## 3 Results and Discussion  
### SDS on CO\({}_{2}\)-Induced Oil Swelling  
CO\({}_{2}\) dissolution in oil is a well-established and published topic as it creates oil swelling and reduces the oil viscosity, subsequently making the oil more mobile [29]. This process is slow and requires high CO\({}_{2}\) pressure to see the measurable change of oil properties on a large scale. Many experiments have been conducted on a microscale to observe the property change and oil swelling at low pressures [30, 31]. In the microfluidic approach, CO\({}_{2}\) dissolution and its rate are usually estimated based on image analysis. Therefore, we conducted a fluorescence-based microscopic experiment to investigate the effect of SDS on CO\({}_{2}\) dissolution in oil. Using fluorescence microscopy, we observed the time-dependent intensity change of oil at the CO\({}_{2}\)-oil interface in a closed-ended microchannel under constant CO\({}_{2}\) pressure. The changes in fluorescence intensity of the oil according to its concentration provide a visual representation of the CO\({}_{2}\) dissolution process, enabling a comparative study under different conditions without the need for dissolution units [29]. Our study is intended to compare the effect of SDS on CO\({}_{2}\) diffusion in oil, i.e., oil swelling, instead of measuring the absolute CO\({}_{2}\) diffusion and dissolution rate in the oil. We analyzed these effects using pure crude oil with 2% (\(w/v\)) SDS. Figure 4 presents the changes in normalized fluorescence intensity along a microchannel filled with pure crude oil and 2% (\(w/v\)) SDS mixed oil at CO\({}_{2}\) pressures of 5 and 10 psig. Each plot includes data collected at 0, 180, and 360 min after oil was pressurized under identical flow conditions. Initially, the fluorescence intensity is zero, indicating no oil presence at that point. The abrupt intensity changes depict the CO\({}_{2}\) -oil interface, which was consistently positioned at the start of CO\({}_{2}\) injection. As CO\({}_{2}\) diffuses into the oil, the fluorescence intensity decreases from the interface along the channel over time (0, 180, 360 min) due to oil swelling. Figure 4a,b show the change in normalized oil intensity in pure oil and SDS mixed oil at 5 psig CO\({}_{2}\) pressure, respectively. It shows that the rate change in intensity is comparatively prominent in SDS mixed oil over time (from 0 min to 180 min and to 360 min). Similarly, the rate change in intensity is more significant at 10 psig CO\({}_{2}\) pressure upon SDS addition. Figure 4d represents the highest intensity change  
Figure 3: **(a)** Illustrative experimental set up for flooding experiment in a micromodel. (**b**) Actual image of the micro reservoir chip. (**c**) Optical microscopy image of the reservoir filled with oil. (**d**) Optical microscopy image of the reservoir after SDS-DI water flooding. or, indirectly, the highest CO2 dissolution in oil among all cases. Overall, the SDS-mixed oil shows higher intensity transitions compared to pure oil, indicating better CO2 diffusion. To quantify the CO2 diffusion rate into oil, exponential curve fitting was applied to the normalized intensity values from 0.2 to 1, excluding initial values, to avoid the CO2-oil interface effect. Figure 5 shows the normalized fluorescent intensity along the microchannel for pure oil and SDS-mixed oil at 180 and 360 min, along with their exponential fits. Although they show some variations in the changes in normalized fluorescence intensity over time, it reaches its saturation, which is 1, at a distance of approximately 2000 or 2500 \(\upmu\)m from the oil-CO2 interface, indicating negligible CO2 diffusion effect at this location. This behavior can be clearly seen in the asymptotic behavior beyond 0.9 intensity in all cases. A shorter distance for the same intensity change implies a steeper exponential curve, which indicates faster CO2 diffusion.