Migration of pollutants in groundwater. II. adsorbable pollutants and numerical dispersion reduction

We discuss here the partial differential equations governing the migration of a decomposing pollutant adsorbing according to a Langmuir isotherm and undergoing 2-dimensional flow in a saturated aquifer. The equation governing the mass transfer of the pollutant to the surfaces within the aquifer are solved in closed form, permitting the use of larger values of the time increment t in the numerical integration of the dispersion-advection equation governing the behavior of the dissolved pollutant. In this numerical integration transverse numerical dispersion is eliminated by using conformal coordinates (velocity potential and stream function), and longitudinal numerical dispersion is very substantially reduced by use of an asymmetrical 4-point formula to represent the advection term. Some representative results are given as contour maps. The mass transfer rate coefficient is estimated as the least positive eigenvalue of a diffusion problem.     

Migration of pollutants in groundwater: I. reduction of numerical dispersion by conformal mapping

The partial differential equations governing the migration of adsorbable pollutants undergoing 2-dimensional flow in saturated aquifers are presented. The analytical solution of these equations is rarely possible, and the use of mesh or grid techniques for numerical integration leads to so-called numerical dispersion, excessive dispersion which is an artifact associated with the numerical method. We discuss here the use of conformal mapping techniques to develop coordinate systems in which numerical dispersion transverse to the direction of flow is eliminated. Some simple illustrations are presented.     

A Linear-Programming-Based Strategy for Bioremediation of Oil-Polluted Marine Environments

A linear programming problem is considered with the aim to determine the optimal discharge point and the optimal discharge rate of a nutrient to be released to a marine environment polluted with oil. The objective is to minimize the total discharge of nutrient into the system provided that the concentrations of nutrient will reach critical values sufficient to eliminate oil residuals in certain affected zones through bioremediation. An initial boundary-value 3D problem for the advection–diffusion equation and its adjoint problems are considered to model, estimate, and control the dispersion of nutrient in a limited region. It is shown that the advection–diffusion problem is well posed, and its solution satisfies the mass balance equation. In each oil-polluted zone, the mean concentration of nutrient is determined by means of an integral formula in which the adjoint model solution serves as a weight function. Critical values of these mean concentrations are used as the constraints of linear programming problem. Some additional constraints are posed in order to limit not only the local discharge of the nutrient, but also the mean concentration of this substance in the whole region. Both constraints serve for environmental protection. The ability of the new method is demonstrated by numerical experiments on the remediation in oil-polluted channel using three control zones. The experiments show that the optimal discharge rate can always be got with a simple combination of step functions.     

Bioremediation With Oxygen-Releasing Solids: A Mathematical Model

The use of oxygen releasing solids in passive wells has become of considerable interest in the bioremediation of groundwater contaminated with hydrocarbons and other biodegradable contaminants. Labor, operating, and maintenance costs of this technology are quite competitive with more conventional techniques in many instances. Because of the small rates of mass transport by transverse dispersion, however, a pin-stripe pattern of alternating contaminant and oxygen distribution is expected downgradient of a line of wells which is unacceptable if it extends beyond the point of compliance downgradient. A mathematical model is presented which permits determination of the maximum well spacing in an array of wells which will yield effective remediation within a specified distance of a plume of contaminated groundwater passing through the array. Transverse dispersion of both oxygen and the contaminant is assumed, and biodegradation is modeled by means of Monod kinetics. Longitudinal numerical dispersion is minimized by the use of a asymmetrical upwind algorithm for modeling advection. Modeling results are presented showing the dependence of model behavior on input parameters.     

Modeling of Hydrodynamics and Cohesive Sediment Processes in an Estuarine System: Study Case in Danshui River

The Danshui River estuarine system is the largest estuarine system in northern Taiwan and is formed by the confluence of Tahan Stream, Hsintien Stream, and Keelung River. A comprehensive one-dimensional (1-D) model was used to model the hydrodynamics and cohesive sediment transport in this branched river estuarine system. The applied unsteady model uses advection/dispersion equation to model the cohesive sediment transport. The erosion and deposition processes are modeled as source/sink terms. The equations are solved numerically using an implicit finite difference scheme. Water surface elevation and longitudinal velocity time series were used to calibrate and verify the hydrodynamics of the system. To calibrate and verify the mixing process, the salinity time series was used and the dispersion coefficient of the advection/dispersion equation was determined. The cohesive sediment module was calibrated by comparing the simulated and field measured sediment concentration data and the erosion coefficient of the system was determined. A minimum mean absolute error of 4.22 mg/L was obtained and the snapshots of model results and field measurements showed a reasonable agreement. Our modeling showed that a 1-D model is capable of simulating the hydrodynamics and sediment processes in this estuary and the sediment concentration has a local maximum at the limit of salinity intrusion. Furthermore, it was indicated that for Q ₅₀ (the flow which is equaled or exceeded 50% times), the turbidity maximum location during neap tide is about 1 km closer to the mouth compared to that during spring tide. It was found that deposition is the dominant sediment transport process in the river during spring–neap periods. It was shown that, while sediment concentration at the upstream depends on the river discharge, the concentration in the downstream is not a function of river discharge.     

STUMOD—a Tool for Predicting Fate and Transport of Nitrogen in Soil Treatment Units

A typical onsite wastewater treatment system consists of a septic tank and a soil treatment unit to treat wastewater before it is discharged through the vadose zone to an aquifer. A tool was developed for the purpose of predicting the fate and transport of nitrogen in soil treatment units (STUMOD or Soil Treatment Unit Model). STUMOD calculates nitrogen species concentrations and the fraction of total nitrogen reaching the aquifer or a specified soil depth. Input data include parameters for hydraulics and nutrient transport and transformation. An analytical solution is used to calculate the profile of pressure based on Darcy’s equation and the relationships between suction head, unsaturated hydraulic conductivity, and soil moisture. Chemical transport is based on simplification of the advection–dispersion equation. STUMOD is relatively simple to use but accounts for important processes such as ammonium sorption, nitrification, and denitrification. STUMOD accounts for the effect of soil moisture content (a surrogate for redox conditions) on nitrification and denitrification reactions. The model has provisions to handle the influence of temperature and organic carbon content on nitrogen transformation. Model outputs, generated based on input parameters obtained from extensive literature review, were compared to a numerical model and data from laboratory tests and field sites. Both measured data and STUMOD outputs show a relatively higher removal in clayey soils compared to sandy soils. Consistent with literature data for most soils, STUMOD predicted ammonium conversion to nitrate within the first foot below the trench infiltrative surface.     

Numerical Simulations of Wind Induced Particle Contamination in Gypsum Landfill Surroundings

The contribution presents numerical simulation of gypsum particles, lifting from a gypsum landfill. First, particle characteristics are presented, resulting from different technologies of gypsum depositing. Next, a laboratory experiment parameter validation tests are described, which served as a means of determination of mass flow of particles from the landfill. The background of the numerical simulations, used in the assessment of landfill impact on the environment, is also described. Simulations consist of two parts: simulation of a long term impact of the particles on the surrounding area, performed by implementation of the Gaussian dispersion model based computer code ISC3, and second, a CFD based simulation for assessing the flow and mass concentration fields in the vicinity of the landfill for several pre-selected flow cases. The results of both computational approaches are presented and compared. In the conclusions, a relation of the simulation results with existing environmental pollution levels is made, and recommendations for landfill management are drawn.     

OSPM - A Parameterised Street Pollution Model

For many practical applications, as e.g. in support of air pollution management, numerical models based on solution of the basic flow and dispersion equations are still too complex. Alternative are models that are basically parameterised semi-empirical models making use of a priori assumptions about the flow and dispersion conditions. However, these models must, be thoroughly tested and their performance and limitations carefully documented. The Danish Operational Street Pollution Model (OSPM) belongs to this category of parameterised models. In the OSPM, concentrations of exhaust gases are calculated using a combination of a plume model for the direct contribution and a box model for the recirculating part of the pollutants in the street. Parameterisation of flow and dispersion conditions in street canyons was deduced from extensive analysis of experimental data and model tests. Results of these tests were used to further improve the model performance, especially with regard to different street configurations and a variety of meteorological conditions.     

A Numerical Study of Airflow and Pollutant Dispersion Inside an Urban Street Canyon Containing an Elevated Expressway

The goal of this study is to investigate numerically the wind flow and pollutant dispersion within an urban street canyon containing an elevated expressway and reveal the impacts of elevated expressway on the atmospheric environment in the canyon. A two-dimensional numerical model for simulating airflow and pollutant dispersion inside urban street canyons is first developed based on the Reynolds-averaged Navier–Stokes equations coupled with the standard k???ε turbulence model and the convection–diffusion equation for passive species transport, and then it is validated against a wind tunnel experiment. It was found that the model-predicted results agree well with the experimental data. Having established this, the wind fields and pollutant distributions in the canyon containing an elevated expressway are evaluated. The numerical results show that the expressway height above the street floor and the gap distance between the expressway and the building wall have considerable influence on airflow and pollutant level inside a canyon: (1) the vortical flow structure in the canyon varies with the expressway height for a constant gap distance, under certain expressway heights, only one main clockwise vortex is formed, while under others one main vortex as well as one or two secondary vortices above and below the expressway are created; (2) the pollutant level within the canyon increases when an expressway is placed in the canyon, especially when the expressway height equals the building height the flow velocities in the canyon are drastically reduced and air exchange in and above the canyon is seriously impeded by the expressway, which leads to a much higher pollution level in the canyon; and (3) the wider gap distance is favorable to pollutant removal from the canyon.     

Experimental and Numerical Analysis of CO Concentration Dispersion of Vehicular Exhaust Emissions in Isolated Environment

Numerical and experimental analyses were applied to carbon monoxide (CO) concentration dispersion to monitor air quality in an enclosed residential complex parking area in Tehran. Firstly, the parking area was preliminary assessed through verifying the characteristics of the problem including the geometry and boundary conditions. Then, proportion of vehicular exhaust emissions was estimated and eventually experimental and numerical analyses were performed. In order to perform numerical calculation, a three-dimensional model was created to numerically simulate the enclosed residential complex parking area by FLUENT software that solves flow governing equations with finite volume method. In FLUENT, species model was selected to assess the dispersion of CO in flow domain. In experimental analysis, CO concentration was measured using sampling bags with a volume of 10 l in 4 min at 6 different points. The sample air was drawn into sampling bags by electric pumps. The findings show that the maximum amount of CO concentration is above the permissible standard recommended by the World Health Organization. Pollutant accumulation was significant in confined areas. In the place where openings exist, the level of accumulation was lower than other areas. The findings obtained from numerical simulation are in complete accord with experimental results.     

Numerical Model Inter-comparison for Wind Flow and Turbulence Around Single-Block Buildings

Wind flow and turbulence within the urban canopy layer can influence the heating and ventilation of buildings, affecting the health and comfort of pedestrians, commuters and building occupants. In addition, the predictive capability of pollutant dispersion models is heavily dependent on wind flow models. For that reason, well-validated microscale models are needed for the simulation of wind fields within built-up urban microenvironments. To address this need, an inter-comparison study of several such models was carried out within the European research network ATREUS. This work was conducted as part of an evaluation study for microscale numerical models, so they could be further implemented to provide reliable wind fields for building energy simulation and pollutant dispersion codes. Four computational fluid dynamics (CFD) models (CHENSI, MIMO, VADIS and FLUENT) were applied to reduced-scale single-block buildings, for which quality-assured and fully documented experimental data were obtained. Simulated wind and turbulence fields around two surface-mounted cubes of different dimensions and wall roughness were compared against experimental data produced in the wind tunnels of the Meteorological Institute of Hamburg University under different inflow and boundary conditions. The models reproduced reasonably well the general flow patterns around the single-block buildings, although over-predictions of the turbulent kinetic energy were observed near stagnation points in the upwind impingement region. Certain discrepancies between the CFD models were also identified and interpreted. Finally, some general recommendations for CFD model evaluation and use in environmental applications are presented.     

Modelling the Competitive Sorption Process of Multiple Solutes During their Transport in Porous Media

A general mathematical model to solve the advection–dispersion transport equation for multiple solutes was developed, where the dual porosity mobile–immobile mass transfer, the two-site non-equilibrium model and first-order transformation reactions were included. The two-site model was expressed with an equilibrium sorption term and a kinetic term. One of three kinetic models could be used: the non-linear, the bilinear and the pore diffusion model. The traditional Freundlich or Langmuir isotherms were employed to simulate no-interaction between the solutes, but with the extended Freundlich or extended Langmuir isotherms, a competitive sorption could be simulated. The transport equation was solved with the Moving Concentration Slope method. The mathematical model was tested and further simplified by using real data from soil column experiments, with 1,2-cis-dichloroethene and trichloroethene as model contaminants and silica gel and real soil samples as porous medium.     

Evaluation of Numerical Modeling Methods for the Management of Produced Water Discharges in the Coastal Region with a Canadian Case Study

This study aims at evaluating two numerical methods for 3D simulation of marine pollutant dispersion problems: the random walk particle tracking (RWPT) method and an explicit second-order finite difference method (FDM) for assessing produced water discharges from offshore oil platform. Test cases in a steady flow field were used to evaluate the efficiency and accuracy of simulating pollutant concentration profiles obtained using both the FDM and RWPT method in comparison with an analytical solution. Additionally, a field study was conducted to simulate the lead concentration distribution of produced water discharged from an oil platform off Canada’s east coast, based on the Princeton Ocean Model modeling the ocean flow in the study area with field verifications. Results indicate that, with proper configuration of grid resolution and particle resolution, both FDM and RWPT method can provide accurate results with reasonable computational costs for complex field cases. Particularly, the satisfactory 3D simulations of marine pollutant dispersion in the far field by both FDM and RWPT numerical methods enable effective assessment and management of offshore waste discharges.     

Numerical simulation on pollutant dispersion from vehicle exhaust in street configurations

The impact of the street configurations on pollutants dispersion from vehicles exhausts within urban canyons was numerically investigated using a computational fluid dynamics (CFD) model. Three-dimensional flow and dispersion of gaseous pollutants were modeled using standard kappa - epsilon turbulence model, which was numerically solved based on Reynolds-averaged Navier-Stokes equations by the commercial CFD code FLUENT. The concentration fields in the urban canyons were examined in three cases of street configurations: (1) a regular-shaped intersection, (2) a T-shaped intersection and (3) a Skew-shaped crossing intersection. Vehicle emissions were simulated as double line sources along the street. The numerical model was validated against wind tunnel results in order to optimize the turbulence model. Numerical predictions agreed reasonably well with wind tunnel results. The results obtained indicate that the mean horizontal velocity was very small in the center near the lower region of street canyon. The lowest turbulent kinetic energy was found at the separation and reattachment points associated with the corner of the down part of the upwind and downwind buildings in the street canyon. The pollutant concentration at the upwind side in the regular-shaped street intersection was higher than that in the T-shaped and Skew-shaped street intersections. Moreover, the results reveal that the street intersections are important factors to predict the flow patterns and pollutant dispersion in street canyon.     

Multipoint source method in air pollution modelling of cold start emission

The paper presents a new method of air pollution modelling on a micro scale. For estimation of concentration of car exhaust pollutants, each car is treated as an instantaneous moving emission source. This approach enables us to model time and spatial changes of emission, especially during cold and cool start of an engine. These stages of engine work are a source of significant pollution concentration in urban areas. In this work, two models are proposed: one for the estimation of emission after cold start of the engine and another for the prediction of pollutant concentration. The first model (defined for individual exhaust gas pollutants) enables us to calculate the emission as a function of time after the cold or cool start, ambient temperature and average speed of motion. This model uses the HBEFA database. The second mathematical model is developed in order to calculate the pollutant dispersion and concentrations. The finite volume method is applied to discretise the set of partial differential equations describing wind flow and pollutant dispersion in the domain considered. Models presented in this paper can be called short-term models on a small spatial scale. The results of numerical simulation of pollutant emission and dispersion are also presented.     

Integral transform solutions for atmospheric pollutant dispersion

A transient two-dimensional advection–diffusion model describing the turbulent dispersion of pollutants in the atmosphere has been solved via the Generalized Integral Transform Technique (GITT), by two different schemes. The first approach performs numerical integration of the transformed system using available routines for initial value problems with automatic error control. In spite of the time-consuming character of such a scheme, its flexibility allows the handling of problems involving time-dependent meteorological parameters such as wind speed and eddy diffusivities. The second approach works fully analytically being thus intrinsically more robust and economic, although not directly applicable in dealing with time-dependent parameters. For the test problem used in this work, both methods agree very well with each other, as well as with a known analytical solution for a simpler formulation used as benchmark. The impact of the longitudinal diffusivity on the stiffness of the ordinary differential equation (ODE) system arising from the integral transformation has been assessed through the processing time demanded to solve it when the numerical approach is used. The observed CPU times show that the analytical approach is clearly preferable unless the problem involves time-dependent parameters.     

Chloride migration in groundwater for a tannery belt in Southern India

Groundwater in a tannery belt in Southern India is being polluted by the discharge of untreated effluents from 80 operating tanneries. Total dissolved solids and chloride (Cl⁻) measurements in open wells in the tannery cluster vary from 27,686 to 39,100 and 12,000 to 13,652 mg/l, respectively. A mass transport model was constructed using Visual MODFLOW Premium 4.4 software to investigate the chloride migration in an area of 75.56 km². Input to the chloride migration model was a groundwater flow model that considered steady and transient conditions. This model was calibrated with field observations; and sensitivity analysis was carried out whereby model parameters, viz., conductivity, dispersivity, and source concentration were altered slightly, and the effect on calibration statistics was evaluated. Results indicated that hydraulic conductivity played a more sensitive role than did dispersivity. The Cl⁻ migration was mainly through advection rather than dispersion. It was found that even if the pollutant load reduced to 50% of the present level, the Cl⁻ concentration in groundwater, even after 6 years, would not be reduced to the permissible limit of drinking water in the tannery belt.     

Study on gas diffusion emitted from different height of point source

The flow and dispersion of stack-gas emitted from different elevated point source around flow obstacles in an urban environment have been investigated, using computational fluid dynamics models (CFD). The results were compared with the experimental results obtained from the diffusion wind tunnel under different conditions of thermal stability (stable, neutral or unstable). The flow and dispersion fields in the boundary layer in an urban environment were examined with different flow obstacles. Gaseous pollutant was discharged in the simulated boundary layer over the flat area. The CFD models used for the simulation were based on the steady-state Reynolds-Average Navier-Stoke equations (RANS) with kappa-epsilon turbulence models; standard kappa-epsilon and RNG kappa-epsilon models. The flow and dispersion data measured in the wind tunnel experiments were compared with the results of the CFD models in order to evaluate the prediction accuracy of the pollutant dispersion. The results of the CFD models showed good agreement with the results of the wind tunnel experiments. The results indicate that the turbulent velocity is reduced by the obstacles models. The maximum dispersion appears around the wake region of the obstacles.