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The difference between semi-continuum model and Richards' equation for unsaturated porous media flow.

ABSTRACT: Semi-continuum modelling of unsaturated porous media flow is based on representing the porous medium as a grid of non-infinitesimal blocks that retain the character of a porous medium. This approach is similar to the hybrid/multiscale modelling. Semi-continuum model is able to physically correctly describe diffusion-like flow, finger-like flow, and the transition between them. This article presents the limit of the semi-continuum model as the block size goes to zero. In the limiting process, the retention curve of each block scales with the block size and in the limit becomes a hysteresis operator of the Prandtl-type used in elasto-plasticity models. Mathematical analysis showed that the limit of the semi-continuum model is a hyperbolic-parabolic partial differential equation with a hysteresis operator of Prandl's type. This limit differs from the standard Richards' equation, which is a parabolic equation and is not able to describe finger-like flow.

SUBMITTER: Vodak R

PROVIDER: S-EPMC9090790 | biostudies-literature | 2022 May

REPOSITORIES: biostudies-literature

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The difference between semi-continuum model and Richards' equation for unsaturated porous media flow.

Vodák Rostislav R Fürst Tomáš T Šír Miloslav M Kmec Jakub J

Scientific reports 20220510 1

Semi-continuum modelling of unsaturated porous media flow is based on representing the porous medium as a grid of non-infinitesimal blocks that retain the character of a porous medium. This approach is similar to the hybrid/multiscale modelling. Semi-continuum model is able to physically correctly describe diffusion-like flow, finger-like flow, and the transition between them. This article presents the limit of the semi-continuum model as the block size goes to zero. In the limiting process, the ...[more]

PMID: 35538096

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Project description:Per- and poly-fluoroalkyl substances (PFAS) adsorb at air-water interfaces during transport in unsaturated porous media. This can cause surfactant-induced flow and enhanced retention that is a function of concentration, which complicates characterization and modeling of PFAS transport under unsaturated conditions. The influence of surfactant-induced flow and nonlinear air-water interfacial adsorption (AWIA) on PFAS transport was investigated with a series of miscible-displacement transport experiments conducted with a several-log range in input concentrations. Perfluorooctane sulfonic acid (PFOS), perfluorooctanoic acid (PFOA), and ammonium perfluoro 2-methyl-3-oxahexanoate (GenX) were used as model PFAS. The results were interpreted in terms of critical reference concentrations associated with PFAS surface activities and their relationship to the relevancy of transport processes such as surfactant-induced flow and nonlinear AWIA for concentration ranges of interest. Analysis of the measured transport behavior of PFAS under unsaturated-flow conditions demonstrated that AWIA was linear when the input concentration was sufficiently below the critical reference concentration. This includes the absence of significant arrival-front self-sharpening and extended elution tailing of the breakthrough curves, as well as the similarity of retardation factors measured for a wide range of input concentrations. Independently-predicted simulations produced with a comprehensive flow and transport model that accounts for transient variably-saturated flow, surfactant-induced flow, nonlinear rate-limited solid-phase sorption, and nonlinear rate-limited AWIA provided excellent predictions of the measured transport. A series of simulations was conducted with the model to test the specific impact of various processes potentially influencing PFOS transport. The simulation results showed that surfactant-induced flow was negligible and that AWIA was effectively linear when the input concentration was sufficiently below the critical reference concentration. PFAS retention associated with AWIA can be considered to be ideal in such cases, thereby supporting the use of simplified mathematical models. Conversely, apparent nonideal transport behavior was observed for experiments conducted with input concentrations similar to or greater than the critical reference concentration.

Dataset Information

The difference between semi-continuum model and Richards' equation for unsaturated porous media flow.

Publications

The difference between semi-continuum model and Richards' equation for unsaturated porous media flow.

Similar Datasets

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