Appendix. A.t. ICMPROPS SOFTWARE PACKAGE

Transcription

1 References 1. World Wide Web Site, - cats/cats.html. 2. Zudkevitch, D. (1975). Imprecise data impacts plant design and operation, Hydrocarbon Process. 54, Zudkevitch, D., and Gray, R. D., Jr. (1975). Impact of fluid properties on the design of equipment for handling LNG, Adv. ryog. Eng. 20, The Technological Importance of Accurate Thermophysical Property Information (1980). Special Publication 590 Natl. Bur. Stand. (U.S.) (J. V. Sengers and M. Klein, eds.). 5. happelear, P. S., hen, R. J. J., and Elliot, D. G. (1977). Pick K correlations carefully, Hydrocarbon Process. 56, Haynes, W. M., Kidnay, A. J., Olien, N. A., and Hiza, M. J. (1984). Status of thermo physical properties data for pure fluids and mixtures of cryogenic interest, Adv. ryog. Eng. 27, Din, F. (1962). Thermodynamic Functions of Gases; Volume 1. Ammonia, arbon Dioxide, and arbon Monoxide; Volume 2. Air, Acetylene, Ethylene, Propane and Argon; Volume 3. Ethane, Methane, and Nitrogen, Butterworths, London. 8. Stewart, R. B., and Timmerhaus, K. D. (1964). The correlation of thermodynamic properties of cryogenic fluids, Adv. ryog. Eng. 9, Diller, D. E. (1976). Thermophysical properties data research on compressed and liquefied gases at the NBS ryogenics Division, Adv. ryog. Eng. 21, Angus, S. (1983). Guidefor the Preparation of Thermodynamic Tables and orrelations of the Fluid State, ODATA Bulletin, No Mason, E. A., and Spurling, T. H. (1969). The Virial Equation of State, Pergamon Press, London. 12. Kamerlingh. Onnes, H. (1901). Expressions of the equation of state of gases and liquids by means of series, ommun. Phys. Lab. Univ. Leiden de Boer, J. (1974). van der Waals in his time and the present revival. Opening address, Physica 73A, Yu, J.-M., Adachi, Y., and Lu, B..-Y. (1986). Selection and design of cubic equations, in Equations of State (K.. hao and R. L. Robinson, eds.), pp , American hemical Society, Washington, D. 15. van der Waals, J. D. (1873). Over de continuiteit vand den gas-envloeistoftoestand, University of Leiden. 16. Redlich, 0., and Kwong, J. N. S. (1949). On the thermodynamics of solutions, V. An equation of state. Fugacities of gaseous solutions, hern. Rev. 44, Soave, G. (1972). Equilibrium constants from a modified Redlich-Kwong equation of state, hern. Eng. Sci. 27, Peng, D., and Robinson, D. B. (1976). A new two-constant equation of state, Ind. Eng. hern. Fundam. 15(1),

2 290 References 19. Harmens, A. (1977). A cubic equation of state for the prediction of N 2 -Ar-0 2 phase equilibrium, ryogenics 17, Harmens, A., and Knapp, H. (1980). Three-parameter cubic equation of state for normal substances, Ind. Eng. hern. Fundam. 19, Schmidt, G., and Wenzel, H. (1980). A modified van der Waals type equation of state, hern. Eng. Sci. 35, Patel, N. c., and Teja, A. S. (1982). A new cubic equation of state for fluids and fluid mixtures, hern. Eng. Sci. 37(3), Adachi, Y., Lu, B. c.-y., and Sugie, H. (1983). Three-parameter equations of state, Fluid Phase Equilibria 13, Peneloux, A., Rauzy, E., and Freze, R. (1982). A consistent correction for Redlich-Kwong Soave volumes, Fluid Phase Equilibria 8, Freze, R., hevalier, J. L., Peneloux, A., and Rauzy, E. (1983). Vapour-liquid equilibria calculations for normal fluid systems using a new cubic equation of state, Fluid Phase Equilibria 15, Adachi, Y., Lu, B..-Y., and Sugie, H. (1983). A four parameter equation of state, Fluid Phase Equilibria 11, Hamam, S. E. M., hung, W. K., Elshayal, L. M., and Lu, B. c.-y. (1977). Generalized temperature-dependent parameters of the Redlich-Kwong equation of state for vaporliquid equilibrium calculations, Ind. Eng. hern. Process Des. Dev. 16, Heyen, G. (1983). A cubic equation of state with extended range of application, Proc. 2nd Int. onf. on Phase Equilibria and Fluid Properties in the hemical Industry, 1980, p. 9; in hemical Engineering Thermodynamics (S. A. Newman, ed.), hap. 15, Ann Arbor Science Publishers, Ann Arbor, MI. 29. Kubic, W. L., Jr. (1982). A modification of the Martin equation of state for calculating vapour-liquid equilibria, Fluid Phase Equilibria 9, Fuller, G. G. (1976). A modified Redlich-Kwong-Soave equation of state capable of representing the liquid state, Ind. Eng. hern. Fundam. 15(4), Jacobsen, R. T, Beyerlein, S. W., Penoncello, S. G., and Lemmon, E. W. (1994). Thermodynamic consistency in property formulations, Adv. ryog. Eng. 39, Beattie, J. A., and Bridgeman, 0.. (1928). A new equation of state for fluids, Proc. Am. Acad. Arts Sci. 63, Beattie, J. A., and Bridgeman, 0.. (1928). A new equation of state for fluids. Application to helium, neon, argon, hydrogen, nitrogen, oxygen, air and methane, J. Am. hern. Soc. 50(12), Benedict, M., Webb, G. B., and Rubin, L.. (1940). An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures, J. hern. Phys. 8, Benellict, M., Webb, G. B., and Rubin, L.. (1951). An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures; onstants for twelve hydrocarbons, hern. Eng. Prog. 47(8), ooper, H. W., and Goldfrank, J.. (1967). B-W-R constants and new correlations, Hydrocarbon Process. 46(12), Schmidt, R., and Wagner, W. (1985). A new form of the equation of state for pure substances and its applications to oxygen, Fluid Phase Equilibria 19, Jacobsen, R. T, Stewart, R. B., Jahangiri, M., and Penoncello, S. G. (1986). A new fundamental equation for thermodynamic property correlations, Adv. ryog. Eng. 31, larke, W. P., Jacobsen, R. T, Lemmon, E. W., Penoncello, S. G., and Beyerlein, S. W. (1994). A revised and extended corresponding states model for predicting thermodynamic properties of N 2 -Ar-0 2 mixtures including vapor-liquid equilibrium, Int. J. 7hermophys. 15(6), 1289.

3 References Leach, J. W. (1967). Molecular Structure orrections for Application of the Theory of orresponding States to Non-Spherical Pure Fluids and Mixtures. Ph.D. dissertation, Rice University, Houston, TX. 41. Lemmon, E. W. (1996). A Generalized Model for the Prediction of the Thermodynamic Properties of Mixtures Including Vapor-Liquid Equilibrium, Ph.D. dissertation, University of Idaho, Moscow. 42. Tillner-Roth, R. (1993). Die Thermodunamischen Eigenschaften von RI52a, R134a und ihren Gemischen, Ph.D. dissertation, University of Hannover, Germany. 43. Hust, J. G., and Mcarty, R. D. (1967). urve-fitting techniques and applications to thermodynamics, ryogenics 7(4), de Reuck, K. M., and Armstrong, J. B. (1979). A method of correlation using a search procedure, based on a stepwise least-squares techniques and its application to an equation of state for propylene, ryogenics 19(9), Bjornn, K. R. (1988). A Linear Least-Squares Regression Algorithmfor the Optimization of Thermodynamic Equations of State, M.S. thesis, University of Idaho, Moscow. 46. Tang, S., Jin, G. X., Sengers, J. V. (1991). Thermodynamic properties of 1,1,1,2-tetrafluoroethane (R134a) in the critical region, Int. J. Thermophys. 12(3), Sengers, J. V. (1994). Effects of critical fluctuations on the thermodynamic and transport properties of supercritical fluids, in Supercritical Fluids, Fundamentals for Applications (E. Kiran and J. M. H. KeveIt Sengers, eds.), pp , Kluwer, Dordrecht. 48. Lemmon, E. W., Jacobsen, R. T, Penoncello, S. G., and Beyerlein, S. W. (1994). omputer programs for the calculation of thermodynamic properties of cryogens and other fluids, Adv. ryog. Eng. 39, Lemmon, E. W., Jacobsen, R. T, Penoncello, S. G., and Beyerlein, S. W. (1995). omputer Programs for alculating Thermodynamic Properties of Fluids of Engineering Interest, Version 4.1, ATS Report 95-1, University of Idaho, Moscow. 50. Jacobsen, R. T, Penoncello, S. G., Beyerlein, S. W., larke, W. P., and Lemmon, E. W. (1992). A thermodynamic property formulation for air, Fluid Phase Equilibria 79, Stewart, R. B., and Jacobsen, R. T (1989). Thermodynamic properties of argon from the triple point to 1200 K at pressures to 1000 MPa, J. Phys. hem. Ref. Data 18(2), Friend, D. G., Huber, M. L., and Gallagher, J. S. (1992). Thermophysical property computer packages from NIST, in omputerized Thermophysical Property Packages (S. G. Penon cello, ed.), American Society of Mechanical Engineers, Symposium Proceedings, HTD Vol. 225, pp Friend, D. G., Ingham, H., and Ely, J. F. (1991). Thermophysical properties of ethane, J. Phys. hem. Ref. Data 20(2), de Reuck, K. M. (1990). International Thermodynamic Tables of the Fluid State-ll Fluorine, International Union of Pure and Applied hemistry, Pergamon Press, London. 55. Mcarty, R. D., and Arp, V. D. (1990). A new wide range equation of state for helium, Adv. ryog. Eng. 35, Mcarty, R. D. (1975). Hydrogen, Technological Survey-Thermophysical Properties, NASA SP-3089, National Aeronautics and Space Administration, Washington, D. 57. Juza, J., and Sifner, O. (1976). Modified equation of state and formulation of thermodynamic properties of krypton in a canonical form in the range from 120 to 423 K and 0 to 300 MPa, Acta Tech. SAV1, Setzmann, u., and Wagner, W. (1991). A new equation of state and tables of thermodynamic properties for methane covering the range from the melting line to 625 K at pressures up to 1000 MPa, J. Phys. hem. Ref. Data 20(6), Katti, R. S. (1985). Thermodynamic Properties of Neon, from the Triple Point to 700 K with Pressures up to 700 MPa. M.S. thesis, University of Idaho, Moscow.

4 292 References 60. Jacobsen, R. T, Stewart, R. B., and Jahangiri, M. (1986). Thermodynamic properties of nitrogen from the freezing line to 2000 K at pressures to 1000 MPa, J. Phys. hern. Ref Data 15(2), Younglove, B. A. (1982). Thermophysical properties of fluids, J. Phys. hern. Ref Data 11(1), Sifner, 0., and Klomfar, J. (1994). Thermodynamic properties of xenon from the triple point to 800 K with pressures up to 350 MPa, J. Phys. hern. Ref Data, 23(1), James, M. L., Smith, G. M., and Wolford, J.. (1977). Applied Numerical Methods for Digital omputation, 2nd ed., Harper & Row Publishers, New York. 64. hambers, G. (1971) A quadratic formula for finding the root of an equation, Math. omput. 25(114).

5 Appendix A.t. IMPROPS SOFTWARE PAKAGE The software package IMPROPS contains subprograms for the calculation of pressure, compressibility factor, energy, entropy, heat capacity, speed of sound, fugacity coefficient, and the second and third virial coefficients, given the independent variables of density and temperature. The Joule-Thomson coefficient, isentropic expansion coefficient, isothermal expansion coefficient, volume expansivity, adiabatic compressibility, adiabatic bulk modulus, isothermal compressibility, and isothermal bulk modulus can also be calculated with this package. Iterative routines are available to solve for state properties when input variables other than density and temperature are specified. Subprograms are also provided to determine properties of coexisting liquid and vapor phases as well as ideal gas caloric properties. These property calculation subprograms can be incorporated in user-written applications. The property calculation package can be interfaced with other programs designed for specific engineering applications using both single fluids and mixtures. An interactive program for calculating the thermodynamic properties is available for calculating properties at single state points for a variety of different input options and can generate eight different types of property tables. The program allows the user to direct the calculated property data to the computer display, to a file, or to a printer as desired. SI and English engineering units and dimensionless input and output are supported in the current version. ombinations of SI and English engineering units and dimensionless input and output can also be specified. A.t.t. Fundamental Equation Subprograms The fundamental equation subprograms are a set of FORTRAN functions and subroutines for calculating thermodynamic properties using the inde- 293

6 294 Appendix Table A.I. Subprograms Used to alculate Thermodynamic Properties with Density and Temperature as Input Variables Subprogram name Property Units ompressibility properties FUNTION PFNDA(D,T) P MPa FUNTION ZFNDA(D,T) Z FUNTION DPDDl(D,T) (op/oph kj/mol FUNTION DPDD2(D,T) OZP/op2h (kj/mol)2 FUNTION DPDT(D,T) (op/otj p MPa/K FUNTION VIR2(T) B(T) dm 3 /mol FUNTION VIR3(T) qt) (dm 3 /mol)2 FUNTION FUGOE(D,T) Energy properties FUNTION AFNDA(D,T) A J/mol FUNTION GFNDA(D,T) G J/mol FUNTION HFNDA(D,T) H J/mol FUNTION UFNDA(D,T) U J/mol Entropy, heat capacities and speed of sound FUNTION SFNDA(D,T) S J/mol'K FUNTION VFNDA(D,T) v J/mol'K FUNTION PFNDA(D,T) p J/mol'K FUNTION WFNDA(D,T) W m/s Other derived properties SUBROUTINE PROPERTY(D,T,JT,KS,KT,BET A,BET AS,BS,KAPPA,BKT)a ajt is the Joule-Thomson coefficient, KS is the isentropic expansion coefficient, KT is the isothermal expansion coefficient, BET A is the volume expansivity, BET AS is the adiabatic compressibility, BS is the adiabatic bulk modulus, KAPPA is the isothermal compressibility, and BKT is the isothermal bulk modulus. Units for these derived properties are given in the nomenclature. pendent variables density (D) and temperature (T). The equations given in Section 4.2 are used in these calculations. Subprograms for calculating these properties are given in Table A.1. The fundamental equation module contains subprograms for directly evaluating rj.o, ~, and their derivatives. These routines are called by many of the functions in Table A.1 and are listed in Table A.2. Different derivative functions of a can be obtained from the subroutine FUNDEQ, depending on the input parameters for IDEL and ITAU as shown in Table A.2. The subroutine FUNDEQ stores the derivative of each term in the equation of state in the array TERMS located in the common block STATE. The variable IAL is set equal to 1 for property calculations. When IAL = 0, FUNDEQ returns a value of zero for FUN.

7 Appendix 295 Table A.2. Subprograms for Evaluating rxo, ii, and their Derivatives Subprogram name Result Ideal Gas Terms FUNTION ALPHAO(DEL, TAU) FUNTION DALP01(TAU) FUNTION DALP02(TAU) Real Gas Terms rxo orxojijt o2rxojot2 SUBROUTINE FUNDEQ(DEL, TAU, IDEL, ITAU, IAL, FUN)b IDEL ITAU FUN (output) o o o o 2 o o 2 ija {)- ij{) oa t Ōt ij2a {)to{)ijt ij 2 a {)2_ ij{)2 ij2a t 2 ījt 2 u v ij"+v(a) {)"tv_- o{)"otv "DEL = (j = pip, and TAU =... = T./T. bindividual terms are calculated and returned via the TERMS array in the commons block /STATE/. The property is calculated if IAL = 1 and the value is returned as FUN. The property package can also be used to calculate ideal gas properties. The logical variable IDGPRP is used to select this option. IDGPRP is contained in the common block FLUIDS. IDGPRP should be assigned a value of.true. if ideal gas properties are desired. A.l.2. Iterative Routines When the pair of variables used to fix the thermodynamic state does not include density or temperature, one of the iterative routines listed in Table A.3 can be used to solve for the remaining independent variable(s). These iterative routines support eight different pairs of input variables.

8 296 Appendix Table A.3. Subprograms to alculate Thermodynamic Properties Using Inputs other than Density and Temperature Subprogram name Solve for density: FUNTION DNEWT(P, T, DEST) FUNTION DOFPT(P, T, IPHASE) FUNTION DOFST(S, T) Solve for temperature: FUNTION TOFDH(D, H) FUNTION TOFDP(D, P) FUNTION TOFDS(D, S) FUNTION TOFDU(D, U) Solve for density and temperature: SUBROUTINE DTOFHP(H, P, D, T) SUBROUTINE DTOFPS(P, S, D, T) Input properties P, T P, T S, T D,H D,P D,S D,U H,P P,S Note: Units for thermodynamic properties are consistent with those given in Table A.l. Two iterative routines, listed in Table A.3, calculate density given the input variables of pressure and temperature. The first of these, DNEWT, is based on a second-order method of Newton. 63 An estimate of the density is needed to begin the iteration. DNEWT is convenient in applications where a good estimate of the density is available. The estimate for density is passed to DNEWT via the argument DEST. The function DOFPT can also be used to solve for density when pressure and temperature are known. DOFPT is based on the method proposed by hambers. 64 The variable IPHASE in the argument list for DOFPT is an integer variable that indicates whether a liquid or vapor calculation is carried out near the saturation line. Setting IPHASE = 1 forces DOFPT to search for the density root in the liquid region. Setting IPHASE = 2 confines the search to the vapor region. This is generally needed only when calculations are carried out near, or on, the saturation line. Otherwise, IPHASE should be set to zero. DOFPT will confine the search for the density root according to the values of P and T. When the temperature is less than the critical value, DOFPT will search the vapor region when P is less than the saturation pressure and search the liquid region when P is greater than the saturation pressure. DNEWT is used when DOFPT fails to converge. In the other iterative routines listed in Table A.3, the method of hambers 64 is also used. Table A.4 lists five subprograms (SATT, SA TP, SATD, SA TH, and SA TS) contained in the iterative module for calculating saturation properties. Only one input property is required when using these subprograms. The final letter of the subroutine name corresponds to the input property. SATT,

9 Appendix 297 Table A.4. Subprograms to alculate Thermodynamic Properties along the Saturation and Melting urves SUBROUTINE SATT(T, IAL, DL, DV, PL, PV) SUBROUTINE SATP(P, IAL, DL, DV, TL, TV) SUBROUTINE SATD(D, IAL, D2, P, T) For these subroutines, IAL = I Pressure and density from ancillary equations IAL = 2 Pressure from ancillary equations and density from the equation of state IAL= 3 Maxwell criterion used to solve for the saturation states SUBROUTINE SATH(H, DI, D2, PI, P2, Tl, T2, IPHASE) SUBROUTINE SATS(S, D, T, IPHASE) For these subroutines, IPHASE = I Saturated liquid properties (Output) IPHASE = 2 Saturated vapor properties (Output) IPHASE = 3 Melting line properties (Input) FUNTION TOFP2P(P, IPHASE) FUNTION TOFD2P(D, IPHASE) For these functions, IPHASE = I Saturated liquid temperature IPHASE = 2 Saturated vapor temperature IPHASE = 3 Melting line temperature SATP, and SATD require a second argument IAL for calculation of the saturation properties as shown in Table A.4. Temperature (T) is the input argument for SATT. For a pure fluid, SATT provides the saturated liquid density (DL), the saturated vapor density (DV), and the saturation pressure (PL or PV). For fluid mixtures, SATT calculates the bubble point density (DL), dew point density (DV), bubble point pressure (PL), and dew point pressure (PV). Pressure (P) is the input argument for SATP. For a pure fluid, SATP provides the saturated liquid density (DL), the saturated vapor density (DV), and the saturation temperature (TL or TV). For fluid mixtures, SATP returns the bubble point density (DL), dew point density (DV), bubble point temperature (TL), and dew point temperature (TV) corresponding to the input pressure (P). SATD requires the density (D) to be known for either the liquid or vapor state. SA TD provides the saturation temperature (T) and pressure (P) for a pure fluid, along with the corresponding density (D2) for the unknown liquid or vapor state. Given the saturation enthalpy (H), SA TH is used to determine whether one or two intersections occur between the saturation curve and the

10 298 Appendix constant enthalpy line. In the case of one intersection, the density (Dl) and temperature (Tl) are provided. When two intersections occur, D2 and T2 are also returned at the intersection with the lower pressure. IPHASE determines the liquid or vapor status of the point(s). To locate the enthalpy on the melting curve, IPHASE must be set to 3 prior to calling the subroutine. SATS calculates the density (D) and temperature (T) given a saturation entropy (S). The liquid or vapor status of the entropy point will be returned in IPHASE. To locate the 'entropy on the melting curve, IPHASE must be set to 3 prior to calling the subroutine. Two functions used for determining the temperature along phase boundaries are also listed in Table A.4. TOFP2P is used to find the saturation temperature given pressure on the saturated liquid line (I PHASE = 1), saturated vapor line (IPHASE = 2), or the freezing liquid line (IPHASE = 3). TOFP2P has the same function as TOFD2P, except the density is the input parameter. Both routines use only the ancillary equations. A.l.3. Fluid-Specific Routines Several of the subprograms listed in Table A.4 use ancillary equations for calculating saturation properties. These equations are fluid specific and interact with the subprograms through the buffer routines listed in Table A.5. Also included in this table is the buffer routine for the ideal gas isobaric heat capacity. These buffer routines use coefficients from the fluid reference file to determine saturation densities, vapor pressures, and ideal gas heat capacities. To add a new fluid to the property package, one must develop or modify a fluid-specific reference file containing the critical properties, the reference state properties, the coefficients and exponents for the fundamental equation of state, the coefficients for the ideal gas heat capacity equation, the vapor and melting pressure equations, and the saturated liquid and saturated vapor density equation. Information about a fluid is read from a fluid reference file by the subroutine READ REF. Fluid constants, coefficients and exponents, fluid identifiers, limits of the formulation, and reference property data are assigned from the fluid reference file, as well as coefficients for the ancillary equations. READ REF places this information in the common blocks NST, EOS, FLUID, LIMITS, ANILLARY, and REFPRP. NST contains critical constants, triple point properties, the acentric factor, and the molecular weight. EOS contains information about the terms in the fundamental equation. FLUID contains the IDGPRP ideal gas flag, the fluid name, and reference number. LIMITS contains data on the boundaries of

11 Appendix 299 Table A.S. Subprograms in the Buffer Routines Subprogram name Result FUNTION D2PEQ(T, IPHASE) IPHASE = 1 Saturated liquid or bubble point density (molfdm 3 ) IPHASE = 2 Saturated vapor or dew point density (moljdm3) IPHASE = 3 Melting or freezing line density (moljdm3). FUNTION P2PEQ(T, IPHASE) IPHASE = 1 Saturation or bubble point pressure (MPa) IPHASE = 2 Saturation or dew point pressure (MPa) IPHASE = 3 Melting or freezing line pressure (MPa) FUNTION H2PEQ(T, IPHASE) IPHASE = 1 Saturated liquid or bubble point enthalpy (J/mol) IPHASE = 2 Saturated vapor or dew point enthalpy (J/mo!) IPHASE = 3 Melting or freezing line enthalpy (J/mol) FUNTION S2PEQ(T, IPHASE) IPHASE = 1 Saturated liquid or bubble point entropy (J/(mol' K)) IPHASE = 2 Saturated vapor or dew point entropy (J/(mol' K» IPHASE = 3 Melting or freezing line entropy (J/(mol' K» FUNTION IDGAS(T, INDX) INDX =0 :/R INDX = 1 J ( ~ / R ) d T INDX = 2 J ( ~ / R T ) d T the formulation. ANILLARY contains the coefficients for the ancillary equations. All routines in the property package that use these common blocks refer to 'INLUDE' files called OMMONS.FOR, OMSTATE.FOR, and OMDRV.FOR. hanges in the common blocks used in the property package are made in these files. Four parameters are used to dimension the arrays in the common blocks. NF specifies the number of fluids that can be loaded at one time, MAXT is the maximum number of coefficients. NS is the maximum number of state points displayed to the screen in single point calculations by IMPROPS. NV is the current number of thermodynamic properties that can be selected by IMPROPS users. Parameters NF, NS, and NV are initialized in OMMONS.FOR. MAXT is initialized in OM STATE.FOR. When including common blocks, OMMONS.FOR should always be included first. OMSTATE.FOR, if needed, should be included second. OMDRV.FOR, if needed, should be included last. The fluid-specific reference file is read by the subroutine READ REF, which is called with two parameters, FNAME and INDX. INDX specifies

12 300 Appendix the storage location for the fluid-specific constants for a given fluid. INDX may have any integer value from 1 to the parameter NF. This feature is convenient when designing programs to examine different working fluids in mixture models. FNAME specifies the fluid reference file name and DOS file specification. A.2. REATING A USER-DEFINED APPLIATION The property calculation package described in this monograph can be interfaced with other programs designed for specific engineering applications. In this section, simple examples of single fluid and multiple fluid applications are given. A.2.t. Single Fluid Applications User-defined application programs can use the routines in the property calculation package by following the strategy outlined below. First, the user should call the READREF subroutine using a statement such as "ALL READREF(FNAME, INDX)". In this statement, FNAME contains the name of the fluid reference file. INDX could be assigned a value of 1 up to the value of NF. The application can use appropriate functions and subroutines from Tables A.I, A.3, A.4, and A.5 to calculate thermodynamic properties at individual state points. If density and temperature inputs are specified, the explicit calculation functions (see Table A.l) can be used to evaluate other thermodynamic state variables. If some other pair of state variables is specified, one of the iterative routines (see Tables A.3 and A.4) will allow the user to solve for either the density or temperature. The remaining state variables can be evaluated once the density and temperature of the state point are known. An application program is given in Example 1. This program calculates the temperature change resulting from a throttling process when nitrogen is expanded from 10 MPa and 300 K to atmospheric pressure. The first executable statement, "ALL READREF(FNAME, 1)", reads the fluidspecific reference file to initialize variables that contain fluid-specific information pertaining to the fundamental equation for nitrogen. The fluid-specific information is available to other subroutines in the package via common blocks. These common blocks are defined in the OMMONS. FOR and OMSTATE.FOR files. onsequently, READREF must be called before execution of the property calculation routines. The second executable statement, "Dl = DOFPT(Pl, Tt, 0)", solves iteratively for the density at state 1 given values for pressure (PI) and

13 Appendix 301 temperature (Tl). "0" is included as the third argument since this state is not near the saturation line. An explanation of the bounding procedures used by DOFPT is given in Section A.L2. Once both density and temperature are known, the thermodynamic properties at state I can be calculated. In this example, the enthalpy at state 1 is calculated using the function HFNDA and the value returned is assigned to the variable HI. Because the fluid enthalpy remains constant during the throttling process, state 2 is defined by the variables H2 = HI and atmospheric pressure, P2 = MPa. For these two input variables, a call to the subroutine DTOFHP returns values for the density (D2) and temperature (T2) at state 2. The desired temperature change is T2-Tl. A.2.2. Multiple Fluid Applications The property package can accommodate more than one fluid at a time. This feature is useful in system modeling when studying more than one working fluid and is also useful in mixture models. READREF must be called for each fluid at the beginning of an application program. Different values of NDX must be used for each fluid. READ REF will assign constants for each fluid in arrays at the position indicated by NDX. The current fluid can be changed by altering the variable NDX which is stored in the FLUIDS common block. If more than two fluids are required in a single application, it will be necessary to increase the parameter NF in the OMMONS.FOR file. Example 2 shows how two fluids are incorporated in a single program. A.2.3. Linking User-Defined Applications with the Property Package The user-defined application program should be compiled and its object code linked with FUNDEQ.OBJ, FUNDIT.OBJ, and BUF ALL.OBJ to produce the executable user-defined application program. Example 1. PROGRAM THROTILE PURPOSE: alculate the temperature change for a throttling process with nitrogen as the working fluid.

14 302 Appendix DESRIPTION OF VARIABLES: D1, D2 H1, H2 P1, P2 T1, T2 DELTA Densities of States 1 and 2. (mol/dm3) Enthalpies of States 1 and 2. (J/mol) Pressures of States 1 and 2. (MPa) Temperatures of States 1 and 2. (K) Temperature Difference from 1 to 2. (K) DELARE FUNTIONS ALLED: REAL *8 DOFPT, HFNDA DELARE LOAL VARIABLES: REAL*8 DELTA, D1, D2, H1, H2, P1, P2, T1, T2 DATA P1, P2, T1 110.DO, DO, 300.DOI HARATER*80 FNAME BEGIN: FNAME = 'NITROGEN' ALL READREF(FNAME, 1) D1 = DOFPT(P1, T1, 0) H1 = HFNDA(D1, T1) H2 = H1 ALL DTOFHP(H2, P2, D2, T2) DELTA = T2 - T1 WRITE (*,' (4F10.4) ') P1, T1, D1, H1 WRITE (*, ' (4F10.4) ') P2, T2, D2, H2 WRITE (*,' (F10.4) ') DELTA END Example 2. PROGRAM MULTIFLD This is a simple example program that demonstrates how to use more than one fluid in an application program. This program calculates the densities of nitrogen and oxygen at the standard conditions of P = MPa and T = K.

15 Appendix INLUDE 'OMMONS. FOR' Declare functions called REAL *8 DOFPT Declare local variables REAL *8 DN2, D02, P, T HARATER*80 FNAME Begin: P = DO T = DO all the reference routine for nitrogen and oxygen FNAME = 'NITROGEN' ALL READREF (FNAME, 1) FNAME = 'OXYGEN' ALL READREF (FNAME, 2) Select nitrogen, then calculate its density NDX= 1 DN2 = DOFPT (P,T,O) Select oxygen, then calculate its density NDX=2 D02 = DOFPT (P,T,O) Write the densities to the screen WRITE(*, *) I DN2 = I, DN2, I, D02 = I, D02 STOP END A.3. USING THE IMPROPS UTILITY PROGRAM IMPROPS provides a DOS-based interactive, menu-driven format for calculating thermodynamic properties. The IMPROPS utility may be used to calculate properties at single state points for a variety of different input options and can be used to generate eight different formats of property tables. The program allows the user to direct the generated property data to the display, to a file, or to a printer as desired. SI and English engineering

16 304 Appendix units and dimensionless input and output are supported in the current version. ombinations of units can also be specified. A.3.t. Menu Structure Most options in IMPROPS menus are accompanied by brief explanation statements in the menu to the right of the option. In some situations IMPROPS prompts the user to enter values for various input properties. Table A.6. Single State Point Property alculation Menu (1) P, T (2) P, D (3) P, H (4) P, S (5) T, D (6) T, S (7) D, H (8) D, S (9) TSAT (10) PSAT (11) T,x (12) P,x (13) Dsat (S) Status () lear (0) Quit (Single phase point given P, T) (Single phase point given P, D) (Single phase point given P, H) (Single phase point given P, S) (Single phase point given T, D) (Single phase point given T, S) (Single phase point given D, H) (Single phase point given D, S) (Saturation point given T) (Saturation point given P) (Saturation point given T and quality) (Saturation point given P and quality) (Saturation point given D) (View program status) (lears all entries from the list) (Return to main menu) Table A.7. Table alculation Menu (1) PT (Isobar table on increments of T) (2) TP (Isotherm table on increments of P) (3) DT (Isochore table on increments of T) (4) HP (Isenthalp table on increments of P) (5) ST (lsentrope table on increments of T) (6) TSAT (Saturation table on increments of T) (7) PSAT (Saturation table on increments of P) (8) TMEL T (Melting table on increments of T) (9) Q (onstant quality table on increments of P) (S) Status (View program status) (N) Tum off printing the value of the quality (M) Multiply Pinc rather than add () hange output file name (0) Quit (Return to main menu)

17 Appendix 305 Requested values can be entered from the keyboard by following the rules offree-format input (separate the values by blanks or commas). Options can also be selected through a configuration file. This file can be created through the SAVE ONFIGURATION command in the main menu and edited with an ASII editor. The saved file will be called "ONF.SA V" unless the user specifies a different filename. POINTS MENU AL. MENU alculate properties at a - single point given two inputs. (1) Point Refer to Table A.6 --.,.- r-- (2) Tables. (3) Status TABLES MENU (0) Quit'" Generate tables along '- MAIN MENU constant property paths. Refer to Table A.7 ( 1) alculate - (2) Options. (3) Status FLUIDS MENU (4) Save onfig. (5) Exit OPTIONS MENU Select a fluid..-- Refer to Table A.S (1) Fluid - (2) Output OUTPUT MENU '--- (3) Units (4) Display Select whether output is sent '-- (5) Idgas to the screen. file or printer.. (6) Status Refer to Table, A.9 (7) Titles (0) Quit" UNITS MENU - hoose a system of units as SI. Engineering. dimensionless or custom. Refer to Tables A.1O-A.l1 DISPLAY MENU '-- hoose a set of variables to display. Refer to Table A.12 Fig, A.I. IMPROPS menu structure,

18 306 Appendix Figure A.l is a diagram of the menu structure for IMPROPS. Tables A.6 through A.12 show the submenus in detail. The last option of each menu is the "Quit" option. This option returns the user to the main menu. Option 5, "Exit," returns the user to the operating system. hoosing the "Status" option will display a screen containing information about current program settings. These include the range of validity of the equation of state, critical constants, output device, fluid name, and units. Table A.S. Fluids Menu (1) Air (2) Argon (3) arbon Monoxide (4) Deuterium (normal) (5) Ethane (6) Fluorine (7) Helium (8) Hydrogen (normal) (9) Krypton (10) Methane (11) Neon (12) Nitrogen (13) Oxygen (14) Parahydrogen (15) Xenon Table A.9. Output Menu (1) (2) (3) (4) (0) Display File Printer No Screen Quit (Display only) (Display and to a file) (Display and to the printer) (Do not send output to display) (Return to the main menu) Table A.to. Units Menu (1) (2) (3) (4) (5) (6) (0) S. I. (molar) S. I. (mass) Engineering Dimensionless Parameters ustom Status Quit (MPa, mol, K, Joules, m, s) (MPa, kg,, kjoules, m, s) (psia, Ibm, F, Btu, flo s) (hoose your own units, see Table A.ll) (View the Status Screen) (Return to the main menu)

19 Appendix 307 Table A.n. ustom Units Menu (1) (2) (3) (4) (5) (6) (7) (0) Temperature Units Pressure Units Density Units Volume Units Energy Units Heat apacity and Entropy Units Speed of Sound Units Quit K,, R, F, Tff. MPa, psia, bar, mmhg, atm, PIP., gage molfdm 3, kg/m 3, Ibm/ft 3, DID. dm 3 /mol, m 3 jkg, ft 3 /lbm, VIV. J/mol, kjjkg, Btu/lbm, kcaljkg, dimensionless" J/mol-K, kjjkg-k, Btu/lbm-R, kcaljkg-k, dimensionless mis, ftls, dimensionless' Return to the Units menu "Dimensionless energy is calculated by dividing by the gas constant and the critical temperature. "Dimensionless heat capacity and entropy are calculated by dividing by the gas constant. 'Dimensionless speed of sound is calculated by dividing by RT., &((T.». Mw y Tc Table A.12. Display Menu (1) Pressure (P) (2) Temperature (T) (3) Density (D) (4) Specific Volume (V) (5) Internal Energy (U) (6) Enthalpy (H) (7) Entropy (S) (8) Isochoric Heat apacity (V) (9) Isobaric Heat apacity (P) (10) Speed of Sound (W) (11) ompressibility Factor (Z) (12) Helmholtz Energy (A) (13) Gibbs Free Energy (G) (14) Second Virial oefficient (B) (15) Third Virial oefficient () (16) Fugacity oefficient (F) (17) First Derivative of Pressure wrt Temperature (PT) (18) First Derivative of Pressure wrt Density (POl) (19)" Second Derivative of Pressure wrt Density (PD2) (23)" Joule-Thomson oefficient (JT) (24) Isentropic Expansion oefficient (KS) (25) Isothermal Expansion oefficient (KT) (26) Volume Expansivity (BETA) (27) Adiabatic ompressibility (BETAS) (28) Adiabatic Bulk Modulus (BS) (29) Isothermal ompressibility (KAPPA) (30) Isothermal Bulk Modulus (BKT) (-1) Erase all current settings (0) Return to the Main Menu "(20), (21), and (22) are reserved for future additions.

20 308 Appendix SI units are the default units for IMPROPS. The output default configuration displays pressure, temperature, density, enthalpy, entropy, isochoric heat capacity, and speed of sound to the screen only. These options can be changed as desired by returning to the main menu, entering the options menu, and selecting the desired choices for properties, units, or output. A.3.2. Saving a onfiguration As stated in Section A.3.1, the chosen options and fluid name can be saved by selecting the SAVE ONFIGURATION option in the main menu. The next time the program is run, the user can select ONF.SA V or type in a different filename. If the user enters 'NUL', IMPROPS will not use a configuration file for that session and will return to the default configuration. A.3.3. Output Options Output can be directed to a file or printer as well as to the screen. Menu screens and prompts are written only to the screen. Output title information (the fluid name, the property names, and the units used) is written to the display and also, by selection, to the output device. The user can choose whether or not to write the title information to the output device by using the TITLES option in the Options menu. Titles will always be written to the screen. Up to seven output properties can be viewed on the screen. More than seven properties can be printed to a file or printer. When point calculation results are written to the screen, they are listed below any previously calculated point or table results. Up to ten lines of previous results will remain displayed as an aid in choosing the next data points. The clear option can be used to remove the lines. These lines will also be removed if the units are changed. A.3.4. Access to Source and Executable omputer ode for IMPROPS The computer programs discussed in this book are available on the worldwide web and may be downloaded by those who wish to use these programs. The web site is given in Ref. 1. Instructions for access to these programs are included on the web site.

21 Index Acentric factor, 298 Adiabatic bulk modulus, 293 Adiabatic compressibility, 293 Air, I, 13 ancillary equations, coefficients and exponents,41 correlation limits, 40 fixed points, 40 fluid constants, 41 fundamental equation, 12 coefficients and exponents, 42 P-H diagram, 54 single phase, 44 two-phase, 43 reference state properties, 41 T-S diagram, 55 Ancillary functions ideal gas heat capacity, 12, 18, 31, 39 melting line, 18, 31, 36 saturated liquid density, 18, 31 saturated vapor density, 18, 31 vapor pressure, 18, 22, 31, 34 Argon, I ancillary equations, coefficients and exponents,56 correlation limits, 56 fixed points, 56 fluid constants, 56 fundamental equation, 12 coefficients and exponents, 57 mixture, 13 P-H diagram, 72 single phase, 59 two-phase, 58 reference state properties, 56 T -S diagram, 73 arbon monoxide ancillary equations, coefficients and exponents,74 arbon monoxide (cont.) correlation limits, 74 fixed points, 74 fluid constants, 74 fundamental equation, coefficients and exponents,75 P-H diagram, 84 single phase, 77 two-phase, 76 reference state properties, 74 T-S diagram, 85 ompressibility factor, 16, 293 omputer calculations, 26 omputer programs accuracy, 4 development, 4 fitting, II iterative calculations, 18 properties, 27 calculation of, 6 estimate, 3 1 tables, II ritical point, 3, 19, 22, 23, 40 Deuterium ancillary equations, 39 coefficients and exponents, 88 correlation limits, 87 fixed points, 87 fluid constants, 87 fundamental equation, coefficients and exponents,89 P-H diagram, 102 single phase, 91 two-phase, 90 reference state properties, 87 T-S diagram, 103, 104 Enthalpy, 7, 12, 19,31,297,298,301,

22 310 Index Equations of state, 3, 5, 7, 18,22,26,32 Beattie-Bridgeman, 10 Benedict--Webb-Rubin, 10 criteria for, 22 critical region, 23 cubic, 8 fundamental equation, II mixture, extended corresponding states, 15 mixtures, 13 cubic, 14 excess properties, 16 pressure explicit, 7, 28 transforming to the fundamental form, 27 virial,7 Ethane, 17 ancillary equations, coefficients and exponents, 105 correlation limits, 105 fixed points, 105 fluid constants, \05 fundamental equation, coefficients and exponents, \06 P-H diagram, 107 single phase, 110 two-phase, 109 reference state properties, 105 T-S diagram, 108 Fluorine ancillary equations, coefficients and exponents, 120 correlation limits, 119 fixed points, 119 fluid constants, 119 fundamental equation, coefficients and exponents, 120 P-H diagram, 131 single phase, 122 two-phase, 121 reference state properties, 119 T-S diagram, 132 Formulations, thermodynamic property, 1,2,36 Fourth pressure virial coefficient, 8 Fourth virial coefficient, 7 Freezing liquid pressure, 31 Fugacity coefficient, 293 Fundamental equation, 4, 7,8,11,12,20,21, 22,25,31 Fundamental equation (cont.) functions for fitting, 21 mixtures, 16 subprograms for, 293, 298, 300 thermodynamic property calculations, 27 Gas constant, 19,39 Helium ancillary equations, coefficients and exponents, 133 correlation limits, 133 fixed points, 133 fluid constants, 133 fundamental equation, coefficients and exponents,134 P-H diagram, 147 single phase, 136 two-phase, 135 reference state properties, 133 T-S diagram, 148, 149 Helmholtz energy, 4, 7, 11, 12, IS, 16, 17,25, 26,30,33,34,40 Hydrocarbon mixtures, 1 Hydrogen, normal ancillary equations, coefficients and exponents, 150 correlation limits, 150 fixed points, 150 fluid constants, 150 fundamental equation, coefficients and exponents, lsi P-H diagram, 162 single phase, 153 two-phase, 152 reference state properties, 150 T-S diagram, 163, 164 Ideal gas, 8, 11,12, 17,20,22,25,26, 33 Ideal gas constant, 33 Isentropic expansion coefficient, 293 Isobaric heat capacity, 23, 31, 298 Isochoric heat capacity, 22, 23, 31, 309 Isothermal bulk modulus, 293 Isothermal compressibility, 293 Isothermal expansion coefficient, 293

23 Index 311 Joule-Thomson coefficient, 293 Krypton ancillary equations, coefficients and exponents, 165 correlation limits, 165 equations of state, 33 fixed points, 165 fluid constants, 165 fundamental equation, coefficients and exponents, 166 P-H diagram, 181, single phase, 169 two-phase, 168 reference state properties, 165 T-8 diagram, 182 Melting line: see Ancillary functions Methane, 17 ancillary equations, coefficients and exponents, 183 correlation limits, 183 fixed points, 183 fluid constants, 183 fundamental equation, coefficients and exponents, 184 Helmholtz energy equation, 34 P-H diagram, 200 single phase, 186 two-phase, 185 reference state properties, 183 T-8 diagram, 201 Natural gas, I Neon,l ancillary equations, coefficients and exponents,202 correlation limits, 202 fixed points, 202 fluid constants, 202 fundamental equation, coefficients and exponents, 203 P-H diagram 217 single phase, 205 two-phase, 203 reference properties, 202 T-8diagram, 218, 219 Nitrogen, 1,300 ancillary equation, coefficients and exponents, 220 correlation limits, 220 fixed points, 220 fluid constants, 220 fundamental equation, 12 coefficients and exponents, 221 mixture, 13 P-H diagram, 237 single phase, 223 two-phase, 222 reference fluid, 16 reference state properties, 220 T-8 diagram, 238 Oxygen, I ancillary equations, coefficients and exponents, 239 correlation limits, 239 fixed points, 239 fluid constants, 239 fundamental equation, II, 12 coefficients and exponents, 240 mixture, 13 P-H diagram, 252 single phase, 242 two-phase, 240 reference state properties, 239 T-8 diagram, 253 Parahydrogen ancillary equations, 39 coefficients and exponents, 255 correlation limits, 254 fixed points, 254 fluid constants, 254 fundamental equation, coefficients and exponents, 256 P-H diagram, 268 single phase, 258 two-phase, 257 reference state properties, 254 T-8 diagram, 269, 270 Property formulations critical region, 23 equations, 11

24 312 Index Reference state properties, 32 Second pressure virial coefficient, 8 Second virial coefficient, 7 Specific volume, 3, 8 Speed of sound, 3, 22, 23, 31, 293, 309 Third pressure virial coefficient, 8 Third viria1 coefficient, 8, 14, 293 Vapor pressure, 20, 22; see also Ancillary functions measurements, 20 subprograms, 298 Volume expansivity, 293 Xenon ancillary equations, coefficients and exponents, 271 correlation limits, 271 equations of state, 33 fixed points, 271 fluid constants, 271 fundamental equation, coefficients and exponents,272 P-H diagram, 286 single phase, 275 two-phase, 274 reference state properties, 271 T-S diagram, 287