Today in the Russian Federation, there are 11 nuclear power plants (NPPs) with 38 operating power units and a total installed capacity of 30.3 GW. The majority of them, 55%, are equipped with a pressurized water reactor (PWR), and the most widely used among them is the VVER–1000 type. Besides the PWRs, NPPs also operate fast breeder reactor (FBR) BN–800 with sodium heat carrier, 2100 MW heat power, 800 MW supplied power, and 39.4% net efficiency. Moreover, a new reactor facility BREST–OD–300 is under development. This FBR has a lead heat carrier, a two–circuit heat transport to the steam turbine and supercritical steam parameters. A common feature of these NPPs is the presence of the steam turbine cycle, which determines the mass and dimensions of the main energy equipment, especially of steam turbines, and rather low thermal efficiency.

A prospective method for increasing the NPP fuel efficiency and its investment reduction is an application of the supercritical carbon dioxide (S–CO₂) working fluid. It allows for use of the Brayton cycle with low auxiliary power consumption, moderate initial temperature, and compact dimensions of the main energy equipment [1,2,3]. This direction has been actively developed since the middle of the past century [4,5,6,7]. This area of development arises scientists′ interests around the world largely because of carbon dioxide′s competitive advantages compared to other working fluids.

The carbon dioxide heat carrier has a low critical temperature of 30.98 °C and a pressure of 7.38 MPa (Figure 1). The low carbon dioxide critical temperature is near to the ambient atmosphere, which allows the working fluid compression near the saturation line (the CO₂ density is quite high at the near–critical parameters) [8,9], reducing the compressor work and the temperature of heat removed from the cycle without the working fluid condensing. Besides, carbon dioxide is less aggressive than water and shows its corrosion activity only in the presence of moisture content in the working fluid or with a water film on a metal surface. The carbon dioxide and water working fluid prices are compatible.

The advantages of carbon dioxide compared to air and water in the role of the working fluid are caused by its thermophysical performance (Table 1) in conditions typical for steam and gas turbine facilities. The high density of carbon dioxide at given turbine inlet and outlet conditions leads to S–CO₂ turbine mass and dimensions being smaller than those of the steam or gas turbines. The airfoil grid friction losses in an S–CO₂ turbine will be smaller than those in a steam or gas turbine because of carbon dioxide′s smaller viscosity [10].

Long-term thermodynamic studies of S–CO₂ power facilities resulted in the development of the five cycles presented in Figure 2.

The simplest S–CO₂ cycle is a closed Brayton cycle with the heat utilization of the exhaust gases (Figure 2a). The recirculating carbon dioxide enters the compressor (C), then the compressed fluid enters the regenerator (RH). The pre-heated flow enters the reactor (R) where its temperature increases. Then, the supercritical fluid is sent to the turbine (T) that drives the electricity generator (G). After the expansion, the turbine exhaust gas enters the regenerator, where it transfers heat to the compressed working fluid. Before it enters the compressor, the cooled CO₂ flow is sent to the cold source, or pre-cooler (PC), where the working fluid is additionally cooled.

The thermal efficiency is about 42% for 550 °C initial temperature, 32 °C compressor inlet temperature, and 25 MPa compressor outlet pressure. Studies of the turbine inlet pressure′s influence upon the S–CO₂ Brayton cycle′s efficiency show that its increase by 2 MPa in the range of 13.8–27.6 MPa causes an efficiency increase of 0.71% [11], and a 150 °C initial temperature increase leads to a thermal efficiency increase of 5.5%.

Reheating (Figure 2b) may increase the S–CO₂ Brayton cycle efficiency. This cycle differs from the previous one (Figure 2a) by the second working fluid supply to the reactor. Pressurized carbon dioxide flow is sent by the compressor to the regenerator, where it is heated by the low-pressure turbine (LPT) outlet flow. Then, the flow is sent to the reactor for its temperature increase up to the cycle initial temperature. After that, the flow is sent to the high-pressure turbine (HPT) flow path, where it expands to half of the initial pressure. Then, the flow re-enters the reactor for reheat. Afterward, the CO₂ flow expands in the LPT and enters the regenerator, where it transmits heat to the compressor outlet flow. From the regenerator outlet, the hot flow is sent to the cooler, and then it re-enters the compressor.

The introduction of the working fluid reheat is followed by an increase of turbine outlet temperature, which increases the reactor inlet temperature and the mean integral temperature of heat supply to the cycle. Thermodynamic studies [7,12] reveal that the efficiency increase is maximal when the high-pressure turbine expansion ratio is equal to the low-pressure turbine one. The cycle efficiency is about 41.5% at 550 °C and 25 MPa initial cycle parameters and the turbine outlet pressure of 7.5 MPa. However, it should be noted that the introduction of an additional superheater will inevitably cause pressure losses in it. A 10% increase in pressure losses in the range of 0–250 kPa reduces the facility efficiency by 0.11%. With a further increase of the superheater pressure losses, application of the reheat will not be reasonable because it reduces the cycle efficiency. The introduction of the secondary reheat allows the supercritical CO₂ Brayton cycle efficiency increase by 0.20 to 0.26% at the heater pressure losses below 125 kPa.

One more method for the efficiency increase of the simplest supercritical CO₂ Brayton cycle is the introduction of intermediate cooling that reduces the compressor energy consumption (Figure 2c). In contrast to the regeneration cycle (Figure 2a), this cycle uses low- pressure compressor (LPC) and high-pressure compressor (HPC) as well as an intermediate cooler (IC). After the low-pressure compressor, the working fluid passes the cooler, where it cools and enters the high-pressure compressor, where it reaches the cycle initial parameters. The maximal increase of this cycle′s thermodynamic efficiency is reached when the second compressor pressure ratio is 1.5–1.9 times higher than the first compressor one. In this case, the S–CO₂ Brayton cycle efficiency increases by 0.8%.

In addition to the above schemes, one more way toward S–CO₂ Brayton cycle efficiency improvement is the use of partial cooling (Figure 2d) [6]. This cycle differs from the cycle with regeneration by the application of a high-temperature regenerator (HTR) and low-temperature regenerator (LTR), condenser (CR), pump (P), and recompressing compressor (RC). The flow pressurized in the compressor is split into two parts: the first is sent to the RC and the second is cooled in the condenser and also compressed by the pump. The second flow of compressed CO₂ is heated in the LTR by the exhaust gas heat and then mixes with the first CO₂ flow in the HTR. After that, the flow is supplied to the reactor, where it is heated up to the cycle′s initial temperature. The reactor exhaust supercritical CO₂ enters the turbine that drives the power generator. Then, the expanded gas is directed to the sequentially connected HTR and LTR for heat utilization. Afterwards, the flow is cooled in the pre-cooler before it enters the compressor. This solution improves the regeneration system efficiency by means of the heat exchangers′ operation at different pressures. The S–CO₂ Brayton cycle has 44.8% efficiency at a 550 °C cycle initial temperature and 25 MPa initial pressure.

Figure 2e shows the supercritical CO₂ Brayton cycle with recompression, which is a simplified modification of the partial cooling cycle presented in Figure 2d. This cycle differs from the partial cooling cycle by the absence of a pump and condenser. The carbon dioxide flow is split into two parts upstream of the pre-cooler. The first part is cooled and supplied to the main compressor, where it reaches the initial parameters. The second part is directly supplied to the recompressing compressor, where it is also compressed up to the initial cycle pressure. After the main compressor, the compressed CO₂ flow enters the LTR, where it is heated by the outlet carbon dioxide flow up to the temperature equal to the second CO₂ flow temperature after the RC. Then, the two flows merge and enter the HTR, where they are also heated up to the reactor inlet temperature by heat utilization of the exhaust gases. Then, the reactor heats the working fluid up to the cycle′s initial temperature. Then, the flow enters the turbine that drives the power generator. After the flow expands in the turbine, the hot exhaust gases are cooled in the sequentially connected HTR and LTR and then split into two flows again.

This scheme solves the problem of low efficiency of the exhaust gases′ heat utilization. This problem is related to the remarkable difference of the regenerator hot and cold flows′ specific heat capacity. This difference is a specific feature of the S–CO₂ Brayton cycle with regeneration. In other words, the split of compressed flow and introduction of the LTR and HTR provides deeper utilization of the exhaust gases heat and smaller heat losses in the cooler. The result of this technical solution is that the S–CO₂ Brayton cycle efficiency increases up to 46%.

Most of the published thermodynamic investigations are obtained at incomparable conditions, at different input data and calculation methods. As a result, one can see different evaluations of similar factors′ influence on thermal efficiency. For example, the study of the S–CO₂ recompression Brayton cycle efficiency [11] shows that a 100 °C increase in the turbine inlet temperature in the 500–1000 °C range increases the efficiency by a 2.0% average, but according to the results in [6], this increase is 3.3%. On the other side, study [7] shows that a 100 °C increase of the turbine inlet temperature in the 550–850 °C range increases the mean cycle efficiency by 4%, and according to [13], in the 550–700 °C range, the same temperature increase leads to the 5% increase in efficiency.

Table 2 summarizes the main results of thermodynamic studies [6,7,11,13,14] of the S–CO₂ recompression Brayton cycle. The results show a remarkable evaluation difference and determine the relevance of the comparison of carbon dioxide cycles under comparable conditions.

To ensure the possibility of an objective comparison of the thermodynamic efficiency of S–CO₂ power cycles, a preliminary optimization of key parameters was carried out using the Aspen Plus software package. Table 3 summarizes the main thermodynamic performance of the five cycles described above. The supercritical CO₂ Brayton cycle with recompression has a maximal net efficiency of 47.28% at the initial temperature and pressure of 550 °C and 35 MPa. The high working fluid temperature at the heat supply source inlet of the S–CO₂ recompression Brayton cycle defines its prospects for the NPP reactor heat utilization.

Despite numerous studies′ results on the CO₂ operating NPPs, many questions are not yet answered. Specifically, the studies do not consider the nuclear reactor influence upon the outer CO₂ circuit [15,16].

2. Structural and Parametric Optimization of S–CO₂ Nuclear Power Plants