Empirical Mathematical Analysis of Electrokinetic Decontamination of Soils Polluted With Heavy Metals

The electrokinetic remediation (EKR) of soils polluted with cadmium and zinc is studied. The dependences of the concentration of C i pollutants in the soil on coordinate x i of its measurement point on the surface (distances to the anode) and on time t i are measured: C i ( x i , t i ). The experimental dependences C i ( x i , t i ) are approximated by our previously developed theoretical function of two variables: C ( x , t ) is the spatiotemporal profile (STP) of pollutant concentrations in the soil during its remediation. The measured dependences C i ( x i , t i ) and the corresponding theoretically calculated surfaces are shown in the figures in the 3D format. A two-stage approximation procedure is described in detail, which makes it possible to avoid getting into the local minimums of the discrepancy error between the function C ( x , t ) and observed experimental values C i ( x i , t i ) and find the desired global minimum of this error. A calculation method is proposed also for the Cd and Zn calculated curves that describe the boundary between the polluted and unpolluted areas adjacent to the soil surface, i.e., areas where the concentration of pollutants is respectively higher and lower than their approximate permissible concentrations (APCs). The curve itself is a geometric set of the STP points, in which the pollutant concentration is approximately equal to the APC. It is shown that the absence of a deviation from the asymptotic behavior of the STP at the intermediate or close to the final stages of the EKR of the soil makes it possible to extrapolate the course of these curves in time and predict in how many days the area of the soil under consideration will be purified without additional measurements, as well as the percentage of the area that will be purified. The experimental dependences of the pollutant concentrations on the coordinate and time and the theoretical curves describing them are also presented in the figures in the 2D format.