1. Introduction
The modern world is undergoing rapid development which is reflected in the increased per capita energy consumption. Developing countries such as India are experiencing exponential growth and, at the same time, awareness of climate change is catching up and governments worldwide are looking at environmentally friendly power generation technologies that are also efficient and sustainable. Renewable energy sources are known to be environmentally friendly and even though power from solar and wind energy is becoming competitive [
1], they are not reliable and sustainable without the support of bulky energy storage devices such as batteries. Conventional power generation technologies involving fossil fuels have the advantage of being mature and well understood while they suffer from an environmental regulations viewpoint [
2]. Several innovative ways of utilizing fossil fuels and reducing their impact on the environment have been explored and are still being investigated [
3]. Some of the methods are fluidized bed combustion [
4], oxy-fuel combustion [
5], chemical looping combustion [
6], etc., which aim at reducing the pollutants at the combustion stage itself. In addition, the application of fossil fuels is being investigated in high-end thermal power plants such as ultra super-critical power plants [
7]. However, they need expensive materials due to high pressure and temperatures. Some technologies are designed to handle the pollutants after the combustion process, and carbon capture and storage (CCS) is one among them [
8]. It would be useful if the captured and stored carbon dioxide could be put to further use. One such application is to use carbon dioxide as a refrigerant while another application is to use it in power generation [
9], such as in s-CO
2 power plants.
The primary benefit of using CO
2 as a working fluid in power generation is that it can replace water as a working fluid, thereby preserving and conserving a more important natural resource. Moreover, large amounts of CO
2 generated by burning fossil fuels (~963 tons/day by a 100 MWe plant) [
10] can be utilized and thereby decrease its contribution to global warming. Other benefits of CO
2 as a working fluid are the fact that it is inert, non-toxic, non-corrosive, has low ozone depletion potential, is accessible and affordable, has good thermal characteristics for heat exchange, a low compression work around critical point, higher thermal efficiency and the equipment is compact due to high density [
11]. In addition to fossil fuels, the necessary heat for a s-CO
2 power plant can also be sourced from geothermal, solar and/or waste heat energies [
12].
Despite having several benefits mentioned above and having been introduced several decades ago in the 1960s by Angelino [
13] and Feher [
14], the power generation technology using s-CO
2 is still at the testing stage with test facilities in the 1–250 kW range and the largest pilot plant being of 10 MWe capacity built by the Gas Turbine Institute, Southwest Research Institute and General Electric Global Research together in San Antonio, Texas, USA [
15]. Several review articles were recently published highlighting the benefits, drawbacks, state-of-the-art and future work to be taken up to make s-CO
2 power a reality at a higher scale [
11,
12,
16,
17,
18,
19,
20]. Sarkar [
16] emphasized the need for more experimental research on transcritical Rankine cycles to carry out a techno-economic comparison of CO
2 with other working fluids. Crespi et al. [
17] have stated that high efficiencies in the range of 50–60% can be achieved by using combined cycle layouts involving s-CO
2. Ahn et al. [
12] suggested that the focus should be on developing pilot power plants bigger than 10 MWe so as to explore the commercial benefits due to scale-up. Yin et al. [
18] carried out a review on the application of s-CO
2 with concentrated solar power and suggested that future research should focus on the materials used, thermodynamic analysis at the design point and off-design point as well as transient modeling. White et al. [
19] highlighted areas of research in the turbomachinery, heat exchangers, materials and control systems. Yu et al. [
20] found that identifying an efficient cycle for a given heat source is an unanswered question and needs to be studied for various heat sources. They also suggested that CO
2-based gas mixtures also need to be evaluated for usage in these power plants.
Based on the reported research and review articles, it can be found that several thermodynamic configurations involving s-CO
2 have been studied. All these studies aimed at maximizing the thermal efficiency either by using a single cycle or a combined cycle. Sun et al. [
21] proposed a bottoming cycle for a coal-fired s-CO
2 power plant to effectively utilize the heat in the exhaust gases. They reported an efficiency of 47% with a double reheat recompression cycle with CO
2 parameters as 620 °C temperature and 30 MPa pressure. Chen et al. [
22] compared two recompression cycles, one with a single reheat and another with a double reheat. They found that the double reheat cycle is more efficient than the single reheat cycle. Moreover, they have evaluated the exergy destruction in the combustion, heat transfer and pressure drop and found that most of the exergy is destructed during combustion followed by heat transfer. Bai et al. [
23] proposed an improved recompression s-CO
2 coal-fired power plant. Rogalev et al. [
24] explored the possibility of replacing steam with s-CO
2 in a nuclear power plant and found it to be an attractive option for a working fluid temperature above 455 °C.
Some studies on the part load performance of s-CO
2 plants have been reported in the literature. Sanchez et al. [
25] analyzed a hybrid system comprising a molten carbonate fuel cell and s-CO
2 cycle to evaluate the control strategies at part loads and concluded that mixed strategies give better results compared to individual control strategies. Fan et al. [
26] considered simple supercritical and trans-critical plants to conduct thermodynamic analysis and determine the control strategy. Yang et al. [
27] studied four simple and separate layouts powered by solar energy and compared different cycles at full and part loads. Tong et al. [
28] studied a coal-powered single reheat recompression cycle and evaluated the boiler’s part load performance. Lee et al. [
29] developed a CFD model to study the part load performance of radial flow turbines used in s-CO
2 plants with a maximum deviation of 10%. Alfani et al. [
30] considered four different system layouts powered by waste heat and carried out a 1st law and techno-economic analysis and optimization. They also compared the performance with organic Rankine cycle technology and concluded that s-CO
2 has a better performance even at part loads. Fan and Dai [
31] combined a simple s-CO
2 with the Kalina cycle and a recompression s-CO
2 with the Kalina cycle and carried out thermo-economic analysis and optimization of the system. They found the recompression-Kalina cycle to be a better performer both thermodynamically and economically. Fan et al. [
32] studied a nuclear energy-powered s-CO
2 plant combined with an organic Rankine cycle to carry out 1st law and economic analysis. Wang et al. [
33] considered a fuel oil-powered recompression cycle and compared different control strategies at part loads. They concluded that inventory and anti-surge control is better than valve controls. Xingyan et al. [
34] studied four different cycles and evaluated their performance based on layout and control strategies. Gini et al. [
35] evaluated a simple recuperated cycle powered by molten salt for control strategy development at part loads. It is evident that some studies on the part load performance of s-CO
2 plants have been reported, and a few studied the specific components [
28,
29] in the plant. There is no study that reported a part load study on a double reheat recompression cycle powered by coal.
Table 1 summarizes the reported literature on part load studies of s-CO
2 power plants.
From the summary of the literature presented above, it can be seen that several thermodynamic cycle layouts have been investigated and reported in the open literature. However, to the best of the authors’ knowledge, there is no study which considered the system design and optimization of a 100 MWe double reheat s-CO
2 power plant and thermodynamic analysis at part loads. Since the existing systems would eventually be scaled up and part load operation would be inevitable and important, as emphasized by Yin et al. [
18], the present study aims to predict the performance at full load as well as part loads of an s-CO
2 power plant. Since it is generally understood that a double reheat recompression cycle has a high efficiency in comparison to other configurations [
17,
22], the same has been considered in the present study. The objectives of the present study are listed below:
To perform a system design of a 100 MWe coal-fired double reheat recompression s-CO
2 system based on the parameters and configurations reported by Chen et al. [
22].
To evaluate its performance at full load as well as at part loads of 80%, 60% and 40% based on 1st and 2nd laws of thermodynamics.
To optimize the performance based on thermal efficiency (1st law efficiency) at full load.
Identify the crucial operational parameters that influence thermal efficiency.
Identify the system components that contribute to high exergy destruction.
2. System Layout Description
The s-CO
2 power plant system layout considered for the present study is a double reheat recompression cycle, as described by Chen et al. [
22]. The schematic of the layout is shown in
Figure 1. Carbon dioxide is heated to the rated supercritical condition in the heater using the heat generated by coal firing. This s-CO
2 expands in the high-pressure turbine, then enters the reheater-1 to undergo a rise in temperature, further expands in the intermediate-pressure turbine followed by a temperature rise in reheater-2 and, finally, expands in the low-pressure turbine. The low-pressure turbine exhaust is still at moderate pressure and temperature and its energy is partly recovered in the high and low-temperature recuperators in which heat is transferred from the low-pressure turbine exhaust to the CO
2 emerging from the compressors. This is meant to save input heat energy in the form of fuel. After the low-temperature recuperator, the s-CO
2 is split into two streams, one of which is cooled in the cooler using ambient air before it enters the main compressor while the other stream is directed into the re-compressor. The main compressor handles cooler s-CO
2 and hence saves energy. After compression and heat exchange in the low-temperature recuperator, both the compressor exit streams are mixed in a direct contact heat exchanger named a ‘junction’ in
Figure 1. Subsequently, heat exchange takes place in the high-temperature recuperator and the CO
2 enters the heater to receive heat from coal combustion. In the figure, the coal flow stream and flue gas stream have not been shown for the sake of simplicity. Part of the power produced by the turbines is consumed by the compressors as indicated by the shaft connecting the turbines and compressors.
The corresponding Temperature vs. Entropy diagram is shown in
Figure 2. Important processes have been marked in the T-S diagram.
The fuel properties and important operating parameters of the plant are shown in
Table 2. Operating parameters are chosen in such a way that the CO
2 remains in a super critical state through the entire operation.
Model Formulation:
The following assumptions were made in the model formulation and analysis:
All components operate at a steady state.
Changes in kinetic and potential energies are neglected for all fluid streams.
All components are perfectly insulated and there is no heat exchange with the surroundings.
The heat exchangers (recuperators and cooler) are the shell and tube type.
The dead state conditions are taken to be 1 bar and 30 °C.
The following equations are framed and solved for all the components in the steady flow system.
The chemical exergy factorized in Equation (13), 1.04, is estimated using the method proposed by Kotas [
36]. The individual equations for mass, energy and exergy balance for each component are shown in
Table 3. Heat and power terms shown in
Table 2 are positive quantities. The subscripts in the equations correspond to the pipe numbers shown in
Figure 1. The exergy destroyed in the equations corresponds to the respective component. Exergy associated with heat transfer is computed using Equation (6) while the flow exergy of each component is evaluated using Equation (9).
The equations shown in
Table 3 are framed and solved by the flow-sheeting software Cycle-Tempo 5.1 based on the inputs given using the graphical user interface. The property values of carbon dioxide are computed using RefProp 10 add-in software.
The system shown in
Figure 1 and the inputs shown in
Table 3 are used to solve the system and the output is validated by comparing the present results with those of Chen et al. [
22] after adjusting some inputs so as to make the model relevant to theirs. The results have been compared to validate the present model and are shown in
Table 4.
The maximum error is found to be less than 4%. This could be due to the different software used by Chen et al. [
22] and in the present work to compute fluid properties. Moreover, the convergence criteria of the two software could be different. Moreover, some commonly used parameters (such as the recompression ratio, chemical exergy factor) which are not provided by Chen et al. [
22] have been assumed or indirectly estimated in the present work. Considering all these reasons, a maximum error of less than 4% is concluded to be reasonable and hence the present model is concluded to be satisfactory.