Evaluation of saline tracer performance during electrical conductivity groundwater monitoring

Saline solutions are the most commonly used hydrological tracers, because they can be easily and economically monitored by in situ instrumentation such as electrical conductivity (EC) loggers in wells or by geoelectrical measurements. Unfortunately, these low-cost techniques only provide information on the total concentration of ions in solution, i.e., they cannot resolve the ionic composition of the aqueous solution. This limitation can introduce a bias in the estimation of aquifer parameters where sorption phenomena between saline tracers and sediments become relevant. In general, only selected anions such as Cl(-) and Br(-) are recognised to be transported unretarded and they are referred to as conservative tracers or mobile anions. However, cations within the saline tracer may interact with the soil matrix through a range of processes such as ion exchange, surface complexation and via physical mass-transfer phenomena. Heterogeneous reactions with minerals or mineral surfaces may not be negligible where aquifers are composed of fine alluvial sediments. The focus of the present study was to examine and to quantify the bias between the aquifer parameters estimated during model-based interpretation of experimental data of EC measurements of saline tracer relative to the aquifer parameters found by specific measurements (i.e. via ionic chromatography, IC) of truly conservative species. To accomplish this, column displacement experiments with alluvial aquifer materials collected from the Po lowlands (Italy) were performed under water saturated conditions. The behaviour of six selected, commonly used saline tracers (i.e., LiCl, KCl, and NaCl; LiBr, KBr, and NaBr) was studied and the data analysed by inverse modelling. The results demonstrate that the use of EC as a tracer can lead to an erroneous parameterisation of the investigated porous media, if the reactions between solute and matrix are neglected. In general, errors were significant except for KCl and KBr, which is due to the weak interaction between dissolved K(+) and the sediment material. The study shows that laboratory scale pre-investigations can help with tracer selection and to optimise the concentration range targeted for in situ multilevel monitoring by unspecific geoelectrical instrumentation.     

Fluorescent dye imaging of the volume sampled by single well forced-gradient tracer tests evaluated in a laboratory-scale aquifer physical model

This study presents a new method to visualise forced-gradient tracer tests in 2-D using a laboratory-scale aquifer physical model. Experiments were designed to investigate the volume of aquifer sampled in vertical dipole flow tracer tests (DFTT) and push-pull tests (PPT), using a miniature monitoring well and straddle packer arrangement equipped with solute injection and recovery chambers. These tests have previously been used to estimate bulk aquifer hydraulic and transport properties for the evaluation of natural attenuation and other remediation approaches. Experiments were performed in a silica glass bead-filled box, using a fluorescent tracer (fluorescein) to deduce conservative solute transport paths. Digital images of fluorescein transport were captured under ultraviolet light and processed to analyse tracer plume geometry and obtain point-concentration breakthrough histories. Inorganic anion mixtures were also used to obtain conventional tracer breakthrough histories. Concentration data from the conservative tracer breakthrough curves was compared with the digital images and a well characterised numerical model. The results show that the peak tracer breakthrough response in dipole flow tracer tests samples a zone of aquifer close to the well screen, while the sampling volume of push-pull tests is limited by the length of the straddle packers used. The effective sampling volume of these single well forced-gradient tests in isotropic conditions can be estimated with simple equations. The experimental approach offers the opportunity to evaluate under controlled conditions the theoretical basis, design and performance of DFTTs and PPTs in porous media in relation to measured flow and transport properties.     

Applications and implications of direct groundwater velocity measurement at the centimetre scale

Three projects involving point velocity probes (PVPs) illustrate the advantages of direct groundwater velocity measurements. In the first, a glacial till and outwash aquifer was characterized using conventional methods and multilevel PVPs for designing a bioremediation program. The PVPs revealed a highly conductive zone that dominated the transport of injected substances. These findings were later confirmed with a natural gradient tracer test. In the second, PVPs were used to map a groundwater velocity field around a dipole recirculation well. The PVPs showed higher than expected velocities near the well, assuming homogeneity in the aquifer, leading to improved representations of the aquifer heterogeneity in a 3D flow model, and an improved match between the modelled and experimental tracer breakthrough curves. In the third study, PVPs detected subtle changes in aquifer permeability downgradient of a biostimulation experiment. The changes were apparently reversible once the oxygen source was depleted, but in locations where the oxygen source lingered, velocities remained low. PVPs can be a useful addition to the hydrogeologist's toolbox, because they can be constructed inexpensively, they provide data in support of models, and they can provide information on flow in unprecedented detail.     

Importance of considering intraborehole flow in solute transport modeling under highly dynamic flow conditions

Correct interpretation of tracer test data is critical for understanding transport processes in the subsurface. This task can be greatly complicated by the presence of intraborehole flows in a highly dynamic flow environment. At a new tracer test site (Hanford IFRC) a dynamic flow field created by changes in the stage of the adjacent Columbia River, coupled with a heterogeneous hydraulic conductivity distribution, leads to considerable variations in vertical hydraulic gradients. These variations, in turn, create intraborehole flows in fully-screened (6.5m) observation wells with frequently alternating upward and downward movement. This phenomenon, in conjunction with a highly permeable aquifer formation and small horizontal hydraulic gradients, makes modeling analysis and model calibration a formidable challenge. Groundwater head data alone were insufficient to define the flow model boundary conditions, and the movement of the tracer was highly sensitive to the dynamics of the flow field. This study shows that model calibration can be significantly improved by explicitly considering (a) dynamic flow model boundary conditions and (b) intraborehole flow. The findings from this study underscore the difficulties in interpreting tracer tests and understanding solute transport under highly dynamic flow conditions.     

Variability of aquifer sorption properties in a field experiment on groundwater transport of organic solutes: Methods and preliminary results

Methods to characterize the organic solute sorption distribution coefficient, organic carbon content, and specific surface area of aquifer solids from the site of a field experiment on solute transport in groundwater were refined for application to small subsamples of 10-cm depth increments taken from 5-cm diameter cores. Initial results indicate that the average sorption characteristics of the Borden aquifer do not vary appreciably along the trajectory of the solute plumes. However, the sorption distribution coefficient of tetrachloroethylene varied over nearly an order of magnitude among 10-cm depth increments in one core sample. Preliminary evidence suggests that the sorption distribution coefficients for four halogenated organic solutes vary proportionally among core strata. However, the distribution coefficients for sorption of tetrachloroethylene on various depth increments are not well correlated with either organic carbon content or specific surface area, suggesting that as yet unidentified mineral phases may play a significant role in sorption of such solutes by the sandy aquifer solids.     

A multi-directional tracer test in the fractured Chalk aquifer of E. Yorkshire, UK

A multi-borehole radial tracer test has been conducted in the confined Chalk aquifer of E. Yorkshire, UK. Three different tracer dyes were injected into three injection boreholes and a central borehole, 25 m from the injection boreholes, was pumped at 330 m(3)/d for 8 days. The breakthrough curves show that initial breakthrough and peak times were fairly similar for all dyes but that recoveries varied markedly from 9 to 57%. The breakthrough curves show a steep rise to a peak and long tail, typical of dual porosity aquifers. The breakthrough curves were simulated using a 1D dual porosity model. Model input parameters were constrained to acceptable ranges determined from estimations of matrix porosity and diffusion coefficient, fracture spacing, initial breakthrough times and bulk transmissivity of the aquifer. The model gave equivalent hydraulic apertures for fractures in the range 363-384 microm, dispersivities of 1 to 5 m and matrix block sizes of 6 to 9 cm. Modelling suggests that matrix block size is the primary controlling parameter for solute transport in the aquifer, particularly for recovery. The observed breakthrough curves suggest results from single injection-borehole tracer tests in the Chalk may give initial breakthrough and peak times reasonably representative of the aquifer but that recovery is highly variable and sensitive to injection and abstraction borehole location. Consideration of aquifer heterogeneity suggests that high recoveries may be indicative of a high flow pathway adjacent, but not necessarily connected, to the injection and abstraction boreholes whereas low recoveries may indicate more distributed flow through many fractures of similar aperture.     

A controlled field experiment on groundwater contamination by a multicomponent DNAPL: dissolved-plume retardation

A natural gradient emplaced-source (ES) controlled field experiment was conducted at the Borden aquifer research site, Ontario, to study the transport of dissolved plumes emanating from residual dense nonaqueous-phase liquid (DNAPL) source zones. The specific objective of the work presented here is to determine the effects of solute and co-solute concentrations on sorption and retardation of dissolved chlorinated solvent-contaminant plumes. The ES field experiment comprised a controlled emplacement of a residual multicomponent DNAPL below the groundwater table and intensive monitoring of dissolved-phase plumes of trichloromethane (TCM), trichloroethylene (TCE), and perchloroethylene (PCE) plumes continuously generated in the aquifer down gradient from gradual source dissolution. Estimates of plume retardation (and dispersion) were obtained from 3-D numerical simulations that incorporated transient source input and flow regimes monitored during the test. PCE, the most retarded solute, surprisingly exhibited a retardation factor approximately 3 times lower than observed in a previous Borden tracer test by Mackay et al. [Water Resour. Res. 22 (1986) 2017] conducted approximately 150 m away. Also, an absence of temporal trend in PCE retardation contrasted with the previous Borden test. Supporting laboratory studies on ES site core indicated that sorption was nonlinear and competitive, i.e. reduced sorption of PCE was observed in the presence of TCE. Consideration of the effects of relatively high co-solute (TCE) concentration (competitive sorption) in addition to PCE concentration effects (nonlinear sorption) was necessary to yield laboratory-based PCE retardation estimates consistent with the field plume values. Concentration- and co-solute-based sorption and retardation analysis was also applied to the previous low-concentration pulse injection test of Mackay et al. [Water Resour. Res. 22 (1986) 2017] and was able to successfully predict the temporal field retardation trends observed in that test. While it is acknowledged that other "nonideal transport" effects may contribute, our analysis predicts differences in the PCE retardation magnitude and trend between the two experiments that are consistent with field observations based on the marked solute concentration differences that resulted from contrasting source conditions. Solute and co-solute concentration effects have heretofore received little attention, but may have wide significance in aquifers contaminated by point-source pollutants because many plumes contain mixed solutes over wide concentration ranges in strata that are likely subject to nonlinear sorption.     

A controlled field experiment on groundwater contamination by a multicomponent DNAPL: creation of the emplaced-source and overview of dissolved plume development

A unique field experiment has been undertaken at the CFB Borden research site to investigate the development of dissolved chlorinated solvent plumes from a residual dense non-aqueous phase liquid (DNAPL) source. The "emplaced-source" tracer test methodology involved a controlled emplacement of a block-shaped source of sand containing chlorinated solvents below the water table. The gradual dissolution of this residual DNAPL solvent source under natural aquifer conditions caused dissolved solvent plumes of trichloromethane (TCM), trichloroethene (TCE) and perchloroethene (PCE) to continuously develop down gradient. Source dissolution and 3-D plume development were successfully monitored via 173 multilevel samplers over a 475-day tracer test period prior to site remediation research being initiated. Detailed groundwater level and hydraulic conductivity data were collected. Development of plumes with concentrations spanning 1-700,000 micrograms/1 is described and key processes controlling their migration identified. Plumes were observed to be narrow due to the weakness of transverse dispersion processes and long due to advection and significant longitudinal dispersion, very limited sorptive retardation and negligible, if any, attenuation due to biodegradation or abiotic reaction. TCM was shown to be essentially conservative, TCE very nearly conservative and PCE, consistent with its greater hydrophobicity, more retarded yet having a greater mobility than observed in previous Borden field tests. The absence of biodegradation was ascribed to the prevailing aerobic conditions and lack of any additional biodegradable carbon substrates. The transient groundwater flow regime caused significant transverse lateral plume movement, plume asymmetry and was likely responsible for most of the, albeit limited, transverse horizontal plume spreading. In agreement with the widespread incidence of extensive TCE and PCE plumes throughout the industrialized world, the experiment indicates such solvent plumes are likely to be highly mobile and persistent, at least in aquifers that are aerobic and have low sorption potential (low foc content).     

Applied tracer tests in fractured rock: Can we predict natural gradient solute transport more accurately than fracture and matrix parameters?

Applied tracer tests provide a means to estimate aquifer parameters in fractured rock. The traditional approach to analysing these tests has been using a single fracture model to find the parameter values that generate the best fit to the measured breakthrough curve. In many cases, the ultimate aim is to predict solute transport under the natural gradient. Usually, no confidence limits are placed on parameter values and the impact of parameter errors on predictions of solute transport is not discussed. The assumption inherent in this approach is that the parameters determined under forced conditions will enable prediction of solute transport under the natural gradient. This paper considers the parameter and prediction uncertainty that might arise from analysis of breakthrough curves obtained from forced gradient applied tracer tests. By adding noise to an exact solution for transport in a single fracture in a porous matrix we create multiple realisations of an initial breakthrough curve. A least squares fitting routine is used to obtain a fit to each realisation, yielding a range of parameter values rather than a single set of absolute values. The suite of parameters is then used to make predictions of solute transport under lower hydraulic gradients and the uncertainty of estimated parameters and subsequent predictions of solute transport is compared. The results of this study show that predictions of breakthrough curve characteristics (first inflection point time, peak arrival time and peak concentration) for groundwater flow speeds with orders of magnitude smaller than that at which a test is conducted can sometimes be determined even more accurately than the fracture and matrix parameters.     

Multi tracer test for the implementation of enhanced in-situ bioremediation at a BTEX-contaminated megasite

At the Centre for Environmental Research Leipzig-Halle (UFZ) research site in Zeitz, Germany, benzene contaminates the lower of two aquifers with concentrations of up to 20 mg/l. Since the benzene plume has a minimum length of approximately 1 km, enhanced natural attenuation measures are being considered as a remediation strategy. This study describes the performance and evaluation of a multi-species reactive tracer test using the tracers fluorescein and bromide as conservative tracers and toluene as reactive tracer. Sampling was performed over a period of six months using a detailed network of multilevel sampling wells. Toluene was only slightly retarded in comparison to bromide, whereas fluorescein was retarded considerably stronger. Therefore, it was not possible to use fluorescein as an in situ tracer for the determination of groundwater velocities. The ionic nature of fluorescein is assumed to be the major reason for its retardation. The results show that the infiltration conditions were suitable to produce a wide spreading of the tracer front along the full thickness of the aquifer. Thus, a large aquifer volume can be treated in future enhanced bioremediation measures. The total quantity of infiltrated toluene (24 l) was degraded under sulfate-reducing conditions over a flow path of 50 m. Benzylsuccinate was identified as a metabolite of toluene degradation under sulfate-reducing conditions at this site. The modelling results show that toluene degradation was described more accurately using Monod kinetics than first-order kinetics. Since toluene was only slightly retarded in comparison to bromide, sorption and desorption processes were considered to be negligible.     

Upscaling heterogeneity in aquifer reactivity via exposure-time concept: forward model

Reactive properties of aquifer solid phase materials play an important role in solute fate and transport in the natural subsurface on time scales ranging from years in contaminant remediation to millennia in dynamics of aqueous geochemistry. Quantitative tools for dealing with the impact of natural heterogeneity in solid phase reactivity on solute fate and transport are limited. Here we describe the use of a structural variable to keep track of solute flux exposure to reactive surfaces. With this approach, we develop a non-reactive tracer model that is useful for determining the signature of multi-scale reactive solid heterogeneity in terms of solute flux distributions at the field scale, given realizations of three-dimensional reactive site density fields. First, a governing Eulerian equation for the non-reactive tracer model is determined by an upscaling technique in which it is found that the exposure time of solution to reactive surface areas evolves via both a macroscopic velocity and a macroscopic dispersion in the artificial dimension of exposure time. Second, we focus on the Lagrangian approach in the context of a streamtube ensemble and demonstrate the use of the distribution of solute flux over the exposure time dimension in modeling two-dimensional transport of a solute undergoing simplified linear reversible reactions, in hypothetical conditions following prior laboratory experiments. The distribution of solute flux over exposure time in a given case is a signature of the impact of heterogeneous aquifer reactivity coupled with a particular physical heterogeneity, boundary conditions, and hydraulic gradient. Rigorous application of this approach in a simulation sense is limited here to linear kinetically controlled reactions.     

Kinematic wave approximation to solute transport along preferred flow paths in soils

A routing procedure is introduced which accounts for the loss of a conservative solute tracer from preferred paths during macropore flow. Water flow is treated as a series of kinematic waves from which the tracer is lost due to mixing previously stored soil water, and an expression for solute loss is added to a previously developed model. The model parameters are estimated through experiments at three different input rates applied to a column of a macroporous forest soil.The results of seven experimental runs indicate that solute losses are consistently highest at the early stages of infiltration and drainage flow. An empirical relationship is proposed which links the frequency distribution of the flow parameter with that for solute loss from the preferred path during transient water flow and solute transport.     

Single-well reactive tracer test and stable isotope analysis for determination of microbial activity in a fast hydrocarbon-contaminated aquifer

Single-well reactive tracer tests, such as the push-pull test are useful tools for characterising in-situ bioattenuation processes in contaminated aquifers. However, the analytical models that are used to interpret push-pull data may be over-simplified, and potentially overlook important processes responsible for the frequent discrepancy between predicted and observed results obtained from push-pull tests. In this study, the limitations underlying the push-pull test methodology were investigated and were supported with results from a push-pull test conducted in a sulphate-reducing aquifer contaminated by crude oil. Poor (<7%) mass recovery was achieved when the push-pull test was performed in a fast-flowing aquifer, preventing a quantifiable reaction rate to be determined. Breakthrough curve data were unexplainable using simplified analytical models, but exhibited trends analogous with tests conducted by others, when >20% mass recoveries were achieved. Push-pull test data collected from sulphate-reducing aquifers indicate that the assumption of a well-mixed batch reactor system is incorrect and that reaction rates obtained from push-pull tests in such systems may be affected by the extraction regime implemented. Evidence of microbial respiration of the reactive tracer was provided by stable sulphur isotope analysis, from which an isotope fractionation factor of +9.9 +/- 8.1 per thousand was estimated. The stable isotope data support the argument that reaction rates calculated using push-pull tests are not uniformly distributed in space and time and are likely to be influenced by heterogeneities in the flow field.     

Linking a one-dimensional pesticide fate model to a three-dimensional groundwater model to simulate pollution risks of shallow and deep groundwater underlying fractured till

The one-dimensional pesticide fate model MACRO was loose-linked to the three-dimensional discrete fracture/matrix diffusion model FRAC3DVS to describe transport of the pesticide mecoprop in a fractured moraine till and local sand aquifer (5-5.5 m depth) overlying a regional limestone aquifer (16 m depth) at Havdrup, Denmark. Alternative approaches to describe the upper boundary in the groundwater model were examined. Field-scale simulations were run to compare a uniform upper boundary condition with a spatially variable upper boundary derived from Monte-Carlo simulations with MACRO. Plot-scale simulations were run to investigate the influence of the temporal resolution of the upper boundary conditions for fluxes in the groundwater model and the effects of different assumptions concerning the macropore/fracture connectivity between the two models. The influence of within-field variability of leaching on simulated mecoprop concentrations in the local aquifer was relatively small. A fully transient simulation with FRAC3DVS gave 20 times larger leaching to the regional aquifer compared to the case with steady-state water flow, assuming full connectivity with respect to macropores/fractures across the boundary between the two models. For fully transient simulations 'disconnecting' the macropores/fractures at the interface between the two models reduced leaching by a factor 24. A fully connected, transient simulation with FRAC3DVS, with spatially uniform upper boundary fluxes derived from a MACRO simulation with 'effective' parameters is therefore recommended for assessing leaching risks to the regional aquifer, at this, and similar sites.     

Use of tracer tests to evaluate the impact of enhanced-solubilization flushing on in-situ biodegradation

Tracer tests were conducted to evaluate the effect of a complexing sugar flush (CSF) on in-situ biodegradation potential at a site contaminated by jet fuel, solvents, and other organic compounds. Technical-grade hydroxypropyl-beta-cyclodextrin was used during the CSF study, which was conducted in a hydraulically isolated cell emplaced in a surficial aquifer. In-situ biodegradation potential was assessed with the use of tracer tests, which were conducted prior to and immediately following the CSF study. Ethanol, hexanol, and benzoate were used as the biodegradable tracers, while bromide was used as a nonreactive tracer. The results indicate that the biodegradation of benzoate was similar for both tracer tests. Conversely, the biodegradation of ethanol (23% increase) and hexanol (41% increase) was greater for the post-CSF tracer test. In addition, analysis of core samples collected from within the test cell indicates that the population density of aerobic jet-fuel degraders increased in the vicinity of the injection wells during the CSF. These results indicate that the cyclodextrin flush did not deleteriously affect the indigenous microbial community. This study illustrates that tracer tests can be used to evaluate the impact of remediation activities on in-situ biodegradation potential.     

Field investigation into unsaturated flow and transport in a fault: model analyses

Results of a fault test performed in the unsaturated zone of Yucca Mountain, Nevada, were analyzed using a three-dimensional numerical model. The fault was explicitly represented as a discrete feature and the surrounding rock was treated as a dual-continuum (fracture-matrix) system. Model calibration against seepage and water-travel-velocity data suggests that lithophysal cavities connected to fractures can considerably enhance the effective fracture porosity and therefore retard water flow in fractures. Comparisons between simulation results and tracer concentration data also indicate that matrix diffusion is an important mechanism for solute transport in unsaturated fractured rock. We found that an increased fault-matrix and fracture-matrix interface areas were needed to match the observed tracer data, which is consistent with previous studies. The study results suggest that the current site-scale model for the unsaturated zone of Yucca Mountain may underestimate radionuclide transport time within the unsaturated zone, because an increased fracture-matrix interface area and the increased effective fracture porosity arising from lithophysal cavities are not considered in the current site-scale model.     

Analytical solution to transport in three-dimensional heterogeneous well capture zones

Solute transport is investigated in a heterogeneous aquifer for combined natural-gradient and well flows. The heterogeneity is associated with the spatially varying hydraulic conductivity K(x, y, z), which is modelled as a log-normal stationary-random function. As such, the conductivity distribution is characterized by four parameters: the arithmetic mean K(A), the variance sigma(Y)(2) (Y=lnK), the horizontal integral scale I of the axisymmetric log-conductivity autocorrelation and the anisotropy ratio e=I(v)/I (I(v) is the vertical integral scale). The well fully penetrates an aquifer of constant thickness B and has given constant discharge QB, while the background aquifer flow is driven by an uniform mean head-gradient, - J. Therefore, for a medium of homogeneous conductivity K(A), the steady-state capture zone has a width 2L=Q/(K(A)|J|) far from the well (herein the term capture zone is used to refer both to the zone from which water is captured by a pumping well and the zone that captures fluid from an injecting well). The main aim is to determine the mean concentration as a function of time in fluid recovered by a pumping well or in a control volume of the aquifer that captures fluid from an injecting well. Relatively simple solutions to these complex problems are achieved by adopting a few assumptions: a thick aquifer B>I(v) of large horizontal extent (so that boundary effects may be neglected), weak heterogeneity sigma(Y)(2)<1, a highly anisotropic formation e<0.2 and neglect of pore-scale dispersion. Transport is analyzed to the first-order in sigma(Y)(2) in terms of the travel time of particles moving from or towards the well along the steady streamlines within the capture zone. Travel-time mean and variance to any point are computed by two quadratures for an exponential log-conductivity two-point covariance. Spreading is reflected by the variance value, which increases with sigma(Y)(2) and I/L. For illustration, the procedure is applied to two particular cases. In the first one, a well continuously injects water at constant concentration. The mean concentration as function of time for different values of the controlling parameters sigma(Y)(2) and I/L is determined within control volumes surrounding the well or in piezometers. In the second case, a solute plume, initially occupying a finite volume Omega(0), is drawn towards a pumping well. The expected solute recovery by the well as a function of time is determined in terms of the previous controlling parameters as well as the location and extent of Omega(0). The methodology is tested against a full three-dimensional simulation of a multi-well forced-gradient flow field test ([Lemke, L., W.B. II, Abriola, L., Goovaerts, P., 2004. Matching solute breakthrough with deterministic and stochastic aquifer models. Ground Water 42], SGS simulations). Although the flow and transport conditions are more complex than the ones pertinent to capture zones in uniform background flow, it was found that after proper adaptation the methodology led to results for the breakthrough curve in good agreement with a full three-dimensional simulation of flow and transport.     

Probability density function of non-reactive solute concentration in heterogeneous porous formations

Available models of solute transport in heterogeneous formations lack in providing complete characterization of the predicted concentration. This is a serious drawback especially in risk analysis where confidence intervals and probability of exceeding threshold values are required. Our contribution to fill this gap of knowledge is a probability distribution model for the local concentration of conservative tracers migrating in heterogeneous aquifers. Our model accounts for dilution, mechanical mixing within the sampling volume and spreading due to formation heterogeneity. It is developed by modeling local concentration dynamics with an Ito Stochastic Differential Equation (SDE) that under the hypothesis of statistical stationarity leads to the Beta probability distribution function (pdf) for the solute concentration. This model shows large flexibility in capturing the smoothing effect of the sampling volume and the associated reduction of the probability of exceeding large concentrations. Furthermore, it is fully characterized by the first two moments of the solute concentration, and these are the same pieces of information required for standard geostatistical techniques employing Normal or Log-Normal distributions. Additionally, we show that in the absence of pore-scale dispersion and for point concentrations the pdf model converges to the binary distribution of [Dagan, G., 1982. Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2, The solute transport. Water Resour. Res. 18 (4), 835-848.], while it approaches the Normal distribution for sampling volumes much larger than the characteristic scale of the aquifer heterogeneity. Furthermore, we demonstrate that the same model with the spatial moments replacing the statistical moments can be applied to estimate the proportion of the plume volume where solute concentrations are above or below critical thresholds. Application of this model to point and vertically averaged bromide concentrations from the first Cape Cod tracer test and to a set of numerical simulations confirms the above findings and for the first time it shows the superiority of the Beta model to both Normal and Log-Normal models in interpreting field data. Furthermore, we show that assuming a-priori that local concentrations are normally or log-normally distributed may result in a severe underestimate of the probability of exceeding large concentrations.