Mathematical Modeling of the Neutralization Process of An Aggressive Impurity in Groundwater: An Express Model

Hydrodynamic modelling for analysis of groundwater flow through permeable reactive barriers (PRBs) is addressed in this paper. Permeable reactive barriers constitute an emerging technology for in situ remediation of groundwater contamination and have many advantages over the traditional ex situ treatment methods. The transport domains during groundwater flow through PRBs often may involve free‐flow or non‐porous sections. To model the fluid mobility efficiently in such situations, the free and porous flow zones (PRBs) must be studied in conjunction with each other. The present paper is devoted to the analysis of groundwater flow through combined free flow domains and PRBs. The free‐flow regime is modelled using the Navier–Stokes equations whereas the permeable barriers are simulated by either the Darcy or the Brinkman equation. In order to couple the governing equations of motions, well‐posed mathematical formulations of matching boundary conditions are prescribed at the interface between the free‐groundwater‐flow zones and the permeable barriers. Combination of the Navier–Stokes equations with the Brinkman equation is more straightforward owing to their analogous forms. However, the Navier–Stokes and Darcy equations are incompatible mathematically and cannot be linked directly. The problem is resolved in this paper by invoking validated hydrodynamical expressions for describing the flow behaviour at the interfaces between free‐flow and porous zones. Three schemes for the analyses of fluid flow in combined domains are applied to the case of groundwater flow through permeable reactive barriers and different model results are compared. Copyright © 2002 John Wiley & Sons, Ltd.

Purpose. Infiltration of contaminated water and accidental spills of chemically hazardous substances into groundwater lead to the formation of large zones of man-made pollution in aquifers. Therefore, it is important to develop protection systems against groundwater pollution. To analyze the effectiveness of such protection systems at the design stage, it is necessary to have scientifically based information on the dynamics of changes in groundwater contamination zones. Such information can be obtained using the method of mathematical modeling. The study aims to create a numerical model for calculating the non-stationary process of geomigration when using chemical protection of groundwater from pollution. Methodology. To describe the dynamics of groundwater flows, two filtration equations are considered, which allow mathematical modeling of the filtration process both for solving planned problems and for solving problems of specialized filtration. A two-dimensional geomigration equation was used to analyze changes in groundwater quality. This equation takes into account the convective transfer of impurities in the filtration flow, dispersion, and the intensity of impurity infiltration into the groundwater flow. This equation is also used to calculate the movement of the neutralizer in groundwater. The numerical integration of the filtration equation was performed using finite difference methods. An implicit splitting scheme was used to numerically integrate the geomigration equation. Findings. A fast-applicable numerical model for calculating groundwater dynamics has been built. The model is also a platform for solving another important task – the calculation of geomigration processes. A numerical model for calculating the unsteady-state geomigration process is proposed, which makes it possible to assess not only the process of formation of contamination zones in the groundwater flow, but also to determine the effectiveness of the method of neutralizing the impurities in the groundwater flow. Originality. Effective numerical models for rapid assessment of changes in groundwater dynamics and quality under the influence of anthropogenic sources have been developed. These models take into account a set of important physical factors that affect the process of geomigration and the process of neutralizing the impurity in the groundwater flow. Practical value. A computer program has been developed that allows determining the effectiveness of the process of neutralizing an aggressive impurity in groundwater by a computational experiment to protect it from anthropogenic pollution.

Problem statement. The task of calculating the dynamics of groundwater in the flooded area during the operation of local drainage is considered. The difficulty of solving this problem consists in the fact that in the presence of building on the flooded territory, it is impossible to use the existing regulatory methods for calculating the drainage. Therefore, there is a need to develop specialized mathematical models for evaluating the change over time in the groundwater level in the flooded area. The purpose of the work is to develop a numerical multi-parameter model and create a computer code based on it to predict changes in the level of groundwater and the level of pollution of the underground aquifer during the operation of drainage in a flooded area. Methodology. The filtration equation for headless underground flow is used to calculate the dynamics of groundwater during the operation of water-lowering wells. A two-dimensional mass transfer equation is used to calculate the impurity concentration in groundwater during the operation of the drainage system, which takes into account the convective transport of the impurity and the transport of the impurity due to dispersion. A locally one-dimensional finite-difference splitting scheme is used for the numerical integration of the filtration equation of headless groundwater. Finite-difference splitting schemes are used for numerical integration of the mass transfer equation of impurities in groundwater during drainage operation. Scientific novelty. An effective numerical model is developed, which allows predicting the change in the level of groundwater during the operation of local drainage. The model also makes it possible to predict the level of groundwater pollution during drainage operations. Practical value. Based on the developed numerical model, a computer code was developed, which is oriented towards the solution for a complex of applied problems related to the design of local drainage systems in flooded areas. Conclusions. A numerical model and computer code is developed that allow to evaluate the dynamics of changes in the groundwater level and the intensity of their pollution during the operation of local drainage. The results of the computational experiment are presented.

Problem statement. Large accumulators of liquid waste (e.g., mine water ponds, tailing ponds, etc.) are long-term sources that change the hydrological regime. A negative consequence of this process is flooding of the territory. In addition, the infiltration of contaminated water from such hazardous sources changes the quality of groundwater. Therefore, it is important to analyze the impact of such anthropogenic sources on the process of flooding and deterioration of groundwater quality. To solve this problem, it is very important to use the method of mathematical modeling as an effective mean of researching problems of this class, since the use of physical modeling is practically impossible within the scope of problems of this class. The purpose of the article. Development of numerical models for predicting changes in the hydrological regime (flooding of the territory) and groundwater quality under the influence of anthropogenic pollution sources. Methodology. To assess the dynamics of changes in the hydrological regime, a two-dimensional equation of filtration of a non-pressure groundwater flow is used. A two-dimensional geomigration equation (planned model) is used to analyze changes in groundwater quality during infiltration of contaminated water from the settling pond. This equation takes into account the convective transfer of contaminants in the filtration flow, dispersion, and the intensity of contaminant infiltration into the groundwater flow. The method of total approximation is used for numerical integration of the filtration equation. For the numerical integration of the geomigration equation, an implicit splitting scheme is used. Scientific novelty. Effective numerical models for rapid assessment of changes in groundwater dynamics and quality under the influence of anthropogenic sources that change the hydrological regime are proposed. The constructed numerical models take into account a set of important physical factors that affect the process of geomigration and flooding of the territory, namely: filtration coefficient, variable depth of free-flowing groundwater, dispersion, intensity of the source of impurity emission into the groundwater flow. This makes it possible to obtain a comprehensive assessment of the process of flooding and groundwater pollution.. Practical significance. A computer code has been created that allows practical usage of the developed numerical models. This code is an effective tool for theoretical study of non-stationary processes of territory flooding and anthropogenic groundwater pollution. Conclusions. A numerical model for calculating groundwater dynamics has been developed. The model allows to predict the level of groundwater rise under the influence of a man-made source of wastewater infiltration from a settling pond. A numerical model for calculating the process of geomigration from an anthropogenic source of emissions has been developed. The model makes it possible to predict the dynamics of contamination zone formation in a non-pressure groundwater flow. The developed numerical models take into account the most important parameters that affect the formation of flooding zones and groundwater contamination.

Generic approach for designing and implementing a passive autocatalytic recombiner PAR-system in nuclear power plant containments

Purpose. The work is aimed at developing a mathematical model that allows to quickly calculate the area of chemical air pollution during the emission of hazardous substances from solid waste landfills. The mathematical model takes into account meteorological parameters, geometric shape of the landfill, intensity of emission of hazardous substances from the landfill. Methodology. The two-dimensional equation of convective diffusion transfer of a conservative impurity from the atmosphere is used to analyze the intensity and size of chemical air pollution during the emission of hazardous substances from the landfill. A difference scheme of splitting is used to numerically solve the equation of convective-diffusive transfer of an impurity. The emission of hazardous substances from the landfill is modeled using the Dirac delta function. Findings. The developed mathematical model takes into account the main physical factors that affect the process of dispersion of hazardous substances from the landfill. On the basis of the developed numerical model, a computational experiment was conducted to assess the impact of the landfill on the environment. Originality. On the basis of the developed numerical model, a computer code was developed that allows predicting chemical pollution of the atmospheric wind and the underlying surface in the event of emission of hazardous substances from the surface of a solid waste landfill. The developed model and computer code make it possible to quickly assess the extent and intensity of environmental pollution from landfills, which is important when selecting sites for new or reconstructed landfills. Practical value. The software implementation of the developed numerical model was carried out, and a computational experiment was conducted to illustrate the effectiveness of using the model to solve applied problems related to the impact of landfills on the environment. The results of the numerical experiment are presented.

Purpose. To analyze the effectiveness of water purification in water treatment systems, an important task is the development of mathematical models that allow determining the degree of water purification at the design stage. The main purpose of the work is to construct numerical models for calculating the filtration process and mass transfer in the filter. Methodology. The calculation of the filtering process of contaminated water in the filter is carried out in two stages. At the first stage, the flow rate field in the filter is calculated. To solve this problem, the classical filtration equations are used. At the second stage of the calculation, the flow of contaminated water in the filter is simulated. To solve this problem, the mass transfer equation is used, which expresses the law of mass conservation. This equation takes into account the transfer of impurities by the filtration flow, the transfer of impurities due to dispersion and the sorption of impurities in the filter material. The solution of the filtration equation is carried out using the alternating triangular method of A. A. Samarskyi. The unknown pressure value based on this method is determined by the explicit formula of point-to-point computation. For numerical integration of the mass transfer equation in the filter, a difference splitting scheme is used. Findings. The current trend in the field of water supply and sanitation is the creation of multidimensional and multifactor mathematical models. Such models make it possible to replace a physical experiment with a computational one. The complex of water treatment facilities necessarily includes water purification filters. The filter efficiency affects the efficiency of other treatment facilities of the technological treatment scheme. A mathematical model has been developed that allows analyzing the water purification process in the filter. Based on the developed numerical model, a package of application programs has been developed for computer simulation of the filter water purification process. The results of a computational experiment on modeling the filtering process of contaminated water in a filter are presented. Originality. The paper proposes a numerical two-dimensional filter model based on the filtration equation and the mass transfer equation. A feature of the developed mathematical models is the possibility of modeling the velocity field and the process of impurity transfer taking into account the geometric shape of the filter. Practical value. The calculation time for one variant of the task based on the developed numerical model is several seconds, which is important for conducting serial calculations in practice. Models can be used as an alternative to laboratory experiments.

Permeable reactive nanofiber barrier integrated with electrokinetic geosynthetics for the remediation of copper contaminated soil under cyclic loading conditions.

Purpose. The problems of farm ventilation, prediction of CO concentration fields inside farms, prediction of artificial soil heating in greenhouses are considered. To solve a complex of such problems, it is necessary to have specialized mathematical models, oriented towards users in design organizations. Development of numerical models for solving heat and mass transfer problems for agricultural facilities (farms, greenhouses). Methodology. To solve the problem of ventilation of the working room (determination of the air flow velocity field in the room), a mathematical model of the motion of a vortex-free flow of an inviscid fluid (Laplace equation for the velocity potential) is used. Numerical integration of the modeling equation is carried out using two schemes: a locally one-dimensional scheme and a conditional approximation scheme. The G. Marchuk model is used to model the mass transfer process. Splitting schemes are used for numerical integration of the modeling equation. Two numerical models are built to analyze thermal fields in a stationary environment: a two-dimensional energy equation and a one-dimensional energy equation. Two difference schemes are used for numerical integration of the two-dimensional energy equation: a conditional approximation scheme and an explicit finite-difference scheme. An implicit splitting scheme is used to solve the one-dimensional energy equation. Findings. The software implementation of the developed numerical models has been carried out. The results of computational experiments are presented. Originality. Effective mathematical models and computer codes have been developed for solving problems of aerodynamics and mass transfer in the working space, as well as the process of heat conduction in a stationary environment. The created numerical models belong to the class of "diagnostic models", that is, computer codes that implement the developed numerical models make it possible to quickly obtain estimated data on thermal or concentration fields in the study area. Practical value. The created computer codes can be used to analyze thermal and concentration fields in agricultural premises (greenhouses, farms) to analyze the efficiency of energy systems and ensure the necessary ventilation and heating modes of the environment.

Analytical solutions for predicting thermal plumes of groundwater heat pump systems

: Permeable reactive barriers for treatment of subsurface organic and inorganic contaminants is recent technology. Little research has been done to its potential problem areas and to measure long-term performance. Observed flow reductions and performance deterioration is typically postulated as a consequence of chemical precipitation. Thus, knowledge about biofouling of these barriers is limited. This study presents a methodology to predict the biofouling potential of permeable reactive barriers through the investigation of dominant microbial groups and using their surface thermodynamic characteristics. Predominant microbial groups were enumerated from soil cores obtained from the permeable barrier at Dover National Test Site, Dover AFB, DE. Hydrophobicity of the microorganisms and their interaction energies with the zero valent iron (ZVI) at different physiological states were quantified. Sulfate reducing bacteria (SRB), anaerobic heterotrophs and aerobic heterotrophs were detected at the site, of which SRB were the dominant group of microorganisms in the ZVI. The Gibbs free energy of SRB cells interaction with ZVI showed highest potential for adhesion at logorithmic state. Predicted observations were confirmed with batch partitioning experiments.

Authors

The quality of groundwater resources globally has been under serious threat due to their exposure to a broad spectrum of anthropogenic pollutants. Permeable reactive barriers (PRBs) are an innovative technology being used for in-situ remediation of polluted groundwater for the past three decades. Metallic iron (Fe0) has been presented as the most efficient reactive medium for PRBs, and Fe0-PRBs can eliminate a large variety of both inorganic and organic compounds from aqueous solutions. Although the performance of installed Fe0-PRBs (using granular Fe0) has been generally satisfactory, there is still uncertainty on how to properly estimate their service life. The long-term porosity loss of a Fe0-PRB is a key factor to determine its service life or its long-term effectiveness. To date, efforts to characterize the long-term porosity loss of Fe0-PRBs have paid little attention to the inherent porosity loss due to the volumetric expansive nature of iron corrosion. The present work is the first attempt to root the estimation of the service life of Fe0-PRBs on the inherent characteristics of Fe0 and its corrosion products. This study presents a review of the Fe0-PRBs literature that reports the porosity loss based on field reports, laboratory column tests, and numerical model studies. Data on reported porosity loss, their estimation methods, and the corresponding geochemical conditions are summarized and analysed. A new mathematical model based on Faraday’s Law is established to describe the porosity change caused by iron corrosion products (FeCPs) in a hypothetical Fe0-based PRB through-flowed by deionized water. Moreover, a three-dimensional (3-D) numerical groundwater flow and transport model of a Fe0-PRB was developed to assess how porosity heterogeneity of the barrier medium may affect groundwater flow over time and influence the long-term effectiveness. A 3-D high resolution aquifer outcrop analogue was utilized to implement aquifer heterogeneity. Contaminant plume migration and groundwater residence time were investigated to evaluate the treatment performance of the PRB. The literature review reveals that the current estimation methods for porosity loss of Fe0-PRBs, which are based on core sample studies and stoichiometric calculations, may significantly underestimate the effect of iron corrosion products. In addition, the Darcy flux has the strongest positive correlation with the long-term porosity loss. The heterogeneity within the aquifer and the barrier should be well studied. Iron corrosion rates derived from the Faraday’s law based mathematical model are up to 7 times larger than the corrosion rate used in previous modeling studies. This suggests that the previous models have underestimated the impact of in-situ generated FeCPs on the porosity loss. The model simulations demonstrate that volume-expansion by Fe0 corrosion products alone can cause to a great extent porosity loss and emphasizes the need for a careful evaluation of the iron corrosion process in individual Fe0-based PRB. The findings of the 3-D model simulation demonstrate that the heterogeneity of porosity reduction of the barrier medium is an important factor in estimating the long-term performance of a continuous-wall Fe0-PRB. Ignoring the porosity heterogeneity of the barrier medium leads to an underestimation of the by-passing flow by 30%-41% in a ten-year simulation, and of contaminant plume spread over time. The overall results of this work provide an important contribution and give practical implications for the future design of Fe0-PRBs. This study developed a new modeling approach to describe the effect of generated iron corrosion products on long-term porosity loss of the PRB system, and a comprehensive 3-D model to simulate the groundwater flow and to assess the long-term effectiveness of the Fe0-PRB. The thesis highlights the potential impact of volume-expansion by Fe0 corrosion products, and the porosity heterogeneity of the barrier medium on the longevity estimation of Fe0-PRBs.

We used permeable reactive subsurface barriers consisting of a C source (wood particles), with very high hydraulic conductivities ( approximately 0.1-1 cm s(-1)), to provide high rates of riparian zone NO3-N removal at two field sites in an agricultural area of southwestern Ontario. At one site, a 0.73-m3 reactor containing fine wood particles was monitored for a 20-mo period and achieved a 33% reduction in mean influent NO3-N concentration of 11.5 mg L(-1) and a mean removal rate of 4.5 mg L(-1) d(-1) (0.7 g m(-2) d(-1)). At the second site, four smaller reactors (0.21 m3 each), two containing fine wood particles and two containing coarse wood particles, were monitored for a 4-mo period and were successful in attenuating mean influent NO3-N concentrations of 23.7 to 35.1 mg L(-1) by 41 to 63%. Mean reaction rates for the two coarse-particle reactors (3.2 and 7.8 mg L(-1) d(-1), or 1.5 and 3.4 g m(-2) d(-1)) were not significantly different (p > 0.2) than the rates observed in the two fine-particle reactors (5.0 and 9.9 mg L(-1) d(-1), or 1.8-3.5 g m(-2) d(-1)). A two-dimensional ground water flow model is used to illustrate how permeable reactive barriers such as these can be used to redirect ground water flow within riparian zones, potentially augmenting NO3- removal in this environment.

The integration of underground tunnels with ground heat exchangers (GHEs), also known as energy tunnels, is a promising technology that has gained attention in energy geotechnics research. This study investigates the coupled effects of groundwater and tunnel-air flows on the energy tunnel system via 3D thermo-hydraulic numerical modelling. It is found that the combination of groundwater flow parallel to the tunnel and limited airflow velocity results in reduced operational efficiency of ground source heat pump (GSHP) due to the strong thermal interference along the tunnel. The study also highlights the importance of real-scale modelling to evaluate the thermal yield of long energy tunnels, particularly when dealing with parallel groundwater flow in geothermal tunnel design.
 The use of shallow geothermal energy is a renewable solution towards net-zero carbon emissions. In recent years, a variety of conventional geotechnical structures, such as piles, retaining walls and tunnels, have been transformed into energy geostructures to also serve as GHEs to harness renewable energy for space heating and cooling purposes [7]. The thermal performance of energy tunnels is significantly affected by the presence of groundwater flow [1, 6] and the airflow in the tunnel [2, 4]. The groundwater flow and tunnel airflow can both be present in the field, however, their coupled effects on the energy tunnel system are hardly explored in the literature. This study aims to bridge this gap via real-scale numerical investigations.
 This study uses 3D thermo-hydraulic numerical modelling developed with the finite element package COMSOL Multiphysics [3]. The numerical model was successfully validated against an energy tunnel model-scale laboratory experiment [5]. Figure 1 shows the overall geometry and boundary conditions of the numerical model. A 48 m long tunnel section is thermally activated with the embedment of HDPE pipes (outer diameter of 25 mm and 2.3 mm thickness) placed in the lining segments at a spacing of 200 mm. A single tunnel ring consists of six segments with absorber pipes joined between them. Every four adjacent rings are connected in series to form a complete loop (with a single inlet and outlet), which is then connected in parallel to a flow and return header pipe(s). The entire thermally activated section comprises six loops, with identical fluid inlet temperature and flow rates, as they are fed by the same flow header pipe. The outlet fluid from each loop is mixed along the return header pipe to the GSHP. A constant 36 kW cooling thermal load is applied, and the simulation is run for ten years to allow the system to reach a steady state condition considering the minimum groundwater flow and airflow. The thermal properties of the ground are prescribed as 2 W/(m·K) and 1100 J/(kg∙K) for thermal conductivity and specific heat capacity, respectively.
 Figure 2 shows the entering water temperature (EWT, header outlet) and the coefficient of performance (COP) of the GSHP after 10 years of operation for different groundwater flow velocities and directions for tunnel air velocities = 0.05 m/s and 2 m/s.
 Results show that an increase in and leads to a decrease in EWT and an increase in COP. However, the effect of groundwater direction and velocity is more significant when airflow is limited ( = 0.05 m/s). The parallel groundwater flow leads to a higher EWT and lower COP than when the flow is inclined and perpendicular to the longitudinal tunnel axis. Consequently, the thermal performance of the system under parallel flow with a higher can be even worse than the perpendicular and inclined flow with a lower . When = 0.05 m/s, the EWT of parallel flow increases by 15% to 20% compared to the perpendicular flow, resulting in a maximum decrease of 15% in the COP. The effect of groundwater flow is much less significant when airflow is fast ( = 2 m/s): for increases from 0.05 to 2 m/d, EWT and COP change by no more than 13% and 5%, respectively, and the impact of groundwater flow direction is minor.