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_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