Analytical Solutions for One-dimensional Advection-dispersion Equation with Uniform and Varying point source in a Heterogeneous Porous medium
Journal Title: International Journal of Modern Research In Engineering & Management. - Year 2019, Vol 2, Issue 4
Abstract
In this study, analytical solutions for one-dimensional advection-dispersion equation in a semi-infinite porous domain with temporally dependent dispersion coefficients are considered. Seepage velocity is taken inversely proportional to spatially and temporally dependent function. It assumed that retardation factor is inversely proportional to square of the spatially dependent function. In this study, two cases for the boundary conditions are taken into consideration. The input condition is considered continuous of uniform and varying input of increasing nature both. The solution is obtained for the proposed mathematical model in a semi-infinite initially not solute free domain. The solution has been obtained by using Laplace Transform Technique. A comprehensive study on the effect of different geological parameters and heterogeneity of the medium on the solute movement during movement processes is carried out for heterogeneous porous medium. The developed analytical solution is illustrated using a hypothetical example and may help benchmark numerical codes and solutions. The effects of parameters on the solute concentrations with respect to position and time are explained with help of different graphs. In real scenario, such mathematical model is helpful for the assessment and effective remediation process. A new time variable is introduced through a known transformation.
Authors and Affiliations
R. R. Yadav
Keywords
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