Development and application of an advection-dispersion model for data analysis of electromigration experiments with intact rock cores

An advection-dispersion model was developed for interpreting the experimental results of electromigration in granitic rock cores. The most important mechanisms governing the movement of the tracer ions, i.e. electromigration, electroosmosis and dispersion were taken into account by the advection-dispersion model, but the influence of aqueous chemistry was ignored. An analytical solution in the Laplace domain was derived and then applied to analyze the measured results of a series of experiments, performed in an updated device with different applied voltages. The modelling results suggested that both studied tracers, i.e. iodide and selenite, are effectively non-sorbing in the intact rock investigated. The effective diffusivities and formation factors evaluated from the model were also found to be in good agreement with data reported in literature and the associated uncertainties are much smaller than those obtained from the classical ideal plug-flow model, which accounts only for the dominant effect of electromigration on ionic transport. To explore further how the quality of parameter identifications would be influenced by neglect of aqueous chemistry, a reactive transport model was also implemented, which may be regarded as a multi-component version of the advection-dispersion model. The analysis showed that the advection-dispersion model works equally well as the reactive transport model but requires much less computational demanding. It can, therefore, be used with great confidence to interpret the experimental results of electromigration for studies of diffusion and sorption behavior of radionuclides in intact rock cores.Peer reviewe

How (not) to Build Quantum PKE in Minicrypt

The seminal work by Impagliazzo and Rudich (STOC\u2789) demonstrated the impossibility of constructing classical public key encryption (PKE) from one-way functions (OWF) in a black-box manner. However, the question remains: can quantum PKE (QPKE) be constructed from quantumly secure OWF? A recent line of work has shown that it is indeed possible to build QPKE from OWF, but with one caveat --- they rely on quantum public keys, which cannot be authenticated and reused. In this work, we re-examine the possibility of perfect complete QPKE in the quantum random oracle model (QROM), where OWF exists. Our first main result: QPKE with classical public keys, secret keys and ciphertext, does not exist in the QROM, if the key generation only makes classical queries. Therefore, a necessary condition for constructing such QPKE from OWF is to have the key generation classically ``un-simulatable’’. Previous discussions (Austrin~et al. CRYPTO\u2722) on the impossibility of QPKE from OWF rely on a seemingly strong conjecture. Our work makes a significant step towards a complete and unconditional quantization of Impagliazzo and Rudich’s results. Our second main result extends to QPKE with quantum public keys. The second main result: QPKE with quantum public keys, classical secret keys and ciphertext, does not exist in the QROM, if the key generation only makes classical queries and the quantum public key is either pure or ``efficiently clonable\u27\u27. The result is tight due to all existing QPKEs constructions. Our result further gives evidence on why existing QPKEs lose reusability. To achieve these results, we use a novel argument based on conditional mutual information and quantum Markov chain by Fawzi and Renner (Communications in Mathematical Physics). We believe the techniques used in the work will find other usefulness in separations in quantum cryptography/complexity

Diffusion and Sorption Studies of Cs, Sr and Co in Intact Crystalline Rock

Three cationic tracers, Sr2+, Co2+ and Cs+ were tested with a modified electromigration device by applying 2V, 3V and 4V voltage gradients over an intact Grimsel granodiorite rock sample. An ideal plug-flow model and an advection-dispersion model were applied to analyze the breakthrough curves. Matrix characterization by C-14-PMMA autoradiography and scanning electron microscopy showed that in the centimeter scale of Grimsel granodiorite rock, the interconnected matrix porosity forms a well-connected network for diffusion. Micrometer-scale fissures are transecting biotite and chlorite minerals, indicating sorption of the studied cations. The ideal plug-flow model indicated that the effective diffusion coefficients (De values) for Sr2+, Co2+ and Cs+ tracer ions within the Grimsel granodiorite rock were 3.20 × 10−13 m2/s, 1.23 × 10−13 m2/s and 2.25 × 10−12 m2/s, respectively. De values were also derived from the advection-dispersion model, from which 2.86 × 10−13 m2/s, 1.35 × 10−13 m2/s and 2.26 × 10−12 m2/s were calculated. The diffusion speed for the tracers was in the sequence of Cs+ > Sr2+ > Co2+ that is in the same sequence as their diffusion in diluted water. The distribution coefficients (Kd values) calculated from the models covered the range of two magnitudes (from 10−7 m3/kg to 10−5 m3/kg). The result indicated that the sorption process of the studied elements did not reach equilibrium during the electromigration process, mainly due to the too much acceleration of the migration speed by the voltage gradients applied over the rock sample

Diffusion and Sorption Studies of Cs, Sr and Co in Intact Crystalline Rock

Three cationic tracers, Sr2+, Co2+ and Cs+ were tested with a modified electromigration device by applying 2V, 3V and 4V voltage gradients over an intact Grimsel granodiorite rock sample. An ideal plug-flow model and an advection-dispersion model were applied to analyze the breakthrough curves. Matrix characterization by C-14-PMMA autoradiography and scanning electron microscopy showed that in the centimeter scale of Grimsel granodiorite rock, the interconnected matrix porosity forms a well-connected network for diffusion. Micrometer-scale fissures are transecting biotite and chlorite minerals, indicating sorption of the studied cations. The ideal plug-flow model indicated that the effective diffusion coefficients (De values) for Sr2+, Co2+ and Cs+ tracer ions within the Grimsel granodiorite rock were 3.20 × 10−13 m2/s, 1.23 × 10−13 m2/s and 2.25 × 10−12 m2/s, respectively. De values were also derived from the advection-dispersion model, from which 2.86 × 10−13 m2/s, 1.35 × 10−13 m2/s and 2.26 × 10−12 m2/s were calculated. The diffusion speed for the tracers was in the sequence of Cs+ > Sr2+ > Co2+ that is in the same sequence as their diffusion in diluted water. The distribution coefficients (Kd values) calculated from the models covered the range of two magnitudes (from 10−7 m3/kg to 10−5 m3/kg). The result indicated that the sorption process of the studied elements did not reach equilibrium during the electromigration process, mainly due to the too much acceleration of the migration speed by the voltage gradients applied over the rock sample

Multi-site surface complexation modelling of Se(IV) sorption on biotite

A surface complexation model of Se(IV) sorption on biotite with one type of strong sorption sites and two types of weak sorption sites were developed based on experimental data obtained from titration, sorption edge and sorption isotherm experiments. Titration data was collected using a batch-wise manner together with back-titration to calibrate the effect of mineral dissolution in 0.01 M KClO4 background electrolytes from pH 3 to 11 in an inert atmosphere glovebox. Further calibrations of the titration curve include proton exchange and cation exchange in which the calculations of cation occupancies on biotite surfaces were taken into account. The sorption edge measurements were determined by measuring the sorption of 10(-9) M total Se with a radioactive Se-75 tracer on converted biotite in 0.01 M KClO4 solution from pH 3 to 11. Se sorption was observed to be strongly dependent on pH. Surface complexation modelling was performed by deriving a set of optimized parameters that can fit titration, sorption edge and sorption isotherm (at pH similar to 7.7) experimental data. A CASTEP code implemented into Materials Studio was used to calculate the site densities and site types on the biotite surfaces. Weak sorption sites with site densities of 3.2 sites/nm(2) and 1.4 sites/nm(2) were derived from the codes and used in the sorption model. A computer code that coupled PHREEQC with Python was developed for the fitting and optimizing processes. The model was validated by sorption data at pH similar to 9.5. The results show that the model can provide quantitative predicts of Se(IV) sorption in groundwater conditions of a deep geological repository and help improve the performance assessments by giving more convincing estimates of the release of radionuclides towards aquifers and biosphere.Peer reviewe

Modelling of the LTDE-SD radionuclide diffusion experiment in crystalline rock at the Aspo Hard Rock Laboratory (Sweden)

This study shows a comparison and analysis of results from a modelling exercise concerning a field experiment involving the transport and retention of different radionuclide tracers in crystalline rock. This exercise was performed within the Swedish Nuclear Fuel and Waste Management Company (SKB) Task Force on Modelling of Groundwater Flow and Transport of Solutes (Task Force GWFTS). Task 9B of the Task Force GWFTS was the second subtask within Task 9 and focused on the modelling of experimental results from the Long Term Sorption Diffusion Experiment in situ tracer test. The test had been performed at a depth of about 410m in the Aspo Hard Rock Laboratory. Synthetic groundwater containing a cocktail of radionuclide tracers was circulated for 198 days on the natural surface of a fracture and in a narrow slim hole drilled in unaltered rock matrix. Overcoring of the rock after the end of the test allowed for the measurement of tracer distribution profiles in the rock from the fracture surface (A cores) and also from the slim hole (D cores). The measured tracer activities in the rock samples showed long profiles (several cm) for non-or weakly-sorbing tracers (Cl-36, Na-22), but also for many of the more strongly-sorbing radionuclides. The understanding of this unexpected feature was one of the main motivations for this modelling exercise. However, re-evaluation and revision of the data during the course of Task 9B provided evidence that the anomalous long tails at low activities for strongly sorbing tracers were artefacts due to cross-contamination during rock sample preparation. A few data points remained for Cs-137, Ba-133, Ni-63 and Cd-109, but most measurements at long distances from the tracer source (>10mm) were now below the reported detection limits. Ten different modelling teams provided results for this exercise, using different concepts and codes. The tracers that were finally considered were Na-22, Cl-36, Co-57, Ni-63, Ba-133, Cs-137, Cd-109, Ra-226 and Np-237. Three main types of models were used: i) analytical solutions to the transport-retention equations, ii) continuum -porous-medium numerical models, and iii) microstructure-based models accounting for small-scale heterogeneity (i.e. mineral grains, porosities and/or microfracture distributions) and potential centimetre-scale fractures. The modelling by the different teams led to some important conclusions, concerning for instance the presence of a disturbed zone (a few mm in thickness) next to the fracture surface and to the wall of the slim hole and the role of micro-fractures and cm-scale fractures in the transport of weakly sorbing tracers. These conclusions could be reached after the re-evaluation and revision of the experimental data (tracer profiles in the rock) and the analysis of the different sets of model results provided by the different teams.Peer reviewe