thermo.thermal_conductivity module¶

thermo.thermal_conductivity.
Sheffy_Johnson
(T, M, Tm)[source]¶ Calculate the thermal conductivity of a liquid as a function of temperature using the SheffyJohnson (1961) method. Requires Temperature, molecular weight, and melting point.
\[k = 1.951 \frac{10.00126(TT_m)}{T_m^{0.216}MW^{0.3}}\]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.
References
[R514] 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): 24549. doi:10.1021/je60010a019 Examples
>>> Sheffy_Johnson(300, 47, 280) 0.17740150413112196

thermo.thermal_conductivity.
Sato_Riedel
(T, M, Tb, Tc)[source]¶ Calculate the thermal conductivity of a liquid as a function of temperature using the CSP method of SatoRiedel [R515], [R516], published in Reid [R517]. Requires temperature, molecular weight, and boiling and critical temperatures.
\[k = \frac{1.1053}{\sqrt{MW}}\frac{3+20(1T_r)^{2/3}} {3+20(1T_{br})^{2/3}}\]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 [R517]. Limited accuracy should be expected. Uncheecked.
References
[R515] (1, 2) Riedel, L.: Chem. Ing. Tech., 21, 349 (1949); 23: 59, 321, 465 (1951) [R516] (1, 2) Maejima, T., private communication, 1973 [R517] (1, 2, 3) Properties of Gases and Liquids”, 3rd Ed., McGrawHill, 1977 Examples
>>> Sato_Riedel(300, 47, 390, 520) 0.21037692461337687

thermo.thermal_conductivity.
Lakshmi_Prasad
(T, M)[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.
\[\lambda = 0.06550.0005T + \frac{1.38550.00197T}{M^{0.5}}\]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.
References
[R518] 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): 21114. doi:10.1016/03009467(92)80037B Examples
>>> Lakshmi_Prasad(273.15, 100) 0.013664450000000009

thermo.thermal_conductivity.
Gharagheizi_liquid
(T, M, Tb, Pc, omega)[source]¶ Estimates the thermal conductivity of a liquid as a function of temperature using the CSP method of Gharagheizi [R519]. A convoluted method claiming highaccuracy and using only statistically significant variable following analalysis.
Requires temperature, molecular weight, boiling temperature and critical pressure and acentric factor.
\[ \begin{align}\begin{aligned}&k = 10^{4}\left[10\omega + 2P_c2T+4+1.908(T_b+\frac{1.009B^2}{MW^2}) +\frac{3.9287MW^4}{B^4}+\frac{A}{B^8}\right]\\&A = 3.8588MW^8(1.0045B+6.5152MW8.9756)\\&B = 16.0407MW+2T_b27.9074\end{aligned}\end{align} \]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.
References
[R519] (1, 2) Gharagheizi, Farhad, Poorandokht IlaniKashkouli, 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): 17028. doi:10.1002/aic.13938 Examples
>>> Gharagheizi_liquid(300, 40, 350, 1E6, 0.27) 0.2171113029534838

thermo.thermal_conductivity.
Nicola_original
(T, M, Tc, omega, Hfus)[source]¶ Estimates the thermal conductivity of a liquid as a function of temperature using the CSP method of Nicola [R520]. A simpler but long method claiming highaccuracy and using only statistically significant variable following analalysis.
Requires temperature, molecular weight, critical temperature, acentric factor and the heat of vaporization.
\[\frac{\lambda}{1 \text{Wm/K}}=0.56940.1436T_r+5.4893\times10^{10} \frac{\Delta_{fus}H}{\text{kmol/J}}+0.0508\omega + \left(\frac{1 \text{kg/kmol}}{MW}\right)^{0.0622}\]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.
References
[R520] (1, 2) 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): 13540. doi:10.1007/s1097301334227 Examples
>>> Nicola_original(300, 142.3, 611.7, 0.49, 201853) 0.2305018632230984

thermo.thermal_conductivity.
Nicola
(T, M, Tc, Pc, omega)[source]¶ Estimates the thermal conductivity of a liquid as a function of temperature using the CSP method of [R521]. A statistically derived equation using any correlated terms.
Requires temperature, molecular weight, critical temperature and pressure, and acentric factor.
\[\frac{\lambda}{0.5147 W/m/K} = 0.2537T_r+\frac{0.0017Pc}{\text{bar}} +0.1501 \omega + \left(\frac{1}{MW}\right)^{0.2999}\]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.
References
[R521] (1, 2) 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

thermo.thermal_conductivity.
Bahadori_liquid
(T, M)[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.
\[ \begin{align}\begin{aligned}K = a + bY + CY^2 + dY^3\\a = A_1 + B_1 X + C_1 X^2 + D_1 X^3\\b = A_2 + B_2 X + C_2 X^2 + D_2 X^3\\c = A_3 + B_3 X + C_3 X^2 + D_3 X^3\\d = A_4 + B_4 X + C_4 X^2 + D_4 X^3\end{aligned}\end{align} \]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.
References
[R522] (1, 2) Bahadori, Alireza, and Saeid Mokhatab. “Estimating Thermal Conductivity of Hydrocarbons.” Chemical Engineering 115, no. 13 (December 2008): 5254 Examples
Data point from [R522].
>>> Bahadori_liquid(273.15, 170) 0.14274278108272603

thermo.thermal_conductivity.
thermal_conductivity_liquid_methods
= ['COOLPROP', 'DIPPR_PERRY_8E', 'VDI_PPDS', 'VDI_TABULAR', 'GHARAGHEIZI_L', 'SHEFFY_JOHNSON', 'SATO_RIEDEL', 'LAKSHMI_PRASAD', 'BAHADORI_L', 'NICOLA', 'NICOLA_ORIGINAL']¶ Holds all lowpressure methods available for the ThermalConductivityLiquid class, for use in iterating over them.

class
thermo.thermal_conductivity.
ThermalConductivityLiquid
(CASRN='', MW=None, Tm=None, Tb=None, Tc=None, Pc=None, omega=None, Hfus=None)[source]¶ Bases:
thermo.utils.TPDependentProperty
Class for dealing with liquid thermal conductivity as a function of temperature and pressure.
For lowpressure (at 1 atm while under the vapor pressure; along the saturation line otherwise) liquids, there is one source of tabular information, one polynomialbased method, 7 correspondingstates estimators, and the external library CoolProp.
For highpressure liquids (also, <1 atm liquids), there are two correspondingstates estimator, and the external library CoolProp.
Parameters: CASs : list[str], optional
The CAS numbers of all species in the mixture
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]
See also
Sheffy_Johnson
,Sato_Riedel
,Lakshmi_Prasad
,Gharagheizi_liquid
,Nicola_original
,Nicola
,Bahadori_liquid
,DIPPR9G
,Missenard
Notes
To iterate over all methods, use the lists stored in
thermal_conductivity_liquid_methods
andthermal_conductivity_liquid_methods_P
for low and high pressure methods respectively.Low pressure methods:
 GHARAGHEIZI_L:
 CSP method, described in
Gharagheizi_liquid
.  SATO_RIEDEL:
 CSP method, described in
Sato_Riedel
.  NICOLA:
 CSP method, described in
Nicola
.  NICOLA_ORIGINAL:
 CSP method, described in
Nicola_original
.  SHEFFY_JOHNSON:
 CSP method, described in
Sheffy_Johnson
.  BAHADORI_L:
 CSP method, described in
Bahadori_liquid
.  LAKSHMI_PRASAD:
 CSP method, described in
Lakshmi_Prasad
.  DIPPR_PERRY_8E:
 A collection of 340 coefficient sets from the DIPPR database published
openly in [R525]. Provides temperature limits for all its fluids.
thermo.dippr.EQ100
is used for its fluids.  VDI_PPDS:
 Coefficients for a equation form developed by the PPDS, published openly in [R524]. Covers a large temperature range, but does not extrapolate well at very high or very low temperatures. 271 compounds.
 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 [R523]. Very slow.
 VDI_TABULAR:
 Tabular data in [R524] along the saturation curve; interpolation is as set by the user or the default.
High pressure methods:
 DIPPR_9G:
 CSP method, described in
DIPPR9G
. Calculates a lowpressure thermal conductivity first, using T_dependent_property.  MISSENARD:
 CSP method, described in
Missenard
. Calculates a lowpressure 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 [R523]. Very slow, but unparalled in accuracy for pressure dependence.
References
[R523] (1, 2, 3) Bell, Ian H., Jorrit Wronski, Sylvain Quoilin, and Vincent Lemort. “Pure and PseudoPure Fluid Thermophysical Property Evaluation and the OpenSource Thermophysical Property Library CoolProp.” Industrial & Engineering Chemistry Research 53, no. 6 (February 12, 2014): 24982508. doi:10.1021/ie4033999. http://www.coolprop.org/ [R524] (1, 2, 3) Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010. [R525] (1, 2) Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGrawHill Professional, 2007. Attributes
TP_cached T_cached interpolation_P interpolation_T interpolation_property interpolation_property_inv method method_P Methods
TP_dependent_property
(T, P)Method to calculate the property with sanity checking and without specifying a specific method. TP_dependent_property_derivative_P
(T, P[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to pressure at constant temperature, of a given order. TP_dependent_property_derivative_T
(T, P[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to temperature at constant pressure, of a given order. TP_or_T_dependent_property
(T, P)T_dependent_property
(T)Method to calculate the property with sanity checking and without specifying a specific method. T_dependent_property_derivative
(T[, order])Method to obtain a derivative of a property with respect to temperature, of a given order. T_dependent_property_integral
(T1, T2)Method to calculate the integral of a property with respect to temperature, using a specified method. T_dependent_property_integral_over_T
(T1, T2)Method to calculate the integral of a property over temperature with respect to temperature, using a specified method. __call__
(T, P)Convenience method to calculate the property; calls TP_dependent_property
.calculate
(T, method)Method to calculate lowpressure liquid thermal conductivity at tempearture T with a given method. calculate_P
(T, P, method)Method to calculate pressuredependent liquid thermal conductivity at temperature T and pressure P with a given method. calculate_derivative
(T, method[, order])Method to calculate a derivative of a property with respect to temperature, of a given order using a specified method. calculate_derivative_P
(P, T, method[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to pressure at constant temperature, of a given order using a specified method. calculate_derivative_T
(T, P, method[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to temperature at constant pressure, of a given order using a specified method. calculate_integral
(T1, T2, method)Method to calculate the integral of a property with respect to temperature, using a specified method. calculate_integral_over_T
(T1, T2, method)Method to calculate the integral of a property over temperature with respect to temperature, using a specified method. extrapolate_tabular
(T)interpolate
(T, name)Method to perform interpolation on a given tabular data set previously added via set_tabular_data
.interpolate_P
(T, P, name)Method to perform interpolation on a given tabular data set previously added via set_tabular_data_P. load_all_methods
()Method which picks out coefficients for the specified chemical from the various dictionaries and DataFrames storing it. plot_TP_dependent_property
([Tmin, Tmax, ...])Method to create a plot of the property vs temperature and pressure according to either a specified list of methods, or user methods (if set), or all methods. plot_T_dependent_property
([Tmin, Tmax, ...])Method to create a plot of the property vs temperature according to either a specified list of methods, or user methods (if set), or all methods. plot_isobar
(P[, Tmin, Tmax, methods_P, pts, ...])Method to create a plot of the property vs temperature at a specific pressure according to either a specified list of methods, or user methods (if set), or all methods. plot_isotherm
(T[, Pmin, Pmax, methods_P, ...])Method to create a plot of the property vs pressure at a specified temperature according to either a specified list of methods, or the user methods (if set), or all methods. select_valid_methods
(T)Method to obtain a sorted list of methods which are valid at T according to test_method_validity. select_valid_methods_P
(T, P)Method to obtain a sorted list methods which are valid at T according to test_method_validity. set_tabular_data
(Ts, properties[, name, ...])Method to set tabular data to be used for interpolation. set_tabular_data_P
(Ts, Ps, properties[, ...])Method to set tabular data to be used for interpolation. set_user_methods
(user_methods[, forced])Method used to select certain property methods as having a higher priority than were set by default. set_user_methods_P
(user_methods_P[, forced_P])Method to set the pressuredependent property methods desired for consideration by the user. solve_prop
(goal[, reset_method])Method to solve for the temperature at which a property is at a specified value. test_method_validity
(T, method)Method to check the validity of a temperaturedependent lowpressure method. test_method_validity_P
(T, P, method)Method to check the validity of a highpressure method. test_property_validity
(prop)Method to test the validity of a calculated property. 
Tmax
= None¶ Maximum temperature at which no method can calculate the liquid thermal conductivity above.

Tmin
= None¶ Minimum temperature at which no method can calculate the liquid thermal conductivity under.

all_methods
= None¶ Set of all lowpressure methods available for a given CASRN and properties; filled by
load_all_methods
.

all_methods_P
= None¶ Set of all highpressure methods available for a given CASRN and properties; filled by
load_all_methods
.

calculate
(T, method)[source]¶ Method to calculate lowpressure 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]

calculate_P
(T, P, method)[source]¶ Method to calculate pressuredependent 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]

interpolation_P
= None¶ No interpolation transformation by default.

interpolation_T
= None¶ No interpolation transformation by default.

interpolation_property
= None¶ No interpolation transformation by default.

interpolation_property_inv
= None¶ No interpolation transformation by default.

load_all_methods
()[source]¶ 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
Tmin
,Tmax
,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.

name
= 'liquid thermal conductivity'¶

property_max
= 10¶ Maximum valid value of liquid thermal conductivity. Generous limit.

property_min
= 0¶ Mimimum valid value of liquid thermal conductivity.

ranked_methods
= ['COOLPROP', 'DIPPR_PERRY_8E', 'VDI_PPDS', 'VDI_TABULAR', 'GHARAGHEIZI_L', 'SHEFFY_JOHNSON', 'SATO_RIEDEL', 'LAKSHMI_PRASAD', 'BAHADORI_L', 'NICOLA', 'NICOLA_ORIGINAL']¶ Default rankings of the lowpressure methods.

ranked_methods_P
= ['COOLPROP', 'DIPPR_9G', 'MISSENARD']¶ Default rankings of the highpressure methods.

sorted_valid_methods
= None¶ sorted_valid_methods, list: Stored methods which were found valid at a specific temperature; set by T_dependent_property.

sorted_valid_methods_P
= None¶ sorted_valid_methods_P, list: Stored methods which were found valid at a specific temperature; set by TP_dependent_property.

tabular_data
= None¶ tabular_data, dict: Stored (Ts, properties) for any tabular data; indexed by provided or autogenerated name.

tabular_data_P
= None¶ tabular_data_P, dict: Stored (Ts, Ps, properties) for any tabular data; indexed by provided or autogenerated name.

tabular_data_interpolators
= None¶ 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.

tabular_data_interpolators_P
= None¶ 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.

tabular_extrapolation_permitted
= True¶ Allow tabular extrapolation by default.

test_method_validity
(T, method)[source]¶ Method to check the validity of a temperaturedependent lowpressure 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
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

test_method_validity_P
(T, P, method)[source]¶ Method to check the validity of a highpressure 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
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

units
= 'W/m/K'¶

user_methods
= None¶ user_methods, list: Stored methods which were specified by the user in a ranked order of preference; set by T_dependent_property.

user_methods_P
= None¶ user_methods_P, list: Stored methods which were specified by the user in a ranked order of preference; set by TP_dependent_property.

thermo.thermal_conductivity.
DIPPR9G
(T, P, Tc, Pc, kl)[source]¶ Adjustes for pressure the thermal conductivity of a liquid using an emperical formula based on [R526], but as given in [R527].
\[k = k^* \left[ 0.98 + 0.0079 P_r T_r^{1.4} + 0.63 T_r^{1.2} \left( \frac{P_r}{30 + P_r}\right)\right]\]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
References
[R526] (1, 2) Missenard, F. A., Thermal Conductivity of Organic Liquids of a Series or a Group of Liquids , Rev. Gen.Thermodyn., 101 649 (1970). [R527] (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
From [R527], for butyl acetate.
>>> DIPPR9G(515.05, 3.92E7, 579.15, 3.212E6, 7.085E2) 0.0864419738671184

thermo.thermal_conductivity.
Missenard
(T, P, Tc, Pc, kl)[source]¶ Adjustes for pressure the thermal conductivity of a liquid using an emperical formula based on [R528], but as given in [R529].
\[\frac{k}{k^*} = 1 + Q P_r^{0.7}\]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.
References
[R528] (1, 2) Missenard, F. A., Thermal Conductivity of Organic Liquids of a Series or a Group of Liquids , Rev. Gen.Thermodyn., 101 649 (1970). [R529] (1, 2, 3) Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGrawHill Professional, 2000. Examples
Example from [R529], toluene; matches.
>>> Missenard(304., 6330E5, 591.8, 41E5, 0.129) 0.2198375777069657

thermo.thermal_conductivity.
DIPPR9H
(ws, ks)[source]¶ Calculates thermal conductivity of a liquid mixture according to mixing rules in [R530] and also in [R531].
\[\lambda_m = \left( \sum_i w_i \lambda_i^{2}\right)^{1/2}\]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 [R531]; 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.
References
[R530] (1, 2) Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. The Properties of Gases and Liquids. McGrawHill Companies, 1987. [R531] (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
>>> DIPPR9H([0.258, 0.742], [0.1692, 0.1528]) 0.15657104706719646

thermo.thermal_conductivity.
Filippov
(ws, ks)[source]¶ Calculates thermal conductivity of a binary liquid mixture according to mixing rules in [R533] as found in [R532].
\[\lambda_m = w_1 \lambda_1 + w_2\lambda_2  0.72 w_1 w_2(\lambda_2\lambda_1)\]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.
References
[R532] (1, 2) Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. The Properties of Gases and Liquids. McGrawHill Companies, 1987. [R533] (1, 2) Filippov, L. P.: Vest. Mosk. Univ., Ser. Fiz. Mat. Estestv. Nauk, (8I0E): 6769A955); Chem. Abstr., 50: 8276 A956). Filippov, L. P., and N. S. Novoselova: Vestn. Mosk. Univ., Ser. F iz. Mat. Estestv.Nauk, CI0B): 3740A955); Chem. Abstr., 49: 11366 A955). Examples
>>> Filippov([0.258, 0.742], [0.1692, 0.1528]) 0.15929167628799998

thermo.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 [R534].
\[\frac{\lambda M}{\eta C_v} = 1 + \frac{9/4}{C_v/R}\]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/gmol.
References
[R534] (1, 2, 3) Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. Properties of Gases and Liquids. McGrawHill Companies, 1987. Examples
2methylbutane at low pressure, 373.15 K. Mathes calculation in [R534].
>>> Eucken(MW=72.151, Cvm=135.9, mu=8.77E6) 0.018792644287722975

thermo.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 [R535].
\[\frac{\lambda M}{\eta C_v} = 1.32 + \frac{1.77}{C_v/R}\]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/gmol.
References
[R535] (1, 2, 3) Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. Properties of Gases and Liquids. McGrawHill Companies, 1987. Examples
2methylbutane at low pressure, 373.15 K. Mathes calculation in [R535].
>>> Eucken_modified(MW=72.151, Cvm=135.9, mu=8.77E6) 0.023593536999201956

thermo.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 [R536], [R537], and presented in [R538].
For monoatomic gases:
\[k = 2.5 \frac{\eta C_v}{MW}\]For linear molecules:
\[k = \frac{\eta}{MW} \left( 1.30 C_v + 14644.00  \frac{2928.80}{T_r}\right)\]For nonlinear molecules:
\[k = \frac{\eta}{MW}(1.15C_v + 16903.36)\]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.
References
[R536] (1, 2) 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. [R537] (1, 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): 2630. doi:10.1002/aic.690100114 [R538] (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
CO:
>>> DIPPR9B(200., 28.01, 20.826, 1.277E5, 132.92, chemtype='linear') 0.01813208676438415

thermo.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 [R539].
\[ \begin{align}\begin{aligned}\frac{\lambda M}{\eta C_v} = \frac{3.75 \Psi}{C_v/R}\\\Psi = 1 + \alpha \left\{[0.215+0.28288\alpha1.061\beta+0.26665Z]/ [0.6366+\beta Z + 1.061 \alpha \beta]\right\}\\\alpha = \frac{C_v}{R}1.5\\\beta = 0.78620.7109\omega + 1.3168\omega^2\\Z=2+10.5T_r^2\end{aligned}\end{align} \]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/gmol.
References
[R539] (1, 2) 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): 813. doi:10.1021/i100013a002 [R540] (1, 2) Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. Properties of Gases and Liquids. McGrawHill Companies, 1987. Examples
2methylbutane at low pressure, 373.15 K. Mathes calculation in [R540].
>>> Chung(T=373.15, MW=72.151, Tc=460.4, omega=0.227, Cvm=135.9, mu=8.77E6) 0.023015653729496946

thermo.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 [R541] as shown in [R542].
\[ \begin{align}\begin{aligned}\lambda = \lambda^* + \frac{\eta^*}{MW}(1.32)\left(C_v  \frac{3R}{2}\right)\\Tr = \text{min}(Tr, 2)\\\theta = 1 + (\omega0.011)\left(0.56553  0.86276\ln Tr  \frac{0.69852}{Tr}\right)\\\psi = [1 + (\omega  0.011)(0.38560  1.1617\ln Tr)]\frac{0.288}{Z_c}\\f = \frac{T_c}{190.4}\theta\\h = \frac{V_c}{9.92E5}\psi\\T_0 = T/f\\\eta_0^*(T_0)= \sum_{n=1}^9 C_n T_0^{(n4)/3}\\\theta_0 = 1944 \eta_0\\\lambda^* = \lambda_0 H\\\eta^* = \eta^*_0 H \frac{MW}{16.04}\\H = \left(\frac{16.04}{MW}\right)^{0.5}f^{0.5}/h^{2/3}\end{aligned}\end{align} \]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/gmol.
References
[R541] (1, 2) 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): 9097. doi:10.1021/i100009a016. [R542] (1, 2, 3) Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. Properties of Gases and Liquids. McGrawHill Companies, 1987. Examples
2methylbutane at low pressure, 373.15 K. Mathes calculation in [R542].
>>> eli_hanley(T=373.15, MW=72.151, Tc=460.4, Vc=3.06E4, Zc=0.267, ... omega=0.227, Cvm=135.9) 0.02247951789135337

thermo.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 [R543]. A convoluted method claiming highaccuracy and using only statistically significant variable following analalysis.
Requires temperature, molecular weight, boiling temperature and critical pressure and acentric factor.
\[ \begin{align}\begin{aligned}k = 7.9505\times 10^{4} + 3.989\times 10^{5} T 5.419\times 10^5 M + 3.989\times 10^{5} A\\A = \frac{\left(2\omega + T  \frac{(2\omega + 3.2825)T}{T_b} + 3.2825\right)}{0.1MP_cT} \times (3.9752\omega + 0.1 P_c + 1.9876B + 6.5243)^2\end{aligned}\end{align} \]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 [R543] is the first point in the supportinf info, for CH4.
References
[R543] (1, 2, 3) Gharagheizi, Farhad, Poorandokht IlaniKashkouli, 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): 17028. doi:10.1002/aic.13938 Examples
>>> Gharagheizi_gas(580., 16.04246, 111.66, 4599000.0, 0.0115478000) 0.09594861261873211

thermo.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.
\[ \begin{align}\begin{aligned}K = a + bY + CY^2 + dY^3\\a = A_1 + B_1 X + C_1 X^2 + D_1 X^3\\b = A_2 + B_2 X + C_2 X^2 + D_2 X^3\\c = A_3 + B_3 X + C_3 X^2 + D_3 X^3\\d = A_4 + B_4 X + C_4 X^2 + D_4 X^3\end{aligned}\end{align} \]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.
References
[R544] Bahadori, Alireza, and Saeid Mokhatab. “Estimating Thermal Conductivity of Hydrocarbons.” Chemical Engineering 115, no. 13 (December 2008): 5254 Examples
>>> Bahadori_gas(40+273.15, 20) # Point from article 0.031968165337873326

thermo.thermal_conductivity.
thermal_conductivity_gas_methods
= ['LINDSAY_BROMLEY', 'SIMPLE']¶ Holds all lowpressure methods available for the ThermalConductivityGas class, for use in iterating over them.

thermo.thermal_conductivity.
thermal_conductivity_gas_methods_P
= ['COOLPROP', 'ELI_HANLEY_DENSE', 'CHUNG_DENSE', 'STIEL_THODOS_DENSE']¶ Holds all highpressure methods available for the ThermalConductivityGas class, for use in iterating over them.

class
thermo.thermal_conductivity.
ThermalConductivityGas
(CASRN='', MW=None, Tb=None, Tc=None, Pc=None, Vc=None, Zc=None, omega=None, dipole=None, Vmg=None, Cvgm=None, mug=None)[source]¶ Bases:
thermo.utils.TPDependentProperty
Class for dealing with gas thermal conductivity as a function of temperature and pressure.
For gases at atmospheric pressure, there are 7 correspondingstates estimators, one source of tabular information, and the external library CoolProp.
For gases under the fluid’s boiling point (at subatmospheric pressures), and highpressure gases above the boiling point, there are three correspondingstates estimators, and the external library CoolProp.
Parameters: CASs : list[str], optional
The CAS numbers of all species in the mixture
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]
See also
Bahadori_gas
,Gharagheizi_gas
,eli_hanley
,Chung
,DIPPR9B
,Eucken_modified
,Eucken
,stiel_thodos_dense
,eli_hanley_dense
,chung_dense
Notes
To iterate over all methods, use the lists stored in
thermal_conductivity_gas_methods
andthermal_conductivity_gas_methods_P
for low and high pressure methods respectively.Low pressure methods:
 GHARAGHEIZI_G:
 CSP method, described in
Gharagheizi_gas
.  DIPPR_9B:
 CSP method, described in
DIPPR9B
.  CHUNG:
 CSP method, described in
Chung
.  ELI_HANLEY:
 CSP method, described in
eli_hanley
.  EUCKEN_MOD:
 CSP method, described in
Eucken_modified
.  EUCKEN:
 CSP method, described in
Eucken
.  BAHADORI_G:
 CSP method, described in
Bahadori_gas
.  DIPPR_PERRY_8E:
 A collection of 345 coefficient sets from the DIPPR database published
openly in [R547]. Provides temperature limits for all its fluids.
thermo.dippr.EQ102
is used for its fluids.  VDI_PPDS:
 Coefficients for a equation form developed by the PPDS, published openly in [R546]. Covers a large temperature range, but does not extrapolate well at very high or very low temperatures. 275 compounds.
 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 [R545]. Very slow.
 VDI_TABULAR:
 Tabular data in [R546] along the saturation curve; interpolation is as set by the user or the default.
High pressure methods:
 STIEL_THODOS_DENSE:
 CSP method, described in
stiel_thodos_dense
. Calculates a lowpressure thermal conductivity first, using T_dependent_property.  ELI_HANLEY_DENSE:
 CSP method, described in
eli_hanley_dense
. Calculates a lowpressure thermal conductivity first, using T_dependent_property.  CHUNG_DENSE:
 CSP method, described in
chung_dense
. Calculates a lowpressure 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 [R545]. Very slow, but unparalled in accuracy for pressure dependence.
References
[R545] (1, 2, 3) Bell, Ian H., Jorrit Wronski, Sylvain Quoilin, and Vincent Lemort. “Pure and PseudoPure Fluid Thermophysical Property Evaluation and the OpenSource Thermophysical Property Library CoolProp.” Industrial & Engineering Chemistry Research 53, no. 6 (February 12, 2014): 24982508. doi:10.1021/ie4033999. http://www.coolprop.org/ [R546] (1, 2, 3) Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010. [R547] (1, 2) Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGrawHill Professional, 2007. Attributes
TP_cached T_cached interpolation_P interpolation_T interpolation_property interpolation_property_inv method method_P Methods
TP_dependent_property
(T, P)Method to calculate the property with sanity checking and without specifying a specific method. TP_dependent_property_derivative_P
(T, P[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to pressure at constant temperature, of a given order. TP_dependent_property_derivative_T
(T, P[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to temperature at constant pressure, of a given order. TP_or_T_dependent_property
(T, P)T_dependent_property
(T)Method to calculate the property with sanity checking and without specifying a specific method. T_dependent_property_derivative
(T[, order])Method to obtain a derivative of a property with respect to temperature, of a given order. T_dependent_property_integral
(T1, T2)Method to calculate the integral of a property with respect to temperature, using a specified method. T_dependent_property_integral_over_T
(T1, T2)Method to calculate the integral of a property over temperature with respect to temperature, using a specified method. __call__
(T, P)Convenience method to calculate the property; calls TP_dependent_property
.calculate
(T, method)Method to calculate lowpressure gas thermal conductivity at tempearture T with a given method. calculate_P
(T, P, method)Method to calculate pressuredependent gas thermal conductivity at temperature T and pressure P with a given method. calculate_derivative
(T, method[, order])Method to calculate a derivative of a property with respect to temperature, of a given order using a specified method. calculate_derivative_P
(P, T, method[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to pressure at constant temperature, of a given order using a specified method. calculate_derivative_T
(T, P, method[, order])Method to calculate a derivative of a temperature and pressure dependent property with respect to temperature at constant pressure, of a given order using a specified method. calculate_integral
(T1, T2, method)Method to calculate the integral of a property with respect to temperature, using a specified method. calculate_integral_over_T
(T1, T2, method)Method to calculate the integral of a property over temperature with respect to temperature, using a specified method. extrapolate_tabular
(T)interpolate
(T, name)Method to perform interpolation on a given tabular data set previously added via set_tabular_data
.interpolate_P
(T, P, name)Method to perform interpolation on a given tabular data set previously added via set_tabular_data_P. load_all_methods
()Method which picks out coefficients for the specified chemical from the various dictionaries and DataFrames storing it. plot_TP_dependent_property
([Tmin, Tmax, ...])Method to create a plot of the property vs temperature and pressure according to either a specified list of methods, or user methods (if set), or all methods. plot_T_dependent_property
([Tmin, Tmax, ...])Method to create a plot of the property vs temperature according to either a specified list of methods, or user methods (if set), or all methods. plot_isobar
(P[, Tmin, Tmax, methods_P, pts, ...])Method to create a plot of the property vs temperature at a specific pressure according to either a specified list of methods, or user methods (if set), or all methods. plot_isotherm
(T[, Pmin, Pmax, methods_P, ...])Method to create a plot of the property vs pressure at a specified temperature according to either a specified list of methods, or the user methods (if set), or all methods. select_valid_methods
(T)Method to obtain a sorted list of methods which are valid at T according to test_method_validity. select_valid_methods_P
(T, P)Method to obtain a sorted list methods which are valid at T according to test_method_validity. set_tabular_data
(Ts, properties[, name, ...])Method to set tabular data to be used for interpolation. set_tabular_data_P
(Ts, Ps, properties[, ...])Method to set tabular data to be used for interpolation. set_user_methods
(user_methods[, forced])Method used to select certain property methods as having a higher priority than were set by default. set_user_methods_P
(user_methods_P[, forced_P])Method to set the pressuredependent property methods desired for consideration by the user. solve_prop
(goal[, reset_method])Method to solve for the temperature at which a property is at a specified value. test_method_validity
(T, method)Method to check the validity of a temperaturedependent lowpressure method. test_method_validity_P
(T, P, method)Method to check the validity of a highpressure method. test_property_validity
(prop)Method to test the validity of a calculated property. 
Tmax
= None¶ Maximum temperature at which no method can calculate the gas thermal conductivity above.

Tmin
= None¶ Minimum temperature at which no method can calculate the gas thermal conductivity under.

all_methods
= None¶ Set of all lowpressure methods available for a given CASRN and properties; filled by
load_all_methods
.

all_methods_P
= None¶ Set of all highpressure methods available for a given CASRN and properties; filled by
load_all_methods
.

calculate
(T, method)[source]¶ Method to calculate lowpressure 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]

calculate_P
(T, P, method)[source]¶ Method to calculate pressuredependent 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]

interpolation_P
= None¶ No interpolation transformation by default.

interpolation_T
= None¶ No interpolation transformation by default.

interpolation_property
= None¶ No interpolation transformation by default.

interpolation_property_inv
= None¶ No interpolation transformation by default.

load_all_methods
()[source]¶ 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
Tmin
,Tmax
,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.

name
= 'gas thermal conductivity'¶

property_max
= 10¶ Maximum valid value of gas thermal conductivity. Generous limit.

property_min
= 0¶ Mimimum valid value of gas thermal conductivity.

ranked_methods
= ['COOLPROP', 'VDI_PPDS', 'DIPPR_PERRY_8E', 'VDI_TABULAR', 'GHARAGHEIZI_G', 'DIPPR_9B', 'CHUNG', 'ELI_HANLEY', 'EUCKEN_MOD', 'EUCKEN', 'BAHADORI_G']¶ Default rankings of the lowpressure methods.

ranked_methods_P
= ['COOLPROP', 'ELI_HANLEY_DENSE', 'CHUNG_DENSE', 'STIEL_THODOS_DENSE']¶ Default rankings of the highpressure methods.

sorted_valid_methods
= None¶ sorted_valid_methods, list: Stored methods which were found valid at a specific temperature; set by T_dependent_property.

sorted_valid_methods_P
= None¶ sorted_valid_methods_P, list: Stored methods which were found valid at a specific temperature; set by TP_dependent_property.

tabular_data
= None¶ tabular_data, dict: Stored (Ts, properties) for any tabular data; indexed by provided or autogenerated name.

tabular_data_P
= None¶ tabular_data_P, dict: Stored (Ts, Ps, properties) for any tabular data; indexed by provided or autogenerated name.

tabular_data_interpolators
= None¶ 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.

tabular_data_interpolators_P
= None¶ 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.

tabular_extrapolation_permitted
= True¶ Allow tabular extrapolation by default.

test_method_validity
(T, method)[source]¶ Method to check the validity of a temperaturedependent lowpressure 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
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

test_method_validity_P
(T, P, method)[source]¶ Method to check the validity of a highpressure 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
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

units
= 'W/m/K'¶

user_methods
= None¶ user_methods, list: Stored methods which were specified by the user in a ranked order of preference; set by T_dependent_property.

user_methods_P
= None¶ user_methods_P, list: Stored methods which were specified by the user in a ranked order of preference; set by TP_dependent_property.

thermo.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 [R548] as shown in [R549].
if rho_r < 0.5:
\[(\lambda\lambda^\circ)\Gamma Z_c^5=1.22\times 10^{2} [\exp(0.535 \rho_r)1]\]if 0.5 < rho_r < 2.0:
\[(\lambda\lambda^\circ)\Gamma Z_c^5=1.22\times 10^{2} [\exp(0.535 \rho_r)1]\]if 2 < rho_r < 2.8:
\[ \begin{align}\begin{aligned}(\lambda\lambda^\circ)\Gamma Z_c^5=1.22\times 10^{2} [\exp(0.535 \rho_r)1]\\\Gamma = 210 \left(\frac{T_cMW^3}{P_c^4}\right)^{1/6}\end{aligned}\end{align} \]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
Lowpressure gas thermal conductivity [W/m/k]
Returns: kg : float
Estimated dense gas thermal conductivity [W/m/k]
Notes
Pc is internally converted to bar.
References
[R548] (1, 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): 2630. doi:10.1002/aic.690100114. [R549] (1, 2) Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. Properties of Gases and Liquids. McGrawHill Companies, 1987. Examples
>>> stiel_thodos_dense(T=378.15, MW=44.013, Tc=309.6, Pc=72.4E5, ... Vc=97.4E6, Zc=0.274, Vm=144E6, kg=2.34E2) 0.041245574404863684

thermo.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 [R550] as shown in [R551].
\[ \begin{align}\begin{aligned}Tr = min(Tr, 2)\\Vr = min(Vr, 2)\\f = \frac{T_c}{190.4}\theta\\h = \frac{V_c}{9.92E5}\psi\\T_0 = T/f\\\rho_0 = \frac{16.04}{V}h\\\theta = 1 + (\omega0.011)\left(0.09057  0.86276\ln Tr + \left( 0.31664  \frac{0.46568}{Tr}\right) (V_r  0.5)\right)\\\psi = [1 + (\omega  0.011)(0.39490(V_r  1.02355)  0.93281(V_r  0.75464)\ln T_r]\frac{0.288}{Z_c}\\\lambda_1 = 1944 \eta_0\\\lambda_2 = \left\{b_1 + b_2\left[b_3  \ln \left(\frac{T_0}{b_4} \right)\right]^2\right\}\rho_0\\\lambda_3 = \exp\left(a_1 + \frac{a_2}{T_0}\right)\left\{\exp[(a_3 + \frac{a_4}{T_0^{1.5}})\rho_0^{0.1} + (\frac{\rho_0}{0.1617}  1) \rho_0^{0.5}(a_5 + \frac{a_6}{T_0} + \frac{a_7}{T_0^2})]  1\right\}\\\lambda^{**} = [\lambda_1 + \lambda_2 + \lambda_3]H\\H = \left(\frac{16.04}{MW}\right)^{0.5}f^{0.5}/h^{2/3}\\X = \left\{\left[1  \frac{T}{f}\left(\frac{df}{dT}\right)_v \right] \frac{0.288}{Z_c}\right\}^{1.5}\\\left(\frac{df}{dT}\right)_v = \frac{T_c}{190.4}\left(\frac{d\theta} {d T}\right)_v\\\left(\frac{d\theta}{d T}\right)_v = (\omega0.011)\left[ \frac{0.86276}{T} + (V_r0.5)\frac{0.46568T_c}{T^2}\right]\end{aligned}\end{align} \]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/gmol.
References
[R550] (1, 2) 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): 9097. doi:10.1021/i100009a016. [R551] (1, 2) Reid, Robert C.; Prausnitz, John M.; Poling, Bruce E. Properties of Gases and Liquids. McGrawHill Companies, 1987. Examples
>>> eli_hanley_dense(T=473., MW=42.081, Tc=364.9, Vc=1.81E4, Zc=0.274, ... omega=0.144, Cvm=82.70, Vm=1.721E4) 0.06038475936515042

thermo.thermal_conductivity.
chung_dense
(T, MW, Tc, Vc, omega, Cvm, Vm, mu, dipole, association=0)[source]¶ Estimates the thermal conductivity of a gas at high pressure as a function of temperature using the reference fluid method of Chung [R552] as shown in [R553].
\[ \begin{align}\begin{aligned}\lambda = \frac{31.2 \eta^\circ \Psi}{M'}(G_2^{1} + B_6 y)+qB_7y^2T_r^{1/2}G_2\\\Psi = 1 + \alpha \left\{[0.215+0.28288\alpha1.061\beta+0.26665Z]/ [0.6366+\beta Z + 1.061 \alpha \beta]\right\}\\\alpha = \frac{C_v}{R}1.5\\\beta = 0.78620.7109\omega + 1.3168\omega^2\\Z=2+10.5T_r^2\\q = 3.586\times 10^{3} (T_c/M')^{1/2}/V_c^{2/3}\\y = \frac{V_c}{6V}\\G_1 = \frac{10.5y}{(1y)^3}\\G_2 = \frac{(B_1/y)[1\exp(B_4y)]+ B_2G_1\exp(B_5y) + B_3G_1} {B_1B_4 + B_2 + B_3}\\B_i = a_i + b_i \omega + c_i \mu_r^4 + d_i \kappa\end{aligned}\end{align} \]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
Lowpressure 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/gmol. Vm internally converted to mL/mol. [R552] is not the latest form as presented in [R552]. Association factor is assumed 0. Relates to the polarity of the gas.
Coefficients as follows: ais = [2.4166E+0, 5.0924E1, 6.6107E+0, 1.4543E+1, 7.9274E1, 5.8634E+0, 9.1089E+1]
bis = [7.4824E1, 1.5094E+0, 5.6207E+0, 8.9139E+0, 8.2019E1, 1.2801E+1, 1.2811E+2]
cis = [9.1858E1, 4.9991E+1, 6.4760E+1, 5.6379E+0, 6.9369E1, 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
[R552] (1, 2, 3, 4) 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): 67179. doi:10.1021/ie00076a024. [R553] (1, 2) Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGrawHill Professional, 2000. Examples
>>> chung_dense(T=473., MW=42.081, Tc=364.9, Vc=184.6E6, omega=0.142, ... Cvm=82.67, Vm=172.1E6, mu=134E7, dipole=0.4) 0.06160570379787278

thermo.thermal_conductivity.
Lindsay_Bromley
(T, ys, ks, mus, Tbs, MWs)[source]¶ Calculates thermal conductivity of a gas mixture according to mixing rules in [R554] and also in [R555].
\[ \begin{align}\begin{aligned}k = \sum \frac{y_i k_i}{\sum y_i A_{ij}}\\A_{ij} = \frac{1}{4} \left\{ 1 + \left[\frac{\eta_i}{\eta_j} \left(\frac{MW_j}{MW_i}\right)^{0.75} \left( \frac{T+S_i}{T+S_j}\right) \right]^{0.5} \right\}^2 \left( \frac{T+S_{ij}}{T+S_i}\right)\\S_{ij} = S_{ji} = (S_i S_j)^{0.5}\end{aligned}\end{align} \]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 [R555]; all results agree. The original source has not been reviewed.
DIPPR Procedure 9D: Method for the Thermal Conductivity of Gas Mixtures
Average deviations of 45% for 77 binary mixtures reviewed in [R555], from 1342 points; also six ternary mixtures (70 points); max deviation observed was 40%. (DIPPR)
TODO: Finish documenting this.
References
[R554] (1, 2) Lindsay, Alexander L., and LeRoy A. Bromley. “Thermal Conductivity of Gas Mixtures.” Industrial & Engineering Chemistry 42, no. 8 (August 1, 1950): 150811. doi:10.1021/ie50488a017. [R555] (1, 2, 3, 4) Danner, Ronald P, and Design Institute for Physical Property Data. Manual for Predicting Chemical Process Design Data. New York, N.Y, 1982. Examples
>>> Lindsay_Bromley(323.15, [0.23, 0.77], [1.939E2, 1.231E2], [1.002E5, 1.015E5], [248.31, 248.93], [46.07, 50.49]) 0.01390264417969313

class
thermo.thermal_conductivity.
ThermalConductivityGasMixture
(MWs=[], Tbs=[], CASs=[], ThermalConductivityGases=[], ViscosityGases=[])[source]¶ Bases:
thermo.utils.MixtureProperty
Class for dealing with thermal conductivity of a gas mixture as a function of temperature, pressure, and composition. Consists of one mixing rule specific to gas thremal conductivity, and mole weighted averaging.
Prefered method is
Lindsay_Bromley
which requires mole fractions, pure component viscosities and thermal conductivities, and the boiling point and molecular weight of each pure component. This is substantially better than the ideal mixing rule based on mole fractions, SIMPLE which is also available.Parameters: MWs : list[float], optional
Molecular weights of all species in the mixture, [g/mol]
Tbs : list[float], optional
Boiling points of all species in the mixture, [K]
CASs : str, optional
The CAS numbers of all species in the mixture
ThermalConductivityGases : list[ThermalConductivityGas], optional
ThermalConductivityGas objects created for all species in the mixture, normally created by
thermo.chemical.Chemical
.ViscosityGases : list[ViscosityGas], optional
ViscosityGas objects created for all species in the mixture, normally created by
thermo.chemical.Chemical
.See also
Notes
To iterate over all methods, use the list stored in
thermal_conductivity_gas_methods
. LINDSAY_BROMLEY:
 Mixing rule described in
Lindsay_Bromley
.  SIMPLE:
 Mixing rule described in
thermo.utils.mixing_simple
.
References
[R556] Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGrawHill Professional, 2000. Attributes
TP_zs_ws_cached method prop_cached Methods
__call__
(T, P, zs, ws)Convenience method to calculate the property; calls mixture_property
.calculate
(T, P, zs, ws, method)Method to calculate thermal conductivity of a gas mixture at temperature T, pressure P, mole fractions zs and weight fractions ws with a given method. calculate_derivative_P
(P, T, zs, ws, method)Method to calculate a derivative of a mixture property with respect to pressure at constant temperature and composition of a given order using a specified method. calculate_derivative_T
(T, P, zs, ws, method)Method to calculate a derivative of a mixture property with respect to temperature at constant pressure and composition of a given order using a specified method. load_all_methods
()Method to initialize the object by precomputing any values which may be used repeatedly and by retrieving mixturespecific variables. mixture_property
(T, P, zs, ws)Method to calculate the property with sanity checking and without specifying a specific method. plot_isobar
(P, zs, ws[, Tmin, Tmax, ...])Method to create a plot of the property vs temperature at a specific pressure and composition according to either a specified list of methods, or user methods (if set), or all methods. plot_isotherm
(T, zs, ws[, Pmin, Pmax, ...])Method to create a plot of the property vs pressure at a specified temperature and composition according to either a specified list of methods, or the user methods (if set), or all methods. plot_property
(zs, ws[, Tmin, Tmax, Pmin, ...])Method to create a plot of the property vs temperature and pressure according to either a specified list of methods, or user methods (if set), or all methods. property_derivative_P
(T, P, zs, ws[, order])Method to calculate a derivative of a mixture property with respect to pressure at constant temperature and composition, of a given order. property_derivative_T
(T, P, zs, ws[, order])Method to calculate a derivative of a mixture property with respect to temperature at constant pressure and composition, of a given order. select_valid_methods
(T, P, zs, ws)Method to obtain a sorted list of methods which are valid at T, P, zs, ws, and possibly Vfls, according to test_method_validity. set_user_method
(user_methods[, forced])Method to set the T, P, and composition dependent property methods desired for consideration by the user. test_method_validity
(T, P, zs, ws, method)Method to test the validity of a specified method for the given conditions. test_property_validity
(prop)Method to test the validity of a calculated property. 
Tmax
= None¶ Maximum temperature at which no method can calculate the gas thermal conductivity above.

Tmin
= None¶ Minimum temperature at which no method can calculate the gas thermal conductivity under.

all_methods
= None¶ Set of all methods available for a given set of information; filled by
load_all_methods
.

calculate
(T, P, zs, ws, method)[source]¶ Method to calculate thermal conductivity of a gas mixture at temperature T, pressure P, mole fractions zs and weight fractions ws with a given method.
This method has no exception handling; see mixture_property for that.
Parameters: T : float
Temperature at which to calculate the property, [K]
P : float
Pressure at which to calculate the property, [Pa]
zs : list[float]
Mole fractions of all species in the mixture, []
ws : list[float]
Weight fractions of all species in the mixture, []
method : str
Name of the method to use
Returns: kg : float
Thermal conductivity of gas mixture, [W/m/K]

load_all_methods
()[source]¶ Method to initialize the object by precomputing any values which may be used repeatedly and by retrieving mixturespecific variables. All data are stored as attributes. This method also sets
Tmin
,Tmax
, andall_methods
as a set of methods which should work to calculate the property.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.

name
= 'gas thermal conductivity'¶

property_max
= 10.0¶ Maximum valid value of gas thermal conductivity. Generous limit.

property_min
= 0.0¶ Mimimum valid value of gas thermal conductivity.

ranked_methods
= ['LINDSAY_BROMLEY', 'SIMPLE']¶

sorted_valid_methods
= None¶ sorted_valid_methods, list: Stored methods which were found valid at a specific temperature; set by mixture_property.

test_method_validity
(T, P, zs, ws, method)[source]¶ Method to test the validity of a specified method for the given conditions. No methods have implemented checks or strict ranges of validity.
Parameters: T : float
Temperature at which to check method validity, [K]
P : float
Pressure at which to check method validity, [Pa]
zs : list[float]
Mole fractions of all species in the mixture, []
ws : list[float]
Weight fractions of all species in the mixture, []
method : str
Method name to use
Returns: validity : bool
Whether or not a specifid method is valid

units
= 'W/m/K'¶

user_methods
= None¶ user_methods, list: Stored methods which were specified by the user in a ranked order of preference; set by mixture_property.