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1. INTRODUCTION
Heat and electricity are supplied to houses, stores, buildings, and/orindustrial sites through a community energy system such as a
combinedheatandpower (CHP) system or cogeneration system. One of the
challenges associated with carrying out this service is that it is very
difficult to determine how to allocate the costs of heat and electricity. There
is no correct answer. Thus, the conflict between producers and purchasers in
terms of profits and losses is inevitable.
In cogeneration, the fuel cost and the capital cost are inputted,
and the electricity cost and the heat cost are outputted. Assuming the sum of
the fuel and capital costs is $100, what is the electricity cost (A) and the
heat cost (B)? The equation is A+B=100, which cannot be solved exactly.
Although there is no correct answer, we must solve the equation to sell or to
buy each product. There are various methodologies to solve the equation.
As introduced in a World Bank technical paper [1], there are various
methods suggested in the field of accounting. The representative methods are
the heat method, the work method, and the benefit distribution method. The
advantage of these methods is that they are very simple. The disadvantage is
that these methods analyze alternative systems such as a power plant and a
heatonly boiler.
Many thermal engineers in the field of thermoeconomics or exergoeconomics have suggested various exergetic methods, which are based on the second law of thermodynamics. The following representative methods were introduced in a review paper [2] on exergoeconomics: the theory of the exergetic cost (TEC) [3, 4], the theory of exergetic costdisaggregating methodology (TECD) [3, 5], thermoeconomic functional analysis (TFA) [7, 8], intelligent functional approach (IFA) [9, 10], lastinfirstout principle (LIFO) [11], specific exergy costing/average cost approach (SPECO/AVCO) [1215], modified productive structure analysis (MOPSA) [1618], and engineering functional analysis (EFA) [19, 20]. The main feature of these methods is that they propose a cost balance equation that can be applied to each component of a thermal system. These equations are based on the exergy balance equation. Therefore, these methods can be reasonable from the viewpoint of thermal engineering. However, there is a disadvantage in that it is not easy to apply these methods to actual systems and solve thermoeconomic problems because too many equations are needed.
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2. WONERGY METHODOLOGY
2.1. A New Cost Allocation Methodology
We have suggested a wonergymethodology [21] that can analyze the cost allocation, cost optimization, and
cost analysis for various thermal systems. The term ¡°wonergy¡± is a new
portmanteau of ¡°worth¡± and ¡°energy¡±, and the definition is an energy that can
equally evaluate the energetic worth of each product. Here, worth is not an
absolute number but a relative concept, which means that there is no correct
answer in the wonergy methodology.
2.2. Equation for Solving the Cost Allocation
In aprevious study [21], we have suggested the equations for the cost allocation of
a cogeneration system as follows:
(1)
(2)
where is the fuel cost flow (including
the environmental pollution cost) [$/h], is the
common capital cost flow, is the
electricityonly capital cost flow [$/h], is the
heatonly capital cost flow [$/h], is the
amount of wonergy input for work production [MJ/h], is theamount of wonergy input for heat production [MJ/h], is the work
cost flow [$/h], and is the heat
cost flow [$/h].
The detailed equations are asfollows:
(3)
(4)
(5)
(6)
(7)
where the subscript F means fuel, HV means heating
value, W means
electricityonly components such as compressor, pump, and turbine, Q means heatonlycomponents such as distributed heat supply, and C means common
components such as combustion chamber, boiler, heater, pipes, etc. is the mass
flow rate, Z is the initial
purchase or construction cost ($), CRF is the annual
capital recovery factor about 16%, i is the interest
rate about 10%, n is the number
of annuities about 10 years, is the
maintenance factor about
6%, A is the annual
cost ($/year) such as personnel expenses or utility bills, and N is the operating
hours per year about 5000.
Finally, each unit cost of work and
heat is calculated as follows:
(8)
(9)
where is the amount
of work output [MJ/h], is the amountof heat output [MJ/h], is the unitcost of work [$/MJ], and is the unitcost of heat [$/MJ].
In these equations, only and are independentvariables, whereas the other terms are given variables. Therefore, the key
point in the wonergy methodology is to calculate the amount of wonergy inputs
required for producing the work and the heat, that is, and .
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2.3. Integration of Various Cost Allocation Methods
2.3.1. Principle of Wonergy on the Cycle of Working Fluid
The components of cogeneration canbe grouped with electricityonly components (compressor, pump, turbine, etc.), heatonly
components (distributed heat supply, etc.), and common components (the others).
As explained in a previous paper [21], the amount of wonergy inflow in commoncomponents is exactly equal to the summation of the amount of wonergy outflow in the electricityonlycomponents and the amount of wonergy outflow in the heatonlycomponents, as in Equation (10).
(10)
2.3.2. Work Efficiency and Heat Efficiency
Coeneration produces work and heat at the same
time. When heat is not produced, the amount of work production becomes the
maximum . When work is not produced, the amount of heatproduction becomes the maximum . Therefore, the work efficiency and the heat
efficiency can be defined as follows:
(11)
(12)
where is equal to the sum of and .
The heat efficiency of Equation (12)
is the value of cogeneration, but the work efficiency of Equation (11) is not
the value of cogeneration. Therefore, there is ambiguity in the work
efficiency .
2.3.3. Merit
¡°Merit¡± means the benefit obtained
from integrating individual systems into a cogeneration system. When a cogeneration
system produces work and heat from fuel , the amount of fuel for producing work is , and the amount of fuel for producing heat is . Therefore, the amount of merit is defined as
follows:
(13)
2.3.4. Wonergy Distribution Table
All the methods introduced in this chapter are
arranged in Table 1. The key point in the wonergy methodology is to calculate
the amount of wonergy inputs required for producing the work and the heat, that
is, and . From these values, the work cost and the heat
cost can be
allocated by Equations (1) and (2).
Table 1. Wonergy distribution table
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2.4. Each Cost Allocation Method
2.4.1. The Heat Method
The heat method applies the heat as
wonergy. That is, this method evaluates each product based on the heat
efficiency. Therefore, the heat of the fuel is , the heat for producing
the heat is , and the heat for producing
the work is the rest from Equation
(10).
This method distributes all the merit
to the work. The
work cost becomes always the
minimum value and the heat cost becomes always the
maximum value. Therefore, the results become the reference values.
2.4.2. The Work Method
The work method applies the work as
wonergy. That is, this method evaluates each product based on the work
efficiency. Therefore, the work of the fuel is , the work for producing the work is , and the work for producingthe heat is the rest from Equation
(10).
This method distributes all the merit to the heat. The
work cost becomes always themaximum value and the heat cost becomes the
minimum value. Therefore, the results become the reference values.
2.4.3. The Benefit Distribution Method
The benefit distribution method
applies the individual fuel as wonergy. That is, this method evaluates each
product based on the individual fuel inputted to a power plant and a
heatonlyboiler. Therefore, the individual fuel for producing
the work is and the individual fuel for producing
the heat is .
The reasonable cost must lie between
the costs determined by the heat method and the work method. That is, a reasonable
method must have a relation with the heat method and the work method. However,
the result of the benefit distribution method has no relation with the results
of the heat method and the work method. Therefore, we judge that the benefit
distribution method is not reasonable.
2.4.4. The Efficiency Method
The efficiency method applies the
fuel divided by efficiency as wonergy. That is, this method evaluates each
product based on efficiency. Therefore, the fuel for producing work
is , and the fuel for producing
heat is .
This method distributes the merit in proportion
to the work efficiency and the heat
efficiency . The result lies in proportion to the results of the
heat method and the work method always. Assuming is zero in the
term of the merit distribution, the results are equal to the heat method
exactly. Assuming is zero in the
term of the merit distribution, the results are equal to the work method
exactly. Therefore, this method can be reasonable.
2.4.5. The Equal Method
The equal method applies the fuel
divided by equal efficiency as wonergy. That is, this method evaluates each
product based on equal efficiency. From the efficiency method, therefore, the
fuel for producing
work is and the fuel for producing
heat is .
This method distributes the merit equally. The
result lies in the middle of the heat method and the work method always.
However, must be larger
than . Therefore, this method can be considered unreasonable
from the viewpoint of thermodynamics.
The precondition of cogeneration is
that there is a demand for electricity production. In general, the electricity
produced in a cogeneration system competes with the electricity produced from
uranium or coal. Consequently, the time restriction can be inevitable in the cogeneration
system. In this case, the work cost should fall and the heat cost should rise.
The equal method suggests the maximum limitation of the heat cost and the
minimum limitation of the work cost, because is never
smaller than . Therefore, in the case that a purchaser is requiredto buy the electricity of cogeneration, this method may be reasonable from the
viewpoint of economics.
2.4.6. The Enthalpy Method
The enthalpy method applies the
enthalpy as wonergy. That is, this method evaluates each product based on the
enthalpy. Therefore, the enthalpy input for producing
work is and the enthalpy input for producing
heat is . In adiabatic conditions, is equal to and is equal to from the first
law of thermoeconomics.
The unit cost of work is always equal
to the unit cost of heat because this method does not distinguish between work
and heat. Also, the results are equal to the heat method exactly. Therefore,
this method can be considered very unreasonable.
2.4.7. The Exergy Method
The exergy method applies the exergy
as wonergy. That is, this method evaluates each product based on the exergy.
Therefore, the exergy input for producingwork is and the exergy input for producing
heat is . The meaning of can be easily
understood. The exergy method only applies the symbol to the symbol . Thus, the meaning of can be easily
understood.
In general, it is wellknown that
exergy evaluates the quality of energy the best. The result of this method is
similar to the result of the efficiency method. Therefore, the exergy method
can be reasonable. The work efficiency of Equation (11) is the value, not of the
cogeneration, but of a power plant. Therefore, the efficiency method using the
work efficiency does not analyze the given state of cogeneration. The exergy
method has no relation with Equation (11) or Equation (12), and it analyzes the
given state of cogeneration exactly. Therefore, the exergy method can be the
most reasonable. Engineers can understand exergy, but economists may be unable
to understand exergy. Therefore, we recommend the efficiency method to
economists and the exergy method to engineers.
2.4.8. The Exergetic Equal Method
The heat efficiency in Equation(12) is the value of cogeneration. However, the work efficiency in Equation
(11) is not the value of cogeneration. Therefore, the new work efficiency of the cogeneration
needs to be calculated. This value can be found from the equation where the
heat cost using the exergy method is equal to the heat cost using the
efficiency method, Equation (2).
(14) )
(15)
Therefore, the exergetic work
efficiency representing
the exergy method is as follows:
(16)
where
The exergetic equal method applies
the fuel divided by the exergetic equal efficiency as wonergy. That is, this
method evaluates each product based on the exergetic equal efficiency.
Therefore, the fuel for producing
work is and the fuel for producing
heat is .
This method can be compared with the
equal method, and the results are similar to each other. Therefore, the
exergetic equal method can be reasonable from the viewpoint of economics. The
equal method using Equation (11) is not to analyze the given state of cogeneration.
The exergetic equal method using Equation (16) analyzes the given state of cogeneration
exactly. Therefore, the exergetic equal method can be more reasonable than the
equal method.
2.4.9.The Exergetic Work Method
The exergetic work method applies the
work divided by exergetic efficiency as wonergy. That is, this method evaluates
each product based on the exergetic work efficiency. Therefore, the work of the fuel is , the work for producing the work is , and the work for producing
the heat is the rest from Equation
(10).
This method can be compared with the
work method, and the results are similar to each other. The work method using Equation
(11) does not analyze the given state of cogeneration. The exergetic work
method using Equation (16) analyzes the given state of cogeneration exactly. Therefore,
the exergetic work method can be more reasonable than the work method.
2.4.10. The Index Method
In the wonergy methodology, the ratio
of wonergy input ¥ê is defined asfollows:
(17)
(18)
The equations applying these terms to Equations (1) and (2) are as follows:
(19)
(20)
From Equations (8), (9), (19), and
(20), the relation among the unit cost of work on the fuel
cost, the unit cost of heat on the fuel
cost, the ratio of wonergy input for producing the work , and the ratio of wonergy input for producing theheat can be
rearranged as follow:
(21)
Finally, ¥ê is an index equal to the ratio of unit cost in the common cost. The core of the index method is to determine the value of ¥ê. Not only the energetic indexes of Table 1, but also a nonenergetic index can be applied to ¥ê. If the producer and the purchaser do not agree onany energetic methods, a third party (such as the government) may be required to determine each ¥ê from nonenergetic indexes.
2.4.11. Accounting
Methods and Engineering Methods
The heat method, the work method, the
benefit distribution method, the efficiency method, and the equal method are
accounting methods, and the enthalpy method, the exergy method, the exergetic
equal method, and the exergetic work method are engineering methods. Here the
result of the enthalpy method is exactly equal to the heat method, the result
of the exergetic work method is similar to the work method, the result of the
exergetic equal method is similar to the equal method, and the result of the
exergy method is similar to the efficiency method. Therefore, we can know that
the method approximating the engineering method is the accounting method.
The benefit distribution method has no relationwith the other accounting methods and all the engineering methods. In general, it is wellknown that this method is most fair. However, we judge that the benefit distribution method is not reasonable.
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3. EXERGY CALCULATION
3.1 What Is Exergy? : Quotation from Wikipedia Encyclopedia
In thermodynamics, the exergy of a
system is the maximum useful work possible during a process that brings the
system into equilibrium with a heat reservoir. When the surroundings are the
reservoir, exergy is the potential of a system to cause a change as it achieves
equilibrium with its environment. Exergy is the energy that is available to be
used. After the system and surroundings reach equilibrium, the exergy is zero.
Determining exergy is also the first goal of thermodynamics.
Energy is never destroyed during a
process; it changes from one form to another (see the first law of
thermodynamics). In contrast, exergy accounts for the irreversibility of a
process due to an increase in entropy (see the second law of thermodynamics).
Exergy is always destroyed when a process involves a temperature change. This
destruction is proportional to the entropy increase of the system together with
its surroundings. The destroyed exergy has been called anergy. For an
isothermal process, exergy and energy are interchangeable terms, and there is
no anergy.
Exergy analysis is performed in the
field of industrial ecology to use energy more efficiently. The term was coined
by Zoran Rant in 1956, but the concept was developed by J. Willard Gibbs in
1873. Ecologists and design engineers often choose a reference state for the
reservoir that may be different from the actual surroundings of the system.
Exergy is a combination property of a
system and its environment because unlike energy, it depends on the state of
both the system and environment. The exergy of a system in equilibrium with the
environment is zero. Exergy is neither a thermodynamic property of matter nor a
thermodynamic potential of a system. Exergy and energy both have units of
joules. The internal energy of a system is always measured from a fixed
reference state and is therefore, always a state function.
The term exergy is also used, by
analogy with its physical definition, in information theory related to
reversible computing. Exergy is also synonymous with: availability, available
energy, exergic energy, essergy (considered archaic), utilizable energy,
available useful work, maximum (or minimum) work, maximum (or minimum) work
content, reversible work, and ideal work.
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3.2 Exergy for the Cost Allocation of CogenerationSystems
The exergy
of a fluid is a function of temperature, pressure, composition, location, and
velocity as follows:
Physical exergy : It is thefunction of the temperature and the pressure between the given state(T,P) and the ambient state(T_{0},P_{0}). The physical exergy is used for analysis ofphysical processes.
Chemical exergy : It is the
function of the chemical composition between the given fluid() and the ambient fluid(). The chemical exergy is used for analysis ofchemical processes.
Kinetic exergy : It is thefunction of the given velocity from the zero velocity.
Potential exergy : It is thefunction of the given location from the ground level.
In general, the kinetic exergy and
the potential exergy are much smaller than the physical exergy in thermal
system. Therefore, these terms can be neglected. Applying the wonergy
methodology to cogeneration, the inlet chemical exergy and the outlet chemical
exergy eliminate each other in the equation. Therefore, there is no need to
calculate the chemical exergy.
Finally, the exergy equation for the
cost allocation of cogeneration systems is as follows:
(22)
where is mass flow
rate, is specific
enthalpy, is specific
entropy, and the subscript means ambient
state.
3.3 Expression of Exergy on Ts Chart
To calculate the exergy of Equation (22), we should know the values of the specific enthalpy and specific entropy. These values can be found with commercial software or numerical programming. We have developed commercial software that can calculate the exergy and plot the line on a Ts chart. The specific exergy lines of air composed with various substances are plotted in Figure 1. The specific exergy lines of water and steam are plotted in Figure 2. Using these charts, system designers can understand the concept of exergy and confirm the values calculated from Equation (22).
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Figure 1. Specific exergy line of air.
Figure 2. Specific exergy line of water
and steam.
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4. COST ALLCOATION OF ELECTRICITY AND HEAT AS FINAL PRODUCTS
4.1 Final Equations of Cost Allocation
A schematic diagram at the
thermodynamic boundary and plant boundary of a cogeneration system is
illustrated in Figure 3. In general, cost allocation methodologies consider
only the thermodynamic boundary such as Equations (1) and (2). However, there
are additional energy flows, as shown in the plant boundary, and they should be
considered in the cost allocation methodology.
Figure 3. A schematic diagram on a cogeneration
system.
The work output in the turbine
is turned into electricity through the
gear of efficiency and the generator of
efficiency . Part of the electricity is supplied to thecondensing pump of , the circulating pump of , and the common components of . The heat output in heat
exchanger is stored in the heat reservoir, and it is turned into heat through efficiency . Part of the heat is supplied to the common components of . Finally, the amount of electricity production is , and the amount of heat production is . In Figure 3, is , is , is , and is .
The cost analysis is as follows. The
electricity cost flow in the generator is equal to . The electricity cost flow inputted to the condensingpump is , which is an electricityonly cost. The electricity cost flowinputted to the heating pump is , which is a heatonly cost. The electricity cost flowinputted to the office is , which is a common cost. The heat cost flow in the heatreservoir is equal to . The heat cost flow inputted to the office is , which is a common cost. These cost flows should be reallocated.
Considering only the fuel cost in Equations
(1) and (2), is divided into
the work cost and the heat cost using the terms of . The fuel cost is a common cost. Like this, thecommon costs and can be dividedinto the work cost and heat cost using the terms of . Finally, the cost allocation equations for theelectricity production and the heat
production are rearranged
as follows:
(23)
(24)
where the values of and can be
calculated from Equations (1) and (2), and the terms of and can be
calculated from Table 1.
Considering only the fuel cost in Equations
(1) and (2) and rearranging these equations, the relations of , , , and are as follows:
(25)
(26)
Therefore, Equations (23) and (24)are as follows:
(27)
(28)
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4.2 Usage Cost and Basic Cost
In general, the sale price of energy
is composed of the usage price and the basic price. Similarly, the cost flow of
Equations (27) and (28) can be divided into the usage cost and the basic cost.
In Equations (1) and (2), the input costs are and . Assuming that is the usage
cost, and in the fuel
cost can be calculated by Equations (27) and (28). Assuming that is the basiccost, and in the capital
cost can be calculated by Equations (27) and (28).
4.3 Importance of Heat Reservoir
In general, the fuel of heating an individual
house is LNG. The unit cost of heat produced in cogeneration is lower than
that of LNG. Therefore, the heat of cogeneration has competitiveness always.
Electricity is produced from uranium, coil, LNG, etc. The unit cost of
electricity produced in cogeneration is lower than that of LNG but much higher than that of uranium. Although there is
no heat reservoir, in the nation without nuclear power plant, cogeneration may
have competitiveness always because the electricity and heat can be produced
and consumed simultaneously. However, if there are nuclear power plants, the production
and the consumption of the electricity in cogeneration do not occur
simultaneously. In this case, the cost loss of electricity can be inevitable,
and any cost allocation method cannot clear the conflict between the producers
and the purchasers in terms of the profits and losses because the unit cost of
electricity in cogeneration is very higher than that in nuclear power plant.
Heat can be stored in a heat
reservoir, but electricity cannot be stored. Therefore, to have competitiveness
always, cogeneration should be operated when there is the demand of
electricity, and the heat should be restored in a heat reservoir.
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5. WONERGY BALANCE EQUATION
5.1 The Energy Balance Equation
The energy balance equation for the kth component and the overall system
can be rearranged as follows:
(29)
(30)
where and are the amountof work and heat of the products, is the amountof heat input from a fuel or energy source, is the changein of the enthalpy flow rate at the stream that inputs the energy to another
stream, is the changein the enthalpy flow rate at the stream that outputs the energy from another
stream, and is the lostheat (heat loss) into the environment.
In Equations (29) and (30), the heat
product of the left
side must
be calculated as the difference between the outlet enthalpy and inlet enthalpy,
and the other terms must be calculated as the difference between the inlet
enthalpy and outlet enthalpy.
5.2 The Exergy Balance Equation
The exergy balance equation for the kth component and the overall system
can be rearranged as follows:
(31)
(32)
where and are the amountof work and exergy of the products, is the amount
of exergy input from a fuel or energy source, is the change
in the exergy flow rate at the stream that inputs the exergy to another stream,
is the change
in the exergy flow rate at the stream that outputs the exergy from another
stream, and is the lost
exergy (exergy destruction or exergy loss).
In Equations (31) and (32), the
exergy product of the left side must be
calculated as the difference between the outlet exergy and inlet exergy, and
the other terms must be calculated between the difference of the inlet exergy
and outlet exergy.
5.3 The Wonergy Balance Equation
The shape of the energy balance equation
of Equations (29) and (30) is basically the same as that of the exergy balance equation
of Equations (31) and (32). Therefore, including enthalpy and exergy in wonergy, and
replacing the symbols of and with , the wonergy balance equation for kth component and overall system can be
rewritten as follows:
(33)
(34)
where the wonergy products of the leftside must be calculated as the difference between the outlet wonergy and inlet
wonergy, and the other terms must be calculated as the difference between the
inlet wonergy and outlet wonergy.
5.4 The Relation between Wonergy and Various Energies
The wonergy is not a specific energy. It is just a word unifying the energies of various species. The concept of unification can be confirmed in the equations and tables in this chapter. Only cogeneration at a steady state was considered in this chapter. If an unsteady state is considered in the energy system, the term of time is added in the energy and exergy balance equations. These equations also can be integrated into the wonergy balance equation. The wonergy can be extended into the nonthermodynamic energies such as Table 1. Therefore, if we understand the concept of wonergy, we can analyze the energy system and allocate the input costs more easily.
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6. COST ALLOCATION IN A GASTURBINE
COGENERATION SYSTEM
6.1 Thermodynamic Analysis
6.1.1. Analysis
of Each State
The gasturbine cogeneration system
in Figure 4 is composed of an aircompressor [1], a fuel injector [2], a
combustion chamber [3], a gasturbine [4], an airpreheater [5], a heat
recovery steam generator(HRSG) [6], pipes [7], and the ambient atmosphere [0].
The mole fractions of air, fuel, and combustion gas are shown in Figure 4, and
the temperature, pressure, and mass flow rate of each state are given in the
schematic diagram. The values of enthalpy and entropy can be calculated using
commercial software or numerical programming, and the value of exergy can be
calculated by Equation (22). We have developed commercial software that can
calculate the properties and plot the lines on a Ts chart. The mass flow rate,
temperature, pressure, enthalpy, entropy, and exergy on each state are shown in
Table 2, and the results, plotted on a Ts diagram, are illustrated in Figure
5.
Figure
4. A heat balance diagram on a gasturbine cogeneration system.
Figure 5. Operating state on the
gasturbine cogeneration system.
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Table
2. Thermodynamic properties of the gasturbine cogeneration
6.1.2. Analysis
of Energy Balance
The results of Equations (29) and (30)
are calculated in Table 3; the low heating value of fuel (LHV) is 49.202 GJ/t.
According to this analysis, almost all of the energy loss occurs in the
ambient. Therefore, we need to consider a plan for improving the ambient
component. However, the 169.4¡É of state 13 is not useful. Therefore, it
can be concluded that the analysis of the energy balance does not offer the
desirable viewpoint.
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Table 3. Analysis of the energy balance of the gasturbine cogeneration
6.1.3. Analysis
of Exergy Balance
The results of Equations (31) and (32)
are calculated in Table 4; the exergy of fuel is 49.151 GJ/t.
According to this analysis, an amount of exergy loss occurs in the combustion
chamber. By raising the adiabatic flame temperature, the exergy loss can fall
off. However, the temperature cannot be raised because air pollutants such as
nitrogen oxide are produced. The direction of improvement is as follows: 1)
install an air compressor, a fuel injector, and a gasturbine of high
efficiency; 2) reduce the temperature difference in the air preheater; 3) increase
the temperature of steam in the HRSG; and 4) install a heat exchanger at state
13 and produce hot water. If we can sell the hot water to a consumer, we will
get additional profits. Similarly, the analysis of exergy balance gives a
wealth of useful information to the system designer. The analysis and
optimization of energy systems were discussed in a paper [21].
Table 4. Analysis of the exergy balance of the gasturbine cogeneration
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6.2 Cost Allocation
6.2.1. Input
Data
All of the input data and equations
for the cost allocation of the gasturbine cogeneration system are given in
Table 5. Here, the analysis of energy balance and exergy balance are not
needed.
The fuel input is 310.0 GJ/h, and the
work output is 119.2 GJ/h. Therefore, this efficiency is 38.46%. Installing a
steamturbine cycle at states 20 and 21, additional work can be obtained by replacing
the steam heat. However, we do not know the amount of additional work exactly.
We assume that the steamturbine cycle can produce the work of efficiency
11.54%. Therefore, the work efficiency is 50.00 %. Because
of this, all the methods except the exergetic methods can be considered
unreasonable.
Table 5. Input
data for the cost allocation of the gasturbine cogeneration
6.2.2. Cost
Allocation
In the cost allocation, the key point
is to find the values of and . These values can be calculated by each term of Table1. Only the data of the thermodynamic boundary in Figure 3 is given in Figure
4. Therefore, the work cost and the heat
cost can be found by
Equations (1) and (2).
The results of the cost allocation are
shown in Table 6, and the charts are illustrated in Figure 6. We can confirm
that the result of the heat method (1) is equal to the result of the enthalpy
method (6), the result of the work method (2) is almost equal to the result of
the exergetic work method (9), the result of the efficiency method (4) is
almost equal to the result of the exergy method (7), and the result of the
equal method (5) is almost equal to the result of the exergetic equal method (8).
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Table 6. Results of the cost allocation on the gasturbine cogeneration
Figure
6. Cost allocation chart on the gasturbine cogeneration system.
6.2.3. Analysis
of the Results
The results of the heat method (1) and
the work method (2) are located at both endpoints, and the other results are
located between them. We assumed the work efficiency . Therefore, there is some ambiguity in the results ofthe work method (2), the benefit distribution method (3), the efficiency method
(4), and the equal method (5). The results of the exergy method (7), the
exergetic equal method (8), and the exergetic work method (9) can be reasonable
because there are no assumptions.
The result of the equal method (5) is
exactly located in the middle of the heat method (1) and the work method (2)
results. The equal method presupposes that the work efficiency is equal to the
heat efficiency in the merit
distribution of Table 1. The benefit distribution method (3) is located in the
leftupper side, which means that the work efficiency is higher than
the heat efficiency in the merit
distribution of Table 1. Therefore, the result of the benefit distribution
method can be considered unreasonable.
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