r"""Chemical Engineering Design Library (ChEDL). Utilities for process modeling.
Copyright (C) 2016, 2017, 2018, 2019 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.
This module contains lookup functions for melting and boiling point, heat of
fusion, various enthalpy of vaporization estimation routines, and dataframes
of fit coefficients.
For reporting bugs, adding feature requests, or submitting pull requests,
please use the `GitHub issue tracker <https://github.com/CalebBell/chemicals/>`_.
.. contents:: :local:
Boiling Point
-------------
.. autofunction:: chemicals.phase_change.Tb
.. autofunction:: chemicals.phase_change.Tb_methods
.. autodata:: chemicals.phase_change.Tb_all_methods
Melting Point
-------------
.. autofunction:: chemicals.phase_change.Tm
.. autofunction:: chemicals.phase_change.Tm_methods
.. autodata:: chemicals.phase_change.Tm_all_methods
Heat of Fusion
--------------
Heat of fusion does not strongly depend on temperature or pressure. This is the
standard value, at 1 atm and the normal melting point.
.. autofunction:: chemicals.phase_change.Hfus
.. autofunction:: chemicals.phase_change.Hfus_methods
.. autodata:: chemicals.phase_change.Hfus_all_methods
Heat of Vaporization at Tb Correlations
---------------------------------------
.. autofunction:: chemicals.phase_change.Riedel
.. autofunction:: chemicals.phase_change.Chen
.. autofunction:: chemicals.phase_change.Liu
.. autofunction:: chemicals.phase_change.Vetere
Heat of Vaporization at T Correlations
--------------------------------------
.. autofunction:: chemicals.phase_change.Pitzer
.. autofunction:: chemicals.phase_change.SMK
.. autofunction:: chemicals.phase_change.MK
.. autofunction:: chemicals.phase_change.Velasco
.. autofunction:: chemicals.phase_change.Clapeyron
.. autofunction:: chemicals.phase_change.Watson
.. autofunction:: chemicals.phase_change.Watson_n
Heat of Vaporization at T Model Equations
-----------------------------------------
.. autofunction:: chemicals.phase_change.Alibakhshi
.. autofunction:: chemicals.phase_change.PPDS12
Heat of Sublimation
-------------------
No specific correlation is provided. This value is fairly strongly temperature
dependent; the dependency comes almost entirely from the vaporization
enthalpy's dependence. To calculate heat of sublimation at any temperature, use
the equation :math:`H_{sub} = H_{fus} + H_{vap}`.
Fit Coefficients
----------------
All of these coefficients are lazy-loaded, so they must be accessed as an
attribute of this module.
.. data:: phase_change_data_Perrys2_150
A collection of 344 coefficient sets from the DIPPR database published
openly in [1]_. Provides temperature limits for all its fluids.
See :obj:`chemicals.dippr.EQ106` for the model equation.
.. data:: phase_change_data_VDI_PPDS_4
Coefficients for a equation form developed by the PPDS, published
openly in [2]_. Extrapolates poorly at low temperatures. See :obj:`PPDS12`
for the model equation.
.. data:: phase_change_data_Alibakhshi_Cs
One-constant limited temperature range regression coefficients presented
in [3]_, with constants for ~2000 chemicals from the DIPPR database.
Valid up to 100 K below the critical point, and 50 K under the boiling
point. See :obj:`Alibakhshi` for the model equation.
.. [1] Green, Don, and Robert Perry. Perry's Chemical Engineers' Handbook,
8E. McGraw-Hill Professional, 2007.
.. [2] Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition.
Berlin; New York:: Springer, 2010.
.. [3] Alibakhshi, Amin. "Enthalpy of Vaporization, Its Temperature
Dependence and Correlation with Surface Tension: A Theoretical Approach."
Fluid Phase Equilibria 432 (January 25, 2017): 62-69.
https://doi.org/10.1016/j.fluid.2016.10.013.
The structure of each dataframe is shown below:
.. ipython::
In [1]: import chemicals
In [2]: chemicals.phase_change.phase_change_data_Perrys2_150
In [3]: chemicals.phase_change.phase_change_data_VDI_PPDS_4
In [4]: chemicals.phase_change.phase_change_data_Alibakhshi_Cs
"""
__all__ = ['Tb_methods', 'Tb', 'Tm_methods', 'Tm',
'Clapeyron', 'Pitzer', 'SMK', 'MK', 'Velasco', 'Riedel', 'Chen',
'Liu', 'Vetere', 'Alibakhshi','PPDS12', 'Watson', 'Watson_n',
'Hfus', 'Hfus_methods']
from fluids.constants import N_A, R, pi
from fluids.numerics import log
from fluids.numerics import numpy as np
from chemicals import data_reader as dr
from chemicals import miscdata
from chemicals.data_reader import (
data_source,
database_constant_lookup,
list_available_methods_from_df_dict,
register_df_source,
retrieve_any_from_df_dict,
retrieve_from_df_dict,
)
from chemicals.utils import PY37, can_load_data, mark_numba_incompatible, os_path_join, source_path
### Register data sources and lazy load them
folder = os_path_join(source_path, 'Phase Change')
register_df_source(folder, 'Yaws Boiling Points.tsv')
register_df_source(folder, 'OpenNotebook Melting Points.tsv')
register_df_source(folder, 'Ghazerati Appendix Vaporization Enthalpy.tsv',
csv_kwargs={'dtype': {'Hvap298': float}})
register_df_source(folder, 'CRC Handbook Heat of Vaporization.tsv')
register_df_source(folder, 'CRC Handbook Heat of Fusion.tsv')
register_df_source(folder, 'Ghazerati Appendix Sublimation Enthalpy.tsv')
register_df_source(folder, 'Table 2-150 Heats of Vaporization of Inorganic and Organic Liquids.tsv')
register_df_source(folder, 'VDI PPDS Enthalpies of vaporization.tsv')
register_df_source(folder, 'Alibakhshi one-coefficient enthalpy of vaporization.tsv')
CRC_ORG = 'CRC_ORG'
CRC_INORG = 'CRC_INORG'
YAWS = 'YAWS'
OPEN_NTBKM = 'OPEN_NTBKM'
CRC = 'CRC'
_phase_change_const_loaded = False
@mark_numba_incompatible
def _load_phase_change_constants():
global Tb_data_Yaws, Tm_ON_data, Hvap_data_Gharagheizi, Hvap_data_CRC
global Hfus_data_CRC, Hsub_data_Gharagheizi, _phase_change_const_loaded
global Tb_sources, Tm_sources, Hfus_sources
Tb_data_Yaws = data_source('Yaws Boiling Points.tsv')
Tm_ON_data = data_source('OpenNotebook Melting Points.tsv')
Hvap_data_Gharagheizi = data_source('Ghazerati Appendix Vaporization Enthalpy.tsv')
Hvap_data_CRC = data_source('CRC Handbook Heat of Vaporization.tsv')
Hfus_data_CRC = data_source('CRC Handbook Heat of Fusion.tsv')
Hsub_data_Gharagheizi = data_source('Ghazerati Appendix Sublimation Enthalpy.tsv')
_phase_change_const_loaded = True
Tb_sources = {
miscdata.HEOS: miscdata.heos_data,
CRC_ORG: miscdata.CRC_organic_data,
CRC_INORG: miscdata.CRC_inorganic_data,
miscdata.COMMON_CHEMISTRY: miscdata.common_chemistry_data,
miscdata.WEBBOOK: miscdata.webbook_data,
YAWS: Tb_data_Yaws,
miscdata.WIKIDATA: miscdata.wikidata_data,
miscdata.JOBACK: miscdata.joback_predictions,
}
Tm_sources = {
OPEN_NTBKM: Tm_ON_data,
CRC_INORG: miscdata.CRC_inorganic_data,
CRC_ORG: miscdata.CRC_organic_data,
miscdata.COMMON_CHEMISTRY: miscdata.common_chemistry_data,
miscdata.WEBBOOK: miscdata.webbook_data,
miscdata.WIKIDATA: miscdata.wikidata_data,
miscdata.JOBACK: miscdata.joback_predictions,
}
Hfus_sources = {
CRC: Hfus_data_CRC,
miscdata.WEBBOOK: miscdata.webbook_data,
miscdata.WIKIDATA: miscdata.wikidata_data,
miscdata.JOBACK: miscdata.joback_predictions,
}
_phase_change_corrs_loaded = False
@mark_numba_incompatible
def _load_phase_change_correlations():
global phase_change_data_Perrys2_150, phase_change_values_Perrys2_150
global phase_change_data_VDI_PPDS_4, phase_change_values_VDI_PPDS_4
global phase_change_data_Alibakhshi_Cs, _phase_change_corrs_loaded
# 66554 for pandas; 19264 bytes for numpy
phase_change_data_Perrys2_150 = data_source('Table 2-150 Heats of Vaporization of Inorganic and Organic Liquids.tsv')
phase_change_values_Perrys2_150 = np.array(phase_change_data_Perrys2_150.values[:, 1:], dtype=float)
# 52187 bytes for pandas, 13056 bytes for numpy
phase_change_data_VDI_PPDS_4 = data_source('VDI PPDS Enthalpies of vaporization.tsv')
phase_change_values_VDI_PPDS_4 = np.array(phase_change_data_VDI_PPDS_4.values[:, 2:], dtype=float)
phase_change_data_Alibakhshi_Cs = data_source('Alibakhshi one-coefficient enthalpy of vaporization.tsv')
_phase_change_corrs_loaded = True
if PY37:
def __getattr__(name):
if name in ('Tb_data_Yaws', 'Tm_ON_data', 'Hvap_data_Gharagheizi',
'Hvap_data_CRC', 'Hfus_data_CRC', 'Hsub_data_Gharagheizi',
'Tb_sources', 'Tm_sources', 'Hfus_sources'):
_load_phase_change_constants()
return globals()[name]
elif name in ('phase_change_data_Perrys2_150',
'phase_change_values_Perrys2_150',
'phase_change_data_VDI_PPDS_4',
'phase_change_values_VDI_PPDS_4',
'phase_change_data_Alibakhshi_Cs'):
_load_phase_change_correlations()
return globals()[name]
raise AttributeError(f"module {__name__} has no attribute {name}")
else:
if can_load_data:
_load_phase_change_constants()
_load_phase_change_correlations()
### Phase change functions
### Boiling Point at 1 atm
Tb_all_methods = (miscdata.HEOS, CRC_INORG, CRC_ORG, miscdata.COMMON_CHEMISTRY,
miscdata.WEBBOOK, YAWS, miscdata.WIKIDATA, miscdata.JOBACK)
"""Tuple of method name keys. See the `Tbg` for the actual references"""
[docs]@mark_numba_incompatible
def Tb_methods(CASRN):
"""Return all methods available to obtain the normal boiling point
for the desired chemical.
Parameters
----------
CASRN : str
CASRN, [-]
Returns
-------
methods : list[str]
Methods which can be used to obtain the Tb with the given inputs.
See Also
--------
Tb
"""
if not _phase_change_const_loaded: _load_phase_change_constants()
return list_available_methods_from_df_dict(Tb_sources, CASRN, 'Tb')
[docs]@mark_numba_incompatible
def Tb(CASRN, method=None):
r'''This function handles the retrieval of a chemical's normal boiling
point. Lookup is based on CASRNs. Will automatically select a data
source to use if no method is provided; returns None if the data is not
available. Function has data for approximately 34000 chemicals.
Parameters
----------
CASRN : str
CASRN [-]
Returns
-------
Tb : float
Boiling temperature, [K]
Other Parameters
----------------
method : string, optional
A string for the method name to use, as defined in the variable,
`Tb_all_methods`.
Notes
-----
The available sources are as follows:
* 'CRC_ORG', a compillation of data on organics
as published in [1]_.
* 'CRC_INORG', a compillation of data on
inorganic as published in [1]_.
* 'WEBBOOK', a NIST resource [6]_ containing mostly experimental
and averaged values
* 'WIKIDATA', data from the Wikidata project [3]_
* 'COMMON_CHEMISTRY', a project from the CAS [4]_
* 'JOBACK', an estimation method for organic substances in [5]_
* 'YAWS', a large compillation of data from a
variety of sources both experimental and predicted;
no data points are sourced in the work of [2]_.
* 'HEOS', a series of values from the NIST REFPROP Database for
Highly Accurate Properties of Industrially Important Fluids
(and other high-precision fundamental equations of state)
Examples
--------
>>> Tb('7732-18-5')
373.124
See Also
--------
Tb_methods
References
----------
.. [1] Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of
Chemistry and Physics, 95E. Boca Raton, FL: CRC press, 2014.
.. [2] Yaws, Carl L. Thermophysical Properties of Chemicals and
Hydrocarbons, Second Edition. Amsterdam Boston: Gulf Professional
Publishing, 2014.
.. [3] Wikidata. Wikidata. Accessed via API. https://www.wikidata.org/
.. [4] "CAS Common Chemistry". https://commonchemistry.cas.org/.
.. [5] Joback, K.G., and R.C. Reid. "Estimation of Pure-Component
Properties from Group-Contributions." Chemical Engineering
Communications 57, no. 1-6 (July 1, 1987): 233-43.
doi:10.1080/00986448708960487.
.. [6] Shen, V.K., Siderius, D.W., Krekelberg, W.P., and Hatch, H.W., Eds.,
NIST WebBook, NIST, http://doi.org/10.18434/T4M88Q
.. [7] Huber, Marcia L., Eric W. Lemmon, Ian H. Bell, and Mark O. McLinden.
"The NIST REFPROP Database for Highly Accurate Properties of Industrially
Important Fluids." Industrial & Engineering Chemistry Research 61, no. 42
(October 26, 2022): 15449-72. https://doi.org/10.1021/acs.iecr.2c01427.
'''
if dr.USE_CONSTANTS_DATABASE and method is None:
val, found = database_constant_lookup(CASRN, 'Tb')
if found: return val
if not _phase_change_const_loaded: _load_phase_change_constants()
if method:
return retrieve_from_df_dict(Tb_sources, CASRN, 'Tb', method)
else:
return retrieve_any_from_df_dict(Tb_sources, CASRN, 'Tb')
### Melting Point
Tm_all_methods = (OPEN_NTBKM, CRC_INORG, CRC_ORG, miscdata.COMMON_CHEMISTRY,
miscdata.WEBBOOK, miscdata.WIKIDATA, miscdata.JOBACK)
"""Tuple of method name keys. See the `Tm` for the actual references"""
[docs]@mark_numba_incompatible
def Tm_methods(CASRN):
"""Return all methods available to obtain the melting point for the desired
chemical.
Parameters
----------
CASRN : str
CASRN, [-]
Returns
-------
methods : list[str]
Methods which can be used to obtain the Tm with the given inputs.
See Also
--------
Tm
"""
if not _phase_change_const_loaded: _load_phase_change_constants()
return list_available_methods_from_df_dict(Tm_sources, CASRN, 'Tm')
[docs]@mark_numba_incompatible
def Tm(CASRN, method=None):
r'''This function handles the retrieval of a chemical's melting
point. Lookup is based on CASRNs. Will automatically select a data
source to use if no method is provided; returns None if the data is not
available. Function has data for approximately 83000 chemicals.
Parameters
----------
CASRN : str
CASRN [-]
Returns
-------
Tm : float
Melting temperature, [K]
Other Parameters
----------------
method : string, optional
A string for the method name to use, as defined by the vairable
`Tm_all_methods`.
Notes
-----
The available sources are as follows:
* 'OPEN_NTBKM, a compillation of data on organics
as published in [1]_ as Open Notebook Melting Points; Averaged
(median) values were used when
multiple points were available. For more information on this
invaluable and excellent collection, see
http://onswebservices.wikispaces.com/meltingpoint.
* 'CRC_ORG', a compillation of data on organics
as published in [2]_.
* 'CRC_INORG', a compillation of data on
inorganic as published in [2]_.
* 'WEBBOOK', a NIST resource [6]_ containing mostly experimental
and averaged values
* 'WIKIDATA', data from the Wikidata project [3]_
* 'COMMON_CHEMISTRY', a project from the CAS [4]_
* 'JOBACK', an estimation method for organic substances in [5]_
Examples
--------
>>> Tm(CASRN='7732-18-5')
273.15
See Also
--------
Tm_methods
References
----------
.. [1] Bradley, Jean-Claude, Antony Williams, and Andrew Lang.
"Jean-Claude Bradley Open Melting Point Dataset", May 20, 2014.
https://figshare.com/articles/Jean_Claude_Bradley_Open_Melting_Point_Datset/1031637.
.. [2] Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of
Chemistry and Physics, 95E. Boca Raton, FL: CRC press, 2014.
.. [3] Wikidata. Wikidata. Accessed via API. https://www.wikidata.org/
.. [4] "CAS Common Chemistry". https://commonchemistry.cas.org/.
.. [5] Joback, K.G., and R.C. Reid. "Estimation of Pure-Component
Properties from Group-Contributions." Chemical Engineering
Communications 57, no. 1-6 (July 1, 1987): 233-43.
doi:10.1080/00986448708960487.
.. [6] Shen, V.K., Siderius, D.W., Krekelberg, W.P., and Hatch, H.W., Eds.,
NIST WebBook, NIST, http://doi.org/10.18434/T4M88Q
'''
if dr.USE_CONSTANTS_DATABASE and method is None:
val, found = database_constant_lookup(CASRN, 'Tm')
if found: return val
if not _phase_change_const_loaded: _load_phase_change_constants()
if method:
return retrieve_from_df_dict(Tm_sources, CASRN, 'Tm', method)
else:
return retrieve_any_from_df_dict(Tm_sources, CASRN, 'Tm')
### Enthalpy of Vaporization at T
[docs]def Clapeyron(T, Tc, Pc, dZ=1, Psat=101325):
r'''Calculates enthalpy of vaporization at arbitrary temperatures using the
Clapeyron equation.
The enthalpy of vaporization is given by:
.. math::
\Delta H_{vap} = RT \Delta Z \frac{\ln (P_c/Psat)}{(1-T_{r})}
Parameters
----------
T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
dZ : float
Change in compressibility factor between liquid and gas, []
Psat : float
Saturation pressure of fluid [Pa], optional
Returns
-------
Hvap : float
Enthalpy of vaporization, [J/mol]
Notes
-----
No original source is available for this equation.
[1]_ claims this equation overpredicts enthalpy by several percent.
Under Tr = 0.8, dZ = 1 is a reasonable assumption.
This equation is most accurate at the normal boiling point.
Internal units are bar.
WARNING: I believe it possible that the adjustment for pressure may be incorrect
Examples
--------
Problem from Perry's examples.
>>> Clapeyron(T=294.0, Tc=466.0, Pc=5.55E6)
26512.36357131963
References
----------
.. [1] Poling, Bruce E. The Properties of Gases and Liquids. 5th edition.
New York: McGraw-Hill Professional, 2000.
'''
Tr = T/Tc
return R*T*dZ*log(Pc/Psat)/(1. - Tr)
[docs]def Pitzer(T, Tc, omega):
r'''Calculates enthalpy of vaporization at arbitrary temperatures using a
fit by [2]_ to the work of Pitzer [1]_; requires a chemical's critical
temperature and acentric factor.
The enthalpy of vaporization is given by:
.. math::
\frac{\Delta_{vap} H}{RT_c}=7.08(1-T_r)^{0.354}+10.95\omega(1-T_r)^{0.456}
Parameters
----------
T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
omega : float
Acentric factor [-]
Returns
-------
Hvap : float
Enthalpy of vaporization, [J/mol]
Notes
-----
This equation is listed in [3]_, page 2-487 as method #2 for estimating
Hvap. This cites [2]_.
The recommended range is 0.6 to 1 Tr. Users should expect up to 5% error.
This function converges to zero at `Tc`. If Tc is larger than T,
0 is returned as the model would return complex numbers.
The original article has been reviewed and found to have a set of tabulated
values which could be used instead of the fit function to provide additional
accuracy.
Examples
--------
Example as in [3]_, p2-487; exp: 37.51 kJ/mol
>>> Pitzer(452, 645.6, 0.35017)
36696.749078320056
References
----------
.. [1] Pitzer, Kenneth S. "The Volumetric and Thermodynamic Properties of
Fluids. I. Theoretical Basis and Virial Coefficients."
Journal of the American Chemical Society 77, no. 13 (July 1, 1955):
3427-33. doi:10.1021/ja01618a001
.. [2] Poling, Bruce E. The Properties of Gases and Liquids. 5th edition.
New York: McGraw-Hill Professional, 2000.
.. [3] Green, Don, and Robert Perry. Perry's Chemical Engineers' Handbook,
Eighth Edition. McGraw-Hill Professional, 2007.
'''
if T >= Tc:
return 0.0
Tr = T/Tc
return R*Tc * (7.08*(1. - Tr)**0.354 + 10.95*omega*(1. - Tr)**0.456)
[docs]def SMK(T, Tc, omega):
r'''Calculates enthalpy of vaporization at arbitrary temperatures using a
the work of [1]_; requires a chemical's critical temperature and
acentric factor.
The enthalpy of vaporization is given by:
.. math::
\frac{\Delta H_{vap}} {RT_c} =
\left( \frac{\Delta H_{vap}} {RT_c} \right)^{(R1)} + \left(
\frac{\omega - \omega^{(R1)}} {\omega^{(R2)} - \omega^{(R1)}} \right)
\left[\left( \frac{\Delta H_{vap}} {RT_c} \right)^{(R2)} - \left(
\frac{\Delta H_{vap}} {RT_c} \right)^{(R1)} \right]
.. math::
\left( \frac{\Delta H_{vap}} {RT_c} \right)^{(R1)}
= 6.537 \tau^{1/3} - 2.467 \tau^{5/6} - 77.251 \tau^{1.208} +
59.634 \tau + 36.009 \tau^2 - 14.606 \tau^3
.. math::
\left( \frac{\Delta H_{vap}} {RT_c} \right)^{(R2)} - \left(
\frac{\Delta H_{vap}} {RT_c} \right)^{(R1)}=-0.133 \tau^{1/3} - 28.215
\tau^{5/6} - 82.958 \tau^{1.208} + 99.00 \tau + 19.105 \tau^2 -2.796 \tau^3
.. math::
\tau = 1-T/T_c
Parameters
----------
T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
omega : float
Acentric factor [-]
Returns
-------
Hvap : float
Enthalpy of vaporization, [J/mol]
Notes
-----
The original article has been reviewed and found to have coefficients with
slightly more precision. Additionally, the form of the equation is slightly
different, but numerically equivalent.
The refence fluids are:
:math:`\omega_0` = benzene = 0.212
:math:`\omega_1` = carbazole = 0.461
A sample problem in the article has been verified. The numerical result
presented by the author requires high numerical accuracy to obtain.
This function converges to zero at `Tc`. If Tc is larger than T,
0 is returned as the model would return complex numbers.
Examples
--------
Problem in [1]_:
>>> SMK(553.15, 751.35, 0.302)
39866.18999046229
References
----------
.. [1] Sivaraman, Alwarappa, Joe W. Magee, and Riki Kobayashi. "Generalized
Correlation of Latent Heats of Vaporization of Coal-Liquid Model Compounds
between Their Freezing Points and Critical Points." Industrial &
Engineering Chemistry Fundamentals 23, no. 1 (February 1, 1984): 97-100.
doi:10.1021/i100013a017.
'''
if T >= Tc:
return 0.0
omegaR1, omegaR2 = 0.212, 0.461
A10 = 6.536924
A20 = -2.466698
A30 = -77.52141
B10 = 59.63435
B20 = 36.09887
B30 = -14.60567
A11 = -0.132584
A21 = -28.21525
A31 = -82.95820
B11 = 99.00008
B21 = 19.10458
B31 = -2.795660
# 1 branch, two powers, 1 division
tau = 1. - T/Tc
tau_16 = tau**(1.0/6.0)
tau_13 = tau_16*tau_16
tau_56 = tau_13*tau_13*tau_16
tau_other = tau**1.2083333333333333 #(1-1/8. + 1/3.))
L0 = (A10*tau_13 + A20*tau_56 + A30*tau_other +
tau*(B10 + tau*(B20 + B30*tau)))
L1 = (A11*tau_13 + A21*tau_56 + A31*tau_other +
tau*(B11 + tau*(B21 + B31*tau)))
domega = 4.016064257028112*(omega - omegaR1) # 4.016... = 1.0/(omegaR2 - omegaR1)
# domega = (omega - omegaR1)/(omegaR2 - omegaR1)
return R*Tc*(L0 + domega*L1)
[docs]def MK(T, Tc, omega):
r'''Calculates enthalpy of vaporization at arbitrary temperatures using a
the work of [1]_; requires a chemical's critical temperature and
acentric factor.
The enthalpy of vaporization is given by:
.. math::
\Delta H_{vap} = \Delta H_{vap}^{(0)} + \omega \Delta H_{vap}^{(1)} + \omega^2 \Delta H_{vap}^{(2)}
.. math::
\frac{\Delta H_{vap}^{(i)}}{RT_c} = b^{(j)} \tau^{1/3} + b_2^{(j)} \tau^{5/6}
+ b_3^{(j)} \tau^{1.2083} + b_4^{(j)}\tau + b_5^{(j)} \tau^2 + b_6^{(j)} \tau^3
.. math::
\tau = 1-T/T_c
Parameters
----------
T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
omega : float
Acentric factor [-]
Returns
-------
Hvap : float
Enthalpy of vaporization, [J/mol]
Notes
-----
The original article has been reviewed. A total of 18 coefficients are used:
WARNING: The correlation has been implemented as described in the article,
but its results seem different and with some error.
Its results match with other functions however.
Has poor behavior for low-temperature use.
This function converges to zero at `Tc`. If Tc is larger than T,
0 is returned as the model would return complex numbers.
Examples
--------
Problem in article for SMK function.
>>> MK(553.15, 751.35, 0.302)
38728.00667307733
References
----------
.. [1] Morgan, David L., and Riki Kobayashi. "Extension of Pitzer CSP
Models for Vapor Pressures and Heats of Vaporization to Long-Chain
Hydrocarbons." Fluid Phase Equilibria 94 (March 15, 1994): 51-87.
doi:10.1016/0378-3812(94)87051-9.
'''
if T >= Tc:
return 0.0
bs0 = [5.2804, 0.080022, 7.2543]
bs1 = [12.8650, 273.23, -346.45]
bs2 = [1.1710, 465.08, -610.48]
bs3 = [-13.1160, -638.51, 839.89]
bs4 = [0.4858, -145.12, 160.05]
bs5 = [-1.0880, 74.049, -50.711]
tau = 1. - T/Tc
tau_third = tau**0.3333
tau_83 = tau**0.8333
tau_other = tau**1.2083
tau2 = tau*tau
tau3 = tau2*tau
H0 = (bs0[0]*tau_third + bs1[0]*tau_83 + bs2[0]*tau_other +
bs3[0]*tau + bs4[0]*tau2 + bs5[0]*tau3)
H1 = (bs0[1]*tau_third + bs1[1]*tau_83 + bs2[1]*tau_other +
bs3[1]*tau + bs4[1]*tau2 + bs5[1]*tau3)
H2 = (bs0[2]*tau_third + bs1[2]*tau_83 + bs2[2]*tau_other +
bs3[2]*tau + bs4[2]*tau2 + bs5[2]*tau3)
return (H0 + omega*(H1 + omega*H2))*R*Tc
[docs]def Velasco(T, Tc, omega):
r'''Calculates enthalpy of vaporization at arbitrary temperatures using a
the work of [1]_; requires a chemical's critical temperature and
acentric factor.
The enthalpy of vaporization is given by:
.. math::
\Delta_{vap} H = RT_c(7.2729 + 10.4962\omega + 0.6061\omega^2)(1-T_r)^{0.38}
Parameters
----------
T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
omega : float
Acentric factor [-]
Returns
-------
Hvap : float
Enthalpy of vaporization, [J/mol]
Notes
-----
The original article has been reviewed. It is regressed from enthalpy of
vaporization values at 0.7Tr, from 121 fluids in REFPROP 9.1.
A value in the article was read to be similar, but slightly too low from
that calculated here.
This function converges to zero at `Tc`. If Tc is larger than T,
0 is returned as the model would return complex numbers.
Examples
--------
From graph, in [1]_ for perfluoro-n-heptane.
>>> Velasco(333.2, 476.0, 0.5559)
33299.428636069264
References
----------
.. [1] Velasco, S., M. J. Santos, and J. A. White. "Extended Corresponding
States Expressions for the Changes in Enthalpy, Compressibility Factor
and Constant-Volume Heat Capacity at Vaporization." The Journal of
Chemical Thermodynamics 85 (June 2015): 68-76.
doi:10.1016/j.jct.2015.01.011.
'''
if T >= Tc:
return 0.0
return (7.2729 + 10.4962*omega + 0.6061*omega**2)*(1-T/Tc)**0.38*R*Tc
### Enthalpy of Vaporization at Normal Boiling Point.
[docs]def Riedel(Tb, Tc, Pc):
r'''Calculates enthalpy of vaporization at the boiling point, using the
Ridel [1]_ CSP method. Required information are critical temperature
and pressure, and boiling point. Equation taken from [2]_ and [3]_.
The enthalpy of vaporization is given by:
.. math::
\Delta_{vap} H=1.093 T_b R\frac{\ln P_c-1.013}{0.930-T_{br}}
Parameters
----------
Tb : float
Boiling temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
Returns
-------
Hvap : float
Enthalpy of vaporization at the normal boiling point, [J/mol]
Notes
-----
This equation has no example calculation in any source. The source has not
been verified. It is equation 4-144 in Perry's. Perry's also claims that
errors seldom surpass 5%.
[2]_ is the source of example work here, showing a calculation at 0.0%
error.
Internal units of pressure are bar.
Examples
--------
Pyridine, 0.0% err vs. exp: 35090 J/mol; from Poling [2]_.
>>> Riedel(388.4, 620.0, 56.3E5)
35089.80179000598
References
----------
.. [1] Riedel, L. "Eine Neue Universelle Dampfdruckformel Untersuchungen
Uber Eine Erweiterung Des Theorems Der Ubereinstimmenden Zustande. Teil
I." Chemie Ingenieur Technik 26, no. 2 (February 1, 1954): 83-89.
doi:10.1002/cite.330260206.
.. [2] Poling, Bruce E. The Properties of Gases and Liquids. 5th edition.
New York: McGraw-Hill Professional, 2000.
.. [3] Green, Don, and Robert Perry. Perry's Chemical Engineers' Handbook,
Eighth Edition. McGraw-Hill Professional, 2007.
'''
Pc = Pc/1E5 # Pa to bar
Tbr = Tb/Tc
return 1.093*Tb*R*(log(Pc) - 1.013)/(0.93 - Tbr)
[docs]def Chen(Tb, Tc, Pc):
r'''Calculates enthalpy of vaporization using the Chen [1]_ correlation
and a chemical's critical temperature, pressure and boiling point.
The enthalpy of vaporization is given by:
.. math::
\Delta H_{vb} = RT_b \frac{3.978 T_r - 3.958 + 1.555 \ln P_c}{1.07 - T_r}
Parameters
----------
Tb : float
Boiling temperature of the fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
Returns
-------
Hvap : float
Enthalpy of vaporization, [J/mol]
Notes
-----
The formulation presented in the original article is similar, but uses
units of atm and calorie instead. The form in [2]_ has adjusted for this.
A method for estimating enthalpy of vaporization at other conditions
has also been developed, but the article is unclear on its implementation.
Based on the Pitzer correlation.
Internal units: bar and K
Examples
--------
Same problem as in Perry's examples.
>>> Chen(294.0, 466.0, 5.55E6)
26705.902558030946
References
----------
.. [1] Chen, N. H. "Generalized Correlation for Latent Heat of Vaporization."
Journal of Chemical & Engineering Data 10, no. 2 (April 1, 1965): 207-10.
doi:10.1021/je60025a047
.. [2] Poling, Bruce E. The Properties of Gases and Liquids. 5th edition.
New York: McGraw-Hill Professional, 2000.
'''
Tbr = Tb/Tc
Pc = Pc/1E5 # Pa to bar
return R*Tb*(3.978*Tbr - 3.958 + 1.555*log(Pc))/(1.07 - Tbr)
[docs]def Liu(Tb, Tc, Pc):
r'''Calculates enthalpy of vaporization at the normal boiling point using
the Liu [1]_ correlation, and a chemical's critical temperature, pressure
and boiling point.
The enthalpy of vaporization is given by:
.. math::
\Delta H_{vap} = RT_b \left[ \frac{T_b}{220}\right]^{0.0627} \frac{
(1-T_{br})^{0.38} \ln(P_c/P_A)}{1-T_{br} + 0.38 T_{br} \ln T_{br}}
Parameters
----------
Tb : float
Boiling temperature of the fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
Returns
-------
Hvap : float
Enthalpy of vaporization, [J/mol]
Notes
-----
This formulation can be adjusted for lower boiling points, due to the use
of a rationalized pressure relationship. The formulation is taken from
the original article.
A correction for alcohols and organic acids based on carbon number,
which only modifies the boiling point, is available but not implemented.
No sample calculations are available in the article.
Internal units: Pa and K
Examples
--------
Same problem as in Perry's examples
>>> Liu(294.0, 466.0, 5.55E6)
26378.575260517395
References
----------
.. [1] LIU, ZHI-YONG. "Estimation of Heat of Vaporization of Pure Liquid at
Its Normal Boiling Temperature." Chemical Engineering Communications
184, no. 1 (February 1, 2001): 221-28. doi:10.1080/00986440108912849.
'''
Tbr = Tb/Tc
return R*Tb*(Tb/220.)**0.0627*(1. - Tbr)**0.38*log(Pc/101325.) \
/ (1 - Tbr + 0.38*Tbr*log(Tbr))
[docs]def Vetere(Tb, Tc, Pc, F=1.0):
r'''Calculates enthalpy of vaporization at the boiling point, using the
Vetere [1]_ CSP method. Required information are critical temperature
and pressure, and boiling point. Equation taken from [2]_.
The enthalpy of vaporization is given by:
.. math::
\frac {\Delta H_{vap}}{RT_b} = \frac{\tau_b^{0.38}
\left[ \ln P_c - 0.513 + \frac{0.5066}{P_cT_{br}^2}\right]}
{\tau_b + F(1-\tau_b^{0.38})\ln T_{br}}
Parameters
----------
Tb : float
Boiling temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
F : float, optional
Constant for a fluid, [-]
Returns
-------
Hvap : float
Enthalpy of vaporization at the boiling point, [J/mol]
Notes
-----
The equation cannot be found in the original source. It is believed that a
second article is its source, or that DIPPR staff have altered the formulation.
Internal units of pressure are bar.
Examples
--------
Example as in [2]_, p2-487; exp: 25.73
>>> Vetere(294.0, 466.0, 5.55E6)
26363.43895706672
References
----------
.. [1] Vetere, Alessandro. "Methods to Predict the Vaporization Enthalpies
at the Normal Boiling Temperature of Pure Compounds Revisited."
Fluid Phase Equilibria 106, no. 1-2 (May 1, 1995): 1-10.
doi:10.1016/0378-3812(94)02627-D.
.. [2] Green, Don, and Robert Perry. Perry's Chemical Engineers' Handbook,
Eighth Edition. McGraw-Hill Professional, 2007.
'''
Tbr = Tb/Tc
taub = 1-Tb/Tc
Pc = Pc/1E5
term = taub**0.38*(log(Pc)-0.513 + 0.5066/Pc/Tbr**2) / (taub + F*(1-taub**0.38)*log(Tbr))
return R*Tb*term
### Enthalpy of Vaporization adjusted for T
[docs]def Watson(T, Hvap_ref, T_ref, Tc, exponent=0.38):
r'''Calculates enthalpy of vaporization of a chemical at a temperature
using the known heat of vaporization at another temperature according to
the Watson [1]_ [2]_ correlation. This is an application of the
corresponding-states principle, with an emperical temperature dependence.
.. math::
\frac{\Delta H_{vap}^{T1}}{\Delta H_{vap}^{T2}} = \left(
\frac{1-T_{r,1}}{1-T_{r,2}} \right)^{0.38}
Parameters
----------
T : float
Temperature for which to calculate heat of vaporization, [K]
Hvap_ref : float
Enthalpy of vaporization at the known temperature point, [J/mol]
T_ref : float
Reference temperature; ideally as close to `T` as posible, [K]
Tc : float
Critical temperature of fluid [K]
exponent : float, optional
A fit exponent can optionally be used instead of the Watson 0.38
exponent, [-]
Returns
-------
Hvap : float
Enthalpy of vaporization at `T`, [J/mol]
Notes
-----
Examples
--------
Predict the enthalpy of vaporization of water at 320 K from a point at
300 K:
>>> Watson(T=320, Hvap_ref=43908, T_ref=300.0, Tc=647.14)
42928.990094915454
The error is 0.38% compared to the correct value of 43048 J/mol.
If the provided temperature is above the critical point, zero is returned.
References
----------
.. [1] Watson, KM. "Thermodynamics of the Liquid State." Industrial &
Engineering Chemistry 35, no. 4 (1943): 398-406.
.. [2] Martin, Joseph J., and John B. Edwards. "Correlation of Latent Heats
of Vaporization.” AIChE Journal 11, no. 2 (1965): 331-33.
https://doi.org/10.1002/aic.690110226.
'''
Tr = T/Tc
if Tr > 1.0:
return 0.0
Trefr = T_ref/Tc
H2 = Hvap_ref*((1.0 - Tr)/(1.0 - Trefr))**exponent
return H2
[docs]def Watson_n(T1, T2, Hvap1, Hvap2, Tc):
r'''Calculates the Watson heat of vaporizaton extrapolation exponent
given two known heats of vaporization.
.. math::
n = \left[ \frac{\ln{\left(\frac{Hvap_{1}}{Hvap_{2}} \right)}}
{\ln{\left(\frac{T_{1} - T_{c}}{T_{2} - T_{c}} \right)}}\right]
Parameters
----------
T1 : float
Temperature of first heat of vaporization point, [K]
T2 : float
Temperature of second heat of vaporization point, [K]
Hvap1 : float
Enthalpy of vaporization at the first known temperature point, [J/mol]
Hvap2 : float
Enthalpy of vaporization at the second known temperature point, [J/mol]
Tc : float
Critical temperature of fluid [K]
Returns
-------
exponent : float
A fit exponent that can be used instead of the Watson 0.38 exponent,
[-]
Notes
-----
This can be useful for extrapolating when a correlation does not reach
the critical point.
Examples
--------
>>> Watson_n(T1=320, T2=300, Hvap1=42928.990094915454, Hvap2=43908, Tc=647.14)
0.380000000000
'''
return log(Hvap1/Hvap2)/log((T1 - Tc)/(T2 - Tc))
### Enthalpy of Vaporization model equations
[docs]def Alibakhshi(T, Tc, C):
r'''Calculates enthalpy of vaporization of a chemical at a temperature
using a theoretically-derived single-coefficient fit equation developed in
[1]_. This model falls apart at ~0.8 Tc.
.. math::
\Delta H_{vap} = \left(4.5\pi N_A\right)^{1/3.}4.2\times 10^{-7}
(T_c - 6) - 0.5RT\ln(T) + CT
Parameters
----------
T : float
Temperature for which to calculate heat of vaporization, [K]
Tc : float
Critical temperature of fluid [K]
C : float
Alibakhshi fit coefficient, [J/mol/K]
Returns
-------
Hvap : float
Enthalpy of vaporization at `T`, [J/mol]
Notes
-----
The authors of [1]_ evaluated their model on 1890 compounds for a
temperature range of 50 K under `Tb` to 100 K below `Tc`, and obtained an
average absolute relative error of 4.5%.
Examples
--------
Predict the enthalpy of vaporization of water at 320 K:
>>> Alibakhshi(T=320.0, Tc=647.14, C=-16.7171)
41961.30490225752
The error is 2.5% compared to the correct value of 43048 J/mol.
References
----------
.. [1] Alibakhshi, Amin. "Enthalpy of Vaporization, Its Temperature
Dependence and Correlation with Surface Tension: A Theoretical Approach."
Fluid Phase Equilibria 432 (January 25, 2017): 62-69.
https://doi.org/10.1016/j.fluid.2016.10.013.
'''
return (4.5*pi*N_A)**(1/3.)*4.2E-7*(Tc-6.) - R/2.*T*log(T) + C*T
[docs]def PPDS12(T, Tc, A, B, C, D, E):
r'''Calculate the enthalpy of vaporization of a fluid using the 5-term
power fit developed by the PPDS and named PPDS equation 12.
.. math::
H_{vap} = RT_c \left(A\tau^{1/3} + B\tau^{2/3} + C\tau + D\tau^2
+ E\tau^6\right)
.. math::
\tau = 1 - \frac{T}{T_c}
Parameters
----------
T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
A : float
Coefficient, [-]
B : float
Coefficient, [-]
C : float
Coefficient, [-]
D : float
Coefficient, [-]
E : float
Coefficient, [-]
Returns
-------
Hvap : float
Enthalpy of vaporization at `T`, [J/mol]
Notes
-----
Coefficients can be found in [1]_, but no other source for these
coefficients has been found.
Examples
--------
Example from [1]_:
>>> PPDS12(300.0, 591.75, 4.60584, 13.97224, -10.592315, 2.120205, 4.277128)
37948.76862035925
Example from [2]_ for benzene; note the coefficients from [2]_ predict
enthalpy of vaporization in kJ/mol, so the output must be adjusted. The same
effect can be obtained by multiplying each of the coefficients by 1000.
>>> 1000.0*PPDS12(300.0, 562.05, 0.00171484, 0.0258604, -0.0243564, 0.00740881, 0.00680068)
33662.4258030
References
----------
.. [1] Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition.
Berlin; New York:: Springer, 2010.
.. [2] "Enthalpy of Vaporization: PPDS12."
https://trc.nist.gov/TDE/TDE_Help/Eqns-Pure-Hvap/PPDS12.htm.
'''
if T >= Tc:
return 0.0
tau = 1. - T/Tc
tau_cbrt = tau**(1/3.)
tau2 = tau*tau
Hvap = R*Tc*(tau_cbrt*(A + B*tau_cbrt) + C*tau
+ tau2*(D + E*tau2*tau2))
return Hvap
### Heat of Fusion
Hfus_all_methods = (CRC, miscdata.WEBBOOK, miscdata.WIKIDATA, miscdata.JOBACK)
"""Tuple of method name keys. See the `Hfus` for the actual references"""
[docs]@mark_numba_incompatible
def Hfus_methods(CASRN):
"""Return all methods available to obtain the heat of fusion for the
desired chemical.
Parameters
----------
CASRN : str
CASRN, [-]
Returns
-------
methods : list[str]
Methods which can be used to obtain the Hfus with the given inputs.
See Also
--------
Hfus
"""
if not _phase_change_const_loaded: _load_phase_change_constants()
return list_available_methods_from_df_dict(Hfus_sources, CASRN, 'Hfus')
[docs]@mark_numba_incompatible
def Hfus(CASRN, method=None):
r'''This function handles the retrieval of a chemical's heat of fusion.
Lookup is based on CASRNs. Will automatically select a data
source to use if no method is provided; returns None if the data is not
available.
Function has data for approximately 22000 chemicals.
Parameters
----------
CASRN : str
CASRN [-]
Returns
-------
Hfus : float
Molar enthalpy of fusion at normal melting point, [J/mol]
Other Parameters
----------------
method : string, optional
A string for the method name to use, as defined by the variable,
`Hfus_all_methods`.
Notes
-----
The available sources are as follows:
* 'CRC', a compillation of data on organics and inorganics as published
in [1]_.
* 'WEBBOOK', a NIST resource [4]_ containing mostly experimental
and averaged values
* 'WIKIDATA', data from the Wikidata project [2]_
* 'JOBACK', an estimation method for organic substances in [3]_
Examples
--------
>>> Hfus('7732-18-5')
6010.0
See Also
--------
Hfus_methods
References
----------
.. [1] Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of
Chemistry and Physics, 95E. Boca Raton, FL: CRC press, 2014.
.. [2] Wikidata. Wikidata. Accessed via API. https://www.wikidata.org/
.. [3] Joback, K.G., and R.C. Reid. "Estimation of Pure-Component
Properties from Group-Contributions." Chemical Engineering
Communications 57, no. 1-6 (July 1, 1987): 233-43.
doi:10.1080/00986448708960487.
.. [4] Shen, V.K., Siderius, D.W., Krekelberg, W.P., and Hatch, H.W., Eds.,
NIST WebBook, NIST, http://doi.org/10.18434/T4M88Q
'''
if dr.USE_CONSTANTS_DATABASE and method is None:
val, found = database_constant_lookup(CASRN, 'Hfus')
if found: return val
if not _phase_change_const_loaded: _load_phase_change_constants()
if method:
return retrieve_from_df_dict(Hfus_sources, CASRN, 'Hfus', method)
else:
return retrieve_any_from_df_dict(Hfus_sources, CASRN, 'Hfus')