Hydraulic transmissivity and heat exchange efficiency of rough fractures: a model based on lowpass filtered apertures
Résumé
Natural open joints in rocks commonly present multiscale self-affine apertures. This geometrical complexity affects fluid transport and heat exchange between the flowing fluid and the surrounding rock. In particular, long range correlations of self-affine apertures induce strong channelling of the flow which influences both mass and heat advection. A key question is to find a geometrical model of the complex aperture that describes at best the macroscopic properties (hydraulic conductivity, heat exchange) with the smallest number of parameters. Solving numerically the Stokes and heat equations with a lubrication approximation, we show that a low pass filtering of the aperture geometry provides efficient estimates of the effective hydraulic and thermal properties (apertures). A detailed study of the influence of the bandwidth of the lowpass filtering on these transport properties is also performed. For instance, keeping the information of amplitude only of the largest Fourier length scales allows us to reach already an accuracy of 9 per cent on the hydraulic and the thermal apertures.
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