-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathpcsaft_pure.py
More file actions
243 lines (217 loc) · 7.73 KB
/
pcsaft_pure.py
File metadata and controls
243 lines (217 loc) · 7.73 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
import torch
import numpy as np
from si_units import KELVIN, KB, ANGSTROM, NAV, PASCAL, MOL, METER, KILO, JOULE
from feos_torch import PcSaft
from .dual import Dual3
A0 = [
0.91056314451539,
0.63612814494991,
2.68613478913903,
-26.5473624914884,
97.7592087835073,
-159.591540865600,
91.2977740839123,
]
A1 = [
-0.30840169182720,
0.18605311591713,
-2.50300472586548,
21.4197936296668,
-65.2558853303492,
83.3186804808856,
-33.7469229297323,
]
A2 = [
-0.09061483509767,
0.45278428063920,
0.59627007280101,
-1.72418291311787,
-4.13021125311661,
13.7766318697211,
-8.67284703679646,
]
B0 = [
0.72409469413165,
2.23827918609380,
-4.00258494846342,
-21.00357681484648,
26.8556413626615,
206.5513384066188,
-355.60235612207947,
]
B1 = [
-0.57554980753450,
0.69950955214436,
3.89256733895307,
-17.21547164777212,
192.6722644652495,
-161.8264616487648,
-165.2076934555607,
]
B2 = [
0.09768831158356,
-0.25575749816100,
-9.15585615297321,
20.64207597439724,
-38.80443005206285,
93.6267740770146,
-29.66690558514725,
]
AD = [
[0.30435038064, 0.95346405973, -1.16100802773],
[-0.13585877707, -1.83963831920, 4.52586067320],
[1.44933285154, 2.01311801180, 0.97512223853],
[0.35569769252, -7.37249576667, -12.2810377713],
[-2.06533084541, 8.23741345333, 5.93975747420],
]
BD = [
[0.21879385627, -0.58731641193, 3.48695755800],
[-1.18964307357, 1.24891317047, -14.9159739347],
[1.16268885692, -0.50852797392, 15.3720218600],
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.0],
]
CD = [
[-0.06467735252, -0.95208758351, -0.62609792333],
[0.19758818347, 2.99242575222, 1.29246858189],
[-0.80875619458, -2.38026356489, 1.65427830900],
[0.69028490492, -0.27012609786, -3.43967436378],
]
class PcSaftPure:
def __init__(self, parameters):
self.m = parameters[:, 0]
self.sigma = parameters[:, 1]
self.epsilon_k = parameters[:, 2]
self.mu2 = (
parameters[:, 3] ** 2
/ (self.m * self.sigma**3 * self.epsilon_k)
* 1e-19
* (JOULE / KELVIN / KB)
)
self.kappa_ab = parameters[:, 4]
self.epsilon_k_ab = parameters[:, 5]
self.na = parameters[:, 6]
self.nb = parameters[:, 7]
self.parameters = parameters.detach().cpu().numpy()
def helmholtz_energy(self, temperature, density):
# temperature dependent segment diameter
d = self.sigma * (1 - 0.12 * (-3 * self.epsilon_k / temperature).exp())
eta = np.pi / 6 * self.m * density * d**3
eta2 = eta * eta
eta3 = eta2 * eta
eta_m1 = 1 / (1 - eta)
eta_m2 = eta_m1 * eta_m1
etas = [1, eta, eta2, eta3, eta2 * eta2, eta2 * eta3, eta3 * eta3]
# hard sphere
hs = self.m * density * (4 * eta - 3 * eta2) * eta_m2
# hard chain
g = (1 - eta / 2) * eta_m1 * eta_m2
hc = -density * (self.m - 1) * g.log()
# dispersion
e = self.epsilon_k / temperature
s3 = self.sigma**3
I1 = 0
I2 = 0
m1 = (self.m - 1) / self.m
m2 = (self.m - 2) / self.m
for i in range(7):
I1 = I1 + (m1 * (m2 * A2[i] + A1[i]) + A0[i]) * etas[i]
I2 = I2 + (m1 * (m2 * B2[i] + B1[i]) + B0[i]) * etas[i]
C1 = 1 / (
1
+ self.m * (8 * eta - 2 * eta2) * eta_m2 * eta_m2
+ (1 - self.m)
* (20 * eta - 27 * eta2 + 12 * eta2 * eta - 2 * eta2 * eta2)
/ ((1 - eta) * (1 - eta) * (2 - eta) * (2 - eta))
)
I = 2 * I1 + C1 * I2 * self.m * e
disp = (-np.pi * density * density * self.m**2 * e * s3) * I
# dipoles
mu2 = self.mu2 * e * s3
m = self.m.clamp(max=2)
m1 = (m - 1) / m
m2 = m1 * (m - 2) / m
J1 = 0
for i in range(5):
a = AD[i][0] + m1 * AD[i][1] + m2 * AD[i][2]
b = BD[i][0] + m1 * BD[i][1] + m2 * BD[i][2]
J1 = J1 + (a + b * e) * etas[i]
J2 = sum((CD[i][0] + m1 * CD[i][1] + m2 * CD[i][2]) * etas[i] for i in range(4))
PI_SQ_43 = 4 / 3 * np.pi**2
# mu is factored out of these expressions to deal with the case where mu=0
phi2 = -density * density * J1 / s3 * np.pi
phi3 = -density * density * density * J2 / s3 * PI_SQ_43
dipole = phi2 * phi2 * mu2 * mu2 / (phi2 - phi3 * mu2)
# association
delta_assoc = (
((self.epsilon_k_ab / temperature).exp() - 1)
* self.sigma**3
* self.kappa_ab
)
k = eta * eta_m1
delta = (1 + k * (1.5 + 0.5 * k)) * eta_m1 * delta_assoc
rhoa = self.na * density
rhob = self.nb * density
aux = 1 + (rhoa - rhob) * delta
sqrt = (aux * aux + 4 * rhob * delta).sqrt()
xa = 2 / (sqrt + 1 + (rhob - rhoa) * delta)
xb = 2 / (sqrt + 1 - (rhob - rhoa) * delta)
assoc = rhoa * (xa.log() - 0.5 * xa + 0.5) + rhob * (xb.log() - 0.5 * xb + 0.5)
return hs + hc + disp + dipole + assoc
def derivatives(self, temperature, density):
a = self.helmholtz_energy(temperature, Dual3.diff(density))
return a.re, density - a.re + density * a.v1, 1 + density * a.v2
def liquid_density(self, temperature, pressure):
density, nans = PcSaft.liquid_density(
self.parameters,
temperature.detach().cpu().numpy(),
pressure.detach().cpu().numpy(),
)
density = torch.from_numpy(density).to(self.m.device)
nans = torch.from_numpy(nans).to(self.m.device)
temperature = temperature[~nans]
pressure = pressure[~nans]
self.reduce(nans)
pressure = pressure / temperature * (PASCAL / (KB * KELVIN) * ANGSTROM**3)
_, p, dp = self.derivatives(temperature, density)
density = density - (p - pressure) / dp
return nans, density / ((KILO * MOL / METER**3) * (NAV * ANGSTROM**3))
def vapor_pressure(self, temperature):
density, nans = PcSaft.vapor_pressure(
self.parameters, temperature.detach().cpu().numpy()
)
density = torch.from_numpy(density).to(self.m.device)
nans = torch.from_numpy(nans).to(self.m.device)
temperature = temperature[~nans]
self.reduce(nans)
rho_V = density[:, 0]
rho_L = density[:, 1]
a_L = self.helmholtz_energy(temperature, rho_L) / rho_L
a_V = self.helmholtz_energy(temperature, rho_V) / rho_V
p = -(a_V - a_L + (rho_V / rho_L).log()) / (1 / rho_V - 1 / rho_L)
return nans, p * temperature * (KB * KELVIN / ANGSTROM**3 / PASCAL)
def equilibrium_liquid_density(self, temperature):
density, nans = PcSaft.vapor_pressure(
self.parameters, temperature.detach().cpu().numpy()
)
density = torch.from_numpy(density).to(self.m.device)
nans = torch.from_numpy(nans).to(self.m.device)
temperature = temperature[~nans]
self.reduce(nans)
rho_V = density[:, 0]
rho_L = density[:, 1]
a_L, p_L, dp_L = self.derivatives(temperature, rho_L)
a_L /= rho_L
a_V = self.helmholtz_energy(temperature, rho_V) / rho_V
p = -(a_V - a_L + (rho_V / rho_L).log()) / (1 / rho_V - 1 / rho_L)
liquid_density = rho_L - (p_L - p) / dp_L
return nans, liquid_density / ((KILO * MOL / METER**3) * (NAV * ANGSTROM**3))
def reduce(self, nans):
self.m = self.m[~nans]
self.sigma = self.sigma[~nans]
self.epsilon_k = self.epsilon_k[~nans]
self.mu2 = self.mu2[~nans]
self.kappa_ab = self.kappa_ab[~nans]
self.epsilon_k_ab = self.epsilon_k_ab[~nans]
self.na = self.na[~nans]
self.nb = self.nb[~nans]