GNGTS 2015 - Atti del 34° Convegno Nazionale

154 GNGTS 2015 S essione 1.3 preliminary stage of design, while in the long period are useful to assess the interference of the geothermal plant in question with other geothermal wells located in the area (i.e. Jolly Hotel and Province of Turin Institute) and other wells in the phase of realization (San Paolo Institute) in order to avoid thermal anomalies. Error design can in fact lead to “ thermal feedback phenomena” : this phenomenon occurs when the distance between the wells (extraction and injection wells) is relative short; in this case, a recall of the thermal plume by the well of extraction it is observed, with a consequent pumping of groundwater with temperatures close to those discharged, compromising the efficiency the geothermal plant (Cultrera, 2012; Piccinini et al. , 2012; Galgaro and Cultrera, 2013). Another phenomenon, known in literature, and partially related to the previous one, is “ thermal breakthrough ” (Banks, 2009; Piccinini et al. , 2012; Galgaro and Cultrera, 2013): it consists in the slow diffusion of the thermal plume upstream. Governing equation. Heat transport and solute transport contain many similarities (Anderson, 2005). Their mathematical representation is similar when the terms describing heat transport are formulated in equivalent solute expressions. SEAWAT leverages these similarities by using MT3DMS to simulate heat transport. The heat transport equation, manipulated by Thorne et al. (2006), highlights the similarity with the solute transport. In Eq. 1 tensors and vectors shown in bold. (1) where: q (m/s) is specific discharge; α (m) is the dispersivity tensor; θ (-) is the volumetric water content; q ’ s (s -1 ) is a source or sink of fluid with density ρ s ; ρ s (kg/m 3 ) is the density of the solid (mass of the solid divided by the volume of the solid); ρ (kg/m 3 ) is the density of the fluid; c Psolid (J/kg· C) is the specific heat capacity of the solid; c Pfluid (J/kg· C) is the specific heat capacity of the fluid; k Tbulk (W/m· C) is the bulk thermal conductivity of the aquifer material; T ( C) is the temperature of the fluid; T s (°C) is the source temperature; t is time (s). ρ b , ρ s , and θ are related by: ρ b ρ s (1 – θ ). Variations in temperature inside a saturated porous medium may give rise to vertical convective motions, which determine the upward movement of the water masses hottest and lighter and the downward movement of the masses more cold and heavy. These motions, can influence the water flow of the system. The form of the equation of density-dependent flow is solved by SEAWAT Eq. 2 (Langevin et al. , 2007; Langevin et al. , 2010) and allows to consider the variations of density and viscosity as a function of temperature. (2) where: μ (kg/m·s) is the fluid dynamic viscosity; μ 0 (kg/m·s) is the reference fluid dynamic viscosity (reference fluid is generally freshwater at temperature T 25 C); K 0 (m/s) is the hydraulic conductivity tensor of material saturated with the reference fluid; h 0 (m) is the hydraulic head (m) measured in terms of the reference fluid of a specified concentration and temperature; z (m) is the cartesian coordinate; S s ,0 (1/m) is the specific storage, defined as the volume of water released from storage per unit volume per unit decline of h 0 ; q ’ s (1/s) is a source or sink of fluid with density ρ s . Computational domain. The flow model was initially implemented with MODFLOW, along with SEAWAT code for the simulation of the heat transport. The domain of the model was discretized by a 1000 x 1000 m uniform grid mesh, with square cells of 10 m 2 . In the area of distribution of the wells, the cell sizes have been reduced until obtaining cells of 1 m 2 . The subsurface was simplified into three layers: 1st layer: unsaturated zone located between the ground surface and the water table; 2nd layer: shallow aquifer;