2. Brief History

3. Fundamental Properties of sCO₂ Cycles

Figure 12.

P-H diagram of CO

₂

with the temperature, density and entropy isopleths suitable for the representation of sCO

₂

power cycles.

3.1. The Conceptual Strengths

3.1.1. Efficient Compression and Expansion Result in High Cycle Efficiency

 

-

Density is high (ρ ≈ 400–600 kg/m³) in the zone close to the critical point (“CP”): the “near-supercritical” region

-

It decreases (down to 100 kg/m³) in the higher enthalpy (“far-supercritical”) region.

-

It still decreases in the “real gas” region (ρ ≈ 50 kg/m³) and even more in the nearly-perfect CO₂ (pink area) region: there, ρ drops to around 10 kg/m³ below 10 bar and its value at 0 °C-1 atm falls to 2 kg/m³.

Let' us look now at a basic (non-recuperated) supercritical cycle (Figure 23) for which thwe researchers take the following input data: (T–, P–) = (45 °C, 75 bar) and (T+, P+) = (550 °C, 225 bar). From Equation (1), the researchers we deduce the following:

Figure 23. Basic sCO₂ Brayton cycle (non-recuperated: (T–, P–) = (45 °C, 75 bar) − (T+, P+) = (550 °C, 225 bar): W_compr/W_exp = 3/17 = 0.18; reversible conditions.

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The reversible mechanical work (W_compr) consumed for the compression performed in the near-supercritical region is very low; indeed, in stage 1 → 2, ρ = 600 kg/m³  (Figure 1) and W_compr ≈ 3 kJ/mol.

-

Reversely, the expansion work (W_exp) which is performed in the far-supercritical region is high; in stage 3 → 4, W_exp is approximately equal to 17 kJ/mol.

Figure 23 shows that the energy consumed by the reversible compression represents approximately 18% of that delivered by the expansion. In comparison, this percentage is about 42% (11/26) in a typical F-class gas turbine, as shown by Figure 34. Moreover, this ratio is still lower in a supercritical steam cycle: around 4%.

Figure 34. Typical air Brayton cycle: (T–, P–) = (20 °C, 1 atm) − (T+, P+) = (1350 °C, 20 bar); reversible conditions: W_compr/W_exp = 11/26 = 0.42.

Indeed,  we must note that the density is the highest (and W_compr the lowest) in the liquid region, where ρ_CO2 typically exceeds 800 kg/m³. This allows for very efficient pumping stages, which represents an inherent efficiency merit of Rankine cycles: for example, the pumping stage A → B (ρ ≈ 900 kg/m³) consumes hardly 0.5 kJ/mol (Figure 23). Such favorable compression and expansion stages result in excellent cycle efficiencies.

3.1.2. Compactness of sCO₂ Power Units

The second key advantage of sCO₂ cycles is the dramatic reduction in size of cycle components, which is again correlated to the high density of supercritical CO₂ ^[27][28][29,30]. Indeed, to control the level of turbulence of the fluid and minimize the resulting losses in static pressure and efficiency, the cross-section of a turbomachine is designed proportional to the volumetric flow of the fluid, i.e., inversely proportional to its density. Although the sCO₂ machines have higher mass flow rates (for the reasons that will be set out in paragraph 4.2.1), their sizes are significantly smaller due to the fluid density effect. Figure 45 presents a notional comparison between the diameters of a sCO₂ turbine and a steam turbine (“ST”) that deliver power output of the same order ^[29][31]. A quantitative comparison will be proposed below (§ 5.1).

Figure 45.

Qualitative comparison between the size of a steam turbine and an sCO

₂ turbine ^[29].

turbine [31].

It is worth noting that the rotation speed of the shaft also conditions the size: the higher the speed, the smaller the diameter.

3.1.3. Other Strengths Linked to Favorable Properties of the CO₂ Molecule

SCO₂ cycles have other important merits linked to advantageous properties of the CO₂ molecule. Firstly, unlike H₂O that has elevated critical properties (374 °C, 221 bar), the critical point of CO₂ is easily accessible (31.1 °C, 73.8 bars). Additionally, compared to hydrocarbons used in Organic Rankine Cycles (ORC), CO₂ does not ignite or explode; its toxicity (risk of asphyxiation) occurs at a much higher concentration in the air and its GWP and ODP data are much lower: for example, the GWP of propane is 3 while that of CO₂ is 1 by definition ^[30][32]. It boasts also a very high thermal resistance, which allows for a wide operation temperature range in power cycles, from for example 200 °C (including e.g., heat recovery cycles and geothermal applications ^[31][33]) up to 1100 °C (including solar ^[32][34] and nuclear ^[33][35] applications). All these characteristics make CO₂ a versatile cycle fluid: while the usages of steam and air are limited respectively to Rankine and Brayton cycles, CO₂ can be used in both and, moreover, not only within power cycles but also within refrigeration ones. Finally, the closed nature of these cycles results in rather clean circuits, apart from the need to stop wear particles by filtration. This contrasts with the complex and costly water treatment of steam cycles and the need of periodical cleanings of gas turbines due to the progressive fouling of their compressors by dust and salts from ambient air.

3.2. The Conceptual Drawbacks

3.2.1. Low Pressure Ratios Cause Low Specific Power Outputs

Although supercritical cycles operate at high pressures, they have low pressure ratios. Indeed, given that the pressure of a true supercritical cycle (Brayton) must exceed 73.8 bars in all stages, the pressure ratio (“Rc”) turns out to be rather limited. For example, if we reasonably limit the value of P+ to 250 bar and start compression at P– = 75 bar, then the Rc is barely 3.3, leading to low enthalpy drops and limited expansion works in the power turbine. Low Rc values result in low turbine outputs. ThWe researchers ccan define the “specific power output” (SPO) of a power generation unit as its electrical output (W_el) divided by the mass flow rate (Q^m) of the fluid passing through the cycle, i.e., SPO = W_el/Q^m. Table 1 compares, in their orders of magnitude, the SPOs of three usual cycles, namely: steam-Rankine; air Brayton and sCO₂ Brayton. The SPOs of the sCO₂ cycles turn out to be roughly 3 times (respectively 15 times) lower than that of an F-class gas turbine cycle (respectively of a steam cycle). Nevertheless, this does not prevent the reduction in equipment size mentioned above owing to the much greater density of supercritical CO₂.

Table 1.

Compared SPO data of typical steam-Rankine, air-Brayton and sCO

₂

Brayton cycles.

Cycle Type	Two-Pressure Steam Rankine	Air Brayton (F-Class Gas Turbine)	sCO2 Brayton (RCBC)
Fluid	H2O	Air & Comb. Gas	CO2
T–/T+ [°C]	20/540	20/1350	45/550
P+/P– [-]	75/0.05	30/1.013	225/75
Rc (press. ratio)	1500	20	3
SPO = Wel/Qm (1)	~1450	~300	~100

⁽¹⁾ the unit of SPO is kWe/(kgCO₂/s) or kJe/kgCO₂.

3.2.2. Low Specific Power Requires Intense Heat Recuperation

As the turbine generates little power, it discharges still hot CO₂. Heat recuperation at its outlet, before heat rejection, is then desirable to improve efficiency. In other words, sCO₂ cycles require intense thermal recuperation.

3.2.3. The Narrow Operability of sCO₂ Rankine Cycles (Figure 1C)

The critical temperature of CO₂ is rather low (Tc = 31.1 °C). Consequently, heat sinks capable of completely condensing CO₂ must have a maximum temperature of about 25 °C. Unfortunately, such cold heat sinks are not so common and will become less available due to the global climate change, which is a strong handicap for sCO₂ Rankine cycles. Two options can be explored to resolve this issue: Option A—Attempts to increase the critical temperature ^[34][35][36,37]: The first possible approach consists in looking for a substance “X” which, once blended with CO₂, would increase the Tc value by e.g., 15 °C. However, ultimately, these attempts show that it looks impossible in practice to find such molecule that would be acceptable from an EHS and cost standpoint. Option B—Moving from a “wet transcritical” to a “dry transcritical” cycle: The second approach consists in passing from a “wet transcritical” (i.e., Rankine) to a “dry transcritical” cycle since the latter does not impose any conditions on the heat sink temperature. In fact, a “dry transcritical” cycles is illustrated in Figure 56, offers an interesting option to both address the narrow operability of the Rankine cycle and improve the efficiency of a true supercritical cycle.

Figure 56.

“Dry transcritical” cycle: the cooling stage is stopped when reaching the 45°C isotherm.

It has also two additional advantages from an efficiency point of view:

-

The Rc value becomes increased from (P₃/P₄) to (P₃/P_4a): thwe researchers thus escape the pressure ratio limitation suffered by true supercritical Brayton) cycles

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There are other improvements in efficiency, which again result from Equation (1); indeed, referring to the chart of Figure 23, the extended expansion causes the density to pass from about 75 kg/m³ (point 4) to about 50 kg/m³ (point 4a); moreover, ρ increases again during the recompression stages from point 5 to point 8.

This option has been actually exploited in the Allam cycle ^[36][37][3,38] as well as in Echogen’s EPS 100 project ^[28][38][30,39]. However, a main drawback is the need for additional compression and cooling stage(s) to perform the bypass sequence. Additionally, it cannot be combined with the double recuperation/recompression cycle described below (§ 5.2), as it would generate excessive added complexity. In conclusion, although sCO₂ transcritical Rankine cycles can be used in winter in cold and temperate climates, their operability is weak in summer and in hot climates. This is the main reason why they are not actually used for power generation, being more suitable for refrigeration applications. This apparent impossibility to improve the operability of sCO₂ Rankine cycles is very detrimental to the deployment of the sCO₂ technology, because these cycles would have provided interesting performances in the field of heat recovery at low temperatures, where Brayton cycles are less efficient, as it will be shown in detail at § 6.2. This was the objective of the EPS100 project which seems however to have been interrupted. Therefore, the rest of this article will focus on sCO₂ Brayton cycles.

3.2.4. The Gap between Conceptual and Practical Evaluation

The conceptual evaluation outlined above, shows very favorable thermodynamics but it relies on ideal conditions. In reality, the actual isentropic efficiencies of turbomachines have a strong impact on performances. Moreover, the technology of sCO₂ power cycles is sometimes said to be in its “infancy” ^[39][40] and there is still progress to be made to reach optimized performances.