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.

Splitting Dynamics of Liquid Slugs at a T‐Junction

“…In this study, the idealized case of liquid slug motion in smooth channels is considered, while in nature channels can have rough surfaces and be nonstraight (Shigorina et al, 2019). Rough surfaces can significantly enhance the effect of contact angle hysteresis (Bonn et al, 2009), resulting in a smaller interface velocities of the liquid slug (Su et al, 2004).…”

Multiscale Smoothed Particle Hydrodynamics Model Development for Simulating Preferential Flow Dynamics in Fractured Porous Media

“…The model is based on a PF-SPH discretization of the Navier-Stokes (NS) equation and can efficiently model flow through fractures or fracture networks and adequately recover all relevant flow dynamics, including the effects of free surface flows and surface tension (A. Kordilla J., 2013;Kordilla et al, 2017;Shigorina et al, 2017Shigorina et al, , 2019. However, in porous-fractured systems, the porous and/or permeable matrix represents an important storage compartment and influences flow dynamics within the highly permeable fractures.…”

Numerical and Analytical Modeling of Flow Partitioning in Partially Saturated Fracture Networks

“…This especially concerns the complex flow dynamics at fracture intersections, which act as critical relay points controlling: (1) the overall connectivity of fracture networks (Adler et al, 2013); (2) the flow partitioning dynamics between connected fracture elements (Xue et al, 2020;Yang et al, 2019;Dragila & Weisbrod, 2004); and, ultimately, (3) the distribution of flow modes on fracture surfaces (Dippenaar & Van Rooy, 2016;Jones et al, 2017;Shigorina et al, 2019), which, in turn, can affect the interaction between porous matrix and fracture (Tokunaga & Wan, 1997;Tokunaga, 2009). Here, the term "partitioning" refers to the process of fluid redistribution at a fracture intersection, which de--4-…”

“…Consequently, experimental results are difficult to cast into meaningful frameworks. This especially concerns the complex flow dynamics at fracture intersections, which act as critical relay points controlling: (1) the overall connectivity of fracture networks (Adler et al, 2013); (2) the flow partitioning dynamics between connected fracture elements (Dragila & Weisbrod, 2004;Xue et al, 2020;Yang et al, 2019); and, ultimately, (3) the distribution of flow modes on fracture surfaces (Dippenaar & Van Rooy, 2016;Jones et al, 2017;Shigorina et al, 2019), which, in turn, can affect the interaction between the porous matrix and fracture (Tokunaga, 2009;Tokunaga & Wan, 1997). Here, the term "partitioning" refers to the process of fluid redistribution at a fracture intersection, which depends on the relation between capillary, inertial, and viscous forces and complexities such as velocity-dependent contact angles (Xue et al, 2020;Yang et al, 2019).…”