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.
Highlights
It has been widely recognized that fractures can play an important role in the transport and fate of contaminants
Characterizing the spreading and mixing processes of conservative solute through the fractures is very important for the understanding of reaction rates and mass transport rates associated with nuclear waste disposal, enhanced oil recovery, and bioremediation [1,2,3,4,5,6]
Hurst on the relationship between the longitudinal and the global. These results indicate that the exponent has little influence on the relationship between the longitudinal and the global scalar dissipation rate (SDR). in
Summary
It has been widely recognized that fractures can play an important role in the transport and fate of contaminants. Characterizing the spreading and mixing processes of conservative solute through the fractures is very important for the understanding of reaction rates and mass transport rates associated with nuclear waste disposal, enhanced oil recovery, and bioremediation [1,2,3,4,5,6]. Since the heterogeneity of geological formations is ubiquitous, a fundamental issue about the difference between spreading and mixing processes of conservative solute needs to be understood. Several authors [9,12,18] emphasized the difference between spreading and mixing. In other words, spreading leads to the stretching and deformation of a solute plume while mixing gives rise to dilution of a conservative solute with time. Spreading and mixing are not the same, but complete conservative solute
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