diff --git a/CoolPropBibTeXLibrary.bib b/CoolPropBibTeXLibrary.bib index 553e45c8..264ae682 100644 --- a/CoolPropBibTeXLibrary.bib +++ b/CoolPropBibTeXLibrary.bib @@ -15,19 +15,6 @@ Timestamp = {2014.12.16} } -@ARTICLE{Kondou-IJR-2015, - author = {Chieko Kondou and Ryuichi Nagata and Noriko Nii and Shigeru Koyama - and Yukihiro Higashi}, - title = {Surface tension of low GWP refrigerants R1243zf, R1234ze(Z), and - R1233zd(E)}, - journal = {Int. J. Refrig.}, - year = {2015}, - volume = {53}, - pages = {80-89}, - owner = {ian}, - timestamp = {2015.07.18} -} - @Article{Abramson-HPR-2011, Title = {{Melting curves of argon and methane}}, Author = {Evan H. Abramson}, @@ -65,6 +52,18 @@ Timestamp = {2014.09.27} } +@Article{Akasaka-2008, + Title = {{A Reliable and Useful Method to Determine the Saturation State from Helmholtz Energy Equations of State}}, + Author = {Ryo Akasaka}, + Journal = {Journal of Thermal Science and Technology}, + Year = {2008}, + Pages = {442-451}, + Volume = {3}, + + Owner = {Belli}, + Timestamp = {2013.03.19} +} + @InProceedings{Akasaka-PU-2014, Title = {{A Thermodynamic Property Model for the R-134a/245fa Mixtures}}, Author = {Ryo Akasaka and Yukihiro Higashi}, @@ -138,6 +137,18 @@ Timestamp = {2013.07.07} } +@Article{Aly-1981, + Title = {Self-Consistent Equations for Calculating the Ideal Gas Specific Heat Capacity, Enthalpy, and Entropy}, + Author = {Fouad A. Aly and Lloyd L. Lee}, + Journal = {Fluid Phase Equilib.}, + Year = {1981}, + Pages = {169-179}, + Volume = {6}, + + Owner = {Belli}, + Timestamp = {2013.08.05} +} + @Book{ASHRAE2001, Title = {{2001 ASHRAE Handbook: Fundamentals}}, Author = {{American Society of Heating, Refrigerating and Air-Conditioning Engineers}}, @@ -298,6 +309,40 @@ Url = {http://pubs.acs.org/doi/abs/10.1021/ie4033999} } +@Conference{Bender-1970, + Title = {{Equations of state exactly representing the phase behavior of pure substances}}, + Author = {E. Bender}, + Booktitle = {Proc. 5th Symp. Thermophys. Prop.}, + Year = {1970}, + Pages = {227-235}, + + Owner = {Belli}, + Timestamp = {2013.05.04} +} + +@Article{Boned-2003, + Title = {{High-pressure dynamic viscosity and density of two synthetic hydrocarbon mixtures representative of some heavy petroleum distillation cuts}}, + Author = {C. Boned and C.K. Z{\'e}berg-Mikkelsen and A. Baylaucq and P. Daug{\'e}}, + Journal = {Fluid Phase Equilibria}, + Year = {2003}, + Pages = {143-164}, + Volume = {212}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + +@InBook{Brent-1973, + Title = {Algorithms for Minimization without Derivatives}, + Author = {R.P. Brent}, + Chapter = {4}, + Publisher = {Prentice-Hall}, + Year = {1973}, + + Owner = {Belli}, + Timestamp = {2013.04.23} +} + @Article{Buecker-JPCRD-2006, Title = {{A Reference Equation of State for the Thermodynamic Properties of Ethane for Temperatures from the Melting Line to 675 K and Pressures up to 900 MPa}}, Author = {D. Buecker and W. Wagner}, @@ -326,6 +371,16 @@ Timestamp = {2013.04.30} } +@Conference{Casella-2008, + Title = {{ExternalMedia: A Library for Easy Re-Use of External Fluid Property Code in Modelica}}, + Author = {Francesco Casella and Christoph Richter}, + Booktitle = {Modelica 2008, March 3rd-4th, 2008}, + Year = {2008}, + + Owner = {Belli}, + Timestamp = {2013.03.28} +} + @TechReport{Chichester-NIST-2008, Title = {{NISTIR 6650: Documentation and Assessment of the Transport Property Model for Mixtures Implemented in NIST REFPROP (Version 8.0)}}, Author = {Justin C. Chichester and Marcia L. Huber}, @@ -336,6 +391,18 @@ Timestamp = {2013.04.08} } +@Article{Chung-IECR-1988, + Title = {{Generalized Multiparameter Correlation for Nonpolar and Polar Fluid Transport Properties}}, + Author = {Ting-Horng Chung and Mohammad Ajlan and Lloyd L. Lee and Kenneth E. Starling}, + Journal = {Ind. Eng. Chem. Res.}, + Year = {1988}, + Pages = {671-679}, + Volume = {27}, + + Owner = {Belli}, + Timestamp = {2013.05.20} +} + @Article{Colonna-FPE-2008, Title = {{Multiparameter equations of state for siloxanes: [(CH3)3-Si-O1/2]2-[O-Si-(CH3)2]i=1,...,3, and [O-Si-(CH3)2]6}}, Author = {P. Colonna and N.R. Nannan and A. Guardone}, @@ -382,6 +449,18 @@ Author = {{Eastman Chemical Company}} } +@Article{EstellaUribe-2003, + Title = {Extended corresponding states model for fluids and fluid mixtures I. Shape factor model for pure fluids}, + Author = {J.F. Estela-Uribe and J.P.M. Trusler}, + Journal = {Fluid Phase Equilibria}, + Year = {2003}, + Pages = {15-40}, + Volume = {204}, + + Owner = {Belli}, + Timestamp = {2013.05.29} +} + @Article{Fenghour-JPCRD-1998, Title = {{The Viscosity of Carbon Dioxide}}, Author = {A. Fenghour and W.A. Wakeham and V. Vesovic}, @@ -527,6 +606,18 @@ Timestamp = {2013.04.08} } +@Article{Guo-1997, + Title = {{Viscosity model based on equations of state for hydrocarbon liquids and gases}}, + Author = {X.-Q. Guo and L.-S. Wang and S.-X. Rong and T.-M. Guo}, + Journal = {Fluid Phase Equilibria}, + Year = {1997}, + Pages = {405-421}, + Volume = {139}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + @Article{Hands-CRYO-1981, Title = {{A Correlation of Thermal Conductivity Data for Helium}}, Author = {B.A. Hands and V.D. Arp}, @@ -554,6 +645,16 @@ Timestamp = {2013.04.08} } +@TechReport{Herrmann-2009, + Title = {ASHRAE RP-1485: Thermodynamic Properties of Real Moist Air, Dry Air, Steam, Water, and Ice}, + Author = {S. Herrmann and H.-J. Kretzschmar and D.P. Gatley}, + Institution = {ASHRAE}, + Year = {2009}, + + Owner = {Belli}, + Timestamp = {2013.05.29} +} + @Article{Herrmann2009, Title = {{Thermodynamic Properties of Real Moist Air, Dry Air, Steam, Water, and Ice (RP-1485)}}, Author = {Herrmann, Sebastian and Kretzschmar, Hans-Joachim and Gatley, Donald P.}, @@ -583,6 +684,19 @@ Timestamp = {2013.04.08} } +@InBook{Huber-1996, + Title = {The Corresponding-States Principle: Dense Fluids}, + Author = {M.L. Huber and H.J.M. Hanley}, + Chapter = {12}, + Editor = {Jurgen Millat and J.H. Dymond and C.A. Nieto de Castro}, + Pages = {283-309}, + Publisher = {Cambridge University Press}, + Year = {1996}, + + Owner = {Belli}, + Timestamp = {2013.05.29} +} + @Article{Huber-FPE-2005, Title = {{Thermal conductivity correlations for minor constituent fluids in natural gas: n-octane, n-nonane and n-decane}}, Author = {M.L. Huber and R.A. Perkins}, @@ -799,6 +913,42 @@ Timestamp = {2014.09.22} } +@Article{Kim-IJR-2008, + Title = {{Cooling performance of several CO2/propane mixtures and glide matching with secondary heat transfer fluid}}, + Author = {Ju Hyok Kim and Jin Min Cho and Min Soo Kim}, + Journal = {Int. J. Refrig.}, + Year = {2008}, + Pages = {800-806}, + Volume = {31}, + + Owner = {Belli}, + Timestamp = {2013.07.10} +} + +@Article{Kiselev-1998, + Title = {{Transport properties of carbon dioxide+ethane and methane+ethane mixtures in the extended critical region}}, + Author = {S.B. Kiselev and M.L. Huber}, + Journal = {Fluid Phase Equilibria}, + Year = {1998}, + Pages = {253-280}, + Volume = {142}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + +@Article{Kiselev-1999, + Title = {{Transport properties of refrigerants R32, R125, R134a, and R125+R32 mixtures in and beyond the critical region}}, + Author = {S.B. Kiselev and R.A. Perkins and M.L. Huber}, + Journal = {International Journal of Refrigeration}, + Year = {1999}, + Pages = {509-520}, + Volume = {22}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + @Article{Kiselev-IECR-2005, Title = {{Generalized SAFT-DFT/DMT Model for the Thermodynamic, Interfacial, and Transport Properties of Associating Fluids: Application for n-Alkanols}}, Author = {S. B. Kiselev and J. F. Ely and I. M. Abdulagatov and M. L. Huber}, @@ -812,6 +962,19 @@ Timestamp = {2013.04.14} } +@Article{Kiselev-1997, + Title = {{Thermodynamic and Transport Properties of Fluids and Fluid Mixtures in the Extended Critical Region}}, + Author = {S. B. Kiselev and V. D. Kulikov}, + Journal = {lnternational Journal of Thermophysics}, + Year = {1997}, + Number = {5}, + Pages = {1143-1182}, + Volume = {18}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + @Article{Klein-IJR-1997, Title = {{An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures}}, Author = {S.A. Klein and M.O. McLinden and A. Laesecke}, @@ -852,6 +1015,15 @@ Timestamp = {2013.04.28} } +@Unpublished{ZITTAU, + Title = {{Hochschule Zittau Thermophysical Property Libraries}}, + Author = {Hans-Joachim Kretzschmar and Ines St{\"o}cker}, + Note = {http://thermodynamik.hs-zigr.de/cmsfg/Stoffwertbibliothek/index.php}, + + Owner = {Belli}, + Timestamp = {2013.08.05} +} + @Book{Kunz-BOOK-2007, Title = {{The GERG-2004 Wide-Range Equation of State for Natural Gases and Other Mixtures}}, Author = {O. Kunz and R. Klimeck and W. Wagner and M. Jaeschke}, @@ -875,6 +1047,18 @@ Timestamp = {2013.07.07} } +@Article{Laesecke-2001, + Title = {{Saturated-Liquid Viscosity of Ten Binary and Ternary Alternative Refrigerant Mixtures. Part I: Measurements}}, + Author = {Arno Laesecke and Richard F. Hafer and Dylan J. Morris}, + Journal = {J. Chem. Eng. Data}, + Year = {2001}, + Pages = {433-445}, + Volume = {46}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + @Article{Laesecke-IJR-1996, Title = {{An improved correlation for the thermal conductivity of HCFC123 (2,2-dichloro-1,1,1-trifluoroethane)}}, Author = {Arno Laesecke and Richard A. Perkins and John B. Howley}, @@ -889,6 +1073,19 @@ Timestamp = {2013.04.13} } +@Article{Latini-1999, + Title = {{A New Approach to the Evaluation of Transport Properties of Azeotropic and Quasi-Azeotropic Refrigerant Mixtures}}, + Author = {G. Latini and G. Passerini and F. Polonara}, + Journal = {International Journal of Thermophysics}, + Year = {1999}, + Number = {1}, + Pages = {73-84}, + Volume = {20}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + @Article{Leachman-JPCRD-2009, Title = {{Fundamental Equations of State for Parahydrogen, Normal Hydrogen, and Orthohydrogen}}, Author = {J.W. Leachman and R.T. Jacobsen and S.G. Penoncello and E.W. Lemmon}, @@ -1221,6 +1418,42 @@ Timestamp = {2014.10.02} } +@Article{Miqueu-2000, + Title = {{An extended scaled equation for the temperature dependence of the surface tension of pure compounds inferred from an analysis of experimental data}}, + Author = {C. Miqueu and D. Broseta and J. Satherley and B. Mendiboure and J. Lachaise and A. Graciaa}, + Journal = {Fluid Phase Equilibria}, + Year = {2000}, + Pages = {169-182}, + Volume = {172}, + + Owner = {Belli}, + Timestamp = {2013.04.23} +} + +@Article{Monsalvo-2006, + Title = {{High-pressure viscosity behavior of x 1,1,1,2-tetrafluoroethane (HFC-134a)+(1-x) triethylene glycol dimethylether (TriEGDME) mixtures: Measurements and modeling}}, + Author = {Mat{\'i}as A. Monsalvo and Antoine Baylaucq and Sergio E. Qui{\~n}ones-Cisneros and Christian Boned}, + Journal = {Fluid Phase Equilibria}, + Year = {2006}, + Pages = {70-79}, + Volume = {247}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + +@Article{Monsalvo-2005, + Title = {{Viscosity measurements and correlations of binary mixtures: 1,1,1,2-tetrafluoroethane (HFC-134a)+tetraethylene glycol dimethylether (TEGDME)}}, + Author = {M.A. Monsalvo and A. Baylaucq and P. Reghem and S.E. Qui{\~n}ones-Cisnerosa and C. Boned}, + Journal = {Fluid Phase Equilibria}, + Year = {2005}, + Pages = {1-8}, + Volume = {233}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + @Article{Mulero-JPCRD-2014, Title = {{Recommended Correlations for the Surface Tension of Several Fluids Included in the REFPROP Program}}, Author = {A. Mulero and I. Cachadi{\~n}a}, @@ -1273,6 +1506,32 @@ Timestamp = {2014.12.10} } +@Article{Nabizadeh-1999, + Title = {{Viscosity of Gaseous R404A, R407C, R410A, and R507}}, + Author = {H. Nabizadeh and F. Mayinger}, + Journal = {International Journal ojr Thermophysics}, + Year = {1999}, + Number = {3}, + Pages = {777-790}, + Volume = {20}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + +@Article{Neufeld-1972, + Title = {{Empirical Equations to Calculate 16 of the Transport Collision Integrals $\Omega$(l,s)* for the Lennard-Jones (12-6) Potential}}, + Author = {Philip D. Neufeld and A. R. Janzen and R. A. Aziz}, + Journal = {J. Chem. Phys.}, + Year = {1972}, + Number = {3}, + Pages = {1100-1102}, + Volume = {57}, + + Owner = {Belli}, + Timestamp = {2013.04.25} +} + @Article{Okada-IJT-1999, Title = {{Surface Tension of HFC Refrigerant Mixtures}}, Author = {M. Okada and T. Shibata and Y. Sato and Y. Higashi}, @@ -1592,6 +1851,16 @@ Timestamp = {2013.07.07} } +@PhdThesis{Quoilin-2011, + Title = {{Sustainable energy conversion through the use of Organic Rankine Cycles for waste heat recovery and solar applications}}, + Author = {Sylvain Quoilin}, + School = {University of Li\`{e}ge}, + Year = {2011}, + + Owner = {Belli}, + Timestamp = {2013.03.30} +} + @Article{Reeves-JCP-1964, Title = {{Melting Curves of Pressure Transmitting Fluids}}, Author = {Larry E. Reeves and Gene J. Scott and Stanley E. Babb Jr.}, @@ -1651,6 +1920,19 @@ Timestamp = {2013.04.08} } +@Article{Royal-2005, + Title = {{Predicting the viscosity of liquid refrigerant blends: comparison with experimental data}}, + Author = {D.D. Royal and V. Vesovic and J.P.M. Trusler and W.A. Wakeham}, + Journal = {International Journal of Refrigeration}, + Year = {2005}, + Pages = {311?319}, + Volume = {28}, + + Owner = {Belli}, + Review = {Only includes liquid mixtures}, + Timestamp = {2013.07.03} +} + @Article{Rui-FPE-2013, Title = {{An equation of state for the thermodynamic properties of 1,1,1,2,3,3-hexafluoropropane (R236ea)}}, Author = {Xinfang Rui and Jiang Pan and Yugang Wang}, @@ -1678,6 +1960,18 @@ Timestamp = {2014.06.09} } +@Article{Scalbrin-2002, + Title = {{A corresponding states predictive viscosity model based on a new scaling parameter: application to hydrocarbons, halocarbons and mixtures}}, + Author = {G. Scalabrin and G. Cristofoli and M. Grigiante}, + Journal = {Int. J. Energy Res.}, + Year = {2002}, + Pages = {1-26}, + Volume = {26}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + @Article{Scalabrin-JPCRD-2006-CO2, Title = {{A Reference Multiparameter Thermal Conductivity Equation for Carbon Dioxide with an Optimized Functional Form}}, Author = {G. Scalabrin and P. Marchi and F. Finezzo and R. Span}, @@ -1774,6 +2068,16 @@ Timestamp = {2013.04.08} } +@Book{Span-BOOK-2000, + Title = {{Multiparameter Equations of State - An Accurate Source of Thermodynamic Property Data}}, + Author = {Roland Span}, + Publisher = {Springer}, + Year = {2000}, + + Owner = {Belli}, + Timestamp = {2013.03.18} +} + @Article{Span-JPCRD-2000, Title = {{A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa}}, Author = {Roland Span and Eric W. Lemmon and Richard T. Jacobsen and Wolfgang Wagner and Akimichi Yokozeki}, @@ -1941,6 +2245,15 @@ Timestamp = {2013.08.05} } +@Unpublished{HelmholtzMedia, + Title = {HelmholtzMedia: Modelica library for the calculation of fluid properties from an equation of state (EoS).}, + Author = {Matthis Thorade}, + Note = {https://github.com/thorade/HelmholtzMedia}, + + Owner = {Belli}, + Timestamp = {2013.05.29} +} + @Article{Thorade-EES-2013, Title = {{Partial derivatives of thermodynamic state properties for dynamic simulation}}, Author = {Thorade, Matthis and Saadat, Ali}, @@ -2009,6 +2322,18 @@ Timestamp = {2013.04.08} } +@Article{Tournier-2008, + Title = {{Properties of noble gases and binary mixtures for closed Brayton Cycle applications}}, + Author = {Jean-Michel P. Tournier and Mohamed S. El-Genk}, + Journal = {Energy Conversion and Management}, + Year = {2008}, + Pages = {469-492}, + Volume = {49}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + @Article{Tufeu-BBPC-1984, Title = {{Thermal Conductivity of Ammonia in a Large Temperature and Pressure Range Including the Critical Region}}, Author = {R. Tufeu and D.Y. Ivanov and Y. Garrabos and B. Le Neindre}, @@ -2022,6 +2347,18 @@ Timestamp = {2013.04.08} } +@Article{Vesovic-2002, + Title = {{Predicting the viscosity of halogenated hydrocarbon mixtures}}, + Author = {V. Vesovic}, + Journal = {Fluid Phase Equilibria}, + Year = {2002}, + Pages = {295-306}, + Volume = {199}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + @Article{Vesovic-JPCRD-1990, Title = {{The Transport Properties of Carbon Dioxide}}, Author = {V. Vesovic and W.A. Wakeham and G.A. Olchowy and J.V. Sengers and J.T.R. Watson and J. Millat}, @@ -2088,6 +2425,15 @@ Timestamp = {2013.05.01} } +@Unpublished{FLUIDCAL, + Title = {FLUIDCAL: Software FLUIDCAL for the Calculation of Thermodynamic Properties for a Great Number of Substances}, + Author = {W. Wagner}, + Note = {http://www.thermo.rub.de/en/prof-w-wagner/software/fluidcal.html}, + + Owner = {Belli}, + Timestamp = {2013.05.29} +} + @Article{Wagner-JPCRD-2002, Title = {{The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use}}, Author = {W. Wagner and A. Pruss}, @@ -2142,6 +2488,19 @@ Timestamp = {2014.08.26} } +@Article{Yokoyama-2006, + Title = {{Viscosity of Gaseous Mixtures of HFC-125 + Propane from 298.15 to 423.15K at Pressures to 6.7 MPa}}, + Author = {C. Yokoyama and T. Nishino and M. Takahashi}, + Journal = {International Journal of Thermophysics,}, + Year = {2006}, + Number = {3}, + Pages = {714-728}, + Volume = {27}, + + Owner = {Belli}, + Timestamp = {2013.07.03} +} + @Article{Younglove-JPCRD-1994, Title = {{An International Standard Equation of State for the Thermodynamic Properties of Refrigerant 123 (2,2-Dichloro-1,1,1-Trifluoroethane)}}, Author = {Ben A. Younglove}, diff --git a/dev/fluids/Novec649.json b/dev/fluids/Novec649.json new file mode 100644 index 00000000..989f4a5d --- /dev/null +++ b/dev/fluids/Novec649.json @@ -0,0 +1,360 @@ +{ + "ALIASES": [ + "Novec1230" + ], + "ANCILLARIES": { + "pL": { + "T_r": 441.81, + "Tmax": 441.81, + "Tmin": 165, + "description": "p' = pc*exp(Tc/T*sum(n_i*theta^t_i))", + "max_abserror_percentage": 1, + "n": [ + -8.4411, + 2.711, + -3.6354, + -5.3872, + -8.1641 + ], + "reducing_value": 1869000.0, + "t": [ + 1, + 1.5, + 2.2, + 4.4, + 15 + ], + "type": "pL", + "using_tau_r": true + }, + "pV": { + "T_r": 441.81, + "Tmax": 441.81, + "Tmin": 165, + "description": "p' = pc*exp(Tc/T*sum(n_i*theta^t_i))", + "max_abserror_percentage": 1, + "n": [ + -8.4411, + 2.711, + -3.6354, + -5.3872, + -8.1641 + ], + "reducing_value": 1869000.0, + "t": [ + 1, + 1.5, + 2.2, + 4.4, + 15 + ], + "type": "pV", + "using_tau_r": true + }, + "rhoL": { + "T_r": 441.81, + "Tmax": 441.81, + "Tmin": 165, + "description": "rho' = rhoc*(1+sum(n_i*theta^t_i))", + "max_abserror_percentage": 1, + "n": [ + 1.5545, + 1.149, + 0.51565 + ], + "reducing_value": 1920.0, + "t": [ + 0.297, + 0.7, + 4.4 + ], + "type": "rhoLnoexp", + "using_tau_r": false + }, + "rhoV": { + "T_r": 441.81, + "Tmax": 441.81, + "Tmin": 165, + "description": "rho'' = rhoc*exp(Tc/T*sum(n_i*theta^t_i))", + "max_abserror_percentage": 1, + "n": [ + -1.6073, + -5.8095, + -17.824, + -61.012, + -151.3 + ], + "reducing_value": 1920.0, + "t": [ + 0.291, + 0.82, + 2.45, + 5.5, + 12 + ], + "type": "rhoV", + "using_tau_r": true + } + }, + "CAS": "756-13-8", + "ENVIRONMENTAL": { + "ASHRAE34": "UNKNOWN", + "FH": -1, + "GWP100": -1.0, + "GWP20": -1.0, + "GWP500": -1.0, + "HH": -1, + "Name": "Novec649", + "ODP": -1.0, + "PH": 0 + }, + "EOS": [ + { + "BibTeX_CP0": "", + "BibTeX_EOS": "McLinden-JCED-2015-PREPRINT", + "STATES": { + "hs_anchor": { + "T": 654.005, + "T_units": "K", + "hmolar": 100494.99108243728, + "hmolar_units": "J/mol", + "p": 3972067.642196921, + 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