Download - ejercicios DTR resueltos.docx
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TABLA 1:
tConcen
trationtm Cn C F Cn t
tmCn
t
tm2Cn
tE(t)
((t
tm)^
2)*E(t
)/s
XA(t) XAs
0 0 75 0 0 0 0 0 0 0 0 0 0 0.511832
34
0.577894
5150 0 162.
5
0 0 0 0 0 0 0 0 0.8218
3
0 0.732749
42
0.845683
56175 0.001 187.
5
0.001
01
0.0010
1
0.0253 0.0253 4.7444
5
889.58
5
0.0010
2
7.643
54
0.8663
5
0.0008
8
0.768443
67
0.884241
6200 0.003 212.
5
0.003
04
0.0030
4
0.1012
2
0.0759
1
16.131
1
3427.8
6
0.0030
6
11.60
39
0.8997
4
0.0027
5
0.797436
7
0.913165
39225 0.0074 232.
5
0.007
49
0.0074
9
0.2135
6
0.1498 34.827
9
8097.5 0.0075
4
10.10
78
0.9247
9
0.0069
7
0.816882
84
0.931006
98240 0.0094 245 0.009
51
0.0095
1
0.3087 0.1189
3
29.137
1
7138.6 0.0095
8
4.474
48
0.9367
1
0.0089
7
0.827647
91
0.940244
86250 0.0097 255 0.009
82
0.0098
2
0.4068
8
0.0981
8
25.035
4
6384.0
3
0.0098
8
1.332
5
0.9435
8
0.0093
3
0.835590
92
0.946736
29260 0.0094 267.
5
0.009
51
0.0095
1
0.5496 0.1189
3
31.813 8509.9
8
0.0095
8
0.024
98
0.9497
1
0.0091 0.844770
6
0.953868
07275 0.0082 287.
5
0.008
3
0.0083 0.7570
9
0.1659
9
47.722
7
13720.
3
0.0083
5
1.496
82
0.9576
8
0.008 0.857935
82
0.963346
63300 0.005 312.
5
0.005
06
0.0050
6
0.8836 0.1265
2
39.537 12355.
3
0.0050
9
7.505
95
0.9682
5
0.0049
3
0.872163
79
0.972504
97325 0.0025 337.
5
0.002
53
0.0025
3
0.9468
6
0.0632
6
21.349
9
7205.6 0.0025
5
10.23
35
0.9761
9
0.0024
9
0.884356
64
0.979374
97350 0.0012 362.
5
0.001
21
0.0012
1
0.9772
3
0.0303
6
11.007 3990.0
5
0.0012
2
9.551
01
0.9821
4
0.0012 0.894884
77
0.984528
41
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375 0.0005 387.
5
0.000
51
0.0005
1
0.9898
8
0.0126
5
4.9025
8
1899.7
5
0.0005
1
6.549
23
0.9866 0.0005 0.904037
99
0.988394
2400 0.0002 425 0.000
2
0.0002 1 0.0075
9
3.2262
1
1371.1
4
0.0002 3.902
28
0.9899
5
0.0002 0.915678
8
0.992459
75450 0 0 --- --- --- --- --- --- 0 0.9943
4
0 --- 0
0.9934
2
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Curves parametersArea under concentration vs. time curve
=
0.988
Residence time V/Q = 32.4 seconds
Residence time ! t"e curve #se$undos%
=
269.43445
Variance o& t s2= 1903.36
Variance o& t"eta = 0.0253027
1. 'ra(car )a curva *#t% para estos datos.
0 50 100 150 200 250 300 350 400 450 500
0
2
4
6
8
10
12
*#t% vs t#s%
E(t) vs t(s)
2. +Qu, &racci-n de materia) reside entre 23 s ! 2 s en
e) reactor0
&racci-n de materia) reside entre 23 s ! 2
s en e) reactor=
3
3. 'ra(car )a curva #t% para estos datos.
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0 50 100 150 200 250 300 350 400 450
0
0.5
1
1.5
#t% vs t#s%
F(t) vs t(s)
4. +Qu, &racci-n de materia) reside menos de 2 s en e)
reactor0
&racci-n de materia) reside menos de 2 sen e) reactor
.44325
. Ca)cu)ar e) tiempo de residencia medio tm.
Ca)cu)ar e) tiempo de residencia
medio tm
25.43
44
5. 'ra(car #t 6 tm%2*#t% como &unci-n de) tiempo.
0 50 100 150 200 250 300 350 400 450 500
02
4
6
8
10
12
14
##t 6 tm%72%8*#t% vs t#s%
((t tm)^2)*E(t)/s vs
t(s)
. Ca)cu)ar )a varian9a 72
Ca)cu)ar )a varian9a
72.
13.3
5
s2
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;. 11 s61> +Qu, conversiones predicen )osmode)os de se$re$aci-n ! tan?ues en serie0
Para una rea!"n #e $r!mer %r#en& 'a %nvers!"n a 'a sa'!#a #e'tanue n est #a#a $%r 'a e$res!"n
. Ca)cu)ar )a conversi-n idea)> si se asume @uo pist-n.
**RCCD< ETR
Ejercicio 1:
Un anlisis de la DTR se efectu en un reactor de fase lquida. Se obtuvieronlos siguientes datos:
t Concentration
0 0
15
0
0
1
5
0.001
!0
0
0.00"
!!
5
0.00#
!#
0
0.00$#
!5
0
0.00$
!%
0
0.00$#
!
5
0.00&!
"00
0.005
FAn .15;;
.24
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"!
5
0.00!5
"5
0
0.001!
"
5
0.0005
#00
0.000!
#5
0
0
1. 'raficar la curva ()t* +ara estos datos.!. ,-u fraccin de /aterial reside entre !"0 s !0 s en el reactor". 'raficar la curva 2)t* +ara estos datos.
#. ,-u fraccin de /aterial reside /enos de !50 s en el reactor5. 3alcular el tie/+o de residencia /edio t/.%. 'raficar )t 4 t/*!()t* co/o funcin del tie/+o.. 3alcular la variana 6!.&. Si se efectu en el reactor una reaccin de +ri/er orden con 7 8 090115
s419 ,-u conversiones +redicen los /odelos de segregacin tanquesen serie
9. 3alcular la conversin ideal9 si se asu/e fluo +istn.
Ejercicio 2:
;as concentraciones de traador9 en un e
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2 0.322.5 0.37
3 0.43.5 0.43
4 0.454.5 0.48
5 0.485.5 0.496 0.5
6.5 0.57 0.51
7.5 0.518 0.51
8.5 0.519 0.51
9.5 0.52
10 0.52
3alcular graficar las curvas ()t* 2)t*9 calcular el tie/+o de residencia /ediot/ la variana =>!
t/mint/se
g
Concentratio
ntm Cn C F Cn t tm
0 0 15 0 0 0 0. 30 0.11 45 0.00045
436
0.000454
36
0.01363
07
0.01363
074
0.6
1 60 0.2 75 0.00082
611
0.000826
11
0.03841
39
0.02478
315
1.8
1. 90 0.27 105 0.00111
524
0.001115
24
0.07187
11
0.03345
72
3.5
2 120 0.32 135 0.00132177 0.00132177 0.111524 0.0396531 5.3
2. 150 0.37 165 0.00152
829
0.001528
29
0.15737
3
0.04584
87
7.5
3 180 0.4 195 0.00165
221
0.001652
21
0.20693
9
0.04956
63
9.6
3. 210 0.43 225 0.00177
613
0.001776
13
0.26022
3
0.05328
39
11.
4 240 0.45 255 0.00185
874
0.001858
74
0.31598
5
0.05576
22
14.
4. 270 0.48 285 0.00198
265
0.001982
65
0.37546
5
0.05947
95
16.
300 0.48 315 0.00198 0.001982 0.43494 0.05947 18.
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265 65 4 95
. 330 0.49 345 0.00202
396
0.002023
96
0.49566
3
0.06071
88
20.
5 360 0.5 375 0.00206
526
0.002065
26
0.55762
1
0.06195
78
23.
5. 390 0.5 405 0.00206
526
0.002065
26
0.61957
9
0.06195
78
25.
420 0.51 435 0.00210657
0.00210657
0.682776
0.0631971
27.
. 450 0.51 465 0.00210
657
0.002106
57
0.74597
3
0.06319
71
29.
; 480 0.51 495 0.00210
657
0.002106
57
0.80917 0.06319
71
31.
;. 510 0.51 525 0.00210
657
0.002106
57
0.87236
7
0.06319
71
33.
540 0.51 555 0.00210
657
0.002106
57
0.93556
4
0.06319
71
35.
. 570 0.52 585 0.00214787
0.00214787
1 0.0644361
37.
1 600 0.52 0 0 0 0 0
1.00000
029
353
TABLA 1:
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TABLA 2:
*#
% #
% #
% Ln #
%
0.04239
11
0 0 1 0 0
0.12717
3
0.16077
3
0.01363
07
0.98636
9
-
0.013724
5
0.162995
0.21195
6
0.29231
5
0.03841
39
0.96158
6
-
0.039171
1
0.303993
0.29673
8
0.39462
6
0.07187
11
0.92812
9
-
0.074584
7
0.425184
0.38152 0.467704
0.111524
0.888476
-0.118248
0.526412
0.46630
2
0.54078
3
0.15737
3
0.84262
7
-
0.171231
0.641782
0.55108
5
0.58463 0.20693
9
0.79306
1
-
0.231855
0.737182
0.63586
7
0.62847
8
0.26022
3
0.73977
7
-
0.301407
0.84955
0.72064
9
0.65770
9
0.31598
5
0.68401
5
-
0.379776
0.961542
0.80543
2
0.70155
7
0.37546
5
0.62453
5
-
0.470747
1.12333
0.89021
4
0.70155
7
0.43494
4
0.56505
6
-
0.570831
1.24157
0.97499
6
0.71617
2
0.49566
3
0.50433
7
-0.68451 1.42003
1.05978 0.73078
8
0.55762
1
0.44237
9
-
0.815588
1.65195
1.14456 0.73078
8
0.61957
9
0.38042
1
-
0.966476
1.921
1.22934 0.74540
4
0.68277
6
0.31722
4
-1.14815 2.34977
1.31413 0.74540
4
0.74597
3
0.25402
7
-1.37031 2.93435
1.39891 0.74540
4
0.80917 0.19083 -1.65637 3.90611
1.48369 0.74540
4
0.87236
7
0.12763
3
-2.05859 5.8402
1.56847 0.74540
4
0.93556
4
0.06443
62
-2.74208 11.5681
1.65325 0.76002 1 2.22E-
16
- 3.42E+15
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a) GAF!C" E(t):
0 100 200 300 400 500 600 700
0
2
4
6
8
10
12
*#t% vs t#se$.%
E(t) vs t(m!n)
#) GAF!C" F(t):
0 100 200 300 400 500 600 700
0
0.2
0.4
0.6
0.8
1
1.2
#t% vs t#se$.%
F(t) vs t(se,un#%s)
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Ejercicio $%
;a /asa de reaccin en un tanque agitado continuo ocu+a un volu/en de? 8 195/". (l fluo volu/trico es @?0 8 "0 ;A/in. Bara /edir la DTR9 seintroduo en el reactor un traador inerte en for/a de escaln. ;a curva 2)t*9 ala salida del reactor9 est re+resentada +or los siguientes datos:
t/min F(t)
5 0.!$
10 0."
15 0.##
!0 0.51
!5 0.5%
"0 0.%1
"5 0.%5
#0 0.%$
#5 0."
50 0.%
%0 0.&1
0 0.&5
&0 0.&&
$0 0.$1
100 0.$"
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Una re+resentacin de 2 co/o funcin de /uestra clara/ente unadesviacin del co/+orta/iento ideal. Una concentracin elevada de traador9/edida a la salida del reactor9 al inicio del e
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Tabla I
T(s) Concentration tm Cn C F Cnt tmCnt tm2Cnt
300 0.00058 450 7.2846e-005 7.2846e-005 0 0.0218538 9.83421 4425.4
600 0.00074 750 9.29415e-005 9.29415e-005 0.0278824 0.0278824 20.9118 15683.9
900 0.00088 1050 0.000110525 0.000110525 0.0610399 0.0331575 34.8154 36556.1
1200 0.00102 1350 0.000128109 0.000128109 0.0994725 0.0384326 51.8839 70043.3
1500 0.00112 1650 0.000140668 0.000140668 0.141673 0.0422005 69.6307 114891
1800 0.00122 1950 0.000153228 0.000153228 0.187641 0.0459683 89.6383 174795
2100 0.0013 2250 0.000163276 0.000163276 0.236624 0.0489827 110.211 247975
2400 0.00138 2550 0.000173323 0.000173323 0.288621 0.051997 132.592 338110
2700 0.00146 2850 0.000183371 0.000183371 0.343632 0.0550113 156.782 446829
3000 0.00152 3300 0.000190907 0.000190907 0.458176 0.114544 377.995 1.24739e+006
3600 0.00162 3900 0.000203466 0.000203466 0.580256 0.12208 476.112 1.85683e+006
4200 0.0017 4500 0.000213514 0.000213514 0.708365 0.128109 576.488 2.5942e+0064800 0.00176 5100 0.00022105 0.00022105 0.840995 0.13263 676.413 3.44971e+006
5400 0.00182 5700 0.000228586 0.000228586 0.978146 0.137151 781.763 4.45605e+006
6000 0.00186 --- --- --- --- --- --- ---
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Tabla II
E() F() I() n I()
0.126225 0.259701 0 1 0 0.259701
0.210374 0.331343 0.0278824 0.972118 -0.0282785 0.340847
0.294524 0.39403 0.0610399 0.93896 -0.0629823 0.419645
0.378674 0.456716 0.0994725 0.900528 -0.104775 0.507165
0.462824 0.501492 0.141673 0.858327 -0.15277 0.584267
0.631123 0.582089 0.236624 0.763376 -0.270005 0.762519
0.715273 0.61791 0.288621 0.711379 -0.34055 0.868609
0.799423 0.653731 0.343632 0.656368 -0.421034 0.995982
0.925648 0.680596 0.458176 0.541824 -0.612815 1.25612
1.09395 0.725373 0.580256 0.419744 -0.868111 1.72813
1.26225 0.761193 0.708365 0.291635 -1.23225 2.61009
1.43055 0.788059 0.840995 0.159005 -1.83882 4.95618
1.59885 0.814925 0.978146 0.0218538 -3.82338 37.2898
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C!r"es #arameters
Area under concentration vs. time curve = 7.962
Residence time V! = 30000 secondsResidence time "# t$e curve = 3565.07 seconds
Variance o% t = 2.34375e+006 s2
Variance o% t$eta =0.184406
First or$er con"ersions
&onversion = 0.984822
'(u) %(o* conversion = 0.999906e(( mi,ed conversion = 0.90268
A,ia( disersion mode( conversion = 0.997416
an/s in serires conversion = 0.995516
&$o(ette-&(outier conversion = 0.98475
evensie( conversion = 0.984753
%o$els #arameters
A,ia( disersion mode( u( = 0.102806
um"er o% tan/s in series = 5.42283
&$o(ette and &(outier mode(
nut %(o* to t$e *e(( mi,ed reactor = 1800 ($
#ass %(o* = 0 ($
e(( mi,ed vo(ume = 1.24101e+007 cm3
eat$ vo(ume = 2.58992e+006 cm3
evensie( mode(
e(( mi,ed vo(ume = 1.24101e+007 cm3
eat$ vo(ume = 2.58992e+006 cm3
'(u) %(o* vo(ume26.9341 cm3
&orre(ation coe%%icient com"ined mode(s = 0.856884
Result:
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;a fraccin de este circuito corto )*
Variance o% t$eta =0.184406
(ventual fraccin de volu/en /uerto )G*.
eat$ vo(ume = 2.58992e+006 cm3
3alcular la conversin que se es+era en este reactor.&onversion = 0.984822