Investigation of Gravity‐Driven Infiltration Instabilities in Smooth and Rough Fractures Using a Pairwise‐Force Smoothed Particle Hydrodynamics Model

Abstract

Core Ideas We study infiltration dynamics in smooth and rough fractures using a 3D SPH model. Roughness induces the formation of flow fingering and preferential flow paths. Fractal roughness leads to a deceleration of average fingertip velocities. The velocity variance of fingers positively correlates with the degree of roughness. Normalized finger velocity and length scale in accordance with analytical predictions. This work investigates small‐scale infiltration dynamics in smooth and rough single fractures using a three‐dimensional multiphase pairwise‐force smoothed particle hydrodynamics (PF‐SPH) model. Gravity‐driven infiltration instabilities in fractures under unsaturated conditions can significantly influence the arrival time of tracers or contaminants, and the rapid and localized recharge dynamics in fractured–porous aquifer systems. Here, we study the influence of roughness and injection rate on fluid flow modes and flow velocity. Three types of fractures are considered with different degrees of roughness, including a smooth fracture. Both the rough and smooth fractures exhibit flow instabilities, fingering, and intermittent flow regimes for low infiltration rates. In agreement with theoretical predictions, a flat fluid front is achieved when the flux q supplied to a fracture is larger than the gravitationally driven saturated flux [q > kρg/μcos(φ), where k is the intrinsic permeability of the fracture, ρ is a density, μ is the viscosity, and φ is the fracture inclination angle measured from the vertical direction]. To characterize the flow instability, we calculate standard deviations of velocity along the fracture width. For the considered infiltration rates, we find that an increase in roughness decreases the flow velocity and increases the standard deviation of velocity. This is caused by a higher likelihood of flow discontinuities in the form of fingering and/or snapping rivulets. To validate our unsaturated flow simulations in fractures, we estimate the scaling of specific discharge with normalized finger velocity, compute the relationship between fingertip length and scaled finger velocity, and find good agreement with experimental results.