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Mathematical modeling of a continuous alcoholic fermentation process in a two-stage tower reactor cascade with flocculating yeast recycle

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Abstract

Experiments of continuous alcoholic fermentation of sugarcane juice with flocculating yeast recycle were conducted in a system of two 0.22-L tower bioreactors in series, operated at a range of dilution rates (D 1 = D 2 = 0.27–0.95 h−1), constant recycle ratio (α = F R /F = 4.0) and a sugar concentration in the feed stream (S 0) around 150 g/L. The data obtained in these experimental conditions were used to adjust the parameters of a mathematical model previously developed for the single-stage process. This model considers each of the tower bioreactors as a perfectly mixed continuous reactor and the kinetics of cell growth and product formation takes into account the limitation by substrate and the inhibition by ethanol and biomass, as well as the substrate consumption for cellular maintenance. The model predictions agreed satisfactorily with the measurements taken in both stages of the cascade. The major differences with respect to the kinetic parameters previously estimated for a single-stage system were observed for the maximum specific growth rate, for the inhibition constants of cell growth and for the specific rate of substrate consumption for cell maintenance. Mathematical models were validated and used to simulate alternative operating conditions as well as to analyze the performance of the two-stage process against that of the single-stage process.

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Abbreviations

D :

Dilution rate (h−1)

D 1 :

Dilution rate for the first reactor (h−1)

D 2 :

Dilution rate for the second reactor (h−1)

F :

Feed volumetric flow rate (L/h)

F R :

Recycle volumetric flow rate (L/h)

K S,X :

Saturation constant for μ X (g/L)

K S,P :

Saturation constant for μ P (g/L)

m :

Specific rate of substrate consumption for cell maintenance (g/g h)

n :

Exponent for ethanol effect on μ X (−)

P m,X :

Ethanol concentration for μ X  = 0 (g/L)

P m,P :

Ethanol concentration for μ P = 0 (g/L)

P i :

Ethanol concentration in the stage i (g/L)

P 1 :

Ethanol concentration in the first reactor (g/L)

P 2 :

Ethanol concentration in the second reactor (g/L)

S 0 :

Sugar concentration in the feed stream (g/L)

S i :

Sugar concentration in the stage i (g/L)

S 1 :

Sugar concentration in the first reactor (g/L)

S 2 :

Sugar concentration in the second reactor (g/L)

\(s_{\text{e}}^{2}\) :

Estimated variance of the experimental errors

\(s_{\text{m}}^{2}\) :

Estimated variance of the errors between model and experiments

V F,1 :

Volume of the first reactor (L)

V F,2 :

Volume of the second reactor (L)

V tot :

Total volume of the reactor system (L)

V S :

Volume of the settler (L)

X i :

Cell concentration in the stage i (g/L)

X 1 :

Cell concentration in the first reactor (g/L)

X 2 :

Cell concentration in the second reactor (g/L)

X e :

Cell concentration in the effluent (g/L)

X m :

Cell concentration for which μ X  = 0 (g/L)

X S :

Cell concentration in the recycle stream to the first reactor (g/L)

w = X S/X 2 :

Cell concentration factor in the settler (−)

Y P/S :

Apparent yield coefficient for substrate-to-ethanol conversion (g/g)

\(Y_{\text{P/S}}^{*}\) :

Stoichiometric coefficient for substrate-to-ethanol conversion (g/g)

\(Y_{{X / {\text{S}}}}^{*}\) :

Stoichiometric coefficient for substrate-to-biomass conversion (g/g)

α = F R/F :

Recycle ratio (−)

β :

Level of significance of the statistical test (=0.05 =5 %)

ɛ :

Estimate of the relative experimental errors of the measured variables

ϕ :

Sum of squares of the normalized residuals (−)

\(\mu_{{X_{i} }}\) :

Specific growth rate in stage i (h−1)

\(\mu_{{X_{1} }}\) :

Specific growth rate in the first reactor (h−1)

\(\mu_{{X_{2} }}\) :

Specific growth rate in the second reactor (h−1)

μ max,X :

Maximum specific growth rate (h−1)

\(\mu_{{{\text{P}}_{i} }}\) :

Specific rate of ethanol production in stage i (g/g h)

\(\mu_{{{\text{P}}_{1} }}\) :

Specific rate of ethanol production in the first reactor (g/g h)

\(\mu_{{{\text{P}}_{2} }}\) :

Specific rate of ethanol production in the second reactor (g/g h)

μ max,P :

Maximum specific rate of ethanol production (g/g h)

\(\mu_{{{\text{S}}_{i} }}\) :

Specific rate of sugar (substrate) consumption in stage i (g/g h)

\(\mu_{{{\text{S}}_{1} }}\) :

Specific rate of sugar consumption in the first reactor (g/g h)

\(\mu_{{{\text{S}}_{2} }}\) :

Specific rate of sugar consumption in the second reactor (g/g h)

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Authors and Affiliations

  1. Departamento de Bioprocessos e Biotecnologia, Faculdade de Ciências Farmacêuticas, UNESP - Univ Estadual Paulista, Rodovia Araraquara-Jaú km 1, Caixa Postal 502, Araraquara, SP, 14801-902, Brazil

    Samuel Conceição de Oliveira

  2. Departamento de Engenharia Química (LEQ), Escola de Engenharia de Lorena (EEL), Universidade de São Paulo (USP), Caixa Postal 116, Lorena, SP, 12602-810, Brazil

    Heizir Ferreira de Castro

  3. Departamento de Biotecnologia (LOT), Escola de Engenharia de Lorena (EEL), Universidade de São Paulo (USP), Caixa Postal 116, Lorena, SP, 12602-810, Brazil

    Alexandre Eliseu Stourdze Visconti

  4. Departamento de Engenharia Química (PQ), Escola Politécnica (EP), Universidade de São Paulo (USP), Av. Prof. Luciano Gualberto, travessa 3, No. 380, São Paulo, SP, 05508-010, Brazil

    Reinaldo Giudici

Authors
  1. Samuel Conceição de Oliveira
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  2. Heizir Ferreira de Castro
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  3. Alexandre Eliseu Stourdze Visconti
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  4. Reinaldo Giudici
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Correspondence to Samuel Conceição de Oliveira.

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de Oliveira, S.C., de Castro, H.F., Visconti, A.E.S. et al. Mathematical modeling of a continuous alcoholic fermentation process in a two-stage tower reactor cascade with flocculating yeast recycle. Bioprocess Biosyst Eng 38, 469–479 (2015). https://doi.org/10.1007/s00449-014-1286-2

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