## 3 Results and Discussion
In Figure 3c, the inhibition due to the high organic carbon content was highlighted when the concentration was 0.2% with a slowing of the TOC removal process. From the fitting of the experimental data using the models previously described, it was defined that a first order kinetic model, and specifically, the Blackman model, better described the experimental data, showing the lowest objective function values (Table 2). In Table 2 are reported all the objective functions (Equation (6)), confirming that the lower values calculated with the Blackman model compared to the Monod and Tessier models, define Blackman as a better representation of the experimental data. Figure 3: TOC removal trends (Blackman equation) during accelerated biodegradation tests of the conditioning mixture A (**a**), B (**b**) and C (**c**) with 2.0 mL of _Bacillus Clausii_ at different dosages as 0.10% (gray), 0.13% (black) and 0.20% (white). Conditions: pH = 6 and 30 \({}^{\circ}\)C.  
Based on the objective functions calculated, Blackman can be considered a suitable model that adequately describes the results of TOC trend in all the investigated concentrations. By considering the Blackman model process (Equation (3)), the mass balance can be defined from integration of Equation (7) with boundary conditions of the initial time and a generic time (t):  
\[\int\mathrm{d}c/\mathrm{d}t=-\int\mathrm{K}\,\mathrm{c} \tag{7}\]  
\[\mathrm{c(t)}=c_{0}\,\exp(-\mathrm{K}\,\mathrm{t}) \tag{8}\]  
Defining K (h\({}^{-1}\)) as:  
\[\mathrm{K}=\mu_{\mathrm{M}}/2\,\mathrm{K_{s}} \tag{9}\]  
The first values of \(\mu_{\mathrm{M}}\) and \(\mathrm{K_{s}}\) for the iterative cycles have been set on the basis of data available in the literature [33; 34; 35]. Table 3 shows the values of the kinetic constants and the estimated reaction time to achieve a 20 or a 50% removal of the initial TOC of the mixtures. Results show that the tested mixtures showed a different behavior. Mixture A, at any dosage tested in this work, showed a fast organics removal with respect to the other mixtures. In particular, though the removal followed the same initial trend at any tested concentration, at the higher dosage (0.20%), a shorter time was required (about 17.33 h) to achieve a 50% reduction of the initial amount of organics. This behavior could be attributed to the typical first kinetic order reaction that is promoted by the high value of \(c_{0}\) (Equation (8)). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Conditioning** & **Concentration** & **\%vol.** & **\(\Phi\)[PERSON]** & **\(\Phi\)Blackman** & **\(\Phi\)Tessier** \\ \hline  & 0.10 & 12.785 & 5.674 & 13.097 \\
**A** & 0.13 & 12.653 & 4.986 & 13.001 \\  & 0.20 & 13.000 & 5.234 & 13.825 \\ \hline  & 0.10 & 13.522 & 3.344 & 13.727 \\
**B** & 0.13 & 12.909 & 3.684 & 13.776 \\  & 0.20 & 12.552 & 3.810 & 13.758 \\ \hline  & 0.10 & 8.653 & 2.957 & 8.833 \\
**C** & 0.13 & 8.481 & 2.481 & 8.209 \\  & 0.20 & 7.999 & 2.280 & 8.011 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Objective function value TOC data fitting by the Monod, Blackman and Tessier models at different conditioning mixture concentrations (0.10, 0.13 and 0.20%). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Conditioning** & **Concentration** & **K** & **t\({}^{*}\)20\%** & **t\({}^{*}\)50\%** \\
**Mixtures** & **[\%vol. ]** & **[1/h]** & **[h]** & **[h]** \\ \hline  & 0.10 & 0.036 & 6.20 & 19.25 \\
**A** & 0.13 & 0.031 & 7.19 & 22.36 \\  & 0.20 & 0.040 & 5.58 & 17.33 \\ \hline  & 0.10 & 0.014 & 15.94 & 49.51 \\
**B** & 0.13 & 0.022 & 10.14 & 31.50 \\  & 0.2 The trend of TOC removal in tests with mixture C was quite different: although a positive effect of the increasing TOC initial value was detected up to 0.13% dosage, a further increase caused a remarkable slowing down of the biodegradation process. When considering the safety data sheets of mixture C, it resulted, in fact, composed of volatile compounds (mono-C10-16-alkyl esters) which are quickly removed (stripping) from the solution through the action of bubbling air into the system.