# Economic Analysis of Gas Turbine Using to Increase Efficiency of the Organic Rankine Cycle

## Abstract

**:**

## 1. Introduction

## 2. System Configuration and Modeling

#### 2.1. Energy Analysis

- The specific enthalpy (h
_{1}) and specific entropy (s_{1}) were calculated using the evaporation pressure of dry saturated steam (with a quality of x = 1). - Considering the isentropic expansion of the vaporized working fluid in the turbine, the specific enthalpy (h
_{2s}) was determined based on the specific entropy (s_{1}) and the condensing pressure. - The specific enthalpy (h
_{3}) was determined using the condensation pressure for dry saturated steam (with a quality of x = 1). - The specific enthalpy (h
_{4}) was determined based on the condensing pressure for the liquid state, specifically on the saturation line (with a quality of x = 0). - Considering the isentropic compression of the working fluid in the pump (s
_{4}= s_{5}) based on specific entropy s_{4}and evaporation pressure, specific enthalpy h_{5s}was determined. - The specific enthalpy (h
_{6}) was determined based on the evaporation pressure for the liquid state, specifically on the boundary line.

_{1}− h

_{2r}denotes the real decline in enthalpy when experiencing an identical pressure drop as encountered during an isentropic transformation. Equation (2) is as follows:

_{5r}− h

_{4}denotes the real decline in enthalpy when experiencing an identical pressure drop as encountered during an isentropic transformation.

- ORC efficiency:

- Power of the ORC cycle:

- Electrical power of the designed ORC power plant:

_{m}is the mechanical efficiency of the turbine, while η

_{g}is the generator efficiency.

#### 2.2. Economic Analysis

- ORC pump [59]:

- ORC preheater [60]:

- ORC evaporator [61]:

- ORC turbine [60]:

- ORC Condenser [62]:

_{max}and ΔT

_{min}represent the highest and lowest temperature differences observed within the heat exchanging equipment, respectively. The values of the heat transfer coefficient U in a heat exchanging system typically rely on factors, such as the material employed and the phase of the flowing heat. For the purposes of this study, it has been assumed that the U values remain constant, as shown in Table 3:

- IO—investment expenditure, USD;
- CF—yearly cash flow, USD/year;
- GT—gas turbine;
- F—working fluid;
- Conf—configuration.

- T
_{SP2}= (240, 245, 250) °C; - T
_{geo_in}= (80–130) °C; - T
_{C}= (60, 65, 70) °C.

- Inc—operational income, USD;
- OCost—operational cost, USD.

- pel—electricity price, USD/MWh;
- nhour—operational number of hours in year: 7446 h;

- png—natural gas price, USD/kg;
- varOM—variable operation and maintenance cost, USD;
- fixOM—fixed operation and maintenance cost, USD.

- pTG—gas turbine price, USD/kW;
- pHE—heat exchanger price, USD.

## 3. Results

## 4. Conclusions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Symbols | |

$\dot{\mathrm{Q}}$ | heat flux [kW] |

$\dot{\mathrm{W}}$ | equipment power [kW] |

$\u2206{\mathrm{T}}_{\mathrm{m}}$ | log mean temperature difference [K] |

A | heat transfer area [m^{2}] |

CF | yearly cash flow [USD/yr] |

fixOM | fixed operation and maintenance costs [USD] |

Inc | operational income [USD] |

IO | investment expenditure [USD] |

MC | depth of the geothermal well [m] |

N | system power [kW] |

Nhour | operational number of hours in year [h] |

OCost | operational cost [USD] |

pel | electricity price [USD/MWh] |

pHE | heat exchanger price [USD] |

png | natural gas price [USD/kg] |

pTG | gas turbine price [USD/kW] |

T | temperature [K] |

U | overall heat transfer coefficient [kW/m^{2}·K] |

varOM | variable operation and maintenance costs [USD] |

Z | equipment investment cost [USD] |

η | efficiency [- or %] |

Subscripts | |

1,…,6,A,B,C | thermodynamic state points |

C | condenser |

Conf | configuration |

E | evaporator |

el | electrical |

F | working fluid |

g | generator |

GEO | geothermal |

HX | heat exchanger |

i | internal |

IN | at inlet |

m | mechanical |

OUT | at outlet |

P | pump |

PH | preheater |

SP | exhaust gases from gas turbine |

T | turbine |

Abbreviation | |

GT | gas turbine |

GT-ORC | gas turbine–ORC combined system |

GW | geothermal well |

GWC | geothermal well cost |

HC | hydrocarbon |

HCFO | hydrochlorofluoroolefin |

HFC | hydrofluorocarbon |

HFO | hydrofluoroolefins |

MM | hexamethyldisiloxane |

ORC | organic Rankine cycle |

SPBT | simple payback time |

VER | vapor expansion ratio |

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**Figure 2.**SPBT values as a function of electricity price and natural gas price for the lowest value SPBT of gas turbines. MD = 2000 m.

**Figure 3.**SPBT values as a function of electricity price and natural gas price for the lowest value SPBT of working fluids (titles of partly figures). MD = 2000 m.

**Figure 4.**SPBT values as a function of electricity price and depth of geothermal well for the lowest value SPBT of working fluids and gas turbine: R1336mzz(Z) and SGT-800. png = 0.4 USD/kg.

**Table 1.**Comparison of the basic technical parameters of the gas turbines. Source: own study based on [54].

Type of the Gas Turbine (GT) | Gas Turbine SGT-50 | Gas Turbine SGT-100 | Gas Turbine SGT-300 | Gas Turbine SGT-400 |
---|---|---|---|---|

Fuel | Natural gas, liquid fuel, dual fuel | |||

Gross efficiency | 26% | 30.2% | 30.6% | 34.8% |

Heat rate | 15,148 kJ/kWh | 11,914 kJ/kWh | 11,773 kJ/kWh | 10,355 kJ/kWh |

Turbine speed | 25,500 rpm | 17,384 rpm | 14,010 rpm | 9500 rpm |

Pressure ration | 7.0:1 | 14.0:1 | 13.7:1 | 16.8:1 |

Exhaust mass flow | 9.5 kg/s | 19.5 kg/s | 30.2 kg/s | 39.4 kg/s |

Exhaust temperature | 600 °C | 545 °C | 542 °C | 555 °C |

Power | 2 MWe | 5.1 MWe | 7.9 MWe | 12.9 MWe |

Type of the Gas Turbine (GT) | Gas Turbine SGT-800 | Gas Turbine SGT-A05 KB5S | Gas Turbine SGT-A05 KB7S | Gas Turbine SGT-A05 KB7HE |

Fuel | Natural gas, liquid fuel, dual fuel | |||

Gross efficiency | 41.1% | 29.7% | 32.3% | 33.2% |

Heat rate | 8759 kJ/kWh | 12,137 kJ/kWh | 11,152 kJ/kWh | 10,848 kJ/kWh |

Turbine speed | 6600 rpm | 14,200 rpm | 14,600 rpm | 14,600 rpm |

Pressure ration | 21.1:1 | 10.3:1 | 13.9:1 | 14.1:1 |

Exhaust mass flow | 135.5 kg/s | 15.4 kg/s | 21.3 kg/s | 21.4 kg/s |

Exhaust temperature | 596 °C | 560 °C | 494 °C | 522 °C |

Power | 62.5 MWe | 4.0 MWe | 5.4 MWe | 5.8 MWe |

Working Fluid (F) | Chemical Class | T_{bp} (K) | T_{CR} (K) | P_{CR} (MPa) | ASHRAE Safety Group | ASHRAE Flammability | ASHRAE Toxicity | ODP | GWP |
---|---|---|---|---|---|---|---|---|---|

R600a | HC | 272.66 | 424.13 | 3.796 | A3 | Yes (highly flammable) | No | 0 | 3 |

R134a | HFC | 247,08 | 374.21 | 4.0593 | A1 | Non-flammable | No | 0 | 1430 |

R152a | HFC | 249.13 | 386.41 | 4.5168 | A2 | Yes (medium flammable) | No | 0 | 124 |

R227ea | HFC | 256.81 | 374.9 | 2.925 | A1 | Non-flammable | No | 0 | 3230 |

R245fa | HFC | 288.29 | 427.16 | 3.651 | A1 | Non-flammable | No | 0 | 1030 |

R1224yd(Z) | HCFO | 287.77 | 428.69 | 3.337 | - | Flammable | Relatively non-toxic | 0 | 0.88 |

R1233zd(E) | HCFO | 291.41 | 439.6 | 3.6237 | A3 | Yes (highly flammable) | Acceptable toxicity | 0 | 7 |

R1234yf | HFO | 243.7 | 367.85 | 3.3822 | A2L | Yes (low flammable) | No | 0 | 4 |

R1243zf | HFO | 247.73 | 376.93 | 3.5179 | - | Yes (highly flammable) | Toxic | 0 | 149 |

R1336mzz(Z) | HFO | 306.6 | 444.5 | 2.903 | A3 | Yes (highly flammable) | No | 0 | 9 |

Equipment | Heating Fluid Type | Heating Fluid Phase | Heated Fluid Type | Heated Fluid Phase | U [kW/m^{2}·K] |
---|---|---|---|---|---|

Heat exchanger | Exhaust gas | Gas | Geothermal brine | Liquid | 0.2 |

Evaporator | Geothermal brine | Liquid | Organic fluid | Liquid/vapor | 0.9 |

Preheater | Geothermal brine | Liquid | Organic fluid | Liquid | 0.9 |

Condenser | Organic fluid | Vapor/liquid | Water | Liquid | 1.0 |

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**MDPI and ACS Style**

Matuszewska, D.
Economic Analysis of Gas Turbine Using to Increase Efficiency of the Organic Rankine Cycle. *Sustainability* **2024**, *16*, 75.
https://doi.org/10.3390/su16010075

**AMA Style**

Matuszewska D.
Economic Analysis of Gas Turbine Using to Increase Efficiency of the Organic Rankine Cycle. *Sustainability*. 2024; 16(1):75.
https://doi.org/10.3390/su16010075

**Chicago/Turabian Style**

Matuszewska, Dominika.
2024. "Economic Analysis of Gas Turbine Using to Increase Efficiency of the Organic Rankine Cycle" *Sustainability* 16, no. 1: 75.
https://doi.org/10.3390/su16010075