Geothermal heat advected by the recharge of underground conduit. Case study of the karstic spring of Lez (Hérault, France)

Abstract

The karstic flow system of the Lez spring is capturing a large proportion of the deep geothermal heat flow as observed by temperature measurements both above and below the underground karst network. For interpreting these data, an analytical model of heat/fluid interaction based on the conservation of mass and energy in a dual conduit/porous medium system is developed. In the model of energy transport, the energy of the fluid includes its enthalpy plus its gravity potential; the hydraulic head is shown to be the correct potential accounting for both pressure and gravity. The thermal features of the model are expressed as a function of a few parameters: from comparison with the actual data, the depth of the conduit appears to lie around 400 m and the number Pe characterizing the recharge is about 6. When estimated with available thermal data, the amount of geothermal energy captured by the flow system in steady state conditions is significantly lower than the actual energy output of the spring. The possible origin of this offset is discussed: effect of gravity potential, 3D convergence of geothermal heat flux lines, transient effect. Moreover, the mapping of the vertical temperature gradient at low depth indicates the general pattern of the recharge zone energy.

Keywords

• Temperature
• Analytical solutions
• Groundwater recharge
• Energy budget
• Karst
• Steady state
• Gravity potential