Thermoeconomic Philosophy Applied to the Operating Analysis and Diagnosis of Energy Utility Systems

Abstract

In this paper, the objectives of thermoeconomic diagnosis are presented. The paper is part of a project, started in 2001 and named TADEUS (Thermoeconomic Approach to the Diagnosis of Energy Utility Systems), aimed at integrating various experiences accumulated by a group of researchers working on thermoeconomic diagnostics, a field of research started by Antonio Valero and co-workers in 1990 and followed by various researchers all over the world. It is shown how, starting from the same basic set of ideas, researchers developed different approaches, each one having particular characteristics that are, nonetheless, complementary to each other.

Full text

Page 1

Int.J. Thermodynamics, Vol.7 (No.2) 33
Int.J. Thermodynamics,
Vol.7, (No.2), pp.33-39, June-2004
ISSN 1301-9724


Thermoeconomic Philosophy Applied to the Operating Analysis
and Diagnosis of Energy Utility Systems


Antonio Valero1, Luis Correas1, Andrea Lazzaretto2, Víctor Rangel1, Mauro Reini3,
Rodolfo Taccani3, Andrea Toffolo2, Vittorio Verda4, And Alejandro Zaleta5
1 CIRCE. University of Zaragoza, SPAIN
2 University of Padova, ITALY
3 University of Trieste, ITALY
4 Politecnico di Torino, ITALY
5 University of Guanajuato, MEXICO


Abstract
In this paper, the objectives of thermoeconomic diagnosis are presented. The paper is
part of a project, started in 2001 and named TADEUS (Thermoeconomic Approach to
the Diagnosis of Energy Utility Systems), aimed at integrating various experiences
accumulated by a group of researchers working on thermoeconomic diagnostics, a field
of research started by Antonio Valero and co-workers in 1990 and followed by various
researchers all over the world. It is shown how, starting from the same basic set of
ideas, researchers developed different approaches, each one having particular
characteristics that are, nonetheless, complementary to each other.
Keywords: Thermoeconomic diagnosis, TADEUS problem.

1. Thermoeconomic Diagnosis
The word "diagnosis" applied to energy
systems means the art of discovering anomalies
by monitoring the operating condition through
hands-on measures. While the aim of techniques
adopted in power plants usually consists of
predicting possible
measurements of thermo-mechanical quantities
(e.g., rotor vibrations, pressures and temperatures
of lubrication and cooling circuits, metal
temperatures, etc.), thermoeconomic diagnosis is
focused on the analysis of system performance in
terms of efficiency.
The objective of such a discipline consists
in the detection of an efficiency deviation, the
location of its main causes, and the quantification
of its effects in terms of additional fuel
consumption or economic impact. Exergy and
thermoeconomic analysis are the main tools on
which this discipline is based and can be applied
to any type of energy system typology. Together
with this type of generality comes another
important characteristic which is its inductive
nature, i.e. the search for the causes of
anomalous behavior is done without knowledge
of the effects provoked by all the possible
anomalies. Other widely adopted methodologies
for the diagnosis of efficiency reductions, such as
gas path analysis (Stamatis, Mathioudakis, and
failures through
Papailiou, 1990) or the fault matrix method
(Saravanamuttoo and MacIsaac, 1983) are
deductive.
The thermoeconomic approach to diagnosis
is a fairly new approach or philosophy. Its cradle
was the University of Zaragoza in the eighties.
The first work on diagnosis was made with the
GAUDEAMO project for Endesa coal power
plants. It was begun in 1981 and lasted until
1986, and its aim was to formulate and apply a
procedure for computer-assisted analysis of
performance tests using systematic exergy audits
(Valero et al., 1986). In the same years, the
theoretical seeds for diagnosis were also sowed.
Illustrations of that work are some papers by
Valero, Lozano and co-workers on “A general
theory of exergy saving” (Valero, Lozano, and
Muñoz, 1986) and “Application of the exergetic
costs theory to a steam boiler in a thermal
generating station” (Lozano and Valero, 1987)
.The first paper states the definition and the
theory for calculating exergetic costs; and the
second applies this concept to the diagnose of a
steam boiler, formulating and first resolving the
question of “what is the additional fuel
consumption of the total plant due to a
discrepancy in the normal functioning of the
boiler as compared to that of the same boiler at
design conditions?”. Both papers were

Page 2

Int.J. Thermodynamics, Vol.7 (No.2)
34
j
recognized with the ASME Edward F. Obert
award in 1986 and 1987. In a letter to ASME
Performance Tests Committee (PTC) by A.
Valero in January of 1988, Valero states:
“…with very little more assessment effort than is
needed at present,…, it would be possible to
increase the quality of the diagnosis of the
plant´s behavior as many times as the number of
independent measures which would have been
taken…. In what remains in this century, and of
course in the next, we will see that performance
tests will become a common practice, and in
general the instrumentation in plants will
become both more accurate and cheaper, thus
increasing the amount of data available. For this
reason it is desirable that the PTC of ASME
should start a conscientious study in order to
propose additional codes and/or methodologies
based on Second Law analyses”. The paper “On
causality in organized energy systems: III.
Theory of perturbations” Valero et al. (1990)
presented for the first time the concepts of
exergy malfunctions and dysfunctions and
analytically demonstrated their relationship with
the impact on raw material consumption of a
component in an organized energy system no
matter how complex. This paper separated the
causation of exergy losses from their localization
and quantification in conventional Second Law
analyses. The paper “Theory of the exergetic
cost” (Lozano and Valero, 1993) divulged those
findings to a broader audience and showed itself
to be a true milestone in the field of applied
thermodynamics.
In the nineties, the seeds grew and Zaragoza
played the role of the “academia” for
thermoeconomic diagnosis. Many master and
Ph.D. degree students were educated in this
philosophy, leading to its continued development
and contributing to the export of this knowledge.
This topic became in these years one of the most
studied topics in thermoeconomics and many
papers were published.
Some of the results that were achieved in
these years are: the mathematical formulation of
the fuel impact formula (Lozano et al., 1994;
Reini, Lazzaretto, and Macor, 1995), the
definition of the indicators for the localization of
anomalies (Stoppato and Lazzaretto, 1996), and
the definition of concepts such as intrinsic
malfunctions, induced
dysfunctions (Torres et al., 1999; Valero, Torres,
and Lerch, 1999).
thermoeconomic diagnosis is to find the causes
and evaluate the impact on fuel, ∆FT, of a given
additional irreversibility. From an exergy balance
it is known that
malfunctions, and
The key idea for

n
TT
j=1
F = P +
∆∆
I
∑
(1)
Thus, an additional fuel consumption is the sum
of additional irreversibilities in the components
and any additional production. However,
location of the irreversibilities is not the same as
causation.
A first solution to the problem of causation
was to relate it with the exergetic cost (Valero,
Lozano, and Muñoz, 1986), i.e.

j
*
P,jT
FkI
∆≅∆
i
(2)
This formula was approximate but predictive
nonetheless. A more precise formula describing
the malfunction of the component was (Lozano
and Valero, 1987; Valero et al., 1990)

*
F,i iT
FkP κ
∆∆≅
(3)
This expression only takes into account the
irreversibility increase due to the variation in
exergy efficiency (malfunction).
Based on these ideas, Reini, Lazzaretto, and
Macor (1995) developed a formula on fuel
impact such that

(4)
nn
*
P,jT0jii
i=1j=0
n
*
P,i0s,i
i=1
∆Fk (x )∆κ P (x )
+ k(x ) ∆P
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
≅
∑ ∑
∑
0
0
This was an important contribution because it
allowed one to assess the impact on fuel as a sum
of contributions of each component, ∆κ, to the
variation of final resources. This equation
considers the exergetic cost and the product for
the reference conditions. It allows one to know
the contribution to the impact on fuel of each
component and to determine the irreversibilities
due to malfunctions. Nonetheless, it too is not
exact, since in fact an error of 1% in ∆κ will
produce an error of 1% in ∆FT.
A few years after this contribution, Torres
et al. (1999) refined this expression to the
following:

(5)
nn
*
P,jT1ji i
i=1j=0
n
*
P,i1s,i
i=1
F = k(x )∆κ P (x )
+ k(x )∆P
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
∆
∑ ∑
∑
This is an exact formula quite close to the
previous one but now the unit exergetic costs are
taken at the actual conditions. Thus, all the
exergies of the system for both the reference and
actual state must be known in order to diagnose.

Page 3

Int.J. Thermodynamics, Vol.7 (No.2) 35
This expression can substituted into equation (1)
and allows one to exactly quantify the impact of
malfuntions on a given system.
With the theory established and several
applications of diagnosis to actual power plants
made, different research groups began making
important contributions. This important activity
also had the consequence of generating non-
thermodynamic entropy, in particular in the
specific nomenclature. For this reason, in 2001,
on the occasion of the ECOS conference in
Istanbul, some of the researchers interested in
this topic decided to define a test case. The idea
was to apply the different procedures to the same
plant, as already done for thermoeconomic
optimization in 1992 (Valero et al., 1994) with
the CGAM problem. The aim of this new effort
was to compare the results and highlight the
main characteristics of each approach. The
objective was also to share this background of
knowledge and experiences with other research
groups interested in thermoeconomic diagnosis,
enlarging the community.
This test has been called the TADEUS
problem (Thermoeconomic
Diagnosis of Energy Utility Systems) in honor of
Prof. Tadeus Kotas. It is consists of a combined
cycle and a couple of operating conditions: the
operating condition to be analyzed and a
reference condition without anomalies.
The TADEUS problem is a significant test
for a number of reasons: 1) most of the
components, in particular in the gas turbine
section, are characterized by efficiencies strongly
dependent on the operating condition; this means
that an intrinsic malfunction
accompanied by induced malfunctions; 2) the
components are closely interconnected, which
results in a propagation of the induced effects
throughout the system.
The combined cycle considered for the
TADEUS problem is comprised of two gas
turbines (125 MWe each), two heat recovery
steam generators, and a steam turbine (about 100
MWe). A schematic of this plant is shown in
Figure 1. TABLE I provides a legend for the
various streams in Figure 1.
A diagnosis procedure is always based on a
comparison between two plant operating
conditions: the actual one, which is the one to be
analyzed in order to detect and locate possible
anomalies, and the reference one, which is an
opportune condition during which the plant is
operating without anomalies.
Analysis and
is often

TABLE I. MAIN POINT OF THE COMBINED
CYCLE PLANT.
Point Description
gt0 Ambient
gt1 Inlet compressor
gt2 Outlet compressor
gt3 Inlet turbine
gt4 Outlet turbine
gt5 Outlet HRSG
gt6 Refrigeration 4° stage turbine
gt7 Refrigeration 3° stage turbine
gt8 Refrigeration 2° stage turbine
gt9 Refrigeration of the rotor
gt10 Fuel
gt11 Mechanical power compressor
gt12 Mechanical power turbine
gt13 Electric power
st1 Inlet high pressure turbine
st2 Outlet high pressure turbine
st3 Low pressure steam
st4 Inlet low pressure turbine
st5 Outlet low pressure turbine
st6 Outlet condenser
st7
st8
st9
st10
st11
Electric power extraction pump
g1 Inlet low pressure economizer
g2 Outlet low pressure economizer
g3 Inlet low pressure evaporator
g4 Outlet low pressure evaporator
g5 Inlet circulation pump
g6 Inlet high pressure economizer
g7 Outlet high pressure economizer
g8 Inlet high pressure evaporator
g9 Outlet high pressure evaporator
g9b Inlet high pressure super-heater
g10 Outlet high pressure super-heater
g11 Outlet low pressure super-heater
g12 Inlet low pressure super-heater
g13 Gas inlet high pressure super-heater
g14 Gas inlet high pressure evaporator
g15 Gas inlet low pressure super-heater
g16 Gas inlet high pressure economizer
g17 Gas inlet low pressure evaporator
g18 Gas inlet low pressure economizer
g19
g20 Electric power circulation pump
Outlet extraction pump
Mechanical power HP turbine
Total mechanical power turbine
Electric power steam turbine
Gas outlet heat recovery steam generator

Page 4

from
HRSG2
HPSHHPEV
LPT
HPT
CONDENSER
LPECO
LPEVHPECOLPSH
from
HRSG2
gt0
gt10
gt1
FILTER
gt3
gt2
gt4
gt6
gt7
gt8
gt9
gt11
gt12gt13
g13 g14g15 g16
g17g18g19
AIR
COMPRESSOR
GAS
TURBINE
g1
g2
g3
g4
g5
g6
g7
g11
g12
g8
g9
g9b
g10
st1
st2
st3
st4
st5
st6
st7
st8
st9
st10
to
HRSG2

Figure 1. Schematic of the combined cycle
power plant proposed for the TADEUS.
2. The TADEUS Problem
The actual operating condition proposed for
the TADEUS problem is shown in TABLES IIA,
IIB, and IIC. This condition was obtained by
using a plant simulator which plays the role of a
real power plant. As in an actual plant, the
diagnosis must be conducted without knowing in
advance if and where anomalies took place.
Moreover, the model is not used to locate the
anomalies detected. It is only used to generate
reliable actual operating conditions.
The model requires the specification of
ambient conditions (temperature, pressure and
relative humidity), the lower heating value of the
fuel, and the total electric power to be produced.
Moreover, several anomalies can be produced by
modifying component design parameters. The
model determines the system state according to
the off-design behavior of the components and
the control system constraints.
The operating condition considered is
characterized by three anomalies in the first gas
turbine and in the first HRSG: 1) filter fouling, 2)
erosion of the gas turbine, and 3) high pressure
super-heater fouling. These are obtained 1) by
increasing the design pressure drop (+25%); 2)
by modifying the design values of the flow
coefficient (+2.5%) and the polytropic efficiency
(-1%) (Diakunchak, 1992); and 3) by increasing
the design approach point temperature (+10%).
The choice of a reference condition is a
crucial part of the diagnosis. In fact, deviations
of some thermodynamic quantities between the
actual operating and
conditions can be due to external causes, which
can be eliminated by simply selecting a different
reference condition. These external causes can be
due to, for instance, 1) plant production: the
efficiency of a plant at its nominal power is
different than at partial load; 2) ambient
conditions: the behavior of components is
generally sensitive to ambient temperature,
pressure and relative humidity; and 3) fuel
quality: a different lower heating value produces
an impact on the combustion products since, for
instance, the same fuel mass flow rate produces a
different temperature. An additional aspect
which impacts the diagnosis result is constituted
by the set-points: if the plant operates with a
different set-point, the whole thermodynamic
picture changes.
reference operating
TABLE IIA. THERMODYNAMIC VARIABLE
VALUES OF THE GAS TURBINES AT THE
ACTUAL OPERATING CONDITION.
TGA GT
°C
phs
kg/s
434.5
434.5
380
388.1
430.7
430.7
1.763
6.707
16.35
17.75
bar
0.987
kJ/kg
-101
-101
283.3
109.9
-560.6
-994
-11.77
82.96
150.4
283.3
kJ/kgK
6.87
6.873
6.981
8.248
8.236
7.461
6.908
6.937
6.954
6.981
gt0
gt1
gt2
gt3
gt4
gt5
gt6
gt7
gt8
gt9
15
15 0.9759
386.7
1145
511.5
117.3
103.3
195.9
261
386.7
12.94
12.81
1.007
0.987
2.207
4.358
6.555
12.94
TGBGT
°C
phs
kg/s
432.4
432.4
378.1 389.6
386.2
428.6 506.6
428.6
1.754 103.9
6.674 197.2
16.27 262.8
17.67 389.6
bar
0.987
kJ/kg
-101
-101
286.5
112.2
-570.8
-998
-11.19
84.29
152.3
286.5
kJ/kgK
6.87
6.873
6.98
8.248
8.229
7.464
6.907
6.936
6.953
6.98
gt0
gt1
gt2
gt3
gt4
gt5
gt6
gt7
gt8
gt9
15
15 0.9781
13.23
115113.1
1.007
0.987
2.227
4.419
6.668
13.23
118
kW
TGA
TGB
gt10
368494 162959 123837 122599
368494 163508 127262 125989

gt11gt12gt13
Int.J. Thermodynamics, Vol.7 (No.2)
36

Page 5

TABLE IIB. THERMODYNAMIC VARIABLE
VALUES OF THE HRSG’S AT THE ACTUAL
OPERATING CONDITION.
HRSG 1GT
°C
phs
kg/s
60.260
60.260 161.70 6.608
241.000 162.70 6.608
241.000 162.70 6.608
50.900 162.70 6.608
50.900 163.60 64.770 694.6
50.900 268.30 54.400 1176.0 2.959
203.600 269.30 54.400 1181.0 2.969
203.600 269.30 54.400 1584.0 3.713
50.900 269.30 54.400 2790.0 5.934
50.900 484.20 52.770 3394.0 6.899
9.366162.70 6.608 2761.0 6.728
9.366261.30 6.410 2979.0 7.193
430.700 511.50 1.007 -560.6
430.700 449.00 1.005 -631.9
430.700 277.30 1.000 -822.6
430.700 272.90 0.999 -827.4
430.700 220.30 0.996 -884.3
430.700 177.70 0.991 -930.0
430.700 117.30 0.987 -994.0

GT
kg/s°Cbar
59.260 53.687.867
59.260 161.70 6.608
237.000 162.70 6.608
237.000 162.70 6.608
49.740 162.70 6.608
49.740 163.60 64.770 694.6
49.740 268.30 54.400 1176.0 2.959
199.000 269.30 54.400 1181.0 2.969
199.000 269.30 54.400 1584.0 3.713
49.740 269.30 54.400 2790.0 5.934
49.740 481.40 52.770 3387.0 6.891
9.518 162.70 6.608 2761.0 6.728
9.518 261.30 6.410 2979.0 7.193
428.600 506.60 1.007 -570.8
428.600 445.90 1.005 -640.1
428.600 277.30 1.000 -827.4
428.600 272.90 0.999 -832.3
428.600 221.20 0.996 -888.1
428.600 177.70 0.991 -934.8
428.600 118.00 0.987 -998.0
bar
7.867
kJ/kg kJ/kgK
225.4
682.8
687.2
768.8
687.2
g1
g2
g3
g4
g5
g6
g7
g8
g9
g9b
g10
g11
g12
g13
g14
g15
g16
g17
g18
g19
53.68 0.751
1.959
1.969
2.157
1.969
1.972
8.236
8.141
7.842
7.833
7.724
7.629
7.461
HRSG 2phs
kJ/kg kJ/kgK
225.4
682.8
687.2
771.5
687.2
g1
g2
g3
g4
g5
g6
g7
g8
g9
g9b
g10
g11
g12
g13
g14
g15
g16
g17
g18
g19
0.751
1.959
1.969
2.163
1.969
1.972
8.229
8.138
7.843
7.834
7.727
7.630
7.464
All these cause of deviations can be
eliminated by considering a reference operating
condition characterized by the same load, the
same ambient conditions, the same fuel quality,
and the same set-points.
The definition and use of the reference case
varies considerably
approaches and is based on the different types of
information that the authors intend to provide
among the various
TABLE IIC. THERMODYNAMIC VARIABLE
VALUES OF THE STEAM TURBINE AT THE
ACTUAL OPERATING CONDITION.
STGT
°C
482.8
190.4
257.8
200.9
53.62 0.1476
53.62 0.1476
53.68
phs
kg/s
100.6
100.6
18.88
119.5
119.5
119.5
119.5
55499 kW
52254 kW
105598 kW
112.1 kW
bar
52.77
4.211
4.211
4.211
kJ/kg kJ/kgK
3390
2839
2979
2861
2424
224.5 0.7503
225.4 0.7507
st1
st2
st3
st4
st5
st6
st7
st8
st9
st10
st11
6.895
7.101
7.384
7.148
7.481
7.867

together with the localization of the anomalies.
In particular, the definition of load is a delicate
part of this procedure. As an example, it can be
assumed to be the "same plant production" or the
"same fuel rate" or the "same mass flow rate of
the process fluid". In TABLES IIIA, IIIB, and
IIIC a reference operating condition charac-
terized by the same electricity production as in
the actual operating condition is provided.
For defining the reference condition, a
reliable plant simulator is very useful, since it
can be used to determine the most useful
reference condition.
condition has been determined, the only cause of
deviation between the actual and reference
conditions is a result of the presence of
anomalies in the plant.
Once this reference
TABLE IIIA. THERMODYNAMIC
VARIABLE VALUES OF THE GAS
TURBINES AT THE REFERENCE
OPERATING CONDITION.
TGA
TGB
gt0
gt1
gt2
gt3
gt4
gt5
gt6
gt7
gt8
gt9
GT
°C
phs
kg/s
425.9
425.9
372.4
380.5
422.2
422.2
1.727
6.573
16.03
17.4
bar
0.987
kJ/kg
-101
-101
281.9
106.6
kJ/kgK
6.87
6.873
6.977
8.255
8.236
7.463
6.906
6.934
6.951
6.977
15
15 0.9781
385.4
1152
509.8
117.2
103.1
195.4
260.2
385.4
13.04
12.91
1.007 -573.9
0.987
2.216 -12.02
4.382
6.596
13.04
-1006
82.4
149.6
281.9
kWgt10 gt11gt12 gt13
TGA-TGB 365450 159148 126263 125000

Int.J. Thermodynamics, Vol.7 (No.2) 37

Page 6

TABLE IIIB. THERMODYNAMIC
VARIABLE VALUES OF THE HRSG’S AT
THE REFERENCE OPERATING
CONDITION.

Int.J. Thermodynamics, Vol.7 (No.2)
38
TABLE IIIC. THERMODYNAMIC
VARIABLE VALUES OF THE STEAM
TURBINE AT THE REFERENCE
OPERATING CONDITION.
STGT
°C
484.9
191.8
257
201.9
53.22 0.1448
53.22 0.1448
53.28
phs
kg/s
99.15
99.15
18.45
117.6
117.6
117.6
117.6
54927 kW
51538 kW
104335 kW
109.1 kW
bar
52.1
4.149
4.149
4.149
kJ/kg
3396
2842
2977
2863
2425
222.8 0.7452
223.7 0.7456
kJ/kgK
6.908
7.115
7.388
7.16
7.493
st1
st2
st3
st4
st5
st6
st7
st8
st9
st10
st11
7.779

4. Conclusions
In the papers which appear in this issue,
some of the latest
thermoeconomic diagnosis
Applications to the TADEUS problem are
presented in order to clarify the different features
of some of the principal thermoeconomic
approaches presently in the literature. The
authors' hope that other research groups may be
able to contribute to the development of
diagnosis by applying their approaches to this
very same system and comparing their results
with those shown in this issue.
developments
are
in
shown.
Nomenclature
Irreversibility in the jth component [kW]
kij Unit exergy consumption
kp,j* Unit exergy cost of the jth component
product
kF,i* Unit exergy cost of the jth component fuel
MF Malfunction [kW]
Pi Product of the ith component [kW]
(xo) Reference operating condition
(x1) Actual operating condition
∆FT Fuel impact [kW]
∆Ij Variation in component irreversibility
[kW]
∆κi Variation in the component’s total unit
exergy consumption
∆κji Variation in the unit consumption of the jth
resource of the ith component
∆PT Variation in total plant production [kW]
∆PS,i Contribution of the jth component to the
variation in plant production [kW]
Ij
References
Stamatis A., Mathioudakis K., Papailiou K.D.,
1990, “Adaptive Simulation of Gas Turbine
Performance,” ASME Journal of Engineering for
Gas Turbines and Power, 112, pp. 168-175.
Saravanamuttoo H.I.H. and MacIsaac B.D. 1983,
“Thermodynamic Models for Pipeline Gas
Turbine Diagnostics,” Journal of Engineering for
Power, Vol. 105, October, pp. 875-884.
Valero A., Lozano M.A., Alconchel J.A., Muñoz
M., and Torres C., 1986, “GAUDEAMO: A
system for energetic/ exergetic optimization of
coal power plants,” ASME, AES Vol. 2-1,
Computer-Aided Engineering of Energy Systems,
Vol. 1, Optimization, ed. R.A. Gaggioli, ASME
Book No H0341 A, pp. 43-49. New York.
Valero, A., Lozano, M. A., and Muñoz, M.,
1986, “A general theory of exergy saving. I. On
the exergetic cost, II On the thermoeconomic
cost, III Energy saving and thermoeconomics,”
ASME, AES: Computer-Aided Engineering and
Energy Systems, Vol. 3, Second Law Analysis
and Modelling, ed. R.A. Gaggioli, ASME Book
No. H0341C, pp. 1-21. New York.
Lozano M.A. and Valero A.,1987, “Application
of the Exergetic Costs Theory to a Steam Boiler
in a Thermal Generating Station,” ASME. AES
vol. 3-2 Analysis and Design of Advanced
Energy Systems: Applications, eds. M.J. Moran,
S.S. Stecco, and G.M. Reistad, ASME Book No.
G0377 B, pp. 41-51.New York, 1987
Valero, A.; Carreras, A.; Torres, C.; Lozano, M.
A., 1990, “On causality in organized energy
systems. I.Purpose, cause, irreversibility, cost /
II. Symbolic exergoeconomics / III. Theory of
Perturbations,” Pergamon Press, A Future for
Energy, eds. S.S. Stecco and M.J. Moran, pp.
387-420.
HRSG 1
HRSG2
g1
g2
g3
g4
g5
g6
g7
g8
g9
g9b
g10
g11
g12
g13
g14
g15
g16
g17
g18
g19
GT
°C
phs
kg/s
58.800
58.800 161.20 6.535
235.200 162.20 6.535
235.200 162.20 6.535
49.580 162.20 6.535
49.580 163.10 63.940
49.580 267.50 53.710 1172.0
198.300 268.50 53.710 1177.0
198.300 268.50 53.710 1582.0
49.580 268.50 53.710 2790.0
49.580 484.90 52.100 3396.0
9.223162.20 6.535
9.223260.50 6.338
422.200 509.80 1.007
422.200 447.60 1.005
422.200 276.50 1.000
422.200 272.10 0.999
422.200 220.10 0.996
422.200 177.20 0.991
422.200 117.20 0.987 -1006.0 7.463
bar
7.779
kJ/kg
223.7
680.9
685.3
767.7
685.3
692.5
kJ/kgK
0.746
1.955
1.965
2.154
1.965
1.967
2.952
2.961
3.708
5.940
6.908
6.731
7.195
8.236
8.141
7.842
7.834
7.726
7.630
53.28
2760.0
2977.0
-573.9
-645.0
-835.1
-839.8
-896.1
-942.1

Page 7

Int.J. Thermodynamics, Vol.7 (No.2) 39
Lozano M.A., and Valero A., 1993, “Theory of
the Exergetic Cost,” Energy: The International
Journal, Vol. 18, n° 9, pp.939-960.
Lozano M.A., Bartolomé J.L., Valero A., and
Reini M., 1994, “Thermoeconomic Diagnosis of
Energy Systems,” Flowers 94 - Florence World
Energy Research Symposium, Florence. Italy.
Reini M., Lazzaretto A., and Macor A., 1995,
“Average Structural and Marginal Costs as
Result of a Unified Formulation of the
Thermoeconomic Problem,” Proceedings of
Second Law Analysis of Energy System: Towards
the 21st Century, Rome.
Stoppato A. and Lazzaretto A., 1996, “The
Exergetic Analysis
Diagnosis,” AES: Thermodynamics and the
Design, Analysis and Improvement of Energy
Systems, ed. Duncan, A. B., Fiszdon, J., O’Neal,
D., and Den Braven, K., ASME Book no
H01022, pp. 191-198.

for Energy System
Torres C., Valero A., Serra L., and Royo J.,
1999, “Structural theory and Thermoeconomic
Diagnosis. Part I: On Malfunction and
Dysfunction Analysis,” ECOS 99. Tokyo. Japan.
Valero A., Torres C., and Lerch F., 1999,
“Structural Theory and
Diagnosis. Part III: Intrinsic and Induced
Malfunctions,” Elsevier
Conversion and Management, 40, 1627-1649.
Valero A.; Lozano M. A.; Serra L.; Tsatsaronis
G.; Pisa J.; Frangopoulos C.; von Spakovsky
M.R., 1994, “CGAM Problem: Definition and
Conventional Solution,” Energy, Pergamon
Press. Vol. 19, No.3, pp. 279-286.
Diakunchak I.S.,
Deterioration in Industrial Gas Turbines,”
Journal of Engineering for Gas Turbines and
Power. Vol. 114. pp. 161-168.
Thermoeconomic
Science,
Energy
1992, “Performance