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SPECIAL SECTION: RESEARCH ADVANCES IN VADOSE ZONE HYDROLOGY THROUGH SIMULATIONS WITH THE TOUGH CODES

Modeling Coupled Evaporation and Seepage in Ventilated Cavities

^a Earth Sciences Division, Lawrence Berkeley National Laboratory, University of California, MS 90R1116, 1 Cyclotron Rd., Berkeley, CA 94720-8126
^b LFR Levine Fricke, Costa Mesa, CA
^* Corresponding author (TAGhezzehei{at}lbl.gov)

Received 29 September 2003.

	ABSTRACT

TOP ABSTRACT INTRODUCTION EVAPORATION IN CAVITIES COUPLED SEEPAGE AND EVAPORATION MATERIALS AND METHODS TOUGH2/iTOUGH2 SEEPAGE MODEL RESULTS AND DISCUSSIONS SUMMARY AND CONCLUSIONS REFERENCES

 
Cavities excavated in unsaturated geological formations are important to activities such as nuclear waste disposal and mining. Such cavities provide a unique setting for simultaneous occurrence of seepage and evaporation. Previously, inverse numerical modeling of field liquid-release tests and associated seepage into cavities were used to provide seepage-related large-scale formation properties, ignoring the impact of evaporation. The applicability of such models was limited to the narrow range of ventilation conditions under which the models were calibrated. The objective of this study was to alleviate this limitation by incorporating evaporation into the seepage models. We modeled evaporation as an isothermal vapor diffusion process. The semiphysical model accounts for the relative humidity (RH), temperature, and ventilation conditions of the cavities. The evaporation boundary layer thickness (BLT) over which diffusion occurs was estimated by calibration against free-water evaporation data collected inside the experimental cavities. The estimated values of BLT were 5 to 7 mm for the open underground drifts and 20 mm for niches closed off by bulkheads. Compared with previous models that neglected the effect of evaporation, this new approach showed significant improvement in capturing seepage fluctuations into open cavities of low RH. At high relative-humidity values (>85%), the effect of evaporation on seepage was very small.

Abbreviations: BLT, boundary layer thickness • ECRB, enhanced characterization of the repository block • RH, relative humidity • YM, Yucca Mountain

	INTRODUCTION

TOP ABSTRACT INTRODUCTION EVAPORATION IN CAVITIES COUPLED SEEPAGE AND EVAPORATION MATERIALS AND METHODS TOUGH2/iTOUGH2 SEEPAGE MODEL RESULTS AND DISCUSSIONS SUMMARY AND CONCLUSIONS REFERENCES

 
SEEPAGE OF LIQUID WATER into cavities is an important phenomenon for subsurface activities such as mining and geologic disposal of nuclear wastes. A key factor affecting the long-term safety of the proposed nuclear waste repository at Yucca Mountain (YM), Nevada, is the seepage of liquid water into waste emplacement cavities. The rate, chemical composition, and spatial and temporal distributions of seepage are critical factors that determine corrosion of waste canisters, integrity of engineered barriers, and dissolution and mobilization of contaminants and their release to groundwater (Bodvarsson et al., 1999; Finsterle et al., 2003). In unsaturated formations, capillary forces hold the pore water tightly in the formation and divert the flow around the cavity, thereby preventing seepage into the cavity. The barrier created by the capillary force is commonly known as a "capillary barrier." Philip and coworkers (Knight et al., 1989; Philip, 1989a, 1989b; Philip et al., 1989a, 1989b) considered steady-state unsaturated flow around capillary barriers and provided analytical solutions for the critical conditions that trigger seepage into various idealized cavity geometries excavated in homogeneous formations. Detailed numerical models have been used to study unsaturated flow in heterogeneous fractured media and seepage into cavities of various geometries under transient conditions (e.g., Birkholzer et al., 1999; Finsterle, 2000; Finsterle and Trautz, 2001; Li and Tsang, 2003). Site-specific seepage models for the proposed nuclear waste repository at YM were developed by calibrating the effective seepage-related parameters against field seepage test data (Finsterle et al., 2003).

Most of the previous numerical models assumed that liquid water leaking into a cavity drips (seeps) immediately from the place of entry. The potential for evaporation to compete with seepage has been generally ignored, and its effect was lumped with the effective flow parameters of the unsaturated medium (Finsterle et al., 2003). In calibration of the analytical model of Philip et al. (1989b) against field seepage data, Trautz and Wang (2002) accounted for the effect of evaporation by adjusting the field seepage data for evaporation. Because the data were obtained from tests conducted in relatively humid cavities, the effect of evaporation on the calibrated seepage-related parameter was not significant. However, recent field measurements of seepage and free-water evaporation in ventilated cavities at YM have shown that seepage rate is significantly influenced by evaporation. The foregoing discussions suggest that the applicability of models that ignore evaporation is limited to similar humidity and temperature conditions under which the calibrations are performed (Finsterle et al., 2003). Such models cannot satisfactorily capture the seepage rate fluctuations when the seepage experiments are conducted under variable humidity and ventilation conditions. More importantly, seepage models that ignore evaporation and that are calibrated against seepage data under ventilated and/or low humidity conditions are not expected to perform well in predicting future (expected nonventilated and humid) seepage conditions. The preceding observations call for a calibrated seepage model that reliably performs over a wide range of ventilation and humidity conditions.

The objective of this study was to improve the portability of calibrated seepage models by reducing the impact of evaporation on the calibrated effective parameters. Thus, we propose to incorporate evaporation from cavity walls into the existing seepage models by assuming a first-order diffusion approximation.

	EVAPORATION IN CAVITIES

TOP ABSTRACT INTRODUCTION EVAPORATION IN CAVITIES COUPLED SEEPAGE AND EVAPORATION MATERIALS AND METHODS TOUGH2/iTOUGH2 SEEPAGE MODEL RESULTS AND DISCUSSIONS SUMMARY AND CONCLUSIONS REFERENCES

 
Fundamentally, evaporation is a two-step process. The first step involves transition from liquid to vapor phase at the liquid–vapor interface (vaporization). The second step is the transport of vapor from the high concentration area at the evaporating surface to the low concentration area of the ambient air. Accurate modeling of these coupled processes is difficult for several reasons: (i) the first step is an endothermic phenomenon, and the parameters that govern this process are strongly temperature dependent; (ii) the vapor concentration gradient in the boundary layer is strongly influenced by the air flow regime; and (iii) the air flow depends on, among other things, the ambient wind velocity, local turbulence, and the roughness of the evaporating surface.

Ho (1997) and Or and Ghezzehei (2000) modeled evaporation from individual water droplets attached to cavity ceilings, assuming constant temperature and humidity conditions. In the present study, we extend these evaporation models to account for evaporation from a variably saturated porous surface. In contrast to the positive capillary pressure on the surfaces of evaporating droplets, the porous surface typically has negative or zero capillary pressure. The evaporation model used in this study is coupled with flow in the porous medium, and the RH of the ambient air could vary.

The formulation we used capitalizes on the observed dependence of evaporation rate on cavity humidity and ventilation conditions, and the availability of high resolution time-series data of RH, temperature, and free-water evaporation rate (Trautz and Wang, 2002).

In the following subsections, we introduce an isothermal vapor diffusion model of evaporation and define the problem domain and boundary conditions. This is followed by estimation of the evaporation model parameters using free-water evaporation data. Finally, a remark on evaporation from a porous surface is provided.

Isothermal Vapor Diffusion Model
The development of the isothermal vapor diffusion model presented in this section closely follows that of Ho (1997), with the exception of the range of vapor pressure on the evaporating surface. In the study of Ho (1997) the vapor pressure on the surface of the evaporating pendent drops depends on the drop radius (positive capillary pressure), while in our study the vapor pressure on the surface of the porous medium depends on the capillary pressure of the liquid held in the pores (negative or zero capillary pressure). To simplify the first step of evaporation (vaporization) we assume the following:

• The absorption of latent heat and its effect on the physical properties of the liquid–vapor interface are negligible.
  
• The time dependence of the vaporization process (e.g., Zhang and Wang, 2002; Zhang et al., 2001) is neglected.
  
• The vapor partial pressure of the interfacial air is assumed to be under thermodynamic equilibrium.
  

At equilibrium, the air above a flat surface of pure water is considered saturated with vapor; its vapor pressure is denoted by p_s (Pa). This saturation vapor pressure rises with temperature. In the temperature range of –10 to 50°C, the saturation vapor pressure is related to interfacial temperature by (Murray, 1966)

[1]

where a = 21.87, b = 265.5°C and c = 6.41 are constants, and T (°C) is the interfacial temperature. For nonflat interfaces (such as capillary menisci) the actual interfacial vapor pressure p is related to the interfacial capillary potential by the classic Kelvin equation:

[2]

where P_C (Pa) is the capillary pressure, _W = 998 kg m^–3 and M_W = 0.018 kg mol^–1 are the density and molecular mass of liquid water, respectively; and R = 8.3143 J K^–1 mol^–1 is the universal gas constant. Note that the RH of air is defined as the ratio of the actual partial pressure p to the saturated vapor pressure p_s:

[3]

The second step of evaporation, vapor removal from the interface, is modeled as a first-order phenomena described by Fickian diffusion (Rohsenow and Choi, 1961). In one dimension and under constant temperature, the vapor mass flux J_V (kg m^–2 s^–1) is given by

[4]

where D_V (m² s^–1) is the vapor diffusion coefficient, which is related to the ambient air pressure, P (Pa), and air temperature T by (Vargaftik, 1975)

[5]

and the vapor concentration C (kg m^–3) is related to vapor pressure by

[6]

Note that the error introduced by the equimolar counterdiffusion equation (Eq. [4]) to represent evaporation (vapor diffusion in stationary gas) is ignored. In the subsequent subsection, we define the problem domain and develop the appropriate boundary conditions needed to solve the vapor diffusion Eq. [4].

Velocity and Concentration Boundary Layers
In admitting diffusive flux as the primary mechanism for vapor removal from the evaporating surface, we assume that airflow above the evaporating surface is fully developed and laminar, as illustrated in Fig. 1a . The free-stream air velocity, U (m s^–1), is retarded in the vicinity of the evaporating surface because of frictional resistance. The air velocity parallel to the evaporating surface increases from U = 0 at z = 0 (no-slip) asymptotically to U = U at a distance sufficiently far away from the surface. For fully laminar flow conditions, the thickness of the boundary layer (_U) of retarded velocity (defined as U 0.99U) is inversely proportional to the square root of the free-stream velocity (Rohsenow and Choi, 1961):

[7]

View larger version (14K): [in this window] [in a new window]   Fig. 1. Schematic description of (a) air velocity and (b) vapor concentration profiles above a free water surface.

[8]

where µ_a (Pa s) and _a are the viscosity and density of air, respectively. At 20°C and 1 atm pressure, the Schmidt number is approximately unity. In the remainder of this paper the subscripts in the boundary layer thickness are dropped and = _U = _C (m). It is evident from Eq. [7] and [8] that the concentration BLT () is inversely related to the square root of the free-stream velocity (U) and can serve as a direct measure of the cavity ventilation condition. In a subsequent subsection, estimation of the BLT will provide further elaboration on the dependence of on ventilation conditions.

Boundary Conditions
The domain of the vapor diffusion Eq. [4] is the concentration boundary layer introduced in the preceding section. The boundary condition on Eq. [4] corresponding to the equilibrium vapor concentration at the evaporating surface (z = 0) is given by (using Eq. [2] and [6]):

[9]

The second boundary condition is at the border of the concentration boundary layer z = , where the vapor concentration is defined by the RH (h) of the ambient air:

[10]

If the boundary conditions change slowly, the evaporation rate can be considered to be at steady state and the concentration gradient dC/dz is constant throughout the boundary layer. Then, the steady-state vapor diffusion Eq. [4] under isothermal conditions is simplified to

[11]

Note that the ratio /D_V is commonly referred to as diffusional resistance, and Eq. [11] is essentially Dalton's equation as used by Penman (1948). The isothermal vapor diffusion Eq. [11] is considered valid for modeling evaporation from cavity surfaces and free water. Fujimaki and Inoue (2003) found Eq. [11] (also known as the bulk transfer equation) to be valid in laboratory evaporation experiments in which the ambient air velocity was on the order of 1 m s^–1. All the variables of this model are directly related to physical conditions in the cavity, and all of them, except , can be independently determined from measured quantities. The boundary layer thickness () can be estimated by calibrating Eq. [11] against free water evaporation data, as discussed in the next section.

Estimation of the Boundary Layer Thickness
Apart from the capillary pressure at the evaporating surface, evaporation from free water and that from a wet porous surface are thus far assumed to be identical processes. Therefore, a controlled evaporation experiment from a still-water surface can be used to estimate the vapor concentration boundary layer thickness, which is also applicable to evaporation from wet cavity surfaces at similar ventilation conditions. Upon substitution of Eq. [1], [5], [9], and [10] in Eq. [11], and noting that the capillary pressure of the free-water surface is P_C = 0, we arrive at a free-water evaporation equation:

[12]

According to the isothermal assumption, T denotes the temperature of the evaporating surface and the surrounding air. Assuming the change in conditions that affect evaporation rate is slow compared with the time it takes to reach steady-state evaporation, Eq. [12] can be fitted to time-series data of evaporation rate data measured at known temperature, pressure, and RH conditions. The best-fit represents the boundary layer thickness at the prevailing ventilation condition. However, it should also be noted that uncertainties associated with the assumed simplifications (including isothermal conditions, flat evaporating surface, and laminar airflow) are lumped into this parameter. Thus, the boundary layer thickness should be considered an effective parameter.

Evaporation from Porous Surface
The surface of an unsaturated porous medium typically consists of solid (matrix of the medium) and pore and fracture (liquid and gas) components, rendering the evaporating surface heterogeneous with respect to vapor concentration, as illustrated in Fig. 2a . During seepage, however, cavity ceilings are usually covered with liquid films (e.g., Trautz and Wang, 2001), and the vapor concentration could be considered locally homogeneous. For simplicity, we extend this assumption of locally uniform distribution of vapor concentration to the entire cavity Fig. 2b. The vapor concentration at any given location on the cavity is assumed to be at capillary equilibrium with the pores and fractures of the porous medium. The datum z = 0 for the vapor diffusion is set on the surface of the cavity (as illustrated in Fig. 2b). Although this assumption is likely to fail at very low saturations (when the liquid is scattered in a few fine pores and fractures), it is expected to be of marginal consequence because the evaporation rate under such conditions is very low. Moreover, as indicated in the preceding section, uncertainties regarding the geometry of the evaporating pan are lumped into the calibrated boundary layer thickness. It should be noted that an unknown error is introduced when applying this boundary layer thickness value to evaporation from rough cavity surfaces that have significantly different geometry from the relatively flat free water surfaces.

View larger version (18K): [in this window] [in a new window]   Fig. 2. Evaporating surface area of a porous medium: (a) partitioning of the surface into nonevaporating solid and evaporating pores; (b) proposed approach of uniform liquid-phase surface. The dark shading denotes vapor in pores and/or fractures.

	COUPLED SEEPAGE AND EVAPORATION

TOP ABSTRACT INTRODUCTION EVAPORATION IN CAVITIES COUPLED SEEPAGE AND EVAPORATION MATERIALS AND METHODS TOUGH2/iTOUGH2 SEEPAGE MODEL RESULTS AND DISCUSSIONS SUMMARY AND CONCLUSIONS REFERENCES

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION EVAPORATION IN CAVITIES COUPLED SEEPAGE AND EVAPORATION MATERIALS AND METHODS TOUGH2/iTOUGH2 SEEPAGE MODEL RESULTS AND DISCUSSIONS SUMMARY AND CONCLUSIONS REFERENCES

 
Field Tests
The data reported in this paper were obtained from field tests and measurements conducted at the proposed nuclear waste repository at YM currently under investigation by the USDOE. Air-injection tests were conducted to characterize the permeability and small-scale heterogeneities of the formation, and liquid-release tests were performed to study seepage phenomena. RH, temperature, and free-water evaporation were monitored at the test site to assess the evaporation conditions. Detailed description of the site and tests conducted at the site are provided elsewhere (Birkholzer et al., 1999; Bodvarsson et al., 1999; Finsterle and Trautz, 2001; Finsterle et al., 2003; Trautz and Wang, 2001, 2002; Wang et al., 1999). This study is concerned with the lower lithophysal welded tuff unit at YM, in which about 80% of the proposed repository is expected to reside. This unit contains many small fractures (<1 m long) and is interspersed with numerous lithophysal cavities (0.15–1 m diam.).

In the lower lithophysal unit, an 800-m-long drift (5-m diam.) for enhanced characterization of the repository block (ECRB) was excavated. Liquid-release and air-injection tests were systematically conducted in this ECRB Cross Drift along boreholes drilled into the ceiling of the Cross Drift at regular intervals. Similar tests were conducted in a short (15 m long) drift excavated off the Cross Drift (niche). Schematic alignment of the cavities is shown in Fig. 3a . This paper is concerned with tests conducted at a Cross Drift borehole designated as LA#2 (Fig. 3b) and a short drift known as Niche 5 (Fig. 3c). The tests and measurements conducted in the Cross Drift and Niche 5 are briefly described below. In the remainder of this paper, drifts and niches are referred to by the generic term cavity.

View larger version (44K): [in this window] [in a new window]   Fig. 3. Schematic alignment of cavities and boreholes: (a) part of the enhanced characterization of the repository block (ECRB) Cross Drift; (b) liquid release test setup in the Cross Drift, including liquid release intervals and liquid injection and seepage collection equipment; and (c) vertical section of Niche 5 along with location of all the test boreholes.

Liquid-Release Tests
Liquid-release tests were conducted in boreholes drilled above cavities to evaluate seepage into waste emplacement drifts. The alignment of the boreholes and test intervals are schematically shown in Fig. 3. The liquid-release boreholes in the Cross Drift were approximately 20 m long, drilled into the ceiling of the Cross Drift at a nominal inclination of 15° from the horizontal. Liquid-release data from Borehole LA#2 were used in this study. The borehole was partitioned into three zones (designated as Zones 1, 2, and 3) available for liquid release testing. The distances from the middle of the liquid-release zones to the drift crown were 1.58, 2.84, and 4.10 m for Zones 1, 2, and 3, respectively. The liquid-release boreholes in Niche 5 were near horizontal. In this study, we used data from tests (Boreholes 4 and 5) that lasted long enough to achieve nearly steady-state seepage. The liquid-release tests were performed by injecting water into a test interval isolated by inflated rubber packers. Water that seeped into the cavities was captured and measured using automated recording devices.

Relative Humidity and Temperature Measurements
The Cross Drift was actively ventilated during regular working hours, thus the RH of the cavity was usually low. Because the primary objective of the liquid-release tests was to calibrate the seepage models, minimization of evaporation was an essential component of the tests. To mitigate the effect of evaporation in the seepage process, the seepage collection interval of the Cross Drift was guarded using curtains on both ends. The RH in Niche 5 was relatively high because it was isolated from the actively ventilated Cross Drift by a bulkhead. To aid in the estimation of evaporation during the liquid-release tests, the RH and temperature of the air inside and outside of the curtains (for the Cross Drift) and in front of and behind the bulkhead (for Niche 5) were monitored using Vaisala HMP45C probes (Vaisala Inc., Helsinki, Finland) (RH measurement range 0–100% noncondensing, accuracy at 20°C ± 2% for 0–90% RH and ±3% for 90–100% RH; temperature measurement range –40 to 60°C, accuracy ±1%). Up to 11 sensors were distributed in different parts of the cavities, and averaged values are reported here.

The evaporation rate from still water was measured by monitoring the level (mass) of water in evaporation pans placed within the space enclosed by the seepage capture tray and end curtains (for the Cross Drift tests) and behind the bulkhead (for Niche 5).

	TOUGH2/iTOUGH2 SEEPAGE MODEL

TOP ABSTRACT INTRODUCTION EVAPORATION IN CAVITIES COUPLED SEEPAGE AND EVAPORATION MATERIALS AND METHODS TOUGH2/iTOUGH2 SEEPAGE MODEL RESULTS AND DISCUSSIONS SUMMARY AND CONCLUSIONS REFERENCES

 
A detailed description of the numerical models developed for flow in a fractured formation around a cavity and associated seepage into the cavity using TOUGH2/iTOUGH is given by Finsterle et al. (2003). A summary of the seepage model follows.

We are concerned with the effective seepage behavior on the scale of a drift segment rather than with individual seepage events from specific dripping locations. Thus, the unsaturated flow through the densely fractured formation and seepage into the cavities is represented by a simplified, heterogeneous continuum model. The matrix is not explicitly represented in this single-continuum model because its contributions to flow and seepage are expected to be small. The effects the matrix and microfractures are accounted for through the estimation of effective parameters (Finsterle et al., 2003).

The TOUGH2 module we used (EOS9) is an integral finite difference simulator that represents unsaturated flow at the scale of individual gridblocks by Richards' equation (Bear, 1972; Pruess et al., 1999)

[13]

where and µ are the density and viscosity of water, is the porosity, and the effective saturation, S_e, is defined as S_e = (S – S_lr)/(1 – S_lr), with S_lr being the residual liquid saturation. The appropriateness of using this continuum approach to simulate water flow through unsaturated fractured rock was shown by Finsterle (2000). The effective permeability, k (m²), and capillary pressure, P_C, are functions of liquid saturation as given by van Genuchten's models (1980)

[14]

[15]

where k_a is the absolute permeability, and 1/ (Pa) and m are fitting parameters with > 0 and 0 < m < 1. While the k_a were considered spatially heterogeneous, the 1/, m, and S_lr parameters were assumed to be homogeneous for a given test bed (Finsterle et al., 2003). The absolute permeability, k_a, was derived from the air-injection tests. The van Genuchten m parameter and the residual saturation were taken to be m = 0.608 and S_lr = 0.01, respectively (Finsterle et al., 2003). The van Genuchten capillary strength parameter 1/ was estimated through inverse modeling. In the numerical seepage model, the condition for seepage is determined by the total water-potential gradient at the connection between the porous medium and the cavity, as depicted in Fig. 4 . The mass flux of seepage water J_W (kg m^–2 s^–1) along the connection between the porous medium and the cavity is given by

[16]

where P denotes the capillary pressure difference across the distance between the last formation node and the cavity node z = 0.05 m. From Eq. [16], and assuming that the capillary pressure in the opening is zero, it follows that downward seepage (J_W > 0) occurs only when the following condition is satisfied:

[17]

where P^*_C is the threshold capillary pressure at the last node adjacent to the opening. The critical capillary pressure P^*_C > –gz depends on the grid size or nodal distance of the numerical model. Thus, the applicability of the calibrated 1/ parameter is limited to the specific numerical scheme used during calibration (Finsterle et al., 2003). According to Eq. [17], the cavity surface does not need to be fully saturated for seepage to commence as in the case of unfractured homogeneous porous media (Philip et al., 1989b).

View larger version (28K): [in this window] [in a new window]   Fig. 4. Schematic description of the overlapping seepage and evaporation gridblocks and the respective connections with the gridblock that represents the cavity wall.

[18]

where the variables with a superscript zero correspond to the cavity wall and those with a superscript denote the cavity air. The capillary pressure of the cavity P_C is equivalent to the RH of the cavity (Eq. [3]), as described by Kelvin's Eq. [2]. The vapor concentrations are computed according to Eq. [9] and [10]. Equation [18] was implemented in iTOUGH2 as an equivalent permeability for the special evaporation connections. Note that k_eq is merely a numerical trick used to represent the concentration gradient–based vapor diffusion equation using the capillary pressure gradient–based flow equations used in iTOUGH2. When the conditions for both evaporation and seepage permit, the total mass flow from the cavity wall to the cavity is considered as the sum of both.

Numerical Meshes
Different numerical models were constructed to simulate liquid-release tests and seepage into the underground openings at different test locations. Three-dimensional meshes of the test sites were generated with grid sizes of 0.3 by 0.1 by 0.1 m for the Cross Drift and 0.1 by 0.1 by 0.1 m for Niche 5 (Fig. 5) . The total mesh size of the models was on the order of 100000 gridblocks. For the Cross Drift meshes, a 5-m diameter, cylindrical cavity was removed from the center of the mesh to represent the cavity. Only one-half of the symmetric mesh was used in the simulations to save computational load. For the Niche 5 meshes, surveyed niche geometry was removed from the numerical mesh to replicate the test sites. The liquid-release boreholes are indicated in Fig. 5 by bold black lines, and the white sections at the middle of the boreholes represent the injection intervals. The Cross Drift borehole is inclined, while the Niche 5 boreholes are parallel to the centerline of the niche. The Cross Drift mesh in Fig. 5a represents the Zone 2 test interval. Figures 5b and 5c illustrate Boreholes 4 and 5, respectively (see also Fig. 3c). Notice that the injection intervals in Boreholes 4 and 5 are located at 3 to 3.5 and 8.5 to 8.8 m, respectively, from the borehole collars; hence, the respective niche outlines are different.

View larger version (87K): [in this window] [in a new window]   Fig. 5. Numerical meshes of (a) Niche 5 with Borehole 4, (b) Niche 5 with Borehole 5, and (c) the Cross Drift, along with a typical realization of the correlated stochastic permeability field. Bold black lines denote the liquid-release boreholes; the white section in the middle of the boreholes is the injection interval.

In the Cross Drift six air-injection tests were performed in borehole intervals approximately 1.8 m in length, providing an estimate of mean log-permeability at the experimental site of –10.73 (corresponding to a permeability of 1.86 x 10^–11 m²) with a standard deviation of 0.21. Variability in permeability on the scale of a gridblock (which is 0.3 m long) is expected to be higher than the measured standard deviation. For the purpose of generating a heterogeneous field, permeability is taken to be lognormally distributed with a standard deviation of one order of magnitude. Because the number of data points was insufficient to reveal the spatial correlation structure of the permeability field, a weak spatial correlation of 0.2 m was prescribed, consistent with the geostatistical results reported by Finsterle et al. (2003). The computed and prescribed geostatistical parameters are reported in Table 1. These parameters were used to constrain generation of spatially correlated permeability fields, using the Gaussian sequential indicator simulation (SISIM) module of the GSLIB (Deutsch and Journel, 1992). Multiple realizations of the permeability field were generated and mapped to the numerical meshes. Representative permeability field realizations for the Cross Drift and Niche 5 are shown in Fig. 5.

	RESULTS AND DISCUSSIONS

TOP ABSTRACT INTRODUCTION EVAPORATION IN CAVITIES COUPLED SEEPAGE AND EVAPORATION MATERIALS AND METHODS TOUGH2/iTOUGH2 SEEPAGE MODEL RESULTS AND DISCUSSIONS SUMMARY AND CONCLUSIONS REFERENCES

 
Evaporation Boundary Layer
The evaporation data collected in Niche 5 were used to calibrate the evaporation model. The data were grouped into three classes based on airflow velocity (ventilation): (i) inside Niche 5 without ventilation, (ii) outside Niche 5 with active ventilation, and (iii) outside Niche 5 without active ventilation, the regime usually encountered during nights and weekends. In Fig. 6 , the measured RH, and temperature, and evaporation rates from still water are plotted. The evaporation model (Eq. [12]) was fitted to the measured data by adjusting the boundary layer thickness. The RH and temperature measurements were conducted at a different time interval from the evaporation rate measurements. Thus, fitting was performed by matching the calculated and measured evaporation rates averaged over selected short durations of significance (such as continuous high or low evaporation rates). The estimates of the boundary layer thickness rounded to the nearest millimeter are listed in Table 2.

View larger version (40K): [in this window] [in a new window]   Fig. 6. Temperature, humidity, and evaporation rate data, along with model fit of the evaporation data for inside and outside of Niche 5.

Coupled Seepage and Evaporation
In this section, simulations of coupled seepage and evaporation are compared with measured seepage rate data. The software iTOUGH2 (Finsterle, 1999) was used to match the simulated seepage rate with the measured values by adjusting the free capillary strength parameter 1/ (Finsterle et al., 2003). The corresponding evaporation rate from the cavity walls was simulated using the cavity RH and calibrated boundary layer thickness.

Niche 5
Two different data sets from liquid release tests conducted in Boreholes 4 (October 2002) and 5 (July 2002) are compared with the Niche 5 seepage models. The liquid release rate, seepage rate, and RH data as well as modeled liquid release rate and fitted seepage rate are shown in Fig. 7 . The best-fit 1/ values were 671 ± 223 and 740 ± 339 Pa for Boreholes 4 (30 inversions) and 5 (24 inversions), respectively. The measured seepage rates attained a steady-state flow rate after several days. Because the early-time transient data are biased by storage (e.g., in lithophysal cavities and matrix) and/or fast flow paths connecting the injection interval to the cavity ceilings, the model was fitted to the late-time steady-state data. In the simulations, the RH was kept constant at 0.85 to match with the lowest steady conditions observed during the Borehole 4 tests.

View larger version (38K): [in this window] [in a new window]   Fig. 7. Calibration of seepage-rate data from liquid-release tests conducted in Niche 5. Calculated seepage rate curves show only one of the multiple inversions.

View larger version (16K): [in this window] [in a new window]   Fig. 8. Effect of high relative humidity on evaporation and seepage rates.

View larger version (52K): [in this window] [in a new window]   Fig. 9. Calibration of seepage-rate data from liquid-release tests conducted in the Enhanced Characterization of the Repository Block (ECRB) cross drift. Calculated seepage rate curves show only one of the multiple inversions.

View larger version (84K): [in this window] [in a new window]   Fig. 10. Liquid saturation distribution simulated with model calibrated against seepage-rate data from liquid-release tests conducted in the Cross Drift Borehole LA#2, Zone 2 on Days 296, 306, 316, and 326. Note the correlation of cavity wall wetness to cavity relative humidity.

	SUMMARY AND CONCLUSIONS

TOP ABSTRACT INTRODUCTION EVAPORATION IN CAVITIES COUPLED SEEPAGE AND EVAPORATION MATERIALS AND METHODS TOUGH2/iTOUGH2 SEEPAGE MODEL RESULTS AND DISCUSSIONS SUMMARY AND CONCLUSIONS REFERENCES

1. The simplified vapor-diffusion approach of modeling evaporation was found to be effective in capturing the roles of the important environmental conditions that affect evaporation—namely, RH, temperature, and ventilation. Calibrated thicknesses of the evaporation boundary layer were obtained for three ventilation conditions representing the conditions at the liquid-release test sites at YM.
   
2. We found that evaporation reduces seepage significantly in tests conducted under ventilated conditions. Therefore, it is important to account for evaporation effects when calibrating a seepage process model against liquid-release test data collected under ventilated conditions. In contrast, the impact of evaporation on seepage rate was minimal in closed-off niches, where RH values were generally high. Thus, when using data obtained from closed-off and/or artificially humidified niches, ignoring the effect of evaporation is expected to introduce little error in the estimation of seepage-relevant parameters.
   
3. The classification of ventilation regimes is based on crude assessment of the cavity environment. The effect of external wind velocity variations (note that the Cross Drift is connected to the air outside the ESF) was not accounted for in the calculations. The match between measured evaporation rate and model predictions could have been improved if accurate measurement of air velocity in the cavities had been made during the test.
   

The calibrated seepage models were tested by comparing blind predictions of seepage rates performed with the calibrated model against liquid release test data that were not used for model calibration. These model tests showed that the models predict seepage rate successfully according to a probabilistic acceptance criterion, which requires that at least 95% of the observed late-time seepage-rate data lie within the 95% simulation uncertainty band calculated by the calibrated model, or if the calibrated model overpredicts the seepage rates (deemed conservative). The model testing exercises and acceptance criterion are discussed in depth by Finsterle et al. (2003) and are not reported here.

	ACKNOWLEDGMENTS

 
Thorough reviews and insightful comments by J. Birkholzer, G. Li, C.K. Ho, R. Fedors, C. Oldenburg, and an anonymous reviewer are gratefully acknowledged. This work was supported by the Director, Office of Civilian Radioactive Waste Management, U.S. Department of Energy, through Memorandum Purchase Order QA-B004220RB3X between Bechtel SAIC Company, LLC, and the Ernest Orlando Lawrence Berkeley National Laboratory (Berkeley Lab). The support is provided to Berkeley Lab through the U.S. Department of Energy Contract no. DE-AC03-76SF00098.

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TOP ABSTRACT INTRODUCTION EVAPORATION IN CAVITIES COUPLED SEEPAGE AND EVAPORATION MATERIALS AND METHODS TOUGH2/iTOUGH2 SEEPAGE MODEL RESULTS AND DISCUSSIONS SUMMARY AND CONCLUSIONS REFERENCES

 

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