# Experimental insights into early cement development in carbonate aquifers: from diffusion to surface-controlled calcite growth

J. Douçot, J-B. Regnet, F. Bourdelle, J. Corvisier, P. Robion, D. Deldicque, C. David, S. Richoz, J. Fortin

► To cite this version:

J. Douçot, J-B. Regnet, F. Bourdelle, J. Corvisier, P. Robion, et al., Experimental insights into early cement development in carbonate aquifers: from diffusion to surface-controlled calcite growth. Geochimica et Cosmochimica Acta, 2026, 417, pp.11-25. 10.1016/j.gca.2026.01.051. hal-05498518

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# Experimental insights into early cement development in carbonate aquifers: from diffusion to surface-controlled calcite growth

J. Douçot<sup>a, *</sup>, J-B. Regnet<sup>a</sup>, F. Bourdelle<sup>a, b</sup>, J. Corvisier<sup>b, c</sup>, P. Robion<sup>a, b</sup>, D. Deldicque<sup>c</sup>, C. David<sup>a, d</sup>, S. Richoz<sup>d</sup>, J. Fortin<sup>c, d</sup>

## ARTICLE INFO

Associate editor: Mariette Wolthers

**Keywords:**

Carbonates early diagenesis

Laboratory diagenesis

Early cements

Aragonite

Calcite

Neomorphism

## ABSTRACT

Despite their geological significance, the thermochemical processes leading to the formation of early carbonate cements remain elusive. To bridge this knowledge gap, we carried out here laboratory-simulated diagenesis on aragonite ooids. They were placed in autoclaves, filled with distilled water, and subjected to varying temperatures and durations. Our results focus on the transformation from aragonite to calcite with temperature-dependent kinetics. At the grain scale, considered as a thermodynamic system on its own, two distinct stages of microstructural evolution were observed. In the first stage, diffusion processes predominate: the ooids experience progressive dissolution while a fringe of calcite cement forms around their periphery. In a second stage, radial diffusion stops and transformations are dominated by surface-controlled processes, characterized by calcite crystal growth within the ooids. The end-result is generally referred to as “neomorphism” in natural analogues. The transition from the diffusion-dominated to the surface-controlled stage is temperature-dependent and does not occur below 150°C. This behaviour can be explained by the progressive growth of the calcite fringe, which isolates the ooid from the surrounding pore water, while internal aragonite dissolution continues within the grain. These experiments show that early calcite cements, similar to those observed in meteoric phreatic environments, can grow without any external CaCO₃ input. They also show that neomorphism in ooids requires the closure of the ooid system, a condition that can occur at any stage of diagenesis. Finally, our experiments support the presence of a diffusive boundary layer, offering a process-based refinement of the traditional ‘thin film’ concept.

## 1. Introduction

Deciphering the diagenetic stages experienced by carbonate rocks remains a major challenge in sedimentary geology (Larsen and Chilingarian, 2010). In particular, this knowledge helps clarify the origin and evolution of carbonate coastal aquifers, which provide a significant share of the world's freshwater resources (Bear et al., 1999). Substantial advances were made in this field between the 1950s and 1970s, when grain-scale studies elucidated the relationships between cement morphologies and their diagenetic environments. It is now well established that each environment has a distinct signature, reflected in the specific microstructures it produces (Bathurst, 1961; Folk, 1964; Bathurst, 1972; Scholle and Umer-Scholle, 2003; Flügel, 2010). Among these, early

meteoric cements are of particular interest, as they form a rigid framework that is chemically stabilized and that partially inhibit mechanical compaction during burial (Purser, 1978; Moore, 2001; Croizé et al., 2010; Volery et al. 2010; Brigaud et al., 2014; Regnet et al., 2015a, 2015b). The natural environments where such cements develop are well documented (Folk, 1964; James and Choquette, 1989; Moore, 2001; Scholle and Umer-Scholle, 2003; Flügel, 2010). They predominantly form during periods of subaerial exposure, when meteoric waters percolate through the sediments. In coastal settings, the result is a hydrogeological structure known as “coastal aquifer”: a lens of freshwater resting above rocks or sediments saturated with seawater. Within the resulting vadose and meteoric-phreatic zones, the interstitial fluid is highly aggressive and possesses a significant dissolving power due to the

<footnote><sup>a</sup> CY Cergy Paris Université, Sorbonne Université, CNRS, Institut des Sciences de la Terre de Paris, ISTE>P, F-95000 Cergy, France</footnote>

<footnote><sup>b</sup> Mines ParisTech, PSL University, Centre de Géosciences, 35 Rue Saint Honoré, Fontainebleau Cedex 77305, France</footnote>

<footnote><sup>c</sup> Laboratoire de Géologie, Ecole Normale Supérieure, CNRS, UMR8538, PSL Research University, 75005 Paris, France</footnote>

<footnote><sup>d</sup> Department of Geology, Lund University, Lund, Sweden</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: judoucot@yahoo.fr (J. Douçot).</footnote>
presence of aqueous CO₂. This drives intense mineralogic trans- formations, mainly the replacement of unstable aragonite to stable low- Mg-calcite (Moore, 2001; Scholle and Umer-Scholle, 2003), including “neomorphic” processes (sensu Dickson, 2003). More specifically, iso- pachous low-Mg calcite cements precipitating in meteoric-phreatic environment have been extensively documented, particularly in Holo- cene sediments from the Bahamas (Bathurst, 1972; Harris, 1979; Halley and Harris, 1979; Budd, 1988; Budd and Land, 1990). These cements develop at grain peripheries, exhibit a tangential growth pattern and typically display the characteristic “dog tooth” morphology (Flügel, 2010). Their formation is often associated with partial internal disso- lution of the host grains. Cement volume, which can be approximated by the extent of aragonite-to-calcite transformation (Halley and Harris, 1979), mostly depends on (i) the time span of exposure to meteoric waters and (ii) the saturation state of the fluids with respect to carbonate mineral species. If the exposure time is sufficiently long, the process can result in porosity inversion and the development of molidic porosity (Scholle and Umer-Scholle, 2003). These criteria are now broadly acknowledged and routinely used to identify early meteoric-phreatic environments in the natural systems, although similar fabrics have oc- casionally been reported to form in marine waters (Melim et al., 1995).

Quantitative studies of early diagenesis in meteoric-phreatic envi- ronments have also been conducted. Research on the cementation ki- netics has been initiated by Halley and Harris (1979), Dravis (1979, 1996), Berner (1980), and Budd (1988). However, the processes con- trolling the growth of the early cements in this specific environment have not yet been fully understood from a thermochemical point of view. It seems challenging for two intrinsic reasons. On one hand, field data generally provides only the end products of diagenesis, making it difficult to reconstruct early stages (Bathurst, 1972; Wilkinson, 1984; Scholle and Umer-Scholle, 2003). On the other hand, most analytical techniques, for evaluating mineralogical transformations and interstitial fluid composition (such as X-Ray-Diffraction and Induced-Coupled- Plasma) yield only bulk or averaged measurements, obscuring grain- scale processes.

Previous studies suggest that the growth of early cements is governed by local dissolution, diffusion and precipitation processes (Berner, 1980; Pingitore, 1982; Lasaga, 1998), which require experimental investiga- tion at the grain scale to be fully understood. To this respect, many laboratory studies have shed light on the processes governing the for- mation of early cements. All the approaches share common features: (i) they used a sedimentary precursor sampled from the field, (ii) they saturated the sedimentary precursor with fluid (seawater, freshwater or brines), (iii) they accelerated the reaction kinetics by different means, or by a combination of these means – temperature increase, pressure in- crease, CO₂ degassing, fluid circulation. Thus, in order to understand the formation of micritic limestones, Hathaway and Robertson (1961, quoted by Bathurst, 1972) subjected an aragonite carbonated mud to a temperature of 400°C and a pressure of 3.45 MPa. They observed a transformation from aragonite to calcite at the microscale, showing that this natural process could be experimentally reproduced. Posterior studies sought to more closely replicate natural conditions. Sharma (1968), imposing sea water fluid flow and CO₂ degassing on quartz and carbonate grains, observed rim cementation and early diagenesis microstructure. Thorstenson and Mackenzie (1972), Badiozamani et al. (1977), using CO₂ degassing and distilled water at temperature ranging from 25 to 75°C, succeeded in recreating vadose and phreatic micro- structures on a skeletal sand, providing valid recognition criteria for field studies. Bhattacharyya and Friedmann (1983) heated an ooid sand filled with distilled water to 250°C and observed neomorphic micro- structures inside the grains. In order to determine changes in organic geochemistry, Ferguson et al. (1984) saturated two different ooid sands with seawater, heated at temperatures ranging from 100 to 210°C. They concluded that organic matter plays a key-role in cement growth ki- netics. Neilson (1990), using also sea water and on different ooid sands, emphasized the role of nucleation and crystal growth to explain cements

morphology. On related topics, Molenaar and Venmans (1992) investi- gated mechanical strength and porosity evolutions for samples produced in the laboratory. More recently, Casella et al. (2017), Pederson et al. (2020) and Forjanes et al. (2022) used hydrothermal treatment on multiple present-day seashells to document, measure and develop geochemical proxies for paleoenvironmental studies. Finally, Hashim and Kaczmarek (2020) explored the control of diagenesis on carbonate micro textures using various aragonite reactants (including ooids), heated to various temperatures from 50°C to 200°C, and saturated with different fluids, demonstrating an inverse relationship between crystal size on temperature, as well as the importance of the sedimentary pre- cursor on crystalline microstructures.

While these studies have greatly advanced our understanding of diagenesis, key questions remain: What thermochemical processes govern early cement growth at the grain scale? Are there distinct stages in the formation of early cements, and what can be learned from tracking their development over time? What are the implications for their geological significance and for our understanding of natural car- bonate systems evolution? To address these questions, we synthesized phreatic-meteoric cements by subjecting a sedimentary precursor to hydrothermal treatment. We then tracked the evolution of microstruc- tures over time, aiming to identify the thermochemical processes that control their formation.

## 2. Materials and methods

### 2.1. Composition of the sedimentary precursor

The sedimentary precursor selected for this study is an ooid sand provided by Calcean®, collected from the shore face of Finley Cay Is- land, Bahamas (Fig. 1a and 1b). The sediment was sorted by grain size, and the 300–600 µm fraction was selected for the experiments, as it contains the highest proportion of ooids. X-ray diffraction analysis confirmed that the sorted sand is composed of 99% aragonite (see Sec- tion 2.3). Grain type, size distribution, aspect ratios were characterized using optical microscopy (Olympus® DSX110) and analysed with ImageJ software. Within the sorted fraction, ooids account for ~90% of the grains with bioclasts comprising the remaining ~10% (based on 53 grains observed). Based on measurements of 100 grains, the average grain diameter is 436 µm (standard deviation of 78 µm). The grains exhibit an average circularity of 0.73 (± 0.09) and an average shape factor 0.82 (± 0.09). It is thus a fair approximation to consider our grains as spheres. To get a precise idea of the internal porosity of a Finley Cay ooid, we first determined the average mass of a single grain by dividing the total mass of a sand volume by the number of grains it contained. From a weight of 0.032 g ± 0.001 g measured on 331 grains, the average ooid mass is therefore m_ooid = 9.36 × 10⁻⁵ g. Knowing the mean ooid radius r_ooid = 218 µm and the density of aragonite (ρ aragonite = 2930 kg m⁻³), we calculated the mass of a porosity-free ideal aragonite sphere using m_ideal = ρ aragonite (4/3)πr_ooid³, which gives m_ideal = 1.27 × 10⁻⁴ g. Then, the porosity Φ_ooid is given by the following equation:

$$ \Phi_{ooid} = 1 - \frac{m_{ooid}}{m_{ideal}} $$

and with the values defined above, the internal porosity Φ_ooid is 24% ± 3.5%.

### 2.2. Experimental protocol

Experiments were carried out using four home-designed autoclaves manufactured by Maximator® (Fig. 2). Each autoclave consists of a three-part stainless-steel body and an internal leakproof Polyether ether ketone (PEEK) bucket, that can be opened on both ends to remove lithified samples. For each experimental run, 60 g ± 0.5 of distilled water were poured into the bucket, followed by 15 g ± 0.5 of sand which
<figure><img src="image_4.png" /><figcaption>Fig. 1. Sedimentary precursor. (a) The Finlay Cay sand before sorting. (b) The Finlay Cay sand after sorting.</figcaption></figure>

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

<figure><img src="image_6.png" /><figcaption>Fig. 2. Autoclave designed for experimental settings.</figcaption></figure>

settled spontaneously, preventing the trapping of air pockets. The autoclaves were then sealed and placed in a Memmert®UN260 oven heated to one of three target temperatures: 120°C, 150°C, and 200°C. Heat diffusion within the autoclave was modelled using a 1D finite difference Python code, showing complete thermal equilibrium after 1 h 42 min, regardless of the target temperature. The autoclaves remained in the oven for a variable length of time, from 6 h to 6 months, after which the resulting microstructures were observed. A summary of the experiments is given in the Table 1. Internal water pressure in the autoclave was calculated using the Wagner regression (Huang, 2018), yielding values of 2.03 bars at 120°C, 4.08 bars at 150°C, and 13.90 bars at 200°C. At the end of each experiment, the temperature was gradually reduced to 20°C over 1 h and 30 min before opening the autoclave. By convention, the experiment is considered to start when the autoclave is placed in the oven, so that the time required to reach thermal equilibrium is included in the total heating duration. Conversely, the

<caption>**Table 1**</caption>

Summary of experiments. Ω<sub>aragonite</sub> was calculated using the free version of the fluid – rock interaction software CHESS. As the calculation corresponds to equilibrium conditions, this value is only indicative because equilibrium is never fully reached in our experiments. Ω<sub>calcite</sub> is not reported, as it is equal to 1 at equilibrium. K<sub>calcite</sub> and K<sub>aragonite</sub> were calculated using the equation given by Plummer and Busenberg (1982), as explained in Supplementary Material, Section A.3.

<table><thead><tr><th>#Experience</th><th>T (°C)</th><th>Duration</th><th>Ω<sub>aragonite</sub></th><th>K<sub>aragonite</sub></th><th>K<sub>calcite</sub></th></tr></thead><tbody><tr><td>01</td><td>120</td><td>2 days</td><td>0.665</td><td>7.50 × 10<sup>-5</sup></td><td>6.84 × 10<sup>-5</sup></td></tr><tr><td>02</td><td>120</td><td>4 days</td><td>0.665</td><td>7.50 × 10<sup>-5</sup></td><td>6.84 × 10<sup>-5</sup></td></tr><tr><td>03</td><td>120</td><td>8 days</td><td>0.665</td><td>7.50 × 10<sup>-5</sup></td><td>6.84 × 10<sup>-5</sup></td></tr><tr><td>04</td><td>120</td><td>12 days</td><td>0.665</td><td>7.50 × 10<sup>-5</sup></td><td>6.84 × 10<sup>-5</sup></td></tr><tr><td>05</td><td>120</td><td>16 days</td><td>0.665</td><td>7.50 × 10<sup>-5</sup></td><td>6.84 × 10<sup>-5</sup></td></tr><tr><td>06</td><td>120</td><td>20 days</td><td>0.665</td><td>7.50 × 10<sup>-5</sup></td><td>6.84 × 10<sup>-5</sup></td></tr><tr><td>07</td><td>120</td><td>28 days</td><td>0.665</td><td>7.50 × 10<sup>-5</sup></td><td>6.84 × 10<sup>-5</sup></td></tr><tr><td>08</td><td>120</td><td>46 days</td><td>0.665</td><td>7.50 × 10<sup>-5</sup></td><td>6.84 × 10<sup>-5</sup></td></tr><tr><td>09</td><td>120</td><td>90 days</td><td>0.665</td><td>7.50 × 10<sup>-5</sup></td><td>6.84 × 10<sup>-5</sup></td></tr><tr><td>10</td><td>120</td><td>180 days</td><td>0.665</td><td>7.50 × 10<sup>-5</sup></td><td>6.84 × 10<sup>-5</sup></td></tr><tr><td>11</td><td>150</td><td>6 h</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>12</td><td>150</td><td>12 h</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>13</td><td>150</td><td>24 h</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>14</td><td>150</td><td>36 h</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>15</td><td>150</td><td>2 days</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>16</td><td>150</td><td>4 days</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>17</td><td>150</td><td>8 days</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>18</td><td>150</td><td>12 days</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>19</td><td>150</td><td>16 days</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>20</td><td>150</td><td>20 days</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>21</td><td>150</td><td>28 days</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>22</td><td>150</td><td>36 days</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>23</td><td>150</td><td>46 days</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>24</td><td>150</td><td>140 days</td><td>0.663</td><td>4.21 × 10<sup>-5</sup></td><td>3.88 × 10<sup>-5</sup></td></tr><tr><td>25</td><td>200</td><td>10 days</td><td>0.660</td><td>1.33 × 10<sup>-5</sup></td><td>1.24 × 10<sup>-5</sup></td></tr></tbody></table>

experiment is deemed to end as soon as the autoclave is removed from the oven.

## 2.3. Sample processing

### 2.3.1. Fluid phase analysis

After each experiment, the fluid was filtered through a 0.45 µm nylon membrane and mixed with HCl (9:1 ratio) to dissolve any residual calcite. The resulting solution was then analyzed for Ca²⁺ concentration using a ThermoScientific iCAP™ Pro X Inductively Coupled Plasma – Optical Emission Spectroscopy (ICP-OES) system. The settings for measurements are as follows: Radio Frequency 1150 W; gas flow rate 0.5 L.min⁻¹ for the auxiliary, 0.6 L.min⁻¹ for the nebulizer; sample flow rate 45 rpm; calcite wavelength 393.366 nm; integration time 15 s; 3 replicates for each measurement; 5 standards were used for Ca²⁺
calibration curves, with 1, 5, 10, 25, and 50 mg.L⁻¹ of CaCl₂; their R² is 0.9985; the Limite Of Detection (LOD) is 0.33 ppm; the Limite Of Quantification (LOQ) is 1.1 ppm; the data is recorded using the QTegra® software.

### 2.3.2. Solid phase analysis

The solid run-products were first dried at room temperature. 2 g of each sample were ground into powder for X-ray diffraction (XRD) analysis, performed with a Brucker® D8 Advance X-ray diffractometer with the following settings: copper cathode, 2θ angles varying from 20° to 60°, 1245 shots. A semi-quantitative analysis is performed on the diffractograms using Topas® software, which employs the Rietveld refinement method. The refinements were carried out using calcite and aragonite crystal structure models imported from the Crystallography Open Database (COD). The remaining run-products is divided into three portions. One portion (a few grams) was embedded in Struers® Epofix epoxy, polished, and examined with a ZEISS Sigma Field Emission Gun Scanning Electron Microscope (SEM), in AsB (Angle sensitive Backscatter) mode, with the following settings: working distance (WD) = 10.3 mm ± 0.3, aperture size (AS) = 120 µm, Electron High Tension (EHT) = 15 kV. For initial state ooids, the EHT was increased to 20 kV. A second portion was examined with the same SEM in In-lens mode (Immersion lens), using WD = 7.7 mm ± 0.3, AS = 60 µm, EHT = 15 kV. The third portion, consisting of a few milligrams, was embedded in Demotec® 70 epoxy, polished, and examined with an Electron Back Scatter Diffraction (EBSD) camera (Oxford Instruments) under the same SEM device. Size and porosity measurements from SEM images were performed using ImageJ® freeware.

## 2.4. Theoretical models

In this study, we consider the gradual transformation from aragonite to calcite through dissolution and in-situ precipitation in an aqueous environment (Flügel, 2010). The overall reactions governing these processes are as follows (Moore, 2001):

$$CaCO_{3(\text{aragonite})} \rightarrow Ca^{2+}_{(aq)} + CO_{3(\text{aq})}^{2-} \quad (1)$$

$$Ca^{2+}_{(aq)} + CO_{3(\text{aq})}^{2-} \rightarrow CaCO_{3(\text{calcite})} \quad (2)$$

Thermochemical models account for these transformations. To describe the rate of crystal dissolution or growth, r (in mol.s⁻¹), we use the relationship proposed by Lasaga (1984, 1998):

$$r = \pm kS_0|1 - \Omega^{\theta}|^{\eta} \quad (3)$$

where Ω is the saturation-state of the fluid with respect to the mineral, k the kinetic rate constant (mol.m⁻².s⁻¹) and S₀ the reaction surface (m²). The two exponents θ and η empirically describe the dependence of the reaction rate on the saturation-state. Ω quantifies the deviation from thermochemical equilibrium. When Ωⁿ < 1, the fluid is undersaturated with respect to the mineral, the reaction rate is negative (i.e. r < 0) and hence the mineral tends to dissolve. Conversely, when Ωⁿ > 1, the fluid is now oversaturated with respect to the mineral and the reaction rate is positive (i.e. r > 0) and the mineral precipitates. The kinetic rate constant k follows an Arrhenius-type temperature dependence:

$$k = Ae^{E_a/RT} \quad (4)$$

where A is the pre-exponential (frequency) factor (mol.m⁻².s⁻¹), Ea the activation energy (J.mol⁻¹), R the universal gas constant (J.K⁻¹.mol⁻¹) and T the absolute temperature (K).

Crystallization proceeds in two stages: (i) a nucleation phase, during which small crystals formed and act as seeds, followed by (ii) a crystal growth phase. Nucleation requires overcoming an energy barrier, represented by the change in nucleation free energy ΔG* (J) (Nielsen, 1964; Bathurst, 1972; Berner, 1980;). The total variation in free energy ΔG (J)

associated with crystal formation is given by:

$$\Delta G = n\Delta\mu + \varphi(n), \quad (5)$$

where n (mol) is the number of moles of the forming crystal, Δμ (J. mol⁻¹) the chemical potential, φ(n) (J) a function describing surface-related energy contributions. The chemical potential is defined as:

$$\Delta\mu = k_b T \ln(\Omega) \quad (6)$$

where k_b (J.K⁻¹) is the Boltzmann constant. φ(n) can be defined as:

$$\varphi(n) = \sigma a(n), \quad (7)$$

where σ (T) (J.m⁻²) is the interfacial surface energy between the crystal and the surrounding fluid, a(n) (m²) the crystal surface area as a function of its number of moles. At a given temperature T, the critical saturation Ω* (Equation (3)) determines the thresholds above which nucleation becomes thermodynamically favourable. Then, the nucleation rate J (nuclei. m⁻².s⁻¹) is described by the classical nucleation theory (Nielsen, 1964; Kashschiev and Van Rosmalen, 2003; Corvisier, 2006):

$$J = J_0 e^{\left(\frac{-\Delta G^*}{k_b T}\right)} \quad (8)$$

where J₀ (m⁻².s⁻¹) a kinetic pre-factor. Finally, to capture the behaviour observed in our experiments and to incorporate the effects of diffusive transport, we give as a reminder the Fick's first law (Berner, 1980; Pingitore, 1981):

$$\vec{F} = -D\vec{\nabla}C \quad (9)$$

where F is the diffusion flux (mol.s⁻¹.m⁻²), D the diffusion coefficient (m².s⁻¹), ∇C(mol.m⁻³.m) the concentration gradient that drives the diffusion flux.

# 3. Results

## 3.1. Macroscopic observations

After the experiments the samples are hardened with respect to their initial state. The time needed for the sample to become cohesive (i.e. lithified), that is, to form a structure that does not disaggregate, decreases as the temperature increases. At 200°C, the sample becomes cohesive after 15 days of heating. At 150°C, cohesion is achieved after 28 days of heating, whereas at 120°C, the sample remains fragile, breaking easily under finger pressure even after 90 days of heating.

## 3.2. Microstructure observations: SEM and EBSD

### 3.2.1. Initial state

In accordance with the terminology of Harris (1979), we will henceforth refer to the central grain of the ooid as the ‘nucleus’, and to the surrounding zone of concentric laminations as the ‘cortex’. SEM images reveal that the ooids possess two distinct types of initial internal porosity in their cortex (Fig. 3a): (i) circular microporosity that follows their growth-related laminations, and (ii) rounded hole porosity. The second type of porosity crosscuts the first, suggesting that it is posterior.

### 3.2.2. Microstructure evolution through time. 150°C

Shortly after the beginning of the experiments (6 h, Fig. 3b), randomly located lumps, with an average thickness of 3 µm, appear at the periphery of the ooids. These features consists of a crystalline mixture comprising two distinct phases: small, pale grey needles (< 1 µm) identified as aragonite, and larger white crystals with well-defined edges identified as calcite. These peripheral lumps vanish after 2 days of heating (Fig. 3c). Two main phenomena accompany this change.
<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Microstructure evolution, 150°C. (a) An ooid profile at its initial stage. Plain arrows: concentric porosity. Dotted arrows: rounded hole porosity. (b) 6 h of heating: lump of aragonite crystal blend (dotted arrow), with calcite crystals (plain arrow). (c) 2 days of heating: Calcite Fringe (plain arrow) and porosity Laminated Zone (dotted arrow). The three zones of the ooid are abbreviated as follows: Crystal Fringe (CF), Lamination Zone (LZ), Aragonite Internal Sphere (AIS). (d) 20 days of heating: grains welded together by the Calcite Fringe; internal calcite crystals (white arrow). (e) 20 days of heating: an ooid with its Calcite Fringe. (f) 28 days of heating: Ooid with internal calcite crystals. (g) 150°C, 46 days of heating. (h) 140 days of heating: the ooid's nucleus has disappeared and has been replaced by large calcite crystals.</figcaption></figure>
(i) A porous zone develops in the cortex, toward the interior of the ooids (Fig. 3c and 3d). This zone exhibits a “layer cake” structure, alternating between porous laminations and laminations composed of aragonite crystals. The number of laminations and the size of the lamination zone increases over time, extending towards the ooid centre (Fig. 3c and 3d). Calcite crystals also appear within this zone (Fig. 3d). This zone will be referred to as the Lamination Zone (LZ).

(ii) Crystals gradually coat the entire ooids periphery, eventually forming a continuous outer fringe (Fig. 3c and 3d). These crystal increase in size over the course of the experiments (Fig. 3c and 3d), displaying a polyhedral morphology, with sharp edges and smooth faces (Fig. 3e). EBSD confirms that the fringe is indeed made of calcite crystals (Fig. 4a). As the fringe thickens, crystal bridges form between adjacent grains, promoting cementation and welding (Fig. 3d). This zone will be referred to as the Calcite Fringe (CF).

After 20 days of heating, a new phenomenon is observed: the alternating structure of porous and aragonite laminations disappears in most ooids, replaced by large crystals ranging from 30 µm to 50 µm in size (Fig. 3f and 3g). EBSD confirms these crystals are calcite (Fig. 4b). At this stage, there is no more porosity in concentric envelopes but new larger voids between calcite crystals can be observed (Fig. 3f and 3g). As long as the experiment continues (up to 140 days, see Fig. 3h), the thickness of the CF does not increase after 20 days, but the entire ooid internal structure (including the nucleus) eventually disappears and is replaced by large calcite crystals.

### 3.2.3. Microstructure evolution through time. 120°C and 200°C

Experiments at 120°C show partially different results. The same development of a porous Lamination Zone and an outer Calcite Fringe is observed. However, the calcite crystals of this fringe are larger but appear less well bonded (Fig. 5a). This characteristic persists throughout the 6 months of the experiment (see Fig. 5b and 5c): the LZ remains intact, and there is no formation of large internal crystals as observed at 150°C. After six months, large calcite crystals are present, but they are restricted to the space between the grains (Fig. 5b and 5c).

In contrast, the single experiment performed at 200°C (for 10 days), produces a thinner Calcite Fringe compared to the 150°C experiments (Fig. 5d). Nevertheless, it displays the same transformation as described above at 150°C: a part of the ooid’s internal structure rapidly disappears and is replaced by large calcite crystals, in less than 10 days.

### 3.3. Size of the crystal fringe, of the lamination zone and porosity measurements

Using SEM images, the thickness evolution of the Calcite Fringe and Lamination Zone was measured. At each time point, 5 to 15 ooids were analysed with at least 10 measurements per ooid. These measurements enabled the calculation of CF and LZ volumes at 150°C and 120°C, assuming a spherical ooid geometry. CF and LZ measurements were interrupted (i) after 20 days at 150°C, due to the disappearance of the LZ in most grains by day 28, (ii) after 46 days at 120°C, once it was no longer possible to distinguish between the CF and calcite-filled inter-granular porosity. All calculated volumes V were normalized to the average initial ooid volume $V_{ooid}$. The results for V and $V/V_{ooid}$ are presented in Fig. 6a and 6b. Analysis indicates that the temporal evolution of both CF and LZ volumes is best described by a logarithmic trend. Fig. 6a and 6b show that the $V_{LZ}/V_{CF}$ ratio is higher at 150°C than at 120°C. Additionally, over the studied timespan, the growth rates of both CF and LZ are higher at 120°C than at 150°C: at 20 days, $V_{LZ, 150°C}/V_{ooid}$ is 0.4 compared to 0.5 for $V_{LZ, 120°C}/V_{ooid}$; similarly, $V_{CF, 150°C}/V_{ooid}$ is 0.2, versus 0.3 for $V_{LZ, 120°C}/V_{ooid}$. These results will be discussed in the light of XRD data.

Porosity within the Lamination Zone ($\Phi_{LZ, measured}$) was quantified using ImageJ® on SEM images (see Appendix A.1 for methodological details). As these represent apparent porosity values, the initial porosity was set to zero. Results are shown in Fig. 6c. During the first days, $\Phi_{LZ, measured}$, at 150°C increases more rapidly than at 120°C. $\Phi_{LZ, measured}$ at 150°C reaches 60% after 20 days, at which point the LZ disappears. In contrast, $\Phi_{LZ, measured}$ at 120°C stabilizes at around 45–50% after 20 days and remains constant until the end of the measurement period.

### 3.4. Nucleation rate measurement and critical supersaturation $\Omega^{*}(\text{calcite})$ calculation

Observation of microstructures evolution over time shows that, from the beginning, calcite crystals form continuously at the periphery of the ooids. Using EBSD (Fig. 4a), the number of calcite nuclei on the ooid perimeter is counted. This approach yields the number of calcite nuclei at a given time $N_c(t)$. It is normalized to the mean surface area S (m²), of an ooid, which was assumed to remain constant throughout the experiment. The nucleation rate $J_{\text{calcite}}$ is then calculated as:

$$J_{\text{calcite}} = \frac{N_c t_{i+1} - N_c t_i}{S}$$

<figure><img src="image_8.png" /><figcaption>**Fig. 4.** EBSD. 150°C. Electron Backscatter Diffraction (EBSD) is an electron microscopy technique that enables the identification of both the type of crystalline networks and the local crystal orientation through the analysis of backscattered diffraction patterns. (a) An ooid after 2 days of heating, EBSD. Yellow points are calcite crystals. Purple points are aragonite crystals or noise (when smaller than 4 pixels). (b) An ooid, after 28 days of heating, EBSD. Green spots are calcite crystals.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Fig. 5.** SEM pictures, 120°C, 200°C. (a) 120°C, 20 days of heating: an ooid with its Calcite Fringe. Notice the pieces of fringe detached from the ooids that supported them, on the sides. (b) An ooid after 180 days of heating at 120°C. Large calcite crystal between the grains (plain arrow). (c) Ooids after 180 days of heating at 120°C. (d) Ooid with internal calcite crystals. 200°C, 10 days of heating.</figcaption></figure>

Where the index i indicates a time step. Results show that $J_{(calcite)}$ is nearly an order of magnitude higher at 150°C ($10^6$ nuclei.m$^{-2}$.s$^{-1}$) than at 120°C ($10^5$ nuclei.m$^{-2}$.s$^{-1}$, Fig. 7a). Additionally, $J_{(calcite)}$ shows a slight increase over time at 150°C, whereas it remains stable at 120°C.

Finally, from $J_{(calcite)}$, Equations (5), (6), (7) and (8) are used to determine the local critical supersaturation $\Omega^{*}_{(calcite)}$ at the nucleation site (Fig. 7b). The details of the calculation are explained in Appendix A.2. The calculated values are $\Omega^{*}_{(calcite, 120°C)} = 8.02 \pm 0.16$ and $\Omega^{*}_{(calcite, 150°C)} = 6.6 \pm 0.16$. Despite variations in $J_{(calcite)}$, the local critical supersaturation $\Omega^{*}_{(calcite)}$ remains relatively stable in both cases. Notably, $\Omega^{*}_{(calcite)}$ is higher at 120°C than at 150°C, as expected (Berner, 1980).

## 3.5. Chemical and mineralogical quantification of the reaction progress

### 3.5.1. ICP measurements

The evolution of $Ca^{2+}$ concentration in fluid samples from experiments conducted at 150°C and 120°C is shown in Fig. 8. It is worth noting that: (i) $Ca^{2+}$ concentrations at both temperatures are of the same order of magnitude, ranging between 150 and $750 \text{ mg.L}^{-1}$; (ii) both curves exhibit similar overall trends. Following a rapid increase to $750 \text{ mg.L}^{-1}$ within the first 24 h of heating, $Ca^{2+}$ concentrations decrease between 4 and 28 days, reaching approximately $150 \text{ mg.L}^{-1}$. This decrease is regular at 120°C and irregular at 150°C. After 28 days, $Ca^{2+}$ concentrations rise again at both temperatures. At 150°C, measurements were stopped after 46 days, at which point the concentration reaches $350 \text{ mg.L}^{-1}$. At 120°C, $Ca^{2+}$ concentration peaks again at $750 \text{ mg/L}$ at 90 days, then stabilizes at $580 \text{ mg/L}$ at 180 days. We would also add that, even though the autoclaves are opened only after they have cooled down, a loss of vapor during the experiment cannot be ruled out. It is

possible that the actual concentration values in Fig. 8 are lower than the measured ones.

### 3.5.2. XRD characterization

Fig. 9a and 9b show the progression of aragonite to calcite transformation over time at 120°C and 150°C (see Section 2.4). At 150°C, the process follows a polyphasic pattern. A rapid transformation occurs between days 2 and 12 with an increase from 5% to 25%. The curve then plateaus until day 20, reaching 30%, before the transformation resumes between 20 and 28 days, following a linear trend that slows after 36 days. By day 46, 70% of aragonite has been transformed to calcite. In contrast, at 120°C, the transformation follows a monotonic trend: a single intense phase between days 2 and 12 increases transformation from 3% to 35%, followed by a gradual rise reaching 50% by day 90. Overall, the aragonite to calcite transformation is temperature-dependant, proceeding more rapidly at 150°C than at 120°C – contrasting with the trends shown in Fig. 6.

## 4. Discussion

### 4.1. Crystallisation processes during aragonite to calcite transformation

The observations reveal two distinct stages during aragonite to calcite transformation in ooids. During the first stage, a layered-porous zone structured in concentric laminations develops in the cortex, inward from the rim, while calcite crystals grow at their periphery. During the second stage, the internal porous structure disappears, progressively replaced by large calcite crystals. The duration of the first stage is strongly temperature-dependent: the transition from the first to the second one occurs before 10 days at 200°C, between 20 and 28 days at
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Volume and LZ porosity evolution for one ooid. (a) CF and LZ volume evolution, 150°C. Measurement stops after 20 days because the LZ disappears after this time. (b) CF and LZ evolution, 120°C. (c) LZ porosity evolution at both temperatures.</figcaption></figure>

150°C, and was not observed in our experiments at 120°C. Bhattacharyya and Friedmann (1983), reported that, under similar experimental conditions at 250°C, internal calcite crystals formed within 24 h, without the development of either an external calcite fringe (CF), or an

internal zone of circular porosity in the lamination (LZ). The following subsections, Figs. 10 and 11 provide an interpretation of the mechanisms underlying these two stages and discuss the key parameters controlling the transition between them.
<figure><img src="image_11.png" /><figcaption>Fig. 7. Nucleation rate and critical supersaturation as functions of time. (a) Calcite nucleation rate at 120°C and 150°C, estimated with EBSD. (b) Critical supersaturation Ω* at 120°C and 150°C.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 8. ICP measurements. Ca²⁺ concentration in the fluid over time, at 150°C and 120°C.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 9. Aragonite to calcite conversion over time. XRD measurements. (a) Diffractograms at different time steps, 150°C. Intensities have been normalized over the highest peak: their values range from 0 to 1. (b) Aragonite to calcite transformations over time, after XRD measurements.</figcaption></figure>

### 4.1.1. First stage: a diffusion-controlled process

Under surface conditions, aragonite is a less stable polymorph of CaCO₃ than calcite: at temperatures lower than 250°C, the solubility of

aragonite is higher than that of calcite (Plummer and Busenberg, 1982; see Table 1 and Appendix A.3). At 150°C, the calcite and aragonite solubility product in distilled water are respectively Kₛulation
<figure><img src="image_14.png" /><figcaption>**Fig. 10.** Model of ooid evolution and cement growth phases. (a) Initial state. (b) Nucleation stage. (c) Diffusion-controlled stage. (d) Surface-controlled stage.</figcaption></figure>

3.88 × 10⁻⁵ and K_s(aragonite, 150°C) = 4.21 × 10⁻⁵. As a result, for all our experiments, aragonite can dissolve while calcite precipitates. Since distilled water is used, the Ca²⁺ and CO₃²⁻ ions that supply the development of the Calcite Fringe (CF) originate from the Lamination Zone (LZ), which thus acts as a dissolution zone. This interpretation is consistent with the observations presented in section 3.2.2 and 3.2.3:

(i) This first lamination-parallel microporosity seems intrinsic to the ooid itself, as it consistently follows its internal laminar structure. It can therefore be interpreted as being inherited from the ooid's original growth steps (Diaz et al., 2019). The second type of porosity, which is overprinting and randomly distributed, is probably microorganism-related and corresponds to what is commonly referred to as 'microborings' (Harris et al., 1979; Fig. 10a). These two types of porosity observed in natural ooids likely account for the relatively high initial porosity Φ_ooid = 24 ± 3.5% (see Section 2.1).

(ii) The “lumps” seen in the early stages at 150°C and 120°C can be interpreted as localized dissolution fronts. Aragonite crystals observed within these lumps (Fig. 3b) are undergoing dissolution. At the grain periphery, aragonite is in contact with undersaturated fluid (Ω(aragonite) < 1, see Equation (3)), initiating dissolution at this interface. As Ca²⁺ ions are consequently released, the local environment becomes supersaturated with respect to calcite (Ω(calcite) > 1), and once the critical supersaturation Ω* is reached (Equation (5), Fig. 7b and 10b), calcite nucleation occurs – typically after approximately 12 h at 150°C.

(iii) The laminated structure of the dissolving LZ can be attributed to the initial porosity within the ooids. Here, a locally high ratio of undersaturated fluid volume to reactive surface area S₀ (Equation (3)) is likely to initiate the dissolution process. Afterward, dissolution kinetics are driven by temperature T (Equation (4)). Additionally, the presence of organic matter within ooids laminations may further enhance dissolution rates. Indeed, many studies show that in carbonate settings, organic matter degrades and produces acids that promote the dissolution of calcite and aragonite (James, 1974; Ferguson et al. 1984; Reuning et al., 2022). This process is further enhanced at higher temperatures (Forjanes et al., 2021).

(iv) The concentric expansion of the LZ volume, towards the ooid centre corresponds to an increase in internal dissolution, while the dissolution products, Ca²⁺ and CO₃²⁻ enable CF growth.

Collectively, these observations support the existence of a *diffusive system* operating from the grain interior to its periphery during this first stage. The chemical gradient (Equation (9)) driving this diffusion is sustained by ongoing calcite nucleation and growth at the fringe. As long as growth continues, it effectively acts as an ionic sink, maintaining a constant supersaturation Ω* in the fluid surrounding the CF. This regime set up here can be described as ‘diffusion-controlled’ crystallization (Steefel and Lasaga, 1994; Lasaga, 1998): the overall kinetics are governed by ions transport rather than by surface reactions rates (Fig. 10c).

#### 4.1.2. A surface-controlled stage

The second stage of aragonite/calcite transformation, observed at temperatures above 120°C, is characterized by the presence of large calcite crystals within the ooid where concentric laminations have disappeared. During this stage, no new nucleation occurs; instead, calcite continues to grow on pre-existing crystals that formed in the lamination zone during the previous stage. This behaviour can be explained by a decrease in supersaturation Ω(calcite), which no longer reaches the energy barrier ΔG* necessary to sustain nucleation (Equations (3), (4) and (5)). As a result, the diffusion-controlled regime described for the first stage is no longer active. Within the confined internal volume of the ooid, calcite growth proceeds predominantly *via* a plurality of faster diffusive ‘surface-controlled’ processes (Fig. 10d). In this regime, overall crystal
<figure><img src="image_15.png" /><figcaption>Fig. 11. CF porosity evolution, calculated thanks to Equation (12). LZ porosity evolution measured is reported in each figure. (a) CF porosity evolution, 150°C. (b) CF porosity evolution, 120°C.</figcaption></figure>

growth kinetics are mainly governed by surface reaction rates, rather than by ion transport, which nevertheless remains active (Lasaga, 1994; Lasaga, 1998).

### 4.1.3. Transition from a diffusion-controlled to a surface-controlled growth process

The transition from the first stage to the second one is characterised by an interruption of the diffusion process towards the ooids’ periphery. This interruption therefore requires the closure of the ooid system and its isolation from the interstitial fluid. This way, the chemical gradient that developed outwards, along the grains cross section, no longer exists (Equation (9)). The closure can be achieved when the calcite rim reaches a critical thickness and its crystals are sufficiently bonded. However, this ooid closed-system hypothesis raises two issues: (i) the degree of openness is difficult to quantify precisely, (ii) it does not necessarily preclude the formation of a radial gradient within the grain, as observed in the first stage.

To shed light on these unresolved points, we propose to consider the porosity of the CF ($\Phi_{CF}$) as an indicator of the degree of openness of the ooid, considered as a system. Thus, we aim to quantify the evolution of $\Phi_{CF}$ by calculating the mass balance of a single ooid during experiments. Indeed, a dissolving ooid can be approximated as a sphere comprising the two previously defined zones — the Calcite Fringe (CF) and the Lamination Zone (LZ) — to which we add a third: the Aragonite Internal Sphere (AIS), which includes the remaining cortex and the nucleus of the ooid (Figs. 3c and 10c). At the initial state, the AIS comprises the entire ooid; the LZ volume is equal to zero; it increases over time. Now, at any time, the total amount of Ca in the CF, per grain, denoted $n_{Ca, CF}$ (mol) can be expressed:

$$n_{Ca,CF} = n_{Ca, init} - n_{Ca, LZ} - n_{Ca, AIS} - n_{Ca, fluid}, \quad (10)$$

where $n_{Ca, init}$, $n_{Ca, LZ}$, $n_{Ca, AIS}$ and $n_{Ca, fluid}$ represent the initial amount of Ca, the amount of Ca in the LZ, in the AIS and in the fluid (mol), respectively. The $n_{Ca, fluid}$ contribution per ooid can be estimated assuming that the ICP data give a good approximation of the total amount of $Ca^{2+}$ ions in the fluid over time. After 4 days, at both temperatures, it is one order of magnitude lower than the amount of $Ca^{2+}$ present in the CF, making it negligible in Equation (10) (Appendix A.4). Assuming the initial radius $R_0$ of the ooid remains constant and defines the boundary between the CF and the LZ, we can express the porosity of CF ($\Phi_{CF}$) as:

$$\Phi_{CF} = 1 - \rho_{ratio} \frac{V_{LZ}}{V_{CF}} (\Phi_{LZ} - \Phi_{AIS}) \quad (11)$$

where $\rho_{ratio}$ is the density ratio of aragonite to calcite, $V_{LZ}$ and $V_{CF}$ are the respective volumes of the LZ and the CF (m$^3$), $\Phi_{LZ}$ the LZ porosity, $\Phi_{AIS}$ the AIS porosity. The initial internal microporosity of the ooid $\Phi_{AIS} = 24\% \pm 3.5\%$ aligns well with published values of 20% for Bahama-type tangential ooids (Oti & Müller, 1979; Richter, 1983). As this value is far from being negligible, $\Phi_{LZ, measured}$ (Fig. 6c) must be modified to access the actual $\Phi_{LZ}$ values. The two porosities initially identified (tangential porosity and microborings) are treated as one. Adding $\Phi_{AIS}$ to the remaining solid parts of the LZ, equation (11) is modified as:

$$\Phi_{CF} = 1 - \rho_{ratio} \frac{V_{LZ}}{V_{CF}} \Phi_{LZ,measured} (1 - \Phi_{AIS}) \quad (12)$$

The equation (12) highlights an inverse linear dependence of $\Phi_{CF}$ on each of the two parameters, the $V_{LZ}/V_{CF}$ ratio and $\Phi_{LZ, measured}$. Fig. 11a and 11b show the evolution of $\Phi_{CF}$ over time, as computed from Equation (12) at 150°C and 120°C, respectively, along with the $\Phi_{LZ, measured}$ from Fig. 5c. Three major results stand out. First, at 150°C, a progressive reduction in the CF porosity is favoured, until it reaches 0 after 12 days (Fig. 11a). The hypothesis of a closing of the ooid system leading to a surface-controlled regime is therefore confirmed. Secondly, the increasing of $\Phi_{LZ, measured}$ at 150°C reflects ongoing dissolution of laminations in the LZ (Fig. 11a), likely dispersing $Ca^{2+}$ within the LZ and disrupting the chemical gradient necessary for diffusion toward the CF. In this regime, calcite supersaturation $\Omega_{calcite}$ is insufficient to induce nucleation ($\Omega_{calcite} < \Omega^{*}_{calcite}$), but high enough to sustain growth on pre-existing crystals which nucleated during the first phase. Finally, at 120°C, $\Phi_{CF}$ increases over time (Fig. 11b). The lower values of $V_{LZ}/V_{CF}$ and $\Phi_{LZ, measured}$ do not support system closure, preventing the transition to stage 2. The system remains in an open diffusion-controlled regime throughout the experiment and evolves towards a porosity inversion (moldic porosity): large calcite crystals, supplied by grains dissolution, fill the space between the ooids (Fig. 5b and 5c).

The duration of the diffusion-controlled regime is strongly temperature-dependent, due to the significant influence of temperature on dissolution kinetics (Equations (3) and (4)). In Bhattacharyya’s (1983) 250°C experiments, the AIS likely dissolved too rapidly for a diffusion regime to develop. At 200°C, LZ laminations dissolve faster than at 150°C, increasing LZ porosity evolution and possibly raising the $V_{LZ}/V_{CF}$ ratio (Equation (12)). The system closes sooner, and the stage 1 to stage 2 transition occurs in less than 10 days. In summary, lower temperatures favour the establishment and persistence of a diffusion-controlled regime, while higher temperatures accelerate dissolution and promote earlier transitions to surface-controlled crystal growth.

### 4.1.4. Comparison of bulk-scale measurements with grain-scale processes

XRD bulk measurements (Fig. 9b) reflect aragonite dissolution and calcite growth observed locally at the grain scale. At 150°C the evolution of aragonite/calcite transformations indicates a two-stages process with an inflection point at 20 days, marking the transition from a diffusion-controlled to a surface-controlled regime. In contrast, the
transformations at 120°C follow a continuous trend, consistent with a persistent diffusion-controlled regime throughout the 90-day period. Moreover, the evolution of the CF local volume (Fig. 6a and 6b) seems to mirror the XRD data from 0 and 20 days at 150°C, and over the entire duration of the experiment at 120°C (Fig. 9b). In both cases, a slowdown in the transformation rate is observed, likely due to a decrease in reactive surface area ($S_0$) as the AIS diminishes (Equation (3)).

## 4.2. Consequences for aragonite to calcite transformation in natural carbonate systems

### 4.2.1. Comparing experimental and natural cementation processes

There are two major differences between our experimental processes and the processes occurring at the onset of early diagenesis in natural systems. First, the reaction temperature in our experiments is higher. As a result, the kinetics of diffusion, nucleation and growth are faster, and the relative contribution of each of these processes is altered compared to natural systems. Secondly, we use an ion-free fluid, whereas interstitial waters in the meteoric-phreatic zone are ion-enriched. This modifies the role of pore waters on the global chemical equilibrium of the system, and create additional issues related to the presence of magnesium as a natural inhibitor of calcite growth.

Despite these differences, it seems reasonable to compare our experimental processes with natural ones, as previously done by Thorstenson and Mackenzie (1972), Badiozamani et al. (1977), Bhattacharyya and Friedmann (1983), and Neilson (1990). This comparison is supported by three key considerations:

(i) A structural analogy is observed between the grain-scale microstructures produced experimentally at 150°C (day 1–20) and 120°C and those occurring in natural meteoric-phreatic environments: calcite cements at the periphery of the ooid, and laminated dissolution features within the cortex (Bathurst, 1972; Harris, 1977; Halley and Harris, 1979; Budd, 1988; Budd and Land, 1989).

(ii) Apart from temperature, the chemical conditions required to produce microstructures at 25°C are similar to those at 120°C: a strongly undersaturated fluid is brought into contact with aragonite grains. The difference in solubility between calcite and aragonite, which is the essential driving force of the transformations, is even higher at 25°C than at 120°C (Busenberg and Plummer, 1986).

(iii) As shown in Section 4.1.3, lowering temperatures from 200°C to 120°C leads to the establishment of a more persistent diffusion regime. Given that this regime lasts up to 180 days at 120°C in our experiments, it is likely to be sustained over much longer timescales in natural systems at 25°C, provided that similar diffusion conditions are maintained (i.e., an open ooid system, see previous Section).

These similar patterns suggest that the same fundamental processes – dissolution, diffusion, nucleation and calcite growth – operate under both experimental and natural conditions.

### 4.2.2. Parameters driving early cement growth: calcium availability and temperature

Since the analogy between artificial and natural microstructures is established, our results first show that natural cements can develop without any external $CaCO_3$ input, relying solely on the internal dissolution of ooids in contact with undersaturated fluids. Although fluid movement occurs at the regional scale in natural systems, it appears negligible in the formation of microstructures, as ours develop in a stationary fluid. Our conclusions are in good agreement with previous laboratory diagenesis studies, which report similar cements in static conditions (Thorstenson and Mackenzie, 1972; Badiozamani et al., 1976; Nielson, 1990). They also echo to the idea suggesting that the stop

of cementation, in confined fresh-water aquifers where similar microstructures are observed, could be attributed to a completed mineralogical stabilization following an early stage of static aragonite-to-calcite transformation (Budd et al., 1993; Maliva et al., 2001). After this initial period only driven by local dissolution/precipitation processes, many limestones enter a long period of stasis, in which little diagenesis occurs because there are no other cementation driving forces (Maliva et al., 2001).

Our crystals, which formed over 20 days at 150°C, exhibit morphologies comparable as those described by Hashim and Kaczmarek (2020) under similar conditions, with the exception of a higher fluid/solid ratio (150 in their protocol, on a mass basis). However, the phreatic meteoric cements produced in our experiments display smaller and more numerous crystals than their natural counterparts (Budd and Land, 1989). This observation aligns with equations (3), (5), (6), (7), and (8), which indicate that increasing temperature enhances nucleation rates. Indeed, we observed a lower nucleation rate and larger crystals at 120°C compared to 150°C (Figs. 3e, 3f and 7a). Similar trends are expected in natural meteoric phreatic environments, where temperatures are typically around 25°C. Interestingly, our finding contrast those of Badiozamani et al. (1977), who reported larger crystals as the temperature increases. A discrepancy that may be attributed to $CO_2$ degassing in their experiment, introducing an additional variable absent in our protocol. Conversely, our results are in strong agreement with Hashim and Kaczmarek (2020), who also found that increasing temperature favours nucleation and result in smaller crystals. Finally, our study supports the consensus that nucleation and growth rates, both strongly temperature-dependent, govern the size and abundance of crystals during diagenesis. Nevertheless, other factors likely influence cementation in natural systems, including the reaction surface area, the partial pressure of $CO_2$, and the concentration of NaCl and Mg in the fluid (Busenberg et al., 1986; Morse and Mackenzie, 1990; Hashim and Kaczmarek, 2021).

### 4.2.3. Origin and timing of neomorphism processes

The formation of calcite crystals within ooids, initially under diffusive-controlled, and later during a surface-controlled growth stage and at temperatures exceeding 120°C, seems to correspond to what is generally referred to as “neomorphism” (Folk, 1965; Bathurst, 1972; Longman, 1980; Wilkinson et al., 1984; Flügel, 2010). Dickson (2003) narrows the definition of neomorphism to the in-situ transformation of aragonite to calcite in the presence of water. This meaning is particularly relevant to the processes observed in our experiments. Specifically, our results align with “aggrading neomorphism” as described by Folk (1965), where smaller crystals reorganize into larger crystals of a polymorph (Flügel, 2010). Although distinguishing neomorphism from external cementation is often challenging in the field (Bathurst, 1976; Flügel, 2010), our samples show unequivocal transformation with no external $CaCO_3$ input, confirming an entirely internal process confined to the ooid.

The origin and environmental conditions of neomorphism have been widely debated (Folk, 1965; Bathurst, 1976; Maliva, 1998; Flügel, 2010; Saller, 2024). It is generally agreed that a phreatic-meteoric environment is required to facilitate aragonite dissolution and calcite precipitation (Folk, 1965; Bathurst, 1976; Flügel, 2010), requiring exposure to undersaturated fluids and sufficient free energy for calcite nucleation (Bathurst, 1976). Our experimental results indicate that, for tangential ooids, an additional condition is necessary: the closure of the ooid-system. At 150°C in our samples, this closure is associated with the development of a Calcite Fringe (Fig. 10b and 10c). In natural environments, closure can also result from external cementation by blocky calcite (Friedman, 1964; Robinson, 1967; Saller, 2024). This highlights the still unresolved question regarding the timing of neomorphic feature formation, specifically the development of “sparitic” crystals within ooids (i.e. coarse interstitial crystal fabrics, sensu Flügel, 2010). Our findings suggest that these features are governed by processes that cannot be placed within a well-defined chronological diagenetic
framework. In particular, grain closure – which initiates internal sparticite crystal growth – may occur at various diagenetic stages.

### 4.2.4. Calcite growth concepts: thin film, diffusive boundary layer and dissolution-reprecipitation

Another ongoing debate concerns the mechanism of aragonite-to-calcite transformations during neomorphism: does this process occur via an aqueous “thin film” passing through the solid medium and acting as a reaction front? The concept was first introduced in rock mechanics by Weyl (1959) to denote a thin solution film separating mineral grains and enabling diffusive mass transport during pressure solution. It became widely used in the 1970s in the study and interpretation of carbonate microstructures (Sandberg et al., 1973; Wardlaw et al., 1978; Maliva, 1978; Pingitore, 1982; Dickson, 2003). It was then reinterpreted as an aqueous film mediating diagenetic dissolution-reprecipitation while preserving fine microstructures of aragonite shells. However, the concept remains controversial and its nature elusive (Dickson, 2003). In this context, Saller (2024) supports instead a framework involving partial dissolution followed by sparticite calcite growth (Flügel, 2010). While our data do not rule out the traditional thin-film concept, they support a more precise process-based model:

(1) The lamination zone (LZ) developed during the diffusion regime closely resembles what Brand and Veizer (1980) refer to as a 'messenger film'. This corresponds to a diffusive grain-boundary layer where the fluid is out of equilibrium with the intragranular bulk fluid. As concluded in Section 4.1.1 and shown in Fig. 10c, this disequilibrium generates a chemical gradient that drives diffusion (Brand and Veizer, 1980). At the grain scale, the Lamination Zone (LZ) also appears to fit with what recent authors refer to as a 'diffusive boundary layer' – a zone in which diagenetic processes are dominated by diffusion at the matrix scale (Fantle et al., 2020).

(2) During the surface-controlled stage of our experiments, we observe a complete structural reorganization, with concentric laminations disappearing and giving way to large sparticite crystals. This transformation is therefore consistent with a dissolution-precipitation process, aligning with Saller's data on Pleistocene carbonates (Saller, 2024). This reorganization also implies multiple micro-diffusive chemical gradients in the vicinity of sparticite calcite crystals (Fig. 10d). These gradient domains may each be considered as a moving diffusive boundary layer.

Consequently, while the term ‘thin film’ remains an initial conceptual framework, it appears less well suited to describing our data than the concepts of a ‘messenger film’ or a grain-scale ‘diffusive boundary layer’. Indeed, these latter terms emphasize a diffusion-controlled process rather than the variable thickness of an interfacial zone. This diffusion zone should be viewed not as a cause, but as a consequence of the prevailing dissolution-precipitation conditions. Its thickness may depend on the regime governing mineralogical transformations, increasing during diffusion-controlled processes and decreasing during surface-controlled ones.

Furthermore, a similar interface-coupled dissolution-reprecipitation (ICDR) mechanism has been proposed by Putnis & Putnis (2022), and the review therein. This model accounts for ion-exchange processes occurring at a crystalline surface in contact with a fluid. This mechanism involves a thin interfacial layer, typically ranging from a few nanometres to a few micrometres, where dissolution of the parent solid and precipitation of the product phase are directly coupled. As a result, a nanoscale porosity develops in the newly formed phase. The ICDR mechanism shows similarities with our experiments during the surface-controlled stage: (i) a dissolution-precipitation process, (ii) a diffusion process within a thin interfacial layer, and (iii) the development of reaction-induced porosity. However, the mechanisms seem to differ in terms of scale. We observe a complete reorganization of the ooid's

internal structure at the grain scale, involving micro-diffusive processes, whereas the ICDR mechanism remains confined to an interfacial layer operating at the mineral-fluid interface as a nanoscale, surface-controlled reaction (Putnis and Putnis, 2022). Ultimately, the ICDR model tends to lie closer to the fast, surface-controlled kinetic endmember than the microstructural transformation observed in our experiments after 20 days at 150°C. Taken together, our observations therefore motivate a process-based refinement of the traditional “thin film” concept, in which dissolution-precipitation conditions determine (i) the thickness of the diffusive boundary layer and (ii) the relative dominance of diffusion- versus surface-controlled kinetics.

## 5. Conclusion

Our study of local processes accompanying the experimental diagenesis of oolitic sands has highlighted two microstructure growth regimes that find their analogues in nature. The first is a diffusion-controlled regime whereby the grain, in contact with meteoric waters, undergoes partial internal dissolution accompanied by the formation of a calcite rim. The second regime, which develops at temperatures above 120°C, is characterized by surface-controlled growth that leads to the precipitation of sparticite calcite within the grain. This regime requires a closed system, due to the development of the calcite fringe. The natural analogue of these internal microstructures, referred to as “neo-morphism”, is thus likely to develop during early diagenesis, provided the system closure occurs. Finally, our data, while not ruling out the traditional concept of an ‘aqueous thin film’, provide support for a more precise process-based model. In this model, the interface is regarded as a diffusive layer whose thickness varies with the balance between diffusion- and surface-controlled kinetics.

## Data availability

Data are available through Mendeley Data at https://doi.org/10.17632/fzndf88vp3.1.

## CRediT authorship contribution statement

J. Douçot: Writing – original draft, Visualization, Validation, Methodology, Investigation, Formal analysis, Conceptualization. J.-B. Regnet: Writing – review & editing, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization. F. Bourdelle: Writing – review & editing, Visualization, Validation, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization. J. Corvisier: Writing – review & editing, Visualization, Validation, Methodology, Investigation. P. Robion: Writing – review & editing, Supervision, Methodology, Investigation, Formal analysis. D. Deldicque: Writing – review & editing, Visualization, Conceptualization. C. David: Writing – review & editing, Validation, Methodology. S. Richoz: Writing – review & editing, Validation, Methodology. J. Fortin: Writing – review & editing, Supervision, Methodology, Investigation, Conceptualization.

## 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

This work has been funded by the ANR JCJC Program (AAP 2023) granted to Jean-Baptiste REGNET under the grant number ANR-23-CE01-0010-01 – PREFAB Project; and by the CY Initiative (grant “Investissements d'Avenir” ANR-16-IDEX-0008; Project CYIn-AAP2022-
Em-0000000020). We would like to thank the LGCgE laboratory – University of Lille for lending us the autoclaves that enabled us to begin this work. We thank François X. Passelègue (University of Côte d'Azur) for actively supporting the start of this research project. We thank Mathis Bergogne (Sorbonne University) for providing the Python code to calculate heat diffusion in our autoclaves. We thank Isabelle Laurent, analytical chemist from the Chemistry Department at CY Cergy Paris University, for her help performing ICP analysis. We also thank Régis Besse and Vincenzo Calcagno, engineers at the Plateforme Microscopie et Analyse at CY Cergy Paris University, for helping to perform XRD analysis and SEM acquisitions. We thank Juan Carlos Laya, (Texas A & M University) and Paul Mitch Harris (University of Miami), for their fruitful discussions in the development of this work. We address our warmest thanks to Christophe Barnes (CY Cergy Paris University) and to Youri Hamon (BRGM) for their critical comments during the preparation of this article. Finally, we express our sincere thanks to Associate Editor Mariette Wolthers, to two anonymous Reviewers, and to Cole A. McCormick, for their rigorous and constructive comments, which greatly helped improve this manuscript. The experimental work has been mainly performed on the NEPII platform at ISTEp laboratory – CY Cergy Paris University, funded by CY Initiative (grant “Investissements d'Avenir" ANR-16-IDEX-0008; Project CYIn-AAP2023-Em-0000000030).

Appendix A. Supplementary material

The appendix section consists of four parts.

Part A.1 presents the method used in ImageJ® to establish a threshold for measuring the porosity of the LZ. This method provides the results shown in Fig. 6c, which in turn are used to calculate the porosity of the CF, as illustrated in Fig. 11. An example of the two threshold limits is shown in Fig. A.1.

Part A.2 details the calculation used to estimate the critical saturation Ω* based on the nucleation rate J. The values used for the calculation are provided. This procedure underlies the results presented in Fig. 7b.

Part A.3 recalls the equations used by Plummer and Busenberg (1982) to calculate the solubility of calcite and aragonite as a function of temperature. A graph of these equations is provided in Fig. A.2.

Part A.4 explains the calculation used to estimate the amount of Ca in the fluid per ooid and shows that this amount is negligible in the mass balance of Equation (10), Section 4.3.1.

Supplementary material to this article can be found online at [http://doi.org/10.1016/j.gca.2026.01.051](http://doi.org/10.1016/j.gca.2026.01.051).

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