Evaluating the Effectiveness of Liquid Diversion around an Underground Opening When Evaporation Is Non-negligible

Interpreting observations of seepage into underground openings is often complicated by evaporative potentials created by the necessity to ventilate the openings. Evaporation removes liquid from the seepage face. By doing so, it reduces both the likelihood of seepage onset and the seepage flux, and thus can enhance the perceived effectiveness of the capillary barrier. We modeled liquid-release tests at the proposed high-level waste repository in Yucca Mountain, using an enhanced version of the EOS9 module of iTOUGH2, which incorporates evaporation as Fickian diffusion. The evaporation boundary layer thickness (BLT) over which diffusion occurs was estimated using free-water evaporation experiments conducted at Yucca Mountain under known relative humidity, temperature, and ventilation conditions. The BLT, which represents the thickness of the laminar flow regime, is inversely related to the ambient airflow velocity. At Yucca Mountain, the estimated values of BLT were 5–7 mm for open underground tunnels and 20 mm for closed niches. Compared to previous models that neglected the effect of evaporation, this new approach shows significant improvement in capturing seepage fluctuations into the open tunnels. This study provides more confidence in the use of the calibrated seepage model for simulations of seepage under different ventilation conditions. INTRODUCTION Continuum models of flow in unsaturated fractured rock and the associated seepage into underground openings can be calibrated against field liquid release tests to provide effective, model-related, and processspecific properties of the porous medium (Finsterle, 2000). Previous calibration exercises ignored the contribution of evaporation in reducing seepage, although the calibration data was obtained from field tests conducted in ventilated cavities (e.g., Finsterle and Trautz, 2001; Trautz and Wang, 2001). Recently, Trautz and Wang (2002) accounted for the role of evaporation in reducing seepage by considering an empirical relationship between relative humidity and free-water evaporation measured in an environment similar to where the seepage tests were conducted. However, the empirical relationship is applicable only to free-water evaporation under similar conditions. Ahlers et al. (2003) used an alternative semiphysical approach to modeling evaporation from a porous medium. They modeled evaporation as an isothermal vapor-diffusion process that accounts for the relative humidity and temperature of the air. Ahlers et al. (2003) updated the EOS9 module of iTOUGH2 to include a special evaporation connection that implements the diffusion equation. The evaporation model assumes evaporation as a vapor diffusion process occurring across a finite boundary layer. The vapor concentration at the rock face was related to the wetness of the rock, and the vapor concentration of the bulk air is related to the humidity. The objectives of this paper are: (1) to provide a calibrated estimate of the boundary layer thickness and (2) to assess the role of evaporation in a seepage calibration model. EVAPORATION BOUNDARY LAYER Theory Evaporation from a free liquid surface involves vapor diffusion by virtue of a vapor-concentration gradient adjacent to the liquid surface, as illustrated by the solid-line curve in Figure 1. The diffusion equation that governs the mass flux of vapor V J [kg m –2 s] is given by dz dC D JV − = , (1) where C [kg m] is vapor density, D [m s] is the vapor diffusion coefficient, and z [m] is physical distance. The air immediately in contact with the liquid water is saturated with vapor, and the saturated vapor concentration is related to the saturated partial pressure of vapor by ° ⋅ ⋅ ° = ° T R M T p C w S ) ( , (2) where w M [0.01802 kg mol ] is the molecular weight of water, R [8.314 J K mol] is the universal gas constant, and ) (T pS [Pa] is the saturated partial pressure of vapor for liquid surface temperature of ° = T T [K]. Similarly, the vapor concentration in the bulk air is related to relative humidity of the air h [dimensionless] and air temperature ∞ = T T by