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
References
Aidoo, K.E.; Hendry, R.; Wood, B.J.B.: Solid substrate fermentations. Advances in Applied Microbiology. 28 (1980) 201–237
Andre, G.; Moo-Young, M.; Robinson, T.M.: Improved method for the dynamic measurement of mass transfer coefficient for application to solid-substrate fermentation. Biotechnol. Bioeng. 23 (1981) 1611–1622
Cooney, C.L.; Wang, D.I.C.; Manteles, R.I.: Measurement of heat evolution and correlation with oxygen consumption during microbialgrowth. Biotechnol. Bioeng. 11 (1968) 269–281
Crank, J.: Free and Moving Boundary Problems. Oxford University Press, London, 1984
Finger, S.M.; Hatch, R.T.; Regan, T.M.: Aerobic microbial growth in semisolid matrices: Heat and mass transfer limitation. Biotechnol. Bioeng. 28 (1976) 1193–1218
Finlayson, B.A.: In: Nonlinear Analysis in Chemical Engineering, McGraw-Hill, New York, 1980
Froment, G.F.; Bischoff, K.B.: In: Chemical Reactor Design and Analysis, John Wiley & Co., New York, 1979
Georgiou, G.; Shuler, M.L.: A computer model for the growth and differentiation of a fungal colony on solid substrate. Biotechnol. Bioeng. 28 (1986) 405–416
Hesseltine, C.W.: Solid state fermentations. Biotechnol. Bioeng. 14 (1972) 517–532
Kobayashi, T.: Van Dedem, G.; Moo-Young, M.: Oxygen transfer into mycelial pellets. Biotechnol. Bioeng. 15 (1973) 27–45
Laukevics, J.J.; Aspite, A.F.; Viesturs, U.S.; Tengerdy, R.P.: Steric hindrance of growth of filamentous fungi in solid substrate fermentation of wheat straw. Biotechnol. Bioeng. 27 (1985) 1687–1691
Lonsane, B.K.; Ghildyal, N.P.; Budiatman, S.; Ramakrishna, S.V.: Engineering aspects of solid state fermentation. J. Enz. Microb. Technol. 7 (1985) 258–265
Mitchell, D.A.; Do, D.D.; Greenfield, P.F.: A semimechanistic mathematical model for growth of Rhizophus oligosporus in a model solid-state fermentation system. Biotechnol. Bioeng. 38 (1991) 353–362
Perry, R.H.; Chilton, C.H.: In: Chemical Engineer's Handbook. Fifth Edition, McGraw-Hill, New York, 1973
Raghava Rao, M.K.; Gowthaman, M.K.; Ghildyal, N.P.; Karanth, N.G.: A mathematical model for solid state fermentation in tray bioreactors. Bioprocess Engineering. 8 (1993) 255–262
Rajagopalan, S.; Modak, J.M.: Heat and Mass Transfer Simulation Studies for Solid-State Fermentation Processes, Chemical Engineering Science 49 (1994) 2187–2193
Rathbun, B.L.; Shuler, M.L.: Heat and mass transfer effects in static solid-substrate fermentations: Design of fermentation chambers. Biotechnol. Bioeng. 25 (1983) 929–937
Saucedo-Castaneda, G.; Gutierrez-Rojas, M.; Bacquet, G.; Raimbault, M.; Vibiegra-Gonzalez, G.: Heat transfer simulation in solid substrate fermentation. Biotechnol. Bioeng. 35 (1990) 802–808
Wittier, R.; Baumgartl, H., Lubbers, D.W.; Schugerl, K.: Investigations of Oxygen Transfer into Penicillium chrysogenum Pellets by Microprobe Measurements. Biotechnol. Bioeng. 28 (1986) 1024–1036
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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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DOI: https://doi.org/10.1007/BF00369700