# Thermodynamic Analysis of Supercritical CO2 Power Cycle with Fluidized Bed Coal Combustion

Authors: Chenchen Geng; Yingjuan Shao; Wenqi Zhong; Xuejiao Liu
Journal: Journal of Combustion
 (2018)

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## Abstract

Closed supercritical carbon dioxide (S-CO2) Brayton cycle is a promising alternative to steam Rankine cycle due to higher cycle efficiency at equivalent turbine inlet conditions, which has been explored to apply to nuclear, solar power, waste heat recovery, and coal-fired power plant. This study establishes 300MW S-CO2 power system based on modified recompression Brayton cycle integrated with coal-fired circulating fluidized bed (CFB) boiler. The influences of two stages split flow on system performance have been investigated in detail. In addition, thermodynamic analysis of critical operating parameters has been carried out, including terminal temperature difference, turbine inlet pressure/temperature, reheat stages, and parameters as well as compressor inlet pressure/temperature. The results show that rational distribution of split ratio to the recompressor (SR1) achieves maximal cycle efficiency where heat capacities of both sides in the low temperature recuperator (LTR) realize an excellent matching. The optimal SR1 decreases in the approximately linear proportion to high pressure turbine (HPT) inlet pressure due to gradually narrowing specific heat differences in the LTR. Secondary split ratio to the economizer of CFB boiler (SR2) can recover moderate flue gas heat caused by narrow temperature range and improve boiler efficiency. Smaller terminal temperature difference corresponds to higher efficiency and brings about larger cost and pressure drops of the recuperators, which probably decrease efficiency conversely. Single reheat improves cycle efficiency by 1.5% under the condition of 600°C/600°C/25Mpa while efficiency improvement for double reheat is less obvious compared to steam Rankine cycle largely due to much lower pressure ratio. Reheat pressure and main compressor (MC) inlet pressure have corresponding optimal values. HPT and low pressure turbine (LPT) inlet temperature both have positive influences on system performance.


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## Body

## 1. Introduction

High efficiency and clean coal-fired power generation technologies are priority research directions in the traditional energy industry. Utilizing double reheat and raising steam parameters are two effective means to improve power plant efficiency, however, which is generally restricted by nickel-based alloys development and expensive equipment cost. More efficient and compact cycles integrated with conventional coal-fired boiler become a breakthrough in improving fossil fuels utilization rate. Closed supercritical carbon dioxide (S-CO2) Brayton cycle is considered as a promising substitute for steam Rankine cycle applied to thermal power generation. S-CO2 is that both pressure and temperature of CO2 are above its critical point (7.38Mpa 30.98°C) which is a suitable working fluid for power generation because of its near-critical properties. CO2 critical temperature is easily achieved and operating at high pressure allows more compact turbomachinery. Furthermore, S-CO2 possesses high density in near-critical region similarity to its liquid phase resulting in less compressor work and higher efficiency. Besides, CO2 is generally abundant, less corrosive, inexpensive, and nontoxic [1].Previous researches show that S-CO2 Brayton cycle is more efficient than supercritical steam Rankine cycle above moderate turbine inlet temperatures and can be coupled with various heat sources. The investigations of its potential applications have extended from nuclear, concentrated solar power (CSP), shipboard propulsion, waste heat recovery, and geothermal to fossil fuel [2, 3]. Detailed analysis began in the late 1960s. Feher [4] proposed CO2 as the working fluid for the regenerative supercritical cycle that operated entirely above the critical pressure and was compressed in the liquid phase. Hoffmann and Feher [5] further designed a 150 kWe power conversion module for a helium-cooled nuclear reactor in 1970. Angelino [6] analyzed different configurations of CO2 condensing cycles including recompression cycle, partial cooling cycle, pre-expansion cycle, and pre-compression cycle. The study pointed out that the efficiency of recompression CO2 cycle was better than reheat steam cycle at turbine inlet temperatures higher than 650°C. These studies have not been given sufficient attention in the following decades because of immature manufacturing technics as well as limitation of heat resource temperature. Dostal et al. [1] revived interest in S-CO2 cycles in the early 20th century; they modified the recompression S-CO2 cycle proposed by Angelino and carried out detailed component design, optimization, and economic analysis as well as control schemes for advanced nuclear reactors. After that, a growing number of studies were carried out involving system design [7], thermodynamic analysis and optimization [8, 9], and experimental loop tests [10, 11] as well as commercial-scale construction [12, 13] for different applications.A considerable amount of heat recovered by recuperators from turbine exhaust brings about a narrow temperature range through the heat source. S-CO2 cycle can well match with nuclear and CSP heat sources due to their nearly constant temperature [14]. However, modifications are indispensable for applications to the coal-fired power plant in order to effectively utilize flue gas heat and improve the gross plant efficiency. Several improvements have been put forward, such as utilizing residual heat to preheat air, improving cycle layouts, extracting a fraction of S-CO2 from different points at high-pressure side to recover flue gas heat, heating recycled flue gas, and adopting cascaded or combined cycles. Muto et al. [15] proposed a double expansion turbine cycle to reduce the pressure difference between gas side and S-CO2 side of heater and introduced an economizer to recover exit gas heat. Moullec [16] explored the potential performance of a coal-fired power plant based on double reheat recompression S-CO2 cycle integrated with a post-combustion carbon capture and storage (CCS). A high temperature air preheating combined with a fraction of fluid split from the main compressor (MC) to the economizer can effectively utilize 100~500°C flue gas heat. The net lower heating value (LHV) plant efficiency without CO2 capture for a maximal temperature and pressure of 620°C and 30Mpa could achieve 50.3% and 4.8% higher than supercritical steam power plant. Mecheri and Moullec [17] investigated the S-CO2 system performance and still recommended the previous layout. Li et al. [18] set up an additional split flow economizer before the air preheater to heat the CO2 from low temperature recuperator (LTR) and had accomplished 5MWe fossil-based S-CO2 recompression and reheat integral test facility design. Bai et al. [19] provided a novel S-CO2 intercooled recompression cycle with additional medium-temperature recuperator and an anabranch applied to a coal-fired power plant, which could achieve 49.5% net LHV efficiency with 29.6Mpa/650°C. Shelton et al. [20] constructed S-CO2 recompression cycle with an oxy-coal circulating fluidized bed (CFB) and CCS, which could realize a nearly constant temperature heat source through heating the recycled flue gas and a fraction of CO2 from the MC exit. The efficiency increment of the S-CO2 cycle plant configured with reheat and intercooling could achieve 2% compared to steam Rankine cycle power. Pratt and Whitney Rocketdyne [21] developed Zero Emission Power and Steam (ZEPS) plant which adopted a pressurized fluidized bed combustor (PFBC) with combined cycle that modified S-CO2 cycle was used as the topping cycle and steam cycle was used as the bottoming cycle. The ZEPS plant efficiency could increase by 9.4% compared with oxy-combustion atmospheric boiler. Thimsen et al. [22] designed an inverted tower coal-fired S-CO2 heater that applied to a 750MWe recompression S-CO2 power cycle with 700°C turbine inlet temperature. A second cascading S-CO2 cycle was employed as the bottoming cycle to cool the combustion products from 530°C to 370°C.CFB boiler with relatively uniform, low heat flux and combustion temperature, and wide fuel flexibility as well as low pollutant emissions can be better coupled with S-CO2 cycle compared to pulverized coal (PC) boiler [14, 23]. Combination of CFB boiler and S-CO2 power cycle is one of the effective means for the coal-dominated energy structure in China to improve energy conversion efficiency and reduce pollutant emissions at their source. The gross system performance requires further analysis and optimization. This study establishes 300MW coal-fired power system based on recompression S-CO2 cycle and single reheat integrated with CFB boiler. Secondary split flow extracted from high-pressure side of the cycle is adopted to accommodate narrow temperature variation through the boiler caused by the necessarily high extent of recuperated heat. A series of parameters sensitivity analysis have been carried out, including two stages split ratio, terminal temperature difference, turbine inlet pressure/temperature, and reheat pressure/temperature as well as compressor inlet pressure/temperature.


## 2. System Configuration and Model

### 2.1. System Configuration

The overall system layout based on modified recompression S-CO2 cycle and single reheat integrated with CFB boiler and the corresponding T-s diagram are shown in Figures 1 and 2. Several different configurations have been put forward, including simple recuperated cycle, recompression cycle, partial cooling cycle, and pre-expansion cycle. However, recompression cycle is considered as a promising alternative with high performance and simple compositions [1]. The recompression cycle effectively alleviates pinch-point problem through adjusting flow rate to compensate specific heat difference and better match temperature variation between cold and hot side fluid in the LTR. Besides, single reheat, a common method used in steam Rankine cycle, can further increase plant efficiency. An additional high pressure CO2 split flow extracted from LTR outlet to the economizer (ECO) can not only utilize flue gas heat but also increase high temperature recuperator (HTR) effectiveness, which is a valid method employed by aforementioned studies.Figure 1
Schematic diagram of recompression S-CO2 cycle with single reheat.Figure 2
T-s diagram of recompression S-CO2 Brayton cycle with single reheat.As Figure1 shows, there exist two split flow locations in the system. Firstly, a portion of S-CO2 exiting from LTR hot side is cooled in the precooler (PC), compressed by the MC and preheated in the LTR sequentially. The remaining flow is directly compressed by the recompressor (RC) and mixes with outlet fluid of LTR cold side. The mixture is divided into two branches again. One branch of S-CO2 exiting from LTR cold side is diverted into the ECO to recover relatively high temperature flue gas heat and another branch is further preheated in the HTR. Two branches of fluid finally converge and are further heated to the desired temperature through the cooling wall (CW) and superheater (SH) of the CFB boiler sequentially. S-CO2 with high pressure and temperature expands through the high pressure turbine (HPT) and is reheated in the low temperature reheater (LRH) and the high temperature reheater (HRH). S-CO2 with moderate pressure expands through the low pressure turbine (LPT) and then passes through the HTR, LTR, and PC to the lowest temperature and pressure.


### 2.2. Mathematical Model

The thermodynamic model for the S-CO2 power system has been established based on mass and energy balance. S-CO2 properties are inquired from REFPROP database, which is developed by the National Institute of Standards and Technology (NIST) [24] based on Span and Wagner equation of state [25]. Thermal parameters of different states in the system are calculated through iteration. In addition, CFB boiler heat balance and efficiency are obtained by preliminary thermal calculation [26].Several assumptions need to be considered in this study:(1) The system operates under steady-state conditions.(2) Heat losses in pipelines and each component are neglected.(3) The temperature and pressure of mixing flows as well as respective branch flows are set to the identical value in order to reduce irreversible loss. The outlet states of LTR cold side and RC are equal. Similarly, the outlet states of HTR cold side and ECO are same.(4) Pressure drops in each component are assumed to be constant with the minimum and maximum pressure variations. The CFB boiler and PC pressure drops are set to 0.7Mpa and 0.05Mpa, respectively. The cold side and hot side pressure drops of LTR and HTR are set to 0.15Mpa and 0.1Mpa separately.Two concepts of the split ratio are defined. The first split ratio (SR1) is defined as the ratio of RC mass flow to the total mass flow and the second split ratio (SR2) is defined as the ratio of ECO mass flow to the total mass flow, both of which are given by (1)SR1=1-h9-h10h3-h2(2)SR2=1-h8-h9h4-h3The compression and expansion in the MC, RC, HPT, and LPT are non-isentropic process. Work consumption of MC and RC and work output of HPT and LPT are expressed as(3)WMC=m1-SR1·h2s-h1ηMC=m1-SR1·h2-h1(4)WRC=m·SR1h3s-h10ηRC=m·SR1h3-h10(5)WHPT=m·h5-h6s·ηHPT=m·h5-h6(6)WLPT=m·h7-h8s·ηLPT=m·h7-h8The temperature difference and effectiveness are frequently used for recuperator model. However, the terminal temperature difference, defined as the achievable minimum temperature at the end of recuperators, is a preference for calculation [27]. The terminal temperature differences of LTR and HTR are set to 8°C, which is a reasonably accomplishable value for current technical equipment. The smaller terminal temperature difference can improve heat transfer capacity, but cause the nonlinear increase of recuperator volumes and capital costs. The temperature relations in the LTR and HTR are defined as(7)t2+Δt≤t10≤t9(8)t3+Δt≤t9≤t8The energy balance equations for the LTR and HTR are expressed as(9)QLTR=m1-SR1·h3-h2=m·h9-h10(10)QHTR=m1-SR2·h4-h3=m·h8-h9Heat absorption in the CFB is expressed as(11)QCFB=mSR2·h5-h3+1-SR2·h5-h4+h7-h6Heat rejection in the PC is expressed as(12)QPC=m1-SR1·h10-h1Thermal efficiency and net efficiency are defined as(13)ηth=WLPT+WHPT-WMC-WRCQCFB·100%(14)ηnet=WLPT+WHPT-WMC-WRC·ηG·100%mcoal·Qnet,ar=ηth·ηG·ηCFBInitial parameters of recompression S-CO2 cycle with CFB, specific compositions of coal, and desulfurizer are listed in Tables 1 and 2.Table 1
Initial parameters.
Parameter Symbol Unit Value Electric power output W e WM 300 MC inlet pressure P 1 Mpa 7.6 MC inlet temperature t 1 °C 32 HPT inlet pressure P 5 Mpa 25 HPT inlet temperature t 5 °C 600 LPT inlet pressure P 7 Mpa 14 LPT inlet temperature t 7 °C 600 Terminal temperature difference Δt °C 8 MC and RC isentropic efficiency η M C, ηRC % 90[16] HPT and LPT isentropic efficiency η H P T, ηLPT % 93[16] Generator efficiency η G % 98.5 Exhaust temperature t p y °C 110 Environment temperature t 0 °C 20Table 2
Compositions of coal and desulfurizer.
Coal and desulfurizer Compositions Unit Value Ultimate analysis of bituminous coal(As-received) Carbon % 62.96 Hydrogen % 4.13 Oxygen % 6.73 Nitrogen % 1.46 Sulfur % 1.22 Moisture % 10.00 Ash % 13.50 Heat value (LHV) Q n e t , a r MJ/kg 24.72 Limestone Calcium carbonate % 95 Moisture % 0.2 Impurities % 4.8


### 2.3. Validation of Thermodynamic Model

The thermodynamic model is validated by literature data [9]. MC inlet pressure of 7.38Mpa and compressor isentropic efficiency of 89% are selected. Other input parameters are identical to Table 1. As Figure 3 shows, the relative errors are below 3%, which are primarily caused by recuperator model. Terminal temperature difference of 8°C corresponds to nearly 95% effectiveness of LTR; however effectiveness of HTR is higher than 95%, leading to larger thermal efficiency.Figure 3
Validation of thermodynamic model by Turchi’s study.


## 2.1. System Configuration

The overall system layout based on modified recompression S-CO2 cycle and single reheat integrated with CFB boiler and the corresponding T-s diagram are shown in Figures 1 and 2. Several different configurations have been put forward, including simple recuperated cycle, recompression cycle, partial cooling cycle, and pre-expansion cycle. However, recompression cycle is considered as a promising alternative with high performance and simple compositions [1]. The recompression cycle effectively alleviates pinch-point problem through adjusting flow rate to compensate specific heat difference and better match temperature variation between cold and hot side fluid in the LTR. Besides, single reheat, a common method used in steam Rankine cycle, can further increase plant efficiency. An additional high pressure CO2 split flow extracted from LTR outlet to the economizer (ECO) can not only utilize flue gas heat but also increase high temperature recuperator (HTR) effectiveness, which is a valid method employed by aforementioned studies.Figure 1
Schematic diagram of recompression S-CO2 cycle with single reheat.Figure 2
T-s diagram of recompression S-CO2 Brayton cycle with single reheat.As Figure1 shows, there exist two split flow locations in the system. Firstly, a portion of S-CO2 exiting from LTR hot side is cooled in the precooler (PC), compressed by the MC and preheated in the LTR sequentially. The remaining flow is directly compressed by the recompressor (RC) and mixes with outlet fluid of LTR cold side. The mixture is divided into two branches again. One branch of S-CO2 exiting from LTR cold side is diverted into the ECO to recover relatively high temperature flue gas heat and another branch is further preheated in the HTR. Two branches of fluid finally converge and are further heated to the desired temperature through the cooling wall (CW) and superheater (SH) of the CFB boiler sequentially. S-CO2 with high pressure and temperature expands through the high pressure turbine (HPT) and is reheated in the low temperature reheater (LRH) and the high temperature reheater (HRH). S-CO2 with moderate pressure expands through the low pressure turbine (LPT) and then passes through the HTR, LTR, and PC to the lowest temperature and pressure.


## 2.2. Mathematical Model

The thermodynamic model for the S-CO2 power system has been established based on mass and energy balance. S-CO2 properties are inquired from REFPROP database, which is developed by the National Institute of Standards and Technology (NIST) [24] based on Span and Wagner equation of state [25]. Thermal parameters of different states in the system are calculated through iteration. In addition, CFB boiler heat balance and efficiency are obtained by preliminary thermal calculation [26].Several assumptions need to be considered in this study:(1) The system operates under steady-state conditions.(2) Heat losses in pipelines and each component are neglected.(3) The temperature and pressure of mixing flows as well as respective branch flows are set to the identical value in order to reduce irreversible loss. The outlet states of LTR cold side and RC are equal. Similarly, the outlet states of HTR cold side and ECO are same.(4) Pressure drops in each component are assumed to be constant with the minimum and maximum pressure variations. The CFB boiler and PC pressure drops are set to 0.7Mpa and 0.05Mpa, respectively. The cold side and hot side pressure drops of LTR and HTR are set to 0.15Mpa and 0.1Mpa separately.Two concepts of the split ratio are defined. The first split ratio (SR1) is defined as the ratio of RC mass flow to the total mass flow and the second split ratio (SR2) is defined as the ratio of ECO mass flow to the total mass flow, both of which are given by (1)SR1=1-h9-h10h3-h2(2)SR2=1-h8-h9h4-h3The compression and expansion in the MC, RC, HPT, and LPT are non-isentropic process. Work consumption of MC and RC and work output of HPT and LPT are expressed as(3)WMC=m1-SR1·h2s-h1ηMC=m1-SR1·h2-h1(4)WRC=m·SR1h3s-h10ηRC=m·SR1h3-h10(5)WHPT=m·h5-h6s·ηHPT=m·h5-h6(6)WLPT=m·h7-h8s·ηLPT=m·h7-h8The temperature difference and effectiveness are frequently used for recuperator model. However, the terminal temperature difference, defined as the achievable minimum temperature at the end of recuperators, is a preference for calculation [27]. The terminal temperature differences of LTR and HTR are set to 8°C, which is a reasonably accomplishable value for current technical equipment. The smaller terminal temperature difference can improve heat transfer capacity, but cause the nonlinear increase of recuperator volumes and capital costs. The temperature relations in the LTR and HTR are defined as(7)t2+Δt≤t10≤t9(8)t3+Δt≤t9≤t8The energy balance equations for the LTR and HTR are expressed as(9)QLTR=m1-SR1·h3-h2=m·h9-h10(10)QHTR=m1-SR2·h4-h3=m·h8-h9Heat absorption in the CFB is expressed as(11)QCFB=mSR2·h5-h3+1-SR2·h5-h4+h7-h6Heat rejection in the PC is expressed as(12)QPC=m1-SR1·h10-h1Thermal efficiency and net efficiency are defined as(13)ηth=WLPT+WHPT-WMC-WRCQCFB·100%(14)ηnet=WLPT+WHPT-WMC-WRC·ηG·100%mcoal·Qnet,ar=ηth·ηG·ηCFBInitial parameters of recompression S-CO2 cycle with CFB, specific compositions of coal, and desulfurizer are listed in Tables 1 and 2.Table 1
Initial parameters.
Parameter Symbol Unit Value Electric power output W e WM 300 MC inlet pressure P 1 Mpa 7.6 MC inlet temperature t 1 °C 32 HPT inlet pressure P 5 Mpa 25 HPT inlet temperature t 5 °C 600 LPT inlet pressure P 7 Mpa 14 LPT inlet temperature t 7 °C 600 Terminal temperature difference Δt °C 8 MC and RC isentropic efficiency η M C, ηRC % 90[16] HPT and LPT isentropic efficiency η H P T, ηLPT % 93[16] Generator efficiency η G % 98.5 Exhaust temperature t p y °C 110 Environment temperature t 0 °C 20Table 2
Compositions of coal and desulfurizer.
Coal and desulfurizer Compositions Unit Value Ultimate analysis of bituminous coal(As-received) Carbon % 62.96 Hydrogen % 4.13 Oxygen % 6.73 Nitrogen % 1.46 Sulfur % 1.22 Moisture % 10.00 Ash % 13.50 Heat value (LHV) Q n e t , a r MJ/kg 24.72 Limestone Calcium carbonate % 95 Moisture % 0.2 Impurities % 4.8


## 2.3. Validation of Thermodynamic Model

The thermodynamic model is validated by literature data [9]. MC inlet pressure of 7.38Mpa and compressor isentropic efficiency of 89% are selected. Other input parameters are identical to Table 1. As Figure 3 shows, the relative errors are below 3%, which are primarily caused by recuperator model. Terminal temperature difference of 8°C corresponds to nearly 95% effectiveness of LTR; however effectiveness of HTR is higher than 95%, leading to larger thermal efficiency.Figure 3
Validation of thermodynamic model by Turchi’s study.


## 3. Results and Discussion

The influences of critical operating parameters on system performance have been investigated comprehensively based on cycle thermodynamics model and CFB thermal balance.


### 3.1. Split Ratio to the RC (SR1)

Figure4 presents effects of SR1 on cycle efficiency at different terminal temperature differences. SR1 is a key manipulated variable influencing the thermal efficiency of the S-CO2 cycle, which has optimal values under given working conditions. Specific heat of S-CO2 varies dramatically with the pressure and temperature, especially near the critical point, and therefore the terminal temperature difference will appear at the cold or hot end of the LTR as SR1 changes. At first, with the increase of SR1, less amount of S-CO2 passes through the PC and MC, resulting in work consumption decrease in the MC and increase in the RC; accordingly, the total work consumption increases. In addition, the outlet temperature of the cold side fluid in HTR continues to rise, leading to a reduction in boiler heat absorption. The extent of decrease of boiler heat absorption is greater than the increase of compressor work consumption, which constantly improves the cycle efficiency until LTR reaches the temperature difference restriction at the hot end. In such a condition, the minimum temperature differences are achieved at both ends of LTR. LTR realizes an excellent temperature matching in which the negative impact of specific heat difference falls to zero and thermal efficiency reaches the maximum. Then, continuing to raise SR1 leads to the sharp decline of LTR effectiveness and thermal efficiency as a result. The later analyses are based on optimal SR1 values under different operating conditions.Figure 4
Effects of SR1 on cycle efficiency at different terminal temperature differences.Figure4 also indicates impacts of different terminal temperature differences on thermal efficiency. The terminal temperature difference represents recuperators heat transfer capability, smaller temperature difference gets better heat transfer capacity and higher cycle efficiency, but it will need greater volumes and higher cost. In addition, larger heat transfer areas increase pressure drops in recuperators, which decrease efficiency conversely. The relevant study indicates that minimum temperature difference lower than 4°C is not economical [28].Figure5 illustrates effects of HPT inlet pressure on optimal SR1. The optimal SR1 declines in the approximately linear proportion to HPT inlet pressure. The same mass flow in recuperator of simple recuperated cycle causes larger heat addition while bypassing the LTR of recompression cycle leads to higher average heat absorption temperature and thermal efficiency improvement. As Figure 5 presents, average specific heat differences between high-pressure and low-pressure side fluids are gradually narrowing with increasing HPT inlet pressure and a greater proportion of S-CO2 is permitted to access to the PC and MC; thereby optimal values of SR1 decrease.Figure 5
Effects of HPT inlet pressure on optimal SR1.


### 3.2. Split Ratio to the ECO (SR2)

Figure6 shows effects of SR2 on boiler efficiency, thermal efficiency, and net efficiency. It demonstrates that the split flow exiting from high-pressure side of the LTR can effectively recover moderate flue gas heat and improve boiler efficiency. Simultaneously, cycle thermal efficiency maintains constant and net efficiency increases accordingly. Boiler heat losses and corresponding efficiency are preliminarily calculated according to semiempirical formulas and historical operation data of steam CFB boiler. Suppose the minimum temperature approach of countercurrent LRH located above the ECO is 55°C and hot air is preheated to 300°C, exhaust gas temperature gradually decreases and boiler efficiency rises with the increase of SR2. Furthermore, thermal efficiency maintains constant because heat recovered by the HTR does not change with a low proportion of S-CO2 entering into the ECO. When SR2 is equal to 0.076, the exhaust temperature falls to 110°C, and thus boiler efficiency is improved to 94%; the net efficiency can reach about 47.2%.Figure 6
Effects of SR2 on boiler efficiency, thermal efficiency, and net efficiency.


### 3.3. HPT Inlet Parameters

Figure7 shows effects of HPT inlet pressure on cycle efficiency at different HPT inlet temperature. The cycle efficiency is improved with the increase of HPT inlet pressure, but the rate of increase gradually slows down and eventually reaches a stable state. At first, the increment of specific work output of the HPT is greater than total specific work consumption of the MC and RC as HPT inlet pressure increases, 1Mpa increase in HPT inlet pressure leads to about 0.5% improvement in cycle efficiency. The increment rate of specific net work continues to fall with HPT inlet pressure rising. In these conditions, the benefit of efficiency improvement is less obvious and materials pressure-resistance requirement becomes stricter, leading to larger material cost.Figure 7
Effects of HPT inlet pressure on cycle efficiency at different HPT inlet temperature.It can also be observed from Figure7 that HPT inlet temperature has a positive influence on system performance. The degree of efficiency improvement caused by HPT inlet temperature is more noticeable under higher HPT inlet pressure. The cycle efficiency is improved by nearly 0.35% with HPT inlet temperature increasing by 20°C under HPT inlet pressure of 20Mpa. The cycle efficiency is improved by nearly 0.6% with HPT inlet pressure of 35Mpa under the same HPT temperature interval.


### 3.4. Reheat Stages and Parameters

Reheat is an effective approach for steam Rankine cycle efficiency improvement by increasing average heat absorption temperature. However, S-CO2 Brayton cycle with lower pressure ratio has different results. As Figure 8 presents, single reheat can improve cycle efficiency, especially under higher HPT inlet pressure. The thermal efficiency is improved by 1.5% with HPT inlet pressure of 25Mpa. However, the efficiency of double reheat is enhanced by only 0.2% under the same condition. Larger reheat stages are undesirable due to more complex configurations and additional capital cost, which may offset the benefit of efficiency increment.Figure 8
Effects of reheat stages on cycle efficiency at different HPT inlet pressure.Figures9 and 10 show effects of LPT inlet pressure on cycle efficiency at different HPT inlet pressure and LPT inlet temperature. As these figures reveal, LPT inlet pressure has optimal values corresponding to different HPT inlet pressure and LPT inlet temperature. Firstly, the tendency of the change of HPT work output is opposite to the variation of LPT work output with increasing reheat pressure. HPT work output decreases and conversely LPT work output increases, which has an optimal reheating pressure. The corresponding optimal reheat pressures with different HPT inlet pressure of 20Mpa, 25Mpa, and 30Mpa are 13Mpa, 14.5Mpa, and 16Mpa respectively, which are slightly higher than the average of minimum and maximum pressures (12.6Mpa, 14.1Mpa, and 15.5Mpa). Figure 10 indicates that the efficiency is improved by nearly 0.5% with the reheat temperature increment of 20°C. Moreover, optimal reheat pressures are similarly affected by reheat temperature. Higher reheat temperature corresponds to lager reheat pressure. Pressure ratios between HPT and LPT need to be redistributed due to various work output under different reheat temperature.Figure 9
Effects of LPT inlet pressure on cycle efficiency at different HPT inlet pressure.Figure 10
Effects of LPT inlet pressure on cycle efficiency at different LPT inlet temperature.Figure11 summarizes optimal reheat pressure values under different HPT inlet pressure and LPT inlet temperature, which can be used as a reference for the conceptual design of a power plant. These values are still affected by the pressure drop in reheater and detailed hydraulic calculation needs to be further carried out.Figure 11
Optimal reheat pressure under different HPT inlet pressure and LPT inlet temperature.


### 3.5. MC Inlet Parameters

Figure12 shows effects of MC inlet pressure on cycle efficiency at different MC inlet temperature. MC inlet pressure similarity has optimal values, which correspond to the pseudocritical pressure of various MC inlet temperature. In addition, optimal MC inlet pressure increases and maximum cycle efficiency decreases with different MC inlet temperature. The specific reason is that turbine work output and compressor work consumption together decrease with increasing MC inlet pressure at first, but work consumption variation, especially in the MC, is greater due to the sharp decline of compressibility factor in the near-critical region, showing the incompressibility property of liquid phase, finally leading to continual rising of cycle efficiency. The benefit of lower compression work consumption near critical point gradually decreases with further increasing MC inlet pressure and temperature. Moreover, the total compressor work consumption increases with MC inlet temperature, resulting in a significant decrease of thermal efficiency especially under optimal MC inlet pressure.Figure 12
Effects of MC inlet pressure on cycle efficiency at different MC inlet temperature.


## 3.1. Split Ratio to the RC (SR1)

Figure4 presents effects of SR1 on cycle efficiency at different terminal temperature differences. SR1 is a key manipulated variable influencing the thermal efficiency of the S-CO2 cycle, which has optimal values under given working conditions. Specific heat of S-CO2 varies dramatically with the pressure and temperature, especially near the critical point, and therefore the terminal temperature difference will appear at the cold or hot end of the LTR as SR1 changes. At first, with the increase of SR1, less amount of S-CO2 passes through the PC and MC, resulting in work consumption decrease in the MC and increase in the RC; accordingly, the total work consumption increases. In addition, the outlet temperature of the cold side fluid in HTR continues to rise, leading to a reduction in boiler heat absorption. The extent of decrease of boiler heat absorption is greater than the increase of compressor work consumption, which constantly improves the cycle efficiency until LTR reaches the temperature difference restriction at the hot end. In such a condition, the minimum temperature differences are achieved at both ends of LTR. LTR realizes an excellent temperature matching in which the negative impact of specific heat difference falls to zero and thermal efficiency reaches the maximum. Then, continuing to raise SR1 leads to the sharp decline of LTR effectiveness and thermal efficiency as a result. The later analyses are based on optimal SR1 values under different operating conditions.Figure 4
Effects of SR1 on cycle efficiency at different terminal temperature differences.Figure4 also indicates impacts of different terminal temperature differences on thermal efficiency. The terminal temperature difference represents recuperators heat transfer capability, smaller temperature difference gets better heat transfer capacity and higher cycle efficiency, but it will need greater volumes and higher cost. In addition, larger heat transfer areas increase pressure drops in recuperators, which decrease efficiency conversely. The relevant study indicates that minimum temperature difference lower than 4°C is not economical [28].Figure5 illustrates effects of HPT inlet pressure on optimal SR1. The optimal SR1 declines in the approximately linear proportion to HPT inlet pressure. The same mass flow in recuperator of simple recuperated cycle causes larger heat addition while bypassing the LTR of recompression cycle leads to higher average heat absorption temperature and thermal efficiency improvement. As Figure 5 presents, average specific heat differences between high-pressure and low-pressure side fluids are gradually narrowing with increasing HPT inlet pressure and a greater proportion of S-CO2 is permitted to access to the PC and MC; thereby optimal values of SR1 decrease.Figure 5
Effects of HPT inlet pressure on optimal SR1.


## 3.2. Split Ratio to the ECO (SR2)

Figure6 shows effects of SR2 on boiler efficiency, thermal efficiency, and net efficiency. It demonstrates that the split flow exiting from high-pressure side of the LTR can effectively recover moderate flue gas heat and improve boiler efficiency. Simultaneously, cycle thermal efficiency maintains constant and net efficiency increases accordingly. Boiler heat losses and corresponding efficiency are preliminarily calculated according to semiempirical formulas and historical operation data of steam CFB boiler. Suppose the minimum temperature approach of countercurrent LRH located above the ECO is 55°C and hot air is preheated to 300°C, exhaust gas temperature gradually decreases and boiler efficiency rises with the increase of SR2. Furthermore, thermal efficiency maintains constant because heat recovered by the HTR does not change with a low proportion of S-CO2 entering into the ECO. When SR2 is equal to 0.076, the exhaust temperature falls to 110°C, and thus boiler efficiency is improved to 94%; the net efficiency can reach about 47.2%.Figure 6
Effects of SR2 on boiler efficiency, thermal efficiency, and net efficiency.


## 3.3. HPT Inlet Parameters

Figure7 shows effects of HPT inlet pressure on cycle efficiency at different HPT inlet temperature. The cycle efficiency is improved with the increase of HPT inlet pressure, but the rate of increase gradually slows down and eventually reaches a stable state. At first, the increment of specific work output of the HPT is greater than total specific work consumption of the MC and RC as HPT inlet pressure increases, 1Mpa increase in HPT inlet pressure leads to about 0.5% improvement in cycle efficiency. The increment rate of specific net work continues to fall with HPT inlet pressure rising. In these conditions, the benefit of efficiency improvement is less obvious and materials pressure-resistance requirement becomes stricter, leading to larger material cost.Figure 7
Effects of HPT inlet pressure on cycle efficiency at different HPT inlet temperature.It can also be observed from Figure7 that HPT inlet temperature has a positive influence on system performance. The degree of efficiency improvement caused by HPT inlet temperature is more noticeable under higher HPT inlet pressure. The cycle efficiency is improved by nearly 0.35% with HPT inlet temperature increasing by 20°C under HPT inlet pressure of 20Mpa. The cycle efficiency is improved by nearly 0.6% with HPT inlet pressure of 35Mpa under the same HPT temperature interval.


## 3.4. Reheat Stages and Parameters

Reheat is an effective approach for steam Rankine cycle efficiency improvement by increasing average heat absorption temperature. However, S-CO2 Brayton cycle with lower pressure ratio has different results. As Figure 8 presents, single reheat can improve cycle efficiency, especially under higher HPT inlet pressure. The thermal efficiency is improved by 1.5% with HPT inlet pressure of 25Mpa. However, the efficiency of double reheat is enhanced by only 0.2% under the same condition. Larger reheat stages are undesirable due to more complex configurations and additional capital cost, which may offset the benefit of efficiency increment.Figure 8
Effects of reheat stages on cycle efficiency at different HPT inlet pressure.Figures9 and 10 show effects of LPT inlet pressure on cycle efficiency at different HPT inlet pressure and LPT inlet temperature. As these figures reveal, LPT inlet pressure has optimal values corresponding to different HPT inlet pressure and LPT inlet temperature. Firstly, the tendency of the change of HPT work output is opposite to the variation of LPT work output with increasing reheat pressure. HPT work output decreases and conversely LPT work output increases, which has an optimal reheating pressure. The corresponding optimal reheat pressures with different HPT inlet pressure of 20Mpa, 25Mpa, and 30Mpa are 13Mpa, 14.5Mpa, and 16Mpa respectively, which are slightly higher than the average of minimum and maximum pressures (12.6Mpa, 14.1Mpa, and 15.5Mpa). Figure 10 indicates that the efficiency is improved by nearly 0.5% with the reheat temperature increment of 20°C. Moreover, optimal reheat pressures are similarly affected by reheat temperature. Higher reheat temperature corresponds to lager reheat pressure. Pressure ratios between HPT and LPT need to be redistributed due to various work output under different reheat temperature.Figure 9
Effects of LPT inlet pressure on cycle efficiency at different HPT inlet pressure.Figure 10
Effects of LPT inlet pressure on cycle efficiency at different LPT inlet temperature.Figure11 summarizes optimal reheat pressure values under different HPT inlet pressure and LPT inlet temperature, which can be used as a reference for the conceptual design of a power plant. These values are still affected by the pressure drop in reheater and detailed hydraulic calculation needs to be further carried out.Figure 11
Optimal reheat pressure under different HPT inlet pressure and LPT inlet temperature.


## 3.5. MC Inlet Parameters

Figure12 shows effects of MC inlet pressure on cycle efficiency at different MC inlet temperature. MC inlet pressure similarity has optimal values, which correspond to the pseudocritical pressure of various MC inlet temperature. In addition, optimal MC inlet pressure increases and maximum cycle efficiency decreases with different MC inlet temperature. The specific reason is that turbine work output and compressor work consumption together decrease with increasing MC inlet pressure at first, but work consumption variation, especially in the MC, is greater due to the sharp decline of compressibility factor in the near-critical region, showing the incompressibility property of liquid phase, finally leading to continual rising of cycle efficiency. The benefit of lower compression work consumption near critical point gradually decreases with further increasing MC inlet pressure and temperature. Moreover, the total compressor work consumption increases with MC inlet temperature, resulting in a significant decrease of thermal efficiency especially under optimal MC inlet pressure.Figure 12
Effects of MC inlet pressure on cycle efficiency at different MC inlet temperature.


## 4. Conclusions

S-CO2 recompression Brayton cycle is a promising alternative to be applied in coal-fired power generation due to special thermophysical properties in the near-critical region and high average heat absorption temperature as well as low pressure ratio, which contribute to higher efficiency and more compact turbomachinery compared to steam Rankine cycle.CFB boiler with lower and uniform combustion temperature can be better integrated with S-CO2 cycle. However, the overall system configuration needs to be further modified to match the narrow temperature range of heat source. This paper constructs recompression S-CO2 Brayton cycle with single reheat based on the CFB boiler. Additional split flow extracted from LTR cold side is adopted in order to utilize flue gas heat effectively. The net efficiency can reach 47.2% under the condition of 600°C/600°C/25Mpa.Influences of critical parameters on system performance have been investigated systematically, including RC split ratio (SR1), ECO split ratio (SR2), HPT inlet pressure and temperature, and reheat layout as well as MC inlet pressure and temperature. The results show that SR1, reheat pressure, and MC inlet pressure have optimal values, among which appropriate temperature matching is achieved between the hot and cold side of the LTR, the optimal reheat pressure is slightly higher than the average pressure and is still affected by reheat temperature, and the optimal MC inlet pressure corresponds to pseudocritical pressure of various MC inlet temperature. Smaller terminal temperature difference corresponds to higher efficiency, but the cost and pressure drops of heat exchangers need to be taken into account. Reasonable SR2 can recover moderate flue gas heat caused by narrow temperature range. Single reheat improves cycle efficiency by 1.5% with HPT inlet pressure of 25Mpa; however, double reheat for efficiency improvement is less obvious compared to steam Rankine cycle largely due to much lower pressure ratio. In addition, HPT and LPT inlet temperature both have positive influences on system performance. The cycle efficiency is improved by nearly 0.5% with HPT or LPT inlet temperature increasing by 20°C under HPT inlet pressure of 25Mpa.



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*Source: 6963292-2018-07-24.xml*