Cinetica de Biorreactores

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5. Cinética en Ingeniería Bioquímica

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5.1. Fundamentos El interés de la Ingeniería Bioquímica es proporcionar procesos viables, que han demostrado ser factibles en el laboratorio área de • Ejemplo clásico de fracaso desalinización • Precaución: costos involucrados en la transferencia de un proceso de laboratorio •

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5.1. Fundamentos Para un diseño adecuado, debe considerarse la economía del proceso en forma global y no sólo considerar el costo del fermentador en sí • Por ejemplo: un diseño con los costos •

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5.2. Factores considerados en el diseño de bio-reactores

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5.2.1. Objetivos y fases del diseño •

Problemas involucrados en el diseño de un reactor (Levenspiel, 1971): 1. Se Sele lecc cció iónn de dell me mejo jorr ti tipo po de

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5.2.1. Objetivos y fases del diseño • Objetivo del diseño: 

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Etapas en el diseño de un fermentador: 1 Selecció iónn de de un una ce cepa ap apro roppia iadda de de

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Etapas en el diseño de un fermentador (cont.): 4. El ár área ea de tr tran ansf sfer eren enci ciaa de de cal calor or y

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Etapas en el diseño de un fermentador (cont.):

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5.2.2. Diferencias entre procesos químicos y bioquímicos 1. La co complejidad reactante

de

la la

mezcla me

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5.2.2. Diferencias entre procesos

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5.2.3. Clasificación de las

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5.4.1. Características generales Variables que afectan la velocidad de reacción: 

En sistemas homogéneos:   Temperatura  pH  Composición

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5.4.1. Características generales Para sistemas heterogéneos: •

Es conveniente considerar la velocidad de reacción para una sola partícula (Rp) Depende de la concentración del

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Distribución de concentración en el fluido alrededor de la partícula (cuando no es afectado por la proximidad de otras partículas) CL u

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Variación de la concentración en la región de una partícula

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Variación de la concentración en la interfase CL

C*

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5.4.1. Características generales •

La influencia de la velocidad del fluido sobre la velocidad de reacción es tal que a

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Efecto de la velocidad del fluido en el perfil de concentración    C  ,

u

Superficie de una partícula biológica  C 

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Efecto de la velocidad del fluido en la velocidad total de reacción C*

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5.4.1. Características generales Bajo condiciones de estado estable, la cinética de esta partícula puede ser modelada por la ecuación de transferencia

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Cinética de primer orden • Si:

N = k1C*

(6)

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Transporte activo (C” > C’; bR > bP   e    d   o   m   u   s   o   n   t   o   a   c   r   e   t   s    d   b    d  u   a   s    d

aP a P = V R a R

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Transporte pasivo (C’ > C’’; bP > bR)   e    d   o   m   u   s   o   n   t   o   a   c   r   e   t   s    d   b    d  u   a   s    d

aP aP = VR aR

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Ecuación generalizada am -Dm dC = ai a Ci dr am (b + Ci) Donde:

(22)

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5.4.2.1. Modelos teóricos Modelo en serie R = R max [[ [1 + (k’2)2 + k3C*] - {[1 + (k’2)2 - k3C*]2 + 4k3C*}1/2]] 2 (k’2)2

(23)

•

El parámetro k’2 representa una limitación de difusión de fase “sólida”, cuando está ausente o es muy pequeña, la ecuación de velocidad para un microorganismo aislado se

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Modelo en paralelo a) Pa Para ra mi micr croo oorg rgan anis ismo moss es esfé féri rico coss D d r2 dC - aRC = 0 r2 dr dr bR + C b) Pa Para ra mic micro roor orga gani nism smos os cilí cilínd ndri rico coss

(25)

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Modelo en paralelo •

Las restricciones para aplicar las ecuaciones anteriores son las

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Modelo en paralelo •

La solución a las ecuaciones 25 y 26 tomando en cuenta las restricciones:

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Modelo en serie C*

C*

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Modelo en paralelo C*

C*

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5.4.2.2. Modelos experimentales •

Ecuación de Monod (1949)

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¿Cómo plantear los fenómenos de

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Características de la masa

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Ecuación de velocidad biológica (Atkinson y col., 1974) Ecuación completa para películas microbianas N= Donde:

l=1

– tanh k2L

k2L 1 tanh k

l

k1LC* 1 + k3C* fP

-1

tanh fP 1 -1

(51) fP 1

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Ecuación de velocidad biológica Ecuaciones reducidas para películas microbianas •

Si k2L < 1 para cualquier k3C* o si k3C* < 0.1 para cualquier k2L: N = tanh fR fR

k1LC* 1 + k3C*

(52)

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Ecuación de velocidad biológica Ecuaciones reducidas para películas microbianas •

Si k2L >20 para cualquier k3C* o si k3C* > 100 para cualquier k2L: Para fR < 1 (Ec. 53)



N = k1LC* 1 + k3C*

(54)

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Ecuación de velocidad biológica reducida

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Ecuación de Velocidad Biológica

para un m.o. en forma de cilindro infinito Modelo cinético de resistencias en serie 

1 C si siddér

a di dif si sión ón

tadd ta

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2. Si la lass con condi dici cion ones es lílími mite te so son: n:

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Integrando la ec. (56):

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3.

Combin Comb inan ando do la lass ec ecua uaci cion ones es (5 (56) 6),, (5 (57) 7) y (58): C* = C +

Ac

ln r

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5. De Defi fini nien endo do coe coefi fici cien ente tess de vel veloc ocid idad ad::

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The world's largest digital library

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