'''Chemical Engineering Design Library (ChEDL). Utilities for process modeling.
Copyright (C) 2019, 2020 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.
'''
__all__ = ['VirialCSP', 'VirialGas',
'VIRIAL_B_ZERO', 'VIRIAL_B_PITZER_CURL', 'VIRIAL_B_ABBOTT', 'VIRIAL_B_TSONOPOULOS',
'VIRIAL_B_TSONOPOULOS_EXTENDED', 'VIRIAL_B_OCONNELL_PRAUSNITZ', 'VIRIAL_B_XIANG', 'VIRIAL_B_MENG', 'VIRIAL_C_XIANG',
'VIRIAL_C_ORBEY_VERA', 'VIRIAL_C_ZERO', 'VIRIAL_B_MODELS', 'VIRIAL_C_MODELS']
from chemicals.utils import dns_to_dn_partials, dxs_to_dn_partials, dxs_to_dns, hash_any_primitive, mixing_simple
from chemicals.virial import (
BVirial_Abbott_mat,
BVirial_Abbott_vec,
BVirial_Meng_mat,
BVirial_Meng_vec,
BVirial_mixture,
BVirial_Oconnell_Prausnitz_mat,
BVirial_Oconnell_Prausnitz_vec,
BVirial_Pitzer_Curl_mat,
BVirial_Pitzer_Curl_vec,
BVirial_Tsonopoulos_extended_mat,
BVirial_Tsonopoulos_extended_vec,
BVirial_Tsonopoulos_mat,
BVirial_Tsonopoulos_vec,
BVirial_Xiang_mat,
BVirial_Xiang_vec,
CVirial_Liu_Xiang_mat,
CVirial_Liu_Xiang_vec,
CVirial_mixture_Orentlicher_Prausnitz,
CVirial_Orbey_Vera_mat,
CVirial_Orbey_Vera_vec,
Lee_Kesler_virial_CSP_Vcijs,
Tarakad_Danner_virial_CSP_omegaijs,
Tarakad_Danner_virial_CSP_Pcijs,
Tarakad_Danner_virial_CSP_Tcijs,
Z_from_virial_density_form,
d2BVirial_mixture_dzizjs,
d2CVirial_mixture_dT2_Orentlicher_Prausnitz,
d2CVirial_mixture_Orentlicher_Prausnitz_dTdzs,
d2CVirial_mixture_Orentlicher_Prausnitz_dzizjs,
d2V_dzizjs_virial,
d3BVirial_mixture_dzizjzks,
d3CVirial_mixture_dT3_Orentlicher_Prausnitz,
d3CVirial_mixture_Orentlicher_Prausnitz_dzizjzks,
dBVirial_mixture_dzs,
dCVirial_mixture_dT_Orentlicher_Prausnitz,
dCVirial_mixture_Orentlicher_Prausnitz_dzs,
dV_dzs_virial,
)
from fluids.constants import R
from fluids.numerics import log, newton
from fluids.numerics import numpy as np
from thermo.heat_capacity import HeatCapacityGas
from thermo.phases.phase import IdealGasDeparturePhase, Phase
try:
array, zeros, ones, delete, npsum, nplog = np.array, np.zeros, np.ones, np.delete, np.sum, np.log
except (ImportError, AttributeError):
pass
VIRIAL_B_ZERO = 'VIRIAL_B_ZERO'
VIRIAL_B_PITZER_CURL = 'VIRIAL_B_PITZER_CURL'
VIRIAL_B_ABBOTT = 'VIRIAL_B_ABBOTT'
VIRIAL_B_TSONOPOULOS = 'VIRIAL_B_TSONOPOULOS'
VIRIAL_B_TSONOPOULOS_EXTENDED = 'VIRIAL_B_TSONOPOULOS_EXTENDED' # requires `a` and `b` parameter
VIRIAL_B_OCONNELL_PRAUSNITZ = "VIRIAL_B_OCONNELL_PRAUSNITZ"
VIRIAL_B_XIANG = 'VIRIAL_B_XIANG'
VIRIAL_B_MENG = 'VIRIAL_B_MENG'
VIRIAL_B_MODELS = (VIRIAL_B_ZERO,
VIRIAL_B_PITZER_CURL,
VIRIAL_B_ABBOTT,
VIRIAL_B_TSONOPOULOS,
VIRIAL_B_TSONOPOULOS_EXTENDED,
VIRIAL_B_OCONNELL_PRAUSNITZ,
VIRIAL_B_XIANG,
VIRIAL_B_MENG)
# reqiures an `a` parameter
VIRIAL_C_XIANG = 'VIRIAL_C_XIANG'
VIRIAL_C_ORBEY_VERA = 'VIRIAL_C_ORBEY_VERA'
VIRIAL_C_ZERO = 'VIRIAL_C_ZERO'
VIRIAL_C_MODELS = (VIRIAL_C_ZERO, VIRIAL_C_XIANG, VIRIAL_C_ORBEY_VERA)
VIRIAL_CROSS_B_ZEROS = VIRIAL_CROSS_C_ZEROS = 'Zeros'
VIRIAL_CROSS_B_TARAKAD_DANNER = 'Tarakad-Danner'
VIRIAL_CROSS_C_TARAKAD_DANNER = 'Tarakad-Danner'
[docs]class VirialCSP:
r'''Class for calculating the `B` virial coefficients of pure components
and their B interaction matrix, and the `C` virial coefficients of pure
components and their mixtures. It is configurable which corresponding
states model is used. Either the `B` or `C` model can be disabled;
if both are off, this will revert to the ideal-gas equation of state.
Parameters
----------
Tcs : list[float]
Critical temperatures of all components, [K]
Pcs : list[float]
Critical pressures of all components, [Pa]
Vcs : list[float]
Critical volumes of all components, [m^3/mol]
omegas : list[float]
Acentric factors of all components, [-]
B_model : str, optional
The model used to calculate the `B` pure component and interaction
virial coefficients, [-]
* **VIRIAL_B_ZERO**: The B virial coefficient is always zero
* **VIRIAL_B_PITZER_CURL** The model of [2]_, :obj:`chemicals.virial.BVirial_Pitzer_Curl`
* **VIRIAL_B_ABBOTT** The model of [3]_, :obj:`chemicals.virial.BVirial_Abbott`
* **VIRIAL_B_TSONOPOULOS** The model of [4]_, :obj:`chemicals.virial.BVirial_Tsonopoulos`
* **VIRIAL_B_TSONOPOULOS_EXTENDED** The model of [5]_ and [6]_, :obj:`chemicals.virial.BVirial_Tsonopoulos_extended`
* **VIRIAL_B_OCONNELL_PRAUSNITZ** The model of [1]_, :obj:`chemicals.virial.BVirial_Oconnell_Prausnitz`
* **VIRIAL_B_XIANG** The model of [7]_, :obj:`chemicals.virial.BVirial_Xiang`
* **VIRIAL_B_MENG** The model of [8]_, :obj:`chemicals.virial.BVirial_Meng`
cross_B_model : str, optional
The model used to calculate the `B` cross virial coefficient
* **VIRIAL_CROSS_B_TARAKAD_DANNER** : This model uses the mixing rules
for estimating interaction critical components according to the
rules :obj:`chemicals.virial.Tarakad_Danner_virial_CSP_Tcijs`,
:obj:`chemicals.virial.Tarakad_Danner_virial_CSP_Pcijs`,
:obj:`chemicals.virial.Lee_Kesler_virial_CSP_Vcijs` and
:obj:`chemicals.virial.Tarakad_Danner_virial_CSP_omegaijs`;
note that this mixing rule has an interaction parameter for the
interaction critical temperature, which defaults to zero and can be
provided. :obj:`chemicals.virial.Meng_Duan_2005_virial_CSP_kijs`
or :obj:`chemicals.virial.Tarakad_Danner_virial_CSP_kijs` are two
sample models for estimating these parameters; additional models are
available in the literature and also the value can be regressed from
experimental values.
cross_B_model_kijs : list[list[float]], optional
Cross parameters `kijs` for **VIRIAL_CROSS_B_TARAKAD_DANNER** cross
rule; specified or set to zero [-]
C_model : str, optional
The model used to calculate the `C` pure component and interaction
virial coefficients, [-]
* **VIRIAL_C_ZERO**: The C virial coefficient is always zero
* **VIRIAL_C_ORBEY_VERA** The model of [9]_, :obj:`chemicals.virial.CVirial_Orbey_Vera`
* **VIRIAL_C_XIANG** The model of [10]_, :obj:`chemicals.virial.CVirial_Liu_Xiang`
B_model_Meng_as : list[list[float]], optional
Meng `a` parameters; this is essentially a correction for polar
behavior, and must be provided for all components as well as their
interactions; see :obj:`chemicals.virial.Meng_virial_a`.
This is used only for the model **VIRIAL_B_MENG** [-]
B_model_Tsonopoulos_extended_as : list[list[float]], optional
Tsonopoulos extended `a` parameters; this is essentially a correction for polar
behavior, and must be provided for all components as well as their
interactions; see :obj:`thermo.functional_groups.BVirial_Tsonopoulos_extended_ab`.
This is used only for the model **VIRIAL_B_TSONOPOULOS_EXTENDED** [-]
B_model_Tsonopoulos_extended_bs : list[list[float]], optional
Meng `a` parameters; this is essentially a correction for polar
behavior, and must be provided for all components as well as their
interactions; see :obj:`thermo.functional_groups.BVirial_Tsonopoulos_extended_ab`.
This is used only for the model **VIRIAL_B_TSONOPOULOS_EXTENDED** [-]
T : float, optional
The specified temperature for the model; the calculations are cached
based only on temperature, use :obj:`VirialCSP.to` to obtain a new
object at a different temperature, [K]
Examples
--------
Notes
-----
References
----------
.. [1] O`Connell, J. P., and J. M. Prausnitz. "Empirical Correlation of
Second Virial Coefficients for Vapor-Liquid Equilibrium Calculations."
Industrial & Engineering Chemistry Process Design and Development 6,
no. 2 (April 1, 1967): 245-50. https://doi.org/10.1021/i260022a016.
.. [2] Pitzer, Kenneth S., and R. F. Curl. "The Volumetric and
Thermodynamic Properties of Fluids. III. Empirical Equation for the
Second Virial Coefficient1." Journal of the American Chemical Society
79, no. 10 (May 1, 1957): 2369-70. doi:10.1021/ja01567a007.
.. [3] Smith, H. C. Van Ness Joseph M. Introduction to Chemical Engineering
Thermodynamics 4E 1987.
.. [4] Tsonopoulos, Constantine. "An Empirical Correlation of Second Virial
Coefficients." AIChE Journal 20, no. 2 (March 1, 1974): 263-72.
doi:10.1002/aic.690200209.
.. [5] Tsonopoulos, C., and J. L. Heidman. "From the Virial to the Cubic
Equation of State." Fluid Phase Equilibria 57, no. 3 (1990): 261-76.
doi:10.1016/0378-3812(90)85126-U
.. [6] Tsonopoulos, Constantine, and John H. Dymond. "Second Virial
Coefficients of Normal Alkanes, Linear 1-Alkanols (and Water), Alkyl
Ethers, and Their Mixtures." Fluid Phase Equilibria, International
Workshop on Vapour-Liquid Equilibria and Related Properties in Binary
and Ternary Mixtures of Ethers, Alkanes and Alkanols, 133, no. 1-2
(June 1997): 11-34. doi:10.1016/S0378-3812(97)00058-7.
.. [7] Xiang, H. W. "The New Simple Extended Corresponding-States
Principle: Vapor Pressure and Second Virial Coefficient." Chemical
Engineering Science 57, no. 8 (April 2002): 1439049.
https://doi.org/10.1016/S0009-2509(02)00017-9.
.. [8] Meng, Long, Yuan-Yuan Duan, and Lei Li. "Correlations for Second and
Third Virial Coefficients of Pure Fluids." Fluid Phase Equilibria 226
(December 10, 2004): 109-20. https://doi.org/10.1016/j.fluid.2004.09.023.
.. [9] Orbey, Hasan, and J. H. Vera. "Correlation for the Third Virial
Coefficient Using Tc, Pc and ω as Parameters." AIChE Journal 29, no. 1
(January 1, 1983): 107-13. https://doi.org/10.1002/aic.690290115.
.. [10] Liu, D. X., and H. W. Xiang. "Corresponding-States Correlation and
Prediction of Third Virial Coefficients for a Wide Range of Substances."
International Journal of Thermophysics 24, no. 6 (November 1, 2003):
1667-80. https://doi.org/10.1023/B:IJOT.0000004098.98614.38.
'''
cross_B_calculated = False
cross_C_calculated = False
pure_B_calculated = False
pure_C_calculated = False
nonstate_constants = ('Tcs', 'Pcs', 'Vcs', 'omegas', 'B_model', 'cross_B_model',
'cross_B_model_kijs', 'C_model', 'B_model_Meng_as',
'B_model_Tsonopoulos_extended_as', 'B_model_Tsonopoulos_extended_bs')
[docs] def __repr__(self):
r'''Method to create a string representation of the VirialCSP object, with
the goal of making it easy to obtain standalone code which reproduces
the current state of the phase. This is extremely helpful in creating
new test cases.
Returns
-------
recreation : str
String which is valid Python and recreates the current state of
the object if ran, [-]
Examples
--------
>>> from thermo import VirialCSP
>>> model = VirialCSP(Tcs=[126.2, 154.58, 150.8], Pcs=[3394387.5, 5042945.25, 4873732.5], Vcs=[8.95e-05, 7.34e-05, 7.49e-05], omegas=[0.04, 0.021, -0.004], B_model='VIRIAL_B_PITZER_CURL', cross_B_model='Tarakad-Danner', C_model='VIRIAL_C_ORBEY_VERA')
>>> model
VirialCSP(Tcs=[126.2, 154.58, 150.8], Pcs=[3394387.5, 5042945.25, 4873732.5], Vcs=[8.95e-05, 7.34e-05, 7.49e-05], omegas=[0.04, 0.021, -0.004], B_model='VIRIAL_B_PITZER_CURL', cross_B_model='Tarakad-Danner', C_model='VIRIAL_C_ORBEY_VERA')
'''
try:
Cpgs = ', '.join(str(o) for o in self.HeatCapacityGases)
except:
Cpgs = ''
base = f'{self.__class__.__name__}('
for s in self.nonstate_constants + ('T',):
if hasattr(self, s) and getattr(self, s) is not None:
val = getattr(self, s)
if type(val) is str:
val = f"'{val}'"
elif isinstance(val, (np.ndarray, list,)):
if not np.any(val):
continue
base += f'{s}={val}, '
if base[-2:] == ', ':
base = base[:-2]
base += ')'
return base
def state_hash(self):
r'''Basic method to calculate a hash of the state of the model and its
model parameters.
Note that the hashes should only be compared on the same system running
in the same process!
Returns
-------
state_hash : int
Hash of the object's model parameters and state, [-]
'''
#print((self.model_hash(), self.T), 'state hash args')
return hash_any_primitive((self.model_hash(), self.T))
def model_hash(self):
r'''Basic method to calculate a hash of the non-state parts of the model
This is useful for comparing to models to
determine if they are the same, i.e. in a VLL flash it is important to
know if both liquids have the same model.
Note that the hashes should only be compared on the same system running
in the same process!
Returns
-------
model_hash : int
Hash of the object's model parameters, [-]
'''
try:
return self._model_hash
except AttributeError:
pass
h = hash(self.__class__.__name__)
for s in self.nonstate_constants:
try:
#print(s,getattr(self, s), hash((h, s, hash_any_primitive(getattr(self, s)))))
h = hash((h, s, hash_any_primitive(getattr(self, s))))
except AttributeError:
pass
self._model_hash = h
return h
def __hash__(self):
r'''Method to calculate and return a hash representing the exact state
of the object.
Returns
-------
hash : int
Hash of the object, [-]
'''
d = self.__dict__
ans = hash_any_primitive((self.__class__.__name__, self.state_hash(), self.model_hash()))
return ans
def __eq__(self, other):
return self.__hash__() == hash(other)
def __init__(self, Tcs, Pcs, Vcs, omegas,
B_model=VIRIAL_B_XIANG,
cross_B_model=VIRIAL_CROSS_B_TARAKAD_DANNER,
# always require kijs in this model
cross_B_model_kijs=None,
C_model=VIRIAL_C_XIANG,
B_model_Meng_as=None,
B_model_Tsonopoulos_extended_as=None,
B_model_Tsonopoulos_extended_bs=None,
T=None,
):
self.Tcs = Tcs
self.Pcs = Pcs
self.Vcs = Vcs
self.omegas = omegas
self.N = N = len(Tcs)
self.scalar = scalar = type(Tcs) is list
self.T = T
self.B_model = B_model
self.cross_B_model = cross_B_model
if cross_B_model_kijs is None:
if scalar:
cross_B_model_kijs = [[0.0]*N for i in range(N)]
else:
cross_B_model_kijs = zeros((N, N))
self.cross_B_model_kijs = cross_B_model_kijs
# Parameters specific to `B` model
if B_model_Meng_as is None:
if scalar:
B_model_Meng_as = [[0.0]*N for i in range(N)]
else:
B_model_Meng_as = zeros((N, N))
B_model_Meng_as_pure = [B_model_Meng_as[i][i] for i in range(N)]
if B_model_Tsonopoulos_extended_as is None:
if scalar:
B_model_Tsonopoulos_extended_as = [[0.0]*N for i in range(N)]
else:
B_model_Tsonopoulos_extended_as = zeros((N, N))
B_model_Tsonopoulos_extended_as_pure = [B_model_Tsonopoulos_extended_as[i][i] for i in range(N)]
if B_model_Tsonopoulos_extended_bs is None:
if scalar:
B_model_Tsonopoulos_extended_bs = [[0.0]*N for i in range(N)]
else:
B_model_Tsonopoulos_extended_bs = zeros((N, N))
B_model_Tsonopoulos_extended_bs_pure = [B_model_Tsonopoulos_extended_bs[i][i] for i in range(N)]
self.B_model_Meng_as = B_model_Meng_as
self.B_model_Tsonopoulos_extended_as = B_model_Tsonopoulos_extended_as
self.B_model_Tsonopoulos_extended_bs = B_model_Tsonopoulos_extended_bs
self.B_model_Meng_as_pure = B_model_Meng_as_pure
self.B_model_Tsonopoulos_extended_as_pure = B_model_Tsonopoulos_extended_as_pure
self.B_model_Tsonopoulos_extended_bs_pure = B_model_Tsonopoulos_extended_bs_pure
# Cross B coefficients
self.cross_B_model_Tcijs = Tarakad_Danner_virial_CSP_Tcijs(Tcs, self.cross_B_model_kijs)
self.cross_B_model_Pcijs = Tarakad_Danner_virial_CSP_Pcijs(Tcs=Tcs, Pcs=Pcs, Vcs=Vcs, Tcijs=self.cross_B_model_Tcijs)
self.cross_B_model_Vcijs = Lee_Kesler_virial_CSP_Vcijs(Vcs=Vcs)
self.cross_B_model_omegaijs = Tarakad_Danner_virial_CSP_omegaijs(omegas=omegas)
self.cross_C_model_Tcijs = self.cross_B_model_Tcijs
self.cross_C_model_Pcijs = self.cross_B_model_Pcijs
self.cross_C_model_Vcijs = self.cross_B_model_Vcijs
self.cross_C_model_omegaijs = self.cross_B_model_omegaijs
self.C_model = C_model
self.C_zero = C_model == VIRIAL_C_ZERO
self.B_zero = B_model == VIRIAL_B_ZERO
[docs] def to(self, T=None):
r'''Method to construct a new object at a new temperature.
Parameters
----------
T : float
Temperature, [K]
Returns
-------
obj : VirialCSP
Object at new temperature, [-]
Notes
-----
Examples
--------
'''
new = self.__class__.__new__(self.__class__)
new.Tcs = self.Tcs
new.Pcs = self.Pcs
new.Vcs = self.Vcs
new.omegas = self.omegas
new.N = self.N
new.scalar = self.scalar
new.B_model = self.B_model
# Parameters specific to `B` model
new.B_model_Meng_as = self.B_model_Meng_as
new.B_model_Tsonopoulos_extended_as = self.B_model_Tsonopoulos_extended_as
new.B_model_Tsonopoulos_extended_bs = self.B_model_Tsonopoulos_extended_bs
new.B_model_Meng_as_pure = self.B_model_Meng_as_pure
new.B_model_Tsonopoulos_extended_as_pure = self.B_model_Tsonopoulos_extended_as_pure
new.B_model_Tsonopoulos_extended_bs_pure = self.B_model_Tsonopoulos_extended_bs_pure
new.cross_B_model = self.cross_B_model
new.cross_B_model_kijs = self.cross_B_model_kijs
new.cross_B_model_Tcijs = self.cross_B_model_Tcijs
new.cross_B_model_Pcijs = self.cross_B_model_Pcijs
new.cross_B_model_Vcijs = self.cross_B_model_Vcijs
new.cross_B_model_omegaijs = self.cross_B_model_omegaijs
new.cross_C_model_Tcijs = self.cross_C_model_Tcijs
new.cross_C_model_Pcijs = self.cross_C_model_Pcijs
new.cross_C_model_Vcijs = self.cross_C_model_Vcijs
new.cross_C_model_omegaijs = self.cross_C_model_omegaijs
new.C_model = self.C_model
new.C_zero = self.C_zero
new.B_zero = self.B_zero
new.T = T
return new
def B_interactions_at_T(self, T):
N = self.N
Tcijs, Pcijs, Vcijs, omegaijs = self.cross_B_model_Tcijs, self.cross_B_model_Pcijs, self.cross_B_model_Vcijs, self.cross_B_model_omegaijs
if self.scalar:
Bs = [[0.0]*N for _ in range(N)]
dB_dTs = [[0.0]*N for _ in range(N)]
d2B_dT2s = [[0.0]*N for _ in range(N)]
d3B_dT3s = [[0.0]*N for _ in range(N)]
else:
Bs = zeros((N, N))
dB_dTs = zeros((N, N))
d2B_dT2s = zeros((N, N))
d3B_dT3s = zeros((N, N))
if self.B_model == VIRIAL_B_ZERO:
return Bs, dB_dTs, d2B_dT2s, d3B_dT3s
elif self.B_model == VIRIAL_B_PITZER_CURL:
Bs_interactions, dB_dTs_interactions, d2B_dT2s_interactions, d3B_dT3s_interactions = BVirial_Pitzer_Curl_mat(T=T, Tcs=Tcijs, Pcs=Pcijs, omegas=omegaijs,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
elif self.B_model == VIRIAL_B_ABBOTT:
Bs_interactions, dB_dTs_interactions, d2B_dT2s_interactions, d3B_dT3s_interactions = BVirial_Abbott_mat(T=T, Tcs=Tcijs, Pcs=Pcijs, omegas=omegaijs,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
elif self.B_model == VIRIAL_B_TSONOPOULOS:
Bs_interactions, dB_dTs_interactions, d2B_dT2s_interactions, d3B_dT3s_interactions = BVirial_Tsonopoulos_mat(T=T, Tcs=Tcijs, Pcs=Pcijs, omegas=omegaijs,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
elif self.B_model == VIRIAL_B_TSONOPOULOS_EXTENDED:
Bs_interactions, dB_dTs_interactions, d2B_dT2s_interactions, d3B_dT3s_interactions = BVirial_Tsonopoulos_extended_mat(T=T, Tcs=Tcijs, Pcs=Pcijs, omegas=omegaijs,
ais=self.B_model_Tsonopoulos_extended_as,
bs=self.B_model_Tsonopoulos_extended_bs,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
elif self.B_model == VIRIAL_B_OCONNELL_PRAUSNITZ:
Bs_interactions, dB_dTs_interactions, d2B_dT2s_interactions, d3B_dT3s_interactions = BVirial_Oconnell_Prausnitz_mat(T=T, Tcs=Tcijs, Pcs=Pcijs, omegas=omegaijs,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
elif self.B_model == VIRIAL_B_XIANG:
Bs_interactions, dB_dTs_interactions, d2B_dT2s_interactions, d3B_dT3s_interactions = BVirial_Xiang_mat(T=T, Tcs=Tcijs, Pcs=Pcijs, Vcs=Vcijs, omegas=omegaijs,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
elif self.B_model == VIRIAL_B_MENG:
Bs_interactions, dB_dTs_interactions, d2B_dT2s_interactions, d3B_dT3s_interactions = BVirial_Meng_mat(T=T, Tcs=Tcijs, Pcs=Pcijs, Vcs=Vcijs, omegas=omegaijs,
ais=self.B_model_Meng_as,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
return Bs_interactions, dB_dTs_interactions, d2B_dT2s_interactions, d3B_dT3s_interactions
def _set_B_and_der_interactions(self):
Bs_interactions, dB_dTs_interactions, d2B_dT2s_interactions, d3B_dT3s_interactions = self.B_interactions_at_T(self.T)
self.Bs_interactions = Bs_interactions
self.dB_dTs_interactions = dB_dTs_interactions
self.d2B_dT2s_interactions = d2B_dT2s_interactions
self.d3B_dT3s_interactions = d3B_dT3s_interactions
self.cross_B_calculated = True
def B_pures_at_T(self, T):
N = self.N
Tcs, Pcs, Vcs, omegas = self.Tcs, self.Pcs, self.Vcs, self.omegas
if self.scalar:
Bs = [0.0]*N
dB_dTs = [0.0]*N
d2B_dT2s = [0.0]*N
d3B_dT3s = [0.0]*N
else:
Bs = zeros(N)
dB_dTs = zeros(N)
d2B_dT2s = zeros(N)
d3B_dT3s = zeros(N)
if self.B_model == VIRIAL_B_ZERO:
return Bs, dB_dTs, d2B_dT2s, d3B_dT3s
elif self.B_model == VIRIAL_B_PITZER_CURL:
Bs_pure, dB_dTs_pure, d2B_dT2s_pure, d3B_dT3s_pure = BVirial_Pitzer_Curl_vec(T=T, Tcs=Tcs, Pcs=Pcs, omegas=omegas,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
elif self.B_model == VIRIAL_B_ABBOTT:
Bs_pure, dB_dTs_pure, d2B_dT2s_pure, d3B_dT3s_pure = BVirial_Abbott_vec(T=T, Tcs=Tcs, Pcs=Pcs, omegas=omegas,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
elif self.B_model == VIRIAL_B_TSONOPOULOS:
Bs_pure, dB_dTs_pure, d2B_dT2s_pure, d3B_dT3s_pure = BVirial_Tsonopoulos_vec(T=T, Tcs=Tcs, Pcs=Pcs, omegas=omegas,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
elif self.B_model == VIRIAL_B_TSONOPOULOS_EXTENDED:
Bs_pure, dB_dTs_pure, d2B_dT2s_pure, d3B_dT3s_pure = BVirial_Tsonopoulos_extended_vec(T=T, Tcs=Tcs, Pcs=Pcs, omegas=omegas,
ais=self.B_model_Tsonopoulos_extended_as_pure,
bs=self.B_model_Tsonopoulos_extended_bs_pure,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
elif self.B_model == VIRIAL_B_OCONNELL_PRAUSNITZ:
Bs_pure, dB_dTs_pure, d2B_dT2s_pure, d3B_dT3s_pure = BVirial_Oconnell_Prausnitz_vec(T=T, Tcs=Tcs, Pcs=Pcs, omegas=omegas,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
elif self.B_model == VIRIAL_B_XIANG:
Bs_pure, dB_dTs_pure, d2B_dT2s_pure, d3B_dT3s_pure = BVirial_Xiang_vec(T=T, Tcs=Tcs, Pcs=Pcs, Vcs=Vcs, omegas=omegas,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
elif self.B_model == VIRIAL_B_MENG:
Bs_pure, dB_dTs_pure, d2B_dT2s_pure, d3B_dT3s_pure = BVirial_Meng_vec(T=T, Tcs=Tcs, Pcs=Pcs, omegas=omegas, Vcs=Vcs,
ais=self.B_model_Meng_as_pure,
Bs=Bs, dB_dTs=dB_dTs, d2B_dT2s=d2B_dT2s, d3B_dT3s=d3B_dT3s)
return Bs_pure, dB_dTs_pure, d2B_dT2s_pure, d3B_dT3s_pure
def _set_B_and_der_pure(self):
Bs_pure, dB_dTs_pure, d2B_dT2s_pure, d3B_dT3s_pure = self.B_pures_at_T(self.T)
self.Bs_pure = Bs_pure
self.dB_dTs_pure = dB_dTs_pure
self.d2B_dT2s_pure = d2B_dT2s_pure
self.d3B_dT3s_pure = d3B_dT3s_pure
self.pure_B_calculated = True
[docs] def B_pures(self):
r'''Method to calculate and return the pure component virial coefficients
at the specified temperature.
Returns
-------
B_pures : list[float]
Second `B` virial coefficients, [m^3/mol]
'''
if not self.pure_B_calculated:
self._set_B_and_der_pure()
return self.Bs_pure
[docs] def dB_dT_pures(self):
r'''Method to calculate and return the first temperature derivative of
pure component virial coefficients at the specified temperature.
Returns
-------
dB_dT_pures : list[float]
Second temperature derivative of second `B` virial coefficients,
[m^3/(mol*K)]
'''
if not self.pure_B_calculated:
self._set_B_and_der_pure()
return self.dB_dTs_pure
[docs] def d2B_dT2_pures(self):
r'''Method to calculate and return the second temperature derivative of
pure component virial coefficients at the specified temperature.
Returns
-------
d2B_dT2_pures : list[float]
Second temperature derivative of second `B` virial coefficients,
[m^3/(mol*K^2)]
'''
if not self.pure_B_calculated:
self._set_B_and_der_pure()
return self.d2B_dT2s_pure
[docs] def d3B_dT3_pures(self):
r'''Method to calculate and return the third temperature derivative of
pure component virial coefficients at the specified temperature.
Returns
-------
d3B_dT3_pures : list[float]
Third temperature derivative of second `B` virial coefficients,
[m^3/(mol*K^3)]
'''
if not self.pure_B_calculated:
self._set_B_and_der_pure()
return self.d3B_dT3s_pure
[docs] def B_interactions(self):
r'''Method to calculate and return the matrix of interaction component
virial coefficients at the specified temperature.
Returns
-------
B_interactions : list[list[float]]
Second `B` virial coefficients interaction matrix, [m^3/mol]
'''
if not self.cross_B_calculated:
self._set_B_and_der_interactions()
return self.Bs_interactions
[docs] def dB_dT_interactions(self):
r'''Method to calculate and return the first temperature derivative of
the `B` virial interaction coefficients at the specified temperature.
Returns
-------
dB_dT_interactions : list[list[float]]
Second temperature derivative of second `B` virial interaction
coefficients, [m^3/(mol*K)]
'''
if not self.cross_B_calculated:
self._set_B_and_der_interactions()
return self.dB_dTs_interactions
[docs] def d2B_dT2_interactions(self):
r'''Method to calculate and return the second temperature derivative of
the `B` virial interaction coefficients at the specified temperature.
Returns
-------
d2B_dT2_interactions : list[list[float]]
Second temperature derivative of second `B` virial interaction
coefficients, [m^3/(mol*K^2)]
'''
if not self.cross_B_calculated:
self._set_B_and_der_interactions()
return self.d2B_dT2s_interactions
[docs] def d3B_dT3_interactions(self):
r'''Method to calculate and return the third temperature derivative of
the `B` virial interaction coefficients at the specified temperature.
Returns
-------
d3B_dT3_interactions : list[list[float]]
Third temperature derivative of second `B` virial interaction
coefficients, [m^3/(mol*K^3)]
'''
if not self.cross_B_calculated:
self._set_B_and_der_interactions()
return self.d3B_dT3s_interactions
def C_interactions_at_T(self, T):
N = self.N
Tcijs, Pcijs, Vcijs, omegaijs = self.cross_C_model_Tcijs, self.cross_C_model_Pcijs, self.cross_C_model_Vcijs, self.cross_C_model_omegaijs
if self.scalar:
Cs = [[0.0]*N for _ in range(N)]
dC_dTs = [[0.0]*N for _ in range(N)]
d2C_dT2s = [[0.0]*N for _ in range(N)]
d3C_dT3s = [[0.0]*N for _ in range(N)]
else:
Cs = zeros((N, N))
dC_dTs = zeros((N, N))
d2C_dT2s = zeros((N, N))
d3C_dT3s = zeros((N, N))
if self.C_model == VIRIAL_C_ZERO:
return Cs, dC_dTs, d2C_dT2s, d3C_dT3s
elif self.C_model == VIRIAL_C_XIANG:
Cs_interactions, dC_dTs_interactions, d2C_dT2s_interactions, d3C_dT3s_interactions = CVirial_Liu_Xiang_mat(T=T, Tcs=Tcijs, Pcs=Pcijs, Vcs=Vcijs, omegas=omegaijs,
Cs=Cs, dC_dTs=dC_dTs, d2C_dT2s=d2C_dT2s, d3C_dT3s=d3C_dT3s)
elif self.C_model == VIRIAL_C_ORBEY_VERA:
Cs_interactions, dC_dTs_interactions, d2C_dT2s_interactions, d3C_dT3s_interactions = CVirial_Orbey_Vera_mat(T=T, Tcs=Tcijs, Pcs=Pcijs, omegas=omegaijs,
Cs=Cs, dC_dTs=dC_dTs, d2C_dT2s=d2C_dT2s, d3C_dT3s=d3C_dT3s)
return Cs_interactions, dC_dTs_interactions, d2C_dT2s_interactions, d3C_dT3s_interactions
def C_pures_at_T(self, T):
N = self.N
Tcs, Pcs, Vcs, omegas = self.Tcs, self.Pcs, self.Vcs, self.omegas
if self.scalar:
Cs = [0.0]*N
dC_dTs = [0.0]*N
d2C_dT2s = [0.0]*N
d3C_dT3s = [0.0]*N
else:
Cs = zeros(N)
dC_dTs = zeros(N)
d2C_dT2s = zeros(N)
d3C_dT3s = zeros(N)
if self.C_model == VIRIAL_C_ZERO:
return Cs, dC_dTs, d2C_dT2s, d3C_dT3s
elif self.C_model == VIRIAL_C_XIANG:
Cs_pure, dC_dTs_pure, d2C_dT2s_pure, d3C_dT3s_pure = CVirial_Liu_Xiang_vec(T=T, Tcs=Tcs, Pcs=Pcs, Vcs=Vcs, omegas=omegas,
Cs=Cs, dC_dTs=dC_dTs, d2C_dT2s=d2C_dT2s, d3C_dT3s=d3C_dT3s)
elif self.C_model == VIRIAL_C_ORBEY_VERA:
Cs_pure, dC_dTs_pure, d2C_dT2s_pure, d3C_dT3s_pure = CVirial_Orbey_Vera_vec(T=T, Tcs=Tcs, Pcs=Pcs, omegas=omegas,
Cs=Cs, dC_dTs=dC_dTs, d2C_dT2s=d2C_dT2s, d3C_dT3s=d3C_dT3s)
return Cs_pure, dC_dTs_pure, d2C_dT2s_pure, d3C_dT3s_pure
def _set_C_and_der_pure(self):
Cs_pure, dC_dTs_pure, d2C_dT2s_pure, d3C_dT3s_pure = self.C_pures_at_T(self.T)
self.Cs_pure = Cs_pure
self.dC_dTs_pure = dC_dTs_pure
self.d2C_dT2s_pure = d2C_dT2s_pure
self.d3C_dT3s_pure = d3C_dT3s_pure
self.pure_C_calculated = True
def _set_C_and_der_interactions(self):
Cs_interactions, dC_dTs_interactions, d2C_dT2s_interactions, d3C_dT3s_interactions = self.C_interactions_at_T(self.T)
self.Cs_interactions = Cs_interactions
self.dC_dTs_interactions = dC_dTs_interactions
self.d2C_dT2s_interactions = d2C_dT2s_interactions
self.d3C_dT3s_interactions = d3C_dT3s_interactions
self.cross_C_calculated = True
[docs] def C_pures(self):
r'''Method to calculate and return the pure component third virial
coefficients at the specified temperature.
Returns
-------
C_pures : list[float]
Third `C` virial coefficients, [m^6/mol^2]
'''
if not self.pure_C_calculated:
self._set_C_and_der_pure()
return self.Cs_pure
[docs] def dC_dT_pures(self):
r'''Method to calculate and return the first temperature derivative of
pure component third virial coefficients at the specified temperature.
Returns
-------
dC_dT_pures : list[float]
First temperature derivative of third `C` virial coefficients,
[m^6/(mol^2*K)]
'''
if not self.pure_C_calculated:
self._set_C_and_der_pure()
return self.dC_dTs_pure
[docs] def d2C_dT2_pures(self):
r'''Method to calculate and return the second temperature derivative of
pure component third virial coefficients at the specified temperature.
Returns
-------
d2C_dT2_pures : list[float]
Second temperature derivative of third `C` virial coefficients,
[m^6/(mol^2*K^2)]
'''
if not self.pure_C_calculated:
self._set_C_and_der_pure()
return self.d2C_dT2s_pure
[docs] def d3C_dT3_pures(self):
r'''Method to calculate and return the third temperature derivative of
pure component third virial coefficients at the specified temperature.
Returns
-------
d3C_dT3_pures : list[float]
Third temperature derivative of third `C` virial coefficients,
[m^6/(mol^2*K^3)]
'''
if not self.pure_C_calculated:
self._set_C_and_der_pure()
return self.d3C_dT3s_pure
[docs] def C_interactions(self):
r'''Method to calculate and return the matrix of interaction third
virial coefficients at the specified temperature.
Returns
-------
C_interactions : list[list[float]]
Interaction third `C` virial coefficients, [m^6/mol^2]
'''
if not self.cross_C_calculated:
self._set_C_and_der_interactions()
return self.Cs_interactions
[docs] def dC_dT_interactions(self):
r'''Method to calculate and return the matrix of first temperature
derivatives of interaction third virial coefficients at the specified
temperature.
Returns
-------
dC_dT_interactions : list[list[float]]
Interaction first temperature derivatives of third `C` virial
coefficients, [m^6/(mol^2*K)]
'''
if not self.cross_C_calculated:
self._set_C_and_der_interactions()
return self.dC_dTs_interactions
[docs] def d2C_dT2_interactions(self):
r'''Method to calculate and return the matrix of second temperature
derivatives of interaction third virial coefficients at the specified
temperature.
Returns
-------
d2C_dT2_interactions : list[list[float]]
Interaction second temperature derivatives of third `C` virial
coefficients, [m^6/(mol^2*K^2)]
'''
if not self.cross_C_calculated:
self._set_C_and_der_interactions()
return self.d2C_dT2s_interactions
[docs] def d3C_dT3_interactions(self):
r'''Method to calculate and return the matrix of third temperature
derivatives of interaction third virial coefficients at the specified
temperature.
Returns
-------
d3C_dT3_interactions : list[list[float]]
Interaction third temperature derivatives of third `C` virial
coefficients, [m^6/(mol^2*K^2)]
'''
if not self.cross_C_calculated:
self._set_C_and_der_interactions()
return self.d3C_dT3s_interactions
[docs]class VirialGas(IdealGasDeparturePhase):
r'''Class for representing a real gas defined by the virial equation of
state (density form), as a phase object. The equation includes the `B`
and `C` coefficients but not further coefficients as they cannot be
accurately estimated. Only limited experimental data for third virial
coefficients is available.
This model is generic, and allows any source of virial coefficients to be
plugged it, so long as it provides the right methods. See :obj:`VirialCSP`.
.. math::
Z = \frac{PV}{RT} = 1 + \frac{B}{V} + \frac{C}{V^2}
Parameters
----------
model : object
Object which provides pure component and interaction second and third
virial coefficients; :obj:`VirialCSP`, [-]
HeatCapacityGases : list[HeatCapacityGas]
Objects proiding pure-component heat capacity correlations, [-]
Hfs : list[float]
Molar ideal-gas standard heats of formation at 298.15 K and 1 atm,
[J/mol]
Gfs : list[float]
Molar ideal-gas standard Gibbs energies of formation at 298.15 K and
1 atm, [J/mol]
T : float, optional
Temperature, [K]
P : float, optional
Pressure, [Pa]
zs : list[float], optional
Mole fractions of each component, [-]
cross_B_model : str, optional
The method used to combine the pure and/or interaction second `B` virial
coefficients into a single `B` coefficient.
* 'linear': :math:`B = \sum_i y_i B_i`
* 'theory': :math:` B = \sum_i \sum_j y_i y_j B(T)`
cross_C_model : str, optional
The method used to combine the pure and/or interaction third `C` virial
coefficients into a single `C` coefficient.
* 'linear': :math:`C = \sum_i y_i C_i`; this is considerably faster
* 'Orentlicher-Prausnitz': :math:`C = \sum_i \sum_j \sum_k y_i y_j y_k C_{ijk}(T)`
where :math:`C_{ijk} = \left(C_{ij}C_{jk}C_{ik}\right)^{1/3}`
Examples
--------
T-P initialization for nitrogen, oxygen, and argon, using Poling's polynomial heat
capacities:
>>> Tcs=[126.2, 154.58, 150.8]
>>> Pcs=[3394387.5, 5042945.25, 4873732.5]
>>> Vcs=[8.95e-05, 7.34e-05, 7.49e-05]
>>> omegas=[0.04, 0.021, -0.004]
>>> model = VirialCSP(Tcs=Tcs, Pcs=Pcs, Vcs=Vcs, omegas=omegas, B_model='VIRIAL_B_PITZER_CURL', cross_B_model='Tarakad-Danner', C_model='VIRIAL_C_ORBEY_VERA')
>>> HeatCapacityGases = [HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*1.79e-12, R*-6e-09, R*6.58e-06, R*-0.001794, R*3.63])),
... HeatCapacityGas(poly_fit=(50.0, 1000.0, [R*-9.9e-13, R*1.57e-09, R*7e-08, R*-0.000261, R*3.539])),
... HeatCapacityGas(poly_fit=(50.0, 1000.0, [0,0,0,0, R*2.5]))]
>>> phase = VirialGas(model=model, T=300, P=1e5, zs=[.78, .21, .01], HeatCapacityGases=HeatCapacityGases, cross_B_model='theory', cross_C_model='Orentlicher-Prausnitz')
>>> phase.V(), phase.isothermal_compressibility(), phase.speed_of_sound()
(0.02493687, 1.00025907e-05, 59.081947)
>>> phase
VirialGas(model=VirialCSP(Tcs=[126.2, 154.58, 150.8], Pcs=[3394387.5, 5042945.25, 4873732.5], Vcs=[8.95e-05, 7.34e-05, 7.49e-05], omegas=[0.04, 0.021, -0.004], B_model='VIRIAL_B_PITZER_CURL', cross_B_model='Tarakad-Danner', C_model='VIRIAL_C_ORBEY_VERA', T=300), HeatCapacityGases=[HeatCapacityGas(extrapolation="linear", method="POLY_FIT", poly_fit=(50.0, 1000.0, [1.48828880864943e-11, -4.9886775708919434e-08, 5.4709164027448316e-05, -0.014916145936966912, 30.18149930389626])), HeatCapacityGas(extrapolation="linear", method="POLY_FIT", poly_fit=(50.0, 1000.0, [-8.231317991971707e-12, 1.3053706310500586e-08, 5.820123832707268e-07, -0.0021700747433379955, 29.424883205644317])), HeatCapacityGas(extrapolation="linear", method="POLY_FIT", poly_fit=(50.0, 1000.0, [0, 0, 0, 0, 20.7861565453831]))], cross_B_model='theory', cross_C_model='Orentlicher-Prausnitz', T=300, P=100000.0, zs=[0.78, 0.21, 0.01])
'''
phase = 'g'
force_phase = 'g'
is_gas = True
is_liquid = False
ideal_gas_basis = True
pure_references = ('HeatCapacityGases',)
pure_reference_types = (HeatCapacityGas, )
model_attributes = ('Hfs', 'Gfs', 'Sfs', 'model',
'cross_B_model', 'cross_C_model') + pure_references
def __init__(self, model, HeatCapacityGases=None, Hfs=None, Gfs=None,
T=None, P=None, zs=None,
cross_B_model='theory', cross_C_model='Orentlicher-Prausnitz'):
self.model = model.to(T=T)
self.HeatCapacityGases = HeatCapacityGases
self.Hfs = Hfs
self.Gfs = Gfs
if cross_B_model not in ('theory', 'linear'):
raise ValueError("Unsupported value for `cross_B_model`")
if cross_C_model not in ('Orentlicher-Prausnitz', 'linear'):
raise ValueError("Unsupported value for `cross_C_model`")
self.cross_B_model = cross_B_model
self.cross_C_model = cross_C_model
# Store the virial cross model as a boolean
# It is likely additional `C` models will be published, the current one is emperical
self.cross_B_coefficients = cross_B_model == 'theory'
self.cross_C_coefficients = cross_C_model == 'Orentlicher-Prausnitz'
if Hfs is not None and Gfs is not None and None not in Hfs and None not in Gfs:
self.Sfs = [(Hfi - Gfi)/298.15 for Hfi, Gfi in zip(Hfs, Gfs)]
else:
self.Sfs = None
for i in (zs, HeatCapacityGases, Hfs, Gfs):
if i is not None:
self.N = len(i)
break
if zs is not None:
self.zs = zs
self.scalar = scalar = type(zs) is list
if T is not None:
self.T = T
self.model.T = T
if P is not None:
self.P = P
if T is not None and P is not None and zs is not None:
Z = Z_from_virial_density_form(T, P, self.B(), self.C())
self._V = Z*self.R*T/P
[docs] def __repr__(self):
r'''Method to create a string representation of the phase object, with
the goal of making it easy to obtain standalone code which reproduces
the current state of the phase. This is extremely helpful in creating
new test cases.
Returns
-------
recreation : str
String which is valid Python and recreates the current state of
the object if ran, [-]
'''
try:
Cpgs = ', '.join(str(o) for o in self.HeatCapacityGases)
except:
Cpgs = ''
base = f'{self.__class__.__name__}(model={self.model}, HeatCapacityGases=[{Cpgs}], '
for s in ('cross_B_model', 'cross_C_model', 'Hfs', 'Gfs', 'T', 'P', 'zs'):
if hasattr(self, s) and getattr(self, s) is not None:
val = getattr(self, s)
if type(val) is str:
val = f"'{val}'"
base += f'{s}={val}, '
if base[-2:] == ', ':
base = base[:-2]
base += ')'
return base
[docs] def V(self):
r'''Method to calculate and return the molar volume.
Returns
-------
V : float
Molar volume [m^3/mol]
'''
return self._V
[docs] def dV_dzs(self):
r'''Method to calculate and return the first mole fraction derivatives
of the molar volume. See :obj:`chemicals.virial.dV_dzs_virial` for
further details.
Returns
-------
dV_dzs : list[float]
First mole fraction derivatives of molar volume
[m^3/mol]
'''
try:
return self._dV_dzs
except:
pass
dB_dzs = self.dB_dzs()
dC_dzs = self.dC_dzs()
B = self.B()
C = self.C()
V = self._V
N = self.N
if self.scalar:
dV_dzs = [0.0]*N
else:
dV_dzs = zeros(N)
self._dV_dzs = dV_dzs_virial(B=B, C=C, V=V, dB_dzs=dB_dzs, dC_dzs=dC_dzs, dV_dzs=dV_dzs)
return dV_dzs
[docs] def d2V_dzizjs(self):
r'''Method to calculate and return the second mole fraction derivatives
of the molar volume. See :obj:`chemicals.virial.d2V_dzizjs_virial` for
further details.
Returns
-------
d2V_dzizjs : list[float]
Second mole fraction derivatives of molar volume
[m^3/mol]
'''
try:
return self._d2V_dzizjs
except:
pass
dB_dzs = self.dB_dzs()
dC_dzs = self.dC_dzs()
d2B_dzizjs = self.d2B_dzizjs()
d2C_dzizjs = self.d2C_dzizjs()
B = self.B()
C = self.C()
V = self._V
dV_dzs = self.dV_dzs()
N = self.N
if self.scalar:
d2V_dzizjs = [[0.0]*N for _ in range(N)]
else:
d2V_dzizjs = zeros((N,N))
self._d2V_dzizjs = d2V_dzizjs_virial(B=B, C=C, V=V, dB_dzs=dB_dzs, dC_dzs=dC_dzs, dV_dzs=dV_dzs,
d2B_dzizjs=d2B_dzizjs, d2C_dzizjs=d2C_dzizjs, d2V_dzizjs=d2V_dzizjs)
return d2V_dzizjs
[docs] def dG_dep_dzs(self):
r'''Method to calculate and return the first mole fraction derivatives
of the departure Gibbs energy.
Returns
-------
dG_dep_dzs : list[float]
First mole fraction derivatives of departure Gibbs energy
[J/mol]
'''
try:
return self._dG_dep_dzs
except:
pass
T = self.T
dB_dzs = self.dB_dzs()
dB_dT = self.dB_dT()
dC_dT = self.dC_dT()
dC_dzs = self.dC_dzs()
dV_dzs = self.dV_dzs()
d2C_dTdzs = self.d2C_dTdzs()
d2B_dTdzs = self.d2B_dTdzs()
B = self.B()
C = self.C()
V = self._V
N = self.N
if self.scalar:
dG_dep_dzs = [0.0]*N
else:
dG_dep_dzs = zeros(N)
for i in range(N):
x0 = V
x1 = x0*x0
x2 = 1.0/x1
x4 = dC_dzs[i]#Derivative(x3, z1)
x6 = 2.0*T
x7 = dV_dzs[i]#Derivative(x0, z1)
x8 = 2.0*x7
x9 = T*dB_dT#Derivative(x5, T)
x10 = x0*B + x1 + C
x11 = log(x10*x2)
x12 = x0*x8
x13 = 1.0/x0
dG_dep_dzs[i] = (R*T*x2*(T*d2C_dTdzs[i] + x0*x6*d2B_dTdzs[i]+ x1*(-x0*dB_dzs[i]
+ 2.0*x10*x13*x7 - x12 - x4 - B*x7)/x10 - x11*x12 - x13*x7*(4.0*x0*x9 - 2.0*x1*x11 - C + x6*dC_dT)
- x4*0.5 + x8*x9))
# self._dG_dep_dzs = dG_dep_dzs_virial(B=B, C=C, V=V, dB_dzs=dB_dzs, dC_dzs=dC_dzs, dG_dep_dzs=dG_dep_dzs)
return dG_dep_dzs
def dG_dep_dns(self):
try:
return self._dG_dep_dns
except:
pass
N = self.N
if self.scalar:
dG_dep_dns = [0.0]*N
else:
dG_dep_dns = zeros(N)
self._dG_dep_dns = dG_dep_dns = dxs_to_dns(self.dG_dep_dzs(), self.zs, dG_dep_dns)
return dG_dep_dns
def dnG_dep_dns(self):
try:
return self._dnG_dep_dns
except:
pass
N = self.N
if self.scalar:
dnG_dep_dns = [0.0]*N
else:
dnG_dep_dns = zeros(N)
self._dnG_dep_dns = dnG_dep_dns = dxs_to_dn_partials(self.dG_dep_dzs(), self.zs, self.G_dep(), dnG_dep_dns)
return dnG_dep_dns
def lnphi(self):
return self.G_dep()/(R*self.T)
[docs] def lnphis(self):
r'''Method to calculate and return the log fugacity coefficients of
the phase.
Returns
-------
lnphis : list[float]
Log fugacity coefficients, [-]
'''
# working!
zs = self.zs
T = self.T
RT_inv = 1.0/(R*T)
lnphi = self.G_dep()*RT_inv
dG_dep_dns = self.dG_dep_dns()
if self.scalar:
dG_dep_dns_RT = [v*RT_inv for v in dG_dep_dns]
else:
dG_dep_dns_RT = RT_inv*dG_dep_dns
out = [0.0]*self.N if self.scalar else zeros(self.N)
log_phis = dns_to_dn_partials(dG_dep_dns_RT, lnphi, out)
return log_phis
[docs] def dP_dT(self):
r'''Method to calculate and return the first derivative of pressure
with respect to temperature.
.. math::
\left(\frac{\partial P}{\partial T}\right)_{V} = \frac{R \left(T
\left(V \frac{d}{d T} B{\left(T \right)} + \frac{d}{d T} C{\left(T
\right)}\right) + V^{2} + V B{\left(T \right)} + C{\left(T \right)}
\right)}{V^{3}}
Returns
-------
dP_dT : float
First derivative of pressure with respect to temperature at constant
volume [Pa/K]
'''
try:
return self._dP_dT
except:
pass
T, V = self.T, self._V
self._dP_dT = dP_dT = self.R*(T*(V*self.dB_dT() + self.dC_dT()) + V*(V + self.B()) + self.C())/(V*V*V)
return dP_dT
[docs] def dP_dV(self):
r'''Method to calculate and return the first derivative of pressure
with respect to volume.
.. math::
\left(\frac{\partial P}{\partial V}\right)_{T} =
- \frac{R T \left(V^{2} + 2 V B{\left(T \right)} + 3 C{\left(T
\right)}\right)}{V^{4}}
Returns
-------
dP_dV : float
First derivative of pressure with respect to volume at constant
temperature [Pa*mol/(m^3)]
'''
try:
return self._dP_dV
except:
pass
T, V = self.T, self._V
self._dP_dV = dP_dV = -self.R*T*(V*V + 2.0*V*self.B() + 3.0*self.C())/(V*V*V*V)
return dP_dV
[docs] def d2P_dTdV(self):
r'''Method to calculate and return the second derivative of pressure
with respect to volume and temperature.
.. math::
\left(\frac{\partial^2 P}{\partial V\partial T}\right)_{T} =
- \frac{R \left(2 T V \frac{d}{d T} B{\left(T \right)} + 3 T
\frac{d}{d T} C{\left(T \right)} + V^{2} + 2 V B{\left(T \right)}
+ 3 C{\left(T \right)}\right)}{V^{4}}
Returns
-------
d2P_dTdV : float
Second derivative of pressure with respect to volume at and
temperature [Pa*mol/(m^3*K)]
'''
try:
return self._d2P_dTdV
except:
pass
T, V = self.T, self._V
V2 = V*V
self._d2P_dTdV = d2P_dTdV = -self.R*(2.0*T*V*self.dB_dT() + 3.0*T*self.dC_dT()
+ V2 + 2.0*V*self.B() + 3.0*self.C())/(V2*V2)
return d2P_dTdV
[docs] def d2P_dV2(self):
r'''Method to calculate and return the second derivative of pressure
with respect to volume.
.. math::
\left(\frac{\partial^2 P}{\partial V^2}\right)_{T} =
\frac{2 R T \left(V^{2} + 3 V B{\left(T \right)}
+ 6 C{\left(T \right)}\right)}{V^{5}}
Returns
-------
d2P_dV2 : float
Second derivative of pressure with respect to volume at constant
temperature [Pa*mol^2/(m^6)]
'''
try:
return self._d2P_dV2
except:
pass
T, V = self.T, self._V
V2 = V*V
self._d2P_dV2 = d2P_dV2 = 2.0*self.R*T*(V2 + 3.0*V*self.B() + 6.0*self.C())/(V2*V2*V)
return d2P_dV2
[docs] def d2P_dT2(self):
r'''Method to calculate and return the second derivative of pressure
with respect to temperature.
.. math::
\left(\frac{\partial^2 P}{\partial T^2}\right)_{V} =
\frac{R \left(T \left(V \frac{d^{2}}{d T^{2}} B{\left(T \right)}
+ \frac{d^{2}}{d T^{2}} C{\left(T \right)}\right) + 2 V \frac{d}{d T}
B{\left(T \right)} + 2 \frac{d}{d T} C{\left(T \right)}\right)}{V^{3}}
Returns
-------
d2P_dT2 : float
Second derivative of pressure with respect to temperature at constant
volume [Pa/K^2]
'''
try:
return self._d2P_dT2
except:
pass
T, V = self.T, self._V
V2 = V*V
self._d2P_dT2 = d2P_dT2 = self.R*(T*(V*self.d2B_dT2() + self.d2C_dT2())
+ 2.0*V*self.dB_dT() + 2.0*self.dC_dT())/(V*V*V)
return d2P_dT2
[docs] def H_dep(self):
r'''Method to calculate and return the molar departure enthalpy.
.. math::
H_{dep} = \frac{R T^{2} \left(2 V \frac{d}{d T} B{\left(T \right)}
+ \frac{d}{d T} C{\left(T \right)}\right)}{2 V^{2}} - R T \left(-1
+ \frac{V^{2} + V B{\left(T \right)} + C{\left(T \right)}}{V^{2}}
\right)
Returns
-------
H_dep : float
Departure enthalpy [J/mol]
Notes
-----
'''
"""
from sympy import *
Z, R, T, V, P = symbols('Z, R, T, V, P')
B, C = symbols('B, C', cls=Function)
base =Eq(P*V/(R*T), 1 + B(T)/V + C(T)/V**2)
P_sln = solve(base, P)[0]
Z = P_sln*V/(R*T)
# Two ways to compute H_dep
Hdep2 = R*T - P_sln*V + integrate(P_sln - T*diff(P_sln, T), (V, oo, V))
Hdep = -R*T*(Z-1) -integrate(diff(Z, T)/V, (V, oo, V))*R*T**2
"""
try:
return self._H_dep
except:
pass
T, V = self.T, self._V
V2 = V*V
RT = self.R*T
self._H_dep = H_dep = RT*(T*(2.0*V*self.dB_dT() + self.dC_dT())/(2.0*V2)
- (-1.0 + (V2 + V*self.B() + self.C())/V2))
return H_dep
[docs] def dH_dep_dT(self):
r'''Method to calculate and return the first temperature derivative of
molar departure enthalpy.
.. math::
\frac{\partial H_{dep}}{\partial T} = \frac{R \left(2 T^{2} V
\frac{d^{2}}{d T^{2}} B{\left(T \right)} + T^{2} \frac{d^{2}}{d T^{2}}
C{\left(T \right)} + 2 T V \frac{d}{d T} B{\left(T \right)}
- 2 V B{\left(T \right)} - 2 C{\left(T \right)}\right)}{2 V^{2}}
Returns
-------
dH_dep_dT : float
First temperature derivative of departure enthalpy [J/(mol*K)]
'''
try:
return self._dH_dep_dT
except:
pass
T, V = self.T, self._V
B = self.B()
C = self.C()
dB_dT = self.dB_dT()
d2B_dT2 = self.d2B_dT2()
d2C_dT2 = self.d2C_dT2()
self._dH_dep_dT = dH_dep_dT = (self.R*(2.0*T*T*V*d2B_dT2 + T*T*d2C_dT2
+ 2.0*T*V*dB_dT - 2.0*V*B - 2.0*C)/(2.0*V*V))
return dH_dep_dT
Cp_dep = dH_dep_dT
def dH_dep_dP_V(self):
r'''Method to calculate and return the first pressure derivative of
molar departure enthalpy at constant volume.
.. math::
\left(\frac{\partial H_{dep}}{\partial P}\right)_{V} =
- R \left(-1 + \frac{V^{2} + V B{\left(P \right)} + C{\left(P \right)}}
{V^{2}}\right) \frac{d}{d P} T{\left(P \right)} - \frac{R \left(- 2 V
\operatorname{dB_{dT}}{\left(P \right)} - \operatorname{dC_{dT}}
{\left(P \right)}\right) T{\left(P \right)} \frac{d}{d P} T{\left(P
\right)}}{V^{2}} - \frac{R \left(V \frac{d}{d P} B{\left(P \right)}
+ \frac{d}{d P} C{\left(P \right)}\right) T{\left(P \right)}}{V^{2}}
- \frac{R \left(- 2 V \frac{d}{d P} \operatorname{dB_{dT}}
{\left(P \right)} - \frac{d}{d P} \operatorname{dC_{dT}}{\left(P
\right)}\right) T^{2}{\left(P \right)}}{2 V^{2}}
Returns
-------
dH_dep_dP_V : float
First pressure derivative of departure enthalpy at constant volume
[J/(mol*Pa)]
'''
"""
from sympy import *
R, V, P = symbols('R, V, P')
dB_dT, dC_dT, T, B, C = symbols('dB_dT, dC_dT, T, B, C', cls=Function)
H_dep_const_V = -R*T(P)**2*(-2*V*dB_dT(P)- dC_dT(P))/(2*V**2) - R*T(P)*(-1 + (V**2 + V*B(P) + C(P))/V**2)
print(diff(H_dep_const_V, P))
"""
T, V = self.T, self._V
B = self.B()
C = self.C()
dB_dT = self.dB_dT()
dC_dT = self.dC_dT()
dB_dP_V = self.dB_dP_V()
dC_dP_V=self.dC_dP_V()
d2B_dTdP_V=self.d2B_dTdP_V()
d2C_dTdP_V=self.d2C_dTdP_V()
dT_dP_V = self.dT_dP_V()
V2 = V*V
dH_dep_dP_V = (-R*(-1.0 + (V2 + V*B + C)/V2)*dT_dP_V - R*(-2.0*V*dB_dT - dC_dT)*T*dT_dP_V/V2
- R*(V*dB_dP_V + dC_dP_V)*T/V2
- R*(-2.0*V*d2B_dTdP_V - d2C_dTdP_V)*T*T/(2.0*V2))
return dH_dep_dP_V
def dS_dep_dP_V(self):
r'''Method to calculate and return the first pressure derivative of
molar departure entropy at constant volume.
.. math::
\left(\frac{\partial S_{dep}}{\partial P}\right)_{V} =
\frac{R \left(V \frac{d}{d P} B{\left(P \right)} + \frac{d}{d P}
C{\left(P \right)}\right)}{V^{2} + V B{\left(P \right)} + C{\left(P \right)}}
+ \frac{- R T{\left(P \right)} \frac{d}{d P} \operatorname{dC_{dT}}
{\left(P \right)} - R \operatorname{dC_{dT}}{\left(P \right)}
\frac{d}{d P} T{\left(P \right)} - R \frac{d}{d P} C{\left(P \right)}
+ V \left(- 2 R T{\left(P \right)} \frac{d}{d P} \operatorname{dB_{dT}}
{\left(P \right)} - 2 R \operatorname{dB_{dT}}{\left(P \right)}
\frac{d}{d P} T{\left(P \right)} - 2 R \frac{d}{d P}
B{\left(P \right)}\right)}{2 V^{2}}
Returns
-------
dS_dep_dP_V : float
First pressure derivative of departure entropy at constant volume
[J/(mol*Pa*K)]
'''
T, V = self.T, self._V
B = self.B()
C = self.C()
dB_dT = self.dB_dT()
dC_dT = self.dC_dT()
dB_dP_V = self.dB_dP_V()
dC_dP_V=self.dC_dP_V()
d2B_dTdP_V=self.d2B_dTdP_V()
d2C_dTdP_V=self.d2C_dTdP_V()
dT_dP_V = self.dT_dP_V()
dS_dep_dP_V = (R*(V*dB_dP_V + dC_dP_V)/(V**2 + V*B
+ C) + (-R*T*d2C_dTdP_V - R*dC_dT*dT_dP_V
- R*dC_dP_V + V*(-2*R*T*d2B_dTdP_V - 2*R*dB_dT*dT_dP_V
- 2*R*dB_dP_V))/(2*V**2))
return dS_dep_dP_V
def dH_dep_dP_T(self):
r'''Method to calculate and return the first pressure derivative of
molar departure enthalpy at constant temperature.
.. math::
\left(\frac{\partial H_{dep}}{\partial P}\right)_{T} =
\frac{R T^{2} dB_{dT} \frac{d}{d P} V{\left(P \right)}}{V^{2}{\left(P
\right)}} + \frac{R T^{2} \left(- 2 dB_{dT} V{\left(P \right)}
- dC_{dT}\right) \frac{d}{d P} V{\left(P \right)}}{V^{3}{\left(P
\right)}} - R T \left(\frac{B \frac{d}{d P} V{\left(P \right)}
+ 2 V{\left(P \right)} \frac{d}{d P} V{\left(P \right)}}{V^{2}
{\left(P \right)}} - \frac{2 \left(B V{\left(P \right)} + C + V^{2}
{\left(P \right)}\right) \frac{d}{d P} V{\left(P \right)}}
{V^{3}{\left(P \right)}}\right)
Returns
-------
dH_dep_dP_T : float
First pressure derivative of departure enthalpy at constant
temperature [J/(mol*Pa)]
'''
"""
from sympy import *
R, P, T, B, C, dB_dT, dC_dT = symbols('R, P, T, B, C, dB_dT, dC_dT')
V = symbols('V', cls=Function)
H_dep_const_T = -R*T**2*(-2*V(P)*dB_dT - dC_dT)/(2*V(P)**2) - R*T*(-1 + (V(P)**2 + V(P)*B + C)/V(P)**2)
print(diff(H_dep_const_T, P))
"""
T, V = self.T, self._V
B = self.B()
C = self.C()
dB_dT = self.dB_dT()
dC_dT = self.dC_dT()
dV_dP = self.dV_dP()
dH_dep_dP_T =(R*T**2*dB_dT*dV_dP/V**2 + R*T**2*(-2*dB_dT*V - dC_dT)*dV_dP/V**3 - R*T*((B*dV_dP + 2*V*dV_dP)/V**2 - 2*(B*V + C + V**2)*dV_dP/V**3))
return dH_dep_dP_T
def dS_dep_dP_T(self):
r'''Method to calculate and return the first pressure derivative of
molar departure entropy at constant temperature.
.. math::
\left(\frac{\partial S_{dep}}{\partial P}\right)_{T} =
\frac{R \left(\frac{B \frac{d}{d P} V{\left(P \right)}
+ 2 V{\left(P \right)} \frac{d}{d P} V{\left(P \right)}}{V^{2}
{\left(P \right)}} - \frac{2 \left(B V{\left(P \right)} + C
+ V^{2}{\left(P \right)}\right) \frac{d}{d P} V{\left(P \right)}}
{V^{3}{\left(P \right)}}\right) V^{2}{\left(P \right)}}{B
V{\left(P \right)} + C + V^{2}{\left(P \right)}} + \frac{\left(
- 2 B R - 2 R T dB_{dT}\right) \frac{d}{d P} V{\left(P \right)}}
{2 V^{2}{\left(P \right)}} - \frac{\left(- C R - R T dC_{dT}
+ \left(- 2 B R - 2 R T dB_{dT}\right) V{\left(P \right)}\right)
\frac{d}{d P} V{\left(P \right)}}{V^{3}{\left(P \right)}}
Returns
-------
dS_dep_dP_T : float
First pressure derivative of departure entropy at constant
temperature [J/(mol*Pa*K)]
'''
"""
from sympy import *
R, P, T, B, C, dB_dT, dC_dT = symbols('R, P, T, B, C, dB_dT, dC_dT')
V = symbols('V', cls=Function)
S_dep_to_diff = R*log((V(P)**2 + V(P)*B + C)/V(P)**2) + (-R*T*dC_dT - R*C + V(P)*(-2*R*T*dB_dT - 2*R*B))/(2*V(P)**2)
print((diff(S_dep_to_diff, P)))
"""
T, V = self.T, self._V
B = self.B()
C = self.C()
dB_dT = self.dB_dT()
dC_dT = self.dC_dT()
dV_dP = self.dV_dP()
dS_dep_dP_T =(R*((B*dV_dP + 2*V*dV_dP)/V**2 - 2*(B*V + C + V**2)*dV_dP/V**3)*V**2/(B*V + C + V**2)
+ (-2*B*R - 2*R*T*dB_dT)*dV_dP/(2*V**2) - (-C*R - R*T*dC_dT + (-2*B*R - 2*R*T*dB_dT)*V)*dV_dP/V**3)
return dS_dep_dP_T
def dH_dep_dV_T(self):
r'''Method to calculate and return the first volume derivative of
molar departure enthalpy at constant temperature.
.. math::
\left(\frac{\partial H_{dep}}{\partial V}\right)_{T} =
\frac{R T^{2} dB_{dT}}{V^{2}} + \frac{R T^{2} \left(- 2 V dB_{dT}
- dC_{dT}\right)}{V^{3}} - R T \left(\frac{B + 2 V}{V^{2}}
- \frac{2 \left(B V + C + V^{2}\right)}{V^{3}}\right)
Returns
-------
dH_dep_dV_T : float
First volume derivative of departure enthalpy at constant
temperature [J/(m^3)]
'''
"""
from sympy import *
R, V, T, B, C, dB_dT, dC_dT = symbols('R, V, T, B, C, dB_dT, dC_dT')
P = symbols('P', cls=Function)
H_dep_const_T = -R*T**2*(-2*V*dB_dT - dC_dT)/(2*V**2) - R*T*(-1 + (V**2 + V*B + C)/V**2)
print(diff(H_dep_const_T, V))
"""
T, V = self.T, self._V
B = self.B()
C = self.C()
dB_dT = self.dB_dT()
dC_dT = self.dC_dT()
return (R*T**2*dB_dT/V**2 + R*T**2*(-2*V*dB_dT - dC_dT)/V**3 - R*T*((B + 2*V)/V**2 - 2*(B*V + C + V**2)/V**3))
def dS_dep_dV_T(self):
r'''Method to calculate and return the first volume derivative of
molar departure entropy at constant temperature.
.. math::
\left(\frac{\partial S_{dep}}{\partial V}\right)_{T} =
\frac{R V^{2} \left(\frac{B + 2 V}{V^{2}} - \frac{2 \left(B V + C
+ V^{2}\right)}{V^{3}}\right)}{B V + C + V^{2}} + \frac{- 2 B R
- 2 R T dB_{dT}}{2 V^{2}} - \frac{- C R - R T dC_{dT} + V \left(
- 2 B R - 2 R T dB_{dT}\right)}{V^{3}}
Returns
-------
dS_dep_dV_T : float
First volume derivative of departure entropy at constant
temperature [J/(m^3*K)]
'''
"""
from sympy import *
R, V, T, B, C, dB_dT, dC_dT = symbols('R, V, T, B, C, dB_dT, dC_dT')
P = symbols('P', cls=Function)
S_dep_const_T = R*log((V**2 + V*B + C)/V**2) + (-R*T*dC_dT - R*C + V*(-2*R*T*dB_dT - 2*R*B))/(2*V**2)
print(latex(diff(S_dep_const_T, V)))
"""
T, V = self.T, self._V
B = self.B()
C = self.C()
dB_dT = self.dB_dT()
dC_dT = self.dC_dT()
return (R*V**2*((B + 2*V)/V**2 - 2*(B*V + C + V**2)/V**3)/(B*V + C + V**2)
+ (-2*B*R - 2*R*T*dB_dT)/(2*V**2) - (-C*R - R*T*dC_dT + V*(-2*B*R - 2*R*T*dB_dT))/V**3)
def dH_dep_dV_P(self):
r'''Method to calculate and return the first volume derivative of
molar departure enthalpy at constant pressure.
.. math::
\left(\frac{\partial H_{dep}}{\partial V}\right)_{P} =
- R \left(-1 + \frac{V^{2} + V B{\left(V \right)} + C{\left(V \right)}}
{V^{2}}\right) \frac{d}{d V} T{\left(V \right)} - R \left(\frac{V
\frac{d}{d V} B{\left(V \right)} + 2 V + B{\left(V \right)}
+ \frac{d}{d V} C{\left(V \right)}}{V^{2}} - \frac{2 \left(V^{2}
+ V B{\left(V \right)} + C{\left(V \right)}\right)}{V^{3}}\right)
T{\left(V \right)} - \frac{R \left(- 2 V \operatorname{dB_{dT}}
{\left(V \right)} - \operatorname{dC_{dT}}{\left(V \right)}\right)
T{\left(V \right)} \frac{d}{d V} T{\left(V \right)}}{V^{2}}
- \frac{R \left(- 2 V \frac{d}{d V} \operatorname{dB_{dT}}{\left(V
\right)} - 2 \operatorname{dB_{dT}}{\left(V \right)}
- \frac{d}{d V} \operatorname{dC_{dT}}{\left(V \right)}\right)
T^{2}{\left(V \right)}}{2 V^{2}} + \frac{R \left(- 2 V
\operatorname{dB_{dT}}{\left(V \right)} - \operatorname{dC_{dT}}
{\left(V \right)}\right) T^{2}{\left(V \right)}}{V^{3}}
Returns
-------
dH_dep_dV_P : float
First volume derivative of departure enthalpy at constant
pressure [J/(m^3)]
'''
"""
from sympy import *
R, V, P = symbols('R, V, P')
dB_dT, dC_dT, T, B, C = symbols('dB_dT, dC_dT, T, B, C', cls=Function)
H_dep_const_P = -R*T(V)**2*(-2*V*dB_dT(V)- dC_dT(V))/(2*V**2) - R*T(V)*(-1 + (V**2 + V*B(V) + C(V))/V**2)
print((diff(H_dep_const_P, V)))
"""
T, V = self.T, self._V
B = self.B()
C = self.C()
dT_dV = self.dT_dV()
dB_dT = self.dB_dT()
dC_dT = self.dC_dT()
dB_dV_P = self.dB_dV_P()
dC_dV_P = self.dC_dV_P()
d2B_dTdV_P = self.d2B_dTdV_P()
d2C_dTdV_P = self.d2C_dTdV_P()
return (-R*(-1 + (V**2 + V*B + C)/V**2)*dT_dV - R*((V*dB_dV_P + 2*V + B + dC_dV_P)/V**2
- 2*(V**2 + V*B + C)/V**3)*T - R*(-2*V*dB_dT - dC_dT)*T*dT_dV/V**2
- R*(-2*V*d2B_dTdV_P - 2*dB_dT - d2C_dTdV_P)*T**2/(2*V**2) + R*(-2*V*dB_dT - dC_dT)*T**2/V**3)
def dS_dep_dV_P(self):
r'''Method to calculate and return the first volume derivative of
molar departure entropy at constant pressure.
.. math::
\left(\frac{\partial S_{dep}}{\partial V}\right)_{P} =
\frac{R V^{2} \left(\frac{V \frac{d}{d V} B{\left(V \right)}
+ 2 V + B{\left(V \right)} + \frac{d}{d V} C{\left(V \right)}}{V^{2}}
- \frac{2 \left(V^{2} + V B{\left(V \right)} + C{\left(V \right)}
\right)}{V^{3}}\right)}{V^{2} + V B{\left(V \right)} + C{\left(V
\right)}} + \frac{- 2 R B{\left(V \right)} - 2 R T{\left(V \right)}
\operatorname{dB_{dT}}{\left(V \right)} - R T{\left(V \right)}
\frac{d}{d V} \operatorname{dC_{dT}}{\left(V \right)}
- R \operatorname{dC_{dT}}{\left(V \right)} \frac{d}{d V} T{\left(V
\right)} - R \frac{d}{d V} C{\left(V \right)} + V \left(- 2 R T
{\left(V \right)} \frac{d}{d V} \operatorname{dB_{dT}}{\left(V
\right)} - 2 R \operatorname{dB_{dT}}{\left(V \right)} \frac{d}
{d V} T{\left(V \right)} - 2 R \frac{d}{d V} B{\left(V \right)}
\right)}{2 V^{2}} - \frac{- R C{\left(V \right)} - R T{\left(V
\right)} \operatorname{dC_{dT}}{\left(V \right)} + V \left(- 2 R
B{\left(V \right)} - 2 R T{\left(V \right)} \operatorname{dB_{dT}}
{\left(V \right)}\right)}{V^{3}}
Returns
-------
dS_dep_dV_P : float
First volume derivative of departure entropy at constant
pressure [J/(m^3)]
'''
"""
from sympy import *
R, V, P = symbols('R, V, P')
dB_dT, dC_dT, T, B, C = symbols('dB_dT, dC_dT, T, B, C', cls=Function)
term = R*log((V**2 + V*B(V) + C(V))/V**2) + (-R*T(V)*dC_dT(V) - R*C(V) + V*(-2*R*T(V)*dB_dT(V) - 2*R*B(V)))/(2*V**2)
print((diff(term, V)))
"""
T, V = self.T, self._V
B = self.B()
C = self.C()
dT_dV = self.dT_dV()
dB_dT = self.dB_dT()
dC_dT = self.dC_dT()
dB_dV_P = self.dB_dV_P()
dC_dV_P = self.dC_dV_P()
d2B_dTdV_P = self.d2B_dTdV_P()
d2C_dTdV_P = self.d2C_dTdV_P()
return (R*V**2*((V*dB_dV_P + 2*V + B + dC_dV_P)/V**2 - 2*(V**2 + V*B + C)/V**3)/(V**2 + V*B + C) + (-2*R*B - 2*R*T*dB_dT - R*T*d2C_dTdV_P - R*dC_dT*dT_dV - R*dC_dV_P + V*(-2*R*T*d2B_dTdV_P - 2*R*dB_dT*dT_dV - 2*R*dB_dV_P))/(2*V**2) - (-R*C - R*T*dC_dT + V*(-2*R*B - 2*R*T*dB_dT))/V**3)
[docs] def S_dep(self):
r'''Method to calculate and return the molar departure entropy.
.. math::
S_{dep} = \frac{R \left(- T \frac{d}{d T} C{\left(T \right)} + 2 V^{2}
\ln{\left(\frac{V^{2} + V B{\left(T \right)} + C{\left(T \right)}}
{V^{2}} \right)} - 2 V \left(T \frac{d}{d T} B{\left(T \right)}
+ B{\left(T \right)}\right) - C{\left(T \right)}\right)}{2 V^{2}}
Returns
-------
S_dep : float
Departure enthalpy [J/(mol*K)]
Notes
-----
'''
"""
dP_dT = diff(P_sln, T)
S_dep = integrate(dP_dT - R/V, (V, oo, V)) + R*log(Z)
"""
try:
return self._S_dep
except:
pass
T, V = self.T, self._V
V2 = V*V
self._S_dep = S_dep = (self.R*(-T*self.dC_dT() + 2*V2*log((V2 + V*self.B() + self.C())/V**2)
- 2*V*(T*self.dB_dT() + self.B()) - self.C())/(2*V2))
return S_dep
[docs] def dS_dep_dT(self):
r'''Method to calculate and return the first temperature derivative of
molar departure entropy.
.. math::
\frac{\partial S_{dep}}{\partial T} = \frac{R \left(2 V^{2} \left(V
\frac{d}{d T} B{\left(T \right)} + \frac{d}{d T} C{\left(T \right)}
\right) - \left(V^{2} + V B{\left(T \right)} + C{\left(T \right)}
\right) \left(T \frac{d^{2}}{d T^{2}} C{\left(T \right)} + 2 V
\left(T \frac{d^{2}}{d T^{2}} B{\left(T \right)} + 2 \frac{d}{d T}
B{\left(T \right)}\right) + 2 \frac{d}{d T} C{\left(T \right)}
\right)\right)}{2 V^{2} \left(V^{2} + V B{\left(T \right)}
+ C{\left(T \right)}\right)}
Returns
-------
dS_dep_dT : float
First temperature derivative of departure enthalpy [J/(mol*K^2)]
'''
try:
return self._dS_dep_dT
except:
pass
T, V = self.T, self._V
V2 = V*V
self._dS_dep_dT = dS_dep_dT = (self.R*(2.0*V2*(V*self.dB_dT() + self.dC_dT()) - (V2 + V*self.B() + self.C())*(T*self.d2C_dT2()
+ 2.0*V*(T*self.d2B_dT2() + 2.0*self.dB_dT()) + 2.0*self.dC_dT()))/(2.0*V2*(V2 + V*self.B() + self.C())))
return dS_dep_dT
dS_dep_dT_P = dS_dep_dT
dS_dep_dT_V = dS_dep_dT
def to_TP_zs(self, T, P, zs):
new = self.__class__.__new__(self.__class__)
new.T = T
new.P = P
new.zs = zs
new.N = self.N
new.scalar = self.scalar
new.cross_B_coefficients = self.cross_B_coefficients
new.cross_C_coefficients = self.cross_C_coefficients
new.cross_B_model = self.cross_B_model
new.cross_C_model = self.cross_C_model
new.HeatCapacityGases = self.HeatCapacityGases
new.model = self.model.to(T)
new.Hfs = self.Hfs
new.Gfs = self.Gfs
new.Sfs = self.Sfs
Z = Z_from_virial_density_form(T, P, new.B(), new.C())
new._V = Z*self.R*T/P
return new
def to(self, zs, T=None, P=None, V=None):
new = self.__class__.__new__(self.__class__)
new.zs = zs
new.scalar = self.scalar
new.N = self.N
new.cross_B_coefficients = self.cross_B_coefficients
new.cross_C_coefficients = self.cross_C_coefficients
new.cross_B_model = self.cross_B_model
new.cross_C_model = self.cross_C_model
new.HeatCapacityGases = self.HeatCapacityGases
new.model = model = self.model.to(T=None)
new.Hfs = self.Hfs
new.Gfs = self.Gfs
new.Sfs = self.Sfs
if T is not None:
new.T = T
new.model.T = T
if P is not None:
new.P = P
B = new.B()
C = new.C()
Z = Z_from_virial_density_form(T, P, B, C)
new._V = Z*self.R*T/P
elif V is not None:
P = new.P = self.R*T*(V*V + V*new.B() + new.C())/(V*V*V)
new._V = V
else:
raise ValueError("Two of T, P, or V are needed")
elif P is not None and V is not None:
new.P = P
new._V = V
# PV specified, solve for T
def err(T):
# Solve for P matching; probably there is a better solution here that does not
# require the cubic solution but this works for now
# TODO: instead of using self.to_TP_zs to allow calculating B and C,
# they should be functional
new_tmp = self.to_TP_zs(T=T, P=P, zs=zs)
B = new_tmp.B()
C = new_tmp.C()
x2 = V*V + V*B + C
x3 = self.R/(V*V*V)
P_err = T*x2*x3 - P
dP_dT = x3*(T*(V*new_tmp.dB_dT() + new_tmp.dC_dT()) + x2)
return P_err, dP_dT
T_ig = P*V/self.R # guess
T = newton(err, T_ig, fprime=True, xtol=1e-15)
new.T = T
new.model.T = T
else:
raise ValueError("Two of T, P, or V are needed")
return new
[docs] def B(self):
r'''Method to calculate and return the `B` second virial coefficient.
Returns
-------
B : float
Second molar virial coefficient [m^3/mol]
'''
try:
return self._B
except:
pass
N = self.N
if N == 1:
self._B = B = self.model.B_pures()[0]
return B
zs = self.zs
if not self.cross_B_coefficients:
Bs = self.model.B_pures()
self._B = B = float(mixing_simple(zs, Bs))
return B
B_interactions = self.model.B_interactions()
self._B = B = float(BVirial_mixture(zs, B_interactions))
return B
[docs] def dB_dT(self):
r'''Method to calculate and return the first temperature derivative of
the `B` second virial coefficient.
Returns
-------
dB_dT : float
First temperature derivative of second molar virial coefficient
[m^3/(mol*K)]
'''
try:
return self._dB_dT
except:
pass
N = self.N
if N == 1:
return self.model.dB_dT_pures()[0]
zs = self.zs
if not self.cross_B_coefficients:
Bs = self.model.dB_dT_pures()
self._dB_dT = dB_dT = float(mixing_simple(zs, Bs))
return dB_dT
dB_dT_interactions = self.model.dB_dT_interactions()
self._dB_dT = dB_dT = float(BVirial_mixture(zs, dB_dT_interactions))
return dB_dT
[docs] def d2B_dT2(self):
r'''Method to calculate and return the second temperature derivative of
the `B` second virial coefficient.
Returns
-------
d2B_dT2 : float
Second temperature derivative of second molar virial coefficient
[m^3/(mol*K^2)]
'''
try:
return self._d2B_dT2
except:
pass
N = self.N
if N == 1:
return self.model.d2B_dT2_pures()[0]
zs = self.zs
if not self.cross_B_coefficients:
Bs = self.model.d2B_dT2_pures()
self._d2B_dT2 = d2B_dT2 = float(mixing_simple(zs, Bs))
return d2B_dT2
d2B_dT2_interactions = self.model.d2B_dT2_interactions()
self._d2B_dT2 = d2B_dT2 = float(BVirial_mixture(zs, d2B_dT2_interactions))
return d2B_dT2
[docs] def d3B_dT3(self):
r'''Method to calculate and return the third temperature derivative of
the `B` second virial coefficient.
Returns
-------
d3B_dT3 : float
Third temperature derivative of second molar virial coefficient
[m^3/(mol*K^3)]
'''
try:
return self._d3B_dT3
except:
pass
N = self.N
if N == 1:
return self.model.d3B_dT3_pures()[0]
zs = self.zs
if not self.cross_B_coefficients:
Bs = self.model.d3B_dT3_pures()
self._d3B_dT3 = d3B_dT3 = float(mixing_simple(zs, Bs))
return d3B_dT3
d3B_dT3_interactions = self.model.d3B_dT3_interactions()
self._d3B_dT3 = d3B_dT3 = float(BVirial_mixture(zs, d3B_dT3_interactions))
return d3B_dT3
[docs] def C(self):
r'''Method to calculate and return the `C` third virial coefficient.
Returns
-------
C : float
Third molar virial coefficient [m^6/mol^2]
'''
try:
return self._C
except:
pass
T = self.T
zs = self.zs
N = self.N
if self.model.C_zero:
self._C = C = 0.0
return C
elif self.N == 1:
self._C = C = self.model.C_pures()[0]
elif not self.cross_C_coefficients:
Cs = self.model.C_pures()
self._C = C = float(mixing_simple(zs, Cs))
return C
else:
Cijs = self.model.C_interactions()
self._C = C = float(CVirial_mixture_Orentlicher_Prausnitz(zs, Cijs))
return C
[docs] def dC_dT(self):
r'''Method to calculate and return the first temperature derivative of
the `C` third virial coefficient.
Returns
-------
dC_dT : float
First temperature derivative of third molar virial coefficient
[m^6/(mol^2*K)]
'''
try:
return self._dC_dT
except:
pass
T = self.T
zs = self.zs
if self.model.C_zero:
self._dC_dT = dC_dT = 0.0
return dC_dT
elif self.N == 1:
self._dC_dT = dC_dT = self.model.dC_dT_pures()[0]
return dC_dT
elif not self.cross_C_coefficients:
dC_dTs = self.model.dC_dT_pures()
self._dC_dT = dC_dT = float(mixing_simple(zs, dC_dTs))
return dC_dT
else:
Cijs = self.model.C_interactions()
dCijs = self.model.dC_dT_interactions()
# TODO
"""
from sympy import *
Cij, Cik, Cjk = symbols('Cij, Cik, Cjk', cls=Function)
T = symbols('T')
# The derivative of this is messy
expr = (Cij(T)*Cik(T)*Cjk(T))**Rational('1/3')
# diff(expr, T, 3)
"""
self._dC_dT = dC_dT = float(dCVirial_mixture_dT_Orentlicher_Prausnitz(zs, Cijs, dCijs))
return dC_dT
[docs] def d2C_dT2(self):
r'''Method to calculate and return the second temperature derivative of
the `C` third virial coefficient.
Returns
-------
d2C_dT2 : float
Second temperature derivative of third molar virial coefficient
[m^6/(mol^2*K^2)]
'''
try:
return self._d2C_dT2
except:
pass
T = self.T
zs = self.zs
if self.model.C_zero:
self._d2C_dT2 = d2C_dT2 = 0.0
return d2C_dT2
elif self.N == 1:
self._d2C_dT2 = d2C_dT2 = self.model.d2C_dT2_pures()[0]
return d2C_dT2
elif not self.cross_C_coefficients:
d2C_dT2s = self.model.d2C_dT2_pures()
self._d2C_dT2 = d2C_dT2 = float(mixing_simple(zs, d2C_dT2s))
return d2C_dT2
else:
Cijs = self.model.C_interactions()
dCijs = self.model.dC_dT_interactions()
d2C_dT2ijs = self.model.d2C_dT2_interactions()
N = self.N
self._d2C_dT2 = d2C_dT2 = float(d2CVirial_mixture_dT2_Orentlicher_Prausnitz(zs, Cijs, dCijs, d2C_dT2ijs))
return d2C_dT2
[docs] def d3C_dT3(self):
r'''Method to calculate and return the third temperature derivative of
the `C` third virial coefficient.
Returns
-------
d3C_dT3 : float
Second temperature derivative of third molar virial coefficient
[m^6/(mol^2*K^3)]
'''
try:
return self._d3C_dT3
except:
pass
T = self.T
zs = self.zs
if self.model.C_zero:
self._d3C_dT3 = d3C_dT3 = 0.0
return d3C_dT3
elif self.N == 1:
self._d3C_dT3 = d3C_dT3 = self.model.d3C_dT3_pures()[0]
return d3C_dT3
elif not self.cross_C_coefficients:
d3C_dT3s = self.model.d3C_dT3_pures()
self._d3C_dT3 = d3C_dT3 = float(mixing_simple(zs, d3C_dT3s))
return d3C_dT3
else:
Cijs = self.model.C_interactions()
dCijs = self.model.dC_dT_interactions()
d2C_dT2ijs = self.model.d2C_dT2_interactions()
d3C_dT3ijs = self.model.d3C_dT3_interactions()
N = self.N
self._d3C_dT3 = d3C_dT3 = float(d3CVirial_mixture_dT3_Orentlicher_Prausnitz(zs, Cijs, dCijs, d2C_dT2ijs, d3C_dT3ijs))
return d3C_dT3
[docs] def dB_dzs(self):
r'''Method to calculate and return the first mole fraction derivatives
of the `B` second virial coefficient.
Returns
-------
dB_dzs : list[float]
First mole fraction derivatives of second molar virial coefficient
[m^3/(mol)]
'''
try:
return self._dB_dzs
except:
pass
zs = self.zs
if not self.cross_B_coefficients:
Bs = self.model.B_pures()
self._dB_dzs = dB_dzs = Bs
return dB_dzs
N = self.N
if self.scalar:
dB_dzs = [0.0]*N
else:
dB_dzs = zeros(N)
B_interactions = self.model.B_interactions()
self._dB_dzs = dB_dzs = dBVirial_mixture_dzs(zs, B_interactions, dB_dzs)
return dB_dzs
[docs] def d2B_dTdzs(self):
r'''Method to calculate and return the temperature derivative of the
first mole fraction derivatives
of the `B` second virial coefficient.
Returns
-------
d2B_dTdzs : list[float]
First temperature derivative of first mole fraction derivatives of
second molar virial coefficient [m^3/(mol*K)]
'''
try:
return self._d2B_dTdzs
except:
pass
zs = self.zs
if not self.cross_B_coefficients:
Bs = self.model.dB_dT_pures()
self._d2B_dTdzs = d2B_dTdzs = Bs
return d2B_dTdzs
N = self.N
if self.scalar:
d2B_dTdzs = [0.0]*N
else:
d2B_dTdzs = zeros(N)
B_interactions = self.model.dB_dT_interactions()
self._d2B_dTdzs = d2B_dTdzs = dBVirial_mixture_dzs(zs, B_interactions, d2B_dTdzs)
return d2B_dTdzs
def d3B_dT2dzs(self):
r'''Method to calculate and return the second temperature derivative of the
first mole fraction derivatives
of the `B` second virial coefficient.
Returns
-------
d3B_dT2dzs : list[float]
Second temperature derivative of first mole fraction derivatives of
second molar virial coefficient [m^3/(mol*K^2)]
'''
try:
return self._d3B_dT2dzs
except:
pass
zs = self.zs
if not self.cross_B_coefficients:
Bs = self.model.d2B_dT2_pures()
self._d3B_dT2dzs = d3B_dT2dzs = Bs
return d3B_dT2dzs
N = self.N
if self.scalar:
d3B_dT2dzs = [0.0]*N
else:
d3B_dT2dzs = zeros(N)
B_interactions = self.model.d2B_dT2_interactions()
self._d3B_dT2dzs = d3B_dT2dzs = dBVirial_mixture_dzs(zs, B_interactions, d3B_dT2dzs)
return d3B_dT2dzs
def d4B_dT3dzs(self):
r'''Method to calculate and return the third temperature derivative of the
first mole fraction derivatives
of the `B` second virial coefficient.
Returns
-------
d4B_dT3dzs : list[float]
Third temperature derivative of first mole fraction derivatives of
second molar virial coefficient [m^3/(mol*K^3)]
'''
try:
return self._d4B_dT3dzs
except:
pass
zs = self.zs
if not self.cross_B_coefficients:
Bs = self.model.d3B_dT3_pures()
self._d4B_dT3dzs = d4B_dT3dzs = Bs
return d4B_dT3dzs
N = self.N
if self.scalar:
d4B_dT3dzs = [0.0]*N
else:
d4B_dT3dzs = zeros(N)
B_interactions = self.model.d3B_dT3_interactions()
self._d4B_dT3dzs = d4B_dT3dzs = dBVirial_mixture_dzs(zs, B_interactions, d4B_dT3dzs)
return d4B_dT3dzs
[docs] def d2B_dzizjs(self):
r'''Method to calculate and return the second mole fraction derivatives
of the `B` second virial coefficient.
Returns
-------
d2B_dzizjs : list[list[float]]
Second mole fraction derivatives of second molar virial coefficient
[m^3/(mol)]
'''
try:
return self._d2B_dzizjs
except:
pass
N = self.N
zs = self.zs
if self.scalar:
d2B_dzizjs = [[0.0]*N for _ in range(N)]
else:
d2B_dzizjs = zeros((N, N))
if not self.cross_B_coefficients:
self._d2B_dzizjs = d2B_dzizjs
return d2B_dzizjs
B_interactions = self.model.B_interactions()
self._d2B_dzizjs = d2B_dzizjs = d2BVirial_mixture_dzizjs(zs, B_interactions, d2B_dzizjs)
return d2B_dzizjs
def d3B_dTdzizjs(self):
r'''Method to calculate and return the first temperature derivative of
the second mole fraction derivatives
of the `B` second virial coefficient.
Returns
-------
d3B_dTdzizjs : list[list[float]]
First temperature derivative of second mole fraction derivatives of
second molar virial coefficient
[m^3/(mol*K)]
'''
try:
return self._d3B_dTdzizjs
except:
pass
N = self.N
zs = self.zs
if self.scalar:
d3B_dTdzizjs = [[0.0]*N for _ in range(N)]
else:
d3B_dTdzizjs = zeros((N, N))
if not self.cross_B_coefficients:
self._d3B_dTdzizjs = d3B_dTdzizjs
return d3B_dTdzizjs
B_interactions = self.model.dB_dT_interactions()
self._d3B_dTdzizjs = d3B_dTdzizjs = d2BVirial_mixture_dzizjs(zs, B_interactions, d3B_dTdzizjs)
return d3B_dTdzizjs
def d4B_dT2dzizjs(self):
r'''Method to calculate and return the second temperature derivative of
the second mole fraction derivatives
of the `B` second virial coefficient.
Returns
-------
d4B_dT2dzizjs : list[list[float]]
Second temperature derivative of second mole fraction derivatives of
second molar virial coefficient
[m^3/(mol*K^2)]
'''
try:
return self._d4B_dT2dzizjs
except:
pass
N = self.N
zs = self.zs
if self.scalar:
d4B_dT2dzizjs = [[0.0]*N for _ in range(N)]
else:
d4B_dT2dzizjs = zeros((N, N))
if not self.cross_B_coefficients:
self._d4B_dT2dzizjs = d4B_dT2dzizjs
return d4B_dT2dzizjs
B_interactions = self.model.d2B_dT2_interactions()
self._d4B_dT2dzizjs = d4B_dT2dzizjs = d2BVirial_mixture_dzizjs(zs, B_interactions, d4B_dT2dzizjs)
return d4B_dT2dzizjs
def d3B_dzizjzks(self):
r'''Method to calculate and return the third mole fraction derivatives
of the `B` second virial coefficient.
Returns
-------
d3B_dzizjzks : list[list[list[float]]]
Third mole fraction derivatives of second molar virial coefficient
[m^3/(mol)]
'''
try:
return self._d3B_dzizjzks
except:
pass
N = self.N
zs = self.zs
if self.scalar:
d3B_dzizjzks = [[[0.0]*N for _ in range(N)] for _ in range(N)]
else:
d3B_dzizjzks = zeros((N, N, N))
if not self.cross_B_coefficients:
self._d3B_dzizjzks = d3B_dzizjzks
return d3B_dzizjzks
B_interactions = self.model.B_interactions()
self._d3B_dzizjzks = d3B_dzizjzks = d3BVirial_mixture_dzizjzks(zs, B_interactions, d3B_dzizjzks)
return d3B_dzizjzks
d4B_dTdzizjzks = d3B_dzizjzks
d5B_dT2dzizjzks = d3B_dzizjzks
d6B_dT3dzizjzks = d3B_dzizjzks
def dB_dns(self):
r'''Method to calculate and return the first mole number derivatives
of the `B` second virial coefficient.
Returns
-------
dB_dns : list[float]
First mole number derivatives of second molar virial coefficient
[m^3/(mol^2)]
'''
try:
return self._dB_dns
except:
pass
N = self.N
if self.scalar:
dB_dns = [0.0]*N
else:
dB_dns = zeros(N)
self._dB_dns = dB_dns = dxs_to_dns(self.dB_dzs(), self.zs, dB_dns)
return dB_dns
def dnB_dns(self):
r'''Method to calculate and return the first partial mole number
derivatives of the `B` second virial coefficient.
Returns
-------
dnB_dns : list[float]
First partial mole number derivatives of second molar virial
coefficient [m^3/(mol)]
'''
try:
return self._dnB_dns
except:
pass
N = self.N
if self.scalar:
dnB_dns = [0.0]*N
else:
dnB_dns = zeros(N)
self._dnB_dns = dnB_dns = dxs_to_dn_partials(self.dB_dzs(), self.zs, self.B(), dnB_dns)
return dnB_dns
[docs] def dC_dzs(self):
r'''Method to calculate and return the first mole fraction derivatives
of the `C` third virial coefficient.
Returns
-------
dC_dzs : list[float]
First mole fraction derivatives of third molar virial coefficient
[m^6/(mol^2)]
'''
try:
return self._dC_dzs
except:
pass
zs = self.zs
if not self.cross_C_coefficients:
Cs = self.model.C_pures()
self._dC_dzs = dC_dzs = Cs
return dC_dzs
N = self.N
if self.scalar:
dC_dzs = [0.0]*N
else:
dC_dzs = zeros(N)
self._dC_dzs = dC_dzs
if not self.model.C_zero:
C_interactions = self.model.C_interactions()
dCVirial_mixture_Orentlicher_Prausnitz_dzs(zs, C_interactions, dC_dzs)
return dC_dzs
[docs] def d2C_dTdzs(self):
r'''Method to calculate and return the first temperature derivative of
the first mole fraction derivatives of the `C` third virial coefficient.
Returns
-------
d2C_dTdzs : list[float]
First temperature derivative of the first mole fraction derivatives
of third molar virial coefficient [m^6/(mol^2*K)]
'''
try:
return self._d2C_dTdzs
except:
pass
zs = self.zs
if not self.cross_C_coefficients:
self._d2C_dTdzs = d2C_dTdzs = self.model.dC_dT_pures()
return d2C_dTdzs
N = self.N
if self.scalar:
d2C_dTdzs = [0.0]*N
else:
d2C_dTdzs = zeros(N)
self._d2C_dTdzs = d2C_dTdzs
if not self.model.C_zero:
C_interactions = self.model.C_interactions()
dC_dT_interactions = self.model.dC_dT_interactions()
d2CVirial_mixture_Orentlicher_Prausnitz_dTdzs(zs, C_interactions, dC_dT_interactions, d2C_dTdzs)
return d2C_dTdzs
[docs] def d2C_dzizjs(self):
r'''Method to calculate and return the second mole fraction derivatives
of the `C` third virial coefficient.
Returns
-------
d2C_dzizjs : list[list[float]]
Second mole fraction derivatives of third molar virial coefficient
[m^6/(mol^2)]
'''
try:
return self._d2C_dzizjs
except:
pass
N = self.N
if self.scalar:
d2C_dzizjs = [[0.0]*N for _ in range(N)]
else:
d2C_dzizjs = zeros((N, N))
zs = self.zs
if not self.cross_C_coefficients:
# Cs = self.model.C_pures()
# for i, C in enumerate(Cs):
# d2C_dzizjs[i][i] = C
self._d2C_dzizjs = d2C_dzizjs
return d2C_dzizjs
self._d2C_dzizjs = d2C_dzizjs
if not self.model.C_zero:
C_interactions = self.model.C_interactions()
d2CVirial_mixture_Orentlicher_Prausnitz_dzizjs(zs, C_interactions, d2C_dzizjs)
return d2C_dzizjs
def d3C_dzizjzks(self):
r'''Method to calculate and return the third mole fraction derivatives
of the `C` third virial coefficient.
Returns
-------
d3C_dzizjzks : list[list[float]]
Third mole fraction derivatives of third molar virial coefficient
[m^6/(mol^2)]
'''
try:
return self._d3C_dzizjzks
except:
pass
N = self.N
if self.scalar:
d3C_dzizjzks = [[[0.0]*N for _ in range(N)] for _ in range(N)]
else:
d3C_dzizjzks = zeros((N, N, N))
zs = self.zs
if not self.cross_C_coefficients:
self._d3C_dzizjzks = d3C_dzizjzks
return d3C_dzizjzks
self._d3C_dzizjzks = d3C_dzizjzks
if not self.model.C_zero:
C_interactions = self.model.C_interactions()
d3CVirial_mixture_Orentlicher_Prausnitz_dzizjzks(zs, C_interactions, d3C_dzizjzks)
return d3C_dzizjzks
def dC_dns(self):
r'''Method to calculate and return the first mole number derivatives
of the `C` third virial coefficient.
Returns
-------
dC_dns : list[float]
First mole number derivatives of third molar virial coefficient
[m^6/(mol^3)]
'''
try:
return self._dC_dns
except:
pass
N = self.N
if self.scalar:
dC_dns = [0.0]*N
else:
dC_dns = zeros(N)
self._dC_dns = dC_dns = dxs_to_dns(self.dC_dzs(), self.zs, dC_dns)
return dC_dns
def dnC_dns(self):
r'''Method to calculate and return the first partial mole number
derivatives of the `C` third virial coefficient.
Returns
-------
dnC_dns : list[float]
First partial mole number derivatives of third molar virial coefficient
[m^6/(mol^2)]
'''
try:
return self._dnC_dns
except:
pass
N = self.N
if self.scalar:
dnC_dns = [0.0]*N
else:
dnC_dns = zeros(N)
self._dnC_dns = dnC_dns = dxs_to_dn_partials(self.dC_dzs(), self.zs, self.C(), dnC_dns)
return dnC_dns
def dB_dP_V(self):
return self.dB_dT()/self.dP_dT()
def dC_dP_V(self):
return self.dC_dT()/self.dP_dT()
def d2B_dTdP_V(self):
return self.d2B_dT2()/self.dP_dT()
def d2C_dTdP_V(self):
return self.d2C_dT2()/self.dP_dT()
def d3B_dT2dP_V(self):
return self.d3B_dT3()/self.dP_dT()
def d3C_dT2dP_V(self):
return self.d3C_dT3()/self.dP_dT()
def dB_dV_P(self):
return self.dB_dT()*self.dT_dV()
def dC_dV_P(self):
return self.dC_dT()*self.dT_dV()
def d2B_dTdV_P(self):
return self.d2B_dT2()*self.dT_dV()
def d2C_dTdV_P(self):
return self.d2C_dT2()*self.dT_dV()
def d3B_dT2dV_P(self):
return self.d3B_dT3()*self.dT_dV()
def d3C_dT2dV_P(self):
return self.d3C_dT3()*self.dT_dV()
# Overrides for precision in regression to ideal gas
def d2T_dV2(self):
if self.model.C_zero and self.model.B_zero:
return 0.0
return super().d2T_dV2()
def d2T_dV2_P(self):
if self.model.C_zero and self.model.B_zero:
return 0.0
return super().d2T_dV2_P()
def d2V_dT2(self):
if self.model.C_zero and self.model.B_zero:
return 0.0
return super().d2V_dT2()
d2V_dT2_P = d2V_dT2
dP_dT_V = dP_dT
dP_dV_T = dP_dV
d2P_dT2_V = d2P_dT2
d2P_dV2_T = d2P_dV2
VirialGas.dH_dT_V = IdealGasDeparturePhase.Cp
VirialGas.d2V_dP2_T = Phase.d2V_dP2
VirialGas.d2T_dP2_V = Phase.d2T_dP2
VirialGas.dV_dP_T = Phase.dV_dP
VirialGas.dV_dT_P = Phase.dV_dT
VirialGas.dT_dP_V = Phase.dT_dP
VirialGas.dT_dV_P = Phase.dT_dV