## 3 Results
### Mathematical Model Development  
The developed mathematical model was able to predict the variation of hydrocarbon and electron acceptors concentrations, over time and at different depths. As shown in Figure 4, hydrocarbon concentrations decreased over time, both in the solid (STPH) and liquid (CTPH) phases. In the first 0.1 m depth, the decrease of STPH starts slowly and accelerates afterwards (Figure 4A), reaching 50% of the initial value after \(\sim\)1.2 years (439 days). For depths higher than 0.4 m (Figure 4A,C), STPH remains relatively constant for 3.2 years (1150 days), after which it decreases consistently, reaching a 50% reduction approximately one year later (1507 days). In the liquid phase, the decrease of hydrocarbon concentration follows a similar tendency (Figure 4B,D); here, \(\sim\)2.3 years (850 days) or \(\sim\)4.5 years (1626 days) are necessary to reach TPH concentrations lower than 1.0 mg/L, at 0.1 m depth or at depths higher than 0.4 m, respectively. After 5 years, hydrocarbons are almost completely removed from both phases, at any depth (Figure 4). The top layers of the soil column are the first to show low TPH concentrations (Figure 4C,D), which may result from hydrocarbons biodegradation by aerobic and/or anoxic microorganisms. However, dissolved oxygen concentration rapidly decreases in depth (Figure S2A), e.g., it reaches null values after 1 day for depths higher than 0.1 m, which limits aerobic biodegradation. As the first layers of the soil column became free of hydrocarbons, oxygen concentration increases again along the time. For example, O\({}_{2}\) values close to 10 mg/L are observed in the first 10-20 cm of the soil column after 3-4 years, and up to \(\sim\)90 cm depth after 5 years (Figure S2A). Aerobic biomass exhibits a peak after 1 year at \(\sim\)25 cm depth and decreases afterwards (Figure S2B). At higher depth (up to 0.5 m) aerobic biomass also grows, but to a less extent and more slowly than in the upper layers (Figure S2B). Nitrate, sulfate and iron are also rapidly consumed by microbial biomass, soon becoming limiting for TPH biodegradation (Figure S3). All these results point that, besides biodegradation, the decrease of STPH and CTPH in the first layers of the soil column is most probably due to transport phenomena. To verify this, a new simulation was then performed considering only the adsorption/desorption and transport processes (i.e., all the biodegradation processes were not included). As observed in Figure 5, the profile of STPH and CTPH in the first layers of the soil column (\(<\)0.2 m) is very similar to the ones obtained when microbial activity is also considered (Figure 4), highlighting that desorption and transport are the main processes influencing TPH removal over time for the top layers of soil. In addition, Peclet number (Pe) was calculated to verify if diffusion or advection was the most important transport phenomenon in the soil column. Thus, assuming a mass diffusion coefficient for hexadecane of 4 \(\times\) 10\({}^{-10}\) m\({}^{2}\)/s [54] and an average water inflow of 3.75 L/d, the Pe was 217, meaning that the advective transport predominates over diffusion in the mass transport process. Figure 3: Cumulative oxygen consumption over time in the aerobic assays (**A**), and time course of NO\({}_{3}\)\({}^{-}\) concentrations (expressed as N) in the anoxic assays (**B**). Figure 4: Variation of hydrocarbon concentration over time (**top**) and in depth (**bottom**), in the solid phase (**A,C**) and in the liquid phase (**B,D**). Figure 5: Variation of hydrocarbon concentration over time, in the solid (**A**) and in the liquid phase (**B**), considering only the adsorption/desorption and transport processes. In deeper soil layers (>0.4 m), however, when just adsorption/desorption and transport processes are considered, STPH and CTPH only begin to decrease after 4 years (Figure 5). By comparison, with Figure 4A,B, it seems that microbial activity has an important role and accelerates TPH removal at higher depths.