Hydrothermal coupling in a rough fracture

Heat exchange during laminar flow is studied at the fracture scale on the basis of the Stokes equation. We used a synthetic aperture model (a self-affine model) that has been shown to be a realistic geometrical description of the fracture morphology. We developed a numerical modelling using a finite difference scheme of the hydrodynamic flow and its coupling with an advection/conduction description of the fluid heat. As a first step, temperature within the surrounding rock is supposed to be constant. Influence of the fracture roughness on the heat flux through the wall, is estimated and a thermalization length is shown to emerge. Implications for the Soultz-sous-For\^{e}ts geothermal project are discussed.