# Economic, Exergoeconomic and Exergoenvironmental Evaluation of Gas Cycle Power Plant Based on Different Compressor Configurations

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}emissions (about 0.7 kg/kWh); all environmental indicators confirmed it is the most environmentally friendly option.

## 1. Introduction

_{2}emissions. Igbong and Fakorede [31] conducted an exergo-economic analysis of a GT plant, studying the effects of turbine inlet temperature and compressor pressure ratio. Arora [32] conducted exergoeconomic research on GT power plant components: the combustion chamber, compressor, and exhaust. Mousafarash and Ameri [33] conducted exergy and exergo-economic analyses of a GT power plant considering its performance at different ambient temperatures and partial loads. Avval et al. [34] conducted an exergy-exergo-economic and exergo-environmental multi-objective optimization analysis of a GT power plant. They studied the influence of different design parameters on turbine exergy efficiency, total cost rate of the system, and CO

_{2}emission, investigating how high ambient temperatures led to a low density of air intake to the compressor, enhancing the performance of the gas cycle while minimizing the losses through highly efficient components (i.e., gas turbine, air compressor, combustion chamber) [35].

- Producing a LCC assessment for a lifespan of 20 years for the given GT engines with respect to ISO conditions and variation in ambient temperature and loading conditions.
- Calculating the payback period of each GT engine studied where the delivered power is assumed to be electricity sold at tariff prices.
- Estimation of exergy costing for all equipment in the given GT engines.
- Estimation of CO
_{2}emissions at ISO conditions that result from each GT engine considering three environmental indicators, environmental destruction coefficient, environmental destruction index, and environmental benign index.

## 2. Methodology

#### 2.1. Description of the Studied GT Engines and Compressor Configurations

#### 2.2. GT Engine Modelling

#### 2.2.1. Modelling Preparations

- (1)
- Typical component maps embedded within the software for the different configurations can be adapted and linearly scaled to satisfy the various engine DP performances.
- (2)
- The turbine components at the DP operate in the choke region.
- (3)
- All processes in the gas cycle are in a steady state.
- (4)
- Natural gas is the fuel, and heat loss from the combustion chamber is equal to 2% of the fuel’s low heating value.

#### 2.2.2. Validation with Manufacturer’s Data

#### 2.3. Economic Analysis

#### 2.3.1. Lifecycle Costing

#### 2.3.2. Discounted Pay-Back Period

#### 2.4. Exergoeconomic Analysis

#### 2.4.1. Exergy Costing

^{th}element in each exergy stream entering a given system, the sum of the costs of capital-investment (${\dot{Z}}_{k}^{CI}$) and operation and maintenance (${\dot{Z}}_{k}^{OM}$), plus the cost rates associated with the stream (${\dot{C}}_{i}$), are equal to the sum of the cost rates of the exiting exergy streams (${\dot{C}}_{e}$). For the k

^{th}element, the general equation relating heat input and power output will be:

#### 2.4.2. Levelization

_{eff}).

^{th}component are given by:

#### 2.4.3. The Exergoeconomic Parameters

^{th}component, ${r}_{k}$ can be expressed as an objective function [42]:

^{th}element are exergetic (exergy destruction and loss) and non-exergetic (including capital investment and/or maintenance and operational costs). To minimize ${r}_{k}$, it is useful to know the relative importance of these two sources. The exergoeconomic factor can determine the relative value of the two sources. The exergoeconomic factor, ${f}_{k}$, can be written as:

#### 2.5. Environmental Indicators

_{2}emissions, since CO

_{2}is the major greenhouse gas. It is also noted that, for a given thermal load, CO

_{2}is proportional to the efficiency of the system; this means inefficient systems significantly adversely affect the environment.

_{ed}), the environmental destruction index (Θ

_{edi}) and the environmental benign index (Θ

_{ebi})–have been applied and assessed. Table 6 shows mathematical expressions for exergy destruction and exergetic efficiency.

#### 2.5.1. Environmental Destruction Coefficient (C_{ed})

#### 2.5.2. Environmental Destruction Index (Θ_{edi})

_{edi}is an indication of the effect an engine (e.g., gas turbine) has on the environment via exergy wastage (e.g., loss and destruction). The desired value is zero, and this is taken as the reference. The target is always to be as close to the reference value as possible. The equation representing the index is:

#### 2.5.3. Environmental Benign Index (Θ_{ebi})

_{ebi}is a measure of how environmentally benign the given energy system is. Θ

_{ebi}is directly and inversely proportional to the Θ

_{edi}:

_{ebi}ranges between zero and +∞. The higher the index the more environmentally beneficial the engine. Higher values of Θ

_{ebi}result from minimizing exergy losses and destruction.

## 3. Results and Discussion

#### 3.1. Economic Analysis

#### 3.2. Exergy Economic Analysis

_{k}, and relative difference in cost, r

_{k}, as percentages for the gas turbine engine with axial compressor. The greatest value for r

_{k}occurs in the combustion chamber (CC); this means that it is the most important component from an exergoeconomic viewpoint. Next is the axial compressor, then the LPT, HPT, and GEN, respectively. The CC, relative to the other components, has a high rate of exergy destruction and a correspondingly low value for f

_{k}.

_{k}for all components is below 50%; this means that a cost saving for the entire system could be attained by enhancing the efficiency of the components, even if this incurs an increase in the cost of capital invested. The cost of inefficiencies in each component can be addressed based on operating conditions and design criteria, with the component with the highest relative cost difference having priority.

_{k}and r

_{k}as a percentage of GT engine with two-stage centrifugal compressor are shown in Figure 5. The CC is again the greatest cost source relative to all other components. A study of the literature confirms that for gas turbines, the CC is accepted as the primary source of exergy destruction, greater than for any of the rotating components. The gas turbine engine with a two-stage centrifugal compressor has a relatively slight effect on r

_{k}and f

_{k}when compared to the axial compressor (reference case), due to its relatively low efficiency and capital cost. However, the impact on LPC and HPC is apparent and there is a need for greater efficiency even if it enhances capital cost because the exergy destruction makes a greater contribution to total cost. From an exergoeconomic perspective, after the CC, the LPC is the next most significant component, followed by the HPC. The gas turbine component’s economic efficiency is reduced slightly relative to turbines in the reference case due to the compressor configuration, which affects operating conditions and the quantity of extracting power.

_{k}and f

_{k}) for the GT engine with axial-centrifugal compressor. The main findings extracted from this figure can be summarized in four points: first, the axial compressor (LPC) shows greater economic efficiency than the centrifugal compressor due to its lower level of irreversibilities, despite its higher investment cost. Second, after the CC, the cold section components have more effect on enhancing the entire system’s cost-effectiveness. Third, the potential for improvement is higher in the centrifugal compressor (HPC). Finally, the irreversibility contributed to the axial compressor is lower than for the reference case. which suggests the target of a relative reduction in investment cost as well.

_{k}and f

_{k}) for the GT engine with centrifugal-centrifugal compressor. From this figure, it is concluded that: first, despite low exergy destruction, the LPT is most important, followed by the combustion chamber, due to varying compressor configurations. The LPC always shows better economic performance than the HPC because of cost due to inefficiencies. Therefore, modifying the design of the compressors by increasing component efficiency or adjusting the operating condition to reduce exergy destruction within the component is necessary. The values of f

_{k}for the intermediate pressure turbine (IPT) and electric generator are 63% and 56%, respectively. These values suggest that capital cost should be reduced at the expense of component efficiency. Moreover, the GT engine with centrifugal-centrifugal compressor configuration enhances the exergoeconomic efficiency for all rotating components compared to the GT with two-stage centrifugal compressor. All turbine components registered higher values of f

_{k}than for any of the previous cases investigated.

#### 3.3. Exergyenvironmental Analysis

_{2}emissions for all four proposed GT engines. CO

_{2}emission is strongly related to engine efficiency, as it is a measure of the fuel consumed in the combustion process. The CO

_{2}value increases as the air-fuel ratio increases until the maximum value is achieved at the stoichiometric air-to-fuel ratio (when oxygen from the air and fuel are in perfect balance for combustion) and then decreases in the presence of excess air, e.g., the air-to-fuel ratio increases further. This leads to an important point: for maximum combustion efficiency, the proportion of carbon dioxide in the flue gases should be just less than its peak value. The gas turbine engine with an axial-centrifugal compressor achieved the lowest value of CO

_{2}emissions per kWh when compared with others.

## 4. Conclusions

- The costs of the net power produced by the GT engines decreased with an increase in production load and with a decrease in ambient temperature.
- The GT with the centrifugal-centrifugal configuration is the most economically feasibility in terms of price per kilowatt power produced and shortest payback period. This was followed, in order, by the axial, axial-centrifugal, and the two-stage configuration.
- The centrifugal compressor has the advantages of low maintenance and high reliability, whereas the advantage of the axial compressor in efficiency has become narrow for small-scale gas turbines. However, all environmental indicators show that the axial-centrifugal configuration is more environmentally benign with lowest value of CO
_{2}emissions per kWh than the other systems considered, due to its high efficiency and lower fuel consumption. - The GT with axial configuration is almost as feasible as the GT with centrifugal-centrifugal configuration at the highest ambient temperature (328 K). This is because the axial compressor has higher efficiency and lower irreversibility compared to two-stage centrifugal, centrifugal-centrifugal, and axial-centrifugal compressors.
- As the power setting is reduced to part-load, the costs associated with exergy destruction and the overall cost for each component grow due to the increase in relative fuel consumption.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A | Uniform cash flow |

AC | Axial compressor |

ACF | Annual return cash flow |

ACIC | Annual capital cost |

${\dot{C}}_{}$ | Cost rate |

$c$ | Average unit cost |

CIC | Initial capital cost |

CC | Combustion chamber |

COE | Cost of electricity |

CRF | Capital recovery factor |

DP | Design point |

DPP | Discounted payback period |

$\stackrel{.}{\mathrm{E}}$ | Exergy rate |

ET | Electricity tariff |

EPC | Equipment purchasing cost |

f | Specefic fuel cost |

${f}_{k}$ | Exergoeconomic factor |

FC | Fuel cost |

GT | Gas turbine |

GEN | Generator |

HP | High pressure |

HPC | High pressure compressor |

HPT | High pressure turbine |

IPT | Intermediate pressure turbine |

ISO | International Standards Organization |

LPC | Low pressure compressor |

LPT | Low pressure turbine |

n | Number of years |

O&M | Operation and maintenance cost |

OM_{f} | Fixed annual operation and mainetance cost |

OM_{vb} | Variable operation and maintenance cost |

$P$ | Pressure |

${P}_{n}$ | N^{th} discharge pressure |

PV | Present value |

PW | Present worth |

PWF | Present worth factor |

$r$ | Tip radius |

r_{k} | Relative difference in cost |

${r}_{n}$ | Nominal escalation rate |

$\mathrm{S}$ | Span length |

$SV$ | Salvage value |

$\stackrel{.}{\mathrm{W}}$ | Work rate |

$\dot{Z}$ | Purchase cost rate |

Greek symbols | |

$\beta $ | Capital charge factor |

$\gamma $ | Heat capacity ratio |

${\eta}_{ex}$ | Exergetic efficiency |

${\eta}_{th}$ | Thermal efficiency |

$\mu $ | Maintenance cost escalation factor |

${\Theta}_{ebi}$ | Environmental benign index |

${\Theta}_{edi}$ | Environmental destruction index |

$\omega $ | Rotational speed |

Subscript | |

$\mathrm{e}$ | Exit |

F | Fuel |

i | Inlet |

k | Component |

x | Total |

w | Work |

xd | Destruction |

GT | Gas turbine |

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**Figure 2.**(

**a**) Lifecycle costs at varying operating load, and (

**b**) Lifecycle costs at varying ambient temperature.

**Figure 3.**The payback period of each configuration based on selling electricity (

**a**) at variant production load and (

**b**) at variant ambient temperature.

**Figure 4.**Exergoeconomic factor (f

_{k}) and relative difference in cost (r

_{k}) for main components of the gas- turbine engine (axial compressor).

**Figure 5.**Exergoeconomic factor (f

_{k}) and relative difference in cost (r

_{k}) for main components of the gas- turbine engine (Two-Stage centrifugal compressor).

**Figure 6.**Exergoeconomic factor (f

_{k}) and relative difference in cost (r

_{k}) for the main components of the GT engine (Axial-centrifugal compressor).

**Figure 7.**Exergoeconomic factor (f

_{k}) and relative difference in cost (r

_{k}) for the main components of the GT engine (Centrifugal-centrifugal compressor).

**Figure 8.**Exergy destruction costs and total cost (${\dot{C}}_{d}+{\dot{Z}}_{k}^{T}$) for GT (axial compressor) at ISO (288 K) and Kuwait conditions (328 K).

**Figure 9.**Exergy destruction costs and total cost (${\dot{C}}_{d}+{\dot{Z}}_{k}^{T}$) for GT engine (Axial-centrifugal compressor) at full and part-load (65%).

No | Model | Size kW | Type of Compressor | Manufacturer |
---|---|---|---|---|

1 | Saturn 20 | 1185 | Axial | Solar Turbine |

2 | M1A-17D | 1653 | Two stage centrifugal | Kawasaki |

3 | PW123 | 1759 | Centrifugal-centrifugal | Pratt & Whitney |

4 | T5317A | 1284 | Axial-centrifugal | Avco Lycoming |

Iteration Targets | Units | Value | |
---|---|---|---|

1. | Overall pressure ratio | - | 6.7 |

2. | Exhaust temperature | K | 793.15 |

3. | Shaft Power Delivered | kW | 1185 |

Iteration Variables | Units | Range Values | Converged Value | |
---|---|---|---|---|

1. | HP compressor pressure ratio | - | 2–20 | 3.42 |

2. | Burner exit temperature | K | 1200–2500 | 1238.75 |

3. | Inlet Corrected Flow | kg/s | 1–10 | 6.99 |

**Table 4.**Saturn 20 Design Point Performance Comparison—simulated and original manufacturer’s values.

Parameter | Unit | Original Manufacturer’s Value | Simulated | Difference | Difference (%) |
---|---|---|---|---|---|

Net Output | kW | 1185 | 1185 | 0 | 0 |

Heat rate, LHV | kJ/kWh | 14,670 | 15,381.7 | −711.7 | −4.85 |

Thermal Efficiency | % | 24.5 | 23.404 | +1.096 | +4.47 |

Exhaust Mass Flow | Kg/h | 23,410 | 25,563.6 | −2153.6 | −9.20 |

Exhaust Temperature | °C | 520 | 520 | 0 | 0 |

Parameter | Input Value |
---|---|

Discount rate | 3% |

Study period | 20 years |

Specific fuel cost | 5 USD/GJ |

Fuel heat rate | 46,800 kJ/kg |

Salvage value | 10% of instlllation cost |

**Table 6.**Exergetic efficiencies and exergy destruction rates for different system elements under steady state conditions.

Component | $\mathbf{Exergy}\mathbf{Destruction}\left({\dot{\mathit{E}}}_{\mathit{x}\mathit{d}}\right)$ | $\mathbf{Exergetic}\mathbf{Efficiency}\left({\mathit{\eta}}_{\mathit{e}\mathit{x}}\right)$ |
---|---|---|

Compressor | ${\dot{E}}_{xd,AC}={\dot{E}}_{xi}-{\dot{E}}_{xe}+{\dot{W}}_{C}$ | ${\eta}_{ex}=\frac{{\dot{E}}_{xi}-{\dot{E}}_{xe}}{{\dot{W}}_{C}}$ |

Combustion Chambers | ${\dot{E}}_{xd,CC}={\dot{E}}_{xi}-{\dot{E}}_{xe}+{\dot{E}}_{xf}$ | ${\eta}_{ex}=\frac{{\dot{E}}_{xe}}{{\dot{E}}_{xi}+{\dot{E}}_{xf}}$ |

Gas Turbines | ${\dot{E}}_{xd,GT}={\dot{E}}_{xi}-{\dot{E}}_{xe}-{\dot{W}}_{GT}$ | ${\eta}_{ex}=\frac{{\dot{W}}_{GT}}{{\dot{E}}_{xi}-{\dot{E}}_{xe}}$ |

The Cycle | ${\dot{E}}_{xd}={\displaystyle \sum}_{k}{\dot{E}}_{xd,k}$ | ${\eta}_{ex}=\frac{{\dot{E}}_{xp}}{{\dot{E}}_{xf}}$ =1 − $\frac{{\dot{E}}_{xd+}{\dot{E}}_{xl}}{{\dot{E}}_{xf}}$ |

No. | Indicator | Axial Configuration | Two-Stage Centrifugal Configuration | Axial-Centrifugal Configuration | Centrifugal-Centrifugal Configuration |
---|---|---|---|---|---|

1 | Environmental Destruction Coefficient [C_{ed}] | 3.846 | 3.987 | 3.704 | 4.065 |

2 | Environmental Destruction Index [Θ_{edi}] | 2.872 | 3.005 | 2.693 | 3.061 |

3 | Environmental Benign Index [Θ_{ebi}] | 0.348 | 0.333 | 0.371 | 0.327 |

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## Share and Cite

**MDPI and ACS Style**

Almutairi, H.H.; Almutairi, A.S.; Suleiman, S.M.; Alenezi, A.H.; Alkhulaifi, K.A.; Alhajeri, H.M. Economic, Exergoeconomic and Exergoenvironmental Evaluation of Gas Cycle Power Plant Based on Different Compressor Configurations. *Processes* **2023**, *11*, 1023.
https://doi.org/10.3390/pr11041023

**AMA Style**

Almutairi HH, Almutairi AS, Suleiman SM, Alenezi AH, Alkhulaifi KA, Alhajeri HM. Economic, Exergoeconomic and Exergoenvironmental Evaluation of Gas Cycle Power Plant Based on Different Compressor Configurations. *Processes*. 2023; 11(4):1023.
https://doi.org/10.3390/pr11041023

**Chicago/Turabian Style**

Almutairi, Hamad H., Abdulrahman S. Almutairi, Suleiman M. Suleiman, Abdulrahman H. Alenezi, Khalid A. Alkhulaifi, and Hamad M. Alhajeri. 2023. "Economic, Exergoeconomic and Exergoenvironmental Evaluation of Gas Cycle Power Plant Based on Different Compressor Configurations" *Processes* 11, no. 4: 1023.
https://doi.org/10.3390/pr11041023