plane directions of compaction in clay-rich systems such as claystones (Gimmi et al., 2014; Robinet et al., 2012; Tyagi et al., 2013; Van Loon et al., 2004a; Wenk et al., 2008), although part of this diffusion anisotropy can also be related to the presence of elongated non-clay particles (Robinet et al., 2012; Tyagi et al., 2013). The preferred orientation of particles can be quantified by the order parameter $\langle P_{2} \rangle$, by analyzing the intensity distribution on a 2D X-ray scattering pattern collected on a slice of hardened samples. This parameter is quite convenient, as it adopts a value of 0 for an isotropic organization, and one when all particles are perfectly oriented relative to each other. Furthermore, Dabat et al. (2019) showed that a single orientation distribution function was associated with a given $\langle P_{2} \rangle$ value. In the recent literature, the quantitative influence of the preferred orientation of clay particles on water diffusion has been clearly demonstrated for a large number of samples composed only of clay minerals (Dabat et al., 2020; Ferrage et al., 2023; Tyagi et al., 2013). For example, Ferrage et al. (2023) showed that a change in the preferred particle orientation from $\langle P_{2} \rangle = 0$ (isotropic organization) to $\langle P_{2} \rangle = 1$ (perfect anisotropic organization) had the same effect on water $D_e$ values normal to the bedding as a decrease in interparticle porosity from 0.4 to 0.15. In addition, the ratio between the effective water diffusion coefficient measured in-plane and along the normal direction to the bedding ($D_e(xy)/D_e(z)$) ranged between one for $\langle P_{2} \rangle = 0$ and approximately five for $\langle P_{2} \rangle = 1$, further evidencing the primary role played by preferred orientations of clay particles on the diffusional properties of water and, likely, cationic or anionic species.

### 3.2.2.5 Impact of water partial saturated conditions on radionuclide transport

There are many situations in which clay-rich porous media can be partially water-saturated. The generation of hydrogen due to the corrosion of canisters may dehydrate host rocks and engineered barriers made of swelling clay materials for more than 100 000 years in deep-geological-waste disposal facilities (ANDRA, 2016; Marschall et al., 2005). Additionally, clay liners placed above the groundwater table are generally unsaturated, especially for landfills located in arid environments (Katsumi et al., 2001). Owing to the CO₂ intrusion into caprocks in carbon geosequestration, caprocks can also be partially water saturated (Minardi et al., 2021; Xiao et al., 2020). In these cases, understanding and parameterizing diffusion processes under partially saturated media are required to evaluate the performance of a clay system and support engineering purposes. This is a challenging task, as illustrated by the fact that only a few reports exist in the literature. For instance, Nunn et al. (2018) presented a new method of using X-ray radiography and iodide tracers for quantifying the degree of partial saturation for shale samples and measuring effective diffusion coefficients ($D_e$) for tracers under such conditions. They showed that the $D_e$ value of iodide decreased by approximately 22% when saturation decreased from 100 wt% to 93.3 wt%.

The diffusion and advective transport of gaseous species, and the effect of saturation on the diffusion of water and cations, was investigated using MD simulation. The simulations showed that surface adsorbed water films provide an important contribution for solute and water transport, even at a low partial water pressure (Owusu et al., 2023; Owusu et al., 2022; Churakov, 2013).

Savoye et al. developed a novel approach to perform diffusion experiments under partially water-saturated conditions in illite-sand mixtures (Savoye et al., 2014) and in Callovo-Oxfordian claystones, intended to host a French disposal facility for high- and intermediate-level long-lived radioactive wastes (Savoye et al., 2012c; Savoye et al., 2010; Savoye et al., 2017). An osmotic method was used to control the partially saturated conditions of the clayey samples over the duration of diffusion experiments. They observed in Callovo-Oxfordian claystones a sharp drop in the $D_e$ values for HTO, ¹²⁵I⁻, and ²²Na⁺ by factors of 6, 50, and 17, respectively, under conditions of 81% water saturation, compared to the values under full-saturation conditions. The strong decrease in $D_e$ for iodide was explained by the anion exclusion phenomenon that restricted iodide to the largest pores, where dehydration was more pronounced. Nevertheless, the distinct behavior of $D_e$ evolution for HTO and sodium remained speculative. Two different processes, for which the relative contributions require further investigation, were proposed. On the one hand, the extent of surface diffusion may be attenuated when dehydration occurs in claystones, reducing the enhanced diffusion phenomenon for cation species (Savoye et al., 2012a)). On the other hand, in addition to HTO diffusing in the liquid phase, HTO diffusing in the vapor form may contribute to the relatively high (compared to that of sodium) HTO diffusive rate, even at 81% water saturation (Savoye et al., 2017). This latter process had already been proposed by Smiles et al. (1995) and, more recently, by Maples et al. (2013), to explain the anomalously widespread distribution of HTO in layers adjacent to low-level radioactive waste burial facilities.

More recently, the same type of investigation was performed in compacted kaolinite, known to be a very weakly surface-charged clay mineral (Wang et al., 2022), in order to estimate the role played by the vapor phase in water diffusion. The results indicated that, from a degree of water saturation of 100% down to 67%, the decrease in the diffusive flux of water in kaolinite was smaller than that observed for anionic and cationic tracers (iodide and sodium) that behaved in the same manner. Based on previous results, a conceptual and numerical model was developed for describing the macroscopic diffusion of water tracers in both liquid and gas phases, in order to induce a decrease of a factor of seven from 100% down to 67% of the diffusive flux. The diffusion of water through both liquid and vapor phases explains why water tracers diffuse faster than ions that only move through the liquid phase.

However, for more complex systems made of surface-charged clay minerals, even though MD showed that surface effects can be enhanced when saturation decreases (Churakov, 2013; Le Crom et al., 2022), the understanding of the evolution of enhanced diffusion phenomena for cation species when dehydrating is still limited. This issue needs to be addressed using simpler clayey media than argillaceous rocks such as compacted illite or vermiculite.

García-Gutiérrez et al. (2023) used the Instant Planar Source method (in this report, referred to as the back-to-back method, described in Section 3.2.3.1.1) to study the diffusion of HTO, ³⁶Cl, and ⁷⁵Se in partially saturated recompacted Callovo-Oxfordian Clay and Spanish Lutite. Upon decreasing the water saturation level from 100% to 60%, they noted a decrease in the apparent diffusion coefficient for the studied radionuclides, showing that, by lowering the saturation, transport becomes hindered.
### 3.2.3 Research methods to extract transport parameters

Several types of migration experiments are used to investigate radionuclide transport in clays. The transport parameters that are extracted from these experiments, by solving the transport equation (Section 3.1) analytically or numerically for the correct initial and boundary conditions, are $D_a$, $D_e$, and the rock capacity factor $\eta R$ (porosity times retardation factor). It is worth noting that $D_a$ and $D_e$ are related as $D_e = \eta RD_a$.

Some decades ago, pioneers in the field described experimental methods and mathematical models for deriving diffusion parameters for application in nuclear waste disposal: Crank (1975), Put et al. (1991), Shackelford (1991), and Shackelford and Daniel (1991).

More recently, some publications with comprehensive overviews became available: Aertsens (2013), Bourg and Tournassat (2015), Van Loon et al. (2012).

In this section, the focus is on classical mass transfer experiments, as these apply, in principle, to all radionuclides of interest in the context of geological disposal, and they can provide direct information on the transport behavior of these radionuclides. Detailed insights into the local mobility of ions in different pores of clay materials can also be obtained using classical and *ab initio* MD simulations. These simulations are particularly useful for understanding the ion transport in narrow pores close to the negatively charged surfaces of clay particles, viz. DDLs (see Churakov and Prasianakis (2018) and references therein). There exists techniques based on NMR, neutron scattering, and electrical conductivity (e.g., impedance spectroscopy),

which also provide important information on transport in porous media, but they require sophisticated equipment and data treatment and are only applicable to a limited set of “tracers.” They mainly provide qualitative information on the transport mechanism, and less quantitative data on the tracer transport parameters. Further information on key references on these methods are available in papers by Bourg and Tournassat (2015) and Van Loon et al. (2012).

Mass transfer-based methods most widely used nowadays are summarized in the present section, highlighting recent developments.

Methods used to derive migration parameters in compact clay materials can be divided in two categories:

1) Transport via diffusion only (the concentration gradient is the only driving force),

2) Transport via a combination of diffusion and an extra flux component as result of a hydraulic or electrical driving force from percolation or electromigration experiments, respectively.

The methods described here are applied for laboratory experiments performed at the cm scale for compacted and fully saturated clay systems. These methods are detailed in Table 5.

#### 3.2.3.1 Category 1 – diffusion only

##### 3.2.3.1.1 Back-to-back diffusion.
This is the simplest form of a diffusion experiment, in which a trace amount (below the

<table><caption>TABLE 5 Summary of various laboratory techniques, based on mass transfer, for diffusion measurements (adapted from Van Loon et al. (2012), with permission from Elsevier).</caption><thead><tr><td>Technique</td><td>Features</td><td>Diffusion parameters</td><td>Suited for</td><td>Less suited for</td></tr></thead><tbody><tr><td>Through-diffusion</td><td>Steady-state technique<br>Time consuming<br>Porous filters may be a problem</td><td>D<sub>e</sub> α = ηR</td><td>Non and weakly sorbing tracers</td><td>Strongly sorbing tracers</td></tr><tr><td>Out-diffusion</td><td>Steady-state technique<br>Time consuming<br>Porous filters may be a problem</td><td>D<sub>e</sub> α = ηR</td><td>Non and weakly sorbing tracers</td><td>Strongly sorbing tracers</td></tr><tr><td>In-diffusion<br>Controlled source</td><td>Transient technique<br>Relatively fast<br>Porous filters may be a problem</td><td>D<sub>e</sub> α = ηR</td><td>All kind of tracers</td><td></td></tr><tr><td>In-diffusion<br>No control on source</td><td>Transient technique<br>Relatively fast</td><td>D<sub>a</sub></td><td>All kind of tracers</td><td></td></tr><tr><td>Back-to-Back diffusion (BtB)</td><td>Transient technique<br>No problem with porous filters</td><td>D<sub>a</sub></td><td>All kind of tracers</td><td>Strongly sorbing tracers (e.g., Cs<sup>+</sup>)</td></tr><tr><td>Column migration<br>experiment – Pulse injection</td><td>Additional hydraulic gradient<br>Clay cores can be conditioned with<br>other pore waters<br>Porous filters may be a problem</td><td>D'<sub>a</sub> ~ D<sub>o</sub>, α = ηR, K</td><td>Non and weakly sorbing tracers</td><td>Strongly sorbing tracers</td></tr><tr><td>Column migration<br>experiment – BtB</td><td>Additional hydraulic gradient<br>No problem with porous filters</td><td>D'<sub>a</sub> ~ D<sub>o</sub>, (α = ηR only for weakly<br>retarded tracers), K, (solubility<br>information)</td><td>All kind of tracers</td><td>Strongly sorbing tracers (e.g., Cs<sup>+</sup>)</td></tr><tr><td>Electromigration</td><td>Additional electrical gradient<br>(acceleration)<br>No problem with porous filters<br>Provides information on the<br>chemical speciation<br>Induces chemical changes in the<br>system</td><td>D<sub>o</sub>, (ion mobility)</td><td>Non, weak to moderately<br>sorbing tracers</td><td></td></tr></tbody></table>
solubility limit) of a diffusing species (radionuclide previously conditioned to be at chemical equilibrium with a clay in the case of redox-sensitive elements to avoid precipitation and reactive transport) is spiked (either directly on the surface or by means of a saturated thin porous disk, which does not interact with the tracer) between two clay cores in a diffusion cell that confines the system (Figure 5A). In the absence of precipitation during transport, diffusion gives rise to a typical Gaussian-shaped tracer profile in the clay core. The diffusion profile is obtained by cutting the clay core into thin slices and measuring the concentration (or radioactivity) of the diffusing species in each slice. This is a simple technique, and there is direct contact between the diffusing species and the clay material (no disturbing influences from confining porous filters, see Section 3.2.3.3). This technique provides the value of the apparent diffusion coefficient ($D_a$) only.

Back-to-back diffusion is a technique of choice for strongly sorbing radionuclides with a simple chemistry, such as cesium ($Cs^+$). However, with redox-sensitive radionuclides (e.g., Se, Tc, U, Np, and Pu), a radionuclide must first be placed at thermodynamic equilibrium with a clay prior starting the diffusion experiments. This is particularly important when reducing conditions are prevailing in the clay. If a redox-sensitive element is introduced in its oxidized state, it will be reduced during transport and may precipitate. Under such an experimental setup, it is impossible to distinguish between sorption and precipitation, and modeling will lead to erroneous overestimated retardation factors ($R$).

#### 3.2.3.1.2 Through-diffusion.
This is probably the most widely used method to determine diffusion parameters. A clay core is confined in a diffusion cell between two porous filter plates connected to water compartments (Figure 5B). One compartment

<figure><img src="image_6.png" /><figcaption>FIGURE 5
Schematic representation of different methods used to determine diffusion parameters of radionuclides in saturated porous materials where diffusion is the only transport mechanism. (A) Back-to-back diffusion, (B) through-Diffusion, (C) in-diffusion. Reprinted from *Bourg and Tournassat* (2015), with permission from Elsevier.</figcaption></figure>
contains diffusing species (high-concentration reservoir, upstream), whereas the other compartment is free of diffusing species (low-concentration reservoir, downstream). In these experiments, the flux arriving at the downstream compartment is monitored until a quasi steady-state flux regime has been attained. From the evolution of the flux with time, the effective diffusive coefficient ($D_e$) and the rock capacity factor ($\eta R$, also called $\alpha$) can be determined independently. As we have access to $\eta R$, these experiments can be linked to batch sorption experiments ($R-K_d$ relation Equation 24). In this technique, decreases in the concentration of the diffusing species in the upstream compartment can be monitored, as well as the concentration profile inside the clay (by post-mortem slicing, stated above). Related analysis of mass balance and observations of the concentrations within a clay sample can be used to crosscheck the results obtained for mass balance and internal consistency. Depending on the experimental conditions (Variable or Constant Concentrations in reservoirs), one defines different sub-types: CC-CC, VC-VC, VC-CC, and CC-VC (Takeda et al., 2008b; Takeda et al., 2008a; Aertsens et al., 2017). It is important to note that the mathematical models used to interpret measurements make use of the correct boundary conditions in line with the experiment, as this can lead to significant differences in the derived parameters. The use of porous filter materials in these experiments can play an important role in transport processes. This is not as important for non-sorbing tracers (anions or HTO), as long as the clay cores are sufficiently thick compared to the combined filter thickness. However, porous filter materials were found to have a pronounced effect on sorbing tracers, either as an extra diffusion barrier (simple cations such as $Sr^{2+}$ or $Cs^+$, Glaus et al. (2015b); Aertsens et al. (2017)) or having a tendency to strongly sorb the diffusing species (transition metals, lanthanides, and actinides) (Altmann et al., 2015). Dierckx et al. (2000) demonstrated the strong sorption of $^{241}$Am onto stainless-steel filters.

A through-diffusion (TD) experiment can be performed via out-diffusion (OD), which is a valuable technique used to crosscheck the results of the TD step. OD is measured after reaching the steady-state flux phase of a TD experiment. Both reservoirs are exchanged by solutions devoid of a diffusing species, viz. the concentration of the diffusing species is kept at an approximately zero level on both sides of a clay sample. OD can also be used to detect slow diffusion pathways. If the contributions of these pathways to the overall flux is only a small fraction (a few percents), the pathways cannot be directly revealed in a TD experiment. In an OD experiment, they will, however, become visible as two-phase flux behavior (Van Loon and Jakob, 2005). OD can also be used to reveal inconsistencies with respect to TD.

#### 3.2.3.1.3 In-diffusion.
The in-diffusion (ID) method can be considered a sub-type of TD experiments. The setup is similar (Figure 5C), but TD is intended to measure the flux going through an entire clay sample, while an ID experiment is not. For sorbing tracers, in particular, it may take extremely long for a tracer to diffuse. In this technique, a decrease in the tracer concentration in an upstream reservoir and the tracer profile in clay are determined, and the combination of this information provides information on the $D_e$ and $\eta R$ (Yaroshchuk and Van Loon, 2008). As with an TD experiment, the presence of a porous filter plate may have an important effect.

The ID method is also commonly applied for *in situ* tests of radionuclide transport (see Section 3.2.4); such tests include the DI, DI-A, DI-B, and DR *in situ* experiments in the Mont Terri Rock Laboratory, as well as the DIR *in situ* tests in Bure URL (overview in Van Loon et al. (2012); Gimmi et al. (2014); Leupin et al. (2017); Delay et al. (2007)). Post-mortem profile analysis is performed on a large clay core recovered by overcoring the borehole used to inject the tracer solution.

### 3.2.3.2 Category 2 – diffusion + extra driving force

In this category, an extra driving force is used to speed up the transport process. These driving forces are either a hydraulic gradient (diffusion-advection experiment) or an electric field (electromigration experiment).

#### 3.2.3.2.1 Column migration experiments applying a hydraulic gradient.
In these experiments, a clay core is confined in a migration cell connected at one side (inlet) with a water vessel that is at elevated pressure so that a hydraulic gradient can be applied (e.g., piston pump, HPLC pump, or pressurized water barrel). At the inlet, an HPLC injection valve is installed, from which a small pulse of tracer can be injected into the water stream in front of the clay core. This mimics a chromatographic column setup (Put et al., 1991) (Figure 6 top). At the other side of the clay core (outlet), water is collected as a function of time, and the amount of tracer flowing out is measured to obtain a breakthrough curve. Because of the presence of an additional hydraulic gradient, not an apparent diffusion coefficient but rather an apparent dispersion coefficient ($D_{disp,a} = D_a + aV_a$) can be obtained. However, as long as the advective term remains limited, the approximation of $D_{disp,a} \sim D_a$ applies. From the $V_{darcy}/V_a$ ration, information on the rock capacity factor $\alpha = \eta R$ can be derived. However, Aertsens et al. (2020) have recently shown that column migration experiments (percolation experiments or infiltration tests) do not provide a correct estimate (overestimation) of the diffusion-accessible porosity ($\eta$) of anions, compared to pure diffusive experiments (TD).

This kind of test is particularly interesting for non-sorbing (or slightly sorbing) tracers. When coupled with a manifold system, several experiments can be performed simultaneously, and successive tracer injections can be performed on the same clay core, if necessary (as no long OD is required) (Aertsens et al., 2003). This method is also useful for investigating the effect of changing chemical conditions, specifically different ionic strengths (Moors, 2005; Aertsens et al., 2009a) and the influence of an alkaline plume (ECOCLAYII, 2005; Wang et al., 2007) or a $NaNO_3$ plume (Bleyen et al., 2018), on transport in percolating water, by first analyzing the diffusion behavior pristine pore water, after which the water transforms into another type of water, followed by new tracer injections, all on the same core.

For sorbing tracers, breakthrough may not be reached even after many years, in which case the tracer profile determined on a clay core at the end of an experiment can provide information on the apparent diffusion coefficient, $D_a$, only. Similarly to the TD and ID tests, a porous filter and an injection loop may cause problems when working with strongly sorbing tracers, which often sorb onto materials (often 316 stainless steel) as well.

Again, it is necessary to emphasize the importance of the chemical speciation of redox-sensitive radionuclides at the start of a percolation experiment. If a radionuclide soluble under
<figure><img src="image_7.png" /><figcaption>**FIGURE 6**

Illustration of migration experiments where an extra hydraulic or electrical gradient is applied to accelerate the transport of the radionuclide of interest. Top and middle: column migration experiments using an extra hydraulic gradient, bottom: electromigration experiment using an extra electrical gradient. Abbreviations: RN: radionuclide, RBCW: real Boom Clay water. (Figures reproduced from (Maes et al., 2004a) annex 14, with permission from SCK CEN).</figcaption></figure>

oxidizing conditions (using radiotracers “as received”) is progressively reduced during its transport in clay, it can precipitate if the solubility limit of its reduced species is exceeded. It is, therefore, essential to guarantee that redox-sensitive species are first at chemical equilibrium with a reducing clay before to start the experiment. Failing to properly achieve this chemical pre-equilibration step can lead to the reduction/precipitation of the redox-sensitive radionuclide during its transport, will make it difficult/impossible to derive quantitative transport parameters from it, or will cause wrong interpretation of the data.

In order to circumvent the problem of radionuclide sorption onto filters, the back-to-back configuration can be used and connected to a hydraulic gradient (Figure 6 middle). For non-sorbing or moderately sorbing tracers, a breakthrough curve can be determined. For strongly sorbing tracers, the clay core can be cut into thin slices and the radionuclide profile inside the clay can be determined to obtain $D_a$ without the problem of sorption on the filters. In these experiments one can also use a solid phase of the

tracer in equilibrium with the pore water. In this case, one has a constant source (instead of a Dirac pulse) of the species controlled by the solubility.

#### 3.2.3.2.2 Electromigration.
By applying an external electrical field to both extremities of a cylindrical clay core confined in an appropriate cell, ions present in the clay pore water are forced to move towards the electrode of opposite charge (this phenomenon is called electromigration), which seriously accelerates their transport (Figure 6 bottom). The velocity with which a charged species moves is linearly proportional to the strength of the applied electrical field. The proportionality coefficient is the ionic mobility, which is related to the apparent diffusion coefficient ($D_a$) of the considered ion. As an effect of the moving cations, a water flow is also created, which is called electro-osmosis. The movement of water (osmosis) towards the cathode in the clay core is directly related to the movement of cations. This is because cations moving in the EDL close to the negatively charged clay surface drag the free water present in the pores and also because water in the hydration shell interacts stronger
with cations than with anions due to the smaller ionic radius of cations. Applying an electrical field to accelerate the transport is particularly interesting for strongly sorbing tracers. A method was developed by Maes et al. (1998), Maes et al. (1999), Maes et al. (2001), and Beauwens et al. (2005) to determine diffusion coefficients for radionuclides in Boom Clay. In addition to using the method in a quantitative way (determination of diffusion coefficients), it can also be used to obtain information on the speciation of the moving species (Maes et al., 2002; Maes et al., 2001) and the migration behavior (stability) of radionuclide-organic matter species/colloids (Maes et al., 2001; Maes et al., 2004b). This method was later on used and adapted for compacted clays (Higashihara et al., 2004; Tanaka et al., 2011) and for granitic rocks (Lofgren and Neretnieks (2006); Li et al. (2019b) see Section 3.3.3.2.2). Information on the apparent diffusion coefficient, D_a, is obtained by performing multiple experiments at varying electrical fields (E) (causing different electromigration velocities). Apparent dispersion coefficients are obtained for each electromigration velocity. To obtain D_a, the linear relationship of the determined dispersion coefficients as function of E is extrapolated to E =0.

Application of strong electrical fields to a clay core triggers significant heat release that may have an influence on the mobility of the diffusing species under investigation. Furthermore, it might disturb the clay core in unexpected ways, for example, electro-consolidation due to electro-osmosis.

### 3.2.3.3 Experimental challenges and technical solutions

As highlighted previously, when a compacted clay sample contacts solution reservoirs, porous filter plates are required in order to maintain the sample integrity related to the swelling behavior of clays. These porous filter plates can introduce artefacts, as they represent an additional diffusion barrier (2–3-mm thickness) specifically for TD and ID experiments, especially when thin clay slabs (5–10-mm thickness) are used (Suzuki et al., 2003; Glaus et al., 2015b; Glaus et al., 2008b; Aertsens et al., 2017). This can be accounted for in modeling, by explicitly considering the diffusion behavior of the filters. However, even when accounting for the filter behavior, there is increased uncertainty in the obtained data. Glaus et al. (2015b) designed so-called flushed filter cells in which the problem of the diffusion barrier, created by the filter, is strongly reduced. This design is based on the work of Jahnke and Radke (1989).

Furthermore, porous filter plates, typically made of fritted stainless steel (to withstand the swelling pressure developed by swelling clay) may exhibit strong sorption properties (especially for transition metals, lanthanides, and actinides at alkaline pH). In fact, any material, other than the clay, that is in contact with the tracer, such as tubing, water vessels, valves, and connectors, may exhibit sorption properties towards the diffusing species and, as such, affect the results of experiments. It is, therefore, advised to first test the sorption to the materials used. Other more “inert” materials such as PEEK, PTFE, and organic polymeric membranes may provide a solution to circumvent sorption (Glaus et al., 2015b). In some cases for clay rocks, it may be possible to avoid filters by using a very small specimen in direct contact with a tracer-containing solution (Van Loon and Muller, 2014).

Investigating the diffusion behavior of strongly sorbing tracers is further challenged by the limited travel distances, which means that

experiments may need considerably long times (years) before a meaningful analysis can be performed. This entails that the chemical and physical conditions of experiments be kept stable during the entire period. Even then, the diffusion profiles that develop within clay often do not extend further than a few millimeters. Soft clays, such as Boom Clay and Ypresian Clay, and London Clay are easy to cut in slices of approximately 0.5–1 mm using a simple knife and a special cutting edge system equipped with a piston mounted on a screw to push the clay core out of the diffusion cell, and using a Palmer to precisely adapt the slice thickness. To enable a precise determination of the shorter diffusion profile in hard and brittle clays or argillites, a more sophisticated profiling technique is needed that goes into the sub-mm range. Van Loon and Eikenberg (2005) developed the abrasive peeling method. Savoye et al. (2013) have used micro-laser-induced breakdown spectroscopy to characterize concentration profiles at sub-mm scales. Rutherford backscattering spectroscopy (RBS), used by Alonso et al. (2009), is another spectroscopic technique and even considers lower scales (tens of nanometers). Moreover, laser ablation mass spectrometry (LA-MS) has been used (Wang et al., 2011; Wang et al., 2013). To study UO₂²⁺ diffusion in Boda Claystone Formation, Czömpöly et al. (see contribution in (Maes et al., 2024)) used μ-XRF. A novel experimental method using TOF-SIMS was tested to investigate Pu diffusion in Opalinus Clay, by Johannes Gutenberg University (contribution of Breckheimer et al. in (Maes et al., 2024)). Glückman (2023) used accelerated mass spectroscopy (AMS) to investigate the diffusion of U(VI) and Am (III) in Opalinus Clay at ultra trace levels (10⁻⁹ mol/m³). These techniques are challenging (calibration, interpretation, sample pre-treatment, and range of application) and are not commonly available.

Linked to the limited penetration depths of diffusion profiles are the artefacts induced at the external surfaces of samples. Sample preparation (and storage) will inevitably create disturbances (physical and chemical) at external surfaces, which will be the first to contact the tracer. Furthermore, when placed in contact with water, by means of a porous filter, some swelling effects will occur, disturbing the clay surface in direct contact with the filter: clay particles may be pushed into the porous filter plates and water may locally soften the clay near the contact interface, resulting in an increased porosity and water content at the filter-clay interface. This will also change the porosity of the filter (clogging) and the properties of the first mm of the clay sample. This is very important when interpreting TD/ID experiments (Glaus et al., 2008b; Glaus et al., 2011).

In addition to experimental difficulties, there are also challenges on the modeling side. Nonetheless, the principles of diffusion are well known and accepted (Crank, 1975; Shackelford, 1991), and mathematical expressions have long been used to obtain parameters for a range of experimental conditions. It has become apparent that the number of experimental factors, which has been neglected before, has a significant effect on the derived parameters, especially for sorbing tracers. These factors include filters, the strict control of boundary conditions, and induced changes at the clay matrix at interfaces (e.g., mechanical disturbances and density and porosity changes due to clay hydration and swelling). Incorporation of all these possible influences into a consistent mathematical model has been proven to be challenging. Many TD studies (especially older studies) may provide data that were
not obtained using a correct mathematical description of the
experimental conditions; as a result, the values of migration
parameters are subject to large uncertainty.

Related to this is the consistency of data obtained from different types of experiments. Several studies (Aertsens et al. (2008a); Aertsens et al. (2009b); Aertsens et al. (2012) (Aertsens et al., 2020)) have indicated that different types of experiments (e.g., ID, TD, or column migration) do not always provide consistent transport parameters. Often, the derived D_a is quite consistent, but not the values for the rock capacity factor α = ηR. This could, in part, be explained by experimental factors that have an important influence on the experimental results (filters in TD), the correct inclusion of the boundary conditions in a mathematical model, and flaws in the conceptual mathematical description of transport processes (Aertsens et al., 2020).

In support of the diffusion program for NAGRA’s deep-drilling campaign in Switzerland (Van Loon et al., 2023), a cross-comparison study was setup between two labs (PSI & SCK CEN) to compare data obtained from TD experiments using HTO, ³⁶Cl⁻, and ²²Na⁺, based on a selection of “twin” samples taken from the Trüllikon1-1 borehole as part of confidence building in methodologies (Van Laer et al., 2023). For all three radionuclides, the variability in the effective diffusion coefficients, estimated independently by both institutes, was less than a factor two. Moreover, the parameter estimations of the capacity factor agreed well. The evaluation revealed that the minor deviations could be attributed predominantly to variations in temperature (experimental conditions) and, to a lesser extent, to minor distinctions in the modeling approach. It is important to acknowledge that local heterogeneity might have also contributed to these differences. The relatively small uncertainties within the methodological approaches provide confidence for application of diffusion parameters in radionuclide transport models.

Despite these efforts, the issue of consistency remained not fully resolved when comparing experimental data obtained from different methodologies, because there was always one important factor that could obscure the results: the nature of the samples. As these studies were performed using core material from natural clay rocks, there was the aspect of local heterogeneities that could influence the outcome. Therefore, a more dedicated study was setup by Durce et al. (2023), where different types of diffusion experiments with HTO and iodide (through diffusion, column migration, and back-to-back methods) were repeatedly performed on the same core plug (originating from Boom Clay cored at HADES URL, Mol, Belgium), hence excluding the heterogeneity aspect. A consistency study showed a good agreement in the apparent and effective diffusion coefficients and accessible porosity for HTO, which did not vary by factors of more than two and 1.6, respectively, between the three setups investigated, i.e., TD, column migration, and back-to-back experiments. On the other hand, the transport parameters obtained for iodide were shown to be more sensitive to the used experimental setup. In column migration (pulse injection, with advection) experiments, and at the scale of a few cm, the dispersion length cannot be neglected for iodide and needs to be known/assessed to extrapolate the diffusion coefficients. Column migration experiments also provide significantly higher accessible porosities than TD experiments, which confirms the findings of Aertsens et al. (2020), that this methodology is not appropriate for the

determination of anion-accessible porosity. The cutting of cores and extrapolation of activity/concentration profiles in back-to-back experiments are practically more challenging, and experimental datasets display high scatter. Yet, overall, under the three experimental setups, the determined diffusion coefficients for iodide did not vary by a factor of more than three for the different samples and orientation investigated.

In experiments with redox-sensitive radionuclides (e.g., Se, Tc, U, Np, and Pu), one has to ensure that speciation is in chemical equilibrium with the reducing conditions prevailing *in situ* in the clay, before the start of migration experiments. Failing to pre-equilibrate a redox-sensitive element with clay prior to starting a diffusion test leads to considerable artefacts, making a quantitative analysis difficult/impossible.

3.2.4 Experimental approaches to upscaling

The mobility of ions in porous clay media depends on the electrostatic interactions in the DDL formed at the surface of negatively charged clay mineral particles and on complex coupled pore-scale transport phenomena controlled by the connectivity of pore spaces (Churakov and Prasianakis, 2018). In principle, the macroscopic mobility, such as that measured in laboratory experiments, can be obtained taking into account the local mobility of ions and the geometry of pore spaces. The local mobility of ions close to mineral surfaces has been extensively characterized using molecular simulations. Molecular simulations provide insights into the nature of the mineral-aqueous interface and allow for discriminating the effect of mean-field electrostatic interaction of ions with a surface, dynamic ion-ion correlation phenomena, and short-range steric effects at interfaces. On a larger scale, fluid transport will be mainly determined by the texture of a rock and connectivity of pore spaces. Pore-scale transport simulations are performed using stochastic methods (Random Walk and Brownian dynamics) and Lattice Boltzmann simulations techniques. One of the most critical parameters for pore-scale modeling is a realistic representation of the pore-scale geometry. While, larger sub-micrometer pores are accessible via computerized tomography (CT) measurements (Keller and Holzer, 2018), smaller nanometer-scale pores are envisaged using numerical modeling (Tyagi et al., 2013; Underwood and Bourg, 2020). Following the idea of a ‘virtual rock laboratory,’ several attempts have been made to merge atomistic and pore-scale simulations to explain observed experimental trends in water and ion transport as a function of compaction state, clay and pore water composition, and saturation degree. Simulation results have shown qualitative agreement with experimental observations (Churakov and Gimmi, 2011; Churakov et al., 2014a; Gimmi and Churakov, 2019).

The purpose of performing macroscopic diffusion/retention experiments is to obtain transport parameter values (and uncertainty ranges) that are relevant for the considered host formation to be used in safety assessment evaluations. This requires that the data obtained can be up-scaled with respect to time and space scales.

Laboratory diffusion experiments suffer from relatively short time scales and challenging sample preparation. Total confinement pressure release can result in decompaction and irreversible distortion of the geometric structure, which may have an impact on the transport properties. Moreover, sample preparation can
result in artefacts and alteration in the chemical environment (e.g., pyrite and clay oxidation, CO₂ degassing, or microbial perturbation), affecting the transport properties. Field experiments may, therefore, be seen as more realistic because tracer migration occurs, after a certain distance from a borehole, in a more or less virgin environment.

Microscopic phenomena determine the behavior of fluid dynamics in porous media. This makes the description of the pore geometry complex both at laboratory and field scales. To tackle flow and transport phenomena at relevant scales (much larger than the pore scale), mass and momentum balances at the pore scale are averaged over volumes or areas containing many pores, and they are considered as a continuum. This is related to the Representative Elementary Volume (REV).

For clays, the typical grain size of a particle measures several tens of micrometers (excluding larger inclusions such as pyrite and carbonate concretions, septaria, fossils, worm tunnels, sand lenses, and other local heterogeneities). The dimension of a REV is in the order of several millimeters. Consequently for natural clay samples, most experimental and modeling scales are larger than the dimensions of a REV. Upscaling does not require adapting hydraulic or transport parameters, as long as macroscopic heterogeneities remain limited (Marivoet et al., 2006).

Within safety evaluations, clay host formations are often considered homogeneous. However, at lower scales, heterogeneity certainly exists and may have important impact on transport parameters.

There are several ways to perform upscaling and to assess the impact of heterogeneities: large-scale tests (laboratory and in situ), natural tracer profiles, and laboratory diffusion/sorption tests on cores sampled over an entire stratigraphy.

Firstly, large-scale transport tests may be considered. These can be conducted in a laboratory using large blocks (up to several decimeters) or in situ URLs (several decimeters up to several meters). The latter experiments are an upscaling both in terms of time (tens of years) and distance (up to decimeters and even several meters). These tests mainly make use of conservative or weakly sorbing tracers in order to obtain measurable tracer profiles over sufficiently large distances still within reasonable time frames (several years to decades).

An example of a large-block experiment consists of large cylindrical drill cores where a radiotracer source is emplaced in a hole drilled at the center. After a given time, subcores are taken to determine the 3D spatial distribution of the tracers (this mimics an ID experiment where the profile in a clay is determined). These experiments provide information about the anisotropy of diffusion coefficients and can be compared to small-scale diffusion experiments. This kind of test was conducted on Opalinus Clay samples (García-Gutiérrez et al. (2006); Cormenzana et al. (2008) and Callovo-Oxfordian Clay (Cormenzana et al., 2008).

A first type of in situ diffusion experiment can be considered as an up-scaling of large-block experiments. In this in situ radial diffusion test, a borehole is drilled in a clay formation. A cylindrical filter screen is emplaced at the bottom of the borehole, enabling circulation of water that contains radiotracers. The borehole is sealed using a packer, an inflatable rubber element sealing the annular space between the down-hole equipment and the borehole wall. The radiotracers diffuse radially into the surrounding

clay rock. After a given time, the experiment is ended, and the borehole is overcored. Subscoring of the part where the tracers were applied enables the determination of the 3D spatial distribution of the tracers. From the tracers' diffusion profiles in the clay rock, combined with the change in the relative concentration (C/C₀, where C₀ is the initial concentration) of the tracers in the reservoir solution as a function of time, the effective diffusion coefficient (D₀) and the rock capacity factor (α = ηR) can be calculated, accounting for anisotropy.

This type of experiment is always affected by a "skin" effect due to the excavation-disturbed zone (EDZ) that exists around the borehole (borehole-disturbed zone, BDZ). This may cause problems in the interpretation of data and is especially a problem for sorbing tracers, as their penetration depth remains limited even after several years. In general, these experimental tests still only provide information on a decimeter-scale distance limited to the overcoring dimensions. The overcoring method also represents a considerable technical challenge, and in the case of failure for unexpected reasons, all the information on the tracers' profile in the clay can be lost in a few minutes at the end of the experiment after several years of work (cf. cement water (CW) experiment at Mont Terri and two of the DIR experiments at Bure). Hence, there are intrinsic limitations related to upscaling in space and time.

This type of test has been conducted at the Mont Terri Rock laboratory on Opalinus Clay (https://www.mont-terri.ch) and includes the so-called DI and DR experiments, those at the Bure URL on Callovo-Oxfordian Clay (https://meusehautemarne.andra.fr), and the so-called DIR experiments (overview in Van Loon et al. (2012); Gimmi et al. (2014), (Van Loon et al., 2004b), Leupin et al. (2017), Delay et al. (2007), Soler et al. (2019)).

A second type of large-scale in situ diffusion experiment makes use of multi-filter piezometers. These tests are particularly applied in the HADES URL on Boom Clay (https://www.euridice.be), owing to its higher plasticity and porosity.

In these tests, a borehole is drilled using compressed air from an underground laboratory into the clay formation, and a stainless-steel cylindrical tube with a series of filter screens (multi-filter piezometer) at well-known distance (up to 0.5–1 m apart) is emplaced into the borehole. After convergence of the clay, the filters are in direct contact with Boom Clay because of its high plasticity, and no packer is needed to hydraulically isolate the different filter intervals. The filters are equipped with one, or sometimes two, stainless steel tubings leading to the gallery and allowing the injection/withdrawal (or recirculation in the case of two tubings) of water. In the injection filter (often the central filter), a radiotracer solution is injected/circulated, and at regular time intervals, water samples are taken from the adjacent filters. This enables the establishment of "break-through" curves for these tracers at different distances. An extension to this test is the emplacement of different multi-filters in a 3D configuration. This also enables sampling in the neighboring piezometer providing excellent 3D spatial information at a scale of several meters.

In Boom Clay, in situ diffusion tests do not significantly suffer from a BDZ, as the damaged clay skin around the filters is rapidly sealed by the fast convergence/creep of the plastic clay around the piezometer casing. As it is not intended to overcore, these piezometers which will remain in place, there is no time constraint, and the diffusion of conservative tracers (HTO and
$H^{14}CO_3^-$) develop over several meters without being affected by the already negligible BDZ. These tests have no end date and they continue to provide reliable data for several years/decades. Hence, these tests are very valuable with respect to upscaling to tens of years and up to several meters.

Examples of these tests in the HADES URL (Boom Clay) are the CP1, TRIBICARB, TRANCOM-R41 H/V, and MEGAS tests (Weetjens et al. (2011); Aertsens (2013); Aertsens et al. (2013); Martens et al. (2010); Weetjens et al. (2014) (Aertsens et al., 2023; Govaerts et al., 2023; Jacops et al., 2023)).

These *in situ* diffusion tests (CP1 and Tribicarb-3D) provide us with confidence that the migration of HTO and $H^{14}CO_3^-$ is correctly understood at the metric scale. Blind predictions at a large scale based on migration parameters obtained at the laboratory scale allow for the validation and verification of water flow and diffusion models. These experiments show that the applied models are consistent with our scientific understanding and adequately represent the relevant phenomena and interactions of conservative tracers at the scale of several meters (Weetjens et al. (2011); Weetjens et al. (2014) (Aertsens et al., 2023)).

At the clay-formation scale (several million years and a 100-m thickness), natural tracer profiles ($\delta^{18}O$, $\delta^{2}H$, He, Cl, Br, and I) provide valuable information regarding migration scenarios in natural systems and dominant transport processes. Despite the initial and boundary conditions not being well known, a careful analysis is useful to check for consistency with results and conclusions from studies at smaller scale. From natural profiles, we can better characterize the dominant transport processes (diffusion and advection) that have occurred during the burial period and may provide information on the effect of larger heterogeneities (distinct clay layers) and confirm the common up-scaling approach. Comprehensive overviews of studies on natural tracer profiles are given by Mazurek et al. (2009) and Mazurek et al. (2011) in the frame of their works performed for the ClayTrac project supported by the OECD/NEA Clay Club.

In order to evaluate the impact of heterogeneities (e.g., due to layering with regular alternation of silt and clay sediments, as observed in Boom Clay) on solute transport parameters, laboratory migration experiments can be conducted on a series of drill cores coming from boreholes drilled in the frame of site characterization campaigns. The general characteristics and microstructural features of a particular clay core can be related to experimentally determined transport parameters. In this way, the effect of heterogeneities on the general solute transport mechanisms can be evaluated. Examples of such studies for Boom Clay and Ypresian Clays include Aertsens et al. (2004), Aertsens et al. (2005a), Aertsens et al. (2005b), Aertsens et al. (2008b), Aertsens et al. (2010b), Aertsens et al. (2010a), Callovo-Oxfordian Clay by ANDRA (2018a), ANDRA (2018b), Descostes et al. (2008), Jacquier et al. (2013), Melkior et al. (2005), Robinet et al. (2012), and Van Loon et al. (2012), while studies for Opalinus Clay include Van Loon et al. (2012) and Van Loon (2014). More recently, a very extensive exploratory program by NAGRA to investigate the Mesozoic sedimentary sequence (comprising Opalinus Clay) of Northern Switzerland (nine deep boreholes (Mazurek et al., 2023)) was concluded. Part of the study comprised measuring the diffusion properties of HTO, $^{36}$Cl$^-$, and $^{22}$Na$^+$ in samples from all the different rock types across the lithostratigraphic

profile of interest in order to assess the spatial distribution of the diffusion properties and to determine the degree of heterogeneity (Glaus et al., 2023; Van Laer et al., 2023; Van Loon et al., 2023). Additionally, the outcome of the study was used to identify correlations between rock properties (mineral composition and microfabric) and diffusion parameters.

The above methods are mainly applicable for conservative tracers (i.e., non-retarded) and weakly sorbing tracers. For radionuclides exhibiting strong interactions with certain mineral phases, small local variations in the clay composition (i.e., in the content of these mineral phases) may have a significant effect. Large-scale experiments for these strongly sorbing elements will not be very helpful because of their very limited diffusion distances even for very long time periods. For these elements, small-scale experiments studying the relationship between sorption and the mineralogical characteristics (variability) of clay formations will be much more relevant. Such experiments are useful for providing reliable uncertainties on the sorption distribution coefficient ($K_d$) values used in safety assessment studies (Bradbury and Baeyens, 2017). Examples of such studies are (Chen et al., 2014b) for Callovo-Oxfordian Clay, and Marques Fernandes et al. (2015) for other clay rocks.

### 3.2.5 Sources of transport data for clay host rocks

In this section, we will provide an extensive (but not complete) overview of available sources with respect to diffusion data obtained for some well-studied clay host rocks (Opalinus Clay, Callovo-Oxfordian argillite, Boom Clay, Toarcian Clay, and Boda Claystone) and single clay phases (e.g., bentonite, smectite, illite, and kaolinite).

#### 3.2.5.1 Opalinus Clay and adjacent overlying or underlying sedimentary formations

The PSI has been conducting diffusion studies on Opalinus Clay since 2000. The materials under investigation originate from different deep boreholes in Northern Switzerland, notably from the Benken borehole in the Zürcher Weinland (BE-DBH), and from the Mont Terri Rock Laboratory, where the Opalinus Clay Formation is horizontally accessible via the safety gallery of a motorway tunnel (Transjurane highway). Thus far, the diffusion of HTO, $D_2O$, $H_2^{18}O$, $^{36}$Cl$^-$, $^{125}$I$^-$, $^{125}IO_3^-$, $^{35}SO_4^{2-}$, Br$^-$, $^{22}Na^+$, $^{85}Sr^{2+}$, $^{134}Cs^+$, $^{60}Co^{2+}$, $^{65}Zn^{2+}$, and $^{152}Eu^{3+}$ has been investigated (Glaus et al., 2008a; Jakob et al., 2009; Leupin et al., 2017; Wu et al., 2009; Van Loon et al., 2003; Van Loon et al., 2004a; Van Loon et al., 2005a; Van Loon and Eikenberg, 2005; Van Loon et al., 2005b; Van Loon and Jakob, 2005; Van Loon, 2014; Van Loon and Mibus, 2015; Van Loon et al., 2018; Glückman, 2023; Maes et al., 2024). More recently, transport studies were reported for $^{233}$U(VI) and $^{243}$A.m.(III) (Glückman, 2023) and for $^{226}Ra^{2+}$ and $^{239}Pu(IV)$, as part of the EURAD WP5 FUTURE project (see respective the contributions of Brandt et al. and Breckheimer et al. in the final technical report (Maes et al., 2024)).

An extensive drilling campaign initiated by NAGRA in three study areas for the potential siting of a deep-geological repository for radioactive waste in sedimentary Mesozoic rocks of northern Switzerland (Mazurek et al., 2023) has provided a unique set of mineralogical, petrophysical, geophysical, and chemical data. Among these, the diffusion properties in terms of the effective
diffusion coefficients and rock capacity factors of HTO, $ ^{36}Cl^{-} $, and $ ^{22}Na^{+} $ were measured perpendicular to the bedding orientation in approximately 130 samples originating from a broad variety of clay-, carbonate-, and silicate-rich rock formations, including Opalinus Clay (Van Loon et al., 2023). The effective diffusion coefficients of non-charged HTO were modeled using empirical functions for porosity and geometry factors, depending on the total clay content, as the sole input variable. The chemical composition of pore water, which differed for the different study areas, had no impact on these empirical functions. In contrast, the diffusion behavior of charged tracer species depended on the pore water composition and showed the characteristic features of surface diffusion in the case of $ ^{22}Na^{+} $, and anion exclusion for $ ^{36}Cl^{-} $. The effective diffusion coefficients and rock capacity factors of these charged species were successfully modeled using an electrostatic approach realized in PhreeqC (Glaus et al., 2023), using again the total clay constant as the main input variable. Two studies (Glaus et al., 2023; Van Loon et al., 2023) were complemented by a cross-laboratory benchmark exercise (Van Laer et al., 2024; Van Laer et al., 2023) in which differences in experimental and modeling approaches were tested using five twin samples from each of the same drill cores.

Furthermore, Opalinus Clay is also used as a reference material in different international studies, such as Joseph et al. (2013), Savoye et al. (2012c), Wigger et al. (2018), Xiang et al. (2016).

### 3.2.5.2 Boom Clay

SCK CEN has been studying diffusion in Boom Clay since 1978. The materials under investigation mainly originate from core material taken from the HADES URL in Mol (Belgium) and deep boreholes (e.g., Mol-1 borehole). Van Laer (2018) provides an overview of all long-term laboratory (Ra, Tc, Be, Ni, Zn, Pa, Zr, Am, Cm, Pu, U, Np, Pa, and NOM) and *in situ* (HTO, $HCO_3^-$, NOM, Am, and Tc) migration experiments on Boom Clay. HTO, $I^-$, and $HCO_3^-$ were used to investigate their variability over an entire host formation using drill core samples (Aertsens et al., 2004; Aertsens et al., 2005a; Aertsens et al., 2008b; Aertsens et al., 2010b; Aertsens et al., 2010a). Transport of Dissolved Organic Matter (DOM) is of particular interest in Boom Clay (Dierckx et al., 2000; Maes et al., 2006; Maes et al., 2011; Durce et al., 2018; Maes et al., 2004b), as it may act both as a vector and a sink for radionuclides.

Moreover, the diffusion of dissolved gases ($H_2$, He, Ne, Ar, $CH_4$, and $C_2H_6$) has been extensively studied by Jacobs et al. (2017b) and Jacobs et al. (2017a). Dedicated compilation reports ("Topical reports") are available that describe the current phenomenological understanding of the transport behavior of so-called reference elements in Boom Clay, based on the available sorption and diffusion experiments conducted: HTO (Bruggeman et al., 2017c), $I^-$ (Bruggeman et al., 2017a), $Sr^{2+}$ (Maes et al., 2017b), $Cs^+$ (Maes et al., 2017a), Se (De Canniere et al., 2010), $Tc$ (Bruggeman et al., 2017b), $Am^{3+}$ (Bruggeman et al., 2017d), U (Salah et al., 2017), and an overview report (Bruggeman and Maes, 2017).

### 3.2.5.3 Callovo-Oxfordian Clay

Different laboratories have performed diffusion experiments on Callovo-Oxfordian Clay and Oxfordian limestone. The following

elements have been studied: HTO, $Cl^-$, $I^-$, $SO_4^{2-}$, $SeO_3^{2-}$, $Li^+$, $Na^+$, $K^+$, $Rb^+$, $Cs^+$, $Zn^{2+}$, $Eu^{3+}$, organic anions, and polymaleic acid (Bazer-Bachi et al., 2006; Melkior et al., 2007; Durce et al., 2014; Dagnelie et al., 2018; ANDRA, 2018a; ANDRA, 2018b; Bazer-Bachi et al., 2007; Descostes et al., 2008; Jacquier et al., 2013; Melkior et al., 2005; Menut et al., 2006; Savoye et al., 2012b; Savoye et al., 2013; Savoye et al., 2015).

Furthermore, for partially saturated conditions of Callovo-Oxfordian Clay, diffusion experiments were performed using HTO, $Cl^-$, $I^-$, $Na^+$, and $Cs^+$ (Savoye et al., 2010; Savoye et al., 2012a; Savoye et al., 2014; Savoye et al., 2017).

In the context of the European Project EURAD WP5-FUTURE, new data from transport studies on samples of Callovo-Oxfordian argillite became available for selenite, $Ra^{2+}$, and $Ba^{2+}$, and they were complemented with sorption data (see contributions of Garcia-Guttierrez et al. in the final technical report of the project (Maes et al., 2024)).

### 3.2.5.4 Toarcian Clay

Diffusion experiments using HTO, $Cl^-$, and $I^-$ on the Toarcian argillite from Tournemire are reported in studies by Motellier et al. (2007), Savoye et al. (2006), and Wittebroodt et al. (2012).

### 3.2.5.5 Boda Claystone

On Boda Claystone, a limited number of experiments using $Cs^+$, $Sr^{2+}$, $Co^{2+}$, $I^-$, $HCO_3^-$, and $TcO_4^-$ are reported by Mell et al. (2006b) and Lazar and Mathé (2012).

In the context of the European Project EURAD WP5-FUTURE, new data from transport studies on samples of Boda Claystone formation became available for selenite (Czömpöly et al., 2023) and $UO_2^{2+}$ (contribution of Czömpöly in Maes et al. (2024)).

### 3.2.5.6 Clay minerals

Diffusion in clay minerals (e.g., bentonite, smectite, illite, and kaolinite) has been widely investigated.

Bourg and Tournassat (2015) provide a comprehensive literature overview on the diffusion studies on different types of bentonite (e.g., MX-80, Kunigel, Volclay KWK, Avonlea, and FEBEX) and smectites (e.g., Kunipia Montmorillonite, Swy-2 Montmorillonite, and Milos). These studies were mainly conducted using conservative tracers such as HTO/HDO, $I^-$/$Cl^-$, $Br^-$, and ion-exchangeable cations such as $Na^+$, $Cs^+$, $Sr^{2+}$, and ($Co^{2+}$). Glaus et al. (2017) published a detailed report on diffusion experiments using HTO, $Na^+$, $Cs^+$, $Sr^{2+}$, $Cl^-$, $SO_4^{2-}$, and $SeO_3^{2-}$ on Milos montmorillonite and Volclay KWK bentonite. They also published diffusion data for HTO, $Na^+$, and $Cl^-$ on kaolinite (Glaus et al., 2010).

In the EC project CATCLAY, the diffusion of a suite of cationic species ($Sr$, $Co$, $Zn$, and $Eu$) in illite (Illite du Puy) was intensively studied (Altmann et al., 2015; Glaus et al., 2015a; Glaus et al., 2020) in combination with dedicated sorption experiments.

In the EC project EURAD WP5 FUTURE, considerable new data from transport studies on different clay materials became available and are compiled in a final technical report (Maes et al., 2024); herewith an overview:

* Illite: Selenate and $Zn^{2+}$ (in competition with $Ni$) (contributions of Van Laer et al.), and $Co^{2+}$ and $Zn^{2+}$ on
<figure><img src="image_8.png" /><figcaption>FIGURE 7</figcaption></figure>

Crystalline rock features: unaltered rock, altered rock zones, fractures with and without mineralization (figure reproduced from Winberg et al., 2000, with permission from SKB).

illite preloaded with different cations (Li, Na; K, and Cs) (contribution of Zerva et al.).

* Compacted vermiculite: $Ca^{2+}$ (contribution of Zerva et al.)

* FEBEX bentonite: HTO, $Cl^{-}$, $Sr^{2+}$, and $Ba^{2+}$ effect of temperature and dry density (contribution of Garcia Guttierez et al.)

* Nontronite

* Effect of water saturation on transport of HTO, $I^{-}$, and $Na^{+}$ on kaolinite, illite, and vermiculite (contribution of Savoye et al., and more information in Section 3.2.2.3)

## 3.3 Transport in crystalline rocks

### 3.3.1 Structural aspects of crystalline rocks

Crystalline formations are geological units, which consist of magmatic and/or metamorphic rocks. Metamorphic rocks have undergone changes in mineralogy, texture, and/or chemical composition as a result of increasing temperature and pressure. The original rock may have been igneous, sedimentary, or another metamorphic rock. Due to their evolution, metamorphic rocks (most frequent representative: gneiss) typically show an ordered and, therewith, anisotropic structure (foliation and schistosity). Magmatic rocks (e.g., granites) usually have a disordered and massive, more isotropic structure owing to the lack of tectonic stress during crystallization. A disordered structure is generally advantageous from the viewpoint of mechanical stability. Nevertheless, many high-grade metamorphic rocks are very mechanically stable owing to their formation and recrystallization under high-pressure and high-temperature conditions.

For the mineralogical and geochemical characterization of magmatic and metamorphic rocks, several classification schemes exist. Granite, diorite, and gneiss as important crystalline rocks mainly consist of (Na, Ca)-feldspar (plagioclase with endmembers albite $Na[AlSi_3O_8]$, anorthite $Ca[Al_2Si_2O_8]$) and (K, Na)-feldspar with endmembers orthoclase/microcline $K[AlSi_3O_8]$ and albite. Further constituents are biotite $(K(Mg,Fe^{2+},Mn^{2+})_3$

[(OH,F)₂](Al,Fe³⁺,Ti³⁺)Si₃O₁₀)], quartz ($SiO_2$), amphiboles (e.g., hornblende, $Ca_2(Mg,Fe,Al)_5(Al,Si)_8O_{22}(OH)_2$), and calcite ($Ca[CO_3]$), and pyrite ($FeS_2$). Potential alteration processes result in albitization, biotite- and hornblende-alteration, and the formation of, for example, epidote ($Ca_2(Fe^{3+},Al)Al_2[O](OH)SiO_4Si_2O_7$), muscovite ($KAl_2[(OH,F)₂AlSi_3O_10]$), chlorite (($Mg,Fe)_3(Si,Al)_4O_{10}(OH)_2·(Mg,Fe)_3(OH)_6$), illite (($K,H_3O)(Al,Mg,Fe)_2(Si,Al)_4O_{10}[(OH)_2(H_2O)]$), smectite (e. g., montmorillonite, ($Na,Ca)_{0.3}(Al,Mg)_2Si_4O_{10}(OH)_2·nH_2O), kaolinite ($Al_4[(OH)_8[Si_4O_10]]$), calcite, stilbite (($Ca,Na)_9[(Si,Al)_{36}O_{72}]·28H_2O$), laumontite ($Ca_4[Al_8Si_{16}O_{48}]·18H_2O$), prehnite ($Ca_2Al[(OH)_2AlSi_3O_10]$), titanite (or sphene) ($CaTi[O]SiO_4$), hematite ($Fe_2O_3$), and pyrite ($FeS_2$) (Sandström and Tullborg, 2009; Plumper and Putnis, 2009; Nishimoto and Yoshida, 2010; Stober and Bucher, 2014; Yuguchi et al., 2015; Niwa et al., 2016). Nishimoto and Yoshida (2010) considered calcite, laumontite, chlorite, epidote, and prehnite along with quartz as the most frequent fracture-filling minerals.

For the assessment of crystalline rocks as host rock for a repository for heat-generating radioactive waste, their hydrogeological properties are particularly important. In metamorphic or magmatic crystalline rocks, the permeability of pore networks plays only a minor role. However, the groundwater flow predominantly occurs through fractures. The formation of fractures is largely controlled by tectonic processes during the uplift of the rocks in depth ranges, which are suitable for radioactive waste disposal. The extent of fracture formation is mainly dependent on rock stability and regional tectonic conditions. However, due to thermodynamic disequilibrium during uplift processes, fractures are frequently mineralized by migrating hydrothermal solutions or groundwater. Thus, the permeability of fractures is significantly modified due to precipitation processes and the infiltration of fines.

To describe transport processes in crystalline rock, one has to distinguish between unaltered and altered rock matrices (Figure 7), as well as between fractures with and without mineralization.

Components of crystalline rock show a large variability in crystal size, often ranging from the millimeter-to-centimeter scale. Newly
formed minerals and alteration products in fractures may comprise much smaller crystal sizes down to the nanometer scale, and they show a large variability of pore diameter, volume, and, hence, porosity (Svensson et al., 2019).

Complex flow fields evolve due to the surface heterogeneity of fractures and complex geometric fracture features, i.e., microscale roughness, reflecting the strong impact of spatial surface variability. Fracture geometry can effectively lead to the retardation of solutes and colloidal phases solely on basis of hydrodynamic processes, without considering physico-chemical processes such as matrix diffusion, sorption, or reduction.

Fracture surfaces vary spatially, for example, due to fracture fillings or geometry variability (Moreno and Neretnieks, 1993; Moreno et al., 1997; Bodin et al., 2003). It was observed that water flows in narrow channels through fractures (Bodin et al., 2003; Moreno et al., 1997), which is referred to as the channeling effect or preferential flow paths and applies to a single fracture as well as fracture networks (Tsang, 1984; Tsang and Tsang, 1987; Tsang, 1992; Park et al., 1997; Moreno et al., 2000; Malloszewski and Zuber, 1992; Shahkarami et al., 2016). Channeling can arise due to: 1) a variable aperture, 2) intersecting fractures, and 3) the offset displacements of fractures (Löfgren et al., 2007) and, among others, affect the hydraulic properties of crystalline rock. It also influences the fracture retention capacity, since matrix diffusion processes can be affected.

## 3.3.2 Main processes controlling transport in crystalline rocks

Reactive transport in fractured crystalline rocks is controlled by the physical and chemical properties of fractures, namely fracture walls and fracture-filling materials.

### 3.3.2.1 Advection in fractures is the dominant transport process

A mechanistic understanding, quantitative description, and prediction of advective transport in fractured porous media are still challenging. The surface building-block size on fracture walls covers a large range of the length scale, from the molecular dimension up to the characteristic extension of fractures in the field scale (Berkowitz, 2002; Pyrak-Nolte and Nolte, 2016). The fracture geometry causes heterogeneity, such as channeling of the flow path, which is also coupled to the adjacent porous and/ or microfractured matrix material. Characterization of the fracture flow, its interplay with the pore space, and upscaling to the field scale relevant for performance assessment is a continuing issue (Wersin, 2017). The fractal nature and partial self-similarity of rough fracture surfaces have been studied for their effects on the geometric constraints of transport models (Cardona et al., 2021; Wang et al., 2022). This topic has recently been discussed in a general review on transport mechanisms (Gao et al., 2023a) and with a focus on RN transport (Zhang et al., 2022)). The complexity increases further when fracture infills (infiltration of fines) and mineralization are considered (Antonellini et al., 2017; Soler, 2016). Fracture-filling materials modify the transport conditions owing to multiple processes of precipitation/crystallization and/or particle aggregation and filtration. As a result, a large diversity of pore shapes, pore size distributions, pore network geometries, and accessible

internal surface areas is reported (James et al., 2018; Jones and Detwiler, 2016; Nollet et al., 2009; Zhang et al., 2015).

Apart from advection through fractures with apertures larger than 100 µm, additional 2D tight flow pathways exist along microfractures and grain boundaries. Consequently, length-scale- depending variability of permeability has been observed and compared to multi-scale porosity and pore network data using multiple methods, such as mercury intrusion porosimetry (MIP) and pore network tomography (e.g., µCT, FIB-SEM, or BIB-SEM) (David et al., 2018).

### 3.3.2.2 Matrix diffusion

A simplified description of fluid transport in fractured crystalline rock is based on the dual-porosity model (e.g., Smith et al., 1991). In the dual-porosity model, diffusion into the rock material adjacent to fractures is included via matrix diffusion. The matrix-controlled transport is determined by the sorption on solid surfaces as well as parameters controlling the diffusion process, particularly the diffusion coefficient and the matrix porosity.

The concept of anion exclusion explains, similarly as in a clay environment (see Section 3.2.2), charge-depending modifications of the mobility of ions. The electrostatic interactions modifying ion mobility are dominant for pore sizes in the nanometer range. While this effect has been often observed in and described for argillaceous rocks, anion exclusion can be significant in crystalline rock matrices as well. Consequently, diffusion coefficients determined in diffusion experiments in crystalline rock matrices using anions tend to be smaller compared to cations or water (Smellie et al., 2014; Tachi et al., 2015; Voutilainen et al., 2019; Kuva et al., 2018).

### 3.3.2.3 Role of sorption and surface-induced processes

Retention processes, which have a common physical background for both clay and crystalline rock environments, are described in Section 2. Some specific issues, specifically focused on crystalline fractured environments, are tackled here.

#### 3.3.2.3.1 Sorption on fracture surfaces, including fracture-filling materials.
In Hakanen et al. (2014), the evaluation of data for rock materials is based on the laboratory-derived $K_d$ values of crushed rocks. Based on the results of the mineral-specific sorption of radionuclides in diffusion experiments and results of sorption to rock surfaces, these distribution coefficients were converted to $K_d$ values for intact rock. From this evaluation, it was suggested that mica minerals and other minerals with high CECs or high surface areas dominate sorption in intact rock.

Nevertheless, such minerals are not restricted to the rock matrix; they are also found in fractures, where they play a critical role in immobilizing contaminants during advective transport. In addition, carbonate minerals such as calcite are commonly found as hydrothermally formed fracture fills and may contribute to contaminant retention in fractured rock as well. While the retention properties of sheet silicates are discussed in detail in Section 3.2, for minerals such as calcite, sorption alone may not be the only process responsible for contaminant retention. Co-precipitation processes, as demonstrated by Smith et al. (2018) for Np(V) sorption on calcite, also play an important role. In addition, carbonate complexes can lead to RN migration in rock fractures without retention, as observed for Pu(IV) by Zavarin et al.
(2005). A detailed study of calcite precipitated in a borehole at the Äspö Hard Rock Laboratory showed that environment-specific partition coefficients can differ from laboratory-derived values, as seen for REEs (Drake et al., 2018).

A combination of microscopic and macroscopic investigations performed by Fukushi et al. (2013) focused on Eu(III) sorption on granite. Here, biotite was identified as the controlling factor for sorption strength. Numerical approaches considering a single-site cation-exchange reaction are able to predict the sorption behavior at pH > 4. The results suggested that sorption on a complex mineral assemblage such as granite could be modeled by using the single most relevant mineral phase (here: biotite) representative of the bulk sorption reaction in a complex mineral assemblage. Similarly, Muuri et al. (2017) and Kyllönen et al. (2008) utilized a multi-site sorption model initially introduced by Bradbury and Baeyens for Cs sorption on illite. They used this model to estimate distribution coefficients for Cs on biotite and biotite-rich rocks. Furthermore, Soderlund et al. (2019) employed the same sorption model, originally developed for Cs, to simulate the sorption of alkaline earth metals on biotite.

Li et al. (2018), Li et al. (2020), and Puhakka et al. (2019) investigated the sorption behavior of Se(IV) on Grimsel granodiorite (mainly plagioclase, K-feldspar, quartz, and biotite) using artificial Grimsel groundwater and different concentrations of Se(IV). A strong Se concentration dependence of Se sorption was observed, and the highest sorption values were found on biotite at low Se concentrations ($<10^{-7}$ mol/L). The distribution coefficients of Ba on Olkiluoto pegmatitic granite and veined gneiss, Grimsel granodiorite, and their main minerals (quartz, plagioclase, K-feldspar, and biotite) were obtained from batch sorption experiments (Muuri et al., 2018; Muuri, 2019). Highest sorption efficiencies were found on biotite and plagioclase. Recent results by Konevnik et al. (2017) suggested a strong increase in the $K_d$ values for Sr(II) and Am(III) for a temperature increase from 20°C to 90°C. Molodtsov et al. (2019) observed that, in the case of Eu(III), plagioclase was the primary mineral responsible for Eu sorption in granite, followed by intermediate sorption on biotite, and, lastly, sorption on quartz. Nevertheless, Molodtsov et al. (2021) reported that Eu(III) sorption on Bukov-magmatized gneiss showed that chlorite and amphibole exhibited the strongest Eu sorption among the complex mineral compositions present in rock.

### 3.3.2.3.2 Surface-induced processes and reactivity.
The presence of specific minerals in crystalline rock can induce processes that lead to reactions, including radionuclide retention. A typical reaction is the species reduction due to the presence of either Fe minerals or Fe-bearing minerals. These processes are specified in detail in Section 2.2.2. An example of this process is the retention of I on pyrite, biotite, and magnetite (Fuhrmann et al., 1998) via the surface reduction of $IO_3^-$ to $I_2$ and oxidation of $S^{2-}$.

Similarly, selenium sorption has been studied, and results suggested that Se(IV) is more readily reduced to Se(0) or Se(-II) when a solution is exposed to metal- or Fe-containing minerals (e.g., biotite) (Videnská et al., 2013; Stamberg et al., 2014; Videnska et al., 2015; Hakanen et al., 2014). The abiotic homogeneous reduction of selenite or selenate to selenide occurs at very low rates. Thus, the reduction reaction in the environment is most likely microbe-mediated, equivalent to the reduction of sulfate to sulfide

(Myneni, 1997; Hockin and Gadd, 2003; Hakanen et al., 2014). Increased Tc sorption was observed for rocks containing Cu, Fe, and Pb sulfides, and additional examples of retention of radionuclides on pyrite, galena, or chalcopyrite via reduction are provided in a review by Suter (1991).

### 3.3.2.3.3 Solid solution.
Solid solutions can be formed during the precipitation of mineral phases on fracture surfaces and in pores close to the fractures (Poonoosamy et al., 2020). These are typically sulfates (e.g., baryte, celestite) or carbonates (e.g., calcite) and can become an important retention mechanism for some radionuclides, such as Ra (see Section 2.3.3 for more details). For example, the precipitation of calcite might occur in crystalline carbonate water at higher pH. Curti (1999) reported that actinides strongly partition into calcite under reducing conditions; nickel(II) incorporation is moderate, while incorporation of ions such as U(VI), Cs(I), Sr(II), and Ra(II) in calcite is weak.

## 3.3.3 Research methods to characterize fracture properties and radionuclide migration

### 3.3.3.1 Advective flow and transport properties (geoPET and PMMA)

Although methods for characterizing bulk-rock properties are highly developed, the characterization of porosity in crystalline rock still remains challenging owing to low pore spaces and a broad range of potential pore sizes (David et al., 2018). Specifically, µCT(spatial resolution in the order of 50 µm) is relevant for transport studies in large and continuous fractures with aperture widths above the instrumental resolution. Methods such as optical microscopy approaches for the quantification of surface roughness variability provide detailed insights into critical surface building blocks of fracture walls (Fischer and Luttge, 2007), but they require preparation of and accessibility to the fracture surface. Apart from the visualization of fractures on relevant scales, other challenging aspects for µCT analysis are, for example, porous fracture fillings and intergrown minerals owing to their highly porous structure that can be of negligible density in contrast to the surrounding fluid (Berg et al., 2016; Menke et al., 2018). Furthermore, the C-14 polymethylmethacrylate (PMMA) method (impregnation with C-14 labelled PMMA resin followed by autoradiography) was developed to obtain information about the spatial distribution of porosity on the core scale (Sammaljärvi et al., 2012). It has been successfully used to characterize the spatial distributions of porosity in REPRO samples from Olkiluoto and has been combined with other techniques (Ikonen et al., 2015), such as electron microscopy for mineralogical characterization (Sammaljärvi et al., 2017). Furthermore, CT tomography analysis can be combined with C-14 PMMA method-based porosity results and SEM-based mineralogical analysis to obtain a 3D structure of crystalline rock.

Radionuclide tracer propagation through rock cores with natural or artificial fractures are studied using positron emission tomography (PET) (Kulenkampff et al., 2008). PET data analysis provides spatiotemporal images of the tracer concentration during conservative transport. In contrast, reactive (sorbing) PET tracers identify reactive sites of rock surfaces during fluid-solid interactions (Kulenkampff et al., 2018). Usually, PET techniques are combined with microcomputed tomography (µCT) data for the identification
of the geometry of fractures, pores, and pore networks. Segmented µCT data yield a structural model for reactive transport modeling (Kahl et al., 2020). Flow-field interpretations based on PET data sequences are used to identify flow heterogeneities (Lippmann-Pipke et al., 2017; Zahasky and Benson, 2018). Both the parametrization and validation of numerical transport models are an important application of PET flow field and velocity data. Pulse migration experiments using the positron-emitting radionuclide F-18 have provided insights into the fluid dynamics of complex fractured crystalline materials. Both the variation of the fracture aperture and the topography of the fracture surface affect the flow field, with consequences for flow channeling and preferential flow paths. Higher flow velocities result in wider and more dispersed flow paths, while lower velocities result in more localized flow and channeling behavior (Pingel et al., 2023).

### 3.3.3.2 Matrix diffusion

#### 3.3.3.2.1 Through-diffusion method.
The most commonly used method to determine the effective diffusion coefficient ($D_e$) of elements in hard materials is the TD experimental method (also see Section 3.2.3.1.2 for clay materials). In this method, a sample is placed between tracer-spiked and tracer-free solutions. The sample is glued to a sample holder, equilibrated in a tracer-free solution, often with synthetic groundwater, and installed between the two reservoirs. The tracer concentration is monitored in the initially tracer-free reservoir (Voutilainen et al., 2017). The apparent and effective diffusion coefficients as well as the geometric factors (G) can be determined from the experimental results based on Fick's second law of diffusion. Another experimental approach used to determine the effective diffusion coefficient involves subjecting sorbing elements to diffusion in rock cubes. In this setup, accurate measurements of concentration decreases in solutions containing the rock cubes are critical (Muuri et al., 2018; Muuri et al., 2017). Recently, the PET technique (see Section 3.3.3.2.4) has been used to calculate spatially resolved effective diffusivities (Bollermann et al., 2022).

In addition to concentration-induced diffusion experiments using aqueous solutions, TD experiments can also be performed in the gas phase. The diffusion coefficients of helium in a nitrogen-filled sample was measured (Kuva et al., 2015). The results showed that helium gas molecules diffused more than 11 000 times faster than atoms and molecules in the water phase.

The experimental arrangement of equilibration-leaching or the OD method can also be used to determine pore diffusion coefficients (Smellie et al., 2014).

#### 3.3.3.2.2 Electromigration.
The through-electromigration method (André et al., 2009; Lofgren and Neretnieks, 2006; Löfgren et al., 2009), adapted from Maes et al. (1998), Maes et al. (1999), and Maes et al. (2001), combines the principle of a TD method with the electromigration method and provides the effective diffusion coefficient ($D_e$), distribution coefficient ($K_d$), and geometric factor (G) for an intact crystalline rock sample in a faster way than traditional block-scale diffusion experiments. It avoids the problem of rock crushing in batch sorption experiments, which can create new surfaces and significantly increase the SSA (which would lead to an overestimation of $K_d$ values). The setup is described in (Lofgren and Neretnieks, 2006). A

small electric field is applied over a rock sample, which is placed between two chambers, one holding an electrolyte with a high tracer concentration (source chamber) and the other holding the same electrolyte initially free of tracers (recipient chamber). André et al. (2009) tested the migration behaviors of $I^-$ and $Cs^+$ ions in samples of intact rock.

In André et al. (2009), a device was found to have difficulties in maintaining a constant electric potential over a rock sample, making the experimental results difficult to interpret. To overcome this problem, Li et al. (2019b) upgraded this device by making use of a potentiostat instead of an ordinary power source and performed iodide ($I^-$) and selenite ($SeO_3^{2-}$) through-electromigration experiments. In addition, $NaHCO_3$ was added as buffer to the background electrolytes to stabilize the pH of the solution during the experiment. As a result, the electromigration device had the capabilities of voltage-self-controlling, continuous-current-recording, and solution-pH-stabilizing.

It should be noted that the classical theory for the interpretation of the experimental results simply applies an ideal plug-flow model that accounts only for the effect of electromigration on ionic transport but neglects contributions of electroosmosis and dispersion. To tackle this problem, an advection-dispersion model was developed by Meng et al. (2020). The model accounts for the influences of electromigration, electroosmosis, and dispersion in ion transport through rock. An analytical solution was derived in the Laplace space and described the transient tracer concentration variation in the recipient chamber.

#### 3.3.3.2.3 C-14 PMMA method.
As stated above (Section 3.3.3.1), the C-14 PMMA method was developed to gain information about pore networks and porosity at the core scale (Sammaljärvi et al., 2012). Relevant datasets act as a basis for the modeling of diffusion in crystalline rock (Kuva et al., 2018; Mazurier et al., 2016; Voutilainen et al., 2017; Voutilainen et al., 2019). Further refinement of image analysis in C-14 PMMA yields pore apertures from C-14 PMMA autoradiographs (Bonnet et al., 2020).

#### 3.3.3.2.4 Flow-field analyses: GeoPET.
Quantitative insights into flow pathway heterogeneity is provided by directly visualizing the propagation of a positron-emitting tracer, such as $^{124}$I and $^{22}$Na, using GeoPET (Kulenkampff et al., 2016; Kulenkampff et al., 2018). This method provides a suite of quantitative tomograms of the spatial tracer distribution. This allows for the derivation of a spatially resolved tensor of molecular diffusion coefficients. A robust algorithm for reconstructing the dominant pathways and flow field ("Darcy velocity") has been developed and is being further improved. PET analysis is being increasingly used for diffusive flux analysis in argillaceous materials and can provide valuable validation of transport simulation results. This is of particular importance owing to the potential variability of pore networks in such materials, which can only be inferred using high resolution methods such as FIB-SEM based on relatively small fields of view (Bollermann et al., 2022).

#### 3.3.3.2.5 In situ vs. laboratory experiments.
Since 2004, two large-scale, long-term in situ diffusion (LTD) experiments have been conducted at the Grimsel Test Site, which aimed to examine in situ matrix diffusion and pore space visualization (Soler et al., 2015; Ikonen et al., 2016b; Ikonen et al., 2016a) (see Section 3.3.4).
Two *in situ* flow experiments have been conducted in Onkalo at the Repro site where the dominant rock type is veined gneiss. Parallel to the *in situ* experiments, the project focused on rock matrix characterization and matrix diffusion in laboratory experiments to compare conditions such as stress relaxation, which might open the pore space and increase the diffusivity of the rock (see Section 3.3.4).

### 3.3.3.3 Sorption

Different approaches exist to characterize relevant mineral-specific sorption processes such as the acid-base behavior of surfaces and retardation, including surface complexation processes, in general. To examine sorption reactions at the solid-liquid interface, commonly applied methods are classical potentiometric titration experiments, column titration experimental setups, so-called batch experiments, and column transport experiments. These techniques are described in Section 2.2.4.

In the following section, a brief overview of titration, batch, and column experimental approaches, that are specific for crystalline rocks, is provided. Detailed information on spectroscopic methods is provided elsewhere (see Section 2.2.4.2) and not within the scope of this chapter.

#### 3.3.3.3.1 Titration experiments.
Potentiometric mineral titration experiments in batch are appropriate for investigating solids with large SSAs, such as clays (see Section 2.2.4). However, crystalline rock samples, in particular, can have very small surface areas. To collect trustworthy information on the acid-base behavior of samples with small SSAs, column potentiometric titration experiments may be applied (Scheidegger et al., 1994; Neumann et al., 2020). The advantage is a significantly larger solid-liquid ratio compared to that of potentiometric batch titrations. Hence, a larger surface area is exposed to a relatively small amount of titrant, making it possible to obtain trustworthy results of changes in surface charge as a function of, for example, ionic strength, pH, and ligands.

#### 3.3.3.3.2 Batch sorption experiments.
Batch sorption experiments can be based on the pre-equilibration of the solid phase in an electrolyte solution before adding a radionuclide, allowing it to sorb over a defined period of time, and can be used for any material, including clays. It is assumed that, after pre-equilibration of a solid, a radionuclide sorbs onto a slightly altered surface, which is expected to represent conditions that are closer to nature, compared to surfaces that have not undergone pre-treatment. Batch sorption results correlate well with data found in the literature and confirm the expected sorption trends that substantiates an approach. Unfortunately, pre-equilibration is time-consuming and may take several weeks to months, depending on the solid phase.

More time-efficient approaches are batch experiments that are carried out without pre-equilibration of a sample. A solid is briefly suspended in an acidic electrolyte that contains an element/radionuclide. Since the sorption of many relevant elements/radionuclides is pH-dependent, no significant surface reactions take place under these initially acidic conditions. Via slow adjustment of a suspension's pH to higher pH conditions, the

radionuclide sorbs onto the surface of the solid systematically. To reach steady-state conditions at surface and to be able to compare the results between the two experimental setups, identical equilibration times should be used when allowing the element/radionuclide to sorb at the surface. In an ongoing research project (SMILE, funding code 02 E 11668A, German Federal Ministry of Economics and Technology), it could be shown that both experimental approaches yield comparable results for quartz and feldspar surfaces. However, the second approach bears complications when using solids that exhibit strong natural buffer capacities and that are prone to dissolution in acidic conditions: Buffer reactions of the mineral surfaces result in pH shifts when comparing initially adjusted pH values with measured pH values after equilibration of a radionuclide with a surface. Minerals that undergo unwanted dissolution processes under acidic conditions may leach silica and other cations from the crystal lattice into the solution that later on, at higher pH, might bias sorption processes and dynamics via competing surface reactions or complexation reactions in solution (formation of aqueous complexes with altered sorption tendencies).

To prevent pH shifts from buffer reactions, and, hence, to precisely control the pH values of solid-electrolyte suspensions, artificial buffers can be added that have been shown not to interfere with sorption processes (Missana et al., 2009). This technique is often used for solids that undergo pre-treatment; however, it may also be applied for batch sorption experiments without pre-equilibration of a surface.

Alonso et al. (2013) and Alonso et al. (2014) proposed combining RBS and micro particle-induced X-ray emission (μPIXE) to analyze radionuclide retention and diffusion at the mineral scale using intact crystalline rocks, thus accounting for their heterogeneity. This method has been tested using different radionuclides (or chemical analogues) and proved successful in the cases of uranium and selenium.

#### 3.3.3.3.3 Dynamic column transport experiments.
Different experimental setups that provide a further understanding of sorption processes at mineral-water interfaces are column experiments. While batch sorption experiments represent sorption processes under static, equilibrium conditions, with column transport experiments, it is possible to collect retardation data under dynamic conditions and/or under equilibrium conditions. In column experiments, a cylinder is homogeneously filled with crushed mineral/rock and closed. For saturated conditions, a background electrolyte with defined chemical conditions is percolated through the column. After the column is saturated and geochemical conditions are adjusted as required, an electrolyte spiked with the radionuclide/contaminant of interest can be introduced into the column. At the end of the column, fractions of the solution that percolated through the column are collected, and information on retardation factors, retention times, mineral dissolution processes, pH evolution, and ionic strength changes, among others, throughout the experiment can be obtained. Since any electrolyte may be introduced into the system, and critical parameters such as pH, ionic strength, and ligand concentrations may change, this experimental system can be used to investigate dynamic transport and retardation processes.
It should be noted that the evaluation of results collected from column experiments in general may provide transport parameters such as retardation factors and distribution coefficients ($R$ and $K_d$, respectively), the Péclet number ($P_e$), or hydrodynamic dispersion coefficients and diffusion coefficients (Stamberg et al., 2014). However, to obtain these parameters, numerical models, such as, e.g., HYDRUS, STANMOD, and 2D/3D transport models, have to be applied.

### 3.3.4 Experimental approach to upscaling

#### 3.3.4.1 Advective transport processes

An extensive experimental program has been run in several underground laboratories, namely the Äspö hard rock laboratory (Sweden) and Grimsel Test Site (Switzerland). Experiments focus on RN migration/retention and fracture properties (see the overview of tracer tests in Löfgren et al. (2007) or references at https://www.grimsel.com/). A generalized view on the understanding of RN migration and retention in fractured rock was provided by projects TRUE-1 and TRUE Block Scale (Andersson et al., 2002b; Andersson et al., 2002a; Poteri et al., 2002). These projects focused on the meter scale up to the block (hundred meter) scale, similar to the Migration project (MI) and Excavation project (EP) at the Grimsel Test Site (Smith et al., 2001; Alexander et al., 2003; Alexander and Frieg, 2009). The Grimsel Test Site project CRIEPIS's Fractured Rock Experiment (C-FSR) provided fundamental knowledge about the properties of fractures, such as aperture, dispersivity, and flow wetted surface, using tracer tests and resin injection (http://www.grimsel.com/gts-phase-vi/c-frs/). Natural fracture properties are most often determined using *in situ* tracer tests in underground laboratories (Löfgren et al., 2007). For practical reasons, the tests are generally performed in reasonably well-connected and hydraulically conductive fractures where groundwater pumping can be performed. The rock mass surrounding fractures is likely to be intersected by swarms or clusters of minor fractures that can only be described stochastically. Information concerning the accumulation of fractures, so-called deformation zones, and individual hydraulically conducting fractures in rock matrices are normally obtained by drilling boreholes and examining the boreholes geologically, hydraulically, and geophysically.

#### 3.3.4.2 Diffusive transport

Since 2004, two LTD experiments were performed at the Grimsel Test Site, which aimed to examine *in situ* matrix diffusion and perform pore space visualization (Soler et al., 2015; Ikonen et al., 2016b; Ikonen et al., 2016a). Full characterization of the spatial porosity distribution in matrices, and its link to mineralogy, was performed by Voutilainen et al. (2017) based on the first LTD monopole experiment in order to better identify microstructure-derived diffusion. The heterogeneous mineral and pore structure of the studied rock, as well as the changing $K_d$ value of cesium, were taken into account for proper interpretation of the results of the *in situ* experiments.

Since 2009, *in situ* experiments have been run within the Repro cluster in the Onkalo URL (Finland) to investigate rock matrix retention properties under *in situ* conditions and to demonstrate that assumptions applied in safety cases are in line with evidence collected on site, *in situ* (Poteri et al., 2018a; Poteri et al., 2018b;

Voutilainen et al., 2019). Two *in situ* flow experiments were conducted in Onkalo at the Repro site where the dominant rock type is veined gneiss. Parallel to the *in situ* experiments, the project is focused on rock matrix characterization and matrix diffusion in laboratory experiments to compare conditions such as stress relaxation, which might open pore spaces and increase the diffusivity of rock. In a study by Voutilainen et al. (2019), the transport of tritiated water (HTO), $ ^{36}Cl$, and $ ^{22}Na$ was studied using laboratory and *in situ* water-phase diffusion experiments (WPDEs). The SKB Groundwater Flow and Transport of Solutes Task Force conducted WPDEs (WPDE-1 and WPDE-2) aimed at predicting tracer breakthrough curves (including those of HTO, $ ^{36}Cl$, $ ^{22}Na$, $ ^{85}Sr$, and $ ^{133}Ba$), as discussed by Soler et al. (2022). These experiments utilized simplified models to evaluate various conceptual approaches. The findings indicated that non-sorbing tracers were primarily influenced by dispersion, while sorbing tracers were impacted by diffusion and sorption parameters, as highlighted in Soler et al. (2019). This underscores the complexity of accurately predicting outcomes in well-designed field experiments, especially when extrapolating from laboratory-based geometries.

Upscaling of the results from numerical simulations at the pore scale can be used to derive key parameters for models at larger scales in crystalline host rocks. The volume-average approach has been applied as an upscaling method for the transport processes in porous media (Molins, 2015). As imaging techniques are progressively improving, “digital rock physics” has become a useful tool for numerically investigating reactive fluid-solid transport (Grathoff et al., 2016). Consequently, the image-based upscaling approach (Keller and Holzer, 2018; Mahrous et al., 2022) can preserve the small-scale information in large-scale simulations. However, one of the challenging aspects of upscaling is confirming whether small-scale measurements are representative of large-scale volumes.

### 3.3.5 Sources of transport data for crystalline rocks

This section presents an extensive (but not complete) overview of available data sources for understanding transport processes specific to crystalline rocks.

#### 3.3.5.1 Transport and retention processes

Fracture surfaces vary spatially owing to factors such as fracture fillings or geometry variability (Moreno and Neretnieks, 1993; Moreno et al., 1997; Bodin et al., 2003). It was observed that water flows in narrow channels through fractures (Bodin et al., 2003; Moreno et al., 1997), which is referred to as the channeling effect or preferential flow paths and applies to a single fracture as well as fracture networks (Tsang, 1984; Tsang and Tsang, 1987; Tsang, 1992; Park et al., 1997; Moreno et al., 2000; Malloszewski and Zuber, 1992; Shahkarami et al., 2016). For an overview of solute transport mechanisms in fractured rock, the RETROCK Project (Nykyri, 2004) and Neretnieks (1993) are recommended. Detailed information on fracture heterogeneity and its influence on transport processes is provided by POSIVA (2012a) and Poteri et al. (2014), who describe phenomena observed at the Olkiluoto site.

An overview of tracer tests can be found in a study by Löfgren et al. (2007) or at the Grimsel Test Site publications list page at https://www.grimsel.com/

A generalized view on understanding of RN migration and retention in fractured rock was provided by the projects TRUE-1
and TRUE Block Scale (Andersson et al., 2002b; Andersson et al., 2002a; Poteri et al., 2002). These projects focused on the meter scale up to the block (hundred meter) scale, similar to the MI and Excavation EP at the Grimsel Test Site (Smith et al., 2001; Alexander et al., 2003; Alexander and Frieg, 2009).

Diffusive transport occurs at the zones adjacent to fractures, enabling radionuclides to enter a connected system of pores in a rock matrix. Recent experimental studies on potential crystalline host rocks and diffusive transport include the Grimsel LTD experiment (Havlova et al., 2013; Martin et al., 2013), investigations at the Olkiluoto site (Aromaa et al., 2019; Voutilainen et al., 2019), and Beishan granite investigations (Yang et al., 2018).

### 3.3.5.2 Sorption processes

Many studies have focused on specific aspects of sorption in crystalline rock, generally using batch sorption experimental setups. A wide range of papers dedicated to batch sorption experiments can be found in Section 2.5.3 (sorption on crystalline rocks and components).

Detailed experimental setups of dynamic sorption column experiments can be obtained from Britz (2018), Palágyi and Vodičková (2009), Palágyi and Stamberg (2010), Palágyi et al. (2012), Videnská et al. (2013), Stamberg et al. (2014), Videnska et al. (2015), Hölttä et al. (1996), Hölttä et al. (1997), Li et al. (2009), Missana et al. (2008a), Dangelmayr et al. (2017), and Porro et al. (2000). These papers present experimental data, different model approaches, advantages, as well as drawbacks compared to batch experiments.

More information on column titration as one of the methods for the determination of retention property experiments is provided by Stolze et al. (2020), García et al. (2019), and Svecova et al. (2008).

### 3.3.5.3 Data used in safety assessment

With respect to sorption on crystalline rock material, compilations of sorption distribution coefficients ($K_d$), including uncertainties to be used in transport calculations for safety assessment, are available in Crawford (2010) and Hakanen et al. (2014). In Hakanen et al. (2014), an evaluation of data for rock material is based on laboratory-derived $K_d$ values of crushed rocks. Based on the results of the mineral-specific sorption of radionuclides in diffusion experiments and results of sorption to rock surfaces, these distribution coefficients determined on crushed rocks were converted to $K_d$ values for intact rock.

## 4 Concluding remarks on remaining research questions and needs

Research on the various topics of radionuclide migration has been conducted for more than 35 years, often co-funded by the European Commission (EC). Within the EC JOPRAD project "Towards a joint program on radioactive waste disposal" (www.joprad.eu), a consortium of WMO, technical support organization, research entity, and actor group representative organizations from European member states identified research development and demonstration (RD&D) priorities of common interest. These RD&D priorities are based on commonly defined remaining key uncertainties and research needs, and they form the basis of a

Strategic Research Agenda (SRA) that is used to coordinate, plan, and conduct future research related to waste disposal in Europe, the so-called European Joint Projects (EJP). Within the SRA (JOPRAD, 2018), different sub-domains were defined by prioritizing the future research needs.

These formed the basis of the EURAD project (https://www.ejp-eurad.eu/, 2021–2024) and the objectives for further research of the different defined work packages. This manuscript, summarizing state-of-the-art knowledge in the field, is one of the main outcomes of the work package "FUTURE," which deals with several of the remaining research questions related to radionuclide retention and transport.

During the EURAD project, the JOPRAD SRA was updated to EURAD SRA 2023, accounting for additional needs identified during the on-going EC project (https://www.ejp-eurad.eu/ strategic-research-agenda). This formed the basis for the different work packages proposed in the EURAD2 project to be started in October 2024.

A summary of the remaining research questions (directly copied from the SRA texts) and needs formulated based on analysis of the data and modes available in the literature, as well as new results obtained in WP-FUTURE, begins with those defined in the SRA and is further extended, or more detailed, where appropriate.

Geochemistry of host rock (intact and disturbed).

The mobility and retention of radionuclides is the result of their speciation within pore water and interaction with the solid phases of rock under intact *in situ*, or altered, conditions. It is, therefore, important to properly constrain the porewater chemistry and to adequately define reference and bounding host rock waters as well as to buffer and backfill pore waters for safety studies.

For the clay pore water chemistry, the main remaining uncertainties concern the correct measurements/determination under the undisturbed *in situ* conditions of non-preservable parameters: pCO₂, pH, and $E_h$. The conditions for the formation of solid solutions of carbonate and sulfate phases are also an open question.

Furthermore, the impact of "perturbations" such as pyrite oxidation, radiolysis, CO₂ degassing, alkaline plume, and iron/ clay interactions are still poorly understood.

Chemical thermodynamics.

Assessment of the long-term performance of a disposal system relies on the understanding and quantification of the thermodynamic driving forces for the degradation of waste matrices and for the mobilization and retention of radionuclides. High-quality thermodynamic data and models can often be used beyond a given disposal configuration, and if one is able to base long-term performance assessments largely on such data, one can attain high credibility and confidence. This can be linked to the NEA-TDB approach, which provides high-quality assurance and clear identification of priorities.

There is a need to further develop transparent and quality-assured TDBs for use in performance assessment studies. This entails determining thermodynamic data for key radionuclides, principal elements of a disposal system, secondary phases, and
solid solutions; obtaining a realistic representation of natural processes; filling in gaps for specific environments and specific species (e.g., organic matter, humic acids, and Fe-hydroxides); and improving the treatment of uncertainties in thermodynamic data.

Another important aspect is related to the database completeness, since the absence of relevant data in any high-quality database inevitably leads to incorrect predictions.

Sorption, site competition, speciation, and transport

Radionuclide transport in the pore water or groundwater of porous and fractured media is the main process challenging the long-term isolation and confinement of radionuclides in deep geological formations. The transport rate of species in groundwater is strongly reduced (1) by the retention of radionuclides on sorption sites present at the surfaces of minerals, engineered barrier materials, and their alteration products, and (2) in fractured media via diffusion into low-permeability rock matrices ("rock matrix diffusion"). The extent of sorption depends on the radionuclide, its speciation in solution, the geochemical boundary conditions, the heterogeneity of surface reactivity, and the permeability of solid phases. Competition for sorption sites between radionuclides and the main elements (e.g., Ca²⁺, Fe²⁺, and Mn²⁺) naturally present in pore water and groundwater may reduce the number of sites available for radionuclides.

Sorption mechanisms (such as surface complexation) should be further characterized to improve coupled chemistry/transport models for various rock types.

Deepening our understanding of sorption via surface complexation.

* Focus on mechanistic understanding: complexation constants, spectroscopic studies, and atomistic modeling to unravel the molecular structure of surface complexes, and provide input to TDBs.

* Impact of competing elements.

* Reversibility of the sorption process (adsorption vs. incorporation).

* Transfer of data from “simple to complex” systems: from dilute to compacted systems and from single-mineral phases to polymineral host rocks.

* Integration of models into reactive transport models to account for the evolution of reactive surface areas.

Well-known heterogeneities of cement-based materials, clay rock, crystalline rocks, bentonite, and corrosion products in speciation and sorption (considering competitive effects) need to be addressed, and transport models considering the variability of barrier properties at all relevant scales need to be developed. This will elucidate the influence of 3D-rock anisotropy/heterogeneity on radionuclide migration.

Complex evaluation of the dependence of sorption process on system constituents and boundary conditions is needed in order to realistically reflect system heterogeneity.

Models that are able to take into account the behavior of radionuclides in complex systems (including the effects of

organic and inorganic ligands, and redox transitions) should be further developed.

Classical transport models for porous media should be extended to include the effect of mobile surface species on the overall diffusion rates of cations and (include) the effects of anion exclusion.

* Coupling the sorption and diffusion models.

* Linking batch sorption data to transport experiments (attention to sorption competition effects) reflecting pore system heterogeneity by conventional description of diffusion process.

* Coupling physico-chemical alterations (mineral assemblage and pore structure geometry) in near- and far-field repositories to diffusive species transport.

* Appropriately using diffusion databases in safety assessment models.

Incorporation of radionuclides in solid phases

In addition to radionuclide retention via sorption, the incorporation of radionuclides in solid phases into waste matrices and along migration paths provides a different and very powerful retention mechanism. This is because incorporated radionuclides are not necessarily released upon contact of a solid with groundwater. This leads to partially irreversible entrapment as a strong safety factor for a repository system, if colloidal transport can be excluded. Important solids in this context are spent fuel and glass, their alteration products, as well as slowly forming and dissolving mineral phases (e.g., carbonates and sulfates) in the far field.

The mechanisms for irreversible entrapment need to be further and better characterized and modeled to enable the quantification of the long-term entrapment of key radionuclides (¹⁴C, Se, and U). There is a strong need for understanding both thermodynamics and kinetics and how to incorporate these aspects in reactive transport models.

Redox influence on radionuclide migration

Redox conditions influence radionuclide migration. Most repository concepts are based on a reducing environment. Under these conditions, actinides and technetium are merely present in a tetravalent redox state, forming solids with very low solubility. This is the principal reason why actinides only contribute a small amount to the overall radiological risk from a geological disposal facility. Much higher solubility and mobility are expected under oxidizing conditions.

Redox conditions can, however, be influenced by waste compounds introduced to the near field (e.g., nitrates and organic matter), and in this context, micro-organisms can also play an important role.

Post-closure safety case uncertainty would be reduced by improving the understanding of:

* The temporal and spatial evolution of redox conditions in engineered barrier systems (for instance, around metallic containers and overpacks and around steel reinforcement structures in concrete).

* The effect of redox perturbations (e.g., arising from the presence of nitrates/organic matter) able to modify the expected oxidation states and the mobility of radionuclides.
* The kinetics of radionuclide reduction/oxidation. Quantification of contributions related to homogeneous and heterogeneous redox reactions.

* The effect of radiolysis on the transport of radionuclides in the near field of a disposal facility. Spatial extension and time evolution of zones affected by radiolytic processes.

* The role of redox-active system constituents (e.g., minerals) on radionuclide mobility

* The knowledge of chemical speciation in source terms.

Further research should involve:

Development of geochemical models for the identification, simulation, and spatial monitoring of local and global anoxic conditions and/or redox transitions, including the associated modeling and transfer to realistic conditions.

Characterizing the mobility of radionuclides under well controlled redox conditions and complex perturbations (e.g., pCO₂, pH, and nitrate levels). There is also a need for well controlled chemical preparation techniques (e.g., reducing agents, purification methods, electrochemical techniques, and the use of a potentiostat) and speciation characterization methods for chemically conditioning radionuclides and tracer sources to be used for redox-sensitive elements before starting sorption and diffusion experiments.

Improve and extend our understanding of coupled sorption and electron-transfer interface reactions governing the retention of redox-sensitive RN on Fe(II)/Fe(III)-bearing minerals, including:

* Complementing TDBs.

* Improving the capacity of sorption models with respect to redox reactions.

* Correlating mineral properties to their retention capacity and reactivity.

* Transferring data from “simple to complex” systems: from dilute to compacted systems and from single minerals to natural host rocks.

* Integrating surface-controlled redox reactions into reactive transport codes.

### Transport of strongly sorbing radionuclides

Strongly sorbing radionuclides are expected to move across a very short distance over geological time periods. Typical strongly sorbing nuclides are trivalent and tetravalent actinides and tetravalent technetium. The actual migration distance is difficult to assess and requires sophisticated solid-state analytical techniques. Migration distances can increase via complexation with organic ligands originating from waste and via complexation/colloid formation with naturally present DOM, even though retention remains very strong.

Even if strongly sorbing radionuclides in a deep geologic repository constitute only a small risk to the environment, a better understanding is desirable to increase confidence, exploring, for instance, the chemical degradation of cement-based materials, the presence of organic molecules, and saline groundwaters.

Further studies are needed to determine and to better:

* Represent heterogeneous media (e.g., cement-based materials, clay rock, crystalline rocks, bentonite, and corrosion products).

* Simulate anoxic environmental conditions in experiments.

* Predict the transport of strongly sorbing nuclides, which is commonly based on the use of so-called effective diffusion coefficients ($D_e$) and sorption distribution coefficients ($R_d$). Recent experimental evidence has demonstrated that $D_e$ values may depend on various characteristics of mineral surfaces and the pertinent pore water composition, as is the case for $R_d$ values. It is, therefore, imperative to further improve the physico-chemical basis for the use of appropriate $D_e$ values in safety assessment studies.

* Characterize the retention of redox-sensitive radionuclides or toxic elements.

### Retardation via isotopic exchange

This refers to the case of $H^{14}CO_3^-$ isotopic exchange with calcite and other carbonates.

The first question to answer is whether this isotopic exchange process can be treated as pure sorption/retardation (linear and reversible equilibrium, $K_d$ approach?) or is it a true incorporation in the solid phase because of precipitation/dissolution equilibrium controlling the $^{14}C$-incorporation?

### Effects of microbial perturbations on radionuclide migration

Microbes and fungal activity can influence radionuclide migration via biosorption, metabolic processes, and the formation of biofilms, among other processes. By releasing organic molecules (siderophores), microbes can produce soluble radionuclide complexes. Microbial activity can also influence the chemical environment and, in particular, the redox state of radionuclides. Nitrates can influence microbial activity. In the absence of microorganisms, the transformation of sulfate to sulfide is, extremely slow, while it is fast in presence of sulfate-reducing bacteria. There is a lot of sulfate in typical repository environments, and sulfide formation may strongly influence the near-field geochemical environment. The geochemical environment and the presence of gases (e.g., $H_2$, $CH_4$, and alkanes) strongly influence microbial populations and activities.

Based on previous and ongoing work (e.g., EC MIND project), the role of microbes is typically addressed in implementers' safety cases by bounding assumptions.

Bounding conditions for predictions of microbial activity may be required for performance assessments. Quantitative information on microbe populations, energy, and carbon source availability (site-specific and waste-specific) would be beneficial in this context.

The impact of microbes on the chemical environment needs to be considered as a function of time to understand and quantify the fate and impact of microbial activity on radionuclide migration.

Assessment of the influence of gas on geochemistry and microbial activity in the near field should be performed by considering void spaces, the release of hydrogen, organic ligands, nitrates, sulfides, and methane, to assess the impact on barrier performance and radionuclide migration.
It would be beneficial to develop methods to upscale from phenomenological descriptions to mechanistic models.

## Organic-radionuclide migration

It is likely that a variety of organic substances will be part of any disposal concept, either from the waste inventory, as superplasticizers or admixture for concrete structures, or from pre-existing organic matter in geological formations. It is possible to consider a variety of substances, likely to be present and known for their stability, mobility, and radionuclide complexation in laboratory (and in situ) transport experiments and models. An example of a very organic-rich waste type is bituminized waste. Organic matter can influence radionuclide migration by creating soluble or colloidal complexes with radionuclides, which would otherwise be insoluble, or by blocking sorption sites. Hyperalkaline water may increase the solubility and mobility of organic matter (R-COOH and Ø-OH dissociation at high pH) along with entrained admixture compounds (such as superplasticizers) arising from cementitious systems. In compact clay rocks present at depth, only small organic molecules can be transported, whereas larger ones are filtered in clay pores.

Further research is required to enhance the understanding of the role of organics (either naturally occurring in clay formations or introduced in wastes and in engineered barrier materials) and their influence on radionuclide migration.

More specifically: (i) the nature of organic molecules generated by organic waste or admixture degradation, (ii) their stability with time, (iii) their effects on radionuclide migration (speciation, solubility, retention, and diffusion as a complex organic/radionuclide), (iv) the effect of cocktails of organic molecules, (v) the nature and release rate of organic compounds resulting from polymer radiolysis and hydrolysis, and (vi) implementation in a reactive transfer model require research.

There is also a need for acquisition of thermodynamic data on these organics for feeding into databases.

## Colloid influence on radionuclide migration

Colloids can be organic or inorganic. Their size is typically smaller than 0.5 µm; therefore, they do not settle during groundwater transport. In a repository, colloids may pre-exist in the groundwater system, or they may be generated via the interaction of groundwater with repository components. Important examples are smectite colloids formed via the interaction of glacial melt water with bentonites (peptization at low ionic strength). Clay rock and swelling clay backfills are filters against colloid transport, which is well documented (BELBaR EC project). When colloids are filtered, they do not contribute to radionuclide migration. When colloids are mobile, colloidal transport is particularly important for radionuclide migration, especially for radionuclides, which are sparingly soluble and strongly sorbed.

An improved understanding of the role of colloid generation and transport for different host rocks is required to increase confidence in post-closure safety cases, such as:

* Mechanistic descriptions of the RN-colloid interaction (e.g., kinetics of complexation, and stability).

* Colloid interaction with the solid (sorption-like).

* Colloid straining/filtering behavior: size-dependent transport.

* Reactive transport modeling of colloid migration and retention: implementation of new insights into the enhanced/inhibited particle retention on rough mineral/rock surfaces.

## Temperature influence on radionuclide migration

Elevated temperatures may change the migration behavior of radionuclides by changing the sorption constants of RN speciation, by changing diffusion coefficients in porous media, or by influencing the stabilities of minerals or organic matter. There are only a few studies on the effect of temperature increases on radionuclide migration and sorption.

There is a need to support concept optimization by studying the temperature effects on groundwater composition, solid-phase transformations, and, for some key radionuclides, the effects of elevated temperature on radionuclide speciation, solubility, sorption, and diffusion.

## Fracture filling

Most groundwater flow and, thus, radionuclide migration in higher-strength rocks take place through a network of interconnected fractures. Fractures become filled with precipitating minerals over time. How this happens depends on various factors, including temperature and reaction kinetics. This may influence the porosity, permeability, organic surface coating, microbial communities, and eventually the sorption of long-lived radionuclides on mineral surfaces.

A thorough understanding of the processes of fracture filling by precipitating minerals with a focus on precipitation kinetics is required to support the safety case of a geological disposal facility for higher-strength rock.

Moreover, fracture system characterization, including pore distribution and sorption properties, in both fracture filling and crystalline host rock is necessary in order to reflect the reality of transport pathway properties. Evaluation of system heterogeneity in connection with retention processes is inevitable.

Investigation of pore networks and the surface topography/rugosity of fractured crystalline rock samples with mineral infills:

* The impact of surface potential variability; the role of grain boundaries; the effect of water saturation, content, and chemistry (pH and ionic strength); as well as the impact of pore size variability (nanometer pore scale: mesopores/macropores).

* Analysis of the velocity field (diffusive vs. advective transport) in and close to fractures, using PET techniques.

* Derivation and quantification of parameter uncertainties to be used in transport modeling in fractured rock.

## Rock matrix diffusion
For relevant long-term safety radionuclides, it would be beneficial to gain an improved understanding of the impact of rock-matrix diffusion on travel time through the geosphere, including the anion exclusion effect, in the development of safety cases. Moreover, a realistic reflection of system heterogeneity would be desirable.

## Heterogeneity

The near and far field surrounding a Geological Disposal Facility is likely to be subject to heterogeneities that are unlikely to be fully represented in models; for example, from a flow perspective, heterogeneities are either generated via the construction of a repository (e.g., voids and EDZ) or exist locally in the geological environment. Integrated modeling taking into account these heterogeneities can provide significant benefits:

* To undertake phenomenological and safety studies to take into account heterogeneities of a system (mineralogy, hydrology, water composition, permeability, porosity, and fracture networks).

* To achieve a modeling capability that can integrate available site data to account for heterogeneities in the near field.

## Performance assessment tools

Modern numerical simulations are efficient tools for addressing the complexity of the flow and transport of radionuclides in porous media at large time and space scales. However, the quality of results depend on the accuracy of the input data, and the influence of each input parameter can also be difficult to quantify (sensitivity analysis and uncertainties). As a result, many mathematical methods to treat parameter sensitivity/uncertainties have been developed, which should be assessed and possibly improved in view of performance assessment calculations.

Research should aim at:

* improving mathematical methods to: (i) analyze the importance of the model input parameters of a simulation on the relevant output of the simulation (sensitivity analysis) and (ii) quantify the effect of uncertainties on these outputs (uncertainty analysis).

* developing a systematic procedure to analyze the data quality and to quantify the input data uncertainty in order to assess the confidence level of the model results.

## Upscaling in support of performance assessment

Upscaling strategies (including bottom-up approaches) are developed to support and justify hypotheses, parameters, and models used in performance assessment calculations. They are based on the understanding and modeling of fundamental processes from the micro-to-macroscopic scale, taking into account spatial heterogeneity, including the multi-scale structuration of rocks/materials.

Upscaling strategy development should aim towards:

* understanding the role of physical/chemical processes at different scales and linking bottom-up and top-down approaches in performance assessments.

* extending upscaling to the materials involved in radioactive waste disposal, such as cementitious-based materials.

* developing multi-scale approaches for coupled processes (including chemical, hydraulic, and mechanical processes).

* developing multi-scale strategies to represent complex phenomena (e.g., redox processes, microbial activity, and mineral transformation).

## Author contributions

NM: Conceptualization, Writing-original draft, Writing-review and editing. SC: Writing-original draft, Writing-review and editing. MG: Writing-original draft. BB: Writing-original draft. RD: Writing-original draft. SG: Writing-original draft. LC: Writing-original draft. FB: Writing-original draft. JP: Writing-original draft. AH: Writing-original draft. VH: Writing-original draft. CF: Writing-original draft. UN: Writing-original draft. SB: Writing-original draft. MS-K: Writing-original draft. OF: Writing-original draft. TM: Writing-original draft.

## Funding

The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. This document is a deliverable of the European Joint Programme on Radioactive Waste Management (EURAD). EURAD has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 847593.

## Acknowledgments

<figure><img src="image_9.png" /></figure>

## Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

## Publisher's note

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