def test_osmoticC(print_result=False):
"""Test the function for calculating osmotic coefficients to see if it is working correctly."""
# NaCl in water
# 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)
pyargs = {
'x': x,
'm': m,
's': s,
'e': e,
'e_assoc': eAB,
'vol_a': volAB,
'k_ij': k_ij,
'z': z,
'dielc': dielc
}
rho = pcsaft_den(t, 2339.3, pyargs, phase='liq')
result = pcsaft_osmoticC(t, rho, pyargs)
calc = result[0]
assert abs((calc - ref) / ref * 100) < 2
if print_result:
print('\n########## Test with aqueous NaCl ##########')
print('----- Osmotic coefficient at 293.15 K -----')
print(' Reference:', ref)
print(' PC-SAFT:', calc)
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
def test_dadt(print_result=False):
"""Test the function for the temperature derivative of the Helmholtz energy."""
# Toluene
x = np.asarray([1.])
m = np.asarray([2.8149])
s = np.asarray([3.7169])
e = np.asarray([285.69])
pyargs = {'x': x, 'm': m, 's': s, 'e': e}
p = 100000.
t = 330.
rho = pcsaft_den(t, p, pyargs, phase='liq')
dadt_eos = pcsaft_dadt(t, rho, pyargs)
# calculating numerical derivative
der1 = pcsaft_ares(t - 1, rho, pyargs)
der2 = pcsaft_ares(t + 1, rho, pyargs)
dadt_num = (der2 - der1) / 2.
assert abs((dadt_eos - dadt_num) / dadt_num * 100) < 2e-2
if print_result:
print('\n########## Test with toluene ##########')
print(' Numerical derivative:', dadt_num)
print(' PC-SAFT derivative:', dadt_eos)
print(' Relative deviation:',
(dadt_eos - dadt_num) / dadt_num * 100, '%')
# 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 = {'x': x, 'm': m, 's': s, 'e': e, 'e_assoc': eAB, 'vol_a': volAB}
p = 100000.
t = 310.
rho = pcsaft_den(t, p, pyargs, phase='liq')
dadt_eos = pcsaft_dadt(t, rho, pyargs)
# calculating numerical derivative
der1 = pcsaft_ares(t - 1, rho, pyargs)
der2 = pcsaft_ares(t + 1, rho, pyargs)
dadt_num = (der2 - der1) / 2.
assert abs((dadt_eos - dadt_num) / dadt_num * 100) < 2e-2
if print_result:
print('\n########## Test with acetic acid ##########')
print(' Numerical derivative:', dadt_num)
print(' PC-SAFT derivative:', dadt_eos)
print(' Relative deviation:',
(dadt_eos - dadt_num) / dadt_num * 100, '%')
# 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)])
pyargs = {'x': x, 'm': m, 's': s, 'e': e, 'e_assoc': eAB, 'vol_a': volAB}
rho = pcsaft_den(t, p, pyargs, phase='liq')
dadt_eos = pcsaft_dadt(t, rho, pyargs)
# calculating numerical derivative
der1 = pcsaft_ares(t - 1, rho, pyargs)
der2 = pcsaft_ares(t + 1, rho, pyargs)
dadt_num = (der2 - der1) / 2.
assert abs((dadt_eos - dadt_num) / dadt_num * 100) < 2e-2
if print_result:
print('\n########## Test with water ##########')
print(' Numerical derivative:', dadt_num)
print(' PC-SAFT derivative:', dadt_eos)
print(' Relative deviation:',
(dadt_eos - dadt_num) / dadt_num * 100, '%')
# 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 = {'x': x, 'm': m, 's': s, 'e': e, 'dipm': dpm, 'dip_num': dip_num}
p = 100000.
t = 370.
rho = pcsaft_den(t, p, pyargs, phase='liq')
dadt_eos = pcsaft_dadt(t, rho, pyargs)
# calculating numerical derivative
der1 = pcsaft_ares(t - 1, rho, pyargs)
der2 = pcsaft_ares(t + 1, rho, pyargs)
dadt_num = (der2 - der1) / 2.
assert abs((dadt_eos - dadt_num) / dadt_num * 100) < 2e-2
if print_result:
print('\n########## Test with dimethyl ether ##########')
print(' Numerical derivative:', dadt_num)
print(' PC-SAFT derivative:', dadt_eos)
print(' Relative deviation:',
(dadt_eos - dadt_num) / dadt_num * 100, '%')
# 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 = {
'x': x,
'm': m,
's': s,
'e': e,
'e_assoc': eAB,
'vol_a': volAB,
'k_ij': k_ij,
'z': z,
'dielc': dielc
}
rho = pcsaft_den(t, p, pyargs, phase='liq')
dadt_eos = pcsaft_dadt(t, rho, pyargs)
# calculating numerical derivative
der1 = pcsaft_ares(t - 1, rho, pyargs)
der2 = pcsaft_ares(t + 1, rho, pyargs)
dadt_num = (der2 - der1) / 2.
assert abs((dadt_eos - dadt_num) / dadt_num * 100) < 2e-2
if print_result:
print('\n########## Test with aqueous NaCl ##########')
print(' Numerical derivative:', dadt_num)
print(' PC-SAFT derivative:', dadt_eos)
print(' Relative deviation:',
(dadt_eos - dadt_num) / dadt_num * 100, '%')
def test_flashPQ(print_result=False):
"""Test the flashPQ function to see if it is working correctly."""
# Binary mixture: methanol-cyclohexane
#0 = methanol, 1 = cyclohexane
x = np.asarray([0.3, 0.7])
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 = {
'x': x,
'm': m,
's': s,
'e': e,
'e_assoc': eAB,
'vol_a': volAB,
'k_ij': k_ij
}
p = 101330
ref = 327.48 # 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
xv_ref = np.asarray([0.59400, 0.40600])
calc, xl, xv = flashPQ(p, 0, pyargs)
assert abs((calc - ref) / ref * 100) < 1
assert np.all(abs((xv - xv_ref) / xv_ref * 100) < 10)
if print_result:
print(
'\n########## Test with methanol-cyclohexane mixture ##########')
print('----- Bubble point temperature at 101330 Pa -----')
print(' Reference:', ref, 'K')
print(' PC-SAFT:', calc, 'K')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
print(' Vapor composition (reference):', xv_ref)
print(' Vapor composition (PC-SAFT):', xv)
print(' Vapor composition relative deviation:',
(xv - xv_ref) / xv_ref * 100)
# NaCl in water
# 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.])
p = 2393.8 # Pa
ref = 298.15 # K, 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.)
s[2] = 2.7927 + 10.11 * np.exp(-0.01775 * ref) - 1.417 * np.exp(
-0.01146 * ref) # temperature dependent segment diameter for water
k_ij[0, 2] = -0.007981 * ref + 2.37999
k_ij[2, 0] = -0.007981 * ref + 2.37999
dielc = dielc_water(ref)
pyargs = {
'x': x,
'm': m,
's': s,
'e': e,
'e_assoc': eAB,
'vol_a': volAB,
'k_ij': k_ij,
'z': z,
'dielc': dielc
}
xv_guess = np.asarray([0., 0., 1.])
calc, xl, xv = flashPQ(p, 0, pyargs, ref)
assert abs((calc - ref) / ref * 100) < 1
if print_result:
print('\n########## Test with aqueous NaCl ##########')
print('----- Bubble point temperature at 2393.8 Pa -----')
print(' Reference:', ref, 'K')
print(' PC-SAFT:', calc, 'K')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
def test_flashTQ(print_result=False):
"""Test the flashTQ function to see if it is working correctly."""
# Toluene
x = np.asarray([1.])
m = np.asarray([2.8149])
s = np.asarray([3.7169])
e = np.asarray([285.69])
pyargs = {'x': x, 'm': m, 's': s, 'e': e}
ref = 3255792.76201971 # source: reference EOS in CoolProp
t = 572.6667
calc, xl, xv = flashTQ(t, 0, pyargs)
assert abs((calc - ref) / ref * 100) < 3
if print_result:
print('########## Test with toluene ##########')
print('----- Vapor pressure at 572.7 K -----')
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# Water
m = np.asarray([1.2047])
e = np.asarray([353.95])
volAB = np.asarray([0.0451])
eAB = np.asarray([2425.67])
ref = 67171.754576141 # source: IAWPS95 EOS
t = 362
s = np.asarray(
[2.7927 + 10.11 * np.exp(-0.01775 * t) - 1.417 * np.exp(-0.01146 * t)])
pyargs = {'x': x, 'm': m, 's': s, 'e': e, 'e_assoc': eAB, 'vol_a': volAB}
calc, xl, xv = flashTQ(t, 0, pyargs)
assert abs((calc - ref) / ref * 100) < 3
if print_result:
print('\n########## Test with water ##########')
print('----- Vapor pressure at 362 K -----')
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# 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 = {'x': x, 'm': m, 's': s, 'e': e, 'e_assoc': eAB, 'vol_a': volAB}
ref = 193261.515187248 # source: DIPPR correlation
t = 413.5385
calc, xl, xv = flashTQ(t, 0, pyargs)
assert abs((calc - ref) / ref * 100) < 3
if print_result:
print('\n########## Test with acetic acid ##########')
print('----- Vapor pressure at 413.5 K -----')
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# 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 = {'x': x, 'm': m, 's': s, 'e': e, 'dipm': dpm, 'dip_num': dip_num}
ref = 625100. # source: DIPPR correlation
t = 300
calc, xl, xv = flashTQ(t, 0, pyargs)
assert abs((calc - ref) / ref * 100) < 3
if print_result:
print('\n########## Test with dimethyl ether ##########')
print('----- Vapor pressure at 300 K -----')
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# Propane
x = np.asarray([1.])
m = np.asarray([2.0020])
s = np.asarray([3.6184])
e = np.asarray([208.11])
pyargs = {'x': x, 'm': m, 's': s, 'e': e}
ref = 1.7551e-4 # source: reference EOS in CoolProp
t = 85.525
calc, xl, xv = flashTQ(t, 0, pyargs)
assert abs((calc - ref) / ref * 100) < 5
if print_result:
print('########## Test with propane ##########')
print('----- Vapor pressure at {} K -----'.format(t))
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
ref = 8.3324e5 # source: reference EOS in CoolProp
t = 293
calc, xl, xv = flashTQ(t, 0, pyargs)
assert abs((calc - ref) / ref * 100) < 3
if print_result:
print('----- Vapor pressure at {} K -----'.format(t))
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
ref = 42.477e5 # source: reference EOS in CoolProp
t = 369.82
calc, xl, xv = flashTQ(t, 0, pyargs)
assert abs((calc - ref) / ref * 100) < 3
if print_result:
print('----- Vapor pressure at {} K -----'.format(t))
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# Binary mixture: methane-benzene
#0 = methane, 1 = benzene
x = np.asarray([0.0252, 0.9748])
m = np.asarray([1.0000, 2.4653])
s = np.asarray([3.7039, 3.6478])
e = np.asarray([150.03, 287.35])
k_ij = np.asarray([[0, 0.037], [0.037, 0]])
pyargs = {'x': x, 'm': m, 's': s, 'e': e, 'k_ij': k_ij}
t = 421.05
ref = 1986983.25 # source: H.-M. Lin, H. M. Sebastian, J. J. Simnick, and K.-C. Chao, “Gas-liquid equilibrium in binary mixtures of methane with N-decane, benzene, and toluene,” J. Chem. Eng. Data, vol. 24, no. 2, pp. 146–149, Apr. 1979.
xv_ref = np.asarray([0.6516, 0.3484])
calc, xl, xv = flashTQ(t, 0, pyargs)
assert abs((calc - ref) / ref * 100) < 10
assert np.all(abs((xv - xv_ref) / xv_ref * 100) < 10)
if print_result:
print('\n########## Test with methane-benzene mixture ##########')
print('----- Bubble point pressure at %s K -----' % t)
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
print(' Vapor composition (reference):', xv_ref)
print(' Vapor composition (PC-SAFT):', xv)
print(' Vapor composition relative deviation:',
(xv - xv_ref) / xv_ref * 100)
# Binary mixture: methanol-cyclohexane
#0 = methanol, 1 = cyclohexane
x = np.asarray([0.3, 0.7])
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 = {
'x': x,
'm': m,
's': s,
'e': e,
'e_assoc': eAB,
'vol_a': volAB,
'k_ij': k_ij
}
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
t = 327.48
xv_ref = np.asarray([0.59400, 0.40600])
calc, xl, xv = flashTQ(t, 0, pyargs)
assert abs((calc - ref) / ref * 100) < 10
assert np.all(abs((xv - xv_ref) / xv_ref * 100) < 10)
if print_result:
print(
'\n########## Test with methanol-cyclohexane mixture ##########')
print('----- Bubble point pressure at 327.48 K -----')
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
print(' Vapor composition (reference):', xv_ref)
print(' Vapor composition (PC-SAFT):', xv)
print(' Vapor composition relative deviation:',
(xv - xv_ref) / xv_ref * 100)
# Binary mixture: water-acetic acid
#0 = water, 1 = acetic acid
m = np.asarray([1.2047, 1.3403])
s = np.asarray([0, 3.8582])
e = np.asarray([353.95, 211.59])
volAB = np.asarray([0.0451, 0.075550])
eAB = np.asarray([2425.67, 3044.4])
k_ij = np.asarray([[0, -0.127], [-0.127, 0]])
xl = np.asarray([0.9898662364, 0.0101337636])
t = 403.574
s[0] = 3.8395 + 1.2828 * np.exp(-0.0074944 * t) - 1.3939 * np.exp(
-0.00056029 * t)
pyargs = {
'x': xl,
'm': m,
's': s,
'e': e,
'e_assoc': eAB,
'vol_a': volAB,
'k_ij': k_ij
}
ref = 273722. # source: Othmer, D. F.; Silvis, S. J.; Spiel, A. Ind. Eng. Chem., 1952, 44, 1864-72 Composition of vapors from boiling binary solutions pressure equilibrium still for studying water - acetic acid system
xv_ref = np.asarray([0.9923666645, 0.0076333355])
calc, xl, xv = flashTQ(t, 0, pyargs)
assert abs((calc - ref) / ref * 100) < 10
assert np.all(abs((xv - xv_ref) / xv_ref * 100) < 15)
if print_result:
print('\n########## Test with water-acetic acid mixture ##########')
print('----- Bubble point pressure at %s K -----' % t)
print(' Liquid composition:', xl)
print(' Reference pressure:', ref, 'Pa')
print(' PC-SAFT pressure:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
print(' Vapor composition (reference):', xv_ref)
print(' Vapor composition (PC-SAFT):', xv)
print(' Vapor composition relative deviation:',
(xv - xv_ref) / xv_ref * 100)
xl = np.asarray([0.2691800943, 0.7308199057])
t = 372.774
s[0] = 3.8395 + 1.2828 * np.exp(-0.0074944 * t) - 1.3939 * np.exp(
-0.00056029 * t)
pyargs = {
'x': xl,
'm': m,
's': s,
'e': e,
'e_assoc': eAB,
'vol_a': volAB,
'k_ij': k_ij
}
ref = 74463. # source: Freeman, J. R.; Wilson, G. M. AIChE Symp. Ser., 1985, 81, 14-25 High temperature vapor-liquid equilibrium measurements on acetic acid/water mixtures
xv_ref = np.asarray([0.3878269411, 0.6121730589])
calc, xl, xv = flashTQ(t, 0, pyargs)
assert abs((calc - ref) / ref * 100) < 10
assert np.all(abs((xv - xv_ref) / xv_ref * 100) < 15)
if print_result:
print('----- Bubble point pressure at %s K -----' % t)
print(' Liquid composition:', xl)
print(' Reference pressure:', ref, 'Pa')
print(' PC-SAFT pressure:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
print(' Vapor composition (reference):', xv_ref)
print(' Vapor composition (PC-SAFT):', xv)
print(' Vapor composition relative deviation:',
(xv - xv_ref) / xv_ref * 100)
# NaCl in water
# 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.])
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 = {
'x': x,
'm': m,
's': s,
'e': e,
'e_assoc': eAB,
'vol_a': volAB,
'k_ij': k_ij,
'z': z,
'dielc': dielc
}
xv_guess = np.asarray([0., 0., 1.])
calc, xl, xv = flashTQ(t, 0, pyargs, ref)
assert abs((calc - ref) / ref * 100) < 10
if print_result:
print('\n########## Test with aqueous NaCl ##########')
print('----- Bubble point pressure at 298.15 K -----')
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
def test_density(print_result=False):
"""Test the density function to see if it is working correctly."""
# Toluene
x = np.asarray([1.])
m = np.asarray([2.8149])
s = np.asarray([3.7169])
e = np.asarray([285.69])
pyargs = {'x': x, 'm': m, 's': s, 'e': e}
ref = 9135.590853014008 # source: reference EOS in CoolProp
calc = pcsaft_den(320, 101325, pyargs, phase='liq')
assert abs((calc - ref) / ref * 100) < 2
if print_result:
print('########## Test with toluene ##########')
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
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)])
pyargs = {'x': x, 'm': m, 's': s, 'e': e, 'e_assoc': eAB, 'vol_a': volAB}
calc = pcsaft_den(t, 101325, pyargs, phase='liq')
assert abs((calc - ref) / ref * 100) < 2
if print_result:
print('\n########## Test with water ##########')
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
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 = {'x': x, 'm': m, 's': s, 'e': e, 'e_assoc': eAB, 'vol_a': volAB}
ref = 17240. # source: DIPPR correlation
calc = pcsaft_den(305, 101325, pyargs, phase='liq')
assert abs((calc - ref) / ref * 100) < 2
if print_result:
print('\n########## Test with acetic acid ##########')
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, '%')
# 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 = {'x': x, 'm': m, 's': s, 'e': e, 'dipm': dpm, 'dip_num': dip_num}
ref = 16110. # source: DIPPR correlation
calc = pcsaft_den(240, 101325, pyargs, phase='liq')
assert abs((calc - ref) / ref * 100) < 2
if print_result:
print('\n########## Test with dimethyl ether ##########')
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
#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]])
pyargs = {
'x': x,
'm': m,
's': s,
'e': e,
'e_assoc': eAB,
'vol_a': volAB,
'k_ij': k_ij
}
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(298.15, 101325, pyargs, phase='liq')
assert abs((calc - ref) / ref * 100) < 2
if print_result:
print(
'\n########## Test with methanol-cyclohexane mixture ##########')
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
# 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)
pyargs = {
'x': x,
'm': m,
's': s,
'e': e,
'e_assoc': eAB,
'vol_a': volAB,
'k_ij': k_ij,
'z': z,
'dielc': dielc
}
calc = pcsaft_den(t, 101325, pyargs, phase='liq')
assert abs((calc - ref) / ref * 100) < 2
if print_result:
print('\n########## Test with aqueous NaCl ##########')
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, '%')
# Propane
x = np.asarray([1.])
m = np.asarray([2.0020])
s = np.asarray([3.6184])
e = np.asarray([208.11])
pyargs = {'x': x, 'm': m, 's': s, 'e': e}
t = 85.525 # K
p = 1.7551e-4 # Pa
ref = 16621.0 # source: reference EOS in CoolProp
calc = pcsaft_den(t, p, pyargs, phase='liq')
assert abs((calc - ref) / ref * 100) < 2
if print_result:
print('########## Test with propane ##########')
print('----- Density at {} K and {} Pa -----'.format(t, p))
print(' Reference:', ref, 'mol m^-3')
print(' PC-SAFT:', calc, 'mol m^-3')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
t = 85.525 # K
p = 1.39e-4 # Pa
ref = 1.9547e-7 # source: reference EOS in CoolProp
calc = pcsaft_den(t, p, pyargs, phase='vap')
assert abs((calc - ref) / ref * 100) < 2
if print_result:
print('----- Density at {} K and {} Pa -----'.format(t, p))
print(' Reference:', ref, 'mol m^-3')
print(' PC-SAFT:', calc, 'mol m^-3')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
t = 293 # K
p = 833240 # Pa
ref = 11346.0 # source: reference EOS in CoolProp
calc = pcsaft_den(t, p, pyargs, phase='liq')
assert abs((calc - ref) / ref * 100) < 2
if print_result:
print('----- Density at {} K and {} Pa -----'.format(t, p))
print(' Reference:', ref, 'mol m^-3')
print(' PC-SAFT:', calc, 'mol m^-3')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
t = 430 # K
p = 2000000 # Pa
ref = 623.59 # source: reference EOS in CoolProp
calc = pcsaft_den(t, p, pyargs, phase='liq')
assert abs((calc - ref) / ref * 100) < 2
if print_result:
print('----- Density at {} K and {} Pa -----'.format(t, p))
print(' Reference:', ref, 'mol m^-3')
print(' PC-SAFT:', calc, 'mol m^-3')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
def test_pressure(print_result=False):
"""Test the pressure function to see if it is working correctly."""
# Toluene
x = np.asarray([1.])
m = np.asarray([2.8149])
s = np.asarray([3.7169])
e = np.asarray([285.69])
pyargs = {'x': x, 'm': m, 's': s, 'e': e}
ref = 101325 # Pa
t = 320 # K
rho = 9033.11420899 # mol m^-3 From density calculation with working PC-SAFT density function
calc = pcsaft_p(t, rho, pyargs)
assert abs((calc - ref) / ref * 100) < 1e-6
if print_result:
print('\n########## Test with toluene ##########')
print('----- Pressure at {} K -----'.format(t))
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# Water
m = np.asarray([1.2047])
e = np.asarray([353.95])
volAB = np.asarray([0.0451])
eAB = np.asarray([2425.67])
ref = 101325 # Pa
t = 274 # K
s = np.asarray(
[2.7927 + 10.11 * np.exp(-0.01775 * t) - 1.417 * np.exp(-0.01146 * t)])
pyargs = {'x': x, 'm': m, 's': s, 'e': e, 'e_assoc': eAB, 'vol_a': volAB}
rho = 55476.44200944 # mol m^-3 From density calculation with working PC-SAFT density function
calc = pcsaft_p(t, rho, pyargs)
assert abs((calc - ref) / ref * 100) < 1e-6
if print_result:
print('\n########## Test with water ##########')
print('----- Pressure at {} K -----'.format(t))
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# 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 = {'x': x, 'm': m, 's': s, 'e': e, 'e_assoc': eAB, 'vol_a': volAB}
ref = 101325 # Pa
t = 305 # K
rho = 16965.43663595 # mol m^-3 From density calculation with working PC-SAFT density function
calc = pcsaft_p(t, rho, pyargs)
assert abs((calc - ref) / ref * 100) < 1e-6
if print_result:
print('\n########## Test with acetic acid ##########')
print('----- Pressure at {} K -----'.format(t))
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# 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 = {'x': x, 'm': m, 's': s, 'e': e, 'dipm': dpm, 'dip_num': dip_num}
ref = 101325 # Pa
t = 240 # K
rho = 15865.69021378 # mol m^-3 From density calculation with working PC-SAFT density function
calc = pcsaft_p(t, rho, pyargs)
assert abs((calc - ref) / ref * 100) < 1e-6
if print_result:
print('\n########## Test with dimethyl ether ##########')
print('----- Pressure at {} K -----'.format(t))
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# Binary mixture: methanol-cyclohexane
#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]])
pyargs = {
'x': x,
'm': m,
's': s,
'e': e,
'e_assoc': eAB,
'vol_a': volAB,
'k_ij': k_ij
}
ref = 101325 # Pa
t = 298.15 # K
rho = 9368.9036823 # mol m^-3 From density calculation with working PC-SAFT density function
calc = pcsaft_p(t, rho, pyargs)
assert abs((calc - ref) / ref * 100) < 1e-6
if print_result:
print(
'\n########## Test with methanol-cyclohexane mixture ##########')
print('----- Pressure at {} K -----'.format(t))
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')
# NaCl in water
# 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 = 101325 # Pa
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)
rho = 55756.67269771 # mol m^-3 From density calculation with working PC-SAFT density function
pyargs = {
'x': x,
'm': m,
's': s,
'e': e,
'e_assoc': eAB,
'vol_a': volAB,
'k_ij': k_ij,
'z': z,
'dielc': dielc
}
calc = pcsaft_p(t, rho, pyargs)
assert abs((calc - ref) / ref * 100) < 1e-6
if print_result:
print('\n########## Test with aqueous NaCl ##########')
print('----- Pressure at {} K -----'.format(t))
print(' Reference:', ref, 'Pa')
print(' PC-SAFT:', calc, 'Pa')
print(' Relative deviation:', (calc - ref) / ref * 100, '%')