Yahia Esmail^1*, Ramez Mohammad¹ and Oulfat Jolaha²

1 Department of Food Science, Lattakia University, Syria.
2 Department of Computer Engineering and Automatic Control, Lattakia University, Syria.

(*Corresponding author: Yahia Esmail, Email: yahia.esmail@tishreen.edu.sy, Tel: +963 936 094505).

Received: 3/ 3/ 2025       Accepted: 5/ 7/ 2025

Abstract

In this study, filtered and purified grape juice was fermented at 25℃, after the juice was inoculated with instant dry yeast Saccharomyces cerevisiae ATCC® 2601™ and the fermentation process took 10 days, a sample was taken every 24 hours to measure the total sugars concentration, biomass and ethanol concentration formed during fermentation. The initial conditions were set as follows: initial sugars concentration S_0=200 ± 0.059g/l, initial alcohol concentration P_0=0g/l, initial yeast concentration X_0=1.5g/l, it was observed that 12.66 ± 0.071g of sugars were consumed after one day of fermentation to produce 10.52 ± 0.22g of ethanol, which represents 83.10% of the consumed sugars, and the biomass increased by 0.66 ± 0.273g, which represents 5.21% of the consumed sugars. The consumption of the substrate continues with the increase in the fermentation period, so that the total consumed sugars reached about 95.74% on the tenth day of fermentation, i.e. at a rate of 191.48 ± 1.291 g, and the maximum alcohol concentration on the tenth day also reached 120.1 ± 0.04g/l. As for the biomass, the maximum concentration of biomass was X_max=15.39 ± 0.04g/l on the tenth day of fermentation, and the growth rate of yeast cells was μ_max=0.674/l. The process of biomass formation, substrate consumption, and alcohol production were modeled according to three special equations as a function of time, which were solved by Runge-Kutta and Euler methods, where the results of the solution by Euler method outperformed the results of the Runge-Kutta method in the measurements of biomass, substrate, and ethanol due to the low value of the coefficient of Determination R^2, the mean absolute error MAE, and the mean square error MSE, where the values reached:

Keywords: Biomass, Substrate, Differential Equations, Runge-Kutta, Euler.

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