The role of injection rate in enhancing capillary trapping in saline aquifer systems

Performing experimental studies in a laboratory on the behavior of \(\textrm{ScCO}_2\) under ambient conditions is difficult. Controlling high pressure and temperature to maintain the supercritical conditions of \(\textrm{CO}_2\) that exist in geological formations is particularly challenging in a laboratory-scale experimental setup. Using proxy fluids in the porous medium under reservoir conditions is a common practice in laboratory-scale studies (Kimbrel et al. 2022; Hu et al. 2020). Hence, silicone oil sourced from Sigma-Aldrich, with physical properties similar to \(\textrm{ScCO}_2\) was used as a proxy fluid in this study. The proxy fluids used in previous experimental studies are listed in Table 2. From here on, the silicone oil is referred to as \(\textrm{proxyScCO}_2\).

The brine used in this study consists of sodium chloride (NaCl) at a concentration of 6000 ppm. The NaCl brine solution was prepared using deionized water as the solvent. The NaCl solute, supplied by Sigma-Aldrich, has a purity of 99.8% and a molecular weight of 58.44 g/mol. To differentiate between the colors of brine and silicone oil during the BAC displacement experiments, Brilliant Blue FCF dye (Sigma-Aldrich) was added to the brine solution. The properties of brine and silicone were measured in the laboratory: Brine viscosity was measured using RST Touch Series rheometers by AMETEK Brookfield and the viscosity of silicon oil was measured using the Anton Paar SVM 3000 Stabinger Viscometer. The interfacial tension was measured by using a force tensiometer (KRUSS). Table 3 presents the physical properties of \(\textrm{proxyScCO}_2\) and brine used in this study.

The 2D micromodel was designed using OpenPNM. The pore morphology was created using coupled Delaunay Voronoi triangulation within a boundary of 35 mm by 10 mm. The micromodel was etched using a wet etching technique on a 10 mm thick glass plate with a length of 55 mm and a width of 30 mm, as shown in Figure 3. A photoresist layer was patterned to define the pore structure, and the exposed regions of the glass substrate were etched using hydrofluoric acid to produce channels of the desired depth and geometry. This method enables precise control over pore features and is widely employed for constructing micromodels that replicate the heterogeneity of reservoir rocks (Karadimitriou et al. 2013; Massimiani et al. 2023). To seal the micromodel, the etched glass plate was bonded to a second glass plate by sintering at a softening temperature of \(700^o\)C in a furnace.

The etched micromodel was placed under a microscope, as illustrated in Figure 4, to identify the average pore space radius, standard deviation of the pore space radius, and model porosity. This process was performed by injecting brine into the micromodel. This step was taken to differentiate between the glass and the pore space during image processing. The pore throats in the etched micromodel have an average radius of 16.33 \(\mu\)m and a standard deviation of 231.98 \(\mu\)m, representing a heterogeneous sandstone. This value resembles that of heterogeneous sandstone (Karadimitriou et al. 2013; Gunda et al. 2011). The porosity (\(\phi\)) is approximately 0.4, calculated using Equation 2 Joseph et al. (2013):where \(NPixel_{brine}\) is the total number of pixels occupied by brine and \(NPixel_{glass}\) is the total number of pixels occupied by glass. Additionally, the pore volume (PV) of the micromodel was approximately 7 \(\upmu\)l and this was estimated by multiplying the size of the pixel by the \(N_{brine}\).

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The diagram of the experimental setup used in this study is shown in Figure 4. The fluid displacement system consists of a micromodel—described in the previous section—a NE-1000 syringe pump for injecting silicone oil and brine, and a microscope equipped with a camera to capture images of the displacement process. The micromodel was assembled and mounted horizontally on the microscope stage. Its inlet was connected to the brine and \(\textrm{proxyScCO}_2\) supply pumps, while the outlet was connected to a fluid drainage container maintained at atmospheric pressure.

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The micromodel was cleaned with acetone and deionized water prior to the experiment. This cleaning procedure was performed to remove any particles or debris that could compromise the accuracy and efficiency of the displacement process. Brine was then injected using a syringe pump along the flow path controlled by valves CFH, as shown in Figure 4, at a flow rate of 50 \(\upmu\)L/min. Injection continued until the micromodel was fully saturated with brine to replicate the conditions of a saline aquifer. All experiments were conducted at ambient temperature (approximately \(25^o\)C) and atmospheric pressure.

After the micromodel was fully saturated with brine, the next phase of the experiment—the BAC injection technique—was conducted. In this phase, \(\textrm{proxyScCO}_2\) and brine were alternately injected into the 2D micromodel over two complete cycles. Each cycle consisted of the injection of one pore volume (1 PV) of \(\textrm{proxyScCO}_2\), followed by 1 PV of brine. In the first cycle, 1 PV of \(\textrm{proxyScCO}_2\) was injected at a flow rate of 0.29 \(\upmu\)L/min, followed by 1 PV of brine at the same flow rate. The second cycle repeated this sequence using the same injection parameters. Both injection cycles were visualized and recorded in real time using the microscope, as illustrated in Figure 4. Subsequently, the experiment was repeated using the same procedure at higher flow rates of 2.89 \(\upmu\)L/min, 28.92 \(\upmu\)L/min, and 96.41 \(\upmu\)L/min.

Table 4 summarizes the injection rate used for each cycle, with each rate corresponding to a specific \(N_{ca}\) value. The Darcy velocity (V) was computed using the relation \(V = \frac{Q}{A}\), where Q is the volumetric flow rate and A is the average cross-sectional area of pores in the micromodel. The values of \(N_{ca}\) shown in the parentheses were calculated using Equation 1. In Table 4, each pair of injection cycles is grouped as a single experimental group (EG), as indicated in the table. These groupings align with the procedures outlined in the preceding paragraph for their respective experiment categories.

The recorded video was converted to an image sequence, which resulted in approximately more than 100 image sequences and this is true for all EG. The processes of conversion were assisted by ImageJ. The image sequence is a RGB (Red, Green and Blue) image and this image was converted to grayscale because the image processing tool works well with grayscale images (Łuczak 2024; Yasin et al. 2024). The post-processing of the image was done using MATLAB (Matrix Laboratory).

The video captured by the microscope consisted of brine, \(\textrm{proxyScCO}_2\), and micromodel. Based on the building material, the micromodel made of glass reflected as a bright image (approaching a zero value of the grayscale image). \(\textrm{ProxyScCO}_2\) and brine have similar grayscale readings. Hence, blue dye was added to brine to create a signal intensity difference between \(\textrm{proxyScCO}_2\) and brine. The three phases were subsequently separated by analyzing the grayscale intensity of the image. Each phase is characterized by a certain range of pixel intensities. By leveraging the different grayscale intensities, we created a binary image that indicates two regions, which are solid and pore space. This was done using a micromodel that was filled only with brine; see Figure 5(a). This brine and micromodel image was split using the adaptive thresholding technique. As a result, the image as shown in Figure 5(b) was created. This thresholding technique is available in MATLAB. Figure 5(b) shows a binary image where the white region represents the pore space and the black region represents the micromodel.

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The constituents, such as \(\textrm{proxyScCO}_2\), brine, and solid, of the converted grayscale image were separated from each other using a median filter and adaptive thresholding shown in Figure 6. The same procedure was followed for all EG mentioned in Table 4. The finalized segmented images of \(\textrm{proxyScCO}_2\) were then used to calculate the saturation of the trapped \(\textrm{proxyScCO}_2\). The saturation of trapped \(\textrm{proxyScCO}_2\) (\(S_{t_{CO_2}}\)) was calculated using Equation 3:

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where \(NPixel_{ScCO_2}\) is the total number of pixels occupied by the trapped \(\textrm{proxyScCO}_2\) and \(NPixel_{porespace}\) is the total number of pixels that are part of the porespace.

Capillary trapping of \(\textrm{proxyScCO}_2\) is strongly influenced by the brine injection rate during BAC displacement experiments. At higher injection rates, viscous forces dominate over capillary forces, resulting in the formation of small \(\textrm{proxyScCO}_2\) droplets and, consequently, lower trapping efficiency. In contrast, at lower injection rates, capillary forces dominate, leading to the entrapment of larger \(\textrm{proxyScCO}_2\) droplets and enhanced capillary trapping. Figure 9 presents the saturation of trapped \(\textrm{proxyScCO}_2\) at four different log(\(\textrm{N}_{ca}\)) values: \(-7.05\) (point A), \(-6.05\) (point B), \(-5.05\) (point C), and \(-4.52\) (point D). As shown in Figure 7, a distinct plateau in \(\textrm{proxyScCO}_2\) saturation is observed for all cases, particularly between points C and D in Figure 9. This plateau indicates that any image within this interval can be used to compute the trapped saturation. Therefore, the image from the final time frame was selected to calculate the saturation of trapped \(\textrm{proxyScCO}_2\) using Equation 3.

The relationship between the log(\(\textrm{N}_{ca}\)) and the trapped ScCO2 saturation indicates a nonlinear relation, where point B shows the highest trapped saturation. The value slightly drops from point B to point A, and the trapped saturation value significantly drops from point B to point D. This stipulates that the capillary number influences the trapped saturation, and since the other parameters in Equation 1 are constant for this study, the primary parameter that influences the trapped saturation is the brine flow rate. However, further studies on log(\(\textrm{N}_{ca}\)) are recommended to strengthen the claims in Figure 9, as studies indicate that log(\(\textrm{N}_{ca}\)) can be as low as \(-8.00\) (Wang et al. 2013; Cao et al. 2016).

Varied flow rates impacted the saturation distributions across the micromodel, as evidenced by the inset photograph in Figure 9. The labels A to D in the inset photograph correspond to the same labels on the graph. At log(\(\textrm{N}_{ca}\)) < \(-6.00\), the saturation topology shows large clusters of trapped \(\textrm{proxyScCO}_2\) (inset photographs A and B, red color). In contrast, at log(\(\textrm{N}_{ca}\)) > \(-5.00\), smaller clusters of trapped \(\textrm{proxyScCO}_2\) are observed (inset photographs C and D, red color). This indicates that variations in capillary number influence the size of trapped \(\textrm{proxyScCO}_2\) clusters. Lenormand et al. (1983, 1988) concluded that flows at log(\(\textrm{N}_{ca}\)) above \(-5.00\) are dominated by viscous forces, while those below are governed by capillary forces. Therefore, it can be inferred that capillary-dominated flow leads to the formation of large trapped \(\textrm{CO}_2\) clusters, whereas viscous-dominated flow results in smaller clusters. These findings are consistent with the studies by Vizika et al. (1994) and Delshad et al. (1986), which also highlight the influence of capillary number on non-wetting phase trapping in porous media. Their work supports the observed trend that capillary number is a key factor controlling trapped \(\textrm{proxyScCO}_2\) saturation.

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Figure 10a shows the effect of capillary number on the trapping capacity [C\({\text {trap}} = \phi S{\text {(nw)r}}\)], which is the fraction of the total volume of the porous medium that can be occupied by the trapped saturation of \(\textrm{ScCO}_{2}\) (Iglauer et al. 2009). As the log(\(N_{ca}\)) increases from \(-\)7.05 (0.29 \(\upmu\)L/min) to \(-\)5.05 (28.92 \(\upmu\)L/min), the capillary trapping capacity of \(\textrm{ScCO}_{2}\) decreases from 0.246 to 0.179. With a further decrease of log (\(N_{ca}\)) to \(-\)4.52 (96.41 \(\upmu\)L/min), the capillary trapping capacity decreases to 0.148.

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At an injection rate of 96.41 \(\upmu\)L/min, the capillary trapping capacity is 0.148, which indicates that at high injection rates, the capillary trapping capacity of \(\textrm{ScCO}_{2}\) is relatively low. As the injection rate decreases to 28.92 \(\upmu\)L/min, the capillary trapping capacity of \(\textrm{ScCO}_{2}\) increases to 0.179, showing a slight improvement. However, as the injection rate continues to decrease to 2.89 \(\upmu\)L/min, the capillary trapping capacity of \(\textrm{ScCO}_{2}\) increases to 0.257. This implies that a moderate flow rate can improve the capillary trapping capacity of \(\textrm{ScCO}_{2}\). At the lowest injection rate of 0.29 \(\upmu\)L/min, the capillary trapping capacity of \(\textrm{ScCO}_{2}\) reduces to 0.246, indicating a slight decrease in the capillary trapping capacity of \(\textrm{ScCO}_{2}\) from its peak value.

High injection rates can negatively impact the capillary trapping capacity of \(\textrm{ScCO}_{2}\) and reducing injection rates to an optimal value can significantly improve the capillary trapping capacity of \(\textrm{ScCO}_{2}\) as illustrated in Figure 10a. Figure 10b illustrates the relationship between capillary trapping capacity \(\textrm{C}_{trap}\) and initial saturation of \(\textrm{proxyScCO}_{2}\). The capillary trapping capacity is calculated using Equation 4. This equation is used to calculate the trapping capacity of \(\textrm{proxyScCO}_{2}\) for initial saturation of \(\textrm{proxyScCO}_{2}\) greater than 0.403 (Iglauer et al. 2009).where \(\textrm{C}_{trap}\) is the trapping capacity and \({\textrm{S}}_{(nw)i}\) is the initial saturation of the non-wetting phase. The relationship between trapping capacity and initial saturation of \(\textrm{proxyScCO}_{2}\) is linear; the trapping capacity of \(\textrm{proxyScCO}_2\) increases as its initial saturation increases. The \(\textrm{C}_{trap}\) increases from 0.0413 to 0.043 as the initial saturation of \(\textrm{proxyScCO}_2\) increases from 0.695 to 0.86.

The Knudsen number was calculated for both \(\textrm{proxyScCO}_2\) and brine to assess the validity of continuum assumptions in the micromodel. The molecular mean free path, approximated by intermolecular spacing, is on the order of 0.3-\(-\)0.5 nm for both fluids. With an average pore diameter of 16.33 \(\mu\)m, the Knudsen numbers are approximately \(3 \times 10^{-5}\) for \(\textrm{proxyScCO}_2\) and \(2 \times 10^{-5}\) for brine. These values are far below the 0.01 threshold for slip flow, confirming that the flow lies firmly within the continuum regime. Accordingly, the micromodel flow behavior can be reliably described by classical Darcy flow without invoking slip flow or Knudsen-type corrections.

Figure 11 demonstrates the relationship between \(\textrm{C}_{trap}\) and initial saturation of \(\textrm{proxyScCO}_{2}\), comparing data from literature with the experimental data obtained in this study (Iglauer et al. 2009; Caubit et al. 2004; Jerauld 1997). The \(\textrm{C}_{trap}\) increases as the initial saturation of \(\textrm{proxyScCO}_{2}\) increases due to IFT between fluids. This aligns with the findings of Iglauer et al. (2009), where capillary trapping is emphasized as a secure mechanism for \(\textrm{proxyScCO}_{2}\) storage in porous rock. The experimental data from this study (red squares) are validated by the experimental data from the literature, confirming that the \(\textrm{ScCO}_{2}\) trapping capacity is consistent with the literature. The differences between the experimental data and Iglauer et al. (2009) the data at the same initial saturation of \(\textrm{proxyScCO}_{2}\) were analyzed through regression analysis. The measure of total variability accounted for by the model was used to assess the goodness of fit by using the goodness of fit (\(\textrm{R}^{2}\)). The value of (\(\textrm{R}^{2}\)) for the linear regression appeared to be 0.918, indicating a good fit of the model.

The comparison with the results of Iglauer et al. (2009) shows the importance of validating and reinforcing the reliability of the experimental results of this study. This comparison of increasing \(\textrm{C}_{trap}\) to prior studies and relating it to the increase in the saturation of the \(\textrm{proxyScCO}_{2}\) to its initial saturation also suggests the secure mechanism of capillary trapping in saline aquifers for \(\textrm{ScCO}_{2}\) storage. Moreover, the consistency between the values characterizing the \(\textrm{proxyScCO}_{2}\) trapping capacity plotted as red squares vs. literature data shown as black squares is also acknowledged, which appears as a strong support for the conclusions made in this study. To compare the differences noted above, regression analysis was performed, and its high determination coefficient (\(\textrm{R}^{2}\)) = 0.918 also supports the outcome of the experiment. This rigorous comparative analysis not only enhances the validity of the current study but also helps to extend the knowledge based on the \(\textrm{ScCO}_{2}\) capillary trapping mechanisms into the existing research findings.

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The trapped saturation of \(\textrm{ProxyScCO}_{2}\) depends on the initial saturation of \(\textrm{ProxyScCO}_{2}\). In this case, higher initial saturation means that more volume of \(\textrm{ProxyScCO}_{2}\) can be immobilized during brine injection. Nonetheless, flow rates rise as log(\(N_{ca}\)) increases so the effectiveness in trapping \(\textrm{ProxyScCO}_{2}\) decreases because viscous forces overcome capillary forces. In BAC cycle 2, the initial saturation of \(\textrm{ProxyScCO}_{2}\) is higher, and the trapped saturation of \(\textrm{ProxyScCO}_{2}\) is higher, but it follows a similar displacement pattern as in BAC cycle 1. Figure 12 illustrates the impact of BAC injection cycles on \(\textrm{ScCO}_{2}\) trapping efficiency during the injection of \(\textrm{ScCO}_{2}\) and brine. The data show that for capillary-dominated flow, the \(\textrm{ScCO}_{2}\) trapping saturation is higher compared to the flow where viscous forces were dominated over capillary forces. The trapped saturation of \(\textrm{ScCO}_{2}\) in BAC cycle 2 is higher than in BAC cycle 1 during the injection of brine at capillary numbers (log(\(N_{ca}\))) of \(-\)4.52, \(-\)5.05, \(-\)7.05, and \(-\)6.05. This variation in the capillary trapping saturation for BAC cycles 1 and 2 is due to the initial \(\textrm{ScCO}_{2}\) saturation in the micromodel. Table 5 summarizes the initial saturation of \(\textrm{ScCO}_{2}\) before brine injection for four capillary numbers (log(\(N_{ca}\))) of \(-\)7.05, \(-\)6.05, \(-\)5.05, and \(-\)4.52. The initial saturation of \(\textrm{ScCO}_{2}\) in BAC cycle 1 is higher than the initial saturation of \(\textrm{ScCO}_{2}\) in BAC cycle 2 for all capillary numbers. The values in brackets in Figure 12 show the percentage difference in trapped saturation between BAC cycles 1 and 2 at different log(\(N_{ca}\)). The values of these parameters describe the change of \(\textrm{ProxyScCO}_{2}\) trapped saturation in BAC cycle 2 compared to that in cycle 1, which shows the change of the trapped \(\textrm{ProxyScCO}_{2}\) saturation under the same circumstances between the two cycles of the experiment.

At log(\(N_{ca}\)) = \(-\)6.05, the percentage difference of 8.21% reveals that the trapped saturation in BAC cycle 2 is relatively 8.21% higher than the trapped saturation in cycle 1. Likewise, at log(\(N_{ca}\)) = \(-\)4.52, the increase in trapped saturation percentage difference of (8.19%) represented a considerably higher stratification in cycle 2. These differences are due to variations in initial \(\textrm{ProxyScCO}_{2}\) saturation and demonstrate how BAC cycle-to-cycle conditions can influence the effectiveness of capillary trapping.

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The influence of initial \(\textrm{ProxyScCO}_{2}\) saturation on capillary trapped saturation of \(\textrm{ProxyScCO}_{2}\) after brine injection is an important factor for predicting the efficiency of \(\textrm{ProxyScCO}_{2}\) capillary trapping in saline aquifers (Land 1968). Higher initial \(\textrm{ProxyScCO}_{2}\) saturation generally leads to higher capillary trapping, as there is more \(\textrm{ProxyScCO}_{2}\) available to be trapped in the pore space (Krevor et al. 2015).

The observed increase in \(\textrm{proxyScCO}_2\) saturation aligns with the findings of Krevor et al. (2015) and Al Mansoori et al. (2009) who reported that the capillary trapping efficiency improves with increasing initial saturation of \(\textrm{ScCO}_{2}\). Figure 13 compares the effect of initial saturation of \(\textrm{proxyScCO}_{2}\) on its capillary trapping in this study with findings of Krevor et al. (2015). Figure 13 shows that capillary trapping of \(\textrm{proxyScCO}_2\) increases with higher initial saturation of \(\textrm{proxyScCO}_2\) and lower capillary numbers, highlighting the significant influence of these factors on trapping efficiency.

This study was focused on capillary trapping of \(\textrm{CO}_2\) as the primary trapping technique of interest for injection rate. Other trapping mechanisms, such as solubility trapping, significantly influence two-phase flow behavior in sandstone saline aquifers. This study was aimed at isolating and examining the effect of injection rate on capillary trapping, as this mechanism is particularly relevant for the conditions under investigation. Nonetheless, solubility trapping must be evaluated to comprehensively comprehend the trapping behavior in actual saline aquifer systems. Subsequent investigations will broaden this research to encompass a more thorough examination of other trapping mechanisms. The results show that \(\textrm{ScCO}_2\) capillary trapping in the micromodel depends strongly on injection rate and initial saturation, with capillary forces favoring larger trapped clusters at low rates and viscous forces reducing trapping at higher rates. BAC injection further enhances trapping by promoting brine imbibition and cluster fragmentation, providing direct pore-scale evidence of mechanisms that are not observable in core-scale studies.

This study is limited by the use of a 2D micromodel and a proxy fluid for \(\textrm{ScCO}_2\), which cannot fully reproduce the mineralogical variability and thermophysical properties of actual reservoirs. In addition, the laboratory pressure and temperature conditions, together with inherent scale effects, restrict the direct applicability of the results, as pore-scale trapping behavior may differ under true reservoir conditions. Long-term processes such as dissolution, mineralization, and potential remobilization were also not assessed. Future work should therefore emphasize experiments and simulations under in situ reservoir conditions, supported by upscaling approaches and long-term evaluations of storage stability to strengthen confidence in permanent \(\textrm{CO}_2\) sequestration.