An axisymmetric diffusion experiment for the determination of diffusion and sorption coefficients of rock samples.

Diffusion anisotropy is a critical property in predicting migration of substances in sedimentary formations with very low permeability. The diffusion anisotropy of sedimentary rocks has been evaluated mainly from laboratory diffusion experiments, in which the directional diffusivities are separately estimated by through-diffusion experiments using different rock samples, or concurrently by in-diffusion experiments in which only the tracer profile in a rock block is measured. To estimate the diffusion anisotropy from a single rock sample, this study proposes an axisymmetric diffusion test, in which tracer diffuses between a cylindrical rock sample and a surrounding solution reservoir. The tracer diffusion between the sample and reservoir can be monitored from the reservoir tracer concentrations, and the tracer profile could also be obtained after dismantling the sample. Semi-analytical solutions are derived for tracer concentrations in both the reservoir and sample, accounting for an anisotropic diffusion tensor of rank two as well as the dilution effects from sampling and replacement of reservoir solution. The transient and steady-state analyses were examined experimentally and numerically for different experimental configurations, but without the need for tracer profiling. These experimental configurations are tested for in- and out-diffusion experiments using Koetoi and Wakkanai mudstones and Shirahama sandstone, and are scrutinized by a numerical approach to identify favorable conditions for parameter estimation. The analysis reveals the difficulty in estimating diffusion anisotropy; test configurations are proposed for enhanced identifiability of diffusion anisotropy. Moreover, it is demonstrated that the axisymmetric diffusion test is efficient in obtaining the sorption parameter from both steady-state and transient data, and in determining the effective diffusion coefficient if isotropic diffusion is assumed. Moreover, measuring reservoir concentrations in an axisymmetric diffusion experiment coupled with tracer profiling may be a promising approach to estimate of diffusion anisotropy of sedimentary rocks.

Electrokinetic coupling in unsaturated porous media.

We consider a charged porous material that is saturated by two fluid phases that are immiscible and continuous on the scale of a representative elementary volume. The wetting phase for the grains is water and the nonwetting phase is assumed to be an electrically insulating viscous fluid. We use a volume-averaging approach to derive the linear constitutive equations for the electrical current density as well as the seepage velocities of the wetting and nonwetting phases on the scale of a representative elementary volume. These macroscopic constitutive equations are obtained by volume-averaging Ampère's law together with the Nernst-Planck equation and the Stokes equations. The material properties entering the macroscopic constitutive equations are explicitly described as functions of the saturation of the water phase, the electrical formation factor, and parameters that describe the capillary pressure function, the relative permeability functions, and the variation of electrical conductivity with saturation. New equations are derived for the streaming potential and electro-osmosis coupling coefficients. A primary drainage and imbibition experiment is simulated numerically to demonstrate that the relative streaming potential coupling coefficient depends not only on the water saturation, but also on the material properties of the sample, as well as the saturation history. We also compare the predicted streaming potential coupling coefficients with experimental data from four dolomite core samples. Measurements on these samples include electrical conductivity, capillary pressure, the streaming potential coupling coefficient at various levels of saturation, and the permeability at saturation of the rock samples. We found very good agreement between these experimental data and the model predictions.

Inverse and predictive modeling of seepage into underground openings.

We discuss the development and calibration of a model for predicting seepage into underground openings. Seepage is a key factor affecting the performance of the potential nuclear-waste repository at Yucca Mountain, Nevada. Three-dimensional numerical models were developed to simulate field tests in which water was released from boreholes above excavated niches. Data from air-injection tests were geostatistically analyzed to infer the heterogeneous structure of the fracture permeability field. The heterogeneous continuum model was then calibrated against the measured amount of water that seeped into the opening. This approach resulted in the estimation of model-related, seepage-specific parameters on the scale of interest. The ability of the calibrated model to predict seepage was examined by comparing calculated with measured seepage rates from additional experiments conducted in different portions of the fracture network. We conclude that an effective capillary strength parameter is suitable to characterize seepage-related features and processes for use in a prediction model of average seepage into potential waste-emplacement drifts.

Flow and transport in the drift shadow in a dual-continuum model.

The current concept for high-level radioactive waste disposal at Yucca Mountain is for the waste to be placed in underground tunnels (or drifts) in the middle of a thick unsaturated zone. Flow modeling and field testing have shown that not all flow encountering a drift will seep into the drift. The underlying reason for the diversion of unsaturated flow around a drift is that capillary forces in the fractures and matrix prevent water entry into the drift unless the capillary pressure in the rock decreases sufficiently to allow for gravity forces to overcome the capillary barrier. As a result of the capillary barrier effect, flow tends to be diverted around the drift, affecting the flow pattern beneath the drift. For some distance beneath the drift, water saturation and flux are reduced. This drift shadow zone is much more pronounced in the fractures than in the matrix due to dominance of gravity over capillary forces in the fractures. Moving downward, away from the drift, the shadow zone asymptotically re-equilibrates to the undisturbed flow conditions due to capillary forces. The behavior of radionuclide transport in this zone of reduced flow is investigated here because this will affect the amount of time required for radionuclides to penetrate the unsaturated zone. The delay of radionuclide movement in the geosphere is one aspect of the potential repository system that could limit public exposure to radioactive waste. The behavior of flow and transport is calculated using a two-dimensional, drift-scale dual-permeability model extending to nine drift diameters below the potential waste emplacement drift. The flow model is first compared with an analytical model for a single continuum. Then, the dual-continuum flow model is investigated with respect to drift-scale and mountain-scale property sets. Transport calculations are performed for a wide range of flow conditions and for different aqueous radionuclides and colloids. Findings indicate that transport times for dissolved or colloidal material released from a drift without seepage are several orders of magnitude longer than if the releases occurred in the undisturbed flow field. Furthermore, the calculations indicate that the transport rate for radionuclides released in the drift shadow is relatively insensitive to flow rates in the fractures, but is sensitive to the flow rate in the matrix.

Migration of a water pulse through fractured porous media.

Contaminant transport from waste-disposal sites is strongly affected by the presence of fractures and the degree of fracture matrix interaction. Characterization of potential contaminant plumes at such sites is difficult, both experimentally and numerically. Simulations of water flow through fractured rock were performed to examine the penetration depth of a large pulse of water entering such a system. Construction water traced with lithium bromide was released during the excavation of a tunnel at Yucca Mountain, Nevada, which is located in an unsaturated fractured tuff formation. Modeling of construction-water migration is qualitatively compared with bromide-to-chloride ratio (Br/Cl) data for pore-water salts extracted from drillcores. The influences of local heterogeneities in the fracture network and variations in hydrogeologic parameters were examined by sensitivity analyses and Monte Carlo simulations. The simulation results are qualitatively consistent with the observed Br/Cl signals, although these data may only indicate a minimum penetration depth, and water may have migrated farther through the fracture network.