^{1}

^{*}

^{1}

^{1}

In this study, the probabilistic exergoeconomic analysis was performed for four industrial gas turbine (GT) units comprising two (GT16 and GT19) units of 100 MW GE engine and two (GT8 and GT12) units of 25 MW Hitachi engine at Transcorp Power Limited, Ughelli. These four industrial GT engine units were modelled and simulated using natural gas as fuel. The design point (DP) simulation results of the modelled GT engines were validated with the available DP thermodynamic data from original equipment manufacturer (OEM). This was done before the off-design point (ODP) simulation was carried out which represents the plant operations. The results obtained from exergy analysis at full load operation show that the turbine has the highest exergy efficiency followed by compressor and combustion having the least. For turbines these were 96.13% for GT8 unit, 98.02% for GT12 unit, 96.26% for GT16 unit, and 96.30% for GT19 unit. Moreover, the combustion chamber has the highest exergy destruction efficiency of 55.16% GT8 unit, 56.58% GT12 unit, 43.90% GT16 unit, and 43.30% GT19 unit respectively. The exergy analysis results obtained from the four units show that the combustion chamber (CC) is the most significant exergy destruction with lowest exergy efficiency and highest exergy destruction efficiency of plant components. The exergoeconomic analysis results from four units showed combustion chamber exergy destruction cost of 531.08 $/h GT8 unit, 584.53 $/h GT12 unit, 2351.81 $/h GT16, and 2315.93 $/h GT19 unit. The probabilistic results and analysis based on the input parameters distributions were evaluated and discussed.

The uncertainty in energy prices and increase in demand coupled with stringent emission regulation has led researchers and industries to seek for more efficient energy systems with reduced thermal losses [

The application of exergy analysis in power plant such as gas turbine is very important because it helps to quantify and locate plant components with major energy losses which will then help the plant engineer make decisions and possibly optimize plant performance and minimize fuel consumption. With second law analysis (exergy) the engineer is able to bring about improvement of plant performance and develop new components or processes with minimum energy losses.

Bejan [

According to Mahamud et al. [_{2} emissions. According to Almutairi et al. [

It is useful to combine second law of thermodynamic with economic principles for the systematic study of energy systems. This combination forms the basis of the relatively new field of thermoeconomics or exergoeconomics. Exergoeconomics combines exergy analysis with conventional cost analysis in order to evaluate and optimize the performance of energy systems. Exergoeconomics is a tool used for improving overall system efficiency and lowering life cycle costs of a thermodynamic system. It incorporates the associated costs of the thermodynamic inefficiencies in the total product cost of an energy system [

According to Anosike [

The most comprehensive approach to take into account a wide range of uncertainties in key risks is to use a probabilistic assessment [

Monte Carlo simulation provides a number of advantages over deterministic analysis:

v Probabilistic Results. Results show not only what could happen, but how likely each outcome is.

v Graphical Results. Because of the data a Monte Carlo simulation generates, it is easy to create graphs of different outcomes and their chances of occurrence. This is important findings to other stakeholders.

v Sensitivity Analysis. With just a few cases, deterministic analysis makes it difficult to see which variables impact the outcome the most. In Monte Carlo simulation, it is easy to see which inputs had the biggest effect on bottom-line results.

v Scenario Analysis. In deterministic models, it is very difficult to model different combinations of values for different inputs to see the effects of truly different scenarios. Using Monte Carlo simulation, analysts can see exactly which inputs had which values together when certain outcomes occurred. This is invaluable for pursuing further analysis.

v Correlation of Inputs. In Monte Carlo simulation, it is possible to model interdependent relationships between inputs variables. It is important for accuracy to represent how, in reality, when some factors go up, others go up or down accordingly.

A probabilistic approach using Monte Carlo simulation and risk analysis is presented, that more accurately defines uncertainties and its impact on plant performance. The problem with this approach is that the true level of success may not be well conveyed.

Specifically in this work, the use of probabilistic tool allows tackling unpredictability of component performance due to varying ambient conditions (at least temperature), as well as power plant part-load operations.

The plant under consideration consists of a 25 MW (GT8 and GT12) Hitachi H25 and 100 MW (GT16 and GT19) GE Frame 9 single shaft open cycles all operated at 50 Hz located at Ughelli, Nigeria. Each generates electricity to the National Grid and use natural gas as fuel. The simplified schematic diagram of the plant is shown in _{net} is available energy for generator.

Energy manifests itself in many forms, which are either internal or transient, and energy can be converted from one form to another [

Exergy is defined as the maximum useful work which could be produced by a stream or system in a specified environment. Exergy is a measure of the maximum capacity of a system to perform useful work as it proceeds to a specified final state in equilibrium with its surroundings. The available work that can be extracted from an energy source depends on the state of the source’s surroundings [

much of the usable work potential, or resource supplied as the input to the system under consideration has been consumed by the process. Exergy provides a quantitative basis to measure the degradation of energy in conversion processes.

Exergy of a stream of matter is distinctly divided into four components: kinetic, potential, physical and chemical, in the absence of nuclear effects, magnetism, electricity etc. The exergy balance of a system can be generally written as:

E ˙ = E ˙ K E + E ˙ P E + E ˙ P H + E ˙ C H E (1)

The kinetic and potential energies of a stream of substance are ordered forms of energy and they depend only on the mass and as such fully convertible to work. Therefore, when evaluated in relation to the environmental reference state, they are equal to kinetic and potential exergy.

E ˙ K E = 1 2 m ˙ V 2 (2)

E ˙ P E = m ˙ g Z (3)

V and Z are important where there is direct interaction of stream with the environment. Kinetic and potential energy are neglected in this study due to their insignificant.

Physical exergy is the maximum useful work that can be extracted from a unit mass of substance passing through a specified state ( T s , P s ) to the environmental state ( T 0 , P 0 ) by physical processes involving only thermal interaction with the environment. The physical exergy consists of two parts, mechanical and thermal exergy [

E ˙ P H = m ˙ [ ( h s − h 0 ) − T 0 ( s s − s 0 ) ] (4)

When the specified state T s is equal to environmental state T 0 , by ideal gas relation, Equation (4) becomes:

E ˙ P H = m ˙ R T o ln ( P P o ) (5)

Chemical exergy represents the maximum useful energy that can be extracted while the flow moves from an environmental state to a dead state due to differences in concentration and molecular structure. In the environmental state, the system is mechanically and thermally at equilibrium state, but not chemically [

E ˙ C H E = m ˙ f L H V (6)

The following assumptions were made considering the second law of thermodynamics analysis:

1) Heat losses from all plant components are negligible.

2) Kinetic and potential energy components of exergy are neglected.

3) Fuel (natural gas) is taken as methane and modeled as an ideal gas.

4) Pressure drop in the combustion chamber assumed to be 3%.

5) The ambient conditions of temperature and pressure are 25˚C and 1.013 bar.

The exergy balance equation for a control volume in steady state according to [

E ˙ x = ∑ j ( 1 − T 0 T j ) Q ˙ j + W ˙ c v + ∑ i m ˙ i e i − ∑ e m ˙ e e e (7)

The subscripts i refer to conditions at inlet, e and j exits of control volume boundaries and o is the reference state.

Also, the thermomechanical exergy stream may be decomposed into mechanical and thermal components of exergy [

E ˙ i M − E ˙ j M = ( E ˙ i T − E ˙ j T ) + ( E ˙ i P − E ˙ j P ) , (8)

where the subscripts i and j denote, respectively, exergy flow streams entering or leaving the plant component. M, T and P represent material components under study, thermal property and mechanical property respectively.

The thermal and mechanical components of the exergy stream for an ideal gas with constant specific heat expressed by [

E ˙ T = m ˙ c p [ ( T − T o ) − T o ln ( T T o ) ] (9)

E ˙ P = m ˙ R T o ln ( P P o ) (10)

where, P o and T o are the pressure and temperature, respectively, at standard state; m ˙ is the mass flow rate of the working fluid; R is the gas constant; c p is the specific heat at constant pressure.

With the decomposition of an exergy stream defined in eqn. (7), the general exergy-balance equation is written as stated by [

E ˙ W = E ˙ C H E + ( ∑ i n l e t E ˙ i T − ∑ e x i t E ˙ e T ) + ( ∑ i n l e t E ˙ i P − ∑ e x i t E ˙ e P ) + T 0 ( ∑ i n l e t S ˙ i − ∑ e x i t S ˙ e + Q ˙ c v T 0 ) (11)

The term E ˙ W in Equation (11) represents the exergy rate of power output by the material component under study; E ˙ C H E denotes the rate of exergy flow of fuel in the plant; S ˙ is the entropy transfer rate; T 0 is the temperature of the source from which the heat is transferred to the working fluid; the fourth right- hand term is the exergy destroyed in the component and Q ˙ c v in the fourth right-hand term denotes the heat transfer rate between the component and the environment.

The exergy balance equation for each component in the power station can be derived from the general exergy balance equation given in Equation (11). The exergy balance equations for each component are as follows using

Compressor:

( E ˙ 1 T − E ˙ 2 T ) + ( E ˙ 1 P − E ˙ 2 P ) + T o ( S ˙ 1 − S ˙ 2 ) = E ˙ W C (12)

Combustion chamber:

E ˙ 5 C H E + ( E ˙ 2 T + E ˙ 5 T − E ˙ 3 T ) + ( E ˙ 2 P + E ˙ 5 P − E ˙ 3 P ) + T o ( S ˙ 2 + S ˙ f − S ˙ 3 + Q ˙ c v / T o ) = 0 (13)

Turbine:

( E ˙ 3 T − E ˙ 4 T ) + ( E ˙ 3 P − E ˙ 4 P ) + T o ( S ˙ 3 − S ˙ 4 ) = E ˙ W T (14)

Chemical exergy of fuel (Methane):

m ˙ f L H V = E ˙ 5 C H E (15)

Exergy is not conserved but destroyed in irreversible systems. The irreversibilities are caused by internal irreversibilities such as friction, unrestrained expansion, mixing and chemical reaction and external irreversibilities arise from heat transfer through a finite temperature difference. The energy associated with material or energy stream is rejected to the environment whenever there is exergy lost in the system [

Exergy destroyed in the compressor, E ˙ D C :

E ˙ D C = T o ( S ˙ 2 − S ˙ 1 ) = m ˙ T o [ c p a ln ( T 2 / T 1 ) − R ln ( P 2 / P 1 ) ] (16)

Combustion chamber, E ˙ D C C :

E ˙ D C C = E ˙ 5 C H E + ( E ˙ 2 T + E ˙ f T − E ˙ 3 T ) + ( E ˙ 2 P + E ˙ f P − E ˙ 3 P ) (17)

Turbine, E ˙ D T :

E ˙ D T = T o ( S ˙ 4 − S ˙ 4 ) = m ˙ T o [ c p g ln ( T 4 / T 3 ) − R ln ( P 4 / P 3 ) ] ̇ (18)

Total exergy destroyed in the plant, E ˙ D p l a n t :

E ˙ D p l a n t = E ˙ D C + E ˙ D C C + E ˙ D T (19)

Exergoeconomic based on the concept that exergy is the only rational basis for assigning monetary costs to the interactions that a system experiences with its surroundings and to the sources of thermodynamic inefficiencies within it [

Exergoeconomic analysis of energy conversion system, Tsatsaronis [

・ Exergy analysis.

・ Economic analysis of each of the plant component.

・ Estimation of exergetic costs associated with each flow and

・ Exergoeconomic evaluation of each system component.

The economic analysis, conducted as part of the exergoeconomic analysis, provides the appropriate monetary (cost) values associated with the investment, operating (excluding fuel), maintenance and fuel costs of the system being analyzed [

P W = P E C − ( S V ) P W F ( i , n ) (20)

The salvage value (SV) at the end of the nth year is taken as 10% of the initial investment for component or purchase equipment cost (PEC). The present worth of the component may be converted to the annualized cost by using the capital recovery factor C R F ( i , n ) [

C ˙ ( $ / year ) = P W × C R F ( i , n ) (21)

where, C R F ( i , n ) = i ( 1 + i ) n / [ ( 1 + i ) n − 1 ] .

The capital recovery factor (CRF) depends on the interest rate as well as estimated equipment lifetime [

Compressor, P E C C :

P E C C = ( 71.1 m ˙ a 0.9 − η s C ) ( P 2 P 1 ) ln ( P 2 P 1 ) (22)

Combustion Chamber, P E C C C :

P E C C C = ( 46.08 m ˙ a 0.995 − P 3 / P 2 ) × [ 1 + exp ( 0.018 T 3 − 26.4 ) ] (23)

Turbine, P E C T :

P E C T = ( 479.34 m ˙ g 0.92 − η T ) ln ( P 3 P 4 ) × [ 1 + exp ( 0.036 T 3 − 54.4 ) ] (24)

For converting capital investment cost into cost per time unit, one may write [

Z ˙ k = C ˙ k φ k N (25)

N is the annual number of operation hours of the unit and maintenance cost is taken into consideration through the factor φ k = 1.06 for each plant component [

The cost associated with fuel is obtained from

C ˙ f = c f m ˙ f L H V (26)

where the fuel cost per energy unit (on an LHV basis) is c f = 0.004 $ / MJ [

The exergy analysis yields the desired information for a complete evaluation of the design and performance of an exergy system from the thermodynamic viewpoint. With this, the plant operator needs to know how much the exergy destruction in a plant component costs and knowing this cost is very useful in improving the cost effectiveness of the plant [

To perform exergy costing calculations, the schematic diagram of the gas turbine power plant components

∑ e C ˙ e , k + C ˙ w , k = C ˙ q , k + ∑ i C ˙ i , k + Z ˙ k (27)

∑ ( c e E ˙ e ) k + c w , k W ˙ k = c q , k E ˙ q , k + ∑ ( c i , k E ˙ i ) k + Z ˙ k (28)

C ˙ j = c j E ˙ j (29)

The cost balance for each component and the required auxiliary equations of

Compressor:

C ˙ 2 = C ˙ 1 + C ˙ 6 + Z ˙ C (30)

Combustion Chamber:

C ˙ 3 = C ˙ 2 + C ˙ 5 + Z ˙ C C (31)

Turbine:

C ˙ 4 + C ˙ 6 + C ˙ 7 = C ˙ 3 + Z ˙ T (32)

The numbers in subscripts denote the states of material streams described in

Component | Fuel | Product | Loss |
---|---|---|---|

C | 1, 6 | 2 | - |

CC | 5 | 3 | - |

T | 3 | 7 | 4 |

C ˙ 3 E ˙ 3 = C ˙ 4 E ˙ 4 or c 3 = c 4 F-rule (33)

C ˙ 6 W ˙ C = C ˙ 7 W ˙ n e t or c 6 = c 7 P-rule (34)

C ˙ f = C ˙ 5 = c f m ˙ f L H V (35)

A zero unit cost is assumed for air entering the air compressor, which is:

C ˙ 1 = 0 (36)

Solving the Equations (30) - (36) simultaneously, one may obtain the cost flow rate and average unit cost at each inlet and outlet of the kth component.

In a complete exergoeconomic evaluation of a plant, certain variables play an important role which is based on the following variable calculated for the kth component. These are the average cost of fuel ( c F , k ) , average cost of product ( c P , k ) , cost rate exergy destruction ( C ˙ D , k ) , relative cost difference r k and exergoeconomic factor f k .

Tsatsaronis [

c F , k = C ˙ F , k E ˙ F , k (37)

c P , k = C ˙ P , k E ˙ P , k (38)

The cost rate associated with exergy destruction is given as:

C ˙ D , k = c F , k E ˙ D , k (39)

The relative cost difference r k is written [

r k = c P , k − c F , k c F , k = Z ˙ k c F , k E ˙ P , k + 1 − ε k ε k (40)

f k = Z ˙ k C ˙ D , k + Z ˙ k (41)

The average operating data used in this analysis were values obtained from operator’s manual and logbook of Transcorp gas turbine power plants for the period of five years (2010-2014) as presented in

In this analysis, standard reference ambient temperature and pressure are assumed 25˚C and 1.013 bar respectively. The exergy flow rates at the inlet and outlet of each component of the plants were evaluated. An exergy balance for the

Plant/Average Operating Data | GT8 | GT12 | GT16 | GT19 |
---|---|---|---|---|

Power output (MW) | 17.50 | 18.20 | 75.10 | 80.15 |

Pressure of inlet air to compressor, P 1 ( MPa ) | 0.1013 | 0.1013 | 0.1013 | 0.1013 |

Temperature of inlet air to compressor, T 1 ( K ) | 298 | 298 | 298 | 298 |

Mass flow rate of air, m ˙ a ( kg / s ) | 78 | 79 | 412 | 414 |

Outlet pressure of air from compressor, P 2 ( MPa ) | 1.108 | 1.110 | 0.981 | 0.985 |

Compression ratio, r_{p} | 10.94 | 10.96 | 9.68 | 9.72 |

Outlet temperature of air from compressor, T 2 ( K ) | 653.16 | 660 | 655 | 654 |

Inlet temperature to gas turbine, T 3 ( K ) | 1425 | 1425 | 1328 | 1330 |

Temperature of exhaust gas, T 4 ( K ) | 846.4 | 835.1 | 824 | 821 |

Pressure of exhaust gas, P 4 ( MPa ) | 0.106 | 0.106 | 0.1075 | 0.1075 |

Mass flow rate of fuel, m ˙ f ( kg / s ) | 1.414 | 1.515 | 7.858 | 7.843 |

Inlet temperature of fuel, T f ( K ) | 298 | 298 | 296.9 | 297 |

Inlet pressure of fuel, P f ( MPa ) | 2.12 | 2.12 | 2.05 | 2.03 |

Isentropic efficiency of compressor, η_{sC} (%) | 85 | 85 | 89 | 89 |

Isentropic efficiency of turbine, η_{sGT} (%) | 89 | 89 | 90 | 90 |

LHV of fuel (kJ/kg) | 47.285 | 47.285 | 47.285 | 47.285 |

Turbine speed (rpm) | 7280 | 7280 | 3000 | 3000 |

Grid Frequency (Hz) | 50 | 50 | 50 | 50 |

components of the gas turbine plants and the total plant is at this point performed and the net exergy flow rates crossing the boundary of each component of the plants, together with the exergy destruction in each component are calculated and are as shown in

The exergy analysis results obtained at full load operation show that the turbine has the highest exergy efficiency of 96.13% for GT8 unit, 98.02% for GT12 unit, 96.26% for GT16 unit, 96.30% for GT19 unit, followed by compressor 94.23% for GT8 unit, 90.89% for GT12 unit, 88.38% for GT16 unit, 88.58% for GT19 unit and combustion chamber having the lowest 44.84% forGT8 unit, 43.42% for GT12 units, 56.10% for GT16 unit, 56.69% for GT19 unit. Moreover, the combustion chamber has the highest exergy destruction efficiency of 55.16% GT8 unit, 56.58% GT12 unit, 43.90% GT16 unit, and 43.30% GT19 unit respectively.

The results of exergy analysis from the four units show that the combustion chamber is the most significant exergy destruction with lowest exergy efficiency and highest exergy destruction efficiency of plant components as shown in

Plant | GT8 | GT12 | GT16 | GT19 |
---|---|---|---|---|

Installed rated power (MW) | 25.00 | 25.00 | 100.00 | 100.00 |

Compressor power W ˙ C (MW) | 28.540 | 29.605 | 152.391 | 152.702 |

Turbine power W ˙ T (MW) | 53.762 | 55.570 | 247.582 | 249.739 |

Exergy rate E ˙ W C (MW) | 27.684 | 28.717 | 147.819 | 148.121 |

Exergy rate E ˙ C H E (MW) | 115.620 | 120.378 | 420.307 | 419.598 |

Exergy rate E ˙ W T (MW) | 53.762 | 55.570 | 247.582 | 249.739 |

Exergy destruction rate E ˙ D C (MW) | 1.598 | 2.614 | 17.170 | 16.920 |

Exergy destruction rate E ˙ D C C (MW) | 64.138 | 68.509 | 186.108 | 183.276 |

Exergy destruction rate E ˙ D T (MW) | 2.079 | 1.103 | 9.257 | 9.228 |

Total exergy destruction rate E ˙ D p l a n t (MW) | 67.816 | 72.226 | 212.537 | 209.424 |

Exergy efficiency ε C (%) | 94.23 | 90.89 | 88.38 | 88.58 |

Exergy efficiency ε C C (%) | 44.84 | 43.42 | 56.10 | 56.69 |

Exergy efficiency ε T (%) | 96.13 | 98.02 | 96.26 | 96.30 |

Total exergy efficiency ε p l a n t (%) | 41.68 | 40.35 | 49.90 | 50.52 |

Exergy destruction efficiency ε D C (%) | 1.37 | 2.16 | 4.05 | 3.99 |

Exergy destruction efficiency ε D C C (%) | 55.16 | 56.58 | 43.9 | 43.30 |

Exergy destruction efficiency ε D T (%) | 1.79 | 0.91 | 2.18 | 2.18 |

Total exergy destruction efficiency ε D p l a n t (%) | 58.32 | 59.65 | 50.13 | 49.48 |

Exergy destruction ratio y D C (%) | 2.36 | 3.62 | 8.08 | 8.08 |

Exergy destruction ratio y D C C (%) | 94.58 | 94.85 | 87.57 | 87.51 |

Exergy destruction ratio y D T (%) | 3.07 | 1.53 | 4.36 | 4.41 |

and degradation occur in this section and in agreement with what was obtained in [

Before now, the method of improving plant component and how to improve it were solely based on thermodynamics. The thermodynamic analysis is very important but the exergonomic analysis which is based on cost associated with exergy of a component has an important role to play and has more significant economically when analyzing a system. The knowledge of the cost of exergy in a component is a very useful parameter for improving the cost-effectiveness of a plant [

Component | C P ( $/GJ) | C F ( $/GJ) | E ˙ D (MW) | C ˙ D ($/h) | Z ˙ ($/h) | C ˙ D + Z ˙ ($/h) | f (%) |
---|---|---|---|---|---|---|---|

C | 10.12 | 7.38 | 1.60 | 42.51 | 190.45 | 232.96 | 81.75 |

CC | 6.81 | 2.30 | 64.14 | 531.08 | 4.88 | 535.96 | 0.91 |

T | 7.38 | 6.81 | 2.08 | 50.99 | 73.45 | 124.44 | 59.02 |

Component | C P ( $/GJ) | C F ( $/GJ) | E ˙ D (MW) | C ˙ D ($/h) | Z ˙ ($/h) | C ˙ D + Z ˙ ($/h) | f (%) |
---|---|---|---|---|---|---|---|

C | 10.16 | 7.36 | 2.61 | 69.15 | 169.70 | 238.85 | 71.05 |

CC | 7.03 | 2.37 | 68.51 | 584.53 | 4.94 | 589.47 | 0.84 |

T | 7.36 | 7.03 | 1.10 | 27.84 | 71.67 | 99.51 | 72.02 |

Component | C P ( $/GJ) | C F ( $/GJ) | E ˙ D (MW) | C ˙ D ($/h) | Z ˙ ($/h) | C ˙ D + Z ˙ ($/h) | f (%) |
---|---|---|---|---|---|---|---|

C | 12.05 | 9.00 | 17.17 | 556.31 | 728.75 | 1285.06 | 56.71 |

CC | 8.32 | 3.51 | 186.12 | 2351.81 | 18.60 | 2370.41 | 0.78 |

T | 9.00 | 8.32 | 9.26 | 277.36 | 331.49 | 608.85 | 54.45 |

Component | C P ( $/GJ) | C F ( $/GJ) | E ˙ D (MW) | C ˙ D ($/h) | Z ˙ ($/h) | C ˙ D + Z ˙ ($/h) | f (%) |
---|---|---|---|---|---|---|---|

C | 12.02 | 8.99 | 16.92 | 547.60 | 736.59 | 1284.19 | 57.46 |

CC | 8.26 | 3.51 | 183.28 | 2315.93 | 18.74 | 2334.67 | 0.80 |

T | 8.99 | 8.26 | 9.23 | 274.46 | 333.71 | 608.17 | 54.82 |

The unit cost of electricity produced in each unit is given as 7.38 $/GJ GT8, 7.362 $/GJ GT12, 9.00 $/GJ GT16 and 8.99 $/GJ GT19. The exergoeconomic parameters considered in this study include average costs per unit of fuel exergy C_{F} and product exergy C_{P}, rate of destruction E ˙ D , cost rate of exergy destruction C D , investment cost rate Z ˙ , and exergoeconomic factor f . The components with the highest value of Z ˙ k + C ˙ D , k and lowest exergoeconomic factor f are considered the most important components from an exergoeconomic viewpoint. This provides a means of determining the level of priority a component should be given attention with respect to improving of the plant.

For the four units considered, the combustion chamber has the highest value of Z ˙ k + C ˙ D , k and lowest value of exergoeconomic factor f , this implies that the component accounts for the highest cost rate of exergy destruction. Hence, the component efficiency should be improved by increasing the capital investment costs Z ˙ k . This can be achieved by increasing the turbine inlet temperature T_{3}. The maximum turbine inlet temperature (TIT) of the combustion chamber is limited by the metallurgical conditions [

Probability distributions were constructed using curve fitting for the input parameters of ambient temperature (AT) and turbine inlet temperature (TIT). The distribution type and statistic for the input parameter are defined in two scenarios as shown in

Parameter | Distribution | Statistics | |||||
---|---|---|---|---|---|---|---|

Min. | Max. | Mean | Median | StdDev | Skewness | ||

AT (K) | Uniform | 288.15 | 315.15 | 300.65 | 300.65 | 8.53 | 0.00 |

TIT (K) | Uniform | 1425.00 | 1518.40 | 1471.70 | 1471.70 | 31.86 | 0.00 |

Parameter | Distribution | Statistics | |||||
---|---|---|---|---|---|---|---|

Min. | Max. | Mean | Median | StdDev | Skewness | ||

AT (K) | Uniform | 288.15 | 315.15 | 300.65 | 300.65 | 8.53 | 0.00 |

TIT (K) | Ext Value Min | 1425 | 1668 | 1594.81 | 1603.90 | 55.31 | −1.14 |

Ambient temperature scenario, the ambient temperature (AT) was used to produce uniform distribution, showing probability cumulative distribution (see

Part-load scenario, the ambient temperature (AT) produced uniform distribution, showing probability cumulative distribution (see

In this study, the probabilistic exergoeconomic analysis was performed for four industrial gas turbine (GT) units comprising of two (GT16 and GT19) units of 100 MW GE engine and two (GT8 and GT12) units of 25 MW Hitachi engine at Transcorp Power Limited, Ughelli. These four industrial GT engine units were modelled and simulated using natural gas as fuel. The design point (DP) simulation results of the modelled GT engines were validated with the available DP thermodynamic data from original equipment manufacturer (OEM).

The results obtained from exergy analysis at full load operation show that the turbine has the highest exergy efficiency of 96.13% for GT8 unit, 98.02% for GT12 unit, 96.26% for GT16 unit, 96.30% for GT19 unit, followed by compressor 94.23% for GT8 unit, 90.89% for GT12 unit, 88.38% for GT16 unit, 88.58% for GT19 unit and combustion chamber having the lowest 44.84% forGT8 unit, 43.42% for GT12 units, 56.10% for GT16 unit, 56.69% for GT19 unit. Moreover, the combustion chamber has the highest exergy destruction efficiency of 55.16% GT8 unit, 56.58% GT12 unit, 43.90% GT16 unit, and 43.30% GT19 unit respectively. The exergy analysis results obtained from the four units show that the combustion chamber (CC) is the most significant exergy destruction with lowest exergy efficiency and highest exergy destruction efficiency of plant components, which is caused by high irreversibility and large temperature difference between the flame and the working fluid [

The results of exergoeconomic analysis from four units show the exergy destruction cost of combustion chamber to be 531.08 $/h GT8 unit, 584.53 $/h GT12 unit, 2351.81 $/h GT16 unit, and 2315.93 $/h GT19 unit. Exergy destruction cost of turbine: 50.99 $/h GT8 unit, 27.84 $/h GT12 unit, 277.36 $/h GT16 unit and 274.46 $/h GT19 unit, also exergy destruction cost of compressor: 42.51 $/h GT8 unit, 69.15 $/h GT12 unit, 556.31 $/h GT16 unit, and 547.60 $/h GT19 unit respectively. The exergoeconomic analysis results from the four units show that the combustion chamber has the highest cost of exergy destruction as compared to other components and lowest value of exergoeconomic factor f , which implies that the component accounts for the highest cost rate of exergy destruction. Hence, the component efficiency should be improved by increasing the capital investment costs Z ˙ k .

The probabilistic analysis results show the possible outputs and their probability of occurrence in each component of the plant. The analysis results show not only what could happen, but how likely it is to happen unlike deterministic analysis (single point estimates). With probability analysis, it shows the probability when component is having low or high exergy destruction and range at which to operate to reduce exergy destruction and increase exergy efficiency in plant.

Special thanks to the Mechanical Engineering Department, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria.

Ogbe, O.P., Anosike, N.B. and Okonkwo, U.C. (2017) Probabilistic Exergoeconomic Analysis of Transcorp Power Plant, Ughelli. Energy and Power Engineering, 9, 588-613. https://doi.org/10.4236/epe.2017.910041

Lists of Symbols

E ˙ ―Exergy flow rate (MW)

E ˙ i ―Exergy flow stream at inlet of the plant component (MW)

E ˙ j ―Exergy flow stream at outlet of the plant component (MW)

E ˙ M ―Material component of exergy (MW)

E ˙ P ―Mechanical component of exergy (MW)

E ˙ T ―Thermal component of exergy (MW)

E ˙ C H E ―Chemical component of exergy (MW)

E ˙ W ―Exergy flow rate of power output (MW)

E ˙ D ―Exergy destruction flow rate (MW)

ε ―Exergy efficiency (%)

ε D ―Exergy destruction efficiency (%)

y D ―Exergy destruction ratio (%)

r k ―Relative cost difference for kth component (%)

Q ˙ c v ―Heat transfer rate between the component and the environment (MW)

S ˙ ―Entropy flow rate (MW/K)

T ―Temperature (Kelvin)

T o ―Reference temperature (Kelvin)

P ―Pressure (Bar)

P o ―Ambient pressure (Bar)

m ˙ ―Mass flow rate (kg/s)

η s ―Isentropic efficiency (%)

C ˙ ―Annualized levelized cost ($/year)

c ˙ ―Levelized cost rate

c ―Average unit exergy cost ($/GJ)

i ―Interest rate (%)

N ―Operating hours per year

n ―Number of years of operation

Z ˙ k ―Capital investment cost rate ($/h)

C F ―Average cost per unit of fuel exergy ($/GJ)

C P ―Average cost per unit of product exergy ($/GJ)

C ˙ D ―Cost rate of exergy destruction ($/h)

f ―Exergoeconomic factor (%)

MW―Megawatt

Superscripts

M―Material under study (Thermomechanical)

P―Mechanical

T―Thermal

CHE―Chemical

W―Power output

Subscripts

i―Inlet

o―Outlet

D―Destruction

k―Stream

a―Air

f―Fuel

g―Flue gas

Submit or recommend next manuscript to SCIRP and we will provide best service for you:

Accepting pre-submission inquiries through Email, Facebook, LinkedIn, Twitter, etc.

A wide selection of journals (inclusive of 9 subjects, more than 200 journals)

Providing 24-hour high-quality service

User-friendly online submission system

Fair and swift peer-review system

Efficient typesetting and proofreading procedure

Display of the result of downloads and visits, as well as the number of cited articles

Maximum dissemination of your research work

Submit your manuscript at: http://papersubmission.scirp.org/

Or contact epe@scirp.org