Chapter 3 Results and Discussions
3.5 RMCOOLCEP-C System
Furthermore, the RMCOOLCEP-C system is then simulated as shown in Figure 2-4 [39]. There is an extra variable, which is the outlet pressure of the first CO2 turbine, emerges in the RMCOOLCEP-C system. The outlet pressure of the first CO2 turbine is also known as the intermediate pressure between both CO2 turbines. The initial intermediate pressure for the simulation is the inlet pressure of the first CO2 turbine divided by 4.5 (6.22 bar). Then, the reheat temperature is 45 oC lower than the TIT (855
oC). This setting follows the constraint that the minimum temperature differences for the reheat process is 45 oC. Under the conditions that TIT is equal to 900 oC, the CO2 pump outlet pressure 29.68 bar and the mass flowrate of recirculating CO2 100 kg/s, the RMCOOLCEP-C system presents higher energy efficiency that is 59.57% and more net power output of the CO2 pump that is 42.84 MW. Besides, the CO2 recovery of the RMCOOLCEP-C system is also 98.60%. Next, the sensitivity analysis for the CO2 pump outlet pressure, TIT and the intermediate pressure is then performed in order to look for the optimized conditions for the RMCOOLCEP-C system.
3.5.1 The Effect of Isentropic Efficiency
In order to approach the real expansion, the isentropic efficiency of the turbine is set to be 90% in the simulation [22]. Isentropic efficiency represents how good the adiabatic and reversible properties are. When isentropic efficiency is 100%, the operation is perfectly adiabatic and reversible, and this makes the energy loss become zero. In contrast, when isentropic efficiency becomes lower, the system becomes irreversible. And under this situation, part of the energy turns into entropy generation, and this transformation causes energy loss. Entropy generation is the entropy generated within the system that
follows the rule that the higher the entropy generation, the larger the energy loss. This is also verified in Equation (3-1). The work done by the turbine in Equation (3-1) would be a negative value, and the negative sign implies that the energy is outputted from turbine to the generator. Since the T1,oSgen term in Equation (3-1) is always greater than zero, the increment of entropy generation leads to decrease the electrical energy produced by turbine. According to the second law of thermodynamics, connecting several turbines in series can decrease energy loss.
Figure 3-9 Schematic diagram for single-stage and two-stage irreversible turbine expansion [40].
Besides, the difference between single and two stage irreversible expansion is also illustrated in Figure 3-9. For a reversible turbine expansion, the work done will be the area under the line of P-V graph, but for an irreversible turbine expansion, the work done by the turbine is the shaded area in the graph at the right hand side of Figure 3-9 while the unshaded area is the entropy generation. Figure 3-9 shows that the work done by turbine will be higher when the expansion changes from single stage to two-stage. In other words, the increment of the expansion stages can enhance the reversibility of the turbine. For example, in the AspenPlus simulation, a turbine is used to make a 106.74 kg/s gas stream in 900 oC go through volume expansion and the pressure change, from 27.97 bar to 1.08 bar. And in this process, the total power output is 54.29 MW. If there is another system with two turbines, the inlet stream of the system that is 106.74 kg/s in 27.97 bar and 900 oC, and the pressure of the outlet stream is kept at 1.08 bar. Under this circumstance, the total power output for these two turbine system can reach 60.49 MW at most. Although the difference is not evident, after the system is scaled up, the difference becomes larger. This leads to a conclusion that when all the conditions are the same, the energy loss is reduced in the system with two turbines.
3.5.2 Sensitivity Analysis for the Intermediate Pressure
On the other hand, the total power output of the two turbines can reach the maximum value by adjusting intermediate pressure. In order to obtain the optimum intermediate pressure for the largest power generation, some calculations are carried out in the following paragraph. The calculations for the single turbine are carried out at the beginning for the purpose of simplifying the problems. Equation (3-2) to Equation (3-4) are the elementary equations that are relevant to the work done by single stage isentropic
studies change from single-stage expansion to two-stage expansion, the formulation is listed in Equation (3-6). Assuming that the working fluid obeys the ideal gas law, the behavior of the working fluid must follow Equation (3-7). When substituting Equation (3-7) into Equation (3-6), Equation (3-8) is obtained. Next, the optimum intermediate pressure (Pinter) can be obtained by differentiating Equation (3-8) to intermediate pressure, and according to this result, optimum intermediate pressure is the geometric mean of the inlet pressure of the first turbine and the outlet pressure of the second turbine shown in Equation (3-9) [41]. Since the RMCOOLCEP-C system also takes the temperature change and the pressure drop during the reheat into consideration, not just the situation with two turbines mentioned above, optimum intermediate pressure is the geometric mean of the inlet pressure of the first turbine and the outlet pressure of the second turbine with
Wtwostg= γ
γ−1P1,iV1,i[2 − (Pi,o
P1,i)
γ−1
γ − (P2,o
P2,i)
γ−1
γ ] (3-8)
Pinter= √P1,iP2,o (3-9)
Figure 3-10 The effect of intermediate pressure between two turbines to the RMCOOLCEP-C system when the CO2 pump outlet pressure is fixed at 29.68 bar and
the TIT is fixed at 900 oC.
Figure 3-10 depicts the effect of the intermediate pressure to the RMCOOLCEP-C system. The intermediate pressures analyzed in Figure 3-10 the are fractions of the pressure of the first turbine inlet stream, and the highest energy efficiency among the fractions is 59.63%. In this analysis, the intermediate pressure that corresponds to the highest energy efficiency is the quarter pressure of the first turbine inlet stream when the
o