## 3 Results and Discussion
### SDS on CO\({}_{2}\)-Induced Oil Swelling
The distance of the intensity changes allows us to evaluate the relative diffusion rate of CO2 in oil under different injection pressures and oil surface tension. Figure 4: An illustrative image showing the intensity profile location in a microchannel. Fluorescent intensity profiles for pure oil and SDS-mixed oil along the channel at three different time intervals: 0 min, 180 min, and 360 min. (**a**) Pure oil at 5 psig CO2 pressure. (**b**) 2% (\(w/v\)) SDS mixed oil at 5 psig CO2 pressure. (**c**) Pure oil at 10 psig CO2 pressure. (**d**) 2% (\(w/v\)) SDS mixed oil at 10 psig CO2 pressure. To perform a comparative evaluation of the CO2 diffusion rates in oil under different conditions, we estimate the distance corresponding to the identical change in normalized fluorescence intensity for different conditions of injection pressure and reduced surface tension of oil upon SDS addition. Table 1 summarizes the distances corresponding to changes in normalized fluorescence intensity (FI) from 0.2 to 0.9 under different conditions. It should be noted that a shorter distance for the same intensity change demonstrates a faster CO2 diffusion rate in oil. The data show that adding SDS results in shorter distances for the same intensity change, indicating faster CO2 diffusion in oil. For instance, the distance for the intensity changes from 0.2 to 0.9 is 895 \(\upmu\)m in SDS-mixed oil at 10 psig and 360 min, compared to 2225.6 \(\upmu\)m in pure oil. This pattern holds reasonably well in all conditions, with SDS-enhanced oil consistently showing shorter distances, thus demonstrating more efficient CO2 diffusion over time. However, at 5 psig and 180 min, the distance for the intensity change from 0.2 to 0.9 in SDS-mixed oil (2320.7 \(\upmu\)m) is unexpectedly higher compared to 5 psig without SDS (2358.2 \(\upmu\)m). This anomaly is attributed to the less accurate fit of the pure oil data at 5 psig, and the difference is within the error range of multiple tests. Additionally, the change in CO2 diffusion upon SDS addition at 5 psig is not as significant as observed at 10 psig. The overall trend, however, still supports the conclusion that adding SDS at higher injection pressure enhances the rate of CO2 diffusion into the oil. Figure 5: Fluorescent intensity profiles for pure oil and SDS-mixed oil at 180 and 360 min, along with their exponential fits. (**a**) Pure oil at 5 psig CO2 pressure. (**b**) 2% (\(w/v\)) SDS mixed oil at 5 psig CO2 pressure. (**c**) Pure oil at 10 psig CO2 pressure. (**d**) 2% (\(w/v\)) SDS mixed oil at 10 psig CO2 pressure. The increase in the rate of SDS-induced CO\({}_{2}\) dissolution into oil is largely attributed to the amphiphilic property of SDS. An amphiphilic molecule such as SDS has both a hydrophobic tail and a hydrophilic head, allowing it to interact with both oil and CO\({}_{2}\)[30]. Upon SDS addition into the system containing oil and CO\({}_{2}\), it reduces the surface tension between them, which makes CO\({}_{2}\) dissolution easier in oil. By adsorbing at the CO\({}_{2}\)-oil interface, the SDS molecules lower interfacial tension (IFT), reducing the energy barrier for CO\({}_{2}\) transport across the interface (Figure 6). This lowered IFT enhances the mass transfer efficiency of CO\({}_{2}\) into the oil phase, enabling finer dispersion of CO\({}_{2}\) and increasing the contact area. Consequently, CO\({}_{2}\) molecules penetrate more effectively into the oil phase, improving their solubility and facilitating oil swelling. In SDS, molecules naturally form structures called micelles, where the hydrophobic tails cluster together in the center, away from water, while the hydrophilic heads face outward, micelle formation is unlikely in oil at the low SDS concentrations used in our study [32]. Instead, SDS molecules aggregate at the CO\({}_{2}\)-oil interface, creating localized microenvironments that enhance CO\({}_{2}\) absorption and solubility.