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Processes 2018, 6(9), 158; https://doi.org/10.3390/pr6090158

Temporal Mixing Behavior of Conservative Solute Transport through 2D Self-Affine Fractures

1
School of Earth Science and Engineering, Hohai University, 8 Fochengxi Rd., Nanjing 210098, China
2
Department of Civil Engineering, University of Toronto, 35 St. George Street, Toronto, ON M5S 1A4, Canada
*
Authors to whom correspondence should be addressed.
Received: 21 August 2018 / Revised: 4 September 2018 / Accepted: 4 September 2018 / Published: 5 September 2018
(This article belongs to the Special Issue Fluid Flow in Fractured Porous Media)
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Abstract

In this work, the influence of the Hurst exponent and Peclet number (Pe) on the temporal mixing behavior of a conservative solute in the self-affine fractures with variable-aperture fracture and constant-aperture distributions were investigated. The mixing was quantified by the scalar dissipation rate (SDR) in fractures. The investigation shows that the variable-aperture distribution leads to local fluctuation of the temporal evolution of the SDR, whereas the temporal evolution of the SDR in the constant-aperture fractures is smoothly decreasing as a power-law function of time. The Peclet number plays a dominant role in the temporal evolution of mixing in both variable-aperture and constant-aperture fractures. In the constant-aperture fracture, the influence of Hurst exponent on the temporal evolution of the SDR becomes negligible when the Peclet number is relatively small. The longitudinal SDR can be related to the global SDR in the constant-aperture fracture when the Peclet number is relatively small. As the Peclet number increases the longitudinal SDR overpredicts the global SDR. In the variable-aperture fractures, predicting the global SDR from the longitudinal SDR is inappropriate due to the non-monotonic increase of the longitudinal concentration second moment, which results in a physically meaningless SDR. View Full-Text
Keywords: mixing; conservative solute; fractal; roughness; fracture mixing; conservative solute; fractal; roughness; fracture
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Dou, Z.; Sleep, B.; Mondal, P.; Guo, Q.; Wang, J.; Zhou, Z. Temporal Mixing Behavior of Conservative Solute Transport through 2D Self-Affine Fractures. Processes 2018, 6, 158.

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