Método General y Ball.

 

Fig. Fig . 2: VELOCIDAD LET L ETAL AL EN FUNCIÓN DEL TIEMPO PARA HALLAR EL F0 (EL ÁREA BAJO LA CURVA) CURVA) 0.3

0.2

       L

0.1

0.0 0

10

20

30

40

50

t (min)

60

70

80

90

100

 

Curso: Tecnología Tecnología de d e Alimentos I Universidad Nacional Agraria La Molina. Lima. Perú. Ing. Carlos Elías Peñafiel

PROBLEMA: Se esteriliza una salsa de tomate en el autoclave. Tiempo

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

t (min) 0 5 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Tº Retorta TR (ºC) 20.0 82.5 94.4 104.6 114.1 115.9 116.1 116.1 115.5 114.9 114.6 114.7 114.6 114.7 115.2 115.4 115.5 115.5

Tº pmf   T (ºC) 16.4 28.1 30.4 55.7 60.3 65.9 71.2 76.8 82.3 86.8 89.5 94.2 96.8 99.3 102.0 104.0 105.7 107.3

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

 

38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 70 74 76 78 80 82 84 86 90

115.6 115.5 115.3 115.3 115.3 115.2 115.2 115.2 115.2 115.2 115.3 115.4 115.3 115.4 115.3 115.3 115.3 115.2 32.7 29.0 29.3 26.5 24.3 21.7

108.7 109.7 110.6 111.4 112.0 112.5 113.0 113.4 113.7 113.9 114.2 114.4 114.6 114.7 114.8 114.9 115.1 115.1 89.8 82.6 83.4 81.5 77.4 66.6

Fig. 1 : MONITOREO DE LA TEMPERATURAS DE LA RETORTA Y DEL PRODUCTO, EN FUNCIÓN DEL TIEMPO

140.0

120.0

   T 100.0   y    R    T 80.0

60.0

40.0

20.0

0.0 0

10

20

30

40

50

60

T (min) TR

T

70

80

90

1 00

MÉTODO GENERAL Para el C. botulinum: Z = 10 ºC y temperatura de 121.1 ºC

Tiempo

F Δt (min)

1 2 3 4 5 6 7

t (min) 0 5 6 8 10 12 14

Tº pmf T (ºC) 16.4 28.1 30.4 55.7 60.3 65.9 71.2

8 9 10 11 12 13

16 18 20 22 24 26

76.8 82.3 86.8 89.5 94.2 96.8

L

F0

Fx((L1+L2)/2)

F0 Acumulado

(min)

5 1 2 2 2 2

10 (1/Z)(T-121.1) 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0

2 2 2 2 2 2

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0

 

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

28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 70 74 76 78 80 82 84 86 90

99.3 102.0 104.0 105.7 107.3 108.7 109.7 110.6 111.4 112.0 112.5 113.0 113.4 113.7 113.9 114.2 114.4 114.6 114.7 114.8 114.9 115.1 115.1 89.8 82.6 83.4 81.5 77.4 66.6

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 2 2 2 2 2 2 4

0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.0 0.0 0.0 0.0 0.0 0.0

F0 =

0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.9 1.0 0.5 0.3 0.0 0.0 0.0 0.0 0.0 7.5

0.0 0.0 0.1 0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.3 1.6 1.9 2.2 2.6 3.0 3.4 3.9 4.3 4.8 5.7 6.7 7.2 7.5 7.5 7.5 7.5 7.5 7.5

F0

 

  o

Fig. 3: F0 ACUMULAD ACUMULADO O

   d   a    l   u   m   u   c   a    0    F

8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0

10

20

30

40

50 t (min)

MÉTODO DE BALL Tiempo

1 2 3 4 5 6 7

t (min) 0 5 6 8 10 12 14

Tº Retorta TR (ºC) 20.0 82.5 94.4 104.6 114.1 115.9 116.1

Tº pmf   T (ºC) 16.4 28.1 30.4 55.7 60.3 65.9 71.2

60

70

80

90

100

8 9 10 11 12 13

16 18 20 22 24 26

116.1 115.5 114.9 114.6 114.7 114.6

76.8 82.3 86.8 89.5 94.2 96.8

14 15 16 17 18 19 20

28 30 32 34 36 38 40

114.7 115.2 115.4 115.5 115.5 115.6 115.5

99.3 102.0 104.0 105.7 107.3 108.7 109.7

2 21 2 23 24 25 26 27 28

4 42 4 46 48 50 52 54 56

1 11 15 5..3 3 115.3 115.2 115.2 115.2 115.2 115.2

111110..46 112.0 112.5 113.0 113.4 113.7 113.9

2 39 0 31

5 68 0 62

1 11 15 5..3 4 115.3

1 11 14 4..2 4 114.6

 

32 33 34 35 36

64 66 70 74 76

115.4 115.3 115.3 115.3 115.2

114.7 114.8 114.9 115.1 115.1

3 37 8 39 40 41 42

7 88 0 82 84 86 90

3 22 9..7 0 29.3 26.5 24.3 21.7

8 89 2..8 6 83.4 81.5 77.4 66.6

SOLUCIÓN PASO 1.-

SE HALLA LA DIFERENCIA ENTRE LA Tº DE LA RETORTA (CUANDO ESTA ES CONSTANTE) T1 Y LA Tº pmf 

Tiempo t (min) 0 5 6 8 10 12 14 16 18 20

TR (ºC) 20.0 82.5 94.4 104.6 114.1 115.9 116.1 116.1 115.5 114.9

Tpmf T (ºC) 16.4 28.1 30.4 55.7 60.3 65.9 71.2 76.8 82.3 86.8

Diferencia T1 - T (ºC) 98.9 87.2 84.9 59.6 55.0 49.4 44.1 38.5 33.0 28.5

T1 = T0 =

115.3 16.4

 

22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 70

114.6 114.7 114.6 114.7 115.2 115.4 115.5 115.5 115.6 115.5 115.3 115.3 115.3 115.2 115.2 115.2 115.2 115.2 115.3 115.4 115.3 115.4 115.3 115.3

89.5 94.2 96.8 99.3 102.0 104.0 105.7 107.3 108.7 109.7 110.6 111.4 112.0 112.5 113.0 113.4 113.7 113.9 114.2 114.4 114.6 114.7 114.8 114.9

25.8 21.1 18.5 16.0 13.3 11.3 9.6 8.0 6.6 5.6 4.7 3.9 3.3 2.8 2.3 1.9 1.6 1.4 1.1 0.9 0.7 0.6 0.5 0.4

140.0 120.0 100.0 80.0 60.0 40.0

74 76 78 80 82 84 86 90

PASO 2 ..-

115.3 115.2 32.7 29.0 29.3 26.5 24.3 21.7

115.1 115.1 89.8 82.6 83.4 81.5 77.4 66.6

0.2 0.2 25.5 32.7 31.9 33.8 37.9 48.7

20.0 0.0

GRAFICANDO EL PERFIL DE TEMPERATURAS

FIG. 4: PERFIL DE TEMPERATURAS, TR Y T 140.0 120.0

   )    C    º    ( 100.0    T

6; 115.9

36; 115.1

80.0 60.0 40.0 20.0 0.0  

0

10

20

 

0

10

20

30

40

50

60

t (min) T1

T

FIG. 5: TÉRMINOS USADOS PARA BALL

En base a los terminos definidos para el método de Ball

70

80

90

100

CUT = Coming Up Time o Tiempo de levante de la temperatura de la retorta. CUT = Tc 12   th = tB =

76  th - 0,58*CUT = 76 - 0.58x12 =

69.0

PASO 3 ..-

TOMANDO EL TIEMPO Y LA DIFERENCI DE Tº CON LA FINALIDAD DE  GRAFICARLOS EN PAPEL SEMILOGARÍTMICO Tomamos los puntos solo de calentamiento Tiempo Diferencia t T1 - T (min) (ºC) 0 98.9 5 87.2 6 84.9 180 12 14 16

55 9..0 6 5 49.4 44.1 38.5

   

 

18 20 22

33.0 28.5 25.8

2 24 6 28 30 32 34 36 38

2 11 8..1 5 16.0 13.3 11.3 9.6 8.0 6.6

4 40 2 44 46 48 50 52 54

5 4..6 7 3.9 3.3 2.8 2.3 1.9 1.6

5 56 8 60 62 64 66 70 74

1 1..4 1 0.9 0.7 0.6 0.5 0.4 0.2

76

0.2

100.0

10.0

1.0 20

0.1

f ( x ) = 221.30 R² = 0.99785

30

4

FIG. 6: DIFERENCIA DE TEMPERATURAS EN FUNCIÓN DEL TIEMPO

100.0    C    º  ,    )    T      1    T    (

 

f(x) = 191.8322310067 exp( - 0.0895101669 x ) R² = 0.9975093867 6 10.0

 

 

 

1.0 10

0.1

20

30

40

50

60

70

80

t (min)

PASO 4 ..--

TOMANDO SOLO LOS DATOS QUE SE ASEMEJAN A UNA LINEA RECTA, CON LA FINALIDAD DE HALLAR LA CURVA AJUSTADA.  A partir de t = 28 min la curva es lineal.

Tiempo t (min) 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 70 74 76

Diferencia T1 - T (ºC) 16.0 13.3 11.3 9.6 8.0 6.6 5.6 4.7 3.9 3.3 2.8 2.3 1.9 1.6 1.4 1.1 0.9 0.7 0.6 0.5 0.4 0.2 0.2

FIG. 7: CURVA AJUSTADA 100.0

   C    º  ,    )    T      T    1    (

f(x) = 221.308723145 221.3087231453 3 exp( - 0.0920225842 0.0920225842 x ) 10.0

R² = 0.9978502577

 

 

 

1.0 20

0.1

30

40

50

t (min)

60

70

80