Practica Biotecnologia
17
Tiempo (h) 0 0.2 25 0.33 0.21 24.8 0.5 0.22 24.8 0.75 0.32 24.6 1 0.47 24.3 1.5 1 23.3 2 2.1 20.7 2.5 4.42 15.7 2.8 6.9 10.2 3 9.4 5.2 3.1 10.9 1.65 3.2 11.6 0.2 3.5 11.7 0 3.7 11.6 0 Ysx global Tiempo (h) Ln X (kgm-3) U (1/h) 0 ### 0.33 ### 0.15 0.5 ### 0.27 0.75 ### 1.50 1 ### 1.54 1.5 ### 1.51 2 ### 1.48 2.5 ### 1.49 2.8 ### 1.48 3 ### 1.55 3.1 ### 1.48 3.2 ### 0.62 3.5 ### 0.03 3.7 ### -0.04 Umax 1.35 S (kg/m3) U (1/) 25 24.8 0.15 24.8 0.27 Concentracion de celulas, x (kgm-3) Concentracion de sustrato (kgm-3)
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Tiempo (h) Yxs
0 0.2 250.33 0.21 24.8 0.050.5 0.22 24.8 0.00
0.75 0.32 24.6 0.501 0.47 24.3 0.50
1.5 1 23.3 0.532 2.1 20.7 0.42
2.5 4.42 15.7 0.462.8 6.9 10.2 0.453 9.4 5.2 0.50
3.1 10.9 1.65 0.423.2 11.6 0.2 0.483.5 11.7 0 0.503.7 11.6 0 0.00
Ysx global 0.46
Tiempo (h) Ln X (kgm-3) U (1/h)
0 -1.609437910.33 -1.56064775 0.150.5 -1.51412773 0.27
0.75 -1.13943428 1.501 -0.75502258 1.54
1.5 0.00000000 1.512 0.74193734 1.48
2.5 1.48613970 1.492.8 1.93152141 1.483 2.24070969 1.55
3.1 2.38876279 1.483.2 2.45100510 0.623.5 2.45958884 0.033.7 2.45100510 -0.04
Umax 1.35
S (kg/m3) U (1/)
2524.8 0.1524.8 0.2724.6 1.5024.3 1.5423.3 1.51
Concentracion de celulas, x (kgm-3)
Concentracion de sustrato (kgm-3)
0 0.5 1 1.5 2 2.5 3 3.5 4
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
2.50
3.00
Tiempo (h)Ln
X
0 5 10 15 20 25 30-0.2
00.20.40.60.8
11.21.41.61.8
S (kg/m3)
u (1
/h)
20.7 1.4815.7 1.4910.2 1.485.2 1.55
1.65 1.480.2 0.620 0.030 -0.04
1/S 1/U
0.0980392156862745 0.67357950.192307692307692 0.64685510.606060606060606 0.6754333
5 1.60662420 34.9497854
Ks/Umax 0.19871/Umax 0.6077
Umax 1.65Ks 0.32697054467665
MODELO DE GOMPERTZ
a b c
YA=a*exp(-exp(b-c*TA))Dep. Var. : YA
0 5 10 15 20 25 30-0.2
00.20.40.60.8
11.21.41.61.8
S (kg/m3)
u (1
/h)
0 2 4 6 8 10 120.000.200.400.600.801.001.201.401.601.80
S (kg/m3
U
0 1 2 3 4 5 60.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
f(x) = 0.198688373206859 x + 0.607736124582049R² = 0.99254314315224
1/S
1/U
0.000 1.000 2.000 3.000 4.000 5.000 6.0000.0000.2000.4000.6000.8001.0001.2001.4001.6001.800
f(x) = 0.198688373206859 x + 0.607736124582049R² = 0.99254314315224
Chart Title
2.041589 1.667028 1.053617
Umax= a*c 2.151052
CONCLUSIONUmax 1.55Uprom 1.35Umax Monnot 1.65Umax Gompertz 2.15
Log (X/Xo)
YA0
0.0211890.0413930.2041200.3710680.6989701.0211891.3443921.5378191.6720981.7363971.7634281.7671561.763428
0 0.5 1 1.5 2 2.5 3 3.5 40
5
10
15
20
25
30Concentracion celulas / sustrato
Concentracion de Celulas Concentracion de Sustrato
Tiempo (h)
Conc
entr
aciò
n (k
gm-3
)
0 0.5 1 1.5 2 2.5 3 3.5 4
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
2.50
3.00
Tiempo (h)
Ln X Se halla Umax (velocidad
maxima) no es integral perfecta.
0 5 10 15 20 25 30-0.2
00.20.40.60.8
11.21.41.61.8
S (kg/m3)
u (1
/h)
𝑢= (𝑈𝑚𝑎𝑥∗𝑆)/(𝐾𝑠+𝑆)1/𝑈= (𝐾𝑠+ 𝑆)/(𝑈𝑚𝑎𝑥∗𝑆)1/𝑈= 𝐾𝑠/𝑈𝑚𝑎𝑥
+ 𝑆/(𝑈𝑚𝑎𝑥∗𝑆)1/𝑈= 1/𝑈𝑚𝑎𝑥
+ 𝐾𝑠/𝑈𝑚𝑎𝑥∗1/𝑆
Siempre debo empezar de 0 para los cultivos
1/S
0 5 10 15 20 25 30-0.2
00.20.40.60.8
11.21.41.61.8
S (kg/m3)
u (1
/h)
0 2 4 6 8 10 120.000.200.400.600.801.001.201.401.601.80
S (kg/m3
U
𝑢= (𝑈𝑚𝑎𝑥∗𝑆)/(𝐾𝑠+𝑆)1/𝑈= (𝐾𝑠+ 𝑆)/(𝑈𝑚𝑎𝑥∗𝑆)1/𝑈= 𝐾𝑠/𝑈𝑚𝑎𝑥
+ 𝑆/(𝑈𝑚𝑎𝑥∗𝑆)1/𝑈= 1/𝑈𝑚𝑎𝑥
+ 𝐾𝑠/𝑈𝑚𝑎𝑥∗1/𝑆
0 1 2 3 4 5 60.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
f(x) = 0.198688373206859 x + 0.607736124582049R² = 0.99254314315224
1/S
1/U
0.000 1.000 2.000 3.000 4.000 5.000 6.0000.0000.2000.4000.6000.8001.0001.2001.4001.6001.800
f(x) = 0.198688373206859 x + 0.607736124582049R² = 0.99254314315224
Chart Title
0 0.5 1 1.5 2 2.5 3 3.5 40
5
10
15
20
25
30Concentracion celulas / sustrato
Concentracion de Celulas Concentracion de Sustrato
Tiempo (h)
Conc
entr
aciò
n (k
gm-3
)
0.040 6.7640.040 3.6540.041 0.6670.041 0.6500.043 0.6620.048 0.6740.064 0.6720.098 0.6740.192 0.6470.606 0.6755.000 1.607
Tiempo (d) Yxs
0 0.64 30120 5 1.95 27.4 0.50240 10 4.21 23.6 0.59360 15 5.54 21 0.51480 20 6.98 18.4 0.55600 25 9.5 14.8 0.70720 30 10.3 13.3 0.53840 35 12 9.7 0.47960 40 12.7 8 0.41
1080 45 13.1 6.8 0.331200 50 13.5 5.7 0.361320 55 13.7 5.1 0.33
Yxs global 0.52
Tiempo (h) Log X (gL-1)
0 -0.193820035 0.29003461 0.0968
10 0.62428210 0.066815 0.74350976 0.023820 0.84385542 0.020125 0.97772361 0.026830 1.01283722 0.007035 1.07918125 0.013340 1.10380372 0.004945 1.11727130 0.002750 1.13033377 0.002655 1.13672057 0.0013
Umax 0.0968
S (gL-1) U
30 027.4 0.096823.6 0.066821 0.0238
18.4 0.020114.8 0.026813.3 0.00709.7 0.01338 0.0049
6.8 0.0027
Concentracion de biomasa x (gL-1 peso seco)
Concentracion de azucar (gL-1)
ɥ (1/h)
5.7 0.00265.1 0.0013
1/S 1/U0.0333333 0.00000.0364964 10.33370.0423729 14.95900.0476190 41.93660.0543478 49.82780.0675676 37.35020.0751880 142.39490.1030928 75.36470.1250000 203.06650.1470588 371.26210.1754386 382.77590.1960784 782.8648
Ks/Umax -4.56981/Umax 0.2585
Umax 3.86847195357834Ks
Log (X/Xo)
YA0.00000 a) Representar U en funcion del tiempo de cultivo . ¿Cuàndo se alcanza la màxima velocidad de crecimiento?0.48385 b) Representar la velocidad especìfica de consumo de azùcar en funciòn del tiempo0.81810 c) ¿Cuàl es el rendimiento observado de biomasa a partir de sustrato? ¿Es Yxs constante?0.937331.037681.171541.206661.273001.297621.311091.324151.33054
0 10 20 30 40 50 600
5
10
15
20
25
30
35
Concentracion celulas/sustrato vs tiempo
Concentracion de Celulas Concentracion de Sustrato
Tiempo (d)
Conc
entr
acio
n gL
-1
14 16 18 20 22 24 260.00
0.20
0.40
0.60
0.80
1.00
1.20
Curva de Crecimiento Logaritmico
Tíempo (d)
Ln X
(gL-
1)
16 18 20 22 24 26 280.0000
0.0200
0.0400
0.0600
0.0800
0.1000
0.1200
Modelo de Monnot
MODELO DE GOMPERTZa b c
1.293490 0.819133 0.138331
Umax 0.17892907
16 18 20 22 24 26 280.0000
0.0200
0.0400
0.0600
0.0800
0.1000
0.1200
Modelo de Monnot
0.0350000 0.0400000 0.0450000 0.0500000 0.0550000 0.06000000.0000
10.0000
20.0000
30.0000
40.0000
50.0000
60.0000
f(x) = 2446.75335350202 x − 81.3510872150044R² = 0.904842984929649
Chart Title
a) Representar U en funcion del tiempo de cultivo . ¿Cuàndo se alcanza la màxima velocidad de crecimiento?
16 18 20 22 24 26 280.0000
0.0200
0.0400
0.0600
0.0800
0.1000
0.1200
Modelo de Monnot
16 18 20 22 24 26 280.0000
0.0200
0.0400
0.0600
0.0800
0.1000
0.1200
Modelo de Monnot
0.0350000 0.0400000 0.0450000 0.0500000 0.0550000 0.06000000.0000
10.0000
20.0000
30.0000
40.0000
50.0000
60.0000
f(x) = 2446.75335350202 x − 81.3510872150044R² = 0.904842984929649
Chart Title
MODELO DE MONOD
Tiempo (h) ° Brix N (*10^6) Yxs0.00 23.7 15 0.00982.50 23.6 25.25 0.0583
24.00 23 35.55 -0.263230.50 21.5 29.85 0.197448.00 20 37.45 0.190178.00 15 63.75 0.000096.00 15 110 0.0000168 15 5.9 0.0000171 15 19.4 0.0000
Rendimiento global: Yxs global 0.091610.9195402299
Tiempo (h) Ln X U (1/h)0.00 2.7082.50 3.229 0.208
24.00 3.571 0.01630.50 3.396 -0.02748.00 3.623 0.01378.00 4.155 0.01896.00 4.700 0.030168 1.775 -0.041171 2.965 0.397
Umax 0.208
S (kg/m3) U (1/)23.723.6 0.20823 0.016
21.5 -0.02720 0.01315 0.01815 0.030
0 20 40 60 80 100 1202.50
3.00
3.50
4.00
4.50
5.00
Tiempo (h)
Ln X
0 20 40 60 80 100 12013
33
53
73
93
113
133
Concentración de Sustrato
Concentración de Biomasa
Tiempo (h)
Conc
entr
ació
n
14 16 18 20 22 24 26
-0.050
0.000
0.050
0.100
0.150
0.200
0.250
HORRIBLE
21 21.5 22 22.5 23 23.5 24
-0.050
0.000
0.050
0.100
0.150
0.200
0.250
f(x) = 0.0959468151042421 x − 2.11221362698362R² = 0.686286236284393
Chart Title
H6
Shyrley: 27°C
H7
Shyrley: 29°C
ºAlcohol1012 1.7 0.2 0.111013 1.84 0.47 0.231014 0.73 0.431015 2.12 1.1 0.59
Rendimiento global: Yps global
Densidad ºBaumé ºBrix
1.98
0 20 40 60 80 100 1202.50
3.00
3.50
4.00
4.50
5.00
Tiempo (h)
Ln X
0 20 40 60 80 100 12013
33
53
73
93
113
133
Concentración de Sustrato
Concentración de Biomasa
Tiempo (h)
Conc
entr
ació
n
14 16 18 20 22 24 26
-0.050
0.000
0.050
0.100
0.150
0.200
0.250
HORRIBLE
21 21.5 22 22.5 23 23.5 24
-0.050
0.000
0.050
0.100
0.150
0.200
0.250
f(x) = 0.0959468151042421 x − 2.11221362698362R² = 0.686286236284393
Chart Title
