- Soil Science Society of America
Wastes buried at the Radioactive Waste Management Complex (RWMC) of the Idaho National Engineering and Environmental Laboratory (INEEL) include activated metals that release radioactive 14C as they corrode. To test and refine transport predictions that describe releases to the environment with time, we conducted a series of transport experiments with nonreactive gas- and aqueous-phase tracers and inorganic 14C species in a large unsaturated soil column filled with sediment representative of that at the RWMC. The tracer tests, hydraulic measurements, and chemical monitoring provided constraints on physical transport parameters, water content, and aqueous–gas partitioning behavior. With those constraints, we estimated a solid–aqueous distribution coefficient for the sediment through inverse modeling of the 14C transport data, using both a simple gas-diffusion model and a multiphase flow and transport simulator (STOMP). Results indicate that 14C transport in this system is well described by a reactive gas diffusion model, with a pH-dependent retardation factor. Fitting transport simulations to the early-time transport data yielded Kd ≈ 0.5 ± 0.1 mL g−1, while soil samples removed approximately 1 yr later yielded Kd values of 0.8 to 2.4 mL g−1. These values are consistent with those derived from smaller-scale experiments, demonstrating that laboratory-based measurements provide a valid means of estimating transport behavior at much larger spatial and temporal scales. Assuming that 14CO2 migration in the RWMC is dominated by gas transport, our results suggest that most 14C released from the RWMC would discharge to the atmosphere rather than to the underlying Snake River Plain aquifer.
- DIC, dissolved inorganic carbon
- INEEL, Idaho National Engineering and Environmental Laboratory
- LLW, Low-Level Waste
- RWMC, Radioactive Waste Management Complex
- SDA, Subsurface Disposal Area
- STOMP, Subsurface Transport Over Multiple Phases [model]
Radioactive carbon released as 14CO2 from wastes emplaced in unsaturated sediments can be transported in both gaseous and dissolved form and may thus impact the overlying atmosphere and underlying groundwater. Analysis of 14C release rates to both those receptors is a concern at the INEEL, where radioactive wastes buried within the RWMC include an estimated 18.5 TBq of 14C (McCarthy et al., 2000) and 14C has been identified as a significant dose contributor relative to the RWMC's performance objectives as a Low-Level Waste (LLW) disposal facility (Case et al., 2000; McCarthy et al., 2000).
Carbon-14 within the RWMC (Fig. 1) is located within the Subsurface Disposal Area (SDA), a 39-ha disposal site where solid radioactive waste has been buried in soil vaults, pits, and trenches, and covered with fine-grained material excavated from a nearby playa. A radiological performance assessment completed in 2000 (McCarthy et al., 2000) conservatively assumed that all 14C released from the SDA would migrate downward, with infiltrating soil moisture, to eventually reach the Snake River Plain aquifer. Conversely, in assessing atmospheric exposures, all 14C was assumed to migrate upward in the gas phase. In addition to these extreme simplifications of transport processes, the assessment also did not consider the effect of partitioning between aqueous and solid phases during liquid transport.
To provide data for more realistic modeling of 14C releases from the SDA, and thereby provide a stronger scientific basis for regulatory decisions, we conducted a series of transport experiments with conservative gas and liquid tracers as well as 14C. Parameters for contaminant transport modeling are typically based on laboratory bench-scale experiments. In this case, to test the ability of unsaturated flow and transport models to predict 14C behavior at larger scales, and to determine flow and transport parameters from measurements at much larger spatial and temporal scales, we conducted the experiments in a large column filled with the same sediment used as cover material at the SDA. Such mesoscale transport experiments are rarely conducted because of the considerable costs and long time periods involved, but are a valuable means of testing transport models at a scale approximating field conditions with control not possible in the field. In this case, the transport parameters derived from these mesoscale experiments should provide a good basis for predictive modeling of 14C transport from the SDA.
Wastes in the SDA are emplaced in a layer of surficial sediment, approximately 2 to 9 m thick, that accumulated in a depression in the basalt flow–covered landscape. Unsaturated fractured basalt, with intermittent aeolian and alluvial interbeds, underlies the fill material and extends to the water table of the Snake River Plain aquifer, which lies about 180 m below the surface (Anderson and Lewis, 1989) at the RWMC. Carbon-14 in the buried waste is primarily contained in activated metals associated with discarded reactor components, where 14C was produced by neutron bombardment of 13C and 14N. These activated metals corrode in the subsurface, slowly releasing 14C that is rapidly oxidized to form 14CO2. Understanding 14C transport from the wastes is therefore primarily a problem of understanding 14CO2 transport.
In arid and semiarid regions, water content in the unsaturated zone is generally low, and CO2 transport occurs primarily by gaseous diffusion, a phenomenon that has been extensively studied (Sheppard et al., 1994). Under these conditions, as Thorstenson et al. (1983) have pointed out, 14CO2 diffuses in response to its own concentration gradient, independent of the concentration gradient of 12CO2 or 13CO2. Differences in the diffusion rates of these isotopes are negligible when considering their independent movement, so 14CO2 transport can be described as CO2 transport. In partially saturated media, the greater fraction of available CO2 is commonly present in dissolved form, as bicarbonate ion. Carbon dioxide transport models typically account for this partitioning into the aqueous phase (Thorstenson et al., 1983) as well as the attendant transport of the dissolved inorganic C (DIC) species (Ross, 1988; Simunek and Suarez, 1993). The distribution of C between CO2, DIC, and solid carbonate is typically described using the thermodynamic constraints for calcite equilibria (Thorstenson et al., 1983). Dissolved carbonate species may interact with the solid matrix in a number of ways that act to retard its movement, including anion sorption and dissolution–precipitation reactions (Simunek and Suarez, 1993; Striegl and Healy, 1990). Isotopic fractionation during these exchanges is, again, negligible (Lu and Ross, 1994) compared with the isotope concentration differences arising from their different origins. While interactions with the solid matrix may be negligible in some conditions (Striegl and Armstrong, 1990), or neglected to provide conservative transport predictions (Lu and Ross, 1994), the inability of carbonate equilibrium transport models to match the observed retardation of downward moving 14CO2 in the unsaturated zone (Thorstenson et al., 1983; Striegl and Healy, 1990) suggests that these phenomena are important. Indeed, several studies of 14CO2 retention have demonstrated that the mass retained by the solid phase can be large compared with other reservoirs for C exchange in the unsaturated zone (Martin, 1991; Striegl and Armstrong, 1990; Garnier, 1985), including the quantity of DIC determined by carbonate equilibria.
Because the surficial fill materials represent the first barrier to gas and liquid transport out of the SDA, one of the primary goals of this study was to develop and test parameters that characterize the transport of 14C in that material. These include contaminant-specific factors, such as aqueous–gas and solid–aqueous partitioning parameters, as well as factors that describe more general controls on the advective and diffusive transport of gaseous and liquid contaminants. Although these parameters could be determined via laboratory-scale experiments, the attendant size restrictions greatly restrict the number of details of the subsurface environment that can be incorporated in a single experiment. Instead, we sought to design a system that would allow us to examine 14C transport behavior at relatively large spatial and temporal scales and at infiltration rates and soil moisture conditions at least broadly representative of those at the SDA. To capture some of the geochemical characteristics of the SDA subsurface, we also sought a system that could incorporate the primary natural control on the partitioning of carbonate species between gas and aqueous phases—microbial respiration and the subsequent redistribution of microbially generated CO2. Soil gas around waste disposal trenches at the SDA where organic debris has been disposed can be as high as 10% CO2 by volume (Hull and Bishop, 2003), which yields a significantly lower pH than typically exists in arid environments with sediments that contain calcite.
MATERIALS AND METHODS
To meet these requirements, we conducted a set of transport experiments in a 2.9-m-tall, 0.91-m-diam. column filled with the same sediment that is used as cover material at the SDA. Also used for studies of C cycling and actinide transport, the column contains an active colony of microbes that consume natural soil organic matter and O2 and respire CO2, producing an approximately exponential increase in CO2 concentration with depth. The column thus provides a relatively large physical model of vadose-zone flow at the SDA that allows monitoring of gas- and liquid-phase transport over relatively long distances and also includes significant variability in the geochemical conditions that have a major influence on carbonate partitioning.
Before conducting a transport experiment with 14C, we performed a set of experiments in the mesoscale column to examine the movement of water, gas, and conservative solute through the sediment. These experiments included an infiltration test; injections of a highly insoluble gas, sulfur hexafluoride, both before and after the transient infiltration period; and an injection of a conservative liquid tracer, lithium bromide, after reaching a quasi-steady-state flow regime. Data from these experiments were used to estimate characteristics of the unsaturated flow system that would affect transport of 14C, including average linear seepage velocity, dispersivity, and gas- and liquid-phase tortuosity. Combining those parameters with calculated aqueous–gas and estimated aqueous–solid partitioning ratios for 14C, we then used the multiphase, multicomponent, flow and transport model, STOMP (Subsurface Transport Over Multiple Phases; White et al., 1995), to design a 14C injection experiment that would be used to improve our estimates of 14C-specific transport characteristics of the SDA sediments. The subsequent transport test involved injection of a 14C-labeled bicarbonate solution.
The mesoscale column is a 0.91-m-diam., 2.9-m-tall, stainless-steel cylinder (Fig. 2) sealed at both ends. The column contains approximately 1.7 m3 of sediment that extends from the bottom of the column to a height of 2.6 m. The headspace above the sediment is sealed at the top with a sheet of Plexiglas and is connected to a gas monitoring and flow control system. Ambient air is circulated through the headspace at a rate of 7 L min−1. This circulation system prevents accumulation of CO2 and provides a constant concentration boundary condition at the sediment surface for gas-phase components. The column is instrumented at 30.5-cm (1-ft) intervals along its length at vertical positions denoted as Levels 1 through 8. Instrumentation includes four tensiometers, four water content reflectometers (Model 615, Campbell Scientific, Logan, UT), 10 sampling lysimeters, eight gas-sampling ports, and six thermocouples (Fig. 2 and 3) . The reflectometers measure water content using time-domain measurement methods. Water content is a critical parameter in gas transport modeling, and field studies have demonstrated that the CS-615 reflectometers can provide dependable and accurate data for at least several years (Delin and Herkelrath, 1999). Seyfried and Murdock (2001) found that the coefficient of variation in water content measurements using the CS-615 reflectometers is <0.05. In addition to monitoring hydraulic head and/or moisture potential at five different levels in the column, we tracked column water balance via periodic measurements of the column inflow, effluent mass, mass removed for liquid sampling, and evaporative loss from the column surface. The latter was calculated from relative humidity measurements of ambient air and column headspace, combined with headspace sweep rate.
The column is fitted with three separate injection arrays capable of injecting gas or liquid. Each of these comprises 24 stainless-steel tubes (1.6-mm i.d.) that can deliver fluid to evenly spaced locations in a horizontal plane within the column. The uppermost array lies on the sediment surface and supplies influent water. The two remaining arrays are situated within the sediment, 1.07 and 1.98 m above the bottom. Solutions for aqueous-phase transport experiments were injected into the middle array (1.98-m height) to minimize nonuniform flow effects due to the periodic application of water at the surface.
A system of 24 syringe-pump-fed tubes applies water to the sediment surface at intervals of 40 min. The applied water is synthetic vadose zone water, formulated to approximate the composition of natural infiltrating soil moisture at the SDA (Table 1). To limit microbial growth, the water is sterilized by autoclaving and treated with ultraviolet radiation immediately preceding application. Water application began on 11 July 2001, at a Darcy flux of about 0.6 cm d−1. After the wetting front reached the effluent lysimeters at the bottom of the column, the flux density was reduced to 0.15 (±4%) cm d−1 and held at that rate for the remainder of the experiment. To withdraw the infiltrating water, constant tension was applied to four 0.05-MPa (0.5-bar) suction lysimeters located in a horizontal plane about 15 cm above the bottom. Thus, near steady-state hydraulic conditions in the column are maintained through application of a consistent flux at the top of the column and constant moisture potential in the lysimeters.
The sediment used in the column is the same as that used as cover at the SDA—surficial sediments from playas adjacent to the SDA. In the Unified soil classification system, the sediment is a calcareous silty-clay. X-ray diffraction analysis indicates that the sediment is 50 to 75% quartz, 10 to 25% plagioclase and K-feldspar, 10 to 20% clay minerals, <5% olivine and pyroxene, <5% calcite and <5% Fe. The fine grain size fraction (<75 μm) is generally 40 to 55% quartz, 30 to 45% clay minerals, 5 to 10% plagioclase and K-feldspar, 5 to 10% calcite, and 5% iron oxides, with trace amounts (<5%) of gypsum and other minerals. Mixed smectite–illite constitutes 50 to 70% of the clay minerals, and kaolinite, illite, and Ca-rich smectite comprise the remaining fraction.
The sediment was obtained from a berm near the SDA, mixed using a backhoe, and passed through a 1.25-mm sieve into 208-L drums for transport to the mesoscale column. The sieved sediment was transferred to the column using 19-L plastic buckets; the weight of each bucket was recorded. The sediment was manually compacted in 15-cm lifts, with bulk density determined following placement of each lift. When the desired density was verified, the lift surface was scarified to avoid layering or segregation by particle size, and the next lift was placed. In situ sensors and sampling devices were positioned on scarified surfaces. At the conclusion of the packing process, the mean bulk density was 1.31 ± 0.05 g cm−3, and mean volumetric water content was between 14 and 16%. The column was then allowed to sit open to the atmosphere for about 2 yr before initiation of the experiments described herein. Calibrated reflectometer measurements made just before the application of water to the column surface indicated that the average volumetric water content of the sediment at the start of this experimental program was approximately 10%. Mass balance monitoring of water content began with the initiation of water flow, and the initial water content for those calculations is based on those reflectometer measurements.
Experiments to Determine General Flow and Transport Parameters
Gas diffusion in porous media is highly dependent on water content because of the nonlinear relationship between gas-filled pore space and tortuosity. Previous experiments at the INEEL (Hull and Hohorst, 2001) with air-dry sediments in small laboratory columns indicated that the reduction in the free-air diffusion coefficient due to tortuosity may be slightly greater in SDA sediments than is described by the commonly used Millington equation (Millington, 1959). To evaluate the relationship between water content and gas diffusivity in the mesoscale column, we conducted four sulfur hexafluoride injection experiments: before water was applied to the column, on 16 Mar. and 4 Apr. 2001, and under near steady-state flow conditions, on 24 Apr. and 7 June 2002. In each test, 10 mL of SF6 were injected into the lower injection array, between Levels 3 and 4. Injections were made with five 10-cm3 disposable syringes connected to five of the 24 injection tubes, selected to distribute the gas evenly over the injection plane. Concentrations of SF6 were then monitored at the eight gas sampling ports until concentrations approached background levels.
To estimate average seepage velocities under the established flow regime, we injected a lithium bromide solution at the upper injection plane (between Levels 6 and 7) on 22 Mar. 2002. The injection consisted of 240 mL of a 9.89 mg L−1 bromide solution, delivered into the 24 injection tubes via gravity flow from 24 10-mL syringes. On 12 Aug. 2002, approximately 5 mo after the Br− tracer test, we injected 2850 mL of a solution containing 60 MBq 14C (as radio-labeled bicarbonate) at the upper injection plane. To minimize disturbance of the flow field and water chemistry, water for the solution was taken from the column itself, withdrawn from lysimeters directly above and below (Levels 6 and 7) the injection plane during the 10-d period preceding the injection. Using a 125-mL Pyrex syringe to inject 120 g of solution into each of the 24 injection tubes, we emplaced the solution over a period of 4.5 h.
Sampling and Analysis
Following each injection, breakthrough curves of the introduced species were monitored at the downstream ports and in the column headspace through sampling and analyses specific to that species. For steady-state flow, aqueous transport experiments, soil water samples were collected using 0.05-MPa (0.5-bar) semiporous stainless-steel lysimeters. Lysimeter tubing was flushed before sample collection and 15 to 25 mL of porewater was removed from each lysimeter, depending on the number of analyses required. Bromide concentrations were measured with a Dionex DX-500 ion chromatograph (Dionex Corp., Sunnyvale, CA); 14C activity was measured via liquid scintillation counting (Beckman LS6000LL, Beckman Coulter, Fullterton, CA). For experiments involving gas-phase transport, gas-sample chambers and tubing were first purged with sample gas. Approximately 500 mL of soil gas was then withdrawn from each sampling level (similar tests at different sampling intervals, and numerical modeling experiments, indicated that these withdrawals had a negligible effect on gas movement). Sulfur hexafluoride concentrations were withdrawn using an automated 12-channel switching device and analyzed with an attached INNOVA 1312 gas analyzer (INNOVA, Ballerup, Denmark). Gas samples for 14C analysis were collected in Tedlar bags containing an aliquot of 0.5 M NaOH solution, and the 14C activity of the gas samples was determined via liquid scintillation counting of the NaOH solution after equilibration.
Flux of 14C from the surface of the column was determined by measuring the cumulative activity of CO2 captured in a 2 M NaOH trap solution through which a split of the head-gas airflow was directed. Calculated trap efficiency was 96% (±1.4%) after a sample collection period of approximately 7 d. At the end of each collection period, the trap weight was recorded, sample aliquots were taken, and the trap solution was refreshed. Head-gas 14C flux was reported as averages of three aliquot determinations. Aliquot weight and isotope activity were combined with CO2 trap efficiency, trap weight, and head-gas split ratio to calculate isotope flux for the period of sampling.
RESULTS AND DISCUSSION
Wetting History and Hydraulic Parameters
Water flow in the column was initiated on 11 July 2001 (Fig. 4) , and water content reflectometers at the lowermost (Level 1) sampling plane detected the wetting front approximately 80 d later (Fig. 4A). At that time, the application rate at the surface was reduced to obtain a steady-state flow of about 0.15 cm d−1. A corresponding sharp increase and subsequent decline in water content was recorded at each of the reflectometers, although instrument response during that time is to some extent inaccurate due to leaching and advection of dissolved salts with the wetting front, which temporarily raised salt concentrations beyond the reflectometer calibration range. We note that the lowermost reflectometer (Level 1) sometimes recorded water contents exceeding the porosity of the sediment and was generally inconsistent with the tensiometer data (Fig. 4B). We therefore considered it only a relative measure of saturation.
The combined reflectometer, tensiometer, and mass balance data (Fig. 4C) indicated that water content in the column reached a near steady-state condition approximately 100 d after flow was initiated, at a volumetric water content of approximately 30%. Although the suction applied to the lysimeters at the base of the column was held nearly constant after that time, the total flux from the lysimeters varied slightly through time, presumably due either to changes in the conductivity of the lysimeters or to subtle changes in the potential gradient and hydraulic conductivity of the sediment. Despite these variations, the cumulative mass balance indicated that volumetric water content remained effectively constant (30 ± 1%) for the entire period during which the transport experiments were conducted. This was generally consistent with the reflectometer data, which, despite several apparent shifts in electrical response, indicated that average water content was consistently maintained in the range of 27 to 30%.
As a third check on water content, we removed two small (5-cm-long, 5-cm-diam.) soil cores from Levels 2 and 8 on 13 Mar. 2002. Moisture content determinations on these samples were 27 and 24%, respectively, slightly lower than indicated by the mass balance and reflectometer data. Finally, on 29 July 2003, vertical cores (4.5-cm diam.) were obtained from six locations along a transect of the column's surface, to a depth (76 cm) that intersected the instrument plane at Level 6. Results of water content determinations on subsamples of those cores taken from the plane of Level 7 yielded an average water content of 26% with a standard deviation of 1%, a value that is within the uncertainty of that measured at the Level 7 reflectometer (28 ± 2%) just before sampling.
Sulfur hexafluoride migrated rapidly through the column following injection, with peak concentrations arriving at the nearest ports (Levels 3 and 4) between 0.5 and 2 h (Fig. 5) . An approximately linear concentration gradient, from the bottom of the column toward the top, generally developed within about 2 d. Maximum late-time SF6 gas concentrations are significantly higher in the second set of tests, under the higher water content associated with the quasi-steady-state flow conditions. This reflects the increased concentration gradient that develops in response to the resultant reduction in gas diffusivity.
Sulfur hexafluoride movement within the column occurs primarily by gas diffusion, the transport equations for which are analogous to those for heat transport. For unidirectional transport, in a system with effectively uniform gas-filled porosity, the applicable continuity expression is 1where Cg is the volumetric gas concentration, τ is the gas-phase tortuosity, and Dm is the free-air diffusion coefficient for the diffusing gas. The gas tracer tests we conducted are essentially equivalent to the introduction of an instantaneous pulse of heat to the interior of an infinite plate, with a no-flux boundary on one side and a constant temperature on the other. An infinite-series type analytical solution for this asymmetric diffusion problem is described in Luikov (1968) and we used that solution to analyze the SF6 data.
In the unsaturated zone, diffusion is strongly controlled by the fraction of the total pore space available for gas movement, due to the nonlinear relationship between fluid tortuosity and fluid saturation (Jury et al., 1991). We chose to use the well-known Millington equation (Jury et al., 1991) to describe that relationship and used the data from the SF6 gas tracer tests to test the applicability of that equation to the SDA sediments. The Millington expression for gas-phase tortuosity is 2where φg is the volumetric air content and φT is the total porosity. While the commonly used Millington expression for tortuosity employs the value 7/3 (2.33) for the exponent, m, several studies have suggested other values for that parameter (Sallam et al., 1984; Jury et al., 1991). In small-column studies using air-dry sediment, Hull and Hohorst (2001) found that a value of 2.6 best described SF6 diffusion in INEEL SDA sediments. In this study, we used the value recommended by Millington (1959) and the analytical solution to Eq.  to perform a least-squares fit of computed breakthrough curves to observed breakthrough curves for all of the eight gas ports and for gas injections conducted both before and after the application of water. Using saturation as a fitting parameter, this analysis indicated an initial water content of 11% and a steady-state flow water content of 25%, values that agree relatively well with the other, more direct, measures of water content. The coefficient of determination for that fit, which includes eight sets of breakthrough curves measured at two different water contents, was 0.86. Comparison of the observed breakthrough curves with those computed with the analytical solution (Fig. 5) demonstrates that the diffusion model, even with the assumption of uniform water content, provides a very accurate description of SF6 transport behavior. Additional least-squares analyses of the data, constraining m or water content, or both, did not provide a significantly improved fit to the data, and we concluded that the standard Millington equation adequately describes gas-phase tortuosity in the SDA sediments.
The primary difference between calculated and observed SF6 concentrations is that the calculated values produced nearly identical early-time responses at sampling levels equidistant from the injection point, while the actual test resulted in significantly higher concentrations at the lower port of each pair of equidistant ports. This phenomenon is evident in data from both the preinfiltration and postinfiltration injections but is significantly greater in the latter. Because the difference is accentuated under wetter conditions, these results may reflect an increase in gas diffusivity with depth, reflecting decreased water content with proximity to the suction lysimeters. Although it could also be related to the effects of gas density on SF6 diffusion, preliminary experiments with a simulator that incorporates gas density-driven diffusion suggested that those effects are negligible.
Bromide breakthrough curves at all ports below the injection plane are well fit (Fig. 6) by a solution to the advection–dispersion equation for equilibrium transport of a slug of conservative solute, 3where Cl is the concentration of solute in the liquid phase, D is the coefficient of hydrodynamic dispersion, and υ is the advective transport velocity. Using CXTFIT2 (Toride et al., 1995) to estimate seepage velocity and hydrodynamic dispersion coefficients by fitting analytical solutions to the observed breakthrough curves at each port, resulting R2 values had a mean of 0.97 and standard deviation of 0.04 (Table 2). While anion exclusion is commonly observed to produce a two-region type of breakthrough curve in Br− transport experiments, we observed no such effect in these data, and fitting calculations using a nonequilibrium type transport solution to the advection–dispersion equation did not provide significantly improved fits. Consistent with column design, and despite column size, the Br− breakthrough curves indicate that flow is effectively one-dimensional. Average linear seepage velocities (ν) calculated using CXTFIT2 were between 0.46 and 0.55 cm d−1, with the maximum velocity calculated from the Level 3 data and the minimum from the first level below the injection plane (Level 6). Interpreted as differences in average water content of the sediment between injection plane and sampling point, this suggests an average water content of 28 ± 3%. This range agrees well with reflectometer data, the mass balance data, and the gravimetric determinations made in March 2002. Although temporal variations in water content could also explain some of the implied water content variability, the reflectometer and mass balance data indicate that water content was relatively constant throughout our experiments. Dispersion coefficients calculated via CXTFIT2 ranged from 0.4 to 0.7 cm2 d−1 (Table 2), with the largest value little more than double the tortuosity-corrected molecular diffusion coefficient for Br−. Calculated dispersivities were effectively negligible, ranging from 0 to 7 mm. This is consistent with the results of Hull and Hohorst (2001), who conducted saturated Br− and tritium transport tests with SDA sediment in 31-cm columns and found that dispersivity, α, was on the order of 0.5 mm.
Carbon-14 Results and Transport Modeling
Gas-phase 14C breakthrough curves (Fig. 7) at virtually all levels in the column display the same characteristic shape as the SF6 curves, but lagged, consistent with gas diffusion–dominated transport retarded by exchanges with other phases. Carbon-14 concentrations at the nearest ports, for example, peaked after approximately 1 d, as opposed to about an hour for SF6. On the basis of these results, we analyzed data from the 14C experiment using two different methods. Given the similarity to the SF6 test results, we used the analytical solution to the same diffusion problem to examine the fit of that model to the 14C transport test. To incorporate aqueous transport effects and spatially and temporally variable transport parameters in a multiphase flow and transport model that could be later extended to SDA transport problems, we also developed a model of the column using the air–water mode of the numerical simulator, STOMP. The applied version uses linear partitioning functions to distribute solute mass between gaseous, aqueous, and solid phases, and accounts for advective and diffusive transport of solutes in both the aqueous and gas phases. Because we also used the model to examine the effect of various aspects of the experimental design on the flow and transport regime, such as the temporal and spatial distribution of fluid application and withdrawal, we developed the latter model as a quadrant of a three-dimensional cylinder, in a cylindrical coordinate system, with 25 nodes in each horizontal plane and 85 nodes along the vertical axis. Boundary conditions for the model include zero-flux boundaries for gas, liquid, and solute at the bottom plane as well as on the vertical walls and cross-sectional planes of the quadrant. At the top of the column, the 14CO2 concentration is fixed at zero, total gas pressure is fixed at the average ambient air pressure, and a constant flux of water is applied to approximate the spatial distribution of the actual injectors. Outflow in the model is simulated by a set of specified liquid-pressure node surfaces 15 cm above the bottom, on the cross-sectional planes of the cylinder at the level of the suction lysimeters. Gas flow at the simulated lysimeter nodes is controlled as a zero-flux plane, so that solute exits the lysimeters only via advection in the liquid phase. Parameters for the van Genuchten–Mualem equations describing relationships between soil moisture, matric potential, and hydraulic conductivity were estimated from measurements of hydraulic properties of the SDA sediments conducted for this study and previous studies (Porro and Keck, 1998).
Carbon-14 Transport Parameters
Parameters needed for simulations of 14C transport include liquid advection rates, aqueous–gas and solid–aqueous partitioning coefficients, and solute diffusivities in the gas and aqueous phases. Our conservative tracer experiments provide good constraints on the aqueous transport velocity and the dependence of gas diffusivity on volumetric air content. Diffusion coefficients for gaseous CO2 and for the aqueous carbonate species (HCO3−) prevalent in the system were taken from the literature (Lide, 2003). While the Br− tracer test indicated that seepage velocity varied slightly with depth, we did not attempt to incorporate that level of detail in our transport simulations. Based on both direct and indirect measures of water content, we assumed that the average water content was approximately 28% and made small adjustments to the van Genuchten–Mualem parameters to provide that value at the injection port under the controlled inflow rate (0.15 cm d−1) under steady-state conditions. We then varied the van Genuchten parameters to produce a set of simulations with mean water contents capturing the estimated uncertainty of that value to assess the effect of that uncertainty on 14C transport predictions. Final parameters for the 14C transport simulations are summarized in Table 3.
The primary remaining parameters are the solid–aqueous and aqueous–gas partitioning functions. Several studies have demonstrated that adsorption of inorganic carbonate species produces a large reservoir of immobile, exchangeable C that retards transport (Striegl and Armstrong, 1990). In this study, we assumed that sorption of inorganic C is reasonably well described using a constant distribution coefficient, or Kd. Dicke and Hohorst (1997) measured a mean Kd of 0.8 mL g−1 (range = 0.1–2.0 mL g−1) in batch 14C adsorption experiments on sediments from the SDA. Hull and Hohorst (2001) also found Kd = 0.8 ± 0.1 mL g−1 in a transport experiment using a small (30.5-cm) column filled with water-saturated SDA sediment. Other studies of 14C sorption on natural materials have produced similar results. Using a variety of natural sediments, Allard et al. (1981) measured Kd values ranging from 1.1 to 3.0 mL g−1, while Martin (1991) measured values ranging from 3.5 to 4.6 mL g−1 for sediments from the Hanford site. Much higher distribution coefficients and a dependence of that parameter on contact time have been observed in several studies. Allard et al. (1981) noted increasing adsorption with time in experiments with calcite, obtaining a Kd of 83 mL g−1 after 6 mo contact time, and Garnier (1985) observed a positive correlation between flow rate and 14C retardation. The contact time in transport experiments depends largely on the mode of transport. In unsaturated sediment transport experiments, 14C transport should be dominated by 14CO2(g) diffusion. We thus expected that Kd values derived from batch experiments on SDA sediments (Dicke and Hohorst, 1997) would predict reasonably well the effect of sorption on redistribution of a spike of 14C applied to one of the injection planes in the column.
The partitioning of CO2 between gas and aqueous phases is determined from the combined solubility of carbonate species present, which depends on several geochemical parameters. Microbial respiration occurs throughout the column and CO2 concentrations increase approximately exponentially with depth. Measured pHs thus typically range from about 7.4 near the top of the column to 6.9 near the bottom. We calculated the dimensionless ratio, Klg, of total DIC per unit volume to gaseous C per unit volume from the measured pH and standard carbonate equilibria expressions (Langmuir, 1997). The calculated ratios were an excellent match (Fig. 8) to those determined from activity measurements in the aqueous and gas phases during the first few weeks following the 14C injection. Although Klg is relatively uniform throughout most of the column, significantly more C is contained in the aqueous phase than in the gas phase near the top of the column, due to the higher pH there and the nonlinear relationship between pH and bicarbonate concentration. We incorporated this variation in the aqueous–gas partitioning ratios in our multiphase transport simulations by assigning an elevation-dependent Klg distribution calculated by interpolation of the observed distribution.
Simulated Carbon-14 Transport and Comparison with Experimental Data
Previous studies of CO2 movement in the unsaturated zone (Thorstenson et al., 1983; Lu and Ross, 1994) indicate that 14C transport can be described by a conceptual model that considers reactive diffusive transport in the gas phase but ignores dissolved-phase transport. The one-dimensional conservation equation describing this transport process, 4is similar to Eq. , except that it includes the dimensionless retardation factor, R, to account for the effects of phase partitioning on diffusive transport (Weeks et al., 1982). The retardation factor is given by 5where ρ is the soil bulk density, φl is the volumetric water content, Klg is the dimensionless ratio of 14C in the aqueous phase to that in the gas phase, and Kd is the sorption coefficient. The shape of the diffusion breakthrough curves is thus dependent on the volumetric air content, through both the retardation factor and tortuosity, and on the partitioning coefficients, through the retardation factor. In this case, we consider the aqueous–gas partitioning ratio, Klg, well constrained by the measured pH and carbonate concentrations. Throughout about 90% of the column, pH is between 6.9 and 7.1; higher pH occurs only relatively near the surface. The average aqueous–gas partitioning ratio is thus approximately 4.5 ± 0.3, depending on the thickness considered. The most uncertain parameters are the sorption Kd, and the water content, which a variety of methods indicate is approximately 28 ± 2%. Assuming that range for the average water content is valid, we can calculate the corresponding range of Kd by fitting breakthrough curves calculated from an analytical solution to the diffusion equation to the observed 14C breakthrough curves. Least-squares fitting to the 14C data yields Kd = 0.45 ± 0.1 mL g−1 for that soil moisture content range, with a coefficient of determination of 0.88 at 28% volumetric water content. These Kd values are well within the range (0.1–2.0 mL g−1) measured by Dicke and Hohorst (1997) and close to the average value obtained in that study. The agreement of the least-squares fit Kd values with those of batch studies on the same sediment and the excellent match between computed and observed breakthrough curves (Fig. 7) also demonstrate that, as predicted, the gas diffusion model provides a good description of 14C transport under the conditions prevalent in the column.
For multiphase transport simulations, we first developed steady-state flow simulations that provided a reasonable match to the flux and water content data characteristic of the transport tests. Carbon-14 transport simulations were then conducted using the best-fit Kd values calculated from the diffusion model. Predictably, the results were very similar (Fig. 9) , and the only notable differences appeared to result from incorporation of nonuniform aqueous–gas partitioning in the numerical simulations. The higher Klg values in the upper part of the column dampened gas peak responses in that region and thereby produced a significant improvement in model fit at Level 8. Curiously, although calculated aqueous/gas ratios at Level 7 were significantly higher than at Level 6, the peak gas-phase responses at both locations were nearly identical, so that incorporation of a nonuniform Klg diminished the quality of the fit at that location. Conversely, the multiphase simulation displays a higher peak in the aqueous Level 7 and Level 8 curves (Fig. 10) than in the gas-phase curves, due to the greater partitioning into that phase. That phenomenon is apparent in the observed breakthrough curves from those levels but is much more pronounced than is predicted by the simulation. In general these simulations with nonuniform aqueous–gas partitioning suggest that such effects can be important where pCO2, and therefore pH, is variable. It is likely that similar variability in adsorption would explain much of the remaining discrepancies between observed and simulated 14C breakthrough curves.
Direct Measurements of Carbon-14 Sorption
Approximately 1 yr after the 14C injection, we collected small soil samples from near the bottom of the column, through ports at Levels 2 and 3, and obtained six ≈76-cm-long (4.5-cm-diam.) soil cores from the top of the column. Gas and water samples were collected on the same date from eight levels in the column. Gas-, aqueous-, and solid-phase activities determined through combined analysis of these gas, water, and soil samples yielded solid–aqueous partitioning ratios of 0.8 to 0.9 mL g−1 near the bottom of the column and between 1.2 and 2.4 mL g−1 near the top. Mass balance (Fig. 11) calculated from these measurements of: sorbed activity, aqueous and gaseous activities from the eight sampling levels, total 14C removed via gas and liquid samples, total 14C lysimeters exiting via the lysimeters at the bottom, and 14C venting into the headspace accounts for 93% of the injected 14C activity. After 1 yr, most (66%) of the injected 14C was removed from the column via upward gas release, while only 4% was removed through downward aqueous transport. Of that remaining in the column, 82% is sorbed to the solid phase. Consistent with other studies of the effects of adsorption on 14C transport in the unsaturated zone (Striegl and Armstrong, 1990; Striegl and Healy, 1990), this demonstrates the large relative magnitude of the sorbed phase and the correspondingly large impact of that reservoir on 14C transport.
Although Kd values measured about 1 yr after the pulse injection were larger than those calculated from analysis of the breakthrough curves, large-scale increases in that parameter with time, such as those noted by Allard et al. (1981), were not observed. On the contrary, the range of Kd values measured in this study (0.3–2.4 mL g−1), determined using entirely different methods and representing times spanning a year, is entirely consistent with the relatively narrow range of values (0.1–2.0 mL g−1) obtained from short-term and small-scale adsorption studies and column studies of SDA sediments. The higher values obtained during the latter part of this study may reflect one or more of several factors that cannot be resolved with the present data, including nonlinearity in the sorption isotherm, a slight temporal dependence in adsorption, and kinetic partitioning effects during the initial spreading of the 14C pulse.
Implications for Carbon-14 Transport at the SDA
Simulations of 14C transport in the mesoscale column, with both a simple gas diffusion model and a multiphase flow and transport model, provide a good match to observed 14C redistribution following a pulse injection and indicate that 14C transport in the column is dominated by gas diffusion. Sediment type and thickness at the SDA are similar to that in the column, while estimated infiltration rates at the SDA are actually lower (Case et al., 2000). Thus, unless saturated flow occurs close to 14C sources, 14C migration at the SDA is also probably dominated by gas-phase transport. If, for the moment, we neglect advective transport and consider a simple one-dimensional model of the SDA, an obvious difference between that system and our column is that the unsaturated zone at the SDA extends approximately 180 m beneath the contaminant source, and 14C may enter the underlying Snake River Plain aquifer by both gas and liquid transport. A one-dimensional model of the SDA might therefore incorporate zero-concentration boundary conditions at both the upper and lower boundaries, as opposed to our column model, which does not permit gas transport through the lower boundary. Assuming a steady-state condition is eventually reached, the one-dimensional diffusion model would predict that relative release rates to each boundary are roughly proportional to the proximity of the source to the boundary. Given the approximately 50 times greater distance to the underlying aquifer, this suggests that most of the 14C released from the SDA would ultimately discharge to the surface. While the considerable depth and fractured nature of the system suggest that atmospheric pressure fluctuations generate significant advective gas movement in the subsurface (Nilson et al., 1991; Holford et al., 1993), that effect would likely enhance upward gas movement at least as much as downward movement. Clearly however, a one-dimensional diffusion model is an oversimplification of the problem, and a realistic estimate of upward and downward fluxes would have to consider the effect of the spatial variability of hydraulic properties, seasonal changes in boundary conditions such as freezing and infiltration of snowmelt, diffusive gas transport across air–sediment and air–water interfaces as well as pressure-driven gas fluxes. These questions will be the focus of subsequent studies that include monitoring and interpretation of 14C in the subsurface of the SDA.
Analysis of the mesoscale unsaturated flow and transport experiments performed in this study demonstrates that 14C transport in the column is well described by a conceptual model that considers reactive diffusive transport in the gas phase but neglects aqueous-phase transport. Physical transport parameters for the large unsaturated flow column were constrained through a combination of gas-phase and aqueous-phase tracer tests. These tests demonstrate that the Millington (1959) equation provides a good description of the relationship between gaseous diffusion and moisture content in the SDA sediment and confirm results of previous studies (Hull and Hohorst, 2001) that dispersivity in the sediment is on the order of several millimeters even over distances of up to a meter. Aqueous–gas partitioning values used in our 14C transport simulations were calculated directly from pH, and aqueous/gas concentration ratios measured during the transport experiment confirmed those calculations and demonstrated the strong dependence of that parameter on pCO2.
Constraints on other transport parameters provide increased confidence in the Kd values we determined by fitting simulated breakthrough curves to observations. Kd values determined in that manner were approximately 0.5 ± 0.1 mL g−1, while values measured from soil, water, and gas phase sampling approximately 1 yr later ranged from 0.8 to 2.4 mL g−1. This range is consistent with that obtained from small batch studies and column studies using SDA sediments and demonstrates that those laboratory-scale measurements provide reliable data for transport modeling even at the large spatial and temporal scale considered in these mesoscale experiments. The models and parameters described in this study should provide a reliable basis for developing transport models of 14CO2 released from activated metals buried in the SDA. As estimated infiltration rates at the SDA (Case et al., 2000) are lower than that maintained in the column, 14C transport at the SDA is also probably dominated by gas movement. Whether or not that includes an advective component, the resultant flux to the atmosphere would be expected to outweigh the flux to the underlying Snake River Plain aquifer. Given the tendency for reactive gas transport to control movement of 14CO2 in the unsaturated zone, this effect should be considered when evaluating risks to atmospheric and groundwater receptors downgradient of the SDA.
The authors would like to thank two anonymous reviewers for comments and suggestions that greatly improved this manuscript. Funding for this project was provided by the U.S. Department of Energy, Office of Environmental Management, under contract DE-AC07-99ID13727.
- Received July 10, 2003.