## 6 Results and Discussions
### Three Membrane Stages Design Technical Analysis  
To seek a technical solution for reducing power demands, which means decreasing the total cost of the process, one more unit was added to the two stages of the membrane, forming a configuration of three membrane units with a compressor before every unit, see Figure 3, Case 3. Different membrane surfaces for the third stage were examined to gain at  
Figure 6: Two stages of membrane with main results of obtaining a 90% recovery and 99% purity. Figure 7: (**a**) First compressor influence on \(\text{CO}_{2}\) capture rate respecting second compressor at the two units of membrane. (**b**) First and second compressor impact on carbon dioxide purity at the two units of membrane. (**c**) First and second compressors effect on total energy consumption at the two units of membrane. least 99% CO\({}_{2}\) purity. The phase where the paper goal was achieved was at 7 bar of the first compressor and 4 bar of the second one. About 298 MW of power was demanded at this optimal point. Figure 8 demonstrates the optimum results of using three membrane stages in terms of the main contents in each process side, CO\({}_{2}\) removal rate, CO\({}_{2}\) captured stream, and compressors' power-consumption requirements. Utilization of a compressor before the third membrane stage affected the membrane process performance in terms of CO\({}_{2}\) recovery and power requirements, where Figure 9a-d show that effect separately. Figure 9a below illustrates the third compressor's effect on the process's efficiency concerning the first compressor. The impact of CP\({}_{3}\) on efficiency expanded clearly at higher first compressor pressures (7 and 8 bar) due to the major flue gas stream arriving at the  
Figure 8: Three stages of membrane with main results to obtain a 90% recovery and 99% purity (optimal). third compressor at elevated \(\mathrm{CP_{1}}\). The figure also demonstrates the importance of using a compressor before the third membrane to reduce the \(\mathrm{CO_{2}}\) flow exiting from the membrane by increasing the driving force around that membrane. The parameters simulated for this figure were at MSA\({}_{1}\), MSA\({}_{2}\), MSA\({}_{3}\), \(\mathrm{CP_{2}}\) of 800,000; 80,000; 8000 m\({}^{2}\), and 4 bar, respectively. Figure 9b presents the influence of increasing \(\mathrm{CP_{3}}\) on total electric power demand for the capture method by examining different first compressor pressures. It is widely obvious that raising the third compressor value led to a reasonable increase in energy consumption because the elevated flue stream reached the carbon dioxide compression station, which helped to boost the electricity needed for pushing that stream. The parameters used for the current figure were like the last figure's parameters. Harnessing a higher surface area for the third membrane module allowed \(\mathrm{N_{2}}\) molecules to go via the membrane unit along with \(\mathrm{CO_{2}}\), which constantly reduced the concentration of carbon dioxide recovered. Raising the first compressor pressure value showed a remarkable boost in \(\mathrm{CO_{2}}\) purity at different MSA\({}_{3}\) due to the raise of flue gas captured and moved toward the third membrane unit, where Figure 9c presents the main \(\mathrm{CO_{2}}\) purity variation at different MSA\({}_{3}\). The impact of first membrane surface was presented in Figure 9d below regarding different first compressor pressures, where the figure demonstrates the highly influential effect of increasing first membrane size on the carbon-capture rate. Enlarging the MSA\({}_{1}\) from 200,000 to 800,000 m\({}^{2}\) guided to almost 33% increase in the carbon dioxide removal rate at 8 bar of \(\mathrm{CP_{1}}\) due to the great amount of \(\mathrm{CO_{2}}\) steam that went through the membrane at larger surfaces. On the other hand, boosting the pressure in the first compressor helped push the \(\mathrm{CO_{2}}\) flow through the membrane which increased the recovery rate.