GNGTS 2016 - Atti del 35° Convegno Nazionale

542 GNGTS 2016 S essione 3.2 5 considers Γ x as uniform, while experimental observations show that the horizontal thermal gradient can depend on depth. Therefore, assuming as a first approximation that Γ x increases linearly with depth, the solution is (4) where Γ xo is the horizontal thermal gradient at the upper limit of the aquifer and D (m -1 ) is a coefficient of variation of Γ x with depth. Eqs. 3 and 4 (see Tab. 1) are rewritten in a simplified form more suitable for the optimization procedure. The coefficients of each model can be obtained by the least squares method. The coefficients contain information on the thermal and hydraulic features of the sediments crossed by the wells. The thermal logs of wells P8 and P10, dominated by advection, were analyzed to infer the horizontal component of the Darcy velocity. The estimation v x requires the horizontal thermal gradient Γ x which in our calculations was assumed to be equal to 4.8·10 -4 K·m -1 (Pasquale et al. , 2010). The value of Γ x influences the determination of v x . In particular, a decrease of one order of magnitude of Γ x causes an equal increase of v x . The density ρ w and specific heat of water c w were respectively assumed to be 1000 kg·m -3 and 4187 J·kg -1 ·K -1 . As no samples of the sediments crossed by the boreholes were available, a thermal conductivity of 1.8 W·m -1 ·K -1 was assumed on the basis of laboratory determinations of sandstone of the Po Basin (Pasquale et al. , 2011). The values of Darcy velocity obtained for P8 and P10 wells by means of the optimization procedure are reported in Tab. 2. The horizontal Darcy velocity obtained for both wells is of the order of 10 –6 m·s –1 . Tab. 1 - Equations in a simplified form of vertical temperature distribution in advective regime with horizontal flow. Tab. 2 - Darcy velocities calculated by analytical models coefficients (see Tab. 1). R 2 is the correlation coefficient. The horizontal velocities found for the other wells sited out of the Maggiore Valley well field - not shown in Tab. 2- range between 10 -7 - 10 -8 m·s -1 . Concluding remarks. The analysis of temperature data recorded in boreholes is a valuable tool for the recognition of underground groundwater flow. Furthermore, through the application