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

Abstract

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.