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SOAIQ.lst
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SOAIQ.lst
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GAMS 44.4.0 06604687 Sep 19, 2023 WEX-WEI x86 64bit/MS Windows - 10/03/23 04:59:11 Page 1
Optimization of Binary Parameters NRTL
C o m p i l a t i o n
2
This is a GAMS-code to estimate Binary interaction parameters for VLE.
6
8 Set
9 i 'Compounds'
10 / ET 'Ethanol'
11 WA 'Water' /
13 PTexp 'Presión and Temperature'
14 / Texp 'Temperature'
15 Pexp 'Presure' /
16
17 PsPar 'Parameters of Antoine Equation'
18 / 1st
19 2nd
20 3rd
21 4th
22 5th /;
23
24 Alias (i,j,h);
25
26 Set k 'Number of experimental points';
27
28
30 Parameter Table xpx(k<,i) 'Composition of experimental Data'
31 * Liq-1 Liq-2
32 ET WA
33 1 1e-16 1.0000
34 2 0.0170 0.9830
35 3 0.0287 0.9713
36 4 0.0516 0.9484
37 5 0.0655 0.9345
38 6 0.1042 0.8958
39 7 0.1355 0.8645
40 8 0.2243 0.7757
41 9 0.3695 0.6305
42 10 0.4924 0.5076
43 11 0.6529 0.3471
44 12 1.0000 1e-16 ;
45
46 Table xpy(k,i) 'Composition of experimental Data'
47 * Vap-1 Vap-2
48 ET WA
49 1 1e-16 1.0000
50 2 0.1543 0.8457
51 3 0.2627 0.7373
52 4 0.3008 0.6992
53 5 0.3770 0.6230
54 6 0.4424 0.5576
55 7 0.4846 0.5154
56 8 0.5504 0.4496
57 9 0.6052 0.3948
58 10 0.6473 0.3527
59 11 0.7212 0.2788
60 12 1.0000 1e-16;
61
62
63
64 Table PT(k,PTexp) 'Experimental Condition'
65 * Presure(Pa) Temperature(K)
66 Pexp Texp
67 1 101.03e3 373.05
68 2 101.03e3 369.80
69 3 101.03e3 366.62
70 4 101.03e3 364.36
71 5 101.03e3 362.07
72 6 101.03e3 359.64
73 7 101.03e3 358.07
74 8 101.03e3 355.92
75 9 101.03e3 353.95
76 10 101.03e3 353.24
77 11 101.03e3 352.45
78 12 101.03e3 351.38;
79
80 Table Psat(i,PsPar) 'Parameters of Antoine Equation for compounds'
81 1st 2nd 3rd 4th 5th
82 ET 73.304 -7122.3 -7.1424 2.8853e-6 2
83 WA 73.649 -7258.2 -7.3037 4.1653e-6 2;
85
86 Positive Variable
87 P(k) 'Presure Model'
88 T(k) 'Temperature of Model'
89 Ps(k,i) 'Saturation Presure of i'
90 x(k,i) 'Liquid fraction of component i'
91 y(k,i) 'Vapor fraction of component i'
93 alpha(i,j) 'Binary interaction alpha'
95 Gex(k,i,j) 'G variable of NRTL'
96 gama(k,i) 'Gamma variable of NRTL (activity)';
97
98 Variable
99 tau(k,i,j) 'Tau variable of NRTL'
101 a(i,j) 'Binary interaction Parameter a'
102 b(i,j) 'Binary interaction Parameter b'
103 Obj 'Objective of optimization';
105 Equation
106 Ant(k,i) 'Antoine equation'
107 taue(k,i,j) 'Tau equation of NRTL'
108 Gexe(k,i,j) 'G equation of NRTL'
109 Gam(k,i) 'Gamma Equation of NRTL'
110 Eq(k,i) 'Equilibrium Equation'
111 Res1(k) 'Balance y'
112 Res2(k) 'Balance x'
113 Res3(i,j) 'alpha verification'
114 Res4(i,j) 'alpha 0'
115 Res5(i) 'Diagonal'
116 Res6(i) 'Diagonal'
117 Obje 'Objective function';
118
119
120 Ant(k,i).. log(Ps(k,i)) =e= Psat(i,'1st') + Psat(i,'2nd')/T(k) +
121 Psat(i,'3rd')*log(T(k)) + Psat(i,'4th')*(T(k) ** Psat(i,'5th'));
122
123 taue(k,i,j).. tau(k,i,j) =e= a(i,j) + b(i,j)/T(k);
124 Gexe(k,i,j).. Gex(k,i,j) =e= exp(-alpha(i,j) * tau(k,i,j));
125
126 Gam(k,i).. gama(k,i) =e= exp((sum(j, tau(k,j,i) * Gex(k,j,i) * x(k,j))/
127 sum(h, Gex(k,h,i) * x(k,h))) + sum(j, (x(k,j) * Gex(k,i,j)/
128 sum(h, Gex(k,h,j) * x(k,h))) * (tau(k,i,j) -
129 sum(h, x(k,h) * tau(k,h,j) * Gex(k,h,j)) /
130 sum(h, x(k,h) * Gex(k,h,j)))));
131
132 Eq(k,i).. P(k) * y(k,i) =e= gama(k,i) * x(k,i) * Ps(k,i);
133
134 Res1(k).. sum(i, y(k,i)) =e= 1;
135 Res2(k).. sum(i, x(k,i)) =e= 1;
136 Res3(i,j).. alpha(i,j) =e= alpha(j,i);
137 Res4(i,j).. alpha(i,i) =e= alpha(i,j);
138 Res5(i).. a(i,i) =e= 0;
139 Res6(i).. b(i,i) =e= 0;
140
141 Obje.. obj =e= sum((k,i), power(x(k,i) - xpx(k,i), 2)) +
142 sum((k,i), power(y(k,i) - xpy(k,i), 2)) +
143 sum(k, power(P(k) - PT(k,'Pexp'), 2)) +
144 sum(k, power(T(k) - PT(k,'Texp'), 2));
145
146 * Initilization parameters
147 alpha.l(i,j) = 0.2;
148
149 a.l(i,j) = 5;
150 b.l(i,j) = 1000;
151 a.l(i,i) = 0;
152 b.l(i,i) = 0;
153
154
155 P.l(k) = PT(k,'Pexp');
156 T.l(k) = PT(k,'Texp');
157 x.l(k,i) = xpx(k,i);
158 y.l(k,i) = xpy(k,i) ;
159 Ps.l(k,i) = exp(Psat(i,'1st') + Psat(i,'2nd')/T.l(k) +
160 Psat(i,'3rd')*log(T.l(k)) + Psat(i,'4th')*(T.l(k) ** Psat(i,'5th')));
161 tau.l(k,i,j) = a.l(i,j) + b.l(i,j)/T.l(k);
162 Gex.l(k,i,j) = exp(-alpha.l(i,j) * tau.l(k,i,j));
163
164 gama.l(k,i) = exp((sum(j, tau.l(k,j,i) * Gex.l(k,j,i) * x.l(k,j))/
165 sum(h, Gex.l(k,h,i) * x.l(k,h))) + sum(j, (x.l(k,j) * Gex.l(k,i,j)/
166 sum(h, Gex.l(k,h,j) * x.l(k,h))) * (tau.l(k,i,j) -
167 sum(h, x.l(k,h) * tau.l(k,h,j) * Gex.l(k,h,j)) /
168 sum(h, x.l(k,h) * Gex.l(k,h,j)))));
169
170 a.lo(i,j) = -10;
171 a.up(i,j) = 10;
172
173 b.lo(i,j) = -2500;
174 b.up(i,j) = 2500;
175
176 alpha.lo(i,j) = 0.2;
177 alpha.up(i,j) = 0.426;
178
179 Model Opti / all /;
180
181 *Options NLP = IPOPT;
182
183 solve Opti using NLP minimizing obj;
184
185 display a.l,b.l,alpha.l,obj.l;
186
187
188
COMPILATION TIME = 0.000 SECONDS 3 MB 44.4.0 06604687 WEX-WEI
GAMS 44.4.0 06604687 Sep 19, 2023 WEX-WEI x86 64bit/MS Windows - 10/03/23 04:59:11 Page 2
Optimization of Binary Parameters NRTL
Equation Listing SOLVE Opti Using NLP From line 183
---- Ant =E= Antoine equation
Ant(1,ET).. - (0.0341851008578408)*T(1) + (4.46956863505746E-6)*Ps(1,ET) =E= 73.304 ; (LHS = 73.304)
Ant(1,WA).. - (0.0356842566410299)*T(1) + (9.91080508487718E-6)*Ps(1,WA) =E= 73.649 ; (LHS = 73.649)
Ant(2,ET).. - (0.0349015995730994)*T(2) + (5.00057129021687E-6)*Ps(2,ET) =E= 73.304 ; (LHS = 73.304)
REMAINING 21 ENTRIES SKIPPED
---- taue =E= Tau equation of NRTL
taue(1,ET,ET).. (0)*T(1) + tau(1,ET,ET) - a(ET,ET) - (0.00268060581691462)*b(ET,ET) =E= 0 ; (LHS = 0)
taue(1,ET,WA).. (0.00718564754567651)*T(1) + tau(1,ET,WA) - a(ET,WA) - (0.00268060581691462)*b(ET,WA) =E= 0 ; (LHS = 0)
taue(1,WA,ET).. (0.00718564754567651)*T(1) + tau(1,WA,ET) - a(WA,ET) - (0.00268060581691462)*b(WA,ET) =E= 0 ; (LHS = 0)
REMAINING 45 ENTRIES SKIPPED
---- Gexe =E= G equation of NRTL
Gexe(1,ET,ET).. (0)*alpha(ET,ET) + Gex(1,ET,ET) + (0.2)*tau(1,ET,ET) =E= 0 ; (LHS = 0)
Gexe(1,ET,WA).. (1.65297593949965)*alpha(ET,WA) + Gex(1,ET,WA) + (0.0430428531004517)*tau(1,ET,WA) =E= 0 ; (LHS = 0)
Gexe(1,WA,ET).. (1.65297593949965)*alpha(WA,ET) + Gex(1,WA,ET) + (0.0430428531004517)*tau(1,WA,ET) =E= 0 ; (LHS = 0)
REMAINING 45 ENTRIES SKIPPED
---- Gam =E= Gamma Equation of NRTL
Gam(1,ET).. (815427.089145807)*x(1,ET) - (9.10048354675632E-11)*x(1,WA) + (8.07379039696102E-11)*Gex(1,ET,ET) - (86879.7435050578)*Gex(1,ET,WA) - (4.28696341396686E-10)*Gex(1,WA,ET) + (18697.7601854656)*Gex(1,WA,WA) + gama(1,ET) - (1.05119187072204E-11)*tau(1,ET,ET) - (2434.41215851599)*tau(1,ET,WA) - (11311.5743179694)*tau(1,WA,ET) + (2434.41215851599)*tau(1,WA,WA) =E= 0 ; (LHS = 0)
Gam(1,WA).. - (7.105427357601E-15)*x(1,ET) + (8.13512808509168E-31)*x(1,WA) - (3.56881817243384E-31)*Gex(1,ET,ET) + (0)*Gex(1,ET,WA) + (2.1316282072803E-30)*Gex(1,WA,ET) + (2.46519032881566E-32)*Gex(1,WA,WA) + gama(1,WA) + (4.64653213236697E-32)*tau(1,ET,ET) + (0)*tau(1,ET,WA) - (5.55111512312578E-32)*tau(1,WA,ET) - (1)*tau(1,WA,WA) =E= 0 ; (LHS = 0)
Gam(2,ET).. (221089.919469868)*x(2,ET) - (3823.528617485)*x(2,WA) + (3712.97339633673)*Gex(2,ET,ET) - (28599.0448914503)*Gex(2,ET,WA) - (17333.930700392)*Gex(2,WA,ET) + (6125.99038717708)*Gex(2,WA,WA) + gama(2,ET) - (541.880202098566)*tau(2,ET,ET) - (801.066188470352)*tau(2,ET,WA) - (3225.63742442107)*tau(2,WA,ET) + (801.066188470352)*tau(2,WA,WA) =E= 0 ; (LHS = 0)
REMAINING 21 ENTRIES SKIPPED
---- Eq =E= Equilibrium Equation
Eq(1,ET).. (1E-16)*P(1) - (1.13115743179694E-12)*Ps(1,ET) - (2530797766.30927)*x(1,ET) + (101030)*y(1,ET) - (2.23735237480506E-11)*gama(1,ET) =E= 0 ; (LHS = -2.53069673630927E-7, INFES = 2.53069673630927E-7 ****)
Eq(1,WA).. (1)*P(1) - (1)*Ps(1,WA) - (100899.976483837)*x(1,WA) + (101030)*y(1,WA) - (100899.976483837)*gama(1,WA) =E= 0 ; (LHS = 130.023516162939, INFES = 130.023516162939 ****)
Eq(2,ET).. (0.1543)*P(2) - (64.0477996508338)*Ps(2,ET) - (753417441.301239)*x(2,ET) + (101030)*y(2,ET) - (3399.61156703412)*gama(2,ET) =E= 0 ; (LHS = -12792507.5731211, INFES = 12792507.5731211 ****)
REMAINING 21 ENTRIES SKIPPED
---- Res1 =E= Balance y
Res1(1).. y(1,ET) + y(1,WA) =E= 1 ; (LHS = 1)
Res1(2).. y(2,ET) + y(2,WA) =E= 1 ; (LHS = 1)
Res1(3).. y(3,ET) + y(3,WA) =E= 1 ; (LHS = 1)
REMAINING 9 ENTRIES SKIPPED
---- Res2 =E= Balance x
Res2(1).. x(1,ET) + x(1,WA) =E= 1 ; (LHS = 1)
Res2(2).. x(2,ET) + x(2,WA) =E= 1 ; (LHS = 1)
Res2(3).. x(3,ET) + x(3,WA) =E= 1 ; (LHS = 1)
REMAINING 9 ENTRIES SKIPPED
---- Res3 =E= alpha verification
Res3(ET,WA).. alpha(ET,WA) - alpha(WA,ET) =E= 0 ; (LHS = 0)
Res3(WA,ET).. - alpha(ET,WA) + alpha(WA,ET) =E= 0 ; (LHS = 0)
---- Res4 =E= alpha 0
Res4(ET,WA).. alpha(ET,ET) - alpha(ET,WA) =E= 0 ; (LHS = 0)
Res4(WA,ET).. - alpha(WA,ET) + alpha(WA,WA) =E= 0 ; (LHS = 0)
---- Res5 =E= Diagonal
Res5(ET).. a(ET,ET) =E= 0 ; (LHS = 0)
Res5(WA).. a(WA,WA) =E= 0 ; (LHS = 0)
---- Res6 =E= Diagonal
Res6(ET).. b(ET,ET) =E= 0 ; (LHS = 0)
Res6(WA).. b(WA,WA) =E= 0 ; (LHS = 0)
---- Obje =E= Objective function
Obje.. (0)*P(1) + (0)*P(2) + (0)*P(3) + (0)*P(4) + (0)*P(5) + (0)*P(6) + (0)*P(7) + (0)*P(8) + (0)*P(9) + (0)*P(10) + (0)*P(11) + (0)*P(12) + (0)*T(1) + (0)*T(2) + (0)*T(3) + (0)*T(4) + (0)*T(5) + (0)*T(6) + (0)*T(7) + (0)*T(8) + (0)*T(9) + (0)*T(10) + (0)*T(11) + (0)*T(12) + (0)*x(1,ET) + (0)*x(1,WA) + (0)*x(2,ET) + (0)*x(2,WA) + (0)*x(3,ET) + (0)*x(3,WA) + (0)*x(4,ET) + (0)*x(4,WA) + (0)*x(5,ET) + (0)*x(5,WA) + (0)*x(6,ET) + (0)*x(6,WA) + (0)*x(7,ET) + (0)*x(7,WA) + (0)*x(8,ET) + (0)*x(8,WA) + (0)*x(9,ET) + (0)*x(9,WA) + (0)*x(10,ET) + (0)*x(10,WA) + (0)*x(11,ET) + (0)*x(11,WA) + (0)*x(12,ET) + (0)*x(12,WA) + (0)*y(1,ET) + (0)*y(1,WA) + (0)*y(2,ET) + (0)*y(2,WA) + (0)*y(3,ET) + (0)*y(3,WA) + (0)*y(4,ET) + (0)*y(4,WA) + (0)*y(5,ET) + (0)*y(5,WA) + (0)*y(6,ET) + (0)*y(6,WA) + (0)*y(7,ET) + (0)*y(7,WA) + (0)*y(8,ET) + (0)*y(8,WA) + (0)*y(9,ET) + (0)*y(9,WA) + (0)*y(10,ET) + (0)*y(10,WA) + (0)*y(11,ET) + (0)*y(11,WA) + (0)*y(12,ET) + (0)*y(12,WA) + Obj =E= 0 ; (LHS = 0)
GAMS 44.4.0 06604687 Sep 19, 2023 WEX-WEI x86 64bit/MS Windows - 10/03/23 04:59:11 Page 3
Optimization of Binary Parameters NRTL
Column Listing SOLVE Opti Using NLP From line 183
---- P Presure Model
P(1)
(.LO, .L, .UP, .M = 0, 101030, +INF, 0)
(1.000000E-16) Eq(1,ET)
(1) Eq(1,WA)
(0) Obje
P(2)
(.LO, .L, .UP, .M = 0, 101030, +INF, 0)
(0.1543) Eq(2,ET)
(0.8457) Eq(2,WA)
(0) Obje
P(3)
(.LO, .L, .UP, .M = 0, 101030, +INF, 0)
(0.2627) Eq(3,ET)
(0.7373) Eq(3,WA)
(0) Obje
REMAINING 9 ENTRIES SKIPPED
---- T Temperature of Model
T(1)
(.LO, .L, .UP, .M = 0, 373.05, +INF, 0)
(-0.0342) Ant(1,ET)
(-0.0357) Ant(1,WA)
(0) taue(1,ET,ET)
(0.0072) taue(1,ET,WA)
(0.0072) taue(1,WA,ET)
(0) taue(1,WA,WA)
(0) Obje
T(2)
(.LO, .L, .UP, .M = 0, 369.8, +INF, 0)
(-0.0349) Ant(2,ET)
(-0.0364) Ant(2,WA)
(0) taue(2,ET,ET)
(0.0073) taue(2,ET,WA)
(0.0073) taue(2,WA,ET)
(0) taue(2,WA,WA)
(0) Obje
T(3)
(.LO, .L, .UP, .M = 0, 366.62, +INF, 0)
(-0.0356) Ant(3,ET)
(-0.0371) Ant(3,WA)
(0) taue(3,ET,ET)
(0.0074) taue(3,ET,WA)
(0.0074) taue(3,WA,ET)
(0) taue(3,WA,WA)
(0) Obje
REMAINING 9 ENTRIES SKIPPED
---- Ps Saturation Presure of i
Ps(1,ET)
(.LO, .L, .UP, .M = 0, 223735.237480506, +INF, 0)
(4.4695686E-6) Ant(1,ET)
(-1.13116E-12) Eq(1,ET)
Ps(1,WA)
(.LO, .L, .UP, .M = 0, 100899.976483837, +INF, 0)
(9.9108051E-6) Ant(1,WA)
(-1) Eq(1,WA)
Ps(2,ET)
(.LO, .L, .UP, .M = 0, 199977.151002007, +INF, 0)
(5.0005713E-6) Ant(2,ET)
(-64.0478) Eq(2,ET)
REMAINING 21 ENTRIES SKIPPED
---- x Liquid fraction of component i
x(1,ET)
(.LO, .L, .UP, .M = 0, 1E-16, +INF, 0)
(815427.0891) Gam(1,ET)
(-7.10543E-15) Gam(1,WA)
(-2.530798E+9) Eq(1,ET)
1 Res2(1)
(0) Obje
x(1,WA)
(.LO, .L, .UP, .M = 0, 1, +INF, 0)
(-9.10048E-11) Gam(1,ET)
(8.135128E-31) Gam(1,WA)
(-100899.9765) Eq(1,WA)
1 Res2(1)
(0) Obje
x(2,ET)
(.LO, .L, .UP, .M = 0, 0.017, +INF, 0)
(221089.9195) Gam(2,ET)
(-1.0244) Gam(2,WA)
(-7.534174E+8) Eq(2,ET)
1 Res2(2)
(0) Obje
REMAINING 21 ENTRIES SKIPPED
---- y Vapor fraction of component i
y(1,ET)
(.LO, .L, .UP, .M = 0, 1E-16, +INF, 0)
(101030) Eq(1,ET)
1 Res1(1)
(0) Obje
y(1,WA)
(.LO, .L, .UP, .M = 0, 1, +INF, 0)
(101030) Eq(1,WA)
1 Res1(1)
(0) Obje
y(2,ET)
(.LO, .L, .UP, .M = 0, 0.1543, +INF, 0)
(101030) Eq(2,ET)
1 Res1(2)
(0) Obje
REMAINING 21 ENTRIES SKIPPED
---- alpha Binary interaction alpha
alpha(ET,ET)
(.LO, .L, .UP, .M = 0.2, 0.2, 0.426, 0)
(0) Gexe(1,ET,ET)
(0) Gexe(2,ET,ET)
(0) Gexe(3,ET,ET)
(0) Gexe(4,ET,ET)
(0) Gexe(5,ET,ET)
(0) Gexe(6,ET,ET)
(0) Gexe(7,ET,ET)
(0) Gexe(8,ET,ET)
(0) Gexe(9,ET,ET)
(0) Gexe(10,ET,ET)
(0) Gexe(11,ET,ET)
(0) Gexe(12,ET,ET)
1 Res4(ET,WA)
alpha(ET,WA)
(.LO, .L, .UP, .M = 0.2, 0.2, 0.426, 0)
(1.653) Gexe(1,ET,WA)
(1.6503) Gexe(2,ET,WA)
(1.6475) Gexe(3,ET,WA)
(1.6456) Gexe(4,ET,WA)
(1.6435) Gexe(5,ET,WA)
(1.6413) Gexe(6,ET,WA)
(1.6399) Gexe(7,ET,WA)
(1.6379) Gexe(8,ET,WA)
(1.6361) Gexe(9,ET,WA)
(1.6354) Gexe(10,ET,WA)
(1.6347) Gexe(11,ET,WA)
(1.6336) Gexe(12,ET,WA)
1 Res3(ET,WA)
-1 Res3(WA,ET)
-1 Res4(ET,WA)
alpha(WA,ET)
(.LO, .L, .UP, .M = 0.2, 0.2, 0.426, 0)
(1.653) Gexe(1,WA,ET)
(1.6503) Gexe(2,WA,ET)
(1.6475) Gexe(3,WA,ET)
(1.6456) Gexe(4,WA,ET)
(1.6435) Gexe(5,WA,ET)
(1.6413) Gexe(6,WA,ET)
(1.6399) Gexe(7,WA,ET)
(1.6379) Gexe(8,WA,ET)
(1.6361) Gexe(9,WA,ET)
(1.6354) Gexe(10,WA,ET)
(1.6347) Gexe(11,WA,ET)
(1.6336) Gexe(12,WA,ET)
-1 Res3(ET,WA)
1 Res3(WA,ET)
-1 Res4(WA,ET)
REMAINING ENTRY SKIPPED
---- Gex G variable of NRTL
Gex(1,ET,ET)
(.LO, .L, .UP, .M = 0, 1, +INF, 0)
1 Gexe(1,ET,ET)
(8.073790E-11) Gam(1,ET)
(-3.56882E-31) Gam(1,WA)
Gex(1,ET,WA)
(.LO, .L, .UP, .M = 0, 0.215214265502258, +INF, 0)
1 Gexe(1,ET,WA)
(-86879.7435) Gam(1,ET)
(0) Gam(1,WA)
Gex(1,WA,ET)
(.LO, .L, .UP, .M = 0, 0.215214265502258, +INF, 0)
1 Gexe(1,WA,ET)
(-4.28696E-10) Gam(1,ET)
(2.131628E-30) Gam(1,WA)
REMAINING 45 ENTRIES SKIPPED
---- gama Gamma variable of NRTL (activity)
gama(1,ET)
(.LO, .L, .UP, .M = 0, 11311.5743179694, +INF, 0)
1 Gam(1,ET)
(-2.23735E-11) Eq(1,ET)
gama(1,WA)
(.LO, .L, .UP, .M = 0, 1, +INF, 0)
1 Gam(1,WA)
(-100899.9765) Eq(1,WA)
gama(2,ET)
(.LO, .L, .UP, .M = 0, 3767.51762651963, +INF, 0)
1 Gam(2,ET)
(-3399.6116) Eq(2,ET)
REMAINING 21 ENTRIES SKIPPED
---- tau Tau variable of NRTL
tau(1,ET,ET)
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
1 taue(1,ET,ET)
(0.2) Gexe(1,ET,ET)
(-1.05119E-11) Gam(1,ET)
(4.646532E-32) Gam(1,WA)
tau(1,ET,WA)
(.LO, .L, .UP, .M = -INF, 7.68060581691462, +INF, 0)
1 taue(1,ET,WA)
(0.043) Gexe(1,ET,WA)
(-2434.4122) Gam(1,ET)
(0) Gam(1,WA)
tau(1,WA,ET)
(.LO, .L, .UP, .M = -INF, 7.68060581691462, +INF, 0)
1 taue(1,WA,ET)
(0.043) Gexe(1,WA,ET)
(-11311.5743) Gam(1,ET)
(-5.55112E-32) Gam(1,WA)
REMAINING 45 ENTRIES SKIPPED
---- a Binary interaction Parameter a
a(ET,ET)
(.LO, .L, .UP, .M = -10, 0, 10, 0)
-1 taue(1,ET,ET)
-1 taue(2,ET,ET)
-1 taue(3,ET,ET)
-1 taue(4,ET,ET)
-1 taue(5,ET,ET)
-1 taue(6,ET,ET)
-1 taue(7,ET,ET)
-1 taue(8,ET,ET)
-1 taue(9,ET,ET)
-1 taue(10,ET,ET)
-1 taue(11,ET,ET)
-1 taue(12,ET,ET)
1 Res5(ET)
a(ET,WA)
(.LO, .L, .UP, .M = -10, 5, 10, 0)
-1 taue(1,ET,WA)
-1 taue(2,ET,WA)
-1 taue(3,ET,WA)
-1 taue(4,ET,WA)
-1 taue(5,ET,WA)
-1 taue(6,ET,WA)
-1 taue(7,ET,WA)
-1 taue(8,ET,WA)
-1 taue(9,ET,WA)
-1 taue(10,ET,WA)
-1 taue(11,ET,WA)
-1 taue(12,ET,WA)
a(WA,ET)
(.LO, .L, .UP, .M = -10, 5, 10, 0)
-1 taue(1,WA,ET)
-1 taue(2,WA,ET)
-1 taue(3,WA,ET)
-1 taue(4,WA,ET)
-1 taue(5,WA,ET)
-1 taue(6,WA,ET)
-1 taue(7,WA,ET)
-1 taue(8,WA,ET)
-1 taue(9,WA,ET)
-1 taue(10,WA,ET)
-1 taue(11,WA,ET)
-1 taue(12,WA,ET)
REMAINING ENTRY SKIPPED
---- b Binary interaction Parameter b
b(ET,ET)
(.LO, .L, .UP, .M = -2500, 0, 2500, 0)
(-0.0027) taue(1,ET,ET)
(-0.0027) taue(2,ET,ET)
(-0.0027) taue(3,ET,ET)
(-0.0027) taue(4,ET,ET)
(-0.0028) taue(5,ET,ET)
(-0.0028) taue(6,ET,ET)
(-0.0028) taue(7,ET,ET)
(-0.0028) taue(8,ET,ET)
(-0.0028) taue(9,ET,ET)
(-0.0028) taue(10,ET,ET)
(-0.0028) taue(11,ET,ET)
(-0.0028) taue(12,ET,ET)
1 Res6(ET)
b(ET,WA)
(.LO, .L, .UP, .M = -2500, 1000, 2500, 0)
(-0.0027) taue(1,ET,WA)
(-0.0027) taue(2,ET,WA)
(-0.0027) taue(3,ET,WA)
(-0.0027) taue(4,ET,WA)
(-0.0028) taue(5,ET,WA)
(-0.0028) taue(6,ET,WA)
(-0.0028) taue(7,ET,WA)
(-0.0028) taue(8,ET,WA)
(-0.0028) taue(9,ET,WA)
(-0.0028) taue(10,ET,WA)
(-0.0028) taue(11,ET,WA)
(-0.0028) taue(12,ET,WA)
b(WA,ET)
(.LO, .L, .UP, .M = -2500, 1000, 2500, 0)
(-0.0027) taue(1,WA,ET)
(-0.0027) taue(2,WA,ET)
(-0.0027) taue(3,WA,ET)
(-0.0027) taue(4,WA,ET)
(-0.0028) taue(5,WA,ET)
(-0.0028) taue(6,WA,ET)
(-0.0028) taue(7,WA,ET)
(-0.0028) taue(8,WA,ET)
(-0.0028) taue(9,WA,ET)
(-0.0028) taue(10,WA,ET)
(-0.0028) taue(11,WA,ET)
(-0.0028) taue(12,WA,ET)
REMAINING ENTRY SKIPPED
---- Obj Objective of optimization
Obj
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
1 Obje
GAMS 44.4.0 06604687 Sep 19, 2023 WEX-WEI x86 64bit/MS Windows - 10/03/23 04:59:11 Page 4
Optimization of Binary Parameters NRTL
Range Statistics SOLVE Opti Using NLP From line 183
RANGE STATISTICS (ABSOLUTE NON-ZERO FINITE VALUES)
RHS [min, max] : [ 1.000E+00, 7.365E+01] - Zero values observed as well
Bound [min, max] : [ 2.000E-01, 2.500E+03] - Zero values observed as well
Matrix [min, max] : [ 1.000E-16, 2.531E+09] - Zero values observed as well
GAMS 44.4.0 06604687 Sep 19, 2023 WEX-WEI x86 64bit/MS Windows - 10/03/23 04:59:11 Page 5
Optimization of Binary Parameters NRTL
Model Statistics SOLVE Opti Using NLP From line 183
MODEL STATISTICS
BLOCKS OF EQUATIONS 12 SINGLE EQUATIONS 201
BLOCKS OF VARIABLES 12 SINGLE VARIABLES 229
NON ZERO ELEMENTS 901 NON LINEAR N-Z 672
CODE LENGTH 3,075 CONSTANT POOL 77
GENERATION TIME = 0.016 SECONDS 4 MB 44.4.0 06604687 WEX-WEI
GAMS 44.4.0 06604687 Sep 19, 2023 WEX-WEI x86 64bit/MS Windows - 10/03/23 04:59:11 Page 6
Optimization of Binary Parameters NRTL
Solution Report SOLVE Opti Using NLP From line 183
S O L V E S U M M A R Y
MODEL Opti OBJECTIVE Obj
TYPE NLP DIRECTION MINIMIZE
SOLVER CONOPT FROM LINE 183
**** SOLVER STATUS 1 Normal Completion
**** MODEL STATUS 2 Locally Optimal
**** OBJECTIVE VALUE 0.2449
RESOURCE USAGE, LIMIT 5.672 10000000000.000
ITERATION COUNT, LIMIT 16365 2147483647
EVALUATION ERRORS 0 0
--- *** This solver runs with a community license. No commercial use.
C O N O P T 3 version 3.17O
Copyright (C) ARKI Consulting and Development A/S
Bagsvaerdvej 246 A
DK-2880 Bagsvaerd, Denmark
The model has 229 variables and 201 constraints
with 901 Jacobian elements, 672 of which are nonlinear.
The Hessian of the Lagrangian has 196 elements on the diagonal,
732 elements below the diagonal, and 224 nonlinear variables.
** Warning ** The value of LFITER is out of range.
LFITER is decreased from 2147483647 to 1000000000.
** Warning ** The variance of the derivatives in the initial
point is large (= 5.3 ). A better initial
point, a better scaling, or better bounds on the
variables will probably help the optimization.
Pre-triangular equations: 4
Post-triangular equations: 1
Definitional equations: 122
** Optimal solution. Reduced gradient less than tolerance.
Tolerance is relaxed due to large 2nd derivatives.
CONOPT time Total 5.672 seconds
of which: Function evaluations 2.324 = 41.0%
1st Derivative evaluations 0.527 = 9.3%
2nd Derivative evaluations 0.226 = 4.0%
Directional 2nd Derivative 1.305 = 23.0%
---- EQU Ant Antoine equation
LOWER LEVEL UPPER MARGINAL
1 .ET 73.3040 73.3040 73.3040 2.7759114E-6
1 .WA 73.6490 73.6490 73.6490 -0.0051
2 .ET 73.3040 73.3040 73.3040 0.0156
2 .WA 73.6490 73.6490 73.6490 0.3631
3 .ET 73.3040 73.3040 73.3040 0.0008
3 .WA 73.6490 73.6490 73.6490 0.2025
4 .ET 73.3040 73.3040 73.3040 0.0001
4 .WA 73.6490 73.6490 73.6490 0.1005
5 .ET 73.3040 73.3040 73.3040 0.0001
5 .WA 73.6490 73.6490 73.6490 0.1304
6 .ET 73.3040 73.3040 73.3040 -0.0001
6 .WA 73.6490 73.6490 73.6490 0.1300
7 .ET 73.3040 73.3040 73.3040 -0.0002
7 .WA 73.6490 73.6490 73.6490 0.1349
8 .ET 73.3040 73.3040 73.3040 -0.3261
8 .WA 73.6490 73.6490 73.6490 -0.3098
9 .ET 73.3040 73.3040 73.3040 -0.2083
9 .WA 73.6490 73.6490 73.6490 -0.2000
10.ET 73.3040 73.3040 73.3040 0.0687
10.WA 73.6490 73.6490 73.6490 -0.0493
11.ET 73.3040 73.3040 73.3040 0.5361
11.WA 73.6490 73.6490 73.6490 0.1719
12.ET 73.3040 73.3040 73.3040 -0.0010
12.WA 73.6490 73.6490 73.6490 EPS
---- EQU taue Tau equation of NRTL
LOWER LEVEL UPPER MARGINAL
1 .ET.ET . . . EPS
1 .ET.WA . . . EPS
1 .WA.ET . . . EPS
1 .WA.WA . . . -0.0051
2 .ET.ET . . . 0.0233
2 .ET.WA . . . -0.0020
2 .WA.ET . . . -0.0077
2 .WA.WA . . . 0.3650
3 .ET.ET . . . 0.0016
3 .ET.WA . . . -0.0001
3 .WA.ET . . . -0.0007
3 .WA.WA . . . 0.2026
4 .ET.ET . . . 2.2437923E-5
4 .ET.WA . . . -7.654891E-6
4 .WA.ET . . . 3.8143510E-5
4 .WA.WA . . . 0.1005
5 .ET.ET . . . 0.0001
5 .ET.WA . . . -1.301842E-5
5 .WA.ET . . . 4.4233658E-5
5 .WA.WA . . . 0.1305
6 .ET.ET . . . -0.0004
6 .ET.WA . . . 1.2971820E-5
6 .WA.ET . . . 0.0003
6 .WA.WA . . . 0.1300
7 .ET.ET . . . -0.0007
7 .ET.WA . . . 2.7923878E-5
7 .WA.ET . . . 0.0005
7 .WA.WA . . . 0.1349
8 .ET.ET . . . -0.3320
8 .ET.WA . . . 0.0339
8 .WA.ET . . . 0.0059
8 .WA.WA . . . -0.3437
9 .ET.ET . . . -0.2121
9 .ET.WA . . . 0.0210
9 .WA.ET . . . 0.0038
9 .WA.WA . . . -0.2210
10.ET.ET . . . 0.0678
10.ET.WA . . . -0.0054
10.WA.ET . . . 0.0009
10.WA.WA . . . -0.0440
11.ET.ET . . . 0.5394
11.ET.WA . . . -0.0474
11.WA.ET . . . -0.0033
11.WA.WA . . . 0.2193
12.ET.ET . . . -0.0010
12.ET.WA . . . EPS
12.WA.ET . . . EPS
12.WA.WA . . . EPS
---- EQU Gexe G equation of NRTL
LOWER LEVEL UPPER MARGINAL
1 .ET.ET . . . EPS
1 .ET.WA . . . EPS
1 .WA.ET . . . EPS
1 .WA.WA . . . EPS
2 .ET.ET . . . -0.0221
2 .ET.WA . . . 0.0873
2 .WA.ET . . . 4.9571
2 .WA.WA . . . -0.0080
3 .ET.ET . . . -0.0027
3 .ET.WA . . . 0.0047
3 .WA.ET . . . 0.6151
3 .WA.WA . . . -0.0004
4 .ET.ET . . . -0.0002
4 .ET.WA . . . 0.0003
4 .WA.ET . . . 0.0482
4 .WA.WA . . . -3.042742E-5
5 .ET.ET . . . -0.0003
5 .ET.WA . . . 0.0006
5 .WA.ET . . . 0.0605
5 .WA.WA . . . -0.0001
6 .ET.ET . . . 0.0005
6 .ET.WA . . . -0.0006
6 .WA.ET . . . -0.1204
6 .WA.WA . . . 0.0001
7 .ET.ET . . . 0.0010
7 .ET.WA . . . -0.0013
7 .WA.ET . . . -0.2320
7 .WA.WA . . . 0.0001
8 .ET.ET . . . 0.0169
8 .ET.WA . . . -1.6942
8 .WA.ET . . . -3.9702
8 .WA.WA . . . 0.1382
9 .ET.ET . . . 0.0108
9 .ET.WA . . . -1.0682
9 .WA.ET . . . -2.5501
9 .WA.WA . . . 0.0857
10.ET.ET . . . 0.0026
10.ET.WA . . . 0.2964
10.WA.ET . . . -0.6072
10.WA.WA . . . -0.0236
11.ET.ET . . . -0.0094
11.ET.WA . . . 2.5259
11.WA.ET . . . 2.2385
11.WA.WA . . . -0.2000
12.ET.ET . . . EPS
12.ET.WA . . . EPS
12.WA.ET . . . EPS
12.WA.WA . . . EPS
---- EQU Gam Gamma Equation of NRTL
LOWER LEVEL UPPER MARGINAL
1 .ET . . . EPS
1 .WA . . . -0.0051
2 .ET . . . 0.0050
2 .WA . . . 0.3508
3 .ET . . . 4.0269796E-5
3 .WA . . . 0.1990
4 .ET . . . 1.6674689E-6
4 .WA . . . 0.0991
5 .ET . . . 1.8562168E-6
5 .WA . . . 0.1288
6 .ET . . . -1.286551E-6
6 .WA . . . 0.1286
7 .ET . . . -2.239866E-6
7 .WA . . . 0.1336
8 .ET . . . -0.2094
8 .WA . . . -0.2908
9 .ET . . . -0.1359
9 .WA . . . -0.1865
10.ET . . . 0.0451
10.WA . . . -0.0458
11.ET . . . 0.3551
11.WA . . . 0.1588
12.ET . . . -0.0010
12.WA . . . EPS
---- EQU Eq Equilibrium Equation
LOWER LEVEL UPPER MARGINAL
1 .ET . . . EPS
1 .WA . . . -5.085146E-8
2 .ET . . . 1.6251511E-6
2 .WA . . . 3.9711595E-6
3 .ET . . . 4.1186322E-8
3 .WA . . . 2.5066148E-6
4 .ET . . . 2.2492756E-9
4 .WA . . . 1.3566342E-6
5 .ET . . . 3.1319585E-9
5 .WA . . . 1.9227547E-6
6 .ET . . . -2.683965E-9
6 .WA . . . 2.1063536E-6
7 .ET . . . -5.248726E-9
7 .WA . . . 2.3255755E-6
8 .ET . . . -5.112481E-6
8 .WA . . . -8.317671E-6
9 .ET . . . -2.975469E-6
9 .WA . . . -6.447650E-6
10.ET . . . 9.5207827E-7
10.WA . . . -1.711018E-6
11.ET . . . 7.1860359E-6
11.WA . . . 6.5050030E-6
12.ET . . . -9.875477E-9
12.WA . . . EPS
---- EQU Res1 Balance y
LOWER LEVEL UPPER MARGINAL
1 1.0000 1.0000 1.0000 0.0026
2 1.0000 1.0000 1.0000 -0.2827
3 1.0000 1.0000 1.0000 -0.1287
4 1.0000 1.0000 1.0000 -0.0686
5 1.0000 1.0000 1.0000 -0.0973
6 1.0000 1.0000 1.0000 -0.1063
7 1.0000 1.0000 1.0000 -0.1172
8 1.0000 1.0000 1.0000 0.6784
9 1.0000 1.0000 1.0000 0.4760
10 1.0000 1.0000 1.0000 0.0383
11 1.0000 1.0000 1.0000 -0.6916
12 1.0000 1.0000 1.0000 0.0005
---- EQU Res2 Balance x
LOWER LEVEL UPPER MARGINAL
1 1.0000 1.0000 1.0000 -0.0051
2 1.0000 1.0000 1.0000 0.3818
3 1.0000 1.0000 1.0000 0.2493
4 1.0000 1.0000 1.0000 0.1939
5 1.0000 1.0000 1.0000 0.2528
6 1.0000 1.0000 1.0000 0.3299
7 1.0000 1.0000 1.0000 0.3975
8 1.0000 1.0000 1.0000 -0.7099
9 1.0000 1.0000 1.0000 -0.4227
10 1.0000 1.0000 1.0000 0.0336
11 1.0000 1.0000 1.0000 0.7305
12 1.0000 1.0000 1.0000 -0.0010
---- EQU Res3 alpha verification
LOWER LEVEL UPPER MARGINAL
ET.WA . . . -0.0571
WA.ET . . . .
---- EQU Res4 alpha 0
LOWER LEVEL UPPER MARGINAL
ET.WA . . . EPS
WA.ET . . . EPS
---- EQU Res5 Diagonal
LOWER LEVEL UPPER MARGINAL
ET . . . 0.0860
WA . . . 0.6691
---- EQU Res6 Diagonal
LOWER LEVEL UPPER MARGINAL
ET . . . 0.0003
WA . . . 0.0018
LOWER LEVEL UPPER MARGINAL
---- EQU Obje . . . 1.0000
Obje Objective function