Paul Cortijo Cinetica de Crecimiento

8/19/2019 Paul Cortijo Cinetica de Crecimiento

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Tabla 01. Datos iniciales

Tiempo (h)

0.00 0.20 25.00.33 0.21 24.8

0.50 0.22 24.80.75 0.32 24.61.00 0.47 24.31.50 1.00 23.32.00 2.10 20.72.50 4.42 15.72.80 6.90 10.23.00 9.40 5.23.10 10.90 1.653.20 11.60 0.23.50 11.70 0.03.70 11.60 0.0

Tiempo (h) Ln(X)

0.00 0.20 -1.6

0.33 0.21 -1.60.50 0.22 -1.50.75 0.32 -1.11.00 0.47 -0.81.50 1.00 0.02.00 2.10 0.72.50 4.42 1.52.80 6.90 1.93.00 9.40 2.23.10 10.90 2.4

3.20 11.60 2.53.50 11.70 2.53.70 11.60 2.5

Tiempo (h) Ln(X)

Concentración eCe!"!a#$ X (%&'m3)

Concentración e#"#trato$ (%&'m3)

. *+,*++T* +L/C (h-1) + C +L T


. CL + +L L/* + L +L/C X (ma

2.5000

3.0000


2/30

0.00 -1.6094

0.33 -1.5606

0.50 -1.5141

0.75 -1.1394

1.00 -0.7550

1.50 0.0000

2.00 0.74192.50 1.4861

2.80 1.9315

3.00 2.2407

3.10 2.3888

3.20 2.4510

3.50 2.4596

3.70 2.4510

Tiempo (h) A:# Tiempo (h)0.00

0.0500 0.330.33

0.50

0.5000 0.250.75

1.00

0.5300 0.501.50

2.000.4640 0.502.50

2.80

0.5000 0.203.00

3.10

0.4828 0.103.20

3.50

#DIV/0! 0.203.70

*enimiento / e# C/TT+.

. +T+*+ C/ +L /+L/ + B/,+*T L/ ,*

Tiempo (h) = T A

0.00 0.2000 0.00

C. CL + +L *++T/ /+*/ + L /


0.00

-2.0000

-1.5000

-1.0000

-0.5000

0.0000

0.5000

1.0000

1.5000

2.0000

.

Ln(X)


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0.33 0.2100 0.02

0.50 0.2200 0.04

0.75 0.3200 0.20

1.00 0.4700 0.37

1.50 1.0000 0.70

2.00 2.1000 1.02

2.50 4.4200 1.342.80 6.9000 1.54

3.00 9.4000 1.67

3.10 10.9000 1.74

3.20 11.6000 1.76

3.50 11.7000 1.77

3.70 11.6000 1.76

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.500.00

0.200.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

B/6,+*TC

T

A

M o d e l : Y A = a * e x p ( - e x p ( b - c * T A ) )

y = ( 2 . 0 4 1 5 9 ) * e x p ( - e x p ( ( 1 . 6 6 7 0 3 ) - ( 1 . 0 5 3 6 2 ) * x ) )

: 1 : 2 : 3

: 4

: 5

: 6

: 7

: !

: 9

: 1 0 : 1 1 : 1 2 : 1 3 : 1 4

- 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0

T A

- 0 . 2

0 . 0

0 . 2

0 . 4

0 . 6

0 . !

1 . 0

1 . 2

1 . 4

1 . 6

1 . !

2 . 0


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+. /+L/ + // +T+ +XC+L

1' (h)

1.55 5.2000 0.65

1.48 1.6500 0.68

0.62 0.2000 1.61

0.03 0.0000 34.95

ma: 1.7221Dm 0.3525

. +CC + // +T+ TTTC

e!ocia (h-1)Concentración e

#"#trato$ (%&'m3)

0.00 1.00 2.00 3.00 4.00 5.000.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

= 0.9973445018

1'

1'

: 1 : 2 : 3

: 4

: 5

- 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0

T A

- 0 . 2

0 . 0

0 . 2

0 . 4

0 . 6


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TTTCma: 1.691172Dm 0.321163*F2 0.99500625


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0.00

0.150.271.501.541.511.481.491.481.551.48

0.620.03-0.04

+,/ (h)

);

0.00 0.50 1.00 1.50

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80.e!ocia

Veloci$a$ esec%&ica ' "-1

(:) = 1.3149631064: - 1.9349408356

Ln(:) en


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1$315@

+T*/ + C*+C++T/

ma: (h-1)

,*T* +L T*T/; + A:# C/TT+;

0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

> = 0.981677956

Tiempo (h)

0.05 0.10 0.15 0.20 0.25 0.300.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

*enimiento oG#erHao Gioma#a en

I tiempo (h)

A:#


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a!or mJ:imo e pro"cción e Gioma#aTiempo e Latencia (h)e!ocia mJ:ima e crecimiento (hF-1)Tiempo e &eneración

a b c R2

2.04 1.6670 1.05 1.00

/G#erHe ,reicte *e#i"a!#1 0.0000 0.01 -0.01

2 0.0212 0.05 -0.03

3 0.0414 0.09 -0.05

4 0.2041 0.18 0.02

5 0.3711 0.32 0.05

6 0.6990 0.69 0.017 1.0212 1.07 -0.05

8 1.3444 1.40 -0.05

9 1.5378 1.55 -0.01

10 1.6721 1.63 0.04

11 1.7364 1.67 0.07

12 1.7634 1.70 0.06

13 1.7672 1.79 -0.02

4.00

1: 1 2 : 1 3 : 1 4

3 . 5 4 . 0


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14 1.7634 1.83 -0.07

1'

0.19

0.61

5.00

-----

0.0000 1.0000 20.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2

6.00

0.0 5.0

-0.50

0.00

0.50

1.00

1.50

2.00

3 . 5 4 . 0

M o d e l : " = ( M * # ) $ ( % & # )

y = ( (1 . 6 9 1 1 7 ) * x ) $ ( ( . 3 2 1 1 6 3 ) & x )

: 1 : 2

1 . 6

1 . !

2 . 0


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M o d e l : " = ( M * # ) $ ( % & # )

y = ( ( 1 . 6 9 1 1 7 ) * x ) $ ( ( . 3 2 1 1 6 3 ) & x )

: 1 : 2

: 3

: 4

0 1 2 3 4 5

#

0 . 0

0 . 2

0 . 4

0 . 6

0 . !

1 . 0

1 . 2

1 . 4

1 . 6

1 . !

2 . 0


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2.00 2.50 3.00 3.50 4.00

2 en


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1$488@@

ma: (h-1)

0.00 0.50 1.00 1.50 2.00 2.50

-2.0000

-1.5000

-1.0000

-0.5000

0.0000

0.5000

1.0000

1.5000

2.0000: = . : - .

*> = 0.9997171066

Tiempo (h)

Ln(X)

0.35 0.40 0.45 0.50 0.55


13/30

2.0415890.6330842.1510520.322236


14/30

.0000 3.0000 4.0000 5.0000 6.0000

en


15/30

6


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Tiempo () Tiempo (h)

0 0 0.64

5 120 1.95

10 240 4.21

15 360 5.5420 480 6.98

25 600 9.50

30 720 10.30

35 840 12.00

40 960 12.70

45 1080 13.10

50 1200 13.50

55 1320 13.70

Ln (X) Tiempo (h) -0.4463 0 0

0.6678 120 9.28+-031.4375 240 6.41-03

1.7120 360 2.29-03

1.9430 480 1.93-03

2.2513 600 2.57-03

2.3321 720 6.74-042.4849 840 1.27-03

2.5416 960 4.72-04

2.5726 1080 2.58-04

2.6027 1200 2.51-04

2.6174 1320 1.23-04

Concentración eGioma#a (&'L pe#o #eco)

1. *+,*++T* +L/C +,+CKC + C*+C+T/ +

2. CL + +L L/* + L +L/C X (ma:);

1.0000

1.5000

2.0000

2.5000

3.0000 = 0.7518403351

Ln(X)


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ma:@ 0.001891

3. *+,*++T* +L/C +,+CMC + C// +

Tiempo (h) L()

30 0 1.48

27.4 120 1.44

23.6 240 1.37

21 360 1.32

18.4 480 1.26

14.8 600 1.17

13.3 720 1.12

9.7 840 0.99

8 960 0.90

6.8 1080 0.835.7 1200 0.76

5.1 1320 0.71

Tiempo (h) A:# Hariaci?n e tiempo0

0.5038461538 120120

240 0.5115384615 120360

4800.7 120

600

7200.4722222222 120

840

9600.3333333333 120

1080

1200

Concentración eN"car (&'L)

4. CL + +L *++T/ /+*/ + L /

0 200 400 600 800 1000 120

-1.0000

-0.5000

0.0000

0.5000

Tiempo (h)


18/30

1320 .

*enimiento / + C/TT+

5. +T+*+ C/ +L /+L/ + B/,+*T L/ ,*+T*

Tiempo (h) = T A

0 0.6 0.0000

120 2.0 0.4839

240 4.2 0.8181

360 5.5 0.9373

480 7.0 1.0377

600 9.5 1.1715

720 10.3 1.2067840 12.0 1.2730

960 12.7 1.2976

1080 13.1 1.3111

1200 13.5 1.3242

1320 13.7 1.3305

Concentración eGioma#a (&'L pe#o

#eco)

0 200 400 600 800 1000 12000.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

1.4000BompertN

M o d e l : Y A = a * e x p ( - e x p ( b - c * T A ) )

y = ( 1 . 2 9 3 4 6 ) * e x p ( - e x p ( ( . ! 1 9 1 7 ! ) - ( . 0 0 5 7 6 4 ) * x ) )

: 3

: 4

: 5

: 6 : 7

: ! : 9 : 1 0 : :

0 . !

1 . 0

1 . 2

1 . 4


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6. /+L/ + //

1' (h)

0 30.0 #DIV/0!

9.28-03 27.4 107.7086666168

6.41-03 23.6 155.9184144962

2.29-03 21.0 437.1077478271

1.93-03 18.4 519.3581757475

2.57-03 14.8 389.3033937612

6.74-04 13.3 1484.1915671092

1.27-03 9.7 785.53178981094.72-04 8.0 2116.575934077

2.58-04 6.8 3869.6899026026

2.51-04 5.7 3989.6992299825

1.23-04 5.1 8159.8529390562

1' (h)

1 107.7086666168 0.0364963504

2 155.9184144962 0.0423728814

3 437.1077478271 0.0476190476

4 519.3581757475 0.0543478261

e!ocia (h-1)Concentración e

#"#trato$ (%&'m3)

1'# (m3'%&)

300

400

500

600

= 0.90

1'

y = . e x p - e x p . - . x

: 1

: 2

: 3

: 4

: 5

: 6 : 7

: ! : 9 : 1 0 : 1 1 :

- 2 0 0 0 2 0 0 4 0 0 6 0 0 ! 0 0 1 0 0 0 1 2 0 0

T A

- 0 . 2

0 . 0

0 . 2

0 . 4

0 . 6

0 . !

1 . 0

1 . 2

1 . 4


20/30

ma: -0.0011793456Dm -30.0764677801

7. /+L/ + // C/ TTTC L+L*

'=4 M

+,ae 1923.409

Model: "=(M*#)$(%) (#peadee

0.035 0.0

100


21/30

30.0

27.4

23.6

21.018.4

14.8

13.3

9.7

8.0

6.8

5.7

5.1

Concentración e N"car(&'L)

C +L T+,/

0 200 400 600 800 1000 1200 14000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

Tiempo (h)

(h-1)

0 200 4000.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

Concentración Gioma#a'#"#trato

(oncent)acin biomasa

(oncent)acin aca)

Ti

0.5000

1.0000

1.5000

2.0000

2.5000

3.0000 = 0.7518403351

Ln(X)


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ma:@@

C* + C +L T+,/

0.0000

3.28-04

5.40-04

4.22-04

4.78-04

7.88-04

3.87-04

1.14-03

6.97-04

5.88-046.39-04

4.03-04

e!ocia e#pecOPca econ#"mo e #"#trato (h-1)

*T* +L T*T/; + A:# C/TT+;

0 1400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

6-0 en &+nci*n $el 7 tiemo

A:#

e!oc. e#p. con#"m. #"#trato (h-

0 200 400 600

-1.0000

-0.5000

0.0000

Tiempo (h)


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+ C*+C++T/

a b c R2

1.293464 0.819178 0.005764 0.97594641

a!or mJ:imo e pro"cción e Gioma#aTiempo e Latencia (h)e!ocia mJ:ima e crecimiento (hF-1)Tiempo e &eneración

N Observed Predicted Residuals1 0.000000 0.01022! -0.01022!

2 0.0211!9 0.04!451 -0.027262

3 0.041393 0.0!94!1 -0.04!0!9

4 0.204120 0.1!4611 0.019509

5 0.37106! 0.32206! 0.04!999

6 0.69!970 0.6!609! 0.012!72

7 1.0211!9 1.072320 -0.051131

! 1.344392 1.395!62 -0.051469

100 120 140 160 180 2000

ariación e tiempo

1400

: :


24/30


25/30

% beed

!276774 1 0.0092!4

2 0.006414

3 0.0022!!

4 0.001925

1) Model +: "=(M*

4 0.045 0.05 0.055 0.06

1'#


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600 800 1000 1200 1400

n


27/30

0.00137

0 1000 2000

0.0000

2.00-04

4.00-04

6.00-04

8.00-04

1.00-03

1.20-03

(ol+mn

Tiempo (h)

)

00 1000 1200 1400


28/30


29/30

20.0 25.0 30.0 35.0


30/30

ed+ced e+dal

0.006367 0.002917

0.0054!4 0.000929

0.004!!0 -0.002592

0.004276 -0.002350

)$(%) (#peadee1)

Paul Cortijo Cinetica de Crecimiento

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