Deuterium !Short name 7782-39-0 !CAS number Deuterium !Full name D2 !Chemical formula {D2} Deuterium !Synonym 4.0282 !Molar mass [g/mol] 18.724 !Triple point temperature [K] 23.661 !Normal boiling point [K] 38.34 !Critical temperature [K] 1679.6 !Critical pressure [kPa] 17.23 !Critical density [mol/L] -0.136 !Acentric factor 0.0 !Dipole moment [Debye]; (exactly zero due to symmetry) NBP !Default reference state 10.0 !Version number 1957 !UN Number :UN: cryogen !Family :Family: ???? !Heating value (upper) [kJ/mol] :Heat: 1S/H2/h1H/i1+1D !Standard InChI String :InChi: UFHFLCQGNIYNRP-VVKOMZTBSA-N !Standard InChI Key :InChiKey: 8d757b40 (hydrogen) !Alternative fluid for mixing rules :AltID: 639b18a0 !Hash number from InChI Key :Hash: !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 ! 04-03-98 EWL, Original version. ! 06-21-10 CKL, Add ancillary equations. ! 12-06-12 EWL, Add surface tension coefficients of Mulero et al. (2012). ! 02-14-13 IAR, Add ancillary equations. ! 02-14-13 IAR, Add new equation of state of Richardson. ! 02-28-13 MLH, Add scaled hydrogen viscosity and thermal conductivity as estimates for deuterium. ! 05-15-17 EWL, Change the hard coded VS0 model to the VS7 reverse Polish notation. ________________________________________________________________________________ #EOS !---Equation of state--- FEQ !Helmholtz equation of state for deuterium of Richardson et al. (2014). :TRUECRITICALPOINT: 38.34 17.23 !True EOS critical point [K, mol/L] (where dP/dD=0 and d^2P/dD^2=0 at constant T) :DOI: 10.1063/1.4864752 ? ?``````````````````````````````````````````````````````````````````````````````` ?Richardson, I.A., Leachman, J.W., and Lemmon, E.W., ? J. Phys. Chem. Ref. Data, 43(1), 013103, 2014. ? ?The uncertainty in density is 0.5% over the full temperature and pressure ranges ? of validity of the equation of state. The uncertainties in vapor pressure and ? saturated liquid density are 2% and 3%, respectively, while speed-of-sound ? values have an uncertainty of 1% in the liquid phase. ? !``````````````````````````````````````````````````````````````````````````````` 18.724 !Lower temperature limit [K] 600.0 !Upper temperature limit [K] 2000000.0 !Upper pressure limit [kPa] 43.351 !Maximum density [mol/L] CPP !Pointer to Cp0 model 4.0282 !Molar mass [g/mol] 18.724 !Triple point temperature [K] 17.189 !Pressure at triple point [kPa] 43.351 !Density at triple point [mol/L] 23.661 !Normal boiling point temperature [K] -0.136 !Acentric factor 38.34 1679.6 17.23 !Tc [K], pc [kPa], rhoc [mol/L] 38.34 17.23 !Reducing parameters [K, mol/L] 8.3144598 !Gas constant [J/mol-K] 14 4 7 12 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms 0.006267958 1.0 4. 0. !a(i),t(i),d(i),l(i) 10.53609 0.462 1. 0. -10.14149 0.5584 1. 0. 0.3560610 0.627 2. 0. 0.1824472 1.201 3. 0. -1.129638 0.309 1. 0. -0.0549812 1.314 3. 0. -0.6791329 1.1166 2. 0. 1.347918 1.25 2. 1. -0.8657582 1.25 2. 1. 1.719146 1.395 1. 2. -1.917977 1.627 1. 2. 0.1233365 1.0 3. 2. -0.07936891 2.5 2. 2. 1.686617 0.635 1. 2. 2. -0.868 -0.613 0.6306 1.460 0. 0. 0. -4.240326 0.664 1. 2. 2. -0.636 -0.584 0.7110 1.7864 0. 0. 0. 1.857114 0.7082 2. 2. 2. -0.668 -0.570 0.6446 1.647 0. 0. 0. -0.5903705 2.25 3. 2. 2. -0.650 -1.056 0.8226 0.541 0. 0. 0. 1.520171 1.524 3. 2. 2. -0.745 -1.010 0.9920 0.969 0. 0. 0. 2.361373 0.67 1. 2. 2. -0.782 -1.025 1.2184 1.892 0. 0. 0. -2.297315 0.709 3. 2. 2. -0.693 -1.029 1.2030 1.076 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 deuterium of Richardson et al. (2014). ? ?``````````````````````````````````````````````````````````````````````````````` ?Richardson, I.A., Leachman, J.W., and Lemmon, E.W., 2014. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1.0 8.3144598 !Reducing parameters for T, Cp0 1 12 0 0 0 0 0 !Nterms: polynomial, exponential, cosh, sinh 2.5 0.0 -3.54145 7174.1 3.0326 8635.0 -3.52422 902.7 -1.73421 181.1 -3.57135 438.5 2.14858 5034.2 6.23107 269.9 -3.30425 229.9 6.23098 666.4 -3.57137 452.8 3.32901 192.0 0.97782 1187.6 #AUX !---Auxiliary function for PX0 PX0 !Helmholtz energy ideal-gas function for deuterium of Richardson et al. (2014). ? ?``````````````````````````````````````````````````````````````````````````````` ?Richardson, I.A., Leachman, J.W., and Lemmon, E.W., 2014. ? !``````````````````````````````````````````````````````````````````````````````` 1 2 12 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 -2.0677350466039846 0.0 !aj, ti for [ai*tau**ti] terms 2.4237150686246927 1.0 !aj, ti for [ai*tau**ti] terms -3.54145 7174.1 !aj, ti for [ai*log(1-exp(-ti/T)] terms 3.0326 8635.0 -3.52422 902.7 -1.73421 181.1 -3.57135 438.5 2.14858 5034.2 6.23107 269.9 -3.30425 229.9 6.23098 666.4 -3.57137 452.8 3.32901 192.0 0.97782 1187.6 #AUX !---Auxiliary function for PH0 PH0 !Ideal gas Helmholtz form for deuterium. ? ?``````````````````````````````````````````````````````````````````````````````` ?Richardson, I.A., Leachman, J.W., and Lemmon, E.W., 2014. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1 2 12 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 -2.0677351753 0.0 !aj, ti for [ai*tau**ti] terms 2.4237151502 1.0 -3.54145 -187.1178925404 !aj, ti for [ai*log(1-exp(ti*tau)] terms 3.0326 -225.2217005738 -3.52422 -23.544600939 -1.73421 -4.7235263432 -3.57135 -11.4371413667 2.14858 -131.3041210224 6.23107 -7.0396452791 -3.30425 -5.9963484611 6.23098 -17.381324987 -3.57137 -11.8101199791 3.32901 -5.0078247261 0.97782 -30.9754825248 -------------------------------------------------------------------------------- @EOS !---Equation of state--- BWR !MBWR equation of state for deuterium of McCarty (1989). ? ?``````````````````````````````````````````````````````````````````````````````` ?McCarty, R.D., ? "Correlations for the Thermophysical Properties of Deuterium," ? unpublished correlation. ? National Institute of Standards and Technology, Boulder, CO, 1989. ? All temperatures on IPTS-68. ? !``````````````````````````````````````````````````````````````````````````````` 18.71 !Lower temperature limit [K] 423.0 !Upper temperature limit [K] 320000.0 !Upper pressure limit [kPa] 43.38 !Maximum density [mol/L] CP1 !Pointer to Cp0 model 4.0282 !Molar mass [g/mol] 18.71 !Triple point temperature [K] 19.462 !Pressure at triple point [kPa] 43.365 !Density at triple point [mol/L] 23.3097 !Normal boiling point temperature [K] -0.175 !Acentric factor 38.34 1665.3 17.327 !Tc [K], pc [kPa], rhoc [mol/L] 38.34 17.327 !Reducing parameters [K, mol/L] 17.3279988559019 !gamma 0.0831434 !Gas constant [L-bar/mol-K] 32 1 !Nterm, Ncoeff per term 0.4894244053982e-4 0.05600164604601 -0.6301493491211 2.538329946038 172.3475985309 0.2956238369436e-4 -0.003926317169317 0.01195764193293 11369.16678824 -0.1916378195727e-6 0.0003153535946452 0.0212293733507 -0.1057999371607e-5 -0.6722062598854e-4 -0.3030166828627 0.1980817195099e-5 -0.1453922641871e-7 0.0001780919116891 -0.1823145348424e-5 -11353.58616578 -1943.542941899 -36.3284766958 108.774511838 -0.04078276062687 0.006460021864005 -0.4480242189217e-4 -0.0002475011206216 -0.883438465676e-8 -0.1081622159862e-8 -0.1478159334303e-10 0.7926922356112e-11 0.5721547329378e-11 @AUX !---Auxiliary function for Cp0 CP1 !Ideal gas heat capacity function for deuterium. ? ?``````````````````````````````````````````````````````````````````````````````` ?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 3 0 0 0 0 0 !Nterms: polynomial, exponential, cosh, sinh 2.4512991 0.0 0.0043563077 1.0 -0.0005316947 1.5 0.000017067184 2.0 -0.53819932e-8 3.0 0.89310438e-12 4.0 18.403263 319.0 -21.257617 361.0 4.1091635 518.0 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ #ETA !---Viscosity--- VS7 !Pure fluid viscosity model from symbolic regression for deuterium 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 uncertainties for deuterium are estimated to be approximately 5% in the gas and ? supercritical regions with larger deviations near the critical region and in the liquid phase. ? !``````````````````````````````````````````````````````````````````````````````` 18.724 !Lower temperature limit [K] 600.0 !Upper temperature limit [K] 2000000.0 !Upper pressure limit [kPa] 43.351 !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 * 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 * CNST * ! !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) 2. 0. 0. 0. 0 ! SQRT(2) for deuterium !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) 1.18 0. 0. 0. 0 ! *1.18 for deuterium NUL !Pointer to the viscosity critical enhancement auxiliary function (none used) ================================================================================ #TCX !---Thermal conductivity--- TC1 !Pure fluid thermal conductivity model for deuterium of Assael et al. (2011). :DOI: 10.1063/1.3606499 ? ?``````````````````````````````````````````````````````````````````````````````` ?unpublished; based on scaling the Assael correlation: ? 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):1-13, 2011. ? ?The uncertainties for deuterium are estimated to be approximately 5% in the gas ? and supercritical regions with larger deviations near the critical region and ? in the liquid phase. ? !``````````````````````````````````````````````````````````````````````````````` 18.724 !Lower temperature limit [K] 600.0 !Upper temperature limit [K] 2000000.0 !Upper pressure limit [kPa] 43.351 !Maximum density [mol/L] 7 4 !# terms for dilute gas function: numerator, denominator 1.0 0.001 !Reducing parameters for T, tcx dilute gas divided by sqrt2 -8779370. 0. 3564210. 1. -34002.5 2. 230.795 3. 0.0676148 4. 1.22675e-4 5. -2.21184e-8 6. 5043050. 0. -24375.3 1. 151.523 2. 1.0 3. 10 0 !# terms for background gas function: numerator, denominator 33.145 15.508 1. !Reducing parameters for T, rho, tcx 0.0363081 0. 1. 0. -0.0207629 0. 2. 0. 0.031481 0. 3. 0. -0.0143097 0. 4. 0. 0.0017498 0. 5. 0. 0.0018337 1. 1. 0. -0.00886716 1. 2. 0. 0.015826 1. 3. 0. -0.0106283 1. 4. 0. 0.00280673 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 deuterium 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) [-] 0.4e-9 !Qd_inverse (modified effective cutoff parameter) [m] 57.51 !Tref (reference temperature) [K] ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ @TRN !---ECS Transport--- ECS !Extended Corresponding States model (Nitrogen reference); fit to limited data for deuterium. ? ?``````````````````````````````````````````````````````````````````````````````` ?*** ESTIMATION METHOD *** NOT STANDARD REFERENCE QUALITY *** ?Unpublished; uses method described in the following reference: ?Huber, M.L., Laesecke, A., and Perkins, R.A. ? "Model for the Viscosity and Thermal Conductivity of Refrigerants, Including ? a New Correlation for the Viscosity of R134a," ? Ind. Eng. Chem. Res., 42(13):3163-3178, 2003. doi: 10.1021/ie0300880 ? ?Estimated uncertainty is 50%. ? ?The Lennard-Jones parameters were taken from Kestin, J. and Nagashima, A.,"Viscosity of the isotopes of hydrogen and their interatomic force potentials", Physics of Fluids, 7:730-734 (1964). ? !``````````````````````````````````````````````````````````````````````````````` 18.724 !Lower temperature limit [K] 600.0 !Upper temperature limit [K] 2000000.0 !Upper pressure limit [kPa] 43.351 !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) 0.2952 !Lennard-Jones coefficient sigma [nm] 35.2 !Lennard-Jones coefficient epsilon/kappa [K] 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 deuterium 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 38.34 !Critical temperature used in fit (dummy) 0.009376 1.258 !Sigma0 and n #PS !---Vapor pressure--- PS5 !Vapor pressure equation for deuterium of Richardson et al. (2014). ? ?``````````````````````````````````````````````````````````````````````````````` ?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. ! 38.34 1679.6 !Reducing parameters 5 0 0 0 0 0 !Number of terms in equation -5.5706 1.0 1.7631 1.5 -0.5458 2.83 1.2154 4.06 -1.1556 5.4 #DL !---Saturated liquid density--- DL1 !Saturated liquid density equation for deuterium of Richardson et al. (2014). ? ?``````````````````````````````````````````````````````````````````````````````` ?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. ! 38.34 17.23 !Reducing parameters 6 0 0 0 0 0 !Number of terms in equation 3.3769 0.512 -5.3693 1.12 11.943 1.8 -17.361 2.55 15.170 3.4 -6.3079 4.4 #DV !---Saturated vapor density--- DV3 !Saturated vapor density equation for deuterium of Richardson et al. (2014). ? ?``````````````````````````````````````````````````````````````````````````````` ?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. ! 38.34 17.23 !Reducing parameters 6 0 0 0 0 0 !Number of terms in equation -3.8111 0.528 -7.3624 2.03 2.2294 3.6 -21.443 5.0 12.796 6.5 -31.334 9.0 @END c 1 2 3 4 5 6 7 8 c2345678901234567890123456789012345678901234567890123456789012345678901234567890 0.2948 !Lennard-Jones coefficient sigma [nm] for ECS method 39.3 !Lennard-Jones coefficient epsilon/kappa [K] for ECS method @ETA !Viscosity model specification VS0 pure fluid viscosity model of Muzny et al. (2013). ? ?``````````````````````````````````````````````````````````````````````````````` ?unpublished; based on scaling the Muzny hydrogen correlation ? 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 uncertainties for deuterium are estimated to be approximately 5% in the gas and supercritical regions ? with larger deviations near the critical region and in the liquid phase. ? !``````````````````````````````````````````````````````````````````````````````` 18.724 !Lower temperature limit [K] 600.0 !Upper temperature limit [K] 2000000.0 !Upper pressure limit [kPa] 43.351 !Maximum density [mol/L] D2 !Pointer to hardcoded thermal conductivity model 0 1 1 0 0 0 0 0 !Number of terms for various pieces 1. 1. 1. !Reducing parameters for T, rho, eta 0. 0. 0. 0. 0 !Dilute gas coeffs 0. 0. 0. 0. 0 !Residual coeffs NUL !Pointer to the viscosity critical enhancement auxiliary function (none used)