## 3 Results
### Assessment of Travel Time on Caposele Aquifer  
The MODFLOW numerical code used to simulate the groundwater flow for the Caposele aquifer is able to compute the travel time of water along the groundwater flow net.  
Figure 10: Relationship between the simulated maximum hydraulic head in the aquifer and the thickness of the saturated zone (TSZ), for different recharge amounts uniformly distributed on the catchment area: mean recharge (R), double recharge (2R) and halved recharge conditions (2R); dots represent the simulation steps carried out.  
Particularly, the MODPATH package is able to calculate the groundwater paths together with the velocity vectors estimated cell-by-cell; the effective porosity value, n\({}_{\text{eff}}\), included in the range 0.01-0.10, was considered for the simulations [30]; then, in order to obtain the travel time for each flow pipe, the MODPATH groundwater flow net was investigated according to the hydraulic approach described by Equations (3)-(7). Table 1 shows the main results obtained by the Caposele aquifer modelling, considering different TSZs, up to a maximum thickness of 2000 m. As the actual effective porosity parameter is not available and no environmental tracers were used to evaluate the actual travel time (Equation (8)), the hydraulic approach adopted using the MODFOW numerical code was able to find the Darcian (mean) travel time range for different scenarios.  
The hydraulic conductivity of the medium was estimated by calibrating the model (Figure 8), after which the Darcian velocity (Equation (1)) and Darcian travel time (Equations (5)-(7)) were also computed. Through a flow simulation, the estimated travel time, applying Equations (5)-(7), ranged from a minimum value of 45.8 years (TSZ = 100 m) to a maximum of 551.8 years (TSZ = 2000 m). Considering all scenarios, the hydraulic analysis highlights that the water particle flows faster considering the flow pipes near the spring zone, while, conversely, water needs more time to reach the spring outlet along the flow pipes that are more distant from the discharge area.  
The hydraulic approach followed to estimate the travel time along the flow net of the Caposele aquifer using the MODFOW numerical code also allows one to underline that the knowledge and the setting of the aquifer TSZ in groundwater modelling is crucial for the assessment of the hydraulic parameters of the aquifer.  
The Darcian travel time trend, observed for the proposed scenarios, clearly points out fast groundwater paths for aquifers with less thickly saturated zones, and flow paths that are slower belonging to aquifers affected by thicker saturated zones.  
In Figure 11, the hydraulic conductivity and Darcian travel time were matched with different TSZs of the model. In particular, the hydraulic conductivity of the medium dropped when the model thickness increased, ranging from a maximum \(K\) = 0.0115 m/s found for models with less thickly saturated zones to a minimum \(K\) = 0.000831 m/s attributable to aquifers with a thickness of 2000 m.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**TSZ** & \(K\) & \(\beta\) & \(\  
The inverse relationship found between the \(K\) values and model thickness is coherent with 3D groundwater modelling. Considering the Caposele discharge as a fixed, unique and constant spring outlet, a thicker aquifer needs a low hydraulic conductivity and a long travel time to satisfy the same discharge of less thick model.