Experiments on vertical transverse mixing in a large-scale heterogeneous model aquifer

Vertical transverse mixing is known to be a controlling factor in natural attenuation of extended biodegradable plumes originating from continuously emitting sources. We perform conservative and reactive tracer tests in a quasi two-dimensional 14 m long sand box in order to quantify vertical mixing in heterogeneous media. The filling mimics natural sediments including a distribution of different hydro-facies, made of different sand mixtures, and micro-structures within the sand lenses. We quantify the concentration distribution of the conservative tracer by the analysis of digital images taken at steady state during the tracer-dye experiment. Heterogeneity causes plume meandering, leading to distorted concentration profiles. Without knowledge about the velocity distribution, it is not possible to determine meaningful vertical dispersion coefficients from the concentration profiles. Using the stream-line pattern resulting from an inverse model of previous experiments in the sand box, we can correct for the plume meandering. The resulting vertical dispersion coefficient is approximately approximately 4 x 10(-)(9) m(2)/s. We observe no distinct increase in the vertical dispersion coefficient with increasing travel distance, indicating that heterogeneity has hardly any impact on vertical transverse mixing. In the reactive tracer test, we continuously inject an alkaline solution over a certain height into the domain that is occupied otherwise by an acidic solution. The outline of the alkaline plume is visualized by adding a pH indicator into both solutions. From the height and length of the reactive plume, we estimate a transverse dispersion coefficient of approximately 3 x 10(-)(9) m(2)/s. Overall, the vertical transverse dispersion coefficients are less than an order of magnitude larger than pore diffusion coefficients and hardly increase due to heterogeneity. Thus, we conclude for the assessment of natural attenuation that reactive plumes might become very large if they are controlled by vertical dispersive mixing.     

Transverse vertical dispersion in groundwater and the capillary fringe

Transverse dispersion is the most relevant process in mass transfer of contaminants across the capillary fringe (both directions), dilution of contaminants, and mixing of electron acceptors and electron donors in biodegrading groundwater plumes. This paper gives an overview on literature values of transverse vertical dispersivities alpha(tv) measured at different flow velocities and compares them to results from well-controlled laboratory-tank experiments on mass transfer of trichloroethene (TCE) across the capillary fringe. The measured values of transverse vertical dispersion in the capillary fringe region were larger than in fully saturated media, which is credited to enhanced tortuosity of the flow paths due to entrapped air within the capillary fringe. In all cases, the values observed for alpha(tv) were < 1 mm. The new measurements and the literature values indicate that alpha(tv) apparently declines with increasing flow velocity. The latter is attributed to incomplete diffusive mixing at the pore scale (pore throats). A simple conceptual model, based on the mean square displacement and the pore size accounting for only partial diffusive mixing at increasing flow velocities, shows very good agreement with measured and published data.     

Wind tunnel study of air entrainment into two-dimensional dense gas plumes at the Chemical Hazards Research Center

Experiments in a neutrally stable wind tunnel boundary layer were made for two-dimensional (quasi-line) sources of carbon dioxide dispersing over two types of uniformly spaced (billboard) surface roughness elements. Velocity and concentration measurements were made with each surface roughness over a wide range of source Richardson number by varying carbon dioxide release rate and wind speed. Concentration measurements were made with a FID gas analyzer using an ethane tracer in the source gas, and velocity measurements were made with independent LDV and HWA systems. For each surface roughness, this paper describes the wind tunnel boundary layer and presents alongwind and vertical concentration profiles in the gas plume. Vertical velocity and concentration profiles were measured at selected downwind distances, and the profiles were integrated to confirm the consistency of the measurements with the mass of carbon dioxide released. The data are intended for development of improved vertical turbulent entrainment correlations for use in dense gas dispersion models applied to hazardous chemical consequence analyses.     

Validation of the lagrangian particle dispersion model FLEXPART against large-scale tracer experiment data

A comprehensive validation of FLEXPART, a recently developed Lagrangian particle dispersion model based on meteorological data from the European Centre for Medium-Range Weather Forecasts, is described in this paper. Measurement data from three large-scale tracer experiments, the Cross-Appalachian Tracer Experiment (CAPTEX), the Across North America Tracer Experiment (ANATEX) and the European Tracer Experiment (ETEX) are used for this purpose. The evaluation is based entirely on comparisons of model results and measurements paired in space and time. It is found that some of the statistical parameters often used for model validation are extremely sensitive to small measurement errors and should not be used in future studies. 40 cases of tracer dispersion are studied, allowing a validation of the model performance under a variety of different meteorological conditions. The model usually performs very well under undisturbed meteorological conditions, but it is less skilful in the presence of fronts. The two ETEX cases reveal the full range of the model’s skill, with the first one being among the best cases studied, and the second one being, by far, the worst. The model performance in terms of the statistical parameters used stays rather constant with time over the periods (up to 117 h) studied here. It is shown that the method used to estimate the concentrations at the receptor locations has a significant effect on the evaluation results. The vertical wind component sometimes has a large influence on the model results, but on the average only a slight improvement over simulations which neglect the vertical wind can be demonstrated. Subgrid variability of mixing heights is important and must be accounted for.     

Choice of dispersion coefficients in reactive transport calculations on smoothed fields

Local dispersion dominates the mixing of compounds that are introduced separately into the subsurface and do not partition into any other than the aqueous phase. Thus, reactions between these compounds are controlled by dispersive mixing if they are not limited by kinetics. I quantify longitudinal dispersive mixing by the longitudinal effective dispersion coefficient of a conservative tracer introduced by a point-like injection [Water Resour. Res. 36 (12) (2000) 3591-3604]. In the upscaling of mixing-controlled reactive transport, I apply the mean velocity and the effective dispersion coefficient to the macroscopic transport calculations, whereas the reactive parameters on the macro-scale are identical to those on the local scale. The applicability of the approach is demonstrated for the transport of compounds undergoing a second-order irreversible bimolecular reaction. Ten realizations of a two-dimensional heterogeneous log-conductivity field are considered. Using the effective dispersion parameters, the overall mass balance is met in the ensemble average, whereas solute spreading is underestimated. I assess the lack of spreading by the difference between the expected macrodispersion and effective dispersion coefficients. I extend the approach to simulations on log-conductivity fields obtained by kriging of regularly spaced conductivity measurements. These fields contain the large-scale features of the true fields but do not resolve the small-scale variability. For the calculations on the kriged fields, the corresponding conditional covariance is substituted into the analytical expressions of effective dispersion, yielding a correction effective dispersion coefficient. The comparison between simulations on the fully resolved fields and on the kriged fields indicates that the approach is valid for wide plumes meeting the ergodicity condition. The high variability of mixing on small scales unresolved by kriging, however, leads to severe uncertainty when mixing-controlled reactions are predicted for narrow plumes.     

Influence of wall roughness on the dispersion of a passive scalar in a turbulent boundary layer

Many towns and cities consist of similarly sized buildings in relatively regular arrangements with smaller scale roughness elements such as roofs, chimneys and balconies. The objective of this study is to investigate how small scale roughness elements modify the influence of the large scale organized roughness on the dispersion of a passive scalar in a turbulent boundary layer. Wind tunnel experiments were performed using a passive tracer released from a line source and concentration profiles were measured with a Flame Ionisation Detector. The measurements are compared with numerical solutions of the advection–diffusion equation.The results show that decreasing the cavity aspect ratio increases the turbulent vertical mass fluxes, and that the small scale roughness enhances these fluxes, but only in the skimming flow regime. Numerical simulations showed that outside the roughness sub-layer (RSL) the changes in surface roughness could be accounted for by a simple variation of the friction velocity, but inside the RSL the spatial variability of the flow imposed by the roughness elements has much more influence. A simple model for a spatially averaged dispersion coefficient in the RSL has been developed and is shown to agree satisfactorily with the concentrations measured in these experiments.     

Concentration field and turbulent fluxes during the mixing of two buoyant plumes

In this work an experimental study of mixing of two identical plumes, carried out in a turbulent neutral boundary layer generated in a wind tunnel, is presented. Measurements have been performed with fast flame ionisation detectors (FFIDs) and a two-component Laser-Doppler Anemometer system. Results allow the study of both the average and the fluctuating concentration field, including the turbulent vertical and longitudinal mass fluxes, in single plumes and during the interaction of two identical plumes. This information gives insight into the details of the mixing phase of the two plumes. Results of trajectories and additional rise (due to plume interactions) have been compared with previous measurements carried out in laminar cross-flows, showing similar behaviour. Concentration distributions in plume cross-sections in turbulent cross-flows differ from those measured in laminar cross-flows. Average vertical and longitudinal velocity measurements into the plume core show the strength of the shielding effect of the upwind plume and some details of interaction between the counter-rotating vortex pairs (CVPs). For large values of the alignment angle φ, between the line joining the stacks and the cross-flow, an average negative vertical velocity is measured in the middle of the plume even if its centre of mass is rising. This downward velocity is induced by the slow interaction of the CVPs and generates a vertical stretching of the plume and negative rise enhancement. Vertical turbulent fluxes change sign on the plume centreline and are of opposite sign with respect to the longitudinal turbulent fluxes. Results indicate a good linearity between vertical turbulent fluxes and concentration gradients, with different proportionality for the top and bottom parts of the plume (especially in the near field) indicating that dispersion could be described by a gradient-transfer model.     

Transverse dispersion of non-reactive tracers in porous media: a new nonlinear relationship to predict dispersion coefficients

Assessing the potential of natural attenuation in groundwater relies on the ability to predict and quantify the processes that occur in contaminant plumes. Transverse dispersion is a significant mass transfer mechanism for mixing of electron acceptors and donors and thus may control the lengths of steady state plumes. Laboratory experiments were carried out using a 2-dimensional acrylic glass tank filled with glass beads, quartz sand and field site material as porous media. Flow velocities and grain sizes were varied in order to cover a large range of Peclet numbers including typical field scenarios. The laboratory study was extended by a comprehensive literature search to compare the new results with earlier work. As a result we propose a new empirical relationship for prediction of transverse dispersion coefficients (Dt) which is based on the Peclet number (Pe). This new relationship indicates a nonlinear dependency on the flow velocity (nu a) and grain size (d), namely a relative decrease of the dispersion coefficient with increasing flow velocity in relatively fast flowing water: Dt/Daq=Dp/Daq+0.28(Pe)0.72 (with Pe=nu a d/Daq; Daq and Dp denote the aqueous and pore diffusion coefficients, resp.).     

Multidimensional, multicomponent, subsurface reactive transport in nonuniform velocity fields: code verification using an advective reactive streamtube approach

High performance computing has made possible the development of high resolution, multidimensional, multicomponent reactive transport models that can be used to analyze complex geochemical environments. However, as increasingly complex processes are included in these models, the accuracy of the numerical formulation coupling the nonlinear processes becomes difficult to verify. Analytical solutions are not available for realistically complex problems and benchmark solutions are not generally available for specific problems. We present an advective reactive streamtube (ARS) transport technique that efficiently provides accurate solutions of nonlinear multicomponent reactive transport in nonuniform multidimensional velocity fields. These solutions can be compared with results from Eulerian-based advection-dispersion-reaction models to evaluate the accuracy of the numerical formulation used. The ARS technique includes mixed equilibrium and kinetic complexation and precipitation-dissolution reactions subject to the following assumptions: (1) transport is purely advective (i.e., no explicit diffusion or dispersion), and (2) chemistry is described by a canonical system of reactions that evolves with time and is unaffected by position in space. Results from the ARS technique are compared with results from the massively parallel, multicomponent reactive transport model MCTRACKER on a test problem involving irreversible oxidation of organic carbon and reaction of the oxidation products with two immobile mineral phases, gypsum and calcite, and fifteen aqueous complexes. Truncation error, operator splitting error, and the nonlinear transformation of these errors in the high-resolution reactive transport model are identified for this problem.     

Modifications necessary to use standard dispersion models at high latitudes

Standard air pollution dispersion models are inappropriate for application at high latitudes. Recent measurements of 10 m mixing heights with 0.5 m s⁻¹ winds in Fairbanks emphasize this inapplicability. It is essential that horizontal and vertical dispersion parameters be specified separately under these conditions. It is also important that the solar radiation input to vertical stability categories at high latitudes be determined on the basis of solar elevation angle, rather than by time after sunrise or before sunset.     

Chemical transport models

Background, aim, and scope  Improving the parameterization of processes in the atmospheric boundary layer (ABL) and surface layer, in air quality and chemical transport models. To do so, an asymmetrical, convective, non-local scheme, with varying upward mixing rates is combined with the non-local, turbulent, kinetic energy scheme for vertical diffusion (COM). For designing it, a function depending on the dimensionless height to the power four in the ABL is suggested, which is empirically derived. Also, we suggested a new method for calculating the in-canopy resistance for dry deposition over a vegetated surface. Materials and methods  The upward mixing rate forming the surface layer is parameterized using the sensible heat flux and the friction and convective velocities. Upward mixing rates varying with height are scaled with an amount of turbulent kinetic energy in layer, while the downward mixing rates are derived from mass conservation. The vertical eddy diffusivity is parameterized using the mean turbulent velocity scale that is obtained by the vertical integration within the ABL. In-canopy resistance is calculated by integration of inverse turbulent transfer coefficient inside the canopy from the effective ground roughness length to the canopy source height and, further, from its the canopy height. Results  This combination of schemes provides a less rapid mass transport out of surface layer into other layers, during convective and non-convective periods, than other local and non-local schemes parameterizing mixing processes in the ABL. The suggested method for calculating the in-canopy resistance for calculating the dry deposition over a vegetated surface differs remarkably from the commonly used one, particularly over forest vegetation. Discussion  In this paper, we studied the performance of a non-local, turbulent, kinetic energy scheme for vertical diffusion combined with a non-local, convective mixing scheme with varying upward mixing in the atmospheric boundary layer (COM) and its impact on the concentration of pollutants calculated with chemical and air-quality models. In addition, this scheme was also compared with a commonly used, local, eddy-diffusivity scheme. Simulated concentrations of NO₂ by the COM scheme and new parameterization of the in-canopy resistance are closer to the observations when compared to those obtained from using the local eddy-diffusivity scheme. Conclusions  Concentrations calculated with the COM scheme and new parameterization of in-canopy resistance, are in general higher and closer to the observations than those obtained by the local, eddy-diffusivity scheme (on the order of 15–22%). Recommendations and perspectives  To examine the performance of the scheme, simulated and measured concentrations of a pollutant (NO₂) were compared for the years 1999 and 2002. The comparison was made for the entire domain used in simulations performed by the chemical European Monitoring and Evaluation Program Unified model (version UNI-ACID, rv2.0) where schemes were incorporated.     

Modelling the solute transport under nonequilibrium conditions on the basis of mass transfer equations

A solute transport model that describes nonequilibrium adsorption in soil/groundwater systems by mass transfer equations for film and intraparticle diffusion is presented. The model is useful in cases where breakthrough curve spreading cannot be explained by dispersion only. To evaluate its validity, the model was applied to several data sets from column experiments. The validity was also proved by a comparison with an analytical solution for the limiting case of predominating dispersion. Furthermore, a sensitivity analysis was performed to illustrate the influence of different process and sorption parameters (pore water velocity, intraparticle mass transfer coefficient, isotherm nonlinearity) on the shape of the calculated breakthrough curves. The application of the proposed model is discussed in comparison to the widely used dispersed flow/local equilibrium model, and a relationship between both models, which is based on a lumped parameter approach, is shown.     

Theoretical analysis of deviations from local equilibrium during sorbing solute transport through idealized stratified aquifers

This paper studies the spreading characteristics of reactive solute plumes in idealized stratified aquifers. The aquifer consists of two layers having different permeabilities with flow parallel to the stratification. The solute is assumed to adsorb onto the aquifer solids according to a first-order reversible kinetic rate law; the adsorption parameters are spatially uniform. We use the Aris moment method to examine analytically the time evolution of the lower-order spatial moments of the depth-averaged contaminant plume for an instantaneous input of mass. The results demonstrate that sorption kinetics cause the total dissolved mass and average velocity of the contaminant plume to decrease with increasing travel time. The plume variance is shown to depend upon three factors: intra-layer longitudinal dispersion, intra-layer kinetics, and vertical averaging. The results indicate that the relative importance of sorption kinetics diminishes as the permeability contrast between the layers increases. We present a simple criterion that can be used to assess the applicability of the local equilibrium assumption in idealized stratified systems.     

Model-based evaluation of controlled-release systems in the remediation of dissolved plumes in groundwater

Controlled-release, semi-passive reactive barrier systems have been recently developed as a long-term treatment option for controlling the spread of contaminant plumes in groundwater. This paper describes a new computer code, and applies it to study coupled processes of solute release, reaction, and mass transport in an in situ remediation scheme using the controlled release of potassium permanganate. Confidence with the modeling approach was developed by model verifications and simulating results of a pilot-scale test-cell experiment. Sensitivity analyses indicated the possibilities of treatment inefficiencies due to inability of transverse dispersion to mix the permanganate (MnO(4)(-)) within the zone of reaction, fluctuations in source strength due to variations in flow velocity, and the small length of treatment zone due to strong soil utilization of MnO(4)(-). Although problems associated with the fluctuating source strength and strong soil utilization can be addressed by optimizing the release rate, the inefficiency of transverse dispersion to create mixing could pose a serious limitation. Through a series of model simulations, a system of injection/withdrawal wells in a doublet arrangement was developed to facilitate lateral spreading and mixing of MnO(4)(-). A well-mixed, stable MnO(4)(-) zone with predetermined size (DxL=8m x 2m) and concentration ranges (1.5-20 mg l(-1)) was created by four 1-day injection/withdrawal pumping periods over 24 d. This type of mixing zone may persist for many years with periodic well mixing and replacements of exhausted controlled-release forms. Coupled use of the generalized code with field hydrologic data will help to optimize the design and operation of controlled-release systems in practice.     

Overview of Petroleum Environmental Research Forum (PERF) dense gas dispersion modeling project

This paper provides a background for and an overview of the results of a comprehensive study of transport and dispersion of dense gas plumes over rough surfaces typical of industrial sites. The Petroleum Environmental Research Forum (PERF) 93-16 project involved model development and evaluations using observations from three wind tunnels and from the Kit Fox field experiment. Detailed discussions of the results of the research are given in the other papers in this special issue. The wind tunnel experiments produced data showing that the resulting best-fit vertical entrainment formula was close to (i.e., within about 30%) the vertical entrainment formulas already in use by current models, which were derived primarily from observations over smooth surfaces. Observations from the Kit Fox field experiment demonstrated the validity of the entrainment curves derived from the wind tunnel data. The Kit Fox data were also used to evaluate algorithms for along-wind dispersion and cloud advection speeds for short-duration releases typical of an industrial site, and to evaluate the HEGADAS dense gas dispersion model.     

Modeling Atmospheric Mercury Deposition in the Vicinity of Power Plants

Abstract

Two mathematical models of the atmospheric fate and transport of mercury (Hg), an Eulerian grid–based model and a Gaussian plume model, are used to calculate the atmospheric deposition of Hg in the vicinity (i.e., within 50 km) of five coal–fired power plants. The former is applied using two different horizontal resolutions: coarse (84 km) and fine (16.7 km). More than 96% of the power plant Hg emissions are calculated with the plume model to be transported beyond 50 km from the plants. The grid–based model predicts a lower fraction to be transported beyond 50 km: >91% with a coarse resolution and >95% with a fine resolution. The contribution of the power plant emissions to total Hg deposition within a radius of 50 km from the plants is calculated to be <8% with the plume model, <14% with the Eulerian model with a coarse resolution, and <10% with the Eulerian model with a fine resolution. The Eulerian grid–based model predicts greater local impacts than the plume model because of artificially enhanced vertical dispersion; the former predicts about twice as much Hg deposition as the latter when the area considered is commensurate with the resolution of the grid–based model. If one compares the local impacts for an area that is significantly less than the grid–based model resolution, then the grid–based model may predict lower local deposition than the plume model, because two compensating errors affect the results obtained with the grid–based model: initial dilution of the power plant emissions within one or more grid cells and enhanced vertical mixing to the ground.     

An efficient Lagrangian stochastic model of vertical dispersion in the convective boundary layer

We consider the one-dimensional case of vertical dispersion in the convective boundary layer (CBL) assuming that the turbulence field is stationary and horizontally homogeneous. The dispersion process is simulated by following Lagrangian trajectories of many independent tracer particles in the turbulent flow field, leading to a prediction of the mean concentration. The particle acceleration is determined using a stochastic differential equation, assuming that the joint evolution of the particle velocity and position is a Markov process. The equation consists of a deterministic term and a random term. While the formulation is standard, attention has been focused in recent years on various ways of calculating the deterministic term using the well-mixed condition incorporating the Fokker–Planck equation. Here we propose a simple parameterisation for the deterministic acceleration term by approximating it as a quadratic function of velocity. Such a function is shown to represent well the acceleration under moderate velocity skewness conditions observed in the CBL. The coefficients in the quadratic form are determined in terms of given turbulence statistics by directly integrating the Fokker–Planck equation. An advantage of this approach is that, unlike in existing Lagrangian stochastic models for the CBL, the use of the turbulence statistics up to the fourth order can be made without assuming any predefined form for the probability distribution function (PDF) of the velocity. The main strength of the model, however, lies in its simplicity and computational efficiency. The dispersion results obtained from the new model are compared with existing laboratory data as well as with those obtained from a more complex Lagrangian model in which the deterministic acceleration term is based on a bi-Gaussian velocity PDF. The comparison shows that the new model performs well.     

High Volume Sampling:Evaluation of an Inverted Sampler for Ambient TSP Measurements

Recent advances in the development of receptor-oriented source apportionment techniques (models) have provided a new approach to evaluating the performance of particulate dispersion models. Rather than limiting performance evaluations to comparisons of particulate mass, receptor model estimates of source impacts can be used to open new opportunities for in-depth analysis of dispersion model performance. Recent experiences in the joint application of receptor and dispersion models have proven valuable in developing increased confidence in source impact projections used for control strategy development. Airshed studies that have followed this approach have identified major errors in emission inventory data bases and provided technical support for modeling assumptions.

This paper focuses on the joint application of dispersion and receptor models to particulate source impact analysis and dispersion model performance and evaluation. The limitations and advantages of each form of modeling are reviewed and case studies are examined. The paper is offered to provide several new perspectives into the model evaluation process in the hope that they may prove useful to those that manage our nation’s air resources.     

Refining emission rate estimates using a coupled receptor–dispersion modeling approach

Receptor modeling techniques like chemical mass balance are used to attribute pollution levels at a point to different sources. Here we analyze the composition of particulate matter and use the source profiles of sources prevalent in a region to estimate quantitative source contributions. In dispersion modeling on the other hand the emission rates of various sources together with meteorological conditions are used to determine the concentrations levels at a point or in a region. The predictions using these two approaches are often inconsistent. In this work these differences are attributed to errors in emission inventory. Here an algorithm for coupling receptor and dispersion models is proposed to reduce the differences of the two predictions and determine the emission rates accurately. The proposed combined approach helps reconcile the differences arising when the two approaches are used in a stand-alone mode. This work is based on assuming that the models are perfect and uses a model-to-model comparison to illustrate the concept.     

A stochastic-advective transport model for NAPL dissolution and degradation in non-uniform flows in porous media

Remediation schemes for contaminated sites are often evaluated to assess their potential for source zone reduction of mass, or treatment of the contaminant between the source and a control plane (CP) to achieve regulatory limits. In this study, we utilize a stochastic stream tube model to explain the behavior of breakthrough curves (BTCs) across a CP. At the local scale, mass dissolution at the source is combined with an advection model with first-order decay for the dissolved plume. Field-scale averaging is then employed to account for spatial variation in mass within the source zone, and variation in the velocity field. Under the assumption of instantaneous mass transfer from the source to the moving liquid, semi-analytical expressions for the BTC and temporal moments are developed, followed by derivation of expressions for effective velocity, dispersion, and degradation coefficients using the method of moments. It is found that degradation strongly influences the behavior of moments and the effective parameters. While increased heterogeneity in the velocity field results in increased dispersion, degradation causes the center of mass of the plume to shift to earlier times, and reduces the dispersion of the BTC by lowering the concentrations in the tail. Modified definitions of effective parameters are presented for degrading solutes to account for the normalization constant (zeroth moment) that keeps changing with time or distance to the CP. It is shown that anomalous dispersion can result for high degradation rates combined with wide variation in velocity fluctuations. Implications of model results on estimating cleanup times and fulfillment of regulatory limits are discussed. Relating mass removal at the source to flux reductions past a control plane is confounded by many factors. Increased heterogeneity in velocity fields causes mass fluxes past a control plane to persist, however, aggressive remediation between the source and CP can reduce these fluxes.