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Energies 2020, 13, 4014 12 of 18 pressures and, at the same time, with a limited quantity of refrigerant, which is an expensive fluid with a relatively high GWP. A direct comparison with other literature results is difficult as comprehensive thermodynamic analyses of mixtures of carbon dioxide for the particular case here considered are not available. Furthermore, different authors assume different parameters and different cycle configurations, according to the specific application and to their particular sensitivity to the design parameters. Nevertheless, in [15], extensive results for recuperative carbon dioxide cycles with different layouts are presented, and for the more elaborate cycle configuration considered (an inter-cooled cycle with a dual split and a dual expansion), at a maximum cycle temperature of 400 ◦C, a total efficiency η of about 0.17–0.18 is reported. In [48], for example, with reference to a glass furnace, a total efficiency η of about 20% for a recovery organic Rankine engine is reported, but the authors assume a minimum cooling temperature for the flue gas equal to 180 ◦C. Obviously, other fluids can be considered as dopants for carbon dioxide (for example, hydrocarbons, some of the new available refrigerants or some of the new technical fluids that are commercially available). In any case, the thermodynamic evaluations require the use of suitable equations of state and, in general, the knowledge of the so-called binary interaction parameters. In the case of the well known Peng–Robinson equation of state, for example, the binary interaction parameters of a mixture ki,j are correlated to the intermolecular interactions between the different molecule pairs of the different molecules composing the mixture. For a mixture of two components, only one binary interaction parameter is necessary, typically identified by the symbol k1,2. The correct value of k1,2 is usually calculated by a regression of the experimental VLE. Then, the coefficient amix bmix of the equation of state for the specific mixture can be defined, for example, by the well known classical van der Waals formulation [47,49] (p. 423): amix = z21a1 + z1z2a1,2 + z2a2 (2) bmix = z1b1+z2b2 (3) where ai and bi are the parameters for the pure components and a1,2 = √a1a2 (1 − k1,2) (4) √ In Figure 12, for 19 different mixtures of carbon dioxide, the values of the parameter a1,2 = a2 (1 − k1,2) are reported as a function of a2. The coefficient a2 is the specific coefficient relative to the second compound of the mixture according the van der Waals equation of state (with a1, the constant coefficient for carbon dioxide) [50]: 27 τ2 a2 = c,2 (5) 64 Pc,2 τc,2 = kBTc,2 (6) kB = NR (7) A where, NA is the Avogadro number, R = 8.3143 J mol−1 K−1 is the gas constant and Tc and Pc are the critical temperature and the critical pressure, respectively. The correlation in Figure 12 can be used for a first estimation of the binary coefficient parameter k1,2 (the Peng–Robinson binary interaction parameter) for binary mixtures of carbon dioxide in case no experimental VLE data are available, thus allowing preliminary calculations of the performances of thermodynamic cycles. Nonetheless, experimental VLE values are obviously preferable.PDF Image | CO2 Mixtures as Working Fluid for High-Temperature Heat Recovery
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