*3.1. Concurrent Displacement*

We used the recovery factor as a quantitative measure of the gas e fficiency to extract the hydrocarbons from the pore. We estimated the recovery factor by normalizing the number of hydrocarbon molecules leaving the systems by the total number of hydrocarbon molecules in the system. Figures 3 and 4 present the performance of di fferent gases to extract single-component hydrocarbon systems with and without constant-rate injection. We observed that both nitrogen and methane yielded similar recovery factors with and without injection. However, nitrogen exhibited faster breakthrough and displacement compared to carbon dioxide and methane, respectively. We could attribute this behavior to the miscibility of each gas in the hydrocarbons [55]. Given that the solubility of nitrogen in decane is only 15% of that of carbon dioxide at 5 MPa and 50 ◦C with more than six times minimum miscibility pressure at a temperature of 343.2 K, nitrogen had a stable displacement front and in turn a faster breakthrough [56–60]. In addition, we observed lower recovery rates for all gases without injection. However, the reduction in the case of CO2 was the most significant, where the breakthrough was not achieved.

**Figure 3.** Final snapshots of single-component systems: (**a**) CO2 with constant-rate injection; (**b**) CO2 without constant-rate injection; (**c**) CH4 with constant-rate injection; (**d**) CH4 without constant-rate injection; (**e**) N2 with constant-rate injection; (**f**) N2 without constant-rate injection. The color code is the same as in Figure 1.

**Figure 4.** Recovery factors for single-component hydrocarbon systems.

On the other hand, carbon dioxide had better results than the rest with continuous injection and worse than the rest without injection. This could be attributed to the superior adsorption and diffusion characteristics of supercritical CO2, which allow the extraction of the trapped hydrocarbons in the pore grooves [61,62]. While carbon dioxide could not achieve the breakthrough without the injection, it did not induce a phase separation. Li et al. [63] experimentally and numerically compared the performance of miscible and immiscible CO2 displacement using the recovery factor. In our case, we believe that the miscibility was initially achieved; however there was no pressure to maintain the miscible front.

Herein, our hydrocarbon system is a multi-component system with a 50:50 mixture of pentane and decane. Figure 5 presents the results of the multi-component systems. Regardless of the boundary conditions, more pentane was extracted compared to decane. Similar to the single-component systems, both nitrogen and methane had similar recovery factors. However, methane and nitrogen had the same displacement speed. In addition, CO2 still yielded a relatively slower and better performance with constant-rate injection. However, it failed to reach the breakthrough without the injection. It is worth noting that the methane performance was quite different than in the single-component system, especially regarding the displacement speed. This behavior could be attributed to a stable displacement front caused by diluting the decane with pentane. Therefore, there is limited room for methane solubility before phase separation. On the other hand, the pentane presence did not affect the carbon dioxide performance.

**Figure 5.** Recovery Factor for multi-component systems with constant-rate injection (**Left**) and without (**Right**).

As the pore width decreased, we observed that the displacement of hydrocarbons became slower. Figure 6 presents the gas performance to extract single-component systems from confined pores (2 nm). For constant-rate injection scenarios, nitrogen started to displace the hydrocarbons faster than the rest. However, both methane and carbon dioxide eventually yielded better recovery rates. We observed a no-production period for all gases at the start, which was shorter for nitrogen. This period might be attributed to the stronger adsorption hydrocarbons experienced as the pore size decreases. Theoretically, higher capillary pressure is required for gases to enter smaller pores. However, our results sugges<sup>t</sup> that both cases, with and without injection, start to displace hydrocarbons around the same time. This behavior could be attributed to the compressibility of the injected fluid. Even though we did not observe significant impacts on the boundary conditions in the early stages, significant effects were observed later on.

**Figure 6.** Recovery factors for single-component systems in confined pores.

It is worth noting that the curve shape of the recovery factor of confined pores differs from the one observed from large pores. In confined pores, we observed more of a convex shape compared to the linear response observed in large pores. In addition, the breakthrough is more transitional instead of the abrupt change observed in large pores. Both observations sugges<sup>t</sup> a stronger adsorption of hydrocarbons on the pore surface under confinement. On the other hand, less recovery is observed without injection. Both methane and carbon dioxide did not reach the breakthrough. However, methane had a slightly better recovery than carbon dioxide.

## *3.2. Countercurrent Displacement*

In this section, we simulate the performance of the gases to extract single-component hydrocarbon systems. The gases were soaked in contact with the hydrocarbon system for 10 ns, while the hydrocarbons were extracted from the pore to the EOR's gas region. Figure 7 presents the results of the Huff and Puff simulations. During the soaking time, CH4 was the most effective in extracting the hydrocarbon, followed by CO2 and then N2. As the puff process started, a large influx of hydrocarbons left the pore. We observed that some of the hydrocarbons returned back to the pore for 5 nm cases, especially with nitrogen or methane. While similar behavior was observed for 2 nm pores, less recovery was observed for all gases. In addition, the CO2 s performance was relatively improved compared to the methane. While reduced compared to the concurrent displacement, the countercurrent displacement's recovery factors were in line with field observations and recent molecular simulation studies [64,65]. The superiority of CO2 over N2 has been previously experimentally and numerically reported. However, we found that CH4 outperformed all of them in this scenario. This behavior could be attributed to the better vaporization characteristics of methane [66,67].

**Figure 7.** Recovery factors observed for Huff and Puff simulation: (**a**) pore width is 5 nm and (**b**) pore width is 2 nm.

Field recommendations include using CO2 for multi-well EOR operations and CH4 for single-well EOR operations. In addition, the injection pressure significantly affects the CO2 performance. Consequently, pressure support should be maintained throughout the operations. While valid, these recommendations were derived based on single-pore simulations with single or binary component hydrocarbons. However, the heterogeneity of the porous media and the complexity of the crude oil mixture might dramatically affect the EOR operations. Therefore, further research is required to quantify the impact of these factors along with more integrated lab and field pilots.
