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CO2 Mixtures as Working Fluid for High-Temperature Heat Recovery

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CO2 Mixtures as Working Fluid for High-Temperature Heat Recovery ( co2-mixtures-as-working-fluid-high-temperature-heat-recovery )

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Energies 2020, 13, 4014 3 of 18 In addition to heat recovery, supercritical and transcritical carbon dioxide cycles have already been considered for a great variety of applications; for example, for solar plants, for nuclear power plants, for the exploitation of geothermal energy, and also for thermo-electric storage [18–21]. 2. The Simple Recuperative Carbon Dioxide Cycle In the thermodynamic exploitation of heat sources with a finite heat capacity, as in the case of hot flue gases, both the thermodynamic cycle efficiency and the effective cooling of the heat source are of paramount importance. This can be expressed, as is well known, by the total efficiency of a waste heat recovery system: W ̇ W ̇ H H 1 − H H 2 η=m ̇ 􏰢H −H 􏰣=m ̇ 􏰢H −H 􏰣H −H =ηthφ (1) H H1 H0 H H1 H2 H1 H0 where ηth is the cycle’s thermodynamic efficiency, φ is the heat recovery factor, and the enthalpy HH0 representstheenthalpycorrespondingtotheminimumtemperatureTH0 atwhichthefluegascanbe cooled (see Table 1). In the following, to simplify the calculations and the general considerations, we assumedavalueofTH0 equaltothedewtemperatureofthefluegas. Table 1. Design parameters assumed for the calculations. Parameter Pressure losses Minimum internal temperature approach in the recuperator, MITAR (◦C) Minimum internal temperature approach in the primary heat exchanger, MITAPHE (◦C) Minimum internal temperature approach in the condenser, MITAC (◦C) Turbine efficiency, ηT Compressor/pump efficiency, ηP Mechanical efficiency of the compressor/pump Mechanical/electrical efficiency of the turbine Cooling air temperature (inlet TC1 /outlet TC2 ) (◦C) Temperatureoftheavailablefluegas,TH1 (◦C) Mass flow of the hot flue gas, m ̇ H (kg s−1) Composition of the flue gas (molar fractions) Dewtemperatureofthefluegas,TH0 (◦C) Thermalpoweravailableinthefluegas,m ̇H(HH1 −HH0)(MW) Assumed Value Neglected 20 50 20 0.85 0.8 0.98 0.95 15/35 450 100 N2 0.58; O2 0.03 CO2 0.28; H2O 0.11 51 44.06 Thus, for a fixed TH1 and a mass flow m ̇ H of flue gas, there is an optimal cycle maximum temperature and an optimal maximum cycle pressure that optimize the total efficiency η. In fact, high maximum cycle temperatures T3 and small expansion ratios rC = P2/P1 result in a relatively high ηth, but a low φ. On the contrary, low values of T3 and high values of rC cause a low ηth and a high φ. Therefore, an optimal compromise between the maximum cycle temperature and the compression ratio must be identified. In Table 1 the main design parameters assumed for all the following calculations are listed. In Figure 1, we show the considered plant scheme, with the compressor conceptually changed to a pump in all cycles with condensation. All the calculations are carried out with Aspen Plus⃝R V9. The model used for all thermodynamic evaluations is the well known Peng–Robinson equation of state. An equation of state is generally considered for the evaluation of the volumetric properties of the real gases in thermodynamic and in fluid-dynamic calculations [22–24] As an example, Figure 2 shows two carbon dioxide thermodynamic cycles at different T3 and different rC values. Cycle (a) has a maximum temperature of 350 ◦C and a compression ratio rC = 3.5, while cycle (b) has T3 = 400 ◦C and rC = 2. The efficiency ηth of cycle (b) is slightly greater than the efficiency of cycle (a), but its lower φ (0.438 against about 0.6) appreciably detracts from the total efficiency η (0.097 versus 0.129).

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