Effect of pH on Spontaneous Imbibition in Calcareous Rocks

Reactive transport in porous media exhibits multifaceted interactions that are dependent on the matrix and fluid properties, and which ultimately alter these properties. A set of calcareous rock samples with unique mineralogy and varying petrophysical properties are selected for this study. A capillary rise experiment is performed in each sample, first with deionized water and then with a dilute, pH 2, HCl solution. Pre‐ and post‐acid petrophysical properties such as porosity, permeability, pore size distribution, and contact angle are measured for each sample along with the capillary rise profile. The latter is tracked by applying image analysis on video recording. The rock mineralogy significantly affects the acidic fluid intrusion into the rock samples. Calcite dissolution is the main reaction that results in the opening of the pore space. This is more prominent in all the carbonate samples where a higher proportion of calcite minerals is present. A higher capillary rise is consistently observed compared to the neutral fluid along with an increase in porosity and the mean pore size. The contact angle also undergoes changes making the carbonate matrix from oil‐wet to neutral‐wet. Coupling capillary interactions with fluid reactivity is often neglected in fluid transport phenomena. This study offers new insights into the relative importance of reactivity at the timescale of spontaneous imbibition. This is important in understanding dissolution and precipitation processes during capillary flow.


Introduction
The geochemical interactions that happen in the subsurface are a result of a combination of fluid, heat, and solute transport along with the chemical reactivity of the minerals present inside the rocks.Thermodynamics is not enough to explain the chemical changes that happen in the minerals since the system is not entirely isolated (Lichtner et al., 2018).Interactions between the fluid, solid phase, and bioorganisms with the minerals contained in the rocks are crucial to explain the cause of the chemical changes inside the rocks.These interactions include, but are not limited to, precipitation and dissolution, adsorption and desorption, microbial reactions, and redox transformation (Matthess, 1982;Siegel & Deutsch, 1997).Additionally, mechanically induced chemical reactions can occur when changes in mechanical properties deform the subsurface, leading to chemical degradation effects (Byrne et al., 2018;Caruso et al., 2009).
Spontaneous invasion of reactive fluids in porous media is significant in a multitude of subsurface processes where chemical and physical processes occur concurrently (Bryant & Thompson, 2001).Pollutants, which are transported with groundwater, can leach and harm the environment (Foster et al., 1982;Hantush et al., 2000;Malyan et al., 2019); soaking time during acidization of an oil well for production enhancement is an important variable to determine the alteration of the petrophysical properties of the rocks (Teklu et al., 2017); and the interaction between the CO 2 , brine, and cap rock during geosequestration can change the petrophysical properties of the cap rock to enable CO 2 leakage (Cerasi et al., 2017;Olabode & Radonjic, 2013).Specifically for groundwater flow, even though the air saturation is small (around 0.25 (Chen et al., 2020)), it significantly impacts the ionic concentration in the water (Stroj et al., 2020).Thus, it is still important to study the capillarity within the fluids-minerals-air interface.
The main forces that drive the spontaneous imbibition are the capillary forces, which are related to the surface tension/energy, and resisted by the viscous forces (Mason & Morrow, 2013).The earliest and simplest analytical solution that successfully characterized the capillary rise behavior was by Lucas (1918), which was later modified by Washburn (1921), for a vertical capillary tube with a constant cross-sectional area and in the absence of gravity.The equation was derived to establish a relationship between the time and capillary height, and a power law relationship was observed.The equation which is famously called the Lucas-Washburn equation (L-W equation) is represented below: where x is the capillary height (m), r is the pore radius (m), σ is the surface tension between the fluid-air interface (N/m), θ is the contact angle (°), μ is the viscosity of the fluid (Pa.s), and t is the time (s).
Over time, the L-W equation has been found to be insufficient to model spontaneous imbibition in porous and permeable medium.The L-W equation assumes the shape of the capillary pores to be idealized parallel cylinders, the flow is considered to be one-dimensional flow, there is no interconnection between the pores, the contact angle is assumed to be static, the tortuosity of the pores is neglected, the effect of gravity is neglected, and the effect of tiny-radius pores on capillary pressure is ignored (Villagrán Zaccardi et al., 2018).These limitations have driven researchers to build modifications and extensions of the L-W equation based on the limitations of the equation.Thus, Fries and Dreyer (2008a) developed an analytical solution for the L-W equation that considered gravity (hydrostatic pressure), viscous pressure loss (Hagen-Poisseuille), and inertial term.Additionally, pore structures in rocks usually exhibit a complex structure which is significantly simplified in the L-W equation.Thus, Benavente et al. (2002) further corrected the L-W equation with a consideration of the pore orientation and deviation by introducing the tortuosity and pore shape factor by deriving the equation for randomly oriented cylindrical pores, which was later enhanced and experimentally verified by Tsunazawa et al. (2016): where ρ is the fluid density, τ is the tortuosity, and g is the gravitational acceleration.
The flow regimes present during the spontaneous imbibition process have also been extensively investigated.Fries and Dreyer (2008b) showed that the inertial flow will occur first and will subsequently be followed by viscous flow.The purely inertial flow was represented by the Quéré (1997) equation (Equation 3) since the equation have a linear relationship between the height and the time and only considering viscous flow as the main drive.While for the viscous flow, the L-W equation (Washburn, 1921) (Equation 1) was used as the equation has a square root relationship between the height and the time.Based on these two equations, Fries and Dreyer (2008b) suggested that the flow regimes could be determined based on the gradient of the dimensionless height and time provided by Ichikawa and Satoda (1994) (Equation 4).The dimensionless time was formulated to encompass the characteristic viscous time, while the dimensionless height was established as the ratio between surface tension and viscous drag (Ichikawa & Satoda, 1994).The early stage of the capillary rise displays purely inertial flow with a higher gradient than the latter stage, which shows purely viscous flow.
Water Resources Research 10.1029/2023WR035307 PRATAMA AND KHAN The imbibition process of reactive fluid has been previously observed and modeled.Fan et al. (2018) observed that the increment of total dissolved solids caused by the chemical leaching of brine-dissolved salts could mobilize dangerous radionuclides such as radium.Eitrheim et al. (2016) showed that the leaching of naturally occurring radioactive materials (NORM) increases the level of uranium (U-238) in horizontal drilling cutting during the Marcellus drilling operation which can be harmful to the environment.However, there has been no work to the best of our knowledge that specifically couples the spontaneous imbibition process and the fluid-rock reactive interactions so far.
In this work, we take a combined experimental-modeling approach to study the impact of fluid reactivity on spontaneous imbibition in calcareous rocks.Multiple capillary rise experiments were conducted using deionized (DI) water and diluted HCl acid (pH 2).The evolution of the petrophysical properties was noted before and after the acid capillary rise and the capillary rise profiles were fitted to the extended L-W equation based on the Tsunazawa et al. (2016) model.The physicochemical changes in the fluid due to the reactive interaction between the rocks and the fluid were also analyzed.The rock samples were soaked with the fluid and changes of the surface tension, fluid density, and fluid chemistry were observed.Connecting capillary interactions with fluid reactivity is frequently overlooked in fluid transport analysis.This research presents new insights on the significance of reactivity concerning spontaneous imbibition timescales.This understanding is crucial for grasping how reactive contaminants move through the vadose zone.

Experimental Methods
The overall experimental workflow is presented in the following.The rock and fluid sample are first prepared and the initial petrophysical and physicochemical characterization is performed respectively.Capillary rise experiments are conducted in each rock sample: first with DI water, then with dilute acid, and then again with DI water.Petrophysical properties of the rock samples are remeasured and microscopy is performed on a select sample to identify the pore-scale changes.Post-reaction fluid is also analyzed.

Sample Preparation and Petrophysical Characterization
Three cylindrical core samples (3.8 cm diameter × 7.6 cm length) from two different carbonate formations (Austin Chalk and Indiana Limestone) and with different petrophysical properties were cored.These samples were chosen due to its high calcite composition (97% and 80% respectively (Loucks et al., 2021;Shaffer, 2020) and for having different petrophysical properties).Each core was labeled according to the respective formation name (AU for Austin Chalk and IL for Indiana Limestone), with numbering based on the expected permeability values.For each sample, the standard petrophysical properties (porosity, permeability, contact angle, and pore size distribution) were measured twice: before and after the acid-based capillary rise experiment.The measurements were performed twice to ensure consistency, and they were taken only after the completion of the water capillary rise measurement.Separately, an IL100 sample with the same dimensions was used specifically for the μCT observation pre-and post-acid capillary rise.
The petrophysical properties were measured using conventional routine-core analysis methods: porosity using Helium gas expansion, liquid permeability using deionized (DI) water injection, contact angle in a water-rock-air system using sessile drop method (detailed in Appendix A), and pore size distribution from nuclear magnetic resonance (NMR) T 2 relaxation time measured on a Geospec benchtop rock core analyzer.
Two repetitions of porosity and permeability measurements were conducted to ensure statistical consistency in the obtained values.Additionally, three separate repetitions of contact angle measurements were carried out at different locations on the same rock surfaces.The results were averaged, and the range was considered as the measurement error.T 2 relaxation time is the time required for hydrogen ions to relax under the magnetic resonance and is directly proportional to the pore size.It can be estimated using Equation 5 assuming the pore to be spherical (Jaeger et al., 2009).

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where T 2 is the T 2 relaxation time (μs), ρ s is the surface relaxivity (μs/s), S is the individual pore surface area (m 2 ), V is the individual pore volume (m 3 ), ϕ is the porosity, and r is the pore radius (μm).
Separately, an acidic solution was prepared by titrating 12M HCl with deionized (DI) water to get a dilute pH 2 solution.DI water was used as the baseline fluid.

Capillary Rise
Spontaneous imbibition behavior can be characterized by a capillary rise experiment (Fries & Dreyer, 2008a).Two beakers (sized 2 L and 100 ml) are used and connected with a siphon/tube (Figure 1b); the large beaker is placed at a higher elevation compared to the small beaker.Initially, the small beaker is empty and the water is siphoned from the large beaker.Once the fluid level reached the top of the small beaker, it starts to spill on the sides and the water level at the top of the small beaker is maintained.The capillary siphon continues to flow until the fluid level in both beakers is equal.An aluminum wire mesh is braced on top of the small beaker and the core sample is placed on top of it.When the fluid reaches the top of the small beaker, it will interact with and imbibe in the core while maintaining the fluid-rock interface.The experiments was performed under standard condition with air as the displaced fluids.The capillary height is measured from the baseline which is the fluid-rock interface.Figure 1b shows the actual imbibition process in action.
The capillary height during the imbibition process is continuously recorded using a Samsung Galaxy Note 9 camera (12.2 MP ISOCELL 2L3 (SAK2L3)) with a resolution of 1,920 × 1,080 (30 fps).The change of fluid saturation will result in a change in color saturation of the core which is captured in the video.Owing to the Fluid moves through the capillary siphon from the large beaker to the small beaker and maintains the fluid level in the small beaker.The imbibition process will be shown by the increment of the fluid height inside the core which is represented by the changes in the color of the core.
experiment's limitations, capillary height was determined by assessing color saturation on the core's surfaces, rather than directly observing the fluid front.
A MATLAB (MathWorks, 2022) script (developed in-house) determines the capillary height for each frame based on this difference in the color saturation.First, the video is read in as a 3D RGB image stack (x-y and t) and the center part (a row of 30 pixels rectangle with the respective core height) of the core is isolated for image analysis (Figure 1b).The scale for each image was 0.15 mm/pixels.The center is chosen as it has the least curvature in the observation window.Next, the RGB image is decomposed into individual color channels and the largest contrast between the dry zone and saturated zone is determined.The blue channel exhibits the largest contrast and is therefore used for the subsequent image analysis.The image is first corrected to minimize the contrast inconsistency caused by external factors (e.g., shadow, movement in background etc.) and then globally segmented; the boundary of the transition zone indicates the imbibition front.From the image stack, the temporal evolution of the imbibition front is tracked as a function of time (Figure 1c).
The capillary rise experiment is conducted three times: first with DI water, then with diluted HCl, and then again with DI water.After each experiment the sample is weighed, oven dried at 75°C for 12 hr, and weighed again.

X-Ray Imaging
A high-resolution X-ray micro computed-tomography (μCT) scan was conducted using a Xradia Versa XRM-500 located within the Center of Integrative Petroleum Research, KFUPM on a separate IL100 sample.The μCT scan is conducted before and after the acid-based capillary rise experiment to analyze the change in pore shape and the porosity distribution between the reacted and non-reacted condition of the core.The sample is scanned with 1,601 projections for 4 hr with the scan parameters of 140 kV voltage, 64 mA current, 1 s exposure time, and resulting in a resolution of 49.03 microns.Multiple glass beads were taped at different position on the core's curved surface for image registration (performed using BigWarp ImageJ plugins (Bogovic et al., 2016)) between pre-and postreacted conditions.
The grayscale image acquired from the μCT scan underwent segmentation to distinguish between pores and grains using adaptive thresholds (Gonzalez & Woods, 2010) with the pixel neighborhood of 55 and 85 for the preand post-reacted image respectively.No filters were employed in this analysis, as the images proved suitable enough for accurate segmentation.Subsequently, a porosity distribution was generated using the segmented images and compared for the pre-and post-reaction scans.

Fluid Interaction With Carbonates
Due to the reactivity of the acidic DI water, the physicochemical interaction between rock and fluid will also alter the fluid properties.Initially, two sets of 5 ml solutions of diluted HCl (pH 2) and DI water (pH 7) each were prepared.The first set was used as the baseline while the second set was introduced to a 1.5 g chip of Austin Chalk (AU) sample.AU was chosen due to its higher mineralogical complexity in comparison to the IL sample, as reported by Feldmann et al. (2021).The IL sample comprises nearly 99% calcites (Shaffer, 2020).The solution is allowed to react for 30 min and fluid sample is withdrawn and passed through a 20 micron filter.Mass spectrometry (ICP-MS) on the four fluid samples (two control sample and two reacted samples, each at 2 pH and 7 pH) is performed to determine the change in fluid chemistry.Furthermore, the density and surface tension (using the pendant drop method (Appendix A)) of the fluid are experimentally determined.Each measurement was conducted three times to ensure result consistency, and the fluids used for the measurements were not reused thereafter.

Model Fitting
The capillary rise (experimental) data was fit to three different equations which model spontaneous imbibition: the Tsunazawa et al. ( 2016) model, the Lucas-Washburn equation (Washburn, 1921), and Quéré equation (Quéré, 1997).The petrophysical properties of the rock samples were used as the fitting parameter: pore size for the L-W equation (Equation 1) and Quéré equation (Equation 3) and pore size and tortuosity for Tsunazawa's model (Equation 2).The rest of the parameters were derived from laboratory measurements.These regressed parameters were then compared between the pre-and post-reaction conditions.Then, the fitting from L-W and Water Resources Research 10.1029/2023WR035307 PRATAMA AND KHAN Quéré equation was used to calculate the dimensionless time and height using Equation 4to determine the flow regimes during the spontaneous imbibition process.

Results and Discussion
Capillary height result from different fluids and rocks have a different behavior.Fluid and rock properties both affected the imbibition process.The interaction between the fluid and the rocks themselves could also alter the petrophysical properties of the rock.Utilizing the methodology mentioned in the previous section, the comparison of the petrophysical properties between pre-and post-acid reactions was analyzed.Acid interaction with the reactive minerals present in the rock also alters the petrophysical properties of the core samples resulting in a change in the water capillary height.The integration between the experimental results and the numerical calculation was also needed to validate this kind of behavior.The results and some insights are highlighted in the following section.

Capillary Rise
Due to the differences in the initial petrophysical properties for each rock, the capillary rise profile and the maximum height achieved are different after 800 s (Figure 2).AU was observed to have the highest capillary height amongst the samples with a maximum capillary height of 20 mm, followed by IL30 at 9 mm and the lowest in IL5 at 6 mm.The capillary front observed in this study is only within the center of the core and only that has appeared on the surface of the rocks.Some limitations still appear and are detailed in the following section.
Generally, acid based capillary height was found to be greater than the initial capillary height but with a similar shape.For IL5, it was consistently higher whereas for the other two samples it was initially lower but increased at a faster rate than with the DI water.The point of crossing, that is, the time at which the acid capillary rise is equal to the DI water capillary rise, is found to be longer in IL30 (∼530 s) compared to AU (∼280 s).
The acid-rock interaction also has an impact on the post-reaction capillary rise experiments, even with water.The most prominent change is observed in IL5, where the post-reaction maximum capillary height is ∼50% higher than the pre-reaction and the post-reaction has a consistently higher height.AU initially shows the same height for pre-and post-reaction, but it got separated in the later stages and the post-reaction shows significantly higher endpoint capillary height.Residual fluid saturation was disregarded in this study, given that the core was thoroughly dried before each capillary rise cycle.
As the effect of acid-rocks interaction, it also changes the water capillary rise profile.In the AU sample, the water capillary rise profile was shown to be lower than the pre-reaction water capillary rise at the beginning, but at some time, it will be overlapping and get higher than the pre-reaction one.The same thing happened with the IL30 sample, but the overlapping point is much later compared to the AU sample.Overall, all of the samples showed a consistent behavior, a higher end-point capillary height compared to the water pre-reaction capillary height.(Washburn, 1921), and Quéré (Quéré, 1997) model with the corresponding R 2 score for each fitting.
Three fitting parameters from Tsunazawa's models (pore size, tortuosity, and contact angle) were obtained (Table 1) based on the Levenberg-Marquardt algorithm (Moré, 1978) fitting method.The pore size was consistently reduced for each sample between the water pre-reaction, acid spontaneous imbibition, and water post-reaction.The highest change was simulated to occur in the IL30 sample while IL5 experienced the lowest changes.Small changes in the tortuosity were observed in all the samples: IL5 and IL30 showed a slight decrease whereas AU showed an increasing trend.

Petrophysical Properties Alteration
The petrophysical properties are changing as the effect of the reaction with acid during the acid-based spontaneous imbibition process.The mass, porosity, permeability, contact angle, and pore size distribution were altered during the process.
Although not statistically significant, comparing the core sample's mass before and after the acid reaction was nonetheless significant.The comparison of it is shown in Table 2.The AU had the maximum mass decrease, whereas the IL30 had the lowest mass reduction.The average reduction in all cases was less than one percent (%), as the reduction detected in all samples did not surpass the value of 1.6 g.
The mass and porosity have a direct relationship: the mass decreases as the void areas inside the core samples grow.All of the core samples saw an increase in porosity (Table 2) with the highest change observed in AU (0.73%) and the smallest in IL30 (0.15%).None of the samples had a significantly large change; all were less than 1%.Note.The fitting parameters in this calculation is the pore size and the tortuosity with an adjustment from the contact angle based on the laboratory measurements and error during the measurement.Note.Each sample experienced changes in the pore scale and opening up of pore spaces, shown by the reduction of mass and increment of the porosity, while the permeability is increased in most of the samples, and reduced in IL30.

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10.1029/2023WR035307 PRATAMA AND KHAN The permeability alteration exhibited a distinct behavior.Most of the samples showed an increase in permeability as a result of the acid reaction (Table 2).However, there was a noticeable and significant permeability drop in IL30.The decrease was measured at 4.6 mD (13.3%) and had the greatest impact on the permeability of all.The AU had the largest permeability rise, measuring 3.8 mD (9.2%).The increase in the IL5 sample is only 1.1 mD (24.4%).Despite having the lowest absolute changes compared to others, its relative changes are the highest among all, making it highly significant.
The pore size distribution was estimated based on the distribution of T 2 relaxation time (Equation 5).The surface relaxivity were used based on experimental measurements present in the literature: 39.65 μm/s for IL5 and IL30 (Lawal et al., 2020) and 23.3 μm/s for AU (Benavides et al., 2020).Two phenomena were observed through the pore size distribution comparison: pore enlargement (increment in the mean of the distribution) and pore size  Water Resources Research 10.1029/2023WR035307 reduction (Figure 4).A slight variation was observed in the changes of the mean pore size distribution.An increment in the mean of the distribution was observed in the IL5 (from 14.98 to 15.68 μm) and AU (from 3.57 to 3.69 μm), while a reduction was observed in the IL30 (from 15.35 to 14.53 μm).The largest of the pore spaces in each sample were observed to be reduced.This is a strong indication that simultaneous dissolution and precipitation were happening in different parts of the pore systems.
The wettability of the rocks was also observed to change due to the acid/rock interaction.The contact angle, measured between deionized water and air, was significantly reduced in each sample (Figure 5a).The highest change is observed in AU, which transitions from neutral-wet to water-wet, and the lowest change is observed in IL30.Even though the time scale of the interaction is considerably low, this has been proved that the acid could alter the wettability of the mineral surfaces, specifically calcite (Rezaei Gomari & Hamouda, 2006;Standnes & Austad, 2003).The alteration in permeability could also be attributed to wettability, wherein the water-wet condition influences the relative permeability of DI water (Owens & Archer, 1971).Given that DI water was employed in the permeability measurements, this change in wettability could potentially impact the liquid permeability.Besides, the fluids that reacted with the rocks also underwent the ionic and surface tension changes (plotted as a bar plot and blue cross in Figure 5b respectively).

Imaging
The μCT scan was performed twice, both before and after the acid-induced capillary rise in the IL100 sample.Specifically, Figure 6a displays a 10 mm thick slice from the bottom of the core.Notably, some pores are either absent or reduced in size due to the spontaneous imbibition process (Figure 6c).In contrast, the unreacted section located 20 mm above the core's bottom (Figure 6b) shows no discernible alterations in the pore structure (Figure 6c).This observation implies that even though the concentration of the reactive fluids is relatively low, in the spontaneous imbibition process, it impacts pore morphology.Intriguingly, this effect persists even in regions below where the fluids have already reacted, indicating that the reactivity continues to influence the pore structure.
Based on the grayscale intensity, the image can be segmented into pore and grain and the porosity can be estimated by calculating the proportion of pore pixels to the sum of the pore and grain pixels (Figure 7).Since the IL100 sample was composed mainly calcites, the grain was assumed to be entirely calcite.Then, the porosity distribution as a function of the core height was generated, as shown in Figure 8b.In Figure 8a, the acid-capillary rise profile indicates a maximum capillary height of approximately 8 mm.To maintain consistency in the analysis, the portion of the core influenced by the 5 mm fluid expulsion was excluded from the study, as it falls outside the scope of the capillary rise process.The examination of the core's porosity distribution uncovers a reduction in porosity within the reacted section.Specifically, a deviation of 0.5%-1% from the pre-reaction state is observed.This reduction becomes more prominent near the interfaces between the fluid and the rock, highlighting the localized nature of the porosity alteration.
The compelling evidence strongly indicates precipitation at the current resolution, leading to a reduction in porosity.This observation aligns with the NMR findings, suggesting a constriction in larger pore sizes.However, it's crucial to acknowledge that the resolution limitations hindered the observation of smaller pores, as they were below the image's level of detail.As a result, the porosity distribution obtained from the imaging data represents a spatial distribution rather than offering a comprehensive overview of the entire porosity spectrum.This limitation arises because the image's resolution is larger than the size of certain pores, emphasizing the necessity for higherresolution imaging techniques to accurately capture the complete range of pore sizes.

Parameters Affecting the Capillary Height
The capillary rise profile is primarily influenced by the petrophysical properties of rocks.However, in cases involving reactive fluids, these petrophysical properties can undergo continuous changes as the fluid reacts with the minerals within the rocks.Consequently, it becomes crucial to analyze the parameters that construct the capillary rise profile.To facilitate this analysis, a sensitivity analysis was conducted on Tsunazawa's model (Appendix B).
Between four distinct parameters contained in Tsunazawa's models, surface tension positively correlated with time, whereas pore size, tortuosity, and contact angle displayed negative correlations.Contact angle and tortuosity Water Resources Research 10.1029/2023WR035307 PRATAMA AND KHAN emerged as the most influential parameters, impacting capillary rise at different time stages.Pore size revealed a unique trend with larger pores initially leading to higher rise followed by stabilization, in contrast to smaller pores which exhibited ongoing elevation.Both numerical calculations and laboratory measurements consistently demonstrated a similar trend concerning pore size.Utilizing the Tsunazawa et al. ( 2016) methodology, the calculation results revealed a reduction in pore size attributed to fitting parameters (Table 1).In parallel, NMR analysis indicated a decrease in size for certain larger pores (Figure 4), aligning with the concept of an ascending capillary profile both in acid and post-acid reactions compared to the pre-acid reaction.Similarly, the μCT scan also showed the reduction of pore sizes.
However, the NMR analysis also revealed an increase in average pore size-an aspect not captured by the numerical calculations.While this finding does not align with the observations in the capillary rise profile, this discrepancy underscores the simultaneous interplay of pore size increment and reduction, influenced by mineral dissolution and precipitation effects during acid-rock interactions.
Even though it is not significant, surface tension was also subjected to testing to monitor changes during the reaction between acid and calcite minerals, as exemplified by thfe AU sample.The surface tension underwent a 25% increase, rising from 67.6 mN/m to 81.3 mN/m (plotted as a blue cross in the secondary y axis in Figure 5b), as a consequence of the acid-rock interaction.Conversely, a marginal reduction in surface tension occurred during the same process with DI water, transitioning from 70.6 to 69.3 mN/m (Figure 5b).These findings illustrate that over time, as the reaction progressed, surface tension exhibited an increase, aligning with the higher capillary height in acid capillary rise.
Other parameters that were observed to have a prominent effect on the capillary height are tortuosity and contact angle (Figure B1).As shown in Figure 5a, the contact angle underwent a reduction after the acid reaction.Similarly, for IL5 and IL30 samples, the tortuosity was also reduced based on the fitting parameters.So, even though the pore size is increasing, the effect of the tortuosity and contact angle outperformed the pore size effect which resulted in a higher capillary height.The AU sample displayed an unusual increase in tortuosity based on fitting parameters; however, the substantial reduction in contact angle could potentially outweigh the influence of other parameters.

Mineral Dissolution and Precipitation During Acid Imbibition
The alteration of petrophysical properties, which include the porosity, pore size, permeability, and wettability, as the effect of acid imbibition was observed.The alteration of porosity, wettability, and pore size affects the capillary rise behavior throughout the core.Even though the bulk porosity showed that the change of the porosity was very minor (<1%), these changes only occur in the reacted part of the core.
Mass spectrometry was also performed on the fluid samples after the reaction with a chip of AU sample (Figure 5b).It showed the distribution for the major cations (Ca 2+ , K + , Al 3+ , and Ba 2+ ) present in the fluid.The pre-reaction samples, DI water (pH 7) and DI water titrated with HCl (pH 2), did not show any of the major cations.Ca 2+ showed the most prominent increase in the acidic DI water (pH 2), where it increased to ∼1,000 ppm indicating the dissolution of calcite.K + and Al 2+ also increased by an order of magnitude implying the dissolution of feldspar.A minute change in Ba 2+ was observed.The DI water (pH 7) also showed high changes in the fluid composition.K + exhibited the largest concentration (∼70 ppm) closely followed by Ca 2+ at ∼30 ppm.The 30x increase in Ca 2+ concentration between the acidic and neutral DI water shows the variation in the amount of calcite dissolution between the two fluids.Since the mineralogy of the IL is more simple (contain 99% calcites), these results also could be the reference for the reaction with IL.On the other hand, no observable change in the Water Resources Research 10.1029/2023WR035307 density of the two fluids was observed.Both exhibited a density of 0.995 g/cm 3 before and after the interaction, and any minute changes were considered to be within the error margin of the instrument.
As indicated by the changes in the fluid properties, calcite dissolution is the main cause of these alterations.Although it is not significant, the fluid composition indicates that feldspars dissolution is also consistently present along with the calcite dissolution (Figure 5b).Calcium ions contained in the fluid are a strong indicator of dissolution of calcite which will exhibit changes in the petrophysical properties of the core (Equation 6).According to Equation 6, in addition to calcium ions, the reaction should also generate CO 2 .This is observed during the AU chip reaction.But not observable during the capillary rise experiments.It is possible that CO 2 is produced within the individual pores but remains undetected by the cameras.Further extensive studies are required to observe and capture this phenomenon during the process.Even with a low acid concentration, calcite dissolution could still be prominent (Alkattan et al., 1998).In the micro-scale, a smoother grain surface has a strong indication that calcite dissolution happened, which is also previously observed by Järvinen et al. (2012).On another hand, Singh et al. (2018) has also observed the increment of porosity distribution during the injection of reactive CO 2 -saturated brine.
Feldspars, specifically potassium feldspars (K-feldspar), are prone to dissolution due to the fluid's reactivity (Equation 7).Feldspar dissolution can happen even at room temperature and pressure conditions (Brantley & Stillings, 1996), which contributes to the changes in the petrophysical properties in the core-scale.Ma et al. (2017) has previously observed the dissolution of K-feldspar with acid which resulted in a smoother grain surface.Despite the slow kinetics of feldspar dissolution (around 5 × 10 8 mol m 2 s 1 ) in acidic condition (Lange et al., 2021;Wild et al., 2016)), the mass spectroscopy data (Figure 5b) revealed the presence of ions characteristic of feldspar composition in the results.This observation suggests that dissolution processes could still occur even within very brief timescales.
Based on Loucks et al. (2021) and Shaffer (2020), the K-feldspar contained in Austin Chalk and Indiana Limestone samples are 20% and 3% respectively.Assuming a biphasic rock consisting of calcite and K-feldspar with the aforementioned mineralogy and only the part of the rock that the fluids have been imbibed to be considered, the mass loss (Equations 6 and 7) of the cores can be estimated as 0.077, 0.834, and 0.140 g for the IL5, AU, and IL30 respectively.
Also, to quantify the dissolution of the minerals within the associated timescales, It could be estimated through the calculation of surface retreat (Arvidson et al., 2004), as follows: Water Resources Research 10.1029/2023WR035307 PRATAMA AND KHAN where ΔH is the surface retreat (m), r is the absolute dissolution rate (mol m 2 s 1 ), Δt is the reaction duration (s), and V m is the molar volume for the minerals (mol m 3 ).Since the rocks assumed to be biphasic rock with the composition of calcite and K-Feldspars, the dissolution rate and molar volume used in this calculation is 7.24 × 10 4 mol m 2 s 1 and 36.94mol cm 3 for calcite and 5.00 × 10 8 mol m 2 s 1 and 140.55 mol cm 3 for Kfeldspar (Alkattan et al., 2002;Cubillas et al., 2005;Wild et al., 2016).
Based on the experimental measurements of acid capillary height in the laboratory, the surface retreat was calculated as a function of the acid exposure time.We assumed that the initial distribution of porosity within the cores was uniformly distributed.Subsequently, the calculations for three different time intervals, specifically 100, 500, and 800 s, were conducted.These calculations allowed us to generate porosity profiles along the length of the core, which are illustrated in Figure 9.As depicted in the figures, an incremental porosity was observed,  Quéré (1997) and Washburn (1921) equation and using the dimensionless formula from Ichikawa and Satoda (1994).The intersection between two lines indicates the transition from the purely inertial to viscous flow regime and is presented in time units.

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10.1029/2023WR035307 PRATAMA AND KHAN particularly in the inlet region.This trend becomes more pronounced as the exposure time increases, albeit the magnitude of change remains relatively small, on the order of 5.
Both of the mass and porosity calculated values are significantly lower compared to the mass and porosity changes observed during the experiment (Table 2).Although the assumptions are a bit heavy handed, but the result shows that something besides the dissolution reaction is happening which is causing the excess loss of mass and increment of porosity.There are potential experimental reasons which could have also resulted in this loss of mass including, but not limited to: repeated loading and unloading of the core during permeability measurement which could have chipped the core and changes in the air humidity after taking core out of the oven.The removal of some part of the core could lead to the porosity measurement error, as the measurement assume the core to be perfectly cylindrical.Further studies need to be conducted to analyze this possibility.
In addition to dissolution, the occurrence of calcite precipitation has been observed, particularly in the context of pore size reduction, specifically within larger pores shown by the μCT scan, NMR and Tsunazawa's fitting parameters.This phenomenon can be primarily attributed to the presence of oversaturated calcium ions and carbon dioxide (CO 2 ) gas, which are generated as byproducts during the dissolution process (Equation 6).Even though is not significant, gas bubbles were observed to appear during the reaction between AU and acid, which is a strong indication that CO 2 gas is produced.However, it was not observed on the rocks surfaces during the acid capillary rise.All of these materials underwent a reaction leading to the precipitation of calcite.This observation aligns with the findings of Eloneva et al. (2008) as they reported that the dissolution byproducts could indeed induce the precipitation of calcite.

Flow Regime Analysis
The dimensionless height is plotted against the dimensionless time in Figure 10 to observe the flow regime changes during the capillary rise.These dimensionless parameters are generated by using the fitting parameters from the Quéré (red steep line) and Lucas-Washburn equations (blue gentle line) as an input in Equation 4. The intersection of these two lines indicates the transition of the flow regime from inertial to viscous flow.As the effect of acid imbibition, the transition point of flow regime in post-reaction water capillary rise was significantly changed throughout the samples.The viscous flow regime appeared earlier in post-reaction water capillary rise.A slight variation was observed in the acid imbibition process: the viscous flow regime appeared later in IL5 and earlier in the other two.
Based on the dimensionless analysis, it is shown that the acid affects the flow regime of post-acid water capillary rise and decreases the time of the inertial flow regime.It is consistently observed that the transition from viscous to inertial flow is decreased between the pre-and post-reaction experiment (Figure 10).With the advent of the reaction, primarily mineral dissolution, the pore size is increasing which is expected to correlate with stronger inertial forces.However, the mineral reactions also reduce the contact angle (Figure 5a) which can accelerate the onset of the viscous flow regime.The current study lacks detailed evidence on this phenomenon, necessitating further investigation.
The flow regime is significant to explain the limitations of the Tsunazawa et al. (2016) model.Since Tsunazawa's model has the same underlying assumption as the L-W model, this model neglects the inertial and viscous forces during the capillary rise.The inertia of the fluid, the capillary force, the weight of the fluid, and the resisting viscous forces will determine the dynamics of capillary rise (Shardt et al., 2014).These forces could also cause the capillary front's oscillation during the capillary rise process (Quéré et al., 1999) The previous studies have also identified two distinct fronts (fluid and particle) as the consequence of these forces on dynamic capillary rise behavior (Bhaduri et al., 2014;Das et al., 2012;Das & Mitra, 2013).
However, some challenges still remain.Due to the heterogeneity of the pore network across the core crosssection, different pore pathways will exhibit different stages of the flow regime and different fluid heights.Therefore, there would exist spatial variation of the dynamic contact angle and will further introduce the fluid slip effect, resulting in a change in the capillary rate (i.e., change of capillary height with time) (Wang et al., 2019).Modeling these aspects is still a big challenge (Cai et al., 2021) and coupling these forces with the fluid-solid interaction, especially with reactive fluid, also needs to be studied further.

Water Resources Research
10.1029/2023WR035307 PRATAMA AND KHAN

Experimental Works
The primary limitation of our experiments lies in the fact that our observations are restricted to the surface of the rocks, rather than providing a direct insight into the true capillary behavior within the intricate pore network systems.Even with our advanced methods, we still encounter slight variations in capillary height within the surface rocks.Moreover, at the level of individual pores, the capillary front is inherently uneven due to the influence of contact angles (David et al., 2011(David et al., , 2015)).These variations are a consequence of the inherent complexity of the pore systems within the rocks (Alyafei & Blunt, 2016;Shou et al., 2014;Zhang et al., 2022).Consequently, it is imperative to develop novel techniques capable of accurately tracking the genuine capillary front within the fracture networks of these rocks, addressing the challenges posed by their intricate structures.

Model Fitting
Even though Tsunazawa's model can fit most of the experimental data accurately, some limitations still need to be further studied.Some parameters, such as the dynamic contact angle, dynamic surface tension, and pore size heterogeneity, were not considered in this model.These parameters are very important to describe the real complex porous media, especially in reactive materials such as carbonates.Each parameter is discussed next.
First, the contact angle changes as acid interacts with the carbonate minerals.During the acid capillary rise experiment, the contact angle alteration will happen continuously as the fluid is imbibing in the pore system.As illustrated by the results (Figure 5a), there is a notable difference in the contact angle before and after the acid reaction.Thus, it is important to introduce this variable to the equation as the dynamic contact angle will be valued lower than the static contact angle, resulting in a higher capillary rise (Figure B1).Siebold et al. (2000) studied the importance of the dynamic contact angle and showed that the contact angle changes as the fluid penetrates the pore system and is proportional to the rate of fluid penetration.Popescu et al. (2008) also proposed that the dynamic contact angle will be velocity-dependent and the result showed a better prediction of capillary height compared to the traditional Washburn's equation.Martic et al. (2003) showed that the front movement during capillary imbibition was strongly influenced by the dynamic nature of the contact angle.This effect become more prominent in carbonate rocks due to the complexity of mineralogy and reactivity (Arif et al., 2017;Sakthivel, 2021).Therefore, a correction for dynamic contact angle needs to be further considered and introduced for a more accurate estimation of the capillary height.
Second, the heterogeneity of the carbonates itself will affect the behavior of the reactive fluid transport in the pore system, either in terms of chemical interaction and/or physical properties.The chemical interaction will be related to the mineralogy of the rocks, which varies from 80%-99% calcite and 1%-3% feldspar.The spatial distribution of the petrophysical properties of the rock though have an impact on the imbibition profile.Previously Hollis et al. (2010) showed that different rock types could show different water imbibition profiles and Adibhatla and Mohanty (2008) showed that the core heterogeneity affects the imbibition-fluid velocity which could deviate the imbibition profile, even though the change is not much.Not only the mineralogy, but the complexity of the pore structure could also play a significant role since the capillary front relies on the preferential fluid path (Alyafei & Blunt, 2016;Shou et al., 2014;Zhang et al., 2022).This complexity could lead to issues in calculating the capillary height and rate, especially when the capillary rise behavior does not follow the conventional Young-Laplace equation (i.e., xρgr 2σ cos (θ) > 1).Examples of these include absence of gravity (Rascón et al., 2016) and when there is no meniscus to hold the fluids (Finn, 2012).Therefore, heterogeneity factors/constants related to the mineralogy and pore structure complexity need to be introduced in the capillary height-time equation.
In addition to investigating petrophysical properties, it is crucial to delve deeper into the fluid characteristics.Specifically, dynamic surface tension warrants further examination within the capillary rise equation.This is especially pertinent due to the introduction of acid, which significantly raises the surface tension of the fluid, as illustrated in Figure 5b.This observation also aligned with the previous study that the reduction of surface tension was observed in acidic condition during the reaction (Lashkarbolooki et al., 2018;Nowrouzi et al., 2019).Consequently, this heightened surface tension amplifies capillary rise, making it imperative to thoroughly study its dynamic nature for a comprehensive understanding.

Conclusion
The investigation highlights the pivotal role of capillary interactions in tandem with fluid reactivity within the porous media.The observed higher capillary height using acid compared to water stemmed from alterations in rock and fluid properties.The alterations in the petrophysical properties of the rock, that is, the porosity, pore size distribution, permeability, and wettability, are due to the chemical interaction(s) between the reactive fluid and pore minerals which significantly influences the capillary rise behavior.These modifications leads to an augmented water capillary height which, supported by numerical fitting, reveals reduction in the average pore size and an increase in the tortuosity.Additionally, an increase in surface tension was observed which also contributed to the increase of the capillary height.
Distinct chemical reactions (calcite dissolution, K-feldspar dissolution, and calcite precipitation) exerted substantial impact on petrophysical properties during acid imbibition.Notably, precipitation predominantly occurred in larger pores, while dissolution was more prominent in smaller pores, delineating a nuanced interplay between reaction kinetics and the pore size.
This study underscores the imperative need to dive deeper into dynamic capillary rise phenomena, encompassing dynamic contact angle variations and heterogeneity factors.Understanding the inconsistent forces during capillary rise is crucial and necessitates further investigation.Furthermore, recognizing the significance of inertial and viscous flow regimes in the capillary rise process warrants a focused exploration at the pore scale.This elucidation could substantially redefine models describing dynamic capillary rise.
It is evident that coupling capillary interactions with fluid reactivity plays a pivotal role which is often overlooked in current fluid transport studies.This research, conducted at core scale an ẉ ithin a short time frame illuminates the substantial impact of reactivity on reactive imbibition.However, to comprehensively grasp the implications, a broader study encompassing longer flow periods on a larger scale is needed which can explain dynamic changes occurring during diverse physiochemical events, such as reactive contaminant transport in the vadose zones, acid transport in acidizing processes, and CO 2 leakage during carbon sequestration.
proportional relationship with time.The contact angle and tortuosity were observed to be the two most sensitive parameters; the former resulting in the capillary rise change in the late times while the latter resulting in the capillary rise to change from the starting time.The pore size sensitivity showed a distinctive trend, with greater pore size indicating higher capillary height in the early stage.In the later stage, the rate of capillary rise for bigger pore sizes slowed and the height stabilized, but smaller pore sizes continued to increase and overlap the larger pore sizes.

Data Availability Statement
All the data generated during this study was obtained at the Center of Integrative Petroleum Research at King Fahd University of Petroleum and Minerals (Saudi Arabia) and can be accessed at Pratama and Khan (2023).The imaging data was processed using MATLAB (MathWorks, 2022) and Fiji (Schindelin et al., 2012).The figures in the manuscript are generated using PGFplots (Feuersänger, 2018).

Figure 1 .
Figure 1.Capillary rise experimental schematic (a), setup (b) and a closer look on the fluid that imbibed inside the core (c).Fluid moves through the capillary siphon from the large beaker to the small beaker and maintains the fluid level in the small beaker.The imbibition process will be shown by the increment of the fluid height inside the core which is represented by the changes in the color of the core.

Figure 2 .
Figure2.The comparison of the capillary height (time-dependent) in every core sample for each condition.The pre-reaction and post reaction was the capillary height observed through the water-based capillary rise experiment before and after the acid-based capillary rise experiment.The fluid that was used was deionized water.Acid was the capillary height that was observed in acid-based capillary height.

Figure 3 .
Figure 3.The fitting of the experimental capillary height to the Tsunazawa et al. (2016) model, L-W equation(Washburn, 1921), and Quéré(Quéré, 1997) model with the corresponding R 2 score for each fitting.

Figure 4 .
Figure 4. Pore size distribution for each sample based on the Nuclear Magnetic Resonance (NMR).The correlation between the T 2 relaxation time and pore radius was used as mentioned in Equation 5.

Figure 5 .
Figure 5. (a) Comparison of the water-air contact angle for all pre-and post-acid reaction core samples.(b) Comparison of the surface tension and mass spectroscopy result of the fluid after the fluid-rock interaction.

Figure 6 .
Figure 6.The (a) 10 mm slices and (b) 20 mm slices of the μCT scan.The left image is scanned in the pre-reaction condition and the right image is in the post-reaction condition.The (c) differences between pre-and post-reaction images.

Figure 7 .
Figure 7.The segmented μCT images in volume view for (a) pre-reaction and (b) post-reaction sample.The white colors represent the pore spaces, while the black colors represent the grains.

Figure 8 .
Figure 8.(a) The acid-based capillary height for IL100.(b) The porosity distribution within the core length for pre-and postreaction.The gray box in (b) is the fluid-rock contact.

Figure 9 .
Figure 9.The incremental of porosity along the core length in different timescales as the effect of the minerals dissolution.

Figure 10 .
Figure 10.The dimensionless height and time for each sample based on theQuéré (1997) andWashburn (1921) equation and using the dimensionless formula fromIchikawa and Satoda (1994).The intersection between two lines indicates the transition from the purely inertial to viscous flow regime and is presented in time units.

Figure B1 .
Figure B1.Sensitivity analysis for each variables based on Tsunazawa et al. (2016) model.

Table 2
Petrophysical Properties Comparison Between Pre-and Post-Acid Reaction Including the Error of the Measurement