Parahydrogen !Short name 1333-74-0p !CAS number Parahydrogen !Full name H2 !Chemical formula {H2} R-702p !Synonym 2.01588 !Molar mass [g/mol] 13.8033 !Triple point temperature [K] 20.271 !Normal boiling point [K] 32.938 !Critical temperature [K] 1285.8 !Critical pressure [kPa] 15.538 !Critical density [mol/L] -0.219 !Acentric factor 0.0 !Dipole moment [Debye]; (exactly zero due to symmetry) NBP !Default reference state 10.0 !Version number 1049 !UN Number :UN: cryogen !Family :Family: 285.83 !Heating value (upper) [kJ/mol] :Heat: A3 !Safety Group (ASHRAE Standard 34, 2010) :Safety: ???? !Standard InChI String :InChi: ???? !Standard InChI Key :InChiKey: 8d757b40 (hydrogen) !Alternative fluid for mixing rules :AltID: 8d757b4a !Hash number from InChI Key :Hash: !Quantum mechanics requires orthohydrogen to retain rotational energy at low temperatures, even below the triple point ! temperature, that manifests in significantly higher ideal-gas thermal properties relative to parahydrogen. The ! traditional reference state determination method of setting the enthalpy and entropy of an ideal-gas equal to zero for a ! saturated liquid at the normal boiling point does not account for this difference and results in false comparisons ! between parahydrogen and orthohydrogen. To allow the orthohydrogen and parahydrogen equations of state to accurately ! reflect these differences, the reference state properties for orthohydrogen have been set in agreement with those ! tabulated in LeRoy et al., J. Phys. Chem., 94:923-929, 1990. ! !Here, the reference state for parahydrogen was left as NBP to conform with that from earlier versions of Refprop. ! If you wish to obtain enthalpy and entropy properties that are consistent with those now used in the orthohydrogen ! fluid file, delete line 14 above that has NBP on it and replace it with the following two lines: !OT0 !Default reference state that agrees with those of LeRoy et al., J. Phys. Chem., 94:923-929, 1990. !25.0 0.1 519.654 123.5089 !The fluid files contain general information about the fluid in the first 15 to 20 lines, followed by sections for the ! equations of state, transport equations, and auxiliary equations. Equations of state are listed first. The NIST recommended ! equations begin with a hash mark (#). The secondary equations begin with the @ symbol. These symbols can be swapped to ! select a secondary equation as primary and the primary as secondary. The equation of state section also contains auxiliary ! equations for the ideal gas heat capacity or ideal gas Helmholtz energy. Below the equations of state (both primary and ! secondary) are the transport equations, first viscosity and then thermal conductivity. These are then followed by the ! secondary equations if available. The transport section also contains auxiliary equations required to calculate either the ! dilute gas state or the critical enhancement. At the end of the file are additional but not necessary auxiliary equations, ! including simple equations for the vapor pressure, saturated liquid and vapor densities, melting line (for some fluids), and ! sublimation line (for even fewer fluids). This section also contains the equations for dielectric constant and surface ! tension if available. The sections are divided by different symbols (these being _-+=^*~) to aid the eye in locating a ! particular section. Secondary equations are indented 10 spaces to avoid confusion with the NIST recommended equations. The ! end of the fluid file is marked with @END. Anything below that is ignored. ! compiled by E.W. Lemmon, NIST Physical and Chemical Properties Division, Boulder, Colorado ! 04-06-98 EWL, Original version. ! 10-20-99 EWL, Add tcx and eta formulations from NIST12, Version 3.1. ! 08-05-04 EWL, Add Harvey and Lemmon dielectric correlation. ! 03-27-07 JWL, Add equation of state of Leachman et al. (2009). ! 10-16-07 EWL, Change upper temp. limit of vis and tcx from 400 to 1000 K based on good graphical extrapolation. ! 07-17-08 EWL, Change incorrect molecular weight from 2.01594 to 2.01588. ! 07-21-08 EWL, Add vapor pressure ancillary. ! 06-17-10 CKL, Add ancillaries for sat. densities. ! 04-07-11 MLH, Add thermal conductivity model of Assael et al. (2011). ! 04-07-11 MLH, Add viscosity model of Quinones-Cisneros et al. (2011) but not as default. ! 11-16-12 MLH, Add new SR model of Muzny for viscosity. ! 12-06-12 EWL, Add surface tension coefficients of Mulero et al. (2012). ! 05-13-17 EWL, Change the ECS LJ sigma from 2.827 to the correct 0.2827. ! 05-15-17 EWL, Change the hard coded VS0 model to the VS7 reverse Polish notation. ! 08-06-17 EWL, Change melting point at Ttrp to match triple point pressure of Leachman et al. ! 02-13-18 IHB, Update sublimation line model to match triple point (w/ AHH). ________________________________________________________________________________ #EOS !---Equation of state--- FEQ !Helmholtz equation of state for parahydrogen of Leachman et al. (2009). :TRUECRITICALPOINT: 32.938 15.538 !True EOS critical point [K, mol/L] (where dP/dD=0 and d^2P/dD^2=0 at constant T) :DOI: 10.1063/1.3160306 ? ?``````````````````````````````````````````````````````````````````````````````` ?Leachman, J.W., Jacobsen, R.T, Penoncello, S.G., and Lemmon, E.W., ? "Fundamental Equations of State for Parahydrogen, Normal Hydrogen, and Orthohydrogen," ? J. Phys. Chem. Ref. Data, 38(3):721-748, 2009. ? ?The uncertainty in density is 0.1% at temperatures from the triple point ? to 250 K and at pressures up to 40 MPa, except in the critical region, ? where an uncertainty of 0.2% in pressure is generally attained. In the ? region between 250 and 450 K and at pressures to 300 MPa, the ? uncertainty in density is 0.04%. At temperatures between 450 and 1000 ? K, the uncertainty in density increases to 1%. At pressures between 300 ? and 2000 MPa, the uncertainty in density is 8%. Speed of sound data are ? represented within 0.5% below 100 MPa. The estimated uncertainty for ? heat capacities is 1.0%. The estimated uncertainties of vapor pressures ? and saturated liquid densities calculated with the Maxwell criterion ? are 0.1% for each property. ? !``````````````````````````````````````````````````````````````````````````````` 13.8033 !Lower temperature limit [K] 1000.0 !Upper temperature limit [K] 2000000.0 !Upper pressure limit [kPa] 104.0 !Maximum density [mol/L] CPP !Pointer to Cp0 model 2.01588 !Molar mass [g/mol] 13.8033 !Triple point temperature [K] 7.041 !Pressure at triple point [kPa] 38.185 !Density at triple point [mol/L] 20.271 !Normal boiling point temperature [K] -0.219 !Acentric factor 32.938 1285.8 15.538 !Tc [K], pc [kPa], rhoc [mol/L] 32.938 15.538 !Reducing parameters [K, mol/L] 8.314472 !Gas constant [J/mol-K] 9 4 5 12 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms 0.01 1.0 4. 0. !a(i),t(i),d(i),l(i) -7.33375 0.6855 1. 0. 2.60375 1.0 1. 0. 4.66279 0.489 1. 0. 0.682390 0.774 2. 0. -1.47078 1.133 2. 0. 0.135801 1.386 3. 0. -1.05327 1.619 1. 1. 0.328239 1.162 3. 1. -0.0577833 3.96 2. 2. 2. -1.7437 -0.194 0.8048 1.5487 0. 0. 0. 0.0449743 5.276 1. 2. 2. -0.5516 -0.2019 1.5248 0.1785 0. 0. 0. 0.0703464 0.99 3. 2. 2. -0.0634 -0.0301 0.6648 1.28 0. 0. 0. -0.0401766 6.791 1. 2. 2. -2.1341 -0.2383 0.6832 0.6319 0. 0. 0. 0.119510 3.190 1. 2. 2. -1.7770 -0.3253 1.4930 1.7104 0. 0. 0. eta beta gamma epsilon EXP[eta*(delta-epsilon)^2+beta*(tau-gamma)^2] #AUX !---Auxiliary function for Cp0 CPP !Ideal gas heat capacity function for parahydrogen of Leachman et al. (2009). ? ?``````````````````````````````````````````````````````````````````````````````` ?Leachman, J.W., Jacobsen, R.T, Penoncello, S.G., and Lemmon, E.W., 2009. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1.0 8.314472 !Reducing parameters for T, Cp0 1 7 0 0 0 0 0 !Nterms: polynomial, exponential, cosh, sinh 2.5 0.0 4.30256 499.0 13.0289 826.5 -47.7365 970.8 50.0013 1166.2 -18.6261 1341.4 0.993973 5395.0 0.536078 10185.0 #AUX !---Auxiliary function for PX0 PX0 !Helmholtz energy ideal-gas function for parahydrogen of Leachman et al. (2009). ? ?``````````````````````````````````````````````````````````````````````````````` ?Leachman, J.W., Jacobsen, R.T, Penoncello, S.G., and Lemmon, E.W., 2009. ? !``````````````````````````````````````````````````````````````````````````````` 1 2 7 0 0 0 0 0 !Nterms: ai*log(tau**ti); ai*tau**ti; ai*log(1-exp(bi*tau)) 1.5 1.0 !ai, ti for [ai*log(tau**ti)] terms -1.4485885457134948 0.0 !aj, ti for [ai*tau**ti] terms 1.8845208741487571 1.0 !aj, ti for [ai*tau**ti] terms 4.30256 499.0 !aj, ti for [ai*log(1-exp(-ti/T)] terms 13.0289 826.5 -47.7365 970.8 50.0013 1166.2 -18.6261 1341.4 0.993973 5395.0 0.536078 10185.0 #AUX !---Auxiliary function for PH0 PH0 !Ideal gas Helmholtz form for parahydrogen. ? ?``````````````````````````````````````````````````````````````````````````````` ?Leachman, J.W., Jacobsen, R.T, Penoncello, S.G., and Lemmon, E.W., 2009. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1 2 7 0 0 0 0 0 !Nterms: ai*log(tau**ti); ai*tau**ti; ai*log(1-exp(bi*tau)); cosh; sinh 1.5 1.0 !ai, ti for [ai*log(tau**ti)] terms -1.4485891134 0.0 !aj, ti for [ai*tau**ti] terms 1.884521239 1.0 4.30256 -15.1496751472 !aj, ti for [ai*log(1-exp(ti*tau)] terms 13.0289 -25.0925982148 -47.7365 -29.4735563787 50.0013 -35.4059141417 -18.6261 -40.724998482 0.993973 -163.7925799988 0.536078 -309.2173173842 -------------------------------------------------------------------------------- @EOS !---Equation of state--- BWR !MBWR equation of state for parahydrogen of Younglove (1982). ? ?``````````````````````````````````````````````````````````````````````````````` ?Younglove, B.A., ? "Thermophysical Properties of Fluids. I. Argon, Ethylene, ? Parahydrogen, Nitrogen, Nitrogen Trifluoride, and Oxygen," ? J. Phys. Chem. Ref. Data, Vol. 11, Suppl. 1, pp. 1-11, 1982. ? ?The uncertainties in density are 0.1% in the liquid phase, 0.25% in the ? vapor phase, and 0.2% in the supercritical region. The uncertainty in ? heat capacity is 3% and the uncertainty in speed of sound is 2% in the ? liquid phase and 1% elsewhere. ? ?Note: ? The ideal gas equation was refit from calculations of piecewise Cp0 equation ? of McCarty ? !``````````````````````````````````````````````````````````````````````````````` 13.8 !Lower temperature limit [K] 400.0 !Upper temperature limit [K] 121000.0 !Upper pressure limit [kPa] 44.0 !Maximum density [mol/L] CP1 !Pointer to Cp0 model 2.01594 !Molar mass [g/mol] 13.8 !Triple point temperature [K] 7.042 !Pressure at triple point [kPa] 38.21 !Density at triple point [mol/L] 20.2769 !Normal boiling point temperature [K] -0.218 !Acentric factor 32.938 1283.77 15.556 !Tc [K], pc [kPa], rhoc [mol/L] 32.938 15.556 !Reducing parameters [K, mol/L] 15.6173762 !gamma 0.0831434 !Gas constant [L-bar/mol-K] 32 1 !Nterm, Ncoeff per term 0.0004675528393416 0.04289274251454 -0.5164085596504 2.961790279801 -30.27194968412 0.1908100320379e-4 -0.001339776859288 0.3056473115421 51.61197159532 0.1999981550224e-6 0.0002896367059356 -0.02257803939041 -0.2287392761826e-5 0.2446261478645e-4 -0.001718181601119 -0.5465142603459e-6 0.4051941401315e-8 0.1157595123961e-5 -0.1269162728389e-7 -49.83023605519 -160.6676092098 -0.192679918531 9.319894638928 -0.0003222596554434 0.001206839307669 -0.384158819747e-6 -0.4036157453608e-4 -0.1250868123513e-9 0.1976107321888e-8 -0.2411883474011e-12 -0.4127551498251e-12 0.891797288361e-11 @AUX !---Auxiliary function for Cp0 CP1 !Ideal gas heat capacity function for parahydrogen. ? ?``````````````````````````````````````````````````````````````````````````````` ?refit by EWL from calculations of piecewise fit of Cp0 by McCarty ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1.0 8.31434 !Reducing parameters for T, Cp0 6 4 0 0 0 0 0 !Nterms: polynomial, exponential, cosh, sinh 2.4995169 0.0 -0.0011125185 1.0 0.00027491461 1.5 -0.000010005269 2.0 0.22695404e-8 3.0 -0.21031029e-12 4.0 12.353388 598.0 -17.777676 778.0 6.4309174 1101.0 7.3347521 6207.0 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ #ETA !---Viscosity--- VS7 !Pure fluid viscosity model from symbolic regression for parahydrogen of Muzny et al. (2013). :DOI: 10.1021/je301273j ? ?``````````````````````````````````````````````````````````````````````````````` ?Muzny, C.D., Huber, M.L., and Kazakov, A.F., ? "Correlation for the Viscosity of Normal Hydrogen Obtained from Symbolic Regression," ? J. Chem. Eng. Data, 58:969-979, 2013. ? ?The estimated uncertainty is 4 % for the saturated liquid from the triple point to 31 K, with larger deviations ? as the critical region is approached. The estimated uncertainty is 4 % for the supercritical fluid phase at pressures to 200 MPa. ? For the limited range of 200 K to 400 K at pressures up to 0.1 MPa, the uncertainty is 0.1 %. ? !``````````````````````````````````````````````````````````````````````````````` 13.8033 !Lower temperature limit [K] 2000.0 !Upper temperature limit [K] 2000000.0 !Upper pressure limit [kPa] 104.0 !Maximum density [mol/L] NUL !Pointer to collision integral model ! !Dilute gas function $DG RED SUMLOGT:5 EXP CNST SQR * INV SUM:1 CNST * SQRT * ! !Second viscosity virial function $VV RED SUM:7 CNST CUBE * ! !Residual function $RF RED SUM:3 SUM:1 SUM:2 / + EXP SUM:1 * ! !Coefficients $CF 0.021357 30.41 1. 0. 0 !Reducing parameters for eta, T, rho 0.209630 0. 0. 0. 0 ! s1*LOG(Ts) Coefficient to match Moldover -0.455274 1. 0. 0. 0 ! s2*LOG(Ts) 0.143602 2. 0. 0. 0 ! s3*LOG(Ts)^2 -0.0335325 3. 0. 0. 0 ! s4*LOG(Ts)^3 0.00276981 4. 0. 0. 0 ! s5*LOG(Ts)^4 0.297 0. 0. 0. 0 ! e3^2*EXP(above) 2.01588 1. 0. 0. 0 ! e2*T (use below) 30.41 0. 0. 0. 0 ! SQRT(e2*T*Tred) !Virial terms 0.6022137 30.41 1. 0. 0 !Reducing parameters for eta, T, rho -0.187 0. 0. 0. 0 ! b2 2.4871 -1. 0. 0. 0 ! b3/Ts 3.7151 -2. 0. 0. 0 ! b4/Ts^2 -11.0972 -3. 0. 0. 0 ! b5/Ts^3 9.0965 -4. 0. 0. 0 ! b6/Ts^4 -3.8292 -5. 0. 0. 0 ! b7/Ts^5 0.5166 -6. 0. 0. 0 ! b8/Ts^6 0.297 0. 0. 0. 0 ! b9^3*sum(above) !Residual function terms 1000. 33.145 45.096479408 0. 0 !Reducing parameters for eta, T, rho 0.0456334068 1. 0. 0. 0 ! a2*Tr 0.232797868 -1. 0. 0. 0 ! a3/Tr 0.363576595 0. 6. 0. 0 ! a6*Dr^6 0.958326120 0. 2. 0. 0 ! a4*Dr^2 0.127941189 0. 0. 0. 0 ! a5 1.0 1. 0. 0. 0 ! [a4*Dr^2 from above]/(a5+Tr) 0.00643449673 0. 2. 0. 0 ! a1*Dr^2*EXP(above) NUL !Pointer to the viscosity critical enhancement auxiliary function (none used) ================================================================================ #TCX !---Thermal conductivity--- TC1 !Pure fluid thermal conductivity model for parahydrogen of Assael et al. (2011). :DOI: 10.1063/1.3606499 ? ?``````````````````````````````````````````````````````````````````````````````` ?Assael, M.J., Assael. J.-A.M., Huber, M.L., Perkins, R.A., and Takata, Y., ? "Correlation of the Thermal Conductivity of Normal and Parahydrogen ? from the Triple Point to 1000 K and up to 100 MPa," ? J. Phys. Chem. Ref. Data, 40(3), 033101, 2011. ? ?For the region from the triple point to 300 K at pressures to 20 MPa, the estimated uncertainty ? is 4%, with the exception of the critical region. The uncertainty is estimated to ? be 6% for temperatures from 400 K to 1000 K and pressures to 100 MPa. The correlation behaves ? in a physically reasonable manner for extrapolations to higher pressures at temperatures ? below 400 K, but will be subject to larger uncertainties. ? !``````````````````````````````````````````````````````````````````````````````` 13.8033 !Lower temperature limit [K] 1000.0 !Upper temperature limit [K] 2000000.0 !Upper pressure limit [kPa] 104.0 !Maximum density [mol/L] 8 7 !# terms for dilute gas function: numerator, denominator 1.0 0.001 !Reducing parameters for T, tcx -1245. 0. 9418.06 1. -305.098 2. 6.88449 3. -0.0558871 4. 2.79243e-4 5. -4.06944e-7 6. 3.42309e-10 7. 14230.4 0. -588.749 1. 14.5983 2. -0.13483 3. 6.19047e-4 4. -9.21777e-7 5. 7.83099e-10 6. 10 0 !# terms for background gas function: numerator, denominator 32.938 15.538 1. !Reducing parameters for T, rho, tcx 0.0265975 0. 1. 0. -0.00133826 0. 2. 0. 0.0130219 0. 3. 0. -0.00567678 0. 4. 0. -0.92338e-4 0. 5. 0. -0.00121727 1. 1. 0. 0.00366663 1. 2. 0. 0.00388715 1. 3. 0. -0.00921055 1. 4. 0. 0.00400723 1. 5. 0. TK3 !Pointer to critical enhancement auxiliary function #AUX !---Auxiliary function for the thermal conductivity critical enhancement TK3 !Simplified thermal conductivity critical enhancement for parahydrogen of Assael et al. (2011). ? ?``````````````````````````````````````````````````````````````````````````````` ?Assael, M.J., Assael. J.-A.M., Huber, M.L., Perkins, R.A., and Takata, Y., 2011. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 9 0 0 0 !# terms: terms, spare, spare, spare 1.0 1.0 1.0 !Reducing parameters for T, rho, tcx [mW/(m-K)] 0.63 !Nu (universal exponent) 1.2415 !Gamma (universal exponent) 1.01 !R0 (universal amplitude) 0.065 !Z (universal exponent--not used for t.c., only viscosity) 1.0 !C (constant in viscosity eqn = 1/[2 - (alpha + gamma)/(2*nu)], but often set to 1) 0.15e-9 !Xi0 (amplitude) [m] 0.052 !Gam0 (amplitude) [-] 0.5e-9 !Qd_inverse (modified effective cutoff parameter) [m] 49.407 !Tref (reference temperature) [K] ******************************************************************************** @ETA !---Viscosity--- VS4 !Pure fluid generalized friction theory viscosity model for parahydrogen of Quinones-Cisneros et al. (2011). ? ?``````````````````````````````````````````````````````````````````````````````` ?Quinones-Cisneros, S.E., Huber, M.L., and Deiters, U.K., ? model of 27-jan-2011 unpublished ? !``````````````````````````````````````````````````````````````````````````````` 13.8033 !Lower temperature limit [K] 1000.0 !Upper temperature limit [K] 2000000.0 !Upper pressure limit [kPa] 104.0 !Maximum density [mol/L] 8 1 2 0 0 0 !Number of terms associated with dilute-gas function NUL !Pointer to reduced effective collision cross-section model; not used 0.2827 !Lennard-Jones coefficient sigma [nm];not used 59.7 !Lennard-Jones coefficient epsilon/kappa [K];not used 32.938 1.0 !Reducing parameters for T, eta 0.0 0.5 !Chapman-Enskog term; not used here !use for extra pieces? 7.7144542105280585 0.0 -36.82065170523866 0.25 68.49882398219104 0.50 -58.00162637079715 0.75 27.013888066380914 1.0 -5.55928755948473 1.25 0.46490717320145977 1.50 1. 0.75 !Additional special terms for numerator 1. 0.0 !Additional special terms for denominator 1. 1.0 !Additional special terms for denominator 7 !Number of terms for initial density dependence 1.0 0.0157768 !Reducing parameters for T (= eps/k), etaB2 (= 0.6022137*sigma**3) -0.187 0.0 !Coefficient, power in T* = T/(eps/k) 75.6327 -1.0 3435.61 -2.0 -312078. -3.0 7779290. -4.0 -99584100. -5.0 408557000. -6.0 -0.03768564675677641 0.02238493598199995 0.006424167560123974 -5.723254060608424e-7 0.0 ! a(0),a(1),a(2) -0.04897821165342249 -0.05786784231898735 0.016640614921653815 -4.352926821749732e-6 0.0 ! b(0),b(1),b(2) 0.0 0.0 0.0 0.0 0.0 ! c(0),c(1),c(2) -3.046799839803415e-5 8.228692086410122e-5 1.8647927082356328e-5 -4.59581250908383e-10 0.0 ! A(0),A(1),A(2) 1.232548095616199e-4 1.2379026782334722e-4 7.504884568669591e-6 1.9436562071471596e-8 0.0 ! B(0),B(1),B(2) 0.0 0.0 0.0 0.0 0.0 ! C(0),C(1),C(2) 3.1464688766415165e-7 4.304432732999407e-7 -7.96709495655157e-8 0.0 0.0 ! D(0),D(1),D(2) 0.0 0.0 0.0 0.0 0.0 ! E(0),E(1),E(2) NUL !Pointer to the viscosity critical enhancement auxiliary function (none used) ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ @TRN !---ECS Transport--- ECS !Extended Corresponding States model (Nitrogen reference); predictive mode for parahydrogen. ? ?``````````````````````````````````````````````````````````````````````````````` ?Klein, S.A., McLinden, M.O., and Laesecke, A., "An Improved Extended Corresponding States Method for Estimation of Viscosity of Pure Refrigerants and Mixtures," Int. J. Refrigeration, 20(3):208-217, 1997. doi: 10.1016/S0140-7007(96)00073-4. ?McLinden, M.O., Klein, S.A., and Perkins, R.A., "An Extended Corresponding States Model for the Thermal Conductivity of Refrigerants and Refrigerant Mixtures," Int. J. Refrigeration, 23(1):43-63, 2000. doi: 10.1016/S0140-7007(99)00024-9 ? ?The Lennard-Jones parameters are for H2 from Reid, R.C., Prausnitz, J.M., and Poling, B.E., "The Properties of Gases and Liquids," 4th edition, New York, McGraw-Hill Book Company, 1987. ? !``````````````````````````````````````````````````````````````````````````````` 13.8 !Lower temperature limit [K] 400.0 !Upper temperature limit [K] 121000.0 !Upper pressure limit [kPa] 66.94 !Maximum density [mol/L] FEQ NITROGEN.FLD VS1 !Model for reference fluid viscosity TC1 !Model for reference fluid thermal conductivity NUL !Large molecule identifier 1 !Lennard-Jones flag (0 or 1) (0 => use estimates) 0.2827 !Lennard-Jones coefficient sigma [nm] for ECS method 59.7 !Lennard-Jones coefficient epsilon/kappa [K] for ECS method 1 0 0 !Number of terms in f_int term in Eucken correlation, spare1, spare2 0.00132 0. 0. 0. !Coefficient, power of T, spare1, spare2 1 0 0 !Number of terms in psi (visc shape factor): poly,spare1,spare2 1.0 0. 0. 0. !Coefficient, power of Tr, power of Dr, spare 1 0 0 !Number of terms in chi (t.c. shape factor): poly,spare1,spare2 1.0 0. 0. 0. !Coefficient, power of Tr, power of Dr, spare TK3 !Pointer to critical enhancement auxiliary function ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #STN !---Surface tension--- ST1 !Surface tension model for parahydrogen of Mulero et al. (2012). :DOI: 10.1063/1.4768782 ? ?``````````````````````````````````````````````````````````````````````````````` ?Mulero, A., Cachadiņa, I., and Parra, M.I., ? "Recommended Correlations for the Surface Tension of Common Fluids," ? J. Phys. Chem. Ref. Data, 41(4), 043105, 2012. doi: 10.1063/1.4768782 ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1 !Number of terms in surface tension model 32.938 !Critical temperature used in fit (dummy) 0.005314 1.06 !Sigma0 and n #DE !---Dielectric constant--- DE3 !Dielectric constant model for parahydrogen of Harvey and Lemmon (2005). :DOI: 10.1007/s10765-005-2351-5 ? ?``````````````````````````````````````````````````````````````````````````````` ?Harvey, A.H. and Lemmon, E.W., ? "Method for Estimating the Dielectric Constant of Natural Gas Mixtures," ? Int. J. Thermophys., 26(1):31-46, 2005. doi: 10.1007/s10765-005-2351-5 ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 273.16 1000.0 1.0 !Reducing parameters for T and D 0 2 3 0 0 0 !Number of terms in dielectric constant model 2.0297 0. 1. 0. !Coefficient, T exp, D exp 0.0069 1. 1. 0. 0.181 0. 2. 0. 0.021 1. 2. 0. -7.4 0. 3. 0. #MLT !---Melting line--- MLP !Melting line model for parahydrogen of Younglove (1982). :DOI: :WEB: https://srd.nist.gov/JPCRD/jpcrdS1Vol11.pdf ? ?``````````````````````````````````````````````````````````````````````````````` ?Younglove, B.A., ? "Thermophysical Properties of Fluids. I. Argon, Ethylene, ? Parahydrogen, Nitrogen, Nitrogen Trifluoride, and Oxygen," ? J. Phys. Chem. Ref. Data, Vol. 11, Suppl. 1, pp. 1-11, 1982. ? !``````````````````````````````````````````````````````````````````````````````` 13.8 !Lower temperature limit [K] 400.0 !Upper temperature limit [K] 0. ! 0. ! 1. 1000. !Reducing temperature and pressure 4 0 0 0 0 0 !Number of terms in melting line equation -26.5289115 0.0 !Coefficients and exponents 0.248578596 1.764739 -21.2823393 0.0 0.125746643 1.955 #SBL !---Sublimation line--- SB2 !Sublimation line model for parahydrogen of Brown and Zeigler (2009). :DOI: 10.1007/978-1-4613-9856-1_76 ? ?``````````````````````````````````````````````````````````````````````````````` ?Based on G.N. Brown and W.T. Ziegler, Adv. Cryo. Eng., 25:662-670, 1979. ? Modified to match the triple point of the equation of state. ? !``````````````````````````````````````````````````````````````````````````````` 0.0 !Lower temperature limit [K] 13.8 !Upper temperature limit [K] 0. ! 0. ! 1.0 1000.0 !Reducing temperature and pressure 6 0 0 0 0 0 !Number of terms in sublimation line equation 4.78288 0.0 !Coefficients and exponents -1.485636e2 -1.0 2.32321e2 -2.0 -5.60207e2 -3.0 6.64126e2 -4.0 -2.8906e2 -5.0 #PS !---Vapor pressure--- PS5 !Vapor pressure equation for parahydrogen of Leachman et al. (2009). ? ?``````````````````````````````````````````````````````````````````````````````` ?Functional Form: P=Pc*EXP[SUM(Ni*Theta^ti)*Tc/T] where Theta=1-T/Tc, Tc and Pc ? are the reducing parameters below, which are followed by rows containing Ni and ti. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 32.938 1285.8 !Reducing parameters 4 0 0 0 0 0 !Number of terms in equation -4.87767 1.0 1.03359 1.5 0.826680 2.65 -0.129412 7.4 #DL !---Saturated liquid density--- DL1 !Saturated liquid density equation for parahydrogen of Lemmon (2010). ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, C.K. and Lemmon, E.W., 2010. ? ?Functional Form: D=Dc*[1+SUM(Ni*Theta^ti)] where Theta=1-T/Tc, Tc and Dc are ? the reducing parameters below, which are followed by rows containing Ni and ti. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 32.938 15.538 !Reducing parameters 5 0 0 0 0 0 !Number of terms in equation -0.13509 0.15 4.0739 0.44 -5.3985 0.7 5.5230 0.99 -2.3643 1.31 #DV !---Saturated vapor density--- DV3 !Saturated vapor density equation for parahydrogen of Lemmon (2010). ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, C.K. and Lemmon, E.W., 2010. ? ?Functional Form: D=Dc*EXP[SUM(Ni*Theta^ti)] where Theta=1-T/Tc, Tc and Dc are ? the reducing parameters below, which are followed by rows containing Ni and ti. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 32.938 15.538 !Reducing parameters 6 0 0 0 0 0 !Number of terms in equation -5.7545 0.53 3.8153 0.7 -12.293 1.7 15.095 2.4 -17.295 3.3 -34.190 10.0 @END c 1 2 3 4 5 6 7 8 c2345678901234567890123456789012345678901234567890123456789012345678901234567890 @ETA !Viscosity model specification VS0 pure fluid viscosity model of McCarty and Weber (1972). ? ?``````````````````````````````````````````````````````````````````````````````` ?McCarty, R.D. and Weber, L.A., ? "Thermophysical properties of parahydrogen from the freezing liquid line to ? 5000 R for pressures to 10,000 psia," ? Natl. Bur. Stand., Tech. Note 617, 1972. ? ?The uncertainty in viscosity ranges from 4% to 15%. ? !``````````````````````````````````````````````````````````````````````````````` 13.8 !Lower temperature limit [K] 1000.0 !Upper temperature limit [K] 121000.0 !Upper pressure limit [kPa] 66.94 !Maximum density [mol/L] H2 !Pointer to hardcoded thermal conductivity model 0 9 8 0 0 0 0 0 !Number of terms for various pieces 1.0 1.0 1.0 !Reducing parameters for T, rho, eta -18.41091042788 0. 0. 0. 0 !Dilute gas coeffs 31.85762039455 0. 0. 0. 0 -23.08233586574 0. 0. 0. 0 9.129812714730 0. 0. 0. 0 -2.163626387630 0. 0. 0. 0 0.3175128582601 0. 0. 0. 0 -0.02773173035271 0. 0. 0. 0 0.001347359367871 0. 0. 0. 0 -0.2775671778154e-4 0. 0. 0. 0 -10.99981128000 0. 0. 0. 0 !Residual coeffs 18.95876508000 0. 0. 0. 0 -381.3005056000 0. 0. 0. 0 59.50473265000 0. 0. 0. 0 1.099399458000 0. 0. 0. 0 8.987269839000 0. 0. 0. 0 1231.422148000 0. 0. 0. 0 0.311 0. 0. 0. 0 NUL !Pointer to the viscosity critical enhancement auxiliary function (none used) @ETA !Viscosity model specification VS0 pure fluid viscosity model from symbolic regression (Muzny, Huber, Kazakov) (2013). ? ?``````````````````````````````````````````````````````````````````````````````` ?Muzny, C.D., Huber, M.L., and Kazakov, A.F., ? "Correlation for the Viscosity of normal hydrogen obtained from symbolic regression" ? submitted to J. Chem. Eng. Data, 2013 ? ?The estimated uncertainty is 4 % for the saturated liquid from the triple point to 31 K, with larger deviations ? as the critical region is approached. The estimated uncertainty is 4 % for the supercritical fluid phase at pressures to 200 MPa. ? For the limited range of 200 K to 400 K at pressures up to 0.1 MPa, the uncertainty is 0.1 %. ? !``````````````````````````````````````````````````````````````````````````````` 13.8033 !Lower temperature limit [K] 2000.0 !Upper temperature limit [K] 2000000.0 !Upper pressure limit [kPa] 104.0 !Maximum density [mol/L] H2A !Pointer to hardcoded model 0 0 0 0 0 0 0 0 !Number of terms for various pieces 1.0 1.0 1.0 !Reducing parameters for T, rho, eta NUL !Pointer to the viscosity critical enhancement auxiliary function (none used) @SBL !---Sublimation line--- SB2 !Sublimation line model for parahydrogen of McCarty et al. (1981). ? ?``````````````````````````````````````````````````````````````````````````````` ?McCarty, R.D., Hord, J., and Roder, H.M., ? "Selected Properties of Hydrogen (Engineering Design Data)," ? NBS Monograph 168, National Bureau of Standards, Boulder, 1981. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 13.8 !Upper temperature limit [K] 0. ! 0. ! 1. 0.13332237 !Reducing temperature and pressure 2 0 1 0 0 0 !Number of terms in sublimation line equation 4.009857354 0.0 !Coefficients and exponents -90.77568949 -1.0 2.489830940 1.0