Association - Dufal et al. modelΒΆ
The following figures show the checks of the results from the model of Dufal against the models implemewnted in CoolProp or calculated values from the paper of Dufal; in the case of methanol, a different EOS is implemented than in REFPROP, but that cannot explain the large deviations.
Note: There appears to be a typo in the methanol parameters as-published
[1]:
import teqp, numpy as np, matplotlib.pyplot as plt, CoolProp.CoolProp as CP
[2]:
Dufal_water = {
"nonpolar": {
"kind": "SAFT-VR-Mie",
"model": {
"coeffs": [
{
"name": "Water",
"BibTeXKey": "Dufal-2015",
"m": 1.0,
"sigma_Angstrom": 3.0555,
"epsilon_over_k": 418.00,
"lambda_r": 35.823,
"lambda_a": 6.0
}
]
}
},
"association": {
"kind": "Dufal",
"model": {
"sigma / m": [3.0555e-10],
"epsilon / J/mol": [3475.445374388054],
"lambda_r": [35.823],
"epsilon_HB / J/mol": [13303.140189045183],
"K_HB / m^3": [496.66e-30],
"kmat": [[0.0]],
"Delta_rule": "Dufal",
"molecule_sites": [["e","e","H","H"]]
}
}
}
Dufal_methanol = {
"nonpolar": {
"kind": "SAFT-VR-Mie",
"model": {
"coeffs": [
{
"name": "Methanol",
"BibTeXKey": "Dufal-2015",
"m": 1.7989,
"sigma_Angstrom": 3.1425,
"epsilon_over_k": 276.96,
"lambda_r": 16.968,
"lambda_a": 6.0
}
]
}
},
"association": {
"kind": "Dufal",
"model": {
"sigma / m": [3.1425e-10],
"epsilon / J/mol": [276.96*8.31446261815324],
"lambda_r": [16.968],
"epsilon_HB / J/mol": [2156.0*8.31446261815324],
"K_HB / m^3": [222.18e-30],
"kmat": [[0.0]],
"Delta_rule": "Dufal",
"molecule_sites": [["e","H","H"]]
}
}
}
Dufal_ammonia = {
"nonpolar": {
"kind": "SAFT-VR-Mie",
"model": {
"coeffs": [
{
"name": "Ammonia",
"BibTeXKey": "Dufal-2015",
"m": 1.0,
"sigma_Angstrom": 3.3309,
"epsilon_over_k": 323.70,
"lambda_r": 36.832,
"lambda_a": 6.0
}
]
}
},
"association": {
"kind": "Dufal",
"model": {
"sigma / m": [3.3309e-10],
"epsilon / J/mol": [323.70*8.31446261815324],
"lambda_r": [36.832],
"epsilon_HB / J/mol": [1105.0*8.31446261815324],
"K_HB / m^3": [560.73e-30],
"kmat": [[0.0]],
"Delta_rule": "Dufal",
"molecule_sites": [["e","H","H","H"]]
}
}
}
# Tabulated values from Dufal for non-bonded fraction for water from the Mie kernel (Eq. 30):
# Note the last "liquid" point in Dufal is actually for the vapor phase
TL_Dufal = [252.10,270.00,290.00,300.00,310.00,314.14,330.00,348.85,350.00,370.00,388.70,390.00,400.00,410.00,416.67,430.00,450.00,450.00,470.00,476.76,490.00,500.00,503.19,510.00,530.00,550.00,556.52,570.00,579.71,590.00,600.00,610.00,620.00]
XL_A_Dufal = [0.060,0.073,0.089,0.098,0.106,0.110,0.124,0.142,0.143,0.162,0.180,0.182,0.192,0.202,0.209,0.223,0.245,0.245,0.267,0.275,0.290,0.302,0.306,0.314,0.339,0.364,0.373,0.391,0.405,0.420,0.435,0.451,0.468]
TV_Dufal = [300.00,314.14,348.85,350.00,370.00,388.70,390.00,400.00,410.00,416.67,430.00,450.00,450.00,470.00,476.76,490.00,500.00,510.00,530.00,550.00,570.00,590.00,600.00,610.00,620.00,638.60]
XV_A_Dufal = [0.998,0.997,0.992,0.992,0.988,0.982,0.982,0.979,0.975,0.973,0.967,0.958,0.958,0.947,0.943,0.935,0.928,0.921,0.906,0.890,0.872,0.852,0.841,0.829,0.816,0.789]
[3]:
model = teqp.make_model({"kind":"genericSAFT", "model":Dufal_water})
anc = teqp.build_ancillaries(model, 676, 7000, 290)
z = np.array([1.0])
for T in np.linspace(290, 678):
rhoL, rhoV = model.pure_VLE_T(T, anc.rhoL(T), anc.rhoV(T), 10)
X_A = model.get_assoc_calcs(T, rhoL, z)['X_A']
plt.plot(T, X_A[0],'o')
X_A = model.get_assoc_calcs(T, rhoV, z)['X_A']
plt.plot(T, X_A[0],'x')
plt.plot(TL_Dufal, XL_A_Dufal)
plt.plot(TV_Dufal, XV_A_Dufal)
plt.gca().set(xlabel='$T$ / K', ylabel='$X_A$ (non-bonded site fraction)');
plt.figure()
Ts = np.linspace(290, 500)
for T in Ts:
rhoL, rhoV = model.pure_VLE_T(T, anc.rhoL(T), anc.rhoV(T), 10)
plt.plot(rhoL, T,'o')
plt.plot(rhoV, T,'x')
plt.plot(CP.PropsSI('Dmolar','T',Ts,'Q',0,'Water'), Ts)
plt.plot(CP.PropsSI('Dmolar','T',Ts,'Q',1,'Water'), Ts)
plt.title('Water')
plt.gca().set(xlabel=r'$\rho$ / mol/m$^3$', ylabel=r'$T$ / K');
[4]:
model = teqp.make_model({"kind":"genericSAFT", "model": Dufal_methanol})
anc = teqp.build_ancillaries(model, 520, 5000, 290)
z = np.array([1.0])
Ts = np.linspace(290, 500)
for T in Ts:
rhoL, rhoV = model.pure_VLE_T(T, anc.rhoL(T), anc.rhoV(T), 10)
plt.plot(rhoL, T,'ko')
plt.plot(rhoV, T,'kx')
plt.plot(CP.PropsSI('Dmolar','T',Ts,'Q',0,'Methanol'), Ts)
plt.plot(CP.PropsSI('Dmolar','T',Ts,'Q',1,'Methanol'), Ts)
plt.title('Methanol')
plt.gca().set(xlabel=r'$\rho$ / mol/m$^3$', ylabel=r'$T$ / K');
[5]:
model = teqp.make_model({"kind":"genericSAFT", "model": Dufal_ammonia})
anc = teqp.build_ancillaries(model, 520, 5000, 290)
z = np.array([1.0])
Ts = np.linspace(290, 380)
for T in Ts:
rhoL, rhoV = model.pure_VLE_T(T, anc.rhoL(T), anc.rhoV(T), 10)
plt.plot(rhoL, T,'ko')
plt.plot(rhoV, T,'kx')
plt.plot(CP.PropsSI('Dmolar','T',Ts,'Q',0,'Ammonia'), Ts)
plt.plot(CP.PropsSI('Dmolar','T',Ts,'Q',1,'Ammonia'), Ts)
plt.title('Ammonia')
plt.gca().set(xlabel=r'$\rho$ / mol/m$^3$', ylabel=r'$T$ / K');
[6]:
# ammonia+water VLE at constant temperature
ammonia = teqp.make_model({"kind":"genericSAFT", "model": Dufal_ammonia})
Dufal_ammoniawater = {
"nonpolar": {
"kind": "SAFT-VR-Mie",
"model": {
"coeffs": [
{
"name": "Ammonia",
"BibTeXKey": "Dufal-2015",
"m": 1.0,
"sigma_Angstrom": 3.3309,
"epsilon_over_k": 323.70,
"lambda_r": 36.832,
"lambda_a": 6.0
},
{
"name": "Water",
"BibTeXKey": "Dufal-2015",
"m": 1.0,
"sigma_Angstrom": 3.0555,
"epsilon_over_k": 418.00,
"lambda_r": 35.823,
"lambda_a": 6.0
}
]
}
},
"association": {
"kind": "Dufal",
"model": {
"sigma / m": [3.3309e-10, 3.0555e-10],
"epsilon / J/mol": [323.70*8.31446261815324, 3475.445374388054],
"lambda_r": [36.832, 35.823],
"epsilon_HB / J/mol": [1105.0*8.31446261815324, 13303.140189045183],
"K_HB / m^3": [560.73e-30, 496.66e-30],
"kmat": [[0.0,0.0],[0,0]],
"Delta_rule": "Dufal",
"molecule_sites": [["e","H","H","H"],["e","e","H","H"]]
}
}
}
T = 298.15
rhoL0, rhoV0 = ammonia.pure_VLE_T(T, anc.rhoL(T), anc.rhoV(T), 10)
ammoniawater = teqp.make_model({"kind":"genericSAFT", "model": Dufal_ammoniawater})
ammoniawater.trace_VLE_isotherm_binary(T, np.array([rhoL0, 0]), np.array([rhoV0, 0]))
[6]:
[{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.3009031150143573,
0.9532863025715441,
-0.026505253934592687,
0.00011053503374651266],
'dt': 1e-05,
'pL / Pa': -1348980.0114703327,
'pV / Pa': 850585.1099931961,
'rhoL / mol/m^3': [35515.45114721886, 0.0],
'rhoV / mol/m^3': [487.03357583366795, 0.0],
't': 0.0,
'xL_0 / mole frac.': 1.0,
'xV_0 / mole frac.': 1.0},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.31109872729343796,
0.9503192359545914,
-0.010532216621598695,
6.375045523910206e-05],
'dt': 4.5e-05,
'pL / Pa': 530725.4885882735,
'pV / Pa': 530725.4885943136,
'rhoL / mol/m^3': [35626.35313673362, 9.532863025498762e-06],
'rhoV / mol/m^3': [262.742533599565, 6.394949560729698e-10],
't': 1e-05,
'xL_0 / mole frac.': 0.9999999997324209,
'xV_0 / mole frac.': 0.9999999999975661},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.3110987287489849,
0.9503192354218599,
-0.010532221696140152,
6.375045478498421e-05],
'dt': 0.00020250000000000002,
'pL / Pa': 530725.4878200889,
'pV / Pa': 530725.4878138459,
'rhoL / mol/m^3': [35626.35312273521, 5.2297228631004934e-05],
'rhoV / mol/m^3': [262.74253312561655, 3.5082654315836237e-09],
't': 5.5e-05,
'xL_0 / mole frac.': 0.9999999985320634,
'xV_0 / mole frac.': 0.9999999999866476},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.3110987353738346,
0.950319233256463,
-0.010532221395738667,
6.375045275703689e-05],
'dt': 0.0009112500000000001,
'pL / Pa': 530725.4843104482,
'pV / Pa': 530725.4843017324,
'rhoL / mol/m^3': [35626.35305973835, 0.0002447368735843725],
'rhoV / mol/m^3': [262.7425309928432, 1.641773232019293e-08],
't': 0.0002575,
'xL_0 / mole frac.': 0.999999993130454,
'xV_0 / mole frac.': 0.999999999937514},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.3110987651829838,
0.9503192235059291,
-0.010532220686610062,
6.375044363083975e-05],
'dt': 0.004100625,
'pL / Pa': 530725.4684955478,
'pV / Pa': 530725.4684972229,
'rhoL / mol/m^3': [35626.352776249725, 0.001110715270445871],
'rhoV / mol/m^3': [262.74252139536407, 7.451032823686246e-08],
't': 0.00116875,
'xL_0 / mole frac.': 0.9999999688232124,
'xV_0 / mole frac.': 0.9999999997164131},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.31109889932897994,
0.9503191796398444,
-0.010532216330687407,
6.375040256373021e-05],
'dt': 0.0184528125,
'pL / Pa': 530725.397386983,
'pV / Pa': 530725.3973768814,
'rhoL / mol/m^3': [35626.35150054978, 0.005007617946395683],
'rhoV / mol/m^3': [262.74247820668023, 3.359269069501529e-07],
't': 0.005269375,
'xL_0 / mole frac.': 0.9999998594406379,
'xV_0 / mole frac.': 0.9999999987214594},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.3110995029837769,
0.9503189822425291,
-0.010532196764242713,
6.375021776229736e-05],
'dt': 0.08303765625,
'pL / Pa': 530725.0773146152,
'pV / Pa': 530725.0773356715,
'rhoL / mol/m^3': [35626.345759893484, 0.02254367776217374],
'rhoV / mol/m^3': [262.7422838578328, 1.5122994272035906e-06],
't': 0.0237221875,
'xL_0 / mole frac.': 0.9999993672193144,
'xV_0 / mole frac.': 0.9999999942441719},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.3111022194027503,
0.95031809395849,
-0.01053210870630424,
6.374938616736466e-05],
'dt': 0.373669453125,
'pL / Pa': 530723.6371623278,
'pV / Pa': 530723.6371566487,
'rhoL / mol/m^3': [35626.319926807926, 0.10145590185693522],
'rhoV / mol/m^3': [262.74140929255907, 6.805933568635144e-06],
't': 0.10675984375,
'xL_0 / mole frac.': 0.9999971522286573,
'xV_0 / mole frac.': 0.9999999740964569},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.3111144427047333,
0.9503140967646987,
-0.01053171245862241,
6.37456442239256e-05],
'dt': 1.6815125390625,
'pL / Pa': 530717.1564760655,
'pV / Pa': 530717.1564786778,
'rhoL / mol/m^3': [35626.20367512748, 0.456559997502588],
'rhoV / mol/m^3': [262.73747383929725, 3.062643269797513e-05],
't': 0.480429296875,
'xL_0 / mole frac.': 0.9999871848779961,
'xV_0 / mole frac.': 0.9999998834333425},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.3111694357864459,
0.950296111088445,
-0.010529929779497732,
6.372881021020651e-05],
'dt': 5.2777905117345005,
'pL / Pa': 530687.9960161746,
'pV / Pa': 530687.9960124324,
'rhoL / mol/m^3': [35625.680486052624, 2.054509945307028],
'rhoV / mol/m^3': [262.7197661316354, 0.0001378013783841202],
't': 2.1619418359375002,
'xL_0 / mole frac.': 0.9999423339725206,
'xV_0 / mole frac.': 0.9999994754817723},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.31134191836451947,
0.9502396771874071,
-0.010524339087906304,
6.367602326602922e-05],
'dt': 11.293354277652224,
'pL / Pa': 530596.4970624149,
'pV / Pa': 530596.49704234,
'rhoL / mol/m^3': [35624.037743711626, 7.069824808594325],
'rhoV / mol/m^3': [262.6642061245047, 0.00047400935551993517],
't': 7.439732347672001,
'xL_0 / mole frac.': 0.9998015827940515,
'xV_0 / mole frac.': 0.9999981953822065},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.31171035841668493,
0.9501190124752473,
-0.010512399750116204,
6.356332582580064e-05],
'dt': 20.219295337907475,
'pL / Pa': 530400.8483027518,
'pV / Pa': 530400.8483113195,
'rhoL / mol/m^3': [35620.51956784696, 17.800536659241242],
'rhoV / mol/m^3': [262.54541848241206, 0.0011924885519618762],
't': 18.733086625324226,
'xL_0 / mole frac.': 0.9995005225665227,
'xV_0 / mole frac.': 0.999995457992973},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.31236784535778556,
0.9499032908210953,
-0.010491103802349255,
6.336242141344015e-05],
'dt': 32.05406109192583,
'pL / Pa': 530051.0387646854,
'pV / Pa': 530051.0387380088,
'rhoL / mol/m^3': [35614.21035243601, 37.00909203195248],
'rhoV / mol/m^3': [262.33308063405644, 0.002475661269434341],
't': 38.9523819632317,
'xL_0 / mole frac.': 0.9989619123101919,
'xV_0 / mole frac.': 0.9999905629976188},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.31340453699814785,
0.9495621263658921,
-0.010457551608343767,
6.304618299002517e-05],
'dt': 46.77777988037518,
'pL / Pa': 529497.7195792794,
'pV / Pa': 529497.7196046263,
'rhoL / mol/m^3': [35604.181060955816, 67.45187959577942],
'rhoV / mol/m^3': [261.9973365749719, 0.00450160846417981],
't': 71.00644305515753,
'xL_0 / mole frac.': 0.9981090890986631,
'xV_0 / mole frac.': 0.9999828184088502},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.3149051477799579,
0.9490660650485994,
-0.010409042097751927,
6.258959691875612e-05],
'dt': 64.35837108709012,
'pL / Pa': 528692.9495015144,
'pV / Pa': 528692.949511752,
'rhoL / mol/m^3': [35589.48553843193, 111.85867700851091],
'rhoV / mol/m^3': [261.5092922019919, 0.007440067314551471],
't': 117.78422293553271,
'xL_0 / mole frac.': 0.9968668216991076,
'xV_0 / mole frac.': 0.9999715503201266},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.3169462807598973,
0.9483870887527648,
-0.010343169685654244,
6.19707783921092e-05],
'dt': 84.80807950481592,
'pL / Pa': 527590.9216072261,
'pV / Pa': 527590.9216132702,
'rhoL / mol/m^3': [35569.15292957848, 172.9171522275068],
'rhoV / mol/m^3': [260.84150827902755, 0.011448261108294243],
't': 182.14259402262283,
'xL_0 / mole frac.': 0.9951620834542673,
'xV_0 / mole frac.': 0.9999561122048983},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.3195953290461591,
0.9474986005168632,
-0.010257871538898754,
6.117151516063689e-05],
'dt': 108.2065363028577,
'pL / Pa': 526147.7891260535,
'pV / Pa': 526147.7891376888,
'rhoL / mol/m^3': [35542.16067078346, 253.31031427913294],
'rhoV / mol/m^3': [259.96795286894064, 0.016669863420093727],
't': 266.95067352743877,
'xL_0 / mole frac.': 0.9929233976447792,
'xV_0 / mole frac.': 0.999935881348501},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.3229098929901436,
0.946375266618026,
-0.010151459077644335,
6.017764829482899e-05],
'dt': 134.71777827306167,
'pL / Pa': 524321.169994995,
'pV / Pa': 524321.1700048461,
'rhoL / mol/m^3': [35507.39838710184, 355.7749759791602],
'rhoV / mol/m^3': [258.8637654924597, 0.023234992065452455],
't': 375.15720983029644,
'xL_0 / mole frac.': 0.9900796571352659,
'xV_0 / mole frac.': 0.9999102504489528},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.32693750736908667,
0.9449928092206256,
-0.010022640272707873,
5.89793414726952e-05],
'dt': 164.60568268475006,
'pL / Pa': 522069.448372066,
'pV / Pa': 522069.4483732332,
'rhoL / mol/m^3': [35463.624176795005, 483.1752282585226],
'rhoV / mol/m^3': [257.50490539395713, 0.03126079809831117],
't': 509.8749881033581,
'xL_0 / mole frac.': 0.9865586022606898,
'xV_0 / mole frac.': 0.9998786158908843},
{'T / K': 298.15,
'c': -1.0,
'drho/dt': [-0.33171556830214927,
0.9433278067268672,
-0.009870536328391875,
5.757126319217159e-05],
'dt': 198.25242509299477,
'pL / Pa': 519350.9265948534,
'pV / Pa': 519350.9266029825,
'rhoL / mol/m^3': [35409.41304487993, 638.5890166367051],
'rhoV / mol/m^3': [255.86771856214293, 0.04085241912014649],
't': 674.4806707881081,
'xL_0 / mole frac.': 0.9822850371694126,
'xV_0 / mole frac.': 0.9998403632243988},
{'T / K': 298.15,
'c': -1.0,
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