VZJ sign up for citetrack
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

Published online 12 October 2005
Published in Vadose Zone J 4:967-976 (2005)
DOI: 10.2136/vzj2004.0179
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Mayers, C. J.
Right arrow Articles by Michel, R. L.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Mayers, C. J.
Right arrow Articles by Michel, R. L.
GeoRef
Right arrow GeoRef Citation
Agricola
Right arrow Articles by Mayers, C. J.
Right arrow Articles by Michel, R. L.
Related Collections
Right arrow Radionuclides
Right arrow Solute Transport Models

ORIGINAL RESEARCH

Modeling Tritium Transport Through a Deep Unsaturated Zone in an Arid Environment

C. J. Mayersa,*, B. J. Andraskia, C. A. Cooperb, S. W. Wheatcraftc, D. A. Stonestromd and R. L. Micheld

a U.S. Geological Survey, WRD, 333 West Nye Lane, Carson City, NV 89706
b Desert Research Institute, 2215 Raggio Parkway, Reno, NV 89512
c Dep. of Geological Sciences, Univ. of Nevada, Reno, NV 89557
d U.S. Geological Survey, WRD, NRP, 345 Middlefield Road, Menlo Park, CA 94025
* Corresponding author (cjmayers{at}usgs.gov)

Received 17 December 2004.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Understanding transport of tritium (3H) in unsaturated zones is critical to evaluating options for waste isolation. Tritium typically is a large component of low-level radioactive waste (LLRW). Studies at the U.S. Geological Survey's Amargosa Desert Research Site (ADRS) in Nevada investigate 3H transport from a closed LLRW facility. Two boreholes are 100 and 160 m from the nearest waste trench and extend to the water table at 110 m. Soil-water vapor samples from the deep boreholes show elevated levels of 3H at all depths. The objectives of this study were to (i) test source thermal and gas-advection mechanisms driving 3H transport and (ii) evaluate model sensitivity to these mechanisms and to selected physical and hydraulic properties including porosity, tortuosity, and anisotropy. A two-dimensional numerical model incorporated a non-isothermal, heterogeneous domain of the unsaturated zone and instantaneous isotopic equilibrium. The TOUGH2 code was used; however, it required modification to account for temperature dependence of both the Henry's law equilibrium constant and isotopic fractionation with respect to tritiated water. Increases in source temperature, pressure, and porosity enhanced 3H migration, but failed to match measured 3H distributions. All anisotropic simulations with a source pressure component resembled, in shape, the upper portion of the 3H distribution of the nearest borehole. Isotopic equilibrium limited migration of 3H, while effects of radioactive decay were negligible. A 500 Pa pressure increase above ambient pressure in conjunction with a high degree of anisotropy (1:100) was necessary for simulated 3H transport to reach the nearest borehole.

Abbreviations: ADRS, Amargosa Desert Research Site • EOS, equation of state • 3H, tritium • 3HHOg, tritiated water vapor • 3HHOl, tritiated liquid water • LLRW, low-level radioactive waste • MHE, maximum horizontal extent • MVE, maximum vertical extent • PS, source-pressure difference above ambient • TS, source temperature


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
UNDERSTANDING TRANSPORT of 3H in unsaturated zones is critical for evaluating options for waste isolation and tracer study results. Smiles et al. (1995) explored the movement of 3H in liquid and gas phases in a deep unsaturated zone using a spherically symmetric diffusion equation. Simulations predicted 3H migrating <30 m in 100 yr. Because of numerical cancellation errors when applying the analytical solution of Carslaw and Jaeger (1959) to a nonpoint source, Smiles et al. (1995) used a point source to approximate initial conditions. Assuming transient effects of 3H concentration do not persist, Knight (1996) derived a more accurate approximation for the initial conditions and found that the quantity of 3H and its distribution dictated the final 3H distribution. Neither of these studies evaluated the effects of temperature dependence of the Henry's law equilibrium constant or isotopic fractionation with respect to 3H.

Studies at the U. S. Geological Survey's ADRS in Nevada are investigating 3H transport from a closed LLRW facility (Fig. 1) . Striegl et al. (1996) attempted to explain elevated concentrations of tritiated water vapor (3HHOg) found throughout the unsaturated zone at a borehole 160 m from the nearest LLRW trench. They used diffusive (Smiles et al., 1995) and advective transport models to simulate an isothermal and homogeneous domain. The models were unable to match observed 3HHOg concentrations. The diffusive model predicted 3H migration to a maximum distance of approximately 10 m from the source after 30 yr. An order of magnitude increase in the effective diffusion coefficient increased the maximum distance by a factor of three. The advective model used a pressure originating from the source. Striegl et al. (1996) determined a 1300 Pa source-pressure-difference sustained for 30 yr was required to move the 3H 100 m, but were unable to justify a source-pressure-difference >100 Pa. Ultimately, a conceptual model of lateral subsurface liquid transport from LLRW trenches was developed as a possible explanation for the observed high concentrations of 3H in the unsaturated zone. However, Striegl et al. (1996) stated that it was not clear how this flow could have occurred and cited previous work at the site that showed no evidence of significant liquid water movement in the subsurface. Thus, the elevated 3H concentrations in the deep and shallow unsaturated zone at the ADRS (Striegl et al., 1996; Healy et al., 1999) have caused speculation regarding the exact mechanisms that control 3H transport in arid unsaturated zones.



View larger version (35K):
[in this window]
[in a new window]
  		Fig. 1. Location map showing the Amargosa Desert Research Site (ADRS) and the low-level radioactive waste (LLRW) facility near Beatty, NV.

 
This study combined field data and numerical modeling to further investigate 3H transport in the deep unsaturated zone at the ADRS. The objectives were to (i) test source thermal and gas-advection mechanisms driving tritium transport and (ii) evaluate model sensitivity to these mechanisms and to selected physical and hydraulic properties including porosity, tortuosity, and anisotropy. Laboratory and field data allowed for conceptualization of flow processes, parameterization of the model, and evaluation of simulation results. The numerical model incorporated a non-isothermal, heterogeneous domain. The TOUGH2 code (Pruess et al., 1999) was used; however, it required modification to account for temperature dependence of both the Henry's law equilibrium constant and isotopic fractionation with respect to tritiated water.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Field Site and Data Collection
The field site is located 17 km south of Beatty and 169 km northwest of Las Vegas (Fig. 1). The unsaturated zone at the ADRS is approximately 110-m thick and comprises alluvial and fluvial deposits. Annual precipitation (1981–2002) averages 105 mm. The unsaturated zone at the ADRS has been drying for approximately 16 000 yr (Scanlon et al., 2003; Walvoord et al., 2004).

The LLRW facility buried waste from 1962 to 1992 in a series of 22 shallow trenches (Fig. 2) . Trenches ranged from 2 to 15 m deep. Before burial, LLRW underwent dewatering or solidification. A 1976 U.S. Nuclear Regulatory Commission (USNRC) investigation, however, indicated that liquid wastes delivered to the LLRW facility between 1962 and 1975 were disposed of directly into the trenches (USNRC, 1976). Steps for burial of LLRW included excavating and stockpiling native sediments and emplacing waste and stockpiled sediments in layers. The LLRW trenches were not lined. During the operational life of the facility, trench covers were kept free of vegetation. Following closure of the LLRW facility a minimum of 2 m of stockpiled native sediments was used to cover all trenches.



View larger version (25K):
[in this window]
[in a new window]
  		Fig. 2. Low-level radioactive waste facility, chemical waste facility, and deep unsaturated zone boreholes.

 
Samples from three unsaturated-zone boreholes (UZB-1, UZB-2, and UZB-3) were analyzed for water content, bulk density, and particle-size; two boreholes (UZB-2 and UZB-3) were instrumented for collection of soil gas samples. Boreholes UZB-1 and UZB-2 are approximately 6-m apart and 160 m from the nearest LLRW trench (Prudic et al., 1997); UZB-3 is approximately 100 m from the nearest LLRW trench (Fig. 2). Boreholes UZB-1, UZB-2, and UZB-3 were drilled to depths of 48 m, 114.6 m, and 114.4 m in November 1992, September 1993, and December 1999, respectively. Water contents were measured by cryodistillation (Prudic et al., 1997). Particle-size distributions were determined by sieving and laser-light scattering (Gee and Or, 2002). Soil-water vapor sampling was based on methods discussed in Striegl (1988). The first soil-water vapor sampling at UZB-2 and UZB-3 began in April 1994 and April 2000, respectively; subsequent sampling occurred annually. Tritium concentrations were measured by direct liquid-scintillation counting (Thatcher et al., 1977).

Numerical Model
The TOUGH2 code solves a nonlinear mass balance equation for all components included in the equation of state (EOS) module and an energy-balance equation for the system. The EOS7R module allows for the following components: water, brine, radionuclide 1 "parent," radionuclide 2 "daughter," and air. The van Genuchten-Mualem model (van Genuchten, 1980; Mualem, 1976) was used to calculate relative permeability and capillary pressure:

[1]

[2]
with

[3]
and

[4]
where krl is relative permeability as a function of water content; Pcap is capillary pressure; {rho} is density of water; g is gravity; {theta} is volumetric water content; {theta}r is residual water content; {theta}s is saturated water content; {psi} is pressure head; and {alpha}, n, and m are curve fitting parameters subject to m = 1 – n–1 and 0 < m < 1. The Corey (1954) gas relative permeability function used is

[5]
with

[6]
where krg is gas relative permeability, and {theta}rg is residual gas content. The diffusive flux equation is

[7]
where f{kappa}ß is diffusive flux of component {kappa} in phase ß (liquid or gas), {phi} is porosity, {tau}0 is a porous medium dependent factor of tortuosity, {tau}ß is a tortuosity coefficient dependent on phase saturation, {rho}ß is phase density, d{kappa}ß is diffusion coefficient of component {kappa} in phase ß, and X{kappa}ß is mass fraction of component {kappa} in phase ß. The Millington model (Millington, 1959) used to calculate the saturation-dependent tortuosity is

[8]
where Sß is phase saturation. The temperature and pressure dependent diffusion coefficient (Vargaftik, 1975) is

[9]
where P is pressure, T is temperature, P0 = 101 325 Pa, T0 = 0°C, and {vartheta} is the temperature dependence which is 1.8. Radioactive decay allows radionuclide 1 to decay into radionuclide 2.


[10]
where M{kappa} is mass of radionuclide {kappa} per unit volume, t is time, and {lambda}{kappa} is the decay constant of radionuclide {kappa}.

To more accurately test 3H transport mechanisms, the TOUGH2 code was modified to include temperature effects on the gas and liquid partitioning of 3H. A function was coded to account for temperature effects on both the Henry's law equilibrium constant and the isotopic fractionation factor for tritiated water:

[11]
with

[12]
where HCRN1 is solubility constant of 3HHOg in water, kH–3H is a temperature dependent Henry's law equilibrium constant for tritiated water, {alpha}3HHO is a temperature dependent fractionation factor for tritiated water, Cg is concentration of 3H in water vapor, Caq is concentration of 3H in liquid water, and R is the ideal gas constant. Fractionation values for 3H were obtained from Ferronsky and Polyakov (1982).

A single source trench was used to represent the 22 trenches at the LLRW facility (Fig. 3) . The total volume of the LLRW trenches is approximately 7.35 x 105 m3 and the greatest trench depth is 15 m below land surface. The three western-most trenches contain approximately 90% of 3H disposed at the LLRW facility (Fig. 2) (Nevada State Health Division, unpublished data, 1992). The model simulated a representative 1-m wide vertical slice of the source trench along the A–A' transect. Projected onto the modeled slice for reference are the relative locations of the UZB-2 and UZB-3 boreholes (Fig. 3). A total 3H radioactivity of approximately 1.27 x 1016 Bq (Nevada State Health Division, unpublished data, 1992) and an assumed backfill and LLRW water content of 0.05 m3 m–3 resulted in a source-trench concentration of 3.46 x 108 Bq L–1.



View larger version (24K):
[in this window]
[in a new window]
  		Fig. 3. Plan view of conceptualized source trench and 600-m transect, A–A'.

 
The model domain extended 585, 1, and 115 m in the x, y, and z directions, respectively (Fig. 4a) . Due to the dimensions of the LLRW trenches and the close proximity of the area of interest to the trenches, the computational grid used Cartesian coordinates. The domain incorporated 2796 cells and the vertical grid spacing ranged from 1 to 4 m, while horizontal grid spacing ranged from 5 to 50 m. Cells close to the source trench and at lithologic contacts had a closer spacing.



View larger version (33K):
[in this window]
[in a new window]
  		Fig. 4. (a) Computational grid and (b) lithology of modeled vertical slice along A–A' transect shown in Fig. 3. Locations of unsaturated zone boreholes UZB-2 and UZB-3 are included for reference (see Fig. 3).

 
Physical and hydraulic property data and other information defined a lithologic model of the site (Fig. 4b). Detailed data available for the upper 5 m of undisturbed sediments and for trench fill material (Andraski, 1996; Andraski and Jacobson, 2000) formed the basis for material properties assigned to the reference model (Table 1). Drillers' logs, gamma logs, particle-size distribution data, air permeability data, a profile description (Fischer, 1992), and photographs of a 20-m deep hazardous waste trench were used to define sediment layers below 5 m. Textural similarities formed the basis for assignment of properties of a sediment layer in the upper 5 m to a deeper sediment layer. Three distinct sediment types defined a layered model and included gravel, sandy gravel, and silty sand with gravel. The top of the water table was defined at 110 m below land surface.


View this table:
[in this window]
[in a new window]
  		Table 1. Material properties of reference model.{dagger}

 
Initial conditions for the reference model were generated using a steady-state simulation. The steady-state simulation used approximations for the two boundary conditions, land surface and 5 m below the water table (Table 2). Temperatures assigned at the land surface and 5 m below the water table were projected from mean daily thermocouple psychrometer data collected for 3 yr (2000–2002) between depths of 10.9 and 103.7 m. Gas-phase pressure at the land surface was based on a 3-yr mean daily of barometric pressure (1998–2000). Gas-phase pressure 5 m below the water table was a hydrostatic value (110 m of air and 5 m of water). Gas saturation at the land surface was based on average measured water potentials (–4 MPa) under native vegetation (Andraski, 1997) and the corresponding soil–water content that was calculated using the van Genuchten (1980) retention model. These boundary conditions resulted in steady-state temperature, pressure, and water content profiles shown in Fig. 5 . The steady-state water content profile generated was, on whole, comparable in shape to the observed profile, but on average was 0.06 m3 m–3 drier.


View this table:
[in this window]
[in a new window]
  		Table 2. Model parameters and reference model boundary conditions.

 


View larger version (32K):
[in this window]
[in a new window]
  		Fig. 5. Simulated steady state temperature, gas phase pressure, and water content profiles.

 
The transport simulation boundaries were: land surface, 5 m below the top of the water table, vertical boundary under the source trench (Fig. 4a, horizontal distance = 0 m), vertical boundary away from the source trench (Fig. 4a, horizontal distance = 585 m), and the horizontal and vertical faces of the source trench. All boundaries in the transport simulations had prescribed thermodynamic conditions except for the vertical axis of symmetry underneath the source trench, which was defined as a no flux boundary. In addition, the prescribed boundaries along the faces of the source trench allowed the initial 3H concentration to diminish by radioactive decay.

Overview of Model Assumptions and Numerical Simulations
All model simulations ran for 40 yr (1962–2002), which allowed comparison with field data collected from 1994 to 2002. Assumptions included instantaneous emplacement of LLRW at time = 0 yr and instantaneous isotopic equilibrium between the gas and liquid phases. The assumption of local equilibrium between aqueous and airborne species is consistent with theory given that in beaker-scale experiments, substantive equilibrium is attained on time scales of minutes (Logan, 1996). The rate-limiting step is diffusion in the liquid phase, and pore-scale liquid dimensions are small. Failure of the local equilibrium assumption would allow tritiated water vapor to move more quickly than theory predicts. Simulations used a maximum time step of 1 yr to avoid time discretization errors that occur when time steps approach the half-life of the simulated radionuclide. In addition to the reference model (described above), simulations were performed with variations in source temperature (TS), source-pressure difference above ambient (PS), material properties (porosity, tortuosity, anisotropic ratios of intrinsic permeability), and various combinations of TS, PS, and material properties (Table 3).


View this table:
[in this window]
[in a new window]
  		Table 3. Summary of simulations.

 
The similarities between LLRW facilities and municipal landfills formed the basis for increased temperatures and pressures in the source trench. The LLRW trenches are unlined and the final covers are monolithic; however, they contain waste similar in type to waste buried at municipal landfills that is radioactive (Crawford and Smith, 1985; Fentiman et al., 1993). The temperatures and pressures within municipal landfills increase as a function of organic biodegradation. Lacking direct measurements from the LLRW facility, temperature, and pressure values were obtained from landfill literature. Temperatures within municipal landfills range from 25 to 45°C and gas pressures range from 250 to 500 Pa above atmospheric pressure (Crawford and Smith, 1985). The TS values tested included 35 and 45°C. The PS values tested were 100, 250, and 500 Pa. The source trench in the reference model had an average temperature of 22°C and average pressure of 9.18 x 104 Pa; temperatures and pressures based on initial conditions varied with depth. Striegl et al. (1996) did not consider biodegradation in the LLRW facility and estimated 100 Pa to be the maximum justifiable pressure difference at ADRS due to temperature and buoyancy effects. Combinations of TS and PS values also were tested and included simulations with a TS of 45°C and PS of 100, 250, and 500 Pa.

Model sensitivity to porosity was tested by setting material porosities to half the original porosity and twice the original porosity. The TOUGH2 code uses relative saturation for mass balance and flow processes, and the mass of the water present in the flow field was scaled appropriately for specified changes in porosity. In both cases, steady-state simulations were run to generate the associated initial conditions. Porosity-sensitivity testing included simulations run under reference model, TS, PS, and TS and PS conditions.

The saturation dependence of tortuosity is poorly understood (Pruess et al., 1999). Given this uncertainty and a reference model simulation using the Millington (1959) tortuosity model, simulations also were run using a relation in which the saturation dependence of tortuosity is based on relative permeability (Pruess et al., 1999),

[13]
where krß is a saturation-dependent relative permeability in phase ß and {tau}0 is subject to the restriction 0 < {tau}0 ≤ 1.0. Model sensitivity to tortuosity was tested by setting tortuosity values to 0.66 and 0.99 for all materials. Tortuosity-sensitivity testing included simulations run under reference model, TS, PS, and TS and PS conditions.

Because of the nature of the alluvial and fluvial sediment deposition at the ADRS, it is likely that permeability is anisotropic with greater permeability along the horizontal plane. Saturated hydraulic conductivity and soil-water retention curves from repacked cores formed the basis for estimating the intrinsic permeability values of all materials (Andraski, 1996). The reference model had isotropic intrinsic permeability values for all materials. Model sensitivity to anisotropy was tested using two anisotropy ratios, 1:10 and 1:100. Freeze and Cherry (1979) state that it is not uncommon for layered heterogeneity to lead to regional anisotropy on the order of 1:100 or greater. Anisotropy-sensitivity included simulations run under reference model, TS, PS, and TS and PS conditions. The source-trench in all simulations remained an isotropic material, due to the homogeneity of the fill material after excavating and backfilling operations.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Field Data
Volumetric water content ranged from 0.05 to 0.14 m3 m–3 (Fig. 6a) . The average water content was 0.09 m3 m–3 above 40 m and 0.12 m3 m–3 below 40 m. Low water contents at the ADRS were a result of differences in thermal vapor conductivity and liquid hydraulic conductivity of up to five orders of magnitude (Andraski and Jacobson, 2000) indicating that vapor transport is dominant in the unsaturated zone.



View larger version (28K):
[in this window]
[in a new window]
  		Fig. 6. (a) Water content at boreholes UZB-1, UZB-2, and UZB-3. Concentration profiles of tritiated water vapor (3HHOg) in units of Bq kg–1 of water in the gas phase at (b) UZB-3 borehole and (c) UZB-2 borehole for selected years (1994 data from Prudic and Striegl, 1995; 1998 data from Prudic et al., 1999).

 
Measurements indicate elevated 3HHOg concentrations throughout the unsaturated zone 100 and 160 m away from the nearest LLRW trench (Fig. 6b and Fig. 6c, respectively). Concentrations of 3HHOg are reported in units of Bq kg–1 of water in the gas phase. All concentrations of 3HHOg at the two boreholes are substantially greater than background concentrations (≤3.0 Bq kg–1). Concentrations of 3HHOg for 2000, 2001, and 2002 at the UZB-3 borehole ranged from 97 to 2704 Bq kg–1 (Fig. 6b). Temporal changes in 3HHOg concentrations vary with depth. For example, the average coefficient of variation within a depth interval over time was 10% above 40 m and 29% below 40 m. High concentrations of 3HHOg at 1.5 m coincide with a coarse gravel layer. A large "diffusive-shaped" bulge from 5 to 35 m consists of a cluster of high concentration depth intervals with a maximum 3HHOg concentration of 1113 Bq kg–1 at a depth of 23.8 m. The bulge crosses several layers of gravel and sandy gravel. Concentrations of 3HHOg for 1994, 1998, and 2002 at the UZB-2 borehole ranged from 16 to 1729 Bq kg–1 (Fig. 6c). The average coefficient of variation within a depth interval over time was 37% above 40 m and 85% below 40 m. High concentrations of 3HHOg at 1.5 and 47.9 m coincide with coarse gravel layers in the unsaturated zone. The tritiated liquid water (3HHOl) concentration of a groundwater sample from UZB-2 in September 1993 was below detection (<0.36 Bq kg–1 of water in the liquid phase). A groundwater sample collected from UZB-3 in March 2000 had a 3HHOl concentration of 0.45 Bq kg–1 of water in the liquid phase.

The UZB-3 and UZB-2 3HHOg profiles are similar in the shallow subsurface and differ at depth. Localized surface spills and the LLRW trenches may constitute two different sources of 3HHOg. A near-surface spill may be the cause of concentration peaks at 1.5 m in both profiles (Andraski et al., 2005). The difference in 3H distributions at depth for the two profiles indicates two different paths from the LLRW trenches may exist. The close proximity to the 15-m deep trenches may explain the diffusive profile present at UZB-3. A vertical transport path beneath the LLRW facility and then lateral transport through the thick, coarse gravel layer at 50 m may explain the deep UZB-2 profile.

Model Results
Reference Model Simulation Results
The reference model incorporated steady-state conditions previously generated assuming no waste. Initially all 3H was assigned to the source trench. The extent of simulated transport was evaluated based on the maximum distance that the leading edge of the 3HHOg plume (defined as 1 Bq kg–1 of water in the gas phase) traveled from the horizontal and vertical faces of the source trench. At time = 40 yr, the reference model simulated 3HHOg migration to a maximum horizontal extent (MHE) of 27 m from the vertical face of the source trench and a maximum vertical extent (MVE) of 18 m from the bottom of the source trench (Fig. 7) . The extent and overall shape of the reference model 3HHOg transport did not match the field data (Fig. 7 and Fig. 6b and 6c, respectively). Compared with the 30-yr model results of Striegl et al. (1996), the reference model increased the horizontal and vertical extents by about 17 and 8 m at time = 30 yr, respectively. Discrepancies between the two model results possibly are because of differences in steady-state water saturations and because a more complex model was used that accounts for temperature effects on the Henry's law equilibrium constant and the isotopic fractionation factor with respect to tritiated water.



View larger version (23K):
[in this window]
[in a new window]
  		Fig. 7. Simulated tritiated water vapor (3HHOg) concentrations in units of Bq kg–1 of water in the gas phase for the reference model simulation at time = 40 yr. Simulated 3HHOg concentration of 1 Bq kg–1 migrated to a maximum horizontal extent (MHE) of 27 m from the vertical face of the source trench and a maximum vertical extent (MVE) of 18 m from the bottom of the source trench.

 
Tritium migrated by diffusion in both the liquid and gas phases. Gas-phase diffusion of 3H dominated due to the low water content of sediments. The average effective-vapor-phase diffusivity (1.9 x 10–5 m2 s–1) was six orders of magnitude larger than the average effective-liquid-phase diffusivity (4.0 x 10–11 m2 s–1). The majority of the 3HHOg migration occurred in the first 10 yr, during which it traveled approximately 82% of the total MHE and MVE simulated at time = 40 yr. The decline in migration rate after time = 10 yr was due to a decreasing 3H concentration gradient at the leading edge of the plume.

Instantaneous isotopic equilibrium was the primary reason the concentration gradient decreased with time. The amount of 3HHOg was very small when compared to the nonradioactive liquid water in the soil matrix. Thus, the liquid water in the soil matrix acted as a large sink for 3H, which in turn, substantially reduced the rate and extent of 3HHOg migration.

Summary of Simulation Results
A summary of the maximum extent of the 3H transport as 3HHOg for TS, PS, and anisotropy simulations is shown in Fig. 8 .



View larger version (17K):
[in this window]
[in a new window]
  		Fig. 8. Summary of simulated tritium (3H) transport as tritiated water vapor (3HHOg) in units of Bq kg–1 showing the effects of source temperature (TS), source-pressure difference above ambient (PS), and anisotropy on the maximum horizontal extent (MHE) from the vertical face of the source trench and the maximum vertical extent (MVE) from the bottom of the source trench at time = 40 yr. The leading edge of the plume was defined as the concentration of 3HHOg = 1 Bq kg–1 of water in the gas phase.

 
Relative to the reference model, both of the isotropic, increased TS (35 and 45°C) simulations enhanced the transport of 3HHOg (Fig. 8). However, the TS values tested were insufficient to enable 3HHOg to reach either borehole. Henry's law equilibrium constant and isotopic fractionation, with respect to 3H, are temperature dependent. An increased temperature resulted in more 3H partitioning into 3HHOg and allowed 3HHOg to migrate further because of the dominance of gas diffusion. The temperature fields generated (not shown) extended less in the horizontal direction than in the vertical direction. The horizontal component was limited by the close proximity of the source trench to the land surface boundary condition (21.8°C) which facilitated rapid heat transfer from the sediments adjacent to the vertical face of the source trench to the surface.

All of the isotropic, increased PS (100, 250, and 500 Pa) simulations enhanced the migration of 3HHOg (Fig. 8). However, the PS values tested were insufficient to enable 3HHOg to reach either borehole. The pressure effect was greater in the horizontal direction due to the greater permeability of the gravel layers in contact with the vertical edge of the source trench, which in turn increased gas velocities in these layers. The pressure gradients generated for the three isotropic PS simulations (not shown) were steepest in the horizontal direction away from the source trench due to the close proximity of the land surface boundary condition. Gas velocities in the horizontal direction (averaged over a distance of 15 m) ranged from 2.8 x 10–6 to 1.0 x 10–5 m s–1. In contrast, gas velocities in the vertical direction (averaged over a distance of 15 m) ranged from 1.0 x 10–6 to 5.3 x 10–6 m s–1.

All of the isotropic, increased TS-and-PS combination simulations enhanced the migration of 3HHOg (Fig. 8). However, the TS-and-PS combinations tested were insufficient to enable 3HHOg to reach either borehole. The combined effects of TS and PS were additive, yielding a 3HHOg field that extended further in the horizontal direction than in the vertical direction. The TS component affected both the horizontal and vertical transport of 3HHOg, whereas the PS component primarily affected the horizontal transport of 3HHOg.

To further evaluate the code modification (Eq. [11] and Eq. [12]), all of the aforementioned simulations were run without the code modification. Results showed the code modifications substantially affected all isotropic simulations that incorporated an increased TS. For example, average MHE and MVE increases of 12 and 24%, respectively, were realized in modified code simulations with an increased TS. In contrast, in simulations without an increased TS, the modified code yielded average MHE and MVE increases of 1 and 1%, respectively.

The porosity simulations yielded little change in the MHE and MVE of the 3HHOg field generated (not shown). One effect of changing the porosity was in the temperature field, which resulted in a small concomitant change in the 3HHOg field. Changing the porosity did not affect the ratio of gas and liquid in the pores; however, the relative soil solid to pore volume did change which resulted in an altered temperature field. Another effect of changing the porosity was the change in the liquid water available for 3H exchange. An increase in water content resulted in more 3H partitioning into the liquid water and a diminished rate of 3HHOg transport. The porosity factor of 0.5 and 2 simulations generated 3HHOg fields that were within 6 and 4 m of their unadjusted counterparts, respectively.

All of the tortuosity simulations based on the relative permeability model slightly increased the MHE and MVE of 3HHOg migration when compared to the Millington (1959) tortuosity model (not shown). This occurred because the relative permeability model used a tortuosity factor of 0.66 or 0.99, whereas the Millington (1959) model resulted tortuosity factors that ranged from 0.57 to 0.69 with an average tortuosity factor of 0.61 (upper 30 m of the unsaturated zone). However, even with a tortuosity factor of 0.99 the enhancement was small. The simulations using a tortuosity factor of 0.66 and 0.99 resulted in increased maximum extents of the 3HHOg fields up to 2 and 6 m of their unadjusted counterparts, respectively. The relatively small effect of tortuosity appears to be due to the dominant effect of instantaneous isotopic equilibrium on the extent of 3H migration.

The anisotropic simulations increased the MHE and MVE of the 3HHOg migration (Fig. 8). The anisotropic MHE increased by as much as 86 m, whereas the largest MVE increase was 3 m when compared to isotropic counterparts at time = 40 yr. Changing the intrinsic permeabilities affected the simulated pressure fields and enhanced 3HHOg transport in the horizontal direction, but did not affect the simulated temperature fields. Changes in TS did influence the anisotropic simulations with increased temperature fields leading to a preferential migration of 3HHOg in the vertical vs. horizontal direction. Two of the 1:100 anisotropic simulations [PS 500 Pa; TS 45°C and PS 500 Pa combination (Fig. 8)] allowed the 3HHOg to migrate a horizontal distance equivalent to that necessary to reach the UZB-3 borehole. Although the simulated 3HHOg plumes extended past UZB-3, the simulated concentrations were a fraction of the measured concentrations shown in Fig. 6b.

An additional simulation was completed to evaluate the effect of radioactive decay on the maximum extent of the 3HHOg transport. The simulation was anisotropic (1:100), TS 45°C, PS 500 Pa and 3H was not allowed to decay. The 3HHOg field generated at time = 40 yr (not shown) had a MHE of 123 m and a MVE of 31 m; these values were only slightly greater ( <2 m) than those for the same simulation that allowed 3H to decay. Thus, radioactive decay was not a limiting factor in the transport of 3HHOg.

Representative "Shape" of Simulated 3HHOg Fields
Results of selected simulations shown in Fig. 9 illustrate variations in the "shape" of the simulated 3HHOg fields. The shape of the 3HHOg field for the TS 45°C simulation (Fig. 9a) reflects diffusive transport enhanced by TS. Relative to the reference model simulation (Fig. 7), the MHE and MVE of the 3HHOg field increased 5 and 6 m at time = 40 yr, respectively. The shape of the 3HHOg field for the PS 500 Pa simulation (Fig. 9b) was similar to that for the TS 45°C simulation (Fig. 9a), but the MVE was smaller. Relative to the reference model, the MHE and MVE of the 3HHOg field increased 12 and 3 m at time = 40 yr, respectively. The combined effects of TS and PS for the isotropic TS 45°C and PS 500 Pa simulation were additive (Fig. 9c). Relative to the reference model, the MHE and MVE of the 3HHOg field increased 15 and 9 m at time = 40 yr, respectively. The simulated 3HHOg fields shown in Fig. 9a, Fig. 9b, and Fig. 9c not only failed to transport 3HHOg to the UZB-3 and UZB-2 boreholes, but did not resemble the measured profile at either UZB-3 or UZB-2 (Fig. 6b and Fig. 6c, respectively).



View larger version (24K):
[in this window]
[in a new window]
  		Fig. 9. Simulated tritiated water vapor (3HHOg) concentrations in units of Bq kg–1 of water in the gas phase at time = 40 yr for (a) source temperature (TS) 45°C simulation [maximum horizontal extent (MHE) = 32 m and a maximum vertical extent (MVE) = 24 m], (b) source-pressure difference above ambient (PS) 500 Pa simulation (MHE = 40 m and MVE = 21 m), (c) TS 45°C and PS 500 Pa simulation (MHE = 42 m and MVE = 28 m), and (d) anisotropic (1:100), TS 45°C, and PS 500 Pa simulation (MHE = 121 m and MVE = 31 m). The MHE and MVE values are based on a simulated 3HHOg concentration of 1 Bq kg–1.

 
The 3HHOg field generated for the anisotropic (1:100) TS 45°C and PS 500 Pa simulation (Fig. 9d) resembled the upper portion of the UZB-3 3HHOg profile (Fig. 6b). Relative to the reference model, the MHE and MVE of the 3HHOg field increased 94 and 13 m at time = 40 yr, respectively. Increasing the horizontal intrinsic permeability resulted in greater 3HHOg transport in the horizontal direction. The anisotropy allowed the pressure imposed at the source trench to escape laterally instead of creating an increased vertical pressure gradient beneath the source trench. This preferential flow enabled 3HHOg to migrate further away from the source trench. All of the anisotropic simulations generated 3HHOg fields that resembled the near surface profiles measured at the UZB-3 3HHOg borehole (Fig. 6b). The simulations showed increased 3HHOg concentrations between land surface and a depth of 46 m, with a peak concentration at approximately 18 m. In contrast with the field data (Fig. 6b and Fig. 6c); however, none of the simulated 3HHOg fields showed vertical migration of 3HHOg below 46 m.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
Field data for water content and concentrations of tritiated water vapor (3HHOg) in the 100-m deep unsaturated zone indicate that 3H movement primarily occurs in the gas phase with preferential transport through coarse-textured sediment layers. The UZB-3 and UZB-2 borehole profiles have the highest concentrations at a 1.5-m depth that correspond with a dry, coarse-gravel layer. At depth, the shapes of the two profiles differ considerably. The high 3HHOg concentrations at UZB-3 (100 m from the nearest LLRW trench) are seen as a bulge between 5 and 35 m. The bulge crosses several layers of sandy gravel and gravel. In contrast, the high 3HHOg concentration at UZB-2 (160 m from the nearest LLRW trench) is present at a single sampling depth, 47.9 m, which is within an individual gravel layer.

All isotropic simulations were insufficient to transport 3HHOg to distances that would reach one or both of the boreholes. The inability to transport 3HHOg resulted from a decreasing concentration gradient because of instantaneous isotopic equilibrium between the liquid and vapor phases. In the reference model simulation, the dominant transport mechanism was diffusion in the gas phase. Code modification incorporating the temperature dependence of both the Henry's law equilibrium constant and fractionation with respect to tritiated water was important in realizing the effects of increased TS. All of the elevated TS simulations enhanced the migration of 3HHOg because the increased temperature field allowed more 3H to partition into 3HHOg. All of the increased source-pressure-difference (PS) simulations enhanced the migration of 3HHOg. The enhancement was greater in the horizontal direction because of the contact between the source trench and the near surface gravel layers. The combined effects of TS and PS were additive, yielding a 3HHOg field that extended further in the horizontal direction than in the vertical direction. The temperature component affected both the horizontal and vertical transport of 3HHOg, whereas the pressure component primarily affected the horizontal transport of 3HHOg. Changes in porosity and tortuosity had little affect on transport of 3HHOg.

The anisotropic simulations showed the greatest enhancement of 3HHOg transport. The horizontal component increased substantially (5–86 m) whereas the vertical component increased only slightly (0–3 m) when compared to the equivalent isotropic simulations. All of the anisotropic simulations with a PS component generated 3HHOg fields that resembled the upper portion (5–50 m) of the measured UZB-3 3HHOg profile. Simulation results indicated that a high degree of anisotropy (1:100) in conjunction with a PS component of 500 Pa was necessary for 3HHOg to reach the UZB-3 borehole.

None of the simulations in this study were able to reproduce observed 3HHOg profiles. Simulations showed that radioactive decay did not limit the migration of 3HHOg. However, isotopic equilibrium in which liquid water in the soil matrix acted as a large sink for the 3HHOg appeared to be a major limiting factor in the migration of 3HHOg. The failure to match simulated 3H profiles to measured profiles is likely due to insufficiencies in the conceptual model. A process that has not yet been accounted for may be driving 3H transport in the deep unsaturated zone. Possible mechanisms driving 3H transport that need to be explored include coupled transport of 3H and volatile organic compounds and the effects of barometric pumping. Additional fieldwork is also needed to better quantify permeabilities and anisotropy.


   ACKNOWLEDGMENTS
 
The authors gratefully acknowledge the Nevada State Health Division for providing unpublished data; M.J. Johnson for his assistance in sample collection; D.E. Prudic for helpful discussions; and M.L. Strobel, K.J. Halford, J.R. Nimmo, E.P. Weeks, and anonymous reviewers for helpful comments on the manuscript.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 





This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Mayers, C. J.
Right arrow Articles by Michel, R. L.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Mayers, C. J.
Right arrow Articles by Michel, R. L.
GeoRef
Right arrow GeoRef Citation
Agricola
Right arrow Articles by Mayers, C. J.
Right arrow Articles by Michel, R. L.
Related Collections
Right arrow Radionuclides
Right arrow Solute Transport Models

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
The SCI Journals Agronomy Journal Crop Science
Journal of Natural Resources
and Life Sciences Education		 Soil Science Society of America Journal
Journal of Plant Registrations Journal of
Environmental Quality		 The Plant Genome