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PUBLICATIONS

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NAT'L INST. OF STAND & TECH

llll llll I II II II AlllDb 3^220

^fCAU O* * NBS TECHNICAL NOTE 1097

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

Interactive FORTRAN Programs for

Micro Computers to Calculate the

Thermophysical Properties of

Twelve Fluids [MIPROPS]

Robert D. McCarty
TM he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

m 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

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: Some divisions within the center are located at Boulder, CO 80303. 'Located at Boulder, CO, with some elements at Gaithersburg, MD.
RESEARCH

k \s) INFORMATION CENTER

Interactive FORTRAN Programs for Micro

Computers to Calculate the

Thermophysical Properties of Twelve

Fluids [MIPROPS]

Robert D. McCarty

Thermophysics Division

Center for Chemical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

Sponsored in part by

National Aeronautics and Space Administration

Lyndon B. Johnson Space Center

Houston, Texas 77058

^—JT"

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued May 1986
National Bureau of Standards Technical Note 1097

Natl. Bur. Stand. (U.S.), Tech Note 1097, 90 pages (May 1986)

CODEN:NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1986

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402
CONTENTS

Page

1. Introduction 1

2

.

Uncertainties of the Calculated Properties 2

3. Computer Routines 2

4

.

Acknowledgments 2

5

.

References 3

Appendix A. Description of Individual Fluids 4

Parahydrogen 5 Helium 6 Nitrogen 7 Oxygen 8 Argon 9 Nitrogen Trifluoride 10 Methane 11 Ethylene 12 Ethane 13 Propane 14 Isobutane 15 Normal Butane 16

Appendix B . Sample Computer Sessions 17

Appendix C . Program Listings 20 Program Listing of MIPROPS 21 Program Listing of HELIUM 64

m

INTERACTIVE FORTRAN PROGRAMS FOR MICRO COMPUTERS TO CALCULATE THE THERMOPHYSICAL PROPERTIES OF TWELVE FLUIDS [MIPROPS]

Robert D. McCarty

Thermophysies Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

The thermophysical and transport properties of selected fluids have been

programmed in FORTRAN 77 which is available for micro computers. The input

variables are any two of P, p, T (pressure, density, and temperature) in the single

phase regions, and either P or T for the saturated liquid or vapor states. The

output is pressure, density, temperature, internal energy, enthalpy, entropy,

specific heat capacities (C

p and C v ), speed of sound and, in most cases, viscosity,

thermal conductivity and dielectric constant.

The fluids included are: helium, hydrogen, nitrogen, oxygen, argon, nitrogen

trifluoride, methane, ethylene, ethane, propane, iso- and normal butane. The

programs give properties in both the liquid and vapor states over a wide range of

temperature and pressure. Copies of the program may be obtained from the Office of

Standard Reference Data, Room A320, Physics Building, National Bureau of Standards,

Gaithersburg, MD 20899.

Key words: argon; computer programs; density; dielectric constant; enthalpy;

entropy; equation of state; ethane, ethylene; heat capacity; helium; hydrogen;

internal energy; isobutane; methane; nitrogen; nitrogen trifluoride; normal butane;

oxygen; pressure; speed of sound; temperature; thermal conductivity; viscosity.

1 . Introduction

Recent technological advances in the field of personal computers have made it possible

and practical to run large FORTRAN programs on these machines. The programs presented here

will run satisfactorily on a wide variety of personal computers on the market today.

The programs are a direct translation of those developed by Younglove [1,2], with five

additional fluids added [3]. The separate program for helium originally appeared in NBS

Technical Note 1025 by McCarty [4] and was, in turn, derived from an earlier evaluation of

helium data [5]. The programs in the above-mentioned documents were written as interactive

FORTRAN IV programs intended to run on large main frames. The programs presented here are translations of the originals to FORTRAN 77 adapted to personal computers and reproduce the

calculations of tne originals exactly.

All of the fluids except helium utilize the same mathematical model of the equation of

state which was originally proposed by Jacobsen [6]. The model for the helium thermodynamic

surface is of a different form, and a separate program was necessary for that fluid. The

mathematical model of the transport properties of the fluids which have been added to those

from NBS Technical Note 1048, has been improved and new routines are utilized for those

fluids.

/
The programs produce the transport properties for all of the fluids except hydrogen,

nitrogen trifluoride, ethylene, ethane and propane. The dielectric constant is also provided

for all of the fluids except argon, ethylene and nitrogen trifluoride.

There is a section devoted to each fluid in Appendix A and the reader is referred to those sections for further information on an individual fluid. Listings of the source code

and sample calculations may be found in Appendices B and C.

2. Uncertainties of the Calculated Properties

When calculating thermodynamic properties from an empirical equation of state, one should

be aware of certain problem areas of the thermodynamic surface. In the critical region

(p c _+ 0.2 p c and T c + 0.05 T c ), the calculated density may be in error by several percent,

while the calculated pressure or temperature will not be as inaccurate. Values of specific

heat capacity and thermal conductivity in the critical region become very large and no realistic estimate of the uncertainty may be made. Saturation boundaries, gas-liquid, and

liquid-solid are potential areas of large uncertainties for derived thermodynamic properties,

especially heat capacities. In the compressed liquid region, calculated pressures will have

an uncertainty of several percent. This is a consequence of the nature of the surface and is in no way the fault of the equation of state.

In each of the sections on the individual fluids, uncertainty estimates are given for

that particular fluid. These estimates do not reflect the potential large uncertainties of

the problem areas outlined above.

3. Computer Routines

The thermophysical properties produced by the computer programs listed in Appendix C are

all calculated using a mathematical model of the equation of state of the fluid and classical

thermodynamic relationships. The reader who is interested in the thermodynamics and

mathematics of the problem is referred to McCarty [7]. In general eleven or twelve significant figures are needed in the property calculations

to prevent round off errors. Sample calculations for each fluid are given in Appenidx A for

the purpose of checking the performance of the programs on individual computers.

Upper and lower temperature and pressure limits for each fluid have been installed in the

programs according to the range of validity as claimed by the original source document. All

of the functions reduce to the ideal gas in the limit of zero pressure, but because of the

very large exponents in some of the terms, the iterative solution for density fails at very

low pressures. Because the models are empirical and cannot be trusted to give even reasonable

results outside their ranges of pressure and temperature, the user is cautioned not to change

the pressure or temperature limits originally set in the programs.

4. Acknowledgments

The author wishes to acknowledge the support of MASA, without which this work would not have been possible, and in particular the support and encouragement of Dr. Timothy Cleghorn at the Johnson Space Center.
5. References

[I] Younglove, 3. A. Interactive fortran program to calculate thermophysical properties of

six fluids. Nat. Bur. Stand. (U.S.) Tech. Note 1048; 1982.

[2] Younglove, B. A. Thermophysical Properties of Fluids. I. Argon, ethylene, parahydrogen,

nitrogen, nitrogen trifluoride, and oxygen. J. Phys. Chem. Ref. Data Vol. 11, Supplement

No. 1; 1982.

[3] Ely, J. F. Thermophysical properties of methane, ethane, propane, normal and isobutane.

to be published.

[4] McCarty, R. D. Interactive FORTRAN IV computer programs for the thermodynamic and

transport properties of selected cryogens [Fluids Pack], Nat. Bur. Stand. (U.S.) Tech.

Note 1025; 1980.

[5] McCarty, R. D. Thermodynamic Properties of Helium 4 and 2 to 1500 K at Pressures to 1 0®

Pa. J. Phys. Chem. Ref. Data Vol. 2, No. 4, 923"1042; 1973

[6] Jacobsen, R. T. ; Stewart, R. B.; McCarty, R. D.; Hanley, H. J. M. Thermophysical

properties of nitrogen from the fusion line to 3500 R [1944 K] for pressures to 150,000 psia [10342 x 1 5 N/rn2

]. Nat. Bur. Stand. (U.S.) Tech. Note 648; 1973 Dec.

[7] McCarty, R. D. Determination of thermodynamic properties from the experimental P-V-T relationships. Vol. II, Experimental thermodynamics of non-reacting fluids. LeNeindre,

3.; Vodar, B., eds. Butterworth and Co., Ltd., London, England; 1975.

[8] Roder, H. M. ; McCarty, R. D. A modified Benedict-Webb-Rubin equation of state for

parahydrogen-II. Nat. Bur. Stand. (U.S.) N3SIR 75-814; 1975.

[9] Stewart, J. W. Dielectric polarizability of fluid parahydrogen. J. Chem. Phys. 40: 3297-3306; 1964.

[10] Weber, L. A. A modified Benedict-Webb-Rubin equation of state for gaseous and liquid

oxygen. Nat. Bur. Stand. (U.S.) N3SIR 78-882; 1978.

[II] Sly, J. F.; Straty, G. C. Dielectric constants and molar polarizabilities of saturated

and compressed fluid nitrogen. J. Chem. Phys. 61: 1480-1485; 1974.

[12] Younglove, B. A. Dielectric constant of compressed gaseous and liquid oxygen. J. Res. Nat. Bur. Stand. (U.S.) 76A: 37-40; 1972.

[13] Stewart, R. B.; Jacobsen, R. T.; Becker, J. H. A thermodynamic property formulation for

argon using a 32 term pressure explicit equation of state. Center for Applied

Thermodynamic Studies Report No. 81 ~3; University of Idaho, Moscow, ID; 1983 July.

[14] Goodwin, R. D.; Weber, L. A. Thermophysical properties of nitrogen trifluoride from 66 to 500 K at pressures to 500 bar. Nat. Bur. Stand. (U.S.) NBSIR 80-1532; 1980 Jul.

[15] McCarty, R. D.; Jacobsen, R. T. An equation of state for fluid ethylene. Nat. Bur. Stand.

(U.S.) Tech. Note 1045; 1981.
Appendix A Description of Individual Fluids
[PARAHYDROGEN]

The source of the hydrogen equation of state is N3SIR 75-814 by Roder and McCarty [8] and

Stewart [9].

Estimated Uncertainties {%)

Property

Pressure

Density

Temperature

Enthapy & Internal Energy

Entropy

Cp and C v Speed of Sound

Liquid Bel ow T c Gas Below

5.0 0.25

0.1 0.25

0.1 0.25

1 .0 3.0

1 .0 1 .0 3-0 2.0

2.0 1 .0

Fluid Above T ( 0.20

0.20

0.20

5.10

1 .0 3-0

1 .0

Fixed Points

Critical Point

Triple Point Liquid

Triple Point Vapor

Pressure, MPa

1 .2838

0.00743

0.00743

Density, M/L

15.556

0.06323

38.2143

Temperature, K 32.933

13.80

Temperature Range 13.8 to 400 K

Pressure Range to 120 MPa

Sample Calculations

THE TEMPERATURE RANGE FOR HYDROGEN IS 13.8 TO 400 K

(-434.8 TO 260 F) WITH PRESSURES TO 120 MPA (17404 PSIA)

FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "1"

1FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "1"

FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "1"

FOR SATURATED LIQUID ENTER "0", FOR VAPOR ENTER "1"

TO ENTER WITH TEMPERATURE ENTER "0", FOR PRESSURE "1"

1ENTER A PRESSURE (MPA) RESTARTS THE PROGRAM

.1

P T DEN E H S CV CP SOUND VI SC COND DIEL

MPA K MOL/L === J/MOL == ==== J/MOL-K === M/S PA-S MW/M-K ==

E + 6 .100 20.23 35.144 -520. -517. 16.1 11.4 19.4 1102. 1.22999

ENTER A PRESSURE (MPA) RESTARTS THE PROGRAM
[HELIUM]

The source of the helium equation of state is McCarty [10].

Estimated Uncertainties (%)

Property Liqu:Id Below T c Gas Below T Pressure 10.0 0.2

Density 0.5 0.2

Temperature 0.5 0.2

Enthapy & Internal Energy 2.0 1 .0 Entropy 2.0 1.0

Cp and C v 2.0 2.0

Speed of Sound 2.0 1 .0 Thermal Conductivity 10.0 10.0

Viscosity 8.0 8.0

Fluid Above Tc 0.2

0.2

0.2

1.0

1.0

0.5

0.5

10.0

10.0

Fixed Points

Critical Point

Lambda Point Liquid

Lambda Point Vapor

Pressure, MPa

0.2275

0.00496

0.00496

Density, M/L

17.399

36.534 3 0.2904

Temperature, K 5.2014

2.172

2.172

Temperature Range 2 - 1 500 K

Pressure Range 0-100 MPa

Sample Calculations

FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "1

FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "1

FOR SATURATED LIQUID ENTER "0", FOR VAPOR ENTER "1"

TO ENTER WITH TEMPERATURE ENTER "0", FOR PRESSURE "1

1ENTER A PRESSUREC MPA)

. 1

P T MPA K DEN E H MOL/L === J/MOL

S

- CV CP SOUND VISC COND DIEL

==== J/MOL-K === M/S PA-S MH/M-K ==

E + 6 .100 4.21 31.291 -24. -20. 14.2 9.5 19.7 173. 31.8 19.6 1.04925
[NITROGEN]

The source of the nitrogen equation of state is Jacobsen, et al. [6] and Ely and Straty [11]

Estimated Uncertainties (%)

Property Liqu:Ld Below T c Gas Below T Pressure 5.0 0.3

Density 0.5 0.3

Temperature 0.5 0.3

Enthapy & Internal Energy 3.0 1.0

Entropy 2.0 1 .0 Cp and C v 5.0 5.0

Speed of Sound 2.0 0.25

Thermal Conductivity 4.0 4.0

Viscosity 2.0 2.0

Fluid Above T c 0.3

0.2

0.2

1.0

1 .0 5.0

1 .0 6.0

2.0

Fixed Points

Critical Point

Triple Point Liquid

Triple Point Vapor

Pressure, MPa

3.4100

0.1246

0.1246

Density, M/L

11 .21 30.977

0.2396

Temperature, K 126.26

63.15

63.15

Temperature Range 63.15 - 1900 K

Pressure Range - 1000 MPa

Sample Calculations

THE RANGE OF TEMPERATURE FOR NITROGEN IS 63.15 TO 1900 K WITH PRESSURES TO 1000 MPA

FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "

1

1FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "

1

FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "

1

FOR SATURATED LIQUID ENTER "0", FOR VAPOR ENTER "1"

TO ENTER WITH TEMPERATURE ENTER "0", FOR PRESSURE "1"

1ENTER A PRESSURE( MPA)

. 1

P T MPA K DEN E H MOL/L === J/MOL

S CV CP SOUND VISC COND DIEL

==== J/MOL-K === M/S PA-S MW/M-K ==

E + 6 .100 77.25 28.881 -3411. -3407. 79.5 27.8 57.8 941. 152.2 133.8 1.43386
[OXYGEN]

The source of the oxygen equation of state is Weber [10] and Younglove [12]

Estimated Uncertainties (%)

Property Liquid Bel ow T c Gas Below T Pressure 5.0 0.25

Density 0.1 0.25

Temperature 0.1 0.20

Enthapy & Internal Energy 0.5 0.25

Entropy 0.5 0.25

Cp and C v 3.0 5.0

Speed of Sound 2.0 0.50

Thermal Conductivity 4.0 4.0

Viscosity 2.0 2.0

Fluid Above T c 0.15

0.15

0.10

0.50

0.50

3.0

0.50

6.0

2.0

Fixed Points

Critical Point

Triple Point Liquid

Triple Point Vapor

Pressure, MPa

5.0422

0.1490 x 10~3

0.1490 x 10~3

Density, M/L

13.63

40.820

0.3275 x 10~3

Temperature, K 154.481

54.359

54.359

Temperature Range 54.359 to 400 K

Pressure Range 0-120 MPa

Sample Calculations

THE RANGE OF TEMPERATURE FOR OXYGEN IS 54. 359 TO 400 K WITH PRESSURES TO 120 MPA

FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "1"

1FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "

1

FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "1"

FOR SATURATED LIQUID ENTER "0", FOR VAPOR ENTER "1"

TO ENTER WITH TEMPERATURE ENTER "0", FOR PRESSURE "1"

1ENTER A PRESSURE( MPA)

. 1

P T DEN E H S CV CP SOUND VISC COND DIEL

MPA K MOL/L === J/MOL == ==== J/MOL-K === M/S PA-S MW/M-K ==

E + 6 .100 90.07 35.677 -4272. -4270. 94.1 29.6 54.2 906. 195.3 152.0 1.48734
[ARGON]

The source of the argon equeition 01 state is ouem11 t, c: U ca-L • L i J J •

Estimated Uncertainties (%)

Property Liqu.Ld Below T c Gas Below T c Flui d Above T c

Pressure 10.0 0.3 0.3

Density 0.25 0.3 0.3

Temperature 0.25 0.3 0.3

Enthapy & Internal Energy 2.0 1.0 1.5

Entropy 1 .0 1 .0 1 .0

C

p and C v 5.0 5.0 5.0

Speed of Sound 5.0 5.0 5.0

Thermal Conductivity 4.0 4.0 6.0

Viscosity 2.0 2.0 2.0

Fixed Points

Critical Point

Triple Point Liquid

Triple Point Vapor

Pressure, MPa

4.8980

0.0689

0.0689

Density, M/L

13-41

35.40

0.1015 x 10"3

Temperature, K 150.86

83.8

83.8

Temperature Range 83.8 to 400 K

Pressure Range 0-100 MPa

Sample Calculations

THE TEMPERATURE RANGE FOR ARGON IS 83. 8 TO 400 K WITH PRESSURES TO 100 MPA

FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "

1

1FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "1"

FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER " 1

FOR SATURATED LIQUID ENTER "0", FOR VAPOR ENTER "1

TO ENTER WITH TEMPERATURE ENTER "0", FOR PRESSURE " 1

1ENTER A PRESSUREC MPA)

. 1

P T DEN E H S CV CP SOUND VISC COND DIEL

MPA K MOL/L === J/M0L == ==== J/MOL-K === M/S PA-S MH/M-K ==

E + 6 .100 87.16 34.914 -4714. -4711. 54.8 22.3 44.7 815. 261.2 128.5
[NITROGEN TRIFLUORIDE]

The source of the nitrogen trifluoride equation of state is Goodwin and Weber [14].

Estimated Uncertainties (%)'

Property Liquid Below T c Gas Below T Pressure 5.0 0.2

Density 0.1 0.2

Temperature 0.1 0.1 Enthapy & Internal Energy 2.0 2.0

Entropy 2.0 2.0

C

p and C v 5.0 5.0

Speed of Sound 5.0 5.0

Fluid Above T c 0.1

0.1

0.1 2.0

2.0

5.0

5.0

Fixed Points

Critical Point

Triple Point Liquid

Triple Point Vapor

Pressure, MPa

4.4607

0.1854 x 10~ 6

0.1854 x 10~ 6

Density, M/L

7.92

26.32

Temperature, K 234.0

66.35

0.33612 x 10~ 6 66.35

Temperature Range 66.36 to 500 K

Pressure Range 0-50 MPa

Sample Calculations

THE RANGE OF TEMPERATURE OFR NITROGEN TRIFLUORIDE IS

66. 36 TO 500 K, WITH PRESSURES TO 50 MPA

FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "1"

1FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "1"

FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER - 1 -

FOR SATURATED LIQUID ENTER "0", FOR VAPOR ENTER "

1

TO ENTER WITH TEMPERATURE ENTER "0", FOR PRESSURE "1"

1ENTER A PRESSUREC MPA)

. 1

P T DEN E H S CV CP SOUND VISC COND DIEL MPA K MOL/L === J/MOL == ==== J/MOL-K === M/ S PA-S MW/M-K ==

E + 6 .100 143.92 21.669 -6846. -6841. 147.6 40.3 72.2 759.

Estimates not from original source.

10
[METHANE]

The source of the methane equation of state is Ely, et al . [3].

Estimated Uncertainties (%)'' Property Liquid Below T c Gas Below T Pressure 5.0 0.25

Density 0.1 0.25

Temperature 0.1 0.25

Enthapy & Internal Energy 1 .0 0.5

Entropy 0.5 0.5

Cp and Cy 2.0 5.0

Speed of Sound 1 .0 0.3

Thermal Conductivity 5.0 5.0

Viscosity 3-0 3-0

Fluid Above T c 0.25

0.25

0.25

0.50

0.50

2.00

0.3

H.O

2.0

Fixed Points

Critical Point

Triple Point Liquid

Triple Point Vapor

Pressure, MPa

4.599

0.01174

0.01174

Density, M/L

10.23

28.151

0.01569 x 10" 6

Temperature, K 190.55

90.68

90.68

Temperature Range 90.68 to 600 K

Pressure Range - 200 MPa

Sample Calculations

THE RANGE OF TEMPERATURE FOR METHANE IS 90.68 TO 600 K WITH PRESSURES TO 200 MPA

FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "1"

1FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "1"

FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "

1

FOR SATURATED LIQUID ENTER "O", FOR VAPOR ENTER "1"

TO ENTER WITH TEMPERATURE ENTER "0", FOR PRESSURE "1"

1ENTER A PRESSURE( MPA)

. 1

P T MPA K DEN E H MOL/L === J/MOL

S CV CP SOUND VISC COND DIEL

==== J/MOL-K === M/S PA-S MW/M-K ==

E + 6 .100 111.47 26.355 -4629. -4625. 79.0 32.9 55.5 1336. 117.6 188.8 1.62653

Estimates not from original source.

11
[ETHYLENE]

The source of the ethylene equation of state is MeCarty and Jacobsen [15]

Estimated Uncertainties {%)'

Property Liquid Below T C Gas Below T Pressure 5.0 0.15

Density 0.15 0.15

Temperature 0.15 0.15

Enthapy & Internal Energy 2.0 1 .0 Entropy 2.0 1 .0 Cp and C v 5.0 2.0

Speed of Sound 3.0 1 .0

Fluid Above Tc 0.15

0.15

0.15

1 .0

1 .0 2.0

1 .0

Fixed Points

Critical Point

Triple Point Liquid

Triple Point Vapor

Pressure, MPa

5.0103

0.12 x 10"3

0.12 x 10"3

Density, M/L

7.634

23.389

0.14 x 10"3

Temperature, K 282.3^3

103.986

103.986

Temperature Range 104 to 400 K

Pressure Range 0-40 MPa

Sample Calculations

THE TEMPERATURE RANGE FOR ETHYLENE IS 104 TO 400 K WITH PRESSURES TO 40 MPA

FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "1"

1FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "

1

FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "

1

FOR SATURATED LIQUID ENTER "0", FOR VAPOR ENTER "1"

TO ENTER WITH TEMPERATURE ENTER "0", FOR PRESSURE "1

ENTER A PRESSURE( MPA)

. 1

P T DEN E H MPA K MOL/L === J/MOL

S CV CP SOUND VISC COND DIEL

==== J/MOL-K === M/S PA-S MW/M-K ==

E + 6 100 169.19 20.256 -8017. -8012. 117.6 38.2 67.9 1312.

'Estimates not from original source.

12
[ETHANE]

The source of the ethane equation of state is Ely, et al . [3].

Estimated Uncertainties {%)

Property Liquid Below T c Gas Below T c Pressure 5.0 0.25

Density 0.1 0.25

Temperature 0.1 0.25

Enthapy & Internal Energy 1 .0 1 .0 Entropy 1 .0 1 .0

C

p and C v 5.0 5.0

Speed of Sound 5.0 5.0

Fluid Above T c 0.15

0.15

0.15

1 .0 1.0

5.0

5.0

Fixed Points

Critical Point

Triple Point Liquid

Triple Point Vapor

Pressure, MPa

4.871

0.1 1308 x 10~ 5 0.11308 x 10" 5

Density, M/L

6.8

21.68

0.1515 x 10~5

Temperature, K 305.33

90.3^8

90. 3^8

Temperature Range 90.33 to 600 K

Pressure Range 0-70 MPa

Sample Calculations

THE RANGE OF TEMPERATURE FOR ETHANE IS 90. 35 TO 600 K WITH PRESSURES TO 70 MPA

FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "1"

1FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "

1

FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "1"

FOR SATURATED LIQUID ENTER "0", FOR VAPOR ENTER "1"

TO ENTER WITH TEMPERATURE ENTER "0", FOR PRESSURE "1"

1ENTER A PRESSURE( MPA)

. 1

P T DEN E H S CV CP SOUND VISC COND DIEL

MPA K MOL/L === J/MOL == ==== J/MOL-K === M/S PA-S MW/M-K ==

E + 6 .100 184.31 18.105 -8263. -8258. 126.8 42.6 73.1 1324. 1.7572!

Estimates not from original source.

13
[PROPANE]

The source of the propane equation of state is Ely, et al. [3].

Estimated Uncertainties (%)'

Property Liquid Below T c Gas Below T Pressure 5.0 0.25

Density 0.1 0.25

Temperature 0.1 0.25

Enthapy & Internal Energy 1 .0 1 .0 Entropy 1 .0 1.0

Cp and C v 5.0 5.0

Speed of Sound 5.0 5.0

Thermal Conductivity 5.0 5.0

Viscosity 3.0 3.0

Fluid Above Tc 0.15

0.15

0.15

1.5

1.5

5.0

5.0

5.0

3.0

Fixed Points

Critical Point

Triple Point Liquid

Triple Point Vapor

Pressure, MPa

4.247

0.1690 x 10~ 9 0.1690 x 10~9

Density, M/L

5.00

16.630

0.2238 x 10~ 9

Temperature, K 369.85

85.47

85.47

Temperature Range 85.47 to 600 K

Pressure Range 0-100 MPa

Sample Calculations

THE RANGE OF TEMPERATURE FOR PROPANE IS 85. 47 TO 600 K WITH PRESSURES TO 100 MPA

FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "1"

1FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "1"

FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "1"

FOR SATURATED LIQUID ENTER "0", FOR VAPOR ENTER "

1

TO ENTER WITH TEMPERATURE ENTER "0", FOR PRESSURE "1"

1ENTER A PRESSURE( MPA)

. 1

P T DEN E H S CV CP SOUND VISC COND DIEL

MPA K MOL/L === J/MOL == ==== J/MOL-K === M/

S

PA-S MW/M-K ==

E + 6 .100 230.78 13.188 -8826. -8818. 171.0 64.0 99.0 1160. 1.80350

Estimates not from original source.

14
[ISOBUTANE]

The source of the isobutane equation of state is Ely, et al. [3]

Estimated Uncertainties {%)'

Property- Li qui:d Below T c Gas Below T c Flui d Above T c Pressure 5.0 0.20 0.15

Density 0.1 0.20 0.15

Temperature 0.1 0.20 0.15

Enthapy & Internal Energy 1 .0 1.0 1.0

Entropy 1 .0 1.0 1.0

Cp and C v 3-0 3.0 3.0

Speed of Sound 3.0 3.0 3-0

Thermal Conductivity 5.0 5.0 5.0

Viscosity 3.0 3-0 3.0

Fixed Points

Critical Point

Triple Point Liquid

Triple Point Vapor

Pressure, MPa

3.690

0.19^81 x 10~ 7

0.19481 x 10~ 7

Density, M/L

3.86

12.755

0.20633 x 10~ 7

Temperature, K 407.85

113.55

113.55

Temperature Range 113-55 to 600 K

Pressure Range 0-35 MPa

Sample Calculations

THE RANGE OF TEMPERATURE FOR ISO BUTANE IS

113.55 TO 600 K WITH PRESSURES TO 35 MPA

FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "1"

1FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "

1

FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "1"

FOR SATURATED LIQUID ENTER "0", FOR VAPOR ENTER "

1

TO ENTER WITH TEMPERATURE ENTER "0", FOR PRESSURE "1"

1ENTER A PRESSURE( MPA)

. 1

P T DEN E H MPA K MOL/L === J/MOLS CV CP SOUND VISC COND DIEL

==== J/MOL-K === M/S PA-S MW/M-K ==

E + 6 .100 261.20 10.220 -7116. -7106. 200.8 92.1 130.4 1010. 229.2 112.2 1.82016

Estimates not from original source.

15
[NORMAL BUTANE]

The source of the normal butane equation of state is Ely, et al . [3]

Estimated Uncertainties {%)

Property Li qui.d Below T c Gas Below T c Flui d Above T c Pressure 5.0 0.20 0.15

Density 0.1 0.20 0.15

Temperature 0.1 0.20 0.15

Enthapy & Internal Energy 1 .0 1.0 1 .0

Entropy 1 .0 1 .0 1.0

Cp and C v 3.0 3.0 3.0

Speed of Sound 3.0 3.0 3.0

Thermal Conductivity 5.0 5.0 5.0

Viscosity 3.0 3.0 3.0

Fixed Points

Critical Point

Triple Point Liquid

Triple Point Vapor

Pressure, MPa

3.796

0.6736 x 10~ 6

0.6736 x 10" 6

Density, M/L

3.92

12.65

0.60071 x 10~ 6

Temperature, K 425.16

13^.86

134.86

Temperature Range 134.65 to 500 K

Pressure Range 0-70 MPa

Sample Calculations

THE RANGE OF TEMPERATURE FOR NORMAL BUTANE IS

1 34. 68 TO 500 K WITH PRESSURES TO 70 MPA

FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "

1

1FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "

1

FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "

1

"

FOR SATURATED LIQUID ENTER "0", FOR VAPOR ENTER "

1

TO ENTER WITH TEMPERATURE ENTER "0", FOR PRESSURE "1"

1ENTER A PRESSUREt MPA)

. 1

P T DEN E H S CV CP SOUND VISC COND DIEL

MPA K MOL/L === J/MOL == ==== J/MOL-K === M/S PA-S MW/M-R

E + 6 .100 272.29 10.348 -5959. -5949. 218.1 95.6 134.4 1036. 204.2 117.2 1.81181

Estimates not from original source.

16
Appendix B Sample Computer Sessions

17
hel ium

THIS PROGRAM PROVIDES THE THERMODYNAMIC PROPERTIES OF HELIUM FROM 2 TO 1500 K UITH PRESSURES TO 100 MPA

UHEN THE PROGRAM ASKS FOR A PRESSURE, DENSITY AND TEMPERATURE,

ENTER ANY TUO AND A ZERO FOR THE THIRD.

TO TERMINATE THE PROGRAM ENTER ZERO FOR ALL THREE.

FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "1"

1FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "1"

1FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "1"

1ENTER A PRESSURE(MPA) , A STARTING TEMPERATURE (K) , A FINAL TEMPERATURE AND A TEMPERATURE INCREMENT AND IN THAT ORDER, TO RESTART PROGRAM ENTER "0,0,0,0"

.1 ,3,10,1

P T DEN E H S CV CP SOUND VISC COND D1EL

MPA K MOL/L === J/MOL == ==== J/MOL-K === M/S PA-S MU/M-K == E+6

.100 3.00 35.794 -39. -36. 9.8 7.6 9.4 222. 38.5 18.1 1.05646

100 4.00 32.477 -27. -24. 13.3 9.1 16 3 185. 33.3 19 6 1 .05114

100 5.00 2.935 52. 86. 39.1 12.7 27 1 120. 13.9 11 1 1 .00456

100 6.00 2.252 67. Ill . 43.7 12.5 24 137. 15.8 12 4 1 .00350

100 7.00 1 .855 81 . 135. 47.3 12.5 22 8 151. 17.6 13 8 1 .00288

100 8.00 1 .586 94. 157. 50.3 12.5 22 2 163. 19.3 15 1 1 .00246

100 9.00 1.389 107. 179. 52.9 12.5 21 9 174. 21 .0 16 3 1 .00216

.100 10.00 1.238 120. 201. 55.2 12.5 21.7 185. 22.6 17.5 1.00192

ENTER A PRESSURE(MPA) , A STARTING TEMPERATURE (K) , A FINAL TEMPERATURE AND A TEMPERATURE INCREMENT AND IN THAT ORDER, TO RESTART PROGRAM ENTER "0,0,0,0"

0,0,0,0

FOR MORE PROPERTIES ENTER 0, TO TERMINATE ENTER 1

1Stop - Program terminated.

18
MIPROPS

FOR INFORMATION ON HOW TO USE THIS PROGRAM, ENTER "0" OTHERWISE, ENTER- "1"

ENTER A NUMBER TO SELECT A FLUID.

ANY ENTRY OTHER THAN A NUMBER HILL TERMINATE THE PROGRAM.

WHEN THE PROGRAM ASKS FOR A PRESSURE, DENSITY AND TEMPERATURE,

ENTER ANY TWO AND A ZERO FOR THE THIRD. TO SELECT ANOTHER

FLUID ENTER ZERO FOR ALL THREE.

SELECT A FLUID BY ENTERING THE CORRESPONDING NUMBER

1=ARG0N, 2=ETHYLENE, 3=PARA HYDROGEN, 4=METHANE

5=NITR0GEN, 6=NITR0GEN TRIFLUORIDE, 7=0XYGEN, 8=ETHANE

9=PR0PANE, 10=ISO BUTANE, 11=N0RMAL BUTANE, 1 2=ST0P

1THE TEMPERATURE RANGE FOR ARGON IS 83. 8 TO 400 K WITH PRESSURES TO 100 MPA

FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER " 1

1FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER "1"

1FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "

1

1ENTER A PRESSUREC MPA) , A STARTING TEMPERATURE( K) , A FINAL TEMPERATURE AND A TEMPERATURE INCREMENT AND IN THAT ORDER, TO RESTART PROGRAM ENTER "0,0,0,0"

1 , 200, 300, 20

P T DEN E H S CV CP SOUND VISC COND DIEL

MPA K MOL/L === J/MOL == ==== J/MOL-K === M/ S PA-S MW/M-K ==

E + 6

1

.

000 200. 00 . 61 9 2384. 3999. 126. 9 12. 7 22. 2 262. 1 6. 3 1 3. 2

1

.

000 220. 00 . 559 2648. 4438. 1 28. 9 1 2. 6 21 . 8 275. 1 7. 7 1 4. 2

1

.

000 240. 00 . 509 2908. 4873. 1 30. 8 1 2. 6 21 . 6 288. 1 9. 1 1 5. 3

1

.

000 260. 00 . 468 31 67. 5304. 132. 6 1 2. 6 21 . 5 301 . 20. 4 1 6. 3

1

.

000 280. 00 . 433 3423. 5732. 134. 2 12. 6 21 . 4 31 2. 21 . 8 1 7. 3

1

.

000 300. 00 . 403 3679. 61 59. 1 35. 6 12. 5 21 . 3 324. 23. 1 1 8. 3 ENTER A PRESSUREC MPA) , A STARTING TEMPERATURE( K) , A FINAL TEMPERATURE AND A TEMPERATURE INCREMENT AND IN THAT ORDER, TO RESTART PROGRAM ENTER "0,0,0,0"

19
Appendix C Program Listings

20
Program Listing of MIPROPS

IMPLICIT REAL*8(A-H)

IMPLICIT REAL*8(0-Z)

IMPLICIT INTEGER*4 (I-N)

DIMENSION G(32),VP(9)

COMMON/DATA/G , R , GAMMA , VP , DTP , PCC , PTP , TCC , TTP , TUL , TLL , PUL , DCC

COMMON/CONT/IF

COMMON/CRIT/EM , EOK , RM , TC , DC , X , PC , SIG

COMMON/DIEL/BX(6) ,PX(6)

1201 FORMAT (//' THIS PROGRAM PROVIDES THE THERMODYNAMIC PROPERTIES OF

111 FLUIDS' ,/,' PARA HYDROGEN, NITROGEN, OXYGEN, ARGON

2'/' NITROGEN TRIFLOURIDE, METHANE, ETHANE, ETHYLENE'/

3' PROPANE, ISO BUTANE AND NORMAL BUTANE'//)

WRITE(* , 1201)

WRITEC* , 1202)

1202 FORMAT (' WRITTEN BY'//

A' ROBERT D. MCCARTY'/

1' THERMOPHYSICS DIVISION'/

2' CENTER FOR CHEMICAL ENGINEERING'/

3

' NATIONAL BUREAU OF STANDARDS '

/

4

BOULDER , COLORADO ' /

/

5' DISTRIBUTED BY' //

A' THE OFFICE OF STANDARD REFERENCE DATA'/

6' NATIONAL BUREAU OF STANDARDS, WASHINGTON, DC'/)

1000 FORMAT (//' FOR INFORMATION ON HOW TO USE THIS PROGRAM, ENTER "0" ' A ' OTHERWISE, ENTER "1"'//)

WRITE(*, 1000)

IP=3

READ(* ,1010)

IF(I.EQ.0)CALL INFO

1010 FORMAT(Il)

110 WRITE(*,1020)

WRITE(*,1030)

SELECT A FLUID BY ENTERING THE CORRESPONDING NUMBER',/)

1=PARA HYDROGEN, 2=NITROGEN, 3=OXYGEN,

4=ARGON, 5=NITROGEN TRIFLUORIDE, 6=METHANE,

7=ETHANE, 8=ETHYLENE, 9=PROPANE,

10=ISO BUTANE, ll=NORMAL BUTANE, 12=STOP',/)

10 20 FORMAT

1030 FORMAT

A,/,

B' ,/,

C ,/,

READ(* , *) IF

CALL FDATA(IF)

120 WRITE(*,1040)

1040 FORMATC' FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "1"',/)

READ(* ,1010) IU

WRITE(* , 1050)

1050 FORMATt* FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER ' A

••'!"' ,/)

READ(* ,1010) IC

WRITE(* ,1060)

1060 FORMATC' FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "1"',/)

READ(* , 1010) IV

160 IF(IC.EQ.0)GO TO 240

IF1IV.EQ.DGO TO 330

170 IF (IU.EQ.O)GO TO 180

WRITE(* , 1080)

READ ( *

, * ) P , D ,

GO TO 190

180 WRITEt* , 1070)

1070 FORMATt' ENTER PRESSURE ( PSIA) , DENSITY (LB/CU FT), AMD TEMPERATURE'

21
A '(F)',/)

READ ( * , * ) P , D , T

P=(P/14.695949D0) * .1013 2 5D0

D=D*16.018 46371D0/EM

T=(T-32.D0) /1.8D0+27 3.15D0

190

1080

200

210

220

230

240

1090

1095

250

1100

260

1110

270

1111

280

1120

ENTER PRESSURE (MPA) , DENSITY (MOL/L) , AND TEMPERATURE (K)

O.0D0 .AND.T.NE.0.0D0)GO TO 210

T, ID

TO 170

T, ID

TO 170

T,IL)

TO 17

T,IU,IV,IC

IF(P.LE.0.0D0.AND.D.LE.0.0D0)GO TO 110

IF(P.GT.0.0D0.AND.D.GT.0.0D0)GO TO 200

IF(P.LE.0.0D0.AND.T.NE.0.0D0)GO TO 220

FORMAT (

A /)

IFtP.NE.

GO TO 110

T=FIND T(P,D)

CALL LIMITS (P,

IF(IL.LE.0)GO

GO TO 230

CALL LIMITS (P,

IF(IL.LE.0)GO

D=FIND D(P,T)

GO TO 230

P=FIND P(D,T)

CALL LIMITS (P,

IF(IL.LE.O) GO

CALL REPRO(P,D,T, IU, IV, IC, IP,TF,DELT)

GO TO 170

WRITE (* ,1090)

FORMAT (' FOR SATURATED LIQUID ENTER "0", FOR VAPOR ENTER "1"',/)

READ( * , 1010) IP

IFIIV.EQ.DGO TO 330

WRITE (* , 1095)

FORMATt' TO ENTER WITH TEMPERATURE ENTER "0", FOR PRESSURE "1"',/)

READt* , 1010) II

IF (II.EQ.l)GO TO 290

IFtIU.EQ.DGO TO 260

FORMAT (' ENTER A TEMPERATURE

WRITEt* , 1100)

READ(* , *)TI

T=(TI-32.D0) /l . 8D0+273.15D0

GO TO 270

WRITEt* , 1110)

FORMAT (' ENTER A TEMPERATURE ( K)

READ( *

, *)T

IF(T.LT. .000001D0)GO TO 110

IF(T.GT.TCC.OR.T.LT.TTP)GO TO 280

P=VPN(T)

IF(IP.EQ.O) ?=P+.00 001D0

D=FIND D(P,T)

CALL RE PRO(P,D,T, IU, IV, IC, IP,TF,DELTI

WRITEt* , 1111)

FORMAT (

' ENTER 1 FOR MORE OR

READ(* , *) I SAT

IF(ISAT.EQ.l)GO TO 250

GO TO 110

Xl=(TTP-27 3 .15D0) *1.8D0+32.D0

X2= (TCC-27 3.15D0) *1 . 8D0+3 2.D0

WRITE (* , 1120)TTP,TCC,X1 ,X2

FORMATt' FOR SATURATION ',F6.2,' < TEMP < ' , Fb .

A ' OR ',F7.2,' < TEMP < ' , F7 . 2

,

' F',/)

GO TO 250

IN DEGREES F" , /)

RESTARTS THE PROGRAM'/)

TO RESTART PROGRAM

22
290 IF(IU.EQ.l)GO TO 300

WRITE(* ,1130)

1130 FORMAT (' ENTER A PRESSURE IN LB/SQ IN RESTARTS THE PROGRAM'/)

READ(*, *)PI

IF(PI.LE.0.0D0)GO TO 110

P=(PI/14.69 59 4 9D0) * .10132 5D0

GO TO 310

300 WRITE(* , 1140)

1140 FORMATt' ENTER A PRESSURE (MPA) RESTARTS THE PROGRAM'/)

READ(* , *)PI

IF(PI.LE.0.0D0)GO TO 110

P=PI

310 IF(P.GT.PCC.OR.P.LT. PTP)GO TO 320

4000 FORMAT (D20. 5)

T=FIND TV(P)

P=VPN(T)

IF(IP.EQ.O) P=P+.0 0001D0

D=FIND D(P,T)

CALL RE PRO(P,D,T, IU, IV, IC, IP,TF,DELT)

GO TO 290

320 PTPF=PTP*14.69 5949D0/.1013 2 5D0

PCCF=PCC*14.69 594 9D0/ .10132 5D0

WRITE (*, 1150) PTP, PCCPTPF, PCCF

1150 FORMAT (' YOUR INPUT PRESSURE IS OUTSIDE THE RANGE OF SATURATION'

A ' PRESSURES'/' FOR THIS FLUID THE RANGE IS ' , F6 . 5 ,

' TO ' , F6 . 3

B ' MPA'/' OR ',F6.2,' TO ',F6.1,' PSIA'/' TRY AGAIN',/)

GO TO 290

330 IF(IC.EQ.l)GO TO 370

IFIIU.EQ.DGO TO 340

WRITE(* , 1160)

1160 FORMAT!' ENTER A STARTING TEMPERATURE, A FINAL TEMPERATURE'

A /' AND A TEMPERATURE INCREMENT, IN DEGREES F AND IN THAT ORDER'/)

READ(* , *)TS,TF,DELT

IF(DELT.LE.0.0D0)GO TO 110

TS=(TS-3 2.D0) /l. 8D0+27 3. 15D0

TF=(TF-3 2.D0) /l . 8D0+27 3 . 15D0

DELT=DELT/1.8D0

IF(TS.LT.TTP.OR.TS.GT.TCC)GO TO 360

IF(TF.LT.TTP.OR.TF.GT.TCC)GO TO 360

GO TO 350

340 WRITE(* ,1170)

1170 FORMAT (' ENTER A STARTING TEMPERATURE, A FINAL TEMPERATURE'

1/' AND A TEMPERATURE INCREMENT IN KELVINS AND IN THAT ORDER',/)

READ(*, *)TS,TF,DELT

IF(DELT.LE.0.0D0)GO TO 110

IF(TS.LT.TTP.OR.TS.GT.TCC)GO TO 360

IFdF.LT.TTP.OR.TF.GT.TCOGO TO 360

350 T=TS

P=VPN(T)

IF(IP.EQ.0.0DQ)P=P+.0 0001D0

D=FIND D(P,T)

CALL RE PRO(P,D,T, IU, IV, IC, IP,TF,DELT)

GO TO 330

360 X1=(TTP-273.15D0) *1.8D0+32

X2=(TCC-27 3.15D0) *1 .8D0+3 2 WRITE (* , 118 0)TTP,TCC,X1,X2

1180 FORMAT(' FOR SATURATION,

A ,13X, 'OR, ' ,F7 .1, ' < TEMP

GO TO 330

DO

DO

,F6

<

' .2, ' <

, F7.1,

TEMP < ' ,F6 . 2,

1 F. TRY AGAIN.

K'

' , / ,/,

)

23
370 IF(IU.EQ.l)GO TO 380

WRITE(* ,1190)

1190 FORMAT(' ENTER PRESSURE ( PSIA) , STARTING TEMPERATURE ( F ), FINAL

A 'TEMPERATURE AND A'/' TEMPERATURE INCREMENT'

2' AND IN THAT ORDER, TO RESTART PROGRAM ENTER "0,0,0,0"',/)

READ ( *

, * ) PI , TS , TF , DELT

IF(DELT.LE.0.0D0)GO TO 110

P=(PI/14.695949D0) * .101325D0

T=(TS-3 2.D0) /1.8D0+27 3.15D0

TF=(TF-32.D0) /l . 8D0+27 3 . 1 5D0

DELT=DELT/1.8D0

CALL LIMITS (P,T, ID

IF(IL.LE.0)GO TO 370

CALL LIMITS (P,TF, ID

IF(IL.LE.0)GO TO 370

GO TO 390

380 WRITE(* , 1200)

1200 FORMAT(' ENTER A PRESSURE (MPA) , A STARTING TEMPERATURE ( K) , A

' 1' FINAL TEMPERATURE AND A'/' TEMPERATURE INCREMENT"

2' AND IN THAT ORDER, TO RESTART PROGRAM ENTER "0,0,0,0"',/)

READ ( *

, * ) PI , TS , TF , DELT

IF(DELT.LE.0.0D0)GO TO 110

T=TS

P = PI

CALL LIMITS (P,T, ID

IF (IL.LE.O)GO TO 370

CALL LIMITS (P,TF, ID

IF (IL.LE.O)GO TO 370

390 D=FIND D(P,T)

CALL RE PRO(P,D,T, IU, IV, IC, IP, TF, DELT)

GO TO 370

99 9 CONTINUE

END

SUBROUTINE REPRO(P,D,T, IU, IV, IC, IP, TF, DELT)

IMPLICIT REAL*8(A-H)

IMPLICIT REAL*8(0-Z)

IMPLICIT INTEGER*4 (I-N)

DIMENSION G(32),VP(9)

COMMON/DATA/G , R , GAMMA , VP , DTP , PCC , PTP , TCC , TTP , TUL , TLL , PUL , DCC

COMMON/CONT/IF

COMMON/CRIT/EM , EOK , RM , TC , DC , X , PC , SIG

COMMON/CPID/GI (11) ,GH(11) ,GL(11)

COMMON/HAN/CR , TCI

N=500

IF(IV.EQ.0)TF=T-1.D0

IF(IU.EQ.0)GO TO 100

WRITE(* , 1000)

WRITE (* ,1010)

WRITE(* , 1020)

GO TO 110

100 WRITE( * , 1000)

WRITEf* , 1030)

WRITE(* , 1040)

110 CONTINUE

DO 210 1=1,

N

IFCEQ.DGO TO 120

IF(D.LT.DCC.OR.T.GT.TCC)GO TO 111

D=FIND D(P,T)

GO TO 120

111 DIN=D

D=FINDM(P,T,DIN)

24
120 H=ENTHAL(P,D,T)

E=H-1000.D0*P/D

S=ENTROP(D,T)

W=SOUND(D,T)

CPP=CP(D,T)

CVV=CV(D,T)

IF(IU.EQ.0)GO TO 160

IF(IF.EQ.6.0R.IF.EQ.2.0R.IF.EQ. 3) GO TO 150

IF(IF.GT.9)GO TO 150

IF(IF.EQ.4) GO TO 140

IF(IF.EQ.1.0R.IF.EQ.7.0R.IF.EQ.9) GO TO 130

WRITE (* ,2000) P,T,D,E,H,S,CVV,CPP,W

GO TO 200

130 EPS=FDIEL(P,D,T)

WRITE (*, 2010) P,T,D,E,H,S,CVV,CPP,W,EPS

GO TO 200

140 TH=THERM(D,T) *1000.D0

V=VISC(D,T)

WRITE (* ,2020) P,T,D,E,H, S , CVV , CPP , W, V, TH

GO TO 200

150 V=VISC(D,T)

TH=THERM(D,T) * 1000. DO

EPS=FDIEL(P,D,T)

WRITE (* ,2030) P,T,D,E,H,S,CVV,CPP,W,V,TH,EPS

GO TO 200

160 H=H/(2.324445D0*EM)

E=E/ (2.324445D0*EM)

S=S/(4.184001D0*EM)

CPP=CPP/ (4.184001D0*EM)

CVV=CVV/ (4.184001D0*EM)

W=W*3.280840D0

PO=(P/.101325D0)*14.695949D0

DO=D*EM/16.01846371D0

TO=T*1.8D0-4 59.67D0

IF(IF.EQ.6.0R.IF.EQ.2.0R.IF.EQ.3) GO TO 190

IFUF.EQ.4) GO TO 180

IF(IF.EQ.l) GO TO 170

WRITE (* ,3000) PO,TO,DO,E,H,S,CVV,CPP,W

GO TO 200

170 EPS=FDIEL(P,D,T)

WRITE (* ,3010) PO,TO,DO,E,H,S,CVV,CPP,W,EPS

GO TO 200

180 V=VISC(D,T) *.067196897D0

TH=THERM(D,T) * .578176D0

WRITE (* ,30 20) PO,TO,DO,E,H,S,CVV,CPP,W,V,TH

GO TO 200

190 V=VISC(D,T) * .067196897D0

TH=THERM(D,T) * .578176D0

EPS=FDIEL(P,D,T)

WRITE (* ,30 30) PO,TO,DO,E,H,S,CVV,CPP,W,V,TH,EPS

200 T=T+DELT

IF(T.GT.TF+.01D0)GO TO 220

IF(IC.EQ.0)P=VPN(T)

IF(IP.EQ.O) P=P+.00001D0

210 CONTINUE

220 CONTINUE

WRITE (* , 1000)

1000 FORMAT {'

'

)

RETURN

25
1010 FORMAT (3X, ' P

' , 5X ,

' T

' , 6X, 'DEN' , 5X ,

' E' ,6X, 'H' ,6X, 'S' ,4X, ' CV ' , 4X,

A ' CP' , 3X, ' SOUND' , 2X, 'VISC , 2X, ' COND ' , 2X, ' DIEL '

1020 FORMAT (3X, * MPA ' ,3X, 'K' ,6X, 'MOL/L' ,2X, ' === J/MOL ==',2X,'====

A ' J/MOL-K ===' , 2X, 'M/S ' , 3X, ' PA-S' ,1X, 'MW/M-K' , 2X , '==' , /,61X, ' E+6 '

1030 FORMAT (3X, ' P

' , 5X ,

' T

' , 7X , 'DENS' , 3X ,

' E' , 8X, ' H' , 5X, ' S

' , 5X, 'CV

A 4X ,' CP ' , 2X ,' SOUND ' , IX , 'VISC , 2X , ' COND ' , 2X ,' DIEL '

1040 FORMAT(3X, 'PSIA' , 2X , 'F' ,7X, 'LB/ ' , 3X, ' ==== BTU/ ===', IX, '======'

A ' BTU/ =====', 2X, 'F/S' , 3X, 'LB/ ' , 2X, 'BTU/ ' , 2X ,

' == ' , /,17X, ' CU FT',

B 6X, 'LB' ,14X, ' LB-F' ,13X, 'FT-S' , IX, ' FT-HR-F' , /,62X, ' E+5 '

2000 FORMAT (F8 . 3 , F7 . 2 , F7 . 3 , 2F7 . , F6 . 1 , F5 . 1 , F6 . 1 , F6 . ) 2010 FORMAT ( F8 . 3 , F7 . 2 , F7 . 3 , 2F7 . , F6 . 1 , F5 . 1 , F6 . 1 , F6 . , 13X , F8 . 5

2020 FORMAT(F8.3,F7.2,F7 .3, 2F7 . , F6 . 1 , F5 . 1 , F6 . 1 , F6 . , F6 . 1 , F6 . 1

20 30 FORMAT(F8.3,F7.2,F7.3,2F7.0,F6.1,F5.1,F6.1,F6.0,F6.1,F6.1,F8.5)

3000 FORMAT(F8.1,F7.2,F7.3,2F7.1, 3F6 . 3,F6.0)

3010 FORMAT(F8.1,F7.2,F7.3,2F7.1, 3F6 . 3 , F6 . , 11X, F8 . 5

3020 FORMAT ( F8 . 1 , F7 . 2 , F7 . 3 , 2F7 . 1 , 3F6 . 3 , F6 . , F5 . 2 , F6 . 4

30 30 FORMAT(F8.1,F7.2,F7.3,2F7 .1, 3F6 . 3,F6.0,F5.2,F6.4,F8.5)

END

SUBROUTINE INFO

WRITE(* , 100)

100 FORMAT(/' ENTER A NUMBER TO SELECT A FLUID.'/

*' ANY ENTRY OTHER THAN A NUMBER WILL TERMINATE THE PROGRAM.'/

*' WHEN THE PROGRAM ASKS FOR A PRESSURE, DENSITY AND TEMPERATURE,'/

*' ENTER ANY TWO AND A ZERO FOR THE THIRD. TO SELECT ANOTHER'/

*' FLUID ENTER ZERO FOR ALL THREE.')

RETURN

END

SUBROUTINE FDATA(IF)

IMPLICIT REAL*8(A-H)

IMPLICIT REAL*8(0-Z)

IMPLICIT INTEGER*4 (I-N)

DIMENSION G(32) ,VP(9) , GV ( 9 ) , GT ( 9 ) , FV ( 4 ) , FT ( 4 ) , EV ( 8 ) , ET ( 8 ) ,A(20)

COMMON/DATA/G , R , GAMMA , VP , DTP , PCC , PTP , TCC , TTP , TUL , TLL , PUL , DCC

COMMON/ SEN/BETA , XO , DELTA , El , E2 , AGAM

COMMON/CRIT/EM, EOK , RM, TC , DC , X , PC , SIG

COMMON/ SATC/ A , DTPV , EG

COMMON/CPID/GK11) ,GH(11) ,GL(11)

COMMON/DATA1 /GV , GT , FV , FT , EV , ET

COMMON/ I SP /N , NW , NWW

COMMON/FIXPT/T0 , SO , HO

COMMON/DIEL/BX ( 6 )

, PX ( 6

COMMON/B/GMW, SEOK, SSIG

COMMON/ A/ SE1 , Gl , Bl , DE , BK , Dl , XZ , ZZ , XI , X2 , X3 , X4

GO TO (3,5,7,1,6,4, 8,2,9,10,11,12) , IF

1 WRITE(*,200)

200 FORMAT (' THE TEMPERATURE RANGE FOR ARGON IS 83.8 TO 400 K' 1/' (-308.8 TO 260 F) WITH PRESSURES TO 100 MPA (14504 PSIA)')

OPEN ( 5 , FILE= ' ARGON . COF '

N=0

NW=0

NWW=0

GO TO 50

2 WRITE(* ,201)

201 FORMAT(' THE TEMPERATURE RANGE FOR ETHYLENE IS 104 TO 400 K' 1/' (-272.4 TO 260 F) WITH PRESSURES TO 40 MPA (5801 PSIA)')

OPEN ( 5 , FILE= ' C2H4 . COF '

N=0

NW=0

NWW=0

26
NWW=0

GO TO 50

3 HRITE( *, 202)

202 FORMATC' THE TEMPERATURE RANGE FOR HYDROGEN IS 13.8 TO 400 K' 1/' WITH PRESSURES TO 120 MPA')

OPEN( 5, FILE=' PH2. COF' ) N=1

NH = NHH = GO TO 50

4 HRITE( *, 203)

203 FORMAT( ' THE RANGE OF TEMPERATURE FOR METHANE IS 90.68 TO 600 K' 1/" WITH PRESSURES TO 200 MPA')

OPEN( 5, FILE = ' METH. COF' ) N=0

NH=1

NHH = GO TO 50

5 WRITEC *, 204)

204 FORMATC" THE RANGE OF TEMPERATURE FOR NITROGEN IS 63.15 TO 1900 K' 1/' WITH PRESSURES TO 1000 MPA')

OPEN( 5, FILE = ' N2. COF' ) N=0

NW=0

NWH = GO TO 50

6 WRITE( *, 205)

205 FORMAT( ' THE RANGE OF TEMPERATURE OFR NITROGEN TRIFLUORIDE IS' 1,/' 66.36 TO 500 K, WITH PRESSURES TO 50 MPA')

OPEN( 5, FILE = ' NF3. COF" ) N=0

NW = NWW = GO TO 50

7 WRITE( *, 206)

206 FORMATC' THE RANGE OF TEMPERATURE FOR OXYGEN IS 54.359 TO 400 K' 1/' WITH PRESSURES TO 120 MPA')

0PEN( 5, FILE = ' 02. COF" ) N=0

NW=0

NWW = GO TO 50

8 WRITE( *, 207)

207 FORMATC' THE RANGE OF TEMPERATURE FOR ETHANE IS 90.35 TO 600 K' 1/' WITH PRESSURES TO 70 MPA')

OPENC 5, FILE = ' C2H6. COF' ) N = NW = 1 NWW = GO TO 50

9 WRITEC *, 208)

208 FORMATC' THE RANGE OF TEMPERATURE FOR PROPANE IS 85.47 TO 600 K' 1/' WITH PRESSURES TO 100 MPA')

OPENC 5, FILE = ' C3H8. COF' ) N=0

NW = 1 NWW = GO TO 50

10 WRITEC *, 209)

209 FORMATC' THE RANGE OF TEMPERATURE FOR ISO BUTANE IS'

1 /' 1 1 3. 55 TO 600 K' 1/' WITH PRESSURES TO 35 MPA')

OPENC 5, FILE = ' ISOB. COF' ) N=0

NW=1

NWW = GO TO 50

11 WRITE(*,210)

27
210 FORMATC' THE RANGE OF

1 /' 134.68 TO 500 K' 1/' WITH PRESSURES TO 70 MPA')

OPEN( 5, FILE = " NORB. COF' ) N=0

NW=1

NWW = GO TO 50

STOP

READ( 5, 1 00) SIG, XO, BETA, DELTA, E1 RE ADC 5, 1 00) EM, EOK, RM, TC, DC, X, PC

FORMATC 7E1 2. 6)

DO 60 1=1 , 32

READC 5, 1 01 ) G( I)

FORMATC 3D20. 1 3)

DO 70 1=1 , 20

READC 5, 1 01 ) AC I)

DO 75 1=1,11

READC 5, 1 01 ) GI( I)

DO 80 1=1,9

READC 5,101) VPC I)

TCC = VP( 8)

PTP=VP( 9)

TTP=VP( 7)

DO 90 1=1,8

READC 5,101) EVC I)

DO 1 1 READC 5 READC 5 READC 5 READC 5

TEMPERATURE FOR NORMAL BUTANE IS'

1 2 50

1 00

60

1 01

70

75

80

90

1 1

95

96

1 02

1

1 1

1 2

1 3

E2, AGAM

GHC I) , GLC I)

GVC I) , GT( I)

ETC I)

1=1,4

1 01 ) FVC I) , FTC I)

1 01 ) DTP, DTPV

1 01 ) TO, SO, HO

102) R, GAMMA, TUL, TLL, PUL, DCC, PCC

DO 95

READC 5, 1=1,61 01 ) BXC I)

4)

PXC I)

IFC NW. EQ. 0) GO TO 96

READC 5, 1 00) SE1 , G1, B1, DE, BK, D1 READC 5, 100) XZ, ZZ, X1, X2, X3, X4

READC 5, 1 00) GMW, SEOK, SSIG, EG

EM=GMW

CONTINUE

CLOSEC 5, STATUS=' KEEP 1 ) FORMATC F10. 8, E14. 8, 3F8. 2, 2F8.

RETURN

END

SUBROUTINE LI MI TSC P, T, I L)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

DIMENSION G( 32) , VPC 9)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

IFC P . GT. PUL) GO TO 10

IFC T . GT. TUL OR. T . LT. TLL) GO TO 1 2 PM=PMELT( T)

IFC P . GT. PM) GO TO 20

IL = 1 RETURN

HRITEC *, 1 1 ) PUL

FORMATC' THE INPUT PRESSURE IS

1/' THE RANGE FOR THIS EQUATION

IL = RETURN

TLLF= ( TLL-273. 1 5D0) *1 . 8D0+32. DO

TULF= ( TUL-273. 1 5D0) *1 . 8D0+32. DO

WRITE(*,13) TLL, TUL, TLLF, TULF

FORMATC 1 THE INPUT TEMPERATURE IS OUT

A /' THE RANGE FOR THIS EQUATION IS

OUT OF THE RANGE OF

IS FROM TO ' , F6. 0,

THIS EQUATION

' MPA' )

OF

F6

RANGE'

2, ' K TO F6. 0, ' K' , /

B 27X, ' IL = RETURNOR F8. 2, TO F6. 0, ' F' )

28
8D0+32. DO

FOR

3,

' THIS

F' ) PRESSURE, TEMP'

DENSITY* MOLES/L)

20 TM=TMELT( P)

TF = ( TM-273. 1 5D0) *1 WRITEC *, 22) TM, TF

22 FORMATC ' SOLID PHASE DETECTED. ',/, ' A ' SHOULD EXCEED ' , F8. 3, ' K, OR' , F9.

IL = END

SUBROUTINE PROPS( PP, DD, TT, K)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

C THE 32 TERM EQUATION OF STATE, INPUT IS

C TEMPERATURE( K) , OUTPUT ( PP) IS PRESSURE* MP A) , OR DP/DD IN

C LITER-MPA/MOLE OR DP/DT MPA/K OR S, H, OR CV AT ONE LIMIT OF

C INTEGRATION

DIMENSION X( 33)

DIMENSION B( 33) , G( 32) , VP( 9)

EQUIVALENCE ( B, X)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

DATA M/32/

D = DD

P = PP

T=TT

GM=GAMMA

D2=D*D

D3=D2*D

D4=D3*D

D5=D4*D

D6=D5*D

D7=D6*D

D8=D7*D

D9=D8*D

D1 0=D9*D

D1 1 =D1 0*D

D1 2=D1 1 *D

D1 3=D1 2*D

TS=DSQRT ( T)

T2 = T3 = T4 = T5 =

T2*T

T3*T

T4*T

F=DEXP ( GM*D2)

GO TO (100,200,300,400,500,600)

ENTRY PRESS

1 00 B( 1 ) = D2*T

B( 2) =D2*TS

B( 3) = D2

B( 4) = D2/T

B( 5) =D2/T2

B( 6) = D3*T

B( 7) = D3

B( 8) = D3/T

B( 9) =D3/T2

B( 1 0) = D4*T

B( 1 1 ) = D4

B( 1 2) = D4/T

B( 1 3) = D5

B( 1 4) = D6/T

B( 1 5) =D6/T2

B( 16) = D7/T

B( 1 7) = D8/T

B( 1 8) =D8/T2

B( 1 9) =D9/T2

B( 20) =D3*F/T2

B( 21 ) =D3*F/T3

B( 22) =D5*F/T2

B( 23) =D5*F/T4

B( 24) =D7*F/T2

29
B( 25) =D7*F/T3

B( 26) =D9*F/T2

B( 27) =D9*F/T4

B( 28) =D1 1 *F/T2

B( 29) =D1 1 *F/T3

B( 30) =D1 3*F/T2

B( 31 ) =D1 3*F/T3

B( 32) =D1 3*F/T4

P = DO 101 1=1, M

1 01 P = P + B( I) *G( I)

P=P+R*D*T

PP = P RETURN

ENTRY DPDD

200 F1 =2. D0*F*GM*D

F21 =3. D0*F*D2 +F1 *D3

F22=5. D0*F*D4 +F1 *D5

F23 = 7. D0*F*D6 +F1 *D7

F24=9. D0*F*D8 +F1 *D9

F25=11. D0*F*D10+F1*D11

F26=13. D0*F*D1 2+F1 *D1

3

B( 1 ) =2. D0*D*T

B( 2) =2. D0*D*TS

B( 3) =2. D0*D

B( 4) =2. D0*D/T

B( 5) =2. D0*D/T2

B( 6) =3. D0*D2*T

B( 7) =3. D0*D2

B( 8) =3. D0*D2/T

B( 9) =3. D0*D2/T2

B( 1 0) =4. D0*D3*T

B( 1 1 ) =4. D0*D3

B( 1 2) =4. D0*D3/T

B( 1 3) =5. D0*D4

B( 1 4) =6. D0*D5/T

B( 1 5) =6. D0*D5/T2

B( 1 6) =7. D0*D6/T

B( 1 7) =8. D0*D7/T

B( 1 8) =8. D0*D7/T2

B( 1 9) =9. D0*D8/T2

B( 20) =F21 /T2

B( 21 ) =F21 /T3

B( 22) =F22/T2

B( 23) =F22/T4

B( 24) =F23/T2

B( 25) =F23/T3

B( 26) =F24/T2

B( 27) =F24/T4

B( 28) =F25/T2

B( 29) =F25/T3

B( 30) =F26/T2

B( 31 ) =F26/T3

B( 32) =F26/T4

P = DO 201 1=1 ,

201 P = P + B( I) *G< I)

P=P+R*T

PP = P RETURN

ENTRY DPDT

300 X( 1 ) =D2

X( 2) =D2/( 2. D0*TS)

X( 3) =0. DO

X( 4)=-D2/T2

X( 5) =-2. D0*D2/T3

X( 6)=D3

X( 7) =0. DO

30
301

X(

X(

X(X(

X(

X(X(

X(X(

X(

X(

X(X(

X(

X(

X(X(

X(

X(

X(

X(

X(

X(X(

X(p = DO

p = pp

RE

EN

PA

RE

S = 400 G1

G2

G3

G4

G5

G6

X(

X(

X(

X(

X(X(

X(

X(

X(

X(

X(

X(

X(

X(

X(

X(

X(

X(

X(X(

X(

X(X(

X(X(

X(

X(X(

8)

9)

1 0)

1 1

)

1 2)

1 3)

1 4) =

1 5) =

1 6) =

1 7) =

1 8) =

1 9) = 20) = 21 ) = 22) = 23) = 24) = 25) = 26) = 27) = 28) = 29) = 30) = 31 ) = 32) =

301

P + G(

= P + R TURN

TRY

RTIA

SPEC

SO-R

= F/(

= ( F*

= ( F*

= ( F*

= ( F*

= ( F*

1 ) = 2) = 3) = 4) = 5) = 6) = 7) = 8) = 9) =

1 0) = 11) =

1 2) =

1 3) =

1 4) =

1 5) =

1 6) =

1 7) =

1 8) =

1 9) = 20) = 21 ) = 22) = 23) = 24) = 25) = 26) = 27) = 28) =

-D3/T2

-2. D0*D3/T3

D4

0. DO

-D4/T2

0. DO

-D6/T2

-2. DO

-D7/T2

-D8/T2

-2. DO*

D6/T3

DO*

DO*

DO*

DO*

DO*

-2. DO*

-3. DO*

-2. DO*

-4. DO*

DO*

DO*

-2. DO*

-3. DO*

-4. DO*

D8/T

D9/T

D3*F

D3*F

D5*F

D5*F

D7*F

D7*F

D9*F

D9*F

D1 1 * D1 1 * D1 3*

D1 3*

D1 3*

3

3/T3

/T4

/T3

/T5

/T3

/T4

/T3

/T5

F/T3

F/T4

F/T3

F/T4

F/T5

1=1 , M

I) *X( I)

*D

DSDN

L OF ENTROPY WITH

T TO THE G COEFFICIENTS

*LOGF( D*R*T/P0)+(DSDN(D)-DSDN(0))*1000. DO +CPOS(T)

2. DO*GM)

DO*GM)

DO*GM)

DO*GM)

DO*GM)

1 0. D0*G5) /( 2. DO*GM)

D2-2. D0*G1 ) /(

D4-4. D0*G2) /(

D6-6. D0*G3) /(

D8-8. D0*G4) /( D1 0- -D

-D/( 2. DO*TS)

0. DO

+ D/T2

2. D0*D/T3

-D2/2. DO

0. DO

D2/( 2. D0*T2)

D2/T3

-D3/3. DO

0. DO

D3/( 3. D0*T2)

0. DO

D5/( 5. D0*T2)

2. D0*D5/( 5. D0*T3)

D6/( 6. D0*T2)

D7/( 7. D0*T2)

2. D0*D7/( 7. D0*T3)

D8/( 4. D0*T3)

2. D0*G1 /T3

3. D0*G1 /T4

2. D0*G2/T3

4. D0*G2/T5

2. D0*G3/T3

3. D0*G3/T4

2. D0*G4/T3

4. D0*G4/T5

2. D0*G5/T3

31
X( 29) =3. D0*G5/T4

X( 30) = 2. D0*G6/T3

X( 31 ) =3. D0*G6/T4

X( 32) =4. D0*G6/T5

P = DO 401 1=1 ,

401 P = P + G( I) *X( I)

PP = P RETURN

C ENTRY DUDN

C TERMS NEEDED FOR ENTHALPY CALCULATION

C H=H0 + (T*DSDN(D)-DSDN(0))*1000. + ( DUDN( D- DUDN( 0) ) * 1 000.

C +( P/D-R*T) *1 000.

500 G1 =F/( 2. D0*GM)

G2 = (F*D2-2.D0*G1)/(2. D0*GM)

G3 = ( F*D4-4. D0*G2) /( 2. D0*GM)

G4 = ( F*D6-6. D0*G3) /( 2. D0*GM)

G5 = ( F*D8-8. D0*G4) /( 2. D0*GM)

G6 = (F*D10-10. D0*G5) /( 2. D0*GM)

X( 1)=D*T

X( 2)=D*TS

X( 3)=D

X( 4)=D/T

X( 5)=D/T2

X( 6) =D2*T/2. DO

X( 7) =D2/2. DO

X( 8) =D2/( 2. D0*T)

X( 9) =D2/( 2. D0*T2)

X( 1 0) =D3*T/3. DO

X( 1 1 ) =D3/3. DO

X( 1 2) =D3/( 3. DO*T)

X( 1 3) =D4/4. DO

X( 1 4) =D5/( 5. DO*T)

X( 1 5) =D5/( 5. D0*T2)

X( 1 6) =D6/( 6. DO*T)

X( 1 7) =D7/( 7. DO*T)

X( 1 8) =D7/( 7. D0*T2)

X( 1 9) =D8/( 8. D0*T2)

X( 20) =G1 /T2

X( 21 ) =G1 /T3

X( 22) =G2/T2

X( 23) =G2/T4

X( 24) =G3/T2

X( 25) =G3/T3

X( 26) =G4/T2

X( 27) =G4/T4

X( 28) =G5/T2

X( 29) =G5/T3

X( 30) =G6/T2

X( 31 ) =G6/T3

X( 32) =G6/T4

P = DO 501 1=1 , M 501 P = P + G( I) *X( I)

PP = P RETURN

C ENTRY TDSDT

C TEMP. TIMES THE PARTIAL OF

C ENTROPY WITH RESPECT TO TEMP.

C CV = CVO + (TDSDN(/) -TDSDN( D) ) *1 000.

600 G1 =F/( 2. DO*GM)

G2=( F*D2-2. D0*G1 ) /(

G3=( F*D4-4. D0*G2) /(

G4=( F*D6-6. D0*G3) /(

G5=( F*D8-8. D0*G4) /(

G6 = ( F*D1 0-1 0. D0*G5) /(

X( 1 ) =0. DO

X( 2) =-D/( 4. DO*TS)

+ CPOH( T)

2. DO*GM)

2. DO*GM)

2. DO*GM)

2. DO*GM)

/( 2. DO*GM)

32
X( 3) =0. DO

X( 4) = 2. D0*D/T2

X( 5) =6. D0*D/T3

X( 6) =0. DO

X( 7) =0. DO

X( 8)=D2/T2

X( 9) =3. D0*D2/T3

X( 1 0) =0. DO

X( 1 1 ) =0. DO

X( 1 2) =( 2. D0*D3) /( 3. D0*T2)

X( 1 3) =0. DO

X( 1 4) =( 2. D0*D5) /( 5. D0*T2)

XM 5) =( 6. D0*D5) /( 5. D0*T3)

X( 1 6) =D6/( 3. D0*T2)

X( 17) =( 2. D0*D7)/(7. D0*T2)

X( 1 8) =( 6. D0*D7) /( 7. D0*T3)

X( 1 9) =( 3. D0*D8) /( 4. D0*T3)

X( 20) =6. D0*G1 /T3

X( 21 ) = 1 2. D0*G1 /T4

X( 22) =6. D0*G2/T3

X( 23) =20. D0*G2/T5

X( 24) =6. D0*G3/T3

X( 25) =1 2. D0*G3/T4

X( 26) =6. D0*G4/T3

X( 27) =20. D0*G4/T5

X( 28) =6. D0*G5/T3

X( 29) = 1 2. D0*G5/T4

X( 30) =6. D0*G6/T3

X( 31 ) =1 2. D0*G6/T4

X( 32) =20. D0*G6/T5

P = DO 601 1=1 , M 601 P = P + G( I) *X( I)

PP = P END

DOUBLE PRECISION FUNCTION

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

ITERATES VAPOR PRESS EQN TO FIND

GIVEN AN INPUT PRESSUREC MP A)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

DIMENSION G( 32) , VP( 9) T = VP( 8)

DO 7 1=1,10

P = VPN( T)

IF( DABS ( P-POBS) -. 000001 D0*P0BS) 8,8,6

6 CONTINUE

C0RR=( POBS-P) /DPDTVP( T, P)

7 T=T+CORR

8 CONTINUE

FINDTV=T

END

DOUBLE PRECISION FUNCTION CV( D, T)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

CALCULATES CV( J/ ( MOL*K)

)

DATA R/8. 31 434D0/

FINDTV( POBS)

TEMP( K) , FOR INPUT OF PRESS(MPA)

INPUT DENS(MOL/L) AND TEMP( K)

DD = D TT = T CALL PROPS( CD, DD, TT, 6)

DD = 0. 0D0

CALL PR0PS( CO, DD, TT, 6)

CV = CPI( TT, 1) +( CO-CD) *1000.

CV=CV-R

END

FUNCTION FINDD( P, T)

DO

33
50D0) GO TO 11

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

DIMENSION G( 32) , VP( 9)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

TT = T IF( TT. GT. VP( 8) *. 99999D0) GO TO 100

IF( P. GT. VPN( TT) ) GO TO 1 01 DD = SATV( TT)

GO TO 102

100 PC=PCC

X = (1. 1 D0/( 9. D0*PC))*P + . 7D0/9. DO

DD=P/( R*T*X)

IF( P/PC. GT. 2D0. AND. T/VPC 8) . LT. 2. 5D0) DD = DTP

GO TO 102

1 01 DD = SATL( TT)

102 CONTINUE

DO 10 1 = 1 , 50

IF( DD. LE. 0. 0D0. OR. DD. GT. CALL PROPSC PP, DD, TT, 1 ) IF( PP. LE. 0. 0D0) GO TO 11 P2 = PP

IFtDABS ( P-P2) -1 . D-7*P) 20, 20, 1 CALL PROPSC PP, DD, TT, 2)

DP = PP

CORR=( P2-P) /DP

IF( DABS ( CORR) -1 . DD=DD-CORR

CALL REGULA( P, DD,

FINDD=DD

END

SUBROUTINE REGULA( PI , DD, TT)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

ITERATES EON OF STATE FOR DENSITY

DIMENSION G( 32) , VP( 9)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

T = TT

P = PI D2=0. ODO

IF( T. LT. TCC) GO TO 10

DO=DCC*TCC/T

1

1

1 1 20

D-7*DD) 20, 20, 1

T)

WHEN SUBPROG FINDD FAILS.

1

1 1

1 2

1 3

GO TO 20

PP = VPN( T)

IF( P. GT. PP) GO TO 15

DO = SATV( T)

DO 11 1=1,150

CALL PROPS( PO, DO,

IF( PO. GE. P) GO TO

DO=DO+. 0001 DO*DO

GO TO 42

D1 =D0

CALL PR0PS( P1 , D1 , IF( P1 LT. P) GO TO

IF( D1 D0 = D1

Z = ( P1 IF( Z. IF( Z. D1 =D1

GO TO

T, 1 )

1 2

T, 1 )

1 4 LE. . 1 D0*PTP) GO TO 42

-P) /P

LT. . 1 DO) Z GT. . 9D0) Z -Z*D1

1 3

1 DO

9D0

1 4 CALL PR0PS( PO,

DO 140 1=1 , 50

D=D1

P3 = P1 IF( DABS( P-P1 ) . P2=P-P1

DO, T, 1 )

LT. . 00001 DO*P) GO TO 40

34
1 20

1 40

15

16

1 7

1 8

20

21

30

31

40

41 102

1 01

42

D1=D1+(D1-D0)*P2/(P1-P0)

IF( DABS( D-D1 ). LE. . 00001 D0*D) GO TO 40

IF( DABS( P-P1 ) . LT. .005D0*P)D2 = FINDM(P,T,D1)

IF( D2. GT. 0. ODO. AND. D2. LT. 50. DO) D1 =D2

D2=0. ODO

T, 1 ) GT. P) GO TO 1 20

LT. P) GO TO 1 20

CALL PR0PS( P1 , D1 IF( PO. GT. P. AND. P1 LT. P.

1 40

IF( PO AND. P1 GO TO

P0 = P3

DO = D CONTINUE

GO TO 41 DO = SATL( T)

DO 16 1=1 , 10

CALL PR0PS( PO, DO, T, 1 ) IF( PO. LE. P) GO TO 17

DO=DO-. 0001 DO*DO

GO TO 42

D1 =D0

CALL PROPS( P1 , D1 , T, 1 ) IF( D1 . GE. 50. DO) GO TO 42

IF( P1 . GT. P) GO TO 14

D0 = D1 Z=( P-P1 ) /P

Z=Z*1 0. DO

IF( T/TCC. LT. . 6 DO) Z = 1 . DO

IF( Z. LT. 1 . DO) Z = 1 . DO

IF( Z. GT. 9. DO) Z = 9. DO

D1 =D1 +. 01 D0*D1 *Z

GO TO 18

CALL PROPSC PO, DO, T, 1 ) IF( P. LE. PO) GO TO 30

D1 =D0

CALL PROPS( P1 , D1 , T, 1 ) IF( P1 . GE. P) GO TO 14

IF( D1 . GE. 50. DO) GO TO 42

D0 = D1 Z=( P-P1 ) /P

Z = Z*1 0. DO

IF( Z. LT. 1 DO) Z=1 . IF( Z. GT. 9D0) Z=9.

D1 =D1 +. 1 D0*D1 *Z

GO TO 21

D1 =D0

CALL PROPS( P1 , D1 , T, 1 ) IF( P1 . LE. P) GO TO 14

IF( D1 . LE. . 1 DO*PTP) GO TO

D0 = D1

Z = ( P1 -P) /P

Z=Z*10. DO

IF( Z. LT. 1 DO) Z=1 . IF( Z. GT. 9D0) Z=9.

D1 =D1 -. 1 D0*D1 *Z

GO TO 31 DD = D1 RETURN

WRITE( * FORMAT(

FORMAT(

1/' DENSITY

RETURN

WRITE( *, 1 02) P, T END

DOUBLE PRECISION FUNCTION

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

DO

DO

42

DO

DO

1 01 ) P, T, D REGULA FAILED AT P=',E11.

DENSITY ITERATION FAILED

RETURNED IS' , E1 7. 8)

4, ' AT

AND T = P = * , F7.

' , F7. 2)

2, ' AND , F7. 2,

CP( D, T)

35
C CALCULATES CP( J / ( MOL*K) ) . INPUT DENSCMOL/L), TEMP( K) . CVEE=CV( D, T)

CALL PROPS( DPT, D, T, 3)

CALL PROPS( DPD, D, T, 2)

CP = CVEE + (T/(D**2)*(DPT**2)/DPD)*1000.D0

END

DOUBLE PRECISION FUNCTION DPDTVP( TT, P)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

C CALCULATES THE DERIVATIVE OF PRESSURE WITH RESPECT TO TEMPERATURE

C AT SATURATION. INPUT IS TEMP( K) , OUTPUT IS DPDT(MPA/K).

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

DIMENSION G( 32) , VP( 9)

T=TT

IF( TT. GT. VP( 8) ) GO TO 1 X=( 1. DO-VPC 7) /T) /( 1 . D0-VP( 7) /VP( 8) ) DXDT = (VP(7)/T**2)/(1.D0-VP(7)/VP(8))

DPDT=VP(1)*DXDT+2. D0*VP(2)*X*DXDT+VP(3)*3. D0*X**2*DXDT+VP(5)*

1((1. D0-X)**VP(6))*DXDT + VP(5)*X*((1. D0-X)**(VP(6)-1. DO) ) *VP( 6)

2*( -DXDT)

DPDTVP=DPDT*P

RETURN

1 DPDTVP=0. 0D0

END

DOUBLE PRECISION FUNCTION FI NDM( P, T, DD)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

C SOLVES FOR DENSI TY( MOL/ L) BY ITERATION. INPUT IS PRESSURE( MPA) , C TEMPERATURE( K) , AND A STARTING VALUE OF DENSITY. THIS FCN IS AN

C ALTERNATIVE FOR FUNCTION FINDD.

TT = T DO 10 1=1,50

CALL PROPS( PP, DD, TT, 1 ) P2 = PP

IFtDABS ( P-P2) -1 . D-7*P) 20, 20, 1

1 CALL PROPSC PP, DD, TT, 1 ) DP = PP

D-7*D) 20, 20, 1

CORR=( P2-P) /DP

D = DD

IF( DABS ( CORR) -1 10 DD=DD-CORR

FINDM=0

RETURN

20 FINDM=DD

END

DOUBLE PRECISION

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

R= . 00831 434D0

DD=D

TT=T

CALL

CALL

DD = CALL

CALL

ENTHAL

END

DOUBLE PRECISION FUNCTION

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

CALCULATES ENTROP Y( J / ( MOL-K)

R= . 00831 434D0

P0= . 1 01 325D0

DD=D

FUNCTION ENTHALC P, D, T)

PROPS( SD, DD, TT, 4)

PROPS( UD, DD, TT, 5)

DO

PROPS( SO, DD, TT, 4)

PROPSt UO, DD, TT, 5)

L=T*( SD-SO) *1 000. D0 + ( UD-UO) *1000. DO + CPK T, 3) +( P/D-R*T) *1 000. DO

ENTROP( D, T)

FROM INPUT OF DENSI TY( MOL/ L) AND TEMP( K) .

36
1

TT=T

CALL PROPS( SD, DD, TT, 4)

DD = CALL PROPSC SO, DD, TT, 4)

ENTROP = ( SD-SO) *1000. D0-R*DLOG( D*R*T/PO) *1000. DO + CPK T, 2)

END

DOUBLE PRECISION FUNCTION SATL( TT)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

CALCULATES DENSI TY( MOL/ L) OF SATURATED LIQUID. INPUT IS TEMP( K)

DIMENSION A( 20)

DIMENSION G( 32) , VP( 9)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

COMMON/SATC/ A, DTPV, EG

COMMON/ISP/N, NW, NWW

IF( NH. EQ. 1 ) GO TO 30

T = TT

K=1 4 KK = 7 IF( T. GE. TCC*. 99999D0) GO TO 20

ITT=TCC

IF( ITT+1 -T. LT. 1 . DO) T=ITT

X=( T-TCC) /( TTP-TCC)

D = A( K) *DLOG( X)

DO 11 1=2, KK

K=K+1

MM=I

IF( MM. GE. 5) MM=MM+1

D = D + A(K)*(1.D0-X**(( MM- 5) /3. DO) ) IF( K. LT. 1 4) GO TO 12

D=DCC+DEXP( D) *( DTP-DCC)

GO TO 13

D=DCC+DEXP( D) *< DTPV-DCC)

SATL=D

IF(ITT + 1-TT. LT. 1)SATL=D-(D-DCC)*(TT-T)

RETURN

SATL=DCC

RETURN

CALL SSATLC DL, TT)

SATL=DL

END

DOUBLE PRECISION FUNCTION SATV( TT)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

CALCULATES DENSI TY( MOL/ L) OF SATURATED VAPOUR. INPUT IS TEMP( K)

DIMENSION A( 20)

DIMENSION G( 32) , VP( 9)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

COMMON/SATC/A, DTPV1 , EG

COMMON/ISP/N, NW, NWW

IF( NW. EQ. 1 ) GO TO 30

K = 1 KK=1 3 T = TT

10 IF( T. GE. TCC*. 99999D0) GO TO 20

ITT=TCC

IF( ITT+1 -T. LT. 1 . DO) T=ITT

X=( T-TCC) /( TTP-TCC)

D = A( K) *DLOG( X)

DO 1 1 1 = 2, KK

K = K + 1 MM=I

IF( MM. GE. 5) MM=MM+1

11 D = D + A(K)*(1.D0-X**(( MM- 5) /3. DO) ) IF( K. LT. 1 4) GO TO 12

D = DCC + DEXP( D) *( DTP-DCC)

GO TO 13

37

1

1

1 2

1 3

20

30
1 2

1 3

20

30

D=DCC+DEXP( D)

SATV=D

IF( ITT + 1 -TT. L RETURN

SATV=DCC

RETURN

CALL SSATV( DV

SATV=DV

END

DOUBLE PRECIS

IMPLICIT REAL

IMPLICIT REAL

IMPLICIT INTE

CALCULATES SPEED

COMMON/CRIT/

CALL PROPS( DP

SOUND = ( ( CP( D, END

DOUBLE PRECIS

IMPLICIT REAL

IMPLICIT REAL

IMPLICIT INTE

CALCULATES VISCO

COMMON/CRIT/

COMMON/ISP/N,

IF( NW. EQ. 1 ) GO

D=DD*GMW/1 000

VISC = DILV( T) + RETURN

1 VISC=VISCE( DD

END

DOUBLE PRECIS

IMPLICIT REAL

IMPLICIT REAL

IMPLICIT INTE

RETURNS THERMAL

COMMON/HAN/CR

COMMON/ISP/N,

COMMON/CRIT/

IF( NW. EQ. 1 ) GO

D=DD*GMW/1 000

CR=CRITC( D, T)

THER = DILT( T) + TCI=THER-CR

THERM=THER

RETURN

THERM=THERME(

END

DOUBLE PRECIS

IMPLICIT REAL

IMPLICIT REAL

IMPLICIT INTE

CALCULATES EX

C0MM0N/DATA1

/

DIMENSION GV(

R2=D**( . 5D0)

R=D**( . 1 DO)

X = EV( 1 ) +EV( 2)

1 +EV( 7) *R2/T

XI =EV( 1 ) +EV( 6 EXCESV= DEXP(

END

DOUBLE PRECIS

IMPLICIT REAL

IMPLICIT REAL

IMPLICIT INTE

C0MM0N/DATA1

/

DIMENSION GV(

CALCULATES EX

*( DTPV-DCC)

T. 1)SATV=D-(D-DCC)*(TT-T)

, TT)

ION FUNCTION SOUNDC D, T)

*8( A-H)

*8( 0-Z)

GER*2( I-N)

OF SOUNDC M/S). INPUT IS DENSI TY( MOL/ L) AND TEMP( K) . W, EOK, RM, TC, DC, X , PC, SIG

, D, T, 2)

T)/CV(D,T))*DP*1000000. DO/W)**. 5D0

ION FUNCTION VISC(DD, T)

*8( A-H)

*8( 0-Z)

GER*4( I-N)

SITY( MICRO PA*S) . INPUT IS DENSI TY( MOL/ L) AND TEMP( K) . GMW, EOK, RM, TC, DC, X , PC, SIG

NW, NWW

TO 1

. DO

FDCV( D, T) +EXCESVC D, T)

, T)

ION FUNCTION THERM( DD, T)

*8( A-H)

*8( 0-Z)

GER*4< I-N)

CONDUCTIVITYC W/( M*K) ) . INPUT IS DENSI TY( MOL/ L) , TEMP( K)

, TCI

NW, NWW

GMW, EOK, RM, TC, DC, X , PC, SIG

TO 1

. DO

10

FDCT( D, T) +EXCESTC D, T) +CR

DD, T)

ION FUNCTION EXCESV( D, T)

*8( A-H)

*8( 0-Z)

GER*4( I-N)

CESS VISCOSITY

GV, GT, FV, FT, EV, ET

9) , GT( 9) , FV( 4) , FTC 4) , EVC 8) , ETC 8)

( ( D-EV( 8) ) /EV( 8) )

*R2 + EV( 3) *R + EV( 4) *R2/( T*T) +EV( 5) *R/T**( 1 . 5D0) +EV( 6) /T

) /T

X) - DEXP( X1 )

ION FUNCTION EXCESTS D, T)

*8( A-H)

*8( 0-Z)

GER*4( I-N)

GV, GT, FV, FT, EV, ET

9) , GT( 9) , FV( 4) , FT( 4) , EV( 8) , ETC 8)

CESS THERMAL CONDUCTIVITY

38
R2 = D**(. 5D0)*((D-ET(8))/ET(8))

R=D**( . 1 DO)

X=ET( 1 ) +ET( 2) *R2 + ET( 3) *R+ET( 4) *R2/( T*T) +ET( 5) *R/T**( 1

1 +ET( 7) *R2/T

X1 =ET( 1 ) +ET( 6) /T

EXCEST= DEXP( X) - DEXP( X1

)

END

DOUBLE PRECISION FUNCTION FDCV( D, T)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

FIRST DENSITY CORRECTION FOR VISC.

COMMON/ D AT A1 /GV,GT,FV,FT,EV,ET

COMMON/CRIT/ GMW, EOK, RM, TC, DC,

DIMENSION GV( 9) , GT( 9) , FV( 4) , FT( 4) ,

5D0) +ET( 6) /T

X , PC, SIG

EV( 8) , ET( 8)

FDCV = (FV(1)+FV(2)*(FV(3) -DLOG( T/FV(4)))**2)*D

END

DOUBLE PRECISION FUNCTION FDCT( D, T)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

FIRST DENSITY CORRECTION FOR THERMAL COND.

COMMON/DATA1 /GV, GT, FV, FT, EV, ET

DIMENSION GV( 9) , GT( 9) , FV( 4) , FT( 4) , EV( 8) , ET( 8)

COMMON/CRIT/ GMW, EOK, RM, TC, DC, X , PC, SIG

FDCT=( FT( 1 ) +FT( 2) *( FT( 3) -DLOG( T/FT(4)))**2)*D

END

FUNCTION CRITCC D, T)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

c CALCULATES CRITICAL ENHANCEMENT FOR THERM. COND.

c INPUT UNITS ARE G/CC, K, OUTPUT IS W/(M*K).

COMMON/CRIT/ GMW, EOK, RM, TC, DC, X , PC, SIG

COMMON/CHECK/DELD, DELT, DSTAR, TSTAR

COMMON/HJM/EPSI, CPCV, RRR, AKT

COMMON/ISP/N, NW, NWW

AV=6. 0225D+23

BK=1 . 38054D-1

6

DELD=DABS ( D-DC) /DC

DELT=DABS ( T-TC) /TC

CALCULATE DISTANCE PARAMETER

R = ( RM**2. 5D0)*(D**0.5D0)*( AV/GMW) **0. 5 DO

R = R*( EOK**0. 5DO) *X/( T**0. 5DO)

RRR=R

GENERAL EQUATION

DX=D*1 OOO. DO/GMH

DX IN MOL/L, D IN G/CM3.

CALL PROPSC DPT, DX, T, 3)

DPDT IN MPA/K.

DPT=DPT*1 . OD+7

DPDT NOW IN DYNES/( CM2*K)

CALL PROPSC DPD, DX, T, 2)

DPDD IN L*MPA/MOL.

DPD = DPD*1. 0D + 7M000. /GMW

DPDD NOW IN DYNE*CM/G.

IF( DPD. LT. 0. ODO) DPD = 1.D0

94 VIS=VISC( DX, T) *( 1 . OD-05)

VISCOSITY NOW IS G/(CM*S).

IF( DELD. GT. 0. 25D0) GO TO 10

8 IF( DELT. GT. 0. 025D0) GO TO 10

9 COMPRES = SENG( D, T)

GO TO 12

10 C0MPRES = 1 . D0/( D*DPD) **0. 5D0

12 EX=BK*T**2*( DPT**2) *COMPRES

EXB=R*( ( BK*T) **0. 5D0) *( D**0. 5D0) *( ( AV/GMW) **0. 5D0)

CRIT = EX/(EXB*6. DO* 3. 14159D0*VIS)

THERMAL COND, CRIT, IS IN ERG/ ( CM*SEC*K)

PUT IN DAMPING FACTOR

39
AKT

SENG( D, T)

BDD = ( ( D-DC) /DC) **4

BTT=( ( T-TC) /TO **2

BXX= -18.66D0*BTT - 4.25D0*BDD

IF( BXX. LT. -1 . D + 2) BXX= -1.D + 2 FACT= DEXP( BXX ) FACT=DEXP ( -1 8. 66D0*BTT - 4.25D0*BDD)

DELC=CRIT*FACT

CRITC = DELC/1 00000. DO

THERMAL COND, CRITC, IS NOW IN W/(M*K)

AKT=COMPRES*COMPRES

EPSI=R*R*BK*T*( AV*D/GMW)

EPSI=EPSI**0. 5D0

CALC CP-CV

CPCV=T*( DPT**2) *AKT/D

END

DOUBLE PRECISION FUNCTION

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

SCALED EQUATION OF STATE FOR CRITICAL REGION

COMMON/CRIT/ GMW, EOK, RM, TC, DC, X , PC, SIG

COMMON/SEN/BETA, XO, DELTA, E1 , E2, AGAM

COMMON/CHECK/DELD, DELT, DSTAR, TSTAR

DSTAR= D/DC

TSTAR=T/TC

BET0=1

.

DO/BETA

XX=DELT/DELD**BETO

AG=AGAM-1 . DO

BET2= 2. ODO*BETA

AGB=AG/BET2

DEL1 =DELTA-1 . DO

AGBB=( AG-BET2) /BET2

XXO=( XX+ XO) /XO

XXB=XX0**BET2

BRAK=1 . DO + E2*XXB

BRAK1 =BRAK**AGB

H=E1 *XX0*BRAK1

HPRIM=( E1 /XO) *BRAK1 + ( AG/ XO) * E1 * E2* ( XXB) * ( BRAK* * AGBB)

RCOM=( DELD**DEL1 ) *( DELTA*H - ( XX/ BETA) * HPRI M ) RC0MP = 1. D0/( RC0M*DSTAR**2)

RCM=RC0MP/( PCM . OD + 7)

RCM IN CM2/DYNE, PC IN MPA

RCM=RCM**0. 5D0

SENG=RCM

END

DOUBLE PRECISION FUNCTION DILV(T)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

DILUTE GAS VISCOSITY

C0MM0N/DATA1 /GV, GT, FV, FT, EV, ET

DIMENSION GV( 9) , GT( 9) , FV( 4) , FT( 4) , EV( 8) , ET( 8)

SUM=0. ODO

TF=T**( 1 . DO/3. DO)

TFF = T**( -4. DO/3. DO)

DO 10 1=1,9

TFF=TFF*TF

1 SUM=SUM+GV( I) *TFF

DILV=SUM

END

DOUBLE PRECISION FUNCTION DILT(T)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

DILUTE GAS THERMAL CONDUCTIVITY.

COMMON/ DAT A 1 / GV, GT, F V, FT, EV, ET

DIMENSION GV( 9) , GT( 9) , FV( 4) , FTC 4) , EV( 8) , ETC 8)

TF = T**( 1 . DO/3. DO)

TF F=T**( -4. DO/3. DO)

40
20

1

1 00

SUM=0

DO 20 1 = 1 , 9 TFF=TFF*TF

SUM=SUM+GT( I) *TFF

DILT=SUM

END

DOUBLE PRECISION FUNCTION FINDP(D, T)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

DIMENSION G( 32) , VP( 9)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL. PUL, DCC

DD = D TT = T IF( TT. LT. TCC) GO TO 10

CALL PROPSC PP, DD, TT, 1 ) FINDP=PP

RETURN

P = VPN( TT)

DV=FINDD( P-. 00 01 DO, TT)

DL=FINDD( P + . 001 DO, TT)

IF( DD. LE. DV. OR. DD. GE. DL) GO TO 1 HRITE( *, 100) DV, DL, DD

CALL PROPSC PP, DV, TT, 1 ) FINDP=PP

D = DV

FORMAT( • THE STATE POINT YOU HAVE SPECIFIED CORRESPONDS

DENSITY IN THE LIQUID VAPOR COEXISTENCE REGION'

THE DENSITY OF THE SATURATED VAPOR IS ',F6.4,'

THE DENSITY OF THE SATURATED LIQUID IS ',F8.4,

AND THE INPUT DENSITY IS ',F8.4,' MOLES/LITER"

SATURATED VAPOR IS ASSUMED')

MOLES/LITER'

MOLES/LITER'

FINDT( P, D)

EQN OF STATE.

TO A

1 / 2/

3/

4/

5/

END

DOUBLE PRECISION FUNCTION

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

RETURNS TEMPERATURE( K) , FROM THE 32-TiJRM MBWR

INPUT IS PRESSURE( MPA) AND DENSI TY( MOL/ L)

.

DIMENSION G( 32) , VP( 9)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL. DCC

PP = P DD=D

IF( P. GE. PCC) GO TO 1 TSAT = FINDTV( PP)

DV = FINDD( PP-. 00001D0, TSAT)

DL=FINDD( PP + . 0001D0, TSAT)

IF( DD. GT. DV. AND. DD. LT. DL) GO TO 30

TT=TSAT

GO TO 2

1 TT=TCC

2 DO 10 1 = 1,10

CALL PROPS( P2, DD, TT, 1 ) IF( DABS( PP-P2) -1. D-7*PP) 20, 20, 11 CALL PROPSC DP, DD, TT, 3)

CORR=( P2-PP) /DP

IF( DABS( CORR) -1 . D-5) 2 0, 20, 1 TT=TT-CORR

FINDT=TT

RETURN

FINDT=TSAT

D = DV

HRITE( *, 1 00) DV, DL, DD

FORMAT( ' THE STATE POINT YOU HAVE SPECIFIED CORRESPONDS TO'

A DENSITY IN THE LIQUID VAPOR COEXISTENCE REGIONDENSITY OF THE SATURATED VAPOR IS',F8.4,' MOLES/LITER'

DENSITY OF THE SATURATED LIQUID IS',F8.4,' MOLES/LITER'

INPUT DENSITY IS',F8.4,' MOLES/LITER'

SATURATED VAPOR CONDITIONS ARE ASSUMED'

)

1 1

10

20

30

1 00

1 /' 2/'

3/ 1 4/

5/

41
C DIE

C CAL

C OUT

C HYD

C CP

C AND

1 1

1 30

1 40

1 60

1 70

1 80

1 5

20

25

40

55

END

DOUBLE PRE

IMPLICIT R IMPLICIT R IMPLICIT I LECTRIC CO

COMMON/DIE

COMMON/ISP

IF( NW. EQ. 1 CM= BX( 1 ) + FDIEL=( 1 . D RETURN

FDIEL=SDIE

END

DOUBLE PRE

IMPLICIT R IMPLICIT R IMPLICIT I CULATES SP

PUT IS IN

ROGEN, ( N = ARE IN THR

T > 1 40 K COMMON/CPI

COMMON/ISP

C0MM0N/H2/

IF( N. NE. 1 ) TX1 =1 40. DO

TX2=40. DO

DO 1 1 J=1

G( J) =GH( J)

IF( T. LT. 1 4 GO TO 180

CALL SHK T

G( 1 0) =G( 1 G( 1 1 ) =G( 1 1 DO 140 J=1

G( J) =GL( J)

CALL SHK T

G( 1 0) =G( 1 G( 1 1 ) =G( 1 1 IF( T. LT. 40

GO TO 180

CALL SHK T

G( 1 0) =G( 1 G( 1 1 ) =G( 1 1 DO 170 J=1

G( J) =0. 0D0

G( 4) =2. 500

CALL SHK T

G( 1 0) =G( 1 G( 1 1 ) =G( 1 1 CONTINUE

U=G( 9) /T

EU=DEXP ( U TS=1 . DO/T*

GO TO ( 20,

CPI = G( 8) *U

DO 25 1 = 1 , TS=TS*T

CPI = CPI+G(

CPI=CPI*8.

RETURN

CPI=G( 8) *(

-G( 1 ) *TS*T

+ G( 6) *T*T/

CPI=CPI*8.

RETURN

CPI=G( 8) *U

CISION FUNCTION FDIEL(P,D,T)

EAL*8( A-H)

EAL*8( O-Z)

NTEGER*4( I-N)

NSTANT. INPUT P( MPA) , D(MOL/L) AND T( K) . L/BX( 6) , PX( 6)

/N, NW, NWW

) GO TO 1 BX(2)*D+ BX(3)*D**2+ BX(4)*D**3 + BX(5)*P + BX(6)*T

+ 2. D0*D*CM) /( 1. D0-D*CM)

L( P, D, T)

CISION

EAL*8.( A EAL*8(

NTEGER*

ECIFIC

J/( MOL*

1 ) , IS

EE TEMP

D/G( 1 1 ) /N, NW, N FHI, FSI

GO TO 1

FUNCTION CPK T, K)

-H)

-Z)

4( I-N)

HEAT, ENTROPY, AND ENTHALPY FOR THE IDEAL GAS.

K) , FOR CP AND S, AND J/MOL FOR H. TREATED AS A SPECIAL CASE AS THE COEFF. FOR

ERATURE RANGES. T < 40 K, 40 < T < 140 K,

, GH( 1 1 ) , GL( 1 1 ) WW

, 11

0. DO) GO

X1 )

) +FHI

) +FSI

, 8

X1 )

) -FHI

) -FSI

. DO) GO

X2)

) +FHI

) +FSI

, 8

031 5D0

X2)

) -FHI

) -FSI

TO 1 30

TO 1 60

)*4

40, 55) , *U*EU/(

7

I) *TS

31 434D0

U/( EU-1

/3. DO-G

2. DO + G( 31 434D0

KEU-1 . DO) **2

. DO) -DLOG( 1. DO-1 . DO/EU))

( 2) *TS*T*T/2. DO-G( 3) /T+G( 4) *DLOG( T) +G( 5) *T

7) *T**3/3. DO

+ G( 1 1 )

*T/( EU-1 . DO) -G( 1) /( 2. D0*T*T)-G(2)/T + G(3) *DLOG< T) +G( 4) *T

42
DO

DO1 . DO/EU) ) - G( 3) /T + G( 4) *DLOG( T) +G( 5) *T +

TEMPERATURE( K)

1

20

30

1+G(5)*T*T/2. D0 + G(6)*T**3/3. D0 + G(7)*T**4/4. DO

CPI=CPI*8. 31434D0 + G( 10)

END

SUBROUTINE SHK T)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

COMMON/ CPID/G( 1 1 ) , GH( 1 1 ) , GL( 1 1 ) C0MM0N/H2/FHI, FSI

1 U=G( 9) /T

EU=DEXP( U)

GHI=G( 8) *U*T/( EU-1 . DO) -G( 1 ) /( 2. D0*T*T)-G(2)/T+G(3) *DL0G( T) +G( 4) *T

A +G(5)*T*T/2. D0 + G(6)*T**3/3. D0 + G(7)*T**4/4. DO

FHI=GHI*8. 31 434D0

U=G( 9) IT

EU=DEXP( U)

TS=1 . D0/T**4

GHS= G( 8) *( U/( EU-1 . DO) -DLOG( 1 . A G( 1 ) *TS*T/3. DO-G( 2) *TS*T*T/2.

B G( 6) *T*T/2. DO + G( 7) *T**3/3. DO

FSI=GHS*8. 31 434D0

END

DOUBLE PRECISION FUNCTION PMELT( T)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

COMPUTES MELTING PRESSURE( MPA) FOR INPUT

COMMON/DIEL/BXC 6) , PX( 6)

COMMON/ISP/N, NW, NWW

IF( N. EQ. 1 ) GO TO 20

PMELT= PX(1)+ PX( 2) *T**PX( 3)

RETURN

IF( T. LT. 22. DO) GO TO 10

PMELT= PX(4)+ PX( 5) *T**PX( 6)

END

TMELT( P)

REAL*8( A-H)

REAL*8( 0-Z)

INTEGER*4( I-N)

COMPUTES MELTING TEMPERATURE( K) FOR INPUT

COMMON/DIEL/BX( 6) , PX( 6)

COMMON/ISP/N, NW, NWW

IF( N. EQ. 1 ) GO TO 20

TMELT = ( ( n -PX(1))/PX(2))**(1

RETURN

IF( P. LT. 31 . 64D0) GO TO 10

TMELT = ( ( P-PX( 4) ) /PX( 5) ) **< 1 END

DOUBLE PRECISION FUNCTION VPN( TT)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

C CALCULATES VAPOR PRESSURE( MPA) , INPUT IS

DIMENSION G( 32) , VP( 9)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

T = TT

X = (1. D0-VP(7)/T)/(1. D0-VP(7)/VP(8))

VPN=VP(9)*DEXP (VP(1)*X + VP(2)*X*X+VP(3)*X**3 + VP(4)*X**4 + VP(5)*X*

1(1. DO-X) **VPi 6) ) END

SUBROUTINE SSATL( D1 , T1

)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

C SATURATED LIQUID AND

C LIQUID DENSITIES ARE

C VAPOR DENSITYES ARE

DIMENSION G( 32) , VP( 9) , A( 20)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

FUNCTION

IMPLICIT

IMPLICIT

IMPLICIT

PRESSURE( MPA)

10

20

30

D0/PX( 3) )

D0/PX( 6) )

TEMP( K)

VAPOR DENSITIES.

FROM R. D. MCCARTY.

FROM R. D. GOODWIN.

43
D0-X1 **< -1 . DO/3. DO) )

. DO-X1 **( 2. DO/3. DO) ) +

20

20

A( 3) *X1 + A( 4) *X1 **(

A( 6) *X1 *X1

SDIEL( P, D, T)

4. DO/3. DO)

INPUT P( MPA) , D(MOL/L) AND T( K)

COMMON/SATC/ A, DTPV, EG

IF( T1 . GE. TCC) GO TO 20

X1 =( T1 -TCC) /( TTP-TCC)

Y1 =A( 7) *DLOG( X1)+ A( 8) *( 1 . DO-1 . D0/.X1 ) + A A( 9) *( 1 . D0-X1 **( -2. DO/3. DO) ) + A(10)*(1.

B A( 1 1 ) *( 1 . D0-X1 **( 1.D0/3.D0))+ A(12)*(1

C A(13)M1. D0-X1 ) D1=DCC+ ( DTP-DCC) *DEXP( Y1

)

RETURN

D1 =DCC

END

SUBROUTINE SSATVt D1 , T1 ) IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

DIMENSION G( 32) , VP( 9) , A( 20)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

COMMON/SATC/ A, DTPV, EG

TT = T1 IF( TT . GE. TCC) GO TO 20

YN=DLOG( DCC/DTPV)

X1 =( TCC-TT) /( TCC -TTP)

Z1 =TCC*X1 /TT

Y1= A(1)*Z1 + A(2)*X1**EG + A +A( 5) *X1 **< 5. DO/3. DO) + D1 =DCC*DEXP( -YN*Y1 ) RETURN

D1 =DCC

END

DOUBLE PRECISION FUNCTION

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

C DIELECTRIC CONSTANT

COMMON/DIEL/BX( 6) , PX( 6)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

DIMENSION G( 32) , VP( 9)

CM= BX(1)+ BX(2)*D + BX(3)*D**2 + BX( 4 ) * DLOG( 1 . DO + TCC/ T) + A BX( 5) *P

SDIEL = ( 1. DO + 2. DO*D*CM) /( 1. DO-D*CM)

END

DOUBLE PRECISION FUNCTION THERME( DD, TT)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

C THERMAL CONDUCTIVITY W/(M*K).

DIMENSION GV( 9) , GT( 9) , FV( 4) , FT( 4) , EV( 8) , C0MM0N/DATA1 /GV, GT, FV, FT, EV, ET

TI = 1 . DO/TT

TRMO= ET( 1 ) + ET(2)*TI + ET(3)*TI*TI

TRM1= ET(4)+ ET(5)*TI + ET(6)*TI*TI

TRM2= ET( 7) + ET( 8) *TI

BACKG = TCONDO( TT) +( TRM0 + TRM1 *DD) *DD/( 1 THERME = BACKG + TCRIT(DD.TT)

END

DOUBLE PRECISION FUNCTION TCOND0( TT)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

C THERMAL CONDUCTIVITY (W/(M*K))

C LOW DENSITY LIMIT.

DIMENSION GV( 9) , GT( 9) , FV( 4) , FT( 4) , EV( 8) , ETC 8)

C0MM0N/DATA1 /GV, GT, FV, FT, EV, ET

COMMON/B/ GMW, EOK,SIG

C R IS GAS CONSTANT IN J/(MOL*K).

R= 8. 31 434D0

C0N1 = 1 5. D0*R/4. DO

C0N2= 2. D0*C0N1 /3. DO

CPO= CPU TT, 1 ) 44

ET( 8)

D0+TRM2*DD)

TT( K)
ETAO

TS

YC

TCONDO

END

DOUBLE

CPO IS SPECIFIC HEAT IN J/(MOL*K),

VSCTYO IS VISCOSITY IN MICRO-PA*S.

= VSCTYO( TT, 0. ODO) /1 OOOOOO. DO

= TT/EOK

= ( GT( 1 ) + GT( 2) /TS) *< CPO- C0N2)

= 1 000. DO*ETAO*( C0N1 + YO/GMW

FACTOR OF 1000 CONVERTS G/MOL TO KG/MOL.

X2*DELD**4. DO

FACT=1 00. DO

TO PA*S.

DO) /( 2. D0*B1 ) )

0. 03D0) GO TO 30

PRECISION FUNCTION TCRITCDD, TT)

CRITICAL ENHANCEMENT W/(M*K), INPUT MOL/L AND K. IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8< 0-Z)

IMPLICIT INTEGER*4( I-N)

DIMENSION G( 32) , VP( 9)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

COMMON/ A/ E1,G1,B1,DE,BK,D1,XZ,ZZ,X1,X2,X3,X4

COMMON/B/ GMW, EOK,SIG

PC1 =PCC*1 . D+6

DELD=DABS( DD-DCC) /DCC

DELT=DABS( TT-TCC) /TCC

FACT= X1 *DELT**4. DO + IF( FACT . GT. 1 00. DO)

DFACT=DEXP( -FACT)

RSTAR=DD/DCC

CONVERTING MICRO-PA*S

VIS= 1 . 0D-06*VISCE( DD, TT)

CALL PROPS( DPD, DD, TT, 2)

CONVERTING M-PA TO PA. DPD=DPD*1. D+6

CALL PROPSC DPT, DD, TT, 3)

DPT=DPT*1 . D+6

IF(DELD . NE. 0. ODO) GO TO 20

CRITICAL ISOCHORE.

10 BGAM=XZ**G1/D1*((1. D0 + E1 ) / E1 ) **( ( G1 -1 CHISTAR=BGAM*( DELT) **( -G1 ) GO TO 50

20 IF(DELD . LE. 0. 2 5D0. AND. DELT . LT. GO TO 40

CRITICAL REGION

30 XX=DELT/DELD**( 1 . D0/B1 ) Y = ( XX + XZ) /XZ

TOP = DELD**( -G1/B1) *< ( 1 . D0 + E1) /( 1

1 ) /( 2. D0*B1 ) ) DIV=D1*(DE+(Y-1. DO) *( DE-1 . D0/B1+E1*Y**(2. D0*B1 ) ) /( 1 . D0 + E1*Y**(2.

1 D0*B1 ) )

CHISTAR=TOP/DIV

GO TO 50

NON CRITICAL REGION

40 CHISTAR=PC1 *DD/( DCC**2*DPD)

50 CHI=CHISTAR**X3

UPPER=X4*BK/PC1*( TT*DPT/RSTAR) **2*CHI*DFACT

SSENG=UPPER/(ZZ*6. DO* 3. 1 41 59D0*VIS)

TCRIT=SSENG

END

DOUBLE PRECISION FUNCTION VISCECDS, TS)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( 0-Z)

IMPLICIT INTEGER*4( I-N)

DIMENSION G( 32) , VP( 9)

DIMENSION GV( 9) , GT( 9) , FV( 4) , FT( 4) , EV( 8) , ET( 8)

C0MM0N/DATA1 /GV, GT, FV, FT, EV, ET

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

ETAO= VSCTYOC TS, DS)

TRM1 = EV( 3) + EV( 4) *TS**( -3. DO/2. DO)

TRM2= EV( 5) + EV(6)/TS + E V( 7) *TS* * ( -2. DO)

TRMX= DEXP(EV(1) + EV(2)/TS)

R1 = DS**0. 1 DO

R2 = ( ( DS-DCC) /DCC) *DS**0. 5D0

VISCE = TRMX*( DEXP( TRM1 *R1 + TRM2*R2) - 1.D0) + ETAO

D0 + E1*Y**(2. D0*B1)))**((G1-1. DO

45
200

END

DOUBL

IMPLI

IMPLI

IMPLI

DIMEN

DIMEN

COMMO

COMMO

DATA

TS = TY = TZ= T E0 = 0.DO

EO

TY

0M22

ETAO

ETA1 = VSCTY

END

DENSITY

K.

ETC 8)

E PRECISION FUNCTION VSCTYO( TX, DX)

VISCOSITY THROUGH LINEAR TERM IN

DENSITY IS IN MOL/L, AND TEMP IN

CIT REAL*8( A-H)

CIT REAL*8( O-Z)

CIT INTEGER*4( I-N)

SION C0( 9)

SION GV( 9) , GT( 9) , FV( 4) , FTC 4) , EV( 8)

N/DATA1 /GV, GT, FV, FT, EV, ET

N/B/ GMW, EOK, SIG

C0/-3. 03281 38281 D+00, 1. 6918880086D+01

4. 1288861858D + 01, -2. 4615921140D + 01

-1. 8739245042D+00, 2. 09661 01 390D-0

1

TX / EOK

1 . DO / TS

S**( 1 . DO/3. DO)

DO

200 J=1 ,

9

=EO+CO( J) *TY

=TY*TZ

= 1 . DO / EO

ETAO IS VISCOSITY AT THE LOW DENSITY LIMIT.

= 2. 6693D0 *DSQRT( GMW * TX) / (SIG*SIG * 0M22)

FV(1) + FV( 2) *( FV( 3) -DLOG( TX/FV( 4) ) ) **2

0=( ETA0+ETA1 *DX)

IN MICRO-PA*S.

-3. 71 8936491 7D+01

,

8. 9488430959D+00,

-9. 6570437074D-03/

46
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63
Program Listing of HELIUM

PROGRAM HELIUM

IMPLICIT REAL*8(A-H)

IMPLICIT REAL*8(0-Z)

IMPLICIT INTEGER*4 (I-N)

COMMON/LIM/TUL , TLL , PUL , TCC , DCC , PCC

1000 FORMAT (//' THIS PROGRAM PROVIDES THE THERMODYNAMIC PROPERTIES

10F HELIUM',/,' FROM 2 TO 1500 K (-456 TO 2240 F)'

A,/' WITH PRESSURES TO 100 MPA (14503 PSIA)'/)

WRITE(*,1000)

CALL INFO

IP = 3 CALL FDATA

TTP=TLL

PTP=.005D0

EM=4.0026

1010 FORMAT (ID

1 CONTINUE

120 WRITE(* ,1040)

1040 FORMAT(' FOR ENGINEERING UNITS ENTER "0", FOR METRIC ENTER "1"',/)

READ(* , 1010) IU

WRITE (* , 1050)

1050 FORMAT (' FOR SATURATION PROPERTIES ENTER "0", FOR FLUID ENTER ' A '"1"' ,/)

READ(* , 1010) IC

WRITE(* ,1060)

1060 FORMAT(' FOR A SINGLE POINT ENTER "0", FOR A TABLE ENTER "1"',/)

READ(* ,1010) IV

160 IF(IC.EQ.0)GO TO 240

IF(IV.EQ.l)GO TO 330

170 IF(IU.EQ.0)GO TO 180

WRITE(* ,1080)

READ(* , *) PI,D,T

GO TO 190

180 WRITE(* ,1070)

1070 FORMAT(' ENTER PRESSURE ( PSIA) , DENSITY ( LB/CU FT), AND TEMPERATURE'

A '(F)',/)

READ(* , *) P,D,T

PI=(P/14.69 59 49D0) *. 101 32

5

D=D*16.018 46 371D0/EM

T=(T-32.D0) /1.8D0+27 3.15D0

190 IF(PI.LE.0.0D0.AND.D.LE.0.0D0)GO TO 110

IF(PI.GT.0.0D0.AND.D.GT.0.0D0)GO TO 200

IF(PI.LE.0.0D0.AND.T.NE.0.0D0)GO TO 220

IF(PI.NE.0.0D0.AND.T.NE.0.0D0)GO TO 210

GO TO 1 1080 FORMAT(' ENTER PRESSURE (MPA) , DENSITY (MOL/L) , AND TEMPERATURE ( K)

A /)

200 P=PI/. 101325

T=FIND T(P,D)

CALL LIMITS (PI, T, ID

IF(IL.LE.0)GO TO 170

GO TO 230

210 P=PI/. 101325

CALL LIMITS (PI, T, ID

IF(IL.LE.0)GO TO 170

D=FIND D(P,T)

64
220

230

240

1090

1095

250

1100

/)

IN DEGREES F, ENTER FOR RESTART',/)

260

1110

270

280

GO TO 230

P=FIND P(D,T)

PI=P*. 101325

CALL LIMITS (PI, T, ID

IF(IL.LE.0)GO TO 170

CALL REPRO(PI,D,T, IU, IV, IC, IP,TF,TDEL)

GO TO 170

WRITE(* , 1090)

FORMAT (' FOR SATURATED LIQUID ENTER "0", FOR VAPOR ENTER " 1 "

' , /

)

READ(* , 1010) IP

IF(IV.EQ.l)GO TO 330

WRITE(*, 1095)

FORMAT (' TO ENTER WITH TEMPERATURE ENTER " " , FOR PRESSURE "1"',

READ(* ,1010) II

IF(II.EQ.l)GO TO 290

IF(IU.EQ.l)GO TO 260

FORMAT (' ENTER A TEMPERATURE

WRITE(* , 1100)

READ(*, *)TI

IF(TI.EQ.0.0D0

T=(TI-32.D0) /l

GO TO 270

WRITE (* , 1110)

FORMATt' ENTER A TEMPERATURE ( K) , ENTER FOR RESTART',/)

READ(* , *)T

IF(T.LT. .000001D0)GO TO

IF ( T . GT . TCC . OR . T . LT . TTP [ P=VPN(T)

IF(IP.EQ.O) P=P+.00001D0

IF(IP.EQ.1)P=P-.00001D0

D=FIND D(P,T)

PI=P* .101325

CALL RE PRO(PI,D,T,IU,IV

GO TO 250

X1=(TTP-27 3.15D0) *1.8D0+32.D0

X2=(TCC-27 3.15D0) *1. 8D0+32.D0

WRITE (* , 11 20) TTP, TCC, XI, X2

GO TO 110

.8D0+273.15D0

110

GO TO 280

IC,IP,TF,TDEL)

1120 SATURATION

' < TEMP < F6

F7

TEMP

' ,/)

F6.2,

290

1130

101325D0

110

300

1140

310

FORMAT (

' FOR

A ' OR '

, F7.2,

GO TO 250

IF(IU.EQ.l)GO TO 300

WRITE(* ,1130)

FORMATT ENTER A PRESSURE IN LB/SQ IN RESTRATS PROGRAM',/)

READ(* , *)P

PI=(P/14.695949D0)

P=PI/.101325D0

IF(PI.LE.0.0D0)GO TO

GO TO 310

WRITE(* , 1140)

FORMAT(' ENTER A PRESSURE (MPA) RESTARTS PROGRAM',/)

READ(* , *) PI

IF(PI.LE.0.0D0)GO TO 110

P=PI/. 101325

IF(PI.GT.PCC.OR.

T=FIND TV(P)

P=VPN(T)

TF(IP.EQ.l) P=PIF(IP.EQ.0)P=P+.

D=FIND D(P,T)

PI=P* .101325

CALL RE PRO (PI

GO TO 290

PI.LT.PTP)GO TO 320

00001D0

00001D0

D,T, IU,IV, IC,IP,TF,TDEL)

65
320 PTPF=PTP*14. 695949/ .101325

PCCF=PCC*14.69 594 9/.101325

WRITE{* ,1150) PTP,PCC,PTPF,PCCF

1150 FORMAT (' YOUR INPUT PRESSURE IS OUTSIDE THE RANGE OF SATURATION'

A ' PRESSURES'/" FOR THIS FLUID THE RANGE IS ' ,F6.5,' TO ' , F6 . 3

,

B' MPA,'/' OR ',F6.5,' TO ' , F6 . 3

,

' PSIA'/' TRY AGAIN',/)

GO TO 290

330 IF(IC.EQ.l)GO TO 370

IF(IU.EQ.l)GO TO 340

WRITE(* ,1160)

1160 FORMAT (' ENTER A STARTING TEMPERATURE, A FINAL TEMPERATURE'

A /' AND A TEMPERATURE INCREMENT, IN DEGREES F AND IN THAT ORDER'/

B ' ENTER 0,0,0 TO RESTART'/)

READ ( *

, * ) TS , TF , TDEL

IF(TDEL.LE.0.0D0)GO TO 110

TS=(TS-32.D0) /1.8D0+27 3.15D0

TF=(TF-32.D0) /l . 8D0+273 . 15D0

TDEL=TDEL/1.8D0

IFdS.LT.TTP.OR.TS.GT.TCOGO TO 360

IFdF.LT.TTP.OR.TF.GT.TCOGO TO 360

GO TO 350

340 WRITE(* ,1170)

1170 FORMAT (' ENTER A STARTING TEMPERATURE, A FINAL TEMPERATURE'

1/' AND A TEMPERATURE INCREMENT IN KELVINS AND IN THAT ORDER',/

2' ENTER 0,0,0 TO RESTART PROGRAM'/)

READ(* , *)TS,TF,TDEL

IF(TDEL.LE.0.0D0)GO TO 110

IFdS.LT.TTP.OR.TS.GT.TCOGO TO 360

IFdF.LT.TTP.OR.TF.GT.TCOGO TO 360

350 T=TS

P=VPN(T)

IF(IP.EQ.0)P=P+.00001D0

IF(IP.EQ.l) P=P-.000 01D0

D=FIND D(P,T)

PI=P* .101325

CALL RE PRO(PI,D,T,IU,IV,IC,IP,TF,TDEL)

GO TO 330

360 X1=(TTP-27 3.15D0) *1.8D0+3 2.D0

X2=(TCC-27 3.15D0) *1.8D0+3 2.D0

WRITE (* ,1180)TTP,TCC,X1,X2

1180 FORMAT (' FOR SATURATION, ' , F6 . 2

,

' < TEMP < ' , F6 . 2

,

' K',/,

A ,13X,'OR, ',F7.1,' < TEMP < ' , F7 . 1

,

' F. TRY AGAIN.',/)

GO TO 330

370 IF(IU.EQ.l)GO TO 380

WRITE(* ,1190)

1190 FORMATf' ENTER PRESSURE ( PSIA) , STARTING TEMPERATURE (F) , FINAL ' A ' TEMPERATURE (F) '/ ' AND A TEMPERATURE INCREMENT, IN THAT ORDER',/

B ' ENTER 0,0,0,0 TO RESTART PROGRAM'/)

READ ( *

, * ) P , TS , TF , TDEL

IF(TDEL.LE.0.0D0)GO TO 110

PI=(P/14.69 5949D0) * . 101325D0

T=(TS-32.D0) /1.8D0+27 3.15D0

TF=(TF-32.D0) /l . 8D0+27 3 . 1 5D0

TDEL=TDEL/1.8D0

P=PI/. 101325

CALL LIMITS (PI,T, ID

IF(IL.LE.0)GO TO 370

CALL LIMITS (PI, TF, ID

IF(IL.LE.0)GO TO 370

GO TO 390

380 WRITE(* ,1200)

1200 FORMAT (' ENTER A PRESSURE (MPA) , A STARTING TEMPERATURE ( K) , A

'

66
1" FINAL TEMPERATURE AND A'/' TEMPERATURE INCREMENT'

2' AND IN THAT ORDER, TO RESTART PROGRAM ENTER "0,0,0,0"',/)

READ ( *

, * ) PI , TS , TF , TDEL

IF(TDEL.LE.0.0D0)GO TO 110

T=TS

P=PI/. 101325

CALL LIMITS(PI,T,IL)

IF(IL.LE.0)GO TO 370

CALL LIMITS(PI,TF,IL)

IF(IL.LE.0)GO TO 370

390 D=FIND D(P,T)

CALL RE PRO(PI,D,T,IU,IV,IC,IP,TF,TDEL)

GO TO 370

110 CONTINUE

WRITE(* , 1210)

1210 FORMAT (//' FOR MORE PROPERTIES ENTER 0, TO TERMINATE ENTER 1' READ(* , 1010) IM

IF(IM.EQ.0)GO TO 1 999 CONTINUE

STOP

END

SUBROUTINE REPRO ( PI , D , T , IU , IV , IC , IP , TF , TDEL

)

IMPLICIT REAL*8(A-H)

IMPLICIT REAL*8(0-Z)

IMPLICIT INTEGER*4 (I-N)

N=500

EM=4.0026

P=PI/. 101325

IF ( IV . EQ . ) TF=T-1 . DO

IF(IU.EQ.0)GO TO 100

WRITE**, 1000)

WRITE(* , 1010)

WRITE(*,1020)

GO TO 110

100 WRITE(* ,1000)

WRITE(*, 1030)

WRITE(* ,1040)

110 CONTINUE

DO 210 1=1,

N

IF(I.EQ.l)GO TO 120

D=FIND D(P,T)

120 H=ENTHAL(P,D,T)

E=H-101.325D0*P/D

S=ENTROP(D,T)

W=SOUND(D,T)

CPP=CP(D,T)

CVV=CV(D,T)

150 V=VISC(D,T)

TH=THERM(D,T) *100.D0

EPS=FDIEL(D)

IF(IU.EQ.0)GO TO 160

PO=P*. 101325

WRITE (* ,2030) PO,T,D,E,H, S , CVV , CPP , W , V , TH , EPS

GO TO 200

160 H=H/(2.324445D0*EM)

E=E/ (2.324445D0*EM)

S=S/ (4.184001DO*EM)

CPP=CPP/ (4. 184001 DO *EM)

CVV=CVV/ (4.184001D0*EM)

W=W*3.280840D0

PO=P*14.695949D0

DO=D*EM/16.018 46 371D0

67
T0=T*1 . 8D0-459 . 67D0

190 V=VISC{D,T) * .0067196897D0

TH=THERM(D,T) * .000 57 8176D0

EPS=FDIEL(P,D,T)

WRITE (*, 3030) PO,TO,DO,E,H, S , CVV , CPP , W , V , TH , EPS

200 T=T+TDEL

IF(T.GT.TF+.01D0)GO TO 220

IF(IC.NE.0)GO TO 210

P=VPN(T)

IF(IP.EQ.0)P=P+.00001D0

IF(IP.EQ.1)P=P-.00001D0

210 CONTINUE

220 CONTINUE

WRITE(* ,1000)

1000 FORMAT ('

'

)

RETURN

1010 FORMAT (3X, ' P

' , 5X ,

' T

' , 6X , 'DEN' , 5X ,

' E

' , 6X ,

' H

' , 6X ,

' S

' , 4X ,

' CV ' , 4X

,

A 'CP' , 3X, 'SOUND' ,2X, 'VISC ,2X, ' COND ' , 2X, 'DIEL'

)

1020 FORMAT(3X, ' MPA ' ,3X, 'K' ,6X, 'MOL/L' , 2X, ' === J/MOL ==',2X,'==== ', A ' J/MOL-K ===' , 2X, 'M/S' , 3X, ' PA-S ' ,1X, 'MW/M-K' ,2X, ' == ' , /,61X, ' E+6 '

)

10 30 FORMAT (3X, ' P

'

, 5X ,' T

' , 7X , 'DENS' , 3X ,

' E

' , 8X ,

' H

' , 5X ,

' S

'

, 5X ,

' CV '

,

A 4X, 'CP' ,2X, ' SOUND' , IX, 'VISC , 2X, 'COND' , 2X, 'DIEL'

)

1040 FORMAT (3X, 'PSIA' , 2X , 'F' ,7X, 'LB/ ' , 3X, ' ==== BTU/ ===', IX, '======'

,

A ' BTU/ =====' ,2X, 'F/S' ,3X, 'LB/' ,2X, 'BTU/ ' ,2X, '==' ,/,17X, 'CU FT',

B 6X, 'LB' ,14X, 'LB-F' ,13X, 'FT-S ' , IX, ' FT-HR-F ' , / , 62X ,' E+5 '

)

2030 FORMAT(F8.3,F7.2,F7.3,2F7.0,F6.1,F5.1,F6.1,F6.0,F6.1,F6.1,F8.5)

30 30 FORMAT (F8.1,F7 . 2 , F7 . 3 , 2F7 .1, 3F6 . 3 , F6 . , F5 . 2 , F6 . 4 , F8 . 5)

END

SUBROUTINE INFO

WRITE (* , 101)

101 FORMAT (' WRITTEN BY'//

A' ROBERT D. MCCARTY'/

1' THERMOPHYSICS DIVISION'/

2' CENTER FOR CHEMICAL ENGINEERING'/

3' NATIONAL BUREAU OF STANDARDS'/

4' BOULDER, COLORADO'//

5' DISTRIBUTED BY' //

A' THE OFFICE OF STANDARD REFERENCE DATA'/

6' NATIONAL BUREAU OF STANDARDS, WASHINGTON, DC'/)

WRITE(* ,100)

100 FORMAT (/ ' WHEN THE PROGRAM ASKS FOR A PRESSURE, DENSITY AND'

*' TEMPERATURE,'/ ' ENTER ANY TWO AND A ZERO FOR THE THIRD.'/

* ' TO TERMINATE THE PROGRAM ENTER ZERO FOR ALL THREE.'/)

RETURN

END

68
SUBROUTINE FDATA(IF)

IMPLICIT REAL*8(A-H)

IMPLICIT REAL*8(0-Z)

IMPLICIT INTEGER*4 (I-N)

DIMENSION B(27, 3)

COMMON/COEF/B

COMMON/LIM/TUL , TLL , PUL , TCC , DCC , PCC

OPEN ( 5 , FILE= ' HELIUM . COF '

DO 60 J=l,3

DO 60 1=1,27

60 READ(5,101)B(I, J)

101 FORMAT (D20. 13)

READ (5,102) TUL , TLL , PUL , TCC , DCC , PCC

CLOSE ( 5 , STATUS= ' KEEP '

102 FORMAT(F10.8,E14.8, 3F8.2,2F8.4)

RETURN

END

SUBROUTINE LIMITS ( PI , T , ID

IMPLICIT REAL*8(A-H)

IMPLICIT REAL*8(0-Z)

IMPLICIT INTEGER*4 (I-N)

COMMON/LIM/TUL , TLL , PUL , TCC , DCC , PCC

P=PI/. 101325

IF(PI.GT. PUDGO TO 10

IF(T .GT. TUL. OR. T . LT . TLL)GO TO 12

PM=PMELT(T)

IF(P .GT. PM) GO TO 20

IL=1

RETURN

10 PULF=PUL*14. 6959496/. 101325

WRITE ( * , 11 ) PUL , PULF

11 FORMAT (' THE INPUT PRESSURE IS OUT OF THE RANGE OF THIS EQUATION ' 1/' THE RANGE FOR THIS EQUATION IS FROM TO ' , F6 . ,

' MPA

2/

OR ' ,F7 .0, ' PSIA'

IL=0

RETURN

12 TLLF= (TLL-273.15D0) *1.8D0+32.D0

TULF= (TUL-273.15D0) *1.8D0+32.D0

WRITE (*, 13) TLL,TUL,TLLF,TULF

13 FORMAT (' THE INPUT TEMPERATURE IS OUT OF RANGE'

A /' THE RANGE FOR THIS EQUATION IS ' , F6 . 2

,

' K TO ',F6.0,' K',/,

B 27X, ' OR ',F8.2,' F TO ',F6.0,' F')

IL=0

RETURN

20 TM=TMELT(P)

TF=(TM-27 3.15D0) *1. 8D0+32.D0

WRITE (*, 22) TM,TF

22 FORMAT (' SOLID PHASE DETECTED.',/,' FOR THIS PRESSURE, TEMP'

A ' SHOULD EXCEED ',F8.3,' K, OR ' , F9 . 3

,

' F')

IL=0

END

DOUBLE PRECISION FUNCTION CV(D,T)

IMPLICIT REAL*8(A-H)

IMPLICIT REAL*8(0-Z)

IMPLICIT INTEGER*4 (I-N)

CALCULATES CV ( J/ (MOL*K) ) . INPUT DENS(MOL/L) AND TEMP(K).

CALL PROPS (PP,D,T,6)

CV=PP

END

DOUBLE PRECISION FUNCTION ENTHAL ( P , D , T)

IMPLICIT REAL*8(A-H)

IMPLICIT REAL*8(0-Z)

IMPLICIT INTEGER*4 (I-N)

69
FROM INPUT OF DENSI TY( MOL/ L) AND TEMP(K)

DD = D TT=T

CALL PROPSC UD, DD, TT, 5)

ENTHAL=( UD)

END

DOUBLE PRECISION FUNCTION ENTROP(D.T)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

CALCULATES ENTROP Y( J / ( MOL- K)

DD = D TT=T

CALL PROPS( SD, DD, TT, 4)

ENTROP=( SD)

END

DOUBLE PRECISION FUNCTION FINDP(D,T)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

DIMENSION G( 32) , VP( 9)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

DD = D TT=T

IF( TT. LT. TCC) GO TO 10

1 CALL PROPS( PP, DD, TT, 1 ) FINDP=PP

RETURN

1 P = VPN( TT)

DV=FINDD( P-. 0001D0, TT)

DL=FINDD( P + . 0001D0, TT)

IF( DD. LE. DV. OR. DD. GE. DL) GO TO 1 HRITE( *, 1 00) DV, DL, DD

CALL PROPS( PP, DV, TT, 1 ) FINDP=PP

D = DV

100 FORMATC ' THE STATE POINT YOU HAVE SPECIFIED CORRESPONDS TO A

1/' DENSITY IN THE LIQUID VAPOR COEXISTENCE REGION'

THE DENSITY OF THE SATURATED VAPOR IS ',F6.4,'

THE DENSITY OF THE SATURATED LIQUID IS ',F8.4,

AND THE INPUT DENSITY IS ',F8.4,' MOLES/LITER'

SATURATED VAPOR IS ASSUMED')

MOLES/LITER'

MOLES/LITER'

2/

3/

4/

5/

END

DOUBLE PRECISION FUNCTION FINDT(P,D)

IMPLICIT REAL*8( A-H)

IMPLICIT REAL*8( O-Z)

IMPLICIT INTEGER*4( I-N)

C RETURNS TEMPERATURE( K) , FROM THE 32-TERM MBWR EQN OF STATE.

C INPUT IS PRESSURE( MPA) AND DENSI TY( MOL/ L) . DIMENSION G( 32) , VP( 9)

COMMON/DATA/G, R, GAMMA, VP, DTP, PCC, PTP, TCC, TTP, TUL, TLL, PUL, DCC

PP = P DD=D

IF( P. GE. PCC) GO TO 1 TSAT=FINDTV( PP)

DV=FINDD( PP-. 00001D0, TSAT)

DL=FINDD(PP + .0001D0,TSAT)

IF( DD. GT. DV. AND. DD. LT. DL) GO TO 30

TT=TSAT

GO TO 2

1 TT=TCC

2 DO 10 1=1,10

CALL PROPSC P2, DD, TT, 1 ) IF( DABS( PP-P2) -1 . D-7*PP) 20, 20, 1 1 11 CALL PROPS( DP, DD, TT, 3)

CORR=( P2-PP) /DP

IF( DABSC CORR) -1. D-5) 20, 20, 10

10 TT=TT-CORR

20 FINDT=TT

70
RETURN

30 FINDT=TSAT

D = DV

WRITEC *, 1 00) DV

1 00 F0RMAT( ' THE S

A DENSITY I DENSITY OF

DENSITY OF

INPUT DENSI

SATURATED V

1 / 2/

3/

4/

5/

END

DOUBLE PRECIS

IMPLICIT REAL*

IMPLICIT REAL*

IMPLICIT INTEG

T=TI

P = PI

IF( T. LT. 5. 2D0)

PM=1 001 . DO

PM=1 . OD + 5 IF( T. LT. 1 5. DO)

IF( PM. LT. P) GO

IF( T. GT. 1 00. DO

PC=2. 2449D0+(

IF( P. LT. PC) GO

PM=200. D0+( T-5

D=1 7. 399D0 + C ( P GO TO 7

2 D = . 0001 DO

IF( T. LT. 4. 2D0)

1 VB = VIRB(T)

RT=0. 0820558D0

P1 =RT/P

D = 1 . /( P1 +VB)

GO TO 7 6 IF( P. LT. VPN( T)

DS=46. 1 8D0+( TDL=SATL( T) *1 00

DEL=DS-DL

PM=PMELT( T)

IF( P. GT. PM) GO

D=DL+DEL*P/PM

7 DO 10 1=1,50

CALL PR0PS( P2,

IF( DABS( P-P2) -

8 CALL PROPSC DP,

C0RR=( P2-P) /DP

IF( DABS( CORR) - 10 D=D-C0RR

FIND D=0. DO

RETURN

20 FIND D=D

RETURN

30 FIND D=0. DO

RETURN

END

SUBROUTINE PRO

IMPLICIT REAL*

IMPLICIT REAL*

IMPLICIT INTEG

DIMENSION A( 26

COMMON/COEF/B

GO T0( 1 000, 300

KP = 1

, DL, DD

TATE POINT YOU HAVE SPECIFIED CORRESPONDS TO'

N THE LIQUID VAPOR COEXISTENCE REGION'

THE SATURATED VAPOR IS' , F8. 4, ' MOLES/LITER'

THE SATURATED LIQUID IS',F8.4,' MOLES/LITER'

TY IS',F8.4," MOLES/LITER'

APOR CONDITIONS ARE ASSUMED'

)

1 000

ION FUNCTION

8 ( A-H)

8 ( 0-Z)

ER*4( I-N)

GO TO 6

FIND D( PI, TI)

PM=PMELT( T)

TO 30

) GO TO 1 -5. 201 4D0) *1 . 76D0

TO 1

. 2D0) *1 2. 31 DO

M-PC) /( PM-PC+1. D0))*2. 33D0*17. 399D0

GO TO 7

*T

) GO TO 2

2. DO) *4. 02D0

0. DO/4. 0026D0

TO 30

D, T, 1 )

1 . D-7*P) 20, 20,

D, T, 2)

1 . D-7*D) 20, 20, 1

PS( PP, DD, TT, ICON)

8 ( A-H)

8 ( O-Z)

ER*4( I-N)

) , B( 27, 3)

0, 2000, 4000, 5000, 6000) ICON

2000

GO TO

ENTRY

KP = 2 GO TO

1DPDT

1

71
3000

4000

5000

6000

1

1 1

1 5

1 00

1ENTROP

1ENTHAL

NE. 0) GO TO 20

GE. 1 5. DO) GO TO 20

GT. 1 0. DO) GO TO 30

GT. 1 7. 3987D0) GO TO

ENTRY DPDD

KP = 3 GO TO

ENTRY

KP = 4 GO TO

ENTRY

KP = 5 GO TO 10

ENTRY CV

KP = 6 K1 =0

KH=1

K=1

KK = 1 K4 = 1 IF( ID. IF( TT. IF( TT. IF( DD. GT. 1 7. 3987D0) GO TO 40

1 = 1 T = TT

D = DD

GO TO ( 9, 1 00, 200, 300, 400, 500) KP

D2=D*D

D3=D2*D

D4=D3*D

D5=D4*D

GAMMA=B( 27, I)

EX=DEXP( D2*GAMMA)

EXD3=EX*D3

EXD5=EX*D5

M=I

N=1

A( N) = D5*D

N=N+1

A( N) =A( N-1 ) /T

N=N+1

DO 2 1=1,6

FI = I A(N)=D5*T**(. 75D0-FI/4. DO)

N=N + 1 DO 3 1=1,4

FI = I A( N) =D4*T**( 1 . 5D0-FI)

N=N+1

DO 1 1=1,8

FI=I

A(N)=D3*T**( 1. 5D0-FI/2. DO)

N=N+1

CONTINUE

DO 4 1=1,3

FI = I A( N) =EXD3*T**< 1 . DO-FI)

N=N+1

DO 5 1=1,3

FI=I

A( N) =EXD5*T**( 1 . DO-FI)

N=N+1

N=N-1

I=M

P=0. DO

DO 15 J=1 ,

P = P + B( J, I) *A( J)

P = P + . 0820558D0*D*T*( 1. +VIRB( T) *D)

IF( KH. LT. 1 ) GO TO 413

GO T0( 50, 50, 30, 40) K D2=D*D

72
D3=D**3

D4=D3*D

D5=D4*D

D6=D5*D

T2=T*T

T3=T2*T

T4=T**4

M=I

GAMMA=B( 27, M)

EX=DEXP( D2*GAMMA)

N=1

R=. 0820558D0

A( N) =0. 0D0

N=N + 1 A( N) =( -1 . DO) *D6/T2

N=N+1

DO 102 1=1,6

FI = I A( N)=D5*T**( . 75D0-FI/4. DO-1. DO) *( . 75D0-FI/4. DO)

102 N=N+1

DO 103 1=1,4

FI = I A( N) =D4*T**( 1 . 5D0-FI/1 . DO-1. DO) *( 1. 5D0-FI)

103 N=N+1

DO 101 1 = 1,8

FI=I

A( N) =D3*T**( 1 . 5D0-FI/2. DO-1. DO) *( 1 . 5D0-FI/2. DO)

101 N=N+1

DO 104 1=1,3

FI=I

A(N)=EX*D3*T**(1. DO-FI-1. DO) *( 1 . DO-FI)

104 N=N+1

DO 1 05 1=1 , 3 FI = I A(N)=EX*D5*T**(1. DO-FI-1. D0)*(1. DO-FI)

105 N=N+1

N=N-1

P = DO 1 1 5 J=1 ,

N

1 1 5 P = P + A( J) *B( J, M)

p=p+R*D*( 1. DO + VIRB( T) *D) +R*D*T*DBDT( T) *D

I=M

GO T0( 50, 50, 30, 40) K 200 D2=D*D

D3=D2*D

D4=D3*D

D5=D4*D

M=I

GAMMA = B( 27, M)

EX=DEXP( D2*GAMMA)

DEX=GAMMA*2. DO*D*EX

N=1

R=0. 0820558D0

A( N) =6. D0*D5

N=N+1

A( N) =A( N-1 ) /T

N=N+1

DO 202 1=1,6

FI=I

A(N)=5. D0*D4*T**(. 75D0-FI/4. DO)

202 N=N+1

DO 203 1=1 ,

4

FI=I

A(N)=D3*4.D0*T**(1. 5D0-FI)

203 N=N+1

DO 201 1=1,8

FI = I A( N)=D2*3. D0*T**( 1. 5D0-FI/2. DO)

73
201 N=N+1

DO 204 1=1,3

FI=I

A(N)=(DEX*D3 + 3. D0*D2*EX)*T**(1. DO-FI)

204 N=N+1

DO 205 1 = 1 , 3 FI = I A(N)=(DEX*D5 + 5.D0*D4*EX)*T**(1. DO-FI)

205 N=N+1

N=N-1

P = DO 21 5 J=1 ,

N

21 5 P = P + A( J) *B( J, M)

I=M

P=P+R*T*(1. DO + 2. DO*D*VIRB< T) ) GO T0( 50, 50, 30, 40) K 300 D2=D*D

D3=D2*D

D4=D3*D

N = 1 R = . 0820558D0

M=I

GAMMA = B( 27, M)

EX=DEXP( D2*GAMMA)

A( N) =0. ODO

N=N+1

A( N) =( D4*D/5. DO) *T**( -2. DO) *C -1. DO)

N=N+1

DO 302 1=1,6

FI=I

A(N)=(D4/4.D0)*T**(.75D0-FI/4.D0-1.D0)*(.75D0-FI/4.D0)

302 N=N+1

DO 303 1=1,4

FI = I A( N) =( D3/3. DO)* T**C1. 5D0-FI-1 . DO) *( 1 . 5 DO-FI)

303 N=N+1

DO 301 1=1,8

FI=I

A( N) =( D2/2. DO) *T**( 1 . 5D0-FI/2. DO-1. DO) *( 1 . 5D0-FI/2. DO)

301 N=N+1

DO 304 1=1,3

FI=I

A(N)=(EX/(2. DO* GAMMA)

)

*T**( 1. DO-FI -1 . D0)*( 1. DO-FI)

304 N=N+1

DO 305 1=1,3

FI = I A( N) =( D2*EX/( 2. DO*GAMMA) -EX/( 2. D0*GAMMA**2) ) * 1T**( 1 . DO-FI -1 . DO) *( 1

.

DO-FI)

305 N=N+1

N=N-1

SINT=D*R*( VIRB(T)+T*DBDT(T))

DO 306 1=1 ,

N

306 SINT=SINT + B( I, M) *A( I) N = 21 EX=1 . DO

D2=0. ODO

DO 310 1=1,3

FI=I

A(N)=(EX/(2. DO* GAMMA) )*T**( 1. DO-FI -1 . D0)*( 1. DO-FI)

310 N=N+1

DO 31 1 1=1,3

FI = I A( N) =( D2*EX/( 2. DO*GAMMA) -EX/( 2. D0*GAMMA**2) ) *

1 T**( 1. DO-FI -1 . DO) *( 1. DO-FI)

311 N=N+1

N=N-1

DO 31 2 1=21 ,

N

312 SINT=SINT-B( I, M) *A( I)

74
P = (9. 371658D0 + 5. 193043D0*DL0G(T/4. 21 4 4 DO) -2 5. 31469D0

1 *( SINT+R*DLOG( R*T*D) ) ) P = P*4. 0026D0

I = M GO TO( 50, 50, 30, 40) K 400 KH=0

GO TO 9 413 PP=P

KH=1

D2=D*D

D3=D*D2

D4=D3*D

N=1

R=. 0820558D0

M=I

GAMMA = B( 27, M)

EX=DEXP( D2*GAMMA)

A( N) =( D4*D) /5. DO

N=N+1

A(N)=(D4*D/5. DO) *( 2. DO/T)

N=N+1

DO 402 1=1 ,

6

FI = I A( N) =( D4/4. DO) *( T**( . 75D0-FI/4. DO) -T**( . 75D0-FI/4. DO)

1 *< . 75D0-FI/4. DO) ) 402 N=N+1

DO 403 1=1 ,

4

FI=I

A( N) =( D3/3. DO) *( T**( 1 . 5D0-FI ) -T**( 1 . 5D0-FI) *( 1 . 5D0-FI) ) 403 N=N+1

DO 401 1=1,8

FI = I A( N) =( D2/2. DO) *( T**( 1 . 5D0-FI/2. DO) -T**( 1 . 5D0-FI/2. DO)

1 *( 1 . 5D0-FI/2. DO) ) 401 N=N+1

DO 404 1=1,3

FI=I

A(N)=(EX/(2. DO* GAMMA) ) *( T**( 1 . D0-FI)-T**(1. DO-FI) *( 1 . DO-FI)

)

404 N=N+1

DO 405 1=1,3

FI=I

A( N) =( D2*EX/( 2. DO*GAMMA) -EX/( 2. D0*GAMMA**2) ) 1*( T**( 1 . D0-FI)-T**(1. DO-FI) *( 1 . DO-FI)

)

405 N=N+1

N = N-1

HINT=R*T*T*D*DBDT( T) *(-1.D0)

DO 406 1=1 ,

N

406 HINT=HINT+B( I, M) *A( I)

N=21

D2=0. ODO

EX=1 . DO

DO 410 1=1,3

FI=I

A( N) =( EX/( 2. DO* GAMMA) )*(T**(1. DO-FI)- T**(1. DO-FI) *( 1 . DO-FI) ) 410 N=N+1

DO 411 1=1,3

FI=I

A(N)=(D2*EX/(2. DO* GAMMA) -EX/( 2. D0*GAMMA**2) )*(T**(1. DO-FI)

1 -T**( 1 . DO-FI) *( 1 . -FI) ) 411 N=N+1

N=N-1

DO 412 1=21 ,

N

412 HINT = HINT-B( I, M) *A( I)

P=21. 8228D0+5. 193043D0*( T-4. 2144D0)+25. 31469D0

1 *( HINT+PP/D-R*T)

P=P*4. 0026D0

I=M

GO T0( 50, 50, 30, 40) K

75
500 D2=D*D

D3=D2*D

D4=D3*D

N=1

R=. 0820558D0

M=I

GAMMA=B( 27, M)

EX=DEXP( D2*GAMMA)

SINT=T*D*R*( 2. *DBDT( T ) +D2DBDT2( T) *T)

A( N) =0. 0D0

N=N+1

A(N)=(D4*D/5. DO) *T**( -2. DO) *( -1 . DO) *( -2. DO)

N=N+1

DO 502 1=1,6

FI=I

A( N) =( D4/4. DO) *T**( . 75D0-FI/4. D0-1 . DO)

1 *< . 75D0-FI/4. DO) *( . 75D0-FI/4. DO-1 . DO)

502 N=N+1

DO 503 1=1,4

FI=I

A( N) =( D3/3. DO)* T**( 1. 5D0-FI-1 . DO) *( 1 . 5D0-FI) *( 1 . 5D0-FI-1. DO)

503 N=N+1

DO 501 1=1,8

FI = I A( N) =( D2/2. DO) *T**( 1 . 5D0-FI/2. DO-1. DO) *( 1 . 5D0-FI/2. DO)

1*( 1. 5D0-FI/2. DO-1 . DO)

501 N=N+1

DO 504 1=1,3

FI = I A( N) =( EX/( 2. DO* GAMMA) ) *T**( 1. DO-FI-1. DO) *( 1. DO-FI)

1*( 1 . DO-FI-1 . DO)

504 N=N+1

DO 505 1=1 ,

FI=I

A(N)=(D2*EX/(2. D0*GAMMA)-EX/(2. DO* GAMMA* *2) ) * 1T**( 1. DO-FI-1. D0)*( 1 . DO-FI) *( 1. DO-FI-1. DO)

505 N=N+1

N=N-1

DO 506 1=1 ,

506 SINT = SINT+B( I, M) *A( I)

P=SINT

EX=1 . DO

D2 = N=21

DO 510 1=1,3

FI=I

A(N)=(EX/(2. DO* GAMMA) ) *T**( 1 . DO-FI-1. DO) *( 1. DO-FI)

1 *( 1 . DO-FI-1 . DO)

510 N=N+1

DO 511 1=1,3

FI = I A(N)=(D2*EX/(2. DO* GAMMA) -EX/( 2. D0*GAMMA**2) ) * 1T**(1. DO-FI-1. DO) *( 1. DO-FI) *( 1 . DO-FI-1. DO)

511 N=N+1

N = N-1

DO 512 1=21 , N

51 2 P = P-B( I, M) *A( I)

P=5. 193043D0*( 3. DO/5. D0)*4. 0026D0-P*101. 3278D0

I=M

GO T0( 50, 50, 30, 40) K 20 K = 2 1=3

T=TT

D=DD

GO TO 8 30 K = 3 GO T0( 33, 34, 35) KK

33 D=DD

76
35

38

40

41

GT. 1 7. 3987D0) GO TO 40

8

8

3) K1 =3

42, 43, 44) K4

:TT

= SATL( T) *1 000. DO/4. 0026D0

T = TT

KK = 2 IF( DD. 1=1

GO TO

34 PTI=P

1 = 3 KK = 3 T = TT

D = DD

GO TO

PTIII=P

F = ( 1 5. DO-T) /5. DO

P=F*PTI+(1. D0-F)*PTIII

IF( KH. LT. 1 ) GO TO 413

PP = P RETURN

IF( K. EQ.

GO TO( 41 K=4

1=2

K4 = 2

D = DD

IF( K1. EQ. 0) T = GO TO 8 42 PIID=P

D=1 7. 3987D0

IF( T. LT. 5. 201 4D0) D = K4 = 3 GO TO 8 43 PIIDC=P

1 = 1 K4 = 4 GO TO 8 44 PIDC=P

P=PIDC+( PIID-PIIDC)

K4 = 1 IF( K1 . EQ. 3) GO TO

PP = P RETURN

50 PP=P

RETURN

END

DOUBLE PRECISION

IMPLICIT REAL*8 ( IMPLICIT REAL*8 ( 0-Z)

IMPLICIT INTEGER*4( I-N)

CALL PR0PS( DPDD, D, T, 2)

CALL PROPS( DPDT, D, T, 3)

CP = CV(D,T)+(T*(DPDT**2)/((D**2)*DPDD))*101.3278D0

RETURN • END

DOUBLE PRECISIONFUNCTION SOUND( D, T)

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( 0-Z)

IMPLICIT INTEGER*4( I-N)

CALL PROPS( DPDD, D, T, 2)

SOUND = ( (CP(D,T)/CV(D,T))*(DPDD*25311.D0))**.5D0

RETURN

END

DOUBLE PRECISION FUNCTION P IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( 0-Z)

IMPLICIT INTEGER*4( I-N)

DIMENSION A( 5)

DATA A/33. 28D0, -44. 1 56D0, 31 . T = TT

IF( T. LE. 5. 2D0) GO TO 7

30

FUNCTION

A-H)

CP( D, T)

MELT( TT)

799D0, -4. 8159D0, . 30313D0/

77
PMELT=-1 7. 80

PMELT=PMELT*

RETURN

7 P=0. 0D0

DO 9 1=1,5

9 P=P+A( I) *T**

PMELT=P*9. 80

RETURN

END

DOUBLE PRECI

IMPLICIT REA

IMPLICIT REA

IMPLICIT INT

DIMENSION A( DATA A/-5. 08

1 7. 447458799

2 3. 937441 484

C COEFFICIENTS

C THIS SUB PRO

C HELIUM. THE

C IN DEGREES K C UNITS ARE AT

C REVISED 2/12

1 B = 0. ODO

DO 5 1=1,9

FI = I 5 B=B+T**( 1 . 5D

VIRB=B

RETURN

END

DOUBLE PRECI

IMPLICIT REA

IMPLICIT REA

IMPLICIT INT

DIMENSION A( C THIS SUB PRO

C HELIUM. THE

C IN DEGREES K DATA A/-5. 08

1 7. 447458799

2 3. 937441 484

C UNITS ARE AT

1 B=0. ODO

DO 5 1=1,9

FI = I 5 B=B+T**( . 5D0

DBDT=B

RETURN

END

DOUBLE PRECI

IMPLICIT REA

IMPLICIT REA

IMPLICIT INT

DIMENSION A( DATA A/-5. 08

1 7. 447458799

2 3. 937441 484

C THIS SUB PRO

C HELIUM. THE

C IN DEGREES K

1 B = 0. ODO

DO 5 1=1,9

FI=I

5 B=B + T**( . 5D0

D2DBDT2=B

RETURN

END

DOUBLE PRECI

DO + 17. 31457D0*T**1. 5 5541 4 DO

. 98066D0/1 . 01 325D0

( 1-1 ) 665D0/1 0. 1 325D0

SION FUNCTION VIRB( T)

L*8 ( A-H)

L*8 ( 0-Z)

EGER*4( I-N)

9)

1 571 0041 D-7, -1 . 1 8D-2, -5. 31 431 747(

3D0, -5. 1 37023922-

FROM PROGRAM 5/:

GRAM CALCULATES

RANGE IS FROM 2 ELVIN

M, DEG KELVIN, AND MOLES/ LI TER, 4 / 3 / 69 - 1 2 5 3 , R. D. MCC ARTY

/70-925

1 68680862D-4,

'68D-1 , -9. 5759

!4D0, 2. 0804456

28/70-1 630

THE SECOND VI TO 1500 DEG

1 . 1 652480354D-2,

219306D-1

,

338D0/

RIAL COEFFICIENT FOR

K. INPUT IS TEMPERATURE

O-FI/2. DO) *A( I)

SION FUNCTION DB

L*8 ( A-H)

L*8 ( 0-Z)

EGER*4( I-N)

9) , V( 45)

GRAM CALCULATES

RANGE IS FROM 2 ELVIN

1 571 0041 D-7, -1 .

8D-2, -5. 31 431 747

3D0, -5. 1 37023922

M, DEG KELVIN, A

DT ( T)

THE SECOND VI

TO 1500 DEG

1 68680862D-4,

68D-1 , -9. 5759

4D0, 2. 0804456

ND MOLES/LITE

RIAL COEFFICIENT FOR

K. INPUT IS TEMPERATURE

1 . 1 652480354D-2,

21 9306D-1

,

338D0/

R, 5/28/70-1630, R. D. MCCARTY

FI/2. D0)*A(I)*(1. 5D0-FI/2. DO)

SION FUNCTION D2DBDT2(T)

L*8 ( A-H)

L*8 ( 0-Z)

EGER*4( I-N)

9)

1 571 0041 D-7, -1 . 1 8D-2, -5. 31 431 747

3D0, -5. 1 37023922

GRAM CALCULATES

RANGE IS FROM 2 ELVIN

1 68680862D-4,

68D-1 , -9. 5759

4D0, 2. 0804456

THE SECOND VI TO 1500 DEG

1 . 1 652480354D-2,

21 9306D-1

,

338D0/

RIAL COEFFICIENT FOR

K. INPUT IS TEMPERATURE

-FI/2. DO-1. DO) *( 1 . 5D0-FI/2. DO) *( . 5D0-FI/2. DO) *A( I)

SION FUNCTION FINDTV(PP)

78
REAL*8 ( A-H)

REAL*8 ( 0-Z)

INTEGER*4( I-N)

8421 05D0) GO TO 12

12

1 13

IMPLICIT

IMPLICIT

IMPLICIT

P=PP

IF( P. LT. . T=5. DO

PCAL=VPN( T)

GO TO 13

PCAL=. 049737D0

IF(DABS(P-PCAL)-. 0000001 DO *PP)11, 11,1

T=2. 1720D0

DO 10 1=1 , 50

DP = DPDTVP( T)

DEL = ( PCAL-P) /DP

T=T-DEL

PCAL=VPN( T)

IF( DABS( P-PCAL) 0000001 DO*P) 1

1

0000001 D0*T) 11,11

11,

10

ITTERATION FAILED AT T=* , E1 4. 7)

DPDTVP( TT)

2 IF( DABS( DEL)

10 CONTINUE

WRITE( *, 1 00)

11 FINDTV=T

RETURN

100 FORMAT( ' TEMPERATURE

END

DOUBLE PRECISION FUNCTION

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( 0-Z)

IMPLICIT INTEGER*4< I-N)

DIMENSION C( 12) , D( 1 4)

DATA C/-3. 9394635287D0, 141. 27497598D0,

1, 11974. 557102D0, -55283. 309818D0,

11 6621 9. 56504D0, -32521 2. 82840D0, 398843. 22750D0,

2-277718. 06992D0, 83395. 2041 83D0, 0. DO, 0.

1640. 7741 565D0

DO/

DATA D/-49. 51 0540356 DO, 651. 923641 7D0, -3707. 5430856D0

1 , 1 2880. 673491 DO,

1 -30048. 545554D0, 49532. 267436D0, -59337. 558548D0, 52311. 296025D0,

2-33950. 2 331 3 4 DO, 16028. 674003D0, -5354. 1038967D0, 11 99. 0301906D0,

3 -161. 46362959D0, 9. 8811553386D0/

P=0. ODO

T=TT-DELT( TT)

IF( T-2. 1 720D0) 10,10,1

1 DO 5 1=1,10

5 P=P+C( I) *T**( 1 -I) *( 2-1)

DPDTVP=P*VPN( T)

RETURN

10 DO 15 1 = 1,14

15 P = P + D( I) *T**( 1 -I) *( 2-1)

DPDTVP=P*VPN( T)

RETURN

END

DOUBLE PRECISION FUNCTION VPN( TT)

IMPLICIT REAL*8 ( IMPLICIT REAL*8 ( IMPLICIT INTEGER*4( I-N)

DIMENSION C( 1 2) , D( 1 4)

DATA C/-3. 9394635287, 141. 27497598, -1640. 7741565, 11974. 557102,

1-55283. 30981 8, 1 6621 9. 56504, -32521 2. 82840, 398843. 22750,

2-277718. 06992, 83395. 204183,0. DO, 0. DO/

DATA D/-49. 51 0540356, 651. 923641 7, -3707. 5430856, 12880. 673491,

1 -30048. 545554, 49532. 267436, -59337. 558548, 5231 1. 296025,

2-33950. 2331 34, 16028. 674003, -5354. 1 038967, 11 99. 0301 906,

3 -161.46362959,9.8811553386/

T=TT

T=T-DELT( T)

P=0. ODO

IF( T-2. 1 720D0) 1 0, 1 0, 1

1 DO 5 1=1 , 1 5 P=P+C( I) *T**( 2-1)

FUNCTION

A-H)

0-Z)

79
VPN=DEXP( P) /. 76D + 6 RETURN

10 DO 15 1=1,14

1 5 P = P + D( I) *T**( 2-1)

VPN=DEXP( P) /. 76D+6

RETURN

END

DOUBLE PRECISION FUNCTION

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( O-Z)

INTEGER*4( I-N)

DELTC TT)

IMPLICIT

T = TT

DELT=. 001 D0+. 002D0*T

RETURN

END

DOUBLE PRECISION FUNCTION SATV( TT)

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( O-Z)

IMPLICIT INTEGER*4( I-N)

DIMENSION GV( 6)

DATA GV/-. 069267495322D0, -. 1 292 53255 3D0, . 293 47 4 707 1 2 DO

, -. 4080665821 2D0, . 35809505624D0, -. 11315580397D0/

DATA DC/. 06964D0/

DATA TC/5. 201 4D0/

T = TT

DCAL=DC

R=( 1 . DO/TO

DO 1 1=1,6

FI = I DCAL=DCAL + GV( I) *R**( FI/3. DO)

SATV=DCAL

RETURN

END

DOUBLE PRECISION FUNCTION SATL( TT)

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( O-Z)

IMPLICIT INTEGER*4( I-N)

DIMENSION GL( 9)

DATA GL/. 12874326484D0, -. 43128217346D0, 1. 7851911824D0

, -3. 3509624489D0, 3. 034421 5824D0, -1. 0981289602D0, 0. DO, 0. DO, 0. DO/

DATA DC/. 06964D0/

DATA TC/5. 201 4D0/

T=TT

DCAL=DC

R=( 1 . DO-T/TC)

DO 2 1=1,6

FI = I DCAL=DCAL+GL(I)*R**(FI/3.D0)

SATL=DCAL

RETURN

END

DOUBLE PRECISION FUNCTION SURFTEN(T)

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( O-Z)

IMPLICIT INTEGER*4( I-N)

SURFTEN = . 5308 DOM 1. -T/5. 201 4 DO)

RETURN

END

DOUBLE PRECISION FUNCTION R INDEX(D,H)

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( O-Z)

IMPLICIT INTEGER*4( I-N)

DD=D*4. 0026D0/1 000. DO

ALG=0. 123396D0-0. 001 4*DD+33701 . 61 7944/D0W**2-1 2325284955. DO/ W**4

FAC=ALG*DD/0. 95555D0

R=((2. D0*FAC+1 . DO) /( FAC-1 . DO))

IF( R. LT. 0. ODO) R=R*( -1 . ) R=R**( . 5D0)

80
FUNCTION

A-H)

O-Z)

TMELTC PP)

/1 . 55541 4D0)

RINDEX=R

RETURN

END

DOUBLE PRECISION

IMPLICIT REAL*8 ( IMPLICIT REAL*8 ( IMPLICIT INTEGER*4( I-N)

P=PP*1 . 01325D0/. 9806 6 DO

IF( P-1 7. 80D0. LT. 0. ODO) GO TO 1 TMELT=( (P-17. 80D0) /1 7. 31 45D0) **( 1 RETURN

1 TMELT=2. DO

RETURN

END

DOUBLE PRECISION FUNCTION FDIEL(D)

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( O-Z)

IMPLICIT INTEGER*4( I-N)

DD=D*4. 0026D0/1000. DO

ALPHA=. 123396D0-. 0014D0*DD

ALPHA=ALPHA*DD *1.04652D0

EPS = (1. DO + 2. DO*ALPHA) /( 1 . DO -A LP HA)

FDIEL=EPS

RETURN

END

DOUBLE PRECISION FUNCTION THERM(DD.TT)

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( O-Z)

IMPLICIT INTEGER*4( I-N)

C HELIUM

C THIS ROUTINE CALCULTATES THERMAL CONDUCTIVITY

C FOR AN INPUT OF DEGREES KELVIN AND DENSITY IN

C THE RANGE OF TEMPERATURE IS FROM 2 TO 2000 K

C FOR TEMPERATURES BELOW 300 K FORMULAS OFD VINCE ARP

C ARE USED, FOR TEMPERATURES ABOVE 300 THE DILUTE GAS

C COMPILATION FROM ENGLAND IS USED FOR BOTH VISCOSITY

C THERMAL CONDUCTIVITY AND THE EXCESS FUNCTIONS FROM

C ARP AND STEWART) THE EXCESS FUNCTIONS ARE CALCULATED FOR TEMPS

C ABOVE 300 K WITH THE TEMPERATURE DEPENDENCE HELD AT 300 K C FOR TEMPS BELOW 300 K TO 100 K THE VISCOSITY EXCESS IS CALC

C FROM STEWARTS ROUTINE BUT THE DILUTE GAS VALUES ARE TAKEN FROM

C THE ENGLISH CORRELATION FOR TEMPS BETWEEN 100 AND 110 T

C DILUTE GAS CALCULATION IS AVARAGED

1 D = DD

T = TT

RHO = D*4. 0026D-3

IF( T. LT. 300. DO) GO TO 5 TH03 = VISCX( 300. DO)*. 00781 736D0

TH0300=CONZ( 300. DO)

DEL300 = DELC( 300. DO, RHO)

THO=VISCX( T) *. 0781 7 36D0+THO30 0-THO3

THE=THO3 00*DEL3 00-THO300

THERM=THO+THE

RETURN

5 THERM=CONZ( T) *DELC( T, RHO) +CRITICC T, RHO)

C OUTPUT IN MW/CM. K RETURN

END

DOUBLE PRECISION FUNCTION VISC(DD,TT)

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( O-Z)

IMPLICIT INTEGER*4( I-N)

D = DD

T=TT

IF( T. LT. 1 00. DO) GO TO 10

IF( T. LT. 300. DO) GO TO 8 ETAO=VISCX( T)

ET030=VISCX( 300. DO)

AND VISCOSITY

MOLES PER LITER

AND GE STEWARD

OF A CRITICAL

AND

THE ROUTINES BY

81
/1 0. DO

IDO, T)

T )

ET0300 = VISCDT( 0. ODO, 300. DO)

ETE300 = VISCDT( D, 300. DO) -ET0300

VISC=ETAO+ETE300

OUTPUT UNITS ARE MICROPOISE

RETURN

8 IF( T. LT. 1 1 0. DO) GO TO 9 ETAO=VISCX( T)

ETEB = VISCDT( D, T) -VISCDT( 0. ODO, T)

VISC=ETA0+ETEB

RETURN

9 ETA1 =VISCDT( 0. ODO, 1 00. DO)

ETA2 = VISCX( 1 1 0. DO)

ETA0=ETA1+( ETA2-ETA1)*( T-100. DO)

VISC = ETAO+VISCDT( D, T) -VISCDT( 0. 0] RETURN

1 VISC = VISCDT( D, T)

RETURN

END

DOUBLE PRECISION FUNCTION VISCXt

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( 0-Z)

IMPLICIT INTEGER*4( I-N)

VISCX = 196. DO*T**. 71 938D0*DEXP( 12. 451D0/T-295. 67D0/T/T-4. 1249D0)

RETURN

END

DOUBLE PRECISION FUNCTION DELC(TEMP, RHO)

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 C 0-Z)

IMPLICIT INTEGER*4( I-N)

K=KZERO*EXPF( B( T) *RH0 + C(T)*RH0 3 THIS PROGRAM RETURNS EXPF( B( T)

1 BB = DLOG( TEMP)

CC=1 . DO/TEMP

BETTY=4. 747066061 2D0-5. 364146815:

2-1. 0702455443D0*BB**3+0. 157134931

B = DEXP( BETTY)

C = 2. 2109006708D0+187. 74174808D0*!

3 + 3645. 239321 6D0* CC* * 3 - 3986 . 69379.

DELC=DEXP( B*RH0+C*RH0*RH0)

RETURN

END

DOUBLE PRECISION FUNCTION CONZ(TEMP)

IMPLICIT REAL*8

IMPLICIT REAL*8

IMPLICIT

KZERO IN

1**2)

RHO + C( T) *RH0**2)

>3D0*BB + 3. 4639703698D0*BB**2

I06D0*BB**4-. 008921 40047D0*BB**5

CC-1281. 0947055D0*CC*CC

I48D0*CC**4

I FUNCTION

C A-H)

( 0-Z)

INTEGER*4( I-N)

MILLIWATTS/CM-K, T IN KELVIN9 22 JUNE 71.

1 ANNE=DL0G( TEMP)

PAT=-4. 361 1 6221 57D0+1

1 +. 090045763885D0*ANNE**3-

C0NZ = DEXP( PAT)

RETURN

END

DOUBLE PRECISION FUNCTION

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( 0-Z)

IMPLICIT INTEGER*4( I-N)

W. G. STEWARD, S DATA 23 JUNE 71 INPUT UNITS ARE KELVIN AND MOL/LITE

OUTPUT UNITS ARE MICROPOISE

TL = DL0G( T)

R=DGC*4. 0026D0/1000. DO

ANNE=-0. 135311743D0/TL+1. 0034784

1-0.

49564551 D0*TL*TL+0. 01 2520841

BETTY=R*( -47. 529 52 59 DO / TL + 8 7 . 679

1+8. 331 28289D0*TL*TL-0. 589252385D

CAR0L = R*R*( 547. 3 092 6 7 DO / TL- 90 4 . 8 1-81. 4504854D0*TL*TL + 5. 37008433D0

DAGMAR=R**3*( -1684. 39324D0/TL+33

92501 59286D0*ANNE-0. 525441 201 65D0*ANNE**2

0054773874708D0*ANNE**4

VISCDT( DGC, T)

1 DO+1 . 20654649D0*TL

6D0*TL**3

9309D0-42. 0741589D0*TL

O^TL^^S)

70586D0+431. 404928D0*TL

*TL**3)

31. 08630D0-1632. 19172D0*TL

82
1+308. 80441 3D0*TL*TL-20. 2936367D0*TL** 3)

VISCDT=DEXP( ANNE+ BETTY+ CAR0L+ DAGMAR)

RETURN

END

DOUBLE PRECISION FUNCTION CRI TI C( TEMP, RHO)

IMPLICIT REAL*8 ( A-H)

IMPLICIT REAL*8 ( O-Z)

IMPLICIT INTEGER*4( I-N)

C CRITICAL ANOMALY FOR HE THERM. CON. , SCALED FROM H-2

C T IN KELVIN, REQUIRES DENSITY IN GRAMS/CC AND CP IN JOULES/MOLE

C THIS DECK OF 18 SEPT 70, I HAVE USED MCCARTY"S HE DECKS OF 7/18/70

4 T=TEMP

5 DML=RHO/0. 0040026D0

6 IF( T . GE. 11. 83D0) GO TO 11 IF( RHO. GT. 0. 1 2D0) GO TO 11

7 CP1 =CP( DML, T)

8 CP2 = CP( DML, 1 1 . 83D0)

9 CRITIC = 0. 0026D0*(CP1-CP2)/4. 0026D0

IF( CRITIC) 11,12,12

CRITIC = 0. 0D0

RETURN

END

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84
NBS-114A (REV. 2-8C) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS/TN-1097

2. Performing Organ. Report No. 3. Publication Date

May 1986

4. TITLE AND SUBTITLE

INTERACTIVE FORTRAN PROGRAMS FOR MICRO COMPUTERS TO CALCULATE THE THERMOPHYSICAL

PROPERTIES OF TWELVE FLUIDS [MIPROPS]

5. AUTHOR(S)

Robert D. McCarty

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

National Aeronautics and Space Administration

Lyndon B. Johnson Space Center

Houston, Texas 77058

10. SUPPLEMENTARY NOTES

H Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less (actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here) The thermophysical and transport properties of selected fluids have been programmed

in FORTRAN 77 which is available for micro computers. The input variables are any

two of P, p, T (pressure, density, and temperature) in the single phase regions, and

either P or T for the saturated liquid or vapor states. The output is pressure,

density, temperature, internal energy, enthalpy, entropy, specific heat capacities

(C and C ), speed of sound and, in most cases, viscosity, thermal conductivity, and

dielectric constant.

The fluids included are: helium, hydrogen, nitrogen, oxygen, argon, nitrogen

trifluoride, methane, ethylene, ethane, propane, iso- and normal butane. The

programs give properties in both the liquid and vapor states over a wide range of

temperature and pressure. Copies of the program may be obtained from the Office of

Standard Reference Data, Room A320, Physics Building, National Bureau of Standards,

Gaithersburg, MD 20899.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

argon; computer programs; density; dielectric constant; enthalpy; entropy; equation of

state; ethane; ethylene; heat capacity; helium; hydrogen; internal energy; isobutane;

methane; nitrogen; nitrogen trifluoride; normal butane; oxygen; pressure; speed of

sound; temperature; thermal conductivity; viscosity.

13. AVAILABILITY

[^Unlimited

| | For Official Distribution. Do Not Release to NTIS

[XJ^Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

^] Order From National Technical Information Service (NTIS), Springfield, VA. 2216 I

14. NO. OF

PRINTED PAGES

90

15. Price

irU.S. GOVERNMENT PRINTING OFFICE:1986—672-047/45229 USCOMM-DC 6043-P80



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