## 4 Discussion  
The experimental tests on microcosms polluted with diesel oil at a constant concentration (70 g\(\cdot\)kg\({}^{-1}\) of soil) but with different water contents (u%) and carbon to nitrogen ratios (C/N) were designed according to the factorial analysis, to get experimental results useful  
* to model the process kinetics;
* to study the interactions between these two operative factors, u% and C/N;
* to optimize the operative conditions to remove pollution in a reasonable time and with good efficiency with limited number of tests but exploiting their links to highlight their interactions, if any. In biological processes, as well as in chemical ones, kinetic modeling is one of the pillars used to plan real processes. Its identification must be derived from experimental tests done at smaller scale than the future application one. In this study, the reaction rate was modeled with a first- and second-order model, to check whether one model was more reliable and robust than the other. Given that the squared regression coefficient, R\({}^{2}\), of a model reflects the variability of the target parameter, with reference to this work, Tables 5-8 report this quantity representing the variability of the residual diesel oil concentration in soil for each run changing the operative factors (u% and C/N). In general, the R\({}^{2}\) values were high in both models, confirming that they were both satisfactory for this application. This has also been shown by other authors [12; 30]. Comparing the R\({}^{2}\) values, the second-order model seemed to give lower variability, especially when the half-life time, t\({}_{1/2}\), was longer. However, at a more careful check, this was also shown by the first-order model. This finding could mean that removal efficiency is estimated with better reliability when reaction kinetics are slower, i.e., when t\({}_{1/2}\) is longer. Regarding the half-life time, t\({}_{1/2}\), the findings were in line with results achieved by other authors [15; 29; 31]; this parameter has a particular relevance when study previsions must be transferred to in situ application, i.e., where its value has influence on the management remediation plan. The analysis of variance allowed us to estimate the influence and interactions of the operative parameters on diesel oil removal efficiency and fluorescein production (indirect measurements of microbial activity). The regression model done at t = 35 days and given by Equation (11) showed that only the linear effects of u% and C/N and the quadratic effect of u% were significant for the removal efficiency; specifically, the water content had a negative effect (\(\beta_{1}\)), while the other significant interactions, shown by \(\beta_{2}\) and \(\beta_{3}\), were positive. The additional ones, from \(\beta_{4}\) to \(\beta_{7}\), had no influence. For the microbial activity, depicted by fluorescein production at t = 30 days (Equation (12)), the effects to be considered were still the same as for diesel oil removal efficiency (\(\beta_{1}\), \(\beta_{2}\), and \(\beta_{3}\)), even if with different trends (they were all positive). Finally, the response surface methodology was applied to optimize the objective parameters already considered in the analysis of variance: diesel oil removal efficiency and fluorescein production. In both cases, the graphical result was a curved surface, due to cubic regression. For u-value, the findings clearly identified the zones where the parameter was higher than in the others; in these zones, the optimum could be found. Using chromatic representation, these results were rather evident. For the fluorescein production, the response surface showed that when the water content was in the range of 8% to 15% b.w., this parameter had limited effect. As we have demonstrated, statistical analysis by analysis of variance and response surface methodology can be adopted successfully for experimental analysis of the degradation process at a laboratory scale.