Non-Equilibrium Solute Transport Models And Parameters Inversion

This thesis deals with mathematical models of solutes transport in porous medium and numerical simulations, and model parameters inversion based on invese problems for convection-dispersion equation(s) and an actual soil-column experiments.1-D solute transport in soil and groundwater can be expressed by convection-dispersion equation(s). In particular, the models parameters describing transport characteristics can not be measured directly for nonlinear solutes transport with complicated physics/chemical reactions. Therefore, inverse problems of parameter inverseion and identification for convetion-dispersion-reaction equation(s) have had widely applications in the researches of solutes transpoprt in soil and groundwater. The main works of this thesis are listed below:1)The equilibrium model with a nonlinear source (sink) term relating with time is discussed, and numerical simulations for the source coefficients inversion are carried out. Furthermore, the inversion algorithm is applied to an actual soil-column experiment to reconstruct the breakthrough data. At last, according to the condition of this experiment, the source coefficients and the unknown adsorption coefficient are jointly determined.2) The non-equilibrium two-site model for solute transportation is described and solved by 6-piont difference scheme numerically, and simulations for multi-parameters joint inversion are performed by the optimal perturbation algorithm.3) A mathematical model is discussed for multi-component solutes transport in porous medium dominated by sulfate, which is a group of advection-dispersion-reaction partial differential equations. Since the model parameters could not be measured directly, an inverse problem for the multi-parameters, which is based on the optimal perturbation iteration algorithm, is put forward, and numerical inversions under different conditions are carried out. Finally, the multi-parameter inversion algorithm here is applied to the actual experiment, and the numerical inversion results basically coincide with the experiment data.