The Semi‐Analytical Solution for Non‐Equilibrium Solute Transport in Dual‐Permeability Porous Media

Abstract

Transport of contaminants through porous media often experiences non-equilibrium conditions and remains a challenging problem for groundwater hydrologists. The porous media heterogeneity is associated with irregular stratification, dead-end pores, fractures, and lenses with different hydraulic conductivities

On the Bimodal Radial Solute Transport in Dual‐Permeability Porous Media

“…Similar conclusions can be found in Sharma et al. (2021). Overall, it is highlighted that the MM model can efficiently capture the complex evolution of tracer for radial flow in a heterogeneous aquifer that can be characterized as a dual‐permeability porous media.…”

“…The optimized values of dispersivity for the MM model is the smaller than those of ADE at the four observation points, and the transfer coefficient of the MM model is higher than that of the MIM model. Similar conclusions can be found in Sharma et al (2021). Overall, it is highlighted that the MM model can efficiently capture the complex evolution of tracer for radial flow in a heterogeneous aquifer that can be characterized as a dual-permeability porous media.…”

“…(2004) investigated the effects of formation heterogeneity on radial solute transport by laboratory tracer test in a tank where a heterogeneous K ‐field was constructed artificially, and distinct double‐peaked BTCs were observed at many observation points. In general, the bimodal BTCs have been commonly observed in solute transport in heterogeneous systems such as karst, structured, and layered porous media, but they cannot be characterized by either ADE or MIM, or multi‐mate MIM (MRMIM) models (Lu et al., 2018; Sharma et al., 2021).…”

A Novel Model of Hydraulic Aperture for Rough Single Fracture: Insights From Fluid Inertial and Fracture Geometry Effects

“…The fluid motion in the rough 3‐D fracture is regarded as a fully developed single‐phase Newtonian fluid with incompressible and steady‐state, which can be described by solving continuity and Navier−Stokes equations (Zhang & Liu, 2024; Zhang et al., 2024c): $$$\left\{\begin{array}{@{}l@{}}\nabla \cdot \boldsymbol{u}=0\\ \rho (\boldsymbol{u}\cdot \nabla )\boldsymbol{u}=-\nabla p+{\mu }_{\mathrm{f}}{\nabla }^{2}\boldsymbol{u}\end{array}\right.$$$ where u is the flow velocity, and u = [ u x , u y , u z ]; ρ is the fluid density; p is the pressure; ∇ is the gradient operator; ∇⋅ is the divergency operator; and ∇ 2 is the Laplace operator.…”

Fluid‐Driven Particle Migration and Its Impact on Hydraulic Transmissivity of Stressed Filled Fractures

“…The pivotal parameter for understanding and predicting fluid flow in filled rock fractures is hydraulic transmissivity, denoting the ability to transmit fluids through porous and fractured media (Min et al., 2004; Walsh, 1981; S. Zhang & Liu, 2024). Over the years, substantial efforts have been dedicated to investigating the effect of confining stress, pressure cycles and filling particle size on the hydraulic transmissivity of filled rock fractures, and a number of general conclusions have been reached: (a) In every scenario, fracture transmissivity is inversely proportional to the confining stress, as it results in the reduction of fracture aperture and thus the densification of the filling material (Morrow et al., 1981); (b) Cyclic fluid pressure induces a decrease in fracture transmissivity, eventually stabilizing at a consistent minimum value after undergoing multiple pressure cycles (Faulkner & Rutter, 2000; Wang et al., 2016); (c) A coarser size of filling particles generally increases fracture transmissivity due to a greater void space (Xiao et al., 2021; Zheng et al., 2018).…”