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# -*- coding: utf-8 -*- 

'''Chemical Engineering Design Library (ChEDL). Utilities for process modeling. 

Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com> 

 

Permission is hereby granted, free of charge, to any person obtaining a copy 

of this software and associated documentation files (the "Software"), to deal 

in the Software without restriction, including without limitation the rights 

to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 

copies of the Software, and to permit persons to whom the Software is 

furnished to do so, subject to the following conditions: 

 

The above copyright notice and this permission notice shall be included in all 

copies or substantial portions of the Software. 

 

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 

IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 

AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 

LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 

OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 

SOFTWARE.''' 

 

from __future__ import division 

 

__all__ = ['Sheffy_Johnson', 'Sato_Riedel', 'Lakshmi_Prasad', 

'Gharagheizi_liquid', 'Nicola_original', 'Nicola', 'Bahadori_liquid', 

'thermal_conductivity_liquid_methods', 'ThermalConductivityLiquid', 'DIPPR9G', 

'Missenard', 'DIPPR9I', 'Filippov', 'thermal_conductivity_liquid_mixture', 

'Eucken', 'Eucken_modified', 'DIPPR9B', 'Chung', 'eli_hanley', 

'Gharagheizi_gas', 'Bahadori_gas', 'thermal_conductivity_gas_methods', 

'thermal_conductivity_gas_methods_P', 'ThermalConductivityGas', 

'stiel_thodos_dense', 'eli_hanley_dense', 'chung_dense', 'Lindsay_Bromley', 

'thermal_conductivity_gas_mixture'] 

 

import numpy as np 

from scipy.interpolate import interp2d 

from scipy.constants import R 

 

from thermo.utils import log, exp 

from thermo.utils import mixing_simple, none_and_length_check, TPDependentProperty 

from thermo.miscdata import _VDISaturationDict, VDI_tabular_data 

from thermo.coolprop import has_CoolProp, coolprop_dict, coolprop_fluids, CoolProp_T_dependent_property, PropsSI, PhaseSI 

from thermo.electrochem import thermal_conductivity_Magomedov, Magomedovk_thermal_cond 

 

### Purely CSP Methods - Liquids 

 

 

def Sheffy_Johnson(T, M, Tm): 

r'''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. 

 

.. math:: 

k = 1.951 \frac{1-0.00126(T-T_m)}{T_m^{0.216}MW^{0.3}} 

 

Parameters 

---------- 

T : float 

Temperature of the fluid [K] 

M : float 

Molecular weight of the fluid [g/mol] 

Tm : float 

Melting point of the fluid [K] 

 

Returns 

------- 

kl : float 

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. 

 

Examples 

-------- 

>>> Sheffy_Johnson(300, 47, 280) 

0.17740150413112196 

 

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 

''' 

kl = 1.951 * (1-0.00126*(T-Tm)) / (Tm**0.216*M**0.3) 

return kl 

 

 

def Sato_Riedel(T, M, Tb, Tc): 

r'''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. 

 

.. math:: 

k = \frac{1.1053}{\sqrt{MW}}\frac{3+20(1-T_r)^{2/3}} 

{3+20(1-T_{br})^{2/3}} 

 

Parameters 

---------- 

T : float 

Temperature of the fluid [K] 

M : float 

Molecular weight of the fluid [g/mol] 

Tb : float 

Boiling temperature of the fluid [K] 

Tc : float 

Critical temperature of the fluid [K] 

 

Returns 

------- 

kl : float 

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. 

 

Examples 

-------- 

>>> Sato_Riedel(300, 47, 390, 520) 

0.2103769246133769 

 

References 

---------- 

.. [1] Riedel, L.: Chem. Ing. Tech., 21, 349 (1949); 23: 59, 321, 465 (1951) 

.. [2] Maejima, T., private communication, 1973 

.. [3] Properties of Gases and Liquids", 3rd Ed., McGraw-Hill, 1977 

''' 

Tr = T/Tc 

Tbr = Tb/Tc 

k = 1.1053 * (3. + 20.*(1-Tr)**(2/3.0)) / M**0.5 / (3+20.*(1-Tbr)**(2/3.0)) 

return k 

 

 

def Lakshmi_Prasad(T, M): 

r'''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. 

 

.. math:: 

\lambda = 0.0655-0.0005T + \frac{1.3855-0.00197T}{M^{0.5}} 

 

Parameters 

---------- 

T : float 

Temperature of the fluid [K] 

M : float 

Molecular weight of the fluid [g/mol] 

 

Returns 

------- 

kl : float 

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. 

 

Examples 

-------- 

>>> Lakshmi_Prasad(273.15, 100) 

0.013664450000000009 

 

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 

''' 

kl = 0.0655 - 0.0005*T + (1.3855 - 0.00197*T)/M**0.5 

return kl 

 

 

def Gharagheizi_liquid(T, M, Tb, Pc, omega): 

r'''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. 

 

.. math:: 

&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 = 3.8588MW^8(1.0045B+6.5152MW-8.9756) 

 

&B = 16.0407MW+2T_b-27.9074 

 

Parameters 

---------- 

T : float 

Temperature of the fluid [K] 

M : float 

Molecular weight of the fluid [g/mol] 

Tb : float 

Boiling temperature of the fluid [K] 

Pc : float 

Critical pressure of the fluid [Pa] 

omega : float 

Acentric factor of the fluid [-] 

 

Returns 

------- 

kl : float 

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. 

 

Examples 

-------- 

>>> Gharagheizi_liquid(300, 40, 350, 1E6, 0.27) 

0.2171113029534838 

 

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 

''' 

Pc = Pc/1E5 

B = 16.0407*M + 2*Tb - 27.9074 

A = 3.8588*M**8 * (1.0045*B + 6.5152*M - 8.9756) 

kl = 1E-4*(10*omega + 2*Pc - 2*T + 4 + 1.908*(Tb + 1.009*B**2/M**2) 

+ 3.9287*M**4/B**4 + A/B**8) 

return kl 

 

 

def Nicola_original(T, M, Tc, omega, Hfus): 

r'''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. 

 

.. math:: 

\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 

---------- 

T : float 

Temperature of the fluid [K] 

M : float 

Molecular weight of the fluid [g/mol] 

Tc : float 

Critical temperature of the fluid [K] 

omega : float 

Acentric factor of the fluid [-] 

Hfus : float 

Heat of fusion of the fluid [J/mol] 

 

Returns 

------- 

kl : float 

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. 

 

Examples 

-------- 

>>> Nicola_original(300, 142.3, 611.7, 0.49, 201853) 

0.2305018632230984 

 

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 

''' 

Tr = T/Tc 

Hfus = Hfus*1000 

kl = -0.5694 - 0.1436*Tr + 5.4893E-10*Hfus + 0.0508*omega + (1/M)**0.0622 

return kl 

 

 

def Nicola(T, M, Tc, Pc, omega): 

r'''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. 

 

.. math:: 

\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 

---------- 

T : float 

Temperature of the fluid [K] 

M : float 

Molecular weight of the fluid [g/mol] 

Tc : float 

Critical temperature of the fluid [K] 

Pc : float 

Critical pressure of the fluid [Pa] 

omega : float 

Acentric factor of the fluid [-] 

 

Returns 

------- 

kl : float 

Estimated liquid thermal conductivity [W/m/k] 

 

Notes 

----- 

A statistical correlation. A revision of an original correlation. 

 

Examples 

-------- 

>>> Nicola(300, 142.3, 611.7, 2110000.0, 0.49) 

0.10863821554584034 

 

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 

''' 

Tr = T/Tc 

Pc = Pc/1E5 

kl = 0.5147*(-0.2537*Tr + 0.0017*Pc + 0.1501*omega + (1./M)**0.2999) 

return kl 

 

 

def Bahadori_liquid(T, M): 

r'''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. 

 

.. math:: 

K = a + bY + CY^2 + dY^3 

 

a = A_1 + B_1 X + C_1 X^2 + D_1 X^3 

 

b = A_2 + B_2 X + C_2 X^2 + D_2 X^3 

 

c = A_3 + B_3 X + C_3 X^2 + D_3 X^3 

 

d = A_4 + B_4 X + C_4 X^2 + D_4 X^3 

 

Parameters 

---------- 

T : float 

Temperature of the fluid [K] 

M : float 

Molecular weight of the fluid [g/mol] 

 

Returns 

------- 

kl : float 

Estimated liquid thermal conductivity [W/m/k] 

 

Notes 

----- 

The accuracy of this equation has not been reviewed. 

 

Examples 

-------- 

Data point from [1]_. 

 

>>> Bahadori_liquid(273.15, 170) 

0.14274278108272603 

 

References 

---------- 

.. [1] Bahadori, Alireza, and Saeid Mokhatab. "Estimating Thermal 

Conductivity of Hydrocarbons." Chemical Engineering 115, no. 13 

(December 2008): 52-54 

''' 

A = [-6.48326E-2, 2.715015E-3, -1.08580E-5, 9.853917E-9] 

B = [1.565612E-2, -1.55833E-4, 5.051114E-7, -4.68030E-10] 

C = [-1.80304E-4, 1.758693E-6, -5.55224E-9, 5.201365E-12] 

D = [5.880443E-7, -5.65898E-9, 1.764384E-11, -1.65944E-14] 

X = M 

Y = T 

a = A[0] + B[0]*X + C[0]*X**2 + D[0]*X**3 

b = A[1] + B[1]*X + C[1]*X**2 + D[1]*X**3 

c = A[2] + B[2]*X + C[2]*X**2 + D[2]*X**3 

d = A[3] + B[3]*X + C[3]*X**2 + D[3]*X**3 

kl = a + b*Y + c*Y**2 + d*Y**3 

return kl 

 

 

VDI_TABULAR = 'VDI_TABULAR' 

COOLPROP = 'COOLPROP' 

GHARAGHEIZI_L = 'GHARAGHEIZI_L' 

NICOLA = 'NICOLA' 

NICOLA_ORIGINAL = 'NICOLA_ORIGINAL' 

SATO_RIEDEL = 'SATO_RIEDEL' 

SHEFFY_JOHNSON = 'SHEFFY_JOHNSON' 

BAHADORI_L = 'BAHADORI_L' 

LAKSHMI_PRASAD = 'LAKSHMI_PRASAD' 

MISSENARD = 'MISSENARD' 

NONE = 'NONE' 

NEGLIGIBLE = 'NEGLIGIBLE' 

DIPPR_9G = 'DIPPR_9G' 

 

thermal_conductivity_liquid_methods = [COOLPROP, VDI_TABULAR, GHARAGHEIZI_L, 

SATO_RIEDEL, NICOLA, NICOLA_ORIGINAL, 

SHEFFY_JOHNSON, BAHADORI_L, 

LAKSHMI_PRASAD] 

'''Holds all low-pressure methods available for the ThermalConductivityLiquid 

class, for use in iterating over them.''' 

 

thermal_conductivity_liquid_methods_P = [COOLPROP, DIPPR_9G, MISSENARD] 

'''Holds all high-pressure methods available for the ThermalConductivityLiquid 

class, for use in iterating over them.''' 

 

class ThermalConductivityLiquid(TPDependentProperty): 

r'''Class for dealing with liquid thermal conductivity as a function of 

temperature and pressure. 

 

For low-pressure (at 1 atm while under the vapor pressure; along the 

saturation line otherwise) liquids, there is one source of tabular 

information, 7 corresponding-states estimators, and the external 

library CoolProp. 

 

For high-pressure liquids (also, <1 atm liquids), there are two 

corresponding-states estimator, and the external library CoolProp. 

 

Parameters 

---------- 

CASRN : str, optional 

The CAS number of the chemical 

MW : float, optional 

Molecular weight, [g/mol] 

Tm : float, optional 

Melting point, [K] 

Tb : float, optional 

Boiling point, [K] 

Tc : float, optional 

Critical temperature, [K] 

Pc : float, optional 

Critical pressure, [Pa] 

omega : float, optional 

Acentric factor, [-] 

Hfus : float, optional 

Heat of fusion, [J/mol] 

 

Notes 

----- 

To iterate over all methods, use the lists stored in 

:obj:`thermal_conductivity_liquid_methods` and 

:obj:`thermal_conductivity_liquid_methods_P` for low and high pressure 

methods respectively. 

 

Low pressure methods: 

 

**GHARAGHEIZI_L**: 

CSP method, described in :obj:`Gharagheizi_liquid`. 

**SATO_RIEDEL**: 

CSP method, described in :obj:`Sato_Riedel`. 

**NICOLA**: 

CSP method, described in :obj:`Nicola`. 

**NICOLA_ORIGINAL**: 

CSP method, described in :obj:`Nicola_original`. 

**SHEFFY_JOHNSON**: 

CSP method, described in :obj:`Sheffy_Johnson`. 

**BAHADORI_L**: 

CSP method, described in :obj:`Bahadori_liquid`. 

**LAKSHMI_PRASAD**: 

CSP method, described in :obj:`Lakshmi_Prasad`. 

**COOLPROP**: 

CoolProp external library; with select fluids from its library. 

Range is limited to that of the equations of state it uses, as 

described in [1]_. Very slow. 

**VDI_TABULAR**: 

Tabular data in [2]_ along the saturation curve; interpolation is as 

set by the user or the default. 

 

High pressure methods: 

 

**DIPPR_9G**: 

CSP method, described in :obj:`DIPPR9G`. Calculates a 

low-pressure thermal conductivity first, using `T_dependent_property`. 

**MISSENARD**: 

CSP method, described in :obj:`Missenard`. Calculates a 

low-pressure thermal conductivity first, using `T_dependent_property`. 

**COOLPROP**: 

CoolProp external library; with select fluids from its library. 

Range is limited to that of the equations of state it uses, as 

described in [1]_. Very slow, but unparalled in accuracy for pressure 

dependence. 

 

See Also 

-------- 

Sheffy_Johnson 

Sato_Riedel 

Lakshmi_Prasad 

Gharagheizi_liquid 

Nicola_original 

Nicola 

Bahadori_liquid 

DIPPR9G 

Missenard 

 

References 

---------- 

.. [1] Bell, Ian H., Jorrit Wronski, Sylvain Quoilin, and Vincent Lemort. 

"Pure and Pseudo-Pure Fluid Thermophysical Property Evaluation and the 

Open-Source Thermophysical Property Library CoolProp." Industrial & 

Engineering Chemistry Research 53, no. 6 (February 12, 2014): 

2498-2508. doi:10.1021/ie4033999. http://www.coolprop.org/ 

.. [2] Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. 

Berlin; New York:: Springer, 2010. 

''' 

name = 'liquid thermal conductivity' 

units = 'W/m/K' 

interpolation_T = None 

'''No interpolation transformation by default.''' 

interpolation_P = None 

'''No interpolation transformation by default.''' 

interpolation_property = None 

'''No interpolation transformation by default.''' 

interpolation_property_inv = None 

'''No interpolation transformation by default.''' 

tabular_extrapolation_permitted = True 

'''Allow tabular extrapolation by default.''' 

property_min = 0 

'''Mimimum valid value of liquid thermal conductivity.''' 

property_max = 10 

'''Maximum valid value of liquid thermal conductivity. Generous limit.''' 

 

ranked_methods = [COOLPROP, VDI_TABULAR, GHARAGHEIZI_L, 

SATO_RIEDEL, NICOLA, NICOLA_ORIGINAL, 

SHEFFY_JOHNSON, BAHADORI_L, LAKSHMI_PRASAD] 

'''Default rankings of the low-pressure methods.''' 

ranked_methods_P = [COOLPROP, DIPPR_9G, MISSENARD] 

'''Default rankings of the high-pressure methods.''' 

 

 

def __init__(self, CASRN='', MW=None, Tm=None, Tb=None, Tc=None, Pc=None, 

omega=None, Hfus=None): 

self.CASRN = CASRN 

self.MW = MW 

self.Tm = Tm 

self.Tb = Tb 

self.Tc = Tc 

self.Pc = Pc 

self.omega = omega 

self.Hfus = Hfus 

 

self.Tmin = None 

'''Minimum temperature at which no method can calculate the 

property under.''' 

self.Tmax = None 

'''Maximum temperature at which no method can calculate the 

property above.''' 

 

self.tabular_data = {} 

'''tabular_data, dict: Stored (Ts, properties) for any 

tabular data; indexed by provided or autogenerated name.''' 

self.tabular_data_interpolators = {} 

'''tabular_data_interpolators, dict: Stored (extrapolator, 

spline) tuples which are interp1d instances for each set of tabular 

data; indexed by tuple of (name, interpolation_T, 

interpolation_property, interpolation_property_inv) to ensure that 

if an interpolation transform is altered, the old interpolator which 

had been created is no longer used.''' 

 

self.tabular_data_P = {} 

'''tabular_data_P, dict: Stored (Ts, Ps, properties) for any 

tabular data; indexed by provided or autogenerated name.''' 

self.tabular_data_interpolators_P = {} 

'''tabular_data_interpolators_P, dict: Stored (extrapolator, 

spline) tuples which are interp2d instances for each set of tabular 

data; indexed by tuple of (name, interpolation_T, interpolation_P, 

interpolation_property, interpolation_property_inv) to ensure that 

if an interpolation transform is altered, the old interpolator which 

had been created is no longer used.''' 

 

self.sorted_valid_methods = [] 

'''sorted_valid_methods, list: Stored methods which were found valid 

at a specific temperature; set by `T_dependent_property`.''' 

self.sorted_valid_methods_P = [] 

'''sorted_valid_methods_P, list: Stored methods which were found valid 

at a specific temperature; set by `TP_dependent_property`.''' 

self.user_methods = [] 

'''user_methods, list: Stored methods which were specified by the user 

in a ranked order of preference; set by `T_dependent_property`.''' 

self.user_methods_P = [] 

'''user_methods_P, list: Stored methods which were specified by the user 

in a ranked order of preference; set by `TP_dependent_property`.''' 

 

self.all_methods = set() 

'''Set of all low-pressure methods available for a given CASRN and 

properties; filled by :obj:`load_all_methods`.''' 

self.all_methods_P = set() 

'''Set of all high-pressure methods available for a given CASRN and 

properties; filled by :obj:`load_all_methods`.''' 

 

self.load_all_methods() 

 

def load_all_methods(self): 

r'''Method which picks out coefficients for the specified chemical 

from the various dictionaries and DataFrames storing it. All data is 

stored as attributes. This method also sets :obj:`Tmin`, :obj:`Tmax`, 

:obj:`all_methods` and obj:`all_methods_P` as a set of methods for 

which the data exists for. 

 

Called on initialization only. See the source code for the variables at 

which the coefficients are stored. The coefficients can safely be 

altered once the class is initialized. This method can be called again 

to reset the parameters. 

''' 

methods, methods_P = [], [] 

Tmins, Tmaxs = [], [] 

if self.CASRN in _VDISaturationDict: 

methods.append(VDI_TABULAR) 

Ts, props = VDI_tabular_data(self.CASRN, 'K (l)') 

self.VDI_Tmin = Ts[0] 

self.VDI_Tmax = Ts[-1] 

self.tabular_data[VDI_TABULAR] = (Ts, props) 

Tmins.append(self.VDI_Tmin); Tmaxs.append(self.VDI_Tmax) 

if has_CoolProp and self.CASRN in coolprop_dict: 

methods.append(COOLPROP); methods_P.append(COOLPROP) 

self.CP_f = coolprop_fluids[self.CASRN] 

Tmins.append(self.CP_f.Tmin); Tmaxs.append(self.CP_f.Tc) 

if self.MW: 

methods.extend([BAHADORI_L, LAKSHMI_PRASAD]) 

# Tmin and Tmax are not extended by these simple models, who often 

# give values of 0; BAHADORI_L even has 3 roots. 

# LAKSHMI_PRASAD works down to 0 K, and has an upper limit of 

# 50.0*(131.0*sqrt(M) + 2771.0)/(50.0*M**0.5 + 197.0) 

# where it becomes 0. 

if all([self.MW, self.Tm]): 

methods.append(SHEFFY_JOHNSON) 

Tmins.append(0); Tmaxs.append(self.Tm + 793.65) 

# Works down to 0, has a nice limit at T = Tm+793.65 from Sympy 

if all([self.Tb, self.Pc, self.omega]): 

methods.append(GHARAGHEIZI_L) 

Tmins.append(self.Tb); Tmaxs.append(self.Tc) 

# Chosen as the model is weird 

if all([self.Tc, self.Pc, self.omega]): 

methods.append(NICOLA) 

if all([self.Tb, self.Tc]): 

methods.append(SATO_RIEDEL) 

if all([self.Hfus, self.Tc, self.omega]): 

methods.append(NICOLA_ORIGINAL) 

if all([self.Tc, self.Pc]): 

methods_P.extend([DIPPR_9G, MISSENARD]) 

self.all_methods = set(methods) 

self.all_methods_P = set(methods_P) 

if Tmins and Tmaxs: 

self.Tmin, self.Tmax = min(Tmins), max(Tmaxs) 

 

def calculate(self, T, method): 

r'''Method to calculate low-pressure liquid thermal conductivity at 

tempearture `T` with a given method. 

 

This method has no exception handling; see `T_dependent_property` 

for that. 

 

Parameters 

---------- 

T : float 

Temperature of the liquid, [K] 

method : str 

Name of the method to use 

 

Returns 

------- 

kl : float 

Thermal conductivity of the liquid at T and a low pressure, [W/m/K] 

''' 

if method == SHEFFY_JOHNSON: 

kl = Sheffy_Johnson(T, self.MW, self.Tm) 

elif method == SATO_RIEDEL: 

kl = Sato_Riedel(T, self.MW, self.Tb, self.Tc) 

elif method == GHARAGHEIZI_L: 

kl = Gharagheizi_liquid(T, self.MW, self.Tb, self.Pc, self.omega) 

elif method == NICOLA: 

kl = Nicola(T, self.MW, self.Tc, self.Pc, self.omega) 

elif method == NICOLA_ORIGINAL: 

kl = Nicola_original(T, self.MW, self.Tc, self.omega, self.Hfus) 

elif method == LAKSHMI_PRASAD: 

kl = Lakshmi_Prasad(T, self.MW) 

elif method == BAHADORI_L: 

kl = Bahadori_liquid(T, self.MW) 

elif method == COOLPROP: 

kl = CoolProp_T_dependent_property(T, self.CASRN, 'L', 'l') 

elif method in self.tabular_data: 

kl = self.interpolate(T, method) 

return kl 

 

def calculate_P(self, T, P, method): 

r'''Method to calculate pressure-dependent liquid thermal conductivity 

at temperature `T` and pressure `P` with a given method. 

 

This method has no exception handling; see `TP_dependent_property` 

for that. 

 

Parameters 

---------- 

T : float 

Temperature at which to calculate liquid thermal conductivity, [K] 

P : float 

Pressure at which to calculate liquid thermal conductivity, [K] 

method : str 

Name of the method to use 

 

Returns 

------- 

kl : float 

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

''' 

if method == DIPPR_9G: 

kl = self.T_dependent_property(T) 

kl = DIPPR9G(T, P, self.Tc, self.Pc, kl) 

elif method == MISSENARD: 

kl = self.T_dependent_property(T) 

kl = Missenard(T, P, self.Tc, self.Pc, kl) 

elif method == COOLPROP: 

kl = PropsSI('L', 'T', T, 'P', P, self.CASRN) 

elif method in self.tabular_data: 

kl = self.interpolate_P(T, P, method) 

return kl 

 

def test_method_validity(self, T, method): 

r'''Method to check the validity of a temperature-dependent 

low-pressure method. For CSP methods, the models **BAHADORI_L**, 

**LAKSHMI_PRASAD**, and **SHEFFY_JOHNSON** are considered valid for all 

temperatures. For methods **GHARAGHEIZI_L**, **NICOLA**, 

and **NICOLA_ORIGINAL**, the methods are considered valid up to 1.5Tc 

and down to 0 K. Method **SATO_RIEDEL** does not work above the 

critical point, so it is valid from 0 K to the critical point. 

 

For tabular data, extrapolation outside of the range is used if 

:obj:`tabular_extrapolation_permitted` is set; if it is, the extrapolation 

is considered valid for all temperatures. 

 

It is not guaranteed that a method will work or give an accurate 

prediction simply because this method considers the method valid. 

 

Parameters 

---------- 

T : float 

Temperature at which to test the method, [K] 

method : str 

Name of the method to test 

 

Returns 

------- 

validity : bool 

Whether or not a method is valid 

''' 

if method == SATO_RIEDEL: 

if T > self.Tc: 

return False 

# Doesn't run, no lower limit though 

elif method in [GHARAGHEIZI_L, NICOLA, NICOLA_ORIGINAL]: 

if T > self.Tc*1.5: 

return False 

# No lower limit, give a wide margin of acceptability here 

elif method in [BAHADORI_L, LAKSHMI_PRASAD, SHEFFY_JOHNSON]: 

pass 

# no limits at all 

elif method == COOLPROP: 

if T < self.CP_f.Tt or T > self.CP_f.Tc: 

return False 

elif method in self.tabular_data: 

# if tabular_extrapolation_permitted, good to go without checking 

if not self.tabular_extrapolation_permitted: 

Ts, properties = self.tabular_data[method] 

if T < Ts[0] or T > Ts[-1]: 

return False 

else: 

raise Exception('Method not valid') 

return True 

 

def test_method_validity_P(self, T, P, method): 

r'''Method to check the validity of a high-pressure method. For 

**COOLPROP**, the fluid must be both a liquid and under the maximum 

pressure of the fluid's EOS. **MISSENARD** has defined limits; 

between 0.5Tc and 0.8Tc, and below 200Pc. The CSP method **DIPPR_9G** 

is considered valid for all temperatures and pressures. 

 

For tabular data, extrapolation outside of the range is used if 

:obj:`tabular_extrapolation_permitted` is set; if it is, the 

extrapolation is considered valid for all temperatures and pressures. 

 

It is not guaranteed that a method will work or give an accurate 

prediction simply because this method considers the method valid. 

 

Parameters 

---------- 

T : float 

Temperature at which to test the method, [K] 

P : float 

Pressure at which to test the method, [Pa] 

method : str 

Name of the method to test 

 

Returns 

------- 

validity : bool 

Whether or not a method is valid 

''' 

validity = True 

if method == MISSENARD: 

if T/self.Tc < 0.5 or T/self.Tc > 0.8 or P/self.Pc > 200: 

validity = False 

elif method == DIPPR_9G: 

if T < 0 or P < 0: 

validity = False 

elif method == COOLPROP: 

validity = PhaseSI('T', T, 'P', P, self.CASRN) in ['liquid', 'supercritical_liquid'] 

elif method in self.tabular_data: 

if not self.tabular_extrapolation_permitted: 

Ts, Ps, properties = self.tabular_data[method] 

if T < Ts[0] or T > Ts[-1] or P < Ps[0] or P > Ps[-1]: 

validity = False 

else: 

raise Exception('Method not valid') 

return validity 

 

 

### Thermal Conductivity of Dense Liquids 

 

def DIPPR9G(T, P, Tc, Pc, kl): 

r'''Adjustes for pressure the thermal conductivity of a liquid using an 

emperical formula based on [1]_, but as given in [2]_. 

 

.. math:: 

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 

---------- 

T : float 

Temperature of fluid [K] 

P : float 

Pressure of fluid [Pa] 

Tc: float 

Critical point of fluid [K] 

Pc : float 

Critical pressure of the fluid [Pa] 

kl : float 

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

 

Returns 

------- 

kl_dense : float 

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 

 

Examples 

-------- 

From [2]_, for butyl acetate. 

 

>>> DIPPR9G(515.05, 3.92E7, 579.15, 3.212E6, 7.085E-2) 

0.0864419738671184 

 

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] Danner, Ronald P, and Design Institute for Physical Property Data. 

Manual for Predicting Chemical Process Design Data. New York, N.Y, 1982. 

''' 

Tr = T/Tc 

Pr = P/Pc 

kl_dense = kl*(0.98 + 0.0079*Pr*Tr**1.4 + 0.63*Tr**1.2*(Pr/(30+Pr))) 

return kl_dense 

 

 

Trs_Missenard = [0.8, 0.7, 0.6, 0.5] 

Prs_Missenard = [1, 5, 10, 50, 100, 200] 

Qs_Missenard = np.array([[0.036, 0.038, 0.038, 0.038, 0.038, 0.038], 

[0.018, 0.025, 0.027, 0.031, 0.032, 0.032], 

[0.015, 0.020, 0.022, 0.024, 0.025, 0.025], 

[0.012, 0.0165, 0.017, 0.019, 0.020, 0.020]]) 

Qfunc_Missenard = interp2d(Prs_Missenard, Trs_Missenard, Qs_Missenard) 

 

 

def Missenard(T, P, Tc, Pc, kl): 

r'''Adjustes for pressure the thermal conductivity of a liquid using an 

emperical formula based on [1]_, but as given in [2]_. 

 

.. math:: 

\frac{k}{k^*} = 1 + Q P_r^{0.7} 

 

Parameters 

---------- 

T : float 

Temperature of fluid [K] 

P : float 

Pressure of fluid [Pa] 

Tc: float 

Critical point of fluid [K] 

Pc : float 

Critical pressure of the fluid [Pa] 

kl : float 

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

 

Returns 

------- 

kl_dense : float 

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. 

 

Examples 

-------- 

Example from [2]_, toluene; matches. 

 

>>> Missenard(304., 6330E5, 591.8, 41E5, 0.129) 

0.21983757770696569 

 

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] Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. 

New York: McGraw-Hill Professional, 2000. 

''' 

Tr = T/Tc 

Pr = P/Pc 

Q = float(Qfunc_Missenard(Pr, Tr)) 

kl_dense = kl*(1 + Q*Pr**0.7) 

return kl_dense 

 

### Thermal conductivity of liquid mixtures 

 

 

def DIPPR9I(ws, ks): 

r'''Calculates thermal conductivity of a liquid mixture according to 

mixing rules in [1]_ and also in [2]_. 

 

.. math:: 

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

 

Parameters 

---------- 

ws : float 

Mass fractions of components 

ks : float 

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

 

Returns 

------- 

kl : float 

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. 

 

Examples 

-------- 

>>> DIPPR9I([0.258, 0.742], [0.1692, 0.1528]) 

0.15657104706719646 

 

References 

---------- 

.. [1] Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. The 

Properties of Gases and Liquids. McGraw-Hill Companies, 1987. 

.. [2] Danner, Ronald P, and Design Institute for Physical Property Data. 

Manual for Predicting Chemical Process Design Data. New York, N.Y, 1982. 

''' 

if not none_and_length_check([ks, ws]): # check same-length inputs 

raise Exception('Function inputs are incorrect format') 

kl = sum(ws[i]/ks[i]**2 for i in range(len(ws)))**(-0.5) 

return kl 

 

 

def Filippov(ws, ks): 

r'''Calculates thermal conductivity of a binary liquid mixture according to 

mixing rules in [2]_ as found in [1]_. 

 

.. math:: 

\lambda_m = w_1 \lambda_1 + w_2\lambda_2 

- 0.72 w_1 w_2(\lambda_2-\lambda_1) 

 

Parameters 

---------- 

ws : float 

Mass fractions of components 

ks : float 

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

 

Returns 

------- 

kl : float 

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. 

 

Examples 

-------- 

>>> Filippov([0.258, 0.742], [0.1692, 0.1528]) 

0.15929167628799998 

 

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). 

''' 

if not none_and_length_check([ks, ws], 2): # check same-length inputs 

raise Exception('Function inputs are incorrect format') 

kl = ws[0]*ks[0] + ws[1]*ks[1] - 0.72*ws[0]*ws[1]*(ks[1] - ks[0]) 

return kl 

 

 

MAGOMEDOV = 'Magomedov' 

DIPPR_9I = 'DIPPR9I' 

FILIPPOV = 'Filippov' 

SIMPLE = 'SIMPLE' 

 

 

def thermal_conductivity_liquid_mixture(T=None, P=None, zs=None, ws=None, 

ks=None, CASRNs=None, 

AvailableMethods=False, Method=None): # pragma: no cover 

'''This function handles the retrival of a mixture's liquid thermal conductivity. 

 

This API is considered experimental, and is expected to be removed in a 

future release in favor of a more complete object-oriented interface. 

 

>>> thermal_conductivity_liquid_mixture(ws=[0.258, 0.742], ks=[0.1692, 

... 0.1528], Method='DIPPR9I') 

0.15657104706719646 

 

>>> thermal_conductivity_liquid_mixture(ws=[0.258, 0.742], ks=[0.1692, 

... 0.1528], Method='Filippov') 

0.15929167628799998 

''' 

def list_methods(): 

methods = [] 

if '7732-18-5' in CASRNs and T and ws: 

wCASRNs = list(CASRNs) 

wCASRNs.remove('7732-18-5') 

if all([i in Magomedovk_thermal_cond.index for i in wCASRNs]): 

methods.append(MAGOMEDOV) 

if none_and_length_check([ks]): 

methods.append(DIPPR_9I) 

if none_and_length_check([ks, ws], 2): 

methods.append(FILIPPOV) 

if none_and_length_check([ks]): 

methods.append(SIMPLE) 

methods.append(NONE) 

return methods 

if AvailableMethods: 

return list_methods() 

if not Method: 

Method = list_methods()[0] 

# This is the calculate, given the method section 

if not none_and_length_check([ks, ws]): 

return None 

# raise Exception('Function inputs are incorrect format') 

if Method == SIMPLE: 

_kl = mixing_simple(zs, ks) 

elif Method == DIPPR_9I: 

_kl = DIPPR9I(ws, ks) 

elif Method == FILIPPOV: 

_kl = Filippov(ws, ks) 

elif Method == MAGOMEDOV: 

k_w = ks[CASRNs.index('7732-18-5')] 

wCASRNs = list(CASRNs) 

wCASRNs.remove('7732-18-5') 

ws2 = list(ws) 

ws2.pop(CASRNs.index('7732-18-5')) 

_kl = thermal_conductivity_Magomedov(T, P, ws2, wCASRNs, k_w) 

elif Method == NONE: 

return None 

else: 

raise Exception('Failure in in function') 

return _kl 

 

#print (thermal_conductivity_liquid_mixture(ws=[0.258, 0.742], ks=[0.1692, 0.1528]), 0) 

#print (thermal_conductivity_liquid_mixture(ws=[0.258, 0.742], ks=[0.1692, 0.1528], Method='Filippov'), 0) 

 

 

### Thermal Conductivity of Gases 

 

def Eucken(MW, Cvm, mu): 

r'''Estimates the thermal conductivity of a gas as a function of 

temperature using the CSP method of Eucken [1]_. 

 

.. math:: 

\frac{\lambda M}{\eta C_v} = 1 + \frac{9/4}{C_v/R} 

 

Parameters 

---------- 

MW : float 

Molecular weight of the gas [g/mol] 

Cvm : float 

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

mu : float 

Gas viscosity [Pa*S] 

 

Returns 

------- 

kg : float 

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. 

 

Examples 

-------- 

2-methylbutane at low pressure, 373.15 K. Mathes calculation in [1]_. 

 

>>> Eucken(MW=72.151, Cvm=135.9, mu=8.77E-6) 

0.018792644287722975 

 

References 

---------- 

.. [1] Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. 

Properties of Gases and Liquids. McGraw-Hill Companies, 1987. 

''' 

MW = MW/1000. 

kg = (1 + 9/4./(Cvm/R))*mu*Cvm/MW 

return kg 

 

 

def Eucken_modified(MW, Cvm, mu): 

r'''Estimates the thermal conductivity of a gas as a function of 

temperature using the Modified CSP method of Eucken [1]_. 

 

.. math:: 

\frac{\lambda M}{\eta C_v} = 1.32 + \frac{1.77}{C_v/R} 

 

Parameters 

---------- 

MW : float 

Molecular weight of the gas [g/mol] 

Cvm : float 

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

mu : float 

Gas viscosity [Pa*S] 

 

Returns 

------- 

kg : float 

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. 

 

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) 

0.023593536999201956 

 

References 

---------- 

.. [1] Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. 

Properties of Gases and Liquids. McGraw-Hill Companies, 1987. 

''' 

MW = MW/1000. 

kg = (1.32 + 1.77/(Cvm/R))*mu*Cvm/MW 

return kg 

 

 

def DIPPR9B(T, MW, Cvm, mu, Tc=None, chemtype=None): 

r'''Calculates the thermal conductivity of a gas using one of several 

emperical equations developed in [1]_, [2]_, and presented in [3]_. 

 

For monoatomic gases: 

 

.. math:: 

k = 2.5 \frac{\eta C_v}{MW} 

 

For linear molecules: 

 

.. math:: 

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

 

For nonlinear molecules: 

 

.. math:: 

k = \frac{\eta}{MW}(1.15C_v + 16903.36) 

 

Parameters 

---------- 

T : float 

Temperature of the fluid [K] 

Tc : float 

Critical temperature of the fluid [K] 

MW : float 

Molwcular weight of fluid [g/mol] 

Cvm : float 

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

mu : float 

Viscosity of gas, [Pa*S] 

 

Returns 

------- 

k_g : float 

Thermal conductivity of gas, [W/m/k] 

 

Notes 

----- 

Tested with DIPPR values. 

Cvm is internally converted to J/kmol/K. 

 

Examples 

-------- 

CO: 

 

>>> DIPPR9B(200., 28.01, 20.826, 1.277E-5, 132.92, chemtype='linear') 

0.01813208676438415 

 

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. 

''' 

Cvm = Cvm*1000. # J/g/K to J/kmol/K 

if not chemtype: 

chemtype = 'linear' 

if chemtype == 'monoatomic': 

k = 2.5*mu*Cvm/MW 

elif chemtype == 'linear': 

Tr = T/Tc 

k = mu/MW*(1.30*Cvm + 14644 - 2928.80/Tr) 

elif chemtype == 'nonlinear': 

k = mu/MW*(1.15*Cvm + 16903.36) 

else: 

raise Exception('Specified chemical type is not an option') 

return k 

 

 

def Chung(T, MW, Tc, omega, Cvm, mu): 

r'''Estimates the thermal conductivity of a gas as a function of 

temperature using the CSP method of Chung [1]_. 

 

.. math:: 

\frac{\lambda M}{\eta C_v} = \frac{3.75 \Psi}{C_v/R} 

 

\Psi = 1 + \alpha \left\{[0.215+0.28288\alpha-1.061\beta+0.26665Z]/ 

[0.6366+\beta Z + 1.061 \alpha \beta]\right\} 

 

\alpha = \frac{C_v}{R}-1.5 

 

\beta = 0.7862-0.7109\omega + 1.3168\omega^2 

 

Z=2+10.5T_r^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] 

omega : float 

Acentric factor of the gas [-] 

Cvm : float 

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

mu : float 

Gas viscosity [Pa*S] 

 

Returns 

------- 

kg : float 

Estimated gas thermal conductivity [W/m/k] 

 

Notes 

----- 

MW internally converted to kg/g-mol. 

 

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) 

0.023015653729496946 

 

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. 

''' 

MW = MW/1000. 

alpha = Cvm/R - 1.5 

beta = 0.7862 - 0.7109*omega + 1.3168*omega**2 

Z = 2 + 10.5*(T/Tc)**2 

psi = 1 + alpha*((0.215 + 0.28288*alpha - 1.061*beta + 0.26665*Z)/(0.6366 + beta*Z + 1.061*alpha*beta)) 

k = 3.75*psi/(Cvm/R)/MW*mu*Cvm 

return k 

 

 

def eli_hanley(T, MW, Tc, Vc, Zc, omega, Cvm): 

r'''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]_. 

 

.. math:: 

\lambda = \lambda^* + \frac{\eta^*}{MW}(1.32)\left(C_v - \frac{3R}{2}\right) 

 

Tr = \text{min}(Tr, 2) 

 

\theta = 1 + (\omega-0.011)\left(0.56553 - 0.86276\ln Tr - \frac{0.69852}{Tr}\right) 

 

\psi = [1 + (\omega - 0.011)(0.38560 - 1.1617\ln Tr)]\frac{0.288}{Z_c} 

 

f = \frac{T_c}{190.4}\theta 

 

h = \frac{V_c}{9.92E-5}\psi 

 

T_0 = T/f 

 

\eta_0^*(T_0)= \sum_{n=1}^9 C_n T_0^{(n-4)/3} 

 

\theta_0 = 1944 \eta_0 

 

\lambda^* = \lambda_0 H 

 

\eta^* = \eta^*_0 H \frac{MW}{16.04} 

 

H = \left(\frac{16.04}{MW}\right)^{0.5}f^{0.5}/h^{2/3} 

 

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] 

 

Returns 

------- 

kg : float 

Estimated gas thermal conductivity [W/m/k] 

 

Notes 

----- 

Reference fluid is Methane. 

MW internally converted to kg/g-mol. 

 

Examples 

-------- 

2-methylbutane at low pressure, 373.15 K. Mathes 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) 

0.022479517891353377 

 

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. 

''' 

Cs = [2.907741307E6, -3.312874033E6, 1.608101838E6, -4.331904871E5, 7.062481330E4, -7.116620750E3, 4.325174400E2, -1.445911210E1, 2.037119479E-1] 

 

Tr = T/Tc 

if Tr > 2: 

Tr = 2 

theta = 1 + (omega - 0.011)*(0.56553 - 0.86276*log(Tr) - 0.69852/Tr) 

psi = (1 + (omega-0.011)*(0.38560 - 1.1617*log(Tr)))*0.288/Zc 

f = Tc/190.4*theta 

h = Vc/9.92E-5*psi 

T0 = T/f 

eta0 = 1E-7*sum([Cs[i]*T0**((i+1-4)/3.) for i in range(len(Cs))]) 

k0 = 1944*eta0 

 

H = (16.04/MW)**0.5*f**0.5/h**(2/3.) 

etas = eta0*H*MW/16.04 

ks = k0*H 

k = ks + etas/(MW/1000.)*1.32*(Cvm-3*R/2.) 

return k 

 

 

def Gharagheizi_gas(T, MW, Tb, Pc, omega): 

r'''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. 

 

.. math:: 

k = 7.9505\times 10^{-4} + 3.989\times 10^{-5} T 

-5.419\times 10^-5 M + 3.989\times 10^{-5} A 

 

A = \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 

---------- 

T : float 

Temperature of the fluid [K] 

MW: float 

Molecular weight of the fluid [g/mol] 

Tb : float 

Boiling temperature of the fluid [K] 

Pc : float 

Critical pressure of the fluid [Pa] 

omega : float 

Acentric factor of the fluid [-] 

 

Returns 

------- 

kg : float 

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. 

 

Examples 

-------- 

>>> Gharagheizi_gas(580., 16.04246, 111.66, 4599000.0, 0.0115478000) 

0.09594861261873211 

 

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 

''' 

Pc = Pc/1E4 

B = T + (2*omega + 2*T - 2*T*(2*omega+3.2825)/Tb + 3.2825)/(2*omega + T - T*(2*omega+3.2825)/Tb + 3.2825) - T*(2*omega+3.2825)/Tb 

A = (2*omega + T - T*(2*omega + 3.2825)/Tb + 3.2825)/(0.1*MW*Pc*T) * (3.9752*omega + 0.1*Pc + 1.9876*B + 6.5243)**2 

k = 7.9505E-4 + 3.989E-5*T - 5.419E-5*MW+3.989E-5*A 

return k 

 

 

def Bahadori_gas(T, MW): 

r'''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. 

 

.. math:: 

K = a + bY + CY^2 + dY^3 

 

a = A_1 + B_1 X + C_1 X^2 + D_1 X^3 

 

b = A_2 + B_2 X + C_2 X^2 + D_2 X^3 

 

c = A_3 + B_3 X + C_3 X^2 + D_3 X^3 

 

d = A_4 + B_4 X + C_4 X^2 + D_4 X^3 

 

Parameters 

---------- 

T : float 

Temperature of the gas [K] 

MW : float 

Molecular weight of the gas [g/mol] 

 

Returns 

------- 

kg : float 

Estimated gas thermal conductivity [W/m/k] 

 

Notes 

----- 

The accuracy of this equation has not been reviewed. 

 

Examples 

-------- 

>>> Bahadori_gas(40+273.15, 20) # Point from article 

0.031968165337873326 

 

References 

---------- 

.. [1] Bahadori, Alireza, and Saeid Mokhatab. "Estimating Thermal 

Conductivity of Hydrocarbons." Chemical Engineering 115, no. 13 

(December 2008): 52-54 

''' 

A = [4.3931323468E-1, -3.88001122207E-2, 9.28616040136E-4, -6.57828995724E-6] 

B = [-2.9624238519E-3, 2.67956145820E-4, -6.40171884139E-6, 4.48579040207E-8] 

C = [7.54249790107E-6, -6.46636219509E-7, 1.5124510261E-8, -1.0376480449E-10] 

D = [-6.0988433456E-9, 5.20752132076E-10, -1.19425545729E-11, 8.0136464085E-14] 

X = T 

Y = MW 

a = A[0] + B[0]*X + C[0]*X**2 + D[0]*X**3 

b = A[1] + B[1]*X + C[1]*X**2 + D[1]*X**3 

c = A[2] + B[2]*X + C[2]*X**2 + D[2]*X**3 

d = A[3] + B[3]*X + C[3]*X**2 + D[3]*X**3 

kg = a + b*Y + c*Y**2 + d*Y**3 

return kg 

 

 

GHARAGHEIZI_G = 'GHARAGHEIZI_G' 

CHUNG = 'CHUNG' 

ELI_HANLEY = 'ELI_HANLEY' 

ELI_HANLEY_DENSE = 'ELI_HANLEY_DENSE' 

CHUNG_DENSE = 'CHUNG_DENSE' 

EUCKEN_MOD = 'EUCKEN_MOD' 

EUCKEN = 'EUCKEN' 

BAHADORI_G = 'BAHADORI_G' 

STIEL_THODOS_DENSE = 'STIEL_THODOS_DENSE' 

DIPPR_9B = 'DIPPR_9B' 

 

thermal_conductivity_gas_methods = [COOLPROP, VDI_TABULAR, GHARAGHEIZI_G, 

DIPPR_9B, CHUNG, ELI_HANLEY, EUCKEN_MOD, 

EUCKEN, BAHADORI_G] 

'''Holds all low-pressure methods available for the ThermalConductivityGas 

class, for use in iterating over them.''' 

thermal_conductivity_gas_methods_P = [COOLPROP, ELI_HANLEY_DENSE, CHUNG_DENSE, 

STIEL_THODOS_DENSE] 

'''Holds all high-pressure methods available for the ThermalConductivityGas 

class, for use in iterating over them.''' 

 

class ThermalConductivityGas(TPDependentProperty): 

r'''Class for dealing with gas thermal conductivity as a function of 

temperature and pressure. 

 

For gases at atmospheric pressure, there are 7 corresponding-states 

estimators, one source of tabular information, and the external library 

CoolProp. 

 

For gases under the fluid's boiling point (at sub-atmospheric pressures), 

and high-pressure gases above the boiling point, there are three 

corresponding-states estimators, and the external library CoolProp. 

 

Parameters 

---------- 

CASRN : str, optional 

The CAS number of the chemical 

MW : float, optional 

Molecular weight, [g/mol] 

Tb : float, optional 

Boiling point, [K] 

Tc : float, optional 

Critical temperature, [K] 

Pc : float, optional 

Critical pressure, [Pa] 

Vc : float, optional 

Critical volume, [m^3/mol] 

Zc : float, optional 

Critical compressibility, [-] 

omega : float, optional 

Acentric factor, [-] 

dipole : float, optional 

Dipole moment of the fluid, [debye] 

Vmg : float or callable, optional 

Molar volume of the fluid at a pressure and temperature or callable for 

the same, [m^3/mol] 

Cvgm : float or callable, optional 

Molar heat capacity of the fluid at a pressure and temperature or  

or callable for the same, [J/mol/K] 

mug : float or callable, optional 

Gas viscosity of the fluid at a pressure and temperature or callable 

for the same, [Pa*S] 

 

Notes 

----- 

To iterate over all methods, use the lists stored in 

:obj:`thermal_conductivity_gas_methods` and 

:obj:`thermal_conductivity_gas_methods_P` for low and high pressure 

methods respectively. 

 

Low pressure methods: 

 

**GHARAGHEIZI_G**: 

CSP method, described in :obj:`Gharagheizi_gas`. 

**DIPPR_9B**: 

CSP method, described in :obj:`DIPPR9B`. 

**CHUNG**: 

CSP method, described in :obj:`Chung`. 

**ELI_HANLEY**: 

CSP method, described in :obj:`eli_hanley`. 

**EUCKEN_MOD**: 

CSP method, described in :obj:`Eucken_modified`. 

**EUCKEN**: 

CSP method, described in :obj:`Eucken`. 

**BAHADORI_G**: 

CSP method, described in :obj:`Bahadori_gas`. 

**COOLPROP**: 

CoolProp external library; with select fluids from its library. 

Range is limited to that of the equations of state it uses, as 

described in [1]_. Very slow. 

**VDI_TABULAR**: 

Tabular data in [2]_ along the saturation curve; interpolation is as 

set by the user or the default. 

 

High pressure methods: 

 

**STIEL_THODOS_DENSE**: 

CSP method, described in :obj:`stiel_thodos_dense`. Calculates a 

low-pressure thermal conductivity first, using `T_dependent_property`. 

**ELI_HANLEY_DENSE**: 

CSP method, described in :obj:`eli_hanley_dense`. Calculates a 

low-pressure thermal conductivity first, using `T_dependent_property`. 

**CHUNG_DENSE**: 

CSP method, described in :obj:`chung_dense`. Calculates a 

low-pressure thermal conductivity first, using `T_dependent_property`. 

**COOLPROP**: 

CoolProp external library; with select fluids from its library. 

Range is limited to that of the equations of state it uses, as 

described in [1]_. Very slow, but unparalled in accuracy for pressure 

dependence. 

 

See Also 

-------- 

Bahadori_gas 

Gharagheizi_gas 

eli_hanley 

Chung 

DIPPR9B 

Eucken_modified 

Eucken 

stiel_thodos_dense 

eli_hanley_dense 

chung_dense 

 

References 

---------- 

.. [1] Bell, Ian H., Jorrit Wronski, Sylvain Quoilin, and Vincent Lemort. 

"Pure and Pseudo-Pure Fluid Thermophysical Property Evaluation and the 

Open-Source Thermophysical Property Library CoolProp." Industrial & 

Engineering Chemistry Research 53, no. 6 (February 12, 2014): 

2498-2508. doi:10.1021/ie4033999. http://www.coolprop.org/ 

.. [2] Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. 

Berlin; New York:: Springer, 2010. 

''' 

name = 'gas thermal conductivity' 

units = 'W/m/K' 

interpolation_T = None 

'''No interpolation transformation by default.''' 

interpolation_P = None 

'''No interpolation transformation by default.''' 

interpolation_property = None 

'''No interpolation transformation by default.''' 

interpolation_property_inv = None 

'''No interpolation transformation by default.''' 

tabular_extrapolation_permitted = True 

'''Allow tabular extrapolation by default.''' 

property_min = 0 

'''Mimimum valid value of gas thermal conductivity.''' 

property_max = 10 

'''Maximum valid value of gas thermal conductivity. Generous limit.''' 

 

ranked_methods = [COOLPROP, VDI_TABULAR, GHARAGHEIZI_G, DIPPR_9B, 

CHUNG, ELI_HANLEY, EUCKEN_MOD, EUCKEN, 

BAHADORI_G] 

'''Default rankings of the low-pressure methods.''' 

ranked_methods_P = [COOLPROP, ELI_HANLEY_DENSE, CHUNG_DENSE, 

STIEL_THODOS_DENSE] 

'''Default rankings of the high-pressure methods.''' 

 

def __init__(self, CASRN='', MW=None, Tb=None, Tc=None, Pc=None, Vc=None, 

Zc=None, omega=None, dipole=None, Vmg=None, Cvgm=None, mug=None): 

self.CASRN = CASRN 

self.MW = MW 

self.Tb = Tb 

self.Tc = Tc 

self.Pc = Pc 

self.Vc = Vc 

self.Zc = Zc 

self.omega = omega 

self.dipole = dipole 

self.Vmg = Vmg 

self.Cvgm = Cvgm 

self.mug = mug 

 

self.Tmin = None 

'''Minimum temperature at which no method can calculate the 

property under.''' 

self.Tmax = None 

'''Maximum temperature at which no method can calculate the 

property above.''' 

 

self.tabular_data = {} 

'''tabular_data, dict: Stored (Ts, properties) for any 

tabular data; indexed by provided or autogenerated name.''' 

self.tabular_data_interpolators = {} 

'''tabular_data_interpolators, dict: Stored (extrapolator, 

spline) tuples which are interp1d instances for each set of tabular 

data; indexed by tuple of (name, interpolation_T, 

interpolation_property, interpolation_property_inv) to ensure that 

if an interpolation transform is altered, the old interpolator which 

had been created is no longer used.''' 

 

self.tabular_data_P = {} 

'''tabular_data_P, dict: Stored (Ts, Ps, properties) for any 

tabular data; indexed by provided or autogenerated name.''' 

self.tabular_data_interpolators_P = {} 

'''tabular_data_interpolators_P, dict: Stored (extrapolator, 

spline) tuples which are interp2d instances for each set of tabular 

data; indexed by tuple of (name, interpolation_T, interpolation_P, 

interpolation_property, interpolation_property_inv) to ensure that 

if an interpolation transform is altered, the old interpolator which 

had been created is no longer used.''' 

 

self.sorted_valid_methods = [] 

'''sorted_valid_methods, list: Stored methods which were found valid 

at a specific temperature; set by `T_dependent_property`.''' 

self.sorted_valid_methods_P = [] 

'''sorted_valid_methods_P, list: Stored methods which were found valid 

at a specific temperature; set by `TP_dependent_property`.''' 

self.user_methods = [] 

'''user_methods, list: Stored methods which were specified by the user 

in a ranked order of preference; set by `T_dependent_property`.''' 

self.user_methods_P = [] 

'''user_methods_P, list: Stored methods which were specified by the user 

in a ranked order of preference; set by `TP_dependent_property`.''' 

 

self.all_methods = set() 

'''Set of all low-pressure methods available for a given CASRN and 

properties; filled by :obj:`load_all_methods`.''' 

self.all_methods_P = set() 

'''Set of all high-pressure methods available for a given CASRN and 

properties; filled by :obj:`load_all_methods`.''' 

 

self.load_all_methods() 

 

def load_all_methods(self): 

r'''Method which picks out coefficients for the specified chemical 

from the various dictionaries and DataFrames storing it. All data is 

stored as attributes. This method also sets :obj:`Tmin`, :obj:`Tmax`, 

:obj:`all_methods` and obj:`all_methods_P` as a set of methods for 

which the data exists for. 

 

Called on initialization only. See the source code for the variables at 

which the coefficients are stored. The coefficients can safely be 

altered once the class is initialized. This method can be called again 

to reset the parameters. 

''' 

methods, methods_P = [], [] 

Tmins, Tmaxs = [], [] 

if self.CASRN in _VDISaturationDict: 

methods.append(VDI_TABULAR) 

Ts, props = VDI_tabular_data(self.CASRN, 'K (g)') 

self.VDI_Tmin = Ts[0] 

self.VDI_Tmax = Ts[-1] 

self.tabular_data[VDI_TABULAR] = (Ts, props) 

Tmins.append(self.VDI_Tmin); Tmaxs.append(self.VDI_Tmax) 

if has_CoolProp and self.CASRN in coolprop_dict: 

methods.append(COOLPROP); methods_P.append(COOLPROP) 

self.CP_f = coolprop_fluids[self.CASRN] 

Tmins.append(self.CP_f.Tmin); Tmaxs.append(self.CP_f.Tc) 

if all((self.MW, self.Tb, self.Pc, self.omega)): 

methods.append(GHARAGHEIZI_G) 

# Turns negative at low T; do not set Tmin 

Tmaxs.append(3000) 

if all((self.Cvgm, self.mug, self.MW, self.Tc)): 

methods.append(DIPPR_9B) 

Tmins.append(0.01); Tmaxs.append(1E4) # No limit here 

if all((self.Cvgm, self.mug, self.MW, self.Tc, self.omega)): 

methods.append(CHUNG) 

Tmins.append(0.01); Tmaxs.append(1E4) # No limit 

if all((self.Cvgm, self.MW, self.Tc, self.Vc, self.Zc, self.omega)): 

methods.append(ELI_HANLEY) 

Tmaxs.append(1E4) # Numeric error at low T 

if all((self.Cvgm, self.mug, self.MW)): 

methods.append(EUCKEN_MOD) 

methods.append(EUCKEN) 

Tmins.append(0.01); Tmaxs.append(1E4) # No limits 

if self.MW: 

methods.append(BAHADORI_G) 

# Terrible method, so don't set methods 

if all([self.MW, self.Tc, self.Vc, self.Zc, self.omega]): 

methods_P.append(ELI_HANLEY_DENSE) 

if all([self.MW, self.Tc, self.Vc, self.omega, self.dipole]): 

methods_P.append(CHUNG_DENSE) 

if all([self.MW, self.Tc, self.Pc, self.Vc, self.Zc]): 

methods_P.append(STIEL_THODOS_DENSE) 

self.all_methods = set(methods) 

self.all_methods_P = set(methods_P) 

if Tmins and Tmaxs: 

self.Tmin, self.Tmax = min(Tmins), max(Tmaxs) 

 

def calculate(self, T, method): 

r'''Method to calculate low-pressure gas thermal conductivity at 

tempearture `T` with a given method. 

 

This method has no exception handling; see `T_dependent_property` 

for that. 

 

Parameters 

---------- 

T : float 

Temperature of the gas, [K] 

method : str 

Name of the method to use 

 

Returns 

------- 

kg : float 

Thermal conductivity of the gas at T and a low pressure, [W/m/K] 

''' 

if method == GHARAGHEIZI_G: 

kg = Gharagheizi_gas(T, self.MW, self.Tb, self.Pc, self.omega) 

elif method == DIPPR_9B: 

Cvgm = self.Cvgm(T) if hasattr(self.Cvgm, '__call__') else self.Cvgm 

mug = self.mug(T) if hasattr(self.mug, '__call__') else self.mug 

kg = DIPPR9B(T, self.MW, Cvgm, mug, self.Tc) 

elif method == CHUNG: 

Cvgm = self.Cvgm(T) if hasattr(self.Cvgm, '__call__') else self.Cvgm 

mug = self.mug(T) if hasattr(self.mug, '__call__') else self.mug 

kg = Chung(T, self.MW, self.Tc, self.omega, Cvgm, mug) 

elif method == ELI_HANLEY: 

Cvgm = self.Cvgm(T) if hasattr(self.Cvgm, '__call__') else self.Cvgm 

kg = eli_hanley(T, self.MW, self.Tc, self.Vc, self.Zc, self.omega, Cvgm) 

elif method == EUCKEN_MOD: 

Cvgm = self.Cvgm(T) if hasattr(self.Cvgm, '__call__') else self.Cvgm 

mug = self.mug(T) if hasattr(self.mug, '__call__') else self.mug 

kg = Eucken_modified(self.MW, Cvgm, mug) 

elif method == EUCKEN: 

Cvgm = self.Cvgm(T) if hasattr(self.Cvgm, '__call__') else self.Cvgm 

mug = self.mug(T) if hasattr(self.mug, '__call__') else self.mug 

kg = Eucken(self.MW, Cvgm, mug) 

elif method == BAHADORI_G: 

kg = Bahadori_gas(T, self.MW) 

elif method == COOLPROP: 

kg = CoolProp_T_dependent_property(T, self.CASRN, 'L', 'g') 

elif method in self.tabular_data: 

kg = self.interpolate(T, method) 

return kg 

 

def calculate_P(self, T, P, method): 

r'''Method to calculate pressure-dependent gas thermal conductivity 

at temperature `T` and pressure `P` with a given method. 

 

This method has no exception handling; see `TP_dependent_property` 

for that. 

 

Parameters 

---------- 

T : float 

Temperature at which to calculate gas thermal conductivity, [K] 

P : float 

Pressure at which to calculate gas thermal conductivity, [K] 

method : str 

Name of the method to use 

 

Returns 

------- 

kg : float 

Thermal conductivity of the gas at T and P, [W/m/K] 

''' 

if method == ELI_HANLEY_DENSE: 

kg = eli_hanley_dense(T, self.MW, self.Tc, self.Vc, self.Zc, self.omega, self.Cvgm, self.Vmg) 

elif method == CHUNG_DENSE: 

kg = chung_dense(T, self.MW, self.Tc, self.Vc, self.omega, self.Cvgm, self.Vmg, self.mug, self.dipole) 

elif method == STIEL_THODOS_DENSE: 

kg = self.T_dependent_property(T) 

kg = stiel_thodos_dense(T, self.MW, self.Tc, self.Pc, self.Vc, self.Zc, self.Vmg, kg) 

elif method == COOLPROP: 

kg = PropsSI('L', 'T', T, 'P', P, self.CASRN) 

elif method in self.tabular_data: 

kg = self.interpolate_P(T, P, method) 

return kg 

 

def test_method_validity(self, T, method): 

r'''Method to check the validity of a temperature-dependent 

low-pressure method. For CSP methods, the all methods are considered 

valid from 0 K and up. 

 

For tabular data, extrapolation outside of the range is used if 

:obj:`tabular_extrapolation_permitted` is set; if it is, the extrapolation 

is considered valid for all temperatures. 

 

It is not guaranteed that a method will work or give an accurate 

prediction simply because this method considers the method valid. 

**GHARAGHEIZI_G** and **BAHADORI_G** are known to sometimes produce 

negative results. 

 

Parameters 

---------- 

T : float 

Temperature at which to test the method, [K] 

method : str 

Name of the method to test 

 

Returns 

------- 

validity : bool 

Whether or not a method is valid 

''' 

if method in [GHARAGHEIZI_G, DIPPR_9B, CHUNG, ELI_HANLEY, EUCKEN_MOD, 

EUCKEN, BAHADORI_G]: 

pass 

elif method == COOLPROP: 

if T < self.CP_f.Tmin or T > self.CP_f.Tmax: 

return False 

elif method in self.tabular_data: 

# if tabular_extrapolation_permitted, good to go without checking 

if not self.tabular_extrapolation_permitted: 

Ts, properties = self.tabular_data[method] 

if T < Ts[0] or T > Ts[-1]: 

return False 

else: 

raise Exception('Method not valid') 

return True 

 

def test_method_validity_P(self, T, P, method): 

r'''Method to check the validity of a high-pressure method. For 

**COOLPROP**, the fluid must be both a gas and under the maximum 

pressure of the fluid's EOS. The CSP method **ELI_HANLEY_DENSE**, 

**CHUNG_DENSE**, and **STIEL_THODOS_DENSE** are considered valid for 

all temperatures and pressures. 

 

For tabular data, extrapolation outside of the range is used if 

:obj:`tabular_extrapolation_permitted` is set; if it is, the 

extrapolation is considered valid for all temperatures and pressures. 

 

It is not guaranteed that a method will work or give an accurate 

prediction simply because this method considers the method valid. 

 

Parameters 

---------- 

T : float 

Temperature at which to test the method, [K] 

P : float 

Pressure at which to test the method, [Pa] 

method : str 

Name of the method to test 

 

Returns 

------- 

validity : bool 

Whether or not a method is valid 

''' 

validity = True 

if method in [ELI_HANLEY_DENSE, CHUNG_DENSE, STIEL_THODOS_DENSE]: 

if T < 0 or P < 0: 

validity = False 

# no better checks known 

elif method == COOLPROP: 

if T < self.CP_f.Tmin or T > self.CP_f.Tmax or P > self.CP_f.Pmax: 

return False 

else: 

return PhaseSI('T', T, 'P', P, self.CASRN) in ['gas', 'supercritical_gas', 'supercritical', 'supercritical_liquid'] 

elif method in self.tabular_data: 

if not self.tabular_extrapolation_permitted: 

Ts, Ps, properties = self.tabular_data[method] 

if T < Ts[0] or T > Ts[-1] or P < Ps[0] or P > Ps[-1]: 

validity = False 

else: 

raise Exception('Method not valid') 

return validity 

 

 

### Thermal Conductivity of dense gases 

 

def stiel_thodos_dense(T, MW, Tc, Pc, Vc, Zc, Vm, kg): 

r'''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 \rho_r < 0.5: 

 

.. math:: 

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

 

if 0.5 < \rho_r < 2.0: 

 

.. math:: 

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

 

if 2 < \rho_r < 2.8: 

 

.. math:: 

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

 

\Gamma = 210 \left(\frac{T_cMW^3}{P_c^4}\right)^{1/6} 

 

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] 

 

Returns 

------- 

kg : float 

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

 

Notes 

----- 

Pc is internally converted to bar. 

 

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 

 

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. 

''' 

gamma = 210*(Tc*MW**3./(Pc/1E5)**4)**(1/6.) 

rhor = Vc/Vm 

if rhor < 0.5: 

term = 1.22E-2*(exp(0.535*rhor) - 1.) 

elif rhor < 2: 

term = 1.14E-2*(exp(0.67*rhor) - 1.069) 

else: 

# Technically only up to 2.8 

term = 2.60E-3*(exp(1.155*rhor) + 2.016) 

diff = term/Zc**5/gamma 

kg = kg + diff 

return kg 

 

 

def eli_hanley_dense(T, MW, Tc, Vc, Zc, omega, Cvm, Vm): 

r'''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]_. 

 

.. math:: 

Tr = min(Tr, 2) 

 

Vr = min(Vr, 2) 

 

f = \frac{T_c}{190.4}\theta 

 

h = \frac{V_c}{9.92E-5}\psi 

 

T_0 = T/f 

 

\rho_0 = \frac{16.04}{V}h 

 

\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) 

 

\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} 

 

\lambda_1 = 1944 \eta_0 

 

\lambda_2 = \left\{b_1 + b_2\left[b_3 - \ln \left(\frac{T_0}{b_4} 

\right)\right]^2\right\}\rho_0 

 

\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\} 

 

\lambda^{**} = [\lambda_1 + \lambda_2 + \lambda_3]H 

 

H = \left(\frac{16.04}{MW}\right)^{0.5}f^{0.5}/h^{2/3} 

 

X = \left\{\left[1 - \frac{T}{f}\left(\frac{df}{dT}\right)_v \right] 

\frac{0.288}{Z_c}\right\}^{1.5} 

 

\left(\frac{df}{dT}\right)_v = \frac{T_c}{190.4}\left(\frac{d\theta} 

{d T}\right)_v 

 

\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 

---------- 

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] 

 

Returns 

------- 

kg : float 

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

 

Notes 

----- 

Reference fluid is Methane. 

MW internally converted to kg/g-mol. 

 

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) 

0.06038475936515042 

 

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. 

''' 

Cs = [2.907741307E6, -3.312874033E6, 1.608101838E6, -4.331904871E5, 

7.062481330E4, -7.116620750E3, 4.325174400E2, -1.445911210E1, 

2.037119479E-1] 

 

Tr = T/Tc 

if Tr > 2: 

Tr = 2 

Vr = Vm/Vc 

if Vr > 2: 

Vr = 2 

theta = 1 + (omega - 0.011)*(0.09057 - 0.86276*log(Tr) + (0.31664 - 0.46568/Tr)*(Vr-0.5)) 

psi = (1 + (omega-0.011)*(0.39490*(Vr-1.02355) - 0.93281*(Vr-0.75464)*log(Tr)))*0.288/Zc 

f = Tc/190.4*theta 

h = Vc/9.92E-5*psi 

T0 = T/f 

rho0 = 16.04/(Vm*1E6)*h # Vm must be in cm^3/mol here. 

eta0 = 1E-7*sum([Cs[i]*T0**((i+1-4)/3.) for i in range(len(Cs))]) 

k1 = 1944*eta0 

b1 = -0.25276920E0 

b2 = 0.334328590E0 

b3 = 1.12 

b4 = 0.1680E3 

k2 = (b1 + b2*(b3 - log(T0/b4))**2)/1000.*rho0 

 

a1 = -7.19771 

a2 = 85.67822 

a3 = 12.47183 

a4 = -984.6252 

a5 = 0.3594685 

a6 = 69.79841 

a7 = -872.8833 

 

k3 = exp(a1 + a2/T0)*(exp((a3 + a4/T0**1.5)*rho0**0.1 + (rho0/0.1617 - 1)*rho0**0.5*(a5 + a6/T0 + a7/T0**2)) - 1)/1000. 

 

if T/Tc > 2: 

dtheta = 0 

else: 

dtheta = (omega - 0.011)*(-0.86276/T + (Vr-0.5)*0.46568*Tc/T**2) 

dfdT = Tc/190.4*dtheta 

X = ((1 - T/f*dfdT)*0.288/Zc)**1.5 

 

H = (16.04/MW)**0.5*f**0.5/h**(2/3.) 

ks = (k1*X + k2 + k3)*H 

 

### Uses calculations similar to those for pure species here 

theta = 1 + (omega - 0.011)*(0.56553 - 0.86276*log(Tr) - 0.69852/Tr) 

psi = (1 + (omega-0.011)*(0.38560 - 1.1617*log(Tr)))*0.288/Zc 

f = Tc/190.4*theta 

h = Vc/9.92E-5*psi 

T0 = T/f 

eta0 = 1E-7*sum([Cs[i]*T0**((i+1-4)/3.) for i in range(len(Cs))]) 

H = (16.04/MW)**0.5*f**0.5/h**(2/3.) 

etas = eta0*H*MW/16.04 

k = ks + etas/(MW/1000.)*1.32*(Cvm-3*R/2.) 

return k 

 

 

def chung_dense(T, MW, Tc, Vc, omega, Cvm, Vm, mu, dipole, association=0): 

r'''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]_. 

 

.. math:: 

\lambda = \frac{31.2 \eta^\circ \Psi}{M'}(G_2^{-1} + B_6 y)+qB_7y^2T_r^{1/2}G_2 

 

\Psi = 1 + \alpha \left\{[0.215+0.28288\alpha-1.061\beta+0.26665Z]/ 

[0.6366+\beta Z + 1.061 \alpha \beta]\right\} 

 

\alpha = \frac{C_v}{R}-1.5 

 

\beta = 0.7862-0.7109\omega + 1.3168\omega^2 

 

Z=2+10.5T_r^2 

 

q = 3.586\times 10^{-3} (T_c/M')^{1/2}/V_c^{2/3} 

 

y = \frac{V_c}{6V} 

 

G_1 = \frac{1-0.5y}{(1-y)^3} 

 

G_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} 

 

B_i = a_i + b_i \omega + c_i \mu_r^4 + d_i \kappa 

 

 

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 [-] 

 

Returns 

------- 

kg : float 

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] 

 

 

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) 

0.06160570379787278 

 

References 

---------- 

.. [1] 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. 

''' 

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] 

Tr = T/Tc 

mur = 131.3*dipole/(Vc*1E6*Tc)**0.5 

 

# From Chung Method 

alpha = Cvm/R - 1.5 

beta = 0.7862 - 0.7109*omega + 1.3168*omega**2 

Z = 2 + 10.5*(T/Tc)**2 

psi = 1 + alpha*((0.215 + 0.28288*alpha - 1.061*beta + 0.26665*Z)/(0.6366 + beta*Z + 1.061*alpha*beta)) 

 

y = Vc/(6*Vm) 

B1, B2, B3, B4, B5, B6, B7 = [ais[i] + bis[i]*omega + cis[i]*mur**4 + dis[i]*association for i in range(7)] 

G1 = (1 - 0.5*y)/(1. - y)**3 

G2 = (B1/y*(1 - exp(-B4*y)) + B2*G1*exp(B5*y) + B3*G1)/(B1*B4 + B2 + B3) 

q = 3.586E-3*(Tc/(MW/1000.))**0.5/(Vc*1E6)**(2/3.) 

k = 31.2*mu*psi/(MW/1000.)*(G2**-1 + B6*y) + q*B7*y**2*Tr**0.5*G2 

return k 

 

 

### Thermal conductivity of gas mixtures 

 

def Lindsay_Bromley(T, ys, ks, mus, Tbs, MWs): 

r'''Calculates thermal conductivity of a gas mixture according to 

mixing rules in [1]_ and also in [2]_. 

 

.. math:: 

k = \sum \frac{y_i k_i}{\sum y_i A_{ij}} 

 

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) 

 

S_{ij} = S_{ji} = (S_i S_j)^{0.5} 

 

Parameters 

---------- 

T : float 

Temperature of gas [K] 

ys : float 

Mole fractions of gas components 

ks : float 

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

mus : float 

Gas viscosities of all components, [Pa*S] 

Tbs : float 

Boiling points of all components, [K] 

MWs : float 

Molecular weights of all components, [g/mol] 

 

Returns 

------- 

kg : float 

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) 

 

TODO: Finish documenting this. 

 

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]) 

0.01390264417969313 

 

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] Danner, Ronald P, and Design Institute for Physical Property Data. 

Manual for Predicting Chemical Process Design Data. New York, N.Y, 1982. 

''' 

if not none_and_length_check([ys, ks, mus, Tbs, MWs]): 

raise Exception('Function inputs are incorrect format') 

 

Ss = [1.5*Tbs[i] for i in range(len(Tbs))] 

Sij = {} 

for i in range(len(ys)): 

for j in range(len(ys)): 

Sij[str(i)+str(j)] = (Ss[i]*Ss[j])**0.5 

Aij = {} 

for i in range(len(ys)): 

for j in range(len(ys)): 

Aij[str(i)+str(j)] = 0.25*(1 + (mus[i]/mus[j]*(MWs[j]/MWs[i])**0.75 

*(T+Ss[i])/(T+Ss[j]))**0.5 )**2 *(T+Sij[str(i)+str(j)])/(T+Ss[i]) 

kg = 0 

for i in range(len(ys)): 

denominator = sum(ys[j]*Aij[str(i)+str(j)] for j in range(len(ys))) 

kg += ys[i]*ks[i]/denominator 

 

return kg 

 

 

 

LINDSAY_BROMLEY = 'Lindsay-Bromley' 

 

def thermal_conductivity_gas_mixture(T=None, ys=None, ws=None, ks=None, 

mus=None, Tbs=None, MWs=None, CASRNs=None, 

AvailableMethods=False, Method=None): # pragma: no cover 

'''This function handles the retrival of a mixture's gas thermal conductivity. 

 

This API is considered experimental, and is expected to be removed in a 

future release in favor of a more complete object-oriented interface. 

 

>>> thermal_conductivity_gas_mixture(T=323.15, ys=[0.23, 0.77], 

... ks=[1.939E-2, 1.231E-2], mus=[1.002E-5, 1.015E-5], Tbs=[248.31, 

... 248.93], MWs=[46.07, 50.49]) 

0.01390264417969313 

''' 

def list_methods(): 

methods = [] 

if T and none_and_length_check([ks, mus, Tbs, MWs]): 

methods.append(LINDSAY_BROMLEY) 

if none_and_length_check([ks]): 

methods.append(SIMPLE) 

methods.append(NONE) 

return methods 

if AvailableMethods: 

return list_methods() 

if not Method: 

Method = list_methods()[0] 

# This is the calculate, given the method section 

if not none_and_length_check([ks, ys]): 

return None 

# raise Exception('Function inputs are incorrect format') 

if Method == SIMPLE: 

_kg = mixing_simple(ys, ks) 

elif Method == LINDSAY_BROMLEY: 

_kg = Lindsay_Bromley(T, ys, ks, mus, Tbs, MWs) 

elif Method == NONE: 

return None 

else: 

raise Exception('Failure in in function') 

return _kg