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Modeling of heat and mass transfer for solid state fermentation process in tray bioreactor

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Abstract

A mathematical model is developed to simulate oxygen consumption, heat generation and cell growth in solid state fermentation (SSF). The fungal growth on the solid substrate particles results in the increase of the cell film thickness around the particles. The model incorporates this increase in the biofilm size which leads to decrease in the porosity of the substrate bed and diffusivity of oxygen in the bed. The model also takes into account the effect of steric hindrance limitations in SSF. The growth of cells around single particle and resulting expansion of biofilm around the particle is analyzed for simplified zero and first order oxygen consumption kinetics. Under conditions of zero order kinetics, the model predicts upper limit on cell density. The model simulations for packed bed of solid particles in tray bioreactor show distinct limitations on growth due to simultaneous heat and mass transport phenomena accompanying solid state fermentation process. The extent of limitation due to heat and/or mass transport phenomena is analyzed during different stages of fermentation. It is expected that the model will lead to better understanding of the transport processes in SSF, and therefore, will assist in optimal design of bioreactors for SSF.

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Abbreviations

a s(t):

Transient interfacial area per unit volume for mass transfer, m−1

A :

Area of the bed, m2

\(C_{O_2 } \) :

Gas phase oxygen concentration in the bed, kg/m3

\(C_{O_2 }^f \) :

Film phase oxygen concentration, kg/m3

C p :

Heat capacity, cal/(kg) (°C)

\(D_{O_2 }^b \) :

Effective diffusivity of oxygen in film, m2/h

\(D_{O_{2_{o}}}^b \) :

Bi-molecular diffusivity of oxygen, m2/h

\(D_{O_2 }^b {\text{ (t)}}\) :

Transient effective diffusivity of oxygen in bed, m2/h

ΔH :

Heat of the reaction, cal/kg Cell

h :

Convective heat transfer coefficient, cal/(m2)(h)(°C)

H :

Separation coefficient

k :

Thermal conductivity, cal/(m)(h)(°C)

K g :

mass transfer coefficient, m/h

\(K_{O_2 } \) :

Saturation parameter for oxygen, kg/m3

L :

Height of the bed, m

n :

Number of particles per unit volume of bed

r :

Radial position coordinate, m

r x :

Cell mass production rate, kg cell mass/m3

R(t) :

Transient radial position coordinate, m

R c :

Particle radius, m

R i :

Initial biofilm radius, m

R max :

Maximum biofilm radius, m

t :

time, h

T :

Temperature, °C

X :

Biomass concentration, kg cell/m3

X max :

Maximum biomass concentration, kg cell/m3

X p :

Biomass, kg cell

y :

Vertical position coordinate, m

\(Y_{O_2 /x} \) :

Oxygen yield coefficient, kg O2/kg Cell

z :

Transformed radial position coordinate

ɛ :

Porosity of the bed

ρ s :

Apparent density of the substrate, kg/m3

ρ x :

Density of the fungal cell, kg/m3

τ :

Tortuosity of the bed

μ m(T):

Maximum growth rate, 1/h

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Authors and Affiliations

  1. Department of Chemical Engineering, Indian Institute of Science, 560012, Bangalore, India

    S. Rajagopalan & J. M. Modak

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  1. S. Rajagopalan
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Rajagopalan, S., Modak, J.M. Modeling of heat and mass transfer for solid state fermentation process in tray bioreactor. Bioprocess Eng. 13, 161–169 (1995). https://doi.org/10.1007/BF00369700

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