thermo.vapor_pressure module¶

thermo.vapor_pressure.
Antoine
(T, A, B, C, base=10.0)[source]¶ Calculates vapor pressure of a chemical using the Antoine equation. Parameters A, B, and C are chemicaldependent. Parameters can be found in numerous sources; however units of the coefficients used vary. Originally proposed by Antoine (1888) [R595].
\[\log_{\text{base}} P^{\text{sat}} = A  \frac{B}{T+C}\]Parameters: T : float
Temperature of fluid, [K]
A, B, C : floats
Regressed coefficients for Antoine equation for a chemical
Returns: Psat : float
Vapor pressure calculated with coefficients [Pa]
Other Parameters: Base : float
Optional base of logarithm; 10 by default
Notes
Assumes coefficients are for calculating vapor pressure in Pascal. Coefficients should be consistent with input temperatures in Kelvin; however, if both the given temperature and units are specific to degrees Celcius, the result will still be correct.
Converting units in input coefficients:
 ln to log10: Divide A and B by ln(10)=2.302585 to change parameters for a ln equation to a log10 equation.
 log10 to ln: Multiply A and B by ln(10)=2.302585 to change parameters for a log equation to a ln equation.
 mmHg to Pa: Add log10(101325/760)= 2.1249 to A.
 kPa to Pa: Add log_{base}(1000)= 6.908 to A for log(base)
 °C to K: Subtract 273.15 from C only!
References
[R594] (1, 2, 3) Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGrawHill Professional, 2000. [R595] (1, 2) Antoine, C. 1888. Tensions des Vapeurs: Nouvelle Relation Entre les Tensions et les Tempé. Compt.Rend. 107:681684. [R596] (1, 2) Yaws, Carl L. The Yaws Handbook of Vapor Pressure: Antoine Coefficients. 1 edition. Houston, Tex: Gulf Publishing Company, 2007. Examples
Methane, coefficients from [R594], at 100 K:
>>> Antoine(100.0, 8.7687, 395.744, 6.469) 34478.367349639906
Tetrafluoromethane, coefficients from [R594], at 180 K
>>> Antoine(180, A=8.95894, B=510.595, C=15.95) 702271.0518579542
Oxygen at 94.91 K, with coefficients from [R596] in units of °C, mmHg, log10, showing the conversion of coefficients A (mmHg to Pa) and C (°C to K)
>>> Antoine(94.91, 6.83706+2.1249, 339.2095, 268.70273.15) 162978.88655572367

thermo.vapor_pressure.
Wagner_original
(T, Tc, Pc, a, b, c, d)[source]¶ Calculates vapor pressure using the Wagner equation (3, 6 form).
Requires critical temperature and pressure as well as four coefficients specific to each chemical.
\[ \begin{align}\begin{aligned}\ln P^{sat}= \ln P_c + \frac{a\tau + b \tau^{1.5} + c\tau^3 + d\tau^6} {T_r}\\\tau = 1  \frac{T}{T_c}\end{aligned}\end{align} \]Parameters: T : float
Temperature of fluid, [K]
Tc : float
Critical temperature, [K]
Pc : float
Critical pressure, [Pa]
a, b, c, d : floats
Parameters for wagner equation. Specific to each chemical. []
Returns: Psat : float
Vapor pressure at T [Pa]
Notes
Warning: Pc is often treated as adjustable constant.
References
[R597] Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGrawHill Professional, 2000. [R598] (1, 2) McGarry, Jack. “Correlation and Prediction of the Vapor Pressures of Pure Liquids over Large Pressure Ranges.” Industrial & Engineering Chemistry Process Design and Development 22, no. 2 (April 1, 1983): 31322. doi:10.1021/i200021a023. Examples
Methane, coefficients from [R598], at 100 K.
>>> Wagner_original(100.0, 190.53, 4596420., a=6.00435, b=1.1885, ... c=0.834082, d=1.22833) 34520.44601450496

thermo.vapor_pressure.
Wagner
(T, Tc, Pc, a, b, c, d)[source]¶ Calculates vapor pressure using the Wagner equation (2.5, 5 form).
Requires critical temperature and pressure as well as four coefficients specific to each chemical.
\[ \begin{align}\begin{aligned}\ln P^{sat}= \ln P_c + \frac{a\tau + b \tau^{1.5} + c\tau^{2.5} + d\tau^5} {T_r}\\\tau = 1  \frac{T}{T_c}\end{aligned}\end{align} \]Parameters: T : float
Temperature of fluid, [K]
Tc : float
Critical temperature, [K]
Pc : float
Critical pressure, [Pa]
a, b, c, d : floats
Parameters for wagner equation. Specific to each chemical. []
Returns: Psat : float
Vapor pressure at T [Pa]
Notes
Warning: Pc is often treated as adjustable constant.
References
[R599] Wagner, W. “New Vapour Pressure Measurements for Argon and Nitrogen and a New Method for Establishing Rational Vapour Pressure Equations.” Cryogenics 13, no. 8 (August 1973): 47082. doi:10.1016/00112275(73)900039 [R600] (1, 2) Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGrawHill Professional, 2000. Examples
Methane, coefficients from [R600], at 100 K.
>>> Wagner(100., 190.551, 4599200, 6.02242, 1.26652, 0.5707, 1.366) 34415.00476263708

thermo.vapor_pressure.
TRC_Antoine_extended
(T, Tc, to, A, B, C, n, E, F)[source]¶ Calculates vapor pressure of a chemical using the TRC Extended Antoine equation. Parameters are chemical dependent, and said to be from the Thermodynamics Research Center (TRC) at Texas A&M. Coefficients for various chemicals can be found in [R601].
\[ \begin{align}\begin{aligned}\log_{10} P^{sat} = A  \frac{B}{T + C} + 0.43429x^n + Ex^8 + Fx^{12}\\x = \max \left(\frac{Tt_o273.15}{T_c}, 0 \right)\end{aligned}\end{align} \]Parameters: T : float
Temperature of fluid, [K]
A, B, C, n, E, F : floats
Regressed coefficients for the Antoine Extended (TRC) equation, specific for each chemical, []
Returns: Psat : float
Vapor pressure calculated with coefficients [Pa]
Notes
Assumes coefficients are for calculating vapor pressure in Pascal. Coefficients should be consistent with input temperatures in Kelvin;
References
[R601] (1, 2, 3) Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGrawHill Professional, 2000. Examples
Tetrafluoromethane, coefficients from [R601], at 180 K:
>>> TRC_Antoine_extended(180.0, 227.51, 120., 8.95894, 510.595, 15.95, ... 2.41377, 93.74, 7425.9) 706317.0898414153

thermo.vapor_pressure.
vapor_pressure_methods
= ['WAGNER_MCGARRY', 'WAGNER_POLING', 'ANTOINE_EXTENDED_POLING', 'DIPPR_PERRY_8E', 'VDI_PPDS', 'COOLPROP', 'ANTOINE_POLING', 'VDI_TABULAR', 'AMBROSE_WALTON', 'LEE_KESLER_PSAT', 'Edalat', 'EOS', 'BOILING_CRITICAL', 'SANJARI']¶ Holds all methods available for the VaporPressure class, for use in iterating over them.

class
thermo.vapor_pressure.
VaporPressure
(Tb=None, Tc=None, Pc=None, omega=None, CASRN='', eos=None)[source]¶ Bases:
thermo.utils.TDependentProperty
Class for dealing with vapor pressure as a function of temperature. Consists of four coefficientbased methods and four data sources, one source of tabular information, four correspondingstates estimators, any provided equation of state, and the external library CoolProp.
Parameters: Tb : float, optional
Boiling point, [K]
Tc : float, optional
Critical temperature, [K]
Pc : float, optional
Critical pressure, [Pa]
omega : float, optional
Acentric factor, []
CASRN : str, optional
The CAS number of the chemical
eos : object, optional
Equation of State object after
thermo.eos.GCEOS
See also
Wagner_original
,Wagner
,TRC_Antoine_extended
,Antoine
,boiling_critical_relation
,Lee_Kesler
,Ambrose_Walton
,Sanjari
,Edalat
Notes
To iterate over all methods, use the list stored in
vapor_pressure_methods
. WAGNER_MCGARRY:
 The Wagner 3,6 original model equation documented in
Wagner_original
, with data for 245 chemicals, from [R602],  WAGNER_POLING:
 The Wagner 2.5, 5 model equation documented in
Wagner
in [R603], with data for 104 chemicals.  ANTOINE_EXTENDED_POLING:
 The TRC extended Antoine model equation documented in
TRC_Antoine_extended
with data for 97 chemicals in [R603].  ANTOINE_POLING:
 Standard Antoine equation, as documented in the function
Antoine
and with data for 325 fluids from [R603]. Coefficients were altered to be in units of Pa and Celcius.  DIPPR_PERRY_8E:
 A collection of 341 coefficient sets from the DIPPR database published
openly in [R606]. Provides temperature limits for all its fluids.
thermo.dippr.EQ101
is used for its fluids.  VDI_PPDS:
 Coefficients for a equation form developed by the PPDS, published openly in [R605].
 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 [R604]. Very slow.
 BOILING_CRITICAL:
 Fundamental relationship in thermodynamics making several
approximations; see
boiling_critical_relation
for details. Least accurate method in most circumstances.  LEE_KESLER_PSAT:
 CSP method documented in
Lee_Kesler
. Widely used.  AMBROSE_WALTON:
 CSP method documented in
Ambrose_Walton
.  SANJARI:
 CSP method documented in
Sanjari
.  EDALAT:
 CSP method documented in
Edalat
.  VDI_TABULAR:
 Tabular data in [R605] along the saturation curve; interpolation is as set by the user or the default.
 EOS:
 Equation of state provided by user; must implement
thermo.eos.GCEOS.Psat
References
[R602] (1, 2) McGarry, Jack. “Correlation and Prediction of the Vapor Pressures of Pure Liquids over Large Pressure Ranges.” Industrial & Engineering Chemistry Process Design and Development 22, no. 2 (April 1, 1983): 31322. doi:10.1021/i200021a023. [R603] (1, 2, 3, 4) Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGrawHill Professional, 2000. [R604] (1, 2) 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/ [R605] (1, 2, 3) Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010. [R606] (1, 2) Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGrawHill Professional, 2007. Attributes
T_cached method Methods
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)Convenience method to calculate the property; calls T_dependent_property
.calculate
(T, method)Method to calculate vapor pressure of a fluid at temperature T 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_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
.interpolation_T
(T)1/T interpolation transformation by default. interpolation_property
(P)log(P) interpolation transformation by default. interpolation_property_inv
(P)exp(P) interpolation transformation by default; reverses load_all_methods
()Method which picks out coefficients for the specified chemical from the various dictionaries and DataFrames storing it. 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. select_valid_methods
(T)Method to obtain a sorted list of 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_user_methods
(user_methods[, forced])Method used to select certain property methods as having a higher priority than were set by default. 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 method. test_property_validity
(prop)Method to test the validity of a calculated property. 
Tmax
= None¶ Maximum temperature at which no method can calculate vapor pressure above; by definition the critical point.

Tmin
= None¶ Minimum temperature at which no method can calculate vapor pressure under.

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

calculate
(T, method)[source]¶ Method to calculate vapor pressure of a fluid at temperature T with a given method.
This method has no exception handling; see T_dependent_property for that.
Parameters: T : float
Temperature at calculate vapor pressure, [K]
method : str
Name of the method to use
Returns: Psat : float
Vapor pressure at T, [pa]

interpolation_T
(T)¶ 1/T interpolation transformation by default.

interpolation_property
(P)¶ log(P) interpolation transformation by default.

interpolation_property_inv
(P)¶ exp(P) interpolation transformation by default; reverses
interpolation_property_inv
.

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
, andall_methods
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.

method
= None¶ The method was which was last used successfully to calculate a property; set only after the first property calculation.

name
= 'Vapor pressure'¶

property_max
= 10000000000.0¶ Maximum valid value of vapor pressure. Set slightly above the critical point estimated for Iridium; Mercury’s 160 MPa critical point is the highest known.

property_min
= 0¶ Mimimum valid value of vapor pressure.

ranked_methods
= ['WAGNER_MCGARRY', 'WAGNER_POLING', 'ANTOINE_EXTENDED_POLING', 'DIPPR_PERRY_8E', 'VDI_PPDS', 'COOLPROP', 'ANTOINE_POLING', 'VDI_TABULAR', 'AMBROSE_WALTON', 'LEE_KESLER_PSAT', 'Edalat', 'BOILING_CRITICAL', 'EOS', 'SANJARI']¶ Default rankings of the available methods.

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

tabular_data
= None¶ tabular_data, dict: Stored (Ts, 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_extrapolation_permitted
= False¶ Disallow tabular extrapolation by default; CSP methods prefered normally.

test_method_validity
(T, method)[source]¶ Method to check the validity of a method. Follows the given ranges for all coefficientbased methods. For CSP methods, the models are considered 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

units
= 'Pa'¶

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.

thermo.vapor_pressure.
boiling_critical_relation
(T, Tb, Tc, Pc)[source]¶ Calculates vapor pressure of a fluid at arbitrary temperatures using a CSP relationship as in [R607]; requires a chemical’s critical temperature and pressure as well as boiling point.
The vapor pressure is given by:
\[ \begin{align}\begin{aligned}\ln P^{sat}_r = h\left( 1  \frac{1}{T_r}\right)\\h = T_{br} \frac{\ln(P_c/101325)}{1T_{br}}\end{aligned}\end{align} \]Parameters: T : float
Temperature of fluid [K]
Tb : float
Boiling temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
Returns: Psat : float
Vapor pressure at T [Pa]
Notes
Units are Pa. Formulation makes intuitive sense; a logarithmic form of interpolation.
References
[R607] (1, 2, 3) Reid, Robert C..; Prausnitz, John M.;; Poling, Bruce E. The Properties of Gases and Liquids. McGrawHill Companies, 1987. Examples
Example as in [R607] for ethylbenzene
>>> boiling_critical_relation(347.2, 409.3, 617.1, 36E5) 15209.467273093938

thermo.vapor_pressure.
Lee_Kesler
(T, Tc, Pc, omega)[source]¶ Calculates vapor pressure of a fluid at arbitrary temperatures using a CSP relationship by [R608]; requires a chemical’s critical temperature and acentric factor.
The vapor pressure is given by:
\[ \begin{align}\begin{aligned}\ln P^{sat}_r = f^{(0)} + \omega f^{(1)}\\f^{(0)} = 5.92714\frac{6.09648}{T_r}1.28862\ln T_r + 0.169347T_r^6\\f^{(1)} = 15.2518\frac{15.6875}{T_r}  13.4721 \ln T_r + 0.43577T_r^6\end{aligned}\end{align} \]Parameters: T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
omega : float
Acentric factor []
Returns: Psat : float
Vapor pressure at T [Pa]
Notes
This equation appears in [R608] in expanded form. The reduced pressure form of the equation ensures predicted vapor pressure cannot surpass the critical pressure.
References
[R608] (1, 2, 3) Lee, Byung Ik, and Michael G. Kesler. “A Generalized Thermodynamic Correlation Based on ThreeParameter Corresponding States.” AIChE Journal 21, no. 3 (1975): 510527. doi:10.1002/aic.690210313. [R609] (1, 2) Reid, Robert C..; Prausnitz, John M.;; Poling, Bruce E. The Properties of Gases and Liquids. McGrawHill Companies, 1987. Examples
Example from [R609]; ethylbenzene at 347.2 K.
>>> Lee_Kesler(347.2, 617.1, 36E5, 0.299) 13078.694162949312

thermo.vapor_pressure.
Ambrose_Walton
(T, Tc, Pc, omega)[source]¶ Calculates vapor pressure of a fluid at arbitrary temperatures using a CSP relationship by [R610]; requires a chemical’s critical temperature and acentric factor.
The vapor pressure is given by:
\[ \begin{align}\begin{aligned}\ln P_r=f^{(0)}+\omega f^{(1)}+\omega^2f^{(2)}\\f^{(0)}=\frac{5.97616\tau + 1.29874\tau^{1.5} 0.60394\tau^{2.5} 1.06841\tau^5}{T_r}\\f^{(1)}=\frac{5.03365\tau + 1.11505\tau^{1.5} 5.41217\tau^{2.5} 7.46628\tau^5}{T_r}\\f^{(2)}=\frac{0.64771\tau + 2.41539\tau^{1.5} 4.26979\tau^{2.5} +3.25259\tau^5}{T_r}\\\tau = 1T_{r}\end{aligned}\end{align} \]Parameters: T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
omega : float
Acentric factor []
Returns: Psat : float
Vapor pressure at T [Pa]
Notes
Somewhat more accurate than the
Lee_Kesler
formulation.References
[R610] (1, 2) Ambrose, D., and J. Walton. “Vapour Pressures up to Their Critical Temperatures of Normal Alkanes and 1Alkanols.” Pure and Applied Chemistry 61, no. 8 (1989): 13951403. doi:10.1351/pac198961081395. [R611] (1, 2) Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGrawHill Professional, 2000. Examples
Example from [R611]; ethylbenzene at 347.25 K.
>>> Ambrose_Walton(347.25, 617.15, 36.09E5, 0.304) 13278.878504306222

thermo.vapor_pressure.
Edalat
(T, Tc, Pc, omega)[source]¶ Calculates vapor pressure of a fluid at arbitrary temperatures using a CSP relationship by [R612]. Requires a chemical’s critical temperature, pressure, and acentric factor. Claimed to have a higher accuracy than the LeeKesler CSP relationship.
The vapor pressure of a chemical at T is given by:
\[ \begin{align}\begin{aligned}\ln(P^{sat}/P_c) = \frac{a\tau + b\tau^{1.5} + c\tau^3 + d\tau^6} {1\tau}\\a = 6.1559  4.0855\omega\\b = 1.5737  1.0540\omega  4.4365\times 10^{3} d\\c = 0.8747  7.8874\omega\\d = \frac{1}{0.4893  0.9912\omega + 3.1551\omega^2}\\\tau = 1  \frac{T}{T_c}\end{aligned}\end{align} \]Parameters: T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
omega : float
Acentric factor []
Returns: Psat : float
Vapor pressure, [Pa]
Notes
[R612] found an average error of 6.06% on 94 compounds and 1106 data points.
References
[R612] (1, 2, 3) Edalat, M., R. B. BozarJomehri, and G. A. Mansoori. “Generalized Equation Predicts Vapor Pressure of Hydrocarbons.” Oil and Gas Journal; 91:5 (February 1, 1993). Examples
>>> Edalat(347.2, 617.1, 36E5, 0.299) 13461.273080743307

thermo.vapor_pressure.
Sanjari
(T, Tc, Pc, omega)[source]¶ Calculates vapor pressure of a fluid at arbitrary temperatures using a CSP relationship by [R613]. Requires a chemical’s critical temperature, pressure, and acentric factor. Although developed for refrigerants, this model should have some general predictive ability.
The vapor pressure of a chemical at T is given by:
\[ \begin{align}\begin{aligned}P^{sat} = P_c\exp(f^{(0)} + \omega f^{(1)} + \omega^2 f^{(2)})\\f^{(0)} = a_1 + \frac{a_2}{T_r} + a_3\ln T_r + a_4 T_r^{1.9}\\f^{(1)} = a_5 + \frac{a_6}{T_r} + a_7\ln T_r + a_8 T_r^{1.9}\\f^{(2)} = a_9 + \frac{a_{10}}{T_r} + a_{11}\ln T_r + a_{12} T_r^{1.9}\end{aligned}\end{align} \]Parameters: T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
omega : float
Acentric factor []
Returns: Psat : float
Vapor pressure, [Pa]
Notes
a[112] are as follows: 6.83377, 5.76051, 0.90654, 1.16906, 5.32034, 28.1460, 58.0352, 23.57466, 18.19967, 16.33839, 65.6995, 35.9739.
For a claimed fluid not included in the regression, R128, the claimed AARD was 0.428%. A recalculation using 200 data points from 125.45 K to 343.90225 K evenly spaced by 1.09775 K as generated by NIST Webbook April 2016 produced an AARD of 0.644%. It is likely that the author’s regression used more precision in its coefficients than was shown here. Nevertheless, the function is reproduced as shown in [R613].
For Tc=808 K, Pc=1100000 Pa, omega=1.1571, this function actually declines after 770 K.
References
[R613] (1, 2, 3) Sanjari, Ehsan, Mehrdad Honarmand, Hamidreza Badihi, and Ali Ghaheri. “An Accurate Generalized Model for Predict Vapor Pressure of Refrigerants.” International Journal of Refrigeration 36, no. 4 (June 2013): 132732. doi:10.1016/j.ijrefrig.2013.01.007. Examples
>>> Sanjari(347.2, 617.1, 36E5, 0.299) 13651.916109552498