## 4 Results and Discussion  
### Kinetic Parameters  
In order to obtain the kinetic parameters of the Monod equation, batch cultivations were carried out inside the quasi-isoactinic photobioreactor for 10 days at a fixed temperature (25 \({}^{\circ}\)C) and incident light intensities of 20, 50, 100, 140, 210, 300 and 450 \(\mu\)E s\({}^{-1}\)m\({}^{-2}\). The growth of microalga _Nannochloropsis gaditana_ at 25 \({}^{\circ}\)C and at different light intensities is shown in Figure 3.  
As can be seen, the growth is well related to the light intensity: the slowest growth is observed under \(I=20\)\(\mu\)E s\({}^{-1}\)m\({}^{-2}\) and it gradually increases with increasing light intensity. The best growth performance is shown by cultures grown between \(I=300\)\(\mu\)E s\({}^{-1}\)m\({}^{-2}\) and \(I=450\)\(\mu\)E s\({}^{-1}\)m\({}^{-2}\). There is no, in any case, very high difference relatively to growth performance from \(I=100\)\(\mu\)E s\({}^{-1}\)m\({}^{-2}\) to \(I=450\)\(\mu\)E s\({}^{-1}\)m\({}^{-2}\), while between \(I=50\)\(\mu\)E s\({}^{-1}\)m\({}^{-2}\) and \(I=100\)\(\mu\)E s\({}^{-1}\)m\({}^{-2}\) there is a distinct difference in accordance to that predicted by the Monod equation [20,21]. In a batch photobioreactor, during the exponential growth phase, the specific growth rate \(\mu\) can be expressed as:  
\[\mu=\frac{\ln X-\ln X_{0}}{t-t_{0}} \tag{13}\]  
where \(X_{0}\) is the biomass concentration at time \(t_{0}\) and \(X\) is the biomass concentration at time \(t\). By employing a linear regression from the data in the exponential phases of Figure 3,  
Figure 3: Growth of microalga _Nannochloropsis gaditana_ at 25 \({}^{\circ}\)C in the quasi-isoactinic photobioreactor under different light intensities. the specific growth rates under each light intensity were obtained and reported in Table 1, together with the values of R\({}^{2}\) and of the relevant \(I_{0}/\mu\). The observed growth rates are in the same range as that previously found for the same strain by other authors [22]. To obtain the kinetic parameters, \(\mu_{max}\) and \(I_{k}\), Equation (10) can be rewritten according to [PERSON] [20] as:  
\[\frac{I_{0}}{\mu}=\frac{1}{\mu_{max}}I_{0}+\frac{I_{K}}{\mu_{max}} \tag{14}\]  
Therefore, a Langmuir plot of \(I_{0}/\mu\) versus \(I_{0}\) should give a straight line with slope \(1/\mu_{max}\) and intercept \(I_{K}/\mu_{max}\) as reported in Figure 4. From the intercept and the slope of the linear regression of Figure 4, the kinetic parameters \(\mu_{max}=0.0256\) h\({}^{-1}\) (0.61 day\({}^{-1}\)) and \(I_{K}=15.28\)\(\mu\) E s\({}^{-1}\)m\({}^{-2}\) were obtained. By using these kinetic parameters, the specific growth rate \(\mu\) as a function of incident light \(I_{0}\) can be plotted, as reported in Figure 5, for the quasi-isoactin  
Figure 4: “Langmuir plot” of experimental values obtained at different light intensities. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(I_{0}\) (\(\mu\)E s\({}^{-1}\)m\({}^{-2}\)) & \(\mu\) (h\({}^{-1}\)) & \(I_{0}/\mu\) (\(\mu\)E h s\({}^{-1}\)m\({}^{-2}\)) & \(\mathbf{R^{2}}\) \\ \hline
20 & 0.0117 & 1709 & 0.9956 \\
50 & 0.0184 & 2717 & 0.9912 \\
100 & 0.0228 & 4386 & 0.9817 \\
140 & 0.0237 & 5907 & 0.9976 \\
210 & 0.0249 & 8434 & 0.9891 \\
300 & 0.0246 & 12195 & 0.9859 \\
450 & 0.0243 & 18519 & 0.9988 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Values of specific growth rates and R\({}^{2}\) calculated at different light intensities at T = 25 \({}^{\circ}\)C in _Nammochloropsis gaditana_. can be seen, the typical Monod curve trend may be easily observed, and the saturation constant (\(l_{k}\)) corresponds to the value of I at which the growth rate is half of the maximal (\(\mu\) = 0.5 \(\mu_{max}\)). It is worth noting that the calculated maximum growth rate \(\mu_{max}\) (0.61 day\({}^{-1}\)) is comparable to typical _Nannochloropsis_ growth rates found by other researchers [23; 24]. [PERSON] et al. found that _Nannochloropsis__oculata_ grown in a saline medium has a maximum growth rate of 0.365 day\({}^{-1}\)[23], while [PERSON] et al.