# Pioneering data on detection, identification and quantification of key carbonate forming minerals using spectral tomography

Kanchana Kularatne, Nicolas E Beaudoin, Pascale Sénéchal, Peter Moonen, Souhail Youssef, Fadi H Nader

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Kanchana Kularatne, Nicolas E Beaudoin, Pascale Sénéchal, Peter Moonen, Souhail Youssef, et al. Pioneering data on detection, identification and quantification of key carbonate forming minerals using spectral tomography. Marine and Petroleum Geology, 2025, 182, pp.107536. 10.1016/j.marpetgeo.2025.107536. hal-05195548

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# Pioneering data on detection, identification and quantification of key carbonate minerals using spectral tomography

Kanchana Kularatne<sup>a, *</sup>, Nicolas E. Beaudoin<sup>a, †</sup>, Pascale Sénéchal<sup>b</sup>, Peter Moonen<sup>b, ‡</sup>,
Souhail Youssef<sup>c, ‡</sup>, Fadi H. Nader<sup>c, d</sup>

## ARTICLE INFO

### Keywords:

Spectral tomography

Time-lapse imaging

Carbonates

Dolomitization

Sedimentology

Mineralogy

Fluid-rock interactions

## ABSTRACT

In this study, we present, for the first time, the spectral computed tomography (sp-CT) signatures of key carbonate rock-forming minerals namely, calcite, magnesian calcite, dolomite, and magnesite. Although the raw spectra of these phases may not be readily distinguishable, we demonstrate that they appear in clusters on a multi-energy histogram derived from laboratory sp-CT. These clusters show a strong correlation with the MgCO₃ mol.% of the carbonate phases. In addition to discriminating among these carbonate phases, we demonstrate the capability of time-resolved sp-CT to monitor mineral replacement reactions in carbonates. As an example, we analyze a series of time-lapse sp-CT images of a carbonate sample undergoing hydrothermal dolomitization in the laboratory. The results reveal a progressive transformation of pure calcite into an Mg-rich carbonate, with the sp-CT data indicating a final composition of approximately 32 mol.% MgCO₃. This estimate, while lower than the 46–50 mol.% MgCO₃ determined through complementary chemical analysis, provides a valuable first-order approximation. This contribution introduces a novel methodology for visualizing, monitoring, and quantifying such chemical reactions in multi-phase carbonate systems, in 2D, 3D and even 4D, offering advantages over destructive techniques such as 3D FIB-tomography. Our findings pave the way to further exploration of carbonate diagenesis and open up new perspectives for the application of spectral tomography in Earth sciences.

## 1. Introduction

Carbonate rocks are commonly found in the geological record and have a great significance for the understanding of the Earth system and the development of resources. They play a critical role in understanding the evolution of life since the Phanerozoic (Ridgwell and Zeebe, 2005), and they are a prime target in the anthropogenic use of the subsurface for resources (Akbar et al., 2000) and storage (Crawshaw and Boek, 2013), along with being a major actor of the natural carbon cycle (Crawshaw and Boek, 2013). These rocks are primarily composed of carbonate minerals such as calcite (pure to very highly magnesian), aragonite, dolomite, magnesite with chemical compositions varying between 100 mol.% of CaCO₃ (calcite) to 100 mol.% of MgCO₃ (magnesite). Being highly reactive rocks, carbonates are heavily impacted by diagenesis, such as dissolution and mineralogical transformations (Whitaker et al., 2004; Fantle et al., 2020). The accurate

detection, quantification (vol%) and estimation of the chemical composition of such carbonate phases are essential for various applications including reservoir (flow properties) characterization (Lucia et al., 2003; Nader et al., 2008; Nader, 2017), understanding geochemical cycles (e.g. Ridgwell and Zeebe, 2005), and predicting potential fluid-rock interactions upon subsurface exploitation (e.g., geothermal energy production, CO₂ storage). To analyze their mineralogical and chemical composition, the commonly used methodologies often involve partially destructive 2D techniques, such as, colouring thin sections and scanning electron microscopy-based energy dispersive spectroscopy (SEM-EDS). Otherwise, destructive methods, such as X-ray powder diffraction (XRD) are applied. Various wet chemical methods (destructive) such as inductively coupled plasma-optical and atomic emission spectrometer (ICP-OES and -AES) and titration methods will return an accurate quantification of the Ca²⁺ and Mg²⁺ content in a sample. Beyond the chemical composition of the rock (that influences

<footnote><sup>a</sup> Université de Pau et des Pays de l'Adour, E2S UPPA, LFCR, CNRS, Pau, France</footnote>

<footnote><sup>b</sup> Université de Pau et Pays de l'Adour, E2S UPPA, CNRS, DMEX, Avenue de l'université, Pau, France</footnote>

<footnote><sup>c</sup> Division of Earth Sciences and Environmental Technologies, IFP Energies Nouvelles, Rueil-Malmaison, France</footnote>

<footnote><sup>d</sup> Department of Earth Sciences, Utrecht University, Utrecht, the Netherlands</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: kanchana.kularatne@univ-pau.fr (K. Kularatne).</footnote>
diagenesis), its internal structure plays also an important role with respect to reservoir properties for flow and storage usages (Lucia et al., 2003).

Laboratory X-ray micro-computed tomography (XCT) (Bultreys et al., 2016; Cnudde and Boone, 2013; Hanna and Ketcham, 2017; Ketcham and Carlson, 2001) has been the prime technique for non-invasive three-dimensional imaging of rocks, also with the capability of time-resolved imaging for non-invasive investigation of dynamic processes (Afrough et al., 2025; Bultreys et al., 2024; Dewanckele et al., 2020; Winardhi et al., 2025). X-rays penetrate through material in varying degrees as mathematically expressed in Beer's law:

$$I = I_0 e^{-\int \mu(s) ds} \quad (1)$$

where I and $I_0$ are the intensity of the incident and transmitted X-ray beam, respectively, and $\mu(s)$ is the local linear attenuation coefficient along the distance s travelled by the X-ray beam though the material (see Cnudde and Boone, 2013 for detailed elaboration). Equation (1) is only valid for a monochromatic X-ray beam. For polychromatic X-ray sources, equation (1) requires integration over the X-ray spectrum.

Projection images are used to reconstruct the internal structure of a scanned volume using suitable algorithms. This process enables the calculation of the local attenuation coefficient ($\mu(s)$) at each point within the volume. The value of $\mu(s)$ depends on both the material's density ($\rho$) and its mass attenuation coefficient ($\mu/\rho$), which varies with X-ray energy and is roughly proportional to the cube of the atomic number ($Z$) in the energy range typically used for CT. However, because $\mu(s)$ is influenced by both density and composition, SCT does not uniquely identify a material unless one of these properties is already known (Cnudde and Boone, 2013).

Carbonates, in particular, have been extensively studied using SCT to visualize porosity and pore networks in order to study mechanical properties and fluid flow (Agrawal et al., 2023; Bultreys et al., 2016, 2022; Centrella et al., 2023; Cnudde and Boone, 2013; Jangda et al., 2024; Mascini et al., 2021; Van Offenwert et al., 2021; Wang et al., 2023), dynamic processes such as dissolution (Gouze et al., 2003; Guren et al., 2023; Menke et al., 2018; Noiriel et al., 2004, 2013, 2016, 2021) and mineralogical replacements (Lefeuvre et al., 2024). The major carbonate minerals (end-member phases, such as calcite, dolomite and magnesite), whose formula weights (calcite = 100.091 gmol⁻¹, dolomite = 184.422 gmol⁻¹, magnesite = 84.331 gmol⁻¹; Robie and Bethke, 1962) and densities (calcite = 2.712 gcm⁻³, dolomite = 2.866 gcm⁻³, magnesite = 3.009 gcm⁻³; Robie and Bethke, 1962) do not significantly differ from each other. Still, it is possible to distinguish them (dolomite, calcite, magnesite) using SCT (e.g. Jonas et al., 2015). Yet, such separation remains challenging when dealing with Aragonite, Mg-Calcite and Calcite. Many techniques have been used to incorporate compositional information into 3D X-ray computed tomography (XCT) volumes. For example, correlative imaging combines 3D SCT with 2D chemical data from complementary methods such as scanning electron microscopy energy dispersive spectroscopy (SEM EDS) (Arif et al., 2021; Boone et al., 2011; Créon et al., 2020; De Boever et al., 2015; Gualda and Rivers, 2006; Godinho et al., 2021a; Kularatne et al., 2024a; Pearce et al., 2019; Saif et al., 2017; Saur et al., 2020; Siddique et al., 2023; Warlo et al., 2021; Wheatland et al., 2020). Another approach is the dual-energy CT (DECT) scanning which can resolve the energy of single photons (Alvarez and Makovski, 1976; Johnson et al., 2007; Li et al., 2024; Maire et al., 2024; Martini et al., 2021; Tsuchiyama et al., 2013; Withers et al., 2021). Unlike conventional single-energy SCT, DECT acquires images at two predefined energy ranges—typically referred to as low and high energy spectra. By capturing attenuation data at both energy levels, DECT enables the reconstruction of various image types, including effective atomic number ($Z_{eff}$) maps, which can help distinguish between phases that are otherwise difficult to differentiate using conventional SCT. However, note that the DECT requires scanning times often longer than a day (Godinho et al., 2021b).

Spectral tomography (sp-CT) has emerged as a powerful non-invasive imaging technique that integrates chemical information with three-dimensional structural information of minerals (Godinho et al., 2021b; Sittner et al., 2021, 2022; So and Nicolaou, 2020; Kularatne et al., 2024b; Sénéchal et al., 2024). This advancement allows for the detailed characterization of materials by providing both compositional and spatial data. In order to obtain chemical information, sp-CT uses a multi-pixel photon-counting detector, such as cadmium telluride or cadmium zinc telluride to detect the energy of the transmitted polychromatic photons within a given range of energy (Fig. 1). So far, sp-CT has been utilized to identify particles containing heavy elements, such as tungsten (W, Z = 74), gold (Au, Z = 79), and lead (Pb, Z = 82) based on the characteristic absorption of energy at the K-edge of these elements. This method has also been applied to identify heavy-elements-bearing minerals, such as barite (BaSO₄), ceria (CeO₂), galena (PbS), and parosite (Ca₁.₁(Ce₀.₉,La₀.₅,Nd₀.₃,Pr₀.₁,Y₀.₁,Sm₀.₁)(CO₃)₃F₁.₇) (Godinho et al., 2021b), employing a methodology similar to SEM-based automated mineralogical classification (Hoal et al., 2009). A recent study has attempted distinguishing common rock forming silicates which are composed of much lighter elements using a spectral data post-processing technique based on a dual-energy concept (please see section 2.2.2) (Kularatne et al., 2024b; Sénéchal et al., 2024). In contrast to SCT, which depends on the local attenuation coefficient ($\mu(s)$) of material (Eqs. (1) and (2)), this sp-CT data post-processing method is able to resolve the linear attenuation coefficient ($\mu$) and the density ($\rho$) of material allowing discrimination of chemically different phases within a sample. Moreover, in contrast to DECT, in the current method, the energy ranges LE and HE are selected posteriori, i.e., after data acquisition, and can be optimized for each material phase separately to maximize the discriminating power from the other material phases. This method has been used to successfully distinguished between eight silicate minerals—plagioclase, orthoclase, pyroxene, amphibole, fayalite, phologophite, pyroximangite + pyroxene, astrophillite + monazite—and magnetite in a monzo-diorite sample (Kularatne et al., 2024b; Sénéchal et al., 2024).

The current study takes this research a step further. Not only do we push the limits to differentiate between various carbonate phases including pure sedimentary, hydrothermal and metamorphic calcite, pure dolomite, pure magnesite, and intermediate Mg-Calcite. But what is more, we perform, for the first time, time-lapse spectral CT to shed light on a mineral replacement reaction. More precisely, we apply sp-CT to a sample of calcite that was subjected to progressive dolomitization in a controlled environment, following the protocol developed by Lefeuvre et al. (2024). Ground-truthing is conducted on the partially dolomitized carbonate using XRD and microprobe quantitative analyses. Thus, we validate the accuracy of sp-CT to quantify the relative proportion of the different carbonate phases.

## 2. Material and methods

### 2.1. Material

#### 2.1.1. Carbonate reference samples

Six natural rock samples were used as reference samples for calibrating the use of sp-CT in carbonate rocks for distinguishing and quantifying carbonate-forming minerals. Compositionally, they are calcite, Mg-calcite, dolomite and magnesite. Provenance, chemical and mineralogical composition of the samples are summarized in Table S1. Three pure calcite samples are used, they are: 1) a cm-scale single crystal of calcite collected in a hydrothermal vein from the Jurassic Meillon Fm. in the Chaînon Béarnais (Motte et al., 2021); 2) a core of Carrara Marble, i.e. an almost (99.8 %) pure CaCO₃ that undergone metamorphism (Lefeuvre et al., 2024); and 3) an oolitic limestone from the Dogger Lavoux formation were collected from the Paris Basin (Youssef et al., 2008; Bemer and Lombard, 2010). In addition, a chalk sample, containing Mg-Calcite from the extensive Upper Cretaceous chalk formation was obtained from Normandy, France (Ballesteros et al., 2020). A
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Principle of spectral tomography (adapted from Sittner et al., 2022) showing a 2D plane of the sample on which sp-CT is performed (left), and the stack of 140 images of the 2D slice, each corresponding to a different energy bin and represented by various colored frames (middle). The reconstructed linear attenuation coefficient of a single pixel of the slice in the range 20–160 keV using the same color code (right). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

polycrystalline fragment of a natural magnesite sample containing a few
veins infilled by dolomite and quartz was obtained from a South African
magnesite mine with unspecified location. Finally, a mini-plug (4 mm
diameter by 1 cm height) was cored from the same oolitic limestone
mentioned above, and hydrothermal dolomitization experiment was
performed following the experimental protocol described below (Sec-
tion 2.1.2). This sample was completely replaced by dolomite as
confirmed by XRD, and served as the reference for dolomite.

2.1.2. Sample and protocol for experimental dolomitization

To evaluate the effectiveness of spectral tomography in studying
mineral replacement reactions in common carbonates, we acquired a
time-lapse sp-CT dataset while progressively replacing CaCO₃ by (Ca,
Mg)CO₃ (dolomitization). The replacement is done experimentally by
reacting a 9 mm diameter, 2 cm height core of oolitic limestone (oolitic
limestone t0) with a solution oversaturated with respect to Mg²⁺, un-
dersaturated with respect to Ca²⁺, and enriched in Zn to promote the
integration of Mg²⁺ into the solid phase (Vandeginste et al., 2019). The
solution was made of 0.3 M of MgCl₂, 0.2 M of CaCl₂ + H₂O, 0.2 M of
ZnCl₂ and 2.0 M of NaCl in milliQ pure water. The reaction occurred in
Parr® Hastelloy 250 ml non-agitated autoclaves sealed with Teflon
gaskets, placed in a furnace at 200 °C for a set amount of days. The
autoclave was heated at a ramp of 5 °C/min to reach 200 °C. After
maintaining the temperature at 200 °C for the 68 h (oolitic limestone
t1), the autoclave was cooled down to room temperature with a ramp of
3 °C/min. Samples were recovered, washed with deionized water, and
dried at 50 °C overnight prior to perform spCT and sp-CT, as described in
section 2.2.2. The sample was then put in a new batch of reactive fluid
and back into the autoclave for another 48 h, with cumulative duration
of 116 h (oolitic limestone t2). A mini-plug of oolitic limestone (4 mm in
diameter and 1 cm in height), used as the dolomite reference sample,
was reacted using the same protocol for 68 continuous hours.

## 2.2. Methods

2.2.1. X-ray diffractometry on powdered sample

X-ray diffractometry (XRD) on powdered samples was performed at
the Université de Pau et des Pays de l'Adour (Pau, France), employing a
Bruker D2 PHASER benchtop XRD system equipped with a Cu tube (Cu
Kα = 1.54184 Å), operated at 30 kV, 10 mA, 300 W. The acquisition
was performed at a step size 30°/min. Diffraction data processing, peak
search, and phase identification were carried out using the EVA Dif-
fracPlus software package (Nash et al., 2013).

2.2.2. sp-CT and Sp-CT analyses

Both spCT and sp-CT were performed using a Tescan UniTOM XL
Spectral (DMEX, Pau, France) equipped with a polychromatic X-ray
source and two detectors. The first is a 16-bit flat panel detector of 2856
× 2856 pixels for conventional tomography (XCT) and the second is a
linear cadmium telluride-detector featuring a sensor width of 307 mm,
subdivided into 384 pixels for spectral tomography (sp-CT).

XCT was performed only on the progressively (experimental) dolo-
mitized oolitic limestone samples (diameter of ~9 mm and height of 20
mm) described in section 2.1.2. Time-lapse spCT imaging was performed
on the initial sample (t0), then after 68 h (t1), and 116 h (t2) of reaction
duration. At each time-step, the reaction was stopped by programmed
cooling of the autoclave from 200 °C to ambient temperature. The
recovered sample was washed with de-ionized water and dried at 50 °C
overnight in oven prior to imaging. The acquisition was performed at 70
kV tube voltage and a target power of 14 W, using an exposure time of
215 ms and targeting a voxel size of 11.5 µm. A series of 1440 angular
projections were collected over 360° sample rotation. Each angular
projection is the average of 4 independent images to improve the signal
to noise ratio. The total acquisition time was around 50 min. The ac-
quired data was reconstructed using Panthera (v 1.4.3.16, Tescan). At
each time-step, sp-CT analysis was conducted as described below.

Sp-CT was conducted on all samples along a randomly chosen plane
of each sample at 160 keV tube voltage and a target power of 20W. The
2D slices of the samples on which Sp-CT analysis were performed are
given in supplementary information (S2, S3). A series of 801 angular
projections were collected over 360° sample rotation. The total acqui-
sition time of Sp-CT was approximately 20 min per sample. The sp-CT
data were reconstructed and analyzed using the Spectral Suite (v2.1,
from Tescan). The reconstructed 2D image has a pixel size of 14 µm. The
reconstructed linear attenuation coefficient at each pixel is comprised of
140 equidistant energy bins of 1 keV between 20 and 160 keV.

The samples used here are composed of elements with atomic
numbers C(Z = 12), Mg(Z = 12) and Ca(Z = 20), with characteristic K-
edge energies 0.283 keV, 1.30333 keV and 4.03834 keV, respectively
(NIST database). Therefore, the detected energy range does not exhibit
absorption edges within the detectable range of the used system
(20–160 keV). Consequently, an approach inspired by DECT is utilized
for the post-processing of data, similar to described in authors previous
works (Kularatne et al., 2024b; Sénéchal et al., 2024). Two energy in-
tervals (LE = low-energy interval and HE = high-energy interval) from
the full detected range are considered (Fig. 2). If μ(LE) and μ(HE) repre-
sent the averaged mass attenuation coefficient over energy ranges LE
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Schematic illustrating the dual-energy-based post-processing technique used in this study. A representative sp-CT raw spectrum is shown, with designated low-energy (LE) and high-energy (HE) ranges. These ranges are selected based on preliminary analysis of the attenuation profiles of target phases to optimize phase contrast. The averaged mass attenuation coefficients over the LE and HE ranges are plotted to generate a multi-energy histogram. Three representative histogram patterns are shown: (a) a distinct spot pattern from a sample with a single chemical composition and uniform density; (b) a spot pattern from a sample with a single chemical composition but varying densities; (c) a spot pattern from a sample containing two distinct chemical compositions, each with fixed density.</figcaption></figure>

and HE, respectively, one can plot μ<sub>(LE)</sub>ρ against μ<sub>(HE)</sub>ρ for each voxel in the dataset, where ρ is the density of material. The plot μ<sub>(LE)</sub>ρ against μ<sub>(HE)</sub>ρ is termed multi-energy histogram. Hereafter, the term “reconstructed linear attenuation coefficient”, (rLAC), will be used in the text to denote μ<sub>(HE)</sub>ρ. In this study, LE and HE ranges were selected as 30–55 keV and 90–120 keV, respectively. These ranges were determined based on preliminary assessment of the attenuation profiles of the target minerals, with the aim of maximizing the phase contrast. On the multi-energy histogram (μ<sub>(LE)</sub>ρ Vs. μ<sub>(HE)</sub>ρ), voxels with the same chemical composition and density will cluster around a spot, whereas phases with the same chemical composition but inhomogeneous in terms of density/porosity, will organize into a line, whereby the slope is chemical-composition-dependent and the distance to the origin is solely a function of density (Fig. 2 & S4). In contrast to DECT, the energy ranges LE and HE are selected posteriori, i.e., after data acquisition, and can be optimized for each material phase separately to maximize the discriminating power from the other material phases.

### 2.2.3. EPMA and SEM analyses

EMPA was performed followed by tomography data acquisition of the oolitic limestone sample which has been reacted for 116 h (Oolitic limestone t2), to obtain the quantitative element distribution maps of Ca and Mg at the reaction front. For this purpose, the sample was sectioned along its vertical axis, embedded in epoxy and polished. EMPA was conducted with a Cameca SXFive microprobe instrument at the Raimond Castaing Microanalysis Centre (Toulouse, France), operating at 15 keV and 20 nA. Distribution maps for O, Mg, Si, Cl, Ca and Zn were generated over a 2.3 mm × 1.2 mm area using a 5 µm beam size and 0.5 s dwell time. Quantification was performed with external standards, including wollastonite (CaSiO₃), periclase (MgO), and tugtupite (Na₄AlBe₃Si₄O₁₂Cl), under conditions of 15 keV, 10 nA, and a 5 µm beam size.

SEM was also carried out on the same sample region using an MEB-

FEG JEOL JSM 6700F equipped with an EDS detector at the same facility. Secondary electron images were acquired at 15 kV accelerating voltage, 84.8 µA current, and a 5.9 mm working distance, while EDS spectra were collected using a 15 kV accelerating voltage, a 6.1 mm working distance, and 38 % dead time.

## 3. Results

### 3.1. Mineralogy and Mg/Ca content in carbonate reference samples

The XRD patterns of reference samples were used to determine both the overall mineralogical content and Mg content using the approach of Montes-Hernandez et al. (2020). The full patterns of the samples are given in supplementary material (S1) and the characteristic (104) reflection of reference samples is given in Fig. 3. The characteristic major peak positions (2θ) of the (104) plane of the analyzed carbonates are: 29.401762 Å (oolitic limestone), 29.511132 Å (calcite), 29.511132 Å (marble), 29.908105 Å (chalk), 30.941045 Å (dolomite) and 32.719322 Å (magnesite). Previous studies show that the MgCO₃ content in carbonates are directly correlated with the d-spacing of the (104) plane (Nash et al., 2013) or the (211) plane (Milliman et al., 1971). We adopted the correlation between the (104) plane and MgCO₃ mol.% content. We also found that the d-spacings of our oolitic limestone, dolomite and magnesite are similar to those of pure calcite, dolomite and magnesite reported by Montes-Hernandez et al. (2020), with confirmed compositions of 0 mol.% MgCO₃ (calcite), 50 mol.% MgCO₃ (dolomite) and 100 mol.% MgCO₃ (magnesite). The red line on Fig. 4 is the linear fit (y = -0.003x + 3.0387; y = d-spacing of (104) plane, x = mol.% of MgCO₃) through these fixed compositions of 0 mol. % MgCO₃ (calcite), 50 mol.% MgCO₃ (dolomite) and 100 mol.% MgCO₃ (magnesite) of our data and those reported by Montes-Hernandez et al. (2020). According to this calibration, calcite, marble and chalk used in
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** X-ray diffraction patterns of the carbonate reference samples showing the characteristic peak position (2θ) of the (104) plane, measured using Cu Kα = 1.54184 Å. The 2θ values are: 29.511132 Å (calcite), 29.511132 Å (marble), 29.401762 Å (oolitic limestone), 29.908105 (chalk) Å, 30.941045 Å (dolomite) and 32.719322 Å (magnesite). The corresponding d-spacings are also given in the figure.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Lattice-constant versus composition curves for $d_{104}$ carbonate peak. The red curve is the fit through pure calcite (100 mol.% CaCO$_3$), dolomite (50 mol. % CaCO$_3$:50 mol.% MgCO$_3$) and pure magnesite (100 mol.% MgCO$_3$) used in this study and also reported by Montes-Hernandez et al. (2020) (MH2020). The green dashed curve and blue dashed curve are experimental fits from Goldschmidt et al. (1958) (GO1958) (y = -0.003x+3.0387) and Goldschmidt et al., 1961 (GO1961) (y = -0.003x+3.04), reported by Milliman et al. (1971). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

this study consist of 3.96 mol.% MgCO$_3$, 3.96 mol.% MgCO$_3$ and 17.05 mol.% MgCO$_3$, respectively. This calibration is also in good agreement with the previous calibrations done based on the d-spacing of (211) plane of carbonates reported by Goldschmidt et al. (1958,1961) and by (Milliman et al., 1971). Chalks are primarily composed of coccolith remnants and therefore expected to consist of low-Mg calcite. However, the chalk sample that has been selected for this study comes from a stratigraphic interval in the Upper Cretaceous chalk formation in Normandy that is known to have been affected by dolomitization (Thiry et al., 2003; Gély and Blanc, 2004). Near the sampled chalk, dolomitization may reach up to 30 % of the bulk rock and has been followed by partial moldic dissolution and calcite replacement, leaving a very small amount of dolomite in the matrix, that may explain the reported 17.05

mol.% MgCO$_3$. In addition, the possibility of having high-Mg calcite nanoparticles embedded within the low-Mg calcite matrix with original coccolith structure (Bianco-Stein et al., 2022), could also prevail and help in further later dolomitization by providing the source of Mg and nucleation sites. Since no clear dolomite rhombs where observed in the investigate chalk (this study), this latter possibility is favored. The investigation of the original source of Mg in the selected chalk sample needs more efforts and is beyond the scope of this study, still these two options provide plausible starting points.

## 3.2. Mineralogy and Mg/Ca content in new phase formed by experimental dolomitization of oolitic limestone

Time-lapse XCT images of the oolitic limestone sample are given in Fig. 5. Oolites and the intergranular porosity (in black) are clearly visible in XCT images (Fig. 5a). After 68 h (t1) of reaction in the Mg-rich solution, at 200 °C (Section 2.1.2.), the outer rim of the oolitic limestone has been replaced by an Mg-rich phase appear as a dark grey rim around the oolitic limestone plug sample. The reaction front appears wavy and often conforms to the contours of the oolites (Fig. 5b). The outer rim of the altered region appears uniform in thickness across the sample. The replacement reaction further continues as indicated by the widening of the reaction rim observed on the sample after 116 h (t2) of reaction (Fig. 5c).

EMPA and SEM back scattered electron (BSE) analysis performed at the interface between reacted and un-reacted area of the sample recovered after 116 h of replacement reaction (Fig. 5c), are given in Fig. 6. Fig. 6a shows the zone where the EMPA analysis was performed. This zone contains unreacted oolitic limestone, the reaction front and the new phase formed. The quantitative EMPA maps of CaO and MgO of the chosen zone (Fig. 6a), are given in Fig. 6b and c respectively. The quantitative EMPA analysis yields a 53 mol.% CaCO$_3$: 47 mol.% MgCO$_3$ composition. Fig. 6d shows the SEM BSE analysis performed within the new phase. The image shows that the replaced area is composed of approximately 2–4 µm rhombohedral crystals. The SEM EDS spectrum of a point analysis performed in the new phase is given in Fig. 6e. The atomic ratio between Ca:Mg of this spectrum yields 1:1. Both these observations confirm that a part of the oolitic limestone sample has been dolomitized during the reaction.
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Time-lapse XCT images showing the oolitic limestone sample: (a) before reaction (t0); (b) after 68 h of reaction (t1); (c) after 116 h of reaction (t2) in Mg-rich solution at 200 °C, 16 bar. During the reaction, Mg is incorporated to the oolitic limestone replacing Ca and forming a new phase, which appears as a dark grey tone on the XCT slices at t1 and t2. The reaction front is visible in some regions; however, segmentation of the replacement product is challenging due to minimal contrast in grey tones. The outer rim of the altered region appears uniform in thickness across the sample.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** (a) EMPA image showing a representative area of the outer border of oolitic limestone t2. Dolomite is formed during the reaction of oolitic limestone with Mg-rich solution at 200 °C, 16 bar, for 116 h. The image shows the dolomite layer (bottom), reaction front and part of the unreacted core of the oolitic limestone; (b) EMPA element distribution maps of (b) CaO showing that high concentration of CaO in the oolitic limestone than in dolomite, and; (c) MgO of the zone in (a) representing 53 mol.% CaCO₃: 47 mol.% MgCO₃. (d) SEM BSE image showing rhombohedral dolomite crystals in the dolomitized zone (e) SEM EDS spectra showing the composition 50 mol.% CaCO₃: 50 mol.% MgCO₃ for dolomite, and 100 mol.% CaCO₃ for oolitic limestone.</figcaption></figure>
### 3.3. Spectral tomography of reference carbonate samples

The detected sp-CT spectra of reference carbonates are shown in Fig. 7a. The slices on which these spectra were collected are shown in supplementary material (S2). Fig. 6a shows the variation of rLAC as a function of X-ray energy from 20 keV to 160 keV. The low energy (LE = 30–55 keV) and high energy (HE = 90–120 keV) ranges selected for post-processing are indicated by the black solid and dashed rectangles in Fig. 7a.

The multi-energy histograms, constructed by plotting rLACs at low energy versus high energy for each carbonate rock sample, are shown in Fig. 7b–g. The multi-energy histograms of calcite and marble comprise dot patterns resembling compact spots, whereas those for chalk, dolomite, and magnesite exhibit a more linear alignment of dots. Each dot represents a pixel with specific chemical composition and density ($μ_{(LE)}ρ$ and $μ_{(HE)}ρ$ described in section 2.2.2.). The average slopes of these dot patterns were determined by connecting the origin (0,0) with the center of gravity of each respective dot pattern. The obtained average slopes are: 2.54 (calcite), 2.58 (marble), 2.24 (chalk), 1.93 (dolomite), 1.53 (magnesite) (Fig. 7b–g).

Fig. 8 shows the normalized histogram of the slopes of each individual pixel of each dot pattern. The average of these distributions corresponds to the average slope determined in the preceding paragraph. A decrease in slope corresponds to an increase in Mg content in the carbonate. For example, the peaks from right to left in Fig. 8 correspond to oolitic limestone (100 mol.% CaCO$_3$), calcite and marble

<figure><img src="image_9.png" /><figcaption>Fig. 8. Normalized histogram of the slope values of carbonate reference samples, obtained from their positions in the multi-energy histograms given in Fig. 7b–g.</figcaption></figure>

(96.04 mol.% CaCO$_3$ ± 3.96 mol.% MgCO$_3$), Mg-calcite (82.95 mol.% CaCO$_3$ with 17.05 mol.% MgCO$_3$), dolomite (50 mol.% CaCO$_3$ and 50 mol.% MgCO$_3$), and magnesite (100 mol.% MgCO$_3$), feature an

<figure><img src="image_10.png" /><figcaption>Fig. 7. Results of sp-CT analysis of carbonate reference samples; (a) spectra of the rLAC (mu) as a function of the energy between 20 keV and 160 keV. The low-energy (LE) range (30–55 keV) and high-energy (HE) range (90–120 keV) are used to construct the multi-energy histograms are also marked on the spectra. Multi-energy histograms of; (b) oolitic limestone (c) calcite; (d) marble; (e) chalk; (f) dolomite; (g) magnesite and their corresponding average slopes are shown here.</figcaption></figure>
increasing percentage of mols of MgCO₃ (MgCO₃ mol.%) and demonstrate the correlation between slope and the Mg content in Ca,Mg-carbonates.

To summarize, the results of sp-CT indicate that each carbonate, with its distinct chemical composition, clusters around a specific slope on the multi-energy histogram (Fig. 7b–g) and these slopes correspond to a specific compositions of Ca,Mg-carbonate as shown in Fig. 8.

## 3.4. Spectral tomography of experimentally dolomitized oolitic limestone

### 3.4.1. Detection of new phase

Time-lapse SCT images of the oolitic limestone going through the replacement reaction (see section 2.1.2) are given in Fig. 5. Images show that the calcite in the initial oolitic limestone has been replaced by a new phase whose LAC is slightly lower than that of the initial oolitic limestone, as indicated by the slightly darker greyscale values on the SCT.

<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Time-lapse sp-CT analysis performed during the replacement of calcite in oolitic limestone by Mg-rich solution at 200 °C. (a) Spectra showing the variation of the rLAC (mu) over the energy range of 20 keV–160 keV at three time steps, t0 (before reaction), t1 = 68 h, t2 = 116 h; (b–d) Corresponding multi-energy histograms derived from the spectra given in (a); (b) at t0, showing a single elongated spot with a slope of 2.57 indicating a single composition with varying densities, likely due to porosity (b), t1 = 68 h, showing two distinct spots: one with the same slope (2.57) as in t0, and a smaller emerging spot on the right with a slope of 2.18, indicating the formation of a new phase. (c), t2 = 116 h (d), showing that the second spot has expanded, suggesting an increasing volume of the newly formed phase.</figcaption></figure>
images (Fig. 5b and c).

Time-lapse spectra collected on the initial oolitic limestone (t0), after reacting for 68 h (t1), and 116 h (t2) are given in Fig. 9. The slices on which sp-CT is performed are given in supplementary material (S3). The spectra of the reconstructed linear attenuation coefficients (rLACs) for t0, t1, and t2 appear very similar (Fig. 9a). The small differences observed in the low energy range (20–30 keV) may be artifacts and cannot be used as a diagnostic feature (Fig. 9a). In contrast, the multi-energy histogram reveals distinct patterns. At t0, the oolitic limestone displays a single elongated spot pattern (Fig. 9b), indicating a uniform chemical composition. However, after 68 h of reaction (t1), the sample exhibits two elongated spot patterns with different slopes, signifying the emergence of a new phase (identified post-mortem as dolomite by SEM EDS) (Fig. 9c). As the reaction progresses, the second spot pattern enlarges, indicating the relative growth of the newly formed phase (Fig. 9d). The plot of slopes against the pixel-normalized intensity counts for experimental oolite sample (t0, t1, and t2) is given in Fig. 10. For comparison, the slopes of the reference carbonate samples shown in Fig. 8 are also included in the plot. This plot shows that the initial oolitic limestone (t0) exhibits a single peak that closely aligns with that of crystalline calcite sample. The peak positions or the slopes, of oolitic limestone (t0) and crystalline calcite are 2.54 and 2.58, respectively, indicating similar compositions. In addition, the reacted oolitic limestone sample (t1) has two peaks, the first with a peak height of ~1.0 and that perfectly aligns with that of (t0), and a new peak which is about 1/3rd of the height of the dominant peak, that appear towards the Mg-rich end (Fig. 10). Moreover, like the reacted oolitic limestone sample (t1), the t2 sample also exhibits two peaks, with the new peak having increased to about 1.7 times the height of the corresponding peak in the t0 sample. The peak positions of the new peaks in the oolitic limestone sample (t1), the (t2) are identical, corresponding to a slope 2.18. This indicates a composition intermediate between dolomite and Mg-calcite (Fig. 10).

### 3.4.2. Identification and quantification of new phase

To determine the composition of the phase formed in the replacement reaction we used the relationship between the slopes of reference

<figure><img src="image_12.png" /></figure>

**Fig. 10.** Normalized histogram of the slope values of oolitic limestone samples at t0, t1 and t2, obtained from their position in the multi-energy histograms given in Fig. 9b and c. Dashed lines indicate the peak positions of reference samples: calcite, Mg-calcite (chalk) and dolomite, for comparison. The initial sample (Oolitic limestone t0) closely aligns with the calcite reference. In the reacted samples (Oolitic limestone t1 and t2), a secondary peak appears on the right, corresponding well to the Mg-calcite reference peak, indicating progressive replacement by a Mg-bearing phase.

carbonates on the multi-energy histogram versus their MgCO₃ mol.% (Fig. 11a). This calibration suggests 32.75 mol.% MgCO₃ for the newly formed phase, in both oolitic limestone sample (t1), the (t2) corresponding to a slope of 2.18 (Fig. 10). SEM-EDS and EMPA were carried out on the same sample after 116 h of reaction (oolitic limestone (t2)). Both results (SEM-EDS: 50 mol.% MgCO₃ and 50 mol.% CaCO₃; EMPA: 47 % MgCO₃ and 53 % CaCO₃, see Fig. 6) are consistent with either ordered or unordered dolomite (50 mol.% CaCO₃: 50 mol.% MgCO₃, Kaczmarek and Sibley, 2011). The newly formed phase was confirmed to be ordered dolomite once the reaction was over using XRD (Fig. 3). The difference between the sp-CT results (32.75 mol.% MgCO₃) and the other methods (~50 mol.% MgCO₃) might be either due to inaccuracies in the sp-CT workflow, or because the dolomitization process may produce a transient phase of very highly magnesian calcite, with irregular patterns and distributions (Lefeuvre et al., 2024). The SEM-EDS data clearly show some dolomite as crystals, yet it is not the whole reacted carbonate but rather specific areas (Fig. 6c). That would suggest that the

<figure><img src="image_13.png" /></figure>

**Fig. 11.** (a) Linear correlation between the slope value of the spot patterns in multi-energy histogram and the MgCO₃ mol.% in carbonate reference samples. The replacement product in the Oolitic limestone after the reaction (at t1 and t2) has a slope of 2.18, corresponding to approximately 32.75 mol.% of MgCO₃. Despite this intermediate composition, the new phase was confirmed to be dolomite through EMPA and SEM EDS analyses; (b) Plot showing the kinetics of the replacement (dolomitization) reaction expressed as the volume percentage of dolomite formed over time, highlighting the capability of sp-CT to monitor dynamic processes. (c–d) sp-CT slice segmentations used for volume quantification at timepoints t1 and t2, indicating dolomite occupying approximately 18 % and 31 % of the total slice area, respectively. The error bars indicate 1σ uncertainty on the slope.
reacted part, during the experiment, involves both dolomite and very high magnesium calcite (VHMC) at a scale below the voxel resolution of the sp-CT. Moreover, direct comparison between EMPA and sp-CT must be done with caution, as both data are not acquired at the same time nor on the same slice of rock. A summary of MgCO₃ mol.% in the carbonate reference samples and the reacted oolitic limestone samples are given in Table 1.

By thresholding based on the slope, sp-CT allows segmenting between calcite and dolomite (Fig. 11c and d). This was impossible based on the conventional sp-CT data as shown in Fig. 5. Here, the segmentation performed on the sp-CT slices indicates the formation of 18 % of dolomite (% by surface area of the sp-CT slice) after 68 h of reaction (Figs. 11b) and 31 % (% by surface area of the sp-CT slice) after 116 h (Fig. 11c). The position of the reaction front is prone to uncertainty, as the histograms of calcite overlaps with the one of the dolomite. More advanced segmentation methods may be required to assess this quantity with confidence. The percentage volume of dolomite formed during the experimental replacement as a function of time is given in Fig. 11b.

# 4. Discussion

## 4.1. Detection, identification and quantification of carbonate minerals

We reported for the first-time spectral signatures of carbonate minerals. The key observations are as follows: (i) although the raw spectra of carbonate-forming minerals appear very similar (Fig. 7a), they occupy a different position in the multi-energy histogram (Fig. 7b–g), enabling the differentiation of carbonate minerals within a sample (Fig. 8); (ii) the slopes observed in the multi-energy histogram show a strong correlation with the MgCO₃ mol.% in carbonates (Fig. 8). This correlation allows for the identification of carbonate phases in a sample based on their composition, hence yielding a calibration that can be used to identify unknown carbonate minerals (Fig. 11a); and (iii) once the carbonate phases are classified using the multi-energy histogram, their abundance can be quantified by counting the number of pixels or voxels associated with each phase, similar to classical sp-CT segmentation by thresholding (Fig. 11c and d). Using this quantification, it is possible to investigate kinetics of mineral replacement reactions in carbonate rocks (Fig. 11b). These findings support the use of sp-CT for detecting, identifying, and quantifying carbonate-forming minerals in rock samples.

**Table 1**

<table><caption>Summary of chemical and sp-CT analyses showing MgCO₃ mol.% in the carbonate samples.</caption><thead><tr><th rowspan="2">Sample</th><th rowspan="2">Provenance</th><th colspan="4">MgCO<sub>3</sub> mol.%</th></tr><tr><th>XRD</th><th>EMPA</th><th>SEM EDS</th><th>sp-CT</th></tr></thead><tbody><tr><td>Calcite</td><td>Natural sample from Jurassic Meillon Fm. in the Chaînon Béarnais, France</td><td>3.96</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Marble</td><td>Natural Carrara marble, Italy</td><td>3.96</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Oolitic limestone</td><td>Natural oolitic limestone, Paris Basin, France</td><td>0</td><td>-</td><td>3.3</td><td>0</td></tr><tr><td>Chalk</td><td>Natural chalk from Normandy, France</td><td>17.5</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Magnesite</td><td>Natural sample, South Africa</td><td>100</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Dolomite</td><td>Experimental, fully dolomitized oolitic limestone</td><td>50</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Partially replaced Oolitic limestone (t1, t2)</td><td>Experimental, fully dolomitized Oolitic limetone</td><td>-</td><td>47</td><td>50</td><td>32.75</td></tr></tbody></table>

Carbonate-forming minerals examined in this study were sourced from natural oolitic limestone, crystalline calcite, marble, chalk, dolomite, and magnesite with MgCO₃ content (mol.%) ranging from 0 % (pure calcite), 3.96 %, 17.05 %, 50 % and 100 % (pure magnesite), respectively (Table 1). These minerals consist entirely of C (Z = 12.000), Mg (Z = 23.985), Ca (Z = 39.962) and O (Z = 15.994) (NIST database), all of which are light elements with no K-edges within the detectable X-ray energy range of the used spectral detector. Consequently, these minerals cannot be identified by the methods described in (Godinho et al., 2021b; Sittner et al., 2021, 2022). A recent study distinguished between eight silicate phases—plagioclase, orthoclase, pyroxene, amphibole, phlogopite, fayalite, mixture of astrophyllite + monzonite, mixture of pyroxangite + pyroxene — along with magnetite in a monzo-diorite sample, all of which also consist of light-elements (Kularatne et al., 2024b). These phases were distinguished using the dual-energy concept-based multi-energy histogram analysis similar to the method employed in the present study. However, there are two key differences between the work of Kularatne et al. (2024b) and the current study: (i) the previous study focused on silicates minerals with different chemical compositions in terms of cations (Na, K, Mg, Ca, Al, Fe, Ti), the ratio between Si:O as well as hydrous and anhydrous phases, whereas the carbonate minerals examined here represent a solid solution between Ca and Mg; and (ii) in the earlier work, the chemical composition of each phase was verified using 2D chemical analysis techniques (SEM-EDS and micro-Raman spectroscopy), while in this study, phase identification of unknown phase was achieved through internal calibration of composition (Figs. 4, 8 and 11).

We demonstrated that this method could effectively track mineral transformations in carbonates, using hydrothermal dolomitization as a case study. While time-lapse sp-CT images revealed the transformation of the original oolitic limestone into a phase with slightly darker grey tone than original oolitic limestone, (Fig. 5), manual thresholding failed to distinguish the two phases due to their similar grey value ranges. Indeed, variations in density and/or chemical composition are often difficult to distinguish in sp-CT images, as their combined effect can also produce similar grey levels. In contrast, time-lapse sp-CT imaging successfully distinguished between the phases and revealed the emergence of a new phase with a distinct composition. Using sp-CT-based segmentation (Fig. 11c and d), we successfully differentiated and quantified the two phases. However, while sp-CT indicated the transformation of oolitic limestone into a compositionally distinct phase, the phase identification was only qualitative in first approximation. 2D chemical analyses (SEM-EDS and EMPA) on the same sample confirmed a CaCO₃:MgCO₃ molar ratio of 50:50 and 53:47, respectively, which represent dolomite (Fig. 6, Table 1). We considered this as the ground truth. In contrast, our sp-CT calibration (Fig. 11) yielded a CaCO₃:MgCO₃ molar ratio of 67:33, which is close to high magnesian calcite composition. While the correlation between histogram slope and MgCO₃ mol.% derived from sp-CT is promising, we acknowledge that the approach currently exhibits systematic underestimation compared to established techniques such as EMPA and XRD. Several sources of uncertainty likely contribute to this discrepancy. First, the sample heterogeneity and the fact that sp-CT was not performed on the same 2D plane as the SEM-EDS and EMPA analyses could have significantly influenced the results. Second, SEM-EDS and EMPA are high resolution imaging techniques, with typical spatial resolutions of approximately ~10 nm and 1 µm, respectively (Reed, 2005). In comparison, the spatial resolution of the reconstructed 2D sp-CT image used in this study is considerably lower, reaching 14 µm. Additionally, SEM-EDS and EMPA were conducted on small surface areas (sample size 2.3 mm × 1.2 mm; Area = 2.8 mm²), whereas sp-CT analyzed a larger area (sample diameter = 9 mm; Area = 63.6 mm²), in which may have affected the representativeness of the chemical composition. Furthermore, the sp-CT technique itself can carry certain uncertainties. For example, pixel averaging within the reconstructed area of the slice may obscure fine-scale compositional variations, while limitations in spectral resolution and poorly understood non-linearities
in X-ray attenuation behavior further complicate precise quantification. Finally, assumptions regarding mineral density and the choice of post-processing thresholds may also introduce systematic biases.

The segmentation of phases using sp-CT multi-energy histograms is currently analogous to manual thresholding in SCT, as no automated algorithm has been developed for this method yet. As a result, the process is prone to user subjectivity, which may lead to inconsistent phase differentiation depending on the operator's interpretation. This lack of automation reduces the reproducibility of results and introduces potential biases, similar to the limitations seen in manual SCT thresholding techniques. In contrast, the average slope of the multi-energy histogram is determined by tracing a line between the center of gravity of the data points and the origin (0,0) of the plot. While this method is objective, the choice of the high and low energy range to be considered is subjective and affects the slopes, which in turn could affect the accuracy of phase differentiation and quantification.

The key advantage of our method over DECT is its flexibility in selecting energy ranges post-acquisition, enabling more effective discrimination between different phases. In DECT, the energy spectra (e. g., low and high keV settings or filter configurations) must be selected *a priori*, which inherently limits adaptability—particularly in heterogeneous or poorly characterized samples. In contrast, this method allows for a posteriori selection of energy ranges, enabling data-driven optimization. This can be tailored, in principle, on a per-mineral basis, offering significant advantages for complex geological or material science applications where the composition may not be fully known at the time of scanning. Additionally, sp-CT intrinsically mitigates beam hardening artifacts due to its photon-counting detection and energy discrimination capabilities. These artifacts often complicate DECT acquisitions, especially when high-Z materials are present, and can reduce the reliability of quantitative analyses.

In this study, we used sp-CT for phase identification and quantification on a two-dimensional slice of the sample (Figs. 5 and 11c and d). However, this method is fully capable of providing chemical information in three dimensions. Achieving 3D analysis requires performing sp-CT (non-invasively) on multiple adjacent 2D planes and reconstructing the entire sample volume, as described in Godinho et al. (2021a) and Sittner et al. (2021, 2022). Currently, three-dimensional chemical information can be obtained using SEM-based focused ion beam (FIB) milling, also known as 3D FIB-tomography (Holzer and Cantoni, 2011; Uchic et al., 2007). However, 3D sp-CT offers two key advantages over 3D FIB-tomography: (i) FIB-tomography is limited to small sample volumes (1 µm³~50 µm³), while 3D sp-CT can analyze volumes up to tens of mm³; and (ii) FIB-tomography is a destructive technique, whereas 3D sp-CT does not require liberating the region of interest. Thus, 3D sp-CT offers a more versatile and non-invasive alternative for analyzing larger sample volumes, while also enabling time-lapse studies, making it a valuable tool for investigating geological materials.

## 4.2. Implications of sp-CT for understanding diagenesis and replacement processes

Diagenesis of carbonate rocks is a complex process that involves fluid-rock interactions, because carbonates are very reactive rocks. Especially, dolomitization is a ubiquitous transformation in carbonate platforms or in basinal contexts. This reaction is still extensively studied, and among the remaining questions, the relationship between reactant supply and crystal growth is an important one, along with the questions of the kinetics of Mg and Ca cation ordering (e.g. Kaczmarek and Sibley, 2011; Kim et al., 2023). One key limitation in our understanding of the dolomitization process is the lack of techniques enabling us to follow the enrichment in Mg in the mineral phase during the reaction. Currently, Mg enrichment can only be quantified after the reaction occurred by destructive techniques such as XRD or EPMA and LA-ICP-MS (Centrella et al., 2023). As 4D SCT approaches developed and allowed to discuss the kinematics of the reactive front propagation, along with local effects

of petrophysics (Weber et al., 2021; Lefeuvre et al., 2024), we argue that sp-CT can be used as a novel tool to quantify the progressive transformation of calcite into dolomite, by providing, in-situ, a quantitative estimate of the Mg content in the mineral phase and its evolution over time.

Further application of sp-CT, such as conducting sp-CT on several slices during a slow reaction, will help to more reliable estimate the volume of phases based on their chemical content, e.g. distinguishing between low Mg calcite and high Mg calcite, in order to use proper mass balance approach to better formulate theories on the replacement mechanisms (Putnis, 2009; Merino and Canals, 2011) until now limited to 2D observations, potentially making quantitative approach arguable (Centrella et al., 2023). Note that while these examples revolve around the dolomitization process, it is likely that equivalent approach is viable for other critical replacement processes, that can be engineered for elementary cycle (e.g. remediation of cadmium in carbonate, Julia et al., 2023), or natural, such as olivine to brucite (Lafay et al., 2012), involved in CO₂capture technology, or as in quantifying hydration of mafic rocks that develop serpentine, a reaction involve in strategic development namely for H₂ exploration (Worman et al., 2016).

## 5. Conclusion

Carbonates are widespread in Earth's lithosphere, and accurate detection, identification and quantification of their constituent minerals are crucial for reservoir characterization, predicting potential fluid-rock interactions in carbonate formations, and ultimately, understanding geochemical cycling. A variety of methods has been previously used to detect, identify and quantify carbonate-forming minerals, though most are either semi-destructive or fully destructive. In this work, we have, for the first time, explored the characteristics of key carbonate-forming minerals non-invasively using spectral computed tomography (sp-CT).

The main findings of this work are summarized as follows.

(i) Although the raw spectra of carbonate minerals with varying Ca/Mg content may not exhibit visually distinguishing features in the 20–160 keV range, they exhibit distinct slopes on the multi-energy histogram constructed using the dual-energy concept.

(ii) By analyzing the slopes of calcite, Mg-calcite, dolomite, and magnesite on the multi-energy histogram, and accurately correlating these with MgCO₃ (mol.%) content, we developed a calibration model for identifying unknown carbonate phases non-invasively using sp-CT.

(iii) Through time-lapse sp-CT combined with a classical hydrothermal autoclave experiment, we successfully tracked the progressive transformation of calcite to dolomite. This method allowed us to non-invasively determine the composition of the new phase formed during the replacement reaction and quantify the percentage of replacement using sp-CT-based segmentation.

This work demonstrated the versatility of sp-CT in distinguishing between phases formed of light-elements such as carbonate-forming minerals, which lack a characteristic K-edge peak within the detectable energy range of most laboratory sp-CT systems. Therefore, we advocate that sp-CT is a promising non-invasive method to access both the phase repartition and the major element content in carbonate rocks, positioning it a cutting-edge tool to exploring diagenetic process and intermediate phase transformations in one of the most exploited rocks of the upper crust.

### CRediT authorship contribution statement

**Kanchana Kularatne:** Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Investigation, Formal analysis, Conceptualization. **Nicolas E. Beaudoin:** Writing – review & editing, Writing – original draft, Supervision, Project administration,
Methodology, Investigation, Funding acquisition, Conceptualization.
**Pascale Sénéchal:** Writing – review & editing, Visualization, Software, Methodology, Formal analysis. **Peter Moonen:** Writing – review & editing, Software, Methodology. **Souhail Youssef:** Writing – review & editing, Resources. **Fadi H. Nader:** Writing – review & editing, Project administration, Funding acquisition.

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.

Acknowledgments

We thank the editor Juan Carlos Laya and the anonymous reviewers for their constructive comments and valuable suggestions, which helped improve the quality of this manuscript. K. Kularatne is funded by the Intercarnot Isifor-IFPEN project CoMiQUE. We thank B. Fasentieux for the preparation of samples at LFCR, Université de Pau et des pays de l'Adour, Philippe de Parseval and Arnaud Priotiett for performing EMPA analysis and Stéphane Le Blond Du Plouy for performing SEM analysis, both at the Centre de microcaractérisation Raimond Castaing at the Université Toulouse III - Paul Sabatier, and Marie-Pierre Isaure for allowing us the access to the XRD. Special thanks to B. Lefevre for his assistance in the laboratory. This work was supported by funding from ANR through the Carnot ISIFoR and the Carnot IFPEN (COMIQUE project).

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.marpetgeo.2025.107536.

Data availability

Data will be made available on request.

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