# Localized versus distributed dissolution in carbonate rocks: The key role of microstructure

Theo Briolet, Elisabeth Bemer, Olivier Sissmann, Jerome Fortin

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Theo Briolet, Elisabeth Bemer, Olivier Sissmann, Jerome Fortin. Localized versus distributed dissolution in carbonate rocks: The key role of microstructure. Geochimica et Cosmochimica Acta, 2025, 397, pp.113-133. 10.1016/j.gca.2025.03.019. hal-05078041

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# Localized versus distributed dissolution in carbonate rocks: The key role of microstructure

Theo Briolet<sup>a,b,*</sup>, Elisabeth Bemer<sup>b</sup>, Olivier Sissmann<sup>b</sup>, Jerome Fortin<sup>a</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

Associate editor: Carl Steefel

**Keywords:**

- Carbonate rock

- Reactive transport

- Dissolution pattern

- Microstructure

- Péclet-Damköhler numbers

## ABSTRACT

Carbonate rocks are widespread and highly reactive, making their study a key topic for various environmental and anthropogenic issues. Dissolution of carbonate rocks is controlled by different factors, related to the fluid (chemical composition, pH, flow velocity) or the rock (mineral content, porosity, permeability, microstructure), and results in different dissolution patterns. To investigate the specific impact of microstructure on dissolution pattern, we perform controlled dissolution experiments under identical experimental conditions on two nearly pure calcite limestones (Euville and Lavoux) characterized by different grain and pore structures. Two distinct dissolution patterns are evidenced by the integration of CT-scanner and thin section observations, implying significant microstructural control. For Euville samples, dissolution is distributed across the entire width of the sample, whereas for Lavoux samples, dissolution is localized in wormhole-type channels. These contrasting responses are explained by differences in pore connectivity, reactivity and accessible specific surface areas. Conventional expressions of Péclet and Damköhler dimensionless numbers fail to differentiate the two studied limestones in a Pe-Da diagram despite their different behavior. Specific expressions are then defined to account for the specific accessibility to the intragranular microporosity and the associated specific surface area. The proposed approach allows a clear positioning of both limestones in areas of Pe-Da diagram consistent with the observed dissolution patterns.

## 1. Introduction

The high reactivity of carbonate rocks to acid solution may trigger a series of physico-chemical processes during fluid flow in rock formations, leading mostly to mineral dissolution (Morse and Arvidson, 2002; Plummer et al., 1978; Plummer and Wigley, 1976) and potentially inducing important modifications of the rock's hydrodynamical, petrophysical, and mechanical properties (Siqueira et al., 2017; Bemer et al., 2016; Vanorio et al., 2011; Noiriel et al., 2004). These processes are involved in various natural phenomena, such as karst formation, and anthropic issues, such as CO₂ storage.

Karst environments are complex geomorphological structures mainly resulting from the infiltration of acidified rainwater in soluble rock formations. Due to their high chemical reactivity and reaction kinetics, carbonate rocks and especially limestones are the most common karstifiable rocks (Goldscheider et al., 2020; Palmer, 2011; Goldscheider and Drew, 2007; Palmer, 1991). The study of karst environments is driven by two key issues: karst aquifers provide 20–25 % of the world's

drinking water (Ford and Williams 2007) and near-surface dissolution can lead to collapse hazards (Gutiérrez et al., 2014; Delle Rose et al., 2004). Karstification processes could, moreover, be affected by the increase of greenhouse gas concentrations in the atmosphere induced by human activities.

Dissolution of carbonate rocks is also a major concern for long-term CO₂ underground storage (Sun et al., 2016; Gaus, 2010; Bachu et al., 2007; Gunter et al., 1996; Dunsmore 1992). IPCC 2022 report reaffirmed the key role of carbon capture and storage (CCS) in the mitigation of climate change (Pörtner et al., 2022). Carbonate formations offer large potential storage capacities, but they will be subject to various chemical and physical interactions with the injected CO₂ (Lombard et al., 2010; Bachu et al., 1994; Gunter et al., 1993). The injection of large amounts of CO₂ may thus result in significant variations of the properties of the host rocks and the surrounding formations that need to be assessed to ensure the storage integrity (Siqueira et al., 2017).

Numerous experimental approaches have been developed to better understand carbonate dissolution processes. Batch experiments can be

<footnote><sup>a</sup> Laboratoire de Géologie, Ecole Normale Supérieure/CNRS UMR 8538, PSL Research University, Paris, France</footnote>

<footnote><sup>b</sup> IFPEN, Direction Sciences de la Terre et Technologies de l'Environnement, 1 et 4 Avenue de Bois-Préau, 92852 Rueil-Malmaison, France</footnote>

<footnote>* Corresponding author at: Laboratoire de Géologie, Ecole Normale Supérieure/CNRS UMR 8538, PSL Research University, Paris, France. E-mail address: briolet@geologie.ens.fr (T. Briolet).</footnote>
used to study the reactivity of single phase or complex minerals (Larson and Emmons, 2021; Pracný et al., 2019; Kirstein et al., 2016; Peng et al., 2015; Kaszuba et al., 2013; Pokrovsky et al., 2009; Sterpenich et al., 2009; Alkattan et al., 1998) and coreflood experiments implement controlled reactive fluid flow within the porous medium thereby allowing the investigation of the influence of hydrodynamical processes. Advanced coreflood experiments are coupled with non-destructive characterization methods to provide information on induced dissolution figures and the evolution of petrophysical properties (Menke et al., 2018, 2016, 2015; Ott and Oedai, 2015; Carroll et al., 2013; Luquot and Gouze, 2009; Bazin and Abdulahad, 1999). Different dissolution patterns have been observed according to the applied experimental conditions and the studied samples. The key controlling factors identified are the injection flow rate (Leger et al., 2022a; Leger et al., 2022b; Egermann et al., 2005; Fredd and Fogler 1998; Daccord et al., 1993; Hoefner and Fogler 1988), the pH and chemical composition of the injected solution (Menke et al., 2017; Luquot et al., 2014; Luquot and Gouze 2009, Egermann et al., 2005), as well as the rock mineral composition (Leger et al., 2022a; Yang et al., 2020; Carroll et al., 2013; Smith et al., 2013). The observed dissolution patterns are usually classified into three main categories: 1) compact dissolution close to the injection face; 2) wormhole development (formation of more or less ramified localized dissolution channels); and 3) uniform dissolution (Golfier et al., 2002). The dimensionless numbers of Péclet (comparing the advection rate to the diffusion rate) and Damköhler (comparing the reaction rate to the advection rate) are commonly used as proxies to relate the dissolution patterns to the experimental conditions (Golfier et al., 2002; Bekri et al., 1995; Daccord et al., 1993a; Daccord et al., 1993b). However, more recent studies suggest that this approach may fail to capture the influence of the complex microstructure of carbonate rocks (Leger et al., 2022a; Leger et al., 2022b; Noiriel, 2015; Smith et al., 2013).

Microstructure encompasses all the small-scale characteristics that describe the rock components (grains, matrix, cement, pores) and their arrangement in a 3D structure. Carbonate rocks are characterized by complex and heterogeneous microstructures resulting from the combination of initial sedimentary processes and further diagenetic modifications (Lønøy, 2006; Mazzullo and Chilingarian, 1992). They typically display bimodal pore networks including macropores and micropores, the latter being usually too small to be resolved on several centimeter samples using scanner or microscanner imaging (Haines et al., 2015; Bauer et al., 2011). The specific microstructure of each carbonate rock will strongly influence the flow and transport fields within the porous medium and hence the alteration processes (Bauer et al., 2024).

Previous studies have explored the impact of local microstructure heterogeneities on the induced dissolution patterns. The obtained results show that preferential flow paths provided by the initial pore network can impact the subsequent dissolution patterns (Menke et al., 2023; Leger et al., 2022a; Leger et al., 2022b; Yang et al., 2020; Al-Khulaifi et al., 2019; Menke et al., 2018; Menke et al., 2017; Smith et al., 2017; Luquot et al., 2014; Carroll et al., 2013; Smith et al., 2013; Vialle et al., 2013; Luquot and Gouze 2009). However, it remains difficult to deconvolute the importance of the different parameters controlling the dissolution of carbonate rocks. To this end, we study the microstructural controls on dissolution in two different limestones with almost identical mineralogical compositions but significantly different microstructures (distinct grain structures and pore networks). An integrated experimental workflow including an extensive characterization of samples before and after coreflood alteration is proposed. The differences in the observed dissolution patterns and estimated dissolution rates are related to the texture of the samples and their petrophysical properties. The dimensionless numbers of Péclet and Damköhler representative of the applied experimental conditions are determined, and the relevance of their relationship to dissolution processes is discussed.

# 2. Materials and methods

## 2.1. Sample selection

Two different limestones are studied: “Euville” and “Lavoux Jaune” (Leger et al., 2022a; Garing et al., 2015). Euville limestone is a grainstone of Oxfordian age from the Eastern Paris Basin, while Lavoux limestone is a grainstone of Bathonian age from the Poitou-Charentes region, France. These limestones have been selected for their nearly pure calcite composition, avoiding any major chemical effect, but significantly different microstructures, already observable at the core scale: Euville samples exhibit larger grains and macropores, while Lavoux samples display an inclined bedding. 40-mm diameter samples are cored from quarry blocks, and CT-scanner imaging is used to select the more homogenous ones: two 80-mm long samples (EUV-1 and LAV-1) and two 100-mm long samples (EUV-2 and LAV-2).

## 2.2. Chemical and microstructure characterization

A detailed characterization of the mineralogical composition and microstructure of Euville and Lavoux limestones is carried out in this study. The chemical composition is determined on 20-mm diameter and 20-mm long samples (one sample per facies). Samples are dissolved in an acid solution and species in solution are quantified by Inductively Coupled Plasma Atomic Emission Spectrometry (ICP-AES) to infer their chemical composition.

Thin sections are made from starting material (one thin section per facies) and from altered samples and observed using an optical microscope and a Scanning Electron Microscope (SEM).

The specific surface area is measured on small 4-mm diameter and 6-mm long samples (two samples per facies) using krypton adsorption and BET (Brunauer, Emmett, and Teller) modeling (Brunauer et al., 1938).

Porosity and pore size distribution are determined through complementary methods to capture distinctive pore structure characteristics. Mercury intrusion porosimetry (MIP) is performed on 20-mm diameter and 20-mm long samples (two samples per facies) to derive the pore throat size distribution and an estimate of the porosity accessible to mercury ($\phi_{Hg}$). Helium porosimetry is performed on the same samples prior to mercury injection, providing an estimate of the porosity accessible to helium ($\phi_{He}$).

The effective porosity of each 20- or 40-mm sample is also measured using the 3-weight method:

$$ \phi_{3w} = \frac{m_{sat} - m_{dry}}{m_{sat} - m_{imm}} \qquad (1) $$

where $m_{dry}$ (g) is the mass of the dry sample, $m_{sat}$ (g) is the mass of the sample saturated with a $25 \text{ g.L}^{-1}$ NaCl brine, and $m_{imm}$ (g) is the mass of the sample immersed in the fluid in which it was saturated.

Nuclear Magnetic Resonance (NMR) analysis is carried out on the two 40-mm diameter and 80-mm long samples after saturation with $25 \text{ g.L}^{-1}$ NaCl brine to derive a pore size distribution reflecting the distribution of the pore volume over surface ratio and estimate the porosity from the brine-saturated pore volume ($\phi_{NMR}$).

## 2.3. Alteration workflow

The limestone samples are altered in a coreflood device (Fig. 1). A series of non-destructive analyses is carried out on each sample in its intact state and after alteration to highlight the impact of the reactive fluid flow on the petrophysical properties.

The samples are imaged with a resolution of 0.625 mm using a medical CT-scanner. A porosity profile along the sample length is obtained from a correlation established between the radiological density and the porosity measured independently on a series of pure calcite samples covering a wide range of porosities. The average porosity value
<figure><img src="image_4.png" /><figcaption>Fig. 1. Schematic view of the coreflood device.</figcaption></figure>

of the different cross-sections provides an estimate of the sample total porosity. Image subtraction between the altered and intact states allows a 3D reconstruction of the induced dissolution pattern. Additional microscanner imaging, allowing higher resolution (20.28 µm for a 40- mm diameter sample), is performed on EUV-2 sample.

The 3-weight method is used to provide a direct estimate of the sample porosity before and after alteration. Water permeability is measured directly in the coreflood device, before and right after the alteration phase, and is monitored during alteration. During permeability measurements, four flow rates Q (m³.s⁻¹) are applied at the inlet and maintained until equilibration of the differential pressure ΔP (Pa). The sample intrinsic permeability k (m²) is then determined using Darcy’s law:

$$k = \mu \frac{LQ}{A\Delta P} \qquad (2)$$

where μ is the fluid dynamic viscosity (Pa.s), L is the sample length (m), and A its cross-sectional area (m²).

Coreflood experiments are performed at room temperature, and a constant confining pressure of 30 bar is applied during the whole experiment. The injected solution is pure Milli-Q® water initially degassed and then kept at equilibrium with a low partial pressure of CO₂ (slightly above 1 bar) using carbon dioxide inflated balloons. The resulting solution has a pH of about 3.9. CO₂ balloons tend to deflate with time and need to be recharged with CO₂ on a regular basis. pH variations induced by the deflation of the balloon have been determined experimentally and are estimated at around 0.1 pH unit. The acid solution is injected at a constant flow rate of 140 cm³.h⁻¹ for 5 days, using a spiral-shaped injection system to ensure, as far as possible, a homogeneous distribution of the fluid across the injection face. The injection system includes two fluid inlets (Fig. 1), one located at the center of the injection system (primarily used) and the second on the periphery (only used for EUV-1 sample).

The outlet pore pressure is kept constant at 2 bar at the downstream end of the device using a back pressure regulator. Differential pressure is

monitored during injection with a differential pressure transducer. Outlet fluids are sampled to monitor dissolution during acid injection. Effluents are acidified using HCl to prevent reprecipitation of dissolved species once CO₂ degasses from the collected fluids and their calcium content is measured by ionic chromatography.

## 3. Results

### 3.1. Facies characterization

The bulk chemical composition derived for each limestone confirms that they are composed almost entirely of pure calcite: more than 98 mol % of CaCO₃, less than 1.5 % of MgCO₃ and less than 0.5 % of SiO₂. Other elements can be found in traces.

Thin section observation (Fig. 2 – A and C) shows that Euville limestone is a grainstone constituted of large angular grains (about 1 mm), mostly crinoid ossicles (more than 95 %). Echinoderm, lamellibranch, and bivalve debris can also be observed sporadically. These observations suggest a distal setting characterized by high hydrodynamic conditions, typically in a mid-ramp depositional environment. Clear and inclusion free syntaxial cement (in white) precipitated on crinoid ossicles can be locally observed, and partly obstructs the intergranular macroporosity (pore-size between 100 and 400 µm). Crinoid axial canal and intragranular microporosity are partly filled with micritic sediments.

Lavoux limestone grains (about 300 µm) are smaller than Euville limestone ones and are mostly highly micriticized ooids, with few echinoderm debris, suggesting an inner ramp depositional environment (Fig. 2 – B and D). Syntaxial cement as well as well crystallized calcite spars precipitated on ooids can be observed and partly obstruct the intergranular macroporosity (pore-size between 100 and 200 µm). Lavoux limestone’s micriticized ooids display higher intragranular microporosity and surface roughness than Euville limestone’s crinoids (Fig. 2 – C and D). These observations are consistent with the almost four times higher specific surface area of Lavoux limestone (0.539 m².g⁻¹)
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Thin sections of Euville limestone (left) and Lavoux limestone (right) observed using optical microscope (A and B, for Euville and Lavoux respectively) and SEM (C and D, for Euville and Lavoux respectively).</figcaption></figure>

compared to Euville limestone (0.138 m²·g⁻¹).

Table 1 compares the different porosity estimates derived on 20-mm diameter and 20-mm long samples using the 3-weight method ($\phi_{3w}$), helium porosimetry ($\phi_{He}$), and MIP ($\phi_{Hg}$). The samples being nearly pure calcite, a theoretical total porosity $\phi_{tot}$ (%) is moreover calculated from dry weight $m_{dry}$ (kg) and bulk volume $V_b$ (m³), using calcite density $\rho_{Ca} = 2.71 \text{ kg.m}^{-3}$:

$$ \phi_{tot} = \frac{V_b - \frac{m_{dry}}{\rho_{Ca}}}{V_b} \qquad (3) $$

Lavoux samples are more porous than Euville samples with $\phi_{tot}$ ranging from 25 % to 28 % and 19 % to 21 %, respectively (Table 1). The porosity values derived from helium porosimetry are in good agreement with the total porosity for Lavoux samples but are around 2 % lower (in porosity units) for Euville samples, indicating the presence of non-accessible porosity within the crinoids in Euville samples. The 3-weight method provides porosity values lower than the total porosity estimates by around 2 % (in porosity units) for Lavoux samples and 5 % (in porosity units) for Euville samples. The discrepancy between 3-weight porosity and helium porosity can be explained by incomplete water saturation due to some pores inaccessible to water but reached by the smaller helium molecules. This issue is even more acute when mercury is

used as a saturating fluid, resulting in lower effective porosity. The larger differences observed for Euville limestone indicate the presence of more difficult-to-access micropores.

MIP data illustrate the bimodal nature of the pore size distribution for Euville and Lavoux limestones (Fig. 3) and highlight clear differences in average size and distribution between macropores and micropores. Euville limestone is characterized by larger pores and a higher fraction of macropores, while Lavoux limestone is characterized by smaller pores and a higher fraction of micropores. The macropore fraction, $f_{macro}$, is estimated using a threshold of 2 µm to separate the microporosity from the macroporosity (Vincent et al., 2011) yielding $f_{macro}^{EUV}$ 0.61 and $f_{macro}^{LAV}$ 0.47.

For Euville limestone, NMR data show a clear bimodal pore size distribution in good agreement with MIP (Fig. 4). In the case of Lavoux limestone, a single broad peak is obtained that does not reflect its bimodal porosity distribution. This is an evidence of diffusional pore coupling, caused by a good connection between micropores and macropores preventing their distinction from NMR data (Vincent et al., 2011; Fleury and Soualem 2009; Fleury et al., 2007). For Euville sample, $\phi_{NMR}$ is higher than $\phi_{3w}$ (Table 2). The 1 % difference (in porosity units) is due to brine remaining within the samples after drying.

**Table 1**

Porosity of Euville and Lavoux limestones measured by different methods. $\phi_{He}$, $\phi_{3w}$, $\phi_{Hg}$ are the porosity using helium porosimetry, 3-weight method and MIP, respectively. $\phi_{tot}$ is the total porosity assuming pure calcite (Eq. (3)).

<table><thead><tr><th>Samples</th><th>Diameter (mm)</th><th>Length (mm)</th><th>φ<sub>tot</sub></th><th>φ<sub>He</sub></th><th>Δφ<sub>tot-He</sub></th><th>φ<sub>3w</sub></th><th>Δφ<sub>tot-3w</sub></th><th>φ<sub>Hg</sub></th><th>Δφ<sub>tot-Hg</sub></th></tr></thead><tbody><tr><td>EUV-MIP-1</td><td>19.54</td><td>13.62</td><td>21.3 %</td><td>19.5 %</td><td>1.8 %</td><td>16.3 %</td><td>5.0 %</td><td>14.4 %</td><td>6.9 %</td></tr><tr><td>EUV-MIP-2</td><td>19.57</td><td>19.42</td><td>19.7 %</td><td>17.7 %</td><td>1.9 %</td><td>15.1 %</td><td>4.6 %</td><td>13.4 %</td><td>6.3 %</td></tr><tr><td>LAV-MIP-1</td><td>19.36</td><td>19.36</td><td>28.2 %</td><td>28.1 %</td><td>0.1 %</td><td>26.1 %</td><td>2.1 %</td><td>24.8 %</td><td>3.4 %</td></tr><tr><td>LAV-MIP-2</td><td>19.52</td><td>19.34</td><td>25.1 %</td><td>24.8 %</td><td>0.3 %</td><td>23.2 %</td><td>1.9 %</td><td>23.9 %</td><td>1.2 %</td></tr></tbody></table>
<figure><img src="image_6.png" /><figcaption>Fig. 3. Mercury intrusion porosimetry data. Solid lines present the pore size distribution, and dotted lines present the cumulative invaded pore volume.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. NMR $T_2$ profiles for EUV-1 (top) and LAV-1 (bottom) samples. Solid lines show the relaxation time distribution, and dashed line the cumulative porosity. As defined by Vincent et al., 2011, the threshold between macropores and micropores (2 µm) is set at $T_2$ = 200 ms (in red on the figure).</figcaption></figure>
<caption>**Table 2**</caption>

Characteristics of the four tested samples before and after alteration. $m_{dry}$ is the mass of the dry sample, $m_{sat}$ is the mass of the sample saturated with $25 \text{ g.L}^{-1}$ NaCl brine, $m_{imm}$ is the mass of the sample immersed in $25 \text{ g.L}^{-1}$ NaCl brine, $\phi_{tot}$ is the porosity calculated using Eq. (3), $\phi_{3w}$ is the porosity estimated using the 3-weight method, $\phi_{CT}$ is the porosity deduced from CT-scanner data, $\phi_{NMR}$ is the porosity estimated from NMR and $k$ is the permeability. Increase factor is calculated as: IF = $k_{altered}/k_{intact}$.

<table><thead><tr><th rowspan="2">Samples</th><th colspan="4">EUV-1</th><th colspan="4">EUV-2</th></tr><tr><th>Intact</th><th>Altered</th><th>Absolute variation</th><th>Relative variation</th><th>Intact</th><th>Altered</th><th>Absolute variation</th><th>Relative variation</th></tr></thead><tbody><tr><td><i>m</i><sub>dry</sub> (g)</td><td>227.68</td><td>217.93</td><td>-9.75</td><td>-4.3 %</td><td>286.72</td><td>278.23</td><td>-8.49</td><td>-3.0 %</td></tr><tr><td><i>m</i><sub>sat</sub> (g)</td><td>240.67</td><td>232.59</td><td>-8.08</td><td>-3.4 %</td><td>303.28</td><td>297.40</td><td>-5.88</td><td>-1.9 %</td></tr><tr><td><i>m</i><sub>imm</sub> (g)</td><td>141.27</td><td>134.52</td><td>-6.75</td><td>-4.8 %</td><td>175.07</td><td>170.96</td><td>-4.11</td><td>-2.3 %</td></tr><tr><td>Φ<sub>tot</sub> (%)</td><td>16.4</td><td>20.4</td><td>4.0</td><td>24 %</td><td>16.6</td><td>19.0</td><td>2.4</td><td>14 %</td></tr><tr><td>Φ<sub>3w</sub> (%)</td><td>13.1</td><td>15.0</td><td>1.9</td><td>15 %</td><td>12.9</td><td>15.2</td><td>2.3</td><td>18 %</td></tr><tr><td>Φ<sub>CT</sub> (%)</td><td>15.9</td><td>19.1</td><td>3.2</td><td>20 %</td><td>15.8</td><td>17.9</td><td>2.1</td><td>13 %</td></tr><tr><td>Φ<sub>NMR</sub> (%)</td><td>14.2</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>k (mD)</td><td>50</td><td>1670</td><td>1620</td><td>33</td><td>40</td><td>1840</td><td>1800</td><td>46</td></tr></tbody></table><table><thead><tr><th rowspan="2">Samples</th><th colspan="4">LAV-1</th><th colspan="4">LAV-2</th></tr><tr><th>Intact</th><th>Altered</th><th>Absolute variation</th><th>Relative variation</th><th>Intact</th><th>Altered</th><th>Absolute variation</th><th>Relative variation</th></tr></thead><tbody><tr><td><i>m</i><sub>dry</sub> (g)</td><td>201.44</td><td>190.91</td><td>-10.53</td><td>-5.2 %</td><td>250.84</td><td>237.20</td><td>-13.64</td><td>-5.4 %</td></tr><tr><td><i>m</i><sub>sat</sub> (g)</td><td>230.01</td><td>221.76</td><td>-8.25</td><td>-3.6 %</td><td>281.46</td><td>271.59</td><td>-9.87</td><td>-3.5 %</td></tr><tr><td><i>m</i><sub>imm</sub> (g)</td><td>127.12</td><td>120.25</td><td>-6.87</td><td>-5.4 %</td><td>155.70</td><td>147.94</td><td>-7.76</td><td>-5.0 %</td></tr><tr><td>Φ<sub>tot</sub> (%)</td><td>28.2</td><td>32.5</td><td>4.3</td><td>15 %</td><td>25.3</td><td>29.4</td><td>4.1</td><td>16 %</td></tr><tr><td>Φ<sub>3w</sub> (%)</td><td>27.8</td><td>30.4</td><td>2.6</td><td>9 %</td><td>24.3</td><td>27.8</td><td>3.5</td><td>14 %</td></tr><tr><td>Φ<sub>CT</sub> (%)</td><td>27.4</td><td>31.6</td><td>4.2</td><td>15 %</td><td>24.3</td><td>28.1</td><td>3.8</td><td>16 %</td></tr><tr><td>Φ<sub>NMR</sub> (%)</td><td>27.1</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>k (mD)</td><td>270</td><td>4400</td><td>4130</td><td>16</td><td>140</td><td>1500</td><td>1360</td><td>11</td></tr></tbody></table>

## 3.2. Impact of alteration at the macroscopic scale

### 3.2.1. Dissolution patterns

3D visualization of dissolution patterns is obtained by subtracting the CT-scanner images acquired in the intact and altered states (Figs. 5 and 6). Despite careful image registration, this process generates incidental noise and therefore requires the application of thresholds to differentiate the actual dissolution-induced porosity increase from the background noise. To avoid bias in interpretation, the obtained 3D dissolution patterns are thus systematically compared with the porosity profiles which provide a quantified dissolution per section and with the series of untreated intact and altered CT-scanner sections (Figs. 5 and 6).

Different dissolution patterns are observed for Lavoux and Euville limestones. Euville samples exhibit some localized dissolution up to about 20 mm from the injection face (Fig. 5). Then, for distances to the inlet beyond 20 mm, dissolution becomes more diffuse (cloudy aspect of subtracted images). Close observation of CT-scanner sections shows evidence of dissolution across the width of the sample such as enlarged macropores (see sections S2.2 and S2.3 in Fig. 5) and areas with increased grey levels indicating unresolved dissolution (see upper half of section S1.2 in Fig. 5). Away from the injection face, the dissolution markers appear to be relatively well distributed over the sections of EUV-1 sample, while areas showing more pronounced dissolution are observed in EUV-2 sample.

The higher resolution of microscanner images acquired for EUV-2 sample allows more in-depth analysis of dissolution processes in Euville limestone (Fig. 7). Comparison of images at different resolutions of altered sections located beyond 20 mm from the injection face (see section S2.2 in Fig. 5 and Fig. 7) shows that even areas with more intense dissolution retain a solid skeleton and therefore do not correspond to dissolution channels. Step-by-step analysis of the series of microscanner images along the sample illustrates the link between the dissolution intensity and the initial porosity distribution (Fig. 7). As Euville limestone is composed of almost pure calcite, the different shades of grey are associated with variations in microporosity, with darker shades corresponding to more porous areas. The intrinsic heterogeneity of EUV-2 sample is illustrated by the three different sections imaged before alteration. The area near the injection face of the sample shows several extensive microporous areas with only a few macropores visible (Fig. 7

– E), while the more distant sections show significantly more developed macroporosity but few microporous areas (Fig. 7 – C, A). The very locally intense dissolution observed at the sample periphery near section S2.1 in the 3D dissolution pattern derived from CT-scanner data (Fig. 5) corresponds to the complete dissolution of a highly microporous zone located just after an upstream zone of significant dissolution (Fig. 7 – F). This preferential dissolution path extends in a fan-shaped structure crossing section S2.2 that develops in more macroporous zones and is characterized by enlarged macropores (Fig. 7 – D, B).

Despite the spiral-shaped injection system, the peripheral acid fluid arrival for EUV-1 sample results in a significant localized dissolution facing the injection point and, even though the acid fluid arrives at the center of EUV-2 sample, dissolution tends to localize on the side of the sample before becoming more diffuse as it moves away from the injection face. The observation of first more localized, then more diffuse dissolution in Euville samples raises the question of a possible impact of the injection system on dissolution initialization.

Unlike Euville samples, Lavoux samples show the development of clear dissolution channels toward the outlet face, with negligible interference from the bedding (Fig. 6). Altered sections in particular show large areas that are completely dissolved. In the case of LAV-1 sample, a dominant wormhole is initiated from an extensive area of localized dissolution facing the injection point and finally crosses the sample from one end to the other. Several minor channels develop at the injection face of LAV-2 sample, but a dominant wormhole eventually emerges and localizes most of the dissolution in the second half without reaching the outlet face. Outside the wormholes, Lavoux limestone appears unaffected by alteration.

Porosity profiles derived from CT-Scanner data provide an average increase in porosity over each cross-section (Figs. 5 and 6) and cannot be used to differentiate between dissolution regimes. Both Lavoux and Euville samples show a larger average porosity increase close to the injection face where far from equilibrium conditions are maintained. The shape of the initial porosity profiles is globally preserved along the length of the samples. For the EUV-2 sample, a similar and small average porosity increase is observed in the area located between 10 and 25 mm from the injection face showing densified dissolution and in the homogeneous dissolution area near the outlet face. Porosity remains unchanged at the very end of the LAV-2 sample as dissolution does not
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Euville samples 3D dissolution patterns derived from image subtraction (at the center), porosity profiles before and after alteration (on the left) and CT-scanner sections before and after alteration (on the right). Position of the CT-scanner sections is indicated on the 3D images and porosity profiles. Positions marked in red indicate the location of thin sections presented in Figs. 11, 12 and 13. S<sub>2-1</sub>, S<sub>2-2</sub> and S<sub>2-3</sub> also indicate the location of the microscanner sections shown in Fig. 7.</figcaption></figure>
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 6. Lavoux samples 3D dissolution patterns derived from image subtraction (at the center), porosity profiles before and after alteration (on the left) and CT-scanner sections before and after alteration (on the right). Position of the CT-scanner sections is indicated on the 3D images and porosity profiles. Positions marked in red indicate the location of thin sections presented in Figs. 14 and 15.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Fig. 7. Microscanner images of EUV-2 sample before (A-C-E) and after alteration (B-D-F). The position of the images is given in Fig. 5.</figcaption></figure>

reach the outlet face.

### 3.2.2. Petrophysical properties

Table 2 gives the petrophysical properties of the samples before and after alteration. Two porosity measurements are provided: the first one is obtained using the 3-weight method, and the second corresponds to the average of the scanner porosity per section. Consistent values are obtained for Lavoux samples, whereas the 3-weight porosity of Euville samples is about 3 % lower (in porosity units) than the porosity estimated from scanner data. As previously shown in section 4.1, this

discrepancy results from the presence of difficult-to-access micropores.

The 3-weight method and the scanner data provide consistent dissolution-induced porosity increases between 2 % and 4 % (in porosity units). The lower mass loss of Euville samples compared to Lavoux samples is associated with a lower absolute porosity increase. When these results are scaled to the sample initial porosity, we obtain a greater relative porosity increase for Euville samples.

Fig. 8 shows the evolution of the apparent permeability deduced from Equation (2) as a function of alteration time. As altered samples may show heterogeneous dissolution patterns, permeability values
<figure><img src="image_13.png" /><figcaption>Fig. 8. Change over time in apparent permeability k normalized to initial permeability k₀.</figcaption></figure>

estimated during alteration from changes in differential pressure for a constant flow rate, as well as those measured at the end of the experiment, should be preferentially referred to as apparent permeabilities. In their original state, Lavoux samples are more porous and 3 to 7 times more permeable than Euville samples. Both limestones show significant permeability increases but follow different trends during alteration (Fig. 8). For Euville samples, permeability increases significantly throughout the alteration experiment, with a higher global increase for EUV-2 sample, while Lavoux samples show only a minor increase in permeability during the first 60 h of alteration. LAV-1 sample shows an intense permeability increase after around 95 h of alteration, corresponding to the wormhole breakthrough observed in Fig. 6. After 120 h of alteration, Euville samples show significantly higher relative change in permeability than Lavoux samples (see increase factors in Table 2). However, the largest final permeability is obtained for LAV-1 sample (Table 2) due to the wormhole reaching the downstream end of the sample.

### 3.2.3. Dissolution rates

As the studied samples are nearly pure calcite limestone, the amount of material dissolved during alteration is equal to the number of moles of calcium ions produced. The outlet fluid analysis provides a global estimate as well as intermediate values. Each fluid sample taken at time $t_i$ corresponds to the total effluent produced between time $t_{i-1}$ and $t_i$. The amount of calcium produced at time $t_i$, $nCa^{2+}(t_i)$ (mol), is then given by:

$$nCa^{2+}(t_i) = \sum_{k=1}^{i} (t_k - t_{k-1}) [Ca^{2+}]_{t_k} Q \quad (4)$$

where $[Ca^{2+}]_{t_k}$ (mol.L⁻¹) is the calcium concentration of the fluid sample taken at time $t_k$ (s) measured by ionic chromatography and Q (L.s⁻¹) is the injection rate.

The evolution of calcite dissolution over time appears to be linear for all samples (Fig. 9 – A), except for LAV-1 sample, which shows a significant change in slope after around 95 h of alteration. For LAV-1 sample, the drop in calcium production rate after 95 h is correlated to the important increase in permeability observed for this sample and can therefore be associated with the wormhole breakthrough. The two distinct regimes identified for the LAV-1 sample correspond then to: 1) dissolution of the rock material through wormhole development until

breakthrough and 2) enlargement of the dominant wormhole. Fig. 9 – A shows that the dissolution rate of LAV-1 sample prior to wormhole breakthrough is similar to the dissolution rate observed for the longer LAV-2 sample, both dissolution rates being higher than the dissolution rates shown by Euville samples. Calcite saturation indexes of the various effluent samples are calculated using JChess thermodynamical modeling software (van der Lee and De Windt, 1999). The obtained saturation indexes indicate that the effluents produced during the alteration experiments prior to any wormhole breakthrough are closer to chemical equilibrium for Lavoux samples compared to Euville samples (Fig. 9 – B). The wormhole breakthrough observed in LAV-1 sample is associated with a sharp decrease in the saturation index, indicating direct transport of the reactive fluid through the wormhole.

The linear evolution of calcite dissolution over time allows the computation of a global mean dissolution rate $R_{mean}$ (mol.s⁻¹) from the total amount of calcium produced $nCa^{2+}_{tot}$ (mol) and the total duration of alteration $t_{tot}$ (s):

$$R_{mean} = \frac{nCa^{2+}_{tot}}{t_{tot}} \quad (5)$$

In our experiment, the total duration of alteration is 120 h. For LAV-1 sample, wormhole breakthrough induces a decrease in the dissolution rate, leading to an underestimation of mean dissolution rates through Equation (5). Thanks to intermediate fluid analysis, we can nevertheless calculate a more representative pre-breakthrough mean dissolution rate (in green in Fig. 10) using the slope of LAV-1 data for $t < 95$ h.

A significantly higher mean dissolution rate is observed for the 100-mm long Lavoux sample (LAV-2) compared to the same length Euville sample (EUV-2). When considering the pre-breakthrough mean dissolution rate, the 80-mm long Lavoux sample (LAV-1) shows a slightly higher mean dissolution rate than the same length Euville sample (EUV-1) (Fig. 10).

### 3.3. Microscopic evidence of dissolution

Observation of the thin sections made from each altered sample (referenced in Figs. 5 and 6) highlights the different responses of Euville and Lavoux limestone with respect to dissolution (Figs. 11 to 15). Clear grain-scale dissolution features are observed in areas showing extensive dissolution: large open dissolution channels and enlarged macropores
<figure><img src="image_14.png" /><figcaption>Fig. 9. A) Cumulative amount of calcium produced during alteration. B) Associated mean saturation indexes (with respect to calcite) calculated using thermodynamic modeling software JChess.</figcaption></figure>

covering several grain sizes (see section S<sub>1.1</sub> in Fig. 11 – A, section S<sub>2.1</sub> Fig. 13 – A, section S<sub>3.3</sub> Fig. 14 – A, section S<sub>4.1</sub> Fig. 15 – A).

Out of the extensive dissolution areas, EUV-1 and EUV-2 samples
retain a solid skeleton with dissolution evidence mainly located on the
now etched cement and grain surfaces (zones 1 and 2 of section S<sub>1-1</sub> in
Fig. 11 – A, zones 1 and 2 of section S<sub>2-1</sub> in Fig. 13 – A), where dissolution
markers can be observed (see section S<sub>1-1</sub> Fig. 11 – A, B). For EUV-1 and
EUV-2 samples, evidence of local dissolution is also observed outside the
extensive dissolution areas (see section S<sub>1-1</sub> in Fig. 11 – B, see section S<sub>2-1</sub>
in Fig. 13 – B), notably in the part of EUV-1 sample showing more diffuse
dissolution (see section S<sub>1-2</sub> in Fig. 12), confirming previous observa-
tions made using CT-scanner and microscanner data suggesting that
dissolution is distributed across the entire width of Euville samples.

The wormholes that develop in LAV-1 and LAV-2 samples cut straight through both ooids and cement (see section S<sub>3.3</sub> in Fig. 14, see section S<sub>4.1</sub> in Fig. 15). The convex shape of the altered cement between two concave altered ooids (see section S<sub>3.3</sub> in Fig. 14 – A) suggests that the ooids are more sensitive to dissolution than the cement. Contrary to Euville samples, no specific dissolution markers are found in Lavoux samples further away from the main dissolution channel. Fig. 14 – B and

Fig. 15 – B show that calcite spars remain intact, confirming the location of dissolution solely in wormholes as previously highlighted by CT-scanner data.

4. Discussion

4.1. Localized versus distributed dissolution

Two different dissolution responses are distinguished for Euville and Lavoux limestones through the combination of CT-scanner and micro-scanner imaging and thin section observation. The highly localized dissolution observed for Lavoux samples (Fig. 6, Fig. 14 – A, Fig. 15 – A) and the associated permeability evolution during alteration, showing minor increase until approaching breakthrough (Fig. 8), are characteristic of a classic wormhole regime (Soulaine et al., 2017). The localization of the dissolution is confirmed by microscale observations (Fig. 14 – B, Fig. 15 – B) showing no dissolution markers outside of the main dissolution channels clearly visible in the CT-scanner images. In contrast, beyond the first approximately 20 mm from the injection face, Euville samples show dissolution distributed over their entire width. The
<figure><img src="image_15.png" /><figcaption>Fig. 10. Global mean Ca²⁺ flux R<sub>mean</sub> (mol.s⁻¹) for each experiment. In green is presented the total mean Ca²⁺ flux inferred considering no wormhole breakthrough.</figcaption></figure>

distributed dissolution pattern is hinted at by the CT-scanner images (Fig. 5) and confirmed by the microscanner images showing that a solid skeleton is preserved even in areas where dissolution is more pronounced (Fig. 7) and by the observation of dissolution markers over the entire surface of the thin sections (Fig. 11 – B, Fig. 12, Fig. 13 – B). Dissolution in EUV-1 sample is relatively well-distributed in the cross sections (Fig. 5). The permeability evolution observed for this sample is consistent with the trend expected for homogeneous dissolution (Fig. 8) (Menke et al., 2023; Egermann et al., 2005). As observed for EUV-2 sample, the distributed dissolution pattern of Euville limestone may display more intense dissolution pathways clearly correlated to more macroporous areas present in the intact sample (Fig. 7). The corresponding increase in permeability is enhanced by the widening of macropores within the more intense dissolution path (Fig. 8).

The explanation for the distinct dissolution responses obtained for the two studied almost pure calcite limestones subjected to similar experimental conditions lies in their differences in microstructure. Despite its lower macroporous fraction and smaller macropores, Lavoux limestone is characterized by higher permeability linked to higher global porosity and better connectivity between macropores and micropores, as highlighted by the diffusional coupling observed in NMR analysis (Fig. 4) and by the consistency between total and effective porosity estimates (Table 1). The injected acid solution is then able to access both macropores and micropores. The flushing of intra-ooid micropores is confirmed by the observation of half-dissolved ooids in thin sections (Fig. 14 – A and Fig. 15 – A). As indicated by the effluent calcite saturation index prior to any wormhole breakthrough, the higher reactivity provided by the larger specific surface area of micritized ooids brings the injected solution closer to equilibrium with calcite as it flows through the porous matrix. Dissolution thus occurs close to areas supplied with fresh acid solution. Localized dissolution nuclei initially develop at the injection surface due to local fluid flow heterogeneities, creating pathways of least resistance to the reactive fluid. Once dissolution channels are initiated, they concentrate the flow of fresh acid solution, which supports their progression along the flow direction mostly regardless of the bedding until the emergence of dominant wormholes.

Euville limestone is characterized by larger macropores, less accessible micropores and poor communication between micropores and macropores, as supported by NMR, MIP, and helium porosimetry. The distributed dissolution within Euville samples is caused by the combined effect of higher fluid velocity in the better connected macropore network (Bauer et al., 2024) and lower reactivity due to lower specific surface

area, allowing the acid solution to remain further from equilibrium while circulating through the porous matrix. Dissolution occurs at the surface of grains bordering macropores, gradually enlarging them, as confirmed by microscanner images and thin section observations. Unlike Lavoux limestone, where whole pieces of ooids have been dissolved, the grain structure of Euville limestone is preserved during alteration. The degree of homogeneity of the dissolution distribution is therefore strongly controlled by the initial microstructure, and more specifically by the spatial distribution of macropores.

The transition from a more localized to a more diffuse dissolution when moving away from the injection face for the Euville samples raises the question of a possible impact of the injection system despite its spiral shape. A more diffuse injection system should be implemented to ensure that the more localized dissolution observed in the first 20 mm of Euville samples is related to inlet flow conditions and does not correspond to the inherent response of these samples.

## 4.2. Consistency with Péclet and Damköhler classification

The two types of dissolution patterns exhibited by Euville and Lavoux limestones will strongly influence the hydromechanical behavior of these formations at a larger scale. Linking these different responses to intrinsic properties of the intact rock and alteration conditions would enable a priori prediction of the dissolution regime. We therefore seek to integrate key microstructure proxies in Péclet and Damköhler numbers to better capture the specific characteristics of microporous carbonates.

Reactive transport is described by an advection–diffusion-reaction equation that, once scaled, introduces Péclet (Pe) and Damköhler (Da) dimensionless numbers that are thus commonly used to classify the different dissolution regimes observed in carbonate rocks (Al-Arji et al., 2021; Kurotori et al., 2019; Al-Khulaifi et al., 2018; Soulaine et al., 2017; Varloteaux et al., 2013a; Varloteaux et al., 2013b; Egermann et al., 2010; Steefel and Maher 2009; Golfier et al., 2002; Bekri et al., 1995; Daccord et al., 1993a).

Péclet number compares the advection rate to the diffusion rate (Golfier et al., 2002):

$$Pe = \frac{v_i L_c}{D} \qquad (7)$$

where $v_i$ is the interstitial fluid velocity (m.s⁻¹), $L_c$ is a characteristic length (m), and $D$ is the molecular diffusion coefficient (m².s⁻¹). The molecular diffusion coefficient corresponds to the molecular diffusion coefficient of the H⁺ ion at 25 °C and according to Lee and Rasaiah,
<figure><img src="image_16.png" /><figcaption>**Fig. 11.** Thin section S₁₋₁ taken in the initial part of the EUV-1 sample showing some localized dissolution. (A) Regions near extensive dissolution areas allowing identification of the local markers of dissolution in Euville limestone (etched interfaces). (B) Regions farther from extensive dissolution areas showing the presence of the identified local dissolution markers.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Fig. 12. Thin section S1-2 taken in the homogeneously altered part of EUV-1 sample, with a focus on two macroporous regions evidencing dissolution markers.</figcaption></figure>

2011, D=7.6 10⁻⁹ m².s⁻¹. The interstitial fluid velocity can be deduced from the experimental data: vᵢ = Q/(Aφₑ), where φₑ is the effective porosity taken equal to φ₃w.

Damköhler number compares the reaction rate to the advection rate. Considering a first order reaction-rate (Morse and Arvidson, 2002; Plummer et al., 1978; Plummer and Wigley, 1976) leads to the following expression (Soulaine et al., 2017):

$$Da = \frac{\kappa L_c}{v_i} \qquad (8)$$

where κ (s⁻¹) is the reaction rate constant. The estimation of κ is not straightforward, and various expressions can be found in the literature. The measured average dissolution rates cannot be used to evaluate this parameter due to the highly localized dissolution in Lavoux limestone. As we consider pure calcite samples, κ can be related to calcite dissolution rate (Menke et al., 2015):

$$\kappa = \frac{r_{Ca}S_s}{n_{Ca}} \qquad (9)$$

where r<sub>Ca</sub> (mol.m⁻².s⁻¹) is the dissolution rate of calcite, S<sub>s</sub> (m⁻¹) the specific surface area, and n<sub>Ca</sub> (mol.m⁻³) the number of moles of calcite per solid volume unit. We take for r<sub>Ca</sub> the value measured by Pokrovsky et al., (2005) in similar experimental conditions (T = 25 °C and pCO₂ = 1.5 bar): 2.55 10⁻⁵ mol.m⁻².s⁻¹ (Pokrovsky et al., 2005). S<sub>s</sub> is calculated from the measured BET specific surface area S<sub>BET</sub> (m².g⁻¹): S<sub>s</sub> = S<sub>BET</sub>m<sub>dry</sub>/V<sub>s</sub>, with V<sub>s</sub> the sample solid volume (m³). Lastly, n<sub>Ca</sub> can be deduced from the molar mass of calcite M<sub>Ca</sub> = 0.1001 kg.mol⁻¹ and the sample characteristics: n<sub>Ca</sub> = m<sub>dry</sub>/(M<sub>Ca</sub>V<sub>s</sub>). The sample solid volume is computed from the bulk volume and the scanner porosity, which encompasses both interconnected and occluded porosity: V<sub>s</sub> = (1-φ<sub>CT</sub>)V<sub>b</sub>. Note that the scanner porosity is very close to the total porosity estimated from Equation (3) (Table 2).

We thus obtain the following expressions of Péclet and Damköhler:

$$Pe = \frac{QL_c}{A\phi_{3w}D} \qquad (10)$$

$$Da = \frac{r_{Ca}S_{BET}M_{Ca}A\phi_{3w}L_c}{Q} \qquad (11)$$

These expressions are well suited for experimental studies as most parameters are either intrinsic (D and M<sub>Ca</sub>), directly related to the experimental conditions (Q and r<sub>Ca</sub>) or easily measurable (A, φ₃w and S<sub>BET</sub>). The only undefined parameter at this stage is the characteristic length (L<sub>c</sub>) which appears both in Pe and Da and should be representative of transport processes at the pore scale (Golfier et al., 2002). As previously detailed, Euville and Lavoux limestones are characterized by very distinct microstructures, with differences in grain structure and pore size distribution controlling their response to dissolution. Besides the measured effective porosity (φ₃w) and specific surface area (S<sub>BET</sub>), the characteristic length (L<sub>c</sub>) is the only parameter related to microstructure in the expressions of Péclet and Damköhler numbers. This parameter therefore needs to be defined with a consistent approach to optimally represent the microstructural characteristics of the two limestones. Different characteristic lengths are considered in the literature and can be estimated either from direct observation of high-resolution images: average pore diameter (d<sub>pore</sub>) and average grain diameter (d<sub>grain</sub>), or computed from macroscopic parameters assuming a model porous structure: √k (standard capillary model) (Golfier et al., 2002) and g<sub>s</sub> (equivalent grain diameter of a cubic packing of regular spheres) (Yang et al., 2020; Voltolini and Ajo-Franklin 2019; Al-Khulaifi et al., 2018; Menke et al., 2017). Some studies even use the sample length L<sub>sample</sub> (Smith et al., 2013).

The Péclet and Damköhler numbers computed from Eqs. (10) and (11) for the four studied samples from the different characteristic lengths are represented in Pe-Da diagram (Fig. 16 – Standard approach). The wide dispersion of the different sets of values confirms the critical importance of defining a relevant characteristic length. Despite the
<figure><img src="image_18.png" /><figcaption>**Fig. 13.** Thin section S₂-1 taken in the initial part of EUV-2 sample showing some localized dissolution. (A) Region near extensive dissolution area characterized by a large open dissolution channel with dissolution markers on its periphery. (B) Region far from extensive dissolution areas showing local dissolution markers evidencing the distribution of dissolution across the sample width.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>**Fig. 14.** Thin section S₃.₃ taken in LAV-1 sample. (A) Region crossed by the main wormhole allowing identification of the local markers of dissolution in Lavoux limestone: etched interfaces and half-dissolved ooids. (B) Region further from the main wormhole with no clear evidence of dissolution and numerous intact calcite spars.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Fig. 15.** Thin section S₄-1 taken in LAV-2 sample. (A) Region crossed by the main wormhole showing etched interfaces and dissolved ooids. (B) Region further from the main wormhole with no clear evidence of dissolution and numerous intact calcite spars.</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>Fig. 16. Pe vs Da diagram for the different characteristic length estimates. Pe and Da computed from Eqs. (10) and (11) (standard approach) for both Lavoux and Euville samples and from Eqs. (12) and (13) (specific approach) for Euville samples.</figcaption></figure>

clearly different dissolution patterns observed, whatever the characteristic length used, the Péclet and Damköhler numbers computed using Eqs. (10) and (11) do not allow to assign Euville and Lavoux samples to different dissolution domain, indicating that the underlying assumptions do not capture the key microstructure characteristics.

Unlike Lavoux limestone, where acid solution flushes both intergranular macropores and intra-ooid micropores, transport in Euville limestone is mainly controlled by the macroporous network, resulting in dissolution primarily at the grain surface. We therefore define a new set of Péclet and Damköhler numbers for Euville samples, replacing total porosity by macroporosity ($\phi_{macro} = f_{macro}\phi_{3w}$) and using a classic geometric model to assess the specific surface area associated with the grain surface: $S_s = \frac{6}{d_{grain}}$ (White et al., 1996). We then obtain the following set of Péclet and Damköhler numbers specific to Euville samples:

$$Pe_{EUV} = \frac{QL_c}{A\phi_{macro}D} \qquad (12)$$

$$Da_{EUV} = \frac{6r_{Ca}M_{Ca}V_{b}(1 - \phi_{CT})A\phi_{macro}L_{c}}{d_{grain}m_{dry}Q} \qquad (13)$$

The specific surface area obtained using the geometric model is two orders of magnitude lower than the specific surface area computed from BET measurements, resulting in significantly lower Da numbers (Fig. 16 – Specific approach). These more realistic assumptions to describe Euville limestone behavior allow a clear distinction between Euville and Lavoux samples by shifting Euville samples towards slightly higher Péclet numbers and significantly lower Damköhler numbers, more compatible with a uniform dissolution regime (Fig. 16 – Specific approach). Since the geometric model does not take surface roughness into account, the effective reactive surface of Euville grains may be underestimated, leading to somewhat higher but still significantly lower Damköhler numbers than those calculated from the measured BET specific surface area. These results show that the accessibility of intra-granular microporosity to reactive fluid is the main differentiating factor between Euville and Lavoux limestones, as it can account for variations

up to two orders of magnitude in Damköhler number values.

The remaining step consists in defining a characteristic length consistent with the behavior of the two limestones studied. For Euville limestone, the average macropore diameter naturally appears to be the most relevant characteristic length:

$$L_c^{EUV} = d_{pore}^{EUV} \qquad (14)$$

For Lavoux samples, the various characteristic lengths proposed fail to account for transport occurring in both intergranular macroporosity and intragranular microporosity. We thus propose to define a characteristic length $L_c^{LAV}$ that extends the average macropore diameter $d_{pore}^{LAV}$ by adding a length $L_{micro}^{LAV}$ accounting for the contribution of the intragranular microporosity:

$$L_c^{LAV} = d_{pore}^{LAV} + L_{micro}^{LAV} \qquad (15)$$

The intragranular microporosity is first deduced from the effective porosity and the macroporosity:

$$\phi_{micro}^{LAV} = \frac{\phi_{3w}^{LAV} - \phi_{macro}^{LAV}}{1 - \phi_{macro}^{LAV}} \qquad (16)$$

An average micropore volume per grain is then computed:

$$V_{micro}^{LAV} = \phi_{micro}^{LAV} \frac{4\pi}{3} \left( \frac{d_{grain}^{LAV}}{2} \right)^3 \qquad (17)$$

And $L_{micro}^{LAV}$ is simply taken as the diameter of a sphere with volume $V_{micro}^{LAV}$:

$$L_{micro}^{LAV} = (\phi_{micro}^{LAV})^{1/3} d_{grain}^{LAV} \qquad (18)$$

The characteristic length of Lavoux limestone is finally obtained by injecting Eq. (18) into Eq. (15):

$$L_c^{LAV} = d_{pore}^{LAV} + (\phi_{micro}^{LAV})^{1/3} d_{grain}^{LAV} \qquad (19)$$
<figure><img src="image_22.png" /><figcaption>**Fig. 17.** Pe vs Da diagram for the specific characteristic lengths and expressions of Péclet and Damköhler numbers derived for Lavoux and Euville samples. The two Euville samples are overlapped.</figcaption></figure>

When reported in Pe-Da diagram, the representative Péclet and Damköhler numbers obtained (using Equation (12) and (13) and $L_c$ the size of the macropores for Euville samples, and Equation (10) and (11) and $L_c^{LAV}$ defined by Equation (19)) seem consistent with the wormhole dissolution regime observed for Lavoux samples and the more diffuse dissolution regime, referred to as distributed, observed for Euville samples (Fig. 17). These results show that guiding the computation of Péclet and Damköhler numbers by a detailed understanding of microstructural controls on reactive transport can provide a relevant classification of dissolution patterns for carbonate samples with a complex microstructure. Dissolution experiments performed at different injection rates would allow to explore other domains in Pe-Da diagram to deepen this analysis.

The computation of global Péclet and Damköhler numbers is only intended to provide information on the expected dissolution regime for different limestones. This approach does not account for the spatial heterogeneity of the pore size distribution at the origin of the more intense dissolution zones observed for EUV-2 sample (Fig. 7), which raises the question of considering the spatial variability of local properties, such as local porosity and macroporosity levels. In addition, the development of dissolution is accompanied by global and local changes, particularly in the case of Lavoux limestone, where wide dissolution channels are formed. The breakthrough of the dominant wormhole observed in LAV-1 sample notably results in sharp variations in permeability (Fig. 8) and effluent saturation index (Fig. 9). The evolution of Péclet and Damköhler numbers over time will impact further development of the dissolution.

In the case of Euville limestone, microscanner and thin section observation (Figs. 7 and 11-13) shows that dissolution essentially leads to the widening of macropores. Global Péclet and Damköhler numbers can therefore continue to be calculated from Eqs. (12) and (13). The dissolution-induced increase in macroporosity and average macropore diameter will not, however, lead to significant changes in global Péclet and Damköhler numbers. In the case of Lavoux limestone, the

development of a wormhole will focus the transport of the reactive fluid at a higher velocity and the diameter of the wormhole becomes the relevant characteristic length. Eqs. (10) and (11) no longer apply to compute global Péclet and Damköhler numbers.

### 4.3. Contribution of reactive transport modeling

Reactive transport modelling offers an interesting approach to explore the spatial variability and temporal evolution of Péclet and Damköhler numbers (Steefel and Hu, 2022). Our experimental study shows that depending on the accessibility of intragranular microporosity, two microporous limestones can respond differently to the circulation of a reactive fluid injected in similar conditions. However, standard modeling approaches at the pore network scale consider a non-porous solid matrix and thus ignore exchanges between intergranular and intragranular porosity (Menke et al., 2023, Soulaine et al., 2017). The global porosity and pore sizes of the model porous media remain moreover relatively high as the whole pore system is represented. Another issue is the need to vary injection and reactivity conditions significantly to induce a change in dissolution figures.

The results obtained in our study contribute to the development of a multi-scale modeling approach integrating the Darcy-Brinkman equation to represent transport in a porous medium consisting of three phases: macropores resolved by imaging, microporous zones associated with an intermediate gray level, and the non-porous solid phase (Bauer et al., 2024). Such an approach allows to address carbonates with intragranular microporosity more or less well connected with intergranular pores. Depending on the level of permeability assigned to the microporous phase, reactive fluid transport will take place through both intergranular and intragranular porosity, as in Lavoux limestone, or be restricted mainly to the intergranular pore network, as in Euville limestone. Tracer injection experiments are being considered to further characterize these phenomena.

Once calibrated, the transport model will enable us to calculate the
local distribution of initial Pe and Da numbers. The next step will be to
couple this model with dissolution laws to determine the evolution of
the transport field as a function of time and ultimately reproduce the
development of dissolution patterns.

5. Summary

We studied the impact of CO₂-acidified fluid flow on two different limestones with nearly pure calcite composition but very different microstructures (crinoidal and micritized oolites) and petrophysical properties (porosity, permeability, pore size distribution, specific surface area).

* For similar injection conditions, two different responses to dissolution are evidenced by CT-scanner and thin section observation. Euville limestone exhibits distributed dissolution over the entire width of the sample and retains a solid skeleton, whereas localized dissolution (wormhole development) is observed in Lavoux limestone.

* These different dissolution responses have been related to two specific properties: 1) The degree of connectivity between micropores and macropores enabling or preventing the circulation of reactive fluid within the intragranular microporosity; 2) The chemical reactivity associated with the accessible specific surface area implying more or less rapid fluid equilibration.

* Based on this in-depth understanding of the dissolution processes in the two studied limestones, we have proposed a specific parametrization of Péclet and Damköhler numbers accounting for the specific accessibility to the intragranular microporosity and the associated specific surface area which led to consistent positioning in Pe-Da diagram with respect to the observed dissolution patterns. We have notably defined a specific characteristic length for each limestone.

CRediT authorship contribution statement

**Theo Briolet:** Writing – original draft, Investigation, Formal analysis. **Elisabeth Bemer:** Writing – review & editing, Methodology, Formal analysis, Conceptualization. **Olivier Sissmann:** Writing – review & editing, Methodology, Conceptualization. **Jerome Fortin:** Writing – review & editing, Supervision.

Data availability

Ca²⁺ concentrations obtained through ionic chromatography measurements are available through Mendeley Data at https://doi.org/10.17632/ht97kyzcm9.1.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors would like to acknowledge Maxime Pélerin for his help and support in the CT-scanner imaging and treatment. They would also like to thank Matthieu Mascle, Souhail Youssef and Nada Ben Amor for their help and the fruitful discussions on the subject.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

**Appendix A. Supplementary material**

In this section, the total amount of dissolved calcite (expressed in mol Ca²⁺) estimated by weighing of the samples prior and after alteration,

and by ionic chromatography, is first presented. The various choices of
characteristic lengths found in literature, and associated Péclet and
Damköhler numbers computed from Equations 10 and 11 (Standard
approach) or from Equations 12 and 13 (Specific approach) are then
presented. The characteristic lengths adopted for Euville and Lavoux
samples are finally presented, as well as the corresponding Péclet and
Damköhler numbers computed respectively from Equations 10 and 11
for Lavoux, and from Equations 12 and 13 for Euville. Supplementary
material to this article can be found online at https://doi.org/10.1016/j.gca.2025.03.019.

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