# The Allam Cycle: A Review of Numerical Modeling Approaches

## Abstract

**:**

_{2}power plants have seen a growing interest in a wide range of applications (e.g., nuclear, waste heat recovery, solar concentrating plants). The Allam Cycle, also known as the Allam-Fetvedt or NET Power cycle, seems to be one of the most interesting direct-fired sCO

_{2}cycles. It is a semi-closed loop, high-pressure, low-pressure ratio, recuperated, direct-fired with oxy-combustion, trans-critical Brayton cycle. Numerical simulations play a key role in the study of this novel cycle. For this reason, the aim of this review is to offer the reader a wide array of modeling solutions, emphasizing the ones most frequently employed and endeavoring to provide guidance on which choices seem to be deemed most appropriate. Furthermore, the review also focuses on the system’s performance and on the opportunities related to the integration of the Allam cycle with a series of processes, e.g., cold energy storage, LNG regasification, biomass or coal gasification, and ammonia production.

## 1. Introduction

_{2}(sCO

_{2}) power cycle has exponentially increased in the last years [1], mainly in externally fired applications such as nuclear, waste heat recovery or solar concentrating plants [1,2,3].

_{2}gas turbines have been considered also for internal combustion plants: the Allam cycle, also known as Allam-Fetvedt or NET Power cycle, has been conceived by NET Power Inc. within this context. It is a semi-closed loop, high-pressure, low-pressure ratio, recuperated, direct-fired, trans-critical Brayton cycle in which the working fluid is mainly composed of carbon dioxide with fuel and combustion-derived impurities as H

_{2}O, inert N

_{2}, Ar, and O

_{2}. In fact, the heat adduction is guaranteed by an oxy-fuel combustion chamber in which the fuel is burnt with oxygen in an ambient mainly based on carbon dioxide in supercritical conditions.

_{2}is used for the turbine cooling, while the majority is directed straight into the combustor and a minor mass flow is mixed with the oxygen, coming from the ASU, in all cases after passing within the regenerator. The flow exiting from the combustor is mainly composed of carbon dioxide, water and some impurities. It is expanded in the turbine and comes to the regenerator, heating the above-mentioned fluxes. Then, the exhaust gases, which are at about 30 bar, pass within the condenser to separate the water from the carbon dioxide mass flow and, finally, the excess of CO

_{2}is captured through the purification and compression unit and the main flow, composed of pure CO

_{2}, returns to the compressor.

_{4}is 25 ppmvd or less.

_{2}-CO

_{2}oxidizer percentages.

## 2. Cycle Definition and Thermodynamic Models

#### 2.1. Natural Gas-Based Allam Cycle

_{2}recirculation feed scenarios. In the first case, the net plant efficiency is 44.5%, while the latter is 55.1%, for a net power of 262.4 and 324.8 MW, respectively.

_{O2}. Results of simulations highlighted that the net electric efficiency of the base case is 54.58%. The authors carried out a sensitivity analysis to various characteristic parameters and a cycle optimization, identifying a net electric efficiency of 54.80% for the maximum efficiency cycle with a considerable difference in the operating conditions. They estimated that the optimal turbine inlet pressure range is between 260 and 300 bar and that the optimal turbine inlet temperature is between 1100 and 1200 °C. They also stated that the cycle efficiency drastically drops below 240 bar.

_{O2}. Results of simulations highlighted that the net electric efficiency is 53.9%, while the exergetic efficiency is equal to 50.1% and the LCOE is equal to 122 €/MWh.

_{O2}(The authors studied three different cases: a base case, and a low and high-efficiency case. The results of simulations gave a cycle efficiency between 47.9% and 57.2%, with a value for the base case of 53.4%, while the exergetic efficiency was equal to 51.3%. The authors highlighted that the Allam cycle appears to have higher efficiency with respect to other oxy-combustion cycles and that recompression could have a certain potential as an improvement of the cycle.

_{2}in supercritical conditions. The turbine, designed by Toshiba, has been modeled through seven cooled gas turbine stages. The cooled gas turbine sub-model integrated into Thermoflex is based on El-Masri’s GASCAN code [31]. The regenerator has been modeled using three two-stream heat exchangers arranged in series. The modeling approach of the ASU had a resulting specific power consumption of 1326 kJ/kg

_{O2}. Simulation results showed a net electric efficiency of 49% for the base case, while the efficiency of the optimized case reached 50.4%.

_{2}gas turbine with optimal thermodynamic parameters of the cycle. The model has been built using Aspen ONE as software, including the model of the air separation unit, determined as the cryogenic high-pressure two-stage. Several approaches have been considered to estimate the CO

_{2}thermodynamic properties: two equations of state (the Peng-Robinson EoS and the Redlich-Kwong EoS) and the NIST REFPROP database. The authors chose to use the NIST-REFPROP database to simulate the Allam cycle because the highest accuracy was highlighted in their comparison with reference data. The open-loop internal cooling of the high-temperature turbine has been considered: the coolant flow fraction has been determined following Wilcock et al. [33] and the cooling losses have been estimated. Results of thermodynamic optimization showed that the highest net efficiency is equal to 56.5% for a turbine inlet temperature and pressure of 1083 °C and 300 bar, a coolant temperature of 200 °C and a turbine outlet pressure of 30 bar. Results of environmental characteristics analysis showed that the specific amount of CO

_{2}emitted to the ambient is 0.0038 kg/kWh, while the total specific investment cost is 1307.5 $/kW. This value is cheaper with respect the costs of CCPP with CCS (2424.3 $/kW).

_{O2}. The ASU was described as a double-column distillation consisting of a main air compressor, an air cooler, an adsorption unit, a booster compressor, a main heat exchanger, two air turbines, an oxygen pump and a distillation unit. Results of simplified simulations showed a net cycle efficiency of 54.4% [35], which can be optimized to 59.7% [36]. In the latest study [39] the authors focused their attention also on the importance of estimating the real-fluid properties: the assumption of ideal gas constant properties may lead to a 25–60% overestimation of the power absorbed by the CO

_{2}compressor, while the turbine power prediction can be overestimated by 3–4%. The authors chose to use a correction factor to consider this aspect.

_{O2}, while for the CPU 139.5 kJ/kg is necessary, both according to [26]. The authors implemented an EoS into the model in which the properties of water and steam are calculated using IAPWS_IF97 formulations [41], CO

_{2}is modeled as a real gas using the correlations of NIST REFPROP and the small quantities of O

_{2}, N

_{2}and Ar are considered as ideal gases. Regarding the base case, the efficiency of the Net Power cycle is 52.36%, while the Graz cycle efficiency is 52.19%, considering CO

_{2}purification in both cases. The authors highlighted a slight difference with respect to the results of Scaccabarozzi et al. [10], which is considered by them as a reference in the absence of experimental data: for them this is due to different isentropic and mechanical efficiencies, which lead to a 0.2% points difference, while the remaining 1.2% points are mainly caused by the different EoS models. The authors also conducted a parametric analysis using the IPSEpro-PSOptimize-module in order to optimize the cycle and, consequently, obtain a higher net efficiency. Regarding the Allam cycle, the optimized net efficiency is 52.72%, while the resulting optimized Graz cycle efficiency is 53.5%. In both cases, the CO

_{2}compression and purification and the O

_{2}generation and compression are considered.

_{O2}, which is equivalent to 1259 kJ/kg

_{O2}. The combustor is modeled as an RGibbs reactor, while the turbine is modeled considering the three-stage turbine cooling method described by Scaccabarozzi et al. [10]. The recuperator is made up of three sections to avoid temperature cross-over effects. The authors considered two different ASU layouts, comparing the case in which the ASU pumps liquid oxygen instead of compressing it. The net thermal efficiency passes from 59.4% (with an O

_{2}compressor) to 64.3% (with an O

_{2}pump) for a net electric power output of 284 and 305.4 MW, respectively. The authors studied also the effects of the ASU operating parameters on the Allam power cycle and compared the carbon footprint (in gCO

_{2}/kWh) of the cycle with natural gas combined cycles.

#### 2.2. Coal-Based Allam Cycle

_{2}system and of the steam Rankine cycle are, respectively, 52.68% and 36.6%. The net efficiency of the optimized coal-based cycle is 42.68%.

_{coal}, while for the ASU is 245 kWh/t

_{O2}. The resulting performance of the base case is a net efficiency of 38.21% for a net power output of 534.89 MW. Results of a parametric study allowed us to increase the performance, up to 38.87%, raising the turbine inlet temperature to 1200 °C and lowering the turbine outlet pressure to 30 bar.

#### 2.3. Model Approaches and Results Comparison

_{2}Brayton cycles. Their analysis concluded that the Span-Wagner EoS [51] exhibited the highest accuracy across the subcritical, supercritical and critical regions, in the temperature range of 300–900 K and the pressure range of 7–20 MPa. Similarly, Rogalev et al. [32] compared two EoS and the NIST REFPROP database against experimental data [52], concluding that the database, which is based on the aforementioned Span-Wagner EoS, presented the minimum average deviation (0.03%) in CO

_{2}specific volume. The other equations of state showed more significant deviations. Wimmer et al. [40] conducted a comparison between their simulation results and those obtained by Scaccabarozzi et al. [10]. Their analysis revealed that a 1.2-point difference in net efficiency could be attributed to variations in the embedded equation of state. They emphasized that different EoS models led to differences in specific enthalpies, particularly at the turbine inlet and outlet.

_{2}, if compared with Soave–Redlich–Kwong (SRK) [43] and Redlich–Kwong, while, over 1000 K, Peng–Robinson and SRK are indistinguishable. At the same time, for sCO

_{2}combustion mixtures, in all the analyzed regimes, the Soave–Redlich–Kwong and Peng–Robinson EoS predict the density by 0.7% and 1.17% with respect to NIST. The authors concluded that the Soave–Redlich–Kwong is the most appropriate EoS for sCO

_{2}mixtures.

_{O2}, as highlighted in Table 2. Moreover, with respect to the ASU, whether the role of thermal integration is considered or not can result in significant differences in the overall evaluation of the system’s performance.

## 3. Modifications and Integration to the Allam Cycle

_{4}and 8.8% H

_{2}) chemical power with a thermal power input of 222 MW renewable electricity and 78.6 MW biomass.

_{O2}. Regarding the classical Allam cycle, the results of the proposed model are coherent with the literature: a net electrical efficiency of 53.06% for a net power output of 407.66 MW. The design performance of the dual-pressure Allam cycle is a net power output of 65.31 MW and a refrigeration capacity of 19.76 MW. The performance indexes of the cogeneration system reported an exergetic efficiency equal to 51.62% for an electricity efficiency of 70.22%. After a parametric analysis and optimization, the optimized dual-pressure Allam cycle presented an electric efficiency of 70.56% and an exergetic efficiency of 51.88%. The specific work was 68.75% higher than the classical case.

_{2}liquefaction. A set of regenerative heat exchangers are introduced for turbine exhaust recovery. The thermodynamic model has been implemented in MATLAB and the properties of pure and mixture CO

_{2}and H

_{2}O have been calculated using the REFPROP database (v.8). The power consumption for oxygen production by ASU is set to 0.42 kWh/kg

_{O2}. The results of this study showed that the output power efficiency and the equivalent net efficiency are 2.15% and 2.96% higher than those of the Allam cycle under the same conditions, respectively: the equivalent net efficiency is 48.05% with respect to the value of 45.09% in both cases, considering a TIT of 900 °C.

_{2}intensities and system costs with respect to the baseline Allam cycle.

_{2}power cycle based on the Allam cycle, with few modifications. The syngas is compressed and preheated in a cooler and then mixed with CO

_{2}exiting the cycle’s HTR, reaching up to 732 °C, passing through another stage of the syngas cooler. Steady state simulations were carried out using Aspen Plus, considering the Peng-Robinson equation of state for the gasification, the ASU, syngas cleaning and CPU sections, and the Lee-Kessler-Plöcker equation of state of the sCO

_{2}power cycle. The capital costs of the plant components have been estimated using the National Energy Technology Laboratory (NETL)’s quality guidelines. The authors compared with reference IGCC plants a baseline case and an improved case. Their results highlighted that the net plant efficiency (on HHV basis) is 37.7% and 40.6 for the baseline and the improved case, respectively. The carbon captured is 97.6% in the first case and 99.4% in the optimized one.

_{2}recycling ratio has a peak because in that case it not only reduces the temperature of turbine blades but leads to a further improvement of the efficiency. The maximum cycle efficiency is 53.19% for a CO

_{2}recycling ratio of 1.158 and a turbine outlet pressure of 24.3 bar.

_{2}emissions associated with traditional ammonia production. The integrated process is studied both in the case of grid-connected and off-grid applications. The integrated process can be divided into the following sections: sCO

_{2}cycle, ASU, steam methane reformer (SMR), HB process, and Pressure swing adsorption (PSA), all modeled using Aspen Plus v11. Regarding the Allam cycle, the authors followed the modeling approach proposed by Mitchell et al. [62]. The authors carried out a termo-economic analysis, obtaining results that the CO

_{2}emission reduction is 68% and 96%, for on-grid and off-grid cases, respectively, when compared to the conventional HB process. From an economic perspective, the study ensures that the process remains economically competitive.

## 4. Simulation of the Combustion Process

_{2}and only a few studies have discussed this topic.

_{2}.

_{2}-CO chemistry as the basis of the kinetics mechanism, based on Ó Conaire et al. [69]. The authors compared the results of their simulations with a limited set of experimental data and they highlighted that this mechanism gave good results.

_{2}[71], while the skeletal mechanism proposed by Smoke was used for fuel blends containing methane in case of adoption of the reactor network model. The Eddy Dissipation Concept (EDC) was used for the turbulent-chemistry interactions. Results of 2D and 3D CFD simulations highlighted that there are no significant temperature or pressure variations in the reaction primary zone and that the estimated CO levels are greater than 100 ppm at 0.99 equivalence ratios, while for an equivalence ratio of 0.9, there is a significant reduction.

_{2}combustion applications. After this evaluation, the authors identified a 23-species gas phase mechanism derived from the Aramco 2.0 mechanism as the more appropriate.

_{2}dilutions and equivalence ratios. The results of their study proved the importance of the development of a mechanism specific to oxy-fuel combustion in direct-fired sCO

_{2}power cycles, focusing also on the role of CH

_{3}O

_{2}chemistry in high-pressure methane combustion. The authors declared that quantitative analysis has proven a superior ability to model ignition delay time against existing chemical kinetic mechanisms.

_{2}2.0 Mech [73]).

## 5. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ASU | Air Separation Unit |

CCPP | Combined Cycle Power Plant |

CCS | Carbon Capture and Storage |

CES | Cold Energy Storage |

CPU | Compression and Purification Unit |

CTEG | Coal to Ethylene Glycol process |

EoS | Equation of State |

HB | Haber-Bosch |

HHV | Higher heating value |

HX | Heat exchanger |

IGCC | Integrated Gasification Combined Cycle |

LHV | Lower Heating Value |

LOX | Liquid Oxygen |

LNG | liquified Natural Gas |

NIST | National Institute of Standards and Technology |

opt | optimized |

ORC | Organic Rankine Cycle |

P | Power |

PEM | Proton Exchange Membrane |

ppm | parts per million |

PR | Pressure Ratio |

RANS | Reynolds averaged Navier Stokes |

sCO_{2} | Supercritical carbon dioxide |

SNG | Synthetic Natural Gas |

TIP | Turbine Inlet Pressure |

TIT | Turbine Inlet Temperature |

TOP | Turbine Outlet Pressure |

TOT | Turbine Outlet Temperature |

Subscripts | |

El | Electrical |

## References

- Xu, J.; Liu, C.; Sun, E.; Xie, J.; Li, M.; Yang, Y.; Liu, J. Perspective of S−CO
_{2}power cycles. Energy**2019**, 186, 115831. [Google Scholar] [CrossRef] - Ahn, Y.; Bae, S.J.; Kim, M.; Cho, S.K.; Baik, S.; Lee, J.I.; Cha, J.E. Review of supercritical CO
_{2}power cycle technology and current status of research and development. Nucl. Eng. Technol.**2015**, 47, 647–661. [Google Scholar] [CrossRef] - Crespi, F.; Gavagnin, G.; Sanchez, D.; Martinez, G.S. Supercritical carbon dioxide cycles for power generation: A review. Appl. Energy
**2017**, 195, 152–183. [Google Scholar] [CrossRef] - Allam, R.J.; Palmer, M.R.; Brown, G.W., Jr.; Fetvedt, J.; Freed, D.; Nomoto, H.; Okita, N.; Jones, C., Jr. High Efficiency and low cost of electricity generation from fossil fuels while eliminating atmospheric emissions including carbon dioxide. Energy Procedia
**2013**, 37, 1135–1149. [Google Scholar] [CrossRef] - Allam, R.J.; Fetvedt, J.E.; Forrest, B.A.; Freed, D.A. The Oxy-Fuel, Supercritical CO
_{2}Allam Cycle: New Cycle Developments to Produce Even Lower-Cost Electricity from Fossil Fuels Without Atmospheric Emissions. In Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, Dusseldorf, Germany, 16–20 June 2014. [Google Scholar] [CrossRef] - Allam, R.J.; Palmer, M.; Brown, G.W. System and Method for High Efficiency Power Generation Using a Carbon Dioxide Circulating Working Fluid. U.S. Patent, 8,596,075 B2, 3 December 2013. [Google Scholar]
- Allam, R.J.; White, V.; Miller, E.J. Purification of Carbon Dioxide. U.S. Patent 8,580,206 B2, 12 November 2013. [Google Scholar]
- Allam, R.; Martin, S.; Forrest, B.; Fetvedt, J.; Lu, X.; Freed, D.; Brown, G.W., Jr.; Sasaki, T.; Itoh, M.; Manning, J. Demonstration of the Allam Cycle: An update on the development status of a high efficiency supercritical carbon dioxide power process employing full carbon capture. Energy Procedia
**2017**, 114, 5948–5966. [Google Scholar] [CrossRef] - Chowdhury, A.; Bugarin, L.; Badhan, A.; Choudhuri, A.; Love, N. Thermodynamic analysis of a directly heated oxyfuelsupercritical power system. Appl. Energy
**2016**, 179, 261–271. [Google Scholar] [CrossRef] - Scaccabarozzi, R.; Gatti, M.; Martelli, E. Thermodynamic Analysis and Numerical Optimization of the NET Power Oxy-Combustion Cycle. Appl. Energy
**2016**, 178, 505–526. [Google Scholar] [CrossRef] - NET Power Website. First Utility Scale Project. Available online: https://netpower.com/first-utility-scale-project/ (accessed on 25 September 2023).
- Nomoto, H.; Itoh, M.; Brown, W.; Fetvedt, J.; Sato, I. Cycle and Turbine Development for the Supercritical Carbon Dioxide Allam Cycle. In Proceedings of the International Conference on Power Engineering, Riga, Latvia, 11–13 May 2015. [Google Scholar]
- Iwai, Y.; Itoh, M.; Morisawa, Y.; Suzuki, S.; Cusano, D.; Harris, M. Development Approach to the Combustor of Gas Turbine for Oxy-fuel, Supercritical CO
_{2}Cycle. In Proceedings of the ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, Volume 9: Oil and Gas Applications; Supercritical CO_{2}Power Cycles, Wind Energy, Montreal, QC, Canada, 15–19 June 2015. ASME GT2015-43160. [Google Scholar] - Suzuki, S.; Iwai, Y.; Itoh, M.; Morisawa, Y.; Jain, P.; Kobayashi, Y. High Pressure Combustion Test of Gas Turbine Combustor for 50MWth Supercritical CO
_{2}Demonstration Power Plant on Allam Cycle. In Proceedings of the International Gas Turbine Congress 2019, Tokyo, Japan, 17–22 November 2019. [Google Scholar] - NET Power Website. Second Quarter 2023 Results Report. Available online: https://netpower.com/press-releases/net-power-reports-second-quarter-2023-results-and-provides-business-update/ (accessed on 25 September 2023).
- Moore, J.J.; Neveu, J.; Bensmiller, J.; Replogle, C.; Lin, J.; Fetvedt, J.; Cormier, I.; Kapat, J.; Fernandez, E.; Paniagua, G. Development of a 300 MWe Utility Scale Oxy-Fuel sCO
_{2}Turbine. In Proceedings of the ASME Turbo Expo Paper no. GT2023-103328, Boston, MA, USA, 26–30 June 2023. [Google Scholar] [CrossRef] - Scopus Document Search. Available online: https://www.scopus.com/ (accessed on 11 September 2023).
- Web of Science Core Collection. Available online: https://www.webofscience.com/ (accessed on 11 September 2023).
- Chan, W.; Morosuk, T.; Li, X.; Li, H. Allam cycle: Review of research and development. Energy Convers. Manag.
**2023**, 294, 117607. [Google Scholar] [CrossRef] - Lee, B.L.; Kesler, M.G. A generalized thermodynamic correlation based on three-parameter corresponding states. AIChE J.
**1975**, 21, 510–527. [Google Scholar] [CrossRef] - Plocker, U.; Knapp, H. Calculation of High-Pressure Vapor-Liquid Equilibria from a Corresponding-States Correlation with Emphasis on Asymmetric Mixtures. Ind. Eng. Chem. Process Des. Dev
**1978**, 17, 324–332. [Google Scholar] [CrossRef] - Malcolm, C. NIST-JANAF thermochemical tables. J. Phys. Chem. Ref. Data Mononograph
**1998**, 1, 1951. [Google Scholar] - El-Masri, M.A. On thermodynamics of gas-turbine cycles: Part 2—A model for expansion in cooled turbines. J. Eng. Gas Turbines Power
**1986**, 108, 151–159. [Google Scholar] [CrossRef] - Peng, D.Y.; Robinson, D.B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam.
**1976**, 15, 59–64. [Google Scholar] [CrossRef] - Gonzalo, R.H.; Petrakopoulou, F. Exergoeconomic Analysis of the Allam Cycle. Energy Fuels
**2019**, 33, 7561–7568. [Google Scholar] [CrossRef] - IEAGHG. Oxy-Combustion Turbine Power Plants, World Energy Outlook, 2015/05; OECED/International Energy Agency: Paris, France, 2016. [Google Scholar] [CrossRef]
- Penkum, M.; Tsatsaronis, G. Exergy Analysis of the Allam Cycle. In Proceedings of the 5th International Symposium–Supercritical CO
_{2}Power Cycles, San Antonio, TX, USA, 28–31 March 2016. [Google Scholar] - Chou, V.H.; Kearney, D.; Turner, M.J.; Woods, M.C.; Zoelle, A.; Black, J.B. Quality Guidelines for Energy System Studies: Process Modeling Design Parameters; Technical Report, DOE/NETL-341/051314; U.S. Department of Energy: Washington, DC, USA, 2014.
- Colleoni, L.; Sindoni, A.; Ravelli, S. Comprehensive Thermodynamic Evaluation of the Natural Gas-Fired Allam Cycle at Full Load. Energies
**2023**, 16, 2597. [Google Scholar] [CrossRef] - Lemmon, E.W.; Bell, I.H.; Huber, M.L.; McLinden, M.O. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 10.0; National Institute of Standards and Technology, Standard Reference Data Program: Gaithersburg, Germany, 2018. [CrossRef]
- El-Masri, M.A. GASCAN―An interactive code for thermal analysis of gas turbine systems. J. Eng. Gas Turbines Power
**1988**, 110, 201–209. [Google Scholar] [CrossRef] - Rogalev, A.; Grigoriev, E.; Kindra, V.; Rogalev, N. Thermodynamic optimization and equipment development for a high efficient fossil fuel power plant with zero emissions. J. Clean. Prod.
**2019**, 236, 117592. [Google Scholar] [CrossRef] - Wilcock, R.C.; Young, J.B.; Horlock, J.H. The effect of turbine blade cooling on the cycle efficiency of gas turbine power cycles. J. Eng. Gas Turbines Power
**2005**, 127, 109–120. [Google Scholar] [CrossRef] - Chan, W.; Lei, X.; Chang, F.; Li, H. Thermodynamic analysis and optimization of Allam cycle with a reheating configuration. Energy Convers. Manag.
**2020**, 224, 113382. [Google Scholar] [CrossRef] - Haseli, Y. Analytical formulation of the performance of the Allam power cycle. In Proceedings of the 2020 ASME Turbo Expo, ASME Paper: GT2020-15070. Virtual, Online, 21–25 September 2020. [Google Scholar] [CrossRef]
- Haseli, Y.; Sifat, N.S. Performance modeling of Allam cycle integrated with a cryogenic air separation process. Comput. Chem. Eng.
**2021**, 148, 107263. [Google Scholar] [CrossRef] - Haseli, Y. Approximate relations for optimum turbine operating parameters in Allam cycle. J. Eng. Gas Turbines Power
**2021**, 143, 064501. [Google Scholar] [CrossRef] - Haseli, Y. Efficiency maximization of Allam cycle at a given combustion temperature. In Proceedings of the 2021 ASME Turbo Expo, Virtual, Online, 7–11 June 2020. ASME Paper: GT2021-59962. [Google Scholar] [CrossRef]
- Haseli, Y.; Naterer, G.F. Optimization of turbine pressures in a net-zero supercritical Allam cycle. J. Clean. Prod.
**2023**, 400, 136639. [Google Scholar] [CrossRef] - Wimmer, K.; Sanz, W. Optimization and comparison of the two promising oxy-combustion cycles NET Power cycle and Graz Cycle. Int. J. Greenh. Gas Control
**2020**, 99, 103055. [Google Scholar] [CrossRef] - Wagner, W.; Kruse, A. Properties of Water and Steam; Springer-Verlag: Berlin/Heidelberg, Germany, 1998. [Google Scholar]
- Fernandes, D.; Wang, S.; Xu, Q.; Buss, R.; Chen, D. Process and carbon footprint analyses of the Allam cycle power plant integrated with an air separation unit. Clean Technol.
**2019**, 1, 22. [Google Scholar] [CrossRef] - Soave, G. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci.
**1972**, 27, 1197–1203. [Google Scholar] [CrossRef] - Scaccabarozzi, R.; Gatti, M.; Martelli, E. Thermodynamic Optimization and Part-load Analysis of the NET Power Cycle. Energy Procedia
**2017**, 114, 551–560. [Google Scholar] [CrossRef] - Martelli, E.; Amaldi, E. PGS-COM: A hybrid method for constrained non-smooth black-box optimization problems. Comput. Chem. Eng.
**2014**, 63, 108–139. [Google Scholar] [CrossRef] - Zaryab, S.A.; Scaccabarozzi, R.; Martelli, E. Advanced part-load control strategies for the Allam cycle. Appl. Therm. Eng.
**2020**, 168, 114822. [Google Scholar] [CrossRef] - Luo, J.; Emelogu, O.; Morosuk, T.; Tsatsaronis, G. Exergy-based investigation of a coal-fired allam cycle. Energy
**2021**, 218, 119471. [Google Scholar] [CrossRef] - Xin, T.; Xu, C.; Yang, Y.; Kindra, V.; Rogalev, A. A new process splitting analytical method for the coal-based Allam cycle: Thermodynamic assessment and process integration. Energy
**2023**, 267, 126634. [Google Scholar] [CrossRef] - Zhao, Y.; Wang, B.; Chi, J.; Xiao, J. Parametric study of a direct-fired supercritical carbon dioxide power cycle coupled to coal gasification process. Energy Convers. Manag.
**2018**, 156, 733–745. [Google Scholar] [CrossRef] - Zhao, Q.; Mecheri, M.; Neveux, T.; Privat, R.; Jaubert, J.-N. 2016 Thermodynamic Model Investigation for Supercritical CO
_{2}Brayton Cycle for Coal-Fired Power Plant Application. In Proceedings of the Fifth International Supercritical CO_{2}Power Cycles Symposium, San Antonio, TX, USA, 29–31 March 2016. Paper No. 93. [Google Scholar] - Span, R.; Wagner, W. A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa. J. Phys. Chem. Ref. Data
**1996**, 25, 1509–1558. [Google Scholar] [CrossRef] - Vargaftik, N.B. Handbook of Thermophysical Properties of Gases and Liquids; Nauka: Moscow, Russia, 1972; p. 721. [Google Scholar]
- Manikantachari, K.R.V.; Martin, S.; Bobren-Diaz, J.O.; Vasu, S. Thermal and Transport Properties for the Simulation of Direct-Fired sCO
_{2}Combustor. ASME. J. Eng. Gas Turbines Power**2017**, 139, 121505. [Google Scholar] [CrossRef] - Rogalev, A.; Rogalev, N.; Kindra, V.; Zlyvko, O.; Vegera, A. A Study of Low-Potential Heat Utilization Methods for Oxy-Fuel Combustion Power Cycles. Energies
**2021**, 14, 3364. [Google Scholar] [CrossRef] - Fernandes, D.; Haque, M.E.; Palanki, S.; Rios, S.G.; Chen, D. DMC controller design for an integrated Allam cycle and air separation plant. Comput. Chem. Eng.
**2020**, 141, 107019. [Google Scholar] [CrossRef] - Fernandes, D.; Wang, S.; Xu, Q.; Chen, D. Dynamic simulations of the Allam cycle power plant integrated with an air separation unit. Int. J. Chem. Eng.
**2019**, 2019, 6035856. [Google Scholar] [CrossRef] - Xie, M.; Chen, L.; Wu, K.; Liu, Z.; Lin, J.; Jiang, C.; Xie, S.; Zhao, Y. A novel peak shaving approach to improving load flexibility of the Allam cycle by integrating cold energy storage. J. Clean. Prod.
**2023**, 386, 135769. [Google Scholar] [CrossRef] - Candelaresi, D.; Spazzafumo, G. Production of Substitute Natural Gas Integrated with Allam Cycle for Power Generation. Energies
**2023**, 16, 2162. [Google Scholar] [CrossRef] - Li, B.; Wang, S.; Qiao, J.; Wang, B.; Song, L. Thermodynamic analysis and optimization of a dual-pressure Allam cycle integrated with the regasification of liquefied natural gas. Energy Convers. Manag.
**2021**, 246, 114660. [Google Scholar] [CrossRef] - Zhu, Z.; Chen, Y.; Wu, J.; Zhang, S.; Zheng, S. A modified Allam cycle without compressors realizing efficient power generation with peak load shifting and CO
_{2}capture. Energy**2019**, 174, 478–487. [Google Scholar] [CrossRef] - Shamsi, M.; Moghaddas, S.; Torabi, O.; Bakhshehshi, S.; Bonyadi, M. Design and analysis of a novel structure for green syngas and power cogeneration based on PEM electrolyzer and Allam cycle. Int. J. Hydrogen Energy
**2023**, 48, 29034–29047. [Google Scholar] [CrossRef] - Mitchell, C.; Avagyan, V.; Chalmers, H.; Lucquiaud, M. An initial assessment of the value of Allam Cycle power plants with liquid oxygen storage in future GB electricity system. Int. J. Greenh. Gas Control
**2019**, 87, 1–18. [Google Scholar] [CrossRef] - Weiland, N.T.; White, C.W. Techno-economic analysis of an integrated gasification direct-fired supercritical CO
_{2}power cycle. Fuel**2018**, 212, 613–625. [Google Scholar] [CrossRef] - Tian, Y.; Feng, H.; Zhang, Y.; Li, Q.; Liu, D. New insight into Allam cycle combined with coal gasification in supercritical water. Energy Convers. Manag.
**2023**, 292, 117432. [Google Scholar] [CrossRef] - Dahl, S.; Fredenslund, A.; Rasmussen, P. The MHV2 Model: A UNIFAC-Based Equation of State Model for Prediction of Gas Solubility and Vapor-Liquof State Model for Prediction of Gas Solubility and Vapor-Liquid Equilibria at Low and High Pressures. Ind. Eng. Chem. Res.
**1991**, 30, 1936–1945. [Google Scholar] [CrossRef] - Zhou, Y.; Xu, Z.; Zhang, J.; Xing, J.; Jia, J.; Cui, P. Development and techno-economic evaluation of coal to ethylene glycol process and Allam power cycle and carbon capture and storage and integration process. Fuel
**2023**, 332, 126121. [Google Scholar] [CrossRef] - Byun, M.; Lim, D.; Lee, B.; Kim, A.; Lee, I.; Brigljević, B.; Lim, H. Economically feasible decarbonization of the Haber-Bosch process through supercritical CO
_{2}Allam cycle integration. Appl. Energy**2022**, 307, 118183. [Google Scholar] [CrossRef] - Chan, W.; Li, H.; Li, X.; Chang, F.; Wang, L.; Feng, Z. Exergoeconomic analysis and optimization of the Allam cycle with liquefied natural gas cold exergy utilization. Energy Convers. Manag.
**2021**, 235, 113972. [Google Scholar] [CrossRef] - Ó’Conaire, M.; Curran, H.J.; Simmie, J.M.; Pitz, W.J.; Westbrook, C.K. A comprehensive modelling study of hydrogen oxidation. Int. J. Chem. Kinet.
**2004**, 36, 603–622. [Google Scholar] [CrossRef] - Abdul-Sater, H.; Lenertz, J.; Bonilha, C.; Lu, X.; Fetvedt, J. A CFD simulation of coal syngas oxy-combustion in a high-pressure supercritical CO
_{2}environment. In Turbo Expo: Power for Land, Sea, and Air; ASME Paper: GT2017-63821; American Society of Mechanical Engineers: New York, NY, USA, 2017; Volume 50848. [Google Scholar] [CrossRef] - Davis, S.G.; Ameya, V.J.; Hai, W.; Fokion, E. An optimized kinetic model of H
_{2}/CO combustion. 1. Proc. Combust. Inst.**2005**, 30, 1283–1292. [Google Scholar] [CrossRef] - Manikantachari, K.R.V.; Vesely, L.; Martin, S.; Bobren-Diaz, J.O.; Vasu, S. Reduced Chemical Kinetic Mechanisms for Oxy/Methane Supercritical CO
_{2}Combustor Simulations. ASME J. Energy Resour. Technol.**2018**, 140, 092202. [Google Scholar] [CrossRef] - Harman-Thomas, J.M.; Pourkashanian, M.; Hughes, K.J. Chemical kinetic mechanism for combustion in supercritical carbon dioxide. In Proceedings of the 4th Eurpean SCO
_{2}Conference Energy Systems, Online, 22–26 March 2021; Volume 255. [Google Scholar] - Harman-Thomas, J.M.; Hughes, K.J.; Pourkashanian, M. The development of a chemical kinetic mechanism for combustion in supercritical carbon dioxide. Energy
**2022**, 255, 124490. [Google Scholar] [CrossRef] - Burke, U.; Metcalfe, W.K.; Burke, S.M.; Heufer, K.A.; Dagaut, P.; Curran, H.J. A detailed chemical kinetic modeling, ignition delay time and jet-stirred reactor study of methanol oxidation. Combust. Flame
**2016**, 165, 125–136. [Google Scholar] [CrossRef] - Burke, S.M.; Burke, U.; Mc Donagh, R.; Mathieu, O.; Osorio, I.; Keesee, C.; Morones, A.; Petersen, E.L.; Wang, W.; DeVerter, T.A.; et al. An experimental and modeling study of propene oxidation. Part 2: Ignition delay time and flame speed measurements. Combust. Flame
**2015**, 162, 296–314. [Google Scholar] [CrossRef] - Burke, S.M.; Metcalfe, O.; Herbinet, F.; Battin-Leclerc, F.M.; Haas, J.; Santner, F.L.; Dryer, H.J.; Curran, H.J. An experimental and modeling study of propene oxidation. Part 1: Speciation measurements in jet-stirred and flow reactors. Combust. Flame
**2014**, 161, 2765–2784. [Google Scholar] [CrossRef] - Kéromnès, A.W.K.; Metcalfe, K.A.; Heufer, N.; Donohoe, A.K.; Das, C.-J.; Sung, J.; Herzler, C.; Naumann, P.; Griebel, O.; Mathieu, M.C.; et al. An experimental and detailed chemical kinetic modeling study of hydrogen and syngas mixture oxidation at elevated pressures. Combust. Flame
**2013**, 160, 995–1011. [Google Scholar] [CrossRef] - Hashemi, H.; Christensen, J.M.; Glarborg, P. High-pressure pyrolysis and oxidation of DME and DME/CH4. Combust. Flame
**2019**, 205, 80–92. [Google Scholar] [CrossRef] - Hashemi, H.; Christensen, J.M.; Gersen, S.; Levinsky, H.; Klippenstein, S.J.; Glarborg, P. High-pressure oxidation of methane. Combust. Flame
**2016**, 172, 349–364. [Google Scholar] [CrossRef] - Smith, G.P.; Golden, D.M.; Frenklach, M.; Moriarty, N.W.; Eiteneer, B.; Goldenberg, M.; Bowman, C.T.; Hanson, R.K.; Song, S.; Gardiner, W.C.; et al. GRI Mechanism 3.0. Available online: http://combustion.berkeley.edu/gri-mech/version30/text30.html (accessed on 15 September 2023).
- Wang, H.; You, X.; Joshi, A.V.; Davis, S.G.; Laskin, A.; Egolfopoulos, F.; Law, C. USC Mech Version II. High-Temperature Combustion Reaction Model of H
_{2}/CO/C1-C4 Compounds. 2007. Available online: https://ignis.usc.edu:80/Mechanisms/USC-Mech%20II/USC_Mech%20II.htm (accessed on 25 September 2023). - Harman-Thomas, J.M.; Kashif, T.A.; Hughes, K.J.; Pourkashanian, M.; Farooq, A. Experimental and modelling study of syngas combustion in CO
_{2}bath gas. Fuel**2023**, 342, 127865. [Google Scholar] [CrossRef]

Description | Value | Ref. |
---|---|---|

Compressor inlet pressure and temperature Turbine inlet pressure | 30 bar, 20 °C | [4] |

Combustor inlet pressure and temperature | 300 bar, 750 °C | [4] |

Turbine inlet pressure and temperature | 300 bar, 1150 °C | [4] |

Natural gas target net efficiency | 58.9% | [5] |

Coal target net efficiency | 51.44% | [5] |

Reheated net efficiency | 57.44% | [5] |

Numerical Analysis | Software | Equation of State/Corrections for sCO_{2} Properties | Other Main Characteristics | Ref. |
---|---|---|---|---|

Thermodynamic analysis | Aspen HYSYS | Lee-Kesler-Plocker | Combustion process: specific heat calculated using the NIST database coupled with Shomate equation | [9] |

Thermodynamic analysis and cycle optimization | Aspen Plus v8.4 | Peng-Robinson | Regenerator modeled as two multi-flow heat exchangers Turbine model: Modified El-Masri model ASU specific electric consumption at 100 bar: 1365 kJ/kg _{O2}. | [10] |

Exergoeconomic analysis | EBSILON Professional 13 | Peng-Robinson | ASU and recuperator modeled as black-box ASU specific electric consumption: 1447 kJ/kg _{O2}.Economic analysis: total revenue requirement method | [25] |

Exergetic analysis | Aspen Plus | Peng-Robinson; Lee-Kesler-Plöcker for CO_{2} recompression modeling | Chemical exergy model: Szargut ASU, CO _{2} purification and cooling tower modeled as black-boxASU Specific consumption: 900 kJ/kg _{O2}CO _{2} Purification: 180 kJ/kg_{CO2} | [27] |

Thermodynamic analysis | Thermoflex 30 | NIST REFPROP | Turbine modeled as seven cooled gas turbines stages. The cooled gas turbine sub-model is based on El-Masri’s code (GASCAN). Regenerator modeled using 3 HX arranged in series. | [29] |

Thermodynamic analysis and optimization | Aspen ONE | NIST REFPROP | ASU: power consumption; 900 kW/(kg/s), Oxygen purity: 91.25% open-loop internal cooling of HT turbines | [32] |

Thermodynamic analysis and optimization of reheated cycle | Aspen Plus v11 | - | El-Masri’s continuous expansion model for the turbine Regenerator modeled as two multi-flow HX in series Combustor simulated with the RGibbs block ASU specific energy consumption: 245 kWh/t _{O2} | [34] |

Thermodynamic analysis | Engineering Equation Solver | Ideal gas EoS | negligible pressure drops, adiabatic behavior of all components, no turbine cooling | [35,36] |

Thermodynamic analysis | Engineering Equation Solver | Ideal gas EoS with correction factors | - | [39] |

Thermodynamic analysis | IPSEpro v7 | Water/steam: IAPWS_IF97 CO_{2}: NIST REFPROPN _{2}, O_{2}, Ar: ideal gas | ASU specific work: 1049 kJ/kg_{O2}, CPU specific work: 139.5 kJ/kg | [40] |

Thermodynamic and carbon footprint analysis | Aspen Plus v10 | Allam cycle: Soave–Redlich–Kwong ASU: Peng-Robinson | ASU number of stages: DSTWU method using the Winn–Underwood–Gilliland method. ASU specific consumption: 1259 kJ/kg _{O2}.Combustor: RGibbs reactor Turbine: three-stage turbine cooling method Recuperator: three sections | [42] |

Part load thermodynamic analysis | Aspen Plus | See [10] | ASU specific energy consumption fixed in the range 40–100% load Regenerator: nine temperature zones Simplified off design curve of the expander: constant non-dimensional mass flow rate | [44] |

Part load thermodynamic analysis | Aspen Plus | See [10] | off-design performance maps of compressors, pumps and turbine. | [46] |

Exergetic analysis | Ebsilon Professional | LibHuGas library LibCO _{2} library for CO_{2} | ASU and Acid gradd removal modeled as black box Cooled turbine: The used method simplified the El-Masri’s model Recuperator: modeled using a series of heat exchangers | [47] |

Process splitting analytical model | Aspen Plus | n.a. | Combustor: Rgibbs block Compression unit and turbine: compr blocks Recuperator: MHeatX block | [48] |

Thermodynamic analysis and parametric study | Aspen Plus | CO_{2}: Peng-RobinsonWater/steam: STEAMNBS property | Combustor: RGibbs block Compression unit: compr block Turbine: El-Masri’s model Recuperator splitted in two sections Coal consumption: 65.93 kg/s (1400 MW) | [49] |

Ref. | Main Thermodynamic Parameters | Main Performance Parameters |
---|---|---|

[9] | Combustor inlet temperatures (K): O_{2}: 89, CH_{4}: 108, CO_{2}: 525 (gaseous rec.), 214 (liquid rec.)TIT (K): 1417 (liquid CO _{2} rec.); 1456 (gaseous CO_{2} rec.) | Net electric Power (MW): 262.4 (liquid CO_{2} rec.); 324.8 (gaseous CO_{2} rec.)Net electric Efficiency (%): 44.5 (liquid CO _{2} rec.); 55.1 (gaseous CO_{2} rec.) |

[10] | Pressure levels (bar/bar) 30/300 (base), 47.153/283.62 (opt) Turbine PR: 8.835 (base); 6.015 (opt) TIT (°C): 1150 (base), 1123.79 (opt) TOT (°C): 741.2 (base), 783.81 (opt) Regenerator pinch point: 5 °C | Net electric Power (MWe): 419.31 (base), 421.06 (opt) Net electric efficiency: 54.58% ((base), 54.80% (opt) |

[25] | TOP (bar): 30 TOT (°C): 767 | Net Power Output (MW): 298.1 Net electric efficiency = 53.94% Exergetic Efficiency = 50.1% LCOE = 122 €/MWh |

[27] | Pressure level (bar/bar): 30/300 TIT (°C) = 1150 | Net Power (MW): 250 Net electric efficiency: 53.4% (base), 47.9 (min), 57.2 (max) Exergetic Efficiency = 51.3% (base), 46% (min), 54.9% (max) |

[29] | TIP [bar]: 292 (base), 303(opt) TIT [°C]: 1158 (base), 1194 (opt) TOP [bar]: 31 (base), 30 (opt) Turbine pressure levels: 292/31 bar TIT: 1158 °C (base), 1200 °C (opt) TOT: 706 °C | Net electric efficiency [%]: 49% (base), 50.4 (opt) Net Power Output [MW}: 281 (base), 301 (opt) ASU penalty (%LHV): 10.64 (base), 10.66 (opt) |

[32] | TIT (°C): 1083 (opt) TIP (bar): 300 | Cycle net efficiency: 56.5% (opt) Total specific investment cost (with CCS): $1307.5/kW |

[34] | Combustor1 Outlet Temperature (°C): 1150 Combustor2 Outlet Temperature (°C): 1200 TIP (bar): 300 (turbine1), 33 (turbine2) TOP (bar): 34 (base), 31.9 (opt) (turbine1), 3 (base), 2.3 (opt) (turbine2) | Net electrical power (MWe): 903.3 (base), 904.6 (opt) Net electric efficiency = 48.92 (base), 49.32 (opt) Exergetic efficiency = 40.5% |

[35,36] | Turbine inlet temperature(K): 1500 (opt) Turbine inlet pressure (bar): 305.5 (opt) Turbine outlet pressure (bar): 28.1 (opt) | Net cycle efficiency: 54.4% (base), 59.7% (opt) |

[39] | Turbine inlet temperature(K): 1431 Turbine inlet pressure (bar): 300 (base), 358 (opt) Turbine outlet pressure (bar): 30 (base), 28.6 (opt) | Net cycle efficiency: 54.4% (base), 58.2% (opt) |

[40] | Combustor outlet temperature (°C): 1150 Turbine pressure levels (bar/bar): 300/34 | Net cycle efficiency: 52.36% (base), 52.72% (opt) Net cycle efficiency (O _{2} purity of 97%): 52.21% (base), 52.19% (opt) |

[42] | Condenser Temperature (°C): −176 (HPC) −192.8 (LPC) | Net Thermal efficiency: 59.4% (O_{2} compressor), 64.3% (O_{2} pump)Net electric power (MW): of 284 (O _{2} compressor) 305.4 net (O_{2} pump) |

[44] | Turbine pressure levels (bar/bar): 288.69/47.02 Combustor inlet temperature (°C): 1127.7 Turbine outlet temperature (°C): 782.7 | Net Electric Power (MWe): 425.26 Net Electric Efficiency: 55.35% |

[46] | TOT (°C) $\le $ 725 | Net electrical efficiency: 41.5% at 15% load (PHVC) |

Ref. | Main Thermodynamic Parameters | Main Performance Parameters |
---|---|---|

[47] | TIT [°C]: 1150 Turbine PR: 10 | Net efficiency: 41.6% Exergetic efficiency: 40.5% |

[48] | TIT (°C): 1150 TIP (bar): 300 | Net efficiency (on HHV basis): 38.8% Net efficiency (opt): 42.68% |

[49] | TIT (°C): 1150 (base), 1200 °C (opt) | Net efficiency: 38.21% (base), 38.87% (opt) |

Layout Specification | Software | EoS | Main Characteristics and Results | Ref. |
---|---|---|---|---|

low potential heat recovery Allam Cycle | AspenONE | Peng-Robinson | Compressed air and oxygen from ASU are considered as heat sources A secondary utilization leads to an improvement of net efficiency of 3.5% | [54] |

DMC controlled Allam—ASU | Aspen Dynamics v11, Aspentech DMC v11 | See [42] | The application of DMC to the power plant improved the carbon dioxide flow rate, keeping the purity at 97% for the EOR case and allowing the medical purity grade. | [55] |

CES-Allam | gPROMS Process Builder | n.a. | Increase in the net electric efficiency from 54.55% to 57.80% in peak period Decrease in net efficiency from 46.98% to 38.81% in valley period The CES-Allam system seems to be more flexible, operating in a wide load range (28.46–105–97%) | [57] |

Allam Cycle + SNG storage | Aspen Plus | Peng-Robinson | The overall efficiency is about 68%, producing 33 MW of net electrical power and 171 MW of SNG (89.2% CH_{4} and 8.8% H_{2}) chemical power with a thermal power in input of 222 MW renewable electricity and 78.6 MW biomass. | [58] |

Dual pressure LNG CES-Allam | Aspen Plus | Peng-Robinson, Lee-Kesler-Plöcker equation for sCO_{2} | The electric efficiency and specific work of the proposed layout are 15.76% and 68.75% higher than the Allam cycle, respectively, while the dual-pressure Allam cycle exergetic efficiency is equal to 51.88%, with an increase of 1.57% compared with the single-pressure case. | [59] |

Z-Allam | MATLAB | REFPROP database | The results of this study showed that the output power efficiency and the equivalent net efficiency are 2.15% and 2.96% higher than those of the Allam cycle under the same conditions, respectively: the equivalent net efficiency is 48.05% with respect the value of 45.09%, in both cases considering a TIT of 900 °C | [60] |

PEM-electrolyzer-Allam-ORC-ammonia/water power cycle | Aspen HYSYS; | Peng-Robinson; | Overall net efficiency: 60.44% Exergetic efficiency: 63.22%. | [61] |

LOX-Allam | gPROMS Process Building | Peng Robinson | Net cycle efficiency: 58% Novel modes of operation of the cycle and its ASU allowed to decouple oxygen production and electricity production. The Introduction of LOX storage allows to partially remove the constraint of the slow dynamics of the ASU and increase the net efficiency by up to 66.10% and the net electricity output by 17.67% when the Allam cycle runs on storage oxygen. | [62] |

Allam + gasification | Aspen Plus | Gasification, ASSU, CPU and syngas cleaning: Peng-Robinson sCO_{2} Power cycle: Lee-Kessler-Plöcker | The net plant efficiency (on HHV basis) is 37.7% and 40.6 for the baseline and the improved case, respectively. The carbon captured is 97.6% in the first case and 99.4% in the optimized one. | [63] |

CAllam Cycle | Aspen Plus | Soave–Redlich–Kwong + MHV2 mixing model | CAllam cycle is the combination of coal gasification in supercritical water and Allam cycle. The maximum cycle efficiency is 53.19% for a CO _{2} recycling ratio of 1.158 and a turbine outlet pressure of 24.3 bar | [64] |

CTEG + Allam cycle | Aspen Plus | Peng-Robinson steam/water: IAPWS-95 method | The thermodynamic performance of CTEG-AC is higher than CTEG by 7.11% (46.83% vs. 39.72%), while the CTEG-ACH performance resulted lower (30.65%) and CTEG-AC process has also the best economic performance. | [66] |

Allam cycle + (SMR) + HB process + PSA | Aspen Plus v11 | Peng Robinson | CO_{2} emission reduction is 68% and 96%, for on-grid and off-grid cases, respectively, when compared to the conventional HB process. From an economic perspective, the study ensures that the process remains economically competitive | [67] |

Allam cycle + LNG regasification | Aspen Plus v11 + MATLAB R2019b | Peng-Robinson | The Allam-LNG cycle presents a net electrical efficiency of 65.7% Results showed also that there exists a conflicting relation between exergetic efficiency and the cost | [68] |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Reale, F.
The Allam Cycle: A Review of Numerical Modeling Approaches. *Energies* **2023**, *16*, 7678.
https://doi.org/10.3390/en16227678

**AMA Style**

Reale F.
The Allam Cycle: A Review of Numerical Modeling Approaches. *Energies*. 2023; 16(22):7678.
https://doi.org/10.3390/en16227678

**Chicago/Turabian Style**

Reale, Fabrizio.
2023. "The Allam Cycle: A Review of Numerical Modeling Approaches" *Energies* 16, no. 22: 7678.
https://doi.org/10.3390/en16227678