Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 679531, 14 pages
Research Article

A Nonlinear Solute Transport Model and Data Reconstruction with Parameter Determination in an Undisturbed Soil-Column Experiment

1Institute of Applied Mathematics, Shandong University of Technology, Shandong, Zibo 255049, China
2Institute of Mining Technology, Inner Mongolia University of Technology, Hohhot, Inner Mongolia 010051, China
3Center of Analysis and Testing, Shandong University of Technology, Shandong, Zibo 255049, China

Received 22 June 2011; Accepted 19 October 2011

Academic Editor: J. Rodellar

Copyright © 2011 Gongsheng Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A real undisturbed soil-column infiltrating experiment in Zibo, Shandong, China, is investigated, and a nonlinear transport model for a solute ion penetrating through the column is put forward by using nonlinear Freundlich's adsorption isotherm. Since Freundlich's exponent and adsorption coefficient and source/sink terms in the model cannot be measured directly, an inverse problem of determining these parameters is encountered based on additional breakthrough data. Furthermore, an optimal perturbation regularization algorithm is introduced to determine the unknown parameters simultaneously. Numerical simulations are carried out and then the inversion algorithm is applied to solve the real inverse problem and reconstruct the measured data successfully. The computational results show that the nonlinear advection-dispersion equation discussed in this paper can be utilized by hydrogeologists to research solute transport behaviors with nonlinear adsorption in porous medium.