Contaminant transport analysis under non-linear sorption in a heterogeneous groundwater system

• Published in: Applied mathematics in science and engineering Vol. 30; no. 1; pp. 736 - 761
• Main Authors: Radha, Rashmi, Singh, Rakesh Kumar, Singh, Mritunjay Kumar
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Ltd 31.12.2022; Taylor & Francis Group
• Subjects: Advection; Contaminants; Dispersion; Exact solutions; Groundwater; groundwater contamination; Groundwater flow; heterogeneous medium; Isotherms; Laplace transforms; non-linear sorption; Parameter robustness; Pollution transport; Sorption; transient flow; Transport phenomena; Unsteady flow
• ISSN: 2769-0911; 2769-0911
• DOI: 10.1080/27690911.2022.2138867

In this study, a one-dimensional non-linear advection–dispersion equation subject to spatial–temporal dependent advection and dispersion coefficients is solved for a heterogeneous groundwater system. The non-linearity of the governing equation is based on the Freundlich and Langmuir sorption isotherms. The groundwater flow is considered to vary exponentially with time. Also, a generalized theory of the dispersion coefficient is used for extensive study of the model problem. The approximate solutions of the model problem are obtained in a semi-infinite and finite heterogeneous media by employing the Crank–Nicolson scheme. The exact solutions are obtained in both domains by the Laplace transform technique subject to linear sorption isotherm and non-transient flow conditions. Further, various graphical solutions are obtained using MATLAB scripts to examine the contaminant transport behaviour. For quantitative evaluation of the proposed model, a root mean square (RMS) error is computed. Overall, the results show that RMS error of the approximate solutions with respect to the exact solutions is within acceptable limits (less than 5%) for different combinations of discretization parameters. The robustness of the proposed model suggests its better suitability for modelling groundwater transport phenomena under the consideration of a non-linear sorption isotherm.