Analytical Model for Contaminant Migration with Time-Dependent Transport Parameters

Abstract

A general analytical model for one-dimensional (1D) contaminant transport in infinite domain with time-dependent transport parameters is presented in this paper. The model is based on the advection-dispersion equation with a time-dependent flow velocity, a time-dependent dispersion coefficient, and a time-dependent distribution coefficient due to sorption. It takes into account a first-order irreversible reaction (decay), an arbitrary initial distribution of the contaminant, and an arbitrary space- and time-dependent sink/source term. The model can handle any time-dependent transport parameter. Analytical solutions are provided for both the advection dominant and the advection-dispersion transport equations. The proposed analytical solutions are general and they can be used for problems where one or more parameters are time-dependent. It is shown that the presented solutions can be reduced to other existent solutions where one transport parameter is assumed to be time-dependent. The general analytical solutions are obtained by using the Fourier transform, and they are presented in integral forms. Several closed-form solutions can be derived from the general integral form. Such closed-form solutions are of great interest since they allow the dependence of the solutions on the underlying physical parameters to be studied in an analytical manner. In particular, the author presents some closed-form solutions for the case of an initial step function and discusses through the numerical examples some insights about the errors that can be made by assuming constant parameters instead of time-dependent ones. These assumptions may lead to overestimated or underestimated concentrations. The proposed analytical solutions are useful for benchmarking numerical solutions to problems in hydrogeology and chemical engineering. They are also of great importance to the investigation of quantitative accuracy assessment. One of the presented closed-form solutions is used to compare with numerical solutions.