A cation exchange model to describe Cs+ sorption at high ionic strength in subsurface sediments at Hanford site, USA

A theoretical and experimental study of cation exchange in high ionic strength electrolytes was performed using pristine subsurface sediments from the U.S. Department of Energy Hanford site. These sediments are representative of the site contaminated sediments impacted by release of high level waste (HLW) solutions containing 137Cs+ in NaNO3 brine. The binary exchange behavior of Cs+–Na+, Cs+–K+, and Na+–K+ was measured over a range in electrolyte concentration. Vanselow selectivity coefficients (Kv) that were calculated from the experimental data using Pitzer model ion activity corrections for aqueous species showed monotonic increases with increasing electrolyte concentrations. The influence of electrolyte concentration was greater on the exchange of Na+–Cs+ than K+–Cs+, an observation consistent with the differences in ion hydration energy of the exchanging cations. A previously developed two-site ion exchange model [Geochimica et Cosmochimica Acta 66 (2002) 193] was modified to include solvent (water) activity changes in the exchanger phase through application of the Gibbs–Duhem equation. This water activity-corrected model well described the ionic strength effect on binary Cs+ exchange, and was extended to the ternary exchange system of Cs+–Na+–K+ on the pristine sediment. The model was also used to predict 137Cs+ distribution between sediment and aqueous phase (Kd) beneath a leaked HLW tank in Hanfordd’s S-SX tank using the analytical aqueous data from the field and the binary ion exchange coefficients for the pristine sediment. The Kd predictions closely followed the trend in the field data and were improved by consideration of water activity effects that were considerable in certain regions of the vadose zone plume

Multispecies diffusion models: A study of uranyl species diffusion

Rigorous numerical description of multispecies diffusion requires coupling of species, charge, and aqueous and surface complexation reactions that collectively affect diffusive fluxes. The applicability of a fully coupled diffusion model is, however, often constrained by the availability of species self-diffusion coefficients, as well as by computational complication in imposing charge conservation. In this study, several diffusion models with variable complexity in charge and species coupling were formulated and compared to describe reactive multispecies diffusion in groundwater. Diffusion of uranyl [U(VI)] species was used as an example in demonstrating the effectiveness of the models in describing multispecies diffusion. Numerical simulations found that a diffusion model with a single, common diffusion coefficient for all species was sufficient to describe multispecies U(VI) diffusion under a steady state condition of major chemical composition, but not under transient chemical conditions. Simulations revealed that for multispecies U(VI) diffusion under transient chemical conditions, a fully coupled diffusion model could be well approximated by a component-based diffusion model when the diffusion coefficient for each chemical component was properly selected. The component-based diffusion model considers the difference in diffusion coefficients between chemical components, but not between the species within each chemical component. This treatment significantly enhanced computational efficiency at the expense of minor charge conservation. The charge balance in the component-based diffusion model can be enforced, if necessary, by adding a secondary migration term resulting from model simplification. The effect of ion activity coefficient gradients on multispecies diffusion is also discussed. The diffusion models were applied to describe U(VI) diffusive mass transfer in intragranular domains in two sediments collected from U.S. Department of Energy’s Hanford 300A, where intragranular diffusion is a rate-limiting process controlling U(VI) adsorption and desorption. The grain-scale reactive diffusion model was able to describe U(VI) adsorption/desorption kinetics that had been previously described using a semiempirical, multirate model. Compared with the multirate model, the diffusion models have the advantage to provide spatiotemporal speciation evolution within the diffusion domains

A cation exchange model to describe Cs+ sorption at high ionic strength in subsurface sediments at Hanford site, USA

A theoretical and experimental study of cation exchange in high ionic strength electrolytes was performed using pristine subsurface sediments from the U.S. Department of Energy Hanford site. These sediments are representative of the site contaminated sediments impacted by release of high level waste (HLW) solutions containing 137Cs+ in NaNO3 brine. The binary exchange behavior of Cs+–Na+, Cs+–K+, and Na+–K+ was measured over a range in electrolyte concentration. Vanselow selectivity coefficients (Kv) that were calculated from the experimental data using Pitzer model ion activity corrections for aqueous species showed monotonic increases with increasing electrolyte concentrations. The influence of electrolyte concentration was greater on the exchange of Na+–Cs+ than K+–Cs+, an observation consistent with the differences in ion hydration energy of the exchanging cations. A previously developed two-site ion exchange model [Geochimica et Cosmochimica Acta 66 (2002) 193] was modified to include solvent (water) activity changes in the exchanger phase through application of the Gibbs–Duhem equation. This water activity-corrected model well described the ionic strength effect on binary Cs+ exchange, and was extended to the ternary exchange system of Cs+–Na+–K+ on the pristine sediment. The model was also used to predict 137Cs+ distribution between sediment and aqueous phase (Kd) beneath a leaked HLW tank in Hanfordd’s S-SX tank using the analytical aqueous data from the field and the binary ion exchange coefficients for the pristine sediment. The Kd predictions closely followed the trend in the field data and were improved by consideration of water activity effects that were considerable in certain regions of the vadose zone plume

Cation exchange reactions controlling desorption of 90Sr2+ from coarse-grained contaminated sediments at the Hanford site, Washington

Nuclear waste that bore 90Sr2+ was accidentally leaked into the vadose zone at the Hanford site, and was immobilized at relatively shallow depths in sediments containing little apparent clay or silt-sized components. Sr2+, 90Sr2+, Mg2+, and Ca2+ was desorbed and total inorganic carbon concentration was monitored during the equilibration of this sediment with varying concentrations of Na+, Ca2+. A cation exchange model previously developed for similar sediments was applied to these results as a predictor of final solution compositions. The model included binary exchange reactions for the four operant cations and an equilibrium dissolution/precipitation reaction for calcite. The model successfully predicted the desorption data. The contaminated sediment was also examined using digital autoradiography, a sensitive tool for imaging the distribution of radioactivity. The exchanger phase containing 90Sr was found to consist of smectite formed from weathering of mesostasis glass in basaltic lithic fragments. These clasts are a significant component of Hanford formation sands. The relatively small but significant cation exchange capacity of these sediments was thus a consequence of reaction with physically sequestered clays in sediment that contained essentially no fine-grained material. The nature of this exchange component explained the relatively slow (scale of days) evolution of desorption solutions. The experimental and model results indicated that there is little risk of migration of 90Sr2+ to the water table

Deep Generative Modeling on Limited Data with Regularization by Nontransferable Pre-trained Models

Deep generative models (DGMs) are data-eager because learning a complex model on limited data suffers from a large variance and easily overfits. Inspired by the classical perspective of the bias-variance tradeoff, we propose regularized deep generative model (Reg-DGM), which leverages a nontransferable pre-trained model to reduce the variance of generative modeling with limited data. Formally, Reg-DGM optimizes a weighted sum of a certain divergence and the expectation of an energy function, where the divergence is between the data and the model distributions, and the energy function is defined by the pre-trained model w.r.t. the model distribution. We analyze a simple yet representative Gaussian-fitting case to demonstrate how the weighting hyperparameter trades off the bias and the variance. Theoretically, we characterize the existence and the uniqueness of the global minimum of Reg-DGM in a non-parametric setting and prove its convergence with neural networks trained by gradient-based methods. Empirically, with various pre-trained feature extractors and a data-dependent energy function, Reg-DGM consistently improves the generation performance of strong DGMs with limited data and achieves competitive results to the state-of-the-art methods

Scale-dependent desorption of uranium from contaminated subsurface sediments

Column experiments were performed to investigate the scale-dependent desorption of uranyl [U(VI)] from a contaminated sediment collected from the Hanford 300 Area at the U.S. Department of Energy (DOE) Hanford Site, Washington. The sediment was a coarse-textured alluvial flood deposit containing significant mass percentage of river cobble. U(VI) was, however, only associated with its minor fine-grained (\u3c2 mm) mass fraction. U(VI) desorption was investigated both from the field-textured sediment using a large column (80 cm length by 15 cm inner diameter) and from its \u3c2 mm U(VI)- associated mass fraction using a small column (10 cm length by 3.4 cm inner diameter). Dynamic advection conditions with intermittent flow and stop-flow events of variable durations were employed to investigate U(VI) desorption kinetics and its scale dependence. A multicomponent kinetic model that integrated a distributed rate of mass transfer with surface complexation reactions successfully described U(VI) release from the fine-grained U(VI)-associated materials. The field-textured sediment in the large column displayed dual-domain tracer-dependent mass transfer properties that affected the breakthrough curves of bromide, pentafluorobenzoic acid (PFBA), and tritium. The tritium breakthrough curve showed stronger nonequilibrium behavior than did PFBA and bromide and required a larger immobile porosity to describe. The dual-domain mass transfer properties were then used to scale the kinetic model of U(VI) desorption developed for the fine-grained materials to describe U(VI) release and reactive transport in the field-textured sediment. Numerical simulations indicated that the kinetic model that was integrated with the dual-domain properties determined from tracer PFBA and Br best described the experimental results. The kinetic model without consideration of the dual-domain properties overpredicted effluent U(VI) concentrations, while the model based on tritium mass transfer underpredicted the rate of U(VI) release. Overall, our results indicated that the kinetics of U(VI) release from the field-textured sediment were different from that of its fine-grained U(VI)-associated mass fraction. However, the desorption kinetics measured on the U(VI)-containing mass fraction could be scaled to describe U(VI) reactive transport in the contaminated field-textured sediment after proper consideration of the physical transport properties of the sediment. The research also demonstrated a modeling approach to integrate geochemical processes into field-scale reactive transport models

Scale-dependent desorption of uranium from contaminated subsurface sediments

Column experiments were performed to investigate the scale-dependent desorption of uranyl [U(VI)] from a contaminated sediment collected from the Hanford 300 Area at the U.S. Department of Energy (DOE) Hanford Site, Washington. The sediment was a coarse-textured alluvial flood deposit containing significant mass percentage of river cobble. U(VI) was, however, only associated with its minor fine-grained (\u3c2 mm) mass fraction. U(VI) desorption was investigated both from the field-textured sediment using a large column (80 cm length by 15 cm inner diameter) and from its \u3c2 mm U(VI)- associated mass fraction using a small column (10 cm length by 3.4 cm inner diameter). Dynamic advection conditions with intermittent flow and stop-flow events of variable durations were employed to investigate U(VI) desorption kinetics and its scale dependence. A multicomponent kinetic model that integrated a distributed rate of mass transfer with surface complexation reactions successfully described U(VI) release from the fine-grained U(VI)-associated materials. The field-textured sediment in the large column displayed dual-domain tracer-dependent mass transfer properties that affected the breakthrough curves of bromide, pentafluorobenzoic acid (PFBA), and tritium. The tritium breakthrough curve showed stronger nonequilibrium behavior than did PFBA and bromide and required a larger immobile porosity to describe. The dual-domain mass transfer properties were then used to scale the kinetic model of U(VI) desorption developed for the fine-grained materials to describe U(VI) release and reactive transport in the field-textured sediment. Numerical simulations indicated that the kinetic model that was integrated with the dual-domain properties determined from tracer PFBA and Br best described the experimental results. The kinetic model without consideration of the dual-domain properties overpredicted effluent U(VI) concentrations, while the model based on tritium mass transfer underpredicted the rate of U(VI) release. Overall, our results indicated that the kinetics of U(VI) release from the field-textured sediment were different from that of its fine-grained U(VI)-associated mass fraction. However, the desorption kinetics measured on the U(VI)-containing mass fraction could be scaled to describe U(VI) reactive transport in the contaminated field-textured sediment after proper consideration of the physical transport properties of the sediment. The research also demonstrated a modeling approach to integrate geochemical processes into field-scale reactive transport models

Influence of Reactive Transport on the Reduction of U(VI) in the Presence of Fe(III) and Nitrate: Implications for U(VI) Immobilization by Bioremidation/Biobarriers

The purposes of this report are to: (1) to determine how flow and transport influence the distribution of U(VI) under field-relevant conditions and the transfer of reductive equivalents to the aqueous and solid phases by DMRB; and (2) to examine the solid-phase stability of bioreduced uranium phases--effects of mass transfer on reoxidation of U(IV) by O{sub 2} and other oxidants (e.g., NO{sub 3}{sup -}, denitrification products)