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

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