N. Maes

Treatment of boundary conditions in through-diffusion: A case study of 85Sr2 + diffusion in compacted illite

Valuable techniques to measure effective diffusion coefficients in porous media are an indispensable prerequisite for a proper understanding of the migration of chemical-toxic and radioactive micropollutants in the subsurface and geosphere. The present article discusses possible pitfalls and difficulties in the classical through-diffusion technique applied to situations where large diffusive fluxes of cations in compacted clay minerals or clay rocks occur. The results obtained from a benchmark study, in which the diffusion of (85)Sr(2+) tracer in compacted illite has been studied using different experimental techniques, are presented. It is shown that these techniques may yield valuable results provided that an appropriate model is used for numerical simulations. It is further shown that effective diffusion coefficients may be systematically underestimated when the concentration at the downstream boundary is not taken adequately into account in modelling, even for very low concentrations. A criterion is derived for quasi steady-state situations, by which it can be decided whether the simplifying assumption of a zero-concentration at the downstream boundary in through-diffusion is justified or not. The application of the criterion requires, however, knowledge of the effective diffusion coefficient of the clay sample. Such knowledge is often absent or only approximately available during the planning phase of a diffusion experiment.

Gas Transfer Through Clay Barriers

Gas transport through clay-rocks can occur by different processes that can be basically subdivided into pressure-driven flow of a bulk gas phase and transport of dissolved gas either by molecular diffusion or advective water flow (Figure 1, Marschall et al., 2005). The relative importance of these transport mechanisms depends on the boundary conditions and the scale of the system. Pressure-driven volume flow (“Darcy flow”) of gas is the most efficient transport mechanism. It requires, however, pressure gradients that are sufficiently large to overcome capillary forces in the typically water-saturated rocks (purely gas-saturated argillaceous rocks are not considered in the present context). These pressure gradients may form as a consequence of the gravity field (buoyancy, compaction) or by gas generation processes (thermogenic, microbial, radiolytic). Dissolved gas may be transported by water flow along a hydraulic gradient. This process is not affected by capillary forces but constrained by the solubility of the gas. It has much lower transport efficiency than bulk gas phase flow. Molecular diffusion of dissolved gas, finally, is occurring essentially without constraints, ubiquitously and perpetually. Effective diffusion distances are, however, proportional to the square root of time, which limits the relevance of this transport process to the range of tens to hundreds of metres on a geological time scale (millions of years). n2 nProcess understanding and the quantification of the controlling parameters, like diffusion coefficients, capillary gas breakthrough pressures and effective gas permeability coefficients, is of great importance for up-scaling purposes in different research disciplines and applications. During the past decades, gas migration through fully water-saturated geological clay-rich barriers has been investigated extensively (Thomas et al., 1968, Pusch and Forsberg, 1983; Horseman et al., 1999; Galle, 2000; Hildenbrand et al., 2002; Marschall et al., 2005; Davy et al., 2009; Harrington et al., 2009, 2012a, 2014). All of these studies aimed at the analysis of experimental data determined for different materials (rocks of different lithotype, composition, compaction state) and pressure/temperature conditions. The clay-rocks investigated in these studies, ranged from unconsolidated to indurated clays and shales, all characterised by small pores (2-100 nm) and very low hydraulic conductivity (K < 10-12 m·s-1) or permeability coefficients (k < 10-19 m²). nStudies concerning radioactive waste disposal include investigations of both the natural host rock formation and synthetic/engineered backfill material at a depth of a few hundred meters (IAEA, 2003, 2009). Within a geological disposal facility, hydrogen is generated by anaerobic corrosion of metals and through radiolysis of water (Rodwell et al., 1999; Yu and Weetjens, 2009). Additionally, methane and carbon dioxide are generated by microbial degradation of organic wastes (Rodwell et al., 1999; Ortiz et al., 2002; Johnson, 2006; Yu and Weetjens, 2009). The focus of carbon capture and storage (CCS) studies is on the analysis of the long-term sealing efficiency of lithologies above depleted reservoirs or saline aquifers, typically at larger depths (hundreds to thousands of meters). During the last decade, several studies were published on the sealing integrity of clay-rocks to carbon dioxide (Hildenbrand et al., 2004; Li et al., 2005; Hangx et al., 2009; Harrington et al., 2009; Skurtveit et al., 2012; Amann-Hildenbrand et al., 2013). In the context of petroleum system analysis, a significant volume of research has been undertaken regarding gas/oil expulsion mechanisms from sources rocks during burial history (Tissot & Pellet, 1971; Appold & Nunn, 2002), secondary migration (Luo et al., 2008) and the capillary sealing capacity of caprocks overlying natural gas accumulations (Berg, 1975; Schowalter, 1979; Krooss, 1992; Schlomer and Kross, 2004; Li et al., 2005; Berne et al., 2010). Recently, more attention has been paid to investigations of the transport efficiency of shales in the context of oil/gas shale production (Bustin et al., 2008; Eseme et al., 2012; Amann-Hildenbrand et al., 2012; Ghanizadeh et al., 2013, 2014). Analysis of the migration mechanisms within partly unlithified strata becomes important when explaining the n3 norigin of overpressure zones, sub-seafloor gas domes and gas seepages (Hovland & Judd, 1988; Boudreau, 2012). nThe conduction of experiments and data evaluation/interpretation requires a profound process understanding and a high level of experience. The acquisition and preparation of adequate samples for laboratory experiments usually constitutes a major challenge and may have serious impact on the representativeness of the experimental results. Information on the success/failure rate of the sample preparation procedure should therefore be provided. Sample specimens “surviving” this procedure are subjected to various experimental protocols to derive information on their gas transport properties. nThe present overview first presents the theoretical background of gas diffusion and advective flow, each followed by a literature review (sections 2 and 3). Different experimental methods are described in sections 4.1 and 4.2. Details are provided on selected experiments performed at the Belgian Nuclear Research Centre (SCK-CEN, Belgium), Ecole Centrale de Lille (France), British Geological Survey (UK), and at RWTH-Aachen University (Germany) (section 4.3). Experimental data are discussed with respect to different petrophysical parameters outlined above: i) gas diffusion, ii) evolution of gas breakthrough, iii) dilation-controlled flow, and iv) effective gas permeability after breakthrough. These experiments were conducted under different pressure and temperature conditions, depending on sample type, burial depth and research focus (e.g. radioactive waste disposal, natural gas exploration, or carbon dioxide storage). The interpretation of the experimental results can be difficult and sometimes a clear discrimination between different mechanisms (and the controlling parameters) is not possible. This holds, for instance, for gas breakthrough experiments where the observed transport can be interpreted as intermittent, continuous, capillary- or dilation-controlled flow. Also, low gas flow rates through samples on the length-scale of centimetres can be equally explained by effective two-phase flow or diffusion of dissolved gas.

Measuring diffusion coefficients of dissolved He and Ar in three potential clay host formations: Boom Clay, Callovo-Oxfordian Clay and Opalinus Clay

Abstract For the long-term management of high- and intermediate-level radioactive waste and/or spent fuel, many countries prefer disposal in a geological repository. In Belgium, Switzerland and France, argillaceous formations are being explored as potential host formations for this purpose. In this context, knowledge of the diffusion coefficient of He is relevant within two research areas: first, diffusion coefficients are used in safety calculations to evaluate the balance between gas generation (mainly H2) and gas dissipation; and, second, the diffusion coefficients of He and Ar are needed in the diffusion models of natural tracers. Owing to the lack of data on the diffusion coefficients of He and Ar for the different clay host formations, diffusion experiments with dissolved He and Ar were performed on Boom Clay, Opalinus Clay and Callovo-Oxfordian Clay. Samples were confined in a diffusion cell, and diffusion coefficients were measured by using the double through-diffusion technique. The diffusion coefficients (Dp or Dpore) for He in Boom Clay, Callovo-Oxfordian Clay and Opalinus Clay are 12.6×10−10, 4.51×10−10 and 7.13×10−10 m2 s−1, respectively. The diffusion coefficients for Ar in Boom Clay, Callovo-Oxfordian Clay and Opalinus Clay are 18.6×10−11, 4.06×10−11 and 3.65×10−11 m2 s−1, respectively.

An improved model for through-diffusion experiments: application to strontium and tritiated water (HTO) diffusion in Boom Clay and compacted illite

Abstract Through-diffusion experiments are conventional experiments to measure the transport parameters of radionuclides in clays. Typically, a regular replacement of the outlet volume by a tracer-free volume is performed. In the classical approach, this type of through-diffusion experiment is modelled by assuming a zero concentration in the outlet volume. Nonetheless, this assumption is not always correct, usually because the outlet volume is insufficiently large or the time between two consecutive replacements of the outlet volume is too long. Therefore, a model was developed disregarding this assumption and, instead, considers the tracer concentration in the outlet volume to evolve, as in the experiments: the flux into the outlet volume increases the tracer concentration and, at each replacement, the tracer concentration in the outlet volume is set to zero. The model was used to reproduce the diffusion of strontium (Sr) and tritiated water (HTO) in illite and Boom Clay. Model results yielded good matches with the tracer evolution in the inlet and the outlet, and the tracer profile in the core at the end of the experiment.

The Dependency of Diffusion Coefficients and Geometric Factor on the Size of the Diffusing Molecule: Observations for Different Clay-Based Materials

In order to investigate in more detail the relation between the size of diffusing molecules and their diffusion coefficients (and geometric factors), diffusion experiments with gases of different size and tritiated water (HTO) have been performed on different clayey samples (Boom Clay, Eigenbilzen Sands, Opalinus Clay, Callovo-Oxfordian Clay, and bentonite with different dry densities). We observed that, for unreactive gases in clayey materials, the effective diffusion coefficient varies with the size of the diffusing molecule and this variation can be described by an exponential or a power law function. The variation of the geometric factor can also be described by an exponential function. The observed experimental relations can be used to estimate diffusion coefficients; by measuring experimentally in clay the effective diffusion coefficient of two unreactive dissolved gases with a different size, the diffusion coefficients of other dissolved gases (with a size in between the two measured gases) can be estimated by using the fitted exponential relationship.

Measurement of Glass Corrosion in Boom Clay Disposal Conditions: First Results of the Experimental Programme 2000-2003 of SCK•CEN

To estimate the lifetime of vitrified high level waste (HLW-glass) in Boom Clay disposal conditions, the dissolution behaviour of waste glass has been studied with experiments performed in surface laboratories and in the HADES underground research facility of SCK·CEN since 1980. We present the main topics and first results of the SCK·CEN programme 2000–2003. This programme focuses on the following items: (1) the diffusion/sorption/precipitation of silica in Boom clay or backfill clay, (2) demonstration of glass dissolution behaviour in realistic test conditions, (3) the effect of presaturation of the clay with silica, and (4) the estimation of near field concentrations of critical isotopes. The experiments have shown so far that Si, released by the glass, is effectively immobilized by Boom Clay, but it can nevertheless diffuse into the clay without immediately precipitating. The dissolution rate of glass SON68 and SM539 is determined in Boom Clay at in situ density and at 30°C (this is the long-term temperature expected near the waste glass packages in a Boom Clay repository). The dissolution rates, based on glass mass losses, are constant during the first year, at ∼ 0.010 g.m−2 .day−1 for glass SON68 and ∼ 0.012 g.m−2 .day−1 for glass SM539. The addition of glass frit causes a decrease of the glass dissolution rate, both with glass SON68 and SM539, and both in Boom Clay and in FoCa-clay. In FoCa-clay at high density with glass frit, the dissolution rates, based on glass mass losses, after 8 months at 30°C are ∼ 0.001 g.m−2 .day−1 (SM539) and ∼0.005 g.m−2 .day−1 (SON68). Because the experiments performed in Boom Clay and FoCa-clay with glass frit simulate realistic conditions (high clay density, low temperature), they can be used to estimate the maximum glass dissolution rate in a (Boom) clay repository. The corresponding minimum lifetime of a glass canister, calculated with the SCK·CEN code for lifetime predictions, is of the order of 105 to 106 years, if we neglect the internal glass surface area (due to cracking). In more diluted clay suspensions with glass frit, the glass dissolution rate is 10−4 to 10−5 g.m−2 .day−1 or even zero. This would correspond to a lifetime of >>106 years. So far, there is no indication that the addition of glass frit leads to secondary phase formation at low temperature (30–40°C). Leach experiments with doped glasses SON68 and SM539 suggest that the maximum concentrations of most critical radionuclides in near field conditions are lower than the best estimate solubilities used for performance assessment studies in Boom Clay. For Se, relatively high concentrations were measured, though. The research programme for the underground laboratory is not discussed.Copyright