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Multiphase Reactive Transport Modeling of Seasonal Infiltration Events and Stable Isotope Fractionation in Unsaturated Zone Pore Water and Vapor at the Hanford Site

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

Michael J. Singleton,* Eric L. Sonnenthal, Mark E. Conrad, Donald J. DePaolo, and Glendon W. Gee ABSTRACT

and diffusive transport). Developing tractable analytical equations for these processes requires simplifying assumptions, which lead to analytical methods that are not easily adapted to field conditions. Previous numerical models have relied on assumptions such as neglecting the temperature dependence of isotope fractionation and treating the isotopic species as nonreactive tracers with concentrations defined by fixed partition coefficients. Prior approaches to predicting the impact of infiltration water on stable isotope profiles include a semiempirical model (Barnes and Allison, 1988), a mixing scheme (Mathieu and Bariac, 1996b), and an analytical model to predict overall average pore water isotope compositions (DePaolo et al., 2004). However, a more general approach is needed to link observed isotope compositions with dynamic hydrological processes, where precipitation events or temperature changes affect the isotopic profile with depth. We use the thermodynamic framework of the TOUGHREACT transport code (Xu and Pruess, 2001; Xu et al., 2003) to develop a general transport model for stable isotopes in vadose zone soil water and consider the impact of infiltration processes on measured stable isotope profiles from the Hanford Site. These reactive transport models of stable isotope transport provide a quantitative method to link the observed isotopic profiles to soil properties, climatic conditions, and net infiltration into the vadose zone.

Numerical simulations of transport and isotope fractionation provide a method to quantitatively interpret vadose zone pore water stable isotope depth profiles based on soil properties, climatic conditions, and infiltration. We incorporate the temperature-dependent equilibration of stable isotopic species between water and water vapor, and their differing diffusive transport properties into the thermodynamic database of the reactive transport code TOUGHREACT. These simulations are used to illustrate the evolution of stable isotope profiles in semiarid regions where recharge during wet seasons disturbs the drying profile traditionally associated with vadose zone pore waters. Alternating wet and dry seasons lead to annual fluctuations in moisture content, capillary pressure, and stable isotope compositions in the vadose zone. Periodic infiltration models capture the effects of seasonal increases in precipitation and predict stable isotope profiles that are distinct from those observed under drying (zero infiltration) conditions. After infiltration, evaporation causes a shift to higher ␦18O and ␦D values, which are preserved in the deeper pore waters. The magnitude of the isotopic composition shift preserved in deep vadose zone pore waters varies inversely with the rate of infiltration.

T

he fraction of precipitation that reaches the deep vadose zone, or the net infiltration, is difficult to predict in arid regions, but important for understanding groundwater recharge and contaminant transport. At the USDOE’s Hanford Site in south-central Washington State, where a large amount of radionuclide contamination is present in the vadose zone, it is critical to know the net water infiltration flux, as this determines how rapidly radionuclides or other contaminants may reach groundwater. The vadose zone hydrological processes that control net infiltration rate also affect the ratios of stable isotopes (i.e., 18O/16O and 2H/1H) in water and water vapor. The transport of stable O and H isotopes in water within drying soil columns has been studied extensively (e.g., Barnes and Allison, 1983, 1984; Allison et al., 1994; Shurbaji et al., 1995; Mathieu and Bariac, 1996a; Melayah et al., 1996). Approaches used to predict stable isotope profiles in drying soils must consider the complex interaction of multiple processes (e.g., drainage, temperature effects on flow and isotope fractionation,

Background: Stable Isotope Measurements The isotopic compositions discussed here are measured relative to a well-defined standard material (Standard Mean Ocean Water [SMOW]). Stable isotope compositions (‰) are calculated as delta values from the isotopic ratio (R ⫽ 18O/16O or 2H/1H), where ␦⫽

冢RR

Sample

Standard

冣

⫺ 1 1000

[1]

Based on this system, typical ocean waters have ␦D and ␦18O values near 0‰ relative to SMOW. Meteoric precipitation over land varies as a function of temperature, latitude, and altitude, but generally has ␦D and ␦18O values that are shifted to values less than zero because of the fractionation of lighter isotopes into the vapor phase during the change from liquid to vapor. Craig (1961) documented a linear relationship, known as the global meteoric water line (GMWL), between

M.J. Singleton, E.L. Sonnenthal, M.E. Conrad, D.J. DePaolo, Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720; and G.W. Gee, Hydrology Group, Environmental Technology Division, Pacific Northwest National Laboratory, Richland, WA. Received 30 Aug. 2003. Special Section: Research Advances in Vadose Zone Hydrology through Simulations with the TOUGH Codes. *Corresponding author ([email protected]).

Abbreviations: GMWL, global meteoric water line; LBNL, Lawrence Berkeley National Laboratory; LMWL, local meteoric water line; PNNL, Pacific Northwest National Laboratory; SMOW, standard mean ocean water.

Published in Vadose Zone Journal 3:775–785 (2004).  Soil Science Society of America 677 S. Segoe Rd., Madison, WI 53711 USA

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Fig. 1. Hydrogen and O isotope compositions of soil waters collected from the Hanford vadose zone. The value of average precipitation used for model input waters is shown as a gray box. Pore water stable isotope data from DePaolo et al. (2004) and unpublished data from ongoing studies are shown as blue diamonds. Also shown are the global meteoric water line of Craig (1961) and the Hanford local meteoric water line, based on data from Graham (1983) and Early et al. (1986).

the ␦D and ␦18O values for meteoric waters collected all over the world. However, in arid and semiarid climates the ␦D and ␦18O values of shallow lakes and soil waters are often shifted to the right of the GMWL (Fig. 1). This behavior can be explained by the strong mass dependence of diffusion-driven transport, which fractionates stable isotopes during evaporation. These processes will be discussed further in the description of the stable isotope model below.

The Hanford Site During the Cold War, Pu for nuclear weapons was produced and separated from other reactor products at the Hanford Site, which led to the contamination of the vadose zone and local groundwater from spills and leaks of radioactive materials. A detailed understanding of fluid flux through the vadose zone under various climatic conditions will help in the prediction of contaminant migration and its potential impact on the Columbia River and other regional water resources. Climate Like many semiarid localities, local precipitation at Hanford exhibits strong seasonal fluctuations, from averages around 26 mm mo⫺1 during the winter months to 7 mm mo⫺1 during the dryer summer months (Gee et al., 1992; Hoitink et al., 2002). The precipitation variations are accompanied by seasonal shifts in average relative humidity and temperature, from approximately 70% at 1⬚C in the winter to 40% at 23⬚C in the summer (Hoitink et al., 2002). Winter rain and snow generally account for more than two-thirds of the annual precipitation at Hanford and have ␦18O values that range from ⫺19 to ⫺16‰ and ␦D

values that range from ⫺142 to ⫺120‰ (Graham, 1983; Early et al., 1986). The ␦18O and ␦D values of summer precipitation are typically higher and plot to the right of the GMWL. It is these summer precipitation samples that impart a lower slope (≈5.8) to the local meteoric water line (LMWL; Fig. 1). It is not clear whether the lower slope of the LMWL reflects evaporation that occurred during precipitation events, or evaporation that took place in the open-top collection devices described in Graham (1983) after precipitation but before sample collection. Due to the small amount of rain and high evaporation potential in the summer, the isotopic compositions of summer precipitation waters are not considered in models from this study. Two samples of near-surface atmospheric vapor collected in August 2002 at the Hanford VZFS300N site have an average ␦18O value of ⫺21‰ and an average ␦D of ⫺146‰. Although the isotopic composition of atmospheric humidity may change in response to regional weather patterns, the August samples represent reasonable values for the summer months, when evaporation is most effective. Vadose Zone Samples An ongoing collaborative effort between investigators at Lawrence Berkeley National Laboratory’s (LBNL) Center for Isotope Geochemistry and the Pacific Northwest National Laboratory (PNNL) has resulted in more than 100 stable isotope measurements of pore waters from sediment core samples collected at Hanford. These cores include both homogenous sediments and layered sedimentary sequences from mostly nonvegetated sites. Evaporation and isotopic equilibration with atmospheric water vapor has shifted the isotopic compositions of unsaturated zone pore waters at Hanford off the LMWL (Fig. 1). Pore waters in the upper 2 m are most strongly affected (Fig. 2) and have ␦18O values up to ⫺3.8‰ and ␦D values up to ⫺75‰. The isotopic compositions of deeper pore waters vary with grain size and moisture content, but generally have average ␦18O values around ⫺14.5‰, representing a shift of ⫹2 to ⫹3‰ from precipitation and local groundwater (DePaolo et al., 2004). METHODS The approach taken to simulate stable isotope transport in this study differs markedly from previous models that account for isotopes as nonreactive tracers. The more flexible approach used here treats the isotopic species of liquid water and water vapor as separate constituents within a multiphase reactive transport model (Singleton et al., 2003). Recently, Wolfsberg and Stauffer (2003) used a similar representation of the isotopic species in a flow and transport code (FEHM) to model vadose zone stable isotope transport (at a fixed temperature) under drying conditions. Our approach considers drying and wetting conditions using the TOUGHREACT code (Xu and Pruess, 2001, Xu et al., 2003), which couples the multicomponent, multiphase hydraulic transport capabilities of TOUGH2 (Pruess, 1991; Pruess et al., 1999) with reactive transport based on thermodynamic principles of chemical equilibrium and kinetics.

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equilibrium constants, defined in the standard thermodynamic form as the quotient of the activities of the products and reactants (e.g., Criss, 1999; Thorstenson and Parkhurst, 2002; Wolfsberg and Stauffer, 2003). The isotope exchange reactions relevant to liquid–vapor fractionation are condensation

H216Ovap

evaporation

1

evaporation

HDOliq

[6]

Both the steam table based vapor–liquid equilibrium and isotopic equilibrium are maintained by using the following temperature-dependent equilibrium values in the TOUGHREACT thermodynamic database:

log K⬘ ⫽ log Fig. 2. Soil water ␦18O values with depth in the Hanford vadose zone. Pore waters in the upper 2 m are most strongly affected by evaporation (Fig. 2) and have ␦18O values up to ⫺3.8‰. Below the evaporation zone, soil water ␦18O values are shifted by approximately ⫹2‰ (dashed line) higher than typical winter precipitation (⫺16.5‰). Pore water stable isotope data from DePaolo et al. (2004) and unpublished data from ongoing studies are shown as blue diamonds.

TOUGHREACT couples multiphase fluid flow (water and air), heat flow, aqueous and gaseous species transport, and kinetic and equilibrium mineral–water–gas reactions. The equations are solved in three distinct parts at each time step. First, the system of equations describing the flow of liquid water, gas (air plus water vapor), and heat are solved simultaneously (i.e., as in TOUGH2). Diffusion of water vapor and air are treated in this step, independent from the transport of the individual isotopic species. Second, the aqueous and gaseous species (including isotopic species) are transported individually using the newly calculated liquid and gas velocities, diffusivities, and the updated properties, such as water saturation, gas pressure, and temperature. Third, mineral– water–gas reactions (including isotopic species) are described by a set of chemical mass-action, kinetic rate expressions for mineral dissolution–precipitation and mass-balance equations, which are solved simultaneously by a Newton–Raphson iterative procedure. At this point, the new concentrations may be used in further iterations between the transport and reaction (i.e., sequential iteration as in Steefel and Lasaga, 1994), or the calculations may proceed to the next time step (sequential noniterative method). This reactive transport approach allows for the development of physical models that describe stable isotope fractionation in tandem with multiphase flow, heat transport, mineral– water–gas reactions and the transport of any number of gaseous and aqueous species. The general equilibrium reaction considered here is the phase change of water: condensation

vapor

liquid

[2]

The temperature-dependent equilibrium constant for this reaction is calculated based on the International Formulation Committee steam table equations (as in Pruess et al., 1999). Similarly, isotope exchange reactions can be described by

[liquid] [vapor]

冢

[7]

冣

[liquid] log K* ⫽ log ␣eq [vapor]

[8]

where K⬘ is the temperature-dependent equilibrium dissociation constant for the more abundant, lighter isotopomer of water (1H216O), as defined by the steam table vapor pressure. The equilibrium constant for the much less abundant, heavier isotopic species (K*) is determined at the temperature of interest using the isotopic fractionation factor (␣eq). The temperature-dependent equilibrium fractionation factor (␣eq) for H and O isotopes of water during liquid–vapor exchange is calculated based on the experimentally determined relation of Horita and Wesolowski (1994), which is valid from the freezing point to the critical temperature of water. We assume that isotopic and phase equilibrium are maintained during each 1000-s time step. In addition to phase changes, the presence of a strong isotopic and vapor concentration gradient (i.e., low humidity in the atmospheric boundary) fractionates water isotopes by diffusion. We follow the assumption that all isotopomers of water have the same molecular diameter, and thus the fractionation of stable isotopes by diffusion is a function of their respective masses (H218O ⬎ HDO ⬎ H2O). The diffusion coefficients for gaseous species are calculated assuming ideal gas behavior as a function of temperature, pressure, molecular weight, and molecular diameter, according to Lasaga (1998), as follows:

D⫽

RT 3√2␲PN Ad 2m

冪8RT ␲M

[9]

where D is the diffusion coefficient (m2 s⫺1), R is the gas constant (8.31451 m2 kg s⫺2 mol⫺1 K⫺1), T is temperature in Kelvin units, P is the gas pressure (kg m⫺1 s⫺2), NA is Avogadro’s number (6.0221367 ⫻ 1023 mol⫺1), dm is the molecular diameter (m), and M is the molecular weight (kg mol⫺1). Transport of gaseous species takes place through advection and diffusion, with the diffusive fluxes following Fick’s Law. The diffusive flux (FD) is therefore expressed as follows:

FD ⫽ DφSg␶䉮(φSgC)

[10]

where φ is the porosity, Sg is the gas saturation, ␶ is the tortuos-

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Table 1. Parameters for calculating unsaturated hydraulic conductivities and capillary pressures using the equations of van Genuchten (1980).† Material


Medium sand Silty sand Clayey silt

␪s (v/v) 0.33 0.35 0.38

␪r (v/v)

␣

0.03 0.05 0.07

m ⫺1 40 10 2

n

Ks

3.6 2.4 1.2

m s⫺1 5 ⫻ 10⫺4 5 ⫻ 10⫺5 5 ⫻ 10⫺7

† Note: ␪s and ␪r are the saturated and residual water contents, ␣ and n are fitting parameters, and Ks is the saturated hydraulic conductivity.

ity, and C is the gas species concentration. For simplicity, a tortuosity value of 0.25 was used for all model calculations. The calculation of aqueous and gaseous species diffusive fluxes involves averaging of the product of the porosity and saturation in adjacent grid blocks. Invoking conservation of diffusive flux across the interface between two grid blocks leads to the requirement of harmonic weighting of the saturation–porosity product. Diffusive transport of isotopic species in the liquid water phase may affect the isotopic profile under conditions of high liquid saturation, small liquid velocities, and during very long time periods. For these conditions the diffusive transport of isotopic species in the liquid can be considered using the selfdiffusion coefficient of water (2.4 ⫻ 10⫺9 m2 s⫺1). However, at low saturations the liquid phase may become discontinuous, effectively preventing any isotopic species transport by liquid diffusion. For the short time scales and unsaturated conditions considered in this study, liquid transport is controlled by capillary and gravity-driven flow. Temperature gradients have a complex effect on the diffusion and isotopic exchange of stable isotopes, since both the isotopic fractionation factors and the diffusion coefficients are temperature dependent. Using TOUGHREACT, the effects of temperature gradients on heat and fluid transport can be simulated, while accounting for temperature dependent changes in chemical and isotopic equilibrium. However, to focus on the effects of infiltration in semiarid climates, and to simplify the interpretation of these results, the effects of temperature gradients and transient temperature profiles will be addressed in a future study. Isothermal models provide a reasonable approximation to field conditions at Hanford in the wet winter months, when measurements of soil temperature (Hoitink et al., 2002) show the least variation with depth. The diffusive fluxes of the isotopic species in the gas phase are dependent on the sediment porosity and texture. Therefore, we consider models of stable isotope transport in a range of sediment types, increasing in grain size from clayey silt to silty sand to medium sand. The dependence of capillary pressure and effective conductivity on moisture content for these unsaturated sediments is based on the equations of van Genuchten (1980). Parameters for these sediments (Table 1) are based on the range of values reported for sediments at the Hanford Site (Kincaid et al., 1998; Zhang et al., 2002). We tested the performance of the model using data collected from a test site known as VZFS300N, described in some detail by Sisson et al. (2002). This site has a sand-filled 7.6m-deep lysimeter in which capillary pressure and drainage measurements have been made for an extended period of time, and from which a series of soil samples were collected for H and O isotope analysis. Samples containing approximately 200 g of material were placed into wide-mouthed, plastic sample bottles and sealed. The pore water in the samples was then collected for isotope analyses using vacuum distillation at 100⬚C. The stable isotope compositions of the water samples were analyzed at the Center for Isotope Geochemistry at LBNL using a VG Instruments (now GV Instruments, Man-

chester, UK) Isoprep automated CO2–H2O equilibration system and Prism Series II isotope ratio mass spectrometer.

RESULTS AND DISCUSSION Evaporation and infiltration in the upper vadose zone is considered within a 7.5-m-deep profile through unsaturated sediments, simulated as a vertically oriented, one-dimensional series of 98 equal volume grid blocks, bounded on the top and bottom by boundary blocks. The top block provides the atmospheric boundary condition, and the bottom boundary block provides an infinite reservoir for draining fluids. The following discussion will focus on the ␦18O values from models and measurements; however, the same general processes are also applicable to ␦D values. Humidity (h) and isotopic composition (Ra) in the atmospheric boundary block are implemented by setting the partial pressure of the dominant vapor isotopomer to PH216O ⫽ h(PH216O)sat

[11]

where (PH216O)sat is the saturated partial pressure. The isotopic composition of atmospheric vapor is then set by Ra ⫽

PH218O PH216O

[12]

The initial conditions for volumetric water content (␪) were established by allowing the flow calculations to run to steady state (no change in ␪) under a constant water input rate of 50 mm yr⫺1 into the top sediment block. Initial ␪ values used for the simulations below are 0.32 for clayey silt, 0.078 for silty sand, and 0.038 for medium sand. All model profiles assume isothermal conditions (20⬚C). The initial soil water ␦18O value for all model nodes is ⫺16.5‰. Removal of soil water by plants may have a significant impact on vadose zone water transport for vegetated arid sites (e.g., Walvoord et al., 2002). Uptake by plant roots does not result in isotopic fractionation (Allison et al., 1983), and could be implemented in TOUGH2 models as a negative water flux in model nodes within the root zone. However, areas that are critical to contaminant transport at the Hanford Site (e.g., tank farms in the 200W and 200E areas) are kept barren of vegetation. In addition, a significant brush fire in 1984 destroyed much of the native shrub-steppe vegetation over more than one-third of the Hanford Site (Gee et al., 1992). Therefore, to improve interpretation of infiltration effects on stable isotope profiles at the Hanford Site, the models in this study are constructed to represent a nonvegetated surface. Stable isotope compositions in the Hanford Site vadose zone record the combined effects of annual wet and dry seasons. To investigate the impact of seasonal infiltration on stable isotope profiles, we will first consider two end-member model scenarios. The first scenario will consider the evolution of pore water ␦18O values under conditions of zero infiltration to illustrate the effects of dry summer months. The second scenario

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Fig. 3. Zero infiltration model results for pore water ␦18O in three hypothetical soil types: clayey silt, silty sand, and medium sand. Starting from an initial pore water ␦18O value similar to winter precipitation at Hanford (⫺16.5‰), the model soils were subjected to 20 yr of evaporation and drainage under an atmosphere with h ⫽ 40% and ␦18Oa ⫽ ⫺21‰. The value of ␦18OMAX that is reached under these atmospheric conditions is shown as a vertical line.

will use a constant infiltration flux to illustrate the impact of near-surface isotope fractionation on net infiltration. These two end-member conditions will then be combined into a periodic infiltration model that best approximates the dynamic conditions of seasonal infiltration.

Zero Infiltration The general features of measured stable isotope profiles in drying soil columns have been described using analytical models (Barnes and Allison, 1983, 1984; Allison et al., 1994) and numerical methods (Shurbaji et al., 1995; Mathieu and Bariac, 1996b; Melayah et al., 1996). Specifically, pore water below the soil–atmosphere interface reaches a peak (␦18OMAX) followed by decreasing ␦18O with depth. Above ␦18OMAX the soil water ␦18O values approach equilibrium with the atmospheric vapor. This transition zone has been referred to as “vapordominated” and consists of sediments that have very low moisture content (Barnes and Allison, 1983; Shurbaji et al., 1995). The vapor-dominated zone is a transition between atmospheric gas with low humidity and pore vapor at the evaporation front. This transition takes place across gradients in concentration and isotopic composition, from atmospheric humidity to 100% humidity at the evaporation front, and from the isotopic composition of atmospheric vapor to pore vapor in isotopic equilibrium with pore water. As demonstrated in Fig. 3, the depth and thickness of the high ␦18O zone is related to soil properties, which determine the transport and distribution of water and water vapor in the column. However, the value for ␦18OMAX in the soil column is controlled by the concentration (i.e., humidity) and isotopic composition of atmo-

spheric vapor (h ⫽ 40% and ␦18Oa ⫽ ⫺21‰ for all three soils). It is important to note that the isotopic ratio of nearsurface soil waters can be increased or decreased without any loss to evaporation, solely due to reequilibration with the atmospheric vapor. As an extreme example, for an atmosphere of 100% humidity that is out of equilibrium with the soil water, the pore water stable isotopic compositions will shift toward equilibrium with atmospheric water vapor near the surface. In the case of 100% relative humidity, the ␦18O profile will reflect solely the diffusive isotopic reequilibration between the soil vapor and the atmosphere, because there is no vapor concentration gradient. The relative importance of this effect at lower humidity is discussed below. Isotopic effects are caused by evaporation as result of the fact that evaporation is a non-equilibrium process. The isotopic fractionation associated with evaporation (␣evap) is a function of humidity (h), the isotopic ratios of the atmospheric vapor (Ra), and the liquid water reservoir (Rliq), the kinetic evaporation fractionation h⫽0 factor at zero humidity (␣evap ), and the temperaturedependent equilibrium fractionation factor (␣eq) (Ehhalt and Knott, 1965; Criss, 1999): ␣evap ⫽

h⫽0 ␣evap (1 ⫺ h) 1 ⫺ ␣eq h Ra/Rliq

[13]

h⫽0 The parameter ␣evap can also be expressed as the product ␣kin␣eq, where ␣kin is referred to as the kinetic fractionation factor. The kinetic fractionation factor depends on the way that water vapor is transported away from the evaporation front (or the surface of the water reservoir in the case of an evaporating pool of liquid water). For purely vapor phase diffusive transport, it is expected that the following will hold:

␣kin ⫽ (D/D⬘)n

[14]

where D is the vapor phase diffusion coefficient for H216O, and D⬘ is the vapor phase diffusion coefficient for either H218O or HD16O. The kinetic fractionation factor is not easy to determine experimentally, partly because of the fact that only the total fractionation factor can be observed and the equilibrium fractionation factor is temperature dependent. At low humidity, evaporation is rapid, and the evaporating water surface cools, so there is uncertainty in the appropriate temperature used to calculate ␣eq (e.g., Cappa et al., 2003). At higher humidity, uncertainty in the humidity makes the determination of ␣kin difficult. Available data suggest that for evaporation into air, n ≈ 0.2 to 0.25 under conditions that would apply to relatively smooth surface waters with typical wind speeds. Stewart (1975) measured stable isotope compositions in evaporating water drops in a dry N2 atmosphere and was able to approach the theoretical maximum value of n ⫽ 2/3 for evaporation into free air. For a water-saturated soil, the soil–atmosphere interface represents the evaporation front. As evaporation proceeds, the soil water at the surface reaches a steadystate value (Rssat) (Zimmerman et al., 1967; Barnes and Allison, 1983):


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Fig. 4. Predicted ␦18OMAX vs. relative humidity for unsaturated soils at 10, 20, and 30ⴗC from numerical model results with zero infiltration. Model calculations are based on reservoir and atmospheric vapor isotopic compositions of ␦18Ores ⫽ ⫺16.5‰ and ␦18Oa ⫽ ⫺21‰. h⫽0 R ssat ⫽ ␣evap (1 ⫺ h)Rres ⫹ ␣eqhRa

[15]

The steady state is reached because evaporation at the soil surface is balanced by upward flow due to capillary forces. The isotopic ratio of the soil water at the surface adjusts relative to the isotopic ratio of atmospheric moisture until the isotopic ratio of the evaporating water (⫽ ␣evapRssat) is equal to the isotopic ratio in the water flowing upward from below (Rres). Equation [15] can be derived from Eq. [13] by setting ␣evap ⫽ Rssat/Rres and Rliq ⫽ Rssat. Because the evaporation in this case is directly into the atmosphere, the value for ␣evap is about 1.015 at 20⬚C for 18O/16O, and the predicted value for Rssat is about 15‰ higher than the reservoir value at h ⫽ 0, varying linearly with humidity so that at h ⫽ 1, Rssat is about 9‰ higher than the reservoir value. For unsaturated soils there are two reasons that ␣kin is different from that expected for evaporation into free air. First, in unsaturated soil, the vapor transport is within a porous medium, so turbulence should not play a role (n ⫽ 1 in Eq. [14]), and the transport will be purely diffusive in the absence of vapor flow. Second, unsaturated soils contain both liquid water and water vapor, which act to buffer the effects of diffusive vapor transport. At the same time that water vapor is being transported through the vapor phase it is exchanging isotopes with the liquid water present in the soil. The precise rate of this exchange relative to the vapor phase transport is not known and to our knowledge has never been directly measured. It is probably dependent on the water content of the soil and other soil properties that dictate the effective surface area of the interface between the liquid and vapor phases in the soil. Model results for zero infiltration can be used to evaluate the value of ␦18OMAX at any humidity and temperature for unsaturated conditions (Fig. 4). TOUGHREACT solves the diffusion, equilibration, and multiphase trans-

port equations directly, and does not rely on predetermined kinetic fractionation factors. This direct approach results in predictions of unsaturated ␦18OMAX that suggest a curvilinear behavior as a function of humidity (Fig. 4). Similar to the relation expected for saturated soils (Eq. [15]), at h ⫽ 1, the value of ␦18OMAX is in equilibrium with atmospheric vapor (i.e., ␣eqRa), and as humidity approaches zero ␦18OMAX is given by kinetic fractionation h⫽0 of the deep liquid (i.e., ␣evap Rres). However, at intermediate values of h, the curvilinear relationship shown in Fig. 4 is due to a relatively complex set of conditions (diffusive fluxes above and below the drying front and the rate of evaporation), which depend on humidity. The net effect is that ␣evap remains close to 1.015 at the humidity values applicable to Hanford summer conditions (h ≈ 0.4), but approaches values nearer unity at higher humidity. The value of ␦18OMAX varies with temperature because of its dependence on the equilibrium fractionation factor (␣eq). This temperature dependence is enhanced with higher humidity, as the equilibration with atmospheric vapor plays a more significant role. At high temperatures, ␣eq approaches unity, resulting in a smaller shift from the initial water value.

Constant Infiltration The examples of drying soil columns discussed in the previous section are useful for understanding the effects of evaporation that predominate during dry months. However, net infiltration ranges from 0.1 to 200 mm yr⫺1 at the Hanford Site (Gee et al., 1992) and has a significant effect on stable isotope profiles in the Hanford vadose zone. Infiltration was implemented in TOUGHREACT simulations by specifying constant or time-dependent water input rates into the uppermost soil grid block. These infiltration models thus represent influx from significant precipitation events, which wet the soil to a depth of at least 8 cm (the size of one grid block). Infiltrating waters are input at the same temperature as the model soil grid blocks (20⬚C) and have an isotopic composition similar to winter precipitation and groundwaters at Hanford (␦18O ⫽ ⫺16.5‰). The initial soil water ␦18O values for all of the models described here were set to ⫺16.5‰, but become shifted to higher values as evaporation and infiltration commence. For a 50 mm yr⫺1 input flux, the time required for all of the initial water to be flushed from the 7.5-m model column ranges from about 4 yr for medium sand to more than 20 yr for clayey silt. Infiltration will first be considered as a constant flux of water into the top block of the soil profile. For simplicity, we assume steady precipitation with no runoff on a bare soil (i.e., no vegetation). This constant infiltration model (Fig. 5) predicts the isotopic shift imparted by evaporation on net infiltration that reaches the deep vadose zone. With constant infiltration, the isotopic composition reaches a steady-state value that reflects the balance of infiltration and evaporation. The net rate of infiltration qnet that is transported below the evaporation front is given by

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Fig. 5. Model steady-state pore water ␦18O values for a constant infiltration of 50 mm yr⫺1 of water with a ␦18O value of ⫺16.5‰. The soil types and atmospheric conditions (h ⫽ 40% and ␦18Oa ⫽ ⫺21‰) are the same as for Fig. 3. The value of ␦18OMAX that would be reached under these atmospheric conditions, but without infiltration, is shown as a vertical line.

qnet ⫽ qinput ⫺ qevap

[16]

where qinput is the input rate (mm yr⫺1) and qevap is the evaporation rate. At steady state, the fraction of water (E) lost to the atmosphere at any given time is E⫽

Minput ⫺ Mdrain Minput

where Minput is the mass of H2 O entering the top of the column, and Mdrain is the mass of H216O exiting draining through the bottom. The steady-state evaporation rate is then [18]

Substituting this relation into Eq. [16] gives the following relation for calculating steady-state net infiltration: qnet ⫽ qinput(1 ⫺ E)

values are shifted to higher values (⫹2.5 and ⫹3.9‰). These shifts to higher ␦18O values occur as water is evaporated after infiltration, decreasing the net infiltration in the coarser soils.

Periodic Infiltration [17]

16

qevap ⫽ Eqinput

Fig. 6. Capillary pressures respond to the annual cycle of wet and dry seasons in the VZFS300N lysimeter at Hanford (solid lines), and in a periodic infiltration model with silty-sand soil properties (dashed lines). Data from Sisson et al. (2002) and online at http:// vadose.pnl.gov (verified 3 June 2004). (1 mbar ⫽ 0.0001 MPa).

[19]

For a constant input rate of 50 mm yr⫺1, the calculated net infiltration rates for these models are 49 mm yr⫺1 for clayey silt, 46.3 mm yr⫺1 for silty sand, and 45.9 mm yr⫺1 for medium sand. In these constant infiltration models, the average ␦18O values of deep pore water are shifted to higher values than the input water (␦18O ⫽ ⫺16.5‰), depending on soil properties as predicted by the analytical model of DePaolo et al. (2004). Smaller grain size increases the liquid saturation in the sediments during infiltration, which in turn limits the amount of vapor loss near the surface under constant water input flux. The finest soil, clayey silt, has the highest liquid saturation ␪ (0.32) and the smallest shift toward higher ␦18O values at depth (⫹0.9‰). With increasing grain size in the silty sand and medium sand, the fraction of water retained in pore space under constant infiltration decreases (0.078 and 0.038, respectively), and the ␦18O

Under a constant infiltration flux, the lack of dry periods prevents the formation of the high ␦18O “bulge” that is commonly observed in arid and semiarid soil cores. As a more realistic alternative, the periodic infiltration model uses pulses of input water to approximate the wet and dry seasons at Hanford. The time-dependent input rate is set so that annually all of the infiltration comes during a 0.3-yr wet period and is followed by a 0.7-yr dry period. Changes in Moisture Content during Periodic Infiltration Changes in moisture content caused by wet and dry seasons are reflected in measurements of capillary pressure (Pcap) in the VZFS300N lysimeter (Sisson et al., 2002), a large (3 m wide by 7.6 m deep) caisson filled with sand from the Hanford formation and allowed to undergo natural recharge and drainage at the Hanford Site since 1978 (Gee, 1987). The lysimeter is instrumented with advanced tensiometers to measure Pcap (Sisson et al., 2002), and drainage is continuously monitored from a tipping cup at the bottom. The lysimeter has been kept vegetation free for more than 20 yr. The average drainage rate measured in the lysimeter during the past several years is 55 ⫾ 10 mm yr⫺1 (Sisson et al., 2002). Capillary pressure reaches a maximum shortly after the wet season, as the accumulated water percolates downward, increasing moisture content (Fig. 6). The time lags between capillary pressure maximums (less nega-


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tive values) recorded by successively deeper tensiometers give an estimate of the downward velocity of the wet season pulse (≈3 m yr⫺1 in 2002 and 7 m yr⫺1 in 2003). Following the post-wet season increase in Pcap, both drainage and evaporation gradually increase with a concurrent drying of the surface (decrease in the capillary pressure in the top several meters of soil) until the wet season of the following year. Model calculations of Pcap for silty sand during simulated wet and dry seasons reasonably match the observed annual variations in capillary pressures recorded by the 0.9- and 1.5-m-deep tensiometers in the lysimeter (Fig. 6). In the silty sand periodic infiltration model, Pcap increases to ⫺0.0043 MPa (⫺43 mbar) at 1.5 m following the wet season, which is simulated by the input of 50 mm of water in the top block of soil over 0.3 yr. Following this increase, Pcap gradually decreases during the following dry season to a minimum of ⫺0.0084 MPa (⫺84 mbar). Model results do not show the degree of damping with depth observed in the deeper tensiometers (Sisson et al., 2002) where the amplitude of Pcap variation decreases to approximately 0.001 MPa (10 mbar) at 2.1 m depth. This discrepancy may result from the model’s bottom boundary, which is not calibrated to capillary pressure conditions in the lysimeter at depth. To consider time scales of days to weeks, it may be necessary to include individual storm events to more accurately capture the measured capillary pressure variations. However, we find that the periodic infiltration model does capture the general form of seasonal variations in capillary pressure near the surface and is adequate for illustrating the impact of annual wet and dry cycles on stable isotope profiles as detailed below. Stable Isotope Profiles during Periodic Infiltration Figures 7A and 7B show the time-dependent pore water ␦18O values predicted using the periodic infiltration model for silty sand. Atmospheric and initial model conditions are the same as those used in the previous models of zero and constant infiltration. During the wet season, 50 mm of isotopically light input water (␦18O ⫽ ⫺16.5‰) infiltrates below the surface (Fig. 7A), resulting in ␦18O values that decrease toward the precipitation value. Below this minimum, ␦18O values increase slightly, where water from the previous dry season has mixed with infiltration water and percolated downward. During the dry season, a high ␦18O zone develops due to evaporation in the top 1 m of the profile (Fig. 7B). Periodic infiltration model results for a silty sand sediment column predict that a second set of these evaporation and preserved rain compositions may be present from the 1- to 2-m depth, where water from the previous infiltration event infiltrated deeper than the evaporation front. Below a depth of about 2.5 m, the pore water ␦18O reaches a steady value that is higher than the initial ␦18O value of the infiltrating water. The general features of the periodic infiltration model are distinct from drying conditions and are consistent with stable isotope profiles observed in the Hanford vadose zone. Specifically, these profiles have high pore

water ␦18O values due to evaporation near the surface, with deep vadose zone pore water ␦18O values that are consistently shifted several per mil higher than winter precipitation (Fig. 2). Dune sand isotope profiles with a subsurface isotopic minimum at the 1- to 2-m depth similar to these model predictions have been documented by Barnes and Allison (1988, their Fig. 12a and 12b) and were also attributed to the infiltration of isotopically light precipitation. Figure 7C shows the post-wet season (equivalent to Time Step 3 in Fig. 7B) ␦18O profiles for the three soil types considered in this study. Periodic infiltration model results for clayey silt predict the smallest shift in the ␦18O of net infiltration. The pulses of infiltration penetrate much deeper in the medium sand model because of its higher effective permeability. A constant ␦18O value for net infiltration in medium sand is not attained in the top 7.5 m considered here, but preliminary models of deeper soil columns indicate a pore water ␦18O at depth that is close to the value for silty sand. There are aspects of the clayey silt model (Fig. 7C) that do not precisely represent the likely conditions in Hanford soils. For example, we have effectively specified net infiltration, and in our model any net infiltration can be imposed on any soil type. However, in Hanford soils, net infiltration is correlated with (and controlled by) soil type (Gee and Ward, 2002). Soils with a large fraction of fine materials are associated with lower net infiltration fluxes than coarse soils. This relation occurs because, for a given amount of initial winter infiltration (which reflects winter precipitation) the water is kept close to the surface by fine soils, and hence the effects of summer evaporation are large and net infiltration is small or negligible. For coarser soils, initial infiltration penetrates to greater depth, and is less affected by summer evaporation. Our current model considers infiltration that penetrates at least 8 cm (the top grid block) into the soil, which may be deeper than the penetration of water into fine soils during typical storm events. To more accurately study finer soils such as clayey silt, it would be necessary to refine the upper grid blocks so that model infiltration more closely approximates the input of precipitation at the surface. Comparison with the Field Experiment Model results from a time step shortly after a wet season infiltration pulse may be compared with samples from an ongoing study, taken from the VZFS300N lysimeter 18 Mar. 2003, shortly after the end of the wet season (Fig. 8). Although this model is not calibrated specifically to the field experiment, the silty sand parameters (Table 1) are similar to parameters determined by inverse models of the lysimeter measurements (Zhang et al., 2003), making a reasonable comparison for considering periodic infiltration under analogous conditions. For an input rate (58.3 mm yr⫺1) adjusted so that at depth the steady state calculated qnet (Eq. [19]) is equal to the measured drainage rate for the lysimeter (55 mm yr⫺1), model predictions using periodic infiltration (Fig. 8, dashed line) indicate a profile similar to the ␦18O



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Fig. 7. A sequence of 0.1-yr time steps from the periodic infiltration model illustrates (A) disturbances to the isotopic profile during the wet season, Steps 1 through 2, and (B) the effects of drainage and evaporation during the dry season, Steps 3 through 9. The atmospheric conditions (h ⫽ 40% and ␦18Oa ⫽ ⫺21‰) are the same as those for Fig. 3 and 5. The soil type is silty sand for Parts A and B. (C) the ␦18O profiles at Time Step 3 for the three soil types considered in this study. Water input (␦18O of ⫺16.5‰) occurs such that annually all of the infiltration (50 mm) comes during the first 0.3-yr wet period and is followed by a 0.7-yr dry period.

data from samples collected in March 2003. In the model profile, infiltration leads to a minimum ␦18O peak (⫺15.8‰) at the 0.7-m depth. Below the minimum, ␦18O increases to a maximum of ⫺13.9‰ at 1.7 m where water evaporated during the previous dry season and infiltration water has mixed. The ␦18O value of net infiltration is predicted to be ⫺14.4‰, similar to the values observed in samples collected from deep within the vadose zone at the Hanford Site (Fig. 2). Various infiltration rates can be considered to predict the effects of changing environments on the ␦18O profile. For example, if the climate became wetter, or the surface was disturbed, infiltration may be expected to increase. A periodic infiltration model with a factor of three in-

crease in water input (qin ⫽ 150 mm yr⫺1; qnet ⫽ 147 mm yr⫺1) predicts a distinct isotopic profile that does not resemble the profile from March 2003 (Fig. 8). With increased infiltration rate, the low ␦18O pulse travels deeper into the profile, causing a broad low 18O zone in the top 3 m (␦18O ⫽ ⫺16.2‰). The deep maximum in ␦18O (⫺14.8‰) that consists of a mixture of old evaporated water and lower ␦18O infiltrating water occurs around the 3.6-m depth. Deep soil waters in this higher infiltration rate model are shifted only 0.7‰ higher than the ␦18O value of input water. A factor of three reduction in the infiltration rate may be considered to predict the isotopic record of consecutive dry years or increased water uptake by


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the effects of seasonal increases in precipitation, and predict stable isotope profiles that are distinct from those observed under drying conditions. Evaporation and equilibration with atmospheric vapor lead to nearsurface pore waters that are strongly shifted off of the meteoric water line during dry seasons. Repeated annual cycles of wet and dry seasons in a semiarid climate result in deep pore water compositions that show little variation and are isotopically heavier than the original precipitation value. The magnitude of the isotopic composition shift in deep vadose zone pore waters varies inversely to the rate of infiltration. ACKNOWLEDGMENTS

Fig. 8. Stable isotope profiles at the beginning of the dry season for pulsed infiltration models. The time-dependent input rates of winter infiltration of 16.7, 58.3, and 150 mm yr⫺1 result in calculated (Eq. [19]) steady-state net infiltration rates of 14.3, 55.0, and 147 mm yr⫺1, respectively. Water input (input water ␦18O of ⫺16.5‰) occurs such that annually all of the infiltration comes during the first 0.3-yr wet period and is followed by a 0.7-yr dry period. The soil type is silty sand, and atmospheric conditions (h ⫽ 40% and ␦18Oa ⫽ ⫺21‰) are the same as those for Fig. 3, 5, and 7. Model results are compared with data collected as part of an ongoing study of the VZFS300N lysimeter in March 2003, shortly after the wet season (diamonds). The lysimeter has a measured drainage rate of 55 ⫾ 10 mm yr⫺1 (Sisson et al., 2002).

plants. Decreasing the annual wet season input of water in the model to 16.7 mm yr⫺1 (qnet ⫽ 14.3 mm yr⫺1) results in a ␦18O shift in the profile, with a small minimum ␦18O of ⫺12.5‰ at 0.3 m (Fig. 8). Below this minimum, ␦18O increases to ⫺9.5‰ at 0.9 m, where input waters have mixed with evaporated water and percolated downward. In this low infiltration rate model, the ␦18O value of deep soil waters is shifted ⫹8.1‰ higher than the input water and is significantly higher than observed deep vadose zone values at Hanford.

SUMMARY AND CONCLUSIONS The reactive transport capabilities of TOUGHREACT are used to implement a new model of stable isotope transport in unsaturated soils. The model considers isotopic fractionation as well as diffusive and advective transport of independent isotopic species in the vapor and liquid phases. Stable isotope profiles are a dynamic record of evaporation and infiltration in the unsaturated zone. Numerical simulations of transport and isotope fractionation provide a method to quantitatively interpret stable isotope depth profiles on the basis of soil properties, climatic conditions, and infiltration through the vadose zone. In semiarid climates, alternating wet and dry seasons lead to annual fluctuations in moisture content, capillary pressure, and stable isotope compositions in the vadose zone. Periodic infiltration models capture

The authors wish to thank P.F. Dobson for a helpful internal review. Funding was provided by the Department of Energy under contract DE-AC06-76RL01830 through the Hanford Science and Technology Program, and by the Director, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division of the U.S. Department of Energy under Contract no. De-AC03-76SF00098.

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