Modeling the continuous lactic acid production process from wheat flour

Abstract

A kinetic model of the simultaneous saccharification, protein hydrolysis, and fermentation (SSPHF) process for lactic acid production from wheat flour has been developed. The model describes the bacterial growth, substrate consumption, lactic acid production, and maltose hydrolysis. The model was fitted and validated with data from SSPHF experiments obtained under different dilution rates. The results of the model are in good agreement with the experimental data. Steady state concentrations of biomass, lactic acid, glucose, and maltose as function of the dilution rate were predicted by the model. This steady state analysis is further useful to determine the operating conditions that maximize lactic acid productivity.

Appendix A: Values of variables at steady state as a function of the dilution rate

The lactic acid concentration at steady state from Eq. 7 can be represented by:

$$ \overset{-}{P}=\left(-\frac{{\overset{-}{D}}^{1/n}}{{\mu_{\max}}^{1/n}}+1\right){P}_{\max } $$

(A.1)

To determine the biomass concentration at steady state, the derivative in Eq. 2 was canceled, thus giving

$$ \overset{-}{P}=\frac{Y_P}{Y_X}\frac{\overline{\mu}}{\overline{D}}\overline{X} $$

(A.2)

where $\overset{-}{X}$ is the biomass concentration at steady state. As $\overline{\mu}=\overline{D}$, the biomass concentration at steady state can be represented as a function of the dilution rate at steady state introducing Eq. 7 in Eq. A.2 as follows:

$$ \overset{-}{X}=\frac{Y_X}{Y_P}\left(-\frac{{\overset{-}{D}}^{1/n}}{{\mu_{\max}}^{1/n}}+1\right){P}_{\max } $$

(A.3)

The glucose concentration at steady state can be represented as a function of the biomass concentration by canceling the dynamics of Eq. 3

$$ \overset{-}{S}=\frac{K_M\overset{-}{M}}{\overset{-}{D}}+{S}_0-\frac{\overset{-}{X}}{Y_X} $$

(A.4)

where $\overset{-}{S}$ and $\overset{-}{M}$ are the glucose and maltose concentrations at steady state, respectively. Equation A.4 shows that $\overline{S}$ depends not only on the biomass concentration but also on the maltose concentration and on the dilution rate. From Eq. 4, it is possible to determine the maltose concentration at steady state:

$$ \overset{-}{M}=\frac{\overset{-}{D}{M}_0}{\overset{-}{D}+{K}_M} $$

(A.5)

Eq. A.5 defines the maltose concentration at steady state as a function of the dilution rate, replacing Eq. A.5 in Eq. A.4, it is possible to obtain:

$$ \overset{-}{S}=\frac{K_M{M}_0}{\left(\overset{-}{D}+{K}_M\right)}+{S}_0-\frac{\overset{-}{X}}{Y_X} $$

(A.6)

From Eqs. A.6 and A.3, the glucose concentration at steady state becomes:

$$ \overset{-}{S}=\frac{K_M{M}_0}{\left(\overset{-}{D}+{K}_M\right)}+{S}_0-\frac{1}{Y_P}\left(-\frac{{\overset{-}{D}}^{1/n}}{{\mu_{\max}}^{1/n}}+1\right){P}_{\max } $$

(A.7)

Eqs. A.1, A.3, A.5, and A.7 allow to express all variables at steady state only in terms of the dilution rate.