Title: Solute transport with decay type input source in one-dimensional heterogeneous groundwater: analytical solution

Authors: Premlata Singh; Gulrana; Arun Dubey; Dilip Kumar Jaiswal

Addresses: Department of Mathematics, Birla Institute of Technology Mesra, Ranchi, Extension Center Patna-800014, India ' Dr. K.P. Jaiswal Inter College, Prayagraj, India ' Faculty of Mathematical and Statistical Sciences, Institute of Natural Sciences and Humanities, Shri Ramswaroop Memorial University, Lucknow-Deva Road, India ' Faculty of Mathematical and Statistical Sciences, Institute of Natural Sciences and Humanities, Shri Ramswaroop Memorial University, Lucknow-Deva Road, India

Abstract: The process of aquifer remediation extends with the growing dependence on groundwater. Mathematical model of solute transport in porous media is important tool used to characterise the extent of approximating the shape, size and position of a contaminant. In the present study, an unsteady solute transport model advection-diffusion equation (ADE) is taken and analytical solutions were obtained by using Laplace integral transformation technique (LITT). The concentration is predicted in presence and absence of source, i.e., firstly initially medium (aquifer/air) is not supposed to be solute free, i.e., initially domain is already polluted/contaminated and secondly the medium is clean, taking decay type exponential input at origin. The dependence of velocity on space variable is of linear non-homogeneous nature due to heterogeneity of the semi-infinite horizontal dispersion medium. The dispersivity is considered square of the velocity which represents the seasonal variation of the year in tropical regions.

Keywords: advection-dispersion equation; groundwater; heterogeneity; pollution; semi-infinite medium.

DOI: 10.1504/IJHST.2025.143131

International Journal of Hydrology Science and Technology, 2025 Vol.19 No.1, pp.40 - 51

Received: 16 Dec 2022
Accepted: 17 Aug 2023
Published online: 03 Dec 2024 *

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