# Thermodynamic Analysis of Partitioned Combined Cycle using Simple Gases
## 3 Model Description
### Pressure/Temperature Ratios for the Brayton Cycle  
The CCGT pressure and temperature ratios are optimized in the original GE model GT. However, sensitization analysis is required for partition cycle. Figure 3 overall represents these results. The optimum pressure and temperature ratios were calculated using conditions bounded by the limits defined in Table 1. In Figure 3a the pressure ratio is plotted against Brayton cycle efficiency. In the Brayton Cycle, it is known that an optimum pressure and temperature ratio is required. However, high combustion temperature does not allow high pressures due to metallurgical limitations. Therefore, the pressure is not high enough to maximize heat to work conversion, resulting in high entropy (second law efficiency) loss. Any fluid that has less heat capacity than CCGT working fluid will inherently present the advantage of heat recovery. It is evident from the simulated data that CO\({}_{2}\)-, Air-, N\({}_{2}\)-, H\({}_{2}\)-, and Ar-based partitioned Brayton cycles had maximum efficiency at pressure ratios of 1168, 105, 102, 79.7, and 19.9, respectively, at mean operating conditions. As the pressure ratio was enormously (impracticably) high for these gases (except Ar), a separate partitioned Rankine cycle was required to make up the entropy loss because of the low turbine inlet pressure. However, for Ar the pressure ratio is achievable with comparable efficiency. This behavior of Ar is because of its lower heat capacity and compressibility factor. Similar behavior for temperature ratios can be inferred and is presented in Figure 3b. Exhaust temperatures of 372, 320, 319, 312, and 308 \({}^{\circ}\)C were calculated for CO\({}_{2}\), Air, N\({}_{2}\), H\({}_{2}\), and Ar, respectively, for the mean operating conditions pressure ratios. Inlet temperature to turbine was fixed at 1435 \({}^{\circ}\)C. These exhaust temperatures do not provide the optimum efficiency value for PCGT, as such low temperatures have an impact on HRSG heat transfer and thus the Q\({}_{\text{R,EX,p}}\) in Equation (2) lowers the overall efficiency. Figure 3: Light blue—Ar, green—H\({}_{2}\), blue—N\({}_{2}\), red—Air, purple—CO\({}_{2}\), (**a**) optimized pressure ratio versus simple cycle efficiency for various adiabatic efficiencies. Dotted lines represent the two limits and the mean operating conditions. Pressure ratio = turbine inlet Pressure/118 kPa. (**b**) Optimized temperature ratio versus simple cycle efficiency for various adiabatic efficiencies. Dotted lines represent the two limits and the mean operating conditions. Temperature ratio = 1435 \({}^{\circ}\)C/Exhaust Temperature. (**c**) Pressure ratio versus temperature ratio. (**d**) Differential of ‘a’, dotted line presents the zero x–axis. The optimum pressure and temperature ratios for Brayton cycle are plotted in Figure 3c. The slope of these lines indirectly illustrates the entropy loss for various gases if the simple cycle is operated below the optimum pressure. The higher the slope, the higher the exergy cost will be. Thus, CO\({}_{2}\) was predicted to offer the highest loss. Figure 3d represents the differential of Figure 3a. These curves are important as they show the effect of excessive pressure drop in the downstream heat exchanger/boiler. The heat exchanger duty is a dynamic feature of fouling. Fouling factor is a design aspect. Although the waste heat recuperation is working on closed systems for partitioned cycle and aggressive fouling factors are not needed, a slight change in pressure drop may have drastic effect on cycle efficiency, as shown in the case of Ar. As an example, an efficiency drop of 3.2% was calculated for only 0.01 bar pressure drop greater than the designed pressure drop. Similar behavior was observed when Ar, as in the case of a new/cleaned heat exchanger, experienced low-pressure drop. This represents the negative effect of the low heat capacity gases. The effect will be much pronounced if the PCGT operates at part load conditions, where efficiency is expected to fall drastically.