M Leger

L Luquot

D Roubinet

Role of mineralogical, structural and hydrodynamic rock properties in conduits formation in three distinct carbonate rock types

Keywords: Carbonate rock, Reactive transport, Dissolution rate, Micro-tomography, Karst, Wormholes

Role of mineralogical, structural and hydrodynamic rock

properties in conduits formation in three distinct carbonate rock types M Leger, L Luquot, Delphine Roubinet

Introduction

The reactivity of carbonate rocks in natural or anthropogenic environment is a well-known fact in the scientific community. Nevertheless, there are still a lot of questions about this reaction process whereas its understanding is particularly essential as carbonate rocks reservoirs play an important role in human development. They are often used for water, oil or gas extraction, as well as for geothermal energy production or CO 2 sequestration [START_REF] Rege | Competition among flow, dissolution, and precipitation in porous media[END_REF][START_REF] Chilingarian | Carbonate reservoir characterization: a geologic-engineering analysis[END_REF][START_REF] Noiriel | Hydraulic Properties and Microgeometry Evolution Accompanying Limestone Dissolution by Acidic Water[END_REF][START_REF] Moore | Carbonate reservoirs: porosity and diagenesis in a sequence stratigraphic framework[END_REF][START_REF] Akono | A review of geochemical-mechanical impacts in geological carbon storage reservoirs[END_REF].

Carbonate rocks display very heterogeneous media due to their high mineralogy variety and the high complexity of their structural properties over scales [START_REF] Choquette | Geologic Nomenclature and Classification of Porosity in Sedimentary Carbonates[END_REF][START_REF] Lucia | Petrophysical parameters estimated from visual descriptions of carbonate rocks[END_REF][START_REF] Lønøy | Making sense of carbonate pore systems[END_REF]. A thermodynamic disequilibrium between a fluid and this medium is responsible for dissolution and karst formation for instance [START_REF] Ford | Karst Hydrogeology and Geomorphology: Ford/Karst Hydrogeology and Geomorphology[END_REF]. In order to better understand dissolution processes inside carbonate rocks, laboratory experiments and numerical simulations are conducted under variable conditions on different carbonate rock types. The two adimensional numbers Péclet (Pe) and Damköhler (Da) are generally used to link the initial conditions of experiments and the resulting dissolution patterns inside the rock [START_REF] Golfier | On the ability of a Darcy-scale model to capture wormhole formation during the dissolution of a porous medium[END_REF]. The Péclet number defines the dominant mechanism, between advection and diffusion, for transport processes occurring inside the rock, whereas the Damköhler number characterizes the importance of this transport compared to reaction [START_REF] Lasaga | Chemical kinetics of water-rock interactions[END_REF][START_REF] De Marsily | Quantitative hydrogeology; groundwater hydrology for engineers[END_REF][START_REF] Daccord | Chemical dissolution of a porous medium by a reactive fluid-I. Model for the "wormholing" phenomenon[END_REF]. They are both dependent on the velocity at which the reactive fluid passes through the system, and on the characteristic length of it. Different experimental conditions are then related to different dissolution patterns, going from uniform dissolution to compact wormholes. The properties of the fluid injected inside the rock are shown as the most decisive factors in the development of dissolution regimes in a lot of experimental and numerical studies [START_REF] Fredd | Influence of transport and reaction on wormhole formation in porous media[END_REF][START_REF] Golfier | On the ability of a Darcy-scale model to capture wormhole formation during the dissolution of a porous medium[END_REF][START_REF] Noiriel | Investigation of porosity and permeability effects from microstructure changes during limestone dissolution[END_REF][START_REF] Luquot | Experimental determination of porosity and permeability changes induced by injection of CO2 into carbonate rocks[END_REF][START_REF] Smith | Evaporite Caprock Integrity: An Experimental Study of Reactive Mineralogy and Pore-Scale Heterogeneity during Brine-CO2 Exposure[END_REF][START_REF] Vialle | Percolation of CO2 -rich fluids in a limestone sample: Evolution of hydraulic, electrical, chemical, and structural properties[END_REF][START_REF] Menke | Dynamic Three-Dimensional Pore-Scale Imaging of Reaction in a Carbonate at Reservoir Conditions[END_REF][START_REF] Rohmer | Mechano-chemical interactions in sedimentary rocks in the context of CO 2 storage: Weak acid, weak effects?[END_REF][START_REF] Lebedev | Carbon geosequestration in limestone: Pore-scale dissolution and geomechanical weakening[END_REF][START_REF] Akono | A review of geochemical-mechanical impacts in geological carbon storage reservoirs[END_REF]. In order to better understand the impact of the dissolution process on the rock, laboratory dissolution experiments are usually conducted on samples where the rock properties were initially characterized by laboratory measurements and/or from 3D-images calculations. Acidic fluid is then injected at various concentrations and flow rates in the samples. The evolution of rock properties, such as porosity, permeability, structural and mechanical properties, is monitored during the experiments. The effects of dissolution on limestone at room and reservoir conditions were studied [START_REF] Fredd | Influence of transport and reaction on wormhole formation in porous media[END_REF][START_REF] Noiriel | Investigation of porosity and permeability effects from microstructure changes during limestone dissolution[END_REF][START_REF] Luquot | Experimental determination of porosity and permeability changes induced by injection of CO2 into carbonate rocks[END_REF][START_REF] Noiriel | Changes in reactive surface area during limestone dissolution: An experimental and modelling study[END_REF][START_REF] Vialle | Laboratory measurements of elastic properties of carbonate rocks during injection of reactive CO2-saturated water: Ef-fect of CO2-rich water in carbonates[END_REF][START_REF] Gharbi | Changes in Pore Structure and Connectivity Induced by CO2 Injection in Carbonates: A Combined Pore-Scale Approach[END_REF][START_REF] Mangane | Permeability impairment of a limestone reservoir triggered by heterogeneous dissolution and particles migration during CO2-rich injection: dissolution-induced particle migration[END_REF][START_REF] Vialle | Percolation of CO2 -rich fluids in a limestone sample: Evolution of hydraulic, electrical, chemical, and structural properties[END_REF][START_REF] Steefel | Micro-Continuum Approaches for Modeling Pore-Scale Geochemical Processes[END_REF][START_REF] Lebedev | Carbon geosequestration in limestone: Pore-scale dissolution and geomechanical weakening[END_REF][START_REF] Akono | A review of geochemical-mechanical impacts in geological carbon storage reservoirs[END_REF], as well as the ones on dolomite, preferentially at reservoir conditions [START_REF] Smith | Evaporite Caprock Integrity: An Experimental Study of Reactive Mineralogy and Pore-Scale Heterogeneity during Brine-CO2 Exposure[END_REF][START_REF] Luhmann | Experimental dissolution of dolomite by CO2-charged brine at 100°C and 150bar: Evolution of porosity, permeability, and reactive surface area[END_REF][START_REF] Tutolo | Experimental Observation of Permeability Changes In Dolomite at CO2 Sequestration Conditions[END_REF][START_REF] Wang | Effect of CO2-brine-rock reactions on pore architecture and permeability in dolostone: Implications for CO2 storage and EOR[END_REF]. Few studies analyze the role of the rock mineralogy or the initial internal rock structure, or concentrate on more complex rocks with pluri-minerals rock composition. Some studies showed that a heterogeneous pore size or pore shape distribution will affect the dissolution mechanisms and lead to different dissolution patterns inside the rock [START_REF] Hoefner | Pore evolution and channel formation during flow and reaction in porous media[END_REF][START_REF] Noiriel | Hydraulic Properties and Microgeometry Evolution Accompanying Limestone Dissolution by Acidic Water[END_REF][START_REF] Vialle | Implications of pore microgeometry heterogeneity for the movement and chemical reactivity of CO2 in carbonates[END_REF][START_REF] Luquot | Experimental Characterization of Porosity Structure and Transport Property Changes in Limestone Undergoing Different Dissolution Regimes[END_REF][START_REF] Wang | Effect of CO2-brine-rock reactions on pore architecture and permeability in dolostone: Implications for CO2 storage and EOR[END_REF]. Others defined new dissolution patterns associated with internal rock structure [START_REF] Menke | Dynamic reservoir-condition microtomography of reactive transport in complex carbonates: Effect of initial pore structure and initial brine pH[END_REF]. Recently, we demonstrated that local heterogeneities have a stronger control on dissolution localization than Pe and Da conditions [START_REF] Leger | Impact of hydrochemical conditions on structural and hydro-mechanical properties of chalk samples during dissolution experiments[END_REF]. At large scale, large structural heterogeneities such as fractures impact the dissolution rate and shape since the dissolution preferentially takes place along these large heterogeneities, leading to dissolution mechanisms controlled by transport [START_REF] Elkhoury | Dissolution and deformation in fractured carbonates caused by flow of CO2-rich brine under reservoir conditions[END_REF][START_REF] Garcia-Rios | The role of mineral heterogeneity on the hydrogeochemical response of two fractured reservoir 40 rocks in contact with dissolved CO2[END_REF].

By studying dissolution patterns on different carbonate types in similar conditions, some studies partially tried to establish the role of local structural properties and mineral composition compared to flow and chemical boundary conditions. Sandstone and limestone show specific responses to dissolution [START_REF] Rohmer | Mechano-chemical interactions in sedimentary rocks in the context of CO 2 storage: Weak acid, weak effects?[END_REF]. Silicates inside sandstone favoring dissolution due to non-reactive grains inside silicates, which leads to a larger reaction surface and then a higher dissolution rate and a more homogeneous dissolution [START_REF] Garcia-Rios | The role of mineral heterogeneity on the hydrogeochemical response of two fractured reservoir 40 rocks in contact with dissolved CO2[END_REF]. Additionally, structural properties inside these two rock types are responsible for different dissolution patterns at local scale inside the studied samples [START_REF] Vialle | Implications of pore microgeometry heterogeneity for the movement and chemical reactivity of CO2 in carbonates[END_REF]. It has been demonstrated that textural differences inside various fractured limestone rock types influence dissolution patterns but do not have a significant impact on dissolution rates [START_REF] Levenson | Calcite dissolution rates in texturally diverse calcareous rocks[END_REF]. These studies do not allow seeing the impact of mineralogy differences in the dissolution of carbonate rock types.

In order to acquire further insights on this matter, the present study predominantly focuses on the differences in dissolution patterns depending on the mineralogy and on the structure of different carbonate rock types, as well as on the experimental hydrodynamic conditions. To this end, three distinct carbonate rock types are selected for their differences in structure and mineralogy: chalk, crinoidal limestone and dolomite. Acid injections are conducted on samples cored from these three rock types at atmospheric conditions. With the same acidic fluid, four Péclet conditions, associated to different flow rates depending on the rock type, were applied to the samples with a homemade experimental device. Samples are characterized with laboratory and images methods before and after these experiments, during which chemical and hydraulic properties are recorded. The rock properties evolution, associated with the initial structural and mineral differences between the three rock types and the experimental conditions, is analyzed in order to determine the influence of each of these parameters on the dissolution patterns induced by the acid injection into the rocks. The discussion of this study will focus on the role of initial properties until the conduits formation.

Materials and Methods

The studied rock samples and the full experimental protocol used here are presented in details in [START_REF] Leger | Importance of Microstructure in Carbonate Rocks: Laboratory and 3D-Imaging Petrophysical Characterization[END_REF] and [START_REF] Leger | Impact of hydrochemical conditions on structural and hydro-mechanical properties of chalk samples during dissolution experiments[END_REF], and the key parts of the experimental protocol are reminded in Supplementary Material. In this section, basic information are provided in order to understand the methodology and the obtained results.

Rock properties and characterization

The eleven cores samples studied are part of three different carbonate types. They were cored in three rock blocks in the same orientation in cores of 20-30 mm length and 18 mm diameter, surrounded with epoxy resin and PVC pipe for a total diameter of 25 mm, i.e., one inch. Scanning Electron Microscopy (SEM) and 3D X-ray micro-tomography (XRMT)

display images where structural differences between the three rocks are shown, especially in pores size and shape. As it can be seen in Figure 1, Euville displays the largest pores followed by Lexos and then Normandie. To characterize the cores samples, petrophysical measurements were done by non-destructive laboratory methods. Porosity, permeability and velocities of P and S waves are carried out on dry and/or saturated samples. Current injection inside the saturated samples gives the rock conductivity and allows to calculate structural properties from Archie's law [START_REF] Archie | The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics[END_REF], such as the formation factor F , cementation index m and electrical tortuosity τ e .

Characterization of pore size distribution between 0.5 and 140 µm is carried out by centrifugation. XRMT images are collected with a pixel size of 12 µm and are analyzed with a homemade software to obtain complementary information about the samples. The properties calculated from the 3D images are porosity, permeability, hydraulic tortuosity τ h and relative pores size S V .

A pore size distribution is also obtained from a probabilistic method displaying chord lengths. Details on rock types, calculation methods and protocols, complete results and discussion on the samples properties are provided in [START_REF] Leger | Importance of Microstructure in Carbonate Rocks: Laboratory and 3D-Imaging Petrophysical Characterization[END_REF].

Experimental protocol

The experimental protocol described here is the same as the one used in [START_REF] Leger | Impact of hydrochemical conditions on structural and hydro-mechanical properties of chalk samples during dissolution experiments[END_REF]

Experimental output

The measurement of pressure difference allows to calculate the evolution of the samples permeability k during the experiment using the Darcy law:

k = QLµ A∆P , ( 1
)
where Q is the flow rate The equivalent volume of dissolved calcite and dolomite in the rock sample between each sampling step, V t i , is calculated by dividing m t i by the density of calcite and dolomite. Finally, the porosity ϕ t i is obtained from

m CaCO3t i = ([Ca] t i -[Ca] t 0 )(t i -t i-1 )Q M Ca M CaCO3 (2)
ϕ t i = ϕ t i-1 + V t i V ech (3) with V ech the sample volume [m 3 ].
The initialization of the previous equation for t = 0 is made by using the initial laboratory porosity ϕ L while the final value at the end of the experiment is labeled ϕ ch .

After dissolution, in order to estimate the impact of the experiments on the rock properties, the same laboratory and imaging characterization as before the experiments is conducted on the samples (Section 2.1). To this purpose, centrifugation is conducted in the direction of the pressure difference and in the opposite one, which allows to characterize a possible anisotropy in pore size distribution.

Results

Hydro-chemical results from percolation experiments

Chemical data obtained over time for all the percolation experiments are displayed in Figure 3. In a general way, we observe that the outlet pH values (pH out ), fluid conductivities (σ f ) and Ca and Mg concentrations ([Ca] and [Mg]) are higher than the inlet values. The increase in these values indicates that calcite and dolomite dissolution is occurring during the experiments. The curve shapes are globally the same for each parameter, with a first point corresponding to the mixing between water at equilibrium with rock and acidic fluid, a plateau reached when the dissolution begins and then a decrease more or less pronounced at different times depending on the samples. We observe that the decrease in the parameters occurs much sooner for the samples from Normandie than for the samples from Euville and Lexos, whatever the Péclet condition applied.

Even if the curves shape are similar, several observations can be done.

The values reached on the plateau for pH, conductivity and Ca and Mg concentrations depend on the rock types and on the Péclet number applied. Firstly, for each rock type, the plateau values reached for pH and conductivity are independent from the Péclet condition applied. As explained in Section 2.3, permeability evolution over time during the percolation experiments is calculated from the differential pressure monitoring, and is displayed in Figure 4. We observe an increase in permeability when we previously observed a decrease in ion concentrations in the effluent.

As previously mentioned and explained in [START_REF] Leger | Impact of hydrochemical conditions on structural and hydro-mechanical properties of chalk samples during dissolution experiments[END_REF], some decreases in permeability can be noticed during the experiments, and are probably due to pores clogging and particles dragging inside the samples [START_REF] Noiriel | Hydraulic Properties and Microgeometry Evolution Accompanying Limestone Dissolution by Acidic Water[END_REF][START_REF] Luquot | Experimental Characterization of Porosity Structure and Transport Property Changes in Limestone Undergoing Different Dissolution Regimes[END_REF][START_REF] Garing | Anticorrelated Porosity-Permeability Changes During the Dissolution of Carbonate Rocks: Experimental Evidences and Modeling[END_REF]. Depending on the Pe applied to the samples, the normalized permeability (k * ) evolves in different ways. An important and sudden increase in permeability occurs at different times depending on the samples, and is due to the percolation inside the core, already defined in previous studies [START_REF] Daccord | Chemical dissolution of a porous medium by a reactive fluid[END_REF][START_REF] Fredd | Influence of transport and reaction on wormhole formation in porous media[END_REF][START_REF] Golfier | On the ability of a Darcy-scale model to capture wormhole formation during the dissolution of a porous medium[END_REF][START_REF] Brosse | Modelling Fluid-Rock Interaction Induced by the Percolation of CO2 -Enriched Solutions in Core Samples: the Role of Reactive Surface Area[END_REF][START_REF] Luquot | Experimental determination of porosity and permeability changes induced by injection of CO2 into carbonate rocks[END_REF][START_REF] Szymczak | Wormhole formation in dissolving fractures[END_REF][START_REF] Guarracino | A fractal model to describe the evolution of multiphase flow properties during mineral dissolution[END_REF][START_REF] Vialle | Percolation of CO2 -rich fluids in a limestone sample: Evolution of hydraulic, electrical, chemical, and structural properties[END_REF][START_REF] Menke | Reservoir condition imaging of reactive transport in heterogeneous carbonates using fast synchrotron tomography -Effect of initial pore structure and flow conditions[END_REF][START_REF] Akono | A review of geochemical-mechanical impacts in geological carbon storage reservoirs[END_REF]. For Normandie and Euville samples, this sharp increase is followed by a more moderate one, less visible for samples submitted to P e 1 . However, permeability of Lexos samples increases gradually during the experiments. Concerning the importance of the increase in permeability, it is not linear with the Péclet numbers applied to the samples. Indeed, N08 P e 2 and L04 P e 3 display both the lowest k * increase, with an increase of only 28 of their permeability. N05 P e 3 and E05 P e 3 present the highest final relative permeability, with 879 and 2035, respectively. Concerning the other samples, those with P e 2 display all similar final k * between 100 and 200 ; whereas N09 P e 1 and E08 P e 1 both increase their permeability of about 400. Finally, E04 P e 4 displays an increase of 186.

Effective petrophysical and hydraulic parameters

In this section, a focus is made on the petrophysical and hydraulic properties obtained from laboratory measurements and 3D X-ray tomographic images before and after the percolation experiments. These results are displayed in Table 2 andTable 4. The sample E01 P e 2 from Euville rock type was not imaged before, so it is not discussed in this part.

Results presented in

[-]).
The index L stands for Laboratory measurements, XR for X Ray tomographic images and ϕ ch is the porosity from chemistry calculations. The sample E01 was not imaged before experiments. For each rock type, the samples are ordered according to increasing Péclet values.

Each rock type does not react in the same way to percolation experiments.

Firstly, concerning Normandie, two groups of samples can be defined. N03 P e 2 and N05 P e 3 samples both increase the most their permeability and decrease the most their structural properties, contrary to N08 P e 2 and N09 P e 1 samples.

Therefore, N03 P e 2 and N05 P e 3 samples begin with the lowest permeability to finally reach the highest. Their high decrease in formation factor and tortuosity leads to similar final values between all the samples. N08 P e 2 is the sample with the lowest increase in permeability, while it displays the highest decrease in formation factor and tortuosity. A full description of this rock type can be found in [START_REF] Leger | Impact of hydrochemical conditions on structural and hydro-mechanical properties of chalk samples during dissolution experiments[END_REF].

Secondly, for Euville rock, the samples E01 P e 2 and E02 P e 2 display the highest increase in porosity, whereas the increase in permeability is the lowest. They also display the highest decrease in formation factors and tortuosities. E05 P e 3 is the sample which increases the most its permeability. However, E08 P e 1 stays the one with the lowest permeability, before and after the experiment. With the highest step in permeability, the sample E05 P e 3 also presents the highest decrease in structural properties, starting with higher values than the other samples and finishing with similar values than all, except E08 P e 1 . Formation factors and tortuosity values do not decrease much for this latter, which displays the highest final values of structural properties.

Finally, the Lexos set is only composed by two samples. Before the percolation experiments, L04 P e 3 has higher initial permeability, formation factor F L and tortuosity τ e . The experiments lead to a higher increase in porosity and permeability for the sample L01 P e 2 , along with a higher decrease in structural factors (F L & F XR and τ e & τ h ). In a general way, we observe that the changes in the pore diameters dis-tributions before and after the percolation experiments are dependent on the rock type. Indeed, samples from Normandie and Euville show a large increase in their proportion of micropores (pores smaller than the XR pixel size equal to 12 µm) with a decrease in large pores proportion. On the opposite, the two samples from Lexos display only few changes between before and after dissolution with a relatively small decrease in micropores proportion, leading to a small increase in macropores proportion. More specifically, concerning

Normandie, the evolution depends on the samples. N03 P e 2 and N05 P e 3 samples display an increase in pores with sizes between 0.5 and 3.7 µm, while a decrease in all the other classes is observed. However, N08 P e 2 and N09 P e 1 samples show a global increase in all the small pore diameters classes. All the samples from Euville rock display similar trends in the evolution of small pores. The proportion of very small pores (smaller than 0.5 µm) globally remains the same, and the proportion of pores with sizes between 0.5 and 9.5 µm increases. Then, the proportion of large pores decreases for the majority of the samples with more pores larger than 73 µm in E01 P e 2 and E02 P e 2 than in the other samples.

Pore size distribution and orientation

The homemade software allows to extract the chord length probability distribution of each sample from the 3D images. The equivalent pore size distributions from these calculations are displayed in Figure 6. On one hand, we observe that the pore size globally increases with the experiments, the quantity of small pores (below 24 µm) decreasing and the quantity of large pores (over 100 µm) increasing. On the other hand, the three rock types show different behaviors, before and after experiments, and samples of each rock type also display differences. Focusing on the global evolution of pore diameters, Normandie samples 361 are divided into two groups. N03 P e 2 and N05 P e 3 change the most with the experiment, dividing by two their quantity of small pores and doubling their quantity of large pores, while N08 P e 2 and N09 P e 1 barely change. This is the same for Euville samples, where E02 P e 2 sample decreases a lot its quantity of small pores compared to the other samples. Conversely, the two samples from Lexos change similarly even if the sample L04 P e 3 keeps more small pores after experiment than L01 P e 2 .

An evolution in the pore shapes is also visible. For the Normandie set,

N05 P e 3 is the only sample displaying spherical pores before the experiments, the others mostly presenting large pores transverse to the flow direction (XY).

The dissolution barely changes N08 P e 2 pore shape, while large pores in the other samples get longer along the flow direction (Z). Concerning Euville samples, they all present spherical pores before the experiments. The sample E08 P e 1 , performed with P e 1 conditions, keeps this shape. However, for the other samples, the large pores enlarge along the flow direction (Z) in different proportion, E02 P e 2 displaying the highest difference between the two directions. Lexos samples also have spherical pores before the experiments and display large pores that are larger in the flow direction than in the transverse one after dissolution.

Resulting main flow paths

Micro-tomography images acquisition allows seeing the resulting main flow paths formed during the dissolution experiments (Figure 7). Preferential flow paths created by the acid injections are clearly visible for all the rock types. Initially, these conduits were not present in the cores but some heterogeneities were, as it is shown in Figure 1. A pre-existing filled channel exists in the central part of N08 P e 2 , while N09 P e 1 displays some micro-cracks. Results for Normandie samples are fully discussed in [START_REF] Leger | Impact of hydrochemical conditions on structural and hydro-mechanical properties of chalk samples during dissolution experiments[END_REF]. E04 P e 4 and E05 P e 3 both present some zones of initial higher porosity. The first one is composed of two areas, one at the inlet and the other one at the outlet, the acid injection creating a conduit between them, where the rock was more cemented. Inside E05 P e 3 , the initial higher porosity zone is located on one side (the left one in Figure 7), inducing a preferential dissolution there. The samples E08 P e 1 and L04 P e 3 both have pre-existing conduits which were not connected to the core sides but help the dissolution process. Additionally, the conduit shapes are different according to the rock type. Dissolution in Normandie chalk samples allows less ramifications than dissolution in Euville crinoidal limestone samples. Indeed, conduits are more linear and precise in the first case. Inside Lexos dolomite samples, dissolution seems to create very linear conduits with few ramifications.

Discussion

Changes in porosity and percolation time

The results presented in Section 3 show that the percolation experiments induce an increase in porosity (ϕ ch from ϕ L , see Equation ( 3)) for the three rock types. The evolution of porosity is calculated from outlet cations concentrations (only Ca or both Ca and Mg depending on the rock type) and is displayed in Figure 8. Porosity does not change in the same way depending on the rock type and the Péclet condition of each sample. In a general way, Normandie samples present the lowest increase in porosity, between 0.08 and 0.35%, whereas porosity in Euville samples increases between 0.39 and 2.06%

and porosity in Lexos between 1.28 and 2.84% (Figure 8). As observed in Section 3.1, a break in the porosity curves occurs at different times for each sample (Figure 8). It is more or less pronounced depending on the samples and it defines the percolation time t p . The corresponding values for each sample are noted in Table 3. For each rock type, we observe in Figure 8 that the higher the Péclet condition applied to the samples, the faster the break in the curves happens and percolation occurs, inducing a lower t p . The sample N08 P e 2 is an exception here due to an important initial heterogeneity, and explanations about this are discussed in [START_REF] Leger | Impact of hydrochemical conditions on structural and hydro-mechanical properties of chalk samples during dissolution experiments[END_REF]. Additionally, concerning rock types only composed of calcite, chalk (Normandie) having a higher initial porosity than crinoidal limestone (Euville), its initial poral volume is higher. To create a conduit, the quantity of rock needed to be dissolved is then less important, inducing a lower increase in its absolute porosity. Inside each rock type, the absolute increase in porosity shown in Figure 8 does not seem correlated with the experimental conditions. For Normandie samples, except N08 P e 2 , porosity increases more when a higher Péclet is applied. In N08 P e 2 , we observe a minimal increase of 0.08% while it is dissolved with P e 2 . For Euville, samples dissolved with P e 2 (E01 P e 2 and E02 P e 2 ) display a larger increase in porosity than E08 P e 1 that is dissolved with P e 1 .

Samples

However, these three samples increase their porosity more than samples for which P e 3 and P e 4 conditions are applied. For Lexos, L01 P e 2 increases more its porosity than L04 P e 3 . However, when considering each Péclet condition applied, the absolute increase in porosity ∆ϕ is always higher in Lexos samples than Euville samples, which have higher increases than Normandie ones.

This result seems inconsistent as dolomite dissolution rate is lower than that of calcite (up to one order of magnitude) in similar conditions [START_REF] Chou | Comparative study of the kinetics and mechanisms of dissolution of carbonate minerals[END_REF][START_REF] Gautelier | An experimental study of dolomite dissolution rates as a function of pH from -0.5 to 5 and temperature from 25 to 80°C[END_REF][START_REF] Morse | The dissolution kinetics of major sedimentary carbonate minerals[END_REF][START_REF] Liu | Comparative study of dissolution rate-determining mechanisms of limestone and dolomite[END_REF][START_REF] Pokrovsky | Dissolution kinetics of calcite, dolomite and magnesite at 25 °C and 0 to 50 atm pCO2[END_REF]. Indeed, in Figure 3, we observe that the outlet Ca concentration for Lexos samples is between one half and one third of Euville samples. This apparent higher porosity increase for Lexos samples than for limestone samples in similar conditions is linked to two different

properties. The first one is the mineral molar volume that is higher for the dolomite than for calcite with 64.3 cm 3 /mol and 37 cm 3 /mol, respectively. The dissolved volume corresponding to one molecule of dolomite is then higher than calcite. The porosity increase in dolomite sample is thus higher than in limestone sample for a same quantity of dissolved mineral.

The second important property is the flow rate. In fact, for a similar Pe number, the imposed constant flow rate is different from one rock type to another due to the differences in pore size distribution. Consequently, flow rates applied to dolomite (Lexos) samples are higher than flow rates applied to calcite (Euville) samples (Table 1).

4.2. Impact of the hydraulic conditions and mineral composition on the dissolution rates Applying higher flow rates for Lexos samples than for Euville samples, in similar Péclet conditions, induces a larger acid renewal inside dolomite samples. It leads to a higher dissolution rate, which is defined as R =

[Ca] × Q and expressed in mol/s, and related to a higher increase in the porosity that is previously described. Indeed, the slope of the increase in this porosity is directly related to the dissolution rate R, standing between 10 -10 and 10 -7 mol/s, depending on the sample (Table 3). This is consistent with existing studies, where for experiments realized in P e 2 conditions, R is about 5 × 10 -8 mol/s in [START_REF] Noiriel | Changes in reactive surface area during limestone dissolution: An experimental and modelling study[END_REF] and 2 × 10 -8 mol/s in [START_REF] Luquot | Experimental Characterization of Porosity Structure and Transport Property Changes in Limestone Undergoing Different Dissolution Regimes[END_REF]; whereas experiments realized with higher Pe lead to R about 8 × 10 -7 mol/s [START_REF] Vialle | Percolation of CO2 -rich fluids in a limestone sample: Evolution of hydraulic, electrical, chemical, and structural properties[END_REF]. Note also that the dissolution rates are similar for the reproductive experiments (E01 P e 2 -E02 P e 2 ). The slope of the increase in porosity and the dissolution rate R are then both correlated with the Péclet conditions applied to the samples. Indeed, inside each rock type, samples dissolved with lower Pe display lower slopes in Figure 8 and lower R in Table 3. At the same time, when considering each Péclet condition, samples from Normandie always have higher porosity slopes and R than samples from Lexos, which are higher than Euville samples.

For identical Pe numbers, different flow rates are used depending on the rock pore diameters. Therefore, conversely, for two different Pe numbers, a similar flow rate could be applied. Indeed, relatively similar flow rates are applied to N03 P e 2 , E04 P e 4 and L04 P e 3 , dissolved with P e 2 , P e 4 and P e 3 , respectively. N03 P e 2 displays a dissolution rate 1.3 times higher than E04 P e 4 , which is 2.3 times higher than L04 P e 3 . The rate between the quantity of dissolved calcite and the quantity of injected acid is calculated as

R ′ = R Q ,
and is displayed in Table 3. Lexos samples rates R ′ are three times lower than Normandie and Euville ones. Therefore, dolomite dissolution is much smaller than calcite one for similar quantity of injected acid. Concerning only samples fully composed of calcite, chalk displays similar but a bit higher R ′ than crinoidal limestone, which can be explained by a higher reactive surface area in Normandie samples characterized by a higher quantity of small grains.

Link between the initial rock structure and dissolution rate

Inside each rock type, we observe that the higher the Péclet number applied to the sample, the higher the dissolution rate. In these conditions, the sample N05 P e 3 has the highest R while E08 Firstly, the higher the Péclet number, the darker the dots representing the samples in Figure 9, showing again that when the acid is injected with high Péclet conditions, the dissolution rate is higher inside the sample. Secondly, samples from Normandie are situated on the bottom of the graph, while

Euville samples are situated on the top and Lexos samples in between. This is due to the difference in formation factors, Normandie having the lowest and Euville the highest. We observe that the lower the formation factor, the darker the dots. The formation factor being defined as the ratio between the electrical conductivity of the fluid and that of the rock sample, it depends on the porosity that is accessible to the fluid and on the heterogeneities of the paths followed by the fluid. Small formation factors are for example associated to fractured rocks where the renewal rate is higher than in porous rocks [START_REF] Schön | Physical properties of rocks: fundamentals and principles of petrophysics[END_REF][START_REF] Roubinet | Relating Topological and Electrical Properties of Fractured Porous Media: Insights into the Characterization of Rock Fracturing[END_REF]. The higher renewal rate is directly linked to a higher dissolution rate. Here, Normandie samples display the lowest formation factors and highest dissolution rates. Therefore, chalk seems to be a more heterogeneous carbonate rock than crinoidal limestone and dolomite, probably due to its very high proportion of small pores associated to its higher porosity, leading to a lower cohesion compared to the two other rock types.

We observed in Section 3.3.2 that the experimental conditions do not seem to deeply affect the evolution of pore shape inside chalk (Normandie) and dolomite (Lexos) samples (Figure 6). However, concerning crinoidal limestone (Euville), a strong difference exists between E01 P e 2 and E02 P e 2 and the other samples of the set. After the experiments, the quantity of small pores sharply decreases and the quantity of large pores increases. A link can be established between the quantity of acid injected into the samples during the experiments and the evolution of pore shape. Indeed, even if the percolation experiment in E08 P e 1 lasts longer than experiments in E01 P e 2 and E02 P e 2 , the difference in flow rates between the experiments leads to a higher total quantity of acid injected inside E01 P e 2 and E02 P e 2 than in E08 P e 1 . Therefore, the total quantity of acid injected into a sample has more impact than the time during which the acid is injected. A very high quantity of acid is then responsible of strong changes in pore shape inside crinoidal limestone. Consequently, it seems that neither the flow condition nor the petrophysical properties changes are the main parameters controlling the reaction but that it is the amount of injected acid and the initial rock properties.

Finally, the conduits shapes displayed in Figure 7 show that dolomite samples are dissolved by creating very linear conduits with few ramifications.

This conduit formation explains the linear increase in permeability during the experiments done on Lexos samples. These two observations can be related to the low dissolution kinetic of dolomite compared to calcite. Indeed, the very low rate R ′ calculated in these samples means a very low quantity of rock dissolved per quantity of injected acid and induces a more localized dissolution than in limestone samples, showing again the strong impact of the initial rock properties on the dissolution process.

Conclusions

This study investigates the impact of mineralogy differences on the dissolution of carbonate rock through percolation experiments in similar conditions conducted on samples from three different carbonate rock type: chalk, crinoidal limestone and dolomite. At first, we demonstrated that inside each rock type, the lower the Péclet condition applied to the samples, the lower the dissolution rate. Looking at each Péclet condition, chalk samples display the highest dissolution rates whereas crinoidal limestone samples display the lowest, and dolomite ones stand in between. Secondly, we highlight that the dolomite dissolution rate is much smaller than the calcite one for similar quantities of acid injected into the samples. This is correlated with a lower dissolution kinetic, inducing localized linear conduits associated with a linear increase in permeability during dissolution experiments.

Then, inside full calcite rock type, the chalk has a larger reactive surface area due to its higher quantity of small grains and it displays slightly higher dissolution rates than crinoidal limestone for similar quantity of acid injected.

For a similar quantity of injected acid during the experiments, the flow rate injected is higher in Normandie chalk and induces a higher renewal rate and a lower formation factor.

Finally, for all rock types studied, the dissolution rate seems to be mainly linked to the mineral composition and the acid flow rate, as well as the amount of injected acid in the case of crinoidal limestone. The initial structure of the rock also plays an important role, as we observed that strong heterogeneities and structural parameters affect the dissolution rate and porosity increase.

pixels histogram and correcting brightness. The two-phase segmentation is done with a region growing method resulting in the macropore and matrix phase, the former corresponding to pores larger than the pixel size and giving the macropore porosity ϕ XR . The sample skeleton is defined as the paths connecting the center of each connected pore and is used to compute the permeability (k XR ), hydraulic tortuosity (τ h ), formation factor (F XR ) and cementation index (m XR ) [START_REF] Kozeny | Uber kapillare Leitung des Wassers im Boden[END_REF][START_REF] Clennell | Tortuosity: a guide through the maze[END_REF][START_REF] Ghanbarian | Tortuosity in Porous Media: A Critical Review[END_REF]. The software also provides the pore volume and surface, giving the surface-volume ratio ( S V ), the pore size distribution with the chord length method [START_REF] Torquato | Chord-Length Distribution Function for Two-Phase Random Media[END_REF] and the proportion of the percolating phase into the volume sample (P V ) from statistics calculations.

Petrophysical properties changes

In this section, we present supplementary data of petrophysical properties that we do not discussed in the main manuscript. In particular, cementation index m L and m XR , P and S waves velocities, relative pore size S V and the proportion of the percolating volume from the full porosity P V are presented in Table 4.

Mechanical factors (V p and V s velocities) are globally larger for Euville and Lexos samples than for Normandie ones. For the Normandie set, N08 P e 2 is the sample with the highest increase in P and S waves velocity. N03 P e 2 and N05 P e 3 both present the lowest increase in V p. A full description of this rock type can be found in [START_REF] Leger | Impact of hydrochemical conditions on structural and hydro-mechanical properties of chalk samples during dissolution experiments[END_REF].

Both E05 P e 3 and E08 P e 1 show a smaller increase in V p than the other samples. A particularity occurs with the sample E05 P e 3 , which is the only one with a decreasing V s over the dissolution.

Finally, both lexos samples present similar values of P waves velocity and cementation index m L . However, L04 P e 3 has a smaller initial S wave velocity. The sample L04 P e 3 displays the highest increase in V p. The two samples differ in V s evolution, which decreases for the sample L01 P e 2 and increases for the sample L04 P e 3 .

For all the rock types, structural properties (m XR ) and surface ratio ( S V )

generally decrease, except for m XR of N09 P e 1 for which we observe no significant changes. No significant changes are also observed for the percolating volume (P V ) for Normandie and Euville samples, while Lexos samples show an important increase.

S

V is lower for Euville than Lexos and then Normandie. Percolating volumes are higher than 93% for all Euville samples, while they stand from 84.7 to 95.9% for Normandie samples, and are below or equal to 68.3% for Lexos samples.

Every sample of each rock type does not change in the same way with dissolution. Concerning Normandie, two groups of samples can be defined.

N03 P e 2 and N05 P e 3 samples both decrease the most their structural properties and surface ratio, contrary to N08 P e 2 and N09 P e 1 samples. However, final S V values are about 100 mm -1 for the samples N03 P e 2 , N05 P e 3 and N09 P e 1 , while it equals 85 mm -1 for the sample N08 P e 2 . For Euville rock type, E02 P e 2 displays the highest decrease in m XR and S V , on the contrary to E04 P e 4 .

For Lexos rock type, the properties of the sample L01 P e 2 change the most between before and after the experiments. We observe that the dissolution barely affects the cementation index of L04 P e 3 , while both samples reach similar final values in m XR , S V and P V . The experiments lead to a higher decrease in structural factors (m L ) for the sample L01 P e 2 .

Samples m L m XR V p V s [-], and P and S wave velocities V p and V s [km/s], ratio of pore surface over pore volume S V [mm -1 ] and proportion of percolating volume P V [%]. The index L stands for Laboratory measurements and XR for 3D microtomographic images. The sample E01 was not imaged before experiments. For each rock type, the samples are ordered according to increasing Péclet values.

  Four samples come from a chalk cave near Le Havre, Normandie, north-western France, and are characterized by flint chalk from the lower Senonian. This group of samples is named Normandie and the samples labels are N03, N05, N08 and N09. A set of five samples was cored into a limestone block from Euville quarry near Nancy, north-eastern France, and is defined as crinoidal limestone from the Oxfordian. It is called Euville and the cores are named E01, E02, E04, E05 and E08. The two last samples were cored in the Lexos quarry near Toulouse, south-western France, described as a reddish recrystallized limestone from the Bajocian lately dolomitized. The set of samples is named Lexos with samples L01 and L04. X-ray Diffraction (XRD) on a Bruker D8 Discover, X-ray Fluorescence (XRF) measurements and Scanning Electron Microscopy (SEM) on a FEI Quanta 200 FEG observations show that Normandie and Euville rocks are fully composed of calcite (CaCO 3 ), whereas Lexos is made up of dolomite (CaMg(CO 3 ) 2 ). The dolomite formula is determined using the Ca and Mg outlet concentrations during the percolation experiments assuming that the dissolution is stoechiometric and no precipitation reaction occurs from the dissolution. For the two experiments on dolomite, constant Ca M g ratio is observed at the outlet and the dolomite formula is established to be Ca 1.06 Mg 0.94 (CO 3 ) 2 .

Figure 1 :

 1 Figure 1: 2D vertical slices from 3D X-ray micro-tomography (XRMT) images of the initial structure of all the samples from the three rock types.

  [m 3 /s], L the sample length [m], µ the dynamic viscosity of water [Pa.s] set to 0.001 Pa.s, A the surface of fluid injection [m 2 ] and ∆P the differential pressure between the inlet and outlet of the sample [Pa]. Concentration of Ca ions for the three rock types and that of Mg for Lexos rock are measured by ICP-AES (Inductively Coupled Plasma Atomic Emission Spectroscopy, Cirad, Montpellier) in the outlet samplings collected at time t i (i = 1, ..., N ) with N the number of samples. The porosity is deduced from these concentrations based on the equivalence between the quantity of Ca or Ca Mg collected in the outlet fluid samples and the quantity of dissolved calcite or dolomite from the rocks, respectively. The calcium carbonate mass dissolved between times t i-1 and t i , m CaCO3t i , is then expressed as

  with[Ca] t i the calcium concentration at the sampling time t i [g/m 3 ], [Ca] t 0 the initial calcium concentration [g/m 3 ], t i -t i-1 the time spent since the last sampling [s], Q the flow rate [m 3 /s], and M Ca and M CaCO3 the molecular masses of calcium and calcium carbonate, respectively [g/mol]. Concerning the dolomite rock type, the proportion of the mass of Ca and Mg from the dolomite formula Ca 1.06 Mg 0.94 (CO 3 ) 2 allows to calculate m CaMg(CO3)2t i .

Figure 3 :

 3 Figure 3: Evolution of the pH at the outlet of the experiments (pH out , first row), the differences in fluid conductivity (σ f , second row) and calcium and magnesium concentrations between the outlet and inlet of the percolating experiments (∆[Ca] and ∆[Mg], third row), with Péclet numbers P e 1 = 0.09 (first column, diamonds), P e 2 = 0.65 (second column, squares), P e 3 = 1.97 (third column, circles) and P e 4 = 5.26 (third column, stars). Samples labels with N stand for Normandie chalk, E for Euville crinoidal limestone and L for Lexos dolomite.

Figure 4 :

 4 Figure 4: Evolution of the normalized rock permeability k * [-] during the percolating experiments, where k * is defined as the permeability of the sample along the experiment normalized by its initial permeability. The dot represents the final value of permeability. Graphics are displayed according to Péclet numbers, in columns (P e 1 , P e 2 and P e 3 &P e 4 ). Due to the large differences in experiments duration, a zoom of Normandie values is displayed on the second row.

1 .Figure 5 :

 15 Figure 5: Pore diameters distribution for each sample in each rock type from centrifugation measurements. The Péclet conditions applied to the samples are: P e 1 (N09, E08), P e 2 (N03, N08, E01, E02, L01), P e 3 (N05, E05, L04) and P e 4 (E04).

Figure 6 :

 6 Figure6: Chord lengths distribution for each sample before (dotted lines) and after (solid lines) percolation. Lines with light colors are for average lengths along X and Y axes, while lines with dark colors are for chord lengths along Z axis. Normandie, Euville and Lexos samples are located on the first, second and third rows, respectively. The Péclet conditions applied to the samples are: P e 1 (N09, E08), P e 2 (N03, N08, E01, E02, L01), P e 3 (N05, E05, L04) and P e 4 (E04).

Figure 7 :

 7 Figure 7: Main path conduits of each sample depending on the four Péclet numbers (in columns) and the rock type (in rows). The samples are all displayed with the acid injection above them. The scale in the bottom right applies to all the samples.

Figure 8 :

 8 Figure 8: Evolution of rock porosity change, ∆ϕ, defined as the porosity measured at time t minus the initial porosity measured in laboratory ∆ϕ(t) = ϕ(t) -ϕ L evaluated from Ca and Mg ions concentrations analyzed in the outlet fluid during percolating experiments and using Equation (3). The graph on the right is a zoom of the graph on the left.

Figure 9 :

 9 Figure 9: Dissolution rate of each sample, depending on the initial formation factor F L and the Péclet number Pe applied during the experiments. The color scale shows darker colors for higher dissolution rates R.

  They are similar 227 for each sample from Normandie and Euville, as they are all considered to be REV. However, we observe a change in the plateau value for Lexos because of the high heterogeneity initially located in L04 P e 3 . Concerning outlet ions concentrations, samples from Normandie display similar values on the plateau regardless of the Péclet number applied to them, while the plateau values for Euville and Lexos samples decrease with the increase in Pe. Secondly, whatever the Pe is, fluid conductivity and ions concentration obtained for dolomite samples (Lexos) are always lower than the ones of full calcite samples (Normandie and Euville). Concerning P e 3 , the outlet pH of L04 P e 3 is lower of 1.5 than the one of N05 P e 3 and E05 P e

3 , whereas the conductivity difference is twice lower. The difference is less pronounced for P e 2 , where L01 P e 2 displays a plateau of pH out lower of 0.5 than Normandie and lower of 1 than Euville, and a plateau of conductivity lower of 1 than Normandie and Euville ones. The lower values of pH out in Lexos experiments are due to the smaller quantity of dolomite molecules dissolved compared to calcite ones. Even if the dissolution of one mole of dolomite consumes two times more H + than one mole of calcite, limestone samples (Normandie and Euville) display more than twice Ca concentration than dolomite samples. Additionally, we observe that the ratio between Ca and Mg is almost constant during the two experiments for Lexos samples and established to be representative of a stoichiometric dissolution. The corresponding formula is then used for mass balance calculation as explained in Section 2.3.

  Table 2 firstly show that the initial properties differ between each rock type. Indeed, Normandie samples are the most porous ones and Euville are the least. Euville samples have the highest formation factors F L & F XR and tortuosities τ e & τ h , while Normandie samples have the lowest, and Lexos samples have parameter values situated between them.However, permeabilities and cementation indexes are relatively similar for the three rock types. More results on initial rock properties and discussion are available in[START_REF] Leger | Importance of Microstructure in Carbonate Rocks: Laboratory and 3D-Imaging Petrophysical Characterization[END_REF] and in Supplementary Material.The final porosities of each sample are obtained from laboratory measurements (ϕ L ), microtomographic images ϕ XR and are also calculated from Ca and Mg concentrations with Equation (3) (ϕ ch ). The dissolution experiments of the three rock types are not responsible for a significant change in porosity, especially in ϕ L where some porosity variations are so tiny that they are included in the error measurement, while permeability k L and k XR increase.

	Samples Péclet ϕ L ϕ XR k L k XR F L F XR τ e τ h	N09 Pe 1 27.2 9.1 0.71 65.2 24.2 31.3 2.57 1.68	N03 Pe 2 38.0 8.3 11.19 12.6 8.3 36.2 1.78 1.74	N08 Pe 2 28.8 9.7 8.14 505 26.6 28.8 2.77 1.67	N05 Pe 3 37.8 7.9 9.07 25.5 7.8 34.1 1.72 1.64	E08 Pe 1 12.6 5.6 0.06 5.4 178.6 140.6 4.75 2.80	E01 Pe 2 13.2 -0.28 -116.2 -3.91 -	E02 Pe 2 14.8 8.0 0.44 10.9 101.0 71.6 3.87 2.40	E05 Pe 3 12.8 5.9 1.47 24.8 222.2 95.6 5.34 2.38	E04 Pe 4 14.6 7.2 3.77 112.2 103.1 65.1 3.87 2.17	L01 Pe 2 18.2 7.4 1.82 1.1 49.0 102.1 2.99 2.74	L04 Pe 3 18.8 4.7 11.61 10.8 68.5 47.1 3.59 1.48	Samples Pe ϕ L ϕ XR ϕ ch k L k XR F L F XR τ e τ h	N09 Pe 1 27.2 10.0 27.4 300 1291 15.0 27.3 2.08 1.65	N03 Pe 2 35.7 8.9 38.3 2500 8059 5.2 24.7 1.36 1.48	N08 Pe 2 29.7 10.4 28.8 230 1497 11.7 25.5 2.03 1.63	N05 Pe 3 36.5 8.8 38.2 8000 11304 5.2 26.6 1.38 1.53	E08 Pe 1 12.9 6.6 13.5 20 28 105.3 87.8 3.68 2.41	E01 Pe 2 14.7 8.2 15.0 50 18231 29.0 56.1 2.06 2.14	E02 Pe 2 16.3 9.8 16.9 70 2092 26.1 39.8 2.06 1.98	E05 Pe 3 12.8 7.1 13.2 3000 7481 50.3 57.0 2.53 2.01	E04 Pe 4 14.8 7.8 15.1 700 5502 41.5 52.6 2.48 2.03	L01 Pe 2 20.6 8.9 21.0 150 229550 13.7 23.1 1.68 1.44	L04 Pe 3 19.3 5.6 20.0 320 5556 25.3 35.5 2.21 1.41
						Initial										Final

Other structural parameters (i.e., formation factor F L & F XR and tortuosity τ e & τ h ), calculated from electrical measurements and X-ray images, decrease.

Table 2 :

 2 Petrophysical properties of samples at initial and final states, i.e., before and after the percolation experiments, from laboratory measurements (porosity ϕ

L [%], permeability k L [mD], formation factor F L [-], electrical tortuosity τ e [-]) and 3D X-ray imaging calculations (porosity ϕ XR [%], permeability k XR [mD], formation factor F XR [-], electrical tortuosity τ h

Table 3 :

 3 Table of experimental properties of each sample. Pe is the Péclet condition applied, R the dissolution rate per acid injection time [mol/s], R ′ the dissolution rate per acid injection volume [mol/m 3 ] and t p is the percolation time [h].

		Pe	t p	R	R ′
	N09	P e 1 7.3 5.86e-9 7.33
	N03	P e 2 1.9 5.17e-8 7.39
	N08	P e 2 0.45 4.49e-8 6.41
	N05	P e 3 1.2 1.31e-7 7.49
	E08	P e 1 893 6.26e-10 6.73
	E01	P e 2 160 3.41e-9 6.82
	E02	P e 2 309 3.45e-9 6.90
	E05	P e 3 11.9 1.58e-8 6.32
	E04	P e 4 4.4 3.86e-8 6.49
	L01	P e 2 105 8.75e-9 2.76
	L04	P e 3 7.7 1.65e-8 2.17

  P e 1 has the lowest. We observe that some samples from different rock types display similar values of R while they are submitted to different Péclet conditions, such as N09 P e 1 with E01 P e 2 and E02 P e 2 , or E04 P e 4 with N03 P e 2 and N08 P e

Table 4 :

 4 N09 P e 2.45 1.43 2.97 1.64 103.0 94.9 N03 P e 2.19 1.44 2.36 1.18 113.0 84.7 N08 P e 2.63 1.44 2.33 1.30 87.6 95.9 N05 P e 2.12 1.39 2.35 1.25 111.4 86.1 E08 P e 2.51 1.71 3.86 2.10 33.7 93.0 E01 P e 2.35 -3.08 1.90 --E02 P e 2.42 1.69 2.32 1.30 41.9 99.1 E05 P e 2.63 1.61 3.73 2.04 37.4 98.9 E04 P e 2.41 1.59 2.56 1.42 40.8 95.1 L01 P e 2.29 1.77 3.40 2.00 68.5 42.1 Initial L04 P e 2.53 1.26 3.10 1.86 65.8 68.3 Samples m L m XR V p V s N09 P e 2.08 1.44 3.89 1.83 98.9 94.8 N03 P e 1.60 1.33 2.76 1.65 103.5 86.4 N08 P e 2.03 1.43 3.74 2.01 85.0 95.7 N05 P e 1.63 1.35 2.80 1.85 100.9 89.1 E08 P e 2.27 1.65 5.33 2.18 33.1 92.5 E01 P e 1.75 1.61 5.27 2.07 29.8 99.6 E02 P e 1.80 1.59 5.08 2.00 34.8 99.5 E05 P e 1.90 1.53 5.45 1.81 34.4 96.8 E04 P e 1.95 1.56 5.32 1.91 38.2 99.1 L01 P e 1.66 1.30 4.74 1.85 57.9 88.3 Final L04 P e 1.96 1.24 4.81 1.94 57.7 88.6 Petrophysical properties of samples at initial and final states, i.e., before and after the percolation experiments from laboratory measurements and 3D X-ray imaging calculations with cementation index m L [-] & m XR

	S V	P V
	S V	P V

Supplementary

Materials and methods

Laboratory measurements

The liquid porosity (ϕ L ) and permeability (k L ) of the rock samples are measured by double-weighing saturated and oven-dried samples and from an experimental device applied to saturated samples, respectively. The electrical impedance is defined by injecting electric current in the saturated samples and used to define the rock conductivity, formation factor (F L ), cementation index (m L ) and electrical tortuosity (τ e ) from the well-known equations provided in [START_REF] Waxman | Electrical conductivities in oil-bearing shaly sands[END_REF]; [START_REF] Archie | The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics[END_REF]; [START_REF] Clennell | Tortuosity: a guide through the maze[END_REF]. The P and S waves velocities (V p and V s) are obtained by injecting ultrasonic frequency waves of 500 kHz with two piezoelectrical transducers. The pore size distribution is obtained by centrifugation. Following the method described by [START_REF] Reatto | Validity of the Centrifuge Method for Determining the Water Reten-tion Properties of Tropical Soils[END_REF]; [START_REF] Rötting | Changes in porosity, permeability, water retention curve and reactive surface area during carbonate rock dissolution[END_REF], increasing velocities are applied on saturated samples. After each cycle of velocity, the water loss is determined by weighing the samples, providing the proportion of a given range of pores size from Young-Laplace equation. Using velocities from 32 to 471 rad/s leads here to pores sizes ranging from approximately 100 to 0.5 µm.

X-ray micro-tomography

3D X-ray micro-tomography (XRMT) images are obtained using the Xray Computed Tomography (XRCT) scanner (EasyTom 150) of the Institute of Evolution Sciences of Montpellier (ISEM, Montpellier, France) with a pixel size of 12 µm. A homemade imaging software [START_REF] Gouze | Non-Fickian dispersion in porous media explained by heterogeneous microscale matrix diffusion[END_REF] is used to treat the images with filters to improve images quality by smoothing the