Comprehensive thermoeconomic, exergoeconomic, and optimization analyses of direct oxy‐combustion supercritical CO2 intercooled and reheated cycles under design and off‐design conditions

This study presents comprehensive energetic, exergetic, exergoeconomic, and economic (4E) performance analyses for four direct oxy‐combustion (DOC) supercritical carbon dioxide (sCO2) power cycles at design, off‐design, and part‐load conditions. These cycles include the dual recuperator cycle (DRC), intercooling cycle (ICC), partial intercooling cycle (PIC), and reheating cycle (RHC). The analyses were conducted at relatively low turbine inlet temperatures (TIT: 550–750°C) with compressor inlet temperature (CIT) varied from 33°C (wet‐cooling) to 50°C (dry‐cooling). Furthermore, single‐ and multiobjective optimization analyses were conducted for each cycle. At design conditions (high‐pressure of Pc,o = 20 MPa, low‐pressure of Pc,o = 5.4 MPa, TIT = 750°C, CIT = 50°C [dry‐cooling]), the PIC has the highest thermal efficiency (47.78%) compared to 38.36% for DRC, 45.71% for ICC, and 44.39% for RHC. At optimized conditions (Pc,o = 30 MPa, Pc,o = 8 MPa, TIT = 744°C, CIT = 30°C [wet‐cooling]), the ICC shows superior energetic performance (52.08%) compared to 47.97% for DRC, 49.20% for PIC, and 48.62% for RHC. At off‐design conditions with a power demand (PD) of 40% of the design load (50 MW), the thermal efficiency is decreased by 21.82% in DRC, 17.71% in ICC, 22.46% in PIC, and 13.60% in RHC. The ICC has the minimum levelized cost of electricity compared to the other cycles with 5.93 ¢/kWh at design conditions (dry‐cooling), 5.65 ¢/kWh at optimized conditions (wet‐cooling), and 7.2 ¢/kWh at minimum PD (21 MW). Therefore, from an economic point of view, the ICC is recommended as the best power block for a sCO2 power cycle driven by oxy‐combustor at moderate TITs. The study also provides constructive comparisons between the DOC‐sCO2 and indirect (nuclear, solar, and waste heat) sCO2 power cycle systems and the future research directions.


| INTRODUCTION
In the recent decade, the worldwide interest in the supercritical carbon dioxide (sCO 2 ) power cycles has been increased steadily. 1 This returns to the distinguishing features of the sCO 2 power cycles, such as compactness, 2 high efficiencies, 3 and ability to capture CO 2 emissions. 4 These sCO 2 power cycles can be integrated with a variety of applications, such as 5 : (1) nuclear reactors (which were reviewed in Wu et al. 6 and analyzed in Du et al. 7 ); (2) concentrated solar power (CSP), which were reviewed in Li et al., 8 presented for dry-cooling conditions in Khatoon et al., 9 and introduced with direct integration as in Son et al., 10 or indirect integration as in Linares et al. 11 ; (3) waste heat recovery through integration with bottoming cycles, 12 direct carbon fuel cell, 13 coupling with high-grade waste heat sources, 14 or specific industries such as steel industry, 15 and direct oxycombustion (DOC) technologies. 16 Therefore, in the open literature, various configurations for the sCO 2 power block are proposed and investigated for these applications. The major proposed configurations were simple recuperator cycle (SRC), dual recuperator cycle (DRC), intercooling cycle (ICC), partial intercooling cycle (PIC), reheating cycle (RHC), recompression cycle (RCC), precompression cycle (PCC), and preheating cycle (PHC). 17 Some of these configurations were thermodynamically and economically assessed and compared for the aforementioned applications with a focus on the CSP technologies 18 and waste heat recovery. 19 The RCC was recommended as the most efficient and economical configuration with an efficiency higher than 50% at heat source temperatures less than 800°C as designed by Saeed et al., 20 analyzed by Khatoon et al., 21 and optimized by Milani et al. 22 However, some of these configurations are not applicable for DOC technologies such as RCC for the reasons mentioned in Sleiti and Al-Ammari. 23 Furthermore, there is a lack of comprehensive comparison between the feasible configurations for the DOC technology based on thermodynamic and economic performance indicators. Moreover, these configurations were not compared at their optimized and offdeign conditions. Thus, the present study is presented to fulfill these gaps, see Figure 1. The next four paragraphs introduce a comprehensive review of the most relevant studies to the present work.
The DOC technologies are mainly developed to generate electricity at high efficiency by capturing CO 2 emissions. Over the past few decades, several DOC-based power cycles have been proposed such as the Graze cycle, 24 MATIANT (contraction of the names of the two designers MAThieu and lANTovski) cycle, 25 the semiclosed oxy-combustion combined cycle (SCOC-CC), 26 and Allam cycle. 16 Currently, the Allam cycle is one of the most promising direct oxy-fuel power cycles, which can capture 98.9% of the combustion products with an energy efficiency of 58.9% 27 for natural gas and 51.44% for gasified coal. 1 However, the design of the Allam cycle's components is quite challenging and costly as it operates at very high pressure (300 bar) and temperature (1150°C). 28 In particular, the regenerator has to handle five cold and hot streams, including turbine exhaust flow, recycled sCO 2 flow, oxidant, turbine coolant flow, and flow that transfers heat from the air separation unit (ASU) to the regenerator to correct the thermodynamic imbalance that occurs in the regenerator. This imposed an extremely large heat transfer area and robust structure to withstand the pressure differences (200-300 bar) and high temperatures (700-750°C). 29 Recently, several studies attempted to introduce some modifications and applications for the Allam cycle to further enhance its efficiency and minimize its operational costs. For instance, Liu et al. 30 proposed chemical looping combustion instead of conventional combustion in the Allam cycle, which could improve its electricity efficiency by 9.5%. Other studies adapted the Allam cycle for polygeneration coal-based 31 or biomass-based 32 systems, integrated it with regasification of liquid natural gas, 19 or Haber-Bosch process. 33 However, these processes still suffer from complexity and high capital investment. Therefore, improving the performance of the Allam cycle or similar DOC cycles should be initialized first by selecting the suitable configuration and operating conditions of the power block to make facilitate their commercialization.
The performance of several sCO 2 power cycles at design conditions was investigated based on energetic, exergetic, exergoeconomic, and economic (4E) analyses by several research groups. For instance, Rogalev et al. 34 proposed construction for a high-power sCO 2 gas turbine based on a thermodynamic study with a specific investment of 1307.5 $/kW, which is 46% lower than that of a combined cycle power plant (2424 $/kW). Li et al. 19 showed that integrating the Allam cycle with regasification of liquified natural gas improves the energy efficiency by 16% over the conventional Allam cycle. However, the exergy efficiency did not exceed 52%, which is lower than those reported for sCO 2 power cycles driven by nuclear (67.28% 35 ) or solar energy (78% 36 ) and similar to sCO 2 power cycles driven by waste energy (52.73% 37 ). This implies that cycles with moderate energy source temperatures (550-750°C) have higher exergy efficiencies than Allam-based cycles. Further, 4E analyses were conducted on integrated cooling-heating-power (CHP) systems where the sCO 2 power block is integrated as a top 38 or bottoming cycle 39 with a focus on freshwater production, 40 hydrogen generation, 41 refrigeration cycle, 42 and waste heat recovery. 43 However, compared to the benefits of these systems, their complexity makes them less attractive for practical applications as their economic feasibility was not confirmed in most of these studies. Only a two 4E analysis studies for DOC-based sCO 2 cycles at moderate turbine inlet temperatures (TITs) were introduced in open literature. One with particular focus on the preheating process as designed in Sleiti et al. 29 and the other one with optimization analysis at dry and wet cooling conditions as conducted in Sleiti et al. 44 However, a comprehensive comparison of different DOC-based sCO 2 cycles is still needed to point out the most feasible and economic configuration, which is performed for the first time in the present study.
While the 4E analyses are useful tools that provide guidelines for preliminary design of the cycle components and give clear insights to which configuration has more potential to be used, they cannot tell the best energetic and economic operating scenarios. This is mainly because of the trade-offs between the operating conditions that yield the highest energetic performance and those that yield a minimum levelized cost of electricity (LCOE). Thus, optimization analysis is necessary to address these trade-offs. Techno-economic optimized analysis of nine sCO 2 power cycles driven by CSP was introduced by Thanganadar et al. 45 They concluded that a recompression cycle with intercooling can reduce the overnight capital cost by 10.8% compared to the basic recompression cycle at TIT of 700°C. But their analysis is limited to the capital cost without reporting the LCOE for these configurations. However, the LCOE for CSP-based Allam and partial cooling sCO 2 power cycles are estimated to be in the range from 8 to 11 ¢/kWh as reported by Crespi et al. 46 In the open literature, only three studies 29,47,48 reported the LCOE for DOC-based sCO 2 power cycles working at TIT between 550 and 750°C. However, these studies are limited to preheating (6.3 ¢/kWh) 47 and flared-power cycles (7.7 ¢/kWh). 48 Therefore, further economic analysis for DOC-based cycles is needed to assess the economic feasibility of various configurations other than preheated and flared cycles, which is one of the major contributions of the present study as shown in Figure 1.
In addition to the 4E and optimization analyses of the sCO 2 power cycle, the off-design analysis is a fundamental step to improve its performance by maintaining stable operation using proper control strategies. Dyreby et al. [49][50][51] have developed modeling methodology to predict the steady-state performance of sCO 2 power cycles at off-design and design conditions. This methodology was used by many researchers to analyze the offdesign performance of several sCO 2 power cycles, such as CSP-based, 52 waste heat-based, 19 nuclear-based, 53 and coal-based 54 cycles. For the Allam cycle, Zaryab et al. 55 introduced a detailed part-load model to evaluate the offdesign performance maps of its compressors, pumps, and turbine. They recommended optimizing the adjustment of compressors' guide vanes and the minimum cycle pressure to achieve higher efficiency at part-load operation. Also, Scaccabarozzi et al. 56 performed part-load analysis for the Allam cycle without considering the ASU into account. They mentioned that as the power load decreases from 100% to 40%, the decrease in the normalized efficiency of the Allam cycle is about 3% lower than that of a combined power cycle. However, only one study in open literature investigated the off-design performance of a DOC-based cycle integrated with CSP by Sleiti and Al-Ammari. 57 As such, the current study introduces a thorough analysis of stand-alone DOCbased sCO 2 power cycles at off-design conditions.
Sleiti and Al-Ammari 23 have performed energetic and exergetic performance analyses for five DOC sCO 2 power cycles, including SRC, DRC, ICC, PIC, and RHC. These analyses were performed at turbine inlet temperatures of (TIT: 550-750°C), compressor inlet temperatures of (CIT: 32-50°C), maximum pressure of (P c,o = 20 MPa), and pressure ratio of (r c : 2-5). They found that the SRC has the lowest energy and exergy efficiencies (34.44% and 79.70%, respectively), PIC achieved the highest thermal efficiency (47.57%), while the highest exergy efficiency of 88.10% is achieved by the RHC. However, merely energy and exergy analyses are not sufficient to decide which cycle is the best fit for the DOC-sCO 2 technology. This is because of the considerable difference in the configuration of each cycle which may negatively affect their economic feasibility. So, further economic analyses are needed to point out which cycle is more feasible from an economic point of view. Furthermore, Sleiti and Al-Ammari 23 concluded that there is a trade-off between the conditions of the optimum energy and exergy efficiency, thus an optimization analysis must be conducted. Moreover, to have a more accurate and comprehensive comparison, these configurations should be investigated and compared at off-design and part-load operation conditions. Therefore, as shown in Figure 1, this study comprehensively addresses these gaps by implementing comprehensive economic, optimization, and off-design analysis for these cycles except the SRC. The SRC is not considered for further analyses due to its poor energetic and exergetic performances. Based on the above and referring to Figure 1, the main contributions of the current study are: (1) Performing comprehensive energetic, exergetic, exergoeconomic, and economic (4E) analyses for four DOC-sCO 2 power cycles, including DRC, ICC, PIC, and RHC. Although several 4E studies in open literature have been conducted on indirect sCO 2 power cycles, this is the first 4E analysis for direct oxycombustion sCO 2 power cycles. (2) Finding the optimal operating conditions of these cycles using both single-and multiobjective optimization analyses. (3) Investigating the off-design performance (including the part-load operation) for each cycle under an arid climate and for various PD scenarios. (4) Comparing the performance indicators (efficiencies, total product unit cost, and LCOE) of these cycles with other common sCO 2 cycles applied for nuclear reactors and concentrated solar power technologies.
The rest of the article is organized into four more sections as follows: Section 2 describes the operating mechanisms and technical features of the investigated cycles. Section 3 presents the energetic, exergetic, exergoeconomic, economic (4E), and off-design models developed for the analyses of these cycles. Section 4 introduces and discusses the obtained results in three main sections, including the design analysis results (Section 4.1), optimization results (Section 4.2), and offdesign analysis results (Section 4.3). Finally, the conclusions and future work suggestions of this study are presented in Section 5.

| DESCRIPTION OF THE INVESTIGATED DIRECT OXY-COMBUSTION SUPERCRITICAL CO CYCLES
The layouts and T-s diagrams of the investigated cycles in this study are presented in Figure 2. The layout of the DRC (Figure 2A) is used as a reference configuration to explain the operating mechanism of each system. Highpurified oxygen is supplied to the oxy-combustor (State 11) using an ASU to be directly combusted with natural gas (assumed as pure methane, State 10). Then, the CO 2 and water vapor (combustion products) enter the turbine (State 1) at high pressure (20-30 bar) and moderate temperatures (550-750°C) and expanded to the lowpressure side (Process 1-2). Next, the turbine outlet flow undergoes the processes from State 2 to 3 and from 3 to 4 in both the high-temperature recuporator (HTR) and low-temperature recuporator (LTR) to preheat the highpressure recycled CO 2 flow. Then, the low-pressure flow is cooled down in the precooler (PC, Process 4-5) and water vapor is condensed and separated via the waster separator (WS, Process 5-6). At State 6, CO 2 flow is compressed to the desired high-pressure (State 7). At State 7, part of the compressed CO 2 is exported to be used in commercial applications or sequestrated. 58 The other part is recycled (referred to as rCO 2 ) to the combustor to mitigate the temperature of the oxy-combustion products after being preheated in the LTR (7-8) and HTR (8)(9). The rCO 2 is then mixed with pressurized oxygen (State 10) and fuel (State 11) and combusted in the combustor to repeat the cycle (see T-s diagram of the DRC in Figure 2A).
In ICC ( Figure 2B), the compression process of the CO 2 flow is performed in two stages (6-7 and 8-9) with an intercooling process through the intercooler (IC) to minimize the compression power. In PIC ( Figure 2C), only a fraction of the rCO 2 flow undergoes the intercooling process (7-8) and the other fraction is F I G U R E 2 Layouts and T-s diagrams of the (A) dual recuperator cycle (DRC), (B) intercooling cycle (ICC), (C) partial intercooling cycle (PIC), and (D) reheating cycle (RHC). ASU, air separation unit; CIT, compressor inlet temperature; TIT, turbine inlet temperature compressed (7′-9′) and mixed with the previous fraction at the exit of the LTR (State 10′). In RHC ( Figure 2D), the expansion process is carried out in two stages through Turbine 1 (1-2) and Turbine 2 (3-4) with a reheating process (2-3) by another oxy-combustor, referred to as reheater (RH).
Compared to the DRC, the main feature of the ICC is that minimized compression power is achieved by applying the intercooling process. For nuclear reactors and solar power technologies, the recompression sCO 2 cycle is recommended as the most efficient configuration as only a fraction of the rCO 2 passes through the LTR, which attenuates its pinch point problem. 1 For the DOC technology, this technique can be only performed by the PIC. Thus, PIC minimizes the compression power and also enhances the performance of the LTR, which makes its energetic performance superior. In addition, the RHC is able to produce larger output power compared to the other cycles. 59 However, the addition of other compressors, IC, RH, and/or turbine to the basic layout of the DRC makes their economic feasibility and off-design control quite challenging. 60 For a fair comparison between these configurations, these configurations must be compared under the same design and off-design conditions. To do that, 4E models must be developed and validated first, as presented in the next section.

| MATHEMATICAL MODEL
This section describes the 4E models that were developed for the analysis of the investigated DOC-sCO 2 power cycles. Throughout the analysis, a steady-state operation is assumed, and kinetic and potential energies variations are neglected.

| Thermodynamic models
The energy and exergy models of each cycle were developed by applying the mass and energy conservation principles of each component, such that: 23 Furthermore, the thermodynamic model of the LTR, HTR, IC, and PC was based on the effectiveness method using Equation (4) 23,62 where variable specific heat of the CO 2 as a function of temperature is taken into consideration as detailed in Sleiti and colleagues. 23,29 The thermal efficiency for each cycle is expressed as the ratio of the net output power (Wṅ et ) to the total input power (Qi n ) as: where the equations of Wṅ et and Qi n are given in the Supporting Information Material (Table S1).
For the exergy model, the physical and chemical exergies are given as 23,63 : where ṅis the molar flow rate, x j is the molar fraction of jth component in a mixture, and e j o is the standard chemical exergy of jth component at T o and P o conditions. To evaluate the exergy efficiency of each cycle, the fuel-product-loss method is used. For kth component, the balanced equation of fuel-product-loss exergies and exergy efficiency are expressed as in Equations (8) and (9), respectively. 64,65 The fuel and product exergies for each component of the present cycles are defined in the Supporting Information Material (Table S2). 59 The overall exergy efficiency of each system is:

| Exergoeconomic and economic models
The product cost per unit exergy is obtained by the exergoeconomic model of each cycle. It is initiated by applying the cost balance equation to each component to obtain the cost rate of each stream, which is given as follows: where Ċk in, , and Ċk out, are inlet and outlet cost rates of each stream. Cq k , and Ċk po, are the cost rates of the thermal energy input and power output of each component (if existed). Zk represents the sum of capital investment, maintenance, and operating costs, which is expressed as in Equation (23) where the capital cost of each component (Z k ) is presented in the Supporting Information Material (Table S3). The plant operation time (τ) per year is taken as (7446 h), while the weighting coefficient (γ k ) is fixed at 0.06. The CRF is the capital recovery factor, which is related to the interest rate (ω = 12%) and the lifetime of the plant (n = 20 years): The total product unit cost (c P,total ) is calculated as follows: For the present cycles, the cost balance equations are presented in the Supporting Information Material (Table S4). The economic assessment of the present cycles is presented in terms of the LCOE 67 : where the project cost (PC) is the sum of the components and installation costs (given in Equation 16), the depreciation tax shield present value (PV DTS ), lifetime operation costs (PV LOC ) are expressed in Equations (17) and (18), respectively. The present value of salvage costs (PV SC ) is assumed to be $0.00, while the lifetime electrical production (LEP) is given in Equation (19).  (19) The design values of the parameters presented in Equations (16)- (19) are also presented in Table 1. Also, the capital cost functions of each component are presented in the Supporting Information Material (Table S3). Furthermore, the direct labor and installation costs were taken as 12% of the capital component cost. 70 T A B L E 1 Parameters at the design point

| Off-design model
The off-design analyses of the present cycles were performed based on the off-design methodology developed by Dyreby et al. 50 using sCO 2 experimental data from Sandia National Laboratory. 50 In this method, the modified flow coefficient (ϕ*), ideal head coefficient (ψ*), and efficiency (η*) are given by Equations (20), (21), and (22), respectively.
where ρ and ṁare the density and mass flow rate at the compressor inlet, respectively. N design , N , D c , and U c are the design shaft speed, operational shaft speed, rotor diameter, and rotor tip speed, respectively. ∆h i represents the ideal enthalpy rise in the compressor. Across the turbine, the mass flow rate is given by Equation (23) asfollows: where C s is called the spouting velocity, which is the velocity that could be achieved if the fluid is isentropically expanded through an ideal nozzle). A nozzle is the effective nozzle area, and ρ in is the fluid density at the turbine outlet.
To obtain the isentropic efficiency at the off-design conditions (η t,off ), first, the ideal aerodynamic efficiency is obtained as: where ν is the ratio of the turbine tip to spouting velocities: Then, η aero,ideal is substituted to obtain η t,off : Finally, under the off-design conditions, the model of the recuperators is given as follows:

| Solution procedures
As shown in Figure 3, the solution of the developed models is carried out in three major steps, including (1) solution of the 4E models at design condition, (2) solution of the single-and multioptimization models (discussed in Section 4.2), and (3) solution of the offdesign model based on the optimized results of Step (2). 4E models were solved based on the design conditions presented in Table 1, which are carefully selected to match the practical ranges recommended for DOC-sCO 2 power cycles. 23 The solution was conducted using the real thermodynamic properties of all fluids available in the library of the Engineering Equation Solver platform. For part-load operation, the PD profile and the ambient conditions were obtained using scaled data for the maximum PD day (September 7) and minimum PD day (February 1) in Qatar. 57,71,72

| Model validation
The developed model for each cycle was validated by comparing the energy analysis results with similar cycles used in other technologies under the same operating conditions as provided in Table 2. The results show a good agreement with a maximum error in the thermal efficiency of 1.83% and a minimum error of 0.71%. The error source may be owed to several reasons, such as the accuracy of the HTR and LTR models used in the references (discretized vs. nondiscretized approach, number of segments, etc.); the source of the thermodynamic properties for each study; and the assumptions made for the analysis.
To validate the off-design analysis model, a comparison was made between the published results by Dyreby et al. 51 and the present model for the DRC under the same conditions ( Figure 4). As the off-design model solution depends on the iterative process for the adjustment of the rotor speed and compressor inlet pressure, the error varies over the range of the CIT and TIT. However, the maximum ARE does not exceed 2.1% (only for a limited number of points), while the average ARE is only 1.15% for CIT and 1.35% for TIT.

| RESULTS OF DESIGN, OPTIMIZATION, AND OFF-DESIGN AND DISCUSSION
The design, optimization, and off-design analysis results are presented and discussed in Sections 4.1, 4.2, and 4.3, respectively. Throughout the discussion, the results of the present study are compared with published simulation results for other sCO 2 cycles implemented in various technologies, particularly nuclear reactors and concentrated solar power technologies.

| Design analysis results
Parametric analyses on the effects of the pressure ratio, TIT, CIT, and compressor outlet pressure on the thermal and exergy efficiencies, c p,total , and LCOE are introduced in this section for each investigated cycle.

| Pressure ratio effect
The thermal efficiency of each cycle increases with the increase of the pressure ratio (r c ) up to an optimum value of r c , which is 4.33 for DRC and ICC, 3.33 for the PIC, and 3.67 for the RHC (see Figure 5A). Up to the optimum r c , the thermal efficiency is improved by 5.58%, 7.73%, 26.70%, and 2.67% in the DRC, ICC, PIC, and RHC, respectively. This means that the PIC is the most sensitive cycle for the variation of r c and has the minimum optimal r c . In contrast (as shown in Figure 5B), the exergy efficiency decreases over the range of r c except for F I G U R E 3 Solution procedures of the 4E, optimization, and off-design models. MOF, multiobjective function the PIC, which decreases first up to r c = 2.67 then increases at r c > 2.67. However, the PIC has the lowest exergy efficiency compared to the other cycles. Also, the decrease of the exergy efficiency has the dominant effect on c p,total , which causes its increase with r c ( Figure 5C). Although PIC has the highest thermal efficiency (49.98%) at its optimal r c (3.33), its LCOE is higher than the ICC by 3.4% as shown in Figure 5D. This points out that the addition of an extra compressor for the PIC has a negative effect on the LCOE more than the improvement achieved in the thermal efficiency. To avoid repetition, a further discussion that explains the technical reasons for the behavior of thermal and exergy efficiencies with the variation of r c can be found in Sleiti and Al-Ammari. 23 This is applied also for Sections 4.1.2 and 4.1.3. Therefore, particular focus will be given to the exergoeconomic and LCOE results. For comparison, the optimal efficiencies of the PIC and ICC cycles (49.98% and 46.17%) are competitive for that of recompression sCO 2 power cycle driven by the nuclear reactor, which was 48.76% (without intercooling) and 50.05% (with intercooling) as reported by Ma et al. 73 However, reported results were obtained at a reactor temperature of 850°C, high pressure of 20 MPa, and CIT of 35°C. This means that the DOC-based PIC and ICC cycles achieve competitive performance at moderate TIT and may have even higher efficiencies than the recompression cycle at low compressor inlet temperatures as discussed in Section 4.1.3. Furthermore, as shown in Figure 5D, it is found that the LCOE of the DRC is the highest (9.98 ¢/kWh as average), which is higher than of other cycles by 54.25% for ICC, 49.20% for PIC, and 33.70% for RHC. However, the LCOE of the DOC-based DRC cycle is lower than those driven by concentrated solar power (e.g., 17.6 ¢/kWh, 74 at TIT = 700°C and CIT = 55°C) and comparable for coal-based sCO 2 power cycles (e.g., 9.0 ¢/kWh, 75 at TIT = 620°C and CIT = 32°C).

| Effect of turbine inlet temperature
Although the Allam cycle has high efficiency (58%), it still has disadvantages at the technical level as it works at TIT of 1150°C and high pressure of 30 MPa, which dictates unconventional designs for its components. 76 In particular, the turbine must be cooled and the recuperator has to withstand high temperatures (up to 750°C). Therefore, as a new approach, it is recommended to develop DOC-sCO 2 power cycles to operate at TIT within the range of 550-750°C. 29,47 Thus, in this section, the economic performance of the investigated cycles is presented within that range, as shown in Figure 6. As the TIT increases from 550 to 750°C, the thermal efficiency is increased by 4.31%, 2.19%, 7.90%, and 6.90% in DRC, ICC, PIC, and RHC, respectively ( Figure 6A). This implies that the ICC is the least sensitive cycle to the TIT, which makes it a preferred configuration for other types of energy sources, such as nuclear reactor, 65 solar power, and waste heat energy. 62 Unlike PIC and RHC, the exergy efficiency of ICC increases by 2.50% with the increase of the TIT as shown in Figure 6B. However, the RHC has the highest exergy efficiency (87.50%) at TIT higher than 640°C. Consequently, RHC has the minimum c p,total (8.88 $/GJ) as shown in Figure 6C. Moreover, the exergy efficiency of the present cycles is about two times higher than that of coal-fired Allam cycle (40.20%) reported by Jing Luo 77 due to: (1) the extremely high TIT (1150°C), which increases the destruction rate through cycle components, and (2) numerous components of the coal-fired Allam cycle are not needed for the presented in this study DOC-based cycles such as gasification unit and syngas coolers.
Economically, as shown in Figure 6D, the LCOE of the present cycles slightly decreases with the increase of the TIT except for the RHC as its performance is significantly affected by this parameter. The stability of the LCOE with the increase of the TIT can be explained as higher TIT yield higher thermal efficiency as well as higher costs for the turbine and recuperators materials. But, for the RHC, the efficiency enhancement was more dominant than the increase of the materials cost. However, ICC still has lower LCOE (5.93 ¢/kWh) than DRC (by 41%), PIC (11%), and RHC (17%). Also, LCOE of ICC cycle in this study is less than one-half the LCOE of a recompression CO 2 cycle (5.93 ¢/kWh) that works at TIT of 750°C, CIT of 50°C, P c,o of 20 MPa, and r c of 2.6 as reported by Noaman et al. 64

| Effect of compressor inlet temperature
The CIT depends on the cooling method performed in the plant such that temperatures less than 35°C are only achievable by wet cooling techniques while dry cooling provides CIT higher than 45°C. 78 However, the economic aspects of each wet and dry cooling approach are considerably different; thus, an economic comparison must be conducted to decide the most feasible and efficient method. 47 For the present cycles, the effects of the CIT on the thermal efficiency, exergy efficiency, c p,total , and LCOE of each cycle are presented in Figure 7. For all cycles, the thermal efficiency is improved only by 2% (average) as the CIT decreases from 50 to 33°C. Also, LCOEs at CIT of 33°C (wet cooling) are 9.51, 5.72, 7.27, and 7.07 ¢/kWh for DRC, ICC, PIC, and RHC, respectively. These LCOEs are lower than at dry cooling conditions (CIT of 50°C) by 4.0%, 3.5%, 2.6%, and 3.9%, respectively. This implies that these DOC-based cycles are less sensitive for the cooling method than the solar-based recompression cycle as its efficiency in dry cooling is about 6% lower than in wet cooling conditions. Therefore, the present cycles are economically feasible even in harsh environmental conditions at which dry cooling methods are more practical than wet cooling methods.

| Effect of compressor outlet pressure
The aforementioned results were presented at constant high pressure (P c,o ) of 20 MPa. However, P c,o has a key F I G U R E 7 Relationship between the compressor inlet temperature and (A) thermal efficiency, (B) exergy efficiency, (C) total product unit cost, and (D) LCOE of each cycle. At r c = 3.67, TIT = 750°C and P c,o = 20 MPa. DRC, dual recuperator cycle; ICC, intercooling cycle; LCOE, levelized cost of electricity; PIC, partial intercooling cycle; RHC, reheating cycle; TIT, turbine inlet temperature role in the performance of the present cycles and affects the value of the optimized pressure ratio. As the ICC shows superior economic performance compared to the other cycles with comparable efficiencies for the PIC, it was selected for further analysis for the highpressure effect. Therefore, the 4E performance indicators for the ICC were simulated over the range of r c (2)(3)(4)(5) at different high pressures (20-30 MPa) as shown in Figure 8. Within this range, the thermal efficiency is increased from 38.44% (at P c,o = 0 MPa and r c = 2) to 46.07% (at P c,o =30 MPa and r c = 3) at the same lowside pressure. Also, it is increased to 48.05% (at P c,o = 30 MPa and r c = 5) but with lower pressures at the lowpressure side. Furthermore, it is found that the optimum r c for the thermal efficiency differs from the optimum one for the LCOE at P c,o less than 25 MPa. For instance, at P c,o of 22.5 MPa, the optimum r c for maximum efficiency is 4.67 while it is 4.00 for minimum LCOE. Moreover, these results are subject to change if the CIT is changed. Therefore, to optimize the 4E performance indicators, an optimization analysis is necessary, which is conducted and presented in the next section.

| Optimization results
For sCO 2 power cycle optimization analysis, the genetic algorithm (GA) approach is recommended as it was less sensitive for the initial guess values, which yield robust results compared to other optimization techniques. 35,44,79 Thus, the GA optimization tool is used in EES to do single-and multiobjective optimization. The highpressure (P c o , ), low-pressure (P c i , ), and the CIT are the major operating conditions that affect the amount of the recycled CO 2 flow rate, fuel flow rate, size of the recuperators and precoolers, and the size of the turbomachinery components (turbines and compressors). Therefore, these parameters are considered as decision variables to be optimized within their practical ranges as: MPa 30, Based on the optimization methodology shown in the Supporting Information Material ( Figure S1), four objective functions were selected, including maximizing the thermal efficiency (η th ), maximizing the exergy efficiency (ε overall ), minimizing c p,total , and minimizing the LCOE as single optimization functions (SOFs). Also, for multiobjective optimization, a multiobjective function (MOF) is defined as follows: where c f unit, and C fuel are the unit fuel cost (26.64 $/GJ) and fuel cost (12 ¢/kWh), respectively. The results of the SOF and MOF for the present cycles are presented in Table 3. Figure 9 compares the results obtained for the 4E performance indicators by the single-bojective and multi-objective optimization fuctions. It is found that Min. c p,total and Max.MOF yield decision parameters at which ICC has more efficient performance than the PIC ( Figure 9A). Therefore, at optimized conditions, ICC shows superior energetic (52.08%) and economic (5.65 ¢/kWh) performances over the other cycles. However, the exergetic performance of the ICC (83.04%) is about 6% lower than that of the RHC Figure 9B. However, the energetic performance of the ICC is more dominant and yields lower c p,total (5.39 $/GJ) than other cycles. In comparison to the optimized efficiency (49%) for a solar-based recompression cycle that works at TIT of 650°C, CIT of 40°C, P c,o of 24.8 MPa, and P c,i of 7.8 MPa reported by Reyes-Belmonte et al., 80 (Table 3). At the optimized designed conditions, the exergy destruction of the components of each cycle is calculated from the fuel and product exergies presented in the supplementary data (Table S5) and analyzed as shown in Figure 10. Also, Table S5 shows the capital cost of each component and the total capital cost of each cycle. It is found that the oxy-combustor is responsible for the major part of exergy destruction of each cycle with a minimum share of 54% in the PIC and a maximum share of 74% in the ICC. This is explained by the chemical reactions and significant temperature difference that occurs through the combustion process. Also, the heat exchanger components (recuperators and precoolers) contribute significantly to the exergy destruction with a maximum of 43% in the PIC as it has two precoolers with a lower recycled flowrate. This reduces the heat transfer coefficient with the cooling fluid and enhances the exergy destruction share. From exergoeconomic point of view, the exergoeconomic factor of each component is calculated as follows: where ŻK and CḊ k , are the cost rate of the component cost and its exergy destruction, respectively. The average exergoeconomic factor of the oxy-combustor (f co = 82.21% as) is higher than that of the turbomachinery (48.98%) and heat exchanger (33.87%) components (Table S5). However, the contribution of the turbomachinery components to the exergy destruction is the least among the other components ( Figure 10). Therefore, improving the design of the combustor and recuperators is essential to enhance the energy performance of the cycles.

| Off-design analysis results
The above results were obtained at constant turbomachinery efficiencies (89% for compressors and 93% for turbines) and fixed output power of 50 MW. However, these parameters are varied with the variation of the CIT, TIT, and PD profiles. Therefore, using the offdesign model, the performance of each cycle is simulated at off-design conditions as shown in Figure 10. First, the thermal efficiency and LCOE were calculated at fixed control variables (FCVs), which are the shaft speed (N c ) and the compressor inlet pressure (P c,i ). Then, N c and P c,i were adjusted to maximize the energy efficiency and minimize the LCOE. The adjustment of the control variables by reducing P c,i (from 8 to 7.7 MPa) and shaft speed (from 13,000 to 10,000 rpm) as the CIT increases from 33 to 50°C. This, in turn, maintains the dense behavior of the sCO 2 and minimizes the compression power. At optimized conditions and FCVs, the thermal efficiency of ICC is higher than other cycles at CIT of 33°C ( Figure 10A). But, at CIT higher than 37°C, the PIC is the most efficient cycle; however, the LCOE of the ICC is the minimum over the range of the CIT ( Figure 10B). Furthermore, the ICC shows superior performance compared to PIC at TIT less than 700°C. Moreover, the adjustment of the control variables considerably improves the thermal efficiency of the ICC by 2.0% at dry cooling conditions (CIT > 40°C) and by 0.6% at TIT > 640°C. This improvement is comparable to that of the recompression cycle investigated by Dyreby et al., 50 which was about 2.5% for the CIT and 1.5% for the TIT. Figure 11 shows the energetic and economic performance of the present cycles at variable PD profiles for two typical days in Qatar (namely, September 7 for Max. PD, and February 1 for Min. PD). It is found that as the PD reduced from 50 to 21 MW (42% of the design output power), the thermal efficiency is reduced by 21.82% in DRC, 17.71% in ICC, 22.46% in PIC, and 13.60% in RHC. This implies that the RHC is the least sensitive cycle for the variation of the PD, thus its LCOE is slightly changing with the PD profile Figure 11D. However, the F I G U R E 10 Comparison of the exergy destruction share of each component in the investigated cycles at their optimized conditions. DRC, dual recuperator cycle; ICC, intercooling cycle; PIC, partial intercooling cycle; RHC, reheating cycle ICC still has the minimum LCOE with an average of 5.65 ¢/kWh at Max. PD, and 7.2 ¢/kWh at Min. PD ( Figure 11B). In addition, the exergetic performance of the ICC is not affected by the conditions at part-load operations as shown in Figure 12. For compression, the thermal efficiency of a recompression cycle, intercooled cycle, and reheating cycle are reduced by 25.5%, 28.7%, and 21.1%, respectively, as PD reduced to 30% from the design load (10 MW) as reported by Yang et al. 81 This confirms the efficient and economic feasibility of the ICC for DOC-based sCO 2 power cycles in a comparable manner for the recompression cycle recommended for nuclear, solar, and waste energy technologies, as shown in Figure 13

| Environmental analysis
To evaluate the CO 2 emissions of the present direct oxy-combustion cycles, the product CO 2 from the combustion process is calculated and compared to that of a conventional natural gas Brayton cycle (BC) with an energy efficiency of 32.0%. The net output power of all cycles is fixed at 50 MW. As shown in Figure 14, the PIC has the minimum CO 2 emissions (0.180 million tons/year 82 ) while the DRC has the maximum CO 2 emissions (0.224 million tons/year) among the direct oxy-combustionbased cycles. These values are proportional to their fuel consumption and energy efficiencies as discussed in Section 4.1. However, the CO2 emissions from the conventional natural gas BC are 20% higher than the DRC and 51% higher than the PIC. Furthermore, the CO 2 emissions from the direct oxycombustion processes are captured and exported as compressed gas to be used in commercial applications or sequestrated, which is not performed in the conventional Brayton cycles. Therefore, the present direct oxy-combustion cycles virtually have zero CO 2 emissions. In this study, comprehensive 4E performance analyses for four DOC-based sCO 2 power cycles at design conditions are introduced. The investigated cycles include DRC, ICC, PIC, and RHC. Then, single-and multiobjective optimization analyses were conducted for each cycle. In addition, the performance of these cycles was assessed at off-design and part-load operation conditions. The main conclusions of this study are: ( Also, it has more practical and feasible design parameters than the Allam cycle, which requires special designs for its components as it operates at TIT higher than 1150°C.
While the present study introduces a thorough analysis for the DOC-based sCO 2 cycles at design and off-design conditions, further optimization analysis based on the detailed model of each cycle component at various control strategies is recommended for future work.

ACKNOWLEDGMENTS
The work presented in this publication was made possible by NPRP-S grant # (11S-1231-170155) from the Qatar National Research Fund (a member of the Qatar Foundation). The findings herein reflect the work, and are solely the responsibility, of the authors.

CONFLICTS OF INTEREST
The authors declare no conflicts of interest.
cross-sectional/surface area (m 2 ) c p,total total product unit cost ($/GJ) D diameter (m) Ėexergy rate (kW) h specific enthalpy (kJ/kg) ṁmass flow rate (kg/s) ṅmolar flow rate (kmol/s) N shaft speed (rpm) P pressure (MPa) P net net power produced by the power cycle Q heat transfer rate (kW) T temperature (°C) Ẇpower produced (or consumed) (kW) Wċ a