System of production and geothermal storage of energy including a surface segment in which the enthalpy (H) of a fluid conveyed into a pipe network, is transformed into mechanical and/or thermal energy, and including an underground segment , said underground segment having at least one injection well with a casing of which, connected to the surface segment pipe network opens into an underground permeable geological formation capable of heating and/or maintaining a temperature of an injected fluid into said geological formation and including at least one production well of which a casing, connected to the surface segment pipe network , ends into said geological formation; the system being characterized in that : - the fluid is an organic working fluid , having a liquefaction pressure PL of less than 10 6 Pa at 15°C temperature, having in liquid phase a density strictly less than 1 compared with water under the same pressure and temperature conditions, and being immiscible with water; - the subsurface geological formation determines a natural trap , forming a reservoir able to contain, in permeable and porous rocks , a desired quantity of the working fluid , and to allow the circulation of said working fluid in said rocks, under upper layers of said trap, which are impermeable for said working fluid in liquid phase, and above an aquifer associated with said trap, said rocks being naturally maintained at temperatures greater than 50°C by a heat flow from lower rocks , in order to constitute an energy storage reservoir in the form of the enthalpy of said working fluid; - the injection well or wells end in a lower part (21 b) of the trap so that the working fluid tends to migrate in the permeable and porous rocks of the trap from the lower part (21 b) towards an upper part (21 a) of said trap, under the buoyancy effect generated by the aquifer on said working fluid and under the effect of thermal convection preventing stratification, in said rocks, of said working fluid subjected to heating upon contact with said rocks, said rocks being heated by heat flow from lower rocks ; - the surface segment , the injection well or wells , the trap , and the production well or wells determine a closed circuit for the working fluid in which said working fluid is confined. - the fluid is an organic working fluid , having a liquefaction pressure PL of less than 10 6 Pa at 15°C temperature, having in liquid phase a density strictly less than 1 compared with water under the same pressure and temperature conditions, and being immiscible with water; - the subsurface geological formation determines a natural trap , forming a reservoir able to contain, in permeable and porous rocks , a desired quantity of the working fluid , and to allow the circulation of said working fluid in said rocks, under upper layers of said trap, which are impermeable for said working fluid in liquid phase, and above an aquifer associated with said trap, said rocks being naturally maintained at temperatures greater than 50°C by a heat flow from lower rocks , in order to constitute an energy storage reservoir in the form of the enthalpy of said working fluid; - the injection well or wells end in a lower part (21 b) of the trap so that the working fluid tends to migrate in the permeable and porous rocks of the trap from the lower part (21 b) towards an upper part (21 a) of said trap, under the buoyancy effect generated by the aquifer on said working fluid and under the effect of thermal convection preventing stratification, in said rocks, of said working fluid subjected to heating upon contact with said rocks, said rocks being heated by heat flow from lower rocks ; - the surface segment , the injection well or wells , the trap , and the production well or wells determine a closed circuit for the working fluid in which said working fluid is confined. <EOS>