Roughness scale dependence of the relationship between tracer longitudinal dispersion and Peclet number in variable‐aperture fractures

• Published in: Hydrological processes 2018-05, Vol.32 (10), p.1461-1475
• Main Authors: Dou, Zhi, Zhou, Zhifang, Wang, Jinguo, Huang, Yong
• Format: Article
• Language: English
• Subjects: Dependence; Dispersion; Dye dispersion; Fractures; Longitudinal dispersion; macrodispersion; multiscale; Peclet number; Roughness; self‐affinity; Solute transport; Solutes; Taylor dispersion; Tracers; variable‐aperture fractures; Wavelet analysis; Waviness
• ISSN: 0885-6087; 1099-1085
• DOI: 10.1002/hyp.11505

The relationship between the longitudinal dispersion (DL) and Peclet number (Pe) is crucial for predicting and simulating tracer through the variable‐aperture fracture. In this study, the roughness of the self‐affine fracture wall was decomposed into primary roughness (relatively large‐scale waviness) and secondary roughness (relatively small‐scale waviness) by a multiscaled wavelet analysis technique. Based on the complete dispersion mechanism (diffusion, macrodispersion, and Taylor dispersion) in the variable‐aperture fracture, three relationships (second‐order, power‐law, and linear relationships) between the DL and Pe were investigated at large and small scales, respectively. Our results showed that the primary roughness mostly controlled the Taylor dispersion mechanism, whereas the secondary roughness was a dominant factor for the macrodispersion mechanism. Increasing the Hurst exponent and removing the secondary roughness led to the decreasing range of Pe where macrodispersion mechanism dominated the solute transport. It was found that estimating the DL from the power‐law relationship based on Taylor dispersion theory resulted in considerable errors, even in the range of Pe where the Taylor dispersion mechanism dominated. The exponent of the power‐law relationship increased as the secondary roughness was removed. Analysing the linear relationship between the DL and Pe revealed that the longitudinal dispersivity αL increased linearly. However, this linear increase became weak as the Taylor dispersion mechanism dominated. In the range of Pe where the macrodispersion mechanism dominated, increasing the Hurst exponent caused the increase of αL and the secondary roughness played a significant role in enhancing the αL. As the Taylor dispersion mechanism dominated, the αL was insensitive to the influence of multiscale roughness in variable‐aperture fractures.