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.

k=1.95110.00126(TTm)Tm0.216MW0.3k = 1.951 \frac{1-0.00126(T-T_m)}{T_m^{0.216}MW^{0.3}}
Parameters
Tfloat

Temperature of the fluid [K]

MWfloat

Molecular weight of the fluid [g/mol]

Tmfloat

Melting point of the fluid [K]

Returns
klfloat

Thermal conductivity of the fluid, W/m/k

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.

k=1.1053MW3+20(1Tr)2/33+20(1Tbr)2/3k = \frac{1.1053}{\sqrt{MW}}\frac{3+20(1-T_r)^{2/3}} {3+20(1-T_{br})^{2/3}}
Parameters
Tfloat

Temperature of the fluid [K]

MWfloat

Molecular weight of the fluid [g/mol]

Tbfloat

Boiling temperature of the fluid [K]

Tcfloat

Critical temperature of the fluid [K]

Returns
klfloat

Estimated liquid thermal conductivity [W/m/k]

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.

λ=0.06550.0005T+1.38550.00197TMW0.5\lambda = 0.0655-0.0005T + \frac{1.3855-0.00197T}{MW^{0.5}}
Parameters
Tfloat

Temperature of the fluid [K]

MWfloat

Molecular weight of the fluid [g/mol]

Returns
klfloat

Estimated liquid thermal conductivity [W/m/k]

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.

k=104[10ω+2Pc2T+4+1.908(Tb+1.009B2MW2)+3.9287MW4B4+AB8]k = 10^{-4}\left[10\omega + 2P_c-2T+4+1.908(T_b+\frac{1.009B^2}{MW^2}) +\frac{3.9287MW^4}{B^4}+\frac{A}{B^8}\right]
A=3.8588MW8(1.0045B+6.5152MW8.9756)A = 3.8588MW^8(1.0045B+6.5152MW-8.9756)
B=16.0407MW+2Tb27.9074B = 16.0407MW+2T_b-27.9074
Parameters
Tfloat

Temperature of the fluid [K]

MWfloat

Molecular weight of the fluid [g/mol]

Tbfloat

Boiling temperature of the fluid [K]

Pcfloat

Critical pressure of the fluid [Pa]

omegafloat

Acentric factor of the fluid [-]

Returns
klfloat

Estimated liquid thermal conductivity [W/m/k]

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.

λ1Wm/K=0.56940.1436Tr+5.4893×1010ΔfusHkmol/J+0.0508ω+(1kg/kmolMW)0.0622\frac{\lambda}{1 \text{Wm/K}}=-0.5694-0.1436T_r+5.4893\times10^{-10} \frac{\Delta_{fus}H}{\text{kmol/J}}+0.0508\omega + \left(\frac{1 \text{kg/kmol}}{MW}\right)^{0.0622}
Parameters
Tfloat

Temperature of the fluid [K]

MWfloat

Molecular weight of the fluid [g/mol]

Tcfloat

Critical temperature of the fluid [K]

omegafloat

Acentric factor of the fluid [-]

Hfusfloat

Heat of fusion of the fluid [J/mol]

Returns
klfloat

Estimated liquid thermal conductivity [W/m/k]

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.

λ0.5147W/m/K=0.2537Tr+0.0017Pcbar+0.1501ω+(1MW)0.2999\frac{\lambda}{0.5147 W/m/K} = -0.2537T_r+\frac{0.0017Pc}{\text{bar}} +0.1501 \omega + \left(\frac{1}{MW}\right)^{-0.2999}
Parameters
Tfloat

Temperature of the fluid [K]

MWfloat

Molecular weight of the fluid [g/mol]

Tcfloat

Critical temperature of the fluid [K]

Pcfloat

Critical pressure of the fluid [Pa]

omegafloat

Acentric factor of the fluid [-]

Returns
klfloat

Estimated liquid thermal conductivity [W/m/k]

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.

K=a+bY+CY2+dY3K = a + bY + CY^2 + dY^3
a=A1+B1X+C1X2+D1X3a = A_1 + B_1 X + C_1 X^2 + D_1 X^3
b=A2+B2X+C2X2+D2X3b = A_2 + B_2 X + C_2 X^2 + D_2 X^3
c=A3+B3X+C3X2+D3X3c = A_3 + B_3 X + C_3 X^2 + D_3 X^3
d=A4+B4X+C4X2+D4X3d = A_4 + B_4 X + C_4 X^2 + D_4 X^3
Parameters
Tfloat

Temperature of the fluid [K]

MWfloat

Molecular weight of the fluid [g/mol]

Returns
klfloat

Estimated liquid thermal conductivity [W/m/k]

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].

λ=λVc2/3TcMW0.5(kTc)1.5NA7/6\lambda^* = \frac{\lambda\cdot V_c^{2/3}\cdot T_c\cdot \text{MW}^{0.5}} {(k\cdot T_c)^{1.5}\cdot N_A^{7/6}}
λ=23(na+401Tr)\lambda^* = \frac{2}{3}\left(n_a + 40\sqrt{1-T_r}\right)
Parameters
Tfloat

Temperature of the fluid [K]

MWfloat

Molecular weight of the fluid [g/mol]

Tcfloat

Critical temperature of the fluid [K]

Vcfloat

Critical volume of the fluid [m^3/mol]

nafloat

Number of atoms in the molecule, [-]

Returns
klfloat

Estimated liquid thermal conductivity [W/m/k]

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].

k=k[0.98+0.0079PrTr1.4+0.63Tr1.2(Pr30+Pr)]k = k^* \left[ 0.98 + 0.0079 P_r T_r^{1.4} + 0.63 T_r^{1.2} \left( \frac{P_r}{30 + P_r}\right)\right]
Parameters
Tfloat

Temperature of fluid [K]

Pfloat

Pressure of fluid [Pa]

Tc: float

Critical point of fluid [K]

Pcfloat

Critical pressure of the fluid [Pa]

klfloat

Thermal conductivity of liquid at 1 atm or saturation, [W/m/K]

Returns
kl_densefloat

Thermal conductivity of liquid at P, [W/m/K]

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].

kk=1+QPr0.7\frac{k}{k^*} = 1 + Q P_r^{0.7}
Parameters
Tfloat

Temperature of fluid [K]

Pfloat

Pressure of fluid [Pa]

Tc: float

Critical point of fluid [K]

Pcfloat

Critical pressure of the fluid [Pa]

klfloat

Thermal conductivity of liquid at 1 atm or saturation, [W/m/K]

Returns
kl_densefloat

Thermal conductivity of liquid at P, [W/m/K]

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].

λm=(iwiλi2)1/2\lambda_m = \left( \sum_i w_i \lambda_i^{-2}\right)^{-1/2}

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
wsfloat

Mass fractions of components

ksfloat

Liquid thermal conductivites of all components, [W/m/K]

Returns
klfloat

Thermal conductivity of liquid mixture, [W/m/K]

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:

λm2=iziMWiλi2iziMWi\lambda_m^{-2} = \frac{\sum_i z_i {MW}_i \lambda_i^{-2}} {\sum_i z_i {MW}_i}

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.

kmix=ijϕiϕjki,jk_{mix} = \sum_{i}\sum_j \phi_i\phi_j k_{i,j}
ki,j=21ki+1kjk_{i,j} = \frac{2}{\frac{1}{k_i} + \frac{1}{k_j}}
ϕi=ziVm,ijnzjVm,j\phi_i = \frac{z_i V_{m,i}}{\sum_j^n z_j V_{m,j}}
Parameters
zslist[float]

Mole fractions of components, [-]

Vmslist[float]

Molar volumes of each component, [m^3/mol]

ksfloat

Liquid thermal conductivites of all components, [W/m/K]

Returns
klfloat

Thermal conductivity of liquid mixture, [W/m/K]

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].

λm=w1λ1+w2λ20.72w1w2(λ2λ1)\lambda_m = w_1 \lambda_1 + w_2\lambda_2 - 0.72 w_1 w_2(\lambda_2-\lambda_1)
Parameters
wsfloat

Mass fractions of components

ksfloat

Liquid thermal conductivites of all components, [W/m/K]

Returns
klfloat

Thermal conductivity of liquid mixture, [W/m/K]

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].

λMWηCv=1+9/4Cv/R\frac{\lambda MW}{\eta C_v} = 1 + \frac{9/4}{C_v/R}
Parameters
MWfloat

Molecular weight of the gas [g/mol]

Cvmfloat

Molar contant volume heat capacity of the gas [J/mol/K]

mufloat

Gas viscosity [Pa*s]

Returns
kgfloat

Estimated gas thermal conductivity [W/m/k]

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].

λMWηCv=1.32+1.77Cv/R\frac{\lambda MW}{\eta C_v} = 1.32 + \frac{1.77}{C_v/R}
Parameters
MWfloat

Molecular weight of the gas [g/mol]

Cvmfloat

Molar contant volume heat capacity of the gas [J/mol/K]

mufloat

Gas viscosity [Pa*s]

Returns
kgfloat

Estimated gas thermal conductivity [W/m/k]

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:

k=2.5ηCvMWk = 2.5 \frac{\eta C_v}{MW}

For linear molecules:

k=ηMW(1.30Cv+14644.002928.80Tr)k = \frac{\eta}{MW} \left( 1.30 C_v + 14644.00 - \frac{2928.80}{T_r}\right)

For nonlinear molecules:

k=ηMW(1.15Cv+16903.36)k = \frac{\eta}{MW}(1.15C_v + 16903.36)
Parameters
Tfloat

Temperature of the fluid [K]

Tcfloat

Critical temperature of the fluid [K]

MWfloat

Molwcular weight of fluid [g/mol]

Cvmfloat

Molar heat capacity at constant volume of fluid, [J/mol/K]

mufloat

Viscosity of gas, [Pa*s]

Returns
k_gfloat

Thermal conductivity of gas, [W/m/k]

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].

λMWηCv=3.75ΨCv/R\frac{\lambda MW}{\eta C_v} = \frac{3.75 \Psi}{C_v/R}
Ψ=1+α{[0.215+0.28288α1.061β+0.26665Z]/[0.6366+βZ+1.061αβ]}\Psi = 1 + \alpha \left\{[0.215+0.28288\alpha-1.061\beta+0.26665Z]/ [0.6366+\beta Z + 1.061 \alpha \beta]\right\}
α=CvR1.5\alpha = \frac{C_v}{R}-1.5
β=0.78620.7109ω+1.3168ω2\beta = 0.7862-0.7109\omega + 1.3168\omega^2
Z=2+10.5Tr2Z=2+10.5T_r^2
Parameters
Tfloat

Temperature of the gas [K]

MWfloat

Molecular weight of the gas [g/mol]

Tcfloat

Critical temperature of the gas [K]

omegafloat

Acentric factor of the gas [-]

Cvmfloat

Molar contant volume heat capacity of the gas [J/mol/K]

mufloat

Gas viscosity [Pa*s]

Returns
kgfloat

Estimated gas thermal conductivity [W/m/k]

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].

λ=λ+ηMW(1.32)(Cv3R2)\lambda = \lambda^* + \frac{\eta^*}{MW}(1.32)\left(C_v - \frac{3R}{2}\right)
Tr=min(Tr,2)Tr = \text{min}(Tr, 2)
θ=1+(ω0.011)(0.565530.86276lnTr0.69852Tr)\theta = 1 + (\omega-0.011)\left(0.56553 - 0.86276\ln Tr - \frac{0.69852}{Tr}\right)
ψ=[1+(ω0.011)(0.385601.1617lnTr)]0.288Zc\psi = [1 + (\omega - 0.011)(0.38560 - 1.1617\ln Tr)]\frac{0.288}{Z_c}
f=Tc190.4θf = \frac{T_c}{190.4}\theta
h=Vc9.92E5ψh = \frac{V_c}{9.92E-5}\psi
T0=T/fT_0 = T/f
η0(T0)=n=19CnT0(n4)/3\eta_0^*(T_0)= \sum_{n=1}^9 C_n T_0^{(n-4)/3}
θ0=1944η0\theta_0 = 1944 \eta_0
λ=λ0H\lambda^* = \lambda_0 H
η=η0HMW16.04\eta^* = \eta^*_0 H \frac{MW}{16.04}
H=(16.04MW)0.5f0.5/h2/3H = \left(\frac{16.04}{MW}\right)^{0.5}f^{0.5}/h^{2/3}
Parameters
Tfloat

Temperature of the gas [K]

MWfloat

Molecular weight of the gas [g/mol]

Tcfloat

Critical temperature of the gas [K]

Vcfloat

Critical volume of the gas [m^3/mol]

Zcfloat

Critical compressibility of the gas []

omegafloat

Acentric factor of the gas [-]

Cvmfloat

Molar contant volume heat capacity of the gas [J/mol/K]

Returns
kgfloat

Estimated gas thermal conductivity [W/m/k]

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.

k=7.9505×104+3.989×105T5.419×105MW+3.989×105Ak = 7.9505\times 10^{-4} + 3.989\times 10^{-5} T -5.419\times 10^-5 MW + 3.989\times 10^{-5} A
A=(2ω+T(2ω+3.2825)TTb+3.2825)0.1MPcT×(3.9752ω+0.1Pc+1.9876B+6.5243)2A = \frac{\left(2\omega + T - \frac{(2\omega + 3.2825)T}{T_b} + 3.2825\right)}{0.1MP_cT} \times (3.9752\omega + 0.1 P_c + 1.9876B + 6.5243)^2
Parameters
Tfloat

Temperature of the fluid [K]

MW: float

Molecular weight of the fluid [g/mol]

Tbfloat

Boiling temperature of the fluid [K]

Pcfloat

Critical pressure of the fluid [Pa]

omegafloat

Acentric factor of the fluid [-]

Returns
kgfloat

Estimated gas thermal conductivity [W/m/k]

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.

K=a+bY+CY2+dY3K = a + bY + CY^2 + dY^3
a=A1+B1X+C1X2+D1X3a = A_1 + B_1 X + C_1 X^2 + D_1 X^3
b=A2+B2X+C2X2+D2X3b = A_2 + B_2 X + C_2 X^2 + D_2 X^3
c=A3+B3X+C3X2+D3X3c = A_3 + B_3 X + C_3 X^2 + D_3 X^3
d=A4+B4X+C4X2+D4X3d = A_4 + B_4 X + C_4 X^2 + D_4 X^3
Parameters
Tfloat

Temperature of the gas [K]

MWfloat

Molecular weight of the gas [g/mol]

Returns
kgfloat

Estimated gas thermal conductivity [W/m/k]

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 ρr<0.5\rho_r < 0.5:

(λλ)ΓZc5=1.22×102[exp(0.535ρr)1](\lambda-\lambda^\circ)\Gamma Z_c^5=1.22\times 10^{-2} [\exp(0.535 \rho_r)-1]

if 0.5<ρr<2.00.5 < \rho_r < 2.0:

(λλ)ΓZc5=1.22×102[exp(0.535ρr)1](\lambda-\lambda^\circ)\Gamma Z_c^5=1.22\times 10^{-2} [\exp(0.535 \rho_r)-1]

if 2<ρr<2.82 < \rho_r < 2.8:

(λλ)ΓZc5=1.22×102[exp(0.535ρr)1](\lambda-\lambda^\circ)\Gamma Z_c^5=1.22\times 10^{-2} [\exp(0.535 \rho_r)-1]
Γ=210(TcMW3Pc4)1/6\Gamma = 210 \left(\frac{T_cMW^3}{P_c^4}\right)^{1/6}
Parameters
Tfloat

Temperature of the gas [K]

MWfloat

Molecular weight of the gas [g/mol]

Tcfloat

Critical temperature of the gas [K]

Pcfloat

Critical pressure of the gas [Pa]

Vcfloat

Critical volume of the gas [m^3/mol]

Zcfloat

Critical compressibility of the gas [-]

Vmfloat

Molar volume of the gas at T and P [m^3/mol]

kgfloat

Low-pressure gas thermal conductivity [W/m/k]

Returns
kgfloat

Estimated dense gas thermal conductivity [W/m/k]

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].

Tr=min(Tr,2)Tr = min(Tr, 2)
Vr=min(Vr,2)Vr = min(Vr, 2)
f=Tc190.4θf = \frac{T_c}{190.4}\theta
h=Vc9.92E5ψh = \frac{V_c}{9.92E-5}\psi
T0=T/fT_0 = T/f
ρ0=16.04Vh\rho_0 = \frac{16.04}{V}h
θ=1+(ω0.011)(0.090570.86276lnTr+(0.316640.46568Tr)(Vr0.5))\theta = 1 + (\omega-0.011)\left(0.09057 - 0.86276\ln Tr + \left( 0.31664 - \frac{0.46568}{Tr}\right) (V_r - 0.5)\right)
ψ=[1+(ω0.011)(0.39490(Vr1.02355)0.93281(Vr0.75464)lnTr]0.288Zc\psi = [1 + (\omega - 0.011)(0.39490(V_r - 1.02355) - 0.93281(V_r - 0.75464)\ln T_r]\frac{0.288}{Z_c}
λ1=1944η0\lambda_1 = 1944 \eta_0
λ2={b1+b2[b3ln(T0b4)]2}ρ0\lambda_2 = \left\{b_1 + b_2\left[b_3 - \ln \left(\frac{T_0}{b_4} \right)\right]^2\right\}\rho_0
λ3=exp(a1+a2T0){exp[(a3+a4T01.5)ρ00.1+(ρ00.16171)ρ00.5(a5+a6T0+a7T02)]1}\lambda_3 = \exp\left(a_1 + \frac{a_2}{T_0}\right)\left\{\exp[(a_3 + \frac{a_4}{T_0^{1.5}})\rho_0^{0.1} + (\frac{\rho_0}{0.1617} - 1) \rho_0^{0.5}(a_5 + \frac{a_6}{T_0} + \frac{a_7}{T_0^2})] - 1\right\}
λ=[λ1+λ2+λ3]H\lambda^{**} = [\lambda_1 + \lambda_2 + \lambda_3]H
H=(16.04MW)0.5f0.5/h2/3H = \left(\frac{16.04}{MW}\right)^{0.5}f^{0.5}/h^{2/3}
X={[1Tf(dfdT)v]0.288Zc}1.5X = \left\{\left[1 - \frac{T}{f}\left(\frac{df}{dT}\right)_v \right] \frac{0.288}{Z_c}\right\}^{1.5}
(dfdT)v=Tc190.4(dθdT)v\left(\frac{df}{dT}\right)_v = \frac{T_c}{190.4}\left(\frac{d\theta} {d T}\right)_v
(dθdT)v=(ω0.011)[0.86276T+(Vr0.5)0.46568TcT2]\left(\frac{d\theta}{d T}\right)_v = (\omega-0.011)\left[ \frac{-0.86276}{T} + (V_r-0.5)\frac{0.46568T_c}{T^2}\right]
Parameters
Tfloat

Temperature of the gas [K]

MWfloat

Molecular weight of the gas [g/mol]

Tcfloat

Critical temperature of the gas [K]

Vcfloat

Critical volume of the gas [m^3/mol]

Zcfloat

Critical compressibility of the gas [-]

omegafloat

Acentric factor of the gas [-]

Cvmfloat

Molar contant volume heat capacity of the gas [J/mol/K]

Vmfloat

Volume of the gas at T and P [m^3/mol]

Returns
kgfloat

Estimated dense gas thermal conductivity [W/m/k]

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].

λ=31.2ηΨM(G21+B6y)+qB7y2Tr1/2G2\lambda = \frac{31.2 \eta^\circ \Psi}{M'}(G_2^{-1} + B_6 y)+qB_7y^2T_r^{1/2}G_2
Ψ=1+α{[0.215+0.28288α1.061β+0.26665Z]/[0.6366+βZ+1.061αβ]}\Psi = 1 + \alpha \left\{[0.215+0.28288\alpha-1.061\beta+0.26665Z]/ [0.6366+\beta Z + 1.061 \alpha \beta]\right\}
α=CvR1.5\alpha = \frac{C_v}{R}-1.5
β=0.78620.7109ω+1.3168ω2\beta = 0.7862-0.7109\omega + 1.3168\omega^2
Z=2+10.5Tr2Z=2+10.5T_r^2
q=3.586×103(Tc/M)1/2/Vc2/3q = 3.586\times 10^{-3} (T_c/M')^{1/2}/V_c^{2/3}
y=Vc6Vy = \frac{V_c}{6V}
G1=10.5y(1y)3G_1 = \frac{1-0.5y}{(1-y)^3}
G2=(B1/y)[1exp(B4y)]+B2G1exp(B5y)+B3G1B1B4+B2+B3G_2 = \frac{(B_1/y)[1-\exp(-B_4y)]+ B_2G_1\exp(B_5y) + B_3G_1} {B_1B_4 + B_2 + B_3}
Bi=ai+biω+ciμr4+diκB_i = a_i + b_i \omega + c_i \mu_r^4 + d_i \kappa
Parameters
Tfloat

Temperature of the gas [K]

MWfloat

Molecular weight of the gas [g/mol]

Tcfloat

Critical temperature of the gas [K]

Vcfloat

Critical volume of the gas [m^3/mol]

omegafloat

Acentric factor of the gas [-]

Cvmfloat

Molar contant volume heat capacity of the gas [J/mol/K]

Vmfloat

Molar volume of the gas at T and P [m^3/mol]

mufloat

Low-pressure gas viscosity [Pa*s]

dipolefloat

Dipole moment [debye]

associationfloat, optional

Association factor [-]

Returns
kgfloat

Estimated dense gas thermal conductivity [W/m/k]

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.

k=iyikijyiAijk = \sum_i \frac{y_i k_i}{\sum_j y_i A_{ij}}
Aij=14{1+[ηiηj(MWjMWi)0.75(T+SiT+Sj)]0.5}2(T+SijT+Si)A_{ij} = \frac{1}{4} \left\{ 1 + \left[\frac{\eta_i}{\eta_j} \left(\frac{MW_j}{MW_i}\right)^{0.75} \left( \frac{T+S_i}{T+S_j}\right) \right]^{0.5} \right\}^2 \left( \frac{T+S_{ij}}{T+S_i}\right)
Sij=Sji=(SiSj)0.5S_{ij} = S_{ji} = (S_i S_j)^{0.5}
Si=1.5TbS_i = 1.5 T_b
Parameters
Tfloat

Temperature of gas [K]

ysfloat

Mole fractions of gas components

ksfloat

Gas thermal conductivites of all components, [W/m/K]

musfloat

Gas viscosities of all components, [Pa*s]

Tbsfloat

Boiling points of all components, [K]

MWsfloat

Molecular weights of all components, [g/mol]

Returns
kgfloat

Thermal conductivity of gas mixture, [W/m/K]

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.

k=yikiyiAijk = \sum \frac{y_i k_i}{\sum y_i A_{ij}}
Aij=(MWjMWi)0.5A_{ij} = \left(\frac{MW_j}{MW_i}\right)^{0.5}
Parameters
zsfloat

Mole fractions of gas components, [-]

ksfloat

gas thermal conductivites of all components, [W/m/K]

MWsfloat

Molecular weights of all components, [g/mol]

MW_rootsfloat, optional

Square roots of molecular weights of all components; speeds up the calculation if provided, [g^0.5/mol^0.5]

Returns
kgfloat

Thermal conductivity of gas mixture, [W/m/K]

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.

λˉ=λˉ0×λˉ1(Tˉ,ρˉ)+λˉ2(Tˉ,ρˉ)\bar\lambda = \bar\lambda_0\times \bar\lambda_1(\bar T, \bar \rho) + \bar\lambda_2(\bar T, \bar\rho)
λˉ0=Tˉk=04LkTˉk\bar\lambda_0 = \frac{\sqrt{\bar T}} {\sum_{k=0}^4 \frac{L_k}{\bar T^k}}
λˉ1(Tˉ,ρˉ)=exp[ρˉi=04((1Tˉ1)ij=05Lij(ρˉ1)j)]\bar \lambda_1(\bar T, \bar \rho) = \exp\left[ \bar\rho \sum_{i=0}^4 \left(\left(\frac{1}{\bar T} - 1 \right)^i \sum_{j=0}^5 L_{ij}(\bar\rho - 1)^j\right)\right]
λˉ2=ΓρˉcˉpTˉμˉZ(y)\bar\lambda_2 = \Gamma\frac{\bar\rho \bar c_p \bar T}{\bar \mu} Z(y)
Z(y)=2πy{[(1κ1)arctan(y)+κ1y][1exp(1y1+y2/3ρˉ2)]}Z(y) = \frac{2}{\pi y} \left\{\left[(1 - \kappa^{-1})\arctan(y) + \kappa^{-1}y\right] - \left[1 - \exp\left(\frac{-1}{y^{-1} + y^{-2}/3\bar\rho^2}\right)\right]\right\}
y=qˉDξ(Tˉ,ρˉ)y = \bar q_D \xi(\bar T, \bar \rho)
ξ=ξ0(ΔχˉΓ0)ν/γ\xi = \xi_0 \left(\frac{\Delta \bar\chi}{\Gamma_0}\right)^{\nu/\gamma}
Δχˉ(Tˉ,ρˉ)=ρˉ[ζ(Tˉ,ρˉ)ζ(TˉR,ρˉ)TˉRTˉ]\Delta \bar\chi(\bar T, \bar \rho) = \bar\rho\left[ \zeta(\bar T, \bar \rho) - \zeta(\bar T_R, \bar \rho)\frac{\bar T_R}{\bar T} \right]
ζ=(ρˉpˉ)Tˉ\zeta = \left(\frac{\partial \bar \rho}{\partial \bar p}\right)_{\bar T}
Parameters
Tfloat

Temperature water [K]

rhofloat

Density of water [kg/m^3]

Cpfloat, optional

Constant pressure heat capacity of water, [J/kg/K]

Cvfloat, optional

Constant volume heat capacity of water, [J/kg/K]

mufloat, optional

Viscosity of water, [Pa*s]

drho_dPfloat, optional

Partial derivative of density with respect to pressure at constant temperature, [kg/m^3/Pa]

drho_dP_Trfloat, 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]

Returns
kfloat

Thermal condiuctivity, [W/m/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.

λ=λ0(T)+λr(τ,δ)+λc(τ,δ)\lambda = \lambda^0(T) + \lambda^r(\tau, \delta) + \lambda^c(\tau, \delta)
λ0=N1[η0(T)1μPas]+N2τt2+N3τt3\lambda^0 = N_1\left[\frac{\eta^0(T)}{1 \mu \text{Pa}\cdot \text{s}} \right] + N_2\tau^{t_2} + N_3\tau^{t_3}
λr=i=4nNiτtiδdiexp(γiδli)\lambda^r = \sum_{i=4}^n N_i \tau^{t_i} \delta^{d_i} \exp(-\gamma_i \delta^{l_i})
λc=ρCpkR0T6πξη(T,ρ)(Ω~Ω~0)\lambda^c = \rho C_p \frac{kR_0 T}{6\pi\xi\cdot \eta(T, \rho)}\left( \tilde \Omega -\tilde \Omega_0\right)
Ω~=2π[(CpCvCp)tan1(ξ/qD)+CvCp(ξ/qD)]\tilde \Omega = \frac{2}{\pi}\left[ \left(\frac{C_p - C_v}{C_p}\right)\tan^{-1} (\xi/q_D) + \frac{C_v} {C_p}(\xi/q_D) \right]
Ω~0=2π{1exp[1qD/ξ+1/3(ξ/qD)2(ρc/ρ)2]}\tilde \Omega_0 = \frac{2}{\pi}\left\{1 - \exp\left[\frac{-1}{q_D/\xi + 1/3(\xi/q_D)^2(\rho_c/\rho)^2} \right] \right\}
ξ=ξ0[χ~(T,ρ)χ~(Tref,ρ)TrefTΓ]ν/γ\xi = \xi_0 \left[\frac{\tilde \chi(T, \rho) - \tilde \chi(T_{ref}, \rho)\frac{T_{ref}}{T}}{\Gamma} \right]^{\nu/\gamma}
χ~(T,ρ)=Pcρρc2(ρP)T\tilde \chi(T, \rho) = \frac{P_c \rho}{\rho_c^2} \left(\frac{\partial \rho}{\partial P} \right)_{T}
Parameters
Tfloat

Temperature air [K]

rhofloat

Molar density of air [mol/m^3]

Cpfloat, optional

Molar constant pressure heat capacity of air, [J/mol/K]

Cvfloat, optional

Molar constant volume heat capacity of air, [J/mol/K]

mufloat, optional

Viscosity of air, [Pa*s]

drho_dPfloat, optional

Partial derivative of density with respect to pressure at constant temperature, [mol/m^3/Pa]

drho_dP_Trfloat, 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]

Returns
kfloat

Thermal condiuctivity of air, [W/m/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.

kl=a0(1+i3aiτi/3)k_l = a_0\left(1 + \sum_i^3 a_i\tau^{i/3} \right)
Parameters
Tfloat

Temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

a0float

Coefficient, [-]

a1float

Coefficient, [-]

a2float

Coefficient, [-]

a3float

Coefficient, [-]

Returns
kfloat

Low pressure liquid thermal conductivity, [W/(m*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.

kg=Tr(i=13aiTri)1k_g = \sqrt{T_r}\left( \sum_{i=1}^3 \frac{a_i}{T_r^i} \right)^{-1}
Parameters
Tfloat

Temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

a1float

Coefficient, [-]

a2float

Coefficient, [-]

a3float

Coefficient, [-]

Returns
kfloat

Low pressure gas thermal conductivity, [W/(m*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.

kl=A+exp(BT+C+DT+ET2)k_l = A + \exp\left(\frac{B}{T} + C + DT + ET^2 \right)
Parameters
Tfloat

Temperature of fluid [K]

Afloat

Coefficient, [W/(m*K)]

Bfloat

Coefficient, [K]

Cfloat

Coefficient, [-]

Dfloat

Coefficient, [1/K]

Efloat

Coefficient, [1/K^2]

Returns
kfloat

Low pressure liquid thermal conductivity, [W/(m*K)]

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]