Stepwise superposition approximation approach for analytical solutions with non-zero initial concentration using existing solutions of zero initial concentration in contaminate transport

Analytical solutions for contaminant transport are widely used for both theoretical and practical purposes.However,many existing solutions are obtained subject to an initial condition of zero concentration,which is often unrealistic in many practical cases.This article proposed a stepwise superposition approximation approach to solve the non-zero initial concentration problem for first-type and third-type boundary conditions by using the existing zero initial concentration solution.Theoretical examples showed that the approach was highly efficient if a proper superposition scheme with relative concentration increments was constructed.The key parameter that controlled the convergence speed was the time increment（△t） multiplied by the rate constant（λ）.The approach served also as an alternative way to make a convenient concentration calculation even if the non-zero initial concentration solution of a problem was known.

FLUID-SOLID COUPLING MATHEMATICAL MODEL OF CONTAMINANT TRANSPORT IN UNSATURATED ZONE AND ITS ASYMPTOTICAL SOLUTION

The process of contaminant transport is a problem of multicomponent and multiphase flow in unsaturated zone. Under the presupposition that gas existence affects water transport, a coupled mathematical model of contaminant transport in unsaturated zone has been established based on fluid_solid interaction mechanics theory. The asymptotical solutions to the nonlinear coupling mathematical model were accomplished by the perturbation and integral transformation method. The distribution law of pore pressure, pore water velocity and contaminant concentration in unsaturated zone has been presented under the conditions of with coupling and without coupling gas phase. An example problem was used to provide a quantitative verification and validation of the model. The asymptotical solution was compared with Faust model solution. The comparison results show reasonable agreement between asymptotical solution and Faust solution, and the gas effect and media deformation has a large impact on the contaminant transport. The theoretical basis is provided for forecasting contaminant transport and the determination of the relationship among pressure_saturation_permeability in laboratory.

3D contaminant migration model with consolidation dependent transport coefficients

Soil consolidation would induce variations of its transport coefficients such as hydraulic conductivity and diffusion coefficient. This paper presents a study of the influence of barrier consolidation on transport coefficients, and a 3D transport model based on mixture theory is proposed for describing the liners that involve circular defects in the geomembrane. The elastoplastic ALPHA model is revised by using the spatially mobilized plane （SMP） criterion for simulating the deformation of the soils. Then, the 3D model coupling the nonlinear consolidation and contaminant advection-diffusion is solved using the finite element software ABAQUS. The results show that the importance of reducing the defect size in the geomembrane and the liner porosity to control the contaminant concentration increase

Flow and transport simulation of Madeira River using three depth-averaged two-equation turbulence closure models

This paper describes a numerical simulation in the Amazon water system, aiming to develop a quasi-three-dimensional numerical tool for refined modeling of turbulent flow and passive transport of mass in natural waters. Three depth-averaged two-equation turbulence closure models, k-ε,k-w, and k-w, were used to close the non-simplified quasi-three-dimensional hydrodynamic fundamental governing equations. The discretized equations were solved with the advanced multi-grid iterative method using non-orthogonal body-fitted coarse and fine grids with collocated variable arrangement. Except for steady flow computation, the processes of contaminant inpouring and plume development at the beginning of discharge, caused by a side-discharge of a tributary, have also been numerically investigated. The three depth-averaged two-equation closure models are all suitable for modeling strong mixing turbulence. The newly established turbulence models such as the k-w model, with a higher order of magnitude of the turbulence parameter, provide a possibility for improving computational precision.

Groundwater fluoride contamination:A reappraisal

Dissolution of fluorite （CaF2） and/or fluorapatite （FAP） [Cas（PO4）3F], pulled by calcite precipitation, is thought to be the dominant mechanism responsible for groundwater fluoride （F） contamination. Here, one dimensional reactive-transport models are developed to test this mechanism using the published dissolution and precipitation rate kinetics for the mineral pair FAP and calcite. Simulation results correctly show positive correlation between the aqueous concentrations of F and CO2 and negative correlation between F- and Ca^2＋. Results also show that precipitation of calcite, contrary to the present understanding, slows down the FAP dissolution by 10G orders of magnitude compared to the FAP dissolution by hydrolysis. For appreciable amount of fluoride contamination rock-water interaction time must be long and of order 106 years.

Numerical investigation of the effect of geosynthetic clay liner chemical incompatibility on flow and contaminant transport through a defective composite liner

A composite liner consisting of a geomembrane(GMB)and a geosynthetic clay liner(GCL)can be compromised by inorganic contaminants because of a defective GMB.When the composite liner with defective GMB is exposed to aggressive leachate conditions,the neglect of the chemical incompatibility of the GCL can potentially result in an underestimation of the leakage rate and flux through the composite liner.This paper proposed a numerical investigation on the effect of chemical incompatibility of GCL on the barrier performance of the composite liner with hole defect.Four cases with leachate solutions having varied cation valencies and ionic strengths were analyzed,in which the hydraulic conductivity of GCL was concentrationdependent.Both the effect of the chemical incompatibility of GCL and the mechanisms were analyzed.The incompatibility of GCL resulted in significant increases in leakage rate and flux through the composite liner by factors of up to 4.9 and 5.0,respectively.The incompatibility-affected area in GCL is located within 0.1 m from the center of the hole in the GMB.The coupled increase in the hydraulic conductivity of GCL and pore water concentration impacts the flux and leakage in a short period of time.With GCL chemical incompatibility considered,advection may dominate the contaminant transport through GCL.

Analysis for remedial alternatives of unregulated municipal solid waste landfills leachate-contaminated groundwater

A groundwater flow and solute transport model was developed using Visual Modflow for forecasting contaminant transport and assessing effects of remedial alternatives based on a case study of an unregulated landfill leachate-contaminated groundwater in eastern China. The results showed that arsenic plume was to reach the pumping well in the downstream farmland after eight years, and the longest lateral and longitudinal distance of arsenic plume was to reach 200 m and 260 m, respectively. But the area of high concentration region of arsenic plume was not to obviously increase from eight years to ten years and the plume was to spread to the downstream river and the farmland region after 20 years; while the landfill＇s ground was hardened, the plume was not to reach the downstream farmland region after eight years; when the pumping well was installed in the plume downstream and discharge rate was 200m3/d, the plume was to be effectively restrained; for leakage-proof barriers, it might effectively protect the groundwater of sensitive objects within an extent time range. But for the continuous point source, the plume was still to circle the leakage-proof barrier; when discharge rate of drainage ditches was 170.26 m3/d, the plume was effectively controlled; the comprehensive method combining ground-harden with drainage ditches could get the best effect in controlling contaminant diffusion, and the discharge rate was to be reduced to 111.43 m3/d. Therefore, the comprehensive remedial alternative combining ground-harden with drainage ditch will be recommended for preventing ground-water contamination when leachate leakage has happened in unregulated landfills.

Source emissions and climate change impacts on the multimedia transport and fate of persistent organic pollutants,Chaohu watershed,eastern China

Emission intensity and climate change control the transport flux and fate of persistent organic pollutants(POPs)inmultiple environmental compartments.This study applied amultimedia model(BETR model)to explore alternations in the spatio-temporal trends of concentrations and transport flux of benzopyrene(BaP),phenanthrene(Phe),perfluorooctane sulfonates(PFOS)and polychlorinated biphenyls(PCBs)in the Chaohu watershed,located in the lower reaches of the Yangtze River,China in response to changes in source emissions and climate.The potential historic and future risks of these pollutants also were assessed.The results suggest that current trends in concentrations and transport were similar to that of their emissions between 2005 and 2018.During the next 100 years,temporal trends and spatial patterns were not predicted to change significantly,which is consistent with climate change.Based on sensitivity and correlation analyses,climate change had significant effects on multi-media concentrations and transport fluxes of BaP,Phe,PFOS and PCBs,and rainfall intensity was the predominant controlling factor.Risk quotients(RQs)of BaP and Phe-in soil increased from 0.42 to 0.95 and 0.06 to 0.35,respectively,from 2005 to 2090,indicating potential risks.The RQs of the other examined contaminants exhibited little potential risk in soil,water,or sediment.Based on spatial patterns,it was inferred that the ecosystem around Lake Chaohu is the most at risk.The study provides insights needed for local pollution control of POPs in the Chaohu watershed.In addition,the developed approach can be applied to other watersheds world-wide.

Contaminant transport in heterogeneous aquifers: A critical review of mechanisms and numerical methods of non-Fickian dispersion

Natural aquifers usually exhibit complex physical and chemical heterogeneities,which are key factors complicating kinetic processes,such as contaminant transport and transformation,posing a great challenge in the remediation of contaminated groundwater.Aquifer heterogeneity usually leads to a distinct feature,the so-called“anomalous transport”in groundwater,which deviates from the phenomenon described by the classical advection-dispersion equation(ADE)based on Fick’s Law.Anomalous transport,also known as non-Fickian dispersion or“anomalous dispersion”in a broad sense,can explain the hydrogeological mechanism that leads to the temporally continuous deterioration of water quality and rapid spatial expansion of pollutant plumes.Contaminants enter and then are retained in the low-permeability matrix from the high-permeability zone via molecular diffusion,chemical adsorption,and other mass exchange effects.This process can be reversed when the concentration of pollutants in high-permeability zones is relatively low.The contaminants slowly return to the high-permeability zones through reverse molecular diffusion,resulting in sub-dispersive anomalous transport leading to the chronic gradual deterioration of water quality.Meanwhile,some contaminants are rapidly transported along the interconnected preferential flow paths,resulting in super-dispersive anomalous transport,which leads to the rapid spread of contaminants.Aquifer heterogeneity is also an important factor that constrains the efficacy of groundwater remediation,while the development,application,and evaluation of groundwater remediation technologies are usually based on the Fickian dispersion process predicted by the ADE equation.Comprehensive studies of the impacts of non-Fickian dispersion on contaminant transport and remediation are still needed.This article reviews the non-Fickian dispersion phenomenon caused by the heterogeneity of geological media,summarizes the processes and current understanding of contaminant migration and transformation in highly heterogeneous aquifers,and evaluates mathematical methods describing the main non-Fickian dispersion features.This critical review also discusses the limitations of existing research and outlines potential future research areas to advance the understanding of mechanisms and modeling of non-Fickian dispersion in heterogeneous media.

Analytical solutions of three-dimensional contaminant transport in uniform flow field in porous media:A library

The purpose of this study is to present a library of analytical solutions for the three-dimensional contaminant transport in uniform flow field in porous media with the first-order decay,linear sorption,and zero-order production.The library is constructed using Green's function method(GFM)in combination with available solutions.The library covers a wide range of solutions for various conditions.The aquifer can be vertically finite,semi-infinitive or infinitive,and laterally semi-infinitive or infinitive.The geometry of the sources can be of point,line,plane or volumetric body;and the source release can be continuous,instantaneous,or by following a given function over time.Dimensionless forms of the solutions are also proposed.A computer code FlowCAS is developed to calculate the solutions.Calculated results demonstrate the correctness of the presented solutions.The library is widely applicable to solve contaminant transport problems of one-or multiple-dimensions in uniform flow fields.

Transport of a volatile contaminant in a free-surface wetland flow

Presented in this paper is an analytical study of a pulsed volatile contaminant emission into a free-surface wetland flow. A simplified model is given for contaminant transport under the combined action of advection, mass dispersion, apparent reaction, and volatilization at the free water surface. The effect of periodic apparent reaction on contaminant transport is separated from the hydraulic effect via an extended transformation, with a limiting case covering the known transformation for constant apparent reaction rate. The analytical solutions of zeroth and first order concentration moments are rigorously derived and illustrated. It was found that the amount of contaminant decreases from the bottom bed to the free-surface under volatilization, and the total amount of contaminant decays with time. It was also found that the moving speed of the mass center of the whole contaminant cloud increases, as the ratio of volatilization coefficient to vertical effective mass dispersivity increases.