LAUSR

Mathematical models not only ensure information about kinetic-metabolic nature of fermentations, but also facilitate their control and optimization. In the study, flexible ten models were evaluated and employed to describe the ethanol fermentation in a biofilm reactor with a carob extract medium (CEM). Findings indicated that W model well fitted the experimental data of cell growth (root mean square error (RMSE) = 0.289 g/L, mean absolute error (MAE) = 0.237 g/L, regression coefficient ( R 2 ) = 0.9944, bias factor (BF) = 1.021, and accuracy factor (AF) = 1.047), ethanol production (RMSE = 1.609 g/L, MAE = 1.277 g/L, R 2  = 0.9774, BF = 1.178, and AF = 1.283), and substrate consumption (RMSE = 2.493 g/L, MAE = 1.546 g/L, R 2  = 0.9931, BF = 1.001 and AF = 1.053). In the prediction of kinetic parameters, W model also gave better and well-directed results compared with the other mathematical models used in the study. When an independent set of experimental data was used in the validation of mathematical models, similar validation results were obtained and W model was also successful. Consequently, W model could be used for more progress of fermentation process in biofilm reactor with CEM, which can serve as a universal equation.