Asymptotic Behavior of Mass Transfer for Solute Transport Through Stratified Porous Medium

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

“…While the first region is associated with macropores or fractures, the second region is associated with micropores or rock matrix. The dual‐porosity models assume that advective flow is limited to the fracture domain and that dissolved solutes can move in and out of micropores or rock matrix due to molecular diffusion or first‐order mass transfer (van Genuchten & Wierenga, 1976; Swami et al., 2014, 2016, 2018). The most popular model based on the dual‐porosity approach is the mobile‐immobile model (MIM) (Gaudet et al., 1977; Skopp et al., 1981; van Genuchten & Wierenga, 1976; Warren & Root, 1963).…”

Karst water resources in a changing world: Review of solute transport modelling approaches

“…Likewise, chemical parameters (i.e., sorption parameters) obtained under the laboratory conditions might largely differ from those measured at the field scale (Faulkner et al, 2009;Witthüse et al, 2003). For instance, the partition coefficient (K d ) and mass transfer coefficient (i.e., first-order mass transfer coefficient) could not be generalized (e.g., Stockmann et al, 2017;Swami et al, 2018) because their values are extremely varied (often by order of magnitudes) at the field-scale measurements depending both on the matrix hydraulic properties (e.g., surface area, matrix porosity, permeability) and on the fracture/conduit characteristics (Howroyd & Novakowski, 2021;Lehmann et al, 2022;Maloszewski & Zuber, 1993;Zhou et al, 2007). Similarly, the values for reactive transport parameters could also be misleading particularly when they are scaled up or extrapolated, because of the oversimplification of the multifaceted processes that are varied both by chemical heterogeneities in the matrix and local/global groundwater chemistry (e.g., Howroyd & Novakowski, 2021;Jiang et al, 2023;Katz et al,1998;Kaufmann et al, 2014;Mohammadi et al, 2021;Maqueda et al, 2023, among many others).…”

A Fundamental Moving Boundary Problem of 1D Commingled Preferential Darcian Flow and Non-Darcian Flow Through Dual-Layered Porous Media

“…Heterogeneity along the direction vertical to the flow (Shen and Reible, 2015;Song et al, 2015;Wu et al, 2016;Afshari et al, 2018;Gao et al, 2018;Swami et al, 2018;Li et al, 2019;Kaffel, 2019;Nijjer et al, 2019;Liu W. C., 2020;Ma et al, 2021;Shen et al, 2022), different from the heterogeneity along the flow direction (Liu et al, 2022), is a critical feature of the porous media in the real world. For example, the vertically stratified oil reservoirs (Song et al, 2015;Gao et al, 2018) with vertical permeability heterogeneity are commonly encountered in petroleum engineering, the contaminant transport (Shen et al, 2015;Swami et al, 2018) in vertically layered formations is frequently involved in environment engineering, and the rainfall infiltration into layered soils (Wu et al, 2016;Afshari et al, 2018;Kaffel, 2019;Nijjer et al, 2019) is very common in municipal engineering. Although the research area on the mass transfer through heterogeneous porous media is very challenging due to the involvement of the nonlinear flow process and complex flow situations in the actual engineering background, abundant research on the seepage flow problems in multi-layer porous media considering the heterogeneity has been carried out in recent years.…”

“…Gao et al (2018) conducted numerical simulation research on the development of low-permeability multi-layer reservoirs, and a stratified hydraulic fracturing method was put forward for oil recovery enhancement. By employing the semi-analytical solution method, Swami et al (2018) studied the asymptotic solute transport behavior in stratified porous media and also proposed an asymptotic relation that could provide valuable information on the mass transfer coefficient during solute transport. Li et al (2019) defined a main flow channel index to identify the type of main flow channel in heterogenous petroleum reservoirs and put forward a quantitative classification method for the main flow channels.…”