Performance Improvement Overview of the Supercritical Carbon Dioxide Brayton Cycle

Abstract

Efficiency and compactness are core strengths of the supercritical carbon dioxide (sCO${}_2$) Brayton cycle, which is considered an alternative to the steam Rankine cycle for moderate-temperature heat sources (350–800 °C). Numerical investigations on system design and analysis have received considerable attention, with the aim of improving the sCO${}_2$ cycle from the viewpoint of thermodynamics. This paper reviews and compares previous studies in the literature to survey different cycle layouts, operating parameters, and working fluids of the sCO${}_2$ cycle. Performance enhancement approaches are categorized into three classes according to characteristics: conventional methods, CO${}_2$ mixtures, and combined cycles. The strengths, weaknesses, and limitations of each categorized method are discussed. This research is expected to provide a roadmap for performance improvement that meets the interests of researchers.

1. Introduction

The supercritical carbon dioxide (sCO${}_2$) Brayton cycle employs supercritical CO${}_2$ working fluid for electricity generation and is characterized by high cycle efficiency, small turbomachinery, high power density, and a simple cycle layout. This emerging technology is adaptable to the majority of heat sources, such as nuclear, solar, fossil fuels, and waste heat, and has attracted significant attention in the last couple of decades [1]. Figure 1 presents publication numbers on a yearly basis with respect to this hot topic since 2002. A body of raw data was collected by Wang [2]. The number of annual publications has risen exponentially. The number of articles published by Chinese researchers has grown since 2014. In 2019, China published more than 80 studies, which accounted for 36.6% of the total documented in an international journal and conference database. Research on nuclear power plants accounts for 42.9% of all sCO${}_2$ cycle research reported in the literature, followed by research on concentrating solar power (CSP) (30.2%) and waste heat recovery (WHR) from gas turbines (9.6%) and fossil power plants (8.2%). Currently, research on the sCO${}_2$ cycle is in the experimental and demonstration stages. The net power tests a 50 MWth plant to demonstrate the zero-emission Allam cycle, which is a variant of the sCO${}_2$ cycle [3]. The Supercritical Transformational Electric Power (STEP) project is being developed by the Southwest Research Institute (SwRI), Gas Technology Institute (GTI), GE Global Research (GE), and the U.S. Department of Energy (DOE) to operate a 10 MWe indirect-fired sCO${}_2$ cycle [4]. In Europe, components have been designed and tested for the sCO₂-HeRo (supercritical CO${}_2$ heat removal system), which is considered a backup cooling system for the reactor core [5]. In China, the Institute of Engineering Thermophysics (IET) built an MW-scale sCO${}_2$ compressor test platform to demonstrate CO${}_2$ compression under subcritical and supercritical conditions [6]. In addition, a printed circuit heat exchanger facility is under development by the IET, with CO${}_2$ operating at a temperature and pressure of 550 °C and 32 MPa, respectively [7].

Compression near the critical point of CO${}_2$ benefits the thermal efficiency of the sCO${}_2$ cycle, but also constrains the application. Power plants operating in hot and/or arid environments are not uncommon, especially for CSP in deserts, taking advantage of the excellent year-round solar radiation. High ambient air temperatures in the range of 25–37 °C [8] and dry air-cooling technologies make it difficult and costly to achieve the desired condition at the inlet of the compressor. High compressor inlet temperatures (CITs) considerably reduce the thermal efficiency of the sCO${}_2$ cycle [9]. In addition, daily and seasonal variations of heat sources and cooling conditions or the use of inefficient cooling systems can hinder the performance of the sCO${}_2$ cycle. A cycle design with low CITs leads to long periods of part-load operation, whereas a high-temperature design penalizes the cycle efficiency [10,11].

Increasing the thermal efficiency of the sCO${}_2$ cycle and the design of new cycles are among the interests of researchers in the field of thermodynamics. Moisseytsev and Sienicki [12] reported several improved methods for the sCO${}_2$ cycle heated by a sodium-cooled fast reactor (SFR). These methods include broad operating ranges (temperature and pressure) and modifications of cycle configuration (reheating, intercooling, recompression, and condensation). Ahn et al. [13] reported on development progress with respect to the sCO${}_2$ cycle and compared single-flow and split-flow cycle layouts. Crespi et al. [14] reviewed and categorized sCO${}_2$ cycles according to their configurations, covering 42 varieties of stand-alone cycles and 38 combined layouts. However, they failed to present details of performance enhancement or include studies on the CO${}_2$ mixture Brayton cycles. Li et al. [15] summarized the development of the sCO${}_2$ cycle in the nuclear and solar industries and categorized designs into single-flow and split-flow layouts. They covered improvement in sCO${}_2$ cycles (like using a bottoming cycle) but focused on the research status rather than the comparison of performance improvement. Wang et al. [16] reviewed and compared six sCO${}_2$ cycles for solar tower CSP. Xu et al. [17] focused on barriers to current research on the sCO${}_2$ cycle.

The research gap lies in a lack of a comprehensive review and interpretation of performance improvement options for the sCO${}_2$ cycle, as well as a comparison of enhanced thermal efficiencies and analysis of the limitations of each method. CO${}_2$ mixtures were previously employed to adjust the critical point of pure CO${}_2$ for power cycles adapting to higher or lower heat sinks [18]. The features and influence of this approach may be aggressive or moderate with respect to other methods. It is not possible to draw a conclusion as to which method is preferable without comparison. In the present paper, we review previously published papers published on methods that could enhance the sCO${}_2$ cycle. Applications, cycle layouts, methods, claimed thermal efficiencies, and operating conditions are presented. Each approach is interpreted and categorized according to its type and characteristics. the claimed performance changes of the sCO${}_2$ cycle are compared from the viewpoints of thermodynamics and economics. In addition, we discuss the strengths, weaknesses, and limitations of each categorized method. This research is expected to provide an intuitive overview of the performance enhancement of sCO${}_2$ cycles.

2. Conventional Method

A conventional method is referred to as a classical approach to improve a power cycle, such as with intercooling, reheating, recuperation, and high operating parameters, which have been applied to the Rankine cycle and Brayton cycle. In the early stages, these options were considered to be handy and extensive. Figure 2 presents four popular schematic diagrams of the sCO${}_2$ cycle layout that have been improved by using the conventional method. Angelino [19] studied the various layouts of the sCO${}_2$ cycle. However, he mainly focused on the transcritical CO${}_2$ (tCO${}_2$) cycle, i.e., the condensation cycle. Later, intercooling, reheating, recompression, partial cooling, and precompression were investigated [9,20,21,22].

Table 1. Numerical study on varied sCO${}_2$ cycles enhanced by the conventional method.

Cycle Layout	Initial Behavior				Improved Behavior		Application	Ref.
	CIT/°C	TIP/MPa	TIT/°C	$\eta$/%	Method	$\eta$/%
Intercooled Recuperated	31	22	550	39	Recompression, Increase TIT	41.8–47	300 MWe Nuclear power	2002 [27]
Recompression	31	20	550	43.1, 45.8	Increase TIT	47, 49.9	600 MWth Nuclear power	2002 [27]
Recuperated	32	20	550	40	Reheating, Intercooling	40.8–41.5	600 MWth Nuclear power	2004 [9]
Recompression	32	20	550–750	45.56–52	Reheating, Increase TIT, Raise TIP	46.775–57	600 MWth Nuclear power	2004 [9]
Recuperated	35	7, 12	800	45.5, 45.8	Intercooling, Partial cooling	47.4–49.7	Nuclear power	2004 [20]
Partial cooling	35	7, 12	800	49.2, 49.7	Intercooling	51.4, 51.9	Nuclear power	2004 [20]
Recompression	31.25	20	472	39.1	Condensation, Liquid phase pumping, Raise TIP	39.5–43.1	250 MWth Nuclear power	2007 [12]
Recompression	32, 50	20, 30	550, 750	36.71–49.83	Reheating	37.65–50.78	600 MWth Nuclear power	2009 [28]
Recuperated	32	25	550–750	40.44–48.2	Precompression, Recompression, Partial cooling, Increase TIT	43.49–54.1	3600 MWth Nuclear power	2011 [29]
Precompression	32	25	550	43.49	Increase TIT	48.8, 52.4	3600 MWth Nuclear power	2011 [29]
Recompression	32	25	550	46.48	Increase TIT	49.9, 52.7	3600 MWth Nuclear power	2011 [29]
Partial cooling	32	25	550	46.12	Increase TIT	50.5, 54.1	3600 MWth Nuclear power	2011 [29]
Recuperated	32	25	550–700	40.7–45.5	Reheating, Increase TIT, Recompression, Partial cooling	42.5–52.8	CSP	2012 [30]
Recompression	32	25	550–700	47.7–52.8	Reheating, Increase TIT	48.9–53.9	CSP	2012 [30]
Partial cooling	32	25	550–700	46.1–52	Reheating, Increase TIT	48.1–53.8	CSP	2012 [30]
Recompression	32	25	500–600	44.5–46	Reheating, Increase TIT	47–49	10 MWe CSP	2012 [31]
Recompression	55.5	25	500–850	40–52	Reheating, Increase TIT	43.14–52.8	CSP	2015 [32]
Recuperated	55.5	25	600	38.5	Reheating, Recompression	39.5, 42.7	CSP	2015 [33]
Recompression	55.5	25	600	42.7	Reheating, Intercooling	43.2–45.3	CSP	2015 [33]
Recompression	32	25	600–800	45.1–52.4	Reheating, Increase TIT	46.5–53.4	2113 MWth Fossil energy	2016 [34]
Recompression	35, 50	20	500–800	39.59–54.58	Intercooling	40.82–55.68	Nuclear power	2017 [21]
Recuperated with reheating	27	25	827	46.3	Intercooling	48.7–49.4	160 MWe Not specified	2017 [35]
Recuperated	-	25	700	36.2	Recompression, Precompression	43.3	104 MWe CSP	2017 [22]
Recompression with reheating	32	25	500	40.98–49.21	Intercooling	41.44–49.4	50 MWe CSP	2017 [36]
Recompression	51	25	750	47	Intercooling	48.6	25 MWe CSP	2017 [37]

summarizes the methods, boundary conditions, and thermal efficiencies declared in the literature. It should be noted that these studies are theoretical and are based on specific component efficiency assumptions, forming many varieties of the sCO${}_2$ cycle, as reviewed by Crespi et al. [14]. Since a heat exchanger contributes 54% to the capital cost of the recompression of the sCO${}_2$ cycle [23], a reduction in pressure loss and the enhancement of heat transfer play important roles in enhancing the performance of the sCO${}_2$ cycle from the point of view of exergy and energy [24,25,26]. This is also true for an increase in turbomachinery efficiency. The reason why Table 1 does not list the improved methods of the components is that these methods are less important than the cycle layout modifications and operating parameters.

Figure 3 shows the thermal efficiency of enhanced sCO${}_2$ cycles as a function of turbine inlet temperature (TIT). Note that the efficiencies of various configurations were collected from published papers on the basis of very different boundary conditions. In order to establish a convincing comparison, the commonly used efficiencies of the sCO${}_2$ cycle were plotted as the reference [9]. It is noted that the reference data were calculated without consideration of cycle losses. It can be seen that the enhanced recuperated sCO${}_2$ cycle has an efficiency in the order of about 3% lower than the reference efficiency at the same TIT. The efficiencies of the improved recompression and partial cooling cycles are higher than the reference efficiencies, except for several points. This is mainly due to high CITs for these cycles, such as 50 °C [28], 51 °C [37], and 55.5 °C [32,33]. Figure 3 also presents the recompression cycle with thermal efficiencies of up to 50% at a TIT of 500 °C. This was achieved not only by reheating but also by the combination of intercooling, high-efficiency turbomachinery, and large recuperator conductance [36,38].

Figure 4 shows the cycle efficiency improvement at various TITs for each specific conventional method. Note that the improvements in efficiency achieved by the reheating or intercooling is obtained with respect to the sCO${}_2$ cycle without modification. As for the methods for the CO${}_2$ condensation cycle, CO${}_2$ liquid-phase pumping, precompression, recompression, and partial cooling, the improvement in efficiency is the efficiency difference for the recuperated sCO${}_2$ cycle. Efficiency gains from increasing TITs are calculated for every 100 °C rise in the TIT. Moreover, the turbine inlet pressure (TIP) is also a crucial factor in changing the efficiency.

For the sCO${}_2$ cycle, the typical conditions at the turbine inlet are 550 °C and 20 MPa [9,39]. It is known that a higher temperature or pressure implies higher cycle efficiency. Figure 4 shows that an order of about 4% additional efficiency is obtained for each 100 °C rise in the TIT. At higher TITs, the efficiency improvement diminishes to 3% [9]. When increasing the TIT from 550 °C to 650 °C, efficiency was improved by 2.8% and 4% for the recuperated (with intercooling) and recompression sCO${}_2$ cycles, respectively [27]. For a precompression layout with higher turbomachinery performance, increasing the temperature to 650 °C improved the efficiency by 5.3% to a value of 48.8% [29]. As for TIPs beyond 20 MPa, the gain in cycle efficiency is very modest. About a 0.3% increase in cycle efficiency was achieved when the TIP was raised from 20 to 22 MPa (at a TIT of 480 °C) [12]. Dostal [9] showed that increasing the pressure from 20 to 25 MPa yielded 1.4% (at a TIT of 650 °C) and 2.0% (at a TIT of 750 °C) efficiency improvements. In contrast, the increase in efficiency was less than 1% when the TIP rose from 25 MPa to 30 MPa. It should be noted that higher temperature and/or pressure conditions represent challenges in terms of material selection. Raising the pressure means increasing the thickness of the pipes, pressure-bearing casings, and heat exchangers, requiring additional capital costs. Moreover, material corrosion should be considered in high turbine inlet conditions.

The sCO${}_2$ cycle takes advantage of the non-ideal properties of CO${}_2$ near the critical point to reduce the compression work. It was shown that higher cycle efficiency could be obtained if the CO${}_2$ is cooled below the pseudocritical temperature at a given supercritical pressure. When the temperature declines across the critical point, the cycle is called the “CO${}_2$ liquid cycle” or “CO${}_2$ condensation cycle”, depending on the compressor inlet pressure crossing the critical point (the latter) or not (the former). The liquid-phase cycle operating at supercritical pressures increased the thermal efficiency by 1.15% at pump inlet conditions of 30 °C and 7.4 MPa [12]. The CO${}_2$ condensation cycle (under pump inlet conditions of 20 °C and 5.75 MPa) achieved an efficiency of 43.1% for a 483 °C SFR, having an efficiency improvement of 3.85% [12]. These two cycles should be carefully treated due to the requirement of a year-round supply of the cold-cooling medium. Moreover, in order to cool CO${}_2$ below the critical temperature, the CO${}_2$ has to pass through the peak specific heat, resulting in a significant increase in the heat transfer area of the cooler.

Reheating improves thermal efficiency by increasing the equivalent Carnot temperature, i.e., the average temperature at which the heat is added to the power cycle. As shown in Figure 4, reheating adds 1–2% to the thermal efficiency. The gains provided by a second reheating configuration, when compared to single reheating, stay below 0.5% and lower at high TITs [9,30,34]. Figure 4 also shows that single-stage reheating could obtain a 2.5% and 3.0% increase in efficiency at TITs of 500 °C and 550 °C, respectively, resulting from a high TIP of 25 MPa and a better component performance [31]. Several factors should be paid attention to regarding the reheating method: (1) The effect of reheating strongly depends on the pressure drop through the reheater. With an increase in pressure drop, the benefit from the reheat decreases until it is negative [9,33]. (2) In contrast to an ideal gas cycle, the pressure ratio split between sCO${}_2$ turbines should be optimized to give equivalent temperatures of heat addition. It was observed that the optimum pressure–ratio split was slightly lower than an equal split [9]. (3) It was shown that using more than one stage of reheating is economically unattractive [9].

Intercooling reduces the average temperature of heat rejection from the sCO${}_2$ cycle. However, the CO${}_2$ compression work is already low, such that the benefit from intercooling is expected to be limited. As shown in Figure 4, intercooling offers a very modest efficiency improvement, which was 0.8% at a TIT of 550 °C (recuperated sCO${}_2$ layout) [9]. With a significant increase in the TIT, the efficiency is slightly increased. It can be seen that efficiency gains can be up to 3% at TITs of higher than 800 °C [20,35]. This is due to the existence of large compression work in the original sCO${}_2$ cycle. It should be noted that the properties of CO${}_2$ are considerably affected by the critical point, and thus, the pressure–ratio split is not equal in order to achieve the same TIP. It was shown that the second compressor provided a 1.5 to 1.9 times higher pressure ratio than the equally split pressure ratio, giving the best cycle performance [9,21]. An equal pressure ratio for the two compressors results in a slightly low thermal efficiency [12]. The disadvantage of intercooling is the additional cost.

The cause of the irreversibility of the recuperator is the pinch-point problem, which largely reduces the performance of the sCO${}_2$ cycle. In order to overcome this problem, compound cycles were introduced [19]. The precompression cycle is another way to increase regeneration [9,40]. As reported in [29], this cycle layout achieved an efficiency improvement of 4% over the recuperated sCO${}_2$ cycle. The partial cooling cycle operates at pressures of about 12 MPa and temperatures of around 700–800 °C. Its efficiency is improved by reducing the average temperature of heat rejection. As can be seen in Figure 4, the efficiency improvement from the partial cooling cycle is larger than that from the precompression cycle. The recompression cycle improves efficiency by reducing the heat rejection from the cycle using an additional compressor before the cooler. The efficiencies of complex cycles (recompression and partial cooling) are consistently about 6% higher than those of the recuperated cycle [30]. At high CITs, the efficiency increase is reduced to a grade of around 4% [20,33].

3. Combined Cycle

Although the sCO${}_2$ cycle has promising thermal efficiency, about 50% of heat addition is still rejected to the heat sink at temperatures of 100 °C to 200 °C. For the purpose of minimizing thermodynamic irreversibility as a consequence of the second law, WHR technologies were employed in the sCO${}_2$ cycle either for power generation or cold supply [2,14]. The WHR technology, or a bottoming cycle, is introduced between the low-temperature recuperator (LTR) and the cooler with an additional heat exchanger, as shown in Figure 5. This approach is recognized as the combined cycle method, by which the recuperator in the topping cycle does not need to have high effectiveness.

Table 2. Numerical study on sCO${}_2$ combined cycles.

Cycle Layout	Initial Behavior					Improved Behavior			Application	Ref.
	CIT/°C	TIP/MPa	TIT/°C	$\eta$/%	Cost	Bottoming Cycle	$\eta$/%	Cost
Recompression	32	22.3	550–750	40.23–47.82	-	tCO${}_2$ cycle	44.25–52.98	-	90–165 kWe nuclear power	2010 [41]
Recuperated	35	22.5	527–727	28.5–33.8	-	ORC (R245fa, isobutane, isopentane, cyclohexane)	36.4–43.96	-	88–115 kWe CSP	2011 [42]
Recuperated	30	-	527–827	28.1–38.7	-	ORC (isopentane, isobutane, n-Butane)	35.3–47.5	-	500 kWe CSP	2013 [43]
Recuperated	55	25	700–850	41.9–46.5	-	ORC (isopentane, n-butene, cis-butene)	48–53	-	CSP	2014 [44]
Recompression	55	25	700-850	46.3–50.6	-	ORC (R236ea, R245fa, isobutane)	50.5–55.75	-	CSP	2014 [44]
Partial cooling	55	25	700–850	46.2–51	-	ORC (R124, R245fa, isobutane)	48.7–53.95	-	CSP	2014 [44]
Recuperated	35	22.5	650	33.8, 36.5	-	tCO${}_2$ cycle	39.5, 41.3	-	326 kWth Fuel cell	2014 [45]
Recuperated	35	22.5	650	39.6	-	tCO${}_2$ cycle	46.1	-	326 kWth Fuel cell	2014 [46]
Recompression	35	20	527	45.32	-	ORC (R123)	52.12	-	570 kWth Nuclear power	2014 [47]
Recompression	35	22.2	550	39.59, 38.3	11.2 $/GJ, 10.87 $/GJ	ORC (Isopentane, n-butane, isobutane, n-pentane, R123, R114, R141b, RC318)	43.68–44.22	10.73 $/GJ, 10.25 $/GJ	600 MWth Nuclear power	2014 [48]
Recompression	32	20	550	44.29	6.2 $/kW	tCO${}_2$ cycle	45.92	6.6 $/kW	84 kWe Nuclear power	2015 [23]
Recuperated	32	20	550	37.46	-	tCO${}_2$ cycle	44.7	-	96 kWe Nuclear power	2015 [49]
Recompression	32	20	550	44.22	-	tCO${}_2$ cycle	47.69	-	81 kWe Nuclear power	2015 [49]
Recompression	32	26.7, 21	550	-	-	tCO${}_2$ cycle	44.99, 43.89	9.98 $/GJ, 9.75 $/GJ	600 MWth Nuclear power	2016 [50]
Recompression	32	28.12–29.53, 20.87–21.16	550	-	-	ORC (R123, R245fa, toluene, isobutane, isopentane, cyclohexane)	44.77–45.23, 43.78–44.08	9.88–9.96 $/GJ, 9.60–9.62 $/GJ	600 MWth nuclear power	2016 [50]
Recompression	35	21.5	550	39.57	11.2 $/GJ, 10.87 $/GJ	Kalina cycle	43.55	10.73 $/GJ, 10.34 $/GJ	600 MWth Nuclear power	2016 [51]
Recompression	35	22	550	39.62	13.73 $/GJ, 13.64 $/GJ	Kalina cycle	42.8	13.04 $/GJ, 12.88 $/GJ	600 MWth Nuclear power	2016 [52]
Recuperated	37	-	655	-	-	ORC (R245fa)	-	0.039 cents/kWh, 0.045 cents/kWh	Fuel cell	2016 [53]
Recompression	33	-	550	-	-	tCO${}_2$ refrigeration	49.9–50.52	10.68–11.05 $/GJ	600 MWth Nuclear power	2017 [54]
Basic	32.5	20	385	51.41	-	tCO${}_2$ cycle	52.53	-	9.25 MWe Exhaust gas	2017 [55]
Recompression	31	21.2	501.8	37.68	-	tCO${}_2$ cycle	50.06	0.046 $/kWh	41.45 MWe Exhaust gas	2017 [56]
Recompression	32	20	550	41.47	-	tCO${}_2$ cycle	43.75	11,243.15 $/h	600 MWth Nuclear power	2017 [57]
Recompression	32	-	600–850	44.5–51.9	-	tCO${}_2$ cycle	47.6–57.1	-	2.7–4.2 MWe Not specified	2018 [58]
Recompression	32	-	750	-	-	ORC (10 zeotropic mixtures)	-	10.93 $/GJ	600 MWth nuclear power	2018 [59]
Recuperated	31	31.06	450.6	-	-	ORC (cyclopentane/R365mfc)	-	3.95–4.34 cents/kWh	Exhaust gas	2018 [60]
Recuperated	40	20	550	-	-	tCO${}_2$ refrigeration	42.3–44.5	-	2.4–3.0 MWe Exhaust gas	2018 [61]
Recuperated	-	25	380	-	-	ORC (R407c, R134a, R245fa, R1234yf, R1234ze)	40.5–41.92	-	3.4–3.7 MWe CSP	2018 [62]
Recuperated, recompression	36	16.4	300	-	-	ORC (R123, R245fa, R600)	17.7–19.1	-	200 kWe Not specified	2018 [63]
Basic	52–55	20	385	-	-	tCO${}_2$ cycle	49.39–51.44	0.042–0.0486 $/kWh	8.886–9.255 MW Exhaust gas	2018 [64]

presents the different configurations of the sCO${}_2$ combined cycle in the literature. The bottoming cycles considered are the organic Rankine cycle (ORC), tCO${}_2$ cycle, and the Kalina cycle. Statistics show that about 56% of combined sCO${}_2$ cycles use the ORC bottoming cycle, and 38% employ the tCO${}_2$ cycle. Only two papers are devoted to the complicated Kalina cycle. It should be noted that the combined cycle method requires a year-round supply of very cold cooling water. The WHR technologies operate at narrow temperature ranges between the heat source and heat sink. The working fluid needs a condensation process to maintain higher performance.

Figure 6 plots the declared thermal efficiencies of the combined sCO${}_2$ system in the literature. Wide dispersion is observed in the chart, showing global efficiencies in the range of 35% to 60%. This is due to the layout and boundary conditions of each combined cycle, as shown in Table 2. The efficiencies, as well as the reference efficiencies, of the stand-alone sCO${}_2$ cycle [9] are further plotted against TIT in Figure 6, showing the clear influence of this parameter on the performance of the combined cycle. The thermal efficiencies of the combined recuperated cycles are nearly 5% lower than reference efficiencies. Figure 7 shows the efficiency improvement after adding a bottoming cycle to the sCO${}_2$ cycle at various TITs. In order to show more details, three common layouts of the topping sCO${}_2$ cycle are distinguished using symbols and colors. The efficiency improvement is defined as the thermal efficiency of the combined sCO${}_2$ cycle over the thermal efficiency of the initial sCO${}_2$ cycle.

$$\begin{array}{c}{\eta }_{initial}=\frac{W_{net,sC{O}_2}}{Q_{in}}\end{array}$$

(1)

$$\begin{array}{c}{\eta }_{combined}=\frac{W_{net,topping}+W_{net,bottom}}{Q_{in}}\end{array}$$

(2)

$$\begin{array}{c}{\eta }_{improvement}={\eta }_{combined}-{\eta }_{initial}\end{array}$$

(3)

ORC employs a refrigeration fluid as the working fluid to convert low-temperature heat into electricity, and this is applicable to the heat sources of geothermal energy [65], solar energy [66], and industrial waste heat [67,68,69]. There is an established industry with over 2000 MW installed. ORC technology was first added to a recuperated sCO${}_2$ cycle (operating at the turbine inlet conditions of 727 °C and 30 MPa) in 2008, showing that the efficiency was improved by 6.1% when using cyclohexane as the working fluid [70]. Some interesting information from the literature review can be found as follows:

• ORC is mainly combined with the recuperated sCO${}_2$ cycle, followed by the recompression and partial cooling cycles. The recuperated sCO${}_2$-ORC combined cycle is slightly less complex than the other two combined cycles. Moreover, the recuperated sCO${}_2$ cycle has a relatively larger amount of waste heat at high temperatures, which is the ideal source for WHR technologies.
• The performance of the recuperated sCO${}_2$ cycle is significantly improved by the additional ORC cycle. As shown in Figure 7, the gain in efficiency ranges from 6 to 13%, which is achieved by the combined cycle compared to the stand-alone recuperated sCO${}_2$ cycle [42]. The CIT and organic fluid are the main contributors to the diversity of performance enhancement [44]. For the recompression sCO${}_2$ cycle, the efficiency was improved by 4–4.6% at a TIT of 550 °C [48] and 4.2–5% at a TIT of higher than 700 °C [44]. Zhang et al. [47] studied a recompression sCO${}_2$-ORC combined cycle, having a thermal efficiency of 52.12% when using a liquefied natural gas (LNG) as the heat sink. About 6.8% of additional efficiency was achieved with respect to the stand-alone cycle due to the small power scale, i.e., 297 kWe, of which the bottoming cycle output accounted for 13%. As for the partial cooling sCO${}_2$ cycle, the gain in efficiency ranged from 2–3% [44] depending on organic fluids.
• The recompression sCO${}_2$-ORC cycle achieves the highest overall efficiency. It can be seen from Figure 6 that most combined recompression cycles have efficiencies that are higher than the reference data at the same TITs, although the cycle boundary conditions are not identical.
• The distinct differences in the organic fluids show limited effects on the performance of the combined cycle. This is true, especially for large-scale sCO${}_2$-ORC-combined cycles [50]. In the literature, both pure substances and zeotropic mixtures [43,59,60] were investigated. The nature of organic fluids decides the efficiency improvement that rises with TIT, like R245fa [42] and Isopentane [44], or falls, like the isobutane and the n-butane/isopentane mixture [43], as shown in Figure 7.

One drawback of the ORC cycle is the pinch problem or constant temperature evaporation in the evaporator. Alternatively, the tCO${}_2$ cycle and Kalina cycle are potentially useful technologies when applied to low-temperature heat sources. CO${}_2$ is an ideal choice as the working fluid for transcritical operations due to its high performance, compactness, and non-flammability. Additionally, it is cost-effective, exhibits low toxicity, and has a negligible environmental impact. The transcritical process makes the tCO${}_2$ cycle absorb heat at the gliding temperature instead of at the constant temperature evaporation in subcritical conditions. There are two objectives for the tCO${}_2$ cycle, which are additional to the sCO${}_2$ cycle.

• For power generation, Yari and Sirousazar [41] first added a tCO${}_2$ cycle to the recompression sCO${}_2$ cycle, showing an efficiency improvement of around 5.1%. They also showed that the performance of the combined cycle was independent of TIT but was strongly affected by the ambient temperature. When increasing the ambient temperature from 15 °C to 25 °C, the gain in efficiency went down from 5.1% to 2.7%. Alsagri and Chiasson [58] reported that the recompression cycle using a split-flow tCO${}_2$ bottoming cycle obtained 2% more efficiency than that with a non-recuperated tCO${}_2$ cycle. As can be seen in Figure 7, the recuperated sCO${}_2$ cycle, for which the heat source is a molten carbonate fuel cell, was improved by 4.8–6.5% in terms of efficiency, depending on the recuperator effectiveness at a CIT of 55 °C [45,46]. When the CIT was lowered to 32 °C, the gain in efficiency for the tCO${}_2$ cycle was up to 7.2% [2].
• For cold production, Akbari and Mahmoudi [54] proposed a recompression sCO${}_2$ cycle combining a tCO${}_2$ refrigeration cycle for both power and refrigeration production. In the combined cycle, a fraction of CO${}_2$ leaving the cooler expends in the refrigeration cycle; after being heated and compressed, it then goes back to the cooler. They showed that the combined cycle produced 240 MW of power and 60 MW of cold simultaneously, or 562 MW of cold only. Manjunath et al. [61] studied a similar combined cycle utilizing the shipboard gas turbine exhaust. The proposed cycle generated a net power output of 3.0 MW (about 14.5% engine power) and a cooling output of 3.1 MW (about 15% engine power).

Although interesting studies have been published on the exergoeconomic performance of the combined sCO${}_2$ cycle, as shown in Table 2, the techno-economic evaluation is still uncertain due to the lack of experimental facilities and standard equipment. Want et al. [23] conducted the thermoeconomic analysis of a combined recompression sCO${}_2$-tCO${}_2$ cycle, showing that the capital cost per net power output was about 6% more expensive than that of the stand-alone sCO${}_2$ cycle. The heat exchanger accounted for 53% of the total cost. Their cost estimation was based on the equipment used in the chemical process. Later, Wang [2] showed that the recompression sCO${}_2$ cycle with a tCO${}_2$ cycle was 5.3% more expensive than the stand-alone cycle using modified cost functions.

The Kalina cycle uses an ammonia/water solution as the working fluid for power generation. The boiling point of the ammonia/water mixture can be adjusted to suit the heat input temperature by the appropriate choice of the mass ratio. As shown in Figure 7, the Kalina cycle improves the recompression sCO${}_2$ cycle by 3.2–4% in terms of efficiency when compared to the sCO${}_2$ cycle in isolation, according to the ammonia concentration in the solution [51,52]. Note that the Kalina cycle itself is much more complicated and hard to operate, which alone and with any additional cost may offset the benefit.

4. CO${}_2$ Mixture

The modification of the thermal–physical properties of the working fluid by adding a small amount of other gases is not uncommon to improve a power cycle. As for the helium Brayton cycle, the use of a He/Xe or He/N${}_2$ binary mixture was successful in reducing the stages of the turbomachinery due to the increment in the molecular weight of the gas mixture [71,72]. For the ORC, zeotropic mixtures have a non-isothermal phase change during evaporation and condensation, which reduces temperature mismatching and exergy destruction [73,74,75,76,77]. In previous studies, CO${}_2$ mixtures were considerably investigated in refrigeration and heat pump systems [78,79,80], as was the transcritical Rankine cycle (TRC) for low-to-medium temperature applications [81,82,83,84].

As for the sCO${}_2$ cycle, the critical point of CO${}_2$ plays a crucial role in the lowest operating boundary and reduction of compression work. The adjustment of the critical point changes the cycle temperature and pressure ranges, providing the possibility of using high-temperature heat sinks. The direction and range of the critical point variation of CO${}_2$ depend on the mixed component and its amount. In this regard, research on CO${}_2—$based mixtures has been performed for various purposes. In 2011, the Sandia National Laboratories (SNL) [85] investigated the effect of secondary gas additions, i.e., SF${}_6$, neon, n-butane, and methane, on the performance of a 50 kW full-scale CO${}_2$ compressor. The Korea Advanced Institute of Science and Technology (KAIST) [18,86,87,88] studied the SFR using the sCO${}_2$ cycle and first proposed the modification of the CO${}_2$ critical point by mixing gases. Several potential gases were selected to consider their thermal stability, property database, and chemical stability in the temperature range of interest. Their goal was to shift the critical point of the pure CO${}_2$ and, thus, expand the operating range of the cycle. The Czech Technical University (CTU) in Prague focused on the effect of gaseous admixtures on the pinch point [89] and cycle performance [90,91]. Both binary and multicomponent mixtures were considered.

Table 3. Numerical study on the supercritical power cycles based on CO${}_2$ mixture.

Cycle Layout	Initial Behavior				Improved Behavior		Application	Ref.
	CIT/°C	TIP/MPa	TIT/°C	$\eta$/%	Additives	$\eta$/%
Recompression	32	20	508	43.27	He, Ar, N${}_2$, O${}_2$	41–45.2	1529 MWth Nuclear power	2011 [92]
Full-scale compressor test	27–50	-	-	-	SF${}_6$, n-Butane, Neon	-	50 kW Compressor	2011 [85]
Recompression	32	20	550	45.37	He, Ar, N${}_2$, O${}_2$	44.02–47.1	600 MWth Nuclear power	2011 [87]
Recompression	32	20	550	45.37	Xe, Ar, N${}_2$, O${}_2$	44.02–46.65	600 MWth nuclear power	2011 [86]
Recuperated	40	30	400	21.5	Benzene	23.5–26.1	Not specified	2012 [93]
Recuperated	32	20	550	39.77	Xe, Kr, Ar, N${}_2$, O${}_2$	39.75–41.46	600 MWth Nuclear power	2013 [18]
Recompression	32	20	550	45.37	Xe, Kr, Ar, N${}_2$, O${}_2$	44–46.69	600 MWth nuclear power	2013 [18]
Recuperated	44	20	550	37.97	H${}_2$S, Cyclohexane	37.88, 38.01	600 MWth nuclear power	2013 [18]
Recompression	44	20	550	41.36	H${}_2$S, Cyclohexane	42.61, 43.23	600 MWth nuclear power	2013 [18]
Recuperated	32	20	600	37.9	N${}_2$, O${}_2$, Ar, Air, He	37.3–37.6	Not specified	2014 [94]
Recompression	32	20	600	42.6	N${}_2$, O${}_2$, Ar, Air, He	42.4–42.5	Not specified	2014 [94]
Recompression	32	20	650	47.82	O${}_2$, He, Ar, Kr	45.9–50.5	600 MWth nuclear power	2015 [95]
Recompression	52	20	650	41.1	n-Butane, Cyclohexane	42.55–43.4	600 MWth nuclear power	2015 [95]
Recompression	34	24	550	32.45	He, CO, O${}_2$, N${}_2$, Ar, H${}_2$, CH${}_4$, H${}_2$S	31.39–32.49	12.5 MWe Not specified	2016 [89]
Precompression	34	24	550	29.45	He, CO, O${}_2$, N${}_2$, Ar, H${}_2$, CH${}_4$, H${}_2$S	28.12–29.48	16.6 MWe Not specified	2016 [89]
Split expansion	34	24	550	29.03	He, CO, O${}_2$, N${}_2$, Ar, H${}_2$, CH${}_4$, H${}_2$S	28.1–29.06	11.2 MWe Not specified	2016 [89]
Recompression	34	24	550	32.45	Air, M-I, M-II, M-H, Air-H, M-IH	29.74–32.31	12.5 MWe Not specified	2017 [90]
Precompression	34	24	550	29.45	Air, M-I, M-II, M-H, Air-H, M-IH	25.83–29.29	16.6 MWe Not specified	2017 [90]
Split expansion	34	24	550	29.03	Air, M-I, M-II, M-H, Air-H, M-IH	26.62–28.91	11.2 MWe Not specified	2017 [90]
Recompression	34	27	550	33.44	He, H${}_2$, CO, O${}_2$, Ar, N${}_2$, CH${}_4$, H${}_2$S, Xe, Kr, SO${}_2$	32.54–33.6	38 MWth not specified	2018 [91]
Precompression	34	27	550	44.44	He, H${}_2$, CO, O${}_2$, Ar, N${}_2$, CH${}_4$, H${}_2$S, Xe, Kr, SO${}_2$	43.14–44.69	38 MWth not specified	2018 [91]
Split expansion	34	27	550	29.83	He, H${}_2$, CO, O${}_2$, Ar, N${}_2$, CH${}_4$, H${}_2$S, Xe, Kr, SO${}_2$	28.83–30.03	38 MWth not specified	2018 [91]
Basic	40	20	300	13.15	SF${}_6$, R32, R22, R123, R134a, Toluene	13.86–14.49	1 MWth not specified	2018 [88]
Recuperated	40	25	551	31.3	TiCl${}_4$	36	CSP	2018 [96]
Recuperated	40	25	800	40.7	TiCl${}_4$	44.7	CSP	2018 [96]
Recompression	40	25	551	38.4	TiCl${}_4$	40.1	CSP	2018 [96]
Recompression	40	25	800	47	TiCl${}_4$	49.9	CSP	2018 [96]
Recuperated	51	25	550, 700	40.4, 47.4	N${}_2$O${}_4$	40.8, 46.7	100 MWth CSP	2019 [97]
Recuperated	51	25	550, 700	40.44, 47.4	N${}_2$O${}_4$, TiCl${}_4$	40.63–49.11	33–38 MWe CSP	2019 [98]
Recuperated, recompression, partial cooling	36	25	550	27.5–30.6	Xe, n-Butane	27.7–30.9	1 MWe CSP	2019 [99]
TRC	15	10, 12	175, 155	-	SF${}_6$	13, 15	Geothermal water	2013 [100]
TRC	25	10	120–240	6.8–15.6	R32, R1270, R161, R1234yf, R134a, R152a, R1234ze	7.5–16.85	20–45 kWe WHR	2014 [81]
TRC	23	11–17	170	8.97	R32, R161, R290, R1234yf, R1234ze	7.54–9.54	112 kWe WHR	2017 [82]
TRC	20	-	150	6.6	R152a, R161, R290, R1270, R1234yf, R1234ze	6.3–9	223 kWe geothermal water	2017 [101]
TRC	20	-	180	5.79	Propane, n-Butane, isobutane, n-pentane, iso-pentane, neo-pentane	7.25–7.61	20 kWe Not specified	2017 [102]
TRC	26	9	277	6.55	R290, R152a, R41, R32, R134a, R161, R1234yf, R1234ze	8.7–11.5	13 kWe WHR	2018 [83]
TRC	30	-	200	-	R134a, R32, R152a, R41, R161, R1270, R1234ze(E), R1234yf	-	20–60 kWe WHR	2018 [84]

surveys gas additives in terms of the sCO${}_2$ cycles, boundary conditions, applications, and thermal efficiencies declared in the original papers. For the Brayton cycles, including the basic, recuperated, recompression, precompression, and split expansion layouts, the CIT is always fixed at 1 °C above the critical temperature, and the TIP is fixed at a certain value. For TRC, the maximum power output is the focus of the purpose of WHR. As can be seen, although most articles considered the recompression cycle with a TIT of 550 °C, large discrepancies in thermal efficiencies were obtained from one paper to another.

Figure 8 plots the declared thermal efficiencies of the supercritical CO${}_2$ mixture for both Brayton and Rankinecycles, as listed in Table 3. There are over 250 data, showing a wide range of cycle efficiencies. As can be seen, most Brayton cycles exhibit efficiencies in the range of 40% to 50%, and for the Rankine cycle, the efficiencies are from 6% to 10%. With low turbomachinery efficiency, the compound cycles have efficiencies of 25–32.5% [89,90]. The Brayton cycles without the recuperator have efficiencies well below 15% [88]. The wide dispersion of efficiencies is due to the cycle layout, as well as boundary conditions, such as TIT, turbomachinery efficiency, the effectiveness of heat exchangers, cooling conditions, and gas additives. Figure 8 also presents the efficiencies against TIT for all the cycles considered. In order to establish a convincing comparison, the commonly used efficiencies of the sCO${}_2$ cycle were plotted as the reference [9]. In general, the recompression layout of the supercritical CO${}_2$ mixture cycles outperforms other layouts and achieves efficiencies close to or even higher than the reference ones.

Figure 9 plots the influence of additives on cycle thermal efficiency. The efficiency change is defined as the thermal efficiency difference between the CO${}_2$ mixture cycle and the pure CO${}_2$ cycle. As can be seen, some additives do not improve cycle efficiency as might be anticipated, which are Ar, N${}_2$, O${}_2$[86,87], CO, CH${}_4$, and H${}_2$[89,91]. These additives alone with He, Xe [86,87], and Kr [18,91] decrease the critical temperature of CO${}_2$. However, the Xe and Kr additives improve the Brayton cycle by up to 2% in terms of efficiency, depending on the mass fraction. It was found that simultaneously lowering the critical temperature and critical pressure of the CO${}_2$ mixture has a positive effect on the total cycle efficiency. The decrease in critical pressure leads to an increase in the cycle operating pressure ratio. It is interesting that the addition of small amounts of Kr leads to an increase and then a decrease in the critical pressure. The reported difference in cycle efficiency was down to −0.7% for the CO${}_2$/Kr binary mixture consisting of 1% mol impurities when compared to pure CO${}_2$[91]. For the CO${}_2$/He mixture, Jeong et al. [18] and Hu et al. [95] showed positive effects, whereas Vesely et al. [89] showed detrimental effects. They all used the REFPROP program, although Jeong et al. [18] pointed out that the properties of the CO${}_2$/He mixture were opposite to the experiment data.

The substances H${}_2$S, cyclohexane, n-butane, toluene, SO${}_2$, R123, R134a, R22, R32, and TiCl${}_4$ have higher critical temperatures than pure CO${}_2$. For these gas additives, the benefit from the compression near the critical point is maintained at high cooling conditions. As can be seen in Figure 9, adding the substances increases the cycle efficiency, ranging from 0 to 2.0%. The CO${}_2$/TiCl${}_4$ mixture makes the Brayton cycle efficiency increase in the range of 1.5% to 5%. The findings in the literature show that adding the above additives to CO${}_2$ cannot stop cycle efficiency from decreasing in a warm environment, although the compression work is still reduced. Adding a gas to CO${}_2$ just mitigates the extent of the efficiency reduction. At a CIT of 44 °C for a dry cooling system, the efficiency of a recompression sCO${}_2$ cycle decreased from 45.4% to 41.4%, whereas adding H${}_2$S and cyclohexane to the working fluid reduced the efficiency to 43.2% and 42.6%, respectively [18]. In addition, the findings show that the higher the ambient temperature, the more obvious the advantages of the method of the CO${}_2$ mixture. A higher ambient temperature requires a higher CIT; thus, a larger amount of gas should be added. Adding TiCl${}_4$ may be a better choice in a high ambient temperature situation, showing an increase in efficiency of 5.5% higher than the pure CO${}_2$ Brayton cycle. In addition, the CO${}_2$/TiCl${}_4$ working fluid reduced the power cycle capital cost by 14.5–17.5% [98]. It is noted that several CO${}_2—$based mixtures were tested using the sCO${}_2$ equipment. The CO${}_2$/n-butane, CO${}_2$/neon, and CO${}_2$/SF${}_6$ mixtures were tested in a full-scale compressor at SNL [85]. The performance of the CO${}_2$/R32 mixture with mass fractions of 0.88:0.12 was tested in the compressor, showing that a slightly higher pressure ratio was achieved [88].

The investigated multicomponent mixtures are Air, M-I, M-II, M-H, Air-H, and M-IH [90]. The basic multicomponent mixture is from the technology of carbon capture and storage. The rest of the mixtures are combinations of pure additives and basic multicomponents. As can be seen in Figure 9, the multicomponent mixtures have a negative effect on the sCO${}_2$ cycle. The effect was small if the purity of CO${}_2$ was over 99%. If the purity of CO${}_2$ drops under 99%, the effect of the mixture deteriorates. The cycle output could be significantly decreased by the M-II mixtures, as shown in Figure 10, which shows the thermal efficiency and power output changes of the sCO${}_2$ cycles when the CO${}_2—$based mixture was applied as the working fluid with respect to the original cycles.

Mixing SF${}_6$ with CO${}_2$ increases the critical temperature, as calculated by the REFPROP program. However, it was found that the CO${}_2$/SF${}_6$ mixture for the Brayton cycle had less efficiency than the pure sCO${}_2$ cycle at the same CIT [88]. As shown in Figure 9, the SF${}_6$ additive reduced the cycle efficiency by 2.1% at most (with a mass fraction of 0.4). This may indicate that the critical point predicted by REFPROP is not close to the experimental value. Earlier, Lewis et al. [85] showed that the addition of SF${}_6$ to a CO${}_2$-dominated mixture reduced the critical temperature until SF${}_6$ became the dominant component. A good prediction of CO${}_2$/SF${}_6$ mixture behavior should be further investigated.

For the Rankine cycle, the substances R1270, R161, R152a, R1234ze, R1234yf, R290, R32, and R134a were blended with CO${}_2$, showing an efficiency gain in the range of −1.5% to 2.5%. The CO${}_2$/R161 mixture exhibited the best cycle efficiency [81] and the most effective economic performance [82]. Note that R161 is highly flammable until the CO${}_2$ fraction is higher than 70% [103]. The CO${}_2$/R290 mixture is commonly used in refrigeration and heat pump systems with good performance, whereas it had decreased efficiency when used in the WHR system, as shown in Figure 9. Note that for the WHR system, the selection of the amount of additive is used to convert as much heat to power as possible; hence, the heat source temperature is not always very high.

The selection of a CO${}_2$ mixture should simultaneously take into account thermal properties, cycle efficiency, heat transfer performance, safety, and environmental issues. To date, the choice of CO${}_2$ mixtures has mainly considered the effect on Brayton cycle efficiency by using the basic law of thermodynamics. The thermal stability of the mixture has been less of a concern. The supercritical CO${}_2$ mixture Brayton cycles operate at a temperature of 350 °C to 700 °C, raising the possibility of bond-breaking reactions and the further decomposition of the additive. Beyond the critical value of thermal stability, organic fluid pyrolysis yields gas, liquid, or solid products. The gaseous products (like non-condensing gases) circulate with the working fluid, whereas the solid products stick to the surface of the heat exchanger, both of which will worsen the heat transfer. In addition, the decomposition products are mixed with the working medium, which changes the thermal properties of the working medium and makes the system deviate from the design condition, resulting in a reduction in system output power [104,105]. More seriously, molecular polymerization may occur, resulting in the blockage of a pipeline and causing a hidden danger to the system safety [106].

Table 4. Physical, safety, and environmental data for promising additives.

Type	Substance	Physical Data				Safety	Environmental Data [116]
		$M$/g·mol${}^{-1}$	$P_c$/MPa	$T_c$/°C	$T_D$/°C		ODP	GWP
Inorganics	H${}_2$S	34.08	9	99.95	<444.6 [107,108]	Highly Flammable	0	-
	SO${}_2$	64.06	7.884	157.49	2000 [110]	B1	0	-
	TiCl${}_4$	189.7	4.661	364.85	>500 [113]	Non Flammable	0	-
	N${}_2$O${}_4$	92.01	9.976	158.2	30 [115]	Non Flammable	0	-
HC	Propane	44.10	4.251	96.74	525 [117]	Highly flammable	0	3.3
	n-Butane	58.12	3.80	152	300–320 [118]	A3	0	~20
	Pentane	72.15	3.37	196.55	280–300 [118]	A3	0	~20
	Cyclohexane	84.16	4.08	280.45	700–800 [119]	Flammable	0	20
	Benzene	78.11	4.907	288.87	<500 [120]	Highly flammable	0	20
	Toluene	92.14	4.126	318.6	350–400 [121,122]	Flammable	0	3.35
HCFC	R123	152.931	3.662	183.68	200–220 [123]	B1	0.01	77
	R125	120.02	3.6177	66.023	396 [124]	A1	0	3420
	R1270	42.08	4.66	92.4	-	A3	0	~20
	R134a	102.032	4.06	101.1	350–370 [122]	A1	0	1430
	R143a	84.04	3.761	72.71	>350 [125]	A2	0	4400
HFC	R152a	66.051	4.52	113.3	160–180 [123]	A2	0	133
	R161	48.06	5.01	102.1	427 [126]	A3	0	12
	R22	86.468	4.99	96.145	-	A1	0.055	1700
	R227ea	170.03	2.925	101.75	>425 [125]	A1	0	3300
	R236fa	152.04	3.2	124.92	380–400 [123]	A1	0	9820
	R32	52.024	5.782	78.1	570–590 [127]	A2	0	675
	R404a	97.60	3.735	72.12	-	-	0	3700
	R407c	86.20	4.632	86.2	-	A1	0	1530
	R41	34.03	5.897	44.13	-	-	0	107
	R410a	72.58	4.901	71.34	-	A1	0	1730

collects the CO${}_2$ mixtures that have positive effects on the power cycle mentioned above. The physical properties, safety, and environmental data are also presented. H${}_2$S is a highly flammable and explosive gas. It was shown that its initial decomposition to hydrogen and sulfur occurred at a temperature below 444.6 °C [107,108]. The equilibrium concentration of hydrogen was less than 1% until the temperature rose up to 550 °C and about 6% at 800 °C [109]. SO${}_2$ is chemically stable and was used as an early refrigerant in home refrigerators. Iron, steel, nickel, copper-nickel alloys, and Inconel nickel-chromium-iron are satisfactory for dry or hot SO${}_2$ but are readily corroded by wet SO${}_2$ gas [110]. The study of TiCl${}_4$ as a heat pipe fluid in the intermediate temperature range of 400–700 K was proposed by Davarakonda and Olminsky [111], and the thermophysical properties were evaluated by NASA [112]. The experimental analysis showed that TiCl${}_4$ was remarkably stable at temperatures up to 500 °C [113]. These considerations and studies support the application of TiCl${}_4$ in high-temperature ORC [114]. N${}_2$O${}_4$ is one of the chemically reactive gases that undergo dissociation reactions at high temperatures and recombination at low temperatures. At temperatures of 30–170 °C, N${}_2$O${}_4$ is unstable and decomposes into NO${}_2$, which undergoes subsequent thermal decomposition into O${}_2$ and NO, depending on the pressure and temperature [115].

Organic compounds are not thermally stable at high temperatures. Between 100 °C and 500 °C, many organic molecules break down, breaking the chemical bonds in their molecules. As can be seen in Table 4, propane, cyclohexane, benzene, R161, and R32 have relatively high decomposition temperatures. Solovyev [117] experimentally showed that propane began thermal decomposition at about 525 °C. The main products were hydrogen, methane, ethane, and ethylene. Tsang [119] proposed that the main initial processes of cyclohexane pyrolysis involved the isomerization of cyclohexane to 1-hexene, followed by the decomposition of 1-hexene. At around 800 °C, the extent of the reaction was extremely small, which is indicative of the great stability of cyclohexane. Zanetti and Egloff [120] showed that the decomposition of benzene began at temperatures as low as 500 °C. In cases below 600 °C, the amounts decomposed were small and chiefly turned into hydrogen and diphenyl at temperatures below 750 °C. As for flammability, benzene was suppressed by a volume fraction of 32% of CO${}_2$ [128].

Several factors should also be considered when modifying the critical point of CO${}_2$.

• The available mixture database is required. The NIST REFPROP is currently used to calculate the thermophysical properties of a CO${}_2$ mixture. Experimental data are quite rare; only the properties of CO${}_2$/xenon can be used so far [129]. However, the REFPROP program suggests the equation of state (EOS) temperature and pressure limits as follows: 161–750 K and 700 MPa for CO${}_2$/Xe, 116–750 K and 200 MPa for CO${}_2$/Kr, 188–760 K and 170 MPa for CO${}_2$/H${}_2$S, and 279–700 K and 80 MPa for CO${}_2$/cyclohexane. In order to estimate the properties at higher temperatures, the temperature range of the REFPROP program has to be extended.
• The critical phenomena of CO${}_2$ mixtures should be considered carefully. The critical line has a continuous or discontinuous form among each critical point of the pure components. As for the discontinuous critical lines, the existence of phase separation could cause instability in the CO${}_2$ mixtures. This could hardly further obtain the optimum design of the compressor.
• The thermal stability of potential additives should be considered as a key selection criterion besides their thermodynamic performance. Otherwise, decomposition products, like non-condensable gases and deposits, may reduce the heat transfer rates, damage the components, and compromise cycle safety. Additional experiments are needed to identify the real phenomena of CO${}_2$ mixtures at high temperatures.
• The chemical effect on cycle components should be considered in the future.

5. Strengths and Weaknesses Analysis

In order to compare the three categorized methods discussed above, the strengths and weaknesses have been identified and are listed in

Table 5. Strengths and weaknesses of sCO${}_2$ cycle improvement methods.

Method	Strengths	Weaknesses
Conventional method	Moderate efficiency rise Technology proven (on steam Rankine cycles)	Adding component(s) Complex layout High TIT Large pressure drop
Combined cycle	⊠ Good waste heat recovery ⊠ Large efficiency rise ⊠ Combined cold and power cogeneration	⊠ Additional components ⊠ Capital cost increase ⊠ Complex layout ⊠ Wet cooling needed
CO${}_2$ mixture	Low efficiency rise Cost-effective Applicable to hot-arid environments	Thermal stability of additives Control of additives Chemical reaction with materials

.

The conventional method provides a moderate enhancement to the sCO${}_2$ cycle. A promising power cycle always comes at the cost of high cycle complexity. More components and complex control strategies would make off-design operations less flexible than the recuperated layout of the sCO${}_2$ cycle. It was found that the recompression sCO${}_2$ cycle is able to yield a high efficiency while still retaining simplicity.

The combined cycle could largely improve the sCO${}_2$ cycle by recovering waste heat from the cooler. At least four more components are required, which increases the capital cost by about 5% [2,23]. The challenging task of this approach is the condensation of the working fluid in the bottoming cycle. Wet cooling or a low-temperature heat sink is mandatory, especially for the tCO${}_2$ bottoming cycle. If the terrestrial ambient temperature is too high or if dry cooling is employed, it is difficult or even impossible to cool the working fluid sufficiently.

The CO${}_2$ mixture method increases the thermal efficiency of the sCO${}_2$ cycle in an economical way. The adjustment of the critical temperature and pressure of the working fluid broadens the applicability of the sCO${}_2$ cycle for a variety of possible heat sinks. The selection of additives plays a crucial role in cycle performance, heat transfer, thermal stability, control, and chemical stability.

6. Conclusions

This paper surveys the available methods of enhanced sCO${}_2$ cycles and uses thermodynamics to gain insight into the effects of cycle modification. These approaches were classified into three categories by type and characteristic: the conventional method, CO${}_2$ mixture, and combined cycle. The comparison of each method was based on the values declared in the original papers, which were investigated under very different operating conditions. An intuitive overview of the performance enhancement is provided for the sCO${}_2$ cycle. In addition, the strengths and limitations of each method are discussed.

In general, the conventional method shows moderate efficiency improvements. Adding a bottoming cycle is a promising option that can significantly improve efficiency. The drawbacks are the requirement of a year-round supply of cold cooling water and about a 5% increase in the capital cost. The modification of the thermal–physical properties of CO${}_2$ is an economical way to change cycle performance. The higher the ambient temperature, the more obvious the advantages of the method of critical point shifting. Thermal stability and the property database are crucial factors for gas mixture selections. Combining the potential methods is a better choice. Further steps toward a comparison of the three methods under the same operating conditions should be conducted.