Identifiability of diffusion and sorption parameters from in situ diffusion experiments by using simultaneously tracer dilution and claystone data

In situ diffusion experiments are performed in geological formations at underground research laboratories to overcome the limitations of laboratory diffusion experiments and investigate scale effects. Tracer concentrations are monitored at the injection interval during the experiment (dilution data) and measured from host rock samples around the injection interval at the end of the experiment (overcoring data). Diffusion and sorption parameters are derived from the inverse numerical modeling of the measured tracer data. The identifiability and the uncertainties of tritium and Na-22(+) diffusion and sorption parameters are studied here by synthetic experiments having the same characteristics as the in situ diffusion and retention (DR) experiment performed on Opalinus Clay. Contrary to previous identifiability analyses of in situ diffusion experiments, which used either dilution or overcoring data at approximate locations, our analysis of the parameter identifiability relies simultaneously on dilution and overcoring data, accounts for the actual position of the overcoring samples in the claystone, uses realistic values of the standard deviation of the measurement errors, relies on model identification criteria to select the most appropriate hypothesis about the existence of a borehole disturbed zone and addresses the effect of errors in the location of the sampling profiles. The simultaneous use of dilution and overcoring data provides accurate parameter estimates in the presence of measurement errors, allows the identification of the right hypothesis about the borehole disturbed zone and diminishes other model uncertainties such as those caused by errors in the volume of the circulation system and the effective diffusion coefficient of the filter. The proper interpretation of the experiment requires the right hypothesis about the borehole disturbed zone. A wrong assumption leads to large estimation errors. The use of model identification criteria helps in the selection of the best model. Small errors in the depth of the overcoring samples lead to large parameter estimation errors. Therefore, attention should be paid to minimize the errors in positioning the depth of the samples. The results of the identifiability analysis do not depend on the particular realization of random numbers. (C) 2012 Elsevier B.V. All rights reserved.

In-situ diffusion of HTO, 22Na+, Cs+ and I- in Opalinus Clay at the Mont Terri underground rock laboratory

The diffusion properties of the Opalinus Clay were studied in the underground research laboratory at Mont Terri (Canton Jura, Switzerland) and the results were compared with diffusion data measured in the laboratory on small-scale samples. The diffusion of HTO, Na-22(+), Cs+ and I- were investigated for a period of 10 months. The diffusion equipment used in the field experiment was designed in such a way that a solution of tracers was circulated through a sintered metal screen placed at the end of a borehole drilled in the formation. The concentration decrease caused by the diffusion of tracers into the rock could be followed with time and allowed first estimations of the effective diffusion coefficient. After 10 months, the diffusion zone was over-cored and the tracer profiles measured. From these profiles, effective diffusion coefficients and rock capacity factors Could be extracted by applying a two-dimensional transport model including diffusion and sorption. The simulations were done with the reactive transport code CRUNCH. In addition, results obtained from through-diffusion experiments oil small-sized samples with HTO, Cl-36(-) and Na-22(+) are presented and compared with the in situ data. In all cases. excellent agreement between the two data sets exists. Results for Cs+ indicated five times higher diffusion rates relative to HTO. Corresponding laboratory diffusion measurements are still lacking. However. our Cs+ data are in qualitative agreement wish through-diffusion data for Callovo-Oxfordian argillite rock samples. which also indicate significantly higher effective diffusivities for Cs+ relative to HTO.

Long-term diffusion experiment at Mont Terri: first results from field and laboratory data

The diffusion of radionuclides is an important safety aspect for nuclear waste disposal in argillaceous host rocks. A long-term diffusion experiment, termed DI-A, is being carried out at the Mont Terri Rock Laboratory in the Opalinus Clay formation. The aim of this experiment is the understanding of the migration and sorption behaviour of cationic and anionic species in consolidated clays. This study reports on the experimental layout and the first results obtained from the DI-A experiment, which include the investigation of HTO, Na-22(+), Cs+, and I- migration during a period of 1 year by analysing these tracers in the water circulating in the borehole. In addition, results obtained from through-diffusion experiments on small-sized samples with HTO, I-, and Cl-36(-) are presented. The decrease of tracer concentrations in the borehole is fastest for Cs+, followed by Na-22(+), HTO, and finally I-. The chemical composition of the artificial pore water in the borehole shows very little variation with time, thus indicating almost no chemical disturbance around the borehole. Through-diffusion experiments in the laboratory that were performed parallel to the bedding plane with two different methods yielded effective diffusion coefficients for HTO of 4-5 X 10(-11) m(2) s(-1) and significantly lower ones for anions Cl- and I- (0.7-1.6 X 10(-11) m(2) s(-1)). The results indicate the importance of anion exclusion effects arising from the negatively charged clay surfaces. Furthermore, they demonstrate the anisotropic diffusion properties of the clay formation with significantly increased diffusion rates parallel to bedding relative to the perpendicular direction. The tracer data of the in situ experiment were successfully described with 2D diffusion models using diffusion and sorption parameters obtained from the above mentioned and other laboratory studies. The modelling results indicate that HTO and I- diffused with no retardation. The retardation of Na+ and Cs+ could be described by empirical sorption expressions from previously derived batch sorption (Cs+) or diffusion (Na+) experiments. Overall, the obtained results demonstrate the feasibility of the technical concept to study the diffusion of nonsorbing and sorbing tracers in consolidated clays. (C) 2004 Elsevier B.V. All rights reserved.

Solute transport in crystalline rocks at Äspö — I: Geological basis and model calibration

Water-conducting faults and fractures were studied in the granite-hosted A¨ spo¨ Hard Rock Laboratory (SE Sweden). On a scale of decametres and larger, steeply dipping faults dominate and contain a variety of different fault rocks (mylonites, cataclasites, fault gouges). On a smaller scale, somewhat less regular fracture patterns were found. Conceptual models of the fault and fracture geometries and of the properties of rock types adjacent to fractures were derived and used as input for the modelling of in situ dipole tracer tests that were conducted in the framework of the Tracer Retention Understanding Experiment (TRUE-1) on a scale of metres. After the identification of all relevant transport and retardation processes, blind predictions of the breakthroughs of conservative to moderately sorbing tracers were calculated and then compared with the experimental data. This paper provides the geological basis and model calibration, while the predictive and inverse modelling work is the topic of the companion paper [J. Contam. Hydrol. 61 (2003) 175]. The TRUE-1 experimental volume is highly fractured and contains the same types of fault rocks and alterations as on the decametric scale. The experimental flow field was modelled on the basis of a 2D-streamtube formalism with an underlying homogeneous and isotropic transmissivity field. Tracer transport was modelled using the dual porosity medium approach, which is linked to the flow model by the flow porosity. Given the substantial pumping rates in the extraction borehole, the transport domain has a maximum width of a few centimetres only. It is concluded that both the uncertainty with regard to the length of individual fractures and the detailed geometry of the network along the flowpath between injection and extraction boreholes are not critical because flow is largely one-dimensional, whether through a single fracture or a network. Process identification and model calibration were based on a single uranine breakthrough (test PDT3), which clearly showed that matrix diffusion had to be included in the model even over the short experimental time scales, evidenced by a characteristic shape of the trailing edge of the breakthrough curve. Using the geological information and therefore considering limited matrix diffusion into a thin fault gouge horizon resulted in a good fit to the experiment. On the other hand, fresh granite was found not to interact noticeably with the tracers over the time scales of the experiments. While fracture-filling gouge materials are very efficient in retarding tracers over short periods of time (hours–days), their volume is very small and, with time progressing, retardation will be dominated by altered wall rock and, finally, by fresh granite. In such rocks, both porosity (and therefore the effective diffusion coefficient) and sorption Kds are more than one order of magnitude smaller compared to fault gouge, thus indicating that long-term retardation is expected to occur but to be less pronounced.

Solute transport in crystalline rocks at Äspö — II: Blind predictions, inverse modelling and lessons learnt from test STT1

Based on the results from detailed structural and petrological characterisation and on up-scaled laboratory values for sorption and diffusion, blind predictions were made for the STT1 dipole tracer test performed in the Swedish A¨ spo¨ Hard Rock Laboratory. The tracers used were nonsorbing, such as uranine and tritiated water, weakly sorbing 22Na+, 85Sr2 +, 47Ca2 +and more strongly sorbing 86Rb+, 133Ba2 +, 137Cs+. Our model consists of two parts: (1) a flow part based on a 2D-streamtube formalism accounting for the natural background flow field and with an underlying homogeneous and isotropic transmissivity field and (2) a transport part in terms of the dual porosity medium approach which is linked to the flow part by the flow porosity. The calibration of the model was done using the data from one single uranine breakthrough (PDT3). The study clearly showed that matrix diffusion into a highly porous material, fault gouge, had to be included in our model evidenced by the characteristic shape of the breakthrough curve and in line with geological observations. After the disclosure of the measurements, it turned out that, in spite of the simplicity of our model, the prediction for the nonsorbing and weakly sorbing tracers was fairly good. The blind prediction for the more strongly sorbing tracers was in general less accurate. The reason for the good predictions is deemed to be the result of the choice of a model structure strongly based on geological observation. The breakthrough curves were inversely modelled to determine in situ values for the transport parameters and to draw consequences on the model structure applied. For good fits, only one additional fracture family in contact with cataclasite had to be taken into account, but no new transport mechanisms had to be invoked. The in situ values for the effective diffusion coefficient for fault gouge are a factor of 2–15 larger than the laboratory data. For cataclasite, both data sets have values comparable to laboratory data. The extracted Kd values for the weakly sorbing tracers are larger than Swedish laboratory data by a factor of 25–60, but agree within a factor of 3–5 for the more strongly sorbing nuclides. The reason for the inconsistency concerning Kds is the use of fresh granite in the laboratory studies, whereas tracers in the field experiments interact only with fracture fault gouge and to a lesser extent with cataclasite both being mineralogically very different (e.g. clay-bearing) from the intact wall rock.

Multi-scale micro-structure generation strategy for up-scaling transport in clays

Clays and claystones are used as backfill and barrier materials in the design of waste repositories, because they act as hydraulic barriers and retain contaminants. Transport through such barriers occurs mainly by molecular diffusion. There is thus an interest to relate the diffusion properties of clays to their structural properties. In previous work, we have developed a concept for up-scaling pore-scale molecular diffusion coefficients using a grid-based model for the sample pore structure. Here we present an operational algorithm which can generate such model pore structures of polymineral materials. The obtained pore maps match the rock’s mineralogical components and its macroscopic properties such as porosity, grain and pore size distributions. Representative ensembles of grains in 2D or 3D are created by a lattice Monte Carlo (MC) method, which minimizes the interfacial energy of grains starting from an initial grain distribution. Pores are generated at grain boundaries and/or within grains. The method is general and allows to generate anisotropic structures with grains of approximately predetermined shapes, or with mixtures of different grain types. A specific focus of this study was on the simulation of clay-like materials. The generated clay pore maps were then used to derive upscaled effective diffusion coefficients for non-sorbing tracers using a homogenization technique. The large number of generated maps allowed to check the relations between micro-structural features of clays and their effective transport parameters, as is required to explain and extrapolate experimental diffusion results. As examples, we present a set of 2D and 3D simulations and investigated the effects of nanopores within particles (interlayer pores) and micropores between particles. Archie’s simple power law is followed in systems with only micropores. When nanopores are present, additional parameters are required; the data reveal that effective diffusion coefficients could be described by a sum of two power functions, related to the micro- and nanoporosity. We further used the model to investigate the relationships between particle orientation and effective transport properties of the sample.

Water–montmorillonite systems: Neutron scattering and tracer throughdiffusion studies

Designs for deep geological respositories of nuclear waste include bentonite as a hydraulic and chemisorption buffer material to protect the biosphere from leakage of radionuclides. Bentonite is chosen because it is a cheap, naturally occurring material with the required properties. It consists essentially of montmorillonite, a swelling clay mineral. Upon contact with groundwater such clays can seal the repository by incorporating water in the interlayers of their crystalline structure. The intercalated water exhibits significantly different properties to bulk water in the surrounding interparticle pores, such as lower diffusion coefficients (González Sánchez et. al. 2008). This doctoral thesis presents water distribution and diffusion behavior on various time and space scales in montmorillonite. Experimental results are presented for Na- and Cs-montmorillonite samples with a range of bulk dry densities (0.8 to 1.7 g/cm3). The experimental methods employed were neutron scattering (backscattering, diffraction, time-of-flight), adsorption measurements (water, nitrogen) and tracer-through diffusion. For the tracer experiments the samples were fully saturated via the liquid phase under volume-constrained conditions. In contrast, for the neutron scattering experiments, the samples were hydrated via the vapor phase and subsequently compacted, leaving a significant fraction of interparticle pores unfilled with water. Owing to these differences in saturation, the water contents of the samples for neutron scattering were characterized by gravimetry whereas those for the tracer experiments were obtained from the bulk dry density. The amount of surface water in interlayer pores could be successfully discriminated from the amount of bulk-like water in interparticle pores in Na- and Csmontmorillonite using neutron spectroscopy. For the first time in the literature, the distribution of water between these two pore environments was deciphered as a function of gravimetric water content. The amount was compared to a geometrical estimation of the amount of interlayer and interparticle water determined by neutron diffraction and adsorption measurements. The relative abundances of the 1 to 4 molecular water layers in the interlayer were determined from the area ratios of the (001)-diffraction peaks. Depending on the characterization method, different fractions of surface water and interlayer water were obtained. Only surface and interlayer water exists in amontmorillonite with water contents up to 0.18 g/g according to spectroscopic measurements and up to 0.32 g/g according to geometrical estimations, respectively. At higher water contents, bulk-like and interparticle water also exists. The amounts increase monotonically, but not linearly, from zero to 0.33 g/g for bulk-like water and to 0.43 g/g for interparticle water. It was found that water most likely redistributes between the surface and interlayer sites during the spectroscopic measurements and therefore the reported fraction is relevant only below about -10 ºC (Anderson, 1967). The redistribution effect can explain the discrepancy in fractions between the methods. In a novel approach the fractions of water in different pore environments were treated as a fixed parameter to derive local diffusion coefficients for water from quasielastic neutron scattering data, in particular for samples with high water contents. Local diffusion coefficients were obtained for the 1 to 4 molecular water layers in the interlayer of 0.5·10–9, 0.9·10–9, 1.5·10–9 and 1.4·10–9 m²/s, respectively, taking account of the different water fractions (molecular water layer, bulk-like water). The diffusive transport of 22Na and HTO through Na-montmorillonite was measured on the laboratory experimental scale (i.e. cm, days) by tracer through-diffusion experiments. We confirmed that diffusion of HTO is independent of the ionic strength of the external solution in contact with the clay sample but dependent on the bulk dry density. In contrast, the diffusion of 22Na was found to depend on both the ionic strength of the pore solution and on the bulk dry density. The ratio of the pore and surface diffusion could be experimentally determined for 22Na from the dependence of the diffusion coefficient on the ionic strength. Activation energies were derived from the temperaturedependent diffusion coefficients via the Arrhenius relation. In samples with high bulk dry density the activation energies are slightly higher than those of bulk water whereas in low density samples they are lower. The activation energies as a function of ionic strengths of the pore solutions are similar for 22Na and HTO. The facts that (i) the slope of the logarithmic effective diffusion coefficients as a function of the logarithmic ionic strength is less than unity for low bulk dry densities and (ii) two water populations can be observed for high gravimetric water contents (low bulk dry densities) support the interlayer and interparticle porosity model proposed by Glaus et al. (2007), Bourg et al. (2006, 2007) and Gimmi and Kosakowski (2011).

Helium in solubility equilibrium with quartz and porefluids in rocks - a new approach in hydrology

Quartz crystals in sandstones at depths of 1200 m–1400 m below the surface appear to reach a solubility equilibrium with the 4He-concentration in the surrounding pore- or groundwater after some time. A rather high 4Heconcentration of 4.5x10E-3 cc STP 4He/cm3 of water measured in a groundwater sample would for instance maintain a He pressure of 0.47 atm in a related volume. This value is equal within analytical error to the pressure deduced from the measured helium content of the quartz and its internal helium-accessible volume. To determine this volume, quartz crystals of 0.1 to 1 mm were separated from sandstones and exposed to a helium gas pressure of 32 atm at a temperature of 290°C for up to 2 months. By crushing, melting or isothermal heating the helium was then extracted from the helium saturated samples. Avolume on the order of 0.1% of the crystal volume is only accessible to helium atoms but not to argon atoms or water molecules. By monitoring the diffusive loss of He from the crystals at 350°C an effective diffusion constant on the order of 10E-9 cm2/s is estimated. Extrapolation to the temperature of 70°C in the sediments at a depth of 1400 m gives a typical time of about 100 000 years to reach equilibrium between helium in porewaters and the internal He-accessible volume of quartz crystals. In a geologic situation with stagnant pore- or groundwaters in sediments it therefore appears to be possible with this new method to deduce a 4He depth profile for porewaters in impermeable rocks based on their mineral record.

The effective Planck mass and the scale of inflation

Observable quantities in cosmology are dimensionless, and therefore independent of the units in which they are measured. This is true of all physical quantities associated with the primordial perturbations that source cosmic microwave background anisotropies such as their amplitude and spectral properties. However, if one were to try and infer an absolute energy scale for inflation—a priori, one of the more immediate corollaries of detecting primordial tensor modes—one necessarily makes reference to a particular choice of units, the natural choice for which is Planck units. In this note, we discuss various aspects of how inferring the energy scale of inflation is complicated by the fact that the effective strength of gravity as seen by inflationary quanta necessarily differs from that seen by gravitational experiments at presently accessible scales. The uncertainty in the former relative to the latter has to do with the unknown spectrum of universally coupled particles between laboratory scales and the putative scale of inflation. These intermediate particles could be in hidden as well as visible sectors or could also be associated with Kaluza–Klein resonances associated with a compactification scale below the scale of inflation. We discuss various implications for cosmological observables.

Experimental determination of barium isotope fractionation during diffusion and adsorption processes at low temperatures

Variations in barium (Ba) stable isotope abundances measured in low and high temperature environments have recently received increasing attention. The actual processes controlling Ba isotope fractionation, however, remain mostly elusive. In this study, we present the first experimental approach to quantify the contribution of diffusion and adsorption on mass- dependent Ba isotope fractionation during transport of aqueous Ba2+ ions through a porous medium. Experiments have been carried out in which a BaCl2 solution of known isotopic composition diffused through u-shaped glass tubes filled with silica hydrogel at 10 C and 25 C for up to 201 days. The diffused Ba was highly fractionated by up to -2.15‰ in d137/134Ba, despite the low relative difference in atomic mass. The time-dependent isotope fractionation can be successfully reproduced by a diffusive transport model accounting for mass-dependent differences in the effective diffusivities of the Ba isotope species (D137Ba/D134Ba = (m134/m137)^b). Values of b extracted from the transport model were in the range of 0.010–0.011. Independently conducted batch experiments revealed that adsorption of Ba onto the surface of silica hydrogel favoured the heavier Ba isotopes (a = 1.00015 ± 0.00008). The contribution of adsorption on the overall isotope fractionation in the diffusion experiments, however, was found to be small. Our results contribute to the understanding of Ba isotope fractionation pro- cesses, which is crucial for interpreting natural isotope variations and the assessment of Ba isotope ratios as geochemical proxies.

Deadspace estimation from CO2 versus molar mass measurements in infants

BACKGROUND: Estimation of respiratory deadspace is often based on the CO2 expirogram, however presence of the CO2 sensor increases equipment deadspace, which in turn influences breathing pattern and calculation of lung volume. In addition, it is necessary to correct for the delay between the sensor and flow signals. We propose a new method for estimation of effective deadspace using the molar mass (MM) signal from an ultrasonic flowmeter device, which does not require delay correction. We hypothesize that this estimation is correlated with that calculated from the CO2 signal using the Fowler method. METHODS: Breath-by-breath CO2, MM and flow measurements were made in a group of 77 term-born healthy infants. Fowler deadspace (Vd,Fowler) was calculated after correcting for the flow-dependent delay in the CO2 signal. Deadspace estimated from the MM signal (Vd,MM) was defined as the volume passing through the flowhead between start of expiration and the 10% rise point in MM. RESULTS: Correlation (r = 0.456, P < 0.0001) was found between Vd,MM and Vd,Fowler averaged over all measurements, with a mean difference of -1.4% (95% CI -4.1 to 1.3%). Vd,MM ranged from 6.6 to 11.4 ml between subjects, while Vd,Fowler ranged from 5.9 to 12.0 ml. Mean intra-measurement CV over 5-10 breaths was 7.8 +/- 5.6% for Vd,MM and 7.8 +/- 3.7% for Vd,Fowler. Mean intra-subject CV was 6.0 +/- 4.5% for Vd,MM and 8.3 +/- 5.9% for Vd,Fowler. Correcting for the CO2 signal delay resulted in a 12% difference (P = 0.022) in Vd,Fowler. Vd,MM could be obtained more frequently than Vd,Fowler in infants with CLD, with a high variability. CONCLUSIONS: Use of the MM signal provides a feasible estimate of Fowler deadspace without introducing additional equipment deadspace. The simple calculation without need for delay correction makes individual adjustment for deadspace in FRC measurements possible. This is especially important given the relative large range of deadspace seen in this homogeneous group of infants.

Prostate carcinoma: diffusion-weighted imaging as potential alternative to conventional MR and 11C-choline PET/CT for detection of bone metastases

In a technical development study approved by the institutional ethics committee, the feasibility of fast diffusion-weighted imaging as a replacement for conventional magnetic resonance (MR) imaging sequences (short inversion time inversion recovery [STIR] and T1-weighted spin echo [SE]) and positron emission tomography (PET)/computed tomography (CT) in the detection of skeletal metastases from prostate cancer was evaluated. MR imaging and carbon 11 ((11)C) choline PET/CT data from 11 consecutive prostate cancer patients with bone metastases were analyzed. Diffusion-weighted imaging appears to be equal, if not superior, to STIR and T1-weighted SE sequences and equally as effective as (11)C-choline PET/CT in detection of bone metastases in these patients. Diffusion-weighted imaging should be considered for further evaluation and comparisons with PET/CT for comprehensive whole-body staging and restaging in prostate and other cancers.

An estimate of heavy quark momentum diffusion coefficient in gluon plasma

We calculate the momentum diffusion coefficient for heavy quarks in SU(3) gluon plasma at temperatures 1-2 times the deconfinement temperature. The momentum diffusion coefficient is extracted from a Monte Carlo calculation of the correlation function of color electric fields, in the leading order of expansion in heavy quark mass. Systematics of the calculation are examined, and compared with perturbtion theory and other estimates.