Diffusive and reactive transport models in clays formations

Resumen

A multi-barrier concept system is often utilized for the disposal of high-level radioactive waste (HLW) in a deep geological repository. Argillaceous rocks have low permeability and high chemical retention capacity. They are host rock candidates for the disposal of radioactive waste. Performance assessment of a repository requires the uses of mathematical and numerical models for diffusive and reactive transport of radionuclides through argillaceous rocks. The FUNMIG (FUNdamental processes of radionuclide MIGration) project aimed at investigating the fundamental processes involved in the migration of radionuclides from a deep geological repository for high level nuclear waste in different host rocks. One of the objectives of the FUNMIG project was to provide tools for scientifically sound performance assessment for radionuclide migration from the near-field to the hydrosphere/biosphere. The FUNMIG was a four-year (2005-2008) project which included a large number of tests such as the large-scale solid-source (SSDE) diffusion experiments (Ciemat, 2006), a mock-up experiment (Ciemat, 2007-2008) and the long-term in situ diffusion and retention (DR) experiments (Nagra, 2006-present). This dissertation presents conceptual and numerical diffusive and reactive transport models for laboratory and in situ experiments in clay formations. The main contributions include: developing and testing diffusive and reactive transport models for real systems, improving the inverse codes and interpreting laboratory and in situ tests performed within the framework of the FUNMIG project. Two codes, CORE2DV4 and INVERSE-CORE2D, have been used in this dissertation. CORE2DV4 is a general-purpose non-isothermal multicomponent reactive transport code dealing with a set of comprehensive local equilibrium and kinetic geochemical processes in two-dimensional saturated/unsaturated porous and fractured media. INVERSE-CORE2D is a finite element code which accounts for both dissolved and sorbed concentration data, allows the estimation of transport and retardation parameters and provides statistical measures of goodness-of-fit as well as approximate confidence intervals. Both codes have been widely used in several research projects dealing with radioactive waste disposal at laboratory and field scales (Dai and Samper, 2004; Samper et al., 2000; 2003; 2006a; 2006b; 2008; 2009; Yang, 2006; Yang et al., 2007). The large-scale solid-source diffusion experiment (SSDE) overcomes some of the uncertainties of in situ diffusion experiments because the tracer diffusion within the experimental setup is not influenced by non-ideal effects such as the filter, the gap and the excavation disturbed zone (EdZ) (García-Gutiérrez et al., 2006). The SSDE performed in samples of Callovo-Oxfordian clay with HTO and 85Sr2+ have been modelled with 2D axi-symmetric finite element models by taking into account the diffusion anisotropy. Relevant diffusion and retention parameters have been identified by sensitivity analyses. HTO parameters have been estimated by solving the inverse problem. Tritium data show axial symmetry with mild fluctuations and allow the accurate estimation of the horizontal effective diffusion, De, which ranges from 4.04 ¿10-11 to 4.51¿10-11 m2/s. The vertical De is smaller than the horizontal De by a factor (anisotropy ratio) which ranges from 1.79 to 3.8. These anisotropy ratios are similar to those reported by ANDRA (2005) and Cormenzana et al. (2008). 85Sr2+ data show a large scatter and provide only crude estimates of Kd and horizontal De. A large¿scale laboratory mock-up experiment (MUE) was performed at CIEMAT facilities to study tracer migration at the bentonite/granite interface and to provide support for the field investigations at the FEBEX in situ test. The migration of HTO, 36Cl- and 137Cs+ in MUE has been modeled with 2D axi-symmetric finite element models. Model results with reference parameters reproduce measured data for HTO and 36Cl- but show large discrepancies for 137Cs+. Relevant diffusion and retention parameters have been identified by sensitivity analyses of tracer concentrations. The interpretation of the 137Cs+ data measured in the tracer chamber has been performed by taking into account the uncertainties in the initial activity C0 and the initial time t0. Optimum values of C0 and t0 have been obtained. The best fit was obtained with a De of the filter equal to 2.03 ¿10-10 m2/s and a Kd of bentonite equal to 5 m3/Kg. The ongoing in situ DR experiments performed at the Mont Terri underground laboratory were designed to study the transport and retention properties of the Opalinus Clay formation. Diffusive and reactive transport models have been developed in this dissertation to study the diffusion and retention processes in Opalinus Clay. The following tasks have been performed: 1) Model testing with a set of reference parameters; 2) Identification of the key parameters as well as the relevance of non-ideal effects by means of average dimensionless sensitivities; 3) Parameter identifiability analyses for the conservative and weakly-sorbing tracers from synthetic dilution data at the tracer interval and synthetic overcoring data along profiles in the rock; 4) Reactive transport model of the sorption of Cs+ onto Opalinus Clay and 5) Interpretation of real in situ DR experiments for 133Ba2+ and HTO. 2D axysymmetric models of the DR experiments have been developed for several groups of tracers. The numerical solutions have been verified by using several spatial discretization schemes with decreasing size of the elements in order to obtain simultaneously an accurate and efficient numerical solution. It has been found that diffusion anisotropy is relevant for the conservative and the weakly-sorbing tracers and its effect in the tracer interval increases with time. Anisotropy, however, is not relevant for the strongly-sorbing tracers within the DR experimental time. Therefore, a 2D axysymmetric model is needed for the interpretation of the conservative and the weakly-sorbing tracers while a 1D axysymmetric grid is sufficient for the interpretation of the strongly-sorbing tracer experiments. Model testing of the DR experiments has been performed with measured dilution data and evaluated in terms of the ratio between the root mean square error, , and the standard deviation of the residuals of measured data, . Results indicate that the model with an EdZ fits the measured data better than a model without EdZ. Model calibration is needed for 133Ba2+, 137Cs+, Cs+ and I- experiments. While for the rest of the tracer experiments, no calibration is needed because the reference model fits well the measured data. Average dimensionless sensitivities have been computed for all the tracers of DR experiments. The key parameters i.e. those showing the largest sensitivities, are tracer dependant, vary with time and change among different profiles. For the investigated parameter ranges, the De of the EdZ, the thickness of the EdZ and the volume of the circulation system are the key parameters for all the tracers. The De of the undisturbed clay is a key parameter for the conservative and the weakly-sorbing tracers but is not a key parameter for the strongly-sorbing tracers when an EdZ is considered. The gap parameters are not relevant for the tracers used in the DR experiments. The De of the filter is a key parameter for the dilution and profile data of the weakly-sorbing tracers and for the dilution data of the conservative and the strongly-sorbing tracers. The De anisotropy and the accessible porosity of the undisturbed clay are key parameters for the conservative and the weakly-sorbing tracers in the profile data while they are not in the dilution data. Therefore, concentrations in overcoring profiles show complementary sensitivities to those of dilution data. The analysis of the parameter identifiability of the DR experiments has been performed for the neutral tracers (HTO), the anionic tracers (Br-) and the weakly-sorbing tracers (22Na+). The result of this analysis indicates that it is difficult to estimate the parameters of the undisturbed clay when tracer dilution data contain noise. The convergence of the estimation algorithm improves when the starting values are smaller than the true parameters. Although the parameters of the undisturbed clay and the EdZ cannot be estimated using tracer dilution data, their joint estimation from overcoring noisy data is possible for standard deviations up to 0.05. Large estimation errors in the parameters of the undisturbed clay and poor fits are obtained when the assumption about the existence of the EdZ is incorrect. The effective diffusion of the filter is a key parameter for the interpretation of the experiments. Small errors in the volume of the circulation system do not affect the estimates of the component of the effective diffusion of the undisturbed clay parallel to bedding. The proper interpretation of in situ DR experiments requires accounting for the filter and the EdZ. Overcoring data allow a more accurate estimation of the parameters of the undisturbed clay than the tracer dilution data. The identifiability of the De of the filter in the DR experiments has been studied. Such identifiability is tracer dependant and depends on the number of synthetic data as well as the amount of noise of the synthetic data. The De of the filter can be derived numerically when more than 6 synthetic data are utilized. However, data errors dominate for less than 6 data thus leading to poor estimates of the De of the filter. The estimate of the De of the filter for all of the tracers improves when more data are used. Data noise makes it difficult the parameter estimation and introduces bias in the De of the filter. Acceptable estimates can be derived for a standard deviation ¿ 0.02. The estimation error of the De of the filter for the sorbing tracers is smaller than that for the conservative tracers. A small starting value of the parameter helps the convergence of the inverse algorithm for the conservative tracers but does not have a large effect on the convergence for the sorbing tracers. A reactive transport model has been developed for studying the Cs+ sorption onto Opalinus Clay and testing the validity of the Kd model. Cs+ sorption occurs mainly via cation exchange. Numerical sensitivities have been computed for the dilution curve of Cs+ at the tracer interval. Concentrations are most sensitive to changes in the De of the filter, the selectivity coefficient KNa-Cs and the De of the EdZ. Cation exchange of Cs+ in the DR experiments takes place mostly within a radial band of 9 cm. Sorption of Cs+ does not depend on the concentration of dissolved Cs+ because the concentration of exchanged Cs+ is much smaller than the concentrations of other exchanged cations in the clay. The sorption of Cs+ decreases slightly with the increase of the ionic strength. Model concentrations fit well the measured dilution Cs+ data, indicating that a reactive transport model provides a good interpretation of the sorption of Cs+ in Opalinus Clay. The dilution curves of Cs+ computed with the reactive transport model and the constant Kd model are similar, indicating the validity of a Kd model in this case. The in situ DR 133Ba2+ and HTO experiments hav been interpreted numerically. 133Ba2+ was injected in the upper interval while HTO was injected in the lower interval. Optimum parameters have been obtained for models with and without EdZ. Results indicate that the best fit for 133Ba2+ is obtained without an EdZ while for HTO is obtained with a 2 cm thick EdZ. These results may indicate the relevance of the EdZ around the lower interval and a lack of relevance of the EdZ around the upper interval. The estimated De of the filter and the undisturbed clay for HTO without EdZ are larger than those estimated with a model with an EdZ to compensate for the larger diffusion coefficient of the EdZ. The estimated Kd of 133Ba2+ ranges from 4.23 ¿ 10-2 to 4.66 ¿ 10-2 L/Kg, which is much larger than the initially postulated value. The interpretation of 133Ba2+ and HTO experiments indicates that the De of the filter plays an important role for tracer diffusion in the DR experiments. Therefore, the De of the filter should be measured in the lab to reduce uncertainties on the estimation of the parameters of the undisturbed clay. The estimation of diffusion anisotropy is not possible from available dilution data of the DR experiments. It is expected that the overcoring data will allow the estimation of the component of the effective diffusion normal to the bedding.