Real Time 3D Observations of Portland Cement Carbonation at CO2 Storage Conditions

Depleted oil reservoirs are considered a viable solution to the global challenge of CO2 storage. A key concern is whether the wells can be suitably sealed with cement to hinder the escape of CO2. Under reservoir conditions, CO2 is in its supercritical state, and the high pressures and temperatures involved make real-time microscopic observations of cement degradation experimentally challenging. Here, we present an in situ 3D dynamic X-ray micro computed tomography (μ-CT) study of well cement carbonation at realistic reservoir stress, pore-pressure, and temperature conditions. The high-resolution time-lapse 3D images allow monitoring the progress of reaction fronts in Portland cement, including density changes, sample deformation, and mineral precipitation and dissolution. By switching between flow and nonflow conditions of CO2-saturated water through cement, we were able to delineate regimes dominated by calcium carbonate precipitation and dissolution. For the first time, we demonstrate experimentally the impact of the flow history on CO2 leakage risk for cement plugging. In-situ μ-CT experiments combined with geochemical modeling provide unique insight into the interactions between CO2 and cement, potentially helping in assessing the risks of CO2 storage in geological reservoirs.

. Scheme of the setup during the experiment Figure S2. Steps for the image processing                  .   Table S1. Mineral and materials present in the cement exposed to CO 2 , their corresponding mass densities and effective linear attenuation coefficients.

S1. Sample preparation and experimental details
Sample preparation. Class G cement (High Sulfate Resistant Well Cement, Norcem AS) was mixed according to API recommended practice 1 with a water/cement mass ratio of 0.44. The slurry was poured into a cylindrical plastic mold with a diameter of 5 mm. To facilitate the chemical and mechanical analysis of the cement carbonation, a cylindrical channel running through the sample was artificially made by inserting a nylon fishing line (diameter 0.4 mm) into the cement slurry. The samples were cured for 3 days at ambient temperature and pressure, and then both the mold and the fishing line were carefully removed. The sample was left for further curing in plastic bags to avoid water evaporation and drying. The curing post-demolding lasted for two weeks before the synchrotron experiment. The cement sample was purposely cleaved by applying a point stress (using a scalpel) normal to the face of the sample immediately prior to the experiment. The two resulting pieces were fit back together and mounted into the sample holder. This additional defect in the cement sample was created to compare the interaction of the fluid with a smooth artificial channel to a rough natural fracture. The fracture extended through the whole sample. The final diameter and length of the sample were 5 mm and 4 mm respectively. While the sample dimensions were dictated in part by the experimental setup, notably Xray contrast and transmission, the sample was still sufficiently much larger than the characteristic Portland grain diameter (~µm) to give realistic insights into the mechanical and chemical processes taking place in the bulk cement.
Experimental details. The cement sample was measured using the HADES triaxial deformation cell 2 , which is X-ray transparent, can apply a confining pressure up to 100 MPa and operate from room temperature to 200 o C. The sample equipment comprises the cell itself, two pumps that control the confining and axial pressures, and two injection pumps that control the fluid pressure (Fig. S1), see Renard et al. 2 A high pressure mixing reactor with a magnetically coupled stirrer was connected to the system. The cement sample was placed inside the rubber gasket, together with two sand spacers (7% porosity, 5 mm diameter, 3 mm length) above and below to achieve a homogenous exposure of CO 2 towards the sample end surfaces The fluid was composed of CO 2 and milliQ water which was previously mixed in the reactor at 3.6 MPa and 16 o C for 4 hours to achieve saturation. Water was chosen instead of the 0.5M NaCl brine commonly used in order to increase the CO 2 saturation and hence the reaction rates. The CO 2 -saturated fluid was transferred to the pumps and pressurized to 28 MPa. The CO 2 -saturated fluid was injected axially into the cement sample from the top. The working pressure and temperature were 28 MPa and 80 o C. To keep the sample in mechanical equilibrium during the experiment, the cement sample was under axial and confining pressures of 31 MPa and 30 MPa, respectively. In the course of the experiment, there were stages of CO 2 flowing through the channel of the cement cylinder and stages of hydrostatic CO 2 conditions. Fig. 1b displays the flow rate as a function of time.
The first tomographic acquisition was performed when the axial and radial pressure were 6 MPa and 5 MPa, respectively, which is defined as time t = 0 in this work. Thereafter the axial and radial pressures were gradually increased to 31 MPa and 30 MPa, respectively. In parallel, CO 2 saturated in water was injected to the system with a flow rate of ~ 50 mL/h and the fluid pressure was increased to 28 MPa. From t = 7 min the system was purged with the fluid for 24 min with a flow rate of 25 m/L. The second measurement was obtained at t = 31 min. From t = 32 min and throughout the remainder of the experiment, alternating static and flow conditions were applied. In periods [32,374] Figure S1. Scheme of the in situ setup during the experiment. The HADES X-ray transparent sample cell is indicated with gray, and the sample itself was placed inside a rubber jacket at the waist of the cell. Four high-pressure pumps were used to control the axial, confining (radial), pore inlet and pore outlet pressures.

S2. X-ray attenuation coefficient of different zones
The Effective Linear Attenuation Coefficient (ELAC) is directly proportional to the grayscale of the Xray µ-CT images, for more details see Mason et al 3 . Table S1. Mineral and materials present in the cement exposed to CO 2 , their corresponding mass densities and effective linear attenuation coefficients.
Material To calculate the ELAC of the different zones, we consider, in a first order of approximation, that carbonate zone and amorphous silica zone are a mixture of calcium carbonate (aragonite) and amorphous aluminosilicate (morderite) 4 and pores 3 .
Here, is the average linear attenuation coefficient of the zone, is the linear attenuation coefficient of the air, is the linear attenuation coefficient of the mineral and f is mineral or porosity fraction. See more details in Mason et al. 3

S3. Image Processing
Image processing was performed by means of automated procedures written in the ImageJ Macro scripting language. The Fiji software, which is a distribution of the Java-based program ImageJ, was applied. Automated procedures, as opposed to manual image segmentation, was required to handle the large amount of image data. ImageJ macros were created with the following objectives:  To quantify the volume of precipitated calcium carbonate in the cylindrical cavity as a function of time.  To measure the amount of reacted cement as a function of time.  To investigate whether there is a deformation of the cement cylinder during the experiment.
The scripts consisted of a series of steps for image enhancement, image segmentation and voxel measurements. The uncertainty of the segmented region volumes in the 3D images was estimated from the minimum and maximum number of voxels that could be considered part of the feature of interest.
The general approach taken is presented schematically in figure S2. Figure S2. Diagram illustrating the general approach taken for image processing.

S3.1. CaCO 3 precipitation in the cylindrical channel
With the aim of measuring the growth and dissolution of CaCO 3 as a function of time, 3D image processing was performed. An action sequence was executed for each time point using an ImageJ Macro consisting of four main steps as presented by figure S3. Figure S3. The steps performed in order to isolate the voxels corresponding to CaCO 3 from the surrounding voxels.
Step 1 was carried out with the purpose of reducing the probability that cement grains located outside the cylindrical cavity were labeled as precipitated CaCO 3 . Steps 2 and 3 served to isolate the voxels corresponding to CaCO 3 from the surrounding voxels. Finally, in step 4, the volume of the detected CaCO 3 grains was measured for each time point. Figure S4 shows the appearance of a slice image after every step. Figure S4. Reconstructed CT slice image displaying the cylindrical channel at t = 340 minutes, after the completion of (a) the first, (b) the second, and (c) the third steps described in figure S3.

S3.2. Reacted cement
Reacted cement developed both near the cylinder end surfaces and near the cylindrical channel. Routines for image processing were designed with the objective to quantify the volume of reacted cement (combined volume of the porous and carbonated zones) in the specimen as a function of time. The procedures for image processing were incorporated in an ImageJ script. The entire cylinder was considered except the topmost and bottommost ~ 45µm of the cement cylinder, which was excluded because of complications during image segmentation caused by the presence of sandstone at the cylinder end surfaces. The routine for image processing is presented in figure S5. First, morphological dilation was carried out using a cubic structuring element. The operation was performed to exploit the fact that unreacted cement has a higher content of bright grains than unreacted cement. Consequently, the morphological dilation increased the displayed intensity of the unreacted cement more than that of the reacted cement. Figure S6 illustrates how the images were transformed by the morphological operation. Next, 3D Gaussian blur was carried out with the purpose of smoothing intensities. Thereafter, 3D single linkage region-growing was performed. Next, morphological dilation was performed once again with the purpose to fill small holes caused by noise and to relabel voxels that were wrongly categorized as background voxels on account of the first dilation operation. Moreover, the volume of CaCO 3 located in the cylindrical channel had to be subtracted from the image foreground. Finally, the number of voxels corresponding to reacted cement was counted. Figure S6. The transformation through image processing of a reconstructed CT slice at t = 620 minutes. a) The CT image prior to the image processing. b) The appearance of the image after the first dilation operations has been performed. c) The image after the Gaussian blur algorithm has been executed.

S4. Portlandite depleted zone
The portlandite depleted zone predicted by several previous studies was not easily detectable in the CT images. A thin region outside the carbonated zone was slightly less dense than the adjacent unreacted cement and may be interpreted as the portlandite depleted zone. However, due to the small density variations in the unreacted cement, it is difficult to visualize the transition between the portlandite depleted zone and unreacted cement. The low contrast between the cement zones is also due to the thick sample holder made of titanium, oil and rubber through which X-rays have to pass. By using image processing, we could estimate the thickness of the portlandite depleted zone to be around 20 µm. Figure S7. The transformation of a reconstructed CT slice image (t = 960 min) by image processing. The image displays reacted cement surrounding the cylindrical channel. Note the thin porous layer with reduced attenuation adjacent to the carbonate front, which can be interpreted as portlandite depleted layer.

S5. Chemical numerical model
In the model, the flow of carbonated fluids through the channel is calculated using the local cubic law. The fluid concentration along the fracture is calculated by solving mass balances for carbon and calcium, accounting for their advection, diffusion, and reaction with cement. The propagation of the reacted layers into the cement is computed using a numerical model developed by Walsh et al. 5 to efficiently simulate the chemical reactions between cement and carbonated fluid. As shown in Fig. S8, from inside the cement to the surface of the channel, the layers modeled correspond to the unreacted cement, the portlandite depleted layer, the calcium carbonate layer, and the amorphous silicate layer. The model assumes that the dissolution and precipitation reactions occur at discrete reaction fronts between these layers. The reactions controlling the movement of each front are based on those originally identified by Kutchko et al. 6 : Outermost Front: CaCO 3(s) → Ca 2+ + CO 3 2-The speeds at which the fronts move depend on the flux of reactants and products into or out of the fronts, which in turn depends on diffusion and reaction rates, the properties of the different layers, and the fluid chemistry. Portlandite dissolution is typically much faster than calcite precipitation or dissolution 7 . Thus, the concentration at the innermost front is assumed to be at portlandite equilibrium. Concentrations at the remaining two fronts depend on relative rates of diffusion and reaction 8 . When reaction is significantly faster than diffusion, equilibrium front concentrations are used, and fluxes are calculated based on diffusion across the front 9 . The assumption of equilibrium concentration prevents the precipitation of calcium carbonate inside the channel (see the upstream end of Fig. S8 (b)). When the layers are thin, and diffusion is faster than reaction, front concentrations are assumed to be equal to the fluid concentration, and the flux is calculated based on the reaction rates 8 . This allows for the precipitation of calcium carbonate within the channel as shown in the downstream end of Fig. S8 (b). Allowing for both conditions gives the model the capability of predicting when three distinct layers grow within the cement and when calcium carbonate precipitates inside the channel 8 .
The model was originally derived and developed in the cartesian coordinate system as it was calibrated to a set of flow through fracture experiments 9 . To model the current experiment, the cylindrical channel is approximated as a parallel plate fracture with the same length along the flow direction. The width (1.26 mm) and aperture (100 µm) were chosen such that the correct surface area and the volume of the channel is simulated. This choice was made because the amount of reaction depends on the surface area of the cement in contact with the carbonated water. Similarly, the concentration of ions in the channel during the hydrostatic phase and the residence time of the water in the periods of flow depend on the volume of the channel. Approximating a cylindrical channel as a parallel plate fracture necessarily results in discrepancies in the magnitudes and slopes of the simulated curves. However, the qualitative trends are expected to be the same as they are largely determined by the flow conditions and the carbonated water and cement chemistry. Figure S8: Schematic for the coupled model. a) The channel in the sample that is being modeled. b) Distribution of layers along the length of the channel. At the upstream end, the porous layer grows as the calcium carbonate zone is confined to within the cement. At the downstream end, the calcium carbonate zone extends beyond the channel surface resulting in precipitation within the channel and the absence of the porous silica zone.
Unlike nucleation and growth of individual calcite/aragonite crystals observed in the cylindrical channel, the model only allows for uniform precipitation as seen in the downstream end of the channel in Fig. S8 (b). This passivates large portions of the channel surface preventing the amorphous silicate layer from growing until the surface precipitate is completely dissolved. The absence of the amorphous silicate layer in the presence of calcium carbonate precipitate within the channel has been hypothesized by Huerta et al. 10 and Luquot et al. 11 and has also been observed in the fracture in this experiment. However, it fundamentally differs from what is observed in the channel in this experiment. Thus, for the purpose of modeling this experiment, a lower effective reaction rate is used for the precipitation inside the channel. The lower effective calcite reaction rate accounts for the smaller surface area over which calcium carbonate precipitates in the channel.
Since, in the experiment, calcium carbonate does not precipitate on a large fraction of the channel surface, the porous layer grows extensively along the channel during the convective phases. The presence of calcium carbonate precipitate prevents the growth of the porous layer in the model. Thus, the growth of the layers within the cement, specifically the amorphous silicate layer, is modeled using equilibrium front concentrations that prevent the precipitation of calcium carbonate on the channel surface and thereby allows the growth of the porous layer 5 . Consequently, all the calcium carbonate is forced to precipitate within the cement.

a) Thin portlandite depleted layer
The growth of the portlandite depleted layer could not be well resolved in the tomography study due to the large uncertainty arising from small density differences at the unreacted cement/portlandite depleted zone interface and its small thickness close to the voxel resolution of 6.5 micrometers. Nevertheless, the thickness of this zone was estimated to be 20 µm, which is around 1/100 of the thickness of the carbonated zone at the end of the experiment.
The growth of the reacted layers within the cement predicted by the diffusion-controlled equilibriumbased model developed by Walsh et al. 5 is sensitive to properties like composition and tortuosity of the unreacted and reacted cement. There are large uncertainties associated with these parameters. Our model's predictions show that modifying the parameters in Table S2 can significantly alter the Δ thicknesses of the reacted layers. For example, increasing decreases the thickness of the portlandite Δ depleted layer and increases the thickness of the calcium carbonate layer.
is a measure of the Δ difference in the amount calcium in the layers on either side of the front . Increasing corresponds Δ to an increase in the amount of portlandite in the cement. The values tabulated in Table S2 were used to model the experiment in this study as it provided good comparison with the experimental data. The predicted layer growth as a function of time is shown in Fig. S9. Note that Fig S9 was generated by assuming all the calcium carbonate precipitates within the cement to allow for the growth of the amorphous layer.

b) Onset of precipitation within the channel
The volume of precipitated CaCO 3 in the channel predicted by the model is shown in Figure S10. To match the experimental observations, the effective precipitation rate in the fracture was reduced by a factor of 100. This was done to mimic localized precipitation because the model assumes uniform precipitation instead of localized precipitation at specific nucleation sites that occupy a small fraction of the surface area of the cement.  As seen in Fig. S10, the precipitation of calcium carbonate begins about 30 minutes into the first hydrostatic phase. In the model, calcium carbonate will precipitate in the channel when the concentrations of calcium and carbonate ions are such that the fluid is supersaturated and calcium carbonate has precipitated in the existing porous layer within the cement. Since the injected fluid has no calcium ions, the incubation period observed in Fig. S10 is the time required for enough calcium to dissolve from the cement, diffuse to the channel and saturate the brine, and precipitate calcium carbonate in the porous layer. The 31-minute injection period resulted in some degradation of the cement even prior to the start of the first hydrostatic phase. This results in a longer incubation time as dissolved calcium ions must travel longer distances to enter the channel and calcium carbonate needs to precipitate in a larger porous layer.

b) Calcium carbonate precipitation in the second hydrostatic phase
In the second hydrostatic phase, the model predicts continued precipitation of calcium carbonate with a negligible incubation period. Unlike the first hydrostatic phase, calcium carbonate precipitate is already present in the fracture at the beginning of the second hydrostatic phase. Thus, the undersaturated brine in the fracture can quickly reach calcium carbonate equilibrium by dissolving small amounts of existing calcium carbonate. Additional calcium entering the channel from the cement makes the brine in the fracture supersaturated and results in further calcium carbonate precipitation. This is not seen in the experiment possibly due to the nature of precipitation occurring in the channel. Unlike the model, in the experiment calcium carbonate is precipitating in discrete nucleation sites. This leaves a large fraction of the channel exposed to attack by carbonated brine during the flow periods of the experiment. Consequently, both calcium carbonate precipitate in the channel and the porous layer in the cement coexist in the same location. As shown in Fig. S8, the model does not allow the presence of precipitation in the channel and growth of porous layer. In the second hydrostatic phase it is possible that due to the presence of the thick porous layer, the brine in the channel does not get oversaturated to yield additional precipitation. The lack of precipitation in the channel and the lack of growth of the porous layer suggest that the brine in the channel is in equilibrium with the precipitated calcium carbonate.       shown are along X, Y and Z, respectively, for a cross section (X-Y) obtained perpendicular to the cylinder axis of the sample. The displacement field is calculated as the difference between a tomogram in the first static stage (t = 90 min) and the first scan. No significant lateral strain around the channel is observed at this early stage of the experiment.