Three-dimensional numerical modelling of thermal transfer through the Vittel aquifer (Vosges, France), including approximated topographical effects

Summary. A geothermal and hydrochemical anomaly was observed in the Lower Triassic sandstone aquifer in the Vittel region (Vosges, France). This anomaly was attributed to a hydrothermal spring under sedimentary cover. In order to localize the hot spring and to quantify more precisely its flow rate and temperature, it is necessary to consider the 3-D thermal problem by taking into account the complex geometry of the domain and the flow rate in the aquifer. A 3-D numerical model of thermal conductive and forced convective transfer, developed for hydrological problems including approximate geometrical and topographical effects, is used which (i) can be directly applied to geologic strata (aquifers) with varying thickness and top and base slope; and (ii) allows calculation of heat flux anomalies associated with fluid flow in such geologically realistic aquifers.
The heat transfer equation is formulated in an orthogonal curvilinear coordinate system. As most geometries dealing with geothermal phenomena in sedimentary basins are nearly horizontal, this formulation can be simplified, leading readily to numerical solution with a finite difference method. The application of the 3-D model to the Vittel aquifer gives temperature results in agreement with measurements. These results provide evidence for the importance of associated forced convection and topographical effects for ground temperature distribution, and show clearly that heat flow in many basins is interpretable only if careful hydrological and thermal studies are made.