Carbon Dioxide Mixtures as Working Fluid for High-Temperature Heat Recovery: A Thermodynamic Comparison with Transcritical Organic Rankine Cycles

This study aims to provide a thermodynamic comparison between supercritical CO2 cycles and ORC cycles utilizing flue gases as waste heat source. Moreover, the possibility of using CO2 mixtures as working fluids in transcritical cycles to enhance the performance of the thermodynamic cycle is explored. ORCs operating with pure working fluids show higher cyclic thermal and total efficiencies compared to supercritical CO2 cycles; thus, they represent a better option for high-temperature waste heat recovery provided that the thermal stability at a higher temperature has been assessed. Based on the improved global thermodynamic performance and good thermal stability of R134a, CO2-R134a is investigated as an illustrative, promising working fluid mixture for transcritical power cycles. The results show that a total efficiency of 0.1476 is obtained for the CO2-R134a mixture (0.3 mole fraction of R134a) at a maximum cycle pressure of 200 bars, which is 15.86% higher than the supercritical carbon dioxide cycle efficiency of 0.1274, obtained at the comparatively high maximum pressure of 300 bars. Steam cycles, owing to their larger number of required turbine stages and lower power output, did not prove to be a suitable option in this application.

Basically, high-temperature waste heat sources are available in refineries (from the process of fluid catalyst cracking, for example, at 700 to 800 • C), in cement plants (at temperatures from 300 to 500 • C) and in steel and glass manufactory processes.
The dust content of the available flue gases is highly variable, depending on the industrial process. For example, in flue gases from cement plants, the dust content may range from 30,000 to 90,000 mg Nm −3 .
The cement industry is one of the largest contributors to carbon dioxide emissions and is very energy-intensive: the production of one ton of cement requires an energy consumption of about 4-5 GJ, with an average emission value of 0.81 kg CO 2 /kg cement [7,8]. Therefore, it is certainly appropriate, necessary and useful to recover energy from flue gases of the cement industry for the production of electricity, given the high available temperatures.
Heat recovery from dusty flue gases, which sometimes also contain sulphur compounds-and are therefore potentially corrosive-is a challenging problem, but the correct materials and suitable technologies are currently available [9,10].
A second important aspect of the problem is the use of advanced high-efficiency thermal power thermodynamic engines. Usually, Rankine cycles with organic fluids are proposed, with good practical results [11][12][13][14]. The steam cycle is another well-known accepted possibility for energy recovery. In recent years, interest in trans-critical and supercritical thermodynamic cycles using carbon dioxide as a working fluid has grown. In [15], for example, a summary of proposals in the literature of carbon dioxide cycles for heat recovery from waste heat is presented. In [7], the authors report a literature overview of power cycles that were proposed for heat recovery in cement plants. The energy efficiencies of the thermodynamic cycles listed in the paper range between 11% and 30%, according to the temperature of the considered heat source (270 to 400 • C), the thermodynamic cycle and working fluid (organic fluids, steam or carbon dioxide).
With regard to carbon dioxide cycles, in [16], a good review of the main advantages and drawbacks of the use of carbon dioxide as a working fluid is presented. Briefly, one advantage is that a very high power density is produced due to the high pressure levels; furthermore, in the supercritical configuration, reasonably high cycle efficiencies even at moderate maximum temperatures can be achieved, but with the need of a large recuperator. However, a corrosive behavior at temperatures greater than 500 • C is exhibited, requiring the use of nickel alloys. About 10 ten testing facilities are operating today globally, and many studies investigating this process are underway.
On the other hand, as regards Rankine cycles operating with organic fluids, there are now at least 1500-2000 installed engines globally with a wide range of applications (geothermal, biomass, solar and heat recovery) and powers (from a few tens of kW to units of a few tens of MW).
According to the analysis developed in [17], carbon dioxide cycles represent a potentially more effective solution than ORC for heat source temperatures greater than 350 • C; this is particularly true if cold water is available, making condensation possible.
In the following, we consider as a case study the heat recovery from flue gases available at 450 • C (a typical maximum reference value for a cement plant) with a mass flow of 100 kg s −1 .
Usually, in a cement plant, two different hot gas streams are available (see, for example [7,11]): from kiln preheaters and from clinker coolers at different exhaust temperatures and with different exhaust mass flows. Here, for simplicity, we assumed the recovery of heat only from the flue gas flow at higher temperature.
Normally, an intermediate heat transfer fluid (diathermal oil or pressurised water) is interposed between the flue gas and the working fluid used in the thermodynamic cycle. Here, to simplify the scheme and the calculations, we considered a direct heat exchanger. On the other hand, some examples of direct heat exchangers are present in industrial practice.
Assuming a simple recuperative supercritical carbon dioxide cycle (the simplest plant configuration considered in literature) as a reference, we developed a performance comparison of transcritical ORC cycles with cycles adopting binary mixtures of carbon dioxide as a working fluid.
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][19][20][21].

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: where η th is the cycle's thermodynamic efficiency, φ is the heat recovery factor, and the enthalpy H H 0 represents the enthalpy corresponding to the minimum temperature T H 0 at which the flue gas can be cooled (see Table 1). In the following, to simplify the calculations and the general considerations, we assumed a value of T H 0 equal to the dew temperature of the flue gas. Thus, for a fixed T H 1 and a mass flowṁ 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 T 3 and small expansion ratios r C = P 2 /P 1 result in a relatively high η th , but a low φ. On the contrary, low values of T 3 and high values of r C cause a low η th 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 Plus R 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][23][24] As an example, Figure 2 shows two carbon dioxide thermodynamic cycles at different T 3 and different r C values. Cycle (a) has a maximum temperature of 350 • C and a compression ratio r C = 3.5, while cycle (b) has T 3 = 400 • C and r C = 2. The efficiency η th 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).
In the following, we assumed a minimum pressure P 1 equal to 100 bar for carbon dioxide cycles, taking advantage of the cycle efficiency of the real gas effects in the compression phase [25]. Figure 3 presents the thermodynamic cycle efficiency and the total efficiency of simple recuperative carbon dioxide cycles. The temperature T H 1 of the flue gas was assumed to be equal to 450 • C (according to Table 1).  As the optimal maximum cycle temperature T 3 is equal to 350 • C, in the following, we assumed for simplicity the same value for all the considered working fluids and for all the discussed cases.
In Figure 4 cycle (a) of Figure 2 is reported in a plane of temperature-transferred power. In this plane, the relations between the thermodynamic cycle and the heat sources are shown. The maximum pressure of this cycle (350 bar) is not feasible in practical applications, although these conditions correspond to the maximum value of η. In any case, the considerations of this case are also extended to cycles with different compression ratios. The heat source is cooled from T H 1 = 350 • C to T H 2 = 217 • C (φ ≈ 0.6) and the remaining potentially available thermal energy (from T H 2 to T H 0 ≈ 51 • C) is lost. The transferred heat in the recuperator is about 2.5 times greater than the net power, and the air mass flow required at the radiator is almost 10 times that of the carbon dioxide circulating in the engine. The high power required by the ventilators could affect the system efficiency and the radiator-i.e., one of the major cycle components. The assumed constraint of an MITA C equal to 20 • C results in a temperature T 1 of 35 • C (corresponding to a reduced temperature T r of 1.01).
These results seem consistent with those obtained in [15], considering that the authors assumed a maximum cycle pressure of 200 bar and a relatively high recuperator efficiency of 95% (five points higher than the efficiency resulting from the present analysis). More advanced plant configurations (with a single split, a dual split and possibly with an intercooler) were not considered here. They performances and a detailed description of the plant arrangements are described, for example, in [15,17,26]. In the following, we concentrate our attention on the transcritical Rankine cycles using organic fluids.

Recuperative Cycles with Organic Working Fluids
Dealing with heat sources with finite heat capacity, the total efficiency in Equation (1) can be optimized adopting an ideal "triangular" cycle. These conditions can be approximated by resorting to working fluids with a critical temperature close to that of the maximum heat source [27,28]. On the other hand, when the critical temperature of the working fluid is much lower than the maximum temperature of the heat source, the ideal thermodynamic cycle approaches the transcritical conditions.
In addition to an adequate critical temperature, another important parameter to consider in the selection of the working fluid is a relatively low molecular complexity to avoid superheating during the adiabatic expansion. Nonetheless, excessively low molecular complexity is still not recommended as it results in an adiabatic expansion in the two-phase region.
The molecular complexity of a working fluid can be quantified, for example, by the molecular complexity parameter σ = T c R (dS/dT) T r =0.7,dew [29] (p. 109). In general, working fluids with σ ≈ 0 show (for reasonable pressure expansion ratios and for a starting point corresponding to the saturated vapor) an adiabatic expansion ending near the upper limit curve (the dew line).
As the molecular complexity is strictly correlated to the isentropic exponent (γ − 1) /γ, working fluids with a small molecular complexity (a relatively large negative value of σ) experience a substantial cooling during an adiabatic expansion (with a fixed pressure expansion ratio [29]; see Section 2.5).
On the other hand, the molecular weight of the fluid directly affects the enthalpy variations: the higher the molecular weight, the lower the number of the turbine stages, and for a fixed input thermal power, the higher the mass low rate. Both if these results have positive effects on the component design.
According to the previous considerations, the fluids listed in Table 2 were chosen. Carbon dioxide is shown in the table as a reference. Water is extensively and successfully used in the traditional Rankine cycles in plants with a high power size (of hundreds of MW).
Refrigerant R-134a (1,1,1,2-tetrafluoroethane, CH 2 FCF 3 ) is a well known refrigerant and together with propane represents a working fluid with a medium molecular complexity (σ ≈ −2). Hydrogen sulphide has a critical temperature similar to that of R-134a and of propane, but it has a smaller molecular complexity (σ ≈ −7); on the contrary, perfluorobutane represents a fluid with a relatively high molecular complexity (σ ≈ 13). Ammonia and chloromethane have a similar critical temperature and similar molecular complexity.
Methanol and dichloromethane represent two fluids with the same critical temperature but with an appreciably different molecular complexity.
Obviously, not all of the fluids listed in Table 2 can actually be proposed as working fluids. For example, hydrogen sulphide is extremely toxic and flammable (see Table 3), while perfluorobutane has a high GWP.
All of the fluids in Table 2 were primarily selected to elucidate the impact of the main properties of the different fluids on the final thermodynamic performances of heat recovery Rankine cycles. Other fluids can be considered for more detailed and more specific analyses aimed at selecting the optimum working fluid. Table 3. Some environmental and safety properties of the considered fluids.

Fluid
Toxicity (a) Flammability (a) Instability/Reactivity (a) GWP (d) ODP Another primary and decisive property that must be taken into account in the selection of the correct working fluid is its thermochemical stability at the devised maximum working temperatures.
Assessing the long-term thermochemical stability of a compound is generally very difficult to achieve, given the several variables involved and the different possible operating conditions: the metallic surfaces and their surface/volume ratio, the presence of contaminants, the final acceptable level of decomposition and the corrosion problems.
As an example, dichloro-methane (methylene chloride) in a quartz vessel starts to decompose at 450 • C and according to a sigmoid curve, after a reaction period of about 350 min, the decomposition reaches a maximum value of about 34% [30]. In a stainless steel (AISI 430F) cylinder, an appreciable decomposition starts at 350 • C [31]. Thus, in general, the presence of different materials and contaminants (air, water, oil) has a strong catalytic effect on the decomposition of the working fluid.
However, as the thermochemical stability is strictly correlated to the chemical stability (at least in an inert environment), we take carbon dioxide (a compound with a well established high chemical stability) as a reference; in Figure 5, values of the ratio ∆H B = ∆ f H 0 /n B are reported as a function of the number of chemical bonds in the molecule n B . As the standard enthalpy of formation, ∆ f H 0 is proportional to the energy required/released during the formation of the molecule, while the parameter ∆H B may be a rough indicator of the relative thermal stability of any working fluid.
Certainly, the thermochemical decomposition of a fluid occurs through many complex reactions and-as in all chemical reactions-the activation energy plays an important role. Thus, compounds that are apparently chemically unstable (with a positive ∆ f H 0 ) can nevertheless show an acceptable chemical and thermochemical stability. Even so, the parameter ∆H B can give an approximate useful indication for the first classification of working fluids. In Figure 5, all flammable compounds have a value of ∆H B close to zero. Titanium tetrachloride TiCl 4 and sulfur hexafluoride SF 6 are also reported in Figure 5. Titanium tetrachloride is a compound that is considered as a possible working fluid in Rankine cycles at high temperatures, as it is industrially produced according a well known process at 700 to 1000 • C [34][35][36]. Sulfur hexafluoride is considered to be thermally very stable at least up to 400 to 600 • C [37] (p. 30).
In the following, for all the Rankine cycles, we assumed a maximum temperature T 3 of 350 • C, which represents a good compromise between the thermal stability limit for organic compounds and a reasonably good heat recovery factor. Figure 6 reports the thermodynamic performances of the Rankine cycles operating with all the working fluids considered here.
The considered steam cycle is a standard superheated cycle (at temperature T 3 ), without feedwater heaters but with a deaerating heater at 5 bar. In the case of steam, a maximum total efficiency η of about 0.15 is reached at the evaporation pressure of 20 bar, with a turbine expansion ratio r T = r T = P 3 /P 1 of 146.
Refrigerant R134a and propane have approximately the same global performance, and perfluoro-butane performs worse. The best performances in terms of total efficiency are obtained by dichloro-methane and methanol. In Figure 7, two cycles with dichloro-methane and methanol are reported in the T-S thermodynamic plane, respectively. Thanks to the small molecular complexity, both fluids do not require a recuperator, and the heat recovery factor is therefore very high. The two cycles show basically the same thermodynamic performance, but the smaller σ parameter for methanol yields a final expansion in the two-phase region (with a vapor quality of about 0.9).

Figure 7.
Thermodynamic cycles with dichloro-methane and with methanol in the T-S thermodynamic plane.
In Figure 8, cycles operating with dichloro-methane and perfluoro-butane in optimized conditions are presented in the temperature-dimensionless transferred power plane. The high molecular complexity of perfluoro-butane (σ ≈ 13) produces a reduced cooling of the vapor during the expansion, requiring the use of a large recuperator (Q R /Ẇ T = 4.7). As a consequence, T H 2 is relatively high (285.34 • C) and φ is rather low (0.428). This result again supports the general thermodynamic convenience of resorting to working fluids with a low molecular complexity to recover energy from waste heat resources, unless the residual heat can be used for different purposes; for example, to preheat combustion air. In this application, considering its global performance, environmental properties in Table 3 and predictably good thermal stability (see Figure 5), the refrigerant R134a seems to represent the best compromise among all of the potential different working fluids considered here. Therefore, in the following section, the thermodynamic performances of mixtures of R134a and carbon dioxide will be investigated.

Transcritical Cycles with Mixtures of Carbon Dioxide
It is possible to vary the critical point of the resulting mixture of two fluids in different proportions and consequently alter its thermodynamic and thermophysical properties. Therefore, it is possible-at least in principle-to find the correct working fluid for any application [25]. For example, it is possible to produce condensation in hot environments or to control the pressure expansion ratio or the minimum and maximum pressures [38][39][40][41]. In particular, mixtures of carbon dioxide as working fluids in closed power cycles have already been considered by some authors in the past [42][43][44][45]. Figure 9a shows the pressure-temperature (P-T) envelopes for different mixtures of carbon dioxide (component 1) and propane (component 2) evaluated by Aspen Plus R V9. The critical locus is calculated by a code based on the approach described in [46], where the Peng-Robinson equation of state in its simpler and original formulation has been implemented [47] (pp. 208, 423). The experimental points available in the data bank of Aspen Plus R V9 are reported for comparison. The developed code is capable of computing both stable and metastable critical points at given composition of any binary mixture without any initial estimation.
In Figure 9b, we present the P-T envelopes and critical loci for mixtures of carbon dioxide and the refrigerant R134a. With the composition of the mixture, the critical temperature and the critical pressures change continuously from that of pure carbon dioxide (z 1 = 1.0) to that of pure R134a (z 1 = 0.0). At z 1 = 0.7, the critical temperature is about 60 • C and the critical pressure is 70 bar, thus allowing condensation with a bubble temperature of 35 • C. Figure 10a,b shows values of the thermodynamic cycle efficiency η th and of the total efficiency η = η th φ as a function of the maximum cycle pressure, respectively, for mixtures of carbon dioxide and R134a. The mixture corresponding to z 1 = 0.7, at P 3 = 200 bar yields an η equal to 0.143-a value only slightly lower than the optimum value for the pure R134a (0.15), but with a halved expansion ratio, as shown in Figure 11. On the other hand, a carbon dioxide cycle with a maximum pressure of 200 bar has a total efficiency of only 0.107.  Table 4 summarizes the supercritical cycles with pure carbon dioxide, pure R134a and a mixture of carbon dioxide/R134a. The results for steam are also included for comparison.
The cycle with pure carbon dioxide at P 3 = 250 bar has a total efficiency η of 0.1215; using pure R134a, we obtain a higher value of η of about 23% (0.15) but with a volume flow ratio of about 11.5 (5.8 times greater than that of the carbon dioxide cycle). The size parameter SP for R134a is greater and this, for the turbine design, represents a slight advantage. The isentropic turbine enthalpy drop, in both cases, is not very high (probably one axial turbine stage could be adequate) and the corresponding isentropic powers fo the turbines are about 10 MW in both cases.
The steam has a good performance (η = 0.15), but compared to R134a and pure carbon dioxide, it results in a rather complex turbine: the expansion has to be divided into two groups (high-pressure (HP) and low-pressure (LP)), with a total volume flow ratio (VFR) of about 68 and a rather low total power of about 7 MW. For this power size, the assumed efficiencies of the steam turbomachinery (0.85 for the turbine and 0.8 for the pump, see Table 1) are probably too optimistic. Furthermore, the high isentropic enthalpy drops require more stages (roughly 6-10 axial stages). These drawbacks negatively impact the steam cycle in the considered case.
The selected mixture represents a good compromise between the simple cycle with carbon dioxide and the cycle with pure R134a, with good thermodynamic efficiency, a rather small turbine enthalpy drop and a reasonable volume flow ratio.
Moreover, the relatively low fraction of refrigerant in the mixture (30%) has the advantages of increasing the total efficiency with respect to the pure carbon dioxide cycle, with lower operating 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 k i,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 k 1,2 .
The correct value of k 1,2 is usually calculated by a regression of the experimental VLE. Then, the coefficient a mix b mix 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): where a i and b i are the parameters for the pure components and In Figure 12, for 19 different mixtures of carbon dioxide, the values of the parameter a 1,2 = √ a 2 (1 − k 1,2 ) are reported as a function of a 2 . The coefficient a 2 is the specific coefficient relative to the second compound of the mixture according the van der Waals equation of state (with a 1 , the constant coefficient for carbon dioxide) [50]: where, N A is the Avogadro number, R = 8.3143 J mol −1 K −1 is the gas constant and T c and P c 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 k 1,2 (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. Table 4. Some results for carbon dioxide in Rankine and transcritical mixture cycles. The maximum temperature T 3 was assumed to be equal to 350 • C for all the listed cycles.

Conclusions
This study focused on the analysis of carbon dioxide mixture working fluids as an alternative to organic fluids, steam and pure carbon dioxide for high-temperature heat recovery in power plants.
In order to explore this concept, a comparative analysis was carried out with transcritical Rankine cycles with organic working fluids, a standard superheated steam cycle, supercritical carbon dioxide cycle and transcritical cycles operating with carbon dioxide mixtures. Flue gases at a temperature of 450 • C and a mass flow of 100 kg s −1 were employed as the heat source for all thermodynamic cycles.
For Rankine cycles, a high critical temperature, low value of molecular complexity and high molecular weight were the three important prerequisites considered in this study for the choice of the working fluids. Therefore, eight working fluids including both lower and higher values of molecular complexity were considered to evaluate the effect of variations in fluid properties on cycle expansion ratios, heat transfer in recuperators, cycle thermal efficiency and total efficiency. Salient points resulting from this study are summarized as follows: • In simple recuperative carbon dioxide cycles, the total efficiency is improved by a comparatively high expansion ratio and low maximum temperature. The opposite occurs in the case of cycle thermodynamic efficiency. However, as a general rule, simple carbon dioxide cycles are ineffective at recovering heat, unless a high fraction of the residual heat in the source could be used in other ways (to preheat combustion air, for example).

•
The results of Rankine cycles with pure organic working fluids show that the heat recovery efficiencies are remarkably better than those of the simple supercritical carbon dioxide power cycles. In relation to the considered specific application, working fluids with a low molecular complexity are to be preferred.

•
Based on its acceptable global thermodynamic performance and presumably good thermal stability, R134a is investigated as an example of a dopant for the design of carbon dioxide mixtures. Thus, the critical points and P-T envelopes of CO 2 -R134a mixtures were calculated at different molar compositions, which helped us to determine the composition of the mixture at the designed condensation temperature and pressure.

•
A transcritical power cycle operating with CO 2 -R134a mixtures showed an appreciable increase in cycle efficiencies as compared to simple supercritical carbon dioxide cycles at all maximum cycle pressures. In the case of the CO 2 -R134a mixture corresponding to the 0.3 mole fraction of R134a, a total efficiency of about 0.15 was obtained at a maximum cycle pressure of 200 bar, compared to the simple supercritical carbon dioxide cycle which presented a total efficiency of 0.12 at the same maximum pressure. • Moreover, in comparison with pure R134a Rankine cycles, the transcritical cycle with a CO 2 -R134a mixture (0.3 mole fraction of R134a) yielded the same total efficiency but with almost half the expansion ratio.
In summary, the transcritical cycle with the CO 2 -R134a mixture (0.3 mole fraction of R134a) showed a good compromise between the simple R134a Rankine cycle and simple supercritical carbon dioxide cycles due to its good thermodynamic efficiencies, lower maximum operating pressures, lower expansion enthalpy drop and reasonable turbine volume flow ratios.
The standard enthalpy of formation per bond is proposed as a rough indicator of the thermal stability of the considered working fluids with reference to pure carbon dioxide; furthermore, a correlation to estimate the binary interaction parameters for carbon dioxide binary mixtures for which experimental VLE data are not available is suggested. This allows the calculation of thermodynamic properties, critical points and P-T envelopes of some new carbon dioxide mixtures and preliminary calculations of the thermodynamic performance of cycles. In this way, is it possible to analyze a broad spectrum of carbon dioxide mixtures to select the most promising components and-only after this preliminary analysis-to carry out the necessary experimental liquid-vapor measurements.
As in all transcritical and supercritical power cycles, the efficiency of the recuperator plays an important role, as the recovered heat is generally very high. For example, the ratioQ R /Ẇ is about 4.5 for simple supercritical carbon dioxide cycles at a maximum pressure of 250 bar and about 2.9 for the mixture CO 2 (0.7)-R134a (0.3).
The use of mixture of carbon dioxide in transcritical power cycles seems a promising solution to obtain (i) reasonable global efficiencies at a reasonable maximum pressure and (ii) with a conceptually simple plant configuration. On the other hand, points to investigate for a better design of the engine are (i) the vapour-liquid equilibria at different temperatures and pressures and, given the important role of the heat exchangers and of the turbomachines, (ii) the main transport properties (viscosity and thermal conductivity) of the most promising mixtures-properties that, for mixtures, are not simple to estimate properly for all of the relevant thermodynamic conditions.

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following abbreviations, symbols and subscripts are used in this manuscript:

C P
Heat capacity at constant pressure (kJ kg −1 K −1 ) C V Heat capacity at constant specific volume (kJ kg −1 K −1 ) m H Mass flow rate of the flu gas (kg s −1 ) MITA R Minimum Internal Temperature Approach in the recuperator ( • C) MITA PHE Minimum Internal Temperature Approach in the primary heat exchanger ( • C) MITA C Minimum Internal Temperature Approach in the radiator/condenser ( • C) P C Condensation pressure (bar) P c Critical pressure (bar) Q R Recovered thermal power in the recuperator (kW) R Gas constant (kJ kg −1 K −1 ) r C Compression ratio (P 2 /P 1 ) r T Expansion ratio (P 3 /P 4 ) S Entropy (kJ kg −1 K −1 )

SP
Size parameter for a stage of axial turbine V 0.5 out,S /∆H 0.25 S T Temperature ( • C or K) T H 1 Maximum temperature of the heat source (thermal oil) ( • C or K) T c Critical temperature ( • C or K) T r Reduced temperature (= T/T c ) T C 1 Cooling air inlet temperature ( • C or K) T C 2 Cooling air outlet temperature ( • C or K) V Volumetric flow rate (m 3 s −1 ) VFR Isentropic flow ratio =V out,S /V in = ρ in /ρ out Ẇ Mechanical or electrical power (kW) W S Isentropic power (kW) z Molar fraction γ Specific heat ratio (C P /C V ) ∆H S Isentropic turbine work (kJ kg −1 )