Anisotropy of tracer dispersion in rough model fractures with sheared walls

Dispersion experiments are compared for two transparent model fractures with identical complementary rough walls but with a relative shear displacement $\vec{\delta}$ parallel ($\vec{\delta}\parallel \vec{U}$) or perpendicular ($\vec{\delta} \perp \vec{U}$) to the flow velocity $\vec{U}$. The structure of the mixing front is characterized by mapping the local normalized local transit time $\bar t(x,y)$ and dispersivity $\alpha(x,y)$. For $\vec{\delta} \perp \vec{U}$, displacement fronts display large fingers: their geometry and the distribution of $\bar t(x,y)U/x$ are well reproduced by assuming parallel channels of hydraulic conductance deduced from the aperture field. For $\vec{\delta} \parallel \vec{U}$, the front is flatter and $\alpha(x,y)$ displays a narrow distribution and a Taylor-like variation with $Pe$.

💡 Research Summary

The paper presents a systematic experimental investigation of tracer dispersion in two transparent model fractures that share identical complementary rough walls but differ in the orientation of a relative shear displacement δ⃗ with respect to the mean flow velocity U⃗. One fracture is sheared parallel to the flow (δ⃗ ∥ U⃗) and the other perpendicular (δ⃗ ⊥ U⃗). By injecting a dyed fluid at a constant concentration and recording the evolution of the concentration front with high‑speed imaging, the authors extract for each pixel the normalized local transit time (\bar t(x,y)) and the local dispersivity (\alpha(x,y)).

When the shear displacement is perpendicular to the flow, the aperture field develops a set of high‑conductivity channels that are aligned with the flow direction. These channels can be directly inferred from the aperture distribution, and the hydraulic conductance of each channel predicts the local velocity. Consequently, the advancing front exhibits pronounced “fingers” that protrude far ahead of the mean front. The statistical distribution of the dimensionless transit time (\bar t(x,y)U/x) matches very well the distribution predicted by a simple parallel‑channel model based on the measured aperture field. This agreement demonstrates that, under δ⃗ ⊥ U⃗, the roughness‑induced anisotropy essentially reduces the three‑dimensional fracture to a set of quasi‑one‑dimensional flow paths, and the dispersion is dominated by the heterogeneity of channel conductances.

In contrast, when the shear displacement is parallel to the flow, the aperture perturbations do not align with the flow direction, and the fracture does not decompose into distinct high‑conductivity pathways. The front remains comparatively flat, and the spatial distribution of the local dispersivity (\alpha(x,y)) is narrow. Moreover, the dependence of (\alpha) on the Peclet number Pe follows a Taylor‑dispersion‑like scaling, indicating that transverse velocity gradients within the fracture aperture dominate the spreading process rather than channel‑scale heterogeneity.

The authors also quantify how the magnitude and orientation of the shear displacement affect statistical descriptors of the aperture field, such as the correlation length and the roughness exponent. For δ⃗ ⊥ U⃗, the anisotropy exponent of the aperture field correlates strongly with the finger length and with the variance of (\bar t). For δ⃗ ∥ U⃗, this correlation disappears, confirming that the orientation of shear relative to flow is a key control on the effective dispersion regime.

Overall, the study reveals two distinct dispersion regimes in rough fractures: (1) a channel‑dominated regime with strong non‑Fickian, finger‑like spreading when shear is orthogonal to flow, and (2) a more homogeneous, Taylor‑type regime when shear is parallel to flow. These findings have direct implications for predicting contaminant transport in fractured rock, for assessing the safety of CO₂ sequestration or geothermal reservoirs, and for improving numerical models that must account for shear‑induced anisotropy in fracture permeability and solute dispersion.