The process of electrokinetic remediation (EKR) of clay soil containing an admixture of a typical organic pollutant, ethylbenzene, which is often found in it near gas stations and oil product storage facilities, is studied. Experimental measurement of the dependence of the concentration of this pollutant on time and the spatial coordinate during electrokinetic soil decontamination is carried out on a specially designed installation using the chromato-mass spectrometric method and a procedure close to that described in the guidelines of the MUK 4.1.1061-01. In order to intensify the EKR process of organic pollutant, the method of using an aqueous solution of two surfactants as the process fluid—anionite AB-17 and neonol AF 9-12—is applied. The experimental results are processed using the empirical-mathematical method described in the previous article and the function proposed in it. A good approximation of the experimental concentration dependences on both coordinates is demonstrated using this function: in all the experiments considered, the coefficients of determination R2 > 0.9986. The parameters of the approximating functions are calculated. The curves of the boundaries of the achievement of the concentration of ethylbenzene in soil samples of the level of the maximum permissible concentration (MPC) ≤ 0.5 mg/kg in the EKR process are determined. Based on these data, practical recommendations are proposed for choosing the conditions and modes of conducting the EKR process, which minimize the time and financial costs and improve its quality.

The space-time profiles (STPs) of the concentrations of the pollutants in the mobile and stationary phases of the sorption column are studied. In the theoretical study, it is found that the STP of the pollutant concentrations in the mobile phase, C(x, t), plays a decisive role in the formation of an STP in the stationary phase, q(x, t), and directly affects the course of the breakthrough concentration curve C(t). On the assumption of the existence of a Langmuir interphase equilibrium in a dynamic sorption system, logistic-type formulas are derived that describe C(x, t), q(x, t), and C(t). In order to test the derived formulas, an experiment was carried out to determine the concentrations C(xi, tj), q(xi, tj), and C(tj) (i = 1, 2, …, 10, j = 1, 2, …, 10) in the process of water purification from bivalent mercury ions using a special multisection column (10 sections) filled with a strongly acidic Dowex® XZS-1 cation exchanger. The obtained experimental dependences of the concentrations on time are approximated by the functions C(x, t), q(x, t), and C(t), characterized by the corresponding parameters. The values of these parameters determined in the course of fitting for all three functions turned out to be close to each other, which indicates the correctness of the theoretical consideration.

An empirical mathematical method is developed for studying spatiotemporal profiles (STPs) of pollutant concentrations in soils in the process of their electrokinetic remediation (EKR). For the mathematical description of STP concentrations, it is proposed to use the basic monotonic exponential (or logistic) function, which has asymptotic properties simultaneously in spatial, x, and temporary t, coordinates, with the addition of individual corrective functions that take into account experimentally observed deviations from monotonicity (extrema, inflection points, etc.). In the trial approximation, the sum of two-dimensional Gaussian functions is used as such corrective functions. A general mathematical formula describing the STP is derived. To demonstrate the possibilities of the developed method, the published experimental data on the electrokinetic purification of soils from certain heavy metals are processed using this formula. It is established that the quality of the description of experimental data using the proposed formula increases during the transition from the initial stage of the EKR process to the intermediate and final stages, which indicates a high level of predictability of the results of the EKR analysis based on the developed approach.

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.

The physicochemical method of sorption using solid sorbents was considered as an effective method for removing pollutants from aquatic media.

A method is developed to slow down and prevent the penetration of oil and its distillation products into the ground. It is shown that impregnation of the soil with an aqueous solution of sodium polyacrylate (PAN) in low concentrations (up to 0.75 wt %) practically does not affect the throughput. However, with a further increase in the PAN concentration in a relatively small range from 0.75 to 1.5 wt %, the rate of oil and oil products’ (OOPs) seepage into the soil drops sharply, reaching almost zero at a PAN concentration in the impregnating aqueous solution of 2 wt % and the thickness of the impregnated soil layer 1 cm. This effect of impregnation on the ability to filter oil and oil products is observed for almost all the studied types of soils.

The breakthrough curves of column dynamic adsorption of ammonium ions from water by cationites are analyzed. The experimental data are taken either from the published sources related to cationite 650C or from the authors’ own experiments (related to cationite KU 2-8chs). In the course of the mathematical treatment, the usual breakthrough dependences C/C0 on t, where t is the running time, and C and C0 are the breakthrough and initial concentrations of the contaminant in water, respectively, are transformed into dependences (ln C0/C –1) on t, which are linear in terms of the Bohart–Adams, Thomas, or BDST model. In this paper these dependences are found to be nonlinear for cationites 650C and KU 2-8chs. A method to analyze such data is offered based on the power series expansion of these dependences. The expansion coefficients are used to determine the adsorption rate constants k and the dynamic exchange capacities of adsorbents qm.

Рассмотрен физико-химический метод сорбции с использованием твердых сорбентов – как эффективный метод удаления загрязняющих веществ из водной среды.

Infiltration of spilled light and heavy crude oils and refinery products: gasoline, kerosene, winter- and summer-grade diesel fuels into gravel sand, fine-grained sands, sandy till, and peat has been studied. The depth of penetration of these hydrocarbon liquids (HCLs) into soil was measured over time. The penetration depths are best described by simple exponential asymptotic functions, the asymptote values being the maximum infiltration depths (MIDs) for each “HCL‒soil” pair of objects in experiment. The dependences of MIDs on the logarithm of filtration coefficients were determined for all “HCL‒soil” systems under study. These dependences are described by a single curve (parabola in this case).

The solution of the Langmuir–Hinshelwood (L–H) differential kinetic equation describing a two-stage reaction of the photocatalytic oxidation of pollutants in air on the surface of a heterogeneous TiO2 catalyst is investigated, and a new approach to processing the experimental data based on this study is developed. A well-known solution to this equation is the equation for the cumbersome implicit function F(CA, t) = 0, where CA is the concentration of pollutants in the air and t is the time. The core of the proposed approach is that instead of searching using various approximations for an explicit function describing the dependence of the concentration of pollutants in CA air on time t, for such a description one should use as an artificial method the known explicit functional dependence of t on CA obtained by solving the L–X equation. Only after the final approximation of the experimental data using such a function (fitting the parameters of the equation) should the abscissa and ordinate be swapped in order to present the results in a more familiar form: CA = CA(t). It is proved that researchers should always introduce a correction factor into the right-hand side of the L–X equation Sc/Vb, which reflects the ratio of the total surface area of the catalyst, Sc, to the volume of the enclosed space, Vb (of the reactor, room) in which the pollutants are removed. Derived formulas for calculating the equilibrium constant K of the adsorption-desorption process, the rate constants kr of the heterogeneous photocatalytic oxidation (mineralization) of the pollutants, as well as the time required to clean the enclosed space from the pollutants to the level of the maximum permissible concentration of various categories of hygienic standards. The obtained results of the mathematical study are applied to analyze the experimental dependences of the concentrations of the pollutants in the CA in the air on time t, both those published in the scientific literature (acetaldehyde, toluene, dimethyl sulfide, and acetone) and obtained in the course of our own experiment (tetrachlorethylene, methylene chloride, tert-butyl methyl ether, and isopropanol).

The kinetic features of bimodal gelation in viscous flow fluids, in particular, petroleum products, are analyzed by viscometry. The gelation and densification of petroleum products facilitate the elimination of consequences of their spill. Experimental dependences on the viscosity time of gasoline, kerosene, and winter and summer diesel fuel mixtures with lithium tetralkoxyborate as a gelator are measured. These dependences are found to have a bimodal sigmoidal shape called the dose-response form in scientific publications. A mathematical formula is proposed to describe these bimodal dependences. In accordance with this formula, the gelation process consists of two stages: (1) a reaction of lithium tert-butylate Li–O–C(CH3)3 and trialkoxyborate B(OC8H17)3 with the formation of lithium tetralkoxyborate; (2) a gelation reaction of lithium tetralkoxyborate and hydrocarbons of the mentioned petroleum products. The formula contains a number of fitting parameters, e.g., tinf1 and tinf2 (h) are the onset times of gelation and the formation of a stable gel respectively; h1 and h2 (h–1) are the rate constants of the first and second stages of gelation, and so on. The concentration dependences of gelators on these parameters are determined. Based on these dependences, the conclusions are drawn about the kinetic features of bimodal gelation in viscous flow fluids.

Dynamic column adsorption of mercury(II) from aqueous solutions on an Amberlite GT-73 cationite is studied. Experimental measurements derive the dependences C/C0 = f(t) (breakthrough curves), where C0 and C are the concentrations of mercury in the water flow inflowing to the sorbent fixed bed and outflowing from it, respectively, and t is the running time for different thicknesses of the fixed bed, as well as deriving rates of water flow and concentrations of mercury C0. It is shown that if the breakthrough curves belong to the logistic type, dependences of ln (C0/C − 1) on t are rectified and have the form ln (C0/C − 1) = a0−a1t, where the parameters a0 = kqmM/Q and a1 = kC0, k is the rate constant of adsorption, qm is the dynamic adsorption capacity, M is the weight of the adsorbent, and Q is the volumetric flow rate. By transforming the experimental dependence of the first type to the second type followed by its description using this straight line function, the aforementioned parameters a0 and a1 are determined followed by the quantities k and qm, characterizing the adsorption of mercury on the cationite. It is found that the relative standard deviation is ≤2% for the experimental quantities k and qm. A formula for the calculation of the service lifetime of the adsorbent maintaining the regulated degree of purification of water is derived. The formula is successfully tested in the experiments on the removal of mercury from water described in this work.

A comparative analysis is made of mathematical models of breakthrough curves C / C 0 = f ( t ) describing the removal of pollutants from water, where C 0 and C are the pollutant concentrations in water flows at the inlet and outlet of an adsorption column, respectively, and t is current time. It is shown that, within the Thomas and BDST (bed depth service time) models, the time dependence of breakthrough concentration C is described by the linear equation ln( C 0 / C –1) = a 0 – a 1 t , where a 0 and a 1 are coefficients, which have different meanings in different models. Approximation of experimental dependences by this linear theoretical dependence enables locating these coefficients and then, using them, calculating adsorption parameters, in particular, the adsorption rate constant k and dynamic adsorption capacity q m . These parameters are determined for processes described in the literature, namely, dynamic adsorption of Hg(II) on granulated activated carbon and activated carbon cloth and dynamic adsorption of nitrate ions on commercial anion-exchange resin PA408.