Analytical solutions for one-dimensional advection–dispersion equation of the pollutant concentration

Abstract

We present simple analytical solutions for the unsteady advection-dispersion equations describing the pollutant concentration C(x, t) in one dimension. The solutions are obtained by using Laplace transformation technique. In this study we divided the river into two regions x ≤ 0 and x ≥ 0 and the origin at x = 0. The variation of C(x, t) with the time t from t = 0 up to t → ∞ (the steady state case) is taken into account in our study. The special case for which the dispersion coefficient D = 0 is studied in detail. The parameters controlling the pollutant concentration along the river are determined.

Remediation of pollution in a river by unsteady aeration with arbitrary initial and boundary conditions

“…The particular river whose water quality was the motivation for this study is the Tha Chin River in Thailand. The previous work published by Wadi et al (2014), in the journal of earth system science presented analytical solutions for the unsteady advection dispersion equations describing the pollutant concentration C(x, t) in one-dimension. On the other hand in the present work, an analytical solution is presented for unsteady equations representing the concentration of the dissolved oxygen Y(x, t).…”

“…(1), describing the pollutant concentration along the river are given by Wadi et al (2014) for the special case when k = 0. The river has been divided into two regions: upstream x 6 0 near the source, where it is assumed that the rate of pollutant along the river q(kg/(m d)) vanishes, the value of Y(x, t) in this region will be denoted by Y 1 (x, t), and downstream 0 6 x 6 LðmÞ (the polluted length of the river), where q = const.…”

“…For the steady state as t ? 1, C 1 (x, t) and C 2 (x, t) are given by Wadi et al (2014) and Pimpunchat et al (2009) …”

“…They determined the best zone from which water is taken for drinking or irrigation. Unsteady analytical solutions for one-dimensional advection-dispersion equation of the pollutant concentration are obtained by Wadi et al (2014). They determined the parameters controlling the pollutant concentration along the river and generalized the earlier solutions obtained by Pimpunchat et al (2007) for the unsteady state.…”

Analytical solution for solute transport from a pulse point source along a medium having concave/convex spatial dispersivity within fractal and Euclidean framework

“…You and Zhan (2013) derived the two semi-analytical solutions for solute transport in a finite column with linear asymptotic and exponential distance-dependent dispersivities and timedependent sources along a uniform flow. Analytical solutions for the one-dimensional advection-dispersion equations have been obtained using the Laplace transform technique into the left and right domains at the origin of the river domain (Wadi et al 2014). In these studies, analytical methods based on Laplace, Fourier, Hankel integral transforms and separation of variables have been used.…”