10
The Conventional Exergoeconomic Analysis
1. The Conventional Exergoeconomic Analysis
The conventional exergoeconomic analysis is a branch of engineering based on
a combination of an exergetic analysis and of an economic analysis applied to an
energy conversion systems in order to pinpoint the components and the processes
with high irreversibilities and to estimate the cost related to these irreversibilities .
Therefore the results of the conventional exergoeconomic analysis allow to focus the
improvements of an energy system to the components responsible of the highest
irreversibilities and so to carry out a more effective optimization of the energy system
under consideration.
1.1 Exergetic Analysis
The exergy analysis allows to further the goal of more effective energy resource
u se, determining the location, the cause and the true magnitude of waste and loss.
Such information can be used in the design of new energy-efficient system and for
increasing the efficiency of existing systems.
11
The Conventional Exergoeconomic Analysis
1.1.1 Exergy definition
Exergy can be defined as the maximum theoretical useful work obtainable from
a system that comes into equilibrium and the heat transfer occurs only with the
environment or as the minimum theoretical useful work required to form a quantity of
matter from substances present in the environment and to bring the matter to a
specified state. On the contrary of the energy the exergy can be destroyed and
generally is not conserved.
Therefore the exergy is a measure of the departure of the state of the system
from that of the environment. So it is necessary to define for the analysis the meaning
of environment. It is modeled as a simple compressible system, large in extent, and
uniform in temperature T
0
and pressure p 0
. The values for T
0
and p 0
are taken for
s implicity equal to the standard conditions (298,15 K and 1 atm), but for real-word
applications the environmental temperature and pressure may be specified differently.
Moreover for calculating the exergy of a stream or of a system it is necessary to refer
to a state, called dead state, characterized by a null value of the exergy. In fact when
pressure, temperature, composition, velocity or elevation of the system are different
from the environment, there is an opportunity to develop work. As the system changes
state toward that of the environment the opportunity diminishes, ceasing to exist
when the two, at rest relative to one another, are in equilibrium. This state of the
system is called the dead state. At the dead state the conditions of mechanical,
thermal and chemical equilibrium between the system and the environment are
satisfied. Another type of equilibrium between the system and the environment can be
defined: the restricted dead state, where only the conditions of mechanical and
thermal equilibrium must be satisfied.
In the absence of nuclear, magnetic, electrical and surface tension effects, the
total exergy of a system E can be divided into four components: physical exergy E
PH
,
k inetic exergy E
KN
, potential exergy E
PT
and chemical exergy E
CH
:
CH PT KN PH
E E E E E + + + =
The sum of kinetic, potential and physical exergies is also indicated as the thermo-
mechanical exergy.
12
The Conventional Exergoeconomic Analysis
Although exergy is an extensive property, it is often convenient to work with it on a
unit-of-mass or molar basis. So the total specific exergy is given by:
CH PT KN PH
e e e e e + + + =
When evaluated relative to the environment, the kinetic and potential energies of a
system are in principle fully convertible to work as the system is brought to rest
relative to the environment and so they correspond to the kinetic and potential
exergies:
2
2
1
V e
KN
=
gz e
PT
=
where V and z denote velocity and elevation relative to coordinates in the
environment.
The meaning of the physical exergy and the chemical exergy is explained in the next
sections.
1.1.1.1 The physical exergy
The physical exergy is the maximal theoretical useful work obtainable as the
c onsidered system, at rest relative to the environment (e KN
=e PT
=0), passes from its
i nitial state where the temperature is T and the pressure is p to the restricted dead
state where the temperature is T
0
and the pressure p 0
.
The physical exergy of a closed system at a specified state (T,p) is given by:
( ) ( ) ( )
0 0 0 0 0
S S T V V p U U E
PH
- - - + - =
where U, V and S are respectively the internal energy, volume and entropy of the
system at the specified state
U
0
,V
0
and S
0
are the value of the same properties when the system is at the
r estricted dead state.
This expression of the physical exergy can be determined by applying the energy and
the entropy balances to a closed system at the rest relative to the environment.
13
The Conventional Exergoeconomic Analysis
For a wide range of practical applications not involving chemical reaction, mixing or
separation of mixture components, knowledge of the physical, kinetic and potential
exergies of a system is sufficient for the exergy analysis. In fact in these cases an
explicit evaluation of the chemical exergy value is not required because is the same at
all states of interest and thus cancels when differences in exergy values between the
states are calculated.
1.1.1.2 The chemical exergy
The chemical exergy is the maximum theoretical useful work obtainable as the
s ystem passes from the restricted dead state to the dead state, where it is in complete
equilibrium with the environment.
For evaluating the chemical exergy the substances comprising the system must be
referred to the properties of a suitably selected set of environmental substances.
Therefore is defined and calculated the standard chemical exergy for this selected set
of environmental substances. The standard chemical exergy represents the chemical
exergy of a substance at the standard values of the environmental temperature T
0
and
p ressure p 0
.
There exist several models to calculate the standard chemical exergy, based on
alternative standard exergy reference environments. The fundamental differences of
these models are in the value of the environmental temperature and pressure and in
the set of the environmental substances.
However to evaluate the standard chemical exergy for a gas, included in the
environmental gas phase, all the models use the following hypothesis: the k th gas
e nters at temperature T
0
and pressure p 0
in a device, expands isothermally with heat
t ransfer only with the environment and exits to the environment at the temperature T
0
a nd at its partial pressure. The maximum theoretical work per mole (i.e. the chemical
exergy per mole) of gas k would be developed when the expansion occurs without
irreversibilities and so it is given by the following equation:
0
0
0
ln
p
p x
T R e
e
k CH
k
- =
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The Conventional Exergoeconomic Analysis
where
0
p x
e
k
is the partial pressure of the k th
gas, the superscript e denotes the environmental
e
k
x is the mole fraction of gas k in the environmental gas phase.
The chemical exergy of a mixture of N gases, each of which is present in the
environmental gas phase, can be obtained in a similar way and is equal to:
k k
CH
k k
CH
x x T R e x e ln
0∑ ∑
+ =
Then it is also necessary to the analysis to know how to evaluate the standard chemical
exergy of a substance not present in the environment. In principle such exergy can be
calculated by considering an idealized reaction (i.e. there are not irreversibilities, all
substances enter and exit in the device unmixed at pressure p 0
and temperature T
0
and
t he heat transfer is at environmental temperature) of the substance with other
substances (usually reference substance) for which the chemical exergies are known.
So the standard chemical exergy of any substance is given by
- + D - =
∑ ∑
R
CH
P
CH CH
e n e n G e
where
ΔG is the change in Gibbs function for the reaction,
the term in curly brackets corresponds to the difference between the standard
chemical exergy of the products and of the reagents.
1.1.2 The exergy balance
As for the extensive properties mass, energy and entropy, exergy balances can
b e written in alternative forms suitable for particular applications of practical interest.
The exergy balance applied to a closed system can be seen as the basis for extending
the exergy balance to more complex cases.
The exergy balance for a closed system is developed by combining the energy and
entropy balances, or better multiplying the entropy balance by the temperature of the
environment T
0
and subtracting the resulting expression from the energy balance
gi ves:
15
The Conventional Exergoeconomic Analysis
( ) ( ) ( )
∫ ∫
- -
- = - - - + - + - 2
1
0 0
2
1
1 2 0 1 2 1 2 1 2
) (
gen
b
S T W
T
Q
T Q S S T PE PE KE KE U U
d d
Collecting the terms involving δQ and considering that the exergy change between two
states of a closed system (neglecting the chemical exergy) is given by
( ) ( ) ( ) ( ) ( )
1 2 1 2 1 2 0 1 2 0 1 2 1 2
PE PE KE KE S S T V V p U U E E - + - + - - - + - = -
Rearranging, the closed system exergy balance results:
( ) ( ) [ ]
gen
b
S T V V p W Q
T
T
E E
0 1 2 0
2
1
0
1 2
1 - - - -
- = - ∫
d
where
1 2
E E - is the exergy change,
( ) [ ]
∫
- - -
- 2
1
1 2 0
0
1 V V p W Q
T
T
b
d is the exergy transfers and depends on the process,
the first term is associated with heat transfer to or from the system during the process,
the second term is associated with the net useful work,
gen
S T
0
is the exergy destruction, also indicated with the symbol E
D
.
The exergy balance can be expressed in various forms that may be more appropriate
for particular applications. A convenient form of the exergy balance for closed system
is the rate equation:
D
j
j
j
E
dt
dV
p W Q
T
T
dt
dE
-
- -
- =
∑ 0
0
1
where
dt dE is the time rate of change of exergy,
.
0
1
j
j
Q
T
T
- is the time rate of exergy transfer associated with heat transfer at the
r ate Q
j occurring at the location on the boundary, where the instantaneous
t emperature is T
j,
dt
dV
p W
0
.
- represents the time rate of exergy transfer associated with the energy
transfer by work,
16
The Conventional Exergoeconomic Analysis
D E
.
is the time rate of exergy destruction due to irreversibilities within the system and
i s related to the rate of entropy generation within the system by the relation:
gen D S T E
=
0
.
In conclusion the exergy balance is applicable to control volumes and because the
exergy is an extensive property, it can be transferred into or out of a control volume
where streams of matter enter and exit. The most general form of the exergy balance
applied to a control volume is:
D
e
e
e
i
i
i
CV
CV
j
j
j
CV
E e m e m
dt
dV
p W Q
T
T
dt
dE
- - +
- -
- =
∑ ∑ ∑ 0
0
1
where the subscripts i and e denote respectively the inlets and the outlet,
dt dE
CV
represents the time rate of change in the exergy of the control
v olume,
j
j
Q
T
T
.
0
1
- is the exergy transfer, also indicated with j q E ,
.
,associated with the
t ime rate of heat transfer
j
Q
.
at the location on the boundary of the control
v olume where the instantaneous temperature is T
j,
dt
dV
p W
CV
CV
0
.
- represents the exergy transfer associated with the time rate of
e nergy transfer by work W E
.
,
i
i e m
.
and
e
e e m
.
are respectively the time rate of exergy transfer at the inlet and
at the outlet of the control volume. The exergy transfer at the inlet and at the
outlet are evaluated relative to the environment used to define exergy. In detail
the exergy associated with a stream of matter entering or exiting a control
volume is the maximum theoretical work that could be obtained were the
stream brought to the dead state, heat transfer occurring with the environment
only. This work can be evaluated in two steps:
- t he stream is brought to the restricted dead state,
17
The Conventional Exergoeconomic Analysis
- the stream is brought from the restricted dead state to dead state,
The contribution given by the first step to the maximum theoretical work is the
sum of the physical, kinetic and potential exergy, instead the contribution of the
second step is the chemical exergy. So the total exergy transfer associated with
a stream is
( ) ( )
CH
e gz V s s T h h e + + + - - - =
2
0 0 0
2
1
where the physical component of the exergy transfer is given by
( ) ( )
0 0 0
s s T h h e
PH
- - - =
,
accounts the time rate of exergy destruction due to irreversibilities within
the control volume.
1.1.2.1 Application of the exergy balance to the components of a system
The exergy balance can be written also in terms of exergy fuel, exergy product,
e xergy destruction and exergy loss. In detail the exergy balance is applied to the
system, that is considered as a black box, in which the inlet must be equal to the
outlet.
Referring to the following picture the exergy balance applied to a system is given by:
tot F E ,
.
is the exergy rate
a ssociated with the fuel, i.e the
exergetic resources expended to generate the exergy of the product. The fuel is
defined to be equal to all the exergy values to be considered at the inlet (including the
exergy of energy streams supplied to the component) plus all the exergy decreases
between inlet and outlet (i.e the exergy removals from the respective material
System
tot P E ,
tot D E ,
tot F E ,
tot L E ,
D E
.
tot L tot D tot P tot F E E E E , , , ,
+ + =
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The Conventional Exergoeconomic Analysis
streams) minus all the exergy increases (between inlet and outlet) that are not in
accord with the purpose of the system;
tot P E ,
.
is the exergy of the product, i.e. the desired result, expressed in exergy terms.
The product is defined to be equal to all the exergy values to be considered at the
outlet plus all the exergy increases between inlet and outlet that are in accord with the
purpose of the system;
tot D E ,
.
is the exergy destruction, i.e. the exergy destroyed due to irreversibilities within
a system;
L E
.
represents the exergy loss, i.e the exergy transfer to the system surroundings.
I t is also possible to apply the same form of the exergy balance to a single component:
The exergy loss of a single
component is considered equal
to zero, because it is assumed
that a single component has
interactions only with other components and not with the system surrounding.
However it is possible to use another approach, where the exergy loss of the single
component is taken into account and so the exergy balance becomes:
k L k D k P k F E E E E , , , ,
+ + =
where
In the method of the exergy analysis the determination of the exergy destruction and
of the exergy loss is fundamental, because they give a quantitative evaluation of the
waste of the energy resources within the system or the components and play an
important role in determining the thermodynamic performance of the system. To
better evaluate the importance of these variables the exergy analysis additionally
k P
E
,
&
k D
E
,
&
k F
E
,
&
k-th
Component
k D k P k F E E E , , ,
+ =
∑
=
k
tot L L E E ,
. .
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The Conventional Exergoeconomic Analysis
often involves the calculation of measures of performance as the exergy destruction
ratio, the exergy loss ratio and the exergetic efficiencies.
The exergy destruction ratio can be calculated in two different ways, in fact the rate of
exergy destruction in a system component can be compared to the exergy rate of the
fuel provided to the overall system or alternatively to the total exergy destruction rate
within the system:
,
,
,
D k
D k
F tot
E
y
E
=
&
&
,
,
,
D k
D k
D tot
E
y
E
* =
&
&
These two exergy destruction ratios are useful for comparisons among various
components of the same system to determine the component responsible for the
maximum exergy destruction. Additionally the y D
can also be used to compare similar
c omponents of different systems using the same fuels.
The exergy loss ratio is defined by comparing the exergy loss to the exergy of the fuel
provided to the overall system:
tot F
L
L
E
E
y
,
=
The exergetic efficiency (also called second-law efficiency) is the ratio between the
exergy product and the exergy fuel (respectively ε tot and ε k are the exergetic efficiency
o f the overall energy system and of the k th component):
tot F
tot L tot D
tot F
tot P
tot
E
E E
E
E
,
, ,
,
,
1
+
- = = e
k F
k D
k F
k P
k
E
E
E
E
,
,
,
,
1
- = = e
Such efficiency provides a true measure of the performance of an energy system from
the thermodynamic viewpoint, because it shows the percentage of the fuel exergy
provided to a system or to a component that is found in the product exergy. The ε is
useful for comparison of similar components and plants.
The exergetic efficiency of a system can be also determined in terms of exergy
destruction ratio and exergy loss ratio:
∑
- - =
k
L k D tot
y y
,
1 e
20
The Conventional Exergoeconomic Analysis
1.2 Economical Analysis
The economical analysis of a power plant is needed to determine the major
c osts involved in the project in order to calculate the necessary variables to lead the
exergoeconomic analysis of the system.
The major costs involved in the realization of a thermal design project are the total
capital investment, the fuel costs, the operating and maintenance expenses and the
cost of the final products.
Each company has its own preferred approach for conducting an economic analysis
and calculating the cost of the main product, however the method used is the revenue
requirement method.
With this approach the cost of the main product can be calculated through four steps:
1. Estimation of the total capital investment.
2 . Determination of the economic, financial, operating a nd market input
parameters for the detailed cost calculation.
3. Calculation of the total revenue requirement.
4. Calculation of the levelized product cost.
1.2.1 Estimation of the Total Capital Investment (TCI)
The total capital investment is the sum of the fixed capital investment (FCI) and
o ther outlays. The term other outlays consists of the startup costs, working capital,
costs of licensing…
The FCI is the capital needed to purchase the land, build all the necessary facilities and
purchase and install the required machinery and equipment for a system. To
determine the FCI is assumed a so-called overnight construction, that is a zero-time
design and construction period.
The cost estimates for the fixed capital investment consist in two cost elements:
- direct costs represent the costs of all permanent equ ipment, materials,
labor and other resources involved in the fabrication, erection and
installation of the permanent facilities,
21
The Conventional Exergoeconomic Analysis
- indirect costs include the engineering and supervisio n costs and the
contingencies cost.
However a detailed description of the cost components of the TCI is given in the
following table 1
:
Table 1.1 Breakdown of total capital investment
I. F ixed-capital investment (FCI)
A. Direct costs (DC)
1. Onsite costs (ONCS)
• Purchased-equipment cost (PEC; 15-40 % of FCI)
• Purchased-equipment installation (20-90 % of PEC; 6-1 4
% of FCI)
• Piping (10-70 % of PEC; 3-20 % of FCI)
• Instrumentation and controls (6-40 % of PEC; 2-8 % of
FCI)
• Electrical equipment and materials (10-15 % of PEC; 2 -10
% of FCI)
2. Offsite costs (OFCS)
• Land (0-10% of PEC; 0-2% of FCI)
• Civil, structural and architectural work (15-90% of P EC; 5-
23% of FCI)
• Service facilities (30-100% of PEC; 8-20% of FCI)
B. I ndirect costs (IC)
1. Engineering and supervision (25-75% of PEC; 6-15 % of DC; 4-
21 % of FCI)
2. Construction costs including contractor’s profit (15 % of DC; 6-
22 % of FCI)
3. Contingencies (8-25% of the sum of the above costs; 5 -20% of
FCI)
II. Other outlays
A. Startup costs (5-12 % of FCI)
B. Working capital (10-20 % of TCI)
C. Costs of licensing, research and development
D. Allowance for funds used during construction (AFUDC)
The onsite costs of the table correspond to the installed equipment cost for all items
built within a specific geographic area called battery limits, over these limits raw
materials, utilities (electricity, water, steam, refrigeration, etc…) , chemicals are
imported and manufactured products and utilities are exported. The offsite costs
include costs associated with the production and distribution of utilities, roads, general
1
see [1]
22
The Conventional Exergoeconomic Analysis
offices, wastewatertreating facilities and storage facilities for raw materials and
finished products.
The estimation of the cost of purchased equipment is the first of the economic
analysis. The best cost estimates can be obtained directly through vendors’ quotations.
Other sources of cost estimates are cost values from past purchase orders, quotations
from experienced professional cost estimators or calculations using the extensive cost
databases often maintained by engineering companies. In addition there exist some
commercially available software. Finally the purchase prices of various equipment
items can be obtained from the literature, where they are usually given in the form of
estimating charts, that have been obtained through the correlation of a large number
of cost and design data.
Obviously all cost data used in an economic analysis must be brought to the same
reference year: the year used as a basis for the cost calculations. For cost data based
on conditions at a different time, this is done with the aid of an appropriate cost index:
=
y
ref
y ref
I
I
C C
where C
ref is the cost at the reference year,
C
y is the original cost,
I
ref represents the cost index for the reference year,
I
y is the cost index for the year when the original cost was obtained.
The cost index is an inflation indicator used to correct the cost of equipment items,
materials, labor and supplies to date of the estimate. There exist several publications
of these cost indexes.
For estimating the total capital investment required for a new system or an expansion
there are some simplified expressions, that are obtained using typical values for the
various cost categories (shown in Table 1.1)
As already mentioned, the total capital investment (TCI) is the sum of the fixed-capital
investment (FCI), startup costs (SUC), working capital (WC), costs of licensing, research
and development (LRD) and allowance for funds used during construction (AFUDC):
TCI=FCI+SUC+WC+LRD+AFUDC
23
The Conventional Exergoeconomic Analysis
whereas the fixed capital investment is the sum of the direct costs (DC) and the
indirect costs (IC):
FCI= DC+IC
The direct costs include the onside costs (ONSC) and the offsite costs (OFSC):
DC=ONSC+OFSC
The onsite costs can be estimated directly from correlations, that can be found in the
literature. The offsite costs may be 100-200% (average value 120 %) of the onsite costs
for the construction of a new facility or between 40 and 50 % (average value 45%) of
the onsite costs for an expansion of an existing facility:
1. 1
The indirect cost IC may be estimated as the 25 % of the direct costs:
IC=0.25 DC
Additionally is possible to assume that:
SUC= 0.10 FCI
WC=0.15 TCI
LRD+AFUDC=0.15 FCI
Therefore the following equivalences are obtained:
TCI=1.47 FCI
and
( ) ( ) OFSC ONSC DC IC DC TCI + = = + = 84 . 1 84 . 1 47 . 1
using the equation 1.1:
=
expansion ONSC
system new ONSC
TCI
67 . 2
05 . 4
Finally the TCI can be evaluated through the PEC (Purchased Equipment Costs), in fact
the FCI for a new system is usually in the range of 280-550 % of the PEC with the
average value being about 430% and for a system expansion the FCI averages about
283 % of the PEC:
=
ONSC
ONSC
OFSC
45 . 0
20 . 1
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