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Pacific Northwest National Lab., P.O. Box 999, MSIN K9-36, Richland, WA 99352
* Corresponding author (vicky.freedman{at}pnl.gov)
Received 26 August 2003.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMODEL DESCRIPTIONAPPLICATIONS AND RESULTSSUMMARY AND CONCLUSIONSREFERENCES |
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Abbreviations: ILAW, Immobilized Low-Activity Waste • STORM, Subsurface Transport Over Reactive Multiphases
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMODEL DESCRIPTIONAPPLICATIONS AND RESULTSSUMMARY AND CONCLUSIONSREFERENCES |
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Because of the environmental hazards these tank farms pose, the current mission is to pretreat the waste so the low-activity fraction can be separated from the high-level and transuranic wastes. The high-level wastes will eventually be sent to a high-level waste repository for permanent disposal. The low-level liquid fraction, however, will be vitrified for onsite disposal in a low-activity waste facility.
Among the issues being examined for the Immobilized Low-Activity Waste (ILAW) disposal facility, the identification of the principal hydrologic properties governing fluid flow through the glass and the surrounding geologic materials is of critical importance to the assessment of the disposal site. It is hypothesized that the hydrologic properties of the geologic media may change because of differences between injected and indigenous fluids. Experimental samples of the vitrified glass matrix exhibit a propensity for dissolution and secondary mineral precipitation (McGrail et al., 1999). In addition, mineral precipitation and dissolution of the backfill material are also expected to occur due to advection and diffusion of the dissolved glass constituents. These changes in mineral and glass volumes may also cause changes in the hydraulic properties of the media.
While several studies have focused on the dynamics and quantitative description of mineral precipitation and dissolution (Bolton et al., 1999; Dijk et al., 2002; Singurindy and Berkowitz, 2003), other studies have focused on the development of mathematical models of hydrologic property changes. Several approaches exist, including statistical analyses of particle grains (Panda and Lake, 1995), discrete descriptions of mineral surface areas and volumes (Steefel and Lasaga, 1994; Legallo et al., 1998), and estimates of changes in pore-size distributions (Baveye and Valocchi, 1989; Clement et al., 1996). The modeling approaches are either macroscopic, which are based on representative elementary volume averaging (Bear, 1979), or microscopic, which are pore-scale modeling techniques.
A continuous biofilm method was recently reported as a microscopic approach for modeling hydraulic property changes due to microbial activity (Taylor et al., 1990; Cunningham et al., 1991). In this method, the biomass in the porous media is assumed to cover each pore with a uniform film. This assumption is consistent with the precipitation and dissolution patterns observed with the ILAW glass materials. Experiments have shown that as the ILAW glass dissolves, secondary mineral precipitates form as a uniform coating (i.e., mineral film) over the glass grains (McGrail et al., 1999). The dissolution of the glass and the formation of secondary mineral precipitates are expected to change the porosity and permeability of the media.
Taylor et al. (1990) used a continuous pore-size distribution function to determine hydraulic property changes due to biofilm growth in saturated media. In this function, the pore radii are unknown, but bounded by minimum and maximum values. Although Taylor et al. (1990) stated that the extension of their work to unsaturated flow is straightforward, it is not easily applied to reactive transport models coupling flow to porosity and permeability changes because the hydraulic parameters used in equations describing unsaturated flow (Brooks and Corey, 1964; van Genuchten, 1980) must also be dynamically updated with changes in the porous medium. This is more easily accomplished when the pore-size distribution is known, as it facilitates the construction of a soil moisture characteristic curve.
We describe the development of a film depositional permeability model applicable to mineral precipitation and dissolution reactions in variably saturated porous media. The film depositional model is implemented in Subsurface Transport Over Reactive Multiphases (STORM), a reactive transport simulator developed at Pacific Northwest National Laboratory (Bacon et al., 2000). STORM has been used for modeling radionuclide release and its fate and transport at the Hanford site for the long-term performance assessments of a low-level, glassified waste disposal facility (Bacon and McGrail, 2001; McGrail et al., 1999).
The film depositional model was specifically developed for application to the disposal facility for two reasons. The first is because secondary mineral precipitates form as a film on the glass. Observations of crushed glass corrosion experiments have shown that as the glass dissolves with time, the secondary minerals of lower density coat its surface. Although glass permeability was not measured, the gradual increase in the volume of the secondary mineral precipitates was indicative of a concomitant decrease in pore size, and hence permeability.
In this work, it is assumed that dissolution occurs in a similar manner. This model of uniform dissolution and precipitation is consistent with surface complexation models that formulate reaction rates based on the surface concentration of specific chemical groups. In such models, the reactive surface is described as a flat terrace, without distinct morphological features. An extension of this model was developed by Duckworth and Martin (2003) and is applicable to flat minerals of ionic crystals that dissolve by step retreat and are far from equilibrium. Yamamoto et al. (1996) also observed this dissolution pattern in their atomic force microscopy study, in which they observed a zeolite to dissolve from terraces in a layer-by-layer sequence.
The second reason for developing this model was because the model offers a viable alternative to empirically based permeability models that do not account for saturation effects on permeability, such as the Fair–Hatch (Fair and Hatch, 1933) and Kozeny–Carmen (Bear, 1972) approaches. The physically based model presented involves utilizing a discrete pore-size distribution to describe the pore space of the medium. In this way, as precipitation and dissolution reactions occur, the unsaturated hydraulic properties of the material can be updated according to the volumetric changes occurring in the media.
In the sections below a brief description of STORM is presented, followed by a detailed description of the development and implementation of the film depositional permeability models. A near-field simulation of the disposal facility is presented to demonstrate the applicability of the film model. An evaluation of model performance is provided in the final section of this paper.
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MODEL DESCRIPTION |
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TOPABSTRACTINTRODUCTIONMODEL DESCRIPTIONAPPLICATIONS AND RESULTSSUMMARY AND CONCLUSIONSREFERENCES |
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In the STORM simulator, the fluid phase is primarily comprised of water with small quantities of dissolved air. Flow of fluid phases is computed from Darcy's law. The resulting flow fields are used to solve conservation equations for reactive aqueous phase transport. Transport of both air and liquid phase components is computed from Fick's Law. Once flow and transport calculations are complete, mineral precipitation and dissolution are calculated, followed by porosity and permeability calculations. For brevity's sake, the governing equations describing flow, transport, and chemical reactions are not presented in this document, but were described in detail by Bacon et al. (2000).
Time stepping in STORM is computed based on the previous time step, the acceleration factor, and the maximum time step. The user is required to choose a minimum and maximum time step that will minimize numerical error, and thereby not violate numerical terms such as the Courant and the grid Peclet numbers (Steefel and MacQuarrie, 1996).
Geochemical Reactions
In the STORM simulator, reactions that only involve aqueous species are assumed to be at equilibrium. However, aqueous-solid phase reactions can be slow and are therefore treated kinetically. Reaction rates in STORM are based on transition state theory and consider the forward rate and the equilibrium constant
 | [1] |
i is the activity coefficient of species i, ci is the concentration (mol M–1), and fi is the factor of the reaction order. The stoichiometric coefficient of species i in reaction j is represented by 
ij. The bars, ||, represent the absolute value. The sign of the reaction is positive for precipitation and negative for dissolution.
Thermodynamic calculations can be performed to determine whether or not a mineral is likely to dissolve or precipitate. To this end, saturation indices (SI) are used in STORM as such an indicator, and are positive when a mineral is supersaturated (precipitation), and negative when a mineral is undersaturated (dissolution). The SI is determined as
 | [2] |
Pore-Size Distribution Model
The film depositional permeability models implemented in this investigation require a discrete definition of the pore-size distribution. A pore-size distribution model based on the work of Arya and Paris (1981) is developed for use with the permeability models. In the Arya and Paris model, particle-size distribution data are used to derive the soil moisture characteristic curve. In this work, the bulk unsaturated hydraulic properties of the porous media, which define the soil moisture characteristic curve, are used to determine a pore-size distribution. This method is described below.
Equations
Since a soil moisture characteristic curve is essentially a pore-size distribution curve, a representative pore-size class and radius for each particle-size fraction on the particle-size distribution curve can be determined. To implement this model in STORM, an arbitrary number of particle-size fractions corresponding to a similar number of pore-size classes is chosen. In this step, a large number of pore-size classes (NP, e.g., 
30) is selected. This is necessary to capture the shape of the soil moisture retention curve.
Using the bulk properties of the media (N, M, and 
), the van Genuchten form of the soil moisture characteristic curve is then used to determine the soil water pressure (
) within each pore-size class and is given as
 | [3] |
is water content (L3 L–3), s is saturated water content (L3 L–3), r is residual water content (L3 L–3), and (1/L), M, and N are empirical fitting coefficients.
The saturation for each pore-size class is assumed to be a fraction of the bulk media saturation (s) and is determined by dividing the water content-pressure head relation into NP equal water content increments from zero to the saturated water content (Jackson, 1972):
 | [4] |
i is the water content corresponding to the ith water content increment.
The soil water pressure for the pore class is determined using Eq. [3]; then the equivalent pore radii (rj) can be obtained from the equation of capillarity:
 | [5] |
is the surface tension of water (M L2 T–1), 
is the contact angle, 
w is the density of water (M L–3), and g is the acceleration of gravity (L T–2). In the isothermal simulations presented in this investigation, the contact angle is assumed to be zero.
Assuming that the pore-size classes are progressively filled with water, the volume of the pore is calculated based on volumetric water content and the bulk density given as
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b is the bulk density (M L–3). Bulk density of the porous media is calculated in STORM as
 | [7] |
p is the particle density of the medium (M L–3), and n is the porosity.
The number of pore-size classes initially used in Eq. [3] is then reduced to a smaller number of pore-size classes. This is done to reduce the computational requirements for the simulations. For the simulations in this investigation, nine pore-size classes were used. Although the final number of pore sizes was selected arbitrarily, the permeability is insensitive to this final number. The magnitude of the permeability is sensitive only to the initial number of pore-size classes because it is with this initial number that the shape of the moisture retention curve is captured. An incremental radius (ri) for each pore-size class is then determined by
 | [8] |
Vp is the volume difference between each of soil pore volumes corresponding to rj and rj–1, and Vi is the incremental volume of the soil pore corresponding to radius, ri. Weighting factors for the number of pores in each class were used, since there are generally fewer very small and very large pores in any given distribution. After determining the initial pore-size distribution, the change in mineral volume is described as a change in film thickness over the entire distribution of pores. This pore-filling sequence is described below.
Mineral Film Thickness
In describing radon diffusion through soil, Nielson et al. (1984) developed a mathematical model based on the characteristics of the soil pore fluid. This included a water pore-filling sequence that assumed that a water film of uniform thickness was present in all pores of sufficient radius, and that smaller pores were more saturated than larger ones. If the water content of the porous media increased, the water films only increased in those pores that were still unsaturated. The volumetric saturation of a soil system was therefore calculated from a given water film thickness and pore-size distribution.
In this work, it is assumed that mineral volume changes occur as films and that there is equal access to all pores and grain surfaces. Hence, the approach used by Nielson et al. (1984) is extended to mineral precipitation and dissolution. Whereas Nielson et al. (1984) defined a parameter (Lf) as a water film thickness (L), it is redefined here as a mineral thickness. This mineral film thickness is given as
 | [9] |
mv is equal to the mineral volume (per unit volume of the porous media). The STORM model calculates volume fractions by assuming mineral grains are spherical in shape and occupy a given volume based on the number of grains and the mineral radius. Assuming that the number of grains remains constant, porosity is calculated based on a rate change in the mineral radius. Initially, the film thickness (Lf) is equal to zero. When mineral precipitation occurs, it is assumed that the mineral volume is distributed evenly over each of the pore surfaces and the pore radius is decreased by Lf (Fig. 1a) . For mineral dissolution, the pore radius is increased by Lf, and the pore volumes also experience a corresponding increase (Fig. 1b). Because Eq. [9] cannot be explicitly solved for Lf, the Lf value for a given change in mineral volume is determined utilizing the bisection method for finding roots of equations. Once the value of the film thickness is determined, it is used to calculate permeability. If the smallest pores in the distribution become clogged, they are eliminated in the calculation of permeability.
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Hydraulic conductivity is then determined by the interconnectivity of the pores. The Mualem and Childs and Collis-George permeabilities (km and kccg, respectively) are given as
 | [10] |
 | [11] |
is the unsaturated moisture content (L3 L–3), and 
is tortuosity (L L–1). Hence, these equations represent the volume of full pores of radii [r,r + r] per unit volume of medium. Only the Mualem model accounts for the interconnectedness of the pore space through the tortuosity parameter. Saturation effects on permeability are accounted for in the Childs and Collis-George model. Both of these factors impact the length of the radii determined for the pore-size distribution implemented in STORM.
Permeability Model Implementation
To determine the discrete pore-size distribution, the soil moisture retention curve is divided into a specified number of pore-size classes. The initial permeabilities calculated by both the Mualem and Childs and Collis-George models are somewhat sensitive to this number. This occurs because there is a minimum number of size fractions that are needed to describe the continuous distribution. There is also a practical limit on this number, which in the Arya and Paris (1981) model, is dictated by sieve sizes. To a limited extent, the initial number of pore-size classes can be used to adjust the magnitude of the permeability. Although the relationship between the magnitude of the permeability and the number of pore-size fractions is nonlinear, generally as the number of pore-size fractions increases, the magnitude of the permeability decreases.
In addition to the pore radii, the tortuosity () is a parameter in the Mualem model. In this analysis, tortuosity is assumed to be constant for all simulations. It is also assumed that hysteresis does not occur and that anistropy effects are negligible. These assumptions de-emphasize the importance of comparing absolute changes in permeability and focus on general trends and sensitivities of the mineral film thicknesses between dissolution and precipitation reactions.
Unsaturated Hydraulic Parameter Updates
To represent hydraulic property changes resulting from chemical reactions with the film permeability model, it is necessary to update the hydraulic parameters. Experimentally, these parameters are usually determined by fitting analytical functions, such as van Genuchten (1980) and Brooks and Corey (1964), to observed retention data. Once the parameter values that describe a soil water retention curve are determined, the unsaturated hydraulic conductivity can be computed.
The difficulty of updating unsaturated hydraulic parameters with a macroscopic flow model is in determining which pores in the medium contain water. Water may not be present in all pores, and only the smaller ones may be saturated. Since solid phase reactions will largely occur in the presence of water, it may not be reasonable to assume that volumetric changes occur throughout the entire pore-size distribution. However, experiments with the proposed glassified waste for the ILAW disposal facility have shown that water is present in all pores in the pore-size distribution, although some pores are only partially filled. Hence, in this work, it is assumed that mineral volumes changes occur throughout the entire distribution of pores.
Since it is assumed that water is present in all pores, it is expected that the shape of the pore-size distribution will remain the same, and only experience a shift in the magnitude of the original pore radii. The pore-size distribution is only calculated once in the STORM model upon initialization. When solid-aqueous phase reactions occur, the new pore-size distribution is determined by summing the updated values of the pore radii and the mineral film thicknesses. Updated values of the pore radii are obtained at every time step from mineral volume changes that are translated to mineral film thicknesses as shown in Eq. [9].
The equation of capillarity as given in Eq. [5] expresses the relationship between the radius of the pore and the capillary pressure. Since the radii are known, the capillary pressure and corresponding water content are determined for each pore. The retention data are then fitted to analytical functions for describing unsaturated flow, in the same way that these parameters are determined by experiments.
The unsaturated hydraulic parameters of the van Genuchten (1980) equation are determined by optimization. Other hydraulic parameters, such as the saturated hydraulic conductivity (Ksat), are assumed to be time invariant. For example, in the van Genuchten equation, parameters , N, and r (Eq. [3]) are the unknowns for the new pore-size distribution. An automated optimization procedure that incorporates the Simplex method of Nelder and Mead (1965) and the simple least squares objective function is used to determine bulk parameter values for the material using an updated pore-size distribution at each time step. These updated parameter values are then used to calculate flow in the next time step.
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APPLICATIONS AND RESULTS |
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TOPABSTRACTINTRODUCTIONMODEL DESCRIPTIONAPPLICATIONS AND RESULTSSUMMARY AND CONCLUSIONSREFERENCES |
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Separate Cases of Precipitation and Dissolution
The first simulation considers a column that is initially supersaturated with respect to calcite (CaCO3) at 25°C. The initial pH in the column is 7.6, and the partial pressure of CO2(g) is 10–1.5 bars. The saturation index (SI) of calcite is 1.85, and the rate constant for calcite precipitation is 7.0 x 10–7 mol m–2 s–1 (Wolery, 1992a). The second simulation simulates a column that is undersaturated with respect to quartz (SiO2) at 100°C. The initial pH in the column is 7.0, the saturation index (SI) of quartz is –8.9, and the rate constant 1.5 x 10–8 mol m–2 s–1 (Wolery, 1992a). Because no carbonate is present in this system, CO2(g) is not included in the simulation. Both columns have an initial saturation of 20% and a porosity of 50%. Input parameters for both the one-dimensional columns are shown in Table 1.
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Permeability Results
Figure 2
shows the relative changes in permeability after 5 d of simulation for the precipitation of calcite. For both of the permeability models, the shape of the permeability profiles is similar. The Childs and Collis-George model predicts nearly a 25% reduction in permeability at the top of the column compared with an 18% reduction predicted by the Mualem model. Permeabilities at the top of the column are lower because the influent water is supersaturated with respect to calcite, causing calcite to precipitate. In the permeability profiles for quartz dissolution shown in Fig. 3
, the shape of the profiles is also similar as the reaction front moves through the column. The Childs and Collis-George model predicts a 9% increase in permeability, whereas a 6% increase is predicted by the Mualem model.
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For quartz dissolution, the permeability increases are more significant as the size of the larger pores increases. As a result, the permeability increase is more significant with the Childs and Collis-George model. This is consistent with the physical reality that the enlargement of relatively small pores has less effect on permeability than an increase in the size of large pores.
Both the Mualem and Childs and Collis-George model yielded physically reasonable results. As suggested by Taylor et al. (1990), however, the Mualem model has a larger database available for verification and is generally preferred over the Childs and Collis-George model.
Further investigation of both the Mualem and Childs and Collis-George permeability models is performed for simultaneous precipitation and dissolution in the next section. The proposed ILAW glassified waste disposal facility is used for this task.
ILAW Glass
Both the Mualem and Childs and Collis-George film models were further tested on multiple mineral assemblages undergoing simultaneous precipitation and dissolution. To this end, simulations were run for the glassified waste to be buried at the Hanford ILAW disposal facility. The proposed design is to bury the glass in a trench. As recharge enters the trench, the glass is expected to undergo dissolution.
The dissolution rate of the glass (Wg) has been determined experimentally to be dependent on both pH and SiO2(aq) concentration and is given as (Bacon and McGrail, 2003)
 | [12] |
is the pH power law coefficient (neutral to basic, 0.5), Ea is the activation energy (75 kJ mol–1), R is the gas constant (8.134 x 10–3 kJ mol–1), T is the temperature (K, assumed constant at 15°C), aSiO2
is the aqueous silica activity (variable calculated by STORM), and Kg is the pseudoequilibrium constant for glass based on SiO2(aq) activity (10–2.853).
Experimental data were used to determine kg, Ea, Kg, and parameters in Eq. [12] (McGrail et al., 2000). Glass dissolution is also considered to be irreversible and is nonlinearly dependent on the pH. As the glass dissolves and the pH and SiO2(aq) concentration increase, SiO2(aq) is transported downstream and is consumed in the formation of secondary mineral precipitates. These secondary mineral assemblages primarily include herschelite, baddeleyite, nontronite-Na and rutile.
In the simulation results presented below, the ILAW repository is represented as a one-dimensional glass column, 2 m long. On the basis of several convergence tests that sought to reduce numerical error and simulation times, the computational grid is set at 10-cm vertical resolution, and the simulation is run out to 10000 yr. Both the physical and chemical properties of the medium used in the simulation presented here are identical to those used in the base case for the 2001 ILAW Performance Assessment. The reader is referred to Bacon and McGrail (2003) for details on the physical and chemical properties used in the simulation.
Porosity and permeability changes are time invariant at the boundaries. A Cauchy concentration boundary is imposed at the top of the column, which is a weighted average of a Dirichlet (fixed) boundary and a Neumann (flux) boundary condition. A constant flux condition is used for flow (4.2 mm yr–1). This flux rate is an average value of annual recharge expected at the ILAW disposal facility.
The results of the simulation presented here utilize the prototypic ILAW glass, LAWABP1 (Bacon and McGrail, 2001), which has been extensively researched and developed for use at the ILAW disposal facility. It is primarily composed of O (55%), Si (14%), Na (13%), B (5%), Al (4%), and La (2%). The glass is expected to be fractured, with little or no porosity in the glass matrix.
Many researchers have used equivalent porous medium techniques to characterize fractured systems (Long et al., 1985; Schwartz and Smith, 1988; Rehfeldt et al., 1992; Pohll et al., 1999). Long et al. (1985) reported that an equivalent porous medium exists for fractured rock when the fractures are relatively dense. Hence, the glass is modeled as an equivalent porous medium with hydraulic properties that correspond to fractured glass. Because of the different assumptions of pore continuities, the initial values of the Mualem (1.039 x 10–11 m2) and Childs and Collis-George (4.461 x 10–11 m2) permeabilities are only approximately equal at the start of each simulation. The initial porosity of the medium is 0.02. All other parameters relevant to hydraulic property changes are listed in Table 3.
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Permeabilities (Fig. 7) are also based on mineral volume changes. As a result, both the Mualem and Childs and Collis-George film depositional permeability models follow the same trends exhibited in the porosity profile. Although both models demonstrate an increase in permeability at the top of the column, the Childs and Collis-George model predicts a greater variability in permeability than the Mualem model. For example, the Mualem model predicts a 45% increase in permeability at the top of the column and a 9% decrease immediately downstream after 10000 yr of simulation. This differs considerably from the peak increase of 72% and decrease of 15% predicted by the Childs and Collis-George model.
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The dissolution rate at the boundary node does not change by a significant measure because the source term for the Cauchy boundary is set to zero to stabilize the numerical solution. As a result, concentrations of the dissolved constituents change much more quickly throughout the column than at the boundary node.
Although this condition may impose an undue constraint at the boundary, it is expected that the influent solution will be undersaturated with respect to the LAWABP1 glass. It also follows that the largest increase in permeability is expected to occur at the top of the column. In the rest of the column, permeability reduction is expected to occur downstream due to secondary mineral precipitation. Simulation results demonstrate that this phenomenon is most pronounced immediately downstream of the boundary. Although not readily apparent in Fig. 4, 5, and 7, small reductions (1 and 2% for the Mualem and Childs and Collis-George models, respectively) do occur in the rest of the column. This result is consistent with the expected behavior of the hydraulic properties of the glass.
Unsaturated Hydraulic Parameter Changes
As the permeability and pore-size distributions change due to solid–aqueous phase reactions, the unsaturated hydraulic parameters (r, N, and ) also change. As indicated in Table 3, the residual saturation (r) is assigned a value of zero to represent the glass as a fractured medium. Increasing the permeability decreases the value of r, but this has no physical meaning. Thus, only changes for N and are reported for the Mualem and Childs and Collis-George film depositional permeability models. Figure 8
shows how the van Genuchten parameter changes for each implementation of the film permeability models. Consistent with theoretical expectations, the larger changes in permeability predicted by the Childs and Collis-George model correspond to larger changes in the parameter relative to the Mualem model. These changes, however, differ by only 2% for both the largest increases and decreases in permeability. For example, there is a difference of more than 25% in the peak permeability values predicted by the two models, yet the corresponding difference in is only 2%. A smaller difference in permeability reduction (6%) is predicted by the models, but this also corresponds to a difference of only 2% in the prediction of . Given that is related to pore size and the inverse of air entry pressure, a larger change in its value may be reasonably expected.
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, the results in Fig. 9 show that the relative changes in N are greater than . These results indicate that the optimization procedure for determining N is sensitive to pore size. The Mualem pore sizes are larger than those calculated with the Childs and Collis-George model. As seen in Fig. 7, the Mualem model has a smaller dependence of permeability on the pore-size distribution. The van Genuchten N, however, is sensitive to changes in the magnitude of the pores within the distribution. As such, despite smaller changes in permeability, the Mualem model predicts larger changes in N.
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The difficulty in obtaining realistic values of the unsaturated hydraulic parameters is likely related to both parameter sensitivity and the representation of the fractured glass as an equivalent porous medium. Changes in both and N for both models demonstrate that N is more sensitive to permeability changes than . The optimized values of the unsaturated hydraulic parameters are also heavily dependent on the pore-size distribution model. In addition, because the value of r is zero, only and N can be changed to account for changes in pressure due to permeability increases. Despite these weaknesses, the largest changes in N for both models generated were within normal ranges of the parameter values. The absolute increase in van Genuchten N is 30% for the Mualem model, and 24% for Childs and Collis-George.
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SUMMARY AND CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMODEL DESCRIPTIONAPPLICATIONS AND RESULTSSUMMARY AND CONCLUSIONSREFERENCES |
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When the film permeability models are applied to glass corrosion simulations, they yield physically realistic results for simultaneous glass dissolution and secondary mineral precipitation. Both the predicted permeability response and the unsaturated hydraulic parameter estimates generally agree with qualitative expectations and physical theory. Although direct verification of the glass corrosion experiments with laboratory data has not yet been performed, qualitative observations of glass dissolution experiments show a decrease in permeability with time, which concurs with model results.
In summary, the film depositional permeability model offers an alternative to empirically based models that do not account for changes in saturation. The film depositional permeability model is physically based, and accounts for saturation effects on permeability, an important factor in the ILAW disposal facility. Changes in permeability for the glass simulation are small because of the slow dissolution behavior of the glass. However, given the long-term nature of the repository, and the complex geochemical and unsaturated flow environments, the film model can represent permeability changes at the ILAW disposal facility that occur due to precipitation and dissolution reactions.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMODEL DESCRIPTIONAPPLICATIONS AND RESULTSSUMMARY AND CONCLUSIONSREFERENCES |
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