Estimation of transport and kinetic parameters using analytical solutions of the 2D advection-dispersion-reaction model

We propose some analytical solutions of the advection-dispersion equation and adopt them to solve a non-linear parameter estimation problem. A solution with no reactive term and another one with a unique coefficient representing the kinetic mechanisms of the solute decay in groundwater are described in detail and are then considered in the estimation procedure. To test the robustness of these analytical solutions if adopted in inverse problems, the anisotropic dispersion and kinetics are estimated using sets of experimental data simulated by Monte Carlo techniques. Cylindrical geometry is considered since large columns are the most common devices adopted to study both dispersion and kinetics mechanisms and, even if the solutions are expressed in terms of Bessel function expansion, they give very good results in terms of reliability and precision of our estimates. Discussion of results is based on the analysis of residuals, variance-covariance matrix and bias of parameters. The influence of location and time of sampling and of the number of samples on the estimates of dispersion and kinetic parameters is also analysed by means of Analysis of Variance and Fisher tests.