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Energies 2020, 13, 2447 7 of 18 ηh—efficiency of the heat exchange (-). The next stage of the cycle is CO2 passing through the turbine to generate mechanical energy (step 5). First, the model assumes a pressure to which the CO2 will expand. Knowing the pressure at the compressor inlet (minimum operating pressure of the cycle—7.7 MPa) and knowing that CO2 after passing through the turbine goes to the recuperator, it is necessary to take into account the pressure drop in the recuperator (no pressure drop was assumed on the cooler) and thus determine the pressure at the turbine outlet. The CO2 temperature in stage 5 is calculated based at the assumption that the turbine expansion can be described by an adiabatic process which is given by Equation (4): T5′ =(T5−T4)·ηT+T4 (4) where: T5′ —actual CO2 temperature after expansion (K), T5—ideal CO2 temperature after expansion (K), T4—CO2 turbine inlet temperature (K), ηp—isentropic efficiency of the compressor (-). Knowing the temperature and pressure of CO2 at the turbine outlet, it is possible to calculate the CO2 enthalpy at stage 5. Thanks to this, the power on the turbine shaft can be calculated based on Equation (5): W = m ·h′ − h (5) 4-5 CO2 4 5 where: W4-5—the power on the turbine shaft (W), mCO2—mass stream of CO2 (kg/s), h′4—specific enthalpy of CO2 at the turbine inlet (J/kg), h5—specific enthalpy of CO2 at the turbine outlet (J/kg). The net power of the system was assumed as the power difference on the turbine shaft and the required power of the compressor by Equation (6): Wnet = W4-5 − W1-2 (6) where: Wnet—the net power of the system (W), W4-5—the power on the turbine shaft (W), W1-2—required compressor power (W). The last stage of the model calculation is stage 6 of the cycle. The cooler has no pressure drop, so that the pressure at the compressor inlet is identical to the inlet pressure to the cooler. Using the CoolProp database, the model determines the CO2 temperature at the inlet to the cooler based on the CO2 pressure and enthalpy in stage 6. The CO2 enthalpy value in stage 6 is calculated according to Equation (7): h6 =h′5−h3−h′2 (7) ηh where: h6—specific enthalpy of CO2 at the recuperator hot side outlet (J/kg), h′5—specific enthalpy of CO2 at the recuperator hot side inlet (J/kg), h3—specific enthalpy of CO2 at the recuperator cold side outlet (J/kg), h′2—specific enthalpy of CO2 at the recuperator cold side inlet (J/kg), ηh—efficiency of the heat exchange (-). For comparative purposes, it was decided to define parameters that would allow to evaluate the energy efficiency of the cycle for different operating conditions. The first parameter is the waste heat utilization rate which is given by Equation (8):PDF Image | Supercritical CO2-Brayton Cycle Nat Gas Compression Station
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