1
SIMULATION OF POWER CYCLE WITH
ENERGY-UTILIZATION DIAGRAM
Thongchai SRINOPHAKUN*
Department of Chemical Engineering, Faculty of Engineering,
Kasetsart University, Bangkok 10903, THAILAND
Sangapong LAOWITHAYANGKUL
Chemical Engineering Practice School, Department of Chemical Engineering,
Faculty of Engineering, King Mongkut's University of Technology Thonburi,
Bangkok 10140, THAILAND
and
Masaru ISHIDA
Research Laboratory of Resources Utilization, Tokyo Institute of Technology
4259 Nagatsuta, Midoriku, Yokohama, JAPAN 226-8503
* To whom all correspondence should be addressed.
* Tel. 66-2-9428555 ext. 1214
* Fax. 66-2-5792083
* E-mail: fengtcs@nontri.ku.ac.th
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ABSTRACT
The graphical representation named Energy-Utilization Diagram (EUD) is a
very useful tool for exergy analysis of chemical process. This technique can be applied to
the power cycle; the combination of heat exchanger and power subsystems. The cooperation of EUD with the process simulator was introduced by retrieve the simulation
results and thermodynamic properties. ASPEN Plus simulator was used in this research
for constructing the EUD routine by programming in Fortran block and external Fortran
files. The Rankine power cycle and the Rankine cycle were selected as a case study for
verifying this routine. The sensitivity analysis of the Rankine cycle showed that the
exergy loss/net generated power ratio (EXL/NGP) decreased with these three conditions:
pump discharge pressure increase, the turbine discharge pressure decrease and steam
temperature increase. The increase of subcooled temperature in condenser affected the
increase of exergy loss/ net generated power ratio. The ratio of exergy loss/net generated
power could be reduced by 12.61% compared to the base case after adjusting the
operating condition. In addition, the modification of the Rankine cycle to the Kalina
cycle could be achieved the purpose of exergy reduction. The ratio of EXL/NGP could
reduce from 2.04805 in the Rankine cycle (improvement case) to be 1.06036 in the
Kalina cycle. Thus the efficiency of power cycle could be improved efficiently.
Keywords
:
Exergy Analysis / EUD / ASPEN Plus / Rankine Cycle / Kalina cycle
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INTRODUCTION
Many researchers conducted exergy analysis in the last two decades. Exergy
analysis could be graphically presented using the Energy-Utilization Diagram (EUD) as a
tool (Ishida, 1981). The EUD is constructed by plotting the energy quality, A, against
energy quantity, H. Many exergy analyses using EUD were performed in the chemical
process and power generation systems (Zheng et al., 1986; Wall et al., 1989; Jin et al.,
1996). Also, Ishida and Zheng (1986) had developed the Graphic Structured CHEMosynthesizER program (GSCHEMER) for calculating and plotting EUD. Now, the exergy
analysis could be linked to ASPEN Plus simulator (Hinderink et al., 1996; Harvey and
Kane, 1996; Bram and De Ruyck, 1996). However, these analyses could only calculate
the quantity of exergy loss in equipment or subsystem by doing the exergy balance over
that equipment or subsystem. The grapical presentation of EUD using ASPEN Plus
simulator is never mentioned in the previous research works.
This research work is extended from the previous research on constructing
EUD by using the Fortran block and external Fortran file in ASPEN Plus simulator. The
benefit of the linking between the EUD routine and the simulator is to reduce the
calculation step of the program because the EUD routine can simultaneously work with
the stream properties and the simulation results.
ENERGY-UTILIZATION DIAGRAM
The definition of exergy is the work that is available in the material stream as a
result of the non-equilibrium conditions relative to the reference condition. Normally, the
4
sea level and atmospheric condition are used as the reference condition (at 25oC). Then
the exergy loss is denoted by  and defined by the following equation.
 = H – T0 S
(1)
When the summation of  in the system is considered, then
 
j

 ( H
j
j
 T0 S j )
j
 T0  S j
j

 H
j
Since
 H
j
j
in the system is zero by the energy conservation law, then
j
 
j
j
  T0  S j
0
(2)
j
In order to determine the level of energy, a new intensive parameter, called
availability factor or energy level (A), was introduced. This parameter is used as an
indicator of the potential of the energy donated and accepted by the processes, where:
A =  / H
(3)
When substitute Equation (1) into Equation (3), the energy level can be defined
in the following formula.
5
A = 1 – (T0 S / H)
(4)
It describes the content of exergy on a certain quantity of energy; in other
words, the exergy content is the maximum fraction of energy which can be converted to
useful work. Basically, the energy transferred between the processes in a system. The
process that releases energy is called "energy donor (ed)", whereas the energy receiving
process is called "energy acceptor (ea)".
The exergy loss in the system is denoted by EXL which is equal to “    j ”.
Hence, for the general system,
EXL     j   H ea ( Aed  Aea )  0
H ea (in positive sign )  H ed
Where
(5)
(6)
When Hea become smaller, Equation (5) can be expressed
EXL     j 
H ea
 (A
ed
 Aea ) dH ea
(7)
0
Consequently, by plotting the energy level of energy donating process (A ed) and
the energy accepting process (Aea) against the transformed energy (dHea), the amount of
exergy loss in the system can be obtained as the area between the curves A ea and Aed.
The energy level difference between Aed and Aea (Aed-Aea) indicates the driving force for
the energy transformation.
(EUD).
This diagram is called the Energy-Utilization Diagram
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Heat exchanger subsystem (Zheng et al., 1986)
For the heat exchanger subsystem, H is defined by Q, also S is Q/T. Then
Equation (4) yields:
A = 1 – T0/T
(8)
Therefore, from Equation (8), the energy level (A) ranges from –  to 1. The
unity is the maximum value of A at infinite temperature (very high temperature). A
becomes zero when its temperature is equal to the reference temperature (T = T0 = 298.15
K). When the temperature is close to zero, the energy level becomes minus infinity. The
energy balances between energy donor and energy acceptor must be considered for
calculating the temperature at any change in Hea. Hence, the energy level of both energy
donor and energy acceptor could be calculated by Equation (8).
Power subsystem (Ishida and Kawamura, 1982)
In power subsystem, in which H is equal to W whereas S = 0. Therefore,
Equation (4) becomes:
A = (H – T0 S) / H = 1
(9)
It means that the energy level of work source (for compressor) and work sink
(for turbine) are always equal to one.
However, the energy level of acceptor
(compressor) and donor (turbine) can be calculated by using Equations (10) and (11),
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then replacing them in Equation (4) to get the equation used to calculate the energy level
in both compressor and turbine.
H  nC p (Tout  Tin )
 T
S  n ln  out
 Tin



Cp
 Pout

 Pin
(10)



R



(11)
Isentropic compressor/turbine
The isentropic efficiency of compressor is defined by Equation (12), whereas
Equation (13) shows the definition of isentropic efficiency of turbine (Avallone and
Baumeister III, 1997).
c 
isentropic work h s out  hin

actual work
hout  hin
(12)
t 
h  hin
actual work
 out
isentropic work h s out  hin
(13)
Also, the isentropic efficiency can be expressed in terms of inlet-outlet
pressure, temperature and the ratio of Cp and Cv (or k) as shown in Equation (14).
c 
1
t
 Tin
( Pout / Pin )( k 1) / k 1
Tout  Tin
(14)
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The enthalpy change in the power system can be calculated from the energy
balance equation and it also equals to the work in power subsystem as expressed in
Equation (15).
H  W  nc p (Tout  Tin )
(15)
The required work (for compressor) or generated work (for turbine) can be
calculated in terms of inlet-outlet pressure as shown in Equation (16) (Ishida and
Kawamura, 1982).
 P ( k 1) / k 
k
 out 
W  nPinVin
1
c (1  k )  Pin 



( k 1) / k

t k  Pout 


 nPinVin
1
(1  k )  Pin 



(16)
Polytropic compressor
Polytropic compressor still uses energy balance equation (Equation (15)).
However, the polytropic efficiency (p) is defined by Equation (17) (Avallone and
Baumeister III, 1997).
k 1
ln( Pout / Pin )
p  k
ln( Tout / Tin )
(17)
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In the polytropic process, the polytropic coefficient (m) is expressed by
Equation (18).
PVm = constant
(18)
The polytropic coefficient (m) can be defined in terms of Cp/Cv ratio and
polytropic efficiency (p) as in Equation (19).
m 1 k 1 1

m
k p
(19)
The required work for polytropic compressor is given by Equation (20) (Ishida
and Kawamura, 1982).
 P  ( m 1) / m 
 m  1
W 
nPinVin  out 
 1

 Pin 

1  m   p
(20)
Pump
The work required by pump in any flowsheet is very low compared to the work
generated by turbine or the compressor work. In addition, the enthalpy, entropy and
temperature change slightly after the pump operation. Hence, it could be assumed that
the temperature increases linearly with pump. Calculation of the energy level of energy
acceptor at any intermediate points is not required. The energy level calculation was
required only at the inlet and outlet stream.
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RANKINE CYCLE
The Rankine cycle is selected as an example for testing the routines by
applying them in the ASPEN Plus simulation program. This cycle consists of two heat
exchangers, one turbine and one pump as shown in Figure 1.
The Rankine cycle is the cycle that is used to produce the electric power. This
power can be generated when the high pressure steam reduces its pressure to a lower
pressure. For this example, the high pressure steam at 2000 kPa and 773.15 K (stream 2)
is fed into turbine to reduce the pressure to 100 kPa. At the outlet condition (stream 3),
the enthalpy of steam is reducing from the inlet condition. The difference of inlet
enthalpy and outlet enthalpy is transformed to the outlet power from the turbine. The
outlet steam is then passed to condenser. The steam is condensed in this heat exchanger
to become saturated liquid after leaving at the outlet (stream 4). The cooling water
(streams 7 and 8) is used in condenser as cooling media. The increase of cooling water
temperature is limited to 10 K, i.e. from 303.15 K to 313.15 K. The condensed liquid
from condenser is then raised to a pressure of 2000 kPa before being fed to the steam
boiler (stream 1). In the boiler, the high pressure liquid changes its phase to become high
pressure steam (superheated steam). The outlet condition of stream 2 is returned back to
be at 2000 kPa and 773.15 K. The exhaust gas (streams 5 and 6) that consists of plenty of
nitrogen is fed into hot side of boiler to release heat to the cold side. The exhaust gas
temperature is decreased from 1273.15 K to 444.25 K.
Figure 1
Rankine cycle
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ENERGY-UTILIZATION DIAGRAM OF RANKINE CYCLE
Heat exchanger subsystem
There are two heat exchangers in Rankine cycle, the boiler and the
condenser.Thus, the EUD can be divided into two sections as shown in Figure 2. In the
boiler section, the hot gas is the energy donor. Its temperature reduced from 1273.15 K
(Aed = 1 – (298.15 / 1273.15) = 0.76582) to 423.95 K (Aed = 1 – (298.15 / 423.95) =
0.29674). The water in the cycle plays the role of energy acceptor. The boiler feed water
changed its phase from liquid at 374.99 K (Aea = 1 – (298.15 / 374.99) = 0.20492) to
become the steam at 773.15 K (Aea = 1- (298.15 / 773.15) = 0.61437). At the middle
points in energy acceptor line, the temperature and energy level were constant at 485.59
K and 0.386, respectively.
Figure 2
EUD of heat exchanger subsystem in Rankine cycle
In the condenser section, the exhaust steam is the energy donor. Its phase has
changed from steam at 493.31 K (Aed = 1- (298.15 / 493.31) = 0.39561) to become
saturated liquid (water) at the hot side outlet (at 374.69 K, Aed = 1 – (298.15 / 374.69) =
0.20427). The cooling water is the energy acceptor in the condenser because of change in
its temperature from 303.15 K (Aea = 1 – (298.15 / 303.15) = 0.01649) to 313.05 K (Aea =
1 – (298.15 / 313.05) = 0.0476). In this section, the phase change occurred only on
energy donor side (Exhaust steam from turbine).
The shaded area of this figure represents the overall exergy loss in heat
exchanger subsystem. The exergy loss was calculated to be 29.274 MW. The exergy
loss in boiler and condenser were equal to 17.513 MW and 11.761 MW, respectively.
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Power subsystem
The power subsystem considered were turbine and pump, which exist in the
Rankine cycle. This subsystem did not need sorting as required in the heat exchanger
subsystem. But the user must separate the generated and consumed work for calculating
the net generated (or consumed) work in cycle. It was separated into two equipment, i.e.
turbine and pump. The generated work from turbine was 13.8 MW but the consumed
work by pump was 0.0746 MW. Thus, the net generated work, which could be calculated
by subtracting pump work from turbine work, was 13.748 MW.
Figure 3 could be plotted for showing the power subsystem EUD for Rankine
cycle by using data from simulation.
Figure 3
EUD of power subsystem in Rankine cycle
The X-axis value illustrates the value of consumed work by pump, generated
work from turbine and the net generated work. The consumed pump work was very low
relative to the generated power from turbine. The pump work was approximately only
0.5% of the turbine work. Table 1 shows the summary of the net generated power and
the overall exergy loss in Rankine cycle.
Table 1 Summary of net generated power and exergy loss in Rankine cycle
It was observed that the main exergy loss existed in the heat exchanger
subsystem (about 90.86%). Only 9.14% of total exergy loss was in power subsystem.
The exergy loss in boiler accounted for 54.35% of the total exergy loss and was the major
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part of exergy loss in system. On the other hand, the exergy loss in pump could be
considered negligible since it was relatively low compared to the total exergy loss (only
0.18%).
SENSITIVITY ANALYSIS OF RANKINE CYCLE
Scopes of the study
Constraints
-
Constant water circulation rate in cycle = 100 tons/hr
-
Constant temperature difference of cooling water in condenser from 303.15 K to
313.05 K
-
Constant temperature difference of hot gas in boiler from 1273.15 K to 423.95 K
Variables to be adjusted
-
Pressure discharge of pump,
-
Pressure discharge of turbine,
-
Outlet temperature of boiler,
-
Subcooled temperature of condenser.
There are some awareness during the simulation stage regarding the input of
improper operating conditions.
-
Liquid phase exists either at outlet conditions or at some intermediate conditions
(Turbine)
-
Cold stream is hotter than hot stream (Boiler and condenser)
-
Feed not all liquid, outlet conditions may be wrong (Pump)
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Results and discussion
In order to compare the exergy loss in each case, a new variable was introduced
to perform sensitivity analysis. Since the net generated power (NGP) were not equal in
each case, the ratio of exergy loss divided by net generated power (EXL/NGP) was a new
variable to study the increase or decrease of exergy loss in system. The results of
sensitivity analysis of operating conditions change show in Table 2.
Table 2 Summary of sensitivity analysis results
Effect of pump discharge pressure
The increase of pump discharge led to the NGP increasing by 1.70% and the
total exergy loss reducing by 0.91%. The main reduction of exergy loss occurred in the
heat exchanger subsystem. The explanation is that the increased pressure raises the
boiling point of water in cycle close to that of the hot gas. Thus, the area between energy
donor and energy acceptor gets closer. In addition, while the different pressure across
turbine increases, the outlet exhaust steam temperature from turbine decreases close to
the cooling water temperature. Hence, the area between cooling water and exhaust
steam/condensate reduced. In contrast, the exergy loss in power subsystem increased
because the pump required additional work for building up the increased pressure. The
higher the pressure difference, the higher the turbine generated work.
In the consideration of EXL/NGP ratio, the increase of pump discharge
pressure led to the decrease of total EXL/NGP ratio by 2.57%. It meant that the increase
of pump pressure has the potential to improve the Rankine cycle efficiency.
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Effect of turbine discharge pressure
The decrease of turbine discharge pressure led the NGP increasing by 2.41%
and the total exergy loss reducing by 0.55%. The main reduction of exergy loss occurred
in the heat exchanger. When the turbine pressure was reduced, the temperature outlet
from turbine was reduced. Then, the temperature difference between exhaust steam and
cooling water was reduced to decrease the exergy loss in the condenser by 3.44%. But
the temperature difference in boiler between boiler feed water and hot gas was then
increased much more than the base case. The boiler must input more heat duty from
energy donor to energy acceptor. Thus, the exergy loss in boiler had increased by 0.75%.
However, after calculation, the overall exergy loss in heat exchanger subsystem was
reduced by 0.93%, whereas the exergy loss in power subsystem was increased 3.24%
because both pump and turbine had a large pressure difference between the outlet and
inlet. Finally, the total EXL/NGP ratio tended to decrease by 2.89% when the turbine
discharge pressure decreased from 100 kPa to 90 kPa. In order to reduce the exergy loss
in the Rankine cycle, the turbine discharge pressure should be decreased.
Effect of boiler outlet temperature
The increase of boiler outlet temperature increased the NGP by 10.97% and the
total exergy loss increased 2.83%. The exergy loss in condenser was greatly increased
from base case. When the temperature outlet from boiler increased, the temperature of
exhaust steam from turbine increased too. Thus, the condenser had to remove more heat
duty from hot side at the same operating pressure. Two units that had the exergy loss
reduction were boiler and turbine. Because the temperature difference between hot gas
and steam in boiler was reduced, the area of exergy loss decreased. If the turbine
operated at higher inlet temperature, the gap between energy donor line and energy
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acceptor line was reduced. The overall exergy loss in the Rankine cycle increased by
2.83%. However, if the EXL/NGP was considered, this ratio was decreased by 7.33% for
the case of boiler outlet temperature increase. In order to improve the cycle, the boiler
outlet temperature is recommended to be increased.
Effect of subcooled temperature in condenser
The increase of subcooled temperature of water in condenser did not give any
exergy loss reduction.
Most of exergy losses were increased after the subcooled
temperature increased. The major change of exergy loss occurred in boiler by increasing
11.85%, whereas the change of exergy loss was about 4.30%. Both heat exchangers were
affected by the increase of subcooled temperature. The temperature difference in boiler
increased between energy donor and energy acceptor. Then the heat duty in boiler
increased. Also, in condenser, the heat duty must increase for cooling the condensate
below the boiling point. The ratio of EXL/NGP was finally increased by 8.00%. Thus,
the increase of subcooled temperature led to the increase of exergy loss. It was not
recommended for the Rankine cycle improvement.
The decrease of EXL/NGP ratio was affected by pump outlet pressure increase,
the turbine outlet pressure decrease and the increase of boiler temperature. Thus, this
conclusion will be used in the next topic for applying into improvement case.
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Improvement case
As mentioned in previous sections, the change of operating condition was used
to check how much exergy loss could be reduced without any modification on the
flowsheet. New operating conditions are listed as below.
-
Increase pump discharge pressure from 2000 kPa to 2175 kPa
-
Decrease turbine discharge pressure from 100 kPa to 90 kPa
-
Increase boiler outlet temperature from 773.15 K to 848.15 K
Table 3 shows the exergy loss of the improvement case.
Table 3 Exergy loss of improvement case compared to base case
All of EXL/NGP ratios reduced after changing the operating conditions. The
main reduction of exergy loss occurred in the heat exchanger subsystem. Boiler could
reduce the exergy loss by 15.17%, while 9.67% was reduced in condenser. Also, the
exergy loss of power subsystem reduced by 9.27% and 4.57% for turbine and pump,
respectively. The overall exergy loss reduction for improvement case was achieved by
reducing EXL/NGP ratio by 12.61%. Thus, the change of operating condition could
reduce the exergy loss by 12.61% without any flowsheet modification.
KALINA CYCLE
In order to improve the power cycle efficiently, the modification of the process
is required. In this case study, the study of the Kalina cycle was performed. The Kalina
cycle was introduced into the engineering society by Kalina (1984). The Kalina cycle
18
uses an ammonia-water mixture as the working liquid in the cycle. The boiling point of
the mixture in boiler is variable temperatures unlike the pure water as in the Rankine
cycle. The variable temperature boiling can maintain temperature closer to that of the hot
gas in the boiler. Thus, the exergy loss could reduce in the Kalina cycle.
Figure 4 shows the Kalina cycle (Wall, 1989). Streams 1 and 2 represent the
hot gas fed to the boiler as the heating media. The ammonia-water vapor (3) from boiler
is then expanded in the turbine to generate the power (4). The turbine exhaust gas (5) is
cooled (6, 7, 8), diluted with the ammonia-poor liquid (9, 10) and condensed (11) in the
absorber by cooling water (12, 13). The saturated liquid leaving the absorber is pumped
(14) to an intermediate pressure and heated (15, 16, 17, 18) in reheater1, reheater2 and
distiller, respectively. The saturated mixture is separated into an ammonia-poor liquid
(19) which is cooled two times (20, 21) and depressurized in a throttle. Whereas an
ammonia-rich vapor (22) is cooled (23) and some of the original condensate (24) is added
to the nearly pure ammonia vapor to obtain an ammonia concentration of about 70% in
the working fluid (25). The mixture is then cooled (26) and condensed (27) by cooling
water (28, 19). The condensate of working fluid is then compressed (30) again, and
reheated in feedwater heater before sending to the boiler (31).
Figure 4
Kalina cycle
ENERGY-UTILIZATION DIAGRAM OF KALINA CYCLE
Figure 5 shows the overall Energy-Utilization Diagram (EUD) of the Kalina
cycle described above. This diagram could separated into many equipment existed in the
process as the note. As observed, the exergy loss represented by the area between the
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energy donor and energy acceptor lines was a smaller area than the exergy loss in the
EUD of Rankine cycle.
In the boiler section, the energy level of energy acceptor
(working mixture fluid) declined its boiling temperature in the middle point of the line.
At this range, the boiling temperature of ammonia-water mixture varied along the energy
transferring in the boiler. The reduction of exergy loss should be improved by changing
the working fluid to become mixture. Comparing EUD in Figure 5 with EUD plot by
Wall et al., 1989, the feature of the curve was observed to be the same together.
However, some of energy transferring in turbine and heat exchanger might be different
because of the Thermodynamics option set was selected in the different set between of
these two works. Also, the operating conditions in this cycle that was simulated by
ASPEN Plus had differed from the work of Wall et al., 1989, the energy level in heat
exchangers was then also slightly different. Table 4 shows the summary of net generated
power and exergy loss in the Kalina cycle.
Table 4 Summary of net generated power and exergy loss in Kalina cycle
From above table, the net generated power in the Kalina cycle could account to
168.32 KW. The exergy loss in heat exchanger subsystem was the major part (about
79%), of total exergy loss. The exergy loss in turbine was increased from the original
Rankine cycle from 9% to 21%. Main exergy loss in cycle was in the boiler about 64%
of total exergy loss. The exergy loss in other heat exchangers was minor sections in this
study. This table also presents that the ratio of exergy loss and net generated power
(EXL/NGP) was much more improvement for the power cycle study. The EXL/NGP
ratio was reduced from 2.04805 in the Rankine cycle improvement case to be 1.06036 in
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the Kalina cycle case. This was a big improvement of the efficiency of power cycle
system.
CONCLUSIONS
1. The concept of exergy analysis and Energy-Utilization diagram (EUD) was used as a
tool for improving and developing the combination process of heat exchanger and
power subsytems. The EUD could be graphically represented for exergy analysis by
showing the amount of heat transferred or generated (or consumed) work on X-axis,
while Y-axis shows the energy level in terms of energy donor and energy acceptor.
The area between the energy level of donor and acceptor indicates the value of exergy
loss in the system. In order to construct the EUD by ASPEN Plus simulator, the EUD
routine was programmed in Fortran block and external Fortran file.
2. The constructed routines were applied to the Rankine cycle. The simulation found
that the main exergy loss existed in the heat exchanger subsystem (about 90% of total
exergy loss), whereas the exergy loss in pump was negligible since its value was
approximately 0.2% of the total exergy loss.
3. Sensitivity analysis of Rankine cycle demonstrated that the total exergy loss per net
generated power ratio (EXL/NGP) tended to decrease when the pump discharge
pressure increased, the turbine discharge pressure decreased or the steam temperature
increased. But the increase in subcooled temperature in condenser led to the increase
in total exergy loss per net generated power increase. This analysis could be used as a
guideline or suggestion for improving the Rankine cycle efficiency or related power
generation cycle. In the improvement case, the ratio of total exergy loss per net
21
generated power could be reduced by 12.61% by adjusting the operating condition
without any flowsheet modification.
4. The modification of flowsheet from the Rankine cycle to the Kalina could reduce the
ratio of EXL/NGP from 2.04805 in the Rankine cycle improvement case to be
1.06036 in Kalina case study. It meant that the modification of flowsheet and the
working fluid change could decrease the exergy loss in the system.
RECOMMENDATIONS
1. This study should extend to perform the sensitivity analysis on the Kalina cycle in
order to find the optimum operating condition for reducing the exergy loss in the
system.
2. From the economic evaluation point of view, the sensitivity analysis should consider
the cost saving of exergy loss reduction (by calculating the operating cost of cooling
water and hot gas and the generated power cost) compared to the increasing cost of
equipment for any case in the sensitivity analysis.
3. The research should be extended to other subsystems to cover all unit operations used
in a real plant. The investigation on the reaction subsystem and distillation column
are suggested for further study.
ACKNOWLEDGEMENTS
The authors would like to express their thanks to all of these professors, Dr.
Goran Wall (Chalmers University of Technology and University of Goteborg, Sweden)
22
and Dr. Yehia M. El-Sayed (Advanced Energy System Analysis, USA), for their warm
consideration and all document and data support in this research.
NOMENCLATURE
A
=
Availability factor or Energy level [dimensionless]
AA
=
Energy level of energy acceptor [dimensionless]
AD
=
Energy level of energy donor [dimensionless]
Cm
=
Mean heat capacity [J/kg-K]
Cp
=
Constant pressure heat capacity [J/kg-K]
Cv
=
Constant volume heat capacity [J/kg-K]
EXL
=
Exergy loss [J/s]
G
=
Gibb’s free energy [J/s]
H
=
Enthalpy [J/s]
h
=
Mass enthalpy [J/kg]
k
=
Ratio of Cp and Cv [dimensionless]
m
=
Polytropic coefficient [dimensionless]
NGP
=
Net generated power [J/s]
n
=
Number of moles [mole]
P
=
Pressure [N/m2]
Q
=
Heat duty [J/s]
R
=
Gas law constant [8314.33 J/kgmol-K]
S
=
Entropy [J/s-K]
s
=
Mass entropy [J/kg-K]
T
=
Temperature [K]
23
V
=
Volume of gas [m3]
W
=
Work [J/s]
Subscript
0
=
Reference condition (at 298.15 K)
c
=
Isentropic compressor
ea
=
Energy acceptor
ed
=
Energy donor
i
=
Integer numbers (1, 2, 3, …)
in
=
Input
j
=
Integer numbers (1, 2, 3, …)
out
=
Output
p
=
Polytropic compressor
t
=
Isentropic turbine
Superscript
s
=
Isentropic operation
Greek letters

=
Exergy change [J/s]

=
Efficiency
24
REFERENCES
1. Avallone, E.A. and Baumeister III, T., 1997, Marks’ Standard Handbook for
Mechanical Engineers, 10th ed., New York, McGraw-Hill, pp. (14-27) – (14-30).
2. Bram, S. and De Ruyck, J., 1996, “Exergy Analysis Tools for Aspen Applied to
Evaporative Cycle Design,” Proceedings of Efficiency, Costs, Optimization,
Simulation and Environmental Aspects of Energy Systems 1996 (ECOS’96), pp.
217-224.
3. Harvey, S. and Kane, N.D., 1996, “Analysis of a Reheat Gas Turbine Cycle with
Chemical
Recuperation Using Aspen,”
Proceedings
of
Efficiency, Costs,
Optimization, Simulation and Environmental Aspects of Energy Systems 1996
(ECOS’96), pp. 297-304.
4. Hinderink, A.P., Kerkhof, F.P.J.M., Lie, A.B.K., De Swaan Arons, J. and Van Der
Kooi, H.J., 1996, “Exergy Analysis with a Flowsheeting Simulator- Part I and II,”
Chemical Engineering Science, Vol. 51, No. 20, pp. 4693-4700.
5. Ishida, M. and Kawamura, K., 1982, “Energy and Exergy Analysis of a Chemical
Process System with Distributed Parameters Based on the Enthalpy-Direction Factor
Diagram,” Industrial & Engineering Chemistry Design and Development, Vol. 21,
pp. 690-695.
6. Ishida, M. and Zheng, D., 1986, “Graphic Exergy Analysis of Chemical Process
Systems by a Graphic Simulator, GSCHEMER,” Computers & Chemical
Engineering, Vol. 10, No. 6, pp. 525-532.
7. Ishida, M., 1981, “A Small But Powerful Language (in Japanese),” TIT Interface,
Vol. 170, No. 51, p. 190.
25
8. Jin, H., Ishida, M., Kobayashi, M. and Nunokawa, M., 1996, “Exergy Evaluation of
Two Current Advanced Power Plants: Supercritical Steam Turbine and Combined
Cycle,” AES-Vol. 36, Proceedings of the ASME Advanced Energy Systems
Division, pp. 493-500.
9. Kalina, A.L., 1984, “Combined Cycle System with Novel Bottoming Cycle,” ASME
Journal of Engineering for Power, Vol. 106, No. 4, pp. 737-742.
10. Wall, G., Chuang, C.C. and Ishida, M., 1989, “Exergy Study of the Kalina Cycle,”
Analysis and Design of Energy Systems: Analysis of Industrial Processes, AESVol. 10-3, pp. 73-77.
11. Zheng, D., Uchiyama, Y. and Ishida, M., 1986, “Energy-Utilization Diagram for Two
Types of LNG Power-Generation Systems,” Energy, Vol. 11, No. 6, pp. 631-639.
26
List of Figures
Figure 1
Rankine cycle
Figure 2
EUD of heat exchanger subsystem in Rankine cycle
Figure 3
EUD of power subsystem in Rankine cycle
Figure 4
Kalina cycle
Figure 5
Overall EUD of Kalina cycle
List of Tables
Table 1
Summary of net generated power and exergy loss in Rankine cycle
Table 2
Summary of sensitivity analysis results
Table 3
Exergy loss of improvement case compared to base case
Table 4
Summary of net generated power and exergy loss in Kalina cycle
27
Energy Level, A
Figure 1
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.00E+00
Rankine cycle
A-DONOR
A-ACCEPT OR
5.00E+07
1.00E+08
Heat Duty (W)
Figure 2
EUD of heat exchanger subsystem in Rankine cycle
1.50E+08
28
1.40
Energy Level, A
1.20
1.00
0.80
AD (T urbine)
AA (T urbine)
AD (Pump)
AA (Pump)
0.60
0.40
0.20
0.00
0.00E+00
5.00E+06
1.00E+07
Work (W)
Figure 3
EUD of power subsystem in Rankine cycle
Figure 4
Kalina cycle
1.50E+07
29
Table 1 Summary of net generated power and exergy loss in Rankine cycle
Net generated power (MW)
Location
13.748
Exergy loss (MW)
% of total exergy loss
Total exergy loss
32.220
100.00%
-
Heat exchanger subsystem
29.274
90.86 %
-
Boiler
17.513
54.35 %
-
Condenser
11.761
36.51 %
-
Power subsystem
2.9455
9.14 %
-
Turbine
2.8862
8.96 %
-
Pump
0.05934
0.18 %
30
1.1
A-DONOR
A-ACCEPTOR
Turbine
Energy Level, A
0.9
0.7
Boiler
0.5
Reheater1
Absorber
Distiller
Reheater2
Condenser
0.3
Feedwater
Heater
0.1
-0.1
0.00E+00
5.00E+05
Figure 5
 H(W)
1.00E+06
Overall EUD of Kalina cycle
1.50E+06
31
Table 2
Summary of sensitivity analysis results
Base case
Increase Ppump
Decrease Pturbine
Increase Tboiler
Increase Tsubcooled
Ppump = 2000 kPa
Changed item
Pturbine = 100 kPa
Ppump =
Pturbine =
Tboiler =
Tsubcooled =
Tboiler = 773.15 K
2175 kPa
%change
90 kPa
%change
848.15 K
%change
40 K
%change
13.748
13.982
1.70%
14.079
2.41%
15.256
10.97%
13.751
0.02%
Tsubcooled = 0 K
NGP (MW)
EXL (MW)
-
Boiler
17.513
17.205
-1.76%
17.645
0.75%
17.317
-1.12%
19.588
11.85%
-
Condenser
-
Turbine
11.761
11.683
-0.66%
11.357
-3.44%
12.907
9.74%
12.267
4.30%
-
Pump
2.8862
2.9734
3.02%
2.9811
3.29%
2.8493
-1.28%
2.8862
0.00%
-
HX subs.
0.05934
0.06480
9.21%
0.05994
1.01%
0.05934
0.00%
0.06395
7.77%
-
Power subs.
-
Total
29.274
4
-1.32%
1
-0.93%
30.224
3.24%
2
8.81%
2.9455
28.889
3.15%
29.002
3.24%
2.9086
-1.25%
31.855
0.16%
32.220
3.0383
-0.91%
3.0411
-0.55%
33.133
2.83%
2.9502
8.02%
31.927
32.043
34.805
EXL/NGP
-
Boiler
1.27386
1.23053 -3.40% 1.25328 -1.62% 1.13507
-
Condenser
-
Turbine
0.85547
0.83561 -2.32% 0.80665 -5.71% 0.84604 10.90% 0.89209
-
1.42447 11.82%
4.28%
32
-
Pump
0.20993
0.21266
1.30%
0.21175
-
HX subs.
-
Power subs.
0.00432
0.00463
7.38%
0.00426 -1.36% 0.00389
0.00465
7.75%
-
Total
2.12933
2.06614 -2.97% 2.05993 -3.26% 1.98111 11.04% 2.31656
8.79%
0.21425
0.21730
0.19065 -9.88% 0.21454
0.14%
2.34358
2.28343 -2.57% 2.27594 -2.89% 2.17176 -6.96% 2.53110
8.00%
1.42%
0.21600
0.86%
0.82%
0.18676 -1.10% 0.20989 -0.02%
-
11.01%
-7.33%
33
Table 3 Exergy loss of improvement case compared to base case
Base case
Changed item
NGP (MW)
Improvement case
Ppump = 2000 kPa
Ppump = 2175 kPa
Pturbine = 100 kPa
Pturbine = 90 kPa
Tboiler = 773.15 K
Tboiler = 848.15 K
13.748
15.886
15.55%
%change
EXL (MW)
-
Boiler
17.513
17.167
-1.98%
-
Condenser
11.761
12.276
4.38%
-
Turbine
-
Pump
2.8862
3.0259
4.84%
-
HX subs.
0.05934
0.06543
10.26%
-
Power subs.
29.274
29.443
0.58%
-
Total
2.9455
3.0913
4.95%
32.220
32.535
0.98%
EXL/NGP
-
Boiler
1.27386
1.08067
-
-
Condenser
0.85547
0.77278
15.17%
-
Turbine
-
Pump
0.20993
0.19048
-9.67%
-
HX subs.
0.00432
0.00412
-9.27%
-
Power subs.
2.12933
1.85345
-4.57%
-
Total
0.21425
0.19460
-
2.34358
2.04805
12.96%
-9.17%
12.61%
34
Table 4 Summary of net generated power and exergy loss in Kalina cycle
Net generated power (KW)
Location
168.32
Exergy loss
% of total
(KW)
EXL/NGP
exergy loss
Total
178.482
1.06036
100.00%
-
Heat exchanger subsystem
141.493
0.84061
79.28%
-
Boiler
114.381
0.67954
64.09%
-
Distiller
6.569
0.03903
3.68%
-
Reheater1
3.485
0.02070
1.95%
-
Reheater2
5.484
0.03258
3.07%
-
Absorber
2.958
0.01757
1.66%
-
Condenser
6.680
0.03969
3.74%
-
Feedwater heater
1.936
0.01150
1.08%
-
Turbine
36.989
0.21975
20.72%
35
APPENDICES
APPENDIX A.: Steps of calculation for heat exchanger subsystem
Read outlet stream of both hot and cold stream
Read calculated transferred heat duty and pressure
drop in hot and cold side
Specify number of sections and divide the duty and
pressure drops in each section.
Duplicate outlet hot and cold streams
Go to other heat
exchangers
Do loop for i = 1 to n+1
Calculate pressure at the
inlet of each section
Supply divided heat duty into hot stream
Call FLASH subroutine
Get inlet temperature of hot stream in each section
Draw divided heat duty from cold stream
Call FLASH subroutine
Get inlet temperature of cold stream in each section
Calculate energy level of energy
donor and energy acceptor
Export data for sorting and plotting in MS Excel
Calculate exergy loss
36
APPENDIX B.: Steps of calculation for isentropic compressor or turbine
Read inlet and outlet stream
Read calculated work and isentropic efficiency
Calculate value of C p/C v ratio and C p
Go to other
compressors/turbines
Specify number of sections and divide the different
pressure in each section.
Do loop for i = 1 to n+1
Calculate required or generated
work in each section
Calculate the outlet temperature in each section
Calculate entropy change in each section
Compressor: Calculate energy level of energy acceptor
Set energy level of energy donor to be 1
Turbine: Calculate energy level of energy donor
Set energy level of energy acceptor to be 1
Plot EUD by MS Excel
Calculate exergy loss
37
APPENDIX C.: Steps of calculation for polytropic compressor
Read inlet and outlet stream
Read calculated work and polytropic efficiency
Calculate value of C p/C v ratio, C p and m
Specify number of sections and divide the different
pressure in each section.
Go to other
compressors
Do loop for i = 1 to n+1
Calculate required work in each
section
Calculate the outlet temperature in each section
Calculate entropy change in each section
Compressor: Calculate energy level of energy acceptor
Set energy level of energy donor to be 1
Plot EUD by MS Excel
Calculate exergy loss
38
APPENDIX D.: Steps of calculation for pump
Go to other pumps
Read inlet and outlet stream
Read calculated work
Pump: Calculate energy level of energy acceptor
Set energy level of energy donor to be 1
Plot EUD by MS Excel
Calculate exergy loss