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Highlights • Investigating multiscale roughness influence on solute transport in a self-affine fracture. • Removing small-scale roughness delayed the breakthrough and shortened tails in BTCs. • The small-scale roughness increased mass exchange rate between immobile and mobile domains. Abstract In this article, the influence of multiscale roughness on transport of a conservative solute through a self-affine fracture was investigated. The fracture roughness was decomposed into two different scales (i.e., a small-scale stationary secondary roughness superimposed on a large-scale non-stationary primary roughness) by a wavelet analysis technique. The fluid flow in the single fracture was characterized by Forchheimer's law and exhibited nonlinear flow features such as eddies and tortuous streamlines. The results indicated that the small-scale secondary roughness was primarily responsible for the nonlinear flow features. Numerical simulations of conservative solute transport showed non-Fickian transport characteristics (i.e., early arrivals and long tails) in breakthrough curves (BTCs) and in residence time distributions (RTDs) with and without consideration of the secondary roughness. Analysis of multiscale BTCs and RTDs showed that the small-scale secondary roughness played a significant role in enhancing the non-Fickian transport characteristics. Removing small-scale secondary roughness delayed the arrival time and shortened the tail. The peak concentrations in BTCs decreased as the secondary roughness was removed, implying that the secondary roughness could also enhance the solute dilution. Fitting the one-dimensional (1D) Fickian advection–dispersion equation (ADE) to the numerical BTCs resulted in considerable errors that decreased with the small-scale secondary roughness being removed. The 1D mobile-immobile model (MIM) provided a better fit to the numerical BTCs and inclusion of the small-scale secondary roughness in numerical simulations resulted in a decreasing MIM mobile domain fraction and an increasing mass exchange rate between immobile and mobile domains. [ABSTRACT FROM AUTHOR]

The solute transport regime is highly dependent upon the heterogeneity of the flow field. In this study, the influence of eddies on conservative solute transport through a two-dimensional (2D) single self-affine fracture was investigated by the Navier-Stokes flow and solute transport simulations. The self-affine rough fracture was generated by the successive random additions (SRA) technique. The simulations showed that eddies had significant influence on the spatial evolution of the solute plume through the fracture. Analysis of breakthrough curves (BTCs) and residence time distributions (RTDs) presented that the solute transport through the fracture was non-Fickian and the developing eddies enhanced the typical non-Fickian characteristics (i.e., “early arrival” and “heavy tail”) in BTCs for a step tracer injection. Increasing the Reynolds number caused the increasing exponent of the power-law tail with the developing eddies. Fitting the non-Fickian BTCs with the classical inverse model (advection–dispersion-equation, ADE) led to a non-negligible error due to the presence of eddies. The continuous time random walk (CTRW) inverse model with truncated power law transition rate probability was alternatively employed and the fitting results showed the robust capability of CTRW in capturing the eddy-induced non-Fickian transport. It was found that the value of parameter β of CTRW decreased as the total eddy volume increased, indicating that the developing eddies might increase the magnitude of non-Fickian transport. Furthermore, the dilution index presenting the exponential of the Shannon entropy of a concentration probability distribution was used to quantify the uniformity of concentration distribution within the fracture. We could conclude that eddies provided strong resistance for solute transport and significantly delayed the mass exchange between the main flow channel and the eddy-controlled zones. Consequently, the delayed mass exchange process directly determined the magnitude of tails in BTCs. The results may enhance our understanding of the role of eddies in the solute transport through fractures. [ABSTRACT FROM AUTHOR]

• Mass transfer for solute transport through unsaturated porous media was investigated. • A non-monotonic relationship was found between dispersivity and residual saturation. • Overall dispersivity in terms of the mobile-immobile-type transport equation was analyzed. • Relative contribution of two mass transfer mechanisms to the overall dispersivity was discussed. The residual non-wetting phase in unsaturated porous media varies the aqueous pore space due to the immiscible characteristics. The varied pore space in turn has significant influence on the mass transfer for aqueous tracer transport through residual unsaturated porous media. In this study, the mass transfer for solute transport through residual unsaturated porous media was investigated. A pore-scale numerical simulation (PSNS) model consisting of both immiscible two-phase flow transport and aqueous-miscible solute transport was developed at pore scale to capture the topology of residual saturation and the tempo-spatial evolution of aqueous tracer in residual unsaturated porous media. The results showed that as the immiscible fluid-fluid displacement pattern varied from compact displacement to capillary fingering, the residual saturation (S rw) increased and the velocity spatial variability in the residual aqueous flow field was enhanced. Inversion of the advection-dispersion-equation (ADE) model and the continuous-time-random-walk (CTRW) model indicated the typical characteristics of anomalous aqueous tracer transport (i.e., early arrivals and long tails) in breakthrough curves (BTCs) in a range of (S rw) from 0.098 to 0.542. A non-monotonic relationship was found between the dispersivity and the S r w. Further, analysis of the overall dispersivity of aqueous tracer in terms of the mobile-immobile-type transport equation showed the coexistence of two mass transfer mechanisms (i.e., the dispersivity of the mobile domain and the solute exchange between the mobile and immobile domains). We introduced a dimensionless dispersivity index to quantify the relative contribution of these two mass transfer mechanisms to the overall dispersivity. However, it was found that the mass transfer of aqueous tracer in residual unsaturated porous media was controlled by the dispersion of aqueous tracer in the mobile domain at low S r w , whereas it was dominated by the solute exchange between the mobile and immobile domains at high S r w. Our study not only highlighted the saturation dependence of mass transfer in residual unsaturated porous media, but also emphasized the importance of the influence of saturation topology on mass transfer. [ABSTRACT FROM AUTHOR]