## 3 Results
### Mathematical Model Development
#### 3.3.2 Bioremediation Scenarios  
Different bioremediation strategies were implemented and the results are depicted in Figure 6. Similar to the previous results, close to the surface (at 0.1 m depth), all scenarios predicted more than 83% TPH removal after two years of simulation (Table 6). In fact, in the scenario with a high concentration of nitrate, after one year a TPH removal of around 82% can be observed. In these first soil layers (<0.5 m), the high TPH removal can be attributed to the presence of the electron acceptors but also to adsorption/desorption and transport processes as previously discussed. In depth, clear differences between the different scenarios can be observed. The implementation of a soil aeration mechanism (Figure 6B) resulted in a faster TPH removal. After one year of the oil spill, the TPH removal was already higher than 19% at 0.5 m depth, reaching values above 50% after 3 years in the presence of oxygen, nitrate and sulfate (Table 6). In the scenarios with the addition of a high concentration of nitrate or sulfate, the results show that near the surface (0.1 m) the model predicts the complete TPH removal in two years (Figure 6C,D, Table 6). These results are in agreement with the literature results, since increasing concentrations of electron acceptors promotes an increase in biodegradation rates [10; 33]. For deeper layers, the removal was lower, mainly due to the depletion of the electron acceptor. Indeed, neither nitrate nor sulfate reaches the end of soil column, meaning that this will not be a problem in terms of groundwater contamination. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Depth** & **Scenario** & **1 Year** & **2 Year** & **3 Year** & **4 Year** & **5 Year** \\ \hline \multirow{8}{*}{0.1 m} & Baseline & 21.9  
Figure 6: Concentration of TPH in solid and liquid phase; (**A**) baseline scenario; (**B**) re-aeration scenario; (**C**) high NO3\({}^{-}\) scenario; and (**D**) high SO4\({}^{2-}\) scenario; (**E**) high Fe (III) scenario; (**F**) 10% STPH scenario. For the scenario with higher initial iron (III) concentration in the soil column (Figure 6E), the results showed similar behavior to the baseline scenario. At surface layers, it is expected to be a 100% removal; for deeper layers (>0.25 m), the TPH removal was not very high (maximum of 40% after four years), although an increase in removal over time was generally observed (Table 6). Some authors suggested that adsorbed hydrocarbons are also directly available for microorganisms [21; 22; 59]. Thus, a scenario where the microorganisms can use the TPH adsorbed to soil (scenario 10%_STPH), though at a lower rate, was designed (Figure 6F). The results showed higher removal efficiencies than in the base scenario but lower that in the high NO\({}_{3}\) and high SO\({}_{4}\) scenarios, in the first layers (Table 6). For depths higher than 1 m, two times higher TPH removal is predicted, relative to the high NO\({}_{3}\) and high SO\({}_{4}\) scenarios (Table 6). This scenario could reflect, for example, the addition of surfactants to contaminated soil. Surfactants reduce the interfacial' tension, increasing the solubility and bioavailability of hydrocarbons, thus facilitating their transport and biodegradation [5; 51]. In summary, and based on mathematical model results, soil re-aeration and surfactants (oxygen and 10%_STPH scenarios) addition are the bioremediation strategies that will guarantee a faster treatment of the oil spill. Nevertheless, the natural attenuation (baseline scenario) could also be considered to be applied, since the technical and economic issues involved in soil re-aeration and the application of dissolved compounds could be challenging. Very few examples of mathematical models were completely validated for one or two bioremediation methodologies [14].