# Confinement properties of zeolite-rich rocks with respect to water and various ionic tracers

Flora Parrotin, Emmanuel Tertre, Sophie Billon, Dimitri Prêt, Serge Lefevre,
Rémi Guichard, Baptiste Dazas, Michael Descostes, Sébastien Savoye

► To cite this version:

Flora Parrotin, Emmanuel Tertre, Sophie Billon, Dimitri Prêt, Serge Lefevre, et al. Confinement properties of zeolite-rich rocks with respect to water and various ionic tracers. Chemical Geology, 2026, 703, pp.123203. 10.1016/j.chemgeo.2025.123203. hal-05443232

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1 Confinement properties of zeolite-rich rocks with respect to water and various ionic

2 tracers

3 Flora Parrotin<sup>a,b,*</sup>, Emmanuel Tertre<sup>a</sup>, Sophie Billon<sup>a</sup>, Dimitri Prêt<sup>a</sup>, Serge Lefevre<sup>c</sup>, Rémi

4 Guichard<sup>a</sup>, Baptiste Dazas<sup>a</sup>, Michaël Descostes<sup>b</sup> & Sébastien Savoye<sup>c</sup>

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6 <sup>a</sup> IC2MP, Equipe HydrASA, UMR 7285 / Université de Poitiers, 86073 Poitiers, France

7 <sup>b</sup> ORANO Mining, Environmental R&D Dpt., 92320 Chatillon, France

8 <sup>c</sup> Université Paris-Saclay, CEA, Service de Physico-Chimie, 91191 Gif-sur-Yvette, France

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10 * Current E-mail address of the corresponding author:

11 Flora PARROTIN: [flora.parrotin@univ-rennes.fr](mailto:flora.parrotin@univ-rennes.fr)

12

13 Keywords:

14 Zeolite-rich rocks, confinement properties, water and ionic tracers, through-diffusion

15 experiments, dual porosity model.

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17 Highlights

18 Water diffusion in analcimolite controlled by pore throat size, not total porosity

19 Dual-porosity model required to reproduce transient diffusion behavior in all facies

20 <sup>36</sup>Cl<sup>-</sup> shows partial anion exclusion and slight sorption in reduced facies analcimolite

21 <sup>22</sup>Na<sup>+</sup> diffuses ~4 × faster than water due to isotopic exchange with analcime framework

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23 Graphical abstract

Through diffusion

<figure><img src="image_2.png" /></figure>

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# ABSTRACT

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The studied materials are zeolite-rich rocks (>70 wt% analcime, named analcimolite) forming a laterally continuous aquitard within the southern part of the Tim Mersoï Basin (Niger).

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This unit, commonly referred to as the Abinky Formation, occurs as three mineralogical facies: a reduced facies containing Fe-chlorite, an oxidized facies with hematite, and an intermediate ‘transition’ facies. This analcimolite unit acts as an aquitard, separating the overlying and underlying sandstone aquifers, the latter locally providing potable water. Due to the low permeability of these analcime-rich rocks, diffusion is expected to be the dominant transport mechanism. However, no data on transport properties in zeolite-rich formations have been reported, and the mobility of water and ionic solutes remains unknown. This study aims to characterize diffusion in the three facies of the Abinky formation, identifying key controls on water and ion transport prior to any anthropogenic perturbation.

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Through-diffusion experiments using water tracers (HDO and HTO) showed that water diffusion (effective diffusion coefficient from 1.3 to $2 \times 10^{-11}$ m²/s) is primarily controlled by pore throat size rather than total porosity. A dual-porosity model was required, distinguishing a fast-transport network (open, low-tortuous zones) from a slow one (confined, tortuous zones). Despite variations in diffusion coefficients, all data are interpreted with capacity factors equal to total external porosity measured by water impregnation (excluding crystal water located in zeolite micropores). This confirms that water behaves as an inert tracer and that micropores contribute negligibly to water migration. For ionic tracers in reduced facies, $ ^{36}Cl^{-} $ is partially excluded from external pores (anionic exclusion) and slightly adsorbed, with an extent of about 0.1 meq/100 g, a very small value compared to the cation exchange capacities of such rocks (up to ~40 meq/100 g for $H^{+}$ and $NH_{4}^{+}$). In contrast, $ ^{22}Na^{+} $ exhibits strong adsorption due to isotopic exchange with $ ^{23}Na^{+} $ in the analcime framework, leading to a diffusivity ~4 times higher than that of water. This dataset is a first step in constraining reactive transport models of water and

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68 solutes in zeolite-rich porous media under environmental conditions and prior to anthropogenic
69 disturbance.

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71 INTRODUCTION

72 Zeolites are aluminosilicates whose network structure provides molecular sieve properties
73 and selective ion retention due to the presence of interconnected pores (cages and channels)
74 (Clifton, 1987; Deer et al., 2004). Owing to these characteristics, they play a key role in
75 numerous applications, including agri-food (Pond et al., 1984; Defang and Nikishov, 2009) and
76 agriculture (Pond et al., 1984; Ming and Allen, 2001; Ming and Boettinger, 2001), water and
77 soil treatment (Mercer and Ames, 1978; Semmens and Seyfarth, 1978; Kalló, 2001; Komarneni
78 and Roy, 1981; Kalita and Chelishchev, 1995), gas separation and enrichment (Hayhurst, 1978;
79 Kotsis et al., 1982), construction materials (Aiello et al., 1995; Colella et al., 2001), and certain
80 biological applications (Tsitsishvili et al., 2020). Today, it is widely recognized that zeolites are
81 common minerals found in a wide variety of geological environments. Fifty-seven species of
82 natural zeolites have been identified (Cejka and van Bekkum, 2005), among which the most
83 frequent are clinoptilolite-heulandite, mordenite, chabazite, analcime, phillipsite, erionite, and
84 ferrierite. A global distribution of zeolite production by country, compiled by Marantos et al.
85 (2012), shows that exploitable deposits are widely distributed worldwide. To date,
86 commercially mined deposits are still predominantly composed of clinoptilolite, chabazite, and
87 mordenite (Marantos et al., 2012).

88 Analcime, or analcite, is a natural sodium zeolite with the theoretical formula
89 NaAlSi<sub>2</sub>O<sub>6</sub>·H<sub>2</sub>O, featuring cages between 0.28 and 0.32 nm in size (Sakirci, 2016; Line et al.,
90 1994; Ming and Mumpton, 1989; Mimura et al., 1995). Due to the small size of its cages,
91 analcime does not exhibit sieving properties for ions and molecules of interest (Na<sup>+</sup>, Cl<sup>-</sup>, and a
92 water tracer), allowing only species with a diameter smaller than its cage size to pass through
(Sakirci, 2016). These properties also make it a zeolite with low cation-exchange capacity, exchanging slightly Na⁺ with some cations such as K⁺, NH₄⁺, H⁺, Ag⁺, Tl⁺, and Rb⁺, while being unable to exchange with others like Li⁺, Cs⁺, Mg²⁺, Ca²⁺, or Ba²⁺, due to constraints imposed by their hydrated ionic radii (Barrer and Hinds, 1953; Barrer, 1981; Dyer et al., 2004; Sakirci, 2016; Pesonen et al., 2021; Parrotin et al., 2024). Analcime is particularly widespread in many geological systems, including sedimentary environments, open and closed hydrological systems, deep-sea sedimentary cavities, hydrothermal alteration settings, geothermal systems, and superficial deposits (Deer et al., 2004; Zhu et al., 2020). It is possible to identify rock formations exceptionally rich in analcime, referred to as analcimolites. Occurrences of analcimolites reported in the literature remain limited and include the Green River Formation (Utah, Eocene; Bradley, 1928), the Popo Agie Member (Wyoming, Triassic; Keller, 1952), the Tim Mersoï Basin (Niger, Jurassic; Joulia et al., 1958), the Mesozoic Formation of the Congo (Vanderstappen and Berbeek, 1959), and the Golden Valley Formation (North Dakota, Late Eocene; Furman, 1970).

The Nigerian analcimolites are located in the Tim Mersoï Basin, where they constitute major stratigraphic units (Joulia, 1958; Millot 1963; Pacquet 1969; Valsardieu 1971). In this basin, ‘analcimolites’ refer to zeolite-rich rocks containing more than 70 wt% analcime. The Abinky Formation, composed entirely of analcimolite, reaches a thickness of several tens of meters. This analcimolite formation is sandwiched between two sandstone aquifers, which also contain significant amounts of analcime: (i) Téloua, located beneath the Abinky Formation, and (ii) Tchirézrine II, positioned above Abinky. In this geological context, Abinky acts as an aquitard, isolating the Téloua aquifer which locally can provide potable water. Note that clay-rich formations have long been considered reference materials for studying confinement properties, with numerous investigations highlighting their ability to isolate aquifers and to act as geological barriers (e.g. Delay et al., 2007; Mazurek et al., 2011; Appelo et al., 2010; Savoye et
al., 2010). By contrast, zeolite-rich rocks have received almost no attention in this context, although zeolites are minerals commonly studied in mineralogy and in water-rock interaction research. In northern Niger, the Abinky Formation provides a natural and model system to investigate confinement properties of an aquitard rich in zeolites. Indeed, this aquitard is highly enriched in zeolites and is dominated by analcime, which is not only one of the simplest zeolites structurally and chemically, but also one with relatively small cages. For this reason, these analcime-rich rocks are good model systems for exploring how zeolitic dual porosity, intracrystalline cages and intergranular domains, controls water and solute transport in potential confining units.

Preliminary studies have identified diffusion as the dominant transport mechanism in Nigerian analcimolites (Dufréchou et al., 2024). To evaluate the impact of mineralogy on diffusion mechanisms, the current study relies on samples from different facies, representative of the Abinky Formation, exhibiting variations in mineral composition and pore structure. The influence of these parameters is examined through the diffusion of inert tracers (i.e., water tracers as HDO and HTO) in through-diffusion experiments, allowing quantification of diffusive transport parameters and identification of the effects of mineralogical and structural properties on solute dynamics within these rocks. Subsequently, the impact of a high zeolite content, and in particular, the presence of analcime, on the diffusion of charged species will be analyzed using tracer-scale diffusion experiments, involving radioisotopes such as ³⁶Cl⁻ (to assess anion exclusion; see Tournassat et al. (2015) among others for definition) and ²²Na⁺ (to investigate isotopic exchange with ²³Na⁺ located in the analcime framework). Indeed, a contrasted behaviour for charged species is widely observed in rocks, especially clay ones. In addition, the occurrence of rigid and well defined intracrystallin pores (i.e., cages) in analcime implies a dual porous medium in such a rock as also encountered for clay materials (Glaus et al., 2007; Tyagi et al., 2013; Ferrage et al., 2023; Tertre et al., 2024) for which the clay interlayer
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spaces are strongly varying in size/volume. Somehow, analcimolite is close to a model dual-
porosity medium. This approach will provide a deeper understanding of how analcime
influences solute mobility within these natural analcime-rich rocks.

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## 2. MATERIAL AND METHOD

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### 2.1. SOLID CHARACTERIZATION

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The analcimolites investigated in this study have already been the subject of previous research, and all details regarding their sampling are described in Parrotin et al. (2024). The Abinky formation was first described by Joulia et al. (1958) and Millot (1963) and subsequently studied in the works of Pacquet (1969) and Valsardieu (1971). Preliminary results, based on 4 core drillings, identified two main facies: a reduced facies, located within the uppermost eight meters of the Abinky, and an oxidized facies, present at greater depths in the lithology. The reduced facies is composed primarily of analcime and Fe-chlorite, whereas the oxidized facies consists mainly of analcime and hematite. Rock cores were kept moist, wrapped in damp cloths, and protected with cellophane. The sampling zones were defined as follows: the reduced facies zone of the Abinky (at the top of the Abinky; sample W009, 163.73 m – 164.23 m), the transition zone (sample X031, 168.44 m – 168.82 m), and the oxidized facies zone (sample X035, 171.84 m – 172.10 m).

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#### 2.1.1. Scanning Electron Microscopy (SEM) observations

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Observations were carried out using a JEOL JSM-5600LV Scanning Electron Microscope (SEM). Fragments of samples with fresh fractures were gold-coated and examined in secondary electron detection (SED) mode to assess surface topography. Thin sections were carbon-coated and analyzed in backscattered electron detection (BED) mode to highlight chemical contrast.

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All observations were performed with a working distance of 11 mm and an accelerating voltage of 15 kV.

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Additional high-resolution observations were conducted using a Field Emission Gun SEM (FEG-SEM), JEOL JSM-7900F, with a working distance of 6 mm and an accelerating voltage of 3 kV. These results, presented in the supplementary information, are necessary to distinguish certain minerals with a size < 1 µm.

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## 2.1.2. X-ray powder diffraction and Rietveld refinement method

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The samples were cut from their cores using a diamond saw cooled by a constant water flow, then dried in an oven at 60° C. These cuts were observed using a binocular microscope (Nikon SMZ800N) equipped with a camera (Nikon Digital Sight DS-SM). Subsequently, the samples were ground using an agate mill (Retsch RM 200). The resulting powder was suspended in Milli-Q® water (18.2 MΩ.cm) at a ratio of 4 g per 10 mL and subjected to a second grinding in an XRD-Mill McCrone microzoning mill (XRD-Mill McCrone) for 7 minutes to achieve a particle size below 5 µm, in accordance with the recommendations of Klug and Alexander (1954) for XRD analysis. After grinding, the suspensions were dried in a ventilated oven at 60° C, followed by three 8-hour dialysis cycles to remove any salt residues. Finally, the material was dried again at 60° C to remove water from interparticular porosity and sieved to 50 µm to disperse aggregates.

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The resulting powders were used to acquire XRD patterns with a Bruker D8 Advance equipped with a LynxEye detector. The diffractograms were obtained in Bragg-Brentano geometry using CuKα₁-₂ radiation (λₚKα₁-₂ = 1.5418 Å) with an angular step of 0.02° 2θ and a counting time of 0.6 s per step, over the 2-65° 2θ angular range. The analytical tube conditions were set to 40 kV and 40 mA. Subsequently, the quantification of crystalline phases was

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performed via Rietveld refinements (Rietveld, 1969) using the BGMN software (Bergmann and Kleeberg, 1998) in combination with the PROFEX interface (Doebelin and Kleeberg, 2015).

### 2.1.3. Mercury Intrusion Porosimetry

Sampling was carried out under water using a 1-cm-diameter corer. Three facies were considered for the study: reduced, transition, and oxidised. For each facies, two samples were collected (i.e., in duplicate) in order to assess intra-facies variability. All samples were dried in an oven at 60 °C, and their dry masses were measured. These six samples were analyzed using Mercury Intrusion Porosimetry (MIP; AutoPore IV 9500 V1.09) to determine the total porosity accessible to mercury, as well as the dry bulk (apparent) and solid (skeletal) densities which are estimated at the lowest and highest mercury injection pressure, respectively. The procedure is based on the use of a non-wetting liquid as a probe, i.e., a liquid with a contact angle greater than 90° between the rock surface and mercury. When increasing pressure, mercury progressively intrudes the connected pores of the samples with decreasing throat sizes. The data are interpreted based on the relationship between the applied pressure and the pore throat radius, described by the Washburn equation (Washburn, 1921) as follows:

$$r = \frac{2\gamma \cos\alpha}{P} \qquad (1)$$

where r is the connected pore entrance radius in meters, γ is the surface tension of mercury and is equal to 485 mN/m, α is the contact angle between air and mercury set at 130°, and P is the pressure difference applied at the interface in Pascals. In this study, the applied pressures ranged from 2 psi (~13.8 kPa) to 28 750 psi (~200 MPa), corresponding to probed pore throat diameters between 90 µm and 6.3 nm.

The cumulative specific intruded volume of mercury (i.e. mL/g) upon intrusion was converted in porosity value (%) according to the relationship provided by Matskova et al. (2017) and using the dry bulk density estimated at low pressure in order to provide cumulative
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throat size distributions. The incremental pore volume between two successive pressure steps
was computed as the difference in cumulative intruded volumes between two successive data
points. These incremental throat size distributions were further used to compute weighted
averages of the pore throat diameters for each sample.

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**2.2. Through diffusion experiments and acquisition of <sup>22</sup>Na<sup>+</sup> rock profile**

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**2.2.1. Experimental setup-up**

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The through-diffusion (TD) method (Boving and Grathwohl, 2001) was used to determine
the diffusion properties of the various tracers through the studied samples. Two water tracers,
HDO and HTO, along with the ions <sup>22</sup>Na<sup>+</sup> and <sup>36</sup>Cl<sup>-</sup>, were selected for these analyses.
Experiments were conducted on all facies for HDO, while tests with HTO, <sup>36</sup>Cl<sup>-</sup>, and <sup>22</sup>Na<sup>+</sup> were
performed exclusively with the reduced facies.

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The through-diffusion experimental setup is adapted from Motellier et al. (2007) (and
subsequently Bachaud, 2010; Frasca, 2011; Savoye et al., 2012, among others). It consists of
two aqueous reservoirs (upstream (~300 mL) and downstream (170 mL)) filled with the
background solution, with openings at the top for sampling. Between the two reservoirs, a
sample rock of known thickness, length, mineralogical composition, and porosity is placed. The
tracer of interest is introduced into the upstream reservoir. For the two water tracers and <sup>36</sup>Cl<sup>-</sup>,
their concentration is maintained constant through periodic renewals (or additions) of the
solution. For <sup>22</sup>Na<sup>+</sup>, its concentration is let free to evolve in the upstream reservoir, because of
its strong interaction towards the material. Under the effect of the concentration gradient, the
tracer diffuses through the sample, causing its concentration in the downstream reservoir to
increase. The solution in the downstream reservoir is regularly renewed with the tracer-free
background solution, maintaining a solute concentration sufficiently low compared to the
upstream reservoir. The concentration in the downstream reservoir, measured before each

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241 renewal, is used to determine the flux of the tracer diffusing through the sample. The transient
242 phase is influenced by the porosity accessible to the diffusing species, its effective diffusion
243 coefficient and its possible sorption in the medium. Once the steady state is reached, the flux
244 becomes constant in the downstream reservoir and is interpreted only by the effective diffusion
245 coefficient of the tracer in the medium.

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2.2.2. Diffusion of HDO, HTO, <sup>36</sup>Cl<sup>-</sup> and <sup>22</sup>Na<sup>+</sup>

248 The diffusion experiments conducted with HTO, <sup>22</sup>Na<sup>+</sup>, and <sup>36</sup>Cl<sup>-</sup> were performed on an
249 analcimolite sample from the reduced facies. At the beginning of the experiment, the upstream
250 and downstream reservoirs contained only a solution of NaHCO<sub>3</sub> at 10<sup>-3</sup> M and NaCl at 10<sup>-2</sup> M,
251 which was maintained for two weeks. This equilibration step had two complementary
252 objectives. First, the presence of 10<sup>-2</sup> M NaCl allowed the solution to fully saturate the pore
253 network in water and reach a stable chemical state, ensuring that the initial diffusion conditions
254 were not affected by transient salinity gradients (e.g., Tertre et al., 2024). Second, adjusting the
255 pH to around 9 ensured the chemical stability of analcime (whose dissolution is negligible under
256 alkaline conditions) while also reproducing the chemical condition of the natural environment
257 where the rocks are located (Parrotin et al., 2024). After this equilibration period, HTO and <sup>36</sup>Cl<sup>-</sup>
258 were spiked into the upstream reservoir as tracers (at a volume activity of 596.5 and
259 356.5 kBq/L, respectively), to conduct a dual tracer experiment. This allows for a direct
260 comparison between the diffusion of an inert tracer such as water (Tits et al., 2003; Van Loon
261 et al., 2003; Descostes et al., 2008), primarily influenced by the pore structure, and that of an
262 anion which is impacted by the negatively charged surface of minerals (e.g., Wigger and Van
263 Loon, 2017). Once these two tracers had reached steady state, <sup>22</sup>Na<sup>+</sup> was subsequently added to
264 the upstream reservoir, also by spiking with a volume activity of 862 kBq/L. In order to
265 minimize disruptions to the equilibrium between the solution and the solid phase, a method
consisting of spiking $^{22}$Na⁺ directly into the existing solution was used, rather than completely emptying the reservoir and replacing it with a new solution containing only $^{22}$Na⁺ (with $NaHCO_3$ 10⁻³ M and $NaCl$ 10⁻² M background solution). From the moment $^{22}$Na⁺ was added, only the diffusion of this cation was monitored. A table summarizing all the experimental conditions of the through-diffusion experiments is presented in Table 1.

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<table><caption>**Table 1:** Summary of the samples and experimental conditions used for the through-diffusion experiments. The underlined elements correspond to the tracers studied.</caption><thead><tr><th></th><th>Facies</th><th>Reduced</th><th>Transition</th><th>Oxidized</th><th>Reduced*</th></tr></thead><tbody><tr><td rowspan="3">Samples</td><td>Height (mm)</td><td>14.7</td><td>13.56</td><td>11.8</td><td>12.41</td></tr><tr><td>Diameter (mm)</td><td>29.25</td><td>29.32</td><td>29.24</td><td>29.30</td></tr><tr><td>Mass (g)</td><td>18.91</td><td>18.13</td><td>16.33</td><td>15.71</td></tr><tr><td rowspan="3">Reservoirs</td><td rowspan="3">Upstream chemical composition</td><td rowspan="3">NaHCO<sub>3</sub> 10<sup>-3</sup> M<br>pH 8.8<br><u>HDO</u> 3.55 M</td><td>NaHCO<sub>3</sub> 10<sup>-3</sup> M<br>pH 8.8</td><td>NaHCO<sub>3</sub> 10<sup>-3</sup> M<br>pH 8.8</td></tr><tr><td>NaCl 10<sup>-2</sup> M</td><td>NaCl 10<sup>-2</sup> M</td></tr><tr><td><u>HTO</u> 596.5 kBq/L<br><u><sup>36</sup>Cl</u> 356.5 kBq/L</td><td><u><sup>22</sup>Na</u>⁺ 862 kBq/L</td></tr><tr><td rowspan="3">Reservoirs</td><td rowspan="3">Downstream chemical composition</td><td rowspan="3">NaHCO<sub>3</sub> 10<sup>-3</sup> M<br>pH 8.8</td><td>NaHCO<sub>3</sub> 10<sup>-3</sup> M<br>pH 8.8</td><td>NaHCO<sub>3</sub> 10<sup>-3</sup> M<br>pH 8.8</td></tr><tr><td>NaCl 10<sup>-2</sup> M</td><td>NaCl 10<sup>-2</sup> M</td></tr><tr><td></td><td></td></tr></tbody></table>

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Another through-diffusion experiment was carried out using HDO as a tracer. The experimental setup was identical to that presented earlier, but this time conducted on all three facies of interest (reduced, transition, and oxidized; see Table 1). These porous media were first saturated with a background solution of $NaHCO_3$ at 10⁻³ M for 15 days, for the same reasons mentioned earlier (i.e., to ensure chemical stability of analcime and full saturation of the pore network). After this equilibration period, only the upstream reservoir was replaced with a solution containing $NaHCO_3$ at 10⁻³ M and HDO (see Table 1), while the downstream reservoir remained unchanged.

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<footnote>*Same sample used first for the diffusion of HTO/$^{36}$Cl⁻, then for $^{22}$Na⁺.</footnote>
### 2.2.3. Aqueous concentration/activity measurements and acquisition of $^{22}$Na$^+$ rock profile in solid

HDO concentrations were determined using a liquid water isotope analyzer (LDR-ICOSTM GLA431 Series Analyzer - ABB). For a solution with a δD value of 200 000‰, the HDO concentration is approximately 3.55 M. For the experiments, the amount of HDO diffusing into the downstream reservoir was calculated considering the natural HDO concentration presented in ultrapure water, estimated at $1.65 \times 10^{-2}$ M (Tertre et al., 2018). The uncertainty in HDO concentrations was assessed at 5% (2σ standard deviation) based on five repeated measurements on the same sample.

The activities of HTO and $^{36}$Cl$^-$ were measured by liquid scintillation using a Packard 2500 counter. The activity of $^{22}$Na$^+$ either in solution and in solid was measured using a gamma counter (Packard 1480 WIZARD, USA). All the data obtained were corrected for radioactive decay considering the start of the experiments.

After 281 days of $^{22}$Na$^+$ diffusion, the diffusion cells were dismantled by removing the sample holder. The sample was dried overnight in the dried atmosphere of the glove box; then, the abrasive peeling technique (Savoye et al., 2017) was applied. This technique enables the abrasion of a sample layer, whose thickness can vary from 10 µm to 250 µm depending on the abrasion duration and the type of the grinding paper (from P220 to P80). The abraded thickness increased with distance with respect to the original surface, in order to collect enough $^{22}$Na$^+$ for activity measurement and to reconstruct the sodium concentration profile within the sample.

#### Data analyses

The tracer fluxes measured in the downstream reservoir (based on concentrations) are interpreted using the classical Fick's second law (Equation 2):

$$ \frac{\partial C}{\partial t} = \frac{De}{\alpha} \cdot \frac{\partial^2 C}{\partial x} = \frac{De}{\varepsilon + \rho_{app} \kappa_d} \cdot \frac{\partial^2 C}{\partial x^2} \quad (2) $$
where C is the concentration (mol/m³ or Bq/m³), t is time (s), D_e is the effective diffusion coefficient (m²/s), α is the rock capacity factor (dimensionless), κ_d is the distribution coefficient (m³/kg), and ρ_app is the apparent bulk density (kg/m³).

The effective diffusion coefficients (D_e) and rock capacity factors (α) for HDO, HTO, and ³⁶Cl⁻ were determined by fitting the experimental diffusive fluxes measured in the downstream reservoir, using the semi-analytical solution Equation 2 and corresponding to Equation 3 reported below, as done by Descostes et al. (2008) and Tertre et al. (2018) for example. This solution is resolved by considering the following boundary conditions:

$C(x, t) = 0$ for $t = 0$

$C(x, t) = C_0$ at $x = 0$ for $t > 0$

$C(x, t) = 0$ at $x = L$ for $t > 0$

where L is the thickness of the sample (m) and C₀ is the tracer concentration in the upstream solution (mol/m³). For HDO, C₀ is corrected to account for the natural HDO concentration present in MilliQ water (1.65 × 10⁻² M).

Thus, the flux (J(x = L, t), in mol/s or Bq/s) in the downstream reservoir for the various tracers can be interpreted using Equation 3, as reported by Crank (1979):

$$J(x = L, t) = \frac{S C_0 D_e}{L} \left[ 1 + 2 \sum_{n=1}^{\infty} (-1)^n \exp\left(\frac{-D_e n^2 \pi^2 t}{\alpha L^2}\right) \right] \quad (3)$$

where S is the cross-sectional area perpendicular to the diffusion direction (basal surface of the samples; m²), C₀ is the tracer concentration in the upstream solution (mol/m³), D_e is the effective diffusion coefficient (m²/s), L is the thickness of the sample (m), t is time (s), and α is the rock capacity factor (dimensionless).

To compare data obtained for experiments differing by sample geometry (thickness and basal surface) and initial concentration of the tracer in the upstream, experimental and modeled fluxes are normalized using Equation 4:
$$333 \qquad F_N = \frac{F}{c_0 \cdot S} L \qquad (4)$$

where $F_N$ is the normalized flux (m²/s), F is the tracer concentration (or activity) measured in the downstream reservoir (mol/s or Bq/s), S is the cross-sectional area perpendicular to the diffusion direction (basal surface of the sample; m²), and L is the sample thickness (m). In the following sections, fluxes are plotted as a function of the barycentric time (weighted average time between two samplings).

For the specific case of $^{22}$Na⁺ diffusion modelling, a single reservoir method with decreasing source concentration for a semi-infinite case was used (Shackelford, 1991). The initial and boundary conditions are:

$$342 \qquad C(x \le 0, t = 0) = c_0 \quad \text{and} \quad C(x > 0, t = 0) = 0 \qquad (5)$$

$$343 \qquad \frac{\partial C(x=0, t>0)}{\partial t} = - \frac{D_e \alpha}{H_f \varepsilon_a} \cdot \frac{\partial C(x=0, t>0)}{\partial t} \qquad (6)$$

$$344 \qquad C(x = \infty, t > 0) = 0 \qquad (7)$$

where the positive x-direction corresponds to the solid and $H_f$ is the length of upstream reservoir, $\varepsilon_a$ is the porosity accessible to a non-reactive species, i.e, HDO/HTO and $\alpha$ is the rock capacity factor determined for $^{22}$Na⁺.

An analytical solution (Equation 8) for these initial and boundary conditions, as given by Shackelford (1991), was used to interpret the Na⁺ data:

$$350 \qquad \frac{c(x,t)}{c_0} = \exp\left[\frac{\alpha x}{H_f} + \frac{\alpha D_e t}{H_f^2}\right] \cdot \operatorname{erfc}\left[\frac{x}{2\sqrt{\frac{D_e t}{\alpha}}} + \frac{\sqrt{D_e \alpha t}}{H_f}\right] \qquad (8)$$

where $C(x,t)$ is the tracer concentration in the rock pore water at distance $x$ after time $t$, and $\operatorname{erfc}(z)$ is the complementary error function of argument $z$ defined with other parameters defined above.
356 **3. RESULTS AND DISCUSSION**

357 **3.1. CHARACTERIZATION OF THE POROUS MEDIUM**

358 **3.1.1. Mineralogy**

359 The study of the lithology revealed two dominant facies within the top of Abinky formation.
360 The reduced facies (Figure 1.A), located at the very top of the Abinky, is primarily observed
361 within the first eight meters. At greater depths, the Abinky is characterized by the presence of
362 the oxidized facies (Figure 1.C). Between these two facies, a gradual transition is identifiable,
363 marked by intermediate samples referred to as "transition facies" (Figure 1.B).

364 The mineralogy of the studied samples is dominated by analcime (NaAlSi₂O₆·H₂O), which
365 exhibits different habits. In all the facies studied, analcime occurs in the form of polycrystalline
366 spherules (Figures 1.D and E) and automorphic monocrystals (Figure 1.F). The analcime
367 spherules in the reduced facies (Figure 1.A and D) and transition facies (Figure 1.B) have cores
368 filled with a mixture of Fe-chlorite and analcime, while cement found between spherules (i.e.
369 outside the polycrystalline analcimes) consists of chlorite and Ti-oxides. In this study, "cement"
370 strictly refers to diagenetic mineral phases filling the porosity. Data illustrating these
371 petrographic features are available in the supplementary information (Figure S.I.1). In the
372 oxidized facies (Figure 1.C and E), the cores of the analcime spherules may be entirely
373 composed of analcime or may be empty (Figure 1.E). Monocrystalline analcimes (Figure 1.F)
374 are located between the analcime spherules and are present in all the observed facies (from
375 nanometric scale (Figure S.I.1) to 50 µm). Hematite is also present as cement between both
376 spherules and monocrystalline analcimes.

377 The chlorite is identified as Fe-chlorite (Parrotin et al., 2024) with an average formula of
378 (Si₂.83Al₁.17)O₁₀(Fe₃.33Al₁.25Mg₁.08Ti₀.1Mn₀.02)(OH)₈. X-Ray diffraction patterns (Figure 1.G)
379 show a decrease in chlorite content (reduction in peak intensity) from the reduced facies to the
380 transition and oxidized facies. Fe-chlorite occurs as cement between the analcime spherules and
monocrystals in the reduced and transition facies with large platy and flexible crystals (~4 µm wide) (Figure S.I.1.A and B). Fe-chlorite is also present within the cores of the analcime spherules in these same facies (Figure S.I.1.C) as part of a Fe-chlorite/nanoanalcime mixture, with particle sizes below one micron. These chlorites are absent in the oxidized facies.

385

<figure><img src="image_4.png" /><figcaption>**Figure 1:** Petrography and mineralogy of the three facies of interest, i.e., reduced, transition, and oxidized.</figcaption></figure>

386

387

388

389

Macroscopic photographs of analcimolites samples from (A) reduced facies (B) transition facies, and (C) oxidized facies, showing polycrystalline analcimes (spherules).
SEM observations (BED mode) on thin sections: (D) the polycrystalline analcime of the reduced facies (filled with a mixture of Fe-chlorites and nanoanalcimes), (E) the polycrystalline analcime of the oxidized facies with an empty heart.

SEM observation (SED mode) of rock fragment: (F) monocrystalline analcime

X-ray diffractograms (G) of the three studied facies (from bottom to top: oxidized, transition, and reduced facies). Chl: chlorite, Anl: analcime, Hem: hematite, Ant: anatase. Note that amorphous phases are accounting for the background intensity upon the Rietveld pattern modelling.

Hematite ($Fe_2O_3$) is absent in the reduced facies but appears locally in certain zones of the transition facies (right-hand area in Figure 1.B and Figure S.I.1.D) as rigid hexagonal platelets 100 - 1000 nm in size, imparting a reddish tint to the cement. Hematite is ubiquitous in the cement of the oxidized facies but is never present within the spherules of analcime in the oxidized facies (which are filled with analcime). Lastly, the presence of anatase ($TiO_2$) and K-felspar are also noted in all the samples. A Rietveld refinement quantification was performed for the three facies, and the results are presented in Table 2.

<table><caption>**Table 2:** Results from XRD Rietveld refinement (in wt% ± 2wt%) and Mercury Intrusion Porosity (MIP) for the three studied facies.</caption><thead><tr><th></th><th></th><th colspan="2">Reduced</th><th colspan="2">Transition</th><th colspan="2">Oxidized</th></tr></thead><tbody><tr><td rowspan="5">XRD Rietveld</td><td>Analcime</td><td colspan="2">69</td><td colspan="2">78</td><td colspan="2">90</td></tr><tr><td>Anatase</td><td colspan="2">2</td><td colspan="2">1</td><td colspan="2">1</td></tr><tr><td>Chlorite - Fe</td><td colspan="2">28</td><td colspan="2">18</td><td colspan="2">2</td></tr><tr><td>Hematite</td><td colspan="2">1</td><td colspan="2">2</td><td colspan="2">6</td></tr><tr><td>K-felspar</td><td colspan="2">2</td><td colspan="2">1</td><td colspan="2">1</td></tr><tr><td rowspan="5">Mercury</td><td>Duplicate</td><td>1</td><td>2</td><td>1</td><td>2</td><td>1</td><td>2</td></tr><tr><td>MIP porosity (-)</td><td>0.181</td><td>0.178</td><td>0.158</td><td>0.155</td><td>0.110</td><td>0.117</td></tr><tr><td>Mean Pore Throat Size (nm)</td><td>45</td><td>69</td><td>132</td><td>186</td><td>671</td><td>584</td></tr><tr><td>Solid density (MIP) (g/cm³)</td><td colspan="2">2.37</td><td colspan="2">2.34</td><td colspan="2">2.31</td></tr><tr><td>Dry Bulk density (MIP) (g/cm³)</td><td colspan="2">1.93</td><td colspan="2">2.00</td><td colspan="2">2.04</td></tr></tbody></table>
There appear to be correlations among the mineral contents. Specifically, analcime shows a positive correlation with hematite, and a negative one with chlorite. However, further sample analyses are required to confirm these trends. Moreover, regarding secondary phases, the quantity of chlorite decreases while that of hematite increases progressively with sample oxidation. Currently, the relationship between chlorite and hematite cannot be definitively established. However, previous studies, particularly those of Billon (2014) performed with the overlying formation (i.e., the sandstone reservoir of Tchirézrine II), have demonstrated that hematite is a product of chlorite oxidation occurring during a wide oxidation event. Ongoing research is investigating this connection.

419

### 3.1.2. Total porosity

The total porosity was measured using Mercury Intrusion Porosimetry (MIP); the results are presented in Table 2. The total porosity, averaged over the duplicates, decreases progressively from the reduced to the oxidized facies, with values of approximately 18%, 16%, and 11%, respectively. The detailed values for each replicate are presented in Table 2. The porosity values discussed correspond to the measurements including all the pores connected by throats larger than 6 nm, which is the commonly accepted lower detection limit of the MIP technique. For all facies and their duplicates, the cumulative throat size distributions show a plateau when reaching the lowest pore throat diameters, indicating that the intrusion reached the smallest accessible connected pores. The absence of a residual upward trend at the end of the curves suggests that the total connected porosity in between the crystals was fully accessed during MIP measurements at first sight (see Figure 2A). This feature validates the bulk values estimated by this technique for analyzing the interparticle pore network (i.e., porosity, dry bulk and solid densities; Table 2) which are generally biased for finely divided materials for which the smallest throat are not invaded by the mercury when the maximum injection pressure is reached
435

(Matskova et al., 2017). Basically, the intra-crystalline pores/cages of analcimes with opening of only 0.32 nm (Sakirci, 2016; Line et al., 1994; Ming and Mumpton, 1989; Mimura et al., 1995) are not accounted for.

436

437

438

<figure><img src="image_5.png" /></figure>

439

<caption>**Figure 2:** (A) MIP cumulative throat size distributions (%) and (B) Incremental throat size distribution obtained for the three studied facies (i.e., reduced, transition, and oxidised), each analysed in duplicate, as a function of pore throat diameter (nm).</caption>

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

Figure 2B shows the evolution of the incremental mercury intrusion volume as a function of throat diameter. The mean pore throat diameters, calculated from the weighted average of the incremental volume distributions (detailed values are presented in Table 2) present rather broad distributions, but reflect a general trend pointing out an evolution towards the degree of oxidation. Results obtained for all samples show three main throat diameter modes to be distinguished, centered around ~60 nm, ~130 nm, and ~500 nm. When the analysis is restricted to the two end-member facies, clear contrasts emerge. In the oxidized facies, the dominant mode is centered around ~500 nm, whereas in the reduced facies, the main mode is centered around ~60 nm. These contrasted distributions can be related to the mineralogical evolution of the cement as a function of the redox state. In the reduced facies, Fe-chlorite is the main contributor to the cement with negligible amount of hematite (28 wt% vs. 1%, respectively, see Table 2) whereas in the oxidized facies, the main contributor to the cement minerals is hematite (see Table 2). The main mode at 60 nm in the reduced facies can be attributed to the Fe-chlorite
cement, in agreement with data reported in the literature for clay-rich rocks (Chalmers et al., 2012; Gaboreau et al., 2016; Matskova et al., 2017). The ~500 nm mode is more likely related to a porosity controlled by the hematite cement.

Pore throat size is inversely correlated to the total porosity of the sample, as expected from the mineralogical evolution of the different facies. Indeed, the presence of chlorites in the reduced and transition facies promotes higher total porosity but with smaller pore throats. Conversely, in the oxidized facies, the presence of hematite instead of chlorite, results in a lower total porosity but larger pore throats. These observations highlight the structural role of mineral phases in controlling pore network properties, particularly the impact of chlorites and hematite cements on pore throat size and the overall pore volume. In addition, across all samples, a dual pore system is consistently detected.

467

## 3.2. DIFFUSION DATA

### 3.2.1. Water diffusion

The experimental fluxes of the water tracer (HDO) for the three studied facies -reduced, transition, and oxidized- are presented in Figures 3.A, B, and C, respectively. The data were obtained without salinity gradient, meaning that both the upstream and downstream reservoir solutions contained a NaHCO₃ concentration of 10⁻³ M. The absence of stirring in these reservoirs ensures that the observed diffusion is exclusively driven by the sole concentration gradient of the tracer between upstream and downstream reservoirs.
<figure><img src="image_6.png" /><figcaption>**Figure 3:** Comparison of water tracer (HDO) fluxes measured experimentally (symbols) in the downstream reservoir with calculated one (lines) by a model based onto a single porosity medium. Data are reported for: (A) reduced, (B) transition, and (C) oxidized facies. $D_e$ and $\alpha$ interpreting experimental data are reported.</figcaption></figure>

Analysis of the Steady-State regime

The experimental data (symbols) are compared to the simulated fluxes (solid and dashed lines representing ± 10% variability on the $D_e$). The effective diffusion coefficients ($D_e$) of HDO are 1.30, 1.53, and $2.01 \times 10^{-11} \text{ m}^2/\text{s}$ for the reduced, transition, and oxidized facies, respectively. The results indicate that the increase in $D_e$ values for HDO is directly related to pore throat size: as pore throat size increases, $D_e$ also increases. Notably, these pore throat sizes are inversely proportional to the total porosity measured by MIP (Table 2). While other studies dealing with clay-rich rocks (argillites) have established a positive relationship between the total porosity accessible to tracers ($\alpha$) and the effective diffusion coefficient ($D_e$) of an inert diffusing tracer (Van Loon et al., 2023; Mazurek et al., 2023), in the present case devoted to analcime-rich
rocks, the D<sub>e</sub> of the water tracer and its rock capacity factor -equivalent to the total measured porosity- is primarily controlled by pore throat size rather than total porosity.

493

494 *Analysis of the transient regime*

The results obtained by an initial model based onto a single pore medium are presented in Figure 3. This model assumes a single-porous system, where the rock capacity factor (α) is equal to the porosity (Table 2). Even though this model correctly interprets the flux measured in the steady-state phase, it fails to accurately reproduce those measured in the transient phase (t < 5 days), where experimental fluxes are systematically oscillating around the simulated one.

o During short time periods, the flux initially increases rapidly (the “first step” of a staircase-like curve). This initial phase is characterized by a steep slope, indicating efficient water tracer transport in low-resistance zones of the medium.

o Subsequently, a gentler slope appears (the “second step” of the staircase-like curve). This second phase corresponds to the involvement of less accessible zones or areas with higher resistance to diffusion.

In all these media, a dual porous network reflects a hierarchically structured organization, where rapid transport occurs in open and connected zones, while slower diffusion occurs in highly confined domains characterized by narrow pore throats and strong tortuosity, leading to purely geometrical restrictions on transport. The experimental data obtained from the analcimolite samples of the studied facies are interpreted using a model based onto two porous media organized in parallel (presented in Figure 4). The total flux (solid black curve) is the result of the sum of two fluxes diffusing through each of the two porous medium, with the objective of reproducing a α<sub>total</sub> equal to the total measured porosity (Table 2) with:
o Porous medium 1 (dashed orange line ($D_{e1}$) in Figure 4) represents zones with large openings, where diffusion is fast due to low constrictivity, tortuosity and resistance to transport, corresponding to low porosity volumes.

o Porous medium 2 (dashed green line ($D_{e2}$) in Figure 4) describes zones with small openings or narrow pore throats, where diffusion is slow due to high resistance to transport, corresponding to high porosity volumes.

$D_e$ and $\alpha$ values of the double porosity models are presented in Table 3.

<figure><img src="image_7.png" /><figcaption>**Figure 4:** Comparison between experimental fluxes (symbols) and those calculated with a double porosity model (lines) for the water tracer (HDO) in the (A) reduced, (B) transition, and (C) oxydized facies. $D_e$ and $\alpha$ associated to each of the double porosity model interpreting experimental data are reported.</figcaption></figure>

First, the transient domain is always better reproduced by this dual porous network approach compared to the use of model based on a single porous medium. In the case of the reduced facies, $D_{e1}$ from porous medium 1 (orange) contributes to 23% to the total flux (see Table 3).
Large openings are scarce in this facies due to the predominance of small pore throats structured by chlorite, making their contribution to diffusive transport minimal. Conversely, $D_{e2}$ from porous medium 2 (green) contributes to 77% to the total flux (see Table 3). Small openings dominate transport, and the reduced pore throat size (45 - 69 nm; Table 2) results in slow but persistent diffusion with high storage capacity. Over longer timescales, flux diffusing through porous medium 2 becomes dominant in the total flux, even though its contribution emerges after that of flow diffusing through porous medium 1.

In the transition facies, $D_{e1}$ from porous medium 1 (orange) increases and contributes to 33% to the total flux (see Table 3). Large openings therefore play a greater role in the overall HDO flux compared to the previous facies. $D_{e2}$ from porosity 2 (green) contributes to 67% to the total flux (see Table 3). With intermediate-sized pore throats (132 - 186 nm; Table 2), small openings significantly contribute to overall diffusion. Over time, a comparable proportion of the flux diffusing through the two types of porous medium is observable.

<table><caption>**Table 3:** Summary of diffusion parameters ($D_e$, in m²/s, and $\alpha$), based onto a model with two types of porosities in parallel, interpreting the experimental flux of water tracer diffusing through the three studied facies.</caption><thead><tr><th rowspan="2"></th><th colspan="4">Reduced</th><th>Transition</th><th>Oxidized</th></tr><tr><th>HDO</th><th>HTO</th><th><sup>36</sup>Cl<sup>-</sup></th><th><sup>22</sup>Na<sup>+</sup></th><th>HDO</th><th>HDO</th></tr></thead><tbody><tr><td>D<sub>e1</sub></td><td>0.30 × 10<sup>-11</sup></td><td>0.25 × 10<sup>-11</sup></td><td>3.20 × 10<sup>-12</sup></td><td></td><td>0.50 × 10<sup>-11</sup></td><td>1.10 × 10<sup>-11</sup></td></tr><tr><td>D<sub>e2</sub></td><td>1.00 × 10<sup>-11</sup></td><td>0.90 × 10<sup>-11</sup></td><td>7.00 × 10<sup>-13</sup></td><td></td><td>1.03 × 10<sup>-11</sup></td><td>0.90 × 10<sup>-11</sup></td></tr><tr><td>D<sub>etotal</sub></td><td><strong>1.30 × 10<sup>-11</sup></strong></td><td><strong>1.15 × 10<sup>-11</sup></strong></td><td><strong>3.90 × 10<sup>-12</sup></strong></td><td><strong>2.90 × 10<sup>-11</sup></strong></td><td><strong>1.53 × 10<sup>-11</sup></strong></td><td><strong>2.00 × 10<sup>-11</sup></strong></td></tr><tr><td>D<sub>e1</sub>/D<sub>etotal</sub> (%)</td><td>23</td><td></td><td></td><td></td><td>33</td><td>55</td></tr><tr><td>D<sub>e1</sub>/D<sub>etotal</sub> (%)</td><td>77</td><td></td><td></td><td></td><td>67</td><td>45</td></tr><tr><td>α<sub>1</sub></td><td>0.01</td><td>0.01</td><td>0.007</td><td></td><td>0.01</td><td>0.03</td></tr><tr><td>α<sub>2</sub></td><td>0.20</td><td>0.19</td><td>0.19</td><td></td><td>0.18</td><td>0.11</td></tr><tr><td>α<sub>total</sub></td><td><strong>0.21</strong></td><td><strong>0.20</strong></td><td><strong>0.197</strong></td><td><strong>462</strong></td><td><strong>0.19</strong></td><td><strong>0.14</strong></td></tr></tbody></table>

In the oxidized facies, $D_{e1}$ from porous medium 1 (orange) contributes to 55% to the total flux (see Table 3). In this facies, large openings dominate transport. The larger pore throat size openings (584 - 671 nm; Table 2) allows for rapid diffusion. The contribution of small pore
throats is significantly reduced due to their lower abundance in the porous medium compared to the dominant population of large pore throats. As a result, flux diffusing through porous medium 2 is less pronounced (45% of the total flux (see Table 3)), and transport remains dominated by rapid diffusion through large openings.

The concept of dual porous medium has been proposed in literature to describe transport behavior in a wide variety of natural and synthetic materials. It was initially formulated for natural reservoirs, where porosity is divided between highly permeable zones (fractures or interconnected pores), where advection dominates, and a low-permeability porous cement, where diffusion is the primary transport mechanism (Warren and Root (1963), from the work of Barenblatt et al. (1960), who studied fractured rocks). However, this model has been quickly extended to other systems, including cements and compacted clays, where advection becomes negligible and dual porous medium was exclusively used to explain diffusion processes. In certain materials, such as swelling clays (bentonites, montmorillonites) and some argillaceous rocks, dual porous medium models correspond to two distinct diffusive compartments. This phenomenon is particularly studied in montmorillonite- and vermiculite-based materials, where porosity is divided between the interlayer space (intraparticle porosity) and interparticle porous medium (Tyagi et al., 2013; Faurel, 2012; Vecchia and Musso, 2016; Tertre et al., 2018; Ferrage et al., 2023; Asaad et al., 2021; Tertre et al., 2024). Some of these studies (Tyagi et al., 2013; Ferrage et al., 2023; Tertre et al., 2024), combining experimental and simulated data, show that the fluxes of water and cations diffusing in these dual porous medium systems is primarily controlled by interparticle porosity, while flux diffusing through the interlayer space is very small due to low mobilities of interlayer species. This observation aligns with trends observed in molecular dynamics simulations (Titiloye and Skipper, 2001; Marry et al., 2002; Malikova et al., 2006), which highlight a strong structuring of interlayer water associated with its strong interactions with clay surfaces, limiting the mobility of interlayer species. This restricted
dynamic of interlayer water was later confirmed by Michot et al. (2016), who demonstrated, using neutron scattering diffusion measurements, a highly confinement of interlayer water in different bi-hydrated smectites.

In this zeolite-rich system, combining both interparticle porosity and intracrystalline cages characteristic of ANA-type zeolites (0.28–0.32 nm), a dual-porosity framework could be considered, accounting for both interparticle and intracrystalline porosity. However, these cages are far too small to allow the diffusion of water molecules at temperature representative of natural environmental conditions, and their contribution would imply diffusivities several orders of magnitude lower than the values measured in this study. The diffusion coefficients reported for HDO/HTO are instead compatible with transport through interparticle pathways whose orders of magnitude are larger than diffusion coefficient of water in ANA cages estimated at $10^{-17}$ – $10^{-16}$ m²/s between 65 and 105° C (Dyer and Molyneux, 1968), making any intracrystalline contribution negligible in our conditions. The dual-porosity model therefore reflects only the heterogeneity of the interparticle network, comprising open domains and narrower, more tortuous microregions. The fact that the total $\alpha$ derived from modelling matches the independently measured interparticle porosity obtained by MIP confirms that water diffusion occurs entirely within this connected interparticle network.

### 3.2.2. $^{36}$Cl-

The entire set of experimental data related to the diffusion of HTO (Figure 5.A) and $^{36}$Cl- (Figure 5.B) in the reduced facies was interpreted using the double porosity model, whose cumulative fit appears as a continuous black line.
<figure><img src="image_8.png" /><figcaption>**Figure 5:** Comparison between experimental fluxes (symbols) measured for water tracer (HTO; A) and anion ($^3$Cl⁻; B) with those calculated with the modelled data (double porous medium model; lines). These data are obtained for the reduced facies. For each tracer, Dₑ and α associated to each of the double porosity model interpreting experimental data are reported.</figcaption></figure>

The sum of the two α coefficients interpreting experimental data corresponds to the total porosity of the sample, estimated at ~ 18% (see Table 2). The global effective diffusion coefficients (Dₑ) interpreting HTO and $^3$Cl⁻ data are 1.15 × 10⁻¹¹ m²/s and 3.90 × 10⁻¹² m²/s, respectively, indicating that the diffusion of $^3$Cl⁻ is approximately three times lower than that of HTO in the same porous medium. The values are presented in Table 3.

To interpret these results, the effective diffusion coefficients (Dₑ) were normalized by dividing them by their free-solution diffusion coefficients (D₀), yielding a dimensionless relative diffusivity for each species. This approach corrects for intrinsic differences in aqueous mobility and highlights the influence of the porous medium on tracer diffusion. First, the diffusion of HTO was compared to that of Cl⁻. Using a D₀ of 2.09 × 10⁻⁹ m²/s for HTO and 1.84 × 10⁻⁹ m²/s for Cl⁻ at 22° C (Mills and Lobo, 1989), the normalized diffusion coefficients obtained are 0.0055 and 0.0021, respectively. Table 4 summarizes the diffusivity values obtained for all experiments conducted on the reduced facies.
<table><caption>**Table 4:** Free-solution diffusion coefficients ($D_0$) used to obtain diffusivities from measured effective diffusion coefficients ($D_e$), interpreting experimental data obtained for various tracers with the reduced facies.</caption><thead><tr><th></th><th>HDO</th><th>HTO</th><th><sup>36</sup>Cl<sup>-</sup></th><th><sup>22</sup>Na<sup>+</sup></th></tr></thead><tbody><tr><th>D<sub>0</sub> (m<sup>2</sup>/s)</th><td>2.08 × 10<sup>-9</sup></td><td>2.09 × 10<sup>-9</sup></td><td>1.84 × 10<sup>-9</sup></td><td>1.27 × 10<sup>-9</sup></td></tr><tr><th>D<sub>e</sub> (m<sup>2</sup>/s)</th><td>1.30 × 10<sup>-11</sup></td><td>1.15 × 10<sup>-11</sup></td><td>3.90 × 10<sup>-12</sup></td><td>2.90 × 10<sup>-11</sup></td></tr><tr><th>Diffusivity</th><td><strong>0.0046</strong></td><td><strong>0.0055</strong></td><td><strong>0.0021</strong></td><td><strong>0.0228</strong></td></tr></tbody></table>

The analysis of HDO diffusion on the same facies provides a reference for experimental variability. With a $D_0$ of $2.08 \times 10^{-9}$ m²/s, the relative diffusivity obtained for HDO is 0.0046. The comparison between HDO and HTO diffusivity reveals a ~16% difference, which represents a reasonable estimate of the experimental variability under our conditions for the same facies (including both analytical uncertainties and intrinsic variability of mineralogy and pore organisation). Any difference exceeding this value can therefore be considered significant. Finally, the comparison of the diffusivity of $^{36}$Cl⁻ and HTO, measured simultaneously on the same sample via co-tracing, highlights a significant diffusivity difference between the two tracers of around 66%. Indeed, the diffusivity of $^{36}$Cl⁻ is about three times lower than that of HTO. This difference could be explained by specific mechanisms related to interactions between the anion and the porous medium. Anion exclusion is the primary hypothesis to explain the reduced diffusion of $^{36}$Cl⁻. In porous media containing negatively charged minerals, negatively charged surfaces repel anions, a phenomenon known as "anion exclusion", which has been demonstrated in clays by many authors, including Van Schaik and Kemper (1966), Tournassat and Steefel (2015), Tournassat and Appelo (2011), Glaus et al. (2010), Zwahlen et al. (2024), Van Loon et al. (2003). As a result, a portion of the total porosity, accessible to water tracers (HDO and HTO), becomes inaccessible to anions. This reduction limits the available diffusion pathways for $^{36}$Cl⁻ which then diffuses through a restricted fraction of the pore network.
Consequently, due to the high negative structural charge of analcime (around 400 meq/100g) and small size of its cages (0.28 – 0.32 nm; Ming and Mumpton, 1989; Mimura et al., 1995), the α value used to describe the diffusion of ³⁶Cl⁻ should be lower than the total porosity. However, the results from the model used to interpret the experimental data (shown in Figure 5.B) indicate that the necessary α value is equivalent to the total interparticle porosity, which appears to contradict the expected effect of anion exclusion. An alternative hypothesis to explain this contradiction relies on the possible sorption of ³⁶Cl⁻ onto minerals surfaces. If a fraction of chloride ions is retained through physicochemical interactions with the material, this would introduce a nonzero distribution coefficient (κ₉). In this case, the α value used to interpret the fluxes would not only represent the porosity (ε) accessible to ³⁶Cl⁻, but would also include a contribution from sorption, as already reported in the literature for this species for different materials (kaolinite, Glaus et al., 2010; phases AFm et C-S-H, Plusquellec et Nonat (2016) and Beaudoin et al. (1990)).

According to Equation 6, derived from Fick's second law (Equation 2):

$$ \alpha = \varepsilon + \rho_{app} \times \kappa_{d} \qquad (6) $$

where the capacity factor α is equal to 0.187. ³⁶Cl⁻ diffusivity is significantly reduced compared to that of HTO suggesting that ³⁶Cl⁻ is partially excluded from a part of the porosity accessible to the water tracer (i.e., anionic exclusion). Then, using the diffusivity ratio between HTO and ³⁶Cl⁻ (~2.6) and assuming identical geometrical factors for both tracers, only about 8% of the water-accessible porosity (i.e., 1.7% in absolute value) would be accessible to chloride. Based on this reduced accessible porosity and the ρₐpp obtained from MIP (1.93 g/cm³), ³⁶Cl⁻ κ₉ can be estimated at around 0.1 mL/g. This value is low compared to literature data for other minerals (e.g., kaolinite) but remains consistent with weak anion sorption. Such a low κ₉ also corresponds to a very small anion exchange capacity (AEC) of 0.1 meq/100 g, especially when compared with the much higher cation exchange capacities reported for similar rocks (416 meq/100 g;
666

Dyer et al., 2004). A combination of anion exclusion and very weak sorption could therefore
explain why α value remains close to total porosity value.

667

668

Anion adsorption on aluminosilicates has been already reported and discussed in the literature.

669

Schell and Jordan (1959) demonstrated that chlorides can adsorb onto clays such as kaolinite, halloysite, pyrophyllite, and bentonite, while Barczyk et al. (2014) reported that anions could also be weakly adsorbed on several zeolites. In our case, ³⁶Cl⁻ adsorption could take place on the edges of the particles irrespective of the mineral considered (clays and zeolites). In our sample, analcime and chlorite could be good candidates to explain the slight ³⁶Cl⁻ sorption observed. Electrokinetic measurements on clays (see Avena and De Pauli (1998) for example) and analcime (see Mäurer and Kraushaar-Czarnetzki (2001) for zeolites) show systematically acidic values for the isoelectric points of these materials. However, the point of zero net proton charge of their edges can be close to 8-9, especially if aluminol and ferrinol edges, due to the presence of analcime and Fe-chlorites, are present (see discussion in Tertre et al (2006) for example for clays). Then, as experiments performed in this study were conducted at a pH close to 9, edges of chlorite and/or analcime can be neutral or slightly positive and could be at the origin of the small amount of ³⁶Cl⁻ adsorbed in analcimolite sample; amount needed to interpret ³⁶Cl⁻ flux measured in the transient stage of the through-diffusion experiments performed with the reduced facies. Other experiments carried out with different facies (differing by their amounts of chlorite and Fe(III) oxy-hydroxides (i.e. oxidized facies)) could be performed in future to go more in depth about the nature of the phase present in analcimolites able to adsorb Cl⁻ at trace concentrations.

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688

### 3.2.3. ²²Na⁺

689

The study of cation diffusion was conducted using ²²Na⁺. The experiment was carried out without a salinity gradient, meaning that both the upstream and downstream reservoirs have the

690
same ionic strength consisting in 10⁻³ M NaHCO₃ and 10⁻² M NaCl. Decrease of ²²Na⁺ activity measured in the upstream reservoir *versus* time, and ²²Na⁺ profile measured in the sample as a function of solid depth at 281 days, for the experiment performed with the reduced facies are presented in Figure 6.

695

<figure><img src="image_9.png" /><figcaption>Figure 6: Data concerning ²²Na⁺ diffusion in an analcimolite from the reduced facies (NaHCO₃ 10⁻³ M and NaCl 10⁻² M in the upstream and downstream reservoirs).</figcaption></figure>

697

A- Comparison between the evolution of ²²Na⁺ activity measured over time in the upstream reservoir (symbols) with the modelled data (line). B- Diffusion profile measured for ²²Na⁺ in the sample as a function of solid depth at 281 days (symbols) compared to the modelled data (dashed line).

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702

The effective diffusion coefficient ($D_e$) of ²²Na⁺ interpreting experiment data (see Figure 6) is equal to $2.9 \times 10^{-11}$ m²/s. For comparison with HTO data, $D_e$ are normalized to the respective free-solution diffusion coefficients ($D_0$) of the interest tracers (HTO and ²²Na⁺) to obtain their diffusivities. The $D_0$ of ²²Na⁺ is considered to be $1.27 \times 10^{-9}$ m²/s (for an ionic strength of 10⁻² M, at 22° C; Mills and Lobo, 1989), resulting in a diffusivity of 0.0228 for ²²Na⁺ (see Table 4).

The diffusivity of HTO, previously discussed in Section 3.2.2 and presented in Table 4, is estimated at 0.0055. This means that the diffusivity of ²²Na⁺ is around 3.7 times higher than that of the water tracer.

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711

To correctly interpret the experimental data, a rock capacity factor ($\alpha$) of 462 for ²²Na⁺ is required. For reference, the $\alpha$ of HTO is equivalent to the total porosity of the material, i.e.,

712
713 0.21. This high capacity factor for $^{22}$Na$^+$ indicates a significant adsorption of this radionuclide
714 within the porous medium. In the reduced facies, the mineralogy (presented in Figure 1 and
715 Table 1) shows that the sample consists of analcime, chlorite, and amorphous phases (rich in Si
716 and Al (see Parrotin et al., 2024)). It is therefore relevant to question the nature of the sodium
717 sorbing phase. Among these minerals, analcime is the most likely candidate due to its cation
718 exchange properties and affinity for Na$^+$ (until 416 meq/100 g (Dyer et al., 2004)).

719 In the samples, sodium is mainly present in the form of non-radioactive $^{23}$Na$^+$. This $^{23}$Na$^+$
720 compensates for the charge of the aluminosilicate framework, making it mobile within the
721 crystalline network (inside the cages), and this mobility is governed by a crystalline diffusion
722 coefficient (D*) upon exchange. The literature reports that the self-diffusion coefficient (D*) of
723 sodium in the framework of analcime is on the order from $10^{-18}$ to $10^{-16}$ m$^2$/s in the temperature
724 range from 20 to 25° C. Dyer and Yusof (1986) estimated a value of $3.38 \times 10^{-18}$ m$^2$/s, obtained
725 by converting the activation energy (Ea) into D* using the Arrhenius equation. Barrer and Rees
726 (1960) reported a coefficient of $1.14 \times 10^{-17}$ m$^2$/s at 25° C. Finally, Dyer et al. (2004) and Ames
727 (1965, 1966) report a broader variability depending on experimental conditions and the
728 materials studied, with values ranging between $10^{-16}$ and $10^{-17}$ m$^2$/s at 20° C. These values
729 confirm that sodium diffusion in analcime cages is particularly slow, which is consistent with
730 the compact structure of this zeolite and its low cation exchange properties (by comparison with
731 other zeolites). During a diffusion experiment conducted in a porous medium composed of
732 analcime particles the diffusion of $^{22}$Na$^+$ within the crystalline structure involves both its
733 penetration into the crystal (governed by the exchange dynamics with $^{23}$Na$^+$) and the isotopic
734 equilibration that progressively modifies the distribution of sodium isotopes inside the solid.
735

736 While Na⁺ in the framework of analcime can be exchanged to some extent with some cations
737 such as K⁺, NH₄⁺, H⁺, Ag⁺, Tl⁺, and Rb⁺, Na⁺ does not exchange with others such as Li⁺, Cs⁺,
738 Mg²⁺, Ca²⁺, or Ba²⁺ due to constraints imposed by their hydrated ionic radii (Barrer and Hinds,
738

1953; Barrer, 1981; Dyer et al., 2004; Sakirci, 2016; Pesonen et al., 2021; Parrotin et al., 2024).

739

In the through-experiment performed here, the main isotope of Na⁺ present in the analcime framework is ²³Na⁺ and is able to be exchanged with ²²Na⁺ injected in the upstream reservoir.

740

741

Some authors reported high exchange capacities (CEC) with respect to ²²Na⁺: from 170 meq/100 g at 25° C (Ames, 1966) to 416 meq/100 g (Dyer et al., 2004). In this study, the value of α = 462 interpreting experimental data corresponds to a κd of 217 mL/g when considering the total interparticle porosity ε of 0.18. This confirms a high amount of exchange between ²³Na⁺ located in the analcime framework and ²²Na⁺, and then a strong interaction with the crystalline structure.

742

743

744

745

746

747

Thus, although isotopic exchange between ²²Na⁺ and ²³Na⁺ is highly favored, it remains constrained by the crystalline diffusion of sodium within the analcime structure. This process imposes a limited transfer kinetics, where the penetration of ²²Na⁺ into the aluminosilicate framework is governed by its slow diffusion coefficient (D*). In other words, the observed exchange is intrinsically driven by the mobility of sodium within the crystalline structure, thereby explaining the high exchange capacities measured despite the low Na⁺ mobility in the analcime framework. Analcimolite with an unexpected dual porous medium for Cl⁻ (anion) and water diffusion within the interparticle pores exhibits a third porous medium (i.e. the intracrystalline pores/cages of zeolite) when dealing with the transfer of Na⁺.

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757

## 4. CONCLUSION AND PERSPECTIVES

758

Zeolite-rich rocks remain poorly documented in terms of their transport properties, despite zeolites themselves being extensively studied for their structural, ion-exchange, and sorption properties in various environmental and industrial contexts. However, little is known about how these intrinsic properties influence solute transport at the rock scale under undisturbed geochemical conditions. This study addresses this gap by investigating diffusion processes in

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762
rocks from the analcime-rich Abinky Formation. This formation, located in Tim Mersoï basin, revealed three distinct facies (reduced, transition, oxidized) characterized by notable mineralogical and porosity variations. Analcime remains the dominant mineral in all facies (~ < 70 wt%), but the nature of the cement evolves with oxidation: Fe-chlorite present in the reduced facies progressively disappears in favor of hematite in oxidized facies. However, no petrographic link between chlorite and hematite has been demonstrated at the formation scale. Thus, further research on the paragenesis of the Abinky formation is needed.

Total porosity decreases from the reduced to the oxidized facies, while pore throat size follows the opposite trend. These variations are directly linked to the mineralogy of the samples: Fe-chlorite promotes higher porosity but with smaller pore throats, whereas hematite leads to lower porosity but with larger pore throats. These structural differences influence the dynamic of the water tracer (HDO) in the samples, and diffusion is primarily controlled by pore throat size and not by the total porosity of the samples. This demonstrates that, in analcime-rich rocks, pore constrictivity exerts a first-order control on diffusive transport, surpassing the influence of bulk porosity, which has direct implications for predictive reactive transport modeling in such media.

The interpretation of through-diffusion experimental data obtained for water and ³⁶Cl⁻ (anion) required a dual-porous network model distinguishing between a fast porous network and a slow one acting in parallel. Although distinct, these compartments remain consistent with the structure of the medium since the sum of the capacity factors α corresponds to the total interparticle porosity, and to a bimodal throat size distribution as measured by MIP. Ongoing studies will aim to better link these two porosity compartments to the fine organization of the pore network and improve the understanding of transport mechanisms occurring in these samples. Diffusion in a third porous network is involved for the interpretation of through diffusion data obtained for ²²Na⁺ (cation), and which corresponds to the cages of analcime
788 crystals where isotopic exchange process between $ ^{23}Na^+ $ (initial cation in the analcime framework) and $ ^{22}Na^+ $ takes place.

790 The study of ionic tracers diffusion highlights specific interactions with the porous medium.
791 The diffusion of $ ^{36}Cl^- $, slower than that of water tracers, suggests an anion exclusion effect
792 limiting its access to certain pore regions. However, the measured $ \alpha $ is equivalent to the total
793 porosity, indicating that a partial adsorption may counterbalance this exclusion. Conversely,
794 $ ^{22}Na^+ $ interacts strongly with analcime through isotopic exchange with $ ^{23}Na^+ $ in the crystalline
795 framework, explaining its high retention and elevated capacity factor $ \alpha $.

796 These data provide the first characterization of the confinement properties of various tracers
797 in analcime-rich rocks under alkaline conditions (pH ≈ 9, the stability domain of analcime),
798 showing that these formations behave as true aquitards, which is particularly critical in a context
799 where the overlying Teloua aquifer locally constitutes a source of drinking water. More broadly,
800 the unusual combination of multi-scale porosity (ranging from nanometric intracrystalline pores
801 (cages) to micrometric pores controlled by mineralogy), anion exclusion, and strong cation
802 exchange capacity gives analcime-rich formations a specific role in the natural attenuation of
803 contaminants and radionuclides, with direct implications for groundwater protection,
804 radioactive waste confinement, and reactive transport predictions in zeolite-bearing geological
805 settings.

806

807 Acknowledgments

808 Authors thank Emmanuelle Chanvry and Denis Virlogieux for the on-site sampling of the
809 Abinky analcimolites in Niger. This work was realized with financial support from Orano
810 Mining and supported by the French government program "Investissements d'Avenir" (EUR
811 INTREE, reference ANR-18-EURE-0010). The authors acknowledge financial support from
812 the European Union (ERDF) and Région Nouvelle Aquitaine.
813

Declaration of Generative AI and AI-assisted technologies in the writing process

814

During the preparation of this work, the author(s) used ChatGPT (OpenAI) in order to improve
the readability and linguistic quality of the English text. After using this tool/service, the
author(s) carefully reviewed and edited the content as needed and take(s) full responsibility for
the content of the publication.

818

819

**Appendix A. Supplementary Material:**

820

The supplementary material provides additional FEG-SEM observations of analcimolites. It
includes micrographs of samples from both reduced and oxidized facies. In the reduced facies,
the images highlight the boundary between polycrystalline analcime and Fe-chlorite located
outside the analcime, as well as aggregates of Fe-chlorite. Other images show the mixture of
nanometric analcime and Fe-chlorite occurring inside polycrystalline analcime. In the oxidized
facies, the supplementary figure documents the presence of hematite located outside
polycrystalline analcime.

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828

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