Hydraulic transmissivity and heat exchange efficiency of open fractures: a model based on lowpass filtered apertures

TL;DR

This paper introduces a lowpass filtering approach to model complex self-affine rock fractures, effectively estimating hydraulic and thermal properties with minimal parameters, simplifying the understanding of fluid and heat transport.

Contribution

The study demonstrates that lowpass filtering of aperture geometries accurately predicts macroscopic hydraulic and thermal properties of fractures, reducing complexity in modeling.

Findings

Lowpass filtering provides 9% accuracy in estimating hydraulic and thermal apertures.

Filtering large Fourier scales captures essential transport properties.

The method simplifies complex fracture geometries for practical modeling.

Abstract

Natural open joints in rocks commonly present multi-scale self-affine apertures. This geometrical complexity affects fluid transport and heat exchange between the flow- ing fluid and the surrounding rock. In particular, long range correlations of self-affine apertures induce strong channeling 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 equa- tions 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% on the hydraulic and the thermal apertures.