Contaminant Transport Processes Research Articles

Enhanced landfill's characterization by using an alternative analytical model for diffusion tests.

Landfills have been extensively used as waste deposits in most of the big cities in the world. Therefore, considerably large urban areas have contamination threats. Engineering solutions applied to prevent or contain soil, and water contamination often involve the application of liners, which are low permeability barriers made of materials such as compacted clay and geomembranes. In many liner applications, once reduced rates of seepage are expected, diffusion has proved to be relevant, if not dominant, to the process of contaminant transport. Normally, diffusivity parameters can be assessed by a single-reservoir pure diffusion test, where a contaminant solution is placed above a saturated soil sample and the solution's concentration is monitored over time. Once the temporal variation of concentration is measured, the process of back-calculating diffusivity parameters is not standardized. In this paper, an analytical model of the diffusive transport of contaminants is revisited considering the initial and boundary conditions of the pure diffusion test. In this model, the contaminant solution reservoir is included in the analysis domain as an equivalent contaminated soil layer. The analytical solution relies on a series evaluation, which may be a drawback to everyday engineering situations. Therefore, we build a high-accuracy exponential approximation to the solution. Expedited evaluation procedures are proposed to provide reasonable estimates for the fitting parameters. Also, in order to illustrate the applicability of the new solution, test datasets of a soil around the Jockey Club Landfill (JCL) site, one of the major landfills in Latin America, have been modeled. We discuss possible issues of considering linear isotherms to model the sorption characteristics of soils, indicating that convex isotherms, if linearly modeled, may lead to overestimated values of the diffusivity parameter.

Determining hyporheic removal rates of trace organic compounds using non-parametric conservative transport with multiple sorption models

Assessing the transport and reactive processes of contaminants in freshwater streams is crucial in managing water resources sustainably. Particularly the hyporheic zone, the sediment-water interface where surface water and groundwater mix, may possess significant contaminant removal capacities due to its myriad physical, chemical, and microbiological processes. However, modelling approaches aiming at assessing the hyporheic zone’s reactivity are either based on simple assumptions, such as, predefining the shape of the residence times distribution (RTD) function, or are computationally not feasible due to a too detailed system characterisation. In addition, parent-daughter reactions of contaminants are barely investigated. The present study introduces a numerical modelling framework for assessing hyporheic reactions of contaminant transformation reactions based on a non-parametric residence time approach combined with multiple sorption models and first-order removal reactions. The proposed framework uses natural electrical conductivity fluctuations to determine conservative transport properties and is demonstrated by interpreting time series of hyporheic point measurements of trace organic compounds, such as pharmaceuticals, and their transformation products using two commonly-used sorption models, namely the simple retardation and the first-order kinetic sorption model. The developed approach gives similar reaction rate coefficient estimates for all contaminants considered for both sorption models tested. The findings highlight that (i) the accurate shape of the RTD is most certainly important for reactive parameter determination and (ii) the daughter reaction rate coefficient may be underestimated if its parent transformation is ignored. The model provides reactive parameter estimates of contaminant transformation reactions with high parameter identifiability and informs which specific parent-daughter-pathway has occurred.

Spatiotemporal characteristics of hydraulic performance and contaminant transport in treatment wetlands

Wetlands have been proven to be efficient and cost-effective ecological treatment systems for municipal and domestic wastewater. It is essential to understand the hydrodynamic characteristics and the related contaminant transport process to optimize the treatment efficiency in free water surface wetlands. Thirty-six tracer experiments were conducted under different water depths and wetland configurations, such as installing static obstacles and dynamic disturbances. The particle image velocimetry and a novel color-concentration transform method were developed to reveal spatiotemporal flow velocity and residence time distribution. The flow fields are categorized into short-circuiting, circulation flow, dead zones, and the corresponding contaminant transport phenomena are flow advection, shear dispersion, and eddy diffusion. The flow circulation dominates the formation of the dead zone and decreases contaminant dissipation. The flow path could have effectively meandered, and the dead zone and short-circuiting could be reduced by increasing the length of the obstacles. The improved flow field is close to the plug flow, indicating enhanced hydraulic performance and treatment efficiency. The dynamic disturbance reflects the movement of fish in wetlands and provides momentum flux to promote the dissipation of pollutants in the circulation field and dead zone, alleviating the deterioration of water quality caused by pollutant accumulation. The findings of this study may provide a critical reference for the optimal design of wetlands.

Conceptualizing a multi‐layered shingle aquifer model based on volcanic stratigraphy and water inflow to lava caves in Jeju Island, Korea

AbstractVolcanic aquifers supply a substantial portion of water resources in many parts of the world, including islands, and their productivity depends strongly on volcanic stratigraphy, which exhibits considerable heterogeneity. We investigated water inflow to lava tube caves formed from numerous basaltic lava flows in the northeastern coastal area of Jeju Island after storm events and monitored relative inflow rates monthly over 1 year to characterize groundwater flow processes in the upper parts of volcanic aquifers, and to evaluate the applicability of the previous hydrogeological models proposed for the island. Considerable water inflow arose shortly after storms from exposed palaeosol layers on the walls of the caves. The monthly monitoring results showed that wall inflow associated with these palaeosol layers is substantial. In both cases, discharge from ceiling drips was much less and more temporally variable compared to wall inflow discharge. Water flowing into the caves was rapidly drained through the floor at all monitoring sites. The lateral extent of the palaeosol layers was identified using drill core logs near the cave and outcrops in the coastal area. Based on these results, we inferred that multiple perched aquifers are formed by low‐permeability palaeosol layers between lava flows, which are connected by vertical flows at discontinuities in the palaeosol layer, eventually reaching the basal aquifer. This study revealed the water inflow processes observed in lava tube caves constrained by palaeosol layers, and established a hydrogeological conceptual model incorporating multiple perched aquifers in both coastal and mountainous areas associated with extensive palaeosol layers formed during volcanic hiatuses. This finding would help elucidate recharge, groundwater flow, and contaminant transport processes in many volcanic aquifers that are not adequately represented by the previous models, and contribute to better management of groundwater in those areas.

Contaminant Transport and Fate

This Special Issue highlights many of the predominant contaminant transport and fate processes that redistribute solutes through natural and engineered surface and subsurface environments [...]

Unsaturated flow effects on solute transport in porous media

A major contaminant transport process in soils is hydrodynamic dispersion by affecting the spreading and arrival of surface-applied pollutants at underlying groundwater reservoirs. When a soil is unsaturated, hydrodynamic dispersion is very much affected by soil water saturation. Centimeter- and decimeter-scale column experiments were carried out to explore the effects of fluid saturation and particle size on the unsaturated solute dispersivity. Measured in-situ breakthrough curves were analyzed in terms of both classical advection–dispersion and dual-porosity (mobile-immobile) type transport equations. A clear non-monotonic relationship was found between the dispersivity and soil water saturation. The extent of non-monotonicity was more pronounced for a relatively coarse-textured sand compared to a finer sand. This finding has been reported rarely before; it explains some of the inconsistencies of saturation-dispersivity relationships in the literature.

Experimental investigations on scale-dependent dispersivity in three-dimensional heterogeneous porous media.

The relationship between the scale-dependent dispersivity and heterogeneous sedimentary structures is investigated through conducting non-reactive tracer experiments in a three-dimensional heterogeneous sand tank. The heterogeneous porous media consists of three sedimentary facies of silty, fine, and medium sands collected from the west of the Songnen Plain, China. Moreover, several corresponding individual facies soil columns were constructed for comparison. A conservative tracer was continuously injected from an upstream source. The effective parameters were estimated by inverse modeling of a one-dimensional transport model. The results show that the scale dependence of the estimated dispersivities was discovered in the individual facies column (with relatively weaker effect) and the heterogeneous porous media (with more significant effect). With increasing transport distances, the dispersivities of the individual facies tend to reach an asymptotic value, while those of the heterogeneous media increase continuously. Furthermore, the results show that a power function can describe the relationship between effective dispersivities and transport distances. The exponent of the function is greater than one for the heterogeneous media, but less than one for the individual facies. The results also indicate that the dispersion plume is macroscopically dominated by the distribution of facies. The heterogeneity of hydraulic conductivity causes the variations of flow velocity, which further enhances the scale dependence of dispersivities. The tracer experiment in heterogeneous media provides the fundamental insight into the understanding of contaminant transport processes.

Geochemical and geophysical indicators of oil and gas wastewater can trace potential exposure pathways following releases to surface waters

Releases of oil and gas (OG) wastewaters can have complex effects on stream-water quality and downstream organisms, due to sediment-water interactions and groundwater/surface water exchange. Previously, elevated concentrations of sodium (Na), chloride (Cl), barium (Ba), strontium (Sr), and lithium (Li), and trace hydrocarbons were determined to be key markers of OG wastewater releases when combined with Sr and radium (Ra) isotopic compositions. Here, we assessed the persistence of an OG wastewater spill in a creek in North Dakota using a combination of geochemical measurements and modeling, hydrologic analysis, and geophysical investigations. OG wastewater comprised 0.1 to 0.3% of the stream-water compositions at downstream sites in February and June 2015 but could not be quantified in 2016 and 2017. However, OG-wastewater markers persisted in sediments and pore water for 2.5 years after the spill and up to 7.2-km downstream from the spill site. Concentrations of OG wastewater constituents were highly variable depending on the hydrologic conditions. Electromagnetic measurements indicated substantially higher electrical conductivity under the bank adjacent to a seep 7.2 km downstream from the spill site. Geomorphic investigations revealed mobilization of sediment is an important contaminant transport process. Labile Ba, Ra, Sr, and ammonium (NH4) concentrations extracted from sediments indicated sediments are a long-term reservoir of these constituents, both in the creek and on the floodplain. Using the drivers of ecological effects identified at this intensively studied site we identified 41 watersheds across the North Dakota landscape that may be subject to similar episodic inputs from OG wastewater spills. Effects of contaminants released to the environment during OG waste management activities remain poorly understood; however, analyses of Ra and Sr isotopic compositions, as well as trace inorganic and organic compound concentrations at these sites in pore-water provide insights into potentials for animal and human exposures well outside source-remediation zones.

Estimating soil water retention for wide ranges of pressure head and bulk density based on a fractional bulk density concept

Soil water retention determines plant water availability and contaminant transport processes in the subsurface environment. However, it is usually difficult to measure soil water retention characteristics. In this study, an analytical model based on a fractional bulk density (FBD) concept was presented for estimating soil water retention curves. The concept allows partitioning of soil pore space according to the relative contribution of certain size fractions of particles to the change in total pore space. The input parameters of the model are particle size distribution (PSD), bulk density, and residual water content at water pressure head of 15,000 cm. The model was tested on 30 sets of water retention data obtained from various types of soils that cover wide ranges of soil texture from clay to sand and soil bulk density from 0.33 g/cm3 to 1.65 g/cm3. Results showed that the FBD model was effective for all soil textures and bulk densities. The estimation was more sensitive to the changes in soil bulk density and residual water content than PSD parameters. The proposed model provides an easy way to evaluate the impacts of soil bulk density on water conservation in soils that are manipulated by mechanical operation.

Atmospheric trace metal deposition to remote Northwest Ontario, Canada: Anthropogenic fluxes and inventories from 1860 to 2010

National and global inventories of anthropogenic trace element emissions to air is a comparatively recent phenomenon (post-1993 in Canada) as is the monitoring of atmospheric metal deposition, the latter being also very spatially limited. Paleo-reconstructive methods offer a contiguous record of environmental contamination providing a needed framework to establish locally relevant “pre-industrial” (~natural) conditions which can be compare with relative and quantitative deviations away from reference conditions. In this study, we reconstruct the history of the long-range, anthropogenic sourced atmospheric trace element deposition to the remote region of Northwestern Ontario Canada (Experimental Lakes Area (ELA)) using dated sediment records from five lakes. Several elements are shown to be highly enriched in lake sediments relative to pre-1860 sediments (Antimony, Lead, Tellurium, Tin, Arsenic, Bismuth, Cadmium and Mercury) and moderately (Zinc, Tungsten, Thallium, Copper, Silver, Selenium, Nickel and Vanadium). Mean decadal anthropogenic atmospheric fluxes (mg m-2 yr-1) are reconstructed for 1860–2010 and compare well with available local (ELA), regional (NW Ontario Canada, N Michigan USA) monitoring data, as well as global assessments of anthropogenic contribution to atmospheric trace metal burdens. Quantitative paleo reconstructions of atmospheric contamination history using the collective signal from multiple lakes provide a rigorous methodology to assess trends, uncertainties, evaluation with monitoring data and, provide an opportunity to explore landscape processes of contaminant transport and storage. Further study of the latter is recommended to understand the latency of legacy anthropogenic contamination of the environment.

Large-strain numerical solution for coupled self-weight consolidation and contaminant transport considering nonlinear compressibility and permeability

Based on the one-dimensional (1D) consolidation equation and advection-dispersion transport equation, this paper presents a large-strain numerical solution for coupled self-weight consolidation and contaminant transport in saturated deforming porous media considering nonlinear compressibility and permeability relationships. The finite difference method is used to solve the governing equations for consolidation and transport. The proposed numerical solution for consolidation accounts for vertical strain, soil self-weight, and nonlinearly changing compressibility and hydraulic conductivity during consolidation. The solution for solute transport accounts for advection, diffusion, mechanical dispersion, linear and nonlinear equilibrium sorption, and porosity-dependent effective diffusion coefficient. The proposed numerical solution is verified against a self-weight consolidation field tank test, an analytical solution in the literature, and the CST1 numerical model. Using the verified solution, a series of parametric study is conducted to investigate the effect of several important parameters on the contaminant transport process for confined disposal of dredged contaminated sediments. The results indicate that the consolidation process and contaminant transport process induced by soil self-weight- can be very different from those induced by the more traditional external surcharge loading. Treating the self-weight loading as traditional external surcharge loading can underestimate the rate of contaminant outflow, especially in the early times. The compressibility and permeability relationships of sediment and the type of loading (i.e., self-weight loading versus external surcharge loading) can all significantly affect the contaminant transport process for confined disposal of dredged contaminated sediment.

Behaviour of contaminant transport in unconfined coastal aquifer: An experimental evaluation

Contamination of groundwater in coastal aquifers is a significant environmental concern for coastal populations across the world. As it not only leads to the depletion of available freshwater resources, but also threatens the ecology and economy of the coastal zones. A quantitative understanding of contaminant transport processes within coastal aquifer systems is, therefore, essential for efficient planning and management of coastal environments. The overarching aim of this research is to investigate the behaviour of contaminant transport patterns for various contaminant transport scenarios in a coastal unconfined aquifer. For this purpose, a series of laboratory-scale experiments have been carried out in the setup of a rectangular flow tank using dye to trace the movement of contaminant plume patterns with homogeneous soil formations. The experimental data indicate that the contaminant travels upward towards the seaward boundary when it approaches the saltwater wedge and then exits around the coastline. Upon installation of the pump, the saltwater intrusion wedge was moving rapidly towards the freshwater aquifer, and the contaminant was also moving along with the saltwater wedge towards the pump location. Experimental results also clearly show that the contaminant plume formed an elongated shape as it approached the saltwater–freshwater interface due to dispersion effects. The findings from this experimental study helped us to have a better understanding of the contaminant transport processes occurring in a coastal unconfined aquifer.

Use of Global Sensitivity and Data-Worth Analysis for an Efficient Estimation of Soil Hydraulic Properties

Accurate simulation of flow and contaminant transport processes through unsaturated soils requires adequate knowledge of the soil parameters. This study deals with the hydraulic characterization of soils using laboratory experiments. A new strategy is developed by combining global sensitivity analysis (GSA) and Bayesian data-worth analysis (DWA) to obtain efficient data that ensure a good estimation of the soil properties. The strategy is applied for the estimation of soil properties from a laboratory infiltration experiment. Results of this study show that GSA allows identification of regions and periods of high sensitivity of each parameter and thereby, the observations prone to contain information for a successful calibration. Further, the sensitivity depicts a nonlinear behavior with regions of high influence and regions of weak influence inside the parameter space. Bayesian DWA, performed a priori, allows to quantify the improvement of the posterior uncertainty of the estimated parameters when adding a type of measurement. The results reveal that an accurate estimation of the soil properties can be obtained if the target parameter values are located in the regions of high influence in the parameter space.

Fill and Spill Hillslope Runoff Representation With a Richards Equation‐Based Model

AbstractIntegrated surface‐subsurface hydrological models (ISSHMs) are well established numerical tools to investigate water flow and contaminant transport processes over a wide range of spatial and temporal scales. However, their ability to correctly reproduce the response of hydrological systems to natural and anthropogenic forcing depends largely on the accuracy of model parameterization, including the level of detail in the representation of the bedrock. This latter is typically incorporated in some way via the bottom boundary of the model domain. Issues of bedrock topography, variable soil depth, and the resulting hillslope storage distribution representation in ISSHMs are vitally important but to date have received little attention. A standard treatment of the bottom boundary, especially in large catchment and continental scale applications, is to model it as a flat or inclined (e.g., parallel to the surface) impermeable base (sometimes with some simple leakage term). This approach does not allow the model to correctly reproduce bedrock‐controlled threshold responses such as the fill and spill process, as observed across many hillslope and catchment scale field studies. It is still unclear whether Richards equation‐based numerical models are actually able to generate such responses. Here we use a Richards equation‐based model (CATHY) to simulate internal transient subsurface stormflow dynamics observed at the well‐characterized Panola experimental hillslope in Georgia (USA). Soil and bedrock properties were calibrated starting from values reported in previous studies at the site. Our simulation results show that the model was able to reproduce threshold mechanisms, which in turn affected both the integrated and distributed hydrologic responses of the Panola hillslope. We then developed a set of virtual experiments with modified boundary conditions and base topography at the soil‐bedrock interface to explore the bedrock boundary control on transient groundwater flow patterns. Our results show that accurate representation of the lower boundary is crucial for ISSHM simulations of hillslope‐scale storm runoff and for connectivity of transient groundwater. We summarize our findings with the development of a new bedrock topographic wetness index that takes into account the unsaturated infiltration dynamics. The index is able to help represent the spatial variability of water table response over the bedrock surface compared to standard surface topography‐based indices. This new index may be useful in larger‐scale ISSHM applications where an exact bedrock topography representation is not feasible or possible.

Effect of bed absorption on contaminant transport in wetland channel with rectangular cross-section

Predicting the evolution of concentration distribution for contaminant transport in wetland flows has a wide range of ecological applications. To account for the ecological effect such as substrate absorption, the influence of bed absorption on the dispersion process of contaminant transport in a wetland channel with rectangular cross-section is analytically investigated in this study by the technique of long-time asymptotic expansion. The combined effects of bed absorption, free-water-surface-effect and the bank-sidewall-effect are demonstrated, by parameter analysis in terms of the bed absorption coefficient and the aspect ratio of the channel section. The studied cases illustrate that bed absorption decreases the total mass of the contaminant cloud retained in the flow and causes the contaminant cloud to concentrate more in the upper layer. The mean advection velocity of the contaminant cloud increases as the intensity of bed absorption amplifies. Environmental dispersivity is augmented with bed absorption in a deep wetland channel, which is inverse in a shallow channel. The effect of bed absorption weakens the positive skewness of the cross-sectional mean concentration distribution when the wetland channel approaches square, while strengthens the negative skewness of the cross-sectional mean concentration distribution when the channel is relatively shallow. Moreover, the cross-sectional mean concentration decays faster under the effect of bed absorption. For applications, the critical length and duration of the influenced region are presented with bed absorption.

1,4-Dioxane cosolvency impacts on trichloroethene dissolution and sorption

Solvent stabilizer 1,4-dioxane, an emerging recalcitrant groundwater contaminant, was commonly added to chlorinated solvents such as trichloroethene (TCE), and the impact of co-disposal on contaminant transport processes remains uncertain. A series of batch equilibrium experiments was conducted with variations of 1,4-dioxane and TCE composition to evaluate aqueous dissolution of the two components and their sorption to aquifer sediments. The solubility of TCE increased with increasing amounts of 1,4-dioxane, indicating that 1,4-dioxane acts as a cosolvent causing solubility enhancement of co-contaminants. The solubilization results compared favorably with predictions using the log-linear cosolvency model. Equilibrium sorption coefficients (Kd and Kf) were also measured for different 1,4-dioxane and TCE compositions, and the findings indicate that both contaminants adsorb to aquifer sediments and TCE Kd values increased with increasing organic matter content. However, the Kd for TCE decreased with increases in 1,4-dioxane concentration, which was attributed to cosolvency impacts on TCE solubility. These findings further advance our understanding of the mass-transfer processes controlling groundwater plumes containing 1,4-dioxane, and also have implications for the remediation of 1,4-dioxane contamination.

A comparative study in aquifer parameter estimation using MFree point collocation method with evolutionary algorithms

Abstract In this study, we present a comparative assessment of simulation-optimization (S-O) models to estimate aquifer parameters such as transmissivity, longitudinal dispersivity, and transverse dispersivity. The groundwater flow and contaminant transport processes are simulated using the mesh-free radial basis point collocation method (RPCM). Four different S-O models are developed by combining the RPCM model separately with genetic algorithm (GA), differential evolution (DE), cat swarm optimization (CSO), and particle swarm optimization (PSO). The objective of the S-O model is to minimize a composite objective function with transmissivity, longitudinal dispersivity, and transverse dispersivity as decision variables. Hydraulic head and contaminant concentration at observation points are the state variables. The S-O models are used to estimate aquifer parameters of a confined aquifer with nine zones. It is found that RPCM-based DE, CSO, and PSO models are more accurate in estimating aquifer parameters than RPCM-GA. However, for noisy observed data, the RPCM-CSO model outperforms other models. The efficiency of the RPCM-CSO model over other models is further established by performing reliability analysis to the noisy observed data set. The comparative study reflects the efficacy of CSO over GA, DE, and PSO.

The Dual‐Domain Porosity Apparatus: Characterizing Dual Porosity at the Sediment/Water Interface

The characterization of pore-space connectivity in porous media at the sediment/water interface is critical in understanding contaminant transport and reactive biogeochemical processes in zones of groundwater and surface-water exchange. Previous in situ studies of dual-domain (i.e., mobile/less-mobile porosity) systems have been limited to solute tracer injections at scales of meters to hundreds of meters and subsequent numerical model parameterization using fluid concentration histories. Pairing fine-scale (e.g., sub-meter) geoelectrical measurements with fluid tracer data over time alleviates dependence on flowpath-scale experiments, enabling spatially targeted characterization of shallow sediment/water interface media where biogeochemical reactivity is often high. The Dual-Domain Porosity Apparatus is a field-tested device capable of variable rate-controlled downward flow experiments. The Dual-Domain Porosity Apparatus facilitates inference of dual-domain parameters, i.e., mobile/less-mobile exchange rate coefficient and the ratio of less mobile to mobile porosity. The Dual-Domain Porosity Apparatus experimental procedure uses water electrical conductivity as a conservative tracer of differential loading and flushing of pore spaces within the region of measurement. Variable injection rates permit the direct quantification of the flow-dependence of dual-domain parameters, which has been theorized for decades but remains challenging to assess using existing experimental methodologies.

The Human Health Risk Assessment Based on Process Simulation and Uncertainty Analysis

Water resource is an important part of human living and production. With the modernization of cities, the problem of groundwater contamination is becoming more and more serious. It is outstanding to effectively assess the risk of groundwater contamination to human health. This paper proposes a human health risk assessment method based on the simulation of contaminant transport process and parameter uncertainty analysis. The method combines health risk assessment with groundwater contaminant transport processes and applies the TOUGH2 program to simulate the temporal and spatial distribution of contaminant in groundwater. In order to improve the accuracy of the assessment results, the influence of the uncertainty of the transport model on human health risk assessment is taken into account. And the key parameter (e.g., the permeability) of the transport model is inversed by Markov chain Monte Carlo simulation method. Based on a sandbox experiment, the human health risk exposed to a typical dense non-aqueous phase liquids contaminant tetrachloroethylene (PCE) is evaluated by considering the parameter uncertainty of the PCE transport model, which confirmed that the method can provide decision-making information for the management and prevention of contaminated sites.

Indicators for contaminant transport in a three-layer wetland with wind

Abstract The effect of global climate change is increasing and it can influence agriculture in many ways, especially in that it makes great threaten on agricultural water resources. Since agricultural water supply is a key issue for agricultural production, indicators for contaminant transport in wetlands should be considered in order to solve agricultural water pollution and promote water protection. In this paper, we analyze the environmental dispersion in a typical three-layer wetland flows with the effect of wind taken into account. The analytical solution for velocity distribution is rigorously derived and the dependence of characteristic parameters on averaged dimensionless velocity is recorded. The asymptotic analysis theory of Gill is employed to measure dispersivity for natural wetland flows with a commonly high Peclet number. Both velocity and environmental dispersion are significantly influenced by wind, in terms of its direction and the magnitude of force. The effects of hydraulics and ecological degradation are considered to obtain the analytical solution for the mean concentration and maximal critical length of the region influenced by the process of contaminant transport.