This document analyzes a triple cycle power plant using methane as fuel based on the second law of thermodynamics. An ideal Brayton cycle is used as the topping cycle. The bottoming cycles are a steam Rankine cycle and an ammonia organic Rankine cycle. The parallel arrangement of the bottoming cycles is selected for analysis due to its improved performance over the series arrangement. Effects of the gas cycle pressure ratio and maximum temperature on the triple cycle's performance and exergetic losses are discussed.

1. Jurnal Ilmiah Teknik Mesin Vol. 4 No.1. April 2010 (1-6)
Second Law Of Thermodynamics Analysis
Of Triple Cycle Power Plant
Matheus M. Dwinanto
Departement of Mechanical Engineering, Faculty of Science and Engineering
University of Nusa Cendana, Kupang
email : m2_dwinanto@yahoo.com
___________________________________________________________________________
Abstract
Triple cycle power plant with methane as a fuel has been analyzed on the basis of second law of thermodynamics.
In this model, ideal Brayton cycle is selected as a topping cycle as it gives higher efficiency at lower pressure ratio compared
intercooler and reheat cycle. In trilple cycle the bottoming cycles are steam Rankine and organic Rankine cycle. Ammonia
has suitable working properties like critical temperature, boiling temperature, etc. Steam cycle consists of a deaerator and
reheater. The bottoming ammonia cycle is a ideal Rankine cycle. Single pressure heat recovery steam and ammonia
generators are selected for simplification of the analysis. The effects of pressure ratio and maximum temperature which are
taken as important parameters regarding the triple cycle are discussed on performance and exergetic losses. On the other
hand, the efficiency of the triple cycle can be raised, especially in the application of recovering low enthalpy content waste
heat. Therefore, by properly combining with a steam Rankine cycle, the ammonia Rankine cycle is expected to efficiently
utilize residual yet available energy to an optimal extent. The arrangement of multiple cycles is compared with combined
cycle having the same sink conditions. The parallel type of arrangement of bottoming cycle is selected due to increased
performance.
Key words : Multiple cycles, triple cycle, exergetic loss, organic Rankine cycle
Abstraksi
Pembangkit daya siklus gabung tiga dengan metana sebagai bahan bakar dianalisa berdasarkan hukum kedua
termodinamika. Dalam model ini, siklus Brayton ideal dipilih sebagai siklus puncak yang memberikan efisiensi yang
tertinggi pada perbandingan tekanan yang rendah dibandingkan siklus yang menggunakan pendingin antara dan pemanas
ulang. Dalam siklus gabung tiga, siklus bagian bawah adalah siklus Rankine dan siklus Rankine organik. Amoniak
mempunyai sifat-sifat kerja yang sesuai seperti temperatur kritis, temperatur didih, dll. Siklus uap terdiri dari deaerator dan
pemanas ulang. Siklus amoniak bagian bawah adalah siklus Rankine ideal. Tekanan uap pemanas ulang dan pembangkit
amoniak dipilih untuk penyederhanaan analisa. Pengaruh perbandingan tekanan dan temperatur maksimum yang mana
diambil sebagai parameter penting berkenaan dengan unjuk kerja dan kerugian dayaguna dari siklus gabung tiga yang
dibahas. Disisi lain, efisiensi siklus gabung tiga dapat dinaikkan terutama dalam penerapan pada recovering entalpi rendah
kandungan pembuangan kalor. Oleh karena itu, semestinya penggabungan dengan sebuah siklus uap Rankine, siklus
Rankine amoniak adalah diharapkan untuk efisiensi memanfaatkan gas sisa yang masih memiliki energi untuk sebuah
tingkat optimal. Susunan siklus bertingkat dibandingkan dengan siklus gabungan mempunyai kesamaan kondisi. Susunan
paralel pada bagian bawah siklus dipilih untuk meningkatkan unjuk kerja.
Kata kunci : Siklus bertingkat, siklus gabung tiga, kerugian dayaguna, siklus Rankine organik
____________________________________________________________________________________________________
1. INTRODUCTION turbine. Small amount of work is obtained from this
The efficiency of the power plant may be turbine but the overall efficiency increases around
improved to around 48% by employing a combined 2% in addition to the combined cycle efficiency.
cycle. Still some heat is rejected to the surroundings Nag [2001] presented the detailed analysis
through the exchaust and condenser. If this heat is of steam cycle and combined cycle power generation.
utilized the efficiency of the plant can futher be Turns [2002] presented the combustion mechanism,
increased. For this a heat recovery ammonia reactions, gas table and equations as function of
generator is placed after the steam turbine. The temperature. These equations are curve fittings for
bottoming cycle is ammonia Rankine cycle. The heat various gases are used to determine the properties of
from the out let of the steam turbine (in series type) the gases. Hung [2002] proposed conceptual
or out let of exhaust (in parallel type) is utilized to arrangement to found a maximum output. El-Wakil
raise the temperature of ammonia in evaporator. In [1984] presented the detailed discussion regarding
the series type arrangement of triple cycle, the the combined cycle its advantages and applications.
rejection in steam cycle goes to heat input to the A detailed thermodynamic analysis of the combined
ammonia cycle. In the parallel type arrangement of power cycle without supplementary firing was given
triple cycle both steam cycle and steam cycle in Horlock [1992]. The chemical physical exergetic
recovers the heat from exhaust of gas turbine. These components are determined by the method given by
ammonia vapors are expanded in a low pressure Kotas [1984].
1

2. Matheus M. Dwinanto/Jurnal Ilmiah Teknik Mesin C Vol. 4 No.1. April 2010 (1-6)
The present work is aimed to study the
following objectives : to select the best optimized
multiple cycle arrangement, to estimate the overall
efficiency of the triple cycle based on the second law
of thermodynamics, and to study the effect of
pressure ratio, maximum temperature of gas cycle in
the performance and exergetic losses.
2. THERMODYNAMIC ANALYSIS OF THE
TRIPLE CYCLE
In this study it is found that the series-type
triple cycle exhibits no significant difference as
compared with the combined cycle. On the other
hand, the efficiency of the parallel type triple cycle
can be raised, especially in the applicationof
recovering low-enthalpy content waste heat.
Figure 2. T – S diagram of
Therefore, the parallel type cycle is selected for the
thermodynamic model of parallel type triple cycle
analysis.
The schematic diagram of triple cycle with
2.1 Assumptions Used in The Analysis
parallel arrangement of multiple cycles is shown in
The following assumption have been made
figure 1 and the corresponding temperature – entropy
during the analysis of the combined cycle :
in the figure 2. This work mainly deals with the
1. Atmospheric condition is taken as 25 oC and 1
detailed study and analysis of triple cycle based on
bar.
the second law of thermodynamics. The expanded
2. Gas cycle pressure ratio and maximum
gases are made to passthrough a single pressure heat
temperature is fixed at 15 and 1200 oC.
recovery steam generator and heat recovery ammonia
3. The inlet condition for high pressure steam
generator in case of parallel type. The remaining is
turbine is taken as 120 bar and 550 oC.
utilized to raise the temperature of the ammonia in
4. The condenser pressure is assumed to be 0,085
the ammonia Rankine cycle. Ammonia is having a
bar.
very low boiling point and easily vaporized by the
5. The temperature difference between condensed
low temperature hot fluid. The ammonia vapors after
steam, ammonia, and outlet cooling water is
expanding from the turbine are at a low temperature.
taken as 8.
6. Steam reheat pressure is taken as 25% of HRSG
pressure.
2.3 Thermodynamic Analysis
7. Isentropic efficiency of gas turbine is taken as
For chemical compounds, molar chemical
90%.
exergy can be calculated from the values of Gibbs
8. Isentropic efficiency of compressor steam and
functon of formation and the values of the chemical
ammonia turbine are taken as 85%.
exergy of the constituent chemical elements taken
9. Pressure drop in HRSG, HRAG, and condenser
from Kotas [1984]. Considering the reversible
is neglected.
reaction of formation of the compound, in which
10. Heat loss in HRSG, HRAG, turbines, condenser,
exergy is conserved, the standard molar chemical
and feed water heater (deaerator) are neglected.
exergy of the compound can be written as :
11. Pinch points in both steam and ammonia cycle is __ __
taken as 10.
0
= g0 + E 0 (1)
f el
__
2.2 Overview of The Termodynamic Model
where g 0 is the standard molar Gibbs function of
f
0
formation and E el is the standard chemical exergy
of constituent elements per mole of the chemical
compounds.
___
0
gf = − 50810 kJ/kgmol
CH (g)
4
Figure 1. Schematic diagram of components for The reaction of formation is,
parallel type cycle C + 2H 2 → CH 4 (2)
2

3. Matheus M. Dwinanto/Jurnal Ilmiah Teknik Mesin C Vol. 4 No.1. April 2010 (1-6)
__ __
0
The equation = g0 + E 0 becomes Exergy,
f el E = E ch + E ph (9)
__ __ __ __
0 (3) Exergetic loss (irreversibility) in compressor,
CH (g) = g0 + 0
C(s) + 2 0 H (g)
4 f 2 I c = E1 + Wc − E 2 (10)
CH (g)
4
__ Exergetic loss in gas turbine combustion chamber,
0 I gtcc = E +E −E (11)
CH (g) = − 50810 + 410530 + 2(238350) CH 2 3
4 4
= 836420 kJ/kg mol
Exergetic loss in gas turbine,
I gt = E 3 − E 4 − Wgt (12)
Therefore, E = 836420 kJ/kg mol.
CH
4
Exergetic loss in heat recovery steam generator,
Without using the value of gamma, with
h11 − h17 + h 20 − h19 − (13)
balancing the entropies in isentropic processes the ( )
I hrsg = m CH E − E − m s
4 6 T0 (S11 − S17 + S20 − S19 )
outlet temperatures can be calculated. For an 4
isentropic compression process in the compressor,
the expression is given as, Exergetic loss in exhaust from hrsg,
S=0=S − SO (T ) + 3.76 S I ex = m CH E 8 (14)
'
O2 (T2 ) ' − S N 2 (T0 ) −
N 2 (T2 )
2 0 4
(4)
[
R u log(P2 /P1 ) + 3.76 log(P2 /P1 ) ] Exergetic loss in steam turbines,
The temperature of the air at state 2’ can be estimated S19 − S11 + S12 − S 20 +
from the above equation. By considering compressor I st = T0 m s (15)
isentropic efficiency, the actual temperature of the (1 − m1 )(S13 − S12 )
compressed air T2 can be calculated. The combustion
equation in gas turbine combustion chamber is, Mass of cooling water required for condenser for
steam cycle,
CH 4 + x (O 2 + 3.76 N 2 ) → CO 2 + 2H 2 O +
(5)
(x − 2) O 2 + 3.76 x N 2
mw =
[ms(1− m1 )(h13 − h14 )] (16)
Where “x” is the amount air to be supplied per kg
[cpw (Tout − Tin )]
mole of methane for gas turbine combustion chamber
which can be calculated by energy balance for the Exergetic loss in condenser,
temperature of T2 and T3. For an isentropic expansion Tout
process in the gas turbine, the expression is given as, m w c pw + (17)
I co = T0 Tin
S = 0 = S3 − S4' (6) m s (1 − m1 )(S14 − S13 )
Total molecules of products combustion chamber, Exergetic loss of hot water from condenser,
m CC = 1 + 2 + (x − 2 ) + 3.76x Tout
I w = m w c pw (Tout − T0 ) − T0 log (18)
T0
2.4 Exergy Analysis
To determine the exergetic losses, the
irreversibilities associated in all the components to be Total (internal + external) exergetic loss in
estimated for second law analysis. The chemical condenser,
exergy and physical exergy can be determined for I cot = I co + I w (19)
each state by using the following equations, Similarly exergetic loss in condenser for ammonia
Chemical exergy, cycle can be determined. Exergetic loss in deaerator,
___ __
E ch = n
k k
0
k + R T0 k
n k ln (P x k ) (7)
[
I deae = T0 m s m1 (S16 − S12 ) + (S16 − S15 ) (20) ]
Exergetic loss in heat recovery ammonia generator,
Physical exergy,
E ph = H − T Sk (8)
k 0
3

4. Matheus M. Dwinanto/Jurnal Ilmiah Teknik Mesin C Vol. 4 No.1. April 2010 (1-6)
h 21 − h 24 −
I hrag = m CH4 (E 6 − E 8 ) − m a (21) Second law efficiency of ammonia cycle,
T0 (S 21 − S 24 )
Wnetac
2,ac = 0
×100% (35)
Exergetic loss in ammonia turbines, m CH4 CH4
I at = T0 m a (S22 − S21 ) (22)
Second law efficiency of triple cycle,
For 1 kg mole of fuel the gas cycle work inputs and Wnet
outputs are : Work input to compressor, 2,tc = 0
×100% (36)
Wc = h 2 − h1 (23)
m CH4 CH4
Work output by high pressure gas turbine,
3. RESULTS AND DISCUSSION
Wgt = h 3 − h 4 (24) In this triple cycle organic Rankine cycle is
added to the combined cycle (Brayton – steam
Net work output by gas cycle, Rankine cycle). The ammonia is selected as working
fluid for the organic Rankine cycle. There are two
Wnetgc = Wgt − Wc (25)
possibilities of arrangement of ammonia cycle to the
combined cycle which are series or parallel
Steam turbine work, combinations. Both the arrangement are compared
(h11 − h19 + h 20 − h12 ) + with the combined cycle (without organic Rankine
cycle) performance. Gas cycle parameters, gas
Wst = m s (26)
(1− m1 )(h12 − h13 ) turbine inlet temperature and maximum temperature
have more domination then the other steam and
Pump work, ammonia cycle parameter. Therefore, the effect of
pressure ratio of gas cycle and maximum cycle
(1− m1 )(h13 − h14 ) + temperature are studied on second law efficiency and
Wps = m s (27)
(h17 − h16 ) exergetic destruction in gas, steam, and ammonia
cycles. In all the three models of the arrangements
the sink temperature is kept constant. The exergetic
Net work from steam cycle, loss in gas cycle includes compressor, combustion
Wnetsc = Wst − Wps (28) chamber, gas turbine, and exhaust. Steam cycle
exergetic loss includes heat recovery steam
generator, steam turbines, condensor, pump, and
Similarly in ammonia cycle deaerator. Ammonia cycle exergetic loss includes
Ammonia turbine work, heat recovery ammonia generator, ammonia turbine,
Wat = m a (h 21 − h 22 ) (29) pump, and condenser.
Pump work, 60
Wpa = m a (h 24 − h 23 ) (30)
55
Second law efficiency of triple
Net work from ammonia cycle, 50
efficiency (%)
Wnetac = Wat − Wpa (31)
45
Net work from triple cycle, 40
Wnet = Wnetgc + Wnetsc + Wnetac (32)
35
Second law efficiency of gas cycle, 30
Wnetgc 0 5 10 15 20 25 30 35 40 45 50 55
2,gc = 0
×100% (33) Pressure ratio
m CH4 CH4
Combined cycle (gas + steam)
Triple cycle - parallel
Triple cycle - series
Second law efficiency of steam cycle, Figure 3. Comparison of triple cycle with
series and parallel arrangement
Wnetsc
×100% of bottoming cycle with
2,sc = 0
(34)
combined cycle and with respect
m CH4 CH4 to pressure ratio of gas cycle.
4

5. Matheus M. Dwinanto/Jurnal Ilmiah Teknik Mesin C Vol. 4 No.1. April 2010 (1-6)
ammonia cycle to the combined cycle in parallel
Figure 3 compares the second law efficiency of improves the performance. At 1200 oC the second
combined cycle with triple cycle with series law efficiency of parallel arrangement is 54% which
arrangement and parallel arrangement with respect to is high compared of others. As mentioned before in
pressure ratio of gas cycle. The series arrangement is this arrangement the waste heat recovery is
not improving the efficiency with the pressure ratio improved. Parallel type arrangement increases the
for the same heat rejection temperature. This is efficiency compared to others ones on the basis of
because the temperature limits of source and sink are pressure ratio and maximum temperature. Therefore
not altered and addition of components in series in the subsequent simulation work parallel
increases the losses. The addition of ammonia cycle arrangement is fixed.
to the combined cycle in parallel improves the The influence of gas pressure ratio on
performance. At the pressure ratio of 15, the second second law efficiency of various cycle in shown
law efficiency of combined cycle, series type triple figure 5. Up to pressure ratio of 35, the gas cycle
cycle and parallel type triple cycle are 52%, 51.3% efficiency increases and then decreases with
and 54% respectively. The figure shows that the increases in pressure ratio. The steam cycle
parallel type the arrangement improves the efficiency efficiency decreases where as the ammonia cycle
to 2%. In the arrangement the waste heat recovery is efficiency increases with increase in the pressure
improved. Exhaust losses are decreased. Therefore ratio.
the efficiency increases with the arrangement.
60
60
S e c o n d la w e f f ic ie n c y o f t r ip le c y c le ( % )
50
S e c o n d L a w E f f ic ie n c y ( % )
55
50 40
45
30
40
35 20
30
10
25
0
20
0 5 10 15 20 25 30 35 40 45 50
800 1000 1200 1400 1600
o Pressure Ratio
Gas turbine inlet temperature C
Combined cycle (gas + steam) Triple cycle - series Gas cycle Ammonia cycle Steam cycle Triple cycle
Triple cycle - parallel
Figure 5. Effect of pressure ratio on second
Figure 4. Comparison of triple cycle with law efficiency of gas, steam,
series and parallel arrangement ammonia and triple cycle with
of bottoming cycle with parallel type.
combined cycle and with respect
to gas turbine inlet temperature For fixed maximum temperature, the increase in
of gas cycle. pressure ratio leads to decrease the gas turbine
exhaust temperature. This reduces the steam cycle
Figure 4 compares the second law efficiency of efficiency. To compensate the reduction in steam
combined cycle with triple cycle with incorporation efficiency, the ammonia cycle efficiency increases as
of ammonia cycle in series arrangement and in the flow rate of ammonia increases where as steam
parallel arrangement with respect to gas turbine inlet flow rate decreases with increase in pressure ratio.
temperature i.e. maximum temperature of the cycle. The triple cycle efficiency increases with the pressure
Here also the series arrangement not improves the ratio up to 15 and then decreases with increase in
efficiency with the temperature for the same heat pressure ratio. Therefore the optimum pressure ratio
sink temperature. The efficiency decreases with for triple cycle is 15. At 15 pressure ratio, the second
series addition of organic cycle to the combined law efficiency of gas, steam, ammonia and triple
cycle due to increased losses. The additon of cycles are 38%, 14%, 2% and 54% respectively.
5

6. Matheus M. Dwinanto/Jurnal Ilmiah Teknik Mesin C Vol. 4 No.1. April 2010 (1-6)
80 rate. The gas and ammonia cycle exergetic loss
70
decreases with increase in the maximum temperature.
On overall basis the triple cycle exergetic loss
60
decreases with increase in the temperature. Therefore
Exergetic loss (%)
50 the efficiency of triple cycle increases with rise in
40 temperature.
30
70
20
60
10
50
Exergetic loss (%)
0
0 5 10 15 20 25 30 35 40 45 50
40
Pressure Ratio
Gas cycle Ammonia cycle Steam cycle Triple cycle 30
Figure 6. Effect of pressure ratio of gas 20
cycle on exergetic destruction 10
of various cycles.
0
The exergetic loss in individual fluid cycle 800 900 1000 1100 1200 1300 1400 1500
and overall triple cycle is shown in figure 6. The o
Gas turbine inlet temperature C
major exergetic destruction occurs in gas cycle due to Gas cycle Ammonia cycle Steam cycle Triple cycle
combustion chamber. At low pressures steam cycle
exergetic loss is more than the ammonia cycle where Figure 8. Effect of maximum temperature
as from pressure ratio of 20, ammonia cycle loss of triple cycle on exergetic loss
dominating the steam cycle. On overall basis, for of various cycles.
triple cycle the exergetic loss decreases and then
increases with increase in the pressure ratio. 4. Conclusions
70 In this work, first to arrangements of series
60 and parallel arrangements are compared with the
combined cycle to select the best triple cycle
Second law efficiency (%)
50
arrangement. The comparison shows that the series
40 type does not improve the efficiency. Therefore,
30
parallel type arrangement of ammonia cycle with the
steam cycle in triple cycle is selected. The variations
20
in performance of gas, steam, ammonia and triple
10 cycle are discussed with respect to gas cycle
0
parameters, which are taken as pressure ratio and
800 900 1000 1100 1200 1300 1400 1500 maximum temperature. The second law efficiency
Gas turbine inlet temperature C
o
and exergetic losses are plotted against to gas
Gas cycle Ammonia cycle Steam cycle Triple cycle
pressure ratio and temperature. The optimum
Figure 7. Effect triple cycle maximum pressure ratio of gas cycle is found as 15 to get
temperature on second law maximum triple cycle efficiency. The effect of gas
efficiency of gas, steam, temperature on performance has more effect than the
ammonia and triple cycle with pressure. Due to incorporation of ammonia cycle the
parallel type efficiency is increased by 2%.
The effect of maximum temperature of triple REFERENCES
cycle on second law efficiency of individual cycles [1] El-Wakil, M. M., Powerplant Technology,
and triple cycle is shown in figure 7. For fixed McGraw-Hill, Ltd, Singapore, 1984.
pressure ratio, the increased maximum temperature [2] Horlock, J. H., Combined Powerplants,
also increases the gas turbine exhaust temperature. Pergamon Press, Oxford, UK, 1992
Therefore gas cycle and also steam cycle efficiency [3] Hung, T. C., “A Conceptual Arrangement of
increases with increase in temperature. Due increased Multiple Cycle Toward Optimal Energy
steam flow rate and decreased ammonia flow rate, Conversion”, ASME Journal Vol. 124, April
the ammonia cycle decreases with the increase in the 2002.
maximum temperature. [4] Kotas, T. J., The Exergy Method of Thermal
Figure 8 shows the exergetic destruction in gas, Plant Analysis, John Wiley & Sons, New
steam, ammonia and overall triple cycle with parallel York 1984
type arrangement. Only the steam cycle exergetic [5] Nag, P. K., Powerplant Engineering, 2nd
loss increases with increase in the maximum Edition, Tata McGraw Hill, New Delhi,
temperature due to increase in the steam mass flow 2001
6