Two-Dimensional Solute Transport with Multiple Point Sources in Semi-infinite Porous Media

Abstract

In the present study, analytical solutions have been developed for two-dimensional solute transport in steady field of groundwater flow with different longitudinal and lateral dispersion coefficients in semi-infinite heterogeneous porous medium for a varying type input point source. Dispersion coefficient is considered squarely proportional to the groundwater velocity along both longitudinal and lateral directions while groundwater velocity is considered linear spatially dependent function in both directions. The flow is assumed to be two-dimensional in a horizontal plane and the nature of pollutant and porous medium are considered chemically non-reactive. The geological formation is initially not solute free. Varying type input condition for multiple point sources through arbitrary time-dependent function is considered at origin. Concentration gradient is considered zero at infinity. New space variables are introduced by certain transformations to get the analytical solutions. The solutions in the real time domain are obtained by using Laplace Integral Transform Technique. The obtained analytical solutions are illustrated graphically to study the effect of various parameters on the solute transport in various time domains for spatially dependent velocity.