## 3 Results and Discussion
### Kinetic Modeling of Product Formation
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Microorganism** & **Substrate** & \(\mu_{max}\) & \(X_{max}\) & \(a\) & \(\beta\) & \(\gamma\) & \(Z\) & **Ref.** \\ \hline _Aspergillius ferrus_ and & Banana waste & 0.0187 & 20.34 & 0.4529 & \(-\)0.00003\(-\)0.28820 & 0.17450 & [29] \\ _Kluvernos marzimus_ & Pineapple waste & 0.0037 & 36.74 & 0.3661 & \(-\)0.0036 & \(-\)29.3869 & 0.0014 & [29] \\ _Escherichia coli_ & Waste cotton & 0.21 & 3.75 & 0.05 & 0.29 & 0.25 & 0.47 & [24] \\ _S. cerevisiae_ ITD00196 & Red Beet Juice & 0.4669 & 6.35 & 5.3184 & \(-\)0.044 & 0.0732 & \(-\)0.0848 & [25] \\ _S. cerevisiae_ ATCC 9763 & Red Beet Juice & 0.3794 & 5.31 & 4.5326 & 0.1047 & 0.074 & 0.095 & [25] \\ _K. marzimus_ DSM 5422 & Whey permeate & 0.75 & - & 5 & 0.4185 & 0.0394 & 0.4287 & [26] \\ _K. marzimus_ DSM 5422 & Lactose & 0.6567 & - & 5 & 0.0686 & 0.0673 & 0.062 & [26] \\ _K. marzimus_ DSM 5422 & Inulin & 0.75 & - & 4.1232 & 0.0033 & 0.0785 & 0 & [26] \\ _K. fragilis_-NCIM 0557 & Sugarcane bagasse & 0.2 & 5.50 & 0.38 & 0.012 & 8.2 & 0.008 & [27] \\ _K. marzimus_ & Crude whey & 0.095 & 12.80 & 0.733 & 0 & 3.3846 & 0.135 & [28] \\ _S. cerevisiae_ and _Candidia tropicalis_ & Corn stover & 0.125 & 3.16 & 2.392 & 0.013 & 0.488 & 0.007 & [47] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Model parameters for different ethanol fermentations. C, in acceleration, log and stationary phases of the fermentation in Medium D, and in the stationary phase of the fermentation in Medium E. Besides, the deceleration phase data of the fermentation in Medium C were slightly underestimated with the LP model. Additionally, Table 1 also shows the success of LP equation, which was evaluated in terms of RMSE, MAE, slope, BF, and AF. The results in Table 1 indicate that the RMSE and MAE values were between 1.43 and 3.46 g/L and between and 0.88 and 2.11 g/L, respectively, showing that higher error values were obtained from Medium A while lower errors were achieved by Medium E. The slope values also varied between 0.92 and 1.07, such that the slope values of Media C and D were equal to each other, which were yielded as 0.97. The values of the slope indicated that the predicted values were close to the experimental values as they were all close to 1. Additionally, the BF values from the predicted data with the LP model were less than 0.87 except for that of Medium C (0.91). On the other hand, AF values from the predicted data with the LP model were 1.00\(\leq\)AF\(\leq\) 1.20 except for that of Media A (1.26) and D (1.21). Thus, although LP model was \"unacceptable\" for Media A, B and D based on the BF values, LP model was \"good\" for Media B, C, and D and was \"acceptable\" for Media A and D depending on the AF values in Table 1. Therefore, it can be concluded that the LP model satisfactorily can be used to predict ethanol production in biofilm reactors. Afterwards, the experimental kinetic parameters related to ethanol production were also estimated using the data from the LP model (Table 2). The results indicate that, except for Medium E, the observed values of \(\Delta P\), \(Y_{P\beta}\) and \(\eta\) were satisfactorily predicted by the LP model. For Medium E, their values were higher speculated by the LP model (Table 2). Nevertheless, the LP model forecasted slightly lower experimental values of \(Y_{P\beta X}\), except for Medium E. During ethanol fermentation, the maximum volumetric productivities of ethanol were estimated to be 2.05, 1.90, 1.22, 1.64, and 1.13 g/L/h, respectively (Table 2). Generally, the fitting kinetic results were satisfactory.