Roko Andričević

Evaluation of Risk from Contaminants Migrating by Groundwater

The general formulation of the environmental risk problem captures the entire process of identifying the source term of the risk agent, its fate and transport through porous media, estimation of human exposure, and conversion of such exposure into the risk level. The contaminant fate and transport is modeled using the solute flux formulation evaluated with its first two moments, which explicitly account for the spatial variability of the velocity field, sorption properties, and parametric uncertainty through the first-order analysis. The risk level is quantified on the basis of carcinogenicity using the risk factor (which describes the risk per unit dose or unit intake) employed to the total doses for individuals potentially consuming radionuclide-contaminated groundwater. As a result of the probabilistic formulation in the solute flux and uncertainty in the water intake and dose-response functions, the total risk level is expressed as a distribution rather than a single estimate. The results indicate that the geologic heterogeneity and uncertainty in the sorption estimate are the two most important factors for the risk evaluation from the physical and chemical processes, while the mean risk factor is a crucial parameter in the risk formulation.

Relative dispersion for solute flux in aquifers

The relative dispersion framework for the non-reactive and reactive solute flux in aquifers is presented in terms of the first two statistical moments. The solute flux is described as a space time process where time refers to the solute flux breakthrough and space refers to the transverse displacement distribution at the control plane. The statistics of the solute flux breakthrough and transversal displacement distributions are derived by analysing the motion of particle pairs. The results indicate that the relative dispersion formulation approaches the absolute dispersion results on increasing the source size (e.g. > 10 heterogeneity scales). The solute flux statistics, when sampling volume is accounted for, show a flattened distribution for the solute flux variance in the space-time domain. For reactive solutes, the solute flux shows a tailing phenomenon in time while solute flux variance exhibits bi-modality in transverse distribution during the recession stage of the solute breakthrough. The solute flux correlation structure is defined as an integral measure over space and time, providing a potentially useful tool for sampling design in the subsurface.

Effects of local dispersion and sampling volume on the evolution of concentration fluctuations in aquifers

The evolution of concentration variance σc2 for conservative solutes in aquifers is presented by accounting for advection heterogeneity, local dispersion, and sampling volume. The concentration variance distribution is obtained by scaling the zero local dispersion form of σc2. The scaling function results from the local dispersion and it is derived in a closed integral form such that it satisfies the measure of total concentration variance, obtained from the Eulerian mass balance using spatially integrated concentration moments. The use of spatially integrated concentration moments avoids the need to apply closing hypothesis on joint moments between velocity and concentration field. This study finds that sampling volume and local dispersion act as a smoothing mechanism on the concentration fluctuations. Contrary to the sampling volume, the smoothing due to the local dispersion is a slow occurring process compared to the advection and increases with transport time. At early stage of transport, the source size, its orientation with respect to the mean flow, and size of the sampling volume are key factors in determining the magnitude of concentration variance. The local dispersion becomes a dominant factor at the later stage and its influence on collected samples is significantly reduced by the presence of sampling volume. The local dispersion dimensionless number is introduced as an indicator for local dispersion importance in modeling the evolution of concentration fluctuations in the subsurface (in the absence of sampling volume). The presented model for concentration variance compares favorably with field data and numerical simulations.

Radionuclide migration using a travel time transport approach and its application in risk analysis

The travel time transport approach for radioactive elements undergoing sorption and decay is employed in assessing the potential health risk at possible locations of human receptors. The principal entity in approach presented is a travel time probability density function conditioned on the set of parameters used to describe different transport processes, like advection, dispersion, sorption, and decay. The importance of accounting for parameter uncertainty and possible correlation between them is described and demonstrated in the study of risk analysis at the Nevada Test Site (NTS), which is located in the southwestern part of the state of Nevada. Because of the lack of sorption, the migration of tritium is found to provide the largest health risk to the accessible environment. Inclusion of the sorption process indicates that the parameter uncertainty and especially negative correlation between the mean velocity and the sorption strength are important in evaluating the arrival time of radionuclides at the prespecified accessible environment. The results from the risk-based screening analysis suggest that tritium, which does not sorb and has a short effective half-life (both physical and biological), is responsible for about 90% of the total risk.

Computational issues in the determination of solute discharge moments and implications for comparison to analytical solutions

Solute discharge moments (mean and variance) are computed using numerical modeling of flow and advective transport in two-dimensional heterogeneous aquifers and are compared to theoretical results. The solute discharge quantifies the temporal evolution of the total contaminant mass crossing a certain compliance boundary. In addition to analyzing the solute discharge moments within a classical absolute dispersion framework, we also analyze relative dispersion formulation, whereby plume meandering (deviation from mean flow path caused by velocity variations at scales larger than plume size) is removed. This study addresses some important issues related to the computation of solute discharge moments from random walk particle tracking experiments, and highlights some of the important differences between absolute and relative dispersion frameworks. Relative dispersion formulation produces maximum uncertainty that coincides with the peak mean discharge. Absolute dispersion, however, results in earlier arrival of the uncertainty peak as compared to the first moment peak. Simulations show that the standard deviation of solute discharge in a relative dispersion framework requires increasingly large temporal sampling windows to smooth out some of the large fluctuations in breakthrough curves associated with advective transport. Using smoothing techniques in particle tracking to distribute the particle mass over a volume rather than at a point significantly reduces the noise in the numerical simulations and removes the need to use large temporal windows. Same effect can be obtained by adding a local dispersion process to the particle tracking experiments used to model advective transport. The effect of the temporal sampling window bears some relevance and important consequences for evaluating risk-related parameters. The expected value of peak solute discharge and its standard deviation are very sensitive to this sampling window and so will be the risk distribution relying on such numerical models.

Modeling ground water flow and radioactive transport in a fractured aquifer.

Three-dimensional numerical modeling is used to characterize ground water flow and contaminant transport at the Shoal nuclear test site in north-central Nevada. The fractured rock aquifer at the site is modeled using an equivalent porous medium approach. Field data are used to characterize the fracture system into classes: large, medium, and no/small fracture zones. Hydraulic conductivities are assigned based on discrete interval measurements. Contaminants from the Shoal test are assumed to all be located within the cavity. Several challenging issues are addressed in this study. Radionuclides are apportioned between surface deposits and volume deposits in nuclear melt glass, based on their volatility and previous observations. Surface-deposited radionuclides are released hydraulically after equilibration of the cavity with the surrounding ground water system, and as a function of ground water flow through the higher-porosity cavity into the low-porosity surrounding aquifer. Processes that are modeled include the release functions, retardation, radioactive decay, prompt injection, and ingrowth of daughter products. Prompt injection of radionuclides away from the cavity is found to increase the arrival of mass at the control plane but is not found to significantly impact calculated concentrations due to increased spreading. Behavior of the other radionuclides is affected by the slow chemical release and retardation behavior. The transport calculations are sensitive to many flow and transport parameters. Most important are the heterogeneity of the flow field and effective porosity. The effect of porosity in radioactive decay is crucial and has not been adequately addressed in the literature. For reactive solutes, retardation and the glass dissolution rate are also critical.

Evaluation of analytical solute discharge moments using numerical modeling in absolute and relative dispersion frameworks

Two-dimensional numerical simulations are used to validate the analytical solutions for the solute discharge moments. In addition to the analysis of classical absolute dispersion we also consider relative dispersion whereby plume meandering (deviation from mean flow path caused by velocity variations at scales larger than plume size) is removed. The numerical simulations are used within a Monte Carlo framework to assess the accuracy and robustness of the analytical predictions of the solute discharge moments (mean and variance). Results show that the analytical predictions deviate from the numerical simulations as the log conductivity variance increases. Deviation occurs for the mean as well as the variance of the solute discharge. The absolute dispersion formulation, however, shows better agreement with the numerical simulations than does the relative dispersion for strong heterogeneity and vice versa for small variability. The relative dispersion results, however, depend on the prediction of the ensemble mean of the plume arrival time, which differs between simulations and analytical solution. Using the first-order analytical estimate for this parameter leads to a much better agreement between the numerical and the analytical results for solute discharge moments in the relative dispersion case.

Evaluation of Sampling in the Subsurface

The evaluation of sampling is presented in the form of a sampling error defined as a difference between the true average and the sampled average of the measured process over the sampling domain. The sampling error is quantified as a product between the process point variance (defined at the scale of a sampling devices support volume) and the sampling variance function, which quantifies the reduction of uncertainty due to the sampling activity. The sampling variance function is expressed analytically as a function of the scale of fluctuation of the measured process. For a single sampling point the sampling variance function defines the reduction in the process point variance as a result of sampling over a certain support volume. The presented evaluation of the sampling performance can be used for designing the monitoring activity and for measurement conditioning of stochastic theories. The presented examples demonstrate the use of sampling evaluation for the purpose of conditioning on the concentration measurements.

Comment on “Stochastic Analysis of the Transport of Kinetically Sorbing Solutes in Aquifers with Randomly Heterogeneous Hydraulic Conductivity” by H. A. M. Quinodoz and A. J. Valocchi

In this comment the alternative probabilistic model for spatial moments of kinetically sorbing solutes was presented. The main advantage of the presented model is the full closed-form solution for general initial conditions which can be extended even for moments higher than second.The only disadvantage is in the accuracy of the first-order approximation in the residence time distribution for very early times. The comparison with the spatial moments obtained by Quinodoz and Valocchi (1993) for the point source case showed consistency in most parts of the transport timescale. The actual limitation of both theories was discussed from the point that they followed a single-particle discplacement concept. It was shown that to compare the stochastic theory, based on a single-particle displacement approach, with field data, either the ergodicity requirement has to be satisfied (very difficult to achive for the kinetically sorbing solutes) or one has to remove the inherent uncertainty in the mean centroid displacement.

Pilot study risk assessment for selected problems at three U.S. Department of Energy facilities

Abstract Objective and realistic human health risk assessments were performed for environmental problems at the Savannah River Site (SRS), the Fernald Environmental Management Project (FEMP), and the Nevada Test Site (NTS). At the SRS, cancer mortality risks were analyzed for projected public exposures to 3 H and 137 Cs released into the Savannah River. For annual human exposures to SRS tritium in Savannah River water, calculated incremental individual lifetime risks in two human receptor populations were small (8×10 −7 ; upper 95 percentile point of the distribution). The 95th percentile point of the distribution for incremental individual lifetime risks from one years exposure to 137 Cs is less than 10 −8 . No deaths are expected in either population as a result of exposures to tritium or cesium released to the Savannah River from the SRS. Routine releases of radon and radon progeny from the K-65 silos at FEMP resulted in individual lifetime risks greater than 1×10 −4 only for onsite workers and fenceline residents. Population risks were less than 1.0 for all identified receptor populations. Assessment of risks from exposure to uranium in ground water released by the FEMP predicted no toxic effects for human receptors. All estimated cancer risks were small. The largest predicted individual lifetime risk was for a well close to the facility (1.3×10 −5 ). For the various above-ground shot sites at the NTS, the highest predicted lifetime cancer risks are for a resident farmer, assuming a loss of institutional control, and exceed 1×10 −4 at the 95th cumulative percentile level. At 50 000 and 100 000 y in the future, the predicted cancer risks are all below 10 −6 . In the assessment of exposure to radionuclides in ground water at the NTS, for an individual onsite near the site boundary, the geometric mean of the maximum potential excess lifetime risk of cancer mortality for an individual is 7×10 −3 . For an individual using water offsite, the geometric mean of the maximum potential excess lifetime risk of cancer mortality is 7×10 −7 .