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Mathematical Modeling of Fed-Batch Ethanol Fermentation Under Very High Gravity and High Cell Density at Different Temperatures

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Abstract

The use of more appropriate kinetic models can assist in improving ethanol fermentation under conditions of very high gravity (VHG) and high cell density (HCD), in order to obtain higher amounts of ethanol in the broth combined with high productivity. The aim of this study was to model fed-batch ethanol fermentation under VHG/HCD conditions, at different temperatures, considering three types of inhibition (substrate, ethanol, and cells). Fermentations were carried out using different temperatures (28 ≤ \(T\) (°C) ≤ 34), inoculum sizes (50 ≤ \({C}_{X0}\) (g L−1) ≤ 125), and substrate concentrations in the must (258 ≤ \({C}_{SM}\) (g L−1) ≤ 436). In the proposed model, the cell inhibition power parameter varied with the temperature and inoculum size, while the cell yield coefficient varied with inoculum size and substrate concentration in the must. Hence, it was possible to propose correlations for the cell inhibition power parameter (\(m=f(T,{C}_{X0})\)) and for the cell yield coefficient (\({Y}_{X/S}=f({C}_{SM},{C}_{X0})\)), as functions of the fermentation conditions. Simulations of fed-batch ethanol fermentations at different temperatures, under VHG/HCD conditions, were performed using the proposed correlations. Experimental validation showed that the model was able to accurately predict the dynamic behavior of the fermentations in terms of the concentrations of viable cells, total cells, ethanol, and substrate.

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Data Availability

All data generated or analyzed during this study are included in this published article.

Abbreviations

\({C}_{E}\)  :

Ethanol concentration (g L−1)

\({C}_{E0}\) :

Initial ethanol concentration (g L−1)

\({C}_{Ef}\) :

Final ethanol concentration (g L−1)

\({C}_{Emax}\) :

Maximum concentration of ethanol after which cell growth ceased (g L−1)

\({C}_{S}\) :

Substrate concentration (g L−1)

\({C}_{SM}\) :

Substrate concentration in the must (g L−1)

\({C}_{S0}\) :

Initial substrate concentration (g L−1)

\({C}_{Sf}\) :

Final substrate concentration (g L−1)

\({C}_{VX}\) :

Viable cell concentration (g L−1)

\({C}_{X}\) :

Total cell concentration (g L−1)

\({C}_{X0}\) :

Initial total cell concentration (g L−1)

\({C}_{Xmax}\) :

Maximum cell concentration after which cell growth ceased (g L−1)

\(F\) :

Feed flow rate of the must (L h−1)

\({K}_{IS}\) :

Substrate inhibition constant (g L−1)

\({K}_{S}\) :

Saturation constant (g L−1)

\(m\) :

Cell inhibition power (dimensionless)

\(n\) :

Product inhibition power (dimensionless)

\({Y}_{E/S}\) :

Ethanol yield coefficient (gE gS−1)

\({Y}_{X/S}\) :

Cell yield coefficient (gX gS−1)

\(\mu\) :

Specific cell growth rate (h−1)

\({\mu }_{max}\) :

Maximum specific cell growth rate (h−1)

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Acknowledgements

The authors are grateful for the financial supports received in this research.

Funding

This study was financed in part by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior- Brazil (CAPES, Finance Code 001). This study was also financially supported by the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP, grant number 2018/11405–5) and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, grant numbers 431460/2016–7, 310098/2017–3, 141300/2019–1, and 140761/2017–9).

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  1. Graduate Program of Chemical Engineering, Federal University of São Carlos, C.P. 676, São Carlos, SP, 13565-905, Brazil

    Ivan I. K. Veloso, Kaio C. S. Rodrigues, Gustavo Batista, Antonio J. G. Cruz & Alberto C. Badino

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  1. Ivan I. K. Veloso
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Contributions

Ivan I. K. Veloso: conceptualization, methodology, validation, investigation, data curation, and writing — original draft. Kaio C. S. Rodrigues: conceptualization, methodology, validation, investigation, data curation, and writing — review & editing. Gustavo Batista: software, writing — review & editing. Antonio J. G. Cruz: supervision and writing — review & editing. Alberto C. Badino: supervision and writing — review & editing, resources, and funding acquisition.

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Correspondence to Alberto C. Badino.

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Veloso, I.I.K., Rodrigues, K.C.S., Batista, G. et al. Mathematical Modeling of Fed-Batch Ethanol Fermentation Under Very High Gravity and High Cell Density at Different Temperatures. Appl Biochem Biotechnol 194, 2632–2649 (2022). https://doi.org/10.1007/s12010-022-03868-x

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