-
-
Notifications
You must be signed in to change notification settings - Fork 89
/
TrueCriticalPoint.vb
3355 lines (2686 loc) · 98.6 KB
/
TrueCriticalPoint.vb
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
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
' Critical Point Calculation Routines (PR & SRK)
' Copyright 2008 Daniel Wagner O. de Medeiros
'
' This file is part of DWSIM.
'
' DWSIM 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.
'
' DWSIM 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 DWSIM. If not, see <http://www.gnu.org/licenses/>.
Imports DWSIM.MathOps.MathEx.Common
Imports DWSIM.MathOps.MathEx
Imports MathNet.Numerics
Imports Community.CsharpSqlite.Sqlite3
Namespace Utilities.TCP
<System.Serializable()> Public Class Methods
Sub New()
End Sub
Function CRITPT_PR(ByVal Vz, ByVal VTc, ByVal VPc, ByVal VVc, ByVal Vw, ByVal VKIj, Optional ByVal Vinf = 0) As ArrayList
Dim res As New ArrayList
Dim V, Vc_sup, Vc_inf, Tcm, Pcm As Double
Dim stmp(2)
Dim n, R As Double
Dim i As Integer
n = Vz.Length - 1
Dim Tc(n), Pc(n) As Double
Dim b As Double
'estimar temperatura e pressao criticas iniciais
R = 8.314
i = 0
Do
Tc(i) = VTc(i)
Pc(i) = VPc(i)
Tcm += Vz(i) * VTc(i)
Pcm += Vz(i) * VPc(i)
i = i + 1
Loop Until i = n + 1
i = 0
b = 0
Do
b += Vz(i) * 0.0778 * R * Tc(i) / Pc(i)
i = i + 1
Loop Until i = n + 1
'estimar temperatura e pressao criticas iniciais
Vc_inf = 4 * b
If Vinf <> 0 Then Vc_inf = Vinf
Vc_sup = b
Dim fV, fV_inf, nsub, delta_Vc As Double
nsub = 100
delta_Vc = (Vc_sup - Vc_inf) / nsub
Do
restart: fV = TRIPLESUM(Vc_inf, Vz, VTc, VPc, VVc, Vw, VKIj)
Vc_inf = Vc_inf + delta_Vc
fV_inf = TRIPLESUM(Vc_inf, Vz, VTc, VPc, VVc, Vw, VKIj)
Loop Until fV * fV_inf < 0 Or Vc_inf <= b
Vc_sup = Vc_inf - delta_Vc
'Vc_inf = Vc_inf - delta_Vc
If Vc_inf <= b Then GoTo Final2
'metodo de Brent para encontrar Vc
Dim aaa, bbb, ccc, ddd, eee, min11, min22, faa, fbb, fcc, ppp, qqq, rrr, sss, tol11, xmm As Double
Dim ITMAX2 As Integer = 100
Dim iter2 As Integer
aaa = Vc_inf
bbb = Vc_sup
ccc = Vc_sup
faa = TRIPLESUM(Vc_inf, Vz, VTc, VPc, VVc, Vw, VKIj)
fbb = TRIPLESUM(Vc_sup, Vz, VTc, VPc, VVc, Vw, VKIj)
fcc = fbb
iter2 = 0
Do
If (fbb > 0 And fcc > 0) Or (fbb < 0 And fcc < 0) Then
ccc = aaa
fcc = faa
ddd = bbb - aaa
eee = ddd
End If
If Math.Abs(fcc) < Math.Abs(fbb) Then
aaa = bbb
bbb = ccc
ccc = aaa
faa = fbb
fbb = fcc
fcc = faa
End If
tol11 = 0.000001
xmm = 0.5 * (ccc - bbb)
If (Math.Abs(xmm) <= tol11) Or (fbb = 0) Then GoTo Final3
If Math.Abs(fbb) < tol11 Then GoTo Final3
If (Math.Abs(eee) >= tol11) And (Math.Abs(faa) > Math.Abs(fbb)) Then
sss = fbb / faa
If aaa = ccc Then
ppp = 2 * xmm * sss
qqq = 1 - sss
Else
qqq = faa / fcc
rrr = fbb / fcc
ppp = sss * (2 * xmm * qqq * (qqq - rrr) - (bbb - aaa) * (rrr - 1))
qqq = (qqq - 1) * (rrr - 1) * (sss - 1)
End If
If ppp > 0 Then qqq = -qqq
ppp = Math.Abs(ppp)
min11 = 3 * xmm * qqq - Math.Abs(tol11 * qqq)
min22 = Math.Abs(eee * qqq)
Dim tvar2 As Double
If min11 < min22 Then tvar2 = min11
If min11 > min22 Then tvar2 = min22
If 2 * ppp < tvar2 Then
eee = ddd
ddd = ppp / qqq
Else
ddd = xmm
eee = ddd
End If
Else
ddd = xmm
eee = ddd
End If
aaa = bbb
faa = fbb
If (Math.Abs(ddd) > tol11) Then
bbb += ddd
Else
bbb += Math.Sign(xmm) * tol11
End If
fbb = TRIPLESUM(bbb, Vz, VTc, VPc, VVc, Vw, VKIj)
iter2 += 1
Loop Until iter2 = ITMAX2
Final3:
V = bbb
Dim T, P
T = TCRIT2(V, Vz, VTc, VPc, VVc, Vw, VKIj)
P = PCRIT(T, V, Vz, VTc, VPc, Vw, VKIj)
If P < 0 Then
Vc_inf += 2 * delta_Vc
GoTo restart
End If
stmp(0) = T
stmp(1) = P
stmp(2) = V
If T > 0.5 * Tcm And T < 2 * Tcm And P > 0.3 * Pcm And P < 2 * Pcm Then
res.Add(stmp.Clone)
End If
If Vc_inf <= b Then
GoTo Final2
Else
Vc_inf += 2 * delta_Vc
GoTo restart
End If
Final2:
CRITPT_PR = res
End Function
Function QIJ_HES_MAT(ByVal T, ByVal V, ByVal Vz, ByVal VTc, ByVal VPc, ByVal VVc, ByVal Vw, ByVal VKIj) As Mapack.Matrix
Dim i, j As Integer
Dim n As Double
Dim am, bm, R As Double
n = Vz.Length - 1
Dim ai(n), b(n), c(n), tmp(2, n + 1), a(n, n), am2(n) As Double
Dim Tc(n), Pc(n), Vc(n), Zc(n), w(n), alpha(n), Tr(n) As Double
'estimar temperatura e pressao criticas iniciais
R = 8.314
i = 0
Do
If Vz(i) <> 0 Then
Tc(i) = VTc(i)
Tr(i) = T / Tc(i)
Pc(i) = VPc(i)
w(i) = Vw(i)
End If
i = i + 1
Loop Until i = n + 1
i = 0
Do
If Vz(i) <> 0 Then
alpha(i) = (1 + (0.37464 + 1.54226 * w(i) - 0.26992 * w(i) ^ 2) * (1 - (T / Tc(i)) ^ 0.5)) ^ 2
ai(i) = 0.45724 * alpha(i) * R ^ 2 * Tc(i) ^ 2 / Pc(i)
b(i) = 0.0778 * R * Tc(i) / Pc(i)
c(i) = (0.37464 + 1.54226 * w(i) - 0.26992 * w(i) ^ 2)
End If
i = i + 1
Loop Until i = n + 1
i = 0
Do
j = 0
Do
a(i, j) = (ai(i) * ai(j)) ^ 0.5 * (1 - VKIj(i, j))
j = j + 1
Loop Until j = n + 1
i = i + 1
Loop Until i = n + 1
i = 0
Do
am2(i) = 0
i = i + 1
Loop Until i = n + 1
i = 0
am = 0
Do
j = 0
Do
am = am + Vz(i) * Vz(j) * a(i, j)
am2(i) = am2(i) + Vz(j) * a(i, j)
j = j + 1
Loop Until j = n + 1
i = i + 1
Loop Until i = n + 1
i = 0
bm = 0
Do
bm = bm + Vz(i) * b(i)
i = i + 1
Loop Until i = n + 1
Dim F1, F2, F3, F4, F5, F6, F7, F8 As Double
Dim K, delta1, delta2 As Double
K = V / bm
delta1 = 2.414
delta2 = -0.414
F1 = 1 / (K - 1)
F2 = 2 / (delta1 - delta2) * (delta1 / (K + delta1) - delta2 / (K + delta2))
F3 = 1 / (delta1 - delta2) * ((delta1 / (K + delta1)) ^ 2 - (delta2 / (K + delta2)) ^ 2)
F4 = 1 / (delta1 - delta2) * ((delta1 / (K + delta1)) ^ 3 - (delta2 / (K + delta2)) ^ 3)
F5 = 2 / (delta1 - delta2) * Math.Log((K + delta1) / (K + delta2))
F6 = F2 - F5
F7 = -F2 / (1 + F1)
F8 = F3 / (1 + F1)
Dim alfa As Double
alfa = am / (bm * R * T)
Dim dnb_dn(n), dnalfa_dn(n) As Double
Dim d2nb_dn(n, n), d2nalfa_dn(n, n) As Double
Dim d3nalfa_dn(n, n, n) As Double
Dim sum_xa(n) As Double
Dim dta(n, n) As Integer
i = 0
Do
j = 0
Do
If i = j Then
dta(i, j) = 1
Else
dta(i, j) = 0
End If
j = j + 1
Loop Until j = n + 1
i = i + 1
Loop Until i = n + 1
i = 0
Do
sum_xa(i) = 0
i = i + 1
Loop Until i = n + 1
i = 0
Do
j = 0
Do
sum_xa(i) += Vz(j) * a(i, j)
j = j + 1
Loop Until j = n + 1
i = i + 1
Loop Until i = n + 1
Dim alfa_(n), beta_(n) As Double
i = 0
Do
beta_(i) = b(i) / bm
alfa_(i) = sum_xa(i) / am
i = i + 1
Loop Until i = n + 1
Dim Q As Mapack.Matrix = New Mapack.Matrix(n + 1, n + 1)
i = 0
Do
j = 0
Do
Q(i, j) = R * T * (dta(i, j) / Vz(i) + (beta_(i) + beta_(j)) * F1 + beta_(i) * beta_(j) * F1 ^ 2) + am / bm * (beta_(i) * beta_(j) * F3 - a(i, j) * F5 / am + (beta_(i) * beta_(j) - alfa_(i) * beta_(j) - alfa_(j) * beta_(i)) * F6)
j = j + 1
Loop Until j = n + 1
i = i + 1
Loop Until i = n + 1
'get maximum value
Dim max As Double = 0
i = 0
Do
j = 0
Do
If Math.Abs(Q(i, j)) > max Then max = Math.Abs(Q(i, j))
j = j + 1
Loop Until j = n + 1
i = i + 1
Loop Until i = n + 1
'i = 0
'Do
' j = 0
' Do
' Q(i, j) = Q(i, j) / max
' j = j + 1
' Loop Until j = n + 1
' i = i + 1
'Loop Until i = n + 1
QIJ_HES_MAT = Q
End Function
Function TRIPLESUM(ByVal V, ByVal Vz, ByVal VTc, ByVal VPc, ByVal VVc, ByVal Vw, ByVal VKIj) As Double
Dim T, Tc_sup, Tc_inf As Double
Dim i, j As Integer
Dim n As Double
Dim am, bm, R As Double
n = Vz.Length - 1
Dim Dn(n)
Dim ai(n), b(n), c(n), tmp(2, n + 1), a(n, n), am2(n) As Double
Dim Tc(n), Pc(n), Vc(n), Zc(n), w(n), alpha(n), Tr(n) As Double
Tc_inf = MathEx.Common.Min(VTc) * 0.5
Tc_sup = MathEx.Common.Max(VTc) * 1.5
Dim fT, fT_inf, nsub, delta_Tc As Double
nsub = 20
delta_Tc = (Tc_sup - Tc_inf) / nsub
Do
fT = QIJ_HES_MAT(Tc_inf, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
Tc_inf = Tc_inf + delta_Tc
fT_inf = QIJ_HES_MAT(Tc_inf, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
Loop Until fT * fT_inf < 0 Or Tc_inf > Tc_sup
Tc_sup = Tc_inf
Tc_inf = Tc_inf - delta_Tc
'metodo de Brent para encontrar Tc
Dim aa, bb, cc, dd, ee, min1, min2, fa, fb, fc, pp, qq, rr, ss, tol1, xm As Double
Dim ITMAX As Integer = 1000
Dim iter As Integer
aa = Tc_inf
bb = Tc_sup
cc = Tc_sup
fa = QIJ_HES_MAT(aa, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
fb = QIJ_HES_MAT(bb, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
fc = fb
iter = 0
Do
If (fb > 0 And fc > 0) Or (fb < 0 And fc < 0) Then
cc = aa
fc = fa
dd = bb - aa
ee = dd
End If
If Math.Abs(fc) < Math.Abs(fb) Then
aa = bb
bb = cc
cc = aa
fa = fb
fb = fc
fc = fa
End If
tol1 = 0.00000001
xm = 0.5 * (cc - bb)
If (Math.Abs(xm) <= tol1) Or (fb = 0) Then GoTo Final
If Math.Abs(fb) < tol1 Then GoTo Final
If (Math.Abs(ee) >= tol1) And (Math.Abs(fa) > Math.Abs(fb)) Then
ss = fb / fa
If aa = cc Then
pp = 2 * xm * ss
qq = 1 - ss
Else
qq = fa / fc
rr = fb / fc
pp = ss * (2 * xm * qq * (qq - rr) - (bb - aa) * (rr - 1))
qq = (qq - 1) * (rr - 1) * (ss - 1)
End If
If pp > 0 Then qq = -qq
pp = Math.Abs(pp)
min1 = 3 * xm * qq - Math.Abs(tol1 * qq)
min2 = Math.Abs(ee * qq)
Dim tvar As Double
If min1 < min2 Then tvar = min1
If min1 > min2 Then tvar = min2
If 2 * pp < tvar Then
ee = dd
dd = pp / qq
Else
dd = xm
ee = dd
End If
Else
dd = xm
ee = dd
End If
aa = bb
fa = fb
If (Math.Abs(dd) > tol1) Then
bb += dd
Else
bb += Math.Sign(xm) * tol1
End If
fb = QIJ_HES_MAT(bb, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
iter += 1
Loop Until iter = ITMAX
Final:
T = bb
If iter = ITMAX Then GoTo Final2
Dim MA As Mapack.Matrix, Dn0(n) As Double
Dim MA_(n, n), MB_(n), Dn0_(n) As Double
'Dim MP As New DLLXnumbers.Xnumbers
MA = QIJ_HES_MAT(T, V, Vz, VTc, VPc, VVc, Vw, VKIj)
Dim m2 As Mapack.Matrix = New Mapack.Matrix(MA.Rows, 1)
For i = 0 To n
For j = 0 To n
MA_(i, j) = MA(i, j)
Next
MB_(i) = Double.Epsilon
Next
Try
Dim trg As New Mapack.LuDecomposition(MA)
i = 0
Do
m2(i, 0) = 0
i = i + 1
Loop Until i = n + 1
m2(n, 0) = trg.UpperTriangularFactor(n, n)
Dim m3 As Mapack.Matrix = trg.UpperTriangularFactor.Solve(m2)
i = 0
Do
Dn0(i) = m3(i, 0)
i = i + 1
Loop Until i = n + 1
Catch ex As Exception
i = 0
Do
Dn0(i) = 0
i = i + 1
Loop Until i = n + 1
End Try
Dim soma_Dn = 0.0#
i = 0
Do
soma_Dn += Math.Abs(Dn0(i))
i = i + 1
Loop Until i = n + 1
i = 0
Do
Dn(i) = Dn0(i) / soma_Dn
i = i + 1
Loop Until i = n + 1
R = 8.314
i = 0
Do
If Vz(i) <> 0 Then
Tc(i) = VTc(i)
Tr(i) = T / Tc(i)
Pc(i) = VPc(i)
w(i) = Vw(i)
End If
i = i + 1
Loop Until i = n + 1
i = 0
Do
If Vz(i) <> 0 Then
alpha(i) = (1 + (0.37464 + 1.54226 * w(i) - 0.26992 * w(i) ^ 2) * (1 - (T / Tc(i)) ^ 0.5)) ^ 2
ai(i) = 0.45724 * alpha(i) * R ^ 2 * Tc(i) ^ 2 / Pc(i)
b(i) = 0.0778 * R * Tc(i) / Pc(i)
c(i) = (0.37464 + 1.54226 * w(i) - 0.26992 * w(i) ^ 2)
End If
i = i + 1
Loop Until i = n + 1
i = 0
Do
j = 0
Do
a(i, j) = (ai(i) * ai(j)) ^ 0.5 * (1 - VKIj(i, j))
j = j + 1
Loop Until j = n + 1
i = i + 1
Loop Until i = n + 1
i = 0
Do
am2(i) = 0
i = i + 1
Loop Until i = n + 1
i = 0
am = 0
Do
j = 0
Do
am = am + Vz(i) * Vz(j) * a(i, j)
am2(i) = am2(i) + Vz(j) * a(i, j)
j = j + 1
Loop Until j = n + 1
i = i + 1
Loop Until i = n + 1
i = 0
bm = 0
Do
bm = bm + Vz(i) * b(i)
i = i + 1
Loop Until i = n + 1
Dim F1, F2, F3, F4, F5, F6, F7, F8 As Double
Dim K, delta1, delta2 As Double
K = V / bm
delta1 = 2.414
delta2 = -0.414
F1 = 1 / (K - 1)
F2 = 2 / (delta1 - delta2) * (delta1 / (K + delta1) - delta2 / (K + delta2))
F3 = 1 / (delta1 - delta2) * ((delta1 / (K + delta1)) ^ 2 - (delta2 / (K + delta2)) ^ 2)
F4 = 1 / (delta1 - delta2) * ((delta1 / (K + delta1)) ^ 3 - (delta2 / (K + delta2)) ^ 3)
F5 = 2 / (delta1 - delta2) * Math.Log((K + delta1) / (K + delta2))
F6 = F2 - F5
F7 = -F2 / (1 + F1)
F8 = F3 / (1 + F1)
Dim sum_xa(n) As Double
i = 0
Do
sum_xa(i) = 0
j = 0
Do
sum_xa(i) += Vz(j) * a(i, j)
j = j + 1
Loop Until j = n + 1
i = i + 1
Loop Until i = n + 1
Dim alfa_(n), beta_(n) As Double
i = 0
Do
beta_(i) = b(i) / bm
alfa_(i) = sum_xa(i) / am
i = i + 1
Loop Until i = n + 1
Dim a_ As Double = 0
Dim b_ As Double = 0
Dim af_ As Double = 0
i = 0
Do
j = 0
Do
a_ += a(i, j) * Dn(i) * Dn(j) / am
j = j + 1
Loop Until j = n + 1
b_ += beta_(i) * Dn(i)
af_ += alfa_(i) * Dn(i)
i = i + 1
Loop Until i = n + 1
Dim n_, sum_Dn3 As Double
n_ = 0
sum_Dn3 = 0
i = 0
Do
n_ = n_ + Dn(i)
sum_Dn3 = sum_Dn3 + Dn(i) ^ 3 / Vz(i) ^ 2
i = i + 1
Loop Until i = n + 1
Dim TS As Double
TS = R * T * (-sum_Dn3 + 3 * n_ * (b_ * F1) ^ 2 + 2 * (b_ * F1) ^ 3) + am / bm * (3 * b_ ^ 2 * (2 * af_ - b_) * (F3 + F6) - 2 * b_ ^ 3 * F4 - 3 * b_ * a_ * F6)
Final2:
TRIPLESUM = TS
End Function
Function TCRIT(ByVal V, ByVal Vz, ByVal VTc, ByVal VPc, ByVal VVc, ByVal Vw, ByVal VKIj)
'Dim MP As New DLLXnumbers.Xnumbers
'MP.DigitsMax = 20
Dim T, Tc_sup, Tc_inf As Double
Dim n As Double
n = Vz.Length - 1
Dim Dn(n)
Dim ai(n), b(n), c(n), tmp(2, n + 1), a(n, n), am2(n)
Dim Tc(n), Pc(n), Vc(n), Zc(n), w(n), alpha(n), Tr(n)
Tc_inf = MathEx.Common.Min(VTc) * 0.5
Tc_sup = MathEx.Common.Min(VTc) * 1.5
Dim fT, fT_inf, nsub, delta_Tc As Double
nsub = 50
delta_Tc = (Tc_sup - Tc_inf) / nsub
Do
fT = QIJ_HES_MAT(Tc_inf, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
Tc_inf = Tc_inf + delta_Tc
fT_inf = QIJ_HES_MAT(Tc_inf, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
Loop Until fT * fT_inf < 0 Or Tc_inf > Tc_sup
Tc_inf = Tc_inf - delta_Tc
Tc_sup = Tc_inf
'metodo de Brent para encontrar Tc
Dim aa, bb, cc, dd, ee, min1, min2, fa, fb, fc, pp, qq, rr, ss, tol1, xm As Double
Dim ITMAX As Integer = 100
Dim iter As Integer
aa = Tc_inf
bb = Tc_sup
cc = Tc_sup
fa = QIJ_HES_MAT(aa, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
fb = QIJ_HES_MAT(bb, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
fc = fb
iter = 0
Do
If (fb > 0 And fc > 0) Or (fb < 0 And fc < 0) Then
cc = aa
fc = fa
dd = bb - aa
ee = dd
End If
If Math.Abs(fc) < Math.Abs(fb) Then
aa = bb
bb = cc
cc = aa
fa = fb
fb = fc
fc = fa
End If
tol1 = 0.000000000001
xm = 0.5 * (cc - bb)
If (Math.Abs(xm) <= tol1) Or (fb = 0) Then GoTo Final
If (Math.Abs(ee) >= tol1) And (Math.Abs(fa) > Math.Abs(fb)) Then
ss = fb / fa
If aa = cc Then
pp = 2 * xm * ss
qq = 1 - ss
Else
qq = fa / fc
rr = fb / fc
pp = ss * (2 * xm * qq * (qq - rr) - (bb - aa) * (rr - 1))
qq = (qq - 1) * (rr - 1) * (ss - 1)
End If
If pp > 0 Then qq = -qq
pp = Math.Abs(pp)
min1 = 3 * xm * qq - Math.Abs(tol1 * qq)
min2 = Math.Abs(ee * qq)
Dim tvar As Double
If min1 < min2 Then tvar = min1
If min1 > min2 Then tvar = min2
If 2 * pp < tvar Then
ee = dd
dd = pp / qq
Else
dd = xm
ee = dd
End If
Else
dd = xm
ee = dd
End If
aa = bb
fa = fb
If (Math.Abs(dd) > tol1) Then
bb += dd
Else
bb += Math.Sign(xm) * tol1
End If
fb = QIJ_HES_MAT(bb, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
iter += 1
Loop Until iter = ITMAX
Final:
T = bb
If iter = ITMAX Then GoTo Final2
Final2:
TCRIT = T
End Function
Function PCRIT(ByVal T, ByVal V, ByVal Vx, ByVal VTc, ByVal VPc, ByVal Vw, ByVal VKIj)
Dim ai(), bi() As Double
Dim n, R, P, coeff(3), tmp() As Double
Dim Tc(), Pc(), W(), alpha(), Vant(0, 4), m(), a(,), b(,), Tr() As Double
n = Vx.Length - 1
ReDim ai(n), bi(n), tmp(n + 1), a(n, n), b(n, n)
ReDim Tc(n), Pc(n), W(n), alpha(n), m(n), Tr(n)
R = 8.314
Dim i, j As Integer
i = 0
Do
Tc(i) = VTc(i)
Tr(i) = T / Tc(i)
Pc(i) = VPc(i)
W(i) = Vw(i)
i = i + 1
Loop Until i = n + 1
i = 0
Do
alpha(i) = (1 + (0.37464 + 1.54226 * W(i) - 0.26992 * W(i) ^ 2) * (1 - (T / Tc(i)) ^ 0.5)) ^ 2
ai(i) = 0.45724 * alpha(i) * R ^ 2 * Tc(i) ^ 2 / Pc(i)
bi(i) = 0.0778 * R * Tc(i) / Pc(i)
i = i + 1
Loop Until i = n + 1
i = 0
Do
j = 0
Do
a(i, j) = (ai(i) * ai(j)) ^ 0.5 * (1 - VKIj(i, j))
j = j + 1
Loop Until j = n + 1
i = i + 1
Loop Until i = n + 1
i = 0
Dim aml = 0.0#
Do
j = 0
Do
aml = aml + Vx(i) * Vx(j) * a(i, j)
j = j + 1
Loop Until j = n + 1
i = i + 1
Loop Until i = n + 1
i = 0
Dim bml = 0.0#
Do
bml = bml + Vx(i) * bi(i)
i = i + 1
Loop Until i = n + 1
P = R * T / (V - bml) - aml / (V ^ 2 + 2 * bml * V - bml ^ 2)
PCRIT = P
End Function
Function STABILITY_CURVE(ByVal Vz As Object, ByVal VTc As Object, ByVal VPc As Object, ByVal VVc As Object, ByVal Vw As Object, ByVal VKIj As Object, Optional ByVal Vmax As Double = 0, Optional ByVal delta As Double = 40, Optional ByVal multipl As Integer = 15) As ArrayList
'Dim MP As New DLLXnumbers.Xnumbers
Dim V, Vmin, deltaV As Double
Dim stmp(2)
Dim n, R, P, T As Double
Dim i As Integer
n = Vz.Length - 1
Dim Tc(n), Pc(n)
Dim b As Double
'estimar temperatura e pressao criticas iniciais
R = 8.314
i = 0
Do
If Vz(i) <> 0 Then
Tc(i) = VTc(i)
Pc(i) = VPc(i)
End If
i = i + 1
Loop Until i = n + 1
i = 0
b = 0
Do
b += Vz(i) * 0.0778 * R * Tc(i) / Pc(i)
i = i + 1
Loop Until i = n + 1
'estimar temperatura e pressao criticas iniciais
If Vmax = 0 Then Vmax = b * multipl
Vmin = b * 1.05
deltaV = (Vmax - Vmin) / 100 ' delta
Dim result As ArrayList = New ArrayList()
V = Vmax
Do
T = TCRIT2(V, Vz, VTc, VPc, VVc, Vw, VKIj)
'P = 0.307 * 8.314 * T / V
P = PCRIT(T, V, Vz, VTc, VPc, Vw, VKIj)
If P < 0 Then Exit Do
result.Add(New Object() {T, P})
V -= deltaV
Loop Until V <= Vmin
STABILITY_CURVE = result
End Function
Function TCRIT2(ByVal V, ByVal Vz, ByVal VTc, ByVal VPc, ByVal VVc, ByVal Vw, ByVal VKIj)
'Dim MP As New DLLXnumbers.Xnumbers
'MP.DigitsMax = 20
Dim T, Tc_sup, Tc_inf As Double
Dim n As Double
n = Vz.Length - 1
Dim Dn(n)
Dim ai(n), b(n), c(n), tmp(2, n + 1), a(n, n), am2(n)
Dim Tc(n), Pc(n), Vc(n), Zc(n), w(n), alpha(n), Tr(n)
Tc_inf = Min(VTc) * 0.5
Tc_sup = Max(VTc) * 1.5
Dim fT, fT_inf, nsub, delta_Tc As Double
nsub = 50
delta_Tc = (Tc_sup - Tc_inf) / nsub
Do
fT = QIJ_HES_MAT(Tc_inf, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
Tc_inf = Tc_inf + delta_Tc
fT_inf = QIJ_HES_MAT(Tc_inf, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
Loop Until fT * fT_inf < 0 Or Tc_inf > Tc_sup
Tc_sup = Tc_inf
Tc_inf = Tc_inf - delta_Tc
'metodo de Brent para encontrar Tc
Dim aa, bb, cc, dd, ee, min1, min2, fa, fb, fc, pp, qq, rr, ss, tol1, xm As Double
Dim ITMAX As Integer = 100
Dim iter As Integer
aa = Tc_inf
bb = Tc_sup
cc = Tc_sup
fa = QIJ_HES_MAT(aa, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
fb = QIJ_HES_MAT(bb, V, Vz, VTc, VPc, VVc, Vw, VKIj).Determinant
fc = fb
iter = 0
Do
If (fb > 0 And fc > 0) Or (fb < 0 And fc < 0) Then
cc = aa
fc = fa
dd = bb - aa
ee = dd
End If
If Math.Abs(fc) < Math.Abs(fb) Then
aa = bb
bb = cc
cc = aa
fa = fb
fb = fc
fc = fa
End If
tol1 = 1.0E-100
xm = 0.5 * (cc - bb)
If (Math.Abs(xm) <= tol1) Or (fb = 0) Then GoTo Final
If Math.Abs(fb) < tol1 Then GoTo Final
If (Math.Abs(ee) >= tol1) And (Math.Abs(fa) > Math.Abs(fb)) Then
ss = fb / fa
If aa = cc Then
pp = 2 * xm * ss
qq = 1 - ss
Else
qq = fa / fc
rr = fb / fc
pp = ss * (2 * xm * qq * (qq - rr) - (bb - aa) * (rr - 1))
qq = (qq - 1) * (rr - 1) * (ss - 1)
End If
If pp > 0 Then qq = -qq
pp = Math.Abs(pp)
min1 = 3 * xm * qq - Math.Abs(tol1 * qq)
min2 = Math.Abs(ee * qq)
Dim tvar As Double
If min1 < min2 Then tvar = min1
If min1 > min2 Then tvar = min2
If 2 * pp < tvar Then
ee = dd
dd = pp / qq
Else
dd = xm
ee = dd