Diffusion of tritiated water and 22Na+ through non-degraded hardened cement pastes

Diffusion experiments through hardened cement pastes (HCP) using tritiated water (HTO) and 22Na(+), considered to be conservative tracers, have been carried out in triplicates in a glove box under a controlled nitrogen atmosphere. Each experiment consisted of a through-diffusion test followed by an out-diffusion test. The experimental data were inversely modelled applying an automated Marquardt-Levenberg procedure. The analysis of the through-diffusion data allowed the extraction of values for the effective diffusion coefficients, D(e), and the rock capacity factor, alpha. Good agreement between measured and calculated tracer breakthrough curves was achieved using both a simple diffusion model without sorption and a diffusion/linear sorption model. The best-fit K(d)-values were found to be consistent with R(d)-values measured in previous batch-sorption experiments. The best-fit values from the through-diffusion tests were then used to predict the results of subsequent out-diffusion experiments. Good agreement between experimental data and predictions was achieved only for the case of linear sorption. Isotopic exchange can only partially account for both the amount of tracer taken up in the batch-sorption tests and the measured retardation in the diffusion experiments and, hence, additional mechanisms have to be invoked to explain the data.     

Diffusion of tritiated water and Na through non-degraded hardened cement pastes

Diffusion experiments through hardened cement pastes (HCP) using tritiated water (HTO) and ²²Na⁺, considered to be conservative tracers, have been carried out in triplicates in a glove box under a controlled nitrogen atmosphere. Each experiment consisted of a through-diffusion test followed by an out-diffusion test.The experimental data were inversely modelled applying an automated Marquardt–Levenberg procedure. The analysis of the through-diffusion data allowed the extraction of values for the effective diffusion coefficients, D_e, and the rock capacity factor, α. Good agreement between measured and calculated tracer breakthrough curves was achieved using both a simple diffusion model without sorption and a diffusion/linear sorption model. The best-fit K_d-values were found to be consistent with R_d-values measured in previous batch-sorption experiments.The best-fit values from the through-diffusion tests were then used to predict the results of subsequent out-diffusion experiments. Good agreement between experimental data and predictions was achieved only for the case of linear sorption.Isotopic exchange can only partially account for both the amount of tracer taken up in the batch-sorption tests and the measured retardation in the diffusion experiments and, hence, additional mechanisms have to be invoked to explain the data.     

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.     

Contribution of the diffusive exchange method to the characterization of pore-water in consolidated argillaceous rocks

Consolidated argillaceous rocks, potential host rocks for nuclear waste disposal, display particular properties (low water content, very small pore size) that require specific methods, especially for the characterization of their pore-water. The diffusive exchange method was applied to the claystone of Tournemire by taking into account the effect of swelling or micro-cracks induced by drilling. The good agreement of diffusion parameters with those obtained from the through-diffusion method showed that the extent of this disturbance was low. This method led to stable isotope content values in pore-water in good agreement with those measured in the fracture fluids located in the vicinity, validating the method. On the contrary, the vacuum distillation technique gave a systematic depletion in heavy isotopes of water, probably induced by an incomplete extraction of pore-water. For the chloride tracer, the determination of the accessible porosity on each sample allowed the estimate of chloride concentration of pore-water to be improved, by taking into account all the petrophysical heterogeneities.     

Improved interpretation of in-diffusion measurements with confined swelling clays

Diffusion is considered the principal transport mechanism of radio-nuclides and other low-molecular-weight pollutants in compacted clays used as barriers at various disposal and storage sites, for example, at projected deep repositories for radioactive waste. Porous filters are routinely used to confine swelling clays in diffusion studies of radio-tracers. The presence of the filter gives rise to considerable mass-transfer limitations at the clay boundary that result in erroneous diffusion parameters. We have solved the problem of in-diffusion with due account for this phenomenon by means of Fourier transforms. By using literature data on the in-diffusion of traces of radioactive cesium in an argillaceous rock (Opalinus clay) and a compacted bentonite (FEBEX bentonite), we have demonstrated that taking into account the mass-transfer limitations considerably improves the quality of the theoretical fit of the time evolution of radio-tracer concentration in the reservoir. Besides that, we have shown that ignoring the mass-transfer limitations leads to a noticeable underestimation of both the effective diffusion coefficient and the specific sorption capacity of the clay.     

A technique for estimating one-dimensional diffusion coefficients in low-permeability sedimentary rock using X-ray radiography: comparison with through-diffusion measurements

The measurement of diffusive properties of low-permeability rocks is of interest to the nuclear power industry, which is considering the option of deep geologic repositories for management of radioactive waste. We present a simple, non-destructive, constant source in-diffusion method for estimating one-dimensional pore diffusion coefficients (D(p)) in geologic materials based on X-ray radiography. Changes in X-ray absorption coefficient (Deltamicro) are used to quantify changes in relative concentration (C/C(0)) of an X-ray attenuating iodide tracer as the tracer solution diffuses through the rock pores. Estimated values of D(p) are then obtained by fitting an analytical solution to the measured concentration profiles over time. Measurements on samples before and after saturation with iodide can also be used to determine iodide-accessible porosity (phi(I)). To evaluate the radiography method, results were compared with traditional steady-state through-diffusion measurements on two rock types: shale and limestone. Values of D(p) of (4.8+/-2.5)x10(-11) m(2).s(-1) (mean+/-standard deviation) were measured for samples of Queenston Formation shale and (2.6+/-1.0)x10(-11) m(2).s(-1) for samples of Cobourg Formation limestone using the radiography method. The range of results for each rock type agree well with D(p) values of (4.6+/-2.0)x10(-11) m(2).s(-1) for shale and (3.5+/-1.8)x10(-11) m(2).s(-1) for limestone, calculated from through-diffusion experiments on adjacent rock samples. Low porosity (0.01 to 0.03) and heterogeneous distribution of porosity in the Cobourg Formation may be responsible for the slightly poorer agreement between radiography and through-diffusion results for limestones. Mean values of phi(I) for shales (0.060) and limestones (0.028) were close to mean porosity measurements made on bulk samples by the independent water loss technique (0.062 and 0.020 for shales and limestones, respectively). Radiography measurements offer the advantage of time-saving for diffusion experiments because the experiment does not require steady-state conditions and also allows for visualization of the small-scale heterogeneities in diffusive properties within rocks at the mm to cm scale.     

Interpretation of out-diffusion experiments on crystalline rocks using random walk modeling

Matrix diffusion in saturated rocks with very low permeability is one of the major mechanisms of solute transport. Laboratory out-diffusion experiments on rock samples may provide an estimate of the bulk diffusion coefficient. However, numerous results have shown that this average parameter does not really depict the complex mechanism of diffusion as a function of the internal heterogeneity of crystalline rocks. Two-dimensional images of the porosity distribution in a granite sample were obtained by impregnation with a radioactive resin and autoradiography. Some examples based on these images and synthetic images were used to perform numerical simulations of out-diffusion using two different random walk methods. The simulated shapes of the out-diffusion curves depend on the spatial distribution of the porosity and on the pore connectivity with the border of the sample. Such relations might explain the multiple nested slopes or the convex shapes often observed on real experimental curves.     

Solute transport properties of compacted Ca-bentonite used in FEBEX project

The present Spanish concept of a deep geological high level waste repository includes an engineered clay barrier around the canister. The clay presents a very high sorption capability for radionuclides and a very small hydraulic conductivity, so that the migration process of solutes is limited by sorption and diffusion processes. Therefore, diffusion and distribution coefficients in compacted bentonite (i.e. in "realistic" liquid to solid ratio conditions) are the main parameters that have to be obtained in order to characterise solute transport that could be produced after the canister breakdown. Through-Diffusion (TD) and In-Diffusion (ID) experiments with HTO, Sr, Cs and Se were carried out using compacted FEBEX bentonite, which is the reference material for the Spanish concept of radioactive waste disposal. Experiments were interpreted by means of available analytical solutions that allow the estimation of diffusion coefficients and, in some cases, distribution coefficients. Analytical solutions are simple to use, but rely on hypotheses that do not hold in all the experiments. These experiments were interpreted also using an automatic parameter estimation code that overcomes the limitations of analytical solutions. Numerical interpretation allows the simultaneous estimation of porosity, diffusion and distribution coefficients, accounts for the role of porous sinters and time-varying boundary concentrations, and can use different types of raw concentration data.     

Diffusive transport through compacted Na- and Ca-bentonite

The effect of exchangeable cation — Na⁺ and Ca ²⁺ — on the diffusive transport of I⁻, Sr ²⁺ and ³H (as HTO) in compacted bentonite was examined using a through-diffusion method. Total intrinsic diffusion coefficients, D_i, were determined from the steady-state flux of the diffusants through the clays, and apparent diffusion coefficients, D_a, were obtained from the time lag technique. The clays were compacted to a dry bulk density of 1.3 Mg/m³, and Na-bentonite was saturated with a solution of 100 mol NaCl/m3 and Ca-bentonite with one of 50 mol CaCl₂/m³. The D_i values for all diffusants are 2 to 6 times higher in the Ca- than Na-clay. We attribute this to the larger quasicrystal, or particle, size of Ca- compared to Na-bentonite. Hence, Ca-bentonite has a greater proportion of relatively large pores; this was confirmed by Hg intrusion porosimetry. This means the diffusion pathways in Ca-bentonite are less tortuous than those in Na-bentonite. Moreover, in some cases the effective porosity, or the porosity available for diffusive transport, may be greater in Ca-bentonite. The D_a values are inversely proportional to the distribution coefficients of the diffusants with the clays.     

Modeling tracer diffusion in fractured and unfractured, unsaturated, porous media

A proposed tracer diffusion test for the Exploratory Shaft Facility at Yucca Mountain, NV, is modeled. For the proposed test, a solution containing conservative tracers will be introduced into a borehole in the geologic medium of interest. The tracers will diffuse and advect from the saturated source region into the unsaturated matrix in the surrounding tuff. After some time, the borehole is to be overcored, and tracer concentrations in the fluid will be measured in the core as a function of distance from emplacement. The data will be used to evaluate diffusive behavior and to derive effective diffusion coefficients for the tracers in the specific tuff. Numerical simulations are used to study the effects of effective diffusion coefficient, porosity, saturation, and fracturing on tracer transport. Results are reported for numerical simulations of tests in the Topopah Spring Member and the Tuff of Calico Hills, which have significantly different porosities and saturations. The simulations make the following predictions: The spread of tracer during the test will be sensitive to the effective diffusion coefficient of the tracer. Tracer will diffuse farther in the Topopah Spring Member than in the Tuff of Calico Hills because of the former's lower porosity and saturation. Tracer transport by advection into the Topopah Spring Member will be greater than that into the Tuff of Calico Hills because of capillary effects. While advection will be a significant mechanism for tracer penetration into the Topopah Spring tuff, it will be less significant for tracer penetration into the Calico Hills tuff. The proximity of a single vertical fracture to the source region determines its effects on tracer transport, especially if the fracture diverts fluid flowing from the source region into the matrix.     

An analytical model for the interpretation of pulse injection experiments performed for testing the spatial variability of clay formations

This paper presents an analytical model to describe pulse injection experiments. This model solves the advection-diffusion equation while taking into account back diffusion from the clay core to the inlet and from the outlet to the clay core. In most analytical models, back diffusion is neglected. For sufficiently high Péclet numbers, this is a good approximation. However, in experiments where the Péclet number is low, back diffusion is important and must be taken into account. An additional advantage of the present model is that both concentration and flux are conserved at the inlet and at the outlet of the clay core. This model is used to fit pulse injection experiments with iodide and tritiated water (HTO) in clay cores. The (new) model is required for fitting the experimental results since in clay layers advection is very slow leading to a low Péclet number. The experiments are performed on clay cores taken from different depths from the Boom Clay and the Ypres Clay layer under the site of the nuclear power plant of Doel (Belgium). The quality of all fits is excellent and the obtained parameter values are coherent. For HTO, the fitted value for the diffusion accessible porosity is consistent with measurements of the water content in Ypres Clay cores. In both types of clays, the apparent diffusion coefficient at zero flow is between 10(-10) and 2 x 10(-10) m(2)/s for iodide and between 2 x 10(-10) and 3 x 10(-10) m(2)/s for HTO. The dispersion length is in the order of 10(-3) m. The average value for the diffusion accessible porosity is between 0.35 and 0.4 for HTO and between 0.2 and 0.25 for iodide.     

Flux density and breakthrough times for water and tracer in a spatially variable, compacted clay soil

Flux density values, computed from observed infiltration and outflow measurements at 184 locations in a 0.3-m-thick, 9m × 23m layer of compacted clay subsoil, are compared to effective flux density values that are based on breakthrough time distributions for water and Br⁻ tracer over the same area. Results suggest that both water and tracer move at similar rates, but considerably faster than expected, on the basis of flux density alone, and that only a small fraction of the total pore space is involved in active transport. The ramifications of these findings are explored against the background of effective porosity, degree of compaction, and observed changes in bulk density with time.     

Modelling of silica diffusion experiments with 32Si in Boom Clay

A mathematical model describing the dissolution of nuclear glass directly disposed in clay combines a first-order dissolution rate law with the diffusion of dissolved silica in clay. According to this model, the main parameters describing the long-term dissolution of the glass are etaR, the product of the diffusion accessible porosity eta and the retardation factor R, and the apparent diffusion coefficient D(app) of dissolved silica in clay. For determining the migration parameters needed for long-term predictions, four Through-Diffusion (T-D) experiments and one percolation test have been performed on undisturbed clay cores. In the Through-Diffusion experiments, the concentration decrease after injection of 32Si (radioactive labelled silica) was measured in the inlet compartment. At the end of the T-D experiments, the clay cores were cut in thin slices and the activity of labelled silica in each slice was determined. The measured activity profiles for these four clay cores are well reproducible. Since no labelled silica could be detected in the outlet compartments, the Through-Diffusion experiments are fitted by two In-Diffusion models: one model assuming linear and reversible sorption equilibrium and a second model taking into account sorption kinetics. Although the kinetic model provides better fits, due to the sufficiently long duration of the experiments, both models give approximately similar values for the fit parameters. The single percolation test leads to an apparent diffusion coefficient value about two to three times lower than those of the Through-Diffusion tests. Therefore, dissolved silica appears to be strongly retarded in Boom Clay. A retardation factor R between 100 and 300 was determined. The corresponding in situ distribution coefficient K(d) is in the range 25-75 cm(3) g(-1). The apparent diffusion coefficient of dissolved silica in Boom Clay is estimated between 2 x 10(-13) and 7 x 10(-13) m(2) s(-1). The pore diffusion coefficient is in the range from 6 x 10(-11) to 1 x 10(-10) m(2) s(-1).     

Direct simulation of heterogeneous diffusion and inversion procedure applied to an out-diffusion experiment. Test case of Palmottu granite

An out-diffusion laboratory experiment using a non-reactive tracer was fitted using the Time Domain Diffusion (TDD) method. This rapid particle tracking method allows simulation of the heterogeneous diffusion based on pore-scale images and local values of diffusivities. The superimposed porosity and mineral 2D maps act as computation grids to condition diffusion pathways. We focused on a Palmottu granite sample, in which the connected pore space has a composite microstructure with cracks linking microporous minerals and is above the percolation threshold. Three main results were achieved: (i) When compared to the fitting obtained with one coefficient (best mean square residual R = 1.6 x 10(-2)), diffusion is shown to be suitably characterised with two coefficients related to cracks and microporous minerals (best R = 6.5 x 10(-4)), (ii) rather than imposing a local apparent diffusion coefficient D(a) independent of the local porosity Phi, a best fit is obtained by applying Archie's relationship D(a) = D(0) x G with G = Phi(m) to each pixel of the calculation grids (G is the geometry factor, D(0) is the diffusion coefficient in free fluid, and m is Archie's exponent), and (iii) the order of magnitude of the fitted diffusion coefficient or Archie's exponents (m=0 for microcracks and m=1.82 for microporous minerals) is physically realistic.     

In situ anion diffusion experiments using radiotracers

Diffusion experiments in compacted bentonite have been carried out in situ using the borehole laboratory CHEMLAB. The "ordinary" anion iodide and the redox-sensitive pertechnetate ion have been investigated. In spite of strongly reducing groundwater conditions, technetium was found to diffuse mostly unreduced as TcO4-, although in some spots in the compacted clay, the activity was significantly higher, which may be explained by reduction of some TcO4- by iron-containing minerals in the bentonite. The measured concentration profiles in the clay cannot be accommodated by assuming one single diffusion process. The experimental data are modeled assuming two diffusion paths, intralamellar diffusion and diffusion in external water. The apparent diffusivity for the intralamellar diffusion was found to be 8.6 x 10(-11) m2 s(-1) for iodide with a capacity factor of 0.1, while the apparent diffusivity for the diffusion in external water was found to be 5 x 10(-14) m2 s(-1) with alpha=2.26. The corresponding values for Tc were found to be Da= 6 x 10(-11) m2 s(-1), alpha=0.1 and Da= 1 x 10(-13) m2 s(-1), alpha=0.46, respectively. The diffusion constants and capacity factors obtained in this study are in accordance with data from laboratory experiments.     

Effect of temperature on the containment properties of argillaceous rocks: The case study of Callovo-Oxfordian claystones

Heat generated by high level radioactive wastes could alter the performance of a clay repository. It was intended to investigate the effect of such a thermal period on the diffusive properties of Callovo-Oxfordian claystones. Thus, through-diffusion experiments with HTO, Cl-36, Na-22 and Cs-137 were performed before, during and after stages of heating at 80°C that lasted for up to one year. A special attention was paid to limit the occurrence of any chemical disturbance. Therefore (i) the temperature was raised to 80°C, then progressively brought back to 21°C, thanks to three intermediate temperature stages, and (ii) specific synthetic solutions were used for each temperature, chemistry of which being close to the equilibrium state, especially with respect to the carbonate and sulphate minerals. It was found that experiments carried out at 80°C showed a clear increase of the effective diffusion coefficient values for the four tracers with respect to those obtained at 21°C (by a factor of 3 for HTO and Cl-36, 5 for Na-22 and 2 for Cs-137). On the other hand, the porosity and rock capacity values did not exhibit any significant discrepancy between 21°C and 80°C, indicating no observable damage of both the pore conducing network and the sorption properties of clay minerals. The Stokes-Einstein relationship, based on the temperature dependency of the viscosity of bulk water, could be used to describe the temperature dependence of the diffusion of HTO and Cl-36 but failed to describe the diffusive evolution of the two sorbing cations, Na-22 and Cs-137. Furthermore, experiments performed after the thermal period led to diffusive properties well matching those obtained before heating. All these results suggest that at the lab scale the heating of rock samples would not alter the claystone containment properties.     

Convergent-flow tracer tests in heterogeneous media: combined experimental-numerical analysis for determination of equivalent transport parameters

In modeling transport within naturally heterogeneous aquifers, it is usually assumed that the transport equations valid at local scales can also be applied at larger scales. At larger scales, the heterogeneous domain is represented by an equivalent homogeneous medium. Convergent-flow tracer tests constitute one of the most frequently used field tests to estimate effective input parameters of equivalent homogeneous aquifers. Traditionally, statistical approaches applied to groundwater flow and solute transport have provided tools to estimate these equivalent parameters. These approaches are based on a number of simplifications including the assumption that the point transmissivity values follow a multilog-normal random function. Several investigators have found that this assumption may not be valid in many field cases. In order to study the applicability of the equivalent homogeneous formulation in a nontraditional stochastic field, a number of experimental and numerical studies were conducted. The results are used to determine the apparent values of porosity and dispersivity that would be obtained if convergent-flow tracer tests were conducted in a deterministically generated heterogeneous transmissivity field displaying anisotropy in the correlation structure. It is shown that in this particular heterogeneous media, apparent porosity strongly depends on connectivity rather than on transmissivity. This dependence on connectivity questions the theoretical results obtained in continuum equivalent fields to estimate effective porosity.     

Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity

Matrix diffusion is an important transport process in geologic materials of low hydraulic conductivity. For predicting the fate and transport of contaminants, a detailed understanding of the diffusion processes in natural porous media is essential. In this study, diffusive tracer transport (iodide) was investigated in a variety of geologically different limestone and sandstone rocks. Porosity, structural and mineralogical composition, hydraulic conductivity, and other rock properties were determined. The effective diffusion coefficients were measured using the time-lag method. The results of the diffusion experiments indicate that there is a close relationship between total porosity and the effective diffusion coefficient of a rock (analogous to Archie's Law). Consequently, the tortousity factor can be expressed as a function of total porosity. The relationship fits best for thicker samples (> 1.0 cm) with high porosities (> 20%), because of the reduced influence of heterogeneity in larger samples. In general, these correlations appear to be a simple way to determine tortuosity and the effective diffusion coefficient from easy to determine rock porosity values.     

A laboratory experiment for determining both the hydraulic and diffusive properties and the initial pore-water composition of an argillaceous rock sample: a test with the Opalinus clay (Mont Terri, Switzerland)

Argillaceous formations are thought to be suitable natural barriers to the release of radionuclides from a radioactive waste repository. However, the safety assessment of a waste repository hosted by an argillaceous rock requires knowledge of several properties of the host rock such as the hydraulic conductivity, diffusion properties and the pore water composition. This paper presents an experimental design that allows the determination of these three types of parameters on the same cylindrical rock sample. The reliability of this method was evaluated using a core sample from a well-investigated indurated argillaceous formation, the Opalinus Clay from the Mont Terri Underground Research Laboratory (URL) (Switzerland). In this test, deuterium- and oxygen-18-depleted water, bromide and caesium were injected as tracer pulses in a reservoir drilled in the centre of a cylindrical core sample. The evolution of these tracers was monitored by means of samplers included in a circulation circuit for a period of 204 days. Then, a hydraulic test (pulse-test type) was performed. Finally, the core sample was dismantled and analysed to determine tracer profiles. Diffusion parameters determined for the four tracers are consistent with those previously obtained from laboratory through-diffusion and in-situ diffusion experiments. The reconstructed initial pore-water composition (chloride and water stable-isotope concentrations) was also consistent with those previously reported. In addition, the hydraulic test led to an estimate of hydraulic conductivity in good agreement with that obtained from in-situ tests.