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At least 163 records · Page 9

Vadose Zone Model for B Plant Area for Composite Analysis

The objectives of the vadose modeling for the updated Hanford Site composite analysis (CA) are to simulate the flow and transport of water and radionuclide releases from the surface to the water table and to provide radionuclide transfer rates for the plateau to river (P2R) model, version 8.3. Water additions include natural recharge and water discharged to the ground as a result of industrial processes associated with Hanford Site operations. Contaminant sources include radionuclides in water discharged to the ground during operations and radionuclides disposed “dry” in solid waste burial grounds or other means. The simulation time starts in 1943 and ends at 12070, which is 10,000 years after assumed Hanford Site closure in 2070. The scope of this ECF is to document the development and results of the B Plant Area vadose zone model. The B Plant Area model encompasses the region around B Plant (221-B) in the western part of 200 East Area. The plant was used to separate plutonium from irradiated fuel using the bismuth-phosphate process from 1945 to 1956, and for strontium and cesium recovery from 1968 to 1985.

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Vadose Zone Model for B-3 Pond for Composite Analysis

The objectives of the vadose modeling for the updated Hanford Site composite analysis (CA) are to simulate the flow and transport of water and radionuclide releases from the surface to the water table and to provide radionuclide transfer rates for the plateau to river (P2R) model, version 8.3. Water additions include natural recharge and water discharged to the ground as a result of industrial processes associated with Hanford Site operations. Contaminant sources include radionuclides in water discharged to the ground during operations and radionuclides disposed “dry” in solid waste burial grounds or other means. The simulation time starts in 1943 and ends at 12070, which is 10,000 years after assumed Hanford Site closure in 2070. The scope of this ECF is to document the development and results of the B-3 Pond vadose zone model. The B-3 Pond model covers the main lobe of the 216-B-3 Pond System located in a topographic low east of the 200 East Area. The pond system operated from 1945 to 1997 and received effluents from the Plutonium Uranium Extraction Plant, B Plant, 284-E Powerhouse, and other 200 East Area facilities.

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Vadose Zone Model for B-3C Pond for Composite Analysis

The objectives of the vadose modeling for the updated Hanford Site composite analysis (CA) are to simulate the flow and transport of water and radionuclide releases from the surface to the water table and to provide radionuclide transfer rates for the plateau to river (P2R) model, version 8.3. Water additions include natural recharge and water discharged to the ground as a result of industrial processes associated with Hanford Site operations. Contaminant sources include radionuclides in water discharged to the ground during operations and radionuclides disposed “dry” in solid waste burial grounds or other means. The simulation time starts in 1943 and ends at 12070, which is 10,000 years after assumed Hanford Site closure in 2070. The scope of this ECF is to document the development and results of the B-3C Pond vadose zone model. The B-3C Pond model covers the 216-B-3C Expansion Pond of the 216-B-3 Pond System located in a topographic low east of the 200 East Area. The pond system operated from 1945 to 1997 and received effluents from the Plutonium Uranium Extraction Plant, B Plant, 284-E Powerhouse, and other 200 East Area facilities.

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Vadose Zone Model for REDOX Ponds Area for Composite Analysis

The objectives of the vadose modeling for the updated Hanford Site composite analysis (CA) are to simulate the flow and transport of water and radionuclide releases from the surface to the water table and to provide radionuclide transfer rates for the plateau to river (P2R) model, version 8.3 (CP-57037, Model Package Report: Plateau to River Groundwater Model, Version 8.3). Water additions include natural recharge and water discharged to the ground as a result of industrial processes associated with Hanford Site operations. Contaminant sources include radionuclides in water discharged to the ground during operations and radionuclides disposed “dry” in solid waste burial grounds or other means. The following 16 radionuclides were selected for this modeling effort: carbon-14 (C-14), chlorine-36 (Cl-36), tritium (H-3), iodine-129 (I-129), neptunium-237 (Np-237), rhenium-187 (Re-187), strontium-90 (Sr-90), technetium-99 (Tc-99), uranium-232 (U-232), uranium-233 (U-233), uranium-234 (U-234), uranium-235 (U-235), uranium-236 (U-236), uranium-238 (U-238), radium-226 (Ra-226), and thorium-230 (Th-230). The simulation time starts in 1943 and ends at 12070, which is 10,000 years after assumed Hanford Site closure in 2070.

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Vadose Zone Model for SALDS for Composite Analysis

The objectives of the vadose modeling for the updated Hanford Site composite analysis (CA) are to simulate the flow and transport of water and radionuclide releases from the surface to the water table and to provide radionuclide transfer rates for the plateau to river (P2R) model, version 8.3 (CP-57037,Model Package Report: Plateau to River Groundwater Model, Version 8.3). Water additions include natural recharge and water discharged to the ground as a result of industrial processes associated with Hanford Site operations. Contaminant sources include radionuclides in water discharged to the ground during operations and radionuclides disposed "dry" in solid waste burial grounds or other means. The following 16 radionuclides were selected for this modeling effort: carbon-14 (C-14), chlorine-36 (Cl-36), tritium (H-3), iodine-129 (I-129), neptunium-237 (Np-237), rhenium-187 (Re-187), strontium-90 (Sr-90), technetium-99 (Tc-99), uranium-232 (U-232), uranium-233 (U-233), uranium-234 (U-234), uranium-235 (U-235), uranium-236 (U-236), uranium-238 (U-238), radium-226 (Ra-226), and thorium-230 (Th-230).

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Vadose Zone Model for T Farms Area for Composite Analysis

The objectives of the vadose modeling for the updated Hanford Site composite analysis (CA) are to simulate the flow and transport of water and radionuclide releases from the surface to the water table and to provide radionuclide transfer rates for the plateau to river (P2R) model, version 8.3 (CP-51031,Model Package Report: Plateau to River Groundwater Model, Version 8.3). Water additions include natural recharge and water discharged to the ground as a result of industrial processes associated with Hanford Site operations. Contaminant sources include radionuclides in water discharged to the ground during operations and radionuclides disposed "dry" in solid waste burial grounds or other means. The following 16 radionuclides were selected for this modeling effort: carbon-14 (C-14), chlorine-36 (Cl-36), tritium (H-3), iodine-129 (1-129), neptunium-237 (Np-237), rhenium-187 (Re-187), strontium-90 (Sr-90), technetium-99 (Tc-99), uranium-232 (U-232), uranium-233 (U-233), uranium-234 (U-234), uranium-235 (U-235), uranium-236 (U-236), uranium-238 (U-238), radium-226 (Ra-226), and thorium-230 (Th-230). The simulation time starts in 1943 and ends at 12070, which is 10,000 years after assumed Hanford Site closure in 2070.

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Vadose Zone Model for B-63 Area for Composite Analysis (Rev. 1)

The objectives of the vadose modeling for the updated Hanford Site composite analysis (CA) are to simulate the flow and transport of water and radionuclide releases from the surface to the water table and to provide radionuclide transfer rates for the plateau to river (P2R) model, version 8.3 (CP-57037, Model Package Report: Plateau to River Groundwater Model, Version 8.3). Water additions include natural recharge and water discharged to the ground as a result of industrial processes associated with Hanford Site operations. Contaminant sources include radionuclides in water discharged to the ground during operations and radionuclides disposed “dry” in solid waste burial grounds or other means. The following 16 radionuclides were selected for this modeling effort; carbon-14 (C-14), chlorine-36 (Cl-36), tritium (H-3), iodine-129 (I-129), neptunium-237 (Np-237), rhenium-187 (Re-187), strontium-90 (Sr-90), technetium-99 (Tc-99), uranium-232 (U-232), uranium-233 (U-233), uranium-234 (U-234), uranium-235 (U-235), uranium-236 (U-236), uranium-238 (U-238), radium-226 (Ra-226), and thorium-230 (Th-230). The simulation time starts in 1943 and ends at 12070, which is 10,000 years after assumed Hanford Site closure in 2070.

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Vadose Zone Model for LLBG-200W A for Composite Analysis

The objectives of the vadose modeling for the updated Hanford Site composite analysis (CA) are to simulate the flow and transport of water and radionuclide releases from the surface to the water table and to provide radionuclide transfer rates for the plateau to river (P2R) model, version 8.3 (CP-57037, Model Package Report: Plateau to River Groundwater Model, Version 8.3). Water additions include natural recharge and water discharged to the ground as a result of industrial processes associated with Hanford Site operations. Contaminant sources include radionuclides in water discharged to the ground during operations and radionuclides disposed “dry” in solid waste burial grounds or other means. The following 16 radionuclides were selected for this modeling effort: carbon-14 (C-14), chlorine-36 (Cl-36), tritium (H-3), iodine-129 (I-129), neptunium-237 (Np-237), rhenium-187 (Re-187), strontium-90 (Sr-90), technetium-99 (Tc-99), uranium-232 (U-232), uranium-233 (U-233), uranium-234 (U-234), uranium-235 (U-235), uranium-236 (U-236), uranium-238 (U-238), radium-226 (Ra-226), and thorium-230 (Th-230). The simulation time starts in 1943 and ends at 12070, which is 10,000 years after assumed Hanford Site closure in 2070.

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Vadose Zone Model for LLBG-200W A for Composite Analysis

The objectives of the vadose modeling for the updated Hanford Site composite analysis (CA) are to simulate the flow and transport of water and radionuclide releases from the surface to the water table and to provide radionuclide transfer rates for the plateau to river (P2R) model, version 8.3 (CP-57037, Model Package Report: Plateau to River Groundwater Model, Version 8.3). Water additions include natural recharge and water discharged to the ground as a results of industrial processes associated with Hanford Site operations. Contaminant sources include radionuclides in water discharged to the ground during operations and radionuclides disposed "dry" in solid waste burial grounds or other means. The following 16 radionuclides were selected for this modeling effort: carbon-14 (C-14), chlorine-36 (Cl-36), tritium (H-3), iodine-129 (I-129), neptunium-237 (Np-237), rhenium-187 (Re-187), strontium-90 (Sr-90), technetium-99 (tc-99), uranium-232 (U-232), uranium-233 (U-233), uranium-234 (U-234), uranium-235 (U-235), uranium-236 (U-236), uranium-238 (U-238), radium-226 (Ra-226), and thorium-230 (Th-230). The simulation time starts in 1943 and ends at 12070, which is 10,000 years after assumed Hanford Site closure in 2070.

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Vadose Zone Model for B-63 Area for Composite Analysis (Rev. 2)

The objectives of the vadose modeling for the updated Hanford Site composite analysis (CA) are to simulate the flow and transport of water and radionuclide releases from the surface to the water table and to provide radionuclide transfer rates for the plateau to river (P2R) model, version 8.3 (CP-57037, Model Package Report: Plateau to River Groundwater Model, Version 8.3). Water additions include natural recharge and water discharged to the ground as a result of industrial processes associated with Hanford Site operations. Contaminant sources include radionuclides in water discharged to the ground during operations and radionuclides disposed “dry” in solid waste burial grounds or other means. The following 16 radionuclides were selected for this modeling effort; carbon-14 (C-14), chlorine-36 (Cl-36), tritium (H-3), iodine-129 (I-129), neptunium-237 (Np-237), rhenium-187 (Re-187), strontium-90 (Sr-90), technetium-99 (Tc-99), uranium-232 (U-232), uranium-233 (U-233), uranium-234 (U-234), uranium-235 (U-235), uranium-236 (U-236), uranium-238 (U-238), radium-226 (Ra-226), and thorium-230 (Th-230). The simulation time starts in 1943 and ends at 12070, which is 10,000 years after assumed Hanford Site closure in 2070.

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BISON Simulated and Experimental Fission Product Release Comparisons from Reradiated AGR-3/4 Compacts During High Temperature Heating Tests

The fuel performance modeling code BISON was used to predict the release of fission products iodine-131 (131I), xenon-133 (133Xe), and krypton-85 (85Kr) from four re-irradiated AGR-3/4 fuel compacts containing tristructural isotropic (TRISO) coated particles during high-temperature isothermal heating tests. The AGR-3/4 fuel compacts were irradiated in the Advanced Test Reactor (ATR) as part of the third and fourth series of planned experiments to support the Advanced Gas Reactor (AGR) Program. They were subsequently stored and re-irradiated in the Neutron Radiography (NRAD) reactor for approximately five days and then stored for another five to eight days before being subjected to isothermal heating tests in the Fuel Accident Condition Simulation (FACS furnace) for 200 to 300 hours at temperatures between 1000°C and 1600°C to evaluate fission product release at elevated temperatures. New nuclide-specific fission product source term models for the three nuclides of interest were developed using the reactor multiphysics code Griffin and implemented into BISON to support this work. The new source term models were incorporated into coupled compact- and particle-scale BISON simulations, which predict spatially- and temporally-resolved radionuclide generation, radioactive decay, transport, and release throughout the entire irradiation history, including the initial ATR irradiation, NRAD re-irradiations, FACS heating tests, and intermediate periods spent in storage. The experimentally measured fission product release from the heating tests were compared to modeling release predictions calculated by BISON to evaluate how well the code compares to experimental results. Overall, the experimental measured and BISON predicted comparative release results varied but generally agreed to within 5 particle equivalents. Comparative release results identified general observations to take into consideration to help refine future models and reduce uncertainties associated with both the measurement results and predictive results. This includes developing new uranium oxycarbide (UCO) specific kernel diffusivities for the three isotopes examined to more accurately reflect the material properties of the fuel form. Deriving new diffusivities will aid in producing a more informed BISON model

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Colloid-facilitated transport of 238 Pu, 233 U and 137 Cs through fractured chalk: Laboratory experiments, modelling, and implications for nuclear waste disposal

The influence of montmorillonite colloids on the mobility of 238 Pu, 233 U and 137 Cs through a chalk fracture was investigated to assess the transport potential for radioactive waste. Radioisotopes of each element, along with the conservative tracer tritium, were injected in the presence and absence of montmorillonite colloids into a naturally fractured chalk core. In parallel, batch experiments were conducted to obtain experimental sorption coefficients (K d , mL/g) for both montmorillonite colloids and the chalk fracture material. Breakthrough curves were modelled to determine diffusivity and sorption of each radionuclide to the chalk and the colloids under advective conditions. Uranium sorbed sparingly to chalk (log K d = 0.7 ± 0.2) in batch sorption experiments. 233 U(VI) breakthrough was controlled primarily by the matrix diffusion and sorption to chalk (15 and 25% recovery with and without colloids, respectively). Cesium, in contrast, sorbed strongly to both the montmorillonite colloids and chalk (batch log K d = 3.2 ± 0.01 and 3.9 ± 0.01, respectively). The high affinity to chalk and low colloid concentrations overwhelmed any colloidal Cs transport, resulting in very low 137 Cs breakthrough (1.1–5.5% mass recovery). Batch and fracture transport results, and the associated modelling revealed that Pu migrates both as Pu (IV) sorbed to montmorillonite colloids and as dissolved Pu(V) (7% recovery). Transport experiments revealed differences in Pu(IV) and Pu(V) transport behavior that could not be quantified in simple batch experiments but are critical to effectively predict transport behavior of redox-sensitive radionuclides. Finally, a brackish groundwater solution was injected after completion of the fracture flow experiments and resulted in remobilization and recovery of 2.2% of the total sorbed radionuclides which remained in the core from previous experiments. In general, our study demonstrates consistency in sorption behavior between batch and advective fracture transport. Finally, the results suggest that colloid-facilitated radionuclide transport will enhance radionuclide migration in fractured chalk for those radionuclides with exceedingly high affinity for colloids.

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Transport processes on the lunar surface - Comparison of model calculations with radionuclides data

Descriptions are given of the experimental methods used in determining Al-26 and Mn-53 activities and of the possible improvements that can be expected in the near future. The results obtained for the seven lunar core sections where both Al-26 and Mn-53 are measured with good depth definition are discussed. It is then shown how meteoritic impacts and the secondary effects they induce modify the Al-26 and Mn-53 activities in a core. Using a Monte Carlo method, 150 possible depositional histories for a core are generated; from these the resulting activity profiles for both Al-26 and Mn-53 are computed, using several possible SCR energy spectra. These model-generated profiles are then compared with the experimental profiles in the seven cores, and plausible scenarios for the depositional history of each of the cores are tentatively inferred.

Langevin, Y.↗

Predicting multiphase flow and tracer transport for an underground chemical explosive test

Detecting radionuclide gas seepage from clandestine underground nuclear tests is central to nonproliferation explosion monitoring research. Yet, early-time (<6 day) gas transport driven by the explosive pressure wave remains poorly constrained due to scarcity of field data. We simulate multi-phase gas transport in the vadose zone using pre-shot data from a recent chemical explosion in P-Tunnel at the Nevada National Security Site, USA. Despite using a simplified 2D-radial model, predictions of tracer arrival matched observations within one order-of-magnitude. Our results show how transient blast forcing rapidly mobilizes gases from the cavity into surrounding rock – critical for optimizing sensor placement and test planning. This unique integration of field data and modeling represents a significant improvement in our ability to predict gas migration from underground explosions. More broadly, it offers insights into the coupled dynamics of pressure waves and contaminant transport in the vadose zone, with implications for monitoring and hazard assessment.

54 ENVIRONMENTAL SCIENCES↗

Characterization of D-T Generator Neutron Flux Spectrum for Cyclic Neutron Activation Analysis Experiments

Improving nuclear data for short-lived fission product yields will further our fundamental understanding of fission, which is needed across various scientific fields and applications. One method of attaining the needed product yield data is through cyclic neutron activation, which allows a target to be irradiated in a neutron environment and then transported for counting of the radionuclides produced, typically via g spectroscopy. Recently, such a system has been constructed and commissioned at Pacific Northwest National Laboratory. Targets are shuttled between the head of a D-T neutron generator and a counting station with a transit time of 2 seconds. As part of the characterization of this system, the neutron flux was studied using two activation targets. The neutron flux from the deuterium-tritium fusion generator was determined to be 9.95(33) x10^8 n/cm2-s with a peak energy of 14.9 MeV and a spread of approximately 4 decades between the epithermal and 14 MeV peak group flux.

cyclic neutron activation, gamma-ray spectroscopy,↗

A Comparison of RESRAD and GoldSim Models for Assessing Radiological Dose for a RCRA Landfill - 20418

US Ecology Idaho (USEI) operates a Resource Conservation and Recovery Act (RCRA) Subtitle C, Hazardous Waste Treatment, Storage, and Disposal (TSD) Facility on a 640-acre property in Owyhee County, Idaho. USEI accepts a wide variety of RCRA-exempt low activity radioactive wastes, including naturally occurring radioactive material (NORM) and technologically enhanced NORM (TENORM) (USEI 2009). The performance of the landfill with regard to radiological operating permit requirements was previously assessed using a model constructed with the residual radioactivity (RESRAD) computer program, developed by Argonne National Laboratory for the U.S. Department of Energy (DOE). RESRAD supports the evaluation of several environmental transport pathways related to a radionuclide-contaminated soil source term, but it was not conceived as a model for the evaluation of landfill radiological performance. A more comprehensive and realistic model is desired in order to better support submissions to both the State of Idaho's Department of Environmental Quality as well as the U.S. Nuclear Regulatory Commission. A Performance Assessment (PA) computer model was developed using GoldSim software for the USEI RCRA Subtitle C landfill. The RESRAD computer model was specifically developed for calculating soil cleanup criteria and radiological dose and cancer risk from residual radioactive material in soil. To evaluate site-specific conditions, users may select from among a number of available environmental transport and exposure pathways and modify 'default' parameter values. In GoldSim, a user must construct the model 'from scratch.' However, this modeling is facilitated by a number of specialized elements available in GoldSim to support a radiological mass transport model. These include elements for defining radiological decay and ingrowth, container failure and radiological release, advective and diffusive transport, and other processes. Advantages afforded by the use of RESRAD for modeling radiological dose for a RCRA Subtitle C landfill include ease of use and reasonable flexibility in specifying site-specific conditions. GoldSim allows for considerably more flexibility and site-specificity than RESRAD, including evaluation of potentially relevant environmental transport processes not supported in RESRAD. The probabilistic modeling capabilities of GoldSim also far exceed those of RESRAD. The pros and cons of RESRAD and GoldSim for this modeling problem are explored with a focus on identifying approaches and critical factors in identifying the appropriate platform. The capabilities of RESRAD and GoldSim for mathematically modeling the disposal system will be contrasted and compared. For example, the existing RESRAD radiological safety assessment evaluated potentially complete exposure pathways related to infiltration to groundwater and upwards diffusion of radon. Additional transport pathways identified in the USEI Idaho facility Conceptual Site Model include deposition of radon decay products in cover material, root uptake of radionuclides in disposed wastes by native plants, and mixing of cover material by burrowing animals. Results of the two models and how the different transport and dose pathways affect results will be discussed. (authors)

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Modeling glass degradation and release of radionuclides from vitrified waste for performance assessment simulations

The release of radionuclides initially encapsulated in a slowly degrading solid waste form and contained in an eventually corroding canister defines the source term for numerical simulations for the assessment of a geologic repository for high-level radioactive waste. While the details of waste degradation, canister corrosion, and dissolution and mobilization of the radionuclides in pore water include complex chemical reaction and transport processes that are coupled to the thermal, hydrological, microbiological, and mechanical conditions in the repository, the source-term model suitable for use in a numerical performance assessment model should be a defensible abstraction of these mechanisms. We developed a radiological source-term model and implemented it into a non-isothermal flow and transport simulator. While the proposed source-term model is applicable to various waste forms, canister systems, and disposal concepts, we specifically considered radionuclide releases from vitrified high-level waste placed in a cylindrical canister disposed in a deep vertical borehole repository. In this model, waste degradation is a function of temperature, and it can be adjusted to evaluate the influence of and propagate uncertainties in pH, passivation reactions, and chemical conditions as well as geometrical factors. The time-dependent, congruent release of safety-relevant radionuclides present in the decaying inventory is then calculated. Finally, the radionuclides are mobilized by diffusive and advective transport according to the thermo-hydraulic conditions prevailing in the near field of the repository, from where they migrate through the geosphere to the accessible environment. We examine the influence of the source-term model’s parameters on performance assessment calculations through sensitivity and uncertainty propagation analyses, identifying influential factors and confirming the upper bound of their impact. These considerations align with the overarching goal of repository design, which is to demonstrate that engineered and natural barriers can collectively delay radionuclide migration for timescales far exceeding human planning, thereby providing multiple, redundant barriers against environmental contamination.

iTOUGH2↗

The Influence of Aqueous Dispersivity on Transport of Radiological Material at LANL MDA G - 20450

Aqueous dispersivity is a phenomenon by which a solute moving in groundwater mixes with water that does not contain the solute and becomes diluted. Solutes take paths of varying lengths through pore networks or experience slower velocities due to interactions with pore walls. Aqueous dispersivity leads to breakthrough curves with earlier arrival than expected in purely advective systems and persistent 'tails,' or late-arriving, dilute concentrations of the solute. Dispersivity can be longitudinal (in the direction of flow) or transverse (orthogonal to flow). LANL has disposed of radioactive material at Material Disposal Area (MDA) G since the late 1950's. Most of the disposed materials at MDA G are low-level waste (LLW), but other types of radioactive wastes are disposed or stored at the site. For example, there is a collection of remote-handled transuranic waste (RH-TRU) waste in 33 shafts, which were intended to be stored retrievably. Aqueous-phase radionuclides included in models of contaminant transport at MDA G are subject to dispersive processes in porous media of the vadose zone and saturated zone. To model dispersivity at MDA G probabilistically, we created site-specific distributions of aqueous dispersivity. First, we performed a comprehensive review of peer-reviewed publications, reports from other performance assessments of MDA G, and documentation from sites that were considered similar based on expert opinion, such as Yucca Mountain. Data were included from a wide range of sources, so that distributions developed based on the data reflect the current state of knowledge in properties of the subsurface environment. Data were grouped based on value type (e.g., determined via experiment or used in a different model), rock type, zone type (saturated or unsaturated), and site, and were weighted in the distributions according to their relevance to the site and zone type. We combined Monte Carlo simulation and bootstrapping techniques to produce approximate distributions of mean aqueous dispersivity. Distributions of dispersivity for saturated and unsaturated zone transport are differentiated by data weight and the length scales over which transport occurs. We find that underestimating or disregarding transverse dispersivity may lead to overstating simulated well capture in the saturated zone at MDA G. Neglecting transverse dispersivity is a common assumption due in part to use of one-dimensional transport models that do not consider solute spreading orthogonal to flow. Also, we find that variability in longitudinal dispersivity is associated with substantial travel time alterations in the MDA G unsaturated zone and in simulated contaminant breakthrough times at a downstream observation plane in the MDA G saturated zone. Finally, at large scales (>1000 m), a linear trend between the dispersivity coefficient and length over which transport occurs may overestimate the dispersivity coefficient. Future modeling work with application to solute spreading could include interacting advective and diffusive zones in the highly fractured basalt below MDA G. (authors)

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