#!/usr/bin/python3
# -*- coding: utf-8 -*-
'''Pychemqt, Chemical Engineering Process simulator
Copyright (C) 2009-2025, Juan José Gómez Romera <jjgomera@gmail.com>
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Virial equation of state implementation
:class:`lib.EoS.virial.Virial`: The main class with all integrated
functionality
Second virial coefficient correlations:
* :func:`lib.EoS.virial.B_Tsonopoulos`
* :func:`lib.EoS.virial.B_IglesiasSilva`
* :func:`lib.EoS.virial.B_Meng`
* :func:`lib.EoS.virial.B_Orbey`
* :func:`lib.EoS.virial.B_Tarakad`
Third virial coefficient correlations:
* :func:`lib.EoS.virial.C_Orbey_Vera`
* :func:`lib.EoS.virial.C_Liu_Xiang`
* :func:`lib.EoS.virial.C_Meng`
.. include:: virial.rst
'''
from numpy import exp, zeros
from numpy.lib.scimath import log
from scipy.constants import R
from numdifftools import Derivative
from lib.eos import EoS
from lib.utilities import refDoc
__doi__ = {
1:
{"autor": "Dymond, J.H., Marsh, K.N., Wilhoit, R.C., Wong, K.C., "
"Frenkel, M.",
"title": "Virial Coefficients of Pure Gases (Landolt-Börnstein - "
"Group IV Physical Chemistry 21A)",
"ref": "Springer-Verlag",
"doi": "10.1007/10693952_16"},
2:
{"autor": "Dymond, J.H., Marsh, K.N., Wilhoit, R.C., Wong, K.C., "
"Frenkel, M.",
"title": "Virial Coefficients of Mixtures "
"(Landolt-Börnstein - Group IV Physical Chemistry 21B)",
"ref": "Springer-Verlag",
"doi": "10.1007/10754889"},
3:
{"autor": "Tsonopoulos, C.",
"title": "An Empirical Correlation of Second Virial Coefficients",
"ref": "AIChE Journal 20(2) (1974) 263-272",
"doi": "10.1002/aic.690200209"},
4:
{"autor": "Orbey, H., Vera, J.H.",
"title": "Correlation for the Third Virial Coefficient Using Tc, Pc "
"and ω as Parameters",
"ref": "AIChE Journal 29(1) (1983) 107-113",
"doi": "10.1002/aic.690290115"},
5:
{"autor": "Liu, D.X., Xiang, H.W.",
"title": "Corresponding-States Correlation and Prediction of Third "
"Virial Coefficients for a Wide Range of Substances",
"ref": "Int. J. Thermophysics 24(6) (2003) 1667-1680",
"doi": "10.1023/b_ijot.0000004098.98614.38"},
6:
{"autor": "Iglesias-Silva, G.A., Hall K.R.",
"title": "An Equation for Prediction and/or Correlation of Second "
"Virial Coefficients",
"ref": "Ind. Eng. Chem. Res. 40(8) (2001) 1968-1974",
"doi": "10.1021/ie0006817"},
7:
{"autor": "Meng, L., Duan, Y.Y. Li, L.",
"title": "Correlations for Second and Third Virial Coefficients of "
"Pure Fluids",
"ref": "Fluid Phase Equilibria 226 (2004) 109-120",
"doi": "10.1016/j.fluid.2004.09.023"},
8:
{"autor": "Orbey, H.",
"title": "A Four Parameter Pitzer-Curl Type Correlation of Second "
"Virial Coefficients",
"ref": "Chemical Engineering Comm. 65(1) (1988) 1-19",
"doi": "10.1080/00986448808940239"},
9:
{"autor": "Tarakad, R.R., Danner, R.P.",
"title": "An Improved Corresponding States Method for Polar Fluids: "
"Correlation of Second Virial Coefficients",
"ref": "AIChE J. 23(5) (1977) 685-695",
"doi": "10.1002/aic.690230510"}}
# Parameters for second virial coefficient for pure compounds, ref [1]_
B_Database = {
98: [3.4162e1, -1.2087e4, -7.6702e5, -1.96e7],
630: [9.1039e1, -5.9081e4, 1.0478e7, 3.0463e9],
113: [-6.0611e3, 4.6389e6, 9.8352e8],
48: [4.8826e1, -1.5614e4, -2.757e5, -4.7684e7],
49: [5.74e1, -3.8829e4, 4.2899e5, -1.4661e9],
102: [2.8415e3, -2.8985e6, 9.583e8, -1.2515e11],
# Chlorine triluoride, pag 36
# 215: [-1.0754e3, 9.3227e5, -2.7872e8],
104: [8.1566e1, -9.7274e4, 2.7321e7, -5.332e9],
105: [1.3171e1, 5.1055e3, -2.9404e7, -5.0383e8],
208: [3.3609e1, -1.0625e4, -6.078e5, -2.22759e7],
# Inorganic fluorides pag 39-46
62: [1.5883e2, -3.0107e5, 1.8189e8, -5.6932e10],
50: [3.6507e1, -7.9791e4, 2.5927e7, -6.7852e9],
63: [1.5198e2, 2.0281e5, 8.1489e7, -1.7248e10],
# Phosphine pag 61
# Krypton pag 69
108: [9.7906e1, -6.2888e4, 1.1825e7, -1.0802e9],
46: [4.0286e1, -9.3378e3, -1.4164e6, 6.1253e7, -2.7198e9],
110: [5.6654e1, 5.4768e4, 9.4786e6, -2.992e9],
107: [1.5894e1, -9.9406e2, -1.2641e5, 2.2721e6],
47: [4.2859e1, -1.7696e4, 5.2007e5, -1.6393e8, 5.0855e9],
51: [2.4794e1, -2.3892e4, -4.9786e6, -8.2606e9],
# Xenon pag 84
636: [-3.0298e2, 1.787e5, -5.2361e7],
215: [8.526e1, -3.6077e4, -1.7214e7, 1.0634e8],
216: [2.0506e2, -2.1105e5, 3.941e7, -1.0597e10],
217: [2.7564e2, -2.5324e5, -7.489e6],
100: [-1.3094e3, 9.9093e5, -3.1965e8],
# trifluoroiodomethane pag 92
218: [8.2106e1, -3.0923e4, -5.9874e6, 9.5915e6],
220: [9.8669e1, -9.879e4, 1.5682e7, -7.9366e9],
642: [4.1796e2, -3.2472e5, 8.1294e6, 2.9564e8],
112: [-3.2242e4, 3.3904e7, -1.1904e10, 1.3609e12],
643: [4.3496e1, -2.6827e4, -3.6456e6, -2.6677e9],
222: [6.6308e2, -9.0425e5, 3.6968e8, -7.0487e10],
645: [1.5688e2, -1.0739e5, 1.2759e7, -6.5037e9],
224: [1.6048e3, -1.751e6, 6.1379e8, -8.4605e10],
115: [2.332e2, -1.9046e5, 1.9734e7, -5.576e9],
225: [4.6669e2, -4.7431e5, 1.4966e8, 2.0299e10],
116: [1.1563e3, -5.7779e5, 3.1037e5],
226: [-2.5351e4, 1.9039e7, -3.8114e9],
2: [4.4344e1, -1.6608e4, -3.543e6, 2.9832e8, 2.3448e10],
117: [2.1043e3, -3.2372e6, 1.6677e9, -3.1011e11],
118: [1.021e2, -1.6761e5, 5.4579e7, -1.6593e10],
229: [-1.9198e2, 2.1731e5, -9.2469e7],
230: [7.9255e2, -4.6603e5, -1.4163e6],
231: [2.3066e2, -2.3e5, 2.1747e7, -1.3611e10],
232: [5.1747e2, -4.6798e5, 4.726e6],
235: [1.3583e2, -9.2618e4],
236: [2.1727e3, -1.6683e6, 4.0046e8, -3.5591e10],
654: [2.8867e2, -2.1746e5],
# 1-cloro-1,2,2,2-tetrafluoroetano pag 118
# 1,1-dicloro-2,2,2-tetrafluoroetano pag 119
119: [1.3094e3, -8.7959e5],
# Pentafluroetano pag 120
# Difluromethoxy-triflurometano pag 122
65: [-7.8931e2, 5.2035e5, -1.0229e8, 1.2008e9],
239: [1.4779e2, -9.305e4, -2.3775e6],
# 1,1,1,2-tetrafluroetano pag 125
122: [2.174e2, -1.945e5],
241: [-1.3226e2, 5.4763e4, -1.875e7, -1.252e10],
# 1,1-dicloro-1-fluoroetano pag 129
479: [6.5521e2, -6.0452e5],
243: [7.0822e2, -6.8308e5, 2.0059e8, -2.8667e10],
# 2,2,2-Trifluroetanol pag 132
125: [3.6936e3, -6.0221e6, 3.2337e9, -6.6701e11],
22: [8.7776e1, -6.0061e4, 1.2857e6, -1.0861e9],
126: [-5.2377e2, 4.5869e5, -1.9557e8],
127: [9.0835e2, -1.2761e6, 5.2426e8, -1.0654e11],
245: [1.3654e3, -1.471e6, 5.0537e8, -6.9611e10],
128: [2.8626e3, -3.53e6, 1.4489e9, -2.2614e11],
129: [1.9619e2, -8.6867e4, -4.5348e7],
130: [-5.2743e4, 6.2086e7, -1.8447e10],
131: [-3.0469e3, 2.3507e6, -5.2465e8],
246: [1.08e3, -5.5106e5],
132: [-5.8568e2, 7.9066e5, -3.5796e8, 3.2306e10],
3: [1.0773e2, -8.2548e4, 5.2387e6, -1.9764e9],
133: [-7.9769e2, 5.3083e5, -1.2938e8],
134: [9.6838e3, -1.3575e7, 6.3248e9, -1.0114e12],
136: [1.187e3, -6.263e5],
138: [2.9097e3, -2.9479e6, 9.6424e8, -1.2336e11],
249: [2.5017e2, -1.0569e5, -4.9303e7],
237: [1.2333e2, -2.4851e4, -3.7728e7],
# 2,2,4,4,5,5-Hexafluro-1,3-dioxonale pag 153
671: [9.1463e2, -4.4617e5],
# Heptafluropropanes pag 153
66: [-4.9112e2, 5.4036e5, -2.1854e8, 1.9163e10],
57: [2.6664e3, -2.2784e6, 6.0977e8, -6.0081e10],
258: [-1.2251e3, 1.337e6, -5.1254e8, 5.6467e10],
23: [1.0101e2, -7.5735e4, -7.9502e6, -2.7987e9],
# 2,2-dicloropropane pag 159
484: [-3.1654e3, 2.2402e6, -4.78e8],
140: [5.1325e3, -6.4311e6, 2.6952e9, -4.2124e11],
261: [-2.3257e4, 1.5352e7, -2.6699e9],
141: [-5.6624e3, 4.3602e6, -9.3449e8],
142: [-2.7935e2, 5.7525e5, -2.8774e8],
682: [-9.2253e2, 7.2399e5, -2.5425e8],
263: [2.6714e2, -3.2743e5, 9.285e7, -3.4217e10],
264: [6.6635e2, -4.3329e5, -1.4434e7],
4: [1.0971e2, -8.4673e4, -8.1215e6, -3.4382e9],
486: [1.0121e3, -5.6471e5, 2.5578e7],
146: [5.6134e3, -8.3867e6, 4.1544e9, -7.2489e11],
145: [1.0296e4, -1.414e7, 6.4638e9, -1.0248e12],
# 2-propanethiol pag 169
147: [-1.4209e3, 1.0335e6, -2.4971e8],
# Trimetilborato pag 170
692: [4.2109e2, -4.3943e5, 1.2859e8, -3.1178e10],
693: [2.0874e3, -1.223e6, 9.7474e7],
# 1,1,1,2,2,3,3,4-octaflurobutano pag 172
# 2-clorotiophene pag 173
273: [6.2291e3, -6.1819e6, 1.9793e9, -2.2748e11],
149: [-3.0669e3, 2.2018e6, -5.088e8],
28: [1.7027e4, -1.6558e7, 5.3391e9, -5.8813e11],
151: [7.8919e2, 4.9648e5],
# 2,5-dihydrofuran pag 175
278: [-6.8713e4, 5.4024e7, -1.0864e10],
492: [3.8855e3, -2.156e6],
24: [1.8449e3, -2.4771e6, 1.1518e9, -2.4483e11, 1.6568e13],
26: [-1.2888e3, 8.6278e5, -2.07e8],
25: [-2.461e3, 1.6351e6, -3.3194e8],
27: [-1.5536, 2.6336e6, -1.6613e9, 4.2568e11, -4.187e13],
448: [-2.4919e3, 1.7921e6, -4.5499e8],
153: [-7.3871e3, 5.8855e6, -1.3266e9],
282: [-6.9621e2, 6.8028e5, -3.0414e8],
155: [-6.583e3, 5.1996e6, -1.167e9],
156: [-3.5353e3, 2.975e6, -7.697e8],
157: [-4.6773e3, 3.8319e6, -9.1872e8],
712: [1.2098e3, -8.7282e5],
284: [8.0474e2, -1.114e6, 4.4699e8, -9.9235e10],
6: [2.272e2, -2.2797e5, 2.9855e7, -1.3706e10],
5: [1.1625e2, -1.0293e5, -1.2475e7, -7.049e9],
160: [1.2021e2, 1.589e6, 1.3878e9, -3.6783e11],
161: [2.8091e3, -1.4181e6],
162: [-2.3331e3, 1.9751e6, -5.4039e8, 1.5345e10],
159: [2.6055e3, -1.431e6],
450: [2.9765e3, -1.5529e6],
294: [7.4083e3, -7.3873e6, 2.3796e9, -2.8822e11],
# Tetrametilsilane pag 193
# Dodecafluoropentano pag 195
295: [3.4839e3, -2.4252e6, 2.68e8],
# 2-metilfuran pag 196
# metiltiofenos pag 197
69: [-2.6712e3, 1.9665e6, -4.4974e8],
297: [2.1158e3, -1.1421e6],
724: [1.2261e3, -8.0976e5],
29: [1.95e4, -1.1193e7, 3.9052e9, -4.7699e11],
165: [-9.9989e3, 8.5387e6, -1.999e9],
# Cyclopentanethiol pag 202
# 2-cloro-2-metylbutane pag 203
9: [4.9697e2, -4.7244e5, 1.031e8, -2.3475e10],
7: [-2.0233e2, 1.8489e5, -1.2348e8, -2.3136e9],
8: [2.9122e2, -3.3475e5, 6.5631e7, -2.8478e10],
# butyl methyl ether pag 208
743: [2.7106e3, -1.6467e6],
# 3,3-dimetil-2-tiabutano pag 209
# 2-methyl-1-butanethiol pag 210
319: [1.0224e3, -1.5575e6, 7.5148e8, -1.8001e11],
320: [-5.0538e1, 2.2888e5, -2.1502e8],
# 2,3-bis(Trifluromethyl)-perfluorobutane pag 212
321: [-3.7991e2, 6.1865e5, -3.4962e8],
# Undecafluoro-2-(trifluoromethyl)-pentane pag 213
172: [-4.7587e2, 6.75e5, -3.9453e8],
322: [3.782e2, -4.2848e5, 7.0203e7, -3.4266e10],
40: [4.7946e2, -6.8047e5, 2.3851e8, -6.2693e10],
174: [-1.8098e3, 2.4621e6, -1.1103e9, 5.3333e10],
622: [-2.0978e4, 2.4607e7, -9.5935e9, 1.166e12],
623: [2.7217e3, -1.6134e6, -2.9073e7],
323: [7.3393e2, -4.9526e4, -3.3521e8],
38: [7.3023e1, -1.2813e5, -1.3635e7, -2.8581e10],
35: [-4.1329e3, 4.2605e6, -1.5173e9, 1.3838e11],
37: [1.3965e3, -8.6726e5],
54: [5.1719e2, -3.8352e5, -4.0872e7],
55: [7.7373e2, -5.3442e5, -4.6235e7],
52: [-7.0489e2, 7.7395e5, -3.2471e8],
53: [7.5391e2, -3.9836e5, -9.7628e7],
10: [1.4421e3, -1.9714e6, 8.1722e8, -1.589e11],
339: [1.2207e3, -6.9533e5, -7.1981e7],
# Hexamethyldisiloxane pag 230
340: [1.1512e4, -1.5192e7, 6.6591e9, -1.0255e12],
524: [2.7009e3, -1.5608e6],
343: [-1.3687e5, 1.5655e8, 4.5344e10],
# fluoro-metil benzenos pag 233
41: [1.9007e3, -2.7592e6, 1.2424e9, -2.4902e11],
344: [-2.2836e3, 2.6153e6, -9.5452e8],
348: [3.1208e3, -2.0276e6],
# 2,4-dimethylpyridine pag 238
349: [2.724e3, -1.8369e6],
# 2,6-dimethylpyridine pag 238
56: [-4.3752e2, 6.8995e5, -3.9007e8],
11: [8.7046e2, -1.3176e6, 5.6372e8, -1.4992e11],
42: [-1.0007e4, 8.9315e6, -2.2448e9],
43: [-6.3438e3, 6.3946e6, -1.8133e9],
44: [3.5344e3, -5.2399e6, 2.5224e9, -5.013e11],
45: [-3.4316e3, 3.2595e6, -9.9758e8],
83: [4.5025e3, -2.9103e6, 1.8712e8],
582: [1.5963e3, -1.0012e6, -7.3728e7],
600: [1.5335e3, -8.8627e5, -1.1686e8],
# Octamethyltrisilosane pag 247
12: [2.5227e3, -3.8225e6, 1.8393e9, -3.9652e11]}
# Parameters for second cross virial coefficient, ref [2]_
Bij_Database = {
"98-48": [3.1874e1, 8.687e3, -1.4896e6, 2.5386e7],
"98-49": [-7.2525e2, 9.6341e5, -4.5827e8, 9.1873e10, -6.7735e12],
"98-104": [1.6897e1, -8.7669e2, -4.8549e6, 1.5096e8],
# Ar-F6S, pag 23
"98-1": [3.3749e1, 8.2782e3, -7.4655e4, 7.1912e7, -5.7163e9],
"98-62": [1.7025e3, -1.8921e6, 6.9275e8, -8.4515e10],
"98-63": [-1.1969e1, 2.1313e4, -8.7141e6],
"98-212": [1.4965e1, 6.8188e3, -2.6724e6, 3.2953e8, -1.3616e10],
# Ar-Kr, pag 29
"98-46": [3.9467e1, -1.4212e4, -1.8873e5, -4.7010e7],
"98-107": [2.9286, 1.2477e4, -4.1259e6, 3.7687e8, -1.2338e10],
"98-47": [4.8775e1, -2.3064e4, 1.7036e6, -1.6031e8],
"98-115": [-7.6625e2, 9.4837e5, -3.5161e8, 3.9333e10],
"98-2": [-1.2034e1, 3.569e4, -1.7184e7, 1.9559e9, -8.5469e10],
"98-3": [9.2713e1, -5.6437e4, 7.0318e6, -9.3813e8],
"98-4": [1.3285e2, -9.7467e4, 1.5052e7, -1.8464e8],
"98-6": [-2.8383e2, 3.3643e5, -1.3313e8, 1.4337e10],
# Ar-C4H12Si, pag 49
"98-9": [9.6764e1, -5.1023e4, -3.848e6],
"48-49": [-2.4271, 2.7027e4, -1.7561e7, 1.6094e9],
"48-1": [4.4409e1, -9.8417e3, 1.7911e5, -7.7626e6],
"48-212": [3.4426e1, -5.6592e3, 7.7493e5, -4.7919e7],
"48-107": [3.3843e1, 6.4861e3, 2.5955e5, -2.4332e7],
"48-2": [2.2044e3, -1.9304e6, 5.6339e8, -5.5377e10],
"48-40": [2.4487e2, -2.4165e5, 7.124e7, -9.9105e9],
"48-12": [2.4481e2, -1.6544e5, 1.32e7],
"49-1": [2.2598e2, -1.7768e5, 4.7952e7, -4.5198e9],
"49-62": [-1.0744e2, 1.1123e5, -4.0394e7],
"49-212": [4.8515e1, -7.9326e3],
"49-46": [1.8683e1, 1.9172e4, -2.0167e7, 3.425e9, -2.1815e11],
"49-2": [1.6073e2, -1.3829e5, 3.5911e7, -4.3948e9],
"49-3": [-2.8002e3, 2.458e6, -7.2439e8, 6.8408e10],
"49-40": [-1.7625e1, -8.5149e4],
"49-38": [-1.9488e2, 3.9274e5, -2.4825e8, 3.8182e10],
# F6S-He, pag 114
# F6S-Kr, pag 115
# F6S-CF4, pag 118
# F6S-CH4, pag 121
# F6S-C4H12Si, pag 122
"1-212": [1.8618e1, -7.5727e2, 6.8549e2, -3.1665e3],
# H2-Kr, pag 125
"1-46": [2.2959e1, -2.6461e3, 4.9944e4, -4.5678e5],
"1-107": [3.5658e1, -7.4422e3, 1.4167e5, -7.5396e6],
# H2-Xe, pag 130
"1-100": [5.8322e3, -5.0461e6, 1.4589e9, -1.4108e11],
"1-218": [6.6438e1, -1.9787e4, 1.4512e6, -1.1631e8],
"1-2": [-1.0011e2, 7.6037e4, -1.2943e7],
"1-40": [7.1836e1, -2.5863e4],
"1-12": [1.0789e2, -3.2428e4],
"62-46": [2.1501e2, -2.1529e5, 7.2238e7, -9.0135e9],
"62-47": [3.6866e1, -1.014e4, -3.3711e6, 2.1458e8],
"62-2": [6.7399e1, -3.5456e4],
"62-117": [2.7643e3, -3.7597e6, 1.7211e9, -2.8931e11],
"62-3": [-2.9694e1, 2.9111e4, -1.5954e7],
"62-134": [-1.6626e3, 1.6933e6, -4.7847e8],
"62-4": [1.9447e2, -1.0179e5],
"62-322": [-8.1996e2, 7.8141e5, -2.1661e8],
"62-10": [1.6413e2, -1.0807e5],
"62-41": [5.6094e3, -8.2825e6, 4.0104e9, -6.5703e11],
"62-11": [-5.7138e2, 4.767e5, -1.2224e8],
"62-12": [1.7899e2, -1.2172e5],
"50-2": [5.4062e1, -2.1818e4, -2.1814e6],
"63-212": [3.6769e1, -8.119e3],
"63-46": [-1.4663e1, 2.5143e4, +9.6702e6],
"63-2": [-7.5406e1, 6.6052e4, -1.8725e7],
# He-Kr, pag 177
"212-108": [2.5168e1, -4.8809e2, -2.3549e5],
"212-46": [1.8417e1, 3.045e3, -7.3264e5, 3.6364e7, -6.3776e8],
"212-110": [4.4476e1, -9.8008e3, 7.9041e5],
"212-107": [1.3558e1, 2.5654e2, -2.8502e4, 2.206e5],
"212-47": [2.6501e1, -2.5239e3, -1.9725e4, -2.9539e4],
# He-Xe, pag 187
"212-218": [9.6369e1, -3.6626e4, 9.6817e6, -9.1723e8],
"212-2": [2.9872e1, -9.6196e2, -2.3581e5, 1.7281e7],
"212-4": [6.2759e1, -1.4565e4, 2.1194e6, 1.9238e8],
"212-6": [-1.2344e1, 5.8166e4, -1.3241e7],
# Kr-Ne, pag 202
# Kr-Xe, pag 204
# Kr-CH4, pag 206
"46-107": [3.2804e1, -5.4303e3, -1.2152e5, 8.2859e6],
"46-47": [3.8110e1, -1.2265e4, 6.6992e5, -3.2660e7, 1.1664e9],
"46-222": [8.1349e2, -9.0416e5, 3.2388e8, -4.0768e10],
"46-2": [2.3092e1, -1.6786e3, -3.3822e6, 7.1634e7],
"46-117": [-3.4678e2, 2.6522e5, -6.9489e7, 4.2123e9],
"46-4": [4.3087e2, -4.013e5, 1.2091e8, -1.3638e10],
"46-40": [1.307e2, -7.2389e4],
"46-38": [-2.5418e2, 2.1825e5, -5.4381e7],
"46-41": [-1.7879e2, 1.2731e5, -3.3317e7],
"46-11": [1.6425e3, -1.5234e6, 4.6319e8, -4.9785e10],
"107-47": [3.2788e1, -8.0888e3, 2.9009e5, -1.6447e7],
# Ne-Xe, pag 243
"107-2": [3.5364e1, -5.7379e3, -1.4498e5, 6.8207e6],
# Xe-C2H6, pag 255
"218-2": [8.6407e1, -5.9805e4, 1.8721e7, -5.6828e9, 5.4603e11],
"220-231": [-2.1738e1, 4.0729e4, -5.2896e7],
"112-140": [-1.6239e4, 1.2491e7, -2.5216e9],
"112-162": [-4.1677e3, 3.8019e6, -9.5242e8],
"112-40": [1.5715e3, -9.3146e5],
"222-40": [-5.7315e2, 5.2812e5, -2.1972e8],
"2-117": [-1.286e3, 8.0897e5, -1.372e8],
"2-22": [7.3929e1, -4.4007e4],
"2-3": [4.9899e1, -2.227e4, -5.8719e6],
"2-4": [1.4877e2, -8.3334e4],
"2-6": [1.2142e2, -8.589e4],
# CH4-C4H12Si, pag 296
"2-8": [-5.3644e2, 3.9304e5, -8.9133e7],
"2-9": [1.3314e2, -8.4264e4, -3.3841e6],
"2-10": [3.0763e2, -1.6881e5],
"2-11": [-1.6715e2, 1.4053e5, -5.3187e7],
"117-40": [6.4967e1, 9.8356e3, -6.7332e7],
"117-38": [9.6586e1, -4.5832e4, -3.4819e7],
"117-10": [-2.7957e2, 3.3896e5, -1.2459e8],
"3-4": [2.7832e2, -1.6449e5],
"3-6": [2.3606e2, -1.7765e5],
"3-8": [-9.987e2, 6.7418e5, -1.5158e8],
"134-40": [4.5376e2, -3.5275e5],
"134-38": [7.8868e1, -2.2292e4, -5.9299e7],
"140-40": [1.4272e3, -7.9349e5],
"4-6": [1.6045e2, -5.6412e4, -4.5336e7],
"4-10": [-4.1284e2, 3.6086e5, -1.4408e8],
"693-6": [9.3979e2, -4.8933e5],
"40-38": [1.8243e3, -9.9756e5]}
[docs]
def _B_Database(T, args):
"""Calculate second virial coefficient, its 1st and 2nd temperature
derivarives from coefficient in database
Parameters
----------
T : float
Temperature, [K]
args : list
Array with polinomial coefficient
Returns
-------
B : float
Second virial coefficient [dm³/mol]
Bt : float
T(∂B/∂T) [dm³/molK]
Btt : float
T²(∂²B/∂T²) [dm³/molK²]
"""
B = 0
Bt = 0
Btt = 0
for i, a in enumerate(args):
B += a/T**i
Bt -= a*i*T**(i-1)
Btt += a*i*(i-1)*T**(i-2)
return B/1000, Bt/1000, Btt/1000
[docs]
@refDoc(__doi__, [3])
def B_Tsonopoulos(T, Tc, Pc, w, mu=None):
r"""Calculate the 2nd virial coefficient using the Tsonopoulos correlation
.. math::
\frac{BP_c}{RT_c} = f^{(0)}+\omega f^{(1)}+f^{(2)}+f^{(3)}
.. math::
f^{(0)} = 0.1445 - \frac{0.33}{T_r} - \frac{0.1385}{T_r^2} -
\frac{0.0121}{T_r^3} - \frac{0.000607}{T_r^8}
.. math::
f^{(1)} = 0.0637 - \frac{0.331}{T_r^2} - \frac{0.423}{T_r^3} -
\frac{0.008}{T_r^8}
.. math::
f^{(2)} = \frac{a}{T_r^6}
.. math::
f^{(3)} = \frac{b}{T_r^8}
.. math::
a = -2.14e-4\mu_r-4.308e-21*\mu_r^8
.. math::
b = 0.00908+0.0006957*\mu_r
Parameters
----------
T : float
Temperature [K]
Tc : float
Critical temperature [K]
Pc : float
Critical pressure
w : float
Acentric factor [-]
mu : float, optional
dipole moment [debye]
Returns
-------
B : float
Second virial coefficient [dm³/mol]
Bt : float
T(∂B/∂T) [dm³/molK]
Btt : float
T²(∂²B/∂T²) [dm³/molK²]
Notes
-----
With the B_database this correlation is only for completeness, the a, b
correlations are general and possibly not applicable to the compounds
not availables in the B_database
Examples
--------
Selected date from Table 2, pag 74 for neon
>>> from lib.mEoS import Ne
>>> D = Ne.momentoDipolar
>>> "%0.4f" % B_Tsonopoulos(262, Ne.Tc, Ne.Pc, Ne.f_acent, D)[0]
'0.0113'
"""
Tr = T/Tc
if mu:
mur = mu**2*Pc/1.01325/Tc**2
a = -2.14e-4*mur-7.831e-21*mur**8
b = 0.00908+0.0006957*mur
else:
a, b = 0, 0
def f(T):
f0 = 0.1445-0.33/Tr-0.1385/Tr**2-0.0121/Tr**3-0.000607/Tr**8
f1 = 0.0637+0.331/Tr**2-0.423/Tr**3-0.008/Tr**8
f2 = 1/Tr**6
f3 = -1/Tr**8
f = f0 + w*f1 + a*f2 + b*f3
return f*R*Tc/Pc*1e3
B = f(T)
B1 = Derivative(f, n=1)(T)
B2 = Derivative(f, n=2)(T)
return B, B1, B2
[docs]
@refDoc(__doi__, [6])
def B_IglesiasSilva(T, Tc, Pc, Vc, w, D):
r"""Calculate the 2nd virial coefficient using the Iglesias-Silva Hall
correlation
.. math::
\frac{B}{b_o} = \left(\frac{T_B}{T}\right)^{0.2}
\left[1-\left(\frac{T_B}{T}\right)^{0.8}\right] \left[\frac{B_c}
{b_o\left(\left(T_B/T_C\right)^{0.2}-\left(T_B/T_C\right)\right)}
\right]^{\left(T_c/T\right)^n}
.. math::
\frac{B_C}{V_C} = -1.1747 - 0.3668\omega - 0.00061\mu_R
.. math::
n = 1.4187 + 1.2058\omega
.. math::
\frac{b_o}{V_C} = 0.1368 - 0.4791\omega + 13.81\left(T_B/T_C\right)^2
\exp\left(-1.95T_B/T_C\right)
.. math::
\frac{T_B}{T_C} = 2.0525 + 0.6428\exp\left(-3.6167\omega\right)
Parameters
----------
T : float
Temperature [K]
Tc : float
Critical temperature [K]
Pc : float
Critical pressure, [Pa]
Vc : float
Critical specific volume, [m³/mol]
w : float
Acentric factor [-]
D : float
dipole moment [debye]
Returns
-------
B : float
Second virial coefficient [dm³/mol]
Bt : float
T(∂B/∂T) [dm³/molK]
Btt : float
T²(∂²B/∂T²) [dm³/molK²]
Examples
--------
Selected date from Table 2, pag 74 for neon
>>> from lib.mEoS import Ne
>>> Vc = Ne.M/Ne.rhoc
>>> D = Ne.momentoDipolar.Debye
>>> "%0.4f" % B_IglesiasSilva(262, Ne.Tc, Ne.Pc, Vc, Ne.f_acent, D)[0]
'0.0102'
"""
# Reduced dipole moment
muR = D**2*Pc/101325/Tc**2
TB = Tc*(2.0525 + 0.6428*exp(-3.6167*w)) # Eq 19
n = 1.4187 + 1.2058*w # Eq 14
bo = Vc*(0.1368-0.4791*w+13.81*(TB/Tc)**2*exp(-1.95*TB/Tc)) # Eq 15
Bc = Vc*(-1.1747-0.3668*w-0.00061*muR)
def f(T):
# Eq 12
return bo*(TB/T)**.2 * (1-(TB/T)**.8) * \
(Bc/bo/((TB/Tc)**.2-TB/Tc))**((Tc/T)**n)
B = f(T)
B1 = Derivative(f, n=1)(T)
B2 = Derivative(f, n=2)(T)
return B, B1, B2
[docs]
@refDoc(__doi__, [7])
def B_Meng(T, Tc, Pc, w, D):
r"""Calculate the 2nd virial coefficient using the Meng-Duan-Li correlation
.. math::
\frac{BP_c}{RT_c} = f^{(0)}+\omega f^{(1)} + f^{(2)}
.. math::
f^{(0)} = 0.13356 - \frac{0.30252}{T_r} - \frac{0.15668}{T_r^2} -
\frac{0.00724}{T_r^3} - \frac{0.00022}{T_r^8}
.. math::
f^{(1)} = 0.17404 - \frac{0.15581}{T_r^2} + \frac{0.38183}{T_r^3} -
\frac{0.44044}{T_r^3} - \frac{0.00541}{T_r^8}
.. math::
f^{(2)} = \frac{a}{T_r^6}
.. math::
a = -3.0309e-6\mu_r^2+9.503e-11\mu_r^4-1.2469e-15\mu_r^6
Parameters
----------
T : float
Temperature [K]
Tc : float
Critical temperature [K]
Pc : float
Critical pressure
w : float
Acentric factor [-]
D : float
dipole moment [debye]
Returns
-------
B : float
Second virial coefficient [dm³/mol]
Bt : float
T(∂B/∂T) [dm³/molK]
Btt : float
T²(∂²B/∂T²) [dm³/molK²]
Examples
--------
Selected date from Table 2, pag 74 for neon
>>> from lib.mEoS import Ne
>>> D = Ne.momentoDipolar.Debye
>>> "%0.4f" % (B_Meng(262, Ne.Tc, Ne.Pc, Ne.f_acent, D)[0])
'0.0099'
"""
mur = D**2*Pc/1.01325/Tc**2
a = -3.0309e-6*mur**2 + 9.503e-11*mur**4 - 1.2469e-15*mur**6
def f(T):
Tr = T/Tc
f0 = .13356 - .30252/Tr - .15668/Tr**2 - .00724/Tr**3 - .00022/Tr**8
f1 = .17404 - .15581/Tr + .38183/Tr**2 - .44044/Tr**3 - .00541/Tr**8
f2 = 1/Tr**6
f = f0 + w*f1 + a*f2
return f*R*Tc/Pc*1e3
# There are a ampliation to associating fluid, only applicable to alcohols,
# amines and water, and with the necessity of chemical type in database
# Meng, L., Duan, Y.-Y.
# An Extended Correlation for Second Virial Coefficients of Associated and
# Quantum Fluids
# Fluid Phase Equilibria 258 (2007) 29-33
# doi: 10.1016/j.fluid.2007.05.010
B = f(T)
B1 = Derivative(f, n=1)(T)
B2 = Derivative(f, n=2)(T)
return B, B1, B2
[docs]
@refDoc(__doi__, [8])
def B_Orbey(T, Tc, Pc, w, id=None):
r"""Calculate the 2nd virial coefficient using the Orbey correlation
.. math::
\frac{BP_c}{RT_c} = f^{(0)} + \omega f^{(1)} + f^{(2)}
.. math::
f^{(0)} = 0.1479 - \frac{0.3321}{T_r} - \frac{0.02907}{T_r^2} -
\frac{0.06849}{T_r^3}
.. math::
f^{(1)} = 0.2473 - \frac{0.6092}{T_r} + \frac{1.0749}{T_r^2} -
\frac{0.7569}{T_r^3}
.. math::
f^{(2)} = \frac{a}{T_r^7}
where a is compound dependend parameters
Parameters
----------
T : float
Temperature [K]
Tc : float
Critical temperature [K]
Pc : float
Critical pressure
w : float
Acentric factor [-]
id : integer
Index of compound in database
Returns
-------
B : float
Second virial coefficient [dm³/mol]
Bt : float
T(∂B/∂T) [dm³/molK]
Btt : float
T²(∂²B/∂T²) [dm³/molK²]
Examples
--------
Using same value of Tsonopoulos correlation as reference
>>> from lib.mEoS import Ne
>>> "%0.4f" % B_Orbey(262, Ne.Tc, Ne.Pc, Ne.f_acent)[0]
'0.0104'
"""
Tr = T/Tc
par = {
100: -0.0021,
220: -0.0021,
224: -0.0060,
115: -0.0065,
225: -0.0550,
226: -0.0320,
117: -0.0350,
227: -0.0038,
118: -0.0230,
102: -0.0010,
235: -0.0030,
236: -0.0069,
119: -0.0050,
65: -0.0300,
125: -0.0730,
126: -0.0031,
128: -0.0340,
129: -0.0092,
131: -0.0140,
132: -0.0085,
133: -0.0120,
134: -0.0040,
137: -0.0015,
249: -0.0115,
138: -0.0130,
66: -0.0010,
140: -0.0230,
141: -0.0045,
142: -0.0145,
264: -0.0030,
486: -0.0054,
304: -0.0150,
305: -0.0083,
165: -0.0140,
166: -0.0080,
309: -0.0066,
7: -0.0020,
318: -0.0012,
319: -0.0077,
322: -0.0013,
174: -0.0100,
323: -0.0020,
# Methyl isobutyl ketone: -0.0210,
41: -0.0025,
45: -0.0023,
42: -0.0050,
43: -0.0055,
145: -0.0060,
147: -0.0030,
270: -0.0116,
67: -0.0046,
27: -0.0020,
25: -0.0020,
26: -0.0020,
153: -0.0130,
157: -0.0045,
155: -0.0065,
156: -0.0082,
162: -0.0005,
290: -0.0015,
294: -0.0040,
29: -0.0080,
34: -0.0018,
44: -0.0066,
71: -0.0066,
72: -0.0022,
74: -0.0022,
75: -0.0022,
76: -0.0021,
77: -0.0013,
208: -0.0090,
62: -0.0090,
63: -0.0220,
51: -0.0060}
if id and id in par:
a = par[id]
else:
a = 0
def f(T):
f0 = 0.1479 - 0.3821/Tr - 0.02907/Tr**2 - 0.06849/Tr**3
f1 = 0.2473 - 0.6092/Tr + 1.0749/Tr**2 - 0.7569/Tr**3
f2 = a/Tr**6
f = f0 + w*f1 + f2
return f*R*Tc/Pc*1e3
B = f(T)
B1 = Derivative(f, n=1)(T)
B2 = Derivative(f, n=2)(T)
return B, B1, B2
[docs]
@refDoc(__doi__, [9])
def B_Tarakad(T, Tc, Pc, id):
r"""Calculate the 2nd virial coefficient using the Tarakad-Danner
correlation
.. math::
B^o = \frac{BP_c}{RT_c} = B_{simple}^o + B_{size-shape}^o + B_{polar}^o
.. math::
B_{simple}^o = 0.1445 - \frac{0.33}{T_r} - \frac{0.1385}{T_r^2} -
\frac{0.0121}{T_r^3} - \frac{0.000607}{T_r^8}
.. math::
B_{size-shape}^o = \left(-0.00787 + \frac{0.0812}{T_R^2} -
\frac{0.0646}{T_R^3}\right)R - \left(\frac{0.00347}{T_R^2} -
\frac{0.000149}{T_R^7}\right)R^2
.. math::
B_{polar}^o = -\frac{0.028}{T_r^7}\Psi
Parameters
----------
T : float
Temperature [K]
Tc : float
Critical temperature [K]
Pc : float
Critical pressure
id : integer
Index of compound in database
Returns
-------
B : float
Second virial coefficient [dm³/mol]
Bt : float
T(∂B/∂T) [dm³/molK]
Btt : float
T²(∂²B/∂T²) [dm³/molK²]
Examples
--------
Using same value of Tsonopoulos correlation as reference
>>> from lib.mEoS import Ne
>>> "%0.4f" % B_Tarakad(262, Ne.Tc, Ne.Pc, Ne.id)[0]
'0.0117'
"""
Tr = T/Tc
par = {
65: (1.094, 0.439),
66: (1.886, 0.133),
67: (2.713, 0),
40: (3.004, 0),
41: (3.443, 0.105),
45: (3.821, 0.101),
42: (3.789, 0.229),
43: (3.897, 0.329),
44: (3.796, 0.308),
71: (4.187, 0.199),
72: (4.130, 0.049),
73: (4.285, 0),
74: (4.166, 0.066),
75: (4.100, 0.179),
76: (4.168, 0.152),
77: (4.341, 0.127),
225: (1.419, 0.867),
643: (2.319, 0.250),
218: (2.635, 0),
247: (2.176, 0.359),
245: (2.498, 0.425),
243: (2.672, 0),
235: (3.380, 0),
691: (4.443, 0),
321: (5.521, 0),
326: (6.022, 0),
320: (4.683, 0),
236: (3.150, 0),
322: (3.345, 0.04),
319: (4.658, 0.323),
642: (2.880, 0),
220: (2.569, 0.119),
216: (3.026, 0),
215: (2.810, 0),
217: (3.304, 0),
115: (1.450, 0.436),
222: (2.342, 0.050),
112: (3.178, 0),
100: (3.458, 0),
132: (2.281, 0.396),
126: (2.995, 0.151),
127: (2.851, 0.071),
479: (3.357, 0.229),
122: (2.122, 0),
658: (3.013, 0.195),
659: (3.013, 0.041),
119: (3.759, 0.061),
224: (1.180, 0.348),
246: (1.988, 0),
116: (1.046, 0.118),
133: (2.127, 0.460),
486: (2.641, 0.255),
162: (3.139, 0.157),
318: (3.547, 0.129),
337: (3.681, 0.154),
280: (2.990, 0.200),
129: (1.901, 0.422),
117: (1.536, 2.146),
134: (2.250, 2.226),
146: (2.736, 1.431),
62: (0.615, 1.220),
145: (2.726, 1.696),
159: (3.182, 1.530),
161: (3.019, 1.749),
160: (3.225, 0.611),
450: (3.151, 1.349),
174: (3.550, 0.634),
140: (2.740, 0.966),
153: (3.139, 0.557),
304: (3.627, 0.797),
305: (3.415, 0.421),
165: (3.482, 0.558),
329: (3.572, 0.925),
131: (2.360, 0.683),
141: (2.870, 0.335),
157: (3.419, 0.260),
142: (2.862, 0.630),
155: (3.348, 0.454),
166: (3.778, 0.425),
156: (3.304, 0.454),
309: (3.712, 0.386),
136: (2.372, 0.077),
269: (2.809, 0.559),
290: (3.207, 0.139),
# Methyl propyl sulfide: 3.317, 0.11,
# Methyl isopropyl sulfide: 3.236, 0,
227: (1.611, 0.197),
137: (2.341, 0.094),
# 2-methyl-2-propanethiol: 3.110, 0,
# 1-pentanethiol: 3.791, 0.097,
113: (0.650, 2.065),
125: (1.821, 3.008),
118: (1.662, 0.903),
249: (2.264, 0.552),
147: (2.736, 0.153),
138: (2.309, 0.660),
294: (3.161, 0.197),
270: (2.789, 0.452),
226: (2.306, 1.398),
108: (0.530, 0.454),
110: (1.191, 0.231),
48: (0.558, 0),
49: (0.992, 0.152),
51: (1.674, 0.512),
50: (0.638, 0.301),
102: (1.424, 0.074),
63: (0.853, 0.917),
630: (2.356, 0),
629: (3.279, 0),
237: (1.423, 0)}
if id and id in par:
R_, fi = par[id]
else:
R_, fi = 0, 0
def f(T):
Bsimple = .1445 - 0.33/Tr - .1385/Tr**2 - .0121/Tr**3 - .000607/Tr**8
Bshape = (-0.00787 + 0.0812/Tr**2 - 0.0646/Tr**3)*R_ - \
(0.00347/Tr**2-0.000149/Tr**7)*R_**2
Bpolar = -0.028/Tr**7*fi
B = Bsimple + Bshape + Bpolar
return B*R*Tc/Pc*1e3
B = f(T)
B1 = Derivative(f, n=1)(T)
B2 = Derivative(f, n=2)(T)
return B, B1, B2
[docs]
@refDoc(__doi__, [4])
def C_OrbeyVera(T, Tc, Pc, w):
r"""Calculate the third virial coefficient using the Orbey-Vera correlation
.. math::
\frac{CP_c^2}{R^2T_c^2} = f^{(0)} + f^{(1)}\omega
.. math::
f^{(0)} = 0.01407+\frac{0.02432}{T_r^{2.8}}-\frac{0.00313}{T_r^{10.5}}
.. math::
f^{(1)} = -0.02676+\frac{0.0177}{T_r^{2.8}}+\frac{0.04}{T_r^3}
-\frac{0.003}{T_r^6}-\frac{0.00228}{T_r^{10.5}}
Parameters
----------
T : float
Temperature [K]
Tc : float
Critical temperature [K]
Pc : float
Critical pressure
w : float
Acentric factor [-]
Returns
-------
C : float
Third virial coefficient [dm⁶/mol²]
C1 : float
T(∂C/∂T) [dm⁶/mol²]
C2 : float
T²(∂²C/∂T²) [dm⁶/mol²]
Examples
--------
Selected points from Table 2 of paper
>>> from lib.mEoS.Benzene import Benzene as Bz
>>> "%.1f" % (C_OrbeyVera(0.877*Bz.Tc, Bz.Tc, Bz.Pc, Bz.f_acent)[0]*1e9)
'41.7'
>>> "%.1f" % (C_OrbeyVera(1.019*Bz.Tc, Bz.Tc, Bz.Pc, Bz.f_acent)[0]*1e9)
'36.0'
"""
def f(T):
Tr = T/Tc
g0 = 0.01407+0.02432/Tr**2.8-0.00313/Tr**10.5
g1 = -0.02676+0.0177/Tr**2.8+0.04/Tr**3-0.003/Tr**6-0.00228/Tr**10.5
g = g0+w*g1
return g*R**2*Tc**2/Pc**2
C = f(T)
C1 = Derivative(f, n=1)(T)
C2 = Derivative(f, n=2)(T)
return C, C1, C2
[docs]
@refDoc(__doi__, [5])
def C_LiuXiang(T, Tc, Pc, w, Zc):
r"""Calculate the third virial coefficient using the Liu-Xiang correlation
.. math::
\frac{CP_c^2}{R^2T_c^2} = f^{(0)} + \omega f^{(1)} + \theta f^{(2)}
.. math::
\theta = \left(Z_c-0.29\right)^2
.. math::
f^{(0)} = a_{00} + \frac{a_{10}}{T_r^3} + \frac{a_20}{T_r^6} +
\frac{a_{30}}{T_r^{11}}
.. math::
f^{(1)} = a_{01} + \frac{a_{11}}{T_r^3} + \frac{a_21}{T_r^6} +
\frac{a_{31}}{T_r^{11}}
.. math::
f^{(2)} = a_{02} + \frac{a_{12}}{T_r^3} + \frac{a_22}{T_r^6} +
\frac{a_{32}}{T_r^{11}}
Parameters
----------
T : float
Temperature [K]
Tc : float
Critical temperature [K]
Pc : float
Critical pressure
w : float
Acentric factor [-]
Zc : float
Critical compresibility factor [-]
Returns
-------
C : float
Third virial coefficient [dm⁶/mol²]
C1 : float
T(∂C/∂T) [dm⁶/mol²]
C2 : float
T²(∂²C/∂T²) [dm⁶/mol²]
"""
X = (Zc-0.29)**2
def f(T):
Tr = T/Tc
g0 = 0.1623538 + 0.3087440/Tr**3 - 0.01790184/Tr**6 - 0.02789157/Tr**11
g1 = -0.5390344 + 1.783526/Tr**3 - 1.055391/Tr**6 + 0.09955867/Tr**11
g2 = 34.22804 - 74.76559/Tr**3 + 279.9220/Tr**6 - 62.85431/Tr**11
g = g0+w*g1+X*g2
return g*R**2*Tc**2/Pc**2*1e-1
C = f(T)
C1 = Derivative(f, n=1)(T)
C2 = Derivative(f, n=2)(T)
return C, C1, C2
[docs]
@refDoc(__doi__, [7])
def C_Meng(T, Tc, Pc, D, B):
r"""Calculate the 3rd virial coefficient using the Meng-Duan-Li correlation
.. math::
\frac{CP_c^2}{R^2T_c^2} = 5.476e-3 + \left(\frac{BP_c}{RT_c}-0.0936
\right)^2 \left(f^{(0)} + \mu_r^4 f^{(1)}x10^{-10}\right)
.. math::
f^{(0)} = 1094.051 - \frac{3334.145}{T_r^{0.1}} +
\frac{3389.848}{T_r^{0.2}} - \frac{1149.58}{T_r^{0.3}}
.. math::
f^{(1)} = 2.0243 - \frac{0.85902}{T_r}
Parameters
----------
T : float
Temperature [K]
Tc : float
Critical temperature [K]
Pc : float
Critical pressure
D : float
dipole moment [debye]
B : list
Second virial coefficient tuple with B, ∂B/∂T, ∂²B/∂T²
Returns
-------
C : float
Third virial coefficient [dm⁶/mol²]
C1 : float
T(∂C/∂T) [dm⁶/mol²]
C2 : float
T²(∂²C/∂T²) [dm⁶/mol²]
"""
mur = D**2*Pc/1.01325/Tc**2
def f(T, *args):
B = args[-1]*1e-3
Br = B*Pc/R/Tc
Tr = T/Tc
f0 = 1094.051 - 3334.145/Tr**0.1 + 3389.848/Tr**0.2 - 1149.58/Tr**0.3
f1 = (2.0243-0.85902/Tr)*1e-10
Cr = (5.476e-3 + (Br-0.0936)**2*(f0+mur**4*f1))
return Cr/Pc**2*R**2*Tc**2
C = f(T, B[0])
C1 = Derivative(f, n=1)(T, B[1])
C2 = Derivative(f, n=2)(T, B[2])
return C, C1, C2
[docs]
class Virial(EoS):
r"""Class to model the virial equation of state
.. math::
Z = \frac{PV}{RT} = 1 + \frac{B}{V} + \frac{C}{V^2} + \cdots
The implementation use the form truncated at third term using the virial
coefficient from database or try to predicted from reference correlations.
This equation is only appropiate for single-phase gas systems.
"""
__title__ = "Virial"
__status__ = "Virial"
METHODS_B = ["Tsonopoulos (1974)", "Iglesias-Silva (2001)", "Meng (2004)"]
METHODS_C = ["Orbey-Vera (1983)", "Liu-Xiang (2003)", "Meng (2004)"]
[docs]
def __init__(self, *args, **kwargs):
EoS.__init__(self, *args, **kwargs)
self._physics(*args)
self.x, self.xi, self.yi, self.Ki = self._Flash()
[docs]
def _Bi(self, T):
"""Second virial coefficient muxture contributions"""
B = []
Bt = []
Btt = []
for cmp in self.componente:
if cmp.id in B_Database:
if cmp.id == 1: # Hydrogen special case
if self.T < 60:
coef = [2.0375e1, -2-2113e3, -2.0892e4, -6.5299e4]
else:
coef = [1.7472e1, 1.2926e2, -2.6988e5, 8.0282e6]
elif cmp.id == 212: # Helium special case
if self.T < 35.1:
coef = [1.5943e1, -3.4601e2, -5.9545e2, 1.9929e3,
2.2269e3]
else:
coef = [9.2479, 1.0876e3, -1.088e5, 2.3869e6]
else:
coef = B_Database[cmp.id]
Bi, Bit, Bitt = _B_Database(T, coef)
else:
# Use general correlation
Bi, Bit, Bitt = B_Tsonopoulos(
T, cmp.Tc, cmp.Pc, cmp.f_acent, cmp.dipole)
B.append(Bi)
Bt.append(Bit)
Btt.append(Bitt)
return B, Bt, Btt
[docs]
def _Ci(self, T):
"""Third virial coefficient mixture contributions"""
C = []
Ct = []
Ctt = []
for comp in self.componente:
if self.kwargs.get("C", 0):
Ci, Cit, Citt = C_OrbeyVera(T, comp.Tc, comp.Pc, comp.f_acent)
else:
Ci, Cit, Citt = C_LiuXiang(
T, comp.Tc, comp.Pc, comp.f_acent, comp.Zc)
C.append(Ci)
Ct.append(Cit)
Ctt.append(Citt)
return C, Ct, Ctt
[docs]
def B(self, T):
"""Second virial coefficient calculation"""
Bi, Bit, Bitt = self._Bi(T)
B, Bt, Btt = 0, 0, 0
for i, xi in enumerate(self.fraccion):
for j, xj in enumerate(self.fraccion):
if i == j:
Bij = Bi[i]
Bijt = Bit[i]
Bijtt = Bitt[i]
elif "%i-%i" % (i, j) in Bij_Database:
id = "%i-%i" % (i, j)
coef = Bij_Database[id]
Bij, Bijt, Bijtt = _B_Database(T, coef)
elif "%i-%i" % (j, i) in Bij_Database:
id = "%i-%i" % (j, i)
coef = Bij_Database[id]
Bij, Bijt, Bijtt = _B_Database(T, coef)
else:
ci = self.componente[i]
cj = self.componente[j]
Tcij = (ci.Tc*cj.Tc)**0.5
Pcij = 4*Tcij*(ci.Zc+cj.Zc)/(ci.Vc**(1/3)+cj.Vc**(1/3))**3
wij = 0.5*(ci.f_acent+cj.f_acent)
Bij, Bijt, Bijtt = B_Tsonopoulos(self.T, Tcij, Pcij, wij)
B += xi*xj*Bij
Bt += xi*xj*Bijt
Btt += xi*xj*Bijtt
return B, Bt, Btt
[docs]
def C(self, T):
"""Third virial coefficient calculation"""
Ci, Cit, Citt = self._Ci(T)
Cij = zeros((len(Ci), len(Ci)))
Cijt = zeros((len(Ci), len(Ci)))
Cijtt = zeros((len(Ci), len(Ci)))
for i, xi in enumerate(self.fraccion):
for j, xj in enumerate(self.fraccion):
if i == j:
Cij[i, j] = Ci[i]
Cijt[i, j] = Cit[i]
Cijtt[i, j] = Citt[i]
else:
ci = self.componente[i]
cj = self.componente[j]
Tcij = (ci.Tc*cj.Tc)**0.5
Vcij = (ci.Vc**(1./3)+cj.Vc**(1./3))**3
Pcij = 4*Tcij*(ci.Zc+cj.Zc)/Vcij
wij = 0.5*(ci.f_acent+cj.f_acent)
if self.kwargs.get("C", 0):
Cij[i, j] = C_OrbeyVera(self.T, Tcij, Pcij, wij)
else:
Zcij = Pcij*Vcij/R/Tcij
Cij[i, j] = C_LiuXiang(
self.T, Tcij, Pcij, wij, Zcij)[0]
C, Ct, Ctt = 0, 0, 0
for i, xi in enumerate(self.fraccion):
for j, xj in enumerate(self.fraccion):
for k, xk in enumerate(self.fraccion):
C += xi*xj*xk*(Cij[i, j]*Cij[j, k]*Cij[j, k])**(1./3)
return C, Ct, Ctt
[docs]
def _physics(self, T, P, mezcla):
"""Properties of Gases calculation. Explanation in [1]_ section 1.4"""
B, B1, B2 = self.B(T)
C, C1, C2 = self.C(T)
self.Z = 1+B*(P/R/T)+(C-B**2)*(P/R/T)**2
V = self.Z*R*T/P
self.U_exc = -R*T*(B1/V+C1/2/V**2)
self.H_exc = R*T*((B-B1)/V+(2*C-C1)/2/V**2)
self.Cv_exc = -R*((2*B1+B2)/V+(2*C1+C2)/2/V**2)
self.Cp_exc = -R*(B2/V-((B-B1)**2-(C-C1)-C2/2)/V**2)
self.S_exc = -R*(log(P)+B1/V+(B**2-C+C1)/2/V**2)
self.A_exc = R*T*(log(P)+(B**2-C/2/V**2))
self.G_exc = R*T*(log(P)+B/V+(B**2+C)/2/V**2)
self.fug = P*exp(B/V+(C+B**2)/2/V**2)
[docs]
def _fug(self, Z, xi):
"""Calculate partial fugacities coefficieint of components, Eq 6-7.9"""
pass
_all = [Virial]
if __name__ == "__main__":
from lib.mezcla import Mezcla
mezcla = Mezcla(2, ids=[10, 38, 22, 61],
caudalUnitarioMolar=[0.3, 0.5, 0.05, 0.15])
eq = Virial(340, 1., mezcla)
print(dir(eq))
print(eq.x)
