def test_osmoticC():
"""Test the function for calculating osmotic coefficients to see if it is working correctly."""
# NaCl in water
print('\n########## Test with aqueous NaCl ##########')
# 0 = Na+, 1 = Cl-, 2 = H2O
x = np.asarray([0.0629838206, 0.0629838206, 0.8740323588])
m = np.asarray([1, 1, 1.2047])
s = np.asarray([2.8232, 2.7599589, 0.])
e = np.asarray([230.00, 170.00, 353.9449])
volAB = np.asarray([0, 0, 0.0451])
eAB = np.asarray([0, 0, 2425.67])
k_ij = np.asarray([[0, 0.317, 0],
[0.317, 0, -0.25],
[0, -0.25, 0]])
z = np.asarray([1., -1., 0.])
ref = 1.116 # source: R. A. Robinson and R. H. Stokes, Electrolyte Solutions: Second Revised Edition. Dover Publications, 1959.
t = 293.15 # K
s[2] = 2.7927 + 10.11*np.exp(-0.01775*t) - 1.417*np.exp(-0.01146*t) # temperature dependent segment diameter for water
k_ij[0,2] = -0.007981*t + 2.37999
k_ij[2,0] = -0.007981*t + 2.37999
dielc = dielc_water(t)
rho = pcsaft_den(x, m, s, e, t, 2339.3, phase='liq', k_ij=k_ij, e_assoc=eAB, vol_a=volAB, z=z, dielc=dielc)
result = pcsaft_osmoticC(x, m, s, e, t, rho, k_ij=k_ij, e_assoc=eAB, vol_a=volAB, z=z, dielc=dielc)
calc = result[0]
print('----- Osmotic coefficient at 293.15 K -----')
print(' Reference:', ref)
print(' PC-SAFT:', calc)
print(' Relative deviation:', (calc-ref)/ref*100, '%')
return None
def test_PTz():
"""Test the function for PTz data to see if it is working correctly."""
# Binary mixture: methanol-cyclohexane
print('\n########## Test with methanol-cyclohexane mixture ##########')
#0 = methanol, 1 = cyclohexane
m = np.asarray([1.5255, 2.5303])
s = np.asarray([3.2300, 3.8499])
e = np.asarray([188.90, 278.11])
volAB = np.asarray([0.035176, 0.])
eAB = np.asarray([2899.5, 0.])
k_ij = np.asarray([[0, 0.051],
[0.051, 0]])
mol = 1.
t = 327.48
p_ref = 101330 # source: Marinichev A.N.; Susarev M.P.: Investigation of Liquid-Vapor Equilibrium in the System Methanol-Cyclohexane at 35, 45 and 55°C and 760 mm Hg. J.Appl.Chem.USSR 38 (1965) 1582-1584
xl_ref = np.asarray([0.3,0.7])
xv_ref = np.asarray([0.59400,0.40600])
beta_ref = 0.6
xtot = (beta_ref*mol*xv_ref + (1-beta_ref)*mol*xl_ref)/mol
rho_l = pcsaft_den(xl_ref, m, s, e, t, p_ref, phase='liq', k_ij=k_ij, e_assoc=eAB, vol_a=volAB)
rho_v = pcsaft_den(xv_ref, m, s, e, t, p_ref, phase='vap', k_ij=k_ij, e_assoc=eAB, vol_a=volAB)
vol = beta_ref*mol/rho_v + (1-beta_ref)*mol/rho_l
result = pcsaft_PTz(p_ref, xl_ref, beta_ref, mol, vol, xtot, m, s, e, t, k_ij=k_ij, e_assoc=eAB, vol_a=volAB)
p_calc = result[0]
xl_calc = result[1]
xv_calc = result[2]
beta_calc = result[3]
print('----- Pressure at 327.48 K -----')
print(' Reference:', p_ref, 'Pa')
print(' PC-SAFT:', p_calc, 'Pa')
print(' Relative deviation:', (p_calc-p_ref)/p_ref*100, '%')
print('----- Liquid phase composition -----')
print(' Reference:', xl_ref)
print(' PC-SAFT:', xl_calc)
print(' Relative deviation:', (xl_calc-xl_ref)/xl_ref*100, '%')
print('----- Vapor phase composition -----')
print(' Reference:', xv_ref)
print(' PC-SAFT:', xv_calc)
print(' Relative deviation:', (xv_calc-xv_ref)/xv_ref*100, '%')
print('----- Beta -----')
print(' Reference:', beta_ref)
print(' PC-SAFT:', beta_calc)
print(' Relative deviation:', (beta_calc-beta_ref)/beta_ref*100, '%')
return None
def test_sres():
"""Test the residual entropy function to see if it is working correctly."""
print('------ 325 K ------')
print('\t\t\t PC-SAFT\t Reference')
t = 325 # K
p = 101325 # Pa
# all reference values are from PC-SAFT implemented in Aspen Plus
# Toluene ----------
x = np.asarray([1.])
m = np.asarray([2.8149])
s = np.asarray([3.7169])
e = np.asarray([285.69])
pyargs = {}
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
calc = pcsaft_sres(x, m, s, e, t, den, pyargs)
print('Toluene, liquid:\t\t', calc, -96.3692, 'J/mol/K')
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='vap')
calc = pcsaft_sres(x, m, s, e, t, den, pyargs)
print('Toluene, vapor:\t\t', calc, -0.71398, 'J/mol/K')
# Acetic acid ---------
m = np.asarray([1.3403])
s = np.asarray([3.8582])
e = np.asarray([211.59])
volAB = np.asarray([0.075550])
eAB = np.asarray([3044.4])
pyargs = {'e_assoc': eAB, 'vol_a': volAB}
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
calc = pcsaft_sres(x, m, s, e, t, den, pyargs)
print('Acetic acid, liquid:\t\t', calc, -98.1127, 'J/mol/K')
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='vap')
calc = pcsaft_sres(x, m, s, e, t, den, pyargs)
print('Acetic acid, vapor:\t\t', calc, -40.8743, 'J/mol/K')
# Butyl acetate ---------
m = np.asarray([2.76462805])
s = np.asarray([4.02244938])
e = np.asarray([263.69902915])
dpm = np.asarray([1.84])
dip_num = np.asarray([4.99688339])
pyargs = {'dipm': dpm, 'dip_num': dip_num}
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
calc = pcsaft_sres(x, m, s, e, t, den, pyargs)
print('Butyl acetate, liquid:\t', calc, -108.9615, 'J/mol/K')
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='vap')
calc = pcsaft_sres(x, m, s, e, t, den, pyargs)
print('Butyl acetate, vapor:\t\t', calc, -1.0361, 'J/mol/K')
return None
def test_gres():
"""Test the residual Gibbs energy function to see if it is working correctly."""
print('------ 325 K ------')
print('\t\t\t PC-SAFT\t Reference')
t = 325 # K
p = 101325 # Pa
# all reference values are from PC-SAFT implemented in Aspen Plus
# Toluene ----------
x = np.asarray([1.])
m = np.asarray([2.8149])
s = np.asarray([3.7169])
e = np.asarray([285.69])
pyargs = {}
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
calc = pcsaft_gres(x, m, s, e, t, den, pyargs)
print('Toluene, liquid:\t\t', calc, -5489.384, 'J/mol')
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='vap')
calc = pcsaft_gres(x, m, s, e, t, den, pyargs)
print('Toluene, vapor:\t\t', calc, -130.6339, 'J/mol')
# Acetic acid ---------
m = np.asarray([1.3403])
s = np.asarray([3.8582])
e = np.asarray([211.59])
volAB = np.asarray([0.075550])
eAB = np.asarray([3044.4])
pyargs = {'e_assoc': eAB, 'vol_a': volAB}
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
calc = pcsaft_gres(x, m, s, e, t, den, pyargs)
print('Acetic acid, liquid:\t\t', calc, -7038.004, 'J/mol')
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='vap')
calc = pcsaft_gres(x, m, s, e, t, den, pyargs)
print('Acetic acid, vapor:\t\t', calc, -2109.459, 'J/mol')
# Butyl acetate ---------
m = np.asarray([2.76462805])
s = np.asarray([4.02244938])
e = np.asarray([263.69902915])
dpm = np.asarray([1.84])
dip_num = np.asarray([4.99688339])
pyargs = {'dipm': dpm, 'dip_num': dip_num}
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
calc = pcsaft_gres(x, m, s, e, t, den, pyargs)
print('Butyl acetate, liquid:\t', calc, -8030.709, 'J/mol')
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='vap')
calc = pcsaft_gres(x, m, s, e, t, den, pyargs)
print('Butyl acetate, vapor:\t\t', calc, -179.7519, 'J/mol')
return None
def test_sres():
"""Test the residual entropy function to see if it is working correctly."""
print('------ 325 K ------')
print('\t\t\t PC-SAFT\t Reference')
t = 325 # K
p = 101325 # Pa
# all reference values are from PC-SAFT implemented in Aspen Plus
# Toluene ----------
x = np.asarray([1.])
m = np.asarray([2.8149])
s = np.asarray([3.7169])
e = np.asarray([285.69])
pyargs = {}
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
calc = pcsaft_sres(x, m, s, e, t, den, pyargs)
print('Toluene, liquid:\t\t', calc, -96.3692, 'J/mol/K')
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='vap')
calc = pcsaft_sres(x, m, s, e, t, den, pyargs)
print('Toluene, vapor:\t\t', calc, -0.71398, 'J/mol/K')
# Acetic acid ---------
m = np.asarray([1.3403])
s = np.asarray([3.8582])
e = np.asarray([211.59])
volAB = np.asarray([0.075550])
eAB = np.asarray([3044.4])
pyargs = {'e_assoc':eAB, 'vol_a':volAB}
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
calc = pcsaft_sres(x, m, s, e, t, den, pyargs)
print('Acetic acid, liquid:\t\t', calc, -98.1127, 'J/mol/K')
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='vap')
calc = pcsaft_sres(x, m, s, e, t, den, pyargs)
print('Acetic acid, vapor:\t\t', calc, -40.8743, 'J/mol/K')
# Dimethyl ether ---------
m = np.asarray([2.2634])
s = np.asarray([3.2723])
e = np.asarray([210.29])
dpm = np.asarray([1.3])
dip_num = np.asarray([1.0])
pyargs = {'dipm':dpm, 'dip_num':dip_num}
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
calc = pcsaft_sres(x, m, s, e, t, den, pyargs)
print('Dimethyl ether, liquid:\t', calc, -75.2232, 'J/mol/K')
den = pcsaft_den(x, m, s, e, t, p, pyargs, phase='vap')
calc = pcsaft_sres(x, m, s, e, t, den, pyargs)
print('Dimethyl ether, vapor:\t\t', calc, -0.17854, 'J/mol/K')
return None
def test_hres():
"""Test the residual enthalpy function to see if it is working correctly."""
print('------ 325 K ------')
print('\t\t\t PC-SAFT\t Reference')
t = 325 # K
p = 101325 # Pa
# all reference values are from PC-SAFT implemented in Aspen Plus
# Toluene ----------
x = np.asarray([1.])
m = np.asarray([2.8149])
s = np.asarray([3.7169])
e = np.asarray([285.69])
den = pcsaft_den(x, m, s, e, t, p, phase='liq')
calc = pcsaft_hres(x, m, s, e, t, den)
print('Toluene, liquid:\t\t', calc, -36809.39, 'J/mol')
den = pcsaft_den(x, m, s, e, t, p, phase='vap')
calc = pcsaft_hres(x, m, s, e, t, den)
print('Toluene, vapor:\t\t', calc, -362.6777, 'J/mol')
# Acetic acid ---------
m = np.asarray([1.3403])
s = np.asarray([3.8582])
e = np.asarray([211.59])
volAB = np.asarray([0.075550])
eAB = np.asarray([3044.4])
den = pcsaft_den(x, m, s, e, t, p, phase='liq', e_assoc=eAB, vol_a=volAB)
calc = pcsaft_hres(x, m, s, e, t, den, e_assoc=eAB, vol_a=volAB)
print('Acetic acid, liquid:\t\t', calc, -38924.64, 'J/mol')
den = pcsaft_den(x, m, s, e, t, p, phase='vap', e_assoc=eAB, vol_a=volAB)
calc = pcsaft_hres(x, m, s, e, t, den, e_assoc=eAB, vol_a=volAB)
print('Acetic acid, vapor:\t\t', calc, -15393.63, 'J/mol')
# Butyl acetate ---------
m = np.asarray([2.76462805])
s = np.asarray([4.02244938])
e = np.asarray([263.69902915])
dpm = np.asarray([1.84])
dip_num = np.asarray([4.99688339])
den = pcsaft_den(x, m, s, e, t, p, phase='liq', dipm=dpm, dip_num=dip_num)
calc = pcsaft_hres(x, m, s, e, t, den, dipm=dpm, dip_num=dip_num)
print('Butyl acetate, liquid:\t', calc, -43443.19, 'J/mol')
den = pcsaft_den(x, m, s, e, t, p, phase='vap', dipm=dpm, dip_num=dip_num)
calc = pcsaft_hres(x, m, s, e, t, den, dipm=dpm, dip_num=dip_num)
print('Butyl acetate, vapor:\t\t', calc, -516.4779, 'J/mol')
return None
def test_hres():
"""Test the residual enthalpy function to see if it is working correctly."""
print('------ 325 K ------')
print('\t\t\t PC-SAFT\t Reference')
t = 325 # K
p = 101325 # Pa
# all reference values are from PC-SAFT implemented in Aspen Plus
# Toluene ----------
x = np.asarray([1.])
m = np.asarray([2.8149])
s = np.asarray([3.7169])
e = np.asarray([285.69])
den = pcsaft_den(x, m, s, e, t, p, phase='liq')
calc = pcsaft_hres(x, m, s, e, t, den)
print('Toluene, liquid:\t\t', calc, -36809.39, 'J/mol')
den = pcsaft_den(x, m, s, e, t, p, phase='vap')
calc = pcsaft_hres(x, m, s, e, t, den)
print('Toluene, vapor:\t\t', calc, -362.6777, 'J/mol')
# Acetic acid ---------
m = np.asarray([1.3403])
s = np.asarray([3.8582])
e = np.asarray([211.59])
volAB = np.asarray([0.075550])
eAB = np.asarray([3044.4])
den = pcsaft_den(x, m, s, e, t, p, phase='liq', e_assoc=eAB, vol_a=volAB)
calc = pcsaft_hres(x, m, s, e, t, den, e_assoc=eAB, vol_a=volAB)
print('Acetic acid, liquid:\t\t', calc, -38924.64, 'J/mol')
den = pcsaft_den(x, m, s, e, t, p, phase='vap', e_assoc=eAB, vol_a=volAB)
calc = pcsaft_hres(x, m, s, e, t, den, e_assoc=eAB, vol_a=volAB)
print('Acetic acid, vapor:\t\t', calc, -15393.63, 'J/mol')
# dimethyl ether ---------
m = np.asarray([2.2634])
s = np.asarray([3.2723])
e = np.asarray([210.29])
dpm = np.asarray([1.3])
dip_num = np.asarray([1.0])
den = pcsaft_den(x, m, s, e, t, p, phase='liq', dipm=dpm, dip_num=dip_num)
calc = pcsaft_hres(x, m, s, e, t, den, dipm=dpm, dip_num=dip_num)
print('dimethyl ether, liquid:\t', calc, -18242.5, 'J/mol')
den = pcsaft_den(x, m, s, e, t, p, phase='vap', dipm=dpm, dip_num=dip_num)
calc = pcsaft_hres(x, m, s, e, t, den, dipm=dpm, dip_num=dip_num)
print('dimethyl ether, vapor:\t\t', calc, -89.6574, 'J/mol')
return None
def test_cp():
"""Test the heat capacity function to see if it is working correctly."""
# Benzene
print('########## Test with benzene ##########')
x = np.asarray([1.])
m = np.asarray([2.4653])
s = np.asarray([3.6478])
e = np.asarray([287.35])
cnsts = np.asarray(
[55238., 173380, 764.25, 72545,
2445.7]) # constants for Aly-Lee equation (obtained from DIPPR)
ref = 140.78 # source: Equation of state from Polt et al. (1992) (available at https://webbook.nist.gov/chemistry/fluid/)
p = 100000.
t = 330.
rho = pcsaft_den(x, m, s, e, t, p, phase='liq')
calc = pcsaft_cp(x, m, s, e, t, rho, cnsts)
print('----- Heat capacity at 330 K -----')
print(' Reference:', ref, 'J mol^-1 K^-1')
print(' PC-SAFT:', calc, 'J mol^-1 K^-1')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# Toluene
print('########## Test with toluene ##########')
x = np.asarray([1.])
m = np.asarray([2.8149])
s = np.asarray([3.7169])
e = np.asarray([285.69])
cnsts = np.asarray(
[58140., 286300, 1440.6, 189800,
650.43]) # constants for Aly-Lee equation (obtained from DIPPR)
ref = 179.79 # source: Equation of state from Polt et al. (1992) (available at https://webbook.nist.gov/chemistry/fluid/)
p = 100000.
t = 370.
rho = pcsaft_den(x, m, s, e, t, p, phase='liq')
calc = pcsaft_cp(x, m, s, e, t, rho, cnsts)
print('----- Heat capacity at 370 K -----')
print(' Reference:', ref, 'J mol^-1 K^-1')
print(' PC-SAFT:', calc, 'J mol^-1 K^-1')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# Water
print('\n########## Test with acetic acid ##########')
m = np.asarray([1.3403])
s = np.asarray([3.8582])
e = np.asarray([211.59])
volAB = np.asarray([0.075550])
eAB = np.asarray([3044.4])
cnsts = np.asarray(
[40200., 136750, 1262, 70030,
569.7]) # constants for Aly-Lee equation (obtained from DIPPR)
ref = 130.3 # source: DIPPR
p = 100000.
t = 325.
rho = pcsaft_den(x, m, s, e, t, p, phase='liq', e_assoc=eAB, vol_a=volAB)
calc = pcsaft_cp(x, m, s, e, t, rho, cnsts, e_assoc=eAB, vol_a=volAB)
""" Note: Large deviations occur with acetic acid and water. This behavior
has been observed before and was described in R. T. C. S. Ribeiro, A. L.
Alberton, M. L. L. Paredes, G. M. Kontogeorgis, and X. Liang, “Extensive
Study of the Capabilities and Limitations of the CPA and sPC-SAFT Equations
of State in Modeling a Wide Range of Acetic Acid Properties,” Ind. Eng.
Chem. Res., vol. 57, no. 16, pp. 5690–5704, Apr. 2018. """
print('----- Heat capacity at 325 K -----')
print(' Reference:', ref, 'J mol^-1 K^-1')
print(' PC-SAFT:', calc, 'J mol^-1 K^-1')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# Butyl acetate
print('\n########## Test with butyl acetate ##########')
m = np.asarray([2.76462805])
s = np.asarray([4.02244938])
e = np.asarray([263.69902915])
dpm = np.asarray([1.84])
dip_num = np.asarray([4.99688339])
cnsts = np.asarray(
[116840., 376900, 1956, 281800,
811.2]) # constants for Aly-Lee equation (obtained from DIPPR)
ref = 234.9 # source: DIPPR correlation
p = 100000.
t = 320.
rho = pcsaft_den(x, m, s, e, t, p, phase='liq', dipm=dpm, dip_num=dip_num)
calc = pcsaft_cp(x, m, s, e, t, rho, cnsts, dipm=dpm, dip_num=dip_num)
print('----- Heat capacity at 320 K -----')
print(' Reference:', ref, 'J mol^-1 K^-1')
print(' PC-SAFT:', calc, 'J mol^-1 K^-1')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
return None
def test_d2adt():
"""Test the function for the second temperature derivative of the Helmholtz energy."""
print('########## Testing pcsaft_d2adt ##########')
# Toluene
print('########## Test with toluene ##########')
x = np.asarray([1.])
m = np.asarray([2.8149])
s = np.asarray([3.7169])
e = np.asarray([285.69])
p = 100000.
t = 330.
rho = pcsaft_den(x, m, s, e, t, p, phase='liq')
d2adt_eos = pcsaft_d2adt(x, m, s, e, t, rho)
# calculating numerical derivative
rho = pcsaft_den(x, m, s, e, t - 1, p, phase='liq')
der1 = pcsaft_dadt(x, m, s, e, t - 1, rho)
rho = pcsaft_den(x, m, s, e, t + 1, p, phase='liq')
der2 = pcsaft_dadt(x, m, s, e, t + 1, rho)
d2adt_num = (der2 - der1) / 2.
print(' Numerical derivative:', d2adt_num)
print(' PC-SAFT derivative:', d2adt_eos)
print(' Relative deviation:', (d2adt_eos - d2adt_num) / d2adt_num * 100,
'%')
# Water
print('########## Test with water ##########')
m = np.asarray([1.2047])
e = np.asarray([353.95])
volAB = np.asarray([0.0451])
eAB = np.asarray([2425.67])
p = 100000.
t = 290.
s = np.asarray(
[2.7927 + 10.11 * np.exp(-0.01775 * t) - 1.417 * np.exp(-0.01146 * t)])
rho = pcsaft_den(x, m, s, e, t, p, phase='liq', e_assoc=eAB, vol_a=volAB)
d2adt_eos = pcsaft_d2adt(x, m, s, e, t, rho, e_assoc=eAB, vol_a=volAB)
# calculating numerical derivative
der1 = pcsaft_dadt(x, m, s, e, t - 1, rho, e_assoc=eAB, vol_a=volAB)
der2 = pcsaft_dadt(x, m, s, e, t + 1, rho, e_assoc=eAB, vol_a=volAB)
d2adt_num = (der2 - der1) / 2.
print(' Numerical derivative:', d2adt_num)
print(' PC-SAFT derivative:', d2adt_eos)
print(' Relative deviation:', (d2adt_eos - d2adt_num) / d2adt_num * 100,
'%')
# Butyl acetate
print('########## Test with butyl acetate ##########')
m = np.asarray([2.76462805])
s = np.asarray([4.02244938])
e = np.asarray([263.69902915])
dpm = np.asarray([1.84])
dip_num = np.asarray([4.99688339])
p = 100000.
t = 370.
rho = pcsaft_den(x, m, s, e, t, p, phase='liq', dipm=dpm, dip_num=dip_num)
d2adt_eos = pcsaft_d2adt(x, m, s, e, t, rho, dipm=dpm, dip_num=dip_num)
# calculating numerical derivative
der1 = pcsaft_dadt(x, m, s, e, t - 1, rho, dipm=dpm, dip_num=dip_num)
der2 = pcsaft_dadt(x, m, s, e, t + 1, rho, dipm=dpm, dip_num=dip_num)
d2adt_num = (der2 - der1) / 2.
print(' Numerical derivative:', d2adt_num)
print(' PC-SAFT derivative:', d2adt_eos)
print(' Relative deviation:', (d2adt_eos - d2adt_num) / d2adt_num * 100,
'%')
# Aqueous NaCl
print('########## Test with aqueous NaCl ##########')
# 0 = Na+, 1 = Cl-, 2 = H2O
x = np.asarray([0.0907304774758426, 0.0907304774758426, 0.818539045048315])
m = np.asarray([1, 1, 1.2047])
s = np.asarray([2.8232, 2.7599589, 0.])
e = np.asarray([230.00, 170.00, 353.9449])
volAB = np.asarray([0, 0, 0.0451])
eAB = np.asarray([0, 0, 2425.67])
k_ij = np.asarray([[0, 0.317, 0], [0.317, 0, -0.25], [0, -0.25, 0]])
z = np.asarray([1., -1., 0.])
t = 298.15 # K
p = 100000. # Pa
s[2] = 2.7927 + 10.11 * np.exp(-0.01775 * t) - 1.417 * np.exp(
-0.01146 * t) # temperature dependent segment diameter for water
k_ij[0, 2] = -0.007981 * t + 2.37999
k_ij[2, 0] = -0.007981 * t + 2.37999
dielc = dielc_water(t)
rho = pcsaft_den(x,
m,
s,
e,
t,
p,
phase='liq',
k_ij=k_ij,
e_assoc=eAB,
vol_a=volAB,
z=z,
dielc=dielc)
d2adt_eos = pcsaft_d2adt(x,
m,
s,
e,
t,
rho,
k_ij=k_ij,
e_assoc=eAB,
vol_a=volAB,
z=z,
dielc=dielc)
# calculating numerical derivative
der1 = pcsaft_dadt(x,
m,
s,
e,
t - 1,
rho,
k_ij=k_ij,
e_assoc=eAB,
vol_a=volAB,
z=z,
dielc=dielc)
der2 = pcsaft_dadt(x,
m,
s,
e,
t + 1,
rho,
k_ij=k_ij,
e_assoc=eAB,
vol_a=volAB,
z=z,
dielc=dielc)
d2adt_num = (der2 - der1) / 2.
print(' Numerical derivative:', d2adt_num)
print(' PC-SAFT derivative:', d2adt_eos)
print(' Relative deviation:', (d2adt_eos - d2adt_num) / d2adt_num * 100,
'%')
return None
def test_density():
"""Test the density function to see if it is working correctly."""
# Toluene
print('########## Test with toluene ##########')
x = np.asarray([1.])
m = np.asarray([2.8149])
s = np.asarray([3.7169])
e = np.asarray([285.69])
ref = 9135.590853014008 # source: reference EOS in CoolProp
calc = pcsaft_den(x, m, s, e, 320, 101325, phase='liq')
print('----- Density at 320 K and 101325 Pa -----')
print(' Reference:', ref, 'mol m^-3')
print(' PC-SAFT:', calc, 'mol m^-3')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# Water
print('\n########## Test with water ##########')
m = np.asarray([1.2047])
e = np.asarray([353.95])
volAB = np.asarray([0.0451])
eAB = np.asarray([2425.67])
ref = 55502.5970532902 # source: IAWPS95 EOS
t = 274
s = np.asarray(
[2.7927 + 10.11 * np.exp(-0.01775 * t) - 1.417 * np.exp(-0.01146 * t)])
calc = pcsaft_den(x,
m,
s,
e,
t,
101325,
phase='liq',
e_assoc=eAB,
vol_a=volAB)
print('----- Density at 274 K and 101325 Pa -----')
print(' Reference:', ref, 'mol m^-3')
print(' PC-SAFT:', calc, 'mol m^-3')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# Acetic acid
print('\n########## Test with acetic acid ##########')
m = np.asarray([1.3403])
s = np.asarray([3.8582])
e = np.asarray([211.59])
volAB = np.asarray([0.075550])
eAB = np.asarray([3044.4])
ref = 17240. # source: DIPPR correlation
calc = pcsaft_den(x,
m,
s,
e,
305,
101325,
phase='liq',
e_assoc=eAB,
vol_a=volAB)
print('----- Density at 305 K and 101325 Pa -----')
print(' Reference:', ref, 'mol m^-3')
print(' PC-SAFT:', calc, 'mol m^-3')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# Butyl acetate
print('\n########## Test with butyl acetate ##########')
m = np.asarray([3.9706])
s = np.asarray([3.5440])
e = np.asarray([241.93])
dpm = np.asarray([1.86])
dip_num = np.asarray([1.0])
ref = 8021. # source: DIPPR correlation
calc = pcsaft_den(x,
m,
s,
e,
240,
101325,
phase='liq',
dipm=dpm,
dip_num=dip_num)
print('----- Density at 240 K and 101325 Pa -----')
print(' Reference:', ref, 'mol m^-3')
print(' PC-SAFT:', calc, 'mol m^-3')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# Binary mixture: methanol-cyclohexane
print('\n########## Test with methanol-cyclohexane mixture ##########')
#0 = methanol, 1 = cyclohexane
x = np.asarray([0.0550, 0.945])
m = np.asarray([1.5255, 2.5303])
s = np.asarray([3.2300, 3.8499])
e = np.asarray([188.90, 278.11])
volAB = np.asarray([0.035176, 0.])
eAB = np.asarray([2899.5, 0.])
k_ij = np.asarray([[0, 0.051], [0.051, 0]])
ref = 9506.1 # source: J. Canosa, A. Rodríguez, and J. Tojo, “Liquid−Liquid Equilibrium and Physical Properties of the Ternary Mixture (Dimethyl Carbonate + Methanol + Cyclohexane) at 298.15 K,” J. Chem. Eng. Data, vol. 46, no. 4, pp. 846–850, Jul. 2001.
calc = pcsaft_den(x,
m,
s,
e,
298.15,
101325,
phase='liq',
k_ij=k_ij,
e_assoc=eAB,
vol_a=volAB)
print('----- Density at 298.15 K and 101325 Pa -----')
print(' Reference:', ref, 'mol m^-3')
print(' PC-SAFT:', calc, 'mol m^-3')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# NaCl in water
print('\n########## Test with aqueous NaCl ##########')
# 0 = Na+, 1 = Cl-, 2 = H2O
x = np.asarray([0.010579869455908, 0.010579869455908, 0.978840261088184])
m = np.asarray([1, 1, 1.2047])
s = np.asarray([2.8232, 2.7599589, 0.])
e = np.asarray([230.00, 170.00, 353.9449])
volAB = np.asarray([0, 0, 0.0451])
eAB = np.asarray([0, 0, 2425.67])
k_ij = np.asarray([[0, 0.317, 0], [0.317, 0, -0.25], [0, -0.25, 0]])
z = np.asarray([1., -1., 0.])
ref = 55507.23 # source: Rodriguez H.; Soto A.; Arce A.; Khoshkbarchi M.K.: Apparent Molar Volume, Isentropic Compressibility, Refractive Index, and Viscosity of DL-Alanine in Aqueous NaCl Solutions. J.Solution Chem. 32 (2003) 53-63
t = 298.15 # K
s[2] = 2.7927 + 10.11 * np.exp(-0.01775 * t) - 1.417 * np.exp(
-0.01146 * t) # temperature dependent segment diameter for water
k_ij[0, 2] = -0.007981 * t + 2.37999
k_ij[2, 0] = -0.007981 * t + 2.37999
dielc = dielc_water(t)
calc = pcsaft_den(x,
m,
s,
e,
t,
101325,
phase='liq',
k_ij=k_ij,
e_assoc=eAB,
vol_a=volAB,
z=z,
dielc=dielc)
print('----- Density at 298.15 K and 101325 Pa -----')
print(' Reference:', ref, 'mol m^-3')
print(' PC-SAFT:', calc, 'mol m^-3')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
return None
def gres(x, m, s, e, t=325, p=101325):
den = pcsaft_den(x, m, s, e, t, p, phase='liq')
calc = pcsaft_gres(x, m, s, e, t, den)
return calc
import sys
import numpy as np
import pandas as pd
from pcsaft_electrolyte import pcsaft_den, pcsaft_hres, pcsaft_gres, pcsaft_sres
def gres(x, m, s, e, t=325, p=101325):
den = pcsaft_den(x, m, s, e, t, p, phase='liq')
calc = pcsaft_gres(x, m, s, e, t, den)
return calc
if __name__ == '__main__':
# print(gres(x,m,s,e))
t = 298.15
p = 101325
df = pd.read_csv('parameters.csv', index_col='name')
data = df.loc[sys.argv[1]]
M = 200000.0 if np.isnan(data['M']) else data['M']
dens = pcsaft_den(x=np.asarray([1.0]),
m=np.asarray([M * data['m/M']]),
s=np.asarray([data['s']]),
e=np.asarray([data['e']]),
t=273.15,
p=101325,
phase='liq')
#dens mol/m3
dens *= M / 1000000
print(dens)
sys.exit()
def test_PTz():
"""Test the function for PTz data to see if it is working correctly."""
# Binary mixture: methanol-cyclohexane
print('\n########## Test with methanol-cyclohexane mixture ##########')
#0 = methanol, 1 = cyclohexane
m = np.asarray([1.5255, 2.5303])
s = np.asarray([3.2300, 3.8499])
e = np.asarray([188.90, 278.11])
volAB = np.asarray([0.035176, 0.])
eAB = np.asarray([2899.5, 0.])
k_ij = np.asarray([[0, 0.051], [0.051, 0]])
pyargs = {'e_assoc': eAB, 'vol_a': volAB, 'k_ij': k_ij}
mol = 1.
t = 327.48
p_ref = 101330 # source: Marinichev A.N.; Susarev M.P.: Investigation of Liquid-Vapor Equilibrium in the System Methanol-Cyclohexane at 35, 45 and 55°C and 760 mm Hg. J.Appl.Chem.USSR 38 (1965) 1582-1584
xl_ref = np.asarray([0.3, 0.7])
xv_ref = np.asarray([0.59400, 0.40600])
beta_ref = 0.6
xtot = (beta_ref * mol * xv_ref + (1 - beta_ref) * mol * xl_ref) / mol
rho_l = pcsaft_den(xl_ref, m, s, e, t, p_ref, pyargs, phase='liq')
rho_v = pcsaft_den(xv_ref, m, s, e, t, p_ref, pyargs, phase='vap')
vol = beta_ref * mol / rho_v + (1 - beta_ref) * mol / rho_l
result = pcsaft_PTz(p_ref, xl_ref, beta_ref, mol, vol, xtot, m, s, e, t,
pyargs)
p_calc = result[0]
xl_calc = result[1]
xv_calc = result[2]
beta_calc = result[3]
print('----- Pressure at 327.48 K -----')
print(' Reference:', p_ref, 'Pa')
print(' PC-SAFT:', p_calc, 'Pa')
print(' Relative deviation:', (p_calc - p_ref) / p_ref * 100, '%')
print('----- Liquid phase composition -----')
print(' Reference:', xl_ref)
print(' PC-SAFT:', xl_calc)
print(' Relative deviation:', (xl_calc - xl_ref) / xl_ref * 100, '%')
print('----- Vapor phase composition -----')
print(' Reference:', xv_ref)
print(' PC-SAFT:', xv_calc)
print(' Relative deviation:', (xv_calc - xv_ref) / xv_ref * 100, '%')
print('----- Beta -----')
print(' Reference:', beta_ref)
print(' PC-SAFT:', beta_calc)
print(' Relative deviation:', (beta_calc - beta_ref) / beta_ref * 100,
'%')
#
# # NaCl in water
print('\n########## Test with aqueous NaCl ##########')
# 0 = Na+, 1 = Cl-, 2 = H2O
m = np.asarray([1, 1, 1.2047])
s = np.asarray([2.8232, 2.7599589, 0.])
e = np.asarray([230.00, 170.00, 353.9449])
volAB = np.asarray([0, 0, 0.0451])
eAB = np.asarray([0, 0, 2425.67])
k_ij = np.asarray([[0, 0.317, 0], [0.317, 0, -0.25], [0, -0.25, 0]])
z = np.asarray([1., -1., 0.])
p_ref = 2393.8 # average of repeat data points from source: A. Apelblat and E. Korin, “The vapour pressures of saturated aqueous solutions of sodium chloride, sodium bromide, sodium nitrate, sodium nitrite, potassium iodate, and rubidium chloride at temperatures from 227 K to 323 K,” J. Chem. Thermodyn., vol. 30, no. 1, pp. 59–71, Jan. 1998. (Solubility calculated using equation from Yaws, Carl L.. (2008). Yaws' Handbook of Properties for Environmental and Green Engineering.)
t = 298.15 # K
s[2] = 2.7927 + 10.11 * np.exp(-0.01775 * t) - 1.417 * np.exp(
-0.01146 * t) # temperature dependent segment diameter for water
k_ij[0, 2] = -0.007981 * t + 2.37999
k_ij[2, 0] = -0.007981 * t + 2.37999
dielc = dielc_water(t)
pyargs = {
'e_assoc': eAB,
'vol_a': volAB,
'k_ij': k_ij,
'z': z,
'dielc': dielc
}
mol = 1.
xl_ref = np.asarray(
[0.0907304774758426, 0.0907304774758426, 0.818539045048315])
xv_ref = np.asarray([0., 0, 1])
beta_ref = 0.001
xtot = (beta_ref * mol * xv_ref + (1 - beta_ref) * mol * xl_ref) / mol
rho_l = pcsaft_den(xl_ref, m, s, e, t, p_ref, pyargs, phase='liq')
rho_v = pcsaft_den(xv_ref, m, s, e, t, p_ref, pyargs, phase='vap')
vol = beta_ref * mol / rho_v + (1 - beta_ref) * mol / rho_l
result = pcsaft_PTz(p_ref, xl_ref, beta_ref, mol, vol, xtot, m, s, e, t,
pyargs)
p_calc = result[0]
xl_calc = result[1]
xv_calc = result[2]
beta_calc = result[3]
print('----- Pressure at 298.15 K -----')
print(' Reference:', p_ref, 'Pa')
print(' PC-SAFT:', p_calc, 'Pa')
print(' Relative deviation:', (p_calc - p_ref) / p_ref * 100, '%')
print('----- Liquid phase composition -----')
print(' Reference:', xl_ref)
print(' PC-SAFT:', xl_calc)
print(' Relative deviation:', (xl_calc - xl_ref) / xl_ref * 100, '%')
print('----- Vapor phase composition -----')
print(' Reference:', xv_ref)
print(' PC-SAFT:', xv_calc)
print(' Relative deviation:', (xv_calc - xv_ref) / xv_ref * 100, '%')
print('----- Beta -----')
print(' Reference:', beta_ref)
print(' PC-SAFT:', beta_calc)
print(' Relative deviation:', (beta_calc - beta_ref) / beta_ref * 100,
'%')
return None
def test_dadt():
"""Test the function for the temperature derivative of the Helmholtz energy."""
print('########## Testing pcsaft_dadt ##########')
# Toluene
print('########## Test with toluene ##########')
x = np.asarray([1.])
m = np.asarray([2.8149])
s = np.asarray([3.7169])
e = np.asarray([285.69])
pyargs = {}
p = 100000.
t = 330.
rho = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
dadt_eos = pcsaft_dadt(x, m, s, e, t, rho, pyargs)
# calculating numerical derivative
der1 = pcsaft_ares(x, m, s, e, t-1, rho, pyargs)
der2 = pcsaft_ares(x, m, s, e, t+1, rho, pyargs)
dadt_num = (der2-der1)/2.
print(' Numerical derivative:', dadt_num)
print(' PC-SAFT derivative:', dadt_eos)
print(' Relative deviation:', (dadt_eos-dadt_num)/dadt_num*100, '%')
# Acetic acid
print('########## Test with acetic acid ##########')
m = np.asarray([1.3403])
s = np.asarray([3.8582])
e = np.asarray([211.59])
volAB = np.asarray([0.075550])
eAB = np.asarray([3044.4])
pyargs = {'e_assoc':eAB, 'vol_a':volAB}
p = 100000.
t = 310.
rho = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
dadt_eos = pcsaft_dadt(x, m, s, e, t, rho, pyargs)
# calculating numerical derivative
der1 = pcsaft_ares(x, m, s, e, t-1, rho, pyargs)
der2 = pcsaft_ares(x, m, s, e, t+1, rho, pyargs)
dadt_num = (der2-der1)/2.
print(' Numerical derivative:', dadt_num)
print(' PC-SAFT derivative:', dadt_eos)
print(' Relative deviation:', (dadt_eos-dadt_num)/dadt_num*100, '%')
# Water
print('########## Test with water ##########')
m = np.asarray([1.2047])
e = np.asarray([353.95])
volAB = np.asarray([0.0451])
eAB = np.asarray([2425.67])
pyargs = {'e_assoc':eAB, 'vol_a':volAB}
p = 100000.
t = 290.
s = np.asarray([2.7927 + 10.11*np.exp(-0.01775*t) - 1.417*np.exp(-0.01146*t)])
rho = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
dadt_eos = pcsaft_dadt(x, m, s, e, t, rho, pyargs)
# calculating numerical derivative
der1 = pcsaft_ares(x, m, s, e, t-1, rho, pyargs)
der2 = pcsaft_ares(x, m, s, e, t+1, rho, pyargs)
dadt_num = (der2-der1)/2.
print(' Numerical derivative:', dadt_num)
print(' PC-SAFT derivative:', dadt_eos)
print(' Relative deviation:', (dadt_eos-dadt_num)/dadt_num*100, '%')
# Dimethyl ether
print('########## Test with dimethyl ether ##########')
m = np.asarray([2.2634])
s = np.asarray([3.2723])
e = np.asarray([210.29])
dpm = np.asarray([1.3])
dip_num = np.asarray([1.0])
pyargs = {'dipm':dpm, 'dip_num':dip_num}
p = 100000.
t = 370.
rho = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
dadt_eos = pcsaft_dadt(x, m, s, e, t, rho, pyargs)
# calculating numerical derivative
der1 = pcsaft_ares(x, m, s, e, t-1, rho, pyargs)
der2 = pcsaft_ares(x, m, s, e, t+1, rho, pyargs)
dadt_num = (der2-der1)/2.
print(' Numerical derivative:', dadt_num)
print(' PC-SAFT derivative:', dadt_eos)
print(' Relative deviation:', (dadt_eos-dadt_num)/dadt_num*100, '%')
# Aqueous NaCl
print('########## Test with aqueous NaCl ##########')
# 0 = Na+, 1 = Cl-, 2 = H2O
x = np.asarray([0.0907304774758426, 0.0907304774758426, 0.818539045048315])
m = np.asarray([1, 1, 1.2047])
s = np.asarray([2.8232, 2.7599589, 0.])
e = np.asarray([230.00, 170.00, 353.9449])
volAB = np.asarray([0, 0, 0.0451])
eAB = np.asarray([0, 0, 2425.67])
k_ij = np.asarray([[0, 0.317, 0],
[0.317, 0, -0.25],
[0, -0.25, 0]])
z = np.asarray([1., -1., 0.])
t = 298.15 # K
p = 100000. # Pa
s[2] = 2.7927 + 10.11*np.exp(-0.01775*t) - 1.417*np.exp(-0.01146*t) # temperature dependent segment diameter for water
k_ij[0,2] = -0.007981*t + 2.37999
k_ij[2,0] = -0.007981*t + 2.37999
dielc = dielc_water(t)
pyargs = {'e_assoc':eAB, 'vol_a':volAB, 'k_ij':k_ij, 'z':z, 'dielc':dielc}
rho = pcsaft_den(x, m, s, e, t, p, pyargs, phase='liq')
dadt_eos = pcsaft_dadt(x, m, s, e, t, rho, pyargs)
# calculating numerical derivative
der1 = pcsaft_ares(x, m, s, e, t-1, rho, pyargs)
der2 = pcsaft_ares(x, m, s, e, t+1, rho, pyargs)
dadt_num = (der2-der1)/2.
print(' Numerical derivative:', dadt_num)
print(' PC-SAFT derivative:', dadt_eos)
print(' Relative deviation:', (dadt_eos-dadt_num)/dadt_num*100, '%')
return None
