Thermodynamic analysis of the Allam cycle and its pressure sensitivity

Abstract

Keywords: Allam cycle; Efficiency; Entropy; Pressure sensitivity

Introduction

Carbon dioxide is the principle greenhouse gas responsible from global warming. Reduction its emission to atmosphere is of great importance in sustainable development.

As the major source of carbon dioxide emission is due to power plants, emission control from power plant stacks has gained enormous attention. Addition of carbon dioxide capturing units to the conventional power plants becomes

*Corresponding author. *E-mail address: duysal@gazi.edu.tr, bzuysal@gazi.edu.tr This paper was recommended for publication in revised form by Editor Muslum Arici Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

essential in addition to other filters used to minimize polluting toxic gases such as sulfur dioxide and nitric oxides as well as particulates. This brings additional cost in power generation. The additional CO2 removal systems can increase the cost of electricity by 50% to 70%. High capital investment and operating costs, high parasitic energy requirements, and additional environmental concerns over scrubbing chemicals have combined to question the sustainability of CO2 capture systems for fossil fuel power plants. Alternatives were then considered to develop economical means to mitigate carbon dioxide emission. Oxycombustion is one of these alternatives which is based on using oxygen instead of air in combustors. This eliminates nitric oxide emission considerably when fossil fuel is used, flue gas cleaning becomes much easier and carbon dioxide emission control becomes quite feasible. Although, air separation unit is an additional cost, the reductions in flue gas handling cost validates its usability. Oxy-combustion has been studied and applied to conventional coal-fired boilers, combined cycles, and high pressure steam-based systems [1, 2]. It is then realized that instead of using steam-based process, use of hot combustion gas at high temperatures directly in turbine eliminates the energy losses that steam-based cycles encounter due to the heat of vaporization and condensation, and improves the efficiency appreciably. Material of construction, on the other hand, limits the maximum temperature that a turbine can handle. This brings in the necessity of diluting combustion gas with carbon dioxide itself. The combustion of hydrocarbons gives carbon dioxide and water. Thus, the natural choice for dilution component

is either water or carbon dioxide. This choice affects the working fluid, i.e. either H2O rich or CO2 rich streams. Currently, CO2 seems to be widely accepted as diluent. Water can be separated from the combustion gas very easily by condensing it. The remaining component in the combustion gas is essentially carbon dioxide which can effectively be recycled to the combustor to adjust the thermal and hydrodynamic conditions to the optimum values and limit the exit temperature of the combustion gas to acceptable values for the turbine. As high pressure and high temperature improve the efficiency of a turbine, the further step to reach high overall efficiency was proposed by Allam et al. [3, 4] to operate the process with carbon dioxide at supercritical conditions. The Allam cycle is a novel system which was originally presented in Kyoto at GHGT-11 [2]. It operates the oxy-combustor at a high pressure under supercritical conditions, uses a single gas turbine, circulates carbon dioxide as the working fluid in a semiclosed-loop and utilizes low-pressure-ratio recuperated Brayton cycle. Of course, another advantage is that the Allam Cycle can run substantially water free [5, 6].

Allam Cycle Description

The basic unit operations of the Allam Cycle using natural gas fuel are shown in Figure 1. The cycle operates with a single turbine with an inlet pressure of about 300 bar and a pressure ratio of 10. Compressed gas fuel, pure oxygen provided by an Air Separation Unit (ASU), and a hot CO2 diluent recycle stream at about 300 bar are fed to the combustor.

The exhaust stream from the burner is expanded through a turbine to about 30 bar, which drops over 700° C. After the turbine, the exhaust flow is cooled in a recuperator, which transfers the heat from the hot exhaust stream to the high pressure CO2 recycling stream. This recycle stream of CO2 serves as a diluting agent in the combustion chamber so that the temperature of the exhaust gas from the combustor is lowered to an acceptable level between 1150–1200oC before its entry to the turbine. The turbine exhaust gas is further cooled close to ambient temperature and combustion water is separated. The remaining component in the turbine exhaust gas is thus essentially only carbon dioxide. The amount equivalent to stoichiometric yield from combustion is removed from the system for sequestration. The remaining part is then recompressed to a pressure of about 300 bar and sent to the recuperator to increase its temperature to about 700oC before introduced to the combustor. The net export of CO2 is about 5% of the total recycling flow, i.e. most of the process inventory is recirculated [6, 7].

Simulation

The Allam Cycle is simulated using Chemcad software in this work (Figure 2). Recently, power generation using natural gas has attracted more attention as it has lower specific CO2 emissions than coal fired power generation [8]. Therefore, methane was chosen as the fuel and its flow rate was taken as 1 kmol/s as a typical value for such a case study. The combustor was operated adiabatically at 285 bar. Methane anf oxygen feeds as well as recycling CO2 were compressed to this pressure before introduced to the combustor. For one mole of CO2 leaving the process, 27 moles of CO2 were recycled as diluent so that CO2 concentration at the combustor exit was 90 mole-% and the temperature of the combustion gases at the turbine entrance was 1170oC. The pressure at the turbine exit was 24 bar and the pressure ratio for the turbine was 8.38. The temperature at the turbine exit was 799oC. The recuparator was used to heat the O2 feed and recycling CO2 streams to 720oC before

fed to the combustor. The temperature of the combustion gas leaving the recuperator was 353oC. In order to utilize its energy, a second heat exchanger was used to produce superheated steam at 7 bar and 233oC at the rate of 175 kg/s. The superheated steam thus produced can either be used as thermal energy elsewhere or can be used in a steam turbine to produce electricity. The later case makes the Allam Cycle a semi-closed oxy-combustion combined cycle. Water condensed in the second heat exchanger is then separated at 60oC and ca 34 bar. One kmol CO2 per second was taken away as the product of the process from the vapor stream at ca 34 bar after cooled down to 55oC. The remaining part of CO2 was recycled.

Results And Discussion

Table 1 summarizes the properties of the species involved in the process, Table 2 the ambient conditions and Table 3 the overall material balance for the process. Performance Energy Balance Steady state energy balance for an open flow system with chemical reaction (combustion) is ( H + EK + EP ) m  − ( H + EK + EP ) m  in out  Energy generated  0 +Q + Ws +  = withchemical reaction 

 Energy generated  0  H m in −  H m out + Q + Ws +  = withchemical reaction  (2) For methane (M) combustion, (3)

Therefore, energy equation becomes [Hm]in – [Hm]out + Q + Ws + mM,in(–∆Hr,M) = 0

Heat generated with combustion can be evaluated using the lower heating value (LHV) of methane. −∆H r , M = −∆H ro, M = 50

It should be noted that Q is considered positive when added to the system and W is taken as positive when work is done on the system. Neglecting the changes in kinetic and potential energies between inlet and outlet of the system,

Energy generated = mM , in ( −∆H r , M ) withchemical reaction

Overall enthalpy balance for the process is summarized in Table 4. Neglecting the heat effects in the compressors and turbine, for 1 kmol/s (16.043 kg/s) methane feed rate, the energy equation can be written numerically as [–427.705 – (–13.828)] – 0.288 + Ws,net,theo + 802.3 = 0 (6) –Ws,net,theo = 388.135 MW

This result is in very good agreement with 392.17 MW obtained from the simulation made by Chemcad software (Table 5). The power requirements of the compressors used in the cycle and the power generated with the turbine are also calculated with Chemcad software. The efficiencies for the turbine and all the compressors were assumed as 95%. The results are tabulated in Table 5.

Table 4. Overall enthalpy balance for the process (Enthalpy = 0 for gaseous state at Tref = 25oC) Inlet streams

Where, S = kJ/kmol · K Cp = kJ/kmol · K R = 8.314 kJ/kmol · K For liquids going from (T1) state to (T2) state, entropy change is T ∆S = C p ln 2 T1

–413.877 Total cooling (Heat recovered from carbon dioxide output stream)

These equations were used to make necessary corrections for the entropy values taken from tables. The entropy generated can be calculated by the following expression, which can easily be obtained from the entropy balance for a flow process at steady state [11, 12];

and the entropy destroyed is given as ψdestroyed = Wrev – Wact = ToSgen

The results are summarized in Table 6. ψdestroyed = 288 MW, in fact, is not lost completely in the process, but 252 MW is used up by the compressors. The rest is due to the heat evolved in compressor and other heat losses.

Using net power generation and basing on lower heating value (LHV) of methane, the energy efficiency of the cycle can be calculated as

Exergy analysis Neglecting potential and kinetic energy terms, the flow thermomechanical exergy, or stream thermomechanical exergy, is defined as

This result agrees very well with 47% reported by Laumb et al. [9] and is close to 54.8% found by Scaccabarozzi et al. [10] employing simulation by Aspen-Plus. The second heat exchanger used after the recuperator definitely improves overall performance.

Chemical exergy of a gas stream consisting of n number of components is defined as

Thermal energy production as steam = [64.946 – (–427.35)] = 492.3 MW

Total exergy is the sum of thermomechanical and chemical exergies.

One may note that this is as important as the output power obtained from gas turbine. Second Law-Entropy Analysis Second law analysis of the Allam cycle was also made. For gases going from (P1, T1, V1) state to (P2, T2, V2) state, entropy change is given as T P = ∆S C p ln 2 − R ln 2 T1 P1

ψ =(h − h0 ) − T0 (s − s0 ) + ∑x kψ k0, ch + RTo ∑x k lnx k (17) = k 1= k 1

Table 6. Entropy balance for the process* (Tref = 25oC, Pref = 1 bar) Inlet

*Water and steam properties are taken from steam tables. Properties of other species are taken from “Yüncü, H., Ekserji Analizi, 2010 [13]”.

Chemical exergies are not needed to be considered for utilities which do not undergo any chemical change in a process. It is enough to consider thermomechanical exergies for utilities. The thermomechanical flow exergy for unit molar flow of the utilities, i.e liquid water and steam, were calculated by the following expressions as recommended by Yüncü [13, 14] and the properties are taken from thermodynamic tables;

ψdestroyed is also referred to as irreversibility rate or lost work (Wlost) and may also be shown by I. Thus, the equivalent expression of the exergy balance for work producing process can also be written as

Stream exergies for input and output streams of Allam cycle are summarized in Table 7. In the process, stream exergy should decrease. Indeed,

The exergy balance for a flow process at steady state can be written as 

One may note that the difference between the exergy flows of feed streams and products gives the ideal work produced for a reversible work-producing process. = Wideal

This shows that the process conforms to the thermodynamic rules and, furthermore, ideal work that can be produced is

Exergy destroyed calculated from the exergy balance is different from the one calculated from ψdestroyed = ToSgen. The difference is about 30%. This may be because of the difficulties and uncertainties involved in estimation of parameters used in exergy calculations. The uncertainties involved can be shown by a simple calculation. If flow exergies of utilities (cooling water and steam) are not included in the exergy balance but instead the exergy generated by the heat exchanger used to generate  T   steam from cooling water is included as  1 − 0  Q  , the  T   choice for T will have a profound effect on the final result.

Total, MW

Table 8. Flow exergies for the process-alternative Inlet streams

Total, MW

T is the temperature of the system boundary at the point of heat exchange. The process stream enters the heat exchanger at 353oC (626 K) and leaves at 60oC (333 K). If arithmetic average is taken, T would be 479.5 K. If geometric average is taken, T would be 456.6 K. If logarithmic mean is taken, T would be 464.2 K. Noting, from enthalpy balance, QHE = 67.776 – (–427.705) = 495.481 MW

and taking the arithmetic average, the exergy balance would be as follows; ψdestroyed is 335.76 MW in this case. If geometric mean is used ψdestroyed will be 351.21 MW and if logarithmic mean is used will be 345.91 MW. These differences in calculations of ψdestroyed from exergy balance leads us to the conclusion that ψdestroyed, estimated from entropy generation, seems to be more dependable. Using this value, the second law efficiency can be calculated from [11–16]

Exergy recovered Exergy destroyed = 1− (29) Exergy supplied Exergy supplied

Total, MW

Exergy supplied is,    ∑ mψ − ∑ mψ  = 848.137 − 79.839 ≅ 768.3 MW (31) out  in  287.81 0.6254 ≡ 62.54% = 768.3

The second law efficiency thus calculated is greater than 48.89% energy efficiency of the cycle as expected. This is in good agreement with similar values reported in literature [7, 16]. Sensitivity to Pressure Critical temperature and critical pressure for carbon dioxide are 31.1oC and 73.9 bar, respectively. As a whole, the Allam cycle operates in trans-critical regime. But the

c­ombustor and the turbine entrance is at supercritical region, i.e. pressure needs to be above 73.9 bar and temperature must be kept above 31.1oC. Therefore, in this work, a sensitivity analysis is also made to see the effect of pressure on power generation. The sensitivity analysis was made using Chemcad software simulation by changing the pressure at inlet of the turbine from 75 to 350 bar (Figure 3). Higher the pressure at inlet of the turbine, higher is the power generated. This is clearly shown in the figure. But, the total power requirement by the compressors of inlet streams, i.e. methane and oxygen, and recycling carbon dioxide also increases. The net power is, however, not very much affected in the range between ca 250 and 350 bar. It is recommended to run the Allam cycle with a single turbine that has an inlet pressure of approximately 300 bar and a pressure ratio of 10 [5]. The sensitivity analysis results given in Figure 3 confirm this and suggest that the optimum pressure range for operation of the system can be between ca 250 and 350 bar. Higher pressure would increase fixed capital investment as well as operating and maintenance costs very much. It should be noted that the gas turbine is the heart of the cycle and dictates tailoring the rest of the process. Commercial gas turbines run safely at temperatures as high as 1300oC. The highest inlet pressure achieved to date is around 310 bar for safe operation [3, 17]. These limits as well as the sensitivity analysis results were considered in this work to choose the pressure at turbine inlet as 285 bar and at outlet as 34 bar, and the carbon dioxide recycling rate such that the temperature at turbine outlet is 1170oC.

Conclusions

Simulation and thermodynamic analysis of the Allam Cycle were made for a typical feed rate of 1 kmol/s of methane as the fuel. Net power output was found as 388 MW. The net power cycle efficiency was determined as 49%. The second law analysis yielded entropy generation rate as 966 W/K and 288 MW exergy destroyed. The second law efficiency was 62.5%. Sensitivity analysis for power generation to pressure indicated that pressure between 250–350 bar at the turbine entrance would be suitable. Recycling rate of CO2 is very important to affect the temperature of combustion gases and 90% CO2 in reactants’ mixture is reasonable to limit the temperature at turbine entry to about 1170oC. Furthermore, addition of a second heat exchanger after the recuperator improves overall performance and total energy recovery.

Nomenclature

Heat capacity [kJ/kmol×K] Kinetic energy [kJ/kg] Potential energy [kJ/kg] Enthalpy [kJ/kg] Heat of reaction [kJ/kg] Mass flow rate, [kg/s] Heat added to the system, [kW] Gas constant, 8.314 [kJ/kmol×K] Entropy [kJ/kmol-K] Temperature [K] Work [kW]

Energy efficiency[–] Second law efficiency [–] Exergy [kJ/kmol] Chemical exergy [kJ/kmol] Thermomechanical exergy [kJ/kmol]

Data Availability Statement

No new data were created in this study. The published publication includes all graphics collected or developed during the study.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

References

1. Ahn Y, Bae SJ, Kim M, Cho SK, Baik S, Lee JI, et al. Co; 2015. [CrossRef] Review of supercritical CO2 power cycle technol- [12] Bejan A. Advanced Engineering Thermodynamics. ogy and current status of research and development. 4th Ed. New Jersey: John & Wiley; 2016. [CrossRef] Nucl Eng Techn 2015;47:647–61. [CrossRef] [13] Yüncü H. Ekserji Analizi-İkinci Kanun Verimi ve
2. Lockwood T. A compararitive review of next-gen- Termoekonomi. Ankara: ODTÜ Basım İşliği; 2010. eration carbon capture technologies for coal-fired [14] Yüncü H. Termodinamik. Ankara: ODTÜ Basım power plant. Energy Procedia 2017;114:2658–70. İşliği; 2016 [CrossRef] [15] Hasan A, Dincer I. Assessment of an Integrated
3. Allam RJ, Palmer MR, Brown Jr GW, Fetvedt J, Gasification Combined Cycle using waste tires for Freed D, Nomoto H, et al. High Efficiency and hydrogen and fresh water production. International low cost of electricity generation from fossil fuels Journal of Hydrogen Energy 2019;44:19730e19741, while eliminating atmospheric emissions includ- [CrossRef] ing carbon dioxide, Energy Procedia (GHGT-11) [16] Hervás GR, Petrakopoulou F. Exergoeconomic anal- 2013;37:1135–49. [CrossRef] ysis of the allam cycle. Energy Fuels 2019;33:7561–8.
4. Allam RJ, Palmer M, Brown Jr GW. System and [CrossRef] method for high efficiency power generation using [17] Zaryankin A, Rogalev A, Osipov S, Kindra V. a carbon dioxide circulating working fluid. USA Supercritical carbon dioxide gas turbines for high- Patent 03 December 2013;8:596, 075 B2. power generation. AIP Conference Proceedings
5. Allam RJ, Fetvedt JE, Forrest BA, Freed DA. The 2018;2047:020026. [CrossRef] Oxy-Fuel, Supercritical CO2 Allam Cycle: New

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