Exergoeconomic Analysis of Combined-Cycle Cogeneration Plants With Supercritical Carbon Dioxide Power Cycle

Cogeneration plants, i.e., combined heat and power (CHP) plants, are currently under operation and are based on conventional commercial technologies. Many technological concepts could be classified as a CHP. The waste thermal energy from a power plant can be further utilized as process heat, district heating, etc. A combined cycle is a technology based on a combination of a topping cycle and a bottoming cycle (Fig. 1), where the waste thermal energy from the topping cycle is the driving energy for the bottoming cycle. A bottoming cycle can be a steam power system for a large-scale application or an organic Rankine cycle (ORC) for a medium to small scale. There are many technical possibilities to produce heat from both topping and bottoming cycles, in addition to electricity. Such technologies are called “combined-cycle cogeneration plants.” The energetic efficiency of cogeneration plants includes both energy effects regardless of which cycle these effects are generated. An energy efficiency [based on the value of the lower heating value (LHV)] of more than 65% could be achieved in comparison to an average of 50% for a detached generation of heat and power. At least 2.2 $¢/kWh worth of fuel could be saved in a CHP approach while providing the same quantity of heat against using a separate boiler [1–3]. Figure 2 shows the potential cost benefits.

Industrial implementation of the supercritical carbon dioxide (sCO₂) cycles for electricity generation is at the level of development despite more than 50 years of research [4–7]. Modern research publications and technical reports demonstrate a strong potential for sCO₂ cycles across a wide range of temperatures and power capacities, particularly in replacing conventional steam Rankine as a bottoming cycle. The benefits of a CHP approach and the sCO₂ technology [8] could lead to efficient and economically feasible power and heat generation.

There are many studies focused on the application of sCO₂ cycles for thermal energy recovery, including the bottoming cycle for gas-turbine systems, and only a few studies have focused on the application of sCO₂ cycles for CHP applications. However, comprehensive energy, exergy, and economic evaluations are reported in a much smaller number of publications. For example, a comparative exergoeconomic analysis between the supercritical CO₂ and the ORC (with the following working fluids: R123, R245fa, toluene, isobutane, isopentane, and cyclohexane) for heat recovery from the transcritical CO₂ cycle has been reported in Ref. [9]. The net power that can be produced within sCO₂ or ORC cycles is 14 MW, and the temperature at the inlet of the turbine is 120 °C. The overall energetic and exergetic efficiency is reported as 44% and 61%, respectively. An exergoeconomics optimization of sCO₂/tCO₂ plants demonstrates a reduction of 2.3% in the product unit cost while reducing the exergetic efficiency is 2.45%. Better economic performance can be achieved only for isobutane as the ORC working fluid (sCO₂/ORC) with a reduction in the product unit cost by 3.36%.

In Ref. [10], the exergoeconomic and exergoenvironmental analyses are applied to complex cogeneration systems consisting of a gas-turbine system (exhaust gas temperature is 530 °C), a sCO₂ recompression cycle, and an organic Rankine cycle. 50 MW of exergy is the total exergy product (power and steam). The reported energetic efficiency is almost 50%, while the exergetic efficiency is 53%. The total cost of produced power and steam is 12.6 $/GJex and 8.74 $/GJex, responding.

Among many known sCO₂ cycles that can be used as a stand-alone technology, the recompression sCO₂ cycles are the most thermodynamically and cost-efficient [11–14].

This article investigates the application of a recompression sCO₂ cycle as a “bottoming cycle” using exergy, economic, and exergoeconomic analyses.

This study considers two CHP plants with single and double sCO₂ bottoming cycles using a recompression layout. For simplicity, throughout the article, the single bottoming cycle is referred to as cycle A, and the double bottoming as cycle B. The simulation of the cycles was conducted using the ebsilon professional [15], which was developed for the design of power plants and the simulation of the thermodynamic processes. The REFPROP library is used to calculate the thermodynamic properties of the working fluid [16], where the Span–Wagner equations of state are implemented, which are currently the most accurate in predicting sCO₂ thermodynamic properties [17]. The environmental conditions are assumed to be as follows: Ambient temperature (and fuel temperature)—15 °C; air relative humidity—60%; ambient pressure—1.013 bar.

The exhaust gas temperature at the exit from the open-cycle gas-turbine system (topping cycle) can be varied in the range of 450–600 °C [18].

Cycle A schematic layout is shown in Fig. 3. The temperature of the exhaust gas is 590 °C and the maximum temperature of the sCO₂ working fluid at the inlet of the sCO₂ turbine is up to 550 °C; nonetheless, the temperature of exhaust gas at the exit of the PHX is still high at 470 °C. For that reason, heat generation is achieved by water heating for direct consumption at temperatures up to 100 °C.

The mass flowrates of the working fluid in the sCO₂ cycle are optimized between the main compressor and recompressor. After the recuperation process in the high-temperature recuperator (HTR) and low-temperature recuperator (LTR), the flow splits before entering the heat consumer. The sCO₂ working fluid is compressed in the main compressor. The second stream is compressed in the recompressor and then combined with the stream coming from the main compressor; both streams are mixed and then pass the HTR. Thermal energy is added to the sCO₂ cycle in the primary heater (PHX). The high-pressure sCO₂ working fluid is expanded in the CO₂ turbine to further generate electricity in Generator 2. The sCO₂ stream cools down after passing HTR and LTR. Also, to avoid the pinch point problem in the cycle, the temperature after the heat consumer is increased up to 37 °C. The flow ratio at the splitter is selected as 40% to achieve a higher temperature for the heating water; this significantly influences the cycle efficiency. Also, the turbine inlet temperature (TIT) is an important parameter that dramatically influences the cycle efficiency. These two parameters should be used for the optimization of the cycle to reach optimal performance, i.e., achieving higher efficiency at lower costs.

Cycle B (Fig. 4) comprises two sCO₂ bottoming cycles: high-temperature cycle (HTC) and low-temperature cycle (LTC). Two heat sources are used to provide the sCO₂ cycles with driving energy. The TIT at the high-temperature cycle is 560 °C, while the TIT of the low-temperature cycle is 375 °C. Since the LTC has a low temperature compared with the HTC, the amount of power that can be produced from this cycle is lower at the same mass flowrate.

Pressure at the main compressor outlet is set to 200 bar for HTC and LTC, while the pressure at the recompressor inlet is set to 76 bar. The lower temperature of the HTC was increased from 37 °C to 39 °C to avoid the pinch point problem.

For a cogeneration system, it is necessary to define the electrical efficiency $(ηel)$ and the total efficiency $(ηtot)$

The equations to calculate the values $ηel$ and $ηth$ were introduced to the ebsilon software.

Table 1 illustrates the assumptions used for simulations. The pressure at the inlet of the main compressor is set to 76.9 bar to make sure the cycle remains supercritical, and the recompressor outlet pressure is assumed to be 200 bar based on the current state of the technology [7]. The design parameters for the turbomachinery were chosen according to Ref. [19].

Cycle A has an electric efficiency of 43.8% and a total efficiency of 75.1%; it can be concluded that the cogeneration system is energetically efficient. For cycle B, the electric efficiency is 45.5% and the total efficiency is 75.6%.

The simulation of cycle A is completed at TIT of 550 °C. A sensitivity analysis was applied to the turbine inlet temperature range from 425 °C to 575 °C. The results (Fig. 5) show that for a difference of 75 K in the value of TIT, the cycle efficiency changes by 1% point.

Within cycle A simulations, the isentropic efficiency of the CO₂ turbine varied between 87% and 92% to identify the impact on the cycle efficiency. Figure 6 shows the results. For a difference of 5% point in the isentropic efficiency, the cycle efficiency changes by 0.1% point.

Modern exergetic analysis helps to identify the thermodynamic inefficiencies at a component and a system level. The real inefficiencies of a system are referred to as exergy destruction (irreversibilities within the system) and exergy losses [20].

The total exergy of a material stream consists of its physical $(E˙jch)$ and chemical exergy $(E˙jph)$⁠, $E˙j=E˙jph+E˙jch$⁠.

The simulation data were extracted from ebsilon and plugged into the vba code in-house Excel vba program developed at the Institute for Energy Engineering of TU Berlin. The reference environment conditions are given in Table 1. The standard molar chemical exergy of CH₄ is 824,348 kJ/kmol (model I in Ref. [20]). For the exergetic analysis of the sSO₂ cycle, only physical exergy is considered.

The exergy balances are written based on the approach “exergy of fuel/exergy of product” [20] as

• for the overall system

  $E˙F,tot=E˙P,tot+E˙D,tot+E˙L,tot$

  (3)
• for the kth system component

  $E˙F,K=E˙P,K+E˙D,K$

  (4)

The exergetic efficiency is defined as

• for the overall system

  $εtot=E˙P,totE˙F,tot$

  (5)
• for the kth system component

  $εk=E˙P,kE˙F,k$

  (6)

The detailed results of the exergy analysis for the components of the stand-alone sCO₂ cycle are given in Table 2, and the distribution of the exergy destruction $(yD,k*)$ among components of a sCO₂ stand-alone system is shown in Fig. 7.

The distribution of the exergy destruction $(yD,k*)$ among all components of cycle A is shown in Fig. 8. The highest rate of exergy destruction occurs in the combustion chamber, representing almost 60% of the total destruction taking place within the system, which agrees with stating that the combustion irreversibility is the most significant in power plants in general. The primary heat consumer ranks second, while the expander comes third.

Focusing on the sCO₂ stand-alone system (Fig. 7), the most significant contributors to exergy destruction are the heat consumer, the low-temperature (LT) recuperator, and the high-temperature (HT) recuperator. However, these components have very low exergy destruction compared to the combustion chamber. The overall cycle A has an exergetic efficiency of 46.6%. The total exergy of fuel fed into the system is 362.5 MW, 169.1 MW of which represents the exergy of product and 29.5 MW as exergy losses for the entire system and around 164.4 MW destructed within the system components.

The distribution of the exergy destruction $(yD,k*)$ among all components of cycle B is shown in Fig. 9. Similar to cycle A, the combustion chamber is the most significant contributor to total exergy destruction within the system. The two heat consumers still have the most significant exergy destruction within the sCO₂ bottoming cycles. The exergetic efficiency of the overall combined cycle increased by 1.5% point compared to cycle A. Around 20% were saved from being lost to the environment in relation to cycle A, while the exergy destructed within the system increased by 8.3%.

The total revenue requirement (TRR) method [20] is used here to evaluate the entire system from an economic perspective and to calculate the levelized cost of electricity (LCOE) of the whole system. For a thermal system, the cost of the final product is an essential metric that affects the selection of the system's design option. Figure 10 illustrates an overview of the whole economic analysis procedure. Economic analysis is based on a large number of assumptions, taking into account economic and technological considerations.

The cost estimation depends on the equipment size, the range of operation, and the construction materials of each component. Since the sCO₂ technology is not yet commercial, the cost estimation for the sCO₂ closed cycle with a 33-MWe CO₂ turbine is estimated based on the DOE Advanced Reactor Concepts program for a 10-MWe sCO₂ closed system [21–24]. Then, the scaling exponent is used to scale (up to 33 MWe) for all components, $CP,new=CP,reference(Xnew/Xreference)α$⁠, with α = 0.66 for the recuperators and heat consumers and α = 0.99 for the turbomachinery. The costs are then adjusted for the estimated year. The estimated purchase cost of the sCO₂ closed-cycle system at Sandia National Laboratories for 10 MWe is equal to $35 M [24]; this includes the components of the cycle: recuperators, heat consumer, turbomachinery, and facility support.

The purchase cost of the gas-turbine system is estimated based on Ref. [25]. As a reference case, the following information for the gas-turbine system (topping) cycle has been used: model—GT13E2; ISO base load—182 MW; efficiency—37.4%; specific price—231 $₂₀₁₀/kW. The share of investment cost for the components of the gas-turbine system is assumed to be 31%—compressor, 6%—combustion chamber, 55%—expander, and 8%—generator.

Total capital investment (TCI) is the sum of the fixed capital investment and other outlays, including the allowance for funds used during construction, start-up costs, and working capital. The routine to calculate the value of TCI can be found in Ref. [20]; for the combined-cycle power plant in Ref. [18], and for the sCO₂ cycle in Ref. [11]. Here, only the final results are reported as: TCI_CycleA = 188.0 M$ and TCI_{Cycle B} = 273.5 M$.

The plant's economic life is assumed to be 20 years with 8000 h/year of baseload operation; an average inflation rate is r_i = 1.9% and a nominal escalation rate n = 3.0%. For calculating the levelized cost, a capital recovery factor (CRF) was calculated

Levelized carrying charges represent the annual obligation associated with the debt and investments made in the project, which represents the capital cost, CAPEX.

Levelized total revenue requirement (TRR_L) is defined as the sum of CC_L, OMC_L, and FC_L (Figs. 11 and 12). The TRR_L calculated for cycle A is 108 M$/year and 120 M$/year for cycle B. The uncertainty of the economic assumptions used for calculating the levelized costs should be tackled in future studies. Sensitivity studies could help reveal how strongly each economic assumption could affect the result of the economic analysis.

The apportioning of levelized costs to the two products (heat and electricity) of the system investigated cannot be achieved using an economic analysis. Hence, calculating separate and correct LCOE and levelized cost of heat (LCOH) values for the CHP system is only possible using exergoeconomic analysis.

An exergoeconomic analysis is a combination of exergy analysis and cost analysis and provides an evaluation at the component level and provides information for lowering the product cost while increasing the exergetic efficiency. To apply an exergoeconomic analysis, it is necessary to apply the exergy analysis in combination with economic principles. This approach is called “exergy costing” [20]. It helps in finding the cost of the exergy destruction within the system and defining measures that could improve the cost-effectiveness of the overall system.

where $CCL$ is the levelized carrying charges, $OMCL$ is levelized operating and maintenance costs, T is annual full load hours, $BMCK$ is the individual component bare module cost, and $BMCtot$ is the total bare module costs.

Using the cost balances rewritten in terms of “exergy of fuel”/“exergy of product” and with the help of auxiliary equations (if required [20]), the cost rates and the cost per unit of exergy can be calculated for each exergy stream:

• for the overall system

  $C˙P,tot=C˙F,tot+Z˙tot−C˙L,tot$

  (16)
• for the kth system component

  $C˙P,k=C˙F,k+Z˙k$

  (17)

The results of the exergoeconomic analysis, the values of $Z˙k$⁠, and the cost rate associated with exergy destruction $(C˙D,k=cF,kE˙D,k)$ for each component for the two cycles are shown in Figs. 13 and 14. For both cycles, the cost rate associated with the combustion chamber has the higher rank, while the primary heat consumer and gas turbine expander come second and third, respectively. For cycle B, the total investment $(Z˙)$ and cost rates of exergy destruction $(C˙D)$ increased in comparison to cycle A, except for its primary heat consumer, which decreased by 18%.

Based on the exergoeconomic results, it is concluded that cycle B has a higher specific cost of the product compared to cycle A (Fig. 15). Also, due to the relatively high costs invested in cycle B, the total cost of the product (levelized cost of the total exergy produced in $¢/kWh) increased by 13.3% from 8.17 to 7.21. In both cases, LCOH is very high, mainly due to the poor performance of heat consumers. However, since the power-to-heat ratio (P/H) is quite high in this design, the effect of this high cost of heat did not change the levelized total cost dramatically.

A benchmark (Fig.16) is conducted to compare the two systems against the most competitive CHP systems in the market [27]. All levelized costs are brought to US dollars for the reference year. The two proposed cycles show a competitive LCOE against other CHP technologies with an average LCOE equal to 6.7 $¢/kWh. Since natural gas is the fuel used in this study, a comparison between CHP systems and gas turbine combined cycles and the Allam cycle (NET power cycle) is carried out since the Allam cycle uses a direct supercritical CO₂ concept [28,29].

This article used the recompression sCO₂ cycle as the modular block for the bottoming cycle since it is the most sCO₂ closed configuration that has received research attention and is highly investigated in the literature. The sCO₂ closed power cycle has shown in the literature a strong performance that has reached thermal efficiencies of up to 50%.

This article aimed to evaluate the possible integration of the sCO₂ closed recompression cycle in a bottoming configuration of the combined-cycle power plants for cogeneration purposes. An exergoeconomic analysis was conducted, which helped identify the system components with the highest cost rates. The levelized cost of the total product generated by the system showed strong competitiveness compared to current technologies in the market.

There are no conflicts of interest. This article does not include research in which human participants were involved. Informed consent is not applicable. This article does not include any research in which animal participants were involved.

The authors attest that all data for this study are included in the article.

c =

Specific cost ($/J_exergy)

y =

Exergy destruction ratio (%)

$m˙$ =

Mass flowrate (kg/s)

$C˙$ =

Cost rate ($/s)

$E˙$ =

Exergy rate (W)

$Q˙$ =

Heat rate (W)

$W˙$ =

Power (W)

$Z˙$ =

Investment cost rate ($/s)

LHV =

Lower heating value (kJ/kg)

 ε =

Exergetic efficiency (%)

η =

Efficiency (%)

ch =

Chemical

D =

Destruction

el =

Electrical

F =

Fuel

k =

kth component

L =

Losses

P =

Product

ph =

Physical

th =

Thermal

tot =

Overall system