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Add two surface tension models from 'Development of corresponding sta…
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…tes model for estimation of the surface tension of chemical compounds'
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@CalebBell
CalebBell committed Nov 20, 2021
1 parent 726058b commit 32a71a1
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138 changes: 125 additions & 13 deletions chemicals/interface.py
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Expand Up @@ -39,6 +39,8 @@
.. autofunction:: chemicals.interface.Miqueu
.. autofunction:: chemicals.interface.Aleem
.. autofunction:: chemicals.interface.Mersmann_Kind_sigma
.. autofunction:: chemicals.interface.sigma_Gharagheizi_1
.. autofunction:: chemicals.interface.sigma_Gharagheizi_2
Mixing Rules
------------
Expand Down Expand Up @@ -139,7 +141,8 @@
'Mersmann_Kind_sigma', 'API10A32',
'Hakim_Steinberg_Stiel', 'Miqueu', 'Aleem',
'Winterfeld_Scriven_Davis', 'Diguilio_Teja', 'Weinaug_Katz',
'Meybodi_Daryasafar_Karimi', 'ISTExpansion']
'Meybodi_Daryasafar_Karimi', 'ISTExpansion', 'sigma_Gharagheizi_1',
'sigma_Gharagheizi_2']

import os
from fluids.numerics import numpy as np
Expand Down Expand Up @@ -223,7 +226,7 @@ def sigma_IAPWS(T):
Returns
-------
sigma : float
Air-water surface tension, [N/m]
Air-liquid surface tension, [N/m]
Notes
-----
Expand Down Expand Up @@ -313,7 +316,7 @@ def REFPROP_sigma(T, Tc, sigma0, n0, sigma1=0.0, n1=0.0, sigma2=0.0, n2=0.0):


def PPDS14(T, Tc, a0, a1, a2):
r'''Calculates air-water surface tension using the [1]_
r'''Calculates air-liquid surface tension using the [1]_
emperical (parameter-regressed) method, called the PPDS 14 equation for
surface tension.
Expand Down Expand Up @@ -362,7 +365,7 @@ def PPDS14(T, Tc, a0, a1, a2):
return a0*tau**a1*(1.0 + a2*tau)

def Watson_sigma(T, Tc, a1, a2, a3=0.0, a4=0.0, a5=0.0):
r'''Calculates air-water surface tension using the Watson [1]_
r'''Calculates air-liquid surface tension using the Watson [1]_
emperical (parameter-regressed) method developed by NIST.
.. math::
Expand Down Expand Up @@ -413,7 +416,7 @@ def Watson_sigma(T, Tc, a1, a2, a3=0.0, a4=0.0, a5=0.0):
return exp(a1 + l*(a2 + Tr*(a3 + Tr*(a4 + a5*Tr))))

def ISTExpansion(T, Tc, a1, a2, a3=0.0, a4=0.0, a5=0.0):
r'''Calculates air-water surface tension using the IST expansion [1]_
r'''Calculates air-liquid surface tension using the IST expansion [1]_
emperical (parameter-regressed) method developed by NIST.
.. math::
Expand Down Expand Up @@ -460,7 +463,7 @@ def ISTExpansion(T, Tc, a1, a2, a3=0.0, a4=0.0, a5=0.0):
return tau*(a1 + tau*(a2 + tau*(a3 + tau*(a4 + a5*tau))))

def Somayajulu(T, Tc, A, B, C):
r'''Calculates air-water surface tension using the [1]_
r'''Calculates air-liquid surface tension using the [1]_
emperical (parameter-regressed) method. Well regressed, no recent data.
.. math::
Expand Down Expand Up @@ -558,7 +561,7 @@ def Jasper(T, a, b):


def Brock_Bird(T, Tb, Tc, Pc):
r'''Calculates air-water surface tension using the [1]_
r'''Calculates air-liquid surface tension using the [1]_
emperical method. Old and tested.
.. math::
Expand Down Expand Up @@ -621,7 +624,7 @@ def Brock_Bird(T, Tb, Tc, Pc):


def Pitzer_sigma(T, Tc, Pc, omega):
r'''Calculates air-water surface tension using the correlation derived
r'''Calculates air-liquid surface tension using the correlation derived
by [1]_ from the works of [2]_ and [3]_. Based on critical property CSP
methods.
Expand Down Expand Up @@ -676,7 +679,7 @@ def Pitzer_sigma(T, Tc, Pc, omega):


def Sastri_Rao(T, Tb, Tc, Pc, chemicaltype=None):
r'''Calculates air-water surface tension using the correlation derived by
r'''Calculates air-liquid surface tension using the correlation derived by
[1]_ based on critical property CSP methods and chemical classes.
.. math::
Expand Down Expand Up @@ -732,7 +735,7 @@ def Sastri_Rao(T, Tb, Tc, Pc, chemicaltype=None):


def Zuo_Stenby(T, Tc, Pc, omega):
r'''Calculates air-water surface tension using the reference fluids
r'''Calculates air-liquid surface tension using the reference fluids
methods of [1]_.
.. math::
Expand Down Expand Up @@ -803,7 +806,7 @@ def Zuo_Stenby(T, Tc, Pc, omega):


def Hakim_Steinberg_Stiel(T, Tc, Pc, omega, StielPolar=0.0):
r'''Calculates air-water surface tension using the reference fluids methods
r'''Calculates air-liquid surface tension using the reference fluids methods
of [1]_.
.. math::
Expand Down Expand Up @@ -865,7 +868,7 @@ def Hakim_Steinberg_Stiel(T, Tc, Pc, omega, StielPolar=0.0):


def Miqueu(T, Tc, Vc, omega):
r'''Calculates air-water surface tension using the methods of [1]_.
r'''Calculates air-liquid surface tension using the methods of [1]_.
.. math::
\sigma = k T_c \left( \frac{N_a}{V_c}\right)^{2/3}
Expand Down Expand Up @@ -1044,6 +1047,115 @@ def Mersmann_Kind_sigma(T, Tm, Tb, Tc, Pc, n_associated=1):
return sigma


def sigma_Gharagheizi_1(T, Tc, MW, omega):
r'''Calculates air-liquid surface tension using the
equation 4 derived in [1]_ by gene expression programming.
.. math::
\sigma = 8.948226\times 10^{-4}\left[\frac{A^2}{MW}\sqrt{\frac{A\omega}{MW}}
\right]^{0.5}
.. math::
A = (T_{c} - T - \omega)
Parameters
----------
T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
MW : float
Molecular weight [g/mol]
omega : float
Acentric factor for fluid, [-]
Returns
-------
sigma : float
Liquid surface tension, N/m
Notes
-----
This equation may fail before the critical point.
Examples
--------
Methane at 93 K, point from [1]_'s supporting material:
>>> sigma_Gharagheizi_1(T=95, Tc=190.564, MW=16.04, omega=0.012)
0.0110389739
References
----------
.. [1] Gharagheizi, Farhad, Ali Eslamimanesh, Mehdi Sattari, Amir H. Mohammadi,
and Dominique Richon. "Development of Corresponding States Model for
Estimation of the Surface Tension of Chemical Compounds." AIChE Journal 59,
no. 2 (2013): 613-21. https://doi.org/10.1002/aic.13824.
'''
# Equation 4
A = (Tc - T - omega)
sigma = 8.948226e-4*sqrt(A*A/MW*sqrt(A*omega/MW))
return sigma

def sigma_Gharagheizi_2(T, Tb, Tc, Pc, Vc):
r'''Calculates air-liquid surface tension using the
equation 6 derived in [1]_ by gene expression programming.
.. math::
\frac{\sigma}{\text{N}/\text{m}} = 10^{-4}\left(\frac{P_c}{\text{bar}}\right)^{2/3}
\left(\frac{T_c}{\text{K}}\right)^{1/3}(1-T_r)^{11/9}
\left[7.728729T_{br} + 2.476318\left(T_{br}^3 + \frac{V_{c}}{\text{m}^3 /\text{kmol}}\right)
\right]
Parameters
----------
T : float
Temperature of fluid [K]
Tb : float
Boiling temperature of the fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
MW : float
Molecular weight [g/mol]
Vc : float
Critical volume of fluid [m^3/mol]
Returns
-------
sigma : float
Liquid surface tension, N/m
Notes
-----
This expression gives does converge to 0 at the critical point.
Examples
--------
Methane at 93 K, point from [1]_'s supporting material:
>>> sigma_Gharagheizi_2(T=95, Tb=111.66, Tc=190.564, Pc=45.99e5, Vc=0.0986e-3)
0.01674894057
References
----------
.. [1] Gharagheizi, Farhad, Ali Eslamimanesh, Mehdi Sattari, Amir H. Mohammadi,
and Dominique Richon. "Development of Corresponding States Model for
Estimation of the Surface Tension of Chemical Compounds." AIChE Journal 59,
no. 2 (2013): 613-21. https://doi.org/10.1002/aic.13824.
'''
# Equation 6
Pc *= 1e-5 # Pc, Pa to bar
Tr = T/Tc
Tbr = Tb/Tc
Tbr2 = Tbr*Tbr
Vc *= 1e3 # m^3/mol to m^3/kmol
sigma = 1e-4*Pc**(2.0/3.0)*Tc**(1.0/3.0)*(1.0 - Tr)**(11/9.)
sigma *= (7.728729*Tbr + 2.476318*(Tbr*Tbr2 + Vc))
return sigma

def API10A32(T, Tc, K_W):
r'''Calculates the interfacial tension between
a liquid petroleum fraction and air, using the oil's pseudocritical
Expand All @@ -1065,7 +1177,7 @@ def API10A32(T, Tc, K_W):
Returns
-------
sigma : float
Air-water surface tension, [N/m]
Air-liquid surface tension, [N/m]
Notes
-----
Expand Down
17 changes: 16 additions & 1 deletion tests/test_interface.py
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Expand Up @@ -206,4 +206,19 @@ def test_ISTExpansion():
assert_close(sigma, 0.02672100905515996, rtol=1e-13)

sigma = ISTExpansion(T=400.0, Tc=776.0, a1=0.037545, a2=0.0363288, a3=1e-4, a4=1e-3, a5=1e-4)
assert_close(sigma, 0.02679017489704166, rtol=1e-15)
assert_close(sigma, 0.02679017489704166, rtol=1e-15)


def test_sigma_Gharagheizi_1():
# point from article supporting material exactly matches
sigma_methane1 = sigma_Gharagheizi_1(T=93.1500015258789, Tc=190.564, MW=16.04246, omega=0.0115478)
assert_close(sigma_methane1, 0.0111974953003432, rtol=1e-13)

# Point that math errors before critical point
# sigma_Gharagheizi_1(T=190.56, Tc=190.564, MW=16.04, omega=0.012)

def test_sigma_Gharagheizi_2():
# point from article supporting material exactly matches

sigma_methane1 = sigma_Gharagheizi_2(T=93.1500015258789, Tb=111.66, Tc=190.564, Pc=45.99*1e5, Vc=0.0986e-3)
assert_close(sigma_methane1, 0.0171460800730683, rtol=1e-13)

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