## 3 Results and Discussion
### Kinetic Modeling of Product Formation  
For product formation, the experimental data, which were utilized to calculate the model kinetic parameters, were used to build the LP model (Equation (12)). Satisfactory fitting results were achieved with \(R^{2}\), which ranged from 0.9217 to 0.9870. When the regression coefficients for the kinetic models analyzed were higher than 0.90, it can be accepted that they explain higher fractions of the total variation [38; 46]. The calculated non-growth associate terms of ethanol (\(\beta\)) in different nutritional compositions were all close to zero, which ranged from 0.0011 to 0.0571 gP/gX.h (Table 1). On the other hand, the growth-associated constants (\(a\)) for ethanol in different medium contents varied from 1.3559-2.6724 gP/g\(X\) (Table 1 and Figure 1B,E,H,K,N). Namely, the value of \(a\) was 24-2359 fold higher than that of \(\beta\) (Table 1). The results indicated that as \(a\
eq 0\) and \(\beta\) value was obtained very close to zero, product formation was growth-associated in PCS biofilm reactor. Some existing results in the literature are given in Table 3. [PERSON] and [PERSON] [29] produced ethanol from banana and pineapple wastes and the experimental data obtained were predicted by the LP model. According to their findings, the empirical constants, \(a\) and \(\beta\), were not equal to zero, even the \(\beta\) values were calculated negative. Therefore, it was reported that ethanol production was growth associated, which assisted the result obtained from this study. It was also stated that the experimental ethanol production data from banana and pineapple wastes fitted well the predicted data from LP model (\(R^{2}\) = 0.98 and 0.91 and RMSD = 0.0019 and 0.0178 g/L, respectively) [29]. In another study, the pyrolysate derived from untreated cotton waste was pretreated with 0.2 M H\({}_{2}\)SO\({}_{4}\) at 120 \({}^{\circ}\)C for 25 min. After detoxification, the acid-hydrolysate pyrolytic sugars were used for ethanol production by _E. coli_. Then the experimental data were estimated by the LP model. It was noted that \(a\) and \(\beta\) were 0.05 gP/gX and 0.29 gP/gX.h, respectively (\(R^{2}\) = 0.996), indicating that ethanol formation was growth associated due to a very small \(\beta\) value [24]. On the other hand, the kinetic modeling of ethanol production from red beet juice using two different _S. cerevisiae_ strains was also performed and the values of \(a\) and \(\beta\) were found to be 5.3143 gP/g\(X\) and -0.044 gP/gX.h for ITD00196 and 4.5326 gP/g\(X\) and 0.1047 gP/gX.h for ATCC 9763 (Table 3). Therefore, \(\beta\) values were 121 and 43-fold smaller than that of \(a\) and show that product formation is growth-associated ([PERSON] et al., 2014). Similarly, [PERSON], et al. [47] modelled the ethanol production from the pretreated corn stover by the co-culture of _S. cerevisiae_ and _C. tropicalis_. When the calculated kinetic parameters related to ethanol production, \(a\) (2.392 gP/g\(X\)) and \(\beta\) (0.013 gP/g\(X\).h), were examined, it was observed that the ethanol production was growth associated due to very small \(\beta\) value, such that the \(a\) value was 184-fold higher than the \(\beta\) value. In conclusion, our results are highly compatible with the existing results in the literature. Subjective comparison of the ethanol production curve with LP model was given by plotting both the observed and predicted data (Figure 3). LP model relatively high predicted the experimental data in the acceleration and log phases of the fermentation in Medium A, in acceleration and log phases of the fermentation in Medium B, in log and stationary phases of the fermentation in Medium