One-dimensional equilibrium model and source parameter determination for soil-column experiment

In this article, we put forward a non-linear transport model for an undisturbed soil-column experiment with the non-linear Freundlich's isotherm. As compared with ordinary models based on linear adsorption, the retardation factor is a non-linear functional of solute concentration, and the production term is a non-linear term related with the solute concentration and an unknown source/sink function. Furthermore, an actual undisturbed soil-column experiment in Zibo, Shandong Province, China is investigated, and an inverse problem of identifying the source/sink parameter is considered with the additional data of breakthrough curves. An optimal perturbation iteration algorithm is applied to determine the unknown source/sink parameter both in the cases of accurate and inaccurate data. The inversion results show that the optimal perturbation algorithm is efficient at least to the problem of this article, and the non-linear mathematical model here could be applied to describe undisturbed soil-column experiments ...

A non-linear mathematical model for an undisturbed soil-column experiment and source parameter identification

A new gradient regularization algorithm for source term inversion in 1D solute transportation with final observations

In this paper, an undisturbed soil-column infiltrating experiment is investigated, and a mathematical model describing multi-components solutes transport behaviors in the column is put forward by combing hydro-chemical analysis with advection dispersion mechanisms, which is a group of advection-dispersionreaction partial differential equations. Since the model involving six reaction coefficients which can not be obtained directly, an optimal perturbation regularization algorithm of determining these parameters is performed, and numerical simulations under different conditions are carried out. Furthermore, the inversion algorithm is applied to solve the real inverse problem by utilizing the measured breakthrough data. The reconstruction data basically coincide with the measured data showing that the inversion algorithm is efficient to the inverse problem of determining multi-parameters in a group of advection-dispersion equations arising in solutes transportation. The model and the inversion coefficients can be utilized to describe the experimental process and the experimental result.

Numerical Inversion of Multi-Parameters in Multi-Components Reactive Solutes Transportation in an Undisturbed Soil-Column Experiment

This paper deals with an inverse problem of determining a time-dependent reaction coefficient arising from a disturbed soil-column infiltrating experiment based on measured breakthrough data. A purpose of doing such experiment is to simulate and study transport behaviors of contaminants when they vertically penetrating through the soils. Data compatibility of the inverse problem is discussed showing a sufficient condition to the solution’s monotonicity and positivity with the help of an adjoint problem. Furthermore, an optimal perturbation regularization algorithm is applied to solve the inverse problem, and two typical numerical examples are presented to support the inversion algorithm. Finally, transport model of a positive solute ion in the soil-column is investigated based on the researches to the inverse problem. An optimal reaction coefficient is determined by the inversion algorithm, and the inversion is of numerical uniqueness. The inversion results not only coincide with data compatibility of the inverse problem, but also agree with the real breakthrough data.

Numerical Inversion of a Time-Dependent Reaction Coefficient in a Soil-Column Infiltrating Experiment

The procedure of cadmium ion transport through unsaturated soils can be described by the convection-diffusion equation, coupled with non-equilibrium sorption effect. The undetermined model parameters in the dimensionless governing equation include the longitudinal dispersivity, the sorption distribution coefficient, the precipitating rate, the dissolving rate and the maximum precipitation. This paper aims at inversing parameter values of the parameter mentioned above for cadmium ion transport in 8 Portugal soils samples and 1 Belgium soils sample under different experimental conditions. Experimental results of 15 groups are obtained in virtue of the laboratory soil column tests for 9 soils samples mentioned above by using self-designed experimental apparatus under different experimental condition. The gradient regularization method is adopted as the inversion method. Based on the experimental results (BTCs), the corresponding model parameters for each experiment are identified by the numerical inversion. The validity and reliability of the gradient regularization method is verified by the numerical simulated experimental results. The computational results confirm the veracity of results presented in this paper.

Model parameter inversion for cadmium ion transport through unsaturated soils

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Model parameter inversion for cadmium ion transport through unsaturated soils