## 6 Results and Discussions
### Two-Membrane Stages Design Technical Analysis  
Two membrane units were designed to overcome the low results in carbon dioxide purity by introducing a low surface for the second membrane unit. For Case 2, two compression units were utilized before each membrane without vacuum pump utilization. After introducing the flue gas into the process at different compressor pressures (3-8 bar) and first membrane surface values, the recovery of carbon dioxide increased with the increase in these parameters, as long as the electricity demand for the process continued. The second compressor and membrane area were considered 2-6 bar and 80,000 m\({}^{2}\), respectively. The results showed that a point of 90% removal efficiency with 99% purity was reached at 7.3 and 2 bar of pressure in the first and second compressors; and 800,000 m\({}^{2}\) of the first membrane surface. At this point, the power demand was around 340 MW, which represents 57% of the total CFPP capacity. Figure 6 clarifies the optimum results of using two membrane stages in terms of the main contents of each process side, CO\({}_{2}\) purity, CO\({}_{2}\) captured stream, and compressors' power consumption.  
The main purpose of presenting Figure 7a-c was to simplify how the feed and second compressor directly influence the CO\({}_{2}\) removal process, purity, and total power consumption.  
Utilization of the membrane's second unit helped to increase the recovery rate of CO\({}_{2}\), as shown in Figure 7a. As observed, a greater first compressor pressure means more flue gas goes through the membrane, which clarifies the vast increase in carbon dioxide removal rate at a higher CP\({}_{1}\). The recirculated stream from the second membrane assisted in reducing carbon dioxide exits from the retenate side, where that stream goes back and integrates with the essential flue, which highly increased the removal efficiency, as demonstrated by the raised second compressor value of 2 to 4 bar. The other parameters harnessed for the figure were 800,000 and 80,000 m\({}^{2}\) of the first and second membrane surfaces, each in order.  
Figure 7b demonstrates CO\({}_{2}\) variation based on the first and second compressors. Increasing the first compressor led to a greater concentration of carbon dioxide removed due to the large stream passing via the first membrane, which increases the amount of CO\({}_{2}\) reaching the second membrane module. The head point shown at 2 bar of CP\({}_{2}\) occurred because low nitrogen molecules passed with carbon dioxide. A purity of 99% can be realized at 7 and 8 bar of the first compressors. The other parameters utilized for the figure were 800,000 and 80,000 m\({}^{2}\) of the first and second membrane surface, respectively.  
Figure 7c below illustrates the considerable influence of first compressor on the total electrical power required for the capture process. The direct decrease in power consumed at 8 bar of first compressor pressure from 2 to 4 bar \(\text{CP}_{2}\) is related to the increase in second membrane efficiency, which led to a reduction in the flue stream back from the retentate to the first compressor. Therefore, the energy needed for the first membrane was decreased. At 3 and 5 bar of the first compressor, the poor effect of increasing \(\text{CP}_{2}\) on electricity required can be observed, which may be interpreted as the low flue gas flow passing through the first compressor. The other indicators utilized were the same as the previous figure.