Anomalous Solute Transport in a Cylindrical Two-Zone Medium with Fractal Structure

Bakhtiyor Khuzhayorov,Bekzodjon Fayziev,N.M.A Nik Long,Azizbek Usmonov

doi:10.3390/app10155349

Bakhtiyor Khuzhayorov, Bekzodjon Fayziev + Show 2 more

Open Access

https://doi.org/10.3390/app10155349

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Abstract

In this paper, a problem of anomalous solute transport in a coaxial cylindrical two-zone porous medium with fractal structure is posed and numerically solved. The porous medium is studied in the form of cylinder with two parts: macropore—with high permeability characteristics in the central part and micropore—with low permeability around it. Anomalous solute transport is modeled by differential equations with a fractional derivative. The solute concentration and pressure fields are determined. Based on numerical results, the influence of the fractional derivatives order on the solute transport process is analysed. It was shown that with a decrease in the order of the derivatives in the diffusion term of the transport equation in the macropore leads to a “fast diffusion” in both zones. Characteristics of the solute transport in both zones mainly depend on the concentration distribution and other hydrodynamic parameters in the macropore.

Highlights

Problems of solute transport and filtration of nonhomogeneous fluids are of great practical importance in many branches of engineering and technology
It was shown that the analytical solution [20] satisfactorily describes the experimental data, the effects of tailing can be well explained by the diffusion exchange of tritium between zones with a mobile and immobile fluid
The medium is treated as a non-homogenous porous medium of fractal structure consists of macropore and micropore

Summary

Introduction

Problems of solute transport and filtration of nonhomogeneous fluids are of great practical importance in many branches of engineering and technology. The poorly permeable zone contains many micropores, where diffusion is the main transport mechanism of solute, while convective transport is insignificant and can be neglected This leads to the restriction of fluid mixing and, the appearance of tailing, even in the case of complete saturation of the media. It was shown that the analytical solution [20] satisfactorily describes the experimental data, the effects of tailing can be well explained by the diffusion exchange of tritium between zones with a mobile and immobile fluid. The complex trajectory of fluid particles and substances in the inter-aggregate media, fractures and porous blocks causes anomalous transport, so that conventional convective transport equations cannot adequately describe solute transport, transport equations must take this anomalous into account Such media can be considered to be fractals [24,25].

Statement of Problem

Numerical Solution of the Problem

Results and Discussion

Conclusions