The effect of coupled transport phenomena in the Opalinus Clay and implications for radionuclide transport

Colloid-facilitated transport of 238Pu, 233U and 137Cs through fractured chalk: Laboratory experiments, modelling, and implications for nuclear waste disposal

The influence of montmorillonite colloids on the mobility of ²³⁸Pu, ²³³U and ¹³⁷Cs through a chalk fracture was investigated to assess the transport potential for radioactive waste. Radioisotopes of each element, along with the conservative tracer tritium, were injected in the presence and absence of montmorillonite colloids into a naturally fractured chalk core. In parallel, batch experiments were conducted to obtain experimental sorption coefficients (K_d, mL/g) for both montmorillonite colloids and the chalk fracture material. Breakthrough curves were modelled to determine diffusivity and sorption of each radionuclide to the chalk and the colloids under advective conditions. Uranium sorbed sparingly to chalk (log K_d = 0.7 ± 0.2) in batch sorption experiments. ²³³U(VI) breakthrough was controlled primarily by the matrix diffusion and sorption to chalk (15 and 25% recovery with and without colloids, respectively). Cesium, in contrast, sorbed strongly to both the montmorillonite colloids and chalk (batch log K_d = 3.2 ± 0.01 and 3.9 ± 0.01, respectively). The high affinity to chalk and low colloid concentrations overwhelmed any colloidal Cs transport, resulting in very low ¹³⁷Cs breakthrough (1.1-5.5% mass recovery). Batch and fracture transport results, and the associated modelling revealed that Pu migrates both as Pu (IV) sorbed to montmorillonite colloids and as dissolved Pu(V) (7% recovery). Transport experiments revealed differences in Pu(IV) and Pu(V) transport behavior that could not be quantified in simple batch experiments but are critical to effectively predict transport behavior of redox-sensitive radionuclides. Finally, a brackish groundwater solution was injected after completion of the fracture flow experiments and resulted in remobilization and recovery of 2.2% of the total sorbed radionuclides which remained in the core from previous experiments. In general, our study demonstrates consistency in sorption behavior between batch and advective fracture transport. The results suggest that colloid-facilitated radionuclide transport will enhance radionuclide migration in fractured chalk for those radionuclides with exceedingly high affinity for colloids.

Critical review of coupled flux formulations for clay membranes based on nonequilibrium thermodynamics

Extensive research conducted over the past several decades has indicated that semipermeable membrane behavior (i.e., the ability of a porous medium to restrict the passage of solutes) may have a significant influence on solute migration through a wide variety of clay-rich soils, including both natural clay formations (aquitards, aquicludes) and engineered clay barriers (e.g., landfill liners and vertical cutoff walls). Restricted solute migration through clay membranes generally has been described using coupled flux formulations based on nonequilibrium (irreversible) thermodynamics. However, these formulations have differed depending on the assumptions inherent in the theoretical development, resulting in some confusion regarding the applicability of the formulations. Accordingly, a critical review of coupled flux formulations for liquid, current, and solutes through a semipermeable clay membrane under isothermal conditions is undertaken with the goals of explicitly resolving differences among the formulations and illustrating the significance of the differences from theoretical and practical perspectives. Formulations based on single-solute systems (i.e., uncharged solute), single-salt systems, and general systems containing multiple cations or anions are presented. Also, expressions relating the phenomenological coefficients in the coupled flux equations to relevant soil properties (e.g., hydraulic conductivity and effective diffusion coefficient) are summarized for each system. A major difference in the formulations is shown to exist depending on whether counter diffusion or salt diffusion is assumed. This difference between counter and salt diffusion is shown to affect the interpretation of values for the effective diffusion coefficient in a clay membrane based on previously published experimental data. Solute transport theories based on both counter and salt diffusion then are used to re-evaluate previously published column test data for the same clay membrane. The results indicate that, despite the theoretical inconsistency between the counter-diffusion assumption and the salt-diffusion conditions of the experiments, the predictive ability of solute transport theory based on the assumption of counter diffusion is not significantly different from that based on the assumption of salt diffusion, provided that the input parameters used in each theory are derived under the same assumption inherent in the theory. Nonetheless, salt-diffusion theory is fundamentally correct and, therefore, is more appropriate for problems involving salt diffusion in clay membranes. Finally, the fact that solute diffusion cannot occur in an ideal or perfect membrane is not explicitly captured in any of the theoretical expressions for total solute flux in clay membranes, but rather is generally accounted for via inclusion of an effective porosity, n(e), or a restrictive tortuosity factor, τ(r), in the formulation of Fick's first law for diffusion. Both n(e) and τ(r) have been correlated as a linear function of membrane efficiency. This linear correlation is supported theoretically by pore-scale modeling of solid-liquid interactions, but experimental support is limited. Additional data are needed to bolster the validity of the linear correlation for clay membranes.

High-precision synthetic computed tomography of reconstructed porous media

Multiscale simulation of transport in disordered and porous media requires microstructures covering several decades in length scale. X-ray and synchrotron computed tomography are presently unable to resolve more than one decade of geometric detail. Recent advances in pore scale modeling [Biswal, Held, Khanna, Wang, and Hilfer, Phys. Rev. E 80, 041301 (2009)] provide strongly correlated microstructures with several decades in microstructural detail. A carefully calibrated microstructure model for Fontainebleau sandstone has been discretized into a suite of three-dimensional microstructures with resolutions from roughly 128 μm down to roughly 500 nm. At the highest resolution the three-dimensional image consists of 32768^{3}=35184372088832 discrete cubic volume elements with gray values between 0 and 216. To the best of our knowledge, this synthetic image is the largest computed tomogram of a porous medium available at present.

A coupled THC model of the FEBEX in situ test with bentonite swelling and chemical and thermal osmosis

The performance assessment of a geological repository for radioactive waste requires quantifying the geochemical evolution of the bentonite engineered barrier. This barrier will be exposed to coupled thermal (T), hydrodynamic (H), mechanical (M) and chemical (C) processes. This paper presents a coupled THC model of the FEBEX (Full-scale Engineered Barrier EXperiment) in situ test which accounts for bentonite swelling and chemical and thermal osmosis. Model results attest the relevance of thermal osmosis and bentonite swelling for the geochemical evolution of the bentonite barrier while chemical osmosis is found to be almost irrelevant. The model has been tested with data collected after the dismantling of heater 1 of the in situ test. The model reproduces reasonably well the measured temperature, relative humidity, water content and inferred geochemical data. However, it fails to mimic the solute concentrations at the heater-bentonite and bentonite-granite interfaces because the model does not account for the volume change of bentonite, the CO(2)(g) degassing and the transport of vapor from the bentonite into the granite. The inferred HCO(3)(-) and pH data cannot be explained solely by solute transport, calcite dissolution and protonation/deprotonation by surface complexation, suggesting that such data may be affected also by other reactions.

A comparision of laboratory and field based determinations of molecular diffusion coefficients in a low permeability geologic medium

Molecular diffusion is the dominant transport mechanism for contaminants in many saturated clay-rich aquitards. The effective coefficient of diffusion (Da) is traditionally determined by conducting laboratory tests on cm-scale core samples that may not be representative of the bulk geologic formation. Here we conducted the first long-term field based in situ diffusion experimentto compare the effect of experimental scale (5 x 10(-5) m3 in the diffusion cells and (5-20) x 10(-2) m3 in the in situ experiments) on De values for clay-rich aquitards. Using a conservative tracer (deuterium), our testing shows De values estimated from in situ testing ((2.5-3.5) x 10(-10) m2 s(-1)) are similar but lower than the average De values measured in the laboratory (4 x 10(-10) m2 s(-1)). The difference was attributed to greater porosity values in the laboratory samples resulting from core barrel extrusion and sample swelling. With representative core sampling and care, laboratory-based diffusion testing remains a viable method to assess solute transport mechanisms in clay aquitards.

Thermodiffusional transport of electrolytes in compact clays

The macroscopic Soret coefficient S(T) was measured for three porous media, namely mica, glass powder, and natural compact clay. At a mean temperature of T = 25 degrees C and with NaCl, S(T) for mica and glass powder was found to be equal to (3.1+/-0.7) x 10(-3) K(-1) and close to values for a free medium in agreement with theoretical predictions which are obtained under the assumption that the pressure gradient and the electric field are negligible on the pore scale. The main result is that for clay S(T) was found five times larger, presumably because of extra couplings with electrical phenomena. This latter measurement was confirmed by an independent technique based on the membrane potential.

Thermodiffusion in compact clays

An experimental cell has been devised in order to measure the Soret coefficients in a compact clay, namely argilite, when a concentration difference of a binary mixture is applied simultaneously with a temperature difference. Temperature gradients have been imposed in the same direction as concentration gradients or in the opposite one. The sign of the Soret coefficients is related to the respective direction of these gradients. Generally, mass transfer was found to be enhanced by the Soret effect. Experimental values of the Soret coefficient are given.

Theory for reactive solute transport through clay membrane barriers

The theoretical development for one-dimensional, coupled migration of solutes with different ionic mobilities through clay soils that behave as ion-restrictive membranes, referred to as clay membrane barriers (CMBs), is presented. The transport formulation is based on principles of irreversible thermodynamics and accounts explicitly for coupling effects of hyperfiltration (ultrafiltration) and chemico-osmotic counter-advection associated with clay membrane behavior in the absence of electrical current. Since, by definition, no solute can enter a "perfect" or "ideal" membrane, the concept of an implicit coupling effect, such that the effective salt-diffusion coefficient, Ds* approaches zero as the chemico-osmotic efficiency coefficient, omega approaches unity is introduced. The theoretical development also illustrates that, even in the absence of membrane behavior, traditional advective-dispersive transport theory based on a constant value of Ds* for the solutes may not be appropriate for simulating transient transport in reactive (ion exchanging) systems. This potential limitation is illustrated through simulations for solute mass flux involving the migration of a binary salt solution (KCl) through a clay barrier with exchange sites saturated with a single exchangeable cation (e.g., Na+) that enters the pore solution upon ion exchange with the salt cation (K+).