Field-scale effective matrix diffusion coefficient for fractured rock: results from literature survey

Matrix diffusion is an important mechanism for solute transport in fractured rock. We recently conducted a literature survey on the effective matrix diffusion coefficient, D_m^e, a key parameter for describing matrix diffusion processes at the field scale. Forty field tracer tests at 15 fractured geologic sites were surveyed and selected for the study, based on data availability and quality. Field-scale D_m^e values were calculated, either directly using data reported in the literature, or by reanalyzing the corresponding field tracer tests. The reanalysis was conducted for the selected tracer tests using analytic or semi-analytic solutions for tracer transport in linear, radial, or interwell flow fields. Surveyed data show that the scale factor of the effective matrix diffusion coefficient (defined as the ratio of D_m^e to the lab-scale matrix diffusion coefficient, D_m, of the same tracer) is generally larger than one, indicating that the effective matrix diffusion coefficient in the field is comparatively larger than the matrix diffusion coefficient at the rock-core scale. This larger value can be attributed to the many mass-transfer processes at different scales in naturally heterogeneous, fractured rock systems.Furthermore, we observed a moderate, on average trend toward systematic increase in the scale factor with observation scale. This trend suggests that the effective matrix diffusion coefficient is likely to be statistically scale-dependent. The scale-factor value ranges from 0.5 to 884 for observation scales from 5 to 2000 m. At a given scale, the scale factor varies by two orders of magnitude, reflecting the influence of differing degrees of fractured rock heterogeneity at different geologic sites. In addition, the surveyed data indicate that field-scale longitudinal dispersivity generally increases with observation scale, which is consistent with previous studies. The scale-dependent field-scale matrix diffusion coefficient (and dispersivity) may have significant implications for assessing long-term, large-scale radionuclide and contaminant transport events in fractured rock, both for nuclear waste disposal and contaminant remediation.     

A hybrid plume model for local-scale atmospheric dispersion

This paper presents a local-scale dispersion model, based on atmospheric boundary layer scaling theory. In the vicinity of the source, Gaussian equations are used in both the horizontal and vertical directions. After a specified transition distance, gradient transfer theory is applied in the vertical direction, while the horizontal dispersion is still assumed to be Gaussian. The dispersion parameters and eddy diffusivity are modelled in a form, which facilitates the use of a meteorological pre-processor. We present a novel model of the vertical eddy diffusivity (K_z), which is a continuous function of height in various atmospheric scaling regions. The model also includes a treatment of the dry deposition of gases and particulate matter. The accuracy of the numerical model was analysed by comparing the model predictions with two analytical solutions; the numerical deviations from these solutions were less than 2% for the computational regime. The model has been tested against the Kincaid experimental field data. The agreement of the predictions and the data is good on the average, although the internal variation of the predictions versus data scatter plot is substantial.     

An evaluation of contaminant migration patterns at two waste disposal sites on fractured porous media in terms of the equivalent porous medium (EPM) model

Contamination has occurred many non-indurated and bedrock systems wherein the groundwater flows almost exclusively through a network of connected, open fractures. The matrix surrounding the fractures often possesses porosity which allows contaminant diffusion into the matrix. If the diffusion rates are fast relative to the fracture groundwater velocity, transport effects may be predicted by considering the system to be an equivalent porous medium (EPM). The rapidity with which fracture/immobile-matrix equilibrium is established will be determined in part by the: fracture aperture (2b); interfracture spacing (2B); porosity in the immobile matrix (θ_im); and the matrix diffusion coefficient (D′). Two systems which are characterized by very different values of the above parameters have been studied by our laboratories. At Alkali Lake, Oregon, the EPM approach describes contaminant transport well. At Bayview Park, Ontario, the EPM approach is not appropriate. Several features of the two sites are compared to illustrate the different nature of these two sites. These features include: (1) natural characteristics of the groundwater systems; (2) contaminant distributions; (3) observed transport; and (4) computed fracture/immobile-matrix diffusion times.     

Simple PDF models for convectively driven vertical diffusion

The mode of vertical velocity in convective boundary layers (CBLs) is usually negative and the probability distribution function (PDF) of w, P_w, is rarely symmetric except near the top and bottom of CBLs. Consequently, vertical diffusion from elevated sources is usually asymmetric and exhibits a descending mode of concentration, causing higher peak surface concentrations than predicted by Gaussian models. The main concentration (χ) effects, we argue, can be modeled using the simplest of PDF diffusion models, with tracers responding to P_w at the source height with straight line trajectories and simple reflection at the surface and z_i, the mixing depth. The critical element is the choice of P_w. Two P_w models are offered, a bi-Gaussian (BG) and a Gaussian-ramp (GR) formulation. Both have some observational support, and the resulting PDF models are mathematically tractable. Analytical solutions for key variables are given; these show some surprising contrasts between the BG and GR models, but both can approximate laboratory and numerical modeling results for ∝χdy patterns. A diverse selection of atmospheric turbulence measurements is presented; for measures that reflect asymmetry in P_w, the data show wide ranges and do not lend support to any particular form of P_w. Recent lidar measurements of oil fog plumes are presented that show a large variability in ∝χdy patterns, even with substantial averaging periods. The only concurrent turbulence measurement that strongly correlates with the observed vertical diffusion of oil fog is the mode of wind elevation angle. A simple adaptation of the BG model is recommended that fits the average peak ∝χdy and distance of occurrence as observed so far.     

An analytical solution to contaminant diffusion in semi-infinite clayey soils with piecewise linear adsorption

The adsorption of contaminants onto soil particles typically is nonlinear if the contaminant concentration is sufficiently high. A simplified piecewise linear adsorption isotherm consistent with experimental results is proposed as an approximation for nonlinear adsorption behavior. This approximation allows for the use of analytical solution to model solute diffusion of contaminants that exhibit nonlinear adsorption. A moving boundary is introduced to represent significant changes in the retardation factor of clay with an increase in solute concentration. The proposed analytical solutions were validated using experimental data presented in the literature. There is negligible difference between the results obtained by the proposed analytical solution and those obtained by the linear model when C_m/C₀ reached 0.5. The results also show that the model based on linear adsorption using the initial secant of the Freundlich isotherm leads to significantly lower estimated breakthrough time for the contaminant of interest than that obtained using the proposed model. The earlier breakthrough is due to an under-estimation of the amount of adsorption. The proposed method is relatively simple to apply and can be used for evaluating experimental results and verifying more complex numerical models.     

The effect of ozone photochemistry on atmospheric and surface temperature changes due to large atmospheric injections of smoke and NOx by a large-scale nuclear war

A coupled one-dimensional radiative-convective and photochemical diffusion model (RCP model), which takes into account the interaction of ozone photochemistry on climate, is used to investigate the possible effects of smoke and NO_x generated by a large-scale nuclear war, on vertical temperature and ozone structure and surface climate. From the results of initial experiments with fixed O₃ it is found that for the nuclear smoke injection scenario adopted in this study (similar to the base line case of Turco etal., 1983), the average sunlight intensities would be reduced drastically (up to 97%), leading to a large cooling near the surface (up to 38 K) and intense heating (up to 110 K) in the upper troposphere and lower stratosphere. Variation of surface albedo, water vapour and clouds with time following the smoke injection would further enhance the surface cooling and prolong the temperature perturbation.Further experimental results with O₃ photochemistry interaction indicate that for the smoke and NO_x nuclear injection scenario considered in this study, the total O₃ column would decrease up to 50%, with a half recovery time of about 2 y. However more than half the total O₃ column reduction is caused by the heating of the stratosphere by smoke injection. The effect of stratospheric O₃ reductions on surface climate is not significant (less than 2.5 K. additional cooling). However the vertical temperature profile is altered in such a way that it would lead to a large increase in the thermal stability of the troposphere, while decreasing it in the stratosphere more than in the case of fixed O₃. Also discussed are the solar u.v.-B flux changes at the surface which result from the presence of smoke in the atmosphere initially and from stratospheric O₃ depletions as the smoke particles are removed from the atmosphere in time.     

Prediction of gas diffusion in complicated terrain by a potential flow model

A numerical model was developed to simulate gaseous diffusion in complicated terrain. This model calculates the air flow as a potential flow by the Boundary Element Method, and gaseous diffusion by an analytical Gaussian equation in the potential flow. Plume spreads σ_y and σ_z are modified by multiregression equations derived from wind tunnel experiments, and the terrain height is elongated depending on the atmospheric stability.First, tracer data from Cinder Cone Butte in the U.S. measured by the U.S.-EPA were predicted by the model in order to examine the prediction accuracy under stable conditions. The averaged ratio of the observed concentration to predicted concentration for 12 runs was better than a factor of 10. Next, tracer data from the Geysers area in the U.S. measured by the U.S.-DOE were used to examine the prediction accuracy under neutral conditions. The ratio of the observed concentration to predicted concentration for two runs under neutral conditions was better than factor of two at most locations, but prediction capability is poor in blocked or separated flow conditions.     

Improving Oxygen Conditions in the Deeper Parts of Bornholm Sea by Pumped Injection of Winter Water

Vertical diffusivity and oxygen consumption in the basin water, the water below the sill level at about 59 m depth, have been estimated by applying budget methods to monitoring data from hydrographical stations BY4 and BY5 for periods without water renewal. From the vertical diffusivity, the mean rate of work against the buoyancy forces below 65 m depth is estimated to about 0.10 mW m⁻². This is slightly higher than published values for East Gotland Sea. The horizontally averaged vertical diffusivity κ can be approximated by the expression κ = a₀N⁻¹ where N is the buoyancy frequency and a₀ ≈ 1.25 × 10⁻⁷ m² s⁻², which is similar to values for a₀ used for depths below the halocline in Baltic proper circulation models for long-term simulations. The contemporary mean rate of oxygen consumption in the basin water is about 75 g O₂ m⁻² year⁻¹, which corresponds to an oxidation of 28 g C m⁻² year⁻¹. The oxygen consumption in the Bornholm Basin doubled from the 1970s to the 2000s, which qualitatively explains the observed increasing frequency and vertical extent of anoxia and hypoxia in the basin water in records from the end of the 1950s to present time. A horizontally averaged vertical advection–diffusion model of the basin water is used to calculate the effects on stratification and oxygen concentration by a forced pump-driven vertical convection. It is shown that the residence time of the basin water may be reduced by pumping down and mixing the so-called winter water into the deepwater. With the present rate of oxygen consumption, a pumped flux of about 25 km³ year⁻¹ would be sufficient to keep the oxygen concentration in the deepwater above 2 mL O₂ L⁻¹.     

A multi-layer model for pollutant dispersion with dry deposition to the ground

This paper presents a semi-analytical solution for the steady advection–diffusion equation that allows simulating the vertical turbulent dispersion of air pollution with deposition to the ground. The performances of the solution, with a proper parameterization of the vertical profiles of wind and eddy diffusivity, were evaluated against Hanford diffusion experiment dataset using two tracers (Doran and Horst, 1985): a non-depositing gas (SF₆) and depositing particles (ZnS). Results show that the dispersion model with the K-parameterization included produces a good fitting of the measured ground-level concentration data and there are no big differences between the parameterizations taken from literature. A comparison with other models was shown and discussed.     

Diffusion of tritiated water and Na through non-degraded hardened cement pastes

Diffusion experiments through hardened cement pastes (HCP) using tritiated water (HTO) and ²²Na⁺, considered to be conservative tracers, have been carried out in triplicates in a glove box under a controlled nitrogen atmosphere. Each experiment consisted of a through-diffusion test followed by an out-diffusion test.The experimental data were inversely modelled applying an automated Marquardt–Levenberg procedure. The analysis of the through-diffusion data allowed the extraction of values for the effective diffusion coefficients, D_e, and the rock capacity factor, α. Good agreement between measured and calculated tracer breakthrough curves was achieved using both a simple diffusion model without sorption and a diffusion/linear sorption model. The best-fit K_d-values were found to be consistent with R_d-values measured in previous batch-sorption experiments.The best-fit values from the through-diffusion tests were then used to predict the results of subsequent out-diffusion experiments. Good agreement between experimental data and predictions was achieved only for the case of linear sorption.Isotopic exchange can only partially account for both the amount of tracer taken up in the batch-sorption tests and the measured retardation in the diffusion experiments and, hence, additional mechanisms have to be invoked to explain the data.     

Diffusive transport through compacted Na- and Ca-bentonite

The effect of exchangeable cation — Na⁺ and Ca ²⁺ — on the diffusive transport of I⁻, Sr ²⁺ and ³H (as HTO) in compacted bentonite was examined using a through-diffusion method. Total intrinsic diffusion coefficients, D_i, were determined from the steady-state flux of the diffusants through the clays, and apparent diffusion coefficients, D_a, were obtained from the time lag technique. The clays were compacted to a dry bulk density of 1.3 Mg/m³, and Na-bentonite was saturated with a solution of 100 mol NaCl/m3 and Ca-bentonite with one of 50 mol CaCl₂/m³. The D_i values for all diffusants are 2 to 6 times higher in the Ca- than Na-clay. We attribute this to the larger quasicrystal, or particle, size of Ca- compared to Na-bentonite. Hence, Ca-bentonite has a greater proportion of relatively large pores; this was confirmed by Hg intrusion porosimetry. This means the diffusion pathways in Ca-bentonite are less tortuous than those in Na-bentonite. Moreover, in some cases the effective porosity, or the porosity available for diffusive transport, may be greater in Ca-bentonite. The D_a values are inversely proportional to the distribution coefficients of the diffusants with the clays.     

A Note on Comparison of Statistical and Analytical Results for Calculating Oxides of Nitrogen Concentrations

A question often asked about analytical diffusion models is “How do the analytical results for calculating pollution concentrations compare with those obtained by statistical techniques?” Miller and Holzworth (1967) have developed a simple analytical diffusion model that yields relative pollution concentrations, x/Q, as a function of afternoon mixing depth, mean transport wind speed, and city size. This analytical model may also be used in reverse to determine apparent afternoon source strengths from observed afternoon pollution concentrations. The apparent source strengths may then be used with the model on independent data to estimate pollution concentrations. It is the purpose of this note to compare results of calculating average afternoon concentrations of oxides of nitrogen (NO_x) by use of the Miller-Holzworth model with those obtained from statistical regression equations.     

Minimum turbulence assumptions and u* and L estimation for dispersion models during low-wind stable conditions

The U.S. Environmental Protection Agency (EPA) short-distance dispersion model, AERMOD, has been shown to overpredict by a factor of as much as 10 when compared with observed concentrations from continuous releases at the Oak Ridge, TN (OR), and Idaho Falls, ID (IF), field experiments during stable periods when wind speeds often dropped below 1 m/sec. Some of this overprediction tendency can be reduced by revising AERMOD's meteorological preprocessor's parameterizations of the friction velocity, u _* , during low-wind stable conditions, thus increasing the calculated σ _v and σ _w and hence the lateral and vertical dispersion rates. Observations show that as the mean wind speed approaches zero at night, there is always significant σ _v and σ _w over time periods of 15 to 60 min, while standard Monin–Obukhov Similarity Theory (MOST) predicts that σ _v and σ _w will approach zero. This paper focuses on the u _* estimation methods and the minimum turbulence (σ _v and σ _w ) assumptions in AERMOD (beta option 4) and two widely used U.S. operational dispersion models, AERMOD (v12345) and SCICHEM. The U.S. EPA has provided results of its tests with the OR and IF data, with its base AERMOD version and its December 2012 modified versions, which assume adjustments to the low-wind u _* and increases in the minimum σ _v parameterization. SCICHEM has relatively small mean bias for both data sets. The revised AERMOD shows much less mean bias, agreeing more with SCICHEM.

Implications:

Suggestions are made for improvements to dispersion models such as AERMOD to correct overpredictions during light-wind stable conditions. Methods for estimating u_*, L, and the minimum turbulence parameters (σ_v and σ_w) are reviewed and compared. SCICHEM and the current operational version and an optional beta version (December 2012) of AERMOD are evaluated with tracer data from low-wind stable field experiments in Idaho Falls and Oak Ridge. It is seen that the operational version of AERMOD overpredicts by a factor of 2 to 10, while the optional beta version of AERMOD and SCICHEM have much less bias.     

Characterization of the olfactory impact around a wastewater treatment plant: Optimization and validation of a hydrogen sulfide determination procedure based on passive diffusion sampling

A monitoring program based on an indirect method was conducted to assess the approximation of the olfactory impact in several wastewater treatment plants (in the present work, only one is shown). The method uses H₂S passive sampling using Palmes-type diffusion tubes impregnated with silver nitrate and fluorometric analysis employing fluorescein mercuric acetate. The analytical procedure was validated in the exposure chamber. Exposure periods of at least 4 days are recommended. The quantification limit of the procedure is 0.61 ppb for a 5-day sampling, which allows the H₂S immission (ground concentration) level to be measured within its low odor threshold, from 0.5 to 300 ppb. Experimental results suggest an exposure time greater than 4 days, while recovery efficiency of the procedure, 93.0 ± 1.8%, seems not to depend on the amount of H₂S collected by the samplers within their application range. The repeatability, expressed as relative standard deviation, is lower than 7%, which is within the limits normally accepted for this type of sampler. Statistical comparison showed that this procedure and the reference method provide analogous accuracy. The proposed procedure was applied in two experimental campaigns, one intensive and the other extensive, and concentrations within the H₂S low odor threshold were quantified at each sampling point. From these results, it can be concluded that the procedure shows good potential for monitoring the olfactory impact around facilities where H₂S emissions are dominant.

Implications: Passive samplers are very attractive tools to experimentally tackle a number of air pollution problems, especially those related to odor impact. Their small size and cost permit a denser sampling design and thus a more detailed spatial characterization than other techniques. On the other hand, the large inherent variability in passive sampler measures requires an uncertainty analysis of the chemical species and analytical procedures used.     

An analytical model for crosswind integrated concentrations released from a continuous source in a finite atmospheric boundary layer

An analytical model for the crosswind integrated concentrations released from a continuous source in a finite atmospheric boundary layer is formulated by considering the wind speed as a power law profile of vertical height above the ground and eddy diffusivity as an explicit function of downwind distance from the source and vertical height. A closed form analytical solution of the resulting advection–diffusion equation for these profiles of wind speed and eddy diffusivity with the physically relevant boundary conditions is derived using the separation of variables technique that leads to a Sturm–Liouville eigen value problem. Various particular cases of the model are deduced.The model is evaluated with the observations obtained from Prairie Grass experiment in various stability classes varying from very unstable to neutral and stable conditions and Hanford diffusion experiment in stable conditions. The agreement is found to be good between the computed and observed concentrations in both the diffusion experiments. For Prairie Grass experiment, the model is predicting 78% cases with in a factor of two and gives a value of NMSE as 0.075. On the other hand, for Hanford observations in stable conditions, it predicts 70% cases with in factor of two. An extensive analysis of statistical measures with the downwind distances from the source reveals that the model is performing well close to the source.     

Numerical model for static chamber measurement of multi-component landfill gas emissions and its application

The quantitative assessment of landfill gas emissions is essential to assess the performance of the landfill cover and gas collection system. The relative error of the measured surface emission of landfill gas may be induced by the static flux chamber technique. This study aims to quantify effects of the size of the chamber, the insertion depth, pressure differential on the relative errors by using an integrated approach of in situ tests, and numerical modeling. A field experiment study of landfill gas emission is conducted by using a static chamber at one landfill site in Xi’an, Northwest China. Additionally, a two-dimensional axisymmetric numerical model for multi-component gas transport in the soil and the static chamber is developed based on the dusty-gas model (DGM). The proposed model is validated by the field data obtained in this study and a set of experimental data in the literature. The results show that DGM model has a better capacity to predict gas transport under a wider range of permeability compared to Blanc’s method. This is due to the fact that DGM model can explain the interaction among gases (e.g., CH₄, CO₂, O₂, and N₂) and the Knudsen diffusion process while these mechanisms are not included in Blanc’s model. Increasing the size and the insertion depth of static chambers can reduce the relative error for the flux of CH₄ and CO₂. For example, increasing the height of chambers from 0.55 to 1.1 m can decrease relative errors of CH₄ and CO₂ flux by 17% and 18%, respectively. Moreover, we find that gas emission fluxes for the case with positive pressure differential (?P_in-out) are greater than that of the case without considering pressure fluctuations. The Monte Carlo method was adopted to carry out the statistical analysis for quantifying the range of relative errors. The agreement of the measured field data and predicted results demonstrated that the proposed model has the capacity to quantify the emission of landfill gas from the landfill cover systems.

     

Reduction of sampling and analytical errors for electron microscopic analysis of atmospheric aerosols

Electron microscopy-energy dispersive spectroscopy (EM/EDS) can be used to determine the elemental composition of individual particles. However, the accuracy with which atmospheric particle compositions can be quantitatively determined is not well understood. In this work we explore sources of sampling and analytical bias and methods of reducing bias. Sulfuric acid [H₂SO₄] and ammonium sulfate [(NH₄)₂SO₄] particles were collected on beryllium, silicon, and carbon substrates with similar deposition densities. While [(NH₄)₂SO₄] particles were observed on all substrates, [H₂SO₄] and ammonia-treated [H₂SO₄] particles could not be found on beryllium substrates. Interactions between the substrate and sulfuric acid particles are implicated. When measured with EM/EDS, [H₂SO₄] particles exposed to ammonia overnight were found having lower beam damage rates (0.000 ± 0.002 fraction s⁻¹) than those without any treatment (0.023 ± 0.006 fraction s⁻¹) For laboratory-generated [C₁₀H₆(SO₃Na)₂] particles, the composition determined using the experimental k-factors evaluated from independent particle standards of similar composition and size shows an error less than 20% for all constituents, while greater than 78% errors were found when k-factors were calculated from the theory. This study suggests (1) that sulfate beam damage can be reduced by exposure of atmospheric particle samples to ammonia before analysis, (2) that beryllium is not a suitable substrate for atmospheric particle analysis, and (3) calibration (k-factor determination) using particle standards of similar size and composition to particles present in the atmosphere shows promise as a way of improving the accuracy of quantitative EM analysis.     

Measurement of nitrogen dioxide profiles by diffusion tubes within a barley canopy

Diffusion tubes have been used for the time-averaged measurement of vertical profiles of N0₂ above and within a canopy of winter barley. The results indicate that diffusion tubes have sufficient precision and reproducibility to be a useful technique in this application.     

WRF-Chem simulation of East Asian air quality: Sensitivity to temporal and vertical emissions distributions

This study develops fine temporal (seasonal, day-of-week, diurnal) and vertical allocations of anthropogenic emissions for the TRACE-P inventory and evaluates their impacts on the East Asian air quality prediction using WRF-Chem simulations in July 2001 at 30-km grid spacing against available surface measurements from EANET and NEMCC. For NO₂ and SO₂, the diurnal and vertical redistributions of emissions play essential roles, while the day-of-week variation is less important. When all incorporated, WRF-Chem best simulates observations of surface NO₂ and SO₂ concentrations, while using the default emissions produces the worst result. The sensitivity is especially large over major cities and industrial areas, where surface NO₂ and SO₂ concentrations are reduced by respectively 3–7 and 6–12 ppbv when using the scaled emissions. The incorporation of all the three redistributions of emissions simulates surface O₃ concentrations higher by 4–8 ppbv at night and 2–4 ppbv in daytime over broad areas of northern, eastern and central China. To this sensitivity, the diurnal redistribution contributes more than the other two.