Vadose Zone Journal 1:68-88 (2002)
© 2002 Soil Science Society of America
Fluid Flow, Heat Transfer, and Solute Transport at Nuclear Waste Storage Tanks in the Hanford Vadose Zone
Karsten Pruess*,a,
Steve Yabusakib,
Carl Steefelc and
Peter Lichtnerd
a Earth Sciences Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720
b Pacific Northwest National Laboratory, Richland, WA 99352
c Energy and Environment Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94551
d Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545
* Corresponding author (K_Pruess{at}lbl.gov)
Received 3 December 2001.
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ABSTRACT
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At the Hanford Site, highly radioactive and chemically aggressive waste fluids have leaked from underground storage tanks into the vadose zone. This paper addresses hydrogeological issues at the 241-SX tank farm, especially focusing on Tank SX-108, which is one of the highest heat load, supernate density and ionic strength tanks at Hanford and a known leaker. The behavior of contaminants in the unsaturated zone near SX-108 is determined by an interplay of multiphase fluid flow and heat transfer processes with reactive chemical transport in a complex geological setting. Numerical simulation studies were performed to obtain a better understanding of mass and energy transport in the unique hydrogeologic system created by the SX tank farm. Problem parameters are patterned after conditions at Tank SX-108, and measured data were used whenever possible. Borrowing from techniques developed in geothermal and petroleum reservoir engineering, our simulations feature a comprehensive description of multiphase processes, including boiling and condensation phenomena, and precipitation and dissolution of solids. We find that the thermal perturbation from the tank causes large-scale redistribution of moisture and alters water seepage patterns. During periods of high heat load, fluid and heat flow near the tank are dominated by vapor–liquid counterflow (heat pipe), which provides a much more efficient mechanism than heat conduction for dissipating tank heat. The heat pipe mechanism is also very effective in concentrating dissolved solids near the heat source, where salts may precipitate even if they were only present in small concentrations in ambient fluids. Tank leaks that released aqueous fluids of high ionic strength into the vadose zone were also modeled. The heat load causes formation dry-out beneath the tank, which is accompanied by precipitation of solutes. These may become remobilized at a later time when tank temperatures decline and previously dried out regions are rewetted. Simulated temperature and moisture distributions compare well with borehole measurements performed in 2000. The temperature maximum observed beneath Tank SX-108 can be explained from past thermal history of the tank; it is not necessary to invoke heat generation from leaked radioactive contaminants. A novel composite medium model is used to explore effects of moisture tension–dependent anisotropy, which is shown to have important impacts on fluid flow and solute transport in the Hanford sediments.
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INTRODUCTION
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A VERY UNUSUAL HYDROGEOLOGIC SYSTEM, namely, the large complex of underground storage tanks at the Hanford reservation is the subject of this study. Located on the Columbia River plateau, a semiarid region in south-central Washington (Fig. 1), the Hanford Site served as a plutonium production facility for nuclear weapons from 1944 to the end of the Cold War era. A total of 177 large underground tanks were constructed in the Hanford vadose zone to store waste fluid streams from the plutonium extraction facilities. Many of the older single-shell tanks have leaked radioactive waste fluids, posing a contamination hazard for the underlying aquifer and ultimately the Columbia River. Our analysis specifically addresses the 241-SX tank farm (Fig. 2), where highly radioactive and chemically aggressive aqueous fluids of high ionic strength have leaked into the vadose zone. Of interest is the nature and extent of subsurface contamination; the past, present, and future migration of contaminants; and hydrogeologic issues posed by possible future remedial actions.
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Fig. 2. Plan view of the 241-SX tank farm, located in the 200 West area, after Conaway et al. (1997). The shaded region around Tank SX-108 indicates an approximate symmetry domain. The locations of monitoring Borehole 41-09-39 and of a slant hole drilled under Tank SX-108 are also shown.
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Construction and operation of the SX storage tanks since the mid 1950s involved massive perturbations of the natural hydrogeologic system. At the SX tank farm, the ground was excavated down to 15.4 m depth, and 15 large cylindrically shaped storage tanks with approximate dimensions of 13.6-m height and 11.8-m radius were emplaced in a regular pattern with 30.4-m spacing between tank centers (Fig. 2, 3). The excavated material was then backfilled, and a gravel layer 1.8 m thick was placed on top. The latter led to a substantial reduction in evapotranspiration and increase in net infiltration. Water migration in the unsaturated zone was profoundly altered by the umbrella effect of the tanks that diverts water around the tank perimeters and by altered hydrogeologic properties in the backfilled region. Additional effects arose from the heat generated by the radioactive wastes in the tanks. Temperatures in several tanks rose to well above the nominal boiling point of 100°C, in one case up to 160°C, for extended time periods (Fig. 4). This caused elevated formation temperatures with vaporization–condensation effects and associated redistribution of moisture and solutes. Tank leaks introduced into the subsurface hot and highly saline aqueous fluids, whose thermophysical properties and flow behavior may be quite different from pure water. Further changes in flow behavior could result from chemical alteration of the sediments because of reactions with the fluids.
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Fig. 3. Approximate geometric parameters for tanks in 241-SX tank farm. The tanks as constructed have a domed top that is approximated here by two straight line segments.
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The physical and chemical processes affecting conditions at and around the tanks are being played out in a complex natural setting that is subject to human alterations and perturbations that are only imperfectly known. Modeling of the impacts of heat-generating tanks and leaked fluids on the Hanford vadose zone involves challenges along four different lines:
Hydrogeological Properties.
The Hanford sediments are heterogeneous, with predominant horizontal or subhorizontal layering. There is considerable variability within layers, as well as complicating features such as pinchouts and clastic dikes (Khaleel and Freeman, 1995; Khaleel et al., 2000).
Complex Coupled Processes.
Fluid flow, heat transfer, and solute transport at the SX tank farm are made substantially more difficult to analyze by boiling and condensation processes induced by the high heat load from the tanks, and by the unusual and extreme thermodynamic and thermophysical properties of the fluids, including high ionic strength, large density and viscosity, chemical reactivity, and heat generation from radioactive decay.
Natural Forcings.
This includes the initial moisture distribution, and rates and timings of deep infiltration events. Further complications arise from nonaverage flow behavior that is promoted by the layered stratigraphy, including lateral flows at certain horizons, and other localized preferential flow effects.
Human Perturbations.
In spite of an extensive monitoring program, there are significant uncertainties in tank temperatures and in the rate of heat release. High radiation levels make it very difficult to perform measurements near the tanks. The timing, magnitude, and composition of fluid leaks is also only partially known.
Each of these four areas involves issues of scale and resolution, in both space and time.
Investigations of hydrogeologic conditions and processes at the Hanford tanks have been conducted for several decades, including field monitoring and sampling within and outside of the tanks (Raymond and Shdo, 1966; Rockhold et al., 1988; Khaleel et al., 2000; Sobczyk, 2000), field experimentation (Sisson and Lu, 1984; Ward and Gee, 2001), laboratory measurements (Khaleel and Freeman, 1995; Khaleel et al., 1995; Khaleel and Relyea, 1997), and modeling (Smoot and Lu, 1994; Kline and Khaleel, 1995; Ward et al., 1997; Rockhold et al., 1997; Rockhold, 1999; Piepho, 1999). These studies have led to continuous improvement of our qualitative and quantitative understanding of the distribution and fate of tank wastes released into the Hanford vadose zone and have provided support for the development and implementation of environmental management options.
From an environmental management perspective, important issues at the SX tank farm include past, present, and future distribution and migration of contaminants for a "no action" scenario, as well as for various remedial measures that may be considered (such as placing covers to reduce net infiltration, or removing tank contents through sluicing; Haass, 1999). A key task for performance assessment is to predict the future rates at which different contaminants may be expected to reach the water table and enter the groundwater system. The complexity and intrinsic variability of hydrogeologic conditions and processes is such that a strictly deterministic description is not possible. Performance assessment must adopt simplified models and representations, which must be complemented by stochastic representations of uncertainties. In order to be credible and acceptable, the simplifications and approximations made in performance assessment models must be based on a sound scientific understanding of the underlying processes.
The purpose of the studies reported here is to contribute to a better understanding of the unique hydrogeologic system created by the Hanford tanks through detailed mechanistic modeling of fluid flow, heat transfer, and mass transport. Our aim is to provide support and guidance for performance assessment, field characterization, and decision making on remedial measures. We focus especially on Tank SX-108, which is one of the highest heat load tanks in the 241-SX tank farm, and is a known leaker. A realistic quantitative model of mass and energy transport near the tanks requires (i) comprehensive treatment of all significant physical and chemical processes, (ii) accurate representation of hydrogeologic conditions at the site, and (iii) realistic parameters for fluids and sediments and for temperature and leak history of the tanks.
These are ambitious goals that can only be reached through a process of iterative refinement, starting from relatively simple models. The main emphasis of the work reported here is on physical effects, focusing on the extent to which various multiphase and nonisothermal processes may impact the migration of moisture and aqueous solutes. The only chemical interactions considered here involve precipitation and dissolution of salts; more complex chemistry such as ion exchange between leaked fluids and clay phases in the sediments, and mineral alteration effects, are considered in ongoing research (Steefel et al., Lichtner et al., 2002, unpublished data). We have attempted to represent significant hydrogeologic features of the Hanford sediments in an approximate way, but have made only limited efforts to capture detailed hydrogeologic conditions at a specific tank. Our specific objectives are to (i) develop an understanding of the main fluid flow and heat transfer processes and hydrogeologic features that determine the behavior of leaked tank wastes, (ii) determine the sensitivity of system behavior to uncertain parameters and conditions, and (iii) use field observations and data to better constrain the amount, distribution, and behavior of leaked fluids. We proceed by first presenting a simplified "base case" that is intended to provide an approximate outlook on system behavior. Specific effects and variations of process descriptions and parameters are then explored in order to gain insight into sensitivities and uncertainties, to develop guidance for future site characterization efforts, and to determine which processes are important for contaminant behavior, and how they can be modeled effectively. Model predictions are evaluated in the context of field observations on subsurface temperatures and moisture distributions.
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Modeling Approach and Specifications
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Modeling of fluid flow, heat transfer, and mass transport at the Hanford tanks is complicated by intrinsic variability of the geologic media and by the complex forcing of the system from natural and human perturbations. Important processes include water seepage from infiltration, umbrella effect and heat output of the tanks, and leakage of fluids with high ionic strength and internal heat generation. Our modeling approach borrows from techniques developed in petroleum and geothermal reservoir engineering and in mining engineering. Several different numerical simulators were used and occasionally enhanced as needed, including FLOTRAN (Lichtner, 2001), NUFT (Nitao, 1998), STOMP (White and Oostrom, 1996), and TOUGH2 (Pruess et al., 1999). These simulators have in the past been applied to numerous field and laboratory problems, where they have been shown to be capable of useful quantitative predictions when adequate characterization data were available. They feature a full multiphase treatment of the simultaneous flow of aqueous and gas phases under gravity, capillary, and viscous forces, using an extended version of Darcy's Law with relative permeability and capillary effects. The aqueous phase may include dissolved solids and gases in addition to water; the gas phase is a mixture of water vapor and air. In some cases, tracers of different solubility and volatility may also be present, and precipitation and dissolution effects may be considered. Fluid properties that determine flow behavior generally depend on temperature, pressure, and composition (salinity). Heat transport occurs by conduction and convection, including latent heat effects from vaporization and condensation. Diffusion of air and vapor is considered, as are effects of vapor pressure lowering from capillary effects, and from salinity of the aqueous phase. Some of the simulations presented below use a simplified treatment, such as isothermal conditions with the gas phase a passive bystander at constant pressure (Richards, 1931), while others include comprehensive multiphase processes and effects of temperature and salinity. Most of the calculations presented here were done with the TOUGH2 simulator (Pruess et al., 1999), using the EWASG fluid property module for multiphase mixtures of water, NaCl, and air (Battistelli et al., 1997). EWASG models air as a single pseudocomponent. The calculations presented below do not include hydrodynamic dispersion.
We have simulated different cases to explore mechanisms and sensitivities. Each case requires several (typically two) modeling segments to describe changes in boundary conditions, formation properties, and sinks and sources from tank construction and from storage and leakage of waste fluids. The modeling process begins with the calculation of a "natural state" that corresponds to hydrogeologic conditions prior to tank construction. The natural state is approximated as steady flow (gravity–capillary equilibrium) under conditions of uniform and time-independent net infiltration. Subsequent emplacement of tanks is modeled by using the previously calculated steady-state conditions as initial conditions and (i) modifying hydrogeologic parameters in the regions occupied by tank and backfill, (ii) altering evapotranspiration conditions at the land surface as appropriate for bare gravel surfaces atop the tanks, and (iii) introducing appropriate time-dependent sources of heat and saline fluids to model radioactive decay heat and fluid leakage from the tanks.
Geometry
Our simulations focus on the centrally located Tank SX-108, which is one of the highest heat load tanks at Hanford and is a known leaker. The starting time of the tank simulations is in November 1955, when Tank SX-108 was first put into service. To simplify the analysis, we consider the vertical planes that bisect the lines between tank centers as planes of symmetry (Fig. 2). This will only be approximately valid even for the centrally located Tank SX-108, because of different heat loads from different tanks and intrinsic variability in hydrogeologic properties. However, this simplification is suitable for a study that focuses on coupled multiphase fluid and heat flow effects. It greatly facilitates the analysis because it is only necessary to model the shaded region in Fig. 2, with no flow conditions applied at the lateral boundaries. We make a further approximation and replace the rectangular model domain by a cylinder with radius chosen in such a way as to preserve the cross-sectional area (i.e., 
R2 = 30.4 x 30.4 m2, so that R = 17.15 m). The simulation model then simplifies to a two-dimensional R–Z section (radius–depth). Geometric parameters used in the model were obtained from a construction diagram of Tank SX-108, and are shown in Fig. 3.
Hydrogeologic Parameters
The dominant hydrogeologic feature at the Hanford Site is the layered structure of the sediments, which is due to the depositional history from a series of cataclysmic floods. However, texture, permeability, and porosity of the individual hydrogeologic units is far from uniform. An intensive program of field sampling and testing, and laboratory analysis, has revealed considerable heterogeneity within individual hydrogeologic units, with permeabilities of bench-scale specimen typically varying over three to four orders of magnitude (Khaleel and Freeman, 1995; Khaleel et al., 1995; Khaleel and Relyea, 1997; Smoot and Lu, 1994; Rockhold, 1999; Khaleel et al., 2000). The predominant large-scale layered structure of the Hanford sediments is significantly perturbed on a local scale; for example, a sloping layer of coarser material has been identified beneath tanks SX-108 and 109 (Price and Fecht, 1976; Khaleel et al., 2000). Additional complications arise from the presence of clastic dikes (Fecht et al., 1999). These form extensive networks of subvertical structures that could play a role in generating localized preferential flow.
The approach taken in this work is to start from a simplified representation of hydrogeologic structure that honors large-scale layering. As the understanding of process-related issues and applicable parameters improves, more specific hydrogeologic features known to exist near SX-108 may be introduced in stepwise fashion. In the present work, the formation is modeled with "layer-cake" stratigraphy, as shown in Table 1 and Fig. 5.
Hydrogeologic parameters include permeability and porosity for all stratigraphic units, as well as relative permeability and capillary pressure functions. Parameters for permeability, porosity, and characteristic curves (capillary pressure and relative permeability) were assigned by selecting values deemed representative from the extensive compilation given by Khaleel and Freeman (1995). A summary of parameters used for the reference case is shown in Tables 2 and 3. For capillary pressure and relative permeability relationships, we use the van Genuchten–Mualem model (Mualem, 1976; van Genuchten, 1980).
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with
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where Slr is the irreducible water saturation and Sls is the "satiated" water saturation, here assumed equal to 1. Parameter m is a pore-size distribution index that determines the shape of the functions, and 
is a capillary strength parameter. The parameter Slr in the capillary pressure function was chosen different from that in the liquid relative permeability function, and was in fact set to zero. This was done to avoid an unphysical feature of van Genuchten's parameterization in which Pcap 
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when krl 0, which will have little impact on unsaturated flow at ambient conditions, but can cause spurious effects in thermally driven systems that may approach dry-out (Pruess, 1997).
Gas relative permeabilities for the Hanford sediments have not been measured. We employ the function of Corey (1954) that is widely used in oil and gas reservoir engineering; it is given by
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with the reduced saturation
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Sgr is the irreducible gas saturation, which we take as Sgr = 0.05. Test calculations have shown that flow behavior is only weakly dependent on gas relative permeability.
Molecular diffusion of air and water vapor in the gas phase is modeled as Fickian (Webb and Pruess, unpublished data, 2001), with diffusive flux of component 
(= air, vapor) given by (Pruess et al., 1999)
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Here, 
is porosity; 
0g is the tortuosity, which includes a porous medium dependent factor 0 and a coefficient that depends on gas phase saturation Sg; g = g
; 
g is density; dg is the diffusion coefficient of component in bulk gas phase; and Xg is the mass fraction of component . The gas phase tortuosity coefficient is taken equal to gas relative permeability, g = krg (Pruess et al., 1999). The vapor–air diffusion coefficient is a function of pressure and temperature, and is given by (Vargaftik, 1975)
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At standard conditions of P0 = 1 atm (0.101325 MPa) 
1.01325 bar, T0 = 0°C, the diffusion coefficient for vapor–air mixtures has a value of 2.13 x 10-5 m2 s-1; parameter 
for the temperature dependence is 1.80 (Vargaftik, 1975).
Experimental and modeling studies have established that in unsaturated porous media, vapor diffusion is enhanced relative to the diffusion of noncondensible gases by pore-level phase change effects (Philip and de Vries, 1957; Cass et al., 1984; Webb and Ho, 1998). Enhancement coefficients are poorly known for field-scale systems, and no such effects have been included in the present study. At temperatures approaching or exceeding the boiling point, macroscopic advection and diffusion of vapor will dominate over pore scale effects.
For the base case we used a rough approximation for formation anisotropy that consists of reducing vertical permeabilities by a factor 3 in all domains except for the backfill, which is believed to be less anisotropic and was assigned a horizontal to vertical permeability ratio of 2. A more detailed analysis and representation of moisture tension–dependent anisotropy was also done, using a novel composite medium model (see below).
Computational Grid
In order to minimize discretization errors, it is desirable to use fine gridding, especially in regions where large gradients in thermodynamic state variables are expected. On the other hand, finer discretization increases the computational work, not only by increasing the number of grid blocks, but also because achievable time steps will be smaller. The grid used here represents a compromise between these conflicting demands. We have limited the number and spatial resolution of grid blocks, but we have provided for finer gridding in regions where important process controls are expected. The computational grid as shown in Fig. 5 has 22 blocks in the R-direction and 44 layers, for a total of 968 grid blocks. The entire tank volume is included in the discretization domain but is omitted from Fig. 5b. The region occupied by the tank is assigned hydrologic properties appropriate for that depth interval (Tables 1 and 2) prior to tank emplacement (1955), and is given zero permeability afterwards. Radial grid increments are 
R = 1 m near the tank center, decrease to 0.53 m near the perimeter of the tank, and then increase to 0.98 m at the outer boundary of the model domain. Vertical thickness of grid layers varies from 0.33 to 4 m. Finer gridding is used near the land surface, near the bottom of the tank, and at lithologic contacts.
Boundary and Initial Conditions
Actual land surface boundary conditions atop the tanks are complex and highly variable. Net infiltration is determined by an interplay of episodic precipitation and snow melt events with evapotranspiration processes that depend on atmospheric conditions of temperature, relative humidity, and wind speed, as well as on thermal radiation and heat supplied from the tanks. No attempt has been made yet to model and resolve these complex mass and heat transport processes on the space and time scales on which they are actually occurring. In this study, we adopt time-independent boundary conditions at the land surface that are intended to capture long-term averages.
Long-term annual average precipitation at the 241-SX tank farm site is in the range of 160 to 190 mm yr-1, but values as high as 300 mm yr-1 have been observed in some years (Hoitink and Burke, 1996; Ward et al., 1997). Depending on soil conditions and vegetative cover, much of the precipitation at Hanford may be lost to evapotranspiration. Net infiltration has been estimated to "vary from less than 0.1 mm yr-1 on a variety of soil and vegetative combinations to greater than 130 mm yr-1 on bare basalt outcrops or bare, gravel-surfaced waste sites" (Gee et al., 1992; cited after Ward et al., 1997).
As suggested in previous modeling studies at Hanford (Kline and Khaleel, 1995; Ward et al., 1997), we assume a net infiltration of 10 mm yr-1 at pre-emplacement conditions. At the bottom of the model domain (68-m depth) water pressure is fixed at 0.1405 MPa (1.405 bar), so that the water table will be at approximately 64 m depth. Initial water saturation for the natural state simulation does not affect the eventual steady state and was chosen as an arbitrary 60%. Temperature boundary conditions are a mean land surface temperature of 12.8°C, and a temperature of 17.26°C at the 68-m depth (Piepho, 1999). Net infiltration at the land surface boundary is increased to 100 mm yr-1 following tank emplacement (Khaleel et al., 2000). Relative humidity at the land surface is held constant at an average value of RH = 50%.
Heat generation from the tank is modeled by specifying actual measured tank temperatures T(t) (see Fig. 4) as time-dependent boundary conditions on the tank surface. The tank fluid has a boiling temperature of approximately 112°C at ambient pressure (Tom Jones, private communication), and this is considered to be the maximum temperature attainable at the sidewall and top of the tank. Considerably higher temperatures may be reached in the solid sludge deposited from the waste fluids at the bottom of the tank. Accordingly, base case temperature assignments on the tank surface are made as follows.
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The temperature data shown in Fig. 4 only cover the period to 1981. For the base case simulation, temperatures after 1981 were fixed at the 1981 values. In the course of this study, additional, more detailed temperature records were found; these were used in some sensitivity studies (see below). Fluid leaks were also modeled.
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Simulated System Behavior
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Before presenting results for the base case simulation, we give a general overview of the main thermohydrologic processes near the tank. A schematic of thermohydrologic processes during a period where tank temperatures are above boiling is shown in Fig. 6. Infiltrating water ponds atop the tank, where a small fraction is vaporized, while most is shed around the tank perimeter at flux rates that are considerably larger than the 100 mm yr-1 applied net infiltration. The large water fluxes provide localized cooling. As water descends it picks up heat released from the tank and boils at increasing rates. A zone of strong boiling with partial or complete formation dry-out forms around the bottom of the tank, and is especially pronounced in the infiltration shadow beneath the tank. The vapor generated by the boiling is transported away from the tank primarily by advection driven by the pressurization resulting from boiling, as well as by molecular diffusion. It condenses in cooler regions at larger distance from the tank, depositing a large amount of latent heat. The condensation zone forms a halo surrounding the boiling and dry-out zones. The boiling and condensation processes cause a redistribution of moisture, which sets up capillary pressure gradients that draw liquid water back towards the tank. Overall this leads to a vapor–liquid counterflow process known as heat pipe, which is a very efficient heat transfer mechanism (Eastman, 1968; Doughty and Pruess, 1988). It rapidly distributes tank heat at substantially larger rates and over a larger volume in the vadose zone than would be possible from heat conduction alone. For a given tank heat generation rate, the heat pipe process substantially reduces tank temperature increases relative to what would be obtained for a conduction-only system. The vapor–liquid counterflow system also gives rise to persistent solute transport to the tank, causing solute concentrations to increase to large values even when concentrations in ambient vadose zone fluids are low.
Specific simulation results obtained for the base case are given as cross sections of temperatures, water saturations, and fluid salinities at different times, as well as time series of various parameters at selected locations marked in Fig. 7. The highly elevated temperatures in the early period, up to 1967, give rise to boiling near the tank and partial formation dry-out. Formation temperatures near the tank rise to above 120°C, and an extensive zone with temperatures near the ambient boiling temperature of 100°C develops (see Fig. 8, 9). This is a heat pipe region in which very efficient heat transport takes place by means of vapor–liquid counterflow. Figure 10 shows the time dependence of water saturations above and below the tank; for comparison we have also included results for an isothermal case in which a Richards' equation approximation was used. It is seen that the tank heat considerably reduces the saturation buildup above the tank relative to what would be predicted for an isothermal case. Saturations in the infiltration shadow below the tank show a modest decline for the isothermal case, while complete dry-out occurs when tank heat effects are considered.
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Fig. 7. Locations for monitoring temporal changes: 30 cm below the tank, 0.5 m from centerline (1); 16.5 cm above tank, 0.5 m from centerline (2); at 4.1 m depth, 29 cm from sidewall (3); 30 cm below the tank, 29 cm from sidewall (4).
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Fig. 10. Time dependence of water saturations at selected locations. "Above tank" is location (2) and "below tank" is location (1) in Fig. 7.
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In order to facilitate understanding of simulated flow behavior, we included a small amount of solute tracer, 0.1 % (w/w) NaCl, in the water infiltrating from the land surface. Figure 11 shows contour diagrams of the mass fraction of infiltrated fluid at three different times. It is seen that during a high heat period in 1965 (Fig. 4) large mass fractions of infiltrated fluid are present in several locations near the tank. A more detailed inspection of simulation results shows that NaCl mass fractions in the aqueous phase in the hot region near the tank reach solubility limits, and a large fraction of infiltrated solute tracer is deposited as solid precipitate. At time 1965.91 precipitated salt amounts to 55.3% of all NaCl that was infiltrated at the land surface. This amount of precipitation is very large, especially when considering that the infiltrating fluid is quite dilute, 0.1% (w/w) NaCl, showing the remarkable capacity of the heat pipe system to concentrate solutes near the heat source. As temperatures decline, the region near the tank is rewetted, both from capillary-driven liquid flow and from vapor condensation. By the end of 1974, all previously precipitated tracer is redissolved (not shown in plots). Over time, the descending solute plume is drawn by capillarity towards the region under the tank, where moisture contents had decreased during the hot phase prior to 1967, see the t = 2000 yr frame in Fig. 11.
The solute tracer in the infiltrating water was arbitrarily modeled as NaCl, but it can represent any nonsorbing solute, such as NO-3, or Tc-99 in the form of TcO-4. Tracer breakthrough curves at different horizons are given for the thermal and isothermal cases in Fig. 12 on a logarithmic scale. These curves were obtained by summing all tracer fluxes that cross a horizon at a certain depth, then dividing this by the total liquid flux across that same horizon, and normalizing with respect to tracer concentration in infiltrated fluid. It is seen that early arrivals of tracer are somewhat enhanced from the tank heat, but thermal effects on aggregated tracer migration are generally modest, except at the 16-m horizon right beneath the tank.
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Fig. 12. Breakthrough curves for a hypothetical solute tracer that was infiltrated at the land surface beginning in 1955.82. Breakthrough curves are shown on a log scale at different depths. Lines are for the base case with tank heat, while symbols are for an isothermal approximation.
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Figure 13 shows rates of vapor diffusion across two different horizons, at the 0.5-m depth, and across the land surface boundary. The mass rates of diffusion obtained in the simulation were also converted to a "cold water equivalent" volumetric rate, so that they may be directly compared with the applied net infiltration of 100 mm yr-1. Diffusive vapor fluxes are highest near the tank, and decrease rapidly due to condensation as the land surface is approached. During high-temperature periods vapor diffusion at the 0.5-m depth amounts to approximately 10% of net infiltration, while at the land surface itself the effect is <4% of net infiltration.
Tank Leak
A separate simulation was performed to investigate the behavior of a tank leak. For this calculation pure water (without solute tracer) was infiltrated at the land surface. The predominant solute in the tank fluid is NaNO3; however, the leak was modeled here as involving a solution of 10% (w/w) NaCl. This was done because a fluid property description for NaCl solutions was readily available for the temperature conditions of interest (Battistelli et al., 1997), while experimental data for NaNO3 solutions appear to be limited to temperatures below 55°C (Isono, 1984; Mahiuddin and Ismail, 1996; Apelblat and Korin, 1998). A new correlation developed by Lorenz et al. (2000) was used to describe the enthalpy of NaCl solutions, as the formulation given by Battistelli et al. (1997) is not valid for temperatures below 100°C. A fluid property package for aqueous solutions of NaNO3 is under development (Xu and Pruess, 2001). Figure 14 taken from Xu and Pruess (2001) compares some thermophysical properties of NaCl and NaNO3 solutions. Kinematic viscosities (µ/) are seen to increase with increasing solute concentrations; that is, viscosity increases more strongly than density, indicating that more concentrated solutions are less mobile than water. At a given mole fraction, NaCl solutions are subject to stronger vapor pressure lowering than NaNO3 solutions. Because of these differences, substitution of NaCl is expected to provide only a rough first approximation for system behavior.
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Fig. 14. Selected thermophysical properties of NaCl and NaNO3 solutions, including (a) kinematic viscosity and (b) vapor pressure (from Xu and Pruess, 2001). NaNO3 data at 90°C represent extrapolations of experimental data.
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Reliable information on location, timing, and magnitude of leaks is not available. For Tank SX-108 it has been estimated that a leak occurred in the 1966 to 1968 time frame, during which approximately 189.27 m3 (50 000 gallons) of fluid were discharged into the unsaturated zone (T. Jones, private communication, 2000). We assume here that the leak occurred over a 1-yr period during 1966, so that average volumetric leak rate is 5.998 x 10-6 m3 s-1.
Another limitation arises from the radial symmetry of our current model, which forces tank leaks to be radially symmetric also. Accordingly, we consider a leak beneath the center of the tank and apply the leak fluid uniformly over a region of 3-m radius. Our simulation includes most but not all effects of salinity on thermodynamic and transport properties of the leaked fluid. Specifically, we include salinity effects on density, viscosity, enthalpy, and vapor pressure of the aqueous phase. Vapor pressure lowering (VPL) from salinity will induce vapor diffusion towards more saline regions, where subsequent vapor condensation will cause water saturations to increase. Our simulations show that salinity-induced VPL can be an important mechanism for redistributing moisture. Fluid salinity is known to affect surface tension; for example, a saturated NaCl solution at T = 20°C has a surface tension approximately 10% larger than pure water (Adamson, 1990). This effect should cause capillary pressures to be somewhat stronger in regions of higher salinity, while the decrease of surface tension with increasing temperatures would weaken capillary pressures in warmer regions. Surface tension of water decreases by 19.2% in the temperature range from 20 to 100°C (Vargaftik, 1975). In the present simulation effects of salinity and temperature on surface tension were neglected.
Results are shown in Fig. 15 and 16. The leaked fluid plume advances downward somewhat more slowly than for an isothermal approximation (not shown), which can be explained from the partial dry-out of the sediments beneath the tank in the thermal regime. A more detailed evaluation can be made by comparing breakthrough curves at different horizons. In Fig. 16 we have plotted flowing leaked fluid mass fractions at different depths, calculated as the ratio of total solute flow rate to total aqueous phase flow rate, and normalized to the solute concentration in leaked fluid (10%, w/w). It is seen that inclusion of thermal effects has negligible impact on the breakthrough time of leaked fluid at the 26-m depth, although the concentration of leaked fluid remains lower in the thermal case for an extended time period of more than 20 yr.
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Fig. 15. Leaked fluid distribution at different times (in years), following a 189.27-m3 (50 000-gallon) tank leak with 10% (w/w) salinity in 1966.
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Fig. 16. Breakthrough curves of leaked fluid released beneath tank center at different horizons. Lines are for the base case with tank heat, while symbols are for an isothermal approximation.
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The solute transport analyses presented here were made under the assumption of a perfectly mixed tracer migrating through a layered, single-porosity porous medium. Future studies will further address multiregion and preferential flow effects (Gwo et al., 1996; Hutson and Wagenet, 1995; Pruess, 1999), as well as competitive sorption of species such as Cs+, Na+, Ca2+, and Mg2+ (Steefel et al., unpublished data, 2002). Also, in addition to leaks of waste fluids from the tanks, there may have been leaks from underground water pipes that are present in the 241-SX tank farm area. Water line leaks have sometimes been invoked by Hanford personnel as possible contributors to mobilizing solutes, but we have not been able to locate any quantitative information on magnitude, timing, or location of such leaks.
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Problem Variations and Comparison with Data
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Simplified Treatment of Salinity Effects
A variation of the nonisothermal tank leak case was run in which all effects of salinity were neglected, except for constraints on total NaCl solubility. This produces some differences in details; for example, when VPL effects from salinity are ignored, moisture transport to the inner part of the saline plume by means of vapor diffusion is suppressed. This leads to lower water saturations there, which in turn considerably increase precipitation of solid salt. More specifically, at t = 1973.66 approximately 29.3% of leaked solute has been precipitated out in the simulation that includes comprehensive salinity effects, while 49.9% has precipitated in the simulation that neglects vapor pressure lowering from salinity. However, such significant differences are limited to a rather small region inside the leaked plume. Patterns of leaked fluid fractions and solute breakthrough curves for the simulation that neglects all salinity effects except the solubility constraints are virtually identical to those for full salinity effects shown in Fig. 15 and 16. It is somewhat surprising that the many changes in fluid properties and flow and transport processes from salinity produce such small net effects. In this regard it should be noted that both fluid density and viscosity µ increase with salinity in a manner such that kinematic viscosity µ/, hence fluid mobility, is little affected (Battistelli et al., 1997; Xu and Pruess, 2001). Effects of vapor diffusion towards regions of higher salinity are limited because vapor pressure is more strongly affected by temperature than by salinity.
Saturation-Dependent Thermal Conductivities
For variably saturated conditions, thermal conductivity is known to depend on water saturation. We adopt a correlation recommended by Somerton et al. (1973)(1974),
 | [9] |
For Kdry we use a value of 0.25 W (m °C)-1 that was measured for SX tank farm sediments (Bouse, 1975) and is in agreement with literature data for dry soils (de Vries, 1963). For fully saturated conditions we use Kwet = 2 W 
-1. According to Eq. [9] the value of K = 0.5 W -1 used in the base case is reached at a small water saturation of Sl = 2.04%. Thus, thermal conductivities from Eq. [9] will be larger than those used in the base case in most regions, with smaller conductivities only for very low water saturation, such as in the dry-out zone beneath the tank. Temperature and saturation distributions obtained using Eq. [9] are very similar to the base case, but there are surprisingly large differences in the concentration and precipitation behavior of solutes. For the case with no tank leak, and infiltrating a 0.1% (w/w) NaCl solution at the land surface, only 2.9% of infiltrated NaCl is deposited as solid precipitate in 1965.91, compared with 55.3% in the calculation with saturation-independent K = 0.5 W -1. Precipitation of solutes from tank leak fluids is also very sensitive to the thermal conduction model, but here the situation is the reversed; namely, the simulation with K = K
gives considerably stronger precipitation, see Table 4. These differences occur because precipitation takes place in different regions and thermodynamic regimes. In the base case, solutes infiltrating from the land surface precipitate primarily around the tank perimeter, starting at approximately the 8-m depth and extending to the bottom of the tank. This precipitation is much weaker when saturation-dependent thermal conductivities are used because in that case there is no formation dry-out around the tank perimeter. In contrast, the solutes released from a leak beneath the center of the tank precipitate in the dry-out zone in the infiltration shadow beneath the tank. For the case with K = K, precipitation is predicted to occur in six grid blocks immediately beneath the center of the tank, occupying from 2.4 to 8.2% of pore space in five of the blocks, and as much as 50.5% of pore space in the sixth block. Such reductions in porosity may cause substantial reductions in permeability, although there is considerable uncertainty about the quantitative aspects of permeability reduction from porosity (Verma and Pruess, 1988; Pape et al., 1999). In our simulations permeability changes were neglected, which is believed to be permissible because very little flow is taking place in the region where salts were deposited. Note that precipitates deposited beneath the tank persist for a long time (decades; see Table 4), even as the region that was dried out during the hottest period returns to two-phase conditions. This is an effect of the infiltration shadow, which reduces water flow to very low rates in that region. From Table 4 it is seen that the amount of precipitate redissolved in a given time period is similar for the two thermal conductivity models.
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Table 4. Simulated results for solute precipitation from tank leak. Percentages indicate fraction of solutes deposited as solids.
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Heat Generation
Another issue is heat generation from fluid that was leaked from Tank SX-108. Gross and spectral gamma logging in vadose zone boreholes has indicated the presence of 137Cs and other radioactive species beneath Tank SX-108 (U.S. Department of Energy, Grand Junction Office, 1995; Serne et al., unpublished data, 2002). Cesium-137 migration is subject to considerable retardation from sorption on clays (Steefel et al., unpublished data, 2002). The slant hole beneath SX-108 showed large 137Cs gamma counts in the depth interval from -16 to -27 m. The concentration of 137Cs in SX-108 tank fluid at the time of the leak has been estimated at 2.85 x 1010 Bq L-1 (0.771 Ci L-1) (Khaleel et al., 2000), which for a hypothesized fluid leak of 189.27 m3 (50 000 gallons) translates into a leaked 137Cs inventory of 5.4 x 1015 Bq (146.0 x 103 Ci), with a thermal power of 0.774 kW. Additional heat would be generated by a host of other radionuclides present in smaller concentrations. Temperature logging performed in Borehole 41-09-39 in 2000 (Fig. 2) showed a broad maximum centered at around the 25-m depth, well below the bottom of Tank SX-108, which suggests that an in situ heat source may be present in that region (Fig. 17). The 41-09-39 temperature profile can be well fitted with a polynomial of order 2 in the depth interval of from -15 to -35 m, with a coefficient of approximately = 0.1 for the leading (z–z0)2 term. A possible condition that can give rise to a parabolic temperature profile is a volumetrically uniform and constant heat generation, for which the coefficient of the quadratic term takes the form = q/2K, with q the heat generation rate per unit volume. For the prevailing water saturation of approximately Sl 
0.4, thermal conductivity is 1.36 W (m °C)-1 from Eq. [9], so that from = 0.1 we infer a value of q 0.272 W m-3. For an order-of-magnitude estimate we further hypothesize that this heat generation may occur over a region of 20-m thickness, the approximate depth interval for which the temperature profile in 41-09-39 is parabolic, and over an area equal to the footprint of the tank. Estimated total in situ heat generation is then 2.384 kW, which is consistent with the estimate of 0.774 kW made above for the contribution of 137Cs in a 189.27-m3 (50 000-gallon) leak. These numbers should be considered first rough order-of-magnitude estimates, as the spatial distribution of leaked fluids is probably rather nonuniform. Considerable lateral variability is indicated by the temperature profile in the slant hole, which has some similarities but also significant differences to the observations in 41-09-39.
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Fig. 17. Simulated temperatures at time 2000.0 compared with data obtained in Borehole 41-0939 and the SX-108 slant hole.
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We proceed now to compare simulated and observed temperatures. The curve labeled "original T" in Fig. 17 corresponds to the base case with revised (Eq. [9]) thermal conductivities, using the SX-108 temperature data as given in Fig. 4. Simulated temperatures are seen to be too high in comparison with 41-09-39 data at shallow depths down to -17 m, and too low from -17 to -40 m. To evaluate impacts of in situ heat generation, a simulation was performed in which a heat source with a strength of 2.5 kW in 1967, and subsequent exponential decay with a decay constant of 
= 0.666 x 10-9 s-1, appropriate for 137Cs with a half-life of 33 yr (Evans, 1982), was placed near z = -30 m. The results from this run are shown as "leak with 2500 W" in Fig. 17. With the added heat generation, simulated temperatures are now in reasonable agreement with 41-09-39 observations in the depth interval from -18 to -36 m, and interpolate between the 41-09-39 and slant hole data at greater depth. Obviously, the in situ heat generation has no effect on the discrepancies between simulated and measured temperatures at shallower depths.
It is difficult to see how lower temperatures may be obtained at shallow depths, except through a revision of the tank temperatures as plotted in Fig. 4. Hanford personnel indeed expressed some doubts about the reliability of Tank SX-108 temperature data for the time period after 1967, and additional temperature measurements from different thermocouple locations inside Tank SX-108 starting in 1981 were located during this study (Tom Jones, private communication, 2001). Figure 18 shows the new temperature data, which are labeled "riser 101" through "riser 104." Interpolated and extrapolated data labeled "top and sidewall" and "bottom" were used in a variation of the base case as temperature specifications on tank top and sidewall, and bottom, respectively. The new data set has much higher tank bottom temperatures after 1967, while top and sidewall temperatures are somewhat lower. The results obtained from these specifications are labeled "revised T after 1967" in Fig. 17. Agreement with 41-09-39 observations is good from shallow depths all the way to -35 m, and at greater depths the simulated temperatures are intermediate between the 41-09-39 and slant hole data. It is especially noteworthy that the "bulge" in 41-09-39 temperatures can be reproduced without any heat generation in situ. We can conclude that current uncertainties about historical tank temperatures preclude an unambiguous identification of an in situ heat source. A likely possibility is that the actual in situ heat source is considerably weaker than 2500 W.
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Fig. 18. Temperature data for Tank SX-108. The data labeled "riser 101" through "riser 104" refer to different thermocouple locations in Tank SX-108, while the curve labeled "SX-108" represents the data used for the base case simulation. The curves labeled "top and sidewall" and "bottom" represent interpolated and extrapolated values used to simulate a variation of the base case.
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Simulated moisture profiles at time t = 2000 yr were plotted for different cases and compared with field data obtained by neutron logging in Borehole 41-09-39 (Fig. 19). Differences between different simulation cases are very small, and the comparison with the field data is reasonable. In the backfill the simulated moisture content is somewhat low, and in the Hanford formation it is a bit too high. Overall moisture levels and depths where changes occur are reproduced fairly well.
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Fig. 19. Simulated moisture contents at time 2000.0 for different cases, compared with data obtained in Borehole 41-09-39.
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Moisture Tension–Dependent Anisotropy
There is much evidence from field and laboratory studies, and theoretical analyses, that permeability in sedimentary formations tends to be anisotropic (Sisson and Lu, 1984; Mualem, 1984; Yeh et al., 1985a,b,c; Mantoglou and Gelhar, 1987a,b,c; Smoot and Lu, 1994; Kline and Khaleel, 1995; Rockhold, 1999; Khaleel et al., 2000). Depending on moisture tension conditions, permeability in the horizontal direction may exceed vertical permeability by factors of from 3 to 10 or more (Polmann et al., 1991). The physical condition that causes this anisotropy is the predominantly horizontal layering of sediments, causing horizontal flow to proceed via "conductors in parallel", while vertical flow involves "resistors in series" (Muskat, 1937). Several authors have developed stochastic approaches for modeling variably saturated flow in heterogeneous media (Mantoglou and Gelhar, 1987a,b,c; Yeh et al., 1985a, b,c; Pruess, 1996). Here we present an initial assessment of moisture tension–dependent anisotropy, using a novel composite medium model in which anisotropy is described by directional relative permeabilities that are generally larger in the horizontal than in the vertical direction. The model assumes that on a grid block scale the medium can be viewed as strictly layered, and that capillary equilibrium prevails locally. Consider a grid block of vertical thickness L that includes horizontal layers i = 1, 2,..., n with thickness l1, l2,..., ln and intrinsic permeability k1, k2,..., kn, assumed isotropic within each of the layers. At a moisture tension 
, hydraulic conductivities of the different layers are given by Ki(). Hydraulic conductivity in the horizontal direction is calculated as arithmetic average over the layers,
 | [10] |
while in the vertical direction, hydraulic conductivity is obtained by adding the flow resistances (harmonic average)
 | [11] |
Here Ks is the saturated hydraulic conductivity in the horizontal direction, and krl,h and krl,v are the relative permeabilities in horizontal and vertical direction, respectively. From Eq. [10] and [11] we obtain the anisotropy ratio as
 | [12] |
where i = li/L are the length fractions of the layers. From Eq. [12] it is clear that Kh/Kv can never be smaller than 1, and will become much larger than 1 if one (or several) of the Ki are small.
A detailed presentation and evaluation of this model is the subject of ongoing work. Here we apply the composite medium model to a simple two-medium system, in which coarse sediments are assumed to be present over a fraction << 1 of vertical thickness, while the remainder (1 - ) consists of a medium with the same properties as used in the base case simulations (see Table 2). As an example, Fig. 20 shows hydraulic conductivities for a two-layer medium in which a fraction 
= 0.9 of vertical thickness has properties as given for the Hanford formation (saturated hydraulic conductivity of 3.7 x 10-4 cm s-1; see Table 2), while a fraction = 0.1 has a conductivity of 3.0 x 10-3 cm s-1 that is almost an order of magnitude larger. Parameters of the capillary pressure–saturation curve are the same for both media, except that, following Leverett (1941), the strength of capillary pressure in the high-k medium was reduced by the square root of the inverse permeability ratio. It is seen that the effective permeability of the coarser medium drops off more rapidly than that of the finer medium for stronger suction pressure (moisture tension). There is a crossover point at a certain intermediate level of suction (
4200 Pa), where effective permeabilities of the fine and coarse medium become equal. At that point the effective horizontal and vertical permeabilities must become equal also, so that the medium behaves isotropic for those particular suction conditions. Effective horizontal permeability (or conductivity) is seen to be slightly larger than vertical permeability for weak suction (large water saturation), while the ratio of horizontal/vertical permeability increases to large values at strong suction conditions (low saturation).
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Fig. 20. Predicted moisture tension dependence of effective horizontal and vertical permeability for a two-layer model of the Hanford formation. Parameters are discussed in the text.
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Simulations of the tank problem using a Richards' equation approximation and incorporating a two-layer model with directional relative permeabilities were performed for two cases, weak and strong anisotropy. In both cases, a more permeable coarse layer was assumed to extend over 10% of vertical thickness. Saturated hydraulic conductivity in the coarse layer was increased relative to the background medium by factors of 10 or 100 for weak and strong anisotropy, respectively, while the strength coefficient in the capillary pressure function for the coarse medium was reduced by factors of 
and 
. These simplifications and approximations seemed appropriate for a first exploration of effects. Laboratory measurements on cores have shown that saturated hydraulic conductivities within a stratigraphic unit may often range over three orders of magnitude (Khaleel and Freeman, 1995). Thus, the factor 100 adopted for our strong anisotropy case does not seem excessive. Backfill is believed to be much less anisotropic than the undisturbed sediments, and permeability was increased by a modest factor 2 for the coarser material.
The "natural" (pre-emplacement) state corresponding to 10 mm yr-1 net infiltration depends on the anisotropy, even though it involves only vertical and no horizontal flow. This is because the presence of coarser layers reduces effective vertical permeability for the relatively dry conditions considered here. Water saturations then must build up to larger values to restore effective hydraulic conductivity to 10 mm yr-1 as required to accommodate net infiltration. Figure 21a shows that increases in water saturations are modest for the mildly anisotropic case, but become very strong for strong anisotropy. Anisotropy factors (Eq. [12]) for the different cases are shown in Fig. 21b. Moisture tension–dependent anisotropy depends on formation parameters and moisture status, and under relatively dry conditions is seen to reach very large values, while becoming small at the wet conditions near the water table.
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Fig. 21. Water saturation (a) profiles and (b) anisotropy factors for steady-state conditions at 1 cm yr-1 net infiltration. Two cases with dynamic anisotropy are shown. The line labeled "static" corresponds to the reference case with a tension-independent anisotropy factor of 3 (2 for backfill).
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Simulated distributions of leaked fluids for both cases are presented in Fig. 22. In the Richards' equation approximation used here, the 189.27-m3 (50 000-gallon) leak was modeled as containing a solute tracer that otherwise does not alter the fluid properties (density, viscosity). The leaked fluid fraction was obtained by dividing simulated solute mass fractions by the mass fraction present in the tank leak. Results for the weakly anisotropic case are virtually indistinguishable from a calculation for static anisotropy (not shown). For strongly anisotropic conditions, the plume has a rather different shape, being more roundish and less elongated in the vertical. It is apparent that for stronger anisotropy the downward migration of solutes is considerably slowed. Breakthrough curves at different horizons are shown in Fig. 23. Breakthrough is seen to generally occur more slowly in the anisotropic case, as expected, but more complex behavior is noted in details. Some early arrivals at low concentrations in the strongly anisotropic case occur because the stronger lateral spreading of the plume allows some solutes to migrate beyond the infiltration shadow of the tank, where downward water fluxes are larger. These impacts on breakthrough curves show some similarities to impacts of tank heat (compare Fig. 16).
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Fig. 22. Leaked fluid fractions at time t = 1980.98 for the case of (a) weak and (b) strong dynamic anisotropy.
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Fig. 23. Breakthrough curves of leaked fluid released beneath the tank center on logarithmic scale for an isothermal approximation to the base case. Symbols are for static (tension-independent) anisotropy, and lines are for the case of strong dynamic anisotropy.
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CONCLUDING REMARKS
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The purpose of the modeling studies presented here is to contribute to a better understanding of contaminant migration at the SX tank farm at Hanford. We have developed and partially calibrated numerical simulation models for the specific conditions found at Tank SX-108, one of the highest heat load tanks at Hanford and a known leaker. Our model includes variably saturated flow with an active gas phase, heat transfer, associated phase change processes (boiling and condensation), solute transport, and precipitation–dissolution effects in regions with dry-out or persistent boiling. Hydrogeologic conditions were represented in a simplified manner, but realistic hydrogeologic, thermal, and operational parameters were used. The simulations cover the time period from when Tank SX-108 was first put into service (November 1955) to 2000. Predictions for subsurface temperatures and moisture distribution agree well with field observations in boreholes obtained in 2000.
Our studies show that for temperatures in excess of the boiling point, the dominant mechanism for fluid flow, heat transfer, and solute transport is a vapor–liquid counterflow process known as heat pipe. This provides a very efficient mechanism for transferring heat away from the tank as well as transporting dissolved solids towards it. The rate of moisture removal from thermally driven vapor diffusion across the land surface boundary was found to be small, amounting to <10 mm yr-1 equivalent infiltration. For realistic hydrothermal conditions and leakage scenarios, our simulations indicated that waste fluids leaked from tanks precipitated out solids. Much of these solids would redissolve at a later time as tank temperatures drop below boiling, but our simulations suggested that a considerable fraction of the original precipitates should persist beneath the tank to the present time. Solid precipitates could provide a long-term source of fluids with high sodium concentrations which, by competing for sorption sites, have a potential for remobilizing species such as 137Cs that would have been sorbed on clay sites further downstream. The precipitation behavior was found to be surprisingly sensitive to details of the heat conduction model used. A new model for subgrid-scale anisotropy was developed which demonstrated considerable dynamic retardation of solutes.
Observations in 2000 in Borehole 41-09-39 near Tank SX-108 showed a broad temperature maximum centered at approximately 25 m depth, considerably below the bottom of the tank. A prevailing view at Hanford had been that this temperature maximum arises from heat generated in situ from leaked radioactive fluids. However, our simulations showed that this temperature maximum can be satisfactorily explained as resulting from higher tank temperatures in the past. (Tank SX-108 is maintained on a regimen of active cooling.) Contributions from radioactive decay heat of sorbed species are possible but not required to match observed temperatures. The model developed here can provide a starting point for predictive simulations of future contaminant behavior in the vadose zone, for a "no action" scenario as well as for different remedial actions that may be considered.
The SX tank farm represents an extremely complex system, in terms of natural attributes and features of the site, physical and chemical processes, and in terms of human disturbances from emplacement and operation of the tanks. In order to be truly useful, numerical modeling must come to grips not only with the complex geology of the site, but also with a realistic representation of the many interacting physical and chemical processes, and with significant uncertainties in heat generation and fluid leakage from the tanks. Such a goal can only be achieved through a continuing process of iterative refinement of field observations and process models, and their eventual integration into a model that fully integrates fluid flow, heat transfer, solute transport, and chemical reactions, while also honoring operational data from the tanks, and incorporating site-specific hydrogeologic features.
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ACKNOWLEDGMENTS
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Helpful discussions with Tianfu Xu are appreciated. For a review of the manuscript and the suggestion of improvements we thank Stefan Finsterle, Tianfu Xu, and Andy Ward. Tom Jones and Ron Corbin provided additional data and valuable suggestions for this study. We thank three anonymous reviewers for their comments and suggestions for improving the paper. This work was supported by the U.S. Department of Energy under Contract No. DE-AC03-76SF00098 through Memorandum Purchase Order 248861-A-B2 between Pacific Northwest National Laboratory and Lawrence Berkeley National Laboratory.
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ABSTRACT
INTRODUCTION
