## 6 Results and Discussions
### One-Membrane Stage Design Technical Analysis  
One membrane unit was used with a compressor before the membrane and a vacuum in the permeate path of the flue gas. Different pressures were assumed for the first compressor to assay the membrane capture performance with a vacuum pump utilization of 0.25 bar (optimized); the simulation showed an elevated capture rate with the increase in pressure. On the other hand, the amount of electricity required was expanded due to the increase in CO\({}_{2}\) removal. That outcome was somewhere close to the declaration of [PERSON] et al. (2022) [33]. Meanwhile, an enlarged membrane area (200,000-800,000 m\({}^{2}\)) provided a CO\({}_{2}\) capture rate that was enormously excess with higher power demands. The target of reaching a 90% removal rate was attained at almost 4.4 bar and 400,000 m\({}^{2}\) of the membrane surface. In terms of CO\({}_{2}\) clarity, the highest value gained at this amount of pressure was around 73%, which is completely poor. Figure 4 demonstrates the optimum result of using a single membrane stage at 3000 GPU in terms of the main contents in each process side, CO\({}_{2}\) purity, CO\({}_{2}\) captured stream, and power consumption. Figure 5a-d were illustrated to clarify the membrane single-stage performance in the current study based on several varied parameters. Figure 5a below represents the first membrane surface effect on the CO\({}_{2}\) recovery rate and purity of the same membrane, where enlarging the membrane area showed a reduction  
in the purity of carbon dioxide and an increase in the capture rate due to the greater amount of CO2 stream that went through the membrane unit, in addition to N2 molecules that passed together with the stream, which produced a greater capture efficiency and less carbon dioxide purity at the same time. Thus, adding more membrane units is highly recommended to achieve both a high capture efficiency and purity. Figure 4: One stage of membrane with main results to obtain 90% recovery. Figure 5: (**a**) The variation in CO2 capture rate and purity regarding different first membrane surface. (**b**) CO2 efficiency regarding membrane surface and compressor pressure for the single membrane stage. (**c**) Compressor pressure and membrane size influence on CO2 capture purity for the single membrane stage. (**d**) Power demand regarding different compressor pressures and membrane surfaces for the single membrane stage. The membrane surface area impact on carbon-capture rate in different feed pressure values is demonstrated in Figure 5b. The figure presents that capture efficiency increases permanently with higher compressor values, reaching 100% where all the flue gas introduced passes via the membrane. The increase in membrane size helped to boost the recovery rate enormously since the stream molecules go through larger surfaces, reaching an efficiency of 100% at 600,000 m\({}^{2}\). The effect of the feed compressor on CO\({}_{2}\) captured purity in several membrane surface areas is exhibited in Figure 5c. Higher pressure and surface area lead to pushing nitrogen and other molecules with the carbon dioxide, which results in a lower purity of CO\({}_{2}\) recovered. As clearly shown in the figure, the top purity reached (82%) was at 3 bar, 200,000 m\({}^{2}\) of compressor pressure, and membrane area, respectively. Due to the large surface area used for one stage, the configuration is not appropriate to obtain a high purity of CO\({}_{2}\). Figure 5d below presents the relationship between compressor and electric power demand regarding several membrane areas. Power consumption lines directly escalate with higher compressor pressures due to the huge energy demand to achieve that amount of pressure. The increase in the energy required at higher membrane surface values can be explained by the greater carbon dioxide stream captured with larger surfaces, which requires more electricity to compress it at 70 bar. In this case, the power required to reach 90% capture efficiency was 239 MW at a 4.4 bar compressor pressure.