An Investigation of the Analytical Solutions to One-Dimensional Transport Equation in Heterogeneous Soils Assuming Three Spatially-Variable Dispersion Coefficients

The phenomenon of transport in aquifers, as heterogeneous porous media, has been the subject of research over the past two decades. Characterizing the role of dispersivity in mass transport in such media is essential to any effort in predicting the movement of contaminant in water resources. In this study, to presume heterogeneity of porous media, three types of spatiallyvaried dispersion coefficients were used. These coefficients including linear, power and exponential functions were inserted separately in the mass transport equation in porous media. Then, these models were solved analytically using boundary conditions of the first- (Dirichlet) and third-kind (Cauchy). To illustrate concentration profiles, data of continuous injection of sodium chloride ions in a laboratory soil column were used. The values of concentration in column at various times were estimated by CXTFIT2.1 code. Concentration profiles of both boundary conditions showed that at early times after the injection, dispersion coefficient of the linear model was more compatible with the experimental data and with elapsing time, results of the power model were better than those of the other two models. Moreover, the results showed that Cauchy and Dirichlet conditions were more appropriate for solving linear and exponential models, respectively.