One-dimensional solute transport for uniform and varying pulse type input point source through heterogeneous medium

Abstract

An analytical solution is developed for conservative solute transport in a one-dimensional heterogeneous porous medium. The solute dispersion parameter is considered uniform, while the seepage flow velocity is considered spatially dependent. Retardation factor is considered inversely proportional to square of the flow velocity. The seepage velocity flow is considered inversely proportional to the spatially dependent function. The solution is derived for two cases: the former one is for uniform pulse type input point source and the latter one is for varying pulse type input point source. The second condition is considered at the far end of the medium. It is of the second type (flux type) of homogeneous nature. Laplace transform technique (LLT) is employed to get the analytical solutions to the present problem. In the process, a new space variable is introduced. The solutions are graphically illustrated. The effects of heterogeneity of the medium on the solute transport behaviour, in the presence and absence of the source pollutant, are also studied. Laplace transformation technique is used to solve the present problems analytically.

Keywords:

• advection–dispersion equation
• retardation factor
• heterogeneous medium
• pulse type point source
• diffusion processes

Acknowledgements

This work is part of the Post Doctoral Fellowship programme of the first author. Financial assistance provided by the funding agency to the first author in the form of Dr D. S. Kothari Post Doctoral Fellowship, University Grant Commission, Government of India, is gratefully acknowledged.