Thermal Conductivity (chemicals.thermal_conductivity)¶
This module contains various thermal conductivity estimation routines, dataframes of fit coefficients, and mixing rules.
For reporting bugs, adding feature requests, or submitting pull requests, please use the GitHub issue tracker.
Pure Low Pressure Liquid Correlations¶
- chemicals.thermal_conductivity.Sheffy_Johnson(T, MW, Tm)[source]¶
Calculate the thermal conductivity of a liquid as a function of temperature using the Sheffy-Johnson (1961) method. Requires Temperature, molecular weight, and melting point.
- Parameters
- Returns
- kl
float
Thermal conductivity of the fluid, W/m/k
- kl
Notes
The origin of this equation has been challenging to trace. It is presently unknown, and untested.
References
- 1
Scheffy, W. J., and E. F. Johnson. “Thermal Conductivities of Liquids at High Temperatures.” Journal of Chemical & Engineering Data 6, no. 2 (April 1, 1961): 245-49. doi:10.1021/je60010a019
Examples
>>> Sheffy_Johnson(300, 47, 280) 0.17740150413112193
- chemicals.thermal_conductivity.Sato_Riedel(T, MW, Tb, Tc)[source]¶
Calculate the thermal conductivity of a liquid as a function of temperature using the CSP method of Sato-Riedel [1], [2], published in Reid [3]. Requires temperature, molecular weight, and boiling and critical temperatures.
- Parameters
- Returns
- kl
float
Estimated liquid thermal conductivity [W/m/k]
- kl
Notes
This equation has a complicated history. It is proposed by Reid [3]. Limited accuracy should be expected. Uncheecked.
References
- 1
Riedel, L.: Chem. Ing. Tech., 21, 349 (1949); 23: 59, 321, 465 (1951)
- 2
Maejima, T., private communication, 1973
- 3(1,2)
Properties of Gases and Liquids”, 3rd Ed., McGraw-Hill, 1977
Examples
>>> Sato_Riedel(300, 47, 390, 520) 0.21037692461337687
- chemicals.thermal_conductivity.Lakshmi_Prasad(T, MW)[source]¶
Estimates thermal conductivity of pure liquids as a function of temperature using a reference fluid approach. Low accuracy but quick. Developed using several organic fluids.
- Parameters
- Returns
- kl
float
Estimated liquid thermal conductivity [W/m/k]
- kl
Notes
This equation returns negative numbers at high T sometimes. This equation is one of those implemented by DDBST. If this results in a negative thermal conductivity, no value is returned.
References
- 1
Lakshmi, D. S., and D. H. L. Prasad. “A Rapid Estimation Method for Thermal Conductivity of Pure Liquids.” The Chemical Engineering Journal 48, no. 3 (April 1992): 211-14. doi:10.1016/0300-9467(92)80037-B
Examples
>>> Lakshmi_Prasad(273.15, 100) 0.013664450
- chemicals.thermal_conductivity.Gharagheizi_liquid(T, MW, Tb, Pc, omega)[source]¶
Estimates the thermal conductivity of a liquid as a function of temperature using the CSP method of Gharagheizi [1]. A convoluted method claiming high-accuracy and using only statistically significant variable following analalysis.
Requires temperature, molecular weight, boiling temperature and critical pressure and acentric factor.
- Parameters
- Returns
- kl
float
Estimated liquid thermal conductivity [W/m/k]
- kl
Notes
Pressure is internally converted into bar, as used in the original equation.
This equation was derived with 19000 points representing 1640 unique compounds.
References
- 1
Gharagheizi, Farhad, Poorandokht Ilani-Kashkouli, Mehdi Sattari, Amir H. Mohammadi, Deresh Ramjugernath, and Dominique Richon. “Development of a General Model for Determination of Thermal Conductivity of Liquid Chemical Compounds at Atmospheric Pressure.” AIChE Journal 59, no. 5 (May 1, 2013): 1702-8. doi:10.1002/aic.13938
Examples
>>> Gharagheizi_liquid(300, 40, 350, 1E6, 0.27) 0.2171113029534838
- chemicals.thermal_conductivity.Nicola_original(T, MW, Tc, omega, Hfus)[source]¶
Estimates the thermal conductivity of a liquid as a function of temperature using the CSP method of Nicola [1]. A simpler but long method claiming high-accuracy and using only statistically significant variable following analalysis.
Requires temperature, molecular weight, critical temperature, acentric factor and the heat of vaporization.
- Parameters
- Returns
- kl
float
Estimated liquid thermal conductivity [W/m/k]
- kl
Notes
A weird statistical correlation. Recent and yet to be reviewed. This correlation has been superceded by the author’s later work. Hfus is internally converted to be in J/kmol.
References
- 1
Nicola, Giovanni Di, Eleonora Ciarrocchi, Mariano Pierantozzi, and Roman Stryjek. “A New Equation for the Thermal Conductivity of Organic Compounds.” Journal of Thermal Analysis and Calorimetry 116, no. 1 (April 1, 2014): 135-40. doi:10.1007/s10973-013-3422-7
Examples
>>> Nicola_original(300, 142.3, 611.7, 0.49, 201853) 0.2305018632230984
- chemicals.thermal_conductivity.Nicola(T, MW, Tc, Pc, omega)[source]¶
Estimates the thermal conductivity of a liquid as a function of temperature using the CSP method of [1]. A statistically derived equation using any correlated terms.
Requires temperature, molecular weight, critical temperature and pressure, and acentric factor.
- Parameters
- Returns
- kl
float
Estimated liquid thermal conductivity [W/m/k]
- kl
Notes
A statistical correlation. A revision of an original correlation.
References
- 1
Di Nicola, Giovanni, Eleonora Ciarrocchi, Gianluca Coccia, and Mariano Pierantozzi. “Correlations of Thermal Conductivity for Liquid Refrigerants at Atmospheric Pressure or near Saturation.” International Journal of Refrigeration. 2014. doi:10.1016/j.ijrefrig.2014.06.003
Examples
>>> Nicola(300, 142.3, 611.7, 2110000.0, 0.49) 0.10863821554584034
- chemicals.thermal_conductivity.Bahadori_liquid(T, MW)[source]¶
Estimates the thermal conductivity of parafin liquid hydrocarbons. Fits their data well, and is useful as only MW is required. X is the Molecular weight, and Y the temperature.
- Parameters
- Returns
- kl
float
Estimated liquid thermal conductivity [W/m/k]
- kl
Notes
The accuracy of this equation has not been reviewed.
References
- 1
Bahadori, Alireza, and Saeid Mokhatab. “Estimating Thermal Conductivity of Hydrocarbons.” Chemical Engineering 115, no. 13 (December 2008): 52-54
Examples
Data point from [1].
>>> Bahadori_liquid(273.15, 170) 0.1427427810827268
- chemicals.thermal_conductivity.kl_Mersmann_Kind(T, MW, Tc, Vc, na)[source]¶
Estimates the thermal conductivity of organic liquid substances according to the method of [1].
- Parameters
- Returns
- kl
float
Estimated liquid thermal conductivity [W/m/k]
- kl
Notes
In the equation, all quantities must be in SI units but N_A is in a kmol basis and Vc is in units of (m^3/kmol); this is converted internally.
References
- 1
Mersmann, Alfons, and Matthias Kind. “Prediction of Mechanical and Thermal Properties of Pure Liquids, of Critical Data, and of Vapor Pressure.” Industrial & Engineering Chemistry Research, January 31, 2017. https://doi.org/10.1021/acs.iecr.6b04323.
Examples
Dodecane at 400 K:
>>> kl_Mersmann_Kind(400, 170.33484, 658.0, ... 0.000754, 38) 0.0895271829899285
Pure High Pressure Liquid Correlations¶
- chemicals.thermal_conductivity.DIPPR9G(T, P, Tc, Pc, kl)[source]¶
Adjustes for pressure the thermal conductivity of a liquid using an emperical formula based on [1], but as given in [2].
- Parameters
- Returns
- kl_dense
float
Thermal conductivity of liquid at P, [W/m/K]
- kl_dense
Notes
This equation is entrely dimensionless; all dimensions cancel. The original source has not been reviewed.
This is DIPPR Procedure 9G: Method for the Thermal Conductivity of Pure Nonhydrocarbon Liquids at High Pressures
References
- 1
Missenard, F. A., Thermal Conductivity of Organic Liquids of a Series or a Group of Liquids , Rev. Gen.Thermodyn., 101 649 (1970).
- 2(1,2)
Danner, Ronald P, and Design Institute for Physical Property Data. Manual for Predicting Chemical Process Design Data. New York, N.Y, 1982.
Examples
From [2], for butyl acetate.
>>> DIPPR9G(515.05, 3.92E7, 579.15, 3.212E6, 7.085E-2) 0.0864419738671184
- chemicals.thermal_conductivity.Missenard(T, P, Tc, Pc, kl)[source]¶
Adjustes for pressure the thermal conductivity of a liquid using an emperical formula based on [1], but as given in [2].
- Parameters
- Returns
- kl_dense
float
Thermal conductivity of liquid at P, [W/m/K]
- kl_dense
Notes
This equation is entirely dimensionless; all dimensions cancel. An interpolation routine is used here from tabulated values of Q. The original source has not been reviewed.
References
- 1
Missenard, F. A., Thermal Conductivity of Organic Liquids of a Series or a Group of Liquids , Rev. Gen.Thermodyn., 101 649 (1970).
- 2(1,2)
Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGraw-Hill Professional, 2000.
Examples
Example from [2], toluene; matches.
>>> Missenard(304., 6330E5, 591.8, 41E5, 0.129) 0.2198375777069657
Liquid Mixing Rules¶
- chemicals.thermal_conductivity.DIPPR9H(ws, ks)[source]¶
Calculates thermal conductivity of a liquid mixture according to mixing rules in [1] and also in [2].
This is also called the Vredeveld (1973) equation. A review in [3] finds this the best model on average. However, they did caution that in some cases a linear mole-fraction mixing rule performs better. This equation according to Poling [1] should not be used if some components have thermal conductivities more than twice other components. They also say this should not be used with water.
- Parameters
- Returns
- kl
float
Thermal conductivity of liquid mixture, [W/m/K]
- kl
Notes
This equation is entirely dimensionless; all dimensions cancel. The example is from [2]; all results agree. The original source has not been reviewed.
DIPPR Procedure 9H: Method for the Thermal Conductivity of Nonaqueous Liquid Mixtures
Average deviations of 3%. for 118 nonaqueous systems with 817 data points. Max deviation 20%. According to DIPPR.
In some sources, this equation is given with the molecular weights included:
References
- 1(1,2)
Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. The Properties of Gases and Liquids. McGraw-Hill Companies, 1987.
- 2(1,2)
Danner, Ronald P, and Design Institute for Physical Property Data. Manual for Predicting Chemical Process Design Data. New York, N.Y, 1982.
- 3
Focke, Walter W. “Correlating Thermal-Conductivity Data for Ternary Liquid Mixtures.” International Journal of Thermophysics 29, no. 4 (August 1, 2008): 1342-60. https://doi.org/10.1007/s10765-008-0465-2.
Examples
>>> DIPPR9H([0.258, 0.742], [0.1692, 0.1528]) 0.15657104706719646
- chemicals.thermal_conductivity.DIPPR9I(zs, Vms, ks)[source]¶
Calculates thermal conductivity of a liquid mixture according to mixing rules in [1]. This is recommended in [2] for aqueous and nonaqueous systems.
- Parameters
- Returns
- kl
float
Thermal conductivity of liquid mixture, [W/m/K]
- kl
Notes
This equation is entirely dimensionless; all dimensions cancel. The example is from [2]; all results agree.
[2] found average deviations of 4-6% for 118 nonaqueous systems and 15 aqueous systems at atmospheric pressure, with a maximum deviation of 33%.
The computational complexity here is N^2, with a division present in the inner loop.
References
- 1
Li, C. C. “Thermal Conductivity of Liquid Mixtures.” AIChE Journal 22, no. 5 (1976): 927-30. https://doi.org/10.1002/aic.690220520.
- 2(1,2,3)
Danner, Ronald P, and Design Institute for Physical Property Data. Manual for Predicting Chemical Process Design Data. New York, N.Y, 1982.
Examples
>>> DIPPR9I(zs=[.682, .318], Vms=[1.723e-2, 7.338e-2], ks=[.6037, .1628]) 0.25397430656658937
- chemicals.thermal_conductivity.Filippov(ws, ks)[source]¶
Calculates thermal conductivity of a binary liquid mixture according to mixing rules in [2] as found in [1].
- Parameters
- Returns
- kl
float
Thermal conductivity of liquid mixture, [W/m/K]
- kl
Notes
This equation is entirely dimensionless; all dimensions cancel. The original source has not been reviewed. Only useful for binary mixtures.
References
- 1
Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. The Properties of Gases and Liquids. McGraw-Hill Companies, 1987.
- 2
Filippov, L. P.: Vest. Mosk. Univ., Ser. Fiz. Mat. Estestv. Nauk, (8I0E): 67-69A955); Chem. Abstr., 50: 8276 A956). Filippov, L. P., and N. S. Novoselova: Vestn. Mosk. Univ., Ser. F iz. Mat. Estestv.Nauk, CI0B): 37-40A955); Chem. Abstr., 49: 11366 A955).
Examples
>>> Filippov([0.258, 0.742], [0.1692, 0.1528]) 0.15929167628799998
Pure Low Pressure Gas Correlations¶
- chemicals.thermal_conductivity.Eucken(MW, Cvm, mu)[source]¶
Estimates the thermal conductivity of a gas as a function of temperature using the CSP method of Eucken [1].
- Parameters
- Returns
- kg
float
Estimated gas thermal conductivity [W/m/k]
- kg
Notes
Temperature dependence is introduced via heat capacity and viscosity. A theoretical equation. No original author located. MW internally converted to kg/g-mol.
References
- 1(1,2)
Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. Properties of Gases and Liquids. McGraw-Hill Companies, 1987.
Examples
2-methylbutane at low pressure, 373.15 K. Mathes calculation in [1].
>>> Eucken(MW=72.151, Cvm=135.9, mu=8.77E-6) 0.018792645058456698
- chemicals.thermal_conductivity.Eucken_modified(MW, Cvm, mu)[source]¶
Estimates the thermal conductivity of a gas as a function of temperature using the Modified CSP method of Eucken [1].
- Parameters
- Returns
- kg
float
Estimated gas thermal conductivity [W/m/k]
- kg
Notes
Temperature dependence is introduced via heat capacity and viscosity. A theoretical equation. No original author located. MW internally converted to kg/g-mol.
References
- 1(1,2)
Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. Properties of Gases and Liquids. McGraw-Hill Companies, 1987.
Examples
2-methylbutane at low pressure, 373.15 K. Mathes calculation in [1].
>>> Eucken_modified(MW=72.151, Cvm=135.9, mu=8.77E-6) 0.02359353760551249
- chemicals.thermal_conductivity.DIPPR9B(T, MW, Cvm, mu, Tc=None, chemtype=None)[source]¶
Calculates the thermal conductivity of a gas using one of several emperical equations developed in [1], [2], and presented in [3].
For monoatomic gases:
For linear molecules:
For nonlinear molecules:
- Parameters
- Returns
- k_g
float
Thermal conductivity of gas, [W/m/k]
- k_g
Notes
Tested with DIPPR values. Cvm is internally converted to J/kmol/K.
References
- 1
Bromley, LeRoy A., Berkeley. University of California, and U.S. Atomic Energy Commission. Thermal Conductivity of Gases at Moderate Pressures. UCRL;1852. Berkeley, CA: University of California Radiation Laboratory, 1952.
- 2
Stiel, Leonard I., and George Thodos. “The Thermal Conductivity of Nonpolar Substances in the Dense Gaseous and Liquid Regions.” AIChE Journal 10, no. 1 (January 1, 1964): 26-30. doi:10.1002/aic.690100114
- 3
Danner, Ronald P, and Design Institute for Physical Property Data. Manual for Predicting Chemical Process Design Data. New York, N.Y, 1982.
Examples
CO:
>>> DIPPR9B(200., 28.01, 20.826, 1.277E-5, 132.92, chemtype='linear') 0.01813208676438415
- chemicals.thermal_conductivity.Chung(T, MW, Tc, omega, Cvm, mu)[source]¶
Estimates the thermal conductivity of a gas as a function of temperature using the CSP method of Chung [1].
- Parameters
- Returns
- kg
float
Estimated gas thermal conductivity [W/m/k]
- kg
Notes
MW internally converted to kg/g-mol.
References
- 1
Chung, Ting Horng, Lloyd L. Lee, and Kenneth E. Starling. “Applications of Kinetic Gas Theories and Multiparameter Correlation for Prediction of Dilute Gas Viscosity and Thermal Conductivity.” Industrial & Engineering Chemistry Fundamentals 23, no. 1 (February 1, 1984): 8-13. doi:10.1021/i100013a002
- 2
Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. Properties of Gases and Liquids. McGraw-Hill Companies, 1987.
Examples
2-methylbutane at low pressure, 373.15 K. Mathes calculation in [2].
>>> Chung(T=373.15, MW=72.151, Tc=460.4, omega=0.227, Cvm=135.9, mu=8.77E-6) 0.023015653797111124
- chemicals.thermal_conductivity.Eli_Hanley(T, MW, Tc, Vc, Zc, omega, Cvm)[source]¶
Estimates the thermal conductivity of a gas as a function of temperature using the reference fluid method of Eli and Hanley [1] as shown in [2].
- Parameters
- T
float
Temperature of the gas [K]
- MW
float
Molecular weight of the gas [g/mol]
- Tc
float
Critical temperature of the gas [K]
- Vc
float
Critical volume of the gas [m^3/mol]
- Zc
float
Critical compressibility of the gas []
- omega
float
Acentric factor of the gas [-]
- Cvm
float
Molar contant volume heat capacity of the gas [J/mol/K]
- T
- Returns
- kg
float
Estimated gas thermal conductivity [W/m/k]
- kg
Notes
Reference fluid is Methane. MW internally converted to kg/g-mol.
References
- 1
Ely, James F., and H. J. M. Hanley. “Prediction of Transport Properties. 2. Thermal Conductivity of Pure Fluids and Mixtures.” Industrial & Engineering Chemistry Fundamentals 22, no. 1 (February 1, 1983): 90-97. doi:10.1021/i100009a016.
- 2(1,2)
Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. Properties of Gases and Liquids. McGraw-Hill Companies, 1987.
Examples
2-methylbutane at low pressure, 373.15 K. Matches calculation in [2].
>>> Eli_Hanley(T=373.15, MW=72.151, Tc=460.4, Vc=3.06E-4, Zc=0.267, ... omega=0.227, Cvm=135.9) 0.02247951724513664
- chemicals.thermal_conductivity.Gharagheizi_gas(T, MW, Tb, Pc, omega)[source]¶
Estimates the thermal conductivity of a gas as a function of temperature using the CSP method of Gharagheizi [1]. A convoluted method claiming high-accuracy and using only statistically significant variable following analalysis.
Requires temperature, molecular weight, boiling temperature and critical pressure and acentric factor.
- Parameters
- Returns
- kg
float
Estimated gas thermal conductivity [W/m/k]
- kg
Notes
Pressure is internally converted into 10*kPa but author used correlation with kPa; overall, errors have been corrected in the presentation of the formula.
This equation was derived with 15927 points and 1574 compounds. Example value from [1] is the first point in the supportinf info, for CH4.
References
- 1(1,2)
Gharagheizi, Farhad, Poorandokht Ilani-Kashkouli, Mehdi Sattari, Amir H. Mohammadi, Deresh Ramjugernath, and Dominique Richon. “Development of a General Model for Determination of Thermal Conductivity of Liquid Chemical Compounds at Atmospheric Pressure.” AIChE Journal 59, no. 5 (May 1, 2013): 1702-8. doi:10.1002/aic.13938
Examples
>>> Gharagheizi_gas(580., 16.04246, 111.66, 4599000.0, 0.0115478000) 0.09594861261873211
- chemicals.thermal_conductivity.Bahadori_gas(T, MW)[source]¶
Estimates the thermal conductivity of hydrocarbons gases at low P. Fits their data well, and is useful as only MW is required. Y is the Molecular weight, and X the temperature.
- Parameters
- Returns
- kg
float
Estimated gas thermal conductivity [W/m/k]
- kg
Notes
The accuracy of this equation has not been reviewed.
References
- 1
Bahadori, Alireza, and Saeid Mokhatab. “Estimating Thermal Conductivity of Hydrocarbons.” Chemical Engineering 115, no. 13 (December 2008): 52-54
Examples
>>> Bahadori_gas(40+273.15, 20.0) # Point from article 0.03196816533787329
Pure High Pressure Gas Correlations¶
- chemicals.thermal_conductivity.Stiel_Thodos_dense(T, MW, Tc, Pc, Vc, Zc, Vm, kg)[source]¶
Estimates the thermal conductivity of a gas at high pressure as a function of temperature using difference method of Stiel and Thodos [1] as shown in [2].
if :
if :
if :
- Parameters
- T
float
Temperature of the gas [K]
- MW
float
Molecular weight of the gas [g/mol]
- Tc
float
Critical temperature of the gas [K]
- Pc
float
Critical pressure of the gas [Pa]
- Vc
float
Critical volume of the gas [m^3/mol]
- Zc
float
Critical compressibility of the gas [-]
- Vm
float
Molar volume of the gas at T and P [m^3/mol]
- kg
float
Low-pressure gas thermal conductivity [W/m/k]
- T
- Returns
- kg
float
Estimated dense gas thermal conductivity [W/m/k]
- kg
Notes
Pc is internally converted to bar.
References
- 1
Stiel, Leonard I., and George Thodos. “The Thermal Conductivity of Nonpolar Substances in the Dense Gaseous and Liquid Regions.” AIChE Journal 10, no. 1 (January 1, 1964): 26-30. doi:10.1002/aic.690100114.
- 2
Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. Properties of Gases and Liquids. McGraw-Hill Companies, 1987.
Examples
>>> Stiel_Thodos_dense(T=378.15, MW=44.013, Tc=309.6, Pc=72.4E5, ... Vc=97.4E-6, Zc=0.274, Vm=144E-6, kg=2.34E-2) 0.041245574404863684
- chemicals.thermal_conductivity.Eli_Hanley_dense(T, MW, Tc, Vc, Zc, omega, Cvm, Vm)[source]¶
Estimates the thermal conductivity of a gas at high pressure as a function of temperature using the reference fluid method of Eli and Hanley [1] as shown in [2].
- Parameters
- T
float
Temperature of the gas [K]
- MW
float
Molecular weight of the gas [g/mol]
- Tc
float
Critical temperature of the gas [K]
- Vc
float
Critical volume of the gas [m^3/mol]
- Zc
float
Critical compressibility of the gas [-]
- omega
float
Acentric factor of the gas [-]
- Cvm
float
Molar contant volume heat capacity of the gas [J/mol/K]
- Vm
float
Volume of the gas at T and P [m^3/mol]
- T
- Returns
- kg
float
Estimated dense gas thermal conductivity [W/m/k]
- kg
Notes
Reference fluid is Methane. MW internally converted to kg/g-mol.
References
- 1
Ely, James F., and H. J. M. Hanley. “Prediction of Transport Properties. 2. Thermal Conductivity of Pure Fluids and Mixtures.” Industrial & Engineering Chemistry Fundamentals 22, no. 1 (February 1, 1983): 90-97. doi:10.1021/i100009a016.
- 2
Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. Properties of Gases and Liquids. McGraw-Hill Companies, 1987.
Examples
>>> Eli_Hanley_dense(T=473., MW=42.081, Tc=364.9, Vc=1.81E-4, Zc=0.274, ... omega=0.144, Cvm=82.70, Vm=1.721E-4) 0.06038475754109959
- chemicals.thermal_conductivity.Chung_dense(T, MW, Tc, Vc, omega, Cvm, Vm, mu, dipole, association=0.0)[source]¶
Estimates the thermal conductivity of a gas at high pressure as a function of temperature using the reference fluid method of Chung [1] as shown in [2].
- Parameters
- T
float
Temperature of the gas [K]
- MW
float
Molecular weight of the gas [g/mol]
- Tc
float
Critical temperature of the gas [K]
- Vc
float
Critical volume of the gas [m^3/mol]
- omega
float
Acentric factor of the gas [-]
- Cvm
float
Molar contant volume heat capacity of the gas [J/mol/K]
- Vm
float
Molar volume of the gas at T and P [m^3/mol]
- mu
float
Low-pressure gas viscosity [Pa*s]
- dipole
float
Dipole moment [debye]
- association
float
,optional
Association factor [-]
- T
- Returns
- kg
float
Estimated dense gas thermal conductivity [W/m/k]
- kg
Notes
MW internally converted to kg/g-mol. Vm internally converted to mL/mol. [1] is not the latest form as presented in [1]. Association factor is assumed 0. Relates to the polarity of the gas.
Coefficients as follows:
ais = [2.4166E+0, -5.0924E-1, 6.6107E+0, 1.4543E+1, 7.9274E-1, -5.8634E+0, 9.1089E+1]
bis = [7.4824E-1, -1.5094E+0, 5.6207E+0, -8.9139E+0, 8.2019E-1, 1.2801E+1, 1.2811E+2]
cis = [-9.1858E-1, -4.9991E+1, 6.4760E+1, -5.6379E+0, -6.9369E-1, 9.5893E+0, -5.4217E+1]
dis = [1.2172E+2, 6.9983E+1, 2.7039E+1, 7.4344E+1, 6.3173E+0, 6.5529E+1, 5.2381E+2]
References
- 1(1,2,3)
Chung, Ting Horng, Mohammad Ajlan, Lloyd L. Lee, and Kenneth E. Starling. “Generalized Multiparameter Correlation for Nonpolar and Polar Fluid Transport Properties.” Industrial & Engineering Chemistry Research 27, no. 4 (April 1, 1988): 671-79. doi:10.1021/ie00076a024.
- 2
Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGraw-Hill Professional, 2000.
Examples
>>> Chung_dense(T=473., MW=42.081, Tc=364.9, Vc=184.6E-6, omega=0.142, ... Cvm=82.67, Vm=172.1E-6, mu=134E-7, dipole=0.4) 0.06160569232570781
Gas Mixing Rules¶
- chemicals.thermal_conductivity.Lindsay_Bromley(T, ys, ks, mus, Tbs, MWs)[source]¶
Calculates thermal conductivity of a gas mixture according to mixing rules in [1] and also in [2]. It is significantly more complicated than other kinetic theory models.
- Parameters
- Returns
- kg
float
Thermal conductivity of gas mixture, [W/m/K]
- kg
Notes
This equation is entirely dimensionless; all dimensions cancel. The example is from [2]; all results agree. The original source has not been reviewed.
DIPPR Procedure 9D: Method for the Thermal Conductivity of Gas Mixtures
Average deviations of 4-5% for 77 binary mixtures reviewed in [2], from 1342 points; also six ternary mixtures (70 points); max deviation observed was 40%. (DIPPR)
References
- 1
Lindsay, Alexander L., and LeRoy A. Bromley. “Thermal Conductivity of Gas Mixtures.” Industrial & Engineering Chemistry 42, no. 8 (August 1, 1950): 1508-11. doi:10.1021/ie50488a017.
- 2(1,2,3)
Danner, Ronald P, and Design Institute for Physical Property Data. Manual for Predicting Chemical Process Design Data. New York, N.Y, 1982.
- 3
Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGraw-Hill Professional, 2000.
Examples
>>> Lindsay_Bromley(323.15, [0.23, 0.77], [1.939E-2, 1.231E-2], [1.002E-5, 1.015E-5], [248.31, 248.93], [46.07, 50.49]) 0.013902644179693132
- chemicals.thermal_conductivity.Wassiljewa_Herning_Zipperer(zs, ks, MWs, MW_roots=None)[source]¶
Calculates thermal conductivity of a gas mixture according to the kinetic theory expression of Wassiljewa with the interaction term from the Herning-Zipperer expression. This is also used for the prediction of gas mixture viscosity.
- Parameters
- Returns
- kg
float
Thermal conductivity of gas mixture, [W/m/K]
- kg
Notes
This equation is entirely dimensionless; all dimensions cancel.
References
- 1
Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGraw-Hill Professional, 2000.
Examples
>>> Wassiljewa_Herning_Zipperer(zs=[.1, .4, .5], ks=[1.002E-5, 1.15E-5, 2e-5], MWs=[40.0, 50.0, 60.0]) 1.5861181979916883e-05
Correlations for Specific Substances¶
- chemicals.thermal_conductivity.k_IAPWS(T, rho, Cp=None, Cv=None, mu=None, drho_dP=None, drho_dP_Tr=None)[source]¶
Calculate the thermal conductivity of water or steam according to the 2011 IAPWS [1] formulation. Critical enhancement is ignored unless parameters for it are provided.
- Parameters
- T
float
Temperature water [K]
- rho
float
Density of water [kg/m^3]
- Cp
float
,optional
Constant pressure heat capacity of water, [J/kg/K]
- Cv
float
,optional
Constant volume heat capacity of water, [J/kg/K]
- mu
float
,optional
Viscosity of water, [Pa*s]
- drho_dP
float
,optional
Partial derivative of density with respect to pressure at constant temperature, [kg/m^3/Pa]
- drho_dP_Tr
float
,optional
Partial derivative of density with respect to pressure at constant temperature (at the reference temperature (970.644 K) and the actual density of water); will be calculated from the industrial formulation fit if omitted, [kg/m^3/Pa]
- T
- Returns
- k
float
Thermal condiuctivity, [W/m/K]
- k
Notes
Gamma = 177.8514;
qd = 0.4E-9;
nu = 0.630;
gamma = 1.239;
zeta0 = 0.13E-9;
Gamma0 = 0.06;
TRC = 1.5
The formulation uses the industrial variant of the critical enhancement. It matches to 5E-6 relative tolerance at the check temperature, and should match even closer outside it.
References
- 1
Huber, M. L., R. A. Perkins, D. G. Friend, J. V. Sengers, M. J. Assael, I. N. Metaxa, K. Miyagawa, R. Hellmann, and E. Vogel. “New International Formulation for the Thermal Conductivity of H2O.” Journal of Physical and Chemical Reference Data 41, no. 3 (September 1, 2012): 033102. doi:10.1063/1.4738955.
Examples
>>> k_IAPWS(647.35, 750.) 0.5976194153179502
Region 1, test 1, from MPEI, exact match:
>>> k_IAPWS(T=620., rho=613.227777440324, Cp=7634.337046792, ... Cv=3037.934412104, mu=70.905106751524E-6, drho_dP=5.209378197916E-6) 0.48148519510200044
Full scientific calculation:
>>> from chemicals.iapws import iapws95_properties, iapws95_P, iapws95_Tc >>> from chemicals.viscosity import mu_IAPWS >>> T, P = 298.15, 1e5 >>> rho, _, _, _, Cv, Cp, _, _, _, _, drho_dP = iapws95_properties(T, P) >>> P_ref = iapws95_P(1.5*iapws95_Tc, rho) >>> _, _, _, _, _, _, _, _, _, _, drho_dP_Tr = iapws95_properties(1.5*iapws95_Tc, P_ref) >>> mu = mu_IAPWS(T, rho, drho_dP, drho_dP_Tr) >>> k_IAPWS(T, rho, Cp, Cv, mu, drho_dP, drho_dP_Tr) 0.60651532815
- chemicals.thermal_conductivity.k_air_lemmon(T, rho, Cp=None, Cv=None, drho_dP=None, drho_dP_Tr=None, mu=None)[source]¶
Calculate the thermal conductivity of air using the Lemmon and Jacobsen (2004) [1] formulation. The critical enhancement term is ignored unless all the rquired parameters for it are provided.
- Parameters
- T
float
Temperature air [K]
- rho
float
Molar density of air [mol/m^3]
- Cp
float
,optional
Molar constant pressure heat capacity of air, [J/mol/K]
- Cv
float
,optional
Molar constant volume heat capacity of air, [J/mol/K]
- drho_dP
float
,optional
Partial derivative of density with respect to pressure at constant temperature, [mol/m^3/Pa]
- drho_dP_Tr
float
,optional
Partial derivative of density with respect to pressure at constant temperature (at the reference temperature (265.262 K) and the actual density of air), [mol/m^3/Pa]
- mu
float
,optional
Viscosity of air, [Pa*s]
- T
- Returns
- k
float
Thermal condiuctivity of air, [W/m/K]
- k
Notes
The constnts are as follows:
Ni = [1.308, 1.405, -1.036, 8.743, 14.76, -16.62, 3.793, -6.142, -0.3778]
ti = [None, -1.1, -0.3, 0.1, 0.0, 0.5, 2.7, 0.3, 1.3]
di = [None, None, None, 1, 2, 3, 7, 7, 11]
li = [None, None, None, 0, 0, 2, 2, 2, 2]
gammai = [None, None, None, 0, 0, 1, 1, 1, 1]
R0 = 1.01; Pc = 3.78502E6 Pa; xi0 = 0.11E-9 nm; qd = 0.31E-9 nm; Tc = 132.6312 K (actually the maxcondentherm); T_ref = 265.262 (2Tc rounded differently); rhoc = 10447.7 mol/m^3 (actually the maxcondentherm); k = 1.380658E-23 J/K; nu = 0.63 and gamma = 1.2415, sigma = 0.36, MW = 28.9586 g/mol.
References
- 1
Lemmon, E. W., and R. T. Jacobsen. “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air.” International Journal of Thermophysics 25, no. 1 (January 1, 2004): 21-69. https://doi.org/10.1023/B:IJOT.0000022327.04529.f3.
Examples
Basic calculation at 300 K and approximately 1 bar:
>>> k_air_lemmon(300, 40.0) 0.0263839695044
Calculation near critical point:
>>> k_air_lemmon(132.64, 10400, 2137.078854678728, 35.24316159996235, 0.07417878614315769, 0.00035919027241528256, 1.7762253265868595e-05) 0.07562307234760
Fit Correlations¶
- chemicals.thermal_conductivity.PPDS8(T, Tc, a0, a1, a2, a3)[source]¶
Calculate the thermal conductivity of a liquid using the 4-term tau polynomial developed by the PPDS and named PPDS equation 8.
- Parameters
- Returns
- k
float
Low pressure liquid thermal conductivity, [W/(m*K)]
- k
References
- 1
“ThermoData Engine (TDE103b V10.1) User`s Guide.” https://trc.nist.gov/TDE/Help/TDE103b/Eqns-Pure-ThermalCondSatL/PPDS8.htm
Examples
Sample coefficients for benzene in [1], at 500 K:
>>> PPDS8(T=500.0, Tc=562.05, a0=0.0641126, a1=0.61057, a2=-1.72442, a3=3.94394) 0.08536381765218425
- chemicals.thermal_conductivity.PPDS3(T, Tc, a1, a2, a3)[source]¶
Calculate the thermal conductivity of a low-pressure gas using the 3-term Tr polynomial developed by the PPDS and named PPDS equation 3.
- Parameters
- Returns
- k
float
Low pressure gas thermal conductivity, [W/(m*K)]
- k
References
- 1
“ThermoData Engine (TDE103b V10.1) User`s Guide.” https://trc.nist.gov/TDE/Help/TDE103b/Eqns-Pure-ThermalCondG/PPDS3-ThermCondGas.htm
Examples
Sample coefficients for pentane in [1], at 400 K:
>>> PPDS3(T=400.0, Tc=470.008, a1=11.6366, a2=25.1191, a3=-7.21674) 0.0251734811601927
- chemicals.thermal_conductivity.Chemsep_16(T, A, B, C, D, E)[source]¶
Calculate the thermal conductivity of a low-pressure liquid using the 5-term T exponential polynomial found in ChemSep.
- Parameters
- Returns
- k
float
Low pressure liquid thermal conductivity, [W/(m*K)]
- k
Notes
This correlation is also used by ChemSep for surface tension. Calculation of negative values is prevented and those are set to 0.
References
- 1
Kooijman, Harry A., and Ross Taylor. The ChemSep Book. Books on Demand Norderstedt, Germany, 2000.
Examples
Sample coefficients for liquid thermal conductivity of n-hexane in [1], at 300 K:
>>> Chemsep_16(300.0, -0.12682, -1.5015, -1.0467, -0.00088709, -9.3679E-07) 0.11924904787869
Fit Coefficients¶
All of these coefficients are lazy-loaded, so they must be accessed as an attribute of this module.
- chemicals.thermal_conductivity.k_data_Perrys_8E_2_315¶
Data from [1] with
chemicals.dippr.EQ100
coefficients for liquids.
- chemicals.thermal_conductivity.k_data_Perrys_8E_2_314¶
Data from [1] with
chemicals.dippr.EQ102
coefficients for gases.
- chemicals.thermal_conductivity.k_data_VDI_PPDS_9¶
Data from [2] with polynomial coefficients for liquids.
- chemicals.thermal_conductivity.k_data_VDI_PPDS_10¶
Data from [2] with polynomial coefficients for gases.
- 1(1,2)
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2(1,2)
Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.
In [1]: import chemicals
In [2]: chemicals.thermal_conductivity.k_data_Perrys_8E_2_315
Out[2]:
Chemical C1 C2 ... C5 Tmin Tmax
CAS ...
50-00-0 Formaldehyde 0.37329 -0.000650 ... 0.0 204.00 234.00
55-21-0 Benzamide 0.28485 -0.000252 ... 0.0 403.00 563.15
56-23-5 Carbon tetrachloride 0.15890 -0.000199 ... 0.0 250.33 349.79
57-55-6 1,2-Propylene glycol 0.21520 -0.000050 ... 0.0 213.15 460.75
60-29-7 Diethyl ether 0.24950 -0.000407 ... 0.0 156.85 433.15
... ... ... ... ... ... ... ...
10028-15-6 Ozone 0.17483 0.000753 ... 0.0 77.35 161.85
10035-10-6 Hydrogen bromide 0.23400 -0.000464 ... 0.0 185.15 290.62
10102-43-9 Nitric oxide 0.18780 0.001029 ... 0.0 110.00 176.40
13511-13-2 Propenylcyclohexene 0.18310 -0.000203 ... 0.0 199.00 431.65
132259-10-0 Air 0.28472 -0.001739 ... 0.0 75.00 125.00
[340 rows x 8 columns]
In [3]: chemicals.thermal_conductivity.k_data_Perrys_8E_2_314
Out[3]:
Chemical C1 ... Tmin Tmax
CAS ...
50-00-0 Formaldehyde 44.847000 ... 254.05 994.05
55-21-0 Benzamide 0.025389 ... 563.15 1000.00
56-23-5 Carbon tetrachloride 0.000166 ... 349.79 1000.00
57-55-6 1,2-Propylene glycol 0.000167 ... 460.75 1000.00
60-29-7 Diethyl ether -0.004489 ... 200.00 600.00
... ... ... ... ... ...
10028-15-6 Ozone 0.004315 ... 161.85 1000.00
10035-10-6 Hydrogen bromide 0.000497 ... 206.45 600.00
10102-43-9 Nitric oxide 0.000410 ... 121.38 750.00
13511-13-2 Propenylcyclohexene 0.000102 ... 431.65 1000.00
132259-10-0 Air 0.000314 ... 70.00 2000.00
[345 rows x 7 columns]
In [4]: chemicals.thermal_conductivity.k_data_VDI_PPDS_9
Out[4]:
Chemical A ... D E
CAS ...
50-00-0 Formaldehyde 0.3834 ... 1.156000e-09 -2.638000e-12
56-23-5 Carbon tetrachloride 0.1509 ... -7.100000e-11 3.980000e-13
56-81-5 Glycerol 0.2562 ... -1.050000e-10 1.020000e-13
60-29-7 Diethyl ether 0.2499 ... -8.600000e-11 7.300000e-14
62-53-3 Aniline 0.2365 ... -3.600000e-11 2.100000e-14
... ... ... ... ... ...
10097-32-2 Bromine -0.1426 ... 2.690200e-08 -1.774400e-11
10102-43-9 Nitric oxide 0.2268 ... -1.993600e-08 1.448400e-11
10102-44-0 Nitrogen dioxide 0.3147 ... 2.620000e-10 -6.980000e-13
10544-72-6 Dinitrogentetroxide 0.1864 ... -5.440000e-10 1.509000e-12
132259-10-0 Air -0.0006 ... 1.114335e-06 -2.670110e-09
[271 rows x 6 columns]
In [5]: chemicals.thermal_conductivity.k_data_VDI_PPDS_10
Out[5]:
Chemical A ... D E
CAS ...
50-00-0 Formaldehyde 8.870000e-04 ... 0.000000e+00 0.000000e+00
56-23-5 Carbon tetrachloride -2.101000e-03 ... 0.000000e+00 0.000000e+00
56-81-5 Glycerol -9.158000e-03 ... 0.000000e+00 0.000000e+00
60-29-7 Diethyl ether -5.130000e-04 ... 0.000000e+00 0.000000e+00
62-53-3 Aniline -9.960000e-03 ... 0.000000e+00 0.000000e+00
... ... ... ... ... ...
10097-32-2 Bromine 5.455000e-03 ... 0.000000e+00 0.000000e+00
10102-43-9 Nitric oxide 1.440000e-04 ... 0.000000e+00 0.000000e+00
10102-44-0 Nitrogen dioxide 6.608500e-02 ... 0.000000e+00 0.000000e+00
10544-72-6 Dinitrogentetroxide 1.460000e-09 ... 0.000000e+00 0.000000e+00
132259-10-0 Air -9.080000e-04 ... 5.696400e-11 -1.563100e-14
[275 rows x 6 columns]