Taking into account water table fluctuations and the interaction of shallow water levels with geothermal systems while modeling their natural state is notoriously difficult. We investigate a new formulation for the non-isothermal compositional gas liquid Darcy flows and its coupling with an advanced soil-atmosphere boundary condition. The latest is needed to model the soil-atmosphere interaction because the coupling between the porous medium and surface flows would not be computationally realistic for geothermal time and space scales. This soil-atmosphere boundary condition is based on mole and energy balance equations expressed at the interface, taking into account the vaporization of the liquid phase in the atmosphere, the convective molar and energy transfer, a liquid outflow condition as well as the precipitation and radiation terms. The compositional model typically accounts for the water component which can vaporize into the gas phase and a set of gaseous components which can dissolve in the liquid phase (air…). Then, we chose a formulation that is based on the pressures, saturations, temperature and phase molar fractions as set of unknowns. No switch of variables is required as this choice of unknowns is combined with an extension of the phase molar fractions of an absent phase by the molar fractions at thermodynamic equilibrium with the present phase. This implies that the set of unknowns does not depend on the set of present phases. More precisely, the phase transitions are expressed as complementary constraints which results that the non-linear system can be solved using semi-smoothed Newton algorithms. The model and its formulation are applied on the Bouillante high temperature geothermal field located in Guadeloupe which show temperature of 250°C around 300m deep and soil with near boiling conditions in some places.

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