Abstract
This chapter aims: ①To investigate the influence of multi-scale roughness on linear, power-law, and second-order polynomial relationships between the DL and Pe; ②To investigate the validation of the different relationships between the DL and Pe. To do this, we generate a series of 2D variable-aperture fractures with the different Hurst exponents. A wavelet analysis method is implemented to decompose the roughness of the fracture wall into the primary roughness and secondary roughness. The BTCs numerically generated from direct simulations are fitted by two inverse models.
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References
Aris R (1956) On the dispersion of a solute in a fluid flowing through a tube. Proceed Roy Soc London a: Mathematic Phys Eng Sci 235(1200):67–77
Bolster D, Dentz M, Le Borgne T (2009) Solute dispersion in channels with periodically varying apertures. Phys Fluids 21(5):056601
Dentz M, Carrera J (2007) Mixing and spreading in stratified flow. Phys Fluids 19(1):017107
Detwiler RL, Rajaram H, Glass RJ (2000) Solute transport in variable-aperture fractures: an investigation of the relative importance of Taylor dispersion and macro-dispersion. Water Resour Res 36(7):1611–1625
Develi K, Babadagli T (1998) Quantification of natural fracture surfaces using fractal geometry. Math Geol 30(8):971–998
Dou Z, Zhou Z, Sleep BE (2013) Influence of wettability on interfacial area during immiscible liquid invasion into a 3D self-affine rough fracture: Lattice Boltzmann simulations. Adv Water Resour 61:1–11
Jacob B (1972) Dynamics of fluids in porous media. Elsevier, Amsterdam
Mallat SG (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 11(7):674–693
Mandelbrot BB (1983) The fractal geometry of nature. Am J Phys 51(3):286
Odling N (1994) Natural fracture profiles, fractal dimension and joint roughness coefficients. Rock Mech Rock Eng 27(3):135–153
Plouraboué F, Hulin JP, Roux S et al (1998) Numerical study of geometrical dispersion in self-affine rough fractures. Phys Rev E 58(3):3334–3346
Qian J, Chen Z, Zhan HB et al (2011) Solute transport in a filled single fracture under non-Darcian flow. Int J Rock Mech Min Sci 48(1):132–140
Roux S, Plouraboué F, Hulin J-P (1998) Tracer dispersion in rough open cracks. Transp Porous Media 32(1):97–116
Wang L, Cardenas MB (2014) Non-Fickian transport through two-dimensional rough fractures: assessment and prediction. Water Resour Res 50(2):871–884
Wang JSY, Narasimhan TN, Scholz CH (1988) Aperture correlation of a fractal fracture. J Geophys Res Solid Earth 93(B3):2216–2224
Wang L, Cardenas MB, Deng W et al (2012) Theory for dynamic longitudinal dispersion in fractures and rivers with poiseuille flow. Geophys Res Lett 5:L05401
Wang L, Cardenas MB, Slottke DT et al (2015) Modification of the local cubic law of fracture flow for weak inertia, tortuosity, and roughness. Water Resour Res 51(4):2064–2080
Wang M, Chen YF, Ma GW et al (2016) Influence of surface roughness on nonlinear flow behaviors in 3D self-affine rough fractures: Lattice Boltzmann simulations. Adv Water Resour 96:373–388
Yeo IW, Ge S (2001) Solute dispersion in rock fractures by non-Darcian flow. Geophys Res Lett 28(20):3983–3986
Zimmerman R, Kumar S, Bodvarsson G (1991) Lubrication theory analysis of the permeability of rough-walled fractures. Int J Rock Mech Mining Sci Geomech Abstr 28(4):325–331
Zou L, **g L, Cvetkovic V (2015) Roughness decomposition and nonlinear fluid flow in a single rock fracture. Int J Rock Mech Min Sci 75:102–118
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Dou, Z., Zhou, Z., Wang, J., Huang, Y. (2024). Multiscale Roughness Influence on Solute Transport in Fracture. In: Mass Transfer Dynamics of Contaminants in Fractured Media. Springer, Singapore. https://doi.org/10.1007/978-981-99-9187-7_9
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DOI: https://doi.org/10.1007/978-981-99-9187-7_9
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