Analytical solutions of contaminant transport in homogeneous and isotropic aquifer in three-dimensional groundwater flow

• Main Authors: Mustafa, Shaymaa, Bahar, Arifah, Abdul Aziz, Zainal, Mohamad Darwish, Mohamad Darwish
• Format: Article
• Published: Springer Science and Business Media Deutschland GmbH 2022
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/103796/; http://dx.doi.org/10.1007/s11356-022-21402-8

Modeling three-dimensional contaminant transport released from arbitrary shape source geometries is useful in hydrological and environmental sciences. This article produces several analytical solutions for three-dimensional contaminant transport in a homogeneous and isotropic aquifer by using Green’s function with the groundwater flow which is assumed to be in three directions. The solutions are obtained for both finite depth aquifer and semi-infinite depth aquifer. Various types of sources are discussed: point, line, plane, or cuboid sources. The continuous and instantaneous sources are also investigated. A MATLAB coding is developed to calculate the numerical integrals which occur at the solutions. Some solutions are verified with the solutions obtained in the literature. This study confirms the effect of groundwater velocities in all directions on the degree and the directions of contaminant spreading. Additionally, the results highlight the significant effect of the geometrical shape of the contaminant sources on contaminant concentrations for instantaneous and continuous sources. In particular, the cuboid source and the horizontal rectangular source provide the highest concentrations. The analytical solutions developed in this article can be applied for a wide range of contaminant transport.