## 4 Results and Discussions
### Effect of the Cycle's Parameters on Its Performance  
The cycle's performance is highly dependent on its selected value parameters. Cycle components are designed on the basis of these parameters. Nevertheless, the selection of cycle parameters under required conditions is tricky and requires extensive cycle simulations. The most sensitive parameters for the recompression sCO\({}_{2}\)-BC are compressor inlet temperature \((T_{1})\) compressor inlet pressure \((P_{1})\), split mass fraction \((x)\), and cycle pressure ratio. The influence of the abovementioned cycle parameters on the cycle's performance was analyzed in the current study, followed by its optimization using the genetic algorithm. Figures 10-13 show the dependence of the cycle's split mass fraction and the cycle's efficiency on the parameters of the cycle--i.e., inlet temperature \((T_{1})\) compressor inlet pressure \((P_{1})\) and cycle's pressure ratio. Figure 10 displays a response of the surface bounded by the two-cycle operating parameters, compressor inlet pressure, and cycle's pressure ratio. Response surface shows that the cycle's efficiency is more sensitive to the pressure ratio than the compressor inlet pressure. The cycle efficiency, which is dependent on the pressure ratio, is relatively prominent at higher values of pressure ratio when the compressor's inlet pressure is close to the critical value of the pressure for sCO\({}_{2}\)--i.e., 7.34 MPa. On the other hand, the cycle's efficiency is equally sensitive to the cycle's pressure ratio for all values of compressor inlet pressure. The cycle's efficiency increases initially when the rise in the value of the \(Pr\) reaches a maximum value and then drops with further increase in the value of the cycle's pressure ratio. Thus, there exists an optimal value of the pressure ratio corresponding to each value of the compressor's inlet pressure \((P_{1})\). This value shifts towards a lower value of the cycle's pressure ratio with an increase in the value of the compressor's inlet pressure \((P_{1})\). Figure 11 shows variations of the optimized split mass fraction with the compressor's inlet pressure \((P_{1})\) and cycle's overall pressure ratio. The graph shows that the optimized split mass fraction is overly sensitive to the compressor's inlet pressure for all the pressure ratio values. The split mass fraction decreases initially with an increase in the value of \((P_{1})\) then it starts increasing with further increase in the value of \((P_{1})\). However, \(x_{opt}\) was also significantly affected by \(Pr\). Initially, \(x_{opt}\) decreased rapidly with an increase in the value of \(Pr\) although this variation leveled off at higher values of \(Pr\).  
Figure 9: Effect of the compressor’s performance on the cycle’s efficiency.  
Figure 11: Variation of the optimized \(x\) with compressor inlet pressure and cycle overall pressure ratio.  
Figure 10: Deviation of \(\eta_{cyc}\) with \(P_{1}\) and \(Pr\).  
temperature and the cycle pressure ratio. The value of \(x_{opt}\) decreased initially and then, after a certain pressure ratio for which its value was minimum, it started increasing. On the other hand, the value of \(x_{opt}\) increased rapidly as the compressor inlet temperature moved away from \(T_{c}\); however, at higher values of \(T_{1}\), the rate of increase in the value of \(x_{opt}\) became smaller. Thus, it can be depicted from here that selection of \(T_{1}\) is crucial for the main and re-compressor sizes.