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Tables for the Thermophysical Properties of Ethane

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Tables for the Thermophysical Properties of Ethane UNITED STATES DEPARTMENT OF COMMERCE TECHNOLOGY ADMINISTRATION NATIONAL INSTITUTE OF STANDARDS nist AND TECHNOLOGY NAT l INST. OF STAND » TECH R.I.C NIST PUBLICATIONS A111D3 T2flT3D NIST Technical Note 1346 /VaZL i Tables for the Thermophysical Properties of Ethane Daniel G. Friend James F. Ely Hepburn Ingham Thermophysics Division Chemical Science and Technology Laboratory National Institute of Standards and Technology Boulder, Colorado 80303-3328 January 1993 * *^TE8 Of U.S. DEPARTMENT OF COMMERCE, Barbara Hackman Franklin, Secretary TECHNOLOGY ADMINISTRATION, Robert M. White, Under Secretary for Technology NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, John W. Lyons, Director National Institute of Standards and Technology Technical Note Natl. Inst. Stand. Technol., Tech. Note 1346, 316 pages (January 1993) CODEN:NTNOEF U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1992 For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325 CONTENTS LIST OF TABLES iv LIST OF FIGURES iv LIST OF SYMBOLS AND UNITS v ABSTRACT viii 1 . INTRODUCTION 1 2. THERMODYNAMIC PROPERTIES AND THEIR ALGEBRAIC REPRESENTATION 2 2 . 1 Fixed Point Constants 2 2 . 2 Liquid- Vapor Saturation Boundary 4 2 . 3 Ideal Gas Equation 5 2.4 Residual Helmholtz Energy 6 2 . 5 Derived Property Equations 6 3. TRANSPORT PROPERTIES AND THEIR ALGEBRAIC REPRESENTATION 11 3 . 1 Dilute Gas Correlations 11 3 . 2 Excess Property Correlations 12 3 . 3 Critical Enhancement Correlation 14 4. SUMMARY OF UNCERTAINTIES ASSOCIATED WITH THE CORRELATIONS 15 4.1 Two -Phase Boundary 15 4 . 2 Ideal Gas Properties 16 4 . 3 Thermodynamic Properties 16 4.4 Transport Properties 20 4.4.1 Viscosity 20 4.4.2 Thermal Conductivity 21 5 . ACKNOWLEDGMENTS 22 6 . REFERENCES 22 7 . APPENDICES 28 Appendix A: Comparisons between experimental data and the correlations 28 Appendix B: Tables for the thermophysical properties of ethane 112 Appendix C: Listing of a FORTRAN 77 program to calculate the thermophysical properties of ethane 283 in .. LIST OF TABLES 1. Fixed point constants and other parameters used in the correlations. 3 2. Coefficients for liquid-vapor boundary correlations 5 3. Coefficients needed for ideal gas Helmholtz energy, eq (5) 6 4. Exponents and coefficients for the residual Helmholtz energy 4> , eq (6) 7 5 Ideal gas Helmholtz energy and its derivatives 8 6 Residual Helmholtz energy and its derivatives 9 7 Thermodynamic property equations 10 8 Coefficients for dilute gas transport properties 12 9 Coefficients for excess transport properties 13 Bl. Properties of ideal gas at 0.1 MPa and dilute gas transport properties 112 B2 . Properties along saturation boundary 121 B3. Properties in the single-phase region along isobars 127 B4 Properties in the single-phase region along isotherms 239 LIST OF FIGURES Al Saturated vapor pressure 30 A2 . Saturated liquid density 36 A3 . Saturated vapor density 42 A4A. Ideal gas entropy 45 A4B. Ideal gas isobaric heat capacity 47 A4C Ideal gas enthalpy 49 A5 . Second virial coefficient 51 A6A PVT data- -pressure deviations 54 A6B. PVT data- -density deviations 59 A7 Isochoric molar heat capacity 67 A8 Isobaric molar heat capacity 70 A9 Molar heat capacity of the saturated liquid 72 A10. Sound speed in the single-phase fluid 74 All Sound speed in the saturated liquid 76 A12 Viscosity at zero density 78 A13 Thermal conductivity at zero density 81 A14 Viscosity at elevated pressures 84 A15 Thermal conductivity at elevated pressures 97 IV 7 , LIST OF SYMBOLS AND UNITS Symbol Description SI Units REFERENCE (used in text) Roman 1 a A Molar Helmholtz energy J»mol eq (4) B Second virial coefficient dm «mol table 7 * (2 2 ) C Coefficients in Q ' eq (10) .table 8 Molar isobaric heat capacity J«mol »K table 7 Molar isochoric heat capacity J«mol *K table 7 Crossover function in A eqs (15,17) c r f Contribution from internal modes eqs (11,12) i n t table 8 G Molar Gibbs energy J«mol table 7 G Coefficients in p eq (2) , table 2 i ctL 9 S Coefficients in r/ eq (13) .table i e H Molar enthalpy J«mol tables 1 , H Coefficients in P eq (1) .table 2 i a J Coefficients in p eq (3) .table 2 i ctV j Coefficients in A eq (14) .table 9 i e x k Boltzmann constant J-K table 1 M Relative molecular mass table 1 r N Avogadro constant mol table 1 A n Coefficients in 4> eq (6) .table 4 i P Pressure MPa id , table 3 Q. Coefficients in <f>* eq (5) i Wavenumber cutoff nm eq (17) Gas constant J«mol «K table 1 Exponent of 5 eqs (6,13,14), tables 2, 9 Molar entropy J»mol »K table 7 , LIST OF SYMBOLS AND UNITS (CONT'D) Symbol Description SI Units REFERENCE (used in text) s. Exponent of r - eqs (6,13 14) tables 2 9 t Reduced temperature, kT/e - eqs (9,10 12) T Temperature, IPTS-68 K - T Reduced temperature, (T -T)/T - eqs (1-3) 1 U Molar internal energy J»molT I' table 7 u Unified atomic mass unit kg table 1 -1 w Speed of sound m»s table 7 Z Compressibility factor, P/RTp - eq (3) Greek - B Scaling° exponent in p T ,p eqs (2,3), ctL CTV table(2) 7 Potential parameter - Ref. [13] 5 Reduced density, p/p - e 2 , Scaling exponent in P , -a eq (1) table 2) e Energy parameter J See e/k e/k Energy parameter K table(l) r\ Shear viscosity /xPa»s eq (7) A Thermal conductivity iW • m • K eq (8) | Correlation length run eqs (15,16) p Molar density mol'dm a Distance parameter nm table 1 r Reduced inverse temperature, T /T - <f> Reduced Helmholtz energy, A/RT eqs (4-6) (2 2)* - CI ' Reduced collision integral eqs (9,10) Superscripts id Ideal gas contribution eq (4) , table 1 r Residual contribution eq (4) VI LIST OF SYMBOLS AND UNITS (CONT'D) Symbol Description SI Units REFERENCE (used in text) Subscripts c Value at critical point table 1 cr Critical contribution eqs (8,15) ex Excess contribution eqs (7,8,13,14) t Value at triple point table 1 tL.tV Value at triple point in liquid, vapor table 1 o Value at saturation boundary eq (1) ctL.ctV Value in saturated liquid, vapor eqs (2,3) 5 Partial derivative with respect to 8 tables 5-7 t Partial derivative with respect to r tables 5-7 Value at zero density eqs (7-9,11) Throughout this paper, extensive physical quantities are given on a molar basis. The elementary entities are the ethane (C„H,) molecules. Vll : TABLES FOR THE THERMOPHYSICAL PROPERTIES OF ETHANE Daniel G. Friend, James F. Ely, and Hepburn Ingham Thermophysics Division National Institute of Standards and Technology Boulder, Colorado 80303 The thermophysical properties of ethane are tabulated for a large range of the fluid state based on recently formulated correlations. For the thermodynamic properties, temperatures from 90 to 625 K at pressures less than 70 MPa are included; for the viscosity, the corresponding range is 90- 500 K with pressures to 60 MPa; for the thermal conductivity the range is 90-600 K with pressures to 70 MPa. In addition to the tables of properties, algebraic expressions and associated tables of coefficients are given to allow additional property calculations. Graphical comparisons between experimental property determinations and the correlation are also given both for primary data used in the formulation of the correlations and for additional data. A listing of a FORTRAN program for the evaluation of ethane thermophysical properties is included. Key words correlation; density; equation of state; heat capacity; ethane; phase boundary; pressure; speed of sound; thermal conductivity; thermophysical properties; transport properties; virial coefficients; viscosity. 1. INTRODUCTION We have recently developed correlations for several of the thermophysical properties of ethane [1], including an equation of state analogous to that proposed by Schmidt and Wagner [2], equations for the liquid-vapor phase boundary, and correlations for the fluid viscosity and thermal conductivity. Details of the development and error analysis of the formulations have been presented elsewhere [1] ; in this paper, we summarize our equations and present extensive graphical comparisons of the correlations with experimental data and tables of properties based on these correlations. We have also included the listing for a FORTRAN program which can be used interactively to calculate properties of ethane. The correlations are similar in form to those published previously for methane [3], and this report is analogous to the earlier Technical Note on the properties of methane [4]. A separate Internal Report [5] gives a full tabular listing of experimental data considered in the development of the ethane correlations. The rationale for these new correlations and the present set of tables was discussed in Ref . [1] . Briefly summarized, earlier extensive works include those of Goodwin et al. [6], Sychev et al. [7], and Younglove and Ely [8]. Our correlations account for some new experimental measurements, and more important, the form of the residual Helmholtz free energy correlation, first proposed by Schmidt and Wagner [2], gives an excellent description of the thermodynamic surface and describes the critical region extremely well for a classical equation of state. The new ancillary equations for the phase boundary incorporate the results of lowest order scaling theory, and both viscosity and thermal conductivity correlations improve the description of the fluid properties when compared to previous correlations. Our current description of the enhancement of the thermal conductivity is based on the very recent mode-coupling work of Olchowy and Sengers [9] . The economic importance of ethane, as a major constituent of natural gas, makes the use of improved thermophysical properties correlations especially desireable.
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