Abstract
A mathematical model describing the transport of a conservative contaminant through a homogeneous finite aquifer under transient flow is presented. We assume the aquifer is subjected to contamination due to the time-dependent source concentration. Both the sinusoidally varying and exponentially decreasing forms of seepage velocity are considered for the purposes of studying seasonal variation problems. We use the parameter-expanding method and seek direct eigenfunctions expansion technique to obtain analytical solution of the model. The results are presented graphically and discussed. It is discovered that the contaminant concentration decreases along temporal and spatial directions as initial dispersion coefficient increases and initial groundwater velocity decreases. This concentration decreases as time increases and differs at each point in the domain.
Highlights
The intensive size of natural resources and the large production of wastes in modern society often pose a threat to the groundwater quality and already have resultant in many incidents of groundwater contamination
The contaminant concentration distribution behaviors along transient groundwater flow for sinusoidally varying velocity are shown in Figures 1 – 8
It is observed that the contaminant concentration increases along temporal direction as initial groundwater velocity increases
Summary
The intensive size of natural resources and the large production of wastes in modern society often pose a threat to the groundwater quality and already have resultant in many incidents of groundwater contamination. Degradation of groundwater quality can take place over large areas from plane or diffuse sources like deep percolation from intensively farmed fields, or it can be caused by point sources such as septic tank, garbage disposal sites, cemeteries, mine spoils and oil spoils or other accidental entry of pollutants into the underground environment. Another possibility is contamination by line sources of poor quality water, like seepage from polluted streams or intrusion of salt water, from oceans [1,2]. Contaminant (solute) transport through a medium is described by a partial differential equation of parabolic type and it is usually known as advection-dispersion equation [3]
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