.12

0.07 0.05

0.01. 0.05

0.17

0.12

,07

,01. .02

,01

,07

63

F-66
METHANE EQUATION OF STATE

10 T,K MOL/L CALCO

6 273. 150 8. 0000 8.0170

6 298. ihZ 8. 000 0 8.0097

6 303. litS 8. 0000 8.0080

6 323. ll»0 8. 000 0 8.0044

6 3<i8. ll>3 8. 0000 8. 0009

6 373. 150 8. 000 0 7. 9984

6 398. 160 8. 000 0 8. 0048

6 273. 150 8.5000 8. 5157

6 298. mz 8. 5000 8.5085

6 3 0 3. li«3 8. 5000 8.5074

6 323. ll»0 8. 500 0 8.5035

6 3ii8. 1W3 3.5000 8.5 014

6 373.150 8. 5000 e.49Be

6 398. 160 8.5000 8.5054

6 273. 150 9. 0000 9. 0173

6 2 9 8 . 1 '2 9. 000 0 9. 0068

6 303. 1<»3 9. 0000 9. 0056

6 323. 1<«0 9. 0000 9.0040

6 3>«8. 1<»3 9. 0000 9. 0004

6 373. 150 9. 000 0 8. 9960

6 398. 160 9. OQOO 9.0022

6 273.150 9.5000 9.5096

6 298. 11(2 9. 5000 9.5037

e 303. IW 9. 5000 9. 4981

6 323. ll>0 9. 5000 9.5006

6 3'»8.1<»3 9.5000 9.4975

6 373.150 9. 5000 9.4976

6 398. 160 9.5000 9.5037

6 273. 150 10. 0000 10. 0044

6 298. li»2 1 0. 000 0 9.9960

6 303. Iif3 1 0. 000 0 9.9916

6 323. li»0 1 0. 000 0 9.9927

6 3it8. Iii3 1 0. 000 0 9.9927

6 373.150 10. 0000 9.9932

6 398. 160 1 0. 000 0 10. 0024

6 273. 150 10. 500 0 10. 4933

6 298. litZ 10.5000 10.4924

6 303.11*3 10.5000 10.4884

6 323. li<0 10. 5000 10.4887

6 3i<8. 1V3 10.5000 10. 4891

6 373. 150 10.5000 10.4897

6 398. 160 10. 5000 10.5010

6 273.150 11. 000 0 10.9948

6 298. 142 11. 0000 10. 9874

6 303. 143 11. 000 0 10.9878

6 323. 140 11. 000 0 10.9878

6 348. 143 11.0000 10.9874

6 373. 150 11. 0000 10.9912

6 398.160 1 1. 0000 11. 0024

6 273.150 11.5000 11.4912

6 298. 142 11.5000 11.4917

6 303.143 11.5000 11.4848

6 323.140 11. 50 0 0 11.4900

D.PCT P.BAR

-0.21 135.410

-0.12 161.873

-0.10 167.135

-0.05 188.142

-0.01 214.218

0.02 240.078

-0.06 266.023

-0.18 143.090

-0.10 171.979

-0.09 177.736

-0.04 200.673

-0.02 229.193

0.02 257.427 -0.06 285.758

-0.19 151.095

-0.08 182.470

-0.06 188.733 -0.04 213.759

-0.00 244.766

0.04 275.434

-0.02 306.209

-0.10 159.307

-0.04 193.423

0.02 200.116

-0.01 227.366

0.03 261.024

0.03 294.478

-0.04 327.865 -0.04 167.979

0.04 204.825

0.08 212.100

0.07 241.534

0.07 278.048

0.07 314.250 -0.02 350.494

0.06 177.002

0.07 216.938

0.11 224.805

0.11 256.572

0.10 296.014

0 . 10 335 . 101 -0.01 374.301

0.05 186.780

0.11 229.688

0.11 238.292

0.11 272. 539 0.11 315.031

0.08 357.297

-0.02 399.523

0.08 197.051

0.07 243.451

0.13 252.507

0.09 289.542

CALCD P,PCT

135. 152 0.19 161-680 0. 12 166.966 0.10 188.0 35 0.06 214.192 0.01

240 . 1 31 -0. 02 265. 8 36 0.07 142.8 45 0.17 171.803 0.10 177.576 0.09 200.584 0.04 229.151 0.02 257.477 -0.02 285.539 0.08 150.812 0.19 182.323 0. 08 188.607 0.07 213.653 0.05 244.752 0.01 275.583 -0.05 306.118 0.03

159 . 144 0.10

193. 339 0.04 200.161 -0.02 227.350 0.01 261.109 -0.03 294.571 -0.03 327.700 0.05 167.899 0.05 204.922 -0. 05 212. 309 -0.10 241.751 -0.09 278.307 -0.09 314.530 -0.09 350.381 0.03 177.129 -0.07 217.128 -0.09 225.111 -0.14 256.925 -0.14

296.419 -0.14 335.544 -0.13

374.250 0.01 186.885 -0.06 230.023 -0.15 238.632 -0.14 272.942 -0.15 315.526 -0.16 357.696 -0.11 399.398 0.03 197.238 -0.10 243.685 -0.10 252.954 -0.18 289.892 -0.12

64

F-67
METH*Ne EQUATION OF STATE

10 T ,K M OL / L C AL CO 0 f PC T P f BAR C AL CO P f PC T D 3 6 • lh3 11. 50 0 0 11. U 8 5

0.13 3 35 . lOU 3 35 . 7 2U -0.18

6 373. 150 11. 5000 11. It953 0. Oi< 380- 866 381.092 -0.06

6 273.150 12. 0000 11.9963 0.03 208. 211 208.296 -O.C

6 296. li»2 12. 0000 11.9906 0.08 257. 950 258.23'. -0.11

6 303. IkZ 12. 0000 11.9900 0.08 267.883 268.199 -0.12

6 323. li«0 12. 0000 11.9907 0.08 307. 555 307.902 -0.11

6 3<48. 11*3 12.0000 11.9887 0.09 356. 651 357.1'»9 -0.1'. 6 373. 150 12. 0000 12. 0011 -0.01 i* 05. 932 '05.875 0.01

6 273.150 12.5000 12.5029 -0.02 220. 275 220. 203 0.03

6 298.1i»2 12.5000 12. '•989 0.01 273. 788 273.825 -0.01

6 303. 11*3 12. 50 0 0 12. '920 0.06 28<». 252 28'.. 523 -0.10

6 323. l'»0 12. 5000 12. <«959 0.03 326. 97<. 327.138 -0.05

6 3i«a. li«3 12. 50 0 0 12. 500<» -0.00 379. 993 379.975 0.00

171, ONRMSPCT = 0.068, PHEANPCT = 0.053

METHANE EQUATION OF STATE

ID

3

3

33

3

3

33

3

33

3

3

3

3

3

33

3

3

3

3

33

33

3

3

33

3

3

33

3

333

33

3

3

3

3

33

3

3

33

3

3

T,K 172.527

171.. 691 177.203

183. 176 190.532

191. 81.9 203. 08'» 213. 01.1 217. 86'. 223. 831

233.51.6 239.797

252.833

263.399

273.380

190. '.29 190. 532

208.57'. 223. 231* 23'.. i.'.O 21.3.733 21.3.773 251.376

262. 190 272.155

272. 185 190. 052 190.532

190.750

191. 032 193. 325 197.737

202. 753

208.22<» 212.165

217. 136 222.926

230. 050 237. 336

21.2.709

21)3. 1.1.4 250. 191. 253. '.1.5 258.51.2 263. 050 268. 301 273.171

190.532

191. 032 191. 551 192.938

195.21.3

MOL/L 2.5593

2.5593

2.5586

2. 5580

2. 5577

2. 5566

2. 5555

2. 551.3

2. 5537

2. 5530 2.5518

2. 5512

2. 51.99 2.51,87

2. 51.71. 6. 1.670

6. 1.686

6. 1.611. 6.1.571

6.1.53 9

6. 1.508 6.1.508

6.1.1.83

6.1.1.52 6. '.'.21 6. 1.1.21 7. 2329

7. 231.8

7. 2329

7. 231.1

7. 2316

7. 2301. 7. 2285 7.2266

7. 2251.

7. 2235

7. 2217

7. 2192

7. 2167

7. 211.8 7. 2129

7. 2123

7. 2111

7. 2092

7. 2079

7. 2061

7. 20'.2

9. 81.0'. 9. 61.01. 9. 8370

9. 836'.

9. 8351

CALCC 2.5632

2.5621

2.5605

2.5588 2.5563

2.5567

2.5551

2.551.1 2.5536

2.5532

2.5528 2.5522 2.5506

2.51.9'. 2.51.82 6.3319

6. 3365

6.1.659

6. 1.701. 6.1.682

6.1.665 6.1.659

6. 1.637 6.4593

6.1.563

6.1.558

6. 9789

7.0271.

7. 0320

7.0511. 7.1510 7.2128

7. 2357

7. 21.36 7.21.69

7.21.67

7.21.65

7. 21.39 7.21.03 7.2372

7.231.0

7. 2329 7.2307

7.2277

7.2251.

7. 2226

7.2197

9.81.01. 8.5313

9. 1955 9.5720 9.7117

D.PCT -0.15

-0.11

-0.07 -0.03

0.05

0.01 0.02

0.01

0.01 -0.01

-0.01. -0.01. -0.03 -0.03

-0.03

2.09

2.01. -0.07

-0.21 -0.22

-0.21. -0.23

-0.21. -0.22 -0.22

-0.21

3.51

2.87

2.78 2.53

-0.10

-0.21. -0.30

-0.32

-0.31.

-0.3'. -0.33

-0.31 -0.29

-0.28

-0.27

-0.26

-0.21. -0.23

-0.22

0.00 13.30 6.52

2.69

1.25

P, BAR

21.. 660

25. 283

25.99'. 27. 666 29.676

30. 038

33. O'.O 35. 672 36.931

38.1.81 'O. 990

1.2.590

1.5. 697

1.8. 559

51. 058

1.1.. 720

kt*. 811. 60. 270

72. 31.6 81. 1.33 88. 913

88. 939

95. 018 103.601

111.1.78 111. 1.91.

1.1.. 989

1.5.1.93

1.5. 710

1.6. 001

1.8. 336 52.722

57.627

62. 909

66. 689

71.1.21 76. 909

83. 611. 90.1.32

95.1.31. 100. 757

102. 376 105. 378

110. 172 114.229

119. 049 123.504

45. 870 46.579

47. 318

49. 282 52.563

CALCO 24.639

25.267

25.983

27.661 29.687 30.039

33.052 35.675

36.932 38.479

40.977

42.576

45. 886 48.547

51.043

44.861 44.974

60.252

72.260

81. 314 88.759

88.791 94.847

103.419

111.272 111.296

45.137

45.626

45.848 46.134

48.423

52.754 57.608 62.849

66.599

71.305

76.759 83.435

90.231

95.223

10 0.537 102.155

105.156

109.945

114.001

118.820 123.275 45.959

46.671 47.409

49.381

52.660

P,PCT

0.09

0.06

0.04

0.02 -0.04

-0.00

-0.01 -0.01

-0.00

0.01

0.03 0.03

0.02

0.03 0.03

-0.36

-0.36

0.03

0.18 -0.33

-0.30

-0.30 -0.29

-0.18 -0.06

0.03

0.10

0.13 0.16

0.19 0.21

0.22 0.22

0.22

0.22

0.21 0.21

0.20

.19

, 19

,19 -0.20

-0.19

-0.20

-0.16

65

F-68
METHANE EQUATION OF STATE

ID

3

3

33

3

333

3

33

3

3

3

3

3

33

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

33

3

3

33

3

33

3

3

3

33

3

3

3

33

3

T,K 197.562

200. <*11 202. 329

206. 370 213.503

223. 6'»7 236. 398

2i«8. li»7 255. 163 273.167 190.532

191. 032 190. 839

191. 0<t0 191. 229

191. '*28 191. 820 192. 075 193.522

195. 158 197.926

200. 575

20<.. 037 207.855

207.855

213. 0<»<« 233. 386

252. 887 273. 016 273. 058

19 0.5 32 191. 032 191. 8<»8 191.873

ig3.2<»e 195.110

197.300

199. 216 200.901

203. 06<» 207.S6'» 213. 197

213.20<« 213.212

223.181* 233.161

2't3. 137 253. 153 263. 12<* 273. 092

273. 150 190.532

191.032

MOL/L

9. 83l»5

9. 8333

9. 8320

9. 8301

9. 827 0 9. 8220

9. 6158

9. 8108

9. 8071 9.7990

10. 2163

10. 2157 10.2128

10. 2128

10. 2128

10. 2128

10. 2128

10. 2128

10. 2115 10.2109

10. 2096

10. 208't 10. 2065

10. 20i»7 10.20'»7

10. 2022

10. 1922

10. 1829

10. 1729

10. 1729

11. 1588

11. 1582

11. 15i»3 11. 15'»3 11. 1537

11. 1531

11. 1518

11. 1506

11. 1500

11. ms?

11. 1«»62 11. 11*31 11. Iif31 11. 11*31 11. 1375

11. 1325

11. 1269 11.1219

11. 1163

11. 1113

11. 1113 11.7672 11.7666

CALCD 9.7582

9. 8072 9.8069

9.6201* 9.8338

9.8372

9.8333

9.8263

9.8215

9.8078

10.2163 8.8398

8. 5302 8.8391

9.2837

9.1*630

9. 6761* 9.7311*

9.91*29

10. 01*18 10.1072

10.1392

10.161.2 10.1759 10.1862

10.1929

10. 2022 10.1918

10.1781 10.1780

7.7000 9.3851

10.6012

10.5372

10.7811 10.9136

10.9678

0055

0306 0525

081*6 1060 1068 1063

1226

1276

1261

1200 1137

1085

1010

9.821*7

10. 3136

D.PCT

0.78

0.27 0.26

0.10 -0.07

-0.16

-0.18 -0.16

-0.15

-0. 09 0.00

13.1*7

16.1*8

13.1*5 9.10

7.31* 5.25

'..71 2.63

1.66

1.00 0.68

-0.09

-0.05

-0.05

31.00 15.89

'..96 5.53

3.34

2.15

1.65

1.30 1.07

0.86 0.55

0.33

0. 33 0.33

0.13

0.01* 0.01

0.02

0.02

0.02

0.09 16.51

12.35

P,eAR

55.870 59.977

63.1*17 68. 503 78.771

93. 389 111. 767 128. 671* 138. 71*9 161*. 501*

1.5. 875

1.6.607

1.6. 31.2 1*6.618

1*6. 900

1*7 .188

1*7.762

1*8. 131

50. 263

52. 700

56. 836

60. 811* 66. 0 36 71. 799 71.833

79. 691 110.688

11*0. 387 170.925

170.987

1*5. 831.

1*6. 61*3

1*7. 983

1*8. 009

50. 21*8 53. 31*0 56. 992

60. 226

63. 092

66. 762

71*. 518

81*. 266

81*. 282

81*. 293 101.660

119. 122 136.601

151*. 123

171.551. 186.977

188. 927

1.5. 823

1*6. 701

CALCO 55.962

60.023

63.1*73 68.531

78.71*1 93.289

111.603

128.1.87 138.551.

161.. 350

1.5.951*

1*6.691*

1*6. 1*09 1*6.706

1*6.986

1*7.281 1*7.863

1*8.21*1* 50.395

52.831* 56.972

60.91*3

66.11*1. 71.6 96 71.696

79.733 110.598

11.0.266 170.830 170.895

1*5.91.1. 1*6.759

1*8.101*

1*8.11.5 50.1*31 53.51.9

57.21*0

60.1*81. 53. 31*8 67.036

71*. 71*6

81*. 1.53

81*. 1*65

81*. 1.79 101.772

119.170 136.612

151.. 152 171.601

189.033

189.135

1*5.960 1.6.632

P.PCT

-0.17 -0.08

-0.09

-0.01*

0.01. 0.11

0.15

0.11. 0.11.

0. 09 -0.17 -0.19

-0.11* -0.19

-0.18 -0.20 -0.21

-0.23

-0.26

-0.25

-0.21. -0.21

-0.16 -0.13

-0.09

-0.05

0.08

0.09

0.06 0.05

-0.21. -0.25

-0.25 -0.28

-0. 36

-0. 39

-0.1.3 -0.1.3

-0.1.1 -0.38

-0.31 -0.22

-0.22

-0.01. -0.01

-0.02

-0.03

-0.03

-0.11

-0.30

-0. 28

66

F-69
METHANE EQUanON OF STATE

10

3

3

33

3

3

3

3

33

3

3

33

3

3

3

3

3

3

3

3

3

3

33

3

3

3

3

33

3

3

3

33

3

3

3

33

3

3

33

3

3

3

3

3

33

T,K

1S2.1»98 195.8i»0 198. 182

203.<«3l» 212.03it 212.035

222.632

233.1.02 233. i»03 237.033

2 37. 0 3i» 2it3. 378

2it3. 381

253.281.

263.<.<»9 268. 300

268. 300

272.691. 272.695 272.698

19 0. 0 32 191. 032 190.532

190.703

191.<.5i. 192. 397 196.505

203. 573 209.295

218.622 228.103

238.550

21.5.920 252.972

260. 108 267. 312

271.. 151

18 8.969

189. 258

189. 767 190. 032

19 0.172

191. 032 190. 1. 1.7 190.532

190.738

191. 075 192. 892

195. 01.8 195. 065 197. 100 200. 010 203. 322

MOL/L 11.7625

11.7607

11.7591.

11. 7563 11.7513

11. 7513

11.71.51

11. 7395 11.7395

11.7370

11.7370 11.7332

11. 7332

11. 7283

11. 7220 11.7195

11. 7195 11.7170

11.7170

11.7170

12. 8681

12. 8675

12. 8681

12. 8636

12. 8636

12. 8630

12. 8605

12. 8562

12. 8521. 12. 81.68 12. 81.06 12. 831.3 12. 8291. 12. 8250

12. 8206

12. 8163

12. 8119

13. 7516

13. 7510 13.7510

13. 751.5 13. 7501. 13. 7539

13.7501.

13.751.5

13.7501. 13.71.97

13. 71.85 13. 71.7 3 13.71.73

13. 71.60 13. 71.1.1 13. 71.16

CALCD

11.1.500 11.581.9 11.6267

11.6773

11.7159

11.7160 11.7336

11.7367

11. 7381 11.7382

11.7379

11.7351.

11. 731.7 11.7291 11.7219

11.7197 11.7195

11.7162

11.7161

11.7157

12.6981. 12.7623

12. 71.1.9 12.7772

12.761.7 12.7310

12. 7831. 12. 8229 12.8393 12.8512

12.8517

12.81.83

12.81.19 12.8382

12.8327 12.8265

12.8191. 13.7572

13. 7517 13.7388

13.7361. 13.7298

13.7281. 13.7288

13.7323

13.7256

13.721.9 13.7165

13. 7181. 13.7167

13.7227

13.7301. 13.7393

O.PCT

2.66

1.1.9 1.13

0.67

0.30

0.30

-0.01

-0.02 -0.01

-0.01

0.00 -0.00

0.00

0.01

0.01

0.01 1.32

0.82

0.96 0.67

.77

,03

,60 .26

,10 -0.03

-0.09

-0.11

-0.10

-0.10 -0.09

-0.08

-0.06

-0.01. -0.01

0.09

.13

.15 0.19 0.16

0.16

0.18

0.18 0.23

0.21 0.22

0.17 0.10

D.02

P,BAR

1.9. 295 55.256

59.511

69. 192

85. 308

85. 310

105.1.07 125.956

125. 973 132.922

132.920

11.5. 053

11.5. 050 163.987

183 . 1.02 192.683 192.678

201. 050 201. 01.9 201. 01.6

1.5. 236

1.7. 21.7

1.6. 239

1.6. 599

1.8. 097

1.9. 969

58. 521

73. 61.2 86. 110 106. 682

127. 755

151. 093 167. 51.6 183. 31.7 199. 300 215. 373 230.576

1.3. 856

m.. 502

1.5.639

1.6. 21.0 1.6.51.9 1.8.523

1.7. 177

1.7. 379

1.7. 81.0

1.8. 615

52. 817

57. 893

57. 928

62. 787

69. 812

77.901.

CALCO

1.9.1.31. 55.1.69

59.71.7

69.1.31.

85.1.91. 85.1.96 105.501

125.987 125.989

132.907

132.909

11.5.023 11.5.029 163.975

183.1.03 192.678

192.678 201.067 201.069

201.075

1.5.317 1.7.332

1.6.319

1.6.661 1.8.188 50.121. 58.703

73.790

86.191

106.61.2 127.621 150.879

167.327

183.081. 199.033

215.126

230.378

1.3.81.9

1.1.. 501

1.5.658

1.6.270

1.6.581. 1.8.575

1.7.217

1.7.1.20

1.7. 888

1.8.666 52.902

57.992

58. 032 62.883

69.882

77.918

P.PCT -0.28

-0.39

-0.1.0 -0.35

-0.22

-0.22 -0.09

-0.02 -0.01

0.01

0.01

0.00

-0.00

-0.01

-0.01

-0.01

-0.18

-0.31

-0.20 -0.09

0.01. 0.10

0.11. 0.13

0.11. 0.13

0.11 0.09

0.02

0.00

,01. ,0708

,11

,08 ,09 10 -0.10

-0.16

67

F-70
METHANE EOUATION OF STATE

10 T,K M

3 2 0 7. 197 1 3. 3 21 3. 323 1 3. 3 222. 792 1 3. 3 227. aitb 1 3.

3 233. 272 13.

3 238. 506 13.

3 2'«2. 985 1 3.

3 21(8.766 13.

3 253. Ill 13.

3 258. 31<» 13.

3 262. 932 13.

3 267. 819 13.

3 267.886 13.

3 273. 153 13.

3 187. 6'»9 m.

3 188. 927 Ik.

3 190.532 Ik.

3 191. IjSS Ik.

3 isit. ao<> Ik.

3 199. 611 Ik.

3 20 3. 05'» Ik.

3 207. 627 Ik.

3 212. 935 Ik.

3 221. 360 Ik.

3 228.637 Ik.

3 236. 599 Ik.

3 2115. 086 Ik.

3 253. 068 Ik.

3 260. 836 Ik.

3 268. 82<> Ik.

3 275.151* Iko

3 183. 351 16.

3 185.267 16.

3 189.259 16.

3 190.532 16.

3 191*. 1*19 16.

3 198. 1*20 16.

3 201. Oi>i» 16.

3 207. 770 16.

3 213.668 16.

3 222.893 16.

3 232.812 16.

3 2111. 295 16.

3 25<». 531 16.

3 261. 826 16.

3 267. 883 16.

3 272.981 16.

3 179. 1<»0 17.

3 179. 830 17.

3 181. 008 17.

3 181<.'»<»1 17.

3 190.532 17.

3 196. 38i» 17.

OL/L CAL6D

7392 13. 7<.l»2 73<»6 13. 7538 7286 13.7523

725'» 13.7507

7217 13.7i«80 7180 13.7it3<»

71<.8 13. 7395

7111 13.7333

7086 13.7291

701.9 13.72<»1 7018 13.7202

6986 13.7152

6986 13.7152

69'.9 13.7105

9705 II*. 9380 9699 11*. 9388 9732 l"*. 91*09 9680 1"*. 91*19 9655 11*. 91*76 9616 11*. 9595

9593 11*. 9652

9562 11*. 9709

952<* 11*. 9732

91*62 11*. 9719

91*06 11*. 9677

9350 II*. 9615

9287 II*. 9535

9225 II*. 91.61. 9169 II*. 9370

9113 II*. 9283 9063 11*. 9227

5231* 16.1*61.5 5215 16.1.636

5181* 16.1*709 5223 16.1.736

511*0 16.1*825 5109 16.1*81.9 508«* 16.1*91.1 5028 16.1.930

1.976 16.1.91.6 1.903 16.1.909

1.822 16.1*853

1*751. 16.1.805

1.61.6 16.1.695

1*566 16.1.630

1.536 16.1.576

1.1.92 16.1.527

561.0 17.531.3

5631* 17.5325

5622 17.5297

5590 17.5256

5595 17.5211.

51.85 17.5178

D.PCT P,B4R

-0.01. 87.1.39

-0 . 11* 102 . 706 -0.17 126.1*32 -0.18 139.171. -0.19 152.881* -0.19 166.109

-0.18 177.1.29 -0.16 192.026 -0.15 203.005

-0.11. 216.11.5 -0.13 227.811

-0.12 21*0.117 -0.12 21.0 . 288 -0.11 253.551

0.22 1.3. 271. 0.21 1.6.771 0.22 51.216

0.17 53.786

0.12 63.256

0.02 77. 101. -0.01. 87.135

-0.10 100. 571. -0.11* 116.265

-0.17 11*1.310 -0.18 163.016 -0.16 186.801

-0.17 212.11.0 -0.16 235.968

-0.13 259.036

-0.11 282.716

-0.11 301.1.72 0.36 36.252

0.35 i.i..8ei. 0.29 56.970

0.29 63.513

0.19 77.509

0.16 91.963

0.09 101.638

0.06 126.173

0. 02 11.7. 682 -0.00 181. 621. -0.02 218.350

-0.03 21.9. 578 -0.03 298.027

-0.03 321*. 591* -0. 03 31*6. 581* -0.02 361*. 997 0.17 33. 01*1* 0.18 35. 61.9 0.19 1.0.651 0.19 51*. 773 0.22 60. 090 0.18 101*. 601

CALCD P.PCT

87,1.01 0.01. 102.521 0.18

126. 121 0.25 138.798 0.27

152.1.1.3 0.29 165.637 0.28 176.931 0.28

191.531. 0.26 202.519 0. 21. 215.655 0.23 227.312 0.22

239.61.0 0.20 239.810 0.20 253.073 0.19

1.3.389 -0.27

1*6.899 -0.27 51.373 -0.31

53.921* -0.26

63. 376 -0.19

77.121. -0.03 87.075 0.07 100.395 0.18 115.965 0.26

11*0.81*8 0.33

162. 1.1.7 0.35 186.156 0.35

211.1.52 0.32 235.229 0.31 258.351 0.26

282.061. 0.22 300.822 0.22 38.720 -1.22

1.5.1*10 -1.17 59.513 -0.92

61*. 106 -0.93

77.961 -0.58

92.391. -0.1.7 101.896 -0.25 126.385 -0.17

11*7-957 -0.05

181.806 0.01

218.21*3 0.05

21.9.380 0.08 297.816 0.07

321*. 362 0.07

31*6.371 0.06

361.. 809 0.05

33.1.19 -1.13

36.251. -1.13

1*1. 101. -1.12 55.317 -0. 99

80.861. -0.97

105. 338 -0.70

68

F-71
METHANE EQUATION OF STATE

10 T ,K

3 2 0 0. 5 37 17.

3 20 8. 822 17.

3 217, 0(,i» 17.

3 225. 0 22 17.

3 23 3. 079 17.

3 2 (, 0 , 9 96 17.

3 2 5 0 . 7 35 17.

3 258 . 6<»6 17.

3 26 6. 750 1 7.

3 2714. 303 17.

3 18 2. 8 3'» 1 8.

3 182. 8 3i» 18.

3 175. 629 18.

3 173. 081 18.

3 188. 292 18.

3 19 0. 5 32 18.

3 193. 6 30 1 8.

3 19 8. 667 1 8. 3 2 0 3. 155 18.

3 208. 21'» 18.

3 21 2. '2<» 18.

3 21 8 . 758 18.

3 223. 7'«2 18.

3 229, 1 35 18.

3 233. 395 18.

3 23 7. 607 18.

3 21(3. 055 18.

3 2'<3. 039 18.

3 253. 126 18.

3 263. 283 18.

3 272.927 18.

3 172.566 19.

3 178.i«80 19.

3 186.850 19.

3 190. 532 19.

3 196. 089 19.

3 20<».181 19.

3 211.525 19.

3 219. 063 19.

3 227. 105 19.

3 235. 300 19.

3 2<«i». 17<» 19.

3 253. 828 19.

3 259. 3<»3 19.

3 267, 733 19.

3 27i». i»69 19.

3 172. 766 21.

3 176. 889 21.

3 181.669 21.

3 189.783 21.

3 190. 532 21.

3 197.315 21.

3 20i». 169 21.

lOL/L CALCO

5<»l»7 17.5219

5379 17.5232

530'* 17.519'! 5235 17.5127

5160 17.5067

5092 17. (.999 5005 17. 1.911 '936 17.i«80i.

'»868 17.1.731

1.799 17.1.665

1*888 18.1.21.5 1.888 18.1.231. 1.956 18.1.325

1.931 18.1.282

1*838 18.1.239

1*871 18.1.237

1.788 18.1.237

1.738 18.1.236

1.695 18.1.231

1.651 18.1*216

1.607 18.4192

1.551 18.1.163

1*501 18.1.137

1*1.52 18.1.092

1.1*11* 18.1*060

1*377 18.1*027

1*321 18.3983

1.277 18.3935

1*227 18.3891

1.131* 18. 3808

1.01.7 18.3716

9962 19.9162

9899 19.9071

9812 19.9009

9838 19.8981. 9719 19.691.7 9631 19.8895

9557 19.8852

91.76 19.8798

9395 19.6726

9311. 19.8662

9220 19.8570

9120 19.81.95

9061. 19.81.52 8977 19.6332

8909 19.8296

2132 21.1170

2088 21.1117

2032 21.1076

1939 21.0980

2000 21.0963

1856 21.0922

1783 21.0883

O.PCT P.BAR

0.13 122.21*1* 0.08 157. 1.26 0.06 192.276

0.06 225.971. 0.05 259.963

0.05 293.223

0. 05 333. 921. 0.08 366.598

0. 08 1.00 . 092 0.08 1.31.136 0.35 65.516

0.35 65.1*91

0.31* 31.376

0.35 1*2. 935 0.32 91. 61*8 0.31* 102.1.01 0.30 117.303

0.27 11.1. 556 0.25 163.181

0.21. 187.511

0.22 207. 691. 0.21 236. 01.9 0.20 261.867

0.20 287. 1.65 0.19 307.683

0.19 327.596

0.18 353.252

0.19 376.587

0.16 1.00.31.8 0.18 1.1.7.525 0.18 1*91.81*0

0.1.0 55. 009

0.1*1 90 . 082

0.1*0 139. 761

0.1*3 161.51*1* 0.39 191*. 310 0.37 21*1. 785

0. 35 281*. 629

0.31* 328. 253

0.31* 371*. 31*1 0. 33 1*21. 001 0.33 1*70. 891 0.31 521*. 859 0.31 555. 1*1*1 0.32 601.053

0.31 638.125

0.1*5 113.831

0.1*6 11*2.805

0.1.5 176.336

0.1.5 232. 523

0.1.8 237. 772

D.1.1. 281.. 367

0.1.2 331. 269

C AL CD P PC T

1 2 2 • 8 50 * 0 . 5 0 157" 892 ~ 0 • 3 0 19 2 • 6 7 9 -0.21

2 26 • 17 "0.20

7C, n T AO * 0 • 1

c ^ 0 " D O D 0 • 1

3 3 ^ • ^ ^ 3 0.16

0 O r • o O i. "0*21

* 0 0 • 9 59 -0.22

* 3 2 • 0 0 "0.21

67 • 093 "2*^0

67.0 93 -2.^5

3 2 .575 -3.82 ^'•292 -3 • 16

9 3 • 357 ~ 1 • 6 6

1 0 • 3 -1.87 119*083 - 1 • 5 2

1 U 3 • 3 5 7 -1.27

16** • 9 86 -1.11

1 8 9 • 3 6 -0.98

2 0 9 • 563 * 0 . 9 0 239*953 -0.80 263*769 -0.73

2 8 9 • 86 -0.70

3 09.7 -0.67

3 29.719 -0.65

35 5 • 16 -0.61

378. 876 -0.61 ^02.691 -0.59

t»t»9.969 -0*55

ti9i».522 -0*55 57.997 -5.*»3 93.600 -3.91

l'*3.7<»0 -2.85

166. 03** -2.76 198.707 -2.26

2^#6.ttt»C -1.93

289.it7e -1.70 333.289 -1.53 379-693 -l.*t3 *»26.58e -1.33

t»76.8'»7 -1.26 530.983 -1.17 561.657 -1.12 607.938 -1.15

6^t»,906 -1.06 119.723 -5.18

1^*9.127 -if.»t3 182. 96'* -3.76 239.883 -3.17

2i*5.650 -3.31 292.177 -2.7** 339.276 -2.U2

69 , F-72
methane: equation of state

ID T,K MOL/L CALCD O.PCT P, BAR CALCD P.PCT

3 21. 1689 21.0822 0.1.1 388. 576 396.886 -2.11.

3 228. '«30 21. 1509 21. 0686 0.39 1.93. 1.61. 502. 362 -1.80

3 235. 779 21. 1'.28 21. 0622 0.38 51.1. 550 550.716 -1.69

3 2<<7. 380 21. 1303 21. 0517 0.37 616. 528 626.128 -1.56

3 252. 9S2 21. 121.1 21. ceo 0.37 652. 311 662. 169 -1.51

3 16 8.7 53 22. 1.109 22. 3126 0.1. 1. 169. 1.22 178.003 -5. C6

3 180. 116 22. 3972 22. 3016 0 .1.3 262 . 685 272.107 -3.59

3 188. 528 22. 3872 22.2931 0.1.2 330 . 1.50 31.0.1.8'. -3.01.

3 190. 532 22. 3918 22. 2910 0.1.5 31.6. 1.1.0 357.386 -3.16

3 196.791 22. 3772 22.2877 0 .1.0 396. 392 1.06.618 -2.58

3 20<«. 366 22. 3679 22. 2811. 0.39 1.55. 919 1.66. 386 -2.30

3 211. 255 22. 3598 22.2755 0.38 509. 1.03 520.115 -2.10

3 218. 293 22. 3517 22. 2700 0 . 37 563. 516 571.. 391. -1.93

3 226. 285 22. 31.17 22.2623 0 . 36 621.. 075 635.168 -1.78

3 23i«.i»20 22. 3321. 22.2550 0.35 685. 032 696. 356 -1.65

NP = 279, DNRMSPCT = 3.196, PMEANPCT = 0.591

METHANE EQUATION OF STATE

10 T »K M OL / L CALCD D , PC T P, BAR CALCD P , PC

6 2 0 3. 0 01. 0. 060 1. 0.0601. -0.03 1. 013 1.013 0.03

8 22 3. 21.9 0. 051.9 0 • 0 51.8 0.08 1 . 013 1.011. -0.08

8 21.8. 175 0. 01.9 3 0 . 0 1.9

0.05 1. 013 1.011. -0.05

8 27 3. 150 0. 01.1.7 0 . 01.1.7 0.02 1. 013 1.013 -0.02

8 29 8 . 1 1.2 0. 01.0 9 0 . 0 1.0 9 0.02 1. 013 1.013 -0.02

8 3 2 3. 1 1.0 0. 0376 0 • 0 37 8 0.01 1. 013 1.013 -0.01

8 37 3. 150 0. 0327 0 . 0 3 27 0.01 1. 013 1.013 -0.01

8 1.23. 170 0 . 029 8 0 . 0 2 68 0.01 1. 013 1.013 -0.01

8 1. 7 3. 193 0. 0258 0.0258 0.01 1. 013 1.013 -0.01

8 2 0 3. 0 61. 1. 39 1 8 1 381.9 -0.22 20. 265 2 0.227 0.19

8 22 3. 21.9 1. 2081. 1.20 79 0.01. 20. 265 2 0.271 -0.03

8 0 . 81. 7 9 0 . 8 1.6 8 0.13 20 . 265 2 0.291 -0.13

8 2 0 3. 0 81. 2. 2701 2.2837 -0.60 30. 397 30.261 0.1.5

8 223. 21.9 1. 9191 1. 9230 -0.20 30 . 397 3 0. 31.6 0.17

8 21.8. 175 1.6396 1.6393 0.01 30. 397 30.1.01 -0.01

8 273. 150 1. 1.1.22 1. 1.1.16 0.01. 30. 397 30.1.08 -0.03

8 323. 11.0 1. 1757 1.1751 0.05 30. 397 30.1.11 -0.01.

8 373. 150 1. 000 1. 0.9989 0.15 30. 397 30.1.1.2 -0.15

8 1.23. 170 0. 8729 0.8717 0.13 30. 397 30.1.38 -0.13

8 1.73. 193 0. 7750 0. 771.8 0.03 30. 397 30.1.06 -0.03

8 203. 081. 3. 1.113 3. 1.1.32 -0.93 1.0. 530 1.0.291 0.59

8 223. 21.9 2.7321. 2.71.12 -0.32 1.0 . 530 1.0.1.26 0.25

8 21.8. 175 2. 2722 2.2737 -0.07 1.0. 530 1.0.507 0.06

8 273. 150 1. 9731. 1.9721 0.07 1.0. 530 1.0.555 -0.06

8 298. 11.2 1. 751.1 1.7539 0.01 1.0. 530 1.0 .535 -0.01

8 323. 11.0 1. 5853 1. 5859 -0.01. 1.0. 530 1.0.516 0.03

8 203. 081. 5. 0533 5. 1569 -2.05 50. 662 50.181 0.95

8 223. 21.9 3. 681.5 3.6997 -0.1.1 50. 662 50.515 0.29

8 273. 150 2.5315 2.5292 0 .09 50 . 662 50.701. -0.08

8 373. 150 1. 6853 1. 6836 0.10 50 . 662 50.71*. -0.10

6 1.23. 170 1. 1.597 1.1.595 0.01 50. 662 50.666 -0.01

8 1.73.193 1. 2919 1.2923 -0.03 50. 662 50 .61.6 0.03

8 2 0 3. 0 81. 7. 9718 8. 1.398 -5.86 60 . 795 59.759 1.70

8 223. 21.9 1.. 8339 1..8523 -0.38 60. 795 60.61.8 0.21.

8 21.8. 175 3. 701.7 3. 7109 -0.17 60 . 795 60.711. 0.13

8 273. 150 3. 1161 3. 111.0 0 .07 60 . 795 60.831 -0.C6

8 298. 11.2 2. 7181. 2.7207 -0.08 60. 795 60.71.8 0.08

8 35 3. 11.0 2.1.350 2.1.332 0.07 60. 795 60.836 -0.07

8 1.23. 170 1. 7532 1.751.5 -0.07 60. 795 60.750 0.07

8 1.73. 193 1. 5505 1.5508 -0.02 60. 795 60 .781. 0.02

8 203. 081. 9. 9826 10. 6796 -6.98 65. 861 61.. 181. 2.55

8 203. 0 81. 1 1. 9996 12. 1.026 -1..31 70. 927 69. 191. 2. 1.1. 8 22 3. 21.9 6. 1880 6. 2519 -1.03 70 . 927 70.503 0.60

8 203. 081. 13.9975 11.. 2780 -2.00 91060 79.009 2.53

8 223. 21.9 7. 7710 7. 6919 -1.56 81. 060 90.31.6 0.68

8 21.8. 175 5. 3793 5. 1.085 -0.51. 91. 060 90. 735 0.1.0

8 273. 150 1.. 3636 1.. 3667 -0.07 81. 060 81.012 0.06

8 299. 11.2 3. 7389 3. 71.30 -0.11 81

060 90.990 0.10

8 323. 11.0 3. 3109 3.3106 Q.Ol 61. 060 81.067 -0.01

8 223. 21.9 9. 1.350 9. 591.2 -1.56 91192 90.251. 1.03

8 2 0 3. 0 81. 15. 9266 16.0518 -0.79 101. 325 99.367 1.93

8 223. 21.9 10. 9398 11.0627 -1.12 101325 100.1.16 0.90

70

F-73
METHANE EQUATION OF STATE

T n O A L U U

6 2 ^ 8 • 175 7 • 25 1 8 7 • 3128

6 2 7 3 • 150 5 • bS*. 9 5 • 7 1 1

^ 29 8* 1 ^2 ' * 79 9 0 • 8 1 0 2

6 32 3* 1 i»0 '• 2 0 ' 8 • 2107

6 2 0 3* 0 8^ lb* y U c 0 1 7 • 0 8 01

g 22 3* 2 *»9 1 3 * 10 5 3 1 3 • 2713

8 2^8* 175 9. 1316 9 • 2139

8 2 7 3 • 150 7 • 057 6 7 - 0 913

6 298* 1 *t2 5 * 88 0 6 5.8991

8 3 2 3* 1 i*fl 5 • 1121 5 • 12 20

8 2 0 3 * 0 6W 1 7* 6717 17. 6199

8 2 2 3- 2 ^9 1 '• 5'*7 1

1 /» conn

8 2^8* 175 10. 7931 10*8623

8 2 7 3 * 150 8 . 396 2 8 • U 3 65

8 29 8* 1 ^2 6. 95 *» '+ 6 • 97 91

8 3 2 3 • 1 '0 6. C 1 5

6 • 0 2 86

8

5 7 n at. 18. 2772 1 8 • 0 5

8 223*2 15. 55 2

15 • 6 9 3 3 8 2^8* 175 12* l^bS 1 2 • 2 3 5 3 8 27 3. 150 9. 637 0 9.6728

8 29 8* 1 *»2 7 . 995 9 8*0221

8 3 2 3* 1 WO 6. 902 2 6*9151

8 2 0 3 • 0 8W 1 8* 773 2 18*8916

8 2 2 3* 2^9 16. 7'+8 ' 1 6 • 65 3

8 2 8 • 1 75 13. 2'*2 2 13* 3^86

8 273* 150 10. 7591 10.7729

8 298. 1'42 8.971.3 9*0029

8 323* 11»0 7.7605 7,7691

8 373. 150 6. 19'.6 6.2011

8 2 0 3. 3 8i« 19. 210'. 19.311**

8 223. 2<»9 16. 9755 17.0931

8 2't8. 175 11.. 151.7 1*«. 2529

8 273. 150 11.7211 11.7i*91

8 298* 11.2 9. 8855 9.90t»G

8 323. lUO 8. 5699 8.5805

8 373* 150 6.81.03 6. e5i*3

8 '•23. 170 5- 7691 5.78ttO

8 '•73. 193 5. 0363 5. 0'**»9 8 20 3. 08i» 2 0. 0835 20* 1691

8 223. 2<»9 18. 2033 18.2918

8 21.8. 175 15. 8229 15.9275

8 273. 150 13. 6611. 13.7030

8 298. Ilt2 11. 8075 11. 63145

8 323. li»0 10. 3751. 10. 383*+

8 373* 150 8. 3661 8. 3816

8 '73* 193 6. 171.7 6. 1893

8 203* 08'« 20. 7751 20. 8527

8 223. 2'»9 19. 0983 19-1863

8 2'<3.175 17. 0283 17.1179

8 273* 150 15. 0986 15.1363

8 298. 11.2 13. 3339 13. 3706

8 323. I'.O 11. 8878 11. 8937

8 37 3. 150 9. 7327 9.7387

O.PCT P.BAR

-0.81. 101.325

-0.28 101.325

-0.23 101.325

-0.1'. 101.325

-1.05 121.590

-1.27 121.590

-0.90 121.590

-0.1.8 121.590

-0.31 121.590

-0.19 121.590

-0.8'. l'.1.855

-0. 98 11.1 . 855

-0.6'. l'.1.855

-O.'.a 11.1.855 -0.35 l'.1.855 -0.22 11.1. 855 -0.70 162.120

-0.91 162.120 -0.73 162.120

-0.37 162.120 -0.33 162. 12C -0.19 162.120 -0.63 182.385

-0.72 182.385

-0.80 182.385

-0.13 182.385

-0*32 182* 385 -0.11 182.385

-0.10 182.385

-0.53 202.650 -0.69 202.650 -0.69 202.650

-0.21. 202. 650 -0.19 202.650

-0.12 202.650

-0.20 202.650 -0.26 202.650

-0.17 202.650

-0.1.3 253. 313

-0.1.9 253. 313 -0.66 253.313

-0.30 253.313

-0.23 253.313

-0.08 253.313

-0.19 253.313

-0.21. 253. 313 -0.37 303*975

-0.'.6 303. 975 -0.53 303.975 -0.25 303.975

-0.27 303.975

-0.05 303.975

-0.06 303.975

C AL C D P y PC T 10 0.691 0 . 6 J 101.087 0.23 101.116 0.21 101.192 0.13 117.50? 3.36 119.693 1.56

12 0.663 0.76

121 .091. 0 . '. 1 121 . 2'.7 0.28 121.370 0.18

137. 3'.7 3.18

1 39 . '» 25 1.71

11.0 .928 0.65

11. 1 . 2 29 0 . '.'. 11. 1 . 3 86 0.33

I'.l . 562 0.21

157 . 3'.9 2.91. 15 8.891 1.99

16 0.678 0.89

16 1 . 1.99 0.36 161.598 0.32

161. 819 0.19

177. 152 2.87 179.0 09 1.85 130.251 1.17 182.115 0.15 181.771 0. 31. 182.176 0.11 182.187 0.11 197.523 2.53 196.562 2.02

200.21.9 1.18

202. 0 31. 0.30 202.216 0.21 202.376 0.1'. 202.208 0.22 202.092 0.28 202.278 0.18

21.7. 61.6 2.21.

21.8. 950 1.72

21.9.523 1.50

252.01.1. 0.50 252.517 0.31

253. 066 0.10 252.763 0.22

252.61.5 0.26 297.721 2*06

298. '.21. 1*83 299.627 1*1.3 30 2.'.'.'. 0.50 302.619 0.1.5 303.760 0.07 303.735 0.08

71

F-74
METHANE EQUATION OF STATE

10

8

8

8

8

88

8

8

8

8

8

88

8

8

88

8

8

8

8

88

88

8

8

1.23.

1*73, 203,

223.

2't8. 273.

298.

323.

373.

Ii23.

<.73. 203.

223.

2'.8. 273.

298. 323.

373.

l»23. 1.73. 203. 223.

2i<8. 273.

298.

323.

373.

1.23. <.73. 203. 223.

21.8. 203.

223.

21.8. 273. 298.

323. 373.

1.23.

1.73. 2G3.

223.

21.8. 20 3. 223.

21.8. 273. 298.

323.

373.

1.23. 1.73.

T,K

170

193

0 81. 21.9 175

150

11.2

11.0 150

170 193

0 81. 21.9 175

150

11.2 mo

150 170

193

0 81. 2<»9 175 150

11.2

11.0 150 170

193

081. 21.9 175

0 81. 21.9 175

150

11.2

11.0 150

170 193

0 81. 21.9 175

0 81. 21.3 175

150

11.2

11*0 150

170

193

MOL/L

8. 261.5

7. 2389

21. 8555

20. 1.1.1.3 18. 7101

17. 0890

15. 5568

11.. 1881. 11.9826

10. 3595

9. 1331. 22. 6621. 21. 1.329 19. 9278

18. 5015

17. 1165

15. 8521

13. 7378

12. 0596

10. 71.89 23. 3596

22.2291.

20. 8623

19. 5731. 18. 301.9 17. 11.25 15. 1352

13. 1.6G3 12. 121.7 23. 9591. 22. 9159

21. 61.06

21.. 1.532 23. 1.668 22. 2969

21. 1777

20. 0986

19. 01.99 17. 21.72 15.6727

11.. 31.03

21.. 9163

23. 9839

22. 860 1 25. 3296

21.. 1.556 23. 1.021. 22. 3610

21. 1.062 20. 1.721. 18. 821.7 17. 3361

16. 0518

CALCD

8.29B1.

7. 2588

21.921.7 20.5136

18.791.7

17. 1395 15.6003

11.. 2201 11.9887

10. 3675 9.1661

22. 761.7 21.5087

19. 9938 18.5387

17.1690 15.9072

13. 7552

12. 0789

10.781.6 23.1.629

22. 311.9 20.9373

19.6173

18. 3698

17.2071

15. 1661

13. 501.9 12. 1720

21.. 0636 22.9976

21.7212

21.. 5931 23.5923

22. 3952

21.21.97

20.161.1. 19. 11.37 17.3053

15. 7361.

II.. 1.151. 25. 0670

21.. 1206

22. 9881. 25.1.967

21.. 5967

23. 5193

22. 1.867 21.5059

20.5800

18.891.7

17.1.253

16. 1550

D.FCT -0.31 -0.28

-0.32

-0. 31. -0.1.5 -0.30 -0.28

-0.22

-0.05

-0.08 -0.36

-0.1.5 -0.35

-0.33

-0.20 -0.31 -0.35

-0.13

-0.16 -0.33

-0 . 1.I. ,3836 -0.22

-0.35

-0.38 -0.20

-0.33

-0. 39

-0.1.1. -0.36

-0.37 -0.57

-0.53

-0.1.1. -0.31. -0.33

-0.1.9 -0. 31. -0.1.1 -0.52

-0.60

-0.57 -0.56

-0.66

-0.58

-0.50 -0.56

-0.1.7 -0.53

-0.37

-0.51

-0.61.

P, BAR

303. 975 303.975

1.05. 300

1.05. 300

1.05. 300

1.05. 300

1.05. 300

1.05 . 300

1.05. 300

1.05. 300

1.05. 300 506.625

506 . 625 506- 625

506 . 625 506.625

506.625

506.625 506.625

506. 625 607. 950 607 . 950 607. 950 607. 950 607. 950

607 . 950 607. 950 607. 950 607. 950 709. 275 709. 275 709. 275 810.600 810.600

810.600

810.600 810.600

810. 600 eiO. 600 810.600 810.600 911.925

911 . 925 911. 925 1013. 250 1013. 250 1013. 250 1013. 250 1013. 250 1013. 250 1013.250

1013. 250 1013. 250

CALCD 302.830

302. 997 397.870

399. 116 399.159

;.02. 177

1.02.901. 1.03.661

1.01.. 985

1.01.. 870

1.03.1.15

1.93. 132

1.98.031. 500.297 503.526

502.711. 502. 821. 505.503

505.371

501.. 209 591. 891 596.311 599.115

603.366

601.81.5

602.331. 605.1.88

601.. 1.91. 601.. 239 690.665

696.331 698.078

782.661.

788.11.0

791..91.C 800.206

801.895 799.062

801.. 135

803. 881. 802. 851. 878.553

881.. 615

888. 985

972. 729 982.178

990.021

990.1.25

996.1.1.0 996. 21.0 1003.187 1001.238 999.865

P.PCT

0.38

0. 32

.83

,53 1.52 0.77

0.59

1.70 1.25

0.61

0.77 0.75

0.22

1.1.5 0.75

1.00 0.92

0.1.0 0.57

0.61 2.62

1.82

1.58

3.1.5 2.77

1.93

1.28

1.07

1.1.2

2.25

1.66 1.68

0.99

1.19 1.32

NP = 158, ONRMSPCT = 0. 952, PHEANPCT = 0.901.

72

F-75
METHANE EQUATION OF STATE

ID

10

10

10

1010

10

10

1010

10

10

10

1010

10

10

10

10

1010

10

10

10

10

10

101010

10

10

1010

10

1010

10

10

10

10

10

1010

10

10

10

10

10

10

1010

10

10

T,K 111. 230 111.230

111. 230 111. 2 30 121. 190 121. 190 121. 190

121. 190 121. 190 131.790

131. 790 131.790

131. 790 131. 790

1'.3. 820

11(3. 820

l"*!. 820 156. 960 156. 960 156.960

156. 960 167.610

167.610

167.610 167.610

179.290

179. 290 179.290

192. 870 132. 870 192. 870 192.870

212. 000 212. 000 212. GOO 212. 000 225.070

225. 070 225. 070 225. 070 237. 570 237.570

237.570

2'.9.i.30

2'.9. '»30 2'i9. '•30 Zitg. <»30 261. 550 261. 550 261.550

261.550

261. 550

MOL/L

27. 9096

28. 30'»6 28. 7271. 29. 360 0 26. 7237

27. 2628

28. 6779

29. 21'»1 29.7000

27. 1518

27. 7008

28. 1770

28.601.1

29. 0360

26. 1.131 27. 2926

28. 1373 25.5297

26. 1575

26. 7i»51 27. 37i»8

21.. 1.618 25. 2653

26. 1370

26. 8381.

21.. 1601. 25. 51.93 26.5111

22. 0601. 23. 581.9

21.. 61.27 25. 7998

21. 21.01. 22. 7739

23. 71.17

21.. 71.63 20.6101

22. 2519

23. 1.797

2i». 7219

17. 91.37 21. 1.638 23. 5793

18. 8076

20. 6016

21. 8579

23. 0256

17.911.7

19. 1.666 20. 7512

21. 7628

22. 7583

CALCD

27. 731.5 26. 1603

28.51.93

29. 1562 26.7088

27. 231.8 28.6520

29. 1851

29.671.3

27. 0691

27. 6061. 28.0758 28.5052

28. 9281

26. 3831. 27.2725

28. 1215 25.6100 26.1825

26.7972

27.1.301

21.. 1.591. 25. 2833

26. 1606

26. 861.0

21.. 11.79 25.5711.

26.51.77 21.9933

23.5581.

21.. 6368 25.8273 21.2565

22. 8011. 23.7996

21.. 8199 20.6353

22. 3362 23.5718

21.. 8386 17.9577

21.5011.

23. 61.11 18. 7 87 3 20. 6352

21.9011. 23.0969

17.9223

19. 1.920 20.8318

21. 871.8 22. 8956

O.FCT

0.63

0.51 0.62

0 .69 0.06

0.10

0.07 0.06 -0.31

-0.10 -0.19

-0.20

0.01 -0.07

-0.09

-0.10

0.05 -0.09

-0.11. 0.30 0.11 0.02 -0.11 -0.08

-0.12

-0.21. -0.30 -0.12

-0.38

-0.39

-0.1.7 -0.08

-0.17 -0.26

0.11 -0.16

-0.20 -0.31

-0.39 -0.51 -0.60

P, BAR

287. 000

1.02 . 000 519. 000 726. 000 218. 000

335 . 000

71.6. 000

91.2. 000

111.1.. 000

1.65. 000 607. 000

71.8. 000 892. 000

101.8. 000

1.83 . 000 705. 000 968. 000

1.95. 000 617 . 000 769. 000 951. 000

1.15. 000 560. 000 751. 000 936. 000

1.88. 000 758. 000 1003. OCO

331.. 000 529. 000

711.. 000 979. 000

1.01. 000 586. 000

71.6. 000 950. 000

1.28. 000 625. 000 823. 000 1087 . 000 302. 000 606. 000

91.6. 000

1.11 . 000 581. 000

71.1.. 000

91.2. 000

1.07. 000 533. 000 680. 000

826 . 000 1001. 000

CALCD 332.699

^l.l.. 02? 576.569

802.530 221.069

31.1.729

751.. 961. 953. 380 1155.226

1.85.579

631.. 053

780 .601. 927.321

1091.271.

1.89.611. 710.618

973.1.05 1.79.273 611. 286 755.207

933.981.

1.15.388

556.501.

71.5.300 928.728

1.89.992 753. 061 992.811

31.0.81.5 532. 999

715.11.3 972.051

399.1.21. 582-081

735.726

933.752

1.25.633 613.326

806. 379 1059.711

301.21.3 601.299

933.956

1.12.503 577.235 737.662

928.819

1.06.1.91. 530.598

669.91.1. 808.821

975.1.21.

10 T,K MOL/L CALCD CPCT P , BAR CALCD

10 278. 710 15. 7751. 15. 7262 0.31 31.8. 000 350.392

10 278. 710 18. 1752 18. 11.36 0.17 500. 000 502.538

10 278.710 19. 5160 19.1.875 0.15 621.. 000 627.018

10 278.710 20.7211 20.7390 -0.09 771.. 000 771.585

10 278. 710 22. 1288 22.181.2 -0.25 999. 000 989.191.

10 293. 1.10 16.7983 16.81.33 -0.27 1.65. 000 1.61.951

10 293. 1.10 18. 81.66 18.9223 -0.1.0 61.0. 000 632.295

10 293.1.10 20. 1776 20.2180 -0.20 791. 000 785.696

10 293.1.10 21. 2089 21.2891. -0.38 91.7. 000 931.. 181. 10 309.290 11.. 2227 11.. 21.01. -0.12 369. 000 368.166

10 309. 290 16. 6691. 16.7201. -0.31 516. 000 512.259

10 309. 290 18. 1.570 18.1.521 0.03 667. 000 667.1.98

10 309.290 19.9283 19.9767 -0.21. 81.7. 000 81.0.1.71. 10 309. 290 21. 2721 21. 3508 -0. 37 1058. 000 101.1.. 1.71.

NP = 66, DNRMSPCT = 0.282, PMEANPCT - 1.937

F.PCT

15.92

10.1.5 11.09

10.51. -1.1.1 -2.01

-1.20 -1.21

-0.98

-1..1.3

-'..i.e

-1.. 36 -3.96

-1..13 -1.37

-0.80 -0.56

3.18 0.93

1.79 1.79 -0.09

0.62

0.76

0.78

-0.1.1 0.65

1.02 -2.05

-0. 76 -0.16

0.71

0.39 0.67

1.38 1.71

0.55

1.87 2.02

2.51

0.25

0.78 1.27 -0.37

0.65

0.85

1.1.0 0.12

0.1.5

1.1.8 2.08

2.56

P.PCT -0.69

-0.51

-0.1.8 0.31

0.98

0.66

1.20 0.67

1.35 0.23

0.73 -0.07

0.77 1.28

73

F-76
Table 15

Calculated P(T) isochores for methane

The following 13 pages give 31 isochores calculated from the

equation of state. They serve to show that the analytically derived

values for derivatives are correct. They also show that curvatures

of the isochores are qualitatively consistent with accepted behavior

per se, and with the behavior of specific heats, Cy , in the critical

region.

74

F-77
METHANE ISOCHORE 1.0 MOL/L HETHflNE ISOCHORE 2.0 MOL/L

T,K P.BAR OP/DD DP/DT D2P/DT2

151*.

10.626 8.<>eo 0.0979 -0. 0 0030 16Z.0 ll.'*02 9.380 0.0960 -0. 00020

170.0 12.16'* 10. 21.6 0.091.6 -0. 0 0015 178.0 12.916 11. 090 0. 0936 -0. 0 0011 ise.o 13.662 11.918 0.0928 -0. 0 0009

191».0 l<*.i*01 12.733 0. C921 -0. 0 0007 202.0 15.136 13.538 0. 0916 -0. 0 0006 210.0 15.867 1'..335 0.0912 -0. 0 0005 218.0 16.595 15.125 0.0906 -0. 0 0001. 226.0 17.320 15.911 0. 0905 -0. 0 0001. 23(t.O 18.0<*3 16.691 Q. 0902 -0. 00003

21*2.0 18.761* 17. '.68 0. C900 -0. 00003

250.0 19.<*8'* 18.21.1 0.0896 -0. 0 0002 258.0 20 .202 19.011 0.0896 -0. 0 0002 266.0 20.918 19.779 0. 0895 -0.00002

27'*.21.63'* 20.5'.'. 0. 0893 -0. 0 0002 282.0 22.3'*8 21. 307 0.0892 -0. 0 0002 290.0 23.061 22.068 0.0891 -0. 0 0001 298.0 23.773 22.828 0. 0890 -0. 0 0001 306.0 2'».<*85 23.586 0. 0889 -0. 0 0001

311*.25.196 0. 0868 -0. 0 0001 322.0 25.906 26. 097 0.0887 -0. 00001

330.0 26.615 25.850 0. 0886 -0. 0 0001 333.0 27.323 26.603 0.0885 -0. 0 0001

31*6.0 28.031 27.35<. 0. 0885 -0. 0 0001

351*.28.739 28. 103 0. 0881. -0. 0 0001 362.0 29.'»'*5 28. 852 0.0883 -0. 0 0001 370.0 30.152 29.600 0.0882 -0. 00001

378.0 30.857 30.31.6 0.0882 -0. 0 0001 386.0 31.562 31. 091 0.0881 -0. 00001

39<».0 32.267 31.836 0.C880 -0. 0 0001

T,K P.BflR DP/CD OP/DT 02P/DT2

170.0 20 .625 6.751 0.2150 -0. 00090

178.0 22.320 7.797 0.2092 -0. 00059

186.0 23.976 6.792 0.2052 -0. 0 001*2

191*.

25.606 9.756 0.2022 -0. 00032

202.0 27.211* 10.696 0.2000 -0. 00025

210.0 26.806 11.620 0. 1981 -0. 00020

218.0 30.385 12.530 0.1967 -0. 00017

226.0^ 31.953 13.1*29 0. 1951. -0. 00011*

231*.

33.512 11*. 320 0.19'.'. -0. 0 0012

21*2.0 35.06'* 15.203 0.1935 -0. 0 0010 250.0 36.609 16.081 0.1928 -0. 00009

258.0 38.11.8 16.953 0. 1921 -0. 00006

266.0 39.68 3 17.820 0.1915 -0. 00007

27<*.0 1*1.212 18.663 0.1910 -0. 00006

282.0 1.2.738 19.51.3 0.1905 -0. 0 0006 290.0 1*1.. 260 20. 399 0.1900 -0. 00005

298.0 1.5.779 21.253 0.1896 -0. 0 0005 306.0 1.7.295 22.103 0.1893 -0. 0 0005

311*.

1.8.807 22.951 0. 1689 -0. 0 0001. 322.0 50.317 23.796 0. 1666 -0. 00001. 330.0 51.821* 21.. 639 0.1883 -0. 00001. 338.0 53.329 25.1.80 0.1880 -0. 0 000'. 31*6.0 51*. 832 26.318 0.1877 -0. 00001*

351*.

56.332 27. 155 0.187'* -0. 00003

362.0 57.830 27.989 0.1871 -0. 00003

370.0 59.326 28.821 0.1869 -0. 00003

378.0 60.820 29.652 0.1866 -0. 00003

386.0 62.312 30.1.80 0. 1861. -0. 0 0003

391*.

63.301 31.307 0.1861 -0. 0 0003

METHANE ISOCHORE 3.0 MOL/L

T,K P,BAR DP/CO OP/OT D2P/0T2

178.0 28.653 '..931. 0. 31.67 -0. 00196

186.0 31.391 6.101. 0. 3369 -0. 00111.

191*.31.. 051. 7. 205 0.3293 -0. 00079

202.0 36.665 8. 268 0. 3239 -0. 00059

210.0 39.239 9. 305 0. 3197 -0. 0 001.6 218.0 1.1 .783 10. 32'. 0. 3165 -0. 00036

226.0 1.1.. 301. 11.328 0. 3138 -0. 0 0030

231..

1.6.806 12.321 0. 3117 -0. 00025

2<*2.0 1.9.292 13.305 0. 3098 -0. D0021

250.0 51.761. 1'..282 0. 3083 -0. 0 0018

258.0 51.. 225 15.252 0. 3069 -0. 0 0016 266.0 56.675 16.216 0. 3057 -0. 00011.

271*.

59.116 17.176 0. 301.6 -0. 0 0013

282.0 61 .55 0 18.131 0. 30 37 -0. 0 0012 290.0 63 .975 19.082 0. 3028 -0. 00011

298.0 66.391. 20.030 0. 3020 -0. 0 0010 306.0 68 .807 20.971. 0. 3012 -0. 00009

311*.71.211. 21.915 0. 30 05 -0. 0 0009

322.0 73.615 22. 853 0. 2998 -0. 0 0006

330 .0 76.011 23.787 0. 2992 -0. 0 0006 338.0 78.1.02 2'.. 719 0. 2985 -0. 0 0008

31*6.0 80 .788 25.61.8 0.2979 -0. 0 0007

351*.

83.169 26.575 0. 2971. -0. 00007

362.0 85.51*6 27.1.98 0. 2968 -0. 0 0007 370.0 87.918 28.1.19 0.2962 -0. 0 0007 378.0 90 .286 29. 338 0. 2957 -0. 0 0007

386.0 92.61*9 30.251. 0. 2952 -0. 00007

391*.

95 .00 9 31. 167 0. 291.7 -0. 0 0006

METHANE ISOCHORE 1.. 0 MOL/L

T,K 166.0

191*.

202.0

210.0

218.0

226.0

231*.

21.2.0 25 0.0 253.0

266.0

271*.

282.0

290.0

298.0 306.0

311*.

322.0 330.0

338.0

3'*6.0

351*.

362.0

370 .0 376.0

386.0

39'..

P,BAR

36.326

1*0.152

1.3.879 1*7.539 51.150

51.. 723 58.265

61.782 65.279

68.757

72 .220 75.669

79.106

82.531

85.91.5 69.35 0 92.71.6 96.133

99.511 102.881

106.2'.'. 109.598

112.91*5 116.285 119.618

122.91*3 126.261

DP/DD

3.8(.3 5.061* 6.228

7.360

8.1.72 9.570

10.657 11.735

12.806

13.672

1'..932 15.988

17.039 18.087

19.132 20.172

21.210

22.21.1. 23.275

21.. 303 25.328

26. 31.9 27.367

28.383

29.395

30.1.01. 31.1*09

DP/DT

0.'.868

0.'.711

0.1.612

0.'.5'*2

0.<*i*88

0.1.1*1*6 0.1.1.11 0.1.383 0.1.359

0.1.338

0.1.320

0.1.303 0.1.288

0.1.275 0.4262

0.1.250 0.1.239

0.1.228

0.1.218

0.1*206

0.1.198 0.1.189

0.1.179

0.1.170 0.1.161 0.1.152

0.1.11.3

02P/0T2

-0. 00262 -0.00160

-0. 00103

-0. 00076

-0. 00059

-0. 0001.7 -0. 00039 -0.00033

-0. 00028

-0. 00021* -0. 00022 -0.00019

-0. 0 0018

-0. 00016

-0. 0 0016

-0. 00011. -0. 0 0011. -0.00013

-0. 00013

-0. 00012

-0. 0 0012 -0.00012

-0. 0 0012

-0. 00011

- 0. 0 0011

-0. 00011

-0. 00011

75

F-78
METHANE ISOCHORE 5.0 MOL/L METHANE ISOCHORE 6.0 MOL/L

T,K 186.0

190.0

19<».0 19S.0 202.0

206.0 210.0

21'*.

218.0 222.0

226.0

230.0

23i*.0 238.0

2'»2.0 2it6.0 250.0

25'*.

258.0

262.0

266.0

270.0

27<».0 27 8.0 282.0

286.0

290.0

29i».0 298.0

302.0

306.0

310.0

31lt.0 318.0 322.0

326.0

330.0

33<».0 338.0

3(t2.0

3<»6.0 350.0

35<».0 358.0

362.0 366.0

370.0

37i«.0 378.0

382.0 386.0

390.0

39^.0

398.0

P.BAR

39.238

<«1.8ie

<»<« .338

'*6.818

<»9.268 54.100

56.<»89 58 .863 61.225

63.576 65.917

68.2<»9 70.573

72.890

75.201 77.505

79.803

82.096

8i».36i» 86.668

88.9lt7 91.222

93.1.92 95.759

98.023 100.282

102.539

10i».792 107.0<.l 109.288

111.531 113.772

116.00 9 118.2<fi» 120. 't75 122.701*

12'*. 929 127.152 129.373

131.59 0 133.805

136.017 138.226

l'»0.<»33 1<.2.636

1<»I«.83 8 li«7.03 6 11*9.232

151.1*25 153.616

155. 80<* 157 .989 160.172

DP/OD

2.083

2.7<.6 3.388

I*. 012

<*.626 5.232

5.833

6. <t30 7. 021* 7.616

8.206

8.791*

9. 380 9.965

10.51(9 11.132

11.711* 12.295 12.875

13.1*51*

11*. 033

11*. 610 15.187

15. 76«* 16. 339

16.911*

17.1*88 18.062

18.631* 19.206

19.777

20.31*8 20.918

21.1*87 22.055 22.622

23.189

23.751*

21*. 319

21*. 883

25.1*1(7 26.009

26.570

27.131

27.691

28.250

28.808 29.365

29.921

30.1(76 31.030

31.581( 32. 136 32.688

OP/DT

0.6558

0.6363

0.621*5 0.6159

0.6093

0.6038

0.5993

0.5951.

0. 5920 0.5891

0. 586i( 0.581*1 0.5820

0.5801

0.5781* 0.5768 0.5753

0.5739

0.5726

0.5711. 0.5703

0.5692

0.5682 0.5672

0.5663

0.5651.

0.561.5 0.5637

0.5628

0.5620 0.5612

0.5605 0.5597

0.5590 0.5582

0.5575

0.5568

0.5561

0.5551*

0.551(7

0.551.0 0.5533

0.5526

0.5520 0.5513

0.5506

0.5500

0.51(93 0.51(86

0.51.80 0.51.73

0.51.67

0.51(60 0.51.53

02P/DT2

-0. 00698

-0. 0 0359

-0. 0 021.6 -0.00187

-0. 0015D

-0. 00121. -0. 00105

-0. 00090

-0. 0 0079

-0. 00C69

-0. 00062

-0. 00055

-0. 00050

-0. 0 001.5 -0. 0 001.2 -0. 0 0038

-0. 0 0036 -0.00033

-0.00031

-0. 00029 -0.00028

-0. 00026

-0. 00025

-0. 0 0021.

- 0. 0 0023

-0- 00022

-0. 00022

-0. 00021

-0. 00020

-0. 00020

-0. 0 0019

-0. 0 0019 -0.00019

-0. 0 0018 -0.00018

-0. 0 0018 -0.00018

-0.00018

-0. 00017

-0. 0 0017

-0. 00017

-0. 00017

-0. 0 0017 -0.00017

-0. 0 0017

-0. 0 0017

-0. 0 0017

-0. 00017

-0. 00017

-0. 0 0017

-0. 0 0016 -0.00016

-0. 00016 -0.00016

T,K 190.0

191..

198.0 202.0

206.0

210.0

211*.

218.0 222.0

226.0 230.0

231*.

238.0

21*2.0

21*6.0 250.0

25<*.0 258.0 262.0

266.0

270.0

27'*.

278.0

282.0

286.0

290.0

291*.

293.0

302.0 306.0

310.0

311*.

318.0

322.0 326.0 330.0

331*.

338.0

31(2.0 3<(6.0 350.0

351*.

358.0 362.0

366.0 370.0

371*.

378.0

382.0 386.0

390.0

391*.

398.0

P.BAR

1.3.906

1.7.082

50 .199 53.275 56.322

59.31.5 62.31.9 65.336

68.310

71.271

71*. 221 77.161

60.093

83.017

85.931.

88 .81*1* 91.71*8

91*. 61*7 97.51*0 100.1*27 103.310 106.188

109.062

111.931

111*. 796 117.657

120.511. 123.367

126.216

129.061 131.902

13i(.7i*0 137.571*

11*0.1*01* 11.3.230 11*6.053

11.8.872 151.688

151.. 500 157.308 160.113

162.911* 165.711

168.505

171.295

171*. 061

176.861* 179.61*3 182.1*19 185.191 187.959

190.721*

193.1*85

DP/OD

1.503 2.172

2. 818

3.1*56

<*. 091

i*.72i( 5. 355 5.986 6.617

7.21(8 7.879

8.509

9.11(0

9. 771

10.1(02 11.033

11.661* 12.296

12.926 13.557

11*. 188

11*. 818

15.1*1(8 16. 078

16. 707

17. 336 17.965

18.593

19.220

19. 81(7 20.1(7I( 21. 099

21.721*

22. 31(8 22.972

23.595

21(.217

21*. 838

25.1*58 26.077

26.695

27. 313 27.929

28.51*5 29.159

29.773

30.385 30.997 31.607

32.216

32. 825

33.1.32

31*. 038

DP/DT

0. 8050

0. 7851. 0.7736

0.7651

0.7585

0.7532

0.71.88

0.71.50

0.71.17

0. 7388

0. 7363

0.731.0 0.7320

0.7301

0.728l( 0.7268

0.7253 0.7239

0.7226 0.7213

0. 7201 0.7190 0.7179

0.7168 0.7157

0. 711.7 0.7137 0.7127

0. 7118

0. 7108 0.7099

0.7089

0.7080

0. 7071 0.7062 0.7052

0.701.3

0. 7031. 0.7025 0.7016

0.7007

0.6998 0.6989

0.6980

0.6971 0.6962

0.6953

0.691.3

0.6931* 0.6925 0.6916

0.6907

0.6898

D2P/DT2

-0. 00697

-0. 00360

-0. 0021*5 -0. 00185

-0. 0011*7 -0. 00121

-0. 00102

-0. 00088

-0. 00076

-0. 00067

-0. 00060

-0. 00051. -0. 0 001(9 -0. 0 001.5 -0. 0 001(1 -0. 0 0038

- 0. 0 0036

-0. 0 0031. -0. 00032

-0. 0 0031

-0. 0 0029

-0. 00028

-0. 00027

-0. 00026

-0. 0 0026

-0. 00025

-0. 00025

-0. 0 0021. -0. 0002i( -0. 0 0021. -0. 00023

-0. 00023 -0.00023

-0. 00023

-0. 00023

-0. O0023

-0. 0 0023

-0. 00023

-0. 0 0023

-0. 00023

-0. 00023

-0. 00023

-0. 00023

-0. 00023 -0.00023

-0. 00023

-0. 00023

-0. 00023

-0. 00023

-0. 00023

-0. 0 0023

-0. 0 0023

-0. 00023

76

F-79
METHANE ISOCHORE 7.0 MOL/L METHANE ISOCHORE 8.0 MOL/L

T,K 190.

Q

l'i'*.0 198.0 202.0

206.0

210.0

21i».0 218.0

222.0

226.0

230.0

23'»-0 238.0

2'»2.0

2'>6.0 250.0

25i».0 258.0 262.0

266.0

270.0

271..0 278.0 282.0 286.0

290.0

29<».0 298.0

302.0 306.0

310.0

31i>.0 318.0

322.0 326.0

330.0

33<».0 338.0

3'»2.0 3'*6.a 350.0

351*.

358.0

363.0

366.0

370.0

37i».0 378.0

382.0 386.0

390.0

39i>.0 398.0

P.BAR

'i».952 48.803

52.572 56.297

59.991

63.66 2 67.31I* 70.951

71.. 576 78.189

81.793

85.388 88.976

92.556

96.13 0 99.698 103.261

106.818

110.370 113.917

117. '59

120 .996

121.. 529 128.056

131.582

135.10 2 138.617

11.2.128

11*5.635

11*9.137 152.635 156.129

159.618

163 .103

166.581. 170.060

173.532

176.999

180.1*61 183.919 187.373

190.821

191.. 266 197.705

201.11*0

201.. 570 207.995

211.1.16

211.. 832

218.21*3

221.61*9 225.050

228. I* 1*6

DP/OD

0. 61.3 1. 322 1.979 2.636

3.295 3.959

1..625 5.295

5.967

6.61.2 7.320 7.999

8.661

9. 361. 10. 01.6 10.731.

11.1.20 12.108 12.796

13.1.85

11.. 175

11.. 861. 15.554

16.21.1. 16.931.

17.621* 18. 311* 19.001* 19.693

20.382

21. 070 21.758

22.i*«t5 23.131

23. 817

21*. 502 25.186

25.869

26.551

27.233

27.913 28.592

29.270

29.91.8 30.623 31.298

31.972

32.6'.'. 33. 315 33.985

3'*. 651. 35. 321 35.987

DP/OT

0.9831.

0.91.98 0.9359

0. 9269

0.9201. 0.9152

0.9111 0.9076

0.901.7 0.9021 0.8998

0.8978

0.6960

0. 891.3 0.8927 0.8913

0.8899

0.8886

0.8871. 0.8861

0.8850

0. 8838 0.8827

0.8816 0.8805

0. 8791* 0.8783 0.8772

0.8761

0.8751

0.871.0 0.8729

0.8718 0.8707

0.8696

0.8685

0.8673 0.8662

0.8651 0.8639

0.8628

0. 8616 0.8605 0.8593

0.6581

0. 8569 0.8557

0.851*5 0.8533

0. 8521 0.8509

0.81*97

0.61.85

D2P/DT2

-0. 01858

-0. 001.60 -0.00269

-0.0 0188

-0. 0 011*3 -0. 00111. -0. 00091. -0.00080

-0. 00069

-0. 00060

-0. 00053

-0. 0 001.8 -0. 0 001.1. -0. 0 001.0 -0.0 0038 -0.00035

-0. 00033

-0. 00032 -0.00031

-0. 00030

-0. 0 0029

-0. 00028

-0. 00028

-0. 00028 -0.00027

-0. 00027

-0. 00027

-0. 00027

-0. 00027

-0. 00027

-0. 00027

-0. 00027

-0. 00027

-0. 00028

-0. 00028

-0. 0 0028

-0. 0 0028 -0.0 0028

-0. 00028 -0.00029

-0. 00029

-0. 00029

-0. 00029

-0. 0 0029

-0. 0 0029

-0. 00030 -0.00030

-0. 00030 -0.00030

-0. 00030

-0. 00030

-0. 00030

-0. 00031

T,K

191*.

198.0 202.0

206.0 210.0

211*.

218.0

222.0 226.0

230.0

231..

238.0

21*2.0

21*6.0 250.0

251*.

258.0

262.0

266.0

270.0

271*.

278.0

282.0

286.0

29 0.0

291*.

298.0

302.0

306.0

310.0

311*.

313.0

322.0

326.0

330.0

331*.

338.0

31*2.0

31*6.0 350.0 354.0

358.0

362.0 366.0 370.0

374.0

378.0

382.0

38 6.0 390.0

394.0

398.0

P.SAR

49.818 54.246

58.638 63.006 67.357

71.696

76.0 25 80.346

84.660

88.968 93.271

97.568 101.861

106.150

110 .434 114.715

118.991 123.263 127.532

131.796

1 36.057 140.313

144.565 148.813

153.056 157.295

161.530 165.760

169 .985 174.206

178.421 182.63 2 186.837 191.038

195.233 199.423

203.607

207.786

211.959

216.126 220.288

224.444

228.594

232.739 236.877

241 .00 9 245.135

249.255

253.369

257.476

261.577 265.672

OP/00

0.754

1.417

2.095 2.785

3.466 4.194

4.910

5.633 6.361

7.093

7.830

8.571 9.314

10.061

10.810

11.561 12.313

13. 068 13.823

14.580 15.337

16.096

16.854 17.613

18.372

19.131

19.890 20.649

21.407

22. 165 22.923

23.680 24.436

25.191 25.945

26.699

27.452

28.203

28.953 29.703

30.451 31.197

31.943

32.687 33.430

34.171

34.911 35.649

36.386

37.121

37.855 38.587

OP/DT

1.1141 1.1016

1.0946

1.0898 1.0862

1.0834 1.0812

0793

0777

0763

0750 0738

0727 0716

0706 1.0696

1. 0686 1.0676

1.0666 1.0656

1. 0646 1.0636

1. 0625

1. 0614 1.0603 1.0592

1.0581 1.0569

1.0557

1.0545

1.0533

0520

0507 0494

0481 0468

0454

1. 0440 1.0426 1.0412

1.0397

1. 0383 1.0368

1. 0353 1.0338 1.C323

0308 C292

0277

0261

0245 1.0229

D2P/0T2 -0.00456

-0. 00222

-0. 00142 -0.00102

-0. 00078

-0. 00062

-0. 00051

-0. 00043

-0. 00038

-0. 00034

-0. 00031

-0. 00029

-0. 00027

-0. 00026

-0. 00025

-0. 00025 -0.00025

-0. 00025

-0. 00025

-0. 00025

-0. 00026

-0. 00026

-0. 00027

-0. 00027

-0. 00028

-0. 00028 -0.00029

-0. 00029

-0. 00030

-0. 00031 -0.00031 -0.00032

-0. 00032

-0. 00033

-0. 00033 -0.00034

-0. 00034

-0. 00035

-0. 00035

-0. 00036

-0. 00036

-0. 00037

-0. 00037

-0. 00037

-0. 00038

-0. 00038

-0. 00038

-0. 00039

-0. 00039

-0. 00039

-0. 00040

-0. 00040

77

F-80
METHANE ISOCHORE 9.0 MOL/L HETHANE ISOCHORE 10.0 HOL/L

T tt 1 f ^ Pr RAP f DM l\ OP / 0 D DP/OT D2P/DT2

4 Q i> n Rfl 1*. 7 7 1 • ?7 8 8 -0. 00238

5P . 50 * 1 ? 7 7 1 • 27 31 -0. 00065

20 2*0 60 •621*951 1 • 27 0 7 -0. 0 001*0

c U D • u 0? * f U X ? can 1 • 26 9 6 -0. 0 002C

9 1 n ft & 1 u • uTft 77 A f U • f ( 0 1 • 26 9 0 -0. 0 0010

C 1. 4' u 75 • 6 5 ^ H • 2 1

-0. 0 0005 218*0 Aft Q 9 A O A Q 1 • 26 66 -0. 00002

222*0 66 * 0 0 2 P * / r f 1 • 26 S5 -0. 0 0001 225,0 91 07 6 6 * 572 1*2665 -0. 0 0001

7 7 ft n jO • L 9 u 7 • 3 7*f i 7fs ft 1 • too** -0. 0 0002

5 7 ft 101.22^ A i A 7 0 • X 0 c 1 • cO 0 o -0. 0 0003

233*0 1 06 .29 6 8*995 1 • 268 2 -0. 0 0005 2^2*0 1 11 369 9.812 1 • 267 9 -0. 0 0006 2^6*0 1 16 * 0 10*633 1 • 26 7 7 -0. 0 0008 250*0 1 21 • 51

1 1 • '5 8 1 • 2673 -0. 0 0010

7 C £i ft X C • (1 O 511 7C & o • £D D 7 -0. 0 0012

25 6*0 1 31 • 6'* 5 13. 115 1 • 26 6** -0. 0 0011* 26 2*0 1 36 •709 13. 9 *t7 1» 2658 -0. 0 0015 266*0 1 .771 1^.780 1 • 26 5

-0. 0 0017 270*0 1 HD • O O U 15*615 1 • 26**^ -0. 0 0019

27 • 0 1 51 * 86 6 16 . **5

!• 26 36 -0. 00021

c I 0 * u 1 56 * 93 9 1 7 * 288 1 • 26 2 8 -0. 0 0022

26 2*0 1 1 Q A Q 1 8 * 126 1 • 2618 -0. 0 0021. 266*0 1 67 •03** 1 8 * 96 1 1 26 0 8 -0. 0 0026

X f C . U f 5

1 Q A n 7 X y . 0 U c1 7 R Q ft -0. 0 0027

5Q U ft 1 77 i i 5 C U * O H U1 71^ ft 7 -0. 00029

296*0 182 • l*f4 21 • *f79 1.2575 -0. 0 0030 302.0 167.172 22* 316 1.2562 -0. 0 0032 306*0 192.19** 23-l5*t 1. 251*9 -0. 00033

310*0 197.211 23.991 1.2536 -0. 0 0031* 31^.0 202*223 2*** 827 1.2522 -0. 0 0035 318.0 207*229 25.663 1.2508 -0. 0 0037 322.0 212.229 26*i*S7 1.21.93 -0. 0 0036 326*0 217.223 27* 331 1. 21»77 -0. 0 0039 330*0 222.211 28*16U 1. 21.62 -0. 0 001*0 33tf«0 227.192 28.995 1.2l»'»6 -0. 0 001.1 338.0 232cl67 29*825 1.21*29 -0. 0 001*2 3^2*0 237*136 30*65*t 1.21*12 -0. 0 001.3 3^6*0 2*t2*097 31*i»82 1.2395 -0. 0 001.3 350*0 2^*7.051 32.388 1.2377 -0. 0 0 01.1* 35(^.0 251.999 35.133 1.2360 -0. 0 001*5 358.0 256*939 33^956 1.231*1 -0. 0 0 01*6 362.0 261*672 3*f *777 1.2323 -0. 0 001*6 366.0 266.798 35.597 1.2301* -0. 0 001*7 370.0 271.716 36**tl5 1.2285 -0. 0 001*6 37*».0 276.626 37*232 1.2266 -0. 0 001*6 37S.0 261*529 38*01*6 1.22<*7 -0. 0 001*9 382.0 286.t*23 38*659 1.2227 -0. 0 001*9 366.0 291.310 39.670 1.2208 -0.00050

390*0 296*189 '0.W79 1.2188 -0. 0 0050 39^.0 301.061 1*1*286 1. 2168 -0. 00050

398.0 305.923 1*2.091 1.211*7 -0. 00051

T V P y 6A R DP / D D no / n T 02P/DT2

19 . 0 50*96 5 0*572 1 . 1*5 2

0. 00129

19 8*0 56 * 8 0 3 1*320 1 . 1*5 7 0 0. 00115

20 2.0 62 . 61* 0 2*106 1 . 1*6 1 1. 0. 00103

206*0 66 . i»9 1* 2.917 1 . 1*652 0. 00091

210.0 71* • 3 63 * 7 1*8 1 . 1*6 8 7 0. 00080

5 1 i* ft ^ X t * u 60 • 2 1*

H . 5 "3 9

* £i7 i 7 0. 00071

213.0 86 .131* 5 * 1* 56 1 • 1* 7 1* 3 0. 00061

yyy n C mU Q5 ft 7 t 7-57 1 . 1* 7 6 6 0. 00053

5 5 1 n c c D . U Q7 Qli.7 7 20 8 1 . 1.7 66 0. 0001.5

c J U * U

i ft 7 A £. X U 0 • o D H 6.096 1 i< ft fi 7 0. 0 0036

57 /« ft A no 7 A A A QO 5 1 • HO X

0. 00032

233.0 115*717 9*891* 1 . 1. 6 2 8 0. 00025

21* 2 * 0 1 21 •65 0 1 0 * 80 0 1 . 1* 8 37 0. 00020

5/i & ft c H 0 * u 1 27 •566 11 711 1 . 1* 6 1* 3 0. 0 0011.

5c? n n 1 33 .525 12 * 626 1 • 1.6 1* 8 0. 0 0009

5R f< n X 0^ . H D 5 1 3 . 5 1*1* * 1* A t: * 0. 0 0001.

5 c A n (1 5 0 * U 1 1*5 • 1* 0 5 X H * **C5 i 1* A c; 7 1 . H 0 3 c -0. 00000

262*0 151 • 31* 6 15 . 388 1 . 1. 8 5

-0. 0 0001.

5 fc. t n £ D 0 • u4 C7 5 A X r * coo 1 c 7'i 5 X D . 0 X c 1 • 1* 6 1* 6 -0. 0 0008

5 7ft ft 1 7 5 5 li 17 • 236 1 . 1. 8 1* 1* -0. 00012

27 i* * 0 169 • 1618*165 1 . 1. 8 39 -0. 0 0015

57 ft ft C r 0 * U 175^095 19 . 0 93 1 . 1.8 3 2 -0. 0 0019

282*0 181*026 20. 022 1 • 1*6 2 1* -0. 00022

236*0 1 86 • 95 ** 2 0*950 1 • 1.6 1

-0. 00025

290.0 1 92 * 8 7 8 21. 879 1 . 1. 8 0 1* -0. 00027

5Q ft 1 96 * 7 9 7 22 . 80 6 1 1*7 93 -0. 00030

296*0 2 01* • 71 2 23.736 1. 1*760 -0. 0 0033

302*0 210*621 2(**66i* 1.1.767 -0. 00035

306.0 216^525 25*591 1.1*752 -0. 0 0037

310.0 222.1*23 26*517 1.1.737 -0. 0 0039

31't.O 228*311* 27. i* 1*3 1.1*721 -0. 0 001.1 313.0 23i*^199 28.367 1.1.7D1* -0. 0 001.3 322.0 21*0.077 29.290 1.1.686 -0. 0 001.5 326.0 21*5.91*6 30.211 1.1.666 -0. 0 001.7 330.0 251.612 31.132 1.1.61*9 -Q. 000<*8

33i».0 257^667 32. 050 1.1.630 -0. 00050

338.0 263.515 32.967 1.1.609 -0. 00051

3W2.0 269.355 33.863 1.1.569 -0. 00052

3^*6.0 275.186 31*. 796 1.1*568 -0. 0 0051. 350.0 281.009 35.708 1.1.51.6 -0. 0 0055

351*.

266.623 36. 616 1. 1.521* -0. 00056

358.0 292*626 37.526 1.1*501 -0. 0 0057

362.0 296*1*21* 36.1*32 1.1*1*78 -0. 0 0056 366.0 301*. 210 39^335 1.1.1*55 -0. 00059

370.0 309.986 1*0.237 1. 1.1.31 -0. 00060

37i»*0 315.755 1*1.136 1.1*1*07 -0. 00061

378.0 321*513 1*2. 031* 1.1.383 -0. 0 0061 382.0 327*261 1*2.929 1.1.356 -0. 00062

386-0 332.999 1*3. 821 1. 1.333 -0. 00063

390.0 336.727 1*1**712 1.1.306 -0. 00063

39f»*0 3'*i*.i»i»5 1*5.600 1.1.282 -0. 0 0061. 398.0 350*153 1*6*1*85 1.1.257 -0. 00061.

78

F-81
METHANE ISOCHORE 11.0 MOL/L METHANE ISOCHORE 12-0 MOL/L

19i«.0 198.0 202.0

206.0 210.0

21<».0 218.0

222.0

226.0

230.0

23i<.0 238.0

2'»2.0

21*6.0 250.0

251*.

238.0

262.0 266.0

270.0

27'».0 278.0

282.0

286.0 290.0

29'*.

298.0 302.0

306.0

310.0

31<».0 318.0

322.0

326.0

330.0

331*.

338.0

31.2.0

3<*6.0 350.0

351*.

35S.0 362.0

366.0 370.0

37i».0 378.0

382.0

386.0

390 .0 39<*.0 398.0

P.BAR

51.588

58.196

6i*.S6t> 71.575 78.322

85.099

91.901 98.725

105.56 7 112.<»2'» 119.295 126.177

133.068 139.967

1<*6.872 153.781

160.69<« 167.608

171*. 52<* 181.'* 1*0 188.355

195.268

202.178 209.085

215.988

222 .886 229.778

236.665

2'.3.5<*5 250 .1*19 257 .28'* 26i..l<»2 270.992 277.832

28<*.66<* 291.1*86 298.298

305.100 311.892

318.673

325.1*1*3 332.202

338.950

31*5.685

352.1*09 359.122

365.821 372.509

379.181*

385.81*6 392.1*96 399.133

OP/DD

0.6<*3

1.1*81 2.362

3.271

i*.203 5.152

6. lie 7.091

8.077

9. 071

10. 072

11. 060 12.093

13. 110

11*. 131

15. 151* 16. 181 17.2B9

18. 238

19. 269

20. 300 21.332

22.361* 23.396

21*. 1.27 25.1*58 26.1.88 27.517

28.51.5 29.571

30.596 31.619

32.61.1 33.660

31.. 678

35.691. 36.787

37. 718

38. 727

39.731. 1.0.738 1.1.739

1.2. 738

1.3.731.

1.1*. 728

1.5.719

1*6.707 1.7.692

1.8.671.

1.9.651. 50.630

51.601.

OP/OT

1.61*26

1.6601* 1.6728 1.6826

1.6907

1.6975 1.7033

1.7083 1.7125

1.7161 1.7192

1. 7217 1.7238 1.7255

1.7268

1. 7278 1.7285

1.7289

1.7290 1.7289

1.7285

1.7279

1.7272

1. 7263 1.7251 1.7239

1.7225 1.7209

1.7192

1.7171* 1.7155

1.7131* 1.7113

1.7090

1.7067

1.701.3 1.7018

1.6992 1.6966

1.6939

1.6911

1.6883

1.6851. 1.6825

1.6795

1.6765

1.6731* 1.6703

1.6672

1.661*0 1.6608 1.6576

02P/DT2

0. 00580

0. 00356

0. 00272

0. 00222

0. 00165 0.00157

0. 00131*

0. 00115

0. 00098 0.00063

0.00070

0. 00056

0. 0 001*7

0. 00037

0. 00029

0. 00021

0. 00013 0.00006

-0. 00000

-0. 00006

-0. 0 0011

-0. 00017

-0. 0 0021

-0. 00026

-0. 00030

-0. 0 0031* -0. 00037

-0. 0001*1 -0. 0 001*1. -0. 0 001.7 -0. 0 0050

-0. 00052

-0. 00055

-0. 00P57

-0. 00059

-0. 00061

-0. 00063

-0. 00065

-0. 00067

-0. 00068 -0.00070

-0. 00071

-0. 00073

-0. 00071* -0. 00075 -0.00076

-0. 00077

-0. 0 0076

-0. 00079

-0. 00080

-0. 00080

-0. 00061

T,K

191*.

198.0 202.0

206.0

210.0

211*.

218.0 222.0

226.0

230.0

231*.

238.0

21*2.0 21*6.0 250.0

251*.

258.0 262.0

266.0

270.0

271*.

278.0

282.0

286.0

290.0

291*.

298.0

302.0

306.0

310.0

311*.

318.0 322.0

326.0

330.0

331*.

338.0

31*2.0

31.6.0 350.0

351..

358.0

362.0 366.0

370.0

371..

378.0

382.0 386.0

390.0

391..

398.0

P.BAR

52.31*6 59.857

67.1*68 75.152

82.891* 90.682

98.511 106.372

111*. 262 122.176

130.110 138.061

11*6.0 26

151*. 00 3 161.989

169.982

177.981

185.98 3 193.988

201.993

209.997

218.000

226.000 233.996

21.1.987 21.9.972 257.951 265.922

273 .886

281.81*0 289.785

297.721

305.61*5 313.559

321.1*61 329.352

337.230

31*5.0 95

352.91.7 360 .786 368.611

376.1.22

381.. 219

392.00

399.766

1.07.521 1.15.258 1.22.979

1.30.685

1.36 .375

1.1*6.01*9 1*53.707

DP/DD

0.951 1.928

2.91*1* 3.987 5.050

6.131

7.226

8. 331

9.i*«*6 10.569

11.698 12.833

13.972

15.111* 16.259

17.1*06 18.555 19.705

20.656

22.007

23.157

21*. 308

25.1*57 26.606

27.751. 28.699

30. 01*1* 31.186

32. 327

33.1*65

31*. 601 35.735

36. 866

37.991.

39. 120

1.0.21.3 1.1.363

1*2.1*80 1*3.591.

1.1*. 705

1.5.813

1.6.917

1.8. 018

1.9. 116 60.210

51. 3T11 52. 386

53.1*72

51*. 553 56.630

66. 703 57.773

OP/DT

1.6610 1.6919

1.9127 1.9287

1.91*17

1. 9521* 1.9615 1.9691

1.9756

1.9811

1.9858

1.9896

1.9928

1.9951* 1.9975

1.9991 2.0002 2.0009

2.0013

2. C013 2.0010

2. 0001* 1.9995

1.9981* 1.9971

1.9955

1.9938 1.9919

1.9898

1.9875

1.9851 1.9625

1.9798

1.9770

1.971*1 1.9711 1.9679

1.961.7 1.9611* 1.9580

1.951*5 1.9510

1.91*71*

1. 91*37 1.9399

1.9361

1.9323

1.9281*

1.921*5 1.9205

1.9165

1. 9121*

D2P/DT2

0. 01021*

0. 00607

0. 001*1*9 0. 00358

0.0 0291*

0. 0021*6

0. 00208 0.00176

0.0011*9

0. 00126

0. 00106

0. 00086

0. 00072

0. 00058

0. 0 001*5 0. 00031.

0. 00023

0. 00013

0. 0 0001. -0. 00001* -0. 00011

-0. 00018

-0. 00025 -0.00031

-0. 00036

-0. 0001.1 -0. 0001.6 -0. 00050

-0. 00055

-0. 00056

-0. 00062

-0. 00066

-0. 00069

-0. 0 0072

-0. 00071. -0. 00077

-0. 00080

-0. 00062

-0. 00081* -0. 00086

-0. 0 0068

-0. 00090

-0. 00091

-0. 00093

-0. 00091* -0. 00095

-0. 00097

-0. 00098

-0. 00099

-0. 00100 -0.00101

-0. 00102

79

F-82
METHANE ISOCHORE 13.0 MOL/L METHANE ISOCHORE lif.O MOL/L

T,K P.BAR DP/DD DP/DT D2P/DT2

19 0.0 '»5.333 0 .675 2.0321 0. 05979

19i».0 53.69'» 1.865 2.1251* 0. 01261

198.

Q

62.280 3. 01*6 2.161*9 0. 00797

202.0 70.997 1*. 253 2. 1923 0. 00591. 206.0 79.810 5.1*77 2.2131* 0. 001.72 210.0 86.699 6.715 2.2305 0. 00386

21i>.D 97.65 0 7.965 2. 21* 1.6 0. 00321

218.0 106.653 9.225 2.2563 0. 00269

222.0 115.698 10.1*93 2.2662 0. 00226

226.0 12i».780 11.767 2. 271*5 0. 00190

230.0 133.892 13. 01.6 2.2815 0. 00159

23<>.0 li»3.033 11*. 329 2. 2873 0. 00133

238.0 152.190 15.616 2.2922 0. 0 0109

2i«2.0 161.367 16.901* 2. 2961 0. 0 0089

2'»6.0 170.557 18.191* 2.2993 0. 0 0070 250.0 179.760 19.1*85 2. 3017 0. 00051.

25<».0 188.971 20.777 2.3036 0. 0 0039

258.

198.18 6 22.068 2. 301*8 0. 0 0025 262.0 207. '09 23.359 2.3056 0. 0 001 3 266.0 216.632 2<*.61.8 2.3059 0. 0 0002 270.0 225.855 25.937 2.3057 -0. 0 0009 27^.0 235.077 27.221. 2.3052 -0. 0 0 018 278.0 21. '.296 28.509 2.301*3 -0. 0 0027 282.0 253.511 29.792 2.3031 -0. 00035

286.0 262.720 31.073 2.3015 -0. 0 0 01.2 290.0 271 .923 32.351 2. 2997 -0. 0 001.9

29'*.281.118 33.627 2.2976 -0. 00055

298.0 290.30'* 31*. 899 2.2953 -0. 00061

302.0 299. '»80 36. 169 2.2928 -0. 0 0066 306.0 308.6<t& 37.1*35 2. 2900 -0. 00071

310.0 317.800 36.698 2. 2871 -0. 00076

31<».0 326.9'»2 39.956 2.2839 -0. 0 0080 318.0 336.071 1*1. 211. 2.2806 -0. 0 0085

322.0 31*5.187 1.2.1.67 2.2772 -0. 0 0068 326.0 351*. 288 1*3. 716 2.2736 -0. 00092

330.0 363.375 1*1*. 961 2.2698 -0. 00095

33<».0 372.1*1*7 1*6. 203 2.2660 -0. 00098

338.0 381.503 1*7.1*1*0 2. 2620 -0. 00101

3i»2.0 390.51*2 1*8.671* 2.2579 -0. 00101.

3<»6.0 399.565 1*9.903 2.2537 -0. 00106

35 0.0 1*08.571 51.126 2.21.91* -0. 00109

35if.0 1*17.560 52. 350 2. 21.50 -0. 00111

358.0 1*26.531 53.567 2. 21.05 -0. 00113

362.0 1*35. 1*8 1* 51*. 780 2.2359 -0. 00115

366.0 1*1*1*. 1*16 55. 986 2.2313 -0. 0 0117 370.0 1*53.331* 57. 193 2.2266 -0. 00118

371..1*62.231 58. 393 2.2219 -0. 00120

37 8.0 1*71.109 59.589 2.2170 -0. 00121

38 2.0 1*79.967 60. 780 2.2122 -0. 00122

386.0 1*88.806 61.967 2. 2073 -0. 00121. 390.0 1*97.625 63.150 2.2023 -0. 00125

39(>.0 506.1*25 61*. 326 2.1973 -0. 00126

398.0 515.201* 65.5B3 2.1922 -0. 00127

T,K P.BAR DP/DD DP/DT D2P/DT2

190.0 1*6.669 2. 152 2. 3821. 0. 02570

191..56.353 3.618 2.1.519 0. 0 126 0 198.0 66.21*9 5. 060 2.1.935 0. 0 0873

202.0 76.267 6.501. 2.521.0 0. 00668

206.0 66.1*33 7.953 2.51.79 0. 00531. 210.0 96.661* 9.1.06 2.5672 0. 001.37

211..

106.966 10.861. 2.5832 0. 00362

218.0 117.326 12. 321* 2.5961. 0. 00301

222.0 127.731. 13. 787 2.6071. 0. 00251

226.0 138.183 15. 251 2.6166 0. 0 0209

230.0 11.6.665 16.716 2.621.2 0. 00172

231*.

159.171. 18.180 2.6301. 0. 0011.1 238.0 169.706 19.61*1. 2.6355 0. 00113

21*2.0 180.257 21.107 2.6395 0. 0 0089

21*6.0 190 .821 22. 568 2.61.26 0. 00067

250.0 201 .397 21.. 027 2.61.1.9 0. 0 001.8

251..211.980 25.1.83 2.61.65 0. 00030

258.0 222.568 26.937 2.61.71. 0. 0 0011. 262.0 233 .156 28.388 2.61.76 0. 0 0000 266.0 21.3.71.8 29.835 2.61.71. -0. 0 0013 270.0 251*. 336 31.280 2.61.66 -0. 0 0025

271*.261.. 921 32.720 2.61.51* -0. 0 0036 278.0 275 .1.99 31*. 156 2.61.38 -0. 0001.6 282.0 286.071 35.589 2.61.18 -0. 0 0055 286.0 296.633 37. 017 2.6391. -0. 00063

290.0 307.186 38.1*1.1 2.6368 -0. 00071

291*.

317.727 39.861 2.6338 -0. 0 0076 293.0 328.256 1.1.276 2.6305 -0. 0 0065 302.0 336 .771 1.2. 687 2.6270 -0. 00091

306.0 31.9.271 1.1.. 092 2.6233 -0. 00096

310.0 359.757 1.5.1.93 2.6193 -0. 00102

311*.

370 .226 1.6. 869 2.6151 -0. 00107

318.0 380 .677 1.8. 281 2. 6108 -0. 00111

322.0 391.111 1.9. 667 2. 6062 -0. 00115

326.0 1.01.527 51. 01.8 2.6015 -0. 00119

330.0 1.11 .921* 52. '21. 2.5967 -0. 00123

331*.1*22.300 53. 795 2.5917 -0. 00126

338.0 1*32.657 55. 161 2.5866 -0. 00130

31*2.0 1*1*2.993 56.521 2.5813 -0. 00133

31*6.0 1*53.308 57.877 2.5760 -0. 00135

350.0 1*63.601 59.227 2.5705 -0. 00138

351*.1*73.871 60.572 2.561.9 -0. 0011.0 358.0 1*81. .120 61.912 2.5593 -0. 0011.2 362.0 1.91.. 31.6 63. 21.6 2.5536 -0. 0 011.1. 366.0 501.. 51.8 61.. 575 2.51.77 -0. 0011.6 370.0 511.. 727 65.899 2.51.I8 -0. 0011.8

371*.521.. 863 67.217 2.5359 -0. 00150

378.0 5 35.011. 68.530 2. 5299 -0. 00151

382.0 51.5.122 69. 838 2. 5238 -0. 00152

386.0 555.205 71.11.1 2.5177 -0. 00151. 39 0.0 565.263 72.1.38 2.5115 -0. 00155

391*.575.297 73.730 2.5053 -0. 00156

398.585.306 75. 016 2.1.990 -0. 00157
METHANE ISOCHORE 15.0 MOL/L METHANE ISOCHORE 16.0 MOL/L

T,K 190.0

isit.a 198.0 202.0

206.0 210.0

21'«.0 218.0

222.0

226.0

230.0

231*. 238.

2<.2, 2'»6, 250,

25'». 258.

262, 266.

27 0, 27i«.0 278.0

232.0 286.0

290.0

29<».0 29 8.0 302.0

306.0 310.0

31<4.a 318.0 322.0

326.0

330.0

33if.O 338.0

3U2.0

3i»6.0 350.0

351*.

358.0 362.0

366.0

370.0

37'«.0 378.0

382.0 386.0

39 0.0

39't.O 398.0

P,8AR

50.016 61.317

72.799

8i».i»17 96.1<»0 1D7.9I»8 119.825

131.759

li»3.7'.0 155.759

167.810 179.885

191.980

20i».090 216.210 228.337

2i*0.i*(,6 252.599

26'.. 728 276.852

288 .969 301.078

313.175

325.260

337.331

3'«9.387 361-<»25

373.ifi»6

385.if'»8 397. 429

i»09.389 '21 .328

'33.2<»3

'1.5.135 1.57.003

1.66. 8<»5

<.eO .663

'.92. '5'. 501*. 216 515.955

527.665

539.31.7 551.000 562.625

57«..220 585.787

597.32'. 608.830 620.307

631.751.

6<»3.170 65I..556 665.910

DP/00

'..768 6.538

8.27'.

9. 995

11. 706

13. '.10 15.108

16.801

18. '.88 20.170

21.8'.7 23.518

25.183

26.81.3 28. '.96 30.1'.'. 31.786

33. '21 35.051

36. 67'^ 38.291

39.901 '1.505

'3.102

''.693

'6.277

'7.855

1.9. '.26 50.991

52.5'^9

51*. 100

55.6^i^ 57. 182

58. 71'^ 60.238 61.756

63. 268

61.. 772 66.27 0 67.762

69.21.7 70.726 72.197

73.662

75.120 76.572

78. 018

79.1.57 80.889 82.316

83.735

85.

86. 556

OP/DT

.7959

.8505

.8890

.9186

.9'.21

. 9612 2.9769

2.9898

3. 000'^ 3.0090

3.0160

3. 0215 3.0258

3.C289

3.0311

3.0323

3. 0328 3.0326 3.0317

3.0303

3.0293

3.0258 3.0229

3.0196 3.0159

3.0118

3.0075

3. 0028 2.9979

2.9928

2.987i^ 2.9818

2.9760

2.9700

2.9638

2.9575 2.9510

2.9'^'^i^ 2.9377 2.9309

2.9239 2.9169

2.9098

2.9026

2.8953

2. 8879 2.8805

2.8730

2. e65'^ 2.8579

2.8502

2.8i^25

2. 83'^8

02P/DT2

0. 0170'^

0. 01118

0. 00833

0. 00655

0. 00528

0. 00'^32 0.00355

0. 00292 0.00239

0. 0019i^

0. 00155

0. 00122

0. 00092

0. 00066

0. 0 00'^2 0. 00022

0. 00003

- 0. 0 0011. -0. 00029

-0. 0001.3 -0. 00056

-0. 00068

-0. 00078

-0. 00088

-0. 00097

-0. 00105 -0.00113

-0. 00120

-0. 00126

-0. 00132

-0. 00138

-0. 0011.3 -0. 0011.7 -0. 00152

-0. 00156

-0. 00160

-0. 00163

-0. 00166

-0. 00169

-0. 00172

-0. 00175

-0. 00177

-0. 00179

-0. 00181

-0. 00163

-0. 00185

-0. 00186 -0.00188

-0. 00189

-0. 00190

-0. 00191

-0. 00192

-0. 00193

T,K 186.0

190.0

19'».0 198.0

202.0 206.0

210.0

21<..0 218.0 222.0

226.0

230 .0 23<..0 238.0

2<.2.0 2'.6.0 250.0

251..

258.0 262.0

266.0

270.0

271..

278.0

28 2.0 286.0

290.0

29'^.a 298.0

302.0

306.0 310.0

31'^.0 318.0

322.0

326.0 330.0

33i^.O 338.0

31.2.0 31.6.0 350.0

35<».0 358.0

362.0 366.0

370.0

37 '.O 378.0

P.BAR

'3.709

56.7I.1 69.971

83.3'^5 96.832

110. '08

12'^.056 137.763

151.516

165.306

179.126

192.968

206.827

220 .697

23'^.572

2'^8.i^51 262.328

276.200

290. 06<. 303.919

317.760

331.587

31.5.397 359.18 8 372.958

386.707

1.00. 1^32 i^l'^.133 1.27.808

''l.'^56 '55.077 '68.668 '82.230

'95.761 509.261

522.730 536.165

5'^9.568 562.937 576.273 589.573

602.839

616. 069 629. 26'^ 61^2. '23

655. 5^6 668.632

681.681

69i^.693

DP/OD

6.830

8.99i^ 11. 085

13. 13i^ 15.15i^ 17.153 19.132

21. 096

23. 01^5 21^.980 26.902

28. 812 30.710

32.597

31^.1.72 36. 337 38.191

1.0.035

1.1.869 '3.693

1^5.507 47.311

i^9.106 50. 891 52.667

51*. 1.31. 56.191

57.939

59.679

61.1.09 63.131

6'^.8i^3 66.51.7

68.21.3 69.930

71.608 73.278

71..939 76.593

78.238

79.871. 81.503

83.123

81^.736 86. 31^0 87.937 89.525

91. 106 92.679

OP/DT

3.2261^ 3.2856

3.3271 3.3588

3. 3837

3.1.037

3.1.199 3.1.329

3.1. 1.33 3.1.516

3.1.580 3.1.628 3.1.662

3.i.68i^

3.i^69'^

3. 1^695 3.1.688

3.1.672

3.1.650

3.1.621 3.1.586

3.1.51.6 3.1.502

3. '.'53

3. '.'.00 3. '.31.3 3.1.283

3.1.220

3.1.151. 3.1.086

3.1.015

3.391.2 3.3867 3.3790

3.3711 3.3630

3.351.9 3.31.65

3. 3381 3.3295

3.3208

3.3120 3.3032

3. 29'*2 3.2852

3.2761 3.2669

3.2577

3.2'^81^

D2P/0T2

0. 0181.2 0.01210

0. 00896

0. 00698

0. 00556

0. OO'.'.O 0. 00362

0. 00292 0.00233

0. 00182 0.00139

0. 00102

0. 00069

0. 0 001.0

0. 00011. -0. 00009

-0. 00029

-0. 0001.8 -0. 00061. -0. 00080

-0. 00093

-0. 00106 -0.00117

-0. 00126 -0.00137

-0.0011.6 -0.00151.

-0. 00161

-0. 00166

-0. 00171. -0.00180

-0. 00185

-0. 00190

-0. 00195

-0. 00199

-0. 00203

-0. 0 0207

-0. 00210 -0.00213

-0. 0 0216

-0. 00218

-0. 00221

-0. 00223 -0.00225

-0. 00227 -0.00226

00230

00231

-0. 00232

81

F-84
METHANE ISOCHORE 17.0 MOL/L METHANE ISOCHORE 18.0 MOL/L

T,K P.BAR DP/OD DP/DT 02P/0T2

182.0 38.199 10.338 3.7669 0. 01560

186.0 53.376 12.913 3. 6185 0. 01077

190.0 68.728 15. 390 3, 8557 0. 00806

19i«.0 8(».210 17.805 3. 881.1 0. 00621. 198.0 99.79 3 20.171 3.9063 0. 0 01.90 202.0 115.<»5'» 22.500 3.9237 0. 00385

206.0 131.177 21.. 796 3.9373 0. 00300

210.0 iit6.9i«e 27. 063 3. 91.79 0. 00231

21<«.0 162.757 29.305 3.9559 0. 00172

218.0 178.593 31.523 3.9618 0. 00122

222.0 19<>.<>'»e 33.719 3.9657 0. 00078

226.0 210.317 35.895 3.9681 0. 0001.1 230.0 226.191 38. 052 3. 9691 0. 0 0008

23't.O 2(>2.06e 1.0.191 3.9688 -0. 00021

238.0 257.91.0 1.2.312 3.9671. -0. 0 001.7 2<»2.0 273.806 1.1.. 1.17 3.9651 -0. 00069

2<fo.O 289.660 1.6.506 3.9619 -0. 00090

250.0 305.500 1.8.580 3.9579 -0. 00108

25l».0 321.323 50.636 3.9533 -0. 0 0125 258.0 337.126 52.682 3.91.80 -0. 0011.0 262.0 352.906 51.. 712 3.91.21 -0. 00153

266.0 368.662 56.729 3.9358 -0. 00165

270.0 381.. 392 58.732 3.9289 -0. 00176

271..<«00.093 60.722 3.9217 -0. 00186

278.0 1.15.765 62.700 3.911.0 -0. 00196

232.0 1.31. 1.05 61.. 661. 3.9060 -0. 0 0 201. 286.0 '.<.7.012 66.617 3.8977 -0. 00212

290.0 <t62.586 68.558 3.8891 -0. 00219

29i>.0 1.78.125 70.1.87 3.8802 -0. 00226

298.0 1.93.627 72.1.81. 3.8711 -0. 00232

392.0 509.093 71.. 310 3. 8617 -0. 00237

306.0 621.. 521 76. 201. 3.8521 -0. 0021.2 310.0 539.910 78.088 3.81.23 -0. 0021.7

31<*.0 555.259 79.960 3.8321. -0. 00251

318.0 570.568 81. 822 3.8223 -0. 00256

322.0 585.837 83.673 3.8120 -0. 0 0 258 326.0 601.061. 85.511. 3. 8016 -0. 00262

330.0 616.21.9 87.31.1. 3.7910 -0. 00265

33<».0 631.392 89. 161. 3.7801. -0. 00268

338.0 61.6.1.92 90.971. 3.7696 -0. 00270

3'»2.0 661.51.9 92. 771. 3.7588 -0. 00272

3i»6.0 676.563 91.. 563 3.71.79 -0. 00271.

35 0.0 691.532 96.31.3 3.7368 -0. 00276

T ,K P.BAR DP/OD OP/OT 02P/DT2

178.0 31. .785 15.922 1.. 1.251 0. 0 1036

182.0 52 .559 18. 8B9 1*. 1.603 0. 00750

186.0 70.1.55 21. 751. 1.. 1.863 0. 0 0561 190.0 88 .1.1. 1 21.. 51.1. 1..5059 0. 0 01.23

191..106.1.96 27.271 I..5206 0. 0 0315

198.0 121.. 60 1 29. 91.7 1.. 5311. 0. 00228

202.0 11.2.71.3 32.577 1..5390 0. 00156

206.0 160 .909 35.167 1.. 61. 1.0 0. 00096

210.0 179.092 37.721 1.. 51.68 0. 0 001.5

211..197.282 1.0. 21.1 1.. 51.78 0. 00001

213.0 215.1.72 1.2. 731 1.. 51.70 -0. 00037

222.0 233.656 1.5. 191 1.. 51.1.9 -0. 0 0070 226.0 251.829 1.7. 6?5 1.. 51.15 -0. 00099

230.0 269.987 50. 031. 1..5371 -0. 00121.

231..288.121. 52.1.18 1..5316 -0. 0 011.7 233.0 306.239 51.. 780 1..5253 -0. 00167

21.2.0 321.. 326 57.119 1..5183 -0. 00185

21.6.0 31.2.381. 59.1.38 1..5106 -0. C 0201

25 0.0 360.1.10 61.737 I..5023 -0. 00215

251..

378. ".OZ 61.. 017 1.. 1.931. -0. 00228

258.0 396.357 66.278 1.. 1.81.0 -0. 0 0 21.0 262.0 1.11.. 273 68.521 It. 1.71.2 -0. 00250

266.0 1.32.150 70.7J.7 1.. 1.61.0 -0. 0 0 260 270 .0 1.1.9.985 72.955 1.. 1.535 -0. 00268

271..

1.67.777 75.11.7 1.. 1.1.26 -0. 00276

278.0 1.85.525 77. 321. 1.. 1.311. -0. 00283

282.0 503.228 79.1.81. 1.. 1.199 -0. 00290

286.0 520.881. 81.630 1.. 1.082 -0. 00296

290.0 538.1.93 83. 760 1.. 3962 -0. 00301

291..

556.051. 85.876 1.. 381.1 -0. 0 0306 298.0 573.566 87.978 1.. 3717 -0. 0 0311

302.0 591.028 90.066 1..3592 -0. 00315

306.0 608.1.39 92. 11.0 1.. 31.65 -0. 00319

310.

625 .800 91.. 201 1..3337 -0. 00322

311..

61.3.109 96. 21.8 1.. 3208 -0. 00325

318.0 660 .366 98.283 1.. 3077 -0. 00328

322.0 677.570 100. 301. 1.. 291.5 -0. 00331

326.0 691.. 722 102.311. i..2ei3 -0. 00333

82

F-85
METHANE ISOCHORE 19.0 MOL/L METHANE ISOCHORE 20.0 MOL/L

T,K

irif.o 178.

182.0

186.0 190.0

19<».0 198.0

202.0

206.0 210.0

Zli*.0 218.

222.0

226.0 230.0

23i».0 238.0

2i»2.0

2'>6.0 250.0

2Si».a 258.0

262.0

266.0

270.0

27i».0 278.0

282.0 286.0

290.0

29<«.0 298.0

302.0

P.BAR

35.388 56.213

77.087 97.993 118.917

139.8<.7 160.775 181.691

202.590

223. 1.6'* 2<«'«.310 265.122

285.897

306.631

327.321

3<»7.965 368.561

389.10 5 '09.597

itSO.OSS

1.50. i»17 <.70.7<»2

i4 91 .009 511.217

531.361. 551. "51

571.<.76 591. '.38 611 .338

6 31.17 3 650. 91.5 670.652 690.295

DP/00

2<».20i« 27.53<. 30.766 33.916

36.999

<.0. 019 '2.985

1.5.900

1.8.770 51.598

51.. 387

57.11.0 59.858

62.51.5 65.201 67.828

70. '26 73.001

75.550

78.07'. 80.575

83.051. 85.511

87.91.7 90.361. 92.760

95. 138

97.1.97 99.838

102.161

101.. 1.68 106.757 109.030

DP/OT 5.198^

5»2132

.2231 .2292

,2322 .2326

.2308

.2271

,2219 .2152

.2071. ,1985 .1887

,1782 ,1669 5.1550

5.11.26

5. 1296 5.1163 5.1025

5.C88I.

5.071.0

5.059'.

5.0'. '.5 5.0293

5.011.0

1..998I. '.9828

'.9669

1^.9510

!. 931^9

It. 9187

'..902't

D2P/DT2

0. OO'^'.l 0. 0 0301.

0. 00197

0. 00111

0. 0001.0 -0. 00019

-0. 00070

-0. 00113

-0. 00150

-0. 00182

-0. 00209

-0. 00231. -0.00255

-0. 00273

-0. 00290

-0. 00301. -0. 00317

-0. 00329

-0. 00339

-0. 0 031.8 -0.00356

-0. 00363

-0. 00370 -0.00376

-0. 00381

-0. 00386

-0. 00390

-0. 00391. -0. 00397

-0. OO'.Ol -0. O0'^03 -0. 00'^06 -0. 00'^08

T,K 170.0

17i».0 178.0

182.0 186.0

190.0

19'..

198.0

202.0

206.0

210.0

21'^.0 218.0

222.0

226.0

230.0

23<^.0 238.0

2'^2.0

2'^6.0 250.0

25i«.a 258.0

262.0

266.0

270.0

27i^.O 278.0

282.0

P,8AR

'2.5'^5 66.852

91.127 115.363 139.553

163.691. 187.780 211.807

235.772

259.672

283.505

307.267

330 .958

351.. 575 378.118

'.01. 58'^

'.2'.. 973

1.1.8.281. 1.71.517

'.9'.. 669

517.7'.2

5'^0.735 563.6i^6 586. '76 609.225

631.892

65'^.'^77 676.979

699. '00

OP/00

35.737 39.397

•2.965

'6. 1^52 '9.866 53.213

56.500

59.730 62.908

66. 038 69. 123 72.165

75.167

78.131

81. 059 83.953

86. 81l^ 89.6115 92. ''S 95.218

97.962

100.681

103. 37i^ 106.0<^3 108.687

111. 309 113.909

116. '86

119.0'^3

OP/DT

6.080i^ 6.0730

6. 061^0 6.0535

6.0'^16 6.0285

6.01'.3

5. 9992 5.9833

5.9667

5. gi.95 5.9317

5.9136

5.8950

5.8761 5.8570

5. 8376 5.6180 5.7982

5.7782

5.7582

5.7380

5. 7177

5.697'. 5.6769

5.6565

5.6360

5.6151.

5.591.8

02P/0T2

-0. 00163

-0. 00205

-0. 002i^5 -0.00281

-0. 00313

-0. 003'^2 -0.00367

-0. 00388

-0. OOi^O? -0. 001^23 -0. 00'^37 -0. 00'^'^9 -0. 00'^59 -0. 00'.68 -0.001.76

-0. 001.82 -0. 001.88 -0.001.93

-0. 00'.97 -0. 00500

-0. 00503 -0.00506

-0. 00508

-0. 00510

-0. 00511

-0. 00512

-0. 00513

-0. 0051'. -0. 00515

83

F-86
METHANE ISOCHORE 21.0 MOL/L HETHANE ISOCHORE 22.0 MOL/L

T,K 160.0

162.0

l(,i*,0 166.0

163.0 170.0

172.0

17<t.O 176.0

178.0

180.0 182.0

IBii.O 186.0

188.0

190.0 192.0

19i«.0 196.0 198.0

200.0

202.0

2ai».0 206.0

208.0

210.0 212.0

21<t.0 216.0

218.0 220.0

222.0

22<>.a 226.0

228.0

230.0

232.0

23<».0 236.0

238.0

2<>a.o 2<»2.0

2<»'».0 2<>6.0

2't8.0 250.0

252.0

25'».0 256.0

258.0

260.0

P.BAR

16.802

31.00 7 1*5.160 59.322

73.<»33 87.515 101.567 115.589

129.582

11.3. 5if6 157. '»81 171.387

185.26'* 199.112

212.931 226.722

2<tO.<»8<> 25i..217 267.922

281.597

295.2i»<» 308.863

322.<t53

336.01<>

3<f9.5i«7 363.052

376.528

389.976

'»03.395

<»16.786

'»30.1't9

<»<»3.it8i» 'f56.791

'»70.070 <t83.322

1.96. 5<»5 509.71.0 522.908

536.0'.9

5<»9.161

562.2'.7 575.30'. 588.335

601.338

611.. 31<. 627.263

61.0.185 653.080

665.91.8 678.789

691.601.

DP/DD

'.'..871 1.6.931 48.966 50.979

52.968

54.936

56.883

58.809

60.715

62.602

64. 471 66.323

68.157

69.975

71.776

73.563

75. 334 77.091 78.834

80.563

82.279

83.982 85.673 87.352

89.019 90.674

92.319

93.952

95.575

97.188 98.790

100.383

101.966

103.540 105.105

106.660 108.207

109.746 111.276

112.797

114. 311 115.817

117.315

118.805

120. 288 121.763

123.231 124.693

126. 147 127.594

129.035

DP/DT 7.1108

7.0945

7,0787 7.0633

7. 0482 7.0333

7. 0185 7.0038 6.9892

6.9747

6. 9602 6.9458

6.9313

6.9169

6.9025

6.8881

6.8738

6.8594

6. 8451 6.8307

6.8164

6.8021

6. 7878 6.7736

6.7593

6.7451

6.7310 6.7168

6.7027

6.6886 6.6745

6.6605

6.6465

6.6325 6.6186

6.6047

6.5908

6.5770 6.5632

6.5495

6.5358

6.5221

6.5084

6.4948

6.4812 6.4677 6.4542

6.4407

6.4273 6.4139

6.4005

D2P/DT2

-0. 00832

-0. 00801

-0.0 or?^

-0. 00762

-0. 00751

-0. 00742

-0. 00736 -0.00731

-0. 00728

-0. 00725

-0. 00723

-0. 00722

-0. 00721

-0. 00720

-0. 00720

-0. 00719 -0.00718 -0.00718

-0. 00717

-0. 00716

-0. 00715 -0.00714

-0. 00713

-0. 00712

-0. 00711 -0.00710

-0. 00708

-0. 00707 -0.00705

-0. 00704

-0. 00702

-0. 00701

-0. 00699

-0. 00697

-0. 00696

-0. 00694

-0. 00692

-0. 00690

-0. 00689

-0. 00687

-0. 00685

-0. 00683

-0. 00681 -0.00680

-0. 00678

-0. 00676 -0.00674

-0.00673

-0. 00671 -0.00669

-0. 00667

T,K 154.0 156.0

158.0

160.0 162.0 164.0

166.0

168.0

170.0 172.0

174.0 176.0

178.0 180.0

182.0

134.0

186.0 183.0

190.0 192.0

194.0

196.0 198.0

200.0

202.0

204.0

206.0

208.0

210.0

212.0

214.0

216.0 218.0

220.0

222.0

224.0 226.0

228.0 230.0

232.0

234.0

236.0

233 .0 240.0

P.BAR

23.671

40.151 56.572

72.935

89.243 105.497

121.696 137.847

153.946 169.996 185.996

201.949

217.854 233.712

249.525

265.291

281 .013 296.691

312 .324 327.914

343.460

358.965 374.426

389.846 405.225

420.562

435.859

451.115 466.332

481.508 496.646

511.744

526.803

541.824

556.807

571.753

586.660

601 .530 616.364

631.160

645.920 660.644

675.331

689.983

OP/DO

61.627

63.836

66. 024 68.192

70.339

72.466 74.572

76.659 78.726

80.775

82. 805

84. 817

86. 811 88.788 90.749

92.693

94.622 96.535

98.433

100.316 102.185

104.041

105.883

107.711

109.527

111.330

113.121

114.900 116.667

118. 423 120.168 121.901 123.624

125.337

127. 039 128.732

130. 414 132.087

133.751 135.405

137.050

138.686

140.314

141.933

OP/OT

8.2554

8.2251 8.1959

8.1677

8.1403 8.1136

8. 0876 8.0620

8. 0370 8.0124

7.9862

7.9644 7.9409

7.9177 7.8947

7.8721

7. 8498 7.8276 7.8057

7.7841

7.7627

7.7414

7.7204 7.6996 7.6789

7.6585

7.6382

7.6181 7.5982 7.5785 7.5589

7.5394

7.5201

7.5010

7.4820

7.4632 7.4444

7.4259 7.4074

7.3891 7.3709

7.3528 7.3349

7.3170

02P/0T2 -0.01548

-0. 01485

-0. 01433

-0. 01389 -0.01351

-0. 01318

-0. 01289

-0. 01263

-0. 01241 -0.81220

-0. 01201

-0. 01184

-0. 01167

-0. 01152

-0. 01138

-0. 01125

-0. 01112 -0.01100

-0. 0 1086 -0.01077

-0. 01067

-0. 01056

-0. 01046

-0. 0 1036

-0. 01027

-0. 01016

-0. 01009 -0.01000

-0. 00992

-0. 00984 -0.00976 -0.00968

-0. 00961 -0.00953

-0.00946 -0.00939

-0. 00932 -0.00926

-0. 00919 -0.00913

-0. 00907

-0. 00901

-0. 00695

-0. 00889

84

F-87
METHANE ISOCHORE 23.0 MOL/L METHANE ISOCHORE 2k. 0 HOL/L

T,K

150.0

152.0

156.0

158.0 163.0 162.0

16i>.0 166.0 168.0

170.0 172.0

17'«.0 176.0

178.0

130.

182.0 Idk.O

186.0

168.0 190.0

192.0

19'».0 196.0 198.0 200.0

202.0

20'*.

206.0

208.0 210.0

212.0

21'».0 216.0

218.0 220.0

222.0

PjBAR

23.128

l»2.20<t 61.190

80 .089

98.90'* 117.63 8 136.293

15«».870 173.372 191.801

210.157

228.'»'ti* 2'«6.66 0 26i».809 282.892

300.908

318 .861

336.7'»9

351*. 576

372.31*1 390 .0i*5 '07.689

1*25.275

'*«t2.803 4.60.273

4*77.687

1*95.01*5 512.3'*e 529.597

51*6.792 563.931* 581.023

598 .061

615.01*7 631.983

61*8.869 665.705

682.1*92 699.230

OP/00

80. 31*6 82.719

85.075

87.1*13 89.732 92.033

91*. 311* 96.577

98. 820 101. 01* I* 103.250

105.1*38 107.607

109.758

111. 892

111*. 009 116.110 118.193

120.261 122.313

121*. 31.9 126. 370 128. 377 130.369

132. 31.7 131.. 311 136.262

138. 199

11*0.123

11*2.035

11.3.931* l'.5.621

11.7.696

11.9.560 151.1.12 153.252

155. 082 156.901

158.710

OP/DT 9.5611 9.5152

9.1.710

'.283 3870

31.69 3079

2698

2326 9.1962

9. 1606 9.1256

9.0911. 9.0577

g. 021.7 8.9921

8.9602 8.9287

8. 8977 8.8672

8. 8371 8.8075

8.7783

8. 71.91. 8.7210 8.6929

8.6552

8.6379 8.6109

8.581.2 8.5578

8.6317

8.5060

8.1.805 8.1.553

8.1.301. 8.1.058

8. 3811* 8.3572

D2P/DT2

-0. 0231*1* -0. 02250

-0. 0 2169 -0.02098

-0.02035

-0.0 1978

-0. 0 1928

-0. 01881

-0. 01839

-0.0 1800 -0.0 1761. -0. 01730

-0.0 1698

-0. 01667

-0. 01639

-0. 01612

-0. 01586 -0.01561

-0. 01537

-0. 01515

-0. 011.93 -0. 0 11*72 -0. 011*51 -0. 011*32 -0. 011.13 -0. 0 1391. -0. 01376

-0. 01359

-0. 0131.3 -0. 01326

-0. 01311

-0. 01295

-0. 01281

-0. 01266

-0. 01252

-0. 01239

-0. 01226

-0. 01213 -0.01201

T,K 136.0

138.0

11.0.0 11.2.0

I'.'i.O I'.&.O

I'.S.O 150.0

152.0

151*.

156.0

158.0

160.0 162.0

161*.

166.0

168.0

170.0 172.0

171..

176.0

178.0 180.0

182.0

131*.

186.0

183.0

190.0

192.0

191*.

196.0

198.0 200.0 202.0

P.BAR

10.1*62 32.552

51*. 517 76.361

98 .087 119.700

l'*l-202 162.596 183.886

205.073

226.160

21*7.11*8 268.01.1 288 .81.0 309.51*7 330.163

350.691 371.131

391.1*86 1.11.757

1.31.91.5 1*52.053

1.72.080 1*92.029 511.900 531.696

551.1*17 571.061. 590.638

610.11.1 629.573

61.8.936 668.231

687.1.58

OP/DO 101.182

103.71.2 106.290

108.821* 111. 31.2 113. 81.3 116. 327 118.792

121.239

123.667

126. 076

128.1.66 130.838

133, 191 135.525

137.81.0

11.0.138

11*2.1.18

11*1*. 680

11*6.925

11*9.152 151. 363 153.558 155.736

157.899

160.01*6 162.177

161*. 291* 166.396

168. 1*61* 170.557

172.617

171*. 663 176.696

10.

10.

10.

OP/OT 11.0771

11.0132

10.9517

10.8922

10. 831*5 10.7781*

10. 7239 10.6708 10.6189

10.5683

.5187

.1*703

.1*228 10.3762

10. 3306 10.2858

10.21.19 10.1987

10. 1563

10.111.7 10.0738

10. 0335 9.9939

9.9550 9.9167

9.8790

9.81*18 9.8053

9.7693

9.7338

9.6988

9.661.3

9.6301* 9.5969

D2P/DT2

-0. 03258

-0.03131*

-0. 03025

-0. 02928

-0. 0281*1 -0. 02763

-0. 02690

-0. 02621* -0.02562

-0. 02501* -0. 021*50 -0. 02399

-0. 02350

-0. 02301* -0. 02260

-0. 02218

-0. 02177 -0.02138

-0.02101

-0. 02061* -0.02029

-0. 01996

-0. 01963

-0. 01931 -0.01901

-0. 01871

-0. 0181*2 -0. 01811* -0. 01787

-0. 01761

-0. 01735

-0. 01711

-0. 0 1687

-0. 01663

METHANE ISOCHORE 25.0 MOL/L METHANE ISOCHORE 26.0 MOL/L

T,K 126.0 128.0

130.0

132.0

131*.

136.0

138.0

11*0.0

11*2.0

li*'*.0 l'*6.0

I'tS.O 150.0 152.0

15'*.

156.0

158.0

160.0

162.0

16<..0 166.0

168.0

170.0

172.3

17'*.

176.0

178.3

183.3 182.0

18'*.0

P.BAR

5.025

30.508 55.832

81.001 106.019

130.890

155.616 180.202

201*. 651 228.965

253.11*6 277.199

301.121*

321*. 926

31*8.605 372.165

395.607

1*18.931*

1*1*2.11*7 1*65.21*9

1.88.21*3 511.129

533.909

556.586 579.162 601.637

621* .011. 61*6.295 668 .1*80 690.572

DP/OD 127.135

129.920

132.696

135.1*61 138.212

11.0.91.8 11.3.667

11.6. 368

11.9. 050 151.712

15i». 355 156.977 159.578

162.159

161.. 720 167.260 169.780 172.279

171.. 759 177.219

179.660

182. 082

181). 1.61* 186.869 169.235

191.583

193.911* 196.227 198.523 200.803

OP/OT 12.7825 12.7015

12.6229

12. 51*61* 12.1*718 12.3990 12.3279

12. 2581* 12.1903

12.1237 12.0583

11.991.3 11.9315

11.6700

11. 8095 11.7502

11.6920

1 1.631.9 11.5788

11.5237

11.1*696

11.1.165

11.361*3 11.3130 11.2625

11.2130

11.161*3

11.1161* 11.0693

11.0230

02P/DT2

-0. 01*113 -0. 03968

-0. 03876

-0. 03775

-0. 03682

-0. 03596 -0.03515

-0. 0 31*1*0 -0. 03368

-0. 03299

-0. 03233

-0. 03170

-0. 03109

-0. 0 3050

-0. 02993 -0.02937

-0.02883

-0. 02830

-0. 02779 -0.02729

-0. 02681

-0. 02631* -0. 02588

-0. 0251*3 -0.021.99

-0. 021.57 -0. 021.15 -0.02375

-0. 02335

-0. 02297

T,K 116.0

118.0

120.0

122.0

121..

126.0 128.0 130.0

132.0

131..

136.0 138.0

11*0.0

11.2.0

11* 1* 11*6

11*3 150 152

151* 156.0

158.0

160.0

162.0

1&<*.0 166.0

P.BAR

10.372

39.669 68.779

97.70 5 126.1*1*9 155.013

183.1*01 211.611. 239.655 267.526

295.231

322.771

350.11.8 377.367

1*01*. 1*29 1*31.336

1.58.092

1.61.. 699 511.159

537.1*75 563.650 589.665

615.583

61*1.31*8 666.980

692.1*83

OP/DD 159.019

162. 123

165. 218

168. 301 171.368

171*. 1*17 177.1*1*7 180.1*55

163.1*1*0 166. 1*02 189. 31.0 192.253

195.11.1 198. 005

200.81.1. 203.657

206.1.1.6 209. 211 211.952

211.. 666 217.361 220.331 222.676

225.302

227.905

230.1.65

DP/OT

111.6956

11.. 6015

11*. 5087

li(. 1*172

11.. 3269

11*. 2378

11*. 11*99

11*. 0633 13.9779 13.8937

13. 6109 13.7292

13.61*69 13.5699

13.1.921

13.1*156

13.31*01* 13.2665

13. 1936

13.1221*

13. 0522 12.9633 12.9155

12. 81*90 12.7836

12.7191*

02P/DT2

-0. 01*739 -0. 01*672 -0. 01*609 -0. 01*51*7 -0. 01*1*85 -0. 01*1*21* -0. 01*363 -0. 01*301 -0. 01*239 -0. 01*176 -0. 01*112 -0. 01*01*8 -0. 03981* -0. 03920

-0. 03856 -0.03792

-0. 03728

-0. 03665

-0. 03602

-0. 0351*0 -0. 031*78 -0. 031*17 -0. 03357

-0. 03296

-0. 0321*0 -0. 03183

85

F-88
HETHftNE ISOCHORE 27.0 MOL/L HETHANE ISOCHORE 27.5 MOL/L

T,K 105.0

106.0 107.

108.0

109.0

110.0 111.0 112.0

113.0

llit.O 115.0

116.0

117.0 118.0

119.0

120.0

121.0

122.0

123.0

i2t>.a 125.0

126.0 127.0

128.0

129.0 130.0

131.0

132.0

133.0

ISit.O 135.0

136.0

137.0 138.0 139.0

li»0.0

litl.O 1<«2.0

li»3.0

li»l».0 l*f5.0

l'«6.0

l'i7.0

l'«8.0

P,BAR

13.613

30 .i»89 i»7.317 6H.095

80 .823 97.501

n't. 129

130 .706

l'»7.231 163.706 180.128

196.1»99 212.818 229.085

2'»5.300 261.1*63

277.57'. 293. 63'* 309.6'«2 325.598

31.1.502 357.356

373.158

388.910

(.Oit.eil 1.20.261 1.35.861

1.51.1.12 1.66.913

1.82.361. 1.97.767 513.121

528.1.26

51.3.681. 556.893

571.. 056 589.171

601.. 21.0 619 .26 3 631.. 239

61.9 .170

661.. 056 678.898

693.691.

DP/DO

195.500

197. 310 199.117 200.919

202.716

201.. 508

206.291. 208.071.

209.81.7 211.613

213.372

215.122 216.866

218.601 220.328

222.01.6 223.756

225.1.58 227.151 228.836

230.512

232.179

233.837

235.1.87 237.128

238.760

21.0.383

21.1.998

21.3. 605

21.5.21)2 21.6.792

21.8.373

21.9.91.5 251.509

253.065

251.. 613

256. 152

257.681. 259.207 260.723

262.231 263.731

265.223

266.708

OP/DT 16.9003

16. 8519 16.6029

16.7531.

16. 7031. 16. 6530 16.6023

16.5512

16.1.999

16.1.1.81. 16. 3967

16. 31. 1.9 16.2930

16. 21.11 16.1891

16.1372

16.0851.

16. 0336 15.9819

15.9301. 15.8791 15.8279

15.7769

15.7261

15.6756 15.6253

15.5753

15.5256

15.1.761

15.1.270 15.3781

15. 3296

15.2811. 15.2336

15.1861 15.1389

15.0921

15.01.57

lit. 9996

II. .9538

III. 9085

111.8635

11.. 8189

11.. 771.6

D2P/DT2

-0. 01.807 -0. 01.870 -0. 01.927 -0. 01.977 -0. 05021

-0. 05059

-0. 05092

-0. 05120

-0. 0511.3 -0. 05161 -0.05175

-0. 05185

-0. 05191

-0. 05193

-0. 05193 -0.05188

-0. 05181 -0.05172

-0. 05159

-0. 0511.1. -0. 05128

-0. 05109

-0. 05088

-0. 05065

-0. 0501.1 -0. 05015

-0. 01.988 -0. 01.959 -0. 01.930 -0. 01.899 -0. 01.868 -0. 01.835 -0. 01.802 -0. 01.768 -0. 01.731. -0. 01.699 -0. 01.663 -0. 01.627 -0. 01.591 -0.01.555

-0. 01.518 -0. 01.1.81 -0. 01.1.1.1. -0. 01.1.06

T,K P.BflR DP/DO OP/DT 02P/0T2

99.0 11.083 211.. 71.5 18.1281 -0. 01.297 100.0 29.190 216.71.8 18. 081.3 -0. 01.1.66 101.0 1.7.251 218.71.5 18. 0388 -0. 01.620 102.0 65.267 220.735 17.9919 -0. 01.760 103.0 83.235 222.718 17.91.37 -0. 01.887

101..101.151. 221.. 692 17.891.2 -0. 05001

105.0 119.023 226.658 17.61.37 -0. 05101. 106.0 136.81.1 228.615 17.7922 -0. 05197

107.0 151.. 607 230. 563 17.7398 -0. 05279

103.0 172.320 232.581 17.6866 -0. 05351

109.0 189.980 231.. 1,28 17.6328 -0. 051.15 110.0 207.585 236.31.6 17.5781. -0. 051.70 111.0 225.136 238. 253 17.5231. -0. 05518

112.0 21.2.632 21.0. 11.9 17.1.680 -0. 05558

113.0 260.072 21.2.035 17.1.123 -0.05592

111..0 277.1.57 21.3.910 17.3562 -0. 05619

115.0 291..785 21.5.773 17.2999 -0. 0561.1 116.0 312.056 21.7.626 17.21.31. -0. 05657

117.0 329.271 21.9.1.68 17.1868 -0. 05668

118.0 31.6.1.30 251.299 17.1301 -0. 05671. 119.0 363 .532 253.118 17.0733 -0. 05676

120.0 380.577 251*. 927 17.0166 -0. 05671. 121.0 397.565 256.725 16.9598 -0. 05668

122.0 1.11.. 1.96 258.511 16.9032 -0. 05659

123.0 1.31.371 260.287 16.81.67 -0. 0561.7

12'..1.1.8.190 262. 052 16.7903 -0. 05631

125.0 1.61.. 952 263.806 16.731.0 -0. 05613

126.0 1.81.658 265.51.9 16.6780 -0. 05592

127.0 1.98.308 267.282 16.6222 -0. 05569

128.0 511.. 902 269.001. 16.5666 -0. 0551.1. 129.0 531.1.1.1 270.716 16.5113 -0. 05517

130.0 51.7.925 272.1.17 16.1.563 -0. 051.88 131.0 561.. 351. 271.. 189 16.1.016 -0. 051.58 132.0 580.728 275.789 16.31.72 -0. 051.26 133.0 597.01.6 277.1.60 16.2931 -0. 05392

131..613.311. 279.121 16. 2393 -0. 05358

135.0 629.527 280.772 16.1859 -0. 05322

136.0 61.5.686 282.I.11. 16.1329 -0. 05285

137.0 661.793 281.. 01.5 16.0802 -0. 0521.8 138.0 677.81.7 285.667 16. 0279 -0. 05210

139.0 693.81.9 287.280 15.9760 -0. 05171

86

F-89
METHANE ISOCHORE 28.0 MOL/L METHANE ISOCHORE 28.5 MOL/L

T,K PjBAR DP/00 OP/OT 02P/0T2

93.0 10.807 23<».663 19.U195 -0. 03101*

9<«.0 30.210 236.926 19.3867 -0. 03't'*8 95.0 i»9.579 239.178 19. 3506 -0. 0 376<* 96.0 68.910 2'.1.1.18 19. 3115 -0. 0'*052 97.0 88.201 2i»3.6«.5 19. 2697 -0. 0'*315 93.0 107. !*!*<) 21*5.860 19.2253 -0. 0'*555 99.0 126.651 21*8.062 19.1786 -0. 01*77'* 100.0 l'»5.80 6 250.250 19. 1299 -0. 0'*971 101.

Q

16<«.910 252. '*2<. 19.0793 -0. 05150

102.0 183.963 251*. 58'* 19.0269 -0. 05312

103.0 202.963 256.729 18.9731 -0. 051*57

lOit.O 221.909 258. 860 18.9178 -0. 05587

105.0 2<»0.798 260.976 18. 861't -0. 05702

106.0 259.631 263.077 18. 8038 -0. 05805

107 .0 278.<»06 265.163 18.7'.53 -0. 05895

108.0 297.122 267.235 18.6860 -0. 05975

109.0 315.778 269.292 18.6259 -0. 0601*3 110.0 33'».373 271. 33'! 18.5651 -0. 06102

111.0 352.908 273. 361 18.5039 -0. 06152

112.0 371.381 275.373 18.^<.21 -0. 06193

113.0 3 89.79 2 277. 371 18. 3800 -0. 06227

ii<».a <»08.1<»1 279. 35<* 18. 3176 -0. 06253

115.0 <»26.<»27 281. 323 18.2550 -0. 06273

116.0 If 'I'*. 650 283.278 18.1922 -0. 06287

117.0 (»62.811 285. 218 18. 1293 -0. 06295

113.0 1*60. <ia<) 287. 1<»5 18. 0663 -0. 06298

119.0 '»98.9'»'4 289.058 18.0033 -0. 06295

120.0 516.916 290.956 17.q<.0i* -0. 06289

121.0 53i».825 292. 8'*2 17.8776 -0. 06278

122.0 552.671 291*. 71<* 17.81<*8 -0. 06263

12 3.0 570.'»5'» 296.572 17.7523 -0. 0621*5

12i«.Q 588.175 298.<*18 17.6900 -0. 06221. 125.0 605.33<t 300.251 17.6278 -0. 06200

126.0 623.<t31 302.071 17.5660 -0. 0 617 3 127.0 &'«0 .966 303.878 17.50'*'* -0. 061'»3 128.0 658.>»itO 305.673 17. <t'*31 -0. 06112

129.0 675.853 307.1.56 17.3822 -0. 06078

130.0 693.205 309.226 17.3216 -0. 0601*2

T,K 96.0

97.0

98.0

99.0 100.0

101.0

102.0

103.0

101*.

105.0

106.0 107.0

108.0

109.0 110.0

111.0

112.0

113.0

llit.O 115.0

116.0

117.0 113.0

119.0

120.0 121.0

P,BAR

198. 1*71 218.926

239.330 259.679

279.972

300.207

320 .381

31*0. 1*93 360.51*2 380.527

1*00. <* 1*5 1*20.297

1*1*0.081 1*59.797

1*79.1*1*1* 1*99.021 518.529

537 .967

557.331* 576.630

595.856 615.012

631*. 096 653.110

672.051* 690.927

OP/OD 277.356

279.785

282. 192

281*. 579

286.91*1* 289.287

291.610 293.912

296.191*

296.1.55 300.696

302.917

305.119

307.301

309.1*61. 311.608

313.731. 315. 81.1 317.930

320. 002 322.056

321.. 093

326. 113

328. 117 330.104

332.075

DP/DT

20.1.801* 20.1*300

20. 3770 20.3216

20.261*1

20. 201*6 20.11*35 20.0808

20.0168

19.9516

19.8853

19. 8181 19.7501 19.6815

19.6123

19.51*27

19.1*727

19.1*02'* 19.3319

19.2613

19.1906 19.1199

19.01*92 18.9787

18.9083

18.8381

D2P/DT2

-0. 01*901 -0. 05176

-0. 051*25 -0. 05650

-0. 05852

-0. 06033

-0. 06191* -0. 06338

-0. 061*65 -0.06577

-0. 06671* -0. 06759

-0. 06831

-0. 06892

-0. 0691*3 -0. 06981* -0. 07016

-0. 0701*0 -0. 07057

-0. 07067

-0. 07070

-0. 07068

-0. 07060

-0. 0701*7 -0.07030

-0. 07008

METHANE ISOCHORE 29.0 MOL/L

T,K 103.0

101*.

105.0 106.0 107.0

108.0

109.0 110.0

111.0

112.0

P,BAR

1*97.378 518.601* 539.753

560.826

581.820 602.737

623.571*

6i»<>.331 665.009

685.607

OP/00

331*. 103 336.527

338. 926

31*1.300

31*3. 6<*9 31.5.971. 31*8.275 350.553 352.809

355.01.2

DP/DT 21.2635

21.1879 21.1112

21.0337 20.9555

20.8767

20. 7971. 20.7177 20.6378

20.5577

02P/DT2

-0. 07507

-0. 87616

-0. 07709

-0. 07788

-0. 07851. -0. 07907

-0. 87950

-0. 07982

-0. 08005

-0. 08019

87

F-90
Table 16

Calculated P(p) isotherms for methane

The following 14 pages give 23 isotherms, calculated from the

equation of state. They serve to show that the analytically derived

values for (8P/9p)t are correct, and that this slope increases monotonically to pressures about twice those existing in the experimental P-p-T

data. Additional columns give derivatives of functions composing the

equation of state, as an aid in trouble- shooting . They show that the

derivatives are consistent with the functions.

88

F-91
METHANE ISOTHERM 90.0 CEG. K

MOL/L

28. 3 28. 28.5

28.6

28. 7 28.8

28.9

29. 0 29.1

29.2

29.3

29.1* 29.5

29.6

29.7

29. 8 29.9 30.0

P,eAR

23. 789

1*8.95 3 7'*. 827

10 l.'»2'» 128.757

156.837

185.677

215.290

2<»5.686 276. 877 308.873

3I» 1.686 375.325 '09.799

i4'»5. 119 481.292

518.327

556.231

DP/DO

2<»8. 135

255. 170 262. 331. 269.626

277. Oi^S 281.. 581, 292. 21.5 300. 023 307.916 315.919

321.. 029

332. 21.1 31.0.552 31.8.956 357. 1.1.9 366. 027

371.. 681. 383. 1.17

XB

0- 006 0.013

0. 019 0.025

0.032

0.038

0. 01.5 0.051 0.057

0. 061. 0.070 0.077

0.083

0.090

0. 096 0.102

0.109

0. 115

DXB/DD

0. 061. 0.061. 0.061.

0.061.

0.061.

0.061.

0.061.

0. 061. 0.061. 0.061.

0.061. 0.061.

0.061.

0.061.

0.061. 0.061.

0.661. 0.063

XC -0.028

-0. 058

-0. 088

-0. 120 -0.153

-0. 186 -0.221

-0. 256

-0. 293

-0. 331

-0. 370

-0. 1.11 -0. 1.53 -0. 1.96 -0.51.0 -0. 586

-0.63'i -0.683

DXC/DD

-0.293 -0.302

-0.311

-0.321

-0.331

-0. 31.1 -0. 352

-0. 363

-0.371. -0.386

-0.398

-0. 1.11 -0. 1.21. -0. 1.38 -0.1.52

-0.1.67

-0.1.82

-0.1.98

XD

-0. 119

-0. 21.8 -0. 382 -0.522 -0.669

-0. 823

-0. 981. -1. 152 -1.328 -1.513

-1.706

-1.909

-2. 122

-2.31.6 -2.580 -2.827

-3.085

-3.357

DXO/DD

-1.257

-1.311. -1.373

-1.1.36 -1.502

-1.571

-1.61.5 -1.722

-1.801. -1.891 -1.982 -2.079

-2.181 -2.289

-2.1.03 -2.521. -2.652

-2.787

XE -0.004

-0. ooe

-0. 012 -0.015

-0.018

-0.020 -0.022

-0. 024 -0.026

-0.027 -0.029

-0.030

-0.030

-0.031 -0.031 -0.032

-0.032 -0.032

OXE/OD

-0.041

-0. 037

-0. 034

-0. 030 -0.027 -0.023

-0.021 -0.018

-0.015

-0.013

-0.011

-0.009

-0.007 -0.005

-0.004

-0.002

-0.001

0. 000

METHANE ISOTHERM 100.0 DEG. K

MOL/L P.BAR OP/00 X8 DXB/DD XC OXC/DD XD DXD/OD XE DXE/DD

27.4 7. 832 210.432 0.002 0. 062 -0. 008 -0.225 -0.031 -0.863 -0. 002 -0.051

27.5 29.190 216.748 0.008 0.062 -0. 031 -0.232 -0. 119 -0.899 -0. 007 -0. 046 27.6 5 1.185 223. 191 0.015 0.062 -0. 054 -0.239 -0.210 -0.936 -0. Oil -0.042

27.7 73.832 229. 763 0.021 0.062 -0. 079 -0. 246 -0.306 -0.975 -0. 015 -0. 038

27. 8 97. 142 236. 463 0.027 0.063 -0. 104 -0.253 -0.405 -1.016 -0. 019 -0. 035 27.9 121.129 243. 292 0.033 0.063 -0. 129 -0. 260 -0.509 -1. 060 -0. 022 -0. 031 28.0 145.805 250. 250 0.040 0. 063 -0. 156 -0.268 -0.617 -1.105 -0. 025 -0. 028 28.1 171.183 257. 336 0.046 0.063 -0. 183 -0. 276 -0.730 -1.153 -0. 028 -0. 025 28.2 197.277 264. 549 0.052 0.063 -0. 211 -0.284 -0.848 -1.204 -0. 030 -0.022 28.3 224.097 271. 889 0.059 0. 064 -0. 240 -0.293 -0.971 -1. 257 -0. 032 -0.019

28.4 251.65 9 279. 354 0.065 0.064 -0. 269 -0.302 -1.100 -1.314 -0. 034 -0. 017 28.5 27 9.97 2 286. 944 0. 071 0. 064 -0. 300 -0.311 -1. 234 -1. 373 -0. 035 -0. 014 26.6 309.051 294. 655 0. 078 0.064 -0. 332 -0.321 -1. 375 -1.436 -0. 037 -0.012

28.7 338.907 302. 486 0. 084 0. 064 -0. 364 -0.331 -1.521 -1.502 -0. 038 -0.010

28.8 36 9.55 2 310. 434 0. 091 0. 064 -0. 398 -0. 341 -1.675 -1.571 -0. 039 -0.008

28.9 400.998 318. 497 0.097 0.064 -0. 432 -0. 352 -1. 836 -1.645 -0. 039 -0. 0O6

29. 0 433.255 326. 671 0.103 0.064 -0. 468 -0. 363 -2.004 -1.722 -0. 040 -0.004

29.466. 336 334. 953 0.110 0.064 -0. 505 -0.374 -2.180 -1.804 -0. 040 -0.003

29.2 500.249 343. 338 0. 116 0.064 -0. 543 -0. 386 -2. 365 -1. 891 -0. 040 -0.002

29.3 53 5.0 07 351. 824 0.123 0.064 -0. 58 2 -0. 398 -2.559 -1.982 -0. 041 -0.000

29.4 57 0.617 360.405 0.129 0.064 -0. 623 -0.411 -2.762 -2.079 -0. 040 0.001 29.5 60 7.091 369. 078 0.136 0.064 -0. 664 -0.424 -2.975 -2.181 -0. 040 0.002 29.6 644.436 377. 837 0.142 0.064 -0. 708 -0.438 -3.198 -2.289 -0. 040 0.003 29.7 68 2.661 386. 677 0.148 0. 064 -0. 752 -0.452 -3.433 -2.403 -0. 040 0.004

METHANE ISOTHERM 110.0 OEG. K

MOL/L

0.1 26.5

26.6

26.7

26.8

26. 9 27.0

27.

27.2

27. 3 27.4

27.5

27.6

27. 7 27.8

27.9 28.0

28.1 28.2

28.3 28.4

28.5

28.6

28.7

28.8

28.9 29.0

29. 1

P.BAR

0.884

2. 572 20.417

38.821 57.796

77.352

97.501

118.257

139.631

161.63 6 184. 28 3 207.585

231.556 256.208

281.552

30 7.603 334.373 361.874

390.120 419.121 448.892 479.444

510.769 542.939

575.905 609.699

644.331 679.813

OP/DD

8.511

175. 698

181. 227

186. 871

192. 631

198. 510

204. 508

210. 628

216. 871 223.237

229. 729

236. 346

243. 089

249. 960

256. 957

264. 082

271. 334

278. 711

286. 215

293. 842

301. 592

309. 464

317. 454

325. 561

333. 782

342. 114

360. 553

359. 096

X8 0.000 0.001

0.006 0.012

0.018

0. 024 0.030 0.036

0.042

0. 049

, 055

, 061

, 067

, 073

. 079

I 086

. 092

,098

0. 105 0.111

0. 117 0.124

0.130 0.137 0.143

0. 149 0.156 0.162

DXB/DD

-0.672

0.059

0.059

0.059

0.060 0.060 0.060

0.061

0.061

0.061 0.062 0.062

0.062 0.062

0.063

0.063

0.063

0.063

0.063

0.064

0. 064 0.064

0.064

0.064

0. 064 0.064

0. 064 0.064

XC

-0. 000 0. 002 •0.020

-0.038

,057

. 076

096

. 116

, 137 159

181

. 204

. 22 8 ,252

I 277

, 302

, 329

, 356

, 384 -0.413

-0. 443

-0. 473 -0.505 -0.538

-0. 571 -0.606

-0.641 -0.678

DXC/DD

2.017

-0. 176 -0.181 -0.186

-0.191

-0.196

-0.202 -0.207

-0.213

-0.219

-0. 225 -0.232

-0.239

-0. 246 -0.253 -0.260

-0.268

-0.276 -0.284

-0.293

-0. 302 -0.311

-0. 321 -0.331

-0.341

-0.352

-0. 363 -0.374

XD 0.000

0. 006

0. 068 0.133

0. 200 0.269 0.342

417

495

577

661

749

841 0.936

-1. 036 1.140

-1. 248 -1.361

-1.479

-1.602

-1. 730

-1. 865 -2.005

-2.152

-2.305

-2.466

-2.635

-2.811

DXD/DO

6.990 -0.611

-0.634

-0.658 -0.683

-0.710

-0.738

. 767

.797 .829

.863

. 899

.936 -0.975

-1. 016 -1.060

-1.105 -1.153

-1.204

-1.257

-1.314

-1.373

-1.436

-1.502

-1.571

-1.645 -1.722

-1. 804

XE -0.000 -0.001

-0.006

-0.011

-0.016

-0.021 -0.025

-0. 028

-0. 032 -0.035

-0. 037 -0.040 -0.042

-0. 044 -0.045

-0.047

-0. 048

-0. 049 -0.049

-0.050

-0.050

-0. 051 -0.051

-0.051

-0.051

-0.050 -0.050

-0. 049

DXE/OD

3.008 -0.059

-0.055

. 050 046 -0.042

-0.038

-0. 035

-0. 031 -0.028

-0.025 -0.022

-0. 020

-0. 017 -0.015 -0.012

-0.010

-0.008

-0. 007 -0.005

-0.003

-0.002 -0.000

0.001

0.002 0.003

0.004

0. 005

89

F-92
METHANE ISOTHERM 120.0 OEG. K

MOL/L

0.1

0.2 25.6 25.7

25.8 25.9

26.0 26.1

26.2

26.3

26. <> 26.5

26.6 26.7

26.8

26.9

27. 0 27.1

27.2

27.3

27. < 27.5

27.6

27.7

27.8 27.9

26. 0 26.1 28.2

28.3

28. i« 28.5

P,BAR

0. 969

1. esi 6.667

21. '.76 36.7i«B 52.512 68.779

85.559

10 2.663 120.701

139.083

158.022

177.529

197.615

218. 291 239.570

261.'»63 283.983

307.11*2 330.952

355.<«26

38 0.577

<»06.<tl6 W2.957

<»60.212

<»88.19<* 516.916

5'»6.389 576.628

eS7.6i>3

639.i»lf8 672.05'.

DP/DD

9. 397

8. 832

1<.5. 509

150. 288

155. 16*

160. litO 165, 218

170.1.00 175. 688

181. 081. 186. 590

192. 209

197. 91.1 203.790

209. 756

215. 81.1 222. 01.6 228. 37'. 231.. 825

21.1. 1.00 21.8. 101

251.. 927

261. 880

268- 959

276. 165

283. 1.98 290. 956

298.51.0 306. 21.9

31'.. OSO

322. 032

3 30. 101.

XB

0. 052 0.002

0.002

0. 007 0.013

0. 019

0. 021* 0. 030 0.036

0. 01.1 0.01.7 0.053

0.059

0. 065

0. 071 0.077 0.063

0.089

0 . 095 0.101 0.107

0. 113 0.119 0.126

0.132

0.138

0. 11.5 0.151

0. 157

0.161. 0.170

0.176

DXB/DD -0.672

-0.399

0.055 0.056

0.056

0.056

0.057

0.057

0.057 0.058

0.058

0. 059 0.059

0.059

0.060

0.060 0.060

0.061 0.061

0.061

0.062

0.062 0.062

0.062

0. 063 0.C63

0.063

0.063 0.063

0.061.

0. 061. 0.061.

XC

-0.1'. I. -0. 001. -0. 005

-0. 019 -0.033

-0. 01.8 •0. 063

-0. 079

-0. 095

-0. 112

-0. 129

-0. 11.6 -0. 161. -0.182

-0. 201 -0.220

-0. 21.0 -0.261

•0. 282

-0. 303

-0. 326

-0. 31.9 -0. 772

-0. 396 0. 1.21 -0.1.1.7 -0.1.73 0.500

•0.529 0.557

0. 587 -0.618

DXC/DD

2.017

1. 012

-0, 11.0 -0. 11.1. -0. 11.7 -0.151

-0.155

-0. 159 -0.163

-0.167

-0.172

-0. 176 -0.181 -0.186

-0.191

-0.196 -0.202

-0.207

-0.213 -0.219 -0.225

-0.232

-0.239

-0.2'.6 -0.253

-0.260 -0.268

-0.276

-0.26'. -0.293

-0.302

-0.311

XO

-0.1.80 -0.011. -0.015

-0. 060 -0.107

-0. 155 -0.206

-0. 258 -0.312

-0.367

-0.1.25

-0.1.85

-0.51.8 -0.612

-0.679

-0.71.9 -0.821 -0.897

-0.975 -1.056

-1. 11.1 -1.229

-1.320

-1.1.16 -1.516 -1.619

-1.727

-1.81.0 -1.956

-2.081

-2. 210

-2. 31.1.

DXD/DO

6.990

3.223

-0.1.1.6 -0.1.61 -0.1.77

-0.1.91. -0.511

-0.530

-0.51.9 -0.569

-0.589

-0.611

-0.631. -0.658 -0.683

-0.710

-0.738

-0.767 -0.797

-0. 829 -0.863

-0.899 -0.936

-0.

-1.

-1. -1.

.975

.016

.060 .105 -1.153

-1.201. -1.257

-1. 311. -1.373

XE -0.181

-0. 007 -0.002

-0. 008

-0.011.

-0. 020

-0. 025

-0. 029

-0.031. -0.037

-0. 01.1 -0. 01.1) -0. 01.7 -0.050

-0.052

-0.051.

-0. 056

-0. 058 -0.059

-C.060

-0.061 -0.062

-0. 062 -0.063

-0.063

-0.063

-0.063

-0. 063 0.062

-0.062 0. 062 -0.061

OXE/00

1.925

1.61.2 -0. 065 -0.061

-0. 056 -0.052

-0. 01.8 -0. 01.1. -0. 01.1 -0. 037

-0.031. -0.031

-0. 028

-0. 025 -0.022

-0.019

-0. 017 -0.015 -0.012

-0.010 -0.008

-0.007

-0.005 -0.003

-0.002 -0.000

0.001 0.002 0.003 0.005

0.006

0. 006

METHftNE ISOTHERM 130.0 OEG. K

MOL/L

0.1

0.2 0.3

21..

2'..

21..

21..

25.0 25.1

25.2

25.3

25.1. 25.5 25.6

25.7

25. 8 25.9

26.0 26.1

26.2

26.3

26.1. 26.5 26.6

26.7 26.8 26.9

27.0

27.

27.2 27.3

27.1. 27.5

27.6 27.7

27.8 27.9

28.0

P,eAR

1.055 2.056

3.006 6.119 17.929

30.11.5

1.2.777 55.832 69.319

S3. 21.6 97.623

112.1.57 127.759

11.3.537 159.802

176. 563 193.830

211. 61<. 229.925

21.8.773 268.170

288.126

308.651.

329.761.

351.1.67 373.777

396.701. 1.20.261

1.1.1.. 1.60

1.6 9. 311.

1.91.. 831. 521.033

51.7.925 575.521

60 3. 835 632.878

662.661. 693.205

DP/DD

10. 271 9.758

9. 21.1. 116. 065

120. 117

121*. 229

128.1.21 132.696

137. 056

11.1. 503

11.6. 038

150. 665

155. 385

160. 200

165. 112

170. 121. 175. 238

180. 1.55 185.778

191. 208

196. 71.9 202. 1.01 208. 167

211.. 01.8 220. 01.6 226. 163

232. 1.01 238. 760

21.5. 21.2 251. 81.8 258. 578

265. 1.35 272.1.17 279. 526

286. 762

29".. 121. 301. 613

309. 226

XB 0.105

0. 051. 0. 020 0.001 0.006

0.011 0.017

0.022

0.027

0.033

0. 038

0. 0'.3 0. 0'.9 0.05'.

0. 060

0. 065 0.071

0. 077 0.082

0. 088

0.091. 0.100

0.105

0.111

0. 117 0.123 0.129

0. 135

0. 11.1 0. 11.7 0. 153 0.160

0. 166 0.172

0.178

0.181. 0.191

Q. 197

DXB/DD

-0.672

-0.399

-0.291. 0.051 0.052

0.052

0.052

0.053

0.053

0.051.

0.05(.

0.05'. 0.055

0.055

0.056 0.056

0.056

0.057

0.057 0.057

0.058 0.058

0.059

0.059

0.059

0.060

0. 060 0.060

0.061

0.061 0.061

0.062

0.062

0.062 0.062 0.063 0.063

0.063

XC -0. 267 -0. 127 -0. 01.5 -0.002

-0. 013 -0.025

-0. 037 -0. 01.9 -0. 061 -0.073

-0. 086

-0. 099 -0. 113 -0.127

-0. 11.1 -0. 155 -0. 170 -0.186

.201 .217 -0. 231. -0. 251 -0.268

-0. 286 -0. 301. -0. 323

31.3 363

383

1.01. 1.26 -0. 1.1.8 -0.1.71 -0. 1.91. -0. 518

-0. 51.3 -0.569

-0. 595

DXC/DD

2. 017 1.012 0.672 -0.110

-0.113

-0.116

-0.118 -0.121

-0.121. -0.127

-0.130 -0.133

-0.137

-0.11.0 -0. 11.1. -0.11.7 -0. 151 -0.155 -0.159

-0. 163 -0.167

-0. 172 -0.176

-0.181

-0.186

-0. 191 -0.196

-0.202

-0. 207

-0. 213

-0. 219 -0.225 -0.232

-0.239

-0. 21.6 -0.253 -0.260

-0. 268

XD -0.853

-0. 387 0.133

-0. 007

-0.01.0 -0.071. -0.109

-0. 11.5 -0.182 0.221

-0.260 0. 301 0. 31.1. 0.388

-0.1.33

-0.1.80 •0.529

.579

.631 .685

.71.1

, 799

. 859

.921

.985

, 053

-1. 122 -1.195

-1.270

-1.31.8

-1. 1.29 -1.511. -1.602

-1.69'.

•1. 789 1.889

1.992

-2. 101

DXO/DD

6.990

3.223 2.029

-0.321. -0.331.

-0.31.5 -0.356

-0.367

-0.379

-0.391

-0.1.01. -0.1.17

-0.1.31

-0.1.1.6 -0.1.61 -0.1.77

-0.1.91. -0.511

-0.530

-0.51.9 -0.569

-0.589

-0.611

-0.631. -0.658 -0.683

-0.710

-0.738

.767

.797 -0.829

-0.863

-0.899

-0.936 -0.975

-1.016

-1. 060 -1.105

XE

0.291. C.176 0.07*

0. 002 0.009

0.015 0.022

0. 027 0.033

0.03S

0.01.2 0.0<»7 0.051

0. 05(t 0.057

0.060

0. 063

0. 066 068

070

071 073

071. 075

076

077

077

078

078

078

078

077

077 076 0.076

0.075

0.071.

0. 071.

OXE/00

1.31.5 1.075 0.997

-0. 073

-0. 069 -0.06*

-0.060 -0.056

-0.052

-0.0*8 -0.0*5

-0.0*1 -0.038

-0.035

-0.031

-0.029

-0. 026 -0.023

-0. 021 -0.018

-0.016

-0. 01* -0.011 -3.C09

-0.008 -0.006

-0.00*

-0. 002 -0.001

0.000 0.002

0.003

0.00*

0.005 0.006

0.007 0.008

0.009

90

F-93
METHANE ISOTHERM UtO.O OEG. K

MOL/L

0.1 0.2

0.3

0.') O.S

0.6 23.6 23.7

23.8 23.9

24.0

2<».l 24. 2 24. 3 24.4

24.5

24.6 24.7

24.8 24.9

25.0

25.1 26.2

25.3 25.4

25.5

25.6

25.7

25. 8 25.9

26. 0 26.1

26.2 26.3

26.4

26.5 26.6

26.7 26.8

26.9

27.0

27.1 27.2

27.3 27.4

P.BflR 1.139

2.229

3.272

4.26 8 5.215 6.114 14.836 24.236

33.977 44.069

54.517

65. 329 76.512

88. 072 100.017

112.355 125.092

138.238

151.799 165.785

180.202

195.061

210.370 226.137

24 2.37 2 259.084

276.283

29 3.97 9 312. 182 330.902 350.148

369.933 390.267

411.161 432.625

454.672

477.314

500.561 524.425

548.920

574.056 599.846

626. 30 3 653.439

681. 267

DP/DD

11. 137

10. 663

10. 193 9.717

9. 234

8. 746

92. 281

95. 685

99. 154 102.688

106. 290 109.961

113.702

117. 515

121. 402

125. 364

129. 403

133. 521

137. 720

142. 002

146. 368

150. 821

155. 363

159. 996 164.721 169.542

174. 459

179. 476 184.594

189. 815

195. 141 200.575

206. 118

211. 772

217. 540

223. 422

229. 421

235. 538 241.775

248. 132 254.613

261. 217

267. 945

274. 798

281. 778

XB 0.157

0.107

0.073

0.046 0.025

0.006 0.004

0.009

0.014 0.019

0.024

0. 028 0.033

0. 0 38 0.043

0.046

0.054 0.059

0. 064

0. 069 0.074

0.060

0.085

0. 090

0. 096

0. 101 0.107

0.112

0.118

0. 123 0.129

0.135

0.141 0.146

0. 152

0. 158 0.164

0.170

0. 176

0. 182

0. 186 0.194

0.200

0.206

0. 212

OXB/DO

-0.672 -0.399

-0. 294 -0.237 -0.199

-0.173

0.047

0.048

0.046 0.046

0. 049 0.049

0.050

0. 050

0. 050 0.051

0. 051 0.052

0.052

0.052 0.053

0.053

0.054 0.054

0.054

0.055

0.055

0.056

0.056

0. 056 0.057

0.057

0.057 0.058

0.058 0.059

0.059

0.059

0.060

0.060

0.060

0.061

0.061

0.061

0.062

XC -0.371

231 149

-0. 092

-0. 047 -0.011 -0.008

-0. 017 -0. 026

-0. 036

-0. 045 -0. 055 -0.065

-0. 075 -0. 085

-0. 096 -0.107

-0. 116 -0.130

-0. 141 -0. 153 -0. 166 -0.178

-0.191

-0. 204

-0. 218 -0.231

-0.246

-0.260

-0.275

-0.290

-0. 306 -0.322

-0. 339 -0. 356

-0. 373 -0. 391 -0.409

-0.428

-0. 447

-0. 467

-0. 488 -0.509

-0.530

-0. 553

OXC/OD

2.017

1.012

0.672

0.500

0. 396

0. 326 -0.088

-0.090

-0. 092

-0. 094 -0.097

-0.099

-0.101 -0.103

-0. 106 -0.108

-0.110 -0.113

-0.116 -0.118

-0. 121 -0.124

-0.127 -0.130

-0.133 -0.137

-0. 140 -0.144 -0.147

-0.151

-0.155

-0.159

-0.163

-0.167 -0.172

-0.176

-0. 181 -0.186

-0. 191

-0. 196

-0. 202 -0.207 -0.213

-0.219

-0.225

XD

-1. 149 -0.683

-0.429 -0.258

-0. 131 -0.031 -0.022

-0.047

-0. 072

-0. 098 -0.125

-0.152

-0.181

-0.210 -0.240

-0.271 -0.303

-0.336

-0.370

-0.405

-0.441

-0.478 -0.517

-0.557

-0.598

-0.640 -0.684

-0.729

-0.776

-0.825

-0.875

-0.927

-0.981 -1.037

-1.095

-1. 155 -1.217

-1.282

-1.349

-1.418

-1.491 -1.566

-1.644 -1.725

-1.810

OXO/OD

6.990

3.223 2.029

1.452

1.115

0.896 -0.242

-0.249

-0.256 -0.264

-0.271

-0.279 -0.288

-0.296

-0.305

-0.315

-0.324 -0.334 -0.345

-0.356

-0.367 -0.379

-3.391 -0.404

-0.417

-0.431

-0.446

-0.461 -0.477

-0.494

-0.511

-0.530 -0.549

-0.569

-0.589

-0.611 -0.634

-0.658

-0.683

-0.710

-0.738

-0.767

-0.797 -0.829

-0.863

XE -0.371 -0.286

.215

.149

. 085 .023

.007

.015 -0.022

-0. 029 -0.035

-0.041 -0.046

-0.051 -0.056

-0. 061 -0.065

-0.069

-0.072

-0.075

-0.078

-0.081 -0.083

-0.065

-0.087

-0.089

-0.090

-0. 092 -0.093

-0.094

-0. 094

-0. 095

-0. 095 -0.095

-0.095

-0.095

-0. 095 -0.095 -0.094

-0.094

-0.093

-0.092

-0.091

-0.090 -0.089

OXE/DD

0.983 0.759

0.678 0.643

0.629 0.631 -0.077

-0.073

-0.069 -0.065

-0.061

-0. 057 -0.053

-0.050

-0.Q46 -0.043

-0.040

-0. 037 -0.034

-0.031

-0. 028 -0.025

-0.023

-0.020

-0.018

-0. 016 -0.Q14

-0.012

-0. 010 -0.008

-0.006 -0.004

-0. 003 -0.001

0.000 0.002

0.003

0.004 0.006

0.007

0. 008 0.009

0. 010 0.010 0.011

METHANE ISOTHERM 150.0 OEG. K

MOL/L

0.2 0.4 0.6

0.8

1.0 22.4

22.6

22.6

23.0 23.2

23.4

23.6

23.8

24. 0 24.2

24.4

24.6

24.8

25. 0 25.2

25.4

25.6 25.8

26.0

26. 2 26.4

26.6 26.8

P.BAR

2.401 4.625

6.672

8.541 10.232

15.461 29.552

44.780

61.190 73.626

97.735

117.965

139.568 162.596

187.104 213.149

24 0.79 2 270.095

30 1.124 333.950

36 8.64 3 40 5.27 9 44 3.93 7 484.699

527.650 572.879

620.477

670.537

DP/00

11.555

10. 679

9. 790

8. 699

3. 012

67. 684

73. 263

79. 058

85. 075

91. 322

97. 608

104. 541 111.532 118.792

126. 333

134. 168

142. 311

150. 776

159. 578

168. 734

178. 258

188. 169

198. 481

209. 211 220.375

231.989

244. 065

256. 617

XB

0. 169 0.099

0. 058 0.028 0.003

0.003

0.012

0.020 0.029

0.038

0.047 0.057

0.066

0.076

0. 086

0. 096

0 .106

0. 116 0.127 0.137 0.146

0.159 0.170

0.161

0.193

0.204 0.216

0. 228

OXB/00 -0.399

-0.237

-0.173

-0.136 -0.114

0.042 0.043

0. 044

0. 045 0.045

0.046

0.047 0.048

0.049

0.050

0.050 0.051 0.052

0.053

0.054

0.054

0.055

0.056

0.057 0.057

0.058 0.059

0.060

XC -0.322

-0. 182

-0. 102

-0. C46 -0.004

-0.005

-0. 019

-0. 034

-0. 049

065 082

099

117 136 -0. 156 -0. 176

-0. 198 -0.220 -0.244 -0.269

-0. 295 -0. 322

351

381 -0. 413

-0. 446

-0. 482

-0. 519

OXC/OD

1.012

0.500

0. 326 0.239

0.186 -0.069

-0.072

-0. 075 -0.078

-0.081

-0.085 -0.086

-0. 092 -0.097 -0.101 -0.106

-0.110 -0.116

-0. 121 -0.127 -0.133

-0. 140 -0.147

-0. 155 -0.163

-0.172

-0.161

-0. 191

XD -0.922

-0.497

-0.270 -0.120

-0.011 -0.013

-0.049

-0.087

-0. 127

-0. 169 -0.214

-0.261

-0. 311 -0.364

-0.420 -0.479

-0.542

-0.609

-0.680

-0.756

-0.837 -0.923

-1. 016

-1. 114 -1.220 1.334

-1.456

-1. 588

OXO/OD

3.223

1.452

0.896

0.629 0.475 -0.175

-0.185 -0.195

-0.206 -0.217

-0.229 -0.242

-0.256

-0.271 -0.288

-0.305 -0.324

-0.345

-0.367

-0.391

-0.417

-0.446

-0.477

-0.511 -0.549

-0.569

-0.634

-0.683

XE -0.362

-0.263

-0.177

-0. 094 -0.010 -0.007

-0.023

-0.037

-0. 050

-0. 062

-0. 072

-0. 081

-0. 089 -0.096

-0.101 -0.106

-0.110 -0.113

-0. 115 -0.116

-0.117

-0.117

-0.116

-0.115

-0.114

-0.112

-0.110

-0.107

OXE/OD

0.557

0.451

0.420

0.414

0.426 -0.085

-O.077

-0.069

-0. 061

-0. 055

-0. 048 042 036 -0.031

-0.026 -0.021 -0.017

-0.012

-0.009

-0.005

-0.002

0.001

0.004

0. 006 0.008

0.010 0.012

0.014

91

F-94
METHftNE ISOTHERM 160.0 DEC. K

MOL/L

0.2

0.<i 0.6 O.S

1.0 1.2

1.1* 21.0 21.2

21.(1 21.6

21.

22.0

22.2

22. I* 22.6

22.8

23.0 23.2

23.it 23.6

23.8

2l«.0

21..

21*. It 24.6

2<«.a 25. 0 25.2

25.'. 25.6

25. 8 26.0

26.2

P.BAR

2.57 3

I.. 979

7.220

9.297 11.209

12.961

1<».556 16.602

26.201

3b. 1*77 '»7.665 59.605

72.935

87.095

102.326

118.670 136.170

1S'».870 17<».816 196.056 218.639

2<f 2.616

268.0'»1

29'*. 970

323. '»61 353.576

385.378

<»18.93'»

'»5<t.313

if9 1.59 0 53 0. ait 1 572. 11*1* 615.583

661.2<»<»

DP /DO

12. 1.39 11.621

10. 791. 9.970

9. 159

8. 363

7. 583

871

1.9. 157 53.628

58. 288

63. 11.2 68. 192

73. '*'*'* 78. 902

8<». 573

90. 1.62 96. 577 102.925

109. 515

116. 357

123. 1.61 130. 838

138. 501

11.6. 1.62 151.. 736

163. 337

172. 279

181. 580

191. 251. 201. 317 211.787 222.678

231.. 006

XB 0.211

0.151

0.111

0.080 0.055

0.031. 0.015

0.001

0. 008 0.016 0.023

0.031

0. 039

0. 01.7 0.056

0.061. 0.073

0. 062

0. 091 0.100 0.109

0.119

0.126 0.138

0. 11.6 0.158 0.169

0. 179 0.190 0.201

0.211

0.223

0.231. 0.21.5

DXB/00 -0.399

-0.237 -0.173

-0.138

-0.111. -0.098

-0.086

0.036

0.037 0.036

0.039

0.01.0

0. 01.0 0.01.1 0.01.2 0.01.3

0.01.1. 0. 01.5

0. 01.5 0.01.6

0.01.7

0.01.6 0.01.9 0.050 0.050

0.051 0.052

0.053

0.051. 0.051. 0.055 0.056

0.057

0.057

XC

.1.01

. 262 -0. 161 -0. 126

-0. 081. -0.050

, 022

. 001 012

. 022

, 031. -0. 01.6 -0.058

-0. 071 -0. C85

,099 .113 -0. 128 -0. 11.1. -0. 161 -0.178 -0.196 -0.215

-0.235

-0.255

-0.277 -0.300

-0.321. -0. 31.8 -0.371. -0.1.02

-0.1.30 -0.1.61 -0.1.92

DXC/DO

1.012 0.500

0.326

0.239

0. 186

0. 151 0.126 -0.052

-0. 051. -0. 056 -0.058

-0.061 -0.063

-0. 066 -0.069

-0. 072

-0. 075

-0. 078 -0.061 -0.065

-0.068 -0.092

-0.097

-0.101 -0.106

-0.110 -0.116

-0.121

-0.127 -0.133

-0. 11.0 -0.11.7 -0.155 -0.163

XO

-1. 117 0.692

0.1.65

•0. 315 -0.206

•0. 122

•0.051. 0.002

0. 028

•0.051. 0.062

•0.111

-0.11.2

•0.171. -0.209

-0.21.5 -0.283

•0.323 0.365

-0.1.09

•0.1.57 •0.506 0.559

0.615

-0.671.

-0. 737

•0.801. •0.875

•0.951

•1. 032 •1.118

•1.211 •1.309

-1.1.15

OXD/OD

3.223

1.1.52 0.896

0.629

0.1.75 0.376

0.307 -0.123 -0.129

-0.136

-0.11.3 -0.150 -0.158

-0.166

-0. 175 -0.185

-0.195

-0.206 -0.217

-0. 229

-0.21.2 -0.256

-0.271 -0.286

-0.305

-0.321. -0. 31.5 -0.367 -0.391

-0.1.17 -0. 1.1.6 -0.1.77 -0.511

-0.51.9

XE

-0. 1.16 -0. 31.3 •0.261

-0.221.

-0. 168 -0.112

-0 . 056 -0.002

-0. 019

-0. 035 -0.050

-0. 061. -0. 076 -0.087

-0. 097

-0. 105 -0.113

-0.120 -0.125

-0.130

-0.131.

•0. 137

-0. 11.0 -0.11.1

-0.11.2 -0.11.3

-0. 11.2 -0.11.2

-0.11.0 -0.136

-0.136

-0.131. -0.131 -0.128

OXE/DD

0. 1.19 328 296

283 276

279 265 -0.092

-0.081. -0. 877 -0.070

-0. 061. -0.058

-0.052

-0. 01.6 -0. 01.1 -0.0 36 -0.031 -0.026 -0.022

-0.018

-0.011. -0.010

-0.006 -0.003

.000 .003

.005

.008

,010 .012

0. Oil. 0.015 0.017

METHftNE ISOTHERM 170.0 DEC.

MOL/L

0.2

0,1* 0.6

0. 8 1.0 1.2

1. <> 1.6 1.8

2.0

2.2

2.1. 19.1. 19.6

19.8

20.0 20.2

20.1. 20.6

20.8

21.0

21.2

21.1. 21.6

21.8

22.0

22.2

22.1. 22.6

22.8

23.0 23.2

23.1* 23.6

23.8 24.0

24.2

24.4

24.6

24.8

25. 0 25.2 25.4

25.6

25.8

P,BAR

2.744

5.330

7.762 10.039

12.164

14.139 15.969

17.656

19.209 20.625

21.910 23.066

24.018

29.566

35.733

42.545

SO. 039 56.248

67.206

76.950

87.515 98.937

111.253

124.501 138.719

153.946

17 0.22 3 187.590 206.069 225.765

246.660

26 8.62 3 292.301

317.143 343.402

371.131 400.388

431.231

463.722 497.926

533.909

571.743 611.502

653.262

697.103

OP/00

13. 317

12. 547 11.772

11. 002

10. 246

9. 510

8. 793

8. 095

7. 415

6. 751

6. 101

5. 462

26. 267

29. 260

32. 416

35. 737

39. 228

42. 890

46. 727

50. 741

54. 936

59. 314 63.879

66.633

73. 581

78. 726

64. 075

69. 630

95. 400

101. 390 107.607

114. 060

120. 757 127.709

134.925

142. 416

150. 199

158. 283

166. 681 175.410

184. 484 193.919

203.731 213.935

224. 547

XB 0.264

0. 203 0.163

0.132

0. 107 0.086

0.068 0.052

0. 037 0.024 0.013

.002

.001

. 007 .013 .019

.025 .032

.039

. 046

. 053 0.060

0.068

, 075

, 063

.091

.100 .106

.116

.125

. 134

.143 0.152

0. 161

.171

,181 .190

.200 .211

.221

.231

.242

.253

.264 0.275

OXB/DO

-0.399

-0. 237 -0.173

-0.138

-0.114

-0.098

-0. 066 -0.076 -0.068

-0.061

-0.055

-0.051

0.D29

0.030

0.031 0.032

0.033 0.034

0.034

0.035

0.036

0.037

0.036 0.039

0.040 0.040

0.041 0.042

0.043 0.044

0.045

0.045

0.046 0.047

0.048 0.049

0.050

0.O50

0.051 0.052

0.053

0.054 0.054

0.055

0.056

XC -0.471 -0.332

-0. 252

,196

, 154

,120

I 093

, 069

OXC/OD

1.012

0.500 0.326

0.239

-0. 049 -0. 032

-0. 016 -0.003

-0. 001 -0.009

-0. 016 -0. 025 -0. 033 -0. 042 -0.051

-0. 061 -0. 071 -0. 082 -0. 093

-0 . 104 -0.116

-0. 128 -0.141

-0.155 -0.169

-0.183

-0. 199

-0. Z14 -0.231

-0.248

-0. 266 -0.285

-0. 305

-0. 326 -0.347

-0.370 -0.394

-0.418

-0.444 -0.472

-0.500

0.186

0.151 0.126

0.108

0.093

0.062 0.072

0. 064 -0.037

-0.036

-0.040

-0. 042 -0.044

-0. 045 -0.047

-0. 049

-0. 052

-0. 054

-0. 056

-0. 058 -0.061

-0. 063

-0. 066 -0.069 -0.072

-0.075

-0. 078

-0. 081

-0. 085

-0. 066

-0. 092

-0. 097 -0.101

-0.106

-0.110 -0.116

-0.121 -0.127

-0.133

-0. 140 -0.147

-0

-0

-0

XO

280 854

627

477

368 284

216 0.160

113

072

037

006 002

019

037

056

075 0.096

118

140 164

190

216 244 0.273 0.304

0. 337 0.371

0.407 0.445

0.485

527

572 619

666

721

777

836

899

966

037 113

194

280 373

DXO/DD

3.223 1.452

0.896

0.629

0.475 0.376

0.307

0.256

0.216

0.188 0.164

0.144 -0.083

-0.087

-0.091

-0. 096 -0.101

-0.106 -0.111

-0.117 -0.123

-0.129

-0.136 -0.143

-0.150 -0.156

-0.166

-0.175 -0.185

-0.195

-0.206 -0.217

-0.229

-0.242

-0.256

-0.271

-0.288

-0.305 -0.324

-0.345

-0.367

-0.391 -0.417

-0.446

-0.477

XE .457

.402

.356

.315

.276 ,236

. 201

.163

.126

.088

.049 .009

,002

.020

.037 ,052

-0. 066 -0.080 -0.092

-0.103

-0.114

. 123

.132

.139

,146 .152

.157 .162 -0.166

-0.169

-0.171

-0.172

-0.173

.174

,173

.173

.171

,170 ,167

. 165 .162

.159

.155 ,151

.147

OXE/00

0.319

0.243

0.214

0.200

0. 192

0. 168 0.186

0.187

0.188 0.192

0.197

0.204 -0.091

-0.085

-0.080

-0. 074 -0.069

-0.064

-0.059

-0.054

-0.050

-0. 045 -0.041

-0. 036 -0.032

-0.028

-0. 024 -0.020 -0.017

-0.013

-0.010 -0.006 -0.003

-0.000

0.003 0.005

0. 008

0. 010 0.012

0.014

0.016 0.017

0.019

0. 020 0.021

92

F-95
METHANE ISOTHERM 180.0 OEG. K

MOL/L P.BAR OP/OD XB OXB/DO xc DXC/DD XD DXO/DD XE DXE/DO

0.5 7.008 13. 098 0.231. -0.199 -0. 35 0 0.396 - 0. 863 1.115 -0.1.28 0. 167 1.0 13.103 11. 299 0. 160 -0.111. -0. 216 0. 186 -0.501. 0.1.75 -0. 355 0-135 1.5 18.326 9.613 0.112 -0.080 -0. 11.3 0.116 -0. 322 0.280 -0.290 0. 126 2.0 22.737 8. 01.9 0.077 -0.061 -0. 091. 0. 082 -0. 208 0.188 -0.228 0. 122 2.5 2 6.39 3 6. 593 0. 050 -0.01.8 -0. 059 0.061 -0.128 0.1 35 -0. 167 0. 122 3.0 29.3<»6 5. 236 0.028 -0.039 -0. 032 0. 01.7 -0. 069 0.102 -0.106 0.123

3.5 3 1.6<«7 3.982 0.010 -0.032 -0. 012 0. 037 -0.025 0.078 -0. 01.1. 0. 126 17.5 36. 125 12. 830 0.006 0.021 -0. 006 -0.021. -0.011. -0. 051 -0.022 -0.076

18.0 1.3.651. 17. 1.20 0. 017 0.023 -0. 019 -0.027 -0. 01.1 -0.058 -0.058 -0. 068 18.5 5 3.681. 22. 81.1 0. 029 0.025 -0. 033 -0.030 -0.072 -0. 066 -0.090 -0.061

19.0 66.61.6 29. 161 0.01.2 0.027 -0. 01.9 -0. 031. -0. 107 -0.075 -0. 119 -0. 053 19.5 8 3. 001. 36. 1.37 0. 056 0.030 -0. 067 -0.038 -0. 11.6 -0.085 -0.11.1. -0. 01.6 20.0 103.250 I.I.. 718 0. 071 0.032 -0. 087 -0. 01.2 -0. 191 -0.096 -0.165 -0.038

20.5 127.897 51.. 01.9 0.088 0.031. -0. 109 -0. 01.6 -0. 21.2 -0.108 -0.182 -0.030

21.0 157. '61 61.. 1.71 0.105 0.036 -0. 133 -0.052 -0.300 -0.123 -0.195 -0.022

21.5 192.558 76. 033 0.121. 0.038 -0. 160 -0.057 -0. 366 -0.139 -0.201. -0.011. 22.0 233.712 88. 788 0. 11.1. 0.01.0 -0. 191 -0.063 -0. 1.1.0 -0.158 -0.209 -0. 007 22.5 281.557 102.811 0.161. 0.01.3 -0. 221. -0.070 -0.521. -0.180 -0.211 -0. 000 23.0 336. 71.9 118. 193 0. 166 0.01.5 -0. 261 -0.078 -0.620 -0.206 -0.209 0.006 23.5 399.998 135. 058 0. 209 0.01.7 -0. 302 -0.087 -0.731 -0.236 -0.205 0.012

2't.O 1.72.080 153. 558 0.233 0.01.9 -0. 31.8 -0. 097 -0.857 -0.271 -0.198 0. 016

2i».5 553.858 173. 876 0.25 8 0.051 -0. 399 -0. 108 -1.003 -0.315 -0. 189 0. 020 25. 0 61.6.295 196. 227 0.281. 0.053 -0. 1.56 -0.121 -1.173 -0.367 -0.178 0.021.

METHANE ISOTHERM 190.0 OEG. K

MOL/L

0.5

1.0 1.5 2.0

2.5

3.0

3.5

1..0 1..5 5.0

5.5 6.0

6.5

7.0 7.5 12.5

13.0

13.5

11..

11..

15.0

15.5

16. 0 16.5

17.0 17.5

18.0

18.5

19.0 19.5

20.0 20.5

21.0 21.5

22.0 22.5

23.0 23.5

21..

21..

P.BAR

7.1.1.7

11.. 032

19.791.

21.. 791. 29.089

32.730 35.767

38.251. 1.0.251 m.818

1.3.017

i»3.906

1.I..536

1.1..952 1.5.190

1.5.112 1.5.333

1.5.817 1.6.669

1.8.017 50.016

52.852

56.71.1 61.937

68.728

77.1.1.2 8 8. 1.1.1 102.123

118.917

139.280

163.691. 192.665 226.722

26 6.1.16 312.321. 365.059

1.25.275

1.93.683 571.061. 658.282

OP/00

11.. 027

12. 327

10. 71.1 9. 277 7.919

6. 661

5. 506

1.. 1.61. 3.51.3

2. 71.6 2. 070

1. 503

1. 033

0. 61.3 0. 321

Q. 231. 0. 675

1. 296

2. 152

3. 291

I.. 768

6. 61.7

8. 991. 11. 881. 15. 390

19. 586

21.. 51.1. 30. 328

36. 999

1.1.. 612

53. 213

62. 81.9 73. 563

85. 1.01. 98.1.33 112. 721. 128. 377

11.5. 515

161.. 291. 181.. 900

XB 0.286

0.212

0.161.

0. 129 0.102

0.080

0. 062

0. 01.8 0. 036 0.027

0.019 0.012

0.007

0.003

0.000 -0.001

0.001 o.oc

0.008

0.012 0.018

0. 021. 0.031

0.039

0.01.8 0.058

0. 069

0. 081

0. 091. 0.108

0.123

0.11.0

0. 157

0. 176

0. 196 0.216

0.238

0.261

0.285

0.310

OXB/OD -0.199

-0.111. -0.080 -0.061

-0.01.8 -0.039 -0.032

-0.026

-0.021

-0.017

-0.011. -0.011

-0.009

-0.007 -0.005

0.003

0.005

0.007 0.008

0.010 0.012 0.C13

0.015 0.017

0.019

0.021 0.023

0.025

0.027

0.030 0.032

0.031. 0.036 0.038

0.01.0 0.01.3

0.01.5

0.01.7 0.01.9 0.051

XC

-0.1.05 -0.272

-0. 198 -0. 150 -0. 115

-0 . 088 -0. 067 -0. 051 -0. 038 -0. 028 -0.019

-0. 013

-0. 007

-0. 003 -0.000

0.001 -0.001

-0.001. -0. 008 -0.013

-0.018

-0. 025

-0. C32 -0. 01.1 -0. 051 -0.062

-0. 075

-0. 089

-0. 105

-0. 123 -0. 11.3 -0.165

-0. 189

-0. 216

-0. 21.6 -0. 28 0 -0.317

-0.358

-0.1.03 -0. 1.51.

DXC/DD

0. 396

0. 186 0.116

0.082

0.061

0. 01.7 0.037

0. 029 0.023 0.019

0.015

0.012 0.009

0. 007 0.005 -0.003

-0.005

-0.007 -0.009

-0.010 -0.012

-0.011. -0.016

-0.019

-0.021

-0. 021. -0. 027 -0.030

-0.031. -0.038

-0. 01.2 -0. 01.6 -0.052

-0. 057

-0. 063

-0. 070

-0. 078 -0.087

-0.097 -0.108

XD -0.978

-0.619

-0.1.37

-0. 323

-0.21.3

-0.181. -0. 11.0 -0.105

-0. 078 -0.057

-0. 039

-0. 026 -0.015

-0.007

-0. 000 0.002

-0.002

-0. 008 -0.016

-0. 025

-0. 037

-0. 050

-0. 066

-0. 081. -0.105

-0. 128 -0.156

-0. 186 -0.222 0.261

-0. 306 0.357

-0.1.15 0.1.81 0.555

•0.639 0.735

0.81.5

•0.972 1.118

DXD/OD

1.115

0.1.75 0.280

0.188 0.135

0.102

0.078

0.061

0.01.8 0.038

0.030

0. 021. 0.019

0.015

0.010 -0.007

-0.010

-0.011. -0.017

-0. 021 -0.025 -0.029

-0.031. -0.039

-0.01.1. -0.051

-0. 058 -0.066

-0. 075 -0.085

-0.096

-0.108 -0.123

-0.139

-0.158

-0.180 -0.206

-0.236

-0.271 -0.315

XE -0.1.67

-0.1.11. -0.369

-0. 328 -0.289

-0.252

-0.216

-0.182

-0.150 -0.120

-0.092 -0.066

-0. 01.3 -0.021

-0. 001 0.008 -0.007

-0.021. -0. 01.3 -0. 062 -0.083

-0.103

-0.12«» -0. 11.1. -0.16<» -0.182

-0.199

-0.215 -0.228

-0.239

-0.21.7 -0.253

-0.255

-0.255

-0.252

-0.21.7 -0.239

-0.229

-0.217

-0.201.

OXE/OD

0.123

0.095 0.085

0.080

0.077

0. 073 0.070

0.066 0.062

058 053

01.9

01.5

01.1 037 -0.032 -0.032 -0.036

-0.038

-0.01.0 -0. JI.1 -0.0^1

-0.01.1

-0.01.0 -0.038

-0.036

-0.033

-0.029

-0.021. -0. 019

-0.011. -0.008 -0.003

0.003

0.008

0.013

0.018 0.022

0.025

0.028
METHANE ISOTHERM 200.0

MOL/L P,8AR OP/DD

0.5 7.885 11.. 91.7 1.0 1'..95 3 13. 337

1.5 21.2'»2 11. 81.1 2. 0 26.81<. 10. 1.63 2.5 31.722 9. 187 3.0 36.016 8. 005

3.5 39. 7<.'. 6. 921

<«. 0 '»2.95'. 5.91.1

l>.5 l»5.703 5. 073

5.0 l»S.0l«6 i». 320 5.5 50.0<<1 3.678

6.0 51.71.1 3. 138 6.5 53.iq<. 2.685

7.0 SI*. '.39 2. 3 07 7.5 55.512 1. 991. e.o 56. 1.1.5 1. 755 e.5 57.283 1.613

q. 0 58.078 1. 589

9.5 5a.ee<. 1. 638

10.0 59.720 1. 709 10.5 60.596 1.800

11.0 51.521. 1. 918 11.5 62.525 2. 105

12. 0 63.652 2. 1.32 12.5 61.. 987 2. 939

13. 0 66.625 3. 61.8 13.5 68. 673 1.. 585

Ik. 0 71.253 5. 782

1<».5 71.. 505 7. 282

15. Q 78.593 9. 136 15.5 83.710 11. 1.03 16. 0 90.076 11.. 11.7 16.5 97.91.8 17.1.36 17.0 107.615 21. 31.0 17.5 119.1.02 25. 928 18.0 133.668 31. 267 18.5 150.805 37.1.22 19.0 17 1.235 1.1.. 1.1.8 19.5 19 5.1.0 7 52. 1.00 20. 0 22 3.79 7 61. 326 20.5 256.903 71. 270 21.0 295.21.1. 82.279

21.5 33 9.36 8 91*. 1.05 22. 0 389.81.6 107. 711 22.5 1.I.7.289 122. 275 23.0 512.31.8 138. 199 23.5 585.735 155. 609

21). 0 66 8.231 171.. 663

OEG. K

XB DXB/DD

0. 338 -0.199

0.261. -0.111. 0.216 -0.080

0.181 -0.061

0. 151. -0.01.8 0.132 -0.039

0.111. -0.032

0.100 -0.026

0.088 -0.021

0. 079 -0.017

0.071 -0. Oil. 0. 065 -0.011

0. 059 -0.009

0. 055 -0.007

0. 052 -0.005

0. 050 -0.003

0. 01.9 -0.001

0. 01.9 -0.000

0. 01.9 -0.000

0. 01.9 0.000

0. 01.9 0.000

0.01.9 0.000

0. 01.9 0.001

0. 050 0.002

0.051 0.003 0.053 0.005

0. 056 0.007

0. 060 0.008

0. 061. 0.010 0.070 0.012

0. 076 0.013

0.083 0.015 0.091 0.017

O.IOD 0.019

0.110 0.021 0.121 0.023 0.133 0.025

0 . 11.6 0.027

0. 160 0.030 0.175 0.032

0. 192 0.031.

0. 209 0.036 0.228 0.038

0.21.8 0. 01.0 0.269 0.01.3 0.290 0.01.5 0.313 0.01.7

0. 337 0.01.9

XC DXC/DO

-0. 1.56 0.396 -0.322 0.186

-0.21.9 0.116 -0.200 0.082 -0.165 0.061

-0. 138 0. 01.7 -0.118 0.037 -0.101 0.029 -0.C88 0.023 -0.078 0.019 -0.070 0.015 -0.063 0.012 -0.058 0.009 -0.053 0.007 -0.050 0.005

-0 . 01.8 0. 003

-0. 01.7 0. 001

-0. 01.7 0. 000

-0. 01.7 0. 000

-0. 01.7 0. 000

-0.01.7 -0.000

-0.01.7 -0.000

-0.01.7 -0.001

-0.01.8 -0.002

-0.01.9 -0.003

-0.051 -0.005

-0. 051. -0. 007 -0.C58 -0.009

-0.06 3 -0.010 -0.068 -0.012

-0. 075 -0. 011. -0.082 -0.016

-0.091 -0.019

-0.101 -0.021

-0.112 -0.021. -0.125 -0.027

-0.139 -0.030

-0. 155 -0. 031. -0.173 -0.038

-0.193 -0.01.2 -0.215 -0.01.6 -0.239 -0.052

-0.266 -0.057

-0.296 -0.063

-0.330 -0.070

-0.367 -0.078

-0 . 1.08 -0. 087

-0.1.5'. -0.097

XD DXO/DO -1.076 1.115 -0.717 0.1.75 -0.536 0.280

-0.ii21 0.188

-0.3'»1 0.135 -0.283 0.102 -0.238 0.078 -0.203 0.061 -0.176 0.01.8 -0.155 0.038

-0. 138 0.030

-0.121. 0.021. -0.113 0.019

-0. 105 0.015

-0. 098 0. 010

-0. 091. 0.006 -0.092 0.002 -0.092 0.000

-0- 092 0.000 -0.092 0.000 -0.092 -0.000 -0.092 -0.000 -0.092 -0.001

-0. 093 -0.001. -0.096 -0.007

-0.100 -0.010

-0.106 -0.011. -0. ll«t -0.017

-0. 121. -0. 021 -0.135 -0.025

-0. 11.8 -0.029

-0.161. -0.031. -0. 182 -0.039

-0.203 -0.01.1. -0.227 -0.051

-0.251. -0.058 -0.285 -0.066

-0. 320 -0.075 -0.359 -0.085

-0.1.01. -0.096

-0.1.55 -0.108 -0.513 -0.123

-0.579 -0.139

-0.653 -0.158

-0.737 -0.180 -0.833 -0.206

-0.91.'. -0.236

-1. 070 -0.271

XE OXE/OD

-0.1.97 0.089

-0.1.60 0.065

-0.1.30 0.056

-0.1.03 0.051 -0.379 0.01.7 -0.356 O.Qi.'. -0. 335 0. 01.1 -0.315 0.037 -0.298 0.033 -0,282 0.029 -0.269 0.025 -0.257 0.022

-0.21.7 0.018 -0.239 0.011. -0.233 0.010 -0.229 0.005 -0.228 0.000 -0.228 -0.002 -0.229 -0.001

-0. 229 0.000 -0.229 0.001 -0.228 0.002 -0.227 0. 001 -0.227 -0.001 -0.228 -0. 005

-0. 232 -0.008 -0.236 -0.011

-0.21.2 -0.013

-0.21.9 -0.015 -0.256 -0. 016

-0.261. -0.016 -0.273 -0. 016 -0.281 -0. 016 -0.288 -0. 015 -0.295 -0. 013 -0.301 -0.011 -0.306 -0. 008

-0. 309 -0.005 -0.310 -0.001 -0.310 0.003 -0.307 o.ooe -0.302 0.012 -0.295 0.016 -0.286 0. 020 -0.275 0.021. -0.263 0.027

-0.21.8 0.030 -0.233 0. 032

94

F-97
METM4NE ISOTHERM 210.0

MOL/L P.BAR OP/DO

0.5 8.322 15. 862

1.0 15.867 Ih. 335 1.5 22.676 12. 919

2.0 28.806 11. 620 2.5 Si*. 312 10. ".18 3.0 39.239 9. 305 3.5 <.3.632 8. 281.

0 <»7.539 7. 360

'•.5 51.010 6. 51.2 5.0 5'.. 100 5. 8 33 5.5 5 6.861 5. 229

6.0 5 9.3i«5 '..721. 6.5 6 1.599 (.. 30<. 7.0 6 3.66 2 3. 959

7.5 65.569 3. 683

8.0 6 7.35 7 3. '.86 e.5 69.073 3. 398 9.0 7 0.778 3. '.<.(. 9.5 72.531 3. 577 10.0 7 361 3. 7'.8 10.5 76.285 3. 95<. 11.0 78.322 1.. 203 11.5 80.503 '..51.3 12. 0 82.89i< 5. 050 12.5 85.589 5. 767 13.0 88.699 6. 715 13.5 92.31.6 7. 917

i<«.a 96.66<< 9. <.06

I'..

10 1.807 11. 221 15.0 10 7.91.8 13. 1.10 15.5 115.288 16. 027 16.0 12 '..056 19. 132 16.5 13<..512 22. 789 17.0 11.6. 9<»8 27. 063 17.5 161.689 32. 019 le.o 179.092 37. 721 18.5 199. 5^5 <.<.. 229 19.0 22 3.1.6<. 51. 598 19.5 251.2 9 5 59. 980 20.0 283.505 69. 123 20.5 320.585 79. 372 21.0 36 3.05 2 90. 67*. 21.5 <.l 1. <«<.<• 103. 085

22. 0 1.66. 332 116. 667 22.5 528.320 131. 503 23.0 598.061 1<.7. 696 23.5 676.261. 165. 376

OEG. K

XB OXB/DO

0.390 -0.199

0.316 -O.!!!. 0.268 -0.080

0.233 -0.061

0. 206 -O.0'.8

O.ie". -0.039

0.166 -0.D32

0.152 -0.026

O.litO -0.021

0.131 -0.017

0.123 -0.011. 0.116 -0.011

0.111 -0.009

0.107 -0.007 O.IC -0.005

0.102 -0.003

0.101 -0.001

0.101 -0.000

O.iCl -0.000

0.101 0.000 0.101 0.000 0.101 0.000 0.101 0.001 0.102 0.002 0.103 0.003 0.105 0.005 0.108 0.007 0.112 0.008 0.116 0.010 0.122 0.012 0.128 0.013 0.135 0.015

0.11.3 0.017 0.152 0.019

0.162 0.021 0.173 0.023 0.185 0.025 0.198 0.027 0.212 0.030 0.227 0.032

0.2'.'. 0.031. 0.261 0.036 0.280 0.038

0 . 300 0. 01.0 0. 320 0. 0'.3 0.31.2 0.01.5

0. 365 0.01.7

XC DXC/DC -0.501 0.396 -0.367 0.186

-0.29<. 0.116

-0.21.5 0. 082 -0.210 0.061

-0.181. 0.01.7 -0.163 0.037

-0 . 11.7 0. 029

-0.131. 0.023 -0.123 0.019 -0.115 0.015 -0.108 0.012 -0.103 0.009 -0.099 0.007 -0.096 0.005

-0.09'. 0.003 -0.093 0.001 -0.092 0.000 -0.092 0.000 -0.092 O.OOO -0.092 -0.000

-0.092 -0.000

-0.093 -0.001

-0.C93 -0.002

-0.095 -0.003

-0.097 -0.005

-0.100 -0.007

-0.103 -0.009

-0.108 -0.010

-0.111. -0.012

-0.120 -0.011. -0.128 -0.016

-0.137 -0.019

-0.11.6 -0.021

-0. 158 -0. 021. -0.170 -0.027 -0.185 -0.030

-0. 200 -0. 031. -0.218 -0.038

-0. 238 -0. 01.2 -0. 260 -0. 01.6 -0.285 -0.052

-0.312 -0.057

-0.31.2 -0.063

-0.375 -0.070

-0.1.12 -0.078

-0. 1.53 -0. 087

XD DXO/DO -1.160 1. 115 -0.802 0.1.75 -0.620 0.280 -0.505 0.188

-0. 1.26 0.135

-0. 367 0.102 -0.322 0.078

-0. 288 0.061 -0.261 0. 01.8 -0.239 0.038

-0. 222 0.030

-0. 208 0.021. -0. 198 0.019 -0.189 0.015 -0.183 0.010

-0. 179 0. 006

-0. 177 0.002 -0.176 0.000

-0. 176 0.000 -0.176 0.000

-0. 176 -0.000

-0. 176 -0.000

-0. 177 -0.001

-0. 178 -0.001. -0. 180 -0.007 -0.185 -0.010

-0. 191 -0.011. -0. 199 -0.017 -0.208 -0.021 -0.219 -0.025 -0.233 -0.029

-0. 21.8 -0.031. -0.266 -0.039

-0.287 -0. 01.1. -0.311 -0.051

-0. 338 -0.058

-0. 369 -0.066

-0.1.01. -0.075

-0 .1.1.1. -0.085

-0.1.89 -0.096

-0.51.0 -0. 108 -0.598 -0.123 -0.663 -0.139

-0.737 -0.158

-0.822 -0.180

-0.918 -0.206

-1. 028 -0.236

XE DXE/DD

-0.520 0.063

-0.1.95 0. 01.2 -0.ii77 0. 031. -0.1.61 0.030

-0.1.1.7 0.027

-0.1.31. 0. 021. -0.1.23 0.021

-0. 1.13 0. 019

-0.1.01. 0.016 -0.397 0. Oil. -0.390 0.011 -0.385 0.009

-0. 381 0.008 -0.378 0. 006 -0.375 O.OOi. -0. 371. 0.001

-0. 371. -0.001

-0. 375 -0.002 -0.376 -0.001

-0. 376 0.000

-C. 376 0.001 -0.375 0.002

-0. 371. 0. 003 -0.373 0.002 -0.372 O.OOC -0.372 -0.001

-0. 373 -0.002

-0.371. -0.003 -0.375 -0.003

-0.377 -0.003

-0.378 -0.003

-0.379 -0. 0O2 -0.380 -0.001 -0.380 0.000 -0.380 0.002 -0.378 0.001. -0.375 O.0O7

-0. 371 0. 010 -0.366 0.013 -0.359 0.016

-0. 350 0.019

-0. 339 0.023 -0.327 0.026 -0.313 0.029 -0.298 0.032 -0.281 0.031. -0.261. 0.036

95

F-98
METHANE ISOTHERM 220

MOL/L P,BAR OP/DO

0.5 8.757 16.771

1.0 16.777 15.322

1.5 21.. 098 13. 982

2.0 30.778 12.756

2.5 36.869 11.623

3.0 l»2.'»15 10.576

3.5 '»7.<.60 9. 615

<.. 0 52.0'f6 8.7'.8

i4.5 56.22'« 7.982

5. 0 50.0<»6 7. 321

5.5 63.562 6.763

6.0 66.825 6.302

6.5 69.878 5.926

7.0 72.765 5.631

7.5 75.521 5.408

8.0 78.187 5.271

8.5 80.812 5.25'> 9.0 83.465 5.382

9.5 86.211 5.611

10.0 89.084 5.890

10.5 92.109 6.217

11.0 95.310 6.602

11.5 98.729 7.096

12.0 102.438 7.777

12.5 106.544 8.690

13.0 111.170 9.858

13.5 116.448 11.303

1<».0 122.524 13. 056 14.5 129.562 15.155

15.0 137.744 17.645

15.5 147.281 20.580

16.0 158.407 24.014

16.5 171.388 28.008

17.0 186.519 32.624

17.5 204.125 37.923

18.0 224.565 43.965

18.5 248.223 50.807

19.0 275.514 58.503

19.5 306.877 67.103

20.0 342.776 76.653

20.5 383.697 87.200

21.0 430.149 98.790

21.5 482.670 111.481

22.0 541.824 125.337

22.5 608.215 140.442

23.0 682.492 156.901

xs DXe/DO

0.442 -0.199

0. 367 -0.114

0. 319 -0.080 0.284 -0.061

0.257 -0.048

0.236 -0.039

0.218 -0.032

0.204 -0.026

0.192 -0.021

0. 182 -0.017

0.174 -0.014

0. 168 -0.011

0. 163 -0.009

0.159 -0.007

0. 156 -0.005

0.154 -0.003

0.153 -0.001

0.152 -0.000

0. 152 -0.000

0.152 0.000 0.152 0.000 0.152 0.000 0-153 0.001

0. 153 0.002

0.155 0.003 0.157 0.005 0.160 0.007 0.163 0.008

0. 168 0.010

0. 173 0.012 0.179 0.013 0.187 0.015 0.194 0.017 0.203 0.019 0.213 0.021 0.224 0.023 0.236 0.025 0.250 0.027 0.264 0.030

0. 279 0.032

0. 295 0.034 0.313 0.036 0.332 0.038

0. 351 0.040

0. 372 0.043

0. 394 0.045

XC DXC/DO

-0.542 0.396 -0.408 0.186 -0.335 0.116 -0.287 0.082 -0.251 0.061 -0.225 0.047 -0.204 0.037 -0.188 0.029 -0.175 0.023 -0.165 0.019 -0.156 0-015 -0.150 0.012 -0.144 0.009 -0.140 0.007 -0.137 0-005 -0.135 0.003 -0.134 0.001 -0.134 0.000 -0-134 0-000 -0.134 0.000 -0.134 -0.000

-0.134 -0.000

-0.134 -O.OCl

-0.134 -0.002

-0.136 -0.003

-0.138 -0.005

-0.141 -0.007

-0.145 -0.009

-0.149 -0.010

-0.155 -0-012

-0.162 -0.014 -0.169 -0.016

-0.178 -0.019

-0.188 -0.021

-0.199 -0.024 -0.212 -0.027

-0.226 -0-030

-0.242 -0.034

-0.260 -0.038

-0.279 -0.042

-0-301 -0-046

-0.326 -0.052

-0.353 -0.057

-0.383 -0.063

-0.416 -0-070

-0.453 -0.078

XO DXD/OD -1-234 1-115 -0.875 0.475 -0.693 0.280 -0.579 0-188 -0.499 0.135 -0.440 0.102

-0. 396 0.078

-0. 361 0.061 -0.334 0.048

-0. 312 0.038 -0-295 0-030

-0. 282 0.024

-0. 271 0.019 -0.262 0.015 -0-256 0-010 -0.252 0.006 -0.250 0.002 -0.249 0.000 -0.249 0.000 -0.249 O.OOD

-0. 249 -0.000 -0.249 -0-000

-0.250 -0.001

-0. 251 -0.004 -0.254 -0.007

-0-258 -0-010 -0.264 -0. 014 -0.272 -0.017

-0.281 -0.021 -0.293 -0.025 -0.306 -0.029

-0. 322 -0. 034

-0. 340 -0-039

-0. 360 -0.044 -0.384 -0.051 -0.411 -0.058

-0-442 -0-066

-0.477 -0.075

-0.517 -0.085 -0.562 -0.096 -0-613 -0-108 -0.671 -0.123

-0.736 -0.139 -0.811 -0.158

-0-895 -0.180 -0.991 -0.206

XE DXE/OC

-0. 540 0.042 -0.524 0.024 -0.514 0.017

-0 .506 0.014 -0.500 0.011 -0.495 0.009 -0.491 0-008 -0.487 0.006 -0.485 0.004 -0.483 0.003 -0-481 0.002 -0.480 0.002 -0.480 0.001 -0.479 0.001 -0-479 -0.000 -0.479 -0.001 -0.480 -0.002 -0.482 -0.002 -0.482 -O.BOl

-0.482 0.000 -0.482 0.001 -0-482 0-002 -0.480 0.003 -0.478 0.003 -0.477 0.003 -0-475 0.003 -0.473 0.003 -0.472 0.004 -0.469 0.005 -0.467 0. 006 -0.464 0.007 -0.460 0.008 -0-456 0-009 -0.451 0.011 -0.445 0.013 -0.438 0.015 -0-430 0.018 -0.420 0.020 -0.409 0.023 -0.397 0.026 -0.383 0.029

-0. 368 0.031

-0. 352 0.034 -0.335 0.036

-0. 316 0.038 -0.296 0.040

96

F-99
METHSNE ISOTHERM 2i«0.0

MOL/L OP/OD

0.5 9.62<. 18. 579

1.0 1 8. 581. 17. 271. 1.5 26.916 16. 071. 2.0 31.. 677 11.. 983

2.5 1.1.915 13. 982

3. 0 1.8.672 13. 060 3.5 51.. 988 12. 219

1.. 0 60.905 11. 1.66

l*.S 66.1.70 10. 810

5.0 71.733 10. 257

5.5 76.71.1. 9. 807

6.0 81.556 9. 1.56 6.5 86.216 9. 196 7.0 90.767 9. 022 7.5 95.251 8. 932

a.o 99.715 8. 91.2 6.5 10 1.. 216 9. 089 9.0 106.633 9. 1.03 9.5 11 3.61.0 9. 839

10.0 11 8.683 10. 31.6 10.5 12 3.998 10. 921. 11.0 129.621 11. 586 11.5 135.606 12. 381. 12.0 11.2. 01.2 13. 1.02 12.5 11.9. 052 11.. 686 13.0 156.776 16. 260 13.5 165.361. 18. 11.6

ll». 0 171.. 980 20. 376

ll».5 185. 803 22. 981. 15.0 19 8.033 26. 0 13 15.5 21 1.895 29. 511. 16. 0 22 7. 631. 33. 536 16.5 21.5.526 38. 135

17. 0 26 5.871. 1.3. 367 17.5 269.008 1.9. 288 le.o 31 5.286 55. 952 18.5 31.5.09 3 63. 1.12 19.0 37 8. 839 71. 718 19.5 1.16.959 80. 915 20.0 1.59. 910 91. 01.9 20.5 50 8. 172 102. 161. 21.0 56 2.21.7 111.. 311 21.5 62 2.661. 127. 51.1. 22.0 689.983 11.1. 933

DEG. K

XB OXB/OD

0. 51.^ -0. 199

0. 1.70 -0.111.

0. 1.22 -0.060

0 . 387 -0.061

0 . 360 -0.01.8

0. 338 -0. 039

0. 321 -0.032

0. 306 -0.026

0. 295 -0.021

0 .285 -0.017

0. 27/ -0.011.

0. 271 - C. Oil

0 . 266 -0.009

0. 262 -0.007

0. 259 -0.005

0 . 257 -0.003

0. 256 -0.001

0. 255 -0.000

0 . 255 -0.000

0. 255 0.000

0 . 255 0.000

0. 255 0.000

0 . 255 0.001

Q. 256 0.002

0. 257 0.003

0 . 259 0.005

0. 262 0.O07

0. 266 0.008

0. 27 1 0.010

0. 276 0.012

0. 282 0.013

0. 269 0.015

0. 297 0.017

0. 306 0.019

0. 316 0.021

0. 327 0.023

0. 339 0. 025

0. 352 0.027

0 . 366 0.030

0. 362 0.032

0 . 398 0.031.

0. 1.16 0.0 36

0 . 1.31. 0.038

0. 1.51. 0. 01.0

XC DXC/OD

-0.611. 0.396

-0.1.81 0.186

-C. 1.07 0 . 116 -0.359 0.082

-0. 321. 0. 06 1 -0. 297 0. 01.7 -0.276 0.037 -0.260 0.029

-0. 21.7 0. 023 -0.237 0.019 -0.228 0.015 -0.222 0.012 -0.216 0.009 -0.212 0.007 -0.209 0.005 -0.207 0.003 -C.206 0.001 -0.206 0.000 -0.206 0.000 -0.206 0.000 -0.206 -0.000

-0.206 -0.000 -0.206 -0.001

-0.207 -0.002

-0.208 -0.003

-0.210 -0.005

-0.213 -0.007

-0.217 -0.009

-0.222 -0.010

-0.227 -0.012

-0.231. -0.011.

-0.21.1 -0.016

-0.25 0 -0.019

-0.260 -0.021

-0. 271 -0. 021. -0. 281. -0. 027 -0.298 -0.030

-0.311. -0.031. -0.332 -0.038

-0. 352 -0. 01.2 -0.371. -0.01.6 -0.398 -0.052

-0.1.25 -0. 057

-0 . 1.55 -0. 063

XD DXD/DD

-1. 353 1.115 -0.995 0.1.75 -0.813 0.280 -0.699 0.186 -0.619 0.135 -0.560 0.102 -0.515 0. 076

-0.1.81 0.061

-0.1.51. 0. 01.8 -0.1.32 0.038

-0.1.15 0.030

- 0. 1.01 0.021. -0. 391 0.019

-0. 382 0.015

-0. 376 0.010

-0. 372 0. 006 -0.370 0.002

-0. 369 0.000 -0.369 0.000

-0. 369 0.000

-0. 369 -0.000 -0.369 -0.000

-0.370 -0.001

-0. 371 -0.001. -0. 371. -0.007

-0. 378 -0.010

-0. 381. -0.011. -0. 392 -0.017

-0.1.01 -0.021

-0. 1.12 -0.025

-0. 1.26 -0.029

-0.1.1.2 -0.031.

-0.1.60 -0.039

-0.1.80 -0. 01.1. -0.501. -0.051 -0.531 -0.058

-0.562 -0. 066 -0.597 -0. 075 -0.637 -0.085

-0.682 -0.096

-0.733 -0.106

-0.791 -0.123 -0.856 -0.139

-0.930 -0.158

XE OXE/OD -0.568 0.012 -0.566 -0.002 -0.569 -0. 007 -0.573 -0. 009 -0.577 -0.010 -0.562 -0.010

-0.587 -0.011 -0.593 -0.011 -0.598 -0.010 -0.603 -0.010 -0.608 -0. 009 -0.612 -0.008 -0.616 -0. 007 -0.619 -0. 005 -0.621 -0.005 -0.623 -0. O0i» -0. 625 -0. 001. -0.627 -0.002

-0.628 -0.001 -0.628 O.QOO -0.628 0. 001 -0.627 0. 003 -0.625 0.001. -0.623 0.006 -0.619 0.007 -0.616 0. OOS -0.611 0.010 -0.606 0.012 -0.600 0. Oil. -0.592 0. 016

-0.581. 0. 018

-0.571. 0.021 -0.563 0.023 -0.551 0.025 -0.538 Q. 028 -0.523 0. 030 -0.508 0.033

-0.1.91 0.035

-0.1.73 0. 037

-0.1.51. 0. 01.0 -0.1.33 0. 01.2 -0.1.12 0.01.1. -0.389 0. 01.5 -0.366 0. 01.7

97

F-lOO
METHftNE ISOTHERM 260

MOL/L P,BAR DP/OD

0.5 lO.i.89 20.376

1.0 20-381 19.203

1.5 29.710 18.13U

2.0 38.532 17.170

2.5 l*f,.695 16.293

3.0 5'». 838 15. <.93 3.5 62. '01 1'».772

it.O 69.62<t li«.137 '.5 76.551* 13. 599

5.0 8 3.2'*1 13.161* 5.5 89.736 12.836

6.0 ge.ogit 12.611

6.5 10 2.36I* 12. '(85 7. 0 10 8.59<» 12. '.52 7.5 111*. 832 12. 515

8.0 121.128 12.690

8.5 127.5'.8 13.019

9.0 13't.l77 13. 531

9.5 lltl.102 11.. 183 10.0 l'4a.375 1'..926 10. 5 156.0it3 15.758

11.0 16i».151 16.69'. 11.5 172.763 17.790

12. 0 18 1.982 19. 130 12.5 191.9'.2 20. 763 13.0 202.798 22.713

13.5 21'.. 712 25. 001. 14.0 227.863 27.663

II.. 5 21.2. 1.1.2 30. 727 15.0 258.661. 31.. 237 15.5 276.761 38.239

16.0 296.993 42.782

16.5 319.642 47.918

17.0 345.019 53.699

17.5 37 3.458 60. 177 16.0 405.320 67.402

18.5 440.992 75.422

19.0 480.863 84.285

19.5 525.425 94.034

20.0 575.071 104.711

20.5 630.298 116.362

21.0 691.604 129.035

XB DXB/DD

0.646 -0.199

0.572 -0.114

0.524 -0.080 0.489 -0.061

0.462 -0.048

0.440 -0.039

0.422 -0.032 0.408 -0.026

0.396 -0.021

0.367 -0.017

0.379 -0.014

0.373 -C.Oll

0.367 -0.009

0.363 -0.007

0.360 -0.005

0.358 -0.C03

0.357 -0.001

0.357 -0.000

0.357 -0.000

0.357 0.000 0.357 0.000 0.357 0.000

0. 357 O.OOl 0.358 0.002

0 . 359 0. 00 3 0.361 0.005 0.364 0.007 0.368 0.008 0.372 0.010 0.376 0.012 0.364 0.013

0.391 0.015 0.399 0.017 0.406 0.019 0.418 0.021 0.429 0.023

0.441 0.025 0.454 0.027 0.468 0.030 0.464 0.032

0.500 0.034 0.517 0.036

XC DXC/OD

-0.676 0.396 -0.542 0.166 -0.468 0.116 -0.420 0.062 -0.385 0.061 -0.358 0.047 -0.337 0.037 -0.321 0.029 -0.308 0.023 -0.298 0.019 -0.290 0.015 -0.263 0.012 -0.278 0.009 -0.273 0.007 -0.270 0.005 -0.268 0.003 -0.267 0.001 -0.26 7 0.000 -0.267 0.0 00 -0.267 0.000 -0.267 -0.0 00 -0.267 -0.000

-0.267 -0.001

-0.268 -0.002

-0.269 -0.003

-0.271 -0.005

-0.274 -0.007 -0.278 -0.009

-0.283 -0.010

-0.266 -0.012

-0.295 -0.014

-0.302 -0.016

-0.311 -0.019

-0.321 -0.021

-0.332 -0.024

-0.345 -0.027

-C.359 -0.030

-0.375 -0.034

-0.393 -0.038

-0.413 -0.042

-0.435 -0.046 -0.459 -0.052

XD DXD/DD

- 1 . 447 1.115

-1. 086 0.475 -0.906 0.280 -0.792 0.186 -0.712 0.135 -0.653 0.102 -0.609 0.078 -0.574 0.061 -0.547 0.048 -0.525 0.038 -0.508 0.030 -0.496 0.024 -0.464 0.019 -0.476 0.015 -0.469 0.010 -0.465 0.006 -0.463 0.002 -0.463 0.000 -0.463 0.000 -0.463 0.000

- 0. 463 -0. OOP -0.463 -0.000

-0. 463 -0.001

-0. 464 -0.004

-0.467 -0.007

-0.471 -0.010

-0.477 -0.014

-0.485 -0.017

-0. 494 -0.021 -0.506 -0.025 -0.519 -0.029

-0.535 -0.034

-0.553 -0. 039 -0.574 -0.044 -0.597 -0. 051 -0.625 -0. 058 -0.655 -0. 066 -0.690 -0.075

-0.730 -0.085

-0.775 -0. 096

-0. 826 -0.108 -0.664 -0.123

XE OXE/00

-0.568 -0. 0O9 -0.595 -0. 019 -0.606 -0.022 -0.617 -0. 023 -0.629 -0.023

-0.640 -0.023 -0.652 -0.022 -0.662 -0.021 -0.672 -0. 019 -0.682 -0.016

-0.690 -0. 016

-0 .697 -0.014 -0.704 -0.011

-0. 709 -0. 009 -0.713 -0. 007 -0.716 -0. 006 -0.718 -0.004

-0.720 -0.003

-0.721 -0.001

-0. 721 0. 000

-0. 721 0. 001 -0.720 0. 003 -0.716 0.005 -0.715 0.007 -0.711 0.009 -0.707 0. Oil -0.700 0.014 -0.693 0.016 -0.664 0. 019

-0. 674 0. 022 -0.662 0. 025 -0.648 0. 028 -0.634 0. 031 -0.617 0. 034 -0.600 0. 037 -0.581 0. 039 -0.560 0 . 042 -0.539 0. 044 -0.516 0. 047 -0.492 0. 049 -0.467 0. 050 -0.441 0.052

98

F-101
METHftNE ISOTHERM 280.0 0E&. K

MOL/L

0.5

1.0

1.5 2.0 2.5

3.0 3.5

tt.O

I*.

5.0

5.5 6.0

6. 5 7.0 7.5

6.0 8.5 9.0

9.5

10.0 10.5

11.0

11.5

12. 0 12.5

13.0 13.5

11*. 0 If*.

15.0

15.5

16.0 16.5

17.0

17.5

18.0 18.5

19.0

19.5 20.0

P.BftR 11.352

22.169

32.<»e6 <»2.357 51.829

6 0.9it2 69.731.

7 8. 2<>8 86.528

91..626 102.598

110.1.97 118.379

126.29'.

13'..296

11.2.1.39 150.798

159. '.6'. 168.531 178.061

18 8. 106 198.723

209. 98^ 222.000

23".. 919

21.8. 901. 26 '..13 0 280.766

299.075

319.219

3<.l.i.6<. 366.076

39 3.3'.5 <.23.589

<.57.H.6

l.9<..363 535.665

581. '.65 632.152

688.200

OP /DO

22. 165

21. 117

20. 170

19. 328

18. 572

17. 892

17. 291

16. 777

16. 361

16. 052

15. 852

15. 763

15. 780

15. 899

16. 121. 16. '.75 16. 991

17. 707

18. 579

19. 557

20. 6'.2 21. 8<t8 23. 233

2'.. 883

26. 8'.7 29. 151

31. 817

3'.. 873

38. 356

1.2. 301.

1.6. 763

51. 780

57. '.0'. 63. 68'. 70. 668

78. '.06 86. 9'.2 96. 320 106.581

117. 767

xe

0.7'./ 0.672

0.62'. 0.589

0.562

0.5'.i 0.523

0.509

0. 1.97

0 .1.87

0. '.79 0.1.73

0. i.68 0. 1.61. 0.1.61

0. 1.59 0.1.58 0.'.57

0.1.57

0. 1.57 0. 1.57 0.1.57 0.1.58

0.1.58

0. 1.60 0.1.62

0.1.65 0.1.68

0.1.73

0.1.78

0. 1.61. 0. 1.91 0.1.99 0.508

0.518 0.529

0.51.1 0.551. 0.569

0.561.

OXB/DO

-0.199

-0.111.

-0. 080 -0.061

-0. O'.S -0.039 -0.032

-0.026

-0.021

-0.017

-0.011. -0.011 -0.009

-0.007

-0.005 -0.003

-0. 001 -0.000

-0.000

0.000

0.000

0.000 0.001 0.002

0.003

0.005

0.007

0.008

0.010

0.012 0.013

0.015 0.017

0.019

0.021 0.023

0.025 0.027

0.030 0.032

XC -0.728

-0 . 591. -0. 521

-0.1.72

-0 . 1.37 -0.1.10 -0.390

-0. 371. 361 350 -0. 31.2 -0. 335 -0.330

-0. 326 -0.323

-0. 321 -0. 320 -C. 319 -0.319

-0. 319

-0. 319 -0. 319

-0. 319 -0.320

-0. 321 -0. 321. -0. 327 -0.330 -0.335

-0. 31.1 -0.3^7

-0. 355

-0. 363

-0. 373

-n . 385 -0. 397

-0.1.11 -0.'.27

-0.'.'.5 -0.1.65

OXC/DO

0.396

0.186 0.116

0. 082 0.061

0. 0'.7 0.037

0.029

0. 023

0. 019 0.015 0.012

0.009

0.007 0.005

0.003

0.001 0.000

0.000 0.000 -0.000

-0.000

-0.001 -0.002 -0.003

-0.005

-0.007 -0.009

-0.010 -0.012

-0.01'. -0. 016

-0. 019 -0.021

-0.021. -0. 027 -0.030

-0. 031. -0.038

-0. 01.2

-1.521

- 1. 162 -0.980

-0.866

-0.786

-0.727 -0.683

-0.61.8 -0.621

-0.600 -0.582

-0.569 -0.558

-0.550

-0.51.3 -0.539

-0.537

-0.537 -0.537 -0.537

-0.537

-0.537

-0.537 -0.538

-0.51.1

-0.51.5 -0.551 -0.559

-0.568

-0.580 -0.593

-0.609

-0.627

-0.61.8 -0.671

-0.699 -0.729

-0.761.

-0.801. -0. B'.9

DXO/OD

1. 115

0.1.75

0. 280 0.188

0.135

0.102

0.078

0.061

0. 01.8 0.038

0.030

0.021. 0.019

0.015

0.010 0.006

0.002

0. 000 0.000

0.000 -0.000

-0.000

-0.001

-0.001. -0.007

-0.010

-0.011. -0.017

-0.021

-0.025 -0.029

-0.031. -0.039

-0.01.1. -0.051 -0.058

-0.066 -0.075

-0. 085 -0.096

XE -0.602 -0.616 -0.632

-0.61.9 -0.665

-0.681

-0.696

-0.710

-0.721. -0.736

-0.7'.7 -0.756

-0.761. -0.770

-0.775 -0.779

-0.782

-0.78^

-0.785

-0.785 -0.785

-C.78^

-0. 782 -0.779

-0. 771. -0.769

-0. 761 -0.753

-0.71.2 -0.730

-0.716 -0.700

-0.682

-0. 663

-0.61.3 -0.620

-0.597

-0.572

-0.51.6 -0.519

OXE/DO

-0.023

-0. 031 -0. 033 -0.033

-0. 032

-0. 031 -0.030

-0. 028

-0. 025

-0. 823 -O.OZO

-0. 017

-0.011. -0.011

-0.009

-0.007 -0.005

-0.003

-0. 001 O.ODO 0.001

0.003 0.005

0. 007

.010 ,013 .016

. 019

,023

,026

,030 ,033

,037

.01.0 .01.3

.01.6 0.01.9 0.051

0. 053 0.055

METHANE ISOTHERM 300.0 OEG. K

MOL/L

0.5

1.0 1.5 2.0

2.5

3.0 3.5

1.. 0

1.. 5 5.0 5.5

6.0

6.5

7.0

7.5

8.0

8.5 9.0

9.5 10.0

10.5

11.0

11.5 12.0

12.5

13.0 13.5

11..

11..

15. 0 15.5

16.0 16.5

17.0

17.5

18. 0 18.5

19.0

P.BAR 12.213

2 3.951

35.2'.8 1.6.158 56.728 66.998

77.007 86.797

96.1.16 105.917

115.356

121.. 792

131.. 282

11. 3.882

153.e'»9 163.61.6

173.91.9

IS'.. 659 195.875

207.667

220.095

233.223

21.7.130 261.938

277.801

291.. 893

31 3.399 333.515

355.1.55

379.1.1.9 1.05.751

1.31.. 636

1.66.1.00 501.365

539.877 582.303

629.031.

68 0.1.82

OP/00

23. 91.7 23. 017

22. 189

21. 1.65 20. 827

20. 266

19. 781. 19. 392

19. 101 18.920

18. 855

la. 907

19. 072

19. 31.8 19. 71.1 20. 270 20.977

21. 898

22. 989

21.. 200 25.533

27. 003 28.667

30. 615

32. 896

35. 531. 38. 551.

1.1. 982

1.5. 651. 50. 209

55. 091

60. 51.5 66. 618

73. 358

SO. 812

89. 021. 98. 038

107. 896

XB

0. 81.6 0.771 0.723 0.688

0.661

0.61.0 0.622

0.608

0.596

0.586

0.578 0.572

0.567

0.563

0. 560 0.558

0.557

0.556

0.556

0.556

0.556 0.556 0.557 0.557

0.559

0.561

0.561. 0.567

0.572

0. 577 0.583

0.590 0.598

0.607

0.617

0.628

0.61.0 0.653

OXB/00

-0.199

-0.111. -0.080 -0.061

-0.01.8 -0.039

-0.0 32 -0.026

-0.021

-0.017

-0.011. -0.011 -0.009

-0.007

-0.005 -0.003

-0.001

-0.000

-0.000

0.000

0.000

0.000

0.001 0.002 0.003

0.005

0.007

0.008

0.010

0.012 0.013

0.015

0.017 0.019

0.021 0.023

0.025

0.027

XC -0. 773

-0.61.0 -0.566

-0.518

-0.1.82 -0. 1.56 -0.1.35

-0.1.19 -0. 1.06 -0. 396

-0. 387 -0. 381 -0. 375

-0. 371 -0. 368

-0. 366

-0. 365

-0. 365 -0. 365

-0. 365

-0. 365 -0.365

-0.365

-0. 365

-0. 367

-0. 369

-0. 37 2 -0. 376 -0.380

-0. 386

-0. 393

-0.1.00 -0. 1.09 -0.1.19 -0. 1.30 -0.1.1.3 -0. 1.57 -0.1.73

DxC/00

0. 396

0. 186 0.116 0.082

0.061

0. 01.7 0.037

0.029

0.023 0.019

0.015 0.012

0.009

0.007

0.005 0-003

0.001

0. 000 0.000

0. 000 -0.00 0 -0.000

-0.001 -0.002

003

005 -0.007

-0.009

-0.010 -0.012

-0.011. -0.016 -0.019

-0. 021

-0.021. -0.027

-0.030

-0. 031.

XD -1.580

-1. 222

-1. 01.0 -0.926

-0.81.6 -0.787

-0. 71.2 -0.708

-0.681 -0.659

-0.61.2 -0.629

-0.618

-0.609

-0.603

-0.599

-0.597

-0.596

-0.596

-0. 596 -0.596

-0.596

-0.597

-0.598

-0.601 -0.605

-0.611 -0.619

-0.628

-0.61.0 -0.653

-0.669

-0.687

-0.707

-0.731 0.758

-0.789

-0.821.

DXO/DO

1.115

0.1.75 0.280 0.188

0.135 0.102

0.078

0.061

0.01.8 0.038

0.030

0.021. 0.019

0.015

0.010 0.006

0.002

0.000

0.000

0.000 -0.000

-0.000

-0.001

-0.001. -0.007

-0.010

-0.011. -0.017

-0.021 -0.025

-0. 029

-0.031. -0.039

-0.01.1. -0.051

-0. 058 -0.066 -0.075

XE 0.612

0.631

0.651

0.671

0.691 0.710

0.728

0. 71.5 0.761

0.775

0.787 0.798

0.807

O.Sll. 0.820

0. 821. 0. 827 0.829

0.830

0.830 0.830

0. 829 0.827

0.821. 0.819

0.813 0.805

0.795 0.783

770

751. 737

718 696

671. 0.61.9 0.623

0. 596

OXE/OD

-0. 03(. .01.0

. 01.1

. 01.0 .039

. 037 .035

. 032

. 030 .026 -0.023

-0. 020

-0. 016 -0.013

-0.010 -0.007

-0.005

-0. 003 -0.001

0.000

0.001 0.003

0.005

0.008

O.flll

0. Oil. 0. 018 0.021 0.025

0. 029 0.033

0.037

0. 040

0. 01.1. 0.01.7 0.050

0.053

0. 056

99

F-102
METHANE ISOTHERM 320.0 SEG. K

MOL/L P.BAR OP/DO

0. 5 13.073 25.723

1. 0 25.728 2i«.908 1.5 37.999 2'».19'i 2.0 i»9.9'«0 23. 585

2.5 61.598 23.063

3.0 73.015 22.618

3.5 8i».230 22. 256

if.O 95.287 21.986

>».5 106. 23^ 21.821

5.0 117.127 21.771

5.5 128.025 21. 8<*2 6.0 138.989 22.036

6.5 150.081 22.352

7.0 161.361 22.788

7.5 172.890 23. 31.9 8.0 18i».735 24.058

8.5 196.980 2'*. 956

9.0 209.730 26.080

9.5 223.091 27.388

10.0 237.139 28.828

10.5 251.9<»1 30.i»0it 11.0 267.568 32.130

11.5 28't.l06 3'*. 066 12.0 301.681* 36. 301 12.5 320.it65 38.881. 13.0 3l»0.631 <»1.8i.l 13.5 362.373 1.5. 195

l^t.O 385.897 1.8.971.

11.. 5 1.11.1.23 53. 212

15. 0 1.39.192 57. 91.9 15.5 1.59.1.62 63. 226 16.0 502.515 69.087

16.5 538.655 75.580

17.0 578.208 82.71.9 17.5 621.521. 90.61.0 18.0 668.975 99.295

METHANE ISOTHERM 31.0.0

MOL/L P.BAR OP/DD

0.5 1 3.932 27.1.96 1.0 27.500 26.790

1.5 1.0.71.0 26. 187

2.0 53.705 25.690

2.5 66.1.1.1. 25. 280

3.0 78.999 21.. 952

3.5 91.1.10 21.. 708

"..Q 10 3.723 21.. 559

<..5 115.988 21.. 520

5.0 128.263 21.. 601

5.5 11.0.610 21.. 810 6.0 153.094 25.148

6.5 165.780 25.615

7.0 178.730 26.210

7.5 192.012 26.91.0 8.0 205.697 27, 827

8.5 219.873 28.915

9.0 23i».652 30. 240 9.5 250.146 31.760

10.0 266.436 33.425

10.5 283.595 35. 237 11.0 301.700 37.213

11.5 320.845 39.411

12.0 341.164 41.922

12.5 362. S2« 44.796

13.0 386.024 48.057

13.5 410.954 51.730

14. D 437.828 55.842

14.5 466.874 60.426

15.0 498.339 65.522

15.5 532.488 71.171

16.0 569.609 77.416

16.5 610.011 84.303

17.0 654.026 91.875

X B OXB/OD XC DXC/DO

0 . 943 -0.199 -0.813 0. 396 0.869 -0.114 -0 . 679 0. 186 0.821 -0. 080 -0 . 606 0. 116 0.766 -0.061 - 0 . 557 0.082 0.759 -0.048 -0 . 522 0.061

0.737 -0. 039 -0 . 496 0. 047 0.719 -0.0 32 -0 . 475 0.0 37 0.705 -0. 026 -0. 459 0. 029 0.693 -0.021 - 0 . 446 0.023

0.684 -0.017 - 0 . 435 0.019

0.676 -0.014 -0 . 427 0. 015 0.669 -0.011 -0 . 420 0.012

0.664 -0.009 -0 . 415 0.009

0 . 660 -0.007 -0 . 411 0.007

0.657 -0.005 -0. 408 0.005

0 . 655 -0.003 -0 . 406 0.00 3 0.654 -0.0 01 -0 .405 0.001 0.654 -0.000 - 0 . 404 0.000

0 . 654 -0.0 0 0 -0 . 404 0.000 0.654 0.000 -0 . 404 0.000 0.654 0.000 -0. 404 -0.000

0*654 0.000 -0 • 404 -0. 000 0.654 0.001 -0 . 405 -0.001

0 , 655 0. 002 -0.405 -0.002

0.656 0.003 -0.406 -0.003

0.658 0.005 -0.409 -0.005

0.661 0.007 -0.412 -0.007

0.665 0.OO8 -0. 415 -0.009

0.66^ 0.010 -0.420 -0.010

0.675 0.012 -0.426 -0.012

0.681 0.013 -0.432 -0.014

0.688 0. 015 -0. 440 -0.016

0.696 0.017 -0. 449 -0.019

0.705 0.019 -0. 458 -0.021

0.715 0.021 -0.470 -0.024

0.726 0. 023 -0.482 -0. 027 /

0E6. K

xe OXB/DO XC DXC/OD

1.039 -0.199 -0. 848 0. 396 0.964 -0.114 -0. 714 0. 186 0.917 -0.080 -0.641 0.116

0.882 -0.061 -0.592 0.082

0.854 -0. 048 -0. 557 0.061

0. 833 -0.039 -0. 531 0. 047 0.815 -0.032 -0.510 0.037 0.801 -0.026 -0. 494 0.029 0.789 -0.021 -0.481 0.023 0.779 -0.017 -0. 470 0.019

0.772 -0.014 - 0 . 46 2 0. 015 0.765 -0.011 -0.455 0.012

0.760 -0.009 -0.45 0 0.009

0.756 -0.007 -0. 446 0.007 0.753 -0.005 -0. 443 0.005 0.751 -0.003 -0.*41 0.003

0.750 -0.001 -0.440 0.001

0. 750 -0.000 -0.439 0.000 0.750 -0.000 -0. 439 0.000

0.750 0.000 -0. 439 0. 000 0.750 0.000 -0.439 -0.000

0.750 0.000 -0.439 -0.000

0.750 0.001 -0. 440 -0.001

0.750 0.002 -0. 440 -0. 002 0.752 0.003 -0. 442 -0.003

0.754 0.005 -0. 444 -0.005

0.757 0.007 -0.447 -0.007

0. 760 0.008 -0.450 -0.009

0.765 0.010 -0. 455 -0. 010 0.770 0.012 -0.461 -0.012

0.776 0.013 -0.467 -0.014

0.784 0.015 -0.475 -0.016

0. 792 0.017 -0. 484 -0.019

0. 800 0.019 -0.493 -0.021

XO 0X0/00 XE DXE/00 -1.629 1.115 -0.620 -0. 041 -1. 271 0.475 -0.642 -0.046

-1. 089 0.280 -0.665 -0. 046 -0.974 0.188 -0.688 -0. 045 -0.895 0.135 -0.711 -0. 044 -0. 836 0.102 -0.732 -0. 041 -0.791 0.078 -0.752 -0. 039 -0.757 0.061 -0.771 -0. 036 -0.730 0.048 -0.788 -0. 032 -0.708 0.038 -0.803 -0. 029 -0.691 0.030 -0.817 -0. 025 -0.677 0.024 -0.828 -0.022

-0.667 0.019 -0.838 -0.018

-0.658 0.015 -0.846 -0.014 -0.652 0.010 -0.852 -0.011 -0.648 0.006 -0.857 -0.008 -0.646 0.002 -0.860 -0.005 -0.645 0.000 -0.862 -0.003

-0 . 645 0.000 -0. 863 -0.001 -0.645 0.000 -0.863 0.000 -0.645 -0.000 -0.863 0. 001 -0.645 -0.000 -0. 862 0.003 -0.646 -0.001 -0.860 0.005 -0.647 -0.004 -0.857 0. 008 -0.649 -0.007 -0. 852 0.012 -0.654 -0.010 -0.845 0.015 -0.660 -0.014 -0.837 0.019 -0.668 -0.017 -0.826 0.023 -0.677 -0.021 -0. 814 0. 027 -0.688 -0.025 -0.799 0.031 -0.702 -0.029 -0.783 0.035 -0.717 -0.034 -0.764 0.039 -0.735 -0. 039 -0.743 e. 043 -0.756 -0. 044 -0.721 0.047 -0.780 -0.051 -0.697 0.050 -0.807 -0.058 -0.671 0.054

XD 0X0/00 XE OXE/OD

-1.670 1.115 -0.626 -0.047 -1.311 0.475 -0.651 -0. 051 -1.129 0.280 -0.676 -0.051

-1. 015 0.188 -0.701 -0.049 -0.935 0.135 -0.725 -0. 047 -0.876 0.102 -0.748 -0. 045 -0.832 0.078 -0.770 -0. 042 -0.797 0.061 -0.790 -0. 038 -0.770 0. 048 -0.808 -0.035 -0.749 0.038 -0.825 -0.031 -0.732 0.030 -0.839 -0. 027 -0.718 0.024 -0.851 -0.023 -0.707 0.019 -0.862 -0.019 -0.699 0.015 -0.870 -0.015 -0.692 0. 010 -0.877 -0.011 -0.688 0.006 -0.882 -0.008

-0.686 0.002 -0. 885 -0.005

-0.686 0.000 -0.887 -0.003

-0.666 0.000 -0.888 -0.001

-0. 686 0.000 -0.888 0.000 -0.686 -0.000 -0.888 0. 001 -0.686 -0.000 -0.887 0.003 -0.686 -0.001 -0.885 0.006 -0.687 -0.004 -0.882 0.009 -0.690 -0.007 -0. 876 0.012 -0.694 -0.010 -0.870 0. 016 -0.700 -0.014 -0.861 0. 020 -0.708 -0.017 -0.850 0.024 -0.718 -0.021 -0.837 0.028 -0.729 -0.025 -0.822 0. 033 -0.742 -0.029 -0.804 0. 037 -0.758 -0.034 -0.785 0. 041 -0.776 -0.039 -0.763 0.045 -0.797 -0. 044 -0.739 0.049

100

F-103
METHANE ISOTHERM 360.0 OEG. K

MOL/L

0.5

1.0 1.5

2.0 2.5

3.0 3.5

'«.0 <..5 5.0 5.5

6.0 6.5

7.0

7.5

e.o

a.

9.0 9.5 10.0

10.5 11.0

11.5

12.0

12.5 13.0

13.5

ik. 0 it*.

15.0 15.5

16. 0 16.5

P.BAR

1<».790 29.269

43.1.72

5r.<.56

7 1.268

81.. 952 98.550

112.109

125.682

139.330

153. 116

16 7.10 8 181.376

195.986 211.009

226.520

21.2.61'. 259. ".07 277.015 295.527

315.020 335.577

35^.298

380.323

1.01.. 828

1.31.010

<»59.073 <.89.236 521.733 556.816

59 '..757 635. 81.8 68a.<.0<.

OP/OD

29. 26". 28.665

28. 169

27. 781

27. 1.83 27. 268

27. 11.1 27. 113

27. 199

27. 1.11 27. 756

28. 237

28. 855

29. 609

30. 507 31.570

32. 81.5

31.. 367

36. 095

37. 979

<»a. 021

«t2. 239

<.<..691

1.7. 1.68 50.620

5<.. 17<. 58. 151

62. 579

67. 1.93 72. 930

78. 931

85. 539

92. 798

XB 1.132

1.058

1.010 0.975

0.91.8 0.926 0.909

0.891. 0.883

0. 873 0.865 0.859

0.851. 0.S50

0.81.7

0.81.5

0.81.1. 0. 81.3 0.81.3

0. 81.3 0.8(i3

0.81.3

0.81.3

0 . 81.1. 0.81.5

0.81.7 0.850

0, 85*1 0. 859

0.861. 0.870 0.877

0.885

OXB/DD

-0.199

-0.111. -0.080

-0. 061

-0.01.8 -0.039 -0.032

-0.026

-0.021 -0.017

-0.011. -0.011 -0.009

-0.007

-0.005

-0.003

-0.001

-0.000

-0.000

0.000

0.000

0.000

0.001 0.002

0.003 0.005

0.007 0.008

0.010 0.012 0.013

0.015 0.017

XC

-0. 879

-0.71.5 -0.672

-0.623 -0.588

-0. 562

-0. 51.1 -0.525

-0.512 -0.502

-0. 1.93 -0.1.87 -0. 1.81 -0.1.77 -0. 1.71. -0 . 1.72 -0.1.71 -0. 1.71 -0.1.71

-0.1.71

-0.1.71

-0.1.71

-0.1.71

-0.1.71 -0. 1.73 -0. 1.75 -0.1.78 -0.1.82 -0. 1.86 -0. 1.92 -0.1.98 -0.506

-0. 515

DXC/DO

0.396 0.186

0.116 0.082

0. 061

0. 01.7 0. 037

0. 029 0.023

0.019 0.015

0.012 0.009

0. 007

0. 005 0.003

0.001 0.000

0.000

0. 000 -0.000

-0.000 -0.001

-0.002 -0.003

-0.005

-0.007 -0.009

-0.010

-0.012

-0.011. -0.016 -0.019

XD

1.701.

1. 31.5 1.163

1. 01.9 0.969

0.910 0.866

0.831

0.801. 0.783

0. 765 0.752

0.71.1 0.733

0.726

0.722

0.720 0.720

0.720 0.720

0.720 0.720 0.720

•0.721

•0.721. •0.728 0.731.

71.2 0.751 0.763

0.776

0.792

0.810

-0

DXD/OD

1.115

0.1.75 0.280

0.188 0.135

0.102

0.078

0.061

0. 01.8 0.038

0.030

0.021.

0. 0x9 0.015

0.010 0.006

0.002

0.000

0.000

0.000 -0.000

-0.000 -0.001

-0.001. -0.007

-O.OIC

-0.011. -0.017 -0.021

-0.025

-0.029

-0.031. -0.039

XE -0.631 -0.657

-0.685

-0.711

-0.737 -0.761

-0.781. -0.805

-0.821.

-0.81.1 -0.856

-0.869

-0.880

-0.889 -0.896

-0.901

-0.901. -0.906

-0.907

-0.907

-0.907 -0.906

-0.901. -0.901

-0.895 -0.888

-0.879

-0.868

-0.851. -0.839

-0.821 -0.800

-0.776

OXE/DO

-0.052

-0.051.

-0.051. -0.092

-0.050

-0.01.7

-0.01.1. -0. 01.0 -0.036

-0.032

-0.028

-0.021. -0.020 -0.016

-0.012

-0.008

-0.006

-0.003

-0.001

0. 000

0. 001 0.003

0.006 0.009

0. 012 0.016

0.020 0.O25

0.029

0.031. 0.038

0.043

0.01.7

MtTHflNE ISOTHERM 380.0 CEG. K

MOL/L

0.5

1.0

1.5 2.0

2.5 3.0

3.5 4.0

4.5

5.0 5.5

6.0

6.5

7.0 7.5

8.0 8.5

9. 0 9.5 10.0 10.5

11.0

11.5

12.0 12.5

13.0

13.5

14.0 14.5

15.0

15.5

P.BAR 15.647 31.034

46.197 61.193

76.072 90.877

105.654

120.450

135.321 150.329

165.542

181.032

196.868

213.124

229.873

247.196

265.190

283.977

303.679

324.388

346. 188 369.167

393.429

419.120 446.424 475.541

506.682

540. 071 575.949

614.573 656.219

OP/00

31. 029

30. 532

30. 141

29. 859 29.670

29. 567

29. 555 29.647

29. 857

30. 199 30.679

31. 302

32. 069 32.980

34. 042

35. 280

36. 7 58 38. 453

40. 384

42. 481

44. 748

47. 200

49. 897 52.931

56. 352

60. 185 64.453

69. 185

74. 412

80. 174

86. 510

XB 1.224

1. 150 1.102

1.067

1.040 1.018

1. 001 0.986

0.975

0.965 0.957

0.951 0.946

0.941 0.938

0.936 0.935

0.935 0.935 0.935

0.935

0.935 0.935 0.936

0.937 0.939

0.942

0.946

0.950 0.956 0.962

OXB/00 -0.199

-0.114

-0.080

-0.061 -0.048 -0.039

-0.032

-0.0 26 -0.021

-0.017 -0.014

-0.011 -0.009

-0.007

-0.009 -0.003

-0.001

-0.000 -0.000

0.000 0.000

0.000

0.001 0.002

0.003

0.005

0.007

0.008

0.010 0.012

0.013

XC -0.907

-0.773

-0.700

-0.651

-0.616

-0.590 -0.569

-0. 553

-0. 540 -0.529

-0.521 -0.514

-0.509

-0. 505 -0.502

-0.500 -0.499

-0. 498

-0. 498 -0.498

-0. 498 -0.498

-0. 499

-0. 499 -0.501

-0.503

-0.506

-0.510

-0.514

-0.520

-0. 526

OXC/OD

0.396

0.186 0.116

0. 082

0. 061 0.047

0.037

0. 029 0.023

0.019

0.015

0.012

0.009

0.007 0.005

0.003

0.001

0.000

0.000

0.000 -0.000

-0.000

-0.001 -0.002

-0.003 -0.005

-0.007

-0.009

-0.010 -0.012

-0.014

xo -1.733

-1.374

-1.192

-1. 078

-0. 998 -0.939

-0.895

-0.860 -0.833

-0.811

-0.794

-0.781

-0.770

-0. 761 -0.755

-0. 751

-0. 749 -0.748

-0. 748

-0. 748 -0.748

-0 . 748

-0. 749 0.750

-0.753

•0.757

-0. 763 -0.771

-0.780 0. 792 0.805

DXO/00

1.115

0.475

0.280 0.188

0.135 0.102

0.078

0.061 0.048

0. 038

0. 030 0.024

0.019

0.015

0.010 0.006 0.002

0.000 0.000

0.000 -0.000

-0.000

-0.001 -0.004

-0.007 -0.010

-0.014

-0.017

-0.021 -0.025 -0.029

XE -0.634 -0.663

-0.691 -0.719

-0. 746 -0.771

-0.795 -0.816

-0.836

-0.854 -0.870

-0.883

-C.894 -0.903

-C.911 -0.916

-0.919

-0.921 -0.922

-0.922

-0.922

-0.921 -0.919

-0.916

-0.910

-0.903

-0. 894 -0.882

-0.868 -0.852

-0.834

OXE/00

-0. 056 -0.057

-0. 057 -0.055

-0. 052

-0. 049 -0.046

-0.042

-0.038

-0.033

-0. 029

-0. 025

-0. 020

-0. 016 -0.012

-0.009

-0.006 -0.003

-0.001

0.000

0.001 0.003

0. 006 0.009

0.013

0. 017 0-021

0.025

0.030

0.035 0.039

101

F-104
METHANE ISOTHERM i»00

MOL/U P,BAR OP/DD

0.5 1 6. 50 3 32. 790

1.0 32.795 32. 39i» 1.5 <>8.91<t 32. 10<> 2.0 bit. 918 31. 926

2.5 80.856 31. 8it3 3.0 96.775 31. 850

3.5 112.722 31. 952

<». 0 128. 7U5 32. 161

<». 5 l't't.90'* 32. <«9<» 5.0 161.262 32. 963

5.5 177.891 33.577

6.0 19<>. e6i« 3<». 3'>0 6.5 21 2.256 35. 25'» 7.0 230.1'»3 36. 319 7.5 2i»a.602 37.5'«'» e. 0 267.717 38.952

8.5 287.592 1.0. 589

9.0 308.352 1*2. i»93 9.5 330.123 Iti*. 622

10.

353.003 <»6.927 10.5 377. 080 i»ll 11.0 <«02.i><i7 52. 090 11.5 1.29.213 55. 025 12.0 <.57.530 58. 306 12.5 l»8 7.5e5 61. 986 13.0 519.586 66. 088 13.5 55 3. 71.

70.636

i<«.a 590.300 75.657

14.5 629.«.89 81. 185

15. 0 671.576 87. 257

XB OXB/DO

1. 31't -0. 199

1. 2<»0 -0. lli» 1.192 -0.080

1.157 -0.061

1.130 -0.048

1.108 -0.039

1. 090 -0.032

1.076 -0.026

1. 06'« -0.021

1. 055 -0.017

1. 0't7 -0.01<i LQitO -0.011

1.035 -0.009

1.031 -0.007

1.028 -0.005

1. 026 -0.003

1.025 -0.001

1.025 -0.000

1.025 -0.000

1.025 0.000

1. 025 0.000 1.025 0.000 1.025 0.001 1.026 0.002

1. 027 0.003 1.029 0.005 1.032 0.007 1.036 0.008

1.0<«0 0.010

1. 0'«6 0.012

XC DXC/DD -0.932 0.396 -0.798 0.186 -0.725 0.116 -0.676 0.082

-0.6i»l 0.061 -0.615 O.aitT -0.59'* 0.037 -0.578 0.029 -0.565 0.023

-0.55<» 0.B19

-0.5'»6 0.015 -0.539 0.012

-0.53<« 0.009 -0.530 0.007 -0.527 0.005 -0.525 0.003

-0.52I* 0.001

-0.52<t 0.000

-0.52<» 0.000 -0.523 0.000

-0.52<» -0.000

-0.521* -0. 000

-0.52'* -0.001

-0.52'. -0.002

-0.526 -0.003

-0.628 -0.005

-0.531 -0.007

-0.535 -0.009

-0.539 -0.010

-0.51.5 -0.012

xo DXO/DD

-1.757 1.115

-1. 398 0.1.75 -1. 217 0.280 -1.102 0.188 -1.022 0.135

-0.96'. 0.102 -0.919 0.078

-0.88<« 0. 061 -0.857 0.0<.8 -0.836 0.038 -0.819 0.030

-0. 805 0.021. -0.79«t 0. 019 -0.786 0.015 -0.780 0.010 -0.776 0.006

-0.77i. 0.002 -0.773 0.000 -0.773 0.000 -0.773 0.000 -0.773 -0.000 -0.773 -0.000 -0.773 -0.001 -0.775 -O.OOt. -0.777 -0.007

-0.782 -0.010

-0.788 -O.Oli. -0.795 -0. 017 -0.805 -0.021

-0. 816 -0.025

XE OXE/DO

-0.637 -0. 058 -0.667 -0. 060 -0.696 -0. 059 -0.725 -0. 056 -0.753 -0. 051. -0.779 -0.050

-0.803 -0. 01.7 -0. 826 -0.01.3 -0. 81.6 -0-039

-0.861. -0.031. -0.880 -0.030

-0. 891. -0.025

-0.906 -0.021 -0.915 -0.016

-0.922 -0.012 -0.928 -0. 009 -0.931 -0.006

-0.933 -0.003

-0.931. -0.001

-0.931. 0.000

-0.931. 0.001 -0.933 0.003 -0.931 0.006 -0.927 0. 009 -0.922 0.013 -0.915 0.017 -0.905 0.021

-0. 893 0.026

-0. 879 0.031 -0.863 0.035

102

F-105
Table 17. Calculated P-p-T locus of the Jouleinversion for raethane.

Thomson

T,K P» BAF MOL/L

16C 'f'f . 67 21.55

165 7C . 15 21.33

170 9'»» 33 21.12

175 117 . 33 20.91

180 139. 2'* 20. 70

185 160 .15 20.50

190 180 . 13 20.29

195 199. 26 2 0 . f 9 2t ti 217 .58 19 . 90

205 235.15 19.70

213 252. 01 19. 51

215 268. 21 19.32

ZZii 283 . 77 19. !' 225 298. 72 1 8. 96

230 3131l 18.78

235 326.92 18.60

ZkQ 3'»C.2L 18. '2

ZU5 352.95 18.25

250 365.21 18.08

255 376.96 17.91

263 388.23 17. 7U

265 399. C3 17.57

270 '09.37 17.'+1

275 '19.2& 17. 2'^ 280 '28.69 17.08

285 '37.66 16.92

290 ('6.2i» 16.76

295 '5'^.3e 16. 6C

300 '62.09 16. '3

3C5 '69. 'L 16.28

310 '76. 3t 16.12

315 '82.79 15.96

323 'e8.89 15. 8C

325 '9'^.6. 15. 6'^

T,iC p |>a,. MoHZ

331) '99.92 15 . '8

335 50'^. 65 15 . 32

3'^0 509. '2 15.17

513.62 15, CI

350 517 . '5 1'^. 85

7 s; t; 7 c U . 7 c X • . o ^

O D U It^ . 5 3 526.61 H^, 38

77o * nu C J . c ^ ±it,ZZ

O f ^ 531.33 lk» C6

3 80 533.08 13. 90

<J o y 53'^ . 5C 393 535 .59 13.58

^ J 536.36 13. '2

V u 536.81 13*26

536.93 13.09

'la 536.73 12.93

(15 536.2^ 12.77

1^20 535.36 12.60

1^25 53'^. 17 12.'^'^ '33 532.65 12.27

'35 530.79 12.10

''0 528.57 11.93

''5 526. CI 11.76

'50 523.06 11.59

'55 519.62 11. '1

'60 516.25 11. 2'^ '65 512. ''^ 11. G6

'70 508. '7 1C.89

'75 50'^.'^2 10.71

'8G 500.3'. 10. 5'^ '85 '96.25 10.37

'9C '92.16 10.20

'95 '88.09 10.

500 'S'^.C'^ 9.88

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F-107

APPENDIX G
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APPENDIX G

The Specific Heats, Cg^rj, and Cy,

of Compressed and Liquefied Methane '

by

B. A. Younglove

The specific heats, ^SAT' '^^ saturated liquid

methane have been measured at 66 temperatures in the

temperature range 95-187 K. The specific heats at

constant volume, Cy, have been measured at 20 densities ranging from 0.8 to 2.8 times the critical density,

at temperatures between 91 and 300 K, and at pressures

to 330 bar (at 280 PVT states in all). The uncertainty

of most of the measurements is estimated to be less

than 0.5%, except near the critical point. These

measurements were performed primarily to provide

input data for accurate thermodynamic properties data

calculations for liquid methane. They are believed to

be the most comprehensive specific heat measurements

available for pure compressed gaseous and liquid methane.

1. Introduction

The specific heat of the saturated liquid has been measured at

66 temperatures between 95 and 187K, These data can be seen in

Figure 1, and as listed in Table 1, Measurements on the specific heat

at constant volume were made at about 280 points from near the triple

point to 300 K and at pressures to near 330 bar. The data were

measured on a path of nearly constant density (isochores). There were

twenty runs made at densities ranging from 8 moles/liter to 28 moles/

liter, the latter being about the density of the liquid at the triple point.

Refer to Figure 2 for a display of Cy versus temperature and to Table 2

for a listing of the data.

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

sponsorship of the American Gas Association.

G-1
2. Method of Measurement

These measurements were all taken with a constant volume

adiabatic calorimeter (Figure 3). The heat capacity, C, is the ratio of

the heat input, DQ, corresponding to a given temperature increase, DT;

cC = ^-CO . (1)

The heat input, DQ, is the product of the cur rent, voltage, and

elasped time that the heater on the calorimeter is operated. The temperature increase, DT, is essentially the increase noted from the steady

state measurements of temperature taken before and after the heating

interval, and CO is the heat capacity of the empty calorimeter.

The heat capacity is divided by the amount of methane, N, as calculated from the initial temperature and pressure measurement using

Goodwin's mathematical representation of the PVT surface of methane;

together with the volume of the calorimeter, V, which is also dependent

on temperature and pressure. This volume, V, is known from previous

expe riments

,

In the case of saturated liquid specific heat capacity, Ca or ^SAT listed in Table 1, the effect of the vapor phase, which is always

present in the calorimeter for this type of measurement, and the effect

of the latent heat of vaporization must be subtracted off the total heat

capacity, C2, or the two-phase heat capacity;

= " - If 1 .

The values of Ca and C2 are shown in columns 9 and 8 respectively of Table 1, The second term of eq (2) is evaluated from the

pressure, temperature and density relation of the liquid phase boundary.

G-2
It is evaluated from

S = ^ (v - N/p) (3)

where p is the density of the saturated liquid, S is referred to as the

"excess" entropy.

The specific heat at constant volume, for the single phase

fluid is evaluated from the total heat capacity by

CV = ^ - Cl , (4)

where C is again evaluated as in eq (1) and CI is the work done by the

methane sample in increasing the volume of the calorimeter as the

pressure increases. This term shown in column 8 of Table 2 can be determined quite accurately once the PVT surface is known. It varies from

0. 5% to 5% of the value of CV. CV is shown in column 9 of Table 2,

3. Results and Discussion of Uncertainties

The uncertainty in the accuracy of the Co measurements is

about 0,5% at temperatures between the triple point and 175 K. Above

that temperature the uncertainty increases to a few percent, and to about

5% near the critical point where Co is increasing very fast. Comparison

2

with the previous data of Wiebe and Brevoort is shown in Figure 4 as

the black circles. Agreement between the two sets of data is within their

estimate of their uncertainty (about 1%) except at lowest temperatures

where larger differences between the two sets of data are seen. The uncertainty in CV is also about 0.5% over the PVT surface except near the critical point, between 180 and 210 K, on runs P, R, S,

and T, where the uncertainty increases to several percent for the larger

values of CV. There are no other measured values of CV for methane

for comparison. However, values of Cp (specific heat at constant pressure) completed from CV using the relation.

G-3
3p

P -2

(5)

V P

3

were compared at P = 137.9 bar (2000 psi) from the data of Jones, et al.

The results are shown in Figure 5 as well as the preliminary calculations

of Cp by Goodwin based only on the equation of state and the Clapeyron

equation.

r The agreement of calculated from eq (5) with the di3 rectly measured values is quite good. The improvement of the .

value from Goodwin's calculation, which in itself is in error mainly

via the latent heat, is clearly seen.

boundary by two methods. First, the data identified by the triangles

(see Table 1, column 9) were computed from Ca by substracting a term

computed from the vapor pressure curve data of Goodwin. ''' The circles

were obtained by extrapolating values of CV along each of the measured

isochores to the liquid-vapor phase boundary. It seems clear that the

latter method produces the more reliable values.

Figure 5 shows CV values computed on the liquid -vapor pha se

G-4
4. References

1. Goodwin, R, D. , private communication

2. Wiebe, R. and Brevoort, M. J. , Journal of the American Chemical

Society, 5^ (1930).

3. Jones, M, L, Jr., Mage, D, T. , Faulkner, R, C, Jr., andKatz,

D. L. , Chemical Engineering Progress Symposium Series, 59

(1963).

G-5
Table Captions

Table 1. Specific heat of saturated liquid methane, Cg^rj,; specific

heat at constant volume of saturated liquid calculated, CV;

specific heat of the two phase (liquid -vapor) system, C2; heat

capacity of the calorimeter (empty) CO, and Heat capacity of

<!" the calorimeter (full) DQ/DT, with temperature, pressure,

density, and temperature increment, DT.

Table 2. Specific heat at constant volume, CV, of methane; heat

correction for calorimeter expansion CI, heat capacity of

empty calorimeter, CO, total heat capacity of calorimeter

(full) DQ/DT, with temperature, pressure, density, and

temperature increment, DT.

G-6
Figure Captions

Figure 1. Specific heat capacity C of saturated liquid methane versus

sat

temperature. Locations of the triple point temperature, T^,

and critical point temperature, T , are indicated.

Figure 2, Specific heat capacity at constant volume CV of gaseous

liquid versus temperature ,

A(Run 19, 28 mol/1)

B(Run 10, 27. 4 mol/1)

C(Run 11, 26. 7 mol/1)

D(Run 12, 25. 8 mol/1)

E(Run 9, 24. 7 mol/1)

F(Run 20, 24 mol/1)

G(Run 14, 23 mol/1)

H(Run 21 , 22. 1 mol/1)

I(Run 8, 21.3 mol/1)

J(Run 17, 19.5 mol/1)

K(Run 18, 18 mol/1)

L(Run 4, 17 mol/1)

M(Run 13, 16. 7 mol/1)

N(Run 16, 16 mol/1)

P(Run 5, 14.4 mol/1)

Q(Run 3, 13.1 mol/1)

R(Run 2, 11.8 mol/1)

S(Run 15, 10.2 mol/1)

T(Run 22, 7. 9 mol/1)

Figure 3. Schematic drawing: The calorimeter and cryostat.

Figure 4. Comparison of C of this work, open circles, to that of

s at

Wiebe and Brevoort, closed circles.

G-7
Figure 5. Comparison of C values of Jones, et al, circles, to values

calculated from CV measurements, triangels, to calculated from PVT and latent heats by Goodwin, solid line.

Figure 6. CV determined by extrapolation of measured CV to the

saturated liquid boundary, circles; and CV calculated from

C , triangles,

sat

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l—l in

r—

(NJ vi o

m, o

CO o

ino

> o

f\l o Oro CNJ o

CO o

(Nl C^

(NJ oCM CNJ (NJ o

ro o

CO (n; o(NJ O

r\j ONCM O

CNJ oro o

CO oCO o

CO

.—1 CO CNJ nj

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ro OCO oro

r—

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o

r-l CO

«cv

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e_Jo

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00

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ro

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in

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(NJ CO o CO -d- <f1^ CO

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00 ON

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CO vO00 ON in

On

COo

o

CO o

^Oln<fr^roocororH^~^-^a^oo^Olnt^l—lOf^"-^cococNI>-^r^ln^-l^^.—ivj-cofNjf^in co<^vDco^C)<^^-^oa^>d-unlnvD^H^-(NJcor\Jcoc\JC^<-^oosD^oc^vOlnoln^-l<^Ln^

v^inajo^cNjcNjcoinc^o-—1'-^>—lco^o^--r^coco01-^coco>j-lncoo^oc\J<^\£)^-a<a

\i. • o.«« 0\ ^-r^r^r-cococooocooNOOOOOO^ONO^ooooooooO'-f'—i"-Ht-!.-<r-ir-i

co<^r^<fco<fo<J-covOvO\OsOoo<}-(NjcocNjcoro^-o>^ooinsd-in«d-inc><tvOoocN

cNioor—(in>—i<^co(ONr^in. (>cNivOr—(in(^CN'cor^rHvi5c\isOroini—lc\J^o<^•-^^ '-HCNiONcor^.-tco{>(Njooor~vOooina^o^<l-cNiror~-ro(>rooo>--<Ln^-rNi<t-<?-rNio

f-Hi—IOOCOfO<^CO>-^^O^OCO<t"^-OOOO^l—

LninroinLninin<}-inunro<t'Lnininin<)-

00 r-H CNJ r\j \0 in

<}- v£) vO v£) <f <J- r-tOOO^ OvO<^^DCOl—lO

Ln<}-v3-ininininininvO

(U

-l-> o

o

I

in CO CNI rH l—l CO CO CO On in o r-l O ro CM O r- o CO rH 00 On o in 00 o ON o vO 00

_J O CO CO <f ro CO <^ ro vO <f ro ON CNI o r- o 00 vO o rH iH vO O ON CM 00 •V. rH <^ CM CM in

LU o o 0^ <}- o I—

o r- O^ ro CNI O C\J 00 00 o iH iH ON rH CO o vO CO nO 0> vO in CO o CT) Q :^

<f <t CO in <h in vJ- (Nl CO CO <}- in in ro CO in <^ <r in CO vO co in vO ro CO vO ro in

_J 00 co CNI (NJ O On 1—1 r~- in O <r CNI CO ro in in iH CNI o fO CO CO O 00 nO O o

CO \ O o r—

1—

r- O CO vD o in ro CNJ r- r- iH o O CNI in CM o sO On rH r-- CO CO ro ON _J CO r- in <r 1—1 r—

l—l 0^ in CO CO ro I—

r-- 1^ vO in CO iH On CO o r-- in On CM 'n O • • d o o o o o o o o O ON o On 0> On 00 CO CO CO CO 00 CO r- r-- vO in in in

CNJ CNJ CNJ CNl CNI CNJ (\1 l—l l—l .—

l—l l—l l—l 1—

iH rH 1—rH rH iH iH rH rH iH rH l—l iH rH rH iH 1—

kD CO OJ vO On vO in o o ro ON (Nl O CNJ CNJ iH OJ O ON CO CO (NJ ON CO (M o in CO

(-0 o o ro On in ro CO <^ r- CNJ <^ ON On 00 <s\ in CO r- <r in rH o in o CO m l—l CO

IlJ or ON O vj in <r in vO ON in (NJ o ro C<1 CO (NJ o O r-~ rH ro in O r-~ r-- 1^ ON O On c> OL <

Cl CD vO 00 CO ON On O O CNJ OvJ co CO ro o vD 00 o c> O o iH ro <^ <) in CO o iH rH

I—

1—1—

1—

f—

1—1 i—i r\j CNI CNg OvJ CNI CNI CNJ CNI CNI CNJ CNI CNI CNI Osl CNI CO ro ro CO CO ro ro co CO <f

a r-l CO vO (M On CO 00 O CO in r- l—l r- o O in CNI O 00 in O o OvJ r~- CO <^ in CNI CNJ iH 1^ ro 00 CO CO CO <r CNJ <}- <t in tn On in c> CO CO O CO CNI CNJ ON CNJ CNI O in iH ro <r CM r-- CM ro LU v: 1—

<f (—

(NJ r—

in in C\J in l—l 1—1 CNJ o rH <!- in o (NJ CNJ O <r On in vO O vO in CM CM iH in vO

h-

.—

t—

CO ro in in in vO On ON o o o rH ro CO CO <f in sD r- CO o rH iH CM <f in o rvO \0 \0 vO nO vO nO nO r- r-- r- r-- r- r- r- r-- 00 CO CO CO CO CO CO CO co

1-H (—1 l—l I—

rH f—l—l 1—l—l r-H r—

r-H iH iH iH iH iH rH ^ iH rH rH l—l 1—

rH rH iH iH iH •H r—

.H -H Q in CO (NJ On r- o O 00 CO CO CO iH rH O o <}- ON rH CNJ o O 1^ CO iH (n; <r rH (NJ CO o o c o o o O o o OJ o c o o iH O rH O o o O CNJ o iH o rH o 1—

CM o O l-^ rH

00 o CO <f ON o CO ON CNI o CO o CNJ o <r <i- CO CM o CM (NJ o (NJ r~ CNJ O CN'

l—l I—

l—l l—l l—l l—l l—l iH iH rH iH rH rH rH iH rH iH rH iH .H

G-10
TABLE 2

ID TEMP

K

2209 200.342

2203 201.339

2210 207.854

2204 203.168

2211 215.402

2212 222.937

2205 222.993

2206 230.373

2213 230.453

2207 237.534

2214 238.128

2208 244.733

2215 245.476

2216 252.815

2218 266.349

15C5 195.780

1523 198.095

1521 198.426

1506 202.601

1502 203.142

1524 203.375

1522 203.731

1525 208.704

1523 209.057

1507 209.526

1503 209.853

1526 214.044

1508 216.467

1504 216.813

1509 223.396

1510 230.790

1511 237.756

1512 244.636

1513 251.488

1514 259.403

1515 266.154

1517 282.516

1518 289.146

1519 295.822

219 195.627

223 196.581

224 203. Q24

225 211.370

205 215.626

226 218.787

206 223.653

227 226.191

CI cv J/MOL.K J/MOL.K

PRESS

BAR

56.917

58.027

65.217

65 .562

73 .451

81.598

81.658

89.583

89.668

97.229

97 .862

104.881

105 .669

113.433

127.671

53.8^3

57.310

57.804

64.048

64.857

65 .206

65 .739

73 .193

73 .722

74 .426

74.915

81 .206

84.845

85.365

95.256

106.373

116.844

127.181

137.466

149.331

159.433

183.843

193.696

203.596

55.318

57.055

70.601

8^.550

92.584

98.572

107.819

112.653

DEN

MOL/L

7.991

7.991

7.988

7.908

7.984

7.980

7.980

7.977

7.977

7.973

7.973

7.970

7.969

7.966

7.959

10.176

10.175

10.174

10.171

10.171

10.171

10.171

10.167

10.167

10. 166

10.166

10. 164

10.161

10.161

10.157

10.151

10.147

10.142

10.137

10.131

10.126

10.114

10.110

10.105

1 1.838

11.839

11.832

11 .826

11.822

11.819

11.815

11.813

DT

K

7.542

5.459

7.559

7.419

7. 5 54

7.511

7.361

7.387

7.484

7.324

7.382

7. 2 92

7.369

7.332

7.246

9.621

7.285

7.393

7. 394

8.023

7.411

8.022

7. 374

DQ/DT

J/K

94.477

94.406

94.152

94 .184

94.22 7

9^1 .677

94.691

95.264

95 . 130

95.819

95.748

96.233

96.374

97.017

97.960

105.430

104,709

103.134

102.930

102.779

102.950

103.224

103.274

CO

J/K

73.734

73.865

74.691

74.729

75. 593

76.439

76.445

77,226

77. 234

77.940

77.998

78.619

78.687

79. 335

80 .436

73. 123

73.436

73.480

74.028

74.098

74, 128

74, 173

74.79 5 74.838

74,895

74,935

75,434

75,715

75,755

76,489

77,268

77,962

78,610

79,221

79,886

80,421

81.599

82.032

82.444

73.102

73.232

74. 198

75. 118

75.618

75.979

76.517

76,789

0. 166

0.167

0. 170

0. 170

0. 175

0.182

0. 182

0. 189

0.189

0.195

0. 196

0.202

0.203

0.210

0.222

0.185

0.189

0. 189

0.194

0.195

0.196

0.197

0.203

0.204

0.203

0.204

0.211

0.213

0.214

0.223

0.233

0.242

0.251

0.261

0.271

0.280

0.301

0.310

0.319

0.204

0.209

0.226

0.242

0.250

0.256

0.265

0.270

35.351

35.004

33 .153

33.141

31.732

31.046

31.059

30.698

30.455

30.419

30.198

3u ,045

3U.034

30.067

29.785

39,325

36.999

36.921

34,818

44.032

34.793

34.382

33.078

33.447

32.879

33,020

32.476

31.750

32.185

31.318

30.432

29.998

29.857

29.650

29.632

29.560

29,922

29,964

30.170

37.165

36. 177

33,223

31.908

31.148

30 .922

30.609

30,347

6.728 102.498

5.257 101.084

5.284 101.071

6.923 100.060

6.470 106.980

5.301 100.142

5.320 99.881

5.334 99.538

5.326 99.856

6.942 99.491

6.955 99.636

5.346 99.736

6.956 99.479

6.945 99.842

6.923 99.937

6.920 100.066

6.901 100.443

6.864 100.993

6.819 101.457

6.782 102.116

6.725 102.604

6.617 104.067

6.625 104.538

6.556 105.109

G-11
TABLE 2--continued.

ID TEV.P

K

207 231.675

223 233.366

2oS 239.625

229 2^t0.92 3

209 2A8.734

210 257.453

211 266.957

212 276.534

214 296.364

30 1 204.751

302 212.016

303 219.265

304 226.524

305 234.072

306 241.245

307 24S.387

309 262.566

310 276.780

313 276.944

314 283.783

311 290.591

312 297.427

501 191.539

528 195.039

502 198.638

520 200.323

503 205.816

521 208.733

504 212.954

522 217.103

505 220.066

523 225.394

506 227.167

524 234.287

507 234.417

508 241.372

525 242.493

509 248.293

510 255.197

511 262.143

514 265.537

512 269.53 8

515 273.495

513 277.494

516 281.439

517 289.349

CI CV

J/MOL.K J/KOl.K

PRESS

BAR

123.117

126.729

13 8.319

140 .803

155.761

17 2.459

190.643

208 .934

246.647

77. 746

9 3.924

110.242

126.697

143 .831

160 .256

176.580

208 .987

241 .398

241 .772

257.318

272.756

288.216

52,228

61.226

70.602

75 .028

89.577

97.366

108 .696

119.884

127.901

142.360

147.180

166 .574

166.928

185 .902

188.962

204.791

223.622

242 .543

251.779

262.650

273.386

284.223

294 . 892

316.229

DEN

MOL/L

11 .803

11.806

11.801

1 1-800

11 .792

11 .784

11.775

11 .766

11 .748

13.088

13.080

13.073

13.065

13.057

13.050

13.042

13.026

13.011

13.010

13 .003

12 .995

12.987

14.388

14.383

14.379

14.377

14.371

14.366

14.3 62

14.356

14.353

14.346

14.344

14.334

14.335

14.326

14.324

14.317

14.308

14.299

14.294

14.289

14.284

14.278

14.273

14.262

DT

K

7.947

7.338

7.906

7.311

7.882

9.556

9.438

9.341

9.271

7.244

7.229

7.214

7. 179

7.166

7. 146

7.078

7.007

6. 874

6.908

6.854

6.847

6. 788

7.056

8.352

7.127

8.432

7.131

8.358

7.102

8.319

7.075

8.245

7.039

8.234

6.969

6.927

8.159

6.910

6. 870

6.820

7.970

7,971

7.928

7.914

7.875

7.793

DO/DT

J/K

103.685

103.858

104.383

104. 171

104.855

105.552

106.408

107. 186

108.845

105.556

105 . 596

105.859

106.293

106.784

107.321

107.969

109. 144

1 10.608

110.434

110.947

111.617

112.344

108.595

107.756

107.453

107.534

107.532

107.655

107.804

107.990

108,187

108,656

108 .887

109.380

109.372

109.898

109.939

110.378

111 .009

111 .759

112.059

112.383

112.890

113.176

113.651

114. 71U

CO

J/K

77.359

77.549

78. 141

78.264

78.979

79. 726

80 .482

81.18 7 82.47o

74.303

75.195

76.033

76.824

77.600

78.295

78.948

80. 140

81.204

81,216

81.684

82.124

82.540

72, 531

73,02 1 73,509

73,732

74.437

74. 799

75.306

75,788

76, 123

76. 704

76.892

77.621

77. 634

78. 307

78.412

78.940

79. 538

80.107

80.373

80.678

80.969

81.255

81.52 7 82. 04^

0.279

0.283

0.293

0.296

0.309

0.323

0.339

0.355

0.388

0.264

0.282

0.299

0.315

0.331

0.34 7

0.362

0.391

0.419

0.4 19

0 .433

0 .446

0.460

0.268

0.281

0.295

0.299

0.315

0.321

0.334

0.34 7

0.356

0.369

0.375

0.392

0.393

0.411

0.412

0.428

0 .44 5 0 .461

0.468

0.478

0.487

0.497

0.506

0.524

3U, 155

30.130

30.04 3

29,653

29,604

29,534

29,632

29,702

30,098

32,393

31,485

30,868

30,478

30 . 165

29,985

29.96 5 2 9 . 9 1 S 3U.309

30 . 1 14

30,1A7

30,375

30 ,687

34,042

32.765

32,000

31,860

31,171

30,94 0

30,585

30.292

30. 152

30.032

30.067

29.826

29.805

29,647

29,585

29,485

29,500

29.656

29.631

29.689

29,885

29,877

30 ,061

30,557

G-12
TABLE 2- - continued

TFMP PRESS

K BAR

70 i 187.947 51.088

70 7 188 .669 53 .498

721 191.577 63.245

702 195.118 75.188

7o8 195 .637 76.943

720 199. 140 88,833

7n3 202.277 99.525

7o9 202 .632 100 .738

704 209.408 123 .943

710 209.569 124.495

711 216.494 148.306

70 5 216.509 148.360

712 223.352 171.937

706 223.900 173 .825

713 230 .437 196.359

714 237.251 219.833

715 244.048 243.213

716 250.777 266.302

717 257.424 289.044

718 264.035 311.587

719 270 .623 333 .970

1601 185.501 42.477

1602 187. 587 49.323

1603 189.591 55.934

16o4 191.595 62 .582

1618 192.871 66 .824

1603 193.605 69.272

1606 195 .61

75.989

1607 197.622 82.719

1608 199.62 8 89 .464

1619 2 00 .03 1 90.821

1620 209.230 121 .946

1609 217.884 15 1.399

1611 223.224 169.616

1610 223.903 171.930

1622 229.42190.764

1612 229.453 190.871

1623 239.424 224.878

1613 241 . 503 231 .959

1614 247.521 252.433

1615 253.443 272.535

1616 259.333 292.473

1617 265.198 312.270

DEN DT DQ/DT

M 0 L / L K

16.104 7 .172 110.110

16.103 6 .957 110.164

16.098 6 .895 110.072

16.093 7 .178 110.019

16.092 6 .947 110 .062

16.087 6 .859 110.111

16.082 7 .135 110.530

16.082 6 .943 110.308

16.071 7 .112 1 10 .909

16.071 6 .933 110.994

16.060 6 .873 111.429

16.060 7 .07 8 111.388

1 6 .049 6 .816 112.095

16.048 7 .007 112.128

16.038 6 .824 112.675

16.027 6 .791 113 .485

16.016 6 .758 113.994

16.005 6 .660 114.660

15.994 6 .627 115.322

1 5.983 6.571 116.177

15.972 6. 544 116.590

1 A . 0 3 R 2 .172 1 1 n . 2 76

16.035 2 .006 110-069

16.032 2 .009 109 . 944

16.029 2 .004 110.119

16.024 6 .135 109.928

16.026 2 .010 109.753

16.023 2 .012 109.895

16.020 2 .003 110.311 X X >^ • _^ X i 16.017 2 .005 1 10.703

16.011 8 .252 110.152

15.996 10 .164 110.765

1 5 .986 6.097 111.290

15.977 6 . 069 111.946

15.976 6 .052 112.026

I 5 .964 10 .032 112 .633

1 5 .967 6 . 063 112.588

1 5 .948 9 .937 113.475

15.948 5 .956 113. 763

15.939 5 .898 114.298

15.929 5 .912 114.868

15.919 5 .842 115.529

15.910 5.849 116.001

CO CI cv

J/K J/MOL.K J/,v,OL.rs

72.012 0.350 32.038

72.118 0.353 31.990

72.537 0.367 31.543

73.032 0.378 31.066

73.103 0.380 31.040

73.576 0.390 30.670

73.987 0.397 30.670

74.032 0.399 30.441

74.881 0.426 30,204

74.901 0.427 30.258

75.718 0.450 29,911

75,720 0.450 29,875

76.484 0.472 29.8o5

76.544 0.473 29.780

77.232 0.494 29.639

77.913 0.515 29,729

78.556 0.536 29,594

79.159 0.557 29.627

79.724 0.577 29,689

80,25o 0.597 29.944

80.759 0.616 29.849

71.648 0.337 32.608

71.959 0.348 32.198

72.252 0.358 31.832

72.539 0.361 31.732

72.719 0.367 31.410

72.822 0.377 31.163

73.100 0.383 31.041

73.373 0.389 31.157

73.640 0.396 30,831

73,693 0.391 30.746

74.859 0.419 30.246

75.877 0.452 29,793

76,470 0.469 29.830

76.544 0.471 29.834

77.128 0.484 29,842

77.131 0.488 29,795

78.122 0.515 29.681

78.319 0.525 29,748

78.871 0.544 29.715

79.389 0.562 29,742

79,880 0.579 29,869

80.347 0.597 29.856

G-13
TABLE 2- -continued.

ID TEMP

K

1309 184.764

1301 187.826

1310 190.103

1302 194.73 3

1311 195.445

1303 201.094

1323 202.937

1312 206.062

1304 206.122

132^ 20S.680

1305 210.401

1313 211.348

1325 214.143

1306 215.024

1314 216.658

1326 219.582

1327 225,003

1317 232.337

1318 237.657

1319 243.097

1320 248.519

1321 253.921

1322 259.304

411 187.325

401 193.924

406 196.587

413 203.953

414 211.988

415 219.901

416 227.768

417 235.598

418 24D.293

419 252.926

1801 178.581

1802 161.649

1803 186.224

1804 192.299

1805 198.354

1806 204.379

1807 210.370

1808 216.641

1809 222.620

1810 228.488

1811 234.30^

1812 240.990

DT DQ/DT

K J/K

5.354 110.741

6.932 110.769

5.347 110.862

6.892 110.968

5.344 111.063

5.855 111.252

6.031 111.551

5.287 111.919

4.249 111.707

5.477 112.228

4.330 112.079

5.286 112.322

5.464 112.494

4.934 112.592

5.219 112.889

5.433 112.992

5,423 113.635

5.178 114.228

5.448 114.856

5.401 115.579

5.387 115.951

5.359 116.619

5.339 117.189

CI CV

J/MOL.K J/MOL.K

PRESS

BAR

45 .449

56.698

65.099

82.255

84.904

105.956

112.841

124.532

124.756

134.336

140 .788

144.339

154.813

158.123

164.252

175.218

195.545

223.009

242.891

26J.174

283.339

303.370

323.264

58.469

83.993

94.337

123.025

154.390

185.282

215.932

245.397

283 .931

313.338

37.972

51.836

72 .545

100 .083

127.540

154.828

181.915

210.187

237.053

263.318

289.242

318.901

DEN

MOL/L

16.723

16.717

16.714

16.706

16. 70 6

16.696

16.693

16.688

16.689

16.683

16.681

16.679

16.674

16.673

16.670

16.665

16.655

16.643

16.633

16.624

16.614

16.604

16.595

17.007

16.997

16.992

16.978

16.964

16.950

16.936

1^.922

16.904

16.890

18.086

18.080

18.068

18.056

18 .044

18.032

18.019

18.006

17.994

17.982

17.970

17.955

8.019

6. 900

7.437

7.970

7.898

7.850

7.807

7.735

7.650

7.598

3. 069

3.085

6.089

6.060

6.039

6.010

5. 964

5.923

5.886

5. 854

5.825

5.797

111.229

111.328

111.563

112.216

113.134

113.769

114.550

115.435

116.261

117.007

112 .484

112 .625

112.813

113.438

113.922

114.564

115.132

115.821

116.615

117. 179

117.723

118.614

CO

J/K

71.537

71.994

72.326

72.979

73.077

73.833

74. 072

74.468

74.475

74.792

75.001

75. 115

75.446

75. 549

75.737

76.069

76.662

77.426

77.952

78.468

78.960

79.430

79.878

71.920

72.867

73.233

74.202

75.192

76. 104

76.955

77.751

78.670

79.345

70.571

71.057

71.756

72.639

73.471

74. 256

74.998

75. 735

76.404

77.031

77.623

78.271

0 . 3 8 i 0.394

0.406

0 .423

0.427

0.446

0.453

0 .465

0 .466

0.4 73

0.481

0.483

0.492

0.496

0.501

0.511

0.530

0.555

0.572

0 .590

0.608

0 .626

0 .644

0.416

0.443

0.452

0.478

0.507

0.535

0.562

0.590

0.623

0.649

0.469

0.496

0.503

0.530

0.554

0.578

0.602

0.627

0.651

0 .674

0.697

0.723

31.721

31.357

31.150

30 .685

3U .679

30.196

30.239

30.204

30.023

30. 184

29,882

29,987

29.847

29.840

29 .924

29.727

29.749

29.585

29.651

29.802

29.686

29.83 1 29.913

31.221

30.513

30.399

30.119

30.033

29.782

29.698

29.743

29.635

29.667

31.280

30.991

30 . 598

30 .377

30.090

29.958

2 9.803

2^.741

29.812

29.742

29.683

29.841

G-14
TABLE 2--continued

,

ID TEMP

K

I7n9 172.603

1710 178.550

1701 181.613

1711 184.637

1702 187.628

1712 190.680

1703 193.640

1713 196.693

170^ 199.616

1714 202.661

1705 205.568

1715 208.615

1706 211.480

1716 214.522

1707 217.573

1717 220.387

1708 223.411

3o7 161.140

Sol 165.189

808 166.828

802 171.921

809 172.488

810 178.091

803 178.582

811 183.640

804 185.182

812 189.153

805 191.734

813 194.626

806 .198.229

814 200.078

2l09 153.984

2101 157.876

2102 162.200

2103 166.497

21o^ 170.767

2105 175.011

2106 179.314

2107 183.514

2108 187.701

CI CV

J/MOL.K J/MOL.K

PRESS

BAR

40 .302

73.409

90 .419

107.182

123.725

140.564

156.357

173.622

189.630

206.260

222.086

238 .633

254.140

270.555

286.970

302.058

318.216

39.441

68.515

80.226

116.429

120 .439

159.906

163.345

198 .640

209.346

236 .787

254.532

274.322

298.849

311.376

30 .846

62 .103

96.526

130 .432

163.847

196.789

229.914

261.982

293.689

DEN

MOL/L

19.500

19.486

19.479

19.4 72

19.465

19.457

19.450

19,443

19.435

19.428

19.421

19.413

19.406

19.398

19.391

19.384

19.376

21.313

21.299

21.296

21 .279

21 .279

21 .262

21.258

21 .244

21.238

21.227

21.218

21.210

21.197

21.193

22.126

22.113

22.098

22.083

22.069

22.054

22.040

22.025

22.011

DT

K

6.087

6.101

6.082

6.065

6. 054

6.039

6.003

5.997

5.980

5.946

5.941

5.92 7

5.895

5.886

5.857

5. 842

5.818

5.723

6.791

5.647

6.676

5.633

5. 566

6.640

13.532

6.587

5.487

6.521

5 .456

6.467

5.439

4.385

4.327

4.314

4.273

4.251

4.233

4.211

4. 186

4. 164

DO/DT

J/K

1 14.035

114.965

115.092

1.1 5 . 5 1 5

115.740

116.187

116.537

116.917

117.239

117.740

117.875

118.353

118.705

118.998

119.326

119.782

120.066

116.134

116.981

117.232

118.171

118.018

118.950

1 18.980

119.742

119.938

120.631

120.927

121 .445

121 .824

122.04^

1 17.42 0

118.099

118.875

119.755

120.349

120.874

121.698

122.103

122.834

CO

J/K

69.577

70.566

71.052

71.517

71. 96^

72.40d

72.827

73.247

73.639

74.036

74.406

74. 784

75. 131

75.490

75.842

76. 158

76.49 1 67.478

68.25 1 68. 554

69.459

69. 557

70.491

70.571

71.365

71. 600

72.188

72.559

72.964

73.454

73. 700

66.016

66. 827

67.684

68.493

69.259

69.985

70.688

71.346

71.976

0.596

0 .608

0.636

0.650

0.663

0.676

0.690

0 .704

0.717

0.731

0. 745

0.759

0.7 72

0.787

0.801

0.814

0.829

0.746

0.772

0.798

0.833

0.831

0.859

0.859

0.890

0.896

0.921

0.933

0.953

0.971

0.985

0.818

0.845

0.927

0.94U

0.951

0.976

1.003

1.029

1.056

30 .637

3^ .586

30,306

30.262

30,094

3 0.082

30.0 2 1 29.980

29.918

29.976

29.798

29.854

29.844

29.783

29.752

29,837

29.789

30 ,544

30,565

3U.507

30 .495

30.336

30.307

30.275

30 ,224

30 , 193

30 ,236

30,175

30 ,229

30 , 139

30 , 109

31,040

30 ,93 1 30 ,800

30 ,832

30.716

30,567

30,615

30.432

30 .468

G-15
TABLE 2- -continued

ID TEMP PRESS

K BAR

1406 148 .82 8 44.459

1407 153.536 10^.131

14o2 155 .969 107.942

1401 156.936 116.449

140S 162.130 161.805

1403 162.555 165 .498

1409 168 .648 217.963

1404 169.076 221.618

1410 175.122 272 .905

140b 175.530 276.347

2001 139.073 45 .399

2002 143.270 88.569

2003 147.448 130.924

200^ 151.599 172.491

£- \J \J 155.908 215.104

2006 160.01 1 255 .209

2007 164.072 294.445

901 130.508 34.766

909 131.693 48.379

904 132.694 59.842

9o2 134.136 76.278

910 137.159 1 10 .410

903 139.337 134.756

911 142.547 170.300

906 143.713 183.112

912 147.886 228,554

907 149 .124 241.915

913 153.185 285.371

908 154.473 299.029

1201 121 . 160 64.484

1202 124.223 104.694

12o3 127.262 144.001

12o^ 130 .274 182.414

uoi 110 .867 44.963

llOo 111.917 60.514

1103 111.855 59.603

1102 116.030 120 .523

uo^ 117.051 135.181

110^ 122.089 206.386

HOB 122 .094 206.433

Il09 127.100 275.431

1103 127. 123 273.769

DEN DT

MOL/L K

22.933 6.789

22.907 6.633

22.906 6.629

22.900 7,882

22.883 6.560

22.881 6.564

22.858 6.496

22.856 6.499

22.834 6.458

22.832 6.440

24.008 4.195

23.990 4.184

23.972 4.155

23.954 4.133

23.935 4.091

23.917 4.084

23.900 4.052

24.785 2.255

24.772 5.484

24.767 5.557

24.761 4.991

24.746 5.421

24.735 5.473

24.720 5.356

24.715 5,439

24,695 5,336

24.689 5.389

24.670 5.287

24.664 5.310

25.872 3.070

25.855 3.048

25.838 3.035

25.822 3.013

26.655 5.194

26.649 5.165

26.649 5.215

26.624 5.136

26.618 5.109

26.588 5.057

26.588 5.U51

26.559 4.981

26.558 5.028

DQ/DT CO

J/K J/K

118.758 64.875

120.057 66.344

120.154 66.435

120.264 66.635

121.193 67.671

121.222 67.753

122.400 68.883

122.320 68.960

123.385 70.003

123.626 70.071

119.866 62.486

120.961 63.554

121.919 64.537

122.597 65.498

123.742 66.422

124.120 67.25o

124.977 68.042

121.056 60.095

121.045 60.443

121.433 60.734

121.346 61.144

122.150 61.977

122.514 62.555

123.309 63.375

123.701 63.663

124.401 64.659

124.607 64.943

125.563 65.844

126.059 66.120

122.005 57.118

122.909 58.138

123.532 59.107

124.390 60.025

121.731 53.349

121.991 53.758

121.835 53.734

123.377 55.306

123.607 55.677

125.308 57.432

125.107 57.434

126.527 59.056

126.592 59.064

CI CV

J/MOL.K J/MOL.K

0.899 31.314

1.015 31.098

1.017 31.100

1,020 31,042

1.042 30,958

1.043 30.925

1.075 30.923

1.078 30.826

1.120 30.798

1.123 30.898

0.988 31.796

1.146 31.655

1.165 31.612

1.191 31.437

1.203 31.550

1.236 31.258

1.268 31.267

1.097 32.662

1.106 32.454

1.136 32.479

1,174 32.166

1.245 32.080

1.258 31.949

1.283 31.911

1,287 31.964

1,303 31.785

1.313 31.732

1.348 31,728

1,359 31,839

1.274 33.145

1.400 32.958

1.420 32.757

1.455 32.691

1.309 33.910

1.354 33.789

1.351 33.724

1.503 33.557

1.510 33.478

1.546 33.415

1.546 33.311

1.574 33.180

1.374 33.210

G-16
TABLE 2- - continued .

T D TEMP PRESS DEN DT DO/ DT

IN BAR MOL / L K J / K

102 .424 48.414 27 .388 5.069 121 .472

lOOi 105 .029 90 .948 27.371 5.078 122.552

" or,

\j \j 107 . 466 129.912 27.355 5.035 123 .275

1002 110.058 170 .73 5 27.338 4.981 124.205

1006 112.446 207.806 27.322 4. 941 125.126

1003 115.142 249.013 27.305 4.914 126.082

loo'i' 117.361 282.491 27.290 4.903 126.695

1912 92.592 40 .274 28.164 3.061 120 .491

1901 92 .609 40.540 28.164 2.871 120.603

1907 93.793 62.384 28.155 2.873 121 .008

1902 95 .465 92.859 28.143 2. 842 122.072

1913 95 .634 95 .885 28.141 3.022 122 . 178

1903 96.675 114.525 28.134 2 .824 122 .424

19o3 98.301 143 .313 28.122 2.807 123 . 144

l9o9 99.505 164.435 28.114 2.821 123.531

1904 101.123 192.506 28.102 2. 793 124.316

1910 102.319 213.085 28.093 2.791 124.573

1905 103.902 240 .032 28.082 2 • 1 49 12 5.401

1911 105 .104 260.314 28 .074 2.766 125.538

1906 106.655 286.252 28.063 2.751 126.307

CO r 1 CV

J / ,ViOI . K J / M n 1 . 49.858 1.475 34.42 8

50.974 1.619 34 , 267

51.986 1.613 34 . 129

53.030 1 .637 34 .049

53.962 1 .646 34.035

54.9 79 ] . 652 33 .999

55.789 1 .673 33.879

45.3 11 1.351 35.326

45.319 1.313 35.415

45 . 899 1.458 35 . 186

46. 701 . 769 35 .003

46. 780 1 .765 35.020

47.269 1 .769 34, 898

48.020 1 . 740 34.913

48.566 1.745 34.830

49 . 288 1.768 34,839

49.812 1.767 34.710

50.495 1.755 34.793

51 .005 1.766 34.600

51. 653 1.781 34.644

G-17
Figure 1 G-18
G-19
Figure 3

G-20


Figure 6

G-23

IB- 10^889 I
*FORM N6S-114A (1-71) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 73-300

2. Gov't Accession No.

4. TITLE AND SUBTITLE THIRD ANNUAL PROGRESS REPORT ON

SURVEY OF CURRENT INFORMATION ON LNG AND

METHANE, THE THERMOPHYSICAL PROPERTIES OF

METHANE, AND METROLOGY

3. Recipient's Accession No.

5. Publication Date March 1973

6. Performing Organization Code

7. AUTHOR(s) Neii A, Oiien, K. U. Goodwin, ±5. A. Y ounglove

,

G. C. Straty, D. B. Mann, and R. J. Richards

8. Performing Organization

NBSIR 73-300

10. Project/Task/ Work Unit No. 2750364

9, PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS, Boulder Labs.

DEPARTMENT OF COMMERCE

Boulder, Colorado 80302

11. Contract/Grant No. The American Gas

As sn.

12. Sponsoring Organization Name and Address

The American Gas Association

1515 Wilson Boulevard

Arlington (Rosslyn), Virginia 22209

13. Type of Report & Period

Covered

Annual Report

14. %>onsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summaty of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) This report summarizes the third year of progress on a licjuefied natural gas

program supported by the American Gas Association, Incorporated. The report is

in three parts and reflects the areas of interest defined by the sponsor. Part I summarizes the work done by the Cryogenic Data Center in acquiring and disseminating published information on liquefied natural gas. Part 2 summarizes the work

done by the Properties of Cryogenic Fluids Section on the experimental determinatior'

of the thermophy sical properties of compressed fluid methane. Part 3 summarizes

the work done by the Cryogenic Metrology Section on liquid level and flow rate

metrology on liquefied natural gas.

17. KEY WORDS (Alphabetical order, separated by semicolons) Densities; equation of State; flow metering;

liquefied natural gas; liquid level; methane; metrology; specific heats; stratification;]

thermophysical properties.

18. AVAILABILITY STATEMENT

[X] UNLIMITED.

I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

239

22. Price

USCOMM-C5C 66244.P'^

«U.S. Government Printing Office: 1 9 7 3-784-21 1/1 130 Regionl